LMFDB - Embedded newform 531.8.a.d.1.10

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-4.01497$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.01497 q^{2} -91.8201 q^{4} +385.807 q^{5} +847.649 q^{7} -1322.21 q^{8} +O(q^{10})$	\(q+6.01497 q^{2} -91.8201 q^{4} +385.807 q^{5} +847.649 q^{7} -1322.21 q^{8} +2320.62 q^{10} +5526.47 q^{11} +2987.05 q^{13} +5098.58 q^{14} +3799.90 q^{16} +6651.02 q^{17} +47421.5 q^{19} -35424.9 q^{20} +33241.6 q^{22} -16902.5 q^{23} +70722.2 q^{25} +17967.0 q^{26} -77831.2 q^{28} -2638.69 q^{29} +138735. q^{31} +192099. q^{32} +40005.7 q^{34} +327029. q^{35} -91219.9 q^{37} +285239. q^{38} -510119. q^{40} -549406. q^{41} -240843. q^{43} -507441. q^{44} -101668. q^{46} +1.17880e6 q^{47} -105035. q^{49} +425392. q^{50} -274271. q^{52} +100058. q^{53} +2.13215e6 q^{55} -1.12077e6 q^{56} -15871.6 q^{58} +205379. q^{59} +71464.3 q^{61} +834486. q^{62} +669085. q^{64} +1.15243e6 q^{65} -912586. q^{67} -610697. q^{68} +1.96707e6 q^{70} +274897. q^{71} -5.34005e6 q^{73} -548685. q^{74} -4.35425e6 q^{76} +4.68451e6 q^{77} +1.12488e6 q^{79} +1.46603e6 q^{80} -3.30466e6 q^{82} +4.95003e6 q^{83} +2.56601e6 q^{85} -1.44866e6 q^{86} -7.30717e6 q^{88} +8.64528e6 q^{89} +2.53197e6 q^{91} +1.55199e6 q^{92} +7.09048e6 q^{94} +1.82956e7 q^{95} -2.69412e6 q^{97} -631782. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) $ 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8} - 6391 q^{10} + 8888 q^{11} - 12702 q^{13} + 17555 q^{14} + 139226 q^{16} + 36167 q^{17} - 71037 q^{19} + 274883 q^{20} - 325182 q^{22} + 269995 q^{23} + 97329 q^{25} + 336906 q^{26} - 901362 q^{28} + 543825 q^{29} - 633109 q^{31} + 837062 q^{32} - 529288 q^{34} + 287621 q^{35} - 867607 q^{37} + 1727169 q^{38} - 815662 q^{40} + 1428939 q^{41} - 477060 q^{43} + 1667926 q^{44} + 5305549 q^{46} + 1217849 q^{47} + 4350738 q^{49} - 4561369 q^{50} + 4175994 q^{52} + 3487068 q^{53} - 960484 q^{55} + 5363196 q^{56} - 3082906 q^{58} + 3491443 q^{59} + 998917 q^{61} + 5742614 q^{62} + 17531621 q^{64} + 6075816 q^{65} - 356026 q^{67} + 16149231 q^{68} - 548798 q^{70} + 12879428 q^{71} - 6176157 q^{73} + 5971906 q^{74} - 17624580 q^{76} - 239687 q^{77} - 18886490 q^{79} + 70463349 q^{80} - 19351611 q^{82} + 22824893 q^{83} - 7973079 q^{85} + 27502196 q^{86} - 62527651 q^{88} + 30609647 q^{89} - 36301521 q^{91} + 41388548 q^{92} + 1010176 q^{94} + 29303629 q^{95} - 26249806 q^{97} + 93110852 q^{98}+O(q^{100}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8 - 6391 * q^10 + 8888 * q^11 - 12702 * q^13 + 17555 * q^14 + 139226 * q^16 + 36167 * q^17 - 71037 * q^19 + 274883 * q^20 - 325182 * q^22 + 269995 * q^23 + 97329 * q^25 + 336906 * q^26 - 901362 * q^28 + 543825 * q^29 - 633109 * q^31 + 837062 * q^32 - 529288 * q^34 + 287621 * q^35 - 867607 * q^37 + 1727169 * q^38 - 815662 * q^40 + 1428939 * q^41 - 477060 * q^43 + 1667926 * q^44 + 5305549 * q^46 + 1217849 * q^47 + 4350738 * q^49 - 4561369 * q^50 + 4175994 * q^52 + 3487068 * q^53 - 960484 * q^55 + 5363196 * q^56 - 3082906 * q^58 + 3491443 * q^59 + 998917 * q^61 + 5742614 * q^62 + 17531621 * q^64 + 6075816 * q^65 - 356026 * q^67 + 16149231 * q^68 - 548798 * q^70 + 12879428 * q^71 - 6176157 * q^73 + 5971906 * q^74 - 17624580 * q^76 - 239687 * q^77 - 18886490 * q^79 + 70463349 * q^80 - 19351611 * q^82 + 22824893 * q^83 - 7973079 * q^85 + 27502196 * q^86 - 62527651 * q^88 + 30609647 * q^89 - 36301521 * q^91 + 41388548 * q^92 + 1010176 * q^94 + 29303629 * q^95 - 26249806 * q^97 + 93110852 * 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 $

$2$	6.01497	0.531654	0.265827	−	0.964021i	$-0.414355\pi$
$2$	6.01497	0.531654	0.265827	+	0.964021i	$0.414355\pi$
$3$	0	0
$3$	0	0
$4$	−91.8201	−0.717345
$5$	385.807	1.38031	0.690153	−	0.723664i	$-0.257543\pi$
$5$	385.807	1.38031	0.690153	+	0.723664i	$0.257543\pi$
$6$	0	0
$7$	847.649	0.934055	0.467028	−	0.884243i	$-0.345325\pi$
$7$	847.649	0.934055	0.467028	+	0.884243i	$0.345325\pi$
$8$	−1322.21	−0.913032
$9$	0	0
$10$	2320.62	0.733844
$11$	5526.47	1.25191	0.625956	−	0.779859i	$-0.284709\pi$
$11$	5526.47	1.25191	0.625956	+	0.779859i	$0.284709\pi$
$12$	0	0
$13$	2987.05	0.377087	0.188543	−	0.982065i	$-0.439623\pi$
$13$	2987.05	0.377087	0.188543	+	0.982065i	$0.439623\pi$
$14$	5098.58	0.496594
$15$	0	0
$16$	3799.90	0.231928
$17$	6651.02	0.328335	0.164167	−	0.986432i	$-0.447506\pi$
$17$	6651.02	0.328335	0.164167	+	0.986432i	$0.447506\pi$
$18$	0	0
$19$	47421.5	1.58613	0.793064	−	0.609139i	$-0.208485\pi$
$19$	47421.5	1.58613	0.793064	+	0.609139i	$0.208485\pi$
$20$	−35424.9	−0.990155
$21$	0	0
$22$	33241.6	0.665583
$23$	−16902.5	−0.289670	−0.144835	−	0.989456i	$-0.546265\pi$
$23$	−16902.5	−0.289670	−0.144835	+	0.989456i	$0.546265\pi$
$24$	0	0
$25$	70722.2	0.905244
$26$	17967.0	0.200479
$27$	0	0
$28$	−77831.2	−0.670040
$29$	−2638.69	−0.0200907	−0.0100454	−	0.999950i	$-0.503198\pi$
$29$	−2638.69	−0.0200907	−0.0100454	+	0.999950i	$0.503198\pi$
$30$	0	0
$31$	138735.	0.836410	0.418205	−	0.908353i	$-0.362659\pi$
$31$	138735.	0.836410	0.418205	+	0.908353i	$0.362659\pi$
$32$	192099.	1.03634
$33$	0	0
$34$	40005.7	0.174560
$35$	327029.	1.28928
$36$	0	0
$37$	−91219.9	−0.296063	−0.148031	−	0.988983i	$-0.547294\pi$
$37$	−91219.9	−0.296063	−0.148031	+	0.988983i	$0.547294\pi$
$38$	285239.	0.843270
$39$	0	0
$40$	−510119.	−1.26026
$41$	−549406.	−1.24494	−0.622472	−	0.782642i	$-0.713871\pi$
$41$	−549406.	−1.24494	−0.622472	+	0.782642i	$0.713871\pi$
$42$	0	0
$43$	−240843.	−0.461949	−0.230974	−	0.972960i	$-0.574191\pi$
$43$	−240843.	−0.461949	−0.230974	+	0.972960i	$0.574191\pi$
$44$	−507441.	−0.898052
$45$	0	0
$46$	−101668.	−0.154004
$47$	1.17880e6	1.65615	0.828074	−	0.560618i	$-0.189437\pi$
$47$	1.17880e6	1.65615	0.828074	+	0.560618i	$0.189437\pi$
$48$	0	0
$49$	−105035.	−0.127540
$50$	425392.	0.481276
$51$	0	0
$52$	−274271.	−0.270501
$53$	100058.	0.0923184	0.0461592	−	0.998934i	$-0.485302\pi$
$53$	100058.	0.0923184	0.0461592	+	0.998934i	$0.485302\pi$
$54$	0	0
$55$	2.13215e6	1.72802
$56$	−1.12077e6	−0.852823
$57$	0	0
$58$	−15871.6	−0.0106813
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	71464.3	0.0403120	0.0201560	−	0.999797i	$-0.493584\pi$
$61$	71464.3	0.0403120	0.0201560	+	0.999797i	$0.493584\pi$
$62$	834486.	0.444680
$63$	0	0
$64$	669085.	0.319045
$65$	1.15243e6	0.520495
$66$	0	0
$67$	−912586.	−0.370691	−0.185345	−	0.982673i	$-0.559340\pi$
$67$	−912586.	−0.370691	−0.185345	+	0.982673i	$0.559340\pi$
$68$	−610697.	−0.235529
$69$	0	0
$70$	1.96707e6	0.685451
$71$	274897.	0.0911520	0.0455760	−	0.998961i	$-0.485488\pi$
$71$	274897.	0.0911520	0.0455760	+	0.998961i	$0.485488\pi$
$72$	0	0
$73$	−5.34005e6	−1.60663	−0.803315	−	0.595555i	$-0.796932\pi$
$73$	−5.34005e6	−1.60663	−0.803315	+	0.595555i	$0.796932\pi$
$74$	−548685.	−0.157403
$75$	0	0
$76$	−4.35425e6	−1.13780
$77$	4.68451e6	1.16935
$78$	0	0
$79$	1.12488e6	0.256692	0.128346	−	0.991729i	$-0.459033\pi$
$79$	1.12488e6	0.256692	0.128346	+	0.991729i	$0.459033\pi$
$80$	1.46603e6	0.320131
$81$	0	0
$82$	−3.30466e6	−0.661878
$83$	4.95003e6	0.950243	0.475122	−	0.879920i	$-0.342404\pi$
$83$	4.95003e6	0.950243	0.475122	+	0.879920i	$0.342404\pi$
$84$	0	0
$85$	2.56601e6	0.453202
$86$	−1.44866e6	−0.245597
$87$	0	0
$88$	−7.30717e6	−1.14304
$89$	8.64528e6	1.29991	0.649956	−	0.759972i	$-0.274787\pi$
$89$	8.64528e6	1.29991	0.649956	+	0.759972i	$0.274787\pi$
$90$	0	0
$91$	2.53197e6	0.352220
$92$	1.55199e6	0.207793
$93$	0	0
$94$	7.09048e6	0.880497
$95$	1.82956e7	2.18934
$96$	0	0
$97$	−2.69412e6	−0.299720	−0.149860	−	0.988707i	$-0.547882\pi$
$97$	−2.69412e6	−0.299720	−0.149860	+	0.988707i	$0.547882\pi$
$98$	−631782.	−0.0678073
$99$	0	0
$100$	−6.49372e6	−0.649372
$101$	−1.51552e7	−1.46365	−0.731826	−	0.681492i	$-0.761332\pi$
$101$	−1.51552e7	−1.46365	−0.731826	+	0.681492i	$0.761332\pi$
$102$	0	0
$103$	−1.40028e7	−1.26266	−0.631328	−	0.775516i	$-0.717490\pi$
$103$	−1.40028e7	−1.26266	−0.631328	+	0.775516i	$0.717490\pi$
$104$	−3.94952e6	−0.344292
$105$	0	0
$106$	601849.	0.0490814
$107$	8.87562e6	0.700415	0.350208	−	0.936672i	$-0.386111\pi$
$107$	8.87562e6	0.700415	0.350208	+	0.936672i	$0.386111\pi$
$108$	0	0
$109$	−2.49654e7	−1.84648	−0.923242	−	0.384219i	$-0.874471\pi$
$109$	−2.49654e7	−1.84648	−0.923242	+	0.384219i	$0.874471\pi$
$110$	1.28248e7	0.918708
$111$	0	0
$112$	3.22098e6	0.216633
$113$	−1.44492e7	−0.942038	−0.471019	−	0.882123i	$-0.656114\pi$
$113$	−1.44492e7	−0.942038	−0.471019	+	0.882123i	$0.656114\pi$
$114$	0	0
$115$	−6.52110e6	−0.399833
$116$	242285.	0.0144120
$117$	0	0
$118$	1.23535e6	0.0692154
$119$	5.63773e6	0.306683
$120$	0	0
$121$	1.10547e7	0.567283
$122$	429856.	0.0214320
$123$	0	0
$124$	−1.27386e7	−0.599994
$125$	−2.85605e6	−0.130792
$126$	0	0
$127$	1.71357e7	0.742315	0.371157	−	0.928570i	$-0.378961\pi$
$127$	1.71357e7	0.742315	0.371157	+	0.928570i	$0.378961\pi$
$128$	−2.05642e7	−0.866716
$129$	0	0
$130$	6.93181e6	0.276723
$131$	1.82887e7	0.710777	0.355388	−	0.934719i	$-0.384349\pi$
$131$	1.82887e7	0.710777	0.355388	+	0.934719i	$0.384349\pi$
$132$	0	0
$133$	4.01968e7	1.48153
$134$	−5.48918e6	−0.197079
$135$	0	0
$136$	−8.79406e6	−0.299780
$137$	4.79157e7	1.59205	0.796023	−	0.605266i	$-0.206933\pi$
$137$	4.79157e7	1.59205	0.796023	+	0.605266i	$0.206933\pi$
$138$	0	0
$139$	2.76336e7	0.872740	0.436370	−	0.899767i	$-0.356264\pi$
$139$	2.76336e7	0.872740	0.436370	+	0.899767i	$0.356264\pi$
$140$	−3.00278e7	−0.924860
$141$	0	0
$142$	1.65350e6	0.0484613
$143$	1.65079e7	0.472079
$144$	0	0
$145$	−1.01803e6	−0.0277313
$146$	−3.21203e7	−0.854170
$147$	0	0
$148$	8.37582e6	0.212379
$149$	−6.17248e6	−0.152865	−0.0764325	−	0.997075i	$-0.524353\pi$
$149$	−6.17248e6	−0.152865	−0.0764325	+	0.997075i	$0.524353\pi$
$150$	0	0
$151$	−2.68093e7	−0.633673	−0.316837	−	0.948480i	$-0.602621\pi$
$151$	−2.68093e7	−0.633673	−0.316837	+	0.948480i	$0.602621\pi$
$152$	−6.27013e7	−1.44819
$153$	0	0
$154$	2.81772e7	0.621692
$155$	5.35249e7	1.15450
$156$	0	0
$157$	1.87147e7	0.385952	0.192976	−	0.981203i	$-0.438186\pi$
$157$	1.87147e7	0.385952	0.192976	+	0.981203i	$0.438186\pi$
$158$	6.76614e6	0.136471
$159$	0	0
$160$	7.41134e7	1.43046
$161$	−1.43274e7	−0.270568
$162$	0	0
$163$	9.00787e7	1.62917	0.814583	−	0.580047i	$-0.196966\pi$
$163$	9.00787e7	1.62917	0.814583	+	0.580047i	$0.196966\pi$
$164$	5.04465e7	0.893053
$165$	0	0
$166$	2.97743e7	0.505200
$167$	6.92715e7	1.15093	0.575463	−	0.817828i	$-0.304822\pi$
$167$	6.92715e7	1.15093	0.575463	+	0.817828i	$0.304822\pi$
$168$	0	0
$169$	−5.38260e7	−0.857806
$170$	1.54345e7	0.240947
$171$	0	0
$172$	2.21142e7	0.331376
$173$	1.01646e8	1.49255	0.746277	−	0.665635i	$-0.231839\pi$
$173$	1.01646e8	1.49255	0.746277	+	0.665635i	$0.231839\pi$
$174$	0	0
$175$	5.99476e7	0.845548
$176$	2.10001e7	0.290353
$177$	0	0
$178$	5.20011e7	0.691103
$179$	−1.59338e7	−0.207650	−0.103825	−	0.994596i	$-0.533108\pi$
$179$	−1.59338e7	−0.207650	−0.103825	+	0.994596i	$0.533108\pi$
$180$	0	0
$181$	8.29983e7	1.04038	0.520192	−	0.854049i	$-0.325860\pi$
$181$	8.29983e7	1.04038	0.520192	+	0.854049i	$0.325860\pi$
$182$	1.52297e7	0.187259
$183$	0	0
$184$	2.23487e7	0.264478
$185$	−3.51933e7	−0.408657
$186$	0	0
$187$	3.67567e7	0.411046
$188$	−1.08238e8	−1.18803
$189$	0	0
$190$	1.10047e8	1.16397
$191$	2.94448e7	0.305768	0.152884	−	0.988244i	$-0.451144\pi$
$191$	2.94448e7	0.305768	0.152884	+	0.988244i	$0.451144\pi$
$192$	0	0
$193$	8.61854e7	0.862945	0.431473	−	0.902126i	$-0.357994\pi$
$193$	8.61854e7	0.862945	0.431473	+	0.902126i	$0.357994\pi$
$194$	−1.62051e7	−0.159347
$195$	0	0
$196$	9.64432e6	0.0914904
$197$	1.74170e8	1.62308	0.811541	−	0.584296i	$-0.198629\pi$
$197$	1.74170e8	1.62308	0.811541	+	0.584296i	$0.198629\pi$
$198$	0	0
$199$	9.07182e7	0.816035	0.408017	−	0.912974i	$-0.366220\pi$
$199$	9.07182e7	0.816035	0.408017	+	0.912974i	$0.366220\pi$
$200$	−9.35098e7	−0.826517
$201$	0	0
$202$	−9.11583e7	−0.778155
$203$	−2.23668e6	−0.0187658
$204$	0	0
$205$	−2.11965e8	−1.71840
$206$	−8.42266e7	−0.671296
$207$	0	0
$208$	1.13505e7	0.0874568
$209$	2.62074e8	1.98569
$210$	0	0
$211$	−1.22589e8	−0.898387	−0.449194	−	0.893434i	$-0.648289\pi$
$211$	−1.22589e8	−0.898387	−0.449194	+	0.893434i	$0.648289\pi$
$212$	−9.18737e6	−0.0662241
$213$	0	0
$214$	5.33866e7	0.372378
$215$	−9.29188e7	−0.637631
$216$	0	0
$217$	1.17598e8	0.781254
$218$	−1.50166e8	−0.981690
$219$	0	0
$220$	−1.95775e8	−1.23959
$221$	1.98669e7	0.123811
$222$	0	0
$223$	−5.48773e7	−0.331380	−0.165690	−	0.986178i	$-0.552985\pi$
$223$	−5.48773e7	−0.331380	−0.165690	+	0.986178i	$0.552985\pi$
$224$	1.62833e8	0.967997
$225$	0	0
$226$	−8.69114e7	−0.500838
$227$	−1.64956e8	−0.936003	−0.468001	−	0.883728i	$-0.655026\pi$
$227$	−1.64956e8	−0.936003	−0.468001	+	0.883728i	$0.655026\pi$
$228$	0	0
$229$	1.18120e8	0.649980	0.324990	−	0.945717i	$-0.394639\pi$
$229$	1.18120e8	0.649980	0.324990	+	0.945717i	$0.394639\pi$
$230$	−3.92243e7	−0.212573
$231$	0	0
$232$	3.48891e6	0.0183435
$233$	1.12335e8	0.581795	0.290898	−	0.956754i	$-0.406046\pi$
$233$	1.12335e8	0.581795	0.290898	+	0.956754i	$0.406046\pi$
$234$	0	0
$235$	4.54791e8	2.28599
$236$	−1.88579e7	−0.0933903
$237$	0	0
$238$	3.39108e7	0.163049
$239$	−2.96755e8	−1.40607	−0.703033	−	0.711158i	$-0.748171\pi$
$239$	−2.96755e8	−1.40607	−0.703033	+	0.711158i	$0.748171\pi$
$240$	0	0
$241$	1.37243e7	0.0631583	0.0315791	−	0.999501i	$-0.489946\pi$
$241$	1.37243e7	0.0631583	0.0315791	+	0.999501i	$0.489946\pi$
$242$	6.64939e7	0.301598
$243$	0	0
$244$	−6.56186e6	−0.0289176
$245$	−4.05232e7	−0.176045
$246$	0	0
$247$	1.41651e8	0.598107
$248$	−1.83437e8	−0.763670
$249$	0	0
$250$	−1.71791e7	−0.0695359
$251$	2.78781e7	0.111277	0.0556385	−	0.998451i	$-0.482281\pi$
$251$	2.78781e7	0.111277	0.0556385	+	0.998451i	$0.482281\pi$
$252$	0	0
$253$	−9.34112e7	−0.362641
$254$	1.03071e8	0.394654
$255$	0	0
$256$	−2.09336e8	−0.779837
$257$	−1.86791e8	−0.686419	−0.343209	−	0.939259i	$-0.611514\pi$
$257$	−1.86791e8	−0.686419	−0.343209	+	0.939259i	$0.611514\pi$
$258$	0	0
$259$	−7.73224e7	−0.276539
$260$	−1.05816e8	−0.373374
$261$	0	0
$262$	1.10006e8	0.377887
$263$	−2.51415e8	−0.852210	−0.426105	−	0.904674i	$-0.640115\pi$
$263$	−2.51415e8	−0.852210	−0.426105	+	0.904674i	$0.640115\pi$
$264$	0	0
$265$	3.86033e7	0.127428
$266$	2.41783e8	0.787661
$267$	0	0
$268$	8.37937e7	0.265913
$269$	4.66642e8	1.46168	0.730838	−	0.682551i	$-0.239130\pi$
$269$	4.66642e8	1.46168	0.730838	+	0.682551i	$0.239130\pi$
$270$	0	0
$271$	4.71085e8	1.43783	0.718914	−	0.695099i	$-0.244640\pi$
$271$	4.71085e8	1.43783	0.718914	+	0.695099i	$0.244640\pi$
$272$	2.52732e7	0.0761500
$273$	0	0
$274$	2.88212e8	0.846417
$275$	3.90844e8	1.13329
$276$	0	0
$277$	−4.94424e8	−1.39772	−0.698860	−	0.715259i	$-0.746309\pi$
$277$	−4.94424e8	−1.39772	−0.698860	+	0.715259i	$0.746309\pi$
$278$	1.66215e8	0.463995
$279$	0	0
$280$	−4.32402e8	−1.17716
$281$	1.88387e8	0.506499	0.253249	−	0.967401i	$-0.418501\pi$
$281$	1.88387e8	0.506499	0.253249	+	0.967401i	$0.418501\pi$
$282$	0	0
$283$	3.45526e8	0.906208	0.453104	−	0.891458i	$-0.350317\pi$
$283$	3.45526e8	0.906208	0.453104	+	0.891458i	$0.350317\pi$
$284$	−2.52411e7	−0.0653874
$285$	0	0
$286$	9.92943e7	0.250982
$287$	−4.65703e8	−1.16285
$288$	0	0
$289$	−3.66103e8	−0.892196
$290$	−6.12340e6	−0.0147435
$291$	0	0
$292$	4.90324e8	1.15251
$293$	−4.35989e8	−1.01260	−0.506301	−	0.862357i	$-0.668988\pi$
$293$	−4.35989e8	−1.01260	−0.506301	+	0.862357i	$0.668988\pi$
$294$	0	0
$295$	7.92367e7	0.179701
$296$	1.20612e8	0.270315
$297$	0	0
$298$	−3.71273e7	−0.0812712
$299$	−5.04886e7	−0.109231
$300$	0	0
$301$	−2.04150e8	−0.431486
$302$	−1.61257e8	−0.336895
$303$	0	0
$304$	1.80197e8	0.367867
$305$	2.75714e7	0.0556429
$306$	0	0
$307$	9.90146e8	1.95306	0.976529	−	0.215387i	$-0.0691013\pi$
$307$	9.90146e8	1.95306	0.976529	+	0.215387i	$0.0691013\pi$
$308$	−4.30132e8	−0.838830
$309$	0	0
$310$	3.21951e8	0.613795
$311$	2.78364e8	0.524750	0.262375	−	0.964966i	$-0.415494\pi$
$311$	2.78364e8	0.524750	0.262375	+	0.964966i	$0.415494\pi$
$312$	0	0
$313$	−7.58142e8	−1.39748	−0.698740	−	0.715376i	$-0.746256\pi$
$313$	−7.58142e8	−1.39748	−0.698740	+	0.715376i	$0.746256\pi$
$314$	1.12568e8	0.205193
$315$	0	0
$316$	−1.03287e8	−0.184137
$317$	3.93211e8	0.693296	0.346648	−	0.937995i	$-0.387320\pi$
$317$	3.93211e8	0.693296	0.346648	+	0.937995i	$0.387320\pi$
$318$	0	0
$319$	−1.45826e7	−0.0251518
$320$	2.58138e8	0.440379
$321$	0	0
$322$	−8.61788e7	−0.143848
$323$	3.15402e8	0.520781
$324$	0	0
$325$	2.11251e8	0.341355
$326$	5.41821e8	0.866152
$327$	0	0
$328$	7.26431e8	1.13667
$329$	9.99212e8	1.54693
$330$	0	0
$331$	−9.50914e7	−0.144126	−0.0720632	−	0.997400i	$-0.522958\pi$
$331$	−9.50914e7	−0.144126	−0.0720632	+	0.997400i	$0.522958\pi$
$332$	−4.54512e8	−0.681652
$333$	0	0
$334$	4.16666e8	0.611894
$335$	−3.52082e8	−0.511667
$336$	0	0
$337$	−6.91531e8	−0.984254	−0.492127	−	0.870524i	$-0.663780\pi$
$337$	−6.91531e8	−0.984254	−0.492127	+	0.870524i	$0.663780\pi$
$338$	−3.23762e8	−0.456055
$339$	0	0
$340$	−2.35611e8	−0.325102
$341$	7.66714e8	1.04711
$342$	0	0
$343$	−7.87108e8	−1.05319
$344$	3.18445e8	0.421774
$345$	0	0
$346$	6.11400e8	0.793522
$347$	5.15844e8	0.662774	0.331387	−	0.943495i	$-0.392484\pi$
$347$	5.15844e8	0.662774	0.331387	+	0.943495i	$0.392484\pi$
$348$	0	0
$349$	−8.89896e8	−1.12060	−0.560300	−	0.828290i	$-0.689314\pi$
$349$	−8.89896e8	−1.12060	−0.560300	+	0.828290i	$0.689314\pi$
$350$	3.60583e8	0.449539
$351$	0	0
$352$	1.06163e9	1.29740
$353$	3.85325e8	0.466246	0.233123	−	0.972447i	$-0.425105\pi$
$353$	3.85325e8	0.466246	0.233123	+	0.972447i	$0.425105\pi$
$354$	0	0
$355$	1.06057e8	0.125818
$356$	−7.93810e8	−0.932485
$357$	0	0
$358$	−9.58411e7	−0.110398
$359$	1.51447e9	1.72755	0.863777	−	0.503875i	$-0.168093\pi$
$359$	1.51447e9	1.72755	0.863777	+	0.503875i	$0.168093\pi$
$360$	0	0
$361$	1.35493e9	1.51580
$362$	4.99232e8	0.553124
$363$	0	0
$364$	−2.32486e8	−0.252663
$365$	−2.06023e9	−2.21764
$366$	0	0
$367$	−8.13769e8	−0.859350	−0.429675	−	0.902984i	$-0.641372\pi$
$367$	−8.13769e8	−0.859350	−0.429675	+	0.902984i	$0.641372\pi$
$368$	−6.42279e7	−0.0671825
$369$	0	0
$370$	−2.11687e8	−0.217264
$371$	8.48144e7	0.0862305
$372$	0	0
$373$	−1.20212e9	−1.19940	−0.599702	−	0.800223i	$-0.704714\pi$
$373$	−1.20212e9	−1.19940	−0.599702	+	0.800223i	$0.704714\pi$
$374$	2.21090e8	0.218534
$375$	0	0
$376$	−1.55863e9	−1.51212
$377$	−7.88190e6	−0.00757594
$378$	0	0
$379$	−4.34931e8	−0.410377	−0.205189	−	0.978722i	$-0.565781\pi$
$379$	−4.34931e8	−0.410377	−0.205189	+	0.978722i	$0.565781\pi$
$380$	−1.67990e9	−1.57051
$381$	0	0
$382$	1.77110e8	0.162563
$383$	−3.58726e7	−0.0326263	−0.0163131	−	0.999867i	$-0.505193\pi$
$383$	−3.58726e7	−0.0326263	−0.0163131	+	0.999867i	$0.505193\pi$
$384$	0	0
$385$	1.80732e9	1.61407
$386$	5.18403e8	0.458788
$387$	0	0
$388$	2.47374e8	0.215003
$389$	1.13638e9	0.978815	0.489407	−	0.872055i	$-0.337213\pi$
$389$	1.13638e9	0.978815	0.489407	+	0.872055i	$0.337213\pi$
$390$	0	0
$391$	−1.12419e8	−0.0951087
$392$	1.38878e8	0.116448
$393$	0	0
$394$	1.04762e9	0.862917
$395$	4.33988e8	0.354314
$396$	0	0
$397$	−5.01657e8	−0.402383	−0.201192	−	0.979552i	$-0.564481\pi$
$397$	−5.01657e8	−0.402383	−0.201192	+	0.979552i	$0.564481\pi$
$398$	5.45667e8	0.433848
$399$	0	0
$400$	2.68738e8	0.209951
$401$	−6.17044e8	−0.477871	−0.238936	−	0.971035i	$-0.576798\pi$
$401$	−6.17044e8	−0.477871	−0.238936	+	0.971035i	$0.576798\pi$
$402$	0	0
$403$	4.14408e8	0.315399
$404$	1.39155e9	1.04994
$405$	0	0
$406$	−1.34536e7	−0.00997692
$407$	−5.04124e8	−0.370644
$408$	0	0
$409$	1.67124e9	1.20783	0.603915	−	0.797048i	$-0.293606\pi$
$409$	1.67124e9	1.20783	0.603915	+	0.797048i	$0.293606\pi$
$410$	−1.27496e9	−0.913595
$411$	0	0
$412$	1.28574e9	0.905760
$413$	1.74089e8	0.121604
$414$	0	0
$415$	1.90976e9	1.31163
$416$	5.73811e8	0.390789
$417$	0	0
$418$	1.57637e9	1.05570
$419$	6.96670e7	0.0462677	0.0231339	−	0.999732i	$-0.492636\pi$
$419$	6.96670e7	0.0462677	0.0231339	+	0.999732i	$0.492636\pi$
$420$	0	0
$421$	−2.02237e9	−1.32091	−0.660457	−	0.750864i	$-0.729637\pi$
$421$	−2.02237e9	−1.32091	−0.660457	+	0.750864i	$0.729637\pi$
$422$	−7.37371e8	−0.477631
$423$	0	0
$424$	−1.32298e8	−0.0842896
$425$	4.70375e8	0.297223
$426$	0	0
$427$	6.05766e7	0.0376537
$428$	−8.14960e8	−0.502439
$429$	0	0
$430$	−5.58904e8	−0.338999
$431$	2.20133e9	1.32439	0.662193	−	0.749333i	$-0.269626\pi$
$431$	2.20133e9	1.32439	0.662193	+	0.749333i	$0.269626\pi$
$432$	0	0
$433$	−1.11885e9	−0.662316	−0.331158	−	0.943575i	$-0.607439\pi$
$433$	−1.11885e9	−0.662316	−0.331158	+	0.943575i	$0.607439\pi$
$434$	7.07351e8	0.415356
$435$	0	0
$436$	2.29232e9	1.32457
$437$	−8.01542e8	−0.459453
$438$	0	0
$439$	3.23226e8	0.182340	0.0911698	−	0.995835i	$-0.470939\pi$
$439$	3.23226e8	0.182340	0.0911698	+	0.995835i	$0.470939\pi$
$440$	−2.81916e9	−1.57774
$441$	0	0
$442$	1.19499e8	0.0658244
$443$	2.28214e9	1.24718	0.623591	−	0.781751i	$-0.285673\pi$
$443$	2.28214e9	1.24718	0.623591	+	0.781751i	$0.285673\pi$
$444$	0	0
$445$	3.33541e9	1.79428
$446$	−3.30086e8	−0.176179
$447$	0	0
$448$	5.67149e8	0.298005
$449$	−2.89839e9	−1.51111	−0.755553	−	0.655087i	$-0.772632\pi$
$449$	−2.89839e9	−1.51111	−0.755553	+	0.655087i	$0.772632\pi$
$450$	0	0
$451$	−3.03627e9	−1.55856
$452$	1.32672e9	0.675766
$453$	0	0
$454$	−9.92205e8	−0.497629
$455$	9.76852e8	0.486171
$456$	0	0
$457$	−1.61157e9	−0.789844	−0.394922	−	0.918715i	$-0.629228\pi$
$457$	−1.61157e9	−0.789844	−0.394922	+	0.918715i	$0.629228\pi$
$458$	7.10490e8	0.345564
$459$	0	0
$460$	5.98768e8	0.286818
$461$	−4.98049e8	−0.236766	−0.118383	−	0.992968i	$-0.537771\pi$
$461$	−4.98049e8	−0.236766	−0.118383	+	0.992968i	$0.537771\pi$
$462$	0	0
$463$	−1.13218e9	−0.530131	−0.265065	−	0.964230i	$-0.585394\pi$
$463$	−1.13218e9	−0.530131	−0.265065	+	0.964230i	$0.585394\pi$
$464$	−1.00268e7	−0.00465959
$465$	0	0
$466$	6.75693e8	0.309313
$467$	−3.04377e9	−1.38294	−0.691470	−	0.722405i	$-0.743037\pi$
$467$	−3.04377e9	−1.38294	−0.691470	+	0.722405i	$0.743037\pi$
$468$	0	0
$469$	−7.73552e8	−0.346246
$470$	2.73556e9	1.21536
$471$	0	0
$472$	−2.71555e8	−0.118867
$473$	−1.33101e9	−0.578319
$474$	0	0
$475$	3.35376e9	1.43583
$476$	−5.17657e8	−0.219997
$477$	0	0
$478$	−1.78497e9	−0.747539
$479$	−1.85843e9	−0.772630	−0.386315	−	0.922367i	$-0.626252\pi$
$479$	−1.85843e9	−0.772630	−0.386315	+	0.922367i	$0.626252\pi$
$480$	0	0
$481$	−2.72479e8	−0.111641
$482$	8.25512e7	0.0335783
$483$	0	0
$484$	−1.01505e9	−0.406937
$485$	−1.03941e9	−0.413705
$486$	0	0
$487$	−3.95871e8	−0.155311	−0.0776555	−	0.996980i	$-0.524743\pi$
$487$	−3.95871e8	−0.155311	−0.0776555	+	0.996980i	$0.524743\pi$
$488$	−9.44909e7	−0.0368062
$489$	0	0
$490$	−2.43746e8	−0.0935948
$491$	−8.60610e8	−0.328111	−0.164056	−	0.986451i	$-0.552458\pi$
$491$	−8.60610e8	−0.328111	−0.164056	+	0.986451i	$0.552458\pi$
$492$	0	0
$493$	−1.75500e7	−0.00659648
$494$	8.52025e8	0.317986
$495$	0	0
$496$	5.27179e8	0.193987
$497$	2.33016e8	0.0851410
$498$	0	0
$499$	2.92320e9	1.05319	0.526595	−	0.850116i	$-0.323469\pi$
$499$	2.92320e9	1.05319	0.526595	+	0.850116i	$0.323469\pi$
$500$	2.62243e8	0.0938228
$501$	0	0
$502$	1.67686e8	0.0591609
$503$	−2.74156e9	−0.960529	−0.480264	−	0.877124i	$-0.659459\pi$
$503$	−2.74156e9	−0.960529	−0.480264	+	0.877124i	$0.659459\pi$
$504$	0	0
$505$	−5.84700e9	−2.02029
$506$	−5.61866e8	−0.192799
$507$	0	0
$508$	−1.57340e9	−0.532495
$509$	−3.66404e9	−1.23154	−0.615769	−	0.787927i	$-0.711154\pi$
$509$	−3.66404e9	−1.23154	−0.615769	+	0.787927i	$0.711154\pi$
$510$	0	0
$511$	−4.52649e9	−1.50068
$512$	1.37307e9	0.452113
$513$	0	0
$514$	−1.12354e9	−0.364937
$515$	−5.40239e9	−1.74285
$516$	0	0
$517$	6.51463e9	2.07335
$518$	−4.65092e8	−0.147023
$519$	0	0
$520$	−1.52375e9	−0.475229
$521$	4.43075e9	1.37260	0.686302	−	0.727317i	$-0.259233\pi$
$521$	4.43075e9	1.37260	0.686302	+	0.727317i	$0.259233\pi$
$522$	0	0
$523$	−5.16773e9	−1.57959	−0.789794	−	0.613372i	$-0.789813\pi$
$523$	−5.16773e9	−1.57959	−0.789794	+	0.613372i	$0.789813\pi$
$524$	−1.67927e9	−0.509872
$525$	0	0
$526$	−1.51226e9	−0.453080
$527$	9.22728e8	0.274623
$528$	0	0
$529$	−3.11913e9	−0.916091
$530$	2.32198e8	0.0677473
$531$	0	0
$532$	−3.69087e9	−1.06277
$533$	−1.64110e9	−0.469451
$534$	0	0
$535$	3.42428e9	0.966787
$536$	1.20663e9	0.338453
$537$	0	0
$538$	2.80684e9	0.777105
$539$	−5.80473e8	−0.159669
$540$	0	0
$541$	5.16094e9	1.40132	0.700662	−	0.713493i	$-0.252888\pi$
$541$	5.16094e9	1.40132	0.700662	+	0.713493i	$0.252888\pi$
$542$	2.83356e9	0.764426
$543$	0	0
$544$	1.27766e9	0.340266
$545$	−9.63183e9	−2.54871
$546$	0	0
$547$	−1.77725e9	−0.464295	−0.232147	−	0.972681i	$-0.574575\pi$
$547$	−1.77725e9	−0.464295	−0.232147	+	0.972681i	$0.574575\pi$
$548$	−4.39962e9	−1.14205
$549$	0	0
$550$	2.35092e9	0.602515
$551$	−1.25131e8	−0.0318664
$552$	0	0
$553$	9.53505e8	0.239765
$554$	−2.97394e9	−0.743102
$555$	0	0
$556$	−2.53732e9	−0.626055
$557$	2.65766e9	0.651637	0.325819	−	0.945432i	$-0.394360\pi$
$557$	2.65766e9	0.651637	0.325819	+	0.945432i	$0.394360\pi$
$558$	0	0
$559$	−7.19409e8	−0.174195
$560$	1.24268e9	0.299020
$561$	0	0
$562$	1.13314e9	0.269282
$563$	2.85664e9	0.674646	0.337323	−	0.941389i	$-0.390478\pi$
$563$	2.85664e9	0.674646	0.337323	+	0.941389i	$0.390478\pi$
$564$	0	0
$565$	−5.57459e9	−1.30030
$566$	2.07833e9	0.481789
$567$	0	0
$568$	−3.63472e8	−0.0832247
$569$	1.18310e9	0.269233	0.134617	−	0.990898i	$-0.457020\pi$
$569$	1.18310e9	0.269233	0.134617	+	0.990898i	$0.457020\pi$
$570$	0	0
$571$	7.04152e8	0.158285	0.0791426	−	0.996863i	$-0.474782\pi$
$571$	7.04152e8	0.158285	0.0791426	+	0.996863i	$0.474782\pi$
$572$	−1.51575e9	−0.338643
$573$	0	0
$574$	−2.80119e9	−0.618231
$575$	−1.19538e9	−0.262222
$576$	0	0
$577$	−5.26118e9	−1.14017	−0.570083	−	0.821587i	$-0.693089\pi$
$577$	−5.26118e9	−1.14017	−0.570083	+	0.821587i	$0.693089\pi$
$578$	−2.20210e9	−0.474339
$579$	0	0
$580$	9.34752e7	0.0198929
$581$	4.19589e9	0.887580
$582$	0	0
$583$	5.52970e8	0.115574
$584$	7.06068e9	1.46690
$585$	0	0
$586$	−2.62246e9	−0.538354
$587$	−7.97467e9	−1.62734	−0.813672	−	0.581324i	$-0.802535\pi$
$587$	−7.97467e9	−1.62734	−0.813672	+	0.581324i	$0.802535\pi$
$588$	0	0
$589$	6.57902e9	1.32665
$590$	4.76607e8	0.0955384
$591$	0	0
$592$	−3.46627e8	−0.0686651
$593$	5.84550e9	1.15115	0.575573	−	0.817750i	$-0.304779\pi$
$593$	5.84550e9	1.15115	0.575573	+	0.817750i	$0.304779\pi$
$594$	0	0
$595$	2.17508e9	0.423316
$596$	5.66758e8	0.109657
$597$	0	0
$598$	−3.03688e8	−0.0580729
$599$	2.93990e9	0.558906	0.279453	−	0.960159i	$-0.409847\pi$
$599$	2.93990e9	0.558906	0.279453	+	0.960159i	$0.409847\pi$
$600$	0	0
$601$	−6.68201e9	−1.25559	−0.627793	−	0.778380i	$-0.716042\pi$
$601$	−6.68201e9	−1.25559	−0.627793	+	0.778380i	$0.716042\pi$
$602$	−1.22796e9	−0.229401
$603$	0	0
$604$	2.46163e9	0.454562
$605$	4.26500e9	0.783024
$606$	0	0
$607$	4.48841e8	0.0814577	0.0407289	−	0.999170i	$-0.487032\pi$
$607$	4.48841e8	0.0814577	0.0407289	+	0.999170i	$0.487032\pi$
$608$	9.10965e9	1.64376
$609$	0	0
$610$	1.65841e8	0.0295827
$611$	3.52115e9	0.624511
$612$	0	0
$613$	7.78075e9	1.36430	0.682150	−	0.731212i	$-0.261045\pi$
$613$	7.78075e9	1.36430	0.682150	+	0.731212i	$0.261045\pi$
$614$	5.95570e9	1.03835
$615$	0	0
$616$	−6.19391e9	−1.06766
$617$	6.97925e9	1.19622	0.598109	−	0.801414i	$-0.295919\pi$
$617$	6.97925e9	1.19622	0.598109	+	0.801414i	$0.295919\pi$
$618$	0	0
$619$	−3.49030e9	−0.591488	−0.295744	−	0.955267i	$-0.595568\pi$
$619$	−3.49030e9	−0.591488	−0.295744	+	0.955267i	$0.595568\pi$
$620$	−4.91466e9	−0.828176
$621$	0	0
$622$	1.67435e9	0.278985
$623$	7.32816e9	1.21419
$624$	0	0
$625$	−6.62706e9	−1.08578
$626$	−4.56021e9	−0.742975
$627$	0	0
$628$	−1.71838e9	−0.276861
$629$	−6.06705e8	−0.0972077
$630$	0	0
$631$	−7.42461e9	−1.17644	−0.588222	−	0.808700i	$-0.700172\pi$
$631$	−7.42461e9	−1.17644	−0.588222	+	0.808700i	$0.700172\pi$
$632$	−1.48733e9	−0.234368
$633$	0	0
$634$	2.36516e9	0.368593
$635$	6.61107e9	1.02462
$636$	0	0
$637$	−3.13745e8	−0.0480938
$638$	−8.77142e7	−0.0133720
$639$	0	0
$640$	−7.93382e9	−1.19633
$641$	2.52065e9	0.378015	0.189007	−	0.981976i	$-0.439473\pi$
$641$	2.52065e9	0.378015	0.189007	+	0.981976i	$0.439473\pi$
$642$	0	0
$643$	−7.35494e9	−1.09104	−0.545520	−	0.838098i	$-0.683668\pi$
$643$	−7.35494e9	−1.09104	−0.545520	+	0.838098i	$0.683668\pi$
$644$	1.31554e9	0.194090
$645$	0	0
$646$	1.89713e9	0.276875
$647$	9.35379e8	0.135776	0.0678879	−	0.997693i	$-0.478374\pi$
$647$	9.35379e8	0.135776	0.0678879	+	0.997693i	$0.478374\pi$
$648$	0	0
$649$	1.13502e9	0.162985
$650$	1.27067e9	0.181483
$651$	0	0
$652$	−8.27103e9	−1.16867
$653$	−1.22407e10	−1.72032	−0.860161	−	0.510022i	$-0.829637\pi$
$653$	−1.22407e10	−1.72032	−0.860161	+	0.510022i	$0.829637\pi$
$654$	0	0
$655$	7.05591e9	0.981089
$656$	−2.08769e9	−0.288737
$657$	0	0
$658$	6.01023e9	0.822433
$659$	−5.21215e9	−0.709444	−0.354722	−	0.934972i	$-0.615425\pi$
$659$	−5.21215e9	−0.709444	−0.354722	+	0.934972i	$0.615425\pi$
$660$	0	0
$661$	−1.11350e10	−1.49964	−0.749820	−	0.661642i	$-0.769860\pi$
$661$	−1.11350e10	−1.49964	−0.749820	+	0.661642i	$0.769860\pi$
$662$	−5.71972e8	−0.0766253
$663$	0	0
$664$	−6.54499e9	−0.867603
$665$	1.55082e10	2.04497
$666$	0	0
$667$	4.46004e7	0.00581967
$668$	−6.36052e9	−0.825610
$669$	0	0
$670$	−2.11776e9	−0.272029
$671$	3.94945e8	0.0504671
$672$	0	0
$673$	9.15611e9	1.15787	0.578933	−	0.815375i	$-0.303469\pi$
$673$	9.15611e9	1.15787	0.578933	+	0.815375i	$0.303469\pi$
$674$	−4.15954e9	−0.523282
$675$	0	0
$676$	4.94231e9	0.615342
$677$	−1.14733e10	−1.42111	−0.710557	−	0.703639i	$-0.751557\pi$
$677$	−1.14733e10	−1.42111	−0.710557	+	0.703639i	$0.751557\pi$
$678$	0	0
$679$	−2.28367e9	−0.279955
$680$	−3.39281e9	−0.413788
$681$	0	0
$682$	4.61176e9	0.556701
$683$	5.63555e9	0.676806	0.338403	−	0.941001i	$-0.390113\pi$
$683$	5.63555e9	0.676806	0.338403	+	0.941001i	$0.390113\pi$
$684$	0	0
$685$	1.84862e10	2.19751
$686$	−4.73443e9	−0.559930
$687$	0	0
$688$	−9.15179e8	−0.107139
$689$	2.98880e8	0.0348120
$690$	0	0
$691$	−6.22407e9	−0.717632	−0.358816	−	0.933408i	$-0.616819\pi$
$691$	−6.22407e9	−0.717632	−0.358816	+	0.933408i	$0.616819\pi$
$692$	−9.33317e9	−1.07068
$693$	0	0
$694$	3.10279e9	0.352366
$695$	1.06612e10	1.20465
$696$	0	0
$697$	−3.65411e9	−0.408758
$698$	−5.35270e9	−0.595771
$699$	0	0
$700$	−5.50439e9	−0.606550
$701$	−8.57820e9	−0.940553	−0.470276	−	0.882519i	$-0.655846\pi$
$701$	−8.57820e9	−0.940553	−0.470276	+	0.882519i	$0.655846\pi$
$702$	0	0
$703$	−4.32579e9	−0.469593
$704$	3.69768e9	0.399416
$705$	0	0
$706$	2.31772e9	0.247881
$707$	−1.28463e10	−1.36713
$708$	0	0
$709$	2.72444e9	0.287088	0.143544	−	0.989644i	$-0.454150\pi$
$709$	2.72444e9	0.287088	0.143544	+	0.989644i	$0.454150\pi$
$710$	6.37932e8	0.0668914
$711$	0	0
$712$	−1.14309e10	−1.18686
$713$	−2.34496e9	−0.242283
$714$	0	0
$715$	6.36885e9	0.651613
$716$	1.46304e9	0.148957
$717$	0	0
$718$	9.10952e9	0.918460
$719$	2.39574e9	0.240375	0.120188	−	0.992751i	$-0.461650\pi$
$719$	2.39574e9	0.240375	0.120188	+	0.992751i	$0.461650\pi$
$720$	0	0
$721$	−1.18695e10	−1.17939
$722$	8.14988e9	0.805881
$723$	0	0
$724$	−7.62091e9	−0.746314
$725$	−1.86614e8	−0.0181870
$726$	0	0
$727$	1.12427e9	0.108517	0.0542586	−	0.998527i	$-0.482720\pi$
$727$	1.12427e9	0.108517	0.0542586	+	0.998527i	$0.482720\pi$
$728$	−3.34780e9	−0.321588
$729$	0	0
$730$	−1.23922e10	−1.17902
$731$	−1.60185e9	−0.151674
$732$	0	0
$733$	1.04255e10	0.977759	0.488880	−	0.872351i	$-0.337406\pi$
$733$	1.04255e10	0.977759	0.488880	+	0.872351i	$0.337406\pi$
$734$	−4.89480e9	−0.456876
$735$	0	0
$736$	−3.24696e9	−0.300196
$737$	−5.04338e9	−0.464072
$738$	0	0
$739$	−1.61439e8	−0.0147147	−0.00735737	−	0.999973i	$-0.502342\pi$
$739$	−1.61439e8	−0.0147147	−0.00735737	+	0.999973i	$0.502342\pi$
$740$	3.23145e9	0.293148
$741$	0	0
$742$	5.10156e8	0.0458447
$743$	−1.59100e10	−1.42302	−0.711508	−	0.702678i	$-0.751987\pi$
$743$	−1.59100e10	−1.42302	−0.711508	+	0.702678i	$0.751987\pi$
$744$	0	0
$745$	−2.38139e9	−0.211000
$746$	−7.23070e9	−0.637668
$747$	0	0
$748$	−3.37500e9	−0.294862
$749$	7.52341e9	0.654226
$750$	0	0
$751$	9.63052e9	0.829679	0.414839	−	0.909895i	$-0.363838\pi$
$751$	9.63052e9	0.829679	0.414839	+	0.909895i	$0.363838\pi$
$752$	4.47934e9	0.384107
$753$	0	0
$754$	−4.74094e7	−0.00402777
$755$	−1.03432e10	−0.874663
$756$	0	0
$757$	−1.23984e10	−1.03880	−0.519398	−	0.854532i	$-0.673844\pi$
$757$	−1.23984e10	−1.03880	−0.519398	+	0.854532i	$0.673844\pi$
$758$	−2.61610e9	−0.218178
$759$	0	0
$760$	−2.41906e10	−1.99894
$761$	3.84482e9	0.316249	0.158125	−	0.987419i	$-0.449455\pi$
$761$	3.84482e9	0.316249	0.158125	+	0.987419i	$0.449455\pi$
$762$	0	0
$763$	−2.11619e10	−1.72472
$764$	−2.70363e9	−0.219341
$765$	0	0
$766$	−2.15773e8	−0.0173459
$767$	6.13478e8	0.0490925
$768$	0	0
$769$	1.85468e10	1.47071	0.735354	−	0.677683i	$-0.237016\pi$
$769$	1.85468e10	1.47071	0.735354	+	0.677683i	$0.237016\pi$
$770$	1.08710e10	0.858125
$771$	0	0
$772$	−7.91355e9	−0.619029
$773$	−9.18489e9	−0.715230	−0.357615	−	0.933869i	$-0.616410\pi$
$773$	−9.18489e9	−0.715230	−0.357615	+	0.933869i	$0.616410\pi$
$774$	0	0
$775$	9.81163e9	0.757156
$776$	3.56220e9	0.273654
$777$	0	0
$778$	6.83530e9	0.520390
$779$	−2.60537e10	−1.97464
$780$	0	0
$781$	1.51921e9	0.114114
$782$	−6.76196e8	−0.0505649
$783$	0	0
$784$	−3.99123e8	−0.0295801
$785$	7.22025e9	0.532732
$786$	0	0
$787$	−1.00821e10	−0.737291	−0.368646	−	0.929570i	$-0.620178\pi$
$787$	−1.00821e10	−0.737291	−0.368646	+	0.929570i	$0.620178\pi$
$788$	−1.59923e10	−1.16431
$789$	0	0
$790$	2.61043e9	0.188372
$791$	−1.22478e10	−0.879916
$792$	0	0
$793$	2.13467e8	0.0152011
$794$	−3.01745e9	−0.213928
$795$	0	0
$796$	−8.32975e9	−0.585378
$797$	1.03385e10	0.723361	0.361681	−	0.932302i	$-0.382203\pi$
$797$	1.03385e10	0.723361	0.361681	+	0.932302i	$0.382203\pi$
$798$	0	0
$799$	7.84025e9	0.543771
$800$	1.35857e10	0.938139
$801$	0	0
$802$	−3.71150e9	−0.254062
$803$	−2.95117e10	−2.01136
$804$	0	0
$805$	−5.52760e9	−0.373466
$806$	2.49265e9	0.167683
$807$	0	0
$808$	2.00384e10	1.33636
$809$	−2.64371e10	−1.75547	−0.877735	−	0.479146i	$-0.840947\pi$
$809$	−2.64371e10	−1.75547	−0.877735	+	0.479146i	$0.840947\pi$
$810$	0	0
$811$	2.22378e10	1.46392	0.731961	−	0.681346i	$-0.238605\pi$
$811$	2.22378e10	1.46392	0.731961	+	0.681346i	$0.238605\pi$
$812$	2.05372e8	0.0134616
$813$	0	0
$814$	−3.03229e9	−0.197054
$815$	3.47530e10	2.24875
$816$	0	0
$817$	−1.14211e10	−0.732710
$818$	1.00524e10	0.642147
$819$	0	0
$820$	1.94626e10	1.23269
$821$	−1.19117e10	−0.751229	−0.375615	−	0.926776i	$-0.622568\pi$
$821$	−1.19117e10	−0.751229	−0.375615	+	0.926776i	$0.622568\pi$
$822$	0	0
$823$	1.73151e9	0.108274	0.0541372	−	0.998534i	$-0.482759\pi$
$823$	1.73151e9	0.108274	0.0541372	+	0.998534i	$0.482759\pi$
$824$	1.85147e10	1.15285
$825$	0	0
$826$	1.04714e9	0.0646510
$827$	−2.70946e10	−1.66576	−0.832882	−	0.553451i	$-0.813311\pi$
$827$	−2.70946e10	−1.66576	−0.832882	+	0.553451i	$0.813311\pi$
$828$	0	0
$829$	1.95311e10	1.19065	0.595326	−	0.803484i	$-0.297023\pi$
$829$	1.95311e10	1.19065	0.595326	+	0.803484i	$0.297023\pi$
$830$	1.14871e10	0.697331
$831$	0	0
$832$	1.99859e9	0.120307
$833$	−6.98589e8	−0.0418759
$834$	0	0
$835$	2.67255e10	1.58863
$836$	−2.40637e10	−1.42442
$837$	0	0
$838$	4.19045e8	0.0245984
$839$	2.20343e10	1.28805	0.644024	−	0.765005i	$-0.277263\pi$
$839$	2.20343e10	1.28805	0.644024	+	0.765005i	$0.277263\pi$
$840$	0	0
$841$	−1.72429e10	−0.999596
$842$	−1.21645e10	−0.702268
$843$	0	0
$844$	1.12562e10	0.644453
$845$	−2.07665e10	−1.18403
$846$	0	0
$847$	9.37053e9	0.529873
$848$	3.80212e8	0.0214112
$849$	0	0
$850$	2.82929e9	0.158020
$851$	1.54184e9	0.0857604
$852$	0	0
$853$	2.56385e10	1.41440	0.707199	−	0.707014i	$-0.249958\pi$
$853$	2.56385e10	1.41440	0.707199	+	0.707014i	$0.249958\pi$
$854$	3.64366e8	0.0200187
$855$	0	0
$856$	−1.17354e10	−0.639502
$857$	1.90552e10	1.03414	0.517072	−	0.855942i	$-0.327022\pi$
$857$	1.90552e10	1.03414	0.517072	+	0.855942i	$0.327022\pi$
$858$	0	0
$859$	1.94648e10	1.04779	0.523896	−	0.851782i	$-0.324478\pi$
$859$	1.94648e10	1.04779	0.523896	+	0.851782i	$0.324478\pi$
$860$	8.53182e9	0.457401
$861$	0	0
$862$	1.32409e10	0.704115
$863$	6.07650e9	0.321822	0.160911	−	0.986969i	$-0.448557\pi$
$863$	6.07650e9	0.321822	0.160911	+	0.986969i	$0.448557\pi$
$864$	0	0
$865$	3.92159e10	2.06018
$866$	−6.72987e9	−0.352123
$867$	0	0
$868$	−1.07979e10	−0.560428
$869$	6.21663e9	0.321356
$870$	0	0
$871$	−2.72594e9	−0.139783
$872$	3.30095e10	1.68590
$873$	0	0
$874$	−4.82126e9	−0.244270
$875$	−2.42092e9	−0.122167
$876$	0	0
$877$	−1.82857e10	−0.915404	−0.457702	−	0.889106i	$-0.651327\pi$
$877$	−1.82857e10	−0.915404	−0.457702	+	0.889106i	$0.651327\pi$
$878$	1.94420e9	0.0969415
$879$	0	0
$880$	8.10198e9	0.400776
$881$	−1.41923e10	−0.699259	−0.349629	−	0.936888i	$-0.613692\pi$
$881$	−1.41923e10	−0.699259	−0.349629	+	0.936888i	$0.613692\pi$
$882$	0	0
$883$	1.61031e10	0.787131	0.393566	−	0.919297i	$-0.371241\pi$
$883$	1.61031e10	0.787131	0.393566	+	0.919297i	$0.371241\pi$
$884$	−1.82418e9	−0.0888149
$885$	0	0
$886$	1.37270e10	0.663068
$887$	1.49039e9	0.0717077	0.0358539	−	0.999357i	$-0.488585\pi$
$887$	1.49039e9	0.0717077	0.0358539	+	0.999357i	$0.488585\pi$
$888$	0	0
$889$	1.45250e10	0.693363
$890$	2.00624e10	0.953933
$891$	0	0
$892$	5.03884e9	0.237713
$893$	5.59007e10	2.62686
$894$	0	0
$895$	−6.14736e9	−0.286621
$896$	−1.74312e10	−0.809561
$897$	0	0
$898$	−1.74338e10	−0.803385
$899$	−3.66078e8	−0.0168041
$900$	0	0
$901$	6.65490e8	0.0303113
$902$	−1.82631e10	−0.828613
$903$	0	0
$904$	1.91049e10	0.860111
$905$	3.20213e10	1.43605
$906$	0	0
$907$	−1.44651e10	−0.643717	−0.321858	−	0.946788i	$-0.604307\pi$
$907$	−1.44651e10	−0.643717	−0.321858	+	0.946788i	$0.604307\pi$
$908$	1.51463e10	0.671436
$909$	0	0
$910$	5.87574e9	0.258475
$911$	2.79187e10	1.22343	0.611717	−	0.791077i	$-0.290479\pi$
$911$	2.79187e10	1.22343	0.611717	+	0.791077i	$0.290479\pi$
$912$	0	0
$913$	2.73562e10	1.18962
$914$	−9.69353e9	−0.419923
$915$	0	0
$916$	−1.08458e10	−0.466259
$917$	1.55024e10	0.663905
$918$	0	0
$919$	1.89312e10	0.804590	0.402295	−	0.915510i	$-0.368213\pi$
$919$	1.89312e10	0.804590	0.402295	+	0.915510i	$0.368213\pi$
$920$	8.62228e9	0.365061
$921$	0	0
$922$	−2.99575e9	−0.125877
$923$	8.21133e8	0.0343722
$924$	0	0
$925$	−6.45127e9	−0.268009
$926$	−6.81005e9	−0.281846
$927$	0	0
$928$	−5.06891e8	−0.0208208
$929$	3.58709e10	1.46787	0.733934	−	0.679221i	$-0.237682\pi$
$929$	3.58709e10	1.46787	0.733934	+	0.679221i	$0.237682\pi$
$930$	0	0
$931$	−4.98092e9	−0.202295
$932$	−1.03146e10	−0.417348
$933$	0	0
$934$	−1.83082e10	−0.735245
$935$	1.41810e10	0.567369
$936$	0	0
$937$	1.18752e10	0.471577	0.235789	−	0.971804i	$-0.424233\pi$
$937$	1.18752e10	0.471577	0.235789	+	0.971804i	$0.424233\pi$
$938$	−4.65289e9	−0.184083
$939$	0	0
$940$	−4.17590e10	−1.63984
$941$	2.99086e10	1.17013	0.585063	−	0.810988i	$-0.301070\pi$
$941$	2.99086e10	1.17013	0.585063	+	0.810988i	$0.301070\pi$
$942$	0	0
$943$	9.28632e9	0.360623
$944$	7.80420e8	0.0301944
$945$	0	0
$946$	−8.00599e9	−0.307465
$947$	1.97326e10	0.755021	0.377510	−	0.926005i	$-0.376780\pi$
$947$	1.97326e10	0.755021	0.377510	+	0.926005i	$0.376780\pi$
$948$	0	0
$949$	−1.59510e10	−0.605838
$950$	2.01728e10	0.763366
$951$	0	0
$952$	−7.45427e9	−0.280011
$953$	−3.05905e10	−1.14488	−0.572442	−	0.819945i	$-0.694004\pi$
$953$	−3.05905e10	−1.14488	−0.572442	+	0.819945i	$0.694004\pi$
$954$	0	0
$955$	1.13600e10	0.422053
$956$	2.72481e10	1.00863
$957$	0	0
$958$	−1.11784e10	−0.410772
$959$	4.06157e10	1.48706
$960$	0	0
$961$	−8.26528e9	−0.300418
$962$	−1.63895e9	−0.0593545
$963$	0	0
$964$	−1.26017e9	−0.0453062
$965$	3.32510e10	1.19113
$966$	0	0
$967$	1.80021e10	0.640221	0.320111	−	0.947380i	$-0.396280\pi$
$967$	1.80021e10	0.640221	0.320111	+	0.947380i	$0.396280\pi$
$968$	−1.46167e10	−0.517947
$969$	0	0
$970$	−6.25203e9	−0.219948
$971$	6.56410e9	0.230095	0.115048	−	0.993360i	$-0.463298\pi$
$971$	6.56410e9	0.230095	0.115048	+	0.993360i	$0.463298\pi$
$972$	0	0
$973$	2.34235e10	0.815188
$974$	−2.38115e9	−0.0825716
$975$	0	0
$976$	2.71557e8	0.00934947
$977$	−1.67236e10	−0.573718	−0.286859	−	0.957973i	$-0.592611\pi$
$977$	−1.67236e10	−0.573718	−0.286859	+	0.957973i	$0.592611\pi$
$978$	0	0
$979$	4.77779e10	1.62737
$980$	3.72085e9	0.126285
$981$	0	0
$982$	−5.17655e9	−0.174442
$983$	6.60882e9	0.221915	0.110957	−	0.993825i	$-0.464608\pi$
$983$	6.60882e9	0.221915	0.110957	+	0.993825i	$0.464608\pi$
$984$	0	0
$985$	6.71959e10	2.24035
$986$	−1.05563e8	−0.00350704
$987$	0	0
$988$	−1.30064e10	−0.429049
$989$	4.07084e9	0.133813
$990$	0	0
$991$	−2.45768e10	−0.802173	−0.401086	−	0.916040i	$-0.631367\pi$
$991$	−2.45768e10	−0.802173	−0.401086	+	0.916040i	$0.631367\pi$
$992$	2.66509e10	0.866803
$993$	0	0
$994$	1.40159e9	0.0452655
$995$	3.49997e10	1.12638
$996$	0	0
$997$	6.18690e10	1.97715	0.988575	−	0.150727i	$-0.0481614\pi$
$997$	6.18690e10	1.97715	0.988575	+	0.150727i	$0.0481614\pi$
$998$	1.75830e10	0.559932
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.d.1.10		17
3.2	odd	2		177.8.a.b.1.8	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.8	✓	17	3.2	odd	2
531.8.a.d.1.10		17	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)

\(f(q)\)	\(=\)	\(q+6.01497 q^{2} -91.8201 q^{4} +385.807 q^{5} +847.649 q^{7} -1322.21 q^{8} +O(q^{10})\)	\(q+6.01497 q^{2} -91.8201 q^{4} +385.807 q^{5} +847.649 q^{7} -1322.21 q^{8} +2320.62 q^{10} +5526.47 q^{11} +2987.05 q^{13} +5098.58 q^{14} +3799.90 q^{16} +6651.02 q^{17} +47421.5 q^{19} -35424.9 q^{20} +33241.6 q^{22} -16902.5 q^{23} +70722.2 q^{25} +17967.0 q^{26} -77831.2 q^{28} -2638.69 q^{29} +138735. q^{31} +192099. q^{32} +40005.7 q^{34} +327029. q^{35} -91219.9 q^{37} +285239. q^{38} -510119. q^{40} -549406. q^{41} -240843. q^{43} -507441. q^{44} -101668. q^{46} +1.17880e6 q^{47} -105035. q^{49} +425392. q^{50} -274271. q^{52} +100058. q^{53} +2.13215e6 q^{55} -1.12077e6 q^{56} -15871.6 q^{58} +205379. q^{59} +71464.3 q^{61} +834486. q^{62} +669085. q^{64} +1.15243e6 q^{65} -912586. q^{67} -610697. q^{68} +1.96707e6 q^{70} +274897. q^{71} -5.34005e6 q^{73} -548685. q^{74} -4.35425e6 q^{76} +4.68451e6 q^{77} +1.12488e6 q^{79} +1.46603e6 q^{80} -3.30466e6 q^{82} +4.95003e6 q^{83} +2.56601e6 q^{85} -1.44866e6 q^{86} -7.30717e6 q^{88} +8.64528e6 q^{89} +2.53197e6 q^{91} +1.55199e6 q^{92} +7.09048e6 q^{94} +1.82956e7 q^{95} -2.69412e6 q^{97} -631782. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8} - 6391 q^{10} + 8888 q^{11} - 12702 q^{13} + 17555 q^{14} + 139226 q^{16} + 36167 q^{17} - 71037 q^{19} + 274883 q^{20} - 325182 q^{22} + 269995 q^{23} + 97329 q^{25} + 336906 q^{26} - 901362 q^{28} + 543825 q^{29} - 633109 q^{31} + 837062 q^{32} - 529288 q^{34} + 287621 q^{35} - 867607 q^{37} + 1727169 q^{38} - 815662 q^{40} + 1428939 q^{41} - 477060 q^{43} + 1667926 q^{44} + 5305549 q^{46} + 1217849 q^{47} + 4350738 q^{49} - 4561369 q^{50} + 4175994 q^{52} + 3487068 q^{53} - 960484 q^{55} + 5363196 q^{56} - 3082906 q^{58} + 3491443 q^{59} + 998917 q^{61} + 5742614 q^{62} + 17531621 q^{64} + 6075816 q^{65} - 356026 q^{67} + 16149231 q^{68} - 548798 q^{70} + 12879428 q^{71} - 6176157 q^{73} + 5971906 q^{74} - 17624580 q^{76} - 239687 q^{77} - 18886490 q^{79} + 70463349 q^{80} - 19351611 q^{82} + 22824893 q^{83} - 7973079 q^{85} + 27502196 q^{86} - 62527651 q^{88} + 30609647 q^{89} - 36301521 q^{91} + 41388548 q^{92} + 1010176 q^{94} + 29303629 q^{95} - 26249806 q^{97} + 93110852 q^{98}+O(q^{100}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8 - 6391 * q^10 + 8888 * q^11 - 12702 * q^13 + 17555 * q^14 + 139226 * q^16 + 36167 * q^17 - 71037 * q^19 + 274883 * q^20 - 325182 * q^22 + 269995 * q^23 + 97329 * q^25 + 336906 * q^26 - 901362 * q^28 + 543825 * q^29 - 633109 * q^31 + 837062 * q^32 - 529288 * q^34 + 287621 * q^35 - 867607 * q^37 + 1727169 * q^38 - 815662 * q^40 + 1428939 * q^41 - 477060 * q^43 + 1667926 * q^44 + 5305549 * q^46 + 1217849 * q^47 + 4350738 * q^49 - 4561369 * q^50 + 4175994 * q^52 + 3487068 * q^53 - 960484 * q^55 + 5363196 * q^56 - 3082906 * q^58 + 3491443 * q^59 + 998917 * q^61 + 5742614 * q^62 + 17531621 * q^64 + 6075816 * q^65 - 356026 * q^67 + 16149231 * q^68 - 548798 * q^70 + 12879428 * q^71 - 6176157 * q^73 + 5971906 * q^74 - 17624580 * q^76 - 239687 * q^77 - 18886490 * q^79 + 70463349 * q^80 - 19351611 * q^82 + 22824893 * q^83 - 7973079 * q^85 + 27502196 * q^86 - 62527651 * q^88 + 30609647 * q^89 - 36301521 * q^91 + 41388548 * q^92 + 1010176 * q^94 + 29303629 * q^95 - 26249806 * q^97 + 93110852 * q^98

Introduction

L-functions

Modular forms

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