LMFDB - Embedded newform 931.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.254102$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93543 q^{2} -1.25410 q^{3} +1.74590 q^{4} -1.68133 q^{5} +2.42723 q^{6} +0.491797 q^{8} -1.42723 q^{9} +O(q^{10})$	\(q-1.93543 q^{2} -1.25410 q^{3} +1.74590 q^{4} -1.68133 q^{5} +2.42723 q^{6} +0.491797 q^{8} -1.42723 q^{9} +3.25410 q^{10} +4.93543 q^{11} -2.18953 q^{12} -1.68133 q^{13} +2.10856 q^{15} -4.44364 q^{16} -5.44364 q^{17} +2.76231 q^{18} -1.00000 q^{19} -2.93543 q^{20} -9.55220 q^{22} +1.81047 q^{23} -0.616763 q^{24} -2.17313 q^{25} +3.25410 q^{26} +5.55220 q^{27} -7.78989 q^{29} -4.08097 q^{30} +1.57277 q^{31} +7.61676 q^{32} -6.18953 q^{33} +10.5358 q^{34} -2.49180 q^{36} -7.55220 q^{37} +1.93543 q^{38} +2.10856 q^{39} -0.826873 q^{40} +6.46004 q^{41} +3.36266 q^{43} +8.61676 q^{44} +2.39964 q^{45} -3.50403 q^{46} +0.697737 q^{47} +5.57277 q^{48} +4.20594 q^{50} +6.82687 q^{51} -2.93543 q^{52} +5.12497 q^{53} -10.7459 q^{54} -8.29809 q^{55} +1.25410 q^{57} +15.0768 q^{58} +5.17313 q^{59} +3.68133 q^{60} +10.0604 q^{61} -3.04399 q^{62} -5.85446 q^{64} +2.82687 q^{65} +11.9794 q^{66} -9.31450 q^{67} -9.50403 q^{68} -2.27051 q^{69} +8.06040 q^{71} -0.701906 q^{72} -10.9958 q^{73} +14.6168 q^{74} +2.72532 q^{75} -1.74590 q^{76} -4.08097 q^{78} +4.37907 q^{79} +7.47122 q^{80} -2.68133 q^{81} -12.5030 q^{82} -4.87503 q^{83} +9.15255 q^{85} -6.50820 q^{86} +9.76931 q^{87} +2.42723 q^{88} +18.2171 q^{89} -4.64435 q^{90} +3.16089 q^{92} -1.97241 q^{93} -1.35042 q^{94} +1.68133 q^{95} -9.55220 q^{96} +2.95601 q^{97} -7.04399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 2 q^{5} + q^{6} + 3 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 2 * q^5 + q^6 + 3 * q^8 + 2 * q^9	$ 3 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 2 q^{5} + q^{6} + 3 q^{8} + 2 q^{9} + 9 q^{10} + 7 q^{11} + 2 q^{12} + 2 q^{13} - 7 q^{15} - 4 q^{16} - 7 q^{17} + 6 q^{18} - 3 q^{19} - q^{20} - 6 q^{22} + 14 q^{23} + 13 q^{24} - q^{25} + 9 q^{26} - 6 q^{27} - 3 q^{29} - 17 q^{30} + 11 q^{31} + 8 q^{32} - 10 q^{33} + 12 q^{34} - 9 q^{36} - 2 q^{38} - 7 q^{39} - 8 q^{40} + 7 q^{41} - 4 q^{43} + 11 q^{44} + 19 q^{45} + 23 q^{46} - 8 q^{47} + 23 q^{48} + q^{50} + 26 q^{51} - q^{52} - q^{53} - 33 q^{54} - 3 q^{55} + 3 q^{57} + 18 q^{58} + 10 q^{59} + 4 q^{60} + 6 q^{61} + 12 q^{62} - 5 q^{64} + 14 q^{65} + 7 q^{66} - 3 q^{67} + 5 q^{68} - 3 q^{69} - 24 q^{72} - q^{73} + 29 q^{74} - 20 q^{75} - 6 q^{76} - 17 q^{78} - 4 q^{79} - 5 q^{80} - q^{81} - 24 q^{82} - 31 q^{83} - 7 q^{85} - 18 q^{86} - 20 q^{87} + q^{88} + 28 q^{89} + 19 q^{90} + 39 q^{92} - 24 q^{93} - 25 q^{94} - 2 q^{95} - 6 q^{96} + 30 q^{97}+O(q^{100}) $ 3 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 2 * q^5 + q^6 + 3 * q^8 + 2 * q^9 + 9 * q^10 + 7 * q^11 + 2 * q^12 + 2 * q^13 - 7 * q^15 - 4 * q^16 - 7 * q^17 + 6 * q^18 - 3 * q^19 - q^20 - 6 * q^22 + 14 * q^23 + 13 * q^24 - q^25 + 9 * q^26 - 6 * q^27 - 3 * q^29 - 17 * q^30 + 11 * q^31 + 8 * q^32 - 10 * q^33 + 12 * q^34 - 9 * q^36 - 2 * q^38 - 7 * q^39 - 8 * q^40 + 7 * q^41 - 4 * q^43 + 11 * q^44 + 19 * q^45 + 23 * q^46 - 8 * q^47 + 23 * q^48 + q^50 + 26 * q^51 - q^52 - q^53 - 33 * q^54 - 3 * q^55 + 3 * q^57 + 18 * q^58 + 10 * q^59 + 4 * q^60 + 6 * q^61 + 12 * q^62 - 5 * q^64 + 14 * q^65 + 7 * q^66 - 3 * q^67 + 5 * q^68 - 3 * q^69 - 24 * q^72 - q^73 + 29 * q^74 - 20 * q^75 - 6 * q^76 - 17 * q^78 - 4 * q^79 - 5 * q^80 - q^81 - 24 * q^82 - 31 * q^83 - 7 * q^85 - 18 * q^86 - 20 * q^87 + q^88 + 28 * q^89 + 19 * q^90 + 39 * q^92 - 24 * q^93 - 25 * q^94 - 2 * q^95 - 6 * q^96 + 30 * q^97

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 $

$2$	−1.93543	−1.36856	−0.684279	−	0.729221i	$-0.739883\pi$
$2$	−1.93543	−1.36856	−0.684279	+	0.729221i	$0.739883\pi$
$3$	−1.25410	−0.724056	−0.362028	−	0.932167i	$-0.617916\pi$
$3$	−1.25410	−0.724056	−0.362028	+	0.932167i	$0.617916\pi$
$4$	1.74590	0.872949
$5$	−1.68133	−0.751914	−0.375957	−	0.926637i	$-0.622686\pi$
$5$	−1.68133	−0.751914	−0.375957	+	0.926637i	$0.622686\pi$
$6$	2.42723	0.990912
$7$	0	0
$7$	0	0
$8$	0.491797	0.173876
$9$	−1.42723	−0.475743
$10$	3.25410	1.02904
$11$	4.93543	1.48809	0.744044	−	0.668130i	$-0.232905\pi$
$11$	4.93543	1.48809	0.744044	+	0.668130i	$0.232905\pi$
$12$	−2.18953	−0.632064
$13$	−1.68133	−0.466317	−0.233159	−	0.972439i	$-0.574906\pi$
$13$	−1.68133	−0.466317	−0.233159	+	0.972439i	$0.574906\pi$
$14$	0	0
$15$	2.10856	0.544428
$16$	−4.44364	−1.11091
$17$	−5.44364	−1.32028	−0.660138	−	0.751145i	$-0.729502\pi$
$17$	−5.44364	−1.32028	−0.660138	+	0.751145i	$0.729502\pi$
$18$	2.76231	0.651082
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.93543	−0.656383
$21$	0	0
$22$	−9.55220	−2.03653
$23$	1.81047	0.377508	0.188754	−	0.982024i	$-0.439555\pi$
$23$	1.81047	0.377508	0.188754	+	0.982024i	$0.439555\pi$
$24$	−0.616763	−0.125896
$25$	−2.17313	−0.434625
$26$	3.25410	0.638182
$27$	5.55220	1.06852
$28$	0	0
$29$	−7.78989	−1.44655	−0.723273	−	0.690562i	$-0.757363\pi$
$29$	−7.78989	−1.44655	−0.723273	+	0.690562i	$0.757363\pi$
$30$	−4.08097	−0.745081
$31$	1.57277	0.282478	0.141239	−	0.989976i	$-0.454891\pi$
$31$	1.57277	0.282478	0.141239	+	0.989976i	$0.454891\pi$
$32$	7.61676	1.34647
$33$	−6.18953	−1.07746
$34$	10.5358	1.80687
$35$	0	0
$36$	−2.49180	−0.415299
$37$	−7.55220	−1.24157	−0.620787	−	0.783980i	$-0.713187\pi$
$37$	−7.55220	−1.24157	−0.620787	+	0.783980i	$0.713187\pi$
$38$	1.93543	0.313969
$39$	2.10856	0.337640
$40$	−0.826873	−0.130740
$41$	6.46004	1.00889	0.504445	−	0.863444i	$-0.331697\pi$
$41$	6.46004	1.00889	0.504445	+	0.863444i	$0.331697\pi$
$42$	0	0
$43$	3.36266	0.512801	0.256401	−	0.966571i	$-0.417463\pi$
$43$	3.36266	0.512801	0.256401	+	0.966571i	$0.417463\pi$
$44$	8.61676	1.29903
$45$	2.39964	0.357718
$46$	−3.50403	−0.516642
$47$	0.697737	0.101775	0.0508877	−	0.998704i	$-0.483795\pi$
$47$	0.697737	0.101775	0.0508877	+	0.998704i	$0.483795\pi$
$48$	5.57277	0.804360
$49$	0	0
$50$	4.20594	0.594810
$51$	6.82687	0.955953
$52$	−2.93543	−0.407071
$53$	5.12497	0.703968	0.351984	−	0.936006i	$-0.385507\pi$
$53$	5.12497	0.703968	0.351984	+	0.936006i	$0.385507\pi$
$54$	−10.7459	−1.46233
$55$	−8.29809	−1.11891
$56$	0	0
$57$	1.25410	0.166110
$58$	15.0768	1.97968
$59$	5.17313	0.673484	0.336742	−	0.941597i	$-0.390675\pi$
$59$	5.17313	0.673484	0.336742	+	0.941597i	$0.390675\pi$
$60$	3.68133	0.475258
$61$	10.0604	1.28810	0.644051	−	0.764983i	$-0.277252\pi$
$61$	10.0604	1.28810	0.644051	+	0.764983i	$0.277252\pi$
$62$	−3.04399	−0.386587
$63$	0	0
$64$	−5.85446	−0.731807
$65$	2.82687	0.350630
$66$	11.9794	1.47457
$67$	−9.31450	−1.13795	−0.568974	−	0.822356i	$-0.692659\pi$
$67$	−9.31450	−1.13795	−0.568974	+	0.822356i	$0.692659\pi$
$68$	−9.50403	−1.15253
$69$	−2.27051	−0.273337
$70$	0	0
$71$	8.06040	0.956593	0.478297	−	0.878198i	$-0.341254\pi$
$71$	8.06040	0.956593	0.478297	+	0.878198i	$0.341254\pi$
$72$	−0.701906	−0.0827205
$73$	−10.9958	−1.28696	−0.643482	−	0.765461i	$-0.722511\pi$
$73$	−10.9958	−1.28696	−0.643482	+	0.765461i	$0.722511\pi$
$74$	14.6168	1.69916
$75$	2.72532	0.314693
$76$	−1.74590	−0.200268
$77$	0	0
$78$	−4.08097	−0.462079
$79$	4.37907	0.492684	0.246342	−	0.969183i	$-0.420771\pi$
$79$	4.37907	0.492684	0.246342	+	0.969183i	$0.420771\pi$
$80$	7.47122	0.835308
$81$	−2.68133	−0.297926
$82$	−12.5030	−1.38072
$83$	−4.87503	−0.535104	−0.267552	−	0.963543i	$-0.586215\pi$
$83$	−4.87503	−0.535104	−0.267552	+	0.963543i	$0.586215\pi$
$84$	0	0
$85$	9.15255	0.992734
$86$	−6.50820	−0.701798
$87$	9.76931	1.04738
$88$	2.42723	0.258743
$89$	18.2171	1.93101	0.965505	−	0.260383i	$-0.0838489\pi$
$89$	18.2171	1.93101	0.965505	+	0.260383i	$0.0838489\pi$
$90$	−4.64435	−0.489557
$91$	0	0
$92$	3.16089	0.329546
$93$	−1.97241	−0.204530
$94$	−1.35042	−0.139286
$95$	1.68133	0.172501
$96$	−9.55220	−0.974917
$97$	2.95601	0.300137	0.150069	−	0.988676i	$-0.452051\pi$
$97$	2.95601	0.300137	0.150069	+	0.988676i	$0.452051\pi$
$98$	0	0
$99$	−7.04399	−0.707948
$100$	−3.79406	−0.379406
$101$	14.9149	1.48408	0.742042	−	0.670354i	$-0.233858\pi$
$101$	14.9149	1.48408	0.742042	+	0.670354i	$0.233858\pi$
$102$	−13.2130	−1.30828
$103$	11.5194	1.13504	0.567519	−	0.823360i	$-0.307903\pi$
$103$	11.5194	1.13504	0.567519	+	0.823360i	$0.307903\pi$
$104$	−0.826873	−0.0810815
$105$	0	0
$106$	−9.91903	−0.963421
$107$	15.6813	1.51597	0.757986	−	0.652271i	$-0.226184\pi$
$107$	15.6813	1.51597	0.757986	+	0.652271i	$0.226184\pi$
$108$	9.69357	0.932764
$109$	−5.04399	−0.483127	−0.241563	−	0.970385i	$-0.577660\pi$
$109$	−5.04399	−0.483127	−0.241563	+	0.970385i	$0.577660\pi$
$110$	16.0604	1.53130
$111$	9.47122	0.898969
$112$	0	0
$113$	16.3257	1.53579	0.767895	−	0.640575i	$-0.221304\pi$
$113$	16.3257	1.53579	0.767895	+	0.640575i	$0.221304\pi$
$114$	−2.42723	−0.227331
$115$	−3.04399	−0.283854
$116$	−13.6004	−1.26276
$117$	2.39964	0.221847
$118$	−10.0122	−0.921701
$119$	0	0
$120$	1.03698	0.0946631
$121$	13.3585	1.21441
$122$	−19.4712	−1.76284
$123$	−8.10155	−0.730492
$124$	2.74590	0.246589
$125$	12.0604	1.07871
$126$	0	0
$127$	13.6126	1.20792	0.603961	−	0.797014i	$-0.293588\pi$
$127$	13.6126	1.20792	0.603961	+	0.797014i	$0.293588\pi$
$128$	−3.90262	−0.344946
$129$	−4.21712	−0.371297
$130$	−5.47122	−0.479858
$131$	−7.44364	−0.650353	−0.325177	−	0.945653i	$-0.605424\pi$
$131$	−7.44364	−0.650353	−0.325177	+	0.945653i	$0.605424\pi$
$132$	−10.8063	−0.940567
$133$	0	0
$134$	18.0276	1.55735
$135$	−9.33508	−0.803435
$136$	−2.67716	−0.229565
$137$	−4.72532	−0.403712	−0.201856	−	0.979415i	$-0.564697\pi$
$137$	−4.72532	−0.403712	−0.201856	+	0.979415i	$0.564697\pi$
$138$	4.39442	0.374077
$139$	−18.7857	−1.59338	−0.796692	−	0.604385i	$-0.793419\pi$
$139$	−18.7857	−1.59338	−0.796692	+	0.604385i	$0.793419\pi$
$140$	0	0
$141$	−0.875034	−0.0736911
$142$	−15.6004	−1.30915
$143$	−8.29809	−0.693921
$144$	6.34209	0.528507
$145$	13.0974	1.08768
$146$	21.2817	1.76128
$147$	0	0
$148$	−13.1854	−1.08383
$149$	18.2775	1.49735	0.748676	−	0.662936i	$-0.230690\pi$
$149$	18.2775	1.49735	0.748676	+	0.662936i	$0.230690\pi$
$150$	−5.27468	−0.430676
$151$	1.57277	0.127990	0.0639951	−	0.997950i	$-0.479616\pi$
$151$	1.57277	0.127990	0.0639951	+	0.997950i	$0.479616\pi$
$152$	−0.491797	−0.0398900
$153$	7.76931	0.628112
$154$	0	0
$155$	−2.64435	−0.212399
$156$	3.68133	0.294742
$157$	−15.6936	−1.25248	−0.626242	−	0.779629i	$-0.715408\pi$
$157$	−15.6936	−1.25248	−0.626242	+	0.779629i	$0.715408\pi$
$158$	−8.47539	−0.674266
$159$	−6.42723	−0.509712
$160$	−12.8063	−1.01243
$161$	0	0
$162$	5.18953	0.407728
$163$	−0.141373	−0.0110732	−0.00553660	−	0.999985i	$-0.501762\pi$
$163$	−0.141373	−0.0110732	−0.00553660	+	0.999985i	$0.501762\pi$
$164$	11.2786	0.880709
$165$	10.4067	0.810157
$166$	9.43530	0.732321
$167$	−13.7141	−1.06123	−0.530616	−	0.847612i	$-0.678039\pi$
$167$	−13.7141	−1.06123	−0.530616	+	0.847612i	$0.678039\pi$
$168$	0	0
$169$	−10.1731	−0.782548
$170$	−17.7141	−1.35861
$171$	1.42723	0.109143
$172$	5.87086	0.447649
$173$	9.52461	0.724143	0.362071	−	0.932150i	$-0.382070\pi$
$173$	9.52461	0.724143	0.362071	+	0.932150i	$0.382070\pi$
$174$	−18.9078	−1.43340
$175$	0	0
$176$	−21.9313	−1.65313
$177$	−6.48763	−0.487640
$178$	−35.2580	−2.64270
$179$	14.6443	1.09457	0.547285	−	0.836946i	$-0.315661\pi$
$179$	14.6443	1.09457	0.547285	+	0.836946i	$0.315661\pi$
$180$	4.18953	0.312269
$181$	14.6772	1.09094	0.545472	−	0.838129i	$-0.316350\pi$
$181$	14.6772	1.09094	0.545472	+	0.838129i	$0.316350\pi$
$182$	0	0
$183$	−12.6168	−0.932658
$184$	0.890381	0.0656398
$185$	12.6977	0.933556
$186$	3.81748	0.279911
$187$	−26.8667	−1.96469
$188$	1.21818	0.0888448
$189$	0	0
$190$	−3.25410	−0.236077
$191$	−18.8667	−1.36515	−0.682573	−	0.730817i	$-0.739139\pi$
$191$	−18.8667	−1.36515	−0.682573	+	0.730817i	$0.739139\pi$
$192$	7.34209	0.529869
$193$	−21.6608	−1.55918	−0.779588	−	0.626293i	$-0.784571\pi$
$193$	−21.6608	−1.55918	−0.779588	+	0.626293i	$0.784571\pi$
$194$	−5.72115	−0.410755
$195$	−3.54519	−0.253876
$196$	0	0
$197$	−14.7376	−1.05001	−0.525004	−	0.851100i	$-0.675936\pi$
$197$	−14.7376	−1.05001	−0.525004	+	0.851100i	$0.675936\pi$
$198$	13.6332	0.968867
$199$	23.4231	1.66042	0.830208	−	0.557453i	$-0.188221\pi$
$199$	23.4231	1.66042	0.830208	+	0.557453i	$0.188221\pi$
$200$	−1.06874	−0.0755711
$201$	11.6813	0.823938
$202$	−28.8667	−2.03105
$203$	0	0
$204$	11.9190	0.834499
$205$	−10.8615	−0.758598
$206$	−22.2950	−1.55337
$207$	−2.58395	−0.179597
$208$	7.47122	0.518036
$209$	−4.93543	−0.341391
$210$	0	0
$211$	14.8667	1.02347	0.511733	−	0.859145i	$-0.329004\pi$
$211$	14.8667	1.02347	0.511733	+	0.859145i	$0.329004\pi$
$212$	8.94767	0.614529
$213$	−10.1086	−0.692627
$214$	−30.3502	−2.07469
$215$	−5.65375	−0.385582
$216$	2.73055	0.185790
$217$	0	0
$218$	9.76231	0.661187
$219$	13.7899	0.931834
$220$	−14.4876	−0.976756
$221$	9.15255	0.615667
$222$	−18.3309	−1.23029
$223$	0.697737	0.0467240	0.0233620	−	0.999727i	$-0.492563\pi$
$223$	0.697737	0.0467240	0.0233620	+	0.999727i	$0.492563\pi$
$224$	0	0
$225$	3.10155	0.206770
$226$	−31.5972	−2.10182
$227$	16.0398	1.06460	0.532300	−	0.846556i	$-0.321328\pi$
$227$	16.0398	1.06460	0.532300	+	0.846556i	$0.321328\pi$
$228$	2.18953	0.145005
$229$	17.4835	1.15534	0.577670	−	0.816271i	$-0.303962\pi$
$229$	17.4835	1.15534	0.577670	+	0.816271i	$0.303962\pi$
$230$	5.89144	0.388470
$231$	0	0
$232$	−3.83104	−0.251520
$233$	3.41082	0.223450	0.111725	−	0.993739i	$-0.464362\pi$
$233$	3.41082	0.223450	0.111725	+	0.993739i	$0.464362\pi$
$234$	−4.64435	−0.303611
$235$	−1.17313	−0.0765264
$236$	9.03175	0.587917
$237$	−5.49180	−0.356731
$238$	0	0
$239$	6.18953	0.400368	0.200184	−	0.979758i	$-0.435846\pi$
$239$	6.18953	0.400368	0.200184	+	0.979758i	$0.435846\pi$
$240$	−9.36967	−0.604810
$241$	−13.1455	−0.846779	−0.423389	−	0.905948i	$-0.639160\pi$
$241$	−13.1455	−0.846779	−0.423389	+	0.905948i	$0.639160\pi$
$242$	−25.8545	−1.66199
$243$	−13.2939	−0.852806
$244$	17.5644	1.12445
$245$	0	0
$246$	15.6800	0.999720
$247$	1.68133	0.106981
$248$	0.773483	0.0491163
$249$	6.11379	0.387446
$250$	−23.3421	−1.47628
$251$	−10.9026	−0.688167	−0.344084	−	0.938939i	$-0.611810\pi$
$251$	−10.9026	−0.688167	−0.344084	+	0.938939i	$0.611810\pi$
$252$	0	0
$253$	8.93543	0.561766
$254$	−26.3463	−1.65311
$255$	−11.4782	−0.718795
$256$	19.2622	1.20389
$257$	−17.0838	−1.06566	−0.532830	−	0.846223i	$-0.678871\pi$
$257$	−17.0838	−1.06566	−0.532830	+	0.846223i	$0.678871\pi$
$258$	8.16195	0.508141
$259$	0	0
$260$	4.93543	0.306083
$261$	11.1180	0.688184
$262$	14.4067	0.890046
$263$	−12.6168	−0.777983	−0.388991	−	0.921241i	$-0.627176\pi$
$263$	−12.6168	−0.777983	−0.388991	+	0.921241i	$0.627176\pi$
$264$	−3.04399	−0.187345
$265$	−8.61676	−0.529324
$266$	0	0
$267$	−22.8461	−1.39816
$268$	−16.2622	−0.993370
$269$	−6.99583	−0.426543	−0.213272	−	0.976993i	$-0.568412\pi$
$269$	−6.99583	−0.426543	−0.213272	+	0.976993i	$0.568412\pi$
$270$	18.0674	1.09955
$271$	11.6056	0.704989	0.352495	−	0.935814i	$-0.385334\pi$
$271$	11.6056	0.704989	0.352495	+	0.935814i	$0.385334\pi$
$272$	24.1895	1.46671
$273$	0	0
$274$	9.14554	0.552502
$275$	−10.7253	−0.646761
$276$	−3.96408	−0.238609
$277$	8.82164	0.530041	0.265021	−	0.964243i	$-0.414621\pi$
$277$	8.82164	0.530041	0.265021	+	0.964243i	$0.414621\pi$
$278$	36.3585	2.18064
$279$	−2.24470	−0.134387
$280$	0	0
$281$	20.4067	1.21736	0.608679	−	0.793416i	$-0.291700\pi$
$281$	20.4067	1.21736	0.608679	+	0.793416i	$0.291700\pi$
$282$	1.69357	0.100851
$283$	30.8255	1.83239	0.916194	−	0.400735i	$-0.131245\pi$
$283$	30.8255	1.83239	0.916194	+	0.400735i	$0.131245\pi$
$284$	14.0726	0.835057
$285$	−2.10856	−0.124900
$286$	16.0604	0.949671
$287$	0	0
$288$	−10.8709	−0.640572
$289$	12.6332	0.743128
$290$	−25.3491	−1.48855
$291$	−3.70713	−0.217316
$292$	−19.1976	−1.12345
$293$	1.77765	0.103852	0.0519258	−	0.998651i	$-0.483464\pi$
$293$	1.77765	0.103852	0.0519258	+	0.998651i	$0.483464\pi$
$294$	0	0
$295$	−8.69774	−0.506402
$296$	−3.71414	−0.215880
$297$	27.4025	1.59005
$298$	−35.3749	−2.04921
$299$	−3.04399	−0.176039
$300$	4.75814	0.274711
$301$	0	0
$302$	−3.04399	−0.175162
$303$	−18.7047	−1.07456
$304$	4.44364	0.254860
$305$	−16.9149	−0.968542
$306$	−15.0370	−0.859607
$307$	10.4272	0.595113	0.297557	−	0.954704i	$-0.403828\pi$
$307$	10.4272	0.595113	0.297557	+	0.954704i	$0.403828\pi$
$308$	0	0
$309$	−14.4465	−0.821831
$310$	5.11796	0.290680
$311$	−31.3062	−1.77521	−0.887605	−	0.460606i	$-0.847632\pi$
$311$	−31.3062	−1.77521	−0.887605	+	0.460606i	$0.847632\pi$
$312$	1.03698	0.0587076
$313$	−22.8545	−1.29181	−0.645905	−	0.763418i	$-0.723520\pi$
$313$	−22.8545	−1.29181	−0.645905	+	0.763418i	$0.723520\pi$
$314$	30.3738	1.71409
$315$	0	0
$316$	7.64541	0.430088
$317$	−7.01641	−0.394081	−0.197040	−	0.980395i	$-0.563133\pi$
$317$	−7.01641	−0.394081	−0.197040	+	0.980395i	$0.563133\pi$
$318$	12.4395	0.697571
$319$	−38.4465	−2.15259
$320$	9.84328	0.550256
$321$	−19.6660	−1.09765
$322$	0	0
$323$	5.44364	0.302892
$324$	−4.68133	−0.260074
$325$	3.65375	0.202673
$326$	0.273618	0.0151543
$327$	6.32568	0.349811
$328$	3.17703	0.175422
$329$	0	0
$330$	−20.1414	−1.10875
$331$	13.6332	0.749347	0.374673	−	0.927157i	$-0.377755\pi$
$331$	13.6332	0.749347	0.374673	+	0.927157i	$0.377755\pi$
$332$	−8.51131	−0.467119
$333$	10.7787	0.590670
$334$	26.5428	1.45236
$335$	15.6608	0.855638
$336$	0	0
$337$	12.6855	0.691023	0.345512	−	0.938414i	$-0.387705\pi$
$337$	12.6855	0.691023	0.345512	+	0.938414i	$0.387705\pi$
$338$	19.6894	1.07096
$339$	−20.4741	−1.11200
$340$	15.9794	0.866606
$341$	7.76231	0.420352
$342$	−2.76231	−0.149368
$343$	0	0
$344$	1.65375	0.0891640
$345$	3.81748	0.205526
$346$	−18.4342	−0.991031
$347$	16.0206	0.860030	0.430015	−	0.902822i	$-0.358508\pi$
$347$	16.0206	0.860030	0.430015	+	0.902822i	$0.358508\pi$
$348$	17.0562	0.914310
$349$	−26.1002	−1.39711	−0.698556	−	0.715555i	$-0.746174\pi$
$349$	−26.1002	−1.39711	−0.698556	+	0.715555i	$0.746174\pi$
$350$	0	0
$351$	−9.33508	−0.498270
$352$	37.5920	2.00366
$353$	−5.32284	−0.283306	−0.141653	−	0.989916i	$-0.545242\pi$
$353$	−5.32284	−0.283306	−0.141653	+	0.989916i	$0.545242\pi$
$354$	12.5564	0.667363
$355$	−13.5522	−0.719276
$356$	31.8052	1.68567
$357$	0	0
$358$	−28.3431	−1.49798
$359$	−18.8063	−0.992558	−0.496279	−	0.868163i	$-0.665301\pi$
$359$	−18.8063	−0.992558	−0.496279	+	0.868163i	$0.665301\pi$
$360$	1.18014	0.0621987
$361$	1.00000	0.0526316
$362$	−28.4067	−1.49302
$363$	−16.7529	−0.879300
$364$	0	0
$365$	18.4876	0.967687
$366$	24.4189	1.27640
$367$	32.0192	1.67139	0.835696	−	0.549193i	$-0.185065\pi$
$367$	32.0192	1.67139	0.835696	+	0.549193i	$0.185065\pi$
$368$	−8.04505	−0.419377
$369$	−9.21996	−0.479972
$370$	−24.5756	−1.27763
$371$	0	0
$372$	−3.44364	−0.178544
$373$	3.37490	0.174746	0.0873728	−	0.996176i	$-0.472153\pi$
$373$	3.37490	0.174746	0.0873728	+	0.996176i	$0.472153\pi$
$374$	51.9987	2.68879
$375$	−15.1250	−0.781050
$376$	0.343145	0.0176963
$377$	13.0974	0.674549
$378$	0	0
$379$	4.22235	0.216887	0.108444	−	0.994103i	$-0.465413\pi$
$379$	4.22235	0.216887	0.108444	+	0.994103i	$0.465413\pi$
$380$	2.93543	0.150585
$381$	−17.0716	−0.874603
$382$	36.5152	1.86828
$383$	1.17313	0.0599440	0.0299720	−	0.999551i	$-0.490458\pi$
$383$	1.17313	0.0599440	0.0299720	+	0.999551i	$0.490458\pi$
$384$	4.89428	0.249760
$385$	0	0
$386$	41.9229	2.13382
$387$	−4.79929	−0.243961
$388$	5.16089	0.262004
$389$	37.9435	1.92381	0.961906	−	0.273381i	$-0.0881419\pi$
$389$	37.9435	1.92381	0.961906	+	0.273381i	$0.0881419\pi$
$390$	6.86147	0.347444
$391$	−9.85552	−0.498415
$392$	0	0
$393$	9.33508	0.470892
$394$	28.5236	1.43700
$395$	−7.36266	−0.370456
$396$	−12.2981	−0.618002
$397$	26.9096	1.35056	0.675278	−	0.737564i	$-0.264024\pi$
$397$	26.9096	1.35056	0.675278	+	0.737564i	$0.264024\pi$
$398$	−45.3337	−2.27238
$399$	0	0
$400$	9.65659	0.482829
$401$	−3.19370	−0.159486	−0.0797430	−	0.996815i	$-0.525410\pi$
$401$	−3.19370	−0.159486	−0.0797430	+	0.996815i	$0.525410\pi$
$402$	−22.6084	−1.12761
$403$	−2.64435	−0.131724
$404$	26.0398	1.29553
$405$	4.50820	0.224014
$406$	0	0
$407$	−37.2733	−1.84757
$408$	3.35743	0.166218
$409$	21.0838	1.04253	0.521264	−	0.853396i	$-0.325461\pi$
$409$	21.0838	1.04253	0.521264	+	0.853396i	$0.325461\pi$
$410$	21.0216	1.03818
$411$	5.92604	0.292310
$412$	20.1117	0.990831
$413$	0	0
$414$	5.00106	0.245789
$415$	8.19654	0.402352
$416$	−12.8063	−0.627880
$417$	23.5592	1.15370
$418$	9.55220	0.467213
$419$	5.33508	0.260636	0.130318	−	0.991472i	$-0.458400\pi$
$419$	5.33508	0.260636	0.130318	+	0.991472i	$0.458400\pi$
$420$	0	0
$421$	16.8820	0.822780	0.411390	−	0.911459i	$-0.365043\pi$
$421$	16.8820	0.822780	0.411390	+	0.911459i	$0.365043\pi$
$422$	−28.7735	−1.40067
$423$	−0.995831	−0.0484190
$424$	2.52044	0.122403
$425$	11.8297	0.573825
$426$	19.5644	0.947900
$427$	0	0
$428$	27.3780	1.32337
$429$	10.4067	0.502438
$430$	10.9424	0.527691
$431$	34.1536	1.64512	0.822561	−	0.568677i	$-0.192545\pi$
$431$	34.1536	1.64512	0.822561	+	0.568677i	$0.192545\pi$
$432$	−24.6719	−1.18703
$433$	−13.5194	−0.649700	−0.324850	−	0.945766i	$-0.605314\pi$
$433$	−13.5194	−0.649700	−0.324850	+	0.945766i	$0.605314\pi$
$434$	0	0
$435$	−16.4254	−0.787540
$436$	−8.80630	−0.421745
$437$	−1.81047	−0.0866063
$438$	−26.6894	−1.27527
$439$	−2.03281	−0.0970209	−0.0485104	−	0.998823i	$-0.515447\pi$
$439$	−2.03281	−0.0970209	−0.0485104	+	0.998823i	$0.515447\pi$
$440$	−4.08097	−0.194553
$441$	0	0
$442$	−17.7141	−0.842576
$443$	29.9159	1.42135	0.710674	−	0.703521i	$-0.248390\pi$
$443$	29.9159	1.42135	0.710674	+	0.703521i	$0.248390\pi$
$444$	16.5358	0.784754
$445$	−30.6290	−1.45195
$446$	−1.35042	−0.0639444
$447$	−22.9219	−1.08417
$448$	0	0
$449$	15.8503	0.748021	0.374011	−	0.927424i	$-0.377982\pi$
$449$	15.8503	0.748021	0.374011	+	0.927424i	$0.377982\pi$
$450$	−6.00284	−0.282977
$451$	31.8831	1.50132
$452$	28.5030	1.34067
$453$	−1.97241	−0.0926721
$454$	−31.0440	−1.45697
$455$	0	0
$456$	0.616763	0.0288826
$457$	18.9547	0.886663	0.443331	−	0.896358i	$-0.353797\pi$
$457$	18.9547	0.886663	0.443331	+	0.896358i	$0.353797\pi$
$458$	−33.8381	−1.58115
$459$	−30.2241	−1.41074
$460$	−5.31450	−0.247790
$461$	15.2541	0.710454	0.355227	−	0.934780i	$-0.384404\pi$
$461$	15.2541	0.710454	0.355227	+	0.934780i	$0.384404\pi$
$462$	0	0
$463$	−29.1976	−1.35693	−0.678464	−	0.734634i	$-0.737354\pi$
$463$	−29.1976	−1.35693	−0.678464	+	0.734634i	$0.737354\pi$
$464$	34.6154	1.60698
$465$	3.31628	0.153789
$466$	−6.60142	−0.305805
$467$	−30.1086	−1.39326	−0.696629	−	0.717432i	$-0.745318\pi$
$467$	−30.1086	−1.39326	−0.696629	+	0.717432i	$0.745318\pi$
$468$	4.18953	0.193661
$469$	0	0
$470$	2.27051	0.104731
$471$	19.6813	0.906868
$472$	2.54413	0.117103
$473$	16.5962	0.763094
$474$	10.6290	0.488206
$475$	2.17313	0.0997099
$476$	0	0
$477$	−7.31450	−0.334908
$478$	−11.9794	−0.547926
$479$	33.2182	1.51778	0.758889	−	0.651220i	$-0.225743\pi$
$479$	33.2182	1.51778	0.758889	+	0.651220i	$0.225743\pi$
$480$	16.0604	0.733054
$481$	12.6977	0.578967
$482$	25.4423	1.15887
$483$	0	0
$484$	23.3226	1.06012
$485$	−4.97003	−0.225677
$486$	25.7295	1.16711
$487$	21.5110	0.974758	0.487379	−	0.873190i	$-0.337953\pi$
$487$	21.5110	0.974758	0.487379	+	0.873190i	$0.337953\pi$
$488$	4.94767	0.223971
$489$	0.177296	0.00801761
$490$	0	0
$491$	−33.4506	−1.50961	−0.754803	−	0.655951i	$-0.772268\pi$
$491$	−33.4506	−1.50961	−0.754803	+	0.655951i	$0.772268\pi$
$492$	−14.1445	−0.637683
$493$	42.4053	1.90984
$494$	−3.25410	−0.146409
$495$	11.8433	0.532316
$496$	−6.98882	−0.313807
$497$	0	0
$498$	−11.8328	−0.530241
$499$	5.79512	0.259425	0.129713	−	0.991552i	$-0.458595\pi$
$499$	5.79512	0.259425	0.129713	+	0.991552i	$0.458595\pi$
$500$	21.0562	0.941663
$501$	17.1989	0.768392
$502$	21.1013	0.941796
$503$	12.6925	0.565931	0.282966	−	0.959130i	$-0.408682\pi$
$503$	12.6925	0.565931	0.282966	+	0.959130i	$0.408682\pi$
$504$	0	0
$505$	−25.0768	−1.11590
$506$	−17.2939	−0.768809
$507$	12.7581	0.566609
$508$	23.7662	1.05445
$509$	−31.9505	−1.41618	−0.708091	−	0.706121i	$-0.750443\pi$
$509$	−31.9505	−1.41618	−0.708091	+	0.706121i	$0.750443\pi$
$510$	22.2153	0.983712
$511$	0	0
$512$	−29.4754	−1.30264
$513$	−5.55220	−0.245135
$514$	33.0646	1.45842
$515$	−19.3679	−0.853451
$516$	−7.36266	−0.324123
$517$	3.44364	0.151451
$518$	0	0
$519$	−11.9448	−0.524320
$520$	1.39025	0.0609663
$521$	6.41499	0.281046	0.140523	−	0.990077i	$-0.455122\pi$
$521$	6.41499	0.281046	0.140523	+	0.990077i	$0.455122\pi$
$522$	−21.5181	−0.941820
$523$	−6.28586	−0.274861	−0.137431	−	0.990511i	$-0.543884\pi$
$523$	−6.28586	−0.274861	−0.137431	+	0.990511i	$0.543884\pi$
$524$	−12.9958	−0.567726
$525$	0	0
$526$	24.4189	1.06471
$527$	−8.56159	−0.372949
$528$	27.5040	1.19696
$529$	−19.7222	−0.857488
$530$	16.6772	0.724410
$531$	−7.38324	−0.320405
$532$	0	0
$533$	−10.8615	−0.470462
$534$	44.2171	1.91346
$535$	−26.3655	−1.13988
$536$	−4.58084	−0.197862
$537$	−18.3655	−0.792530
$538$	13.5400	0.583749
$539$	0	0
$540$	−16.2981	−0.701358
$541$	8.03281	0.345358	0.172679	−	0.984978i	$-0.444758\pi$
$541$	8.03281	0.345358	0.172679	+	0.984978i	$0.444758\pi$
$542$	−22.4618	−0.964818
$543$	−18.4067	−0.789905
$544$	−41.4629	−1.77771
$545$	8.48062	0.363270
$546$	0	0
$547$	−33.0510	−1.41316	−0.706579	−	0.707634i	$-0.749763\pi$
$547$	−33.0510	−1.41316	−0.706579	+	0.707634i	$0.749763\pi$
$548$	−8.24993	−0.352420
$549$	−14.3585	−0.612806
$550$	20.7581	0.885130
$551$	7.78989	0.331860
$552$	−1.11663	−0.0475269
$553$	0	0
$554$	−17.0737	−0.725392
$555$	−15.9243	−0.675947
$556$	−32.7980	−1.39094
$557$	−5.56443	−0.235773	−0.117886	−	0.993027i	$-0.537612\pi$
$557$	−5.56443	−0.235773	−0.117886	+	0.993027i	$0.537612\pi$
$558$	4.34447	0.183916
$559$	−5.65375	−0.239128
$560$	0	0
$561$	33.6936	1.42254
$562$	−39.4957	−1.66603
$563$	−31.2059	−1.31517	−0.657587	−	0.753379i	$-0.728423\pi$
$563$	−31.2059	−1.31517	−0.657587	+	0.753379i	$0.728423\pi$
$564$	−1.52772	−0.0643286
$565$	−27.4489	−1.15478
$566$	−59.6608	−2.50773
$567$	0	0
$568$	3.96408	0.166329
$569$	−44.4311	−1.86265	−0.931325	−	0.364189i	$-0.881346\pi$
$569$	−44.4311	−1.86265	−0.931325	+	0.364189i	$0.881346\pi$
$570$	4.08097	0.170933
$571$	17.8349	0.746369	0.373185	−	0.927757i	$-0.378266\pi$
$571$	17.8349	0.746369	0.373185	+	0.927757i	$0.378266\pi$
$572$	−14.4876	−0.605758
$573$	23.6608	0.988442
$574$	0	0
$575$	−3.93437	−0.164075
$576$	8.35565	0.348152
$577$	−36.0674	−1.50151	−0.750753	−	0.660583i	$-0.770309\pi$
$577$	−36.0674	−1.50151	−0.750753	+	0.660583i	$0.770309\pi$
$578$	−24.4506	−1.01701
$579$	27.1648	1.12893
$580$	22.8667	0.949488
$581$	0	0
$582$	7.17491	0.297410
$583$	25.2939	1.04757
$584$	−5.40771	−0.223773
$585$	−4.03459	−0.166810
$586$	−3.44053	−0.142127
$587$	−11.7969	−0.486910	−0.243455	−	0.969912i	$-0.578281\pi$
$587$	−11.7969	−0.486910	−0.243455	+	0.969912i	$0.578281\pi$
$588$	0	0
$589$	−1.57277	−0.0648049
$590$	16.8339	0.693040
$591$	18.4824	0.760264
$592$	33.5592	1.37927
$593$	2.79406	0.114738	0.0573691	−	0.998353i	$-0.481729\pi$
$593$	2.79406	0.114738	0.0573691	+	0.998353i	$0.481729\pi$
$594$	−53.0357	−2.17608
$595$	0	0
$596$	31.9107	1.30711
$597$	−29.3749	−1.20223
$598$	5.89144	0.240919
$599$	−19.6660	−0.803530	−0.401765	−	0.915743i	$-0.631603\pi$
$599$	−19.6660	−0.803530	−0.401765	+	0.915743i	$0.631603\pi$
$600$	1.34030	0.0547177
$601$	−13.1801	−0.537629	−0.268814	−	0.963192i	$-0.586632\pi$
$601$	−13.1801	−0.537629	−0.268814	+	0.963192i	$0.586632\pi$
$602$	0	0
$603$	13.2939	0.541370
$604$	2.74590	0.111729
$605$	−22.4600	−0.913131
$606$	36.2018	1.47060
$607$	−16.0192	−0.650201	−0.325101	−	0.945679i	$-0.605398\pi$
$607$	−16.0192	−0.650201	−0.325101	+	0.945679i	$0.605398\pi$
$608$	−7.61676	−0.308901
$609$	0	0
$610$	32.7376	1.32551
$611$	−1.17313	−0.0474596
$612$	13.5644	0.548310
$613$	17.6555	0.713100	0.356550	−	0.934276i	$-0.383953\pi$
$613$	17.6555	0.713100	0.356550	+	0.934276i	$0.383953\pi$
$614$	−20.1812	−0.814447
$615$	13.6214	0.549267
$616$	0	0
$617$	−32.1278	−1.29342	−0.646708	−	0.762737i	$-0.723855\pi$
$617$	−32.1278	−1.29342	−0.646708	+	0.762737i	$0.723855\pi$
$618$	27.9602	1.12472
$619$	−22.7047	−0.912581	−0.456290	−	0.889831i	$-0.650822\pi$
$619$	−22.7047	−0.912581	−0.456290	+	0.889831i	$0.650822\pi$
$620$	−4.61676	−0.185414
$621$	10.0521	0.403375
$622$	60.5910	2.42948
$623$	0	0
$624$	−9.36967	−0.375087
$625$	−9.41188	−0.376475
$626$	44.2333	1.76792
$627$	6.18953	0.247186
$628$	−27.3994	−1.09335
$629$	41.1114	1.63922
$630$	0	0
$631$	−4.00523	−0.159446	−0.0797228	−	0.996817i	$-0.525404\pi$
$631$	−4.00523	−0.159446	−0.0797228	+	0.996817i	$0.525404\pi$
$632$	2.15361	0.0856660
$633$	−18.6443	−0.741046
$634$	13.5798	0.539322
$635$	−22.8873	−0.908254
$636$	−11.2213	−0.444953
$637$	0	0
$638$	74.4106	2.94594
$639$	−11.5040	−0.455093
$640$	6.56159	0.259370
$641$	14.3533	0.566920	0.283460	−	0.958984i	$-0.408518\pi$
$641$	14.3533	0.566920	0.283460	+	0.958984i	$0.408518\pi$
$642$	38.0622	1.50219
$643$	43.0685	1.69845	0.849227	−	0.528027i	$-0.177068\pi$
$643$	43.0685	1.69845	0.849227	+	0.528027i	$0.177068\pi$
$644$	0	0
$645$	7.09037	0.279183
$646$	−10.5358	−0.414525
$647$	−13.8349	−0.543908	−0.271954	−	0.962310i	$-0.587670\pi$
$647$	−13.8349	−0.543908	−0.271954	+	0.962310i	$0.587670\pi$
$648$	−1.31867	−0.0518022
$649$	25.5316	1.00220
$650$	−7.07158	−0.277370
$651$	0	0
$652$	−0.246823	−0.00966634
$653$	17.1648	0.671710	0.335855	−	0.941914i	$-0.390975\pi$
$653$	17.1648	0.671710	0.335855	+	0.941914i	$0.390975\pi$
$654$	−12.2429	−0.478736
$655$	12.5152	0.489010
$656$	−28.7061	−1.12078
$657$	15.6936	0.612264
$658$	0	0
$659$	24.5564	0.956580	0.478290	−	0.878202i	$-0.341257\pi$
$659$	24.5564	0.956580	0.478290	+	0.878202i	$0.341257\pi$
$660$	18.1690	0.707226
$661$	−29.6761	−1.15427	−0.577133	−	0.816650i	$-0.695829\pi$
$661$	−29.6761	−1.15427	−0.577133	+	0.816650i	$0.695829\pi$
$662$	−26.3861	−1.02552
$663$	−11.4782	−0.445778
$664$	−2.39753	−0.0930420
$665$	0	0
$666$	−20.8615	−0.808365
$667$	−14.1033	−0.546083
$668$	−23.9435	−0.926402
$669$	−0.875034	−0.0338308
$670$	−30.3103	−1.17099
$671$	49.6524	1.91681
$672$	0	0
$673$	−30.6412	−1.18113	−0.590566	−	0.806989i	$-0.701096\pi$
$673$	−30.6412	−1.18113	−0.590566	+	0.806989i	$0.701096\pi$
$674$	−24.5519	−0.945705
$675$	−12.0656	−0.464406
$676$	−17.7612	−0.683125
$677$	12.2294	0.470012	0.235006	−	0.971994i	$-0.424489\pi$
$677$	12.2294	0.470012	0.235006	+	0.971994i	$0.424489\pi$
$678$	39.6262	1.52183
$679$	0	0
$680$	4.50119	0.172613
$681$	−20.1156	−0.770830
$682$	−15.0234	−0.575276
$683$	31.8021	1.21687	0.608437	−	0.793602i	$-0.291797\pi$
$683$	31.8021	1.21687	0.608437	+	0.793602i	$0.291797\pi$
$684$	2.49180	0.0952762
$685$	7.94483	0.303556
$686$	0	0
$687$	−21.9260	−0.836530
$688$	−14.9424	−0.569675
$689$	−8.61676	−0.328273
$690$	−7.38847	−0.281274
$691$	5.23353	0.199093	0.0995464	−	0.995033i	$-0.468261\pi$
$691$	5.23353	0.199093	0.0995464	+	0.995033i	$0.468261\pi$
$692$	16.6290	0.632140
$693$	0	0
$694$	−31.0067	−1.17700
$695$	31.5850	1.19809
$696$	4.80452	0.182115
$697$	−35.1661	−1.33201
$698$	50.5152	1.91203
$699$	−4.27752	−0.161791
$700$	0	0
$701$	37.2804	1.40806	0.704030	−	0.710170i	$-0.251382\pi$
$701$	37.2804	1.40806	0.704030	+	0.710170i	$0.251382\pi$
$702$	18.0674	0.681910
$703$	7.55220	0.284836
$704$	−28.8943	−1.08899
$705$	1.47122	0.0554094
$706$	10.3020	0.387721
$707$	0	0
$708$	−11.3267	−0.425685
$709$	−8.35148	−0.313647	−0.156823	−	0.987627i	$-0.550125\pi$
$709$	−8.35148	−0.313647	−0.156823	+	0.987627i	$0.550125\pi$
$710$	26.2294	0.984370
$711$	−6.24993	−0.234391
$712$	8.95912	0.335757
$713$	2.84745	0.106638
$714$	0	0
$715$	13.9518	0.521769
$716$	25.5675	0.955504
$717$	−7.76231	−0.289889
$718$	36.3983	1.35837
$719$	5.01641	0.187080	0.0935402	−	0.995616i	$-0.470182\pi$
$719$	5.01641	0.187080	0.0935402	+	0.995616i	$0.470182\pi$
$720$	−10.6631	−0.397392
$721$	0	0
$722$	−1.93543	−0.0720293
$723$	16.4858	0.613115
$724$	25.6248	0.952339
$725$	16.9284	0.628706
$726$	32.4241	1.20337
$727$	−21.4314	−0.794847	−0.397423	−	0.917635i	$-0.630096\pi$
$727$	−21.4314	−0.794847	−0.397423	+	0.917635i	$0.630096\pi$
$728$	0	0
$729$	24.7159	0.915405
$730$	−35.7816	−1.32433
$731$	−18.3051	−0.677039
$732$	−22.0276	−0.814163
$733$	−34.1864	−1.26270	−0.631352	−	0.775496i	$-0.717500\pi$
$733$	−34.1864	−1.26270	−0.631352	+	0.775496i	$0.717500\pi$
$734$	−61.9711	−2.28739
$735$	0	0
$736$	13.7899	0.508302
$737$	−45.9711	−1.69337
$738$	17.8446	0.656869
$739$	−41.7938	−1.53741	−0.768705	−	0.639604i	$-0.779098\pi$
$739$	−41.7938	−1.53741	−0.768705	+	0.639604i	$0.779098\pi$
$740$	22.1690	0.814947
$741$	−2.10856	−0.0774599
$742$	0	0
$743$	−0.697737	−0.0255975	−0.0127988	−	0.999918i	$-0.504074\pi$
$743$	−0.697737	−0.0255975	−0.0127988	+	0.999918i	$0.504074\pi$
$744$	−0.970027	−0.0355629
$745$	−30.7306	−1.12588
$746$	−6.53189	−0.239149
$747$	6.95779	0.254572
$748$	−46.9065	−1.71507
$749$	0	0
$750$	29.2733	1.06891
$751$	−22.6496	−0.826495	−0.413247	−	0.910619i	$-0.635606\pi$
$751$	−22.6496	−0.826495	−0.413247	+	0.910619i	$0.635606\pi$
$752$	−3.10049	−0.113063
$753$	13.6730	0.498272
$754$	−25.3491	−0.923160
$755$	−2.64435	−0.0962377
$756$	0	0
$757$	21.0492	0.765047	0.382523	−	0.923946i	$-0.375055\pi$
$757$	21.0492	0.765047	0.382523	+	0.923946i	$0.375055\pi$
$758$	−8.17207	−0.296823
$759$	−11.2059	−0.406750
$760$	0.826873	0.0299938
$761$	12.7857	0.463482	0.231741	−	0.972778i	$-0.425558\pi$
$761$	12.7857	0.463482	0.231741	+	0.972778i	$0.425558\pi$
$762$	33.0409	1.19694
$763$	0	0
$764$	−32.9393	−1.19170
$765$	−13.0628	−0.472286
$766$	−2.27051	−0.0820368
$767$	−8.69774	−0.314057
$768$	−24.1567	−0.871681
$769$	−24.4119	−0.880315	−0.440157	−	0.897921i	$-0.645077\pi$
$769$	−24.4119	−0.880315	−0.440157	+	0.897921i	$0.645077\pi$
$770$	0	0
$771$	21.4248	0.771597
$772$	−37.8175	−1.36108
$773$	16.1291	0.580125	0.290062	−	0.957008i	$-0.406324\pi$
$773$	16.1291	0.580125	0.290062	+	0.957008i	$0.406324\pi$
$774$	9.28870	0.333875
$775$	−3.41783	−0.122772
$776$	1.45375	0.0521868
$777$	0	0
$778$	−73.4371	−2.63285
$779$	−6.46004	−0.231455
$780$	−6.18953	−0.221621
$781$	39.7816	1.42350
$782$	19.0747	0.682109
$783$	−43.2510	−1.54566
$784$	0	0
$785$	26.3861	0.941759
$786$	−18.0674	−0.644443
$787$	19.4835	0.694510	0.347255	−	0.937771i	$-0.387114\pi$
$787$	19.4835	0.694510	0.347255	+	0.937771i	$0.387114\pi$
$788$	−25.7303	−0.916603
$789$	15.8227	0.563303
$790$	14.2499	0.506990
$791$	0	0
$792$	−3.46421	−0.123095
$793$	−16.9149	−0.600664
$794$	−52.0818	−1.84831
$795$	10.8063	0.383260
$796$	40.8943	1.44946
$797$	2.81463	0.0996995	0.0498497	−	0.998757i	$-0.484126\pi$
$797$	2.81463	0.0996995	0.0498497	+	0.998757i	$0.484126\pi$
$798$	0	0
$799$	−3.79823	−0.134372
$800$	−16.5522	−0.585208
$801$	−26.0000	−0.918665
$802$	6.18120	0.218266
$803$	−54.2692	−1.91512
$804$	20.3944	0.719256
$805$	0	0
$806$	5.11796	0.180272
$807$	8.77348	0.308841
$808$	7.33508	0.258047
$809$	−20.0276	−0.704132	−0.352066	−	0.935975i	$-0.614521\pi$
$809$	−20.0276	−0.704132	−0.352066	+	0.935975i	$0.614521\pi$
$810$	−8.72532	−0.306577
$811$	22.5878	0.793167	0.396583	−	0.917999i	$-0.370196\pi$
$811$	22.5878	0.793167	0.396583	+	0.917999i	$0.370196\pi$
$812$	0	0
$813$	−14.5546	−0.510452
$814$	72.1400	2.52851
$815$	0.237695	0.00832609
$816$	−30.3361	−1.06198
$817$	−3.36266	−0.117645
$818$	−40.8063	−1.42676
$819$	0	0
$820$	−18.9630	−0.662217
$821$	−2.31344	−0.0807396	−0.0403698	−	0.999185i	$-0.512854\pi$
$821$	−2.31344	−0.0807396	−0.0403698	+	0.999185i	$0.512854\pi$
$822$	−11.4694	−0.400043
$823$	10.3156	0.359578	0.179789	−	0.983705i	$-0.442459\pi$
$823$	10.3156	0.359578	0.179789	+	0.983705i	$0.442459\pi$
$824$	5.66519	0.197356
$825$	13.4506	0.468291
$826$	0	0
$827$	39.6095	1.37736	0.688678	−	0.725067i	$-0.258191\pi$
$827$	39.6095	1.37736	0.688678	+	0.725067i	$0.258191\pi$
$828$	−4.51131	−0.156779
$829$	38.0552	1.32171	0.660855	−	0.750513i	$-0.270194\pi$
$829$	38.0552	1.32171	0.660855	+	0.750513i	$0.270194\pi$
$830$	−15.8639	−0.550642
$831$	−11.0632	−0.383780
$832$	9.84328	0.341254
$833$	0	0
$834$	−45.5972	−1.57890
$835$	23.0580	0.797955
$836$	−8.61676	−0.298017
$837$	8.73233	0.301834
$838$	−10.3257	−0.356695
$839$	−31.1596	−1.07575	−0.537874	−	0.843025i	$-0.680772\pi$
$839$	−31.1596	−1.07575	−0.537874	+	0.843025i	$0.680772\pi$
$840$	0	0
$841$	31.6824	1.09250
$842$	−32.6741	−1.12602
$843$	−25.5920	−0.881436
$844$	25.9557	0.893433
$845$	17.1044	0.588409
$846$	1.92736	0.0662641
$847$	0	0
$848$	−22.7735	−0.782045
$849$	−38.6584	−1.32675
$850$	−22.8956	−0.785313
$851$	−13.6730	−0.468704
$852$	−17.6485	−0.604628
$853$	10.6719	0.365400	0.182700	−	0.983169i	$-0.441516\pi$
$853$	10.6719	0.365400	0.182700	+	0.983169i	$0.441516\pi$
$854$	0	0
$855$	−2.39964	−0.0820661
$856$	7.71203	0.263592
$857$	29.1442	0.995547	0.497774	−	0.867307i	$-0.334151\pi$
$857$	29.1442	0.995547	0.497774	+	0.867307i	$0.334151\pi$
$858$	−20.1414	−0.687615
$859$	5.81437	0.198384	0.0991918	−	0.995068i	$-0.468374\pi$
$859$	5.81437	0.198384	0.0991918	+	0.995068i	$0.468374\pi$
$860$	−9.87086	−0.336594
$861$	0	0
$862$	−66.1020	−2.25144
$863$	−22.6496	−0.771001	−0.385500	−	0.922708i	$-0.625971\pi$
$863$	−22.6496	−0.771001	−0.385500	+	0.922708i	$0.625971\pi$
$864$	42.2898	1.43873
$865$	−16.0140	−0.544493
$866$	26.1658	0.889152
$867$	−15.8433	−0.538066
$868$	0	0
$869$	21.6126	0.733157
$870$	31.7903	1.07779
$871$	15.6608	0.530644
$872$	−2.48062	−0.0840043
$873$	−4.21890	−0.142788
$874$	3.50403	0.118526
$875$	0	0
$876$	24.0757	0.813444
$877$	9.70058	0.327565	0.163783	−	0.986496i	$-0.447630\pi$
$877$	9.70058	0.327565	0.163783	+	0.986496i	$0.447630\pi$
$878$	3.93437	0.132779
$879$	−2.22936	−0.0751943
$880$	36.8737	1.24301
$881$	−3.82581	−0.128895	−0.0644475	−	0.997921i	$-0.520528\pi$
$881$	−3.82581	−0.128895	−0.0644475	+	0.997921i	$0.520528\pi$
$882$	0	0
$883$	−25.5522	−0.859900	−0.429950	−	0.902853i	$-0.641469\pi$
$883$	−25.5522	−0.859900	−0.429950	+	0.902853i	$0.641469\pi$
$884$	15.9794	0.537446
$885$	10.9078	0.366663
$886$	−57.9002	−1.94520
$887$	−13.4725	−0.452364	−0.226182	−	0.974085i	$-0.572624\pi$
$887$	−13.4725	−0.452364	−0.226182	+	0.974085i	$0.572624\pi$
$888$	4.65791	0.156309
$889$	0	0
$890$	59.2804	1.98708
$891$	−13.2335	−0.443340
$892$	1.21818	0.0407876
$893$	−0.697737	−0.0233489
$894$	44.3637	1.48374
$895$	−24.6220	−0.823022
$896$	0	0
$897$	3.81748	0.127462
$898$	−30.6772	−1.02371
$899$	−12.2517	−0.408618
$900$	5.41499	0.180500
$901$	−27.8984	−0.929432
$902$	−61.7076	−2.05464
$903$	0	0
$904$	8.02891	0.267038
$905$	−24.6772	−0.820297
$906$	3.81748	0.126827
$907$	−7.32674	−0.243280	−0.121640	−	0.992574i	$-0.538815\pi$
$907$	−7.32674	−0.243280	−0.121640	+	0.992574i	$0.538815\pi$
$908$	28.0039	0.929342
$909$	−21.2869	−0.706042
$910$	0	0
$911$	−21.6537	−0.717421	−0.358710	−	0.933449i	$-0.616783\pi$
$911$	−21.6537	−0.717421	−0.358710	+	0.933449i	$0.616783\pi$
$912$	−5.57277	−0.184533
$913$	−24.0604	−0.796283
$914$	−36.6855	−1.21345
$915$	21.2130	0.701279
$916$	30.5243	1.00855
$917$	0	0
$918$	58.4968	1.93068
$919$	39.8678	1.31512	0.657558	−	0.753404i	$-0.271589\pi$
$919$	39.8678	1.31512	0.657558	+	0.753404i	$0.271589\pi$
$920$	−1.49702	−0.0493555
$921$	−13.0768	−0.430895
$922$	−29.5233	−0.972297
$923$	−13.5522	−0.446076
$924$	0	0
$925$	16.4119	0.539619
$926$	56.5100	1.85703
$927$	−16.4408	−0.539987
$928$	−59.3337	−1.94773
$929$	4.36683	0.143271	0.0716355	−	0.997431i	$-0.477178\pi$
$929$	4.36683	0.143271	0.0716355	+	0.997431i	$0.477178\pi$
$930$	−6.41844	−0.210469
$931$	0	0
$932$	5.95495	0.195061
$933$	39.2611	1.28535
$934$	58.2731	1.90675
$935$	45.1718	1.47728
$936$	1.18014	0.0385740
$937$	−14.9599	−0.488719	−0.244359	−	0.969685i	$-0.578578\pi$
$937$	−14.9599	−0.488719	−0.244359	+	0.969685i	$0.578578\pi$
$938$	0	0
$939$	28.6618	0.935343
$940$	−2.04816	−0.0668036
$941$	−4.72532	−0.154041	−0.0770206	−	0.997030i	$-0.524541\pi$
$941$	−4.72532	−0.154041	−0.0770206	+	0.997030i	$0.524541\pi$
$942$	−38.0919	−1.24110
$943$	11.6957	0.380864
$944$	−22.9875	−0.748179
$945$	0	0
$946$	−32.1208	−1.04434
$947$	29.5124	0.959023	0.479512	−	0.877536i	$-0.340814\pi$
$947$	29.5124	0.959023	0.479512	+	0.877536i	$0.340814\pi$
$948$	−9.58812	−0.311408
$949$	18.4876	0.600134
$950$	−4.20594	−0.136459
$951$	8.79929	0.285336
$952$	0	0
$953$	15.1114	0.489506	0.244753	−	0.969585i	$-0.421293\pi$
$953$	15.1114	0.489506	0.244753	+	0.969585i	$0.421293\pi$
$954$	14.1567	0.458341
$955$	31.7212	1.02647
$956$	10.8063	0.349501
$957$	48.2158	1.55860
$958$	−64.2915	−2.07717
$959$	0	0
$960$	−12.3445	−0.398416
$961$	−28.5264	−0.920206
$962$	−24.5756	−0.792350
$963$	−22.3808	−0.721213
$964$	−22.9508	−0.739195
$965$	36.4189	1.17237
$966$	0	0
$967$	−2.95779	−0.0951161	−0.0475580	−	0.998868i	$-0.515144\pi$
$967$	−2.95779	−0.0951161	−0.0475580	+	0.998868i	$0.515144\pi$
$968$	6.56966	0.211157
$969$	−6.82687	−0.219311
$970$	9.61915	0.308852
$971$	35.3924	1.13580	0.567898	−	0.823099i	$-0.307757\pi$
$971$	35.3924	1.13580	0.567898	+	0.823099i	$0.307757\pi$
$972$	−23.2098	−0.744456
$973$	0	0
$974$	−41.6332	−1.33401
$975$	−4.58217	−0.146747
$976$	−44.7047	−1.43096
$977$	−50.0140	−1.60009	−0.800045	−	0.599940i	$-0.795191\pi$
$977$	−50.0140	−1.60009	−0.800045	+	0.599940i	$0.795191\pi$
$978$	−0.343145	−0.0109726
$979$	89.9094	2.87352
$980$	0	0
$981$	7.19893	0.229844
$982$	64.7415	2.06598
$983$	35.0028	1.11642	0.558209	−	0.829701i	$-0.311489\pi$
$983$	35.0028	1.11642	0.558209	+	0.829701i	$0.311489\pi$
$984$	−3.98432	−0.127015
$985$	24.7787	0.789515
$986$	−82.0726	−2.61373
$987$	0	0
$988$	2.93543	0.0933885
$989$	6.08798	0.193587
$990$	−22.9219	−0.728505
$991$	15.0081	0.476747	0.238374	−	0.971174i	$-0.423386\pi$
$991$	15.0081	0.476747	0.238374	+	0.971174i	$0.423386\pi$
$992$	11.9794	0.380347
$993$	−17.0974	−0.542569
$994$	0	0
$995$	−39.3819	−1.24849
$996$	10.6741	0.338220
$997$	−57.6144	−1.82467	−0.912333	−	0.409449i	$-0.865721\pi$
$997$	−57.6144	−1.82467	−0.912333	+	0.409449i	$0.865721\pi$
$998$	−11.2161	−0.355038
$999$	−41.9313	−1.32665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.k.1.1		3
3.2	odd	2		8379.2.a.bo.1.3		3
7.2	even	3		931.2.f.m.704.3		6
7.3	odd	6		931.2.f.l.324.3		6
7.4	even	3		931.2.f.m.324.3		6
7.5	odd	6		931.2.f.l.704.3		6
7.6	odd	2		133.2.a.d.1.1	✓	3
21.20	even	2		1197.2.a.k.1.3		3
28.27	even	2		2128.2.a.p.1.2		3
35.34	odd	2		3325.2.a.r.1.3		3
56.13	odd	2		8512.2.a.bi.1.2		3
56.27	even	2		8512.2.a.bp.1.2		3
133.132	even	2		2527.2.a.f.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.a.d.1.1	✓	3	7.6	odd	2
931.2.a.k.1.1		3	1.1	even	1	trivial
931.2.f.l.324.3		6	7.3	odd	6
931.2.f.l.704.3		6	7.5	odd	6
931.2.f.m.324.3		6	7.4	even	3
931.2.f.m.704.3		6	7.2	even	3
1197.2.a.k.1.3		3	21.20	even	2
2128.2.a.p.1.2		3	28.27	even	2
2527.2.a.f.1.3		3	133.132	even	2
3325.2.a.r.1.3		3	35.34	odd	2
8379.2.a.bo.1.3		3	3.2	odd	2
8512.2.a.bi.1.2		3	56.13	odd	2
8512.2.a.bp.1.2		3	56.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q-1.93543 q^{2} -1.25410 q^{3} +1.74590 q^{4} -1.68133 q^{5} +2.42723 q^{6} +0.491797 q^{8} -1.42723 q^{9} +O(q^{10})\)	\(q-1.93543 q^{2} -1.25410 q^{3} +1.74590 q^{4} -1.68133 q^{5} +2.42723 q^{6} +0.491797 q^{8} -1.42723 q^{9} +3.25410 q^{10} +4.93543 q^{11} -2.18953 q^{12} -1.68133 q^{13} +2.10856 q^{15} -4.44364 q^{16} -5.44364 q^{17} +2.76231 q^{18} -1.00000 q^{19} -2.93543 q^{20} -9.55220 q^{22} +1.81047 q^{23} -0.616763 q^{24} -2.17313 q^{25} +3.25410 q^{26} +5.55220 q^{27} -7.78989 q^{29} -4.08097 q^{30} +1.57277 q^{31} +7.61676 q^{32} -6.18953 q^{33} +10.5358 q^{34} -2.49180 q^{36} -7.55220 q^{37} +1.93543 q^{38} +2.10856 q^{39} -0.826873 q^{40} +6.46004 q^{41} +3.36266 q^{43} +8.61676 q^{44} +2.39964 q^{45} -3.50403 q^{46} +0.697737 q^{47} +5.57277 q^{48} +4.20594 q^{50} +6.82687 q^{51} -2.93543 q^{52} +5.12497 q^{53} -10.7459 q^{54} -8.29809 q^{55} +1.25410 q^{57} +15.0768 q^{58} +5.17313 q^{59} +3.68133 q^{60} +10.0604 q^{61} -3.04399 q^{62} -5.85446 q^{64} +2.82687 q^{65} +11.9794 q^{66} -9.31450 q^{67} -9.50403 q^{68} -2.27051 q^{69} +8.06040 q^{71} -0.701906 q^{72} -10.9958 q^{73} +14.6168 q^{74} +2.72532 q^{75} -1.74590 q^{76} -4.08097 q^{78} +4.37907 q^{79} +7.47122 q^{80} -2.68133 q^{81} -12.5030 q^{82} -4.87503 q^{83} +9.15255 q^{85} -6.50820 q^{86} +9.76931 q^{87} +2.42723 q^{88} +18.2171 q^{89} -4.64435 q^{90} +3.16089 q^{92} -1.97241 q^{93} -1.35042 q^{94} +1.68133 q^{95} -9.55220 q^{96} +2.95601 q^{97} -7.04399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 2 q^{5} + q^{6} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 2 * q^5 + q^6 + 3 * q^8 + 2 * q^9	\( 3 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 2 q^{5} + q^{6} + 3 q^{8} + 2 q^{9} + 9 q^{10} + 7 q^{11} + 2 q^{12} + 2 q^{13} - 7 q^{15} - 4 q^{16} - 7 q^{17} + 6 q^{18} - 3 q^{19} - q^{20} - 6 q^{22} + 14 q^{23} + 13 q^{24} - q^{25} + 9 q^{26} - 6 q^{27} - 3 q^{29} - 17 q^{30} + 11 q^{31} + 8 q^{32} - 10 q^{33} + 12 q^{34} - 9 q^{36} - 2 q^{38} - 7 q^{39} - 8 q^{40} + 7 q^{41} - 4 q^{43} + 11 q^{44} + 19 q^{45} + 23 q^{46} - 8 q^{47} + 23 q^{48} + q^{50} + 26 q^{51} - q^{52} - q^{53} - 33 q^{54} - 3 q^{55} + 3 q^{57} + 18 q^{58} + 10 q^{59} + 4 q^{60} + 6 q^{61} + 12 q^{62} - 5 q^{64} + 14 q^{65} + 7 q^{66} - 3 q^{67} + 5 q^{68} - 3 q^{69} - 24 q^{72} - q^{73} + 29 q^{74} - 20 q^{75} - 6 q^{76} - 17 q^{78} - 4 q^{79} - 5 q^{80} - q^{81} - 24 q^{82} - 31 q^{83} - 7 q^{85} - 18 q^{86} - 20 q^{87} + q^{88} + 28 q^{89} + 19 q^{90} + 39 q^{92} - 24 q^{93} - 25 q^{94} - 2 q^{95} - 6 q^{96} + 30 q^{97}+O(q^{100}) \) 3 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 2 * q^5 + q^6 + 3 * q^8 + 2 * q^9 + 9 * q^10 + 7 * q^11 + 2 * q^12 + 2 * q^13 - 7 * q^15 - 4 * q^16 - 7 * q^17 + 6 * q^18 - 3 * q^19 - q^20 - 6 * q^22 + 14 * q^23 + 13 * q^24 - q^25 + 9 * q^26 - 6 * q^27 - 3 * q^29 - 17 * q^30 + 11 * q^31 + 8 * q^32 - 10 * q^33 + 12 * q^34 - 9 * q^36 - 2 * q^38 - 7 * q^39 - 8 * q^40 + 7 * q^41 - 4 * q^43 + 11 * q^44 + 19 * q^45 + 23 * q^46 - 8 * q^47 + 23 * q^48 + q^50 + 26 * q^51 - q^52 - q^53 - 33 * q^54 - 3 * q^55 + 3 * q^57 + 18 * q^58 + 10 * q^59 + 4 * q^60 + 6 * q^61 + 12 * q^62 - 5 * q^64 + 14 * q^65 + 7 * q^66 - 3 * q^67 + 5 * q^68 - 3 * q^69 - 24 * q^72 - q^73 + 29 * q^74 - 20 * q^75 - 6 * q^76 - 17 * q^78 - 4 * q^79 - 5 * q^80 - q^81 - 24 * q^82 - 31 * q^83 - 7 * q^85 - 18 * q^86 - 20 * q^87 + q^88 + 28 * q^89 + 19 * q^90 + 39 * q^92 - 24 * q^93 - 25 * q^94 - 2 * q^95 - 6 * q^96 + 30 * q^97

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