LMFDB - Embedded newform 6027.2.a.bc.1.6

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:	$8$
Coefficient field:	8.8.7457527933.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 $ x^8 - 3x^7 - 6x^6 + 23x^5 - 4x^4 - 27x^3 + 8x^2 + 8*x + 1
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			1.6
Root			$1.70821$ 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)

$f(q)$	$=$	$q+1.66803 q^{2} +1.00000 q^{3} +0.782321 q^{4} +4.32429 q^{5} +1.66803 q^{6} -2.03112 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.66803 q^{2} +1.00000 q^{3} +0.782321 q^{4} +4.32429 q^{5} +1.66803 q^{6} -2.03112 q^{8} +1.00000 q^{9} +7.21304 q^{10} +5.84934 q^{11} +0.782321 q^{12} +4.56081 q^{13} +4.32429 q^{15} -4.95262 q^{16} +1.48730 q^{17} +1.66803 q^{18} -7.25900 q^{19} +3.38298 q^{20} +9.75686 q^{22} +3.99375 q^{23} -2.03112 q^{24} +13.6995 q^{25} +7.60756 q^{26} +1.00000 q^{27} -3.99637 q^{29} +7.21304 q^{30} -3.33775 q^{31} -4.19886 q^{32} +5.84934 q^{33} +2.48086 q^{34} +0.782321 q^{36} +0.681013 q^{37} -12.1082 q^{38} +4.56081 q^{39} -8.78317 q^{40} +1.00000 q^{41} -7.66175 q^{43} +4.57606 q^{44} +4.32429 q^{45} +6.66169 q^{46} -6.16952 q^{47} -4.95262 q^{48} +22.8512 q^{50} +1.48730 q^{51} +3.56801 q^{52} -2.70607 q^{53} +1.66803 q^{54} +25.2942 q^{55} -7.25900 q^{57} -6.66606 q^{58} +0.715360 q^{59} +3.38298 q^{60} +3.33773 q^{61} -5.56747 q^{62} +2.90141 q^{64} +19.7223 q^{65} +9.75686 q^{66} -7.99827 q^{67} +1.16355 q^{68} +3.99375 q^{69} +7.51068 q^{71} -2.03112 q^{72} -0.453895 q^{73} +1.13595 q^{74} +13.6995 q^{75} -5.67887 q^{76} +7.60756 q^{78} -6.22766 q^{79} -21.4166 q^{80} +1.00000 q^{81} +1.66803 q^{82} -7.75509 q^{83} +6.43153 q^{85} -12.7800 q^{86} -3.99637 q^{87} -11.8807 q^{88} +14.2235 q^{89} +7.21304 q^{90} +3.12439 q^{92} -3.33775 q^{93} -10.2909 q^{94} -31.3900 q^{95} -4.19886 q^{96} -7.48789 q^{97} +5.84934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9} + 8 q^{10} + 11 q^{11} + 13 q^{12} + 10 q^{13} + 7 q^{15} - 17 q^{16} + 3 q^{17} + q^{18} + 6 q^{19} + 11 q^{20} + 15 q^{22} + 14 q^{23} + 6 q^{24} + 25 q^{25} + 24 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} + 3 q^{32} + 11 q^{33} - 4 q^{34} + 13 q^{36} - 20 q^{37} + 10 q^{38} + 10 q^{39} - 3 q^{40} + 8 q^{41} + 7 q^{43} + 7 q^{45} - 5 q^{46} + 14 q^{47} - 17 q^{48} - 5 q^{50} + 3 q^{51} + 23 q^{52} + 7 q^{53} + q^{54} + 48 q^{55} + 6 q^{57} - 20 q^{58} + 22 q^{59} + 11 q^{60} - 33 q^{62} - 10 q^{64} - 14 q^{65} + 15 q^{66} + 12 q^{67} - 27 q^{68} + 14 q^{69} - 5 q^{71} + 6 q^{72} + 2 q^{73} + 6 q^{74} + 25 q^{75} + 43 q^{76} + 24 q^{78} - 15 q^{79} - 7 q^{80} + 8 q^{81} + q^{82} + 15 q^{83} - 43 q^{85} + 31 q^{86} + 2 q^{87} + 17 q^{88} + 29 q^{89} + 8 q^{90} + 19 q^{92} + 16 q^{93} + 20 q^{94} + 14 q^{95} + 3 q^{96} + 19 q^{97} + 11 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9 + 8 * q^10 + 11 * q^11 + 13 * q^12 + 10 * q^13 + 7 * q^15 - 17 * q^16 + 3 * q^17 + q^18 + 6 * q^19 + 11 * q^20 + 15 * q^22 + 14 * q^23 + 6 * q^24 + 25 * q^25 + 24 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 + 3 * q^32 + 11 * q^33 - 4 * q^34 + 13 * q^36 - 20 * q^37 + 10 * q^38 + 10 * q^39 - 3 * q^40 + 8 * q^41 + 7 * q^43 + 7 * q^45 - 5 * q^46 + 14 * q^47 - 17 * q^48 - 5 * q^50 + 3 * q^51 + 23 * q^52 + 7 * q^53 + q^54 + 48 * q^55 + 6 * q^57 - 20 * q^58 + 22 * q^59 + 11 * q^60 - 33 * q^62 - 10 * q^64 - 14 * q^65 + 15 * q^66 + 12 * q^67 - 27 * q^68 + 14 * q^69 - 5 * q^71 + 6 * q^72 + 2 * q^73 + 6 * q^74 + 25 * q^75 + 43 * q^76 + 24 * q^78 - 15 * q^79 - 7 * q^80 + 8 * q^81 + q^82 + 15 * q^83 - 43 * q^85 + 31 * q^86 + 2 * q^87 + 17 * q^88 + 29 * q^89 + 8 * q^90 + 19 * q^92 + 16 * q^93 + 20 * q^94 + 14 * q^95 + 3 * q^96 + 19 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.66803	1.17947	0.589737	−	0.807595i	$-0.299231\pi$
$2$	1.66803	1.17947	0.589737	+	0.807595i	$0.299231\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.782321	0.391160
$5$	4.32429	1.93388	0.966941	−	0.255001i	$-0.0820757\pi$
$5$	4.32429	1.93388	0.966941	+	0.255001i	$0.0820757\pi$
$6$	1.66803	0.680970
$7$	0	0
$7$	0	0
$8$	−2.03112	−0.718111
$9$	1.00000	0.333333
$10$	7.21304	2.28096
$11$	5.84934	1.76364	0.881821	−	0.471585i	$-0.156318\pi$
$11$	5.84934	1.76364	0.881821	+	0.471585i	$0.156318\pi$
$12$	0.782321	0.225837
$13$	4.56081	1.26494	0.632470	−	0.774585i	$-0.282041\pi$
$13$	4.56081	1.26494	0.632470	+	0.774585i	$0.282041\pi$
$14$	0	0
$15$	4.32429	1.11653
$16$	−4.95262	−1.23815
$17$	1.48730	0.360724	0.180362	−	0.983600i	$-0.442273\pi$
$17$	1.48730	0.360724	0.180362	+	0.983600i	$0.442273\pi$
$18$	1.66803	0.393158
$19$	−7.25900	−1.66533	−0.832665	−	0.553778i	$-0.813186\pi$
$19$	−7.25900	−1.66533	−0.832665	+	0.553778i	$0.813186\pi$
$20$	3.38298	0.756458
$21$	0	0
$22$	9.75686	2.08017
$23$	3.99375	0.832754	0.416377	−	0.909192i	$-0.363300\pi$
$23$	3.99375	0.832754	0.416377	+	0.909192i	$0.363300\pi$
$24$	−2.03112	−0.414602
$25$	13.6995	2.73990
$26$	7.60756	1.49196
$27$	1.00000	0.192450
$28$	0	0
$29$	−3.99637	−0.742107	−0.371053	−	0.928612i	$-0.621003\pi$
$29$	−3.99637	−0.742107	−0.371053	+	0.928612i	$0.621003\pi$
$30$	7.21304	1.31692
$31$	−3.33775	−0.599478	−0.299739	−	0.954021i	$-0.596900\pi$
$31$	−3.33775	−0.599478	−0.299739	+	0.954021i	$0.596900\pi$
$32$	−4.19886	−0.742260
$33$	5.84934	1.01824
$34$	2.48086	0.425465
$35$	0	0
$36$	0.782321	0.130387
$37$	0.681013	0.111958	0.0559789	−	0.998432i	$-0.482172\pi$
$37$	0.681013	0.111958	0.0559789	+	0.998432i	$0.482172\pi$
$38$	−12.1082	−1.96421
$39$	4.56081	0.730313
$40$	−8.78317	−1.38874
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−7.66175	−1.16841	−0.584203	−	0.811607i	$-0.698593\pi$
$43$	−7.66175	−1.16841	−0.584203	+	0.811607i	$0.698593\pi$
$44$	4.57606	0.689867
$45$	4.32429	0.644627
$46$	6.66169	0.982213
$47$	−6.16952	−0.899917	−0.449958	−	0.893050i	$-0.648561\pi$
$47$	−6.16952	−0.899917	−0.449958	+	0.893050i	$0.648561\pi$
$48$	−4.95262	−0.714849
$49$	0	0
$50$	22.8512	3.23164
$51$	1.48730	0.208264
$52$	3.56801	0.494794
$53$	−2.70607	−0.371707	−0.185853	−	0.982577i	$-0.559505\pi$
$53$	−2.70607	−0.371707	−0.185853	+	0.982577i	$0.559505\pi$
$54$	1.66803	0.226990
$55$	25.2942	3.41067
$56$	0	0
$57$	−7.25900	−0.961478
$58$	−6.66606	−0.875296
$59$	0.715360	0.0931319	0.0465660	−	0.998915i	$-0.485172\pi$
$59$	0.715360	0.0931319	0.0465660	+	0.998915i	$0.485172\pi$
$60$	3.38298	0.436741
$61$	3.33773	0.427353	0.213677	−	0.976904i	$-0.431456\pi$
$61$	3.33773	0.427353	0.213677	+	0.976904i	$0.431456\pi$
$62$	−5.56747	−0.707069
$63$	0	0
$64$	2.90141	0.362677
$65$	19.7223	2.44624
$66$	9.75686	1.20099
$67$	−7.99827	−0.977145	−0.488572	−	0.872523i	$-0.662482\pi$
$67$	−7.99827	−0.977145	−0.488572	+	0.872523i	$0.662482\pi$
$68$	1.16355	0.141101
$69$	3.99375	0.480791
$70$	0	0
$71$	7.51068	0.891354	0.445677	−	0.895194i	$-0.352963\pi$
$71$	7.51068	0.891354	0.445677	+	0.895194i	$0.352963\pi$
$72$	−2.03112	−0.239370
$73$	−0.453895	−0.0531244	−0.0265622	−	0.999647i	$-0.508456\pi$
$73$	−0.453895	−0.0531244	−0.0265622	+	0.999647i	$0.508456\pi$
$74$	1.13595	0.132051
$75$	13.6995	1.58188
$76$	−5.67887	−0.651411
$77$	0	0
$78$	7.60756	0.861386
$79$	−6.22766	−0.700666	−0.350333	−	0.936625i	$-0.613932\pi$
$79$	−6.22766	−0.700666	−0.350333	+	0.936625i	$0.613932\pi$
$80$	−21.4166	−2.39444
$81$	1.00000	0.111111
$82$	1.66803	0.184203
$83$	−7.75509	−0.851232	−0.425616	−	0.904904i	$-0.639943\pi$
$83$	−7.75509	−0.851232	−0.425616	+	0.904904i	$0.639943\pi$
$84$	0	0
$85$	6.43153	0.697597
$86$	−12.7800	−1.37811
$87$	−3.99637	−0.428456
$88$	−11.8807	−1.26649
$89$	14.2235	1.50769	0.753846	−	0.657051i	$-0.228196\pi$
$89$	14.2235	1.50769	0.753846	+	0.657051i	$0.228196\pi$
$90$	7.21304	0.760321
$91$	0	0
$92$	3.12439	0.325740
$93$	−3.33775	−0.346109
$94$	−10.2909	−1.06143
$95$	−31.3900	−3.22055
$96$	−4.19886	−0.428544
$97$	−7.48789	−0.760280	−0.380140	−	0.924929i	$-0.624124\pi$
$97$	−7.48789	−0.760280	−0.380140	+	0.924929i	$0.624124\pi$
$98$	0	0
$99$	5.84934	0.587881
$100$	10.7174	1.07174
$101$	−12.1787	−1.21183	−0.605915	−	0.795529i	$-0.707193\pi$
$101$	−12.1787	−1.21183	−0.605915	+	0.795529i	$0.707193\pi$
$102$	2.48086	0.245642
$103$	11.2578	1.10926	0.554630	−	0.832097i	$-0.312860\pi$
$103$	11.2578	1.10926	0.554630	+	0.832097i	$0.312860\pi$
$104$	−9.26356	−0.908367
$105$	0	0
$106$	−4.51380	−0.438419
$107$	−16.9596	−1.63954	−0.819772	−	0.572691i	$-0.805900\pi$
$107$	−16.9596	−1.63954	−0.819772	+	0.572691i	$0.805900\pi$
$108$	0.782321	0.0752788
$109$	−15.8268	−1.51593	−0.757967	−	0.652293i	$-0.773807\pi$
$109$	−15.8268	−1.51593	−0.757967	+	0.652293i	$0.773807\pi$
$110$	42.1915	4.02280
$111$	0.681013	0.0646389
$112$	0	0
$113$	0.0411977	0.00387555	0.00193778	−	0.999998i	$-0.499383\pi$
$113$	0.0411977	0.00387555	0.00193778	+	0.999998i	$0.499383\pi$
$114$	−12.1082	−1.13404
$115$	17.2701	1.61045
$116$	−3.12644	−0.290283
$117$	4.56081	0.421647
$118$	1.19324	0.109847
$119$	0	0
$120$	−8.78317	−0.801790
$121$	23.2147	2.11043
$122$	5.56744	0.504052
$123$	1.00000	0.0901670
$124$	−2.61119	−0.234492
$125$	37.6191	3.36476
$126$	0	0
$127$	−6.47454	−0.574522	−0.287261	−	0.957852i	$-0.592745\pi$
$127$	−6.47454	−0.574522	−0.287261	+	0.957852i	$0.592745\pi$
$128$	13.2374	1.17003
$129$	−7.66175	−0.674580
$130$	32.8973	2.88528
$131$	−13.6986	−1.19685	−0.598425	−	0.801179i	$-0.704207\pi$
$131$	−13.6986	−1.19685	−0.598425	+	0.801179i	$0.704207\pi$
$132$	4.57606	0.398295
$133$	0	0
$134$	−13.3414	−1.15252
$135$	4.32429	0.372176
$136$	−3.02090	−0.259040
$137$	0.100390	0.00857690	0.00428845	−	0.999991i	$-0.498635\pi$
$137$	0.100390	0.00857690	0.00428845	+	0.999991i	$0.498635\pi$
$138$	6.66169	0.567081
$139$	14.5020	1.23005	0.615023	−	0.788509i	$-0.289147\pi$
$139$	14.5020	1.23005	0.615023	+	0.788509i	$0.289147\pi$
$140$	0	0
$141$	−6.16952	−0.519567
$142$	12.5280	1.05133
$143$	26.6777	2.23090
$144$	−4.95262	−0.412718
$145$	−17.2815	−1.43515
$146$	−0.757110	−0.0626589
$147$	0	0
$148$	0.532771	0.0437935
$149$	−6.42022	−0.525965	−0.262982	−	0.964801i	$-0.584706\pi$
$149$	−6.42022	−0.525965	−0.262982	+	0.964801i	$0.584706\pi$
$150$	22.8512	1.86579
$151$	−6.61736	−0.538513	−0.269256	−	0.963069i	$-0.586778\pi$
$151$	−6.61736	−0.538513	−0.269256	+	0.963069i	$0.586778\pi$
$152$	14.7439	1.19589
$153$	1.48730	0.120241
$154$	0	0
$155$	−14.4334	−1.15932
$156$	3.56801	0.285670
$157$	5.84014	0.466094	0.233047	−	0.972465i	$-0.425130\pi$
$157$	5.84014	0.466094	0.233047	+	0.972465i	$0.425130\pi$
$158$	−10.3879	−0.826418
$159$	−2.70607	−0.214605
$160$	−18.1571	−1.43544
$161$	0	0
$162$	1.66803	0.131053
$163$	13.2696	1.03935	0.519677	−	0.854363i	$-0.326052\pi$
$163$	13.2696	1.03935	0.519677	+	0.854363i	$0.326052\pi$
$164$	0.782321	0.0610890
$165$	25.2942	1.96915
$166$	−12.9357	−1.00401
$167$	−0.628977	−0.0486717	−0.0243359	−	0.999704i	$-0.507747\pi$
$167$	−0.628977	−0.0486717	−0.0243359	+	0.999704i	$0.507747\pi$
$168$	0	0
$169$	7.80095	0.600073
$170$	10.7280	0.822798
$171$	−7.25900	−0.555110
$172$	−5.99395	−0.457034
$173$	18.9619	1.44164	0.720822	−	0.693120i	$-0.243765\pi$
$173$	18.9619	1.44164	0.720822	+	0.693120i	$0.243765\pi$
$174$	−6.66606	−0.505352
$175$	0	0
$176$	−28.9695	−2.18366
$177$	0.715360	0.0537698
$178$	23.7253	1.77828
$179$	4.54253	0.339525	0.169762	−	0.985485i	$-0.445700\pi$
$179$	4.54253	0.339525	0.169762	+	0.985485i	$0.445700\pi$
$180$	3.38298	0.252153
$181$	15.5935	1.15905	0.579526	−	0.814954i	$-0.303238\pi$
$181$	15.5935	1.15905	0.579526	+	0.814954i	$0.303238\pi$
$182$	0	0
$183$	3.33773	0.246732
$184$	−8.11180	−0.598010
$185$	2.94490	0.216513
$186$	−5.56747	−0.408226
$187$	8.69974	0.636188
$188$	−4.82654	−0.352012
$189$	0	0
$190$	−52.3595	−3.79856
$191$	−9.20449	−0.666013	−0.333007	−	0.942924i	$-0.608063\pi$
$191$	−9.20449	−0.666013	−0.333007	+	0.942924i	$0.608063\pi$
$192$	2.90141	0.209392
$193$	18.1234	1.30455	0.652276	−	0.757982i	$-0.273814\pi$
$193$	18.1234	1.30455	0.652276	+	0.757982i	$0.273814\pi$
$194$	−12.4900	−0.896731
$195$	19.7223	1.41234
$196$	0	0
$197$	−22.1458	−1.57782	−0.788910	−	0.614509i	$-0.789354\pi$
$197$	−22.1458	−1.57782	−0.788910	+	0.614509i	$0.789354\pi$
$198$	9.75686	0.693390
$199$	18.5760	1.31682	0.658410	−	0.752660i	$-0.271229\pi$
$199$	18.5760	1.31682	0.658410	+	0.752660i	$0.271229\pi$
$200$	−27.8254	−1.96755
$201$	−7.99827	−0.564155
$202$	−20.3145	−1.42932
$203$	0	0
$204$	1.16355	0.0814646
$205$	4.32429	0.302022
$206$	18.7783	1.30834
$207$	3.99375	0.277585
$208$	−22.5879	−1.56619
$209$	−42.4604	−2.93704
$210$	0	0
$211$	−13.4151	−0.923531	−0.461765	−	0.887002i	$-0.652784\pi$
$211$	−13.4151	−0.923531	−0.461765	+	0.887002i	$0.652784\pi$
$212$	−2.11701	−0.145397
$213$	7.51068	0.514624
$214$	−28.2891	−1.93380
$215$	−33.1317	−2.25956
$216$	−2.03112	−0.138201
$217$	0	0
$218$	−26.3996	−1.78801
$219$	−0.453895	−0.0306714
$220$	19.7882	1.33412
$221$	6.78330	0.456294
$222$	1.13595	0.0762399
$223$	10.4122	0.697255	0.348627	−	0.937261i	$-0.386648\pi$
$223$	10.4122	0.697255	0.348627	+	0.937261i	$0.386648\pi$
$224$	0	0
$225$	13.6995	0.913299
$226$	0.0687189	0.00457111
$227$	10.5305	0.698934	0.349467	−	0.936949i	$-0.386363\pi$
$227$	10.5305	0.698934	0.349467	+	0.936949i	$0.386363\pi$
$228$	−5.67887	−0.376092
$229$	13.6437	0.901598	0.450799	−	0.892625i	$-0.351139\pi$
$229$	13.6437	0.901598	0.450799	+	0.892625i	$0.351139\pi$
$230$	28.8071	1.89948
$231$	0	0
$232$	8.11712	0.532915
$233$	15.9722	1.04637	0.523186	−	0.852219i	$-0.324743\pi$
$233$	15.9722	1.04637	0.523186	+	0.852219i	$0.324743\pi$
$234$	7.60756	0.497321
$235$	−26.6788	−1.74033
$236$	0.559641	0.0364295
$237$	−6.22766	−0.404530
$238$	0	0
$239$	−2.04562	−0.132320	−0.0661600	−	0.997809i	$-0.521075\pi$
$239$	−2.04562	−0.132320	−0.0661600	+	0.997809i	$0.521075\pi$
$240$	−21.4166	−1.38243
$241$	−23.6978	−1.52651	−0.763254	−	0.646099i	$-0.776400\pi$
$241$	−23.6978	−1.52651	−0.763254	+	0.646099i	$0.776400\pi$
$242$	38.7229	2.48920
$243$	1.00000	0.0641500
$244$	2.61118	0.167164
$245$	0	0
$246$	1.66803	0.106350
$247$	−33.1069	−2.10654
$248$	6.77939	0.430492
$249$	−7.75509	−0.491459
$250$	62.7498	3.96865
$251$	13.4627	0.849760	0.424880	−	0.905250i	$-0.360316\pi$
$251$	13.4627	0.849760	0.424880	+	0.905250i	$0.360316\pi$
$252$	0	0
$253$	23.3608	1.46868
$254$	−10.7997	−0.677634
$255$	6.43153	0.402758
$256$	16.2775	1.01734
$257$	−10.3493	−0.645569	−0.322785	−	0.946472i	$-0.604619\pi$
$257$	−10.3493	−0.645569	−0.322785	+	0.946472i	$0.604619\pi$
$258$	−12.7800	−0.795650
$259$	0	0
$260$	15.4291	0.956874
$261$	−3.99637	−0.247369
$262$	−22.8496	−1.41166
$263$	−0.788038	−0.0485925	−0.0242962	−	0.999705i	$-0.507734\pi$
$263$	−0.788038	−0.0485925	−0.0242962	+	0.999705i	$0.507734\pi$
$264$	−11.8807	−0.731208
$265$	−11.7018	−0.718837
$266$	0	0
$267$	14.2235	0.870467
$268$	−6.25722	−0.382220
$269$	−19.3210	−1.17802	−0.589010	−	0.808126i	$-0.700482\pi$
$269$	−19.3210	−1.17802	−0.589010	+	0.808126i	$0.700482\pi$
$270$	7.21304	0.438972
$271$	−16.0597	−0.975560	−0.487780	−	0.872966i	$-0.662193\pi$
$271$	−16.0597	−0.975560	−0.487780	+	0.872966i	$0.662193\pi$
$272$	−7.36604	−0.446632
$273$	0	0
$274$	0.167454	0.0101162
$275$	80.1330	4.83220
$276$	3.12439	0.188066
$277$	4.09759	0.246201	0.123100	−	0.992394i	$-0.460716\pi$
$277$	4.09759	0.246201	0.123100	+	0.992394i	$0.460716\pi$
$278$	24.1898	1.45081
$279$	−3.33775	−0.199826
$280$	0	0
$281$	8.67302	0.517389	0.258694	−	0.965959i	$-0.416708\pi$
$281$	8.67302	0.517389	0.258694	+	0.965959i	$0.416708\pi$
$282$	−10.2909	−0.612816
$283$	−15.3327	−0.911433	−0.455716	−	0.890125i	$-0.650617\pi$
$283$	−15.3327	−0.911433	−0.455716	+	0.890125i	$0.650617\pi$
$284$	5.87576	0.348662
$285$	−31.3900	−1.85939
$286$	44.4992	2.63129
$287$	0	0
$288$	−4.19886	−0.247420
$289$	−14.7879	−0.869878
$290$	−28.8260	−1.69272
$291$	−7.48789	−0.438948
$292$	−0.355091	−0.0207802
$293$	−0.0222887	−0.00130212	−0.000651059	−	1.00000i	$-0.500207\pi$
$293$	−0.0222887	−0.00130212	−0.000651059		1.00000i	$0.500207\pi$
$294$	0	0
$295$	3.09342	0.180106
$296$	−1.38322	−0.0803981
$297$	5.84934	0.339413
$298$	−10.7091	−0.620362
$299$	18.2147	1.05338
$300$	10.7174	0.618769
$301$	0	0
$302$	−11.0379	−0.635162
$303$	−12.1787	−0.699651
$304$	35.9510	2.06193
$305$	14.4333	0.826450
$306$	2.48086	0.141822
$307$	3.14402	0.179439	0.0897195	−	0.995967i	$-0.471403\pi$
$307$	3.14402	0.179439	0.0897195	+	0.995967i	$0.471403\pi$
$308$	0	0
$309$	11.2578	0.640431
$310$	−24.0753	−1.36739
$311$	−26.5894	−1.50774	−0.753872	−	0.657021i	$-0.771816\pi$
$311$	−26.5894	−1.50774	−0.753872	+	0.657021i	$0.771816\pi$
$312$	−9.26356	−0.524446
$313$	−6.25270	−0.353423	−0.176712	−	0.984263i	$-0.556546\pi$
$313$	−6.25270	−0.353423	−0.176712	+	0.984263i	$0.556546\pi$
$314$	9.74153	0.549746
$315$	0	0
$316$	−4.87203	−0.274073
$317$	22.0285	1.23724	0.618621	−	0.785689i	$-0.287691\pi$
$317$	22.0285	1.23724	0.618621	+	0.785689i	$0.287691\pi$
$318$	−4.51380	−0.253121
$319$	−23.3761	−1.30881
$320$	12.5466	0.701374
$321$	−16.9596	−0.946591
$322$	0	0
$323$	−10.7963	−0.600724
$324$	0.782321	0.0434623
$325$	62.4807	3.46581
$326$	22.1341	1.22589
$327$	−15.8268	−0.875225
$328$	−2.03112	−0.112150
$329$	0	0
$330$	42.1915	2.32257
$331$	31.0654	1.70751	0.853756	−	0.520674i	$-0.174319\pi$
$331$	31.0654	1.70751	0.853756	+	0.520674i	$0.174319\pi$
$332$	−6.06697	−0.332968
$333$	0.681013	0.0373193
$334$	−1.04915	−0.0574070
$335$	−34.5869	−1.88968
$336$	0	0
$337$	−20.5844	−1.12130	−0.560652	−	0.828052i	$-0.689449\pi$
$337$	−20.5844	−1.12130	−0.560652	+	0.828052i	$0.689449\pi$
$338$	13.0122	0.707771
$339$	0.0411977	0.00223755
$340$	5.03152	0.272872
$341$	−19.5236	−1.05726
$342$	−12.1082	−0.654738
$343$	0	0
$344$	15.5620	0.839045
$345$	17.2701	0.929793
$346$	31.6289	1.70038
$347$	−13.6978	−0.735336	−0.367668	−	0.929957i	$-0.619844\pi$
$347$	−13.6978	−0.735336	−0.367668	+	0.929957i	$0.619844\pi$
$348$	−3.12644	−0.167595
$349$	19.6067	1.04952	0.524761	−	0.851250i	$-0.324155\pi$
$349$	19.6067	1.04952	0.524761	+	0.851250i	$0.324155\pi$
$350$	0	0
$351$	4.56081	0.243438
$352$	−24.5605	−1.30908
$353$	6.16984	0.328387	0.164194	−	0.986428i	$-0.447498\pi$
$353$	6.16984	0.328387	0.164194	+	0.986428i	$0.447498\pi$
$354$	1.19324	0.0634201
$355$	32.4784	1.72377
$356$	11.1274	0.589749
$357$	0	0
$358$	7.57707	0.400461
$359$	−23.6085	−1.24601	−0.623003	−	0.782219i	$-0.714088\pi$
$359$	−23.6085	−1.24601	−0.623003	+	0.782219i	$0.714088\pi$
$360$	−8.78317	−0.462914
$361$	33.6931	1.77332
$362$	26.0103	1.36707
$363$	23.2147	1.21846
$364$	0	0
$365$	−1.96277	−0.102736
$366$	5.56744	0.291015
$367$	25.2440	1.31773	0.658864	−	0.752262i	$-0.271037\pi$
$367$	25.2440	1.31773	0.658864	+	0.752262i	$0.271037\pi$
$368$	−19.7795	−1.03108
$369$	1.00000	0.0520579
$370$	4.91218	0.255372
$371$	0	0
$372$	−2.61119	−0.135384
$373$	20.9243	1.08342	0.541708	−	0.840566i	$-0.317778\pi$
$373$	20.9243	1.08342	0.541708	+	0.840566i	$0.317778\pi$
$374$	14.5114	0.750367
$375$	37.6191	1.94264
$376$	12.5311	0.646240
$377$	−18.2267	−0.938720
$378$	0	0
$379$	−28.3554	−1.45652	−0.728261	−	0.685300i	$-0.759671\pi$
$379$	−28.3554	−1.45652	−0.728261	+	0.685300i	$0.759671\pi$
$380$	−24.5571	−1.25975
$381$	−6.47454	−0.331701
$382$	−15.3534	−0.785546
$383$	1.47971	0.0756094	0.0378047	−	0.999285i	$-0.487964\pi$
$383$	1.47971	0.0756094	0.0378047	+	0.999285i	$0.487964\pi$
$384$	13.2374	0.675516
$385$	0	0
$386$	30.2304	1.53869
$387$	−7.66175	−0.389469
$388$	−5.85793	−0.297391
$389$	13.4225	0.680549	0.340275	−	0.940326i	$-0.389480\pi$
$389$	13.4225	0.680549	0.340275	+	0.940326i	$0.389480\pi$
$390$	32.8973	1.66582
$391$	5.93991	0.300394
$392$	0	0
$393$	−13.6986	−0.691002
$394$	−36.9398	−1.86100
$395$	−26.9302	−1.35501
$396$	4.57606	0.229956
$397$	0.598620	0.0300439	0.0150219	−	0.999887i	$-0.495218\pi$
$397$	0.598620	0.0300439	0.0150219	+	0.999887i	$0.495218\pi$
$398$	30.9853	1.55315
$399$	0	0
$400$	−67.8483	−3.39242
$401$	−11.6312	−0.580835	−0.290418	−	0.956900i	$-0.593794\pi$
$401$	−11.6312	−0.580835	−0.290418	+	0.956900i	$0.593794\pi$
$402$	−13.3414	−0.665406
$403$	−15.2228	−0.758304
$404$	−9.52769	−0.474020
$405$	4.32429	0.214876
$406$	0	0
$407$	3.98347	0.197454
$408$	−3.02090	−0.149557
$409$	30.0222	1.48450	0.742250	−	0.670123i	$-0.233758\pi$
$409$	30.0222	1.48450	0.742250	+	0.670123i	$0.233758\pi$
$410$	7.21304	0.356227
$411$	0.100390	0.00495188
$412$	8.80717	0.433898
$413$	0	0
$414$	6.66169	0.327404
$415$	−33.5353	−1.64618
$416$	−19.1502	−0.938915
$417$	14.5020	0.710167
$418$	−70.8251	−3.46417
$419$	8.22375	0.401756	0.200878	−	0.979616i	$-0.435620\pi$
$419$	8.22375	0.401756	0.200878	+	0.979616i	$0.435620\pi$
$420$	0	0
$421$	−0.696747	−0.0339574	−0.0169787	−	0.999856i	$-0.505405\pi$
$421$	−0.696747	−0.0339574	−0.0169787	+	0.999856i	$0.505405\pi$
$422$	−22.3767	−1.08928
$423$	−6.16952	−0.299972
$424$	5.49636	0.266927
$425$	20.3753	0.988347
$426$	12.5280	0.606985
$427$	0	0
$428$	−13.2678	−0.641324
$429$	26.6777	1.28801
$430$	−55.2646	−2.66509
$431$	−27.0930	−1.30502	−0.652512	−	0.757779i	$-0.726285\pi$
$431$	−27.0930	−1.30502	−0.652512	+	0.757779i	$0.726285\pi$
$432$	−4.95262	−0.238283
$433$	15.1891	0.729943	0.364972	−	0.931019i	$-0.381079\pi$
$433$	15.1891	0.729943	0.364972	+	0.931019i	$0.381079\pi$
$434$	0	0
$435$	−17.2815	−0.828582
$436$	−12.3816	−0.592973
$437$	−28.9906	−1.38681
$438$	−0.757110	−0.0361761
$439$	26.1419	1.24769	0.623843	−	0.781550i	$-0.285570\pi$
$439$	26.1419	1.24769	0.623843	+	0.781550i	$0.285570\pi$
$440$	−51.3757	−2.44924
$441$	0	0
$442$	11.3147	0.538187
$443$	−2.63221	−0.125060	−0.0625300	−	0.998043i	$-0.519917\pi$
$443$	−2.63221	−0.125060	−0.0625300	+	0.998043i	$0.519917\pi$
$444$	0.532771	0.0252842
$445$	61.5067	2.91570
$446$	17.3679	0.822394
$447$	−6.42022	−0.303666
$448$	0	0
$449$	−10.7630	−0.507935	−0.253968	−	0.967213i	$-0.581736\pi$
$449$	−10.7630	−0.507935	−0.253968	+	0.967213i	$0.581736\pi$
$450$	22.8512	1.07721
$451$	5.84934	0.275435
$452$	0.0322298	0.00151596
$453$	−6.61736	−0.310911
$454$	17.5652	0.824375
$455$	0	0
$456$	14.7439	0.690448
$457$	−12.8296	−0.600143	−0.300071	−	0.953917i	$-0.597011\pi$
$457$	−12.8296	−0.600143	−0.300071	+	0.953917i	$0.597011\pi$
$458$	22.7580	1.06341
$459$	1.48730	0.0694213
$460$	13.5108	0.629944
$461$	−32.7222	−1.52403	−0.762013	−	0.647562i	$-0.775789\pi$
$461$	−32.7222	−1.52403	−0.762013	+	0.647562i	$0.775789\pi$
$462$	0	0
$463$	−1.48288	−0.0689155	−0.0344577	−	0.999406i	$-0.510970\pi$
$463$	−1.48288	−0.0689155	−0.0344577	+	0.999406i	$0.510970\pi$
$464$	19.7925	0.918842
$465$	−14.4334	−0.669333
$466$	26.6420	1.23417
$467$	22.6643	1.04878	0.524390	−	0.851478i	$-0.324293\pi$
$467$	22.6643	1.04878	0.524390	+	0.851478i	$0.324293\pi$
$468$	3.56801	0.164931
$469$	0	0
$470$	−44.5010	−2.05268
$471$	5.84014	0.269100
$472$	−1.45299	−0.0668791
$473$	−44.8162	−2.06065
$474$	−10.3879	−0.477133
$475$	−99.4446	−4.56283
$476$	0	0
$477$	−2.70607	−0.123902
$478$	−3.41215	−0.156068
$479$	−11.8541	−0.541628	−0.270814	−	0.962632i	$-0.587293\pi$
$479$	−11.8541	−0.541628	−0.270814	+	0.962632i	$0.587293\pi$
$480$	−18.1571	−0.828754
$481$	3.10597	0.141620
$482$	−39.5286	−1.80048
$483$	0	0
$484$	18.1614	0.825517
$485$	−32.3798	−1.47029
$486$	1.66803	0.0756633
$487$	−35.4706	−1.60732	−0.803662	−	0.595086i	$-0.797118\pi$
$487$	−35.4706	−1.60732	−0.803662	+	0.595086i	$0.797118\pi$
$488$	−6.77935	−0.306887
$489$	13.2696	0.600072
$490$	0	0
$491$	−2.57948	−0.116410	−0.0582052	−	0.998305i	$-0.518538\pi$
$491$	−2.57948	−0.116410	−0.0582052	+	0.998305i	$0.518538\pi$
$492$	0.782321	0.0352697
$493$	−5.94381	−0.267696
$494$	−55.2233	−2.48461
$495$	25.2942	1.13689
$496$	16.5306	0.742246
$497$	0	0
$498$	−12.9357	−0.579663
$499$	15.4774	0.692863	0.346432	−	0.938075i	$-0.387393\pi$
$499$	15.4774	0.692863	0.346432	+	0.938075i	$0.387393\pi$
$500$	29.4302	1.31616
$501$	−0.628977	−0.0281006
$502$	22.4562	1.00227
$503$	5.92655	0.264252	0.132126	−	0.991233i	$-0.457820\pi$
$503$	5.92655	0.264252	0.132126	+	0.991233i	$0.457820\pi$
$504$	0	0
$505$	−52.6644	−2.34354
$506$	38.9665	1.73227
$507$	7.80095	0.346452
$508$	−5.06516	−0.224730
$509$	−32.1538	−1.42519	−0.712597	−	0.701573i	$-0.752481\pi$
$509$	−32.1538	−1.42519	−0.712597	+	0.701573i	$0.752481\pi$
$510$	10.7280	0.475043
$511$	0	0
$512$	0.676573	0.0299006
$513$	−7.25900	−0.320493
$514$	−17.2629	−0.761432
$515$	48.6818	2.14518
$516$	−5.99395	−0.263869
$517$	−36.0876	−1.58713
$518$	0	0
$519$	18.9619	0.832334
$520$	−40.0583	−1.75667
$521$	4.96065	0.217330	0.108665	−	0.994078i	$-0.465342\pi$
$521$	4.96065	0.217330	0.108665	+	0.994078i	$0.465342\pi$
$522$	−6.66606	−0.291765
$523$	17.8989	0.782664	0.391332	−	0.920250i	$-0.372014\pi$
$523$	17.8989	0.782664	0.391332	+	0.920250i	$0.372014\pi$
$524$	−10.7167	−0.468161
$525$	0	0
$526$	−1.31447	−0.0573136
$527$	−4.96425	−0.216246
$528$	−28.9695	−1.26074
$529$	−7.04997	−0.306520
$530$	−19.5190	−0.847850
$531$	0.715360	0.0310440
$532$	0	0
$533$	4.56081	0.197550
$534$	23.7253	1.02669
$535$	−73.3381	−3.17068
$536$	16.2455	0.701698
$537$	4.54253	0.196025
$538$	−32.2279	−1.38945
$539$	0	0
$540$	3.38298	0.145580
$541$	31.0548	1.33515	0.667576	−	0.744542i	$-0.267332\pi$
$541$	31.0548	1.33515	0.667576	+	0.744542i	$0.267332\pi$
$542$	−26.7881	−1.15065
$543$	15.5935	0.669179
$544$	−6.24497	−0.267751
$545$	−68.4398	−2.93164
$546$	0	0
$547$	−14.2599	−0.609709	−0.304854	−	0.952399i	$-0.598608\pi$
$547$	−14.2599	−0.609709	−0.304854	+	0.952399i	$0.598608\pi$
$548$	0.0785372	0.00335494
$549$	3.33773	0.142451
$550$	133.664	5.69946
$551$	29.0096	1.23585
$552$	−8.11180	−0.345261
$553$	0	0
$554$	6.83490	0.290387
$555$	2.94490	0.125004
$556$	11.3452	0.481145
$557$	−22.0405	−0.933885	−0.466942	−	0.884288i	$-0.654644\pi$
$557$	−22.0405	−0.933885	−0.466942	+	0.884288i	$0.654644\pi$
$558$	−5.56747	−0.235690
$559$	−34.9438	−1.47796
$560$	0	0
$561$	8.69974	0.367303
$562$	14.4668	0.610247
$563$	−31.1001	−1.31071	−0.655356	−	0.755320i	$-0.727481\pi$
$563$	−31.1001	−1.31071	−0.655356	+	0.755320i	$0.727481\pi$
$564$	−4.82654	−0.203234
$565$	0.178151	0.00749486
$566$	−25.5753	−1.07501
$567$	0	0
$568$	−15.2551	−0.640091
$569$	8.53952	0.357995	0.178998	−	0.983849i	$-0.442715\pi$
$569$	8.53952	0.357995	0.178998	+	0.983849i	$0.442715\pi$
$570$	−52.3595	−2.19310
$571$	−0.459320	−0.0192220	−0.00961098	−	0.999954i	$-0.503059\pi$
$571$	−0.459320	−0.0192220	−0.00961098	+	0.999954i	$0.503059\pi$
$572$	20.8705	0.872640
$573$	−9.20449	−0.384523
$574$	0	0
$575$	54.7123	2.28166
$576$	2.90141	0.120892
$577$	−25.7043	−1.07008	−0.535042	−	0.844825i	$-0.679704\pi$
$577$	−25.7043	−1.07008	−0.535042	+	0.844825i	$0.679704\pi$
$578$	−24.6667	−1.02600
$579$	18.1234	0.753183
$580$	−13.5196	−0.561372
$581$	0	0
$582$	−12.4900	−0.517728
$583$	−15.8287	−0.655558
$584$	0.921917	0.0381492
$585$	19.7223	0.815415
$586$	−0.0371782	−0.00153582
$587$	28.9538	1.19505	0.597526	−	0.801849i	$-0.296150\pi$
$587$	28.9538	1.19505	0.597526	+	0.801849i	$0.296150\pi$
$588$	0	0
$589$	24.2287	0.998328
$590$	5.15992	0.212431
$591$	−22.1458	−0.910955
$592$	−3.37280	−0.138621
$593$	−3.54980	−0.145773	−0.0728865	−	0.997340i	$-0.523221\pi$
$593$	−3.54980	−0.145773	−0.0728865	+	0.997340i	$0.523221\pi$
$594$	9.75686	0.400329
$595$	0	0
$596$	−5.02267	−0.205736
$597$	18.5760	0.760266
$598$	30.3827	1.24244
$599$	25.4327	1.03915	0.519576	−	0.854424i	$-0.326090\pi$
$599$	25.4327	1.03915	0.519576	+	0.854424i	$0.326090\pi$
$600$	−27.8254	−1.13597
$601$	32.6848	1.33324	0.666621	−	0.745397i	$-0.267740\pi$
$601$	32.6848	1.33324	0.666621	+	0.745397i	$0.267740\pi$
$602$	0	0
$603$	−7.99827	−0.325715
$604$	−5.17690	−0.210645
$605$	100.387	4.08133
$606$	−20.3145	−0.825220
$607$	23.9828	0.973432	0.486716	−	0.873560i	$-0.338195\pi$
$607$	23.9828	0.973432	0.486716	+	0.873560i	$0.338195\pi$
$608$	30.4795	1.23611
$609$	0	0
$610$	24.0752	0.974777
$611$	−28.1380	−1.13834
$612$	1.16355	0.0470336
$613$	−38.2382	−1.54442	−0.772212	−	0.635364i	$-0.780850\pi$
$613$	−38.2382	−1.54442	−0.772212	+	0.635364i	$0.780850\pi$
$614$	5.24432	0.211644
$615$	4.32429	0.174372
$616$	0	0
$617$	−4.29122	−0.172758	−0.0863790	−	0.996262i	$-0.527530\pi$
$617$	−4.29122	−0.172758	−0.0863790	+	0.996262i	$0.527530\pi$
$618$	18.7783	0.755372
$619$	−20.2026	−0.812009	−0.406005	−	0.913871i	$-0.633078\pi$
$619$	−20.2026	−0.812009	−0.406005	+	0.913871i	$0.633078\pi$
$620$	−11.2916	−0.453480
$621$	3.99375	0.160264
$622$	−44.3518	−1.77835
$623$	0	0
$624$	−22.5879	−0.904240
$625$	94.1786	3.76715
$626$	−10.4297	−0.416854
$627$	−42.4604	−1.69570
$628$	4.56886	0.182318
$629$	1.01287	0.0403859
$630$	0	0
$631$	33.0298	1.31490	0.657448	−	0.753500i	$-0.271636\pi$
$631$	33.0298	1.31490	0.657448	+	0.753500i	$0.271636\pi$
$632$	12.6491	0.503156
$633$	−13.4151	−0.533201
$634$	36.7441	1.45930
$635$	−27.9978	−1.11106
$636$	−2.11701	−0.0839450
$637$	0	0
$638$	−38.9920	−1.54371
$639$	7.51068	0.297118
$640$	57.2422	2.26270
$641$	−21.8364	−0.862487	−0.431243	−	0.902236i	$-0.641925\pi$
$641$	−21.8364	−0.862487	−0.431243	+	0.902236i	$0.641925\pi$
$642$	−28.2891	−1.11648
$643$	22.4974	0.887209	0.443605	−	0.896223i	$-0.353699\pi$
$643$	22.4974	0.887209	0.443605	+	0.896223i	$0.353699\pi$
$644$	0	0
$645$	−33.1317	−1.30456
$646$	−18.0086	−0.708539
$647$	−13.4779	−0.529871	−0.264936	−	0.964266i	$-0.585351\pi$
$647$	−13.4779	−0.529871	−0.264936	+	0.964266i	$0.585351\pi$
$648$	−2.03112	−0.0797901
$649$	4.18438	0.164251
$650$	104.220	4.08783
$651$	0	0
$652$	10.3811	0.406554
$653$	−36.2358	−1.41802	−0.709008	−	0.705200i	$-0.750857\pi$
$653$	−36.2358	−1.41802	−0.709008	+	0.705200i	$0.750857\pi$
$654$	−26.3996	−1.03231
$655$	−59.2367	−2.31457
$656$	−4.95262	−0.193367
$657$	−0.453895	−0.0177081
$658$	0	0
$659$	−10.3387	−0.402737	−0.201369	−	0.979516i	$-0.564539\pi$
$659$	−10.3387	−0.402737	−0.201369	+	0.979516i	$0.564539\pi$
$660$	19.7882	0.770255
$661$	26.6528	1.03667	0.518337	−	0.855177i	$-0.326551\pi$
$661$	26.6528	1.03667	0.518337	+	0.855177i	$0.326551\pi$
$662$	51.8181	2.01397
$663$	6.78330	0.263441
$664$	15.7516	0.611279
$665$	0	0
$666$	1.13595	0.0440171
$667$	−15.9605	−0.617993
$668$	−0.492062	−0.0190384
$669$	10.4122	0.402560
$670$	−57.6919	−2.22883
$671$	19.5235	0.753698
$672$	0	0
$673$	1.94492	0.0749711	0.0374856	−	0.999297i	$-0.488065\pi$
$673$	1.94492	0.0749711	0.0374856	+	0.999297i	$0.488065\pi$
$674$	−34.3354	−1.32255
$675$	13.6995	0.527294
$676$	6.10284	0.234725
$677$	16.1164	0.619402	0.309701	−	0.950834i	$-0.399771\pi$
$677$	16.1164	0.619402	0.309701	+	0.950834i	$0.399771\pi$
$678$	0.0687189	0.00263913
$679$	0	0
$680$	−13.0632	−0.500952
$681$	10.5305	0.403530
$682$	−32.5660	−1.24702
$683$	32.2129	1.23259	0.616295	−	0.787515i	$-0.288633\pi$
$683$	32.2129	1.23259	0.616295	+	0.787515i	$0.288633\pi$
$684$	−5.67887	−0.217137
$685$	0.434116	0.0165867
$686$	0	0
$687$	13.6437	0.520538
$688$	37.9457	1.44667
$689$	−12.3418	−0.470187
$690$	28.8071	1.09667
$691$	−15.9137	−0.605384	−0.302692	−	0.953088i	$-0.597885\pi$
$691$	−15.9137	−0.605384	−0.302692	+	0.953088i	$0.597885\pi$
$692$	14.8343	0.563914
$693$	0	0
$694$	−22.8483	−0.867310
$695$	62.7110	2.37876
$696$	8.11712	0.307679
$697$	1.48730	0.0563356
$698$	32.7045	1.23788
$699$	15.9722	0.604123
$700$	0	0
$701$	7.53082	0.284435	0.142218	−	0.989835i	$-0.454577\pi$
$701$	7.53082	0.284435	0.142218	+	0.989835i	$0.454577\pi$
$702$	7.60756	0.287129
$703$	−4.94347	−0.186447
$704$	16.9714	0.639632
$705$	−26.6788	−1.00478
$706$	10.2915	0.387325
$707$	0	0
$708$	0.559641	0.0210326
$709$	3.97882	0.149428	0.0747138	−	0.997205i	$-0.476196\pi$
$709$	3.97882	0.149428	0.0747138	+	0.997205i	$0.476196\pi$
$710$	54.1749	2.03315
$711$	−6.22766	−0.233555
$712$	−28.8898	−1.08269
$713$	−13.3301	−0.499218
$714$	0	0
$715$	115.362	4.31430
$716$	3.55372	0.132809
$717$	−2.04562	−0.0763950
$718$	−39.3796	−1.46963
$719$	−34.2235	−1.27632	−0.638161	−	0.769903i	$-0.720305\pi$
$719$	−34.2235	−1.27632	−0.638161	+	0.769903i	$0.720305\pi$
$720$	−21.4166	−0.798148
$721$	0	0
$722$	56.2011	2.09159
$723$	−23.6978	−0.881330
$724$	12.1991	0.453375
$725$	−54.7482	−2.03330
$726$	38.7229	1.43714
$727$	−28.3533	−1.05156	−0.525782	−	0.850619i	$-0.676227\pi$
$727$	−28.3533	−1.05156	−0.525782	+	0.850619i	$0.676227\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−3.27396	−0.121175
$731$	−11.3953	−0.421472
$732$	2.61118	0.0965120
$733$	21.1863	0.782532	0.391266	−	0.920278i	$-0.372037\pi$
$733$	21.1863	0.782532	0.391266	+	0.920278i	$0.372037\pi$
$734$	42.1078	1.55423
$735$	0	0
$736$	−16.7692	−0.618120
$737$	−46.7846	−1.72333
$738$	1.66803	0.0614010
$739$	5.01966	0.184651	0.0923257	−	0.995729i	$-0.470570\pi$
$739$	5.01966	0.184651	0.0923257	+	0.995729i	$0.470570\pi$
$740$	2.30385	0.0846914
$741$	−33.1069	−1.21621
$742$	0	0
$743$	5.80215	0.212860	0.106430	−	0.994320i	$-0.466058\pi$
$743$	5.80215	0.212860	0.106430	+	0.994320i	$0.466058\pi$
$744$	6.77939	0.248544
$745$	−27.7629	−1.01715
$746$	34.9023	1.27786
$747$	−7.75509	−0.283744
$748$	6.80598	0.248851
$749$	0	0
$750$	62.7498	2.29130
$751$	−4.60198	−0.167929	−0.0839643	−	0.996469i	$-0.526758\pi$
$751$	−4.60198	−0.167929	−0.0839643	+	0.996469i	$0.526758\pi$
$752$	30.5552	1.11424
$753$	13.4627	0.490609
$754$	−30.4026	−1.10720
$755$	−28.6154	−1.04142
$756$	0	0
$757$	−9.87582	−0.358943	−0.179471	−	0.983763i	$-0.557439\pi$
$757$	−9.87582	−0.358943	−0.179471	+	0.983763i	$0.557439\pi$
$758$	−47.2977	−1.71793
$759$	23.3608	0.847943
$760$	63.7571	2.31271
$761$	19.2921	0.699339	0.349670	−	0.936873i	$-0.386294\pi$
$761$	19.2921	0.699339	0.349670	+	0.936873i	$0.386294\pi$
$762$	−10.7997	−0.391232
$763$	0	0
$764$	−7.20086	−0.260518
$765$	6.43153	0.232532
$766$	2.46819	0.0891794
$767$	3.26262	0.117806
$768$	16.2775	0.587363
$769$	−25.6251	−0.924066	−0.462033	−	0.886863i	$-0.652880\pi$
$769$	−25.6251	−0.924066	−0.462033	+	0.886863i	$0.652880\pi$
$770$	0	0
$771$	−10.3493	−0.372719
$772$	14.1783	0.510289
$773$	−16.4298	−0.590938	−0.295469	−	0.955352i	$-0.595476\pi$
$773$	−16.4298	−0.590938	−0.295469	+	0.955352i	$0.595476\pi$
$774$	−12.7800	−0.459369
$775$	−45.7255	−1.64251
$776$	15.2088	0.545965
$777$	0	0
$778$	22.3892	0.802691
$779$	−7.25900	−0.260081
$780$	15.4291	0.552451
$781$	43.9325	1.57203
$782$	9.90795	0.354308
$783$	−3.99637	−0.142819
$784$	0	0
$785$	25.2545	0.901371
$786$	−22.8496	−0.815019
$787$	4.68820	0.167116	0.0835582	−	0.996503i	$-0.473372\pi$
$787$	4.68820	0.167116	0.0835582	+	0.996503i	$0.473372\pi$
$788$	−17.3251	−0.617181
$789$	−0.788038	−0.0280549
$790$	−44.9204	−1.59820
$791$	0	0
$792$	−11.8807	−0.422163
$793$	15.2228	0.540576
$794$	0.998516	0.0354360
$795$	−11.7018	−0.415021
$796$	14.5324	0.515087
$797$	5.03067	0.178196	0.0890978	−	0.996023i	$-0.471602\pi$
$797$	5.03067	0.178196	0.0890978	+	0.996023i	$0.471602\pi$
$798$	0	0
$799$	−9.17594	−0.324621
$800$	−57.5222	−2.03372
$801$	14.2235	0.502564
$802$	−19.4012	−0.685081
$803$	−2.65499	−0.0936924
$804$	−6.25722	−0.220675
$805$	0	0
$806$	−25.3921	−0.894400
$807$	−19.3210	−0.680131
$808$	24.7365	0.870229
$809$	0.167803	0.00589965	0.00294982	−	0.999996i	$-0.499061\pi$
$809$	0.167803	0.00589965	0.00294982	+	0.999996i	$0.499061\pi$
$810$	7.21304	0.253440
$811$	−47.1839	−1.65685	−0.828426	−	0.560098i	$-0.810763\pi$
$811$	−47.1839	−1.65685	−0.828426	+	0.560098i	$0.810763\pi$
$812$	0	0
$813$	−16.0597	−0.563240
$814$	6.64455	0.232891
$815$	57.3816	2.00999
$816$	−7.36604	−0.257863
$817$	55.6167	1.94578
$818$	50.0779	1.75093
$819$	0	0
$820$	3.38298	0.118139
$821$	26.6236	0.929169	0.464585	−	0.885529i	$-0.346204\pi$
$821$	26.6236	0.929169	0.464585	+	0.885529i	$0.346204\pi$
$822$	0.167454	0.00584061
$823$	−17.5847	−0.612964	−0.306482	−	0.951876i	$-0.599152\pi$
$823$	−17.5847	−0.612964	−0.306482	+	0.951876i	$0.599152\pi$
$824$	−22.8659	−0.796571
$825$	80.1330	2.78987
$826$	0	0
$827$	21.5130	0.748082	0.374041	−	0.927412i	$-0.377972\pi$
$827$	21.5130	0.748082	0.374041	+	0.927412i	$0.377972\pi$
$828$	3.12439	0.108580
$829$	29.8147	1.03551	0.517754	−	0.855529i	$-0.326768\pi$
$829$	29.8147	1.03551	0.517754	+	0.855529i	$0.326768\pi$
$830$	−55.9378	−1.94163
$831$	4.09759	0.142144
$832$	13.2328	0.458764
$833$	0	0
$834$	24.1898	0.837625
$835$	−2.71988	−0.0941253
$836$	−33.2176	−1.14886
$837$	−3.33775	−0.115370
$838$	13.7174	0.473861
$839$	12.9236	0.446171	0.223085	−	0.974799i	$-0.428387\pi$
$839$	12.9236	0.446171	0.223085	+	0.974799i	$0.428387\pi$
$840$	0	0
$841$	−13.0291	−0.449278
$842$	−1.16219	−0.0400519
$843$	8.67302	0.298715
$844$	−10.4949	−0.361249
$845$	33.7336	1.16047
$846$	−10.2909	−0.353810
$847$	0	0
$848$	13.4021	0.460230
$849$	−15.3327	−0.526216
$850$	33.9866	1.16573
$851$	2.71980	0.0932334
$852$	5.87576	0.201300
$853$	−5.26193	−0.180165	−0.0900824	−	0.995934i	$-0.528713\pi$
$853$	−5.26193	−0.180165	−0.0900824	+	0.995934i	$0.528713\pi$
$854$	0	0
$855$	−31.3900	−1.07352
$856$	34.4470	1.17737
$857$	−36.4007	−1.24342	−0.621712	−	0.783246i	$-0.713563\pi$
$857$	−36.4007	−1.24342	−0.621712	+	0.783246i	$0.713563\pi$
$858$	44.4992	1.51918
$859$	7.06055	0.240903	0.120451	−	0.992719i	$-0.461566\pi$
$859$	7.06055	0.240903	0.120451	+	0.992719i	$0.461566\pi$
$860$	−25.9196	−0.883850
$861$	0	0
$862$	−45.1919	−1.53924
$863$	18.9497	0.645054	0.322527	−	0.946560i	$-0.395468\pi$
$863$	18.9497	0.645054	0.322527	+	0.946560i	$0.395468\pi$
$864$	−4.19886	−0.142848
$865$	81.9966	2.78797
$866$	25.3359	0.860950
$867$	−14.7879	−0.502224
$868$	0	0
$869$	−36.4277	−1.23572
$870$	−28.8260	−0.977292
$871$	−36.4786	−1.23603
$872$	32.1462	1.08861
$873$	−7.48789	−0.253427
$874$	−48.3572	−1.63571
$875$	0	0
$876$	−0.355091	−0.0119974
$877$	−35.6780	−1.20476	−0.602380	−	0.798209i	$-0.705781\pi$
$877$	−35.6780	−1.20476	−0.602380	+	0.798209i	$0.705781\pi$
$878$	43.6055	1.47161
$879$	−0.0222887	−0.000751778 0
$880$	−125.273	−4.22294
$881$	15.4830	0.521635	0.260818	−	0.965388i	$-0.416008\pi$
$881$	15.4830	0.521635	0.260818	+	0.965388i	$0.416008\pi$
$882$	0	0
$883$	−45.3288	−1.52543	−0.762717	−	0.646732i	$-0.776135\pi$
$883$	−45.3288	−1.52543	−0.762717	+	0.646732i	$0.776135\pi$
$884$	5.30671	0.178484
$885$	3.09342	0.103984
$886$	−4.39060	−0.147505
$887$	50.8827	1.70847	0.854237	−	0.519884i	$-0.174025\pi$
$887$	50.8827	1.70847	0.854237	+	0.519884i	$0.174025\pi$
$888$	−1.38322	−0.0464179
$889$	0	0
$890$	102.595	3.43899
$891$	5.84934	0.195960
$892$	8.14571	0.272738
$893$	44.7845	1.49866
$894$	−10.7091	−0.358166
$895$	19.6432	0.656601
$896$	0	0
$897$	18.2147	0.608172
$898$	−17.9529	−0.599097
$899$	13.3389	0.444877
$900$	10.7174	0.357247
$901$	−4.02474	−0.134084
$902$	9.75686	0.324868
$903$	0	0
$904$	−0.0836776	−0.00278308
$905$	67.4307	2.24147
$906$	−11.0379	−0.366711
$907$	−32.7943	−1.08892	−0.544458	−	0.838788i	$-0.683265\pi$
$907$	−32.7943	−1.08892	−0.544458	+	0.838788i	$0.683265\pi$
$908$	8.23823	0.273395
$909$	−12.1787	−0.403944
$910$	0	0
$911$	24.4758	0.810920	0.405460	−	0.914113i	$-0.367111\pi$
$911$	24.4758	0.810920	0.405460	+	0.914113i	$0.367111\pi$
$912$	35.9510	1.19046
$913$	−45.3622	−1.50127
$914$	−21.4001	−0.707853
$915$	14.4333	0.477151
$916$	10.6737	0.352669
$917$	0	0
$918$	2.48086	0.0818807
$919$	−5.45846	−0.180058	−0.0900289	−	0.995939i	$-0.528696\pi$
$919$	−5.45846	−0.180058	−0.0900289	+	0.995939i	$0.528696\pi$
$920$	−35.0778	−1.15648
$921$	3.14402	0.103599
$922$	−54.5816	−1.79755
$923$	34.2548	1.12751
$924$	0	0
$925$	9.32953	0.306753
$926$	−2.47349	−0.0812841
$927$	11.2578	0.369753
$928$	16.7802	0.550836
$929$	−38.6111	−1.26679	−0.633395	−	0.773829i	$-0.718339\pi$
$929$	−38.6111	−1.26679	−0.633395	+	0.773829i	$0.718339\pi$
$930$	−24.0753	−0.789462
$931$	0	0
$932$	12.4954	0.409299
$933$	−26.5894	−0.870496
$934$	37.8048	1.23701
$935$	37.6202	1.23031
$936$	−9.26356	−0.302789
$937$	−7.88640	−0.257638	−0.128819	−	0.991668i	$-0.541119\pi$
$937$	−7.88640	−0.257638	−0.128819	+	0.991668i	$0.541119\pi$
$938$	0	0
$939$	−6.25270	−0.204049
$940$	−20.8714	−0.680749
$941$	−0.520002	−0.0169516	−0.00847579	−	0.999964i	$-0.502698\pi$
$941$	−0.520002	−0.0169516	−0.00847579	+	0.999964i	$0.502698\pi$
$942$	9.74153	0.317396
$943$	3.99375	0.130054
$944$	−3.54290	−0.115312
$945$	0	0
$946$	−74.7547	−2.43048
$947$	−7.62438	−0.247759	−0.123879	−	0.992297i	$-0.539534\pi$
$947$	−7.62438	−0.247759	−0.123879	+	0.992297i	$0.539534\pi$
$948$	−4.87203	−0.158236
$949$	−2.07013	−0.0671992
$950$	−165.877	−5.38175
$951$	22.0285	0.714322
$952$	0	0
$953$	15.0822	0.488559	0.244279	−	0.969705i	$-0.421449\pi$
$953$	15.0822	0.488559	0.244279	+	0.969705i	$0.421449\pi$
$954$	−4.51380	−0.146140
$955$	−39.8029	−1.28799
$956$	−1.60033	−0.0517584
$957$	−23.3761	−0.755642
$958$	−19.7730	−0.638836
$959$	0	0
$960$	12.5466	0.404939
$961$	−19.8594	−0.640626
$962$	5.18084	0.167037
$963$	−16.9596	−0.546514
$964$	−18.5393	−0.597109
$965$	78.3709	2.52285
$966$	0	0
$967$	34.1646	1.09866	0.549330	−	0.835606i	$-0.314883\pi$
$967$	34.1646	1.09866	0.549330	+	0.835606i	$0.314883\pi$
$968$	−47.1520	−1.51552
$969$	−10.7963	−0.346828
$970$	−54.0105	−1.73417
$971$	53.8374	1.72773	0.863863	−	0.503727i	$-0.168038\pi$
$971$	53.8374	1.72773	0.863863	+	0.503727i	$0.168038\pi$
$972$	0.782321	0.0250929
$973$	0	0
$974$	−59.1659	−1.89580
$975$	62.4807	2.00098
$976$	−16.5305	−0.529129
$977$	−42.6087	−1.36317	−0.681587	−	0.731737i	$-0.738710\pi$
$977$	−42.6087	−1.36317	−0.681587	+	0.731737i	$0.738710\pi$
$978$	22.1341	0.707769
$979$	83.1983	2.65903
$980$	0	0
$981$	−15.8268	−0.505311
$982$	−4.30265	−0.137303
$983$	26.9565	0.859780	0.429890	−	0.902881i	$-0.358552\pi$
$983$	26.9565	0.859780	0.429890	+	0.902881i	$0.358552\pi$
$984$	−2.03112	−0.0647499
$985$	−95.7647	−3.05132
$986$	−9.91444	−0.315740
$987$	0	0
$988$	−25.9002	−0.823996
$989$	−30.5991	−0.972996
$990$	42.1915	1.34093
$991$	−38.6693	−1.22837	−0.614185	−	0.789162i	$-0.710515\pi$
$991$	−38.6693	−1.22837	−0.614185	+	0.789162i	$0.710515\pi$
$992$	14.0147	0.444969
$993$	31.0654	0.985832
$994$	0	0
$995$	80.3281	2.54657
$996$	−6.06697	−0.192239
$997$	−18.0152	−0.570548	−0.285274	−	0.958446i	$-0.592085\pi$
$997$	−18.0152	−0.570548	−0.285274	+	0.958446i	$0.592085\pi$
$998$	25.8167	0.817215
$999$	0.681013	0.0215463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bc.1.6		8
7.3	odd	6		861.2.i.d.247.3	✓	16
7.5	odd	6		861.2.i.d.739.3	yes	16
7.6	odd	2		6027.2.a.bb.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.d.247.3	✓	16	7.3	odd	6
861.2.i.d.739.3	yes	16	7.5	odd	6
6027.2.a.bb.1.6		8	7.6	odd	2
6027.2.a.bc.1.6		8	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)

\(f(q)\)	\(=\)	\(q+1.66803 q^{2} +1.00000 q^{3} +0.782321 q^{4} +4.32429 q^{5} +1.66803 q^{6} -2.03112 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.66803 q^{2} +1.00000 q^{3} +0.782321 q^{4} +4.32429 q^{5} +1.66803 q^{6} -2.03112 q^{8} +1.00000 q^{9} +7.21304 q^{10} +5.84934 q^{11} +0.782321 q^{12} +4.56081 q^{13} +4.32429 q^{15} -4.95262 q^{16} +1.48730 q^{17} +1.66803 q^{18} -7.25900 q^{19} +3.38298 q^{20} +9.75686 q^{22} +3.99375 q^{23} -2.03112 q^{24} +13.6995 q^{25} +7.60756 q^{26} +1.00000 q^{27} -3.99637 q^{29} +7.21304 q^{30} -3.33775 q^{31} -4.19886 q^{32} +5.84934 q^{33} +2.48086 q^{34} +0.782321 q^{36} +0.681013 q^{37} -12.1082 q^{38} +4.56081 q^{39} -8.78317 q^{40} +1.00000 q^{41} -7.66175 q^{43} +4.57606 q^{44} +4.32429 q^{45} +6.66169 q^{46} -6.16952 q^{47} -4.95262 q^{48} +22.8512 q^{50} +1.48730 q^{51} +3.56801 q^{52} -2.70607 q^{53} +1.66803 q^{54} +25.2942 q^{55} -7.25900 q^{57} -6.66606 q^{58} +0.715360 q^{59} +3.38298 q^{60} +3.33773 q^{61} -5.56747 q^{62} +2.90141 q^{64} +19.7223 q^{65} +9.75686 q^{66} -7.99827 q^{67} +1.16355 q^{68} +3.99375 q^{69} +7.51068 q^{71} -2.03112 q^{72} -0.453895 q^{73} +1.13595 q^{74} +13.6995 q^{75} -5.67887 q^{76} +7.60756 q^{78} -6.22766 q^{79} -21.4166 q^{80} +1.00000 q^{81} +1.66803 q^{82} -7.75509 q^{83} +6.43153 q^{85} -12.7800 q^{86} -3.99637 q^{87} -11.8807 q^{88} +14.2235 q^{89} +7.21304 q^{90} +3.12439 q^{92} -3.33775 q^{93} -10.2909 q^{94} -31.3900 q^{95} -4.19886 q^{96} -7.48789 q^{97} +5.84934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9} + 8 q^{10} + 11 q^{11} + 13 q^{12} + 10 q^{13} + 7 q^{15} - 17 q^{16} + 3 q^{17} + q^{18} + 6 q^{19} + 11 q^{20} + 15 q^{22} + 14 q^{23} + 6 q^{24} + 25 q^{25} + 24 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} + 3 q^{32} + 11 q^{33} - 4 q^{34} + 13 q^{36} - 20 q^{37} + 10 q^{38} + 10 q^{39} - 3 q^{40} + 8 q^{41} + 7 q^{43} + 7 q^{45} - 5 q^{46} + 14 q^{47} - 17 q^{48} - 5 q^{50} + 3 q^{51} + 23 q^{52} + 7 q^{53} + q^{54} + 48 q^{55} + 6 q^{57} - 20 q^{58} + 22 q^{59} + 11 q^{60} - 33 q^{62} - 10 q^{64} - 14 q^{65} + 15 q^{66} + 12 q^{67} - 27 q^{68} + 14 q^{69} - 5 q^{71} + 6 q^{72} + 2 q^{73} + 6 q^{74} + 25 q^{75} + 43 q^{76} + 24 q^{78} - 15 q^{79} - 7 q^{80} + 8 q^{81} + q^{82} + 15 q^{83} - 43 q^{85} + 31 q^{86} + 2 q^{87} + 17 q^{88} + 29 q^{89} + 8 q^{90} + 19 q^{92} + 16 q^{93} + 20 q^{94} + 14 q^{95} + 3 q^{96} + 19 q^{97} + 11 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9 + 8 * q^10 + 11 * q^11 + 13 * q^12 + 10 * q^13 + 7 * q^15 - 17 * q^16 + 3 * q^17 + q^18 + 6 * q^19 + 11 * q^20 + 15 * q^22 + 14 * q^23 + 6 * q^24 + 25 * q^25 + 24 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 + 3 * q^32 + 11 * q^33 - 4 * q^34 + 13 * q^36 - 20 * q^37 + 10 * q^38 + 10 * q^39 - 3 * q^40 + 8 * q^41 + 7 * q^43 + 7 * q^45 - 5 * q^46 + 14 * q^47 - 17 * q^48 - 5 * q^50 + 3 * q^51 + 23 * q^52 + 7 * q^53 + q^54 + 48 * q^55 + 6 * q^57 - 20 * q^58 + 22 * q^59 + 11 * q^60 - 33 * q^62 - 10 * q^64 - 14 * q^65 + 15 * q^66 + 12 * q^67 - 27 * q^68 + 14 * q^69 - 5 * q^71 + 6 * q^72 + 2 * q^73 + 6 * q^74 + 25 * q^75 + 43 * q^76 + 24 * q^78 - 15 * q^79 - 7 * q^80 + 8 * q^81 + q^82 + 15 * q^83 - 43 * q^85 + 31 * q^86 + 2 * q^87 + 17 * q^88 + 29 * q^89 + 8 * q^90 + 19 * q^92 + 16 * q^93 + 20 * q^94 + 14 * q^95 + 3 * q^96 + 19 * q^97 + 11 * q^99

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