LMFDB - Embedded newform 7942.2.a.bj.1.1

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			1.1
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	$-0.783608\pi$
$3$	−2.69399	−1.55538	−0.777689	+	0.628649i	$0.783608\pi$
$4$	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	$-0.701039\pi$
$13$	−4.25761	−1.18085	−0.590424	+	0.807093i	$0.701039\pi$
$14$	−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	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	−5.38799	−0.983708
$31$	6.64560	1.19358	0.596792	−	0.802396i	$-0.296442\pi$
$31$	6.64560	1.19358	0.596792	+	0.802396i	$0.296442\pi$
$32$	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	$-0.882033\pi$
$37$	−11.3396	−1.86422	−0.932109	+	0.362178i	$0.882033\pi$
$38$	0	0
$39$	11.4700	1.83667
$40$	2.00000	0.316228
$41$	−2.56361	−0.400369	−0.200185	−	0.979758i	$-0.564154\pi$
$41$	−2.56361	−0.400369	−0.200185	+	0.979758i	$0.564154\pi$
$42$	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	$-0.234779\pi$
$53$	10.7760	1.48019	0.740097	+	0.672500i	$0.234779\pi$
$54$	−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	$-0.335649\pi$
$67$	8.08198	0.987372	0.493686	+	0.869640i	$0.335649\pi$
$68$	7.95160	0.964273
$69$	−25.2912	−3.04470
$70$	−1.38799	−0.165896
$71$	2.43639	0.289146	0.144573	−	0.989494i	$-0.453819\pi$
$71$	2.43639	0.289146	0.144573	+	0.989494i	$0.453819\pi$
$72$	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	$-0.691956\pi$
$79$	−10.0820	−1.13431	−0.567156	+	0.823610i	$0.691956\pi$
$80$	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	$-0.343580\pi$
$89$	8.90321	0.943738	0.471869	+	0.881669i	$0.343580\pi$
$90$	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	$-0.613974\pi$
$97$	−6.90321	−0.700914	−0.350457	+	0.936579i	$0.613974\pi$
$98$	−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	$-0.332240\pi$
$103$	10.2092	1.00594	0.502972	+	0.864303i	$0.332240\pi$
$104$	−4.25761	−0.417493
$105$	3.73924	0.364912
$106$	10.7760	1.04666
$107$	8.98519	0.868631	0.434316	−	0.900761i	$-0.356990\pi$
$107$	8.98519	0.868631	0.434316	+	0.900761i	$0.356990\pi$
$108$	−3.38799	−0.326009
$109$	6.51837	0.624347	0.312173	−	0.950025i	$-0.398943\pi$
$109$	6.51837	0.624347	0.312173	+	0.950025i	$0.398943\pi$
$110$	2.00000	0.190693
$111$	30.5488	2.89956
$112$	−0.693995	−0.0655763
$113$	−4.90321	−0.461255	−0.230627	−	0.973042i	$-0.574078\pi$
$113$	−4.90321	−0.461255	−0.230627	+	0.973042i	$0.574078\pi$
$114$	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	$-0.464404\pi$
$127$	2.51522	0.223189	0.111595	+	0.993754i	$0.464404\pi$
$128$	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	$-0.332612\pi$
$151$	12.3364	1.00393	0.501963	+	0.864889i	$0.332612\pi$
$152$	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	$-0.246061\pi$
$167$	18.5004	1.43160	0.715802	+	0.698303i	$0.246061\pi$
$168$	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	$-0.532067\pi$
$173$	−2.64560	−0.201141	−0.100571	+	0.994930i	$0.532067\pi$
$174$	−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	$-0.695028\pi$
$179$	−15.3880	−1.15015	−0.575076	+	0.818100i	$0.695028\pi$
$180$	8.51522	0.634687
$181$	14.2124	1.05640	0.528198	−	0.849121i	$-0.322868\pi$
$181$	14.2124	1.05640	0.528198	+	0.849121i	$0.322868\pi$
$182$	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	$-0.652710\pi$
$193$	−12.8244	−0.923119	−0.461559	+	0.887109i	$0.652710\pi$
$194$	−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	$-0.590671\pi$
$211$	−8.16397	−0.562031	−0.281015	+	0.959703i	$0.590671\pi$
$212$	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	$-0.339414\pi$
$223$	14.4364	0.966732	0.483366	+	0.875418i	$0.339414\pi$
$224$	−0.693995	−0.0463695
$225$	−4.25761	−0.283841
$226$	−4.90321	−0.326156
$227$	−6.90636	−0.458391	−0.229196	−	0.973380i	$-0.573610\pi$
$227$	−6.90636	−0.458391	−0.229196	+	0.973380i	$0.573610\pi$
$228$	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	$-0.543820\pi$
$241$	−4.26076	−0.274460	−0.137230	+	0.990539i	$0.543820\pi$
$242$	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	$-0.328876\pi$
$257$	16.4184	1.02415	0.512077	+	0.858940i	$0.328876\pi$
$258$	−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	$-0.401885\pi$
$269$	9.95160	0.606760	0.303380	+	0.952870i	$0.401885\pi$
$270$	−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	$-0.635608\pi$
$281$	−13.8548	−0.826509	−0.413254	+	0.910616i	$0.635608\pi$
$282$	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	$-0.744376\pi$
$293$	−23.7760	−1.38901	−0.694504	+	0.719489i	$0.744376\pi$
$294$	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	$-0.217880\pi$
$307$	27.1492	1.54948	0.774742	+	0.632277i	$0.217880\pi$
$308$	−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	$-0.723309\pi$
$317$	−22.9820	−1.29080	−0.645400	+	0.763845i	$0.723309\pi$
$318$	−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	$-0.519071\pi$
$331$	−2.17878	−0.119757	−0.0598783	+	0.998206i	$0.519071\pi$
$332$	−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	$-0.269520\pi$
$337$	24.3216	1.32488	0.662442	+	0.749113i	$0.269520\pi$
$338$	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	$-0.364357\pi$
$373$	15.9664	0.826710	0.413355	+	0.910570i	$0.364357\pi$
$374$	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	$-0.425318\pi$
$379$	9.05155	0.464947	0.232474	+	0.972603i	$0.425318\pi$
$380$	0	0
$381$	−6.77598	−0.347144
$382$	7.79079	0.398611
$383$	24.1640	1.23472	0.617361	−	0.786680i	$-0.288202\pi$
$383$	24.1640	1.23472	0.617361	+	0.786680i	$0.288202\pi$
$384$	−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	$-0.657366\pi$
$401$	−19.0032	−0.948972	−0.474486	+	0.880263i	$0.657366\pi$
$402$	−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	$-0.816665\pi$
$409$	−33.9220	−1.67733	−0.838667	+	0.544644i	$0.816665\pi$
$410$	−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	$-0.687740\pi$
$421$	−22.8244	−1.11239	−0.556196	+	0.831051i	$0.687740\pi$
$422$	−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	$-0.360949\pi$
$431$	17.5668	0.846161	0.423081	+	0.906092i	$0.360949\pi$
$432$	−3.38799	−0.163005
$433$	33.1912	1.59507	0.797535	−	0.603273i	$-0.206137\pi$
$433$	33.1912	1.59507	0.797535	+	0.603273i	$0.206137\pi$
$434$	−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	$-0.395713\pi$
$439$	13.4848	0.643594	0.321797	+	0.946809i	$0.395713\pi$
$440$	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	$-0.551595\pi$
$449$	−6.83919	−0.322761	−0.161381	+	0.986892i	$0.551595\pi$
$450$	−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	$-0.200932\pi$
$487$	35.6308	1.61459	0.807293	+	0.590151i	$0.200932\pi$
$488$	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	$-0.509110\pi$
$509$	−1.29120	−0.0572312	−0.0286156	+	0.999590i	$0.509110\pi$
$510$	−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	$-0.804336\pi$
$521$	−37.2944	−1.63390	−0.816948	+	0.576712i	$0.804336\pi$
$522$	4.25761	0.186350
$523$	22.2092	0.971141	0.485570	−	0.874198i	$-0.338612\pi$
$523$	22.2092	0.971141	0.485570	+	0.874198i	$0.338612\pi$
$524$	−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	$-0.516587\pi$
$547$	−2.43639	−0.104172	−0.0520862	+	0.998643i	$0.516587\pi$
$548$	−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	$-0.472034\pi$
$563$	4.16397	0.175490	0.0877452	+	0.996143i	$0.472034\pi$
$564$	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	$-0.320137\pi$
$569$	25.5456	1.07093	0.535465	+	0.844558i	$0.320137\pi$
$570$	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	$-0.314397\pi$
$599$	26.9516	1.10121	0.550606	+	0.834765i	$0.314397\pi$
$600$	2.69399	0.109982
$601$	28.5824	1.16590	0.582950	−	0.812508i	$-0.301898\pi$
$601$	28.5824	1.16590	0.582950	+	0.812508i	$0.301898\pi$
$602$	−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	$-0.475290\pi$
$607$	3.82122	0.155099	0.0775493	+	0.996989i	$0.475290\pi$
$608$	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	$-0.473416\pi$
$641$	4.22402	0.166839	0.0834194	+	0.996515i	$0.473416\pi$
$642$	−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	$-0.250832\pi$
$659$	36.2092	1.41051	0.705255	+	0.708953i	$0.250832\pi$
$660$	−5.38799	−0.209727
$661$	6.04840	0.235255	0.117628	−	0.993058i	$-0.462471\pi$
$661$	6.04840	0.235255	0.117628	+	0.993058i	$0.462471\pi$
$662$	−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	$-0.344991\pi$
$673$	24.2795	0.935908	0.467954	+	0.883753i	$0.344991\pi$
$674$	24.3216	0.936834
$675$	3.38799	0.130404
$676$	5.12723	0.197201
$677$	−41.9064	−1.61059	−0.805296	−	0.592873i	$-0.797994\pi$
$677$	−41.9064	−1.61059	−0.805296	+	0.592873i	$0.797994\pi$
$678$	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	$-0.353089\pi$
$683$	23.2764	0.890646	0.445323	+	0.895370i	$0.353089\pi$
$684$	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	$-0.765182\pi$
$743$	−40.3427	−1.48003	−0.740016	+	0.672589i	$0.765182\pi$
$744$	−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	$-0.554898\pi$
$751$	−9.40595	−0.343228	−0.171614	+	0.985164i	$0.554898\pi$
$752$	−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	$-0.474958\pi$
$773$	4.37002	0.157179	0.0785894	+	0.996907i	$0.474958\pi$
$774$	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	$-0.667273\pi$
$787$	−28.1460	−1.00330	−0.501648	+	0.865072i	$0.667273\pi$
$788$	−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	$-0.547361\pi$
$797$	−8.37002	−0.296481	−0.148241	+	0.988951i	$0.547361\pi$
$798$	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	$-0.361658\pi$
$811$	23.9820	0.842123	0.421062	+	0.907032i	$0.361658\pi$
$812$	−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	$-0.448830\pi$
$827$	9.20606	0.320126	0.160063	+	0.987107i	$0.448830\pi$
$828$	39.9704	1.38907
$829$	−27.4973	−0.955019	−0.477510	−	0.878627i	$-0.658460\pi$
$829$	−27.4973	−0.955019	−0.477510	+	0.878627i	$0.658460\pi$
$830$	−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	$-0.604960\pi$
$839$	−18.7580	−0.647599	−0.323799	+	0.946126i	$0.604960\pi$
$840$	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	$-0.318529\pi$
$857$	31.6004	1.07945	0.539724	+	0.841842i	$0.318529\pi$
$858$	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	$-0.368979\pi$
$863$	23.5067	0.800178	0.400089	+	0.916476i	$0.368979\pi$
$864$	−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	$-0.592495\pi$
$877$	−16.9696	−0.573022	−0.286511	+	0.958077i	$0.592495\pi$
$878$	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	$-0.579377\pi$
$887$	−14.7003	−0.493588	−0.246794	+	0.969068i	$0.579377\pi$
$888$	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	$-0.678061\pi$
$907$	−31.9641	−1.06135	−0.530675	+	0.847576i	$0.678061\pi$
$908$	−6.90636	−0.229196
$909$	−1.09679	−0.0363784
$910$	5.90952	0.195899
$911$	−55.6128	−1.84254	−0.921268	−	0.388930i	$-0.872845\pi$
$911$	−55.6128	−1.84254	−0.921268	+	0.388930i	$0.872845\pi$
$912$	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	$-0.551750\pi$
$941$	−9.93048	−0.323724	−0.161862	+	0.986813i	$0.551750\pi$
$942$	−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	$-0.463676\pi$
$953$	7.03043	0.227738	0.113869	+	0.993496i	$0.463676\pi$
$954$	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	$-0.712633\pi$
$971$	−38.6035	−1.23885	−0.619423	+	0.785058i	$0.712633\pi$
$972$	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	$-0.418284\pi$
$977$	15.8728	0.507815	0.253908	+	0.967229i	$0.418284\pi$
$978$	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	$-0.664147\pi$
$983$	−30.9220	−0.986258	−0.493129	+	0.869956i	$0.664147\pi$
$984$	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	$-0.546045\pi$
$991$	−9.07567	−0.288298	−0.144149	+	0.989556i	$0.546045\pi$
$992$	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.bj.1.1		3
19.8	odd	6		418.2.e.i.45.1	✓	6
19.12	odd	6		418.2.e.i.353.1	yes	6
19.18	odd	2		7942.2.a.bd.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.e.i.45.1	✓	6	19.8	odd	6
418.2.e.i.353.1	yes	6	19.12	odd	6
7942.2.a.bd.1.3		3	19.18	odd	2
7942.2.a.bj.1.1		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
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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