LMFDB - Embedded newform 2842.2.a.z.1.4

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:	$0$
Dimension:	$5$
Coefficient field:	5.5.1019601.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 10x^{3} - x^{2} + 24x + 7 $ x^5 - 10x^3 - x^2 + 24x + 7
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			1.4
Root			$-1.80092$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.40697 q^{3} +1.00000 q^{4} -2.20789 q^{5} +2.40697 q^{6} +1.00000 q^{8} +2.79350 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.40697 q^{3} +1.00000 q^{4} -2.20789 q^{5} +2.40697 q^{6} +1.00000 q^{8} +2.79350 q^{9} -2.20789 q^{10} -1.18745 q^{11} +2.40697 q^{12} +1.24330 q^{13} -5.31432 q^{15} +1.00000 q^{16} +5.96459 q^{17} +2.79350 q^{18} +2.19486 q^{19} -2.20789 q^{20} -1.18745 q^{22} +7.74172 q^{23} +2.40697 q^{24} -0.125238 q^{25} +1.24330 q^{26} -0.497031 q^{27} -1.00000 q^{29} -5.31432 q^{30} +9.31097 q^{31} +1.00000 q^{32} -2.85816 q^{33} +5.96459 q^{34} +2.79350 q^{36} -6.90400 q^{37} +2.19486 q^{38} +2.99259 q^{39} -2.20789 q^{40} +10.1520 q^{41} -5.76077 q^{43} -1.18745 q^{44} -6.16774 q^{45} +7.74172 q^{46} -5.82274 q^{47} +2.40697 q^{48} -0.125238 q^{50} +14.3566 q^{51} +1.24330 q^{52} +1.68146 q^{53} -0.497031 q^{54} +2.62175 q^{55} +5.28297 q^{57} -1.00000 q^{58} -7.97761 q^{59} -5.31432 q^{60} +8.11523 q^{61} +9.31097 q^{62} +1.00000 q^{64} -2.74507 q^{65} -2.85816 q^{66} +12.1445 q^{67} +5.96459 q^{68} +18.6341 q^{69} +4.61064 q^{71} +2.79350 q^{72} +0.0394827 q^{73} -6.90400 q^{74} -0.301444 q^{75} +2.19486 q^{76} +2.99259 q^{78} -2.42334 q^{79} -2.20789 q^{80} -9.57685 q^{81} +10.1520 q^{82} +5.46282 q^{83} -13.1691 q^{85} -5.76077 q^{86} -2.40697 q^{87} -1.18745 q^{88} -7.26832 q^{89} -6.16774 q^{90} +7.74172 q^{92} +22.4112 q^{93} -5.82274 q^{94} -4.84601 q^{95} +2.40697 q^{96} +3.23923 q^{97} -3.31715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 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 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9	$ 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9} + 7 q^{10} + 3 q^{12} + 10 q^{13} - 10 q^{15} + 5 q^{16} + 8 q^{17} + 8 q^{18} + 2 q^{19} + 7 q^{20} + q^{23} + 3 q^{24} + 12 q^{25} + 10 q^{26} + 15 q^{27} - 5 q^{29} - 10 q^{30} + 11 q^{31} + 5 q^{32} + 9 q^{33} + 8 q^{34} + 8 q^{36} - 8 q^{37} + 2 q^{38} + 18 q^{39} + 7 q^{40} + 23 q^{41} - 3 q^{43} + 4 q^{45} + q^{46} + 16 q^{47} + 3 q^{48} + 12 q^{50} + 7 q^{51} + 10 q^{52} + 7 q^{53} + 15 q^{54} + 6 q^{55} - 34 q^{57} - 5 q^{58} - 9 q^{59} - 10 q^{60} + 15 q^{61} + 11 q^{62} + 5 q^{64} + 5 q^{65} + 9 q^{66} - 4 q^{67} + 8 q^{68} + 14 q^{69} - 22 q^{71} + 8 q^{72} - 8 q^{74} - 34 q^{75} + 2 q^{76} + 18 q^{78} - 13 q^{79} + 7 q^{80} + 17 q^{81} + 23 q^{82} + 28 q^{83} - 7 q^{85} - 3 q^{86} - 3 q^{87} + 17 q^{89} + 4 q^{90} + q^{92} + 17 q^{93} + 16 q^{94} - 9 q^{95} + 3 q^{96} + 42 q^{97} - 42 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9 + 7 * q^10 + 3 * q^12 + 10 * q^13 - 10 * q^15 + 5 * q^16 + 8 * q^17 + 8 * q^18 + 2 * q^19 + 7 * q^20 + q^23 + 3 * q^24 + 12 * q^25 + 10 * q^26 + 15 * q^27 - 5 * q^29 - 10 * q^30 + 11 * q^31 + 5 * q^32 + 9 * q^33 + 8 * q^34 + 8 * q^36 - 8 * q^37 + 2 * q^38 + 18 * q^39 + 7 * q^40 + 23 * q^41 - 3 * q^43 + 4 * q^45 + q^46 + 16 * q^47 + 3 * q^48 + 12 * q^50 + 7 * q^51 + 10 * q^52 + 7 * q^53 + 15 * q^54 + 6 * q^55 - 34 * q^57 - 5 * q^58 - 9 * q^59 - 10 * q^60 + 15 * q^61 + 11 * q^62 + 5 * q^64 + 5 * q^65 + 9 * q^66 - 4 * q^67 + 8 * q^68 + 14 * q^69 - 22 * q^71 + 8 * q^72 - 8 * q^74 - 34 * q^75 + 2 * q^76 + 18 * q^78 - 13 * q^79 + 7 * q^80 + 17 * q^81 + 23 * q^82 + 28 * q^83 - 7 * q^85 - 3 * q^86 - 3 * q^87 + 17 * q^89 + 4 * q^90 + q^92 + 17 * q^93 + 16 * q^94 - 9 * q^95 + 3 * q^96 + 42 * q^97 - 42 * 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
$3$	2.40697	1.38966	0.694832	−	0.719172i	$-0.255479\pi$
$3$	2.40697	1.38966	0.694832	+	0.719172i	$0.255479\pi$
$4$	1.00000	0.500000
$5$	−2.20789	−0.987397	−0.493698	−	0.869633i	$-0.664355\pi$
$5$	−2.20789	−0.987397	−0.493698	+	0.869633i	$0.664355\pi$
$6$	2.40697	0.982641
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	2.79350	0.931168
$10$	−2.20789	−0.698195
$11$	−1.18745	−0.358030	−0.179015	−	0.983846i	$-0.557291\pi$
$11$	−1.18745	−0.358030	−0.179015	+	0.983846i	$0.557291\pi$
$12$	2.40697	0.694832
$13$	1.24330	0.344830	0.172415	−	0.985024i	$-0.444843\pi$
$13$	1.24330	0.344830	0.172415	+	0.985024i	$0.444843\pi$
$14$	0	0
$15$	−5.31432	−1.37215
$16$	1.00000	0.250000
$17$	5.96459	1.44662	0.723312	−	0.690521i	$-0.242619\pi$
$17$	5.96459	1.44662	0.723312	+	0.690521i	$0.242619\pi$
$18$	2.79350	0.658435
$19$	2.19486	0.503536	0.251768	−	0.967788i	$-0.418988\pi$
$19$	2.19486	0.503536	0.251768	+	0.967788i	$0.418988\pi$
$20$	−2.20789	−0.493698
$21$	0	0
$22$	−1.18745	−0.253165
$23$	7.74172	1.61426	0.807130	−	0.590373i	$-0.201020\pi$
$23$	7.74172	1.61426	0.807130	+	0.590373i	$0.201020\pi$
$24$	2.40697	0.491321
$25$	−0.125238	−0.0250476
$26$	1.24330	0.243831
$27$	−0.497031	−0.0956537
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−5.31432	−0.970257
$31$	9.31097	1.67230	0.836150	−	0.548501i	$-0.184801\pi$
$31$	9.31097	1.67230	0.836150	+	0.548501i	$0.184801\pi$
$32$	1.00000	0.176777
$33$	−2.85816	−0.497541
$34$	5.96459	1.02292
$35$	0	0
$36$	2.79350	0.465584
$37$	−6.90400	−1.13501	−0.567505	−	0.823370i	$-0.692091\pi$
$37$	−6.90400	−1.13501	−0.567505	+	0.823370i	$0.692091\pi$
$38$	2.19486	0.356054
$39$	2.99259	0.479197
$40$	−2.20789	−0.349097
$41$	10.1520	1.58548	0.792741	−	0.609559i	$-0.208653\pi$
$41$	10.1520	1.58548	0.792741	+	0.609559i	$0.208653\pi$
$42$	0	0
$43$	−5.76077	−0.878509	−0.439254	−	0.898363i	$-0.644757\pi$
$43$	−5.76077	−0.878509	−0.439254	+	0.898363i	$0.644757\pi$
$44$	−1.18745	−0.179015
$45$	−6.16774	−0.919432
$46$	7.74172	1.14145
$47$	−5.82274	−0.849334	−0.424667	−	0.905350i	$-0.639609\pi$
$47$	−5.82274	−0.849334	−0.424667	+	0.905350i	$0.639609\pi$
$48$	2.40697	0.347416
$49$	0	0
$50$	−0.125238	−0.0177113
$51$	14.3566	2.01032
$52$	1.24330	0.172415
$53$	1.68146	0.230967	0.115483	−	0.993309i	$-0.463158\pi$
$53$	1.68146	0.230967	0.115483	+	0.993309i	$0.463158\pi$
$54$	−0.497031	−0.0676374
$55$	2.62175	0.353517
$56$	0	0
$57$	5.28297	0.699746
$58$	−1.00000	−0.131306
$59$	−7.97761	−1.03860	−0.519298	−	0.854593i	$-0.673807\pi$
$59$	−7.97761	−1.03860	−0.519298	+	0.854593i	$0.673807\pi$
$60$	−5.31432	−0.686075
$61$	8.11523	1.03905	0.519524	−	0.854456i	$-0.326109\pi$
$61$	8.11523	1.03905	0.519524	+	0.854456i	$0.326109\pi$
$62$	9.31097	1.18249
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.74507	−0.340484
$66$	−2.85816	−0.351815
$67$	12.1445	1.48368	0.741842	−	0.670575i	$-0.233953\pi$
$67$	12.1445	1.48368	0.741842	+	0.670575i	$0.233953\pi$
$68$	5.96459	0.723312
$69$	18.6341	2.24328
$70$	0	0
$71$	4.61064	0.547182	0.273591	−	0.961846i	$-0.411789\pi$
$71$	4.61064	0.547182	0.273591	+	0.961846i	$0.411789\pi$
$72$	2.79350	0.329218
$73$	0.0394827	0.00462110	0.00231055	−	0.999997i	$-0.499265\pi$
$73$	0.0394827	0.00462110	0.00231055	+	0.999997i	$0.499265\pi$
$74$	−6.90400	−0.802574
$75$	−0.301444	−0.0348078
$76$	2.19486	0.251768
$77$	0	0
$78$	2.99259	0.338844
$79$	−2.42334	−0.272647	−0.136323	−	0.990664i	$-0.543529\pi$
$79$	−2.42334	−0.272647	−0.136323	+	0.990664i	$0.543529\pi$
$80$	−2.20789	−0.246849
$81$	−9.57685	−1.06409
$82$	10.1520	1.12110
$83$	5.46282	0.599622	0.299811	−	0.953999i	$-0.403076\pi$
$83$	5.46282	0.599622	0.299811	+	0.953999i	$0.403076\pi$
$84$	0	0
$85$	−13.1691	−1.42839
$86$	−5.76077	−0.621200
$87$	−2.40697	−0.258054
$88$	−1.18745	−0.126583
$89$	−7.26832	−0.770440	−0.385220	−	0.922825i	$-0.625874\pi$
$89$	−7.26832	−0.770440	−0.385220	+	0.922825i	$0.625874\pi$
$90$	−6.16774	−0.650137
$91$	0	0
$92$	7.74172	0.807130
$93$	22.4112	2.32394
$94$	−5.82274	−0.600570
$95$	−4.84601	−0.497190
$96$	2.40697	0.245660
$97$	3.23923	0.328894	0.164447	−	0.986386i	$-0.447416\pi$
$97$	3.23923	0.328894	0.164447	+	0.986386i	$0.447416\pi$
$98$	0	0
$99$	−3.31715	−0.333386
$100$	−0.125238	−0.0125238
$101$	9.00718	0.896247	0.448124	−	0.893972i	$-0.352092\pi$
$101$	9.00718	0.896247	0.448124	+	0.893972i	$0.352092\pi$
$102$	14.3566	1.42151
$103$	6.22971	0.613832	0.306916	−	0.951737i	$-0.400703\pi$
$103$	6.22971	0.613832	0.306916	+	0.951737i	$0.400703\pi$
$104$	1.24330	0.121916
$105$	0	0
$106$	1.68146	0.163318
$107$	−16.2648	−1.57238	−0.786189	−	0.617986i	$-0.787949\pi$
$107$	−16.2648	−1.57238	−0.786189	+	0.617986i	$0.787949\pi$
$108$	−0.497031	−0.0478269
$109$	−2.87281	−0.275165	−0.137582	−	0.990490i	$-0.543933\pi$
$109$	−2.87281	−0.275165	−0.137582	+	0.990490i	$0.543933\pi$
$110$	2.62175	0.249975
$111$	−16.6177	−1.57728
$112$	0	0
$113$	−1.01001	−0.0950134	−0.0475067	−	0.998871i	$-0.515128\pi$
$113$	−1.01001	−0.0950134	−0.0475067	+	0.998871i	$0.515128\pi$
$114$	5.28297	0.494795
$115$	−17.0928	−1.59392
$116$	−1.00000	−0.0928477
$117$	3.47316	0.321094
$118$	−7.97761	−0.734398
$119$	0	0
$120$	−5.31432	−0.485128
$121$	−9.58996	−0.871815
$122$	8.11523	0.734719
$123$	24.4356	2.20329
$124$	9.31097	0.836150
$125$	11.3159	1.01213
$126$	0	0
$127$	4.78015	0.424170	0.212085	−	0.977251i	$-0.431975\pi$
$127$	4.78015	0.424170	0.212085	+	0.977251i	$0.431975\pi$
$128$	1.00000	0.0883883
$129$	−13.8660	−1.22083
$130$	−2.74507	−0.240758
$131$	−10.8450	−0.947528	−0.473764	−	0.880652i	$-0.657105\pi$
$131$	−10.8450	−0.947528	−0.473764	+	0.880652i	$0.657105\pi$
$132$	−2.85816	−0.248771
$133$	0	0
$134$	12.1445	1.04912
$135$	1.09739	0.0944482
$136$	5.96459	0.511459
$137$	−0.620466	−0.0530100	−0.0265050	−	0.999649i	$-0.508438\pi$
$137$	−0.620466	−0.0530100	−0.0265050	+	0.999649i	$0.508438\pi$
$138$	18.6341	1.58624
$139$	−10.8612	−0.921233	−0.460616	−	0.887599i	$-0.652372\pi$
$139$	−10.8612	−0.921233	−0.460616	+	0.887599i	$0.652372\pi$
$140$	0	0
$141$	−14.0152	−1.18029
$142$	4.61064	0.386916
$143$	−1.47636	−0.123459
$144$	2.79350	0.232792
$145$	2.20789	0.183355
$146$	0.0394827	0.00326761
$147$	0	0
$148$	−6.90400	−0.567505
$149$	−6.98665	−0.572369	−0.286184	−	0.958175i	$-0.592387\pi$
$149$	−6.98665	−0.572369	−0.286184	+	0.958175i	$0.592387\pi$
$150$	−0.301444	−0.0246128
$151$	6.84496	0.557035	0.278517	−	0.960431i	$-0.410157\pi$
$151$	6.84496	0.557035	0.278517	+	0.960431i	$0.410157\pi$
$152$	2.19486	0.178027
$153$	16.6621	1.34705
$154$	0	0
$155$	−20.5576	−1.65122
$156$	2.99259	0.239599
$157$	18.3243	1.46244	0.731220	−	0.682141i	$-0.238951\pi$
$157$	18.3243	1.46244	0.731220	+	0.682141i	$0.238951\pi$
$158$	−2.42334	−0.192790
$159$	4.04723	0.320967
$160$	−2.20789	−0.174549
$161$	0	0
$162$	−9.57685	−0.752428
$163$	−20.6653	−1.61863	−0.809315	−	0.587375i	$-0.800161\pi$
$163$	−20.6653	−1.61863	−0.809315	+	0.587375i	$0.800161\pi$
$164$	10.1520	0.792741
$165$	6.31048	0.491271
$166$	5.46282	0.423997
$167$	21.9158	1.69590	0.847949	−	0.530079i	$-0.177838\pi$
$167$	21.9158	1.69590	0.847949	+	0.530079i	$0.177838\pi$
$168$	0	0
$169$	−11.4542	−0.881093
$170$	−13.1691	−1.01003
$171$	6.13136	0.468877
$172$	−5.76077	−0.439254
$173$	−14.1727	−1.07753	−0.538764	−	0.842457i	$-0.681108\pi$
$173$	−14.1727	−1.07753	−0.538764	+	0.842457i	$0.681108\pi$
$174$	−2.40697	−0.182472
$175$	0	0
$176$	−1.18745	−0.0895074
$177$	−19.2019	−1.44330
$178$	−7.26832	−0.544784
$179$	−22.3800	−1.67276	−0.836381	−	0.548149i	$-0.815333\pi$
$179$	−22.3800	−1.67276	−0.836381	+	0.548149i	$0.815333\pi$
$180$	−6.16774	−0.459716
$181$	−15.5160	−1.15330	−0.576649	−	0.816992i	$-0.695640\pi$
$181$	−15.5160	−1.15330	−0.576649	+	0.816992i	$0.695640\pi$
$182$	0	0
$183$	19.5331	1.44393
$184$	7.74172	0.570727
$185$	15.2432	1.12071
$186$	22.4112	1.64327
$187$	−7.08265	−0.517935
$188$	−5.82274	−0.424667
$189$	0	0
$190$	−4.84601	−0.351566
$191$	7.95133	0.575338	0.287669	−	0.957730i	$-0.407120\pi$
$191$	7.95133	0.575338	0.287669	+	0.957730i	$0.407120\pi$
$192$	2.40697	0.173708
$193$	−3.38051	−0.243334	−0.121667	−	0.992571i	$-0.538824\pi$
$193$	−3.38051	−0.243334	−0.121667	+	0.992571i	$0.538824\pi$
$194$	3.23923	0.232563
$195$	−6.60729	−0.473158
$196$	0	0
$197$	0.885106	0.0630612	0.0315306	−	0.999503i	$-0.489962\pi$
$197$	0.885106	0.0630612	0.0315306	+	0.999503i	$0.489962\pi$
$198$	−3.31715	−0.235739
$199$	11.6138	0.823281	0.411640	−	0.911346i	$-0.364956\pi$
$199$	11.6138	0.823281	0.411640	+	0.911346i	$0.364956\pi$
$200$	−0.125238	−0.00885567
$201$	29.2314	2.06182
$202$	9.00718	0.633743
$203$	0	0
$204$	14.3566	1.00516
$205$	−22.4145	−1.56550
$206$	6.22971	0.434045
$207$	21.6265	1.50315
$208$	1.24330	0.0862074
$209$	−2.60629	−0.180281
$210$	0	0
$211$	−24.0646	−1.65668	−0.828338	−	0.560229i	$-0.810713\pi$
$211$	−24.0646	−1.65668	−0.828338	+	0.560229i	$0.810713\pi$
$212$	1.68146	0.115483
$213$	11.0977	0.760399
$214$	−16.2648	−1.11184
$215$	12.7191	0.867437
$216$	−0.497031	−0.0338187
$217$	0	0
$218$	−2.87281	−0.194571
$219$	0.0950337	0.00642178
$220$	2.62175	0.176759
$221$	7.41577	0.498839
$222$	−16.6177	−1.11531
$223$	3.62968	0.243062	0.121531	−	0.992588i	$-0.461220\pi$
$223$	3.62968	0.243062	0.121531	+	0.992588i	$0.461220\pi$
$224$	0	0
$225$	−0.349853	−0.0233235
$226$	−1.01001	−0.0671846
$227$	12.6807	0.841649	0.420825	−	0.907142i	$-0.361741\pi$
$227$	12.6807	0.841649	0.420825	+	0.907142i	$0.361741\pi$
$228$	5.28297	0.349873
$229$	−19.9214	−1.31645	−0.658223	−	0.752823i	$-0.728691\pi$
$229$	−19.9214	−1.31645	−0.658223	+	0.752823i	$0.728691\pi$
$230$	−17.0928	−1.12707
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	−13.6959	−0.897247	−0.448623	−	0.893721i	$-0.648086\pi$
$233$	−13.6959	−0.897247	−0.448623	+	0.893721i	$0.648086\pi$
$234$	3.47316	0.227048
$235$	12.8560	0.838630
$236$	−7.97761	−0.519298
$237$	−5.83290	−0.378888
$238$	0	0
$239$	16.6929	1.07977	0.539886	−	0.841738i	$-0.318467\pi$
$239$	16.6929	1.07977	0.539886	+	0.841738i	$0.318467\pi$
$240$	−5.31432	−0.343038
$241$	−16.8099	−1.08282	−0.541411	−	0.840758i	$-0.682110\pi$
$241$	−16.8099	−1.08282	−0.541411	+	0.840758i	$0.682110\pi$
$242$	−9.58996	−0.616466
$243$	−21.5601	−1.38308
$244$	8.11523	0.519524
$245$	0	0
$246$	24.4356	1.55796
$247$	2.72887	0.173634
$248$	9.31097	0.591247
$249$	13.1488	0.833274
$250$	11.3159	0.715683
$251$	−3.73348	−0.235655	−0.117828	−	0.993034i	$-0.537593\pi$
$251$	−3.73348	−0.235655	−0.117828	+	0.993034i	$0.537593\pi$
$252$	0	0
$253$	−9.19291	−0.577953
$254$	4.78015	0.299933
$255$	−31.6977	−1.98499
$256$	1.00000	0.0625000
$257$	30.5436	1.90526	0.952630	−	0.304132i	$-0.0983664\pi$
$257$	30.5436	1.90526	0.952630	+	0.304132i	$0.0983664\pi$
$258$	−13.8660	−0.863259
$259$	0	0
$260$	−2.74507	−0.170242
$261$	−2.79350	−0.172914
$262$	−10.8450	−0.670004
$263$	−16.6182	−1.02472	−0.512361	−	0.858770i	$-0.671229\pi$
$263$	−16.6182	−1.02472	−0.512361	+	0.858770i	$0.671229\pi$
$264$	−2.85816	−0.175907
$265$	−3.71248	−0.228056
$266$	0	0
$267$	−17.4946	−1.07065
$268$	12.1445	0.741842
$269$	−15.3894	−0.938308	−0.469154	−	0.883116i	$-0.655441\pi$
$269$	−15.3894	−0.938308	−0.469154	+	0.883116i	$0.655441\pi$
$270$	1.09739	0.0667849
$271$	−22.9214	−1.39237	−0.696187	−	0.717860i	$-0.745122\pi$
$271$	−22.9214	−1.39237	−0.696187	+	0.717860i	$0.745122\pi$
$272$	5.96459	0.361656
$273$	0	0
$274$	−0.620466	−0.0374837
$275$	0.148714	0.00896779
$276$	18.6341	1.12164
$277$	−24.0528	−1.44519	−0.722596	−	0.691270i	$-0.757051\pi$
$277$	−24.0528	−1.44519	−0.722596	+	0.691270i	$0.757051\pi$
$278$	−10.8612	−0.651410
$279$	26.0102	1.55719
$280$	0	0
$281$	1.73325	0.103397	0.0516984	−	0.998663i	$-0.483537\pi$
$281$	1.73325	0.103397	0.0516984	+	0.998663i	$0.483537\pi$
$282$	−14.0152	−0.834591
$283$	−17.6940	−1.05180	−0.525899	−	0.850547i	$-0.676271\pi$
$283$	−17.6940	−1.05180	−0.525899	+	0.850547i	$0.676271\pi$
$284$	4.61064	0.273591
$285$	−11.6642	−0.690927
$286$	−1.47636	−0.0872988
$287$	0	0
$288$	2.79350	0.164609
$289$	18.5763	1.09272
$290$	2.20789	0.129652
$291$	7.79673	0.457053
$292$	0.0394827	0.00231055
$293$	−26.8620	−1.56929	−0.784647	−	0.619942i	$-0.787156\pi$
$293$	−26.8620	−1.56929	−0.784647	+	0.619942i	$0.787156\pi$
$294$	0	0
$295$	17.6137	1.02551
$296$	−6.90400	−0.401287
$297$	0.590200	0.0342469
$298$	−6.98665	−0.404726
$299$	9.62529	0.556645
$300$	−0.301444	−0.0174039
$301$	0	0
$302$	6.84496	0.393883
$303$	21.6800	1.24548
$304$	2.19486	0.125884
$305$	−17.9175	−1.02595
$306$	16.6621	0.952508
$307$	−14.3480	−0.818881	−0.409440	−	0.912337i	$-0.634276\pi$
$307$	−14.3480	−0.818881	−0.409440	+	0.912337i	$0.634276\pi$
$308$	0	0
$309$	14.9947	0.853020
$310$	−20.5576	−1.16759
$311$	1.63601	0.0927696	0.0463848	−	0.998924i	$-0.485230\pi$
$311$	1.63601	0.0927696	0.0463848	+	0.998924i	$0.485230\pi$
$312$	2.99259	0.169422
$313$	0.732076	0.0413794	0.0206897	−	0.999786i	$-0.493414\pi$
$313$	0.732076	0.0413794	0.0206897	+	0.999786i	$0.493414\pi$
$314$	18.3243	1.03410
$315$	0	0
$316$	−2.42334	−0.136323
$317$	19.7271	1.10798	0.553992	−	0.832522i	$-0.313104\pi$
$317$	19.7271	1.10798	0.553992	+	0.832522i	$0.313104\pi$
$318$	4.04723	0.226958
$319$	1.18745	0.0664844
$320$	−2.20789	−0.123425
$321$	−39.1489	−2.18508
$322$	0	0
$323$	13.0915	0.728428
$324$	−9.57685	−0.532047
$325$	−0.155709	−0.00863715
$326$	−20.6653	−1.14454
$327$	−6.91476	−0.382387
$328$	10.1520	0.560552
$329$	0	0
$330$	6.31048	0.347381
$331$	33.3950	1.83555	0.917776	−	0.397097i	$-0.129983\pi$
$331$	33.3950	1.83555	0.917776	+	0.397097i	$0.129983\pi$
$332$	5.46282	0.299811
$333$	−19.2863	−1.05689
$334$	21.9158	1.19918
$335$	−26.8136	−1.46498
$336$	0	0
$337$	−10.5851	−0.576607	−0.288304	−	0.957539i	$-0.593091\pi$
$337$	−10.5851	−0.576607	−0.288304	+	0.957539i	$0.593091\pi$
$338$	−11.4542	−0.623027
$339$	−2.43105	−0.132037
$340$	−13.1691	−0.714196
$341$	−11.0563	−0.598733
$342$	6.13136	0.331546
$343$	0	0
$344$	−5.76077	−0.310600
$345$	−41.1420	−2.21501
$346$	−14.1727	−0.761927
$347$	23.3463	1.25330	0.626648	−	0.779302i	$-0.284426\pi$
$347$	23.3463	1.25330	0.626648	+	0.779302i	$0.284426\pi$
$348$	−2.40697	−0.129027
$349$	7.42792	0.397607	0.198804	−	0.980039i	$-0.436294\pi$
$349$	7.42792	0.397607	0.198804	+	0.980039i	$0.436294\pi$
$350$	0	0
$351$	−0.617959	−0.0329842
$352$	−1.18745	−0.0632913
$353$	−32.5393	−1.73189	−0.865946	−	0.500137i	$-0.833283\pi$
$353$	−32.5393	−1.73189	−0.865946	+	0.500137i	$0.833283\pi$
$354$	−19.2019	−1.02057
$355$	−10.1798	−0.540286
$356$	−7.26832	−0.385220
$357$	0	0
$358$	−22.3800	−1.18282
$359$	7.25600	0.382957	0.191478	−	0.981497i	$-0.438672\pi$
$359$	7.25600	0.382957	0.191478	+	0.981497i	$0.438672\pi$
$360$	−6.16774	−0.325068
$361$	−14.1826	−0.746451
$362$	−15.5160	−0.815504
$363$	−23.0827	−1.21153
$364$	0	0
$365$	−0.0871733	−0.00456286
$366$	19.5331	1.02101
$367$	−24.1847	−1.26243	−0.631215	−	0.775608i	$-0.717443\pi$
$367$	−24.1847	−1.26243	−0.631215	+	0.775608i	$0.717443\pi$
$368$	7.74172	0.403565
$369$	28.3597	1.47635
$370$	15.2432	0.792459
$371$	0	0
$372$	22.4112	1.16197
$373$	−24.0550	−1.24552	−0.622759	−	0.782414i	$-0.713988\pi$
$373$	−24.0550	−1.24552	−0.622759	+	0.782414i	$0.713988\pi$
$374$	−7.08265	−0.366235
$375$	27.2371	1.40652
$376$	−5.82274	−0.300285
$377$	−1.24330	−0.0640332
$378$	0	0
$379$	27.4551	1.41027	0.705137	−	0.709071i	$-0.250885\pi$
$379$	27.4551	1.41027	0.705137	+	0.709071i	$0.250885\pi$
$380$	−4.84601	−0.248595
$381$	11.5057	0.589454
$382$	7.95133	0.406825
$383$	−1.30301	−0.0665807	−0.0332904	−	0.999446i	$-0.510599\pi$
$383$	−1.30301	−0.0665807	−0.0332904	+	0.999446i	$0.510599\pi$
$384$	2.40697	0.122830
$385$	0	0
$386$	−3.38051	−0.172063
$387$	−16.0927	−0.818039
$388$	3.23923	0.164447
$389$	17.1482	0.869449	0.434724	−	0.900564i	$-0.356846\pi$
$389$	17.1482	0.869449	0.434724	+	0.900564i	$0.356846\pi$
$390$	−6.60729	−0.334573
$391$	46.1762	2.33523
$392$	0	0
$393$	−26.1035	−1.31675
$394$	0.885106	0.0445910
$395$	5.35045	0.269211
$396$	−3.31715	−0.166693
$397$	−19.3432	−0.970809	−0.485404	−	0.874290i	$-0.661328\pi$
$397$	−19.3432	−0.970809	−0.485404	+	0.874290i	$0.661328\pi$
$398$	11.6138	0.582147
$399$	0	0
$400$	−0.125238	−0.00626190
$401$	32.6583	1.63088	0.815440	−	0.578842i	$-0.196495\pi$
$401$	32.6583	1.63088	0.815440	+	0.578842i	$0.196495\pi$
$402$	29.2314	1.45793
$403$	11.5763	0.576658
$404$	9.00718	0.448124
$405$	21.1446	1.05068
$406$	0	0
$407$	8.19816	0.406368
$408$	14.3566	0.710756
$409$	4.34907	0.215048	0.107524	−	0.994202i	$-0.465708\pi$
$409$	4.34907	0.215048	0.107524	+	0.994202i	$0.465708\pi$
$410$	−22.4145	−1.10698
$411$	−1.49344	−0.0736661
$412$	6.22971	0.306916
$413$	0	0
$414$	21.6265	1.06289
$415$	−12.0613	−0.592065
$416$	1.24330	0.0609578
$417$	−26.1425	−1.28020
$418$	−2.60629	−0.127478
$419$	18.3596	0.896925	0.448462	−	0.893802i	$-0.351972\pi$
$419$	18.3596	0.896925	0.448462	+	0.893802i	$0.351972\pi$
$420$	0	0
$421$	2.64832	0.129071	0.0645355	−	0.997915i	$-0.479443\pi$
$421$	2.64832	0.129071	0.0645355	+	0.997915i	$0.479443\pi$
$422$	−24.0646	−1.17145
$423$	−16.2659	−0.790873
$424$	1.68146	0.0816591
$425$	−0.746993	−0.0362345
$426$	11.0977	0.537683
$427$	0	0
$428$	−16.2648	−0.786189
$429$	−3.55355	−0.171567
$430$	12.7191	0.613370
$431$	1.64865	0.0794128	0.0397064	−	0.999211i	$-0.487358\pi$
$431$	1.64865	0.0794128	0.0397064	+	0.999211i	$0.487358\pi$
$432$	−0.497031	−0.0239134
$433$	6.12954	0.294567	0.147284	−	0.989094i	$-0.452947\pi$
$433$	6.12954	0.294567	0.147284	+	0.989094i	$0.452947\pi$
$434$	0	0
$435$	5.31432	0.254802
$436$	−2.87281	−0.137582
$437$	16.9920	0.812839
$438$	0.0950337	0.00454089
$439$	−10.3136	−0.492240	−0.246120	−	0.969239i	$-0.579156\pi$
$439$	−10.3136	−0.492240	−0.246120	+	0.969239i	$0.579156\pi$
$440$	2.62175	0.124987
$441$	0	0
$442$	7.41577	0.352732
$443$	8.40137	0.399161	0.199581	−	0.979881i	$-0.436042\pi$
$443$	8.40137	0.399161	0.199581	+	0.979881i	$0.436042\pi$
$444$	−16.6177	−0.788642
$445$	16.0476	0.760730
$446$	3.62968	0.171870
$447$	−16.8167	−0.795400
$448$	0	0
$449$	9.90897	0.467633	0.233817	−	0.972281i	$-0.424878\pi$
$449$	9.90897	0.467633	0.233817	+	0.972281i	$0.424878\pi$
$450$	−0.349853	−0.0164922
$451$	−12.0550	−0.567650
$452$	−1.01001	−0.0475067
$453$	16.4756	0.774091
$454$	12.6807	0.595136
$455$	0	0
$456$	5.28297	0.247398
$457$	−21.5372	−1.00747	−0.503734	−	0.863859i	$-0.668041\pi$
$457$	−21.5372	−1.00747	−0.503734	+	0.863859i	$0.668041\pi$
$458$	−19.9214	−0.930867
$459$	−2.96459	−0.138375
$460$	−17.0928	−0.796958
$461$	−22.0453	−1.02675	−0.513376	−	0.858164i	$-0.671605\pi$
$461$	−22.0453	−1.02675	−0.513376	+	0.858164i	$0.671605\pi$
$462$	0	0
$463$	−18.1202	−0.842116	−0.421058	−	0.907034i	$-0.638341\pi$
$463$	−18.1202	−0.842116	−0.421058	+	0.907034i	$0.638341\pi$
$464$	−1.00000	−0.0464238
$465$	−49.4814	−2.29465
$466$	−13.6959	−0.634449
$467$	24.8321	1.14909	0.574547	−	0.818471i	$-0.305178\pi$
$467$	24.8321	1.14909	0.574547	+	0.818471i	$0.305178\pi$
$468$	3.47316	0.160547
$469$	0	0
$470$	12.8560	0.593001
$471$	44.1061	2.03230
$472$	−7.97761	−0.367199
$473$	6.84062	0.314532
$474$	−5.83290	−0.267914
$475$	−0.274880	−0.0126124
$476$	0	0
$477$	4.69718	0.215069
$478$	16.6929	0.763514
$479$	12.5423	0.573071	0.286536	−	0.958070i	$-0.407496\pi$
$479$	12.5423	0.573071	0.286536	+	0.958070i	$0.407496\pi$
$480$	−5.31432	−0.242564
$481$	−8.58375	−0.391385
$482$	−16.8099	−0.765670
$483$	0	0
$484$	−9.58996	−0.435907
$485$	−7.15186	−0.324749
$486$	−21.5601	−0.977986
$487$	−15.2869	−0.692714	−0.346357	−	0.938103i	$-0.612581\pi$
$487$	−15.2869	−0.692714	−0.346357	+	0.938103i	$0.612581\pi$
$488$	8.11523	0.367359
$489$	−49.7407	−2.24935
$490$	0	0
$491$	29.0450	1.31078	0.655391	−	0.755290i	$-0.272504\pi$
$491$	29.0450	1.31078	0.655391	+	0.755290i	$0.272504\pi$
$492$	24.4356	1.10164
$493$	−5.96459	−0.268631
$494$	2.72887	0.122778
$495$	7.32388	0.329184
$496$	9.31097	0.418075
$497$	0	0
$498$	13.1488	0.589214
$499$	16.7064	0.747881	0.373941	−	0.927453i	$-0.378006\pi$
$499$	16.7064	0.747881	0.373941	+	0.927453i	$0.378006\pi$
$500$	11.3159	0.506064
$501$	52.7507	2.35673
$502$	−3.73348	−0.166634
$503$	43.1520	1.92405	0.962026	−	0.272959i	$-0.0880025\pi$
$503$	43.1520	1.92405	0.962026	+	0.272959i	$0.0880025\pi$
$504$	0	0
$505$	−19.8868	−0.884952
$506$	−9.19291	−0.408675
$507$	−27.5699	−1.22442
$508$	4.78015	0.212085
$509$	−8.97640	−0.397872	−0.198936	−	0.980013i	$-0.563749\pi$
$509$	−8.97640	−0.397872	−0.198936	+	0.980013i	$0.563749\pi$
$510$	−31.6977	−1.40360
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.09092	−0.0481651
$514$	30.5436	1.34722
$515$	−13.7545	−0.606096
$516$	−13.8660	−0.610416
$517$	6.91422	0.304087
$518$	0	0
$519$	−34.1132	−1.49740
$520$	−2.74507	−0.120379
$521$	20.0148	0.876866	0.438433	−	0.898764i	$-0.355534\pi$
$521$	20.0148	0.876866	0.438433	+	0.898764i	$0.355534\pi$
$522$	−2.79350	−0.122268
$523$	33.8886	1.48185	0.740923	−	0.671589i	$-0.234388\pi$
$523$	33.8886	1.48185	0.740923	+	0.671589i	$0.234388\pi$
$524$	−10.8450	−0.473764
$525$	0	0
$526$	−16.6182	−0.724588
$527$	55.5361	2.41919
$528$	−2.85816	−0.124385
$529$	36.9343	1.60584
$530$	−3.71248	−0.161260
$531$	−22.2855	−0.967107
$532$	0	0
$533$	12.6220	0.546721
$534$	−17.4946	−0.757066
$535$	35.9108	1.55256
$536$	12.1445	0.524561
$537$	−53.8681	−2.32458
$538$	−15.3894	−0.663484
$539$	0	0
$540$	1.09739	0.0472241
$541$	21.7815	0.936460	0.468230	−	0.883607i	$-0.344892\pi$
$541$	21.7815	0.936460	0.468230	+	0.883607i	$0.344892\pi$
$542$	−22.9214	−0.984557
$543$	−37.3466	−1.60270
$544$	5.96459	0.255730
$545$	6.34283	0.271697
$546$	0	0
$547$	−10.7968	−0.461639	−0.230819	−	0.972997i	$-0.574141\pi$
$547$	−10.7968	−0.461639	−0.230819	+	0.972997i	$0.574141\pi$
$548$	−0.620466	−0.0265050
$549$	22.6699	0.967529
$550$	0.148714	0.00634118
$551$	−2.19486	−0.0935043
$552$	18.6341	0.793120
$553$	0	0
$554$	−24.0528	−1.02191
$555$	36.6900	1.55741
$556$	−10.8612	−0.460616
$557$	26.5352	1.12433	0.562166	−	0.827024i	$-0.309968\pi$
$557$	26.5352	1.12433	0.562166	+	0.827024i	$0.309968\pi$
$558$	26.0102	1.10110
$559$	−7.16237	−0.302936
$560$	0	0
$561$	−17.0477	−0.719755
$562$	1.73325	0.0731126
$563$	20.8544	0.878909	0.439455	−	0.898265i	$-0.355172\pi$
$563$	20.8544	0.878909	0.439455	+	0.898265i	$0.355172\pi$
$564$	−14.0152	−0.590145
$565$	2.22998	0.0938159
$566$	−17.6940	−0.743734
$567$	0	0
$568$	4.61064	0.193458
$569$	13.5630	0.568592	0.284296	−	0.958737i	$-0.408240\pi$
$569$	13.5630	0.568592	0.284296	+	0.958737i	$0.408240\pi$
$570$	−11.6642	−0.488559
$571$	−22.0408	−0.922380	−0.461190	−	0.887301i	$-0.652577\pi$
$571$	−22.0408	−0.922380	−0.461190	+	0.887301i	$0.652577\pi$
$572$	−1.47636	−0.0617296
$573$	19.1386	0.799526
$574$	0	0
$575$	−0.969558	−0.0404334
$576$	2.79350	0.116396
$577$	−5.96000	−0.248118	−0.124059	−	0.992275i	$-0.539591\pi$
$577$	−5.96000	−0.248118	−0.124059	+	0.992275i	$0.539591\pi$
$578$	18.5763	0.772672
$579$	−8.13679	−0.338153
$580$	2.20789	0.0916775
$581$	0	0
$582$	7.79673	0.323185
$583$	−1.99666	−0.0826930
$584$	0.0394827	0.00163381
$585$	−7.66835	−0.317047
$586$	−26.8620	−1.10966
$587$	−17.1038	−0.705949	−0.352974	−	0.935633i	$-0.614830\pi$
$587$	−17.1038	−0.705949	−0.352974	+	0.935633i	$0.614830\pi$
$588$	0	0
$589$	20.4363	0.842063
$590$	17.6137	0.725143
$591$	2.13042	0.0876339
$592$	−6.90400	−0.283753
$593$	43.4796	1.78549	0.892747	−	0.450558i	$-0.148775\pi$
$593$	43.4796	1.78549	0.892747	+	0.450558i	$0.148775\pi$
$594$	0.590200	0.0242162
$595$	0	0
$596$	−6.98665	−0.286184
$597$	27.9541	1.14408
$598$	9.62529	0.393607
$599$	−38.1048	−1.55692	−0.778461	−	0.627693i	$-0.783999\pi$
$599$	−38.1048	−1.55692	−0.778461	+	0.627693i	$0.783999\pi$
$600$	−0.301444	−0.0123064
$601$	48.5105	1.97878	0.989391	−	0.145275i	$-0.0464067\pi$
$601$	48.5105	1.97878	0.989391	+	0.145275i	$0.0464067\pi$
$602$	0	0
$603$	33.9256	1.38156
$604$	6.84496	0.278517
$605$	21.1735	0.860827
$606$	21.6800	0.880690
$607$	−48.5022	−1.96864	−0.984322	−	0.176382i	$-0.943560\pi$
$607$	−48.5022	−1.96864	−0.984322	+	0.176382i	$0.943560\pi$
$608$	2.19486	0.0890135
$609$	0	0
$610$	−17.9175	−0.725459
$611$	−7.23942	−0.292876
$612$	16.6621	0.673525
$613$	5.66312	0.228731	0.114366	−	0.993439i	$-0.463516\pi$
$613$	5.66312	0.228731	0.114366	+	0.993439i	$0.463516\pi$
$614$	−14.3480	−0.579036
$615$	−53.9511	−2.17552
$616$	0	0
$617$	24.7525	0.996496	0.498248	−	0.867034i	$-0.333977\pi$
$617$	24.7525	0.996496	0.498248	+	0.867034i	$0.333977\pi$
$618$	14.9947	0.603176
$619$	−7.75434	−0.311673	−0.155837	−	0.987783i	$-0.549807\pi$
$619$	−7.75434	−0.311673	−0.155837	+	0.987783i	$0.549807\pi$
$620$	−20.5576	−0.825612
$621$	−3.84788	−0.154410
$622$	1.63601	0.0655980
$623$	0	0
$624$	2.99259	0.119799
$625$	−24.3581	−0.974325
$626$	0.732076	0.0292597
$627$	−6.27326	−0.250530
$628$	18.3243	0.731220
$629$	−41.1795	−1.64193
$630$	0	0
$631$	39.3718	1.56737	0.783684	−	0.621160i	$-0.213338\pi$
$631$	39.3718	1.56737	0.783684	+	0.621160i	$0.213338\pi$
$632$	−2.42334	−0.0963952
$633$	−57.9228	−2.30222
$634$	19.7271	0.783463
$635$	−10.5540	−0.418824
$636$	4.04723	0.160483
$637$	0	0
$638$	1.18745	0.0470116
$639$	12.8798	0.509518
$640$	−2.20789	−0.0872744
$641$	−12.4755	−0.492752	−0.246376	−	0.969174i	$-0.579240\pi$
$641$	−12.4755	−0.492752	−0.246376	+	0.969174i	$0.579240\pi$
$642$	−39.1489	−1.54508
$643$	−17.0296	−0.671581	−0.335790	−	0.941937i	$-0.609003\pi$
$643$	−17.0296	−0.671581	−0.335790	+	0.941937i	$0.609003\pi$
$644$	0	0
$645$	30.6145	1.20545
$646$	13.0915	0.515076
$647$	32.0895	1.26157	0.630785	−	0.775958i	$-0.282733\pi$
$647$	32.0895	1.26157	0.630785	+	0.775958i	$0.282733\pi$
$648$	−9.57685	−0.376214
$649$	9.47301	0.371848
$650$	−0.155709	−0.00610739
$651$	0	0
$652$	−20.6653	−0.809315
$653$	−37.2834	−1.45901	−0.729506	−	0.683975i	$-0.760250\pi$
$653$	−37.2834	−1.45901	−0.729506	+	0.683975i	$0.760250\pi$
$654$	−6.91476	−0.270388
$655$	23.9444	0.935586
$656$	10.1520	0.396370
$657$	0.110295	0.00430302
$658$	0	0
$659$	−18.0912	−0.704734	−0.352367	−	0.935862i	$-0.614623\pi$
$659$	−18.0912	−0.704734	−0.352367	+	0.935862i	$0.614623\pi$
$660$	6.31048	0.245635
$661$	27.2099	1.05834	0.529172	−	0.848514i	$-0.322503\pi$
$661$	27.2099	1.05834	0.529172	+	0.848514i	$0.322503\pi$
$662$	33.3950	1.29793
$663$	17.8495	0.693219
$664$	5.46282	0.211999
$665$	0	0
$666$	−19.2863	−0.747331
$667$	−7.74172	−0.299761
$668$	21.9158	0.847949
$669$	8.73654	0.337774
$670$	−26.8136	−1.03590
$671$	−9.63643	−0.372010
$672$	0	0
$673$	−26.8539	−1.03514	−0.517572	−	0.855640i	$-0.673164\pi$
$673$	−26.8539	−1.03514	−0.517572	+	0.855640i	$0.673164\pi$
$674$	−10.5851	−0.407723
$675$	0.0622472	0.00239590
$676$	−11.4542	−0.440546
$677$	−18.5177	−0.711693	−0.355846	−	0.934545i	$-0.615807\pi$
$677$	−18.5177	−0.711693	−0.355846	+	0.934545i	$0.615807\pi$
$678$	−2.43105	−0.0933641
$679$	0	0
$680$	−13.1691	−0.505013
$681$	30.5221	1.16961
$682$	−11.0563	−0.423368
$683$	−41.2661	−1.57900	−0.789502	−	0.613748i	$-0.789661\pi$
$683$	−41.2661	−1.57900	−0.789502	+	0.613748i	$0.789661\pi$
$684$	6.13136	0.234438
$685$	1.36992	0.0523419
$686$	0	0
$687$	−47.9503	−1.82942
$688$	−5.76077	−0.219627
$689$	2.09057	0.0796442
$690$	−41.1420	−1.56625
$691$	−37.7308	−1.43535	−0.717674	−	0.696379i	$-0.754793\pi$
$691$	−37.7308	−1.43535	−0.717674	+	0.696379i	$0.754793\pi$
$692$	−14.1727	−0.538764
$693$	0	0
$694$	23.3463	0.886215
$695$	23.9802	0.909622
$696$	−2.40697	−0.0912360
$697$	60.5527	2.29360
$698$	7.42792	0.281151
$699$	−32.9656	−1.24687
$700$	0	0
$701$	48.1772	1.81963	0.909814	−	0.415017i	$-0.136224\pi$
$701$	48.1772	1.81963	0.909814	+	0.415017i	$0.136224\pi$
$702$	−0.617959	−0.0233234
$703$	−15.1533	−0.571519
$704$	−1.18745	−0.0447537
$705$	30.9439	1.16541
$706$	−32.5393	−1.22463
$707$	0	0
$708$	−19.2019	−0.721650
$709$	−11.4135	−0.428642	−0.214321	−	0.976763i	$-0.568754\pi$
$709$	−11.4135	−0.428642	−0.214321	+	0.976763i	$0.568754\pi$
$710$	−10.1798	−0.382040
$711$	−6.76960	−0.253880
$712$	−7.26832	−0.272392
$713$	72.0829	2.69953
$714$	0	0
$715$	3.25963	0.121903
$716$	−22.3800	−0.836381
$717$	40.1792	1.50052
$718$	7.25600	0.270791
$719$	−17.6674	−0.658883	−0.329441	−	0.944176i	$-0.606860\pi$
$719$	−17.6674	−0.658883	−0.329441	+	0.944176i	$0.606860\pi$
$720$	−6.16774	−0.229858
$721$	0	0
$722$	−14.1826	−0.527821
$723$	−40.4609	−1.50476
$724$	−15.5160	−0.576649
$725$	0.125238	0.00465122
$726$	−23.0827	−0.856681
$727$	−24.8691	−0.922342	−0.461171	−	0.887311i	$-0.652571\pi$
$727$	−24.8691	−0.922342	−0.461171	+	0.887311i	$0.652571\pi$
$728$	0	0
$729$	−23.1639	−0.857924
$730$	−0.0871733	−0.00322643
$731$	−34.3606	−1.27087
$732$	19.5331	0.721965
$733$	14.3888	0.531463	0.265732	−	0.964047i	$-0.414386\pi$
$733$	14.3888	0.531463	0.265732	+	0.964047i	$0.414386\pi$
$734$	−24.1847	−0.892673
$735$	0	0
$736$	7.74172	0.285364
$737$	−14.4210	−0.531203
$738$	28.3597	1.04394
$739$	−4.18020	−0.153771	−0.0768855	−	0.997040i	$-0.524498\pi$
$739$	−4.18020	−0.153771	−0.0768855	+	0.997040i	$0.524498\pi$
$740$	15.2432	0.560353
$741$	6.56832	0.241293
$742$	0	0
$743$	45.1899	1.65786	0.828928	−	0.559355i	$-0.188951\pi$
$743$	45.1899	1.65786	0.828928	+	0.559355i	$0.188951\pi$
$744$	22.4112	0.821635
$745$	15.4257	0.565155
$746$	−24.0550	−0.880715
$747$	15.2604	0.558349
$748$	−7.08265	−0.258967
$749$	0	0
$750$	27.2371	0.994559
$751$	23.2797	0.849489	0.424744	−	0.905313i	$-0.360364\pi$
$751$	23.2797	0.849489	0.424744	+	0.905313i	$0.360364\pi$
$752$	−5.82274	−0.212334
$753$	−8.98638	−0.327482
$754$	−1.24330	−0.0452783
$755$	−15.1129	−0.550014
$756$	0	0
$757$	30.8864	1.12258	0.561292	−	0.827618i	$-0.310304\pi$
$757$	30.8864	1.12258	0.561292	+	0.827618i	$0.310304\pi$
$758$	27.4551	0.997214
$759$	−22.1271	−0.803161
$760$	−4.84601	−0.175783
$761$	−26.3359	−0.954676	−0.477338	−	0.878720i	$-0.658398\pi$
$761$	−26.3359	−0.954676	−0.477338	+	0.878720i	$0.658398\pi$
$762$	11.5057	0.416807
$763$	0	0
$764$	7.95133	0.287669
$765$	−36.7880	−1.33007
$766$	−1.30301	−0.0470797
$767$	−9.91857	−0.358139
$768$	2.40697	0.0868540
$769$	−19.8275	−0.714996	−0.357498	−	0.933914i	$-0.616370\pi$
$769$	−19.8275	−0.714996	−0.357498	+	0.933914i	$0.616370\pi$
$770$	0	0
$771$	73.5176	2.64767
$772$	−3.38051	−0.121667
$773$	19.1675	0.689407	0.344704	−	0.938712i	$-0.387979\pi$
$773$	19.1675	0.689407	0.344704	+	0.938712i	$0.387979\pi$
$774$	−16.0927	−0.578441
$775$	−1.16609	−0.0418871
$776$	3.23923	0.116282
$777$	0	0
$778$	17.1482	0.614793
$779$	22.2823	0.798347
$780$	−6.60729	−0.236579
$781$	−5.47490	−0.195907
$782$	46.1762	1.65126
$783$	0.497031	0.0177624
$784$	0	0
$785$	−40.4580	−1.44401
$786$	−26.1035	−0.931080
$787$	13.5325	0.482380	0.241190	−	0.970478i	$-0.422462\pi$
$787$	13.5325	0.482380	0.241190	+	0.970478i	$0.422462\pi$
$788$	0.885106	0.0315306
$789$	−39.9995	−1.42402
$790$	5.35045	0.190361
$791$	0	0
$792$	−3.31715	−0.117870
$793$	10.0897	0.358295
$794$	−19.3432	−0.686465
$795$	−8.93583	−0.316921
$796$	11.6138	0.411640
$797$	21.2360	0.752216	0.376108	−	0.926576i	$-0.377262\pi$
$797$	21.2360	0.752216	0.376108	+	0.926576i	$0.377262\pi$
$798$	0	0
$799$	−34.7302	−1.22867
$800$	−0.125238	−0.00442783
$801$	−20.3041	−0.717409
$802$	32.6583	1.15321
$803$	−0.0468837	−0.00165449
$804$	29.2314	1.03091
$805$	0	0
$806$	11.5763	0.407759
$807$	−37.0418	−1.30393
$808$	9.00718	0.316871
$809$	−28.5898	−1.00516	−0.502582	−	0.864529i	$-0.667617\pi$
$809$	−28.5898	−1.00516	−0.502582	+	0.864529i	$0.667617\pi$
$810$	21.1446	0.742945
$811$	12.8153	0.450007	0.225004	−	0.974358i	$-0.427761\pi$
$811$	12.8153	0.450007	0.225004	+	0.974358i	$0.427761\pi$
$812$	0	0
$813$	−55.1710	−1.93493
$814$	8.19816	0.287345
$815$	45.6266	1.59823
$816$	14.3566	0.502581
$817$	−12.6441	−0.442361
$818$	4.34907	0.152062
$819$	0	0
$820$	−22.4145	−0.782750
$821$	13.3000	0.464173	0.232087	−	0.972695i	$-0.425445\pi$
$821$	13.3000	0.464173	0.232087	+	0.972695i	$0.425445\pi$
$822$	−1.49344	−0.0520898
$823$	−38.2658	−1.33386	−0.666930	−	0.745120i	$-0.732392\pi$
$823$	−38.2658	−1.33386	−0.666930	+	0.745120i	$0.732392\pi$
$824$	6.22971	0.217022
$825$	0.357950	0.0124622
$826$	0	0
$827$	−47.0423	−1.63582	−0.817910	−	0.575346i	$-0.804868\pi$
$827$	−47.0423	−1.63582	−0.817910	+	0.575346i	$0.804868\pi$
$828$	21.6265	0.751574
$829$	13.3705	0.464375	0.232188	−	0.972671i	$-0.425412\pi$
$829$	13.3705	0.464375	0.232188	+	0.972671i	$0.425412\pi$
$830$	−12.0613	−0.418653
$831$	−57.8943	−2.00833
$832$	1.24330	0.0431037
$833$	0	0
$834$	−26.1425	−0.905241
$835$	−48.3876	−1.67452
$836$	−2.60629	−0.0901405
$837$	−4.62784	−0.159962
$838$	18.3596	0.634222
$839$	−17.0873	−0.589919	−0.294959	−	0.955510i	$-0.595306\pi$
$839$	−17.0873	−0.589919	−0.294959	+	0.955510i	$0.595306\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	2.64832	0.0912670
$843$	4.17187	0.143687
$844$	−24.0646	−0.828338
$845$	25.2896	0.869988
$846$	−16.2659	−0.559231
$847$	0	0
$848$	1.68146	0.0577417
$849$	−42.5889	−1.46165
$850$	−0.746993	−0.0256216
$851$	−53.4489	−1.83220
$852$	11.0977	0.380200
$853$	−44.1225	−1.51073	−0.755363	−	0.655307i	$-0.772539\pi$
$853$	−44.1225	−1.51073	−0.755363	+	0.655307i	$0.772539\pi$
$854$	0	0
$855$	−13.5373	−0.462967
$856$	−16.2648	−0.555919
$857$	16.1697	0.552347	0.276173	−	0.961108i	$-0.410934\pi$
$857$	16.1697	0.552347	0.276173	+	0.961108i	$0.410934\pi$
$858$	−3.55355	−0.121316
$859$	−33.0463	−1.12753	−0.563763	−	0.825937i	$-0.690647\pi$
$859$	−33.0463	−1.12753	−0.563763	+	0.825937i	$0.690647\pi$
$860$	12.7191	0.433718
$861$	0	0
$862$	1.64865	0.0561534
$863$	−0.750553	−0.0255491	−0.0127746	−	0.999918i	$-0.504066\pi$
$863$	−0.750553	−0.0255491	−0.0127746	+	0.999918i	$0.504066\pi$
$864$	−0.497031	−0.0169093
$865$	31.2916	1.06395
$866$	6.12954	0.208290
$867$	44.7126	1.51852
$868$	0	0
$869$	2.87759	0.0976156
$870$	5.31432	0.180172
$871$	15.0992	0.511618
$872$	−2.87281	−0.0972855
$873$	9.04881	0.306256
$874$	16.9920	0.574764
$875$	0	0
$876$	0.0950337	0.00321089
$877$	42.5336	1.43626	0.718129	−	0.695910i	$-0.244999\pi$
$877$	42.5336	1.43626	0.718129	+	0.695910i	$0.244999\pi$
$878$	−10.3136	−0.348066
$879$	−64.6560	−2.18079
$880$	2.62175	0.0883793
$881$	−41.6234	−1.40233	−0.701165	−	0.713000i	$-0.747336\pi$
$881$	−41.6234	−1.40233	−0.701165	+	0.713000i	$0.747336\pi$
$882$	0	0
$883$	3.11629	0.104872	0.0524358	−	0.998624i	$-0.483302\pi$
$883$	3.11629	0.104872	0.0524358	+	0.998624i	$0.483302\pi$
$884$	7.41577	0.249419
$885$	42.3955	1.42511
$886$	8.40137	0.282250
$887$	−15.1513	−0.508731	−0.254366	−	0.967108i	$-0.581867\pi$
$887$	−15.1513	−0.508731	−0.254366	+	0.967108i	$0.581867\pi$
$888$	−16.6177	−0.557654
$889$	0	0
$890$	16.0476	0.537918
$891$	11.3720	0.380977
$892$	3.62968	0.121531
$893$	−12.7801	−0.427671
$894$	−16.8167	−0.562433
$895$	49.4126	1.65168
$896$	0	0
$897$	23.1678	0.773549
$898$	9.90897	0.330667
$899$	−9.31097	−0.310538
$900$	−0.349853	−0.0116618
$901$	10.0292	0.334122
$902$	−12.0550	−0.401389
$903$	0	0
$904$	−1.01001	−0.0335923
$905$	34.2576	1.13876
$906$	16.4756	0.547365
$907$	−56.0289	−1.86041	−0.930204	−	0.367042i	$-0.880371\pi$
$907$	−56.0289	−1.86041	−0.930204	+	0.367042i	$0.880371\pi$
$908$	12.6807	0.420825
$909$	25.1616	0.834557
$910$	0	0
$911$	25.0412	0.829653	0.414827	−	0.909900i	$-0.363842\pi$
$911$	25.0412	0.829653	0.414827	+	0.909900i	$0.363842\pi$
$912$	5.28297	0.174937
$913$	−6.48683	−0.214683
$914$	−21.5372	−0.712388
$915$	−43.1269	−1.42573
$916$	−19.9214	−0.658223
$917$	0	0
$918$	−2.96459	−0.0978459
$919$	−44.0916	−1.45445	−0.727224	−	0.686400i	$-0.759190\pi$
$919$	−44.0916	−1.45445	−0.727224	+	0.686400i	$0.759190\pi$
$920$	−17.0928	−0.563534
$921$	−34.5351	−1.13797
$922$	−22.0453	−0.726023
$923$	5.73241	0.188684
$924$	0	0
$925$	0.864643	0.0284293
$926$	−18.1202	−0.595466
$927$	17.4027	0.571580
$928$	−1.00000	−0.0328266
$929$	49.2826	1.61691	0.808456	−	0.588557i	$-0.200304\pi$
$929$	49.2826	1.61691	0.808456	+	0.588557i	$0.200304\pi$
$930$	−49.4814	−1.62256
$931$	0	0
$932$	−13.6959	−0.448623
$933$	3.93782	0.128919
$934$	24.8321	0.812533
$935$	15.6377	0.511407
$936$	3.47316	0.113524
$937$	−38.6362	−1.26219	−0.631094	−	0.775706i	$-0.717394\pi$
$937$	−38.6362	−1.26219	−0.631094	+	0.775706i	$0.717394\pi$
$938$	0	0
$939$	1.76209	0.0575035
$940$	12.8560	0.419315
$941$	0.563605	0.0183730	0.00918649	−	0.999958i	$-0.497076\pi$
$941$	0.563605	0.0183730	0.00918649	+	0.999958i	$0.497076\pi$
$942$	44.1061	1.43705
$943$	78.5942	2.55938
$944$	−7.97761	−0.259649
$945$	0	0
$946$	6.84062	0.222408
$947$	7.71967	0.250856	0.125428	−	0.992103i	$-0.459970\pi$
$947$	7.71967	0.250856	0.125428	+	0.992103i	$0.459970\pi$
$948$	−5.83290	−0.189444
$949$	0.0490889	0.00159349
$950$	−0.274880	−0.00891830
$951$	47.4825	1.53973
$952$	0	0
$953$	−60.2876	−1.95291	−0.976453	−	0.215729i	$-0.930787\pi$
$953$	−60.2876	−1.95291	−0.976453	+	0.215729i	$0.930787\pi$
$954$	4.69718	0.152077
$955$	−17.5556	−0.568087
$956$	16.6929	0.539886
$957$	2.85816	0.0923911
$958$	12.5423	0.405223
$959$	0	0
$960$	−5.31432	−0.171519
$961$	55.6942	1.79659
$962$	−8.58375	−0.276751
$963$	−45.4358	−1.46415
$964$	−16.8099	−0.541411
$965$	7.46378	0.240268
$966$	0	0
$967$	25.9669	0.835040	0.417520	−	0.908668i	$-0.362899\pi$
$967$	25.9669	0.835040	0.417520	+	0.908668i	$0.362899\pi$
$968$	−9.58996	−0.308233
$969$	31.5107	1.01227
$970$	−7.15186	−0.229632
$971$	−28.5034	−0.914718	−0.457359	−	0.889282i	$-0.651205\pi$
$971$	−28.5034	−0.914718	−0.457359	+	0.889282i	$0.651205\pi$
$972$	−21.5601	−0.691540
$973$	0	0
$974$	−15.2869	−0.489823
$975$	−0.374786	−0.0120027
$976$	8.11523	0.259762
$977$	−50.8821	−1.62786	−0.813932	−	0.580960i	$-0.802677\pi$
$977$	−50.8821	−1.62786	−0.813932	+	0.580960i	$0.802677\pi$
$978$	−49.7407	−1.59053
$979$	8.63077	0.275841
$980$	0	0
$981$	−8.02520	−0.256225
$982$	29.0450	0.926863
$983$	−2.28810	−0.0729791	−0.0364895	−	0.999334i	$-0.511618\pi$
$983$	−2.28810	−0.0729791	−0.0364895	+	0.999334i	$0.511618\pi$
$984$	24.4356	0.778980
$985$	−1.95421	−0.0622664
$986$	−5.96459	−0.189951
$987$	0	0
$988$	2.72887	0.0868171
$989$	−44.5983	−1.41814
$990$	7.32388	0.232768
$991$	−28.1233	−0.893366	−0.446683	−	0.894692i	$-0.647395\pi$
$991$	−28.1233	−0.893366	−0.446683	+	0.894692i	$0.647395\pi$
$992$	9.31097	0.295624
$993$	80.3807	2.55080
$994$	0	0
$995$	−25.6420	−0.812905
$996$	13.1488	0.416637
$997$	−17.8838	−0.566384	−0.283192	−	0.959063i	$-0.591393\pi$
$997$	−17.8838	−0.566384	−0.283192	+	0.959063i	$0.591393\pi$
$998$	16.7064	0.528832
$999$	3.43150	0.108568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.z.1.4		5
7.2	even	3		406.2.e.a.291.2	yes	10
7.4	even	3		406.2.e.a.233.2	✓	10
7.6	odd	2		2842.2.a.x.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.a.233.2	✓	10	7.4	even	3
406.2.e.a.291.2	yes	10	7.2	even	3
2842.2.a.x.1.2		5	7.6	odd	2
2842.2.a.z.1.4		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.40697 q^{3} +1.00000 q^{4} -2.20789 q^{5} +2.40697 q^{6} +1.00000 q^{8} +2.79350 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.40697 q^{3} +1.00000 q^{4} -2.20789 q^{5} +2.40697 q^{6} +1.00000 q^{8} +2.79350 q^{9} -2.20789 q^{10} -1.18745 q^{11} +2.40697 q^{12} +1.24330 q^{13} -5.31432 q^{15} +1.00000 q^{16} +5.96459 q^{17} +2.79350 q^{18} +2.19486 q^{19} -2.20789 q^{20} -1.18745 q^{22} +7.74172 q^{23} +2.40697 q^{24} -0.125238 q^{25} +1.24330 q^{26} -0.497031 q^{27} -1.00000 q^{29} -5.31432 q^{30} +9.31097 q^{31} +1.00000 q^{32} -2.85816 q^{33} +5.96459 q^{34} +2.79350 q^{36} -6.90400 q^{37} +2.19486 q^{38} +2.99259 q^{39} -2.20789 q^{40} +10.1520 q^{41} -5.76077 q^{43} -1.18745 q^{44} -6.16774 q^{45} +7.74172 q^{46} -5.82274 q^{47} +2.40697 q^{48} -0.125238 q^{50} +14.3566 q^{51} +1.24330 q^{52} +1.68146 q^{53} -0.497031 q^{54} +2.62175 q^{55} +5.28297 q^{57} -1.00000 q^{58} -7.97761 q^{59} -5.31432 q^{60} +8.11523 q^{61} +9.31097 q^{62} +1.00000 q^{64} -2.74507 q^{65} -2.85816 q^{66} +12.1445 q^{67} +5.96459 q^{68} +18.6341 q^{69} +4.61064 q^{71} +2.79350 q^{72} +0.0394827 q^{73} -6.90400 q^{74} -0.301444 q^{75} +2.19486 q^{76} +2.99259 q^{78} -2.42334 q^{79} -2.20789 q^{80} -9.57685 q^{81} +10.1520 q^{82} +5.46282 q^{83} -13.1691 q^{85} -5.76077 q^{86} -2.40697 q^{87} -1.18745 q^{88} -7.26832 q^{89} -6.16774 q^{90} +7.74172 q^{92} +22.4112 q^{93} -5.82274 q^{94} -4.84601 q^{95} +2.40697 q^{96} +3.23923 q^{97} -3.31715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9} + 7 q^{10} + 3 q^{12} + 10 q^{13} - 10 q^{15} + 5 q^{16} + 8 q^{17} + 8 q^{18} + 2 q^{19} + 7 q^{20} + q^{23} + 3 q^{24} + 12 q^{25} + 10 q^{26} + 15 q^{27} - 5 q^{29} - 10 q^{30} + 11 q^{31} + 5 q^{32} + 9 q^{33} + 8 q^{34} + 8 q^{36} - 8 q^{37} + 2 q^{38} + 18 q^{39} + 7 q^{40} + 23 q^{41} - 3 q^{43} + 4 q^{45} + q^{46} + 16 q^{47} + 3 q^{48} + 12 q^{50} + 7 q^{51} + 10 q^{52} + 7 q^{53} + 15 q^{54} + 6 q^{55} - 34 q^{57} - 5 q^{58} - 9 q^{59} - 10 q^{60} + 15 q^{61} + 11 q^{62} + 5 q^{64} + 5 q^{65} + 9 q^{66} - 4 q^{67} + 8 q^{68} + 14 q^{69} - 22 q^{71} + 8 q^{72} - 8 q^{74} - 34 q^{75} + 2 q^{76} + 18 q^{78} - 13 q^{79} + 7 q^{80} + 17 q^{81} + 23 q^{82} + 28 q^{83} - 7 q^{85} - 3 q^{86} - 3 q^{87} + 17 q^{89} + 4 q^{90} + q^{92} + 17 q^{93} + 16 q^{94} - 9 q^{95} + 3 q^{96} + 42 q^{97} - 42 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9 + 7 * q^10 + 3 * q^12 + 10 * q^13 - 10 * q^15 + 5 * q^16 + 8 * q^17 + 8 * q^18 + 2 * q^19 + 7 * q^20 + q^23 + 3 * q^24 + 12 * q^25 + 10 * q^26 + 15 * q^27 - 5 * q^29 - 10 * q^30 + 11 * q^31 + 5 * q^32 + 9 * q^33 + 8 * q^34 + 8 * q^36 - 8 * q^37 + 2 * q^38 + 18 * q^39 + 7 * q^40 + 23 * q^41 - 3 * q^43 + 4 * q^45 + q^46 + 16 * q^47 + 3 * q^48 + 12 * q^50 + 7 * q^51 + 10 * q^52 + 7 * q^53 + 15 * q^54 + 6 * q^55 - 34 * q^57 - 5 * q^58 - 9 * q^59 - 10 * q^60 + 15 * q^61 + 11 * q^62 + 5 * q^64 + 5 * q^65 + 9 * q^66 - 4 * q^67 + 8 * q^68 + 14 * q^69 - 22 * q^71 + 8 * q^72 - 8 * q^74 - 34 * q^75 + 2 * q^76 + 18 * q^78 - 13 * q^79 + 7 * q^80 + 17 * q^81 + 23 * q^82 + 28 * q^83 - 7 * q^85 - 3 * q^86 - 3 * q^87 + 17 * q^89 + 4 * q^90 + q^92 + 17 * q^93 + 16 * q^94 - 9 * q^95 + 3 * q^96 + 42 * q^97 - 42 * q^99

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