LMFDB - Embedded newform 8281.2.a.by.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, 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("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.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:	$66.1241179138$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.7674048.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.70320$ of defining polynomial
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70320 q^{2} +0.345949 q^{3} +5.30727 q^{4} +3.25812 q^{5} -0.935168 q^{6} -8.94020 q^{8} -2.88032 q^{9} +O(q^{10})$	\(q-2.70320 q^{2} +0.345949 q^{3} +5.30727 q^{4} +3.25812 q^{5} -0.935168 q^{6} -8.94020 q^{8} -2.88032 q^{9} -8.80735 q^{10} +1.84603 q^{11} +1.83605 q^{12} +1.12715 q^{15} +13.5526 q^{16} -2.15314 q^{17} +7.78607 q^{18} -2.40096 q^{19} +17.2917 q^{20} -4.99017 q^{22} +1.81263 q^{23} -3.09285 q^{24} +5.61537 q^{25} -2.03429 q^{27} -2.73406 q^{29} -3.04689 q^{30} +1.74236 q^{31} -18.7549 q^{32} +0.638632 q^{33} +5.82036 q^{34} -15.2866 q^{36} +5.93565 q^{37} +6.49025 q^{38} -29.1283 q^{40} -4.22131 q^{41} -8.68223 q^{43} +9.79737 q^{44} -9.38444 q^{45} -4.89989 q^{46} +5.87774 q^{47} +4.68850 q^{48} -15.1794 q^{50} -0.744877 q^{51} -9.30628 q^{53} +5.49909 q^{54} +6.01459 q^{55} -0.830609 q^{57} +7.39071 q^{58} -10.7523 q^{59} +5.98206 q^{60} -10.1101 q^{61} -4.70994 q^{62} +23.5929 q^{64} -1.72635 q^{66} +0.826916 q^{67} -11.4273 q^{68} +0.627077 q^{69} +2.35425 q^{71} +25.7506 q^{72} +3.19482 q^{73} -16.0452 q^{74} +1.94263 q^{75} -12.7425 q^{76} +0.801911 q^{79} +44.1559 q^{80} +7.93720 q^{81} +11.4110 q^{82} +9.97031 q^{83} -7.01520 q^{85} +23.4698 q^{86} -0.945847 q^{87} -16.5039 q^{88} +15.1135 q^{89} +25.3680 q^{90} +9.62010 q^{92} +0.602768 q^{93} -15.8887 q^{94} -7.82261 q^{95} -6.48823 q^{96} +9.23171 q^{97} -5.31715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 6 * q - 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 12 * q^8 + 4 * q^9	$ 6 q - 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 12 q^{8} + 4 q^{9} - 12 q^{10} - 4 q^{11} - 2 q^{12} - 20 q^{15} + 8 q^{16} + 4 q^{17} + 16 q^{18} + 2 q^{19} + 26 q^{20} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 10 q^{25} - 6 q^{27} - 8 q^{29} + 8 q^{30} - 14 q^{31} - 8 q^{32} + 16 q^{33} - 2 q^{34} - 10 q^{36} - 12 q^{37} + 2 q^{38} - 46 q^{40} + 28 q^{41} + 2 q^{43} + 20 q^{44} + 16 q^{45} - 20 q^{46} + 14 q^{47} - 2 q^{48} - 32 q^{50} - 26 q^{51} - 22 q^{53} + 14 q^{54} - 6 q^{55} - 4 q^{58} - 2 q^{59} + 14 q^{61} + 4 q^{62} + 26 q^{64} + 26 q^{66} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 4 q^{71} - 8 q^{72} + 36 q^{73} - 6 q^{74} - 46 q^{75} - 26 q^{76} - 28 q^{79} + 36 q^{80} - 2 q^{81} - 14 q^{82} + 26 q^{83} + 20 q^{85} + 24 q^{86} - 2 q^{87} - 14 q^{88} + 42 q^{89} + 12 q^{90} + 12 q^{92} + 4 q^{94} - 22 q^{95} - 42 q^{96} + 24 q^{97} - 16 q^{99}+O(q^{100}) $ 6 * q - 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 12 * q^8 + 4 * q^9 - 12 * q^10 - 4 * q^11 - 2 * q^12 - 20 * q^15 + 8 * q^16 + 4 * q^17 + 16 * q^18 + 2 * q^19 + 26 * q^20 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 10 * q^25 - 6 * q^27 - 8 * q^29 + 8 * q^30 - 14 * q^31 - 8 * q^32 + 16 * q^33 - 2 * q^34 - 10 * q^36 - 12 * q^37 + 2 * q^38 - 46 * q^40 + 28 * q^41 + 2 * q^43 + 20 * q^44 + 16 * q^45 - 20 * q^46 + 14 * q^47 - 2 * q^48 - 32 * q^50 - 26 * q^51 - 22 * q^53 + 14 * q^54 - 6 * q^55 - 4 * q^58 - 2 * q^59 + 14 * q^61 + 4 * q^62 + 26 * q^64 + 26 * q^66 - 24 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^71 - 8 * q^72 + 36 * q^73 - 6 * q^74 - 46 * q^75 - 26 * q^76 - 28 * q^79 + 36 * q^80 - 2 * q^81 - 14 * q^82 + 26 * q^83 + 20 * q^85 + 24 * q^86 - 2 * q^87 - 14 * q^88 + 42 * q^89 + 12 * q^90 + 12 * q^92 + 4 * q^94 - 22 * q^95 - 42 * q^96 + 24 * q^97 - 16 * q^99

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 $

$2$	−2.70320	−1.91145	−0.955724	−	0.294264i	$-0.904925\pi$
$2$	−2.70320	−1.91145	−0.955724	+	0.294264i	$0.904925\pi$
$3$	0.345949	0.199734	0.0998669	−	0.995001i	$-0.468158\pi$
$3$	0.345949	0.199734	0.0998669	+	0.995001i	$0.468158\pi$
$4$	5.30727	2.65363
$5$	3.25812	1.45708	0.728539	−	0.685005i	$-0.240200\pi$
$5$	3.25812	1.45708	0.728539	+	0.685005i	$0.240200\pi$
$6$	−0.935168	−0.381781
$7$	0	0
$7$	0	0
$8$	−8.94020	−3.16084
$9$	−2.88032	−0.960106
$10$	−8.80735	−2.78513
$11$	1.84603	0.556598	0.278299	−	0.960494i	$-0.410229\pi$
$11$	1.84603	0.556598	0.278299	+	0.960494i	$0.410229\pi$
$12$	1.83605	0.530021
$13$	0	0
$13$	0	0
$14$	0	0
$15$	1.12715	0.291028
$16$	13.5526	3.38814
$17$	−2.15314	−0.522213	−0.261107	−	0.965310i	$-0.584087\pi$
$17$	−2.15314	−0.522213	−0.261107	+	0.965310i	$0.584087\pi$
$18$	7.78607	1.83519
$19$	−2.40096	−0.550817	−0.275408	−	0.961327i	$-0.588813\pi$
$19$	−2.40096	−0.550817	−0.275408	+	0.961327i	$0.588813\pi$
$20$	17.2917	3.86655
$21$	0	0
$22$	−4.99017	−1.06391
$23$	1.81263	0.377959	0.188979	−	0.981981i	$-0.439482\pi$
$23$	1.81263	0.377959	0.188979	+	0.981981i	$0.439482\pi$
$24$	−3.09285	−0.631326
$25$	5.61537	1.12307
$26$	0	0
$27$	−2.03429	−0.391500
$28$	0	0
$29$	−2.73406	−0.507703	−0.253851	−	0.967243i	$-0.581697\pi$
$29$	−2.73406	−0.507703	−0.253851	+	0.967243i	$0.581697\pi$
$30$	−3.04689	−0.556284
$31$	1.74236	0.312937	0.156468	−	0.987683i	$-0.449989\pi$
$31$	1.74236	0.312937	0.156468	+	0.987683i	$0.449989\pi$
$32$	−18.7549	−3.31542
$33$	0.638632	0.111172
$34$	5.82036	0.998183
$35$	0	0
$36$	−15.2866	−2.54777
$37$	5.93565	0.975815	0.487908	−	0.872895i	$-0.337760\pi$
$37$	5.93565	0.975815	0.487908	+	0.872895i	$0.337760\pi$
$38$	6.49025	1.05286
$39$	0	0
$40$	−29.1283	−4.60558
$41$	−4.22131	−0.659259	−0.329629	−	0.944110i	$-0.606924\pi$
$41$	−4.22131	−0.659259	−0.329629	+	0.944110i	$0.606924\pi$
$42$	0	0
$43$	−8.68223	−1.32403	−0.662014	−	0.749492i	$-0.730298\pi$
$43$	−8.68223	−1.32403	−0.662014	+	0.749492i	$0.730298\pi$
$44$	9.79737	1.47701
$45$	−9.38444	−1.39895
$46$	−4.89989	−0.722449
$47$	5.87774	0.857357	0.428678	−	0.903457i	$-0.358979\pi$
$47$	5.87774	0.857357	0.428678	+	0.903457i	$0.358979\pi$
$48$	4.68850	0.676727
$49$	0	0
$50$	−15.1794	−2.14670
$51$	−0.744877	−0.104304
$52$	0	0
$53$	−9.30628	−1.27832	−0.639158	−	0.769076i	$-0.720717\pi$
$53$	−9.30628	−1.27832	−0.639158	+	0.769076i	$0.720717\pi$
$54$	5.49909	0.748331
$55$	6.01459	0.811007
$56$	0	0
$57$	−0.830609	−0.110017
$58$	7.39071	0.970447
$59$	−10.7523	−1.39982	−0.699912	−	0.714229i	$-0.746778\pi$
$59$	−10.7523	−1.39982	−0.699912	+	0.714229i	$0.746778\pi$
$60$	5.98206	0.772281
$61$	−10.1101	−1.29446	−0.647231	−	0.762294i	$-0.724073\pi$
$61$	−10.1101	−1.29446	−0.647231	+	0.762294i	$0.724073\pi$
$62$	−4.70994	−0.598163
$63$	0	0
$64$	23.5929	2.94911
$65$	0	0
$66$	−1.72635	−0.212499
$67$	0.826916	0.101024	0.0505119	−	0.998723i	$-0.483915\pi$
$67$	0.826916	0.101024	0.0505119	+	0.998723i	$0.483915\pi$
$68$	−11.4273	−1.38576
$69$	0.627077	0.0754912
$70$	0	0
$71$	2.35425	0.279398	0.139699	−	0.990194i	$-0.455387\pi$
$71$	2.35425	0.279398	0.139699	+	0.990194i	$0.455387\pi$
$72$	25.7506	3.03474
$73$	3.19482	0.373925	0.186963	−	0.982367i	$-0.440136\pi$
$73$	3.19482	0.373925	0.186963	+	0.982367i	$0.440136\pi$
$74$	−16.0452	−1.86522
$75$	1.94263	0.224316
$76$	−12.7425	−1.46167
$77$	0	0
$78$	0	0
$79$	0.801911	0.0902220	0.0451110	−	0.998982i	$-0.485636\pi$
$79$	0.801911	0.0902220	0.0451110	+	0.998982i	$0.485636\pi$
$80$	44.1559	4.93678
$81$	7.93720	0.881911
$82$	11.4110	1.26014
$83$	9.97031	1.09438	0.547192	−	0.837007i	$-0.315697\pi$
$83$	9.97031	1.09438	0.547192	+	0.837007i	$0.315697\pi$
$84$	0	0
$85$	−7.01520	−0.760905
$86$	23.4698	2.53081
$87$	−0.945847	−0.101405
$88$	−16.5039	−1.75932
$89$	15.1135	1.60202	0.801012	−	0.598648i	$-0.204295\pi$
$89$	15.1135	1.60202	0.801012	+	0.598648i	$0.204295\pi$
$90$	25.3680	2.67402
$91$	0	0
$92$	9.62010	1.00296
$93$	0.602768	0.0625041
$94$	−15.8887	−1.63879
$95$	−7.82261	−0.802583
$96$	−6.48823	−0.662202
$97$	9.23171	0.937338	0.468669	−	0.883374i	$-0.344734\pi$
$97$	9.23171	0.937338	0.468669	+	0.883374i	$0.344734\pi$
$98$	0	0
$99$	−5.31715	−0.534394
$100$	29.8023	2.98023
$101$	−14.8234	−1.47498	−0.737491	−	0.675357i	$-0.763989\pi$
$101$	−14.8234	−1.47498	−0.737491	+	0.675357i	$0.763989\pi$
$102$	2.01355	0.199371
$103$	4.28286	0.422003	0.211001	−	0.977486i	$-0.432328\pi$
$103$	4.28286	0.422003	0.211001	+	0.977486i	$0.432328\pi$
$104$	0	0
$105$	0	0
$106$	25.1567	2.44343
$107$	−19.1258	−1.84896	−0.924479	−	0.381233i	$-0.875500\pi$
$107$	−19.1258	−1.84896	−0.924479	+	0.381233i	$0.875500\pi$
$108$	−10.7965	−1.03890
$109$	−4.27153	−0.409139	−0.204569	−	0.978852i	$-0.565579\pi$
$109$	−4.27153	−0.409139	−0.204569	+	0.978852i	$0.565579\pi$
$110$	−16.2586	−1.55020
$111$	2.05343	0.194903
$112$	0	0
$113$	2.74976	0.258676	0.129338	−	0.991601i	$-0.458715\pi$
$113$	2.74976	0.258676	0.129338	+	0.991601i	$0.458715\pi$
$114$	2.24530	0.210291
$115$	5.90576	0.550715
$116$	−14.5104	−1.34726
$117$	0	0
$118$	29.0655	2.67569
$119$	0	0
$120$	−10.0769	−0.919891
$121$	−7.59218	−0.690198
$122$	27.3295	2.47430
$123$	−1.46036	−0.131676
$124$	9.24717	0.830420
$125$	2.00495	0.179329
$126$	0	0
$127$	−9.73438	−0.863786	−0.431893	−	0.901925i	$-0.642154\pi$
$127$	−9.73438	−0.863786	−0.431893	+	0.901925i	$0.642154\pi$
$128$	−26.2666	−2.32166
$129$	−3.00361	−0.264453
$130$	0	0
$131$	18.6615	1.63046	0.815230	−	0.579138i	$-0.196611\pi$
$131$	18.6615	1.63046	0.815230	+	0.579138i	$0.196611\pi$
$132$	3.38939	0.295009
$133$	0	0
$134$	−2.23532	−0.193102
$135$	−6.62797	−0.570445
$136$	19.2495	1.65063
$137$	−8.42156	−0.719502	−0.359751	−	0.933048i	$-0.617138\pi$
$137$	−8.42156	−0.719502	−0.359751	+	0.933048i	$0.617138\pi$
$138$	−1.69511	−0.144298
$139$	17.6362	1.49588	0.747941	−	0.663765i	$-0.231043\pi$
$139$	17.6362	1.49588	0.747941	+	0.663765i	$0.231043\pi$
$140$	0	0
$141$	2.03340	0.171243
$142$	−6.36399	−0.534054
$143$	0	0
$144$	−39.0357	−3.25298
$145$	−8.90791	−0.739762
$146$	−8.63623	−0.714739
$147$	0	0
$148$	31.5021	2.58946
$149$	4.02104	0.329416	0.164708	−	0.986342i	$-0.447332\pi$
$149$	4.02104	0.329416	0.164708	+	0.986342i	$0.447332\pi$
$150$	−5.25132	−0.428768
$151$	−18.9010	−1.53814	−0.769069	−	0.639165i	$-0.779280\pi$
$151$	−18.9010	−1.53814	−0.769069	+	0.639165i	$0.779280\pi$
$152$	21.4650	1.74104
$153$	6.20173	0.501380
$154$	0	0
$155$	5.67682	0.455973
$156$	0	0
$157$	11.5735	0.923670	0.461835	−	0.886966i	$-0.347191\pi$
$157$	11.5735	0.923670	0.461835	+	0.886966i	$0.347191\pi$
$158$	−2.16772	−0.172455
$159$	−3.21950	−0.255323
$160$	−61.1056	−4.83082
$161$	0	0
$162$	−21.4558	−1.68573
$163$	−4.40542	−0.345059	−0.172529	−	0.985004i	$-0.555194\pi$
$163$	−4.40542	−0.345059	−0.172529	+	0.985004i	$0.555194\pi$
$164$	−22.4037	−1.74943
$165$	2.08074	0.161985
$166$	−26.9517	−2.09186
$167$	−9.01909	−0.697918	−0.348959	−	0.937138i	$-0.613465\pi$
$167$	−9.01909	−0.697918	−0.348959	+	0.937138i	$0.613465\pi$
$168$	0	0
$169$	0	0
$170$	18.9635	1.45443
$171$	6.91552	0.528843
$172$	−46.0789	−3.51349
$173$	−6.09200	−0.463166	−0.231583	−	0.972815i	$-0.574391\pi$
$173$	−6.09200	−0.463166	−0.231583	+	0.972815i	$0.574391\pi$
$174$	2.55681	0.193831
$175$	0	0
$176$	25.0184	1.88583
$177$	−3.71974	−0.279592
$178$	−40.8547	−3.06219
$179$	3.87964	0.289978	0.144989	−	0.989433i	$-0.453685\pi$
$179$	3.87964	0.289978	0.144989	+	0.989433i	$0.453685\pi$
$180$	−49.8057	−3.71230
$181$	−6.58392	−0.489379	−0.244690	−	0.969601i	$-0.578686\pi$
$181$	−6.58392	−0.489379	−0.244690	+	0.969601i	$0.578686\pi$
$182$	0	0
$183$	−3.49757	−0.258548
$184$	−16.2052	−1.19467
$185$	19.3391	1.42184
$186$	−1.62940	−0.119473
$187$	−3.97476	−0.290663
$188$	31.1948	2.27511
$189$	0	0
$190$	21.1460	1.53410
$191$	−13.7434	−0.994435	−0.497218	−	0.867626i	$-0.665645\pi$
$191$	−13.7434	−0.994435	−0.497218	+	0.867626i	$0.665645\pi$
$192$	8.16195	0.589038
$193$	−22.7530	−1.63780	−0.818899	−	0.573937i	$-0.805415\pi$
$193$	−22.7530	−1.63780	−0.818899	+	0.573937i	$0.805415\pi$
$194$	−24.9551	−1.79167
$195$	0	0
$196$	0	0
$197$	−14.5272	−1.03502	−0.517509	−	0.855678i	$-0.673141\pi$
$197$	−14.5272	−1.03502	−0.517509	+	0.855678i	$0.673141\pi$
$198$	14.3733	1.02147
$199$	−23.8404	−1.69000	−0.845001	−	0.534765i	$-0.820400\pi$
$199$	−23.8404	−1.69000	−0.845001	+	0.534765i	$0.820400\pi$
$200$	−50.2025	−3.54985
$201$	0.286071	0.0201779
$202$	40.0705	2.81935
$203$	0	0
$204$	−3.95326	−0.276784
$205$	−13.7536	−0.960591
$206$	−11.5774	−0.806637
$207$	−5.22095	−0.362881
$208$	0	0
$209$	−4.43223	−0.306584
$210$	0	0
$211$	4.31527	0.297076	0.148538	−	0.988907i	$-0.452543\pi$
$211$	4.31527	0.297076	0.148538	+	0.988907i	$0.452543\pi$
$212$	−49.3909	−3.39218
$213$	0.814450	0.0558052
$214$	51.7007	3.53419
$215$	−28.2878	−1.92921
$216$	18.1870	1.23747
$217$	0	0
$218$	11.5468	0.782047
$219$	1.10525	0.0746856
$220$	31.9210	2.15212
$221$	0	0
$222$	−5.55083	−0.372548
$223$	23.3947	1.56662	0.783312	−	0.621629i	$-0.213529\pi$
$223$	23.3947	1.56662	0.783312	+	0.621629i	$0.213529\pi$
$224$	0	0
$225$	−16.1741	−1.07827
$226$	−7.43315	−0.494446
$227$	−26.7229	−1.77366	−0.886829	−	0.462097i	$-0.847097\pi$
$227$	−26.7229	−1.77366	−0.886829	+	0.462097i	$0.847097\pi$
$228$	−4.40826	−0.291944
$229$	−3.00670	−0.198688	−0.0993442	−	0.995053i	$-0.531674\pi$
$229$	−3.00670	−0.198688	−0.0993442	+	0.995053i	$0.531674\pi$
$230$	−15.9644	−1.05266
$231$	0	0
$232$	24.4431	1.60477
$233$	−11.7148	−0.767462	−0.383731	−	0.923445i	$-0.625361\pi$
$233$	−11.7148	−0.767462	−0.383731	+	0.923445i	$0.625361\pi$
$234$	0	0
$235$	19.1504	1.24924
$236$	−57.0651	−3.71462
$237$	0.277420	0.0180204
$238$	0	0
$239$	1.42797	0.0923677	0.0461838	−	0.998933i	$-0.485294\pi$
$239$	1.42797	0.0923677	0.0461838	+	0.998933i	$0.485294\pi$
$240$	15.2757	0.986043
$241$	2.67969	0.172614	0.0863069	−	0.996269i	$-0.472493\pi$
$241$	2.67969	0.172614	0.0863069	+	0.996269i	$0.472493\pi$
$242$	20.5232	1.31928
$243$	8.84874	0.567647
$244$	−53.6569	−3.43503
$245$	0	0
$246$	3.94764	0.251692
$247$	0	0
$248$	−15.5770	−0.989143
$249$	3.44922	0.218586
$250$	−5.41978	−0.342777
$251$	−10.9339	−0.690143	−0.345072	−	0.938576i	$-0.612145\pi$
$251$	−10.9339	−0.690143	−0.345072	+	0.938576i	$0.612145\pi$
$252$	0	0
$253$	3.34616	0.210371
$254$	26.3139	1.65108
$255$	−2.42690	−0.151978
$256$	23.8178	1.48861
$257$	−4.15138	−0.258956	−0.129478	−	0.991582i	$-0.541330\pi$
$257$	−4.15138	−0.258956	−0.129478	+	0.991582i	$0.541330\pi$
$258$	8.11935	0.505488
$259$	0	0
$260$	0	0
$261$	7.87497	0.487448
$262$	−50.4456	−3.11654
$263$	4.05360	0.249955	0.124978	−	0.992160i	$-0.460114\pi$
$263$	4.05360	0.249955	0.124978	+	0.992160i	$0.460114\pi$
$264$	−5.70949	−0.351395
$265$	−30.3210	−1.86260
$266$	0	0
$267$	5.22849	0.319979
$268$	4.38866	0.268080
$269$	−4.00022	−0.243898	−0.121949	−	0.992536i	$-0.538914\pi$
$269$	−4.00022	−0.243898	−0.121949	+	0.992536i	$0.538914\pi$
$270$	17.9167	1.09038
$271$	−2.78502	−0.169178	−0.0845888	−	0.996416i	$-0.526958\pi$
$271$	−2.78502	−0.169178	−0.0845888	+	0.996416i	$0.526958\pi$
$272$	−29.1806	−1.76933
$273$	0	0
$274$	22.7651	1.37529
$275$	10.3661	0.625101
$276$	3.32807	0.200326
$277$	16.6924	1.00295	0.501474	−	0.865173i	$-0.332791\pi$
$277$	16.6924	1.00295	0.501474	+	0.865173i	$0.332791\pi$
$278$	−47.6741	−2.85930
$279$	−5.01855	−0.300453
$280$	0	0
$281$	−13.3731	−0.797774	−0.398887	−	0.917000i	$-0.630603\pi$
$281$	−13.3731	−0.797774	−0.398887	+	0.917000i	$0.630603\pi$
$282$	−5.49668	−0.327322
$283$	18.8862	1.12267	0.561335	−	0.827589i	$-0.310288\pi$
$283$	18.8862	1.12267	0.561335	+	0.827589i	$0.310288\pi$
$284$	12.4946	0.741419
$285$	−2.70623	−0.160303
$286$	0	0
$287$	0	0
$288$	54.0200	3.18316
$289$	−12.3640	−0.727293
$290$	24.0798	1.41402
$291$	3.19370	0.187218
$292$	16.9558	0.992262
$293$	3.41790	0.199676	0.0998380	−	0.995004i	$-0.468168\pi$
$293$	3.41790	0.199676	0.0998380	+	0.995004i	$0.468168\pi$
$294$	0	0
$295$	−35.0322	−2.03965
$296$	−53.0659	−3.08439
$297$	−3.75536	−0.217908
$298$	−10.8697	−0.629663
$299$	0	0
$300$	10.3101	0.595252
$301$	0	0
$302$	51.0930	2.94007
$303$	−5.12814	−0.294604
$304$	−32.5391	−1.86625
$305$	−32.9399	−1.88613
$306$	−16.7645	−0.958362
$307$	−16.3679	−0.934165	−0.467083	−	0.884214i	$-0.654695\pi$
$307$	−16.3679	−0.934165	−0.467083	+	0.884214i	$0.654695\pi$
$308$	0	0
$309$	1.48165	0.0842883
$310$	−15.3456	−0.871569
$311$	−23.6979	−1.34378	−0.671891	−	0.740650i	$-0.734518\pi$
$311$	−23.6979	−1.34378	−0.671891	+	0.740650i	$0.734518\pi$
$312$	0	0
$313$	5.18025	0.292805	0.146403	−	0.989225i	$-0.453231\pi$
$313$	5.18025	0.292805	0.146403	+	0.989225i	$0.453231\pi$
$314$	−31.2856	−1.76555
$315$	0	0
$316$	4.25596	0.239416
$317$	−6.06537	−0.340665	−0.170332	−	0.985387i	$-0.554484\pi$
$317$	−6.06537	−0.340665	−0.170332	+	0.985387i	$0.554484\pi$
$318$	8.70294	0.488037
$319$	−5.04715	−0.282586
$320$	76.8686	4.29709
$321$	−6.61655	−0.369300
$322$	0	0
$323$	5.16959	0.287644
$324$	42.1248	2.34027
$325$	0	0
$326$	11.9087	0.659562
$327$	−1.47773	−0.0817188
$328$	37.7394	2.08381
$329$	0	0
$330$	−5.62465	−0.309627
$331$	−17.2749	−0.949512	−0.474756	−	0.880118i	$-0.657464\pi$
$331$	−17.2749	−0.949512	−0.474756	+	0.880118i	$0.657464\pi$
$332$	52.9151	2.90410
$333$	−17.0966	−0.936886
$334$	24.3804	1.33403
$335$	2.69419	0.147200
$336$	0	0
$337$	8.35464	0.455106	0.227553	−	0.973766i	$-0.426927\pi$
$337$	8.35464	0.455106	0.227553	+	0.973766i	$0.426927\pi$
$338$	0	0
$339$	0.951279	0.0516664
$340$	−37.2315	−2.01916
$341$	3.21644	0.174180
$342$	−18.6940	−1.01086
$343$	0	0
$344$	77.6208	4.18504
$345$	2.04309	0.109997
$346$	16.4679	0.885318
$347$	28.8220	1.54725	0.773623	−	0.633646i	$-0.218443\pi$
$347$	28.8220	1.54725	0.773623	+	0.633646i	$0.218443\pi$
$348$	−5.01986	−0.269093
$349$	−11.7221	−0.627467	−0.313734	−	0.949511i	$-0.601580\pi$
$349$	−11.7221	−0.627467	−0.313734	+	0.949511i	$0.601580\pi$
$350$	0	0
$351$	0	0
$352$	−34.6220	−1.84536
$353$	−17.8362	−0.949326	−0.474663	−	0.880168i	$-0.657430\pi$
$353$	−17.8362	−0.949326	−0.474663	+	0.880168i	$0.657430\pi$
$354$	10.0552	0.534426
$355$	7.67043	0.407104
$356$	80.2113	4.25119
$357$	0	0
$358$	−10.4874	−0.554278
$359$	5.68162	0.299864	0.149932	−	0.988696i	$-0.452094\pi$
$359$	5.68162	0.299864	0.149932	+	0.988696i	$0.452094\pi$
$360$	83.8987	4.42185
$361$	−13.2354	−0.696601
$362$	17.7976	0.935423
$363$	−2.62651	−0.137856
$364$	0	0
$365$	10.4091	0.544838
$366$	9.45462	0.494201
$367$	19.6316	1.02476	0.512381	−	0.858758i	$-0.328764\pi$
$367$	19.6316	1.02476	0.512381	+	0.858758i	$0.328764\pi$
$368$	24.5658	1.28058
$369$	12.1587	0.632958
$370$	−52.2773	−2.71777
$371$	0	0
$372$	3.19905	0.165863
$373$	32.0645	1.66024	0.830119	−	0.557586i	$-0.188272\pi$
$373$	32.0645	1.66024	0.830119	+	0.557586i	$0.188272\pi$
$374$	10.7445	0.555587
$375$	0.693612	0.0358180
$376$	−52.5482	−2.70997
$377$	0	0
$378$	0	0
$379$	−19.0231	−0.977150	−0.488575	−	0.872522i	$-0.662483\pi$
$379$	−19.0231	−0.977150	−0.488575	+	0.872522i	$0.662483\pi$
$380$	−41.5167	−2.12976
$381$	−3.36760	−0.172527
$382$	37.1510	1.90081
$383$	0.699829	0.0357596	0.0178798	−	0.999840i	$-0.494308\pi$
$383$	0.699829	0.0357596	0.0178798	+	0.999840i	$0.494308\pi$
$384$	−9.08689	−0.463714
$385$	0	0
$386$	61.5059	3.13057
$387$	25.0076	1.27121
$388$	48.9951	2.48735
$389$	−20.0547	−1.01681	−0.508407	−	0.861117i	$-0.669765\pi$
$389$	−20.0547	−1.01681	−0.508407	+	0.861117i	$0.669765\pi$
$390$	0	0
$391$	−3.90284	−0.197375
$392$	0	0
$393$	6.45592	0.325658
$394$	39.2698	1.97838
$395$	2.61272	0.131460
$396$	−28.2195	−1.41809
$397$	22.2803	1.11822	0.559108	−	0.829095i	$-0.311144\pi$
$397$	22.2803	1.11822	0.559108	+	0.829095i	$0.311144\pi$
$398$	64.4453	3.23035
$399$	0	0
$400$	76.1027	3.80513
$401$	4.80749	0.240074	0.120037	−	0.992769i	$-0.461699\pi$
$401$	4.80749	0.240074	0.120037	+	0.992769i	$0.461699\pi$
$402$	−0.773306	−0.0385690
$403$	0	0
$404$	−78.6717	−3.91406
$405$	25.8604	1.28501
$406$	0	0
$407$	10.9574	0.543137
$408$	6.65935	0.329687
$409$	36.8035	1.81981	0.909907	−	0.414811i	$-0.136152\pi$
$409$	36.8035	1.81981	0.909907	+	0.414811i	$0.136152\pi$
$410$	37.1786	1.83612
$411$	−2.91343	−0.143709
$412$	22.7303	1.11984
$413$	0	0
$414$	14.1132	0.693628
$415$	32.4845	1.59460
$416$	0	0
$417$	6.10122	0.298778
$418$	11.9812	0.586019
$419$	−29.2667	−1.42977	−0.714887	−	0.699240i	$-0.753522\pi$
$419$	−29.2667	−1.42977	−0.714887	+	0.699240i	$0.753522\pi$
$420$	0	0
$421$	−7.53862	−0.367410	−0.183705	−	0.982981i	$-0.558809\pi$
$421$	−7.53862	−0.367410	−0.183705	+	0.982981i	$0.558809\pi$
$422$	−11.6650	−0.567845
$423$	−16.9298	−0.823154
$424$	83.2000	4.04055
$425$	−12.0907	−0.586484
$426$	−2.20162	−0.106669
$427$	0	0
$428$	−101.506	−4.90646
$429$	0	0
$430$	76.4674	3.68759
$431$	−31.2261	−1.50411	−0.752055	−	0.659101i	$-0.770937\pi$
$431$	−31.2261	−1.50411	−0.752055	+	0.659101i	$0.770937\pi$
$432$	−27.5699	−1.32646
$433$	−5.88404	−0.282769	−0.141384	−	0.989955i	$-0.545155\pi$
$433$	−5.88404	−0.282769	−0.141384	+	0.989955i	$0.545155\pi$
$434$	0	0
$435$	−3.08169	−0.147755
$436$	−22.6702	−1.08570
$437$	−4.35204	−0.208186
$438$	−2.98770	−0.142758
$439$	9.95642	0.475194	0.237597	−	0.971364i	$-0.423640\pi$
$439$	9.95642	0.475194	0.237597	+	0.971364i	$0.423640\pi$
$440$	−53.7716	−2.56346
$441$	0	0
$442$	0	0
$443$	−35.8813	−1.70477	−0.852385	−	0.522915i	$-0.824845\pi$
$443$	−35.8813	−1.70477	−0.852385	+	0.522915i	$0.824845\pi$
$444$	10.8981	0.517202
$445$	49.2416	2.33427
$446$	−63.2404	−2.99452
$447$	1.39108	0.0657956
$448$	0	0
$449$	3.99528	0.188549	0.0942744	−	0.995546i	$-0.469947\pi$
$449$	3.99528	0.188549	0.0942744	+	0.995546i	$0.469947\pi$
$450$	43.7217	2.06106
$451$	−7.79266	−0.366942
$452$	14.5937	0.686432
$453$	−6.53877	−0.307218
$454$	72.2371	3.39026
$455$	0	0
$456$	7.42580	0.347745
$457$	41.2222	1.92829	0.964147	−	0.265369i	$-0.0854937\pi$
$457$	41.2222	1.92829	0.964147	+	0.265369i	$0.0854937\pi$
$458$	8.12770	0.379783
$459$	4.38011	0.204446
$460$	31.3435	1.46140
$461$	24.7266	1.15163	0.575816	−	0.817579i	$-0.304684\pi$
$461$	24.7266	1.15163	0.575816	+	0.817579i	$0.304684\pi$
$462$	0	0
$463$	24.4057	1.13423	0.567115	−	0.823639i	$-0.308060\pi$
$463$	24.4057	1.13423	0.567115	+	0.823639i	$0.308060\pi$
$464$	−37.0536	−1.72017
$465$	1.96389	0.0910733
$466$	31.6674	1.46696
$467$	4.44860	0.205857	0.102928	−	0.994689i	$-0.467179\pi$
$467$	4.44860	0.205857	0.102928	+	0.994689i	$0.467179\pi$
$468$	0	0
$469$	0	0
$470$	−51.7673	−2.38785
$471$	4.00386	0.184488
$472$	96.1273	4.42462
$473$	−16.0276	−0.736951
$474$	−0.749922	−0.0344450
$475$	−13.4823	−0.618608
$476$	0	0
$477$	26.8051	1.22732
$478$	−3.86008	−0.176556
$479$	−31.6766	−1.44734	−0.723671	−	0.690145i	$-0.757547\pi$
$479$	−31.6766	−1.44734	−0.723671	+	0.690145i	$0.757547\pi$
$480$	−21.1394	−0.964879
$481$	0	0
$482$	−7.24372	−0.329942
$483$	0	0
$484$	−40.2938	−1.83153
$485$	30.0780	1.36577
$486$	−23.9199	−1.08503
$487$	−26.9156	−1.21966	−0.609832	−	0.792531i	$-0.708763\pi$
$487$	−26.9156	−1.21966	−0.609832	+	0.792531i	$0.708763\pi$
$488$	90.3860	4.09158
$489$	−1.52405	−0.0689200
$490$	0	0
$491$	9.72716	0.438980	0.219490	−	0.975615i	$-0.429561\pi$
$491$	9.72716	0.438980	0.219490	+	0.975615i	$0.429561\pi$
$492$	−7.75052	−0.349421
$493$	5.88682	0.265129
$494$	0	0
$495$	−17.3239	−0.778653
$496$	23.6134	1.06027
$497$	0	0
$498$	−9.32392	−0.417815
$499$	7.87525	0.352545	0.176272	−	0.984341i	$-0.443596\pi$
$499$	7.87525	0.352545	0.176272	+	0.984341i	$0.443596\pi$
$500$	10.6408	0.475872
$501$	−3.12015	−0.139398
$502$	29.5565	1.31917
$503$	9.75206	0.434823	0.217411	−	0.976080i	$-0.430239\pi$
$503$	9.75206	0.434823	0.217411	+	0.976080i	$0.430239\pi$
$504$	0	0
$505$	−48.2964	−2.14916
$506$	−9.04533	−0.402114
$507$	0	0
$508$	−51.6630	−2.29217
$509$	23.0256	1.02059	0.510295	−	0.859999i	$-0.329536\pi$
$509$	23.0256	1.02059	0.510295	+	0.859999i	$0.329536\pi$
$510$	6.56039	0.290499
$511$	0	0
$512$	−11.8512	−0.523752
$513$	4.88424	0.215645
$514$	11.2220	0.494981
$515$	13.9541	0.614891
$516$	−15.9410	−0.701762
$517$	10.8505	0.477203
$518$	0	0
$519$	−2.10752	−0.0925100
$520$	0	0
$521$	−0.486481	−0.0213131	−0.0106566	−	0.999943i	$-0.503392\pi$
$521$	−0.486481	−0.0213131	−0.0106566	+	0.999943i	$0.503392\pi$
$522$	−21.2876	−0.931733
$523$	34.6270	1.51413	0.757065	−	0.653339i	$-0.226632\pi$
$523$	34.6270	1.51413	0.757065	+	0.653339i	$0.226632\pi$
$524$	99.0414	4.32664
$525$	0	0
$526$	−10.9577	−0.477777
$527$	−3.75154	−0.163420
$528$	8.65510	0.376665
$529$	−19.7144	−0.857147
$530$	81.9636	3.56027
$531$	30.9699	1.34398
$532$	0	0
$533$	0	0
$534$	−14.1336	−0.611622
$535$	−62.3141	−2.69408
$536$	−7.39279	−0.319320
$537$	1.34216	0.0579185
$538$	10.8134	0.466198
$539$	0	0
$540$	−35.1764	−1.51375
$541$	−22.5384	−0.969002	−0.484501	−	0.874791i	$-0.660999\pi$
$541$	−22.5384	−0.969002	−0.484501	+	0.874791i	$0.660999\pi$
$542$	7.52844	0.323374
$543$	−2.27770	−0.0977456
$544$	40.3818	1.73136
$545$	−13.9172	−0.596146
$546$	0	0
$547$	39.3716	1.68341	0.841704	−	0.539940i	$-0.181553\pi$
$547$	39.3716	1.68341	0.841704	+	0.539940i	$0.181553\pi$
$548$	−44.6955	−1.90930
$549$	29.1202	1.24282
$550$	−28.0217	−1.19485
$551$	6.56436	0.279651
$552$	−5.60619	−0.238615
$553$	0	0
$554$	−45.1227	−1.91708
$555$	6.69034	0.283989
$556$	93.6000	3.96952
$557$	−0.726975	−0.0308029	−0.0154015	−	0.999881i	$-0.504903\pi$
$557$	−0.726975	−0.0308029	−0.0154015	+	0.999881i	$0.504903\pi$
$558$	13.5661	0.574300
$559$	0	0
$560$	0	0
$561$	−1.37506	−0.0580552
$562$	36.1502	1.52490
$563$	−41.6077	−1.75355	−0.876777	−	0.480897i	$-0.840311\pi$
$563$	−41.6077	−1.75355	−0.876777	+	0.480897i	$0.840311\pi$
$564$	10.7918	0.454417
$565$	8.95907	0.376911
$566$	−51.0532	−2.14593
$567$	0	0
$568$	−21.0474	−0.883130
$569$	−25.3888	−1.06435	−0.532177	−	0.846633i	$-0.678626\pi$
$569$	−25.3888	−1.06435	−0.532177	+	0.846633i	$0.678626\pi$
$570$	7.31546	0.306411
$571$	16.9992	0.711393	0.355697	−	0.934602i	$-0.384244\pi$
$571$	16.9992	0.711393	0.355697	+	0.934602i	$0.384244\pi$
$572$	0	0
$573$	−4.75451	−0.198622
$574$	0	0
$575$	10.1786	0.424476
$576$	−67.9551	−2.83146
$577$	15.9759	0.665084	0.332542	−	0.943088i	$-0.392094\pi$
$577$	15.9759	0.665084	0.332542	+	0.943088i	$0.392094\pi$
$578$	33.4223	1.39018
$579$	−7.87139	−0.327124
$580$	−47.2767	−1.96306
$581$	0	0
$582$	−8.63320	−0.357858
$583$	−17.1796	−0.711508
$584$	−28.5623	−1.18192
$585$	0	0
$586$	−9.23926	−0.381670
$587$	15.9815	0.659627	0.329814	−	0.944046i	$-0.393014\pi$
$587$	15.9815	0.659627	0.329814	+	0.944046i	$0.393014\pi$
$588$	0	0
$589$	−4.18333	−0.172371
$590$	94.6989	3.89869
$591$	−5.02566	−0.206728
$592$	80.4433	3.30620
$593$	−29.0532	−1.19307	−0.596536	−	0.802586i	$-0.703457\pi$
$593$	−29.0532	−1.19307	−0.596536	+	0.802586i	$0.703457\pi$
$594$	10.1515	0.416520
$595$	0	0
$596$	21.3407	0.874151
$597$	−8.24757	−0.337551
$598$	0	0
$599$	3.45554	0.141190	0.0705948	−	0.997505i	$-0.477510\pi$
$599$	3.45554	0.141190	0.0705948	+	0.997505i	$0.477510\pi$
$600$	−17.3675	−0.709026
$601$	−15.5304	−0.633497	−0.316748	−	0.948510i	$-0.602591\pi$
$601$	−15.5304	−0.633497	−0.316748	+	0.948510i	$0.602591\pi$
$602$	0	0
$603$	−2.38178	−0.0969936
$604$	−100.313	−4.08166
$605$	−24.7363	−1.00567
$606$	13.8624	0.563120
$607$	−15.4784	−0.628250	−0.314125	−	0.949382i	$-0.601711\pi$
$607$	−15.4784	−0.628250	−0.314125	+	0.949382i	$0.601711\pi$
$608$	45.0296	1.82619
$609$	0	0
$610$	89.0429	3.60524
$611$	0	0
$612$	32.9142	1.33048
$613$	−7.13223	−0.288068	−0.144034	−	0.989573i	$-0.546007\pi$
$613$	−7.13223	−0.288068	−0.144034	+	0.989573i	$0.546007\pi$
$614$	44.2456	1.78561
$615$	−4.75803	−0.191862
$616$	0	0
$617$	4.96685	0.199958	0.0999789	−	0.994990i	$-0.468122\pi$
$617$	4.96685	0.199958	0.0999789	+	0.994990i	$0.468122\pi$
$618$	−4.00520	−0.161113
$619$	−42.3570	−1.70247	−0.851235	−	0.524784i	$-0.824146\pi$
$619$	−42.3570	−1.70247	−0.851235	+	0.524784i	$0.824146\pi$
$620$	30.1284	1.20999
$621$	−3.68741	−0.147971
$622$	64.0600	2.56857
$623$	0	0
$624$	0	0
$625$	−21.5445	−0.861779
$626$	−14.0032	−0.559682
$627$	−1.53333	−0.0612352
$628$	61.4239	2.45108
$629$	−12.7803	−0.509583
$630$	0	0
$631$	−6.26775	−0.249515	−0.124758	−	0.992187i	$-0.539815\pi$
$631$	−6.26775	−0.249515	−0.124758	+	0.992187i	$0.539815\pi$
$632$	−7.16924	−0.285177
$633$	1.49286	0.0593361
$634$	16.3959	0.651163
$635$	−31.7158	−1.25860
$636$	−17.0868	−0.677534
$637$	0	0
$638$	13.6434	0.540149
$639$	−6.78098	−0.268251
$640$	−85.5797	−3.38283
$641$	−31.5637	−1.24669	−0.623345	−	0.781947i	$-0.714227\pi$
$641$	−31.5637	−1.24669	−0.623345	+	0.781947i	$0.714227\pi$
$642$	17.8858	0.705897
$643$	18.2504	0.719725	0.359863	−	0.933005i	$-0.382824\pi$
$643$	18.2504	0.719725	0.359863	+	0.933005i	$0.382824\pi$
$644$	0	0
$645$	−9.78613	−0.385329
$646$	−13.9744	−0.549816
$647$	−23.0273	−0.905298	−0.452649	−	0.891689i	$-0.649521\pi$
$647$	−23.0273	−0.905298	−0.452649	+	0.891689i	$0.649521\pi$
$648$	−70.9601	−2.78758
$649$	−19.8490	−0.779140
$650$	0	0
$651$	0	0
$652$	−23.3807	−0.915660
$653$	28.8124	1.12752	0.563759	−	0.825939i	$-0.309355\pi$
$653$	28.8124	1.12752	0.563759	+	0.825939i	$0.309355\pi$
$654$	3.99460	0.156201
$655$	60.8014	2.37571
$656$	−57.2096	−2.23366
$657$	−9.20210	−0.359008
$658$	0	0
$659$	−31.2228	−1.21627	−0.608134	−	0.793835i	$-0.708082\pi$
$659$	−31.2228	−1.21627	−0.608134	+	0.793835i	$0.708082\pi$
$660$	11.0431	0.429850
$661$	−26.5582	−1.03299	−0.516496	−	0.856289i	$-0.672764\pi$
$661$	−26.5582	−1.03299	−0.516496	+	0.856289i	$0.672764\pi$
$662$	46.6973	1.81494
$663$	0	0
$664$	−89.1366	−3.45917
$665$	0	0
$666$	46.2154	1.79081
$667$	−4.95584	−0.191891
$668$	−47.8667	−1.85202
$669$	8.09337	0.312908
$670$	−7.28293	−0.281364
$671$	−18.6635	−0.720495
$672$	0	0
$673$	−19.7386	−0.760867	−0.380434	−	0.924808i	$-0.624225\pi$
$673$	−19.7386	−0.760867	−0.380434	+	0.924808i	$0.624225\pi$
$674$	−22.5842	−0.869912
$675$	−11.4233	−0.439683
$676$	0	0
$677$	13.1440	0.505163	0.252582	−	0.967576i	$-0.418720\pi$
$677$	13.1440	0.505163	0.252582	+	0.967576i	$0.418720\pi$
$678$	−2.57149	−0.0987576
$679$	0	0
$680$	62.7172	2.40510
$681$	−9.24475	−0.354260
$682$	−8.69468	−0.332936
$683$	−6.76255	−0.258762	−0.129381	−	0.991595i	$-0.541299\pi$
$683$	−6.76255	−0.258762	−0.129381	+	0.991595i	$0.541299\pi$
$684$	36.7025	1.40336
$685$	−27.4385	−1.04837
$686$	0	0
$687$	−1.04017	−0.0396848
$688$	−117.666	−4.48599
$689$	0	0
$690$	−5.52288	−0.210253
$691$	−9.17090	−0.348877	−0.174439	−	0.984668i	$-0.555811\pi$
$691$	−9.17090	−0.348877	−0.174439	+	0.984668i	$0.555811\pi$
$692$	−32.3319	−1.22907
$693$	0	0
$694$	−77.9115	−2.95748
$695$	57.4609	2.17962
$696$	8.45605	0.320526
$697$	9.08908	0.344273
$698$	31.6870	1.19937
$699$	−4.05272	−0.153288
$700$	0	0
$701$	−47.4700	−1.79292	−0.896459	−	0.443127i	$-0.853869\pi$
$701$	−47.4700	−1.79292	−0.896459	+	0.443127i	$0.853869\pi$
$702$	0	0
$703$	−14.2512	−0.537495
$704$	43.5532	1.64147
$705$	6.62507	0.249515
$706$	48.2148	1.81459
$707$	0	0
$708$	−19.7416	−0.741936
$709$	34.9719	1.31340	0.656699	−	0.754153i	$-0.271952\pi$
$709$	34.9719	1.31340	0.656699	+	0.754153i	$0.271952\pi$
$710$	−20.7347	−0.778158
$711$	−2.30976	−0.0866227
$712$	−135.117	−5.06374
$713$	3.15825	0.118277
$714$	0	0
$715$	0	0
$716$	20.5903	0.769496
$717$	0.494005	0.0184490
$718$	−15.3585	−0.573175
$719$	8.36101	0.311813	0.155907	−	0.987772i	$-0.450170\pi$
$719$	8.36101	0.311813	0.155907	+	0.987772i	$0.450170\pi$
$720$	−127.183	−4.73984
$721$	0	0
$722$	35.7779	1.33152
$723$	0.927035	0.0344768
$724$	−34.9427	−1.29863
$725$	−15.3528	−0.570188
$726$	7.09997	0.263505
$727$	−27.4014	−1.01626	−0.508131	−	0.861280i	$-0.669663\pi$
$727$	−27.4014	−1.01626	−0.508131	+	0.861280i	$0.669663\pi$
$728$	0	0
$729$	−20.7504	−0.768532
$730$	−28.1379	−1.04143
$731$	18.6941	0.691425
$732$	−18.5625	−0.686092
$733$	12.1569	0.449026	0.224513	−	0.974471i	$-0.427921\pi$
$733$	12.1569	0.449026	0.224513	+	0.974471i	$0.427921\pi$
$734$	−53.0681	−1.95878
$735$	0	0
$736$	−33.9956	−1.25309
$737$	1.52651	0.0562297
$738$	−32.8674	−1.20987
$739$	48.4439	1.78204	0.891019	−	0.453966i	$-0.149991\pi$
$739$	48.4439	1.78204	0.891019	+	0.453966i	$0.149991\pi$
$740$	102.638	3.77304
$741$	0	0
$742$	0	0
$743$	−16.9906	−0.623326	−0.311663	−	0.950193i	$-0.600886\pi$
$743$	−16.9906	−0.623326	−0.311663	+	0.950193i	$0.600886\pi$
$744$	−5.38886	−0.197565
$745$	13.1010	0.479985
$746$	−86.6767	−3.17346
$747$	−28.7177	−1.05073
$748$	−21.0951	−0.771313
$749$	0	0
$750$	−1.87497	−0.0684642
$751$	43.0323	1.57027	0.785136	−	0.619323i	$-0.212593\pi$
$751$	43.0323	1.57027	0.785136	+	0.619323i	$0.212593\pi$
$752$	79.6585	2.90485
$753$	−3.78258	−0.137845
$754$	0	0
$755$	−61.5817	−2.24119
$756$	0	0
$757$	29.1785	1.06051	0.530255	−	0.847838i	$-0.322096\pi$
$757$	29.1785	1.06051	0.530255	+	0.847838i	$0.322096\pi$
$758$	51.4231	1.86777
$759$	1.15760	0.0420183
$760$	69.9357	2.53683
$761$	29.4251	1.06666	0.533330	−	0.845907i	$-0.320941\pi$
$761$	29.4251	1.06666	0.533330	+	0.845907i	$0.320941\pi$
$762$	9.10328	0.329777
$763$	0	0
$764$	−72.9398	−2.63887
$765$	20.2060	0.730550
$766$	−1.89178	−0.0683526
$767$	0	0
$768$	8.23976	0.297327
$769$	−17.1864	−0.619759	−0.309879	−	0.950776i	$-0.600289\pi$
$769$	−17.1864	−0.619759	−0.309879	+	0.950776i	$0.600289\pi$
$770$	0	0
$771$	−1.43617	−0.0517223
$772$	−120.756	−4.34612
$773$	21.9601	0.789851	0.394926	−	0.918713i	$-0.370770\pi$
$773$	21.9601	0.789851	0.394926	+	0.918713i	$0.370770\pi$
$774$	−67.6004	−2.42985
$775$	9.78399	0.351451
$776$	−82.5333	−2.96277
$777$	0	0
$778$	54.2118	1.94359
$779$	10.1352	0.363131
$780$	0	0
$781$	4.34600	0.155512
$782$	10.5501	0.377272
$783$	5.56188	0.198765
$784$	0	0
$785$	37.7081	1.34586
$786$	−17.4516	−0.622478
$787$	2.33567	0.0832578	0.0416289	−	0.999133i	$-0.486745\pi$
$787$	2.33567	0.0832578	0.0416289	+	0.999133i	$0.486745\pi$
$788$	−77.0996	−2.74656
$789$	1.40234	0.0499246
$790$	−7.06271	−0.251280
$791$	0	0
$792$	47.5364	1.68913
$793$	0	0
$794$	−60.2280	−2.13741
$795$	−10.4895	−0.372025
$796$	−126.527	−4.48465
$797$	−27.8040	−0.984869	−0.492434	−	0.870350i	$-0.663893\pi$
$797$	−27.8040	−0.984869	−0.492434	+	0.870350i	$0.663893\pi$
$798$	0	0
$799$	−12.6556	−0.447723
$800$	−105.315	−3.72346
$801$	−43.5316	−1.53811
$802$	−12.9956	−0.458890
$803$	5.89773	0.208126
$804$	1.51825	0.0535447
$805$	0	0
$806$	0	0
$807$	−1.38387	−0.0487147
$808$	132.524	4.66218
$809$	15.0203	0.528087	0.264043	−	0.964511i	$-0.414944\pi$
$809$	15.0203	0.528087	0.264043	+	0.964511i	$0.414944\pi$
$810$	−69.9056	−2.45623
$811$	−43.6933	−1.53428	−0.767139	−	0.641481i	$-0.778320\pi$
$811$	−43.6933	−1.53428	−0.767139	+	0.641481i	$0.778320\pi$
$812$	0	0
$813$	−0.963474	−0.0337905
$814$	−29.6199	−1.03818
$815$	−14.3534	−0.502778
$816$	−10.0950	−0.353395
$817$	20.8456	0.729297
$818$	−99.4870	−3.47848
$819$	0	0
$820$	−72.9939	−2.54906
$821$	18.0701	0.630651	0.315326	−	0.948984i	$-0.397886\pi$
$821$	18.0701	0.630651	0.315326	+	0.948984i	$0.397886\pi$
$822$	7.87557	0.274692
$823$	4.45550	0.155309	0.0776544	−	0.996980i	$-0.475257\pi$
$823$	4.45550	0.155309	0.0776544	+	0.996980i	$0.475257\pi$
$824$	−38.2896	−1.33388
$825$	3.58615	0.124854
$826$	0	0
$827$	−11.8352	−0.411549	−0.205774	−	0.978599i	$-0.565971\pi$
$827$	−11.8352	−0.411549	−0.205774	+	0.978599i	$0.565971\pi$
$828$	−27.7090	−0.962953
$829$	3.53894	0.122913	0.0614563	−	0.998110i	$-0.480426\pi$
$829$	3.53894	0.122913	0.0614563	+	0.998110i	$0.480426\pi$
$830$	−87.8120	−3.04800
$831$	5.77471	0.200323
$832$	0	0
$833$	0	0
$834$	−16.4928	−0.571099
$835$	−29.3853	−1.01692
$836$	−23.5230	−0.813561
$837$	−3.54447	−0.122515
$838$	79.1137	2.73294
$839$	33.4853	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$839$	33.4853	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$840$	0	0
$841$	−21.5249	−0.742238
$842$	20.3784	0.702285
$843$	−4.62642	−0.159343
$844$	22.9023	0.788330
$845$	0	0
$846$	45.7645	1.57342
$847$	0	0
$848$	−126.124	−4.33112
$849$	6.53368	0.224235
$850$	32.6835	1.12103
$851$	10.7591	0.368818
$852$	4.32250	0.148087
$853$	22.0871	0.756248	0.378124	−	0.925755i	$-0.376569\pi$
$853$	22.0871	0.756248	0.378124	+	0.925755i	$0.376569\pi$
$854$	0	0
$855$	22.5316	0.770565
$856$	170.988	5.84426
$857$	6.89363	0.235482	0.117741	−	0.993044i	$-0.462435\pi$
$857$	6.89363	0.235482	0.117741	+	0.993044i	$0.462435\pi$
$858$	0	0
$859$	37.4834	1.27892	0.639459	−	0.768825i	$-0.279158\pi$
$859$	37.4834	1.27892	0.639459	+	0.768825i	$0.279158\pi$
$860$	−150.131	−5.11942
$861$	0	0
$862$	84.4103	2.87503
$863$	−17.5248	−0.596552	−0.298276	−	0.954480i	$-0.596412\pi$
$863$	−17.5248	−0.596552	−0.298276	+	0.954480i	$0.596412\pi$
$864$	38.1528	1.29799
$865$	−19.8485	−0.674869
$866$	15.9057	0.540498
$867$	−4.27731	−0.145265
$868$	0	0
$869$	1.48035	0.0502174
$870$	8.33040	0.282427
$871$	0	0
$872$	38.1883	1.29322
$873$	−26.5903	−0.899944
$874$	11.7644	0.397937
$875$	0	0
$876$	5.86584	0.198188
$877$	46.7491	1.57860	0.789302	−	0.614005i	$-0.210443\pi$
$877$	46.7491	1.57860	0.789302	+	0.614005i	$0.210443\pi$
$878$	−26.9142	−0.908309
$879$	1.18242	0.0398821
$880$	81.5131	2.74781
$881$	2.91875	0.0983350	0.0491675	−	0.998791i	$-0.484343\pi$
$881$	2.91875	0.0983350	0.0491675	+	0.998791i	$0.484343\pi$
$882$	0	0
$883$	−28.5505	−0.960801	−0.480400	−	0.877049i	$-0.659509\pi$
$883$	−28.5505	−0.960801	−0.480400	+	0.877049i	$0.659509\pi$
$884$	0	0
$885$	−12.1194	−0.407388
$886$	96.9941	3.25858
$887$	−0.422914	−0.0142001	−0.00710004	−	0.999975i	$-0.502260\pi$
$887$	−0.422914	−0.0142001	−0.00710004	+	0.999975i	$0.502260\pi$
$888$	−18.3581	−0.616058
$889$	0	0
$890$	−133.110	−4.46184
$891$	14.6523	0.490870
$892$	124.162	4.15725
$893$	−14.1122	−0.472247
$894$	−3.76035	−0.125765
$895$	12.6404	0.422521
$896$	0	0
$897$	0	0
$898$	−10.8000	−0.360401
$899$	−4.76372	−0.158879
$900$	−85.8401	−2.86134
$901$	20.0377	0.667553
$902$	21.0651	0.701391
$903$	0	0
$904$	−24.5834	−0.817633
$905$	−21.4512	−0.713063
$906$	17.6756	0.587232
$907$	−22.4284	−0.744723	−0.372361	−	0.928088i	$-0.621452\pi$
$907$	−22.4284	−0.744723	−0.372361	+	0.928088i	$0.621452\pi$
$908$	−141.825	−4.70664
$909$	42.6961	1.41614
$910$	0	0
$911$	−32.5788	−1.07938	−0.539692	−	0.841863i	$-0.681459\pi$
$911$	−32.5788	−1.07938	−0.539692	+	0.841863i	$0.681459\pi$
$912$	−11.2569	−0.372752
$913$	18.4055	0.609132
$914$	−111.432	−3.68583
$915$	−11.3955	−0.376724
$916$	−15.9574	−0.527247
$917$	0	0
$918$	−11.8403	−0.390788
$919$	−9.87913	−0.325883	−0.162941	−	0.986636i	$-0.552098\pi$
$919$	−9.87913	−0.325883	−0.162941	+	0.986636i	$0.552098\pi$
$920$	−52.7987	−1.74072
$921$	−5.66246	−0.186584
$922$	−66.8408	−2.20129
$923$	0	0
$924$	0	0
$925$	33.3309	1.09591
$926$	−65.9734	−2.16802
$927$	−12.3360	−0.405168
$928$	51.2769	1.68325
$929$	29.9136	0.981434	0.490717	−	0.871319i	$-0.336735\pi$
$929$	29.9136	0.981434	0.490717	+	0.871319i	$0.336735\pi$
$930$	−5.30878	−0.174082
$931$	0	0
$932$	−62.1736	−2.03656
$933$	−8.19826	−0.268399
$934$	−12.0255	−0.393485
$935$	−12.9502	−0.423518
$936$	0	0
$937$	31.8296	1.03983	0.519914	−	0.854219i	$-0.325964\pi$
$937$	31.8296	1.03983	0.519914	+	0.854219i	$0.325964\pi$
$938$	0	0
$939$	1.79210	0.0584831
$940$	101.636	3.31501
$941$	42.0885	1.37205	0.686023	−	0.727580i	$-0.259355\pi$
$941$	42.0885	1.37205	0.686023	+	0.727580i	$0.259355\pi$
$942$	−10.8232	−0.352640
$943$	−7.65167	−0.249173
$944$	−145.721	−4.74280
$945$	0	0
$946$	43.3258	1.40864
$947$	−60.3377	−1.96071	−0.980357	−	0.197234i	$-0.936804\pi$
$947$	−60.3377	−1.96071	−0.980357	+	0.197234i	$0.936804\pi$
$948$	1.47234	0.0478195
$949$	0	0
$950$	36.4452	1.18244
$951$	−2.09831	−0.0680423
$952$	0	0
$953$	−17.3754	−0.562844	−0.281422	−	0.959584i	$-0.590806\pi$
$953$	−17.3754	−0.562844	−0.281422	+	0.959584i	$0.590806\pi$
$954$	−72.4593	−2.34596
$955$	−44.7776	−1.44897
$956$	7.57862	0.245110
$957$	−1.74606	−0.0564421
$958$	85.6281	2.76652
$959$	0	0
$960$	26.5926	0.858274
$961$	−27.9642	−0.902070
$962$	0	0
$963$	55.0883	1.77520
$964$	14.2218	0.458054
$965$	−74.1322	−2.38640
$966$	0	0
$967$	18.8630	0.606594	0.303297	−	0.952896i	$-0.401913\pi$
$967$	18.8630	0.606594	0.303297	+	0.952896i	$0.401913\pi$
$968$	67.8756	2.18160
$969$	1.78842	0.0574522
$970$	−81.3068	−2.61061
$971$	1.56446	0.0502060	0.0251030	−	0.999685i	$-0.492009\pi$
$971$	1.56446	0.0502060	0.0251030	+	0.999685i	$0.492009\pi$
$972$	46.9626	1.50633
$973$	0	0
$974$	72.7582	2.33132
$975$	0	0
$976$	−137.017	−4.38582
$977$	−27.8755	−0.891817	−0.445909	−	0.895078i	$-0.647119\pi$
$977$	−27.8755	−0.891817	−0.445909	+	0.895078i	$0.647119\pi$
$978$	4.11981	0.131737
$979$	27.8999	0.891684
$980$	0	0
$981$	12.3034	0.392817
$982$	−26.2944	−0.839088
$983$	33.4239	1.06606	0.533029	−	0.846097i	$-0.321054\pi$
$983$	33.4239	1.06606	0.533029	+	0.846097i	$0.321054\pi$
$984$	13.0559	0.416207
$985$	−47.3313	−1.50810
$986$	−15.9132	−0.506780
$987$	0	0
$988$	0	0
$989$	−15.7376	−0.500428
$990$	46.8300	1.48835
$991$	−18.9110	−0.600726	−0.300363	−	0.953825i	$-0.597108\pi$
$991$	−18.9110	−0.600726	−0.300363	+	0.953825i	$0.597108\pi$
$992$	−32.6777	−1.03752
$993$	−5.97622	−0.189650
$994$	0	0
$995$	−77.6750	−2.46246
$996$	18.3059	0.580046
$997$	−43.5775	−1.38011	−0.690057	−	0.723755i	$-0.742415\pi$
$997$	−43.5775	−1.38011	−0.690057	+	0.723755i	$0.742415\pi$
$998$	−21.2884	−0.673871
$999$	−12.0748	−0.382031

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.by.1.1		6
7.6	odd	2		1183.2.a.m.1.1		6
13.2	odd	12		637.2.q.h.589.1		12
13.7	odd	12		637.2.q.h.491.1		12
13.12	even	2		8281.2.a.ch.1.6		6
91.2	odd	12		637.2.k.g.459.6		12
91.20	even	12		91.2.q.a.36.1	✓	12
91.33	even	12		637.2.u.h.361.6		12
91.34	even	4		1183.2.c.i.337.1		12
91.41	even	12		91.2.q.a.43.1	yes	12
91.46	odd	12		637.2.k.g.569.1		12
91.54	even	12		637.2.k.h.459.6		12
91.59	even	12		637.2.k.h.569.1		12
91.67	odd	12		637.2.u.i.30.6		12
91.72	odd	12		637.2.u.i.361.6		12
91.80	even	12		637.2.u.h.30.6		12
91.83	even	4		1183.2.c.i.337.12		12
91.90	odd	2		1183.2.a.p.1.6		6
273.20	odd	12		819.2.ct.a.127.6		12
273.41	odd	12		819.2.ct.a.316.6		12
364.111	odd	12		1456.2.cc.c.673.4		12
364.223	odd	12		1456.2.cc.c.225.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.1	✓	12	91.20	even	12
91.2.q.a.43.1	yes	12	91.41	even	12
637.2.k.g.459.6		12	91.2	odd	12
637.2.k.g.569.1		12	91.46	odd	12
637.2.k.h.459.6		12	91.54	even	12
637.2.k.h.569.1		12	91.59	even	12
637.2.q.h.491.1		12	13.7	odd	12
637.2.q.h.589.1		12	13.2	odd	12
637.2.u.h.30.6		12	91.80	even	12
637.2.u.h.361.6		12	91.33	even	12
637.2.u.i.30.6		12	91.67	odd	12
637.2.u.i.361.6		12	91.72	odd	12
819.2.ct.a.127.6		12	273.20	odd	12
819.2.ct.a.316.6		12	273.41	odd	12
1183.2.a.m.1.1		6	7.6	odd	2
1183.2.a.p.1.6		6	91.90	odd	2
1183.2.c.i.337.1		12	91.34	even	4
1183.2.c.i.337.12		12	91.83	even	4
1456.2.cc.c.225.4		12	364.223	odd	12
1456.2.cc.c.673.4		12	364.111	odd	12
8281.2.a.by.1.1		6	1.1	even	1	trivial
8281.2.a.ch.1.6		6	13.12	even	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:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70320 q^{2} +0.345949 q^{3} +5.30727 q^{4} +3.25812 q^{5} -0.935168 q^{6} -8.94020 q^{8} -2.88032 q^{9} +O(q^{10})\)	\(q-2.70320 q^{2} +0.345949 q^{3} +5.30727 q^{4} +3.25812 q^{5} -0.935168 q^{6} -8.94020 q^{8} -2.88032 q^{9} -8.80735 q^{10} +1.84603 q^{11} +1.83605 q^{12} +1.12715 q^{15} +13.5526 q^{16} -2.15314 q^{17} +7.78607 q^{18} -2.40096 q^{19} +17.2917 q^{20} -4.99017 q^{22} +1.81263 q^{23} -3.09285 q^{24} +5.61537 q^{25} -2.03429 q^{27} -2.73406 q^{29} -3.04689 q^{30} +1.74236 q^{31} -18.7549 q^{32} +0.638632 q^{33} +5.82036 q^{34} -15.2866 q^{36} +5.93565 q^{37} +6.49025 q^{38} -29.1283 q^{40} -4.22131 q^{41} -8.68223 q^{43} +9.79737 q^{44} -9.38444 q^{45} -4.89989 q^{46} +5.87774 q^{47} +4.68850 q^{48} -15.1794 q^{50} -0.744877 q^{51} -9.30628 q^{53} +5.49909 q^{54} +6.01459 q^{55} -0.830609 q^{57} +7.39071 q^{58} -10.7523 q^{59} +5.98206 q^{60} -10.1101 q^{61} -4.70994 q^{62} +23.5929 q^{64} -1.72635 q^{66} +0.826916 q^{67} -11.4273 q^{68} +0.627077 q^{69} +2.35425 q^{71} +25.7506 q^{72} +3.19482 q^{73} -16.0452 q^{74} +1.94263 q^{75} -12.7425 q^{76} +0.801911 q^{79} +44.1559 q^{80} +7.93720 q^{81} +11.4110 q^{82} +9.97031 q^{83} -7.01520 q^{85} +23.4698 q^{86} -0.945847 q^{87} -16.5039 q^{88} +15.1135 q^{89} +25.3680 q^{90} +9.62010 q^{92} +0.602768 q^{93} -15.8887 q^{94} -7.82261 q^{95} -6.48823 q^{96} +9.23171 q^{97} -5.31715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 6 * q - 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 12 * q^8 + 4 * q^9	\( 6 q - 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 12 q^{8} + 4 q^{9} - 12 q^{10} - 4 q^{11} - 2 q^{12} - 20 q^{15} + 8 q^{16} + 4 q^{17} + 16 q^{18} + 2 q^{19} + 26 q^{20} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 10 q^{25} - 6 q^{27} - 8 q^{29} + 8 q^{30} - 14 q^{31} - 8 q^{32} + 16 q^{33} - 2 q^{34} - 10 q^{36} - 12 q^{37} + 2 q^{38} - 46 q^{40} + 28 q^{41} + 2 q^{43} + 20 q^{44} + 16 q^{45} - 20 q^{46} + 14 q^{47} - 2 q^{48} - 32 q^{50} - 26 q^{51} - 22 q^{53} + 14 q^{54} - 6 q^{55} - 4 q^{58} - 2 q^{59} + 14 q^{61} + 4 q^{62} + 26 q^{64} + 26 q^{66} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 4 q^{71} - 8 q^{72} + 36 q^{73} - 6 q^{74} - 46 q^{75} - 26 q^{76} - 28 q^{79} + 36 q^{80} - 2 q^{81} - 14 q^{82} + 26 q^{83} + 20 q^{85} + 24 q^{86} - 2 q^{87} - 14 q^{88} + 42 q^{89} + 12 q^{90} + 12 q^{92} + 4 q^{94} - 22 q^{95} - 42 q^{96} + 24 q^{97} - 16 q^{99}+O(q^{100}) \) 6 * q - 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 12 * q^8 + 4 * q^9 - 12 * q^10 - 4 * q^11 - 2 * q^12 - 20 * q^15 + 8 * q^16 + 4 * q^17 + 16 * q^18 + 2 * q^19 + 26 * q^20 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 10 * q^25 - 6 * q^27 - 8 * q^29 + 8 * q^30 - 14 * q^31 - 8 * q^32 + 16 * q^33 - 2 * q^34 - 10 * q^36 - 12 * q^37 + 2 * q^38 - 46 * q^40 + 28 * q^41 + 2 * q^43 + 20 * q^44 + 16 * q^45 - 20 * q^46 + 14 * q^47 - 2 * q^48 - 32 * q^50 - 26 * q^51 - 22 * q^53 + 14 * q^54 - 6 * q^55 - 4 * q^58 - 2 * q^59 + 14 * q^61 + 4 * q^62 + 26 * q^64 + 26 * q^66 - 24 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^71 - 8 * q^72 + 36 * q^73 - 6 * q^74 - 46 * q^75 - 26 * q^76 - 28 * q^79 + 36 * q^80 - 2 * q^81 - 14 * q^82 + 26 * q^83 + 20 * q^85 + 24 * q^86 - 2 * q^87 - 14 * q^88 + 42 * q^89 + 12 * q^90 + 12 * q^92 + 4 * q^94 - 22 * q^95 - 42 * q^96 + 24 * q^97 - 16 * q^99

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