LMFDB - Embedded newform 531.8.a.f.1.19

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			1.19
Root			$20.5214$ 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)

$f(q)$	$=$	$q+19.5214 q^{2} +253.086 q^{4} +89.3612 q^{5} +1245.27 q^{7} +2441.86 q^{8} +O(q^{10})$	\(q+19.5214 q^{2} +253.086 q^{4} +89.3612 q^{5} +1245.27 q^{7} +2441.86 q^{8} +1744.46 q^{10} +7324.44 q^{11} +8540.60 q^{13} +24309.5 q^{14} +15273.6 q^{16} +36007.9 q^{17} -3702.00 q^{19} +22616.1 q^{20} +142984. q^{22} -18369.7 q^{23} -70139.6 q^{25} +166725. q^{26} +315161. q^{28} -212266. q^{29} +139015. q^{31} -14395.6 q^{32} +702926. q^{34} +111279. q^{35} -485828. q^{37} -72268.3 q^{38} +218208. q^{40} -103557. q^{41} -510383. q^{43} +1.85372e6 q^{44} -358603. q^{46} +89050.0 q^{47} +727157. q^{49} -1.36922e6 q^{50} +2.16151e6 q^{52} -1.11781e6 q^{53} +654521. q^{55} +3.04078e6 q^{56} -4.14373e6 q^{58} +205379. q^{59} +2.54420e6 q^{61} +2.71377e6 q^{62} -2.23605e6 q^{64} +763198. q^{65} +2.86443e6 q^{67} +9.11310e6 q^{68} +2.17232e6 q^{70} -4.18037e6 q^{71} +361702. q^{73} -9.48406e6 q^{74} -936925. q^{76} +9.12092e6 q^{77} +4.78177e6 q^{79} +1.36487e6 q^{80} -2.02158e6 q^{82} -2.22497e6 q^{83} +3.21771e6 q^{85} -9.96340e6 q^{86} +1.78853e7 q^{88} -6.14697e6 q^{89} +1.06354e7 q^{91} -4.64911e6 q^{92} +1.73838e6 q^{94} -330815. q^{95} +5.76701e6 q^{97} +1.41952e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	19.5214	1.72547	0.862734	−	0.505659i	$-0.168751\pi$
$2$	19.5214	1.72547	0.862734	+	0.505659i	$0.168751\pi$
$3$	0	0
$3$	0	0
$4$	253.086	1.97724
$5$	89.3612	0.319708	0.159854	−	0.987141i	$-0.448898\pi$
$5$	89.3612	0.319708	0.159854	+	0.987141i	$0.448898\pi$
$6$	0	0
$7$	1245.27	1.37221	0.686105	−	0.727502i	$-0.259319\pi$
$7$	1245.27	1.37221	0.686105	+	0.727502i	$0.259319\pi$
$8$	2441.86	1.68619
$9$	0	0
$10$	1744.46	0.551646
$11$	7324.44	1.65921	0.829603	−	0.558354i	$-0.188567\pi$
$11$	7324.44	1.65921	0.829603	+	0.558354i	$0.188567\pi$
$12$	0	0
$13$	8540.60	1.07817	0.539084	−	0.842252i	$-0.318771\pi$
$13$	8540.60	1.07817	0.539084	+	0.842252i	$0.318771\pi$
$14$	24309.5	2.36770
$15$	0	0
$16$	15273.6	0.932228
$17$	36007.9	1.77757	0.888785	−	0.458325i	$-0.151551\pi$
$17$	36007.9	1.77757	0.888785	+	0.458325i	$0.151551\pi$
$18$	0	0
$19$	−3702.00	−0.123822	−0.0619112	−	0.998082i	$-0.519720\pi$
$19$	−3702.00	−0.123822	−0.0619112	+	0.998082i	$0.519720\pi$
$20$	22616.1	0.632139
$21$	0	0
$22$	142984.	2.86291
$23$	−18369.7	−0.314814	−0.157407	−	0.987534i	$-0.550313\pi$
$23$	−18369.7	−0.314814	−0.157407	+	0.987534i	$0.550313\pi$
$24$	0	0
$25$	−70139.6	−0.897786
$26$	166725.	1.86034
$27$	0	0
$28$	315161.	2.71319
$29$	−212266.	−1.61617	−0.808085	−	0.589067i	$-0.799496\pi$
$29$	−212266.	−1.61617	−0.808085	+	0.589067i	$0.799496\pi$
$30$	0	0
$31$	139015.	0.838100	0.419050	−	0.907963i	$-0.362363\pi$
$31$	139015.	0.838100	0.419050	+	0.907963i	$0.362363\pi$
$32$	−14395.6	−0.0776614
$33$	0	0
$34$	702926.	3.06714
$35$	111279.	0.438707
$36$	0	0
$37$	−485828.	−1.57680	−0.788400	−	0.615163i	$-0.789090\pi$
$37$	−485828.	−1.57680	−0.788400	+	0.615163i	$0.789090\pi$
$38$	−72268.3	−0.213651
$39$	0	0
$40$	218208.	0.539089
$41$	−103557.	−0.234658	−0.117329	−	0.993093i	$-0.537433\pi$
$41$	−103557.	−0.234658	−0.117329	+	0.993093i	$0.537433\pi$
$42$	0	0
$43$	−510383.	−0.978940	−0.489470	−	0.872020i	$-0.662810\pi$
$43$	−510383.	−0.978940	−0.489470	+	0.872020i	$0.662810\pi$
$44$	1.85372e6	3.28064
$45$	0	0
$46$	−358603.	−0.543201
$47$	89050.0	0.125110	0.0625549	−	0.998042i	$-0.480075\pi$
$47$	89050.0	0.125110	0.0625549	+	0.998042i	$0.480075\pi$
$48$	0	0
$49$	727157.	0.882962
$50$	−1.36922e6	−1.54910
$51$	0	0
$52$	2.16151e6	2.13179
$53$	−1.11781e6	−1.03134	−0.515669	−	0.856788i	$-0.672457\pi$
$53$	−1.11781e6	−1.03134	−0.515669	+	0.856788i	$0.672457\pi$
$54$	0	0
$55$	654521.	0.530462
$56$	3.04078e6	2.31381
$57$	0	0
$58$	−4.14373e6	−2.78865
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	2.54420e6	1.43515	0.717575	−	0.696481i	$-0.245252\pi$
$61$	2.54420e6	1.43515	0.717575	+	0.696481i	$0.245252\pi$
$62$	2.71377e6	1.44611
$63$	0	0
$64$	−2.23605e6	−1.06623
$65$	763198.	0.344699
$66$	0	0
$67$	2.86443e6	1.16353	0.581764	−	0.813358i	$-0.302363\pi$
$67$	2.86443e6	1.16353	0.581764	+	0.813358i	$0.302363\pi$
$68$	9.11310e6	3.51467
$69$	0	0
$70$	2.17232e6	0.756975
$71$	−4.18037e6	−1.38615	−0.693076	−	0.720864i	$-0.743745\pi$
$71$	−4.18037e6	−1.38615	−0.693076	+	0.720864i	$0.743745\pi$
$72$	0	0
$73$	361702.	0.108823	0.0544116	−	0.998519i	$-0.482672\pi$
$73$	361702.	0.108823	0.0544116	+	0.998519i	$0.482672\pi$
$74$	−9.48406e6	−2.72072
$75$	0	0
$76$	−936925.	−0.244826
$77$	9.12092e6	2.27678
$78$	0	0
$79$	4.78177e6	1.09117	0.545586	−	0.838055i	$-0.316307\pi$
$79$	4.78177e6	1.09117	0.545586	+	0.838055i	$0.316307\pi$
$80$	1.36487e6	0.298041
$81$	0	0
$82$	−2.02158e6	−0.404895
$83$	−2.22497e6	−0.427121	−0.213561	−	0.976930i	$-0.568506\pi$
$83$	−2.22497e6	−0.427121	−0.213561	+	0.976930i	$0.568506\pi$
$84$	0	0
$85$	3.21771e6	0.568304
$86$	−9.96340e6	−1.68913
$87$	0	0
$88$	1.78853e7	2.79774
$89$	−6.14697e6	−0.924264	−0.462132	−	0.886811i	$-0.652915\pi$
$89$	−6.14697e6	−0.924264	−0.462132	+	0.886811i	$0.652915\pi$
$90$	0	0
$91$	1.06354e7	1.47947
$92$	−4.64911e6	−0.622462
$93$	0	0
$94$	1.73838e6	0.215873
$95$	−330815.	−0.0395870
$96$	0	0
$97$	5.76701e6	0.641578	0.320789	−	0.947151i	$-0.396052\pi$
$97$	5.76701e6	0.641578	0.320789	+	0.947151i	$0.396052\pi$
$98$	1.41952e7	1.52352
$99$	0	0
$100$	−1.77514e7	−1.77514
$101$	3.90753e6	0.377379	0.188689	−	0.982037i	$-0.439576\pi$
$101$	3.90753e6	0.377379	0.188689	+	0.982037i	$0.439576\pi$
$102$	0	0
$103$	1.41123e7	1.27253	0.636263	−	0.771473i	$-0.280480\pi$
$103$	1.41123e7	1.27253	0.636263	+	0.771473i	$0.280480\pi$
$104$	2.08550e7	1.81800
$105$	0	0
$106$	−2.18212e7	−1.77954
$107$	9.34061e6	0.737109	0.368555	−	0.929606i	$-0.379853\pi$
$107$	9.34061e6	0.737109	0.368555	+	0.929606i	$0.379853\pi$
$108$	0	0
$109$	−1.87310e7	−1.38538	−0.692690	−	0.721235i	$-0.743575\pi$
$109$	−1.87310e7	−1.38538	−0.692690	+	0.721235i	$0.743575\pi$
$110$	1.27772e7	0.915295
$111$	0	0
$112$	1.90198e7	1.27921
$113$	−1.17683e7	−0.767253	−0.383627	−	0.923488i	$-0.625325\pi$
$113$	−1.17683e7	−0.767253	−0.383627	+	0.923488i	$0.625325\pi$
$114$	0	0
$115$	−1.64154e6	−0.100649
$116$	−5.37215e7	−3.19555
$117$	0	0
$118$	4.00929e6	0.224637
$119$	4.48396e7	2.43920
$120$	0	0
$121$	3.41603e7	1.75296
$122$	4.96665e7	2.47630
$123$	0	0
$124$	3.51828e7	1.65712
$125$	−1.32491e7	−0.606738
$126$	0	0
$127$	−3.19821e7	−1.38546	−0.692731	−	0.721197i	$-0.743592\pi$
$127$	−3.19821e7	−1.38546	−0.692731	+	0.721197i	$0.743592\pi$
$128$	−4.18082e7	−1.76208
$129$	0	0
$130$	1.48987e7	0.594768
$131$	−1.71083e6	−0.0664900	−0.0332450	−	0.999447i	$-0.510584\pi$
$131$	−1.71083e6	−0.0664900	−0.0332450	+	0.999447i	$0.510584\pi$
$132$	0	0
$133$	−4.60999e6	−0.169910
$134$	5.59178e7	2.00763
$135$	0	0
$136$	8.79263e7	2.99732
$137$	−7.90990e6	−0.262814	−0.131407	−	0.991328i	$-0.541950\pi$
$137$	−7.90990e6	−0.262814	−0.131407	+	0.991328i	$0.541950\pi$
$138$	0	0
$139$	4.01922e7	1.26937	0.634687	−	0.772769i	$-0.281129\pi$
$139$	4.01922e7	1.26937	0.634687	+	0.772769i	$0.281129\pi$
$140$	2.81632e7	0.867428
$141$	0	0
$142$	−8.16069e7	−2.39176
$143$	6.25551e7	1.78890
$144$	0	0
$145$	−1.89683e7	−0.516703
$146$	7.06094e6	0.187771
$147$	0	0
$148$	−1.22956e8	−3.11771
$149$	−3.82194e7	−0.946525	−0.473263	−	0.880921i	$-0.656924\pi$
$149$	−3.82194e7	−0.946525	−0.473263	+	0.880921i	$0.656924\pi$
$150$	0	0
$151$	1.65925e7	0.392187	0.196093	−	0.980585i	$-0.437174\pi$
$151$	1.65925e7	0.392187	0.196093	+	0.980585i	$0.437174\pi$
$152$	−9.03978e6	−0.208788
$153$	0	0
$154$	1.78053e8	3.92851
$155$	1.24226e7	0.267948
$156$	0	0
$157$	−1.11725e7	−0.230411	−0.115206	−	0.993342i	$-0.536753\pi$
$157$	−1.11725e7	−0.230411	−0.115206	+	0.993342i	$0.536753\pi$
$158$	9.33469e7	1.88278
$159$	0	0
$160$	−1.28641e6	−0.0248290
$161$	−2.28752e7	−0.431991
$162$	0	0
$163$	−8.88579e7	−1.60709	−0.803544	−	0.595246i	$-0.797055\pi$
$163$	−8.88579e7	−1.60709	−0.803544	+	0.595246i	$0.797055\pi$
$164$	−2.62088e7	−0.463975
$165$	0	0
$166$	−4.34347e7	−0.736984
$167$	−1.26497e7	−0.210172	−0.105086	−	0.994463i	$-0.533512\pi$
$167$	−1.26497e7	−0.210172	−0.105086	+	0.994463i	$0.533512\pi$
$168$	0	0
$169$	1.01933e7	0.162446
$170$	6.28143e7	0.980590
$171$	0	0
$172$	−1.29171e8	−1.93560
$173$	−4.22459e7	−0.620331	−0.310166	−	0.950683i	$-0.600384\pi$
$173$	−4.22459e7	−0.620331	−0.310166	+	0.950683i	$0.600384\pi$
$174$	0	0
$175$	−8.73428e7	−1.23195
$176$	1.11871e8	1.54676
$177$	0	0
$178$	−1.19998e8	−1.59479
$179$	−4.55937e6	−0.0594182	−0.0297091	−	0.999559i	$-0.509458\pi$
$179$	−4.55937e6	−0.0594182	−0.0297091	+	0.999559i	$0.509458\pi$
$180$	0	0
$181$	9.44145e7	1.18349	0.591744	−	0.806126i	$-0.298440\pi$
$181$	9.44145e7	1.18349	0.591744	+	0.806126i	$0.298440\pi$
$182$	2.07617e8	2.55278
$183$	0	0
$184$	−4.48563e7	−0.530836
$185$	−4.34142e7	−0.504116
$186$	0	0
$187$	2.63738e8	2.94935
$188$	2.25373e7	0.247372
$189$	0	0
$190$	−6.45799e6	−0.0683061
$191$	1.79091e6	0.0185977	0.00929883	−	0.999957i	$-0.497040\pi$
$191$	1.79091e6	0.0185977	0.00929883	+	0.999957i	$0.497040\pi$
$192$	0	0
$193$	−4.11127e7	−0.411647	−0.205824	−	0.978589i	$-0.565987\pi$
$193$	−4.11127e7	−0.411647	−0.205824	+	0.978589i	$0.565987\pi$
$194$	1.12580e8	1.10702
$195$	0	0
$196$	1.84034e8	1.74583
$197$	1.69978e7	0.158402	0.0792009	−	0.996859i	$-0.474763\pi$
$197$	1.69978e7	0.158402	0.0792009	+	0.996859i	$0.474763\pi$
$198$	0	0
$199$	−7.65553e7	−0.688635	−0.344318	−	0.938853i	$-0.611890\pi$
$199$	−7.65553e7	−0.688635	−0.344318	+	0.938853i	$0.611890\pi$
$200$	−1.71271e8	−1.51384
$201$	0	0
$202$	7.62806e7	0.651155
$203$	−2.64328e8	−2.21772
$204$	0	0
$205$	−9.25398e6	−0.0750222
$206$	2.75492e8	2.19570
$207$	0	0
$208$	1.30446e8	1.00510
$209$	−2.71151e7	−0.205447
$210$	0	0
$211$	1.77538e8	1.30108	0.650538	−	0.759474i	$-0.274544\pi$
$211$	1.77538e8	1.30108	0.650538	+	0.759474i	$0.274544\pi$
$212$	−2.82901e8	−2.03920
$213$	0	0
$214$	1.82342e8	1.27186
$215$	−4.56084e7	−0.312976
$216$	0	0
$217$	1.73111e8	1.15005
$218$	−3.65657e8	−2.39043
$219$	0	0
$220$	1.65650e8	1.04885
$221$	3.07529e8	1.91652
$222$	0	0
$223$	−5.03971e7	−0.304325	−0.152163	−	0.988355i	$-0.548624\pi$
$223$	−5.03971e7	−0.304325	−0.152163	+	0.988355i	$0.548624\pi$
$224$	−1.79264e7	−0.106568
$225$	0	0
$226$	−2.29734e8	−1.32387
$227$	2.09561e8	1.18910	0.594552	−	0.804057i	$-0.297329\pi$
$227$	2.09561e8	1.18910	0.594552	+	0.804057i	$0.297329\pi$
$228$	0	0
$229$	2.52968e8	1.39201	0.696004	−	0.718038i	$-0.254959\pi$
$229$	2.52968e8	1.39201	0.696004	+	0.718038i	$0.254959\pi$
$230$	−3.20452e7	−0.173666
$231$	0	0
$232$	−5.18324e8	−2.72517
$233$	9.82362e7	0.508775	0.254387	−	0.967102i	$-0.418126\pi$
$233$	9.82362e7	0.508775	0.254387	+	0.967102i	$0.418126\pi$
$234$	0	0
$235$	7.95762e6	0.0399987
$236$	5.19786e7	0.257414
$237$	0	0
$238$	8.75333e8	4.20876
$239$	2.30093e8	1.09021	0.545107	−	0.838367i	$-0.316489\pi$
$239$	2.30093e8	1.09021	0.545107	+	0.838367i	$0.316489\pi$
$240$	0	0
$241$	1.15969e8	0.533684	0.266842	−	0.963740i	$-0.414020\pi$
$241$	1.15969e8	0.533684	0.266842	+	0.963740i	$0.414020\pi$
$242$	6.66858e8	3.02468
$243$	0	0
$244$	6.43903e8	2.83763
$245$	6.49797e7	0.282291
$246$	0	0
$247$	−3.16173e7	−0.133501
$248$	3.39456e8	1.41319
$249$	0	0
$250$	−2.58642e8	−1.04691
$251$	−2.23254e8	−0.891132	−0.445566	−	0.895249i	$-0.646998\pi$
$251$	−2.23254e8	−0.891132	−0.445566	+	0.895249i	$0.646998\pi$
$252$	0	0
$253$	−1.34548e8	−0.522342
$254$	−6.24337e8	−2.39057
$255$	0	0
$256$	−5.29942e8	−1.97419
$257$	−2.74537e8	−1.00887	−0.504435	−	0.863450i	$-0.668299\pi$
$257$	−2.74537e8	−1.00887	−0.504435	+	0.863450i	$0.668299\pi$
$258$	0	0
$259$	−6.04988e8	−2.16370
$260$	1.93155e8	0.681552
$261$	0	0
$262$	−3.33978e7	−0.114726
$263$	3.81892e8	1.29448	0.647240	−	0.762287i	$-0.275923\pi$
$263$	3.81892e8	1.29448	0.647240	+	0.762287i	$0.275923\pi$
$264$	0	0
$265$	−9.98886e7	−0.329728
$266$	−8.99937e7	−0.293175
$267$	0	0
$268$	7.24949e8	2.30057
$269$	−4.94791e8	−1.54985	−0.774924	−	0.632054i	$-0.782212\pi$
$269$	−4.94791e8	−1.54985	−0.774924	+	0.632054i	$0.782212\pi$
$270$	0	0
$271$	−4.99405e8	−1.52427	−0.762133	−	0.647421i	$-0.775848\pi$
$271$	−4.99405e8	−1.52427	−0.762133	+	0.647421i	$0.775848\pi$
$272$	5.49971e8	1.65710
$273$	0	0
$274$	−1.54413e8	−0.453477
$275$	−5.13733e8	−1.48961
$276$	0	0
$277$	3.71789e8	1.05104	0.525518	−	0.850782i	$-0.323872\pi$
$277$	3.71789e8	1.05104	0.525518	+	0.850782i	$0.323872\pi$
$278$	7.84608e8	2.19026
$279$	0	0
$280$	2.71728e8	0.739744
$281$	3.96353e8	1.06564	0.532820	−	0.846229i	$-0.321132\pi$
$281$	3.96353e8	1.06564	0.532820	+	0.846229i	$0.321132\pi$
$282$	0	0
$283$	4.66718e8	1.22406	0.612029	−	0.790835i	$-0.290353\pi$
$283$	4.66718e8	1.22406	0.612029	+	0.790835i	$0.290353\pi$
$284$	−1.05800e9	−2.74075
$285$	0	0
$286$	1.22117e9	3.08669
$287$	−1.28956e8	−0.322001
$288$	0	0
$289$	8.86230e8	2.15975
$290$	−3.70289e8	−0.891554
$291$	0	0
$292$	9.15419e7	0.215169
$293$	−7.12153e8	−1.65400	−0.827002	−	0.562199i	$-0.809955\pi$
$293$	−7.12153e8	−1.65400	−0.827002	+	0.562199i	$0.809955\pi$
$294$	0	0
$295$	1.83529e7	0.0416225
$296$	−1.18633e9	−2.65878
$297$	0	0
$298$	−7.46098e8	−1.63320
$299$	−1.56888e8	−0.339423
$300$	0	0
$301$	−6.35565e8	−1.34331
$302$	3.23910e8	0.676705
$303$	0	0
$304$	−5.65429e7	−0.115431
$305$	2.27353e8	0.458830
$306$	0	0
$307$	−3.34586e8	−0.659969	−0.329985	−	0.943986i	$-0.607044\pi$
$307$	−3.34586e8	−0.659969	−0.329985	+	0.943986i	$0.607044\pi$
$308$	2.30838e9	4.50173
$309$	0	0
$310$	2.42506e8	0.462335
$311$	3.86109e8	0.727861	0.363931	−	0.931426i	$-0.381434\pi$
$311$	3.86109e8	0.727861	0.363931	+	0.931426i	$0.381434\pi$
$312$	0	0
$313$	−2.20042e8	−0.405602	−0.202801	−	0.979220i	$-0.565004\pi$
$313$	−2.20042e8	−0.405602	−0.202801	+	0.979220i	$0.565004\pi$
$314$	−2.18104e8	−0.397567
$315$	0	0
$316$	1.21020e9	2.15751
$317$	−8.94081e8	−1.57641	−0.788205	−	0.615412i	$-0.788989\pi$
$317$	−8.94081e8	−1.57641	−0.788205	+	0.615412i	$0.788989\pi$
$318$	0	0
$319$	−1.55473e9	−2.68156
$320$	−1.99816e8	−0.340883
$321$	0	0
$322$	−4.46557e8	−0.745387
$323$	−1.33301e8	−0.220103
$324$	0	0
$325$	−5.99034e8	−0.967965
$326$	−1.73463e9	−2.77298
$327$	0	0
$328$	−2.52872e8	−0.395678
$329$	1.10891e8	0.171677
$330$	0	0
$331$	−7.07133e8	−1.07177	−0.535887	−	0.844290i	$-0.680023\pi$
$331$	−7.07133e8	−1.07177	−0.535887	+	0.844290i	$0.680023\pi$
$332$	−5.63110e8	−0.844520
$333$	0	0
$334$	−2.46941e8	−0.362644
$335$	2.55969e8	0.371990
$336$	0	0
$337$	−1.35974e9	−1.93532	−0.967659	−	0.252263i	$-0.918825\pi$
$337$	−1.35974e9	−1.93532	−0.967659	+	0.252263i	$0.918825\pi$
$338$	1.98987e8	0.280296
$339$	0	0
$340$	8.14358e8	1.12367
$341$	1.01821e9	1.39058
$342$	0	0
$343$	−1.20026e8	−0.160600
$344$	−1.24628e9	−1.65068
$345$	0	0
$346$	−8.24701e8	−1.07036
$347$	−5.60992e8	−0.720782	−0.360391	−	0.932801i	$-0.617357\pi$
$347$	−5.60992e8	−0.720782	−0.360391	+	0.932801i	$0.617357\pi$
$348$	0	0
$349$	8.60301e8	1.08333	0.541666	−	0.840594i	$-0.317794\pi$
$349$	8.60301e8	1.08333	0.541666	+	0.840594i	$0.317794\pi$
$350$	−1.70506e9	−2.12569
$351$	0	0
$352$	−1.05440e8	−0.128856
$353$	−1.92431e8	−0.232843	−0.116421	−	0.993200i	$-0.537142\pi$
$353$	−1.92431e8	−0.232843	−0.116421	+	0.993200i	$0.537142\pi$
$354$	0	0
$355$	−3.73563e8	−0.443165
$356$	−1.55571e9	−1.82749
$357$	0	0
$358$	−8.90055e7	−0.102524
$359$	−8.07007e8	−0.920549	−0.460275	−	0.887777i	$-0.652249\pi$
$359$	−8.07007e8	−0.920549	−0.460275	+	0.887777i	$0.652249\pi$
$360$	0	0
$361$	−8.80167e8	−0.984668
$362$	1.84311e9	2.04207
$363$	0	0
$364$	2.69166e9	2.92527
$365$	3.23222e7	0.0347917
$366$	0	0
$367$	8.62205e8	0.910498	0.455249	−	0.890364i	$-0.349550\pi$
$367$	8.62205e8	0.910498	0.455249	+	0.890364i	$0.349550\pi$
$368$	−2.80572e8	−0.293478
$369$	0	0
$370$	−8.47507e8	−0.869836
$371$	−1.39197e9	−1.41521
$372$	0	0
$373$	6.66530e8	0.665026	0.332513	−	0.943099i	$-0.392103\pi$
$373$	6.66530e8	0.665026	0.332513	+	0.943099i	$0.392103\pi$
$374$	5.14854e9	5.08901
$375$	0	0
$376$	2.17448e8	0.210959
$377$	−1.81288e9	−1.74250
$378$	0	0
$379$	9.61803e8	0.907505	0.453752	−	0.891128i	$-0.350085\pi$
$379$	9.61803e8	0.907505	0.453752	+	0.891128i	$0.350085\pi$
$380$	−8.37248e7	−0.0782729
$381$	0	0
$382$	3.49612e7	0.0320896
$383$	2.17300e9	1.97635	0.988177	−	0.153316i	$-0.0489951\pi$
$383$	2.17300e9	1.97635	0.988177	+	0.153316i	$0.0489951\pi$
$384$	0	0
$385$	8.15057e8	0.727906
$386$	−8.02578e8	−0.710283
$387$	0	0
$388$	1.45955e9	1.26855
$389$	1.17218e9	1.00965	0.504823	−	0.863223i	$-0.331558\pi$
$389$	1.17218e9	1.00965	0.504823	+	0.863223i	$0.331558\pi$
$390$	0	0
$391$	−6.61454e8	−0.559604
$392$	1.77562e9	1.48884
$393$	0	0
$394$	3.31821e8	0.273317
$395$	4.27305e8	0.348857
$396$	0	0
$397$	7.82092e8	0.627323	0.313662	−	0.949535i	$-0.398444\pi$
$397$	7.82092e8	0.627323	0.313662	+	0.949535i	$0.398444\pi$
$398$	−1.49447e9	−1.18822
$399$	0	0
$400$	−1.07128e9	−0.836941
$401$	−2.15777e8	−0.167109	−0.0835547	−	0.996503i	$-0.526627\pi$
$401$	−2.15777e8	−0.167109	−0.0835547	+	0.996503i	$0.526627\pi$
$402$	0	0
$403$	1.18727e9	0.903612
$404$	9.88942e8	0.746167
$405$	0	0
$406$	−5.16007e9	−3.82661
$407$	−3.55842e9	−2.61624
$408$	0	0
$409$	9.36539e8	0.676853	0.338427	−	0.940993i	$-0.390105\pi$
$409$	9.36539e8	0.676853	0.338427	+	0.940993i	$0.390105\pi$
$410$	−1.80651e8	−0.129448
$411$	0	0
$412$	3.57162e9	2.51608
$413$	2.55753e8	0.178647
$414$	0	0
$415$	−1.98826e8	−0.136554
$416$	−1.22947e8	−0.0837321
$417$	0	0
$418$	−5.29325e8	−0.354491
$419$	1.51618e9	1.00694	0.503468	−	0.864014i	$-0.332057\pi$
$419$	1.51618e9	1.00694	0.503468	+	0.864014i	$0.332057\pi$
$420$	0	0
$421$	1.17128e9	0.765020	0.382510	−	0.923951i	$-0.375060\pi$
$421$	1.17128e9	0.765020	0.382510	+	0.923951i	$0.375060\pi$
$422$	3.46579e9	2.24496
$423$	0	0
$424$	−2.72953e9	−1.73903
$425$	−2.52558e9	−1.59588
$426$	0	0
$427$	3.16822e9	1.96933
$428$	2.36398e9	1.45744
$429$	0	0
$430$	−8.90342e8	−0.540029
$431$	2.53301e9	1.52393	0.761966	−	0.647616i	$-0.224234\pi$
$431$	2.53301e9	1.52393	0.761966	+	0.647616i	$0.224234\pi$
$432$	0	0
$433$	−8.09828e8	−0.479386	−0.239693	−	0.970849i	$-0.577047\pi$
$433$	−8.09828e8	−0.479386	−0.239693	+	0.970849i	$0.577047\pi$
$434$	3.37938e9	1.98437
$435$	0	0
$436$	−4.74057e9	−2.73923
$437$	6.80046e7	0.0389810
$438$	0	0
$439$	−3.58859e8	−0.202441	−0.101220	−	0.994864i	$-0.532275\pi$
$439$	−3.58859e8	−0.202441	−0.101220	+	0.994864i	$0.532275\pi$
$440$	1.59825e9	0.894460
$441$	0	0
$442$	6.00340e9	3.30689
$443$	−6.60227e8	−0.360811	−0.180406	−	0.983592i	$-0.557741\pi$
$443$	−6.60227e8	−0.360811	−0.180406	+	0.983592i	$0.557741\pi$
$444$	0	0
$445$	−5.49301e8	−0.295495
$446$	−9.83823e8	−0.525103
$447$	0	0
$448$	−2.78448e9	−1.46309
$449$	−2.36774e9	−1.23445	−0.617223	−	0.786788i	$-0.711742\pi$
$449$	−2.36774e9	−1.23445	−0.617223	+	0.786788i	$0.711742\pi$
$450$	0	0
$451$	−7.58497e8	−0.389346
$452$	−2.97839e9	−1.51704
$453$	0	0
$454$	4.09093e9	2.05176
$455$	9.50389e8	0.473000
$456$	0	0
$457$	−5.43383e8	−0.266317	−0.133159	−	0.991095i	$-0.542512\pi$
$457$	−5.43383e8	−0.266317	−0.133159	+	0.991095i	$0.542512\pi$
$458$	4.93830e9	2.40186
$459$	0	0
$460$	−4.15451e8	−0.199006
$461$	2.48172e9	1.17978	0.589888	−	0.807485i	$-0.299172\pi$
$461$	2.48172e9	1.17978	0.589888	+	0.807485i	$0.299172\pi$
$462$	0	0
$463$	−8.54133e8	−0.399937	−0.199969	−	0.979802i	$-0.564084\pi$
$463$	−8.54133e8	−0.399937	−0.199969	+	0.979802i	$0.564084\pi$
$464$	−3.24206e9	−1.50664
$465$	0	0
$466$	1.91771e9	0.877874
$467$	2.93944e9	1.33554	0.667768	−	0.744370i	$-0.267250\pi$
$467$	2.93944e9	1.33554	0.667768	+	0.744370i	$0.267250\pi$
$468$	0	0
$469$	3.56700e9	1.59661
$470$	1.55344e8	0.0690164
$471$	0	0
$472$	5.01507e8	0.219523
$473$	−3.73827e9	−1.62426
$474$	0	0
$475$	2.59657e8	0.111166
$476$	1.13483e10	4.82287
$477$	0	0
$478$	4.49175e9	1.88113
$479$	−2.95208e9	−1.22731	−0.613655	−	0.789574i	$-0.710302\pi$
$479$	−2.95208e9	−1.22731	−0.613655	+	0.789574i	$0.710302\pi$
$480$	0	0
$481$	−4.14926e9	−1.70006
$482$	2.26389e9	0.920854
$483$	0	0
$484$	8.64551e9	3.46602
$485$	5.15347e8	0.205118
$486$	0	0
$487$	2.92137e9	1.14613	0.573067	−	0.819508i	$-0.305753\pi$
$487$	2.92137e9	1.14613	0.573067	+	0.819508i	$0.305753\pi$
$488$	6.21259e9	2.41993
$489$	0	0
$490$	1.26850e9	0.487083
$491$	2.30204e9	0.877664	0.438832	−	0.898569i	$-0.355392\pi$
$491$	2.30204e9	0.877664	0.438832	+	0.898569i	$0.355392\pi$
$492$	0	0
$493$	−7.64324e9	−2.87285
$494$	−6.17215e8	−0.230352
$495$	0	0
$496$	2.12326e9	0.781300
$497$	−5.20570e9	−1.90209
$498$	0	0
$499$	2.78031e9	1.00171	0.500855	−	0.865531i	$-0.333019\pi$
$499$	2.78031e9	1.00171	0.500855	+	0.865531i	$0.333019\pi$
$500$	−3.35317e9	−1.19967
$501$	0	0
$502$	−4.35825e9	−1.53762
$503$	−1.47758e8	−0.0517682	−0.0258841	−	0.999665i	$-0.508240\pi$
$503$	−1.47758e8	−0.0517682	−0.0258841	+	0.999665i	$0.508240\pi$
$504$	0	0
$505$	3.49182e8	0.120651
$506$	−2.62656e9	−0.901283
$507$	0	0
$508$	−8.09424e9	−2.73938
$509$	−3.57719e9	−1.20235	−0.601174	−	0.799118i	$-0.705300\pi$
$509$	−3.57719e9	−1.20235	−0.601174	+	0.799118i	$0.705300\pi$
$510$	0	0
$511$	4.50417e8	0.149328
$512$	−4.99377e9	−1.64431
$513$	0	0
$514$	−5.35936e9	−1.74077
$515$	1.26109e9	0.406837
$516$	0	0
$517$	6.52242e8	0.207583
$518$	−1.18102e10	−3.73340
$519$	0	0
$520$	1.86363e9	0.581229
$521$	−3.95864e9	−1.22635	−0.613174	−	0.789948i	$-0.710107\pi$
$521$	−3.95864e9	−1.22635	−0.613174	+	0.789948i	$0.710107\pi$
$522$	0	0
$523$	2.06403e9	0.630898	0.315449	−	0.948943i	$-0.397845\pi$
$523$	2.06403e9	0.630898	0.315449	+	0.948943i	$0.397845\pi$
$524$	−4.32987e8	−0.131466
$525$	0	0
$526$	7.45507e9	2.23358
$527$	5.00564e9	1.48978
$528$	0	0
$529$	−3.06738e9	−0.900892
$530$	−1.94997e9	−0.568934
$531$	0	0
$532$	−1.16673e9	−0.335953
$533$	−8.84438e8	−0.253001
$534$	0	0
$535$	8.34688e8	0.235660
$536$	6.99455e9	1.96193
$537$	0	0
$538$	−9.65903e9	−2.67421
$539$	5.32602e9	1.46502
$540$	0	0
$541$	2.06045e9	0.559464	0.279732	−	0.960078i	$-0.409754\pi$
$541$	2.06045e9	0.559464	0.279732	+	0.960078i	$0.409754\pi$
$542$	−9.74911e9	−2.63007
$543$	0	0
$544$	−5.18356e8	−0.138049
$545$	−1.67383e9	−0.442918
$546$	0	0
$547$	−2.64555e9	−0.691131	−0.345565	−	0.938395i	$-0.612313\pi$
$547$	−2.64555e9	−0.691131	−0.345565	+	0.938395i	$0.612313\pi$
$548$	−2.00189e9	−0.519646
$549$	0	0
$550$	−1.00288e10	−2.57028
$551$	7.85808e8	0.200118
$552$	0	0
$553$	5.95460e9	1.49732
$554$	7.25786e9	1.81353
$555$	0	0
$556$	1.01721e10	2.50985
$557$	−3.48363e9	−0.854160	−0.427080	−	0.904214i	$-0.640458\pi$
$557$	−3.48363e9	−0.854160	−0.427080	+	0.904214i	$0.640458\pi$
$558$	0	0
$559$	−4.35897e9	−1.05546
$560$	1.69963e9	0.408975
$561$	0	0
$562$	7.73738e9	1.83873
$563$	−3.13162e9	−0.739587	−0.369793	−	0.929114i	$-0.620572\pi$
$563$	−3.13162e9	−0.739587	−0.369793	+	0.929114i	$0.620572\pi$
$564$	0	0
$565$	−1.05163e9	−0.245297
$566$	9.11101e9	2.11207
$567$	0	0
$568$	−1.02079e10	−2.33732
$569$	−3.45119e9	−0.785373	−0.392686	−	0.919672i	$-0.628454\pi$
$569$	−3.45119e9	−0.785373	−0.392686	+	0.919672i	$0.628454\pi$
$570$	0	0
$571$	5.86089e8	0.131746	0.0658729	−	0.997828i	$-0.479017\pi$
$571$	5.86089e8	0.131746	0.0658729	+	0.997828i	$0.479017\pi$
$572$	1.58318e10	3.53708
$573$	0	0
$574$	−2.51742e9	−0.555601
$575$	1.28844e9	0.282636
$576$	0	0
$577$	−5.35377e9	−1.16023	−0.580115	−	0.814534i	$-0.696993\pi$
$577$	−5.35377e9	−1.16023	−0.580115	+	0.814534i	$0.696993\pi$
$578$	1.73005e10	3.72658
$579$	0	0
$580$	−4.80062e9	−1.02164
$581$	−2.77069e9	−0.586101
$582$	0	0
$583$	−8.18731e9	−1.71120
$584$	8.83227e8	0.183496
$585$	0	0
$586$	−1.39022e10	−2.85393
$587$	2.38474e9	0.486639	0.243319	−	0.969946i	$-0.421764\pi$
$587$	2.38474e9	0.486639	0.243319	+	0.969946i	$0.421764\pi$
$588$	0	0
$589$	−5.14634e8	−0.103775
$590$	3.58275e8	0.0718183
$591$	0	0
$592$	−7.42035e9	−1.46994
$593$	1.25715e9	0.247569	0.123785	−	0.992309i	$-0.460497\pi$
$593$	1.25715e9	0.247569	0.123785	+	0.992309i	$0.460497\pi$
$594$	0	0
$595$	4.00692e9	0.779833
$596$	−9.67281e9	−1.87150
$597$	0	0
$598$	−3.06268e9	−0.585662
$599$	7.96256e9	1.51377	0.756884	−	0.653550i	$-0.226721\pi$
$599$	7.96256e9	1.51377	0.756884	+	0.653550i	$0.226721\pi$
$600$	0	0
$601$	−4.51895e9	−0.849134	−0.424567	−	0.905396i	$-0.639574\pi$
$601$	−4.51895e9	−0.849134	−0.424567	+	0.905396i	$0.639574\pi$
$602$	−1.24071e10	−2.31784
$603$	0	0
$604$	4.19934e9	0.775446
$605$	3.05261e9	0.560438
$606$	0	0
$607$	8.55255e8	0.155216	0.0776078	−	0.996984i	$-0.475272\pi$
$607$	8.55255e8	0.155216	0.0776078	+	0.996984i	$0.475272\pi$
$608$	5.32926e7	0.00961622
$609$	0	0
$610$	4.43826e9	0.791695
$611$	7.60540e8	0.134889
$612$	0	0
$613$	1.13272e10	1.98615	0.993074	−	0.117495i	$-0.0374863\pi$
$613$	1.13272e10	1.98615	0.993074	+	0.117495i	$0.0374863\pi$
$614$	−6.53160e9	−1.13876
$615$	0	0
$616$	2.22720e10	3.83908
$617$	4.99511e9	0.856144	0.428072	−	0.903745i	$-0.359193\pi$
$617$	4.99511e9	0.856144	0.428072	+	0.903745i	$0.359193\pi$
$618$	0	0
$619$	−9.00840e9	−1.52662	−0.763309	−	0.646034i	$-0.776427\pi$
$619$	−9.00840e9	−1.52662	−0.763309	+	0.646034i	$0.776427\pi$
$620$	3.14398e9	0.529796
$621$	0	0
$622$	7.53740e9	1.25590
$623$	−7.65465e9	−1.26829
$624$	0	0
$625$	4.29570e9	0.703807
$626$	−4.29553e9	−0.699853
$627$	0	0
$628$	−2.82762e9	−0.455577
$629$	−1.74936e10	−2.80287
$630$	0	0
$631$	2.46728e9	0.390945	0.195473	−	0.980709i	$-0.437376\pi$
$631$	2.46728e9	0.390945	0.195473	+	0.980709i	$0.437376\pi$
$632$	1.16764e10	1.83992
$633$	0	0
$634$	−1.74537e10	−2.72004
$635$	−2.85796e9	−0.442944
$636$	0	0
$637$	6.21036e9	0.951982
$638$	−3.03505e10	−4.62694
$639$	0	0
$640$	−3.73603e9	−0.563353
$641$	−9.81230e9	−1.47153	−0.735763	−	0.677239i	$-0.763176\pi$
$641$	−9.81230e9	−1.47153	−0.735763	+	0.677239i	$0.763176\pi$
$642$	0	0
$643$	−2.14527e9	−0.318232	−0.159116	−	0.987260i	$-0.550864\pi$
$643$	−2.14527e9	−0.318232	−0.159116	+	0.987260i	$0.550864\pi$
$644$	−5.78941e9	−0.854149
$645$	0	0
$646$	−2.60223e9	−0.379780
$647$	6.47241e8	0.0939510	0.0469755	−	0.998896i	$-0.485042\pi$
$647$	6.47241e8	0.0939510	0.0469755	+	0.998896i	$0.485042\pi$
$648$	0	0
$649$	1.50429e9	0.216010
$650$	−1.16940e10	−1.67019
$651$	0	0
$652$	−2.24887e10	−3.17759
$653$	1.02494e10	1.44046	0.720231	−	0.693734i	$-0.244036\pi$
$653$	1.02494e10	1.44046	0.720231	+	0.693734i	$0.244036\pi$
$654$	0	0
$655$	−1.52882e8	−0.0212574
$656$	−1.58169e9	−0.218755
$657$	0	0
$658$	2.16476e9	0.296223
$659$	−6.02759e9	−0.820436	−0.410218	−	0.911987i	$-0.634547\pi$
$659$	−6.02759e9	−0.820436	−0.410218	+	0.911987i	$0.634547\pi$
$660$	0	0
$661$	−6.67043e9	−0.898357	−0.449178	−	0.893442i	$-0.648283\pi$
$661$	−6.67043e9	−0.898357	−0.449178	+	0.893442i	$0.648283\pi$
$662$	−1.38043e10	−1.84931
$663$	0	0
$664$	−5.43308e9	−0.720208
$665$	−4.11955e8	−0.0543218
$666$	0	0
$667$	3.89925e9	0.508793
$668$	−3.20148e9	−0.415559
$669$	0	0
$670$	4.99689e9	0.641856
$671$	1.86349e10	2.38121
$672$	0	0
$673$	−1.14815e10	−1.45194	−0.725968	−	0.687728i	$-0.758608\pi$
$673$	−1.14815e10	−1.45194	−0.725968	+	0.687728i	$0.758608\pi$
$674$	−2.65441e10	−3.33933
$675$	0	0
$676$	2.57978e9	0.321195
$677$	−5.08614e8	−0.0629982	−0.0314991	−	0.999504i	$-0.510028\pi$
$677$	−5.08614e8	−0.0629982	−0.0314991	+	0.999504i	$0.510028\pi$
$678$	0	0
$679$	7.18149e9	0.880380
$680$	7.85721e9	0.958268
$681$	0	0
$682$	1.98769e10	2.39940
$683$	−1.22165e10	−1.46715	−0.733574	−	0.679610i	$-0.762149\pi$
$683$	−1.22165e10	−1.46715	−0.733574	+	0.679610i	$0.762149\pi$
$684$	0	0
$685$	−7.06838e8	−0.0840239
$686$	−2.34308e9	−0.277111
$687$	0	0
$688$	−7.79539e9	−0.912595
$689$	−9.54673e9	−1.11196
$690$	0	0
$691$	1.36598e10	1.57496	0.787482	−	0.616337i	$-0.211384\pi$
$691$	1.36598e10	1.57496	0.787482	+	0.616337i	$0.211384\pi$
$692$	−1.06919e10	−1.22654
$693$	0	0
$694$	−1.09514e10	−1.24368
$695$	3.59162e9	0.405830
$696$	0	0
$697$	−3.72887e9	−0.417121
$698$	1.67943e10	1.86925
$699$	0	0
$700$	−2.21053e10	−2.43586
$701$	−2.89789e9	−0.317737	−0.158869	−	0.987300i	$-0.550785\pi$
$701$	−2.89789e9	−0.317737	−0.158869	+	0.987300i	$0.550785\pi$
$702$	0	0
$703$	1.79854e9	0.195243
$704$	−1.63778e10	−1.76909
$705$	0	0
$706$	−3.75652e9	−0.401762
$707$	4.86593e9	0.517843
$708$	0	0
$709$	3.72879e9	0.392922	0.196461	−	0.980512i	$-0.437055\pi$
$709$	3.72879e9	0.392922	0.196461	+	0.980512i	$0.437055\pi$
$710$	−7.29249e9	−0.764666
$711$	0	0
$712$	−1.50101e10	−1.55848
$713$	−2.55366e9	−0.263846
$714$	0	0
$715$	5.59000e9	0.571927
$716$	−1.15391e9	−0.117484
$717$	0	0
$718$	−1.57539e10	−1.58838
$719$	−5.51005e9	−0.552846	−0.276423	−	0.961036i	$-0.589149\pi$
$719$	−5.51005e9	−0.552846	−0.276423	+	0.961036i	$0.589149\pi$
$720$	0	0
$721$	1.75736e10	1.74617
$722$	−1.71821e10	−1.69901
$723$	0	0
$724$	2.38950e10	2.34004
$725$	1.48882e10	1.45097
$726$	0	0
$727$	−4.92800e9	−0.475664	−0.237832	−	0.971306i	$-0.576437\pi$
$727$	−4.92800e9	−0.475664	−0.237832	+	0.971306i	$0.576437\pi$
$728$	2.59701e10	2.49467
$729$	0	0
$730$	6.30975e8	0.0600319
$731$	−1.83778e10	−1.74013
$732$	0	0
$733$	−1.65782e10	−1.55480	−0.777400	−	0.629006i	$-0.783462\pi$
$733$	−1.65782e10	−1.55480	−0.777400	+	0.629006i	$0.783462\pi$
$734$	1.68315e10	1.57103
$735$	0	0
$736$	2.64443e8	0.0244489
$737$	2.09804e10	1.93053
$738$	0	0
$739$	3.89003e9	0.354566	0.177283	−	0.984160i	$-0.443269\pi$
$739$	3.89003e9	0.354566	0.177283	+	0.984160i	$0.443269\pi$
$740$	−1.09875e10	−0.996757
$741$	0	0
$742$	−2.71733e10	−2.44190
$743$	−1.57972e9	−0.141293	−0.0706464	−	0.997501i	$-0.522506\pi$
$743$	−1.57972e9	−0.141293	−0.0706464	+	0.997501i	$0.522506\pi$
$744$	0	0
$745$	−3.41533e9	−0.302612
$746$	1.30116e10	1.14748
$747$	0	0
$748$	6.67484e10	5.83157
$749$	1.16316e10	1.01147
$750$	0	0
$751$	−1.21876e10	−1.04997	−0.524987	−	0.851110i	$-0.675930\pi$
$751$	−1.21876e10	−1.04997	−0.524987	+	0.851110i	$0.675930\pi$
$752$	1.36012e9	0.116631
$753$	0	0
$754$	−3.53899e10	−3.00663
$755$	1.48273e9	0.125385
$756$	0	0
$757$	5.00276e9	0.419154	0.209577	−	0.977792i	$-0.432791\pi$
$757$	5.00276e9	0.419154	0.209577	+	0.977792i	$0.432791\pi$
$758$	1.87758e10	1.56587
$759$	0	0
$760$	−8.07806e8	−0.0667512
$761$	5.46141e9	0.449219	0.224610	−	0.974449i	$-0.427889\pi$
$761$	5.46141e9	0.449219	0.224610	+	0.974449i	$0.427889\pi$
$762$	0	0
$763$	−2.33252e10	−1.90103
$764$	4.53256e8	0.0367720
$765$	0	0
$766$	4.24202e10	3.41013
$767$	1.75406e9	0.140366
$768$	0	0
$769$	9.03628e9	0.716552	0.358276	−	0.933616i	$-0.383365\pi$
$769$	9.03628e9	0.716552	0.358276	+	0.933616i	$0.383365\pi$
$770$	1.59111e10	1.25598
$771$	0	0
$772$	−1.04051e10	−0.813924
$773$	1.95485e10	1.52225	0.761124	−	0.648606i	$-0.224648\pi$
$773$	1.95485e10	1.52225	0.761124	+	0.648606i	$0.224648\pi$
$774$	0	0
$775$	−9.75045e9	−0.752435
$776$	1.40822e10	1.08182
$777$	0	0
$778$	2.28826e10	1.74211
$779$	3.83368e8	0.0290559
$780$	0	0
$781$	−3.06189e10	−2.29991
$782$	−1.29125e10	−0.965578
$783$	0	0
$784$	1.11063e10	0.823122
$785$	−9.98393e8	−0.0736644
$786$	0	0
$787$	1.51346e10	1.10677	0.553386	−	0.832925i	$-0.313335\pi$
$787$	1.51346e10	1.10677	0.553386	+	0.832925i	$0.313335\pi$
$788$	4.30190e9	0.313198
$789$	0	0
$790$	8.34160e9	0.601942
$791$	−1.46547e10	−1.05283
$792$	0	0
$793$	2.17290e10	1.54733
$794$	1.52676e10	1.08243
$795$	0	0
$796$	−1.93751e10	−1.36159
$797$	−2.16967e10	−1.51806	−0.759031	−	0.651055i	$-0.774327\pi$
$797$	−2.16967e10	−1.51806	−0.759031	+	0.651055i	$0.774327\pi$
$798$	0	0
$799$	3.20650e9	0.222391
$800$	1.00970e9	0.0697234
$801$	0	0
$802$	−4.21228e9	−0.288342
$803$	2.64927e9	0.180560
$804$	0	0
$805$	−2.04416e9	−0.138111
$806$	2.31772e10	1.55915
$807$	0	0
$808$	9.54165e9	0.636332
$809$	−8.84688e9	−0.587450	−0.293725	−	0.955890i	$-0.594895\pi$
$809$	−8.84688e9	−0.587450	−0.293725	+	0.955890i	$0.594895\pi$
$810$	0	0
$811$	2.76914e10	1.82294	0.911470	−	0.411367i	$-0.134949\pi$
$811$	2.76914e10	1.82294	0.911470	+	0.411367i	$0.134949\pi$
$812$	−6.68979e10	−4.38497
$813$	0	0
$814$	−6.94655e10	−4.51423
$815$	−7.94045e9	−0.513799
$816$	0	0
$817$	1.88944e9	0.121215
$818$	1.82826e10	1.16789
$819$	0	0
$820$	−2.34205e9	−0.148337
$821$	−5.11977e8	−0.0322886	−0.0161443	−	0.999870i	$-0.505139\pi$
$821$	−5.11977e8	−0.0322886	−0.0161443	+	0.999870i	$0.505139\pi$
$822$	0	0
$823$	−1.36623e9	−0.0854327	−0.0427163	−	0.999087i	$-0.513601\pi$
$823$	−1.36623e9	−0.0854327	−0.0427163	+	0.999087i	$0.513601\pi$
$824$	3.44602e10	2.14572
$825$	0	0
$826$	4.99266e9	0.308249
$827$	−1.32162e10	−0.812525	−0.406263	−	0.913756i	$-0.633168\pi$
$827$	−1.32162e10	−0.812525	−0.406263	+	0.913756i	$0.633168\pi$
$828$	0	0
$829$	−1.17083e10	−0.713764	−0.356882	−	0.934149i	$-0.616160\pi$
$829$	−1.17083e10	−0.713764	−0.356882	+	0.934149i	$0.616160\pi$
$830$	−3.88137e9	−0.235620
$831$	0	0
$832$	−1.90972e10	−1.14957
$833$	2.61834e10	1.56953
$834$	0	0
$835$	−1.13040e9	−0.0671936
$836$	−6.86246e9	−0.406217
$837$	0	0
$838$	2.95980e10	1.73744
$839$	−1.41233e10	−0.825597	−0.412799	−	0.910822i	$-0.635449\pi$
$839$	−1.41233e10	−0.825597	−0.412799	+	0.910822i	$0.635449\pi$
$840$	0	0
$841$	2.78068e10	1.61200
$842$	2.28650e10	1.32002
$843$	0	0
$844$	4.49324e10	2.57253
$845$	9.10883e8	0.0519355
$846$	0	0
$847$	4.25389e10	2.40544
$848$	−1.70729e10	−0.961442
$849$	0	0
$850$	−4.93029e10	−2.75363
$851$	8.92451e9	0.496399
$852$	0	0
$853$	−1.96723e10	−1.08526	−0.542629	−	0.839973i	$-0.682571\pi$
$853$	−1.96723e10	−1.08526	−0.542629	+	0.839973i	$0.682571\pi$
$854$	6.18482e10	3.39801
$855$	0	0
$856$	2.28085e10	1.24291
$857$	1.19022e8	0.00645942	0.00322971	−	0.999995i	$-0.498972\pi$
$857$	1.19022e8	0.00645942	0.00322971	+	0.999995i	$0.498972\pi$
$858$	0	0
$859$	−1.81362e10	−0.976271	−0.488136	−	0.872768i	$-0.662323\pi$
$859$	−1.81362e10	−0.976271	−0.488136	+	0.872768i	$0.662323\pi$
$860$	−1.15429e10	−0.618827
$861$	0	0
$862$	4.94479e10	2.62950
$863$	−1.14426e9	−0.0606020	−0.0303010	−	0.999541i	$-0.509647\pi$
$863$	−1.14426e9	−0.0606020	−0.0303010	+	0.999541i	$0.509647\pi$
$864$	0	0
$865$	−3.77515e9	−0.198325
$866$	−1.58090e10	−0.827164
$867$	0	0
$868$	4.38121e10	2.27392
$869$	3.50238e10	1.81048
$870$	0	0
$871$	2.44640e10	1.25448
$872$	−4.57386e10	−2.33601
$873$	0	0
$874$	1.32755e9	0.0672605
$875$	−1.64987e10	−0.832573
$876$	0	0
$877$	−1.63691e10	−0.819457	−0.409728	−	0.912208i	$-0.634377\pi$
$877$	−1.63691e10	−0.819457	−0.409728	+	0.912208i	$0.634377\pi$
$878$	−7.00544e9	−0.349305
$879$	0	0
$880$	9.99691e9	0.494511
$881$	−1.77394e10	−0.874022	−0.437011	−	0.899456i	$-0.643963\pi$
$881$	−1.77394e10	−0.874022	−0.437011	+	0.899456i	$0.643963\pi$
$882$	0	0
$883$	−2.34714e10	−1.14730	−0.573649	−	0.819102i	$-0.694472\pi$
$883$	−2.34714e10	−1.14730	−0.573649	+	0.819102i	$0.694472\pi$
$884$	7.78313e10	3.78941
$885$	0	0
$886$	−1.28886e10	−0.622568
$887$	−1.33151e10	−0.640635	−0.320318	−	0.947310i	$-0.603790\pi$
$887$	−1.33151e10	−0.640635	−0.320318	+	0.947310i	$0.603790\pi$
$888$	0	0
$889$	−3.98264e10	−1.90114
$890$	−1.07231e10	−0.509867
$891$	0	0
$892$	−1.27548e10	−0.601723
$893$	−3.29663e8	−0.0154914
$894$	0	0
$895$	−4.07431e8	−0.0189965
$896$	−5.20625e10	−2.41795
$897$	0	0
$898$	−4.62217e10	−2.12999
$899$	−2.95081e10	−1.35451
$900$	0	0
$901$	−4.02499e10	−1.83327
$902$	−1.48069e10	−0.671804
$903$	0	0
$904$	−2.87365e10	−1.29373
$905$	8.43700e9	0.378371
$906$	0	0
$907$	1.60529e10	0.714379	0.357189	−	0.934032i	$-0.383735\pi$
$907$	1.60529e10	0.714379	0.357189	+	0.934032i	$0.383735\pi$
$908$	5.30370e10	2.35114
$909$	0	0
$910$	1.85530e10	0.816146
$911$	4.74722e9	0.208030	0.104015	−	0.994576i	$-0.466831\pi$
$911$	4.74722e9	0.208030	0.104015	+	0.994576i	$0.466831\pi$
$912$	0	0
$913$	−1.62967e10	−0.708682
$914$	−1.06076e10	−0.459522
$915$	0	0
$916$	6.40228e10	2.75233
$917$	−2.13044e9	−0.0912383
$918$	0	0
$919$	7.61932e9	0.323826	0.161913	−	0.986805i	$-0.448234\pi$
$919$	7.61932e9	0.323826	0.161913	+	0.986805i	$0.448234\pi$
$920$	−4.00841e9	−0.169713
$921$	0	0
$922$	4.84467e10	2.03566
$923$	−3.57029e10	−1.49451
$924$	0	0
$925$	3.40758e10	1.41563
$926$	−1.66739e10	−0.690079
$927$	0	0
$928$	3.05570e9	0.125514
$929$	2.16983e10	0.887913	0.443956	−	0.896048i	$-0.353574\pi$
$929$	2.16983e10	0.887913	0.443956	+	0.896048i	$0.353574\pi$
$930$	0	0
$931$	−2.69194e9	−0.109330
$932$	2.48622e10	1.00597
$933$	0	0
$934$	5.73821e10	2.30442
$935$	2.35679e10	0.942933
$936$	0	0
$937$	1.48556e10	0.589930	0.294965	−	0.955508i	$-0.404692\pi$
$937$	1.48556e10	0.589930	0.294965	+	0.955508i	$0.404692\pi$
$938$	6.96329e10	2.75489
$939$	0	0
$940$	2.01396e9	0.0790869
$941$	−2.41515e9	−0.0944889	−0.0472445	−	0.998883i	$-0.515044\pi$
$941$	−2.41515e9	−0.0944889	−0.0472445	+	0.998883i	$0.515044\pi$
$942$	0	0
$943$	1.90231e9	0.0738737
$944$	3.13688e9	0.121366
$945$	0	0
$946$	−7.29764e10	−2.80261
$947$	3.87782e10	1.48376	0.741878	−	0.670534i	$-0.233935\pi$
$947$	3.87782e10	1.48376	0.741878	+	0.670534i	$0.233935\pi$
$948$	0	0
$949$	3.08915e9	0.117330
$950$	5.06887e9	0.191813
$951$	0	0
$952$	1.09492e11	4.11295
$953$	−2.86112e10	−1.07081	−0.535403	−	0.844597i	$-0.679840\pi$
$953$	−2.86112e10	−1.07081	−0.535403	+	0.844597i	$0.679840\pi$
$954$	0	0
$955$	1.60038e8	0.00594583
$956$	5.82335e10	2.15561
$957$	0	0
$958$	−5.76289e10	−2.11768
$959$	−9.84997e9	−0.360637
$960$	0	0
$961$	−8.18745e9	−0.297589
$962$	−8.09995e10	−2.93339
$963$	0	0
$964$	2.93503e10	1.05522
$965$	−3.67388e9	−0.131607
$966$	0	0
$967$	9.52974e9	0.338913	0.169457	−	0.985538i	$-0.445799\pi$
$967$	9.52974e9	0.338913	0.169457	+	0.985538i	$0.445799\pi$
$968$	8.34148e10	2.95583
$969$	0	0
$970$	1.00603e10	0.353924
$971$	1.04348e10	0.365777	0.182889	−	0.983134i	$-0.441455\pi$
$971$	1.04348e10	0.365777	0.182889	+	0.983134i	$0.441455\pi$
$972$	0	0
$973$	5.00501e10	1.74185
$974$	5.70294e10	1.97762
$975$	0	0
$976$	3.88592e10	1.33789
$977$	1.28963e10	0.442418	0.221209	−	0.975226i	$-0.429000\pi$
$977$	1.28963e10	0.442418	0.221209	+	0.975226i	$0.429000\pi$
$978$	0	0
$979$	−4.50232e10	−1.53354
$980$	1.64455e10	0.558155
$981$	0	0
$982$	4.49392e10	1.51438
$983$	5.00120e10	1.67933	0.839666	−	0.543103i	$-0.182751\pi$
$983$	5.00120e10	1.67933	0.839666	+	0.543103i	$0.182751\pi$
$984$	0	0
$985$	1.51894e9	0.0506424
$986$	−1.49207e11	−4.95701
$987$	0	0
$988$	−8.00190e9	−0.263964
$989$	9.37557e9	0.308184
$990$	0	0
$991$	−4.09158e9	−0.133547	−0.0667734	−	0.997768i	$-0.521270\pi$
$991$	−4.09158e9	−0.133547	−0.0667734	+	0.997768i	$0.521270\pi$
$992$	−2.00121e9	−0.0650880
$993$	0	0
$994$	−1.01623e11	−3.28200
$995$	−6.84107e9	−0.220163
$996$	0	0
$997$	6.09915e10	1.94911	0.974555	−	0.224150i	$-0.0719604\pi$
$997$	6.09915e10	1.94911	0.974555	+	0.224150i	$0.0719604\pi$
$998$	5.42757e10	1.72842
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.f.1.19		20
3.2	odd	2		59.8.a.b.1.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.8.a.b.1.2	✓	20	3.2	odd	2
531.8.a.f.1.19		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)

\(f(q)\)	\(=\)	\(q+19.5214 q^{2} +253.086 q^{4} +89.3612 q^{5} +1245.27 q^{7} +2441.86 q^{8} +O(q^{10})\)	\(q+19.5214 q^{2} +253.086 q^{4} +89.3612 q^{5} +1245.27 q^{7} +2441.86 q^{8} +1744.46 q^{10} +7324.44 q^{11} +8540.60 q^{13} +24309.5 q^{14} +15273.6 q^{16} +36007.9 q^{17} -3702.00 q^{19} +22616.1 q^{20} +142984. q^{22} -18369.7 q^{23} -70139.6 q^{25} +166725. q^{26} +315161. q^{28} -212266. q^{29} +139015. q^{31} -14395.6 q^{32} +702926. q^{34} +111279. q^{35} -485828. q^{37} -72268.3 q^{38} +218208. q^{40} -103557. q^{41} -510383. q^{43} +1.85372e6 q^{44} -358603. q^{46} +89050.0 q^{47} +727157. q^{49} -1.36922e6 q^{50} +2.16151e6 q^{52} -1.11781e6 q^{53} +654521. q^{55} +3.04078e6 q^{56} -4.14373e6 q^{58} +205379. q^{59} +2.54420e6 q^{61} +2.71377e6 q^{62} -2.23605e6 q^{64} +763198. q^{65} +2.86443e6 q^{67} +9.11310e6 q^{68} +2.17232e6 q^{70} -4.18037e6 q^{71} +361702. q^{73} -9.48406e6 q^{74} -936925. q^{76} +9.12092e6 q^{77} +4.78177e6 q^{79} +1.36487e6 q^{80} -2.02158e6 q^{82} -2.22497e6 q^{83} +3.21771e6 q^{85} -9.96340e6 q^{86} +1.78853e7 q^{88} -6.14697e6 q^{89} +1.06354e7 q^{91} -4.64911e6 q^{92} +1.73838e6 q^{94} -330815. q^{95} +5.76701e6 q^{97} +1.41952e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 15 q^{2} + 1535 q^{4} - 570 q^{5} + 1040 q^{7} - 2145 q^{8}+O(q^{10}) \) 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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