LMFDB - Embedded newform 531.8.a.h.1.4

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

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-16.9368 q^{2} +158.854 q^{4} -242.916 q^{5} -217.217 q^{7} -522.560 q^{8} +O(q^{10})$	\(q-16.9368 q^{2} +158.854 q^{4} -242.916 q^{5} -217.217 q^{7} -522.560 q^{8} +4114.21 q^{10} -2478.81 q^{11} -263.412 q^{13} +3678.95 q^{14} -11482.8 q^{16} +5400.90 q^{17} -48619.9 q^{19} -38588.1 q^{20} +41982.9 q^{22} +68140.5 q^{23} -19116.9 q^{25} +4461.34 q^{26} -34505.7 q^{28} +14476.0 q^{29} +66883.2 q^{31} +261369. q^{32} -91473.7 q^{34} +52765.5 q^{35} -568384. q^{37} +823463. q^{38} +126938. q^{40} -723821. q^{41} +457005. q^{43} -393767. q^{44} -1.15408e6 q^{46} +774421. q^{47} -776360. q^{49} +323778. q^{50} -41843.9 q^{52} -946119. q^{53} +602141. q^{55} +113509. q^{56} -245176. q^{58} -205379. q^{59} +578754. q^{61} -1.13278e6 q^{62} -2.95694e6 q^{64} +63986.9 q^{65} +3.55539e6 q^{67} +857953. q^{68} -893676. q^{70} +1.39078e6 q^{71} -4.59983e6 q^{73} +9.62658e6 q^{74} -7.72345e6 q^{76} +538439. q^{77} -2.06025e6 q^{79} +2.78935e6 q^{80} +1.22592e7 q^{82} +4.52988e6 q^{83} -1.31196e6 q^{85} -7.74018e6 q^{86} +1.29533e6 q^{88} -3.81525e6 q^{89} +57217.5 q^{91} +1.08244e7 q^{92} -1.31162e7 q^{94} +1.18105e7 q^{95} -1.49256e7 q^{97} +1.31490e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−16.9368	−1.49701	−0.748506	−	0.663128i	$-0.769228\pi$
$2$	−16.9368	−1.49701	−0.748506	+	0.663128i	$0.769228\pi$
$3$	0	0
$3$	0	0
$4$	158.854	1.24104
$5$	−242.916	−0.869082	−0.434541	−	0.900652i	$-0.643089\pi$
$5$	−242.916	−0.869082	−0.434541	+	0.900652i	$0.643089\pi$
$6$	0	0
$7$	−217.217	−0.239360	−0.119680	−	0.992813i	$-0.538187\pi$
$7$	−217.217	−0.239360	−0.119680	+	0.992813i	$0.538187\pi$
$8$	−522.560	−0.360846
$9$	0	0
$10$	4114.21	1.30103
$11$	−2478.81	−0.561524	−0.280762	−	0.959777i	$-0.590587\pi$
$11$	−2478.81	−0.561524	−0.280762	+	0.959777i	$0.590587\pi$
$12$	0	0
$13$	−263.412	−0.0332532	−0.0166266	−	0.999862i	$-0.505293\pi$
$13$	−263.412	−0.0332532	−0.0166266	+	0.999862i	$0.505293\pi$
$14$	3678.95	0.358324
$15$	0	0
$16$	−11482.8	−0.700854
$17$	5400.90	0.266621	0.133311	−	0.991074i	$-0.457439\pi$
$17$	5400.90	0.266621	0.133311	+	0.991074i	$0.457439\pi$
$18$	0	0
$19$	−48619.9	−1.62621	−0.813105	−	0.582118i	$-0.802224\pi$
$19$	−48619.9	−1.62621	−0.813105	+	0.582118i	$0.802224\pi$
$20$	−38588.1	−1.07857
$21$	0	0
$22$	41982.9	0.840608
$23$	68140.5	1.16777	0.583886	−	0.811836i	$-0.301532\pi$
$23$	68140.5	1.16777	0.583886	+	0.811836i	$0.301532\pi$
$24$	0	0
$25$	−19116.9	−0.244696
$26$	4461.34	0.0497804
$27$	0	0
$28$	−34505.7	−0.297056
$29$	14476.0	0.110219	0.0551093	−	0.998480i	$-0.482449\pi$
$29$	14476.0	0.110219	0.0551093	+	0.998480i	$0.482449\pi$
$30$	0	0
$31$	66883.2	0.403229	0.201614	−	0.979465i	$-0.435381\pi$
$31$	66883.2	0.403229	0.201614	+	0.979465i	$0.435381\pi$
$32$	261369.	1.41003
$33$	0	0
$34$	−91473.7	−0.399135
$35$	52765.5	0.208023
$36$	0	0
$37$	−568384.	−1.84474	−0.922371	−	0.386305i	$-0.873751\pi$
$37$	−568384.	−1.84474	−0.922371	+	0.386305i	$0.873751\pi$
$38$	823463.	2.43445
$39$	0	0
$40$	126938.	0.313605
$41$	−723821.	−1.64016	−0.820082	−	0.572246i	$-0.806072\pi$
$41$	−723821.	−1.64016	−0.820082	+	0.572246i	$0.806072\pi$
$42$	0	0
$43$	457005.	0.876559	0.438279	−	0.898839i	$-0.355588\pi$
$43$	457005.	0.876559	0.438279	+	0.898839i	$0.355588\pi$
$44$	−393767.	−0.696876
$45$	0	0
$46$	−1.15408e6	−1.74817
$47$	774421.	1.08801	0.544007	−	0.839080i	$-0.316906\pi$
$47$	774421.	1.08801	0.544007	+	0.839080i	$0.316906\pi$
$48$	0	0
$49$	−776360.	−0.942707
$50$	323778.	0.366313
$51$	0	0
$52$	−41843.9	−0.0412687
$53$	−946119.	−0.872932	−0.436466	−	0.899721i	$-0.643770\pi$
$53$	−946119.	−0.872932	−0.436466	+	0.899721i	$0.643770\pi$
$54$	0	0
$55$	602141.	0.488010
$56$	113509.	0.0863719
$57$	0	0
$58$	−245176.	−0.164998
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	578754.	0.326467	0.163234	−	0.986587i	$-0.447808\pi$
$61$	578754.	0.326467	0.163234	+	0.986587i	$0.447808\pi$
$62$	−1.13278e6	−0.603638
$63$	0	0
$64$	−2.95694e6	−1.40998
$65$	63986.9	0.0288997
$66$	0	0
$67$	3.55539e6	1.44420	0.722098	−	0.691791i	$-0.243178\pi$
$67$	3.55539e6	1.44420	0.722098	+	0.691791i	$0.243178\pi$
$68$	857953.	0.330889
$69$	0	0
$70$	−893676.	−0.311413
$71$	1.39078e6	0.461163	0.230582	−	0.973053i	$-0.425937\pi$
$71$	1.39078e6	0.461163	0.230582	+	0.973053i	$0.425937\pi$
$72$	0	0
$73$	−4.59983e6	−1.38392	−0.691961	−	0.721934i	$-0.743253\pi$
$73$	−4.59983e6	−1.38392	−0.691961	+	0.721934i	$0.743253\pi$
$74$	9.62658e6	2.76160
$75$	0	0
$76$	−7.72345e6	−2.01820
$77$	538439.	0.134406
$78$	0	0
$79$	−2.06025e6	−0.470137	−0.235068	−	0.971979i	$-0.575531\pi$
$79$	−2.06025e6	−0.470137	−0.235068	+	0.971979i	$0.575531\pi$
$80$	2.78935e6	0.609100
$81$	0	0
$82$	1.22592e7	2.45535
$83$	4.52988e6	0.869588	0.434794	−	0.900530i	$-0.356821\pi$
$83$	4.52988e6	0.869588	0.434794	+	0.900530i	$0.356821\pi$
$84$	0	0
$85$	−1.31196e6	−0.231716
$86$	−7.74018e6	−1.31222
$87$	0	0
$88$	1.29533e6	0.202623
$89$	−3.81525e6	−0.573665	−0.286833	−	0.957981i	$-0.592602\pi$
$89$	−3.81525e6	−0.573665	−0.286833	+	0.957981i	$0.592602\pi$
$90$	0	0
$91$	57217.5	0.00795947
$92$	1.08244e7	1.44926
$93$	0	0
$94$	−1.31162e7	−1.62877
$95$	1.18105e7	1.41331
$96$	0	0
$97$	−1.49256e7	−1.66047	−0.830234	−	0.557415i	$-0.811793\pi$
$97$	−1.49256e7	−1.66047	−0.830234	+	0.557415i	$0.811793\pi$
$98$	1.31490e7	1.41124
$99$	0	0
$100$	−3.03679e6	−0.303679
$101$	−1.68323e7	−1.62562	−0.812809	−	0.582530i	$-0.802063\pi$
$101$	−1.68323e7	−1.62562	−0.812809	+	0.582530i	$0.802063\pi$
$102$	0	0
$103$	−1.41617e7	−1.27698	−0.638490	−	0.769630i	$-0.720440\pi$
$103$	−1.41617e7	−1.27698	−0.638490	+	0.769630i	$0.720440\pi$
$104$	137648.	0.0119993
$105$	0	0
$106$	1.60242e7	1.30679
$107$	9.86769e6	0.778704	0.389352	−	0.921089i	$-0.372699\pi$
$107$	9.86769e6	0.778704	0.389352	+	0.921089i	$0.372699\pi$
$108$	0	0
$109$	−9.90684e6	−0.732727	−0.366364	−	0.930472i	$-0.619397\pi$
$109$	−9.90684e6	−0.732727	−0.366364	+	0.930472i	$0.619397\pi$
$110$	−1.01983e7	−0.730557
$111$	0	0
$112$	2.49426e6	0.167756
$113$	−1.02390e7	−0.667546	−0.333773	−	0.942653i	$-0.608322\pi$
$113$	−1.02390e7	−0.667546	−0.333773	+	0.942653i	$0.608322\pi$
$114$	0	0
$115$	−1.65524e7	−1.01489
$116$	2.29956e6	0.136786
$117$	0	0
$118$	3.47845e6	0.194894
$119$	−1.17317e6	−0.0638184
$120$	0	0
$121$	−1.33427e7	−0.684691
$122$	−9.80222e6	−0.488726
$123$	0	0
$124$	1.06246e7	0.500424
$125$	2.36216e7	1.08174
$126$	0	0
$127$	1.89909e7	0.822683	0.411341	−	0.911481i	$-0.365060\pi$
$127$	1.89909e7	0.822683	0.411341	+	0.911481i	$0.365060\pi$
$128$	1.66258e7	0.700725
$129$	0	0
$130$	−1.08373e6	−0.0432633
$131$	−5.03667e7	−1.95747	−0.978733	−	0.205139i	$-0.934235\pi$
$131$	−5.03667e7	−1.95747	−0.978733	+	0.205139i	$0.934235\pi$
$132$	0	0
$133$	1.05611e7	0.389249
$134$	−6.02168e7	−2.16198
$135$	0	0
$136$	−2.82230e6	−0.0962092
$137$	4.79599e6	0.159351	0.0796757	−	0.996821i	$-0.474612\pi$
$137$	4.79599e6	0.159351	0.0796757	+	0.996821i	$0.474612\pi$
$138$	0	0
$139$	−1.41239e7	−0.446070	−0.223035	−	0.974810i	$-0.571596\pi$
$139$	−1.41239e7	−0.446070	−0.223035	+	0.974810i	$0.571596\pi$
$140$	8.38199e6	0.258166
$141$	0	0
$142$	−2.35553e7	−0.690366
$143$	652946.	0.0186724
$144$	0	0
$145$	−3.51644e6	−0.0957890
$146$	7.79062e7	2.07175
$147$	0	0
$148$	−9.02898e7	−2.28941
$149$	−1.48745e7	−0.368376	−0.184188	−	0.982891i	$-0.558966\pi$
$149$	−1.48745e7	−0.368376	−0.184188	+	0.982891i	$0.558966\pi$
$150$	0	0
$151$	−1.68819e7	−0.399027	−0.199514	−	0.979895i	$-0.563936\pi$
$151$	−1.68819e7	−0.399027	−0.199514	+	0.979895i	$0.563936\pi$
$152$	2.54068e7	0.586810
$153$	0	0
$154$	−9.11941e6	−0.201208
$155$	−1.62470e7	−0.350439
$156$	0	0
$157$	−8.42487e7	−1.73746	−0.868729	−	0.495288i	$-0.835063\pi$
$157$	−8.42487e7	−1.73746	−0.868729	+	0.495288i	$0.835063\pi$
$158$	3.48939e7	0.703800
$159$	0	0
$160$	−6.34906e7	−1.22543
$161$	−1.48013e7	−0.279517
$162$	0	0
$163$	1.04094e8	1.88266	0.941328	−	0.337494i	$-0.109579\pi$
$163$	1.04094e8	1.88266	0.941328	+	0.337494i	$0.109579\pi$
$164$	−1.14982e8	−2.03552
$165$	0	0
$166$	−7.67215e7	−1.30178
$167$	−6.27818e7	−1.04310	−0.521550	−	0.853220i	$-0.674646\pi$
$167$	−6.27818e7	−1.04310	−0.521550	+	0.853220i	$0.674646\pi$
$168$	0	0
$169$	−6.26791e7	−0.998894
$170$	2.22204e7	0.346881
$171$	0	0
$172$	7.25969e7	1.08785
$173$	−9.98012e7	−1.46546	−0.732731	−	0.680518i	$-0.761755\pi$
$173$	−9.98012e7	−1.46546	−0.732731	+	0.680518i	$0.761755\pi$
$174$	0	0
$175$	4.15252e6	0.0585704
$176$	2.84636e7	0.393546
$177$	0	0
$178$	6.46180e7	0.858783
$179$	3.52277e7	0.459091	0.229546	−	0.973298i	$-0.426276\pi$
$179$	3.52277e7	0.459091	0.229546	+	0.973298i	$0.426276\pi$
$180$	0	0
$181$	−1.17490e8	−1.47275	−0.736373	−	0.676576i	$-0.763463\pi$
$181$	−1.17490e8	−1.47275	−0.736373	+	0.676576i	$0.763463\pi$
$182$	−969079.	−0.0119154
$183$	0	0
$184$	−3.56075e7	−0.421385
$185$	1.38069e8	1.60323
$186$	0	0
$187$	−1.33878e7	−0.149714
$188$	1.23020e8	1.35027
$189$	0	0
$190$	−2.00032e8	−2.11574
$191$	1.22580e8	1.27293	0.636464	−	0.771306i	$-0.280396\pi$
$191$	1.22580e8	1.27293	0.636464	+	0.771306i	$0.280396\pi$
$192$	0	0
$193$	1.75455e8	1.75677	0.878387	−	0.477950i	$-0.158620\pi$
$193$	1.75455e8	1.75677	0.878387	+	0.477950i	$0.158620\pi$
$194$	2.52791e8	2.48574
$195$	0	0
$196$	−1.23328e8	−1.16994
$197$	5.26629e6	0.0490764	0.0245382	−	0.999699i	$-0.492188\pi$
$197$	5.26629e6	0.0490764	0.0245382	+	0.999699i	$0.492188\pi$
$198$	0	0
$199$	−2.15015e8	−1.93412	−0.967058	−	0.254556i	$-0.918071\pi$
$199$	−2.15015e8	−1.93412	−0.967058	+	0.254556i	$0.918071\pi$
$200$	9.98972e6	0.0882975
$201$	0	0
$202$	2.85084e8	2.43357
$203$	−3.14443e6	−0.0263819
$204$	0	0
$205$	1.75827e8	1.42544
$206$	2.39853e8	1.91165
$207$	0	0
$208$	3.02470e6	0.0233056
$209$	1.20519e8	0.913155
$210$	0	0
$211$	−6.82790e7	−0.500378	−0.250189	−	0.968197i	$-0.580493\pi$
$211$	−6.82790e7	−0.500378	−0.250189	+	0.968197i	$0.580493\pi$
$212$	−1.50294e8	−1.08335
$213$	0	0
$214$	−1.67127e8	−1.16573
$215$	−1.11014e8	−0.761802
$216$	0	0
$217$	−1.45282e7	−0.0965167
$218$	1.67790e8	1.09690
$219$	0	0
$220$	9.56523e7	0.605642
$221$	−1.42266e6	−0.00886601
$222$	0	0
$223$	−6.19558e7	−0.374124	−0.187062	−	0.982348i	$-0.559896\pi$
$223$	−6.19558e7	−0.374124	−0.187062	+	0.982348i	$0.559896\pi$
$224$	−5.67738e7	−0.337505
$225$	0	0
$226$	1.73415e8	0.999324
$227$	−1.60196e8	−0.908995	−0.454497	−	0.890748i	$-0.650181\pi$
$227$	−1.60196e8	−0.908995	−0.454497	+	0.890748i	$0.650181\pi$
$228$	0	0
$229$	3.53705e7	0.194633	0.0973166	−	0.995253i	$-0.468974\pi$
$229$	3.53705e7	0.194633	0.0973166	+	0.995253i	$0.468974\pi$
$230$	2.80344e8	1.51930
$231$	0	0
$232$	−7.56457e6	−0.0397719
$233$	2.61988e8	1.35686	0.678431	−	0.734665i	$-0.262660\pi$
$233$	2.61988e8	1.35686	0.678431	+	0.734665i	$0.262660\pi$
$234$	0	0
$235$	−1.88119e8	−0.945574
$236$	−3.26252e7	−0.161570
$237$	0	0
$238$	1.98697e7	0.0955369
$239$	−1.85538e8	−0.879104	−0.439552	−	0.898217i	$-0.644863\pi$
$239$	−1.85538e8	−0.879104	−0.439552	+	0.898217i	$0.644863\pi$
$240$	0	0
$241$	1.32257e8	0.608639	0.304320	−	0.952570i	$-0.401571\pi$
$241$	1.32257e8	0.608639	0.304320	+	0.952570i	$0.401571\pi$
$242$	2.25982e8	1.02499
$243$	0	0
$244$	9.19372e7	0.405160
$245$	1.88590e8	0.819290
$246$	0	0
$247$	1.28070e7	0.0540766
$248$	−3.49505e7	−0.145503
$249$	0	0
$250$	−4.00073e8	−1.61938
$251$	−1.04039e7	−0.0415276	−0.0207638	−	0.999784i	$-0.506610\pi$
$251$	−1.04039e7	−0.0415276	−0.0207638	+	0.999784i	$0.506610\pi$
$252$	0	0
$253$	−1.68907e8	−0.655731
$254$	−3.21644e8	−1.23157
$255$	0	0
$256$	9.69016e7	0.360987
$257$	4.70421e8	1.72870	0.864352	−	0.502887i	$-0.167729\pi$
$257$	4.70421e8	1.72870	0.864352	+	0.502887i	$0.167729\pi$
$258$	0	0
$259$	1.23463e8	0.441557
$260$	1.01645e7	0.0358659
$261$	0	0
$262$	8.53049e8	2.93035
$263$	5.30219e8	1.79726	0.898628	−	0.438711i	$-0.144565\pi$
$263$	5.30219e8	1.79726	0.898628	+	0.438711i	$0.144565\pi$
$264$	0	0
$265$	2.29827e8	0.758649
$266$	−1.78870e8	−0.582710
$267$	0	0
$268$	5.64787e8	1.79231
$269$	5.56832e8	1.74418	0.872090	−	0.489346i	$-0.162765\pi$
$269$	5.56832e8	1.74418	0.872090	+	0.489346i	$0.162765\pi$
$270$	0	0
$271$	3.97339e8	1.21274	0.606372	−	0.795181i	$-0.292624\pi$
$271$	3.97339e8	1.21274	0.606372	+	0.795181i	$0.292624\pi$
$272$	−6.20174e7	−0.186863
$273$	0	0
$274$	−8.12284e7	−0.238551
$275$	4.73870e7	0.137403
$276$	0	0
$277$	6.70163e8	1.89453	0.947265	−	0.320452i	$-0.103835\pi$
$277$	6.70163e8	1.89453	0.947265	+	0.320452i	$0.103835\pi$
$278$	2.39213e8	0.667772
$279$	0	0
$280$	−2.75732e7	−0.0750643
$281$	3.99134e7	0.107312	0.0536558	−	0.998559i	$-0.482913\pi$
$281$	3.99134e7	0.107312	0.0536558	+	0.998559i	$0.482913\pi$
$282$	0	0
$283$	4.32518e8	1.13436	0.567181	−	0.823593i	$-0.308034\pi$
$283$	4.32518e8	1.13436	0.567181	+	0.823593i	$0.308034\pi$
$284$	2.20931e8	0.572324
$285$	0	0
$286$	−1.10588e7	−0.0279529
$287$	1.57226e8	0.392589
$288$	0	0
$289$	−3.81169e8	−0.928913
$290$	5.95571e7	0.143397
$291$	0	0
$292$	−7.30700e8	−1.71751
$293$	−3.25609e8	−0.756239	−0.378120	−	0.925757i	$-0.623429\pi$
$293$	−3.25609e8	−0.756239	−0.378120	+	0.925757i	$0.623429\pi$
$294$	0	0
$295$	4.98898e7	0.113145
$296$	2.97015e8	0.665667
$297$	0	0
$298$	2.51926e8	0.551463
$299$	−1.79490e7	−0.0388321
$300$	0	0
$301$	−9.92693e7	−0.209813
$302$	2.85925e8	0.597348
$303$	0	0
$304$	5.58292e8	1.13973
$305$	−1.40589e8	−0.283727
$306$	0	0
$307$	1.82809e8	0.360589	0.180295	−	0.983613i	$-0.442295\pi$
$307$	1.82809e8	0.360589	0.180295	+	0.983613i	$0.442295\pi$
$308$	8.55330e7	0.166804
$309$	0	0
$310$	2.75171e8	0.524611
$311$	1.23788e8	0.233354	0.116677	−	0.993170i	$-0.462776\pi$
$311$	1.23788e8	0.233354	0.116677	+	0.993170i	$0.462776\pi$
$312$	0	0
$313$	−3.00225e8	−0.553404	−0.276702	−	0.960956i	$-0.589241\pi$
$313$	−3.00225e8	−0.553404	−0.276702	+	0.960956i	$0.589241\pi$
$314$	1.42690e9	2.60099
$315$	0	0
$316$	−3.27278e8	−0.583461
$317$	1.40738e8	0.248145	0.124072	−	0.992273i	$-0.460404\pi$
$317$	1.40738e8	0.248145	0.124072	+	0.992273i	$0.460404\pi$
$318$	0	0
$319$	−3.58831e7	−0.0618903
$320$	7.18288e8	1.22539
$321$	0	0
$322$	2.50686e8	0.418441
$323$	−2.62591e8	−0.433582
$324$	0	0
$325$	5.03561e6	0.00813692
$326$	−1.76302e9	−2.81836
$327$	0	0
$328$	3.78240e8	0.591846
$329$	−1.68218e8	−0.260427
$330$	0	0
$331$	6.58548e8	0.998136	0.499068	−	0.866563i	$-0.333676\pi$
$331$	6.58548e8	0.998136	0.499068	+	0.866563i	$0.333676\pi$
$332$	7.19588e8	1.07920
$333$	0	0
$334$	1.06332e9	1.56153
$335$	−8.63662e8	−1.25512
$336$	0	0
$337$	6.20382e7	0.0882988	0.0441494	−	0.999025i	$-0.485942\pi$
$337$	6.20382e7	0.0882988	0.0441494	+	0.999025i	$0.485942\pi$
$338$	1.06158e9	1.49536
$339$	0	0
$340$	−2.08410e8	−0.287570
$341$	−1.65791e8	−0.226422
$342$	0	0
$343$	3.47526e8	0.465006
$344$	−2.38813e8	−0.316302
$345$	0	0
$346$	1.69031e9	2.19381
$347$	−1.52990e9	−1.96567	−0.982833	−	0.184495i	$-0.940935\pi$
$347$	−1.52990e9	−1.96567	−0.982833	+	0.184495i	$0.940935\pi$
$348$	0	0
$349$	−4.75606e7	−0.0598906	−0.0299453	−	0.999552i	$-0.509533\pi$
$349$	−4.75606e7	−0.0598906	−0.0299453	+	0.999552i	$0.509533\pi$
$350$	−7.03301e7	−0.0876805
$351$	0	0
$352$	−6.47883e8	−0.791766
$353$	−9.50971e8	−1.15068	−0.575341	−	0.817913i	$-0.695131\pi$
$353$	−9.50971e8	−1.15068	−0.575341	+	0.817913i	$0.695131\pi$
$354$	0	0
$355$	−3.37843e8	−0.400789
$356$	−6.06067e8	−0.711944
$357$	0	0
$358$	−5.96643e8	−0.687265
$359$	1.03471e9	1.18029	0.590143	−	0.807298i	$-0.299071\pi$
$359$	1.03471e9	1.18029	0.590143	+	0.807298i	$0.299071\pi$
$360$	0	0
$361$	1.47002e9	1.64456
$362$	1.98991e9	2.20472
$363$	0	0
$364$	9.08921e6	0.00987805
$365$	1.11737e9	1.20274
$366$	0	0
$367$	−2.55152e8	−0.269443	−0.134722	−	0.990883i	$-0.543014\pi$
$367$	−2.55152e8	−0.269443	−0.134722	+	0.990883i	$0.543014\pi$
$368$	−7.82443e8	−0.818437
$369$	0	0
$370$	−2.33845e9	−2.40006
$371$	2.05513e8	0.208945
$372$	0	0
$373$	−8.04964e7	−0.0803148	−0.0401574	−	0.999193i	$-0.512786\pi$
$373$	−8.04964e7	−0.0803148	−0.0401574	+	0.999193i	$0.512786\pi$
$374$	2.26746e8	0.224124
$375$	0	0
$376$	−4.04682e8	−0.392605
$377$	−3.81314e6	−0.00366512
$378$	0	0
$379$	4.26920e8	0.402818	0.201409	−	0.979507i	$-0.435448\pi$
$379$	4.26920e8	0.402818	0.201409	+	0.979507i	$0.435448\pi$
$380$	1.87615e9	1.75398
$381$	0	0
$382$	−2.07611e9	−1.90559
$383$	−1.10298e9	−1.00317	−0.501584	−	0.865109i	$-0.667249\pi$
$383$	−1.10298e9	−1.00317	−0.501584	+	0.865109i	$0.667249\pi$
$384$	0	0
$385$	−1.30795e8	−0.116810
$386$	−2.97164e9	−2.62991
$387$	0	0
$388$	−2.37098e9	−2.06071
$389$	−5.39468e8	−0.464667	−0.232334	−	0.972636i	$-0.574636\pi$
$389$	−5.39468e8	−0.464667	−0.232334	+	0.972636i	$0.574636\pi$
$390$	0	0
$391$	3.68020e8	0.311353
$392$	4.05695e8	0.340172
$393$	0	0
$394$	−8.91939e7	−0.0734680
$395$	5.00467e8	0.408588
$396$	0	0
$397$	1.57605e9	1.26417	0.632084	−	0.774900i	$-0.282200\pi$
$397$	1.57605e9	1.26417	0.632084	+	0.774900i	$0.282200\pi$
$398$	3.64165e9	2.89539
$399$	0	0
$400$	2.19515e8	0.171496
$401$	−1.42291e9	−1.10198	−0.550989	−	0.834512i	$-0.685749\pi$
$401$	−1.42291e9	−1.10198	−0.550989	+	0.834512i	$0.685749\pi$
$402$	0	0
$403$	−1.76178e7	−0.0134086
$404$	−2.67387e9	−2.01746
$405$	0	0
$406$	5.32564e7	0.0394940
$407$	1.40891e9	1.03587
$408$	0	0
$409$	2.50740e9	1.81214	0.906069	−	0.423129i	$-0.139068\pi$
$409$	2.50740e9	1.81214	0.906069	+	0.423129i	$0.139068\pi$
$410$	−2.97795e9	−2.13390
$411$	0	0
$412$	−2.24963e9	−1.58479
$413$	4.46118e7	0.0311620
$414$	0	0
$415$	−1.10038e9	−0.755743
$416$	−6.88476e7	−0.0468881
$417$	0	0
$418$	−2.04121e9	−1.36700
$419$	1.23395e9	0.819502	0.409751	−	0.912197i	$-0.365616\pi$
$419$	1.23395e9	0.819502	0.409751	+	0.912197i	$0.365616\pi$
$420$	0	0
$421$	−1.74480e9	−1.13961	−0.569807	−	0.821778i	$-0.692982\pi$
$421$	−1.74480e9	−1.13961	−0.569807	+	0.821778i	$0.692982\pi$
$422$	1.15642e9	0.749072
$423$	0	0
$424$	4.94404e8	0.314994
$425$	−1.03248e8	−0.0652412
$426$	0	0
$427$	−1.25715e8	−0.0781431
$428$	1.56752e9	0.966405
$429$	0	0
$430$	1.88021e9	1.14043
$431$	5.78704e8	0.348166	0.174083	−	0.984731i	$-0.444304\pi$
$431$	5.78704e8	0.348166	0.174083	+	0.984731i	$0.444304\pi$
$432$	0	0
$433$	−2.11949e9	−1.25465	−0.627326	−	0.778756i	$-0.715851\pi$
$433$	−2.11949e9	−1.25465	−0.627326	+	0.778756i	$0.715851\pi$
$434$	2.46060e8	0.144487
$435$	0	0
$436$	−1.57374e9	−0.909347
$437$	−3.31298e9	−1.89904
$438$	0	0
$439$	−3.07170e9	−1.73282	−0.866408	−	0.499336i	$-0.833577\pi$
$439$	−3.07170e9	−1.73282	−0.866408	+	0.499336i	$0.833577\pi$
$440$	−3.14655e8	−0.176096
$441$	0	0
$442$	2.40952e7	0.0132725
$443$	2.64415e9	1.44502	0.722509	−	0.691361i	$-0.242989\pi$
$443$	2.64415e9	1.44502	0.722509	+	0.691361i	$0.242989\pi$
$444$	0	0
$445$	9.26786e8	0.498562
$446$	1.04933e9	0.560067
$447$	0	0
$448$	6.42299e8	0.337492
$449$	8.25285e8	0.430271	0.215135	−	0.976584i	$-0.430981\pi$
$449$	8.25285e8	0.430271	0.215135	+	0.976584i	$0.430981\pi$
$450$	0	0
$451$	1.79421e9	0.920991
$452$	−1.62650e9	−0.828454
$453$	0	0
$454$	2.71320e9	1.36078
$455$	−1.38990e7	−0.00691743
$456$	0	0
$457$	2.23621e9	1.09599	0.547994	−	0.836482i	$-0.315392\pi$
$457$	2.23621e9	1.09599	0.547994	+	0.836482i	$0.315392\pi$
$458$	−5.99061e8	−0.291368
$459$	0	0
$460$	−2.62941e9	−1.25952
$461$	3.28827e9	1.56320	0.781599	−	0.623781i	$-0.214404\pi$
$461$	3.28827e9	1.56320	0.781599	+	0.623781i	$0.214404\pi$
$462$	0	0
$463$	1.72422e9	0.807344	0.403672	−	0.914904i	$-0.367734\pi$
$463$	1.72422e9	0.807344	0.403672	+	0.914904i	$0.367734\pi$
$464$	−1.66224e8	−0.0772471
$465$	0	0
$466$	−4.43722e9	−2.03124
$467$	3.38450e9	1.53775	0.768874	−	0.639400i	$-0.220817\pi$
$467$	3.38450e9	1.53775	0.768874	+	0.639400i	$0.220817\pi$
$468$	0	0
$469$	−7.72293e8	−0.345682
$470$	3.18613e9	1.41554
$471$	0	0
$472$	1.07323e8	0.0469781
$473$	−1.13283e9	−0.492209
$474$	0	0
$475$	9.29461e8	0.397927
$476$	−1.86362e8	−0.0792015
$477$	0	0
$478$	3.14241e9	1.31603
$479$	−9.78770e8	−0.406917	−0.203459	−	0.979084i	$-0.565218\pi$
$479$	−9.78770e8	−0.406917	−0.203459	+	0.979084i	$0.565218\pi$
$480$	0	0
$481$	1.49719e8	0.0613436
$482$	−2.24001e9	−0.911140
$483$	0	0
$484$	−2.11954e9	−0.849732
$485$	3.62566e9	1.44308
$486$	0	0
$487$	6.12048e8	0.240123	0.120062	−	0.992766i	$-0.461691\pi$
$487$	6.12048e8	0.240123	0.120062	+	0.992766i	$0.461691\pi$
$488$	−3.02434e8	−0.117804
$489$	0	0
$490$	−3.19410e9	−1.22649
$491$	−2.35954e9	−0.899584	−0.449792	−	0.893133i	$-0.648502\pi$
$491$	−2.35954e9	−0.899584	−0.449792	+	0.893133i	$0.648502\pi$
$492$	0	0
$493$	7.81833e7	0.0293866
$494$	−2.16910e8	−0.0809533
$495$	0	0
$496$	−7.68006e8	−0.282604
$497$	−3.02101e8	−0.110384
$498$	0	0
$499$	2.16687e9	0.780694	0.390347	−	0.920668i	$-0.372355\pi$
$499$	2.16687e9	0.780694	0.390347	+	0.920668i	$0.372355\pi$
$500$	3.75238e9	1.34249
$501$	0	0
$502$	1.76208e8	0.0621673
$503$	−4.41651e9	−1.54736	−0.773680	−	0.633576i	$-0.781586\pi$
$503$	−4.41651e9	−1.54736	−0.773680	+	0.633576i	$0.781586\pi$
$504$	0	0
$505$	4.08883e9	1.41280
$506$	2.86074e9	0.981637
$507$	0	0
$508$	3.01677e9	1.02099
$509$	−1.59369e9	−0.535664	−0.267832	−	0.963466i	$-0.586307\pi$
$509$	−1.59369e9	−0.535664	−0.267832	+	0.963466i	$0.586307\pi$
$510$	0	0
$511$	9.99162e8	0.331255
$512$	−3.76930e9	−1.24113
$513$	0	0
$514$	−7.96741e9	−2.58789
$515$	3.44009e9	1.10980
$516$	0	0
$517$	−1.91964e9	−0.610946
$518$	−2.09106e9	−0.661016
$519$	0	0
$520$	−3.34370e7	−0.0104283
$521$	−5.70010e8	−0.176584	−0.0882918	−	0.996095i	$-0.528141\pi$
$521$	−5.70010e8	−0.176584	−0.0882918	+	0.996095i	$0.528141\pi$
$522$	0	0
$523$	−1.56589e9	−0.478635	−0.239318	−	0.970941i	$-0.576924\pi$
$523$	−1.56589e9	−0.478635	−0.239318	+	0.970941i	$0.576924\pi$
$524$	−8.00094e9	−2.42930
$525$	0	0
$526$	−8.98019e9	−2.69051
$527$	3.61230e8	0.107509
$528$	0	0
$529$	1.23830e9	0.363690
$530$	−3.89253e9	−1.13571
$531$	0	0
$532$	1.67767e9	0.483075
$533$	1.90663e8	0.0545407
$534$	0	0
$535$	−2.39702e9	−0.676757
$536$	−1.85791e9	−0.521132
$537$	0	0
$538$	−9.43092e9	−2.61106
$539$	1.92444e9	0.529352
$540$	0	0
$541$	1.39129e9	0.377770	0.188885	−	0.981999i	$-0.439513\pi$
$541$	1.39129e9	0.377770	0.188885	+	0.981999i	$0.439513\pi$
$542$	−6.72964e9	−1.81549
$543$	0	0
$544$	1.41163e9	0.375945
$545$	2.40653e9	0.636800
$546$	0	0
$547$	8.01349e8	0.209347	0.104673	−	0.994507i	$-0.466620\pi$
$547$	8.01349e8	0.209347	0.104673	+	0.994507i	$0.466620\pi$
$548$	7.61860e8	0.197762
$549$	0	0
$550$	−8.02583e8	−0.205693
$551$	−7.03820e8	−0.179238
$552$	0	0
$553$	4.47521e8	0.112532
$554$	−1.13504e10	−2.83613
$555$	0	0
$556$	−2.24363e9	−0.553592
$557$	4.66112e9	1.14287	0.571435	−	0.820647i	$-0.306387\pi$
$557$	4.66112e9	1.14287	0.571435	+	0.820647i	$0.306387\pi$
$558$	0	0
$559$	−1.20380e8	−0.0291484
$560$	−6.05895e8	−0.145794
$561$	0	0
$562$	−6.76004e8	−0.160647
$563$	−2.50367e9	−0.591285	−0.295643	−	0.955299i	$-0.595534\pi$
$563$	−2.50367e9	−0.591285	−0.295643	+	0.955299i	$0.595534\pi$
$564$	0	0
$565$	2.48721e9	0.580152
$566$	−7.32545e9	−1.69815
$567$	0	0
$568$	−7.26767e8	−0.166409
$569$	−3.69811e9	−0.841563	−0.420781	−	0.907162i	$-0.638244\pi$
$569$	−3.69811e9	−0.841563	−0.420781	+	0.907162i	$0.638244\pi$
$570$	0	0
$571$	7.32968e9	1.64763	0.823813	−	0.566861i	$-0.191842\pi$
$571$	7.32968e9	1.64763	0.823813	+	0.566861i	$0.191842\pi$
$572$	1.03723e8	0.0231733
$573$	0	0
$574$	−2.66290e9	−0.587711
$575$	−1.30263e9	−0.285749
$576$	0	0
$577$	4.41924e9	0.957705	0.478853	−	0.877895i	$-0.341053\pi$
$577$	4.41924e9	0.957705	0.478853	+	0.877895i	$0.341053\pi$
$578$	6.45576e9	1.39059
$579$	0	0
$580$	−5.58600e8	−0.118878
$581$	−9.83968e8	−0.208144
$582$	0	0
$583$	2.34525e9	0.490172
$584$	2.40369e9	0.499383
$585$	0	0
$586$	5.51475e9	1.13210
$587$	8.26687e9	1.68697	0.843486	−	0.537152i	$-0.180500\pi$
$587$	8.26687e9	1.68697	0.843486	+	0.537152i	$0.180500\pi$
$588$	0	0
$589$	−3.25186e9	−0.655734
$590$	−8.44972e8	−0.169379
$591$	0	0
$592$	6.52663e9	1.29289
$593$	−7.69929e9	−1.51621	−0.758105	−	0.652132i	$-0.773875\pi$
$593$	−7.69929e9	−1.51621	−0.758105	+	0.652132i	$0.773875\pi$
$594$	0	0
$595$	2.84981e8	0.0554634
$596$	−2.36287e9	−0.457171
$597$	0	0
$598$	3.03998e8	0.0581321
$599$	−2.34929e9	−0.446625	−0.223313	−	0.974747i	$-0.571687\pi$
$599$	−2.34929e9	−0.446625	−0.223313	+	0.974747i	$0.571687\pi$
$600$	0	0
$601$	−3.55592e9	−0.668176	−0.334088	−	0.942542i	$-0.608428\pi$
$601$	−3.55592e9	−0.668176	−0.334088	+	0.942542i	$0.608428\pi$
$602$	1.68130e9	0.314092
$603$	0	0
$604$	−2.68175e9	−0.495210
$605$	3.24115e9	0.595053
$606$	0	0
$607$	−2.15522e9	−0.391138	−0.195569	−	0.980690i	$-0.562655\pi$
$607$	−2.15522e9	−0.391138	−0.195569	+	0.980690i	$0.562655\pi$
$608$	−1.27077e10	−2.29301
$609$	0	0
$610$	2.38111e9	0.424743
$611$	−2.03992e8	−0.0361800
$612$	0	0
$613$	1.50389e9	0.263697	0.131849	−	0.991270i	$-0.457909\pi$
$613$	1.50389e9	0.263697	0.131849	+	0.991270i	$0.457909\pi$
$614$	−3.09619e9	−0.539806
$615$	0	0
$616$	−2.81367e8	−0.0484999
$617$	5.65990e9	0.970088	0.485044	−	0.874490i	$-0.338804\pi$
$617$	5.65990e9	0.970088	0.485044	+	0.874490i	$0.338804\pi$
$618$	0	0
$619$	−2.39264e9	−0.405472	−0.202736	−	0.979233i	$-0.564983\pi$
$619$	−2.39264e9	−0.405472	−0.202736	+	0.979233i	$0.564983\pi$
$620$	−2.58089e9	−0.434910
$621$	0	0
$622$	−2.09656e9	−0.349334
$623$	8.28739e8	0.137312
$624$	0	0
$625$	−4.24455e9	−0.695428
$626$	5.08484e9	0.828452
$627$	0	0
$628$	−1.33832e10	−2.15626
$629$	−3.06979e9	−0.491848
$630$	0	0
$631$	1.87051e9	0.296386	0.148193	−	0.988958i	$-0.452654\pi$
$631$	1.87051e9	0.296386	0.148193	+	0.988958i	$0.452654\pi$
$632$	1.07660e9	0.169647
$633$	0	0
$634$	−2.38365e9	−0.371476
$635$	−4.61319e9	−0.714979
$636$	0	0
$637$	2.04502e8	0.0313480
$638$	6.07743e8	0.0926505
$639$	0	0
$640$	−4.03867e9	−0.608988
$641$	1.58676e9	0.237962	0.118981	−	0.992897i	$-0.462037\pi$
$641$	1.58676e9	0.237962	0.118981	+	0.992897i	$0.462037\pi$
$642$	0	0
$643$	6.53546e9	0.969477	0.484739	−	0.874659i	$-0.338915\pi$
$643$	6.53546e9	0.969477	0.484739	+	0.874659i	$0.338915\pi$
$644$	−2.35124e9	−0.346893
$645$	0	0
$646$	4.44744e9	0.649078
$647$	−5.98982e9	−0.869459	−0.434729	−	0.900561i	$-0.643156\pi$
$647$	−5.98982e9	−0.869459	−0.434729	+	0.900561i	$0.643156\pi$
$648$	0	0
$649$	5.09095e8	0.0731042
$650$	−8.52869e7	−0.0121811
$651$	0	0
$652$	1.65358e10	2.33646
$653$	−9.26026e9	−1.30145	−0.650725	−	0.759314i	$-0.725535\pi$
$653$	−9.26026e9	−1.30145	−0.650725	+	0.759314i	$0.725535\pi$
$654$	0	0
$655$	1.22349e10	1.70120
$656$	8.31148e9	1.14952
$657$	0	0
$658$	2.84906e9	0.389862
$659$	−9.04375e9	−1.23098	−0.615488	−	0.788147i	$-0.711041\pi$
$659$	−9.04375e9	−1.23098	−0.615488	+	0.788147i	$0.711041\pi$
$660$	0	0
$661$	5.89717e8	0.0794216	0.0397108	−	0.999211i	$-0.487356\pi$
$661$	5.89717e8	0.0794216	0.0397108	+	0.999211i	$0.487356\pi$
$662$	−1.11537e10	−1.49422
$663$	0	0
$664$	−2.36714e9	−0.313787
$665$	−2.56545e9	−0.338289
$666$	0	0
$667$	9.86399e8	0.128710
$668$	−9.97312e9	−1.29453
$669$	0	0
$670$	1.46276e10	1.87894
$671$	−1.43462e9	−0.183319
$672$	0	0
$673$	−8.68423e9	−1.09819	−0.549097	−	0.835759i	$-0.685028\pi$
$673$	−8.68423e9	−1.09819	−0.549097	+	0.835759i	$0.685028\pi$
$674$	−1.05073e9	−0.132184
$675$	0	0
$676$	−9.95681e9	−1.23967
$677$	2.76879e9	0.342949	0.171475	−	0.985189i	$-0.445147\pi$
$677$	2.76879e9	0.342949	0.171475	+	0.985189i	$0.445147\pi$
$678$	0	0
$679$	3.24209e9	0.397449
$680$	6.85581e8	0.0836137
$681$	0	0
$682$	2.80795e9	0.338957
$683$	−6.69854e9	−0.804467	−0.402233	−	0.915537i	$-0.631766\pi$
$683$	−6.69854e9	−0.804467	−0.402233	+	0.915537i	$0.631766\pi$
$684$	0	0
$685$	−1.16502e9	−0.138489
$686$	−5.88597e9	−0.696119
$687$	0	0
$688$	−5.24769e9	−0.614340
$689$	2.49219e8	0.0290278
$690$	0	0
$691$	9.57434e9	1.10392	0.551958	−	0.833872i	$-0.313881\pi$
$691$	9.57434e9	1.10392	0.551958	+	0.833872i	$0.313881\pi$
$692$	−1.58538e10	−1.81870
$693$	0	0
$694$	2.59115e10	2.94263
$695$	3.43092e9	0.387671
$696$	0	0
$697$	−3.90928e9	−0.437303
$698$	8.05523e8	0.0896569
$699$	0	0
$700$	6.59642e8	0.0726884
$701$	1.69082e10	1.85389	0.926944	−	0.375200i	$-0.122426\pi$
$701$	1.69082e10	1.85389	0.926944	+	0.375200i	$0.122426\pi$
$702$	0	0
$703$	2.76348e10	2.99994
$704$	7.32969e9	0.791737
$705$	0	0
$706$	1.61064e10	1.72259
$707$	3.65626e9	0.389107
$708$	0	0
$709$	4.31037e9	0.454206	0.227103	−	0.973871i	$-0.427075\pi$
$709$	4.31037e9	0.454206	0.227103	+	0.973871i	$0.427075\pi$
$710$	5.72196e9	0.599985
$711$	0	0
$712$	1.99370e9	0.207005
$713$	4.55746e9	0.470879
$714$	0	0
$715$	−1.58611e8	−0.0162279
$716$	5.59605e9	0.569753
$717$	0	0
$718$	−1.75246e10	−1.76690
$719$	1.20241e10	1.20643	0.603216	−	0.797578i	$-0.293886\pi$
$719$	1.20241e10	1.20643	0.603216	+	0.797578i	$0.293886\pi$
$720$	0	0
$721$	3.07616e9	0.305657
$722$	−2.48974e10	−2.46192
$723$	0	0
$724$	−1.86638e10	−1.82774
$725$	−2.76735e8	−0.0269700
$726$	0	0
$727$	−1.04773e10	−1.01130	−0.505650	−	0.862739i	$-0.668747\pi$
$727$	−1.04773e10	−1.01130	−0.505650	+	0.862739i	$0.668747\pi$
$728$	−2.98996e7	−0.00287214
$729$	0	0
$730$	−1.89247e10	−1.80052
$731$	2.46824e9	0.233709
$732$	0	0
$733$	7.55226e9	0.708294	0.354147	−	0.935190i	$-0.384771\pi$
$733$	7.55226e9	0.708294	0.354147	+	0.935190i	$0.384771\pi$
$734$	4.32144e9	0.403360
$735$	0	0
$736$	1.78098e10	1.64659
$737$	−8.81313e9	−0.810950
$738$	0	0
$739$	1.91408e10	1.74463	0.872315	−	0.488944i	$-0.162618\pi$
$739$	1.91408e10	1.74463	0.872315	+	0.488944i	$0.162618\pi$
$740$	2.19328e10	1.98968
$741$	0	0
$742$	−3.48073e9	−0.312793
$743$	−4.38494e9	−0.392196	−0.196098	−	0.980584i	$-0.562827\pi$
$743$	−4.38494e9	−0.392196	−0.196098	+	0.980584i	$0.562827\pi$
$744$	0	0
$745$	3.61326e9	0.320149
$746$	1.36335e9	0.120232
$747$	0	0
$748$	−2.12670e9	−0.185802
$749$	−2.14343e9	−0.186390
$750$	0	0
$751$	−1.05805e10	−0.911522	−0.455761	−	0.890102i	$-0.650633\pi$
$751$	−1.05805e10	−0.911522	−0.455761	+	0.890102i	$0.650633\pi$
$752$	−8.89252e9	−0.762539
$753$	0	0
$754$	6.45822e7	0.00548672
$755$	4.10088e9	0.346787
$756$	0	0
$757$	−1.55390e10	−1.30193	−0.650964	−	0.759108i	$-0.725635\pi$
$757$	−1.55390e10	−1.30193	−0.650964	+	0.759108i	$0.725635\pi$
$758$	−7.23064e9	−0.603024
$759$	0	0
$760$	−6.17172e9	−0.509987
$761$	2.22274e8	0.0182828	0.00914140	−	0.999958i	$-0.497090\pi$
$761$	2.22274e8	0.0182828	0.00914140	+	0.999958i	$0.497090\pi$
$762$	0	0
$763$	2.15194e9	0.175385
$764$	1.94723e10	1.57976
$765$	0	0
$766$	1.86810e10	1.50175
$767$	5.40992e7	0.00432920
$768$	0	0
$769$	8.96433e9	0.710846	0.355423	−	0.934706i	$-0.384337\pi$
$769$	8.96433e9	0.710846	0.355423	+	0.934706i	$0.384337\pi$
$770$	2.21525e9	0.174866
$771$	0	0
$772$	2.78717e10	2.18023
$773$	1.98270e10	1.54393	0.771966	−	0.635664i	$-0.219274\pi$
$773$	1.98270e10	1.54393	0.771966	+	0.635664i	$0.219274\pi$
$774$	0	0
$775$	−1.27860e9	−0.0986685
$776$	7.79952e9	0.599173
$777$	0	0
$778$	9.13683e9	0.695612
$779$	3.51921e10	2.66725
$780$	0	0
$781$	−3.44748e9	−0.258954
$782$	−6.23307e9	−0.466099
$783$	0	0
$784$	8.91478e9	0.660700
$785$	2.04653e10	1.50999
$786$	0	0
$787$	5.39717e9	0.394688	0.197344	−	0.980334i	$-0.436768\pi$
$787$	5.39717e9	0.394688	0.197344	+	0.980334i	$0.436768\pi$
$788$	8.36570e8	0.0609060
$789$	0	0
$790$	−8.47628e9	−0.611660
$791$	2.22408e9	0.159784
$792$	0	0
$793$	−1.52451e8	−0.0108561
$794$	−2.66933e10	−1.89247
$795$	0	0
$796$	−3.41559e10	−2.40032
$797$	−1.96733e10	−1.37649	−0.688245	−	0.725479i	$-0.741618\pi$
$797$	−1.96733e10	−1.37649	−0.688245	+	0.725479i	$0.741618\pi$
$798$	0	0
$799$	4.18257e9	0.290088
$800$	−4.99656e9	−0.345029
$801$	0	0
$802$	2.40995e10	1.64967
$803$	1.14021e10	0.777105
$804$	0	0
$805$	3.59547e9	0.242924
$806$	2.98389e8	0.0200729
$807$	0	0
$808$	8.79589e9	0.586597
$809$	5.51345e9	0.366103	0.183052	−	0.983103i	$-0.441402\pi$
$809$	5.51345e9	0.366103	0.183052	+	0.983103i	$0.441402\pi$
$810$	0	0
$811$	−1.71960e10	−1.13202	−0.566010	−	0.824398i	$-0.691514\pi$
$811$	−1.71960e10	−1.13202	−0.566010	+	0.824398i	$0.691514\pi$
$812$	−4.99504e8	−0.0327411
$813$	0	0
$814$	−2.38624e10	−1.55070
$815$	−2.52862e10	−1.63618
$816$	0	0
$817$	−2.22195e10	−1.42547
$818$	−4.24672e10	−2.71279
$819$	0	0
$820$	2.79308e10	1.76903
$821$	2.04467e10	1.28950	0.644752	−	0.764392i	$-0.276961\pi$
$821$	2.04467e10	1.28950	0.644752	+	0.764392i	$0.276961\pi$
$822$	0	0
$823$	−1.02663e10	−0.641971	−0.320986	−	0.947084i	$-0.604014\pi$
$823$	−1.02663e10	−0.641971	−0.320986	+	0.947084i	$0.604014\pi$
$824$	7.40032e9	0.460792
$825$	0	0
$826$	−7.55580e8	−0.0466498
$827$	1.56962e10	0.964997	0.482499	−	0.875897i	$-0.339729\pi$
$827$	1.56962e10	0.964997	0.482499	+	0.875897i	$0.339729\pi$
$828$	0	0
$829$	−3.62556e8	−0.0221021	−0.0110511	−	0.999939i	$-0.503518\pi$
$829$	−3.62556e8	−0.0221021	−0.0110511	+	0.999939i	$0.503518\pi$
$830$	1.86369e10	1.13136
$831$	0	0
$832$	7.78893e8	0.0468863
$833$	−4.19304e9	−0.251346
$834$	0	0
$835$	1.52507e10	0.906540
$836$	1.91449e10	1.13327
$837$	0	0
$838$	−2.08992e10	−1.22680
$839$	7.63658e9	0.446408	0.223204	−	0.974772i	$-0.428348\pi$
$839$	7.63658e9	0.446408	0.223204	+	0.974772i	$0.428348\pi$
$840$	0	0
$841$	−1.70403e10	−0.987852
$842$	2.95512e10	1.70602
$843$	0	0
$844$	−1.08464e10	−0.620991
$845$	1.52258e10	0.868121
$846$	0	0
$847$	2.89826e9	0.163887
$848$	1.08641e10	0.611798
$849$	0	0
$850$	1.74869e9	0.0976669
$851$	−3.87300e10	−2.15424
$852$	0	0
$853$	7.70662e9	0.425150	0.212575	−	0.977145i	$-0.431815\pi$
$853$	7.70662e9	0.425150	0.212575	+	0.977145i	$0.431815\pi$
$854$	2.12921e9	0.116981
$855$	0	0
$856$	−5.15646e9	−0.280992
$857$	4.93233e9	0.267682	0.133841	−	0.991003i	$-0.457269\pi$
$857$	4.93233e9	0.267682	0.133841	+	0.991003i	$0.457269\pi$
$858$	0	0
$859$	−1.75155e10	−0.942861	−0.471430	−	0.881903i	$-0.656262\pi$
$859$	−1.75155e10	−0.942861	−0.471430	+	0.881903i	$0.656262\pi$
$860$	−1.76349e10	−0.945429
$861$	0	0
$862$	−9.80136e9	−0.521208
$863$	−1.21725e10	−0.644676	−0.322338	−	0.946625i	$-0.604469\pi$
$863$	−1.21725e10	−0.644676	−0.322338	+	0.946625i	$0.604469\pi$
$864$	0	0
$865$	2.42433e10	1.27361
$866$	3.58973e10	1.87823
$867$	0	0
$868$	−2.30785e9	−0.119781
$869$	5.10695e9	0.263993
$870$	0	0
$871$	−9.36532e8	−0.0480241
$872$	5.17692e9	0.264401
$873$	0	0
$874$	5.61112e10	2.84289
$875$	−5.13102e9	−0.258926
$876$	0	0
$877$	−3.33113e10	−1.66761	−0.833803	−	0.552062i	$-0.813841\pi$
$877$	−3.33113e10	−1.66761	−0.833803	+	0.552062i	$0.813841\pi$
$878$	5.20246e10	2.59405
$879$	0	0
$880$	−6.91426e9	−0.342024
$881$	2.94155e10	1.44931	0.724653	−	0.689113i	$-0.242000\pi$
$881$	2.94155e10	1.44931	0.724653	+	0.689113i	$0.242000\pi$
$882$	0	0
$883$	−1.01463e10	−0.495958	−0.247979	−	0.968765i	$-0.579766\pi$
$883$	−1.01463e10	−0.495958	−0.247979	+	0.968765i	$0.579766\pi$
$884$	−2.25995e8	−0.0110031
$885$	0	0
$886$	−4.47833e10	−2.16321
$887$	−1.07032e10	−0.514969	−0.257485	−	0.966282i	$-0.582894\pi$
$887$	−1.07032e10	−0.514969	−0.257485	+	0.966282i	$0.582894\pi$
$888$	0	0
$889$	−4.12515e9	−0.196917
$890$	−1.56967e10	−0.746353
$891$	0	0
$892$	−9.84191e9	−0.464304
$893$	−3.76523e10	−1.76934
$894$	0	0
$895$	−8.55738e9	−0.398988
$896$	−3.61141e9	−0.167725
$897$	0	0
$898$	−1.39777e10	−0.644120
$899$	9.68199e8	0.0444433
$900$	0	0
$901$	−5.10990e9	−0.232742
$902$	−3.03881e10	−1.37873
$903$	0	0
$904$	5.35047e9	0.240881
$905$	2.85403e10	1.27994
$906$	0	0
$907$	1.56967e10	0.698527	0.349264	−	0.937024i	$-0.386432\pi$
$907$	1.56967e10	0.698527	0.349264	+	0.937024i	$0.386432\pi$
$908$	−2.54477e10	−1.12810
$909$	0	0
$910$	2.35405e8	0.0103555
$911$	−1.32484e10	−0.580561	−0.290280	−	0.956942i	$-0.593749\pi$
$911$	−1.32484e10	−0.580561	−0.290280	+	0.956942i	$0.593749\pi$
$912$	0	0
$913$	−1.12287e10	−0.488294
$914$	−3.78741e10	−1.64071
$915$	0	0
$916$	5.61873e9	0.241548
$917$	1.09405e10	0.468538
$918$	0	0
$919$	8.96719e9	0.381112	0.190556	−	0.981676i	$-0.438971\pi$
$919$	8.96719e9	0.381112	0.190556	+	0.981676i	$0.438971\pi$
$920$	8.64963e9	0.366218
$921$	0	0
$922$	−5.56926e10	−2.34013
$923$	−3.66348e8	−0.0153351
$924$	0	0
$925$	1.08657e10	0.451401
$926$	−2.92027e10	−1.20860
$927$	0	0
$928$	3.78357e9	0.155412
$929$	−1.06115e10	−0.434230	−0.217115	−	0.976146i	$-0.569665\pi$
$929$	−1.06115e10	−0.434230	−0.217115	+	0.976146i	$0.569665\pi$
$930$	0	0
$931$	3.77465e10	1.53304
$932$	4.16177e10	1.68392
$933$	0	0
$934$	−5.73224e10	−2.30203
$935$	3.25211e9	0.130114
$936$	0	0
$937$	−1.24424e10	−0.494099	−0.247049	−	0.969003i	$-0.579461\pi$
$937$	−1.24424e10	−0.494099	−0.247049	+	0.969003i	$0.579461\pi$
$938$	1.30801e10	0.517490
$939$	0	0
$940$	−2.98834e10	−1.17350
$941$	1.22144e10	0.477867	0.238934	−	0.971036i	$-0.423202\pi$
$941$	1.22144e10	0.477867	0.238934	+	0.971036i	$0.423202\pi$
$942$	0	0
$943$	−4.93215e10	−1.91534
$944$	2.35832e9	0.0912434
$945$	0	0
$946$	1.91864e10	0.736842
$947$	4.23338e10	1.61980	0.809901	−	0.586566i	$-0.199521\pi$
$947$	4.23338e10	1.61980	0.809901	+	0.586566i	$0.199521\pi$
$948$	0	0
$949$	1.21165e9	0.0460198
$950$	−1.57421e10	−0.595701
$951$	0	0
$952$	6.13051e8	0.0230286
$953$	8.59082e9	0.321521	0.160761	−	0.986993i	$-0.448605\pi$
$953$	8.59082e9	0.321521	0.160761	+	0.986993i	$0.448605\pi$
$954$	0	0
$955$	−2.97767e10	−1.10628
$956$	−2.94734e10	−1.09101
$957$	0	0
$958$	1.65772e10	0.609160
$959$	−1.04177e9	−0.0381423
$960$	0	0
$961$	−2.30392e10	−0.837407
$962$	−2.53575e9	−0.0918320
$963$	0	0
$964$	2.10095e10	0.755348
$965$	−4.26209e10	−1.52678
$966$	0	0
$967$	1.19944e10	0.426567	0.213283	−	0.976990i	$-0.431584\pi$
$967$	1.19944e10	0.426567	0.213283	+	0.976990i	$0.431584\pi$
$968$	6.97236e9	0.247068
$969$	0	0
$970$	−6.14070e10	−2.16031
$971$	−3.97129e9	−0.139208	−0.0696040	−	0.997575i	$-0.522174\pi$
$971$	−3.97129e9	−0.139208	−0.0696040	+	0.997575i	$0.522174\pi$
$972$	0	0
$973$	3.06795e9	0.106771
$974$	−1.03661e10	−0.359467
$975$	0	0
$976$	−6.64571e9	−0.228806
$977$	3.34808e10	1.14859	0.574295	−	0.818648i	$-0.305276\pi$
$977$	3.34808e10	1.14859	0.574295	+	0.818648i	$0.305276\pi$
$978$	0	0
$979$	9.45727e9	0.322127
$980$	2.99582e10	1.01677
$981$	0	0
$982$	3.99629e10	1.34669
$983$	−2.68068e10	−0.900134	−0.450067	−	0.892995i	$-0.648600\pi$
$983$	−2.68068e10	−0.900134	−0.450067	+	0.892995i	$0.648600\pi$
$984$	0	0
$985$	−1.27927e9	−0.0426515
$986$	−1.32417e9	−0.0439921
$987$	0	0
$988$	2.03445e9	0.0671115
$989$	3.11405e10	1.02362
$990$	0	0
$991$	−4.71616e10	−1.53933	−0.769664	−	0.638449i	$-0.779576\pi$
$991$	−4.71616e10	−1.53933	−0.769664	+	0.638449i	$0.779576\pi$
$992$	1.74812e10	0.568565
$993$	0	0
$994$	5.11662e9	0.165246
$995$	5.22305e10	1.68091
$996$	0	0
$997$	2.80681e9	0.0896975	0.0448487	−	0.998994i	$-0.485719\pi$
$997$	2.80681e9	0.0896975	0.0448487	+	0.998994i	$0.485719\pi$
$998$	−3.66997e10	−1.16871
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.h.1.4	yes	33
3.2	odd	2		531.8.a.g.1.30	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.8.a.g.1.30	✓	33	3.2	odd	2
531.8.a.h.1.4	yes	33	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)

\(f(q)\)	\(=\)	\(q-16.9368 q^{2} +158.854 q^{4} -242.916 q^{5} -217.217 q^{7} -522.560 q^{8} +O(q^{10})\)	\(q-16.9368 q^{2} +158.854 q^{4} -242.916 q^{5} -217.217 q^{7} -522.560 q^{8} +4114.21 q^{10} -2478.81 q^{11} -263.412 q^{13} +3678.95 q^{14} -11482.8 q^{16} +5400.90 q^{17} -48619.9 q^{19} -38588.1 q^{20} +41982.9 q^{22} +68140.5 q^{23} -19116.9 q^{25} +4461.34 q^{26} -34505.7 q^{28} +14476.0 q^{29} +66883.2 q^{31} +261369. q^{32} -91473.7 q^{34} +52765.5 q^{35} -568384. q^{37} +823463. q^{38} +126938. q^{40} -723821. q^{41} +457005. q^{43} -393767. q^{44} -1.15408e6 q^{46} +774421. q^{47} -776360. q^{49} +323778. q^{50} -41843.9 q^{52} -946119. q^{53} +602141. q^{55} +113509. q^{56} -245176. q^{58} -205379. q^{59} +578754. q^{61} -1.13278e6 q^{62} -2.95694e6 q^{64} +63986.9 q^{65} +3.55539e6 q^{67} +857953. q^{68} -893676. q^{70} +1.39078e6 q^{71} -4.59983e6 q^{73} +9.62658e6 q^{74} -7.72345e6 q^{76} +538439. q^{77} -2.06025e6 q^{79} +2.78935e6 q^{80} +1.22592e7 q^{82} +4.52988e6 q^{83} -1.31196e6 q^{85} -7.74018e6 q^{86} +1.29533e6 q^{88} -3.81525e6 q^{89} +57217.5 q^{91} +1.08244e7 q^{92} -1.31162e7 q^{94} +1.18105e7 q^{95} -1.49256e7 q^{97} +1.31490e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 24 q^{2} + 1776 q^{4} + 1000 q^{5} + 154 q^{7} + 4608 q^{8}+O(q^{10}) \) 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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