LMFDB - Embedded newform 531.8.a.c.1.17

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			1.17
Root			$-22.1687$ 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)

$f(q)$	$=$	$q+22.1687 q^{2} +363.451 q^{4} -258.765 q^{5} +411.003 q^{7} +5219.64 q^{8} +O(q^{10})$	\(q+22.1687 q^{2} +363.451 q^{4} -258.765 q^{5} +411.003 q^{7} +5219.64 q^{8} -5736.49 q^{10} -437.879 q^{11} +13224.5 q^{13} +9111.39 q^{14} +69190.8 q^{16} -24930.4 q^{17} +38005.6 q^{19} -94048.5 q^{20} -9707.20 q^{22} -79710.8 q^{23} -11165.5 q^{25} +293169. q^{26} +149379. q^{28} +64355.4 q^{29} +241791. q^{31} +865756. q^{32} -552675. q^{34} -106353. q^{35} +353659. q^{37} +842535. q^{38} -1.35066e6 q^{40} -246146. q^{41} -151362. q^{43} -159147. q^{44} -1.76708e6 q^{46} +512816. q^{47} -654620. q^{49} -247524. q^{50} +4.80644e6 q^{52} +141087. q^{53} +113308. q^{55} +2.14528e6 q^{56} +1.42668e6 q^{58} +205379. q^{59} +846302. q^{61} +5.36020e6 q^{62} +1.03362e7 q^{64} -3.42203e6 q^{65} +3.36339e6 q^{67} -9.06099e6 q^{68} -2.35771e6 q^{70} +4.07342e6 q^{71} -4.42831e6 q^{73} +7.84015e6 q^{74} +1.38132e7 q^{76} -179969. q^{77} -4.19495e6 q^{79} -1.79042e7 q^{80} -5.45672e6 q^{82} +6.96295e6 q^{83} +6.45114e6 q^{85} -3.35550e6 q^{86} -2.28557e6 q^{88} +2.48793e6 q^{89} +5.43529e6 q^{91} -2.89710e7 q^{92} +1.13685e7 q^{94} -9.83454e6 q^{95} +8.97300e6 q^{97} -1.45121e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	22.1687	1.95945	0.979727	−	0.200338i	$-0.0642039\pi$
$2$	22.1687	1.95945	0.979727	+	0.200338i	$0.0642039\pi$
$3$	0	0
$3$	0	0
$4$	363.451	2.83946
$5$	−258.765	−0.925787	−0.462894	−	0.886414i	$-0.653189\pi$
$5$	−258.765	−0.925787	−0.462894	+	0.886414i	$0.653189\pi$
$6$	0	0
$7$	411.003	0.452899	0.226450	−	0.974023i	$-0.427288\pi$
$7$	411.003	0.452899	0.226450	+	0.974023i	$0.427288\pi$
$8$	5219.64	3.60434
$9$	0	0
$10$	−5736.49	−1.81404
$11$	−437.879	−0.0991927	−0.0495964	−	0.998769i	$-0.515793\pi$
$11$	−437.879	−0.0991927	−0.0495964	+	0.998769i	$0.515793\pi$
$12$	0	0
$13$	13224.5	1.66946	0.834730	−	0.550659i	$-0.185624\pi$
$13$	13224.5	1.66946	0.834730	+	0.550659i	$0.185624\pi$
$14$	9111.39	0.887435
$15$	0	0
$16$	69190.8	4.22307
$17$	−24930.4	−1.23072	−0.615359	−	0.788247i	$-0.710989\pi$
$17$	−24930.4	−1.23072	−0.615359	+	0.788247i	$0.710989\pi$
$18$	0	0
$19$	38005.6	1.27119	0.635595	−	0.772023i	$-0.280755\pi$
$19$	38005.6	1.27119	0.635595	+	0.772023i	$0.280755\pi$
$20$	−94048.5	−2.62874
$21$	0	0
$22$	−9707.20	−0.194364
$23$	−79710.8	−1.36606	−0.683030	−	0.730390i	$-0.739338\pi$
$23$	−79710.8	−1.36606	−0.683030	+	0.730390i	$0.739338\pi$
$24$	0	0
$25$	−11165.5	−0.142918
$26$	293169.	3.27123
$27$	0	0
$28$	149379.	1.28599
$29$	64355.4	0.489996	0.244998	−	0.969524i	$-0.421213\pi$
$29$	64355.4	0.489996	0.244998	+	0.969524i	$0.421213\pi$
$30$	0	0
$31$	241791.	1.45772	0.728862	−	0.684661i	$-0.240050\pi$
$31$	241791.	1.45772	0.728862	+	0.684661i	$0.240050\pi$
$32$	865756.	4.67058
$33$	0	0
$34$	−552675.	−2.41154
$35$	−106353.	−0.419288
$36$	0	0
$37$	353659.	1.14783	0.573916	−	0.818914i	$-0.305424\pi$
$37$	353659.	1.14783	0.573916	+	0.818914i	$0.305424\pi$
$38$	842535.	2.49084
$39$	0	0
$40$	−1.35066e6	−3.33685
$41$	−246146.	−0.557761	−0.278881	−	0.960326i	$-0.589963\pi$
$41$	−246146.	−0.557761	−0.278881	+	0.960326i	$0.589963\pi$
$42$	0	0
$43$	−151362.	−0.290321	−0.145160	−	0.989408i	$-0.546370\pi$
$43$	−151362.	−0.290321	−0.145160	+	0.989408i	$0.546370\pi$
$44$	−159147.	−0.281654
$45$	0	0
$46$	−1.76708e6	−2.67673
$47$	512816.	0.720475	0.360238	−	0.932861i	$-0.382696\pi$
$47$	512816.	0.720475	0.360238	+	0.932861i	$0.382696\pi$
$48$	0	0
$49$	−654620.	−0.794882
$50$	−247524.	−0.280041
$51$	0	0
$52$	4.80644e6	4.74036
$53$	141087.	0.130173	0.0650867	−	0.997880i	$-0.479268\pi$
$53$	141087.	0.130173	0.0650867	+	0.997880i	$0.479268\pi$
$54$	0	0
$55$	113308.	0.0918314
$56$	2.14528e6	1.63240
$57$	0	0
$58$	1.42668e6	0.960124
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	846302.	0.477388	0.238694	−	0.971095i	$-0.423281\pi$
$61$	846302.	0.477388	0.238694	+	0.971095i	$0.423281\pi$
$62$	5.36020e6	2.85634
$63$	0	0
$64$	1.03362e7	4.92871
$65$	−3.42203e6	−1.54556
$66$	0	0
$67$	3.36339e6	1.36620	0.683101	−	0.730324i	$-0.260631\pi$
$67$	3.36339e6	1.36620	0.683101	+	0.730324i	$0.260631\pi$
$68$	−9.06099e6	−3.49458
$69$	0	0
$70$	−2.35771e6	−0.821576
$71$	4.07342e6	1.35069	0.675344	−	0.737503i	$-0.263995\pi$
$71$	4.07342e6	1.35069	0.675344	+	0.737503i	$0.263995\pi$
$72$	0	0
$73$	−4.42831e6	−1.33232	−0.666159	−	0.745810i	$-0.732063\pi$
$73$	−4.42831e6	−1.33232	−0.666159	+	0.745810i	$0.732063\pi$
$74$	7.84015e6	2.24912
$75$	0	0
$76$	1.38132e7	3.60949
$77$	−179969.	−0.0449243
$78$	0	0
$79$	−4.19495e6	−0.957265	−0.478633	−	0.878015i	$-0.658867\pi$
$79$	−4.19495e6	−0.957265	−0.478633	+	0.878015i	$0.658867\pi$
$80$	−1.79042e7	−3.90967
$81$	0	0
$82$	−5.45672e6	−1.09291
$83$	6.96295e6	1.33666	0.668329	−	0.743866i	$-0.267010\pi$
$83$	6.96295e6	1.33666	0.668329	+	0.743866i	$0.267010\pi$
$84$	0	0
$85$	6.45114e6	1.13938
$86$	−3.35550e6	−0.568870
$87$	0	0
$88$	−2.28557e6	−0.357524
$89$	2.48793e6	0.374088	0.187044	−	0.982352i	$-0.440109\pi$
$89$	2.48793e6	0.374088	0.187044	+	0.982352i	$0.440109\pi$
$90$	0	0
$91$	5.43529e6	0.756097
$92$	−2.89710e7	−3.87887
$93$	0	0
$94$	1.13685e7	1.41174
$95$	−9.83454e6	−1.17685
$96$	0	0
$97$	8.97300e6	0.998244	0.499122	−	0.866532i	$-0.333656\pi$
$97$	8.97300e6	0.998244	0.499122	+	0.866532i	$0.333656\pi$
$98$	−1.45121e7	−1.55754
$99$	0	0
$100$	−4.05810e6	−0.405810
$101$	1.29861e6	0.125417	0.0627084	−	0.998032i	$-0.480026\pi$
$101$	1.29861e6	0.125417	0.0627084	+	0.998032i	$0.480026\pi$
$102$	0	0
$103$	1.51079e7	1.36230	0.681150	−	0.732144i	$-0.261480\pi$
$103$	1.51079e7	1.36230	0.681150	+	0.732144i	$0.261480\pi$
$104$	6.90268e7	6.01729
$105$	0	0
$106$	3.12772e6	0.255069
$107$	−6.86606e6	−0.541832	−0.270916	−	0.962603i	$-0.587327\pi$
$107$	−6.86606e6	−0.541832	−0.270916	+	0.962603i	$0.587327\pi$
$108$	0	0
$109$	−1.26929e7	−0.938790	−0.469395	−	0.882988i	$-0.655528\pi$
$109$	−1.26929e7	−0.938790	−0.469395	+	0.882988i	$0.655528\pi$
$110$	2.51189e6	0.179939
$111$	0	0
$112$	2.84376e7	1.91262
$113$	1.90547e7	1.24230	0.621151	−	0.783691i	$-0.286665\pi$
$113$	1.90547e7	1.24230	0.621151	+	0.783691i	$0.286665\pi$
$114$	0	0
$115$	2.06264e7	1.26468
$116$	2.33900e7	1.39132
$117$	0	0
$118$	4.55298e6	0.255099
$119$	−1.02465e7	−0.557391
$120$	0	0
$121$	−1.92954e7	−0.990161
$122$	1.87614e7	0.935419
$123$	0	0
$124$	8.78793e7	4.13915
$125$	2.31053e7	1.05810
$126$	0	0
$127$	3.81929e7	1.65451	0.827254	−	0.561828i	$-0.189902\pi$
$127$	3.81929e7	1.65451	0.827254	+	0.561828i	$0.189902\pi$
$128$	1.18324e8	4.98700
$129$	0	0
$130$	−7.58620e7	−3.02846
$131$	−4.40577e7	−1.71227	−0.856135	−	0.516752i	$-0.827141\pi$
$131$	−4.40577e7	−1.71227	−0.856135	+	0.516752i	$0.827141\pi$
$132$	0	0
$133$	1.56204e7	0.575721
$134$	7.45619e7	2.67701
$135$	0	0
$136$	−1.30128e8	−4.43592
$137$	2.64599e7	0.879156	0.439578	−	0.898204i	$-0.355128\pi$
$137$	2.64599e7	0.879156	0.439578	+	0.898204i	$0.355128\pi$
$138$	0	0
$139$	−2.17850e7	−0.688029	−0.344014	−	0.938964i	$-0.611787\pi$
$139$	−2.17850e7	−0.688029	−0.344014	+	0.938964i	$0.611787\pi$
$140$	−3.86542e7	−1.19055
$141$	0	0
$142$	9.03024e7	2.64661
$143$	−5.79071e6	−0.165598
$144$	0	0
$145$	−1.66530e7	−0.453632
$146$	−9.81698e7	−2.61061
$147$	0	0
$148$	1.28538e8	3.25922
$149$	−5.57470e6	−0.138061	−0.0690303	−	0.997615i	$-0.521991\pi$
$149$	−5.57470e6	−0.138061	−0.0690303	+	0.997615i	$0.521991\pi$
$150$	0	0
$151$	−3.98105e7	−0.940975	−0.470487	−	0.882407i	$-0.655922\pi$
$151$	−3.98105e7	−0.940975	−0.470487	+	0.882407i	$0.655922\pi$
$152$	1.98376e8	4.58180
$153$	0	0
$154$	−3.98969e6	−0.0880271
$155$	−6.25673e7	−1.34954
$156$	0	0
$157$	−2.43241e7	−0.501635	−0.250818	−	0.968034i	$-0.580699\pi$
$157$	−2.43241e7	−0.501635	−0.250818	+	0.968034i	$0.580699\pi$
$158$	−9.29966e7	−1.87572
$159$	0	0
$160$	−2.24028e8	−4.32396
$161$	−3.27614e7	−0.618687
$162$	0	0
$163$	1.62611e7	0.294098	0.147049	−	0.989129i	$-0.453022\pi$
$163$	1.62611e7	0.294098	0.147049	+	0.989129i	$0.453022\pi$
$164$	−8.94618e7	−1.58374
$165$	0	0
$166$	1.54360e8	2.61912
$167$	−2.00507e7	−0.333136	−0.166568	−	0.986030i	$-0.553268\pi$
$167$	−2.00507e7	−0.333136	−0.166568	+	0.986030i	$0.553268\pi$
$168$	0	0
$169$	1.12138e8	1.78710
$170$	1.43013e8	2.23257
$171$	0	0
$172$	−5.50128e7	−0.824354
$173$	−1.22817e8	−1.80342	−0.901712	−	0.432338i	$-0.857689\pi$
$173$	−1.22817e8	−1.80342	−0.901712	+	0.432338i	$0.857689\pi$
$174$	0	0
$175$	−4.58903e6	−0.0647274
$176$	−3.02972e7	−0.418898
$177$	0	0
$178$	5.51542e7	0.733008
$179$	4.55080e7	0.593065	0.296532	−	0.955023i	$-0.404170\pi$
$179$	4.55080e7	0.593065	0.296532	+	0.955023i	$0.404170\pi$
$180$	0	0
$181$	−1.43158e8	−1.79448	−0.897241	−	0.441541i	$-0.854432\pi$
$181$	−1.43158e8	−1.79448	−0.897241	+	0.441541i	$0.854432\pi$
$182$	1.20493e8	1.48154
$183$	0	0
$184$	−4.16061e8	−4.92374
$185$	−9.15147e7	−1.06265
$186$	0	0
$187$	1.09165e7	0.122078
$188$	1.86383e8	2.04576
$189$	0	0
$190$	−2.18019e8	−2.30599
$191$	−5.12128e7	−0.531817	−0.265908	−	0.963998i	$-0.585672\pi$
$191$	−5.12128e7	−0.531817	−0.265908	+	0.963998i	$0.585672\pi$
$192$	0	0
$193$	9.92991e7	0.994248	0.497124	−	0.867680i	$-0.334389\pi$
$193$	9.92991e7	0.994248	0.497124	+	0.867680i	$0.334389\pi$
$194$	1.98920e8	1.95601
$195$	0	0
$196$	−2.37922e8	−2.25704
$197$	1.34248e8	1.25105	0.625527	−	0.780202i	$-0.284884\pi$
$197$	1.34248e8	1.25105	0.625527	+	0.780202i	$0.284884\pi$
$198$	0	0
$199$	−6.47369e7	−0.582326	−0.291163	−	0.956674i	$-0.594042\pi$
$199$	−6.47369e7	−0.582326	−0.291163	+	0.956674i	$0.594042\pi$
$200$	−5.82796e7	−0.515124
$201$	0	0
$202$	2.87886e7	0.245748
$203$	2.64502e7	0.221919
$204$	0	0
$205$	6.36940e7	0.516368
$206$	3.34922e8	2.66936
$207$	0	0
$208$	9.15010e8	7.05025
$209$	−1.66419e7	−0.126093
$210$	0	0
$211$	−3.50321e7	−0.256731	−0.128365	−	0.991727i	$-0.540973\pi$
$211$	−3.50321e7	−0.256731	−0.128365	+	0.991727i	$0.540973\pi$
$212$	5.12783e7	0.369622
$213$	0	0
$214$	−1.52212e8	−1.06169
$215$	3.91673e7	0.268775
$216$	0	0
$217$	9.93769e7	0.660201
$218$	−2.81385e8	−1.83952
$219$	0	0
$220$	4.11819e7	0.260751
$221$	−3.29692e8	−2.05464
$222$	0	0
$223$	2.00970e8	1.21357	0.606783	−	0.794867i	$-0.292460\pi$
$223$	2.00970e8	1.21357	0.606783	+	0.794867i	$0.292460\pi$
$224$	3.55828e8	2.11530
$225$	0	0
$226$	4.22417e8	2.43423
$227$	−2.01923e8	−1.14577	−0.572883	−	0.819637i	$-0.694175\pi$
$227$	−2.01923e8	−1.14577	−0.572883	+	0.819637i	$0.694175\pi$
$228$	0	0
$229$	−8.98434e7	−0.494381	−0.247191	−	0.968967i	$-0.579507\pi$
$229$	−8.98434e7	−0.494381	−0.247191	+	0.968967i	$0.579507\pi$
$230$	4.57260e8	2.47808
$231$	0	0
$232$	3.35912e8	1.76611
$233$	−2.22230e8	−1.15095	−0.575476	−	0.817819i	$-0.695183\pi$
$233$	−2.22230e8	−1.15095	−0.575476	+	0.817819i	$0.695183\pi$
$234$	0	0
$235$	−1.32699e8	−0.667007
$236$	7.46452e7	0.369666
$237$	0	0
$238$	−2.27151e8	−1.09218
$239$	−1.33230e8	−0.631262	−0.315631	−	0.948882i	$-0.602216\pi$
$239$	−1.33230e8	−0.631262	−0.315631	+	0.948882i	$0.602216\pi$
$240$	0	0
$241$	5.22856e7	0.240615	0.120307	−	0.992737i	$-0.461612\pi$
$241$	5.22856e7	0.240615	0.120307	+	0.992737i	$0.461612\pi$
$242$	−4.27754e8	−1.94017
$243$	0	0
$244$	3.07589e8	1.35552
$245$	1.69393e8	0.735892
$246$	0	0
$247$	5.02604e8	2.12220
$248$	1.26206e9	5.25412
$249$	0	0
$250$	5.12214e8	2.07330
$251$	2.01583e8	0.804629	0.402314	−	0.915502i	$-0.368206\pi$
$251$	2.01583e8	0.804629	0.402314	+	0.915502i	$0.368206\pi$
$252$	0	0
$253$	3.49037e7	0.135503
$254$	8.46686e8	3.24193
$255$	0	0
$256$	1.30006e9	4.84309
$257$	−2.23672e7	−0.0821949	−0.0410975	−	0.999155i	$-0.513085\pi$
$257$	−2.23672e7	−0.0821949	−0.0410975	+	0.999155i	$0.513085\pi$
$258$	0	0
$259$	1.45355e8	0.519852
$260$	−1.24374e9	−4.38857
$261$	0	0
$262$	−9.76702e8	−3.35512
$263$	−2.02431e8	−0.686170	−0.343085	−	0.939304i	$-0.611472\pi$
$263$	−2.02431e8	−0.686170	−0.343085	+	0.939304i	$0.611472\pi$
$264$	0	0
$265$	−3.65085e7	−0.120513
$266$	3.46284e8	1.12810
$267$	0	0
$268$	1.22243e9	3.87928
$269$	−6.24827e8	−1.95716	−0.978581	−	0.205862i	$-0.934000\pi$
$269$	−6.24827e8	−1.95716	−0.978581	+	0.205862i	$0.934000\pi$
$270$	0	0
$271$	−3.54191e8	−1.08105	−0.540525	−	0.841328i	$-0.681774\pi$
$271$	−3.54191e8	−1.08105	−0.540525	+	0.841328i	$0.681774\pi$
$272$	−1.72496e9	−5.19741
$273$	0	0
$274$	5.86581e8	1.72267
$275$	4.88912e6	0.0141764
$276$	0	0
$277$	−6.00748e8	−1.69829	−0.849147	−	0.528156i	$-0.822884\pi$
$277$	−6.00748e8	−1.69829	−0.849147	+	0.528156i	$0.822884\pi$
$278$	−4.82946e8	−1.34816
$279$	0	0
$280$	−5.55125e8	−1.51126
$281$	5.54600e8	1.49110	0.745551	−	0.666448i	$-0.232186\pi$
$281$	5.54600e8	1.49110	0.745551	+	0.666448i	$0.232186\pi$
$282$	0	0
$283$	1.85734e8	0.487124	0.243562	−	0.969885i	$-0.421684\pi$
$283$	1.85734e8	0.487124	0.243562	+	0.969885i	$0.421684\pi$
$284$	1.48049e9	3.83522
$285$	0	0
$286$	−1.28372e8	−0.324482
$287$	−1.01166e8	−0.252610
$288$	0	0
$289$	2.11188e8	0.514668
$290$	−3.69174e8	−0.888870
$291$	0	0
$292$	−1.60947e9	−3.78306
$293$	−8.06147e8	−1.87231	−0.936154	−	0.351590i	$-0.885641\pi$
$293$	−8.06147e8	−1.87231	−0.936154	+	0.351590i	$0.885641\pi$
$294$	0	0
$295$	−5.31450e7	−0.120527
$296$	1.84597e9	4.13717
$297$	0	0
$298$	−1.23584e8	−0.270523
$299$	−1.05413e9	−2.28058
$300$	0	0
$301$	−6.22103e7	−0.131486
$302$	−8.82546e8	−1.84380
$303$	0	0
$304$	2.62964e9	5.36832
$305$	−2.18994e8	−0.441959
$306$	0	0
$307$	−5.41975e8	−1.06904	−0.534522	−	0.845155i	$-0.679508\pi$
$307$	−5.41975e8	−1.06904	−0.534522	+	0.845155i	$0.679508\pi$
$308$	−6.54100e7	−0.127561
$309$	0	0
$310$	−1.38703e9	−2.64436
$311$	2.23407e8	0.421149	0.210575	−	0.977578i	$-0.432466\pi$
$311$	2.23407e8	0.421149	0.210575	+	0.977578i	$0.432466\pi$
$312$	0	0
$313$	−6.53332e8	−1.20428	−0.602142	−	0.798389i	$-0.705686\pi$
$313$	−6.53332e8	−1.20428	−0.602142	+	0.798389i	$0.705686\pi$
$314$	−5.39234e8	−0.982932
$315$	0	0
$316$	−1.52466e9	−2.71812
$317$	−3.82141e8	−0.673777	−0.336889	−	0.941544i	$-0.609375\pi$
$317$	−3.82141e8	−0.673777	−0.336889	+	0.941544i	$0.609375\pi$
$318$	0	0
$319$	−2.81799e7	−0.0486040
$320$	−2.67466e9	−4.56293
$321$	0	0
$322$	−7.26276e8	−1.21229
$323$	−9.47497e8	−1.56448
$324$	0	0
$325$	−1.47657e8	−0.238596
$326$	3.60486e8	0.576272
$327$	0	0
$328$	−1.28479e9	−2.01036
$329$	2.10769e8	0.326303
$330$	0	0
$331$	−1.19439e8	−0.181030	−0.0905148	−	0.995895i	$-0.528851\pi$
$331$	−1.19439e8	−0.181030	−0.0905148	+	0.995895i	$0.528851\pi$
$332$	2.53069e9	3.79539
$333$	0	0
$334$	−4.44497e8	−0.652764
$335$	−8.70328e8	−1.26481
$336$	0	0
$337$	6.48790e8	0.923421	0.461710	−	0.887031i	$-0.347236\pi$
$337$	6.48790e8	0.923421	0.461710	+	0.887031i	$0.347236\pi$
$338$	2.48595e9	3.50173
$339$	0	0
$340$	2.34467e9	3.23523
$341$	−1.05875e8	−0.144596
$342$	0	0
$343$	−6.07529e8	−0.812901
$344$	−7.90056e8	−1.04641
$345$	0	0
$346$	−2.72270e9	−3.53372
$347$	1.32744e9	1.70553	0.852766	−	0.522292i	$-0.174923\pi$
$347$	1.32744e9	1.70553	0.852766	+	0.522292i	$0.174923\pi$
$348$	0	0
$349$	−2.41076e7	−0.0303575	−0.0151787	−	0.999885i	$-0.504832\pi$
$349$	−2.41076e7	−0.0303575	−0.0151787	+	0.999885i	$0.504832\pi$
$350$	−1.01733e8	−0.126830
$351$	0	0
$352$	−3.79096e8	−0.463287
$353$	1.15393e9	1.39626	0.698132	−	0.715969i	$-0.254015\pi$
$353$	1.15393e9	1.39626	0.698132	+	0.715969i	$0.254015\pi$
$354$	0	0
$355$	−1.05406e9	−1.25045
$356$	9.04241e8	1.06221
$357$	0	0
$358$	1.00885e9	1.16208
$359$	1.33636e8	0.152438	0.0762190	−	0.997091i	$-0.475715\pi$
$359$	1.33636e8	0.152438	0.0762190	+	0.997091i	$0.475715\pi$
$360$	0	0
$361$	5.50557e8	0.615924
$362$	−3.17361e9	−3.51621
$363$	0	0
$364$	1.97546e9	2.14691
$365$	1.14589e9	1.23344
$366$	0	0
$367$	6.96923e8	0.735959	0.367980	−	0.929834i	$-0.380050\pi$
$367$	6.96923e8	0.735959	0.367980	+	0.929834i	$0.380050\pi$
$368$	−5.51525e9	−5.76897
$369$	0	0
$370$	−2.02876e9	−2.08221
$371$	5.79872e7	0.0589554
$372$	0	0
$373$	−2.37598e7	−0.0237062	−0.0118531	−	0.999930i	$-0.503773\pi$
$373$	−2.37598e7	−0.0237062	−0.0118531	+	0.999930i	$0.503773\pi$
$374$	2.42005e8	0.239207
$375$	0	0
$376$	2.67671e9	2.59684
$377$	8.51065e8	0.818028
$378$	0	0
$379$	6.51339e8	0.614568	0.307284	−	0.951618i	$-0.400580\pi$
$379$	6.51339e8	0.614568	0.307284	+	0.951618i	$0.400580\pi$
$380$	−3.57437e9	−3.34162
$381$	0	0
$382$	−1.13532e9	−1.04207
$383$	−7.66231e8	−0.696889	−0.348445	−	0.937329i	$-0.613290\pi$
$383$	−7.66231e8	−0.696889	−0.348445	+	0.937329i	$0.613290\pi$
$384$	0	0
$385$	4.65699e7	0.0415903
$386$	2.20133e9	1.94818
$387$	0	0
$388$	3.26124e9	2.83447
$389$	9.02040e8	0.776966	0.388483	−	0.921456i	$-0.372999\pi$
$389$	9.02040e8	0.776966	0.388483	+	0.921456i	$0.372999\pi$
$390$	0	0
$391$	1.98723e9	1.68124
$392$	−3.41688e9	−2.86502
$393$	0	0
$394$	2.97610e9	2.45138
$395$	1.08551e9	0.886224
$396$	0	0
$397$	−4.92346e8	−0.394915	−0.197458	−	0.980311i	$-0.563268\pi$
$397$	−4.92346e8	−0.394915	−0.197458	+	0.980311i	$0.563268\pi$
$398$	−1.43513e9	−1.14104
$399$	0	0
$400$	−7.72547e8	−0.603552
$401$	8.45019e8	0.654427	0.327213	−	0.944950i	$-0.393890\pi$
$401$	8.45019e8	0.654427	0.327213	+	0.944950i	$0.393890\pi$
$402$	0	0
$403$	3.19756e9	2.43361
$404$	4.71983e8	0.356116
$405$	0	0
$406$	5.86367e8	0.434839
$407$	−1.54860e8	−0.113857
$408$	0	0
$409$	−1.44863e9	−1.04695	−0.523474	−	0.852042i	$-0.675364\pi$
$409$	−1.44863e9	−1.04695	−0.523474	+	0.852042i	$0.675364\pi$
$410$	1.41201e9	1.01180
$411$	0	0
$412$	5.49097e9	3.86820
$413$	8.44113e7	0.0589624
$414$	0	0
$415$	−1.80177e9	−1.23746
$416$	1.14491e10	7.79734
$417$	0	0
$418$	−3.68929e8	−0.247073
$419$	1.06290e9	0.705902	0.352951	−	0.935642i	$-0.385178\pi$
$419$	1.06290e9	0.705902	0.352951	+	0.935642i	$0.385178\pi$
$420$	0	0
$421$	−1.46411e9	−0.956282	−0.478141	−	0.878283i	$-0.658689\pi$
$421$	−1.46411e9	−0.956282	−0.478141	+	0.878283i	$0.658689\pi$
$422$	−7.76617e8	−0.503052
$423$	0	0
$424$	7.36424e8	0.469189
$425$	2.78360e8	0.175892
$426$	0	0
$427$	3.47832e8	0.216208
$428$	−2.49548e9	−1.53851
$429$	0	0
$430$	8.68289e8	0.526653
$431$	−9.71394e8	−0.584420	−0.292210	−	0.956354i	$-0.594391\pi$
$431$	−9.71394e8	−0.584420	−0.292210	+	0.956354i	$0.594391\pi$
$432$	0	0
$433$	−1.99519e9	−1.18107	−0.590535	−	0.807012i	$-0.701083\pi$
$433$	−1.99519e9	−1.18107	−0.590535	+	0.807012i	$0.701083\pi$
$434$	2.20306e9	1.29363
$435$	0	0
$436$	−4.61325e9	−2.66566
$437$	−3.02946e9	−1.73652
$438$	0	0
$439$	−3.32793e9	−1.87737	−0.938683	−	0.344782i	$-0.887953\pi$
$439$	−3.32793e9	−1.87737	−0.938683	+	0.344782i	$0.887953\pi$
$440$	5.91426e8	0.330991
$441$	0	0
$442$	−7.30883e9	−4.02596
$443$	−6.61628e8	−0.361577	−0.180789	−	0.983522i	$-0.557865\pi$
$443$	−6.61628e8	−0.361577	−0.180789	+	0.983522i	$0.557865\pi$
$444$	0	0
$445$	−6.43791e8	−0.346326
$446$	4.45523e9	2.37793
$447$	0	0
$448$	4.24823e9	2.23221
$449$	−2.39627e9	−1.24932	−0.624661	−	0.780896i	$-0.714763\pi$
$449$	−2.39627e9	−1.24932	−0.624661	+	0.780896i	$0.714763\pi$
$450$	0	0
$451$	1.07782e8	0.0553259
$452$	6.92544e9	3.52747
$453$	0	0
$454$	−4.47637e9	−2.24507
$455$	−1.40646e9	−0.699985
$456$	0	0
$457$	5.13759e8	0.251798	0.125899	−	0.992043i	$-0.459818\pi$
$457$	5.13759e8	0.251798	0.125899	+	0.992043i	$0.459818\pi$
$458$	−1.99171e9	−0.968717
$459$	0	0
$460$	7.49668e9	3.59101
$461$	−1.60015e9	−0.760687	−0.380344	−	0.924845i	$-0.624194\pi$
$461$	−1.60015e9	−0.760687	−0.380344	+	0.924845i	$0.624194\pi$
$462$	0	0
$463$	7.65148e8	0.358271	0.179136	−	0.983824i	$-0.442670\pi$
$463$	7.65148e8	0.358271	0.179136	+	0.983824i	$0.442670\pi$
$464$	4.45280e9	2.06929
$465$	0	0
$466$	−4.92655e9	−2.25524
$467$	−2.99058e9	−1.35877	−0.679386	−	0.733782i	$-0.737754\pi$
$467$	−2.99058e9	−1.35877	−0.679386	+	0.733782i	$0.737754\pi$
$468$	0	0
$469$	1.38236e9	0.618752
$470$	−2.94176e9	−1.30697
$471$	0	0
$472$	1.07200e9	0.469245
$473$	6.62784e7	0.0287977
$474$	0	0
$475$	−4.24350e8	−0.181676
$476$	−3.72409e9	−1.58269
$477$	0	0
$478$	−2.95354e9	−1.23693
$479$	1.96100e9	0.815275	0.407637	−	0.913144i	$-0.366353\pi$
$479$	1.96100e9	0.815275	0.407637	+	0.913144i	$0.366353\pi$
$480$	0	0
$481$	4.67695e9	1.91626
$482$	1.15910e9	0.471473
$483$	0	0
$484$	−7.01294e9	−2.81152
$485$	−2.32190e9	−0.924161
$486$	0	0
$487$	−4.21150e9	−1.65229	−0.826143	−	0.563460i	$-0.809470\pi$
$487$	−4.21150e9	−1.65229	−0.826143	+	0.563460i	$0.809470\pi$
$488$	4.41739e9	1.72066
$489$	0	0
$490$	3.75522e9	1.44195
$491$	−1.16149e9	−0.442824	−0.221412	−	0.975180i	$-0.571066\pi$
$491$	−1.16149e9	−0.442824	−0.221412	+	0.975180i	$0.571066\pi$
$492$	0	0
$493$	−1.60441e9	−0.603047
$494$	1.11421e10	4.15835
$495$	0	0
$496$	1.67297e10	6.15607
$497$	1.67419e9	0.611725
$498$	0	0
$499$	2.79801e9	1.00808	0.504042	−	0.863679i	$-0.331846\pi$
$499$	2.79801e9	1.00808	0.504042	+	0.863679i	$0.331846\pi$
$500$	8.39763e9	3.00443
$501$	0	0
$502$	4.46883e9	1.57663
$503$	2.19333e9	0.768452	0.384226	−	0.923239i	$-0.374468\pi$
$503$	2.19333e9	0.768452	0.384226	+	0.923239i	$0.374468\pi$
$504$	0	0
$505$	−3.36037e8	−0.116109
$506$	7.73769e8	0.265512
$507$	0	0
$508$	1.38812e10	4.69791
$509$	1.63668e9	0.550112	0.275056	−	0.961428i	$-0.411304\pi$
$509$	1.63668e9	0.550112	0.275056	+	0.961428i	$0.411304\pi$
$510$	0	0
$511$	−1.82005e9	−0.603405
$512$	1.36750e10	4.50281
$513$	0	0
$514$	−4.95851e8	−0.161057
$515$	−3.90939e9	−1.26120
$516$	0	0
$517$	−2.24551e8	−0.0714659
$518$	3.22232e9	1.01863
$519$	0	0
$520$	−1.78618e10	−5.57074
$521$	8.21908e8	0.254619	0.127310	−	0.991863i	$-0.459366\pi$
$521$	8.21908e8	0.254619	0.127310	+	0.991863i	$0.459366\pi$
$522$	0	0
$523$	8.10572e8	0.247763	0.123881	−	0.992297i	$-0.460466\pi$
$523$	8.10572e8	0.247763	0.123881	+	0.992297i	$0.460466\pi$
$524$	−1.60128e10	−4.86192
$525$	0	0
$526$	−4.48763e9	−1.34452
$527$	−6.02797e9	−1.79405
$528$	0	0
$529$	2.94899e9	0.866120
$530$	−8.09346e8	−0.236139
$531$	0	0
$532$	5.67725e9	1.63474
$533$	−3.25514e9	−0.931160
$534$	0	0
$535$	1.77670e9	0.501621
$536$	1.75557e10	4.92425
$537$	0	0
$538$	−1.38516e10	−3.83497
$539$	2.86644e8	0.0788465
$540$	0	0
$541$	5.84572e9	1.58726	0.793629	−	0.608402i	$-0.208189\pi$
$541$	5.84572e9	1.58726	0.793629	+	0.608402i	$0.208189\pi$
$542$	−7.85196e9	−2.11827
$543$	0	0
$544$	−2.15837e10	−5.74816
$545$	3.28449e9	0.869120
$546$	0	0
$547$	−7.90478e8	−0.206507	−0.103253	−	0.994655i	$-0.532925\pi$
$547$	−7.90478e8	−0.206507	−0.103253	+	0.994655i	$0.532925\pi$
$548$	9.61686e9	2.49633
$549$	0	0
$550$	1.08385e8	0.0277780
$551$	2.44587e9	0.622877
$552$	0	0
$553$	−1.72414e9	−0.433544
$554$	−1.33178e10	−3.32773
$555$	0	0
$556$	−7.91779e9	−1.95363
$557$	−4.59101e9	−1.12568	−0.562840	−	0.826566i	$-0.690291\pi$
$557$	−4.59101e9	−1.12568	−0.562840	+	0.826566i	$0.690291\pi$
$558$	0	0
$559$	−2.00168e9	−0.484679
$560$	−7.35867e9	−1.77068
$561$	0	0
$562$	1.22947e10	2.92175
$563$	1.87013e9	0.441663	0.220832	−	0.975312i	$-0.429123\pi$
$563$	1.87013e9	0.441663	0.220832	+	0.975312i	$0.429123\pi$
$564$	0	0
$565$	−4.93069e9	−1.15011
$566$	4.11749e9	0.954497
$567$	0	0
$568$	2.12618e10	4.86833
$569$	3.29999e8	0.0750965	0.0375482	−	0.999295i	$-0.488045\pi$
$569$	3.29999e8	0.0750965	0.0375482	+	0.999295i	$0.488045\pi$
$570$	0	0
$571$	8.31103e9	1.86822	0.934111	−	0.356982i	$-0.116194\pi$
$571$	8.31103e9	1.86822	0.934111	+	0.356982i	$0.116194\pi$
$572$	−2.10464e9	−0.470210
$573$	0	0
$574$	−2.24273e9	−0.494977
$575$	8.90008e8	0.195234
$576$	0	0
$577$	−3.65097e9	−0.791212	−0.395606	−	0.918420i	$-0.629465\pi$
$577$	−3.65097e9	−0.791212	−0.395606	+	0.918420i	$0.629465\pi$
$578$	4.68177e9	1.00847
$579$	0	0
$580$	−6.05253e9	−1.28807
$581$	2.86179e9	0.605371
$582$	0	0
$583$	−6.17792e7	−0.0129123
$584$	−2.31142e10	−4.80212
$585$	0	0
$586$	−1.78712e10	−3.66870
$587$	−3.05418e9	−0.623248	−0.311624	−	0.950206i	$-0.600873\pi$
$587$	−3.05418e9	−0.623248	−0.311624	+	0.950206i	$0.600873\pi$
$588$	0	0
$589$	9.18944e9	1.85304
$590$	−1.17815e9	−0.236168
$591$	0	0
$592$	2.44699e10	4.84738
$593$	4.80493e9	0.946227	0.473113	−	0.881002i	$-0.343130\pi$
$593$	4.80493e9	0.946227	0.473113	+	0.881002i	$0.343130\pi$
$594$	0	0
$595$	2.65143e9	0.516026
$596$	−2.02613e9	−0.392018
$597$	0	0
$598$	−2.33687e10	−4.46870
$599$	−3.86139e9	−0.734090	−0.367045	−	0.930203i	$-0.619631\pi$
$599$	−3.86139e9	−0.734090	−0.367045	+	0.930203i	$0.619631\pi$
$600$	0	0
$601$	1.96007e9	0.368308	0.184154	−	0.982897i	$-0.441045\pi$
$601$	1.96007e9	0.368308	0.184154	+	0.982897i	$0.441045\pi$
$602$	−1.37912e9	−0.257641
$603$	0	0
$604$	−1.44691e10	−2.67186
$605$	4.99299e9	0.916678
$606$	0	0
$607$	−4.97911e9	−0.903632	−0.451816	−	0.892111i	$-0.649224\pi$
$607$	−4.97911e9	−0.903632	−0.451816	+	0.892111i	$0.649224\pi$
$608$	3.29036e10	5.93719
$609$	0	0
$610$	−4.85480e9	−0.865999
$611$	6.78171e9	1.20280
$612$	0	0
$613$	2.72401e9	0.477636	0.238818	−	0.971064i	$-0.423240\pi$
$613$	2.72401e9	0.477636	0.238818	+	0.971064i	$0.423240\pi$
$614$	−1.20149e10	−2.09474
$615$	0	0
$616$	−9.39375e8	−0.161922
$617$	−7.00273e9	−1.20024	−0.600122	−	0.799909i	$-0.704881\pi$
$617$	−7.00273e9	−1.20024	−0.600122	+	0.799909i	$0.704881\pi$
$618$	0	0
$619$	8.54432e9	1.44797	0.723986	−	0.689815i	$-0.242308\pi$
$619$	8.54432e9	1.44797	0.723986	+	0.689815i	$0.242308\pi$
$620$	−2.27401e10	−3.83197
$621$	0	0
$622$	4.95265e9	0.825223
$623$	1.02255e9	0.169424
$624$	0	0
$625$	−5.10655e9	−0.836657
$626$	−1.44835e10	−2.35974
$627$	0	0
$628$	−8.84062e9	−1.42437
$629$	−8.81687e9	−1.41266
$630$	0	0
$631$	9.15178e9	1.45012	0.725058	−	0.688688i	$-0.241813\pi$
$631$	9.15178e9	1.45012	0.725058	+	0.688688i	$0.241813\pi$
$632$	−2.18961e10	−3.45030
$633$	0	0
$634$	−8.47157e9	−1.32024
$635$	−9.88299e9	−1.53172
$636$	0	0
$637$	−8.65699e9	−1.32702
$638$	−6.24711e8	−0.0952373
$639$	0	0
$640$	−3.06183e10	−4.61690
$641$	−7.04336e9	−1.05627	−0.528137	−	0.849159i	$-0.677109\pi$
$641$	−7.04336e9	−1.05627	−0.528137	+	0.849159i	$0.677109\pi$
$642$	0	0
$643$	−6.27887e9	−0.931415	−0.465708	−	0.884939i	$-0.654200\pi$
$643$	−6.27887e9	−0.931415	−0.465708	+	0.884939i	$0.654200\pi$
$644$	−1.19071e10	−1.75674
$645$	0	0
$646$	−2.10048e10	−3.06552
$647$	4.23121e9	0.614185	0.307093	−	0.951680i	$-0.400644\pi$
$647$	4.23121e9	0.614185	0.307093	+	0.951680i	$0.400644\pi$
$648$	0	0
$649$	−8.99312e7	−0.0129138
$650$	−3.27337e9	−0.467517
$651$	0	0
$652$	5.91009e9	0.835080
$653$	−3.22584e9	−0.453364	−0.226682	−	0.973969i	$-0.572788\pi$
$653$	−3.22584e9	−0.453364	−0.226682	+	0.973969i	$0.572788\pi$
$654$	0	0
$655$	1.14006e10	1.58520
$656$	−1.70310e10	−2.35547
$657$	0	0
$658$	4.67247e9	0.639375
$659$	−1.14067e10	−1.55261	−0.776303	−	0.630360i	$-0.782907\pi$
$659$	−1.14067e10	−1.55261	−0.776303	+	0.630360i	$0.782907\pi$
$660$	0	0
$661$	−5.33531e9	−0.718546	−0.359273	−	0.933233i	$-0.616975\pi$
$661$	−5.33531e9	−0.718546	−0.359273	+	0.933233i	$0.616975\pi$
$662$	−2.64782e9	−0.354719
$663$	0	0
$664$	3.63441e10	4.81776
$665$	−4.04202e9	−0.532995
$666$	0	0
$667$	−5.12982e9	−0.669363
$668$	−7.28743e9	−0.945926
$669$	0	0
$670$	−1.92940e10	−2.47834
$671$	−3.70578e8	−0.0473534
$672$	0	0
$673$	−4.70152e9	−0.594547	−0.297273	−	0.954792i	$-0.596077\pi$
$673$	−4.70152e9	−0.594547	−0.297273	+	0.954792i	$0.596077\pi$
$674$	1.43828e10	1.80940
$675$	0	0
$676$	4.07565e10	5.07439
$677$	1.06147e10	1.31477	0.657384	−	0.753555i	$-0.271663\pi$
$677$	1.06147e10	1.31477	0.657384	+	0.753555i	$0.271663\pi$
$678$	0	0
$679$	3.68793e9	0.452104
$680$	3.36726e10	4.10672
$681$	0	0
$682$	−2.34712e9	−0.283328
$683$	−1.13835e10	−1.36711	−0.683556	−	0.729898i	$-0.739568\pi$
$683$	−1.13835e10	−1.36711	−0.683556	+	0.729898i	$0.739568\pi$
$684$	0	0
$685$	−6.84690e9	−0.813911
$686$	−1.34681e10	−1.59284
$687$	0	0
$688$	−1.04729e10	−1.22605
$689$	1.86580e9	0.217319
$690$	0	0
$691$	−1.20923e10	−1.39423	−0.697117	−	0.716958i	$-0.745534\pi$
$691$	−1.20923e10	−1.39423	−0.697117	+	0.716958i	$0.745534\pi$
$692$	−4.46380e10	−5.12075
$693$	0	0
$694$	2.94275e10	3.34191
$695$	5.63721e9	0.636968
$696$	0	0
$697$	6.13652e9	0.686447
$698$	−5.34435e8	−0.0594841
$699$	0	0
$700$	−1.66789e9	−0.183791
$701$	7.42546e9	0.814161	0.407080	−	0.913392i	$-0.366547\pi$
$701$	7.42546e9	0.814161	0.407080	+	0.913392i	$0.366547\pi$
$702$	0	0
$703$	1.34410e10	1.45911
$704$	−4.52603e9	−0.488892
$705$	0	0
$706$	2.55811e10	2.73592
$707$	5.33734e8	0.0568011
$708$	0	0
$709$	−1.74012e10	−1.83366	−0.916828	−	0.399283i	$-0.869259\pi$
$709$	−1.74012e10	−1.83366	−0.916828	+	0.399283i	$0.869259\pi$
$710$	−2.33671e10	−2.45020
$711$	0	0
$712$	1.29861e10	1.34834
$713$	−1.92734e10	−1.99134
$714$	0	0
$715$	1.49844e9	0.153309
$716$	1.65399e10	1.68398
$717$	0	0
$718$	2.96254e9	0.298695
$719$	1.32945e10	1.33389	0.666947	−	0.745105i	$-0.267601\pi$
$719$	1.32945e10	1.33389	0.666947	+	0.745105i	$0.267601\pi$
$720$	0	0
$721$	6.20937e9	0.616985
$722$	1.22051e10	1.20687
$723$	0	0
$724$	−5.20307e10	−5.09536
$725$	−7.18558e8	−0.0700291
$726$	0	0
$727$	−1.92881e9	−0.186174	−0.0930870	−	0.995658i	$-0.529673\pi$
$727$	−1.92881e9	−0.186174	−0.0930870	+	0.995658i	$0.529673\pi$
$728$	2.83702e10	2.72523
$729$	0	0
$730$	2.54029e10	2.41687
$731$	3.77353e9	0.357303
$732$	0	0
$733$	−1.50113e10	−1.40785	−0.703924	−	0.710276i	$-0.748570\pi$
$733$	−1.50113e10	−1.40785	−0.703924	+	0.710276i	$0.748570\pi$
$734$	1.54499e10	1.44208
$735$	0	0
$736$	−6.90101e10	−6.38029
$737$	−1.47276e9	−0.135517
$738$	0	0
$739$	1.34293e9	0.122404	0.0612022	−	0.998125i	$-0.480507\pi$
$739$	1.34293e9	0.122404	0.0612022	+	0.998125i	$0.480507\pi$
$740$	−3.32611e10	−3.01735
$741$	0	0
$742$	1.28550e9	0.115520
$743$	2.17047e10	1.94130	0.970650	−	0.240497i	$-0.0773104\pi$
$743$	2.17047e10	1.94130	0.970650	+	0.240497i	$0.0773104\pi$
$744$	0	0
$745$	1.44254e9	0.127815
$746$	−5.26723e8	−0.0464511
$747$	0	0
$748$	3.96762e9	0.346636
$749$	−2.82197e9	−0.245395
$750$	0	0
$751$	2.45348e9	0.211370	0.105685	−	0.994400i	$-0.466297\pi$
$751$	2.45348e9	0.211370	0.105685	+	0.994400i	$0.466297\pi$
$752$	3.54821e10	3.04262
$753$	0	0
$754$	1.88670e10	1.60289
$755$	1.03016e10	0.871143
$756$	0	0
$757$	9.08326e9	0.761038	0.380519	−	0.924773i	$-0.375745\pi$
$757$	9.08326e9	0.761038	0.380519	+	0.924773i	$0.375745\pi$
$758$	1.44393e10	1.20422
$759$	0	0
$760$	−5.13327e10	−4.24177
$761$	−2.38536e10	−1.96204	−0.981021	−	0.193902i	$-0.937885\pi$
$761$	−2.38536e10	−1.96204	−0.981021	+	0.193902i	$0.937885\pi$
$762$	0	0
$763$	−5.21682e9	−0.425177
$764$	−1.86133e10	−1.51007
$765$	0	0
$766$	−1.69863e10	−1.36552
$767$	2.71603e9	0.217345
$768$	0	0
$769$	1.44982e10	1.14967	0.574834	−	0.818270i	$-0.305067\pi$
$769$	1.44982e10	1.14967	0.574834	+	0.818270i	$0.305067\pi$
$770$	1.03239e9	0.0814943
$771$	0	0
$772$	3.60903e10	2.82313
$773$	1.48061e10	1.15296	0.576479	−	0.817112i	$-0.304426\pi$
$773$	1.48061e10	1.15296	0.576479	+	0.817112i	$0.304426\pi$
$774$	0	0
$775$	−2.69971e9	−0.208335
$776$	4.68358e10	3.59801
$777$	0	0
$778$	1.99970e10	1.52243
$779$	−9.35492e9	−0.709021
$780$	0	0
$781$	−1.78367e9	−0.133978
$782$	4.40542e10	3.29430
$783$	0	0
$784$	−4.52937e10	−3.35684
$785$	6.29424e9	0.464408
$786$	0	0
$787$	1.47489e10	1.07857	0.539286	−	0.842122i	$-0.318694\pi$
$787$	1.47489e10	1.07857	0.539286	+	0.842122i	$0.318694\pi$
$788$	4.87926e10	3.55232
$789$	0	0
$790$	2.40643e10	1.73651
$791$	7.83153e9	0.562638
$792$	0	0
$793$	1.11919e10	0.796979
$794$	−1.09147e10	−0.773818
$795$	0	0
$796$	−2.35287e10	−1.65349
$797$	−1.53056e10	−1.07090	−0.535448	−	0.844568i	$-0.679857\pi$
$797$	−1.53056e10	−1.07090	−0.535448	+	0.844568i	$0.679857\pi$
$798$	0	0
$799$	−1.27847e10	−0.886702
$800$	−9.66656e9	−0.667509
$801$	0	0
$802$	1.87330e10	1.28232
$803$	1.93906e9	0.132156
$804$	0	0
$805$	8.47751e9	0.572773
$806$	7.08857e10	4.76855
$807$	0	0
$808$	6.77830e9	0.452044
$809$	−2.54329e8	−0.0168879	−0.00844396	−	0.999964i	$-0.502688\pi$
$809$	−2.54329e8	−0.0168879	−0.00844396	+	0.999964i	$0.502688\pi$
$810$	0	0
$811$	1.23140e10	0.810637	0.405318	−	0.914176i	$-0.367161\pi$
$811$	1.23140e10	0.810637	0.405318	+	0.914176i	$0.367161\pi$
$812$	9.61336e9	0.630129
$813$	0	0
$814$	−3.43304e9	−0.223097
$815$	−4.20780e9	−0.272272
$816$	0	0
$817$	−5.75262e9	−0.369053
$818$	−3.21141e10	−2.05144
$819$	0	0
$820$	2.31496e10	1.46621
$821$	−5.18812e9	−0.327197	−0.163598	−	0.986527i	$-0.552310\pi$
$821$	−5.18812e9	−0.327197	−0.163598	+	0.986527i	$0.552310\pi$
$822$	0	0
$823$	−4.12489e9	−0.257937	−0.128968	−	0.991649i	$-0.541167\pi$
$823$	−4.12489e9	−0.257937	−0.128968	+	0.991649i	$0.541167\pi$
$824$	7.88576e10	4.91019
$825$	0	0
$826$	1.87129e9	0.115534
$827$	−5.89785e9	−0.362597	−0.181298	−	0.983428i	$-0.558030\pi$
$827$	−5.89785e9	−0.362597	−0.181298	+	0.983428i	$0.558030\pi$
$828$	0	0
$829$	−2.77208e10	−1.68991	−0.844957	−	0.534835i	$-0.820374\pi$
$829$	−2.77208e10	−1.68991	−0.844957	+	0.534835i	$0.820374\pi$
$830$	−3.99429e10	−2.42475
$831$	0	0
$832$	1.36691e11	8.22828
$833$	1.63200e10	0.978277
$834$	0	0
$835$	5.18842e9	0.308413
$836$	−6.04850e9	−0.358035
$837$	0	0
$838$	2.35632e10	1.38318
$839$	−1.84332e10	−1.07754	−0.538771	−	0.842452i	$-0.681111\pi$
$839$	−1.84332e10	−1.07754	−0.538771	+	0.842452i	$0.681111\pi$
$840$	0	0
$841$	−1.31083e10	−0.759904
$842$	−3.24574e10	−1.87379
$843$	0	0
$844$	−1.27325e10	−0.728977
$845$	−2.90174e10	−1.65447
$846$	0	0
$847$	−7.93047e9	−0.448443
$848$	9.76194e9	0.549731
$849$	0	0
$850$	6.17087e9	0.344652
$851$	−2.81904e10	−1.56801
$852$	0	0
$853$	−3.15892e10	−1.74268	−0.871339	−	0.490682i	$-0.836748\pi$
$853$	−3.15892e10	−1.74268	−0.871339	+	0.490682i	$0.836748\pi$
$854$	7.71099e9	0.423650
$855$	0	0
$856$	−3.58383e10	−1.95294
$857$	1.55096e10	0.841722	0.420861	−	0.907125i	$-0.361728\pi$
$857$	1.55096e10	0.841722	0.420861	+	0.907125i	$0.361728\pi$
$858$	0	0
$859$	−2.86456e10	−1.54199	−0.770997	−	0.636839i	$-0.780241\pi$
$859$	−2.86456e10	−1.54199	−0.770997	+	0.636839i	$0.780241\pi$
$860$	1.42354e10	0.763177
$861$	0	0
$862$	−2.15345e10	−1.14514
$863$	3.05356e10	1.61722	0.808609	−	0.588346i	$-0.200221\pi$
$863$	3.05356e10	1.61722	0.808609	+	0.588346i	$0.200221\pi$
$864$	0	0
$865$	3.17808e10	1.66959
$866$	−4.42307e10	−2.31425
$867$	0	0
$868$	3.61186e10	1.87462
$869$	1.83688e9	0.0949537
$870$	0	0
$871$	4.44790e10	2.28082
$872$	−6.62524e10	−3.38372
$873$	0	0
$874$	−6.71592e10	−3.40263
$875$	9.49633e9	0.479212
$876$	0	0
$877$	−1.42738e10	−0.714562	−0.357281	−	0.933997i	$-0.616296\pi$
$877$	−1.42738e10	−0.714562	−0.357281	+	0.933997i	$0.616296\pi$
$878$	−7.37759e10	−3.67861
$879$	0	0
$880$	7.83987e9	0.387810
$881$	5.85758e9	0.288604	0.144302	−	0.989534i	$-0.453906\pi$
$881$	5.85758e9	0.288604	0.144302	+	0.989534i	$0.453906\pi$
$882$	0	0
$883$	3.15376e10	1.54158	0.770790	−	0.637089i	$-0.219862\pi$
$883$	3.15376e10	1.54158	0.770790	+	0.637089i	$0.219862\pi$
$884$	−1.19827e11	−5.83405
$885$	0	0
$886$	−1.46674e10	−0.708494
$887$	−1.06379e10	−0.511829	−0.255914	−	0.966699i	$-0.582376\pi$
$887$	−1.06379e10	−0.511829	−0.255914	+	0.966699i	$0.582376\pi$
$888$	0	0
$889$	1.56974e10	0.749325
$890$	−1.42720e10	−0.678609
$891$	0	0
$892$	7.30426e10	3.44587
$893$	1.94899e10	0.915861
$894$	0	0
$895$	−1.17759e10	−0.549052
$896$	4.86316e10	2.25861
$897$	0	0
$898$	−5.31222e10	−2.44799
$899$	1.55606e10	0.714278
$900$	0	0
$901$	−3.51737e9	−0.160207
$902$	2.38939e9	0.108408
$903$	0	0
$904$	9.94585e10	4.47767
$905$	3.70442e10	1.66131
$906$	0	0
$907$	−1.21567e10	−0.540993	−0.270497	−	0.962721i	$-0.587188\pi$
$907$	−1.21567e10	−0.540993	−0.270497	+	0.962721i	$0.587188\pi$
$908$	−7.33891e10	−3.25335
$909$	0	0
$910$	−3.11795e10	−1.37159
$911$	1.79794e10	0.787881	0.393941	−	0.919136i	$-0.371112\pi$
$911$	1.79794e10	0.787881	0.393941	+	0.919136i	$0.371112\pi$
$912$	0	0
$913$	−3.04893e9	−0.132587
$914$	1.13894e10	0.493387
$915$	0	0
$916$	−3.26537e10	−1.40378
$917$	−1.81078e10	−0.775486
$918$	0	0
$919$	3.12747e10	1.32919	0.664597	−	0.747202i	$-0.268603\pi$
$919$	3.12747e10	1.32919	0.664597	+	0.747202i	$0.268603\pi$
$920$	1.07662e11	4.55834
$921$	0	0
$922$	−3.54731e10	−1.49053
$923$	5.38688e10	2.25492
$924$	0	0
$925$	−3.94876e9	−0.164046
$926$	1.69623e10	0.702016
$927$	0	0
$928$	5.57161e10	2.28856
$929$	4.19833e9	0.171799	0.0858997	−	0.996304i	$-0.472624\pi$
$929$	4.19833e9	0.171799	0.0858997	+	0.996304i	$0.472624\pi$
$930$	0	0
$931$	−2.48792e10	−1.01045
$932$	−8.07697e10	−3.26808
$933$	0	0
$934$	−6.62972e10	−2.66245
$935$	−2.82482e9	−0.113019
$936$	0	0
$937$	−4.93627e10	−1.96024	−0.980122	−	0.198393i	$-0.936428\pi$
$937$	−4.93627e10	−1.96024	−0.980122	+	0.198393i	$0.936428\pi$
$938$	3.06451e10	1.21242
$939$	0	0
$940$	−4.82296e10	−1.89394
$941$	−5.81164e9	−0.227371	−0.113685	−	0.993517i	$-0.536266\pi$
$941$	−5.81164e9	−0.227371	−0.113685	+	0.993517i	$0.536266\pi$
$942$	0	0
$943$	1.96205e10	0.761936
$944$	1.42103e10	0.549797
$945$	0	0
$946$	1.46931e9	0.0564278
$947$	3.48866e10	1.33485	0.667427	−	0.744676i	$-0.267396\pi$
$947$	3.48866e10	1.33485	0.667427	+	0.744676i	$0.267396\pi$
$948$	0	0
$949$	−5.85619e10	−2.22425
$950$	−9.40729e9	−0.355985
$951$	0	0
$952$	−5.34829e10	−2.00903
$953$	−8.20632e9	−0.307131	−0.153565	−	0.988138i	$-0.549076\pi$
$953$	−8.20632e9	−0.307131	−0.153565	+	0.988138i	$0.549076\pi$
$954$	0	0
$955$	1.32521e10	0.492349
$956$	−4.84226e10	−1.79244
$957$	0	0
$958$	4.34729e10	1.59749
$959$	1.08751e10	0.398169
$960$	0	0
$961$	3.09505e10	1.12496
$962$	1.03682e11	3.75482
$963$	0	0
$964$	1.90032e10	0.683216
$965$	−2.56952e10	−0.920462
$966$	0	0
$967$	1.16190e10	0.413213	0.206607	−	0.978424i	$-0.433758\pi$
$967$	1.16190e10	0.413213	0.206607	+	0.978424i	$0.433758\pi$
$968$	−1.00715e11	−3.56887
$969$	0	0
$970$	−5.14735e10	−1.81085
$971$	4.87190e9	0.170778	0.0853889	−	0.996348i	$-0.472787\pi$
$971$	4.87190e9	0.170778	0.0853889	+	0.996348i	$0.472787\pi$
$972$	0	0
$973$	−8.95371e9	−0.311607
$974$	−9.33634e10	−3.23758
$975$	0	0
$976$	5.85563e10	2.01604
$977$	2.06779e10	0.709375	0.354688	−	0.934985i	$-0.384587\pi$
$977$	2.06779e10	0.709375	0.354688	+	0.934985i	$0.384587\pi$
$978$	0	0
$979$	−1.08941e9	−0.0371068
$980$	6.15660e10	2.08954
$981$	0	0
$982$	−2.57487e10	−0.867692
$983$	1.54356e8	0.00518306	0.00259153	−	0.999997i	$-0.499175\pi$
$983$	1.54356e8	0.00518306	0.00259153	+	0.999997i	$0.499175\pi$
$984$	0	0
$985$	−3.47388e10	−1.15821
$986$	−3.55676e10	−1.18164
$987$	0	0
$988$	1.82672e11	6.02590
$989$	1.20652e10	0.396596
$990$	0	0
$991$	−2.23061e10	−0.728057	−0.364029	−	0.931388i	$-0.618599\pi$
$991$	−2.23061e10	−0.728057	−0.364029	+	0.931388i	$0.618599\pi$
$992$	2.09332e11	6.80841
$993$	0	0
$994$	3.71145e10	1.19865
$995$	1.67517e10	0.539110
$996$	0	0
$997$	3.27229e10	1.04573	0.522865	−	0.852416i	$-0.324863\pi$
$997$	3.27229e10	1.04573	0.522865	+	0.852416i	$0.324863\pi$
$998$	6.20281e10	1.97529
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.c.1.17		17
3.2	odd	2		177.8.a.c.1.1	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.1	✓	17	3.2	odd	2
531.8.a.c.1.17		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)

\(f(q)\)	\(=\)	\(q+22.1687 q^{2} +363.451 q^{4} -258.765 q^{5} +411.003 q^{7} +5219.64 q^{8} +O(q^{10})\)	\(q+22.1687 q^{2} +363.451 q^{4} -258.765 q^{5} +411.003 q^{7} +5219.64 q^{8} -5736.49 q^{10} -437.879 q^{11} +13224.5 q^{13} +9111.39 q^{14} +69190.8 q^{16} -24930.4 q^{17} +38005.6 q^{19} -94048.5 q^{20} -9707.20 q^{22} -79710.8 q^{23} -11165.5 q^{25} +293169. q^{26} +149379. q^{28} +64355.4 q^{29} +241791. q^{31} +865756. q^{32} -552675. q^{34} -106353. q^{35} +353659. q^{37} +842535. q^{38} -1.35066e6 q^{40} -246146. q^{41} -151362. q^{43} -159147. q^{44} -1.76708e6 q^{46} +512816. q^{47} -654620. q^{49} -247524. q^{50} +4.80644e6 q^{52} +141087. q^{53} +113308. q^{55} +2.14528e6 q^{56} +1.42668e6 q^{58} +205379. q^{59} +846302. q^{61} +5.36020e6 q^{62} +1.03362e7 q^{64} -3.42203e6 q^{65} +3.36339e6 q^{67} -9.06099e6 q^{68} -2.35771e6 q^{70} +4.07342e6 q^{71} -4.42831e6 q^{73} +7.84015e6 q^{74} +1.38132e7 q^{76} -179969. q^{77} -4.19495e6 q^{79} -1.79042e7 q^{80} -5.45672e6 q^{82} +6.96295e6 q^{83} +6.45114e6 q^{85} -3.35550e6 q^{86} -2.28557e6 q^{88} +2.48793e6 q^{89} +5.43529e6 q^{91} -2.89710e7 q^{92} +1.13685e7 q^{94} -9.83454e6 q^{95} +8.97300e6 q^{97} -1.45121e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 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

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