LMFDB - Embedded newform 3381.2.a.bc.1.4

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			1.4
Root			$-0.289957$ 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)

$f(q)$	$=$	$q+0.289957 q^{2} -1.00000 q^{3} -1.91593 q^{4} +2.32621 q^{5} -0.289957 q^{6} -1.13545 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.289957 q^{2} -1.00000 q^{3} -1.91593 q^{4} +2.32621 q^{5} -0.289957 q^{6} -1.13545 q^{8} +1.00000 q^{9} +0.674501 q^{10} +0.730971 q^{11} +1.91593 q^{12} -0.115233 q^{13} -2.32621 q^{15} +3.50262 q^{16} +0.789022 q^{17} +0.289957 q^{18} -6.92342 q^{19} -4.45685 q^{20} +0.211950 q^{22} -1.00000 q^{23} +1.13545 q^{24} +0.411258 q^{25} -0.0334127 q^{26} -1.00000 q^{27} -6.26700 q^{29} -0.674501 q^{30} +1.49584 q^{31} +3.28651 q^{32} -0.730971 q^{33} +0.228782 q^{34} -1.91593 q^{36} +4.14294 q^{37} -2.00749 q^{38} +0.115233 q^{39} -2.64129 q^{40} +8.20805 q^{41} +1.50333 q^{43} -1.40049 q^{44} +2.32621 q^{45} -0.289957 q^{46} -3.78787 q^{47} -3.50262 q^{48} +0.119247 q^{50} -0.789022 q^{51} +0.220778 q^{52} -6.81735 q^{53} -0.289957 q^{54} +1.70039 q^{55} +6.92342 q^{57} -1.81716 q^{58} -6.18845 q^{59} +4.45685 q^{60} -2.39074 q^{61} +0.433729 q^{62} -6.05229 q^{64} -0.268057 q^{65} -0.211950 q^{66} -8.37206 q^{67} -1.51171 q^{68} +1.00000 q^{69} -1.53737 q^{71} -1.13545 q^{72} +9.90095 q^{73} +1.20127 q^{74} -0.411258 q^{75} +13.2647 q^{76} +0.0334127 q^{78} +0.483967 q^{79} +8.14783 q^{80} +1.00000 q^{81} +2.37998 q^{82} -1.84208 q^{83} +1.83543 q^{85} +0.435901 q^{86} +6.26700 q^{87} -0.829981 q^{88} +3.06457 q^{89} +0.674501 q^{90} +1.91593 q^{92} -1.49584 q^{93} -1.09832 q^{94} -16.1053 q^{95} -3.28651 q^{96} +14.8351 q^{97} +0.730971 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.289957	0.205030	0.102515	−	0.994731i	$-0.467311\pi$
$2$	0.289957	0.205030	0.102515	+	0.994731i	$0.467311\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.91593	−0.957963
$5$	2.32621	1.04031	0.520157	−	0.854071i	$-0.325874\pi$
$5$	2.32621	1.04031	0.520157	+	0.854071i	$0.325874\pi$
$6$	−0.289957	−0.118374
$7$	0	0
$7$	0	0
$8$	−1.13545	−0.401442
$9$	1.00000	0.333333
$10$	0.674501	0.213296
$11$	0.730971	0.220396	0.110198	−	0.993910i	$-0.464851\pi$
$11$	0.730971	0.220396	0.110198	+	0.993910i	$0.464851\pi$
$12$	1.91593	0.553080
$13$	−0.115233	−0.0319599	−0.0159800	−	0.999872i	$-0.505087\pi$
$13$	−0.115233	−0.0319599	−0.0159800	+	0.999872i	$0.505087\pi$
$14$	0	0
$15$	−2.32621	−0.600625
$16$	3.50262	0.875655
$17$	0.789022	0.191366	0.0956830	−	0.995412i	$-0.469496\pi$
$17$	0.789022	0.191366	0.0956830	+	0.995412i	$0.469496\pi$
$18$	0.289957	0.0683435
$19$	−6.92342	−1.58834	−0.794170	−	0.607695i	$-0.792094\pi$
$19$	−6.92342	−1.58834	−0.794170	+	0.607695i	$0.792094\pi$
$20$	−4.45685	−0.996581
$21$	0	0
$22$	0.211950	0.0451879
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.13545	0.231773
$25$	0.411258	0.0822516
$26$	−0.0334127	−0.00655276
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.26700	−1.16375	−0.581877	−	0.813277i	$-0.697681\pi$
$29$	−6.26700	−1.16375	−0.581877	+	0.813277i	$0.697681\pi$
$30$	−0.674501	−0.123146
$31$	1.49584	0.268661	0.134330	−	0.990937i	$-0.457112\pi$
$31$	1.49584	0.268661	0.134330	+	0.990937i	$0.457112\pi$
$32$	3.28651	0.580978
$33$	−0.730971	−0.127246
$34$	0.228782	0.0392358
$35$	0	0
$36$	−1.91593	−0.319321
$37$	4.14294	0.681095	0.340548	−	0.940227i	$-0.389388\pi$
$37$	4.14294	0.681095	0.340548	+	0.940227i	$0.389388\pi$
$38$	−2.00749	−0.325658
$39$	0.115233	0.0184521
$40$	−2.64129	−0.417625
$41$	8.20805	1.28188	0.640941	−	0.767590i	$-0.278544\pi$
$41$	8.20805	1.28188	0.640941	+	0.767590i	$0.278544\pi$
$42$	0	0
$43$	1.50333	0.229256	0.114628	−	0.993408i	$-0.463432\pi$
$43$	1.50333	0.229256	0.114628	+	0.993408i	$0.463432\pi$
$44$	−1.40049	−0.211131
$45$	2.32621	0.346771
$46$	−0.289957	−0.0427518
$47$	−3.78787	−0.552518	−0.276259	−	0.961083i	$-0.589095\pi$
$47$	−3.78787	−0.552518	−0.276259	+	0.961083i	$0.589095\pi$
$48$	−3.50262	−0.505559
$49$	0	0
$50$	0.119247	0.0168641
$51$	−0.789022	−0.110485
$52$	0.220778	0.0306164
$53$	−6.81735	−0.936434	−0.468217	−	0.883613i	$-0.655104\pi$
$53$	−6.81735	−0.936434	−0.468217	+	0.883613i	$0.655104\pi$
$54$	−0.289957	−0.0394581
$55$	1.70039	0.229281
$56$	0	0
$57$	6.92342	0.917029
$58$	−1.81716	−0.238605
$59$	−6.18845	−0.805668	−0.402834	−	0.915273i	$-0.631975\pi$
$59$	−6.18845	−0.805668	−0.402834	+	0.915273i	$0.631975\pi$
$60$	4.45685	0.575376
$61$	−2.39074	−0.306103	−0.153051	−	0.988218i	$-0.548910\pi$
$61$	−2.39074	−0.306103	−0.153051	+	0.988218i	$0.548910\pi$
$62$	0.433729	0.0550836
$63$	0	0
$64$	−6.05229	−0.756537
$65$	−0.268057	−0.0332483
$66$	−0.211950	−0.0260892
$67$	−8.37206	−1.02281	−0.511405	−	0.859340i	$-0.670875\pi$
$67$	−8.37206	−1.02281	−0.511405	+	0.859340i	$0.670875\pi$
$68$	−1.51171	−0.183321
$69$	1.00000	0.120386
$70$	0	0
$71$	−1.53737	−0.182452	−0.0912260	−	0.995830i	$-0.529079\pi$
$71$	−1.53737	−0.182452	−0.0912260	+	0.995830i	$0.529079\pi$
$72$	−1.13545	−0.133814
$73$	9.90095	1.15882	0.579409	−	0.815037i	$-0.303283\pi$
$73$	9.90095	1.15882	0.579409	+	0.815037i	$0.303283\pi$
$74$	1.20127	0.139645
$75$	−0.411258	−0.0474880
$76$	13.2647	1.52157
$77$	0	0
$78$	0.0334127	0.00378324
$79$	0.483967	0.0544505	0.0272253	−	0.999629i	$-0.491333\pi$
$79$	0.483967	0.0544505	0.0272253	+	0.999629i	$0.491333\pi$
$80$	8.14783	0.910955
$81$	1.00000	0.111111
$82$	2.37998	0.262825
$83$	−1.84208	−0.202195	−0.101097	−	0.994877i	$-0.532235\pi$
$83$	−1.84208	−0.202195	−0.101097	+	0.994877i	$0.532235\pi$
$84$	0	0
$85$	1.83543	0.199081
$86$	0.435901	0.0470044
$87$	6.26700	0.671893
$88$	−0.829981	−0.0884762
$89$	3.06457	0.324844	0.162422	−	0.986721i	$-0.448069\pi$
$89$	3.06457	0.324844	0.162422	+	0.986721i	$0.448069\pi$
$90$	0.674501	0.0710986
$91$	0	0
$92$	1.91593	0.199749
$93$	−1.49584	−0.155111
$94$	−1.09832	−0.113283
$95$	−16.1053	−1.65237
$96$	−3.28651	−0.335428
$97$	14.8351	1.50628	0.753140	−	0.657860i	$-0.228538\pi$
$97$	14.8351	1.50628	0.753140	+	0.657860i	$0.228538\pi$
$98$	0	0
$99$	0.730971	0.0734654
$100$	−0.787940	−0.0787940
$101$	10.8469	1.07931	0.539654	−	0.841887i	$-0.318555\pi$
$101$	10.8469	1.07931	0.539654	+	0.841887i	$0.318555\pi$
$102$	−0.228782	−0.0226528
$103$	−9.39923	−0.926134	−0.463067	−	0.886323i	$-0.653251\pi$
$103$	−9.39923	−0.926134	−0.463067	+	0.886323i	$0.653251\pi$
$104$	0.130841	0.0128301
$105$	0	0
$106$	−1.97674	−0.191998
$107$	−17.7498	−1.71593	−0.857967	−	0.513704i	$-0.828273\pi$
$107$	−17.7498	−1.71593	−0.857967	+	0.513704i	$0.828273\pi$
$108$	1.91593	0.184360
$109$	−9.77303	−0.936087	−0.468043	−	0.883705i	$-0.655041\pi$
$109$	−9.77303	−0.936087	−0.468043	+	0.883705i	$0.655041\pi$
$110$	0.493041	0.0470096
$111$	−4.14294	−0.393231
$112$	0	0
$113$	−3.68270	−0.346440	−0.173220	−	0.984883i	$-0.555417\pi$
$113$	−3.68270	−0.346440	−0.173220	+	0.984883i	$0.555417\pi$
$114$	2.00749	0.188019
$115$	−2.32621	−0.216920
$116$	12.0071	1.11483
$117$	−0.115233	−0.0106533
$118$	−1.79438	−0.165186
$119$	0	0
$120$	2.64129	0.241116
$121$	−10.4657	−0.951426
$122$	−0.693211	−0.0627604
$123$	−8.20805	−0.740095
$124$	−2.86591	−0.257367
$125$	−10.6744	−0.954746
$126$	0	0
$127$	−3.53396	−0.313588	−0.156794	−	0.987631i	$-0.550116\pi$
$127$	−3.53396	−0.313588	−0.156794	+	0.987631i	$0.550116\pi$
$128$	−8.32792	−0.736091
$129$	−1.50333	−0.132361
$130$	−0.0777249	−0.00681692
$131$	−4.35221	−0.380254	−0.190127	−	0.981759i	$-0.560890\pi$
$131$	−4.35221	−0.380254	−0.190127	+	0.981759i	$0.560890\pi$
$132$	1.40049	0.121897
$133$	0	0
$134$	−2.42754	−0.209707
$135$	−2.32621	−0.200208
$136$	−0.895894	−0.0768223
$137$	−17.1154	−1.46227	−0.731133	−	0.682235i	$-0.761008\pi$
$137$	−17.1154	−1.46227	−0.731133	+	0.682235i	$0.761008\pi$
$138$	0.289957	0.0246828
$139$	5.41785	0.459536	0.229768	−	0.973245i	$-0.426203\pi$
$139$	5.41785	0.459536	0.229768	+	0.973245i	$0.426203\pi$
$140$	0	0
$141$	3.78787	0.318996
$142$	−0.445770	−0.0374082
$143$	−0.0842321	−0.00704385
$144$	3.50262	0.291885
$145$	−14.5784	−1.21067
$146$	2.87085	0.237593
$147$	0	0
$148$	−7.93756	−0.652464
$149$	−15.2241	−1.24721	−0.623604	−	0.781740i	$-0.714332\pi$
$149$	−15.2241	−1.24721	−0.623604	+	0.781740i	$0.714332\pi$
$150$	−0.119247	−0.00973649
$151$	14.3805	1.17027	0.585136	−	0.810935i	$-0.301041\pi$
$151$	14.3805	1.17027	0.585136	+	0.810935i	$0.301041\pi$
$152$	7.86119	0.637627
$153$	0.789022	0.0637887
$154$	0	0
$155$	3.47964	0.279491
$156$	−0.220778	−0.0176764
$157$	−4.46641	−0.356458	−0.178229	−	0.983989i	$-0.557037\pi$
$157$	−4.46641	−0.356458	−0.178229	+	0.983989i	$0.557037\pi$
$158$	0.140330	0.0111640
$159$	6.81735	0.540651
$160$	7.64511	0.604399
$161$	0	0
$162$	0.289957	0.0227812
$163$	0.785722	0.0615425	0.0307713	−	0.999526i	$-0.490204\pi$
$163$	0.785722	0.0615425	0.0307713	+	0.999526i	$0.490204\pi$
$164$	−15.7260	−1.22800
$165$	−1.70039	−0.132375
$166$	−0.534124	−0.0414560
$167$	5.52754	0.427734	0.213867	−	0.976863i	$-0.431394\pi$
$167$	5.52754	0.427734	0.213867	+	0.976863i	$0.431394\pi$
$168$	0	0
$169$	−12.9867	−0.998979
$170$	0.532196	0.0408176
$171$	−6.92342	−0.529447
$172$	−2.88027	−0.219618
$173$	−9.95116	−0.756573	−0.378286	−	0.925689i	$-0.623487\pi$
$173$	−9.95116	−0.756573	−0.378286	+	0.925689i	$0.623487\pi$
$174$	1.81716	0.137759
$175$	0	0
$176$	2.56031	0.192991
$177$	6.18845	0.465153
$178$	0.888593	0.0666029
$179$	−17.4916	−1.30739	−0.653693	−	0.756760i	$-0.726781\pi$
$179$	−17.4916	−1.30739	−0.653693	+	0.756760i	$0.726781\pi$
$180$	−4.45685	−0.332194
$181$	−19.8587	−1.47608	−0.738042	−	0.674754i	$-0.764250\pi$
$181$	−19.8587	−1.47608	−0.738042	+	0.674754i	$0.764250\pi$
$182$	0	0
$183$	2.39074	0.176729
$184$	1.13545	0.0837064
$185$	9.63736	0.708553
$186$	−0.433729	−0.0318025
$187$	0.576752	0.0421763
$188$	7.25728	0.529291
$189$	0	0
$190$	−4.66985	−0.338787
$191$	14.1099	1.02095	0.510477	−	0.859892i	$-0.329469\pi$
$191$	14.1099	1.02095	0.510477	+	0.859892i	$0.329469\pi$
$192$	6.05229	0.436787
$193$	−12.7248	−0.915953	−0.457976	−	0.888964i	$-0.651426\pi$
$193$	−12.7248	−0.915953	−0.457976	+	0.888964i	$0.651426\pi$
$194$	4.30155	0.308833
$195$	0.268057	0.0191959
$196$	0	0
$197$	−14.1582	−1.00873	−0.504364	−	0.863491i	$-0.668273\pi$
$197$	−14.1582	−1.00873	−0.504364	+	0.863491i	$0.668273\pi$
$198$	0.211950	0.0150626
$199$	−4.23945	−0.300527	−0.150263	−	0.988646i	$-0.548012\pi$
$199$	−4.23945	−0.300527	−0.150263	+	0.988646i	$0.548012\pi$
$200$	−0.466963	−0.0330193
$201$	8.37206	0.590520
$202$	3.14514	0.221291
$203$	0	0
$204$	1.51171	0.105841
$205$	19.0937	1.33356
$206$	−2.72537	−0.189886
$207$	−1.00000	−0.0695048
$208$	−0.403618	−0.0279859
$209$	−5.06082	−0.350064
$210$	0	0
$211$	−26.3917	−1.81688	−0.908440	−	0.418015i	$-0.862726\pi$
$211$	−26.3917	−1.81688	−0.908440	+	0.418015i	$0.862726\pi$
$212$	13.0615	0.897069
$213$	1.53737	0.105339
$214$	−5.14667	−0.351819
$215$	3.49706	0.238498
$216$	1.13545	0.0772575
$217$	0	0
$218$	−2.83376	−0.191926
$219$	−9.90095	−0.669044
$220$	−3.25783	−0.219643
$221$	−0.0909215	−0.00611604
$222$	−1.20127	−0.0806242
$223$	−9.57370	−0.641102	−0.320551	−	0.947231i	$-0.603868\pi$
$223$	−9.57370	−0.641102	−0.320551	+	0.947231i	$0.603868\pi$
$224$	0	0
$225$	0.411258	0.0274172
$226$	−1.06783	−0.0710307
$227$	−22.8593	−1.51723	−0.758614	−	0.651540i	$-0.774123\pi$
$227$	−22.8593	−1.51723	−0.758614	+	0.651540i	$0.774123\pi$
$228$	−13.2647	−0.878479
$229$	−2.08062	−0.137492	−0.0687458	−	0.997634i	$-0.521900\pi$
$229$	−2.08062	−0.137492	−0.0687458	+	0.997634i	$0.521900\pi$
$230$	−0.674501	−0.0444753
$231$	0	0
$232$	7.11586	0.467179
$233$	5.01702	0.328676	0.164338	−	0.986404i	$-0.447451\pi$
$233$	5.01702	0.328676	0.164338	+	0.986404i	$0.447451\pi$
$234$	−0.0334127	−0.00218425
$235$	−8.81139	−0.574792
$236$	11.8566	0.771800
$237$	−0.483967	−0.0314370
$238$	0	0
$239$	20.5640	1.33018	0.665089	−	0.746764i	$-0.268394\pi$
$239$	20.5640	1.33018	0.665089	+	0.746764i	$0.268394\pi$
$240$	−8.14783	−0.525940
$241$	26.6259	1.71513	0.857563	−	0.514379i	$-0.171978\pi$
$241$	26.6259	1.71513	0.857563	+	0.514379i	$0.171978\pi$
$242$	−3.03460	−0.195071
$243$	−1.00000	−0.0641500
$244$	4.58048	0.293235
$245$	0	0
$246$	−2.37998	−0.151742
$247$	0.797808	0.0507633
$248$	−1.69845	−0.107852
$249$	1.84208	0.116737
$250$	−3.09511	−0.195752
$251$	−1.18435	−0.0747552	−0.0373776	−	0.999301i	$-0.511900\pi$
$251$	−1.18435	−0.0747552	−0.0373776	+	0.999301i	$0.511900\pi$
$252$	0	0
$253$	−0.730971	−0.0459558
$254$	−1.02469	−0.0642951
$255$	−1.83543	−0.114939
$256$	9.68985	0.605616
$257$	−9.21806	−0.575006	−0.287503	−	0.957780i	$-0.592825\pi$
$257$	−9.21806	−0.575006	−0.287503	+	0.957780i	$0.592825\pi$
$258$	−0.435901	−0.0271380
$259$	0	0
$260$	0.513577	0.0318507
$261$	−6.26700	−0.387918
$262$	−1.26195	−0.0779637
$263$	−22.1016	−1.36284	−0.681422	−	0.731891i	$-0.738638\pi$
$263$	−22.1016	−1.36284	−0.681422	+	0.731891i	$0.738638\pi$
$264$	0.829981	0.0510818
$265$	−15.8586	−0.974185
$266$	0	0
$267$	−3.06457	−0.187549
$268$	16.0402	0.979813
$269$	29.3526	1.78966	0.894829	−	0.446408i	$-0.147297\pi$
$269$	29.3526	1.78966	0.894829	+	0.446408i	$0.147297\pi$
$270$	−0.674501	−0.0410488
$271$	15.8453	0.962533	0.481266	−	0.876574i	$-0.340177\pi$
$271$	15.8453	0.962533	0.481266	+	0.876574i	$0.340177\pi$
$272$	2.76364	0.167571
$273$	0	0
$274$	−4.96272	−0.299809
$275$	0.300618	0.0181279
$276$	−1.91593	−0.115325
$277$	24.4377	1.46832	0.734160	−	0.678977i	$-0.237576\pi$
$277$	24.4377	1.46832	0.734160	+	0.678977i	$0.237576\pi$
$278$	1.57094	0.0942189
$279$	1.49584	0.0895535
$280$	0	0
$281$	−9.53666	−0.568910	−0.284455	−	0.958689i	$-0.591813\pi$
$281$	−9.53666	−0.568910	−0.284455	+	0.958689i	$0.591813\pi$
$282$	1.09832	0.0654040
$283$	4.22846	0.251356	0.125678	−	0.992071i	$-0.459889\pi$
$283$	4.22846	0.251356	0.125678	+	0.992071i	$0.459889\pi$
$284$	2.94548	0.174782
$285$	16.1053	0.953997
$286$	−0.0244237	−0.00144420
$287$	0	0
$288$	3.28651	0.193659
$289$	−16.3774	−0.963379
$290$	−4.22710	−0.248224
$291$	−14.8351	−0.869652
$292$	−18.9695	−1.11010
$293$	30.9919	1.81057	0.905283	−	0.424809i	$-0.139659\pi$
$293$	30.9919	1.81057	0.905283	+	0.424809i	$0.139659\pi$
$294$	0	0
$295$	−14.3956	−0.838147
$296$	−4.70410	−0.273420
$297$	−0.730971	−0.0424152
$298$	−4.41434	−0.255716
$299$	0.115233	0.00666411
$300$	0.787940	0.0454917
$301$	0	0
$302$	4.16974	0.239941
$303$	−10.8469	−0.623139
$304$	−24.2501	−1.39084
$305$	−5.56136	−0.318443
$306$	0.228782	0.0130786
$307$	−15.9601	−0.910888	−0.455444	−	0.890264i	$-0.650520\pi$
$307$	−15.9601	−0.910888	−0.455444	+	0.890264i	$0.650520\pi$
$308$	0	0
$309$	9.39923	0.534704
$310$	1.00894	0.0573042
$311$	−15.3225	−0.868860	−0.434430	−	0.900706i	$-0.643050\pi$
$311$	−15.3225	−0.868860	−0.434430	+	0.900706i	$0.643050\pi$
$312$	−0.130841	−0.00740744
$313$	−16.7734	−0.948086	−0.474043	−	0.880502i	$-0.657206\pi$
$313$	−16.7734	−0.948086	−0.474043	+	0.880502i	$0.657206\pi$
$314$	−1.29507	−0.0730848
$315$	0	0
$316$	−0.927244	−0.0521616
$317$	32.4011	1.81982	0.909912	−	0.414801i	$-0.136149\pi$
$317$	32.4011	1.81982	0.909912	+	0.414801i	$0.136149\pi$
$318$	1.97674	0.110850
$319$	−4.58100	−0.256487
$320$	−14.0789	−0.787035
$321$	17.7498	0.990695
$322$	0	0
$323$	−5.46273	−0.303954
$324$	−1.91593	−0.106440
$325$	−0.0473906	−0.00262876
$326$	0.227825	0.0126181
$327$	9.77303	0.540450
$328$	−9.31983	−0.514601
$329$	0	0
$330$	−0.493041	−0.0271410
$331$	25.9585	1.42681	0.713404	−	0.700753i	$-0.247152\pi$
$331$	25.9585	1.42681	0.713404	+	0.700753i	$0.247152\pi$
$332$	3.52929	0.193695
$333$	4.14294	0.227032
$334$	1.60275	0.0876985
$335$	−19.4752	−1.06404
$336$	0	0
$337$	19.2372	1.04791	0.523957	−	0.851744i	$-0.324455\pi$
$337$	19.2372	1.04791	0.523957	+	0.851744i	$0.324455\pi$
$338$	−3.76559	−0.204821
$339$	3.68270	0.200017
$340$	−3.51655	−0.190712
$341$	1.09341	0.0592117
$342$	−2.00749	−0.108553
$343$	0	0
$344$	−1.70696	−0.0920329
$345$	2.32621	0.125239
$346$	−2.88541	−0.155120
$347$	21.7166	1.16581	0.582905	−	0.812541i	$-0.301916\pi$
$347$	21.7166	1.16581	0.582905	+	0.812541i	$0.301916\pi$
$348$	−12.0071	−0.643649
$349$	−33.3948	−1.78758	−0.893792	−	0.448482i	$-0.851965\pi$
$349$	−33.3948	−1.78758	−0.893792	+	0.448482i	$0.851965\pi$
$350$	0	0
$351$	0.115233	0.00615069
$352$	2.40234	0.128045
$353$	27.5424	1.46593	0.732967	−	0.680264i	$-0.238135\pi$
$353$	27.5424	1.46593	0.732967	+	0.680264i	$0.238135\pi$
$354$	1.79438	0.0953705
$355$	−3.57624	−0.189807
$356$	−5.87149	−0.311188
$357$	0	0
$358$	−5.07182	−0.268054
$359$	−13.1409	−0.693550	−0.346775	−	0.937948i	$-0.612723\pi$
$359$	−13.1409	−0.693550	−0.346775	+	0.937948i	$0.612723\pi$
$360$	−2.64129	−0.139208
$361$	28.9337	1.52283
$362$	−5.75816	−0.302642
$363$	10.4657	0.549306
$364$	0	0
$365$	23.0317	1.20553
$366$	0.693211	0.0362347
$367$	−29.9839	−1.56514	−0.782572	−	0.622560i	$-0.786093\pi$
$367$	−29.9839	−1.56514	−0.782572	+	0.622560i	$0.786093\pi$
$368$	−3.50262	−0.182587
$369$	8.20805	0.427294
$370$	2.79442	0.145275
$371$	0	0
$372$	2.86591	0.148591
$373$	15.4492	0.799930	0.399965	−	0.916530i	$-0.369022\pi$
$373$	15.4492	0.799930	0.399965	+	0.916530i	$0.369022\pi$
$374$	0.167233	0.00864743
$375$	10.6744	0.551223
$376$	4.30094	0.221804
$377$	0.722167	0.0371935
$378$	0	0
$379$	−28.0665	−1.44168	−0.720840	−	0.693101i	$-0.756244\pi$
$379$	−28.0665	−1.44168	−0.720840	+	0.693101i	$0.756244\pi$
$380$	30.8566	1.58291
$381$	3.53396	0.181050
$382$	4.09125	0.209327
$383$	−20.8640	−1.06610	−0.533051	−	0.846083i	$-0.678954\pi$
$383$	−20.8640	−1.06610	−0.533051	+	0.846083i	$0.678954\pi$
$384$	8.32792	0.424982
$385$	0	0
$386$	−3.68965	−0.187798
$387$	1.50333	0.0764186
$388$	−28.4230	−1.44296
$389$	3.07301	0.155808	0.0779039	−	0.996961i	$-0.475177\pi$
$389$	3.07301	0.155808	0.0779039	+	0.996961i	$0.475177\pi$
$390$	0.0777249	0.00393575
$391$	−0.789022	−0.0399026
$392$	0	0
$393$	4.35221	0.219540
$394$	−4.10526	−0.206820
$395$	1.12581	0.0566456
$396$	−1.40049	−0.0703771
$397$	−34.4854	−1.73077	−0.865385	−	0.501107i	$-0.832926\pi$
$397$	−34.4854	−1.73077	−0.865385	+	0.501107i	$0.832926\pi$
$398$	−1.22926	−0.0616171
$399$	0	0
$400$	1.44048	0.0720240
$401$	−33.9427	−1.69502	−0.847508	−	0.530783i	$-0.821898\pi$
$401$	−33.9427	−1.69502	−0.847508	+	0.530783i	$0.821898\pi$
$402$	2.42754	0.121074
$403$	−0.172370	−0.00858638
$404$	−20.7819	−1.03394
$405$	2.32621	0.115590
$406$	0	0
$407$	3.02837	0.150111
$408$	0.895894	0.0443534
$409$	14.3206	0.708109	0.354055	−	0.935225i	$-0.384803\pi$
$409$	14.3206	0.708109	0.354055	+	0.935225i	$0.384803\pi$
$410$	5.53634	0.273420
$411$	17.1154	0.844239
$412$	18.0082	0.887202
$413$	0	0
$414$	−0.289957	−0.0142506
$415$	−4.28507	−0.210346
$416$	−0.378715	−0.0185680
$417$	−5.41785	−0.265313
$418$	−1.46742	−0.0717738
$419$	14.0322	0.685520	0.342760	−	0.939423i	$-0.388638\pi$
$419$	14.0322	0.685520	0.342760	+	0.939423i	$0.388638\pi$
$420$	0	0
$421$	−33.9644	−1.65532	−0.827662	−	0.561227i	$-0.810329\pi$
$421$	−33.9644	−1.65532	−0.827662	+	0.561227i	$0.810329\pi$
$422$	−7.65246	−0.372516
$423$	−3.78787	−0.184173
$424$	7.74075	0.375924
$425$	0.324492	0.0157402
$426$	0.445770	0.0215976
$427$	0	0
$428$	34.0072	1.64380
$429$	0.0842321	0.00406677
$430$	1.01400	0.0488993
$431$	22.9625	1.10607	0.553033	−	0.833159i	$-0.313470\pi$
$431$	22.9625	1.10607	0.553033	+	0.833159i	$0.313470\pi$
$432$	−3.50262	−0.168520
$433$	19.1710	0.921299	0.460650	−	0.887582i	$-0.347616\pi$
$433$	19.1710	0.921299	0.460650	+	0.887582i	$0.347616\pi$
$434$	0	0
$435$	14.5784	0.698979
$436$	18.7244	0.896736
$437$	6.92342	0.331192
$438$	−2.87085	−0.137174
$439$	−29.5226	−1.40904	−0.704518	−	0.709686i	$-0.748837\pi$
$439$	−29.5226	−1.40904	−0.704518	+	0.709686i	$0.748837\pi$
$440$	−1.93071	−0.0920430
$441$	0	0
$442$	−0.0263633	−0.00125398
$443$	−12.2761	−0.583253	−0.291627	−	0.956532i	$-0.594196\pi$
$443$	−12.2761	−0.583253	−0.291627	+	0.956532i	$0.594196\pi$
$444$	7.93756	0.376700
$445$	7.12884	0.337939
$446$	−2.77596	−0.131445
$447$	15.2241	0.720076
$448$	0	0
$449$	33.5155	1.58169	0.790847	−	0.612014i	$-0.209640\pi$
$449$	33.5155	1.58169	0.790847	+	0.612014i	$0.209640\pi$
$450$	0.119247	0.00562136
$451$	5.99985	0.282522
$452$	7.05579	0.331876
$453$	−14.3805	−0.675657
$454$	−6.62822	−0.311078
$455$	0	0
$456$	−7.86119	−0.368134
$457$	−26.8780	−1.25730	−0.628650	−	0.777688i	$-0.716392\pi$
$457$	−26.8780	−1.25730	−0.628650	+	0.777688i	$0.716392\pi$
$458$	−0.603291	−0.0281900
$459$	−0.789022	−0.0368284
$460$	4.45685	0.207802
$461$	−33.3536	−1.55343	−0.776715	−	0.629852i	$-0.783115\pi$
$461$	−33.3536	−1.55343	−0.776715	+	0.629852i	$0.783115\pi$
$462$	0	0
$463$	−15.9403	−0.740806	−0.370403	−	0.928871i	$-0.620780\pi$
$463$	−15.9403	−0.740806	−0.370403	+	0.928871i	$0.620780\pi$
$464$	−21.9509	−1.01905
$465$	−3.47964	−0.161364
$466$	1.45472	0.0673885
$467$	3.72521	0.172382	0.0861912	−	0.996279i	$-0.472530\pi$
$467$	3.72521	0.172382	0.0861912	+	0.996279i	$0.472530\pi$
$468$	0.220778	0.0102055
$469$	0	0
$470$	−2.55492	−0.117850
$471$	4.46641	0.205801
$472$	7.02667	0.323429
$473$	1.09889	0.0505271
$474$	−0.140330	−0.00644555
$475$	−2.84731	−0.130644
$476$	0	0
$477$	−6.81735	−0.312145
$478$	5.96269	0.272727
$479$	1.02488	0.0468278	0.0234139	−	0.999726i	$-0.492546\pi$
$479$	1.02488	0.0468278	0.0234139	+	0.999726i	$0.492546\pi$
$480$	−7.64511	−0.348950
$481$	−0.477404	−0.0217678
$482$	7.72036	0.351653
$483$	0	0
$484$	20.0515	0.911430
$485$	34.5097	1.56700
$486$	−0.289957	−0.0131527
$487$	8.12755	0.368294	0.184147	−	0.982899i	$-0.441048\pi$
$487$	8.12755	0.368294	0.184147	+	0.982899i	$0.441048\pi$
$488$	2.71456	0.122882
$489$	−0.785722	−0.0355316
$490$	0	0
$491$	−3.42514	−0.154574	−0.0772871	−	0.997009i	$-0.524626\pi$
$491$	−3.42514	−0.154574	−0.0772871	+	0.997009i	$0.524626\pi$
$492$	15.7260	0.708984
$493$	−4.94480	−0.222703
$494$	0.231330	0.0104080
$495$	1.70039	0.0764270
$496$	5.23935	0.235254
$497$	0	0
$498$	0.534124	0.0239347
$499$	−5.97802	−0.267613	−0.133806	−	0.991007i	$-0.542720\pi$
$499$	−5.97802	−0.267613	−0.133806	+	0.991007i	$0.542720\pi$
$500$	20.4513	0.914611
$501$	−5.52754	−0.246952
$502$	−0.343409	−0.0153271
$503$	30.6662	1.36734	0.683669	−	0.729793i	$-0.260383\pi$
$503$	30.6662	1.36734	0.683669	+	0.729793i	$0.260383\pi$
$504$	0	0
$505$	25.2322	1.12282
$506$	−0.211950	−0.00942233
$507$	12.9867	0.576761
$508$	6.77079	0.300405
$509$	43.2957	1.91905	0.959523	−	0.281629i	$-0.0908747\pi$
$509$	43.2957	1.91905	0.959523	+	0.281629i	$0.0908747\pi$
$510$	−0.532196	−0.0235660
$511$	0	0
$512$	19.4655	0.860260
$513$	6.92342	0.305676
$514$	−2.67284	−0.117894
$515$	−21.8646	−0.963469
$516$	2.88027	0.126797
$517$	−2.76882	−0.121773
$518$	0	0
$519$	9.95116	0.436808
$520$	0.304365	0.0133473
$521$	39.8977	1.74795	0.873974	−	0.485972i	$-0.161534\pi$
$521$	39.8977	1.74795	0.873974	+	0.485972i	$0.161534\pi$
$522$	−1.81716	−0.0795349
$523$	18.5692	0.811974	0.405987	−	0.913879i	$-0.366928\pi$
$523$	18.5692	0.811974	0.405987	+	0.913879i	$0.366928\pi$
$524$	8.33850	0.364269
$525$	0	0
$526$	−6.40851	−0.279424
$527$	1.18025	0.0514125
$528$	−2.56031	−0.111423
$529$	1.00000	0.0434783
$530$	−4.59831	−0.199738
$531$	−6.18845	−0.268556
$532$	0	0
$533$	−0.945840	−0.0409689
$534$	−0.888593	−0.0384532
$535$	−41.2897	−1.78511
$536$	9.50605	0.410599
$537$	17.4916	0.754820
$538$	8.51098	0.366934
$539$	0	0
$540$	4.45685	0.191792
$541$	−41.0597	−1.76529	−0.882646	−	0.470037i	$-0.844240\pi$
$541$	−41.0597	−1.76529	−0.882646	+	0.470037i	$0.844240\pi$
$542$	4.59445	0.197349
$543$	19.8587	0.852218
$544$	2.59313	0.111179
$545$	−22.7341	−0.973824
$546$	0	0
$547$	13.7117	0.586268	0.293134	−	0.956071i	$-0.405302\pi$
$547$	13.7117	0.586268	0.293134	+	0.956071i	$0.405302\pi$
$548$	32.7918	1.40080
$549$	−2.39074	−0.102034
$550$	0.0871662	0.00371678
$551$	43.3891	1.84844
$552$	−1.13545	−0.0483279
$553$	0	0
$554$	7.08588	0.301050
$555$	−9.63736	−0.409083
$556$	−10.3802	−0.440219
$557$	−0.0927102	−0.00392826	−0.00196413	−	0.999998i	$-0.500625\pi$
$557$	−0.0927102	−0.00392826	−0.00196413	+	0.999998i	$0.500625\pi$
$558$	0.433729	0.0183612
$559$	−0.173234	−0.00732700
$560$	0	0
$561$	−0.576752	−0.0243505
$562$	−2.76522	−0.116644
$563$	41.4979	1.74893	0.874464	−	0.485091i	$-0.161214\pi$
$563$	41.4979	1.74893	0.874464	+	0.485091i	$0.161214\pi$
$564$	−7.25728	−0.305587
$565$	−8.56675	−0.360406
$566$	1.22607	0.0515355
$567$	0	0
$568$	1.74560	0.0732439
$569$	14.9403	0.626328	0.313164	−	0.949699i	$-0.398611\pi$
$569$	14.9403	0.626328	0.313164	+	0.949699i	$0.398611\pi$
$570$	4.66985	0.195599
$571$	24.4660	1.02387	0.511935	−	0.859024i	$-0.328929\pi$
$571$	24.4660	1.02387	0.511935	+	0.859024i	$0.328929\pi$
$572$	0.161382	0.00674774
$573$	−14.1099	−0.589448
$574$	0	0
$575$	−0.411258	−0.0171507
$576$	−6.05229	−0.252179
$577$	−13.9226	−0.579605	−0.289802	−	0.957086i	$-0.593590\pi$
$577$	−13.9226	−0.579605	−0.289802	+	0.957086i	$0.593590\pi$
$578$	−4.74875	−0.197522
$579$	12.7248	0.528826
$580$	27.9311	1.15977
$581$	0	0
$582$	−4.30155	−0.178305
$583$	−4.98328	−0.206386
$584$	−11.2420	−0.465198
$585$	−0.268057	−0.0110828
$586$	8.98631	0.371221
$587$	−16.3231	−0.673728	−0.336864	−	0.941553i	$-0.609366\pi$
$587$	−16.3231	−0.673728	−0.336864	+	0.941553i	$0.609366\pi$
$588$	0	0
$589$	−10.3563	−0.426725
$590$	−4.17412	−0.171846
$591$	14.1582	0.582389
$592$	14.5111	0.596404
$593$	43.6987	1.79449	0.897244	−	0.441534i	$-0.145566\pi$
$593$	43.6987	1.79449	0.897244	+	0.441534i	$0.145566\pi$
$594$	−0.211950	−0.00869642
$595$	0	0
$596$	29.1683	1.19478
$597$	4.23945	0.173509
$598$	0.0334127	0.00136635
$599$	11.0256	0.450495	0.225247	−	0.974302i	$-0.427681\pi$
$599$	11.0256	0.450495	0.225247	+	0.974302i	$0.427681\pi$
$600$	0.466963	0.0190637
$601$	−6.86484	−0.280023	−0.140011	−	0.990150i	$-0.544714\pi$
$601$	−6.86484	−0.280023	−0.140011	+	0.990150i	$0.544714\pi$
$602$	0	0
$603$	−8.37206	−0.340937
$604$	−27.5520	−1.12108
$605$	−24.3454	−0.989781
$606$	−3.14514	−0.127762
$607$	18.6522	0.757069	0.378534	−	0.925587i	$-0.376428\pi$
$607$	18.6522	0.757069	0.378534	+	0.925587i	$0.376428\pi$
$608$	−22.7539	−0.922791
$609$	0	0
$610$	−1.61256	−0.0652905
$611$	0.436489	0.0176584
$612$	−1.51171	−0.0611071
$613$	16.0601	0.648663	0.324331	−	0.945944i	$-0.394861\pi$
$613$	16.0601	0.648663	0.324331	+	0.945944i	$0.394861\pi$
$614$	−4.62773	−0.186760
$615$	−19.0937	−0.769931
$616$	0	0
$617$	11.5349	0.464376	0.232188	−	0.972671i	$-0.425412\pi$
$617$	11.5349	0.464376	0.232188	+	0.972671i	$0.425412\pi$
$618$	2.72537	0.109631
$619$	−20.2528	−0.814030	−0.407015	−	0.913421i	$-0.633430\pi$
$619$	−20.2528	−0.814030	−0.407015	+	0.913421i	$0.633430\pi$
$620$	−6.66672	−0.267742
$621$	1.00000	0.0401286
$622$	−4.44287	−0.178143
$623$	0	0
$624$	0.403618	0.0161577
$625$	−26.8872	−1.07549
$626$	−4.86355	−0.194387
$627$	5.06082	0.202110
$628$	8.55730	0.341473
$629$	3.26887	0.130338
$630$	0	0
$631$	9.38947	0.373789	0.186894	−	0.982380i	$-0.440158\pi$
$631$	9.38947	0.373789	0.186894	+	0.982380i	$0.440158\pi$
$632$	−0.549520	−0.0218587
$633$	26.3917	1.04898
$634$	9.39491	0.373119
$635$	−8.22073	−0.326230
$636$	−13.0615	−0.517923
$637$	0	0
$638$	−1.32829	−0.0525876
$639$	−1.53737	−0.0608173
$640$	−19.3725	−0.765765
$641$	2.03391	0.0803348	0.0401674	−	0.999193i	$-0.487211\pi$
$641$	2.03391	0.0803348	0.0401674	+	0.999193i	$0.487211\pi$
$642$	5.14667	0.203123
$643$	−11.7666	−0.464029	−0.232015	−	0.972712i	$-0.574532\pi$
$643$	−11.7666	−0.464029	−0.232015	+	0.972712i	$0.574532\pi$
$644$	0	0
$645$	−3.49706	−0.137697
$646$	−1.58396	−0.0623199
$647$	−12.1599	−0.478053	−0.239027	−	0.971013i	$-0.576828\pi$
$647$	−12.1599	−0.478053	−0.239027	+	0.971013i	$0.576828\pi$
$648$	−1.13545	−0.0446047
$649$	−4.52358	−0.177566
$650$	−0.0137412	−0.000538975 0
$651$	0	0
$652$	−1.50538	−0.0589554
$653$	−33.8366	−1.32413	−0.662065	−	0.749447i	$-0.730320\pi$
$653$	−33.8366	−1.32413	−0.662065	+	0.749447i	$0.730320\pi$
$654$	2.83376	0.110809
$655$	−10.1242	−0.395583
$656$	28.7497	1.12249
$657$	9.90095	0.386273
$658$	0	0
$659$	15.7293	0.612727	0.306363	−	0.951915i	$-0.400888\pi$
$659$	15.7293	0.612727	0.306363	+	0.951915i	$0.400888\pi$
$660$	3.25783	0.126811
$661$	31.1757	1.21259	0.606297	−	0.795238i	$-0.292654\pi$
$661$	31.1757	1.21259	0.606297	+	0.795238i	$0.292654\pi$
$662$	7.52685	0.292539
$663$	0.0909215	0.00353110
$664$	2.09159	0.0811694
$665$	0	0
$666$	1.20127	0.0465484
$667$	6.26700	0.242659
$668$	−10.5904	−0.409753
$669$	9.57370	0.370141
$670$	−5.64696	−0.218161
$671$	−1.74756	−0.0674639
$672$	0	0
$673$	9.23484	0.355977	0.177988	−	0.984033i	$-0.443041\pi$
$673$	9.23484	0.355977	0.177988	+	0.984033i	$0.443041\pi$
$674$	5.57795	0.214854
$675$	−0.411258	−0.0158293
$676$	24.8816	0.956984
$677$	45.5403	1.75026	0.875128	−	0.483891i	$-0.160777\pi$
$677$	45.5403	1.75026	0.875128	+	0.483891i	$0.160777\pi$
$678$	1.06783	0.0410096
$679$	0	0
$680$	−2.08404	−0.0799193
$681$	22.8593	0.875972
$682$	0.317043	0.0121402
$683$	12.2292	0.467938	0.233969	−	0.972244i	$-0.424829\pi$
$683$	12.2292	0.467938	0.233969	+	0.972244i	$0.424829\pi$
$684$	13.2647	0.507190
$685$	−39.8140	−1.52121
$686$	0	0
$687$	2.08062	0.0793808
$688$	5.26559	0.200749
$689$	0.785585	0.0299284
$690$	0.674501	0.0256778
$691$	−22.4785	−0.855123	−0.427562	−	0.903986i	$-0.640627\pi$
$691$	−22.4785	−0.855123	−0.427562	+	0.903986i	$0.640627\pi$
$692$	19.0657	0.724769
$693$	0	0
$694$	6.29688	0.239026
$695$	12.6031	0.478062
$696$	−7.11586	−0.269726
$697$	6.47634	0.245309
$698$	−9.68306	−0.366509
$699$	−5.01702	−0.189761
$700$	0	0
$701$	−27.0133	−1.02028	−0.510139	−	0.860092i	$-0.670406\pi$
$701$	−27.0133	−1.02028	−0.510139	+	0.860092i	$0.670406\pi$
$702$	0.0334127	0.00126108
$703$	−28.6833	−1.08181
$704$	−4.42405	−0.166738
$705$	8.81139	0.331856
$706$	7.98611	0.300561
$707$	0	0
$708$	−11.8566	−0.445599
$709$	26.6975	1.00264	0.501322	−	0.865261i	$-0.332847\pi$
$709$	26.6975	1.00264	0.501322	+	0.865261i	$0.332847\pi$
$710$	−1.03696	−0.0389163
$711$	0.483967	0.0181502
$712$	−3.47966	−0.130406
$713$	−1.49584	−0.0560196
$714$	0	0
$715$	−0.195942	−0.00732781
$716$	33.5127	1.25243
$717$	−20.5640	−0.767978
$718$	−3.81029	−0.142199
$719$	34.7361	1.29544	0.647720	−	0.761879i	$-0.275723\pi$
$719$	34.7361	1.29544	0.647720	+	0.761879i	$0.275723\pi$
$720$	8.14783	0.303652
$721$	0	0
$722$	8.38953	0.312226
$723$	−26.6259	−0.990228
$724$	38.0478	1.41403
$725$	−2.57736	−0.0957206
$726$	3.03460	0.112624
$727$	6.54111	0.242596	0.121298	−	0.992616i	$-0.461294\pi$
$727$	6.54111	0.242596	0.121298	+	0.992616i	$0.461294\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.67820	0.247171
$731$	1.18616	0.0438718
$732$	−4.58048	−0.169299
$733$	51.7999	1.91327	0.956637	−	0.291283i	$-0.0940822\pi$
$733$	51.7999	1.91327	0.956637	+	0.291283i	$0.0940822\pi$
$734$	−8.69402	−0.320902
$735$	0	0
$736$	−3.28651	−0.121142
$737$	−6.11973	−0.225423
$738$	2.37998	0.0876083
$739$	−40.4751	−1.48890	−0.744451	−	0.667677i	$-0.767289\pi$
$739$	−40.4751	−1.48890	−0.744451	+	0.667677i	$0.767289\pi$
$740$	−18.4645	−0.678767
$741$	−0.797808	−0.0293082
$742$	0	0
$743$	−41.4092	−1.51916	−0.759579	−	0.650415i	$-0.774595\pi$
$743$	−41.4092	−1.51916	−0.759579	+	0.650415i	$0.774595\pi$
$744$	1.69845	0.0622682
$745$	−35.4145	−1.29749
$746$	4.47960	0.164010
$747$	−1.84208	−0.0673982
$748$	−1.10501	−0.0404033
$749$	0	0
$750$	3.09511	0.113017
$751$	25.5101	0.930876	0.465438	−	0.885081i	$-0.345897\pi$
$751$	25.5101	0.930876	0.465438	+	0.885081i	$0.345897\pi$
$752$	−13.2675	−0.483815
$753$	1.18435	0.0431600
$754$	0.209397	0.00762580
$755$	33.4522	1.21745
$756$	0	0
$757$	45.9268	1.66924	0.834619	−	0.550827i	$-0.185688\pi$
$757$	45.9268	1.66924	0.834619	+	0.550827i	$0.185688\pi$
$758$	−8.13808	−0.295588
$759$	0.730971	0.0265326
$760$	18.2868	0.663331
$761$	8.18381	0.296663	0.148331	−	0.988938i	$-0.452610\pi$
$761$	8.18381	0.296663	0.148331	+	0.988938i	$0.452610\pi$
$762$	1.02469	0.0371208
$763$	0	0
$764$	−27.0334	−0.978035
$765$	1.83543	0.0663602
$766$	−6.04966	−0.218583
$767$	0.713115	0.0257491
$768$	−9.68985	−0.349652
$769$	15.3794	0.554596	0.277298	−	0.960784i	$-0.410561\pi$
$769$	15.3794	0.554596	0.277298	+	0.960784i	$0.410561\pi$
$770$	0	0
$771$	9.21806	0.331980
$772$	24.3798	0.877448
$773$	−0.201716	−0.00725521	−0.00362760	−	0.999993i	$-0.501155\pi$
$773$	−0.201716	−0.00725521	−0.00362760	+	0.999993i	$0.501155\pi$
$774$	0.435901	0.0156681
$775$	0.615176	0.0220978
$776$	−16.8446	−0.604684
$777$	0	0
$778$	0.891041	0.0319454
$779$	−56.8278	−2.03607
$780$	−0.513577	−0.0183890
$781$	−1.12377	−0.0402117
$782$	−0.228782	−0.00818124
$783$	6.26700	0.223964
$784$	0	0
$785$	−10.3898	−0.370828
$786$	1.26195	0.0450123
$787$	−36.2719	−1.29296	−0.646478	−	0.762933i	$-0.723759\pi$
$787$	−36.2719	−1.29296	−0.646478	+	0.762933i	$0.723759\pi$
$788$	27.1260	0.966323
$789$	22.1016	0.786838
$790$	0.326436	0.0116141
$791$	0	0
$792$	−0.829981	−0.0294921
$793$	0.275493	0.00978303
$794$	−9.99926	−0.354861
$795$	15.8586	0.562446
$796$	8.12247	0.287893
$797$	25.4967	0.903138	0.451569	−	0.892236i	$-0.350864\pi$
$797$	25.4967	0.903138	0.451569	+	0.892236i	$0.350864\pi$
$798$	0	0
$799$	−2.98871	−0.105733
$800$	1.35160	0.0477864
$801$	3.06457	0.108281
$802$	−9.84190	−0.347530
$803$	7.23731	0.255399
$804$	−16.0402	−0.565696
$805$	0	0
$806$	−0.0499799	−0.00176047
$807$	−29.3526	−1.03326
$808$	−12.3161	−0.433280
$809$	16.5243	0.580963	0.290482	−	0.956881i	$-0.406184\pi$
$809$	16.5243	0.580963	0.290482	+	0.956881i	$0.406184\pi$
$810$	0.674501	0.0236995
$811$	−35.0068	−1.22925	−0.614627	−	0.788818i	$-0.710694\pi$
$811$	−35.0068	−1.22925	−0.614627	+	0.788818i	$0.710694\pi$
$812$	0	0
$813$	−15.8453	−0.555719
$814$	0.878097	0.0307773
$815$	1.82776	0.0640235
$816$	−2.76364	−0.0967469
$817$	−10.4082	−0.364136
$818$	4.15236	0.145184
$819$	0	0
$820$	−36.5820	−1.27750
$821$	34.9634	1.22023	0.610116	−	0.792312i	$-0.291123\pi$
$821$	34.9634	1.22023	0.610116	+	0.792312i	$0.291123\pi$
$822$	4.96272	0.173095
$823$	−29.7247	−1.03614	−0.518069	−	0.855339i	$-0.673349\pi$
$823$	−29.7247	−1.03614	−0.518069	+	0.855339i	$0.673349\pi$
$824$	10.6724	0.371789
$825$	−0.300618	−0.0104662
$826$	0	0
$827$	8.29301	0.288376	0.144188	−	0.989550i	$-0.453943\pi$
$827$	8.29301	0.288376	0.144188	+	0.989550i	$0.453943\pi$
$828$	1.91593	0.0665830
$829$	1.76447	0.0612826	0.0306413	−	0.999530i	$-0.490245\pi$
$829$	1.76447	0.0612826	0.0306413	+	0.999530i	$0.490245\pi$
$830$	−1.24248	−0.0431273
$831$	−24.4377	−0.847735
$832$	0.697425	0.0241789
$833$	0	0
$834$	−1.57094	−0.0543973
$835$	12.8582	0.444977
$836$	9.69615	0.335348
$837$	−1.49584	−0.0517037
$838$	4.06874	0.140552
$839$	−25.9251	−0.895035	−0.447517	−	0.894275i	$-0.647692\pi$
$839$	−25.9251	−0.895035	−0.447517	+	0.894275i	$0.647692\pi$
$840$	0	0
$841$	10.2753	0.354321
$842$	−9.84821	−0.339392
$843$	9.53666	0.328460
$844$	50.5645	1.74050
$845$	−30.2099	−1.03925
$846$	−1.09832	−0.0377610
$847$	0	0
$848$	−23.8786	−0.819993
$849$	−4.22846	−0.145120
$850$	0.0940886	0.00322721
$851$	−4.14294	−0.142018
$852$	−2.94548	−0.100911
$853$	23.2110	0.794729	0.397365	−	0.917661i	$-0.369925\pi$
$853$	23.2110	0.794729	0.397365	+	0.917661i	$0.369925\pi$
$854$	0	0
$855$	−16.1053	−0.550791
$856$	20.1540	0.688848
$857$	−12.4312	−0.424643	−0.212322	−	0.977200i	$-0.568102\pi$
$857$	−12.4312	−0.424643	−0.212322	+	0.977200i	$0.568102\pi$
$858$	0.0244237	0.000833811 0
$859$	5.94580	0.202868	0.101434	−	0.994842i	$-0.467657\pi$
$859$	5.94580	0.202868	0.101434	+	0.994842i	$0.467657\pi$
$860$	−6.70011	−0.228472
$861$	0	0
$862$	6.65815	0.226777
$863$	46.2512	1.57441	0.787204	−	0.616692i	$-0.211528\pi$
$863$	46.2512	1.57441	0.787204	+	0.616692i	$0.211528\pi$
$864$	−3.28651	−0.111809
$865$	−23.1485	−0.787073
$866$	5.55876	0.188894
$867$	16.3774	0.556207
$868$	0	0
$869$	0.353766	0.0120007
$870$	4.22710	0.143312
$871$	0.964739	0.0326889
$872$	11.0968	0.375784
$873$	14.8351	0.502094
$874$	2.00749	0.0679044
$875$	0	0
$876$	18.9695	0.640919
$877$	−12.7311	−0.429899	−0.214950	−	0.976625i	$-0.568959\pi$
$877$	−12.7311	−0.429899	−0.214950	+	0.976625i	$0.568959\pi$
$878$	−8.56028	−0.288895
$879$	−30.9919	−1.04533
$880$	5.95583	0.200771
$881$	22.2712	0.750334	0.375167	−	0.926957i	$-0.377585\pi$
$881$	22.2712	0.750334	0.375167	+	0.926957i	$0.377585\pi$
$882$	0	0
$883$	39.1941	1.31899	0.659493	−	0.751711i	$-0.270771\pi$
$883$	39.1941	1.31899	0.659493	+	0.751711i	$0.270771\pi$
$884$	0.174199	0.00585894
$885$	14.3956	0.483904
$886$	−3.55953	−0.119585
$887$	−7.54606	−0.253372	−0.126686	−	0.991943i	$-0.540434\pi$
$887$	−7.54606	−0.253372	−0.126686	+	0.991943i	$0.540434\pi$
$888$	4.70410	0.157859
$889$	0	0
$890$	2.06706	0.0692879
$891$	0.730971	0.0244885
$892$	18.3425	0.614152
$893$	26.2250	0.877587
$894$	4.41434	0.147638
$895$	−40.6892	−1.36009
$896$	0	0
$897$	−0.115233	−0.00384752
$898$	9.71805	0.324295
$899$	−9.37442	−0.312655
$900$	−0.787940	−0.0262647
$901$	−5.37904	−0.179202
$902$	1.73970	0.0579256
$903$	0	0
$904$	4.18152	0.139075
$905$	−46.1955	−1.53559
$906$	−4.16974	−0.138530
$907$	17.4927	0.580836	0.290418	−	0.956900i	$-0.406206\pi$
$907$	17.4927	0.580836	0.290418	+	0.956900i	$0.406206\pi$
$908$	43.7968	1.45345
$909$	10.8469	0.359770
$910$	0	0
$911$	1.76174	0.0583691	0.0291846	−	0.999574i	$-0.490709\pi$
$911$	1.76174	0.0583691	0.0291846	+	0.999574i	$0.490709\pi$
$912$	24.2501	0.803001
$913$	−1.34651	−0.0445629
$914$	−7.79347	−0.257785
$915$	5.56136	0.183853
$916$	3.98632	0.131712
$917$	0	0
$918$	−0.228782	−0.00755094
$919$	−19.9587	−0.658377	−0.329189	−	0.944264i	$-0.606775\pi$
$919$	−19.9587	−0.658377	−0.329189	+	0.944264i	$0.606775\pi$
$920$	2.64129	0.0870809
$921$	15.9601	0.525902
$922$	−9.67109	−0.318500
$923$	0.177156	0.00583115
$924$	0	0
$925$	1.70382	0.0560212
$926$	−4.62199	−0.151888
$927$	−9.39923	−0.308711
$928$	−20.5965	−0.676115
$929$	−16.9400	−0.555783	−0.277892	−	0.960612i	$-0.589636\pi$
$929$	−16.9400	−0.555783	−0.277892	+	0.960612i	$0.589636\pi$
$930$	−1.00894	−0.0330846
$931$	0	0
$932$	−9.61223	−0.314859
$933$	15.3225	0.501637
$934$	1.08015	0.0353436
$935$	1.34165	0.0438766
$936$	0.130841	0.00427669
$937$	−2.54779	−0.0832327	−0.0416163	−	0.999134i	$-0.513251\pi$
$937$	−2.54779	−0.0832327	−0.0416163	+	0.999134i	$0.513251\pi$
$938$	0	0
$939$	16.7734	0.547378
$940$	16.8820	0.550629
$941$	−43.0016	−1.40181	−0.700906	−	0.713253i	$-0.747221\pi$
$941$	−43.0016	−1.40181	−0.700906	+	0.713253i	$0.747221\pi$
$942$	1.29507	0.0421955
$943$	−8.20805	−0.267291
$944$	−21.6758	−0.705487
$945$	0	0
$946$	0.318631	0.0103596
$947$	−46.4295	−1.50875	−0.754377	−	0.656441i	$-0.772061\pi$
$947$	−46.4295	−1.50875	−0.754377	+	0.656441i	$0.772061\pi$
$948$	0.927244	0.0301155
$949$	−1.14092	−0.0370358
$950$	−0.825598	−0.0267859
$951$	−32.4011	−1.05068
$952$	0	0
$953$	−23.0858	−0.747824	−0.373912	−	0.927464i	$-0.621984\pi$
$953$	−23.0858	−0.747824	−0.373912	+	0.927464i	$0.621984\pi$
$954$	−1.97674	−0.0639992
$955$	32.8225	1.06211
$956$	−39.3992	−1.27426
$957$	4.58100	0.148083
$958$	0.297170	0.00960112
$959$	0	0
$960$	14.0789	0.454395
$961$	−28.7625	−0.927822
$962$	−0.138427	−0.00446305
$963$	−17.7498	−0.571978
$964$	−51.0132	−1.64303
$965$	−29.6006	−0.952878
$966$	0	0
$967$	−6.48746	−0.208623	−0.104311	−	0.994545i	$-0.533264\pi$
$967$	−6.48746	−0.208623	−0.104311	+	0.994545i	$0.533264\pi$
$968$	11.8832	0.381942
$969$	5.46273	0.175488
$970$	10.0063	0.321283
$971$	23.6355	0.758499	0.379250	−	0.925294i	$-0.376182\pi$
$971$	23.6355	0.758499	0.379250	+	0.925294i	$0.376182\pi$
$972$	1.91593	0.0614533
$973$	0	0
$974$	2.35664	0.0755116
$975$	0.0473906	0.00151771
$976$	−8.37385	−0.268040
$977$	9.62430	0.307909	0.153954	−	0.988078i	$-0.450799\pi$
$977$	9.62430	0.307909	0.153954	+	0.988078i	$0.450799\pi$
$978$	−0.227825	−0.00728506
$979$	2.24011	0.0715943
$980$	0	0
$981$	−9.77303	−0.312029
$982$	−0.993142	−0.0316924
$983$	31.7316	1.01208	0.506041	−	0.862509i	$-0.331108\pi$
$983$	31.7316	1.01208	0.506041	+	0.862509i	$0.331108\pi$
$984$	9.31983	0.297105
$985$	−32.9349	−1.04939
$986$	−1.43378	−0.0456608
$987$	0	0
$988$	−1.52854	−0.0486293
$989$	−1.50333	−0.0478031
$990$	0.493041	0.0156699
$991$	4.46149	0.141724	0.0708620	−	0.997486i	$-0.477425\pi$
$991$	4.46149	0.141724	0.0708620	+	0.997486i	$0.477425\pi$
$992$	4.91608	0.156086
$993$	−25.9585	−0.823768
$994$	0	0
$995$	−9.86186	−0.312642
$996$	−3.52929	−0.111830
$997$	−25.4916	−0.807328	−0.403664	−	0.914907i	$-0.632264\pi$
$997$	−25.4916	−0.807328	−0.403664	+	0.914907i	$0.632264\pi$
$998$	−1.73337	−0.0548688
$999$	−4.14294	−0.131077

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bc.1.4		6
7.2	even	3		483.2.i.f.277.3	✓	12
7.4	even	3		483.2.i.f.415.3	yes	12
7.6	odd	2		3381.2.a.bd.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.f.277.3	✓	12	7.2	even	3
483.2.i.f.415.3	yes	12	7.4	even	3
3381.2.a.bc.1.4		6	1.1	even	1	trivial
3381.2.a.bd.1.4		6	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+0.289957 q^{2} -1.00000 q^{3} -1.91593 q^{4} +2.32621 q^{5} -0.289957 q^{6} -1.13545 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.289957 q^{2} -1.00000 q^{3} -1.91593 q^{4} +2.32621 q^{5} -0.289957 q^{6} -1.13545 q^{8} +1.00000 q^{9} +0.674501 q^{10} +0.730971 q^{11} +1.91593 q^{12} -0.115233 q^{13} -2.32621 q^{15} +3.50262 q^{16} +0.789022 q^{17} +0.289957 q^{18} -6.92342 q^{19} -4.45685 q^{20} +0.211950 q^{22} -1.00000 q^{23} +1.13545 q^{24} +0.411258 q^{25} -0.0334127 q^{26} -1.00000 q^{27} -6.26700 q^{29} -0.674501 q^{30} +1.49584 q^{31} +3.28651 q^{32} -0.730971 q^{33} +0.228782 q^{34} -1.91593 q^{36} +4.14294 q^{37} -2.00749 q^{38} +0.115233 q^{39} -2.64129 q^{40} +8.20805 q^{41} +1.50333 q^{43} -1.40049 q^{44} +2.32621 q^{45} -0.289957 q^{46} -3.78787 q^{47} -3.50262 q^{48} +0.119247 q^{50} -0.789022 q^{51} +0.220778 q^{52} -6.81735 q^{53} -0.289957 q^{54} +1.70039 q^{55} +6.92342 q^{57} -1.81716 q^{58} -6.18845 q^{59} +4.45685 q^{60} -2.39074 q^{61} +0.433729 q^{62} -6.05229 q^{64} -0.268057 q^{65} -0.211950 q^{66} -8.37206 q^{67} -1.51171 q^{68} +1.00000 q^{69} -1.53737 q^{71} -1.13545 q^{72} +9.90095 q^{73} +1.20127 q^{74} -0.411258 q^{75} +13.2647 q^{76} +0.0334127 q^{78} +0.483967 q^{79} +8.14783 q^{80} +1.00000 q^{81} +2.37998 q^{82} -1.84208 q^{83} +1.83543 q^{85} +0.435901 q^{86} +6.26700 q^{87} -0.829981 q^{88} +3.06457 q^{89} +0.674501 q^{90} +1.91593 q^{92} -1.49584 q^{93} -1.09832 q^{94} -16.1053 q^{95} -3.28651 q^{96} +14.8351 q^{97} +0.730971 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 6 q^{3} + 3 q^{4} + 3 q^{5} + q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 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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