LMFDB - Embedded newform 7942.2.a.bd.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1940.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 8x - 2 $ x^3 - 8*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.69399$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.69399 q^{3} +1.00000 q^{4} +2.00000 q^{5} -2.69399 q^{6} -0.693995 q^{7} -1.00000 q^{8} +4.25761 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.69399 q^{3} +1.00000 q^{4} +2.00000 q^{5} -2.69399 q^{6} -0.693995 q^{7} -1.00000 q^{8} +4.25761 q^{9} -2.00000 q^{10} +1.00000 q^{11} +2.69399 q^{12} +4.25761 q^{13} +0.693995 q^{14} +5.38799 q^{15} +1.00000 q^{16} +7.95160 q^{17} -4.25761 q^{18} +2.00000 q^{20} -1.86962 q^{21} -1.00000 q^{22} +9.38799 q^{23} -2.69399 q^{24} -1.00000 q^{25} -4.25761 q^{26} +3.38799 q^{27} -0.693995 q^{28} -1.00000 q^{29} -5.38799 q^{30} -6.64560 q^{31} -1.00000 q^{32} +2.69399 q^{33} -7.95160 q^{34} -1.38799 q^{35} +4.25761 q^{36} +11.3396 q^{37} +11.4700 q^{39} -2.00000 q^{40} +2.56361 q^{41} +1.86962 q^{42} +2.43639 q^{43} +1.00000 q^{44} +8.51522 q^{45} -9.38799 q^{46} -10.2092 q^{47} +2.69399 q^{48} -6.51837 q^{49} +1.00000 q^{50} +21.4216 q^{51} +4.25761 q^{52} -10.7760 q^{53} -3.38799 q^{54} +2.00000 q^{55} +0.693995 q^{56} +1.00000 q^{58} +5.38799 q^{60} +7.13038 q^{61} +6.64560 q^{62} -2.95476 q^{63} +1.00000 q^{64} +8.51522 q^{65} -2.69399 q^{66} -8.08198 q^{67} +7.95160 q^{68} +25.2912 q^{69} +1.38799 q^{70} -2.43639 q^{71} -4.25761 q^{72} +3.43639 q^{73} -11.3396 q^{74} -2.69399 q^{75} -0.693995 q^{77} -11.4700 q^{78} +10.0820 q^{79} +2.00000 q^{80} -3.64560 q^{81} -2.56361 q^{82} -3.82438 q^{83} -1.86962 q^{84} +15.9032 q^{85} -2.43639 q^{86} -2.69399 q^{87} -1.00000 q^{88} -8.90321 q^{89} -8.51522 q^{90} -2.95476 q^{91} +9.38799 q^{92} -17.9032 q^{93} +10.2092 q^{94} -2.69399 q^{96} +6.90321 q^{97} +6.51837 q^{98} +4.25761 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 + 7 * q^9	$ 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} + 7 q^{9} - 6 q^{10} + 3 q^{11} + 7 q^{13} - 6 q^{14} + 3 q^{16} + 10 q^{17} - 7 q^{18} + 6 q^{20} - 16 q^{21} - 3 q^{22} + 12 q^{23} - 3 q^{25} - 7 q^{26} - 6 q^{27} + 6 q^{28} - 3 q^{29} + 2 q^{31} - 3 q^{32} - 10 q^{34} + 12 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{39} - 6 q^{40} + 10 q^{41} + 16 q^{42} + 5 q^{43} + 3 q^{44} + 14 q^{45} - 12 q^{46} - 11 q^{47} + 7 q^{49} + 3 q^{50} + 10 q^{51} + 7 q^{52} + 6 q^{54} + 6 q^{55} - 6 q^{56} + 3 q^{58} + 11 q^{61} - 2 q^{62} + 20 q^{63} + 3 q^{64} + 14 q^{65} + 10 q^{68} + 32 q^{69} - 12 q^{70} - 5 q^{71} - 7 q^{72} + 8 q^{73} - 4 q^{74} + 6 q^{77} + 6 q^{78} + 6 q^{79} + 6 q^{80} + 11 q^{81} - 10 q^{82} + 7 q^{83} - 16 q^{84} + 20 q^{85} - 5 q^{86} - 3 q^{88} + q^{89} - 14 q^{90} + 20 q^{91} + 12 q^{92} - 26 q^{93} + 11 q^{94} - 7 q^{97} - 7 q^{98} + 7 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 + 7 * q^9 - 6 * q^10 + 3 * q^11 + 7 * q^13 - 6 * q^14 + 3 * q^16 + 10 * q^17 - 7 * q^18 + 6 * q^20 - 16 * q^21 - 3 * q^22 + 12 * q^23 - 3 * q^25 - 7 * q^26 - 6 * q^27 + 6 * q^28 - 3 * q^29 + 2 * q^31 - 3 * q^32 - 10 * q^34 + 12 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^39 - 6 * q^40 + 10 * q^41 + 16 * q^42 + 5 * q^43 + 3 * q^44 + 14 * q^45 - 12 * q^46 - 11 * q^47 + 7 * q^49 + 3 * q^50 + 10 * q^51 + 7 * q^52 + 6 * q^54 + 6 * q^55 - 6 * q^56 + 3 * q^58 + 11 * q^61 - 2 * q^62 + 20 * q^63 + 3 * q^64 + 14 * q^65 + 10 * q^68 + 32 * q^69 - 12 * q^70 - 5 * q^71 - 7 * q^72 + 8 * q^73 - 4 * q^74 + 6 * q^77 + 6 * q^78 + 6 * q^79 + 6 * q^80 + 11 * q^81 - 10 * q^82 + 7 * q^83 - 16 * q^84 + 20 * q^85 - 5 * q^86 - 3 * q^88 + q^89 - 14 * q^90 + 20 * q^91 + 12 * q^92 - 26 * q^93 + 11 * q^94 - 7 * q^97 - 7 * q^98 + 7 * 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
$3$	2.69399	1.55538	0.777689	−	0.628649i	$-0.216392\pi$
$3$	2.69399	1.55538	0.777689	+	0.628649i	$0.216392\pi$
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	−2.69399	−1.09982
$7$	−0.693995	−0.262305	−0.131153	−	0.991362i	$-0.541868\pi$
$7$	−0.693995	−0.262305	−0.131153	+	0.991362i	$0.541868\pi$
$8$	−1.00000	−0.353553
$9$	4.25761	1.41920
$10$	−2.00000	−0.632456
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.69399	0.777689
$13$	4.25761	1.18085	0.590424	−	0.807093i	$-0.298961\pi$
$13$	4.25761	1.18085	0.590424	+	0.807093i	$0.298961\pi$
$14$	0.693995	0.185478
$15$	5.38799	1.39117
$16$	1.00000	0.250000
$17$	7.95160	1.92855	0.964273	−	0.264909i	$-0.0853418\pi$
$17$	7.95160	1.92855	0.964273	+	0.264909i	$0.0853418\pi$
$18$	−4.25761	−1.00353
$19$	0	0
$19$	0	0
$20$	2.00000	0.447214
$21$	−1.86962	−0.407984
$22$	−1.00000	−0.213201
$23$	9.38799	1.95753	0.978766	−	0.204983i	$-0.0657138\pi$
$23$	9.38799	1.95753	0.978766	+	0.204983i	$0.0657138\pi$
$24$	−2.69399	−0.549909
$25$	−1.00000	−0.200000
$26$	−4.25761	−0.834986
$27$	3.38799	0.652019
$28$	−0.693995	−0.131153
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	−5.38799	−0.983708
$31$	−6.64560	−1.19358	−0.596792	−	0.802396i	$-0.703558\pi$
$31$	−6.64560	−1.19358	−0.596792	+	0.802396i	$0.703558\pi$
$32$	−1.00000	−0.176777
$33$	2.69399	0.468964
$34$	−7.95160	−1.36369
$35$	−1.38799	−0.234613
$36$	4.25761	0.709601
$37$	11.3396	1.86422	0.932109	−	0.362178i	$-0.117967\pi$
$37$	11.3396	1.86422	0.932109	+	0.362178i	$0.117967\pi$
$38$	0	0
$39$	11.4700	1.83667
$40$	−2.00000	−0.316228
$41$	2.56361	0.400369	0.200185	−	0.979758i	$-0.435846\pi$
$41$	2.56361	0.400369	0.200185	+	0.979758i	$0.435846\pi$
$42$	1.86962	0.288488
$43$	2.43639	0.371545	0.185773	−	0.982593i	$-0.440521\pi$
$43$	2.43639	0.371545	0.185773	+	0.982593i	$0.440521\pi$
$44$	1.00000	0.150756
$45$	8.51522	1.26937
$46$	−9.38799	−1.38418
$47$	−10.2092	−1.48917	−0.744583	−	0.667530i	$-0.767352\pi$
$47$	−10.2092	−1.48917	−0.744583	+	0.667530i	$0.767352\pi$
$48$	2.69399	0.388845
$49$	−6.51837	−0.931196
$50$	1.00000	0.141421
$51$	21.4216	2.99962
$52$	4.25761	0.590424
$53$	−10.7760	−1.48019	−0.740097	−	0.672500i	$-0.765221\pi$
$53$	−10.7760	−1.48019	−0.740097	+	0.672500i	$0.765221\pi$
$54$	−3.38799	−0.461047
$55$	2.00000	0.269680
$56$	0.693995	0.0927390
$57$	0	0
$58$	1.00000	0.131306
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	5.38799	0.695586
$61$	7.13038	0.912952	0.456476	−	0.889736i	$-0.349111\pi$
$61$	7.13038	0.912952	0.456476	+	0.889736i	$0.349111\pi$
$62$	6.64560	0.843992
$63$	−2.95476	−0.372265
$64$	1.00000	0.125000
$65$	8.51522	1.05618
$66$	−2.69399	−0.331608
$67$	−8.08198	−0.987372	−0.493686	−	0.869640i	$-0.664351\pi$
$67$	−8.08198	−0.987372	−0.493686	+	0.869640i	$0.664351\pi$
$68$	7.95160	0.964273
$69$	25.2912	3.04470
$70$	1.38799	0.165896
$71$	−2.43639	−0.289146	−0.144573	−	0.989494i	$-0.546181\pi$
$71$	−2.43639	−0.289146	−0.144573	+	0.989494i	$0.546181\pi$
$72$	−4.25761	−0.501764
$73$	3.43639	0.402199	0.201099	−	0.979571i	$-0.435549\pi$
$73$	3.43639	0.402199	0.201099	+	0.979571i	$0.435549\pi$
$74$	−11.3396	−1.31820
$75$	−2.69399	−0.311076
$76$	0	0
$77$	−0.693995	−0.0790880
$78$	−11.4700	−1.29872
$79$	10.0820	1.13431	0.567156	−	0.823610i	$-0.308044\pi$
$79$	10.0820	1.13431	0.567156	+	0.823610i	$0.308044\pi$
$80$	2.00000	0.223607
$81$	−3.64560	−0.405066
$82$	−2.56361	−0.283104
$83$	−3.82438	−0.419780	−0.209890	−	0.977725i	$-0.567311\pi$
$83$	−3.82438	−0.419780	−0.209890	+	0.977725i	$0.567311\pi$
$84$	−1.86962	−0.203992
$85$	15.9032	1.72494
$86$	−2.43639	−0.262722
$87$	−2.69399	−0.288827
$88$	−1.00000	−0.106600
$89$	−8.90321	−0.943738	−0.471869	−	0.881669i	$-0.656420\pi$
$89$	−8.90321	−0.943738	−0.471869	+	0.881669i	$0.656420\pi$
$90$	−8.51522	−0.897583
$91$	−2.95476	−0.309743
$92$	9.38799	0.978766
$93$	−17.9032	−1.85648
$94$	10.2092	1.05300
$95$	0	0
$96$	−2.69399	−0.274955
$97$	6.90321	0.700914	0.350457	−	0.936579i	$-0.386026\pi$
$97$	6.90321	0.700914	0.350457	+	0.936579i	$0.386026\pi$
$98$	6.51837	0.658455
$99$	4.25761	0.427906
$100$	−1.00000	−0.100000
$101$	−0.257608	−0.0256330	−0.0128165	−	0.999918i	$-0.504080\pi$
$101$	−0.257608	−0.0256330	−0.0128165	+	0.999918i	$0.504080\pi$
$102$	−21.4216	−2.12105
$103$	−10.2092	−1.00594	−0.502972	−	0.864303i	$-0.667760\pi$
$103$	−10.2092	−1.00594	−0.502972	+	0.864303i	$0.667760\pi$
$104$	−4.25761	−0.417493
$105$	−3.73924	−0.364912
$106$	10.7760	1.04666
$107$	−8.98519	−0.868631	−0.434316	−	0.900761i	$-0.643010\pi$
$107$	−8.98519	−0.868631	−0.434316	+	0.900761i	$0.643010\pi$
$108$	3.38799	0.326009
$109$	−6.51837	−0.624347	−0.312173	−	0.950025i	$-0.601057\pi$
$109$	−6.51837	−0.624347	−0.312173	+	0.950025i	$0.601057\pi$
$110$	−2.00000	−0.190693
$111$	30.5488	2.89956
$112$	−0.693995	−0.0655763
$113$	4.90321	0.461255	0.230627	−	0.973042i	$-0.425922\pi$
$113$	4.90321	0.461255	0.230627	+	0.973042i	$0.425922\pi$
$114$	0	0
$115$	18.7760	1.75087
$116$	−1.00000	−0.0928477
$117$	18.1272	1.67586
$118$	0	0
$119$	−5.51837	−0.505868
$120$	−5.38799	−0.491854
$121$	1.00000	0.0909091
$122$	−7.13038	−0.645554
$123$	6.90636	0.622726
$124$	−6.64560	−0.596792
$125$	−12.0000	−1.07331
$126$	2.95476	0.263231
$127$	−2.51522	−0.223189	−0.111595	−	0.993754i	$-0.535596\pi$
$127$	−2.51522	−0.223189	−0.111595	+	0.993754i	$0.535596\pi$
$128$	−1.00000	−0.0883883
$129$	6.56361	0.577894
$130$	−8.51522	−0.746834
$131$	−14.9852	−1.30926	−0.654631	−	0.755949i	$-0.727176\pi$
$131$	−14.9852	−1.30926	−0.654631	+	0.755949i	$0.727176\pi$
$132$	2.69399	0.234482
$133$	0	0
$134$	8.08198	0.698177
$135$	6.77598	0.583183
$136$	−7.95160	−0.681844
$137$	−7.03359	−0.600920	−0.300460	−	0.953794i	$-0.597140\pi$
$137$	−7.03359	−0.600920	−0.300460	+	0.953794i	$0.597140\pi$
$138$	−25.2912	−2.15293
$139$	20.1640	1.71029	0.855143	−	0.518393i	$-0.173469\pi$
$139$	20.1640	1.71029	0.855143	+	0.518393i	$0.173469\pi$
$140$	−1.38799	−0.117307
$141$	−27.5036	−2.31622
$142$	2.43639	0.204457
$143$	4.25761	0.356039
$144$	4.25761	0.354801
$145$	−2.00000	−0.166091
$146$	−3.43639	−0.284397
$147$	−17.5605	−1.44836
$148$	11.3396	0.932109
$149$	−13.4216	−1.09954	−0.549769	−	0.835317i	$-0.685284\pi$
$149$	−13.4216	−1.09954	−0.549769	+	0.835317i	$0.685284\pi$
$150$	2.69399	0.219964
$151$	−12.3364	−1.00393	−0.501963	−	0.864889i	$-0.667388\pi$
$151$	−12.3364	−1.00393	−0.501963	+	0.864889i	$0.667388\pi$
$152$	0	0
$153$	33.8548	2.73700
$154$	0.693995	0.0559237
$155$	−13.2912	−1.06757
$156$	11.4700	0.918333
$157$	10.7760	0.860017	0.430008	−	0.902825i	$-0.358511\pi$
$157$	10.7760	0.860017	0.430008	+	0.902825i	$0.358511\pi$
$158$	−10.0820	−0.802080
$159$	−29.0304	−2.30226
$160$	−2.00000	−0.158114
$161$	−6.51522	−0.513471
$162$	3.64560	0.286425
$163$	−16.4184	−1.28599	−0.642995	−	0.765870i	$-0.722308\pi$
$163$	−16.4184	−1.28599	−0.642995	+	0.765870i	$0.722308\pi$
$164$	2.56361	0.200185
$165$	5.38799	0.419454
$166$	3.82438	0.296829
$167$	−18.5004	−1.43160	−0.715802	−	0.698303i	$-0.753939\pi$
$167$	−18.5004	−1.43160	−0.715802	+	0.698303i	$0.753939\pi$
$168$	1.86962	0.144244
$169$	5.12723	0.394402
$170$	−15.9032	−1.21972
$171$	0	0
$172$	2.43639	0.185773
$173$	2.64560	0.201141	0.100571	−	0.994930i	$-0.467933\pi$
$173$	2.64560	0.201141	0.100571	+	0.994930i	$0.467933\pi$
$174$	2.69399	0.204231
$175$	0.693995	0.0524611
$176$	1.00000	0.0753778
$177$	0	0
$178$	8.90321	0.667323
$179$	15.3880	1.15015	0.575076	−	0.818100i	$-0.304972\pi$
$179$	15.3880	1.15015	0.575076	+	0.818100i	$0.304972\pi$
$180$	8.51522	0.634687
$181$	−14.2124	−1.05640	−0.528198	−	0.849121i	$-0.677132\pi$
$181$	−14.2124	−1.05640	−0.528198	+	0.849121i	$0.677132\pi$
$182$	2.95476	0.219021
$183$	19.2092	1.41999
$184$	−9.38799	−0.692092
$185$	22.6792	1.66741
$186$	17.9032	1.31273
$187$	7.95160	0.581479
$188$	−10.2092	−0.744583
$189$	−2.35125	−0.171028
$190$	0	0
$191$	7.79079	0.563722	0.281861	−	0.959455i	$-0.409048\pi$
$191$	7.79079	0.563722	0.281861	+	0.959455i	$0.409048\pi$
$192$	2.69399	0.194422
$193$	12.8244	0.923119	0.461559	−	0.887109i	$-0.347290\pi$
$193$	12.8244	0.923119	0.461559	+	0.887109i	$0.347290\pi$
$194$	−6.90321	−0.495621
$195$	22.9399	1.64276
$196$	−6.51837	−0.465598
$197$	−1.09679	−0.0781434	−0.0390717	−	0.999236i	$-0.512440\pi$
$197$	−1.09679	−0.0781434	−0.0390717	+	0.999236i	$0.512440\pi$
$198$	−4.25761	−0.302575
$199$	13.5636	0.961499	0.480750	−	0.876858i	$-0.340365\pi$
$199$	13.5636	0.961499	0.480750	+	0.876858i	$0.340365\pi$
$200$	1.00000	0.0707107
$201$	−21.7728	−1.53574
$202$	0.257608	0.0181252
$203$	0.693995	0.0487089
$204$	21.4216	1.49981
$205$	5.12723	0.358101
$206$	10.2092	0.711309
$207$	39.9704	2.77813
$208$	4.25761	0.295212
$209$	0	0
$210$	3.73924	0.258032
$211$	8.16397	0.562031	0.281015	−	0.959703i	$-0.409329\pi$
$211$	8.16397	0.562031	0.281015	+	0.959703i	$0.409329\pi$
$212$	−10.7760	−0.740097
$213$	−6.56361	−0.449731
$214$	8.98519	0.614215
$215$	4.87277	0.332320
$216$	−3.38799	−0.230523
$217$	4.61201	0.313084
$218$	6.51837	0.441480
$219$	9.25761	0.625571
$220$	2.00000	0.134840
$221$	33.8548	2.27732
$222$	−30.5488	−2.05030
$223$	−14.4364	−0.966732	−0.483366	−	0.875418i	$-0.660586\pi$
$223$	−14.4364	−0.966732	−0.483366	+	0.875418i	$0.660586\pi$
$224$	0.693995	0.0463695
$225$	−4.25761	−0.283841
$226$	−4.90321	−0.326156
$227$	6.90636	0.458391	0.229196	−	0.973380i	$-0.426390\pi$
$227$	6.90636	0.458391	0.229196	+	0.973380i	$0.426390\pi$
$228$	0	0
$229$	4.92117	0.325200	0.162600	−	0.986692i	$-0.448012\pi$
$229$	4.92117	0.325200	0.162600	+	0.986692i	$0.448012\pi$
$230$	−18.7760	−1.23805
$231$	−1.86962	−0.123012
$232$	1.00000	0.0656532
$233$	20.9820	1.37458	0.687289	−	0.726384i	$-0.258800\pi$
$233$	20.9820	1.37458	0.687289	+	0.726384i	$0.258800\pi$
$234$	−18.1272	−1.18501
$235$	−20.4184	−1.33195
$236$	0	0
$237$	27.1608	1.76428
$238$	5.51837	0.357703
$239$	−1.22402	−0.0791753	−0.0395877	−	0.999216i	$-0.512604\pi$
$239$	−1.22402	−0.0791753	−0.0395877	+	0.999216i	$0.512604\pi$
$240$	5.38799	0.347793
$241$	4.26076	0.274460	0.137230	−	0.990539i	$-0.456180\pi$
$241$	4.26076	0.274460	0.137230	+	0.990539i	$0.456180\pi$
$242$	−1.00000	−0.0642824
$243$	−19.9852	−1.28205
$244$	7.13038	0.456476
$245$	−13.0367	−0.832887
$246$	−6.90636	−0.440333
$247$	0	0
$248$	6.64560	0.421996
$249$	−10.3029	−0.652917
$250$	12.0000	0.758947
$251$	14.5972	0.921367	0.460684	−	0.887564i	$-0.347604\pi$
$251$	14.5972	0.921367	0.460684	+	0.887564i	$0.347604\pi$
$252$	−2.95476	−0.186132
$253$	9.38799	0.590218
$254$	2.51522	0.157819
$255$	42.8432	2.68294
$256$	1.00000	0.0625000
$257$	−16.4184	−1.02415	−0.512077	−	0.858940i	$-0.671124\pi$
$257$	−16.4184	−1.02415	−0.512077	+	0.858940i	$0.671124\pi$
$258$	−6.56361	−0.408633
$259$	−7.86962	−0.488994
$260$	8.51522	0.528091
$261$	−4.25761	−0.263539
$262$	14.9852	0.925788
$263$	23.6488	1.45824	0.729122	−	0.684383i	$-0.239929\pi$
$263$	23.6488	1.45824	0.729122	+	0.684383i	$0.239929\pi$
$264$	−2.69399	−0.165804
$265$	−21.5520	−1.32393
$266$	0	0
$267$	−23.9852	−1.46787
$268$	−8.08198	−0.493686
$269$	−9.95160	−0.606760	−0.303380	−	0.952870i	$-0.598115\pi$
$269$	−9.95160	−0.606760	−0.303380	+	0.952870i	$0.598115\pi$
$270$	−6.77598	−0.412373
$271$	−12.0000	−0.728948	−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000	−0.728948	−0.364474	+	0.931214i	$0.618751\pi$
$272$	7.95160	0.482137
$273$	−7.96010	−0.481767
$274$	7.03359	0.424915
$275$	−1.00000	−0.0603023
$276$	25.2912	1.52235
$277$	0.869618	0.0522503	0.0261252	−	0.999659i	$-0.491683\pi$
$277$	0.869618	0.0522503	0.0261252	+	0.999659i	$0.491683\pi$
$278$	−20.1640	−1.20935
$279$	−28.2944	−1.69394
$280$	1.38799	0.0829482
$281$	13.8548	0.826509	0.413254	−	0.910616i	$-0.364392\pi$
$281$	13.8548	0.826509	0.413254	+	0.910616i	$0.364392\pi$
$282$	27.5036	1.63781
$283$	−10.4184	−0.619311	−0.309655	−	0.950849i	$-0.600214\pi$
$283$	−10.4184	−0.619311	−0.309655	+	0.950849i	$0.600214\pi$
$284$	−2.43639	−0.144573
$285$	0	0
$286$	−4.25761	−0.251758
$287$	−1.77913	−0.105019
$288$	−4.25761	−0.250882
$289$	46.2280	2.71929
$290$	2.00000	0.117444
$291$	18.5972	1.09019
$292$	3.43639	0.201099
$293$	23.7760	1.38901	0.694504	−	0.719489i	$-0.255624\pi$
$293$	23.7760	1.38901	0.694504	+	0.719489i	$0.255624\pi$
$294$	17.5605	1.02415
$295$	0	0
$296$	−11.3396	−0.659100
$297$	3.38799	0.196591
$298$	13.4216	0.777491
$299$	39.9704	2.31155
$300$	−2.69399	−0.155538
$301$	−1.69084	−0.0974584
$302$	12.3364	0.709882
$303$	−0.693995	−0.0398690
$304$	0	0
$305$	14.2608	0.816569
$306$	−33.8548	−1.93535
$307$	−27.1492	−1.54948	−0.774742	−	0.632277i	$-0.782120\pi$
$307$	−27.1492	−1.54948	−0.774742	+	0.632277i	$0.782120\pi$
$308$	−0.693995	−0.0395440
$309$	−27.5036	−1.56462
$310$	13.2912	0.754889
$311$	6.98519	0.396094	0.198047	−	0.980193i	$-0.436540\pi$
$311$	6.98519	0.396094	0.198047	+	0.980193i	$0.436540\pi$
$312$	−11.4700	−0.649359
$313$	8.16081	0.461276	0.230638	−	0.973040i	$-0.425919\pi$
$313$	8.16081	0.461276	0.230638	+	0.973040i	$0.425919\pi$
$314$	−10.7760	−0.608124
$315$	−5.90952	−0.332963
$316$	10.0820	0.567156
$317$	22.9820	1.29080	0.645400	−	0.763845i	$-0.276691\pi$
$317$	22.9820	1.29080	0.645400	+	0.763845i	$0.276691\pi$
$318$	29.0304	1.62795
$319$	−1.00000	−0.0559893
$320$	2.00000	0.111803
$321$	−24.2061	−1.35105
$322$	6.51522	0.363079
$323$	0	0
$324$	−3.64560	−0.202533
$325$	−4.25761	−0.236170
$326$	16.4184	0.909332
$327$	−17.5605	−0.971096
$328$	−2.56361	−0.141552
$329$	7.08514	0.390616
$330$	−5.38799	−0.296599
$331$	2.17878	0.119757	0.0598783	−	0.998206i	$-0.480929\pi$
$331$	2.17878	0.119757	0.0598783	+	0.998206i	$0.480929\pi$
$332$	−3.82438	−0.209890
$333$	48.2795	2.64570
$334$	18.5004	1.01230
$335$	−16.1640	−0.883132
$336$	−1.86962	−0.101996
$337$	−24.3216	−1.32488	−0.662442	−	0.749113i	$-0.730480\pi$
$337$	−24.3216	−1.32488	−0.662442	+	0.749113i	$0.730480\pi$
$338$	−5.12723	−0.278884
$339$	13.2092	0.717426
$340$	15.9032	0.862472
$341$	−6.64560	−0.359879
$342$	0	0
$343$	9.38168	0.506563
$344$	−2.43639	−0.131361
$345$	50.5824	2.72326
$346$	−2.64560	−0.142228
$347$	0.566768	0.0304257	0.0152129	−	0.999884i	$-0.495157\pi$
$347$	0.566768	0.0304257	0.0152129	+	0.999884i	$0.495157\pi$
$348$	−2.69399	−0.144413
$349$	13.1577	0.704313	0.352157	−	0.935941i	$-0.385448\pi$
$349$	13.1577	0.704313	0.352157	+	0.935941i	$0.385448\pi$
$350$	−0.693995	−0.0370956
$351$	14.4247	0.769935
$352$	−1.00000	−0.0533002
$353$	−17.5215	−0.932577	−0.466288	−	0.884633i	$-0.654409\pi$
$353$	−17.5215	−0.932577	−0.466288	+	0.884633i	$0.654409\pi$
$354$	0	0
$355$	−4.87277	−0.258620
$356$	−8.90321	−0.471869
$357$	−14.8665	−0.786817
$358$	−15.3880	−0.813281
$359$	36.6792	1.93585	0.967927	−	0.251233i	$-0.0808360\pi$
$359$	36.6792	1.93585	0.967927	+	0.251233i	$0.0808360\pi$
$360$	−8.51522	−0.448791
$361$	0	0
$362$	14.2124	0.746985
$363$	2.69399	0.141398
$364$	−2.95476	−0.154871
$365$	6.87277	0.359737
$366$	−19.2092	−1.00408
$367$	−6.24280	−0.325871	−0.162936	−	0.986637i	$-0.552096\pi$
$367$	−6.24280	−0.325871	−0.162936	+	0.986637i	$0.552096\pi$
$368$	9.38799	0.489383
$369$	10.9149	0.568205
$370$	−22.6792	−1.17903
$371$	7.47847	0.388263
$372$	−17.9032	−0.928238
$373$	−15.9664	−0.826710	−0.413355	−	0.910570i	$-0.635643\pi$
$373$	−15.9664	−0.826710	−0.413355	+	0.910570i	$0.635643\pi$
$374$	−7.95160	−0.411168
$375$	−32.3279	−1.66941
$376$	10.2092	0.526500
$377$	−4.25761	−0.219278
$378$	2.35125	0.120935
$379$	−9.05155	−0.464947	−0.232474	−	0.972603i	$-0.574682\pi$
$379$	−9.05155	−0.464947	−0.232474	+	0.972603i	$0.574682\pi$
$380$	0	0
$381$	−6.77598	−0.347144
$382$	−7.79079	−0.398611
$383$	−24.1640	−1.23472	−0.617361	−	0.786680i	$-0.711798\pi$
$383$	−24.1640	−1.23472	−0.617361	+	0.786680i	$0.711798\pi$
$384$	−2.69399	−0.137477
$385$	−1.38799	−0.0707385
$386$	−12.8244	−0.652744
$387$	10.3732	0.527298
$388$	6.90321	0.350457
$389$	0.145191	0.00736149	0.00368075	−	0.999993i	$-0.498828\pi$
$389$	0.145191	0.00736149	0.00368075	+	0.999993i	$0.498828\pi$
$390$	−22.9399	−1.16161
$391$	74.6496	3.77519
$392$	6.51837	0.329227
$393$	−40.3700	−2.03640
$394$	1.09679	0.0552557
$395$	20.1640	1.01456
$396$	4.25761	0.213953
$397$	−2.66041	−0.133522	−0.0667610	−	0.997769i	$-0.521267\pi$
$397$	−2.66041	−0.133522	−0.0667610	+	0.997769i	$0.521267\pi$
$398$	−13.5636	−0.679882
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	19.0032	0.948972	0.474486	−	0.880263i	$-0.342634\pi$
$401$	19.0032	0.948972	0.474486	+	0.880263i	$0.342634\pi$
$402$	21.7728	1.08593
$403$	−28.2944	−1.40944
$404$	−0.257608	−0.0128165
$405$	−7.29120	−0.362302
$406$	−0.693995	−0.0344424
$407$	11.3396	0.562083
$408$	−21.4216	−1.06053
$409$	33.9220	1.67733	0.838667	−	0.544644i	$-0.183335\pi$
$409$	33.9220	1.67733	0.838667	+	0.544644i	$0.183335\pi$
$410$	−5.12723	−0.253216
$411$	−18.9484	−0.934658
$412$	−10.2092	−0.502972
$413$	0	0
$414$	−39.9704	−1.96444
$415$	−7.64875	−0.375463
$416$	−4.25761	−0.208746
$417$	54.3216	2.66014
$418$	0	0
$419$	−16.6940	−0.815555	−0.407778	−	0.913081i	$-0.633696\pi$
$419$	−16.6940	−0.815555	−0.407778	+	0.913081i	$0.633696\pi$
$420$	−3.73924	−0.182456
$421$	22.8244	1.11239	0.556196	−	0.831051i	$-0.312260\pi$
$421$	22.8244	1.11239	0.556196	+	0.831051i	$0.312260\pi$
$422$	−8.16397	−0.397416
$423$	−43.4668	−2.11343
$424$	10.7760	0.523328
$425$	−7.95160	−0.385709
$426$	6.56361	0.318008
$427$	−4.94845	−0.239472
$428$	−8.98519	−0.434316
$429$	11.4700	0.553776
$430$	−4.87277	−0.234986
$431$	−17.5668	−0.846161	−0.423081	−	0.906092i	$-0.639051\pi$
$431$	−17.5668	−0.846161	−0.423081	+	0.906092i	$0.639051\pi$
$432$	3.38799	0.163005
$433$	−33.1912	−1.59507	−0.797535	−	0.603273i	$-0.793863\pi$
$433$	−33.1912	−1.59507	−0.797535	+	0.603273i	$0.793863\pi$
$434$	−4.61201	−0.221384
$435$	−5.38799	−0.258334
$436$	−6.51837	−0.312173
$437$	0	0
$438$	−9.25761	−0.442346
$439$	−13.4848	−0.643594	−0.321797	−	0.946809i	$-0.604287\pi$
$439$	−13.4848	−0.643594	−0.321797	+	0.946809i	$0.604287\pi$
$440$	−2.00000	−0.0953463
$441$	−27.7527	−1.32156
$442$	−33.8548	−1.61031
$443$	−2.43954	−0.115906	−0.0579531	−	0.998319i	$-0.518457\pi$
$443$	−2.43954	−0.115906	−0.0579531	+	0.998319i	$0.518457\pi$
$444$	30.5488	1.44978
$445$	−17.8064	−0.844105
$446$	14.4364	0.683583
$447$	−36.1577	−1.71020
$448$	−0.693995	−0.0327882
$449$	6.83919	0.322761	0.161381	−	0.986892i	$-0.448405\pi$
$449$	6.83919	0.322761	0.161381	+	0.986892i	$0.448405\pi$
$450$	4.25761	0.200706
$451$	2.56361	0.120716
$452$	4.90321	0.230627
$453$	−33.2343	−1.56148
$454$	−6.90636	−0.324132
$455$	−5.90952	−0.277042
$456$	0	0
$457$	−19.9516	−0.933297	−0.466648	−	0.884443i	$-0.654539\pi$
$457$	−19.9516	−0.933297	−0.466648	+	0.884443i	$0.654539\pi$
$458$	−4.92117	−0.229951
$459$	26.9399	1.25745
$460$	18.7760	0.875435
$461$	17.3911	0.809986	0.404993	−	0.914320i	$-0.367274\pi$
$461$	17.3911	0.809986	0.404993	+	0.914320i	$0.367274\pi$
$462$	1.86962	0.0869825
$463$	10.9852	0.510525	0.255263	−	0.966872i	$-0.417838\pi$
$463$	10.9852	0.510525	0.255263	+	0.966872i	$0.417838\pi$
$464$	−1.00000	−0.0464238
$465$	−35.8064	−1.66048
$466$	−20.9820	−0.971974
$467$	−1.82122	−0.0842761	−0.0421380	−	0.999112i	$-0.513417\pi$
$467$	−1.82122	−0.0842761	−0.0421380	+	0.999112i	$0.513417\pi$
$468$	18.1272	0.837931
$469$	5.60886	0.258993
$470$	20.4184	0.941832
$471$	29.0304	1.33765
$472$	0	0
$473$	2.43639	0.112025
$474$	−27.1608	−1.24754
$475$	0	0
$476$	−5.51837	−0.252934
$477$	−45.8799	−2.10070
$478$	1.22402	0.0559854
$479$	4.79079	0.218897	0.109448	−	0.993992i	$-0.465092\pi$
$479$	4.79079	0.218897	0.109448	+	0.993992i	$0.465092\pi$
$480$	−5.38799	−0.245927
$481$	48.2795	2.20136
$482$	−4.26076	−0.194072
$483$	−17.5520	−0.798642
$484$	1.00000	0.0454545
$485$	13.8064	0.626917
$486$	19.9852	0.906547
$487$	−35.6308	−1.61459	−0.807293	−	0.590151i	$-0.799068\pi$
$487$	−35.6308	−1.61459	−0.807293	+	0.590151i	$0.799068\pi$
$488$	−7.13038	−0.322777
$489$	−44.2311	−2.00020
$490$	13.0367	0.588940
$491$	−6.41842	−0.289659	−0.144830	−	0.989457i	$-0.546263\pi$
$491$	−6.41842	−0.289659	−0.144830	+	0.989457i	$0.546263\pi$
$492$	6.90636	0.311363
$493$	−7.95160	−0.358122
$494$	0	0
$495$	8.51522	0.382731
$496$	−6.64560	−0.298396
$497$	1.69084	0.0758445
$498$	10.3029	0.461682
$499$	2.51522	0.112597	0.0562983	−	0.998414i	$-0.482070\pi$
$499$	2.51522	0.112597	0.0562983	+	0.998414i	$0.482070\pi$
$500$	−12.0000	−0.536656
$501$	−49.8400	−2.22669
$502$	−14.5972	−0.651505
$503$	25.2912	1.12768	0.563839	−	0.825884i	$-0.309324\pi$
$503$	25.2912	1.12768	0.563839	+	0.825884i	$0.309324\pi$
$504$	2.95476	0.131615
$505$	−0.515216	−0.0229268
$506$	−9.38799	−0.417347
$507$	13.8127	0.613445
$508$	−2.51522	−0.111595
$509$	1.29120	0.0572312	0.0286156	−	0.999590i	$-0.490890\pi$
$509$	1.29120	0.0572312	0.0286156	+	0.999590i	$0.490890\pi$
$510$	−42.8432	−1.89713
$511$	−2.38483	−0.105499
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	16.4184	0.724186
$515$	−20.4184	−0.899743
$516$	6.56361	0.288947
$517$	−10.2092	−0.449001
$518$	7.86962	0.345771
$519$	7.12723	0.312851
$520$	−8.51522	−0.373417
$521$	37.2944	1.63390	0.816948	−	0.576712i	$-0.195664\pi$
$521$	37.2944	1.63390	0.816948	+	0.576712i	$0.195664\pi$
$522$	4.25761	0.186350
$523$	−22.2092	−0.971141	−0.485570	−	0.874198i	$-0.661388\pi$
$523$	−22.2092	−0.971141	−0.485570	+	0.874198i	$0.661388\pi$
$524$	−14.9852	−0.654631
$525$	1.86962	0.0815968
$526$	−23.6488	−1.03113
$527$	−52.8432	−2.30188
$528$	2.69399	0.117241
$529$	65.1343	2.83193
$530$	21.5520	0.936157
$531$	0	0
$532$	0	0
$533$	10.9149	0.472775
$534$	23.9852	1.03794
$535$	−17.9704	−0.776927
$536$	8.08198	0.349089
$537$	41.4552	1.78892
$538$	9.95160	0.429044
$539$	−6.51837	−0.280766
$540$	6.77598	0.291592
$541$	−29.7791	−1.28030	−0.640152	−	0.768248i	$-0.721129\pi$
$541$	−29.7791	−1.28030	−0.640152	+	0.768248i	$0.721129\pi$
$542$	12.0000	0.515444
$543$	−38.2880	−1.64310
$544$	−7.95160	−0.340922
$545$	−13.0367	−0.558433
$546$	7.96010	0.340661
$547$	2.43639	0.104172	0.0520862	−	0.998643i	$-0.483413\pi$
$547$	2.43639	0.104172	0.0520862	+	0.998643i	$0.483413\pi$
$548$	−7.03359	−0.300460
$549$	30.3584	1.29566
$550$	1.00000	0.0426401
$551$	0	0
$552$	−25.2912	−1.07646
$553$	−6.99684	−0.297536
$554$	−0.869618	−0.0369465
$555$	61.0976	2.59345
$556$	20.1640	0.855143
$557$	23.7424	1.00600	0.502999	−	0.864287i	$-0.332230\pi$
$557$	23.7424	1.00600	0.502999	+	0.864287i	$0.332230\pi$
$558$	28.2944	1.19780
$559$	10.3732	0.438739
$560$	−1.38799	−0.0586533
$561$	21.4216	0.904420
$562$	−13.8548	−0.584430
$563$	−4.16397	−0.175490	−0.0877452	−	0.996143i	$-0.527966\pi$
$563$	−4.16397	−0.175490	−0.0877452	+	0.996143i	$0.527966\pi$
$564$	−27.5036	−1.15811
$565$	9.80641	0.412559
$566$	10.4184	0.437919
$567$	2.53003	0.106251
$568$	2.43639	0.102229
$569$	−25.5456	−1.07093	−0.535465	−	0.844558i	$-0.679863\pi$
$569$	−25.5456	−1.07093	−0.535465	+	0.844558i	$0.679863\pi$
$570$	0	0
$571$	−8.98519	−0.376019	−0.188009	−	0.982167i	$-0.560203\pi$
$571$	−8.98519	−0.376019	−0.188009	+	0.982167i	$0.560203\pi$
$572$	4.25761	0.178020
$573$	20.9883	0.876801
$574$	1.77913	0.0742596
$575$	−9.38799	−0.391506
$576$	4.25761	0.177400
$577$	4.90005	0.203992	0.101996	−	0.994785i	$-0.467477\pi$
$577$	4.90005	0.203992	0.101996	+	0.994785i	$0.467477\pi$
$578$	−46.2280	−1.92283
$579$	34.5488	1.43580
$580$	−2.00000	−0.0830455
$581$	2.65410	0.110111
$582$	−18.5972	−0.770879
$583$	−10.7760	−0.446295
$584$	−3.43639	−0.142199
$585$	36.2545	1.49894
$586$	−23.7760	−0.982177
$587$	24.6940	1.01923	0.509615	−	0.860402i	$-0.329788\pi$
$587$	24.6940	1.01923	0.509615	+	0.860402i	$0.329788\pi$
$588$	−17.5605	−0.724181
$589$	0	0
$590$	0	0
$591$	−2.95476	−0.121543
$592$	11.3396	0.466054
$593$	21.2912	0.874325	0.437162	−	0.899383i	$-0.355984\pi$
$593$	21.2912	0.874325	0.437162	+	0.899383i	$0.355984\pi$
$594$	−3.38799	−0.139011
$595$	−11.0367	−0.452462
$596$	−13.4216	−0.549769
$597$	36.5403	1.49550
$598$	−39.9704	−1.63451
$599$	−26.9516	−1.10121	−0.550606	−	0.834765i	$-0.685603\pi$
$599$	−26.9516	−1.10121	−0.550606	+	0.834765i	$0.685603\pi$
$600$	2.69399	0.109982
$601$	−28.5824	−1.16590	−0.582950	−	0.812508i	$-0.698102\pi$
$601$	−28.5824	−1.16590	−0.582950	+	0.812508i	$0.698102\pi$
$602$	1.69084	0.0689135
$603$	−34.4099	−1.40128
$604$	−12.3364	−0.501963
$605$	2.00000	0.0813116
$606$	0.693995	0.0281916
$607$	−3.82122	−0.155099	−0.0775493	−	0.996989i	$-0.524710\pi$
$607$	−3.82122	−0.155099	−0.0775493	+	0.996989i	$0.524710\pi$
$608$	0	0
$609$	1.86962	0.0757608
$610$	−14.2608	−0.577401
$611$	−43.4668	−1.75848
$612$	33.8548	1.36850
$613$	−24.0703	−0.972191	−0.486096	−	0.873906i	$-0.661579\pi$
$613$	−24.0703	−0.972191	−0.486096	+	0.873906i	$0.661579\pi$
$614$	27.1492	1.09565
$615$	13.8127	0.556983
$616$	0.693995	0.0279618
$617$	−2.51837	−0.101386	−0.0506929	−	0.998714i	$-0.516143\pi$
$617$	−2.51837	−0.101386	−0.0506929	+	0.998714i	$0.516143\pi$
$618$	27.5036	1.10636
$619$	43.6488	1.75439	0.877196	−	0.480133i	$-0.159412\pi$
$619$	43.6488	1.75439	0.877196	+	0.480133i	$0.159412\pi$
$620$	−13.2912	−0.533787
$621$	31.8064	1.27635
$622$	−6.98519	−0.280081
$623$	6.17878	0.247548
$624$	11.4700	0.459166
$625$	−19.0000	−0.760000
$626$	−8.16081	−0.326172
$627$	0	0
$628$	10.7760	0.430008
$629$	90.1679	3.59523
$630$	5.90952	0.235441
$631$	−10.7876	−0.429449	−0.214724	−	0.976675i	$-0.568885\pi$
$631$	−10.7876	−0.429449	−0.214724	+	0.976675i	$0.568885\pi$
$632$	−10.0820	−0.401040
$633$	21.9937	0.874171
$634$	−22.9820	−0.912733
$635$	−5.03043	−0.199627
$636$	−29.0304	−1.15113
$637$	−27.7527	−1.09960
$638$	1.00000	0.0395904
$639$	−10.3732	−0.410357
$640$	−2.00000	−0.0790569
$641$	−4.22402	−0.166839	−0.0834194	−	0.996515i	$-0.526584\pi$
$641$	−4.22402	−0.166839	−0.0834194	+	0.996515i	$0.526584\pi$
$642$	24.2061	0.955337
$643$	33.3732	1.31611	0.658055	−	0.752970i	$-0.271379\pi$
$643$	33.3732	1.31611	0.658055	+	0.752970i	$0.271379\pi$
$644$	−6.51522	−0.256735
$645$	13.1272	0.516884
$646$	0	0
$647$	10.7580	0.422941	0.211471	−	0.977384i	$-0.432175\pi$
$647$	10.7580	0.422941	0.211471	+	0.977384i	$0.432175\pi$
$648$	3.64560	0.143213
$649$	0	0
$650$	4.25761	0.166997
$651$	12.4247	0.486964
$652$	−16.4184	−0.642995
$653$	−18.6308	−0.729079	−0.364540	−	0.931188i	$-0.618774\pi$
$653$	−18.6308	−0.729079	−0.364540	+	0.931188i	$0.618774\pi$
$654$	17.5605	0.686668
$655$	−29.9704	−1.17104
$656$	2.56361	0.100092
$657$	14.6308	0.570801
$658$	−7.08514	−0.276207
$659$	−36.2092	−1.41051	−0.705255	−	0.708953i	$-0.749168\pi$
$659$	−36.2092	−1.41051	−0.705255	+	0.708953i	$0.749168\pi$
$660$	5.38799	0.209727
$661$	−6.04840	−0.235255	−0.117628	−	0.993058i	$-0.537529\pi$
$661$	−6.04840	−0.235255	−0.117628	+	0.993058i	$0.537529\pi$
$662$	−2.17878	−0.0846806
$663$	91.2047	3.54210
$664$	3.82438	0.148415
$665$	0	0
$666$	−48.2795	−1.87079
$667$	−9.38799	−0.363504
$668$	−18.5004	−0.715802
$669$	−38.8916	−1.50363
$670$	16.1640	0.624469
$671$	7.13038	0.275265
$672$	1.86962	0.0721221
$673$	−24.2795	−0.935908	−0.467954	−	0.883753i	$-0.655009\pi$
$673$	−24.2795	−0.935908	−0.467954	+	0.883753i	$0.655009\pi$
$674$	24.3216	0.936834
$675$	−3.38799	−0.130404
$676$	5.12723	0.197201
$677$	41.9064	1.61059	0.805296	−	0.592873i	$-0.202006\pi$
$677$	41.9064	1.61059	0.805296	+	0.592873i	$0.202006\pi$
$678$	−13.2092	−0.507297
$679$	−4.79079	−0.183854
$680$	−15.9032	−0.609860
$681$	18.6057	0.712972
$682$	6.64560	0.254473
$683$	−23.2764	−0.890646	−0.445323	−	0.895370i	$-0.646911\pi$
$683$	−23.2764	−0.890646	−0.445323	+	0.895370i	$0.646911\pi$
$684$	0	0
$685$	−14.0672	−0.537479
$686$	−9.38168	−0.358194
$687$	13.2576	0.505809
$688$	2.43639	0.0928864
$689$	−45.8799	−1.74788
$690$	−50.5824	−1.92564
$691$	−41.4700	−1.57759	−0.788796	−	0.614655i	$-0.789295\pi$
$691$	−41.4700	−1.57759	−0.788796	+	0.614655i	$0.789295\pi$
$692$	2.64560	0.100571
$693$	−2.95476	−0.112242
$694$	−0.566768	−0.0215142
$695$	40.3279	1.52973
$696$	2.69399	0.102116
$697$	20.3848	0.772131
$698$	−13.1577	−0.498025
$699$	56.5255	2.13799
$700$	0.693995	0.0262305
$701$	43.6792	1.64974	0.824870	−	0.565322i	$-0.191248\pi$
$701$	43.6792	1.64974	0.824870	+	0.565322i	$0.191248\pi$
$702$	−14.4247	−0.544426
$703$	0	0
$704$	1.00000	0.0376889
$705$	−55.0071	−2.07169
$706$	17.5215	0.659431
$707$	0.178779	0.00672366
$708$	0	0
$709$	−7.55196	−0.283620	−0.141810	−	0.989894i	$-0.545292\pi$
$709$	−7.55196	−0.283620	−0.141810	+	0.989894i	$0.545292\pi$
$710$	4.87277	0.182872
$711$	42.9251	1.60982
$712$	8.90321	0.333662
$713$	−62.3888	−2.33648
$714$	14.8665	0.556363
$715$	8.51522	0.318451
$716$	15.3880	0.575076
$717$	−3.29751	−0.123148
$718$	−36.6792	−1.36886
$719$	35.1156	1.30959	0.654795	−	0.755807i	$-0.272755\pi$
$719$	35.1156	1.30959	0.654795	+	0.755807i	$0.272755\pi$
$720$	8.51522	0.317343
$721$	7.08514	0.263864
$722$	0	0
$723$	11.4785	0.426889
$724$	−14.2124	−0.528198
$725$	1.00000	0.0371391
$726$	−2.69399	−0.0999835
$727$	−27.4731	−1.01892	−0.509461	−	0.860494i	$-0.670155\pi$
$727$	−27.4731	−1.01892	−0.509461	+	0.860494i	$0.670155\pi$
$728$	2.95476	0.109511
$729$	−42.9032	−1.58901
$730$	−6.87277	−0.254373
$731$	19.3732	0.716543
$732$	19.2092	0.709993
$733$	8.06321	0.297821	0.148911	−	0.988851i	$-0.452423\pi$
$733$	8.06321	0.297821	0.148911	+	0.988851i	$0.452423\pi$
$734$	6.24280	0.230426
$735$	−35.1209	−1.29545
$736$	−9.38799	−0.346046
$737$	−8.08198	−0.297704
$738$	−10.9149	−0.401782
$739$	−14.5668	−0.535847	−0.267924	−	0.963440i	$-0.586337\pi$
$739$	−14.5668	−0.535847	−0.267924	+	0.963440i	$0.586337\pi$
$740$	22.6792	0.833703
$741$	0	0
$742$	−7.47847	−0.274543
$743$	40.3427	1.48003	0.740016	−	0.672589i	$-0.234818\pi$
$743$	40.3427	1.48003	0.740016	+	0.672589i	$0.234818\pi$
$744$	17.9032	0.656363
$745$	−26.8432	−0.983457
$746$	15.9664	0.584572
$747$	−16.2827	−0.595753
$748$	7.95160	0.290739
$749$	6.23568	0.227847
$750$	32.3279	1.18045
$751$	9.40595	0.343228	0.171614	−	0.985164i	$-0.445102\pi$
$751$	9.40595	0.343228	0.171614	+	0.985164i	$0.445102\pi$
$752$	−10.2092	−0.372292
$753$	39.3248	1.43307
$754$	4.25761	0.155053
$755$	−24.6729	−0.897938
$756$	−2.35125	−0.0855140
$757$	27.8127	1.01087	0.505435	−	0.862865i	$-0.331332\pi$
$757$	27.8127	1.01087	0.505435	+	0.862865i	$0.331332\pi$
$758$	9.05155	0.328767
$759$	25.2912	0.918012
$760$	0	0
$761$	−47.0976	−1.70729	−0.853643	−	0.520858i	$-0.825612\pi$
$761$	−47.0976	−1.70729	−0.853643	+	0.520858i	$0.825612\pi$
$762$	6.77598	0.245468
$763$	4.52372	0.163770
$764$	7.79079	0.281861
$765$	67.7096	2.44805
$766$	24.1640	0.873080
$767$	0	0
$768$	2.69399	0.0972112
$769$	−51.0367	−1.84043	−0.920216	−	0.391411i	$-0.871987\pi$
$769$	−51.0367	−1.84043	−0.920216	+	0.391411i	$0.871987\pi$
$770$	1.38799	0.0500197
$771$	−44.2311	−1.59295
$772$	12.8244	0.461559
$773$	−4.37002	−0.157179	−0.0785894	−	0.996907i	$-0.525042\pi$
$773$	−4.37002	−0.157179	−0.0785894	+	0.996907i	$0.525042\pi$
$774$	−10.3732	−0.372856
$775$	6.64560	0.238717
$776$	−6.90321	−0.247811
$777$	−21.2007	−0.760571
$778$	−0.145191	−0.00520536
$779$	0	0
$780$	22.9399	0.821382
$781$	−2.43639	−0.0871808
$782$	−74.6496	−2.66946
$783$	−3.38799	−0.121077
$784$	−6.51837	−0.232799
$785$	21.5520	0.769222
$786$	40.3700	1.43995
$787$	28.1460	1.00330	0.501648	−	0.865072i	$-0.332727\pi$
$787$	28.1460	1.00330	0.501648	+	0.865072i	$0.332727\pi$
$788$	−1.09679	−0.0390717
$789$	63.7096	2.26812
$790$	−20.1640	−0.717402
$791$	−3.40280	−0.120990
$792$	−4.25761	−0.151288
$793$	30.3584	1.07806
$794$	2.66041	0.0944143
$795$	−58.0609	−2.05921
$796$	13.5636	0.480750
$797$	8.37002	0.296481	0.148241	−	0.988951i	$-0.452639\pi$
$797$	8.37002	0.296481	0.148241	+	0.988951i	$0.452639\pi$
$798$	0	0
$799$	−81.1796	−2.87193
$800$	1.00000	0.0353553
$801$	−37.9064	−1.33936
$802$	−19.0032	−0.671025
$803$	3.43639	0.121267
$804$	−21.7728	−0.767868
$805$	−13.0304	−0.459262
$806$	28.2944	0.996626
$807$	−26.8096	−0.943741
$808$	0.257608	0.00906262
$809$	−41.3037	−1.45216	−0.726080	−	0.687611i	$-0.758660\pi$
$809$	−41.3037	−1.45216	−0.726080	+	0.687611i	$0.758660\pi$
$810$	7.29120	0.256186
$811$	−23.9820	−0.842123	−0.421062	−	0.907032i	$-0.638342\pi$
$811$	−23.9820	−0.842123	−0.421062	+	0.907032i	$0.638342\pi$
$812$	0.693995	0.0243544
$813$	−32.3279	−1.13379
$814$	−11.3396	−0.397453
$815$	−32.8368	−1.15022
$816$	21.4216	0.749905
$817$	0	0
$818$	−33.9220	−1.18605
$819$	−12.5802	−0.439588
$820$	5.12723	0.179051
$821$	−31.6760	−1.10550	−0.552751	−	0.833347i	$-0.686422\pi$
$821$	−31.6760	−1.10550	−0.552751	+	0.833347i	$0.686422\pi$
$822$	18.9484	0.660903
$823$	−13.4036	−0.467221	−0.233610	−	0.972330i	$-0.575054\pi$
$823$	−13.4036	−0.467221	−0.233610	+	0.972330i	$0.575054\pi$
$824$	10.2092	0.355655
$825$	−2.69399	−0.0937929
$826$	0	0
$827$	−9.20606	−0.320126	−0.160063	−	0.987107i	$-0.551170\pi$
$827$	−9.20606	−0.320126	−0.160063	+	0.987107i	$0.551170\pi$
$828$	39.9704	1.38907
$829$	27.4973	0.955019	0.477510	−	0.878627i	$-0.341540\pi$
$829$	27.4973	0.955019	0.477510	+	0.878627i	$0.341540\pi$
$830$	7.64875	0.265492
$831$	2.34275	0.0812690
$832$	4.25761	0.147606
$833$	−51.8315	−1.79586
$834$	−54.3216	−1.88100
$835$	−37.0008	−1.28047
$836$	0	0
$837$	−22.5152	−0.778240
$838$	16.6940	0.576684
$839$	18.7580	0.647599	0.323799	−	0.946126i	$-0.395040\pi$
$839$	18.7580	0.647599	0.323799	+	0.946126i	$0.395040\pi$
$840$	3.73924	0.129016
$841$	−28.0000	−0.965517
$842$	−22.8244	−0.786580
$843$	37.3248	1.28553
$844$	8.16397	0.281015
$845$	10.2545	0.352764
$846$	43.4668	1.49442
$847$	−0.693995	−0.0238459
$848$	−10.7760	−0.370049
$849$	−28.0672	−0.963263
$850$	7.95160	0.272738
$851$	106.456	3.64926
$852$	−6.56361	−0.224866
$853$	7.57924	0.259508	0.129754	−	0.991546i	$-0.458581\pi$
$853$	7.57924	0.259508	0.129754	+	0.991546i	$0.458581\pi$
$854$	4.94845	0.169332
$855$	0	0
$856$	8.98519	0.307107
$857$	−31.6004	−1.07945	−0.539724	−	0.841842i	$-0.681471\pi$
$857$	−31.6004	−1.07945	−0.539724	+	0.841842i	$0.681471\pi$
$858$	−11.4700	−0.391578
$859$	−33.4489	−1.14126	−0.570630	−	0.821207i	$-0.693301\pi$
$859$	−33.4489	−1.14126	−0.570630	+	0.821207i	$0.693301\pi$
$860$	4.87277	0.166160
$861$	−4.79298	−0.163344
$862$	17.5668	0.598327
$863$	−23.5067	−0.800178	−0.400089	−	0.916476i	$-0.631021\pi$
$863$	−23.5067	−0.800178	−0.400089	+	0.916476i	$0.631021\pi$
$864$	−3.38799	−0.115262
$865$	5.29120	0.179906
$866$	33.1912	1.12788
$867$	124.538	4.22953
$868$	4.61201	0.156542
$869$	10.0820	0.342008
$870$	5.38799	0.182670
$871$	−34.4099	−1.16594
$872$	6.51837	0.220740
$873$	29.3911	0.994740
$874$	0	0
$875$	8.32794	0.281536
$876$	9.25761	0.312786
$877$	16.9696	0.573022	0.286511	−	0.958077i	$-0.407505\pi$
$877$	16.9696	0.573022	0.286511	+	0.958077i	$0.407505\pi$
$878$	13.4848	0.455089
$879$	64.0524	2.16043
$880$	2.00000	0.0674200
$881$	−37.0640	−1.24872	−0.624359	−	0.781137i	$-0.714640\pi$
$881$	−37.0640	−1.24872	−0.624359	+	0.781137i	$0.714640\pi$
$882$	27.7527	0.934481
$883$	−53.5371	−1.80167	−0.900834	−	0.434163i	$-0.857044\pi$
$883$	−53.5371	−1.80167	−0.900834	+	0.434163i	$0.857044\pi$
$884$	33.8548	1.13866
$885$	0	0
$886$	2.43954	0.0819580
$887$	14.7003	0.493588	0.246794	−	0.969068i	$-0.420623\pi$
$887$	14.7003	0.493588	0.246794	+	0.969068i	$0.420623\pi$
$888$	−30.5488	−1.02515
$889$	1.74555	0.0585438
$890$	17.8064	0.596872
$891$	−3.64560	−0.122132
$892$	−14.4364	−0.483366
$893$	0	0
$894$	36.1577	1.20929
$895$	30.7760	1.02873
$896$	0.693995	0.0231847
$897$	107.680	3.59533
$898$	−6.83919	−0.228227
$899$	6.64560	0.221643
$900$	−4.25761	−0.141920
$901$	−85.6863	−2.85462
$902$	−2.56361	−0.0853590
$903$	−4.55511	−0.151585
$904$	−4.90321	−0.163078
$905$	−28.4247	−0.944870
$906$	33.2343	1.10414
$907$	31.9641	1.06135	0.530675	−	0.847576i	$-0.321939\pi$
$907$	31.9641	1.06135	0.530675	+	0.847576i	$0.321939\pi$
$908$	6.90636	0.229196
$909$	−1.09679	−0.0363784
$910$	5.90952	0.195899
$911$	55.6128	1.84254	0.921268	−	0.388930i	$-0.127155\pi$
$911$	55.6128	1.84254	0.921268	+	0.388930i	$0.127155\pi$
$912$	0	0
$913$	−3.82438	−0.126568
$914$	19.9516	0.659940
$915$	38.4184	1.27007
$916$	4.92117	0.162600
$917$	10.3996	0.343427
$918$	−26.9399	−0.889151
$919$	34.6581	1.14326	0.571632	−	0.820510i	$-0.306310\pi$
$919$	34.6581	1.14326	0.571632	+	0.820510i	$0.306310\pi$
$920$	−18.7760	−0.619026
$921$	−73.1397	−2.41003
$922$	−17.3911	−0.572747
$923$	−10.3732	−0.341437
$924$	−1.86962	−0.0615059
$925$	−11.3396	−0.372844
$926$	−10.9852	−0.360996
$927$	−43.4668	−1.42764
$928$	1.00000	0.0328266
$929$	3.19359	0.104778	0.0523891	−	0.998627i	$-0.483316\pi$
$929$	3.19359	0.104778	0.0523891	+	0.998627i	$0.483316\pi$
$930$	35.8064	1.17414
$931$	0	0
$932$	20.9820	0.687289
$933$	18.8181	0.616076
$934$	1.82122	0.0595922
$935$	15.9032	0.520090
$936$	−18.1272	−0.592507
$937$	45.1039	1.47348	0.736740	−	0.676176i	$-0.236364\pi$
$937$	45.1039	1.47348	0.736740	+	0.676176i	$0.236364\pi$
$938$	−5.60886	−0.183136
$939$	21.9852	0.717460
$940$	−20.4184	−0.665975
$941$	9.93048	0.323724	0.161862	−	0.986813i	$-0.448250\pi$
$941$	9.93048	0.323724	0.161862	+	0.986813i	$0.448250\pi$
$942$	−29.0304	−0.945863
$943$	24.0672	0.783735
$944$	0	0
$945$	−4.70249	−0.152972
$946$	−2.43639	−0.0792138
$947$	6.42473	0.208776	0.104388	−	0.994537i	$-0.466712\pi$
$947$	6.42473	0.208776	0.104388	+	0.994537i	$0.466712\pi$
$948$	27.1608	0.882142
$949$	14.6308	0.474935
$950$	0	0
$951$	61.9135	2.00768
$952$	5.51837	0.178851
$953$	−7.03043	−0.227738	−0.113869	−	0.993496i	$-0.536324\pi$
$953$	−7.03043	−0.227738	−0.113869	+	0.993496i	$0.536324\pi$
$954$	45.8799	1.48542
$955$	15.5816	0.504208
$956$	−1.22402	−0.0395877
$957$	−2.69399	−0.0870845
$958$	−4.79079	−0.154783
$959$	4.88127	0.157625
$960$	5.38799	0.173897
$961$	13.1640	0.424644
$962$	−48.2795	−1.55659
$963$	−38.2554	−1.23276
$964$	4.26076	0.137230
$965$	25.6488	0.825663
$966$	17.5520	0.564725
$967$	−17.9032	−0.575728	−0.287864	−	0.957671i	$-0.592945\pi$
$967$	−17.9032	−0.575728	−0.287864	+	0.957671i	$0.592945\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−13.8064	−0.443297
$971$	38.6035	1.23885	0.619423	−	0.785058i	$-0.287367\pi$
$971$	38.6035	1.23885	0.619423	+	0.785058i	$0.287367\pi$
$972$	−19.9852	−0.641025
$973$	−13.9937	−0.448617
$974$	35.6308	1.14168
$975$	−11.4700	−0.367333
$976$	7.13038	0.228238
$977$	−15.8728	−0.507815	−0.253908	−	0.967229i	$-0.581716\pi$
$977$	−15.8728	−0.507815	−0.253908	+	0.967229i	$0.581716\pi$
$978$	44.2311	1.41436
$979$	−8.90321	−0.284548
$980$	−13.0367	−0.416443
$981$	−27.7527	−0.886075
$982$	6.41842	0.204820
$983$	30.9220	0.986258	0.493129	−	0.869956i	$-0.335853\pi$
$983$	30.9220	0.986258	0.493129	+	0.869956i	$0.335853\pi$
$984$	−6.90636	−0.220167
$985$	−2.19359	−0.0698935
$986$	7.95160	0.253231
$987$	19.0873	0.607556
$988$	0	0
$989$	22.8728	0.727312
$990$	−8.51522	−0.270631
$991$	9.07567	0.288298	0.144149	−	0.989556i	$-0.453955\pi$
$991$	9.07567	0.288298	0.144149	+	0.989556i	$0.453955\pi$
$992$	6.64560	0.210998
$993$	5.86962	0.186267
$994$	−1.69084	−0.0536302
$995$	27.1272	0.859991
$996$	−10.3029	−0.326458
$997$	44.5824	1.41194	0.705969	−	0.708242i	$-0.250512\pi$
$997$	44.5824	1.41194	0.705969	+	0.708242i	$0.250512\pi$
$998$	−2.51522	−0.0796178
$999$	38.4184	1.21551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bd.1.3		3
19.7	even	3		418.2.e.i.353.1	yes	6
19.11	even	3		418.2.e.i.45.1	✓	6
19.18	odd	2		7942.2.a.bj.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.e.i.45.1	✓	6	19.11	even	3
418.2.e.i.353.1	yes	6	19.7	even	3
7942.2.a.bd.1.3		3	1.1	even	1	trivial
7942.2.a.bj.1.1		3	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.69399 q^{3} +1.00000 q^{4} +2.00000 q^{5} -2.69399 q^{6} -0.693995 q^{7} -1.00000 q^{8} +4.25761 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.69399 q^{3} +1.00000 q^{4} +2.00000 q^{5} -2.69399 q^{6} -0.693995 q^{7} -1.00000 q^{8} +4.25761 q^{9} -2.00000 q^{10} +1.00000 q^{11} +2.69399 q^{12} +4.25761 q^{13} +0.693995 q^{14} +5.38799 q^{15} +1.00000 q^{16} +7.95160 q^{17} -4.25761 q^{18} +2.00000 q^{20} -1.86962 q^{21} -1.00000 q^{22} +9.38799 q^{23} -2.69399 q^{24} -1.00000 q^{25} -4.25761 q^{26} +3.38799 q^{27} -0.693995 q^{28} -1.00000 q^{29} -5.38799 q^{30} -6.64560 q^{31} -1.00000 q^{32} +2.69399 q^{33} -7.95160 q^{34} -1.38799 q^{35} +4.25761 q^{36} +11.3396 q^{37} +11.4700 q^{39} -2.00000 q^{40} +2.56361 q^{41} +1.86962 q^{42} +2.43639 q^{43} +1.00000 q^{44} +8.51522 q^{45} -9.38799 q^{46} -10.2092 q^{47} +2.69399 q^{48} -6.51837 q^{49} +1.00000 q^{50} +21.4216 q^{51} +4.25761 q^{52} -10.7760 q^{53} -3.38799 q^{54} +2.00000 q^{55} +0.693995 q^{56} +1.00000 q^{58} +5.38799 q^{60} +7.13038 q^{61} +6.64560 q^{62} -2.95476 q^{63} +1.00000 q^{64} +8.51522 q^{65} -2.69399 q^{66} -8.08198 q^{67} +7.95160 q^{68} +25.2912 q^{69} +1.38799 q^{70} -2.43639 q^{71} -4.25761 q^{72} +3.43639 q^{73} -11.3396 q^{74} -2.69399 q^{75} -0.693995 q^{77} -11.4700 q^{78} +10.0820 q^{79} +2.00000 q^{80} -3.64560 q^{81} -2.56361 q^{82} -3.82438 q^{83} -1.86962 q^{84} +15.9032 q^{85} -2.43639 q^{86} -2.69399 q^{87} -1.00000 q^{88} -8.90321 q^{89} -8.51522 q^{90} -2.95476 q^{91} +9.38799 q^{92} -17.9032 q^{93} +10.2092 q^{94} -2.69399 q^{96} +6.90321 q^{97} +6.51837 q^{98} +4.25761 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} + 7 q^{9} - 6 q^{10} + 3 q^{11} + 7 q^{13} - 6 q^{14} + 3 q^{16} + 10 q^{17} - 7 q^{18} + 6 q^{20} - 16 q^{21} - 3 q^{22} + 12 q^{23} - 3 q^{25} - 7 q^{26} - 6 q^{27} + 6 q^{28} - 3 q^{29} + 2 q^{31} - 3 q^{32} - 10 q^{34} + 12 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{39} - 6 q^{40} + 10 q^{41} + 16 q^{42} + 5 q^{43} + 3 q^{44} + 14 q^{45} - 12 q^{46} - 11 q^{47} + 7 q^{49} + 3 q^{50} + 10 q^{51} + 7 q^{52} + 6 q^{54} + 6 q^{55} - 6 q^{56} + 3 q^{58} + 11 q^{61} - 2 q^{62} + 20 q^{63} + 3 q^{64} + 14 q^{65} + 10 q^{68} + 32 q^{69} - 12 q^{70} - 5 q^{71} - 7 q^{72} + 8 q^{73} - 4 q^{74} + 6 q^{77} + 6 q^{78} + 6 q^{79} + 6 q^{80} + 11 q^{81} - 10 q^{82} + 7 q^{83} - 16 q^{84} + 20 q^{85} - 5 q^{86} - 3 q^{88} + q^{89} - 14 q^{90} + 20 q^{91} + 12 q^{92} - 26 q^{93} + 11 q^{94} - 7 q^{97} - 7 q^{98} + 7 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 + 7 * q^9 - 6 * q^10 + 3 * q^11 + 7 * q^13 - 6 * q^14 + 3 * q^16 + 10 * q^17 - 7 * q^18 + 6 * q^20 - 16 * q^21 - 3 * q^22 + 12 * q^23 - 3 * q^25 - 7 * q^26 - 6 * q^27 + 6 * q^28 - 3 * q^29 + 2 * q^31 - 3 * q^32 - 10 * q^34 + 12 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^39 - 6 * q^40 + 10 * q^41 + 16 * q^42 + 5 * q^43 + 3 * q^44 + 14 * q^45 - 12 * q^46 - 11 * q^47 + 7 * q^49 + 3 * q^50 + 10 * q^51 + 7 * q^52 + 6 * q^54 + 6 * q^55 - 6 * q^56 + 3 * q^58 + 11 * q^61 - 2 * q^62 + 20 * q^63 + 3 * q^64 + 14 * q^65 + 10 * q^68 + 32 * q^69 - 12 * q^70 - 5 * q^71 - 7 * q^72 + 8 * q^73 - 4 * q^74 + 6 * q^77 + 6 * q^78 + 6 * q^79 + 6 * q^80 + 11 * q^81 - 10 * q^82 + 7 * q^83 - 16 * q^84 + 20 * q^85 - 5 * q^86 - 3 * q^88 + q^89 - 14 * q^90 + 20 * q^91 + 12 * q^92 - 26 * q^93 + 11 * q^94 - 7 * q^97 - 7 * q^98 + 7 * q^99

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