LMFDB - Embedded newform 6027.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.785.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x + 5 $ x^3 - x^2 - 6*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.812716$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.812716 q^{2} +1.00000 q^{3} -1.33949 q^{4} +1.00000 q^{5} +0.812716 q^{6} -2.71406 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.812716 q^{2} +1.00000 q^{3} -1.33949 q^{4} +1.00000 q^{5} +0.812716 q^{6} -2.71406 q^{8} +1.00000 q^{9} +0.812716 q^{10} -5.15221 q^{11} -1.33949 q^{12} +2.18728 q^{13} +1.00000 q^{15} +0.473224 q^{16} -5.86627 q^{17} +0.812716 q^{18} -5.33949 q^{19} -1.33949 q^{20} -4.18728 q^{22} +7.49170 q^{23} -2.71406 q^{24} -4.00000 q^{25} +1.77764 q^{26} +1.00000 q^{27} -3.96492 q^{29} +0.812716 q^{30} +4.77764 q^{31} +5.81272 q^{32} -5.15221 q^{33} -4.76761 q^{34} -1.33949 q^{36} +9.96492 q^{37} -4.33949 q^{38} +2.18728 q^{39} -2.71406 q^{40} +1.00000 q^{41} +9.05355 q^{43} +6.90134 q^{44} +1.00000 q^{45} +6.08863 q^{46} +8.49170 q^{47} +0.473224 q^{48} -3.25087 q^{50} -5.86627 q^{51} -2.92985 q^{52} +7.52678 q^{53} +0.812716 q^{54} -5.15221 q^{55} -5.33949 q^{57} -3.22236 q^{58} -0.964925 q^{59} -1.33949 q^{60} +4.90134 q^{61} +3.88287 q^{62} +3.77764 q^{64} +2.18728 q^{65} -4.18728 q^{66} -2.47322 q^{67} +7.85782 q^{68} +7.49170 q^{69} +16.0536 q^{71} -2.71406 q^{72} +3.66051 q^{73} +8.09866 q^{74} -4.00000 q^{75} +7.15221 q^{76} +1.77764 q^{78} -12.1522 q^{79} +0.473224 q^{80} +1.00000 q^{81} +0.812716 q^{82} +15.2944 q^{83} -5.86627 q^{85} +7.35797 q^{86} -3.96492 q^{87} +13.9834 q^{88} +3.77764 q^{89} +0.812716 q^{90} -10.0351 q^{92} +4.77764 q^{93} +6.90134 q^{94} -5.33949 q^{95} +5.81272 q^{96} +7.87630 q^{97} -5.15221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + 7 q^{4} + 3 q^{5} + q^{6} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + 7 * q^4 + 3 * q^5 + q^6 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + 7 q^{4} + 3 q^{5} + q^{6} + 3 q^{9} + q^{10} - 3 q^{11} + 7 q^{12} + 8 q^{13} + 3 q^{15} + 11 q^{16} + 3 q^{17} + q^{18} - 5 q^{19} + 7 q^{20} - 14 q^{22} - q^{23} - 12 q^{25} - 10 q^{26} + 3 q^{27} + 2 q^{29} + q^{30} - q^{31} + 16 q^{32} - 3 q^{33} + 13 q^{34} + 7 q^{36} + 16 q^{37} - 2 q^{38} + 8 q^{39} + 3 q^{41} + 8 q^{43} + 14 q^{44} + 3 q^{45} + 13 q^{46} + 2 q^{47} + 11 q^{48} - 4 q^{50} + 3 q^{51} + 19 q^{52} + 13 q^{53} + q^{54} - 3 q^{55} - 5 q^{57} - 25 q^{58} + 11 q^{59} + 7 q^{60} + 8 q^{61} + 38 q^{62} - 4 q^{64} + 8 q^{65} - 14 q^{66} - 17 q^{67} + 48 q^{68} - q^{69} + 29 q^{71} + 22 q^{73} + 31 q^{74} - 12 q^{75} + 9 q^{76} - 10 q^{78} - 24 q^{79} + 11 q^{80} + 3 q^{81} + q^{82} + 9 q^{83} + 3 q^{85} - 22 q^{86} + 2 q^{87} - 5 q^{88} - 4 q^{89} + q^{90} - 44 q^{92} - q^{93} + 14 q^{94} - 5 q^{95} + 16 q^{96} + 15 q^{97} - 3 q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + 7 * q^4 + 3 * q^5 + q^6 + 3 * q^9 + q^10 - 3 * q^11 + 7 * q^12 + 8 * q^13 + 3 * q^15 + 11 * q^16 + 3 * q^17 + q^18 - 5 * q^19 + 7 * q^20 - 14 * q^22 - q^23 - 12 * q^25 - 10 * q^26 + 3 * q^27 + 2 * q^29 + q^30 - q^31 + 16 * q^32 - 3 * q^33 + 13 * q^34 + 7 * q^36 + 16 * q^37 - 2 * q^38 + 8 * q^39 + 3 * q^41 + 8 * q^43 + 14 * q^44 + 3 * q^45 + 13 * q^46 + 2 * q^47 + 11 * q^48 - 4 * q^50 + 3 * q^51 + 19 * q^52 + 13 * q^53 + q^54 - 3 * q^55 - 5 * q^57 - 25 * q^58 + 11 * q^59 + 7 * q^60 + 8 * q^61 + 38 * q^62 - 4 * q^64 + 8 * q^65 - 14 * q^66 - 17 * q^67 + 48 * q^68 - q^69 + 29 * q^71 + 22 * q^73 + 31 * q^74 - 12 * q^75 + 9 * q^76 - 10 * q^78 - 24 * q^79 + 11 * q^80 + 3 * q^81 + q^82 + 9 * q^83 + 3 * q^85 - 22 * q^86 + 2 * q^87 - 5 * q^88 - 4 * q^89 + q^90 - 44 * q^92 - q^93 + 14 * q^94 - 5 * q^95 + 16 * q^96 + 15 * q^97 - 3 * 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 $

$2$	0.812716	0.574677	0.287339	−	0.957829i	$-0.407230\pi$
$2$	0.812716	0.574677	0.287339	+	0.957829i	$0.407230\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.33949	−0.669746
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	0.812716	0.331790
$7$	0	0
$7$	0	0
$8$	−2.71406	−0.959565
$9$	1.00000	0.333333
$10$	0.812716	0.257003
$11$	−5.15221	−1.55345	−0.776725	−	0.629840i	$-0.783120\pi$
$11$	−5.15221	−1.55345	−0.776725	+	0.629840i	$0.783120\pi$
$12$	−1.33949	−0.386678
$13$	2.18728	0.606643	0.303322	−	0.952888i	$-0.401904\pi$
$13$	2.18728	0.606643	0.303322	+	0.952888i	$0.401904\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	0.473224	0.118306
$17$	−5.86627	−1.42278	−0.711390	−	0.702798i	$-0.751934\pi$
$17$	−5.86627	−1.42278	−0.711390	+	0.702798i	$0.751934\pi$
$18$	0.812716	0.191559
$19$	−5.33949	−1.22496	−0.612482	−	0.790485i	$-0.709829\pi$
$19$	−5.33949	−1.22496	−0.612482	+	0.790485i	$0.709829\pi$
$20$	−1.33949	−0.299520
$21$	0	0
$22$	−4.18728	−0.892732
$23$	7.49170	1.56213	0.781064	−	0.624451i	$-0.214677\pi$
$23$	7.49170	1.56213	0.781064	+	0.624451i	$0.214677\pi$
$24$	−2.71406	−0.554005
$25$	−4.00000	−0.800000
$26$	1.77764	0.348624
$27$	1.00000	0.192450
$28$	0	0
$29$	−3.96492	−0.736268	−0.368134	−	0.929773i	$-0.620003\pi$
$29$	−3.96492	−0.736268	−0.368134	+	0.929773i	$0.620003\pi$
$30$	0.812716	0.148381
$31$	4.77764	0.858090	0.429045	−	0.903283i	$-0.358850\pi$
$31$	4.77764	0.858090	0.429045	+	0.903283i	$0.358850\pi$
$32$	5.81272	1.02755
$33$	−5.15221	−0.896884
$34$	−4.76761	−0.817639
$35$	0	0
$36$	−1.33949	−0.223249
$37$	9.96492	1.63822	0.819112	−	0.573634i	$-0.194467\pi$
$37$	9.96492	1.63822	0.819112	+	0.573634i	$0.194467\pi$
$38$	−4.33949	−0.703959
$39$	2.18728	0.350246
$40$	−2.71406	−0.429131
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	9.05355	1.38065	0.690327	−	0.723498i	$-0.257467\pi$
$43$	9.05355	1.38065	0.690327	+	0.723498i	$0.257467\pi$
$44$	6.90134	1.04042
$45$	1.00000	0.149071
$46$	6.08863	0.897719
$47$	8.49170	1.23864	0.619321	−	0.785138i	$-0.287408\pi$
$47$	8.49170	1.23864	0.619321	+	0.785138i	$0.287408\pi$
$48$	0.473224	0.0683040
$49$	0	0
$50$	−3.25087	−0.459742
$51$	−5.86627	−0.821442
$52$	−2.92985	−0.406297
$53$	7.52678	1.03388	0.516941	−	0.856021i	$-0.327071\pi$
$53$	7.52678	1.03388	0.516941	+	0.856021i	$0.327071\pi$
$54$	0.812716	0.110597
$55$	−5.15221	−0.694724
$56$	0	0
$57$	−5.33949	−0.707233
$58$	−3.22236	−0.423116
$59$	−0.964925	−0.125623	−0.0628113	−	0.998025i	$-0.520007\pi$
$59$	−0.964925	−0.125623	−0.0628113	+	0.998025i	$0.520007\pi$
$60$	−1.33949	−0.172928
$61$	4.90134	0.627553	0.313776	−	0.949497i	$-0.398406\pi$
$61$	4.90134	0.627553	0.313776	+	0.949497i	$0.398406\pi$
$62$	3.88287	0.493125
$63$	0	0
$64$	3.77764	0.472205
$65$	2.18728	0.271299
$66$	−4.18728	−0.515419
$67$	−2.47322	−0.302152	−0.151076	−	0.988522i	$-0.548274\pi$
$67$	−2.47322	−0.302152	−0.151076	+	0.988522i	$0.548274\pi$
$68$	7.85782	0.952901
$69$	7.49170	0.901895
$70$	0	0
$71$	16.0536	1.90521	0.952603	−	0.304216i	$-0.0983945\pi$
$71$	16.0536	1.90521	0.952603	+	0.304216i	$0.0983945\pi$
$72$	−2.71406	−0.319855
$73$	3.66051	0.428430	0.214215	−	0.976787i	$-0.431281\pi$
$73$	3.66051	0.428430	0.214215	+	0.976787i	$0.431281\pi$
$74$	8.09866	0.941450
$75$	−4.00000	−0.461880
$76$	7.15221	0.820415
$77$	0	0
$78$	1.77764	0.201278
$79$	−12.1522	−1.36723	−0.683615	−	0.729843i	$-0.739593\pi$
$79$	−12.1522	−1.36723	−0.683615	+	0.729843i	$0.739593\pi$
$80$	0.473224	0.0529081
$81$	1.00000	0.111111
$82$	0.812716	0.0897495
$83$	15.2944	1.67878	0.839389	−	0.543532i	$-0.182913\pi$
$83$	15.2944	1.67878	0.839389	+	0.543532i	$0.182913\pi$
$84$	0	0
$85$	−5.86627	−0.636286
$86$	7.35797	0.793430
$87$	−3.96492	−0.425085
$88$	13.9834	1.49064
$89$	3.77764	0.400429	0.200215	−	0.979752i	$-0.435836\pi$
$89$	3.77764	0.400429	0.200215	+	0.979752i	$0.435836\pi$
$90$	0.812716	0.0856678
$91$	0	0
$92$	−10.0351	−1.04623
$93$	4.77764	0.495418
$94$	6.90134	0.711819
$95$	−5.33949	−0.547820
$96$	5.81272	0.593258
$97$	7.87630	0.799717	0.399858	−	0.916577i	$-0.369059\pi$
$97$	7.87630	0.799717	0.399858	+	0.916577i	$0.369059\pi$
$98$	0	0
$99$	−5.15221	−0.517816
$100$	5.35797	0.535797
$101$	3.96492	0.394525	0.197262	−	0.980351i	$-0.436795\pi$
$101$	3.96492	0.394525	0.197262	+	0.980351i	$0.436795\pi$
$102$	−4.76761	−0.472064
$103$	−9.45663	−0.931789	−0.465895	−	0.884840i	$-0.654267\pi$
$103$	−9.45663	−0.931789	−0.465895	+	0.884840i	$0.654267\pi$
$104$	−5.93642	−0.582114
$105$	0	0
$106$	6.11713	0.594149
$107$	4.81272	0.465263	0.232631	−	0.972565i	$-0.425266\pi$
$107$	4.81272	0.465263	0.232631	+	0.972565i	$0.425266\pi$
$108$	−1.33949	−0.128893
$109$	−13.1707	−1.26152	−0.630761	−	0.775977i	$-0.717257\pi$
$109$	−13.1707	−1.26152	−0.630761	+	0.775977i	$0.717257\pi$
$110$	−4.18728	−0.399242
$111$	9.96492	0.945829
$112$	0	0
$113$	4.81272	0.452742	0.226371	−	0.974041i	$-0.427314\pi$
$113$	4.81272	0.452742	0.226371	+	0.974041i	$0.427314\pi$
$114$	−4.33949	−0.406431
$115$	7.49170	0.698605
$116$	5.31099	0.493113
$117$	2.18728	0.202214
$118$	−0.784210	−0.0721924
$119$	0	0
$120$	−2.71406	−0.247759
$121$	15.5453	1.41320
$122$	3.98340	0.360640
$123$	1.00000	0.0901670
$124$	−6.39961	−0.574702
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−6.76761	−0.600528	−0.300264	−	0.953856i	$-0.597075\pi$
$127$	−6.76761	−0.600528	−0.300264	+	0.953856i	$0.597075\pi$
$128$	−8.55528	−0.756187
$129$	9.05355	0.797121
$130$	1.77764	0.155909
$131$	13.4281	1.17322	0.586610	−	0.809869i	$-0.300462\pi$
$131$	13.4281	1.17322	0.586610	+	0.809869i	$0.300462\pi$
$132$	6.90134	0.600685
$133$	0	0
$134$	−2.01003	−0.173640
$135$	1.00000	0.0860663
$136$	15.9214	1.36525
$137$	−1.87630	−0.160303	−0.0801515	−	0.996783i	$-0.525540\pi$
$137$	−1.87630	−0.160303	−0.0801515	+	0.996783i	$0.525540\pi$
$138$	6.08863	0.518298
$139$	−4.46319	−0.378563	−0.189282	−	0.981923i	$-0.560616\pi$
$139$	−4.46319	−0.378563	−0.189282	+	0.981923i	$0.560616\pi$
$140$	0	0
$141$	8.49170	0.715130
$142$	13.0470	1.09488
$143$	−11.2693	−0.942390
$144$	0.473224	0.0394353
$145$	−3.96492	−0.329269
$146$	2.97495	0.246209
$147$	0	0
$148$	−13.3479	−1.09719
$149$	−12.8497	−1.05269	−0.526343	−	0.850272i	$-0.676437\pi$
$149$	−12.8497	−1.05269	−0.526343	+	0.850272i	$0.676437\pi$
$150$	−3.25087	−0.265432
$151$	5.98340	0.486922	0.243461	−	0.969911i	$-0.421717\pi$
$151$	5.98340	0.486922	0.243461	+	0.969911i	$0.421717\pi$
$152$	14.4917	1.17543
$153$	−5.86627	−0.474260
$154$	0	0
$155$	4.77764	0.383749
$156$	−2.92985	−0.234576
$157$	3.65048	0.291340	0.145670	−	0.989333i	$-0.453466\pi$
$157$	3.65048	0.291340	0.145670	+	0.989333i	$0.453466\pi$
$158$	−9.87630	−0.785716
$159$	7.52678	0.596912
$160$	5.81272	0.459536
$161$	0	0
$162$	0.812716	0.0638530
$163$	−9.18728	−0.719604	−0.359802	−	0.933029i	$-0.617156\pi$
$163$	−9.18728	−0.719604	−0.359802	+	0.933029i	$0.617156\pi$
$164$	−1.33949	−0.104597
$165$	−5.15221	−0.401099
$166$	12.4300	0.964755
$167$	−7.72409	−0.597708	−0.298854	−	0.954299i	$-0.596604\pi$
$167$	−7.72409	−0.597708	−0.298854	+	0.954299i	$0.596604\pi$
$168$	0	0
$169$	−8.21579	−0.631984
$170$	−4.76761	−0.365659
$171$	−5.33949	−0.408321
$172$	−12.1272	−0.924687
$173$	−5.03508	−0.382810	−0.191405	−	0.981511i	$-0.561304\pi$
$173$	−5.03508	−0.382810	−0.191405	+	0.981511i	$0.561304\pi$
$174$	−3.22236	−0.244286
$175$	0	0
$176$	−2.43815	−0.183782
$177$	−0.964925	−0.0725282
$178$	3.07015	0.230118
$179$	3.52678	0.263604	0.131802	−	0.991276i	$-0.457924\pi$
$179$	3.52678	0.263604	0.131802	+	0.991276i	$0.457924\pi$
$180$	−1.33949	−0.0998399
$181$	−15.9834	−1.18804	−0.594018	−	0.804451i	$-0.702459\pi$
$181$	−15.9834	−1.18804	−0.594018	+	0.804451i	$0.702459\pi$
$182$	0	0
$183$	4.90134	0.362318
$184$	−20.3329	−1.49896
$185$	9.96492	0.732636
$186$	3.88287	0.284706
$187$	30.2242	2.21022
$188$	−11.3746	−0.829576
$189$	0	0
$190$	−4.33949	−0.314820
$191$	17.7961	1.28768	0.643841	−	0.765159i	$-0.277340\pi$
$191$	17.7961	1.28768	0.643841	+	0.765159i	$0.277340\pi$
$192$	3.77764	0.272628
$193$	−20.5202	−1.47708	−0.738538	−	0.674211i	$-0.764484\pi$
$193$	−20.5202	−1.47708	−0.738538	+	0.674211i	$0.764484\pi$
$194$	6.40120	0.459579
$195$	2.18728	0.156635
$196$	0	0
$197$	11.0185	0.785034	0.392517	−	0.919745i	$-0.371604\pi$
$197$	11.0185	0.785034	0.392517	+	0.919745i	$0.371604\pi$
$198$	−4.18728	−0.297577
$199$	20.4115	1.44693	0.723467	−	0.690359i	$-0.242547\pi$
$199$	20.4115	1.44693	0.723467	+	0.690359i	$0.242547\pi$
$200$	10.8562	0.767652
$201$	−2.47322	−0.174448
$202$	3.22236	0.226724
$203$	0	0
$204$	7.85782	0.550158
$205$	1.00000	0.0698430
$206$	−7.68555	−0.535478
$207$	7.49170	0.520709
$208$	1.03508	0.0717696
$209$	27.5102	1.90292
$210$	0	0
$211$	−14.3930	−0.990858	−0.495429	−	0.868648i	$-0.664989\pi$
$211$	−14.3930	−0.990858	−0.495429	+	0.868648i	$0.664989\pi$
$212$	−10.0821	−0.692439
$213$	16.0536	1.09997
$214$	3.91137	0.267376
$215$	9.05355	0.617447
$216$	−2.71406	−0.184668
$217$	0	0
$218$	−10.7040	−0.724968
$219$	3.66051	0.247354
$220$	6.90134	0.465288
$221$	−12.8312	−0.863119
$222$	8.09866	0.543546
$223$	−15.2593	−1.02184	−0.510920	−	0.859629i	$-0.670695\pi$
$223$	−15.2593	−1.02184	−0.510920	+	0.859629i	$0.670695\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	3.91137	0.260181
$227$	13.4031	0.889593	0.444797	−	0.895632i	$-0.353276\pi$
$227$	13.4031	0.889593	0.444797	+	0.895632i	$0.353276\pi$
$228$	7.15221	0.473667
$229$	23.9834	1.58487	0.792434	−	0.609958i	$-0.208814\pi$
$229$	23.9834	1.58487	0.792434	+	0.609958i	$0.208814\pi$
$230$	6.08863	0.401472
$231$	0	0
$232$	10.7610	0.706497
$233$	20.4281	1.33829	0.669145	−	0.743132i	$-0.266660\pi$
$233$	20.4281	1.33829	0.669145	+	0.743132i	$0.266660\pi$
$234$	1.77764	0.116208
$235$	8.49170	0.553937
$236$	1.29251	0.0841352
$237$	−12.1522	−0.789371
$238$	0	0
$239$	−13.6439	−0.882551	−0.441276	−	0.897372i	$-0.645474\pi$
$239$	−13.6439	−0.882551	−0.441276	+	0.897372i	$0.645474\pi$
$240$	0.473224	0.0305465
$241$	29.5988	1.90663	0.953313	−	0.301983i	$-0.0976486\pi$
$241$	29.5988	1.90663	0.953313	+	0.301983i	$0.0976486\pi$
$242$	12.6339	0.812137
$243$	1.00000	0.0641500
$244$	−6.56531	−0.420301
$245$	0	0
$246$	0.812716	0.0518169
$247$	−11.6790	−0.743116
$248$	−12.9668	−0.823393
$249$	15.2944	0.969242
$250$	−7.31445	−0.462606
$251$	8.96492	0.565861	0.282931	−	0.959140i	$-0.408693\pi$
$251$	8.96492	0.565861	0.282931	+	0.959140i	$0.408693\pi$
$252$	0	0
$253$	−38.5988	−2.42669
$254$	−5.50015	−0.345110
$255$	−5.86627	−0.367360
$256$	−14.5083	−0.906769
$257$	−19.7510	−1.23203	−0.616017	−	0.787733i	$-0.711255\pi$
$257$	−19.7510	−1.23203	−0.616017	+	0.787733i	$0.711255\pi$
$258$	7.35797	0.458087
$259$	0	0
$260$	−2.92985	−0.181702
$261$	−3.96492	−0.245423
$262$	10.9133	0.674223
$263$	−13.8763	−0.855649	−0.427825	−	0.903862i	$-0.640720\pi$
$263$	−13.8763	−0.855649	−0.427825	+	0.903862i	$0.640720\pi$
$264$	13.9834	0.860619
$265$	7.52678	0.462366
$266$	0	0
$267$	3.77764	0.231188
$268$	3.31286	0.202365
$269$	7.18728	0.438216	0.219108	−	0.975701i	$-0.429685\pi$
$269$	7.18728	0.438216	0.219108	+	0.975701i	$0.429685\pi$
$270$	0.812716	0.0494603
$271$	6.09866	0.370467	0.185234	−	0.982695i	$-0.440696\pi$
$271$	6.09866	0.370467	0.185234	+	0.982695i	$0.440696\pi$
$272$	−2.77606	−0.168323
$273$	0	0
$274$	−1.52490	−0.0921224
$275$	20.6088	1.24276
$276$	−10.0351	−0.604041
$277$	27.7426	1.66689	0.833445	−	0.552603i	$-0.186365\pi$
$277$	27.7426	1.66689	0.833445	+	0.552603i	$0.186365\pi$
$278$	−3.62731	−0.217552
$279$	4.77764	0.286030
$280$	0	0
$281$	−6.25087	−0.372895	−0.186448	−	0.982465i	$-0.559697\pi$
$281$	−6.25087	−0.372895	−0.186448	+	0.982465i	$0.559697\pi$
$282$	6.90134	0.410969
$283$	−16.4817	−0.979734	−0.489867	−	0.871797i	$-0.662955\pi$
$283$	−16.4817	−0.979734	−0.489867	+	0.871797i	$0.662955\pi$
$284$	−21.5036	−1.27600
$285$	−5.33949	−0.316284
$286$	−9.15878	−0.541570
$287$	0	0
$288$	5.81272	0.342518
$289$	17.4131	1.02430
$290$	−3.22236	−0.189223
$291$	7.87630	0.461717
$292$	−4.90322	−0.286939
$293$	−9.40307	−0.549333	−0.274667	−	0.961539i	$-0.588568\pi$
$293$	−9.40307	−0.549333	−0.274667	+	0.961539i	$0.588568\pi$
$294$	0	0
$295$	−0.964925	−0.0561801
$296$	−27.0454	−1.57198
$297$	−5.15221	−0.298961
$298$	−10.4431	−0.604955
$299$	16.3865	0.947654
$300$	5.35797	0.309342
$301$	0	0
$302$	4.86281	0.279823
$303$	3.96492	0.227779
$304$	−2.52678	−0.144921
$305$	4.90134	0.280650
$306$	−4.76761	−0.272546
$307$	−9.03508	−0.515659	−0.257829	−	0.966190i	$-0.583007\pi$
$307$	−9.03508	−0.515659	−0.257829	+	0.966190i	$0.583007\pi$
$308$	0	0
$309$	−9.45663	−0.537969
$310$	3.88287	0.220532
$311$	−2.26746	−0.128576	−0.0642880	−	0.997931i	$-0.520478\pi$
$311$	−2.26746	−0.128576	−0.0642880	+	0.997931i	$0.520478\pi$
$312$	−5.93642	−0.336084
$313$	−14.9649	−0.845868	−0.422934	−	0.906161i	$-0.639000\pi$
$313$	−14.9649	−0.845868	−0.422934	+	0.906161i	$0.639000\pi$
$314$	2.96680	0.167426
$315$	0	0
$316$	16.2778	0.915697
$317$	−14.3846	−0.807919	−0.403960	−	0.914777i	$-0.632366\pi$
$317$	−14.3846	−0.807919	−0.403960	+	0.914777i	$0.632366\pi$
$318$	6.11713	0.343032
$319$	20.4281	1.14376
$320$	3.77764	0.211177
$321$	4.81272	0.268620
$322$	0	0
$323$	31.3229	1.74285
$324$	−1.33949	−0.0744162
$325$	−8.74913	−0.485315
$326$	−7.46666	−0.413540
$327$	−13.1707	−0.728341
$328$	−2.71406	−0.149859
$329$	0	0
$330$	−4.18728	−0.230502
$331$	16.3830	0.900492	0.450246	−	0.892905i	$-0.351336\pi$
$331$	16.3830	0.900492	0.450246	+	0.892905i	$0.351336\pi$
$332$	−20.4867	−1.12435
$333$	9.96492	0.546075
$334$	−6.27749	−0.343489
$335$	−2.47322	−0.135127
$336$	0	0
$337$	27.2076	1.48209	0.741047	−	0.671453i	$-0.234329\pi$
$337$	27.2076	1.48209	0.741047	+	0.671453i	$0.234329\pi$
$338$	−6.67711	−0.363187
$339$	4.81272	0.261391
$340$	7.85782	0.426150
$341$	−24.6154	−1.33300
$342$	−4.33949	−0.234653
$343$	0	0
$344$	−24.5719	−1.32483
$345$	7.49170	0.403340
$346$	−4.09209	−0.219992
$347$	−21.5703	−1.15795	−0.578977	−	0.815344i	$-0.696548\pi$
$347$	−21.5703	−1.15795	−0.578977	+	0.815344i	$0.696548\pi$
$348$	5.31099	0.284699
$349$	36.9734	1.97914	0.989570	−	0.144055i	$-0.0460144\pi$
$349$	36.9734	1.97914	0.989570	+	0.144055i	$0.0460144\pi$
$350$	0	0
$351$	2.18728	0.116749
$352$	−29.9483	−1.59625
$353$	5.98997	0.318814	0.159407	−	0.987213i	$-0.449042\pi$
$353$	5.98997	0.318814	0.159407	+	0.987213i	$0.449042\pi$
$354$	−0.784210	−0.0416803
$355$	16.0536	0.852034
$356$	−5.06012	−0.268186
$357$	0	0
$358$	2.86627	0.151487
$359$	1.35609	0.0715717	0.0357859	−	0.999359i	$-0.488607\pi$
$359$	1.35609	0.0715717	0.0357859	+	0.999359i	$0.488607\pi$
$360$	−2.71406	−0.143044
$361$	9.51018	0.500536
$362$	−12.9900	−0.682738
$363$	15.5453	0.815914
$364$	0	0
$365$	3.66051	0.191600
$366$	3.98340	0.208216
$367$	−6.82275	−0.356144	−0.178072	−	0.984017i	$-0.556986\pi$
$367$	−6.82275	−0.356144	−0.178072	+	0.984017i	$0.556986\pi$
$368$	3.54525	0.184809
$369$	1.00000	0.0520579
$370$	8.09866	0.421029
$371$	0	0
$372$	−6.39961	−0.331804
$373$	5.59036	0.289458	0.144729	−	0.989471i	$-0.453769\pi$
$373$	5.59036	0.289458	0.144729	+	0.989471i	$0.453769\pi$
$374$	24.5637	1.27016
$375$	−9.00000	−0.464758
$376$	−23.0470	−1.18856
$377$	−8.67242	−0.446652
$378$	0	0
$379$	5.10710	0.262334	0.131167	−	0.991360i	$-0.458128\pi$
$379$	5.10710	0.262334	0.131167	+	0.991360i	$0.458128\pi$
$380$	7.15221	0.366901
$381$	−6.76761	−0.346715
$382$	14.4632	0.740001
$383$	24.9483	1.27480	0.637400	−	0.770533i	$-0.280010\pi$
$383$	24.9483	1.27480	0.637400	+	0.770533i	$0.280010\pi$
$384$	−8.55528	−0.436585
$385$	0	0
$386$	−16.6771	−0.848842
$387$	9.05355	0.460218
$388$	−10.5502	−0.535607
$389$	−7.48167	−0.379336	−0.189668	−	0.981848i	$-0.560741\pi$
$389$	−7.48167	−0.379336	−0.189668	+	0.981848i	$0.560741\pi$
$390$	1.77764	0.0900144
$391$	−43.9483	−2.22256
$392$	0	0
$393$	13.4281	0.677359
$394$	8.95490	0.451141
$395$	−12.1522	−0.611444
$396$	6.90134	0.346806
$397$	26.2443	1.31716	0.658582	−	0.752509i	$-0.271157\pi$
$397$	26.2443	1.31716	0.658582	+	0.752509i	$0.271157\pi$
$398$	16.5888	0.831520
$399$	0	0
$400$	−1.89290	−0.0946448
$401$	5.56531	0.277918	0.138959	−	0.990298i	$-0.455624\pi$
$401$	5.56531	0.277918	0.138959	+	0.990298i	$0.455624\pi$
$402$	−2.01003	−0.100251
$403$	10.4501	0.520554
$404$	−5.31099	−0.264231
$405$	1.00000	0.0496904
$406$	0	0
$407$	−51.3414	−2.54490
$408$	15.9214	0.788227
$409$	33.9032	1.67641	0.838203	−	0.545358i	$-0.183606\pi$
$409$	33.9032	1.67641	0.838203	+	0.545358i	$0.183606\pi$
$410$	0.812716	0.0401372
$411$	−1.87630	−0.0925509
$412$	12.6671	0.624062
$413$	0	0
$414$	6.08863	0.299240
$415$	15.2944	0.750772
$416$	12.7141	0.623358
$417$	−4.46319	−0.218564
$418$	22.3580	1.09356
$419$	18.1422	0.886303	0.443152	−	0.896447i	$-0.353860\pi$
$419$	18.1422	0.886303	0.443152	+	0.896447i	$0.353860\pi$
$420$	0	0
$421$	−29.9483	−1.45959	−0.729796	−	0.683665i	$-0.760385\pi$
$421$	−29.9483	−1.45959	−0.729796	+	0.683665i	$0.760385\pi$
$422$	−11.6975	−0.569424
$423$	8.49170	0.412881
$424$	−20.4281	−0.992077
$425$	23.4651	1.13822
$426$	13.0470	0.632128
$427$	0	0
$428$	−6.44660	−0.311608
$429$	−11.2693	−0.544089
$430$	7.35797	0.354833
$431$	9.94833	0.479194	0.239597	−	0.970872i	$-0.422985\pi$
$431$	9.94833	0.479194	0.239597	+	0.970872i	$0.422985\pi$
$432$	0.473224	0.0227680
$433$	15.2593	0.733316	0.366658	−	0.930356i	$-0.380502\pi$
$433$	15.2593	0.733316	0.366658	+	0.930356i	$0.380502\pi$
$434$	0	0
$435$	−3.96492	−0.190104
$436$	17.6420	0.844900
$437$	−40.0019	−1.91355
$438$	2.97495	0.142149
$439$	−6.37457	−0.304242	−0.152121	−	0.988362i	$-0.548610\pi$
$439$	−6.37457	−0.304242	−0.152121	+	0.988362i	$0.548610\pi$
$440$	13.9834	0.666633
$441$	0	0
$442$	−10.4281	−0.496015
$443$	−11.0720	−0.526048	−0.263024	−	0.964789i	$-0.584720\pi$
$443$	−11.0720	−0.526048	−0.263024	+	0.964789i	$0.584720\pi$
$444$	−13.3479	−0.633465
$445$	3.77764	0.179077
$446$	−12.4015	−0.587228
$447$	−12.8497	−0.607769
$448$	0	0
$449$	−36.6173	−1.72808	−0.864038	−	0.503426i	$-0.832073\pi$
$449$	−36.6173	−1.72808	−0.864038	+	0.503426i	$0.832073\pi$
$450$	−3.25087	−0.153247
$451$	−5.15221	−0.242608
$452$	−6.44660	−0.303222
$453$	5.98340	0.281125
$454$	10.8929	0.511229
$455$	0	0
$456$	14.4917	0.678636
$457$	6.91794	0.323608	0.161804	−	0.986823i	$-0.448269\pi$
$457$	6.91794	0.323608	0.161804	+	0.986823i	$0.448269\pi$
$458$	19.4917	0.910787
$459$	−5.86627	−0.273814
$460$	−10.0351	−0.467888
$461$	18.7676	0.874095	0.437047	−	0.899438i	$-0.356024\pi$
$461$	18.7676	0.874095	0.437047	+	0.899438i	$0.356024\pi$
$462$	0	0
$463$	3.53334	0.164208	0.0821042	−	0.996624i	$-0.473836\pi$
$463$	3.53334	0.164208	0.0821042	+	0.996624i	$0.473836\pi$
$464$	−1.87630	−0.0871049
$465$	4.77764	0.221558
$466$	16.6023	0.769085
$467$	9.06358	0.419413	0.209706	−	0.977764i	$-0.432749\pi$
$467$	9.06358	0.419413	0.209706	+	0.977764i	$0.432749\pi$
$468$	−2.92985	−0.135432
$469$	0	0
$470$	6.90134	0.318335
$471$	3.65048	0.168205
$472$	2.61886	0.120543
$473$	−46.6458	−2.14478
$474$	−9.87630	−0.453633
$475$	21.3580	0.979971
$476$	0	0
$477$	7.52678	0.344627
$478$	−11.0886	−0.507182
$479$	−37.3063	−1.70457	−0.852284	−	0.523079i	$-0.824783\pi$
$479$	−37.3063	−1.70457	−0.852284	+	0.523079i	$0.824783\pi$
$480$	5.81272	0.265313
$481$	21.7961	0.993817
$482$	24.0554	1.09569
$483$	0	0
$484$	−20.8227	−0.946488
$485$	7.87630	0.357644
$486$	0.812716	0.0368656
$487$	1.84779	0.0837314	0.0418657	−	0.999123i	$-0.486670\pi$
$487$	1.84779	0.0837314	0.0418657	+	0.999123i	$0.486670\pi$
$488$	−13.3025	−0.602178
$489$	−9.18728	−0.415463
$490$	0	0
$491$	15.7610	0.711286	0.355643	−	0.934622i	$-0.384262\pi$
$491$	15.7610	0.711286	0.355643	+	0.934622i	$0.384262\pi$
$492$	−1.33949	−0.0603890
$493$	23.2593	1.04755
$494$	−9.49170	−0.427052
$495$	−5.15221	−0.231575
$496$	2.26089	0.101517
$497$	0	0
$498$	12.4300	0.557002
$499$	−32.1071	−1.43731	−0.718656	−	0.695366i	$-0.755242\pi$
$499$	−32.1071	−1.43731	−0.718656	+	0.695366i	$0.755242\pi$
$500$	12.0554	0.539135
$501$	−7.72409	−0.345087
$502$	7.28594	0.325187
$503$	−20.3680	−0.908164	−0.454082	−	0.890960i	$-0.650033\pi$
$503$	−20.3680	−0.908164	−0.454082	+	0.890960i	$0.650033\pi$
$504$	0	0
$505$	3.96492	0.176437
$506$	−31.3699	−1.39456
$507$	−8.21579	−0.364876
$508$	9.06516	0.402202
$509$	36.6339	1.62377	0.811884	−	0.583819i	$-0.198442\pi$
$509$	36.6339	1.62377	0.811884	+	0.583819i	$0.198442\pi$
$510$	−4.76761	−0.211113
$511$	0	0
$512$	5.31943	0.235088
$513$	−5.33949	−0.235744
$514$	−16.0520	−0.708022
$515$	−9.45663	−0.416709
$516$	−12.1272	−0.533869
$517$	−43.7510	−1.92417
$518$	0	0
$519$	−5.03508	−0.221015
$520$	−5.93642	−0.260329
$521$	37.0536	1.62335	0.811673	−	0.584112i	$-0.198557\pi$
$521$	37.0536	1.62335	0.811673	+	0.584112i	$0.198557\pi$
$522$	−3.22236	−0.141039
$523$	−40.1090	−1.75384	−0.876922	−	0.480633i	$-0.840407\pi$
$523$	−40.1090	−1.75384	−0.876922	+	0.480633i	$0.840407\pi$
$524$	−17.9869	−0.785760
$525$	0	0
$526$	−11.2775	−0.491722
$527$	−28.0269	−1.22087
$528$	−2.43815	−0.106107
$529$	33.1256	1.44024
$530$	6.11713	0.265711
$531$	−0.964925	−0.0418742
$532$	0	0
$533$	2.18728	0.0947418
$534$	3.07015	0.132858
$535$	4.81272	0.208072
$536$	6.71248	0.289935
$537$	3.52678	0.152192
$538$	5.84122	0.251833
$539$	0	0
$540$	−1.33949	−0.0576426
$541$	−40.1506	−1.72621	−0.863105	−	0.505024i	$-0.831484\pi$
$541$	−40.1506	−1.72621	−0.863105	+	0.505024i	$0.831484\pi$
$542$	4.95648	0.212899
$543$	−15.9834	−0.685913
$544$	−34.0990	−1.46198
$545$	−13.1707	−0.564170
$546$	0	0
$547$	−18.7260	−0.800665	−0.400332	−	0.916370i	$-0.631105\pi$
$547$	−18.7260	−0.800665	−0.400332	+	0.916370i	$0.631105\pi$
$548$	2.51329	0.107362
$549$	4.90134	0.209184
$550$	16.7491	0.714186
$551$	21.1707	0.901902
$552$	−20.3329	−0.865427
$553$	0	0
$554$	22.5468	0.957923
$555$	9.96492	0.422988
$556$	5.97841	0.253541
$557$	36.6993	1.55500	0.777500	−	0.628882i	$-0.216487\pi$
$557$	36.6993	1.55500	0.777500	+	0.628882i	$0.216487\pi$
$558$	3.88287	0.164375
$559$	19.8027	0.837564
$560$	0	0
$561$	30.2242	1.27607
$562$	−5.08018	−0.214294
$563$	1.11367	0.0469357	0.0234679	−	0.999725i	$-0.492529\pi$
$563$	1.11367	0.0469357	0.0234679	+	0.999725i	$0.492529\pi$
$564$	−11.3746	−0.478956
$565$	4.81272	0.202472
$566$	−13.3949	−0.563031
$567$	0	0
$568$	−43.5703	−1.82817
$569$	33.9568	1.42354	0.711771	−	0.702412i	$-0.247893\pi$
$569$	33.9568	1.42354	0.711771	+	0.702412i	$0.247893\pi$
$570$	−4.33949	−0.181761
$571$	3.14875	0.131771	0.0658855	−	0.997827i	$-0.479013\pi$
$571$	3.14875	0.131771	0.0658855	+	0.997827i	$0.479013\pi$
$572$	15.0952	0.631162
$573$	17.7961	0.743443
$574$	0	0
$575$	−29.9668	−1.24970
$576$	3.77764	0.157402
$577$	−15.6724	−0.652451	−0.326226	−	0.945292i	$-0.605777\pi$
$577$	−15.6724	−0.652451	−0.326226	+	0.945292i	$0.605777\pi$
$578$	14.1519	0.588642
$579$	−20.5202	−0.852791
$580$	5.31099	0.220527
$581$	0	0
$582$	6.40120	0.265338
$583$	−38.7795	−1.60608
$584$	−9.93484	−0.411106
$585$	2.18728	0.0904331
$586$	−7.64203	−0.315689
$587$	−8.27937	−0.341726	−0.170863	−	0.985295i	$-0.554656\pi$
$587$	−8.27937	−0.341726	−0.170863	+	0.985295i	$0.554656\pi$
$588$	0	0
$589$	−25.5102	−1.05113
$590$	−0.784210	−0.0322854
$591$	11.0185	0.453240
$592$	4.71564	0.193812
$593$	1.74069	0.0714815	0.0357407	−	0.999361i	$-0.488621\pi$
$593$	1.74069	0.0714815	0.0357407	+	0.999361i	$0.488621\pi$
$594$	−4.18728	−0.171806
$595$	0	0
$596$	17.2120	0.705032
$597$	20.4115	0.835388
$598$	13.3176	0.544595
$599$	22.0185	0.899651	0.449825	−	0.893117i	$-0.351486\pi$
$599$	22.0185	0.899651	0.449825	+	0.893117i	$0.351486\pi$
$600$	10.8562	0.443204
$601$	47.2963	1.92925	0.964627	−	0.263617i	$-0.0849155\pi$
$601$	47.2963	1.92925	0.964627	+	0.263617i	$0.0849155\pi$
$602$	0	0
$603$	−2.47322	−0.100717
$604$	−8.01472	−0.326114
$605$	15.5453	0.632004
$606$	3.22236	0.130899
$607$	−6.67242	−0.270825	−0.135412	−	0.990789i	$-0.543236\pi$
$607$	−6.67242	−0.270825	−0.135412	+	0.990789i	$0.543236\pi$
$608$	−31.0370	−1.25871
$609$	0	0
$610$	3.98340	0.161283
$611$	18.5738	0.751414
$612$	7.85782	0.317634
$613$	−25.1873	−1.01730	−0.508652	−	0.860972i	$-0.669856\pi$
$613$	−25.1873	−1.01730	−0.508652	+	0.860972i	$0.669856\pi$
$614$	−7.34295	−0.296337
$615$	1.00000	0.0403239
$616$	0	0
$617$	2.51176	0.101120	0.0505598	−	0.998721i	$-0.483899\pi$
$617$	2.51176	0.101120	0.0505598	+	0.998721i	$0.483899\pi$
$618$	−7.68555	−0.309158
$619$	0.287819	0.0115684	0.00578420	−	0.999983i	$-0.498159\pi$
$619$	0.287819	0.0115684	0.00578420	+	0.999983i	$0.498159\pi$
$620$	−6.39961	−0.257015
$621$	7.49170	0.300632
$622$	−1.84280	−0.0738897
$623$	0	0
$624$	1.03508	0.0414362
$625$	11.0000	0.440000
$626$	−12.1622	−0.486101
$627$	27.5102	1.09865
$628$	−4.88979	−0.195124
$629$	−58.4569	−2.33083
$630$	0	0
$631$	−33.6358	−1.33902	−0.669509	−	0.742804i	$-0.733496\pi$
$631$	−33.6358	−1.33902	−0.669509	+	0.742804i	$0.733496\pi$
$632$	32.9818	1.31195
$633$	−14.3930	−0.572072
$634$	−11.6906	−0.464293
$635$	−6.76761	−0.268564
$636$	−10.0821	−0.399780
$637$	0	0
$638$	16.6023	0.657290
$639$	16.0536	0.635069
$640$	−8.55528	−0.338177
$641$	43.9934	1.73764	0.868818	−	0.495132i	$-0.164880\pi$
$641$	43.9934	1.73764	0.868818	+	0.495132i	$0.164880\pi$
$642$	3.91137	0.154370
$643$	8.74257	0.344773	0.172387	−	0.985029i	$-0.444852\pi$
$643$	8.74257	0.344773	0.172387	+	0.985029i	$0.444852\pi$
$644$	0	0
$645$	9.05355	0.356483
$646$	25.4566	1.00158
$647$	21.0720	0.828427	0.414213	−	0.910180i	$-0.364057\pi$
$647$	21.0720	0.828427	0.414213	+	0.910180i	$0.364057\pi$
$648$	−2.71406	−0.106618
$649$	4.97149	0.195148
$650$	−7.11056	−0.278899
$651$	0	0
$652$	12.3063	0.481952
$653$	29.1237	1.13970	0.569849	−	0.821749i	$-0.307002\pi$
$653$	29.1237	1.13970	0.569849	+	0.821749i	$0.307002\pi$
$654$	−10.7040	−0.418561
$655$	13.4281	0.524680
$656$	0.473224	0.0184763
$657$	3.66051	0.142810
$658$	0	0
$659$	31.8681	1.24141	0.620703	−	0.784045i	$-0.286847\pi$
$659$	31.8681	1.24141	0.620703	+	0.784045i	$0.286847\pi$
$660$	6.90134	0.268634
$661$	−7.91137	−0.307717	−0.153858	−	0.988093i	$-0.549170\pi$
$661$	−7.91137	−0.307717	−0.153858	+	0.988093i	$0.549170\pi$
$662$	13.3147	0.517492
$663$	−12.8312	−0.498322
$664$	−41.5099	−1.61090
$665$	0	0
$666$	8.09866	0.313817
$667$	−29.7040	−1.15014
$668$	10.3464	0.400313
$669$	−15.2593	−0.589959
$670$	−2.01003	−0.0776542
$671$	−25.2527	−0.974871
$672$	0	0
$673$	32.4150	1.24951	0.624753	−	0.780823i	$-0.285200\pi$
$673$	32.4150	1.24951	0.624753	+	0.780823i	$0.285200\pi$
$674$	22.1121	0.851726
$675$	−4.00000	−0.153960
$676$	11.0050	0.423269
$677$	26.5368	1.01989	0.509946	−	0.860206i	$-0.329665\pi$
$677$	26.5368	1.01989	0.509946	+	0.860206i	$0.329665\pi$
$678$	3.91137	0.150215
$679$	0	0
$680$	15.9214	0.610558
$681$	13.4031	0.513607
$682$	−20.0053	−0.766044
$683$	−39.6624	−1.51764	−0.758820	−	0.651301i	$-0.774224\pi$
$683$	−39.6624	−1.51764	−0.758820	+	0.651301i	$0.774224\pi$
$684$	7.15221	0.273472
$685$	−1.87630	−0.0716896
$686$	0	0
$687$	23.9834	0.915024
$688$	4.28436	0.163340
$689$	16.4632	0.627198
$690$	6.08863	0.231790
$691$	34.3930	1.30837	0.654187	−	0.756333i	$-0.273011\pi$
$691$	34.3930	1.30837	0.654187	+	0.756333i	$0.273011\pi$
$692$	6.74444	0.256385
$693$	0	0
$694$	−17.5305	−0.665450
$695$	−4.46319	−0.169299
$696$	10.7610	0.407896
$697$	−5.86627	−0.222201
$698$	30.0489	1.13737
$699$	20.4281	0.772662
$700$	0	0
$701$	−18.3949	−0.694767	−0.347383	−	0.937723i	$-0.612930\pi$
$701$	−18.3949	−0.694767	−0.347383	+	0.937723i	$0.612930\pi$
$702$	1.77764	0.0670927
$703$	−53.2076	−2.00676
$704$	−19.4632	−0.733547
$705$	8.49170	0.319816
$706$	4.86815	0.183215
$707$	0	0
$708$	1.29251	0.0485755
$709$	−8.34606	−0.313443	−0.156721	−	0.987643i	$-0.550092\pi$
$709$	−8.34606	−0.313443	−0.156721	+	0.987643i	$0.550092\pi$
$710$	13.0470	0.489645
$711$	−12.1522	−0.455743
$712$	−10.2527	−0.384238
$713$	35.7927	1.34045
$714$	0	0
$715$	−11.2693	−0.421449
$716$	−4.72409	−0.176547
$717$	−13.6439	−0.509541
$718$	1.10212	0.0411306
$719$	29.1541	1.08726	0.543632	−	0.839324i	$-0.317049\pi$
$719$	29.1541	1.08726	0.543632	+	0.839324i	$0.317049\pi$
$720$	0.473224	0.0176360
$721$	0	0
$722$	7.72908	0.287646
$723$	29.5988	1.10079
$724$	21.4096	0.795683
$725$	15.8597	0.589014
$726$	12.6339	0.468887
$727$	−23.9298	−0.887509	−0.443754	−	0.896148i	$-0.646354\pi$
$727$	−23.9298	−0.887509	−0.443754	+	0.896148i	$0.646354\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.97495	0.110108
$731$	−53.1106	−1.96437
$732$	−6.56531	−0.242661
$733$	10.1672	0.375535	0.187768	−	0.982214i	$-0.439875\pi$
$733$	10.1672	0.375535	0.187768	+	0.982214i	$0.439875\pi$
$734$	−5.54496	−0.204668
$735$	0	0
$736$	43.5471	1.60517
$737$	12.7426	0.469378
$738$	0.812716	0.0299165
$739$	−23.3664	−0.859548	−0.429774	−	0.902937i	$-0.641407\pi$
$739$	−23.3664	−0.859548	−0.429774	+	0.902937i	$0.641407\pi$
$740$	−13.3479	−0.490680
$741$	−11.6790	−0.429038
$742$	0	0
$743$	23.7861	0.872627	0.436313	−	0.899795i	$-0.356284\pi$
$743$	23.7861	0.872627	0.436313	+	0.899795i	$0.356284\pi$
$744$	−12.9668	−0.475386
$745$	−12.8497	−0.470775
$746$	4.54337	0.166345
$747$	15.2944	0.559592
$748$	−40.4851	−1.48028
$749$	0	0
$750$	−7.31445	−0.267086
$751$	22.9233	0.836482	0.418241	−	0.908336i	$-0.362647\pi$
$751$	22.9233	0.836482	0.418241	+	0.908336i	$0.362647\pi$
$752$	4.01848	0.146539
$753$	8.96492	0.326700
$754$	−7.04821	−0.256681
$755$	5.98340	0.217758
$756$	0	0
$757$	−20.4632	−0.743747	−0.371874	−	0.928283i	$-0.621285\pi$
$757$	−20.4632	−0.743747	−0.371874	+	0.928283i	$0.621285\pi$
$758$	4.15063	0.150758
$759$	−38.5988	−1.40105
$760$	14.4917	0.525669
$761$	−42.6154	−1.54481	−0.772404	−	0.635132i	$-0.780946\pi$
$761$	−42.6154	−1.54481	−0.772404	+	0.635132i	$0.780946\pi$
$762$	−5.50015	−0.199249
$763$	0	0
$764$	−23.8378	−0.862420
$765$	−5.86627	−0.212095
$766$	20.2759	0.732598
$767$	−2.11056	−0.0762081
$768$	−14.5083	−0.523523
$769$	−47.4735	−1.71194	−0.855969	−	0.517026i	$-0.827039\pi$
$769$	−47.4735	−1.71194	−0.855969	+	0.517026i	$0.827039\pi$
$770$	0	0
$771$	−19.7510	−0.711315
$772$	27.4867	0.989266
$773$	36.0119	1.29526	0.647629	−	0.761956i	$-0.275761\pi$
$773$	36.0119	1.29526	0.647629	+	0.761956i	$0.275761\pi$
$774$	7.35797	0.264477
$775$	−19.1106	−0.686472
$776$	−21.3767	−0.767380
$777$	0	0
$778$	−6.08048	−0.217996
$779$	−5.33949	−0.191307
$780$	−2.92985	−0.104905
$781$	−82.7112	−2.95964
$782$	−35.7175	−1.27726
$783$	−3.96492	−0.141695
$784$	0	0
$785$	3.65048	0.130291
$786$	10.9133	0.389263
$787$	−7.66896	−0.273369	−0.136684	−	0.990615i	$-0.543645\pi$
$787$	−7.66896	−0.273369	−0.136684	+	0.990615i	$0.543645\pi$
$788$	−14.7592	−0.525773
$789$	−13.8763	−0.494009
$790$	−9.87630	−0.351383
$791$	0	0
$792$	13.9834	0.496879
$793$	10.7206	0.380701
$794$	21.3292	0.756944
$795$	7.52678	0.266947
$796$	−27.3411	−0.969079
$797$	17.0035	0.602293	0.301147	−	0.953578i	$-0.402631\pi$
$797$	17.0035	0.602293	0.301147	+	0.953578i	$0.402631\pi$
$798$	0	0
$799$	−49.8146	−1.76231
$800$	−23.2509	−0.822042
$801$	3.77764	0.133476
$802$	4.52302	0.159713
$803$	−18.8597	−0.665544
$804$	3.31286	0.116836
$805$	0	0
$806$	8.49293	0.299151
$807$	7.18728	0.253004
$808$	−10.7610	−0.378572
$809$	−8.73066	−0.306954	−0.153477	−	0.988152i	$-0.549047\pi$
$809$	−8.73066	−0.306954	−0.153477	+	0.988152i	$0.549047\pi$
$810$	0.812716	0.0285559
$811$	−20.6339	−0.724554	−0.362277	−	0.932071i	$-0.618000\pi$
$811$	−20.6339	−0.724554	−0.362277	+	0.932071i	$0.618000\pi$
$812$	0	0
$813$	6.09866	0.213889
$814$	−41.7260	−1.46249
$815$	−9.18728	−0.321817
$816$	−2.77606	−0.0971815
$817$	−48.3414	−1.69125
$818$	27.5537	0.963393
$819$	0	0
$820$	−1.33949	−0.0467771
$821$	26.7360	0.933093	0.466546	−	0.884497i	$-0.345498\pi$
$821$	26.7360	0.933093	0.466546	+	0.884497i	$0.345498\pi$
$822$	−1.52490	−0.0531869
$823$	−48.7595	−1.69965	−0.849824	−	0.527067i	$-0.823292\pi$
$823$	−48.7595	−1.69965	−0.849824	+	0.527067i	$0.823292\pi$
$824$	25.6658	0.894112
$825$	20.6088	0.717508
$826$	0	0
$827$	13.2427	0.460494	0.230247	−	0.973132i	$-0.426047\pi$
$827$	13.2427	0.460494	0.230247	+	0.973132i	$0.426047\pi$
$828$	−10.0351	−0.348743
$829$	11.5619	0.401560	0.200780	−	0.979636i	$-0.435652\pi$
$829$	11.5619	0.401560	0.200780	+	0.979636i	$0.435652\pi$
$830$	12.4300	0.431452
$831$	27.7426	0.962379
$832$	8.26277	0.286460
$833$	0	0
$834$	−3.62731	−0.125604
$835$	−7.72409	−0.267303
$836$	−36.8497	−1.27447
$837$	4.77764	0.165139
$838$	14.7444	0.509338
$839$	−36.1375	−1.24760	−0.623802	−	0.781582i	$-0.714413\pi$
$839$	−36.1375	−1.24760	−0.623802	+	0.781582i	$0.714413\pi$
$840$	0	0
$841$	−13.2794	−0.457909
$842$	−24.3395	−0.838794
$843$	−6.25087	−0.215291
$844$	19.2794	0.663623
$845$	−8.21579	−0.282632
$846$	6.90134	0.237273
$847$	0	0
$848$	3.56185	0.122314
$849$	−16.4817	−0.565649
$850$	19.0704	0.654111
$851$	74.6542	2.55911
$852$	−21.5036	−0.736701
$853$	38.2593	1.30997	0.654987	−	0.755640i	$-0.272674\pi$
$853$	38.2593	1.30997	0.654987	+	0.755640i	$0.272674\pi$
$854$	0	0
$855$	−5.33949	−0.182607
$856$	−13.0620	−0.446450
$857$	−30.8431	−1.05358	−0.526790	−	0.849995i	$-0.676605\pi$
$857$	−30.8431	−1.05358	−0.526790	+	0.849995i	$0.676605\pi$
$858$	−9.15878	−0.312676
$859$	13.7942	0.470653	0.235327	−	0.971916i	$-0.424384\pi$
$859$	13.7942	0.470653	0.235327	+	0.971916i	$0.424384\pi$
$860$	−12.1272	−0.413533
$861$	0	0
$862$	8.08517	0.275382
$863$	−18.3295	−0.623942	−0.311971	−	0.950092i	$-0.600989\pi$
$863$	−18.3295	−0.623942	−0.311971	+	0.950092i	$0.600989\pi$
$864$	5.81272	0.197753
$865$	−5.03508	−0.171198
$866$	12.4015	0.421420
$867$	17.4131	0.591380
$868$	0	0
$869$	62.6107	2.12392
$870$	−3.22236	−0.109248
$871$	−5.40964	−0.183299
$872$	35.7460	1.21051
$873$	7.87630	0.266572
$874$	−32.5102	−1.09967
$875$	0	0
$876$	−4.90322	−0.165665
$877$	−20.6373	−0.696873	−0.348437	−	0.937332i	$-0.613287\pi$
$877$	−20.6373	−0.696873	−0.348437	+	0.937332i	$0.613287\pi$
$878$	−5.18071	−0.174841
$879$	−9.40307	−0.317158
$880$	−2.43815	−0.0821900
$881$	40.6007	1.36787	0.683936	−	0.729542i	$-0.260267\pi$
$881$	40.6007	1.36787	0.683936	+	0.729542i	$0.260267\pi$
$882$	0	0
$883$	54.8431	1.84562	0.922809	−	0.385259i	$-0.125888\pi$
$883$	54.8431	1.84562	0.922809	+	0.385259i	$0.125888\pi$
$884$	17.1873	0.578071
$885$	−0.964925	−0.0324356
$886$	−8.99842	−0.302308
$887$	−56.1910	−1.88671	−0.943355	−	0.331784i	$-0.892349\pi$
$887$	−56.1910	−1.88671	−0.943355	+	0.331784i	$0.892349\pi$
$888$	−27.0454	−0.907584
$889$	0	0
$890$	3.07015	0.102912
$891$	−5.15221	−0.172605
$892$	20.4397	0.684373
$893$	−45.3414	−1.51729
$894$	−10.4431	−0.349271
$895$	3.52678	0.117887
$896$	0	0
$897$	16.3865	0.547128
$898$	−29.7595	−0.993086
$899$	−18.9430	−0.631784
$900$	5.35797	0.178599
$901$	−44.1541	−1.47099
$902$	−4.18728	−0.139421
$903$	0	0
$904$	−13.0620	−0.434436
$905$	−15.9834	−0.531306
$906$	4.86281	0.161556
$907$	18.0620	0.599739	0.299869	−	0.953980i	$-0.403057\pi$
$907$	18.0620	0.599739	0.299869	+	0.953980i	$0.403057\pi$
$908$	−17.9533	−0.595802
$909$	3.96492	0.131508
$910$	0	0
$911$	12.1337	0.402008	0.201004	−	0.979590i	$-0.435579\pi$
$911$	12.1337	0.402008	0.201004	+	0.979590i	$0.435579\pi$
$912$	−2.52678	−0.0836699
$913$	−78.7999	−2.60790
$914$	5.62232	0.185970
$915$	4.90134	0.162033
$916$	−32.1256	−1.06146
$917$	0	0
$918$	−4.76761	−0.157355
$919$	−55.1475	−1.81915	−0.909574	−	0.415541i	$-0.863592\pi$
$919$	−55.1475	−1.81915	−0.909574	+	0.415541i	$0.863592\pi$
$920$	−20.3329	−0.670357
$921$	−9.03508	−0.297716
$922$	15.2527	0.502322
$923$	35.1137	1.15578
$924$	0	0
$925$	−39.8597	−1.31058
$926$	2.87161	0.0943669
$927$	−9.45663	−0.310596
$928$	−23.0470	−0.756554
$929$	14.3545	0.470956	0.235478	−	0.971880i	$-0.424334\pi$
$929$	14.3545	0.470956	0.235478	+	0.971880i	$0.424334\pi$
$930$	3.88287	0.127324
$931$	0	0
$932$	−27.3633	−0.896315
$933$	−2.26746	−0.0742334
$934$	7.36612	0.241027
$935$	30.2242	0.988438
$936$	−5.93642	−0.194038
$937$	55.8331	1.82399	0.911993	−	0.410205i	$-0.134543\pi$
$937$	55.8331	1.82399	0.911993	+	0.410205i	$0.134543\pi$
$938$	0	0
$939$	−14.9649	−0.488362
$940$	−11.3746	−0.370997
$941$	32.8697	1.07152	0.535761	−	0.844370i	$-0.320025\pi$
$941$	32.8697	1.07152	0.535761	+	0.844370i	$0.320025\pi$
$942$	2.96680	0.0966637
$943$	7.49170	0.243963
$944$	−0.456626	−0.0148619
$945$	0	0
$946$	−37.9098	−1.23255
$947$	12.6355	0.410597	0.205299	−	0.978699i	$-0.434183\pi$
$947$	12.6355	0.410597	0.205299	+	0.978699i	$0.434183\pi$
$948$	16.2778	0.528678
$949$	8.00657	0.259904
$950$	17.3580	0.563167
$951$	−14.3846	−0.466453
$952$	0	0
$953$	42.7125	1.38359	0.691796	−	0.722093i	$-0.256820\pi$
$953$	42.7125	1.38359	0.691796	+	0.722093i	$0.256820\pi$
$954$	6.11713	0.198050
$955$	17.7961	0.575869
$956$	18.2759	0.591085
$957$	20.4281	0.660347
$958$	−30.3194	−0.979576
$959$	0	0
$960$	3.77764	0.121923
$961$	−8.17415	−0.263682
$962$	17.7141	0.571124
$963$	4.81272	0.155088
$964$	−39.6474	−1.27696
$965$	−20.5202	−0.660569
$966$	0	0
$967$	48.3764	1.55568	0.777841	−	0.628461i	$-0.216315\pi$
$967$	48.3764	1.55568	0.777841	+	0.628461i	$0.216315\pi$
$968$	−42.1907	−1.35606
$969$	31.3229	1.00624
$970$	6.40120	0.205530
$971$	−18.8681	−0.605508	−0.302754	−	0.953069i	$-0.597906\pi$
$971$	−18.8681	−0.605508	−0.302754	+	0.953069i	$0.597906\pi$
$972$	−1.33949	−0.0429642
$973$	0	0
$974$	1.50173	0.0481185
$975$	−8.74913	−0.280197
$976$	2.31943	0.0742433
$977$	−15.8513	−0.507126	−0.253563	−	0.967319i	$-0.581603\pi$
$977$	−15.8513	−0.507126	−0.253563	+	0.967319i	$0.581603\pi$
$978$	−7.46666	−0.238757
$979$	−19.4632	−0.622046
$980$	0	0
$981$	−13.1707	−0.420508
$982$	12.8093	0.408760
$983$	−7.71406	−0.246040	−0.123020	−	0.992404i	$-0.539258\pi$
$983$	−7.71406	−0.246040	−0.123020	+	0.992404i	$0.539258\pi$
$984$	−2.71406	−0.0865211
$985$	11.0185	0.351078
$986$	18.9032	0.602001
$987$	0	0
$988$	15.6439	0.497699
$989$	67.8265	2.15676
$990$	−4.18728	−0.133081
$991$	−0.611943	−0.0194390	−0.00971950	−	0.999953i	$-0.503094\pi$
$991$	−0.611943	−0.0194390	−0.00971950	+	0.999953i	$0.503094\pi$
$992$	27.7711	0.881732
$993$	16.3830	0.519899
$994$	0	0
$995$	20.4115	0.647089
$996$	−20.4867	−0.649146
$997$	−25.8866	−0.819838	−0.409919	−	0.912122i	$-0.634443\pi$
$997$	−25.8866	−0.819838	−0.409919	+	0.912122i	$0.634443\pi$
$998$	−26.0940	−0.825990
$999$	9.96492	0.315276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.t.1.2		3
7.3	odd	6		861.2.i.b.247.2	✓	6
7.5	odd	6		861.2.i.b.739.2	yes	6
7.6	odd	2		6027.2.a.r.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.b.247.2	✓	6	7.3	odd	6
861.2.i.b.739.2	yes	6	7.5	odd	6
6027.2.a.r.1.2		3	7.6	odd	2
6027.2.a.t.1.2		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+0.812716 q^{2} +1.00000 q^{3} -1.33949 q^{4} +1.00000 q^{5} +0.812716 q^{6} -2.71406 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.812716 q^{2} +1.00000 q^{3} -1.33949 q^{4} +1.00000 q^{5} +0.812716 q^{6} -2.71406 q^{8} +1.00000 q^{9} +0.812716 q^{10} -5.15221 q^{11} -1.33949 q^{12} +2.18728 q^{13} +1.00000 q^{15} +0.473224 q^{16} -5.86627 q^{17} +0.812716 q^{18} -5.33949 q^{19} -1.33949 q^{20} -4.18728 q^{22} +7.49170 q^{23} -2.71406 q^{24} -4.00000 q^{25} +1.77764 q^{26} +1.00000 q^{27} -3.96492 q^{29} +0.812716 q^{30} +4.77764 q^{31} +5.81272 q^{32} -5.15221 q^{33} -4.76761 q^{34} -1.33949 q^{36} +9.96492 q^{37} -4.33949 q^{38} +2.18728 q^{39} -2.71406 q^{40} +1.00000 q^{41} +9.05355 q^{43} +6.90134 q^{44} +1.00000 q^{45} +6.08863 q^{46} +8.49170 q^{47} +0.473224 q^{48} -3.25087 q^{50} -5.86627 q^{51} -2.92985 q^{52} +7.52678 q^{53} +0.812716 q^{54} -5.15221 q^{55} -5.33949 q^{57} -3.22236 q^{58} -0.964925 q^{59} -1.33949 q^{60} +4.90134 q^{61} +3.88287 q^{62} +3.77764 q^{64} +2.18728 q^{65} -4.18728 q^{66} -2.47322 q^{67} +7.85782 q^{68} +7.49170 q^{69} +16.0536 q^{71} -2.71406 q^{72} +3.66051 q^{73} +8.09866 q^{74} -4.00000 q^{75} +7.15221 q^{76} +1.77764 q^{78} -12.1522 q^{79} +0.473224 q^{80} +1.00000 q^{81} +0.812716 q^{82} +15.2944 q^{83} -5.86627 q^{85} +7.35797 q^{86} -3.96492 q^{87} +13.9834 q^{88} +3.77764 q^{89} +0.812716 q^{90} -10.0351 q^{92} +4.77764 q^{93} +6.90134 q^{94} -5.33949 q^{95} +5.81272 q^{96} +7.87630 q^{97} -5.15221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + 7 q^{4} + 3 q^{5} + q^{6} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + 7 * q^4 + 3 * q^5 + q^6 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + 7 q^{4} + 3 q^{5} + q^{6} + 3 q^{9} + q^{10} - 3 q^{11} + 7 q^{12} + 8 q^{13} + 3 q^{15} + 11 q^{16} + 3 q^{17} + q^{18} - 5 q^{19} + 7 q^{20} - 14 q^{22} - q^{23} - 12 q^{25} - 10 q^{26} + 3 q^{27} + 2 q^{29} + q^{30} - q^{31} + 16 q^{32} - 3 q^{33} + 13 q^{34} + 7 q^{36} + 16 q^{37} - 2 q^{38} + 8 q^{39} + 3 q^{41} + 8 q^{43} + 14 q^{44} + 3 q^{45} + 13 q^{46} + 2 q^{47} + 11 q^{48} - 4 q^{50} + 3 q^{51} + 19 q^{52} + 13 q^{53} + q^{54} - 3 q^{55} - 5 q^{57} - 25 q^{58} + 11 q^{59} + 7 q^{60} + 8 q^{61} + 38 q^{62} - 4 q^{64} + 8 q^{65} - 14 q^{66} - 17 q^{67} + 48 q^{68} - q^{69} + 29 q^{71} + 22 q^{73} + 31 q^{74} - 12 q^{75} + 9 q^{76} - 10 q^{78} - 24 q^{79} + 11 q^{80} + 3 q^{81} + q^{82} + 9 q^{83} + 3 q^{85} - 22 q^{86} + 2 q^{87} - 5 q^{88} - 4 q^{89} + q^{90} - 44 q^{92} - q^{93} + 14 q^{94} - 5 q^{95} + 16 q^{96} + 15 q^{97} - 3 q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + 7 * q^4 + 3 * q^5 + q^6 + 3 * q^9 + q^10 - 3 * q^11 + 7 * q^12 + 8 * q^13 + 3 * q^15 + 11 * q^16 + 3 * q^17 + q^18 - 5 * q^19 + 7 * q^20 - 14 * q^22 - q^23 - 12 * q^25 - 10 * q^26 + 3 * q^27 + 2 * q^29 + q^30 - q^31 + 16 * q^32 - 3 * q^33 + 13 * q^34 + 7 * q^36 + 16 * q^37 - 2 * q^38 + 8 * q^39 + 3 * q^41 + 8 * q^43 + 14 * q^44 + 3 * q^45 + 13 * q^46 + 2 * q^47 + 11 * q^48 - 4 * q^50 + 3 * q^51 + 19 * q^52 + 13 * q^53 + q^54 - 3 * q^55 - 5 * q^57 - 25 * q^58 + 11 * q^59 + 7 * q^60 + 8 * q^61 + 38 * q^62 - 4 * q^64 + 8 * q^65 - 14 * q^66 - 17 * q^67 + 48 * q^68 - q^69 + 29 * q^71 + 22 * q^73 + 31 * q^74 - 12 * q^75 + 9 * q^76 - 10 * q^78 - 24 * q^79 + 11 * q^80 + 3 * q^81 + q^82 + 9 * q^83 + 3 * q^85 - 22 * q^86 + 2 * q^87 - 5 * q^88 - 4 * q^89 + q^90 - 44 * q^92 - q^93 + 14 * q^94 - 5 * q^95 + 16 * q^96 + 15 * q^97 - 3 * q^99

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