LMFDB - Embedded newform 43.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +1.41421 q^{3} +3.41421 q^{5} -2.00000 q^{6} -3.41421 q^{7} +2.82843 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +1.41421 q^{3} +3.41421 q^{5} -2.00000 q^{6} -3.41421 q^{7} +2.82843 q^{8} -1.00000 q^{9} -4.82843 q^{10} -3.82843 q^{11} -1.82843 q^{13} +4.82843 q^{14} +4.82843 q^{15} -4.00000 q^{16} +2.17157 q^{17} +1.41421 q^{18} +0.828427 q^{19} -4.82843 q^{21} +5.41421 q^{22} +6.65685 q^{23} +4.00000 q^{24} +6.65685 q^{25} +2.58579 q^{26} -5.65685 q^{27} -4.24264 q^{29} -6.82843 q^{30} -3.00000 q^{31} -5.41421 q^{33} -3.07107 q^{34} -11.6569 q^{35} +8.48528 q^{37} -1.17157 q^{38} -2.58579 q^{39} +9.65685 q^{40} +1.82843 q^{41} +6.82843 q^{42} +1.00000 q^{43} -3.41421 q^{45} -9.41421 q^{46} +6.00000 q^{47} -5.65685 q^{48} +4.65685 q^{49} -9.41421 q^{50} +3.07107 q^{51} +13.8284 q^{53} +8.00000 q^{54} -13.0711 q^{55} -9.65685 q^{56} +1.17157 q^{57} +6.00000 q^{58} -4.82843 q^{59} -0.242641 q^{61} +4.24264 q^{62} +3.41421 q^{63} +8.00000 q^{64} -6.24264 q^{65} +7.65685 q^{66} -7.48528 q^{67} +9.41421 q^{69} +16.4853 q^{70} -3.17157 q^{71} -2.82843 q^{72} -16.2426 q^{73} -12.0000 q^{74} +9.41421 q^{75} +13.0711 q^{77} +3.65685 q^{78} +4.82843 q^{79} -13.6569 q^{80} -5.00000 q^{81} -2.58579 q^{82} +3.34315 q^{83} +7.41421 q^{85} -1.41421 q^{86} -6.00000 q^{87} -10.8284 q^{88} -1.75736 q^{89} +4.82843 q^{90} +6.24264 q^{91} -4.24264 q^{93} -8.48528 q^{94} +2.82843 q^{95} +1.82843 q^{97} -6.58579 q^{98} +3.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{5} - 4 q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 2 * q + 4 * q^5 - 4 * q^6 - 4 * q^7 - 2 * q^9	$ 2 q + 4 q^{5} - 4 q^{6} - 4 q^{7} - 2 q^{9} - 4 q^{10} - 2 q^{11} + 2 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} + 10 q^{17} - 4 q^{19} - 4 q^{21} + 8 q^{22} + 2 q^{23} + 8 q^{24} + 2 q^{25} + 8 q^{26} - 8 q^{30} - 6 q^{31} - 8 q^{33} + 8 q^{34} - 12 q^{35} - 8 q^{38} - 8 q^{39} + 8 q^{40} - 2 q^{41} + 8 q^{42} + 2 q^{43} - 4 q^{45} - 16 q^{46} + 12 q^{47} - 2 q^{49} - 16 q^{50} - 8 q^{51} + 22 q^{53} + 16 q^{54} - 12 q^{55} - 8 q^{56} + 8 q^{57} + 12 q^{58} - 4 q^{59} + 8 q^{61} + 4 q^{63} + 16 q^{64} - 4 q^{65} + 4 q^{66} + 2 q^{67} + 16 q^{69} + 16 q^{70} - 12 q^{71} - 24 q^{73} - 24 q^{74} + 16 q^{75} + 12 q^{77} - 4 q^{78} + 4 q^{79} - 16 q^{80} - 10 q^{81} - 8 q^{82} + 18 q^{83} + 12 q^{85} - 12 q^{87} - 16 q^{88} - 12 q^{89} + 4 q^{90} + 4 q^{91} - 2 q^{97} - 16 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q + 4 * q^5 - 4 * q^6 - 4 * q^7 - 2 * q^9 - 4 * q^10 - 2 * q^11 + 2 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 + 10 * q^17 - 4 * q^19 - 4 * q^21 + 8 * q^22 + 2 * q^23 + 8 * q^24 + 2 * q^25 + 8 * q^26 - 8 * q^30 - 6 * q^31 - 8 * q^33 + 8 * q^34 - 12 * q^35 - 8 * q^38 - 8 * q^39 + 8 * q^40 - 2 * q^41 + 8 * q^42 + 2 * q^43 - 4 * q^45 - 16 * q^46 + 12 * q^47 - 2 * q^49 - 16 * q^50 - 8 * q^51 + 22 * q^53 + 16 * q^54 - 12 * q^55 - 8 * q^56 + 8 * q^57 + 12 * q^58 - 4 * q^59 + 8 * q^61 + 4 * q^63 + 16 * q^64 - 4 * q^65 + 4 * q^66 + 2 * q^67 + 16 * q^69 + 16 * q^70 - 12 * q^71 - 24 * q^73 - 24 * q^74 + 16 * q^75 + 12 * q^77 - 4 * q^78 + 4 * q^79 - 16 * q^80 - 10 * q^81 - 8 * q^82 + 18 * q^83 + 12 * q^85 - 12 * q^87 - 16 * q^88 - 12 * q^89 + 4 * q^90 + 4 * q^91 - 2 * q^97 - 16 * q^98 + 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 $

$2$	−1.41421	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	−1.41421	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$3$	1.41421	0.816497	0.408248	−	0.912871i	$-0.366140\pi$
$3$	1.41421	0.816497	0.408248	+	0.912871i	$0.366140\pi$
$4$	0	0
$5$	3.41421	1.52688	0.763441	−	0.645877i	$-0.223508\pi$
$5$	3.41421	1.52688	0.763441	+	0.645877i	$0.223508\pi$
$6$	−2.00000	−0.816497
$7$	−3.41421	−1.29045	−0.645226	−	0.763992i	$-0.723237\pi$
$7$	−3.41421	−1.29045	−0.645226	+	0.763992i	$0.723237\pi$
$8$	2.82843	1.00000
$9$	−1.00000	−0.333333
$10$	−4.82843	−1.52688
$11$	−3.82843	−1.15431	−0.577157	−	0.816633i	$-0.695838\pi$
$11$	−3.82843	−1.15431	−0.577157	+	0.816633i	$0.695838\pi$
$12$	0	0
$13$	−1.82843	−0.507114	−0.253557	−	0.967320i	$-0.581601\pi$
$13$	−1.82843	−0.507114	−0.253557	+	0.967320i	$0.581601\pi$
$14$	4.82843	1.29045
$15$	4.82843	1.24669
$16$	−4.00000	−1.00000
$17$	2.17157	0.526684	0.263342	−	0.964703i	$-0.415175\pi$
$17$	2.17157	0.526684	0.263342	+	0.964703i	$0.415175\pi$
$18$	1.41421	0.333333
$19$	0.828427	0.190054	0.0950271	−	0.995475i	$-0.469706\pi$
$19$	0.828427	0.190054	0.0950271	+	0.995475i	$0.469706\pi$
$20$	0	0
$21$	−4.82843	−1.05365
$22$	5.41421	1.15431
$23$	6.65685	1.38805	0.694025	−	0.719951i	$-0.255836\pi$
$23$	6.65685	1.38805	0.694025	+	0.719951i	$0.255836\pi$
$24$	4.00000	0.816497
$25$	6.65685	1.33137
$26$	2.58579	0.507114
$27$	−5.65685	−1.08866
$28$	0	0
$29$	−4.24264	−0.787839	−0.393919	−	0.919145i	$-0.628881\pi$
$29$	−4.24264	−0.787839	−0.393919	+	0.919145i	$0.628881\pi$
$30$	−6.82843	−1.24669
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	0	0
$33$	−5.41421	−0.942494
$34$	−3.07107	−0.526684
$35$	−11.6569	−1.97037
$36$	0	0
$37$	8.48528	1.39497	0.697486	−	0.716599i	$-0.254302\pi$
$37$	8.48528	1.39497	0.697486	+	0.716599i	$0.254302\pi$
$38$	−1.17157	−0.190054
$39$	−2.58579	−0.414057
$40$	9.65685	1.52688
$41$	1.82843	0.285552	0.142776	−	0.989755i	$-0.454397\pi$
$41$	1.82843	0.285552	0.142776	+	0.989755i	$0.454397\pi$
$42$	6.82843	1.05365
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0	0
$45$	−3.41421	−0.508961
$46$	−9.41421	−1.38805
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	−5.65685	−0.816497
$49$	4.65685	0.665265
$50$	−9.41421	−1.33137
$51$	3.07107	0.430036
$52$	0	0
$53$	13.8284	1.89948	0.949740	−	0.313039i	$-0.101347\pi$
$53$	13.8284	1.89948	0.949740	+	0.313039i	$0.101347\pi$
$54$	8.00000	1.08866
$55$	−13.0711	−1.76250
$56$	−9.65685	−1.29045
$57$	1.17157	0.155179
$58$	6.00000	0.787839
$59$	−4.82843	−0.628608	−0.314304	−	0.949322i	$-0.601771\pi$
$59$	−4.82843	−0.628608	−0.314304	+	0.949322i	$0.601771\pi$
$60$	0	0
$61$	−0.242641	−0.0310670	−0.0155335	−	0.999879i	$-0.504945\pi$
$61$	−0.242641	−0.0310670	−0.0155335	+	0.999879i	$0.504945\pi$
$62$	4.24264	0.538816
$63$	3.41421	0.430150
$64$	8.00000	1.00000
$65$	−6.24264	−0.774304
$66$	7.65685	0.942494
$67$	−7.48528	−0.914473	−0.457236	−	0.889345i	$-0.651161\pi$
$67$	−7.48528	−0.914473	−0.457236	+	0.889345i	$0.651161\pi$
$68$	0	0
$69$	9.41421	1.13334
$70$	16.4853	1.97037
$71$	−3.17157	−0.376396	−0.188198	−	0.982131i	$-0.560265\pi$
$71$	−3.17157	−0.376396	−0.188198	+	0.982131i	$0.560265\pi$
$72$	−2.82843	−0.333333
$73$	−16.2426	−1.90106	−0.950529	−	0.310637i	$-0.899458\pi$
$73$	−16.2426	−1.90106	−0.950529	+	0.310637i	$0.899458\pi$
$74$	−12.0000	−1.39497
$75$	9.41421	1.08706
$76$	0	0
$77$	13.0711	1.48959
$78$	3.65685	0.414057
$79$	4.82843	0.543240	0.271620	−	0.962405i	$-0.412441\pi$
$79$	4.82843	0.543240	0.271620	+	0.962405i	$0.412441\pi$
$80$	−13.6569	−1.52688
$81$	−5.00000	−0.555556
$82$	−2.58579	−0.285552
$83$	3.34315	0.366958	0.183479	−	0.983024i	$-0.441264\pi$
$83$	3.34315	0.366958	0.183479	+	0.983024i	$0.441264\pi$
$84$	0	0
$85$	7.41421	0.804184
$86$	−1.41421	−0.152499
$87$	−6.00000	−0.643268
$88$	−10.8284	−1.15431
$89$	−1.75736	−0.186280	−0.0931399	−	0.995653i	$-0.529690\pi$
$89$	−1.75736	−0.186280	−0.0931399	+	0.995653i	$0.529690\pi$
$90$	4.82843	0.508961
$91$	6.24264	0.654407
$92$	0	0
$93$	−4.24264	−0.439941
$94$	−8.48528	−0.875190
$95$	2.82843	0.290191
$96$	0	0
$97$	1.82843	0.185649	0.0928243	−	0.995683i	$-0.470411\pi$
$97$	1.82843	0.185649	0.0928243	+	0.995683i	$0.470411\pi$
$98$	−6.58579	−0.665265
$99$	3.82843	0.384771
$100$	0	0
$101$	5.82843	0.579950	0.289975	−	0.957034i	$-0.406353\pi$
$101$	5.82843	0.579950	0.289975	+	0.957034i	$0.406353\pi$
$102$	−4.34315	−0.430036
$103$	0.514719	0.0507167	0.0253584	−	0.999678i	$-0.491927\pi$
$103$	0.514719	0.0507167	0.0253584	+	0.999678i	$0.491927\pi$
$104$	−5.17157	−0.507114
$105$	−16.4853	−1.60880
$106$	−19.5563	−1.89948
$107$	−0.343146	−0.0331732	−0.0165866	−	0.999862i	$-0.505280\pi$
$107$	−0.343146	−0.0331732	−0.0165866	+	0.999862i	$0.505280\pi$
$108$	0	0
$109$	−19.9706	−1.91283	−0.956416	−	0.292006i	$-0.905677\pi$
$109$	−19.9706	−1.91283	−0.956416	+	0.292006i	$0.905677\pi$
$110$	18.4853	1.76250
$111$	12.0000	1.13899
$112$	13.6569	1.29045
$113$	−6.82843	−0.642364	−0.321182	−	0.947017i	$-0.604080\pi$
$113$	−6.82843	−0.642364	−0.321182	+	0.947017i	$0.604080\pi$
$114$	−1.65685	−0.155179
$115$	22.7279	2.11939
$116$	0	0
$117$	1.82843	0.169038
$118$	6.82843	0.628608
$119$	−7.41421	−0.679660
$120$	13.6569	1.24669
$121$	3.65685	0.332441
$122$	0.343146	0.0310670
$123$	2.58579	0.233153
$124$	0	0
$125$	5.65685	0.505964
$126$	−4.82843	−0.430150
$127$	3.82843	0.339718	0.169859	−	0.985468i	$-0.445669\pi$
$127$	3.82843	0.339718	0.169859	+	0.985468i	$0.445669\pi$
$128$	−11.3137	−1.00000
$129$	1.41421	0.124515
$130$	8.82843	0.774304
$131$	9.65685	0.843723	0.421862	−	0.906660i	$-0.361377\pi$
$131$	9.65685	0.843723	0.421862	+	0.906660i	$0.361377\pi$
$132$	0	0
$133$	−2.82843	−0.245256
$134$	10.5858	0.914473
$135$	−19.3137	−1.66226
$136$	6.14214	0.526684
$137$	−14.4853	−1.23756	−0.618781	−	0.785564i	$-0.712373\pi$
$137$	−14.4853	−1.23756	−0.618781	+	0.785564i	$0.712373\pi$
$138$	−13.3137	−1.13334
$139$	5.48528	0.465255	0.232628	−	0.972566i	$-0.425268\pi$
$139$	5.48528	0.465255	0.232628	+	0.972566i	$0.425268\pi$
$140$	0	0
$141$	8.48528	0.714590
$142$	4.48528	0.376396
$143$	7.00000	0.585369
$144$	4.00000	0.333333
$145$	−14.4853	−1.20294
$146$	22.9706	1.90106
$147$	6.58579	0.543187
$148$	0	0
$149$	8.48528	0.695141	0.347571	−	0.937654i	$-0.387007\pi$
$149$	8.48528	0.695141	0.347571	+	0.937654i	$0.387007\pi$
$150$	−13.3137	−1.08706
$151$	18.2426	1.48457	0.742283	−	0.670087i	$-0.233743\pi$
$151$	18.2426	1.48457	0.742283	+	0.670087i	$0.233743\pi$
$152$	2.34315	0.190054
$153$	−2.17157	−0.175561
$154$	−18.4853	−1.48959
$155$	−10.2426	−0.822709
$156$	0	0
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	−6.82843	−0.543240
$159$	19.5563	1.55092
$160$	0	0
$161$	−22.7279	−1.79121
$162$	7.07107	0.555556
$163$	−11.7574	−0.920907	−0.460454	−	0.887684i	$-0.652313\pi$
$163$	−11.7574	−0.920907	−0.460454	+	0.887684i	$0.652313\pi$
$164$	0	0
$165$	−18.4853	−1.43908
$166$	−4.72792	−0.366958
$167$	−14.3137	−1.10763	−0.553814	−	0.832640i	$-0.686828\pi$
$167$	−14.3137	−1.10763	−0.553814	+	0.832640i	$0.686828\pi$
$168$	−13.6569	−1.05365
$169$	−9.65685	−0.742835
$170$	−10.4853	−0.804184
$171$	−0.828427	−0.0633514
$172$	0	0
$173$	23.6569	1.79860	0.899299	−	0.437335i	$-0.144078\pi$
$173$	23.6569	1.79860	0.899299	+	0.437335i	$0.144078\pi$
$174$	8.48528	0.643268
$175$	−22.7279	−1.71807
$176$	15.3137	1.15431
$177$	−6.82843	−0.513256
$178$	2.48528	0.186280
$179$	−4.58579	−0.342758	−0.171379	−	0.985205i	$-0.554822\pi$
$179$	−4.58579	−0.342758	−0.171379	+	0.985205i	$0.554822\pi$
$180$	0	0
$181$	7.31371	0.543624	0.271812	−	0.962350i	$-0.412377\pi$
$181$	7.31371	0.543624	0.271812	+	0.962350i	$0.412377\pi$
$182$	−8.82843	−0.654407
$183$	−0.343146	−0.0253661
$184$	18.8284	1.38805
$185$	28.9706	2.12996
$186$	6.00000	0.439941
$187$	−8.31371	−0.607959
$188$	0	0
$189$	19.3137	1.40487
$190$	−4.00000	−0.290191
$191$	−6.14214	−0.444429	−0.222215	−	0.974998i	$-0.571329\pi$
$191$	−6.14214	−0.444429	−0.222215	+	0.974998i	$0.571329\pi$
$192$	11.3137	0.816497
$193$	15.9706	1.14959	0.574793	−	0.818299i	$-0.305083\pi$
$193$	15.9706	1.14959	0.574793	+	0.818299i	$0.305083\pi$
$194$	−2.58579	−0.185649
$195$	−8.82843	−0.632217
$196$	0	0
$197$	−14.1421	−1.00759	−0.503793	−	0.863825i	$-0.668062\pi$
$197$	−14.1421	−1.00759	−0.503793	+	0.863825i	$0.668062\pi$
$198$	−5.41421	−0.384771
$199$	7.65685	0.542780	0.271390	−	0.962469i	$-0.412517\pi$
$199$	7.65685	0.542780	0.271390	+	0.962469i	$0.412517\pi$
$200$	18.8284	1.33137
$201$	−10.5858	−0.746664
$202$	−8.24264	−0.579950
$203$	14.4853	1.01667
$204$	0	0
$205$	6.24264	0.436005
$206$	−0.727922	−0.0507167
$207$	−6.65685	−0.462683
$208$	7.31371	0.507114
$209$	−3.17157	−0.219382
$210$	23.3137	1.60880
$211$	−0.142136	−0.00978502	−0.00489251	−	0.999988i	$-0.501557\pi$
$211$	−0.142136	−0.00978502	−0.00489251	+	0.999988i	$0.501557\pi$
$212$	0	0
$213$	−4.48528	−0.307326
$214$	0.485281	0.0331732
$215$	3.41421	0.232847
$216$	−16.0000	−1.08866
$217$	10.2426	0.695316
$218$	28.2426	1.91283
$219$	−22.9706	−1.55221
$220$	0	0
$221$	−3.97056	−0.267089
$222$	−16.9706	−1.13899
$223$	4.10051	0.274590	0.137295	−	0.990530i	$-0.456159\pi$
$223$	4.10051	0.274590	0.137295	+	0.990530i	$0.456159\pi$
$224$	0	0
$225$	−6.65685	−0.443790
$226$	9.65685	0.642364
$227$	−6.34315	−0.421009	−0.210505	−	0.977593i	$-0.567511\pi$
$227$	−6.34315	−0.421009	−0.210505	+	0.977593i	$0.567511\pi$
$228$	0	0
$229$	−25.9706	−1.71618	−0.858092	−	0.513497i	$-0.828350\pi$
$229$	−25.9706	−1.71618	−0.858092	+	0.513497i	$0.828350\pi$
$230$	−32.1421	−2.11939
$231$	18.4853	1.21624
$232$	−12.0000	−0.787839
$233$	4.82843	0.316321	0.158160	−	0.987413i	$-0.449444\pi$
$233$	4.82843	0.316321	0.158160	+	0.987413i	$0.449444\pi$
$234$	−2.58579	−0.169038
$235$	20.4853	1.33631
$236$	0	0
$237$	6.82843	0.443554
$238$	10.4853	0.679660
$239$	14.4853	0.936975	0.468487	−	0.883470i	$-0.344799\pi$
$239$	14.4853	0.936975	0.468487	+	0.883470i	$0.344799\pi$
$240$	−19.3137	−1.24669
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	−5.17157	−0.332441
$243$	9.89949	0.635053
$244$	0	0
$245$	15.8995	1.01578
$246$	−3.65685	−0.233153
$247$	−1.51472	−0.0963792
$248$	−8.48528	−0.538816
$249$	4.72792	0.299620
$250$	−8.00000	−0.505964
$251$	23.1421	1.46072	0.730359	−	0.683063i	$-0.239353\pi$
$251$	23.1421	1.46072	0.730359	+	0.683063i	$0.239353\pi$
$252$	0	0
$253$	−25.4853	−1.60225
$254$	−5.41421	−0.339718
$255$	10.4853	0.656614
$256$	0	0
$257$	−1.75736	−0.109621	−0.0548105	−	0.998497i	$-0.517455\pi$
$257$	−1.75736	−0.109621	−0.0548105	+	0.998497i	$0.517455\pi$
$258$	−2.00000	−0.124515
$259$	−28.9706	−1.80014
$260$	0	0
$261$	4.24264	0.262613
$262$	−13.6569	−0.843723
$263$	0.142136	0.00876446	0.00438223	−	0.999990i	$-0.498605\pi$
$263$	0.142136	0.00876446	0.00438223	+	0.999990i	$0.498605\pi$
$264$	−15.3137	−0.942494
$265$	47.2132	2.90028
$266$	4.00000	0.245256
$267$	−2.48528	−0.152097
$268$	0	0
$269$	−3.00000	−0.182913	−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000	−0.182913	−0.0914566	+	0.995809i	$0.529152\pi$
$270$	27.3137	1.66226
$271$	−25.9706	−1.57760	−0.788800	−	0.614650i	$-0.789297\pi$
$271$	−25.9706	−1.57760	−0.788800	+	0.614650i	$0.789297\pi$
$272$	−8.68629	−0.526684
$273$	8.82843	0.534321
$274$	20.4853	1.23756
$275$	−25.4853	−1.53682
$276$	0	0
$277$	7.89949	0.474635	0.237317	−	0.971432i	$-0.423732\pi$
$277$	7.89949	0.474635	0.237317	+	0.971432i	$0.423732\pi$
$278$	−7.75736	−0.465255
$279$	3.00000	0.179605
$280$	−32.9706	−1.97037
$281$	−8.65685	−0.516425	−0.258212	−	0.966088i	$-0.583133\pi$
$281$	−8.65685	−0.516425	−0.258212	+	0.966088i	$0.583133\pi$
$282$	−12.0000	−0.714590
$283$	18.3137	1.08864	0.544318	−	0.838879i	$-0.316788\pi$
$283$	18.3137	1.08864	0.544318	+	0.838879i	$0.316788\pi$
$284$	0	0
$285$	4.00000	0.236940
$286$	−9.89949	−0.585369
$287$	−6.24264	−0.368491
$288$	0	0
$289$	−12.2843	−0.722604
$290$	20.4853	1.20294
$291$	2.58579	0.151581
$292$	0	0
$293$	10.3431	0.604253	0.302127	−	0.953268i	$-0.402303\pi$
$293$	10.3431	0.604253	0.302127	+	0.953268i	$0.402303\pi$
$294$	−9.31371	−0.543187
$295$	−16.4853	−0.959810
$296$	24.0000	1.39497
$297$	21.6569	1.25666
$298$	−12.0000	−0.695141
$299$	−12.1716	−0.703900
$300$	0	0
$301$	−3.41421	−0.196792
$302$	−25.7990	−1.48457
$303$	8.24264	0.473527
$304$	−3.31371	−0.190054
$305$	−0.828427	−0.0474356
$306$	3.07107	0.175561
$307$	26.7990	1.52950	0.764750	−	0.644328i	$-0.222863\pi$
$307$	26.7990	1.52950	0.764750	+	0.644328i	$0.222863\pi$
$308$	0	0
$309$	0.727922	0.0414100
$310$	14.4853	0.822709
$311$	−13.9706	−0.792198	−0.396099	−	0.918208i	$-0.629636\pi$
$311$	−13.9706	−0.792198	−0.396099	+	0.918208i	$0.629636\pi$
$312$	−7.31371	−0.414057
$313$	−25.2132	−1.42513	−0.712567	−	0.701604i	$-0.752468\pi$
$313$	−25.2132	−1.42513	−0.712567	+	0.701604i	$0.752468\pi$
$314$	14.1421	0.798087
$315$	11.6569	0.656789
$316$	0	0
$317$	25.8284	1.45067	0.725334	−	0.688397i	$-0.241685\pi$
$317$	25.8284	1.45067	0.725334	+	0.688397i	$0.241685\pi$
$318$	−27.6569	−1.55092
$319$	16.2426	0.909413
$320$	27.3137	1.52688
$321$	−0.485281	−0.0270858
$322$	32.1421	1.79121
$323$	1.79899	0.100098
$324$	0	0
$325$	−12.1716	−0.675157
$326$	16.6274	0.920907
$327$	−28.2426	−1.56182
$328$	5.17157	0.285552
$329$	−20.4853	−1.12939
$330$	26.1421	1.43908
$331$	21.4142	1.17703	0.588516	−	0.808486i	$-0.299712\pi$
$331$	21.4142	1.17703	0.588516	+	0.808486i	$0.299712\pi$
$332$	0	0
$333$	−8.48528	−0.464991
$334$	20.2426	1.10763
$335$	−25.5563	−1.39629
$336$	19.3137	1.05365
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	13.6569	0.742835
$339$	−9.65685	−0.524488
$340$	0	0
$341$	11.4853	0.621963
$342$	1.17157	0.0633514
$343$	8.00000	0.431959
$344$	2.82843	0.152499
$345$	32.1421	1.73047
$346$	−33.4558	−1.79860
$347$	−4.58579	−0.246178	−0.123089	−	0.992396i	$-0.539280\pi$
$347$	−4.58579	−0.246178	−0.123089	+	0.992396i	$0.539280\pi$
$348$	0	0
$349$	−20.2426	−1.08356	−0.541782	−	0.840519i	$-0.682250\pi$
$349$	−20.2426	−1.08356	−0.541782	+	0.840519i	$0.682250\pi$
$350$	32.1421	1.71807
$351$	10.3431	0.552076
$352$	0	0
$353$	5.82843	0.310216	0.155108	−	0.987898i	$-0.450427\pi$
$353$	5.82843	0.310216	0.155108	+	0.987898i	$0.450427\pi$
$354$	9.65685	0.513256
$355$	−10.8284	−0.574713
$356$	0	0
$357$	−10.4853	−0.554940
$358$	6.48528	0.342758
$359$	−21.3431	−1.12645	−0.563224	−	0.826304i	$-0.690439\pi$
$359$	−21.3431	−1.12645	−0.563224	+	0.826304i	$0.690439\pi$
$360$	−9.65685	−0.508961
$361$	−18.3137	−0.963879
$362$	−10.3431	−0.543624
$363$	5.17157	0.271437
$364$	0	0
$365$	−55.4558	−2.90269
$366$	0.485281	0.0253661
$367$	9.79899	0.511503	0.255752	−	0.966743i	$-0.417677\pi$
$367$	9.79899	0.511503	0.255752	+	0.966743i	$0.417677\pi$
$368$	−26.6274	−1.38805
$369$	−1.82843	−0.0951841
$370$	−40.9706	−2.12996
$371$	−47.2132	−2.45119
$372$	0	0
$373$	8.48528	0.439351	0.219676	−	0.975573i	$-0.429500\pi$
$373$	8.48528	0.439351	0.219676	+	0.975573i	$0.429500\pi$
$374$	11.7574	0.607959
$375$	8.00000	0.413118
$376$	16.9706	0.875190
$377$	7.75736	0.399524
$378$	−27.3137	−1.40487
$379$	30.3137	1.55711	0.778555	−	0.627576i	$-0.215953\pi$
$379$	30.3137	1.55711	0.778555	+	0.627576i	$0.215953\pi$
$380$	0	0
$381$	5.41421	0.277379
$382$	8.68629	0.444429
$383$	−20.4853	−1.04675	−0.523374	−	0.852103i	$-0.675327\pi$
$383$	−20.4853	−1.04675	−0.523374	+	0.852103i	$0.675327\pi$
$384$	−16.0000	−0.816497
$385$	44.6274	2.27442
$386$	−22.5858	−1.14959
$387$	−1.00000	−0.0508329
$388$	0	0
$389$	−16.6274	−0.843044	−0.421522	−	0.906818i	$-0.638504\pi$
$389$	−16.6274	−0.843044	−0.421522	+	0.906818i	$0.638504\pi$
$390$	12.4853	0.632217
$391$	14.4558	0.731063
$392$	13.1716	0.665265
$393$	13.6569	0.688897
$394$	20.0000	1.00759
$395$	16.4853	0.829465
$396$	0	0
$397$	29.4558	1.47835	0.739173	−	0.673515i	$-0.235216\pi$
$397$	29.4558	1.47835	0.739173	+	0.673515i	$0.235216\pi$
$398$	−10.8284	−0.542780
$399$	−4.00000	−0.200250
$400$	−26.6274	−1.33137
$401$	−12.5147	−0.624955	−0.312478	−	0.949925i	$-0.601159\pi$
$401$	−12.5147	−0.624955	−0.312478	+	0.949925i	$0.601159\pi$
$402$	14.9706	0.746664
$403$	5.48528	0.273241
$404$	0	0
$405$	−17.0711	−0.848268
$406$	−20.4853	−1.01667
$407$	−32.4853	−1.61024
$408$	8.68629	0.430036
$409$	−16.8701	−0.834171	−0.417085	−	0.908867i	$-0.636948\pi$
$409$	−16.8701	−0.834171	−0.417085	+	0.908867i	$0.636948\pi$
$410$	−8.82843	−0.436005
$411$	−20.4853	−1.01046
$412$	0	0
$413$	16.4853	0.811188
$414$	9.41421	0.462683
$415$	11.4142	0.560302
$416$	0	0
$417$	7.75736	0.379880
$418$	4.48528	0.219382
$419$	−23.8995	−1.16757	−0.583783	−	0.811909i	$-0.698428\pi$
$419$	−23.8995	−1.16757	−0.583783	+	0.811909i	$0.698428\pi$
$420$	0	0
$421$	−15.6569	−0.763068	−0.381534	−	0.924355i	$-0.624604\pi$
$421$	−15.6569	−0.763068	−0.381534	+	0.924355i	$0.624604\pi$
$422$	0.201010	0.00978502
$423$	−6.00000	−0.291730
$424$	39.1127	1.89948
$425$	14.4558	0.701211
$426$	6.34315	0.307326
$427$	0.828427	0.0400904
$428$	0	0
$429$	9.89949	0.477952
$430$	−4.82843	−0.232847
$431$	23.2843	1.12156	0.560782	−	0.827964i	$-0.310501\pi$
$431$	23.2843	1.12156	0.560782	+	0.827964i	$0.310501\pi$
$432$	22.6274	1.08866
$433$	21.7574	1.04559	0.522796	−	0.852458i	$-0.324889\pi$
$433$	21.7574	1.04559	0.522796	+	0.852458i	$0.324889\pi$
$434$	−14.4853	−0.695316
$435$	−20.4853	−0.982194
$436$	0	0
$437$	5.51472	0.263805
$438$	32.4853	1.55221
$439$	11.4853	0.548163	0.274081	−	0.961707i	$-0.411626\pi$
$439$	11.4853	0.548163	0.274081	+	0.961707i	$0.411626\pi$
$440$	−36.9706	−1.76250
$441$	−4.65685	−0.221755
$442$	5.61522	0.267089
$443$	7.85786	0.373338	0.186669	−	0.982423i	$-0.440231\pi$
$443$	7.85786	0.373338	0.186669	+	0.982423i	$0.440231\pi$
$444$	0	0
$445$	−6.00000	−0.284427
$446$	−5.79899	−0.274590
$447$	12.0000	0.567581
$448$	−27.3137	−1.29045
$449$	33.2132	1.56743	0.783714	−	0.621122i	$-0.213323\pi$
$449$	33.2132	1.56743	0.783714	+	0.621122i	$0.213323\pi$
$450$	9.41421	0.443790
$451$	−7.00000	−0.329617
$452$	0	0
$453$	25.7990	1.21214
$454$	8.97056	0.421009
$455$	21.3137	0.999202
$456$	3.31371	0.155179
$457$	0.727922	0.0340508	0.0170254	−	0.999855i	$-0.494580\pi$
$457$	0.727922	0.0340508	0.0170254	+	0.999855i	$0.494580\pi$
$458$	36.7279	1.71618
$459$	−12.2843	−0.573381
$460$	0	0
$461$	42.6274	1.98536	0.992678	−	0.120788i	$-0.0385420\pi$
$461$	42.6274	1.98536	0.992678	+	0.120788i	$0.0385420\pi$
$462$	−26.1421	−1.21624
$463$	−30.7279	−1.42805	−0.714024	−	0.700121i	$-0.753129\pi$
$463$	−30.7279	−1.42805	−0.714024	+	0.700121i	$0.753129\pi$
$464$	16.9706	0.787839
$465$	−14.4853	−0.671739
$466$	−6.82843	−0.316321
$467$	23.6569	1.09471	0.547354	−	0.836901i	$-0.315635\pi$
$467$	23.6569	1.09471	0.547354	+	0.836901i	$0.315635\pi$
$468$	0	0
$469$	25.5563	1.18008
$470$	−28.9706	−1.33631
$471$	−14.1421	−0.651635
$472$	−13.6569	−0.628608
$473$	−3.82843	−0.176031
$474$	−9.65685	−0.443554
$475$	5.51472	0.253033
$476$	0	0
$477$	−13.8284	−0.633160
$478$	−20.4853	−0.936975
$479$	−6.65685	−0.304159	−0.152080	−	0.988368i	$-0.548597\pi$
$479$	−6.65685	−0.304159	−0.152080	+	0.988368i	$0.548597\pi$
$480$	0	0
$481$	−15.5147	−0.707410
$482$	−5.65685	−0.257663
$483$	−32.1421	−1.46252
$484$	0	0
$485$	6.24264	0.283464
$486$	−14.0000	−0.635053
$487$	22.3431	1.01246	0.506232	−	0.862397i	$-0.331038\pi$
$487$	22.3431	1.01246	0.506232	+	0.862397i	$0.331038\pi$
$488$	−0.686292	−0.0310670
$489$	−16.6274	−0.751918
$490$	−22.4853	−1.01578
$491$	13.4142	0.605375	0.302687	−	0.953090i	$-0.402116\pi$
$491$	13.4142	0.605375	0.302687	+	0.953090i	$0.402116\pi$
$492$	0	0
$493$	−9.21320	−0.414942
$494$	2.14214	0.0963792
$495$	13.0711	0.587501
$496$	12.0000	0.538816
$497$	10.8284	0.485721
$498$	−6.68629	−0.299620
$499$	−25.7574	−1.15306	−0.576529	−	0.817077i	$-0.695593\pi$
$499$	−25.7574	−1.15306	−0.576529	+	0.817077i	$0.695593\pi$
$500$	0	0
$501$	−20.2426	−0.904374
$502$	−32.7279	−1.46072
$503$	−30.7696	−1.37195	−0.685973	−	0.727627i	$-0.740623\pi$
$503$	−30.7696	−1.37195	−0.685973	+	0.727627i	$0.740623\pi$
$504$	9.65685	0.430150
$505$	19.8995	0.885516
$506$	36.0416	1.60225
$507$	−13.6569	−0.606522
$508$	0	0
$509$	0.514719	0.0228145	0.0114073	−	0.999935i	$-0.496369\pi$
$509$	0.514719	0.0228145	0.0114073	+	0.999935i	$0.496369\pi$
$510$	−14.8284	−0.656614
$511$	55.4558	2.45322
$512$	22.6274	1.00000
$513$	−4.68629	−0.206905
$514$	2.48528	0.109621
$515$	1.75736	0.0774385
$516$	0	0
$517$	−22.9706	−1.01024
$518$	40.9706	1.80014
$519$	33.4558	1.46855
$520$	−17.6569	−0.774304
$521$	16.9289	0.741670	0.370835	−	0.928699i	$-0.379072\pi$
$521$	16.9289	0.741670	0.370835	+	0.928699i	$0.379072\pi$
$522$	−6.00000	−0.262613
$523$	−39.2132	−1.71467	−0.857337	−	0.514756i	$-0.827883\pi$
$523$	−39.2132	−1.71467	−0.857337	+	0.514756i	$0.827883\pi$
$524$	0	0
$525$	−32.1421	−1.40280
$526$	−0.201010	−0.00876446
$527$	−6.51472	−0.283786
$528$	21.6569	0.942494
$529$	21.3137	0.926683
$530$	−66.7696	−2.90028
$531$	4.82843	0.209536
$532$	0	0
$533$	−3.34315	−0.144808
$534$	3.51472	0.152097
$535$	−1.17157	−0.0506515
$536$	−21.1716	−0.914473
$537$	−6.48528	−0.279861
$538$	4.24264	0.182913
$539$	−17.8284	−0.767925
$540$	0	0
$541$	8.79899	0.378298	0.189149	−	0.981948i	$-0.439427\pi$
$541$	8.79899	0.378298	0.189149	+	0.981948i	$0.439427\pi$
$542$	36.7279	1.57760
$543$	10.3431	0.443867
$544$	0	0
$545$	−68.1838	−2.92067
$546$	−12.4853	−0.534321
$547$	9.00000	0.384812	0.192406	−	0.981315i	$-0.438371\pi$
$547$	9.00000	0.384812	0.192406	+	0.981315i	$0.438371\pi$
$548$	0	0
$549$	0.242641	0.0103557
$550$	36.0416	1.53682
$551$	−3.51472	−0.149732
$552$	26.6274	1.13334
$553$	−16.4853	−0.701025
$554$	−11.1716	−0.474635
$555$	40.9706	1.73910
$556$	0	0
$557$	−9.00000	−0.381342	−0.190671	−	0.981654i	$-0.561066\pi$
$557$	−9.00000	−0.381342	−0.190671	+	0.981654i	$0.561066\pi$
$558$	−4.24264	−0.179605
$559$	−1.82843	−0.0773342
$560$	46.6274	1.97037
$561$	−11.7574	−0.496396
$562$	12.2426	0.516425
$563$	39.6274	1.67010	0.835048	−	0.550177i	$-0.185440\pi$
$563$	39.6274	1.67010	0.835048	+	0.550177i	$0.185440\pi$
$564$	0	0
$565$	−23.3137	−0.980815
$566$	−25.8995	−1.08864
$567$	17.0711	0.716917
$568$	−8.97056	−0.376396
$569$	13.3431	0.559374	0.279687	−	0.960091i	$-0.409769\pi$
$569$	13.3431	0.559374	0.279687	+	0.960091i	$0.409769\pi$
$570$	−5.65685	−0.236940
$571$	−3.07107	−0.128520	−0.0642601	−	0.997933i	$-0.520469\pi$
$571$	−3.07107	−0.128520	−0.0642601	+	0.997933i	$0.520469\pi$
$572$	0	0
$573$	−8.68629	−0.362875
$574$	8.82843	0.368491
$575$	44.3137	1.84801
$576$	−8.00000	−0.333333
$577$	33.0711	1.37677	0.688383	−	0.725347i	$-0.258321\pi$
$577$	33.0711	1.37677	0.688383	+	0.725347i	$0.258321\pi$
$578$	17.3726	0.722604
$579$	22.5858	0.938633
$580$	0	0
$581$	−11.4142	−0.473541
$582$	−3.65685	−0.151581
$583$	−52.9411	−2.19260
$584$	−45.9411	−1.90106
$585$	6.24264	0.258101
$586$	−14.6274	−0.604253
$587$	33.7990	1.39503	0.697517	−	0.716568i	$-0.254288\pi$
$587$	33.7990	1.39503	0.697517	+	0.716568i	$0.254288\pi$
$588$	0	0
$589$	−2.48528	−0.102404
$590$	23.3137	0.959810
$591$	−20.0000	−0.822690
$592$	−33.9411	−1.39497
$593$	−9.07107	−0.372504	−0.186252	−	0.982502i	$-0.559634\pi$
$593$	−9.07107	−0.372504	−0.186252	+	0.982502i	$0.559634\pi$
$594$	−30.6274	−1.25666
$595$	−25.3137	−1.03776
$596$	0	0
$597$	10.8284	0.443178
$598$	17.2132	0.703900
$599$	36.6569	1.49776	0.748879	−	0.662706i	$-0.230592\pi$
$599$	36.6569	1.49776	0.748879	+	0.662706i	$0.230592\pi$
$600$	26.6274	1.08706
$601$	−24.9706	−1.01857	−0.509285	−	0.860598i	$-0.670090\pi$
$601$	−24.9706	−1.01857	−0.509285	+	0.860598i	$0.670090\pi$
$602$	4.82843	0.196792
$603$	7.48528	0.304824
$604$	0	0
$605$	12.4853	0.507599
$606$	−11.6569	−0.473527
$607$	−32.9706	−1.33823	−0.669117	−	0.743157i	$-0.733327\pi$
$607$	−32.9706	−1.33823	−0.669117	+	0.743157i	$0.733327\pi$
$608$	0	0
$609$	20.4853	0.830105
$610$	1.17157	0.0474356
$611$	−10.9706	−0.443821
$612$	0	0
$613$	6.82843	0.275798	0.137899	−	0.990446i	$-0.455965\pi$
$613$	6.82843	0.275798	0.137899	+	0.990446i	$0.455965\pi$
$614$	−37.8995	−1.52950
$615$	8.82843	0.355997
$616$	36.9706	1.48959
$617$	19.9706	0.803985	0.401992	−	0.915643i	$-0.368318\pi$
$617$	19.9706	0.803985	0.401992	+	0.915643i	$0.368318\pi$
$618$	−1.02944	−0.0414100
$619$	28.9706	1.16443	0.582213	−	0.813037i	$-0.302187\pi$
$619$	28.9706	1.16443	0.582213	+	0.813037i	$0.302187\pi$
$620$	0	0
$621$	−37.6569	−1.51112
$622$	19.7574	0.792198
$623$	6.00000	0.240385
$624$	10.3431	0.414057
$625$	−13.9706	−0.558823
$626$	35.6569	1.42513
$627$	−4.48528	−0.179125
$628$	0	0
$629$	18.4264	0.734709
$630$	−16.4853	−0.656789
$631$	46.7696	1.86187	0.930933	−	0.365189i	$-0.118996\pi$
$631$	46.7696	1.86187	0.930933	+	0.365189i	$0.118996\pi$
$632$	13.6569	0.543240
$633$	−0.201010	−0.00798944
$634$	−36.5269	−1.45067
$635$	13.0711	0.518710
$636$	0	0
$637$	−8.51472	−0.337365
$638$	−22.9706	−0.909413
$639$	3.17157	0.125465
$640$	−38.6274	−1.52688
$641$	−29.5563	−1.16741	−0.583703	−	0.811967i	$-0.698397\pi$
$641$	−29.5563	−1.16741	−0.583703	+	0.811967i	$0.698397\pi$
$642$	0.686292	0.0270858
$643$	−26.4853	−1.04448	−0.522239	−	0.852799i	$-0.674903\pi$
$643$	−26.4853	−1.04448	−0.522239	+	0.852799i	$0.674903\pi$
$644$	0	0
$645$	4.82843	0.190119
$646$	−2.54416	−0.100098
$647$	−1.17157	−0.0460593	−0.0230296	−	0.999735i	$-0.507331\pi$
$647$	−1.17157	−0.0460593	−0.0230296	+	0.999735i	$0.507331\pi$
$648$	−14.1421	−0.555556
$649$	18.4853	0.725611
$650$	17.2132	0.675157
$651$	14.4853	0.567723
$652$	0	0
$653$	15.1716	0.593710	0.296855	−	0.954923i	$-0.404062\pi$
$653$	15.1716	0.593710	0.296855	+	0.954923i	$0.404062\pi$
$654$	39.9411	1.56182
$655$	32.9706	1.28827
$656$	−7.31371	−0.285552
$657$	16.2426	0.633686
$658$	28.9706	1.12939
$659$	16.3137	0.635492	0.317746	−	0.948176i	$-0.397074\pi$
$659$	16.3137	0.635492	0.317746	+	0.948176i	$0.397074\pi$
$660$	0	0
$661$	−17.0000	−0.661223	−0.330612	−	0.943767i	$-0.607255\pi$
$661$	−17.0000	−0.661223	−0.330612	+	0.943767i	$0.607255\pi$
$662$	−30.2843	−1.17703
$663$	−5.61522	−0.218077
$664$	9.45584	0.366958
$665$	−9.65685	−0.374477
$666$	12.0000	0.464991
$667$	−28.2426	−1.09356
$668$	0	0
$669$	5.79899	0.224202
$670$	36.1421	1.39629
$671$	0.928932	0.0358610
$672$	0	0
$673$	−16.7279	−0.644814	−0.322407	−	0.946601i	$-0.604492\pi$
$673$	−16.7279	−0.644814	−0.322407	+	0.946601i	$0.604492\pi$
$674$	7.07107	0.272367
$675$	−37.6569	−1.44941
$676$	0	0
$677$	11.1716	0.429358	0.214679	−	0.976685i	$-0.431129\pi$
$677$	11.1716	0.429358	0.214679	+	0.976685i	$0.431129\pi$
$678$	13.6569	0.524488
$679$	−6.24264	−0.239571
$680$	20.9706	0.804184
$681$	−8.97056	−0.343753
$682$	−16.2426	−0.621963
$683$	−46.4558	−1.77758	−0.888792	−	0.458311i	$-0.848454\pi$
$683$	−46.4558	−1.77758	−0.888792	+	0.458311i	$0.848454\pi$
$684$	0	0
$685$	−49.4558	−1.88961
$686$	−11.3137	−0.431959
$687$	−36.7279	−1.40126
$688$	−4.00000	−0.152499
$689$	−25.2843	−0.963254
$690$	−45.4558	−1.73047
$691$	−26.7279	−1.01678	−0.508389	−	0.861128i	$-0.669759\pi$
$691$	−26.7279	−1.01678	−0.508389	+	0.861128i	$0.669759\pi$
$692$	0	0
$693$	−13.0711	−0.496529
$694$	6.48528	0.246178
$695$	18.7279	0.710391
$696$	−16.9706	−0.643268
$697$	3.97056	0.150396
$698$	28.6274	1.08356
$699$	6.82843	0.258275
$700$	0	0
$701$	−29.6569	−1.12012	−0.560062	−	0.828451i	$-0.689223\pi$
$701$	−29.6569	−1.12012	−0.560062	+	0.828451i	$0.689223\pi$
$702$	−14.6274	−0.552076
$703$	7.02944	0.265120
$704$	−30.6274	−1.15431
$705$	28.9706	1.09109
$706$	−8.24264	−0.310216
$707$	−19.8995	−0.748398
$708$	0	0
$709$	−38.1127	−1.43135	−0.715676	−	0.698432i	$-0.753881\pi$
$709$	−38.1127	−1.43135	−0.715676	+	0.698432i	$0.753881\pi$
$710$	15.3137	0.574713
$711$	−4.82843	−0.181080
$712$	−4.97056	−0.186280
$713$	−19.9706	−0.747903
$714$	14.8284	0.554940
$715$	23.8995	0.893790
$716$	0	0
$717$	20.4853	0.765037
$718$	30.1838	1.12645
$719$	−22.6274	−0.843860	−0.421930	−	0.906628i	$-0.638647\pi$
$719$	−22.6274	−0.843860	−0.421930	+	0.906628i	$0.638647\pi$
$720$	13.6569	0.508961
$721$	−1.75736	−0.0654475
$722$	25.8995	0.963879
$723$	5.65685	0.210381
$724$	0	0
$725$	−28.2426	−1.04891
$726$	−7.31371	−0.271437
$727$	−24.9706	−0.926107	−0.463053	−	0.886330i	$-0.653246\pi$
$727$	−24.9706	−0.926107	−0.463053	+	0.886330i	$0.653246\pi$
$728$	17.6569	0.654407
$729$	29.0000	1.07407
$730$	78.4264	2.90269
$731$	2.17157	0.0803185
$732$	0	0
$733$	16.9706	0.626822	0.313411	−	0.949618i	$-0.398528\pi$
$733$	16.9706	0.626822	0.313411	+	0.949618i	$0.398528\pi$
$734$	−13.8579	−0.511503
$735$	22.4853	0.829382
$736$	0	0
$737$	28.6569	1.05559
$738$	2.58579	0.0951841
$739$	−39.4558	−1.45141	−0.725703	−	0.688008i	$-0.758485\pi$
$739$	−39.4558	−1.45141	−0.725703	+	0.688008i	$0.758485\pi$
$740$	0	0
$741$	−2.14214	−0.0786933
$742$	66.7696	2.45119
$743$	15.1127	0.554431	0.277216	−	0.960808i	$-0.410588\pi$
$743$	15.1127	0.554431	0.277216	+	0.960808i	$0.410588\pi$
$744$	−12.0000	−0.439941
$745$	28.9706	1.06140
$746$	−12.0000	−0.439351
$747$	−3.34315	−0.122319
$748$	0	0
$749$	1.17157	0.0428083
$750$	−11.3137	−0.413118
$751$	−11.7574	−0.429032	−0.214516	−	0.976720i	$-0.568817\pi$
$751$	−11.7574	−0.429032	−0.214516	+	0.976720i	$0.568817\pi$
$752$	−24.0000	−0.875190
$753$	32.7279	1.19267
$754$	−10.9706	−0.399524
$755$	62.2843	2.26676
$756$	0	0
$757$	3.51472	0.127745	0.0638723	−	0.997958i	$-0.479655\pi$
$757$	3.51472	0.127745	0.0638723	+	0.997958i	$0.479655\pi$
$758$	−42.8701	−1.55711
$759$	−36.0416	−1.30823
$760$	8.00000	0.290191
$761$	19.1127	0.692835	0.346417	−	0.938080i	$-0.387398\pi$
$761$	19.1127	0.692835	0.346417	+	0.938080i	$0.387398\pi$
$762$	−7.65685	−0.277379
$763$	68.1838	2.46842
$764$	0	0
$765$	−7.41421	−0.268061
$766$	28.9706	1.04675
$767$	8.82843	0.318776
$768$	0	0
$769$	44.7696	1.61443	0.807216	−	0.590257i	$-0.200973\pi$
$769$	44.7696	1.61443	0.807216	+	0.590257i	$0.200973\pi$
$770$	−63.1127	−2.27442
$771$	−2.48528	−0.0895052
$772$	0	0
$773$	8.10051	0.291355	0.145677	−	0.989332i	$-0.453464\pi$
$773$	8.10051	0.291355	0.145677	+	0.989332i	$0.453464\pi$
$774$	1.41421	0.0508329
$775$	−19.9706	−0.717364
$776$	5.17157	0.185649
$777$	−40.9706	−1.46981
$778$	23.5147	0.843044
$779$	1.51472	0.0542704
$780$	0	0
$781$	12.1421	0.434480
$782$	−20.4437	−0.731063
$783$	24.0000	0.857690
$784$	−18.6274	−0.665265
$785$	−34.1421	−1.21859
$786$	−19.3137	−0.688897
$787$	9.79899	0.349296	0.174648	−	0.984631i	$-0.444121\pi$
$787$	9.79899	0.349296	0.174648	+	0.984631i	$0.444121\pi$
$788$	0	0
$789$	0.201010	0.00715615
$790$	−23.3137	−0.829465
$791$	23.3137	0.828940
$792$	10.8284	0.384771
$793$	0.443651	0.0157545
$794$	−41.6569	−1.47835
$795$	66.7696	2.36807
$796$	0	0
$797$	35.3137	1.25088	0.625438	−	0.780274i	$-0.284920\pi$
$797$	35.3137	1.25088	0.625438	+	0.780274i	$0.284920\pi$
$798$	5.65685	0.200250
$799$	13.0294	0.460948
$800$	0	0
$801$	1.75736	0.0620932
$802$	17.6985	0.624955
$803$	62.1838	2.19442
$804$	0	0
$805$	−77.5980	−2.73497
$806$	−7.75736	−0.273241
$807$	−4.24264	−0.149348
$808$	16.4853	0.579950
$809$	−5.65685	−0.198884	−0.0994422	−	0.995043i	$-0.531706\pi$
$809$	−5.65685	−0.198884	−0.0994422	+	0.995043i	$0.531706\pi$
$810$	24.1421	0.848268
$811$	23.2721	0.817193	0.408597	−	0.912715i	$-0.366018\pi$
$811$	23.2721	0.817193	0.408597	+	0.912715i	$0.366018\pi$
$812$	0	0
$813$	−36.7279	−1.28810
$814$	45.9411	1.61024
$815$	−40.1421	−1.40612
$816$	−12.2843	−0.430036
$817$	0.828427	0.0289830
$818$	23.8579	0.834171
$819$	−6.24264	−0.218136
$820$	0	0
$821$	−52.1127	−1.81875	−0.909373	−	0.415982i	$-0.863438\pi$
$821$	−52.1127	−1.81875	−0.909373	+	0.415982i	$0.863438\pi$
$822$	28.9706	1.01046
$823$	−54.6569	−1.90522	−0.952609	−	0.304197i	$-0.901612\pi$
$823$	−54.6569	−1.90522	−0.952609	+	0.304197i	$0.901612\pi$
$824$	1.45584	0.0507167
$825$	−36.0416	−1.25481
$826$	−23.3137	−0.811188
$827$	−1.65685	−0.0576145	−0.0288072	−	0.999585i	$-0.509171\pi$
$827$	−1.65685	−0.0576145	−0.0288072	+	0.999585i	$0.509171\pi$
$828$	0	0
$829$	23.7990	0.826573	0.413287	−	0.910601i	$-0.364381\pi$
$829$	23.7990	0.826573	0.413287	+	0.910601i	$0.364381\pi$
$830$	−16.1421	−0.560302
$831$	11.1716	0.387538
$832$	−14.6274	−0.507114
$833$	10.1127	0.350384
$834$	−10.9706	−0.379880
$835$	−48.8701	−1.69122
$836$	0	0
$837$	16.9706	0.586588
$838$	33.7990	1.16757
$839$	−48.8701	−1.68718	−0.843591	−	0.536986i	$-0.819563\pi$
$839$	−48.8701	−1.68718	−0.843591	+	0.536986i	$0.819563\pi$
$840$	−46.6274	−1.60880
$841$	−11.0000	−0.379310
$842$	22.1421	0.763068
$843$	−12.2426	−0.421659
$844$	0	0
$845$	−32.9706	−1.13422
$846$	8.48528	0.291730
$847$	−12.4853	−0.428999
$848$	−55.3137	−1.89948
$849$	25.8995	0.888868
$850$	−20.4437	−0.701211
$851$	56.4853	1.93629
$852$	0	0
$853$	46.5980	1.59548	0.797742	−	0.602999i	$-0.206028\pi$
$853$	46.5980	1.59548	0.797742	+	0.602999i	$0.206028\pi$
$854$	−1.17157	−0.0400904
$855$	−2.82843	−0.0967302
$856$	−0.970563	−0.0331732
$857$	7.65685	0.261553	0.130777	−	0.991412i	$-0.458253\pi$
$857$	7.65685	0.261553	0.130777	+	0.991412i	$0.458253\pi$
$858$	−14.0000	−0.477952
$859$	16.9706	0.579028	0.289514	−	0.957174i	$-0.406506\pi$
$859$	16.9706	0.579028	0.289514	+	0.957174i	$0.406506\pi$
$860$	0	0
$861$	−8.82843	−0.300872
$862$	−32.9289	−1.12156
$863$	−47.2548	−1.60857	−0.804287	−	0.594242i	$-0.797452\pi$
$863$	−47.2548	−1.60857	−0.804287	+	0.594242i	$0.797452\pi$
$864$	0	0
$865$	80.7696	2.74625
$866$	−30.7696	−1.04559
$867$	−17.3726	−0.590004
$868$	0	0
$869$	−18.4853	−0.627070
$870$	28.9706	0.982194
$871$	13.6863	0.463742
$872$	−56.4853	−1.91283
$873$	−1.82843	−0.0618829
$874$	−7.79899	−0.263805
$875$	−19.3137	−0.652923
$876$	0	0
$877$	36.7990	1.24261	0.621307	−	0.783567i	$-0.286602\pi$
$877$	36.7990	1.24261	0.621307	+	0.783567i	$0.286602\pi$
$878$	−16.2426	−0.548163
$879$	14.6274	0.493371
$880$	52.2843	1.76250
$881$	36.2548	1.22146	0.610728	−	0.791840i	$-0.290877\pi$
$881$	36.2548	1.22146	0.610728	+	0.791840i	$0.290877\pi$
$882$	6.58579	0.221755
$883$	−8.02944	−0.270212	−0.135106	−	0.990831i	$-0.543138\pi$
$883$	−8.02944	−0.270212	−0.135106	+	0.990831i	$0.543138\pi$
$884$	0	0
$885$	−23.3137	−0.783682
$886$	−11.1127	−0.373338
$887$	58.9706	1.98004	0.990019	−	0.140935i	$-0.0450108\pi$
$887$	58.9706	1.98004	0.990019	+	0.140935i	$0.0450108\pi$
$888$	33.9411	1.13899
$889$	−13.0711	−0.438390
$890$	8.48528	0.284427
$891$	19.1421	0.641286
$892$	0	0
$893$	4.97056	0.166334
$894$	−16.9706	−0.567581
$895$	−15.6569	−0.523351
$896$	38.6274	1.29045
$897$	−17.2132	−0.574732
$898$	−46.9706	−1.56743
$899$	12.7279	0.424500
$900$	0	0
$901$	30.0294	1.00043
$902$	9.89949	0.329617
$903$	−4.82843	−0.160680
$904$	−19.3137	−0.642364
$905$	24.9706	0.830050
$906$	−36.4853	−1.21214
$907$	−19.9706	−0.663112	−0.331556	−	0.943436i	$-0.607574\pi$
$907$	−19.9706	−0.663112	−0.331556	+	0.943436i	$0.607574\pi$
$908$	0	0
$909$	−5.82843	−0.193317
$910$	−30.1421	−0.999202
$911$	−4.24264	−0.140565	−0.0702825	−	0.997527i	$-0.522390\pi$
$911$	−4.24264	−0.140565	−0.0702825	+	0.997527i	$0.522390\pi$
$912$	−4.68629	−0.155179
$913$	−12.7990	−0.423585
$914$	−1.02944	−0.0340508
$915$	−1.17157	−0.0387310
$916$	0	0
$917$	−32.9706	−1.08878
$918$	17.3726	0.573381
$919$	−12.5147	−0.412822	−0.206411	−	0.978465i	$-0.566178\pi$
$919$	−12.5147	−0.412822	−0.206411	+	0.978465i	$0.566178\pi$
$920$	64.2843	2.11939
$921$	37.8995	1.24883
$922$	−60.2843	−1.98536
$923$	5.79899	0.190876
$924$	0	0
$925$	56.4853	1.85722
$926$	43.4558	1.42805
$927$	−0.514719	−0.0169056
$928$	0	0
$929$	39.1716	1.28518	0.642589	−	0.766211i	$-0.277860\pi$
$929$	39.1716	1.28518	0.642589	+	0.766211i	$0.277860\pi$
$930$	20.4853	0.671739
$931$	3.85786	0.126436
$932$	0	0
$933$	−19.7574	−0.646827
$934$	−33.4558	−1.09471
$935$	−28.3848	−0.928281
$936$	5.17157	0.169038
$937$	−51.0122	−1.66650	−0.833248	−	0.552900i	$-0.813521\pi$
$937$	−51.0122	−1.66650	−0.833248	+	0.552900i	$0.813521\pi$
$938$	−36.1421	−1.18008
$939$	−35.6569	−1.16362
$940$	0	0
$941$	−31.6274	−1.03102	−0.515512	−	0.856882i	$-0.672398\pi$
$941$	−31.6274	−1.03102	−0.515512	+	0.856882i	$0.672398\pi$
$942$	20.0000	0.651635
$943$	12.1716	0.396361
$944$	19.3137	0.628608
$945$	65.9411	2.14506
$946$	5.41421	0.176031
$947$	−5.82843	−0.189398	−0.0946992	−	0.995506i	$-0.530189\pi$
$947$	−5.82843	−0.189398	−0.0946992	+	0.995506i	$0.530189\pi$
$948$	0	0
$949$	29.6985	0.964054
$950$	−7.79899	−0.253033
$951$	36.5269	1.18447
$952$	−20.9706	−0.679660
$953$	−24.0416	−0.778785	−0.389392	−	0.921072i	$-0.627315\pi$
$953$	−24.0416	−0.778785	−0.389392	+	0.921072i	$0.627315\pi$
$954$	19.5563	0.633160
$955$	−20.9706	−0.678591
$956$	0	0
$957$	22.9706	0.742533
$958$	9.41421	0.304159
$959$	49.4558	1.59701
$960$	38.6274	1.24669
$961$	−22.0000	−0.709677
$962$	21.9411	0.707410
$963$	0.343146	0.0110577
$964$	0	0
$965$	54.5269	1.75528
$966$	45.4558	1.46252
$967$	−40.9411	−1.31658	−0.658289	−	0.752765i	$-0.728719\pi$
$967$	−40.9411	−1.31658	−0.658289	+	0.752765i	$0.728719\pi$
$968$	10.3431	0.332441
$969$	2.54416	0.0817301
$970$	−8.82843	−0.283464
$971$	−3.14214	−0.100836	−0.0504180	−	0.998728i	$-0.516055\pi$
$971$	−3.14214	−0.100836	−0.0504180	+	0.998728i	$0.516055\pi$
$972$	0	0
$973$	−18.7279	−0.600390
$974$	−31.5980	−1.01246
$975$	−17.2132	−0.551264
$976$	0.970563	0.0310670
$977$	−23.3137	−0.745872	−0.372936	−	0.927857i	$-0.621649\pi$
$977$	−23.3137	−0.745872	−0.372936	+	0.927857i	$0.621649\pi$
$978$	23.5147	0.751918
$979$	6.72792	0.215025
$980$	0	0
$981$	19.9706	0.637611
$982$	−18.9706	−0.605375
$983$	−62.5269	−1.99430	−0.997149	−	0.0754527i	$-0.975960\pi$
$983$	−62.5269	−1.99430	−0.997149	+	0.0754527i	$0.975960\pi$
$984$	7.31371	0.233153
$985$	−48.2843	−1.53846
$986$	13.0294	0.414942
$987$	−28.9706	−0.922143
$988$	0	0
$989$	6.65685	0.211676
$990$	−18.4853	−0.587501
$991$	11.5563	0.367100	0.183550	−	0.983010i	$-0.441241\pi$
$991$	11.5563	0.367100	0.183550	+	0.983010i	$0.441241\pi$
$992$	0	0
$993$	30.2843	0.961042
$994$	−15.3137	−0.485721
$995$	26.1421	0.828761
$996$	0	0
$997$	2.92893	0.0927602	0.0463801	−	0.998924i	$-0.485231\pi$
$997$	2.92893	0.0927602	0.0463801	+	0.998924i	$0.485231\pi$
$998$	36.4264	1.15306
$999$	−48.0000	−1.51865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.a.b.1.1	✓	2
3.2	odd	2		387.2.a.h.1.2		2
4.3	odd	2		688.2.a.f.1.1		2
5.2	odd	4		1075.2.b.f.474.1		4
5.3	odd	4		1075.2.b.f.474.4		4
5.4	even	2		1075.2.a.i.1.2		2
7.6	odd	2		2107.2.a.b.1.1		2
8.3	odd	2		2752.2.a.m.1.2		2
8.5	even	2		2752.2.a.l.1.1		2
11.10	odd	2		5203.2.a.f.1.2		2
12.11	even	2		6192.2.a.bd.1.1		2
13.12	even	2		7267.2.a.b.1.2		2
15.14	odd	2		9675.2.a.bf.1.1		2
43.42	odd	2		1849.2.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.a.b.1.1	✓	2	1.1	even	1	trivial
387.2.a.h.1.2		2	3.2	odd	2
688.2.a.f.1.1		2	4.3	odd	2
1075.2.a.i.1.2		2	5.4	even	2
1075.2.b.f.474.1		4	5.2	odd	4
1075.2.b.f.474.4		4	5.3	odd	4
1849.2.a.f.1.2		2	43.42	odd	2
2107.2.a.b.1.1		2	7.6	odd	2
2752.2.a.l.1.1		2	8.5	even	2
2752.2.a.m.1.2		2	8.3	odd	2
5203.2.a.f.1.2		2	11.10	odd	2
6192.2.a.bd.1.1		2	12.11	even	2
7267.2.a.b.1.2		2	13.12	even	2
9675.2.a.bf.1.1		2	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +1.41421 q^{3} +3.41421 q^{5} -2.00000 q^{6} -3.41421 q^{7} +2.82843 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +1.41421 q^{3} +3.41421 q^{5} -2.00000 q^{6} -3.41421 q^{7} +2.82843 q^{8} -1.00000 q^{9} -4.82843 q^{10} -3.82843 q^{11} -1.82843 q^{13} +4.82843 q^{14} +4.82843 q^{15} -4.00000 q^{16} +2.17157 q^{17} +1.41421 q^{18} +0.828427 q^{19} -4.82843 q^{21} +5.41421 q^{22} +6.65685 q^{23} +4.00000 q^{24} +6.65685 q^{25} +2.58579 q^{26} -5.65685 q^{27} -4.24264 q^{29} -6.82843 q^{30} -3.00000 q^{31} -5.41421 q^{33} -3.07107 q^{34} -11.6569 q^{35} +8.48528 q^{37} -1.17157 q^{38} -2.58579 q^{39} +9.65685 q^{40} +1.82843 q^{41} +6.82843 q^{42} +1.00000 q^{43} -3.41421 q^{45} -9.41421 q^{46} +6.00000 q^{47} -5.65685 q^{48} +4.65685 q^{49} -9.41421 q^{50} +3.07107 q^{51} +13.8284 q^{53} +8.00000 q^{54} -13.0711 q^{55} -9.65685 q^{56} +1.17157 q^{57} +6.00000 q^{58} -4.82843 q^{59} -0.242641 q^{61} +4.24264 q^{62} +3.41421 q^{63} +8.00000 q^{64} -6.24264 q^{65} +7.65685 q^{66} -7.48528 q^{67} +9.41421 q^{69} +16.4853 q^{70} -3.17157 q^{71} -2.82843 q^{72} -16.2426 q^{73} -12.0000 q^{74} +9.41421 q^{75} +13.0711 q^{77} +3.65685 q^{78} +4.82843 q^{79} -13.6569 q^{80} -5.00000 q^{81} -2.58579 q^{82} +3.34315 q^{83} +7.41421 q^{85} -1.41421 q^{86} -6.00000 q^{87} -10.8284 q^{88} -1.75736 q^{89} +4.82843 q^{90} +6.24264 q^{91} -4.24264 q^{93} -8.48528 q^{94} +2.82843 q^{95} +1.82843 q^{97} -6.58579 q^{98} +3.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{5} - 4 q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 2 * q + 4 * q^5 - 4 * q^6 - 4 * q^7 - 2 * q^9	\( 2 q + 4 q^{5} - 4 q^{6} - 4 q^{7} - 2 q^{9} - 4 q^{10} - 2 q^{11} + 2 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} + 10 q^{17} - 4 q^{19} - 4 q^{21} + 8 q^{22} + 2 q^{23} + 8 q^{24} + 2 q^{25} + 8 q^{26} - 8 q^{30} - 6 q^{31} - 8 q^{33} + 8 q^{34} - 12 q^{35} - 8 q^{38} - 8 q^{39} + 8 q^{40} - 2 q^{41} + 8 q^{42} + 2 q^{43} - 4 q^{45} - 16 q^{46} + 12 q^{47} - 2 q^{49} - 16 q^{50} - 8 q^{51} + 22 q^{53} + 16 q^{54} - 12 q^{55} - 8 q^{56} + 8 q^{57} + 12 q^{58} - 4 q^{59} + 8 q^{61} + 4 q^{63} + 16 q^{64} - 4 q^{65} + 4 q^{66} + 2 q^{67} + 16 q^{69} + 16 q^{70} - 12 q^{71} - 24 q^{73} - 24 q^{74} + 16 q^{75} + 12 q^{77} - 4 q^{78} + 4 q^{79} - 16 q^{80} - 10 q^{81} - 8 q^{82} + 18 q^{83} + 12 q^{85} - 12 q^{87} - 16 q^{88} - 12 q^{89} + 4 q^{90} + 4 q^{91} - 2 q^{97} - 16 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 4 * q^5 - 4 * q^6 - 4 * q^7 - 2 * q^9 - 4 * q^10 - 2 * q^11 + 2 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 + 10 * q^17 - 4 * q^19 - 4 * q^21 + 8 * q^22 + 2 * q^23 + 8 * q^24 + 2 * q^25 + 8 * q^26 - 8 * q^30 - 6 * q^31 - 8 * q^33 + 8 * q^34 - 12 * q^35 - 8 * q^38 - 8 * q^39 + 8 * q^40 - 2 * q^41 + 8 * q^42 + 2 * q^43 - 4 * q^45 - 16 * q^46 + 12 * q^47 - 2 * q^49 - 16 * q^50 - 8 * q^51 + 22 * q^53 + 16 * q^54 - 12 * q^55 - 8 * q^56 + 8 * q^57 + 12 * q^58 - 4 * q^59 + 8 * q^61 + 4 * q^63 + 16 * q^64 - 4 * q^65 + 4 * q^66 + 2 * q^67 + 16 * q^69 + 16 * q^70 - 12 * q^71 - 24 * q^73 - 24 * q^74 + 16 * q^75 + 12 * q^77 - 4 * q^78 + 4 * q^79 - 16 * q^80 - 10 * q^81 - 8 * q^82 + 18 * q^83 + 12 * q^85 - 12 * q^87 - 16 * q^88 - 12 * q^89 + 4 * q^90 + 4 * q^91 - 2 * q^97 - 16 * q^98 + 2 * q^99

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