LMFDB - Embedded newform 1859.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.756.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 2 $ x^3 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.60168$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.60168 q^{3} -1.00000 q^{4} -3.76873 q^{5} -2.60168 q^{6} -0.167055 q^{7} +3.00000 q^{8} +3.76873 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.60168 q^{3} -1.00000 q^{4} -3.76873 q^{5} -2.60168 q^{6} -0.167055 q^{7} +3.00000 q^{8} +3.76873 q^{9} +3.76873 q^{10} -1.00000 q^{11} -2.60168 q^{12} +0.167055 q^{14} -9.80504 q^{15} -1.00000 q^{16} +4.37041 q^{17} -3.76873 q^{18} +3.37041 q^{19} +3.76873 q^{20} -0.434624 q^{21} +1.00000 q^{22} -5.20336 q^{23} +7.80504 q^{24} +9.20336 q^{25} +2.00000 q^{27} +0.167055 q^{28} +1.93579 q^{29} +9.80504 q^{30} -6.86925 q^{31} -5.00000 q^{32} -2.60168 q^{33} -4.37041 q^{34} +0.629587 q^{35} -3.76873 q^{36} -8.63798 q^{37} -3.37041 q^{38} -11.3062 q^{40} +1.26757 q^{41} +0.434624 q^{42} -7.20336 q^{43} +1.00000 q^{44} -14.2034 q^{45} +5.20336 q^{46} +10.1391 q^{47} -2.60168 q^{48} -6.97209 q^{49} -9.20336 q^{50} +11.3704 q^{51} +1.33411 q^{53} -2.00000 q^{54} +3.76873 q^{55} -0.501166 q^{56} +8.76873 q^{57} -1.93579 q^{58} -2.13915 q^{59} +9.80504 q^{60} -4.80504 q^{61} +6.86925 q^{62} -0.629587 q^{63} +7.00000 q^{64} +2.60168 q^{66} +4.13915 q^{67} -4.37041 q^{68} -13.5375 q^{69} -0.629587 q^{70} -6.00000 q^{71} +11.3062 q^{72} -14.2420 q^{73} +8.63798 q^{74} +23.9442 q^{75} -3.37041 q^{76} +0.167055 q^{77} -14.5738 q^{79} +3.76873 q^{80} -6.10284 q^{81} -1.26757 q^{82} +10.5738 q^{83} +0.434624 q^{84} -16.4709 q^{85} +7.20336 q^{86} +5.03630 q^{87} -3.00000 q^{88} -14.3062 q^{89} +14.2034 q^{90} +5.20336 q^{92} -17.8716 q^{93} -10.1391 q^{94} -12.7022 q^{95} -13.0084 q^{96} -3.56538 q^{97} +6.97209 q^{98} -3.76873 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{4} - 3 q^{5} + 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 + 9 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 3 q^{4} - 3 q^{5} + 9 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{11} - 6 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 6 q^{19} + 3 q^{20} + 6 q^{21} + 3 q^{22} + 12 q^{25} + 6 q^{27} - 3 q^{29} + 6 q^{30} - 6 q^{31} - 15 q^{32} + 3 q^{34} + 18 q^{35} - 3 q^{36} - 3 q^{37} + 6 q^{38} - 9 q^{40} - 3 q^{41} - 6 q^{42} - 6 q^{43} + 3 q^{44} - 27 q^{45} + 6 q^{47} + 3 q^{49} - 12 q^{50} + 18 q^{51} + 3 q^{53} - 6 q^{54} + 3 q^{55} + 18 q^{57} + 3 q^{58} + 18 q^{59} + 6 q^{60} + 9 q^{61} + 6 q^{62} - 18 q^{63} + 21 q^{64} - 12 q^{67} + 3 q^{68} - 24 q^{69} - 18 q^{70} - 18 q^{71} + 9 q^{72} - 9 q^{73} + 3 q^{74} + 24 q^{75} + 6 q^{76} - 12 q^{79} + 3 q^{80} - 9 q^{81} + 3 q^{82} - 6 q^{84} - 27 q^{85} + 6 q^{86} - 9 q^{88} - 18 q^{89} + 27 q^{90} - 36 q^{93} - 6 q^{94} - 24 q^{95} - 18 q^{97} - 3 q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 + 9 * q^8 + 3 * q^9 + 3 * q^10 - 3 * q^11 - 6 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 6 * q^19 + 3 * q^20 + 6 * q^21 + 3 * q^22 + 12 * q^25 + 6 * q^27 - 3 * q^29 + 6 * q^30 - 6 * q^31 - 15 * q^32 + 3 * q^34 + 18 * q^35 - 3 * q^36 - 3 * q^37 + 6 * q^38 - 9 * q^40 - 3 * q^41 - 6 * q^42 - 6 * q^43 + 3 * q^44 - 27 * q^45 + 6 * q^47 + 3 * q^49 - 12 * q^50 + 18 * q^51 + 3 * q^53 - 6 * q^54 + 3 * q^55 + 18 * q^57 + 3 * q^58 + 18 * q^59 + 6 * q^60 + 9 * q^61 + 6 * q^62 - 18 * q^63 + 21 * q^64 - 12 * q^67 + 3 * q^68 - 24 * q^69 - 18 * q^70 - 18 * q^71 + 9 * q^72 - 9 * q^73 + 3 * q^74 + 24 * q^75 + 6 * q^76 - 12 * q^79 + 3 * q^80 - 9 * q^81 + 3 * q^82 - 6 * q^84 - 27 * q^85 + 6 * q^86 - 9 * q^88 - 18 * q^89 + 27 * q^90 - 36 * q^93 - 6 * q^94 - 24 * q^95 - 18 * q^97 - 3 * q^98 - 3 * 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 $

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	2.60168	1.50208	0.751040	−	0.660257i	$-0.229552\pi$
$3$	2.60168	1.50208	0.751040	+	0.660257i	$0.229552\pi$
$4$	−1.00000	−0.500000
$5$	−3.76873	−1.68543	−0.842715	−	0.538361i	$-0.819044\pi$
$5$	−3.76873	−1.68543	−0.842715	+	0.538361i	$0.819044\pi$
$6$	−2.60168	−1.06213
$7$	−0.167055	−0.0631409	−0.0315705	−	0.999502i	$-0.510051\pi$
$7$	−0.167055	−0.0631409	−0.0315705	+	0.999502i	$0.510051\pi$
$8$	3.00000	1.06066
$9$	3.76873	1.25624
$10$	3.76873	1.19178
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.60168	−0.751040
$13$	0	0
$13$	0	0
$14$	0.167055	0.0446474
$15$	−9.80504	−2.53165
$16$	−1.00000	−0.250000
$17$	4.37041	1.05998	0.529990	−	0.848004i	$-0.322195\pi$
$17$	4.37041	1.05998	0.529990	+	0.848004i	$0.322195\pi$
$18$	−3.76873	−0.888299
$19$	3.37041	0.773226	0.386613	−	0.922242i	$-0.373645\pi$
$19$	3.37041	0.773226	0.386613	+	0.922242i	$0.373645\pi$
$20$	3.76873	0.842715
$21$	−0.434624	−0.0948427
$22$	1.00000	0.213201
$23$	−5.20336	−1.08498	−0.542488	−	0.840064i	$-0.682517\pi$
$23$	−5.20336	−1.08498	−0.542488	+	0.840064i	$0.682517\pi$
$24$	7.80504	1.59320
$25$	9.20336	1.84067
$26$	0	0
$27$	2.00000	0.384900
$28$	0.167055	0.0315705
$29$	1.93579	0.359467	0.179734	−	0.983715i	$-0.442476\pi$
$29$	1.93579	0.359467	0.179734	+	0.983715i	$0.442476\pi$
$30$	9.80504	1.79015
$31$	−6.86925	−1.23375	−0.616877	−	0.787060i	$-0.711602\pi$
$31$	−6.86925	−1.23375	−0.616877	+	0.787060i	$0.711602\pi$
$32$	−5.00000	−0.883883
$33$	−2.60168	−0.452894
$34$	−4.37041	−0.749520
$35$	0.629587	0.106420
$36$	−3.76873	−0.628122
$37$	−8.63798	−1.42008	−0.710038	−	0.704164i	$-0.751322\pi$
$37$	−8.63798	−1.42008	−0.710038	+	0.704164i	$0.751322\pi$
$38$	−3.37041	−0.546753
$39$	0	0
$40$	−11.3062	−1.78767
$41$	1.26757	0.197961	0.0989805	−	0.995089i	$-0.468442\pi$
$41$	1.26757	0.197961	0.0989805	+	0.995089i	$0.468442\pi$
$42$	0.434624	0.0670639
$43$	−7.20336	−1.09850	−0.549251	−	0.835657i	$-0.685087\pi$
$43$	−7.20336	−1.09850	−0.549251	+	0.835657i	$0.685087\pi$
$44$	1.00000	0.150756
$45$	−14.2034	−2.11731
$46$	5.20336	0.767193
$47$	10.1391	1.47895	0.739473	−	0.673186i	$-0.235075\pi$
$47$	10.1391	1.47895	0.739473	+	0.673186i	$0.235075\pi$
$48$	−2.60168	−0.375520
$49$	−6.97209	−0.996013
$50$	−9.20336	−1.30155
$51$	11.3704	1.59218
$52$	0	0
$53$	1.33411	0.183254	0.0916271	−	0.995793i	$-0.470793\pi$
$53$	1.33411	0.183254	0.0916271	+	0.995793i	$0.470793\pi$
$54$	−2.00000	−0.272166
$55$	3.76873	0.508176
$56$	−0.501166	−0.0669711
$57$	8.76873	1.16145
$58$	−1.93579	−0.254182
$59$	−2.13915	−0.278493	−0.139247	−	0.990258i	$-0.544468\pi$
$59$	−2.13915	−0.278493	−0.139247	+	0.990258i	$0.544468\pi$
$60$	9.80504	1.26582
$61$	−4.80504	−0.615222	−0.307611	−	0.951512i	$-0.599530\pi$
$61$	−4.80504	−0.615222	−0.307611	+	0.951512i	$0.599530\pi$
$62$	6.86925	0.872395
$63$	−0.629587	−0.0793205
$64$	7.00000	0.875000
$65$	0	0
$66$	2.60168	0.320245
$67$	4.13915	0.505677	0.252839	−	0.967508i	$-0.418636\pi$
$67$	4.13915	0.505677	0.252839	+	0.967508i	$0.418636\pi$
$68$	−4.37041	−0.529990
$69$	−13.5375	−1.62972
$70$	−0.629587	−0.0752500
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	11.3062	1.33245
$73$	−14.2420	−1.66690	−0.833450	−	0.552596i	$-0.813637\pi$
$73$	−14.2420	−1.66690	−0.833450	+	0.552596i	$0.813637\pi$
$74$	8.63798	1.00415
$75$	23.9442	2.76484
$76$	−3.37041	−0.386613
$77$	0.167055	0.0190377
$78$	0	0
$79$	−14.5738	−1.63968	−0.819839	−	0.572595i	$-0.805937\pi$
$79$	−14.5738	−1.63968	−0.819839	+	0.572595i	$0.805937\pi$
$80$	3.76873	0.421357
$81$	−6.10284	−0.678094
$82$	−1.26757	−0.139980
$83$	10.5738	1.16062	0.580311	−	0.814395i	$-0.302931\pi$
$83$	10.5738	1.16062	0.580311	+	0.814395i	$0.302931\pi$
$84$	0.434624	0.0474214
$85$	−16.4709	−1.78652
$86$	7.20336	0.776758
$87$	5.03630	0.539948
$88$	−3.00000	−0.319801
$89$	−14.3062	−1.51645	−0.758227	−	0.651990i	$-0.773934\pi$
$89$	−14.3062	−1.51645	−0.758227	+	0.651990i	$0.773934\pi$
$90$	14.2034	1.49717
$91$	0	0
$92$	5.20336	0.542488
$93$	−17.8716	−1.85320
$94$	−10.1391	−1.04577
$95$	−12.7022	−1.30322
$96$	−13.0084	−1.32766
$97$	−3.56538	−0.362009	−0.181005	−	0.983482i	$-0.557935\pi$
$97$	−3.56538	−0.362009	−0.181005	+	0.983482i	$0.557935\pi$
$98$	6.97209	0.704288
$99$	−3.76873	−0.378772
$100$	−9.20336	−0.920336
$101$	−12.0363	−1.19766	−0.598828	−	0.800877i	$-0.704367\pi$
$101$	−12.0363	−1.19766	−0.598828	+	0.800877i	$0.704367\pi$
$102$	−11.3704	−1.12584
$103$	−6.40672	−0.631273	−0.315636	−	0.948880i	$-0.602218\pi$
$103$	−6.40672	−0.631273	−0.315636	+	0.948880i	$0.602218\pi$
$104$	0	0
$105$	1.63798	0.159851
$106$	−1.33411	−0.129580
$107$	−13.7045	−1.32487	−0.662433	−	0.749121i	$-0.730476\pi$
$107$	−13.7045	−1.32487	−0.662433	+	0.749121i	$0.730476\pi$
$108$	−2.00000	−0.192450
$109$	8.84134	0.846847	0.423423	−	0.905932i	$-0.360828\pi$
$109$	8.84134	0.846847	0.423423	+	0.905932i	$0.360828\pi$
$110$	−3.76873	−0.359335
$111$	−22.4733	−2.13307
$112$	0.167055	0.0157852
$113$	4.56538	0.429474	0.214737	−	0.976672i	$-0.431110\pi$
$113$	4.56538	0.429474	0.214737	+	0.976672i	$0.431110\pi$
$114$	−8.76873	−0.821267
$115$	19.6101	1.82865
$116$	−1.93579	−0.179734
$117$	0	0
$118$	2.13915	0.196925
$119$	−0.730100	−0.0669282
$120$	−29.4151	−2.68522
$121$	1.00000	0.0909091
$122$	4.80504	0.435028
$123$	3.29781	0.297353
$124$	6.86925	0.616877
$125$	−15.8413	−1.41689
$126$	0.629587	0.0560880
$127$	−1.33178	−0.118176	−0.0590882	−	0.998253i	$-0.518819\pi$
$127$	−1.33178	−0.118176	−0.0590882	+	0.998253i	$0.518819\pi$
$128$	3.00000	0.265165
$129$	−18.7408	−1.65004
$130$	0	0
$131$	13.7045	1.19737	0.598685	−	0.800985i	$-0.295690\pi$
$131$	13.7045	1.19737	0.598685	+	0.800985i	$0.295690\pi$
$132$	2.60168	0.226447
$133$	−0.563045	−0.0488222
$134$	−4.13915	−0.357568
$135$	−7.53747	−0.648722
$136$	13.1112	1.12428
$137$	13.6403	1.16537	0.582685	−	0.812698i	$-0.302002\pi$
$137$	13.6403	1.16537	0.582685	+	0.812698i	$0.302002\pi$
$138$	13.5375	1.15239
$139$	0.869248	0.0737286	0.0368643	−	0.999320i	$-0.488263\pi$
$139$	0.869248	0.0737286	0.0368643	+	0.999320i	$0.488263\pi$
$140$	−0.629587	−0.0532098
$141$	26.3788	2.22150
$142$	6.00000	0.503509
$143$	0	0
$144$	−3.76873	−0.314061
$145$	−7.29548	−0.605856
$146$	14.2420	1.17868
$147$	−18.1391	−1.49609
$148$	8.63798	0.710038
$149$	−1.16706	−0.0956089	−0.0478044	−	0.998857i	$-0.515222\pi$
$149$	−1.16706	−0.0956089	−0.0478044	+	0.998857i	$0.515222\pi$
$150$	−23.9442	−1.95503
$151$	10.7408	0.874076	0.437038	−	0.899443i	$-0.356028\pi$
$151$	10.7408	0.874076	0.437038	+	0.899443i	$0.356028\pi$
$152$	10.1112	0.820130
$153$	16.4709	1.33160
$154$	−0.167055	−0.0134617
$155$	25.8884	2.07940
$156$	0	0
$157$	−4.59328	−0.366584	−0.183292	−	0.983059i	$-0.558675\pi$
$157$	−4.59328	−0.366584	−0.183292	+	0.983059i	$0.558675\pi$
$158$	14.5738	1.15943
$159$	3.47093	0.275262
$160$	18.8437	1.48972
$161$	0.869248	0.0685063
$162$	6.10284	0.479485
$163$	−11.3425	−0.888414	−0.444207	−	0.895924i	$-0.646514\pi$
$163$	−11.3425	−0.888414	−0.444207	+	0.895924i	$0.646514\pi$
$164$	−1.26757	−0.0989805
$165$	9.80504	0.763321
$166$	−10.5738	−0.820684
$167$	−17.2760	−1.33685	−0.668427	−	0.743778i	$-0.733032\pi$
$167$	−17.2760	−1.33685	−0.668427	+	0.743778i	$0.733032\pi$
$168$	−1.30387	−0.100596
$169$	0	0
$170$	16.4709	1.26326
$171$	12.7022	0.971361
$172$	7.20336	0.549251
$173$	−12.8413	−0.976309	−0.488155	−	0.872757i	$-0.662330\pi$
$173$	−12.8413	−0.976309	−0.488155	+	0.872757i	$0.662330\pi$
$174$	−5.03630	−0.381801
$175$	−1.53747	−0.116222
$176$	1.00000	0.0753778
$177$	−5.56538	−0.418319
$178$	14.3062	1.07230
$179$	−4.93579	−0.368918	−0.184459	−	0.982840i	$-0.559053\pi$
$179$	−4.93579	−0.368918	−0.184459	+	0.982840i	$0.559053\pi$
$180$	14.2034	1.05866
$181$	0.637982	0.0474208	0.0237104	−	0.999719i	$-0.492452\pi$
$181$	0.637982	0.0474208	0.0237104	+	0.999719i	$0.492452\pi$
$182$	0	0
$183$	−12.5012	−0.924113
$184$	−15.6101	−1.15079
$185$	32.5543	2.39344
$186$	17.8716	1.31041
$187$	−4.37041	−0.319596
$188$	−10.1391	−0.739473
$189$	−0.334110	−0.0243030
$190$	12.7022	0.921514
$191$	26.1391	1.89136	0.945681	−	0.325096i	$-0.105396\pi$
$191$	26.1391	1.89136	0.945681	+	0.325096i	$0.105396\pi$
$192$	18.2118	1.31432
$193$	11.1391	0.801813	0.400907	−	0.916119i	$-0.368695\pi$
$193$	11.1391	0.801813	0.400907	+	0.916119i	$0.368695\pi$
$194$	3.56538	0.255979
$195$	0	0
$196$	6.97209	0.498007
$197$	−15.5375	−1.10700	−0.553499	−	0.832850i	$-0.686708\pi$
$197$	−15.5375	−1.10700	−0.553499	+	0.832850i	$0.686708\pi$
$198$	3.76873	0.267832
$199$	−11.6766	−0.827733	−0.413867	−	0.910337i	$-0.635822\pi$
$199$	−11.6766	−0.827733	−0.413867	+	0.910337i	$0.635822\pi$
$200$	27.6101	1.95233
$201$	10.7687	0.759568
$202$	12.0363	0.846871
$203$	−0.323384	−0.0226971
$204$	−11.3704	−0.796088
$205$	−4.77713	−0.333649
$206$	6.40672	0.446377
$207$	−19.6101	−1.36299
$208$	0	0
$209$	−3.37041	−0.233136
$210$	−1.63798	−0.113032
$211$	−4.57377	−0.314871	−0.157436	−	0.987529i	$-0.550323\pi$
$211$	−4.57377	−0.314871	−0.157436	+	0.987529i	$0.550323\pi$
$212$	−1.33411	−0.0916271
$213$	−15.6101	−1.06958
$214$	13.7045	0.936822
$215$	27.1475	1.85145
$216$	6.00000	0.408248
$217$	1.14754	0.0779003
$218$	−8.84134	−0.598811
$219$	−37.0531	−2.50382
$220$	−3.76873	−0.254088
$221$	0	0
$222$	22.4733	1.50831
$223$	9.06421	0.606984	0.303492	−	0.952834i	$-0.401847\pi$
$223$	9.06421	0.606984	0.303492	+	0.952834i	$0.401847\pi$
$224$	0.835276	0.0558092
$225$	34.6850	2.31233
$226$	−4.56538	−0.303684
$227$	13.2034	0.876338	0.438169	−	0.898893i	$-0.355627\pi$
$227$	13.2034	0.876338	0.438169	+	0.898893i	$0.355627\pi$
$228$	−8.76873	−0.580724
$229$	−2.02791	−0.134008	−0.0670039	−	0.997753i	$-0.521344\pi$
$229$	−2.02791	−0.134008	−0.0670039	+	0.997753i	$0.521344\pi$
$230$	−19.6101	−1.29305
$231$	0.434624	0.0285962
$232$	5.80737	0.381272
$233$	−12.7408	−0.834679	−0.417340	−	0.908751i	$-0.637037\pi$
$233$	−12.7408	−0.834679	−0.417340	+	0.908751i	$0.637037\pi$
$234$	0	0
$235$	−38.2118	−2.49266
$236$	2.13915	0.139247
$237$	−37.9163	−2.46293
$238$	0.730100	0.0473254
$239$	−4.07261	−0.263435	−0.131717	−	0.991287i	$-0.542049\pi$
$239$	−4.07261	−0.263435	−0.131717	+	0.991287i	$0.542049\pi$
$240$	9.80504	0.632912
$241$	18.9828	1.22279	0.611395	−	0.791325i	$-0.290608\pi$
$241$	18.9828	1.22279	0.611395	+	0.791325i	$0.290608\pi$
$242$	−1.00000	−0.0642824
$243$	−21.8776	−1.40345
$244$	4.80504	0.307611
$245$	26.2760	1.67871
$246$	−3.29781	−0.210261
$247$	0	0
$248$	−20.6077	−1.30859
$249$	27.5096	1.74335
$250$	15.8413	1.00189
$251$	10.3402	0.652666	0.326333	−	0.945255i	$-0.394187\pi$
$251$	10.3402	0.652666	0.326333	+	0.945255i	$0.394187\pi$
$252$	0.629587	0.0396602
$253$	5.20336	0.327132
$254$	1.33178	0.0835633
$255$	−42.8521	−2.68350
$256$	−17.0000	−1.06250
$257$	24.1755	1.50802	0.754012	−	0.656861i	$-0.228116\pi$
$257$	24.1755	1.50802	0.754012	+	0.656861i	$0.228116\pi$
$258$	18.7408	1.16675
$259$	1.44302	0.0896649
$260$	0	0
$261$	7.29548	0.451579
$262$	−13.7045	−0.846668
$263$	−10.7408	−0.662308	−0.331154	−	0.943577i	$-0.607438\pi$
$263$	−10.7408	−0.662308	−0.331154	+	0.943577i	$0.607438\pi$
$264$	−7.80504	−0.480367
$265$	−5.02791	−0.308862
$266$	0.563045	0.0345225
$267$	−37.2201	−2.27784
$268$	−4.13915	−0.252839
$269$	17.6659	1.07711	0.538554	−	0.842591i	$-0.318971\pi$
$269$	17.6659	1.07711	0.538554	+	0.842591i	$0.318971\pi$
$270$	7.53747	0.458716
$271$	−8.74083	−0.530967	−0.265484	−	0.964115i	$-0.585532\pi$
$271$	−8.74083	−0.530967	−0.265484	+	0.964115i	$0.585532\pi$
$272$	−4.37041	−0.264995
$273$	0	0
$274$	−13.6403	−0.824041
$275$	−9.20336	−0.554983
$276$	13.5375	0.814860
$277$	29.2118	1.75516	0.877582	−	0.479426i	$-0.159155\pi$
$277$	29.2118	1.75516	0.877582	+	0.479426i	$0.159155\pi$
$278$	−0.869248	−0.0521340
$279$	−25.8884	−1.54990
$280$	1.88876	0.112875
$281$	10.8050	0.644574	0.322287	−	0.946642i	$-0.395548\pi$
$281$	10.8050	0.644574	0.322287	+	0.946642i	$0.395548\pi$
$282$	−26.3788	−1.57084
$283$	10.2397	0.608685	0.304342	−	0.952563i	$-0.401563\pi$
$283$	10.2397	0.608685	0.304342	+	0.952563i	$0.401563\pi$
$284$	6.00000	0.356034
$285$	−33.0470	−1.95754
$286$	0	0
$287$	−0.211754	−0.0124994
$288$	−18.8437	−1.11037
$289$	2.10051	0.123560
$290$	7.29548	0.428405
$291$	−9.27596	−0.543767
$292$	14.2420	0.833450
$293$	−3.96370	−0.231562	−0.115781	−	0.993275i	$-0.536937\pi$
$293$	−3.96370	−0.231562	−0.115781	+	0.993275i	$0.536937\pi$
$294$	18.1391	1.05790
$295$	8.06188	0.469381
$296$	−25.9139	−1.50622
$297$	−2.00000	−0.116052
$298$	1.16706	0.0676057
$299$	0	0
$300$	−23.9442	−1.38242
$301$	1.20336	0.0693604
$302$	−10.7408	−0.618065
$303$	−31.3146	−1.79898
$304$	−3.37041	−0.193306
$305$	18.1089	1.03691
$306$	−16.4709	−0.941580
$307$	−14.2397	−0.812700	−0.406350	−	0.913717i	$-0.633199\pi$
$307$	−14.2397	−0.812700	−0.406350	+	0.913717i	$0.633199\pi$
$308$	−0.167055	−0.00951885
$309$	−16.6682	−0.948222
$310$	−25.8884	−1.47036
$311$	11.8776	0.673519	0.336760	−	0.941591i	$-0.390669\pi$
$311$	11.8776	0.673519	0.336760	+	0.941591i	$0.390669\pi$
$312$	0	0
$313$	7.89949	0.446505	0.223253	−	0.974761i	$-0.428332\pi$
$313$	7.89949	0.446505	0.223253	+	0.974761i	$0.428332\pi$
$314$	4.59328	0.259214
$315$	2.37274	0.133689
$316$	14.5738	0.819839
$317$	−27.3230	−1.53461	−0.767306	−	0.641281i	$-0.778403\pi$
$317$	−27.3230	−1.53461	−0.767306	+	0.641281i	$0.778403\pi$
$318$	−3.47093	−0.194640
$319$	−1.93579	−0.108383
$320$	−26.3811	−1.47475
$321$	−35.6548	−1.99006
$322$	−0.869248	−0.0484413
$323$	14.7301	0.819605
$324$	6.10284	0.339047
$325$	0	0
$326$	11.3425	0.628203
$327$	23.0023	1.27203
$328$	3.80271	0.209969
$329$	−1.69380	−0.0933821
$330$	−9.80504	−0.539750
$331$	−4.74083	−0.260579	−0.130290	−	0.991476i	$-0.541591\pi$
$331$	−4.74083	−0.260579	−0.130290	+	0.991476i	$0.541591\pi$
$332$	−10.5738	−0.580311
$333$	−32.5543	−1.78396
$334$	17.2760	0.945299
$335$	−15.5993	−0.852283
$336$	0.434624	0.0237107
$337$	−32.4430	−1.76728	−0.883642	−	0.468163i	$-0.844916\pi$
$337$	−32.4430	−1.76728	−0.883642	+	0.468163i	$0.844916\pi$
$338$	0	0
$339$	11.8776	0.645105
$340$	16.4709	0.893261
$341$	6.86925	0.371991
$342$	−12.7022	−0.686856
$343$	2.33411	0.126030
$344$	−21.6101	−1.16514
$345$	51.0191	2.74678
$346$	12.8413	0.690355
$347$	−11.8329	−0.635226	−0.317613	−	0.948220i	$-0.602881\pi$
$347$	−11.8329	−0.635226	−0.317613	+	0.948220i	$0.602881\pi$
$348$	−5.03630	−0.269974
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	1.53747	0.0821812
$351$	0	0
$352$	5.00000	0.266501
$353$	10.2034	0.543070	0.271535	−	0.962429i	$-0.412469\pi$
$353$	10.2034	0.543070	0.271535	+	0.962429i	$0.412469\pi$
$354$	5.56538	0.295796
$355$	22.6124	1.20014
$356$	14.3062	0.758227
$357$	−1.89949	−0.100531
$358$	4.93579	0.260865
$359$	13.5375	0.714480	0.357240	−	0.934013i	$-0.383718\pi$
$359$	13.5375	0.714480	0.357240	+	0.934013i	$0.383718\pi$
$360$	−42.6101	−2.24575
$361$	−7.64031	−0.402122
$362$	−0.637982	−0.0335316
$363$	2.60168	0.136553
$364$	0	0
$365$	53.6743	2.80944
$366$	12.5012	0.653446
$367$	−11.1475	−0.581897	−0.290949	−	0.956739i	$-0.593971\pi$
$367$	−11.1475	−0.581897	−0.290949	+	0.956739i	$0.593971\pi$
$368$	5.20336	0.271244
$369$	4.77713	0.248687
$370$	−32.5543	−1.69242
$371$	−0.222870	−0.0115708
$372$	17.8716	0.926598
$373$	−27.3123	−1.41418	−0.707088	−	0.707126i	$-0.749991\pi$
$373$	−27.3123	−1.41418	−0.707088	+	0.707126i	$0.749991\pi$
$374$	4.37041	0.225989
$375$	−41.2141	−2.12829
$376$	30.4174	1.56866
$377$	0	0
$378$	0.334110	0.0171848
$379$	−18.4067	−0.945490	−0.472745	−	0.881199i	$-0.656737\pi$
$379$	−18.4067	−0.945490	−0.472745	+	0.881199i	$0.656737\pi$
$380$	12.7022	0.651609
$381$	−3.46486	−0.177510
$382$	−26.1391	−1.33740
$383$	25.8716	1.32198	0.660988	−	0.750397i	$-0.270137\pi$
$383$	25.8716	1.32198	0.660988	+	0.750397i	$0.270137\pi$
$384$	7.80504	0.398299
$385$	−0.629587	−0.0320867
$386$	−11.1391	−0.566968
$387$	−27.1475	−1.37999
$388$	3.56538	0.181005
$389$	20.7153	1.05030	0.525152	−	0.851008i	$-0.324008\pi$
$389$	20.7153	1.05030	0.525152	+	0.851008i	$0.324008\pi$
$390$	0	0
$391$	−22.7408	−1.15005
$392$	−20.9163	−1.05643
$393$	35.6548	1.79855
$394$	15.5375	0.782766
$395$	54.9247	2.76356
$396$	3.76873	0.189386
$397$	21.5822	1.08318	0.541589	−	0.840643i	$-0.317823\pi$
$397$	21.5822	1.08318	0.541589	+	0.840643i	$0.317823\pi$
$398$	11.6766	0.585296
$399$	−1.46486	−0.0733348
$400$	−9.20336	−0.460168
$401$	−0.203358	−0.0101552	−0.00507761	−	0.999987i	$-0.501616\pi$
$401$	−0.203358	−0.0101552	−0.00507761	+	0.999987i	$0.501616\pi$
$402$	−10.7687	−0.537096
$403$	0	0
$404$	12.0363	0.598828
$405$	23.0000	1.14288
$406$	0.323384	0.0160493
$407$	8.63798	0.428169
$408$	34.1112	1.68876
$409$	−0.0921180	−0.00455494	−0.00227747	−	0.999997i	$-0.500725\pi$
$409$	−0.0921180	−0.00455494	−0.00227747	+	0.999997i	$0.500725\pi$
$410$	4.77713	0.235926
$411$	35.4877	1.75048
$412$	6.40672	0.315636
$413$	0.357356	0.0175843
$414$	19.6101	0.963783
$415$	−39.8497	−1.95615
$416$	0	0
$417$	2.26150	0.110746
$418$	3.37041	0.164852
$419$	10.1284	0.494806	0.247403	−	0.968913i	$-0.420423\pi$
$419$	10.1284	0.494806	0.247403	+	0.968913i	$0.420423\pi$
$420$	−1.63798	−0.0799253
$421$	6.58217	0.320795	0.160398	−	0.987052i	$-0.448722\pi$
$421$	6.58217	0.320795	0.160398	+	0.987052i	$0.448722\pi$
$422$	4.57377	0.222648
$423$	38.2118	1.85792
$424$	4.00233	0.194370
$425$	40.2225	1.95108
$426$	15.6101	0.756311
$427$	0.802706	0.0388457
$428$	13.7045	0.662433
$429$	0	0
$430$	−27.1475	−1.30917
$431$	−17.4988	−0.842889	−0.421445	−	0.906854i	$-0.638477\pi$
$431$	−17.4988	−0.842889	−0.421445	+	0.906854i	$0.638477\pi$
$432$	−2.00000	−0.0962250
$433$	−8.69380	−0.417797	−0.208899	−	0.977937i	$-0.566988\pi$
$433$	−8.69380	−0.417797	−0.208899	+	0.977937i	$0.566988\pi$
$434$	−1.14754	−0.0550838
$435$	−18.9805	−0.910045
$436$	−8.84134	−0.423423
$437$	−17.5375	−0.838931
$438$	37.0531	1.77047
$439$	−24.5738	−1.17284	−0.586421	−	0.810006i	$-0.699464\pi$
$439$	−24.5738	−1.17284	−0.586421	+	0.810006i	$0.699464\pi$
$440$	11.3062	0.539002
$441$	−26.2760	−1.25124
$442$	0	0
$443$	−17.2699	−0.820518	−0.410259	−	0.911969i	$-0.634562\pi$
$443$	−17.2699	−0.820518	−0.410259	+	0.911969i	$0.634562\pi$
$444$	22.4733	1.06653
$445$	53.9163	2.55588
$446$	−9.06421	−0.429203
$447$	−3.03630	−0.143612
$448$	−1.16939	−0.0552483
$449$	−16.3230	−0.770330	−0.385165	−	0.922848i	$-0.625855\pi$
$449$	−16.3230	−0.770330	−0.385165	+	0.922848i	$0.625855\pi$
$450$	−34.6850	−1.63507
$451$	−1.26757	−0.0596875
$452$	−4.56538	−0.214737
$453$	27.9442	1.31293
$454$	−13.2034	−0.619664
$455$	0	0
$456$	26.3062	1.23190
$457$	−21.4174	−1.00187	−0.500933	−	0.865486i	$-0.667010\pi$
$457$	−21.4174	−1.00187	−0.500933	+	0.865486i	$0.667010\pi$
$458$	2.02791	0.0947579
$459$	8.74083	0.407987
$460$	−19.6101	−0.914324
$461$	17.8074	0.829372	0.414686	−	0.909965i	$-0.363891\pi$
$461$	17.8074	0.829372	0.414686	+	0.909965i	$0.363891\pi$
$462$	−0.434624	−0.0202205
$463$	−4.80271	−0.223201	−0.111600	−	0.993753i	$-0.535598\pi$
$463$	−4.80271	−0.223201	−0.111600	+	0.993753i	$0.535598\pi$
$464$	−1.93579	−0.0898668
$465$	67.3532	3.12343
$466$	12.7408	0.590207
$467$	−2.80737	−0.129910	−0.0649548	−	0.997888i	$-0.520690\pi$
$467$	−2.80737	−0.129910	−0.0649548	+	0.997888i	$0.520690\pi$
$468$	0	0
$469$	−0.691466	−0.0319289
$470$	38.2118	1.76258
$471$	−11.9502	−0.550638
$472$	−6.41744	−0.295387
$473$	7.20336	0.331211
$474$	37.9163	1.74155
$475$	31.0191	1.42325
$476$	0.730100	0.0334641
$477$	5.02791	0.230212
$478$	4.07261	0.186277
$479$	−11.8329	−0.540661	−0.270331	−	0.962768i	$-0.587133\pi$
$479$	−11.8329	−0.540661	−0.270331	+	0.962768i	$0.587133\pi$
$480$	49.0252	2.23768
$481$	0	0
$482$	−18.9828	−0.864644
$483$	2.26150	0.102902
$484$	−1.00000	−0.0454545
$485$	13.4370	0.610141
$486$	21.8776	0.992390
$487$	16.4174	0.743945	0.371973	−	0.928244i	$-0.378682\pi$
$487$	16.4174	0.743945	0.371973	+	0.928244i	$0.378682\pi$
$488$	−14.4151	−0.652541
$489$	−29.5096	−1.33447
$490$	−26.2760	−1.18703
$491$	7.83294	0.353496	0.176748	−	0.984256i	$-0.443442\pi$
$491$	7.83294	0.353496	0.176748	+	0.984256i	$0.443442\pi$
$492$	−3.29781	−0.148677
$493$	8.46020	0.381028
$494$	0	0
$495$	14.2034	0.638393
$496$	6.86925	0.308438
$497$	1.00233	0.0449607
$498$	−27.5096	−1.23273
$499$	−12.2722	−0.549381	−0.274690	−	0.961533i	$-0.588575\pi$
$499$	−12.2722	−0.549381	−0.274690	+	0.961533i	$0.588575\pi$
$500$	15.8413	0.708446
$501$	−44.9465	−2.00806
$502$	−10.3402	−0.461505
$503$	1.10891	0.0494438	0.0247219	−	0.999694i	$-0.492130\pi$
$503$	1.10891	0.0494438	0.0247219	+	0.999694i	$0.492130\pi$
$504$	−1.88876	−0.0841320
$505$	45.3616	2.01857
$506$	−5.20336	−0.231317
$507$	0	0
$508$	1.33178	0.0590882
$509$	23.8692	1.05799	0.528993	−	0.848626i	$-0.322570\pi$
$509$	23.8692	1.05799	0.528993	+	0.848626i	$0.322570\pi$
$510$	42.8521	1.89752
$511$	2.37920	0.105250
$512$	11.0000	0.486136
$513$	6.74083	0.297615
$514$	−24.1755	−1.06633
$515$	24.1452	1.06397
$516$	18.7408	0.825019
$517$	−10.1391	−0.445919
$518$	−1.44302	−0.0634026
$519$	−33.4090	−1.46649
$520$	0	0
$521$	18.3318	0.803130	0.401565	−	0.915831i	$-0.368466\pi$
$521$	18.3318	0.803130	0.401565	+	0.915831i	$0.368466\pi$
$522$	−7.29548	−0.319314
$523$	−10.4407	−0.456539	−0.228270	−	0.973598i	$-0.573307\pi$
$523$	−10.4407	−0.456539	−0.228270	+	0.973598i	$0.573307\pi$
$524$	−13.7045	−0.598685
$525$	−4.00000	−0.174574
$526$	10.7408	0.468322
$527$	−30.0215	−1.30776
$528$	2.60168	0.113224
$529$	4.07494	0.177171
$530$	5.02791	0.218398
$531$	−8.06188	−0.349856
$532$	0.563045	0.0244111
$533$	0	0
$534$	37.2201	1.61067
$535$	51.6487	2.23297
$536$	12.4174	0.536352
$537$	−12.8413	−0.554145
$538$	−17.6659	−0.761631
$539$	6.97209	0.300309
$540$	7.53747	0.324361
$541$	11.0554	0.475310	0.237655	−	0.971350i	$-0.423621\pi$
$541$	11.0554	0.475310	0.237655	+	0.971350i	$0.423621\pi$
$542$	8.74083	0.375451
$543$	1.65983	0.0712299
$544$	−21.8521	−0.936900
$545$	−33.3207	−1.42730
$546$	0	0
$547$	25.3532	1.08403	0.542013	−	0.840370i	$-0.317662\pi$
$547$	25.3532	1.08403	0.542013	+	0.840370i	$0.317662\pi$
$548$	−13.6403	−0.582685
$549$	−18.1089	−0.772869
$550$	9.20336	0.392433
$551$	6.52441	0.277949
$552$	−40.6124	−1.72858
$553$	2.43462	0.103531
$554$	−29.2118	−1.24109
$555$	84.6957	3.59513
$556$	−0.869248	−0.0368643
$557$	−20.3425	−0.861940	−0.430970	−	0.902366i	$-0.641828\pi$
$557$	−20.3425	−0.861940	−0.430970	+	0.902366i	$0.641828\pi$
$558$	25.8884	1.09594
$559$	0	0
$560$	−0.629587	−0.0266049
$561$	−11.3704	−0.480059
$562$	−10.8050	−0.455783
$563$	−6.77480	−0.285524	−0.142762	−	0.989757i	$-0.545598\pi$
$563$	−6.77480	−0.285524	−0.142762	+	0.989757i	$0.545598\pi$
$564$	−26.3788	−1.11075
$565$	−17.2057	−0.723849
$566$	−10.2397	−0.430405
$567$	1.01951	0.0428155
$568$	−18.0000	−0.755263
$569$	16.8739	0.707391	0.353696	−	0.935361i	$-0.384925\pi$
$569$	16.8739	0.707391	0.353696	+	0.935361i	$0.384925\pi$
$570$	33.0470	1.38419
$571$	44.9973	1.88308	0.941539	−	0.336905i	$-0.109380\pi$
$571$	44.9973	1.88308	0.941539	+	0.336905i	$0.109380\pi$
$572$	0	0
$573$	68.0057	2.84098
$574$	0.211754	0.00883844
$575$	−47.8884	−1.99708
$576$	26.3811	1.09921
$577$	19.5119	0.812291	0.406145	−	0.913808i	$-0.366873\pi$
$577$	19.5119	0.812291	0.406145	+	0.913808i	$0.366873\pi$
$578$	−2.10051	−0.0873698
$579$	28.9805	1.20439
$580$	7.29548	0.302928
$581$	−1.76640	−0.0732828
$582$	9.27596	0.384501
$583$	−1.33411	−0.0552532
$584$	−42.7260	−1.76801
$585$	0	0
$586$	3.96370	0.163739
$587$	−16.6789	−0.688414	−0.344207	−	0.938894i	$-0.611852\pi$
$587$	−16.6789	−0.688414	−0.344207	+	0.938894i	$0.611852\pi$
$588$	18.1391	0.748046
$589$	−23.1522	−0.953970
$590$	−8.06188	−0.331902
$591$	−40.4235	−1.66280
$592$	8.63798	0.355019
$593$	29.4128	1.20784	0.603919	−	0.797046i	$-0.293605\pi$
$593$	29.4128	1.20784	0.603919	+	0.797046i	$0.293605\pi$
$594$	2.00000	0.0820610
$595$	2.75155	0.112803
$596$	1.16706	0.0478044
$597$	−30.3788	−1.24332
$598$	0	0
$599$	6.12842	0.250400	0.125200	−	0.992131i	$-0.460043\pi$
$599$	6.12842	0.250400	0.125200	+	0.992131i	$0.460043\pi$
$600$	71.8326	2.93255
$601$	25.0061	1.02002	0.510009	−	0.860169i	$-0.329642\pi$
$601$	25.0061	1.02002	0.510009	+	0.860169i	$0.329642\pi$
$602$	−1.20336	−0.0490452
$603$	15.5993	0.635255
$604$	−10.7408	−0.437038
$605$	−3.76873	−0.153221
$606$	31.3146	1.27207
$607$	32.4407	1.31673	0.658363	−	0.752700i	$-0.271249\pi$
$607$	32.4407	1.31673	0.658363	+	0.752700i	$0.271249\pi$
$608$	−16.8521	−0.683442
$609$	−0.841340	−0.0340928
$610$	−18.1089	−0.733208
$611$	0	0
$612$	−16.4709	−0.665798
$613$	16.5714	0.669314	0.334657	−	0.942340i	$-0.391380\pi$
$613$	16.5714	0.669314	0.334657	+	0.942340i	$0.391380\pi$
$614$	14.2397	0.574666
$615$	−12.4286	−0.501168
$616$	0.501166	0.0201925
$617$	17.8692	0.719389	0.359694	−	0.933070i	$-0.382881\pi$
$617$	17.8692	0.719389	0.359694	+	0.933070i	$0.382881\pi$
$618$	16.6682	0.670494
$619$	27.4151	1.10191	0.550953	−	0.834536i	$-0.314264\pi$
$619$	27.4151	1.10191	0.550953	+	0.834536i	$0.314264\pi$
$620$	−25.8884	−1.03970
$621$	−10.4067	−0.417607
$622$	−11.8776	−0.476250
$623$	2.38993	0.0957503
$624$	0	0
$625$	13.6850	0.547400
$626$	−7.89949	−0.315727
$627$	−8.76873	−0.350190
$628$	4.59328	0.183292
$629$	−37.7516	−1.50525
$630$	−2.37274	−0.0945324
$631$	−6.54586	−0.260587	−0.130293	−	0.991475i	$-0.541592\pi$
$631$	−6.54586	−0.260587	−0.130293	+	0.991475i	$0.541592\pi$
$632$	−43.7213	−1.73914
$633$	−11.8995	−0.472962
$634$	27.3230	1.08513
$635$	5.01912	0.199178
$636$	−3.47093	−0.137631
$637$	0	0
$638$	1.93579	0.0766386
$639$	−22.6124	−0.894533
$640$	−11.3062	−0.446917
$641$	2.07494	0.0819551	0.0409775	−	0.999160i	$-0.486953\pi$
$641$	2.07494	0.0819551	0.0409775	+	0.999160i	$0.486953\pi$
$642$	35.6548	1.40718
$643$	12.2676	0.483786	0.241893	−	0.970303i	$-0.422232\pi$
$643$	12.2676	0.483786	0.241893	+	0.970303i	$0.422232\pi$
$644$	−0.869248	−0.0342532
$645$	70.6292	2.78102
$646$	−14.7301	−0.579548
$647$	47.0871	1.85118	0.925592	−	0.378523i	$-0.123568\pi$
$647$	47.0871	1.85118	0.925592	+	0.378523i	$0.123568\pi$
$648$	−18.3085	−0.719227
$649$	2.13915	0.0839689
$650$	0	0
$651$	2.98554	0.117013
$652$	11.3425	0.444207
$653$	−21.1028	−0.825818	−0.412909	−	0.910772i	$-0.635487\pi$
$653$	−21.1028	−0.825818	−0.412909	+	0.910772i	$0.635487\pi$
$654$	−23.0023	−0.899462
$655$	−51.6487	−2.01808
$656$	−1.26757	−0.0494902
$657$	−53.6743	−2.09403
$658$	1.69380	0.0660311
$659$	−18.3895	−0.716355	−0.358177	−	0.933654i	$-0.616602\pi$
$659$	−18.3895	−0.716355	−0.358177	+	0.933654i	$0.616602\pi$
$660$	−9.80504	−0.381661
$661$	−16.6938	−0.649313	−0.324657	−	0.945832i	$-0.605249\pi$
$661$	−16.6938	−0.649313	−0.324657	+	0.945832i	$0.605249\pi$
$662$	4.74083	0.184257
$663$	0	0
$664$	31.7213	1.23103
$665$	2.12197	0.0822864
$666$	32.5543	1.26145
$667$	−10.0726	−0.390013
$668$	17.2760	0.668427
$669$	23.5822	0.911739
$670$	15.5993	0.602655
$671$	4.80504	0.185496
$672$	2.17312	0.0838299
$673$	29.6185	1.14171	0.570854	−	0.821052i	$-0.306612\pi$
$673$	29.6185	1.14171	0.570854	+	0.821052i	$0.306612\pi$
$674$	32.4430	1.24966
$675$	18.4067	0.708475
$676$	0	0
$677$	−22.6124	−0.869065	−0.434533	−	0.900656i	$-0.643086\pi$
$677$	−22.6124	−0.869065	−0.434533	+	0.900656i	$0.643086\pi$
$678$	−11.8776	−0.456158
$679$	0.595615	0.0228576
$680$	−49.4128	−1.89489
$681$	34.3509	1.31633
$682$	−6.86925	−0.263037
$683$	−33.1429	−1.26818	−0.634089	−	0.773260i	$-0.718625\pi$
$683$	−33.1429	−1.26818	−0.634089	+	0.773260i	$0.718625\pi$
$684$	−12.7022	−0.485680
$685$	−51.4067	−1.96415
$686$	−2.33411	−0.0891167
$687$	−5.27596	−0.201291
$688$	7.20336	0.274625
$689$	0	0
$690$	−51.0191	−1.94226
$691$	−16.2057	−0.616493	−0.308247	−	0.951306i	$-0.599742\pi$
$691$	−16.2057	−0.616493	−0.308247	+	0.951306i	$0.599742\pi$
$692$	12.8413	0.488155
$693$	0.629587	0.0239160
$694$	11.8329	0.449172
$695$	−3.27596	−0.124264
$696$	15.1089	0.572702
$697$	5.53980	0.209835
$698$	30.0000	1.13552
$699$	−33.1475	−1.25376
$700$	1.53747	0.0581109
$701$	16.7855	0.633981	0.316990	−	0.948429i	$-0.397328\pi$
$701$	16.7855	0.633981	0.316990	+	0.948429i	$0.397328\pi$
$702$	0	0
$703$	−29.1136	−1.09804
$704$	−7.00000	−0.263822
$705$	−99.4147	−3.74418
$706$	−10.2034	−0.384008
$707$	2.01073	0.0756212
$708$	5.56538	0.209160
$709$	−27.6292	−1.03764	−0.518818	−	0.854885i	$-0.673628\pi$
$709$	−27.6292	−1.03764	−0.518818	+	0.854885i	$0.673628\pi$
$710$	−22.6124	−0.848628
$711$	−54.9247	−2.05984
$712$	−42.9186	−1.60844
$713$	35.7432	1.33859
$714$	1.89949	0.0710865
$715$	0	0
$716$	4.93579	0.184459
$717$	−10.5956	−0.395700
$718$	−13.5375	−0.505214
$719$	9.40905	0.350898	0.175449	−	0.984488i	$-0.443862\pi$
$719$	9.40905	0.350898	0.175449	+	0.984488i	$0.443862\pi$
$720$	14.2034	0.529328
$721$	1.07028	0.0398591
$722$	7.64031	0.284343
$723$	49.3872	1.83673
$724$	−0.637982	−0.0237104
$725$	17.8158	0.661661
$726$	−2.60168	−0.0965574
$727$	20.6682	0.766542	0.383271	−	0.923636i	$-0.374798\pi$
$727$	20.6682	0.766542	0.383271	+	0.923636i	$0.374798\pi$
$728$	0	0
$729$	−38.6101	−1.43000
$730$	−53.6743	−1.98657
$731$	−31.4817	−1.16439
$732$	12.5012	0.462056
$733$	−26.1368	−0.965385	−0.482693	−	0.875790i	$-0.660341\pi$
$733$	−26.1368	−0.965385	−0.482693	+	0.875790i	$0.660341\pi$
$734$	11.1475	0.411463
$735$	68.3616	2.52156
$736$	26.0168	0.958992
$737$	−4.13915	−0.152467
$738$	−4.77713	−0.175849
$739$	16.4793	0.606202	0.303101	−	0.952958i	$-0.401978\pi$
$739$	16.4793	0.606202	0.303101	+	0.952958i	$0.401978\pi$
$740$	−32.5543	−1.19672
$741$	0	0
$742$	0.222870	0.00818182
$743$	−29.6440	−1.08753	−0.543767	−	0.839236i	$-0.683003\pi$
$743$	−29.6440	−1.08753	−0.543767	+	0.839236i	$0.683003\pi$
$744$	−53.6147	−1.96561
$745$	4.39832	0.161142
$746$	27.3123	0.999973
$747$	39.8497	1.45803
$748$	4.37041	0.159798
$749$	2.28941	0.0836533
$750$	41.2141	1.50493
$751$	25.3486	0.924982	0.462491	−	0.886624i	$-0.346956\pi$
$751$	25.3486	0.924982	0.462491	+	0.886624i	$0.346956\pi$
$752$	−10.1391	−0.369737
$753$	26.9018	0.980357
$754$	0	0
$755$	−40.4793	−1.47319
$756$	0.334110	0.0121515
$757$	31.7320	1.15332	0.576660	−	0.816984i	$-0.304356\pi$
$757$	31.7320	1.15332	0.576660	+	0.816984i	$0.304356\pi$
$758$	18.4067	0.668562
$759$	13.5375	0.491379
$760$	−38.1066	−1.38227
$761$	43.8837	1.59078	0.795392	−	0.606096i	$-0.207265\pi$
$761$	43.8837	1.59078	0.795392	+	0.606096i	$0.207265\pi$
$762$	3.46486	0.125519
$763$	−1.47699	−0.0534707
$764$	−26.1391	−0.945681
$765$	−62.0745	−2.24431
$766$	−25.8716	−0.934778
$767$	0	0
$768$	−44.2285	−1.59596
$769$	15.6147	0.563082	0.281541	−	0.959549i	$-0.409154\pi$
$769$	15.6147	0.563082	0.281541	+	0.959549i	$0.409154\pi$
$770$	0.629587	0.0226887
$771$	62.8968	2.26517
$772$	−11.1391	−0.400907
$773$	22.2504	0.800291	0.400145	−	0.916452i	$-0.368960\pi$
$773$	22.2504	0.800291	0.400145	+	0.916452i	$0.368960\pi$
$774$	27.1475	0.975798
$775$	−63.2201	−2.27093
$776$	−10.6961	−0.383969
$777$	3.75427	0.134684
$778$	−20.7153	−0.742678
$779$	4.27223	0.153069
$780$	0	0
$781$	6.00000	0.214697
$782$	22.7408	0.813210
$783$	3.87158	0.138359
$784$	6.97209	0.249003
$785$	17.3109	0.617851
$786$	−35.6548	−1.27176
$787$	−53.9828	−1.92428	−0.962140	−	0.272556i	$-0.912131\pi$
$787$	−53.9828	−1.92428	−0.962140	+	0.272556i	$0.912131\pi$
$788$	15.5375	0.553499
$789$	−27.9442	−0.994839
$790$	−54.9247	−1.95413
$791$	−0.762670	−0.0271174
$792$	−11.3062	−0.401748
$793$	0	0
$794$	−21.5822	−0.765922
$795$	−13.0810	−0.463935
$796$	11.6766	0.413867
$797$	−32.9912	−1.16861	−0.584304	−	0.811535i	$-0.698633\pi$
$797$	−32.9912	−1.16861	−0.584304	+	0.811535i	$0.698633\pi$
$798$	1.46486	0.0518556
$799$	44.3123	1.56766
$800$	−46.0168	−1.62694
$801$	−53.9163	−1.90504
$802$	0.203358	0.00718083
$803$	14.2420	0.502589
$804$	−10.7687	−0.379784
$805$	−3.27596	−0.115463
$806$	0	0
$807$	45.9610	1.61790
$808$	−36.1089	−1.27031
$809$	−32.7771	−1.15238	−0.576191	−	0.817315i	$-0.695462\pi$
$809$	−32.7771	−1.15238	−0.576191	+	0.817315i	$0.695462\pi$
$810$	−23.0000	−0.808138
$811$	−4.94185	−0.173532	−0.0867660	−	0.996229i	$-0.527653\pi$
$811$	−4.94185	−0.173532	−0.0867660	+	0.996229i	$0.527653\pi$
$812$	0.323384	0.0113485
$813$	−22.7408	−0.797556
$814$	−8.63798	−0.302761
$815$	42.7469	1.49736
$816$	−11.3704	−0.398044
$817$	−24.2783	−0.849390
$818$	0.0921180	0.00322083
$819$	0	0
$820$	4.77713	0.166825
$821$	19.8158	0.691575	0.345787	−	0.938313i	$-0.387612\pi$
$821$	19.8158	0.691575	0.345787	+	0.938313i	$0.387612\pi$
$822$	−35.4877	−1.23778
$823$	28.1499	0.981243	0.490621	−	0.871373i	$-0.336770\pi$
$823$	28.1499	0.981243	0.490621	+	0.871373i	$0.336770\pi$
$824$	−19.2201	−0.669566
$825$	−23.9442	−0.833630
$826$	−0.357356	−0.0124340
$827$	−33.0578	−1.14953	−0.574765	−	0.818318i	$-0.694907\pi$
$827$	−33.0578	−1.14953	−0.574765	+	0.818318i	$0.694907\pi$
$828$	19.6101	0.681497
$829$	−14.9721	−0.520002	−0.260001	−	0.965608i	$-0.583723\pi$
$829$	−14.9721	−0.520002	−0.260001	+	0.965608i	$0.583723\pi$
$830$	39.8497	1.38320
$831$	75.9996	2.63640
$832$	0	0
$833$	−30.4709	−1.05576
$834$	−2.26150	−0.0783095
$835$	65.1085	2.25317
$836$	3.37041	0.116568
$837$	−13.7385	−0.474872
$838$	−10.1284	−0.349880
$839$	13.0131	0.449261	0.224630	−	0.974444i	$-0.427883\pi$
$839$	13.0131	0.449261	0.224630	+	0.974444i	$0.427883\pi$
$840$	4.91395	0.169547
$841$	−25.2527	−0.870783
$842$	−6.58217	−0.226836
$843$	28.1112	0.968203
$844$	4.57377	0.157436
$845$	0	0
$846$	−38.2118	−1.31375
$847$	−0.167055	−0.00574008
$848$	−1.33411	−0.0458135
$849$	26.6403	0.914293
$850$	−40.2225	−1.37962
$851$	44.9465	1.54075
$852$	15.6101	0.534792
$853$	−25.3448	−0.867791	−0.433895	−	0.900963i	$-0.642861\pi$
$853$	−25.3448	−0.867791	−0.433895	+	0.900963i	$0.642861\pi$
$854$	−0.802706	−0.0274680
$855$	−47.8712	−1.63716
$856$	−41.1136	−1.40523
$857$	49.5627	1.69303	0.846514	−	0.532366i	$-0.178697\pi$
$857$	49.5627	1.69303	0.846514	+	0.532366i	$0.178697\pi$
$858$	0	0
$859$	−55.6208	−1.89776	−0.948879	−	0.315641i	$-0.897780\pi$
$859$	−55.6208	−1.89776	−0.948879	+	0.315641i	$0.897780\pi$
$860$	−27.1475	−0.925724
$861$	−0.550916	−0.0187752
$862$	17.4988	0.596013
$863$	−10.6124	−0.361250	−0.180625	−	0.983552i	$-0.557812\pi$
$863$	−10.6124	−0.361250	−0.180625	+	0.983552i	$0.557812\pi$
$864$	−10.0000	−0.340207
$865$	48.3956	1.64550
$866$	8.69380	0.295427
$867$	5.46486	0.185596
$868$	−1.14754	−0.0389502
$869$	14.5738	0.494381
$870$	18.9805	0.643499
$871$	0	0
$872$	26.5240	0.898217
$873$	−13.4370	−0.454772
$874$	17.5375	0.593214
$875$	2.64638	0.0894639
$876$	37.0531	1.25191
$877$	−53.8474	−1.81830	−0.909149	−	0.416471i	$-0.863267\pi$
$877$	−53.8474	−1.81830	−0.909149	+	0.416471i	$0.863267\pi$
$878$	24.5738	0.829325
$879$	−10.3123	−0.347824
$880$	−3.76873	−0.127044
$881$	−1.20103	−0.0404636	−0.0202318	−	0.999795i	$-0.506440\pi$
$881$	−1.20103	−0.0404636	−0.0202318	+	0.999795i	$0.506440\pi$
$882$	26.2760	0.884758
$883$	58.4793	1.96799	0.983993	−	0.178207i	$-0.0570298\pi$
$883$	58.4793	1.96799	0.983993	+	0.178207i	$0.0570298\pi$
$884$	0	0
$885$	20.9744	0.705048
$886$	17.2699	0.580194
$887$	−27.3364	−0.917868	−0.458934	−	0.888470i	$-0.651769\pi$
$887$	−27.3364	−0.917868	−0.458934	+	0.888470i	$0.651769\pi$
$888$	−67.4198	−2.26246
$889$	0.222481	0.00746176
$890$	−53.9163	−1.80728
$891$	6.10284	0.204453
$892$	−9.06421	−0.303492
$893$	34.1731	1.14356
$894$	3.03630	0.101549
$895$	18.6017	0.621786
$896$	−0.501166	−0.0167428
$897$	0	0
$898$	16.3230	0.544705
$899$	−13.2974	−0.443494
$900$	−34.6850	−1.15617
$901$	5.83061	0.194246
$902$	1.26757	0.0422054
$903$	3.13075	0.104185
$904$	13.6961	0.455526
$905$	−2.40439	−0.0799245
$906$	−27.9442	−0.928383
$907$	−17.6598	−0.586385	−0.293192	−	0.956053i	$-0.594718\pi$
$907$	−17.6598	−0.586385	−0.293192	+	0.956053i	$0.594718\pi$
$908$	−13.2034	−0.438169
$909$	−45.3616	−1.50455
$910$	0	0
$911$	−20.8074	−0.689379	−0.344689	−	0.938717i	$-0.612016\pi$
$911$	−20.8074	−0.689379	−0.344689	+	0.938717i	$0.612016\pi$
$912$	−8.76873	−0.290362
$913$	−10.5738	−0.349941
$914$	21.4174	0.708426
$915$	47.1136	1.55753
$916$	2.02791	0.0670039
$917$	−2.28941	−0.0756030
$918$	−8.74083	−0.288490
$919$	57.3700	1.89246	0.946231	−	0.323491i	$-0.104857\pi$
$919$	57.3700	1.89246	0.946231	+	0.323491i	$0.104857\pi$
$920$	58.8302	1.93958
$921$	−37.0470	−1.22074
$922$	−17.8074	−0.586454
$923$	0	0
$924$	−0.434624	−0.0142981
$925$	−79.4984	−2.61389
$926$	4.80271	0.157827
$927$	−24.1452	−0.793033
$928$	−9.67895	−0.317727
$929$	−47.1452	−1.54678	−0.773392	−	0.633928i	$-0.781442\pi$
$929$	−47.1452	−1.54678	−0.773392	+	0.633928i	$0.781442\pi$
$930$	−67.3532	−2.20860
$931$	−23.4988	−0.770143
$932$	12.7408	0.417340
$933$	30.9018	1.01168
$934$	2.80737	0.0918599
$935$	16.4709	0.538657
$936$	0	0
$937$	24.2820	0.793259	0.396630	−	0.917979i	$-0.370180\pi$
$937$	24.2820	0.793259	0.396630	+	0.917979i	$0.370180\pi$
$938$	0.691466	0.0225772
$939$	20.5519	0.670687
$940$	38.2118	1.24633
$941$	−12.7408	−0.415339	−0.207670	−	0.978199i	$-0.566588\pi$
$941$	−12.7408	−0.415339	−0.207670	+	0.978199i	$0.566588\pi$
$942$	11.9502	0.389360
$943$	−6.59561	−0.214783
$944$	2.13915	0.0696233
$945$	1.25917	0.0409609
$946$	−7.20336	−0.234201
$947$	11.0749	0.359887	0.179944	−	0.983677i	$-0.442408\pi$
$947$	11.0749	0.359887	0.179944	+	0.983677i	$0.442408\pi$
$948$	37.9163	1.23146
$949$	0	0
$950$	−31.0191	−1.00639
$951$	−71.0857	−2.30511
$952$	−2.19030	−0.0709880
$953$	50.3677	1.63157	0.815785	−	0.578356i	$-0.196305\pi$
$953$	50.3677	1.63157	0.815785	+	0.578356i	$0.196305\pi$
$954$	−5.02791	−0.162785
$955$	−98.5115	−3.18776
$956$	4.07261	0.131717
$957$	−5.03630	−0.162801
$958$	11.8329	0.382305
$959$	−2.27868	−0.0735826
$960$	−68.6353	−2.21519
$961$	16.1866	0.522147
$962$	0	0
$963$	−51.6487	−1.66436
$964$	−18.9828	−0.611395
$965$	−41.9805	−1.35140
$966$	−2.26150	−0.0727627
$967$	−47.7213	−1.53461	−0.767307	−	0.641280i	$-0.778404\pi$
$967$	−47.7213	−1.53461	−0.767307	+	0.641280i	$0.778404\pi$
$968$	3.00000	0.0964237
$969$	38.3230	1.23111
$970$	−13.4370	−0.431435
$971$	−30.7469	−0.986715	−0.493357	−	0.869827i	$-0.664231\pi$
$971$	−30.7469	−0.986715	−0.493357	+	0.869827i	$0.664231\pi$
$972$	21.8776	0.701726
$973$	−0.145212	−0.00465529
$974$	−16.4174	−0.526049
$975$	0	0
$976$	4.80504	0.153805
$977$	22.6426	0.724402	0.362201	−	0.932100i	$-0.382025\pi$
$977$	22.6426	0.724402	0.362201	+	0.932100i	$0.382025\pi$
$978$	29.5096	0.943612
$979$	14.3062	0.457228
$980$	−26.2760	−0.839355
$981$	33.3207	1.06385
$982$	−7.83294	−0.249959
$983$	−2.40672	−0.0767623	−0.0383812	−	0.999263i	$-0.512220\pi$
$983$	−2.40672	−0.0767623	−0.0383812	+	0.999263i	$0.512220\pi$
$984$	9.89342	0.315391
$985$	58.5566	1.86577
$986$	−8.46020	−0.269428
$987$	−4.40672	−0.140267
$988$	0	0
$989$	37.4817	1.19185
$990$	−14.2034	−0.451412
$991$	13.2094	0.419611	0.209806	−	0.977743i	$-0.432717\pi$
$991$	13.2094	0.419611	0.209806	+	0.977743i	$0.432717\pi$
$992$	34.3462	1.09049
$993$	−12.3341	−0.391411
$994$	−1.00233	−0.0317920
$995$	44.0061	1.39509
$996$	−27.5096	−0.871674
$997$	17.2565	0.546517	0.273259	−	0.961941i	$-0.411899\pi$
$997$	17.2565	0.546517	0.273259	+	0.961941i	$0.411899\pi$
$998$	12.2722	0.388471
$999$	−17.2760	−0.546587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.e.1.3		3
13.4	even	6		143.2.e.a.133.1	yes	6
13.10	even	6		143.2.e.a.100.1	✓	6
13.12	even	2		1859.2.a.h.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.a.100.1	✓	6	13.10	even	6
143.2.e.a.133.1	yes	6	13.4	even	6
1859.2.a.e.1.3		3	1.1	even	1	trivial
1859.2.a.h.1.3		3	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.60168 q^{3} -1.00000 q^{4} -3.76873 q^{5} -2.60168 q^{6} -0.167055 q^{7} +3.00000 q^{8} +3.76873 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.60168 q^{3} -1.00000 q^{4} -3.76873 q^{5} -2.60168 q^{6} -0.167055 q^{7} +3.00000 q^{8} +3.76873 q^{9} +3.76873 q^{10} -1.00000 q^{11} -2.60168 q^{12} +0.167055 q^{14} -9.80504 q^{15} -1.00000 q^{16} +4.37041 q^{17} -3.76873 q^{18} +3.37041 q^{19} +3.76873 q^{20} -0.434624 q^{21} +1.00000 q^{22} -5.20336 q^{23} +7.80504 q^{24} +9.20336 q^{25} +2.00000 q^{27} +0.167055 q^{28} +1.93579 q^{29} +9.80504 q^{30} -6.86925 q^{31} -5.00000 q^{32} -2.60168 q^{33} -4.37041 q^{34} +0.629587 q^{35} -3.76873 q^{36} -8.63798 q^{37} -3.37041 q^{38} -11.3062 q^{40} +1.26757 q^{41} +0.434624 q^{42} -7.20336 q^{43} +1.00000 q^{44} -14.2034 q^{45} +5.20336 q^{46} +10.1391 q^{47} -2.60168 q^{48} -6.97209 q^{49} -9.20336 q^{50} +11.3704 q^{51} +1.33411 q^{53} -2.00000 q^{54} +3.76873 q^{55} -0.501166 q^{56} +8.76873 q^{57} -1.93579 q^{58} -2.13915 q^{59} +9.80504 q^{60} -4.80504 q^{61} +6.86925 q^{62} -0.629587 q^{63} +7.00000 q^{64} +2.60168 q^{66} +4.13915 q^{67} -4.37041 q^{68} -13.5375 q^{69} -0.629587 q^{70} -6.00000 q^{71} +11.3062 q^{72} -14.2420 q^{73} +8.63798 q^{74} +23.9442 q^{75} -3.37041 q^{76} +0.167055 q^{77} -14.5738 q^{79} +3.76873 q^{80} -6.10284 q^{81} -1.26757 q^{82} +10.5738 q^{83} +0.434624 q^{84} -16.4709 q^{85} +7.20336 q^{86} +5.03630 q^{87} -3.00000 q^{88} -14.3062 q^{89} +14.2034 q^{90} +5.20336 q^{92} -17.8716 q^{93} -10.1391 q^{94} -12.7022 q^{95} -13.0084 q^{96} -3.56538 q^{97} +6.97209 q^{98} -3.76873 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{4} - 3 q^{5} + 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 + 9 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{4} - 3 q^{5} + 9 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{11} - 6 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 6 q^{19} + 3 q^{20} + 6 q^{21} + 3 q^{22} + 12 q^{25} + 6 q^{27} - 3 q^{29} + 6 q^{30} - 6 q^{31} - 15 q^{32} + 3 q^{34} + 18 q^{35} - 3 q^{36} - 3 q^{37} + 6 q^{38} - 9 q^{40} - 3 q^{41} - 6 q^{42} - 6 q^{43} + 3 q^{44} - 27 q^{45} + 6 q^{47} + 3 q^{49} - 12 q^{50} + 18 q^{51} + 3 q^{53} - 6 q^{54} + 3 q^{55} + 18 q^{57} + 3 q^{58} + 18 q^{59} + 6 q^{60} + 9 q^{61} + 6 q^{62} - 18 q^{63} + 21 q^{64} - 12 q^{67} + 3 q^{68} - 24 q^{69} - 18 q^{70} - 18 q^{71} + 9 q^{72} - 9 q^{73} + 3 q^{74} + 24 q^{75} + 6 q^{76} - 12 q^{79} + 3 q^{80} - 9 q^{81} + 3 q^{82} - 6 q^{84} - 27 q^{85} + 6 q^{86} - 9 q^{88} - 18 q^{89} + 27 q^{90} - 36 q^{93} - 6 q^{94} - 24 q^{95} - 18 q^{97} - 3 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 + 9 * q^8 + 3 * q^9 + 3 * q^10 - 3 * q^11 - 6 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 6 * q^19 + 3 * q^20 + 6 * q^21 + 3 * q^22 + 12 * q^25 + 6 * q^27 - 3 * q^29 + 6 * q^30 - 6 * q^31 - 15 * q^32 + 3 * q^34 + 18 * q^35 - 3 * q^36 - 3 * q^37 + 6 * q^38 - 9 * q^40 - 3 * q^41 - 6 * q^42 - 6 * q^43 + 3 * q^44 - 27 * q^45 + 6 * q^47 + 3 * q^49 - 12 * q^50 + 18 * q^51 + 3 * q^53 - 6 * q^54 + 3 * q^55 + 18 * q^57 + 3 * q^58 + 18 * q^59 + 6 * q^60 + 9 * q^61 + 6 * q^62 - 18 * q^63 + 21 * q^64 - 12 * q^67 + 3 * q^68 - 24 * q^69 - 18 * q^70 - 18 * q^71 + 9 * q^72 - 9 * q^73 + 3 * q^74 + 24 * q^75 + 6 * q^76 - 12 * q^79 + 3 * q^80 - 9 * q^81 + 3 * q^82 - 6 * q^84 - 27 * q^85 + 6 * q^86 - 9 * q^88 - 18 * q^89 + 27 * q^90 - 36 * q^93 - 6 * q^94 - 24 * q^95 - 18 * q^97 - 3 * q^98 - 3 * q^99

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