LMFDB - Embedded newform 6042.2.a.bb.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 16x^{7} + 76x^{6} + 30x^{5} - 366x^{4} + 300x^{3} + 101x^{2} - 106x + 16 $ x^9 - 4x^8 - 16x^7 + 76x^6 + 30x^5 - 366x^4 + 300x^3 + 101x^2 - 106x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.613026$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.133530 q^{5} -1.00000 q^{6} -1.61303 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.133530 q^{5} -1.00000 q^{6} -1.61303 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.133530 q^{10} +2.62913 q^{11} -1.00000 q^{12} -4.22862 q^{13} -1.61303 q^{14} +0.133530 q^{15} +1.00000 q^{16} +4.31475 q^{17} +1.00000 q^{18} -1.00000 q^{19} -0.133530 q^{20} +1.61303 q^{21} +2.62913 q^{22} -1.63540 q^{23} -1.00000 q^{24} -4.98217 q^{25} -4.22862 q^{26} -1.00000 q^{27} -1.61303 q^{28} -1.99919 q^{29} +0.133530 q^{30} -0.126146 q^{31} +1.00000 q^{32} -2.62913 q^{33} +4.31475 q^{34} +0.215387 q^{35} +1.00000 q^{36} +0.989323 q^{37} -1.00000 q^{38} +4.22862 q^{39} -0.133530 q^{40} +9.19422 q^{41} +1.61303 q^{42} -6.57466 q^{43} +2.62913 q^{44} -0.133530 q^{45} -1.63540 q^{46} -5.21171 q^{47} -1.00000 q^{48} -4.39815 q^{49} -4.98217 q^{50} -4.31475 q^{51} -4.22862 q^{52} +1.00000 q^{53} -1.00000 q^{54} -0.351067 q^{55} -1.61303 q^{56} +1.00000 q^{57} -1.99919 q^{58} +7.07682 q^{59} +0.133530 q^{60} -9.64227 q^{61} -0.126146 q^{62} -1.61303 q^{63} +1.00000 q^{64} +0.564646 q^{65} -2.62913 q^{66} -10.8116 q^{67} +4.31475 q^{68} +1.63540 q^{69} +0.215387 q^{70} -2.67507 q^{71} +1.00000 q^{72} +13.4975 q^{73} +0.989323 q^{74} +4.98217 q^{75} -1.00000 q^{76} -4.24085 q^{77} +4.22862 q^{78} +10.3723 q^{79} -0.133530 q^{80} +1.00000 q^{81} +9.19422 q^{82} +8.53170 q^{83} +1.61303 q^{84} -0.576147 q^{85} -6.57466 q^{86} +1.99919 q^{87} +2.62913 q^{88} -18.4051 q^{89} -0.133530 q^{90} +6.82087 q^{91} -1.63540 q^{92} +0.126146 q^{93} -5.21171 q^{94} +0.133530 q^{95} -1.00000 q^{96} -17.1005 q^{97} -4.39815 q^{98} +2.62913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9} - 5 q^{10} + 3 q^{11} - 9 q^{12} - 4 q^{13} - 5 q^{14} + 5 q^{15} + 9 q^{16} - 16 q^{17} + 9 q^{18} - 9 q^{19} - 5 q^{20} + 5 q^{21} + 3 q^{22} - 9 q^{24} + 8 q^{25} - 4 q^{26} - 9 q^{27} - 5 q^{28} - 2 q^{29} + 5 q^{30} - 10 q^{31} + 9 q^{32} - 3 q^{33} - 16 q^{34} - q^{35} + 9 q^{36} - 14 q^{37} - 9 q^{38} + 4 q^{39} - 5 q^{40} - 21 q^{41} + 5 q^{42} - 4 q^{43} + 3 q^{44} - 5 q^{45} - 8 q^{47} - 9 q^{48} - 14 q^{49} + 8 q^{50} + 16 q^{51} - 4 q^{52} + 9 q^{53} - 9 q^{54} - 14 q^{55} - 5 q^{56} + 9 q^{57} - 2 q^{58} - 12 q^{59} + 5 q^{60} - 13 q^{61} - 10 q^{62} - 5 q^{63} + 9 q^{64} - 13 q^{65} - 3 q^{66} + 22 q^{67} - 16 q^{68} - q^{70} - 13 q^{71} + 9 q^{72} - 17 q^{73} - 14 q^{74} - 8 q^{75} - 9 q^{76} - 25 q^{77} + 4 q^{78} - 5 q^{80} + 9 q^{81} - 21 q^{82} - 24 q^{83} + 5 q^{84} - 16 q^{85} - 4 q^{86} + 2 q^{87} + 3 q^{88} - 23 q^{89} - 5 q^{90} - 11 q^{91} + 10 q^{93} - 8 q^{94} + 5 q^{95} - 9 q^{96} - 29 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9 - 5 * q^10 + 3 * q^11 - 9 * q^12 - 4 * q^13 - 5 * q^14 + 5 * q^15 + 9 * q^16 - 16 * q^17 + 9 * q^18 - 9 * q^19 - 5 * q^20 + 5 * q^21 + 3 * q^22 - 9 * q^24 + 8 * q^25 - 4 * q^26 - 9 * q^27 - 5 * q^28 - 2 * q^29 + 5 * q^30 - 10 * q^31 + 9 * q^32 - 3 * q^33 - 16 * q^34 - q^35 + 9 * q^36 - 14 * q^37 - 9 * q^38 + 4 * q^39 - 5 * q^40 - 21 * q^41 + 5 * q^42 - 4 * q^43 + 3 * q^44 - 5 * q^45 - 8 * q^47 - 9 * q^48 - 14 * q^49 + 8 * q^50 + 16 * q^51 - 4 * q^52 + 9 * q^53 - 9 * q^54 - 14 * q^55 - 5 * q^56 + 9 * q^57 - 2 * q^58 - 12 * q^59 + 5 * q^60 - 13 * q^61 - 10 * q^62 - 5 * q^63 + 9 * q^64 - 13 * q^65 - 3 * q^66 + 22 * q^67 - 16 * q^68 - q^70 - 13 * q^71 + 9 * q^72 - 17 * q^73 - 14 * q^74 - 8 * q^75 - 9 * q^76 - 25 * q^77 + 4 * q^78 - 5 * q^80 + 9 * q^81 - 21 * q^82 - 24 * q^83 + 5 * q^84 - 16 * q^85 - 4 * q^86 + 2 * q^87 + 3 * q^88 - 23 * q^89 - 5 * q^90 - 11 * q^91 + 10 * q^93 - 8 * q^94 + 5 * q^95 - 9 * q^96 - 29 * q^97 - 14 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.133530	−0.0597163	−0.0298582	−	0.999554i	$-0.509506\pi$
$5$	−0.133530	−0.0597163	−0.0298582	+	0.999554i	$0.509506\pi$
$6$	−1.00000	−0.408248
$7$	−1.61303	−0.609666	−0.304833	−	0.952406i	$-0.598601\pi$
$7$	−1.61303	−0.609666	−0.304833	+	0.952406i	$0.598601\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.133530	−0.0422258
$11$	2.62913	0.792712	0.396356	−	0.918097i	$-0.370275\pi$
$11$	2.62913	0.792712	0.396356	+	0.918097i	$0.370275\pi$
$12$	−1.00000	−0.288675
$13$	−4.22862	−1.17281	−0.586404	−	0.810019i	$-0.699457\pi$
$13$	−4.22862	−1.17281	−0.586404	+	0.810019i	$0.699457\pi$
$14$	−1.61303	−0.431099
$15$	0.133530	0.0344772
$16$	1.00000	0.250000
$17$	4.31475	1.04648	0.523240	−	0.852185i	$-0.324723\pi$
$17$	4.31475	1.04648	0.523240	+	0.852185i	$0.324723\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.133530	−0.0298582
$21$	1.61303	0.351991
$22$	2.62913	0.560532
$23$	−1.63540	−0.341004	−0.170502	−	0.985357i	$-0.554539\pi$
$23$	−1.63540	−0.341004	−0.170502	+	0.985357i	$0.554539\pi$
$24$	−1.00000	−0.204124
$25$	−4.98217	−0.996434
$26$	−4.22862	−0.829300
$27$	−1.00000	−0.192450
$28$	−1.61303	−0.304833
$29$	−1.99919	−0.371240	−0.185620	−	0.982622i	$-0.559429\pi$
$29$	−1.99919	−0.371240	−0.185620	+	0.982622i	$0.559429\pi$
$30$	0.133530	0.0243791
$31$	−0.126146	−0.0226564	−0.0113282	−	0.999936i	$-0.503606\pi$
$31$	−0.126146	−0.0226564	−0.0113282	+	0.999936i	$0.503606\pi$
$32$	1.00000	0.176777
$33$	−2.62913	−0.457672
$34$	4.31475	0.739974
$35$	0.215387	0.0364070
$36$	1.00000	0.166667
$37$	0.989323	0.162644	0.0813218	−	0.996688i	$-0.474086\pi$
$37$	0.989323	0.162644	0.0813218	+	0.996688i	$0.474086\pi$
$38$	−1.00000	−0.162221
$39$	4.22862	0.677121
$40$	−0.133530	−0.0211129
$41$	9.19422	1.43590	0.717948	−	0.696097i	$-0.245082\pi$
$41$	9.19422	1.43590	0.717948	+	0.696097i	$0.245082\pi$
$42$	1.61303	0.248895
$43$	−6.57466	−1.00263	−0.501313	−	0.865266i	$-0.667150\pi$
$43$	−6.57466	−1.00263	−0.501313	+	0.865266i	$0.667150\pi$
$44$	2.62913	0.396356
$45$	−0.133530	−0.0199054
$46$	−1.63540	−0.241126
$47$	−5.21171	−0.760205	−0.380103	−	0.924944i	$-0.624111\pi$
$47$	−5.21171	−0.760205	−0.380103	+	0.924944i	$0.624111\pi$
$48$	−1.00000	−0.144338
$49$	−4.39815	−0.628307
$50$	−4.98217	−0.704585
$51$	−4.31475	−0.604186
$52$	−4.22862	−0.586404
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	−0.351067	−0.0473378
$56$	−1.61303	−0.215550
$57$	1.00000	0.132453
$58$	−1.99919	−0.262506
$59$	7.07682	0.921324	0.460662	−	0.887576i	$-0.347612\pi$
$59$	7.07682	0.921324	0.460662	+	0.887576i	$0.347612\pi$
$60$	0.133530	0.0172386
$61$	−9.64227	−1.23457	−0.617283	−	0.786741i	$-0.711767\pi$
$61$	−9.64227	−1.23457	−0.617283	+	0.786741i	$0.711767\pi$
$62$	−0.126146	−0.0160205
$63$	−1.61303	−0.203222
$64$	1.00000	0.125000
$65$	0.564646	0.0700358
$66$	−2.62913	−0.323623
$67$	−10.8116	−1.32084	−0.660422	−	0.750895i	$-0.729623\pi$
$67$	−10.8116	−1.32084	−0.660422	+	0.750895i	$0.729623\pi$
$68$	4.31475	0.523240
$69$	1.63540	0.196879
$70$	0.215387	0.0257437
$71$	−2.67507	−0.317473	−0.158736	−	0.987321i	$-0.550742\pi$
$71$	−2.67507	−0.317473	−0.158736	+	0.987321i	$0.550742\pi$
$72$	1.00000	0.117851
$73$	13.4975	1.57976	0.789879	−	0.613263i	$-0.210144\pi$
$73$	13.4975	1.57976	0.789879	+	0.613263i	$0.210144\pi$
$74$	0.989323	0.115006
$75$	4.98217	0.575291
$76$	−1.00000	−0.114708
$77$	−4.24085	−0.483290
$78$	4.22862	0.478797
$79$	10.3723	1.16698	0.583489	−	0.812121i	$-0.301687\pi$
$79$	10.3723	1.16698	0.583489	+	0.812121i	$0.301687\pi$
$80$	−0.133530	−0.0149291
$81$	1.00000	0.111111
$82$	9.19422	1.01533
$83$	8.53170	0.936476	0.468238	−	0.883602i	$-0.344889\pi$
$83$	8.53170	0.936476	0.468238	+	0.883602i	$0.344889\pi$
$84$	1.61303	0.175996
$85$	−0.576147	−0.0624920
$86$	−6.57466	−0.708964
$87$	1.99919	0.214335
$88$	2.62913	0.280266
$89$	−18.4051	−1.95094	−0.975471	−	0.220129i	$-0.929352\pi$
$89$	−18.4051	−1.95094	−0.975471	+	0.220129i	$0.929352\pi$
$90$	−0.133530	−0.0140753
$91$	6.82087	0.715022
$92$	−1.63540	−0.170502
$93$	0.126146	0.0130807
$94$	−5.21171	−0.537546
$95$	0.133530	0.0136999
$96$	−1.00000	−0.102062
$97$	−17.1005	−1.73629	−0.868144	−	0.496312i	$-0.834687\pi$
$97$	−17.1005	−1.73629	−0.868144	+	0.496312i	$0.834687\pi$
$98$	−4.39815	−0.444280
$99$	2.62913	0.264237
$100$	−4.98217	−0.498217
$101$	−8.85011	−0.880619	−0.440310	−	0.897846i	$-0.645131\pi$
$101$	−8.85011	−0.880619	−0.440310	+	0.897846i	$0.645131\pi$
$102$	−4.31475	−0.427224
$103$	−7.32779	−0.722029	−0.361014	−	0.932560i	$-0.617570\pi$
$103$	−7.32779	−0.722029	−0.361014	+	0.932560i	$0.617570\pi$
$104$	−4.22862	−0.414650
$105$	−0.215387	−0.0210196
$106$	1.00000	0.0971286
$107$	13.8487	1.33880	0.669402	−	0.742900i	$-0.266550\pi$
$107$	13.8487	1.33880	0.669402	+	0.742900i	$0.266550\pi$
$108$	−1.00000	−0.0962250
$109$	−5.47884	−0.524778	−0.262389	−	0.964962i	$-0.584510\pi$
$109$	−5.47884	−0.524778	−0.262389	+	0.964962i	$0.584510\pi$
$110$	−0.351067	−0.0334729
$111$	−0.989323	−0.0939024
$112$	−1.61303	−0.152417
$113$	−3.67754	−0.345954	−0.172977	−	0.984926i	$-0.555339\pi$
$113$	−3.67754	−0.345954	−0.172977	+	0.984926i	$0.555339\pi$
$114$	1.00000	0.0936586
$115$	0.218374	0.0203635
$116$	−1.99919	−0.185620
$117$	−4.22862	−0.390936
$118$	7.07682	0.651474
$119$	−6.95980	−0.638004
$120$	0.133530	0.0121895
$121$	−4.08769	−0.371608
$122$	−9.64227	−0.872970
$123$	−9.19422	−0.829015
$124$	−0.126146	−0.0113282
$125$	1.33292	0.119220
$126$	−1.61303	−0.143700
$127$	1.16929	0.103758	0.0518788	−	0.998653i	$-0.483479\pi$
$127$	1.16929	0.103758	0.0518788	+	0.998653i	$0.483479\pi$
$128$	1.00000	0.0883883
$129$	6.57466	0.578866
$130$	0.564646	0.0495228
$131$	12.5935	1.10030	0.550150	−	0.835066i	$-0.314571\pi$
$131$	12.5935	1.10030	0.550150	+	0.835066i	$0.314571\pi$
$132$	−2.62913	−0.228836
$133$	1.61303	0.139867
$134$	−10.8116	−0.933978
$135$	0.133530	0.0114924
$136$	4.31475	0.369987
$137$	0.0110498	0.000944049 0	0.000472025	−	1.00000i	$-0.499850\pi$
$137$	0.0110498	0.000944049 0	0.000472025		1.00000i	$0.499850\pi$
$138$	1.63540	0.139214
$139$	−17.1342	−1.45330	−0.726650	−	0.687008i	$-0.758924\pi$
$139$	−17.1342	−1.45330	−0.726650	+	0.687008i	$0.758924\pi$
$140$	0.215387	0.0182035
$141$	5.21171	0.438905
$142$	−2.67507	−0.224487
$143$	−11.1176	−0.929699
$144$	1.00000	0.0833333
$145$	0.266951	0.0221691
$146$	13.4975	1.11706
$147$	4.39815	0.362753
$148$	0.989323	0.0813218
$149$	−3.15657	−0.258597	−0.129298	−	0.991606i	$-0.541272\pi$
$149$	−3.15657	−0.258597	−0.129298	+	0.991606i	$0.541272\pi$
$150$	4.98217	0.406792
$151$	0.744742	0.0606063	0.0303031	−	0.999541i	$-0.490353\pi$
$151$	0.744742	0.0606063	0.0303031	+	0.999541i	$0.490353\pi$
$152$	−1.00000	−0.0811107
$153$	4.31475	0.348827
$154$	−4.24085	−0.341738
$155$	0.0168442	0.00135296
$156$	4.22862	0.338560
$157$	−6.83316	−0.545345	−0.272673	−	0.962107i	$-0.587908\pi$
$157$	−6.83316	−0.545345	−0.272673	+	0.962107i	$0.587908\pi$
$158$	10.3723	0.825177
$159$	−1.00000	−0.0793052
$160$	−0.133530	−0.0105565
$161$	2.63794	0.207899
$162$	1.00000	0.0785674
$163$	−7.48549	−0.586309	−0.293154	−	0.956065i	$-0.594705\pi$
$163$	−7.48549	−0.586309	−0.293154	+	0.956065i	$0.594705\pi$
$164$	9.19422	0.717948
$165$	0.351067	0.0273305
$166$	8.53170	0.662188
$167$	−13.2934	−1.02868	−0.514338	−	0.857588i	$-0.671962\pi$
$167$	−13.2934	−1.02868	−0.514338	+	0.857588i	$0.671962\pi$
$168$	1.61303	0.124448
$169$	4.88122	0.375478
$170$	−0.576147	−0.0441885
$171$	−1.00000	−0.0764719
$172$	−6.57466	−0.501313
$173$	2.38713	0.181490	0.0907452	−	0.995874i	$-0.471075\pi$
$173$	2.38713	0.181490	0.0907452	+	0.995874i	$0.471075\pi$
$174$	1.99919	0.151558
$175$	8.03637	0.607492
$176$	2.62913	0.198178
$177$	−7.07682	−0.531927
$178$	−18.4051	−1.37952
$179$	14.0684	1.05153	0.525763	−	0.850631i	$-0.323780\pi$
$179$	14.0684	1.05153	0.525763	+	0.850631i	$0.323780\pi$
$180$	−0.133530	−0.00995272
$181$	−13.3591	−0.992975	−0.496487	−	0.868044i	$-0.665377\pi$
$181$	−13.3591	−0.992975	−0.496487	+	0.868044i	$0.665377\pi$
$182$	6.82087	0.505597
$183$	9.64227	0.712777
$184$	−1.63540	−0.120563
$185$	−0.132104	−0.00971248
$186$	0.126146	0.00924945
$187$	11.3440	0.829558
$188$	−5.21171	−0.380103
$189$	1.61303	0.117330
$190$	0.133530	0.00968727
$191$	−15.4021	−1.11446	−0.557228	−	0.830359i	$-0.688135\pi$
$191$	−15.4021	−1.11446	−0.557228	+	0.830359i	$0.688135\pi$
$192$	−1.00000	−0.0721688
$193$	−17.0041	−1.22398	−0.611990	−	0.790866i	$-0.709631\pi$
$193$	−17.0041	−1.22398	−0.611990	+	0.790866i	$0.709631\pi$
$194$	−17.1005	−1.22774
$195$	−0.564646	−0.0404352
$196$	−4.39815	−0.314153
$197$	22.1158	1.57568	0.787842	−	0.615877i	$-0.211198\pi$
$197$	22.1158	1.57568	0.787842	+	0.615877i	$0.211198\pi$
$198$	2.62913	0.186844
$199$	−5.89946	−0.418202	−0.209101	−	0.977894i	$-0.567054\pi$
$199$	−5.89946	−0.418202	−0.209101	+	0.977894i	$0.567054\pi$
$200$	−4.98217	−0.352293
$201$	10.8116	0.762590
$202$	−8.85011	−0.622692
$203$	3.22474	0.226333
$204$	−4.31475	−0.302093
$205$	−1.22770	−0.0857464
$206$	−7.32779	−0.510552
$207$	−1.63540	−0.113668
$208$	−4.22862	−0.293202
$209$	−2.62913	−0.181861
$210$	−0.215387	−0.0148631
$211$	6.11370	0.420884	0.210442	−	0.977606i	$-0.432510\pi$
$211$	6.11370	0.420884	0.210442	+	0.977606i	$0.432510\pi$
$212$	1.00000	0.0686803
$213$	2.67507	0.183293
$214$	13.8487	0.946678
$215$	0.877913	0.0598731
$216$	−1.00000	−0.0680414
$217$	0.203476	0.0138129
$218$	−5.47884	−0.371074
$219$	−13.4975	−0.912073
$220$	−0.351067	−0.0236689
$221$	−18.2454	−1.22732
$222$	−0.989323	−0.0663990
$223$	−21.6950	−1.45280	−0.726402	−	0.687270i	$-0.758809\pi$
$223$	−21.6950	−1.45280	−0.726402	+	0.687270i	$0.758809\pi$
$224$	−1.61303	−0.107775
$225$	−4.98217	−0.332145
$226$	−3.67754	−0.244626
$227$	−25.8441	−1.71533	−0.857665	−	0.514208i	$-0.828086\pi$
$227$	−25.8441	−1.71533	−0.857665	+	0.514208i	$0.828086\pi$
$228$	1.00000	0.0662266
$229$	−7.66717	−0.506661	−0.253330	−	0.967380i	$-0.581526\pi$
$229$	−7.66717	−0.506661	−0.253330	+	0.967380i	$0.581526\pi$
$230$	0.218374	0.0143992
$231$	4.24085	0.279028
$232$	−1.99919	−0.131253
$233$	−28.1465	−1.84394	−0.921970	−	0.387262i	$-0.873421\pi$
$233$	−28.1465	−1.84394	−0.921970	+	0.387262i	$0.873421\pi$
$234$	−4.22862	−0.276433
$235$	0.695918	0.0453967
$236$	7.07682	0.460662
$237$	−10.3723	−0.673754
$238$	−6.95980	−0.451137
$239$	−21.1835	−1.37025	−0.685125	−	0.728426i	$-0.740252\pi$
$239$	−21.1835	−1.37025	−0.685125	+	0.728426i	$0.740252\pi$
$240$	0.133530	0.00861931
$241$	17.2517	1.11128	0.555639	−	0.831423i	$-0.312474\pi$
$241$	17.2517	1.11128	0.555639	+	0.831423i	$0.312474\pi$
$242$	−4.08769	−0.262766
$243$	−1.00000	−0.0641500
$244$	−9.64227	−0.617283
$245$	0.587284	0.0375202
$246$	−9.19422	−0.586202
$247$	4.22862	0.269061
$248$	−0.126146	−0.00801026
$249$	−8.53170	−0.540675
$250$	1.33292	0.0843010
$251$	−6.50097	−0.410338	−0.205169	−	0.978727i	$-0.565774\pi$
$251$	−6.50097	−0.410338	−0.205169	+	0.978727i	$0.565774\pi$
$252$	−1.61303	−0.101611
$253$	−4.29967	−0.270318
$254$	1.16929	0.0733677
$255$	0.576147	0.0360798
$256$	1.00000	0.0625000
$257$	−5.27041	−0.328759	−0.164380	−	0.986397i	$-0.552562\pi$
$257$	−5.27041	−0.328759	−0.164380	+	0.986397i	$0.552562\pi$
$258$	6.57466	0.409320
$259$	−1.59580	−0.0991584
$260$	0.564646	0.0350179
$261$	−1.99919	−0.123747
$262$	12.5935	0.778030
$263$	−10.6499	−0.656703	−0.328352	−	0.944556i	$-0.606493\pi$
$263$	−10.6499	−0.656703	−0.328352	+	0.944556i	$0.606493\pi$
$264$	−2.62913	−0.161812
$265$	−0.133530	−0.00820267
$266$	1.61303	0.0989010
$267$	18.4051	1.12638
$268$	−10.8116	−0.660422
$269$	23.0252	1.40387	0.701936	−	0.712240i	$-0.252319\pi$
$269$	23.0252	1.40387	0.701936	+	0.712240i	$0.252319\pi$
$270$	0.133530	0.00812636
$271$	15.3554	0.932773	0.466386	−	0.884581i	$-0.345556\pi$
$271$	15.3554	0.932773	0.466386	+	0.884581i	$0.345556\pi$
$272$	4.31475	0.261620
$273$	−6.82087	−0.412818
$274$	0.0110498	0.000667544 0
$275$	−13.0988	−0.789885
$276$	1.63540	0.0984394
$277$	20.6944	1.24341	0.621704	−	0.783253i	$-0.286441\pi$
$277$	20.6944	1.24341	0.621704	+	0.783253i	$0.286441\pi$
$278$	−17.1342	−1.02764
$279$	−0.126146	−0.00755215
$280$	0.215387	0.0128718
$281$	13.3508	0.796442	0.398221	−	0.917290i	$-0.369628\pi$
$281$	13.3508	0.796442	0.398221	+	0.917290i	$0.369628\pi$
$282$	5.21171	0.310353
$283$	−6.28533	−0.373624	−0.186812	−	0.982396i	$-0.559816\pi$
$283$	−6.28533	−0.373624	−0.186812	+	0.982396i	$0.559816\pi$
$284$	−2.67507	−0.158736
$285$	−0.133530	−0.00790962
$286$	−11.1176	−0.657396
$287$	−14.8305	−0.875417
$288$	1.00000	0.0589256
$289$	1.61707	0.0951217
$290$	0.266951	0.0156759
$291$	17.1005	1.00245
$292$	13.4975	0.789879
$293$	12.1608	0.710442	0.355221	−	0.934782i	$-0.384406\pi$
$293$	12.1608	0.710442	0.355221	+	0.934782i	$0.384406\pi$
$294$	4.39815	0.256505
$295$	−0.944967	−0.0550181
$296$	0.989323	0.0575032
$297$	−2.62913	−0.152557
$298$	−3.15657	−0.182855
$299$	6.91548	0.399932
$300$	4.98217	0.287646
$301$	10.6051	0.611268
$302$	0.744742	0.0428551
$303$	8.85011	0.508426
$304$	−1.00000	−0.0573539
$305$	1.28753	0.0737237
$306$	4.31475	0.246658
$307$	−4.81443	−0.274774	−0.137387	−	0.990517i	$-0.543870\pi$
$307$	−4.81443	−0.274774	−0.137387	+	0.990517i	$0.543870\pi$
$308$	−4.24085	−0.241645
$309$	7.32779	0.416864
$310$	0.0168442	0.000956686 0
$311$	−9.89104	−0.560869	−0.280435	−	0.959873i	$-0.590479\pi$
$311$	−9.89104	−0.560869	−0.280435	+	0.959873i	$0.590479\pi$
$312$	4.22862	0.239398
$313$	−14.5455	−0.822159	−0.411079	−	0.911600i	$-0.634848\pi$
$313$	−14.5455	−0.822159	−0.411079	+	0.911600i	$0.634848\pi$
$314$	−6.83316	−0.385617
$315$	0.215387	0.0121357
$316$	10.3723	0.583489
$317$	−20.8908	−1.17335	−0.586673	−	0.809824i	$-0.699562\pi$
$317$	−20.8908	−1.17335	−0.586673	+	0.809824i	$0.699562\pi$
$318$	−1.00000	−0.0560772
$319$	−5.25612	−0.294286
$320$	−0.133530	−0.00746454
$321$	−13.8487	−0.772959
$322$	2.63794	0.147007
$323$	−4.31475	−0.240079
$324$	1.00000	0.0555556
$325$	21.0677	1.16863
$326$	−7.48549	−0.414583
$327$	5.47884	0.302981
$328$	9.19422	0.507666
$329$	8.40662	0.463472
$330$	0.351067	0.0193256
$331$	12.9259	0.710469	0.355235	−	0.934777i	$-0.384401\pi$
$331$	12.9259	0.710469	0.355235	+	0.934777i	$0.384401\pi$
$332$	8.53170	0.468238
$333$	0.989323	0.0542146
$334$	−13.2934	−0.727383
$335$	1.44367	0.0788760
$336$	1.61303	0.0879978
$337$	28.6006	1.55797	0.778987	−	0.627040i	$-0.215734\pi$
$337$	28.6006	1.55797	0.778987	+	0.627040i	$0.215734\pi$
$338$	4.88122	0.265503
$339$	3.67754	0.199736
$340$	−0.576147	−0.0312460
$341$	−0.331653	−0.0179600
$342$	−1.00000	−0.0540738
$343$	18.3855	0.992724
$344$	−6.57466	−0.354482
$345$	−0.218374	−0.0117569
$346$	2.38713	0.128333
$347$	4.67496	0.250965	0.125482	−	0.992096i	$-0.459952\pi$
$347$	4.67496	0.250965	0.125482	+	0.992096i	$0.459952\pi$
$348$	1.99919	0.107168
$349$	7.55630	0.404479	0.202240	−	0.979336i	$-0.435178\pi$
$349$	7.55630	0.404479	0.202240	+	0.979336i	$0.435178\pi$
$350$	8.03637	0.429562
$351$	4.22862	0.225707
$352$	2.62913	0.140133
$353$	−11.5838	−0.616543	−0.308271	−	0.951298i	$-0.599751\pi$
$353$	−11.5838	−0.616543	−0.308271	+	0.951298i	$0.599751\pi$
$354$	−7.07682	−0.376129
$355$	0.357202	0.0189583
$356$	−18.4051	−0.975471
$357$	6.95980	0.368352
$358$	14.0684	0.743541
$359$	3.40679	0.179803	0.0899017	−	0.995951i	$-0.471345\pi$
$359$	3.40679	0.179803	0.0899017	+	0.995951i	$0.471345\pi$
$360$	−0.133530	−0.00703764
$361$	1.00000	0.0526316
$362$	−13.3591	−0.702139
$363$	4.08769	0.214548
$364$	6.82087	0.357511
$365$	−1.80231	−0.0943373
$366$	9.64227	0.504009
$367$	28.7617	1.50135	0.750675	−	0.660671i	$-0.229728\pi$
$367$	28.7617	1.50135	0.750675	+	0.660671i	$0.229728\pi$
$368$	−1.63540	−0.0852510
$369$	9.19422	0.478632
$370$	−0.132104	−0.00686776
$371$	−1.61303	−0.0837441
$372$	0.126146	0.00654035
$373$	−35.0116	−1.81283	−0.906415	−	0.422388i	$-0.861192\pi$
$373$	−35.0116	−1.81283	−0.906415	+	0.422388i	$0.861192\pi$
$374$	11.3440	0.586586
$375$	−1.33292	−0.0688315
$376$	−5.21171	−0.268773
$377$	8.45381	0.435393
$378$	1.61303	0.0829651
$379$	−4.60077	−0.236326	−0.118163	−	0.992994i	$-0.537701\pi$
$379$	−4.60077	−0.236326	−0.118163	+	0.992994i	$0.537701\pi$
$380$	0.133530	0.00684993
$381$	−1.16929	−0.0599044
$382$	−15.4021	−0.788040
$383$	−34.3439	−1.75489	−0.877445	−	0.479677i	$-0.840754\pi$
$383$	−34.3439	−1.75489	−0.877445	+	0.479677i	$0.840754\pi$
$384$	−1.00000	−0.0510310
$385$	0.566280	0.0288603
$386$	−17.0041	−0.865484
$387$	−6.57466	−0.334209
$388$	−17.1005	−0.868144
$389$	−27.5303	−1.39584	−0.697921	−	0.716174i	$-0.745891\pi$
$389$	−27.5303	−1.39584	−0.697921	+	0.716174i	$0.745891\pi$
$390$	−0.564646	−0.0285920
$391$	−7.05634	−0.356854
$392$	−4.39815	−0.222140
$393$	−12.5935	−0.635259
$394$	22.1158	1.11418
$395$	−1.38501	−0.0696876
$396$	2.62913	0.132119
$397$	−36.8429	−1.84909	−0.924545	−	0.381073i	$-0.875555\pi$
$397$	−36.8429	−1.84909	−0.924545	+	0.381073i	$0.875555\pi$
$398$	−5.89946	−0.295713
$399$	−1.61303	−0.0807523
$400$	−4.98217	−0.249108
$401$	−0.474617	−0.0237013	−0.0118506	−	0.999930i	$-0.503772\pi$
$401$	−0.474617	−0.0237013	−0.0118506	+	0.999930i	$0.503772\pi$
$402$	10.8116	0.539232
$403$	0.533422	0.0265716
$404$	−8.85011	−0.440310
$405$	−0.133530	−0.00663515
$406$	3.22474	0.160041
$407$	2.60106	0.128930
$408$	−4.31475	−0.213612
$409$	17.6713	0.873790	0.436895	−	0.899513i	$-0.356078\pi$
$409$	17.6713	0.873790	0.436895	+	0.899513i	$0.356078\pi$
$410$	−1.22770	−0.0606319
$411$	−0.0110498	−0.000545047 0
$412$	−7.32779	−0.361014
$413$	−11.4151	−0.561700
$414$	−1.63540	−0.0803754
$415$	−1.13924	−0.0559229
$416$	−4.22862	−0.207325
$417$	17.1342	0.839063
$418$	−2.62913	−0.128595
$419$	−0.564609	−0.0275829	−0.0137915	−	0.999905i	$-0.504390\pi$
$419$	−0.564609	−0.0275829	−0.0137915	+	0.999905i	$0.504390\pi$
$420$	−0.215387	−0.0105098
$421$	27.7792	1.35387	0.676937	−	0.736041i	$-0.263307\pi$
$421$	27.7792	1.35387	0.676937	+	0.736041i	$0.263307\pi$
$422$	6.11370	0.297610
$423$	−5.21171	−0.253402
$424$	1.00000	0.0485643
$425$	−21.4968	−1.04275
$426$	2.67507	0.129608
$427$	15.5532	0.752673
$428$	13.8487	0.669402
$429$	11.1176	0.536762
$430$	0.877913	0.0423367
$431$	1.66576	0.0802369	0.0401185	−	0.999195i	$-0.487226\pi$
$431$	1.66576	0.0802369	0.0401185	+	0.999195i	$0.487226\pi$
$432$	−1.00000	−0.0481125
$433$	−37.9454	−1.82354	−0.911769	−	0.410704i	$-0.865283\pi$
$433$	−37.9454	−1.82354	−0.911769	+	0.410704i	$0.865283\pi$
$434$	0.203476	0.00976717
$435$	−0.266951	−0.0127993
$436$	−5.47884	−0.262389
$437$	1.63540	0.0782317
$438$	−13.4975	−0.644933
$439$	26.1242	1.24684	0.623419	−	0.781888i	$-0.285743\pi$
$439$	26.1242	1.24684	0.623419	+	0.781888i	$0.285743\pi$
$440$	−0.351067	−0.0167365
$441$	−4.39815	−0.209436
$442$	−18.2454	−0.867847
$443$	25.5672	1.21473	0.607367	−	0.794421i	$-0.292226\pi$
$443$	25.5672	1.21473	0.607367	+	0.794421i	$0.292226\pi$
$444$	−0.989323	−0.0469512
$445$	2.45763	0.116503
$446$	−21.6950	−1.02729
$447$	3.15657	0.149301
$448$	−1.61303	−0.0762083
$449$	24.5924	1.16059	0.580294	−	0.814407i	$-0.302938\pi$
$449$	24.5924	1.16059	0.580294	+	0.814407i	$0.302938\pi$
$450$	−4.98217	−0.234862
$451$	24.1728	1.13825
$452$	−3.67754	−0.172977
$453$	−0.744742	−0.0349910
$454$	−25.8441	−1.21292
$455$	−0.910789	−0.0426985
$456$	1.00000	0.0468293
$457$	−30.1161	−1.40877	−0.704386	−	0.709818i	$-0.748777\pi$
$457$	−30.1161	−1.40877	−0.704386	+	0.709818i	$0.748777\pi$
$458$	−7.66717	−0.358263
$459$	−4.31475	−0.201395
$460$	0.218374	0.0101818
$461$	−16.4104	−0.764310	−0.382155	−	0.924098i	$-0.624818\pi$
$461$	−16.4104	−0.764310	−0.382155	+	0.924098i	$0.624818\pi$
$462$	4.24085	0.197302
$463$	34.2993	1.59402	0.797012	−	0.603964i	$-0.206413\pi$
$463$	34.2993	1.59402	0.797012	+	0.603964i	$0.206413\pi$
$464$	−1.99919	−0.0928100
$465$	−0.0168442	−0.000781131 0
$466$	−28.1465	−1.30386
$467$	25.1535	1.16397	0.581983	−	0.813201i	$-0.302277\pi$
$467$	25.1535	1.16397	0.581983	+	0.813201i	$0.302277\pi$
$468$	−4.22862	−0.195468
$469$	17.4394	0.805274
$470$	0.695918	0.0321003
$471$	6.83316	0.314855
$472$	7.07682	0.325737
$473$	−17.2856	−0.794794
$474$	−10.3723	−0.476416
$475$	4.98217	0.228598
$476$	−6.95980	−0.319002
$477$	1.00000	0.0457869
$478$	−21.1835	−0.968913
$479$	−14.3286	−0.654691	−0.327345	−	0.944905i	$-0.606154\pi$
$479$	−14.3286	−0.654691	−0.327345	+	0.944905i	$0.606154\pi$
$480$	0.133530	0.00609477
$481$	−4.18347	−0.190750
$482$	17.2517	0.785793
$483$	−2.63794	−0.120030
$484$	−4.08769	−0.185804
$485$	2.28342	0.103685
$486$	−1.00000	−0.0453609
$487$	−18.0676	−0.818721	−0.409360	−	0.912373i	$-0.634248\pi$
$487$	−18.0676	−0.818721	−0.409360	+	0.912373i	$0.634248\pi$
$488$	−9.64227	−0.436485
$489$	7.48549	0.338505
$490$	0.587284	0.0265308
$491$	26.7700	1.20811	0.604057	−	0.796941i	$-0.293550\pi$
$491$	26.7700	1.20811	0.604057	+	0.796941i	$0.293550\pi$
$492$	−9.19422	−0.414507
$493$	−8.62600	−0.388495
$494$	4.22862	0.190255
$495$	−0.351067	−0.0157793
$496$	−0.126146	−0.00566411
$497$	4.31496	0.193552
$498$	−8.53170	−0.382315
$499$	−1.46345	−0.0655130	−0.0327565	−	0.999463i	$-0.510429\pi$
$499$	−1.46345	−0.0655130	−0.0327565	+	0.999463i	$0.510429\pi$
$500$	1.33292	0.0596098
$501$	13.2934	0.593906
$502$	−6.50097	−0.290153
$503$	19.5011	0.869510	0.434755	−	0.900549i	$-0.356835\pi$
$503$	19.5011	0.869510	0.434755	+	0.900549i	$0.356835\pi$
$504$	−1.61303	−0.0718499
$505$	1.18175	0.0525873
$506$	−4.29967	−0.191144
$507$	−4.88122	−0.216782
$508$	1.16929	0.0518788
$509$	14.6392	0.648872	0.324436	−	0.945908i	$-0.394825\pi$
$509$	14.6392	0.648872	0.324436	+	0.945908i	$0.394825\pi$
$510$	0.576147	0.0255122
$511$	−21.7717	−0.963125
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−5.27041	−0.232468
$515$	0.978478	0.0431169
$516$	6.57466	0.289433
$517$	−13.7022	−0.602624
$518$	−1.59580	−0.0701156
$519$	−2.38713	−0.104783
$520$	0.564646	0.0247614
$521$	5.27515	0.231109	0.115554	−	0.993301i	$-0.463136\pi$
$521$	5.27515	0.231109	0.115554	+	0.993301i	$0.463136\pi$
$522$	−1.99919	−0.0875021
$523$	−15.2457	−0.666649	−0.333324	−	0.942812i	$-0.608170\pi$
$523$	−15.2457	−0.666649	−0.333324	+	0.942812i	$0.608170\pi$
$524$	12.5935	0.550150
$525$	−8.03637	−0.350736
$526$	−10.6499	−0.464359
$527$	−0.544287	−0.0237095
$528$	−2.62913	−0.114418
$529$	−20.3255	−0.883716
$530$	−0.133530	−0.00580016
$531$	7.07682	0.307108
$532$	1.61303	0.0699335
$533$	−38.8788	−1.68403
$534$	18.4051	0.796469
$535$	−1.84921	−0.0799485
$536$	−10.8116	−0.466989
$537$	−14.0684	−0.607098
$538$	23.0252	0.992687
$539$	−11.5633	−0.498066
$540$	0.133530	0.00574621
$541$	−8.92435	−0.383688	−0.191844	−	0.981425i	$-0.561447\pi$
$541$	−8.92435	−0.383688	−0.191844	+	0.981425i	$0.561447\pi$
$542$	15.3554	0.659570
$543$	13.3591	0.573294
$544$	4.31475	0.184993
$545$	0.731588	0.0313378
$546$	−6.82087	−0.291906
$547$	34.8424	1.48975	0.744877	−	0.667202i	$-0.232508\pi$
$547$	34.8424	1.48975	0.744877	+	0.667202i	$0.232508\pi$
$548$	0.0110498	0.000472025 0
$549$	−9.64227	−0.411522
$550$	−13.0988	−0.558533
$551$	1.99919	0.0851683
$552$	1.63540	0.0696072
$553$	−16.7308	−0.711467
$554$	20.6944	0.879222
$555$	0.132104	0.00560750
$556$	−17.1342	−0.726650
$557$	−26.5900	−1.12666	−0.563328	−	0.826233i	$-0.690479\pi$
$557$	−26.5900	−1.12666	−0.563328	+	0.826233i	$0.690479\pi$
$558$	−0.126146	−0.00534017
$559$	27.8017	1.17589
$560$	0.215387	0.00910176
$561$	−11.3440	−0.478945
$562$	13.3508	0.563169
$563$	−4.82097	−0.203180	−0.101590	−	0.994826i	$-0.532393\pi$
$563$	−4.82097	−0.203180	−0.101590	+	0.994826i	$0.532393\pi$
$564$	5.21171	0.219452
$565$	0.491061	0.0206591
$566$	−6.28533	−0.264192
$567$	−1.61303	−0.0677407
$568$	−2.67507	−0.112244
$569$	−37.6597	−1.57877	−0.789387	−	0.613895i	$-0.789602\pi$
$569$	−37.6597	−1.57877	−0.789387	+	0.613895i	$0.789602\pi$
$570$	−0.133530	−0.00559295
$571$	41.3495	1.73042	0.865212	−	0.501406i	$-0.167184\pi$
$571$	41.3495	1.73042	0.865212	+	0.501406i	$0.167184\pi$
$572$	−11.1176	−0.464849
$573$	15.4021	0.643432
$574$	−14.8305	−0.619014
$575$	8.14783	0.339788
$576$	1.00000	0.0416667
$577$	−10.0971	−0.420348	−0.210174	−	0.977664i	$-0.567403\pi$
$577$	−10.0971	−0.420348	−0.210174	+	0.977664i	$0.567403\pi$
$578$	1.61707	0.0672612
$579$	17.0041	0.706665
$580$	0.266951	0.0110845
$581$	−13.7619	−0.570938
$582$	17.1005	0.708837
$583$	2.62913	0.108887
$584$	13.4975	0.558529
$585$	0.564646	0.0233453
$586$	12.1608	0.502358
$587$	0.919873	0.0379672	0.0189836	−	0.999820i	$-0.493957\pi$
$587$	0.919873	0.0379672	0.0189836	+	0.999820i	$0.493957\pi$
$588$	4.39815	0.181377
$589$	0.126146	0.00519774
$590$	−0.944967	−0.0389037
$591$	−22.1158	−0.909722
$592$	0.989323	0.0406609
$593$	7.29854	0.299715	0.149858	−	0.988708i	$-0.452118\pi$
$593$	7.29854	0.299715	0.149858	+	0.988708i	$0.452118\pi$
$594$	−2.62913	−0.107874
$595$	0.929341	0.0380993
$596$	−3.15657	−0.129298
$597$	5.89946	0.241449
$598$	6.91548	0.282795
$599$	18.3289	0.748899	0.374450	−	0.927247i	$-0.377832\pi$
$599$	18.3289	0.748899	0.374450	+	0.927247i	$0.377832\pi$
$600$	4.98217	0.203396
$601$	36.9406	1.50684	0.753418	−	0.657542i	$-0.228404\pi$
$601$	36.9406	1.50684	0.753418	+	0.657542i	$0.228404\pi$
$602$	10.6051	0.432231
$603$	−10.8116	−0.440281
$604$	0.744742	0.0303031
$605$	0.545828	0.0221911
$606$	8.85011	0.359511
$607$	30.0817	1.22098	0.610489	−	0.792025i	$-0.290973\pi$
$607$	30.0817	1.22098	0.610489	+	0.792025i	$0.290973\pi$
$608$	−1.00000	−0.0405554
$609$	−3.22474	−0.130673
$610$	1.28753	0.0521305
$611$	22.0383	0.891575
$612$	4.31475	0.174413
$613$	36.2610	1.46457	0.732284	−	0.680999i	$-0.238454\pi$
$613$	36.2610	1.46457	0.732284	+	0.680999i	$0.238454\pi$
$614$	−4.81443	−0.194295
$615$	1.22770	0.0495057
$616$	−4.24085	−0.170869
$617$	31.0327	1.24933	0.624664	−	0.780894i	$-0.285236\pi$
$617$	31.0327	1.24933	0.624664	+	0.780894i	$0.285236\pi$
$618$	7.32779	0.294767
$619$	−34.5903	−1.39030	−0.695151	−	0.718863i	$-0.744663\pi$
$619$	−34.5903	−1.39030	−0.695151	+	0.718863i	$0.744663\pi$
$620$	0.0168442	0.000676479 0
$621$	1.63540	0.0656263
$622$	−9.89104	−0.396594
$623$	29.6880	1.18942
$624$	4.22862	0.169280
$625$	24.7329	0.989315
$626$	−14.5455	−0.581354
$627$	2.62913	0.104997
$628$	−6.83316	−0.272673
$629$	4.26868	0.170203
$630$	0.215387	0.00858122
$631$	−10.9521	−0.435996	−0.217998	−	0.975949i	$-0.569953\pi$
$631$	−10.9521	−0.435996	−0.217998	+	0.975949i	$0.569953\pi$
$632$	10.3723	0.412589
$633$	−6.11370	−0.242998
$634$	−20.8908	−0.829680
$635$	−0.156135	−0.00619602
$636$	−1.00000	−0.0396526
$637$	18.5981	0.736883
$638$	−5.25612	−0.208092
$639$	−2.67507	−0.105824
$640$	−0.133530	−0.00527823
$641$	40.7161	1.60819	0.804095	−	0.594501i	$-0.202650\pi$
$641$	40.7161	1.60819	0.804095	+	0.594501i	$0.202650\pi$
$642$	−13.8487	−0.546565
$643$	2.32251	0.0915908	0.0457954	−	0.998951i	$-0.485418\pi$
$643$	2.32251	0.0915908	0.0457954	+	0.998951i	$0.485418\pi$
$644$	2.63794	0.103949
$645$	−0.877913	−0.0345678
$646$	−4.31475	−0.169762
$647$	−8.90313	−0.350018	−0.175009	−	0.984567i	$-0.555995\pi$
$647$	−8.90313	−0.350018	−0.175009	+	0.984567i	$0.555995\pi$
$648$	1.00000	0.0392837
$649$	18.6059	0.730345
$650$	21.0677	0.826343
$651$	−0.203476	−0.00797486
$652$	−7.48549	−0.293154
$653$	−29.0492	−1.13678	−0.568391	−	0.822758i	$-0.692434\pi$
$653$	−29.0492	−1.13678	−0.568391	+	0.822758i	$0.692434\pi$
$654$	5.47884	0.214240
$655$	−1.68161	−0.0657059
$656$	9.19422	0.358974
$657$	13.4975	0.526586
$658$	8.40662	0.327724
$659$	−9.84870	−0.383651	−0.191825	−	0.981429i	$-0.561441\pi$
$659$	−9.84870	−0.383651	−0.191825	+	0.981429i	$0.561441\pi$
$660$	0.351067	0.0136653
$661$	29.1238	1.13279	0.566393	−	0.824135i	$-0.308338\pi$
$661$	29.1238	1.13279	0.566393	+	0.824135i	$0.308338\pi$
$662$	12.9259	0.502378
$663$	18.2454	0.708594
$664$	8.53170	0.331094
$665$	−0.215387	−0.00835235
$666$	0.989323	0.0383355
$667$	3.26947	0.126594
$668$	−13.2934	−0.514338
$669$	21.6950	0.838776
$670$	1.44367	0.0557737
$671$	−25.3508	−0.978655
$672$	1.61303	0.0622238
$673$	−2.74603	−0.105852	−0.0529258	−	0.998598i	$-0.516855\pi$
$673$	−2.74603	−0.105852	−0.0529258	+	0.998598i	$0.516855\pi$
$674$	28.6006	1.10165
$675$	4.98217	0.191764
$676$	4.88122	0.187739
$677$	−49.9286	−1.91891	−0.959455	−	0.281862i	$-0.909048\pi$
$677$	−49.9286	−1.91891	−0.959455	+	0.281862i	$0.909048\pi$
$678$	3.67754	0.141235
$679$	27.5835	1.05856
$680$	−0.576147	−0.0220942
$681$	25.8441	0.990347
$682$	−0.331653	−0.0126997
$683$	27.5156	1.05286	0.526428	−	0.850220i	$-0.323531\pi$
$683$	27.5156	1.05286	0.526428	+	0.850220i	$0.323531\pi$
$684$	−1.00000	−0.0382360
$685$	−0.00147548	−5.63751e−5 0
$686$	18.3855	0.701962
$687$	7.66717	0.292521
$688$	−6.57466	−0.250657
$689$	−4.22862	−0.161098
$690$	−0.218374	−0.00831337
$691$	−28.4306	−1.08155	−0.540776	−	0.841167i	$-0.681869\pi$
$691$	−28.4306	−1.08155	−0.540776	+	0.841167i	$0.681869\pi$
$692$	2.38713	0.0907452
$693$	−4.24085	−0.161097
$694$	4.67496	0.177459
$695$	2.28792	0.0867857
$696$	1.99919	0.0757790
$697$	39.6708	1.50264
$698$	7.55630	0.286010
$699$	28.1465	1.06460
$700$	8.03637	0.303746
$701$	−26.4739	−0.999904	−0.499952	−	0.866053i	$-0.666649\pi$
$701$	−26.4739	−0.999904	−0.499952	+	0.866053i	$0.666649\pi$
$702$	4.22862	0.159599
$703$	−0.989323	−0.0373130
$704$	2.62913	0.0990890
$705$	−0.695918	−0.0262098
$706$	−11.5838	−0.435962
$707$	14.2755	0.536884
$708$	−7.07682	−0.265963
$709$	34.0152	1.27747	0.638733	−	0.769428i	$-0.279459\pi$
$709$	34.0152	1.27747	0.638733	+	0.769428i	$0.279459\pi$
$710$	0.357202	0.0134055
$711$	10.3723	0.388992
$712$	−18.4051	−0.689762
$713$	0.206298	0.00772594
$714$	6.95980	0.260464
$715$	1.48453	0.0555182
$716$	14.0684	0.525763
$717$	21.1835	0.791114
$718$	3.40679	0.127140
$719$	−8.78146	−0.327493	−0.163747	−	0.986502i	$-0.552358\pi$
$719$	−8.78146	−0.327493	−0.163747	+	0.986502i	$0.552358\pi$
$720$	−0.133530	−0.00497636
$721$	11.8199	0.440197
$722$	1.00000	0.0372161
$723$	−17.2517	−0.641597
$724$	−13.3591	−0.496487
$725$	9.96030	0.369916
$726$	4.08769	0.151708
$727$	−7.30238	−0.270830	−0.135415	−	0.990789i	$-0.543237\pi$
$727$	−7.30238	−0.270830	−0.135415	+	0.990789i	$0.543237\pi$
$728$	6.82087	0.252798
$729$	1.00000	0.0370370
$730$	−1.80231	−0.0667065
$731$	−28.3680	−1.04923
$732$	9.64227	0.356388
$733$	−30.7741	−1.13667	−0.568334	−	0.822798i	$-0.692412\pi$
$733$	−30.7741	−1.13667	−0.568334	+	0.822798i	$0.692412\pi$
$734$	28.7617	1.06162
$735$	−0.587284	−0.0216623
$736$	−1.63540	−0.0602816
$737$	−28.4250	−1.04705
$738$	9.19422	0.338444
$739$	50.1079	1.84325	0.921625	−	0.388081i	$-0.126862\pi$
$739$	50.1079	1.84325	0.921625	+	0.388081i	$0.126862\pi$
$740$	−0.132104	−0.00485624
$741$	−4.22862	−0.155342
$742$	−1.61303	−0.0592160
$743$	22.9835	0.843184	0.421592	−	0.906786i	$-0.361471\pi$
$743$	22.9835	0.843184	0.421592	+	0.906786i	$0.361471\pi$
$744$	0.126146	0.00462473
$745$	0.421497	0.0154424
$746$	−35.0116	−1.28186
$747$	8.53170	0.312159
$748$	11.3440	0.414779
$749$	−22.3383	−0.816224
$750$	−1.33292	−0.0486712
$751$	−52.2155	−1.90537	−0.952685	−	0.303958i	$-0.901692\pi$
$751$	−52.2155	−1.90537	−0.952685	+	0.303958i	$0.901692\pi$
$752$	−5.21171	−0.190051
$753$	6.50097	0.236909
$754$	8.45381	0.307869
$755$	−0.0994452	−0.00361918
$756$	1.61303	0.0586652
$757$	7.23634	0.263009	0.131505	−	0.991316i	$-0.458019\pi$
$757$	7.23634	0.263009	0.131505	+	0.991316i	$0.458019\pi$
$758$	−4.60077	−0.167108
$759$	4.29967	0.156068
$760$	0.133530	0.00484363
$761$	30.7093	1.11321	0.556606	−	0.830777i	$-0.312103\pi$
$761$	30.7093	1.11321	0.556606	+	0.830777i	$0.312103\pi$
$762$	−1.16929	−0.0423588
$763$	8.83751	0.319939
$764$	−15.4021	−0.557228
$765$	−0.576147	−0.0208307
$766$	−34.3439	−1.24089
$767$	−29.9252	−1.08054
$768$	−1.00000	−0.0360844
$769$	−24.8575	−0.896385	−0.448193	−	0.893937i	$-0.647932\pi$
$769$	−24.8575	−0.896385	−0.448193	+	0.893937i	$0.647932\pi$
$770$	0.566280	0.0204073
$771$	5.27041	0.189809
$772$	−17.0041	−0.611990
$773$	−25.0247	−0.900077	−0.450039	−	0.893009i	$-0.648590\pi$
$773$	−25.0247	−0.900077	−0.450039	+	0.893009i	$0.648590\pi$
$774$	−6.57466	−0.236321
$775$	0.628479	0.0225756
$776$	−17.1005	−0.613871
$777$	1.59580	0.0572491
$778$	−27.5303	−0.987010
$779$	−9.19422	−0.329417
$780$	−0.564646	−0.0202176
$781$	−7.03311	−0.251664
$782$	−7.05634	−0.252334
$783$	1.99919	0.0714452
$784$	−4.39815	−0.157077
$785$	0.912430	0.0325660
$786$	−12.5935	−0.449196
$787$	11.1088	0.395987	0.197994	−	0.980203i	$-0.436557\pi$
$787$	11.1088	0.395987	0.197994	+	0.980203i	$0.436557\pi$
$788$	22.1158	0.787842
$789$	10.6499	0.379148
$790$	−1.38501	−0.0492766
$791$	5.93196	0.210916
$792$	2.62913	0.0934220
$793$	40.7735	1.44791
$794$	−36.8429	−1.30750
$795$	0.133530	0.00473581
$796$	−5.89946	−0.209101
$797$	12.3499	0.437457	0.218729	−	0.975786i	$-0.429809\pi$
$797$	12.3499	0.437457	0.218729	+	0.975786i	$0.429809\pi$
$798$	−1.61303	−0.0571005
$799$	−22.4872	−0.795540
$800$	−4.98217	−0.176146
$801$	−18.4051	−0.650314
$802$	−0.474617	−0.0167593
$803$	35.4865	1.25229
$804$	10.8116	0.381295
$805$	−0.352243	−0.0124149
$806$	0.533422	0.0187890
$807$	−23.0252	−0.810526
$808$	−8.85011	−0.311346
$809$	1.99289	0.0700661	0.0350331	−	0.999386i	$-0.488846\pi$
$809$	1.99289	0.0700661	0.0350331	+	0.999386i	$0.488846\pi$
$810$	−0.133530	−0.00469176
$811$	−3.86650	−0.135771	−0.0678856	−	0.997693i	$-0.521625\pi$
$811$	−3.86650	−0.135771	−0.0678856	+	0.997693i	$0.521625\pi$
$812$	3.22474	0.113166
$813$	−15.3554	−0.538537
$814$	2.60106	0.0911670
$815$	0.999535	0.0350122
$816$	−4.31475	−0.151046
$817$	6.57466	0.230018
$818$	17.6713	0.617863
$819$	6.82087	0.238341
$820$	−1.22770	−0.0428732
$821$	25.9962	0.907275	0.453637	−	0.891186i	$-0.350126\pi$
$821$	25.9962	0.907275	0.453637	+	0.891186i	$0.350126\pi$
$822$	−0.0110498	−0.000385406 0
$823$	−30.2042	−1.05285	−0.526426	−	0.850221i	$-0.676468\pi$
$823$	−30.2042	−1.05285	−0.526426	+	0.850221i	$0.676468\pi$
$824$	−7.32779	−0.255276
$825$	13.0988	0.456040
$826$	−11.4151	−0.397182
$827$	40.1589	1.39646	0.698231	−	0.715872i	$-0.253971\pi$
$827$	40.1589	1.39646	0.698231	+	0.715872i	$0.253971\pi$
$828$	−1.63540	−0.0568340
$829$	7.45575	0.258949	0.129474	−	0.991583i	$-0.458671\pi$
$829$	7.45575	0.258949	0.129474	+	0.991583i	$0.458671\pi$
$830$	−1.13924	−0.0395435
$831$	−20.6944	−0.717881
$832$	−4.22862	−0.146601
$833$	−18.9769	−0.657511
$834$	17.1342	0.593307
$835$	1.77507	0.0614287
$836$	−2.62913	−0.0909303
$837$	0.126146	0.00436023
$838$	−0.564609	−0.0195041
$839$	−55.4823	−1.91546	−0.957730	−	0.287668i	$-0.907120\pi$
$839$	−55.4823	−1.91546	−0.957730	+	0.287668i	$0.907120\pi$
$840$	−0.215387	−0.00743156
$841$	−25.0032	−0.862181
$842$	27.7792	0.957333
$843$	−13.3508	−0.459826
$844$	6.11370	0.210442
$845$	−0.651788	−0.0224222
$846$	−5.21171	−0.179182
$847$	6.59354	0.226557
$848$	1.00000	0.0343401
$849$	6.28533	0.215712
$850$	−21.4968	−0.737335
$851$	−1.61794	−0.0554622
$852$	2.67507	0.0916465
$853$	−18.1796	−0.622457	−0.311228	−	0.950335i	$-0.600740\pi$
$853$	−18.1796	−0.622457	−0.311228	+	0.950335i	$0.600740\pi$
$854$	15.5532	0.532220
$855$	0.133530	0.00456662
$856$	13.8487	0.473339
$857$	5.06935	0.173166	0.0865829	−	0.996245i	$-0.472405\pi$
$857$	5.06935	0.173166	0.0865829	+	0.996245i	$0.472405\pi$
$858$	11.1176	0.379548
$859$	−0.439370	−0.0149911	−0.00749556	−	0.999972i	$-0.502386\pi$
$859$	−0.439370	−0.0149911	−0.00749556	+	0.999972i	$0.502386\pi$
$860$	0.877913	0.0299366
$861$	14.8305	0.505422
$862$	1.66576	0.0567361
$863$	54.0716	1.84062	0.920309	−	0.391193i	$-0.127938\pi$
$863$	54.0716	1.84062	0.920309	+	0.391193i	$0.127938\pi$
$864$	−1.00000	−0.0340207
$865$	−0.318753	−0.0108379
$866$	−37.9454	−1.28944
$867$	−1.61707	−0.0549186
$868$	0.203476	0.00690643
$869$	27.2702	0.925077
$870$	−0.266951	−0.00905049
$871$	45.7180	1.54910
$872$	−5.47884	−0.185537
$873$	−17.1005	−0.578763
$874$	1.63540	0.0553182
$875$	−2.15003	−0.0726842
$876$	−13.4975	−0.456037
$877$	14.5542	0.491459	0.245730	−	0.969338i	$-0.420972\pi$
$877$	14.5542	0.491459	0.245730	+	0.969338i	$0.420972\pi$
$878$	26.1242	0.881648
$879$	−12.1608	−0.410174
$880$	−0.351067	−0.0118345
$881$	−0.480999	−0.0162053	−0.00810264	−	0.999967i	$-0.502579\pi$
$881$	−0.480999	−0.0162053	−0.00810264	+	0.999967i	$0.502579\pi$
$882$	−4.39815	−0.148093
$883$	−21.6236	−0.727693	−0.363846	−	0.931459i	$-0.618537\pi$
$883$	−21.6236	−0.727693	−0.363846	+	0.931459i	$0.618537\pi$
$884$	−18.2454	−0.613660
$885$	0.944967	0.0317647
$886$	25.5672	0.858947
$887$	9.56880	0.321289	0.160644	−	0.987012i	$-0.448643\pi$
$887$	9.56880	0.321289	0.160644	+	0.987012i	$0.448643\pi$
$888$	−0.989323	−0.0331995
$889$	−1.88609	−0.0632575
$890$	2.45763	0.0823801
$891$	2.62913	0.0880791
$892$	−21.6950	−0.726402
$893$	5.21171	0.174403
$894$	3.15657	0.105572
$895$	−1.87856	−0.0627932
$896$	−1.61303	−0.0538874
$897$	−6.91548	−0.230901
$898$	24.5924	0.820660
$899$	0.252189	0.00841097
$900$	−4.98217	−0.166072
$901$	4.31475	0.143745
$902$	24.1728	0.804865
$903$	−10.6051	−0.352915
$904$	−3.67754	−0.122313
$905$	1.78384	0.0592968
$906$	−0.744742	−0.0247424
$907$	9.95699	0.330616	0.165308	−	0.986242i	$-0.447138\pi$
$907$	9.95699	0.330616	0.165308	+	0.986242i	$0.447138\pi$
$908$	−25.8441	−0.857665
$909$	−8.85011	−0.293540
$910$	−0.910789	−0.0301924
$911$	26.6428	0.882714	0.441357	−	0.897332i	$-0.354497\pi$
$911$	26.6428	0.882714	0.441357	+	0.897332i	$0.354497\pi$
$912$	1.00000	0.0331133
$913$	22.4309	0.742356
$914$	−30.1161	−0.996152
$915$	−1.28753	−0.0425644
$916$	−7.66717	−0.253330
$917$	−20.3137	−0.670816
$918$	−4.31475	−0.142408
$919$	30.2094	0.996518	0.498259	−	0.867028i	$-0.333973\pi$
$919$	30.2094	0.996518	0.498259	+	0.867028i	$0.333973\pi$
$920$	0.218374	0.00719959
$921$	4.81443	0.158641
$922$	−16.4104	−0.540449
$923$	11.3119	0.372334
$924$	4.24085	0.139514
$925$	−4.92897	−0.162064
$926$	34.2993	1.12715
$927$	−7.32779	−0.240676
$928$	−1.99919	−0.0656266
$929$	−9.03931	−0.296570	−0.148285	−	0.988945i	$-0.547375\pi$
$929$	−9.03931	−0.296570	−0.148285	+	0.988945i	$0.547375\pi$
$930$	−0.0168442	−0.000552343 0
$931$	4.39815	0.144143
$932$	−28.1465	−0.921970
$933$	9.89104	0.323818
$934$	25.1535	0.823049
$935$	−1.51477	−0.0495381
$936$	−4.22862	−0.138217
$937$	13.6489	0.445889	0.222944	−	0.974831i	$-0.428433\pi$
$937$	13.6489	0.445889	0.222944	+	0.974831i	$0.428433\pi$
$938$	17.4394	0.569415
$939$	14.5455	0.474674
$940$	0.695918	0.0226983
$941$	15.3848	0.501531	0.250766	−	0.968048i	$-0.419318\pi$
$941$	15.3848	0.501531	0.250766	+	0.968048i	$0.419318\pi$
$942$	6.83316	0.222636
$943$	−15.0362	−0.489646
$944$	7.07682	0.230331
$945$	−0.215387	−0.00700654
$946$	−17.2856	−0.562004
$947$	−14.4249	−0.468747	−0.234373	−	0.972147i	$-0.575304\pi$
$947$	−14.4249	−0.468747	−0.234373	+	0.972147i	$0.575304\pi$
$948$	−10.3723	−0.336877
$949$	−57.0756	−1.85275
$950$	4.98217	0.161643
$951$	20.8908	0.677431
$952$	−6.95980	−0.225569
$953$	−22.9920	−0.744784	−0.372392	−	0.928076i	$-0.621462\pi$
$953$	−22.9920	−0.744784	−0.372392	+	0.928076i	$0.621462\pi$
$954$	1.00000	0.0323762
$955$	2.05664	0.0665512
$956$	−21.1835	−0.685125
$957$	5.25612	0.169906
$958$	−14.3286	−0.462936
$959$	−0.0178236	−0.000575555 0
$960$	0.133530	0.00430965
$961$	−30.9841	−0.999487
$962$	−4.18347	−0.134880
$963$	13.8487	0.446268
$964$	17.2517	0.555639
$965$	2.27055	0.0730916
$966$	−2.63794	−0.0848743
$967$	−16.3183	−0.524761	−0.262381	−	0.964964i	$-0.584508\pi$
$967$	−16.3183	−0.524761	−0.262381	+	0.964964i	$0.584508\pi$
$968$	−4.08769	−0.131383
$969$	4.31475	0.138610
$970$	2.28342	0.0733162
$971$	46.6222	1.49618	0.748088	−	0.663599i	$-0.230972\pi$
$971$	46.6222	1.49618	0.748088	+	0.663599i	$0.230972\pi$
$972$	−1.00000	−0.0320750
$973$	27.6378	0.886028
$974$	−18.0676	−0.578923
$975$	−21.0677	−0.674706
$976$	−9.64227	−0.308641
$977$	16.1011	0.515120	0.257560	−	0.966262i	$-0.417081\pi$
$977$	16.1011	0.515120	0.257560	+	0.966262i	$0.417081\pi$
$978$	7.48549	0.239359
$979$	−48.3895	−1.54653
$980$	0.587284	0.0187601
$981$	−5.47884	−0.174926
$982$	26.7700	0.854265
$983$	22.0476	0.703208	0.351604	−	0.936149i	$-0.385636\pi$
$983$	22.0476	0.703208	0.351604	+	0.936149i	$0.385636\pi$
$984$	−9.19422	−0.293101
$985$	−2.95311	−0.0940940
$986$	−8.62600	−0.274708
$987$	−8.40662	−0.267586
$988$	4.22862	0.134530
$989$	10.7522	0.341900
$990$	−0.351067	−0.0111576
$991$	9.58266	0.304403	0.152202	−	0.988349i	$-0.451364\pi$
$991$	9.58266	0.304403	0.152202	+	0.988349i	$0.451364\pi$
$992$	−0.126146	−0.00400513
$993$	−12.9259	−0.410190
$994$	4.31496	0.136862
$995$	0.787754	0.0249735
$996$	−8.53170	−0.270337
$997$	10.2333	0.324091	0.162045	−	0.986783i	$-0.448191\pi$
$997$	10.2333	0.324091	0.162045	+	0.986783i	$0.448191\pi$
$998$	−1.46345	−0.0463247
$999$	−0.989323	−0.0313008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bb.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bb.1.5	✓	9	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.133530 q^{5} -1.00000 q^{6} -1.61303 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.133530 q^{5} -1.00000 q^{6} -1.61303 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.133530 q^{10} +2.62913 q^{11} -1.00000 q^{12} -4.22862 q^{13} -1.61303 q^{14} +0.133530 q^{15} +1.00000 q^{16} +4.31475 q^{17} +1.00000 q^{18} -1.00000 q^{19} -0.133530 q^{20} +1.61303 q^{21} +2.62913 q^{22} -1.63540 q^{23} -1.00000 q^{24} -4.98217 q^{25} -4.22862 q^{26} -1.00000 q^{27} -1.61303 q^{28} -1.99919 q^{29} +0.133530 q^{30} -0.126146 q^{31} +1.00000 q^{32} -2.62913 q^{33} +4.31475 q^{34} +0.215387 q^{35} +1.00000 q^{36} +0.989323 q^{37} -1.00000 q^{38} +4.22862 q^{39} -0.133530 q^{40} +9.19422 q^{41} +1.61303 q^{42} -6.57466 q^{43} +2.62913 q^{44} -0.133530 q^{45} -1.63540 q^{46} -5.21171 q^{47} -1.00000 q^{48} -4.39815 q^{49} -4.98217 q^{50} -4.31475 q^{51} -4.22862 q^{52} +1.00000 q^{53} -1.00000 q^{54} -0.351067 q^{55} -1.61303 q^{56} +1.00000 q^{57} -1.99919 q^{58} +7.07682 q^{59} +0.133530 q^{60} -9.64227 q^{61} -0.126146 q^{62} -1.61303 q^{63} +1.00000 q^{64} +0.564646 q^{65} -2.62913 q^{66} -10.8116 q^{67} +4.31475 q^{68} +1.63540 q^{69} +0.215387 q^{70} -2.67507 q^{71} +1.00000 q^{72} +13.4975 q^{73} +0.989323 q^{74} +4.98217 q^{75} -1.00000 q^{76} -4.24085 q^{77} +4.22862 q^{78} +10.3723 q^{79} -0.133530 q^{80} +1.00000 q^{81} +9.19422 q^{82} +8.53170 q^{83} +1.61303 q^{84} -0.576147 q^{85} -6.57466 q^{86} +1.99919 q^{87} +2.62913 q^{88} -18.4051 q^{89} -0.133530 q^{90} +6.82087 q^{91} -1.63540 q^{92} +0.126146 q^{93} -5.21171 q^{94} +0.133530 q^{95} -1.00000 q^{96} -17.1005 q^{97} -4.39815 q^{98} +2.62913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 5 q^{5} - 9 q^{6} - 5 q^{7} + 9 q^{8} + 9 q^{9} - 5 q^{10} + 3 q^{11} - 9 q^{12} - 4 q^{13} - 5 q^{14} + 5 q^{15} + 9 q^{16} - 16 q^{17} + 9 q^{18} - 9 q^{19} - 5 q^{20} + 5 q^{21} + 3 q^{22} - 9 q^{24} + 8 q^{25} - 4 q^{26} - 9 q^{27} - 5 q^{28} - 2 q^{29} + 5 q^{30} - 10 q^{31} + 9 q^{32} - 3 q^{33} - 16 q^{34} - q^{35} + 9 q^{36} - 14 q^{37} - 9 q^{38} + 4 q^{39} - 5 q^{40} - 21 q^{41} + 5 q^{42} - 4 q^{43} + 3 q^{44} - 5 q^{45} - 8 q^{47} - 9 q^{48} - 14 q^{49} + 8 q^{50} + 16 q^{51} - 4 q^{52} + 9 q^{53} - 9 q^{54} - 14 q^{55} - 5 q^{56} + 9 q^{57} - 2 q^{58} - 12 q^{59} + 5 q^{60} - 13 q^{61} - 10 q^{62} - 5 q^{63} + 9 q^{64} - 13 q^{65} - 3 q^{66} + 22 q^{67} - 16 q^{68} - q^{70} - 13 q^{71} + 9 q^{72} - 17 q^{73} - 14 q^{74} - 8 q^{75} - 9 q^{76} - 25 q^{77} + 4 q^{78} - 5 q^{80} + 9 q^{81} - 21 q^{82} - 24 q^{83} + 5 q^{84} - 16 q^{85} - 4 q^{86} + 2 q^{87} + 3 q^{88} - 23 q^{89} - 5 q^{90} - 11 q^{91} + 10 q^{93} - 8 q^{94} + 5 q^{95} - 9 q^{96} - 29 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 5 * q^5 - 9 * q^6 - 5 * q^7 + 9 * q^8 + 9 * q^9 - 5 * q^10 + 3 * q^11 - 9 * q^12 - 4 * q^13 - 5 * q^14 + 5 * q^15 + 9 * q^16 - 16 * q^17 + 9 * q^18 - 9 * q^19 - 5 * q^20 + 5 * q^21 + 3 * q^22 - 9 * q^24 + 8 * q^25 - 4 * q^26 - 9 * q^27 - 5 * q^28 - 2 * q^29 + 5 * q^30 - 10 * q^31 + 9 * q^32 - 3 * q^33 - 16 * q^34 - q^35 + 9 * q^36 - 14 * q^37 - 9 * q^38 + 4 * q^39 - 5 * q^40 - 21 * q^41 + 5 * q^42 - 4 * q^43 + 3 * q^44 - 5 * q^45 - 8 * q^47 - 9 * q^48 - 14 * q^49 + 8 * q^50 + 16 * q^51 - 4 * q^52 + 9 * q^53 - 9 * q^54 - 14 * q^55 - 5 * q^56 + 9 * q^57 - 2 * q^58 - 12 * q^59 + 5 * q^60 - 13 * q^61 - 10 * q^62 - 5 * q^63 + 9 * q^64 - 13 * q^65 - 3 * q^66 + 22 * q^67 - 16 * q^68 - q^70 - 13 * q^71 + 9 * q^72 - 17 * q^73 - 14 * q^74 - 8 * q^75 - 9 * q^76 - 25 * q^77 + 4 * q^78 - 5 * q^80 + 9 * q^81 - 21 * q^82 - 24 * q^83 + 5 * q^84 - 16 * q^85 - 4 * q^86 + 2 * q^87 + 3 * q^88 - 23 * q^89 - 5 * q^90 - 11 * q^91 + 10 * q^93 - 8 * q^94 + 5 * q^95 - 9 * q^96 - 29 * q^97 - 14 * q^98 + 3 * q^99

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