LMFDB - Embedded newform 531.8.a.g.1.8

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:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-14.1831 q^{2} +73.1601 q^{4} +347.413 q^{5} +522.395 q^{7} +777.799 q^{8} +O(q^{10})$	\(q-14.1831 q^{2} +73.1601 q^{4} +347.413 q^{5} +522.395 q^{7} +777.799 q^{8} -4927.40 q^{10} -8111.00 q^{11} -1020.63 q^{13} -7409.17 q^{14} -20396.1 q^{16} +12904.9 q^{17} +37644.1 q^{19} +25416.8 q^{20} +115039. q^{22} +76971.6 q^{23} +42571.0 q^{25} +14475.7 q^{26} +38218.5 q^{28} +46125.9 q^{29} -283279. q^{31} +189721. q^{32} -183031. q^{34} +181487. q^{35} +158719. q^{37} -533910. q^{38} +270218. q^{40} -549684. q^{41} -561641. q^{43} -593402. q^{44} -1.09169e6 q^{46} -580625. q^{47} -550647. q^{49} -603789. q^{50} -74669.3 q^{52} -1.26696e6 q^{53} -2.81787e6 q^{55} +406318. q^{56} -654209. q^{58} +205379. q^{59} +2.99918e6 q^{61} +4.01777e6 q^{62} -80136.5 q^{64} -354580. q^{65} +885038. q^{67} +944123. q^{68} -2.57404e6 q^{70} -1.83083e6 q^{71} +1.64078e6 q^{73} -2.25113e6 q^{74} +2.75405e6 q^{76} -4.23714e6 q^{77} +5.91230e6 q^{79} -7.08587e6 q^{80} +7.79622e6 q^{82} +2.52150e6 q^{83} +4.48333e6 q^{85} +7.96581e6 q^{86} -6.30873e6 q^{88} -1.27983e7 q^{89} -533171. q^{91} +5.63125e6 q^{92} +8.23506e6 q^{94} +1.30781e7 q^{95} -8.05056e6 q^{97} +7.80988e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8}+O(q^{10}) $ 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8} + 5042 q^{10} - 13310 q^{11} - 14172 q^{13} - 16464 q^{14} + 95772 q^{16} - 39304 q^{17} - 56302 q^{19} + 17936 q^{20} + 152764 q^{22} - 17988 q^{23} + 468523 q^{25} + 27624 q^{26} - 59896 q^{28} - 474564 q^{29} + 188186 q^{31} - 251068 q^{32} + 169888 q^{34} - 514500 q^{35} + 1148200 q^{37} - 446594 q^{38} + 501214 q^{40} - 1246152 q^{41} + 62268 q^{43} - 2555520 q^{44} - 1289942 q^{46} - 1485654 q^{47} + 3829555 q^{49} - 6430160 q^{50} - 2624804 q^{52} - 4086740 q^{53} - 1119118 q^{55} - 8448352 q^{56} + 2966706 q^{58} + 6777507 q^{59} + 2436146 q^{61} - 9005952 q^{62} + 11117562 q^{64} - 16730354 q^{65} - 2652248 q^{67} - 15929124 q^{68} + 3359254 q^{70} - 7356324 q^{71} + 1900454 q^{73} - 25386964 q^{74} - 16047360 q^{76} - 20774826 q^{77} - 5912712 q^{79} - 13568404 q^{80} + 1579434 q^{82} + 1052766 q^{83} + 18372730 q^{85} - 43499960 q^{86} + 18209214 q^{88} - 174788 q^{89} - 18891512 q^{91} - 46033270 q^{92} + 365448 q^{94} - 31505580 q^{95} + 14418540 q^{97} + 15964056 q^{98}+O(q^{100}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8 + 5042 * q^10 - 13310 * q^11 - 14172 * q^13 - 16464 * q^14 + 95772 * q^16 - 39304 * q^17 - 56302 * q^19 + 17936 * q^20 + 152764 * q^22 - 17988 * q^23 + 468523 * q^25 + 27624 * q^26 - 59896 * q^28 - 474564 * q^29 + 188186 * q^31 - 251068 * q^32 + 169888 * q^34 - 514500 * q^35 + 1148200 * q^37 - 446594 * q^38 + 501214 * q^40 - 1246152 * q^41 + 62268 * q^43 - 2555520 * q^44 - 1289942 * q^46 - 1485654 * q^47 + 3829555 * q^49 - 6430160 * q^50 - 2624804 * q^52 - 4086740 * q^53 - 1119118 * q^55 - 8448352 * q^56 + 2966706 * q^58 + 6777507 * q^59 + 2436146 * q^61 - 9005952 * q^62 + 11117562 * q^64 - 16730354 * q^65 - 2652248 * q^67 - 15929124 * q^68 + 3359254 * q^70 - 7356324 * q^71 + 1900454 * q^73 - 25386964 * q^74 - 16047360 * q^76 - 20774826 * q^77 - 5912712 * q^79 - 13568404 * q^80 + 1579434 * q^82 + 1052766 * q^83 + 18372730 * q^85 - 43499960 * q^86 + 18209214 * q^88 - 174788 * q^89 - 18891512 * q^91 - 46033270 * q^92 + 365448 * q^94 - 31505580 * q^95 + 14418540 * q^97 + 15964056 * 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 $

$2$	−14.1831	−1.25362	−0.626810	−	0.779172i	$-0.715640\pi$
$2$	−14.1831	−1.25362	−0.626810	+	0.779172i	$0.715640\pi$
$3$	0	0
$3$	0	0
$4$	73.1601	0.571564
$5$	347.413	1.24294	0.621472	−	0.783437i	$-0.286535\pi$
$5$	347.413	1.24294	0.621472	+	0.783437i	$0.286535\pi$
$6$	0	0
$7$	522.395	0.575646	0.287823	−	0.957684i	$-0.407069\pi$
$7$	522.395	0.575646	0.287823	+	0.957684i	$0.407069\pi$
$8$	777.799	0.537097
$9$	0	0
$10$	−4927.40	−1.55818
$11$	−8111.00	−1.83738	−0.918692	−	0.394974i	$-0.870754\pi$
$11$	−8111.00	−1.83738	−0.918692	+	0.394974i	$0.870754\pi$
$12$	0	0
$13$	−1020.63	−0.128845	−0.0644223	−	0.997923i	$-0.520520\pi$
$13$	−1020.63	−0.128845	−0.0644223	+	0.997923i	$0.520520\pi$
$14$	−7409.17	−0.721641
$15$	0	0
$16$	−20396.1	−1.24488
$17$	12904.9	0.637064	0.318532	−	0.947912i	$-0.396810\pi$
$17$	12904.9	0.637064	0.318532	+	0.947912i	$0.396810\pi$
$18$	0	0
$19$	37644.1	1.25910	0.629549	−	0.776961i	$-0.283240\pi$
$19$	37644.1	1.25910	0.629549	+	0.776961i	$0.283240\pi$
$20$	25416.8	0.710421
$21$	0	0
$22$	115039.	2.30338
$23$	76971.6	1.31912	0.659558	−	0.751654i	$-0.270744\pi$
$23$	76971.6	1.31912	0.659558	+	0.751654i	$0.270744\pi$
$24$	0	0
$25$	42571.0	0.544909
$26$	14475.7	0.161522
$27$	0	0
$28$	38218.5	0.329018
$29$	46125.9	0.351198	0.175599	−	0.984462i	$-0.443814\pi$
$29$	46125.9	0.351198	0.175599	+	0.984462i	$0.443814\pi$
$30$	0	0
$31$	−283279.	−1.70784	−0.853922	−	0.520401i	$-0.825783\pi$
$31$	−283279.	−1.70784	−0.853922	+	0.520401i	$0.825783\pi$
$32$	189721.	1.02351
$33$	0	0
$34$	−183031.	−0.798636
$35$	181487.	0.715496
$36$	0	0
$37$	158719.	0.515138	0.257569	−	0.966260i	$-0.417079\pi$
$37$	158719.	0.515138	0.257569	+	0.966260i	$0.417079\pi$
$38$	−533910.	−1.57843
$39$	0	0
$40$	270218.	0.667581
$41$	−549684.	−1.24557	−0.622787	−	0.782391i	$-0.714000\pi$
$41$	−549684.	−1.24557	−0.622787	+	0.782391i	$0.714000\pi$
$42$	0	0
$43$	−561641.	−1.07726	−0.538629	−	0.842543i	$-0.681057\pi$
$43$	−561641.	−1.07726	−0.538629	+	0.842543i	$0.681057\pi$
$44$	−593402.	−1.05018
$45$	0	0
$46$	−1.09169e6	−1.65367
$47$	−580625.	−0.815743	−0.407872	−	0.913039i	$-0.633729\pi$
$47$	−580625.	−0.815743	−0.407872	+	0.913039i	$0.633729\pi$
$48$	0	0
$49$	−550647.	−0.668632
$50$	−603789.	−0.683109
$51$	0	0
$52$	−74669.3	−0.0736428
$53$	−1.26696e6	−1.16895	−0.584475	−	0.811411i	$-0.698700\pi$
$53$	−1.26696e6	−1.16895	−0.584475	+	0.811411i	$0.698700\pi$
$54$	0	0
$55$	−2.81787e6	−2.28377
$56$	406318.	0.309178
$57$	0	0
$58$	−654209.	−0.440269
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	2.99918e6	1.69179	0.845897	−	0.533346i	$-0.179065\pi$
$61$	2.99918e6	1.69179	0.845897	+	0.533346i	$0.179065\pi$
$62$	4.01777e6	2.14099
$63$	0	0
$64$	−80136.5	−0.0382121
$65$	−354580.	−0.160147
$66$	0	0
$67$	885038.	0.359501	0.179751	−	0.983712i	$-0.442471\pi$
$67$	885038.	0.359501	0.179751	+	0.983712i	$0.442471\pi$
$68$	944123.	0.364122
$69$	0	0
$70$	−2.57404e6	−0.896960
$71$	−1.83083e6	−0.607078	−0.303539	−	0.952819i	$-0.598168\pi$
$71$	−1.83083e6	−0.607078	−0.303539	+	0.952819i	$0.598168\pi$
$72$	0	0
$73$	1.64078e6	0.493653	0.246826	−	0.969060i	$-0.420612\pi$
$73$	1.64078e6	0.493653	0.246826	+	0.969060i	$0.420612\pi$
$74$	−2.25113e6	−0.645787
$75$	0	0
$76$	2.75405e6	0.719655
$77$	−4.23714e6	−1.05768
$78$	0	0
$79$	5.91230e6	1.34915	0.674577	−	0.738204i	$-0.264326\pi$
$79$	5.91230e6	1.34915	0.674577	+	0.738204i	$0.264326\pi$
$80$	−7.08587e6	−1.54731
$81$	0	0
$82$	7.79622e6	1.56148
$83$	2.52150e6	0.484045	0.242023	−	0.970271i	$-0.422189\pi$
$83$	2.52150e6	0.484045	0.242023	+	0.970271i	$0.422189\pi$
$84$	0	0
$85$	4.48333e6	0.791834
$86$	7.96581e6	1.35047
$87$	0	0
$88$	−6.30873e6	−0.986853
$89$	−1.27983e7	−1.92437	−0.962184	−	0.272401i	$-0.912182\pi$
$89$	−1.27983e7	−1.92437	−0.962184	+	0.272401i	$0.912182\pi$
$90$	0	0
$91$	−533171.	−0.0741689
$92$	5.63125e6	0.753958
$93$	0	0
$94$	8.23506e6	1.02263
$95$	1.30781e7	1.56499
$96$	0	0
$97$	−8.05056e6	−0.895623	−0.447811	−	0.894128i	$-0.647796\pi$
$97$	−8.05056e6	−0.895623	−0.447811	+	0.894128i	$0.647796\pi$
$98$	7.80988e6	0.838210
$99$	0	0
$100$	3.11450e6	0.311450
$101$	−1.37719e7	−1.33005	−0.665025	−	0.746821i	$-0.731579\pi$
$101$	−1.37719e7	−1.33005	−0.665025	+	0.746821i	$0.731579\pi$
$102$	0	0
$103$	1.08632e7	0.979548	0.489774	−	0.871849i	$-0.337079\pi$
$103$	1.08632e7	0.979548	0.489774	+	0.871849i	$0.337079\pi$
$104$	−793844.	−0.0692020
$105$	0	0
$106$	1.79694e7	1.46542
$107$	−1.53133e7	−1.20844	−0.604222	−	0.796816i	$-0.706516\pi$
$107$	−1.53133e7	−1.20844	−0.604222	+	0.796816i	$0.706516\pi$
$108$	0	0
$109$	3.30226e6	0.244241	0.122120	−	0.992515i	$-0.461031\pi$
$109$	3.30226e6	0.244241	0.122120	+	0.992515i	$0.461031\pi$
$110$	3.99661e7	2.86297
$111$	0	0
$112$	−1.06548e7	−0.716609
$113$	3.63305e6	0.236863	0.118431	−	0.992962i	$-0.462213\pi$
$113$	3.63305e6	0.236863	0.118431	+	0.992962i	$0.462213\pi$
$114$	0	0
$115$	2.67409e7	1.63959
$116$	3.37458e6	0.200732
$117$	0	0
$118$	−2.91291e6	−0.163207
$119$	6.74144e6	0.366723
$120$	0	0
$121$	4.63012e7	2.37598
$122$	−4.25376e7	−2.12087
$123$	0	0
$124$	−2.07247e7	−0.976142
$125$	−1.23519e7	−0.565653
$126$	0	0
$127$	−1.53527e7	−0.665076	−0.332538	−	0.943090i	$-0.607905\pi$
$127$	−1.53527e7	−0.665076	−0.332538	+	0.943090i	$0.607905\pi$
$128$	−2.31478e7	−0.975605
$129$	0	0
$130$	5.02904e6	0.200763
$131$	3.55234e7	1.38059	0.690295	−	0.723528i	$-0.257481\pi$
$131$	3.55234e7	1.38059	0.690295	+	0.723528i	$0.257481\pi$
$132$	0	0
$133$	1.96651e7	0.724795
$134$	−1.25526e7	−0.450678
$135$	0	0
$136$	1.00374e7	0.342165
$137$	−5.35794e7	−1.78023	−0.890115	−	0.455736i	$-0.849376\pi$
$137$	−5.35794e7	−1.78023	−0.890115	+	0.455736i	$0.849376\pi$
$138$	0	0
$139$	−3.96342e7	−1.25175	−0.625875	−	0.779923i	$-0.715258\pi$
$139$	−3.96342e7	−1.25175	−0.625875	+	0.779923i	$0.715258\pi$
$140$	1.32776e7	0.408951
$141$	0	0
$142$	2.59669e7	0.761045
$143$	8.27832e6	0.236737
$144$	0	0
$145$	1.60248e7	0.436520
$146$	−2.32714e7	−0.618853
$147$	0	0
$148$	1.16119e7	0.294434
$149$	3.88860e7	0.963034	0.481517	−	0.876437i	$-0.340086\pi$
$149$	3.88860e7	0.963034	0.481517	+	0.876437i	$0.340086\pi$
$150$	0	0
$151$	4.65915e7	1.10125	0.550627	−	0.834751i	$-0.314389\pi$
$151$	4.65915e7	1.10125	0.550627	+	0.834751i	$0.314389\pi$
$152$	2.92796e7	0.676257
$153$	0	0
$154$	6.00958e7	1.32593
$155$	−9.84149e7	−2.12275
$156$	0	0
$157$	4.17377e7	0.860755	0.430377	−	0.902649i	$-0.358381\pi$
$157$	4.17377e7	0.860755	0.430377	+	0.902649i	$0.358381\pi$
$158$	−8.38547e7	−1.69133
$159$	0	0
$160$	6.59117e7	1.27216
$161$	4.02095e7	0.759344
$162$	0	0
$163$	3.15764e7	0.571091	0.285546	−	0.958365i	$-0.407825\pi$
$163$	3.15764e7	0.571091	0.285546	+	0.958365i	$0.407825\pi$
$164$	−4.02150e7	−0.711925
$165$	0	0
$166$	−3.57627e7	−0.606809
$167$	−8.95917e7	−1.48854	−0.744269	−	0.667880i	$-0.767202\pi$
$167$	−8.95917e7	−1.48854	−0.744269	+	0.667880i	$0.767202\pi$
$168$	0	0
$169$	−6.17068e7	−0.983399
$170$	−6.35875e7	−0.992659
$171$	0	0
$172$	−4.10897e7	−0.615721
$173$	7.49892e7	1.10113	0.550563	−	0.834793i	$-0.314413\pi$
$173$	7.49892e7	1.10113	0.550563	+	0.834793i	$0.314413\pi$
$174$	0	0
$175$	2.22389e7	0.313675
$176$	1.65433e8	2.28732
$177$	0	0
$178$	1.81520e8	2.41243
$179$	7.21642e7	0.940451	0.470226	−	0.882546i	$-0.344172\pi$
$179$	7.21642e7	0.940451	0.470226	+	0.882546i	$0.344172\pi$
$180$	0	0
$181$	−2.22359e6	−0.0278727	−0.0139363	−	0.999903i	$-0.504436\pi$
$181$	−2.22359e6	−0.0278727	−0.0139363	+	0.999903i	$0.504436\pi$
$182$	7.56201e6	0.0929796
$183$	0	0
$184$	5.98684e7	0.708493
$185$	5.51412e7	0.640287
$186$	0	0
$187$	−1.04672e8	−1.17053
$188$	−4.24786e7	−0.466249
$189$	0	0
$190$	−1.85487e8	−1.96190
$191$	1.82389e7	0.189400	0.0947002	−	0.995506i	$-0.469811\pi$
$191$	1.82389e7	0.189400	0.0947002	+	0.995506i	$0.469811\pi$
$192$	0	0
$193$	−1.99194e7	−0.199446	−0.0997229	−	0.995015i	$-0.531796\pi$
$193$	−1.99194e7	−0.199446	−0.0997229	+	0.995015i	$0.531796\pi$
$194$	1.14182e8	1.12277
$195$	0	0
$196$	−4.02854e7	−0.382165
$197$	1.41820e7	0.132162	0.0660810	−	0.997814i	$-0.478950\pi$
$197$	1.41820e7	0.132162	0.0660810	+	0.997814i	$0.478950\pi$
$198$	0	0
$199$	−4.37149e7	−0.393227	−0.196614	−	0.980481i	$-0.562994\pi$
$199$	−4.37149e7	−0.393227	−0.196614	+	0.980481i	$0.562994\pi$
$200$	3.31117e7	0.292669
$201$	0	0
$202$	1.95328e8	1.66738
$203$	2.40959e7	0.202166
$204$	0	0
$205$	−1.90968e8	−1.54818
$206$	−1.54073e8	−1.22798
$207$	0	0
$208$	2.08168e7	0.160396
$209$	−3.05332e8	−2.31345
$210$	0	0
$211$	2.55912e7	0.187543	0.0937716	−	0.995594i	$-0.470108\pi$
$211$	2.55912e7	0.187543	0.0937716	+	0.995594i	$0.470108\pi$
$212$	−9.26907e7	−0.668130
$213$	0	0
$214$	2.17190e8	1.51493
$215$	−1.95122e8	−1.33897
$216$	0	0
$217$	−1.47983e8	−0.983114
$218$	−4.68362e7	−0.306185
$219$	0	0
$220$	−2.06156e8	−1.30532
$221$	−1.31711e7	−0.0820822
$222$	0	0
$223$	−6.12718e7	−0.369993	−0.184997	−	0.982739i	$-0.559227\pi$
$223$	−6.12718e7	−0.369993	−0.184997	+	0.982739i	$0.559227\pi$
$224$	9.91094e7	0.589179
$225$	0	0
$226$	−5.15278e7	−0.296936
$227$	−1.21259e8	−0.688058	−0.344029	−	0.938959i	$-0.611792\pi$
$227$	−1.21259e8	−0.688058	−0.344029	+	0.938959i	$0.611792\pi$
$228$	0	0
$229$	−1.26372e8	−0.695385	−0.347693	−	0.937609i	$-0.613035\pi$
$229$	−1.26372e8	−0.695385	−0.347693	+	0.937609i	$0.613035\pi$
$230$	−3.79269e8	−2.05542
$231$	0	0
$232$	3.58767e7	0.188627
$233$	2.25521e8	1.16799	0.583997	−	0.811756i	$-0.301488\pi$
$233$	2.25521e8	1.16799	0.583997	+	0.811756i	$0.301488\pi$
$234$	0	0
$235$	−2.01717e8	−1.01392
$236$	1.50256e7	0.0744112
$237$	0	0
$238$	−9.56145e7	−0.459732
$239$	−1.64981e7	−0.0781700	−0.0390850	−	0.999236i	$-0.512444\pi$
$239$	−1.64981e7	−0.0781700	−0.0390850	+	0.999236i	$0.512444\pi$
$240$	0	0
$241$	2.28946e8	1.05360	0.526798	−	0.849990i	$-0.323392\pi$
$241$	2.28946e8	1.05360	0.526798	+	0.849990i	$0.323392\pi$
$242$	−6.56694e8	−2.97858
$243$	0	0
$244$	2.19420e8	0.966968
$245$	−1.91302e8	−0.831071
$246$	0	0
$247$	−3.84207e7	−0.162228
$248$	−2.20334e8	−0.917277
$249$	0	0
$250$	1.75189e8	0.709114
$251$	1.57555e8	0.628891	0.314445	−	0.949276i	$-0.398181\pi$
$251$	1.57555e8	0.628891	0.314445	+	0.949276i	$0.398181\pi$
$252$	0	0
$253$	−6.24317e8	−2.42372
$254$	2.17749e8	0.833753
$255$	0	0
$256$	3.38564e8	1.26125
$257$	−5.02698e8	−1.84732	−0.923659	−	0.383217i	$-0.874816\pi$
$257$	−5.02698e8	−1.84732	−0.923659	+	0.383217i	$0.874816\pi$
$258$	0	0
$259$	8.29140e7	0.296537
$260$	−2.59411e7	−0.0915339
$261$	0	0
$262$	−5.03831e8	−1.73074
$263$	−3.26465e8	−1.10660	−0.553302	−	0.832981i	$-0.686632\pi$
$263$	−3.26465e8	−1.10660	−0.553302	+	0.832981i	$0.686632\pi$
$264$	0	0
$265$	−4.40158e8	−1.45294
$266$	−2.78912e8	−0.908617
$267$	0	0
$268$	6.47495e7	0.205478
$269$	3.31961e8	1.03981	0.519904	−	0.854224i	$-0.325968\pi$
$269$	3.31961e8	1.03981	0.519904	+	0.854224i	$0.325968\pi$
$270$	0	0
$271$	−1.60418e8	−0.489622	−0.244811	−	0.969571i	$-0.578726\pi$
$271$	−1.60418e8	−0.489622	−0.244811	+	0.969571i	$0.578726\pi$
$272$	−2.63209e8	−0.793067
$273$	0	0
$274$	7.59922e8	2.23173
$275$	−3.45293e8	−1.00121
$276$	0	0
$277$	1.11916e8	0.316383	0.158192	−	0.987408i	$-0.449434\pi$
$277$	1.11916e8	0.316383	0.158192	+	0.987408i	$0.449434\pi$
$278$	5.62135e8	1.56922
$279$	0	0
$280$	1.41160e8	0.384290
$281$	1.98790e7	0.0534468	0.0267234	−	0.999643i	$-0.491493\pi$
$281$	1.98790e7	0.0534468	0.0267234	+	0.999643i	$0.491493\pi$
$282$	0	0
$283$	7.52585e8	1.97380	0.986900	−	0.161333i	$-0.0515792\pi$
$283$	7.52585e8	1.97380	0.986900	+	0.161333i	$0.0515792\pi$
$284$	−1.33944e8	−0.346984
$285$	0	0
$286$	−1.17412e8	−0.296778
$287$	−2.87152e8	−0.717010
$288$	0	0
$289$	−2.43803e8	−0.594150
$290$	−2.27281e8	−0.547230
$291$	0	0
$292$	1.20040e8	0.282154
$293$	3.79259e8	0.880843	0.440422	−	0.897791i	$-0.354829\pi$
$293$	3.79259e8	0.880843	0.440422	+	0.897791i	$0.354829\pi$
$294$	0	0
$295$	7.13514e7	0.161817
$296$	1.23452e8	0.276679
$297$	0	0
$298$	−5.51524e8	−1.20728
$299$	−7.85594e7	−0.169961
$300$	0	0
$301$	−2.93398e8	−0.620119
$302$	−6.60812e8	−1.38055
$303$	0	0
$304$	−7.67793e8	−1.56742
$305$	1.04195e9	2.10281
$306$	0	0
$307$	2.90654e8	0.573313	0.286656	−	0.958033i	$-0.407456\pi$
$307$	2.90654e8	0.573313	0.286656	+	0.958033i	$0.407456\pi$
$308$	−3.09990e8	−0.604533
$309$	0	0
$310$	1.39583e9	2.66113
$311$	−1.17056e8	−0.220665	−0.110333	−	0.993895i	$-0.535192\pi$
$311$	−1.17056e8	−0.220665	−0.110333	+	0.993895i	$0.535192\pi$
$312$	0	0
$313$	−8.65416e8	−1.59522	−0.797608	−	0.603176i	$-0.793902\pi$
$313$	−8.65416e8	−1.59522	−0.797608	+	0.603176i	$0.793902\pi$
$314$	−5.91969e8	−1.07906
$315$	0	0
$316$	4.32545e8	0.771127
$317$	−5.65864e8	−0.997711	−0.498855	−	0.866685i	$-0.666246\pi$
$317$	−5.65864e8	−0.997711	−0.498855	+	0.866685i	$0.666246\pi$
$318$	0	0
$319$	−3.74128e8	−0.645286
$320$	−2.78405e7	−0.0474954
$321$	0	0
$322$	−5.70295e8	−0.951929
$323$	4.85793e8	0.802126
$324$	0	0
$325$	−4.34492e7	−0.0702085
$326$	−4.47850e8	−0.715931
$327$	0	0
$328$	−4.27544e8	−0.668994
$329$	−3.03315e8	−0.469579
$330$	0	0
$331$	−2.71063e8	−0.410839	−0.205420	−	0.978674i	$-0.565856\pi$
$331$	−2.71063e8	−0.410839	−0.205420	+	0.978674i	$0.565856\pi$
$332$	1.84473e8	0.276663
$333$	0	0
$334$	1.27069e9	1.86606
$335$	3.07474e8	0.446840
$336$	0	0
$337$	−4.73795e8	−0.674350	−0.337175	−	0.941442i	$-0.609471\pi$
$337$	−4.73795e8	−0.674350	−0.337175	+	0.941442i	$0.609471\pi$
$338$	8.75194e8	1.23281
$339$	0	0
$340$	3.28001e8	0.452584
$341$	2.29768e9	3.13797
$342$	0	0
$343$	−7.17869e8	−0.960541
$344$	−4.36844e8	−0.578591
$345$	0	0
$346$	−1.06358e9	−1.38039
$347$	−7.74737e8	−0.995408	−0.497704	−	0.867347i	$-0.665823\pi$
$347$	−7.74737e8	−0.995408	−0.497704	+	0.867347i	$0.665823\pi$
$348$	0	0
$349$	−6.21693e8	−0.782865	−0.391432	−	0.920207i	$-0.628020\pi$
$349$	−6.21693e8	−0.782865	−0.391432	+	0.920207i	$0.628020\pi$
$350$	−3.15416e8	−0.393229
$351$	0	0
$352$	−1.53883e9	−1.88058
$353$	−1.54031e9	−1.86379	−0.931897	−	0.362722i	$-0.881847\pi$
$353$	−1.54031e9	−1.86379	−0.931897	+	0.362722i	$0.881847\pi$
$354$	0	0
$355$	−6.36056e8	−0.754564
$356$	−9.36327e8	−1.09990
$357$	0	0
$358$	−1.02351e9	−1.17897
$359$	−1.07879e9	−1.23057	−0.615286	−	0.788304i	$-0.710960\pi$
$359$	−1.07879e9	−1.23057	−0.615286	+	0.788304i	$0.710960\pi$
$360$	0	0
$361$	5.23208e8	0.585328
$362$	3.15373e7	0.0349418
$363$	0	0
$364$	−3.90069e7	−0.0423922
$365$	5.70030e8	0.613582
$366$	0	0
$367$	−2.26451e8	−0.239135	−0.119567	−	0.992826i	$-0.538151\pi$
$367$	−2.26451e8	−0.239135	−0.119567	+	0.992826i	$0.538151\pi$
$368$	−1.56992e9	−1.64214
$369$	0	0
$370$	−7.82072e8	−0.802677
$371$	−6.61851e8	−0.672902
$372$	0	0
$373$	8.24182e8	0.822323	0.411161	−	0.911563i	$-0.365123\pi$
$373$	8.24182e8	0.822323	0.411161	+	0.911563i	$0.365123\pi$
$374$	1.48457e9	1.46740
$375$	0	0
$376$	−4.51610e8	−0.438133
$377$	−4.70775e7	−0.0452500
$378$	0	0
$379$	1.48000e9	1.39644	0.698221	−	0.715882i	$-0.253975\pi$
$379$	1.48000e9	1.39644	0.698221	+	0.715882i	$0.253975\pi$
$380$	9.56793e8	0.894490
$381$	0	0
$382$	−2.58683e8	−0.237436
$383$	−7.22943e7	−0.0657519	−0.0328760	−	0.999459i	$-0.510467\pi$
$383$	−7.22943e7	−0.0657519	−0.0328760	+	0.999459i	$0.510467\pi$
$384$	0	0
$385$	−1.47204e9	−1.31464
$386$	2.82518e8	0.250029
$387$	0	0
$388$	−5.88980e8	−0.511905
$389$	−1.82632e9	−1.57309	−0.786545	−	0.617533i	$-0.788132\pi$
$389$	−1.82632e9	−1.57309	−0.786545	+	0.617533i	$0.788132\pi$
$390$	0	0
$391$	9.93309e8	0.840361
$392$	−4.28293e8	−0.359120
$393$	0	0
$394$	−2.01145e8	−0.165681
$395$	2.05401e9	1.67692
$396$	0	0
$397$	−4.09390e8	−0.328376	−0.164188	−	0.986429i	$-0.552500\pi$
$397$	−4.09390e8	−0.328376	−0.164188	+	0.986429i	$0.552500\pi$
$398$	6.20012e8	0.492958
$399$	0	0
$400$	−8.68282e8	−0.678345
$401$	−1.18389e9	−0.916869	−0.458435	−	0.888728i	$-0.651590\pi$
$401$	−1.18389e9	−0.916869	−0.458435	+	0.888728i	$0.651590\pi$
$402$	0	0
$403$	2.89123e8	0.220046
$404$	−1.00755e9	−0.760209
$405$	0	0
$406$	−3.41755e8	−0.253439
$407$	−1.28737e9	−0.946506
$408$	0	0
$409$	1.87185e9	1.35282	0.676408	−	0.736527i	$-0.263536\pi$
$409$	1.87185e9	1.35282	0.676408	+	0.736527i	$0.263536\pi$
$410$	2.70851e9	1.94083
$411$	0	0
$412$	7.94750e8	0.559874
$413$	1.07289e8	0.0749427
$414$	0	0
$415$	8.76003e8	0.601641
$416$	−1.93635e8	−0.131873
$417$	0	0
$418$	4.33055e9	2.90018
$419$	1.15678e9	0.768251	0.384125	−	0.923281i	$-0.374503\pi$
$419$	1.15678e9	0.768251	0.384125	+	0.923281i	$0.374503\pi$
$420$	0	0
$421$	2.45085e8	0.160077	0.0800387	−	0.996792i	$-0.474496\pi$
$421$	2.45085e8	0.160077	0.0800387	+	0.996792i	$0.474496\pi$
$422$	−3.62962e8	−0.235108
$423$	0	0
$424$	−9.85438e8	−0.627840
$425$	5.49374e8	0.347142
$426$	0	0
$427$	1.56675e9	0.973875
$428$	−1.12033e9	−0.690702
$429$	0	0
$430$	2.76743e9	1.67856
$431$	−3.03863e9	−1.82813	−0.914065	−	0.405567i	$-0.867074\pi$
$431$	−3.03863e9	−1.82813	−0.914065	+	0.405567i	$0.867074\pi$
$432$	0	0
$433$	−2.66856e9	−1.57968	−0.789840	−	0.613313i	$-0.789837\pi$
$433$	−2.66856e9	−1.57968	−0.789840	+	0.613313i	$0.789837\pi$
$434$	2.09886e9	1.23245
$435$	0	0
$436$	2.41593e8	0.139599
$437$	2.89753e9	1.66090
$438$	0	0
$439$	2.22892e9	1.25738	0.628692	−	0.777654i	$-0.283590\pi$
$439$	2.22892e9	1.25738	0.628692	+	0.777654i	$0.283590\pi$
$440$	−2.19174e9	−1.22660
$441$	0	0
$442$	1.86807e8	0.102900
$443$	−1.08311e9	−0.591914	−0.295957	−	0.955201i	$-0.595639\pi$
$443$	−1.08311e9	−0.591914	−0.295957	+	0.955201i	$0.595639\pi$
$444$	0	0
$445$	−4.44631e9	−2.39188
$446$	8.69024e8	0.463831
$447$	0	0
$448$	−4.18629e7	−0.0219966
$449$	−2.12604e9	−1.10843	−0.554216	−	0.832373i	$-0.686982\pi$
$449$	−2.12604e9	−1.10843	−0.554216	+	0.832373i	$0.686982\pi$
$450$	0	0
$451$	4.45849e9	2.28860
$452$	2.65794e8	0.135382
$453$	0	0
$454$	1.71983e9	0.862563
$455$	−1.85231e8	−0.0921877
$456$	0	0
$457$	−1.43049e9	−0.701097	−0.350549	−	0.936545i	$-0.614005\pi$
$457$	−1.43049e9	−0.701097	−0.350549	+	0.936545i	$0.614005\pi$
$458$	1.79234e9	0.871749
$459$	0	0
$460$	1.95637e9	0.937128
$461$	−4.00329e9	−1.90311	−0.951554	−	0.307483i	$-0.900513\pi$
$461$	−4.00329e9	−1.90311	−0.951554	+	0.307483i	$0.900513\pi$
$462$	0	0
$463$	2.13866e9	1.00140	0.500700	−	0.865621i	$-0.333076\pi$
$463$	2.13866e9	1.00140	0.500700	+	0.865621i	$0.333076\pi$
$464$	−9.40789e8	−0.437199
$465$	0	0
$466$	−3.19858e9	−1.46422
$467$	1.07482e8	0.0488344	0.0244172	−	0.999702i	$-0.492227\pi$
$467$	1.07482e8	0.0488344	0.0244172	+	0.999702i	$0.492227\pi$
$468$	0	0
$469$	4.62339e8	0.206945
$470$	2.86097e9	1.27107
$471$	0	0
$472$	1.59744e8	0.0699240
$473$	4.55547e9	1.97934
$474$	0	0
$475$	1.60255e9	0.686094
$476$	4.93205e8	0.209606
$477$	0	0
$478$	2.33993e8	0.0979955
$479$	2.67480e8	0.111203	0.0556015	−	0.998453i	$-0.482292\pi$
$479$	2.67480e8	0.111203	0.0556015	+	0.998453i	$0.482292\pi$
$480$	0	0
$481$	−1.61993e8	−0.0663727
$482$	−3.24717e9	−1.32081
$483$	0	0
$484$	3.38740e9	1.35802
$485$	−2.79687e9	−1.11321
$486$	0	0
$487$	−5.06255e8	−0.198618	−0.0993088	−	0.995057i	$-0.531663\pi$
$487$	−5.06255e8	−0.198618	−0.0993088	+	0.995057i	$0.531663\pi$
$488$	2.33276e9	0.908657
$489$	0	0
$490$	2.71326e9	1.04185
$491$	6.82368e8	0.260156	0.130078	−	0.991504i	$-0.458477\pi$
$491$	6.82368e8	0.260156	0.130078	+	0.991504i	$0.458477\pi$
$492$	0	0
$493$	5.95250e8	0.223736
$494$	5.44924e8	0.203372
$495$	0	0
$496$	5.77778e9	2.12606
$497$	−9.56417e8	−0.349462
$498$	0	0
$499$	−5.05913e9	−1.82274	−0.911368	−	0.411593i	$-0.864973\pi$
$499$	−5.05913e9	−1.82274	−0.911368	+	0.411593i	$0.864973\pi$
$500$	−9.03669e8	−0.323306
$501$	0	0
$502$	−2.23462e9	−0.788390
$503$	2.46180e9	0.862513	0.431256	−	0.902229i	$-0.358070\pi$
$503$	2.46180e9	0.862513	0.431256	+	0.902229i	$0.358070\pi$
$504$	0	0
$505$	−4.78453e9	−1.65318
$506$	8.85474e9	3.03843
$507$	0	0
$508$	−1.12321e9	−0.380133
$509$	−3.24116e9	−1.08940	−0.544702	−	0.838630i	$-0.683357\pi$
$509$	−3.24116e9	−1.08940	−0.544702	+	0.838630i	$0.683357\pi$
$510$	0	0
$511$	8.57137e8	0.284169
$512$	−1.83898e9	−0.605524
$513$	0	0
$514$	7.12982e9	2.31583
$515$	3.77401e9	1.21752
$516$	0	0
$517$	4.70945e9	1.49883
$518$	−1.17598e9	−0.371745
$519$	0	0
$520$	−2.75792e8	−0.0860142
$521$	3.22198e8	0.0998138	0.0499069	−	0.998754i	$-0.484108\pi$
$521$	3.22198e8	0.0998138	0.0499069	+	0.998754i	$0.484108\pi$
$522$	0	0
$523$	−2.62851e9	−0.803441	−0.401720	−	0.915762i	$-0.631588\pi$
$523$	−2.62851e9	−0.803441	−0.401720	+	0.915762i	$0.631588\pi$
$524$	2.59890e9	0.789095
$525$	0	0
$526$	4.63029e9	1.38726
$527$	−3.65568e9	−1.08801
$528$	0	0
$529$	2.51980e9	0.740067
$530$	6.24280e9	1.82143
$531$	0	0
$532$	1.43870e9	0.414266
$533$	5.61023e8	0.160485
$534$	0	0
$535$	−5.32005e9	−1.50203
$536$	6.88382e8	0.193087
$537$	0	0
$538$	−4.70823e9	−1.30353
$539$	4.46630e9	1.22853
$540$	0	0
$541$	2.50223e8	0.0679418	0.0339709	−	0.999423i	$-0.489185\pi$
$541$	2.50223e8	0.0679418	0.0339709	+	0.999423i	$0.489185\pi$
$542$	2.27522e9	0.613800
$543$	0	0
$544$	2.44833e9	0.652040
$545$	1.14725e9	0.303577
$546$	0	0
$547$	−4.97823e9	−1.30053	−0.650263	−	0.759709i	$-0.725341\pi$
$547$	−4.97823e9	−1.30053	−0.650263	+	0.759709i	$0.725341\pi$
$548$	−3.91988e9	−1.01751
$549$	0	0
$550$	4.89733e9	1.25513
$551$	1.73637e9	0.442193
$552$	0	0
$553$	3.08855e9	0.776635
$554$	−1.58732e9	−0.396624
$555$	0	0
$556$	−2.89964e9	−0.715455
$557$	−6.42734e9	−1.57593	−0.787967	−	0.615717i	$-0.788866\pi$
$557$	−6.42734e9	−1.57593	−0.787967	+	0.615717i	$0.788866\pi$
$558$	0	0
$559$	5.73227e8	0.138799
$560$	−3.70162e9	−0.890705
$561$	0	0
$562$	−2.81945e8	−0.0670020
$563$	6.88214e9	1.62534	0.812669	−	0.582725i	$-0.198014\pi$
$563$	6.88214e9	1.62534	0.812669	+	0.582725i	$0.198014\pi$
$564$	0	0
$565$	1.26217e9	0.294407
$566$	−1.06740e10	−2.47440
$567$	0	0
$568$	−1.42402e9	−0.326060
$569$	6.73673e8	0.153305	0.0766525	−	0.997058i	$-0.475577\pi$
$569$	6.73673e8	0.153305	0.0766525	+	0.997058i	$0.475577\pi$
$570$	0	0
$571$	5.99921e9	1.34855	0.674276	−	0.738480i	$-0.264456\pi$
$571$	5.99921e9	1.34855	0.674276	+	0.738480i	$0.264456\pi$
$572$	6.05643e8	0.135310
$573$	0	0
$574$	4.07270e9	0.898858
$575$	3.27676e9	0.718798
$576$	0	0
$577$	−5.88307e9	−1.27494	−0.637468	−	0.770477i	$-0.720018\pi$
$577$	−5.88307e9	−1.27494	−0.637468	+	0.770477i	$0.720018\pi$
$578$	3.45788e9	0.744838
$579$	0	0
$580$	1.17237e9	0.249499
$581$	1.31722e9	0.278639
$582$	0	0
$583$	1.02763e10	2.14781
$584$	1.27620e9	0.265139
$585$	0	0
$586$	−5.37906e9	−1.10424
$587$	−1.17128e9	−0.239017	−0.119508	−	0.992833i	$-0.538132\pi$
$587$	−1.17128e9	−0.239017	−0.119508	+	0.992833i	$0.538132\pi$
$588$	0	0
$589$	−1.06638e10	−2.15034
$590$	−1.01198e9	−0.202858
$591$	0	0
$592$	−3.23725e9	−0.641284
$593$	9.74774e8	0.191961	0.0959804	−	0.995383i	$-0.469401\pi$
$593$	9.74774e8	0.191961	0.0959804	+	0.995383i	$0.469401\pi$
$594$	0	0
$595$	2.34207e9	0.455816
$596$	2.84491e9	0.550435
$597$	0	0
$598$	1.11422e9	0.213066
$599$	4.18211e9	0.795064	0.397532	−	0.917588i	$-0.369867\pi$
$599$	4.18211e9	0.795064	0.397532	+	0.917588i	$0.369867\pi$
$600$	0	0
$601$	2.97120e9	0.558304	0.279152	−	0.960247i	$-0.409947\pi$
$601$	2.97120e9	0.558304	0.279152	+	0.960247i	$0.409947\pi$
$602$	4.16130e9	0.777393
$603$	0	0
$604$	3.40864e9	0.629437
$605$	1.60856e10	2.95321
$606$	0	0
$607$	6.29111e9	1.14174	0.570870	−	0.821041i	$-0.306606\pi$
$607$	6.29111e9	1.14174	0.570870	+	0.821041i	$0.306606\pi$
$608$	7.14190e9	1.28870
$609$	0	0
$610$	−1.47781e10	−2.63612
$611$	5.92603e8	0.105104
$612$	0	0
$613$	−4.19579e9	−0.735702	−0.367851	−	0.929885i	$-0.619906\pi$
$613$	−4.19579e9	−0.735702	−0.367851	+	0.929885i	$0.619906\pi$
$614$	−4.12237e9	−0.718716
$615$	0	0
$616$	−3.29565e9	−0.568078
$617$	6.32858e9	1.08470	0.542348	−	0.840154i	$-0.317535\pi$
$617$	6.32858e9	1.08470	0.542348	+	0.840154i	$0.317535\pi$
$618$	0	0
$619$	−1.00319e10	−1.70007	−0.850034	−	0.526727i	$-0.823419\pi$
$619$	−1.00319e10	−1.70007	−0.850034	+	0.526727i	$0.823419\pi$
$620$	−7.20004e9	−1.21329
$621$	0	0
$622$	1.66022e9	0.276630
$623$	−6.68577e9	−1.10775
$624$	0	0
$625$	−7.61708e9	−1.24798
$626$	1.22743e10	1.99980
$627$	0	0
$628$	3.05353e9	0.491976
$629$	2.04825e9	0.328176
$630$	0	0
$631$	−1.16344e10	−1.84348	−0.921742	−	0.387803i	$-0.873234\pi$
$631$	−1.16344e10	−1.84348	−0.921742	+	0.387803i	$0.873234\pi$
$632$	4.59858e9	0.724626
$633$	0	0
$634$	8.02570e9	1.25075
$635$	−5.33373e9	−0.826653
$636$	0	0
$637$	5.62006e8	0.0861496
$638$	5.30629e9	0.808944
$639$	0	0
$640$	−8.04184e9	−1.21262
$641$	8.17369e8	0.122579	0.0612894	−	0.998120i	$-0.480479\pi$
$641$	8.17369e8	0.122579	0.0612894	+	0.998120i	$0.480479\pi$
$642$	0	0
$643$	−1.27383e10	−1.88961	−0.944803	−	0.327638i	$-0.893748\pi$
$643$	−1.27383e10	−1.88961	−0.944803	+	0.327638i	$0.893748\pi$
$644$	2.94173e9	0.434013
$645$	0	0
$646$	−6.89005e9	−1.00556
$647$	9.76722e9	1.41777	0.708885	−	0.705324i	$-0.249198\pi$
$647$	9.76722e9	1.41777	0.708885	+	0.705324i	$0.249198\pi$
$648$	0	0
$649$	−1.66583e9	−0.239207
$650$	6.16244e8	0.0880148
$651$	0	0
$652$	2.31013e9	0.326415
$653$	−1.38778e9	−0.195040	−0.0975201	−	0.995234i	$-0.531091\pi$
$653$	−1.38778e9	−0.195040	−0.0975201	+	0.995234i	$0.531091\pi$
$654$	0	0
$655$	1.23413e10	1.71600
$656$	1.12114e10	1.55059
$657$	0	0
$658$	4.30195e9	0.588674
$659$	2.05987e9	0.280376	0.140188	−	0.990125i	$-0.455229\pi$
$659$	2.05987e9	0.280376	0.140188	+	0.990125i	$0.455229\pi$
$660$	0	0
$661$	2.12923e9	0.286759	0.143379	−	0.989668i	$-0.454203\pi$
$661$	2.12923e9	0.286759	0.143379	+	0.989668i	$0.454203\pi$
$662$	3.84451e9	0.515037
$663$	0	0
$664$	1.96122e9	0.259979
$665$	6.83191e9	0.900879
$666$	0	0
$667$	3.55039e9	0.463271
$668$	−6.55454e9	−0.850794
$669$	0	0
$670$	−4.36093e9	−0.560167
$671$	−2.43263e10	−3.10848
$672$	0	0
$673$	−1.03831e10	−1.31303	−0.656513	−	0.754315i	$-0.727969\pi$
$673$	−1.03831e10	−1.31303	−0.656513	+	0.754315i	$0.727969\pi$
$674$	6.71987e9	0.845379
$675$	0	0
$676$	−4.51448e9	−0.562075
$677$	1.75650e9	0.217565	0.108782	−	0.994066i	$-0.465305\pi$
$677$	1.75650e9	0.217565	0.108782	+	0.994066i	$0.465305\pi$
$678$	0	0
$679$	−4.20557e9	−0.515562
$680$	3.48713e9	0.425292
$681$	0	0
$682$	−3.25881e10	−3.93382
$683$	−1.35391e10	−1.62599	−0.812994	−	0.582272i	$-0.802164\pi$
$683$	−1.35391e10	−1.62599	−0.812994	+	0.582272i	$0.802164\pi$
$684$	0	0
$685$	−1.86142e10	−2.21273
$686$	1.01816e10	1.20415
$687$	0	0
$688$	1.14553e10	1.34105
$689$	1.29309e9	0.150613
$690$	0	0
$691$	−4.11941e9	−0.474965	−0.237482	−	0.971392i	$-0.576322\pi$
$691$	−4.11941e9	−0.474965	−0.237482	+	0.971392i	$0.576322\pi$
$692$	5.48622e9	0.629364
$693$	0	0
$694$	1.09882e10	1.24786
$695$	−1.37694e10	−1.55586
$696$	0	0
$697$	−7.09361e9	−0.793510
$698$	8.81752e9	0.981415
$699$	0	0
$700$	1.62700e9	0.179285
$701$	−1.40168e10	−1.53687	−0.768433	−	0.639930i	$-0.778963\pi$
$701$	−1.40168e10	−1.53687	−0.768433	+	0.639930i	$0.778963\pi$
$702$	0	0
$703$	5.97484e9	0.648609
$704$	6.49987e8	0.0702103
$705$	0	0
$706$	2.18464e10	2.33649
$707$	−7.19435e9	−0.765638
$708$	0	0
$709$	1.84363e10	1.94273	0.971364	−	0.237596i	$-0.0763594\pi$
$709$	1.84363e10	1.94273	0.971364	+	0.237596i	$0.0763594\pi$
$710$	9.02124e9	0.945936
$711$	0	0
$712$	−9.95452e9	−1.03357
$713$	−2.18044e10	−2.25284
$714$	0	0
$715$	2.87600e9	0.294251
$716$	5.27954e9	0.537528
$717$	0	0
$718$	1.53006e10	1.54267
$719$	−9.38221e9	−0.941356	−0.470678	−	0.882305i	$-0.655991\pi$
$719$	−9.38221e9	−0.941356	−0.470678	+	0.882305i	$0.655991\pi$
$720$	0	0
$721$	5.67485e9	0.563873
$722$	−7.42071e9	−0.733779
$723$	0	0
$724$	−1.62678e8	−0.0159310
$725$	1.96363e9	0.191371
$726$	0	0
$727$	−1.28628e10	−1.24155	−0.620776	−	0.783988i	$-0.713182\pi$
$727$	−1.28628e10	−1.24155	−0.620776	+	0.783988i	$0.713182\pi$
$728$	−4.14700e8	−0.0398358
$729$	0	0
$730$	−8.08479e9	−0.769199
$731$	−7.24792e9	−0.686281
$732$	0	0
$733$	2.95776e9	0.277395	0.138698	−	0.990335i	$-0.455708\pi$
$733$	2.95776e9	0.277395	0.138698	+	0.990335i	$0.455708\pi$
$734$	3.21177e9	0.299784
$735$	0	0
$736$	1.46032e10	1.35013
$737$	−7.17855e9	−0.660542
$738$	0	0
$739$	−1.20547e10	−1.09875	−0.549375	−	0.835576i	$-0.685134\pi$
$739$	−1.20547e10	−1.09875	−0.549375	+	0.835576i	$0.685134\pi$
$740$	4.03413e9	0.365965
$741$	0	0
$742$	9.38710e9	0.843563
$743$	1.52375e10	1.36287	0.681434	−	0.731880i	$-0.261357\pi$
$743$	1.52375e10	1.36287	0.681434	+	0.731880i	$0.261357\pi$
$744$	0	0
$745$	1.35095e10	1.19700
$746$	−1.16895e10	−1.03088
$747$	0	0
$748$	−7.65778e9	−0.669033
$749$	−7.99960e9	−0.695636
$750$	0	0
$751$	7.81976e9	0.673680	0.336840	−	0.941562i	$-0.390642\pi$
$751$	7.81976e9	0.673680	0.336840	+	0.941562i	$0.390642\pi$
$752$	1.18425e10	1.01550
$753$	0	0
$754$	6.67704e8	0.0567263
$755$	1.61865e10	1.36880
$756$	0	0
$757$	−1.95010e10	−1.63388	−0.816942	−	0.576719i	$-0.804333\pi$
$757$	−1.95010e10	−1.63388	−0.816942	+	0.576719i	$0.804333\pi$
$758$	−2.09909e10	−1.75061
$759$	0	0
$760$	1.01721e10	0.840550
$761$	7.65488e9	0.629639	0.314820	−	0.949151i	$-0.398056\pi$
$761$	7.65488e9	0.629639	0.314820	+	0.949151i	$0.398056\pi$
$762$	0	0
$763$	1.72508e9	0.140596
$764$	1.33436e9	0.108254
$765$	0	0
$766$	1.02536e9	0.0824280
$767$	−2.09616e8	−0.0167741
$768$	0	0
$769$	1.48573e9	0.117814	0.0589072	−	0.998263i	$-0.481238\pi$
$769$	1.48573e9	0.117814	0.0589072	+	0.998263i	$0.481238\pi$
$770$	2.08781e10	1.64806
$771$	0	0
$772$	−1.45730e9	−0.113996
$773$	1.41154e10	1.09917	0.549583	−	0.835439i	$-0.314786\pi$
$773$	1.41154e10	1.09917	0.549583	+	0.835439i	$0.314786\pi$
$774$	0	0
$775$	−1.20595e10	−0.930619
$776$	−6.26172e9	−0.481036
$777$	0	0
$778$	2.59029e10	1.97206
$779$	−2.06924e10	−1.56830
$780$	0	0
$781$	1.48499e10	1.11544
$782$	−1.40882e10	−1.05349
$783$	0	0
$784$	1.12310e10	0.832365
$785$	1.45002e10	1.06987
$786$	0	0
$787$	−2.01995e10	−1.47717	−0.738583	−	0.674163i	$-0.764505\pi$
$787$	−2.01995e10	−1.47717	−0.738583	+	0.674163i	$0.764505\pi$
$788$	1.03756e9	0.0755390
$789$	0	0
$790$	−2.91322e10	−2.10222
$791$	1.89788e9	0.136349
$792$	0	0
$793$	−3.06105e9	−0.217979
$794$	5.80642e9	0.411658
$795$	0	0
$796$	−3.19819e9	−0.224754
$797$	1.57650e10	1.10304	0.551518	−	0.834163i	$-0.314049\pi$
$797$	1.57650e10	1.10304	0.551518	+	0.834163i	$0.314049\pi$
$798$	0	0
$799$	−7.49290e9	−0.519680
$800$	8.07663e9	0.557719
$801$	0	0
$802$	1.67913e10	1.14941
$803$	−1.33084e10	−0.907030
$804$	0	0
$805$	1.39693e10	0.943821
$806$	−4.10065e9	−0.275855
$807$	0	0
$808$	−1.07117e10	−0.714366
$809$	1.46891e10	0.975383	0.487691	−	0.873016i	$-0.337839\pi$
$809$	1.46891e10	0.975383	0.487691	+	0.873016i	$0.337839\pi$
$810$	0	0
$811$	−1.19514e10	−0.786763	−0.393382	−	0.919375i	$-0.628695\pi$
$811$	−1.19514e10	−0.786763	−0.393382	+	0.919375i	$0.628695\pi$
$812$	1.76286e9	0.115551
$813$	0	0
$814$	1.82589e10	1.18656
$815$	1.09700e10	0.709834
$816$	0	0
$817$	−2.11425e10	−1.35637
$818$	−2.65486e10	−1.69592
$819$	0	0
$820$	−1.39712e10	−0.884882
$821$	−1.96015e8	−0.0123620	−0.00618100	−	0.999981i	$-0.501967\pi$
$821$	−1.96015e8	−0.0123620	−0.00618100	+	0.999981i	$0.501967\pi$
$822$	0	0
$823$	1.45005e10	0.906743	0.453371	−	0.891322i	$-0.350221\pi$
$823$	1.45005e10	0.906743	0.453371	+	0.891322i	$0.350221\pi$
$824$	8.44935e9	0.526112
$825$	0	0
$826$	−1.52169e9	−0.0939497
$827$	2.38967e10	1.46916	0.734580	−	0.678523i	$-0.237379\pi$
$827$	2.38967e10	1.46916	0.734580	+	0.678523i	$0.237379\pi$
$828$	0	0
$829$	−3.76640e8	−0.0229607	−0.0114804	−	0.999934i	$-0.503654\pi$
$829$	−3.76640e8	−0.0229607	−0.0114804	+	0.999934i	$0.503654\pi$
$830$	−1.24244e10	−0.754229
$831$	0	0
$832$	8.17896e7	0.00492342
$833$	−7.10603e9	−0.425961
$834$	0	0
$835$	−3.11254e10	−1.85017
$836$	−2.23381e10	−1.32228
$837$	0	0
$838$	−1.64068e10	−0.963095
$839$	6.46027e8	0.0377645	0.0188823	−	0.999822i	$-0.493989\pi$
$839$	6.46027e8	0.0377645	0.0188823	+	0.999822i	$0.493989\pi$
$840$	0	0
$841$	−1.51223e10	−0.876660
$842$	−3.47607e9	−0.200676
$843$	0	0
$844$	1.87225e9	0.107193
$845$	−2.14378e10	−1.22231
$846$	0	0
$847$	2.41875e10	1.36772
$848$	2.58410e10	1.45520
$849$	0	0
$850$	−7.79182e9	−0.435184
$851$	1.22169e10	0.679526
$852$	0	0
$853$	−1.77737e10	−0.980519	−0.490259	−	0.871577i	$-0.663098\pi$
$853$	−1.77737e10	−0.980519	−0.490259	+	0.871577i	$0.663098\pi$
$854$	−2.22214e10	−1.22087
$855$	0	0
$856$	−1.19107e10	−0.649051
$857$	−1.59949e10	−0.868056	−0.434028	−	0.900899i	$-0.642908\pi$
$857$	−1.59949e10	−0.868056	−0.434028	+	0.900899i	$0.642908\pi$
$858$	0	0
$859$	1.41375e10	0.761020	0.380510	−	0.924777i	$-0.375748\pi$
$859$	1.41375e10	0.761020	0.380510	+	0.924777i	$0.375748\pi$
$860$	−1.42751e10	−0.765306
$861$	0	0
$862$	4.30972e10	2.29178
$863$	−1.13489e10	−0.601058	−0.300529	−	0.953773i	$-0.597163\pi$
$863$	−1.13489e10	−0.601058	−0.300529	+	0.953773i	$0.597163\pi$
$864$	0	0
$865$	2.60522e10	1.36864
$866$	3.78484e10	1.98032
$867$	0	0
$868$	−1.08265e10	−0.561912
$869$	−4.79547e10	−2.47892
$870$	0	0
$871$	−9.03295e8	−0.0463198
$872$	2.56849e9	0.131181
$873$	0	0
$874$	−4.10959e10	−2.08213
$875$	−6.45258e9	−0.325616
$876$	0	0
$877$	−1.21568e10	−0.608585	−0.304292	−	0.952579i	$-0.598420\pi$
$877$	−1.21568e10	−0.608585	−0.304292	+	0.952579i	$0.598420\pi$
$878$	−3.16130e10	−1.57628
$879$	0	0
$880$	5.74735e10	2.84301
$881$	8.54283e6	0.000420907 0	0.000210453	−	1.00000i	$-0.499933\pi$
$881$	8.54283e6	0.000420907 0	0.000210453		1.00000i	$0.499933\pi$
$882$	0	0
$883$	4.25559e9	0.208016	0.104008	−	0.994576i	$-0.466833\pi$
$883$	4.25559e9	0.208016	0.104008	+	0.994576i	$0.466833\pi$
$884$	−9.63599e8	−0.0469152
$885$	0	0
$886$	1.53618e10	0.742035
$887$	−2.65326e10	−1.27658	−0.638288	−	0.769798i	$-0.720357\pi$
$887$	−2.65326e10	−1.27658	−0.638288	+	0.769798i	$0.720357\pi$
$888$	0	0
$889$	−8.02016e9	−0.382849
$890$	6.30624e10	2.99851
$891$	0	0
$892$	−4.48265e9	−0.211475
$893$	−2.18571e10	−1.02710
$894$	0	0
$895$	2.50708e10	1.16893
$896$	−1.20923e10	−0.561603
$897$	0	0
$898$	3.01538e10	1.38955
$899$	−1.30665e10	−0.599792
$900$	0	0
$901$	−1.63499e10	−0.744696
$902$	−6.32351e10	−2.86903
$903$	0	0
$904$	2.82578e9	0.127218
$905$	−7.72503e8	−0.0346442
$906$	0	0
$907$	1.30701e10	0.581639	0.290820	−	0.956778i	$-0.406072\pi$
$907$	1.30701e10	0.581639	0.290820	+	0.956778i	$0.406072\pi$
$908$	−8.87136e9	−0.393269
$909$	0	0
$910$	2.62714e9	0.115568
$911$	−9.33341e9	−0.409003	−0.204501	−	0.978866i	$-0.565557\pi$
$911$	−9.33341e9	−0.409003	−0.204501	+	0.978866i	$0.565557\pi$
$912$	0	0
$913$	−2.04519e10	−0.889377
$914$	2.02888e10	0.878909
$915$	0	0
$916$	−9.24537e9	−0.397457
$917$	1.85572e10	0.794731
$918$	0	0
$919$	1.62411e10	0.690256	0.345128	−	0.938556i	$-0.387835\pi$
$919$	1.62411e10	0.690256	0.345128	+	0.938556i	$0.387835\pi$
$920$	2.07991e10	0.880616
$921$	0	0
$922$	5.67790e10	2.38577
$923$	1.86860e9	0.0782187
$924$	0	0
$925$	6.75683e9	0.280703
$926$	−3.03328e10	−1.25538
$927$	0	0
$928$	8.75108e9	0.359454
$929$	4.61407e10	1.88812	0.944060	−	0.329774i	$-0.106972\pi$
$929$	4.61407e10	1.88812	0.944060	+	0.329774i	$0.106972\pi$
$930$	0	0
$931$	−2.07286e10	−0.841873
$932$	1.64991e10	0.667582
$933$	0	0
$934$	−1.52442e9	−0.0612197
$935$	−3.63643e10	−1.45490
$936$	0	0
$937$	1.16823e10	0.463915	0.231957	−	0.972726i	$-0.425487\pi$
$937$	1.16823e10	0.463915	0.231957	+	0.972726i	$0.425487\pi$
$938$	−6.55740e9	−0.259431
$939$	0	0
$940$	−1.47576e10	−0.579521
$941$	−5.84004e8	−0.0228482	−0.0114241	−	0.999935i	$-0.503636\pi$
$941$	−5.84004e8	−0.0228482	−0.0114241	+	0.999935i	$0.503636\pi$
$942$	0	0
$943$	−4.23100e10	−1.64306
$944$	−4.18893e9	−0.162069
$945$	0	0
$946$	−6.46107e10	−2.48134
$947$	2.16535e9	0.0828522	0.0414261	−	0.999142i	$-0.486810\pi$
$947$	2.16535e9	0.0828522	0.0414261	+	0.999142i	$0.486810\pi$
$948$	0	0
$949$	−1.67463e9	−0.0636045
$950$	−2.27291e10	−0.860101
$951$	0	0
$952$	5.24349e9	0.196966
$953$	−1.53392e10	−0.574086	−0.287043	−	0.957918i	$-0.592672\pi$
$953$	−1.53392e10	−0.574086	−0.287043	+	0.957918i	$0.592672\pi$
$954$	0	0
$955$	6.33642e9	0.235414
$956$	−1.20700e9	−0.0446791
$957$	0	0
$958$	−3.79369e9	−0.139406
$959$	−2.79896e10	−1.02478
$960$	0	0
$961$	5.27343e10	1.91673
$962$	2.29757e9	0.0832062
$963$	0	0
$964$	1.67498e10	0.602197
$965$	−6.92025e9	−0.247900
$966$	0	0
$967$	3.99566e10	1.42100	0.710502	−	0.703695i	$-0.248468\pi$
$967$	3.99566e10	1.42100	0.710502	+	0.703695i	$0.248468\pi$
$968$	3.60130e10	1.27613
$969$	0	0
$970$	3.96683e10	1.39554
$971$	5.20126e10	1.82323	0.911614	−	0.411048i	$-0.134837\pi$
$971$	5.20126e10	1.82323	0.911614	+	0.411048i	$0.134837\pi$
$972$	0	0
$973$	−2.07047e10	−0.720565
$974$	7.18026e9	0.248991
$975$	0	0
$976$	−6.11715e10	−2.10608
$977$	−6.11345e9	−0.209728	−0.104864	−	0.994487i	$-0.533441\pi$
$977$	−6.11345e9	−0.209728	−0.104864	+	0.994487i	$0.533441\pi$
$978$	0	0
$979$	1.03807e11	3.53580
$980$	−1.39957e10	−0.475010
$981$	0	0
$982$	−9.67809e9	−0.326137
$983$	−6.44828e9	−0.216524	−0.108262	−	0.994122i	$-0.534529\pi$
$983$	−6.44828e9	−0.216524	−0.108262	+	0.994122i	$0.534529\pi$
$984$	0	0
$985$	4.92703e9	0.164270
$986$	−8.44249e9	−0.280480
$987$	0	0
$988$	−2.81086e9	−0.0927236
$989$	−4.32304e10	−1.42103
$990$	0	0
$991$	4.02808e10	1.31474	0.657370	−	0.753568i	$-0.271669\pi$
$991$	4.02808e10	1.31474	0.657370	+	0.753568i	$0.271669\pi$
$992$	−5.37441e10	−1.74799
$993$	0	0
$994$	1.35650e10	0.438093
$995$	−1.51871e10	−0.488759
$996$	0	0
$997$	2.21675e10	0.708408	0.354204	−	0.935168i	$-0.384752\pi$
$997$	2.21675e10	0.708408	0.354204	+	0.935168i	$0.384752\pi$
$998$	7.17541e10	2.28502
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.g.1.8	✓	33
3.2	odd	2		531.8.a.h.1.26	yes	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.8.a.g.1.8	✓	33	1.1	even	1	trivial
531.8.a.h.1.26	yes	33	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q-14.1831 q^{2} +73.1601 q^{4} +347.413 q^{5} +522.395 q^{7} +777.799 q^{8} +O(q^{10})\)	\(q-14.1831 q^{2} +73.1601 q^{4} +347.413 q^{5} +522.395 q^{7} +777.799 q^{8} -4927.40 q^{10} -8111.00 q^{11} -1020.63 q^{13} -7409.17 q^{14} -20396.1 q^{16} +12904.9 q^{17} +37644.1 q^{19} +25416.8 q^{20} +115039. q^{22} +76971.6 q^{23} +42571.0 q^{25} +14475.7 q^{26} +38218.5 q^{28} +46125.9 q^{29} -283279. q^{31} +189721. q^{32} -183031. q^{34} +181487. q^{35} +158719. q^{37} -533910. q^{38} +270218. q^{40} -549684. q^{41} -561641. q^{43} -593402. q^{44} -1.09169e6 q^{46} -580625. q^{47} -550647. q^{49} -603789. q^{50} -74669.3 q^{52} -1.26696e6 q^{53} -2.81787e6 q^{55} +406318. q^{56} -654209. q^{58} +205379. q^{59} +2.99918e6 q^{61} +4.01777e6 q^{62} -80136.5 q^{64} -354580. q^{65} +885038. q^{67} +944123. q^{68} -2.57404e6 q^{70} -1.83083e6 q^{71} +1.64078e6 q^{73} -2.25113e6 q^{74} +2.75405e6 q^{76} -4.23714e6 q^{77} +5.91230e6 q^{79} -7.08587e6 q^{80} +7.79622e6 q^{82} +2.52150e6 q^{83} +4.48333e6 q^{85} +7.96581e6 q^{86} -6.30873e6 q^{88} -1.27983e7 q^{89} -533171. q^{91} +5.63125e6 q^{92} +8.23506e6 q^{94} +1.30781e7 q^{95} -8.05056e6 q^{97} +7.80988e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8}+O(q^{10}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8	\( 33 q - 24 q^{2} + 1776 q^{4} - 1000 q^{5} + 154 q^{7} - 4608 q^{8} + 5042 q^{10} - 13310 q^{11} - 14172 q^{13} - 16464 q^{14} + 95772 q^{16} - 39304 q^{17} - 56302 q^{19} + 17936 q^{20} + 152764 q^{22} - 17988 q^{23} + 468523 q^{25} + 27624 q^{26} - 59896 q^{28} - 474564 q^{29} + 188186 q^{31} - 251068 q^{32} + 169888 q^{34} - 514500 q^{35} + 1148200 q^{37} - 446594 q^{38} + 501214 q^{40} - 1246152 q^{41} + 62268 q^{43} - 2555520 q^{44} - 1289942 q^{46} - 1485654 q^{47} + 3829555 q^{49} - 6430160 q^{50} - 2624804 q^{52} - 4086740 q^{53} - 1119118 q^{55} - 8448352 q^{56} + 2966706 q^{58} + 6777507 q^{59} + 2436146 q^{61} - 9005952 q^{62} + 11117562 q^{64} - 16730354 q^{65} - 2652248 q^{67} - 15929124 q^{68} + 3359254 q^{70} - 7356324 q^{71} + 1900454 q^{73} - 25386964 q^{74} - 16047360 q^{76} - 20774826 q^{77} - 5912712 q^{79} - 13568404 q^{80} + 1579434 q^{82} + 1052766 q^{83} + 18372730 q^{85} - 43499960 q^{86} + 18209214 q^{88} - 174788 q^{89} - 18891512 q^{91} - 46033270 q^{92} + 365448 q^{94} - 31505580 q^{95} + 14418540 q^{97} + 15964056 q^{98}+O(q^{100}) \) 33 * q - 24 * q^2 + 1776 * q^4 - 1000 * q^5 + 154 * q^7 - 4608 * q^8 + 5042 * q^10 - 13310 * q^11 - 14172 * q^13 - 16464 * q^14 + 95772 * q^16 - 39304 * q^17 - 56302 * q^19 + 17936 * q^20 + 152764 * q^22 - 17988 * q^23 + 468523 * q^25 + 27624 * q^26 - 59896 * q^28 - 474564 * q^29 + 188186 * q^31 - 251068 * q^32 + 169888 * q^34 - 514500 * q^35 + 1148200 * q^37 - 446594 * q^38 + 501214 * q^40 - 1246152 * q^41 + 62268 * q^43 - 2555520 * q^44 - 1289942 * q^46 - 1485654 * q^47 + 3829555 * q^49 - 6430160 * q^50 - 2624804 * q^52 - 4086740 * q^53 - 1119118 * q^55 - 8448352 * q^56 + 2966706 * q^58 + 6777507 * q^59 + 2436146 * q^61 - 9005952 * q^62 + 11117562 * q^64 - 16730354 * q^65 - 2652248 * q^67 - 15929124 * q^68 + 3359254 * q^70 - 7356324 * q^71 + 1900454 * q^73 - 25386964 * q^74 - 16047360 * q^76 - 20774826 * q^77 - 5912712 * q^79 - 13568404 * q^80 + 1579434 * q^82 + 1052766 * q^83 + 18372730 * q^85 - 43499960 * q^86 + 18209214 * q^88 - 174788 * q^89 - 18891512 * q^91 - 46033270 * q^92 + 365448 * q^94 - 31505580 * q^95 + 14418540 * q^97 + 15964056 * q^98

Introduction

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