LMFDB - Embedded newform 139.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [139,2,Mod(1,139)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(139, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("139.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	139.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:	$1.10992058810$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 11x^{5} + 8x^{4} + 35x^{3} - 10x^{2} - 32x - 8 $ x^7 - x^6 - 11x^5 + 8x^4 + 35x^3 - 10x^2 - 32*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.28572$ of defining polynomial
Character	$\chi$	$=$	139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.28572 q^{2} -3.03631 q^{3} +3.22451 q^{4} +3.97653 q^{5} -6.94014 q^{6} -0.589281 q^{7} +2.79888 q^{8} +6.21915 q^{9} +O(q^{10})$	\(q+2.28572 q^{2} -3.03631 q^{3} +3.22451 q^{4} +3.97653 q^{5} -6.94014 q^{6} -0.589281 q^{7} +2.79888 q^{8} +6.21915 q^{9} +9.08923 q^{10} -1.38959 q^{11} -9.79058 q^{12} -3.36469 q^{13} -1.34693 q^{14} -12.0740 q^{15} -0.0515721 q^{16} -7.97644 q^{17} +14.2152 q^{18} +1.27608 q^{19} +12.8223 q^{20} +1.78924 q^{21} -3.17622 q^{22} +0.987077 q^{23} -8.49824 q^{24} +10.8128 q^{25} -7.69072 q^{26} -9.77432 q^{27} -1.90014 q^{28} +3.80145 q^{29} -27.5977 q^{30} +2.49968 q^{31} -5.71563 q^{32} +4.21923 q^{33} -18.2319 q^{34} -2.34329 q^{35} +20.0537 q^{36} +4.32765 q^{37} +2.91676 q^{38} +10.2162 q^{39} +11.1298 q^{40} +0.260254 q^{41} +4.08969 q^{42} -2.44284 q^{43} -4.48075 q^{44} +24.7306 q^{45} +2.25618 q^{46} -6.74203 q^{47} +0.156589 q^{48} -6.65275 q^{49} +24.7150 q^{50} +24.2189 q^{51} -10.8495 q^{52} +8.41699 q^{53} -22.3413 q^{54} -5.52576 q^{55} -1.64932 q^{56} -3.87456 q^{57} +8.68905 q^{58} +4.54940 q^{59} -38.9326 q^{60} -10.3800 q^{61} +5.71356 q^{62} -3.66482 q^{63} -12.9612 q^{64} -13.3798 q^{65} +9.64397 q^{66} +7.40056 q^{67} -25.7201 q^{68} -2.99707 q^{69} -5.35611 q^{70} +6.43153 q^{71} +17.4066 q^{72} +11.7293 q^{73} +9.89179 q^{74} -32.8309 q^{75} +4.11472 q^{76} +0.818860 q^{77} +23.3514 q^{78} +6.81628 q^{79} -0.205078 q^{80} +11.0204 q^{81} +0.594867 q^{82} +8.02368 q^{83} +5.76940 q^{84} -31.7186 q^{85} -5.58363 q^{86} -11.5424 q^{87} -3.88930 q^{88} +2.71727 q^{89} +56.5273 q^{90} +1.98275 q^{91} +3.18284 q^{92} -7.58978 q^{93} -15.4104 q^{94} +5.07436 q^{95} +17.3544 q^{96} +4.08668 q^{97} -15.2063 q^{98} -8.64209 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) $ 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9} - 4 q^{10} + 2 q^{11} - 8 q^{12} + 6 q^{13} + 7 q^{14} - 3 q^{15} + 5 q^{16} + 5 q^{17} - 10 q^{18} - 10 q^{19} + 12 q^{20} - 5 q^{21} - 18 q^{22} - q^{23} - 21 q^{24} + 14 q^{25} - 8 q^{26} - 11 q^{27} - 28 q^{28} + 30 q^{29} - 41 q^{30} - 20 q^{31} - 12 q^{32} - 20 q^{33} - 17 q^{34} - 7 q^{35} + 2 q^{36} + 6 q^{37} + 6 q^{38} + 11 q^{39} - 22 q^{40} + 19 q^{41} + 6 q^{42} - 12 q^{43} + 25 q^{44} + 27 q^{45} + 22 q^{46} - 3 q^{47} + 15 q^{48} - 8 q^{49} + 12 q^{50} + 23 q^{51} - 8 q^{52} + 38 q^{53} - 7 q^{54} + 7 q^{55} + 21 q^{56} - 19 q^{57} - 21 q^{58} - 14 q^{59} - 8 q^{60} + 4 q^{61} - q^{62} - 18 q^{63} - 16 q^{64} + 10 q^{65} + 18 q^{66} + 9 q^{67} - 25 q^{68} + 9 q^{69} + 20 q^{70} + 24 q^{71} + 41 q^{72} - 5 q^{73} + 9 q^{74} - 21 q^{75} + 3 q^{76} - 13 q^{77} + 20 q^{78} + 8 q^{79} + 11 q^{80} + 39 q^{81} + 56 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 39 q^{86} - 25 q^{87} - 29 q^{88} + 10 q^{89} + 72 q^{90} + 7 q^{91} + 29 q^{92} - 15 q^{93} - 36 q^{94} - 21 q^{95} - 11 q^{96} - 5 q^{97} - 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9 - 4 * q^10 + 2 * q^11 - 8 * q^12 + 6 * q^13 + 7 * q^14 - 3 * q^15 + 5 * q^16 + 5 * q^17 - 10 * q^18 - 10 * q^19 + 12 * q^20 - 5 * q^21 - 18 * q^22 - q^23 - 21 * q^24 + 14 * q^25 - 8 * q^26 - 11 * q^27 - 28 * q^28 + 30 * q^29 - 41 * q^30 - 20 * q^31 - 12 * q^32 - 20 * q^33 - 17 * q^34 - 7 * q^35 + 2 * q^36 + 6 * q^37 + 6 * q^38 + 11 * q^39 - 22 * q^40 + 19 * q^41 + 6 * q^42 - 12 * q^43 + 25 * q^44 + 27 * q^45 + 22 * q^46 - 3 * q^47 + 15 * q^48 - 8 * q^49 + 12 * q^50 + 23 * q^51 - 8 * q^52 + 38 * q^53 - 7 * q^54 + 7 * q^55 + 21 * q^56 - 19 * q^57 - 21 * q^58 - 14 * q^59 - 8 * q^60 + 4 * q^61 - q^62 - 18 * q^63 - 16 * q^64 + 10 * q^65 + 18 * q^66 + 9 * q^67 - 25 * q^68 + 9 * q^69 + 20 * q^70 + 24 * q^71 + 41 * q^72 - 5 * q^73 + 9 * q^74 - 21 * q^75 + 3 * q^76 - 13 * q^77 + 20 * q^78 + 8 * q^79 + 11 * q^80 + 39 * q^81 + 56 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 39 * q^86 - 25 * q^87 - 29 * q^88 + 10 * q^89 + 72 * q^90 + 7 * q^91 + 29 * q^92 - 15 * q^93 - 36 * q^94 - 21 * q^95 - 11 * q^96 - 5 * q^97 - 49 * q^98 - 31 * 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 $

$2$	2.28572	1.61625	0.808123	−	0.589013i	$-0.200483\pi$
$2$	2.28572	1.61625	0.808123	+	0.589013i	$0.200483\pi$
$3$	−3.03631	−1.75301	−0.876506	−	0.481391i	$-0.840132\pi$
$3$	−3.03631	−1.75301	−0.876506	+	0.481391i	$0.840132\pi$
$4$	3.22451	1.61225
$5$	3.97653	1.77836	0.889179	−	0.457559i	$-0.151276\pi$
$5$	3.97653	1.77836	0.889179	+	0.457559i	$0.151276\pi$
$6$	−6.94014	−2.83330
$7$	−0.589281	−0.222727	−0.111364	−	0.993780i	$-0.535522\pi$
$7$	−0.589281	−0.222727	−0.111364	+	0.993780i	$0.535522\pi$
$8$	2.79888	0.989552
$9$	6.21915	2.07305
$10$	9.08923	2.87427
$11$	−1.38959	−0.418978	−0.209489	−	0.977811i	$-0.567180\pi$
$11$	−1.38959	−0.418978	−0.209489	+	0.977811i	$0.567180\pi$
$12$	−9.79058	−2.82630
$13$	−3.36469	−0.933196	−0.466598	−	0.884469i	$-0.654521\pi$
$13$	−3.36469	−0.933196	−0.466598	+	0.884469i	$0.654521\pi$
$14$	−1.34693	−0.359982
$15$	−12.0740	−3.11748
$16$	−0.0515721	−0.0128930
$17$	−7.97644	−1.93457	−0.967286	−	0.253690i	$-0.918356\pi$
$17$	−7.97644	−1.93457	−0.967286	+	0.253690i	$0.918356\pi$
$18$	14.2152	3.35056
$19$	1.27608	0.292752	0.146376	−	0.989229i	$-0.453239\pi$
$19$	1.27608	0.292752	0.146376	+	0.989229i	$0.453239\pi$
$20$	12.8223	2.86716
$21$	1.78924	0.390443
$22$	−3.17622	−0.677172
$23$	0.987077	0.205820	0.102910	−	0.994691i	$-0.467185\pi$
$23$	0.987077	0.205820	0.102910	+	0.994691i	$0.467185\pi$
$24$	−8.49824	−1.73470
$25$	10.8128	2.16256
$26$	−7.69072	−1.50828
$27$	−9.77432	−1.88107
$28$	−1.90014	−0.359093
$29$	3.80145	0.705912	0.352956	−	0.935640i	$-0.385176\pi$
$29$	3.80145	0.705912	0.352956	+	0.935640i	$0.385176\pi$
$30$	−27.5977	−5.03862
$31$	2.49968	0.448955	0.224478	−	0.974479i	$-0.427932\pi$
$31$	2.49968	0.448955	0.224478	+	0.974479i	$0.427932\pi$
$32$	−5.71563	−1.01039
$33$	4.21923	0.734473
$34$	−18.2319	−3.12674
$35$	−2.34329	−0.396089
$36$	20.0537	3.34228
$37$	4.32765	0.711461	0.355731	−	0.934589i	$-0.384232\pi$
$37$	4.32765	0.711461	0.355731	+	0.934589i	$0.384232\pi$
$38$	2.91676	0.473160
$39$	10.2162	1.63590
$40$	11.1298	1.75978
$41$	0.260254	0.0406448	0.0203224	−	0.999793i	$-0.493531\pi$
$41$	0.260254	0.0406448	0.0203224	+	0.999793i	$0.493531\pi$
$42$	4.08969	0.631053
$43$	−2.44284	−0.372529	−0.186265	−	0.982500i	$-0.559638\pi$
$43$	−2.44284	−0.372529	−0.186265	+	0.982500i	$0.559638\pi$
$44$	−4.48075	−0.675499
$45$	24.7306	3.68663
$46$	2.25618	0.332655
$47$	−6.74203	−0.983426	−0.491713	−	0.870757i	$-0.663629\pi$
$47$	−6.74203	−0.983426	−0.491713	+	0.870757i	$0.663629\pi$
$48$	0.156589	0.0226016
$49$	−6.65275	−0.950393
$50$	24.7150	3.49523
$51$	24.2189	3.39133
$52$	−10.8495	−1.50455
$53$	8.41699	1.15616	0.578081	−	0.815979i	$-0.303802\pi$
$53$	8.41699	1.15616	0.578081	+	0.815979i	$0.303802\pi$
$54$	−22.3413	−3.04027
$55$	−5.52576	−0.745093
$56$	−1.64932	−0.220400
$57$	−3.87456	−0.513198
$58$	8.68905	1.14093
$59$	4.54940	0.592282	0.296141	−	0.955144i	$-0.404300\pi$
$59$	4.54940	0.592282	0.296141	+	0.955144i	$0.404300\pi$
$60$	−38.9326	−5.02617
$61$	−10.3800	−1.32903	−0.664514	−	0.747276i	$-0.731361\pi$
$61$	−10.3800	−1.32903	−0.664514	+	0.747276i	$0.731361\pi$
$62$	5.71356	0.725623
$63$	−3.66482	−0.461725
$64$	−12.9612	−1.62015
$65$	−13.3798	−1.65956
$66$	9.64397	1.18709
$67$	7.40056	0.904122	0.452061	−	0.891987i	$-0.350689\pi$
$67$	7.40056	0.904122	0.452061	+	0.891987i	$0.350689\pi$
$68$	−25.7201	−3.11902
$69$	−2.99707	−0.360804
$70$	−5.35611	−0.640177
$71$	6.43153	0.763282	0.381641	−	0.924311i	$-0.375359\pi$
$71$	6.43153	0.763282	0.381641	+	0.924311i	$0.375359\pi$
$72$	17.4066	2.05139
$73$	11.7293	1.37281	0.686406	−	0.727218i	$-0.259187\pi$
$73$	11.7293	1.37281	0.686406	+	0.727218i	$0.259187\pi$
$74$	9.89179	1.14990
$75$	−32.8309	−3.79099
$76$	4.11472	0.471991
$77$	0.818860	0.0933178
$78$	23.3514	2.64402
$79$	6.81628	0.766891	0.383446	−	0.923563i	$-0.374737\pi$
$79$	6.81628	0.766891	0.383446	+	0.923563i	$0.374737\pi$
$80$	−0.205078	−0.0229284
$81$	11.0204	1.22449
$82$	0.594867	0.0656920
$83$	8.02368	0.880714	0.440357	−	0.897823i	$-0.354852\pi$
$83$	8.02368	0.880714	0.440357	+	0.897823i	$0.354852\pi$
$84$	5.76940	0.629493
$85$	−31.7186	−3.44036
$86$	−5.58363	−0.602099
$87$	−11.5424	−1.23747
$88$	−3.88930	−0.414601
$89$	2.71727	0.288030	0.144015	−	0.989576i	$-0.453999\pi$
$89$	2.71727	0.288030	0.144015	+	0.989576i	$0.453999\pi$
$90$	56.5273	5.95850
$91$	1.98275	0.207848
$92$	3.18284	0.331833
$93$	−7.58978	−0.787024
$94$	−15.4104	−1.58946
$95$	5.07436	0.520619
$96$	17.3544	1.77123
$97$	4.08668	0.414939	0.207470	−	0.978241i	$-0.433477\pi$
$97$	4.08668	0.414939	0.207470	+	0.978241i	$0.433477\pi$
$98$	−15.2063	−1.53607
$99$	−8.64209	−0.868562
$100$	34.8659	3.48659
$101$	−0.265684	−0.0264365	−0.0132183	−	0.999913i	$-0.504208\pi$
$101$	−0.265684	−0.0264365	−0.0132183	+	0.999913i	$0.504208\pi$
$102$	55.3576	5.48122
$103$	−11.8428	−1.16691	−0.583454	−	0.812146i	$-0.698299\pi$
$103$	−11.8428	−1.16691	−0.583454	+	0.812146i	$0.698299\pi$
$104$	−9.41734	−0.923446
$105$	7.11495	0.694348
$106$	19.2389	1.86864
$107$	9.56139	0.924335	0.462167	−	0.886793i	$-0.347072\pi$
$107$	9.56139	0.924335	0.462167	+	0.886793i	$0.347072\pi$
$108$	−31.5174	−3.03276
$109$	1.27767	0.122378	0.0611892	−	0.998126i	$-0.480511\pi$
$109$	1.27767	0.122378	0.0611892	+	0.998126i	$0.480511\pi$
$110$	−12.6303	−1.20425
$111$	−13.1401	−1.24720
$112$	0.0303905	0.00287163
$113$	−10.8619	−1.02181	−0.510903	−	0.859639i	$-0.670689\pi$
$113$	−10.8619	−1.02181	−0.510903	+	0.859639i	$0.670689\pi$
$114$	−8.85616	−0.829455
$115$	3.92514	0.366021
$116$	12.2578	1.13811
$117$	−20.9255	−1.93456
$118$	10.3987	0.957273
$119$	4.70036	0.430882
$120$	−33.7935	−3.08491
$121$	−9.06903	−0.824457
$122$	−23.7258	−2.14804
$123$	−0.790210	−0.0712508
$124$	8.06023	0.723830
$125$	23.1147	2.06745
$126$	−8.37676	−0.746261
$127$	−13.9253	−1.23567	−0.617834	−	0.786308i	$-0.711990\pi$
$127$	−13.9253	−1.23567	−0.617834	+	0.786308i	$0.711990\pi$
$128$	−18.1943	−1.60817
$129$	7.41720	0.653048
$130$	−30.5824	−2.68225
$131$	20.9022	1.82624	0.913118	−	0.407695i	$-0.133667\pi$
$131$	20.9022	1.82624	0.913118	+	0.407695i	$0.133667\pi$
$132$	13.6049	1.18416
$133$	−0.751968	−0.0652039
$134$	16.9156	1.46128
$135$	−38.8679	−3.34521
$136$	−22.3251	−1.91436
$137$	1.72782	0.147618	0.0738089	−	0.997272i	$-0.476484\pi$
$137$	1.72782	0.147618	0.0738089	+	0.997272i	$0.476484\pi$
$138$	−6.85045	−0.583149
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−7.55596	−0.638595
$141$	20.4708	1.72396
$142$	14.7007	1.23365
$143$	4.67555	0.390989
$144$	−0.320735	−0.0267279
$145$	15.1166	1.25536
$146$	26.8099	2.21880
$147$	20.1998	1.66605
$148$	13.9545	1.14706
$149$	1.02784	0.0842040	0.0421020	−	0.999113i	$-0.486595\pi$
$149$	1.02784	0.0842040	0.0421020	+	0.999113i	$0.486595\pi$
$150$	−75.0423	−6.12717
$151$	−19.0920	−1.55368	−0.776842	−	0.629696i	$-0.783179\pi$
$151$	−19.0920	−1.55368	−0.776842	+	0.629696i	$0.783179\pi$
$152$	3.57158	0.289694
$153$	−49.6067	−4.01046
$154$	1.87168	0.150825
$155$	9.94004	0.798403
$156$	32.9422	2.63749
$157$	−18.0068	−1.43710	−0.718550	−	0.695476i	$-0.755194\pi$
$157$	−18.0068	−1.43710	−0.718550	+	0.695476i	$0.755194\pi$
$158$	15.5801	1.23949
$159$	−25.5565	−2.02677
$160$	−22.7284	−1.79684
$161$	−0.581665	−0.0458416
$162$	25.1895	1.97907
$163$	−2.05837	−0.161224	−0.0806118	−	0.996746i	$-0.525687\pi$
$163$	−2.05837	−0.161224	−0.0806118	+	0.996746i	$0.525687\pi$
$164$	0.839190	0.0655297
$165$	16.7779	1.30616
$166$	18.3399	1.42345
$167$	5.68056	0.439575	0.219787	−	0.975548i	$-0.429464\pi$
$167$	5.68056	0.439575	0.219787	+	0.975548i	$0.429464\pi$
$168$	5.00785	0.386364
$169$	−1.67888	−0.129145
$170$	−72.4997	−5.56047
$171$	7.93612	0.606890
$172$	−7.87694	−0.600611
$173$	2.21460	0.168373	0.0841864	−	0.996450i	$-0.473171\pi$
$173$	2.21460	0.168373	0.0841864	+	0.996450i	$0.473171\pi$
$174$	−26.3826	−2.00006
$175$	−6.37177	−0.481661
$176$	0.0716643	0.00540190
$177$	−13.8134	−1.03828
$178$	6.21091	0.465527
$179$	20.5804	1.53825	0.769124	−	0.639100i	$-0.220693\pi$
$179$	20.5804	1.53825	0.769124	+	0.639100i	$0.220693\pi$
$180$	79.7441	5.94377
$181$	10.3422	0.768726	0.384363	−	0.923182i	$-0.374421\pi$
$181$	10.3422	0.768726	0.384363	+	0.923182i	$0.374421\pi$
$182$	4.53200	0.335934
$183$	31.5170	2.32980
$184$	2.76271	0.203669
$185$	17.2090	1.26523
$186$	−17.3481	−1.27202
$187$	11.0840	0.810543
$188$	−21.7397	−1.58553
$189$	5.75982	0.418965
$190$	11.5986	0.841448
$191$	5.27440	0.381642	0.190821	−	0.981625i	$-0.438885\pi$
$191$	5.27440	0.381642	0.190821	+	0.981625i	$0.438885\pi$
$192$	39.3541	2.84014
$193$	−4.46237	−0.321209	−0.160604	−	0.987019i	$-0.551344\pi$
$193$	−4.46237	−0.321209	−0.160604	+	0.987019i	$0.551344\pi$
$194$	9.34099	0.670644
$195$	40.6251	2.90922
$196$	−21.4518	−1.53227
$197$	−17.4078	−1.24026	−0.620128	−	0.784500i	$-0.712919\pi$
$197$	−17.4078	−1.24026	−0.620128	+	0.784500i	$0.712919\pi$
$198$	−19.7534	−1.40381
$199$	−1.15104	−0.0815951	−0.0407976	−	0.999167i	$-0.512990\pi$
$199$	−1.15104	−0.0815951	−0.0407976	+	0.999167i	$0.512990\pi$
$200$	30.2637	2.13996
$201$	−22.4703	−1.58494
$202$	−0.607278	−0.0427280
$203$	−2.24012	−0.157226
$204$	78.0940	5.46768
$205$	1.03491	0.0722810
$206$	−27.0694	−1.88601
$207$	6.13878	0.426675
$208$	0.173524	0.0120317
$209$	−1.77323	−0.122657
$210$	16.2628	1.12224
$211$	−23.5554	−1.62162	−0.810811	−	0.585308i	$-0.800973\pi$
$211$	−23.5554	−1.62162	−0.810811	+	0.585308i	$0.800973\pi$
$212$	27.1406	1.86403
$213$	−19.5281	−1.33804
$214$	21.8546	1.49395
$215$	−9.71401	−0.662490
$216$	−27.3571	−1.86142
$217$	−1.47301	−0.0999946
$218$	2.92039	0.197794
$219$	−35.6138	−2.40656
$220$	−17.8178	−1.20128
$221$	26.8382	1.80533
$222$	−30.0345	−2.01578
$223$	11.1201	0.744657	0.372329	−	0.928101i	$-0.378559\pi$
$223$	11.1201	0.744657	0.372329	+	0.928101i	$0.378559\pi$
$224$	3.36811	0.225041
$225$	67.2464	4.48309
$226$	−24.8273	−1.65149
$227$	−8.93935	−0.593325	−0.296663	−	0.954982i	$-0.595874\pi$
$227$	−8.93935	−0.593325	−0.296663	+	0.954982i	$0.595874\pi$
$228$	−12.4936	−0.827406
$229$	24.1692	1.59715	0.798573	−	0.601898i	$-0.205589\pi$
$229$	24.1692	1.59715	0.798573	+	0.601898i	$0.205589\pi$
$230$	8.97176	0.591581
$231$	−2.48631	−0.163587
$232$	10.6398	0.698537
$233$	18.4029	1.20562	0.602808	−	0.797886i	$-0.294048\pi$
$233$	18.4029	1.20562	0.602808	+	0.797886i	$0.294048\pi$
$234$	−47.8298	−3.12673
$235$	−26.8099	−1.74888
$236$	14.6696	0.954908
$237$	−20.6963	−1.34437
$238$	10.7437	0.696411
$239$	−12.2242	−0.790717	−0.395359	−	0.918527i	$-0.629380\pi$
$239$	−12.2242	−0.790717	−0.395359	+	0.918527i	$0.629380\pi$
$240$	0.622680	0.0401938
$241$	−14.5310	−0.936023	−0.468012	−	0.883722i	$-0.655029\pi$
$241$	−14.5310	−0.936023	−0.468012	+	0.883722i	$0.655029\pi$
$242$	−20.7292	−1.33253
$243$	−4.13824	−0.265469
$244$	−33.4705	−2.14273
$245$	−26.4549	−1.69014
$246$	−1.80620	−0.115159
$247$	−4.29360	−0.273195
$248$	6.99629	0.444265
$249$	−24.3623	−1.54390
$250$	52.8338	3.34150
$251$	−17.7274	−1.11894	−0.559472	−	0.828850i	$-0.688996\pi$
$251$	−17.7274	−1.11894	−0.559472	+	0.828850i	$0.688996\pi$
$252$	−11.8173	−0.744417
$253$	−1.37164	−0.0862340
$254$	−31.8293	−1.99715
$255$	96.3072	6.03099
$256$	−15.6648	−0.979047
$257$	−1.82162	−0.113629	−0.0568146	−	0.998385i	$-0.518094\pi$
$257$	−1.82162	−0.113629	−0.0568146	+	0.998385i	$0.518094\pi$
$258$	16.9536	1.05549
$259$	−2.55020	−0.158462
$260$	−43.1432	−2.67563
$261$	23.6418	1.46339
$262$	47.7766	2.95165
$263$	−22.1213	−1.36406	−0.682028	−	0.731326i	$-0.738902\pi$
$263$	−22.1213	−1.36406	−0.682028	+	0.731326i	$0.738902\pi$
$264$	11.8091	0.726800
$265$	33.4704	2.05607
$266$	−1.71879	−0.105386
$267$	−8.25046	−0.504920
$268$	23.8631	1.45767
$269$	−9.14050	−0.557306	−0.278653	−	0.960392i	$-0.589888\pi$
$269$	−9.14050	−0.557306	−0.278653	+	0.960392i	$0.589888\pi$
$270$	−88.8410	−5.40669
$271$	−20.2083	−1.22757	−0.613783	−	0.789475i	$-0.710353\pi$
$271$	−20.2083	−1.22757	−0.613783	+	0.789475i	$0.710353\pi$
$272$	0.411362	0.0249425
$273$	−6.02022	−0.364360
$274$	3.94932	0.238587
$275$	−15.0254	−0.906065
$276$	−9.66406	−0.581708
$277$	−2.01465	−0.121049	−0.0605244	−	0.998167i	$-0.519277\pi$
$277$	−2.01465	−0.121049	−0.0605244	+	0.998167i	$0.519277\pi$
$278$	2.28572	0.137088
$279$	15.5459	0.930707
$280$	−6.55858	−0.391950
$281$	−22.5703	−1.34643	−0.673215	−	0.739447i	$-0.735087\pi$
$281$	−22.5703	−1.34643	−0.673215	+	0.739447i	$0.735087\pi$
$282$	46.7906	2.78634
$283$	29.7284	1.76717	0.883585	−	0.468271i	$-0.155123\pi$
$283$	29.7284	1.76717	0.883585	+	0.468271i	$0.155123\pi$
$284$	20.7385	1.23060
$285$	−15.4073	−0.912651
$286$	10.6870	0.631934
$287$	−0.153363	−0.00905270
$288$	−35.5464	−2.09459
$289$	46.6236	2.74257
$290$	34.5523	2.02898
$291$	−12.4084	−0.727393
$292$	37.8212	2.21332
$293$	13.6344	0.796530	0.398265	−	0.917270i	$-0.369612\pi$
$293$	13.6344	0.796530	0.398265	+	0.917270i	$0.369612\pi$
$294$	46.1710	2.69275
$295$	18.0908	1.05329
$296$	12.1126	0.704028
$297$	13.5823	0.788127
$298$	2.34935	0.136094
$299$	−3.32120	−0.192070
$300$	−105.864	−6.11204
$301$	1.43952	0.0829723
$302$	−43.6389	−2.51114
$303$	0.806697	0.0463436
$304$	−0.0658101	−0.00377447
$305$	−41.2765	−2.36349
$306$	−113.387	−6.48190
$307$	5.04105	0.287708	0.143854	−	0.989599i	$-0.454050\pi$
$307$	5.04105	0.287708	0.143854	+	0.989599i	$0.454050\pi$
$308$	2.64042	0.150452
$309$	35.9584	2.04560
$310$	22.7201	1.29042
$311$	12.7325	0.721996	0.360998	−	0.932567i	$-0.382436\pi$
$311$	12.7325	0.721996	0.360998	+	0.932567i	$0.382436\pi$
$312$	28.5939	1.61881
$313$	3.74960	0.211940	0.105970	−	0.994369i	$-0.466205\pi$
$313$	3.74960	0.211940	0.105970	+	0.994369i	$0.466205\pi$
$314$	−41.1585	−2.32271
$315$	−14.5733	−0.821112
$316$	21.9791	1.23642
$317$	26.0321	1.46211	0.731053	−	0.682321i	$-0.239029\pi$
$317$	26.0321	1.46211	0.731053	+	0.682321i	$0.239029\pi$
$318$	−58.4151	−3.27575
$319$	−5.28247	−0.295762
$320$	−51.5405	−2.88120
$321$	−29.0313	−1.62037
$322$	−1.32952	−0.0740914
$323$	−10.1786	−0.566351
$324$	35.5352	1.97418
$325$	−36.3817	−2.01809
$326$	−4.70484	−0.260577
$327$	−3.87939	−0.214531
$328$	0.728418	0.0402201
$329$	3.97295	0.219036
$330$	38.3495	2.11107
$331$	14.5572	0.800139	0.400069	−	0.916485i	$-0.368986\pi$
$331$	14.5572	0.800139	0.400069	+	0.916485i	$0.368986\pi$
$332$	25.8724	1.41993
$333$	26.9143	1.47489
$334$	12.9841	0.710461
$335$	29.4285	1.60785
$336$	−0.0922748	−0.00503400
$337$	−10.9554	−0.596779	−0.298390	−	0.954444i	$-0.596449\pi$
$337$	−10.9554	−0.596779	−0.298390	+	0.954444i	$0.596449\pi$
$338$	−3.83746	−0.208730
$339$	32.9802	1.79124
$340$	−102.277	−5.54673
$341$	−3.47353	−0.188102
$342$	18.1397	0.980885
$343$	8.04530	0.434405
$344$	−6.83719	−0.368637
$345$	−11.9179	−0.641639
$346$	5.06195	0.272132
$347$	−15.7979	−0.848073	−0.424037	−	0.905645i	$-0.639387\pi$
$347$	−15.7979	−0.848073	−0.424037	+	0.905645i	$0.639387\pi$
$348$	−37.2185	−1.99512
$349$	−4.18777	−0.224166	−0.112083	−	0.993699i	$-0.535752\pi$
$349$	−4.18777	−0.224166	−0.112083	+	0.993699i	$0.535752\pi$
$350$	−14.5641	−0.778482
$351$	32.8875	1.75541
$352$	7.94240	0.423331
$353$	−0.422258	−0.0224745	−0.0112373	−	0.999937i	$-0.503577\pi$
$353$	−0.422258	−0.0224745	−0.0112373	+	0.999937i	$0.503577\pi$
$354$	−31.5735	−1.67811
$355$	25.5752	1.35739
$356$	8.76185	0.464377
$357$	−14.2717	−0.755341
$358$	47.0409	2.48619
$359$	−21.1717	−1.11740	−0.558701	−	0.829369i	$-0.688700\pi$
$359$	−21.1717	−1.11740	−0.558701	+	0.829369i	$0.688700\pi$
$360$	69.2180	3.64811
$361$	−17.3716	−0.914296
$362$	23.6392	1.24245
$363$	27.5363	1.44528
$364$	6.39337	0.335104
$365$	46.6420	2.44135
$366$	72.0389	3.76553
$367$	−36.3415	−1.89701	−0.948507	−	0.316757i	$-0.897406\pi$
$367$	−36.3415	−1.89701	−0.948507	+	0.316757i	$0.897406\pi$
$368$	−0.0509057	−0.00265364
$369$	1.61856	0.0842587
$370$	39.3350	2.04493
$371$	−4.95997	−0.257509
$372$	−24.4733	−1.26888
$373$	−13.6453	−0.706529	−0.353265	−	0.935523i	$-0.614928\pi$
$373$	−13.6453	−0.706529	−0.353265	+	0.935523i	$0.614928\pi$
$374$	25.3349	1.31004
$375$	−70.1834	−3.62426
$376$	−18.8701	−0.973151
$377$	−12.7907	−0.658755
$378$	13.1653	0.677151
$379$	−13.3908	−0.687841	−0.343920	−	0.938999i	$-0.611755\pi$
$379$	−13.3908	−0.687841	−0.343920	+	0.938999i	$0.611755\pi$
$380$	16.3623	0.839369
$381$	42.2814	2.16614
$382$	12.0558	0.616828
$383$	2.15406	0.110067	0.0550337	−	0.998484i	$-0.482473\pi$
$383$	2.15406	0.110067	0.0550337	+	0.998484i	$0.482473\pi$
$384$	55.2435	2.81913
$385$	3.25622	0.165953
$386$	−10.1997	−0.519153
$387$	−15.1924	−0.772271
$388$	13.1775	0.668987
$389$	24.1996	1.22697	0.613484	−	0.789707i	$-0.289767\pi$
$389$	24.1996	1.22697	0.613484	+	0.789707i	$0.289767\pi$
$390$	92.8575	4.70202
$391$	−7.87336	−0.398173
$392$	−18.6202	−0.940463
$393$	−63.4655	−3.20141
$394$	−39.7894	−2.00456
$395$	27.1051	1.36381
$396$	−27.8665	−1.40034
$397$	−25.3852	−1.27405	−0.637024	−	0.770844i	$-0.719835\pi$
$397$	−25.3852	−1.27405	−0.637024	+	0.770844i	$0.719835\pi$
$398$	−2.63095	−0.131878
$399$	2.28321	0.114303
$400$	−0.557639	−0.0278819
$401$	30.8033	1.53824	0.769122	−	0.639102i	$-0.220694\pi$
$401$	30.8033	1.53824	0.769122	+	0.639102i	$0.220694\pi$
$402$	−51.3609	−2.56165
$403$	−8.41063	−0.418963
$404$	−0.856699	−0.0426224
$405$	43.8228	2.17757
$406$	−5.12029	−0.254116
$407$	−6.01367	−0.298087
$408$	67.7857	3.35589
$409$	16.9638	0.838804	0.419402	−	0.907801i	$-0.362240\pi$
$409$	16.9638	0.838804	0.419402	+	0.907801i	$0.362240\pi$
$410$	2.36551	0.116824
$411$	−5.24620	−0.258776
$412$	−38.1873	−1.88135
$413$	−2.68088	−0.131917
$414$	14.0315	0.689611
$415$	31.9064	1.56622
$416$	19.2313	0.942892
$417$	−3.03631	−0.148689
$418$	−4.05310	−0.198244
$419$	−33.3672	−1.63010	−0.815048	−	0.579393i	$-0.803289\pi$
$419$	−33.3672	−1.63010	−0.815048	+	0.579393i	$0.803289\pi$
$420$	22.9422	1.11947
$421$	−3.05533	−0.148908	−0.0744539	−	0.997224i	$-0.523721\pi$
$421$	−3.05533	−0.148908	−0.0744539	+	0.997224i	$0.523721\pi$
$422$	−53.8410	−2.62094
$423$	−41.9297	−2.03869
$424$	23.5581	1.14408
$425$	−86.2476	−4.18362
$426$	−44.6357	−2.16261
$427$	6.11676	0.296011
$428$	30.8308	1.49026
$429$	−14.1964	−0.685408
$430$	−22.2035	−1.07075
$431$	3.51577	0.169349	0.0846744	−	0.996409i	$-0.473015\pi$
$431$	3.51577	0.169349	0.0846744	+	0.996409i	$0.473015\pi$
$432$	0.504083	0.0242527
$433$	−9.71612	−0.466927	−0.233463	−	0.972366i	$-0.575006\pi$
$433$	−9.71612	−0.466927	−0.233463	+	0.972366i	$0.575006\pi$
$434$	−3.36689	−0.161616
$435$	−45.8986	−2.20067
$436$	4.11985	0.197305
$437$	1.25959	0.0602542
$438$	−81.4030	−3.88959
$439$	4.92358	0.234990	0.117495	−	0.993073i	$-0.462514\pi$
$439$	4.92358	0.234990	0.117495	+	0.993073i	$0.462514\pi$
$440$	−15.4659	−0.737308
$441$	−41.3744	−1.97021
$442$	61.3446	2.91787
$443$	−27.4238	−1.30294	−0.651472	−	0.758673i	$-0.725848\pi$
$443$	−27.4238	−1.30294	−0.651472	+	0.758673i	$0.725848\pi$
$444$	−42.3702	−2.01080
$445$	10.8053	0.512220
$446$	25.4174	1.20355
$447$	−3.12084	−0.147611
$448$	7.63777	0.360851
$449$	21.8886	1.03299	0.516494	−	0.856291i	$-0.327237\pi$
$449$	21.8886	1.03299	0.516494	+	0.856291i	$0.327237\pi$
$450$	153.706	7.24578
$451$	−0.361647	−0.0170293
$452$	−35.0244	−1.64741
$453$	57.9691	2.72362
$454$	−20.4328	−0.958960
$455$	7.88445	0.369629
$456$	−10.8444	−0.507837
$457$	−23.4953	−1.09906	−0.549532	−	0.835473i	$-0.685194\pi$
$457$	−23.4953	−1.09906	−0.549532	+	0.835473i	$0.685194\pi$
$458$	55.2440	2.58138
$459$	77.9643	3.63906
$460$	12.6566	0.590119
$461$	0.809532	0.0377037	0.0188518	−	0.999822i	$-0.493999\pi$
$461$	0.809532	0.0377037	0.0188518	+	0.999822i	$0.493999\pi$
$462$	−5.68300	−0.264397
$463$	35.1962	1.63571	0.817853	−	0.575427i	$-0.195164\pi$
$463$	35.1962	1.63571	0.817853	+	0.575427i	$0.195164\pi$
$464$	−0.196049	−0.00910135
$465$	−30.1810	−1.39961
$466$	42.0639	1.94857
$467$	−20.6924	−0.957530	−0.478765	−	0.877943i	$-0.658915\pi$
$467$	−20.6924	−0.957530	−0.478765	+	0.877943i	$0.658915\pi$
$468$	−67.4744	−3.11900
$469$	−4.36101	−0.201373
$470$	−61.2798	−2.82663
$471$	54.6741	2.51925
$472$	12.7332	0.586094
$473$	3.39455	0.156081
$474$	−47.3059	−2.17283
$475$	13.7980	0.633094
$476$	15.1564	0.694690
$477$	52.3465	2.39678
$478$	−27.9411	−1.27799
$479$	31.4244	1.43582	0.717909	−	0.696137i	$-0.245099\pi$
$479$	31.4244	1.43582	0.717909	+	0.696137i	$0.245099\pi$
$480$	69.0103	3.14987
$481$	−14.5612	−0.663933
$482$	−33.2137	−1.51284
$483$	1.76611	0.0803609
$484$	−29.2431	−1.32923
$485$	16.2508	0.737910
$486$	−9.45886	−0.429063
$487$	38.9012	1.76278	0.881392	−	0.472386i	$-0.156607\pi$
$487$	38.9012	1.76278	0.881392	+	0.472386i	$0.156607\pi$
$488$	−29.0524	−1.31514
$489$	6.24983	0.282627
$490$	−60.4683	−2.73168
$491$	26.6748	1.20382	0.601909	−	0.798565i	$-0.294407\pi$
$491$	26.6748	1.20382	0.601909	+	0.798565i	$0.294407\pi$
$492$	−2.54804	−0.114874
$493$	−30.3221	−1.36564
$494$	−9.81397	−0.441551
$495$	−34.3655	−1.54462
$496$	−0.128914	−0.00578840
$497$	−3.78997	−0.170004
$498$	−55.6855	−2.49532
$499$	−33.5973	−1.50402	−0.752011	−	0.659150i	$-0.770916\pi$
$499$	−33.5973	−1.50402	−0.752011	+	0.659150i	$0.770916\pi$
$500$	74.5336	3.33325
$501$	−17.2479	−0.770579
$502$	−40.5198	−1.80849
$503$	−19.0102	−0.847621	−0.423811	−	0.905751i	$-0.639308\pi$
$503$	−19.0102	−0.847621	−0.423811	+	0.905751i	$0.639308\pi$
$504$	−10.2574	−0.456900
$505$	−1.05650	−0.0470136
$506$	−3.13517	−0.139375
$507$	5.09760	0.226393
$508$	−44.9022	−1.99221
$509$	31.1683	1.38151	0.690756	−	0.723088i	$-0.257278\pi$
$509$	31.1683	1.38151	0.690756	+	0.723088i	$0.257278\pi$
$510$	220.131	9.74757
$511$	−6.91186	−0.305763
$512$	0.583455	0.0257853
$513$	−12.4728	−0.550687
$514$	−4.16370	−0.183653
$515$	−47.0934	−2.07518
$516$	23.9168	1.05288
$517$	9.36867	0.412034
$518$	−5.82904	−0.256113
$519$	−6.72420	−0.295160
$520$	−37.4483	−1.64222
$521$	−16.7361	−0.733221	−0.366611	−	0.930374i	$-0.619482\pi$
$521$	−16.7361	−0.733221	−0.366611	+	0.930374i	$0.619482\pi$
$522$	54.0385	2.36520
$523$	1.68244	0.0735678	0.0367839	−	0.999323i	$-0.488289\pi$
$523$	1.68244	0.0735678	0.0367839	+	0.999323i	$0.488289\pi$
$524$	67.3994	2.94435
$525$	19.3466	0.844357
$526$	−50.5630	−2.20465
$527$	−19.9385	−0.868536
$528$	−0.217595	−0.00946959
$529$	−22.0257	−0.957638
$530$	76.5039	3.32312
$531$	28.2934	1.22783
$532$	−2.42473	−0.105125
$533$	−0.875672	−0.0379296
$534$	−18.8582	−0.816075
$535$	38.0212	1.64380
$536$	20.7132	0.894676
$537$	−62.4882	−2.69657
$538$	−20.8926	−0.900744
$539$	9.24461	0.398194
$540$	−125.330	−5.39333
$541$	11.8790	0.510717	0.255359	−	0.966846i	$-0.417806\pi$
$541$	11.8790	0.510717	0.255359	+	0.966846i	$0.417806\pi$
$542$	−46.1904	−1.98405
$543$	−31.4019	−1.34759
$544$	45.5904	1.95467
$545$	5.08068	0.217632
$546$	−13.7605	−0.588896
$547$	6.30966	0.269781	0.134891	−	0.990860i	$-0.456932\pi$
$547$	6.30966	0.269781	0.134891	+	0.990860i	$0.456932\pi$
$548$	5.57138	0.237997
$549$	−64.5550	−2.75514
$550$	−34.3438	−1.46442
$551$	4.85095	0.206658
$552$	−8.38842	−0.357035
$553$	−4.01670	−0.170807
$554$	−4.60493	−0.195645
$555$	−52.2519	−2.21797
$556$	3.22451	0.136750
$557$	14.2077	0.601998	0.300999	−	0.953625i	$-0.402680\pi$
$557$	14.2077	0.601998	0.300999	+	0.953625i	$0.402680\pi$
$558$	35.5335	1.50425
$559$	8.21938	0.347643
$560$	0.120849	0.00510679
$561$	−33.6544	−1.42089
$562$	−51.5893	−2.17616
$563$	22.5612	0.950841	0.475421	−	0.879759i	$-0.342296\pi$
$563$	22.5612	0.950841	0.475421	+	0.879759i	$0.342296\pi$
$564$	66.0084	2.77945
$565$	−43.1928	−1.81714
$566$	67.9507	2.85618
$567$	−6.49409	−0.272726
$568$	18.0010	0.755307
$569$	8.49484	0.356122	0.178061	−	0.984019i	$-0.443018\pi$
$569$	8.49484	0.356122	0.178061	+	0.984019i	$0.443018\pi$
$570$	−35.2168	−1.47507
$571$	12.3006	0.514764	0.257382	−	0.966310i	$-0.417140\pi$
$571$	12.3006	0.514764	0.257382	+	0.966310i	$0.417140\pi$
$572$	15.0763	0.630373
$573$	−16.0147	−0.669023
$574$	−0.350543	−0.0146314
$575$	10.6731	0.445097
$576$	−80.6075	−3.35865
$577$	33.7010	1.40299	0.701495	−	0.712675i	$-0.252516\pi$
$577$	33.7010	1.40299	0.701495	+	0.712675i	$0.252516\pi$
$578$	106.568	4.43266
$579$	13.5491	0.563083
$580$	48.7436	2.02397
$581$	−4.72820	−0.196159
$582$	−28.3621	−1.17565
$583$	−11.6962	−0.484407
$584$	32.8289	1.35847
$585$	−83.2108	−3.44034
$586$	31.1644	1.28739
$587$	22.4455	0.926424	0.463212	−	0.886247i	$-0.346697\pi$
$587$	22.4455	0.926424	0.463212	+	0.886247i	$0.346697\pi$
$588$	65.1343	2.68609
$589$	3.18978	0.131433
$590$	41.3505	1.70238
$591$	52.8555	2.17418
$592$	−0.223186	−0.00917290
$593$	1.10495	0.0453747	0.0226874	−	0.999743i	$-0.492778\pi$
$593$	1.10495	0.0453747	0.0226874	+	0.999743i	$0.492778\pi$
$594$	31.0454	1.27381
$595$	18.6911	0.766262
$596$	3.31428	0.135758
$597$	3.49491	0.143037
$598$	−7.59134	−0.310433
$599$	−33.0966	−1.35229	−0.676144	−	0.736769i	$-0.736350\pi$
$599$	−33.0966	−1.35229	−0.676144	+	0.736769i	$0.736350\pi$
$600$	−91.8897	−3.75138
$601$	−33.3385	−1.35991	−0.679953	−	0.733256i	$-0.738000\pi$
$601$	−33.3385	−1.35991	−0.679953	+	0.733256i	$0.738000\pi$
$602$	3.29033	0.134104
$603$	46.0252	1.87429
$604$	−61.5622	−2.50493
$605$	−36.0633	−1.46618
$606$	1.84388	0.0749026
$607$	13.7062	0.556316	0.278158	−	0.960535i	$-0.410276\pi$
$607$	13.7062	0.556316	0.278158	+	0.960535i	$0.410276\pi$
$608$	−7.29359	−0.295794
$609$	6.80170	0.275619
$610$	−94.3465	−3.81998
$611$	22.6848	0.917729
$612$	−159.957	−6.46588
$613$	0.208150	0.00840711	0.00420355	−	0.999991i	$-0.498662\pi$
$613$	0.208150	0.00840711	0.00420355	+	0.999991i	$0.498662\pi$
$614$	11.5224	0.465007
$615$	−3.14229	−0.126709
$616$	2.29189	0.0923428
$617$	20.5634	0.827849	0.413925	−	0.910311i	$-0.364158\pi$
$617$	20.5634	0.827849	0.413925	+	0.910311i	$0.364158\pi$
$618$	82.1908	3.30620
$619$	17.3778	0.698472	0.349236	−	0.937035i	$-0.386441\pi$
$619$	17.3778	0.698472	0.349236	+	0.937035i	$0.386441\pi$
$620$	32.0517	1.28723
$621$	−9.64800	−0.387161
$622$	29.1030	1.16692
$623$	−1.60123	−0.0641521
$624$	−0.526872	−0.0210918
$625$	37.8525	1.51410
$626$	8.57052	0.342547
$627$	5.38407	0.215019
$628$	−58.0630	−2.31697
$629$	−34.5193	−1.37637
$630$	−33.3104	−1.32712
$631$	−39.4836	−1.57182	−0.785908	−	0.618344i	$-0.787804\pi$
$631$	−39.4836	−1.57182	−0.785908	+	0.618344i	$0.787804\pi$
$632$	19.0779	0.758879
$633$	71.5214	2.84272
$634$	59.5019	2.36312
$635$	−55.3743	−2.19746
$636$	−82.4073	−3.26766
$637$	22.3844	0.886903
$638$	−12.0742	−0.478024
$639$	39.9986	1.58232
$640$	−72.3503	−2.85990
$641$	−4.40943	−0.174162	−0.0870811	−	0.996201i	$-0.527754\pi$
$641$	−4.40943	−0.174162	−0.0870811	+	0.996201i	$0.527754\pi$
$642$	−66.3574	−2.61892
$643$	17.1006	0.674381	0.337191	−	0.941436i	$-0.390523\pi$
$643$	17.1006	0.674381	0.337191	+	0.941436i	$0.390523\pi$
$644$	−1.87558	−0.0739083
$645$	29.4947	1.16135
$646$	−23.2653	−0.915362
$647$	25.6061	1.00668	0.503340	−	0.864088i	$-0.332104\pi$
$647$	25.6061	1.00668	0.503340	+	0.864088i	$0.332104\pi$
$648$	30.8446	1.21169
$649$	−6.32182	−0.248153
$650$	−83.1582	−3.26173
$651$	4.47251	0.175292
$652$	−6.63721	−0.259933
$653$	−21.1155	−0.826313	−0.413157	−	0.910660i	$-0.635574\pi$
$653$	−21.1155	−0.826313	−0.413157	+	0.910660i	$0.635574\pi$
$654$	−8.86718	−0.346734
$655$	83.1183	3.24770
$656$	−0.0134218	−0.000524035 0
$657$	72.9463	2.84591
$658$	9.08103	0.354016
$659$	−24.3696	−0.949303	−0.474652	−	0.880174i	$-0.657426\pi$
$659$	−24.3696	−0.949303	−0.474652	+	0.880174i	$0.657426\pi$
$660$	54.1004	2.10586
$661$	24.0495	0.935417	0.467708	−	0.883883i	$-0.345080\pi$
$661$	24.0495	0.935417	0.467708	+	0.883883i	$0.345080\pi$
$662$	33.2738	1.29322
$663$	−81.4891	−3.16477
$664$	22.4573	0.871512
$665$	−2.99023	−0.115956
$666$	61.5185	2.38379
$667$	3.75233	0.145291
$668$	18.3170	0.708705
$669$	−33.7640	−1.30539
$670$	67.2653	2.59869
$671$	14.4240	0.556834
$672$	−10.2266	−0.394500
$673$	−13.7203	−0.528879	−0.264440	−	0.964402i	$-0.585187\pi$
$673$	−13.7203	−0.528879	−0.264440	+	0.964402i	$0.585187\pi$
$674$	−25.0410	−0.964542
$675$	−105.688	−4.06792
$676$	−5.41357	−0.208214
$677$	35.3726	1.35948	0.679740	−	0.733453i	$-0.262093\pi$
$677$	35.3726	1.35948	0.679740	+	0.733453i	$0.262093\pi$
$678$	75.3833	2.89508
$679$	−2.40820	−0.0924182
$680$	−88.7763	−3.40442
$681$	27.1426	1.04011
$682$	−7.93952	−0.304020
$683$	23.7553	0.908972	0.454486	−	0.890754i	$-0.349823\pi$
$683$	23.7553	0.908972	0.454486	+	0.890754i	$0.349823\pi$
$684$	25.5901	0.978461
$685$	6.87074	0.262518
$686$	18.3893	0.702106
$687$	−73.3851	−2.79982
$688$	0.125982	0.00480303
$689$	−28.3205	−1.07893
$690$	−27.2410	−1.03705
$691$	2.29511	0.0873100	0.0436550	−	0.999047i	$-0.486100\pi$
$691$	2.29511	0.0873100	0.0436550	+	0.999047i	$0.486100\pi$
$692$	7.14099	0.271460
$693$	5.09262	0.193452
$694$	−36.1094	−1.37070
$695$	3.97653	0.150838
$696$	−32.3057	−1.22454
$697$	−2.07590	−0.0786303
$698$	−9.57207	−0.362308
$699$	−55.8769	−2.11346
$700$	−20.5458	−0.776559
$701$	39.9586	1.50922	0.754608	−	0.656176i	$-0.227827\pi$
$701$	39.9586	1.50922	0.754608	+	0.656176i	$0.227827\pi$
$702$	75.1716	2.83717
$703$	5.52242	0.208282
$704$	18.0108	0.678806
$705$	81.4029	3.06581
$706$	−0.965163	−0.0363244
$707$	0.156562	0.00588814
$708$	−44.5413	−1.67396
$709$	12.8582	0.482898	0.241449	−	0.970413i	$-0.422377\pi$
$709$	12.8582	0.482898	0.241449	+	0.970413i	$0.422377\pi$
$710$	58.4576	2.19387
$711$	42.3914	1.58980
$712$	7.60530	0.285021
$713$	2.46737	0.0924039
$714$	−32.6212	−1.22082
$715$	18.5924	0.695318
$716$	66.3615	2.48005
$717$	37.1164	1.38614
$718$	−48.3926	−1.80600
$719$	−2.24754	−0.0838191	−0.0419096	−	0.999121i	$-0.513344\pi$
$719$	−2.24754	−0.0838191	−0.0419096	+	0.999121i	$0.513344\pi$
$720$	−1.27541	−0.0475318
$721$	6.97875	0.259902
$722$	−39.7066	−1.47773
$723$	44.1205	1.64086
$724$	33.3483	1.23938
$725$	41.1043	1.52658
$726$	62.9403	2.33593
$727$	−8.17350	−0.303138	−0.151569	−	0.988447i	$-0.548433\pi$
$727$	−8.17350	−0.303138	−0.151569	+	0.988447i	$0.548433\pi$
$728$	5.54946	0.205677
$729$	−20.4961	−0.759116
$730$	106.610	3.94583
$731$	19.4851	0.720684
$732$	101.627	3.75623
$733$	−17.3886	−0.642264	−0.321132	−	0.947034i	$-0.604063\pi$
$733$	−17.3886	−0.642264	−0.321132	+	0.947034i	$0.604063\pi$
$734$	−83.0665	−3.06604
$735$	80.3250	2.96283
$736$	−5.64177	−0.207958
$737$	−10.2838	−0.378807
$738$	3.69956	0.136183
$739$	−44.2030	−1.62603	−0.813017	−	0.582239i	$-0.802177\pi$
$739$	−44.2030	−1.62603	−0.813017	+	0.582239i	$0.802177\pi$
$740$	55.4906	2.03988
$741$	13.0367	0.478915
$742$	−11.3371	−0.416198
$743$	45.9059	1.68412	0.842061	−	0.539382i	$-0.181342\pi$
$743$	45.9059	1.68412	0.842061	+	0.539382i	$0.181342\pi$
$744$	−21.2429	−0.778801
$745$	4.08724	0.149745
$746$	−31.1894	−1.14193
$747$	49.9005	1.82576
$748$	35.7405	1.30680
$749$	−5.63434	−0.205874
$750$	−160.419	−5.85769
$751$	8.75571	0.319500	0.159750	−	0.987157i	$-0.448931\pi$
$751$	8.75571	0.319500	0.159750	+	0.987157i	$0.448931\pi$
$752$	0.347701	0.0126793
$753$	53.8258	1.96152
$754$	−29.2359	−1.06471
$755$	−75.9198	−2.76301
$756$	18.5726	0.675478
$757$	−50.7922	−1.84607	−0.923037	−	0.384712i	$-0.874301\pi$
$757$	−50.7922	−1.84607	−0.923037	+	0.384712i	$0.874301\pi$
$758$	−30.6077	−1.11172
$759$	4.16470	0.151169
$760$	14.2025	0.515179
$761$	3.88986	0.141007	0.0705036	−	0.997512i	$-0.477539\pi$
$761$	3.88986	0.141007	0.0705036	+	0.997512i	$0.477539\pi$
$762$	96.6434	3.50102
$763$	−0.752905	−0.0272570
$764$	17.0073	0.615304
$765$	−197.262	−7.13204
$766$	4.92358	0.177896
$767$	−15.3073	−0.552715
$768$	47.5630	1.71628
$769$	0.112820	0.00406839	0.00203420	−	0.999998i	$-0.499352\pi$
$769$	0.112820	0.00406839	0.00203420	+	0.999998i	$0.499352\pi$
$770$	7.44281	0.268220
$771$	5.53098	0.199193
$772$	−14.3890	−0.517870
$773$	−33.2676	−1.19655	−0.598275	−	0.801291i	$-0.704147\pi$
$773$	−33.2676	−1.19655	−0.598275	+	0.801291i	$0.704147\pi$
$774$	−34.7255	−1.24818
$775$	27.0285	0.970892
$776$	11.4381	0.410604
$777$	7.74319	0.277785
$778$	55.3135	1.98308
$779$	0.332104	0.0118989
$780$	130.996	4.69040
$781$	−8.93720	−0.319798
$782$	−17.9963	−0.643546
$783$	−37.1566	−1.32787
$784$	0.343097	0.0122534
$785$	−71.6046	−2.55568
$786$	−145.064	−5.17427
$787$	−0.317823	−0.0113291	−0.00566457	−	0.999984i	$-0.501803\pi$
$787$	−0.317823	−0.0113291	−0.00566457	+	0.999984i	$0.501803\pi$
$788$	−56.1317	−1.99961
$789$	67.1670	2.39121
$790$	61.9547	2.20425
$791$	6.40073	0.227584
$792$	−24.1881	−0.859488
$793$	34.9256	1.24024
$794$	−58.0234	−2.05917
$795$	−101.626	−3.60432
$796$	−3.71154	−0.131552
$797$	13.5414	0.479660	0.239830	−	0.970815i	$-0.422908\pi$
$797$	13.5414	0.479660	0.239830	+	0.970815i	$0.422908\pi$
$798$	5.21876	0.184742
$799$	53.7774	1.90251
$800$	−61.8019	−2.18503
$801$	16.8991	0.597100
$802$	70.4077	2.48618
$803$	−16.2990	−0.575178
$804$	−72.4558	−2.55532
$805$	−2.31301	−0.0815229
$806$	−19.2243	−0.677148
$807$	27.7533	0.976964
$808$	−0.743616	−0.0261603
$809$	−7.15051	−0.251399	−0.125699	−	0.992068i	$-0.540117\pi$
$809$	−7.15051	−0.251399	−0.125699	+	0.992068i	$0.540117\pi$
$810$	100.167	3.51950
$811$	−36.0381	−1.26547	−0.632734	−	0.774369i	$-0.718067\pi$
$811$	−36.0381	−1.26547	−0.632734	+	0.774369i	$0.718067\pi$
$812$	−7.22329	−0.253488
$813$	61.3585	2.15194
$814$	−13.7456	−0.481782
$815$	−8.18515	−0.286713
$816$	−1.24902	−0.0437245
$817$	−3.11725	−0.109059
$818$	38.7744	1.35571
$819$	12.3310	0.430880
$820$	3.33706	0.116535
$821$	−31.8220	−1.11060	−0.555298	−	0.831651i	$-0.687396\pi$
$821$	−31.8220	−1.11060	−0.555298	+	0.831651i	$0.687396\pi$
$822$	−11.9913	−0.418246
$823$	−22.6241	−0.788628	−0.394314	−	0.918976i	$-0.629018\pi$
$823$	−22.6241	−0.788628	−0.394314	+	0.918976i	$0.629018\pi$
$824$	−33.1466	−1.15472
$825$	45.6216	1.58834
$826$	−6.12772	−0.213211
$827$	−40.1727	−1.39694	−0.698470	−	0.715639i	$-0.746136\pi$
$827$	−40.1727	−1.39694	−0.698470	+	0.715639i	$0.746136\pi$
$828$	19.7945	0.687907
$829$	−25.3627	−0.880882	−0.440441	−	0.897782i	$-0.645178\pi$
$829$	−25.3627	−0.880882	−0.440441	+	0.897782i	$0.645178\pi$
$830$	72.9291	2.53140
$831$	6.11711	0.212200
$832$	43.6103	1.51191
$833$	53.0653	1.83860
$834$	−6.94014	−0.240317
$835$	22.5889	0.781721
$836$	−5.71779	−0.197754
$837$	−24.4326	−0.844516
$838$	−76.2681	−2.63464
$839$	−0.442819	−0.0152878	−0.00764391	−	0.999971i	$-0.502433\pi$
$839$	−0.442819	−0.0152878	−0.00764391	+	0.999971i	$0.502433\pi$
$840$	19.9139	0.687094
$841$	−14.5489	−0.501688
$842$	−6.98363	−0.240672
$843$	68.5302	2.36031
$844$	−75.9546	−2.61446
$845$	−6.67613	−0.229666
$846$	−95.8394	−3.29503
$847$	5.34421	0.183629
$848$	−0.434082	−0.0149064
$849$	−90.2645	−3.09787
$850$	−197.138	−6.76177
$851$	4.27172	0.146433
$852$	−62.9684	−2.15726
$853$	−4.51015	−0.154425	−0.0772123	−	0.997015i	$-0.524602\pi$
$853$	−4.51015	−0.154425	−0.0772123	+	0.997015i	$0.524602\pi$
$854$	13.9812	0.478426
$855$	31.5582	1.07927
$856$	26.7611	0.914677
$857$	−0.451099	−0.0154092	−0.00770462	−	0.999970i	$-0.502452\pi$
$857$	−0.451099	−0.0154092	−0.00770462	+	0.999970i	$0.502452\pi$
$858$	−32.4489	−1.10779
$859$	34.1338	1.16463	0.582315	−	0.812963i	$-0.302147\pi$
$859$	34.1338	1.16463	0.582315	+	0.812963i	$0.302147\pi$
$860$	−31.3229	−1.06810
$861$	0.465655	0.0158695
$862$	8.03606	0.273709
$863$	35.4425	1.20648	0.603238	−	0.797561i	$-0.293877\pi$
$863$	35.4425	1.20648	0.603238	+	0.797561i	$0.293877\pi$
$864$	55.8664	1.90061
$865$	8.80642	0.299427
$866$	−22.2083	−0.754669
$867$	−141.564	−4.80775
$868$	−4.74974	−0.161217
$869$	−9.47185	−0.321311
$870$	−104.911	−3.55682
$871$	−24.9006	−0.843723
$872$	3.57603	0.121100
$873$	25.4156	0.860189
$874$	2.87906	0.0973857
$875$	−13.6211	−0.460476
$876$	−114.837	−3.87998
$877$	18.6839	0.630911	0.315456	−	0.948940i	$-0.397843\pi$
$877$	18.6839	0.630911	0.315456	+	0.948940i	$0.397843\pi$
$878$	11.2539	0.379801
$879$	−41.3982	−1.39633
$880$	0.284975	0.00960651
$881$	25.8647	0.871404	0.435702	−	0.900091i	$-0.356500\pi$
$881$	25.8647	0.871404	0.435702	+	0.900091i	$0.356500\pi$
$882$	−94.5703	−3.18435
$883$	−18.5287	−0.623541	−0.311771	−	0.950157i	$-0.600922\pi$
$883$	−18.5287	−0.623541	−0.311771	+	0.950157i	$0.600922\pi$
$884$	86.5400	2.91066
$885$	−54.9293	−1.84643
$886$	−62.6831	−2.10588
$887$	−6.91346	−0.232131	−0.116066	−	0.993242i	$-0.537028\pi$
$887$	−6.91346	−0.232131	−0.116066	+	0.993242i	$0.537028\pi$
$888$	−36.7774	−1.23417
$889$	8.20590	0.275217
$890$	24.6979	0.827875
$891$	−15.3138	−0.513033
$892$	35.8569	1.20058
$893$	−8.60335	−0.287900
$894$	−7.13335	−0.238575
$895$	81.8384	2.73556
$896$	10.7216	0.358182
$897$	10.0842	0.336701
$898$	50.0312	1.66956
$899$	9.50241	0.316923
$900$	216.836	7.22788
$901$	−67.1376	−2.23668
$902$	−0.826623	−0.0275235
$903$	−4.37081	−0.145451
$904$	−30.4012	−1.01113
$905$	41.1259	1.36707
$906$	132.501	4.40205
$907$	−12.8246	−0.425833	−0.212917	−	0.977070i	$-0.568296\pi$
$907$	−12.8246	−0.425833	−0.212917	+	0.977070i	$0.568296\pi$
$908$	−28.8250	−0.956591
$909$	−1.65233	−0.0548043
$910$	18.0216	0.597411
$911$	−11.4505	−0.379372	−0.189686	−	0.981845i	$-0.560747\pi$
$911$	−11.4505	−0.379372	−0.189686	+	0.981845i	$0.560747\pi$
$912$	0.199820	0.00661669
$913$	−11.1497	−0.369000
$914$	−53.7036	−1.77636
$915$	125.328	4.14322
$916$	77.9338	2.57500
$917$	−12.3173	−0.406752
$918$	178.204	5.88162
$919$	33.7945	1.11478	0.557388	−	0.830252i	$-0.311804\pi$
$919$	33.7945	1.11478	0.557388	+	0.830252i	$0.311804\pi$
$920$	10.9860	0.362197
$921$	−15.3062	−0.504356
$922$	1.85036	0.0609384
$923$	−21.6401	−0.712292
$924$	−8.01712	−0.263744
$925$	46.7940	1.53858
$926$	80.4486	2.64370
$927$	−73.6523	−2.41906
$928$	−21.7277	−0.713247
$929$	47.9433	1.57297	0.786485	−	0.617609i	$-0.211899\pi$
$929$	47.9433	1.57297	0.786485	+	0.617609i	$0.211899\pi$
$930$	−68.9853	−2.26212
$931$	−8.48943	−0.278230
$932$	59.3404	1.94376
$933$	−38.6598	−1.26567
$934$	−47.2970	−1.54760
$935$	44.0759	1.44144
$936$	−58.5678	−1.91435
$937$	35.3844	1.15596	0.577979	−	0.816052i	$-0.303842\pi$
$937$	35.3844	1.15596	0.577979	+	0.816052i	$0.303842\pi$
$938$	−9.96803	−0.325468
$939$	−11.3849	−0.371533
$940$	−86.4486	−2.81964
$941$	−5.23428	−0.170633	−0.0853163	−	0.996354i	$-0.527190\pi$
$941$	−5.23428	−0.170633	−0.0853163	+	0.996354i	$0.527190\pi$
$942$	124.970	4.07173
$943$	0.256890	0.00836550
$944$	−0.234622	−0.00763631
$945$	22.9041	0.745070
$946$	7.75898	0.252266
$947$	14.6034	0.474548	0.237274	−	0.971443i	$-0.423746\pi$
$947$	14.6034	0.474548	0.237274	+	0.971443i	$0.423746\pi$
$948$	−66.7353	−2.16746
$949$	−39.4655	−1.28110
$950$	31.5383	1.02324
$951$	−79.0413	−2.56309
$952$	13.1557	0.426380
$953$	43.4793	1.40843	0.704217	−	0.709985i	$-0.251298\pi$
$953$	43.4793	1.40843	0.704217	+	0.709985i	$0.251298\pi$
$954$	119.649	3.87379
$955$	20.9738	0.678696
$956$	−39.4170	−1.27484
$957$	16.0392	0.518474
$958$	71.8274	2.32064
$959$	−1.01817	−0.0328785
$960$	156.493	5.05078
$961$	−24.7516	−0.798439
$962$	−33.2828	−1.07308
$963$	59.4637	1.91619
$964$	−46.8553	−1.50911
$965$	−17.7448	−0.571224
$966$	4.03684	0.129883
$967$	55.9224	1.79834	0.899171	−	0.437597i	$-0.144170\pi$
$967$	55.9224	1.79834	0.899171	+	0.437597i	$0.144170\pi$
$968$	−25.3831	−0.815843
$969$	30.9052	0.992819
$970$	37.1447	1.19265
$971$	49.6121	1.59213	0.796064	−	0.605213i	$-0.206912\pi$
$971$	49.6121	1.59213	0.796064	+	0.605213i	$0.206912\pi$
$972$	−13.3438	−0.428002
$973$	−0.589281	−0.0188915
$974$	88.9173	2.84909
$975$	110.466	3.53774
$976$	0.535321	0.0171352
$977$	25.6989	0.822181	0.411091	−	0.911595i	$-0.365148\pi$
$977$	25.6989	0.822181	0.411091	+	0.911595i	$0.365148\pi$
$978$	14.2853	0.456795
$979$	−3.77590	−0.120678
$980$	−85.3038	−2.72493
$981$	7.94600	0.253696
$982$	60.9711	1.94567
$983$	31.7436	1.01246	0.506231	−	0.862398i	$-0.331038\pi$
$983$	31.7436	1.01246	0.506231	+	0.862398i	$0.331038\pi$
$984$	−2.21170	−0.0705064
$985$	−69.2228	−2.20562
$986$	−69.3077	−2.20721
$987$	−12.0631	−0.383972
$988$	−13.8448	−0.440460
$989$	−2.41127	−0.0766738
$990$	−78.5499	−2.49648
$991$	−56.7020	−1.80120	−0.900599	−	0.434652i	$-0.856871\pi$
$991$	−56.7020	−1.80120	−0.900599	+	0.434652i	$0.856871\pi$
$992$	−14.2872	−0.453620
$993$	−44.2003	−1.40265
$994$	−8.66281	−0.274768
$995$	−4.57715	−0.145105
$996$	−78.5565	−2.48916
$997$	−26.2957	−0.832793	−0.416396	−	0.909183i	$-0.636707\pi$
$997$	−26.2957	−0.832793	−0.416396	+	0.909183i	$0.636707\pi$
$998$	−76.7940	−2.43087
$999$	−42.2998	−1.33831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	139.2.a.c.1.6	✓	7
3.2	odd	2		1251.2.a.k.1.2		7
4.3	odd	2		2224.2.a.o.1.6		7
5.4	even	2		3475.2.a.e.1.2		7
7.6	odd	2		6811.2.a.p.1.6		7
8.3	odd	2		8896.2.a.bd.1.2		7
8.5	even	2		8896.2.a.be.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
139.2.a.c.1.6	✓	7	1.1	even	1	trivial
1251.2.a.k.1.2		7	3.2	odd	2
2224.2.a.o.1.6		7	4.3	odd	2
3475.2.a.e.1.2		7	5.4	even	2
6811.2.a.p.1.6		7	7.6	odd	2
8896.2.a.bd.1.2		7	8.3	odd	2
8896.2.a.be.1.6		7	8.5	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:	\( N \)	\(=\)	\( 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	139.a (trivial)

\(f(q)\)	\(=\)	\(q+2.28572 q^{2} -3.03631 q^{3} +3.22451 q^{4} +3.97653 q^{5} -6.94014 q^{6} -0.589281 q^{7} +2.79888 q^{8} +6.21915 q^{9} +O(q^{10})\)	\(q+2.28572 q^{2} -3.03631 q^{3} +3.22451 q^{4} +3.97653 q^{5} -6.94014 q^{6} -0.589281 q^{7} +2.79888 q^{8} +6.21915 q^{9} +9.08923 q^{10} -1.38959 q^{11} -9.79058 q^{12} -3.36469 q^{13} -1.34693 q^{14} -12.0740 q^{15} -0.0515721 q^{16} -7.97644 q^{17} +14.2152 q^{18} +1.27608 q^{19} +12.8223 q^{20} +1.78924 q^{21} -3.17622 q^{22} +0.987077 q^{23} -8.49824 q^{24} +10.8128 q^{25} -7.69072 q^{26} -9.77432 q^{27} -1.90014 q^{28} +3.80145 q^{29} -27.5977 q^{30} +2.49968 q^{31} -5.71563 q^{32} +4.21923 q^{33} -18.2319 q^{34} -2.34329 q^{35} +20.0537 q^{36} +4.32765 q^{37} +2.91676 q^{38} +10.2162 q^{39} +11.1298 q^{40} +0.260254 q^{41} +4.08969 q^{42} -2.44284 q^{43} -4.48075 q^{44} +24.7306 q^{45} +2.25618 q^{46} -6.74203 q^{47} +0.156589 q^{48} -6.65275 q^{49} +24.7150 q^{50} +24.2189 q^{51} -10.8495 q^{52} +8.41699 q^{53} -22.3413 q^{54} -5.52576 q^{55} -1.64932 q^{56} -3.87456 q^{57} +8.68905 q^{58} +4.54940 q^{59} -38.9326 q^{60} -10.3800 q^{61} +5.71356 q^{62} -3.66482 q^{63} -12.9612 q^{64} -13.3798 q^{65} +9.64397 q^{66} +7.40056 q^{67} -25.7201 q^{68} -2.99707 q^{69} -5.35611 q^{70} +6.43153 q^{71} +17.4066 q^{72} +11.7293 q^{73} +9.89179 q^{74} -32.8309 q^{75} +4.11472 q^{76} +0.818860 q^{77} +23.3514 q^{78} +6.81628 q^{79} -0.205078 q^{80} +11.0204 q^{81} +0.594867 q^{82} +8.02368 q^{83} +5.76940 q^{84} -31.7186 q^{85} -5.58363 q^{86} -11.5424 q^{87} -3.88930 q^{88} +2.71727 q^{89} +56.5273 q^{90} +1.98275 q^{91} +3.18284 q^{92} -7.58978 q^{93} -15.4104 q^{94} +5.07436 q^{95} +17.3544 q^{96} +4.08668 q^{97} -15.2063 q^{98} -8.64209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9} - 4 q^{10} + 2 q^{11} - 8 q^{12} + 6 q^{13} + 7 q^{14} - 3 q^{15} + 5 q^{16} + 5 q^{17} - 10 q^{18} - 10 q^{19} + 12 q^{20} - 5 q^{21} - 18 q^{22} - q^{23} - 21 q^{24} + 14 q^{25} - 8 q^{26} - 11 q^{27} - 28 q^{28} + 30 q^{29} - 41 q^{30} - 20 q^{31} - 12 q^{32} - 20 q^{33} - 17 q^{34} - 7 q^{35} + 2 q^{36} + 6 q^{37} + 6 q^{38} + 11 q^{39} - 22 q^{40} + 19 q^{41} + 6 q^{42} - 12 q^{43} + 25 q^{44} + 27 q^{45} + 22 q^{46} - 3 q^{47} + 15 q^{48} - 8 q^{49} + 12 q^{50} + 23 q^{51} - 8 q^{52} + 38 q^{53} - 7 q^{54} + 7 q^{55} + 21 q^{56} - 19 q^{57} - 21 q^{58} - 14 q^{59} - 8 q^{60} + 4 q^{61} - q^{62} - 18 q^{63} - 16 q^{64} + 10 q^{65} + 18 q^{66} + 9 q^{67} - 25 q^{68} + 9 q^{69} + 20 q^{70} + 24 q^{71} + 41 q^{72} - 5 q^{73} + 9 q^{74} - 21 q^{75} + 3 q^{76} - 13 q^{77} + 20 q^{78} + 8 q^{79} + 11 q^{80} + 39 q^{81} + 56 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 39 q^{86} - 25 q^{87} - 29 q^{88} + 10 q^{89} + 72 q^{90} + 7 q^{91} + 29 q^{92} - 15 q^{93} - 36 q^{94} - 21 q^{95} - 11 q^{96} - 5 q^{97} - 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9 - 4 * q^10 + 2 * q^11 - 8 * q^12 + 6 * q^13 + 7 * q^14 - 3 * q^15 + 5 * q^16 + 5 * q^17 - 10 * q^18 - 10 * q^19 + 12 * q^20 - 5 * q^21 - 18 * q^22 - q^23 - 21 * q^24 + 14 * q^25 - 8 * q^26 - 11 * q^27 - 28 * q^28 + 30 * q^29 - 41 * q^30 - 20 * q^31 - 12 * q^32 - 20 * q^33 - 17 * q^34 - 7 * q^35 + 2 * q^36 + 6 * q^37 + 6 * q^38 + 11 * q^39 - 22 * q^40 + 19 * q^41 + 6 * q^42 - 12 * q^43 + 25 * q^44 + 27 * q^45 + 22 * q^46 - 3 * q^47 + 15 * q^48 - 8 * q^49 + 12 * q^50 + 23 * q^51 - 8 * q^52 + 38 * q^53 - 7 * q^54 + 7 * q^55 + 21 * q^56 - 19 * q^57 - 21 * q^58 - 14 * q^59 - 8 * q^60 + 4 * q^61 - q^62 - 18 * q^63 - 16 * q^64 + 10 * q^65 + 18 * q^66 + 9 * q^67 - 25 * q^68 + 9 * q^69 + 20 * q^70 + 24 * q^71 + 41 * q^72 - 5 * q^73 + 9 * q^74 - 21 * q^75 + 3 * q^76 - 13 * q^77 + 20 * q^78 + 8 * q^79 + 11 * q^80 + 39 * q^81 + 56 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 39 * q^86 - 25 * q^87 - 29 * q^88 + 10 * q^89 + 72 * q^90 + 7 * q^91 + 29 * q^92 - 15 * q^93 - 36 * q^94 - 21 * q^95 - 11 * q^96 - 5 * q^97 - 49 * q^98 - 31 * q^99

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