LMFDB - Embedded newform 3381.2.a.bd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.7997584.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 7x^{4} + 5x^{3} + 12x^{2} - 4x - 2 $ x^6 - x^5 - 7x^4 + 5x^3 + 12x^2 - 4x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.83264$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83264 q^{2} +1.00000 q^{3} +1.35859 q^{4} +0.943490 q^{5} -1.83264 q^{6} +1.17548 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.83264 q^{2} +1.00000 q^{3} +1.35859 q^{4} +0.943490 q^{5} -1.83264 q^{6} +1.17548 q^{8} +1.00000 q^{9} -1.72908 q^{10} +2.08680 q^{11} +1.35859 q^{12} -3.64405 q^{13} +0.943490 q^{15} -4.87142 q^{16} -0.299440 q^{17} -1.83264 q^{18} +0.579464 q^{19} +1.28181 q^{20} -3.82436 q^{22} -1.00000 q^{23} +1.17548 q^{24} -4.10983 q^{25} +6.67825 q^{26} +1.00000 q^{27} -5.89363 q^{29} -1.72908 q^{30} +6.02387 q^{31} +6.57660 q^{32} +2.08680 q^{33} +0.548767 q^{34} +1.35859 q^{36} -1.23744 q^{37} -1.06195 q^{38} -3.64405 q^{39} +1.10906 q^{40} -8.42024 q^{41} -9.08583 q^{43} +2.83510 q^{44} +0.943490 q^{45} +1.83264 q^{46} -5.06246 q^{47} -4.87142 q^{48} +7.53185 q^{50} -0.299440 q^{51} -4.95075 q^{52} +2.32577 q^{53} -1.83264 q^{54} +1.96887 q^{55} +0.579464 q^{57} +10.8009 q^{58} -2.08015 q^{59} +1.28181 q^{60} -12.4540 q^{61} -11.0396 q^{62} -2.30974 q^{64} -3.43812 q^{65} -3.82436 q^{66} -4.13763 q^{67} -0.406815 q^{68} -1.00000 q^{69} -11.6439 q^{71} +1.17548 q^{72} +11.5700 q^{73} +2.26778 q^{74} -4.10983 q^{75} +0.787251 q^{76} +6.67825 q^{78} +17.1584 q^{79} -4.59613 q^{80} +1.00000 q^{81} +15.4313 q^{82} -10.9740 q^{83} -0.282519 q^{85} +16.6511 q^{86} -5.89363 q^{87} +2.45300 q^{88} -2.67561 q^{89} -1.72908 q^{90} -1.35859 q^{92} +6.02387 q^{93} +9.27770 q^{94} +0.546718 q^{95} +6.57660 q^{96} -0.589843 q^{97} +2.08680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9	$ 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{10} - 14 q^{11} + 3 q^{12} - 3 q^{15} - 7 q^{16} - 15 q^{17} - q^{18} + q^{19} - 17 q^{20} - 6 q^{22} - 6 q^{23} - 3 q^{24} + 9 q^{25} + 15 q^{26} + 6 q^{27} - 6 q^{29} + 3 q^{30} + 11 q^{31} + 3 q^{32} - 14 q^{33} - 15 q^{34} + 3 q^{36} - 5 q^{37} - 14 q^{38} + 17 q^{40} - 18 q^{41} - 37 q^{43} - 10 q^{44} - 3 q^{45} + q^{46} - 3 q^{47} - 7 q^{48} - 30 q^{50} - 15 q^{51} + 7 q^{52} - 15 q^{53} - q^{54} + 2 q^{55} + q^{57} + 4 q^{58} + 2 q^{59} - 17 q^{60} + 12 q^{61} - 36 q^{62} - 23 q^{64} - 17 q^{65} - 6 q^{66} - 10 q^{67} + q^{68} - 6 q^{69} - 21 q^{71} - 3 q^{72} + 8 q^{73} - 16 q^{74} + 9 q^{75} - 18 q^{76} + 15 q^{78} - 17 q^{79} - 3 q^{80} + 6 q^{81} + 48 q^{82} - 12 q^{83} - 13 q^{85} + 22 q^{86} - 6 q^{87} - 2 q^{88} - 18 q^{89} + 3 q^{90} - 3 q^{92} + 11 q^{93} - 3 q^{94} - 16 q^{95} + 3 q^{96} + 2 q^{97} - 14 q^{99}+O(q^{100}) $ 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9 + 3 * q^10 - 14 * q^11 + 3 * q^12 - 3 * q^15 - 7 * q^16 - 15 * q^17 - q^18 + q^19 - 17 * q^20 - 6 * q^22 - 6 * q^23 - 3 * q^24 + 9 * q^25 + 15 * q^26 + 6 * q^27 - 6 * q^29 + 3 * q^30 + 11 * q^31 + 3 * q^32 - 14 * q^33 - 15 * q^34 + 3 * q^36 - 5 * q^37 - 14 * q^38 + 17 * q^40 - 18 * q^41 - 37 * q^43 - 10 * q^44 - 3 * q^45 + q^46 - 3 * q^47 - 7 * q^48 - 30 * q^50 - 15 * q^51 + 7 * q^52 - 15 * q^53 - q^54 + 2 * q^55 + q^57 + 4 * q^58 + 2 * q^59 - 17 * q^60 + 12 * q^61 - 36 * q^62 - 23 * q^64 - 17 * q^65 - 6 * q^66 - 10 * q^67 + q^68 - 6 * q^69 - 21 * q^71 - 3 * q^72 + 8 * q^73 - 16 * q^74 + 9 * q^75 - 18 * q^76 + 15 * q^78 - 17 * q^79 - 3 * q^80 + 6 * q^81 + 48 * q^82 - 12 * q^83 - 13 * q^85 + 22 * q^86 - 6 * q^87 - 2 * q^88 - 18 * q^89 + 3 * q^90 - 3 * q^92 + 11 * q^93 - 3 * q^94 - 16 * q^95 + 3 * q^96 + 2 * q^97 - 14 * 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 $

$2$	−1.83264	−1.29588	−0.647938	−	0.761693i	$-0.724368\pi$
$2$	−1.83264	−1.29588	−0.647938	+	0.761693i	$0.724368\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.35859	0.679293
$5$	0.943490	0.421941	0.210971	−	0.977492i	$-0.432338\pi$
$5$	0.943490	0.421941	0.210971	+	0.977492i	$0.432338\pi$
$6$	−1.83264	−0.748174
$7$	0	0
$7$	0	0
$8$	1.17548	0.415597
$9$	1.00000	0.333333
$10$	−1.72908	−0.546783
$11$	2.08680	0.629194	0.314597	−	0.949225i	$-0.398131\pi$
$11$	2.08680	0.629194	0.314597	+	0.949225i	$0.398131\pi$
$12$	1.35859	0.392190
$13$	−3.64405	−1.01068	−0.505339	−	0.862921i	$-0.668632\pi$
$13$	−3.64405	−1.01068	−0.505339	+	0.862921i	$0.668632\pi$
$14$	0	0
$15$	0.943490	0.243608
$16$	−4.87142	−1.21785
$17$	−0.299440	−0.0726249	−0.0363124	−	0.999340i	$-0.511561\pi$
$17$	−0.299440	−0.0726249	−0.0363124	+	0.999340i	$0.511561\pi$
$18$	−1.83264	−0.431958
$19$	0.579464	0.132938	0.0664690	−	0.997788i	$-0.478827\pi$
$19$	0.579464	0.132938	0.0664690	+	0.997788i	$0.478827\pi$
$20$	1.28181	0.286622
$21$	0	0
$22$	−3.82436	−0.815357
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.17548	0.239945
$25$	−4.10983	−0.821965
$26$	6.67825	1.30971
$27$	1.00000	0.192450
$28$	0	0
$29$	−5.89363	−1.09442	−0.547210	−	0.836995i	$-0.684310\pi$
$29$	−5.89363	−1.09442	−0.547210	+	0.836995i	$0.684310\pi$
$30$	−1.72908	−0.315686
$31$	6.02387	1.08192	0.540960	−	0.841048i	$-0.318061\pi$
$31$	6.02387	1.08192	0.540960	+	0.841048i	$0.318061\pi$
$32$	6.57660	1.16259
$33$	2.08680	0.363265
$34$	0.548767	0.0941128
$35$	0	0
$36$	1.35859	0.226431
$37$	−1.23744	−0.203433	−0.101717	−	0.994813i	$-0.532433\pi$
$37$	−1.23744	−0.203433	−0.101717	+	0.994813i	$0.532433\pi$
$38$	−1.06195	−0.172271
$39$	−3.64405	−0.583515
$40$	1.10906	0.175357
$41$	−8.42024	−1.31502	−0.657510	−	0.753446i	$-0.728390\pi$
$41$	−8.42024	−1.31502	−0.657510	+	0.753446i	$0.728390\pi$
$42$	0	0
$43$	−9.08583	−1.38558	−0.692788	−	0.721142i	$-0.743618\pi$
$43$	−9.08583	−1.38558	−0.692788	+	0.721142i	$0.743618\pi$
$44$	2.83510	0.427407
$45$	0.943490	0.140647
$46$	1.83264	0.270209
$47$	−5.06246	−0.738436	−0.369218	−	0.929343i	$-0.620374\pi$
$47$	−5.06246	−0.738436	−0.369218	+	0.929343i	$0.620374\pi$
$48$	−4.87142	−0.703128
$49$	0	0
$50$	7.53185	1.06516
$51$	−0.299440	−0.0419300
$52$	−4.95075	−0.686546
$53$	2.32577	0.319469	0.159734	−	0.987160i	$-0.448936\pi$
$53$	2.32577	0.319469	0.159734	+	0.987160i	$0.448936\pi$
$54$	−1.83264	−0.249391
$55$	1.96887	0.265483
$56$	0	0
$57$	0.579464	0.0767518
$58$	10.8009	1.41823
$59$	−2.08015	−0.270812	−0.135406	−	0.990790i	$-0.543234\pi$
$59$	−2.08015	−0.270812	−0.135406	+	0.990790i	$0.543234\pi$
$60$	1.28181	0.165481
$61$	−12.4540	−1.59457	−0.797287	−	0.603600i	$-0.793732\pi$
$61$	−12.4540	−1.59457	−0.797287	+	0.603600i	$0.793732\pi$
$62$	−11.0396	−1.40203
$63$	0	0
$64$	−2.30974	−0.288718
$65$	−3.43812	−0.426447
$66$	−3.82436	−0.470747
$67$	−4.13763	−0.505493	−0.252746	−	0.967533i	$-0.581334\pi$
$67$	−4.13763	−0.505493	−0.252746	+	0.967533i	$0.581334\pi$
$68$	−0.406815	−0.0493335
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−11.6439	−1.38188	−0.690938	−	0.722914i	$-0.742802\pi$
$71$	−11.6439	−1.38188	−0.690938	+	0.722914i	$0.742802\pi$
$72$	1.17548	0.138532
$73$	11.5700	1.35416	0.677082	−	0.735908i	$-0.263244\pi$
$73$	11.5700	1.35416	0.677082	+	0.735908i	$0.263244\pi$
$74$	2.26778	0.263624
$75$	−4.10983	−0.474562
$76$	0.787251	0.0903039
$77$	0	0
$78$	6.67825	0.756163
$79$	17.1584	1.93047	0.965235	−	0.261382i	$-0.0841783\pi$
$79$	17.1584	1.93047	0.965235	+	0.261382i	$0.0841783\pi$
$80$	−4.59613	−0.513863
$81$	1.00000	0.111111
$82$	15.4313	1.70410
$83$	−10.9740	−1.20455	−0.602274	−	0.798289i	$-0.705739\pi$
$83$	−10.9740	−1.20455	−0.602274	+	0.798289i	$0.705739\pi$
$84$	0	0
$85$	−0.282519	−0.0306434
$86$	16.6511	1.79553
$87$	−5.89363	−0.631864
$88$	2.45300	0.261491
$89$	−2.67561	−0.283614	−0.141807	−	0.989894i	$-0.545291\pi$
$89$	−2.67561	−0.283614	−0.141807	+	0.989894i	$0.545291\pi$
$90$	−1.72908	−0.182261
$91$	0	0
$92$	−1.35859	−0.141642
$93$	6.02387	0.624647
$94$	9.27770	0.956921
$95$	0.546718	0.0560921
$96$	6.57660	0.671222
$97$	−0.589843	−0.0598895	−0.0299447	−	0.999552i	$-0.509533\pi$
$97$	−0.589843	−0.0598895	−0.0299447	+	0.999552i	$0.509533\pi$
$98$	0	0
$99$	2.08680	0.209731
$100$	−5.58355	−0.558355
$101$	−6.22834	−0.619743	−0.309872	−	0.950778i	$-0.600286\pi$
$101$	−6.22834	−0.619743	−0.309872	+	0.950778i	$0.600286\pi$
$102$	0.548767	0.0543360
$103$	18.6455	1.83719	0.918597	−	0.395195i	$-0.129323\pi$
$103$	18.6455	1.83719	0.918597	+	0.395195i	$0.129323\pi$
$104$	−4.28352	−0.420034
$105$	0	0
$106$	−4.26230	−0.413992
$107$	−0.648883	−0.0627299	−0.0313650	−	0.999508i	$-0.509985\pi$
$107$	−0.648883	−0.0627299	−0.0313650	+	0.999508i	$0.509985\pi$
$108$	1.35859	0.130730
$109$	−13.6533	−1.30775	−0.653876	−	0.756602i	$-0.726858\pi$
$109$	−13.6533	−1.30775	−0.653876	+	0.756602i	$0.726858\pi$
$110$	−3.60825	−0.344033
$111$	−1.23744	−0.117452
$112$	0	0
$113$	0.547279	0.0514836	0.0257418	−	0.999669i	$-0.491805\pi$
$113$	0.547279	0.0514836	0.0257418	+	0.999669i	$0.491805\pi$
$114$	−1.06195	−0.0994608
$115$	−0.943490	−0.0879809
$116$	−8.00700	−0.743431
$117$	−3.64405	−0.336893
$118$	3.81217	0.350939
$119$	0	0
$120$	1.10906	0.101243
$121$	−6.64526	−0.604115
$122$	22.8238	2.06637
$123$	−8.42024	−0.759227
$124$	8.18395	0.734940
$125$	−8.59503	−0.768763
$126$	0	0
$127$	−1.01278	−0.0898693	−0.0449347	−	0.998990i	$-0.514308\pi$
$127$	−1.01278	−0.0898693	−0.0449347	+	0.998990i	$0.514308\pi$
$128$	−8.92027	−0.788448
$129$	−9.08583	−0.799962
$130$	6.30086	0.552622
$131$	15.0311	1.31327	0.656635	−	0.754209i	$-0.271979\pi$
$131$	15.0311	1.31327	0.656635	+	0.754209i	$0.271979\pi$
$132$	2.83510	0.246764
$133$	0	0
$134$	7.58281	0.655055
$135$	0.943490	0.0812027
$136$	−0.351987	−0.0301827
$137$	9.27867	0.792730	0.396365	−	0.918093i	$-0.370271\pi$
$137$	9.27867	0.792730	0.396365	+	0.918093i	$0.370271\pi$
$138$	1.83264	0.156005
$139$	−6.58750	−0.558744	−0.279372	−	0.960183i	$-0.590126\pi$
$139$	−6.58750	−0.558744	−0.279372	+	0.960183i	$0.590126\pi$
$140$	0	0
$141$	−5.06246	−0.426336
$142$	21.3391	1.79074
$143$	−7.60440	−0.635912
$144$	−4.87142	−0.405951
$145$	−5.56058	−0.461781
$146$	−21.2037	−1.75483
$147$	0	0
$148$	−1.68116	−0.138191
$149$	−5.88903	−0.482448	−0.241224	−	0.970469i	$-0.577549\pi$
$149$	−5.88903	−0.482448	−0.241224	+	0.970469i	$0.577549\pi$
$150$	7.53185	0.614973
$151$	13.1539	1.07045	0.535223	−	0.844711i	$-0.320228\pi$
$151$	13.1539	1.07045	0.535223	+	0.844711i	$0.320228\pi$
$152$	0.681151	0.0552486
$153$	−0.299440	−0.0242083
$154$	0	0
$155$	5.68346	0.456507
$156$	−4.95075	−0.396377
$157$	8.42558	0.672434	0.336217	−	0.941784i	$-0.390852\pi$
$157$	8.42558	0.672434	0.336217	+	0.941784i	$0.390852\pi$
$158$	−31.4452	−2.50165
$159$	2.32577	0.184445
$160$	6.20496	0.490545
$161$	0	0
$162$	−1.83264	−0.143986
$163$	4.15736	0.325630	0.162815	−	0.986657i	$-0.447943\pi$
$163$	4.15736	0.325630	0.162815	+	0.986657i	$0.447943\pi$
$164$	−11.4396	−0.893284
$165$	1.96887	0.153277
$166$	20.1114	1.56095
$167$	3.04445	0.235587	0.117793	−	0.993038i	$-0.462418\pi$
$167$	3.04445	0.235587	0.117793	+	0.993038i	$0.462418\pi$
$168$	0	0
$169$	0.279097	0.0214690
$170$	0.517756	0.0397101
$171$	0.579464	0.0443127
$172$	−12.3439	−0.941211
$173$	−16.0543	−1.22059	−0.610293	−	0.792176i	$-0.708948\pi$
$173$	−16.0543	−1.22059	−0.610293	+	0.792176i	$0.708948\pi$
$174$	10.8009	0.818816
$175$	0	0
$176$	−10.1657	−0.766267
$177$	−2.08015	−0.156354
$178$	4.90345	0.367529
$179$	−5.34509	−0.399511	−0.199755	−	0.979846i	$-0.564015\pi$
$179$	−5.34509	−0.399511	−0.199755	+	0.979846i	$0.564015\pi$
$180$	1.28181	0.0955406
$181$	11.6201	0.863716	0.431858	−	0.901942i	$-0.357858\pi$
$181$	11.6201	0.863716	0.431858	+	0.901942i	$0.357858\pi$
$182$	0	0
$183$	−12.4540	−0.920628
$184$	−1.17548	−0.0866579
$185$	−1.16751	−0.0858369
$186$	−11.0396	−0.809464
$187$	−0.624872	−0.0456951
$188$	−6.87779	−0.501614
$189$	0	0
$190$	−1.00194	−0.0726883
$191$	−17.0751	−1.23551	−0.617757	−	0.786369i	$-0.711958\pi$
$191$	−17.0751	−1.23551	−0.617757	+	0.786369i	$0.711958\pi$
$192$	−2.30974	−0.166691
$193$	−4.65052	−0.334752	−0.167376	−	0.985893i	$-0.553529\pi$
$193$	−4.65052	−0.334752	−0.167376	+	0.985893i	$0.553529\pi$
$194$	1.08097	0.0776093
$195$	−3.43812	−0.246209
$196$	0	0
$197$	0.254912	0.0181618	0.00908088	−	0.999959i	$-0.497109\pi$
$197$	0.254912	0.0181618	0.00908088	+	0.999959i	$0.497109\pi$
$198$	−3.82436	−0.271786
$199$	−5.47597	−0.388181	−0.194091	−	0.980984i	$-0.562176\pi$
$199$	−5.47597	−0.388181	−0.194091	+	0.980984i	$0.562176\pi$
$200$	−4.83104	−0.341606
$201$	−4.13763	−0.291846
$202$	11.4143	0.803110
$203$	0	0
$204$	−0.406815	−0.0284827
$205$	−7.94441	−0.554861
$206$	−34.1705	−2.38077
$207$	−1.00000	−0.0695048
$208$	17.7517	1.23086
$209$	1.20923	0.0836438
$210$	0	0
$211$	−3.18599	−0.219332	−0.109666	−	0.993968i	$-0.534978\pi$
$211$	−3.18599	−0.219332	−0.109666	+	0.993968i	$0.534978\pi$
$212$	3.15975	0.217013
$213$	−11.6439	−0.797827
$214$	1.18917	0.0812902
$215$	−8.57238	−0.584632
$216$	1.17548	0.0799816
$217$	0	0
$218$	25.0217	1.69468
$219$	11.5700	0.781827
$220$	2.67488	0.180341
$221$	1.09117	0.0734003
$222$	2.26778	0.152203
$223$	22.7674	1.52462	0.762309	−	0.647213i	$-0.224066\pi$
$223$	22.7674	1.52462	0.762309	+	0.647213i	$0.224066\pi$
$224$	0	0
$225$	−4.10983	−0.273988
$226$	−1.00297	−0.0667164
$227$	−10.4521	−0.693729	−0.346864	−	0.937915i	$-0.612754\pi$
$227$	−10.4521	−0.693729	−0.346864	+	0.937915i	$0.612754\pi$
$228$	0.787251	0.0521370
$229$	10.7678	0.711559	0.355779	−	0.934570i	$-0.384215\pi$
$229$	10.7678	0.711559	0.355779	+	0.934570i	$0.384215\pi$
$230$	1.72908	0.114012
$231$	0	0
$232$	−6.92787	−0.454837
$233$	11.7508	0.769818	0.384909	−	0.922955i	$-0.374233\pi$
$233$	11.7508	0.769818	0.384909	+	0.922955i	$0.374233\pi$
$234$	6.67825	0.436571
$235$	−4.77638	−0.311577
$236$	−2.82606	−0.183961
$237$	17.1584	1.11456
$238$	0	0
$239$	−12.5491	−0.811734	−0.405867	−	0.913932i	$-0.633030\pi$
$239$	−12.5491	−0.811734	−0.405867	+	0.913932i	$0.633030\pi$
$240$	−4.59613	−0.296679
$241$	10.6305	0.684768	0.342384	−	0.939560i	$-0.388766\pi$
$241$	10.6305	0.684768	0.342384	+	0.939560i	$0.388766\pi$
$242$	12.1784	0.782858
$243$	1.00000	0.0641500
$244$	−16.9199	−1.08318
$245$	0	0
$246$	15.4313	0.983864
$247$	−2.11159	−0.134358
$248$	7.08097	0.449642
$249$	−10.9740	−0.695447
$250$	15.7516	0.996220
$251$	17.4415	1.10090	0.550450	−	0.834868i	$-0.314456\pi$
$251$	17.4415	1.10090	0.550450	+	0.834868i	$0.314456\pi$
$252$	0	0
$253$	−2.08680	−0.131196
$254$	1.85606	0.116459
$255$	−0.282519	−0.0176920
$256$	20.9672	1.31045
$257$	−18.7261	−1.16810	−0.584050	−	0.811718i	$-0.698533\pi$
$257$	−18.7261	−1.16810	−0.584050	+	0.811718i	$0.698533\pi$
$258$	16.6511	1.03665
$259$	0	0
$260$	−4.67098	−0.289682
$261$	−5.89363	−0.364807
$262$	−27.5466	−1.70183
$263$	29.9086	1.84424	0.922121	−	0.386902i	$-0.126455\pi$
$263$	29.9086	1.84424	0.922121	+	0.386902i	$0.126455\pi$
$264$	2.45300	0.150972
$265$	2.19434	0.134797
$266$	0	0
$267$	−2.67561	−0.163745
$268$	−5.62133	−0.343377
$269$	−22.6461	−1.38076	−0.690378	−	0.723449i	$-0.742556\pi$
$269$	−22.6461	−1.38076	−0.690378	+	0.723449i	$0.742556\pi$
$270$	−1.72908	−0.105229
$271$	12.7364	0.773679	0.386839	−	0.922147i	$-0.373567\pi$
$271$	12.7364	0.773679	0.386839	+	0.922147i	$0.373567\pi$
$272$	1.45870	0.0884465
$273$	0	0
$274$	−17.0045	−1.02728
$275$	−8.57639	−0.517176
$276$	−1.35859	−0.0817772
$277$	−29.0127	−1.74320	−0.871601	−	0.490216i	$-0.836918\pi$
$277$	−29.0127	−1.74320	−0.871601	+	0.490216i	$0.836918\pi$
$278$	12.0725	0.724063
$279$	6.02387	0.360640
$280$	0	0
$281$	−12.4466	−0.742504	−0.371252	−	0.928532i	$-0.621071\pi$
$281$	−12.4466	−0.742504	−0.371252	+	0.928532i	$0.621071\pi$
$282$	9.27770	0.552479
$283$	−9.36397	−0.556630	−0.278315	−	0.960490i	$-0.589776\pi$
$283$	−9.36397	−0.556630	−0.278315	+	0.960490i	$0.589776\pi$
$284$	−15.8192	−0.938699
$285$	0.546718	0.0323848
$286$	13.9362	0.824063
$287$	0	0
$288$	6.57660	0.387530
$289$	−16.9103	−0.994726
$290$	10.1906	0.598411
$291$	−0.589843	−0.0345772
$292$	15.7188	0.919874
$293$	−5.69521	−0.332717	−0.166359	−	0.986065i	$-0.553201\pi$
$293$	−5.69521	−0.332717	−0.166359	+	0.986065i	$0.553201\pi$
$294$	0	0
$295$	−1.96260	−0.114267
$296$	−1.45459	−0.0845461
$297$	2.08680	0.121088
$298$	10.7925	0.625192
$299$	3.64405	0.210741
$300$	−5.58355	−0.322367
$301$	0	0
$302$	−24.1063	−1.38716
$303$	−6.22834	−0.357809
$304$	−2.82281	−0.161899
$305$	−11.7502	−0.672817
$306$	0.548767	0.0313709
$307$	−17.0596	−0.973642	−0.486821	−	0.873502i	$-0.661844\pi$
$307$	−17.0596	−0.973642	−0.486821	+	0.873502i	$0.661844\pi$
$308$	0	0
$309$	18.6455	1.06070
$310$	−10.4158	−0.591576
$311$	16.5243	0.937005	0.468503	−	0.883462i	$-0.344794\pi$
$311$	16.5243	0.937005	0.468503	+	0.883462i	$0.344794\pi$
$312$	−4.28352	−0.242507
$313$	1.49388	0.0844389	0.0422195	−	0.999108i	$-0.486557\pi$
$313$	1.49388	0.0844389	0.0422195	+	0.999108i	$0.486557\pi$
$314$	−15.4411	−0.871391
$315$	0	0
$316$	23.3112	1.31135
$317$	−18.2234	−1.02353	−0.511765	−	0.859126i	$-0.671008\pi$
$317$	−18.2234	−1.02353	−0.511765	+	0.859126i	$0.671008\pi$
$318$	−4.26230	−0.239018
$319$	−12.2988	−0.688602
$320$	−2.17922	−0.121822
$321$	−0.648883	−0.0362171
$322$	0	0
$323$	−0.173515	−0.00965461
$324$	1.35859	0.0754770
$325$	14.9764	0.830742
$326$	−7.61897	−0.421976
$327$	−13.6533	−0.755031
$328$	−9.89786	−0.546518
$329$	0	0
$330$	−3.60825	−0.198627
$331$	−22.9549	−1.26171	−0.630857	−	0.775899i	$-0.717297\pi$
$331$	−22.9549	−1.26171	−0.630857	+	0.775899i	$0.717297\pi$
$332$	−14.9091	−0.818241
$333$	−1.23744	−0.0678111
$334$	−5.57939	−0.305291
$335$	−3.90381	−0.213288
$336$	0	0
$337$	22.2266	1.21076	0.605381	−	0.795936i	$-0.293021\pi$
$337$	22.2266	1.21076	0.605381	+	0.795936i	$0.293021\pi$
$338$	−0.511486	−0.0278212
$339$	0.547279	0.0297241
$340$	−0.383826	−0.0208159
$341$	12.5706	0.680737
$342$	−1.06195	−0.0574237
$343$	0	0
$344$	−10.6802	−0.575840
$345$	−0.943490	−0.0507958
$346$	29.4218	1.58173
$347$	−5.40842	−0.290339	−0.145170	−	0.989407i	$-0.546373\pi$
$347$	−5.40842	−0.290339	−0.145170	+	0.989407i	$0.546373\pi$
$348$	−8.00700	−0.429220
$349$	−10.3938	−0.556369	−0.278184	−	0.960528i	$-0.589733\pi$
$349$	−10.3938	−0.556369	−0.278184	+	0.960528i	$0.589733\pi$
$350$	0	0
$351$	−3.64405	−0.194505
$352$	13.7241	0.731495
$353$	13.0691	0.695596	0.347798	−	0.937570i	$-0.386930\pi$
$353$	13.0691	0.695596	0.347798	+	0.937570i	$0.386930\pi$
$354$	3.81217	0.202615
$355$	−10.9859	−0.583071
$356$	−3.63505	−0.192657
$357$	0	0
$358$	9.79565	0.517716
$359$	−19.2232	−1.01456	−0.507281	−	0.861781i	$-0.669349\pi$
$359$	−19.2232	−1.01456	−0.507281	+	0.861781i	$0.669349\pi$
$360$	1.10906	0.0584525
$361$	−18.6642	−0.982327
$362$	−21.2955	−1.11927
$363$	−6.64526	−0.348786
$364$	0	0
$365$	10.9162	0.571378
$366$	22.8238	1.19302
$367$	1.77510	0.0926592	0.0463296	−	0.998926i	$-0.485248\pi$
$367$	1.77510	0.0926592	0.0463296	+	0.998926i	$0.485248\pi$
$368$	4.87142	0.253940
$369$	−8.42024	−0.438340
$370$	2.13963	0.111234
$371$	0	0
$372$	8.18395	0.424318
$373$	−7.44021	−0.385240	−0.192620	−	0.981273i	$-0.561698\pi$
$373$	−7.44021	−0.385240	−0.192620	+	0.981273i	$0.561698\pi$
$374$	1.14517	0.0592152
$375$	−8.59503	−0.443845
$376$	−5.95085	−0.306892
$377$	21.4767	1.10611
$378$	0	0
$379$	−4.31050	−0.221415	−0.110708	−	0.993853i	$-0.535312\pi$
$379$	−4.31050	−0.221415	−0.110708	+	0.993853i	$0.535312\pi$
$380$	0.742763	0.0381029
$381$	−1.01278	−0.0518861
$382$	31.2927	1.60107
$383$	−34.6915	−1.77265	−0.886326	−	0.463062i	$-0.846751\pi$
$383$	−34.6915	−1.77265	−0.886326	+	0.463062i	$0.846751\pi$
$384$	−8.92027	−0.455211
$385$	0	0
$386$	8.52275	0.433796
$387$	−9.08583	−0.461858
$388$	−0.801352	−0.0406825
$389$	33.1439	1.68046	0.840230	−	0.542230i	$-0.182420\pi$
$389$	33.1439	1.68046	0.840230	+	0.542230i	$0.182420\pi$
$390$	6.30086	0.319056
$391$	0.299440	0.0151433
$392$	0	0
$393$	15.0311	0.758217
$394$	−0.467164	−0.0235354
$395$	16.1888	0.814545
$396$	2.83510	0.142469
$397$	28.4564	1.42818	0.714092	−	0.700052i	$-0.246840\pi$
$397$	28.4564	1.42818	0.714092	+	0.700052i	$0.246840\pi$
$398$	10.0355	0.503035
$399$	0	0
$400$	20.0207	1.00103
$401$	−37.8811	−1.89169	−0.945846	−	0.324615i	$-0.894765\pi$
$401$	−37.8811	−1.89169	−0.945846	+	0.324615i	$0.894765\pi$
$402$	7.58281	0.378196
$403$	−21.9513	−1.09347
$404$	−8.46174	−0.420987
$405$	0.943490	0.0468824
$406$	0	0
$407$	−2.58228	−0.127999
$408$	−0.351987	−0.0174260
$409$	−0.957146	−0.0473278	−0.0236639	−	0.999720i	$-0.507533\pi$
$409$	−0.957146	−0.0473278	−0.0236639	+	0.999720i	$0.507533\pi$
$410$	14.5593	0.719031
$411$	9.27867	0.457683
$412$	25.3315	1.24799
$413$	0	0
$414$	1.83264	0.0900696
$415$	−10.3538	−0.508249
$416$	−23.9655	−1.17500
$417$	−6.58750	−0.322591
$418$	−2.21608	−0.108392
$419$	40.7600	1.99126	0.995628	−	0.0934066i	$-0.0297756\pi$
$419$	40.7600	1.99126	0.995628	+	0.0934066i	$0.0297756\pi$
$420$	0	0
$421$	−26.0184	−1.26806	−0.634031	−	0.773308i	$-0.718601\pi$
$421$	−26.0184	−1.26806	−0.634031	+	0.773308i	$0.718601\pi$
$422$	5.83878	0.284227
$423$	−5.06246	−0.246145
$424$	2.73390	0.132770
$425$	1.23065	0.0596951
$426$	21.3391	1.03388
$427$	0	0
$428$	−0.881564	−0.0426120
$429$	−7.60440	−0.367144
$430$	15.7101	0.757610
$431$	−31.4441	−1.51461	−0.757305	−	0.653061i	$-0.773485\pi$
$431$	−31.4441	−1.51461	−0.757305	+	0.653061i	$0.773485\pi$
$432$	−4.87142	−0.234376
$433$	−3.61281	−0.173621	−0.0868103	−	0.996225i	$-0.527667\pi$
$433$	−3.61281	−0.173621	−0.0868103	+	0.996225i	$0.527667\pi$
$434$	0	0
$435$	−5.56058	−0.266609
$436$	−18.5492	−0.888347
$437$	−0.579464	−0.0277195
$438$	−21.2037	−1.01315
$439$	−18.0511	−0.861530	−0.430765	−	0.902464i	$-0.641756\pi$
$439$	−18.0511	−0.861530	−0.430765	+	0.902464i	$0.641756\pi$
$440$	2.31438	0.110334
$441$	0	0
$442$	−1.99973	−0.0951177
$443$	−35.3301	−1.67858	−0.839291	−	0.543683i	$-0.817030\pi$
$443$	−35.3301	−1.67858	−0.839291	+	0.543683i	$0.817030\pi$
$444$	−1.68116	−0.0797844
$445$	−2.52441	−0.119669
$446$	−41.7246	−1.97571
$447$	−5.88903	−0.278541
$448$	0	0
$449$	5.95593	0.281078	0.140539	−	0.990075i	$-0.455116\pi$
$449$	5.95593	0.281078	0.140539	+	0.990075i	$0.455116\pi$
$450$	7.53185	0.355055
$451$	−17.5714	−0.827403
$452$	0.743525	0.0349725
$453$	13.1539	0.618022
$454$	19.1549	0.898986
$455$	0	0
$456$	0.681151	0.0318978
$457$	31.9674	1.49537	0.747685	−	0.664053i	$-0.231165\pi$
$457$	31.9674	1.49537	0.747685	+	0.664053i	$0.231165\pi$
$458$	−19.7336	−0.922091
$459$	−0.299440	−0.0139767
$460$	−1.28181	−0.0597648
$461$	−7.10536	−0.330930	−0.165465	−	0.986216i	$-0.552912\pi$
$461$	−7.10536	−0.330930	−0.165465	+	0.986216i	$0.552912\pi$
$462$	0	0
$463$	−42.0816	−1.95570	−0.977848	−	0.209314i	$-0.932877\pi$
$463$	−42.0816	−1.95570	−0.977848	+	0.209314i	$0.932877\pi$
$464$	28.7103	1.33284
$465$	5.68346	0.263564
$466$	−21.5350	−0.997588
$467$	−26.4507	−1.22399	−0.611995	−	0.790861i	$-0.709633\pi$
$467$	−26.4507	−1.22399	−0.611995	+	0.790861i	$0.709633\pi$
$468$	−4.95075	−0.228849
$469$	0	0
$470$	8.75341	0.403765
$471$	8.42558	0.388230
$472$	−2.44518	−0.112549
$473$	−18.9603	−0.871796
$474$	−31.4452	−1.44433
$475$	−2.38150	−0.109271
$476$	0	0
$477$	2.32577	0.106490
$478$	22.9980	1.05191
$479$	25.2828	1.15520	0.577601	−	0.816319i	$-0.303989\pi$
$479$	25.2828	1.15520	0.577601	+	0.816319i	$0.303989\pi$
$480$	6.20496	0.283216
$481$	4.50928	0.205605
$482$	−19.4818	−0.887373
$483$	0	0
$484$	−9.02816	−0.410371
$485$	−0.556511	−0.0252698
$486$	−1.83264	−0.0831304
$487$	19.9765	0.905222	0.452611	−	0.891708i	$-0.350493\pi$
$487$	19.9765	0.905222	0.452611	+	0.891708i	$0.350493\pi$
$488$	−14.6395	−0.662700
$489$	4.15736	0.188002
$490$	0	0
$491$	−41.0091	−1.85072	−0.925358	−	0.379095i	$-0.876235\pi$
$491$	−41.0091	−1.85072	−0.925358	+	0.379095i	$0.876235\pi$
$492$	−11.4396	−0.515738
$493$	1.76479	0.0794821
$494$	3.86980	0.174111
$495$	1.96887	0.0884943
$496$	−29.3448	−1.31762
$497$	0	0
$498$	20.1114	0.901212
$499$	14.0469	0.628825	0.314412	−	0.949286i	$-0.398193\pi$
$499$	14.0469	0.628825	0.314412	+	0.949286i	$0.398193\pi$
$500$	−11.6771	−0.522215
$501$	3.04445	0.136016
$502$	−31.9641	−1.42663
$503$	−12.8463	−0.572787	−0.286393	−	0.958112i	$-0.592456\pi$
$503$	−12.8463	−0.572787	−0.286393	+	0.958112i	$0.592456\pi$
$504$	0	0
$505$	−5.87638	−0.261495
$506$	3.82436	0.170014
$507$	0.279097	0.0123951
$508$	−1.37594	−0.0610476
$509$	26.7812	1.18706	0.593528	−	0.804813i	$-0.297734\pi$
$509$	26.7812	1.18706	0.593528	+	0.804813i	$0.297734\pi$
$510$	0.517756	0.0229266
$511$	0	0
$512$	−20.5848	−0.909730
$513$	0.579464	0.0255839
$514$	34.3182	1.51371
$515$	17.5918	0.775188
$516$	−12.3439	−0.543409
$517$	−10.5644	−0.464620
$518$	0	0
$519$	−16.0543	−0.704705
$520$	−4.04146	−0.177230
$521$	26.8305	1.17546	0.587732	−	0.809056i	$-0.300021\pi$
$521$	26.8305	1.17546	0.587732	+	0.809056i	$0.300021\pi$
$522$	10.8009	0.472744
$523$	16.0946	0.703768	0.351884	−	0.936044i	$-0.385541\pi$
$523$	16.0946	0.703768	0.351884	+	0.936044i	$0.385541\pi$
$524$	20.4210	0.892095
$525$	0	0
$526$	−54.8118	−2.38991
$527$	−1.80379	−0.0785743
$528$	−10.1657	−0.442404
$529$	1.00000	0.0434783
$530$	−4.02144	−0.174680
$531$	−2.08015	−0.0902708
$532$	0	0
$533$	30.6838	1.32906
$534$	4.90345	0.212193
$535$	−0.612215	−0.0264683
$536$	−4.86373	−0.210081
$537$	−5.34509	−0.230658
$538$	41.5022	1.78929
$539$	0	0
$540$	1.28181	0.0551604
$541$	−0.676959	−0.0291047	−0.0145524	−	0.999894i	$-0.504632\pi$
$541$	−0.676959	−0.0291047	−0.0145524	+	0.999894i	$0.504632\pi$
$542$	−23.3412	−1.00259
$543$	11.6201	0.498667
$544$	−1.96930	−0.0844330
$545$	−12.8818	−0.551795
$546$	0	0
$547$	−8.38777	−0.358635	−0.179318	−	0.983791i	$-0.557389\pi$
$547$	−8.38777	−0.358635	−0.179318	+	0.983791i	$0.557389\pi$
$548$	12.6059	0.538496
$549$	−12.4540	−0.531525
$550$	15.7175	0.670195
$551$	−3.41515	−0.145490
$552$	−1.17548	−0.0500320
$553$	0	0
$554$	53.1699	2.25897
$555$	−1.16751	−0.0495579
$556$	−8.94968	−0.379551
$557$	−2.49888	−0.105881	−0.0529404	−	0.998598i	$-0.516859\pi$
$557$	−2.49888	−0.105881	−0.0529404	+	0.998598i	$0.516859\pi$
$558$	−11.0396	−0.467344
$559$	33.1092	1.40037
$560$	0	0
$561$	−0.624872	−0.0263821
$562$	22.8103	0.962193
$563$	40.4580	1.70510	0.852551	−	0.522645i	$-0.175055\pi$
$563$	40.4580	1.70510	0.852551	+	0.522645i	$0.175055\pi$
$564$	−6.87779	−0.289607
$565$	0.516352	0.0217231
$566$	17.1608	0.721323
$567$	0	0
$568$	−13.6872	−0.574303
$569$	−12.4802	−0.523199	−0.261599	−	0.965177i	$-0.584250\pi$
$569$	−12.4802	−0.523199	−0.261599	+	0.965177i	$0.584250\pi$
$570$	−1.00194	−0.0419666
$571$	−30.9927	−1.29700	−0.648502	−	0.761213i	$-0.724604\pi$
$571$	−30.9927	−1.29700	−0.648502	+	0.761213i	$0.724604\pi$
$572$	−10.3312	−0.431971
$573$	−17.0751	−0.713324
$574$	0	0
$575$	4.10983	0.171392
$576$	−2.30974	−0.0962394
$577$	−10.5302	−0.438379	−0.219190	−	0.975682i	$-0.570341\pi$
$577$	−10.5302	−0.438379	−0.219190	+	0.975682i	$0.570341\pi$
$578$	30.9906	1.28904
$579$	−4.65052	−0.193269
$580$	−7.55452	−0.313684
$581$	0	0
$582$	1.08097	0.0448077
$583$	4.85341	0.201008
$584$	13.6003	0.562786
$585$	−3.43812	−0.142149
$586$	10.4373	0.431160
$587$	−7.06244	−0.291498	−0.145749	−	0.989322i	$-0.546559\pi$
$587$	−7.06244	−0.291498	−0.145749	+	0.989322i	$0.546559\pi$
$588$	0	0
$589$	3.49062	0.143828
$590$	3.59675	0.148076
$591$	0.254912	0.0104857
$592$	6.02806	0.247752
$593$	−39.8925	−1.63819	−0.819094	−	0.573660i	$-0.805523\pi$
$593$	−39.8925	−1.63819	−0.819094	+	0.573660i	$0.805523\pi$
$594$	−3.82436	−0.156916
$595$	0	0
$596$	−8.00075	−0.327723
$597$	−5.47597	−0.224117
$598$	−6.67825	−0.273094
$599$	11.8646	0.484773	0.242386	−	0.970180i	$-0.422070\pi$
$599$	11.8646	0.484773	0.242386	+	0.970180i	$0.422070\pi$
$600$	−4.83104	−0.197226
$601$	−15.0105	−0.612290	−0.306145	−	0.951985i	$-0.599039\pi$
$601$	−15.0105	−0.612290	−0.306145	+	0.951985i	$0.599039\pi$
$602$	0	0
$603$	−4.13763	−0.168498
$604$	17.8706	0.727146
$605$	−6.26974	−0.254901
$606$	11.4143	0.463676
$607$	4.19990	0.170469	0.0852343	−	0.996361i	$-0.472836\pi$
$607$	4.19990	0.170469	0.0852343	+	0.996361i	$0.472836\pi$
$608$	3.81090	0.154553
$609$	0	0
$610$	21.5340	0.871887
$611$	18.4479	0.746321
$612$	−0.406815	−0.0164445
$613$	30.9865	1.25153	0.625766	−	0.780011i	$-0.284786\pi$
$613$	30.9865	1.25153	0.625766	+	0.780011i	$0.284786\pi$
$614$	31.2641	1.26172
$615$	−7.94441	−0.320349
$616$	0	0
$617$	1.93041	0.0777153	0.0388577	−	0.999245i	$-0.487628\pi$
$617$	1.93041	0.0777153	0.0388577	+	0.999245i	$0.487628\pi$
$618$	−34.1705	−1.37454
$619$	−33.2844	−1.33781	−0.668907	−	0.743346i	$-0.733237\pi$
$619$	−33.2844	−1.33781	−0.668907	+	0.743346i	$0.733237\pi$
$620$	7.72147	0.310102
$621$	−1.00000	−0.0401286
$622$	−30.2831	−1.21424
$623$	0	0
$624$	17.7517	0.710636
$625$	12.4398	0.497593
$626$	−2.73775	−0.109422
$627$	1.20923	0.0482918
$628$	11.4469	0.456780
$629$	0.370538	0.0147743
$630$	0	0
$631$	4.49815	0.179068	0.0895342	−	0.995984i	$-0.471462\pi$
$631$	4.49815	0.179068	0.0895342	+	0.995984i	$0.471462\pi$
$632$	20.1694	0.802297
$633$	−3.18599	−0.126632
$634$	33.3971	1.32637
$635$	−0.955543	−0.0379196
$636$	3.15975	0.125292
$637$	0	0
$638$	22.5394	0.892343
$639$	−11.6439	−0.460625
$640$	−8.41618	−0.332679
$641$	−26.8209	−1.05936	−0.529681	−	0.848197i	$-0.677688\pi$
$641$	−26.8209	−1.05936	−0.529681	+	0.848197i	$0.677688\pi$
$642$	1.18917	0.0469329
$643$	21.1912	0.835701	0.417850	−	0.908516i	$-0.362784\pi$
$643$	21.1912	0.835701	0.417850	+	0.908516i	$0.362784\pi$
$644$	0	0
$645$	−8.57238	−0.337537
$646$	0.317991	0.0125112
$647$	−3.28238	−0.129044	−0.0645218	−	0.997916i	$-0.520552\pi$
$647$	−3.28238	−0.129044	−0.0645218	+	0.997916i	$0.520552\pi$
$648$	1.17548	0.0461774
$649$	−4.34086	−0.170393
$650$	−27.4464	−1.07654
$651$	0	0
$652$	5.64813	0.221198
$653$	32.7912	1.28322	0.641610	−	0.767031i	$-0.278267\pi$
$653$	32.7912	1.28322	0.641610	+	0.767031i	$0.278267\pi$
$654$	25.0217	0.978426
$655$	14.1816	0.554123
$656$	41.0185	1.60150
$657$	11.5700	0.451388
$658$	0	0
$659$	11.1625	0.434828	0.217414	−	0.976079i	$-0.430238\pi$
$659$	11.1625	0.434828	0.217414	+	0.976079i	$0.430238\pi$
$660$	2.67488	0.104120
$661$	−8.39461	−0.326513	−0.163256	−	0.986584i	$-0.552200\pi$
$661$	−8.39461	−0.326513	−0.163256	+	0.986584i	$0.552200\pi$
$662$	42.0681	1.63502
$663$	1.09117	0.0423777
$664$	−12.8997	−0.500606
$665$	0	0
$666$	2.26778	0.0878747
$667$	5.89363	0.228202
$668$	4.13614	0.160032
$669$	22.7674	0.880239
$670$	7.15430	0.276395
$671$	−25.9891	−1.00330
$672$	0	0
$673$	30.3183	1.16869	0.584343	−	0.811507i	$-0.301352\pi$
$673$	30.3183	1.16869	0.584343	+	0.811507i	$0.301352\pi$
$674$	−40.7335	−1.56900
$675$	−4.10983	−0.158187
$676$	0.379177	0.0145837
$677$	10.3013	0.395910	0.197955	−	0.980211i	$-0.436570\pi$
$677$	10.3013	0.395910	0.197955	+	0.980211i	$0.436570\pi$
$678$	−1.00297	−0.0385187
$679$	0	0
$680$	−0.332096	−0.0127353
$681$	−10.4521	−0.400524
$682$	−23.0375	−0.882151
$683$	−48.1741	−1.84333	−0.921666	−	0.387984i	$-0.873172\pi$
$683$	−48.1741	−1.84333	−0.921666	+	0.387984i	$0.873172\pi$
$684$	0.787251	0.0301013
$685$	8.75433	0.334486
$686$	0	0
$687$	10.7678	0.410819
$688$	44.2608	1.68743
$689$	−8.47521	−0.322880
$690$	1.72908	0.0658250
$691$	36.7195	1.39687	0.698437	−	0.715671i	$-0.253879\pi$
$691$	36.7195	1.39687	0.698437	+	0.715671i	$0.253879\pi$
$692$	−21.8111	−0.829135
$693$	0	0
$694$	9.91171	0.376243
$695$	−6.21523	−0.235757
$696$	−6.92787	−0.262600
$697$	2.52136	0.0955032
$698$	19.0482	0.720985
$699$	11.7508	0.444455
$700$	0	0
$701$	35.3581	1.33546	0.667728	−	0.744406i	$-0.267267\pi$
$701$	35.3581	1.33546	0.667728	+	0.744406i	$0.267267\pi$
$702$	6.67825	0.252054
$703$	−0.717049	−0.0270440
$704$	−4.81998	−0.181660
$705$	−4.77638	−0.179889
$706$	−23.9509	−0.901405
$707$	0	0
$708$	−2.82606	−0.106210
$709$	−10.9962	−0.412969	−0.206485	−	0.978450i	$-0.566202\pi$
$709$	−10.9962	−0.412969	−0.206485	+	0.978450i	$0.566202\pi$
$710$	20.1332	0.755587
$711$	17.1584	0.643490
$712$	−3.14514	−0.117869
$713$	−6.02387	−0.225596
$714$	0	0
$715$	−7.17468	−0.268318
$716$	−7.26176	−0.271385
$717$	−12.5491	−0.468655
$718$	35.2293	1.31475
$719$	36.5754	1.36403	0.682016	−	0.731337i	$-0.261103\pi$
$719$	36.5754	1.36403	0.682016	+	0.731337i	$0.261103\pi$
$720$	−4.59613	−0.171288
$721$	0	0
$722$	34.2049	1.27297
$723$	10.6305	0.395351
$724$	15.7869	0.586716
$725$	24.2218	0.899575
$726$	12.1784	0.451983
$727$	12.9513	0.480337	0.240169	−	0.970731i	$-0.422797\pi$
$727$	12.9513	0.480337	0.240169	+	0.970731i	$0.422797\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−20.0054	−0.740434
$731$	2.72066	0.100627
$732$	−16.9199	−0.625376
$733$	−6.26355	−0.231350	−0.115675	−	0.993287i	$-0.536903\pi$
$733$	−6.26355	−0.231350	−0.115675	+	0.993287i	$0.536903\pi$
$734$	−3.25312	−0.120075
$735$	0	0
$736$	−6.57660	−0.242417
$737$	−8.63442	−0.318053
$738$	15.4313	0.568034
$739$	32.4215	1.19264	0.596322	−	0.802745i	$-0.296628\pi$
$739$	32.4215	1.19264	0.596322	+	0.802745i	$0.296628\pi$
$740$	−1.58616	−0.0583084
$741$	−2.11159	−0.0775714
$742$	0	0
$743$	−4.32354	−0.158615	−0.0793076	−	0.996850i	$-0.525271\pi$
$743$	−4.32354	−0.158615	−0.0793076	+	0.996850i	$0.525271\pi$
$744$	7.08097	0.259601
$745$	−5.55624	−0.203565
$746$	13.6353	0.499222
$747$	−10.9740	−0.401516
$748$	−0.848942	−0.0310404
$749$	0	0
$750$	15.7516	0.575168
$751$	−12.0432	−0.439461	−0.219730	−	0.975561i	$-0.570518\pi$
$751$	−12.0432	−0.439461	−0.219730	+	0.975561i	$0.570518\pi$
$752$	24.6614	0.899308
$753$	17.4415	0.635605
$754$	−39.3591	−1.43337
$755$	12.4105	0.451665
$756$	0	0
$757$	17.8806	0.649880	0.324940	−	0.945735i	$-0.394656\pi$
$757$	17.8806	0.649880	0.324940	+	0.945735i	$0.394656\pi$
$758$	7.89961	0.286927
$759$	−2.08680	−0.0757461
$760$	0.642659	0.0233117
$761$	−26.2960	−0.953231	−0.476615	−	0.879112i	$-0.658137\pi$
$761$	−26.2960	−0.953231	−0.476615	+	0.879112i	$0.658137\pi$
$762$	1.85606	0.0672379
$763$	0	0
$764$	−23.1980	−0.839276
$765$	−0.282519	−0.0102145
$766$	63.5772	2.29714
$767$	7.58016	0.273704
$768$	20.9672	0.756588
$769$	32.2632	1.16344	0.581720	−	0.813389i	$-0.302380\pi$
$769$	32.2632	1.16344	0.581720	+	0.813389i	$0.302380\pi$
$770$	0	0
$771$	−18.7261	−0.674403
$772$	−6.31813	−0.227394
$773$	10.5757	0.380380	0.190190	−	0.981747i	$-0.439090\pi$
$773$	10.5757	0.380380	0.190190	+	0.981747i	$0.439090\pi$
$774$	16.6511	0.598511
$775$	−24.7571	−0.889301
$776$	−0.693351	−0.0248899
$777$	0	0
$778$	−60.7409	−2.17767
$779$	−4.87922	−0.174816
$780$	−4.67098	−0.167248
$781$	−24.2985	−0.869468
$782$	−0.548767	−0.0196239
$783$	−5.89363	−0.210621
$784$	0	0
$785$	7.94945	0.283728
$786$	−27.5466	−0.982554
$787$	27.5234	0.981103	0.490552	−	0.871412i	$-0.336795\pi$
$787$	27.5234	0.981103	0.490552	+	0.871412i	$0.336795\pi$
$788$	0.346320	0.0123371
$789$	29.9086	1.06477
$790$	−29.6683	−1.05555
$791$	0	0
$792$	2.45300	0.0871636
$793$	45.3831	1.61160
$794$	−52.1504	−1.85075
$795$	2.19434	0.0778251
$796$	−7.43958	−0.263689
$797$	43.4629	1.53953	0.769767	−	0.638324i	$-0.220372\pi$
$797$	43.4629	1.53953	0.769767	+	0.638324i	$0.220372\pi$
$798$	0	0
$799$	1.51590	0.0536288
$800$	−27.0287	−0.955609
$801$	−2.67561	−0.0945381
$802$	69.4226	2.45140
$803$	24.1442	0.852032
$804$	−5.62133	−0.198249
$805$	0	0
$806$	40.2289	1.41700
$807$	−22.6461	−0.797180
$808$	−7.32132	−0.257563
$809$	42.8145	1.50528	0.752639	−	0.658434i	$-0.228781\pi$
$809$	42.8145	1.50528	0.752639	+	0.658434i	$0.228781\pi$
$810$	−1.72908	−0.0607537
$811$	−45.2610	−1.58933	−0.794664	−	0.607049i	$-0.792353\pi$
$811$	−45.2610	−1.58933	−0.794664	+	0.607049i	$0.792353\pi$
$812$	0	0
$813$	12.7364	0.446684
$814$	4.73240	0.165871
$815$	3.92243	0.137397
$816$	1.45870	0.0510646
$817$	−5.26491	−0.184196
$818$	1.75411	0.0613310
$819$	0	0
$820$	−10.7932	−0.376913
$821$	−36.3213	−1.26762	−0.633812	−	0.773487i	$-0.718511\pi$
$821$	−36.3213	−1.26762	−0.633812	+	0.773487i	$0.718511\pi$
$822$	−17.0045	−0.593100
$823$	52.1001	1.81610	0.908048	−	0.418865i	$-0.137572\pi$
$823$	52.1001	1.81610	0.908048	+	0.418865i	$0.137572\pi$
$824$	21.9175	0.763532
$825$	−8.57639	−0.298592
$826$	0	0
$827$	−21.6989	−0.754545	−0.377273	−	0.926102i	$-0.623138\pi$
$827$	−21.6989	−0.754545	−0.377273	+	0.926102i	$0.623138\pi$
$828$	−1.35859	−0.0472141
$829$	13.5755	0.471497	0.235749	−	0.971814i	$-0.424246\pi$
$829$	13.5755	0.471497	0.235749	+	0.971814i	$0.424246\pi$
$830$	18.9749	0.658627
$831$	−29.0127	−1.00644
$832$	8.41682	0.291801
$833$	0	0
$834$	12.0725	0.418038
$835$	2.87241	0.0994037
$836$	1.64284	0.0568187
$837$	6.02387	0.208216
$838$	−74.6986	−2.58042
$839$	40.6915	1.40483	0.702413	−	0.711770i	$-0.252106\pi$
$839$	40.6915	1.40483	0.702413	+	0.711770i	$0.252106\pi$
$840$	0	0
$841$	5.73489	0.197755
$842$	47.6826	1.64325
$843$	−12.4466	−0.428685
$844$	−4.32843	−0.148991
$845$	0.263325	0.00905866
$846$	9.27770	0.318974
$847$	0	0
$848$	−11.3298	−0.389066
$849$	−9.36397	−0.321370
$850$	−2.25534	−0.0773575
$851$	1.23744	0.0424187
$852$	−15.8192	−0.541958
$853$	53.5882	1.83482	0.917412	−	0.397938i	$-0.130274\pi$
$853$	53.5882	1.83482	0.917412	+	0.397938i	$0.130274\pi$
$854$	0	0
$855$	0.546718	0.0186974
$856$	−0.762752	−0.0260703
$857$	15.1853	0.518719	0.259360	−	0.965781i	$-0.416489\pi$
$857$	15.1853	0.518719	0.259360	+	0.965781i	$0.416489\pi$
$858$	13.9362	0.475773
$859$	37.9385	1.29444	0.647222	−	0.762302i	$-0.275931\pi$
$859$	37.9385	1.29444	0.647222	+	0.762302i	$0.275931\pi$
$860$	−11.6463	−0.397136
$861$	0	0
$862$	57.6259	1.96275
$863$	34.9640	1.19019	0.595094	−	0.803656i	$-0.297115\pi$
$863$	34.9640	1.19019	0.595094	+	0.803656i	$0.297115\pi$
$864$	6.57660	0.223741
$865$	−15.1471	−0.515015
$866$	6.62099	0.224991
$867$	−16.9103	−0.574305
$868$	0	0
$869$	35.8062	1.21464
$870$	10.1906	0.345493
$871$	15.0777	0.510890
$872$	−16.0493	−0.543497
$873$	−0.589843	−0.0199632
$874$	1.06195	0.0359210
$875$	0	0
$876$	15.7188	0.531089
$877$	39.0428	1.31838	0.659191	−	0.751976i	$-0.270899\pi$
$877$	39.0428	1.31838	0.659191	+	0.751976i	$0.270899\pi$
$878$	33.0812	1.11644
$879$	−5.69521	−0.192095
$880$	−9.59121	−0.323320
$881$	−21.5235	−0.725145	−0.362572	−	0.931956i	$-0.618101\pi$
$881$	−21.5235	−0.725145	−0.362572	+	0.931956i	$0.618101\pi$
$882$	0	0
$883$	−17.0630	−0.574217	−0.287109	−	0.957898i	$-0.592694\pi$
$883$	−17.0630	−0.574217	−0.287109	+	0.957898i	$0.592694\pi$
$884$	1.48245	0.0498603
$885$	−1.96260	−0.0659720
$886$	64.7474	2.17523
$887$	−43.1464	−1.44871	−0.724357	−	0.689425i	$-0.757863\pi$
$887$	−43.1464	−1.44871	−0.724357	+	0.689425i	$0.757863\pi$
$888$	−1.45459	−0.0488127
$889$	0	0
$890$	4.62635	0.155076
$891$	2.08680	0.0699104
$892$	30.9315	1.03566
$893$	−2.93351	−0.0981663
$894$	10.7925	0.360955
$895$	−5.04304	−0.168570
$896$	0	0
$897$	3.64405	0.121671
$898$	−10.9151	−0.364242
$899$	−35.5025	−1.18407
$900$	−5.58355	−0.186118
$901$	−0.696428	−0.0232014
$902$	32.2020	1.07221
$903$	0	0
$904$	0.643318	0.0213964
$905$	10.9635	0.364438
$906$	−24.1063	−0.800879
$907$	−9.48595	−0.314976	−0.157488	−	0.987521i	$-0.550340\pi$
$907$	−9.48595	−0.314976	−0.157488	+	0.987521i	$0.550340\pi$
$908$	−14.2000	−0.471245
$909$	−6.22834	−0.206581
$910$	0	0
$911$	17.7773	0.588988	0.294494	−	0.955653i	$-0.404849\pi$
$911$	17.7773	0.588988	0.294494	+	0.955653i	$0.404849\pi$
$912$	−2.82281	−0.0934725
$913$	−22.9005	−0.757895
$914$	−58.5848	−1.93781
$915$	−11.7502	−0.388451
$916$	14.6290	0.483357
$917$	0	0
$918$	0.548767	0.0181120
$919$	3.50669	0.115675	0.0578376	−	0.998326i	$-0.481579\pi$
$919$	3.50669	0.115675	0.0578376	+	0.998326i	$0.481579\pi$
$920$	−1.10906	−0.0365645
$921$	−17.0596	−0.562132
$922$	13.0216	0.428843
$923$	42.4309	1.39663
$924$	0	0
$925$	5.08565	0.167215
$926$	77.1206	2.53434
$927$	18.6455	0.612398
$928$	−38.7601	−1.27236
$929$	−15.2444	−0.500153	−0.250076	−	0.968226i	$-0.580456\pi$
$929$	−15.2444	−0.500153	−0.250076	+	0.968226i	$0.580456\pi$
$930$	−10.4158	−0.341546
$931$	0	0
$932$	15.9644	0.522932
$933$	16.5243	0.540980
$934$	48.4747	1.58614
$935$	−0.589560	−0.0192807
$936$	−4.28352	−0.140011
$937$	16.0219	0.523414	0.261707	−	0.965147i	$-0.415715\pi$
$937$	16.0219	0.523414	0.261707	+	0.965147i	$0.415715\pi$
$938$	0	0
$939$	1.49388	0.0487508
$940$	−6.48912	−0.211652
$941$	8.29938	0.270552	0.135276	−	0.990808i	$-0.456808\pi$
$941$	8.29938	0.270552	0.135276	+	0.990808i	$0.456808\pi$
$942$	−15.4411	−0.503098
$943$	8.42024	0.274201
$944$	10.1333	0.329810
$945$	0	0
$946$	34.7475	1.12974
$947$	48.3210	1.57022	0.785111	−	0.619355i	$-0.212606\pi$
$947$	48.3210	1.57022	0.785111	+	0.619355i	$0.212606\pi$
$948$	23.3112	0.757111
$949$	−42.1616	−1.36862
$950$	4.36443	0.141601
$951$	−18.2234	−0.590935
$952$	0	0
$953$	12.0181	0.389303	0.194652	−	0.980872i	$-0.437642\pi$
$953$	12.0181	0.389303	0.194652	+	0.980872i	$0.437642\pi$
$954$	−4.26230	−0.137997
$955$	−16.1102	−0.521314
$956$	−17.0490	−0.551405
$957$	−12.2988	−0.397565
$958$	−46.3344	−1.49700
$959$	0	0
$960$	−2.17922	−0.0703340
$961$	5.28706	0.170550
$962$	−8.26390	−0.266439
$963$	−0.648883	−0.0209100
$964$	14.4424	0.465158
$965$	−4.38772	−0.141246
$966$	0	0
$967$	20.9914	0.675036	0.337518	−	0.941319i	$-0.390413\pi$
$967$	20.9914	0.675036	0.337518	+	0.941319i	$0.390413\pi$
$968$	−7.81141	−0.251068
$969$	−0.173515	−0.00557409
$970$	1.01989	0.0327466
$971$	5.29526	0.169933	0.0849665	−	0.996384i	$-0.472922\pi$
$971$	5.29526	0.169933	0.0849665	+	0.996384i	$0.472922\pi$
$972$	1.35859	0.0435767
$973$	0	0
$974$	−36.6098	−1.17305
$975$	14.9764	0.479629
$976$	60.6688	1.94196
$977$	−26.6768	−0.853466	−0.426733	−	0.904378i	$-0.640336\pi$
$977$	−26.6768	−0.853466	−0.426733	+	0.904378i	$0.640336\pi$
$978$	−7.61897	−0.243628
$979$	−5.58347	−0.178448
$980$	0	0
$981$	−13.6533	−0.435917
$982$	75.1551	2.39830
$983$	−6.63941	−0.211764	−0.105882	−	0.994379i	$-0.533767\pi$
$983$	−6.63941	−0.211764	−0.105882	+	0.994379i	$0.533767\pi$
$984$	−9.89786	−0.315532
$985$	0.240507	0.00766320
$986$	−3.23423	−0.102999
$987$	0	0
$988$	−2.86878	−0.0912681
$989$	9.08583	0.288912
$990$	−3.60825	−0.114678
$991$	30.3443	0.963917	0.481958	−	0.876194i	$-0.339926\pi$
$991$	30.3443	0.963917	0.481958	+	0.876194i	$0.339926\pi$
$992$	39.6166	1.25783
$993$	−22.9549	−0.728451
$994$	0	0
$995$	−5.16652	−0.163790
$996$	−14.9091	−0.472412
$997$	−46.9848	−1.48802	−0.744011	−	0.668167i	$-0.767079\pi$
$997$	−46.9848	−1.48802	−0.744011	+	0.668167i	$0.767079\pi$
$998$	−25.7429	−0.814878
$999$	−1.23744	−0.0391507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bd.1.2		6
7.3	odd	6		483.2.i.f.415.5	yes	12
7.5	odd	6		483.2.i.f.277.5	✓	12
7.6	odd	2		3381.2.a.bc.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.f.277.5	✓	12	7.5	odd	6
483.2.i.f.415.5	yes	12	7.3	odd	6
3381.2.a.bc.1.2		6	7.6	odd	2
3381.2.a.bd.1.2		6	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.83264 q^{2} +1.00000 q^{3} +1.35859 q^{4} +0.943490 q^{5} -1.83264 q^{6} +1.17548 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.83264 q^{2} +1.00000 q^{3} +1.35859 q^{4} +0.943490 q^{5} -1.83264 q^{6} +1.17548 q^{8} +1.00000 q^{9} -1.72908 q^{10} +2.08680 q^{11} +1.35859 q^{12} -3.64405 q^{13} +0.943490 q^{15} -4.87142 q^{16} -0.299440 q^{17} -1.83264 q^{18} +0.579464 q^{19} +1.28181 q^{20} -3.82436 q^{22} -1.00000 q^{23} +1.17548 q^{24} -4.10983 q^{25} +6.67825 q^{26} +1.00000 q^{27} -5.89363 q^{29} -1.72908 q^{30} +6.02387 q^{31} +6.57660 q^{32} +2.08680 q^{33} +0.548767 q^{34} +1.35859 q^{36} -1.23744 q^{37} -1.06195 q^{38} -3.64405 q^{39} +1.10906 q^{40} -8.42024 q^{41} -9.08583 q^{43} +2.83510 q^{44} +0.943490 q^{45} +1.83264 q^{46} -5.06246 q^{47} -4.87142 q^{48} +7.53185 q^{50} -0.299440 q^{51} -4.95075 q^{52} +2.32577 q^{53} -1.83264 q^{54} +1.96887 q^{55} +0.579464 q^{57} +10.8009 q^{58} -2.08015 q^{59} +1.28181 q^{60} -12.4540 q^{61} -11.0396 q^{62} -2.30974 q^{64} -3.43812 q^{65} -3.82436 q^{66} -4.13763 q^{67} -0.406815 q^{68} -1.00000 q^{69} -11.6439 q^{71} +1.17548 q^{72} +11.5700 q^{73} +2.26778 q^{74} -4.10983 q^{75} +0.787251 q^{76} +6.67825 q^{78} +17.1584 q^{79} -4.59613 q^{80} +1.00000 q^{81} +15.4313 q^{82} -10.9740 q^{83} -0.282519 q^{85} +16.6511 q^{86} -5.89363 q^{87} +2.45300 q^{88} -2.67561 q^{89} -1.72908 q^{90} -1.35859 q^{92} +6.02387 q^{93} +9.27770 q^{94} +0.546718 q^{95} +6.57660 q^{96} -0.589843 q^{97} +2.08680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9	\( 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{10} - 14 q^{11} + 3 q^{12} - 3 q^{15} - 7 q^{16} - 15 q^{17} - q^{18} + q^{19} - 17 q^{20} - 6 q^{22} - 6 q^{23} - 3 q^{24} + 9 q^{25} + 15 q^{26} + 6 q^{27} - 6 q^{29} + 3 q^{30} + 11 q^{31} + 3 q^{32} - 14 q^{33} - 15 q^{34} + 3 q^{36} - 5 q^{37} - 14 q^{38} + 17 q^{40} - 18 q^{41} - 37 q^{43} - 10 q^{44} - 3 q^{45} + q^{46} - 3 q^{47} - 7 q^{48} - 30 q^{50} - 15 q^{51} + 7 q^{52} - 15 q^{53} - q^{54} + 2 q^{55} + q^{57} + 4 q^{58} + 2 q^{59} - 17 q^{60} + 12 q^{61} - 36 q^{62} - 23 q^{64} - 17 q^{65} - 6 q^{66} - 10 q^{67} + q^{68} - 6 q^{69} - 21 q^{71} - 3 q^{72} + 8 q^{73} - 16 q^{74} + 9 q^{75} - 18 q^{76} + 15 q^{78} - 17 q^{79} - 3 q^{80} + 6 q^{81} + 48 q^{82} - 12 q^{83} - 13 q^{85} + 22 q^{86} - 6 q^{87} - 2 q^{88} - 18 q^{89} + 3 q^{90} - 3 q^{92} + 11 q^{93} - 3 q^{94} - 16 q^{95} + 3 q^{96} + 2 q^{97} - 14 q^{99}+O(q^{100}) \) 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9 + 3 * q^10 - 14 * q^11 + 3 * q^12 - 3 * q^15 - 7 * q^16 - 15 * q^17 - q^18 + q^19 - 17 * q^20 - 6 * q^22 - 6 * q^23 - 3 * q^24 + 9 * q^25 + 15 * q^26 + 6 * q^27 - 6 * q^29 + 3 * q^30 + 11 * q^31 + 3 * q^32 - 14 * q^33 - 15 * q^34 + 3 * q^36 - 5 * q^37 - 14 * q^38 + 17 * q^40 - 18 * q^41 - 37 * q^43 - 10 * q^44 - 3 * q^45 + q^46 - 3 * q^47 - 7 * q^48 - 30 * q^50 - 15 * q^51 + 7 * q^52 - 15 * q^53 - q^54 + 2 * q^55 + q^57 + 4 * q^58 + 2 * q^59 - 17 * q^60 + 12 * q^61 - 36 * q^62 - 23 * q^64 - 17 * q^65 - 6 * q^66 - 10 * q^67 + q^68 - 6 * q^69 - 21 * q^71 - 3 * q^72 + 8 * q^73 - 16 * q^74 + 9 * q^75 - 18 * q^76 + 15 * q^78 - 17 * q^79 - 3 * q^80 + 6 * q^81 + 48 * q^82 - 12 * q^83 - 13 * q^85 + 22 * q^86 - 6 * q^87 - 2 * q^88 - 18 * q^89 + 3 * q^90 - 3 * q^92 + 11 * q^93 - 3 * q^94 - 16 * q^95 + 3 * q^96 + 2 * q^97 - 14 * q^99

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