LMFDB - Embedded newform 531.8.a.c.1.7

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} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 $ x^17 - 2x^16 - 1669x^15 + 2385x^14 + 1108684x^13 - 848131x^12 - 377920980x^11 + 12724944x^10 + 71331230512x^9 + 50741131904x^8 - 7480805165760x^7 - 10751966150272x^6 + 413177144536320x^5 + 886760582981376x^4 - 10454479722123264x^3 - 29180140031461376x^2 + 79787300207378432x + 248723246810300416
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
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			1.7
Root			$7.49302$ 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)

$f(q)$	$=$	$q-7.49302 q^{2} -71.8546 q^{4} -400.807 q^{5} -272.200 q^{7} +1497.52 q^{8} +O(q^{10})$	\(q-7.49302 q^{2} -71.8546 q^{4} -400.807 q^{5} -272.200 q^{7} +1497.52 q^{8} +3003.25 q^{10} -1287.50 q^{11} +9535.11 q^{13} +2039.60 q^{14} -2023.52 q^{16} +35497.8 q^{17} -14418.3 q^{19} +28799.8 q^{20} +9647.27 q^{22} -51239.1 q^{23} +82520.9 q^{25} -71446.8 q^{26} +19558.9 q^{28} +79916.8 q^{29} +228626. q^{31} -176520. q^{32} -265986. q^{34} +109100. q^{35} -139882. q^{37} +108037. q^{38} -600214. q^{40} -497679. q^{41} +299840. q^{43} +92512.8 q^{44} +383936. q^{46} -280623. q^{47} -749450. q^{49} -618331. q^{50} -685142. q^{52} -1.78864e6 q^{53} +516038. q^{55} -407624. q^{56} -598818. q^{58} +205379. q^{59} +3.36147e6 q^{61} -1.71310e6 q^{62} +1.58168e6 q^{64} -3.82174e6 q^{65} -585455. q^{67} -2.55068e6 q^{68} -817487. q^{70} -2.83547e6 q^{71} -758408. q^{73} +1.04814e6 q^{74} +1.03602e6 q^{76} +350458. q^{77} +3.27559e6 q^{79} +811040. q^{80} +3.72912e6 q^{82} -9.92122e6 q^{83} -1.42278e7 q^{85} -2.24671e6 q^{86} -1.92805e6 q^{88} +634907. q^{89} -2.59546e6 q^{91} +3.68177e6 q^{92} +2.10271e6 q^{94} +5.77895e6 q^{95} +8.12879e6 q^{97} +5.61564e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) $ 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8} + 6521 q^{10} + 1764 q^{11} + 18192 q^{13} + 7827 q^{14} + 139226 q^{16} + 15507 q^{17} + 52083 q^{19} - 721 q^{20} - 234434 q^{22} - 63823 q^{23} + 202153 q^{25} + 367956 q^{26} + 182306 q^{28} + 502955 q^{29} + 347531 q^{31} + 243908 q^{32} - 330872 q^{34} - 92641 q^{35} + 447615 q^{37} - 775669 q^{38} + 2203270 q^{40} - 940335 q^{41} + 478562 q^{43} + 596924 q^{44} - 3078663 q^{46} - 703121 q^{47} + 1895082 q^{49} + 876967 q^{50} + 6278296 q^{52} + 1005974 q^{53} + 5212846 q^{55} - 3425294 q^{56} + 6710166 q^{58} + 3491443 q^{59} + 11510749 q^{61} - 5996234 q^{62} + 29496941 q^{64} - 11094180 q^{65} + 14007144 q^{67} - 19688159 q^{68} + 30909708 q^{70} - 5229074 q^{71} + 5452211 q^{73} - 12819662 q^{74} + 41929340 q^{76} - 9930777 q^{77} + 15275654 q^{79} - 36576105 q^{80} + 32025935 q^{82} - 7826609 q^{83} + 11836945 q^{85} - 51649136 q^{86} + 30223741 q^{88} + 6436185 q^{89} + 11633535 q^{91} - 43357972 q^{92} - 4494252 q^{94} - 23741055 q^{95} + 26377540 q^{97} - 26517816 q^{98}+O(q^{100}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8 + 6521 * q^10 + 1764 * q^11 + 18192 * q^13 + 7827 * q^14 + 139226 * q^16 + 15507 * q^17 + 52083 * q^19 - 721 * q^20 - 234434 * q^22 - 63823 * q^23 + 202153 * q^25 + 367956 * q^26 + 182306 * q^28 + 502955 * q^29 + 347531 * q^31 + 243908 * q^32 - 330872 * q^34 - 92641 * q^35 + 447615 * q^37 - 775669 * q^38 + 2203270 * q^40 - 940335 * q^41 + 478562 * q^43 + 596924 * q^44 - 3078663 * q^46 - 703121 * q^47 + 1895082 * q^49 + 876967 * q^50 + 6278296 * q^52 + 1005974 * q^53 + 5212846 * q^55 - 3425294 * q^56 + 6710166 * q^58 + 3491443 * q^59 + 11510749 * q^61 - 5996234 * q^62 + 29496941 * q^64 - 11094180 * q^65 + 14007144 * q^67 - 19688159 * q^68 + 30909708 * q^70 - 5229074 * q^71 + 5452211 * q^73 - 12819662 * q^74 + 41929340 * q^76 - 9930777 * q^77 + 15275654 * q^79 - 36576105 * q^80 + 32025935 * q^82 - 7826609 * q^83 + 11836945 * q^85 - 51649136 * q^86 + 30223741 * q^88 + 6436185 * q^89 + 11633535 * q^91 - 43357972 * q^92 - 4494252 * q^94 - 23741055 * q^95 + 26377540 * q^97 - 26517816 * 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 $

$2$	−7.49302	−0.662296	−0.331148	−	0.943579i	$-0.607436\pi$
$2$	−7.49302	−0.662296	−0.331148	+	0.943579i	$0.607436\pi$
$3$	0	0
$3$	0	0
$4$	−71.8546	−0.561364
$5$	−400.807	−1.43397	−0.716985	−	0.697089i	$-0.754478\pi$
$5$	−400.807	−1.43397	−0.716985	+	0.697089i	$0.754478\pi$
$6$	0	0
$7$	−272.200	−0.299948	−0.149974	−	0.988690i	$-0.547919\pi$
$7$	−272.200	−0.299948	−0.149974	+	0.988690i	$0.547919\pi$
$8$	1497.52	1.03408
$9$	0	0
$10$	3003.25	0.949712
$11$	−1287.50	−0.291657	−0.145829	−	0.989310i	$-0.546585\pi$
$11$	−1287.50	−0.291657	−0.145829	+	0.989310i	$0.546585\pi$
$12$	0	0
$13$	9535.11	1.20372	0.601858	−	0.798603i	$-0.294427\pi$
$13$	9535.11	1.20372	0.601858	+	0.798603i	$0.294427\pi$
$14$	2039.60	0.198654
$15$	0	0
$16$	−2023.52	−0.123506
$17$	35497.8	1.75239	0.876195	−	0.481957i	$-0.160074\pi$
$17$	35497.8	1.75239	0.876195	+	0.481957i	$0.160074\pi$
$18$	0	0
$19$	−14418.3	−0.482255	−0.241128	−	0.970493i	$-0.577517\pi$
$19$	−14418.3	−0.482255	−0.241128	+	0.970493i	$0.577517\pi$
$20$	28799.8	0.804979
$21$	0	0
$22$	9647.27	0.193163
$23$	−51239.1	−0.878120	−0.439060	−	0.898458i	$-0.644688\pi$
$23$	−51239.1	−0.878120	−0.439060	+	0.898458i	$0.644688\pi$
$24$	0	0
$25$	82520.9	1.05627
$26$	−71446.8	−0.797216
$27$	0	0
$28$	19558.9	0.168380
$29$	79916.8	0.608478	0.304239	−	0.952596i	$-0.401598\pi$
$29$	79916.8	0.608478	0.304239	+	0.952596i	$0.401598\pi$
$30$	0	0
$31$	228626.	1.37835	0.689175	−	0.724595i	$-0.257973\pi$
$31$	228626.	1.37835	0.689175	+	0.724595i	$0.257973\pi$
$32$	−176520.	−0.952288
$33$	0	0
$34$	−265986.	−1.16060
$35$	109100.	0.430116
$36$	0	0
$37$	−139882.	−0.454001	−0.227000	−	0.973895i	$-0.572892\pi$
$37$	−139882.	−0.454001	−0.227000	+	0.973895i	$0.572892\pi$
$38$	108037.	0.319395
$39$	0	0
$40$	−600214.	−1.48285
$41$	−497679.	−1.12773	−0.563866	−	0.825866i	$-0.690686\pi$
$41$	−497679.	−1.12773	−0.563866	+	0.825866i	$0.690686\pi$
$42$	0	0
$43$	299840.	0.575109	0.287554	−	0.957764i	$-0.407158\pi$
$43$	299840.	0.575109	0.287554	+	0.957764i	$0.407158\pi$
$44$	92512.8	0.163726
$45$	0	0
$46$	383936.	0.581575
$47$	−280623.	−0.394258	−0.197129	−	0.980378i	$-0.563162\pi$
$47$	−280623.	−0.394258	−0.197129	+	0.980378i	$0.563162\pi$
$48$	0	0
$49$	−749450.	−0.910031
$50$	−618331.	−0.699561
$51$	0	0
$52$	−685142.	−0.675723
$53$	−1.78864e6	−1.65028	−0.825140	−	0.564928i	$-0.808904\pi$
$53$	−1.78864e6	−1.65028	−0.825140	+	0.564928i	$0.808904\pi$
$54$	0	0
$55$	516038.	0.418228
$56$	−407624.	−0.310172
$57$	0	0
$58$	−598818.	−0.402992
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	3.36147e6	1.89616	0.948080	−	0.318033i	$-0.103022\pi$
$61$	3.36147e6	1.89616	0.948080	+	0.318033i	$0.103022\pi$
$62$	−1.71310e6	−0.912875
$63$	0	0
$64$	1.58168e6	0.754202
$65$	−3.82174e6	−1.72609
$66$	0	0
$67$	−585455.	−0.237811	−0.118905	−	0.992906i	$-0.537939\pi$
$67$	−585455.	−0.237811	−0.118905	+	0.992906i	$0.537939\pi$
$68$	−2.55068e6	−0.983729
$69$	0	0
$70$	−817487.	−0.284864
$71$	−2.83547e6	−0.940202	−0.470101	−	0.882612i	$-0.655783\pi$
$71$	−2.83547e6	−0.940202	−0.470101	+	0.882612i	$0.655783\pi$
$72$	0	0
$73$	−758408.	−0.228178	−0.114089	−	0.993471i	$-0.536395\pi$
$73$	−758408.	−0.228178	−0.114089	+	0.993471i	$0.536395\pi$
$74$	1.04814e6	0.300683
$75$	0	0
$76$	1.03602e6	0.270721
$77$	350458.	0.0874820
$78$	0	0
$79$	3.27559e6	0.747471	0.373736	−	0.927535i	$-0.378077\pi$
$79$	3.27559e6	0.747471	0.373736	+	0.927535i	$0.378077\pi$
$80$	811040.	0.177104
$81$	0	0
$82$	3.72912e6	0.746892
$83$	−9.92122e6	−1.90455	−0.952273	−	0.305246i	$-0.901261\pi$
$83$	−9.92122e6	−1.90455	−0.952273	+	0.305246i	$0.901261\pi$
$84$	0	0
$85$	−1.42278e7	−2.51287
$86$	−2.24671e6	−0.380892
$87$	0	0
$88$	−1.92805e6	−0.301598
$89$	634907.	0.0954652	0.0477326	−	0.998860i	$-0.484800\pi$
$89$	634907.	0.0954652	0.0477326	+	0.998860i	$0.484800\pi$
$90$	0	0
$91$	−2.59546e6	−0.361052
$92$	3.68177e6	0.492945
$93$	0	0
$94$	2.10271e6	0.261116
$95$	5.77895e6	0.691539
$96$	0	0
$97$	8.12879e6	0.904325	0.452163	−	0.891936i	$-0.350653\pi$
$97$	8.12879e6	0.904325	0.452163	+	0.891936i	$0.350653\pi$
$98$	5.61564e6	0.602710
$99$	0	0
$100$	−5.92951e6	−0.592951
$101$	−4.69794e6	−0.453715	−0.226857	−	0.973928i	$-0.572845\pi$
$101$	−4.69794e6	−0.453715	−0.226857	+	0.973928i	$0.572845\pi$
$102$	0	0
$103$	6.17390e6	0.556710	0.278355	−	0.960478i	$-0.410211\pi$
$103$	6.17390e6	0.556710	0.278355	+	0.960478i	$0.410211\pi$
$104$	1.42790e7	1.24474
$105$	0	0
$106$	1.34023e7	1.09297
$107$	1.35523e6	0.106948	0.0534738	−	0.998569i	$-0.482971\pi$
$107$	1.35523e6	0.106948	0.0534738	+	0.998569i	$0.482971\pi$
$108$	0	0
$109$	1.04846e7	0.775457	0.387729	−	0.921774i	$-0.373260\pi$
$109$	1.04846e7	0.775457	0.387729	+	0.921774i	$0.373260\pi$
$110$	−3.86669e6	−0.276990
$111$	0	0
$112$	550803.	0.0370453
$113$	7.14003e6	0.465506	0.232753	−	0.972536i	$-0.425227\pi$
$113$	7.14003e6	0.465506	0.232753	+	0.972536i	$0.425227\pi$
$114$	0	0
$115$	2.05370e7	1.25920
$116$	−5.74239e6	−0.341578
$117$	0	0
$118$	−1.53891e6	−0.0862236
$119$	−9.66253e6	−0.525625
$120$	0	0
$121$	−1.78295e7	−0.914936
$122$	−2.51876e7	−1.25582
$123$	0	0
$124$	−1.64278e7	−0.773756
$125$	−1.76189e6	−0.0806854
$126$	0	0
$127$	−7.91805e6	−0.343009	−0.171504	−	0.985183i	$-0.554863\pi$
$127$	−7.91805e6	−0.343009	−0.171504	+	0.985183i	$0.554863\pi$
$128$	1.07430e7	0.452783
$129$	0	0
$130$	2.86363e7	1.14318
$131$	2.93961e7	1.14246	0.571230	−	0.820790i	$-0.306466\pi$
$131$	2.93961e7	1.14246	0.571230	+	0.820790i	$0.306466\pi$
$132$	0	0
$133$	3.92467e6	0.144651
$134$	4.38683e6	0.157501
$135$	0	0
$136$	5.31585e7	1.81212
$137$	−9.93494e6	−0.330098	−0.165049	−	0.986285i	$-0.552778\pi$
$137$	−9.93494e6	−0.330098	−0.165049	+	0.986285i	$0.552778\pi$
$138$	0	0
$139$	2.35079e7	0.742440	0.371220	−	0.928545i	$-0.378939\pi$
$139$	2.35079e7	0.742440	0.371220	+	0.928545i	$0.378939\pi$
$140$	−7.83932e6	−0.241452
$141$	0	0
$142$	2.12463e7	0.622692
$143$	−1.22765e7	−0.351073
$144$	0	0
$145$	−3.20312e7	−0.872539
$146$	5.68277e6	0.151121
$147$	0	0
$148$	1.00512e7	0.254860
$149$	2.98820e7	0.740044	0.370022	−	0.929023i	$-0.379350\pi$
$149$	2.98820e7	0.740044	0.370022	+	0.929023i	$0.379350\pi$
$150$	0	0
$151$	−3.58463e7	−0.847277	−0.423639	−	0.905831i	$-0.639247\pi$
$151$	−3.58463e7	−0.847277	−0.423639	+	0.905831i	$0.639247\pi$
$152$	−2.15916e7	−0.498693
$153$	0	0
$154$	−2.62599e6	−0.0579389
$155$	−9.16347e7	−1.97651
$156$	0	0
$157$	−6.40578e7	−1.32106	−0.660531	−	0.750799i	$-0.729669\pi$
$157$	−6.40578e7	−1.32106	−0.660531	+	0.750799i	$0.729669\pi$
$158$	−2.45440e7	−0.495047
$159$	0	0
$160$	7.07502e7	1.36555
$161$	1.39473e7	0.263390
$162$	0	0
$163$	−4.23392e7	−0.765749	−0.382874	−	0.923800i	$-0.625066\pi$
$163$	−4.23392e7	−0.765749	−0.382874	+	0.923800i	$0.625066\pi$
$164$	3.57605e7	0.633068
$165$	0	0
$166$	7.43399e7	1.26137
$167$	−6.08959e7	−1.01177	−0.505883	−	0.862602i	$-0.668833\pi$
$167$	−6.08959e7	−1.01177	−0.505883	+	0.862602i	$0.668833\pi$
$168$	0	0
$169$	2.81699e7	0.448933
$170$	1.06609e8	1.66426
$171$	0	0
$172$	−2.15449e7	−0.322845
$173$	1.00814e8	1.48033	0.740165	−	0.672425i	$-0.234747\pi$
$173$	1.00814e8	1.48033	0.740165	+	0.672425i	$0.234747\pi$
$174$	0	0
$175$	−2.24622e7	−0.316825
$176$	2.60528e6	0.0360214
$177$	0	0
$178$	−4.75737e6	−0.0632262
$179$	−1.28687e8	−1.67707	−0.838533	−	0.544851i	$-0.816586\pi$
$179$	−1.28687e8	−1.67707	−0.838533	+	0.544851i	$0.816586\pi$
$180$	0	0
$181$	−7.12899e7	−0.893620	−0.446810	−	0.894629i	$-0.647440\pi$
$181$	−7.12899e7	−0.893620	−0.446810	+	0.894629i	$0.647440\pi$
$182$	1.94479e7	0.239123
$183$	0	0
$184$	−7.67313e7	−0.908051
$185$	5.60657e7	0.651023
$186$	0	0
$187$	−4.57035e7	−0.511097
$188$	2.01641e7	0.221322
$189$	0	0
$190$	−4.33018e7	−0.458003
$191$	−7.68302e7	−0.797839	−0.398920	−	0.916986i	$-0.630615\pi$
$191$	−7.68302e7	−0.797839	−0.398920	+	0.916986i	$0.630615\pi$
$192$	0	0
$193$	1.34702e8	1.34873	0.674364	−	0.738399i	$-0.264418\pi$
$193$	1.34702e8	1.34873	0.674364	+	0.738399i	$0.264418\pi$
$194$	−6.09092e7	−0.598931
$195$	0	0
$196$	5.38514e7	0.510859
$197$	−1.09326e8	−1.01881	−0.509405	−	0.860527i	$-0.670134\pi$
$197$	−1.09326e8	−1.01881	−0.509405	+	0.860527i	$0.670134\pi$
$198$	0	0
$199$	−5.09514e7	−0.458322	−0.229161	−	0.973389i	$-0.573598\pi$
$199$	−5.09514e7	−0.458322	−0.229161	+	0.973389i	$0.573598\pi$
$200$	1.23576e8	1.09227
$201$	0	0
$202$	3.52018e7	0.300493
$203$	−2.17534e7	−0.182512
$204$	0	0
$205$	1.99473e8	1.61713
$206$	−4.62612e7	−0.368707
$207$	0	0
$208$	−1.92945e7	−0.148666
$209$	1.85636e7	0.140653
$210$	0	0
$211$	−1.44274e8	−1.05730	−0.528651	−	0.848839i	$-0.677302\pi$
$211$	−1.44274e8	−1.05730	−0.528651	+	0.848839i	$0.677302\pi$
$212$	1.28522e8	0.926408
$213$	0	0
$214$	−1.01548e7	−0.0708310
$215$	−1.20178e8	−0.824688
$216$	0	0
$217$	−6.22321e7	−0.413433
$218$	−7.85611e7	−0.513582
$219$	0	0
$220$	−3.70798e7	−0.234778
$221$	3.38476e8	2.10938
$222$	0	0
$223$	1.97785e8	1.19433	0.597167	−	0.802117i	$-0.296293\pi$
$223$	1.97785e8	1.19433	0.597167	+	0.802117i	$0.296293\pi$
$224$	4.80487e7	0.285637
$225$	0	0
$226$	−5.35004e7	−0.308303
$227$	3.33997e8	1.89519	0.947593	−	0.319479i	$-0.103508\pi$
$227$	3.33997e8	1.89519	0.947593	+	0.319479i	$0.103508\pi$
$228$	0	0
$229$	−5.10139e7	−0.280714	−0.140357	−	0.990101i	$-0.544825\pi$
$229$	−5.10139e7	−0.280714	−0.140357	+	0.990101i	$0.544825\pi$
$230$	−1.53884e8	−0.833961
$231$	0	0
$232$	1.19677e8	0.629218
$233$	1.21435e8	0.628923	0.314461	−	0.949270i	$-0.398176\pi$
$233$	1.21435e8	0.628923	0.314461	+	0.949270i	$0.398176\pi$
$234$	0	0
$235$	1.12476e8	0.565354
$236$	−1.47574e7	−0.0730834
$237$	0	0
$238$	7.24015e7	0.348119
$239$	−2.41270e7	−0.114317	−0.0571585	−	0.998365i	$-0.518204\pi$
$239$	−2.41270e7	−0.114317	−0.0571585	+	0.998365i	$0.518204\pi$
$240$	0	0
$241$	−5.58221e7	−0.256890	−0.128445	−	0.991717i	$-0.540999\pi$
$241$	−5.58221e7	−0.256890	−0.128445	+	0.991717i	$0.540999\pi$
$242$	1.33597e8	0.605958
$243$	0	0
$244$	−2.41537e8	−1.06444
$245$	3.00384e8	1.30496
$246$	0	0
$247$	−1.37480e8	−0.580498
$248$	3.42371e8	1.42533
$249$	0	0
$250$	1.32019e7	0.0534376
$251$	−1.85785e8	−0.741570	−0.370785	−	0.928719i	$-0.620911\pi$
$251$	−1.85785e8	−0.741570	−0.370785	+	0.928719i	$0.620911\pi$
$252$	0	0
$253$	6.59703e7	0.256110
$254$	5.93301e7	0.227173
$255$	0	0
$256$	−2.82952e8	−1.05408
$257$	4.53248e8	1.66560	0.832799	−	0.553575i	$-0.186737\pi$
$257$	4.53248e8	1.66560	0.832799	+	0.553575i	$0.186737\pi$
$258$	0	0
$259$	3.80760e7	0.136177
$260$	2.74609e8	0.968966
$261$	0	0
$262$	−2.20266e8	−0.756646
$263$	−4.28480e8	−1.45240	−0.726199	−	0.687485i	$-0.758715\pi$
$263$	−4.28480e8	−1.45240	−0.726199	+	0.687485i	$0.758715\pi$
$264$	0	0
$265$	7.16899e8	2.36645
$266$	−2.94076e7	−0.0958020
$267$	0	0
$268$	4.20677e7	0.133499
$269$	2.65173e7	0.0830609	0.0415305	−	0.999137i	$-0.486777\pi$
$269$	2.65173e7	0.0830609	0.0415305	+	0.999137i	$0.486777\pi$
$270$	0	0
$271$	1.36921e8	0.417905	0.208952	−	0.977926i	$-0.432995\pi$
$271$	1.36921e8	0.417905	0.208952	+	0.977926i	$0.432995\pi$
$272$	−7.18305e7	−0.216430
$273$	0	0
$274$	7.44427e7	0.218623
$275$	−1.06246e8	−0.308068
$276$	0	0
$277$	4.27728e8	1.20917	0.604586	−	0.796540i	$-0.293338\pi$
$277$	4.27728e8	1.20917	0.604586	+	0.796540i	$0.293338\pi$
$278$	−1.76145e8	−0.491715
$279$	0	0
$280$	1.63378e8	0.444776
$281$	3.52657e8	0.948157	0.474079	−	0.880482i	$-0.342781\pi$
$281$	3.52657e8	0.948157	0.474079	+	0.880482i	$0.342781\pi$
$282$	0	0
$283$	5.10806e8	1.33969	0.669844	−	0.742502i	$-0.266361\pi$
$283$	5.10806e8	1.33969	0.669844	+	0.742502i	$0.266361\pi$
$284$	2.03742e8	0.527796
$285$	0	0
$286$	9.19878e7	0.232514
$287$	1.35468e8	0.338261
$288$	0	0
$289$	8.49757e8	2.07087
$290$	2.40010e8	0.577879
$291$	0	0
$292$	5.44952e7	0.128091
$293$	−1.53209e8	−0.355835	−0.177917	−	0.984045i	$-0.556936\pi$
$293$	−1.53209e8	−0.355835	−0.177917	+	0.984045i	$0.556936\pi$
$294$	0	0
$295$	−8.23172e7	−0.186687
$296$	−2.09476e8	−0.469476
$297$	0	0
$298$	−2.23906e8	−0.490128
$299$	−4.88570e8	−1.05701
$300$	0	0
$301$	−8.16165e7	−0.172503
$302$	2.68597e8	0.561148
$303$	0	0
$304$	2.91757e7	0.0595613
$305$	−1.34730e9	−2.71903
$306$	0	0
$307$	7.83772e8	1.54598	0.772992	−	0.634415i	$-0.218759\pi$
$307$	7.83772e8	1.54598	0.772992	+	0.634415i	$0.218759\pi$
$308$	−2.51820e7	−0.0491093
$309$	0	0
$310$	6.86621e8	1.30903
$311$	7.44813e7	0.140406	0.0702030	−	0.997533i	$-0.477635\pi$
$311$	7.44813e7	0.140406	0.0702030	+	0.997533i	$0.477635\pi$
$312$	0	0
$313$	4.78847e8	0.882657	0.441328	−	0.897346i	$-0.354507\pi$
$313$	4.78847e8	0.882657	0.441328	+	0.897346i	$0.354507\pi$
$314$	4.79986e8	0.874934
$315$	0	0
$316$	−2.35366e8	−0.419604
$317$	3.22619e8	0.568829	0.284415	−	0.958701i	$-0.408201\pi$
$317$	3.22619e8	0.568829	0.284415	+	0.958701i	$0.408201\pi$
$318$	0	0
$319$	−1.02893e8	−0.177467
$320$	−6.33946e8	−1.08150
$321$	0	0
$322$	−1.04507e8	−0.174442
$323$	−5.11819e8	−0.845099
$324$	0	0
$325$	7.86846e8	1.27145
$326$	3.17249e8	0.507152
$327$	0	0
$328$	−7.45282e8	−1.16617
$329$	7.63857e7	0.118257
$330$	0	0
$331$	1.02925e9	1.56000	0.779998	−	0.625782i	$-0.215220\pi$
$331$	1.02925e9	1.56000	0.779998	+	0.625782i	$0.215220\pi$
$332$	7.12885e8	1.06914
$333$	0	0
$334$	4.56294e8	0.670089
$335$	2.34654e8	0.341014
$336$	0	0
$337$	3.61784e7	0.0514926	0.0257463	−	0.999669i	$-0.491804\pi$
$337$	3.61784e7	0.0514926	0.0257463	+	0.999669i	$0.491804\pi$
$338$	−2.11077e8	−0.297326
$339$	0	0
$340$	1.02233e9	1.41064
$341$	−2.94356e8	−0.402006
$342$	0	0
$343$	4.28169e8	0.572910
$344$	4.49015e8	0.594711
$345$	0	0
$346$	−7.55400e8	−0.980417
$347$	−1.13436e9	−1.45746	−0.728729	−	0.684802i	$-0.759889\pi$
$347$	−1.13436e9	−1.45746	−0.728729	+	0.684802i	$0.759889\pi$
$348$	0	0
$349$	−3.76547e8	−0.474166	−0.237083	−	0.971489i	$-0.576191\pi$
$349$	−3.76547e8	−0.474166	−0.237083	+	0.971489i	$0.576191\pi$
$350$	1.68310e8	0.209832
$351$	0	0
$352$	2.27269e8	0.277742
$353$	1.14395e9	1.38419	0.692097	−	0.721805i	$-0.256687\pi$
$353$	1.14395e9	1.38419	0.692097	+	0.721805i	$0.256687\pi$
$354$	0	0
$355$	1.13648e9	1.34822
$356$	−4.56210e7	−0.0535908
$357$	0	0
$358$	9.64257e8	1.11071
$359$	1.69002e9	1.92780	0.963900	−	0.266265i	$-0.0857897\pi$
$359$	1.69002e9	1.92780	0.963900	+	0.266265i	$0.0857897\pi$
$360$	0	0
$361$	−6.85984e8	−0.767430
$362$	5.34177e8	0.591841
$363$	0	0
$364$	1.86496e8	0.202682
$365$	3.03975e8	0.327200
$366$	0	0
$367$	−1.11560e9	−1.17809	−0.589046	−	0.808100i	$-0.700496\pi$
$367$	−1.11560e9	−1.17809	−0.589046	+	0.808100i	$0.700496\pi$
$368$	1.03683e8	0.108453
$369$	0	0
$370$	−4.20102e8	−0.431170
$371$	4.86869e8	0.494998
$372$	0	0
$373$	−1.06668e9	−1.06427	−0.532134	−	0.846660i	$-0.678610\pi$
$373$	−1.06668e9	−1.06427	−0.532134	+	0.846660i	$0.678610\pi$
$374$	3.42457e8	0.338497
$375$	0	0
$376$	−4.20237e8	−0.407697
$377$	7.62015e8	0.732435
$378$	0	0
$379$	9.06012e7	0.0854864	0.0427432	−	0.999086i	$-0.486390\pi$
$379$	9.06012e7	0.0854864	0.0427432	+	0.999086i	$0.486390\pi$
$380$	−4.15245e8	−0.388205
$381$	0	0
$382$	5.75691e8	0.528406
$383$	−1.02770e9	−0.934700	−0.467350	−	0.884072i	$-0.654791\pi$
$383$	−1.02770e9	−0.934700	−0.467350	+	0.884072i	$0.654791\pi$
$384$	0	0
$385$	−1.40466e8	−0.125446
$386$	−1.00933e9	−0.893257
$387$	0	0
$388$	−5.84091e8	−0.507656
$389$	−1.62652e9	−1.40099	−0.700495	−	0.713657i	$-0.747038\pi$
$389$	−1.62652e9	−1.40099	−0.700495	+	0.713657i	$0.747038\pi$
$390$	0	0
$391$	−1.81888e9	−1.53881
$392$	−1.12231e9	−0.941050
$393$	0	0
$394$	8.19184e8	0.674753
$395$	−1.31288e9	−1.07185
$396$	0	0
$397$	−1.41716e8	−0.113672	−0.0568359	−	0.998384i	$-0.518101\pi$
$397$	−1.41716e8	−0.113672	−0.0568359	+	0.998384i	$0.518101\pi$
$398$	3.81780e8	0.303545
$399$	0	0
$400$	−1.66983e8	−0.130455
$401$	1.70702e9	1.32200	0.661002	−	0.750384i	$-0.270132\pi$
$401$	1.70702e9	1.32200	0.661002	+	0.750384i	$0.270132\pi$
$402$	0	0
$403$	2.17997e9	1.65914
$404$	3.37569e8	0.254699
$405$	0	0
$406$	1.62999e8	0.120877
$407$	1.80099e8	0.132413
$408$	0	0
$409$	−1.96299e9	−1.41869	−0.709345	−	0.704862i	$-0.751009\pi$
$409$	−1.96299e9	−1.41869	−0.709345	+	0.704862i	$0.751009\pi$
$410$	−1.49466e9	−1.07102
$411$	0	0
$412$	−4.43623e8	−0.312517
$413$	−5.59043e7	−0.0390499
$414$	0	0
$415$	3.97649e9	2.73106
$416$	−1.68313e9	−1.14628
$417$	0	0
$418$	−1.39097e8	−0.0931540
$419$	−2.45844e9	−1.63271	−0.816357	−	0.577547i	$-0.804010\pi$
$419$	−2.45844e9	−1.63271	−0.816357	+	0.577547i	$0.804010\pi$
$420$	0	0
$421$	6.57370e8	0.429361	0.214681	−	0.976684i	$-0.431129\pi$
$421$	6.57370e8	0.429361	0.214681	+	0.976684i	$0.431129\pi$
$422$	1.08105e9	0.700247
$423$	0	0
$424$	−2.67852e9	−1.70653
$425$	2.92931e9	1.85099
$426$	0	0
$427$	−9.14994e8	−0.568749
$428$	−9.73799e7	−0.0600366
$429$	0	0
$430$	9.00495e8	0.546187
$431$	1.65546e9	0.995976	0.497988	−	0.867184i	$-0.334072\pi$
$431$	1.65546e9	0.995976	0.497988	+	0.867184i	$0.334072\pi$
$432$	0	0
$433$	−1.96267e9	−1.16182	−0.580910	−	0.813968i	$-0.697303\pi$
$433$	−1.96267e9	−1.16182	−0.580910	+	0.813968i	$0.697303\pi$
$434$	4.66306e8	0.273815
$435$	0	0
$436$	−7.53365e8	−0.435314
$437$	7.38781e8	0.423478
$438$	0	0
$439$	6.65374e8	0.375353	0.187677	−	0.982231i	$-0.439904\pi$
$439$	6.65374e8	0.375353	0.187677	+	0.982231i	$0.439904\pi$
$440$	7.72775e8	0.432483
$441$	0	0
$442$	−2.53621e9	−1.39703
$443$	−2.45181e8	−0.133991	−0.0669953	−	0.997753i	$-0.521341\pi$
$443$	−2.45181e8	−0.133991	−0.0669953	+	0.997753i	$0.521341\pi$
$444$	0	0
$445$	−2.54475e8	−0.136894
$446$	−1.48201e9	−0.791003
$447$	0	0
$448$	−4.30533e8	−0.226221
$449$	−1.56613e9	−0.816516	−0.408258	−	0.912867i	$-0.633864\pi$
$449$	−1.56613e9	−0.816516	−0.408258	+	0.912867i	$0.633864\pi$
$450$	0	0
$451$	6.40762e8	0.328911
$452$	−5.13044e8	−0.261318
$453$	0	0
$454$	−2.50265e9	−1.25517
$455$	1.04028e9	0.517737
$456$	0	0
$457$	2.77494e9	1.36002	0.680012	−	0.733201i	$-0.261974\pi$
$457$	2.77494e9	1.36002	0.680012	+	0.733201i	$0.261974\pi$
$458$	3.82249e8	0.185916
$459$	0	0
$460$	−1.47568e9	−0.706868
$461$	−1.84492e9	−0.877051	−0.438525	−	0.898719i	$-0.644499\pi$
$461$	−1.84492e9	−0.877051	−0.438525	+	0.898719i	$0.644499\pi$
$462$	0	0
$463$	−1.44653e9	−0.677322	−0.338661	−	0.940908i	$-0.609974\pi$
$463$	−1.44653e9	−0.677322	−0.338661	+	0.940908i	$0.609974\pi$
$464$	−1.61713e8	−0.0751506
$465$	0	0
$466$	−9.09914e8	−0.416533
$467$	1.95804e9	0.889636	0.444818	−	0.895621i	$-0.353268\pi$
$467$	1.95804e9	0.889636	0.444818	+	0.895621i	$0.353268\pi$
$468$	0	0
$469$	1.59361e8	0.0713309
$470$	−8.42782e8	−0.374432
$471$	0	0
$472$	3.07558e8	0.134626
$473$	−3.86044e8	−0.167735
$474$	0	0
$475$	−1.18981e9	−0.509390
$476$	6.94297e8	0.295067
$477$	0	0
$478$	1.80784e8	0.0757116
$479$	3.02650e9	1.25825	0.629124	−	0.777305i	$-0.283414\pi$
$479$	3.02650e9	1.25825	0.629124	+	0.777305i	$0.283414\pi$
$480$	0	0
$481$	−1.33379e9	−0.546488
$482$	4.18277e8	0.170137
$483$	0	0
$484$	1.28113e9	0.513612
$485$	−3.25807e9	−1.29677
$486$	0	0
$487$	−1.90649e9	−0.747967	−0.373983	−	0.927435i	$-0.622008\pi$
$487$	−1.90649e9	−0.747967	−0.373983	+	0.927435i	$0.622008\pi$
$488$	5.03385e9	1.96079
$489$	0	0
$490$	−2.25079e9	−0.864267
$491$	−2.37779e9	−0.906544	−0.453272	−	0.891372i	$-0.649743\pi$
$491$	−2.37779e9	−0.906544	−0.453272	+	0.891372i	$0.649743\pi$
$492$	0	0
$493$	2.83687e9	1.06629
$494$	1.03014e9	0.384462
$495$	0	0
$496$	−4.62629e8	−0.170234
$497$	7.71817e8	0.282012
$498$	0	0
$499$	−1.25478e9	−0.452081	−0.226041	−	0.974118i	$-0.572578\pi$
$499$	−1.25478e9	−0.452081	−0.226041	+	0.974118i	$0.572578\pi$
$500$	1.26600e8	0.0452939
$501$	0	0
$502$	1.39209e9	0.491139
$503$	1.13501e9	0.397660	0.198830	−	0.980034i	$-0.436286\pi$
$503$	1.13501e9	0.397660	0.198830	+	0.980034i	$0.436286\pi$
$504$	0	0
$505$	1.88297e9	0.650613
$506$	−4.94317e8	−0.169621
$507$	0	0
$508$	5.68949e8	0.192553
$509$	4.34255e9	1.45960	0.729798	−	0.683663i	$-0.239614\pi$
$509$	4.34255e9	1.45960	0.729798	+	0.683663i	$0.239614\pi$
$510$	0	0
$511$	2.06439e8	0.0684414
$512$	7.45063e8	0.245329
$513$	0	0
$514$	−3.39620e9	−1.10312
$515$	−2.47454e9	−0.798305
$516$	0	0
$517$	3.61302e8	0.114988
$518$	−2.85305e8	−0.0901892
$519$	0	0
$520$	−5.72311e9	−1.78493
$521$	−1.60678e9	−0.497764	−0.248882	−	0.968534i	$-0.580063\pi$
$521$	−1.60678e9	−0.497764	−0.248882	+	0.968534i	$0.580063\pi$
$522$	0	0
$523$	−1.33872e9	−0.409198	−0.204599	−	0.978846i	$-0.565589\pi$
$523$	−1.33872e9	−0.409198	−0.204599	+	0.978846i	$0.565589\pi$
$524$	−2.11225e9	−0.641336
$525$	0	0
$526$	3.21061e9	0.961917
$527$	8.11572e9	2.41541
$528$	0	0
$529$	−7.79382e8	−0.228905
$530$	−5.37174e9	−1.56729
$531$	0	0
$532$	−2.82006e8	−0.0812021
$533$	−4.74542e9	−1.35747
$534$	0	0
$535$	−5.43187e8	−0.153360
$536$	−8.76728e8	−0.245917
$537$	0	0
$538$	−1.98695e8	−0.0550109
$539$	9.64917e8	0.265417
$540$	0	0
$541$	2.04184e9	0.554410	0.277205	−	0.960811i	$-0.410592\pi$
$541$	2.04184e9	0.554410	0.277205	+	0.960811i	$0.410592\pi$
$542$	−1.02595e9	−0.276777
$543$	0	0
$544$	−6.26606e9	−1.66878
$545$	−4.20228e9	−1.11198
$546$	0	0
$547$	4.97747e9	1.30033	0.650164	−	0.759794i	$-0.274700\pi$
$547$	4.97747e9	1.30033	0.650164	+	0.759794i	$0.274700\pi$
$548$	7.13871e8	0.185305
$549$	0	0
$550$	7.96101e8	0.204032
$551$	−1.15226e9	−0.293442
$552$	0	0
$553$	−8.91616e8	−0.224202
$554$	−3.20497e9	−0.800830
$555$	0	0
$556$	−1.68915e9	−0.416780
$557$	−4.71080e9	−1.15505	−0.577526	−	0.816372i	$-0.695982\pi$
$557$	−4.71080e9	−1.15505	−0.577526	+	0.816372i	$0.695982\pi$
$558$	0	0
$559$	2.85901e9	0.692267
$560$	−2.20765e8	−0.0531218
$561$	0	0
$562$	−2.64247e9	−0.627961
$563$	4.24894e9	1.00346	0.501731	−	0.865024i	$-0.332697\pi$
$563$	4.24894e9	1.00346	0.501731	+	0.865024i	$0.332697\pi$
$564$	0	0
$565$	−2.86177e9	−0.667521
$566$	−3.82748e9	−0.887269
$567$	0	0
$568$	−4.24616e9	−0.972249
$569$	−5.26230e9	−1.19752	−0.598759	−	0.800929i	$-0.704339\pi$
$569$	−5.26230e9	−1.19752	−0.598759	+	0.800929i	$0.704339\pi$
$570$	0	0
$571$	−3.29668e9	−0.741056	−0.370528	−	0.928821i	$-0.620823\pi$
$571$	−3.29668e9	−0.741056	−0.370528	+	0.928821i	$0.620823\pi$
$572$	8.82120e8	0.197080
$573$	0	0
$574$	−1.01507e9	−0.224029
$575$	−4.22829e9	−0.927529
$576$	0	0
$577$	−3.50100e9	−0.758713	−0.379356	−	0.925251i	$-0.623855\pi$
$577$	−3.50100e9	−0.758713	−0.379356	+	0.925251i	$0.623855\pi$
$578$	−6.36725e9	−1.37153
$579$	0	0
$580$	2.30159e9	0.489812
$581$	2.70056e9	0.571265
$582$	0	0
$583$	2.30288e9	0.481316
$584$	−1.13573e9	−0.235955
$585$	0	0
$586$	1.14800e9	0.235668
$587$	3.06924e9	0.626322	0.313161	−	0.949700i	$-0.398612\pi$
$587$	3.06924e9	0.626322	0.313161	+	0.949700i	$0.398612\pi$
$588$	0	0
$589$	−3.29640e9	−0.664716
$590$	6.16805e8	0.123642
$591$	0	0
$592$	2.83055e8	0.0560718
$593$	9.06218e9	1.78460	0.892300	−	0.451442i	$-0.149090\pi$
$593$	9.06218e9	1.78460	0.892300	+	0.451442i	$0.149090\pi$
$594$	0	0
$595$	3.87280e9	0.753730
$596$	−2.14716e9	−0.415434
$597$	0	0
$598$	3.66087e9	0.700052
$599$	−5.53085e9	−1.05147	−0.525736	−	0.850648i	$-0.676210\pi$
$599$	−5.53085e9	−1.05147	−0.525736	+	0.850648i	$0.676210\pi$
$600$	0	0
$601$	2.64790e9	0.497555	0.248777	−	0.968561i	$-0.419971\pi$
$601$	2.64790e9	0.497555	0.248777	+	0.968561i	$0.419971\pi$
$602$	6.11555e8	0.114248
$603$	0	0
$604$	2.57573e9	0.475631
$605$	7.14619e9	1.31199
$606$	0	0
$607$	1.49005e9	0.270421	0.135210	−	0.990817i	$-0.456829\pi$
$607$	1.49005e9	0.270421	0.135210	+	0.990817i	$0.456829\pi$
$608$	2.54512e9	0.459246
$609$	0	0
$610$	1.00953e10	1.80080
$611$	−2.67577e9	−0.474575
$612$	0	0
$613$	6.01176e9	1.05412	0.527060	−	0.849828i	$-0.323294\pi$
$613$	6.01176e9	1.05412	0.527060	+	0.849828i	$0.323294\pi$
$614$	−5.87282e9	−1.02390
$615$	0	0
$616$	5.24816e8	0.0904638
$617$	−1.06578e10	−1.82671	−0.913356	−	0.407161i	$-0.866519\pi$
$617$	−1.06578e10	−1.82671	−0.913356	+	0.407161i	$0.866519\pi$
$618$	0	0
$619$	−3.27736e9	−0.555401	−0.277700	−	0.960668i	$-0.589572\pi$
$619$	−3.27736e9	−0.555401	−0.277700	+	0.960668i	$0.589572\pi$
$620$	6.58438e9	1.10954
$621$	0	0
$622$	−5.58090e8	−0.0929903
$623$	−1.72822e8	−0.0286346
$624$	0	0
$625$	−5.74076e9	−0.940567
$626$	−3.58801e9	−0.584580
$627$	0	0
$628$	4.60285e9	0.741597
$629$	−4.96552e9	−0.795586
$630$	0	0
$631$	−5.83790e9	−0.925026	−0.462513	−	0.886613i	$-0.653052\pi$
$631$	−5.83790e9	−0.925026	−0.462513	+	0.886613i	$0.653052\pi$
$632$	4.90524e9	0.772949
$633$	0	0
$634$	−2.41739e9	−0.376733
$635$	3.17361e9	0.491864
$636$	0	0
$637$	−7.14609e9	−1.09542
$638$	7.70978e8	0.117536
$639$	0	0
$640$	−4.30586e9	−0.649277
$641$	9.30439e9	1.39536	0.697678	−	0.716412i	$-0.254217\pi$
$641$	9.30439e9	1.39536	0.697678	+	0.716412i	$0.254217\pi$
$642$	0	0
$643$	7.27839e9	1.07969	0.539843	−	0.841766i	$-0.318484\pi$
$643$	7.27839e9	1.07969	0.539843	+	0.841766i	$0.318484\pi$
$644$	−1.00218e9	−0.147858
$645$	0	0
$646$	3.83507e9	0.559705
$647$	8.75508e9	1.27085	0.635426	−	0.772162i	$-0.280824\pi$
$647$	8.75508e9	1.27085	0.635426	+	0.772162i	$0.280824\pi$
$648$	0	0
$649$	−2.64425e8	−0.0379705
$650$	−5.89585e9	−0.842073
$651$	0	0
$652$	3.04227e9	0.429864
$653$	−5.51167e8	−0.0774617	−0.0387308	−	0.999250i	$-0.512331\pi$
$653$	−5.51167e8	−0.0774617	−0.0387308	+	0.999250i	$0.512331\pi$
$654$	0	0
$655$	−1.17822e10	−1.63825
$656$	1.00706e9	0.139281
$657$	0	0
$658$	−5.72360e8	−0.0783210
$659$	−2.23902e8	−0.0304761	−0.0152381	−	0.999884i	$-0.504851\pi$
$659$	−2.23902e8	−0.0304761	−0.0152381	+	0.999884i	$0.504851\pi$
$660$	0	0
$661$	1.42160e10	1.91458	0.957288	−	0.289137i	$-0.0933682\pi$
$661$	1.42160e10	1.91458	0.957288	+	0.289137i	$0.0933682\pi$
$662$	−7.71221e9	−1.03318
$663$	0	0
$664$	−1.48572e10	−1.96946
$665$	−1.57303e9	−0.207426
$666$	0	0
$667$	−4.09486e9	−0.534317
$668$	4.37565e9	0.567970
$669$	0	0
$670$	−1.75827e9	−0.225852
$671$	−4.32789e9	−0.553029
$672$	0	0
$673$	−1.15239e10	−1.45730	−0.728648	−	0.684888i	$-0.759851\pi$
$673$	−1.15239e10	−1.45730	−0.728648	+	0.684888i	$0.759851\pi$
$674$	−2.71085e8	−0.0341033
$675$	0	0
$676$	−2.02414e9	−0.252015
$677$	1.31983e10	1.63477	0.817385	−	0.576092i	$-0.195423\pi$
$677$	1.31983e10	1.63477	0.817385	+	0.576092i	$0.195423\pi$
$678$	0	0
$679$	−2.21266e9	−0.271250
$680$	−2.13063e10	−2.59852
$681$	0	0
$682$	2.20561e9	0.266247
$683$	1.04211e10	1.25153	0.625766	−	0.780010i	$-0.284786\pi$
$683$	1.04211e10	1.25153	0.625766	+	0.780010i	$0.284786\pi$
$684$	0	0
$685$	3.98199e9	0.473351
$686$	−3.20828e9	−0.379436
$687$	0	0
$688$	−6.06732e8	−0.0710292
$689$	−1.70549e10	−1.98647
$690$	0	0
$691$	1.27099e10	1.46544	0.732721	−	0.680529i	$-0.238250\pi$
$691$	1.27099e10	1.46544	0.732721	+	0.680529i	$0.238250\pi$
$692$	−7.24394e9	−0.831005
$693$	0	0
$694$	8.49976e9	0.965269
$695$	−9.42211e9	−1.06464
$696$	0	0
$697$	−1.76665e10	−1.97622
$698$	2.82148e9	0.314038
$699$	0	0
$700$	1.61401e9	0.177854
$701$	9.44240e9	1.03531	0.517654	−	0.855590i	$-0.326806\pi$
$701$	9.44240e9	1.03531	0.517654	+	0.855590i	$0.326806\pi$
$702$	0	0
$703$	2.01687e9	0.218944
$704$	−2.03641e9	−0.219968
$705$	0	0
$706$	−8.57167e9	−0.916745
$707$	1.27878e9	0.136091
$708$	0	0
$709$	5.62595e9	0.592835	0.296417	−	0.955058i	$-0.404208\pi$
$709$	5.62595e9	0.592835	0.296417	+	0.955058i	$0.404208\pi$
$710$	−8.51564e9	−0.892921
$711$	0	0
$712$	9.50783e8	0.0987191
$713$	−1.17146e10	−1.21036
$714$	0	0
$715$	4.92049e9	0.503427
$716$	9.24678e9	0.941445
$717$	0	0
$718$	−1.26634e10	−1.27677
$719$	−1.77080e9	−0.177672	−0.0888360	−	0.996046i	$-0.528315\pi$
$719$	−1.77080e9	−0.177672	−0.0888360	+	0.996046i	$0.528315\pi$
$720$	0	0
$721$	−1.68054e9	−0.166984
$722$	5.14009e9	0.508266
$723$	0	0
$724$	5.12251e9	0.501647
$725$	6.59480e9	0.642715
$726$	0	0
$727$	−2.42657e9	−0.234219	−0.117110	−	0.993119i	$-0.537363\pi$
$727$	−2.42657e9	−0.234219	−0.117110	+	0.993119i	$0.537363\pi$
$728$	−3.88674e9	−0.373359
$729$	0	0
$730$	−2.27769e9	−0.216703
$731$	1.06437e10	1.00781
$732$	0	0
$733$	7.37181e9	0.691370	0.345685	−	0.938351i	$-0.387647\pi$
$733$	7.37181e9	0.691370	0.345685	+	0.938351i	$0.387647\pi$
$734$	8.35925e9	0.780245
$735$	0	0
$736$	9.04471e9	0.836223
$737$	7.53774e8	0.0693593
$738$	0	0
$739$	−1.11711e6	−0.000101822 0	−5.09108e−5	−	1.00000i	$-0.500016\pi$
$739$	−1.11711e6	−0.000101822 0	−5.09108e−5		1.00000i	$0.500016\pi$
$740$	−4.02858e9	−0.365461
$741$	0	0
$742$	−3.64812e9	−0.327835
$743$	6.56798e9	0.587450	0.293725	−	0.955890i	$-0.405105\pi$
$743$	6.56798e9	0.587450	0.293725	+	0.955890i	$0.405105\pi$
$744$	0	0
$745$	−1.19769e10	−1.06120
$746$	7.99262e9	0.704861
$747$	0	0
$748$	3.28401e9	0.286912
$749$	−3.68895e8	−0.0320787
$750$	0	0
$751$	5.66489e9	0.488036	0.244018	−	0.969771i	$-0.421534\pi$
$751$	5.66489e9	0.488036	0.244018	+	0.969771i	$0.421534\pi$
$752$	5.67846e8	0.0486932
$753$	0	0
$754$	−5.70980e9	−0.485088
$755$	1.43674e10	1.21497
$756$	0	0
$757$	−8.32870e9	−0.697817	−0.348908	−	0.937157i	$-0.613448\pi$
$757$	−8.32870e9	−0.697817	−0.348908	+	0.937157i	$0.613448\pi$
$758$	−6.78877e8	−0.0566173
$759$	0	0
$760$	8.65407e9	0.715110
$761$	1.51950e10	1.24984	0.624918	−	0.780690i	$-0.285132\pi$
$761$	1.51950e10	1.24984	0.624918	+	0.780690i	$0.285132\pi$
$762$	0	0
$763$	−2.85390e9	−0.232597
$764$	5.52061e9	0.447878
$765$	0	0
$766$	7.70060e9	0.619048
$767$	1.95831e9	0.156711
$768$	0	0
$769$	5.04268e9	0.399871	0.199935	−	0.979809i	$-0.435927\pi$
$769$	5.04268e9	0.399871	0.199935	+	0.979809i	$0.435927\pi$
$770$	1.05251e9	0.0830826
$771$	0	0
$772$	−9.67898e9	−0.757128
$773$	−8.09728e9	−0.630537	−0.315269	−	0.949002i	$-0.602095\pi$
$773$	−8.09728e9	−0.630537	−0.315269	+	0.949002i	$0.602095\pi$
$774$	0	0
$775$	1.88664e10	1.45591
$776$	1.21730e10	0.935149
$777$	0	0
$778$	1.21875e10	0.927870
$779$	7.17569e9	0.543854
$780$	0	0
$781$	3.65067e9	0.274217
$782$	1.36289e10	1.01915
$783$	0	0
$784$	1.51653e9	0.112394
$785$	2.56748e10	1.89436
$786$	0	0
$787$	−1.32475e10	−0.968773	−0.484387	−	0.874854i	$-0.660957\pi$
$787$	−1.32475e10	−0.968773	−0.484387	+	0.874854i	$0.660957\pi$
$788$	7.85560e9	0.571923
$789$	0	0
$790$	9.83741e9	0.709882
$791$	−1.94352e9	−0.139628
$792$	0	0
$793$	3.20520e10	2.28244
$794$	1.06188e9	0.0752843
$795$	0	0
$796$	3.66110e9	0.257286
$797$	1.25069e10	0.875076	0.437538	−	0.899200i	$-0.355851\pi$
$797$	1.25069e10	0.875076	0.437538	+	0.899200i	$0.355851\pi$
$798$	0	0
$799$	−9.96151e9	−0.690894
$800$	−1.45666e10	−1.00587
$801$	0	0
$802$	−1.27907e10	−0.875557
$803$	9.76451e8	0.0665497
$804$	0	0
$805$	−5.59017e9	−0.377693
$806$	−1.63346e10	−1.09884
$807$	0	0
$808$	−7.03524e9	−0.469179
$809$	−2.07620e10	−1.37864	−0.689319	−	0.724458i	$-0.742090\pi$
$809$	−2.07620e10	−1.37864	−0.689319	+	0.724458i	$0.742090\pi$
$810$	0	0
$811$	−8.31574e8	−0.0547429	−0.0273715	−	0.999625i	$-0.508714\pi$
$811$	−8.31574e8	−0.0547429	−0.0273715	+	0.999625i	$0.508714\pi$
$812$	1.56308e9	0.102456
$813$	0	0
$814$	−1.34948e9	−0.0876964
$815$	1.69698e10	1.09806
$816$	0	0
$817$	−4.32318e9	−0.277349
$818$	1.47088e10	0.939592
$819$	0	0
$820$	−1.43331e10	−0.907800
$821$	7.46166e9	0.470581	0.235290	−	0.971925i	$-0.424396\pi$
$821$	7.46166e9	0.470581	0.235290	+	0.971925i	$0.424396\pi$
$822$	0	0
$823$	−1.83123e10	−1.14510	−0.572550	−	0.819870i	$-0.694046\pi$
$823$	−1.83123e10	−1.14510	−0.572550	+	0.819870i	$0.694046\pi$
$824$	9.24551e9	0.575686
$825$	0	0
$826$	4.18892e8	0.0258626
$827$	−2.57787e10	−1.58487	−0.792433	−	0.609960i	$-0.791186\pi$
$827$	−2.57787e10	−1.58487	−0.792433	+	0.609960i	$0.791186\pi$
$828$	0	0
$829$	−2.26603e10	−1.38142	−0.690710	−	0.723132i	$-0.742702\pi$
$829$	−2.26603e10	−1.38142	−0.690710	+	0.723132i	$0.742702\pi$
$830$	−2.97959e10	−1.80877
$831$	0	0
$832$	1.50815e10	0.907845
$833$	−2.66038e10	−1.59473
$834$	0	0
$835$	2.44075e10	1.45084
$836$	−1.33388e9	−0.0789577
$837$	0	0
$838$	1.84211e10	1.08134
$839$	9.57948e9	0.559983	0.279992	−	0.960002i	$-0.409668\pi$
$839$	9.57948e9	0.559983	0.279992	+	0.960002i	$0.409668\pi$
$840$	0	0
$841$	−1.08632e10	−0.629755
$842$	−4.92569e9	−0.284364
$843$	0	0
$844$	1.03668e10	0.593532
$845$	−1.12907e10	−0.643756
$846$	0	0
$847$	4.85320e9	0.274433
$848$	3.61935e9	0.203819
$849$	0	0
$850$	−2.19494e10	−1.22590
$851$	7.16744e9	0.398667
$852$	0	0
$853$	2.74400e10	1.51378	0.756889	−	0.653544i	$-0.226718\pi$
$853$	2.74400e10	1.51378	0.756889	+	0.653544i	$0.226718\pi$
$854$	6.85607e9	0.376680
$855$	0	0
$856$	2.02948e9	0.110593
$857$	1.29104e10	0.700657	0.350329	−	0.936627i	$-0.386070\pi$
$857$	1.29104e10	0.700657	0.350329	+	0.936627i	$0.386070\pi$
$858$	0	0
$859$	2.65615e10	1.42981	0.714903	−	0.699224i	$-0.246471\pi$
$859$	2.65615e10	1.42981	0.714903	+	0.699224i	$0.246471\pi$
$860$	8.63533e9	0.462950
$861$	0	0
$862$	−1.24044e10	−0.659631
$863$	−1.29749e10	−0.687173	−0.343586	−	0.939121i	$-0.611642\pi$
$863$	−1.29749e10	−0.687173	−0.343586	+	0.939121i	$0.611642\pi$
$864$	0	0
$865$	−4.04068e10	−2.12275
$866$	1.47063e10	0.769469
$867$	0	0
$868$	4.47166e9	0.232087
$869$	−4.21732e9	−0.218005
$870$	0	0
$871$	−5.58238e9	−0.286257
$872$	1.57008e10	0.801889
$873$	0	0
$874$	−5.53570e9	−0.280468
$875$	4.79588e8	0.0242014
$876$	0	0
$877$	−1.08321e10	−0.542270	−0.271135	−	0.962541i	$-0.587399\pi$
$877$	−1.08321e10	−0.542270	−0.271135	+	0.962541i	$0.587399\pi$
$878$	−4.98566e9	−0.248595
$879$	0	0
$880$	−1.04421e9	−0.0516535
$881$	−1.78817e10	−0.881034	−0.440517	−	0.897744i	$-0.645205\pi$
$881$	−1.78817e10	−0.881034	−0.440517	+	0.897744i	$0.645205\pi$
$882$	0	0
$883$	2.05428e9	0.100415	0.0502073	−	0.998739i	$-0.484012\pi$
$883$	2.05428e9	0.100415	0.0502073	+	0.998739i	$0.484012\pi$
$884$	−2.43211e10	−1.18413
$885$	0	0
$886$	1.83715e9	0.0887414
$887$	−2.26672e10	−1.09060	−0.545299	−	0.838242i	$-0.683584\pi$
$887$	−2.26672e10	−1.09060	−0.545299	+	0.838242i	$0.683584\pi$
$888$	0	0
$889$	2.15530e9	0.102885
$890$	1.90679e9	0.0906644
$891$	0	0
$892$	−1.42118e10	−0.670457
$893$	4.04611e9	0.190133
$894$	0	0
$895$	5.15787e10	2.40486
$896$	−2.92424e9	−0.135811
$897$	0	0
$898$	1.17350e10	0.540775
$899$	1.82710e10	0.838695
$900$	0	0
$901$	−6.34929e10	−2.89193
$902$	−4.80124e9	−0.217836
$903$	0	0
$904$	1.06923e10	0.481373
$905$	2.85735e10	1.28142
$906$	0	0
$907$	−3.69882e10	−1.64603	−0.823015	−	0.568020i	$-0.807710\pi$
$907$	−3.69882e10	−1.64603	−0.823015	+	0.568020i	$0.807710\pi$
$908$	−2.39992e10	−1.06389
$909$	0	0
$910$	−7.79483e9	−0.342895
$911$	3.70589e10	1.62397	0.811986	−	0.583677i	$-0.198387\pi$
$911$	3.70589e10	1.62397	0.811986	+	0.583677i	$0.198387\pi$
$912$	0	0
$913$	1.27736e10	0.555475
$914$	−2.07927e10	−0.900739
$915$	0	0
$916$	3.66559e9	0.157583
$917$	−8.00164e9	−0.342678
$918$	0	0
$919$	−3.58106e10	−1.52197	−0.760986	−	0.648768i	$-0.775285\pi$
$919$	−3.58106e10	−1.52197	−0.760986	+	0.648768i	$0.775285\pi$
$920$	3.07544e10	1.30212
$921$	0	0
$922$	1.38240e10	0.580867
$923$	−2.70366e10	−1.13174
$924$	0	0
$925$	−1.15432e10	−0.479546
$926$	1.08389e10	0.448587
$927$	0	0
$928$	−1.41069e10	−0.579446
$929$	3.54484e10	1.45058	0.725291	−	0.688443i	$-0.241705\pi$
$929$	3.54484e10	1.45058	0.725291	+	0.688443i	$0.241705\pi$
$930$	0	0
$931$	1.08058e10	0.438867
$932$	−8.72565e9	−0.353055
$933$	0	0
$934$	−1.46716e10	−0.589202
$935$	1.83182e10	0.732897
$936$	0	0
$937$	3.58282e10	1.42278	0.711388	−	0.702800i	$-0.248067\pi$
$937$	3.58282e10	1.42278	0.711388	+	0.702800i	$0.248067\pi$
$938$	−1.19410e9	−0.0472421
$939$	0	0
$940$	−8.08189e9	−0.317370
$941$	5.81166e9	0.227372	0.113686	−	0.993517i	$-0.463734\pi$
$941$	5.81166e9	0.227372	0.113686	+	0.993517i	$0.463734\pi$
$942$	0	0
$943$	2.55006e10	0.990284
$944$	−4.15588e8	−0.0160791
$945$	0	0
$946$	2.89264e9	0.111090
$947$	−3.32826e10	−1.27348	−0.636740	−	0.771079i	$-0.719717\pi$
$947$	−3.32826e10	−1.27348	−0.636740	+	0.771079i	$0.719717\pi$
$948$	0	0
$949$	−7.23151e9	−0.274661
$950$	8.91528e9	0.337367
$951$	0	0
$952$	−1.44698e10	−0.543541
$953$	1.73227e9	0.0648322	0.0324161	−	0.999474i	$-0.489680\pi$
$953$	1.73227e9	0.0648322	0.0324161	+	0.999474i	$0.489680\pi$
$954$	0	0
$955$	3.07941e10	1.14408
$956$	1.73364e9	0.0641735
$957$	0	0
$958$	−2.26776e10	−0.833332
$959$	2.70429e9	0.0990122
$960$	0	0
$961$	2.47572e10	0.899848
$962$	9.99415e9	0.361937
$963$	0	0
$964$	4.01108e9	0.144209
$965$	−5.39895e10	−1.93403
$966$	0	0
$967$	3.35118e10	1.19180	0.595902	−	0.803057i	$-0.296795\pi$
$967$	3.35118e10	1.19180	0.595902	+	0.803057i	$0.296795\pi$
$968$	−2.67000e10	−0.946122
$969$	0	0
$970$	2.44128e10	0.858848
$971$	2.03751e10	0.714219	0.357110	−	0.934063i	$-0.383762\pi$
$971$	2.03751e10	0.714219	0.357110	+	0.934063i	$0.383762\pi$
$972$	0	0
$973$	−6.39885e9	−0.222693
$974$	1.42853e10	0.495375
$975$	0	0
$976$	−6.80200e9	−0.234187
$977$	−4.03720e10	−1.38500	−0.692498	−	0.721419i	$-0.743490\pi$
$977$	−4.03720e10	−1.38500	−0.692498	+	0.721419i	$0.743490\pi$
$978$	0	0
$979$	−8.17443e8	−0.0278431
$980$	−2.15840e10	−0.732556
$981$	0	0
$982$	1.78169e10	0.600400
$983$	−1.10528e10	−0.371139	−0.185569	−	0.982631i	$-0.559413\pi$
$983$	−1.10528e10	−0.371139	−0.185569	+	0.982631i	$0.559413\pi$
$984$	0	0
$985$	4.38187e10	1.46094
$986$	−2.12567e10	−0.706199
$987$	0	0
$988$	9.87859e9	0.325871
$989$	−1.53635e10	−0.505014
$990$	0	0
$991$	3.39895e10	1.10940	0.554699	−	0.832051i	$-0.312833\pi$
$991$	3.39895e10	1.10940	0.554699	+	0.832051i	$0.312833\pi$
$992$	−4.03570e10	−1.31259
$993$	0	0
$994$	−5.78324e9	−0.186775
$995$	2.04217e10	0.657219
$996$	0	0
$997$	5.14554e10	1.64436	0.822182	−	0.569225i	$-0.192757\pi$
$997$	5.14554e10	1.64436	0.822182	+	0.569225i	$0.192757\pi$
$998$	9.40211e9	0.299412
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.c.1.7		17
3.2	odd	2		177.8.a.c.1.11	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.11	✓	17	3.2	odd	2
531.8.a.c.1.7		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)

\(f(q)\)	\(=\)	\(q-7.49302 q^{2} -71.8546 q^{4} -400.807 q^{5} -272.200 q^{7} +1497.52 q^{8} +O(q^{10})\)	\(q-7.49302 q^{2} -71.8546 q^{4} -400.807 q^{5} -272.200 q^{7} +1497.52 q^{8} +3003.25 q^{10} -1287.50 q^{11} +9535.11 q^{13} +2039.60 q^{14} -2023.52 q^{16} +35497.8 q^{17} -14418.3 q^{19} +28799.8 q^{20} +9647.27 q^{22} -51239.1 q^{23} +82520.9 q^{25} -71446.8 q^{26} +19558.9 q^{28} +79916.8 q^{29} +228626. q^{31} -176520. q^{32} -265986. q^{34} +109100. q^{35} -139882. q^{37} +108037. q^{38} -600214. q^{40} -497679. q^{41} +299840. q^{43} +92512.8 q^{44} +383936. q^{46} -280623. q^{47} -749450. q^{49} -618331. q^{50} -685142. q^{52} -1.78864e6 q^{53} +516038. q^{55} -407624. q^{56} -598818. q^{58} +205379. q^{59} +3.36147e6 q^{61} -1.71310e6 q^{62} +1.58168e6 q^{64} -3.82174e6 q^{65} -585455. q^{67} -2.55068e6 q^{68} -817487. q^{70} -2.83547e6 q^{71} -758408. q^{73} +1.04814e6 q^{74} +1.03602e6 q^{76} +350458. q^{77} +3.27559e6 q^{79} +811040. q^{80} +3.72912e6 q^{82} -9.92122e6 q^{83} -1.42278e7 q^{85} -2.24671e6 q^{86} -1.92805e6 q^{88} +634907. q^{89} -2.59546e6 q^{91} +3.68177e6 q^{92} +2.10271e6 q^{94} +5.77895e6 q^{95} +8.12879e6 q^{97} +5.61564e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8} + 6521 q^{10} + 1764 q^{11} + 18192 q^{13} + 7827 q^{14} + 139226 q^{16} + 15507 q^{17} + 52083 q^{19} - 721 q^{20} - 234434 q^{22} - 63823 q^{23} + 202153 q^{25} + 367956 q^{26} + 182306 q^{28} + 502955 q^{29} + 347531 q^{31} + 243908 q^{32} - 330872 q^{34} - 92641 q^{35} + 447615 q^{37} - 775669 q^{38} + 2203270 q^{40} - 940335 q^{41} + 478562 q^{43} + 596924 q^{44} - 3078663 q^{46} - 703121 q^{47} + 1895082 q^{49} + 876967 q^{50} + 6278296 q^{52} + 1005974 q^{53} + 5212846 q^{55} - 3425294 q^{56} + 6710166 q^{58} + 3491443 q^{59} + 11510749 q^{61} - 5996234 q^{62} + 29496941 q^{64} - 11094180 q^{65} + 14007144 q^{67} - 19688159 q^{68} + 30909708 q^{70} - 5229074 q^{71} + 5452211 q^{73} - 12819662 q^{74} + 41929340 q^{76} - 9930777 q^{77} + 15275654 q^{79} - 36576105 q^{80} + 32025935 q^{82} - 7826609 q^{83} + 11836945 q^{85} - 51649136 q^{86} + 30223741 q^{88} + 6436185 q^{89} + 11633535 q^{91} - 43357972 q^{92} - 4494252 q^{94} - 23741055 q^{95} + 26377540 q^{97} - 26517816 q^{98}+O(q^{100}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8 + 6521 * q^10 + 1764 * q^11 + 18192 * q^13 + 7827 * q^14 + 139226 * q^16 + 15507 * q^17 + 52083 * q^19 - 721 * q^20 - 234434 * q^22 - 63823 * q^23 + 202153 * q^25 + 367956 * q^26 + 182306 * q^28 + 502955 * q^29 + 347531 * q^31 + 243908 * q^32 - 330872 * q^34 - 92641 * q^35 + 447615 * q^37 - 775669 * q^38 + 2203270 * q^40 - 940335 * q^41 + 478562 * q^43 + 596924 * q^44 - 3078663 * q^46 - 703121 * q^47 + 1895082 * q^49 + 876967 * q^50 + 6278296 * q^52 + 1005974 * q^53 + 5212846 * q^55 - 3425294 * q^56 + 6710166 * q^58 + 3491443 * q^59 + 11510749 * q^61 - 5996234 * q^62 + 29496941 * q^64 - 11094180 * q^65 + 14007144 * q^67 - 19688159 * q^68 + 30909708 * q^70 - 5229074 * q^71 + 5452211 * q^73 - 12819662 * q^74 + 41929340 * q^76 - 9930777 * q^77 + 15275654 * q^79 - 36576105 * q^80 + 32025935 * q^82 - 7826609 * q^83 + 11836945 * q^85 - 51649136 * q^86 + 30223741 * q^88 + 6436185 * q^89 + 11633535 * q^91 - 43357972 * q^92 - 4494252 * q^94 - 23741055 * q^95 + 26377540 * q^97 - 26517816 * q^98

Introduction

L-functions

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