LMFDB - Embedded newform 539.2.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(1,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("539.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.19869$ of defining polynomial
Character	$\chi$	$=$	539.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83424 q^{2} +2.19869 q^{3} +1.36445 q^{4} +0.635552 q^{5} +4.03293 q^{6} -1.16576 q^{8} +1.83424 q^{9} +O(q^{10})$	\(q+1.83424 q^{2} +2.19869 q^{3} +1.36445 q^{4} +0.635552 q^{5} +4.03293 q^{6} -1.16576 q^{8} +1.83424 q^{9} +1.16576 q^{10} -1.00000 q^{11} +3.00000 q^{12} +1.80131 q^{13} +1.39738 q^{15} -4.86718 q^{16} +2.83424 q^{17} +3.36445 q^{18} +5.56314 q^{19} +0.867178 q^{20} -1.83424 q^{22} +2.16576 q^{23} -2.56314 q^{24} -4.59607 q^{25} +3.30404 q^{26} -2.56314 q^{27} -10.4303 q^{29} +2.56314 q^{30} -6.43032 q^{31} -6.59607 q^{32} -2.19869 q^{33} +5.19869 q^{34} +2.50273 q^{36} +6.06587 q^{37} +10.2042 q^{38} +3.96052 q^{39} -0.740899 q^{40} -7.53566 q^{41} -4.86718 q^{43} -1.36445 q^{44} +1.16576 q^{45} +3.97252 q^{46} +2.83424 q^{47} -10.7014 q^{48} -8.43032 q^{50} +6.23163 q^{51} +2.45779 q^{52} +7.46980 q^{53} -4.70142 q^{54} -0.635552 q^{55} +12.2316 q^{57} -19.1317 q^{58} -11.8068 q^{59} +1.90666 q^{60} +4.33151 q^{61} -11.7948 q^{62} -2.36445 q^{64} +1.14483 q^{65} -4.03293 q^{66} -1.60262 q^{67} +3.86718 q^{68} +4.76183 q^{69} +4.29204 q^{71} -2.13828 q^{72} +15.9935 q^{73} +11.1263 q^{74} -10.1053 q^{75} +7.59061 q^{76} +7.26456 q^{78} +4.76183 q^{79} -3.09334 q^{80} -11.1383 q^{81} -13.8222 q^{82} +9.23163 q^{83} +1.80131 q^{85} -8.92759 q^{86} -22.9330 q^{87} +1.16576 q^{88} -0.364448 q^{89} +2.13828 q^{90} +2.95506 q^{92} -14.1383 q^{93} +5.19869 q^{94} +3.53566 q^{95} -14.5027 q^{96} +2.59607 q^{97} -1.83424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{3} + 4 q^{4} + 2 q^{5} + q^{6} - 9 q^{8}+O(q^{10}) $ 3 * q + q^3 + 4 * q^4 + 2 * q^5 + q^6 - 9 * q^8	$ 3 q + q^{3} + 4 q^{4} + 2 q^{5} + q^{6} - 9 q^{8} + 9 q^{10} - 3 q^{11} + 9 q^{12} + 11 q^{13} - 7 q^{15} + 2 q^{16} + 3 q^{17} + 10 q^{18} + 11 q^{19} - 14 q^{20} + 12 q^{23} - 2 q^{24} + 3 q^{25} - q^{26} - 2 q^{27} - 9 q^{29} + 2 q^{30} + 3 q^{31} - 3 q^{32} - q^{33} + 10 q^{34} - 9 q^{36} - 4 q^{37} - 8 q^{38} - 5 q^{39} + 3 q^{40} + 5 q^{41} + 2 q^{43} - 4 q^{44} + 9 q^{45} - 10 q^{46} + 3 q^{47} - 10 q^{48} - 3 q^{50} + 2 q^{51} + 7 q^{52} + 17 q^{53} + 8 q^{54} - 2 q^{55} + 20 q^{57} - 13 q^{58} - 8 q^{59} + 6 q^{60} + 24 q^{61} - 13 q^{62} - 7 q^{64} + 15 q^{65} - q^{66} - 16 q^{67} - 5 q^{68} + 3 q^{69} + 7 q^{71} + 10 q^{72} + 20 q^{73} + 22 q^{74} - 25 q^{75} + 39 q^{76} - 6 q^{78} + 3 q^{79} - 9 q^{80} - 17 q^{81} - 41 q^{82} + 11 q^{83} + 11 q^{85} - 21 q^{86} - 30 q^{87} + 9 q^{88} - q^{89} - 10 q^{90} + 25 q^{92} - 26 q^{93} + 10 q^{94} - 17 q^{95} - 27 q^{96} - 9 q^{97}+O(q^{100}) $ 3 * q + q^3 + 4 * q^4 + 2 * q^5 + q^6 - 9 * q^8 + 9 * q^10 - 3 * q^11 + 9 * q^12 + 11 * q^13 - 7 * q^15 + 2 * q^16 + 3 * q^17 + 10 * q^18 + 11 * q^19 - 14 * q^20 + 12 * q^23 - 2 * q^24 + 3 * q^25 - q^26 - 2 * q^27 - 9 * q^29 + 2 * q^30 + 3 * q^31 - 3 * q^32 - q^33 + 10 * q^34 - 9 * q^36 - 4 * q^37 - 8 * q^38 - 5 * q^39 + 3 * q^40 + 5 * q^41 + 2 * q^43 - 4 * q^44 + 9 * q^45 - 10 * q^46 + 3 * q^47 - 10 * q^48 - 3 * q^50 + 2 * q^51 + 7 * q^52 + 17 * q^53 + 8 * q^54 - 2 * q^55 + 20 * q^57 - 13 * q^58 - 8 * q^59 + 6 * q^60 + 24 * q^61 - 13 * q^62 - 7 * q^64 + 15 * q^65 - q^66 - 16 * q^67 - 5 * q^68 + 3 * q^69 + 7 * q^71 + 10 * q^72 + 20 * q^73 + 22 * q^74 - 25 * q^75 + 39 * q^76 - 6 * q^78 + 3 * q^79 - 9 * q^80 - 17 * q^81 - 41 * q^82 + 11 * q^83 + 11 * q^85 - 21 * q^86 - 30 * q^87 + 9 * q^88 - q^89 - 10 * q^90 + 25 * q^92 - 26 * q^93 + 10 * q^94 - 17 * q^95 - 27 * q^96 - 9 * q^97

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 $

$2$	1.83424	1.29701	0.648503	−	0.761212i	$-0.275395\pi$
$2$	1.83424	1.29701	0.648503	+	0.761212i	$0.275395\pi$
$3$	2.19869	1.26941	0.634707	−	0.772752i	$-0.281121\pi$
$3$	2.19869	1.26941	0.634707	+	0.772752i	$0.281121\pi$
$4$	1.36445	0.682224
$5$	0.635552	0.284227	0.142114	−	0.989850i	$-0.454610\pi$
$5$	0.635552	0.284227	0.142114	+	0.989850i	$0.454610\pi$
$6$	4.03293	1.64644
$7$	0	0
$7$	0	0
$8$	−1.16576	−0.412157
$9$	1.83424	0.611414
$10$	1.16576	0.368645
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.00000	0.866025
$13$	1.80131	0.499593	0.249797	−	0.968298i	$-0.419636\pi$
$13$	1.80131	0.499593	0.249797	+	0.968298i	$0.419636\pi$
$14$	0	0
$15$	1.39738	0.360803
$16$	−4.86718	−1.21679
$17$	2.83424	0.687405	0.343702	−	0.939079i	$-0.388319\pi$
$17$	2.83424	0.687405	0.343702	+	0.939079i	$0.388319\pi$
$18$	3.36445	0.793008
$19$	5.56314	1.27627	0.638136	−	0.769924i	$-0.279706\pi$
$19$	5.56314	1.27627	0.638136	+	0.769924i	$0.279706\pi$
$20$	0.867178	0.193907
$21$	0	0
$22$	−1.83424	−0.391062
$23$	2.16576	0.451592	0.225796	−	0.974175i	$-0.427502\pi$
$23$	2.16576	0.451592	0.225796	+	0.974175i	$0.427502\pi$
$24$	−2.56314	−0.523199
$25$	−4.59607	−0.919215
$26$	3.30404	0.647975
$27$	−2.56314	−0.493276
$28$	0	0
$29$	−10.4303	−1.93686	−0.968431	−	0.249283i	$-0.919805\pi$
$29$	−10.4303	−1.93686	−0.968431	+	0.249283i	$0.919805\pi$
$30$	2.56314	0.467963
$31$	−6.43032	−1.15492	−0.577460	−	0.816419i	$-0.695956\pi$
$31$	−6.43032	−1.15492	−0.577460	+	0.816419i	$0.695956\pi$
$32$	−6.59607	−1.16603
$33$	−2.19869	−0.382743
$34$	5.19869	0.891568
$35$	0	0
$36$	2.50273	0.417122
$37$	6.06587	0.997223	0.498611	−	0.866826i	$-0.333843\pi$
$37$	6.06587	0.997223	0.498611	+	0.866826i	$0.333843\pi$
$38$	10.2042	1.65533
$39$	3.96052	0.634191
$40$	−0.740899	−0.117146
$41$	−7.53566	−1.17687	−0.588436	−	0.808543i	$-0.700256\pi$
$41$	−7.53566	−1.17687	−0.588436	+	0.808543i	$0.700256\pi$
$42$	0	0
$43$	−4.86718	−0.742238	−0.371119	−	0.928585i	$-0.621026\pi$
$43$	−4.86718	−0.742238	−0.371119	+	0.928585i	$0.621026\pi$
$44$	−1.36445	−0.205698
$45$	1.16576	0.173781
$46$	3.97252	0.585717
$47$	2.83424	0.413417	0.206708	−	0.978403i	$-0.433725\pi$
$47$	2.83424	0.413417	0.206708	+	0.978403i	$0.433725\pi$
$48$	−10.7014	−1.54462
$49$	0	0
$50$	−8.43032	−1.19223
$51$	6.23163	0.872602
$52$	2.45779	0.340834
$53$	7.46980	1.02606	0.513028	−	0.858372i	$-0.328524\pi$
$53$	7.46980	1.02606	0.513028	+	0.858372i	$0.328524\pi$
$54$	−4.70142	−0.639782
$55$	−0.635552	−0.0856978
$56$	0	0
$57$	12.2316	1.62012
$58$	−19.1317	−2.51212
$59$	−11.8068	−1.53711	−0.768555	−	0.639784i	$-0.779024\pi$
$59$	−11.8068	−1.53711	−0.768555	+	0.639784i	$0.779024\pi$
$60$	1.90666	0.246148
$61$	4.33151	0.554593	0.277297	−	0.960784i	$-0.410561\pi$
$61$	4.33151	0.554593	0.277297	+	0.960784i	$0.410561\pi$
$62$	−11.7948	−1.49794
$63$	0	0
$64$	−2.36445	−0.295556
$65$	1.14483	0.141998
$66$	−4.03293	−0.496420
$67$	−1.60262	−0.195791	−0.0978954	−	0.995197i	$-0.531211\pi$
$67$	−1.60262	−0.195791	−0.0978954	+	0.995197i	$0.531211\pi$
$68$	3.86718	0.468964
$69$	4.76183	0.573257
$70$	0	0
$71$	4.29204	0.509371	0.254685	−	0.967024i	$-0.418028\pi$
$71$	4.29204	0.509371	0.254685	+	0.967024i	$0.418028\pi$
$72$	−2.13828	−0.251999
$73$	15.9935	1.87189	0.935946	−	0.352143i	$-0.114547\pi$
$73$	15.9935	1.87189	0.935946	+	0.352143i	$0.114547\pi$
$74$	11.1263	1.29340
$75$	−10.1053	−1.16686
$76$	7.59061	0.870703
$77$	0	0
$78$	7.26456	0.822549
$79$	4.76183	0.535748	0.267874	−	0.963454i	$-0.413679\pi$
$79$	4.76183	0.535748	0.267874	+	0.963454i	$0.413679\pi$
$80$	−3.09334	−0.345846
$81$	−11.1383	−1.23759
$82$	−13.8222	−1.52641
$83$	9.23163	1.01330	0.506651	−	0.862151i	$-0.330883\pi$
$83$	9.23163	1.01330	0.506651	+	0.862151i	$0.330883\pi$
$84$	0	0
$85$	1.80131	0.195379
$86$	−8.92759	−0.962687
$87$	−22.9330	−2.45868
$88$	1.16576	0.124270
$89$	−0.364448	−0.0386314	−0.0193157	−	0.999813i	$-0.506149\pi$
$89$	−0.364448	−0.0386314	−0.0193157	+	0.999813i	$0.506149\pi$
$90$	2.13828	0.225395
$91$	0	0
$92$	2.95506	0.308087
$93$	−14.1383	−1.46607
$94$	5.19869	0.536204
$95$	3.53566	0.362751
$96$	−14.5027	−1.48018
$97$	2.59607	0.263591	0.131796	−	0.991277i	$-0.457926\pi$
$97$	2.59607	0.263591	0.131796	+	0.991277i	$0.457926\pi$
$98$	0	0
$99$	−1.83424	−0.184348
$100$	−6.27110	−0.627110
$101$	9.90011	0.985098	0.492549	−	0.870285i	$-0.336065\pi$
$101$	9.90011	0.985098	0.492549	+	0.870285i	$0.336065\pi$
$102$	11.4303	1.13177
$103$	−6.23163	−0.614020	−0.307010	−	0.951706i	$-0.599329\pi$
$103$	−6.23163	−0.614020	−0.307010	+	0.951706i	$0.599329\pi$
$104$	−2.09989	−0.205911
$105$	0	0
$106$	13.7014	1.33080
$107$	11.0988	1.07296	0.536481	−	0.843912i	$-0.319753\pi$
$107$	11.0988	1.07296	0.536481	+	0.843912i	$0.319753\pi$
$108$	−3.49727	−0.336525
$109$	−14.3040	−1.37008	−0.685039	−	0.728506i	$-0.740215\pi$
$109$	−14.3040	−1.37008	−0.685039	+	0.728506i	$0.740215\pi$
$110$	−1.16576	−0.111151
$111$	13.3370	1.26589
$112$	0	0
$113$	−8.68942	−0.817432	−0.408716	−	0.912662i	$-0.634023\pi$
$113$	−8.68942	−0.817432	−0.408716	+	0.912662i	$0.634023\pi$
$114$	22.4358	2.10130
$115$	1.37645	0.128355
$116$	−14.2316	−1.32137
$117$	3.30404	0.305458
$118$	−21.6565	−1.99364
$119$	0	0
$120$	−1.62901	−0.148707
$121$	1.00000	0.0909091
$122$	7.94505	0.719311
$123$	−16.5686	−1.49394
$124$	−8.77383	−0.787914
$125$	−6.09880	−0.545494
$126$	0	0
$127$	20.9989	1.86335	0.931676	−	0.363290i	$-0.118346\pi$
$127$	20.9989	1.86335	0.931676	+	0.363290i	$0.118346\pi$
$128$	8.85517	0.782694
$129$	−10.7014	−0.942208
$130$	2.09989	0.184172
$131$	13.7014	1.19710	0.598549	−	0.801086i	$-0.295744\pi$
$131$	13.7014	1.19710	0.598549	+	0.801086i	$0.295744\pi$
$132$	−3.00000	−0.261116
$133$	0	0
$134$	−2.93959	−0.253942
$135$	−1.62901	−0.140203
$136$	−3.30404	−0.283319
$137$	7.26456	0.620653	0.310327	−	0.950630i	$-0.399562\pi$
$137$	7.26456	0.620653	0.310327	+	0.950630i	$0.399562\pi$
$138$	8.73436	0.743518
$139$	2.60262	0.220751	0.110376	−	0.993890i	$-0.464795\pi$
$139$	2.60262	0.220751	0.110376	+	0.993890i	$0.464795\pi$
$140$	0	0
$141$	6.23163	0.524798
$142$	7.87264	0.660657
$143$	−1.80131	−0.150633
$144$	−8.92759	−0.743966
$145$	−6.62901	−0.550509
$146$	29.3359	2.42786
$147$	0	0
$148$	8.27656	0.680329
$149$	−1.00000	−0.0819232	−0.0409616	−	0.999161i	$-0.513042\pi$
$149$	−1.00000	−0.0819232	−0.0409616	+	0.999161i	$0.513042\pi$
$150$	−18.5357	−1.51343
$151$	1.73544	0.141228	0.0706140	−	0.997504i	$-0.477504\pi$
$151$	1.73544	0.141228	0.0706140	+	0.997504i	$0.477504\pi$
$152$	−6.48527	−0.526025
$153$	5.19869	0.420289
$154$	0	0
$155$	−4.08680	−0.328260
$156$	5.40393	0.432660
$157$	7.93959	0.633648	0.316824	−	0.948484i	$-0.397383\pi$
$157$	7.93959	0.633648	0.316824	+	0.948484i	$0.397383\pi$
$158$	8.73436	0.694868
$159$	16.4238	1.30249
$160$	−4.19215	−0.331418
$161$	0	0
$162$	−20.4303	−1.60516
$163$	−16.0055	−1.25364	−0.626822	−	0.779162i	$-0.715645\pi$
$163$	−16.0055	−1.25364	−0.626822	+	0.779162i	$0.715645\pi$
$164$	−10.2820	−0.802891
$165$	−1.39738	−0.108786
$166$	16.9330	1.31426
$167$	−1.15921	−0.0897026	−0.0448513	−	0.998994i	$-0.514281\pi$
$167$	−1.15921	−0.0897026	−0.0448513	+	0.998994i	$0.514281\pi$
$168$	0	0
$169$	−9.75529	−0.750407
$170$	3.30404	0.253408
$171$	10.2042	0.780331
$172$	−6.64101	−0.506372
$173$	0.993456	0.0755311	0.0377655	−	0.999287i	$-0.487976\pi$
$173$	0.993456	0.0755311	0.0377655	+	0.999287i	$0.487976\pi$
$174$	−42.0648	−3.18892
$175$	0	0
$176$	4.86718	0.366877
$177$	−25.9594	−1.95123
$178$	−0.668486	−0.0501052
$179$	−19.6619	−1.46960	−0.734801	−	0.678282i	$-0.762725\pi$
$179$	−19.6619	−1.46960	−0.734801	+	0.678282i	$0.762725\pi$
$180$	1.59061	0.118557
$181$	23.8726	1.77444	0.887220	−	0.461347i	$-0.152634\pi$
$181$	23.8726	1.77444	0.887220	+	0.461347i	$0.152634\pi$
$182$	0	0
$183$	9.52366	0.704009
$184$	−2.52475	−0.186127
$185$	3.85517	0.283438
$186$	−25.9330	−1.90150
$187$	−2.83424	−0.207260
$188$	3.86718	0.282043
$189$	0	0
$190$	6.48527	0.470491
$191$	−11.1317	−0.805464	−0.402732	−	0.915318i	$-0.631939\pi$
$191$	−11.1317	−0.805464	−0.402732	+	0.915318i	$0.631939\pi$
$192$	−5.19869	−0.375183
$193$	3.61462	0.260186	0.130093	−	0.991502i	$-0.458472\pi$
$193$	3.61462	0.260186	0.130093	+	0.991502i	$0.458472\pi$
$194$	4.76183	0.341880
$195$	2.51712	0.180255
$196$	0	0
$197$	2.41831	0.172298	0.0861489	−	0.996282i	$-0.472544\pi$
$197$	2.41831	0.172298	0.0861489	+	0.996282i	$0.472544\pi$
$198$	−3.36445	−0.239101
$199$	18.4962	1.31116	0.655580	−	0.755126i	$-0.272424\pi$
$199$	18.4962	1.31116	0.655580	+	0.755126i	$0.272424\pi$
$200$	5.35790	0.378861
$201$	−3.52366	−0.248540
$202$	18.1592	1.27768
$203$	0	0
$204$	8.50273	0.595310
$205$	−4.78931	−0.334500
$206$	−11.4303	−0.796388
$207$	3.97252	0.276110
$208$	−8.76729	−0.607902
$209$	−5.56314	−0.384810
$210$	0	0
$211$	−7.85517	−0.540773	−0.270386	−	0.962752i	$-0.587151\pi$
$211$	−7.85517	−0.540773	−0.270386	+	0.962752i	$0.587151\pi$
$212$	10.1921	0.700000
$213$	9.43686	0.646603
$214$	20.3579	1.39164
$215$	−3.09334	−0.210964
$216$	2.98800	0.203307
$217$	0	0
$218$	−26.2371	−1.77700
$219$	35.1647	2.37621
$220$	−0.867178	−0.0584651
$221$	5.10535	0.343423
$222$	24.4633	1.64187
$223$	−20.3370	−1.36186	−0.680932	−	0.732346i	$-0.738425\pi$
$223$	−20.3370	−1.36186	−0.680932	+	0.732346i	$0.738425\pi$
$224$	0	0
$225$	−8.43032	−0.562021
$226$	−15.9385	−1.06021
$227$	−7.21962	−0.479183	−0.239592	−	0.970874i	$-0.577014\pi$
$227$	−7.21962	−0.479183	−0.239592	+	0.970874i	$0.577014\pi$
$228$	16.6894	1.10528
$229$	−12.0713	−0.797696	−0.398848	−	0.917017i	$-0.630590\pi$
$229$	−12.0713	−0.797696	−0.398848	+	0.917017i	$0.630590\pi$
$230$	2.52475	0.166477
$231$	0	0
$232$	12.1592	0.798291
$233$	−7.54221	−0.494106	−0.247053	−	0.969002i	$-0.579462\pi$
$233$	−7.54221	−0.494106	−0.247053	+	0.969002i	$0.579462\pi$
$234$	6.06041	0.396181
$235$	1.80131	0.117504
$236$	−16.1097	−1.04865
$237$	10.4698	0.680086
$238$	0	0
$239$	−9.84625	−0.636901	−0.318450	−	0.947940i	$-0.603162\pi$
$239$	−9.84625	−0.636901	−0.318450	+	0.947940i	$0.603162\pi$
$240$	−6.80131	−0.439023
$241$	1.67503	0.107898	0.0539491	−	0.998544i	$-0.482819\pi$
$241$	1.67503	0.107898	0.0539491	+	0.998544i	$0.482819\pi$
$242$	1.83424	0.117910
$243$	−16.8002	−1.07773
$244$	5.91013	0.378357
$245$	0	0
$246$	−30.3908	−1.93765
$247$	10.0209	0.637617
$248$	7.49619	0.476008
$249$	20.2975	1.28630
$250$	−11.1867	−0.707508
$251$	−19.7738	−1.24811	−0.624057	−	0.781379i	$-0.714517\pi$
$251$	−19.7738	−1.24811	−0.624057	+	0.781379i	$0.714517\pi$
$252$	0	0
$253$	−2.16576	−0.136160
$254$	38.5171	2.41678
$255$	3.96052	0.248017
$256$	20.9714	1.31072
$257$	−2.71997	−0.169667	−0.0848335	−	0.996395i	$-0.527036\pi$
$257$	−2.71997	−0.169667	−0.0848335	+	0.996395i	$0.527036\pi$
$258$	−19.6290	−1.22205
$259$	0	0
$260$	1.56205	0.0968745
$261$	−19.1317	−1.18422
$262$	25.1317	1.55264
$263$	12.6949	0.782800	0.391400	−	0.920221i	$-0.371991\pi$
$263$	12.6949	0.782800	0.391400	+	0.920221i	$0.371991\pi$
$264$	2.56314	0.157750
$265$	4.74744	0.291633
$266$	0	0
$267$	−0.801309	−0.0490393
$268$	−2.18669	−0.133573
$269$	7.09334	0.432489	0.216244	−	0.976339i	$-0.430619\pi$
$269$	7.09334	0.432489	0.216244	+	0.976339i	$0.430619\pi$
$270$	−2.98800	−0.181844
$271$	18.2162	1.10655	0.553276	−	0.832998i	$-0.313377\pi$
$271$	18.2162	1.10655	0.553276	+	0.832998i	$0.313377\pi$
$272$	−13.7948	−0.836430
$273$	0	0
$274$	13.3250	0.804991
$275$	4.59607	0.277154
$276$	6.49727	0.391090
$277$	13.8486	0.832084	0.416042	−	0.909345i	$-0.363417\pi$
$277$	13.8486	0.832084	0.416042	+	0.909345i	$0.363417\pi$
$278$	4.77383	0.286316
$279$	−11.7948	−0.706134
$280$	0	0
$281$	21.0329	1.25472	0.627360	−	0.778730i	$-0.284136\pi$
$281$	21.0329	1.25472	0.627360	+	0.778730i	$0.284136\pi$
$282$	11.4303	0.680665
$283$	−0.352445	−0.0209507	−0.0104753	−	0.999945i	$-0.503334\pi$
$283$	−0.352445	−0.0209507	−0.0104753	+	0.999945i	$0.503334\pi$
$284$	5.85626	0.347505
$285$	7.77383	0.460482
$286$	−3.30404	−0.195372
$287$	0	0
$288$	−12.0988	−0.712929
$289$	−8.96707	−0.527474
$290$	−12.1592	−0.714014
$291$	5.70796	0.334607
$292$	21.8222	1.27705
$293$	3.46325	0.202325	0.101163	−	0.994870i	$-0.467744\pi$
$293$	3.46325	0.202325	0.101163	+	0.994870i	$0.467744\pi$
$294$	0	0
$295$	−7.50381	−0.436889
$296$	−7.07133	−0.411013
$297$	2.56314	0.148728
$298$	−1.83424	−0.106255
$299$	3.90120	0.225612
$300$	−13.7882	−0.796063
$301$	0	0
$302$	3.18322	0.183174
$303$	21.7673	1.25050
$304$	−27.0768	−1.55296
$305$	2.75290	0.157631
$306$	9.53566	0.545118
$307$	6.51473	0.371815	0.185908	−	0.982567i	$-0.440477\pi$
$307$	6.51473	0.371815	0.185908	+	0.982567i	$0.440477\pi$
$308$	0	0
$309$	−13.7014	−0.779447
$310$	−7.49619	−0.425755
$311$	−11.6301	−0.659482	−0.329741	−	0.944071i	$-0.606961\pi$
$311$	−11.6301	−0.659482	−0.329741	+	0.944071i	$0.606961\pi$
$312$	−4.61701	−0.261386
$313$	27.0977	1.53165	0.765827	−	0.643047i	$-0.222330\pi$
$313$	27.0977	1.53165	0.765827	+	0.643047i	$0.222330\pi$
$314$	14.5631	0.821845
$315$	0	0
$316$	6.49727	0.365500
$317$	3.86172	0.216896	0.108448	−	0.994102i	$-0.465412\pi$
$317$	3.86172	0.216896	0.108448	+	0.994102i	$0.465412\pi$
$318$	30.1252	1.68934
$319$	10.4303	0.583986
$320$	−1.50273	−0.0840051
$321$	24.4028	1.36203
$322$	0	0
$323$	15.7673	0.877315
$324$	−15.1976	−0.844311
$325$	−8.27895	−0.459233
$326$	−29.3579	−1.62598
$327$	−31.4502	−1.73920
$328$	8.78475	0.485057
$329$	0	0
$330$	−2.56314	−0.141096
$331$	6.15028	0.338050	0.169025	−	0.985612i	$-0.445938\pi$
$331$	6.15028	0.338050	0.169025	+	0.985612i	$0.445938\pi$
$332$	12.5961	0.691299
$333$	11.1263	0.609716
$334$	−2.12628	−0.116345
$335$	−1.01855	−0.0556491
$336$	0	0
$337$	−11.7607	−0.640649	−0.320324	−	0.947308i	$-0.603792\pi$
$337$	−11.7607	−0.640649	−0.320324	+	0.947308i	$0.603792\pi$
$338$	−17.8936	−0.973282
$339$	−19.1053	−1.03766
$340$	2.45779	0.133292
$341$	6.43032	0.348221
$342$	18.7169	1.01209
$343$	0	0
$344$	5.67395	0.305919
$345$	3.02639	0.162935
$346$	1.82224	0.0979642
$347$	−0.840787	−0.0451358	−0.0225679	−	0.999745i	$-0.507184\pi$
$347$	−0.840787	−0.0451358	−0.0225679	+	0.999745i	$0.507184\pi$
$348$	−31.2910	−1.67737
$349$	−9.13174	−0.488811	−0.244405	−	0.969673i	$-0.578593\pi$
$349$	−9.13174	−0.488811	−0.244405	+	0.969673i	$0.578593\pi$
$350$	0	0
$351$	−4.61701	−0.246438
$352$	6.59607	0.351572
$353$	−22.7278	−1.20968	−0.604840	−	0.796347i	$-0.706763\pi$
$353$	−22.7278	−1.20968	−0.604840	+	0.796347i	$0.706763\pi$
$354$	−47.6159	−2.53076
$355$	2.72781	0.144777
$356$	−0.497270	−0.0263553
$357$	0	0
$358$	−36.0648	−1.90608
$359$	−26.2185	−1.38376	−0.691881	−	0.722012i	$-0.743218\pi$
$359$	−26.2185	−1.38376	−0.691881	+	0.722012i	$0.743218\pi$
$360$	−1.35899	−0.0716250
$361$	11.9485	0.628869
$362$	43.7882	2.30146
$363$	2.19869	0.115401
$364$	0	0
$365$	10.1647	0.532043
$366$	17.4687	0.913104
$367$	3.82224	0.199519	0.0997597	−	0.995012i	$-0.468193\pi$
$367$	3.82224	0.199519	0.0997597	+	0.995012i	$0.468193\pi$
$368$	−10.5411	−0.549494
$369$	−13.8222	−0.719557
$370$	7.07133	0.367621
$371$	0	0
$372$	−19.2910	−1.00019
$373$	15.1077	0.782249	0.391124	−	0.920338i	$-0.372086\pi$
$373$	15.1077	0.782249	0.391124	+	0.920338i	$0.372086\pi$
$374$	−5.19869	−0.268818
$375$	−13.4094	−0.692458
$376$	−3.30404	−0.170393
$377$	−18.7882	−0.967643
$378$	0	0
$379$	−11.3765	−0.584369	−0.292185	−	0.956362i	$-0.594382\pi$
$379$	−11.3765	−0.584369	−0.292185	+	0.956362i	$0.594382\pi$
$380$	4.82423	0.247478
$381$	46.1701	2.36537
$382$	−20.4183	−1.04469
$383$	−8.88572	−0.454039	−0.227020	−	0.973890i	$-0.572898\pi$
$383$	−8.88572	−0.454039	−0.227020	+	0.973890i	$0.572898\pi$
$384$	19.4698	0.993564
$385$	0	0
$386$	6.63009	0.337463
$387$	−8.92759	−0.453815
$388$	3.54221	0.179828
$389$	−19.8990	−1.00892	−0.504460	−	0.863435i	$-0.668309\pi$
$389$	−19.8990	−1.00892	−0.504460	+	0.863435i	$0.668309\pi$
$390$	4.61701	0.233791
$391$	6.13828	0.310426
$392$	0	0
$393$	30.1252	1.51962
$394$	4.43578	0.223471
$395$	3.02639	0.152274
$396$	−2.50273	−0.125767
$397$	34.8606	1.74961	0.874803	−	0.484480i	$-0.160991\pi$
$397$	34.8606	1.74961	0.874803	+	0.484480i	$0.160991\pi$
$398$	33.9265	1.70058
$399$	0	0
$400$	22.3699	1.11850
$401$	11.3963	0.569104	0.284552	−	0.958661i	$-0.408155\pi$
$401$	11.3963	0.569104	0.284552	+	0.958661i	$0.408155\pi$
$402$	−6.46325	−0.322358
$403$	−11.5830	−0.576990
$404$	13.5082	0.672058
$405$	−7.07896	−0.351756
$406$	0	0
$407$	−6.06587	−0.300674
$408$	−7.26456	−0.359649
$409$	4.08789	0.202133	0.101066	−	0.994880i	$-0.467775\pi$
$409$	4.08789	0.202133	0.101066	+	0.994880i	$0.467775\pi$
$410$	−8.78475	−0.433848
$411$	15.9725	0.787867
$412$	−8.50273	−0.418899
$413$	0	0
$414$	7.28658	0.358116
$415$	5.86718	0.288008
$416$	−11.8816	−0.582542
$417$	5.72235	0.280225
$418$	−10.2042	−0.499101
$419$	−32.8002	−1.60240	−0.801198	−	0.598399i	$-0.795804\pi$
$419$	−32.8002	−1.60240	−0.801198	+	0.598399i	$0.795804\pi$
$420$	0	0
$421$	−8.52128	−0.415302	−0.207651	−	0.978203i	$-0.566582\pi$
$421$	−8.52128	−0.415302	−0.207651	+	0.978203i	$0.566582\pi$
$422$	−14.4083	−0.701385
$423$	5.19869	0.252769
$424$	−8.70796	−0.422896
$425$	−13.0264	−0.631873
$426$	17.3095	0.838648
$427$	0	0
$428$	15.1437	0.732000
$429$	−3.96052	−0.191216
$430$	−5.67395	−0.273622
$431$	−16.7344	−0.806066	−0.403033	−	0.915186i	$-0.632044\pi$
$431$	−16.7344	−0.806066	−0.403033	+	0.915186i	$0.632044\pi$
$432$	12.4753	0.600216
$433$	25.8661	1.24305	0.621523	−	0.783396i	$-0.286514\pi$
$433$	25.8661	1.24305	0.621523	+	0.783396i	$0.286514\pi$
$434$	0	0
$435$	−14.5751	−0.698825
$436$	−19.5171	−0.934700
$437$	12.0484	0.576353
$438$	64.5006	3.08196
$439$	9.56860	0.456684	0.228342	−	0.973581i	$-0.426670\pi$
$439$	9.56860	0.456684	0.228342	+	0.973581i	$0.426670\pi$
$440$	0.740899	0.0353210
$441$	0	0
$442$	9.36445	0.445421
$443$	19.0329	0.904282	0.452141	−	0.891946i	$-0.350660\pi$
$443$	19.0329	0.904282	0.452141	+	0.891946i	$0.350660\pi$
$444$	18.1976	0.863620
$445$	−0.231626	−0.0109801
$446$	−37.3030	−1.76635
$447$	−2.19869	−0.103995
$448$	0	0
$449$	33.3424	1.57353	0.786763	−	0.617255i	$-0.211755\pi$
$449$	33.3424	1.57353	0.786763	+	0.617255i	$0.211755\pi$
$450$	−15.4633	−0.728945
$451$	7.53566	0.354841
$452$	−11.8563	−0.557672
$453$	3.81570	0.179277
$454$	−13.2425	−0.621503
$455$	0	0
$456$	−14.2591	−0.667744
$457$	11.9605	0.559490	0.279745	−	0.960074i	$-0.409750\pi$
$457$	11.9605	0.559490	0.279745	+	0.960074i	$0.409750\pi$
$458$	−22.1418	−1.03462
$459$	−7.26456	−0.339081
$460$	1.87810	0.0875667
$461$	−12.4896	−0.581701	−0.290850	−	0.956769i	$-0.593938\pi$
$461$	−12.4896	−0.581701	−0.290850	+	0.956769i	$0.593938\pi$
$462$	0	0
$463$	12.3095	0.572071	0.286035	−	0.958219i	$-0.407662\pi$
$463$	12.3095	0.572071	0.286035	+	0.958219i	$0.407662\pi$
$464$	50.7662	2.35676
$465$	−8.98561	−0.416698
$466$	−13.8342	−0.640859
$467$	−32.7607	−1.51599	−0.757993	−	0.652262i	$-0.773820\pi$
$467$	−32.7607	−1.51599	−0.757993	+	0.652262i	$0.773820\pi$
$468$	4.50819	0.208391
$469$	0	0
$470$	3.30404	0.152404
$471$	17.4567	0.804363
$472$	13.7638	0.633531
$473$	4.86718	0.223793
$474$	19.2042	0.882076
$475$	−25.5686	−1.17317
$476$	0	0
$477$	13.7014	0.627345
$478$	−18.0604	−0.826064
$479$	−25.9780	−1.18696	−0.593482	−	0.804847i	$-0.702247\pi$
$479$	−25.9780	−1.18696	−0.593482	+	0.804847i	$0.702247\pi$
$480$	−9.21724	−0.420707
$481$	10.9265	0.498206
$482$	3.07241	0.139945
$483$	0	0
$484$	1.36445	0.0620204
$485$	1.64994	0.0749199
$486$	−30.8157	−1.39783
$487$	14.5357	0.658674	0.329337	−	0.944212i	$-0.393175\pi$
$487$	14.5357	0.658674	0.329337	+	0.944212i	$0.393175\pi$
$488$	−5.04949	−0.228580
$489$	−35.1911	−1.59139
$490$	0	0
$491$	−39.3952	−1.77788	−0.888941	−	0.458023i	$-0.848558\pi$
$491$	−39.3952	−1.77788	−0.888941	+	0.458023i	$0.848558\pi$
$492$	−22.6070	−1.01920
$493$	−29.5621	−1.33141
$494$	18.3808	0.826992
$495$	−1.16576	−0.0523969
$496$	31.2975	1.40530
$497$	0	0
$498$	37.2305	1.66834
$499$	−26.2305	−1.17424	−0.587120	−	0.809500i	$-0.699738\pi$
$499$	−26.2305	−1.17424	−0.587120	+	0.809500i	$0.699738\pi$
$500$	−8.32150	−0.372149
$501$	−2.54875	−0.113870
$502$	−36.2700	−1.61881
$503$	−3.94613	−0.175949	−0.0879747	−	0.996123i	$-0.528039\pi$
$503$	−3.94613	−0.175949	−0.0879747	+	0.996123i	$0.528039\pi$
$504$	0	0
$505$	6.29204	0.279992
$506$	−3.97252	−0.176600
$507$	−21.4489	−0.952577
$508$	28.6519	1.27122
$509$	−16.9056	−0.749326	−0.374663	−	0.927161i	$-0.622242\pi$
$509$	−16.9056	−0.749326	−0.374663	+	0.927161i	$0.622242\pi$
$510$	7.26456	0.321680
$511$	0	0
$512$	20.7564	0.917311
$513$	−14.2591	−0.629555
$514$	−4.98908	−0.220059
$515$	−3.96052	−0.174521
$516$	−14.6015	−0.642797
$517$	−2.83424	−0.124650
$518$	0	0
$519$	2.18430	0.0958803
$520$	−1.33459	−0.0585255
$521$	−1.55768	−0.0682432	−0.0341216	−	0.999418i	$-0.510863\pi$
$521$	−1.55768	−0.0682432	−0.0341216	+	0.999418i	$0.510863\pi$
$522$	−35.0923	−1.53595
$523$	12.5027	0.546706	0.273353	−	0.961914i	$-0.411867\pi$
$523$	12.5027	0.546706	0.273353	+	0.961914i	$0.411867\pi$
$524$	18.6949	0.816689
$525$	0	0
$526$	23.2855	1.01530
$527$	−18.2251	−0.793897
$528$	10.7014	0.465720
$529$	−18.3095	−0.796065
$530$	8.70796	0.378250
$531$	−21.6565	−0.939811
$532$	0	0
$533$	−13.5741	−0.587958
$534$	−1.46980	−0.0636043
$535$	7.05387	0.304965
$536$	1.86826	0.0806966
$537$	−43.2305	−1.86554
$538$	13.0109	0.560941
$539$	0	0
$540$	−2.22270	−0.0956497
$541$	−16.5621	−0.712058	−0.356029	−	0.934475i	$-0.615870\pi$
$541$	−16.5621	−0.712058	−0.356029	+	0.934475i	$0.615870\pi$
$542$	33.4129	1.43521
$543$	52.4886	2.25250
$544$	−18.6949	−0.801536
$545$	−9.09096	−0.389414
$546$	0	0
$547$	−6.64448	−0.284097	−0.142049	−	0.989860i	$-0.545369\pi$
$547$	−6.64448	−0.284097	−0.142049	+	0.989860i	$0.545369\pi$
$548$	9.91211	0.423425
$549$	7.94505	0.339086
$550$	8.43032	0.359470
$551$	−58.0253	−2.47196
$552$	−5.55114	−0.236272
$553$	0	0
$554$	25.4018	1.07922
$555$	8.47634	0.359801
$556$	3.55114	0.150602
$557$	13.1119	0.555569	0.277784	−	0.960643i	$-0.410400\pi$
$557$	13.1119	0.555569	0.277784	+	0.960643i	$0.410400\pi$
$558$	−21.6345	−0.915860
$559$	−8.76729	−0.370817
$560$	0	0
$561$	−6.23163	−0.263099
$562$	38.5795	1.62738
$563$	−30.4886	−1.28494	−0.642470	−	0.766311i	$-0.722090\pi$
$563$	−30.4886	−1.28494	−0.642470	+	0.766311i	$0.722090\pi$
$564$	8.50273	0.358030
$565$	−5.52258	−0.232337
$566$	−0.646470	−0.0271732
$567$	0	0
$568$	−5.00347	−0.209941
$569$	−35.3579	−1.48228	−0.741140	−	0.671350i	$-0.765715\pi$
$569$	−35.3579	−1.48228	−0.741140	+	0.671350i	$0.765715\pi$
$570$	14.2591	0.597248
$571$	−41.2844	−1.72770	−0.863849	−	0.503750i	$-0.831953\pi$
$571$	−41.2844	−1.72770	−0.863849	+	0.503750i	$0.831953\pi$
$572$	−2.45779	−0.102765
$573$	−24.4753	−1.02247
$574$	0	0
$575$	−9.95398	−0.415110
$576$	−4.33697	−0.180707
$577$	−8.70251	−0.362290	−0.181145	−	0.983456i	$-0.557980\pi$
$577$	−8.70251	−0.362290	−0.181145	+	0.983456i	$0.557980\pi$
$578$	−16.4478	−0.684137
$579$	7.94743	0.330284
$580$	−9.04494	−0.375571
$581$	0	0
$582$	10.4698	0.433987
$583$	−7.46980	−0.309367
$584$	−18.6445	−0.771514
$585$	2.09989	0.0868197
$586$	6.35245	0.262417
$587$	23.0539	0.951535	0.475767	−	0.879571i	$-0.342170\pi$
$587$	23.0539	0.951535	0.475767	+	0.879571i	$0.342170\pi$
$588$	0	0
$589$	−35.7727	−1.47399
$590$	−13.7638	−0.566648
$591$	5.31713	0.218717
$592$	−29.5237	−1.21341
$593$	−30.0988	−1.23601	−0.618005	−	0.786174i	$-0.712059\pi$
$593$	−30.0988	−1.23601	−0.618005	+	0.786174i	$0.712059\pi$
$594$	4.70142	0.192902
$595$	0	0
$596$	−1.36445	−0.0558900
$597$	40.6674	1.66441
$598$	7.15574	0.292620
$599$	29.2515	1.19518	0.597591	−	0.801801i	$-0.296125\pi$
$599$	29.2515	1.19518	0.597591	+	0.801801i	$0.296125\pi$
$600$	11.7804	0.480932
$601$	26.8222	1.09410	0.547051	−	0.837099i	$-0.315750\pi$
$601$	26.8222	1.09410	0.547051	+	0.837099i	$0.315750\pi$
$602$	0	0
$603$	−2.93959	−0.119709
$604$	2.36792	0.0963492
$605$	0.635552	0.0258389
$606$	39.9265	1.62190
$607$	−32.2096	−1.30735	−0.653674	−	0.756776i	$-0.726773\pi$
$607$	−32.2096	−1.30735	−0.653674	+	0.756776i	$0.726773\pi$
$608$	−36.6949	−1.48817
$609$	0	0
$610$	5.04949	0.204448
$611$	5.10535	0.206540
$612$	7.09334	0.286731
$613$	44.5950	1.80117	0.900587	−	0.434675i	$-0.143137\pi$
$613$	44.5950	1.80117	0.900587	+	0.434675i	$0.143137\pi$
$614$	11.9496	0.482247
$615$	−10.5302	−0.424619
$616$	0	0
$617$	−0.531290	−0.0213889	−0.0106945	−	0.999943i	$-0.503404\pi$
$617$	−0.531290	−0.0213889	−0.0106945	+	0.999943i	$0.503404\pi$
$618$	−25.1317	−1.01095
$619$	−41.7453	−1.67788	−0.838942	−	0.544221i	$-0.816825\pi$
$619$	−41.7453	−1.67788	−0.838942	+	0.544221i	$0.816825\pi$
$620$	−5.57623	−0.223947
$621$	−5.55114	−0.222759
$622$	−21.3324	−0.855352
$623$	0	0
$624$	−19.2766	−0.771680
$625$	19.1043	0.764170
$626$	49.7038	1.98656
$627$	−12.2316	−0.488484
$628$	10.8332	0.432290
$629$	17.1921	0.685496
$630$	0	0
$631$	−0.217238	−0.00864810	−0.00432405	−	0.999991i	$-0.501376\pi$
$631$	−0.217238	−0.00864810	−0.00432405	+	0.999991i	$0.501376\pi$
$632$	−5.55114	−0.220812
$633$	−17.2711	−0.686465
$634$	7.08333	0.281315
$635$	13.3459	0.529616
$636$	22.4094	0.888590
$637$	0	0
$638$	19.1317	0.757433
$639$	7.87264	0.311437
$640$	5.62792	0.222463
$641$	−9.69050	−0.382752	−0.191376	−	0.981517i	$-0.561295\pi$
$641$	−9.69050	−0.382752	−0.191376	+	0.981517i	$0.561295\pi$
$642$	44.7607	1.76657
$643$	−16.4633	−0.649247	−0.324624	−	0.945843i	$-0.605238\pi$
$643$	−16.4633	−0.649247	−0.324624	+	0.945843i	$0.605238\pi$
$644$	0	0
$645$	−6.80131	−0.267801
$646$	28.9210	1.13788
$647$	−0.873721	−0.0343495	−0.0171748	−	0.999853i	$-0.505467\pi$
$647$	−0.873721	−0.0343495	−0.0171748	+	0.999853i	$0.505467\pi$
$648$	12.9845	0.510080
$649$	11.8068	0.463456
$650$	−15.1856	−0.595628
$651$	0	0
$652$	−21.8386	−0.855266
$653$	−39.9330	−1.56270	−0.781350	−	0.624093i	$-0.785469\pi$
$653$	−39.9330	−1.56270	−0.781350	+	0.624093i	$0.785469\pi$
$654$	−57.6872	−2.25575
$655$	8.70796	0.340248
$656$	36.6774	1.43201
$657$	29.3359	1.14450
$658$	0	0
$659$	−6.89465	−0.268578	−0.134289	−	0.990942i	$-0.542875\pi$
$659$	−6.89465	−0.268578	−0.134289	+	0.990942i	$0.542875\pi$
$660$	−1.90666	−0.0742165
$661$	40.0144	1.55638	0.778190	−	0.628029i	$-0.216138\pi$
$661$	40.0144	1.55638	0.778190	+	0.628029i	$0.216138\pi$
$662$	11.2811	0.438453
$663$	11.2251	0.435946
$664$	−10.7618	−0.417640
$665$	0	0
$666$	20.4083	0.790806
$667$	−22.5895	−0.874670
$668$	−1.58169	−0.0611973
$669$	−44.7147	−1.72877
$670$	−1.86826	−0.0721773
$671$	−4.33151	−0.167216
$672$	0	0
$673$	31.3788	1.20957	0.604783	−	0.796391i	$-0.293260\pi$
$673$	31.3788	1.20957	0.604783	+	0.796391i	$0.293260\pi$
$674$	−21.5721	−0.830925
$675$	11.7804	0.453427
$676$	−13.3106	−0.511945
$677$	36.5315	1.40402	0.702010	−	0.712167i	$-0.252286\pi$
$677$	36.5315	1.40402	0.702010	+	0.712167i	$0.252286\pi$
$678$	−35.0439	−1.34585
$679$	0	0
$680$	−2.09989	−0.0805270
$681$	−15.8737	−0.608282
$682$	11.7948	0.451645
$683$	−15.2700	−0.584291	−0.292146	−	0.956374i	$-0.594369\pi$
$683$	−15.2700	−0.584291	−0.292146	+	0.956374i	$0.594369\pi$
$684$	13.9230	0.532360
$685$	4.61701	0.176407
$686$	0	0
$687$	−26.5411	−1.01261
$688$	23.6894	0.903151
$689$	13.4554	0.512610
$690$	5.55114	0.211328
$691$	38.3843	1.46021	0.730104	−	0.683336i	$-0.239472\pi$
$691$	38.3843	1.46021	0.730104	+	0.683336i	$0.239472\pi$
$692$	1.35552	0.0515291
$693$	0	0
$694$	−1.54221	−0.0585414
$695$	1.65410	0.0627435
$696$	26.7344	1.01336
$697$	−21.3579	−0.808988
$698$	−16.7498	−0.633990
$699$	−16.5830	−0.627226
$700$	0	0
$701$	17.9056	0.676284	0.338142	−	0.941095i	$-0.390202\pi$
$701$	17.9056	0.676284	0.338142	+	0.941095i	$0.390202\pi$
$702$	−8.46871	−0.319631
$703$	33.7453	1.27273
$704$	2.36445	0.0891135
$705$	3.96052	0.149162
$706$	−41.6883	−1.56896
$707$	0	0
$708$	−35.4203	−1.33118
$709$	34.3994	1.29190	0.645948	−	0.763382i	$-0.276462\pi$
$709$	34.3994	1.29190	0.645948	+	0.763382i	$0.276462\pi$
$710$	5.00347	0.187777
$711$	8.73436	0.327564
$712$	0.424858	0.0159222
$713$	−13.9265	−0.521552
$714$	0	0
$715$	−1.14483	−0.0428140
$716$	−26.8277	−1.00260
$717$	−21.6489	−0.808491
$718$	−48.0912	−1.79475
$719$	−49.4172	−1.84295	−0.921476	−	0.388436i	$-0.873016\pi$
$719$	−49.4172	−1.84295	−0.921476	+	0.388436i	$0.873016\pi$
$720$	−5.67395	−0.211455
$721$	0	0
$722$	21.9165	0.815647
$723$	3.68287	0.136968
$724$	32.5730	1.21057
$725$	47.9385	1.78039
$726$	4.03293	0.149676
$727$	19.8201	0.735086	0.367543	−	0.930007i	$-0.380199\pi$
$727$	19.8201	0.735086	0.367543	+	0.930007i	$0.380199\pi$
$728$	0	0
$729$	−3.52366	−0.130506
$730$	18.6445	0.690063
$731$	−13.7948	−0.510218
$732$	12.9945	0.480292
$733$	30.6476	1.13199	0.565997	−	0.824408i	$-0.308492\pi$
$733$	30.6476	1.13199	0.565997	+	0.824408i	$0.308492\pi$
$734$	7.01092	0.258778
$735$	0	0
$736$	−14.2855	−0.526570
$737$	1.60262	0.0590332
$738$	−25.3534	−0.933270
$739$	17.1019	0.629103	0.314551	−	0.949240i	$-0.398146\pi$
$739$	17.1019	0.629103	0.314551	+	0.949240i	$0.398146\pi$
$740$	5.26019	0.193368
$741$	22.0329	0.809400
$742$	0	0
$743$	−6.97252	−0.255797	−0.127899	−	0.991787i	$-0.540823\pi$
$743$	−6.97252	−0.255797	−0.127899	+	0.991787i	$0.540823\pi$
$744$	16.4818	0.604252
$745$	−0.635552	−0.0232848
$746$	27.7113	1.01458
$747$	16.9330	0.619548
$748$	−3.86718	−0.141398
$749$	0	0
$750$	−24.5961	−0.898122
$751$	15.2327	0.555849	0.277925	−	0.960603i	$-0.410353\pi$
$751$	15.2327	0.555849	0.277925	+	0.960603i	$0.410353\pi$
$752$	−13.7948	−0.503043
$753$	−43.4766	−1.58437
$754$	−34.4622	−1.25504
$755$	1.10296	0.0401409
$756$	0	0
$757$	−14.5326	−0.528196	−0.264098	−	0.964496i	$-0.585074\pi$
$757$	−14.5326	−0.528196	−0.264098	+	0.964496i	$0.585074\pi$
$758$	−20.8672	−0.757930
$759$	−4.76183	−0.172843
$760$	−4.12172	−0.149511
$761$	1.71342	0.0621116	0.0310558	−	0.999518i	$-0.490113\pi$
$761$	1.71342	0.0621116	0.0310558	+	0.999518i	$0.490113\pi$
$762$	84.6872	3.06790
$763$	0	0
$764$	−15.1887	−0.549507
$765$	3.30404	0.119458
$766$	−16.2986	−0.588892
$767$	−21.2676	−0.767930
$768$	46.1097	1.66384
$769$	36.5874	1.31937	0.659687	−	0.751540i	$-0.270689\pi$
$769$	36.5874	1.31937	0.659687	+	0.751540i	$0.270689\pi$
$770$	0	0
$771$	−5.98037	−0.215378
$772$	4.93196	0.177505
$773$	−26.8212	−0.964690	−0.482345	−	0.875981i	$-0.660215\pi$
$773$	−26.8212	−0.964690	−0.482345	+	0.875981i	$0.660215\pi$
$774$	−16.3754	−0.588600
$775$	29.5542	1.06162
$776$	−3.02639	−0.108641
$777$	0	0
$778$	−36.4997	−1.30858
$779$	−41.9219	−1.50201
$780$	3.43448	0.122974
$781$	−4.29204	−0.153581
$782$	11.2591	0.402625
$783$	26.7344	0.955408
$784$	0	0
$785$	5.04602	0.180100
$786$	55.2569	1.97095
$787$	−4.95159	−0.176505	−0.0882526	−	0.996098i	$-0.528128\pi$
$787$	−4.95159	−0.176505	−0.0882526	+	0.996098i	$0.528128\pi$
$788$	3.29966	0.117546
$789$	27.9121	0.993698
$790$	5.55114	0.197501
$791$	0	0
$792$	2.13828	0.0759805
$793$	7.80239	0.277071
$794$	63.9429	2.26925
$795$	10.4382	0.370203
$796$	25.2371	0.894505
$797$	26.6818	0.945117	0.472559	−	0.881299i	$-0.343330\pi$
$797$	26.6818	0.945117	0.472559	+	0.881299i	$0.343330\pi$
$798$	0	0
$799$	8.03293	0.284185
$800$	30.3160	1.07183
$801$	−0.668486	−0.0236198
$802$	20.9036	0.738131
$803$	−15.9935	−0.564397
$804$	−4.80785	−0.169560
$805$	0	0
$806$	−21.2460	−0.748359
$807$	15.5961	0.549008
$808$	−11.5411	−0.406015
$809$	−39.5400	−1.39015	−0.695077	−	0.718935i	$-0.744630\pi$
$809$	−39.5400	−1.39015	−0.695077	+	0.718935i	$0.744630\pi$
$810$	−12.9845	−0.456230
$811$	33.4543	1.17474	0.587370	−	0.809318i	$-0.300163\pi$
$811$	33.4543	1.17474	0.587370	+	0.809318i	$0.300163\pi$
$812$	0	0
$813$	40.0517	1.40467
$814$	−11.1263	−0.389976
$815$	−10.1723	−0.356320
$816$	−30.3304	−1.06178
$817$	−27.0768	−0.947297
$818$	7.49818	0.262168
$819$	0	0
$820$	−6.53476	−0.228204
$821$	56.8619	1.98450	0.992248	−	0.124277i	$-0.0396611\pi$
$821$	56.8619	1.98450	0.992248	+	0.124277i	$0.0396611\pi$
$822$	29.2975	1.02187
$823$	−40.1756	−1.40043	−0.700217	−	0.713931i	$-0.746913\pi$
$823$	−40.1756	−1.40043	−0.700217	+	0.713931i	$0.746913\pi$
$824$	7.26456	0.253073
$825$	10.1053	0.351823
$826$	0	0
$827$	−5.73544	−0.199441	−0.0997204	−	0.995015i	$-0.531795\pi$
$827$	−5.73544	−0.199441	−0.0997204	+	0.995015i	$0.531795\pi$
$828$	5.42030	0.188369
$829$	35.5961	1.23630	0.618151	−	0.786059i	$-0.287882\pi$
$829$	35.5961	1.23630	0.618151	+	0.786059i	$0.287882\pi$
$830$	10.7618	0.373549
$831$	30.4489	1.05626
$832$	−4.25910	−0.147658
$833$	0	0
$834$	10.4962	0.363453
$835$	−0.736740	−0.0254959
$836$	−7.59061	−0.262527
$837$	16.4818	0.569694
$838$	−60.1636	−2.07832
$839$	41.7727	1.44216	0.721078	−	0.692854i	$-0.243647\pi$
$839$	41.7727	1.44216	0.721078	+	0.692854i	$0.243647\pi$
$840$	0	0
$841$	79.7915	2.75143
$842$	−15.6301	−0.538649
$843$	46.2449	1.59276
$844$	−10.7180	−0.368928
$845$	−6.19999	−0.213286
$846$	9.53566	0.327843
$847$	0	0
$848$	−36.3568	−1.24850
$849$	−0.774918	−0.0265951
$850$	−23.8936	−0.819543
$851$	13.1372	0.450337
$852$	12.8761	0.441128
$853$	−49.7871	−1.70468	−0.852340	−	0.522989i	$-0.824817\pi$
$853$	−49.7871	−1.70468	−0.852340	+	0.522989i	$0.824817\pi$
$854$	0	0
$855$	6.48527	0.221791
$856$	−12.9385	−0.442229
$857$	−25.4787	−0.870337	−0.435168	−	0.900349i	$-0.643311\pi$
$857$	−25.4787	−0.870337	−0.435168	+	0.900349i	$0.643311\pi$
$858$	−7.26456	−0.248008
$859$	−16.1616	−0.551427	−0.275713	−	0.961240i	$-0.588914\pi$
$859$	−16.1616	−0.551427	−0.275713	+	0.961240i	$0.588914\pi$
$860$	−4.22071	−0.143925
$861$	0	0
$862$	−30.6949	−1.04547
$863$	2.89903	0.0986840	0.0493420	−	0.998782i	$-0.484288\pi$
$863$	2.89903	0.0986840	0.0493420	+	0.998782i	$0.484288\pi$
$864$	16.9067	0.575176
$865$	0.631393	0.0214680
$866$	47.4447	1.61224
$867$	−19.7158	−0.669584
$868$	0	0
$869$	−4.76183	−0.161534
$870$	−26.7344	−0.906380
$871$	−2.88681	−0.0978158
$872$	16.6750	0.564688
$873$	4.76183	0.161164
$874$	22.0997	0.747534
$875$	0	0
$876$	47.9804	1.62111
$877$	−8.41484	−0.284149	−0.142075	−	0.989856i	$-0.545377\pi$
$877$	−8.41484	−0.284149	−0.142075	+	0.989856i	$0.545377\pi$
$878$	17.5511	0.592322
$879$	7.61462	0.256835
$880$	3.09334	0.104277
$881$	−41.5335	−1.39930	−0.699649	−	0.714486i	$-0.746660\pi$
$881$	−41.5335	−1.39930	−0.699649	+	0.714486i	$0.746660\pi$
$882$	0	0
$883$	−56.4753	−1.90054	−0.950272	−	0.311422i	$-0.899195\pi$
$883$	−56.4753	−1.90054	−0.950272	+	0.311422i	$0.899195\pi$
$884$	6.96598	0.234291
$885$	−16.4986	−0.554593
$886$	34.9110	1.17286
$887$	34.5795	1.16107	0.580533	−	0.814237i	$-0.302844\pi$
$887$	34.5795	1.16107	0.580533	+	0.814237i	$0.302844\pi$
$888$	−15.5477	−0.521746
$889$	0	0
$890$	−0.424858	−0.0142413
$891$	11.1383	0.373146
$892$	−27.7487	−0.929097
$893$	15.7673	0.527632
$894$	−4.03293	−0.134882
$895$	−12.4962	−0.417701
$896$	0	0
$897$	8.57753	0.286395
$898$	61.1581	2.04087
$899$	67.0702	2.23692
$900$	−11.5027	−0.383424
$901$	21.1712	0.705315
$902$	13.8222	0.460230
$903$	0	0
$904$	10.1297	0.336910
$905$	15.1723	0.504344
$906$	6.99892	0.232523
$907$	8.40284	0.279012	0.139506	−	0.990221i	$-0.455449\pi$
$907$	8.40284	0.279012	0.139506	+	0.990221i	$0.455449\pi$
$908$	−9.85080	−0.326910
$909$	18.1592	0.602303
$910$	0	0
$911$	−0.593689	−0.0196698	−0.00983489	−	0.999952i	$-0.503131\pi$
$911$	−0.593689	−0.0196698	−0.00983489	+	0.999952i	$0.503131\pi$
$912$	−59.5335	−1.97135
$913$	−9.23163	−0.305522
$914$	21.9385	0.725661
$915$	6.05278	0.200099
$916$	−16.4707	−0.544207
$917$	0	0
$918$	−13.3250	−0.439790
$919$	−16.3370	−0.538907	−0.269454	−	0.963013i	$-0.586843\pi$
$919$	−16.3370	−0.538907	−0.269454	+	0.963013i	$0.586843\pi$
$920$	−1.60461	−0.0529023
$921$	14.3239	0.471988
$922$	−22.9090	−0.754469
$923$	7.73128	0.254478
$924$	0	0
$925$	−27.8792	−0.916662
$926$	22.5786	0.741979
$927$	−11.4303	−0.375421
$928$	68.7991	2.25844
$929$	−8.90120	−0.292039	−0.146019	−	0.989282i	$-0.546646\pi$
$929$	−8.90120	−0.292039	−0.146019	+	0.989282i	$0.546646\pi$
$930$	−16.4818	−0.540459
$931$	0	0
$932$	−10.2910	−0.337091
$933$	−25.5710	−0.837156
$934$	−60.0912	−1.96624
$935$	−1.80131	−0.0589091
$936$	−3.85171	−0.125897
$937$	−45.2360	−1.47780	−0.738898	−	0.673817i	$-0.764653\pi$
$937$	−45.2360	−1.47780	−0.738898	+	0.673817i	$0.764653\pi$
$938$	0	0
$939$	59.5795	1.94430
$940$	2.45779	0.0801643
$941$	6.93305	0.226011	0.113005	−	0.993594i	$-0.463952\pi$
$941$	6.93305	0.226011	0.113005	+	0.993594i	$0.463952\pi$
$942$	32.0198	1.04326
$943$	−16.3204	−0.531466
$944$	57.4656	1.87035
$945$	0	0
$946$	8.92759	0.290261
$947$	20.7433	0.674066	0.337033	−	0.941493i	$-0.390577\pi$
$947$	20.7433	0.674066	0.337033	+	0.941493i	$0.390577\pi$
$948$	14.2855	0.463971
$949$	28.8092	0.935185
$950$	−46.8990	−1.52161
$951$	8.49073	0.275331
$952$	0	0
$953$	20.2076	0.654589	0.327295	−	0.944922i	$-0.393863\pi$
$953$	20.2076	0.654589	0.327295	+	0.944922i	$0.393863\pi$
$954$	25.1317	0.813670
$955$	−7.07480	−0.228935
$956$	−13.4347	−0.434509
$957$	22.9330	0.741320
$958$	−47.6499	−1.53950
$959$	0	0
$960$	−3.30404	−0.106637
$961$	10.3490	0.333838
$962$	20.0419	0.646176
$963$	20.3579	0.656024
$964$	2.28549	0.0736107
$965$	2.29728	0.0739520
$966$	0	0
$967$	−7.98254	−0.256701	−0.128351	−	0.991729i	$-0.540968\pi$
$967$	−7.98254	−0.256701	−0.128351	+	0.991729i	$0.540968\pi$
$968$	−1.16576	−0.0374688
$969$	34.6674	1.11368
$970$	3.02639	0.0971715
$971$	13.7793	0.442199	0.221099	−	0.975251i	$-0.429036\pi$
$971$	13.7793	0.442199	0.221099	+	0.975251i	$0.429036\pi$
$972$	−22.9230	−0.735257
$973$	0	0
$974$	26.6619	0.854304
$975$	−18.2029	−0.582958
$976$	−21.0822	−0.674826
$977$	12.0209	0.384584	0.192292	−	0.981338i	$-0.438408\pi$
$977$	12.0209	0.384584	0.192292	+	0.981338i	$0.438408\pi$
$978$	−64.5490	−2.06405
$979$	0.364448	0.0116478
$980$	0	0
$981$	−26.2371	−0.837686
$982$	−72.2604	−2.30592
$983$	44.6543	1.42425	0.712126	−	0.702052i	$-0.247733\pi$
$983$	44.6543	1.42425	0.712126	+	0.702052i	$0.247733\pi$
$984$	19.3150	0.615738
$985$	1.53696	0.0489718
$986$	−54.2240	−1.72684
$987$	0	0
$988$	13.6730	0.434997
$989$	−10.5411	−0.335188
$990$	−2.13828	−0.0679590
$991$	−22.9660	−0.729538	−0.364769	−	0.931098i	$-0.618852\pi$
$991$	−22.9660	−0.729538	−0.364769	+	0.931098i	$0.618852\pi$
$992$	42.4148	1.34667
$993$	13.5226	0.429126
$994$	0	0
$995$	11.7553	0.372668
$996$	27.6949	0.877546
$997$	−1.34898	−0.0427225	−0.0213612	−	0.999772i	$-0.506800\pi$
$997$	−1.34898	−0.0427225	−0.0213612	+	0.999772i	$0.506800\pi$
$998$	−48.1132	−1.52300
$999$	−15.5477	−0.491906

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.a.i.1.3		3
3.2	odd	2		4851.2.a.bn.1.1		3
4.3	odd	2		8624.2.a.ck.1.1		3
7.2	even	3		539.2.e.l.67.1		6
7.3	odd	6		77.2.e.b.23.1	✓	6
7.4	even	3		539.2.e.l.177.1		6
7.5	odd	6		77.2.e.b.67.1	yes	6
7.6	odd	2		539.2.a.h.1.3		3
11.10	odd	2		5929.2.a.w.1.1		3
21.5	even	6		693.2.i.g.298.3		6
21.17	even	6		693.2.i.g.100.3		6
21.20	even	2		4851.2.a.bo.1.1		3
28.3	even	6		1232.2.q.k.177.1		6
28.19	even	6		1232.2.q.k.529.1		6
28.27	even	2		8624.2.a.cl.1.3		3
77.3	odd	30		847.2.n.e.9.3		24
77.5	odd	30		847.2.n.e.487.3		24
77.10	even	6		847.2.e.d.485.3		6
77.17	even	30		847.2.n.d.366.3		24
77.19	even	30		847.2.n.d.130.3		24
77.24	even	30		847.2.n.d.807.1		24
77.26	odd	30		847.2.n.e.753.3		24
77.31	odd	30		847.2.n.e.807.3		24
77.38	odd	30		847.2.n.e.366.1		24
77.40	even	30		847.2.n.d.753.1		24
77.47	odd	30		847.2.n.e.130.1		24
77.52	even	30		847.2.n.d.9.1		24
77.54	even	6		847.2.e.d.606.3		6
77.59	odd	30		847.2.n.e.632.1		24
77.61	even	30		847.2.n.d.487.1		24
77.68	even	30		847.2.n.d.81.3		24
77.73	even	30		847.2.n.d.632.3		24
77.75	odd	30		847.2.n.e.81.1		24
77.76	even	2		5929.2.a.v.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.1	✓	6	7.3	odd	6
77.2.e.b.67.1	yes	6	7.5	odd	6
539.2.a.h.1.3		3	7.6	odd	2
539.2.a.i.1.3		3	1.1	even	1	trivial
539.2.e.l.67.1		6	7.2	even	3
539.2.e.l.177.1		6	7.4	even	3
693.2.i.g.100.3		6	21.17	even	6
693.2.i.g.298.3		6	21.5	even	6
847.2.e.d.485.3		6	77.10	even	6
847.2.e.d.606.3		6	77.54	even	6
847.2.n.d.9.1		24	77.52	even	30
847.2.n.d.81.3		24	77.68	even	30
847.2.n.d.130.3		24	77.19	even	30
847.2.n.d.366.3		24	77.17	even	30
847.2.n.d.487.1		24	77.61	even	30
847.2.n.d.632.3		24	77.73	even	30
847.2.n.d.753.1		24	77.40	even	30
847.2.n.d.807.1		24	77.24	even	30
847.2.n.e.9.3		24	77.3	odd	30
847.2.n.e.81.1		24	77.75	odd	30
847.2.n.e.130.1		24	77.47	odd	30
847.2.n.e.366.1		24	77.38	odd	30
847.2.n.e.487.3		24	77.5	odd	30
847.2.n.e.632.1		24	77.59	odd	30
847.2.n.e.753.3		24	77.26	odd	30
847.2.n.e.807.3		24	77.31	odd	30
1232.2.q.k.177.1		6	28.3	even	6
1232.2.q.k.529.1		6	28.19	even	6
4851.2.a.bn.1.1		3	3.2	odd	2
4851.2.a.bo.1.1		3	21.20	even	2
5929.2.a.v.1.1		3	77.76	even	2
5929.2.a.w.1.1		3	11.10	odd	2
8624.2.a.ck.1.1		3	4.3	odd	2
8624.2.a.cl.1.3		3	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.a (trivial)

\(f(q)\)	\(=\)	\(q+1.83424 q^{2} +2.19869 q^{3} +1.36445 q^{4} +0.635552 q^{5} +4.03293 q^{6} -1.16576 q^{8} +1.83424 q^{9} +O(q^{10})\)	\(q+1.83424 q^{2} +2.19869 q^{3} +1.36445 q^{4} +0.635552 q^{5} +4.03293 q^{6} -1.16576 q^{8} +1.83424 q^{9} +1.16576 q^{10} -1.00000 q^{11} +3.00000 q^{12} +1.80131 q^{13} +1.39738 q^{15} -4.86718 q^{16} +2.83424 q^{17} +3.36445 q^{18} +5.56314 q^{19} +0.867178 q^{20} -1.83424 q^{22} +2.16576 q^{23} -2.56314 q^{24} -4.59607 q^{25} +3.30404 q^{26} -2.56314 q^{27} -10.4303 q^{29} +2.56314 q^{30} -6.43032 q^{31} -6.59607 q^{32} -2.19869 q^{33} +5.19869 q^{34} +2.50273 q^{36} +6.06587 q^{37} +10.2042 q^{38} +3.96052 q^{39} -0.740899 q^{40} -7.53566 q^{41} -4.86718 q^{43} -1.36445 q^{44} +1.16576 q^{45} +3.97252 q^{46} +2.83424 q^{47} -10.7014 q^{48} -8.43032 q^{50} +6.23163 q^{51} +2.45779 q^{52} +7.46980 q^{53} -4.70142 q^{54} -0.635552 q^{55} +12.2316 q^{57} -19.1317 q^{58} -11.8068 q^{59} +1.90666 q^{60} +4.33151 q^{61} -11.7948 q^{62} -2.36445 q^{64} +1.14483 q^{65} -4.03293 q^{66} -1.60262 q^{67} +3.86718 q^{68} +4.76183 q^{69} +4.29204 q^{71} -2.13828 q^{72} +15.9935 q^{73} +11.1263 q^{74} -10.1053 q^{75} +7.59061 q^{76} +7.26456 q^{78} +4.76183 q^{79} -3.09334 q^{80} -11.1383 q^{81} -13.8222 q^{82} +9.23163 q^{83} +1.80131 q^{85} -8.92759 q^{86} -22.9330 q^{87} +1.16576 q^{88} -0.364448 q^{89} +2.13828 q^{90} +2.95506 q^{92} -14.1383 q^{93} +5.19869 q^{94} +3.53566 q^{95} -14.5027 q^{96} +2.59607 q^{97} -1.83424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{3} + 4 q^{4} + 2 q^{5} + q^{6} - 9 q^{8}+O(q^{10}) \) 3 * q + q^3 + 4 * q^4 + 2 * q^5 + q^6 - 9 * q^8	\( 3 q + q^{3} + 4 q^{4} + 2 q^{5} + q^{6} - 9 q^{8} + 9 q^{10} - 3 q^{11} + 9 q^{12} + 11 q^{13} - 7 q^{15} + 2 q^{16} + 3 q^{17} + 10 q^{18} + 11 q^{19} - 14 q^{20} + 12 q^{23} - 2 q^{24} + 3 q^{25} - q^{26} - 2 q^{27} - 9 q^{29} + 2 q^{30} + 3 q^{31} - 3 q^{32} - q^{33} + 10 q^{34} - 9 q^{36} - 4 q^{37} - 8 q^{38} - 5 q^{39} + 3 q^{40} + 5 q^{41} + 2 q^{43} - 4 q^{44} + 9 q^{45} - 10 q^{46} + 3 q^{47} - 10 q^{48} - 3 q^{50} + 2 q^{51} + 7 q^{52} + 17 q^{53} + 8 q^{54} - 2 q^{55} + 20 q^{57} - 13 q^{58} - 8 q^{59} + 6 q^{60} + 24 q^{61} - 13 q^{62} - 7 q^{64} + 15 q^{65} - q^{66} - 16 q^{67} - 5 q^{68} + 3 q^{69} + 7 q^{71} + 10 q^{72} + 20 q^{73} + 22 q^{74} - 25 q^{75} + 39 q^{76} - 6 q^{78} + 3 q^{79} - 9 q^{80} - 17 q^{81} - 41 q^{82} + 11 q^{83} + 11 q^{85} - 21 q^{86} - 30 q^{87} + 9 q^{88} - q^{89} - 10 q^{90} + 25 q^{92} - 26 q^{93} + 10 q^{94} - 17 q^{95} - 27 q^{96} - 9 q^{97}+O(q^{100}) \) 3 * q + q^3 + 4 * q^4 + 2 * q^5 + q^6 - 9 * q^8 + 9 * q^10 - 3 * q^11 + 9 * q^12 + 11 * q^13 - 7 * q^15 + 2 * q^16 + 3 * q^17 + 10 * q^18 + 11 * q^19 - 14 * q^20 + 12 * q^23 - 2 * q^24 + 3 * q^25 - q^26 - 2 * q^27 - 9 * q^29 + 2 * q^30 + 3 * q^31 - 3 * q^32 - q^33 + 10 * q^34 - 9 * q^36 - 4 * q^37 - 8 * q^38 - 5 * q^39 + 3 * q^40 + 5 * q^41 + 2 * q^43 - 4 * q^44 + 9 * q^45 - 10 * q^46 + 3 * q^47 - 10 * q^48 - 3 * q^50 + 2 * q^51 + 7 * q^52 + 17 * q^53 + 8 * q^54 - 2 * q^55 + 20 * q^57 - 13 * q^58 - 8 * q^59 + 6 * q^60 + 24 * q^61 - 13 * q^62 - 7 * q^64 + 15 * q^65 - q^66 - 16 * q^67 - 5 * q^68 + 3 * q^69 + 7 * q^71 + 10 * q^72 + 20 * q^73 + 22 * q^74 - 25 * q^75 + 39 * q^76 - 6 * q^78 + 3 * q^79 - 9 * q^80 - 17 * q^81 - 41 * q^82 + 11 * q^83 + 11 * q^85 - 21 * q^86 - 30 * q^87 + 9 * q^88 - q^89 - 10 * q^90 + 25 * q^92 - 26 * q^93 + 10 * q^94 - 17 * q^95 - 27 * q^96 - 9 * q^97

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