LMFDB - Embedded newform 5929.2.a.bt.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.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:	$47.3433033584$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 10x^{5} + 35x^{4} - 30x^{3} - 30x^{2} + 30x - 5 $ x^8 - x^7 - 11x^6 + 10x^5 + 35x^4 - 30x^3 - 30x^2 + 30x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.11447$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.11447 q^{2} +2.85882 q^{3} -0.757964 q^{4} -3.45608 q^{5} +3.18606 q^{6} -3.07366 q^{8} +5.17284 q^{9} +O(q^{10})$	\(q+1.11447 q^{2} +2.85882 q^{3} -0.757964 q^{4} -3.45608 q^{5} +3.18606 q^{6} -3.07366 q^{8} +5.17284 q^{9} -3.85168 q^{10} -2.16688 q^{12} +2.05965 q^{13} -9.88030 q^{15} -1.90956 q^{16} -1.93373 q^{17} +5.76496 q^{18} -1.62296 q^{19} +2.61958 q^{20} -0.807136 q^{23} -8.78703 q^{24} +6.94447 q^{25} +2.29541 q^{26} +6.21176 q^{27} +7.97368 q^{29} -11.0113 q^{30} -0.788420 q^{31} +4.01918 q^{32} -2.15508 q^{34} -3.92083 q^{36} +10.0618 q^{37} -1.80873 q^{38} +5.88817 q^{39} +10.6228 q^{40} +2.12613 q^{41} +3.08043 q^{43} -17.8777 q^{45} -0.899526 q^{46} -7.56632 q^{47} -5.45909 q^{48} +7.73938 q^{50} -5.52818 q^{51} -1.56114 q^{52} +10.8224 q^{53} +6.92280 q^{54} -4.63975 q^{57} +8.88640 q^{58} +3.29664 q^{59} +7.48891 q^{60} +1.07663 q^{61} -0.878667 q^{62} +8.29836 q^{64} -7.11832 q^{65} +2.40314 q^{67} +1.46570 q^{68} -2.30745 q^{69} -3.18859 q^{71} -15.8995 q^{72} -1.22628 q^{73} +11.2135 q^{74} +19.8530 q^{75} +1.23015 q^{76} +6.56217 q^{78} -9.48182 q^{79} +6.59959 q^{80} +2.23976 q^{81} +2.36950 q^{82} +16.0694 q^{83} +6.68312 q^{85} +3.43303 q^{86} +22.7953 q^{87} +4.43830 q^{89} -19.9241 q^{90} +0.611780 q^{92} -2.25395 q^{93} -8.43241 q^{94} +5.60908 q^{95} +11.4901 q^{96} -6.46807 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} + 7 q^{4} - 10 q^{5} + q^{6} + 14 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 + 7 * q^4 - 10 * q^5 + q^6 + 14 * q^9	$ 8 q + q^{2} - 4 q^{3} + 7 q^{4} - 10 q^{5} + q^{6} + 14 q^{9} - 6 q^{10} - 9 q^{12} + 6 q^{13} + 11 q^{15} + q^{16} + 5 q^{17} + 8 q^{18} + 13 q^{19} - 23 q^{20} + 16 q^{23} + 10 q^{24} + 16 q^{25} + 6 q^{26} - 10 q^{27} + 9 q^{29} - 36 q^{30} - 9 q^{31} + 16 q^{32} + 12 q^{34} - 14 q^{36} + 7 q^{37} + 10 q^{38} + 13 q^{39} - 5 q^{40} + 10 q^{41} - 4 q^{43} - 35 q^{45} + 4 q^{46} - 16 q^{47} + 3 q^{48} + 6 q^{50} + 13 q^{51} + 41 q^{52} + 37 q^{53} - 30 q^{54} + 2 q^{57} - 15 q^{58} - q^{59} + 5 q^{60} - 19 q^{61} + 18 q^{62} - 4 q^{64} - 4 q^{65} - 19 q^{67} - 9 q^{68} - 20 q^{69} + 13 q^{71} - 35 q^{72} + 25 q^{73} + 33 q^{74} + 13 q^{75} - 26 q^{76} - 29 q^{78} - 4 q^{80} + 8 q^{81} + 13 q^{82} + 25 q^{83} + 3 q^{85} + 4 q^{86} + 36 q^{87} - 37 q^{89} + 2 q^{90} + 35 q^{92} + 21 q^{93} + 42 q^{94} + 21 q^{95} + 6 q^{96} - 15 q^{97}+O(q^{100}) $ 8 * q + q^2 - 4 * q^3 + 7 * q^4 - 10 * q^5 + q^6 + 14 * q^9 - 6 * q^10 - 9 * q^12 + 6 * q^13 + 11 * q^15 + q^16 + 5 * q^17 + 8 * q^18 + 13 * q^19 - 23 * q^20 + 16 * q^23 + 10 * q^24 + 16 * q^25 + 6 * q^26 - 10 * q^27 + 9 * q^29 - 36 * q^30 - 9 * q^31 + 16 * q^32 + 12 * q^34 - 14 * q^36 + 7 * q^37 + 10 * q^38 + 13 * q^39 - 5 * q^40 + 10 * q^41 - 4 * q^43 - 35 * q^45 + 4 * q^46 - 16 * q^47 + 3 * q^48 + 6 * q^50 + 13 * q^51 + 41 * q^52 + 37 * q^53 - 30 * q^54 + 2 * q^57 - 15 * q^58 - q^59 + 5 * q^60 - 19 * q^61 + 18 * q^62 - 4 * q^64 - 4 * q^65 - 19 * q^67 - 9 * q^68 - 20 * q^69 + 13 * q^71 - 35 * q^72 + 25 * q^73 + 33 * q^74 + 13 * q^75 - 26 * q^76 - 29 * q^78 - 4 * q^80 + 8 * q^81 + 13 * q^82 + 25 * q^83 + 3 * q^85 + 4 * q^86 + 36 * q^87 - 37 * q^89 + 2 * q^90 + 35 * q^92 + 21 * q^93 + 42 * q^94 + 21 * q^95 + 6 * q^96 - 15 * q^97

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 $

$2$	1.11447	0.788047	0.394023	−	0.919100i	$-0.371083\pi$
$2$	1.11447	0.788047	0.394023	+	0.919100i	$0.371083\pi$
$3$	2.85882	1.65054	0.825270	−	0.564739i	$-0.191023\pi$
$3$	2.85882	1.65054	0.825270	+	0.564739i	$0.191023\pi$
$4$	−0.757964	−0.378982
$5$	−3.45608	−1.54561	−0.772803	−	0.634647i	$-0.781146\pi$
$5$	−3.45608	−1.54561	−0.772803	+	0.634647i	$0.781146\pi$
$6$	3.18606	1.30070
$7$	0	0
$7$	0	0
$8$	−3.07366	−1.08670
$9$	5.17284	1.72428
$10$	−3.85168	−1.21801
$11$	0	0
$11$	0	0
$12$	−2.16688	−0.625525
$13$	2.05965	0.571245	0.285622	−	0.958342i	$-0.407800\pi$
$13$	2.05965	0.571245	0.285622	+	0.958342i	$0.407800\pi$
$14$	0	0
$15$	−9.88030	−2.55108
$16$	−1.90956	−0.477390
$17$	−1.93373	−0.468998	−0.234499	−	0.972116i	$-0.575345\pi$
$17$	−1.93373	−0.468998	−0.234499	+	0.972116i	$0.575345\pi$
$18$	5.76496	1.35881
$19$	−1.62296	−0.372333	−0.186166	−	0.982518i	$-0.559606\pi$
$19$	−1.62296	−0.372333	−0.186166	+	0.982518i	$0.559606\pi$
$20$	2.61958	0.585757
$21$	0	0
$22$	0	0
$23$	−0.807136	−0.168299	−0.0841497	−	0.996453i	$-0.526817\pi$
$23$	−0.807136	−0.168299	−0.0841497	+	0.996453i	$0.526817\pi$
$24$	−8.78703	−1.79365
$25$	6.94447	1.38889
$26$	2.29541	0.450168
$27$	6.21176	1.19545
$28$	0	0
$29$	7.97368	1.48067	0.740337	−	0.672235i	$-0.234666\pi$
$29$	7.97368	1.48067	0.740337	+	0.672235i	$0.234666\pi$
$30$	−11.0113	−2.01037
$31$	−0.788420	−0.141604	−0.0708022	−	0.997490i	$-0.522556\pi$
$31$	−0.788420	−0.141604	−0.0708022	+	0.997490i	$0.522556\pi$
$32$	4.01918	0.710497
$33$	0	0
$34$	−2.15508	−0.369592
$35$	0	0
$36$	−3.92083	−0.653471
$37$	10.0618	1.65414	0.827072	−	0.562096i	$-0.190005\pi$
$37$	10.0618	1.65414	0.827072	+	0.562096i	$0.190005\pi$
$38$	−1.80873	−0.293415
$39$	5.88817	0.942862
$40$	10.6228	1.67961
$41$	2.12613	0.332046	0.166023	−	0.986122i	$-0.446907\pi$
$41$	2.12613	0.332046	0.166023	+	0.986122i	$0.446907\pi$
$42$	0	0
$43$	3.08043	0.469761	0.234880	−	0.972024i	$-0.424530\pi$
$43$	3.08043	0.469761	0.234880	+	0.972024i	$0.424530\pi$
$44$	0	0
$45$	−17.8777	−2.66506
$46$	−0.899526	−0.132628
$47$	−7.56632	−1.10366	−0.551831	−	0.833956i	$-0.686070\pi$
$47$	−7.56632	−1.10366	−0.551831	+	0.833956i	$0.686070\pi$
$48$	−5.45909	−0.787952
$49$	0	0
$50$	7.73938	1.09451
$51$	−5.52818	−0.774100
$52$	−1.56114	−0.216492
$53$	10.8224	1.48658	0.743289	−	0.668971i	$-0.233265\pi$
$53$	10.8224	1.48658	0.743289	+	0.668971i	$0.233265\pi$
$54$	6.92280	0.942073
$55$	0	0
$56$	0	0
$57$	−4.63975	−0.614550
$58$	8.88640	1.16684
$59$	3.29664	0.429186	0.214593	−	0.976704i	$-0.431158\pi$
$59$	3.29664	0.429186	0.214593	+	0.976704i	$0.431158\pi$
$60$	7.48891	0.966814
$61$	1.07663	0.137848	0.0689240	−	0.997622i	$-0.478043\pi$
$61$	1.07663	0.137848	0.0689240	+	0.997622i	$0.478043\pi$
$62$	−0.878667	−0.111591
$63$	0	0
$64$	8.29836	1.03729
$65$	−7.11832	−0.882919
$66$	0	0
$67$	2.40314	0.293590	0.146795	−	0.989167i	$-0.453104\pi$
$67$	2.40314	0.293590	0.146795	+	0.989167i	$0.453104\pi$
$68$	1.46570	0.177742
$69$	−2.30745	−0.277785
$70$	0	0
$71$	−3.18859	−0.378417	−0.189208	−	0.981937i	$-0.560592\pi$
$71$	−3.18859	−0.378417	−0.189208	+	0.981937i	$0.560592\pi$
$72$	−15.8995	−1.87378
$73$	−1.22628	−0.143525	−0.0717624	−	0.997422i	$-0.522862\pi$
$73$	−1.22628	−0.143525	−0.0717624	+	0.997422i	$0.522862\pi$
$74$	11.2135	1.30354
$75$	19.8530	2.29243
$76$	1.23015	0.141107
$77$	0	0
$78$	6.56217	0.743020
$79$	−9.48182	−1.06679	−0.533394	−	0.845867i	$-0.679084\pi$
$79$	−9.48182	−1.06679	−0.533394	+	0.845867i	$0.679084\pi$
$80$	6.59959	0.737857
$81$	2.23976	0.248862
$82$	2.36950	0.261668
$83$	16.0694	1.76385	0.881923	−	0.471394i	$-0.156249\pi$
$83$	16.0694	1.76385	0.881923	+	0.471394i	$0.156249\pi$
$84$	0	0
$85$	6.68312	0.724886
$86$	3.43303	0.370193
$87$	22.7953	2.44391
$88$	0	0
$89$	4.43830	0.470459	0.235230	−	0.971940i	$-0.424416\pi$
$89$	4.43830	0.470459	0.235230	+	0.971940i	$0.424416\pi$
$90$	−19.9241	−2.10019
$91$	0	0
$92$	0.611780	0.0637825
$93$	−2.25395	−0.233724
$94$	−8.43241	−0.869737
$95$	5.60908	0.575479
$96$	11.4901	1.17270
$97$	−6.46807	−0.656733	−0.328366	−	0.944550i	$-0.606498\pi$
$97$	−6.46807	−0.656733	−0.328366	+	0.944550i	$0.606498\pi$
$98$	0	0
$99$	0	0
$100$	−5.26366	−0.526366
$101$	15.4449	1.53682	0.768412	−	0.639955i	$-0.221047\pi$
$101$	15.4449	1.53682	0.768412	+	0.639955i	$0.221047\pi$
$102$	−6.16097	−0.610027
$103$	−8.90812	−0.877743	−0.438872	−	0.898550i	$-0.644622\pi$
$103$	−8.90812	−0.877743	−0.438872	+	0.898550i	$0.644622\pi$
$104$	−6.33067	−0.620773
$105$	0	0
$106$	12.0613	1.17149
$107$	3.51219	0.339536	0.169768	−	0.985484i	$-0.445698\pi$
$107$	3.51219	0.339536	0.169768	+	0.985484i	$0.445698\pi$
$108$	−4.70829	−0.453055
$109$	3.87655	0.371306	0.185653	−	0.982615i	$-0.440560\pi$
$109$	3.87655	0.371306	0.185653	+	0.982615i	$0.440560\pi$
$110$	0	0
$111$	28.7648	2.73023
$112$	0	0
$113$	10.6539	1.00224	0.501118	−	0.865379i	$-0.332922\pi$
$113$	10.6539	1.00224	0.501118	+	0.865379i	$0.332922\pi$
$114$	−5.17084	−0.484294
$115$	2.78952	0.260124
$116$	−6.04376	−0.561149
$117$	10.6543	0.984986
$118$	3.67399	0.338218
$119$	0	0
$120$	30.3687	2.77227
$121$	0	0
$122$	1.19987	0.108631
$123$	6.07823	0.548056
$124$	0.597594	0.0536655
$125$	−6.72025	−0.601078
$126$	0	0
$127$	19.4509	1.72599	0.862994	−	0.505214i	$-0.168586\pi$
$127$	19.4509	1.72599	0.862994	+	0.505214i	$0.168586\pi$
$128$	1.20989	0.106941
$129$	8.80638	0.775359
$130$	−7.93313	−0.695782
$131$	−5.11284	−0.446711	−0.223355	−	0.974737i	$-0.571701\pi$
$131$	−5.11284	−0.446711	−0.223355	+	0.974737i	$0.571701\pi$
$132$	0	0
$133$	0	0
$134$	2.67822	0.231363
$135$	−21.4683	−1.84770
$136$	5.94362	0.509661
$137$	9.10052	0.777510	0.388755	−	0.921341i	$-0.372905\pi$
$137$	9.10052	0.777510	0.388755	+	0.921341i	$0.372905\pi$
$138$	−2.57158	−0.218907
$139$	13.0166	1.10405	0.552026	−	0.833827i	$-0.313855\pi$
$139$	13.0166	1.10405	0.552026	+	0.833827i	$0.313855\pi$
$140$	0	0
$141$	−21.6307	−1.82164
$142$	−3.55358	−0.298210
$143$	0	0
$144$	−9.87786	−0.823155
$145$	−27.5577	−2.28854
$146$	−1.36664	−0.113104
$147$	0	0
$148$	−7.62646	−0.626891
$149$	−3.14650	−0.257771	−0.128886	−	0.991659i	$-0.541140\pi$
$149$	−3.14650	−0.257771	−0.128886	+	0.991659i	$0.541140\pi$
$150$	22.1255	1.80654
$151$	2.86696	0.233310	0.116655	−	0.993172i	$-0.462783\pi$
$151$	2.86696	0.233310	0.116655	+	0.993172i	$0.462783\pi$
$152$	4.98843	0.404615
$153$	−10.0029	−0.808684
$154$	0	0
$155$	2.72484	0.218864
$156$	−4.46302	−0.357328
$157$	21.4895	1.71505	0.857524	−	0.514443i	$-0.172001\pi$
$157$	21.4895	1.71505	0.857524	+	0.514443i	$0.172001\pi$
$158$	−10.5672	−0.840679
$159$	30.9394	2.45365
$160$	−13.8906	−1.09815
$161$	0	0
$162$	2.49614	0.196115
$163$	−8.22245	−0.644032	−0.322016	−	0.946734i	$-0.604361\pi$
$163$	−8.22245	−0.644032	−0.322016	+	0.946734i	$0.604361\pi$
$164$	−1.61153	−0.125840
$165$	0	0
$166$	17.9088	1.38999
$167$	21.7086	1.67986	0.839930	−	0.542695i	$-0.182596\pi$
$167$	21.7086	1.67986	0.839930	+	0.542695i	$0.182596\pi$
$168$	0	0
$169$	−8.75783	−0.673679
$170$	7.44811	0.571244
$171$	−8.39531	−0.642006
$172$	−2.33485	−0.178031
$173$	8.04563	0.611698	0.305849	−	0.952080i	$-0.401060\pi$
$173$	8.04563	0.611698	0.305849	+	0.952080i	$0.401060\pi$
$174$	25.4046	1.92592
$175$	0	0
$176$	0	0
$177$	9.42449	0.708388
$178$	4.94634	0.370744
$179$	−3.62091	−0.270640	−0.135320	−	0.990802i	$-0.543206\pi$
$179$	−3.62091	−0.270640	−0.135320	+	0.990802i	$0.543206\pi$
$180$	13.5507	1.01001
$181$	−15.8179	−1.17574	−0.587868	−	0.808957i	$-0.700033\pi$
$181$	−15.8179	−1.17574	−0.587868	+	0.808957i	$0.700033\pi$
$182$	0	0
$183$	3.07788	0.227524
$184$	2.48086	0.182891
$185$	−34.7743	−2.55665
$186$	−2.51195	−0.184185
$187$	0	0
$188$	5.73500	0.418268
$189$	0	0
$190$	6.25113	0.453504
$191$	0.429081	0.0310472	0.0155236	−	0.999880i	$-0.495058\pi$
$191$	0.429081	0.0310472	0.0155236	+	0.999880i	$0.495058\pi$
$192$	23.7235	1.71210
$193$	−15.1748	−1.09231	−0.546154	−	0.837685i	$-0.683909\pi$
$193$	−15.1748	−1.09231	−0.546154	+	0.837685i	$0.683909\pi$
$194$	−7.20845	−0.517536
$195$	−20.3500	−1.45729
$196$	0	0
$197$	−20.8082	−1.48252	−0.741262	−	0.671216i	$-0.765772\pi$
$197$	−20.8082	−1.48252	−0.741262	+	0.671216i	$0.765772\pi$
$198$	0	0
$199$	−8.44567	−0.598698	−0.299349	−	0.954144i	$-0.596769\pi$
$199$	−8.44567	−0.598698	−0.299349	+	0.954144i	$0.596769\pi$
$200$	−21.3449	−1.50932
$201$	6.87014	0.484582
$202$	17.2128	1.21109
$203$	0	0
$204$	4.19016	0.293370
$205$	−7.34808	−0.513212
$206$	−9.92781	−0.691703
$207$	−4.17518	−0.290195
$208$	−3.93303	−0.272707
$209$	0	0
$210$	0	0
$211$	−9.85927	−0.678740	−0.339370	−	0.940653i	$-0.610214\pi$
$211$	−9.85927	−0.678740	−0.339370	+	0.940653i	$0.610214\pi$
$212$	−8.20303	−0.563386
$213$	−9.11561	−0.624592
$214$	3.91422	0.267570
$215$	−10.6462	−0.726065
$216$	−19.0928	−1.29910
$217$	0	0
$218$	4.32028	0.292606
$219$	−3.50570	−0.236893
$220$	0	0
$221$	−3.98281	−0.267913
$222$	32.0574	2.15155
$223$	−17.3959	−1.16491	−0.582457	−	0.812861i	$-0.697909\pi$
$223$	−17.3959	−1.16491	−0.582457	+	0.812861i	$0.697909\pi$
$224$	0	0
$225$	35.9227	2.39484
$226$	11.8734	0.789809
$227$	12.6315	0.838381	0.419190	−	0.907898i	$-0.362314\pi$
$227$	12.6315	0.838381	0.419190	+	0.907898i	$0.362314\pi$
$228$	3.51676	0.232903
$229$	−4.57341	−0.302220	−0.151110	−	0.988517i	$-0.548285\pi$
$229$	−4.57341	−0.302220	−0.151110	+	0.988517i	$0.548285\pi$
$230$	3.10883	0.204990
$231$	0	0
$232$	−24.5084	−1.60905
$233$	23.8569	1.56292	0.781458	−	0.623957i	$-0.214476\pi$
$233$	23.8569	1.56292	0.781458	+	0.623957i	$0.214476\pi$
$234$	11.8738	0.776215
$235$	26.1498	1.70582
$236$	−2.49873	−0.162654
$237$	−27.1068	−1.76078
$238$	0	0
$239$	8.83814	0.571692	0.285846	−	0.958276i	$-0.407725\pi$
$239$	8.83814	0.571692	0.285846	+	0.958276i	$0.407725\pi$
$240$	18.8670	1.21786
$241$	−18.9464	−1.22045	−0.610224	−	0.792229i	$-0.708921\pi$
$241$	−18.9464	−1.22045	−0.610224	+	0.792229i	$0.708921\pi$
$242$	0	0
$243$	−12.2322	−0.784696
$244$	−0.816045	−0.0522419
$245$	0	0
$246$	6.77398	0.431893
$247$	−3.34273	−0.212693
$248$	2.42333	0.153882
$249$	45.9395	2.91130
$250$	−7.48950	−0.473678
$251$	2.86691	0.180958	0.0904790	−	0.995898i	$-0.471160\pi$
$251$	2.86691	0.180958	0.0904790	+	0.995898i	$0.471160\pi$
$252$	0	0
$253$	0	0
$254$	21.6774	1.36016
$255$	19.1058	1.19645
$256$	−15.2483	−0.953021
$257$	−22.4159	−1.39826	−0.699132	−	0.714993i	$-0.746430\pi$
$257$	−22.4159	−1.39826	−0.699132	+	0.714993i	$0.746430\pi$
$258$	9.81442	0.611019
$259$	0	0
$260$	5.39543	0.334611
$261$	41.2466	2.55310
$262$	−5.69808	−0.352029
$263$	0.990706	0.0610895	0.0305448	−	0.999533i	$-0.490276\pi$
$263$	0.990706	0.0610895	0.0305448	+	0.999533i	$0.490276\pi$
$264$	0	0
$265$	−37.4032	−2.29766
$266$	0	0
$267$	12.6883	0.776511
$268$	−1.82149	−0.111265
$269$	7.19036	0.438404	0.219202	−	0.975679i	$-0.429655\pi$
$269$	7.19036	0.438404	0.219202	+	0.975679i	$0.429655\pi$
$270$	−23.9257	−1.45607
$271$	27.1643	1.65011	0.825056	−	0.565050i	$-0.191143\pi$
$271$	27.1643	1.65011	0.825056	+	0.565050i	$0.191143\pi$
$272$	3.69257	0.223895
$273$	0	0
$274$	10.1422	0.612714
$275$	0	0
$276$	1.74897	0.105275
$277$	20.9856	1.26090	0.630451	−	0.776229i	$-0.282870\pi$
$277$	20.9856	1.26090	0.630451	+	0.776229i	$0.282870\pi$
$278$	14.5065	0.870045
$279$	−4.07837	−0.244166
$280$	0	0
$281$	−28.1580	−1.67977	−0.839883	−	0.542768i	$-0.817376\pi$
$281$	−28.1580	−1.67977	−0.839883	+	0.542768i	$0.817376\pi$
$282$	−24.1067	−1.43553
$283$	26.1917	1.55694	0.778469	−	0.627684i	$-0.215997\pi$
$283$	26.1917	1.55694	0.778469	+	0.627684i	$0.215997\pi$
$284$	2.41684	0.143413
$285$	16.0353	0.949851
$286$	0	0
$287$	0	0
$288$	20.7906	1.22510
$289$	−13.2607	−0.780041
$290$	−30.7121	−1.80348
$291$	−18.4910	−1.08396
$292$	0.929473	0.0543933
$293$	4.46385	0.260781	0.130391	−	0.991463i	$-0.458377\pi$
$293$	4.46385	0.260781	0.130391	+	0.991463i	$0.458377\pi$
$294$	0	0
$295$	−11.3934	−0.663351
$296$	−30.9264	−1.79756
$297$	0	0
$298$	−3.50667	−0.203136
$299$	−1.66242	−0.0961402
$300$	−15.0479	−0.868788
$301$	0	0
$302$	3.19513	0.183859
$303$	44.1542	2.53659
$304$	3.09914	0.177748
$305$	−3.72091	−0.213059
$306$	−11.1479	−0.637281
$307$	−12.8841	−0.735334	−0.367667	−	0.929957i	$-0.619843\pi$
$307$	−12.8841	−0.735334	−0.367667	+	0.929957i	$0.619843\pi$
$308$	0	0
$309$	−25.4667	−1.44875
$310$	3.03674	0.172475
$311$	−26.8199	−1.52081	−0.760407	−	0.649447i	$-0.775001\pi$
$311$	−26.8199	−1.52081	−0.760407	+	0.649447i	$0.775001\pi$
$312$	−18.0982	−1.02461
$313$	−3.58869	−0.202845	−0.101422	−	0.994843i	$-0.532339\pi$
$313$	−3.58869	−0.202845	−0.101422	+	0.994843i	$0.532339\pi$
$314$	23.9493	1.35154
$315$	0	0
$316$	7.18688	0.404294
$317$	−16.9181	−0.950213	−0.475106	−	0.879928i	$-0.657590\pi$
$317$	−16.9181	−0.950213	−0.475106	+	0.879928i	$0.657590\pi$
$318$	34.4809	1.93359
$319$	0	0
$320$	−28.6798	−1.60325
$321$	10.0407	0.560418
$322$	0	0
$323$	3.13836	0.174623
$324$	−1.69766	−0.0943144
$325$	14.3032	0.793399
$326$	−9.16365	−0.507528
$327$	11.0823	0.612855
$328$	−6.53501	−0.360836
$329$	0	0
$330$	0	0
$331$	−1.23826	−0.0680610	−0.0340305	−	0.999421i	$-0.510834\pi$
$331$	−1.23826	−0.0680610	−0.0340305	+	0.999421i	$0.510834\pi$
$332$	−12.1800	−0.668466
$333$	52.0479	2.85221
$334$	24.1935	1.32381
$335$	−8.30544	−0.453774
$336$	0	0
$337$	−20.4806	−1.11565	−0.557824	−	0.829959i	$-0.688364\pi$
$337$	−20.4806	−1.11565	−0.557824	+	0.829959i	$0.688364\pi$
$338$	−9.76031	−0.530891
$339$	30.4576	1.65423
$340$	−5.06556	−0.274719
$341$	0	0
$342$	−9.35630	−0.505931
$343$	0	0
$344$	−9.46818	−0.510490
$345$	7.97474	0.429346
$346$	8.96659	0.482047
$347$	27.2699	1.46392	0.731961	−	0.681346i	$-0.238605\pi$
$347$	27.2699	1.46392	0.731961	+	0.681346i	$0.238605\pi$
$348$	−17.2780	−0.926199
$349$	−7.98434	−0.427392	−0.213696	−	0.976900i	$-0.568550\pi$
$349$	−7.98434	−0.427392	−0.213696	+	0.976900i	$0.568550\pi$
$350$	0	0
$351$	12.7941	0.682897
$352$	0	0
$353$	−5.93472	−0.315873	−0.157937	−	0.987449i	$-0.550484\pi$
$353$	−5.93472	−0.315873	−0.157937	+	0.987449i	$0.550484\pi$
$354$	10.5033	0.558243
$355$	11.0200	0.584883
$356$	−3.36407	−0.178296
$357$	0	0
$358$	−4.03538	−0.213277
$359$	28.4203	1.49996	0.749982	−	0.661458i	$-0.230062\pi$
$359$	28.4203	1.49996	0.749982	+	0.661458i	$0.230062\pi$
$360$	54.9501	2.89612
$361$	−16.3660	−0.861368
$362$	−17.6285	−0.926535
$363$	0	0
$364$	0	0
$365$	4.23810	0.221832
$366$	3.43020	0.179299
$367$	30.4014	1.58694	0.793471	−	0.608608i	$-0.208272\pi$
$367$	30.4014	1.58694	0.793471	+	0.608608i	$0.208272\pi$
$368$	1.54128	0.0803445
$369$	10.9982	0.572541
$370$	−38.7547	−2.01476
$371$	0	0
$372$	1.70841	0.0885771
$373$	14.4226	0.746772	0.373386	−	0.927676i	$-0.378197\pi$
$373$	14.4226	0.746772	0.373386	+	0.927676i	$0.378197\pi$
$374$	0	0
$375$	−19.2120	−0.992103
$376$	23.2563	1.19935
$377$	16.4230	0.845828
$378$	0	0
$379$	−22.4072	−1.15098	−0.575490	−	0.817809i	$-0.695189\pi$
$379$	−22.4072	−1.15098	−0.575490	+	0.817809i	$0.695189\pi$
$380$	−4.25148	−0.218096
$381$	55.6066	2.84881
$382$	0.478196	0.0244667
$383$	−33.6785	−1.72089	−0.860446	−	0.509541i	$-0.829815\pi$
$383$	−33.6785	−1.72089	−0.860446	+	0.509541i	$0.829815\pi$
$384$	3.45887	0.176510
$385$	0	0
$386$	−16.9118	−0.860790
$387$	15.9346	0.809999
$388$	4.90256	0.248890
$389$	2.42783	0.123096	0.0615479	−	0.998104i	$-0.480396\pi$
$389$	2.42783	0.123096	0.0615479	+	0.998104i	$0.480396\pi$
$390$	−22.6794	−1.14841
$391$	1.56078	0.0789321
$392$	0	0
$393$	−14.6167	−0.737313
$394$	−23.1900	−1.16830
$395$	32.7699	1.64883
$396$	0	0
$397$	5.89696	0.295960	0.147980	−	0.988990i	$-0.452723\pi$
$397$	5.89696	0.295960	0.147980	+	0.988990i	$0.452723\pi$
$398$	−9.41242	−0.471802
$399$	0	0
$400$	−13.2609	−0.663045
$401$	11.2396	0.561278	0.280639	−	0.959813i	$-0.409454\pi$
$401$	11.2396	0.561278	0.280639	+	0.959813i	$0.409454\pi$
$402$	7.65654	0.381873
$403$	−1.62387	−0.0808908
$404$	−11.7067	−0.582429
$405$	−7.74079	−0.384643
$406$	0	0
$407$	0	0
$408$	16.9917	0.841216
$409$	−29.3344	−1.45049	−0.725246	−	0.688490i	$-0.758274\pi$
$409$	−29.3344	−1.45049	−0.725246	+	0.688490i	$0.758274\pi$
$410$	−8.18919	−0.404435
$411$	26.0167	1.28331
$412$	6.75204	0.332649
$413$	0	0
$414$	−4.65310	−0.228688
$415$	−55.5371	−2.72621
$416$	8.27811	0.405868
$417$	37.2120	1.82228
$418$	0	0
$419$	20.2858	0.991027	0.495514	−	0.868600i	$-0.334980\pi$
$419$	20.2858	0.991027	0.495514	+	0.868600i	$0.334980\pi$
$420$	0	0
$421$	−3.06003	−0.149137	−0.0745683	−	0.997216i	$-0.523758\pi$
$421$	−3.06003	−0.149137	−0.0745683	+	0.997216i	$0.523758\pi$
$422$	−10.9878	−0.534879
$423$	−39.1394	−1.90302
$424$	−33.2645	−1.61547
$425$	−13.4287	−0.651389
$426$	−10.1590	−0.492207
$427$	0	0
$428$	−2.66211	−0.128678
$429$	0	0
$430$	−11.8648	−0.572173
$431$	7.54197	0.363284	0.181642	−	0.983365i	$-0.441859\pi$
$431$	7.54197	0.363284	0.181642	+	0.983365i	$0.441859\pi$
$432$	−11.8617	−0.570698
$433$	32.1616	1.54559	0.772794	−	0.634657i	$-0.218859\pi$
$433$	32.1616	1.54559	0.772794	+	0.634657i	$0.218859\pi$
$434$	0	0
$435$	−78.7823	−3.77732
$436$	−2.93828	−0.140718
$437$	1.30995	0.0626633
$438$	−3.90698	−0.186683
$439$	4.66725	0.222756	0.111378	−	0.993778i	$-0.464474\pi$
$439$	4.66725	0.222756	0.111378	+	0.993778i	$0.464474\pi$
$440$	0	0
$441$	0	0
$442$	−4.43871	−0.211128
$443$	17.2772	0.820862	0.410431	−	0.911892i	$-0.365378\pi$
$443$	17.2772	0.820862	0.410431	+	0.911892i	$0.365378\pi$
$444$	−21.8027	−1.03471
$445$	−15.3391	−0.727144
$446$	−19.3871	−0.918007
$447$	−8.99527	−0.425461
$448$	0	0
$449$	−16.7401	−0.790013	−0.395007	−	0.918678i	$-0.629258\pi$
$449$	−16.7401	−0.790013	−0.395007	+	0.918678i	$0.629258\pi$
$450$	40.0346	1.88725
$451$	0	0
$452$	−8.07529	−0.379829
$453$	8.19612	0.385088
$454$	14.0774	0.660683
$455$	0	0
$456$	14.2610	0.667833
$457$	−21.6974	−1.01496	−0.507481	−	0.861663i	$-0.669423\pi$
$457$	−21.6974	−1.01496	−0.507481	+	0.861663i	$0.669423\pi$
$458$	−5.09692	−0.238163
$459$	−12.0119	−0.560665
$460$	−2.11436	−0.0985825
$461$	6.07778	0.283070	0.141535	−	0.989933i	$-0.454796\pi$
$461$	6.07778	0.283070	0.141535	+	0.989933i	$0.454796\pi$
$462$	0	0
$463$	−5.14719	−0.239210	−0.119605	−	0.992822i	$-0.538163\pi$
$463$	−5.14719	−0.239210	−0.119605	+	0.992822i	$0.538163\pi$
$464$	−15.2262	−0.706860
$465$	7.78982	0.361244
$466$	26.5877	1.23165
$467$	3.91927	0.181362	0.0906812	−	0.995880i	$-0.471096\pi$
$467$	3.91927	0.181362	0.0906812	+	0.995880i	$0.471096\pi$
$468$	−8.07555	−0.373292
$469$	0	0
$470$	29.1431	1.34427
$471$	61.4346	2.83076
$472$	−10.1327	−0.466397
$473$	0	0
$474$	−30.2096	−1.38757
$475$	−11.2706	−0.517131
$476$	0	0
$477$	55.9828	2.56328
$478$	9.84982	0.450520
$479$	15.1129	0.690527	0.345263	−	0.938506i	$-0.387790\pi$
$479$	15.1129	0.690527	0.345263	+	0.938506i	$0.387790\pi$
$480$	−39.7106	−1.81253
$481$	20.7237	0.944922
$482$	−21.1152	−0.961770
$483$	0	0
$484$	0	0
$485$	22.3541	1.01505
$486$	−13.6324	−0.618377
$487$	25.0768	1.13634	0.568169	−	0.822912i	$-0.307652\pi$
$487$	25.0768	1.13634	0.568169	+	0.822912i	$0.307652\pi$
$488$	−3.30919	−0.149800
$489$	−23.5065	−1.06300
$490$	0	0
$491$	37.2208	1.67975	0.839875	−	0.542780i	$-0.182628\pi$
$491$	37.2208	1.67975	0.839875	+	0.542780i	$0.182628\pi$
$492$	−4.60708	−0.207703
$493$	−15.4189	−0.694434
$494$	−3.72536	−0.167612
$495$	0	0
$496$	1.50554	0.0676006
$497$	0	0
$498$	51.1980	2.29424
$499$	−31.8134	−1.42416	−0.712081	−	0.702098i	$-0.752247\pi$
$499$	−31.8134	−1.42416	−0.712081	+	0.702098i	$0.752247\pi$
$500$	5.09371	0.227798
$501$	62.0609	2.77267
$502$	3.19508	0.142603
$503$	19.2058	0.856346	0.428173	−	0.903697i	$-0.359157\pi$
$503$	19.2058	0.856346	0.428173	+	0.903697i	$0.359157\pi$
$504$	0	0
$505$	−53.3788	−2.37532
$506$	0	0
$507$	−25.0370	−1.11193
$508$	−14.7431	−0.654119
$509$	−2.51549	−0.111497	−0.0557485	−	0.998445i	$-0.517754\pi$
$509$	−2.51549	−0.111497	−0.0557485	+	0.998445i	$0.517754\pi$
$510$	21.2928	0.942861
$511$	0	0
$512$	−19.4135	−0.857966
$513$	−10.0814	−0.445106
$514$	−24.9817	−1.10190
$515$	30.7872	1.35664
$516$	−6.67492	−0.293847
$517$	0	0
$518$	0	0
$519$	23.0010	1.00963
$520$	21.8793	0.959470
$521$	−14.8968	−0.652639	−0.326320	−	0.945260i	$-0.605809\pi$
$521$	−14.8968	−0.652639	−0.326320	+	0.945260i	$0.605809\pi$
$522$	45.9679	2.01196
$523$	9.90502	0.433116	0.216558	−	0.976270i	$-0.430517\pi$
$523$	9.90502	0.433116	0.216558	+	0.976270i	$0.430517\pi$
$524$	3.87535	0.169295
$525$	0	0
$526$	1.10411	0.0481414
$527$	1.52459	0.0664122
$528$	0	0
$529$	−22.3485	−0.971675
$530$	−41.6846	−1.81066
$531$	17.0530	0.740036
$532$	0	0
$533$	4.37910	0.189680
$534$	14.1407	0.611927
$535$	−12.1384	−0.524789
$536$	−7.38643	−0.319045
$537$	−10.3515	−0.446701
$538$	8.01342	0.345483
$539$	0	0
$540$	16.2722	0.700245
$541$	−22.0084	−0.946214	−0.473107	−	0.881005i	$-0.656868\pi$
$541$	−22.0084	−0.946214	−0.473107	+	0.881005i	$0.656868\pi$
$542$	30.2737	1.30037
$543$	−45.2205	−1.94060
$544$	−7.77199	−0.333222
$545$	−13.3977	−0.573892
$546$	0	0
$547$	−10.8643	−0.464523	−0.232261	−	0.972653i	$-0.574612\pi$
$547$	−10.8643	−0.464523	−0.232261	+	0.972653i	$0.574612\pi$
$548$	−6.89787	−0.294662
$549$	5.56922	0.237689
$550$	0	0
$551$	−12.9410	−0.551303
$552$	7.09233	0.301869
$553$	0	0
$554$	23.3878	0.993650
$555$	−99.4133	−4.21986
$556$	−9.86610	−0.418416
$557$	33.6126	1.42421	0.712106	−	0.702072i	$-0.247742\pi$
$557$	33.6126	1.42421	0.712106	+	0.702072i	$0.247742\pi$
$558$	−4.54521	−0.192414
$559$	6.34461	0.268348
$560$	0	0
$561$	0	0
$562$	−31.3811	−1.32373
$563$	2.05348	0.0865440	0.0432720	−	0.999063i	$-0.486222\pi$
$563$	2.05348	0.0865440	0.0432720	+	0.999063i	$0.486222\pi$
$564$	16.3953	0.690367
$565$	−36.8208	−1.54906
$566$	29.1898	1.22694
$567$	0	0
$568$	9.80065	0.411226
$569$	3.27416	0.137260	0.0686300	−	0.997642i	$-0.478137\pi$
$569$	3.27416	0.137260	0.0686300	+	0.997642i	$0.478137\pi$
$570$	17.8708	0.748527
$571$	−43.8897	−1.83673	−0.918363	−	0.395738i	$-0.870489\pi$
$571$	−43.8897	−1.83673	−0.918363	+	0.395738i	$0.870489\pi$
$572$	0	0
$573$	1.22666	0.0512446
$574$	0	0
$575$	−5.60513	−0.233750
$576$	42.9261	1.78859
$577$	43.8904	1.82718	0.913591	−	0.406635i	$-0.133298\pi$
$577$	43.8904	1.82718	0.913591	+	0.406635i	$0.133298\pi$
$578$	−14.7786	−0.614709
$579$	−43.3821	−1.80290
$580$	20.8877	0.867315
$581$	0	0
$582$	−20.6076	−0.854214
$583$	0	0
$584$	3.76915	0.155969
$585$	−36.8219	−1.52240
$586$	4.97481	0.205508
$587$	−2.79166	−0.115224	−0.0576121	−	0.998339i	$-0.518349\pi$
$587$	−2.79166	−0.115224	−0.0576121	+	0.998339i	$0.518349\pi$
$588$	0	0
$589$	1.27957	0.0527239
$590$	−12.6976	−0.522752
$591$	−59.4869	−2.44696
$592$	−19.2136	−0.789673
$593$	−23.2526	−0.954871	−0.477435	−	0.878667i	$-0.658434\pi$
$593$	−23.2526	−0.954871	−0.477435	+	0.878667i	$0.658434\pi$
$594$	0	0
$595$	0	0
$596$	2.38493	0.0976907
$597$	−24.1446	−0.988175
$598$	−1.85271	−0.0757630
$599$	10.4595	0.427362	0.213681	−	0.976904i	$-0.431455\pi$
$599$	10.4595	0.427362	0.213681	+	0.976904i	$0.431455\pi$
$600$	−61.0213	−2.49118
$601$	−22.3096	−0.910029	−0.455015	−	0.890484i	$-0.650366\pi$
$601$	−22.3096	−0.910029	−0.455015	+	0.890484i	$0.650366\pi$
$602$	0	0
$603$	12.4311	0.506232
$604$	−2.17306	−0.0884204
$605$	0	0
$606$	49.2083	1.99895
$607$	−18.9884	−0.770716	−0.385358	−	0.922767i	$-0.625922\pi$
$607$	−18.9884	−0.770716	−0.385358	+	0.922767i	$0.625922\pi$
$608$	−6.52296	−0.264541
$609$	0	0
$610$	−4.14683	−0.167900
$611$	−15.5840	−0.630461
$612$	7.58182	0.306477
$613$	20.1617	0.814323	0.407161	−	0.913356i	$-0.366519\pi$
$613$	20.1617	0.814323	0.407161	+	0.913356i	$0.366519\pi$
$614$	−14.3589	−0.579478
$615$	−21.0068	−0.847077
$616$	0	0
$617$	7.03919	0.283387	0.141694	−	0.989911i	$-0.454745\pi$
$617$	7.03919	0.283387	0.141694	+	0.989911i	$0.454745\pi$
$618$	−28.3818	−1.14168
$619$	31.0831	1.24933	0.624667	−	0.780891i	$-0.285235\pi$
$619$	31.0831	1.24933	0.624667	+	0.780891i	$0.285235\pi$
$620$	−2.06533	−0.0829457
$621$	−5.01373	−0.201194
$622$	−29.8898	−1.19847
$623$	0	0
$624$	−11.2438	−0.450113
$625$	−11.4966	−0.459866
$626$	−3.99947	−0.159851
$627$	0	0
$628$	−16.2883	−0.649973
$629$	−19.4567	−0.775791
$630$	0	0
$631$	21.9720	0.874690	0.437345	−	0.899294i	$-0.355919\pi$
$631$	21.9720	0.874690	0.437345	+	0.899294i	$0.355919\pi$
$632$	29.1439	1.15928
$633$	−28.1859	−1.12029
$634$	−18.8546	−0.748812
$635$	−67.2238	−2.66770
$636$	−23.4510	−0.929891
$637$	0	0
$638$	0	0
$639$	−16.4941	−0.652496
$640$	−4.18149	−0.165288
$641$	−13.2909	−0.524961	−0.262480	−	0.964937i	$-0.584540\pi$
$641$	−13.2909	−0.524961	−0.262480	+	0.964937i	$0.584540\pi$
$642$	11.1900	0.441636
$643$	−14.6904	−0.579333	−0.289666	−	0.957128i	$-0.593544\pi$
$643$	−14.6904	−0.579333	−0.289666	+	0.957128i	$0.593544\pi$
$644$	0	0
$645$	−30.4355	−1.19840
$646$	3.49760	0.137611
$647$	6.14523	0.241594	0.120797	−	0.992677i	$-0.461455\pi$
$647$	6.14523	0.241594	0.120797	+	0.992677i	$0.461455\pi$
$648$	−6.88426	−0.270439
$649$	0	0
$650$	15.9404	0.625236
$651$	0	0
$652$	6.23232	0.244077
$653$	−40.6691	−1.59151	−0.795753	−	0.605622i	$-0.792924\pi$
$653$	−40.6691	−1.59151	−0.795753	+	0.605622i	$0.792924\pi$
$654$	12.3509	0.482959
$655$	17.6704	0.690438
$656$	−4.05998	−0.158516
$657$	−6.34333	−0.247477
$658$	0	0
$659$	18.0090	0.701531	0.350765	−	0.936463i	$-0.385921\pi$
$659$	18.0090	0.701531	0.350765	+	0.936463i	$0.385921\pi$
$660$	0	0
$661$	17.1420	0.666745	0.333373	−	0.942795i	$-0.391813\pi$
$661$	17.1420	0.666745	0.333373	+	0.942795i	$0.391813\pi$
$662$	−1.38000	−0.0536353
$663$	−11.3861	−0.442201
$664$	−49.3919	−1.91678
$665$	0	0
$666$	58.0057	2.24767
$667$	−6.43584	−0.249197
$668$	−16.4543	−0.636637
$669$	−49.7317	−1.92274
$670$	−9.25613	−0.357596
$671$	0	0
$672$	0	0
$673$	−23.1926	−0.894008	−0.447004	−	0.894532i	$-0.647509\pi$
$673$	−23.1926	−0.894008	−0.447004	+	0.894532i	$0.647509\pi$
$674$	−22.8249	−0.879183
$675$	43.1374	1.66036
$676$	6.63812	0.255312
$677$	27.5705	1.05962	0.529811	−	0.848116i	$-0.322263\pi$
$677$	27.5705	1.05962	0.529811	+	0.848116i	$0.322263\pi$
$678$	33.9440	1.30361
$679$	0	0
$680$	−20.5416	−0.787735
$681$	36.1111	1.38378
$682$	0	0
$683$	21.9351	0.839322	0.419661	−	0.907681i	$-0.362149\pi$
$683$	21.9351	0.839322	0.419661	+	0.907681i	$0.362149\pi$
$684$	6.36335	0.243309
$685$	−31.4521	−1.20172
$686$	0	0
$687$	−13.0746	−0.498826
$688$	−5.88227	−0.224259
$689$	22.2905	0.849200
$690$	8.88758	0.338344
$691$	25.6666	0.976404	0.488202	−	0.872731i	$-0.337653\pi$
$691$	25.6666	0.976404	0.488202	+	0.872731i	$0.337653\pi$
$692$	−6.09830	−0.231823
$693$	0	0
$694$	30.3913	1.15364
$695$	−44.9863	−1.70643
$696$	−70.0650	−2.65581
$697$	−4.11137	−0.155729
$698$	−8.89828	−0.336805
$699$	68.2025	2.57966
$700$	0	0
$701$	−18.4135	−0.695467	−0.347733	−	0.937593i	$-0.613049\pi$
$701$	−18.4135	−0.695467	−0.347733	+	0.937593i	$0.613049\pi$
$702$	14.2586	0.538154
$703$	−16.3298	−0.615892
$704$	0	0
$705$	74.7575	2.81553
$706$	−6.61404	−0.248923
$707$	0	0
$708$	−7.14342	−0.268466
$709$	23.6621	0.888647	0.444323	−	0.895866i	$-0.353444\pi$
$709$	23.6621	0.888647	0.444323	+	0.895866i	$0.353444\pi$
$710$	12.2815	0.460915
$711$	−49.0480	−1.83944
$712$	−13.6418	−0.511249
$713$	0.636362	0.0238319
$714$	0	0
$715$	0	0
$716$	2.74452	0.102568
$717$	25.2666	0.943600
$718$	31.6734	1.18204
$719$	−11.1222	−0.414790	−0.207395	−	0.978257i	$-0.566498\pi$
$719$	−11.1222	−0.414790	−0.207395	+	0.978257i	$0.566498\pi$
$720$	34.1387	1.27227
$721$	0	0
$722$	−18.2394	−0.678799
$723$	−54.1644	−2.01440
$724$	11.9894	0.445583
$725$	55.3730	2.05650
$726$	0	0
$727$	−42.4803	−1.57551	−0.787753	−	0.615991i	$-0.788756\pi$
$727$	−42.4803	−1.57551	−0.787753	+	0.615991i	$0.788756\pi$
$728$	0	0
$729$	−41.6889	−1.54403
$730$	4.72323	0.174814
$731$	−5.95671	−0.220317
$732$	−2.33292	−0.0862274
$733$	−22.1884	−0.819548	−0.409774	−	0.912187i	$-0.634393\pi$
$733$	−22.1884	−0.819548	−0.409774	+	0.912187i	$0.634393\pi$
$734$	33.8814	1.25058
$735$	0	0
$736$	−3.24402	−0.119576
$737$	0	0
$738$	12.2571	0.451189
$739$	29.4481	1.08327	0.541633	−	0.840615i	$-0.317806\pi$
$739$	29.4481	1.08327	0.541633	+	0.840615i	$0.317806\pi$
$740$	26.3576	0.968926
$741$	−9.55627	−0.351058
$742$	0	0
$743$	16.9059	0.620217	0.310109	−	0.950701i	$-0.399635\pi$
$743$	16.9059	0.620217	0.310109	+	0.950701i	$0.399635\pi$
$744$	6.92787	0.253988
$745$	10.8745	0.398412
$746$	16.0735	0.588491
$747$	83.1244	3.04136
$748$	0	0
$749$	0	0
$750$	−21.4111	−0.781823
$751$	−1.55147	−0.0566138	−0.0283069	−	0.999599i	$-0.509012\pi$
$751$	−1.55147	−0.0566138	−0.0283069	+	0.999599i	$0.509012\pi$
$752$	14.4484	0.526877
$753$	8.19598	0.298678
$754$	18.3029	0.666552
$755$	−9.90845	−0.360605
$756$	0	0
$757$	12.5467	0.456016	0.228008	−	0.973659i	$-0.426779\pi$
$757$	12.5467	0.456016	0.228008	+	0.973659i	$0.426779\pi$
$758$	−24.9721	−0.907027
$759$	0	0
$760$	−17.2404	−0.625375
$761$	9.03436	0.327495	0.163748	−	0.986502i	$-0.447642\pi$
$761$	9.03436	0.327495	0.163748	+	0.986502i	$0.447642\pi$
$762$	61.9717	2.24500
$763$	0	0
$764$	−0.325228	−0.0117663
$765$	34.5707	1.24991
$766$	−37.5336	−1.35614
$767$	6.78993	0.245170
$768$	−43.5922	−1.57300
$769$	16.1383	0.581963	0.290981	−	0.956729i	$-0.406018\pi$
$769$	16.1383	0.581963	0.290981	+	0.956729i	$0.406018\pi$
$770$	0	0
$771$	−64.0829	−2.30789
$772$	11.5020	0.413965
$773$	18.4134	0.662285	0.331143	−	0.943581i	$-0.392566\pi$
$773$	18.4134	0.662285	0.331143	+	0.943581i	$0.392566\pi$
$774$	17.7585	0.638317
$775$	−5.47516	−0.196674
$776$	19.8806	0.713673
$777$	0	0
$778$	2.70573	0.0970053
$779$	−3.45063	−0.123632
$780$	15.4246	0.552288
$781$	0	0
$782$	1.73944	0.0622022
$783$	49.5306	1.77008
$784$	0	0
$785$	−74.2694	−2.65079
$786$	−16.2898	−0.581037
$787$	−46.9870	−1.67491	−0.837453	−	0.546509i	$-0.815957\pi$
$787$	−46.9870	−1.67491	−0.837453	+	0.546509i	$0.815957\pi$
$788$	15.7719	0.561850
$789$	2.83225	0.100831
$790$	36.5210	1.29936
$791$	0	0
$792$	0	0
$793$	2.21748	0.0787450
$794$	6.57197	0.233230
$795$	−106.929	−3.79238
$796$	6.40152	0.226896
$797$	3.12454	0.110677	0.0553385	−	0.998468i	$-0.482376\pi$
$797$	3.12454	0.110677	0.0553385	+	0.998468i	$0.482376\pi$
$798$	0	0
$799$	14.6312	0.517615
$800$	27.9111	0.986805
$801$	22.9586	0.811203
$802$	12.5261	0.442314
$803$	0	0
$804$	−5.20732	−0.183648
$805$	0	0
$806$	−1.80975	−0.0637457
$807$	20.5559	0.723604
$808$	−47.4724	−1.67007
$809$	−32.7257	−1.15057	−0.575286	−	0.817952i	$-0.695109\pi$
$809$	−32.7257	−1.15057	−0.575286	+	0.817952i	$0.695109\pi$
$810$	−8.62685	−0.303117
$811$	−32.6613	−1.14689	−0.573447	−	0.819243i	$-0.694394\pi$
$811$	−32.6613	−1.14689	−0.573447	+	0.819243i	$0.694394\pi$
$812$	0	0
$813$	77.6578	2.72358
$814$	0	0
$815$	28.4174	0.995419
$816$	10.5564	0.369548
$817$	−4.99941	−0.174907
$818$	−32.6922	−1.14306
$819$	0	0
$820$	5.56958	0.194498
$821$	−7.43142	−0.259358	−0.129679	−	0.991556i	$-0.541395\pi$
$821$	−7.43142	−0.259358	−0.129679	+	0.991556i	$0.541395\pi$
$822$	28.9948	1.01131
$823$	6.55866	0.228621	0.114310	−	0.993445i	$-0.463534\pi$
$823$	6.55866	0.228621	0.114310	+	0.993445i	$0.463534\pi$
$824$	27.3805	0.953846
$825$	0	0
$826$	0	0
$827$	23.8538	0.829479	0.414739	−	0.909940i	$-0.363873\pi$
$827$	23.8538	0.829479	0.414739	+	0.909940i	$0.363873\pi$
$828$	3.16464	0.109979
$829$	26.1431	0.907989	0.453994	−	0.891005i	$-0.349999\pi$
$829$	26.1431	0.907989	0.453994	+	0.891005i	$0.349999\pi$
$830$	−61.8942	−2.14838
$831$	59.9940	2.08117
$832$	17.0917	0.592549
$833$	0	0
$834$	41.4716	1.43604
$835$	−75.0265	−2.59640
$836$	0	0
$837$	−4.89747	−0.169281
$838$	22.6079	0.780976
$839$	−34.2890	−1.18379	−0.591893	−	0.806016i	$-0.701619\pi$
$839$	−34.2890	−1.18379	−0.591893	+	0.806016i	$0.701619\pi$
$840$	0	0
$841$	34.5795	1.19240
$842$	−3.41030	−0.117527
$843$	−80.4986	−2.77252
$844$	7.47297	0.257230
$845$	30.2677	1.04124
$846$	−43.6195	−1.49967
$847$	0	0
$848$	−20.6661	−0.709678
$849$	74.8774	2.56979
$850$	−14.9659	−0.513325
$851$	−8.12121	−0.278392
$852$	6.90931	0.236709
$853$	−21.3842	−0.732181	−0.366090	−	0.930579i	$-0.619304\pi$
$853$	−21.3842	−0.732181	−0.366090	+	0.930579i	$0.619304\pi$
$854$	0	0
$855$	29.0149	0.992287
$856$	−10.7953	−0.368975
$857$	−42.8697	−1.46440	−0.732200	−	0.681090i	$-0.761506\pi$
$857$	−42.8697	−1.46440	−0.732200	+	0.681090i	$0.761506\pi$
$858$	0	0
$859$	30.3915	1.03695	0.518473	−	0.855094i	$-0.326501\pi$
$859$	30.3915	1.03695	0.518473	+	0.855094i	$0.326501\pi$
$860$	8.06944	0.275165
$861$	0	0
$862$	8.40527	0.286285
$863$	11.8184	0.402304	0.201152	−	0.979560i	$-0.435532\pi$
$863$	11.8184	0.402304	0.201152	+	0.979560i	$0.435532\pi$
$864$	24.9661	0.849365
$865$	−27.8063	−0.945444
$866$	35.8430	1.21800
$867$	−37.9099	−1.28749
$868$	0	0
$869$	0	0
$870$	−87.8003	−2.97671
$871$	4.94963	0.167712
$872$	−11.9152	−0.403499
$873$	−33.4583	−1.13239
$874$	1.45989	0.0493816
$875$	0	0
$876$	2.65719	0.0897783
$877$	−9.20488	−0.310827	−0.155413	−	0.987850i	$-0.549671\pi$
$877$	−9.20488	−0.310827	−0.155413	+	0.987850i	$0.549671\pi$
$878$	5.20149	0.175542
$879$	12.7613	0.430429
$880$	0	0
$881$	41.9030	1.41175	0.705874	−	0.708338i	$-0.250555\pi$
$881$	41.9030	1.41175	0.705874	+	0.708338i	$0.250555\pi$
$882$	0	0
$883$	−16.0478	−0.540053	−0.270026	−	0.962853i	$-0.587032\pi$
$883$	−16.0478	−0.540053	−0.270026	+	0.962853i	$0.587032\pi$
$884$	3.01883	0.101534
$885$	−32.5718	−1.09489
$886$	19.2548	0.646878
$887$	33.8483	1.13652	0.568258	−	0.822850i	$-0.307618\pi$
$887$	33.8483	1.13652	0.568258	+	0.822850i	$0.307618\pi$
$888$	−88.4131	−2.96695
$889$	0	0
$890$	−17.0949	−0.573024
$891$	0	0
$892$	13.1855	0.441482
$893$	12.2798	0.410929
$894$	−10.0249	−0.335284
$895$	12.5141	0.418302
$896$	0	0
$897$	−4.75255	−0.158683
$898$	−18.6563	−0.622568
$899$	−6.28660	−0.209670
$900$	−27.2281	−0.907603
$901$	−20.9277	−0.697202
$902$	0	0
$903$	0	0
$904$	−32.7465	−1.08913
$905$	54.6679	1.81722
$906$	9.13431	0.303467
$907$	−44.1013	−1.46436	−0.732181	−	0.681111i	$-0.761497\pi$
$907$	−44.1013	−1.46436	−0.732181	+	0.681111i	$0.761497\pi$
$908$	−9.57421	−0.317731
$909$	79.8940	2.64992
$910$	0	0
$911$	49.5756	1.64251	0.821257	−	0.570558i	$-0.193273\pi$
$911$	49.5756	1.64251	0.821257	+	0.570558i	$0.193273\pi$
$912$	8.85988	0.293380
$913$	0	0
$914$	−24.1810	−0.799837
$915$	−10.6374	−0.351662
$916$	3.46648	0.114536
$917$	0	0
$918$	−13.3868	−0.441831
$919$	−40.7926	−1.34563	−0.672813	−	0.739813i	$-0.734914\pi$
$919$	−40.7926	−1.34563	−0.672813	+	0.739813i	$0.734914\pi$
$920$	−8.57404	−0.282678
$921$	−36.8333	−1.21370
$922$	6.77348	0.223073
$923$	−6.56740	−0.216169
$924$	0	0
$925$	69.8737	2.29743
$926$	−5.73637	−0.188509
$927$	−46.0803	−1.51348
$928$	32.0476	1.05201
$929$	−41.3929	−1.35806	−0.679029	−	0.734112i	$-0.737599\pi$
$929$	−41.3929	−1.35806	−0.679029	+	0.734112i	$0.737599\pi$
$930$	8.68150	0.284677
$931$	0	0
$932$	−18.0827	−0.592318
$933$	−76.6731	−2.51016
$934$	4.36790	0.142922
$935$	0	0
$936$	−32.7476	−1.07039
$937$	−1.59644	−0.0521534	−0.0260767	−	0.999660i	$-0.508301\pi$
$937$	−1.59644	−0.0521534	−0.0260767	+	0.999660i	$0.508301\pi$
$938$	0	0
$939$	−10.2594	−0.334803
$940$	−19.8206	−0.646477
$941$	−7.10787	−0.231710	−0.115855	−	0.993266i	$-0.536961\pi$
$941$	−7.10787	−0.231710	−0.115855	+	0.993266i	$0.536961\pi$
$942$	68.4668	2.23077
$943$	−1.71608	−0.0558832
$944$	−6.29513	−0.204889
$945$	0	0
$946$	0	0
$947$	−2.45986	−0.0799347	−0.0399674	−	0.999201i	$-0.512725\pi$
$947$	−2.45986	−0.0799347	−0.0399674	+	0.999201i	$0.512725\pi$
$948$	20.5460	0.667303
$949$	−2.52570	−0.0819878
$950$	−12.5607	−0.407523
$951$	−48.3656	−1.56836
$952$	0	0
$953$	−28.6000	−0.926446	−0.463223	−	0.886242i	$-0.653307\pi$
$953$	−28.6000	−0.926446	−0.463223	+	0.886242i	$0.653307\pi$
$954$	62.3910	2.01998
$955$	−1.48294	−0.0479867
$956$	−6.69900	−0.216661
$957$	0	0
$958$	16.8428	0.544168
$959$	0	0
$960$	−81.9903	−2.64622
$961$	−30.3784	−0.979948
$962$	23.0959	0.744643
$963$	18.1680	0.585456
$964$	14.3607	0.462528
$965$	52.4454	1.68828
$966$	0	0
$967$	−0.213338	−0.00686047	−0.00343024	−	0.999994i	$-0.501092\pi$
$967$	−0.213338	−0.00686047	−0.00343024	+	0.999994i	$0.501092\pi$
$968$	0	0
$969$	8.97201	0.288223
$970$	24.9129	0.799907
$971$	0.828199	0.0265782	0.0132891	−	0.999912i	$-0.495770\pi$
$971$	0.828199	0.0265782	0.0132891	+	0.999912i	$0.495770\pi$
$972$	9.27157	0.297386
$973$	0	0
$974$	27.9473	0.895488
$975$	40.8903	1.30954
$976$	−2.05589	−0.0658073
$977$	9.75714	0.312159	0.156079	−	0.987745i	$-0.450114\pi$
$977$	9.75714	0.312159	0.156079	+	0.987745i	$0.450114\pi$
$978$	−26.1972	−0.837694
$979$	0	0
$980$	0	0
$981$	20.0528	0.640236
$982$	41.4813	1.32372
$983$	−45.1198	−1.43910	−0.719548	−	0.694442i	$-0.755651\pi$
$983$	−45.1198	−1.43910	−0.719548	+	0.694442i	$0.755651\pi$
$984$	−18.6824	−0.595573
$985$	71.9148	2.29140
$986$	−17.1839	−0.547246
$987$	0	0
$988$	2.53367	0.0806069
$989$	−2.48632	−0.0790604
$990$	0	0
$991$	53.5405	1.70077	0.850384	−	0.526162i	$-0.176369\pi$
$991$	53.5405	1.70077	0.850384	+	0.526162i	$0.176369\pi$
$992$	−3.16880	−0.100609
$993$	−3.53997	−0.112337
$994$	0	0
$995$	29.1889	0.925351
$996$	−34.8205	−1.10333
$997$	31.1607	0.986869	0.493435	−	0.869783i	$-0.335741\pi$
$997$	31.1607	0.986869	0.493435	+	0.869783i	$0.335741\pi$
$998$	−35.4549	−1.12231
$999$	62.5013	1.97745

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bt.1.6		8
7.6	odd	2		847.2.a.p.1.6		8
11.5	even	5		539.2.f.e.344.2		16
11.9	even	5		539.2.f.e.246.2		16
11.10	odd	2		5929.2.a.bs.1.3		8
21.20	even	2		7623.2.a.ct.1.3		8
77.5	odd	30		539.2.q.g.410.3		32
77.6	even	10		847.2.f.x.729.3		16
77.9	even	15		539.2.q.f.312.2		32
77.13	even	10		847.2.f.x.323.3		16
77.16	even	15		539.2.q.f.410.3		32
77.20	odd	10		77.2.f.b.15.2	✓	16
77.27	odd	10		77.2.f.b.36.2	yes	16
77.31	odd	30		539.2.q.g.422.3		32
77.38	odd	30		539.2.q.g.520.2		32
77.41	even	10		847.2.f.v.372.2		16
77.48	odd	10		847.2.f.w.148.3		16
77.53	even	15		539.2.q.f.422.3		32
77.60	even	15		539.2.q.f.520.2		32
77.62	even	10		847.2.f.v.148.2		16
77.69	odd	10		847.2.f.w.372.3		16
77.75	odd	30		539.2.q.g.312.2		32
77.76	even	2		847.2.a.o.1.3		8
231.20	even	10		693.2.m.i.631.3		16
231.104	even	10		693.2.m.i.190.3		16
231.230	odd	2		7623.2.a.cw.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.2	✓	16	77.20	odd	10
77.2.f.b.36.2	yes	16	77.27	odd	10
539.2.f.e.246.2		16	11.9	even	5
539.2.f.e.344.2		16	11.5	even	5
539.2.q.f.312.2		32	77.9	even	15
539.2.q.f.410.3		32	77.16	even	15
539.2.q.f.422.3		32	77.53	even	15
539.2.q.f.520.2		32	77.60	even	15
539.2.q.g.312.2		32	77.75	odd	30
539.2.q.g.410.3		32	77.5	odd	30
539.2.q.g.422.3		32	77.31	odd	30
539.2.q.g.520.2		32	77.38	odd	30
693.2.m.i.190.3		16	231.104	even	10
693.2.m.i.631.3		16	231.20	even	10
847.2.a.o.1.3		8	77.76	even	2
847.2.a.p.1.6		8	7.6	odd	2
847.2.f.v.148.2		16	77.62	even	10
847.2.f.v.372.2		16	77.41	even	10
847.2.f.w.148.3		16	77.48	odd	10
847.2.f.w.372.3		16	77.69	odd	10
847.2.f.x.323.3		16	77.13	even	10
847.2.f.x.729.3		16	77.6	even	10
5929.2.a.bs.1.3		8	11.10	odd	2
5929.2.a.bt.1.6		8	1.1	even	1	trivial
7623.2.a.ct.1.3		8	21.20	even	2
7623.2.a.cw.1.6		8	231.230	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q+1.11447 q^{2} +2.85882 q^{3} -0.757964 q^{4} -3.45608 q^{5} +3.18606 q^{6} -3.07366 q^{8} +5.17284 q^{9} +O(q^{10})\)	\(q+1.11447 q^{2} +2.85882 q^{3} -0.757964 q^{4} -3.45608 q^{5} +3.18606 q^{6} -3.07366 q^{8} +5.17284 q^{9} -3.85168 q^{10} -2.16688 q^{12} +2.05965 q^{13} -9.88030 q^{15} -1.90956 q^{16} -1.93373 q^{17} +5.76496 q^{18} -1.62296 q^{19} +2.61958 q^{20} -0.807136 q^{23} -8.78703 q^{24} +6.94447 q^{25} +2.29541 q^{26} +6.21176 q^{27} +7.97368 q^{29} -11.0113 q^{30} -0.788420 q^{31} +4.01918 q^{32} -2.15508 q^{34} -3.92083 q^{36} +10.0618 q^{37} -1.80873 q^{38} +5.88817 q^{39} +10.6228 q^{40} +2.12613 q^{41} +3.08043 q^{43} -17.8777 q^{45} -0.899526 q^{46} -7.56632 q^{47} -5.45909 q^{48} +7.73938 q^{50} -5.52818 q^{51} -1.56114 q^{52} +10.8224 q^{53} +6.92280 q^{54} -4.63975 q^{57} +8.88640 q^{58} +3.29664 q^{59} +7.48891 q^{60} +1.07663 q^{61} -0.878667 q^{62} +8.29836 q^{64} -7.11832 q^{65} +2.40314 q^{67} +1.46570 q^{68} -2.30745 q^{69} -3.18859 q^{71} -15.8995 q^{72} -1.22628 q^{73} +11.2135 q^{74} +19.8530 q^{75} +1.23015 q^{76} +6.56217 q^{78} -9.48182 q^{79} +6.59959 q^{80} +2.23976 q^{81} +2.36950 q^{82} +16.0694 q^{83} +6.68312 q^{85} +3.43303 q^{86} +22.7953 q^{87} +4.43830 q^{89} -19.9241 q^{90} +0.611780 q^{92} -2.25395 q^{93} -8.43241 q^{94} +5.60908 q^{95} +11.4901 q^{96} -6.46807 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} + 7 q^{4} - 10 q^{5} + q^{6} + 14 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 + 7 * q^4 - 10 * q^5 + q^6 + 14 * q^9	\( 8 q + q^{2} - 4 q^{3} + 7 q^{4} - 10 q^{5} + q^{6} + 14 q^{9} - 6 q^{10} - 9 q^{12} + 6 q^{13} + 11 q^{15} + q^{16} + 5 q^{17} + 8 q^{18} + 13 q^{19} - 23 q^{20} + 16 q^{23} + 10 q^{24} + 16 q^{25} + 6 q^{26} - 10 q^{27} + 9 q^{29} - 36 q^{30} - 9 q^{31} + 16 q^{32} + 12 q^{34} - 14 q^{36} + 7 q^{37} + 10 q^{38} + 13 q^{39} - 5 q^{40} + 10 q^{41} - 4 q^{43} - 35 q^{45} + 4 q^{46} - 16 q^{47} + 3 q^{48} + 6 q^{50} + 13 q^{51} + 41 q^{52} + 37 q^{53} - 30 q^{54} + 2 q^{57} - 15 q^{58} - q^{59} + 5 q^{60} - 19 q^{61} + 18 q^{62} - 4 q^{64} - 4 q^{65} - 19 q^{67} - 9 q^{68} - 20 q^{69} + 13 q^{71} - 35 q^{72} + 25 q^{73} + 33 q^{74} + 13 q^{75} - 26 q^{76} - 29 q^{78} - 4 q^{80} + 8 q^{81} + 13 q^{82} + 25 q^{83} + 3 q^{85} + 4 q^{86} + 36 q^{87} - 37 q^{89} + 2 q^{90} + 35 q^{92} + 21 q^{93} + 42 q^{94} + 21 q^{95} + 6 q^{96} - 15 q^{97}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 + 7 * q^4 - 10 * q^5 + q^6 + 14 * q^9 - 6 * q^10 - 9 * q^12 + 6 * q^13 + 11 * q^15 + q^16 + 5 * q^17 + 8 * q^18 + 13 * q^19 - 23 * q^20 + 16 * q^23 + 10 * q^24 + 16 * q^25 + 6 * q^26 - 10 * q^27 + 9 * q^29 - 36 * q^30 - 9 * q^31 + 16 * q^32 + 12 * q^34 - 14 * q^36 + 7 * q^37 + 10 * q^38 + 13 * q^39 - 5 * q^40 + 10 * q^41 - 4 * q^43 - 35 * q^45 + 4 * q^46 - 16 * q^47 + 3 * q^48 + 6 * q^50 + 13 * q^51 + 41 * q^52 + 37 * q^53 - 30 * q^54 + 2 * q^57 - 15 * q^58 - q^59 + 5 * q^60 - 19 * q^61 + 18 * q^62 - 4 * q^64 - 4 * q^65 - 19 * q^67 - 9 * q^68 - 20 * q^69 + 13 * q^71 - 35 * q^72 + 25 * q^73 + 33 * q^74 + 13 * q^75 - 26 * q^76 - 29 * q^78 - 4 * q^80 + 8 * q^81 + 13 * q^82 + 25 * q^83 + 3 * q^85 + 4 * q^86 + 36 * q^87 - 37 * q^89 + 2 * q^90 + 35 * q^92 + 21 * q^93 + 42 * q^94 + 21 * q^95 + 6 * q^96 - 15 * q^97

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