LMFDB - Embedded newform 8673.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8673,2,Mod(1,8673)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8673, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8673.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8673 = 3 \cdot 7^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8673.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:	$69.2542536731$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.86081$ of defining polynomial
Character	$\chi$	$=$	8673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.86081 q^{2} +1.00000 q^{3} +1.46260 q^{4} +3.32340 q^{5} -1.86081 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.86081 q^{2} +1.00000 q^{3} +1.46260 q^{4} +3.32340 q^{5} -1.86081 q^{6} +1.00000 q^{8} +1.00000 q^{9} -6.18421 q^{10} +0.398207 q^{11} +1.46260 q^{12} -2.39821 q^{13} +3.32340 q^{15} -4.78600 q^{16} -7.10941 q^{17} -1.86081 q^{18} -1.53740 q^{19} +4.86081 q^{20} -0.740987 q^{22} +3.25901 q^{23} +1.00000 q^{24} +6.04502 q^{25} +4.46260 q^{26} +1.00000 q^{27} -3.93561 q^{29} -6.18421 q^{30} -7.78600 q^{31} +6.90582 q^{32} +0.398207 q^{33} +13.2292 q^{34} +1.46260 q^{36} +1.25901 q^{37} +2.86081 q^{38} -2.39821 q^{39} +3.32340 q^{40} +7.50761 q^{41} -9.69182 q^{43} +0.582418 q^{44} +3.32340 q^{45} -6.06439 q^{46} -8.71120 q^{47} -4.78600 q^{48} -11.2486 q^{50} -7.10941 q^{51} -3.50761 q^{52} +10.7666 q^{53} -1.86081 q^{54} +1.32340 q^{55} -1.53740 q^{57} +7.32340 q^{58} -1.00000 q^{59} +4.86081 q^{60} -0.989588 q^{61} +14.4882 q^{62} -3.27839 q^{64} -7.97021 q^{65} -0.740987 q^{66} +5.45219 q^{67} -10.3982 q^{68} +3.25901 q^{69} +15.0450 q^{71} +1.00000 q^{72} -4.73202 q^{73} -2.34278 q^{74} +6.04502 q^{75} -2.24860 q^{76} +4.46260 q^{78} +7.04502 q^{79} -15.9058 q^{80} +1.00000 q^{81} -13.9702 q^{82} -13.0796 q^{83} -23.6274 q^{85} +18.0346 q^{86} -3.93561 q^{87} +0.398207 q^{88} +16.4328 q^{89} -6.18421 q^{90} +4.76663 q^{92} -7.78600 q^{93} +16.2099 q^{94} -5.10941 q^{95} +6.90582 q^{96} -14.7666 q^{97} +0.398207 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9} - 5 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} + 9 q^{20} - 11 q^{22} + q^{23} + 3 q^{24} - q^{25} + 11 q^{26} + 3 q^{27} - 11 q^{29} - 5 q^{30} - 13 q^{31} - 4 q^{32} - 2 q^{33} + 7 q^{34} + 2 q^{36} - 5 q^{37} + 3 q^{38} - 4 q^{39} + 2 q^{40} + q^{41} + 6 q^{43} - 15 q^{44} + 2 q^{45} - 19 q^{46} - 11 q^{47} - 4 q^{48} - 21 q^{50} - 3 q^{51} + 11 q^{52} + 2 q^{53} - 4 q^{55} - 7 q^{57} + 14 q^{58} - 3 q^{59} + 9 q^{60} + q^{61} + 2 q^{62} - 21 q^{64} - 11 q^{66} + 10 q^{67} - 28 q^{68} + q^{69} + 26 q^{71} + 3 q^{72} - 7 q^{73} - 19 q^{74} - q^{75} + 6 q^{76} + 11 q^{78} + 2 q^{79} - 23 q^{80} + 3 q^{81} - 18 q^{82} + 3 q^{83} - 35 q^{85} + 31 q^{86} - 11 q^{87} - 2 q^{88} + 23 q^{89} - 5 q^{90} - 16 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} - 4 q^{96} - 14 q^{97} - 2 q^{99}+O(q^{100}) $ 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9 - 5 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 + 9 * q^20 - 11 * q^22 + q^23 + 3 * q^24 - q^25 + 11 * q^26 + 3 * q^27 - 11 * q^29 - 5 * q^30 - 13 * q^31 - 4 * q^32 - 2 * q^33 + 7 * q^34 + 2 * q^36 - 5 * q^37 + 3 * q^38 - 4 * q^39 + 2 * q^40 + q^41 + 6 * q^43 - 15 * q^44 + 2 * q^45 - 19 * q^46 - 11 * q^47 - 4 * q^48 - 21 * q^50 - 3 * q^51 + 11 * q^52 + 2 * q^53 - 4 * q^55 - 7 * q^57 + 14 * q^58 - 3 * q^59 + 9 * q^60 + q^61 + 2 * q^62 - 21 * q^64 - 11 * q^66 + 10 * q^67 - 28 * q^68 + q^69 + 26 * q^71 + 3 * q^72 - 7 * q^73 - 19 * q^74 - q^75 + 6 * q^76 + 11 * q^78 + 2 * q^79 - 23 * q^80 + 3 * q^81 - 18 * q^82 + 3 * q^83 - 35 * q^85 + 31 * q^86 - 11 * q^87 - 2 * q^88 + 23 * q^89 - 5 * q^90 - 16 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 - 4 * q^96 - 14 * q^97 - 2 * 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 $

$2$	−1.86081	−1.31579	−0.657894	−	0.753110i	$-0.728553\pi$
$2$	−1.86081	−1.31579	−0.657894	+	0.753110i	$0.728553\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.46260	0.731299
$5$	3.32340	1.48627	0.743136	−	0.669141i	$-0.233338\pi$
$5$	3.32340	1.48627	0.743136	+	0.669141i	$0.233338\pi$
$6$	−1.86081	−0.759671
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−6.18421	−1.95562
$11$	0.398207	0.120064	0.0600320	−	0.998196i	$-0.480880\pi$
$11$	0.398207	0.120064	0.0600320	+	0.998196i	$0.480880\pi$
$12$	1.46260	0.422216
$13$	−2.39821	−0.665143	−0.332572	−	0.943078i	$-0.607916\pi$
$13$	−2.39821	−0.665143	−0.332572	+	0.943078i	$0.607916\pi$
$14$	0	0
$15$	3.32340	0.858099
$16$	−4.78600	−1.19650
$17$	−7.10941	−1.72428	−0.862142	−	0.506666i	$-0.830878\pi$
$17$	−7.10941	−1.72428	−0.862142	+	0.506666i	$0.830878\pi$
$18$	−1.86081	−0.438596
$19$	−1.53740	−0.352704	−0.176352	−	0.984327i	$-0.556430\pi$
$19$	−1.53740	−0.352704	−0.176352	+	0.984327i	$0.556430\pi$
$20$	4.86081	1.08691
$21$	0	0
$22$	−0.740987	−0.157979
$23$	3.25901	0.679551	0.339776	−	0.940507i	$-0.389649\pi$
$23$	3.25901	0.679551	0.339776	+	0.940507i	$0.389649\pi$
$24$	1.00000	0.204124
$25$	6.04502	1.20900
$26$	4.46260	0.875188
$27$	1.00000	0.192450
$28$	0	0
$29$	−3.93561	−0.730824	−0.365412	−	0.930846i	$-0.619072\pi$
$29$	−3.93561	−0.730824	−0.365412	+	0.930846i	$0.619072\pi$
$30$	−6.18421	−1.12908
$31$	−7.78600	−1.39841	−0.699204	−	0.714923i	$-0.746462\pi$
$31$	−7.78600	−1.39841	−0.699204	+	0.714923i	$0.746462\pi$
$32$	6.90582	1.22079
$33$	0.398207	0.0693190
$34$	13.2292	2.26879
$35$	0	0
$36$	1.46260	0.243766
$37$	1.25901	0.206981	0.103490	−	0.994630i	$-0.466999\pi$
$37$	1.25901	0.206981	0.103490	+	0.994630i	$0.466999\pi$
$38$	2.86081	0.464084
$39$	−2.39821	−0.384021
$40$	3.32340	0.525476
$41$	7.50761	1.17249	0.586246	−	0.810133i	$-0.300605\pi$
$41$	7.50761	1.17249	0.586246	+	0.810133i	$0.300605\pi$
$42$	0	0
$43$	−9.69182	−1.47799	−0.738995	−	0.673711i	$-0.764699\pi$
$43$	−9.69182	−1.47799	−0.738995	+	0.673711i	$0.764699\pi$
$44$	0.582418	0.0878028
$45$	3.32340	0.495424
$46$	−6.06439	−0.894146
$47$	−8.71120	−1.27066	−0.635330	−	0.772241i	$-0.719136\pi$
$47$	−8.71120	−1.27066	−0.635330	+	0.772241i	$0.719136\pi$
$48$	−4.78600	−0.690800
$49$	0	0
$50$	−11.2486	−1.59079
$51$	−7.10941	−0.995516
$52$	−3.50761	−0.486419
$53$	10.7666	1.47891	0.739455	−	0.673206i	$-0.235083\pi$
$53$	10.7666	1.47891	0.739455	+	0.673206i	$0.235083\pi$
$54$	−1.86081	−0.253224
$55$	1.32340	0.178448
$56$	0	0
$57$	−1.53740	−0.203634
$58$	7.32340	0.961610
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	4.86081	0.627527
$61$	−0.989588	−0.126704	−0.0633519	−	0.997991i	$-0.520179\pi$
$61$	−0.989588	−0.126704	−0.0633519	+	0.997991i	$0.520179\pi$
$62$	14.4882	1.84001
$63$	0	0
$64$	−3.27839	−0.409799
$65$	−7.97021	−0.988583
$66$	−0.740987	−0.0912092
$67$	5.45219	0.666091	0.333045	−	0.942911i	$-0.391924\pi$
$67$	5.45219	0.666091	0.333045	+	0.942911i	$0.391924\pi$
$68$	−10.3982	−1.26097
$69$	3.25901	0.392339
$70$	0	0
$71$	15.0450	1.78551	0.892757	−	0.450538i	$-0.148768\pi$
$71$	15.0450	1.78551	0.892757	+	0.450538i	$0.148768\pi$
$72$	1.00000	0.117851
$73$	−4.73202	−0.553842	−0.276921	−	0.960893i	$-0.589314\pi$
$73$	−4.73202	−0.553842	−0.276921	+	0.960893i	$0.589314\pi$
$74$	−2.34278	−0.272343
$75$	6.04502	0.698018
$76$	−2.24860	−0.257932
$77$	0	0
$78$	4.46260	0.505290
$79$	7.04502	0.792626	0.396313	−	0.918115i	$-0.370289\pi$
$79$	7.04502	0.792626	0.396313	+	0.918115i	$0.370289\pi$
$80$	−15.9058	−1.77832
$81$	1.00000	0.111111
$82$	−13.9702	−1.54275
$83$	−13.0796	−1.43567	−0.717837	−	0.696211i	$-0.754868\pi$
$83$	−13.0796	−1.43567	−0.717837	+	0.696211i	$0.754868\pi$
$84$	0	0
$85$	−23.6274	−2.56275
$86$	18.0346	1.94472
$87$	−3.93561	−0.421942
$88$	0.398207	0.0424491
$89$	16.4328	1.74187	0.870937	−	0.491394i	$-0.163513\pi$
$89$	16.4328	1.74187	0.870937	+	0.491394i	$0.163513\pi$
$90$	−6.18421	−0.651873
$91$	0	0
$92$	4.76663	0.496955
$93$	−7.78600	−0.807371
$94$	16.2099	1.67192
$95$	−5.10941	−0.524214
$96$	6.90582	0.704822
$97$	−14.7666	−1.49932	−0.749662	−	0.661821i	$-0.769784\pi$
$97$	−14.7666	−1.49932	−0.749662	+	0.661821i	$0.769784\pi$
$98$	0	0
$99$	0.398207	0.0400214
$100$	8.84143	0.884143
$101$	0.278388	0.0277007	0.0138503	−	0.999904i	$-0.495591\pi$
$101$	0.278388	0.0277007	0.0138503	+	0.999904i	$0.495591\pi$
$102$	13.2292	1.30989
$103$	15.0152	1.47949	0.739747	−	0.672885i	$-0.234945\pi$
$103$	15.0152	1.47949	0.739747	+	0.672885i	$0.234945\pi$
$104$	−2.39821	−0.235164
$105$	0	0
$106$	−20.0346	−1.94593
$107$	1.16898	0.113010	0.0565048	−	0.998402i	$-0.482004\pi$
$107$	1.16898	0.113010	0.0565048	+	0.998402i	$0.482004\pi$
$108$	1.46260	0.140739
$109$	−4.89059	−0.468434	−0.234217	−	0.972184i	$-0.575253\pi$
$109$	−4.89059	−0.468434	−0.234217	+	0.972184i	$0.575253\pi$
$110$	−2.46260	−0.234800
$111$	1.25901	0.119500
$112$	0	0
$113$	−15.5630	−1.46405	−0.732024	−	0.681279i	$-0.761424\pi$
$113$	−15.5630	−1.46405	−0.732024	+	0.681279i	$0.761424\pi$
$114$	2.86081	0.267939
$115$	10.8310	1.01000
$116$	−5.75622	−0.534451
$117$	−2.39821	−0.221714
$118$	1.86081	0.171301
$119$	0	0
$120$	3.32340	0.303384
$121$	−10.8414	−0.985585
$122$	1.84143	0.166715
$123$	7.50761	0.676939
$124$	−11.3878	−1.02265
$125$	3.47301	0.310636
$126$	0	0
$127$	4.39821	0.390278	0.195139	−	0.980776i	$-0.437484\pi$
$127$	4.39821	0.390278	0.195139	+	0.980776i	$0.437484\pi$
$128$	−7.71120	−0.681580
$129$	−9.69182	−0.853318
$130$	14.8310	1.30077
$131$	−17.6620	−1.54314	−0.771570	−	0.636145i	$-0.780528\pi$
$131$	−17.6620	−1.54314	−0.771570	+	0.636145i	$0.780528\pi$
$132$	0.582418	0.0506929
$133$	0	0
$134$	−10.1455	−0.876434
$135$	3.32340	0.286033
$136$	−7.10941	−0.609627
$137$	−10.7666	−0.919855	−0.459928	−	0.887956i	$-0.652125\pi$
$137$	−10.7666	−0.919855	−0.459928	+	0.887956i	$0.652125\pi$
$138$	−6.06439	−0.516235
$139$	−9.82061	−0.832973	−0.416486	−	0.909142i	$-0.636739\pi$
$139$	−9.82061	−0.832973	−0.416486	+	0.909142i	$0.636739\pi$
$140$	0	0
$141$	−8.71120	−0.733615
$142$	−27.9959	−2.34936
$143$	−0.954984	−0.0798598
$144$	−4.78600	−0.398834
$145$	−13.0796	−1.08620
$146$	8.80538	0.728738
$147$	0	0
$148$	1.84143	0.151365
$149$	−5.01938	−0.411203	−0.205602	−	0.978636i	$-0.565915\pi$
$149$	−5.01938	−0.411203	−0.205602	+	0.978636i	$0.565915\pi$
$150$	−11.2486	−0.918444
$151$	7.35801	0.598786	0.299393	−	0.954130i	$-0.403216\pi$
$151$	7.35801	0.598786	0.299393	+	0.954130i	$0.403216\pi$
$152$	−1.53740	−0.124700
$153$	−7.10941	−0.574761
$154$	0	0
$155$	−25.8760	−2.07841
$156$	−3.50761	−0.280834
$157$	1.73057	0.138115	0.0690574	−	0.997613i	$-0.478001\pi$
$157$	1.73057	0.138115	0.0690574	+	0.997613i	$0.478001\pi$
$158$	−13.1094	−1.04293
$159$	10.7666	0.853849
$160$	22.9508	1.81442
$161$	0	0
$162$	−1.86081	−0.146199
$163$	−8.58242	−0.672227	−0.336113	−	0.941822i	$-0.609113\pi$
$163$	−8.58242	−0.672227	−0.336113	+	0.941822i	$0.609113\pi$
$164$	10.9806	0.857443
$165$	1.32340	0.103027
$166$	24.3386	1.88904
$167$	−6.49239	−0.502396	−0.251198	−	0.967936i	$-0.580825\pi$
$167$	−6.49239	−0.502396	−0.251198	+	0.967936i	$0.580825\pi$
$168$	0	0
$169$	−7.24860	−0.557585
$170$	43.9661	3.37204
$171$	−1.53740	−0.117568
$172$	−14.1752	−1.08085
$173$	20.5437	1.56191	0.780953	−	0.624590i	$-0.214734\pi$
$173$	20.5437	1.56191	0.780953	+	0.624590i	$0.214734\pi$
$174$	7.32340	0.555186
$175$	0	0
$176$	−1.90582	−0.143657
$177$	−1.00000	−0.0751646
$178$	−30.5783	−2.29194
$179$	−23.9702	−1.79162	−0.895809	−	0.444439i	$-0.853403\pi$
$179$	−23.9702	−1.79162	−0.895809	+	0.444439i	$0.853403\pi$
$180$	4.86081	0.362303
$181$	−14.7112	−1.09347	−0.546737	−	0.837304i	$-0.684130\pi$
$181$	−14.7112	−1.09347	−0.546737	+	0.837304i	$0.684130\pi$
$182$	0	0
$183$	−0.989588	−0.0731524
$184$	3.25901	0.240258
$185$	4.18421	0.307629
$186$	14.4882	1.06233
$187$	−2.83102	−0.207025
$188$	−12.7410	−0.929232
$189$	0	0
$190$	9.50761	0.689755
$191$	2.91623	0.211011	0.105506	−	0.994419i	$-0.466354\pi$
$191$	2.91623	0.211011	0.105506	+	0.994419i	$0.466354\pi$
$192$	−3.27839	−0.236597
$193$	−0.646809	−0.0465583	−0.0232791	−	0.999729i	$-0.507411\pi$
$193$	−0.646809	−0.0465583	−0.0232791	+	0.999729i	$0.507411\pi$
$194$	27.4778	1.97279
$195$	−7.97021	−0.570759
$196$	0	0
$197$	−5.87122	−0.418307	−0.209153	−	0.977883i	$-0.567071\pi$
$197$	−5.87122	−0.418307	−0.209153	+	0.977883i	$0.567071\pi$
$198$	−0.740987	−0.0526596
$199$	−11.1004	−0.786890	−0.393445	−	0.919348i	$-0.628717\pi$
$199$	−11.1004	−0.786890	−0.393445	+	0.919348i	$0.628717\pi$
$200$	6.04502	0.427447
$201$	5.45219	0.384568
$202$	−0.518027	−0.0364482
$203$	0	0
$204$	−10.3982	−0.728020
$205$	24.9508	1.74264
$206$	−27.9404	−1.94670
$207$	3.25901	0.226517
$208$	11.4778	0.795844
$209$	−0.612205	−0.0423471
$210$	0	0
$211$	−13.4778	−0.927852	−0.463926	−	0.885874i	$-0.653560\pi$
$211$	−13.4778	−0.927852	−0.463926	+	0.885874i	$0.653560\pi$
$212$	15.7473	1.08153
$213$	15.0450	1.03087
$214$	−2.17525	−0.148697
$215$	−32.2099	−2.19669
$216$	1.00000	0.0680414
$217$	0	0
$218$	9.10044	0.616360
$219$	−4.73202	−0.319761
$220$	1.93561	0.130499
$221$	17.0498	1.14690
$222$	−2.34278	−0.157237
$223$	−16.7368	−1.12078	−0.560391	−	0.828228i	$-0.689349\pi$
$223$	−16.7368	−1.12078	−0.560391	+	0.828228i	$0.689349\pi$
$224$	0	0
$225$	6.04502	0.403001
$226$	28.9598	1.92638
$227$	14.0346	0.931509	0.465755	−	0.884914i	$-0.345783\pi$
$227$	14.0346	0.931509	0.465755	+	0.884914i	$0.345783\pi$
$228$	−2.24860	−0.148917
$229$	12.2445	0.809136	0.404568	−	0.914508i	$-0.367422\pi$
$229$	12.2445	0.809136	0.404568	+	0.914508i	$0.367422\pi$
$230$	−20.1544	−1.32894
$231$	0	0
$232$	−3.93561	−0.258385
$233$	1.87122	0.122588	0.0612938	−	0.998120i	$-0.480477\pi$
$233$	1.87122	0.122588	0.0612938	+	0.998120i	$0.480477\pi$
$234$	4.46260	0.291729
$235$	−28.9508	−1.88854
$236$	−1.46260	−0.0952070
$237$	7.04502	0.457623
$238$	0	0
$239$	−13.9910	−0.905005	−0.452502	−	0.891763i	$-0.649469\pi$
$239$	−13.9910	−0.905005	−0.452502	+	0.891763i	$0.649469\pi$
$240$	−15.9058	−1.02672
$241$	−27.5333	−1.77357	−0.886786	−	0.462179i	$-0.847068\pi$
$241$	−27.5333	−1.77357	−0.886786	+	0.462179i	$0.847068\pi$
$242$	20.1738	1.29682
$243$	1.00000	0.0641500
$244$	−1.44737	−0.0926583
$245$	0	0
$246$	−13.9702	−0.890708
$247$	3.68701	0.234599
$248$	−7.78600	−0.494412
$249$	−13.0796	−0.828887
$250$	−6.46260	−0.408731
$251$	2.61702	0.165185	0.0825925	−	0.996583i	$-0.473680\pi$
$251$	2.61702	0.165185	0.0825925	+	0.996583i	$0.473680\pi$
$252$	0	0
$253$	1.29776	0.0815897
$254$	−8.18421	−0.513523
$255$	−23.6274	−1.47961
$256$	20.9058	1.30661
$257$	−20.3892	−1.27185	−0.635923	−	0.771752i	$-0.719380\pi$
$257$	−20.3892	−1.27185	−0.635923	+	0.771752i	$0.719380\pi$
$258$	18.0346	1.12279
$259$	0	0
$260$	−11.6572	−0.722950
$261$	−3.93561	−0.243608
$262$	32.8656	2.03044
$263$	−23.8552	−1.47098	−0.735488	−	0.677538i	$-0.763047\pi$
$263$	−23.8552	−1.47098	−0.735488	+	0.677538i	$0.763047\pi$
$264$	0.398207	0.0245080
$265$	35.7819	2.19806
$266$	0	0
$267$	16.4328	1.00567
$268$	7.97436	0.487112
$269$	28.2999	1.72547	0.862737	−	0.505653i	$-0.168748\pi$
$269$	28.2999	1.72547	0.862737	+	0.505653i	$0.168748\pi$
$270$	−6.18421	−0.376359
$271$	23.4134	1.42226	0.711132	−	0.703058i	$-0.248183\pi$
$271$	23.4134	1.42226	0.711132	+	0.703058i	$0.248183\pi$
$272$	34.0256	2.06311
$273$	0	0
$274$	20.0346	1.21033
$275$	2.40717	0.145158
$276$	4.76663	0.286917
$277$	15.6918	0.942830	0.471415	−	0.881911i	$-0.343743\pi$
$277$	15.6918	0.942830	0.471415	+	0.881911i	$0.343743\pi$
$278$	18.2742	1.09602
$279$	−7.78600	−0.466136
$280$	0	0
$281$	−5.63158	−0.335952	−0.167976	−	0.985791i	$-0.553723\pi$
$281$	−5.63158	−0.335952	−0.167976	+	0.985791i	$0.553723\pi$
$282$	16.2099	0.965283
$283$	−10.8310	−0.643837	−0.321919	−	0.946767i	$-0.604328\pi$
$283$	−10.8310	−0.643837	−0.321919	+	0.946767i	$0.604328\pi$
$284$	22.0048	1.30575
$285$	−5.10941	−0.302655
$286$	1.77704	0.105079
$287$	0	0
$288$	6.90582	0.406929
$289$	33.5437	1.97316
$290$	24.3386	1.42921
$291$	−14.7666	−0.865635
$292$	−6.92105	−0.405024
$293$	−33.9959	−1.98606	−0.993029	−	0.117866i	$-0.962395\pi$
$293$	−33.9959	−1.98606	−0.993029	+	0.117866i	$0.962395\pi$
$294$	0	0
$295$	−3.32340	−0.193496
$296$	1.25901	0.0731787
$297$	0.398207	0.0231063
$298$	9.34008	0.541056
$299$	−7.81579	−0.451999
$300$	8.84143	0.510460
$301$	0	0
$302$	−13.6918	−0.787876
$303$	0.278388	0.0159930
$304$	7.35801	0.422011
$305$	−3.28880	−0.188316
$306$	13.2292	0.756265
$307$	4.25756	0.242992	0.121496	−	0.992592i	$-0.461231\pi$
$307$	4.25756	0.242992	0.121496	+	0.992592i	$0.461231\pi$
$308$	0	0
$309$	15.0152	0.854187
$310$	48.1503	2.73475
$311$	−21.5374	−1.22127	−0.610637	−	0.791911i	$-0.709087\pi$
$311$	−21.5374	−1.22127	−0.610637	+	0.791911i	$0.709087\pi$
$312$	−2.39821	−0.135772
$313$	3.96540	0.224137	0.112069	−	0.993700i	$-0.464252\pi$
$313$	3.96540	0.224137	0.112069	+	0.993700i	$0.464252\pi$
$314$	−3.22026	−0.181730
$315$	0	0
$316$	10.3040	0.579647
$317$	7.58097	0.425790	0.212895	−	0.977075i	$-0.431711\pi$
$317$	7.58097	0.425790	0.212895	+	0.977075i	$0.431711\pi$
$318$	−20.0346	−1.12348
$319$	−1.56719	−0.0877457
$320$	−10.8954	−0.609072
$321$	1.16898	0.0652462
$322$	0	0
$323$	10.9300	0.608162
$324$	1.46260	0.0812555
$325$	−14.4972	−0.804160
$326$	15.9702	0.884508
$327$	−4.89059	−0.270450
$328$	7.50761	0.414539
$329$	0	0
$330$	−2.46260	−0.135562
$331$	−0.667633	−0.0366964	−0.0183482	−	0.999832i	$-0.505841\pi$
$331$	−0.667633	−0.0366964	−0.0183482	+	0.999832i	$0.505841\pi$
$332$	−19.1302	−1.04991
$333$	1.25901	0.0689935
$334$	12.0811	0.661047
$335$	18.1198	0.989991
$336$	0	0
$337$	7.47783	0.407343	0.203672	−	0.979039i	$-0.434713\pi$
$337$	7.47783	0.407343	0.203672	+	0.979039i	$0.434713\pi$
$338$	13.4882	0.733664
$339$	−15.5630	−0.845268
$340$	−34.5574	−1.87414
$341$	−3.10044	−0.167898
$342$	2.86081	0.154695
$343$	0	0
$344$	−9.69182	−0.522548
$345$	10.8310	0.583122
$346$	−38.2278	−2.05514
$347$	−29.0200	−1.55788	−0.778939	−	0.627100i	$-0.784242\pi$
$347$	−29.0200	−1.55788	−0.778939	+	0.627100i	$0.784242\pi$
$348$	−5.75622	−0.308566
$349$	16.8746	0.903276	0.451638	−	0.892201i	$-0.350840\pi$
$349$	16.8746	0.903276	0.451638	+	0.892201i	$0.350840\pi$
$350$	0	0
$351$	−2.39821	−0.128007
$352$	2.74995	0.146573
$353$	2.98062	0.158643	0.0793213	−	0.996849i	$-0.474725\pi$
$353$	2.98062	0.158643	0.0793213	+	0.996849i	$0.474725\pi$
$354$	1.86081	0.0989007
$355$	50.0007	2.65376
$356$	24.0346	1.27383
$357$	0	0
$358$	44.6039	2.35739
$359$	−1.85039	−0.0976600	−0.0488300	−	0.998807i	$-0.515549\pi$
$359$	−1.85039	−0.0976600	−0.0488300	+	0.998807i	$0.515549\pi$
$360$	3.32340	0.175159
$361$	−16.6364	−0.875600
$362$	27.3747	1.43878
$363$	−10.8414	−0.569028
$364$	0	0
$365$	−15.7264	−0.823159
$366$	1.84143	0.0962531
$367$	−7.97021	−0.416042	−0.208021	−	0.978124i	$-0.566702\pi$
$367$	−7.97021	−0.416042	−0.208021	+	0.978124i	$0.566702\pi$
$368$	−15.5976	−0.813084
$369$	7.50761	0.390831
$370$	−7.78600	−0.404775
$371$	0	0
$372$	−11.3878	−0.590430
$373$	1.31859	0.0682739	0.0341369	−	0.999417i	$-0.489132\pi$
$373$	1.31859	0.0682739	0.0341369	+	0.999417i	$0.489132\pi$
$374$	5.26798	0.272401
$375$	3.47301	0.179345
$376$	−8.71120	−0.449246
$377$	9.43841	0.486103
$378$	0	0
$379$	20.5783	1.05703	0.528517	−	0.848922i	$-0.322748\pi$
$379$	20.5783	1.05703	0.528517	+	0.848922i	$0.322748\pi$
$380$	−7.47301	−0.383357
$381$	4.39821	0.225327
$382$	−5.42655	−0.277646
$383$	−21.8802	−1.11803	−0.559013	−	0.829159i	$-0.688820\pi$
$383$	−21.8802	−1.11803	−0.559013	+	0.829159i	$0.688820\pi$
$384$	−7.71120	−0.393511
$385$	0	0
$386$	1.20359	0.0612609
$387$	−9.69182	−0.492663
$388$	−21.5976	−1.09645
$389$	−6.29921	−0.319383	−0.159691	−	0.987167i	$-0.551050\pi$
$389$	−6.29921	−0.319383	−0.159691	+	0.987167i	$0.551050\pi$
$390$	14.8310	0.750998
$391$	−23.1697	−1.17174
$392$	0	0
$393$	−17.6620	−0.890932
$394$	10.9252	0.550403
$395$	23.4134	1.17806
$396$	0.582418	0.0292676
$397$	12.1198	0.608276	0.304138	−	0.952628i	$-0.401632\pi$
$397$	12.1198	0.608276	0.304138	+	0.952628i	$0.401632\pi$
$398$	20.6558	1.03538
$399$	0	0
$400$	−28.9315	−1.44657
$401$	−16.3338	−0.815672	−0.407836	−	0.913055i	$-0.633716\pi$
$401$	−16.3338	−0.815672	−0.407836	+	0.913055i	$0.633716\pi$
$402$	−10.1455	−0.506010
$403$	18.6724	0.930141
$404$	0.407170	0.0202575
$405$	3.32340	0.165141
$406$	0	0
$407$	0.501348	0.0248509
$408$	−7.10941	−0.351968
$409$	−37.0665	−1.83282	−0.916410	−	0.400240i	$-0.868927\pi$
$409$	−37.0665	−1.83282	−0.916410	+	0.400240i	$0.868927\pi$
$410$	−46.4287	−2.29295
$411$	−10.7666	−0.531079
$412$	21.9612	1.08195
$413$	0	0
$414$	−6.06439	−0.298049
$415$	−43.4689	−2.13380
$416$	−16.5616	−0.811999
$417$	−9.82061	−0.480917
$418$	1.13919	0.0557198
$419$	−14.6468	−0.715543	−0.357772	−	0.933809i	$-0.616463\pi$
$419$	−14.6468	−0.715543	−0.357772	+	0.933809i	$0.616463\pi$
$420$	0	0
$421$	−3.32340	−0.161973	−0.0809864	−	0.996715i	$-0.525807\pi$
$421$	−3.32340	−0.161973	−0.0809864	+	0.996715i	$0.525807\pi$
$422$	25.0796	1.22086
$423$	−8.71120	−0.423553
$424$	10.7666	0.522874
$425$	−42.9765	−2.08467
$426$	−27.9959	−1.35640
$427$	0	0
$428$	1.70975	0.0826439
$429$	−0.954984	−0.0461071
$430$	59.9363	2.89038
$431$	2.73202	0.131597	0.0657985	−	0.997833i	$-0.479041\pi$
$431$	2.73202	0.131597	0.0657985	+	0.997833i	$0.479041\pi$
$432$	−4.78600	−0.230267
$433$	36.1038	1.73504	0.867519	−	0.497404i	$-0.165713\pi$
$433$	36.1038	1.73504	0.867519	+	0.497404i	$0.165713\pi$
$434$	0	0
$435$	−13.0796	−0.627120
$436$	−7.15297	−0.342565
$437$	−5.01041	−0.239681
$438$	8.80538	0.420737
$439$	37.9571	1.81159	0.905797	−	0.423712i	$-0.139273\pi$
$439$	37.9571	1.81159	0.905797	+	0.423712i	$0.139273\pi$
$440$	1.32340	0.0630908
$441$	0	0
$442$	−31.7264	−1.50907
$443$	1.84625	0.0877179	0.0438589	−	0.999038i	$-0.486035\pi$
$443$	1.84625	0.0877179	0.0438589	+	0.999038i	$0.486035\pi$
$444$	1.84143	0.0873904
$445$	54.6129	2.58890
$446$	31.1440	1.47471
$447$	−5.01938	−0.237408
$448$	0	0
$449$	27.9494	1.31901	0.659507	−	0.751699i	$-0.270765\pi$
$449$	27.9494	1.31901	0.659507	+	0.751699i	$0.270765\pi$
$450$	−11.2486	−0.530264
$451$	2.98959	0.140774
$452$	−22.7625	−1.07066
$453$	7.35801	0.345709
$454$	−26.1157	−1.22567
$455$	0	0
$456$	−1.53740	−0.0719954
$457$	−23.2501	−1.08759	−0.543796	−	0.839218i	$-0.683013\pi$
$457$	−23.2501	−1.08759	−0.543796	+	0.839218i	$0.683013\pi$
$458$	−22.7846	−1.06465
$459$	−7.10941	−0.331839
$460$	15.8414	0.738611
$461$	−20.4447	−0.952203	−0.476102	−	0.879390i	$-0.657951\pi$
$461$	−20.4447	−0.952203	−0.476102	+	0.879390i	$0.657951\pi$
$462$	0	0
$463$	−12.6122	−0.586139	−0.293069	−	0.956091i	$-0.594677\pi$
$463$	−12.6122	−0.586139	−0.293069	+	0.956091i	$0.594677\pi$
$464$	18.8358	0.874432
$465$	−25.8760	−1.19997
$466$	−3.48197	−0.161299
$467$	1.89204	0.0875533	0.0437766	−	0.999041i	$-0.486061\pi$
$467$	1.89204	0.0875533	0.0437766	+	0.999041i	$0.486061\pi$
$468$	−3.50761	−0.162140
$469$	0	0
$470$	53.8719	2.48492
$471$	1.73057	0.0797407
$472$	−1.00000	−0.0460287
$473$	−3.85936	−0.177453
$474$	−13.1094	−0.602135
$475$	−9.29362	−0.426420
$476$	0	0
$477$	10.7666	0.492970
$478$	26.0346	1.19080
$479$	3.51658	0.160677	0.0803383	−	0.996768i	$-0.474400\pi$
$479$	3.51658	0.160677	0.0803383	+	0.996768i	$0.474400\pi$
$480$	22.9508	1.04756
$481$	−3.01938	−0.137672
$482$	51.2340	2.33365
$483$	0	0
$484$	−15.8567	−0.720757
$485$	−49.0755	−2.22840
$486$	−1.86081	−0.0844079
$487$	21.2203	0.961582	0.480791	−	0.876835i	$-0.340350\pi$
$487$	21.2203	0.961582	0.480791	+	0.876835i	$0.340350\pi$
$488$	−0.989588	−0.0447965
$489$	−8.58242	−0.388110
$490$	0	0
$491$	12.4536	0.562025	0.281012	−	0.959704i	$-0.409330\pi$
$491$	12.4536	0.562025	0.281012	+	0.959704i	$0.409330\pi$
$492$	10.9806	0.495045
$493$	27.9798	1.26015
$494$	−6.86081	−0.308682
$495$	1.32340	0.0594826
$496$	37.2638	1.67320
$497$	0	0
$498$	24.3386	1.09064
$499$	33.0755	1.48066	0.740331	−	0.672243i	$-0.234669\pi$
$499$	33.0755	1.48066	0.740331	+	0.672243i	$0.234669\pi$
$500$	5.07962	0.227168
$501$	−6.49239	−0.290058
$502$	−4.86977	−0.217348
$503$	−12.5824	−0.561022	−0.280511	−	0.959851i	$-0.590504\pi$
$503$	−12.5824	−0.561022	−0.280511	+	0.959851i	$0.590504\pi$
$504$	0	0
$505$	0.925197	0.0411707
$506$	−2.41489	−0.107355
$507$	−7.24860	−0.321922
$508$	6.43281	0.285410
$509$	−28.0465	−1.24314	−0.621569	−	0.783360i	$-0.713504\pi$
$509$	−28.0465	−1.24314	−0.621569	+	0.783360i	$0.713504\pi$
$510$	43.9661	1.94685
$511$	0	0
$512$	−23.4793	−1.03765
$513$	−1.53740	−0.0678779
$514$	37.9404	1.67348
$515$	49.9017	2.19893
$516$	−14.1752	−0.624030
$517$	−3.46886	−0.152560
$518$	0	0
$519$	20.5437	0.901767
$520$	−7.97021	−0.349517
$521$	37.7956	1.65586	0.827928	−	0.560834i	$-0.189519\pi$
$521$	37.7956	1.65586	0.827928	+	0.560834i	$0.189519\pi$
$522$	7.32340	0.320537
$523$	17.1946	0.751868	0.375934	−	0.926646i	$-0.377322\pi$
$523$	17.1946	0.751868	0.375934	+	0.926646i	$0.377322\pi$
$524$	−25.8325	−1.12850
$525$	0	0
$526$	44.3899	1.93549
$527$	55.3539	2.41125
$528$	−1.90582	−0.0829402
$529$	−12.3788	−0.538210
$530$	−66.5831	−2.89218
$531$	−1.00000	−0.0433963
$532$	0	0
$533$	−18.0048	−0.779875
$534$	−30.5783	−1.32325
$535$	3.88500	0.167963
$536$	5.45219	0.235499
$537$	−23.9702	−1.03439
$538$	−52.6606	−2.27036
$539$	0	0
$540$	4.86081	0.209176
$541$	−3.94939	−0.169797	−0.0848987	−	0.996390i	$-0.527057\pi$
$541$	−3.94939	−0.169797	−0.0848987	+	0.996390i	$0.527057\pi$
$542$	−43.5679	−1.87140
$543$	−14.7112	−0.631318
$544$	−49.0963	−2.10499
$545$	−16.2534	−0.696220
$546$	0	0
$547$	17.1094	0.731545	0.365773	−	0.930704i	$-0.380805\pi$
$547$	17.1094	0.731545	0.365773	+	0.930704i	$0.380805\pi$
$548$	−15.7473	−0.672689
$549$	−0.989588	−0.0422346
$550$	−4.47928	−0.190997
$551$	6.05061	0.257765
$552$	3.25901	0.138713
$553$	0	0
$554$	−29.1994	−1.24057
$555$	4.18421	0.177610
$556$	−14.3636	−0.609152
$557$	3.29362	0.139555	0.0697775	−	0.997563i	$-0.477771\pi$
$557$	3.29362	0.139555	0.0697775	+	0.997563i	$0.477771\pi$
$558$	14.4882	0.613336
$559$	23.2430	0.983074
$560$	0	0
$561$	−2.83102	−0.119526
$562$	10.4793	0.442042
$563$	−3.10459	−0.130843	−0.0654214	−	0.997858i	$-0.520839\pi$
$563$	−3.10459	−0.130843	−0.0654214	+	0.997858i	$0.520839\pi$
$564$	−12.7410	−0.536492
$565$	−51.7223	−2.17597
$566$	20.1544	0.847154
$567$	0	0
$568$	15.0450	0.631275
$569$	14.4024	0.603778	0.301889	−	0.953343i	$-0.402383\pi$
$569$	14.4024	0.603778	0.301889	+	0.953343i	$0.402383\pi$
$570$	9.50761	0.398230
$571$	−34.1198	−1.42787	−0.713935	−	0.700212i	$-0.753089\pi$
$571$	−34.1198	−1.42787	−0.713935	+	0.700212i	$0.753089\pi$
$572$	−1.39676	−0.0584014
$573$	2.91623	0.121827
$574$	0	0
$575$	19.7008	0.821580
$576$	−3.27839	−0.136600
$577$	43.6143	1.81569	0.907844	−	0.419308i	$-0.137727\pi$
$577$	43.6143	1.81569	0.907844	+	0.419308i	$0.137727\pi$
$578$	−62.4183	−2.59626
$579$	−0.646809	−0.0268804
$580$	−19.1302	−0.794340
$581$	0	0
$582$	27.4778	1.13899
$583$	4.28735	0.177564
$584$	−4.73202	−0.195813
$585$	−7.97021	−0.329528
$586$	63.2597	2.61323
$587$	−10.6170	−0.438211	−0.219106	−	0.975701i	$-0.570314\pi$
$587$	−10.6170	−0.438211	−0.219106	+	0.975701i	$0.570314\pi$
$588$	0	0
$589$	11.9702	0.493224
$590$	6.18421	0.254600
$591$	−5.87122	−0.241510
$592$	−6.02564	−0.247652
$593$	0.621168	0.0255083	0.0127541	−	0.999919i	$-0.495940\pi$
$593$	0.621168	0.0255083	0.0127541	+	0.999919i	$0.495940\pi$
$594$	−0.740987	−0.0304031
$595$	0	0
$596$	−7.34133	−0.300713
$597$	−11.1004	−0.454311
$598$	14.5437	0.594735
$599$	3.01523	0.123199	0.0615995	−	0.998101i	$-0.480380\pi$
$599$	3.01523	0.123199	0.0615995	+	0.998101i	$0.480380\pi$
$600$	6.04502	0.246787
$601$	6.24378	0.254689	0.127345	−	0.991859i	$-0.459355\pi$
$601$	6.24378	0.254689	0.127345	+	0.991859i	$0.459355\pi$
$602$	0	0
$603$	5.45219	0.222030
$604$	10.7618	0.437892
$605$	−36.0305	−1.46485
$606$	−0.518027	−0.0210434
$607$	0.526989	0.0213898	0.0106949	−	0.999943i	$-0.496596\pi$
$607$	0.526989	0.0213898	0.0106949	+	0.999943i	$0.496596\pi$
$608$	−10.6170	−0.430577
$609$	0	0
$610$	6.11982	0.247784
$611$	20.8913	0.845170
$612$	−10.3982	−0.420323
$613$	44.6564	1.80366	0.901828	−	0.432094i	$-0.142225\pi$
$613$	44.6564	1.80366	0.901828	+	0.432094i	$0.142225\pi$
$614$	−7.92250	−0.319726
$615$	24.9508	1.00611
$616$	0	0
$617$	−44.5831	−1.79485	−0.897424	−	0.441170i	$-0.854564\pi$
$617$	−44.5831	−1.79485	−0.897424	+	0.441170i	$0.854564\pi$
$618$	−27.9404	−1.12393
$619$	39.6531	1.59379	0.796896	−	0.604117i	$-0.206474\pi$
$619$	39.6531	1.59379	0.796896	+	0.604117i	$0.206474\pi$
$620$	−37.8462	−1.51994
$621$	3.25901	0.130780
$622$	40.0769	1.60694
$623$	0	0
$624$	11.4778	0.459481
$625$	−18.6829	−0.747314
$626$	−7.37883	−0.294917
$627$	−0.612205	−0.0244491
$628$	2.53114	0.101003
$629$	−8.95084	−0.356893
$630$	0	0
$631$	−6.30818	−0.251125	−0.125562	−	0.992086i	$-0.540073\pi$
$631$	−6.30818	−0.251125	−0.125562	+	0.992086i	$0.540073\pi$
$632$	7.04502	0.280236
$633$	−13.4778	−0.535696
$634$	−14.1067	−0.560249
$635$	14.6170	0.580059
$636$	15.7473	0.624419
$637$	0	0
$638$	2.91623	0.115455
$639$	15.0450	0.595172
$640$	−25.6274	−1.01301
$641$	16.5062	0.651954	0.325977	−	0.945378i	$-0.394307\pi$
$641$	16.5062	0.651954	0.325977	+	0.945378i	$0.394307\pi$
$642$	−2.17525	−0.0858502
$643$	22.1455	0.873332	0.436666	−	0.899624i	$-0.356159\pi$
$643$	22.1455	0.873332	0.436666	+	0.899624i	$0.356159\pi$
$644$	0	0
$645$	−32.2099	−1.26826
$646$	−20.3386	−0.800213
$647$	12.4376	0.488974	0.244487	−	0.969653i	$-0.421381\pi$
$647$	12.4376	0.488974	0.244487	+	0.969653i	$0.421381\pi$
$648$	1.00000	0.0392837
$649$	−0.398207	−0.0156310
$650$	26.9765	1.05810
$651$	0	0
$652$	−12.5526	−0.491599
$653$	−10.3941	−0.406751	−0.203376	−	0.979101i	$-0.565191\pi$
$653$	−10.3941	−0.406751	−0.203376	+	0.979101i	$0.565191\pi$
$654$	9.10044	0.355856
$655$	−58.6981	−2.29352
$656$	−35.9315	−1.40289
$657$	−4.73202	−0.184614
$658$	0	0
$659$	−46.5139	−1.81192	−0.905962	−	0.423360i	$-0.860851\pi$
$659$	−46.5139	−1.81192	−0.905962	+	0.423360i	$0.860851\pi$
$660$	1.93561	0.0753435
$661$	31.3788	1.22050	0.610248	−	0.792211i	$-0.291070\pi$
$661$	31.3788	1.22050	0.610248	+	0.792211i	$0.291070\pi$
$662$	1.24234	0.0482847
$663$	17.0498	0.662161
$664$	−13.0796	−0.507588
$665$	0	0
$666$	−2.34278	−0.0907809
$667$	−12.8262	−0.496633
$668$	−9.49575	−0.367402
$669$	−16.7368	−0.647084
$670$	−33.7175	−1.30262
$671$	−0.394061	−0.0152126
$672$	0	0
$673$	23.2936	0.897903	0.448951	−	0.893556i	$-0.351798\pi$
$673$	23.2936	0.897903	0.448951	+	0.893556i	$0.351798\pi$
$674$	−13.9148	−0.535977
$675$	6.04502	0.232673
$676$	−10.6018	−0.407761
$677$	0.775591	0.0298084	0.0149042	−	0.999889i	$-0.495256\pi$
$677$	0.775591	0.0298084	0.0149042	+	0.999889i	$0.495256\pi$
$678$	28.9598	1.11219
$679$	0	0
$680$	−23.6274	−0.906071
$681$	14.0346	0.537807
$682$	5.76932	0.220919
$683$	−13.5810	−0.519661	−0.259831	−	0.965654i	$-0.583667\pi$
$683$	−13.5810	−0.519661	−0.259831	+	0.965654i	$0.583667\pi$
$684$	−2.24860	−0.0859774
$685$	−35.7819	−1.36715
$686$	0	0
$687$	12.2445	0.467155
$688$	46.3851	1.76842
$689$	−25.8206	−0.983687
$690$	−20.1544	−0.767266
$691$	−18.6981	−0.711309	−0.355654	−	0.934618i	$-0.615742\pi$
$691$	−18.6981	−0.711309	−0.355654	+	0.934618i	$0.615742\pi$
$692$	30.0471	1.14222
$693$	0	0
$694$	54.0007	2.04984
$695$	−32.6378	−1.23802
$696$	−3.93561	−0.149179
$697$	−53.3747	−2.02171
$698$	−31.4003	−1.18852
$699$	1.87122	0.0707760
$700$	0	0
$701$	−46.7625	−1.76619	−0.883097	−	0.469190i	$-0.844546\pi$
$701$	−46.7625	−1.76619	−0.883097	+	0.469190i	$0.844546\pi$
$702$	4.46260	0.168430
$703$	−1.93561	−0.0730029
$704$	−1.30548	−0.0492021
$705$	−28.9508	−1.09035
$706$	−5.54636	−0.208740
$707$	0	0
$708$	−1.46260	−0.0549678
$709$	2.98477	0.112095	0.0560477	−	0.998428i	$-0.482150\pi$
$709$	2.98477	0.112095	0.0560477	+	0.998428i	$0.482150\pi$
$710$	−93.0415	−3.49179
$711$	7.04502	0.264209
$712$	16.4328	0.615846
$713$	−25.3747	−0.950289
$714$	0	0
$715$	−3.17380	−0.118693
$716$	−35.0588	−1.31021
$717$	−13.9910	−0.522505
$718$	3.44322	0.128500
$719$	33.0915	1.23410	0.617052	−	0.786922i	$-0.288327\pi$
$719$	33.0915	1.23410	0.617052	+	0.786922i	$0.288327\pi$
$720$	−15.9058	−0.592775
$721$	0	0
$722$	30.9571	1.15210
$723$	−27.5333	−1.02397
$724$	−21.5166	−0.799657
$725$	−23.7908	−0.883569
$726$	20.1738	0.748720
$727$	−25.9100	−0.960948	−0.480474	−	0.877009i	$-0.659535\pi$
$727$	−25.9100	−0.960948	−0.480474	+	0.877009i	$0.659535\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	29.2638	1.08310
$731$	68.9031	2.54847
$732$	−1.44737	−0.0534963
$733$	3.43426	0.126847	0.0634237	−	0.997987i	$-0.479798\pi$
$733$	3.43426	0.126847	0.0634237	+	0.997987i	$0.479798\pi$
$734$	14.8310	0.547423
$735$	0	0
$736$	22.5062	0.829588
$737$	2.17110	0.0799735
$738$	−13.9702	−0.514251
$739$	19.0014	0.698980	0.349490	−	0.936940i	$-0.386355\pi$
$739$	19.0014	0.698980	0.349490	+	0.936940i	$0.386355\pi$
$740$	6.11982	0.224969
$741$	3.68701	0.135446
$742$	0	0
$743$	−13.1607	−0.482819	−0.241409	−	0.970423i	$-0.577610\pi$
$743$	−13.1607	−0.482819	−0.241409	+	0.970423i	$0.577610\pi$
$744$	−7.78600	−0.285449
$745$	−16.6814	−0.611160
$746$	−2.45364	−0.0898340
$747$	−13.0796	−0.478558
$748$	−4.14064	−0.151397
$749$	0	0
$750$	−6.46260	−0.235981
$751$	−14.6981	−0.536341	−0.268170	−	0.963371i	$-0.586419\pi$
$751$	−14.6981	−0.536341	−0.268170	+	0.963371i	$0.586419\pi$
$752$	41.6918	1.52034
$753$	2.61702	0.0953696
$754$	−17.5630	−0.639608
$755$	24.4536	0.889959
$756$	0	0
$757$	3.27984	0.119208	0.0596039	−	0.998222i	$-0.481016\pi$
$757$	3.27984	0.119208	0.0596039	+	0.998222i	$0.481016\pi$
$758$	−38.2922	−1.39083
$759$	1.29776	0.0471058
$760$	−5.10941	−0.185338
$761$	15.5810	0.564810	0.282405	−	0.959295i	$-0.408868\pi$
$761$	15.5810	0.564810	0.282405	+	0.959295i	$0.408868\pi$
$762$	−8.18421	−0.296483
$763$	0	0
$764$	4.26528	0.154312
$765$	−23.6274	−0.854252
$766$	40.7148	1.47108
$767$	2.39821	0.0865943
$768$	20.9058	0.754374
$769$	−11.0402	−0.398120	−0.199060	−	0.979987i	$-0.563789\pi$
$769$	−11.0402	−0.398120	−0.199060	+	0.979987i	$0.563789\pi$
$770$	0	0
$771$	−20.3892	−0.734301
$772$	−0.946021	−0.0340480
$773$	−39.8600	−1.43367	−0.716833	−	0.697245i	$-0.754409\pi$
$773$	−39.8600	−1.43367	−0.716833	+	0.697245i	$0.754409\pi$
$774$	18.0346	0.648240
$775$	−47.0665	−1.69068
$776$	−14.7666	−0.530091
$777$	0	0
$778$	11.7216	0.420240
$779$	−11.5422	−0.413543
$780$	−11.6572	−0.417395
$781$	5.99104	0.214376
$782$	43.1142	1.54176
$783$	−3.93561	−0.140647
$784$	0	0
$785$	5.75140	0.205276
$786$	32.8656	1.17228
$787$	−24.0692	−0.857975	−0.428987	−	0.903311i	$-0.641129\pi$
$787$	−24.0692	−0.857975	−0.428987	+	0.903311i	$0.641129\pi$
$788$	−8.58723	−0.305908
$789$	−23.8552	−0.849268
$790$	−43.5679	−1.55007
$791$	0	0
$792$	0.398207	0.0141497
$793$	2.37324	0.0842761
$794$	−22.5526	−0.800363
$795$	35.7819	1.26905
$796$	−16.2355	−0.575452
$797$	−10.3088	−0.365158	−0.182579	−	0.983191i	$-0.558445\pi$
$797$	−10.3088	−0.365158	−0.182579	+	0.983191i	$0.558445\pi$
$798$	0	0
$799$	61.9315	2.19098
$800$	41.7458	1.47594
$801$	16.4328	0.580625
$802$	30.3941	1.07325
$803$	−1.88433	−0.0664965
$804$	7.97436	0.281234
$805$	0	0
$806$	−34.7458	−1.22387
$807$	28.2999	0.996203
$808$	0.278388	0.00979367
$809$	24.7119	0.868823	0.434412	−	0.900715i	$-0.356956\pi$
$809$	24.7119	0.868823	0.434412	+	0.900715i	$0.356956\pi$
$810$	−6.18421	−0.217291
$811$	16.3088	0.572681	0.286341	−	0.958128i	$-0.407561\pi$
$811$	16.3088	0.572681	0.286341	+	0.958128i	$0.407561\pi$
$812$	0	0
$813$	23.4134	0.821145
$814$	−0.932912	−0.0326986
$815$	−28.5228	−0.999112
$816$	34.0256	1.19114
$817$	14.9002	0.521293
$818$	68.9736	2.41160
$819$	0	0
$820$	36.4931	1.27439
$821$	−39.5076	−1.37883	−0.689413	−	0.724369i	$-0.742131\pi$
$821$	−39.5076	−1.37883	−0.689413	+	0.724369i	$0.742131\pi$
$822$	20.0346	0.698787
$823$	−0.655771	−0.0228588	−0.0114294	−	0.999935i	$-0.503638\pi$
$823$	−0.655771	−0.0228588	−0.0114294	+	0.999935i	$0.503638\pi$
$824$	15.0152	0.523080
$825$	2.40717	0.0838069
$826$	0	0
$827$	33.5035	1.16503	0.582515	−	0.812820i	$-0.302069\pi$
$827$	33.5035	1.16503	0.582515	+	0.812820i	$0.302069\pi$
$828$	4.76663	0.165652
$829$	−28.1752	−0.978567	−0.489283	−	0.872125i	$-0.662742\pi$
$829$	−28.1752	−0.978567	−0.489283	+	0.872125i	$0.662742\pi$
$830$	80.8871	2.80763
$831$	15.6918	0.544343
$832$	7.86226	0.272575
$833$	0	0
$834$	18.2742	0.632785
$835$	−21.5768	−0.746697
$836$	−0.895410	−0.0309684
$837$	−7.78600	−0.269124
$838$	27.2549	0.941504
$839$	21.9315	0.757158	0.378579	−	0.925569i	$-0.376413\pi$
$839$	21.9315	0.757158	0.378579	+	0.925569i	$0.376413\pi$
$840$	0	0
$841$	−13.5110	−0.465896
$842$	6.18421	0.213122
$843$	−5.63158	−0.193962
$844$	−19.7126	−0.678537
$845$	−24.0900	−0.828722
$846$	16.2099	0.557306
$847$	0	0
$848$	−51.5291	−1.76952
$849$	−10.8310	−0.371720
$850$	79.9709	2.74298
$851$	4.10314	0.140654
$852$	22.0048	0.753873
$853$	22.9903	0.787171	0.393586	−	0.919288i	$-0.371234\pi$
$853$	22.9903	0.787171	0.393586	+	0.919288i	$0.371234\pi$
$854$	0	0
$855$	−5.10941	−0.174738
$856$	1.16898	0.0399550
$857$	16.5574	0.565592	0.282796	−	0.959180i	$-0.408738\pi$
$857$	16.5574	0.565592	0.282796	+	0.959180i	$0.408738\pi$
$858$	1.77704	0.0606671
$859$	3.50280	0.119514	0.0597570	−	0.998213i	$-0.480967\pi$
$859$	3.50280	0.119514	0.0597570	+	0.998213i	$0.480967\pi$
$860$	−47.1101	−1.60644
$861$	0	0
$862$	−5.08377	−0.173154
$863$	−19.1994	−0.653557	−0.326778	−	0.945101i	$-0.605963\pi$
$863$	−19.1994	−0.653557	−0.326778	+	0.945101i	$0.605963\pi$
$864$	6.90582	0.234941
$865$	68.2749	2.32142
$866$	−67.1822	−2.28294
$867$	33.5437	1.13920
$868$	0	0
$869$	2.80538	0.0951659
$870$	24.3386	0.825157
$871$	−13.0755	−0.443046
$872$	−4.89059	−0.165616
$873$	−14.7666	−0.499775
$874$	9.32340	0.315369
$875$	0	0
$876$	−6.92105	−0.233841
$877$	52.8864	1.78585	0.892924	−	0.450207i	$-0.148650\pi$
$877$	52.8864	1.78585	0.892924	+	0.450207i	$0.148650\pi$
$878$	−70.6308	−2.38367
$879$	−33.9959	−1.14665
$880$	−6.33382	−0.213513
$881$	6.86562	0.231309	0.115654	−	0.993290i	$-0.463104\pi$
$881$	6.86562	0.231309	0.115654	+	0.993290i	$0.463104\pi$
$882$	0	0
$883$	−51.6233	−1.73726	−0.868631	−	0.495460i	$-0.835000\pi$
$883$	−51.6233	−1.73726	−0.868631	+	0.495460i	$0.835000\pi$
$884$	24.9371	0.838724
$885$	−3.32340	−0.111715
$886$	−3.43551	−0.115418
$887$	−19.7126	−0.661886	−0.330943	−	0.943651i	$-0.607367\pi$
$887$	−19.7126	−0.661886	−0.330943	+	0.943651i	$0.607367\pi$
$888$	1.25901	0.0422497
$889$	0	0
$890$	−101.624	−3.40644
$891$	0.398207	0.0133405
$892$	−24.4793	−0.819627
$893$	13.3926	0.448167
$894$	9.34008	0.312379
$895$	−79.6627	−2.66283
$896$	0	0
$897$	−7.81579	−0.260962
$898$	−52.0084	−1.73554
$899$	30.6427	1.02199
$900$	8.84143	0.294714
$901$	−76.5443	−2.55006
$902$	−5.56304	−0.185229
$903$	0	0
$904$	−15.5630	−0.517619
$905$	−48.8913	−1.62520
$906$	−13.6918	−0.454880
$907$	−40.5366	−1.34600	−0.672998	−	0.739644i	$-0.734994\pi$
$907$	−40.5366	−1.34600	−0.672998	+	0.739644i	$0.734994\pi$
$908$	20.5270	0.681212
$909$	0.278388	0.00923356
$910$	0	0
$911$	54.5949	1.80881	0.904406	−	0.426674i	$-0.140315\pi$
$911$	54.5949	1.80881	0.904406	+	0.426674i	$0.140315\pi$
$912$	7.35801	0.243648
$913$	−5.20840	−0.172373
$914$	43.2638	1.43104
$915$	−3.28880	−0.108724
$916$	17.9087	0.591721
$917$	0	0
$918$	13.2292	0.436630
$919$	−6.95565	−0.229446	−0.114723	−	0.993398i	$-0.536598\pi$
$919$	−6.95565	−0.229446	−0.114723	+	0.993398i	$0.536598\pi$
$920$	10.8310	0.357088
$921$	4.25756	0.140292
$922$	38.0436	1.25290
$923$	−36.0811	−1.18762
$924$	0	0
$925$	7.61076	0.250240
$926$	23.4689	0.771235
$927$	15.0152	0.493165
$928$	−27.1786	−0.892182
$929$	−16.5478	−0.542916	−0.271458	−	0.962450i	$-0.587506\pi$
$929$	−16.5478	−0.542916	−0.271458	+	0.962450i	$0.587506\pi$
$930$	48.1503	1.57891
$931$	0	0
$932$	2.73684	0.0896482
$933$	−21.5374	−0.705103
$934$	−3.52072	−0.115202
$935$	−9.40862	−0.307695
$936$	−2.39821	−0.0783879
$937$	28.6766	0.936824	0.468412	−	0.883510i	$-0.344826\pi$
$937$	28.6766	0.936824	0.468412	+	0.883510i	$0.344826\pi$
$938$	0	0
$939$	3.96540	0.129406
$940$	−42.3434	−1.38109
$941$	24.1198	0.786284	0.393142	−	0.919478i	$-0.371388\pi$
$941$	24.1198	0.786284	0.393142	+	0.919478i	$0.371388\pi$
$942$	−3.22026	−0.104922
$943$	24.4674	0.796769
$944$	4.78600	0.155771
$945$	0	0
$946$	7.18151	0.233491
$947$	33.0617	1.07436	0.537180	−	0.843467i	$-0.319489\pi$
$947$	33.0617	1.07436	0.537180	+	0.843467i	$0.319489\pi$
$948$	10.3040	0.334659
$949$	11.3484	0.368384
$950$	17.2936	0.561079
$951$	7.58097	0.245830
$952$	0	0
$953$	−6.79641	−0.220157	−0.110079	−	0.993923i	$-0.535110\pi$
$953$	−6.79641	−0.220157	−0.110079	+	0.993923i	$0.535110\pi$
$954$	−20.0346	−0.648644
$955$	9.69182	0.313620
$956$	−20.4633	−0.661829
$957$	−1.56719	−0.0506600
$958$	−6.54367	−0.211416
$959$	0	0
$960$	−10.8954	−0.351648
$961$	29.6218	0.955543
$962$	5.61847	0.181147
$963$	1.16898	0.0376699
$964$	−40.2701	−1.29701
$965$	−2.14961	−0.0691983
$966$	0	0
$967$	−43.7479	−1.40684	−0.703419	−	0.710775i	$-0.748344\pi$
$967$	−43.7479	−1.40684	−0.703419	+	0.710775i	$0.748344\pi$
$968$	−10.8414	−0.348457
$969$	10.9300	0.351123
$970$	91.3199	2.93211
$971$	−30.3434	−0.973768	−0.486884	−	0.873467i	$-0.661866\pi$
$971$	−30.3434	−0.973768	−0.486884	+	0.873467i	$0.661866\pi$
$972$	1.46260	0.0469129
$973$	0	0
$974$	−39.4868	−1.26524
$975$	−14.4972	−0.464282
$976$	4.73617	0.151601
$977$	47.2638	1.51210	0.756052	−	0.654512i	$-0.227126\pi$
$977$	47.2638	1.51210	0.756052	+	0.654512i	$0.227126\pi$
$978$	15.9702	0.510671
$979$	6.54367	0.209137
$980$	0	0
$981$	−4.89059	−0.156145
$982$	−23.1738	−0.739506
$983$	−30.9854	−0.988282	−0.494141	−	0.869382i	$-0.664517\pi$
$983$	−30.9854	−0.988282	−0.494141	+	0.869382i	$0.664517\pi$
$984$	7.50761	0.239334
$985$	−19.5124	−0.621718
$986$	−52.0651	−1.65809
$987$	0	0
$988$	5.39261	0.171562
$989$	−31.5858	−1.00437
$990$	−2.46260	−0.0782665
$991$	−18.8131	−0.597618	−0.298809	−	0.954313i	$-0.596589\pi$
$991$	−18.8131	−0.597618	−0.298809	+	0.954313i	$0.596589\pi$
$992$	−53.7687	−1.70716
$993$	−0.667633	−0.0211867
$994$	0	0
$995$	−36.8913	−1.16953
$996$	−19.1302	−0.606165
$997$	−16.5020	−0.522624	−0.261312	−	0.965254i	$-0.584155\pi$
$997$	−16.5020	−0.522624	−0.261312	+	0.965254i	$0.584155\pi$
$998$	−61.5470	−1.94824
$999$	1.25901	0.0398334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8673.2.a.s.1.1		3
7.6	odd	2		177.2.a.d.1.1	✓	3
21.20	even	2		531.2.a.d.1.3		3
28.27	even	2		2832.2.a.t.1.1		3
35.34	odd	2		4425.2.a.w.1.3		3
84.83	odd	2		8496.2.a.bl.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.a.d.1.1	✓	3	7.6	odd	2
531.2.a.d.1.3		3	21.20	even	2
2832.2.a.t.1.1		3	28.27	even	2
4425.2.a.w.1.3		3	35.34	odd	2
8496.2.a.bl.1.3		3	84.83	odd	2
8673.2.a.s.1.1		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8673 = 3 \cdot 7^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8673.a (trivial)

\(f(q)\)	\(=\)	\(q-1.86081 q^{2} +1.00000 q^{3} +1.46260 q^{4} +3.32340 q^{5} -1.86081 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.86081 q^{2} +1.00000 q^{3} +1.46260 q^{4} +3.32340 q^{5} -1.86081 q^{6} +1.00000 q^{8} +1.00000 q^{9} -6.18421 q^{10} +0.398207 q^{11} +1.46260 q^{12} -2.39821 q^{13} +3.32340 q^{15} -4.78600 q^{16} -7.10941 q^{17} -1.86081 q^{18} -1.53740 q^{19} +4.86081 q^{20} -0.740987 q^{22} +3.25901 q^{23} +1.00000 q^{24} +6.04502 q^{25} +4.46260 q^{26} +1.00000 q^{27} -3.93561 q^{29} -6.18421 q^{30} -7.78600 q^{31} +6.90582 q^{32} +0.398207 q^{33} +13.2292 q^{34} +1.46260 q^{36} +1.25901 q^{37} +2.86081 q^{38} -2.39821 q^{39} +3.32340 q^{40} +7.50761 q^{41} -9.69182 q^{43} +0.582418 q^{44} +3.32340 q^{45} -6.06439 q^{46} -8.71120 q^{47} -4.78600 q^{48} -11.2486 q^{50} -7.10941 q^{51} -3.50761 q^{52} +10.7666 q^{53} -1.86081 q^{54} +1.32340 q^{55} -1.53740 q^{57} +7.32340 q^{58} -1.00000 q^{59} +4.86081 q^{60} -0.989588 q^{61} +14.4882 q^{62} -3.27839 q^{64} -7.97021 q^{65} -0.740987 q^{66} +5.45219 q^{67} -10.3982 q^{68} +3.25901 q^{69} +15.0450 q^{71} +1.00000 q^{72} -4.73202 q^{73} -2.34278 q^{74} +6.04502 q^{75} -2.24860 q^{76} +4.46260 q^{78} +7.04502 q^{79} -15.9058 q^{80} +1.00000 q^{81} -13.9702 q^{82} -13.0796 q^{83} -23.6274 q^{85} +18.0346 q^{86} -3.93561 q^{87} +0.398207 q^{88} +16.4328 q^{89} -6.18421 q^{90} +4.76663 q^{92} -7.78600 q^{93} +16.2099 q^{94} -5.10941 q^{95} +6.90582 q^{96} -14.7666 q^{97} +0.398207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9} - 5 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} + 9 q^{20} - 11 q^{22} + q^{23} + 3 q^{24} - q^{25} + 11 q^{26} + 3 q^{27} - 11 q^{29} - 5 q^{30} - 13 q^{31} - 4 q^{32} - 2 q^{33} + 7 q^{34} + 2 q^{36} - 5 q^{37} + 3 q^{38} - 4 q^{39} + 2 q^{40} + q^{41} + 6 q^{43} - 15 q^{44} + 2 q^{45} - 19 q^{46} - 11 q^{47} - 4 q^{48} - 21 q^{50} - 3 q^{51} + 11 q^{52} + 2 q^{53} - 4 q^{55} - 7 q^{57} + 14 q^{58} - 3 q^{59} + 9 q^{60} + q^{61} + 2 q^{62} - 21 q^{64} - 11 q^{66} + 10 q^{67} - 28 q^{68} + q^{69} + 26 q^{71} + 3 q^{72} - 7 q^{73} - 19 q^{74} - q^{75} + 6 q^{76} + 11 q^{78} + 2 q^{79} - 23 q^{80} + 3 q^{81} - 18 q^{82} + 3 q^{83} - 35 q^{85} + 31 q^{86} - 11 q^{87} - 2 q^{88} + 23 q^{89} - 5 q^{90} - 16 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} - 4 q^{96} - 14 q^{97} - 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9 - 5 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 + 9 * q^20 - 11 * q^22 + q^23 + 3 * q^24 - q^25 + 11 * q^26 + 3 * q^27 - 11 * q^29 - 5 * q^30 - 13 * q^31 - 4 * q^32 - 2 * q^33 + 7 * q^34 + 2 * q^36 - 5 * q^37 + 3 * q^38 - 4 * q^39 + 2 * q^40 + q^41 + 6 * q^43 - 15 * q^44 + 2 * q^45 - 19 * q^46 - 11 * q^47 - 4 * q^48 - 21 * q^50 - 3 * q^51 + 11 * q^52 + 2 * q^53 - 4 * q^55 - 7 * q^57 + 14 * q^58 - 3 * q^59 + 9 * q^60 + q^61 + 2 * q^62 - 21 * q^64 - 11 * q^66 + 10 * q^67 - 28 * q^68 + q^69 + 26 * q^71 + 3 * q^72 - 7 * q^73 - 19 * q^74 - q^75 + 6 * q^76 + 11 * q^78 + 2 * q^79 - 23 * q^80 + 3 * q^81 - 18 * q^82 + 3 * q^83 - 35 * q^85 + 31 * q^86 - 11 * q^87 - 2 * q^88 + 23 * q^89 - 5 * q^90 - 16 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 - 4 * q^96 - 14 * q^97 - 2 * q^99

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