LMFDB - Embedded newform 2842.2.a.t.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, 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("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.974241.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 9x^{3} - 2x^{2} + 11x + 3 $ x^5 - x^4 - 9x^3 - 2x^2 + 11*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.76647$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.42629 q^{3} +1.00000 q^{4} -0.260736 q^{5} -2.42629 q^{6} -1.00000 q^{8} +2.88687 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.42629 q^{3} +1.00000 q^{4} -0.260736 q^{5} -2.42629 q^{6} -1.00000 q^{8} +2.88687 q^{9} +0.260736 q^{10} +2.14760 q^{11} +2.42629 q^{12} -6.34036 q^{13} -0.632619 q^{15} +1.00000 q^{16} -2.22705 q^{17} -2.88687 q^{18} -8.43775 q^{19} -0.260736 q^{20} -2.14760 q^{22} +4.38533 q^{23} -2.42629 q^{24} -4.93202 q^{25} +6.34036 q^{26} -0.274492 q^{27} -1.00000 q^{29} +0.632619 q^{30} +3.04515 q^{31} -1.00000 q^{32} +5.21070 q^{33} +2.22705 q^{34} +2.88687 q^{36} -7.24517 q^{37} +8.43775 q^{38} -15.3835 q^{39} +0.260736 q^{40} -10.7302 q^{41} +0.195049 q^{43} +2.14760 q^{44} -0.752709 q^{45} -4.38533 q^{46} -12.2245 q^{47} +2.42629 q^{48} +4.93202 q^{50} -5.40345 q^{51} -6.34036 q^{52} -0.390391 q^{53} +0.274492 q^{54} -0.559957 q^{55} -20.4724 q^{57} +1.00000 q^{58} +14.7537 q^{59} -0.632619 q^{60} +9.83960 q^{61} -3.04515 q^{62} +1.00000 q^{64} +1.65316 q^{65} -5.21070 q^{66} +9.53790 q^{67} -2.22705 q^{68} +10.6401 q^{69} +2.18856 q^{71} -2.88687 q^{72} -4.18350 q^{73} +7.24517 q^{74} -11.9665 q^{75} -8.43775 q^{76} +15.3835 q^{78} -4.48597 q^{79} -0.260736 q^{80} -9.32660 q^{81} +10.7302 q^{82} -1.91389 q^{83} +0.580670 q^{85} -0.195049 q^{86} -2.42629 q^{87} -2.14760 q^{88} -11.8209 q^{89} +0.752709 q^{90} +4.38533 q^{92} +7.38841 q^{93} +12.2245 q^{94} +2.20002 q^{95} -2.42629 q^{96} +0.283480 q^{97} +6.19984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9} + q^{10} + 4 q^{11} - 3 q^{12} - 8 q^{15} + 5 q^{16} - 10 q^{17} - 8 q^{18} - 8 q^{19} - q^{20} - 4 q^{22} + 9 q^{23} + 3 q^{24} - 9 q^{27} - 5 q^{29} + 8 q^{30} - 3 q^{31} - 5 q^{32} - 7 q^{33} + 10 q^{34} + 8 q^{36} + 10 q^{37} + 8 q^{38} - 26 q^{39} + q^{40} - 19 q^{41} + 3 q^{43} + 4 q^{44} + 14 q^{45} - 9 q^{46} - 36 q^{47} - 3 q^{48} + 31 q^{51} - 3 q^{53} + 9 q^{54} - 10 q^{55} - 18 q^{57} + 5 q^{58} + 5 q^{59} - 8 q^{60} - 3 q^{61} + 3 q^{62} + 5 q^{64} + 29 q^{65} + 7 q^{66} - 2 q^{67} - 10 q^{68} + 18 q^{69} + 2 q^{71} - 8 q^{72} + 2 q^{73} - 10 q^{74} - 22 q^{75} - 8 q^{76} + 26 q^{78} + 17 q^{79} - q^{80} - 7 q^{81} + 19 q^{82} - 30 q^{83} - 11 q^{85} - 3 q^{86} + 3 q^{87} - 4 q^{88} - 29 q^{89} - 14 q^{90} + 9 q^{92} + 37 q^{93} + 36 q^{94} - 17 q^{95} + 3 q^{96} + 40 q^{99}+O(q^{100}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9 + q^10 + 4 * q^11 - 3 * q^12 - 8 * q^15 + 5 * q^16 - 10 * q^17 - 8 * q^18 - 8 * q^19 - q^20 - 4 * q^22 + 9 * q^23 + 3 * q^24 - 9 * q^27 - 5 * q^29 + 8 * q^30 - 3 * q^31 - 5 * q^32 - 7 * q^33 + 10 * q^34 + 8 * q^36 + 10 * q^37 + 8 * q^38 - 26 * q^39 + q^40 - 19 * q^41 + 3 * q^43 + 4 * q^44 + 14 * q^45 - 9 * q^46 - 36 * q^47 - 3 * q^48 + 31 * q^51 - 3 * q^53 + 9 * q^54 - 10 * q^55 - 18 * q^57 + 5 * q^58 + 5 * q^59 - 8 * q^60 - 3 * q^61 + 3 * q^62 + 5 * q^64 + 29 * q^65 + 7 * q^66 - 2 * q^67 - 10 * q^68 + 18 * q^69 + 2 * q^71 - 8 * q^72 + 2 * q^73 - 10 * q^74 - 22 * q^75 - 8 * q^76 + 26 * q^78 + 17 * q^79 - q^80 - 7 * q^81 + 19 * q^82 - 30 * q^83 - 11 * q^85 - 3 * q^86 + 3 * q^87 - 4 * q^88 - 29 * q^89 - 14 * q^90 + 9 * q^92 + 37 * q^93 + 36 * q^94 - 17 * q^95 + 3 * q^96 + 40 * 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
$2$	−1.00000	−0.707107
$3$	2.42629	1.40082	0.700409	−	0.713742i	$-0.253001\pi$
$3$	2.42629	1.40082	0.700409	+	0.713742i	$0.253001\pi$
$4$	1.00000	0.500000
$5$	−0.260736	−0.116605	−0.0583023	−	0.998299i	$-0.518569\pi$
$5$	−0.260736	−0.116605	−0.0583023	+	0.998299i	$0.518569\pi$
$6$	−2.42629	−0.990527
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	2.88687	0.962289
$10$	0.260736	0.0824519
$11$	2.14760	0.647527	0.323763	−	0.946138i	$-0.395052\pi$
$11$	2.14760	0.647527	0.323763	+	0.946138i	$0.395052\pi$
$12$	2.42629	0.700409
$13$	−6.34036	−1.75850	−0.879249	−	0.476362i	$-0.841955\pi$
$13$	−6.34036	−1.75850	−0.879249	+	0.476362i	$0.841955\pi$
$14$	0	0
$15$	−0.632619	−0.163342
$16$	1.00000	0.250000
$17$	−2.22705	−0.540138	−0.270069	−	0.962841i	$-0.587047\pi$
$17$	−2.22705	−0.540138	−0.270069	+	0.962841i	$0.587047\pi$
$18$	−2.88687	−0.680441
$19$	−8.43775	−1.93575	−0.967876	−	0.251428i	$-0.919100\pi$
$19$	−8.43775	−1.93575	−0.967876	+	0.251428i	$0.919100\pi$
$20$	−0.260736	−0.0583023
$21$	0	0
$22$	−2.14760	−0.457870
$23$	4.38533	0.914404	0.457202	−	0.889363i	$-0.348852\pi$
$23$	4.38533	0.914404	0.457202	+	0.889363i	$0.348852\pi$
$24$	−2.42629	−0.495264
$25$	−4.93202	−0.986403
$26$	6.34036	1.24345
$27$	−0.274492	−0.0528261
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.632619	0.115500
$31$	3.04515	0.546925	0.273463	−	0.961883i	$-0.411831\pi$
$31$	3.04515	0.546925	0.273463	+	0.961883i	$0.411831\pi$
$32$	−1.00000	−0.176777
$33$	5.21070	0.907067
$34$	2.22705	0.381935
$35$	0	0
$36$	2.88687	0.481145
$37$	−7.24517	−1.19110	−0.595549	−	0.803319i	$-0.703066\pi$
$37$	−7.24517	−1.19110	−0.595549	+	0.803319i	$0.703066\pi$
$38$	8.43775	1.36878
$39$	−15.3835	−2.46333
$40$	0.260736	0.0412259
$41$	−10.7302	−1.67577	−0.837887	−	0.545844i	$-0.816209\pi$
$41$	−10.7302	−1.67577	−0.837887	+	0.545844i	$0.816209\pi$
$42$	0	0
$43$	0.195049	0.0297447	0.0148723	−	0.999889i	$-0.495266\pi$
$43$	0.195049	0.0297447	0.0148723	+	0.999889i	$0.495266\pi$
$44$	2.14760	0.323763
$45$	−0.752709	−0.112207
$46$	−4.38533	−0.646581
$47$	−12.2245	−1.78312	−0.891560	−	0.452902i	$-0.850389\pi$
$47$	−12.2245	−1.78312	−0.891560	+	0.452902i	$0.850389\pi$
$48$	2.42629	0.350204
$49$	0	0
$50$	4.93202	0.697493
$51$	−5.40345	−0.756635
$52$	−6.34036	−0.879249
$53$	−0.390391	−0.0536243	−0.0268121	−	0.999640i	$-0.508536\pi$
$53$	−0.390391	−0.0536243	−0.0268121	+	0.999640i	$0.508536\pi$
$54$	0.274492	0.0373537
$55$	−0.559957	−0.0755045
$56$	0	0
$57$	−20.4724	−2.71163
$58$	1.00000	0.131306
$59$	14.7537	1.92076	0.960382	−	0.278687i	$-0.0898993\pi$
$59$	14.7537	1.92076	0.960382	+	0.278687i	$0.0898993\pi$
$60$	−0.632619	−0.0816708
$61$	9.83960	1.25983	0.629916	−	0.776664i	$-0.283089\pi$
$61$	9.83960	1.25983	0.629916	+	0.776664i	$0.283089\pi$
$62$	−3.04515	−0.386734
$63$	0	0
$64$	1.00000	0.125000
$65$	1.65316	0.205049
$66$	−5.21070	−0.641393
$67$	9.53790	1.16524	0.582620	−	0.812745i	$-0.302028\pi$
$67$	9.53790	1.16524	0.582620	+	0.812745i	$0.302028\pi$
$68$	−2.22705	−0.270069
$69$	10.6401	1.28091
$70$	0	0
$71$	2.18856	0.259734	0.129867	−	0.991531i	$-0.458545\pi$
$71$	2.18856	0.259734	0.129867	+	0.991531i	$0.458545\pi$
$72$	−2.88687	−0.340221
$73$	−4.18350	−0.489642	−0.244821	−	0.969568i	$-0.578729\pi$
$73$	−4.18350	−0.489642	−0.244821	+	0.969568i	$0.578729\pi$
$74$	7.24517	0.842234
$75$	−11.9665	−1.38177
$76$	−8.43775	−0.967876
$77$	0	0
$78$	15.3835	1.74184
$79$	−4.48597	−0.504712	−0.252356	−	0.967635i	$-0.581205\pi$
$79$	−4.48597	−0.504712	−0.252356	+	0.967635i	$0.581205\pi$
$80$	−0.260736	−0.0291511
$81$	−9.32660	−1.03629
$82$	10.7302	1.18495
$83$	−1.91389	−0.210077	−0.105038	−	0.994468i	$-0.533497\pi$
$83$	−1.91389	−0.210077	−0.105038	+	0.994468i	$0.533497\pi$
$84$	0	0
$85$	0.580670	0.0629825
$86$	−0.195049	−0.0210327
$87$	−2.42629	−0.260125
$88$	−2.14760	−0.228935
$89$	−11.8209	−1.25301	−0.626505	−	0.779418i	$-0.715515\pi$
$89$	−11.8209	−1.25301	−0.626505	+	0.779418i	$0.715515\pi$
$90$	0.752709	0.0793425
$91$	0	0
$92$	4.38533	0.457202
$93$	7.38841	0.766142
$94$	12.2245	1.26086
$95$	2.20002	0.225717
$96$	−2.42629	−0.247632
$97$	0.283480	0.0287830	0.0143915	−	0.999896i	$-0.495419\pi$
$97$	0.283480	0.0287830	0.0143915	+	0.999896i	$0.495419\pi$
$98$	0	0
$99$	6.19984	0.623108
$100$	−4.93202	−0.493202
$101$	10.9123	1.08581	0.542905	−	0.839794i	$-0.317324\pi$
$101$	10.9123	1.08581	0.542905	+	0.839794i	$0.317324\pi$
$102$	5.40345	0.535022
$103$	11.5444	1.13750	0.568751	−	0.822509i	$-0.307427\pi$
$103$	11.5444	1.13750	0.568751	+	0.822509i	$0.307427\pi$
$104$	6.34036	0.621723
$105$	0	0
$106$	0.390391	0.0379181
$107$	9.96649	0.963497	0.481748	−	0.876310i	$-0.340002\pi$
$107$	9.96649	0.963497	0.481748	+	0.876310i	$0.340002\pi$
$108$	−0.274492	−0.0264130
$109$	−9.82477	−0.941042	−0.470521	−	0.882389i	$-0.655934\pi$
$109$	−9.82477	−0.941042	−0.470521	+	0.882389i	$0.655934\pi$
$110$	0.559957	0.0533898
$111$	−17.5789	−1.66851
$112$	0	0
$113$	−1.20430	−0.113291	−0.0566456	−	0.998394i	$-0.518041\pi$
$113$	−1.20430	−0.113291	−0.0566456	+	0.998394i	$0.518041\pi$
$114$	20.4724	1.91742
$115$	−1.14341	−0.106624
$116$	−1.00000	−0.0928477
$117$	−18.3038	−1.69218
$118$	−14.7537	−1.35819
$119$	0	0
$120$	0.632619	0.0577500
$121$	−6.38780	−0.580709
$122$	−9.83960	−0.890835
$123$	−26.0345	−2.34745
$124$	3.04515	0.273463
$125$	2.58963	0.231624
$126$	0	0
$127$	4.82334	0.428002	0.214001	−	0.976833i	$-0.431350\pi$
$127$	4.82334	0.428002	0.214001	+	0.976833i	$0.431350\pi$
$128$	−1.00000	−0.0883883
$129$	0.473244	0.0416668
$130$	−1.65316	−0.144991
$131$	−14.0889	−1.23095	−0.615475	−	0.788156i	$-0.711036\pi$
$131$	−14.0889	−1.23095	−0.615475	+	0.788156i	$0.711036\pi$
$132$	5.21070	0.453533
$133$	0	0
$134$	−9.53790	−0.823949
$135$	0.0715699	0.00615976
$136$	2.22705	0.190968
$137$	−13.0249	−1.11279	−0.556396	−	0.830917i	$-0.687816\pi$
$137$	−13.0249	−1.11279	−0.556396	+	0.830917i	$0.687816\pi$
$138$	−10.6401	−0.905742
$139$	16.8987	1.43333	0.716664	−	0.697419i	$-0.245668\pi$
$139$	16.8987	1.43333	0.716664	+	0.697419i	$0.245668\pi$
$140$	0	0
$141$	−29.6600	−2.49783
$142$	−2.18856	−0.183660
$143$	−13.6166	−1.13867
$144$	2.88687	0.240572
$145$	0.260736	0.0216529
$146$	4.18350	0.346229
$147$	0	0
$148$	−7.24517	−0.595549
$149$	−0.491974	−0.0403040	−0.0201520	−	0.999797i	$-0.506415\pi$
$149$	−0.491974	−0.0403040	−0.0201520	+	0.999797i	$0.506415\pi$
$150$	11.9665	0.977060
$151$	2.10185	0.171046	0.0855230	−	0.996336i	$-0.472744\pi$
$151$	2.10185	0.171046	0.0855230	+	0.996336i	$0.472744\pi$
$152$	8.43775	0.684392
$153$	−6.42919	−0.519769
$154$	0	0
$155$	−0.793979	−0.0637739
$156$	−15.3835	−1.23167
$157$	−9.92354	−0.791985	−0.395993	−	0.918254i	$-0.629599\pi$
$157$	−9.92354	−0.791985	−0.395993	+	0.918254i	$0.629599\pi$
$158$	4.48597	0.356885
$159$	−0.947199	−0.0751178
$160$	0.260736	0.0206130
$161$	0	0
$162$	9.32660	0.732767
$163$	6.75259	0.528904	0.264452	−	0.964399i	$-0.414809\pi$
$163$	6.75259	0.528904	0.264452	+	0.964399i	$0.414809\pi$
$164$	−10.7302	−0.837887
$165$	−1.35862	−0.105768
$166$	1.91389	0.148547
$167$	−7.22428	−0.559032	−0.279516	−	0.960141i	$-0.590174\pi$
$167$	−7.22428	−0.559032	−0.279516	+	0.960141i	$0.590174\pi$
$168$	0	0
$169$	27.2001	2.09232
$170$	−0.580670	−0.0445354
$171$	−24.3587	−1.86275
$172$	0.195049	0.0148723
$173$	−8.60818	−0.654468	−0.327234	−	0.944943i	$-0.606117\pi$
$173$	−8.60818	−0.654468	−0.327234	+	0.944943i	$0.606117\pi$
$174$	2.42629	0.183936
$175$	0	0
$176$	2.14760	0.161882
$177$	35.7966	2.69064
$178$	11.8209	0.886012
$179$	21.0797	1.57557	0.787786	−	0.615949i	$-0.211227\pi$
$179$	21.0797	1.57557	0.787786	+	0.615949i	$0.211227\pi$
$180$	−0.752709	−0.0561036
$181$	8.59244	0.638671	0.319336	−	0.947642i	$-0.396540\pi$
$181$	8.59244	0.638671	0.319336	+	0.947642i	$0.396540\pi$
$182$	0	0
$183$	23.8737	1.76479
$184$	−4.38533	−0.323291
$185$	1.88907	0.138888
$186$	−7.38841	−0.541744
$187$	−4.78281	−0.349754
$188$	−12.2245	−0.891560
$189$	0	0
$190$	−2.20002	−0.159606
$191$	8.52165	0.616605	0.308302	−	0.951288i	$-0.400239\pi$
$191$	8.52165	0.616605	0.308302	+	0.951288i	$0.400239\pi$
$192$	2.42629	0.175102
$193$	13.1790	0.948645	0.474322	−	0.880351i	$-0.342693\pi$
$193$	13.1790	0.948645	0.474322	+	0.880351i	$0.342693\pi$
$194$	−0.283480	−0.0203527
$195$	4.01103	0.287236
$196$	0	0
$197$	−5.96908	−0.425279	−0.212640	−	0.977131i	$-0.568206\pi$
$197$	−5.96908	−0.425279	−0.212640	+	0.977131i	$0.568206\pi$
$198$	−6.19984	−0.440604
$199$	−13.3315	−0.945042	−0.472521	−	0.881319i	$-0.656656\pi$
$199$	−13.3315	−0.945042	−0.472521	+	0.881319i	$0.656656\pi$
$200$	4.93202	0.348746
$201$	23.1417	1.63229
$202$	−10.9123	−0.767784
$203$	0	0
$204$	−5.40345	−0.378317
$205$	2.79774	0.195403
$206$	−11.5444	−0.804336
$207$	12.6599	0.879921
$208$	−6.34036	−0.439625
$209$	−18.1209	−1.25345
$210$	0	0
$211$	9.91857	0.682823	0.341411	−	0.939914i	$-0.389095\pi$
$211$	9.91857	0.682823	0.341411	+	0.939914i	$0.389095\pi$
$212$	−0.390391	−0.0268121
$213$	5.31008	0.363840
$214$	−9.96649	−0.681295
$215$	−0.0508562	−0.00346836
$216$	0.274492	0.0186768
$217$	0	0
$218$	9.82477	0.665417
$219$	−10.1504	−0.685898
$220$	−0.559957	−0.0377523
$221$	14.1203	0.949832
$222$	17.5789	1.17982
$223$	19.5885	1.31174	0.655872	−	0.754872i	$-0.272301\pi$
$223$	19.5885	1.31174	0.655872	+	0.754872i	$0.272301\pi$
$224$	0	0
$225$	−14.2381	−0.949205
$226$	1.20430	0.0801090
$227$	−15.6918	−1.04150	−0.520751	−	0.853708i	$-0.674348\pi$
$227$	−15.6918	−1.04150	−0.520751	+	0.853708i	$0.674348\pi$
$228$	−20.4724	−1.35582
$229$	14.4197	0.952879	0.476440	−	0.879207i	$-0.341927\pi$
$229$	14.4197	0.952879	0.476440	+	0.879207i	$0.341927\pi$
$230$	1.14341	0.0753943
$231$	0	0
$232$	1.00000	0.0656532
$233$	−10.0291	−0.657029	−0.328515	−	0.944499i	$-0.606548\pi$
$233$	−10.0291	−0.657029	−0.328515	+	0.944499i	$0.606548\pi$
$234$	18.3038	1.19655
$235$	3.18735	0.207920
$236$	14.7537	0.960382
$237$	−10.8843	−0.707009
$238$	0	0
$239$	−0.920380	−0.0595344	−0.0297672	−	0.999557i	$-0.509477\pi$
$239$	−0.920380	−0.0595344	−0.0297672	+	0.999557i	$0.509477\pi$
$240$	−0.632619	−0.0408354
$241$	7.64883	0.492704	0.246352	−	0.969180i	$-0.420768\pi$
$241$	7.64883	0.492704	0.246352	+	0.969180i	$0.420768\pi$
$242$	6.38780	0.410623
$243$	−21.8055	−1.39883
$244$	9.83960	0.629916
$245$	0	0
$246$	26.0345	1.65990
$247$	53.4983	3.40402
$248$	−3.04515	−0.193367
$249$	−4.64365	−0.294279
$250$	−2.58963	−0.163783
$251$	−10.3042	−0.650395	−0.325197	−	0.945646i	$-0.605431\pi$
$251$	−10.3042	−0.650395	−0.325197	+	0.945646i	$0.605431\pi$
$252$	0	0
$253$	9.41794	0.592101
$254$	−4.82334	−0.302643
$255$	1.40887	0.0882270
$256$	1.00000	0.0625000
$257$	4.43144	0.276425	0.138213	−	0.990403i	$-0.455864\pi$
$257$	4.43144	0.276425	0.138213	+	0.990403i	$0.455864\pi$
$258$	−0.473244	−0.0294629
$259$	0	0
$260$	1.65316	0.102524
$261$	−2.88687	−0.178693
$262$	14.0889	0.870413
$263$	8.75489	0.539850	0.269925	−	0.962881i	$-0.413001\pi$
$263$	8.75489	0.539850	0.269925	+	0.962881i	$0.413001\pi$
$264$	−5.21070	−0.320696
$265$	0.101789	0.00625283
$266$	0	0
$267$	−28.6808	−1.75524
$268$	9.53790	0.582620
$269$	−21.7855	−1.32828	−0.664141	−	0.747607i	$-0.731203\pi$
$269$	−21.7855	−1.32828	−0.664141	+	0.747607i	$0.731203\pi$
$270$	−0.0715699	−0.00435561
$271$	16.9776	1.03132	0.515658	−	0.856794i	$-0.327547\pi$
$271$	16.9776	1.03132	0.515658	+	0.856794i	$0.327547\pi$
$272$	−2.22705	−0.135035
$273$	0	0
$274$	13.0249	0.786863
$275$	−10.5920	−0.638722
$276$	10.6401	0.640457
$277$	−0.608653	−0.0365704	−0.0182852	−	0.999833i	$-0.505821\pi$
$277$	−0.608653	−0.0365704	−0.0182852	+	0.999833i	$0.505821\pi$
$278$	−16.8987	−1.01352
$279$	8.79094	0.526300
$280$	0	0
$281$	−25.5555	−1.52451	−0.762256	−	0.647276i	$-0.775908\pi$
$281$	−25.5555	−1.52451	−0.762256	+	0.647276i	$0.775908\pi$
$282$	29.6600	1.76623
$283$	−24.7141	−1.46910	−0.734551	−	0.678553i	$-0.762607\pi$
$283$	−24.7141	−1.46910	−0.734551	+	0.678553i	$0.762607\pi$
$284$	2.18856	0.129867
$285$	5.33788	0.316189
$286$	13.6166	0.805164
$287$	0	0
$288$	−2.88687	−0.170110
$289$	−12.0403	−0.708251
$290$	−0.260736	−0.0153109
$291$	0.687804	0.0403198
$292$	−4.18350	−0.244821
$293$	−20.9908	−1.22630	−0.613148	−	0.789968i	$-0.710097\pi$
$293$	−20.9908	−1.22630	−0.613148	+	0.789968i	$0.710097\pi$
$294$	0	0
$295$	−3.84681	−0.223970
$296$	7.24517	0.421117
$297$	−0.589500	−0.0342063
$298$	0.491974	0.0284993
$299$	−27.8045	−1.60798
$300$	−11.9665	−0.690885
$301$	0	0
$302$	−2.10185	−0.120948
$303$	26.4763	1.52102
$304$	−8.43775	−0.483938
$305$	−2.56553	−0.146902
$306$	6.42919	0.367532
$307$	−24.9164	−1.42205	−0.711027	−	0.703164i	$-0.751770\pi$
$307$	−24.9164	−1.42205	−0.711027	+	0.703164i	$0.751770\pi$
$308$	0	0
$309$	28.0100	1.59343
$310$	0.793979	0.0450950
$311$	−3.38252	−0.191805	−0.0959025	−	0.995391i	$-0.530574\pi$
$311$	−3.38252	−0.191805	−0.0959025	+	0.995391i	$0.530574\pi$
$312$	15.3835	0.870920
$313$	−27.7834	−1.57041	−0.785206	−	0.619235i	$-0.787443\pi$
$313$	−27.7834	−1.57041	−0.785206	+	0.619235i	$0.787443\pi$
$314$	9.92354	0.560018
$315$	0	0
$316$	−4.48597	−0.252356
$317$	−13.6437	−0.766304	−0.383152	−	0.923685i	$-0.625161\pi$
$317$	−13.6437	−0.766304	−0.383152	+	0.923685i	$0.625161\pi$
$318$	0.947199	0.0531163
$319$	−2.14760	−0.120243
$320$	−0.260736	−0.0145756
$321$	24.1816	1.34968
$322$	0	0
$323$	18.7913	1.04557
$324$	−9.32660	−0.518144
$325$	31.2707	1.73459
$326$	−6.75259	−0.373992
$327$	−23.8377	−1.31823
$328$	10.7302	0.592475
$329$	0	0
$330$	1.35862	0.0747893
$331$	−12.1576	−0.668244	−0.334122	−	0.942530i	$-0.608440\pi$
$331$	−12.1576	−0.668244	−0.334122	+	0.942530i	$0.608440\pi$
$332$	−1.91389	−0.105038
$333$	−20.9158	−1.14618
$334$	7.22428	0.395295
$335$	−2.48687	−0.135872
$336$	0	0
$337$	12.7616	0.695168	0.347584	−	0.937649i	$-0.387002\pi$
$337$	12.7616	0.695168	0.347584	+	0.937649i	$0.387002\pi$
$338$	−27.2001	−1.47949
$339$	−2.92198	−0.158700
$340$	0.580670	0.0314913
$341$	6.53977	0.354149
$342$	24.3587	1.31717
$343$	0	0
$344$	−0.195049	−0.0105163
$345$	−2.77424	−0.149360
$346$	8.60818	0.462779
$347$	−3.20642	−0.172130	−0.0860648	−	0.996290i	$-0.527429\pi$
$347$	−3.20642	−0.172130	−0.0860648	+	0.996290i	$0.527429\pi$
$348$	−2.42629	−0.130063
$349$	−3.95168	−0.211529	−0.105764	−	0.994391i	$-0.533729\pi$
$349$	−3.95168	−0.211529	−0.105764	+	0.994391i	$0.533729\pi$
$350$	0	0
$351$	1.74038	0.0928945
$352$	−2.14760	−0.114468
$353$	15.0305	0.799995	0.399998	−	0.916516i	$-0.369011\pi$
$353$	15.0305	0.799995	0.399998	+	0.916516i	$0.369011\pi$
$354$	−35.7966	−1.90257
$355$	−0.570636	−0.0302862
$356$	−11.8209	−0.626505
$357$	0	0
$358$	−21.0797	−1.11410
$359$	−12.5777	−0.663823	−0.331912	−	0.943310i	$-0.607694\pi$
$359$	−12.5777	−0.663823	−0.331912	+	0.943310i	$0.607694\pi$
$360$	0.752709	0.0396713
$361$	52.1956	2.74714
$362$	−8.59244	−0.451609
$363$	−15.4986	−0.813468
$364$	0	0
$365$	1.09079	0.0570944
$366$	−23.8737	−1.24790
$367$	15.2524	0.796166	0.398083	−	0.917349i	$-0.369676\pi$
$367$	15.2524	0.796166	0.398083	+	0.917349i	$0.369676\pi$
$368$	4.38533	0.228601
$369$	−30.9766	−1.61258
$370$	−1.88907	−0.0982083
$371$	0	0
$372$	7.38841	0.383071
$373$	−14.9777	−0.775517	−0.387759	−	0.921761i	$-0.626751\pi$
$373$	−14.9777	−0.775517	−0.387759	+	0.921761i	$0.626751\pi$
$374$	4.78281	0.247313
$375$	6.28319	0.324462
$376$	12.2245	0.630428
$377$	6.34036	0.326545
$378$	0	0
$379$	0.578081	0.0296940	0.0148470	−	0.999890i	$-0.495274\pi$
$379$	0.578081	0.0296940	0.0148470	+	0.999890i	$0.495274\pi$
$380$	2.20002	0.112859
$381$	11.7028	0.599553
$382$	−8.52165	−0.436005
$383$	28.9218	1.47783	0.738917	−	0.673797i	$-0.235338\pi$
$383$	28.9218	1.47783	0.738917	+	0.673797i	$0.235338\pi$
$384$	−2.42629	−0.123816
$385$	0	0
$386$	−13.1790	−0.670793
$387$	0.563080	0.0286230
$388$	0.283480	0.0143915
$389$	−9.91719	−0.502821	−0.251411	−	0.967881i	$-0.580894\pi$
$389$	−9.91719	−0.502821	−0.251411	+	0.967881i	$0.580894\pi$
$390$	−4.01103	−0.203107
$391$	−9.76633	−0.493905
$392$	0	0
$393$	−34.1836	−1.72434
$394$	5.96908	0.300718
$395$	1.16965	0.0588516
$396$	6.19984	0.311554
$397$	−10.3356	−0.518729	−0.259365	−	0.965779i	$-0.583513\pi$
$397$	−10.3356	−0.518729	−0.259365	+	0.965779i	$0.583513\pi$
$398$	13.3315	0.668245
$399$	0	0
$400$	−4.93202	−0.246601
$401$	−20.8127	−1.03933	−0.519667	−	0.854369i	$-0.673944\pi$
$401$	−20.8127	−1.03933	−0.519667	+	0.854369i	$0.673944\pi$
$402$	−23.1417	−1.15420
$403$	−19.3073	−0.961767
$404$	10.9123	0.542905
$405$	2.43178	0.120836
$406$	0	0
$407$	−15.5598	−0.771268
$408$	5.40345	0.267511
$409$	−9.80067	−0.484612	−0.242306	−	0.970200i	$-0.577904\pi$
$409$	−9.80067	−0.484612	−0.242306	+	0.970200i	$0.577904\pi$
$410$	−2.79774	−0.138171
$411$	−31.6022	−1.55882
$412$	11.5444	0.568751
$413$	0	0
$414$	−12.6599	−0.622198
$415$	0.499020	0.0244959
$416$	6.34036	0.310862
$417$	41.0010	2.00783
$418$	18.1209	0.886324
$419$	−0.564842	−0.0275943	−0.0137972	−	0.999905i	$-0.504392\pi$
$419$	−0.564842	−0.0275943	−0.0137972	+	0.999905i	$0.504392\pi$
$420$	0	0
$421$	28.1593	1.37240	0.686201	−	0.727412i	$-0.259277\pi$
$421$	28.1593	1.37240	0.686201	+	0.727412i	$0.259277\pi$
$422$	−9.91857	−0.482829
$423$	−35.2904	−1.71588
$424$	0.390391	0.0189590
$425$	10.9838	0.532794
$426$	−5.31008	−0.257274
$427$	0	0
$428$	9.96649	0.481748
$429$	−33.0377	−1.59507
$430$	0.0508562	0.00245250
$431$	28.1658	1.35670	0.678350	−	0.734739i	$-0.262695\pi$
$431$	28.1658	1.35670	0.678350	+	0.734739i	$0.262695\pi$
$432$	−0.274492	−0.0132065
$433$	−17.6927	−0.850259	−0.425130	−	0.905132i	$-0.639771\pi$
$433$	−17.6927	−0.850259	−0.425130	+	0.905132i	$0.639771\pi$
$434$	0	0
$435$	0.632619	0.0303318
$436$	−9.82477	−0.470521
$437$	−37.0023	−1.77006
$438$	10.1504	0.485003
$439$	28.1245	1.34231	0.671154	−	0.741318i	$-0.265799\pi$
$439$	28.1245	1.34231	0.671154	+	0.741318i	$0.265799\pi$
$440$	0.559957	0.0266949
$441$	0	0
$442$	−14.1203	−0.671633
$443$	−6.21048	−0.295069	−0.147534	−	0.989057i	$-0.547134\pi$
$443$	−6.21048	−0.295069	−0.147534	+	0.989057i	$0.547134\pi$
$444$	−17.5789	−0.834256
$445$	3.08212	0.146107
$446$	−19.5885	−0.927543
$447$	−1.19367	−0.0564586
$448$	0	0
$449$	−5.87960	−0.277475	−0.138738	−	0.990329i	$-0.544304\pi$
$449$	−5.87960	−0.277475	−0.138738	+	0.990329i	$0.544304\pi$
$450$	14.2381	0.671189
$451$	−23.0442	−1.08511
$452$	−1.20430	−0.0566456
$453$	5.09969	0.239604
$454$	15.6918	0.736454
$455$	0	0
$456$	20.4724	0.958708
$457$	−34.2340	−1.60140	−0.800700	−	0.599065i	$-0.795539\pi$
$457$	−34.2340	−1.60140	−0.800700	+	0.599065i	$0.795539\pi$
$458$	−14.4197	−0.673788
$459$	0.611307	0.0285334
$460$	−1.14341	−0.0533118
$461$	7.77623	0.362175	0.181088	−	0.983467i	$-0.442038\pi$
$461$	7.77623	0.362175	0.181088	+	0.983467i	$0.442038\pi$
$462$	0	0
$463$	−6.50388	−0.302261	−0.151130	−	0.988514i	$-0.548291\pi$
$463$	−6.50388	−0.302261	−0.151130	+	0.988514i	$0.548291\pi$
$464$	−1.00000	−0.0464238
$465$	−1.92642	−0.0893356
$466$	10.0291	0.464590
$467$	5.00733	0.231712	0.115856	−	0.993266i	$-0.463039\pi$
$467$	5.00733	0.231712	0.115856	+	0.993266i	$0.463039\pi$
$468$	−18.3038	−0.846092
$469$	0	0
$470$	−3.18735	−0.147022
$471$	−24.0774	−1.10943
$472$	−14.7537	−0.679093
$473$	0.418887	0.0192605
$474$	10.8843	0.499931
$475$	41.6151	1.90943
$476$	0	0
$477$	−1.12701	−0.0516020
$478$	0.920380	0.0420972
$479$	35.2838	1.61216	0.806080	−	0.591807i	$-0.201585\pi$
$479$	35.2838	1.61216	0.806080	+	0.591807i	$0.201585\pi$
$480$	0.632619	0.0288750
$481$	45.9370	2.09455
$482$	−7.64883	−0.348395
$483$	0	0
$484$	−6.38780	−0.290355
$485$	−0.0739133	−0.00335623
$486$	21.8055	0.989119
$487$	4.73153	0.214406	0.107203	−	0.994237i	$-0.465811\pi$
$487$	4.73153	0.214406	0.107203	+	0.994237i	$0.465811\pi$
$488$	−9.83960	−0.445418
$489$	16.3837	0.740898
$490$	0	0
$491$	−18.5337	−0.836413	−0.418206	−	0.908352i	$-0.637341\pi$
$491$	−18.5337	−0.836413	−0.418206	+	0.908352i	$0.637341\pi$
$492$	−26.0345	−1.17373
$493$	2.22705	0.100301
$494$	−53.4983	−2.40700
$495$	−1.61652	−0.0726572
$496$	3.04515	0.136731
$497$	0	0
$498$	4.64365	0.208087
$499$	−8.49139	−0.380127	−0.190063	−	0.981772i	$-0.560869\pi$
$499$	−8.49139	−0.380127	−0.190063	+	0.981772i	$0.560869\pi$
$500$	2.58963	0.115812
$501$	−17.5282	−0.783101
$502$	10.3042	0.459899
$503$	−25.6049	−1.14167	−0.570833	−	0.821066i	$-0.693380\pi$
$503$	−25.6049	−1.14167	−0.570833	+	0.821066i	$0.693380\pi$
$504$	0	0
$505$	−2.84522	−0.126610
$506$	−9.41794	−0.418679
$507$	65.9953	2.93095
$508$	4.82334	0.214001
$509$	2.16096	0.0957829	0.0478914	−	0.998853i	$-0.484750\pi$
$509$	2.16096	0.0957829	0.0478914	+	0.998853i	$0.484750\pi$
$510$	−1.40887	−0.0623859
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	2.31610	0.102258
$514$	−4.43144	−0.195462
$515$	−3.01003	−0.132638
$516$	0.473244	0.0208334
$517$	−26.2533	−1.15462
$518$	0	0
$519$	−20.8859	−0.916790
$520$	−1.65316	−0.0724957
$521$	−38.3906	−1.68192	−0.840961	−	0.541096i	$-0.818009\pi$
$521$	−38.3906	−1.68192	−0.840961	+	0.541096i	$0.818009\pi$
$522$	2.88687	0.126355
$523$	36.1101	1.57898	0.789492	−	0.613761i	$-0.210344\pi$
$523$	36.1101	1.57898	0.789492	+	0.613761i	$0.210344\pi$
$524$	−14.0889	−0.615475
$525$	0	0
$526$	−8.75489	−0.381731
$527$	−6.78169	−0.295415
$528$	5.21070	0.226767
$529$	−3.76889	−0.163865
$530$	−0.101789	−0.00442142
$531$	42.5919	1.84833
$532$	0	0
$533$	68.0332	2.94685
$534$	28.6808	1.24114
$535$	−2.59862	−0.112348
$536$	−9.53790	−0.411975
$537$	51.1454	2.20709
$538$	21.7855	0.939238
$539$	0	0
$540$	0.0715699	0.00307988
$541$	−6.89449	−0.296417	−0.148209	−	0.988956i	$-0.547351\pi$
$541$	−6.89449	−0.296417	−0.148209	+	0.988956i	$0.547351\pi$
$542$	−16.9776	−0.729251
$543$	20.8477	0.894662
$544$	2.22705	0.0954838
$545$	2.56167	0.109730
$546$	0	0
$547$	−39.4686	−1.68756	−0.843779	−	0.536691i	$-0.819674\pi$
$547$	−39.4686	−1.68756	−0.843779	+	0.536691i	$0.819674\pi$
$548$	−13.0249	−0.556396
$549$	28.4056	1.21232
$550$	10.5920	0.451645
$551$	8.43775	0.359460
$552$	−10.6401	−0.452871
$553$	0	0
$554$	0.608653	0.0258592
$555$	4.58344	0.194556
$556$	16.8987	0.716664
$557$	21.9613	0.930530	0.465265	−	0.885171i	$-0.345959\pi$
$557$	21.9613	0.930530	0.465265	+	0.885171i	$0.345959\pi$
$558$	−8.79094	−0.372150
$559$	−1.23668	−0.0523059
$560$	0	0
$561$	−11.6045	−0.489941
$562$	25.5555	1.07799
$563$	17.4707	0.736303	0.368151	−	0.929766i	$-0.379991\pi$
$563$	17.4707	0.736303	0.368151	+	0.929766i	$0.379991\pi$
$564$	−29.6600	−1.24891
$565$	0.314005	0.0132103
$566$	24.7141	1.03881
$567$	0	0
$568$	−2.18856	−0.0918300
$569$	11.0179	0.461896	0.230948	−	0.972966i	$-0.425817\pi$
$569$	11.0179	0.461896	0.230948	+	0.972966i	$0.425817\pi$
$570$	−5.33788	−0.223579
$571$	4.82287	0.201831	0.100915	−	0.994895i	$-0.467823\pi$
$571$	4.82287	0.201831	0.100915	+	0.994895i	$0.467823\pi$
$572$	−13.6166	−0.569337
$573$	20.6760	0.863751
$574$	0	0
$575$	−21.6285	−0.901971
$576$	2.88687	0.120286
$577$	11.9775	0.498629	0.249314	−	0.968423i	$-0.419795\pi$
$577$	11.9775	0.498629	0.249314	+	0.968423i	$0.419795\pi$
$578$	12.0403	0.500809
$579$	31.9760	1.32888
$580$	0.260736	0.0108265
$581$	0	0
$582$	−0.687804	−0.0285104
$583$	−0.838404	−0.0347231
$584$	4.18350	0.173114
$585$	4.77244	0.197316
$586$	20.9908	0.867122
$587$	−28.0949	−1.15960	−0.579800	−	0.814759i	$-0.696869\pi$
$587$	−28.0949	−1.15960	−0.579800	+	0.814759i	$0.696869\pi$
$588$	0	0
$589$	−25.6942	−1.05871
$590$	3.84681	0.158371
$591$	−14.4827	−0.595738
$592$	−7.24517	−0.297775
$593$	−25.6900	−1.05496	−0.527481	−	0.849567i	$-0.676863\pi$
$593$	−25.6900	−1.05496	−0.527481	+	0.849567i	$0.676863\pi$
$594$	0.589500	0.0241875
$595$	0	0
$596$	−0.491974	−0.0201520
$597$	−32.3459	−1.32383
$598$	27.8045	1.13701
$599$	−8.23688	−0.336550	−0.168275	−	0.985740i	$-0.553820\pi$
$599$	−8.23688	−0.336550	−0.168275	+	0.985740i	$0.553820\pi$
$600$	11.9665	0.488530
$601$	−12.0901	−0.493166	−0.246583	−	0.969122i	$-0.579308\pi$
$601$	−12.0901	−0.493166	−0.246583	+	0.969122i	$0.579308\pi$
$602$	0	0
$603$	27.5347	1.12130
$604$	2.10185	0.0855230
$605$	1.66553	0.0677133
$606$	−26.4763	−1.07553
$607$	−25.0685	−1.01750	−0.508749	−	0.860915i	$-0.669892\pi$
$607$	−25.0685	−1.01750	−0.508749	+	0.860915i	$0.669892\pi$
$608$	8.43775	0.342196
$609$	0	0
$610$	2.56553	0.103875
$611$	77.5074	3.13561
$612$	−6.42919	−0.259885
$613$	−33.6592	−1.35948	−0.679741	−	0.733453i	$-0.737908\pi$
$613$	−33.6592	−1.35948	−0.679741	+	0.733453i	$0.737908\pi$
$614$	24.9164	1.00554
$615$	6.78813	0.273724
$616$	0	0
$617$	−29.3861	−1.18304	−0.591519	−	0.806291i	$-0.701472\pi$
$617$	−29.3861	−1.18304	−0.591519	+	0.806291i	$0.701472\pi$
$618$	−28.0100	−1.12673
$619$	−41.3752	−1.66301	−0.831504	−	0.555518i	$-0.812520\pi$
$619$	−41.3752	−1.66301	−0.831504	+	0.555518i	$0.812520\pi$
$620$	−0.793979	−0.0318870
$621$	−1.20374	−0.0483044
$622$	3.38252	0.135627
$623$	0	0
$624$	−15.3835	−0.615834
$625$	23.9849	0.959395
$626$	27.7834	1.11045
$627$	−43.9666	−1.75586
$628$	−9.92354	−0.395993
$629$	16.1353	0.643358
$630$	0	0
$631$	−3.03083	−0.120656	−0.0603278	−	0.998179i	$-0.519215\pi$
$631$	−3.03083	−0.120656	−0.0603278	+	0.998179i	$0.519215\pi$
$632$	4.48597	0.178442
$633$	24.0653	0.956510
$634$	13.6437	0.541859
$635$	−1.25762	−0.0499070
$636$	−0.947199	−0.0375589
$637$	0	0
$638$	2.14760	0.0850244
$639$	6.31809	0.249940
$640$	0.260736	0.0103065
$641$	25.6543	1.01328	0.506642	−	0.862157i	$-0.330887\pi$
$641$	25.6543	1.01328	0.506642	+	0.862157i	$0.330887\pi$
$642$	−24.1816	−0.954370
$643$	11.3614	0.448048	0.224024	−	0.974584i	$-0.428081\pi$
$643$	11.3614	0.448048	0.224024	+	0.974584i	$0.428081\pi$
$644$	0	0
$645$	−0.123392	−0.00485854
$646$	−18.7913	−0.739332
$647$	19.0817	0.750181	0.375090	−	0.926988i	$-0.377612\pi$
$647$	19.0817	0.750181	0.375090	+	0.926988i	$0.377612\pi$
$648$	9.32660	0.366383
$649$	31.6850	1.24375
$650$	−31.2707	−1.22654
$651$	0	0
$652$	6.75259	0.264452
$653$	48.3668	1.89274	0.946370	−	0.323086i	$-0.104720\pi$
$653$	48.3668	1.89274	0.946370	+	0.323086i	$0.104720\pi$
$654$	23.8377	0.932128
$655$	3.67347	0.143534
$656$	−10.7302	−0.418943
$657$	−12.0772	−0.471177
$658$	0	0
$659$	−7.57465	−0.295067	−0.147533	−	0.989057i	$-0.547133\pi$
$659$	−7.57465	−0.295067	−0.147533	+	0.989057i	$0.547133\pi$
$660$	−1.35862	−0.0528840
$661$	44.4433	1.72864	0.864322	−	0.502940i	$-0.167748\pi$
$661$	44.4433	1.72864	0.864322	+	0.502940i	$0.167748\pi$
$662$	12.1576	0.472520
$663$	34.2598	1.33054
$664$	1.91389	0.0742734
$665$	0	0
$666$	20.9158	0.810473
$667$	−4.38533	−0.169801
$668$	−7.22428	−0.279516
$669$	47.5274	1.83751
$670$	2.48687	0.0960762
$671$	21.1316	0.815774
$672$	0	0
$673$	−22.7141	−0.875564	−0.437782	−	0.899081i	$-0.644236\pi$
$673$	−22.7141	−0.875564	−0.437782	+	0.899081i	$0.644236\pi$
$674$	−12.7616	−0.491558
$675$	1.35380	0.0521078
$676$	27.2001	1.04616
$677$	1.67725	0.0644621	0.0322310	−	0.999480i	$-0.489739\pi$
$677$	1.67725	0.0644621	0.0322310	+	0.999480i	$0.489739\pi$
$678$	2.92198	0.112218
$679$	0	0
$680$	−0.580670	−0.0222677
$681$	−38.0729	−1.45895
$682$	−6.53977	−0.250421
$683$	49.9200	1.91014	0.955069	−	0.296385i	$-0.0957811\pi$
$683$	49.9200	1.91014	0.955069	+	0.296385i	$0.0957811\pi$
$684$	−24.3587	−0.931377
$685$	3.39606	0.129757
$686$	0	0
$687$	34.9863	1.33481
$688$	0.195049	0.00743617
$689$	2.47521	0.0942982
$690$	2.77424	0.105614
$691$	−25.5835	−0.973240	−0.486620	−	0.873614i	$-0.661770\pi$
$691$	−25.5835	−0.973240	−0.486620	+	0.873614i	$0.661770\pi$
$692$	−8.60818	−0.327234
$693$	0	0
$694$	3.20642	0.121714
$695$	−4.40609	−0.167132
$696$	2.42629	0.0919682
$697$	23.8966	0.905149
$698$	3.95168	0.149573
$699$	−24.3335	−0.920378
$700$	0	0
$701$	29.5973	1.11787	0.558936	−	0.829211i	$-0.311210\pi$
$701$	29.5973	1.11787	0.558936	+	0.829211i	$0.311210\pi$
$702$	−1.74038	−0.0656864
$703$	61.1329	2.30567
$704$	2.14760	0.0809408
$705$	7.73343	0.291258
$706$	−15.0305	−0.565682
$707$	0	0
$708$	35.7966	1.34532
$709$	0.307107	0.0115337	0.00576683	−	0.999983i	$-0.498164\pi$
$709$	0.307107	0.0115337	0.00576683	+	0.999983i	$0.498164\pi$
$710$	0.570636	0.0214156
$711$	−12.9504	−0.485678
$712$	11.8209	0.443006
$713$	13.3540	0.500111
$714$	0	0
$715$	3.55032	0.132775
$716$	21.0797	0.787786
$717$	−2.23311	−0.0833969
$718$	12.5777	0.469394
$719$	−22.2426	−0.829511	−0.414755	−	0.909933i	$-0.636133\pi$
$719$	−22.2426	−0.829511	−0.414755	+	0.909933i	$0.636133\pi$
$720$	−0.752709	−0.0280518
$721$	0	0
$722$	−52.1956	−1.94252
$723$	18.5583	0.690189
$724$	8.59244	0.319336
$725$	4.93202	0.183171
$726$	15.4986	0.575208
$727$	23.8821	0.885739	0.442869	−	0.896586i	$-0.353961\pi$
$727$	23.8821	0.885739	0.442869	+	0.896586i	$0.353961\pi$
$728$	0	0
$729$	−24.9267	−0.923210
$730$	−1.09079	−0.0403719
$731$	−0.434383	−0.0160662
$732$	23.8737	0.882397
$733$	2.31726	0.0855899	0.0427949	−	0.999084i	$-0.486374\pi$
$733$	2.31726	0.0855899	0.0427949	+	0.999084i	$0.486374\pi$
$734$	−15.2524	−0.562975
$735$	0	0
$736$	−4.38533	−0.161645
$737$	20.4836	0.754524
$738$	30.9766	1.14027
$739$	−20.4310	−0.751566	−0.375783	−	0.926708i	$-0.622626\pi$
$739$	−20.4310	−0.751566	−0.375783	+	0.926708i	$0.622626\pi$
$740$	1.88907	0.0694438
$741$	129.802	4.76841
$742$	0	0
$743$	16.7514	0.614550	0.307275	−	0.951621i	$-0.400583\pi$
$743$	16.7514	0.614550	0.307275	+	0.951621i	$0.400583\pi$
$744$	−7.38841	−0.270872
$745$	0.128275	0.00469963
$746$	14.9777	0.548373
$747$	−5.52515	−0.202155
$748$	−4.78281	−0.174877
$749$	0	0
$750$	−6.28319	−0.229430
$751$	27.2245	0.993438	0.496719	−	0.867911i	$-0.334538\pi$
$751$	27.2245	0.993438	0.496719	+	0.867911i	$0.334538\pi$
$752$	−12.2245	−0.445780
$753$	−25.0009	−0.911084
$754$	−6.34036	−0.230902
$755$	−0.548027	−0.0199447
$756$	0	0
$757$	7.31697	0.265940	0.132970	−	0.991120i	$-0.457549\pi$
$757$	7.31697	0.265940	0.132970	+	0.991120i	$0.457549\pi$
$758$	−0.578081	−0.0209969
$759$	22.8506	0.829426
$760$	−2.20002	−0.0798032
$761$	24.8920	0.902334	0.451167	−	0.892440i	$-0.351008\pi$
$761$	24.8920	0.902334	0.451167	+	0.892440i	$0.351008\pi$
$762$	−11.7028	−0.423948
$763$	0	0
$764$	8.52165	0.308302
$765$	1.67632	0.0606074
$766$	−28.9218	−1.04499
$767$	−93.5435	−3.37766
$768$	2.42629	0.0875511
$769$	47.5147	1.71342	0.856712	−	0.515795i	$-0.172503\pi$
$769$	47.5147	1.71342	0.856712	+	0.515795i	$0.172503\pi$
$770$	0	0
$771$	10.7519	0.387221
$772$	13.1790	0.474322
$773$	−35.8534	−1.28956	−0.644778	−	0.764370i	$-0.723050\pi$
$773$	−35.8534	−1.28956	−0.644778	+	0.764370i	$0.723050\pi$
$774$	−0.563080	−0.0202395
$775$	−15.0187	−0.539489
$776$	−0.283480	−0.0101763
$777$	0	0
$778$	9.91719	0.355548
$779$	90.5386	3.24388
$780$	4.01103	0.143618
$781$	4.70016	0.168185
$782$	9.76633	0.349243
$783$	0.274492	0.00980955
$784$	0	0
$785$	2.58742	0.0923490
$786$	34.1836	1.21929
$787$	4.53121	0.161520	0.0807601	−	0.996734i	$-0.474265\pi$
$787$	4.53121	0.161520	0.0807601	+	0.996734i	$0.474265\pi$
$788$	−5.96908	−0.212640
$789$	21.2419	0.756231
$790$	−1.16965	−0.0416144
$791$	0	0
$792$	−6.19984	−0.220302
$793$	−62.3865	−2.21541
$794$	10.3356	0.366797
$795$	0.246969	0.00875908
$796$	−13.3315	−0.472521
$797$	1.22332	0.0433324	0.0216662	−	0.999765i	$-0.493103\pi$
$797$	1.22332	0.0433324	0.0216662	+	0.999765i	$0.493103\pi$
$798$	0	0
$799$	27.2244	0.963131
$800$	4.93202	0.174373
$801$	−34.1253	−1.20576
$802$	20.8127	0.734921
$803$	−8.98450	−0.317056
$804$	23.1417	0.816145
$805$	0	0
$806$	19.3073	0.680072
$807$	−52.8578	−1.86068
$808$	−10.9123	−0.383892
$809$	−46.2305	−1.62538	−0.812689	−	0.582697i	$-0.801997\pi$
$809$	−46.2305	−1.62538	−0.812689	+	0.582697i	$0.801997\pi$
$810$	−2.43178	−0.0854439
$811$	−20.0839	−0.705241	−0.352621	−	0.935766i	$-0.614709\pi$
$811$	−20.0839	−0.705241	−0.352621	+	0.935766i	$0.614709\pi$
$812$	0	0
$813$	41.1925	1.44469
$814$	15.5598	0.545369
$815$	−1.76064	−0.0616726
$816$	−5.40345	−0.189159
$817$	−1.64577	−0.0575783
$818$	9.80067	0.342672
$819$	0	0
$820$	2.79774	0.0977014
$821$	27.8598	0.972314	0.486157	−	0.873871i	$-0.338398\pi$
$821$	27.8598	0.972314	0.486157	+	0.873871i	$0.338398\pi$
$822$	31.6022	1.10225
$823$	54.1598	1.88789	0.943946	−	0.330099i	$-0.107082\pi$
$823$	54.1598	1.88789	0.943946	+	0.330099i	$0.107082\pi$
$824$	−11.5444	−0.402168
$825$	−25.6993	−0.894734
$826$	0	0
$827$	−16.8852	−0.587157	−0.293579	−	0.955935i	$-0.594846\pi$
$827$	−16.8852	−0.587157	−0.293579	+	0.955935i	$0.594846\pi$
$828$	12.6599	0.439961
$829$	46.3467	1.60969	0.804844	−	0.593486i	$-0.202249\pi$
$829$	46.3467	1.60969	0.804844	+	0.593486i	$0.202249\pi$
$830$	−0.499020	−0.0173212
$831$	−1.47677	−0.0512285
$832$	−6.34036	−0.219812
$833$	0	0
$834$	−41.0010	−1.41975
$835$	1.88363	0.0651856
$836$	−18.1209	−0.626726
$837$	−0.835870	−0.0288919
$838$	0.564842	0.0195121
$839$	24.9065	0.859866	0.429933	−	0.902861i	$-0.358537\pi$
$839$	24.9065	0.859866	0.429933	+	0.902861i	$0.358537\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−28.1593	−0.970434
$843$	−62.0049	−2.13556
$844$	9.91857	0.341411
$845$	−7.09204	−0.243974
$846$	35.2904	1.21331
$847$	0	0
$848$	−0.390391	−0.0134061
$849$	−59.9636	−2.05794
$850$	−10.9838	−0.376742
$851$	−31.7725	−1.08915
$852$	5.31008	0.181920
$853$	13.4612	0.460903	0.230451	−	0.973084i	$-0.425980\pi$
$853$	13.4612	0.460903	0.230451	+	0.973084i	$0.425980\pi$
$854$	0	0
$855$	6.35117	0.217205
$856$	−9.96649	−0.340648
$857$	−28.3203	−0.967403	−0.483702	−	0.875233i	$-0.660708\pi$
$857$	−28.3203	−0.967403	−0.483702	+	0.875233i	$0.660708\pi$
$858$	33.0377	1.12789
$859$	−21.8641	−0.745995	−0.372997	−	0.927832i	$-0.621670\pi$
$859$	−21.8641	−0.745995	−0.372997	+	0.927832i	$0.621670\pi$
$860$	−0.0508562	−0.00173418
$861$	0	0
$862$	−28.1658	−0.959331
$863$	32.4502	1.10462	0.552308	−	0.833640i	$-0.313747\pi$
$863$	32.4502	1.10462	0.552308	+	0.833640i	$0.313747\pi$
$864$	0.274492	0.00933842
$865$	2.24446	0.0763139
$866$	17.6927	0.601224
$867$	−29.2131	−0.992130
$868$	0	0
$869$	−9.63409	−0.326814
$870$	−0.632619	−0.0214478
$871$	−60.4737	−2.04907
$872$	9.82477	0.332709
$873$	0.818369	0.0276976
$874$	37.0023	1.25162
$875$	0	0
$876$	−10.1504	−0.342949
$877$	−4.92965	−0.166462	−0.0832312	−	0.996530i	$-0.526524\pi$
$877$	−4.92965	−0.166462	−0.0832312	+	0.996530i	$0.526524\pi$
$878$	−28.1245	−0.949155
$879$	−50.9297	−1.71782
$880$	−0.559957	−0.0188761
$881$	13.9409	0.469682	0.234841	−	0.972034i	$-0.424543\pi$
$881$	13.9409	0.469682	0.234841	+	0.972034i	$0.424543\pi$
$882$	0	0
$883$	44.4387	1.49548	0.747740	−	0.663992i	$-0.231139\pi$
$883$	44.4387	1.49548	0.747740	+	0.663992i	$0.231139\pi$
$884$	14.1203	0.474916
$885$	−9.33346	−0.313741
$886$	6.21048	0.208645
$887$	3.19391	0.107241	0.0536204	−	0.998561i	$-0.482924\pi$
$887$	3.19391	0.107241	0.0536204	+	0.998561i	$0.482924\pi$
$888$	17.5789	0.589908
$889$	0	0
$890$	−3.08212	−0.103313
$891$	−20.0298	−0.671025
$892$	19.5885	0.655872
$893$	103.147	3.45168
$894$	1.19367	0.0399223
$895$	−5.49623	−0.183719
$896$	0	0
$897$	−67.4618	−2.25248
$898$	5.87960	0.196205
$899$	−3.04515	−0.101561
$900$	−14.2381	−0.474603
$901$	0.869418	0.0289645
$902$	23.0442	0.767287
$903$	0	0
$904$	1.20430	0.0400545
$905$	−2.24036	−0.0744720
$906$	−5.09969	−0.169426
$907$	20.0688	0.666372	0.333186	−	0.942861i	$-0.391876\pi$
$907$	20.0688	0.666372	0.333186	+	0.942861i	$0.391876\pi$
$908$	−15.6918	−0.520751
$909$	31.5022	1.04486
$910$	0	0
$911$	−5.18802	−0.171887	−0.0859434	−	0.996300i	$-0.527390\pi$
$911$	−5.18802	−0.171887	−0.0859434	+	0.996300i	$0.527390\pi$
$912$	−20.4724	−0.677909
$913$	−4.11028	−0.136030
$914$	34.2340	1.13236
$915$	−6.22472	−0.205783
$916$	14.4197	0.476440
$917$	0	0
$918$	−0.611307	−0.0201761
$919$	10.2725	0.338859	0.169429	−	0.985542i	$-0.445808\pi$
$919$	10.2725	0.338859	0.169429	+	0.985542i	$0.445808\pi$
$920$	1.14341	0.0376972
$921$	−60.4543	−1.99204
$922$	−7.77623	−0.256097
$923$	−13.8763	−0.456743
$924$	0	0
$925$	35.7333	1.17490
$926$	6.50388	0.213731
$927$	33.3271	1.09461
$928$	1.00000	0.0328266
$929$	4.27777	0.140349	0.0701745	−	0.997535i	$-0.477644\pi$
$929$	4.27777	0.140349	0.0701745	+	0.997535i	$0.477644\pi$
$930$	1.92642	0.0631698
$931$	0	0
$932$	−10.0291	−0.328515
$933$	−8.20696	−0.268684
$934$	−5.00733	−0.163845
$935$	1.24705	0.0407829
$936$	18.3038	0.598277
$937$	59.1093	1.93102	0.965508	−	0.260374i	$-0.0838460\pi$
$937$	59.1093	1.93102	0.965508	+	0.260374i	$0.0838460\pi$
$938$	0	0
$939$	−67.4106	−2.19986
$940$	3.18735	0.103960
$941$	−35.6173	−1.16109	−0.580545	−	0.814228i	$-0.697161\pi$
$941$	−35.6173	−1.16109	−0.580545	+	0.814228i	$0.697161\pi$
$942$	24.0774	0.784483
$943$	−47.0554	−1.53233
$944$	14.7537	0.480191
$945$	0	0
$946$	−0.418887	−0.0136192
$947$	−56.0906	−1.82270	−0.911349	−	0.411634i	$-0.864958\pi$
$947$	−56.0906	−1.82270	−0.911349	+	0.411634i	$0.864958\pi$
$948$	−10.8843	−0.353504
$949$	26.5249	0.861034
$950$	−41.6151	−1.35017
$951$	−33.1034	−1.07345
$952$	0	0
$953$	30.7780	0.996998	0.498499	−	0.866890i	$-0.333885\pi$
$953$	30.7780	0.996998	0.498499	+	0.866890i	$0.333885\pi$
$954$	1.12701	0.0364882
$955$	−2.22190	−0.0718989
$956$	−0.920380	−0.0297672
$957$	−5.21070	−0.168438
$958$	−35.2838	−1.13997
$959$	0	0
$960$	−0.632619	−0.0204177
$961$	−21.7271	−0.700873
$962$	−45.9370	−1.48107
$963$	28.7719	0.927162
$964$	7.64883	0.246352
$965$	−3.43623	−0.110616
$966$	0	0
$967$	18.2916	0.588217	0.294108	−	0.955772i	$-0.404977\pi$
$967$	18.2916	0.588217	0.294108	+	0.955772i	$0.404977\pi$
$968$	6.38780	0.205312
$969$	45.5930	1.46466
$970$	0.0739133	0.00237321
$971$	−19.2108	−0.616503	−0.308251	−	0.951305i	$-0.599744\pi$
$971$	−19.2108	−0.616503	−0.308251	+	0.951305i	$0.599744\pi$
$972$	−21.8055	−0.699413
$973$	0	0
$974$	−4.73153	−0.151608
$975$	75.8718	2.42984
$976$	9.83960	0.314958
$977$	11.6484	0.372665	0.186332	−	0.982487i	$-0.440340\pi$
$977$	11.6484	0.372665	0.186332	+	0.982487i	$0.440340\pi$
$978$	−16.3837	−0.523894
$979$	−25.3865	−0.811357
$980$	0	0
$981$	−28.3628	−0.905555
$982$	18.5337	0.591433
$983$	1.00446	0.0320372	0.0160186	−	0.999872i	$-0.494901\pi$
$983$	1.00446	0.0320372	0.0160186	+	0.999872i	$0.494901\pi$
$984$	26.0345	0.829950
$985$	1.55635	0.0495895
$986$	−2.22705	−0.0709236
$987$	0	0
$988$	53.4983	1.70201
$989$	0.855353	0.0271986
$990$	1.61652	0.0513764
$991$	−47.5781	−1.51137	−0.755684	−	0.654936i	$-0.772695\pi$
$991$	−47.5781	−1.51137	−0.755684	+	0.654936i	$0.772695\pi$
$992$	−3.04515	−0.0966836
$993$	−29.4979	−0.936088
$994$	0	0
$995$	3.47599	0.110196
$996$	−4.64365	−0.147140
$997$	13.6822	0.433320	0.216660	−	0.976247i	$-0.430484\pi$
$997$	13.6822	0.433320	0.216660	+	0.976247i	$0.430484\pi$
$998$	8.49139	0.268790
$999$	1.98874	0.0629211

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.t.1.5		5
7.2	even	3		406.2.e.d.291.1	yes	10
7.4	even	3		406.2.e.d.233.1	✓	10
7.6	odd	2		2842.2.a.u.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.d.233.1	✓	10	7.4	even	3
406.2.e.d.291.1	yes	10	7.2	even	3
2842.2.a.t.1.5		5	1.1	even	1	trivial
2842.2.a.u.1.1		5	7.6	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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.42629 q^{3} +1.00000 q^{4} -0.260736 q^{5} -2.42629 q^{6} -1.00000 q^{8} +2.88687 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.42629 q^{3} +1.00000 q^{4} -0.260736 q^{5} -2.42629 q^{6} -1.00000 q^{8} +2.88687 q^{9} +0.260736 q^{10} +2.14760 q^{11} +2.42629 q^{12} -6.34036 q^{13} -0.632619 q^{15} +1.00000 q^{16} -2.22705 q^{17} -2.88687 q^{18} -8.43775 q^{19} -0.260736 q^{20} -2.14760 q^{22} +4.38533 q^{23} -2.42629 q^{24} -4.93202 q^{25} +6.34036 q^{26} -0.274492 q^{27} -1.00000 q^{29} +0.632619 q^{30} +3.04515 q^{31} -1.00000 q^{32} +5.21070 q^{33} +2.22705 q^{34} +2.88687 q^{36} -7.24517 q^{37} +8.43775 q^{38} -15.3835 q^{39} +0.260736 q^{40} -10.7302 q^{41} +0.195049 q^{43} +2.14760 q^{44} -0.752709 q^{45} -4.38533 q^{46} -12.2245 q^{47} +2.42629 q^{48} +4.93202 q^{50} -5.40345 q^{51} -6.34036 q^{52} -0.390391 q^{53} +0.274492 q^{54} -0.559957 q^{55} -20.4724 q^{57} +1.00000 q^{58} +14.7537 q^{59} -0.632619 q^{60} +9.83960 q^{61} -3.04515 q^{62} +1.00000 q^{64} +1.65316 q^{65} -5.21070 q^{66} +9.53790 q^{67} -2.22705 q^{68} +10.6401 q^{69} +2.18856 q^{71} -2.88687 q^{72} -4.18350 q^{73} +7.24517 q^{74} -11.9665 q^{75} -8.43775 q^{76} +15.3835 q^{78} -4.48597 q^{79} -0.260736 q^{80} -9.32660 q^{81} +10.7302 q^{82} -1.91389 q^{83} +0.580670 q^{85} -0.195049 q^{86} -2.42629 q^{87} -2.14760 q^{88} -11.8209 q^{89} +0.752709 q^{90} +4.38533 q^{92} +7.38841 q^{93} +12.2245 q^{94} +2.20002 q^{95} -2.42629 q^{96} +0.283480 q^{97} +6.19984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9} + q^{10} + 4 q^{11} - 3 q^{12} - 8 q^{15} + 5 q^{16} - 10 q^{17} - 8 q^{18} - 8 q^{19} - q^{20} - 4 q^{22} + 9 q^{23} + 3 q^{24} - 9 q^{27} - 5 q^{29} + 8 q^{30} - 3 q^{31} - 5 q^{32} - 7 q^{33} + 10 q^{34} + 8 q^{36} + 10 q^{37} + 8 q^{38} - 26 q^{39} + q^{40} - 19 q^{41} + 3 q^{43} + 4 q^{44} + 14 q^{45} - 9 q^{46} - 36 q^{47} - 3 q^{48} + 31 q^{51} - 3 q^{53} + 9 q^{54} - 10 q^{55} - 18 q^{57} + 5 q^{58} + 5 q^{59} - 8 q^{60} - 3 q^{61} + 3 q^{62} + 5 q^{64} + 29 q^{65} + 7 q^{66} - 2 q^{67} - 10 q^{68} + 18 q^{69} + 2 q^{71} - 8 q^{72} + 2 q^{73} - 10 q^{74} - 22 q^{75} - 8 q^{76} + 26 q^{78} + 17 q^{79} - q^{80} - 7 q^{81} + 19 q^{82} - 30 q^{83} - 11 q^{85} - 3 q^{86} + 3 q^{87} - 4 q^{88} - 29 q^{89} - 14 q^{90} + 9 q^{92} + 37 q^{93} + 36 q^{94} - 17 q^{95} + 3 q^{96} + 40 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9 + q^10 + 4 * q^11 - 3 * q^12 - 8 * q^15 + 5 * q^16 - 10 * q^17 - 8 * q^18 - 8 * q^19 - q^20 - 4 * q^22 + 9 * q^23 + 3 * q^24 - 9 * q^27 - 5 * q^29 + 8 * q^30 - 3 * q^31 - 5 * q^32 - 7 * q^33 + 10 * q^34 + 8 * q^36 + 10 * q^37 + 8 * q^38 - 26 * q^39 + q^40 - 19 * q^41 + 3 * q^43 + 4 * q^44 + 14 * q^45 - 9 * q^46 - 36 * q^47 - 3 * q^48 + 31 * q^51 - 3 * q^53 + 9 * q^54 - 10 * q^55 - 18 * q^57 + 5 * q^58 + 5 * q^59 - 8 * q^60 - 3 * q^61 + 3 * q^62 + 5 * q^64 + 29 * q^65 + 7 * q^66 - 2 * q^67 - 10 * q^68 + 18 * q^69 + 2 * q^71 - 8 * q^72 + 2 * q^73 - 10 * q^74 - 22 * q^75 - 8 * q^76 + 26 * q^78 + 17 * q^79 - q^80 - 7 * q^81 + 19 * q^82 - 30 * q^83 - 11 * q^85 - 3 * q^86 + 3 * q^87 - 4 * q^88 - 29 * q^89 - 14 * q^90 + 9 * q^92 + 37 * q^93 + 36 * q^94 - 17 * q^95 + 3 * q^96 + 40 * q^99

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