LMFDB - Embedded newform 2001.2.a.o.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 $ x^20 - 2x^19 - 33x^18 + 64x^17 + 453x^16 - 846x^15 - 3353x^14 + 5985x^13 + 14484x^12 - 24566x^11 - 36791x^10 + 59410x^9 + 52109x^8 - 82362x^7 - 34967x^6 + 60661x^5 + 5201x^4 - 19624x^3 + 2768x^2 + 1408*x - 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$1.20801$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.20801 q^{2} +1.00000 q^{3} -0.540713 q^{4} +2.72981 q^{5} +1.20801 q^{6} -1.05258 q^{7} -3.06921 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.20801 q^{2} +1.00000 q^{3} -0.540713 q^{4} +2.72981 q^{5} +1.20801 q^{6} -1.05258 q^{7} -3.06921 q^{8} +1.00000 q^{9} +3.29764 q^{10} +0.0950928 q^{11} -0.540713 q^{12} +1.29615 q^{13} -1.27153 q^{14} +2.72981 q^{15} -2.62620 q^{16} +6.72257 q^{17} +1.20801 q^{18} +1.49041 q^{19} -1.47604 q^{20} -1.05258 q^{21} +0.114873 q^{22} +1.00000 q^{23} -3.06921 q^{24} +2.45186 q^{25} +1.56577 q^{26} +1.00000 q^{27} +0.569144 q^{28} +1.00000 q^{29} +3.29764 q^{30} +3.03307 q^{31} +2.96593 q^{32} +0.0950928 q^{33} +8.12092 q^{34} -2.87334 q^{35} -0.540713 q^{36} +5.28694 q^{37} +1.80043 q^{38} +1.29615 q^{39} -8.37835 q^{40} -5.16061 q^{41} -1.27153 q^{42} +0.852332 q^{43} -0.0514180 q^{44} +2.72981 q^{45} +1.20801 q^{46} +9.07477 q^{47} -2.62620 q^{48} -5.89208 q^{49} +2.96187 q^{50} +6.72257 q^{51} -0.700848 q^{52} +8.68851 q^{53} +1.20801 q^{54} +0.259585 q^{55} +3.23058 q^{56} +1.49041 q^{57} +1.20801 q^{58} +7.14371 q^{59} -1.47604 q^{60} -11.2692 q^{61} +3.66398 q^{62} -1.05258 q^{63} +8.83528 q^{64} +3.53825 q^{65} +0.114873 q^{66} +13.9103 q^{67} -3.63498 q^{68} +1.00000 q^{69} -3.47102 q^{70} -10.8505 q^{71} -3.06921 q^{72} -12.7611 q^{73} +6.38667 q^{74} +2.45186 q^{75} -0.805885 q^{76} -0.100093 q^{77} +1.56577 q^{78} -4.38026 q^{79} -7.16903 q^{80} +1.00000 q^{81} -6.23406 q^{82} -2.83783 q^{83} +0.569144 q^{84} +18.3513 q^{85} +1.02962 q^{86} +1.00000 q^{87} -0.291859 q^{88} +2.67707 q^{89} +3.29764 q^{90} -1.36430 q^{91} -0.540713 q^{92} +3.03307 q^{93} +10.9624 q^{94} +4.06853 q^{95} +2.96593 q^{96} -9.23470 q^{97} -7.11768 q^{98} +0.0950928 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9} + 7 q^{10} + 30 q^{12} + 21 q^{13} - q^{14} - q^{15} + 58 q^{16} - 4 q^{17} + 2 q^{18} + 7 q^{19} - 20 q^{20} + 9 q^{21} + 7 q^{22} + 20 q^{23} + 6 q^{24} + 47 q^{25} + 8 q^{26} + 20 q^{27} + 11 q^{28} + 20 q^{29} + 7 q^{30} + 28 q^{31} + 14 q^{32} + 16 q^{34} + 9 q^{35} + 30 q^{36} + 14 q^{37} - 20 q^{38} + 21 q^{39} + 34 q^{40} + 7 q^{41} - q^{42} + 3 q^{43} - q^{44} - q^{45} + 2 q^{46} + 3 q^{47} + 58 q^{48} + 35 q^{49} - 24 q^{50} - 4 q^{51} + 73 q^{52} - 19 q^{53} + 2 q^{54} + 29 q^{55} - 30 q^{56} + 7 q^{57} + 2 q^{58} + 20 q^{59} - 20 q^{60} + 15 q^{61} + 12 q^{62} + 9 q^{63} + 82 q^{64} - 28 q^{65} + 7 q^{66} + 20 q^{67} - 23 q^{68} + 20 q^{69} - 24 q^{70} + 63 q^{71} + 6 q^{72} + 19 q^{73} + 16 q^{74} + 47 q^{75} - 44 q^{76} - 7 q^{77} + 8 q^{78} + 32 q^{79} - 56 q^{80} + 20 q^{81} - 20 q^{82} - 21 q^{83} + 11 q^{84} + 4 q^{85} - 6 q^{86} + 20 q^{87} + 55 q^{88} - 13 q^{89} + 7 q^{90} + 70 q^{91} + 30 q^{92} + 28 q^{93} - 12 q^{94} + 9 q^{95} + 14 q^{96} - 9 q^{97} + 31 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9 + 7 * q^10 + 30 * q^12 + 21 * q^13 - q^14 - q^15 + 58 * q^16 - 4 * q^17 + 2 * q^18 + 7 * q^19 - 20 * q^20 + 9 * q^21 + 7 * q^22 + 20 * q^23 + 6 * q^24 + 47 * q^25 + 8 * q^26 + 20 * q^27 + 11 * q^28 + 20 * q^29 + 7 * q^30 + 28 * q^31 + 14 * q^32 + 16 * q^34 + 9 * q^35 + 30 * q^36 + 14 * q^37 - 20 * q^38 + 21 * q^39 + 34 * q^40 + 7 * q^41 - q^42 + 3 * q^43 - q^44 - q^45 + 2 * q^46 + 3 * q^47 + 58 * q^48 + 35 * q^49 - 24 * q^50 - 4 * q^51 + 73 * q^52 - 19 * q^53 + 2 * q^54 + 29 * q^55 - 30 * q^56 + 7 * q^57 + 2 * q^58 + 20 * q^59 - 20 * q^60 + 15 * q^61 + 12 * q^62 + 9 * q^63 + 82 * q^64 - 28 * q^65 + 7 * q^66 + 20 * q^67 - 23 * q^68 + 20 * q^69 - 24 * q^70 + 63 * q^71 + 6 * q^72 + 19 * q^73 + 16 * q^74 + 47 * q^75 - 44 * q^76 - 7 * q^77 + 8 * q^78 + 32 * q^79 - 56 * q^80 + 20 * q^81 - 20 * q^82 - 21 * q^83 + 11 * q^84 + 4 * q^85 - 6 * q^86 + 20 * q^87 + 55 * q^88 - 13 * q^89 + 7 * q^90 + 70 * q^91 + 30 * q^92 + 28 * q^93 - 12 * q^94 + 9 * q^95 + 14 * q^96 - 9 * q^97 + 31 * q^98

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 $

$2$	1.20801	0.854192	0.427096	−	0.904206i	$-0.359537\pi$
$2$	1.20801	0.854192	0.427096	+	0.904206i	$0.359537\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.540713	−0.270357
$5$	2.72981	1.22081	0.610404	−	0.792090i	$-0.291007\pi$
$5$	2.72981	1.22081	0.610404	+	0.792090i	$0.291007\pi$
$6$	1.20801	0.493168
$7$	−1.05258	−0.397838	−0.198919	−	0.980016i	$-0.563743\pi$
$7$	−1.05258	−0.397838	−0.198919	+	0.980016i	$0.563743\pi$
$8$	−3.06921	−1.08513
$9$	1.00000	0.333333
$10$	3.29764	1.04280
$11$	0.0950928	0.0286716	0.0143358	−	0.999897i	$-0.495437\pi$
$11$	0.0950928	0.0286716	0.0143358	+	0.999897i	$0.495437\pi$
$12$	−0.540713	−0.156091
$13$	1.29615	0.359488	0.179744	−	0.983713i	$-0.442473\pi$
$13$	1.29615	0.359488	0.179744	+	0.983713i	$0.442473\pi$
$14$	−1.27153	−0.339830
$15$	2.72981	0.704834
$16$	−2.62620	−0.656550
$17$	6.72257	1.63046	0.815231	−	0.579136i	$-0.196610\pi$
$17$	6.72257	1.63046	0.815231	+	0.579136i	$0.196610\pi$
$18$	1.20801	0.284731
$19$	1.49041	0.341923	0.170962	−	0.985278i	$-0.445313\pi$
$19$	1.49041	0.341923	0.170962	+	0.985278i	$0.445313\pi$
$20$	−1.47604	−0.330054
$21$	−1.05258	−0.229692
$22$	0.114873	0.0244910
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.06921	−0.626499
$25$	2.45186	0.490372
$26$	1.56577	0.307072
$27$	1.00000	0.192450
$28$	0.569144	0.107558
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	3.29764	0.602063
$31$	3.03307	0.544756	0.272378	−	0.962190i	$-0.412190\pi$
$31$	3.03307	0.544756	0.272378	+	0.962190i	$0.412190\pi$
$32$	2.96593	0.524308
$33$	0.0950928	0.0165535
$34$	8.12092	1.39273
$35$	−2.87334	−0.485683
$36$	−0.540713	−0.0901189
$37$	5.28694	0.869167	0.434584	−	0.900631i	$-0.356896\pi$
$37$	5.28694	0.869167	0.434584	+	0.900631i	$0.356896\pi$
$38$	1.80043	0.292068
$39$	1.29615	0.207551
$40$	−8.37835	−1.32473
$41$	−5.16061	−0.805951	−0.402976	−	0.915211i	$-0.632024\pi$
$41$	−5.16061	−0.805951	−0.402976	+	0.915211i	$0.632024\pi$
$42$	−1.27153	−0.196201
$43$	0.852332	0.129979	0.0649897	−	0.997886i	$-0.479299\pi$
$43$	0.852332	0.129979	0.0649897	+	0.997886i	$0.479299\pi$
$44$	−0.0514180	−0.00775155
$45$	2.72981	0.406936
$46$	1.20801	0.178111
$47$	9.07477	1.32369	0.661845	−	0.749640i	$-0.269773\pi$
$47$	9.07477	1.32369	0.661845	+	0.749640i	$0.269773\pi$
$48$	−2.62620	−0.379060
$49$	−5.89208	−0.841725
$50$	2.96187	0.418871
$51$	6.72257	0.941348
$52$	−0.700848	−0.0971901
$53$	8.68851	1.19346	0.596729	−	0.802443i	$-0.296467\pi$
$53$	8.68851	1.19346	0.596729	+	0.802443i	$0.296467\pi$
$54$	1.20801	0.164389
$55$	0.259585	0.0350025
$56$	3.23058	0.431705
$57$	1.49041	0.197410
$58$	1.20801	0.158619
$59$	7.14371	0.930031	0.465016	−	0.885302i	$-0.346049\pi$
$59$	7.14371	0.930031	0.465016	+	0.885302i	$0.346049\pi$
$60$	−1.47604	−0.190557
$61$	−11.2692	−1.44288	−0.721438	−	0.692479i	$-0.756519\pi$
$61$	−11.2692	−1.44288	−0.721438	+	0.692479i	$0.756519\pi$
$62$	3.66398	0.465326
$63$	−1.05258	−0.132613
$64$	8.83528	1.10441
$65$	3.53825	0.438866
$66$	0.114873	0.0141399
$67$	13.9103	1.69941	0.849707	−	0.527256i	$-0.176779\pi$
$67$	13.9103	1.69941	0.849707	+	0.527256i	$0.176779\pi$
$68$	−3.63498	−0.440806
$69$	1.00000	0.120386
$70$	−3.47102	−0.414867
$71$	−10.8505	−1.28772	−0.643859	−	0.765144i	$-0.722668\pi$
$71$	−10.8505	−1.28772	−0.643859	+	0.765144i	$0.722668\pi$
$72$	−3.06921	−0.361709
$73$	−12.7611	−1.49357	−0.746786	−	0.665064i	$-0.768404\pi$
$73$	−12.7611	−1.49357	−0.746786	+	0.665064i	$0.768404\pi$
$74$	6.38667	0.742435
$75$	2.45186	0.283116
$76$	−0.805885	−0.0924413
$77$	−0.100093	−0.0114066
$78$	1.56577	0.177288
$79$	−4.38026	−0.492818	−0.246409	−	0.969166i	$-0.579251\pi$
$79$	−4.38026	−0.492818	−0.246409	+	0.969166i	$0.579251\pi$
$80$	−7.16903	−0.801522
$81$	1.00000	0.111111
$82$	−6.23406	−0.688437
$83$	−2.83783	−0.311492	−0.155746	−	0.987797i	$-0.549778\pi$
$83$	−2.83783	−0.311492	−0.155746	+	0.987797i	$0.549778\pi$
$84$	0.569144	0.0620987
$85$	18.3513	1.99048
$86$	1.02962	0.111027
$87$	1.00000	0.107211
$88$	−0.291859	−0.0311123
$89$	2.67707	0.283769	0.141884	−	0.989883i	$-0.454684\pi$
$89$	2.67707	0.283769	0.141884	+	0.989883i	$0.454684\pi$
$90$	3.29764	0.347601
$91$	−1.36430	−0.143018
$92$	−0.540713	−0.0563733
$93$	3.03307	0.314515
$94$	10.9624	1.13069
$95$	4.06853	0.417423
$96$	2.96593	0.302709
$97$	−9.23470	−0.937642	−0.468821	−	0.883293i	$-0.655321\pi$
$97$	−9.23470	−0.937642	−0.468821	+	0.883293i	$0.655321\pi$
$98$	−7.11768	−0.718995
$99$	0.0950928	0.00955719
$100$	−1.32575	−0.132575
$101$	−6.95395	−0.691943	−0.345972	−	0.938245i	$-0.612451\pi$
$101$	−6.95395	−0.691943	−0.345972	+	0.938245i	$0.612451\pi$
$102$	8.12092	0.804091
$103$	17.3902	1.71351	0.856753	−	0.515727i	$-0.172478\pi$
$103$	17.3902	1.71351	0.856753	+	0.515727i	$0.172478\pi$
$104$	−3.97816	−0.390091
$105$	−2.87334	−0.280409
$106$	10.4958	1.01944
$107$	15.0267	1.45268	0.726341	−	0.687335i	$-0.241219\pi$
$107$	15.0267	1.45268	0.726341	+	0.687335i	$0.241219\pi$
$108$	−0.540713	−0.0520302
$109$	−17.8192	−1.70677	−0.853383	−	0.521284i	$-0.825453\pi$
$109$	−17.8192	−1.70677	−0.853383	+	0.521284i	$0.825453\pi$
$110$	0.313581	0.0298988
$111$	5.28694	0.501814
$112$	2.76429	0.261200
$113$	−6.63665	−0.624323	−0.312162	−	0.950029i	$-0.601053\pi$
$113$	−6.63665	−0.624323	−0.312162	+	0.950029i	$0.601053\pi$
$114$	1.80043	0.168626
$115$	2.72981	0.254556
$116$	−0.540713	−0.0502040
$117$	1.29615	0.119829
$118$	8.62966	0.794425
$119$	−7.07603	−0.648659
$120$	−8.37835	−0.764835
$121$	−10.9910	−0.999178
$122$	−13.6133	−1.23249
$123$	−5.16061	−0.465316
$124$	−1.64002	−0.147279
$125$	−6.95594	−0.622158
$126$	−1.27153	−0.113277
$127$	−17.4909	−1.55206	−0.776032	−	0.630693i	$-0.782771\pi$
$127$	−17.4909	−1.55206	−0.776032	+	0.630693i	$0.782771\pi$
$128$	4.74123	0.419070
$129$	0.852332	0.0750436
$130$	4.27424	0.374876
$131$	20.0165	1.74885	0.874423	−	0.485164i	$-0.161240\pi$
$131$	20.0165	1.74885	0.874423	+	0.485164i	$0.161240\pi$
$132$	−0.0514180	−0.00447536
$133$	−1.56877	−0.136030
$134$	16.8038	1.45162
$135$	2.72981	0.234945
$136$	−20.6329	−1.76926
$137$	−10.8950	−0.930823	−0.465411	−	0.885094i	$-0.654094\pi$
$137$	−10.8950	−0.930823	−0.465411	+	0.885094i	$0.654094\pi$
$138$	1.20801	0.102833
$139$	−8.06409	−0.683987	−0.341993	−	0.939702i	$-0.611102\pi$
$139$	−8.06409	−0.683987	−0.341993	+	0.939702i	$0.611102\pi$
$140$	1.55365	0.131308
$141$	9.07477	0.764233
$142$	−13.1075	−1.09996
$143$	0.123255	0.0103071
$144$	−2.62620	−0.218850
$145$	2.72981	0.226698
$146$	−15.4155	−1.27580
$147$	−5.89208	−0.485970
$148$	−2.85872	−0.234985
$149$	−6.47063	−0.530094	−0.265047	−	0.964235i	$-0.585388\pi$
$149$	−6.47063	−0.530094	−0.265047	+	0.964235i	$0.585388\pi$
$150$	2.96187	0.241836
$151$	−16.8594	−1.37200	−0.686001	−	0.727601i	$-0.740635\pi$
$151$	−16.8594	−1.37200	−0.686001	+	0.727601i	$0.740635\pi$
$152$	−4.57437	−0.371031
$153$	6.72257	0.543487
$154$	−0.120913	−0.00974344
$155$	8.27971	0.665043
$156$	−0.700848	−0.0561127
$157$	15.2976	1.22088	0.610442	−	0.792061i	$-0.290992\pi$
$157$	15.2976	1.22088	0.610442	+	0.792061i	$0.290992\pi$
$158$	−5.29140	−0.420961
$159$	8.68851	0.689044
$160$	8.09644	0.640079
$161$	−1.05258	−0.0829549
$162$	1.20801	0.0949102
$163$	13.4200	1.05114	0.525569	−	0.850751i	$-0.323852\pi$
$163$	13.4200	1.05114	0.525569	+	0.850751i	$0.323852\pi$
$164$	2.79041	0.217894
$165$	0.259585	0.0202087
$166$	−3.42813	−0.266074
$167$	−5.28341	−0.408843	−0.204421	−	0.978883i	$-0.565531\pi$
$167$	−5.28341	−0.408843	−0.204421	+	0.978883i	$0.565531\pi$
$168$	3.23058	0.249245
$169$	−11.3200	−0.870768
$170$	22.1686	1.70025
$171$	1.49041	0.113974
$172$	−0.460867	−0.0351408
$173$	19.7703	1.50311	0.751553	−	0.659672i	$-0.229305\pi$
$173$	19.7703	1.50311	0.751553	+	0.659672i	$0.229305\pi$
$174$	1.20801	0.0915790
$175$	−2.58078	−0.195088
$176$	−0.249733	−0.0188243
$177$	7.14371	0.536954
$178$	3.23392	0.242393
$179$	−14.4299	−1.07854	−0.539270	−	0.842133i	$-0.681300\pi$
$179$	−14.4299	−1.07854	−0.539270	+	0.842133i	$0.681300\pi$
$180$	−1.47604	−0.110018
$181$	−20.0238	−1.48836	−0.744179	−	0.667980i	$-0.767159\pi$
$181$	−20.0238	−1.48836	−0.744179	+	0.667980i	$0.767159\pi$
$182$	−1.64809	−0.122165
$183$	−11.2692	−0.833045
$184$	−3.06921	−0.226265
$185$	14.4323	1.06109
$186$	3.66398	0.268656
$187$	0.639268	0.0467479
$188$	−4.90685	−0.357869
$189$	−1.05258	−0.0765639
$190$	4.91483	0.356559
$191$	7.53689	0.545350	0.272675	−	0.962106i	$-0.412092\pi$
$191$	7.53689	0.545350	0.272675	+	0.962106i	$0.412092\pi$
$192$	8.83528	0.637631
$193$	13.7002	0.986164	0.493082	−	0.869983i	$-0.335870\pi$
$193$	13.7002	0.986164	0.493082	+	0.869983i	$0.335870\pi$
$194$	−11.1556	−0.800926
$195$	3.53825	0.253380
$196$	3.18593	0.227566
$197$	−14.2870	−1.01791	−0.508954	−	0.860794i	$-0.669968\pi$
$197$	−14.2870	−1.01791	−0.508954	+	0.860794i	$0.669968\pi$
$198$	0.114873	0.00816367
$199$	25.8998	1.83599	0.917993	−	0.396596i	$-0.129809\pi$
$199$	25.8998	1.83599	0.917993	+	0.396596i	$0.129809\pi$
$200$	−7.52526	−0.532116
$201$	13.9103	0.981157
$202$	−8.40043	−0.591052
$203$	−1.05258	−0.0738766
$204$	−3.63498	−0.254500
$205$	−14.0875	−0.983912
$206$	21.0075	1.46366
$207$	1.00000	0.0695048
$208$	−3.40396	−0.236022
$209$	0.141727	0.00980348
$210$	−3.47102	−0.239523
$211$	1.77461	0.122169	0.0610846	−	0.998133i	$-0.480544\pi$
$211$	1.77461	0.122169	0.0610846	+	0.998133i	$0.480544\pi$
$212$	−4.69799	−0.322660
$213$	−10.8505	−0.743464
$214$	18.1523	1.24087
$215$	2.32670	0.158680
$216$	−3.06921	−0.208833
$217$	−3.19255	−0.216724
$218$	−21.5257	−1.45791
$219$	−12.7611	−0.862314
$220$	−0.140361	−0.00946315
$221$	8.71348	0.586132
$222$	6.38667	0.428645
$223$	11.2214	0.751443	0.375721	−	0.926733i	$-0.377395\pi$
$223$	11.2214	0.751443	0.375721	+	0.926733i	$0.377395\pi$
$224$	−3.12188	−0.208589
$225$	2.45186	0.163457
$226$	−8.01713	−0.533292
$227$	0.0481254	0.00319419	0.00159710	−	0.999999i	$-0.499492\pi$
$227$	0.0481254	0.00319419	0.00159710	+	0.999999i	$0.499492\pi$
$228$	−0.805885	−0.0533710
$229$	−17.3588	−1.14710	−0.573552	−	0.819169i	$-0.694435\pi$
$229$	−17.3588	−1.14710	−0.573552	+	0.819169i	$0.694435\pi$
$230$	3.29764	0.217440
$231$	−0.100093	−0.00658562
$232$	−3.06921	−0.201503
$233$	5.44641	0.356806	0.178403	−	0.983957i	$-0.442907\pi$
$233$	5.44641	0.356806	0.178403	+	0.983957i	$0.442907\pi$
$234$	1.56577	0.102357
$235$	24.7724	1.61597
$236$	−3.86270	−0.251440
$237$	−4.38026	−0.284528
$238$	−8.54792	−0.554079
$239$	−0.363333	−0.0235020	−0.0117510	−	0.999931i	$-0.503741\pi$
$239$	−0.363333	−0.0235020	−0.0117510	+	0.999931i	$0.503741\pi$
$240$	−7.16903	−0.462759
$241$	19.8759	1.28032	0.640159	−	0.768243i	$-0.278869\pi$
$241$	19.8759	1.28032	0.640159	+	0.768243i	$0.278869\pi$
$242$	−13.2772	−0.853489
$243$	1.00000	0.0641500
$244$	6.09342	0.390091
$245$	−16.0842	−1.02758
$246$	−6.23406	−0.397469
$247$	1.93180	0.122917
$248$	−9.30913	−0.591130
$249$	−2.83783	−0.179840
$250$	−8.40284	−0.531442
$251$	−24.4211	−1.54144	−0.770722	−	0.637172i	$-0.780104\pi$
$251$	−24.4211	−1.54144	−0.770722	+	0.637172i	$0.780104\pi$
$252$	0.569144	0.0358527
$253$	0.0950928	0.00597843
$254$	−21.1291	−1.32576
$255$	18.3513	1.14920
$256$	−11.9431	−0.746444
$257$	−16.3921	−1.02251	−0.511255	−	0.859429i	$-0.670819\pi$
$257$	−16.3921	−1.02251	−0.511255	+	0.859429i	$0.670819\pi$
$258$	1.02962	0.0641017
$259$	−5.56492	−0.345787
$260$	−1.91318	−0.118650
$261$	1.00000	0.0618984
$262$	24.1801	1.49385
$263$	5.90552	0.364150	0.182075	−	0.983285i	$-0.441719\pi$
$263$	5.90552	0.364150	0.182075	+	0.983285i	$0.441719\pi$
$264$	−0.291859	−0.0179627
$265$	23.7180	1.45698
$266$	−1.89509	−0.116196
$267$	2.67707	0.163834
$268$	−7.52149	−0.459448
$269$	20.8869	1.27350	0.636749	−	0.771071i	$-0.280279\pi$
$269$	20.8869	1.27350	0.636749	+	0.771071i	$0.280279\pi$
$270$	3.29764	0.200688
$271$	19.0989	1.16018	0.580089	−	0.814553i	$-0.303018\pi$
$271$	19.0989	1.16018	0.580089	+	0.814553i	$0.303018\pi$
$272$	−17.6548	−1.07048
$273$	−1.36430	−0.0825715
$274$	−13.1613	−0.795101
$275$	0.233154	0.0140597
$276$	−0.540713	−0.0325471
$277$	−27.6649	−1.66222	−0.831110	−	0.556108i	$-0.812294\pi$
$277$	−27.6649	−1.66222	−0.831110	+	0.556108i	$0.812294\pi$
$278$	−9.74149	−0.584256
$279$	3.03307	0.181585
$280$	8.81887	0.527029
$281$	−14.6598	−0.874532	−0.437266	−	0.899332i	$-0.644053\pi$
$281$	−14.6598	−0.874532	−0.437266	+	0.899332i	$0.644053\pi$
$282$	10.9624	0.652802
$283$	10.6965	0.635842	0.317921	−	0.948117i	$-0.397015\pi$
$283$	10.6965	0.635842	0.317921	+	0.948117i	$0.397015\pi$
$284$	5.86701	0.348143
$285$	4.06853	0.240999
$286$	0.148893	0.00880423
$287$	5.43195	0.320638
$288$	2.96593	0.174769
$289$	28.1929	1.65841
$290$	3.29764	0.193644
$291$	−9.23470	−0.541348
$292$	6.90009	0.403797
$293$	−30.1483	−1.76128	−0.880642	−	0.473782i	$-0.842888\pi$
$293$	−30.1483	−1.76128	−0.880642	+	0.473782i	$0.842888\pi$
$294$	−7.11768	−0.415112
$295$	19.5010	1.13539
$296$	−16.2267	−0.943158
$297$	0.0950928	0.00551785
$298$	−7.81658	−0.452802
$299$	1.29615	0.0749585
$300$	−1.32575	−0.0765424
$301$	−0.897147	−0.0517107
$302$	−20.3664	−1.17195
$303$	−6.95395	−0.399494
$304$	−3.91412	−0.224490
$305$	−30.7628	−1.76147
$306$	8.12092	0.464242
$307$	−9.53172	−0.544004	−0.272002	−	0.962297i	$-0.587686\pi$
$307$	−9.53172	−0.544004	−0.272002	+	0.962297i	$0.587686\pi$
$308$	0.0541215	0.00308386
$309$	17.3902	0.989293
$310$	10.0020	0.568074
$311$	−31.4611	−1.78400	−0.891999	−	0.452038i	$-0.850697\pi$
$311$	−31.4611	−1.78400	−0.891999	+	0.452038i	$0.850697\pi$
$312$	−3.97816	−0.225219
$313$	8.56299	0.484009	0.242004	−	0.970275i	$-0.422195\pi$
$313$	8.56299	0.484009	0.242004	+	0.970275i	$0.422195\pi$
$314$	18.4797	1.04287
$315$	−2.87334	−0.161894
$316$	2.36847	0.133237
$317$	20.2256	1.13598	0.567990	−	0.823035i	$-0.307721\pi$
$317$	20.2256	1.13598	0.567990	+	0.823035i	$0.307721\pi$
$318$	10.4958	0.588575
$319$	0.0950928	0.00532418
$320$	24.1186	1.34827
$321$	15.0267	0.838706
$322$	−1.27153	−0.0708594
$323$	10.0194	0.557493
$324$	−0.540713	−0.0300396
$325$	3.17799	0.176283
$326$	16.2115	0.897874
$327$	−17.8192	−0.985402
$328$	15.8390	0.874560
$329$	−9.55191	−0.526614
$330$	0.313581	0.0172621
$331$	−15.0603	−0.827788	−0.413894	−	0.910325i	$-0.635832\pi$
$331$	−15.0603	−0.827788	−0.413894	+	0.910325i	$0.635832\pi$
$332$	1.53445	0.0842141
$333$	5.28694	0.289722
$334$	−6.38241	−0.349230
$335$	37.9725	2.07466
$336$	2.76429	0.150804
$337$	−26.5968	−1.44882	−0.724409	−	0.689370i	$-0.757887\pi$
$337$	−26.5968	−1.44882	−0.724409	+	0.689370i	$0.757887\pi$
$338$	−13.6746	−0.743803
$339$	−6.63665	−0.360453
$340$	−9.92281	−0.538140
$341$	0.288424	0.0156190
$342$	1.80043	0.0973560
$343$	13.5699	0.732708
$344$	−2.61598	−0.141044
$345$	2.72981	0.146968
$346$	23.8827	1.28394
$347$	−9.67344	−0.519298	−0.259649	−	0.965703i	$-0.583607\pi$
$347$	−9.67344	−0.519298	−0.259649	+	0.965703i	$0.583607\pi$
$348$	−0.540713	−0.0289853
$349$	20.8327	1.11515	0.557573	−	0.830128i	$-0.311733\pi$
$349$	20.8327	1.11515	0.557573	+	0.830128i	$0.311733\pi$
$350$	−3.11760	−0.166643
$351$	1.29615	0.0691836
$352$	0.282039	0.0150327
$353$	−34.5661	−1.83977	−0.919885	−	0.392189i	$-0.871718\pi$
$353$	−34.5661	−1.83977	−0.919885	+	0.392189i	$0.871718\pi$
$354$	8.62966	0.458661
$355$	−29.6198	−1.57206
$356$	−1.44753	−0.0767188
$357$	−7.07603	−0.374503
$358$	−17.4314	−0.921280
$359$	10.6404	0.561579	0.280790	−	0.959769i	$-0.409404\pi$
$359$	10.6404	0.561579	0.280790	+	0.959769i	$0.409404\pi$
$360$	−8.37835	−0.441578
$361$	−16.7787	−0.883088
$362$	−24.1890	−1.27134
$363$	−10.9910	−0.576876
$364$	0.737698	0.0386659
$365$	−34.8353	−1.82336
$366$	−13.6133	−0.711580
$367$	2.37107	0.123769	0.0618844	−	0.998083i	$-0.480289\pi$
$367$	2.37107	0.123769	0.0618844	+	0.998083i	$0.480289\pi$
$368$	−2.62620	−0.136900
$369$	−5.16061	−0.268650
$370$	17.4344	0.906371
$371$	−9.14535	−0.474803
$372$	−1.64002	−0.0850313
$373$	−10.9807	−0.568562	−0.284281	−	0.958741i	$-0.591755\pi$
$373$	−10.9807	−0.568562	−0.284281	+	0.958741i	$0.591755\pi$
$374$	0.772242	0.0399317
$375$	−6.95594	−0.359203
$376$	−27.8523	−1.43637
$377$	1.29615	0.0667553
$378$	−1.27153	−0.0654002
$379$	−8.30310	−0.426502	−0.213251	−	0.976997i	$-0.568405\pi$
$379$	−8.30310	−0.426502	−0.213251	+	0.976997i	$0.568405\pi$
$380$	−2.19991	−0.112853
$381$	−17.4909	−0.896085
$382$	9.10464	0.465834
$383$	−17.7406	−0.906500	−0.453250	−	0.891383i	$-0.649736\pi$
$383$	−17.7406	−0.906500	−0.453250	+	0.891383i	$0.649736\pi$
$384$	4.74123	0.241950
$385$	−0.273234	−0.0139253
$386$	16.5500	0.842373
$387$	0.852332	0.0433265
$388$	4.99333	0.253498
$389$	−0.601566	−0.0305006	−0.0152503	−	0.999884i	$-0.504855\pi$
$389$	−0.601566	−0.0305006	−0.0152503	+	0.999884i	$0.504855\pi$
$390$	4.27424	0.216435
$391$	6.72257	0.339975
$392$	18.0840	0.913380
$393$	20.0165	1.00970
$394$	−17.2588	−0.869488
$395$	−11.9573	−0.601636
$396$	−0.0514180	−0.00258385
$397$	32.5222	1.63224	0.816121	−	0.577881i	$-0.196120\pi$
$397$	32.5222	1.63224	0.816121	+	0.577881i	$0.196120\pi$
$398$	31.2872	1.56828
$399$	−1.56877	−0.0785369
$400$	−6.43908	−0.321954
$401$	−34.7143	−1.73355	−0.866774	−	0.498701i	$-0.833811\pi$
$401$	−34.7143	−1.73355	−0.866774	+	0.498701i	$0.833811\pi$
$402$	16.8038	0.838096
$403$	3.93133	0.195834
$404$	3.76009	0.187072
$405$	2.72981	0.135645
$406$	−1.27153	−0.0631048
$407$	0.502750	0.0249204
$408$	−20.6329	−1.02148
$409$	37.2317	1.84099	0.920496	−	0.390753i	$-0.127785\pi$
$409$	37.2317	1.84099	0.920496	+	0.390753i	$0.127785\pi$
$410$	−17.0178	−0.840449
$411$	−10.8950	−0.537411
$412$	−9.40311	−0.463258
$413$	−7.51932	−0.370001
$414$	1.20801	0.0593704
$415$	−7.74674	−0.380272
$416$	3.84431	0.188483
$417$	−8.06409	−0.394900
$418$	0.171208	0.00837405
$419$	−11.2359	−0.548911	−0.274455	−	0.961600i	$-0.588498\pi$
$419$	−11.2359	−0.548911	−0.274455	+	0.961600i	$0.588498\pi$
$420$	1.55365	0.0758106
$421$	29.5588	1.44061	0.720304	−	0.693658i	$-0.244002\pi$
$421$	29.5588	1.44061	0.720304	+	0.693658i	$0.244002\pi$
$422$	2.14374	0.104356
$423$	9.07477	0.441230
$424$	−26.6668	−1.29506
$425$	16.4828	0.799533
$426$	−13.1075	−0.635061
$427$	11.8618	0.574030
$428$	−8.12512	−0.392742
$429$	0.123255	0.00595080
$430$	2.81068	0.135543
$431$	−10.8552	−0.522876	−0.261438	−	0.965220i	$-0.584197\pi$
$431$	−10.8552	−0.522876	−0.261438	+	0.965220i	$0.584197\pi$
$432$	−2.62620	−0.126353
$433$	28.1930	1.35487	0.677434	−	0.735583i	$-0.263092\pi$
$433$	28.1930	1.35487	0.677434	+	0.735583i	$0.263092\pi$
$434$	−3.85663	−0.185124
$435$	2.72981	0.130884
$436$	9.63506	0.461436
$437$	1.49041	0.0712960
$438$	−15.4155	−0.736582
$439$	−23.1590	−1.10532	−0.552659	−	0.833408i	$-0.686387\pi$
$439$	−23.1590	−1.10532	−0.552659	+	0.833408i	$0.686387\pi$
$440$	−0.796721	−0.0379822
$441$	−5.89208	−0.280575
$442$	10.5260	0.500669
$443$	−21.2269	−1.00852	−0.504261	−	0.863551i	$-0.668235\pi$
$443$	−21.2269	−1.00852	−0.504261	+	0.863551i	$0.668235\pi$
$444$	−2.85872	−0.135669
$445$	7.30789	0.346427
$446$	13.5556	0.641876
$447$	−6.47063	−0.306050
$448$	−9.29983	−0.439376
$449$	−9.30415	−0.439090	−0.219545	−	0.975602i	$-0.570457\pi$
$449$	−9.30415	−0.439090	−0.219545	+	0.975602i	$0.570457\pi$
$450$	2.96187	0.139624
$451$	−0.490737	−0.0231079
$452$	3.58853	0.168790
$453$	−16.8594	−0.792125
$454$	0.0581359	0.00272845
$455$	−3.72429	−0.174597
$456$	−4.57437	−0.214215
$457$	−39.1723	−1.83240	−0.916202	−	0.400718i	$-0.868761\pi$
$457$	−39.1723	−1.83240	−0.916202	+	0.400718i	$0.868761\pi$
$458$	−20.9696	−0.979847
$459$	6.72257	0.313783
$460$	−1.47604	−0.0688209
$461$	7.73012	0.360027	0.180014	−	0.983664i	$-0.442386\pi$
$461$	7.73012	0.360027	0.180014	+	0.983664i	$0.442386\pi$
$462$	−0.120913	−0.00562538
$463$	−0.502209	−0.0233396	−0.0116698	−	0.999932i	$-0.503715\pi$
$463$	−0.502209	−0.0233396	−0.0116698	+	0.999932i	$0.503715\pi$
$464$	−2.62620	−0.121918
$465$	8.27971	0.383963
$466$	6.57931	0.304781
$467$	−17.9365	−0.830001	−0.415001	−	0.909821i	$-0.636219\pi$
$467$	−17.9365	−0.830001	−0.415001	+	0.909821i	$0.636219\pi$
$468$	−0.700848	−0.0323967
$469$	−14.6417	−0.676090
$470$	29.9253	1.38035
$471$	15.2976	0.704878
$472$	−21.9255	−1.00920
$473$	0.0810507	0.00372671
$474$	−5.29140	−0.243042
$475$	3.65427	0.167670
$476$	3.82611	0.175369
$477$	8.68851	0.397820
$478$	−0.438909	−0.0200752
$479$	−17.7497	−0.811004	−0.405502	−	0.914094i	$-0.632903\pi$
$479$	−17.7497	−0.811004	−0.405502	+	0.914094i	$0.632903\pi$
$480$	8.09644	0.369550
$481$	6.85268	0.312456
$482$	24.0102	1.09364
$483$	−1.05258	−0.0478940
$484$	5.94296	0.270134
$485$	−25.2090	−1.14468
$486$	1.20801	0.0547964
$487$	0.542296	0.0245738	0.0122869	−	0.999925i	$-0.496089\pi$
$487$	0.542296	0.0245738	0.0122869	+	0.999925i	$0.496089\pi$
$488$	34.5876	1.56571
$489$	13.4200	0.606875
$490$	−19.4299	−0.877754
$491$	11.3071	0.510282	0.255141	−	0.966904i	$-0.417878\pi$
$491$	11.3071	0.510282	0.255141	+	0.966904i	$0.417878\pi$
$492$	2.79041	0.125801
$493$	6.72257	0.302769
$494$	2.33363	0.104995
$495$	0.259585	0.0116675
$496$	−7.96547	−0.357660
$497$	11.4210	0.512303
$498$	−3.42813	−0.153618
$499$	23.1334	1.03560	0.517798	−	0.855503i	$-0.326752\pi$
$499$	23.1334	1.03560	0.517798	+	0.855503i	$0.326752\pi$
$500$	3.76117	0.168205
$501$	−5.28341	−0.236046
$502$	−29.5009	−1.31669
$503$	−23.1463	−1.03204	−0.516022	−	0.856575i	$-0.672588\pi$
$503$	−23.1463	−1.03204	−0.516022	+	0.856575i	$0.672588\pi$
$504$	3.23058	0.143902
$505$	−18.9829	−0.844730
$506$	0.114873	0.00510673
$507$	−11.3200	−0.502738
$508$	9.45755	0.419611
$509$	2.91911	0.129387	0.0646937	−	0.997905i	$-0.479393\pi$
$509$	2.91911	0.129387	0.0646937	+	0.997905i	$0.479393\pi$
$510$	22.1686	0.981641
$511$	13.4321	0.594199
$512$	−23.9099	−1.05668
$513$	1.49041	0.0658032
$514$	−19.8018	−0.873419
$515$	47.4719	2.09186
$516$	−0.460867	−0.0202886
$517$	0.862945	0.0379523
$518$	−6.72248	−0.295369
$519$	19.7703	0.867819
$520$	−10.8596	−0.476226
$521$	21.6716	0.949450	0.474725	−	0.880134i	$-0.342548\pi$
$521$	21.6716	0.949450	0.474725	+	0.880134i	$0.342548\pi$
$522$	1.20801	0.0528731
$523$	14.3768	0.628654	0.314327	−	0.949315i	$-0.398221\pi$
$523$	14.3768	0.628654	0.314327	+	0.949315i	$0.398221\pi$
$524$	−10.8232	−0.472812
$525$	−2.58078	−0.112634
$526$	7.13392	0.311054
$527$	20.3900	0.888204
$528$	−0.249733	−0.0108682
$529$	1.00000	0.0434783
$530$	28.6515	1.24454
$531$	7.14371	0.310010
$532$	0.848257	0.0367766
$533$	−6.68894	−0.289730
$534$	3.23392	0.139946
$535$	41.0199	1.77345
$536$	−42.6936	−1.84408
$537$	−14.4299	−0.622696
$538$	25.2316	1.08781
$539$	−0.560294	−0.0241336
$540$	−1.47604	−0.0635189
$541$	11.6330	0.500142	0.250071	−	0.968227i	$-0.419546\pi$
$541$	11.6330	0.500142	0.250071	+	0.968227i	$0.419546\pi$
$542$	23.0717	0.991015
$543$	−20.0238	−0.859304
$544$	19.9387	0.854864
$545$	−48.6429	−2.08363
$546$	−1.64809	−0.0705319
$547$	−9.07153	−0.387871	−0.193935	−	0.981014i	$-0.562125\pi$
$547$	−9.07153	−0.387871	−0.193935	+	0.981014i	$0.562125\pi$
$548$	5.89107	0.251654
$549$	−11.2692	−0.480959
$550$	0.281652	0.0120097
$551$	1.49041	0.0634936
$552$	−3.06921	−0.130634
$553$	4.61057	0.196061
$554$	−33.4194	−1.41985
$555$	14.4323	0.612618
$556$	4.36036	0.184920
$557$	19.3611	0.820355	0.410178	−	0.912006i	$-0.365467\pi$
$557$	19.3611	0.820355	0.410178	+	0.912006i	$0.365467\pi$
$558$	3.66398	0.155109
$559$	1.10475	0.0467261
$560$	7.54597	0.318876
$561$	0.639268	0.0269899
$562$	−17.7092	−0.747017
$563$	17.8870	0.753845	0.376923	−	0.926245i	$-0.376982\pi$
$563$	17.8870	0.753845	0.376923	+	0.926245i	$0.376982\pi$
$564$	−4.90685	−0.206616
$565$	−18.1168	−0.762179
$566$	12.9215	0.543130
$567$	−1.05258	−0.0442042
$568$	33.3024	1.39734
$569$	10.4808	0.439378	0.219689	−	0.975570i	$-0.429496\pi$
$569$	10.4808	0.439378	0.219689	+	0.975570i	$0.429496\pi$
$570$	4.91483	0.205859
$571$	19.1917	0.803149	0.401575	−	0.915826i	$-0.368463\pi$
$571$	19.1917	0.803149	0.401575	+	0.915826i	$0.368463\pi$
$572$	−0.0666456	−0.00278659
$573$	7.53689	0.314858
$574$	6.56184	0.273886
$575$	2.45186	0.102250
$576$	8.83528	0.368137
$577$	−18.9756	−0.789966	−0.394983	−	0.918689i	$-0.629249\pi$
$577$	−18.9756	−0.789966	−0.394983	+	0.918689i	$0.629249\pi$
$578$	34.0573	1.41660
$579$	13.7002	0.569362
$580$	−1.47604	−0.0612894
$581$	2.98704	0.123923
$582$	−11.1556	−0.462415
$583$	0.826215	0.0342183
$584$	39.1664	1.62072
$585$	3.53825	0.146289
$586$	−36.4195	−1.50447
$587$	43.8136	1.80838	0.904190	−	0.427130i	$-0.140475\pi$
$587$	43.8136	1.80838	0.904190	+	0.427130i	$0.140475\pi$
$588$	3.18593	0.131385
$589$	4.52052	0.186265
$590$	23.5573	0.969840
$591$	−14.2870	−0.587689
$592$	−13.8846	−0.570652
$593$	13.1914	0.541707	0.270853	−	0.962621i	$-0.412694\pi$
$593$	13.1914	0.541707	0.270853	+	0.962621i	$0.412694\pi$
$594$	0.114873	0.00471330
$595$	−19.3162	−0.791888
$596$	3.49875	0.143315
$597$	25.8998	1.06001
$598$	1.56577	0.0640289
$599$	26.1663	1.06913	0.534564	−	0.845128i	$-0.320476\pi$
$599$	26.1663	1.06913	0.534564	+	0.845128i	$0.320476\pi$
$600$	−7.52526	−0.307217
$601$	−3.58376	−0.146185	−0.0730923	−	0.997325i	$-0.523287\pi$
$601$	−3.58376	−0.146185	−0.0730923	+	0.997325i	$0.523287\pi$
$602$	−1.08376	−0.0441708
$603$	13.9103	0.566471
$604$	9.11612	0.370930
$605$	−30.0032	−1.21980
$606$	−8.40043	−0.341244
$607$	37.6954	1.53001	0.765005	−	0.644024i	$-0.222736\pi$
$607$	37.6954	1.53001	0.765005	+	0.644024i	$0.222736\pi$
$608$	4.42046	0.179273
$609$	−1.05258	−0.0426527
$610$	−37.1618	−1.50464
$611$	11.7623	0.475851
$612$	−3.63498	−0.146935
$613$	−27.3706	−1.10549	−0.552745	−	0.833351i	$-0.686419\pi$
$613$	−27.3706	−1.10549	−0.552745	+	0.833351i	$0.686419\pi$
$614$	−11.5144	−0.464684
$615$	−14.0875	−0.568062
$616$	0.307205	0.0123776
$617$	37.2694	1.50041	0.750205	−	0.661205i	$-0.229955\pi$
$617$	37.2694	1.50041	0.750205	+	0.661205i	$0.229955\pi$
$618$	21.0075	0.845046
$619$	14.1754	0.569759	0.284879	−	0.958563i	$-0.408046\pi$
$619$	14.1754	0.569759	0.284879	+	0.958563i	$0.408046\pi$
$620$	−4.47695	−0.179799
$621$	1.00000	0.0401286
$622$	−38.0053	−1.52388
$623$	−2.81783	−0.112894
$624$	−3.40396	−0.136268
$625$	−31.2477	−1.24991
$626$	10.3442	0.413436
$627$	0.141727	0.00566004
$628$	−8.27163	−0.330074
$629$	35.5418	1.41714
$630$	−3.47102	−0.138289
$631$	−29.1365	−1.15991	−0.579953	−	0.814650i	$-0.696929\pi$
$631$	−29.1365	−1.15991	−0.579953	+	0.814650i	$0.696929\pi$
$632$	13.4439	0.534770
$633$	1.77461	0.0705344
$634$	24.4327	0.970345
$635$	−47.7468	−1.89477
$636$	−4.69799	−0.186288
$637$	−7.63704	−0.302590
$638$	0.114873	0.00454787
$639$	−10.8505	−0.429239
$640$	12.9427	0.511604
$641$	−13.6557	−0.539367	−0.269684	−	0.962949i	$-0.586919\pi$
$641$	−13.6557	−0.539367	−0.269684	+	0.962949i	$0.586919\pi$
$642$	18.1523	0.716416
$643$	16.8084	0.662859	0.331429	−	0.943480i	$-0.392469\pi$
$643$	16.8084	0.662859	0.331429	+	0.943480i	$0.392469\pi$
$644$	0.569144	0.0224274
$645$	2.32670	0.0916139
$646$	12.1035	0.476206
$647$	−15.6785	−0.616386	−0.308193	−	0.951324i	$-0.599724\pi$
$647$	−15.6785	−0.616386	−0.308193	+	0.951324i	$0.599724\pi$
$648$	−3.06921	−0.120570
$649$	0.679315	0.0266655
$650$	3.83904	0.150579
$651$	−3.19255	−0.125126
$652$	−7.25640	−0.284182
$653$	31.6408	1.23820	0.619099	−	0.785313i	$-0.287498\pi$
$653$	31.6408	1.23820	0.619099	+	0.785313i	$0.287498\pi$
$654$	−21.5257	−0.841722
$655$	54.6411	2.13501
$656$	13.5528	0.529148
$657$	−12.7611	−0.497857
$658$	−11.5388	−0.449829
$659$	−16.4824	−0.642062	−0.321031	−	0.947069i	$-0.604029\pi$
$659$	−16.4824	−0.642062	−0.321031	+	0.947069i	$0.604029\pi$
$660$	−0.140361	−0.00546355
$661$	2.37429	0.0923490	0.0461745	−	0.998933i	$-0.485297\pi$
$661$	2.37429	0.0923490	0.0461745	+	0.998933i	$0.485297\pi$
$662$	−18.1930	−0.707089
$663$	8.71348	0.338404
$664$	8.70989	0.338009
$665$	−4.28245	−0.166066
$666$	6.38667	0.247478
$667$	1.00000	0.0387202
$668$	2.85681	0.110533
$669$	11.2214	0.433846
$670$	45.8711	1.77215
$671$	−1.07162	−0.0413695
$672$	−3.12188	−0.120429
$673$	−11.7196	−0.451757	−0.225879	−	0.974155i	$-0.572525\pi$
$673$	−11.7196	−0.451757	−0.225879	+	0.974155i	$0.572525\pi$
$674$	−32.1291	−1.23757
$675$	2.45186	0.0943721
$676$	6.12087	0.235418
$677$	−46.0678	−1.77053	−0.885265	−	0.465086i	$-0.846023\pi$
$677$	−46.0678	−1.77053	−0.885265	+	0.465086i	$0.846023\pi$
$678$	−8.01713	−0.307896
$679$	9.72026	0.373029
$680$	−56.3240	−2.15993
$681$	0.0481254	0.00184417
$682$	0.348418	0.0133416
$683$	−15.3863	−0.588740	−0.294370	−	0.955692i	$-0.595110\pi$
$683$	−15.3863	−0.588740	−0.294370	+	0.955692i	$0.595110\pi$
$684$	−0.805885	−0.0308138
$685$	−29.7413	−1.13636
$686$	16.3926	0.625873
$687$	−17.3588	−0.662281
$688$	−2.23840	−0.0853380
$689$	11.2616	0.429034
$690$	3.29764	0.125539
$691$	21.9023	0.833204	0.416602	−	0.909089i	$-0.363221\pi$
$691$	21.9023	0.833204	0.416602	+	0.909089i	$0.363221\pi$
$692$	−10.6901	−0.406375
$693$	−0.100093	−0.00380221
$694$	−11.6856	−0.443580
$695$	−22.0134	−0.835017
$696$	−3.06921	−0.116338
$697$	−34.6925	−1.31407
$698$	25.1660	0.952549
$699$	5.44641	0.206002
$700$	1.39546	0.0527434
$701$	32.8062	1.23907	0.619536	−	0.784968i	$-0.287321\pi$
$701$	32.8062	1.23907	0.619536	+	0.784968i	$0.287321\pi$
$702$	1.56577	0.0590960
$703$	7.87970	0.297189
$704$	0.840172	0.0316652
$705$	24.7724	0.932982
$706$	−41.7562	−1.57152
$707$	7.31958	0.275281
$708$	−3.86270	−0.145169
$709$	12.0699	0.453295	0.226647	−	0.973977i	$-0.427224\pi$
$709$	12.0699	0.453295	0.226647	+	0.973977i	$0.427224\pi$
$710$	−35.7810	−1.34284
$711$	−4.38026	−0.164273
$712$	−8.21647	−0.307925
$713$	3.03307	0.113590
$714$	−8.54792	−0.319898
$715$	0.336462	0.0125830
$716$	7.80244	0.291591
$717$	−0.363333	−0.0135689
$718$	12.8537	0.479696
$719$	25.7940	0.961955	0.480978	−	0.876733i	$-0.340282\pi$
$719$	25.7940	0.961955	0.480978	+	0.876733i	$0.340282\pi$
$720$	−7.16903	−0.267174
$721$	−18.3045	−0.681697
$722$	−20.2688	−0.754327
$723$	19.8759	0.739192
$724$	10.8272	0.402388
$725$	2.45186	0.0910598
$726$	−13.2772	−0.492762
$727$	−13.2122	−0.490014	−0.245007	−	0.969521i	$-0.578790\pi$
$727$	−13.2122	−0.490014	−0.245007	+	0.969521i	$0.578790\pi$
$728$	4.18733	0.155193
$729$	1.00000	0.0370370
$730$	−42.0814	−1.55750
$731$	5.72986	0.211926
$732$	6.09342	0.225219
$733$	24.8191	0.916714	0.458357	−	0.888768i	$-0.348438\pi$
$733$	24.8191	0.916714	0.458357	+	0.888768i	$0.348438\pi$
$734$	2.86427	0.105722
$735$	−16.0842	−0.593276
$736$	2.96593	0.109326
$737$	1.32277	0.0487248
$738$	−6.23406	−0.229479
$739$	−20.0451	−0.737370	−0.368685	−	0.929554i	$-0.620192\pi$
$739$	−20.0451	−0.737370	−0.368685	+	0.929554i	$0.620192\pi$
$740$	−7.80376	−0.286872
$741$	1.93180	0.0709664
$742$	−11.0477	−0.405572
$743$	−19.4968	−0.715269	−0.357635	−	0.933862i	$-0.616417\pi$
$743$	−19.4968	−0.715269	−0.357635	+	0.933862i	$0.616417\pi$
$744$	−9.30913	−0.341289
$745$	−17.6636	−0.647143
$746$	−13.2648	−0.485660
$747$	−2.83783	−0.103831
$748$	−0.345661	−0.0126386
$749$	−15.8167	−0.577931
$750$	−8.40284	−0.306828
$751$	−5.18641	−0.189255	−0.0946274	−	0.995513i	$-0.530166\pi$
$751$	−5.18641	−0.189255	−0.0946274	+	0.995513i	$0.530166\pi$
$752$	−23.8322	−0.869070
$753$	−24.4211	−0.889953
$754$	1.56577	0.0570218
$755$	−46.0230	−1.67495
$756$	0.569144	0.0206996
$757$	33.3241	1.21119	0.605593	−	0.795774i	$-0.292936\pi$
$757$	33.3241	1.21119	0.605593	+	0.795774i	$0.292936\pi$
$758$	−10.0302	−0.364314
$759$	0.0950928	0.00345165
$760$	−12.4872	−0.452957
$761$	8.82878	0.320043	0.160021	−	0.987114i	$-0.448844\pi$
$761$	8.82878	0.320043	0.160021	+	0.987114i	$0.448844\pi$
$762$	−21.1291	−0.765428
$763$	18.7561	0.679016
$764$	−4.07530	−0.147439
$765$	18.3513	0.663494
$766$	−21.4308	−0.774325
$767$	9.25934	0.334335
$768$	−11.9431	−0.430960
$769$	28.8580	1.04065	0.520323	−	0.853970i	$-0.325812\pi$
$769$	28.8580	1.04065	0.520323	+	0.853970i	$0.325812\pi$
$770$	−0.330069	−0.0118949
$771$	−16.3921	−0.590346
$772$	−7.40790	−0.266616
$773$	−5.63551	−0.202695	−0.101348	−	0.994851i	$-0.532315\pi$
$773$	−5.63551	−0.202695	−0.101348	+	0.994851i	$0.532315\pi$
$774$	1.02962	0.0370091
$775$	7.43667	0.267133
$776$	28.3432	1.01746
$777$	−5.56492	−0.199640
$778$	−0.726698	−0.0260534
$779$	−7.69142	−0.275574
$780$	−1.91318	−0.0685029
$781$	−1.03181	−0.0369209
$782$	8.12092	0.290404
$783$	1.00000	0.0357371
$784$	15.4738	0.552635
$785$	41.7596	1.49046
$786$	24.1801	0.862475
$787$	−28.0128	−0.998548	−0.499274	−	0.866444i	$-0.666400\pi$
$787$	−28.0128	−0.998548	−0.499274	+	0.866444i	$0.666400\pi$
$788$	7.72518	0.275198
$789$	5.90552	0.210242
$790$	−14.4445	−0.513912
$791$	6.98560	0.248379
$792$	−0.291859	−0.0103708
$793$	−14.6066	−0.518697
$794$	39.2871	1.39425
$795$	23.7180	0.841190
$796$	−14.0044	−0.496371
$797$	−55.2666	−1.95764	−0.978822	−	0.204715i	$-0.934373\pi$
$797$	−55.2666	−1.95764	−0.978822	+	0.204715i	$0.934373\pi$
$798$	−1.89509	−0.0670856
$799$	61.0057	2.15823
$800$	7.27205	0.257106
$801$	2.67707	0.0945896
$802$	−41.9352	−1.48078
$803$	−1.21349	−0.0428231
$804$	−7.52149	−0.265262
$805$	−2.87334	−0.101272
$806$	4.74908	0.167279
$807$	20.8869	0.735254
$808$	21.3431	0.750847
$809$	5.09682	0.179195	0.0895974	−	0.995978i	$-0.471442\pi$
$809$	5.09682	0.179195	0.0895974	+	0.995978i	$0.471442\pi$
$810$	3.29764	0.115867
$811$	−44.0762	−1.54773	−0.773863	−	0.633353i	$-0.781678\pi$
$811$	−44.0762	−1.54773	−0.773863	+	0.633353i	$0.781678\pi$
$812$	0.569144	0.0199730
$813$	19.0989	0.669829
$814$	0.607327	0.0212868
$815$	36.6341	1.28324
$816$	−17.6548	−0.618042
$817$	1.27032	0.0444430
$818$	44.9763	1.57256
$819$	−1.36430	−0.0476727
$820$	7.61728	0.266007
$821$	−0.900882	−0.0314410	−0.0157205	−	0.999876i	$-0.505004\pi$
$821$	−0.900882	−0.0314410	−0.0157205	+	0.999876i	$0.505004\pi$
$822$	−13.1613	−0.459052
$823$	16.8019	0.585678	0.292839	−	0.956162i	$-0.405400\pi$
$823$	16.8019	0.585678	0.292839	+	0.956162i	$0.405400\pi$
$824$	−53.3741	−1.85937
$825$	0.233154	0.00811739
$826$	−9.08340	−0.316052
$827$	−45.8691	−1.59502	−0.797512	−	0.603303i	$-0.793851\pi$
$827$	−45.8691	−1.59502	−0.797512	+	0.603303i	$0.793851\pi$
$828$	−0.540713	−0.0187911
$829$	5.68550	0.197466	0.0987328	−	0.995114i	$-0.468521\pi$
$829$	5.68550	0.197466	0.0987328	+	0.995114i	$0.468521\pi$
$830$	−9.35813	−0.324826
$831$	−27.6649	−0.959683
$832$	11.4519	0.397023
$833$	−39.6099	−1.37240
$834$	−9.74149	−0.337320
$835$	−14.4227	−0.499119
$836$	−0.0766338	−0.00265044
$837$	3.03307	0.104838
$838$	−13.5731	−0.468875
$839$	−36.1884	−1.24936	−0.624681	−	0.780880i	$-0.714771\pi$
$839$	−36.1884	−1.24936	−0.624681	+	0.780880i	$0.714771\pi$
$840$	8.81887	0.304280
$841$	1.00000	0.0344828
$842$	35.7073	1.23056
$843$	−14.6598	−0.504911
$844$	−0.959555	−0.0330293
$845$	−30.9014	−1.06304
$846$	10.9624	0.376895
$847$	11.5689	0.397511
$848$	−22.8178	−0.783566
$849$	10.6965	0.367103
$850$	19.9114	0.682954
$851$	5.28694	0.181234
$852$	5.86701	0.201001
$853$	53.4179	1.82899	0.914497	−	0.404593i	$-0.132587\pi$
$853$	53.4179	1.82899	0.914497	+	0.404593i	$0.132587\pi$
$854$	14.3291	0.490332
$855$	4.06853	0.139141
$856$	−46.1199	−1.57635
$857$	48.9105	1.67075	0.835376	−	0.549679i	$-0.185250\pi$
$857$	48.9105	1.67075	0.835376	+	0.549679i	$0.185250\pi$
$858$	0.148893	0.00508313
$859$	−34.0344	−1.16124	−0.580619	−	0.814175i	$-0.697190\pi$
$859$	−34.0344	−1.16124	−0.580619	+	0.814175i	$0.697190\pi$
$860$	−1.25808	−0.0429002
$861$	5.43195	0.185120
$862$	−13.1132	−0.446636
$863$	−45.5204	−1.54953	−0.774766	−	0.632248i	$-0.782132\pi$
$863$	−45.5204	−1.54953	−0.774766	+	0.632248i	$0.782132\pi$
$864$	2.96593	0.100903
$865$	53.9691	1.83500
$866$	34.0574	1.15732
$867$	28.1929	0.957481
$868$	1.72626	0.0585929
$869$	−0.416531	−0.0141299
$870$	3.29764	0.111800
$871$	18.0299	0.610919
$872$	54.6907	1.85206
$873$	−9.23470	−0.312547
$874$	1.80043	0.0609004
$875$	7.32168	0.247518
$876$	6.90009	0.233133
$877$	23.1936	0.783192	0.391596	−	0.920137i	$-0.371923\pi$
$877$	23.1936	0.783192	0.391596	+	0.920137i	$0.371923\pi$
$878$	−27.9763	−0.944153
$879$	−30.1483	−1.01688
$880$	−0.681723	−0.0229809
$881$	−22.6964	−0.764661	−0.382331	−	0.924026i	$-0.624878\pi$
$881$	−22.6964	−0.764661	−0.382331	+	0.924026i	$0.624878\pi$
$882$	−7.11768	−0.239665
$883$	43.9771	1.47995	0.739974	−	0.672636i	$-0.234838\pi$
$883$	43.9771	1.47995	0.739974	+	0.672636i	$0.234838\pi$
$884$	−4.71150	−0.158465
$885$	19.5010	0.655517
$886$	−25.6423	−0.861470
$887$	15.2109	0.510733	0.255367	−	0.966844i	$-0.417804\pi$
$887$	15.2109	0.510733	0.255367	+	0.966844i	$0.417804\pi$
$888$	−16.2267	−0.544532
$889$	18.4105	0.617470
$890$	8.82799	0.295915
$891$	0.0950928	0.00318573
$892$	−6.06758	−0.203158
$893$	13.5251	0.452601
$894$	−7.81658	−0.261425
$895$	−39.3909	−1.31669
$896$	−4.99052	−0.166722
$897$	1.29615	0.0432773
$898$	−11.2395	−0.375067
$899$	3.03307	0.101159
$900$	−1.32575	−0.0441918
$901$	58.4091	1.94589
$902$	−0.592814	−0.0197386
$903$	−0.897147	−0.0298552
$904$	20.3692	0.677471
$905$	−54.6612	−1.81700
$906$	−20.3664	−0.676627
$907$	−7.95460	−0.264128	−0.132064	−	0.991241i	$-0.542160\pi$
$907$	−7.95460	−0.264128	−0.132064	+	0.991241i	$0.542160\pi$
$908$	−0.0260220	−0.000863572 0
$909$	−6.95395	−0.230648
$910$	−4.49898	−0.149140
$911$	0.300857	0.00996784	0.00498392	−	0.999988i	$-0.498414\pi$
$911$	0.300857	0.00996784	0.00498392	+	0.999988i	$0.498414\pi$
$912$	−3.91412	−0.129609
$913$	−0.269857	−0.00893098
$914$	−47.3205	−1.56522
$915$	−30.7628	−1.01699
$916$	9.38616	0.310128
$917$	−21.0689	−0.695757
$918$	8.12092	0.268030
$919$	−4.08143	−0.134634	−0.0673170	−	0.997732i	$-0.521444\pi$
$919$	−4.08143	−0.134634	−0.0673170	+	0.997732i	$0.521444\pi$
$920$	−8.37835	−0.276226
$921$	−9.53172	−0.314081
$922$	9.33805	0.307532
$923$	−14.0639	−0.462920
$924$	0.0541215	0.00178047
$925$	12.9628	0.426215
$926$	−0.606673	−0.0199365
$927$	17.3902	0.571169
$928$	2.96593	0.0973616
$929$	22.6934	0.744547	0.372274	−	0.928123i	$-0.378578\pi$
$929$	22.6934	0.744547	0.372274	+	0.928123i	$0.378578\pi$
$930$	10.0020	0.327978
$931$	−8.78161	−0.287806
$932$	−2.94495	−0.0964649
$933$	−31.4611	−1.02999
$934$	−21.6674	−0.708980
$935$	1.74508	0.0570702
$936$	−3.97816	−0.130030
$937$	36.1651	1.18146	0.590731	−	0.806869i	$-0.298839\pi$
$937$	36.1651	1.18146	0.590731	+	0.806869i	$0.298839\pi$
$938$	−17.6873	−0.577511
$939$	8.56299	0.279443
$940$	−13.3948	−0.436889
$941$	34.0213	1.10906	0.554532	−	0.832163i	$-0.312897\pi$
$941$	34.0213	1.10906	0.554532	+	0.832163i	$0.312897\pi$
$942$	18.4797	0.602100
$943$	−5.16061	−0.168052
$944$	−18.7608	−0.610612
$945$	−2.87334	−0.0934698
$946$	0.0979099	0.00318333
$947$	53.2033	1.72888	0.864438	−	0.502740i	$-0.167675\pi$
$947$	53.2033	1.72888	0.864438	+	0.502740i	$0.167675\pi$
$948$	2.36847	0.0769242
$949$	−16.5403	−0.536922
$950$	4.41440	0.143222
$951$	20.2256	0.655858
$952$	21.7178	0.703878
$953$	31.5026	1.02047	0.510234	−	0.860036i	$-0.329559\pi$
$953$	31.5026	1.02047	0.510234	+	0.860036i	$0.329559\pi$
$954$	10.4958	0.339814
$955$	20.5743	0.665768
$956$	0.196459	0.00635394
$957$	0.0950928	0.00307391
$958$	−21.4418	−0.692753
$959$	11.4679	0.370316
$960$	24.1186	0.778425
$961$	−21.8005	−0.703241
$962$	8.27811	0.266897
$963$	15.0267	0.484227
$964$	−10.7472	−0.346142
$965$	37.3990	1.20392
$966$	−1.27153	−0.0409107
$967$	−1.81425	−0.0583423	−0.0291711	−	0.999574i	$-0.509287\pi$
$967$	−1.81425	−0.0583423	−0.0291711	+	0.999574i	$0.509287\pi$
$968$	33.7335	1.08424
$969$	10.0194	0.321869
$970$	−30.4527	−0.977777
$971$	−51.7766	−1.66159	−0.830795	−	0.556579i	$-0.812114\pi$
$971$	−51.7766	−1.66159	−0.830795	+	0.556579i	$0.812114\pi$
$972$	−0.540713	−0.0173434
$973$	8.48809	0.272116
$974$	0.655099	0.0209907
$975$	3.17799	0.101777
$976$	29.5953	0.947321
$977$	−27.9076	−0.892843	−0.446421	−	0.894823i	$-0.647302\pi$
$977$	−27.9076	−0.892843	−0.446421	+	0.894823i	$0.647302\pi$
$978$	16.2115	0.518388
$979$	0.254570	0.00813609
$980$	8.69697	0.277814
$981$	−17.8192	−0.568922
$982$	13.6591	0.435879
$983$	−7.30632	−0.233036	−0.116518	−	0.993189i	$-0.537173\pi$
$983$	−7.30632	−0.233036	−0.116518	+	0.993189i	$0.537173\pi$
$984$	15.8390	0.504928
$985$	−39.0008	−1.24267
$986$	8.12092	0.258623
$987$	−9.55191	−0.304041
$988$	−1.04455	−0.0332316
$989$	0.852332	0.0271026
$990$	0.313581	0.00996627
$991$	11.8211	0.375508	0.187754	−	0.982216i	$-0.439879\pi$
$991$	11.8211	0.375508	0.187754	+	0.982216i	$0.439879\pi$
$992$	8.99590	0.285620
$993$	−15.0603	−0.477924
$994$	13.7967	0.437605
$995$	70.7015	2.24139
$996$	1.53445	0.0486210
$997$	−19.3020	−0.611300	−0.305650	−	0.952144i	$-0.598874\pi$
$997$	−19.3020	−0.611300	−0.305650	+	0.952144i	$0.598874\pi$
$998$	27.9454	0.884597
$999$	5.28694	0.167271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.o.1.14	✓	20
3.2	odd	2		6003.2.a.s.1.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.o.1.14	✓	20	1.1	even	1	trivial
6003.2.a.s.1.7		20	3.2	odd	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+1.20801 q^{2} +1.00000 q^{3} -0.540713 q^{4} +2.72981 q^{5} +1.20801 q^{6} -1.05258 q^{7} -3.06921 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.20801 q^{2} +1.00000 q^{3} -0.540713 q^{4} +2.72981 q^{5} +1.20801 q^{6} -1.05258 q^{7} -3.06921 q^{8} +1.00000 q^{9} +3.29764 q^{10} +0.0950928 q^{11} -0.540713 q^{12} +1.29615 q^{13} -1.27153 q^{14} +2.72981 q^{15} -2.62620 q^{16} +6.72257 q^{17} +1.20801 q^{18} +1.49041 q^{19} -1.47604 q^{20} -1.05258 q^{21} +0.114873 q^{22} +1.00000 q^{23} -3.06921 q^{24} +2.45186 q^{25} +1.56577 q^{26} +1.00000 q^{27} +0.569144 q^{28} +1.00000 q^{29} +3.29764 q^{30} +3.03307 q^{31} +2.96593 q^{32} +0.0950928 q^{33} +8.12092 q^{34} -2.87334 q^{35} -0.540713 q^{36} +5.28694 q^{37} +1.80043 q^{38} +1.29615 q^{39} -8.37835 q^{40} -5.16061 q^{41} -1.27153 q^{42} +0.852332 q^{43} -0.0514180 q^{44} +2.72981 q^{45} +1.20801 q^{46} +9.07477 q^{47} -2.62620 q^{48} -5.89208 q^{49} +2.96187 q^{50} +6.72257 q^{51} -0.700848 q^{52} +8.68851 q^{53} +1.20801 q^{54} +0.259585 q^{55} +3.23058 q^{56} +1.49041 q^{57} +1.20801 q^{58} +7.14371 q^{59} -1.47604 q^{60} -11.2692 q^{61} +3.66398 q^{62} -1.05258 q^{63} +8.83528 q^{64} +3.53825 q^{65} +0.114873 q^{66} +13.9103 q^{67} -3.63498 q^{68} +1.00000 q^{69} -3.47102 q^{70} -10.8505 q^{71} -3.06921 q^{72} -12.7611 q^{73} +6.38667 q^{74} +2.45186 q^{75} -0.805885 q^{76} -0.100093 q^{77} +1.56577 q^{78} -4.38026 q^{79} -7.16903 q^{80} +1.00000 q^{81} -6.23406 q^{82} -2.83783 q^{83} +0.569144 q^{84} +18.3513 q^{85} +1.02962 q^{86} +1.00000 q^{87} -0.291859 q^{88} +2.67707 q^{89} +3.29764 q^{90} -1.36430 q^{91} -0.540713 q^{92} +3.03307 q^{93} +10.9624 q^{94} +4.06853 q^{95} +2.96593 q^{96} -9.23470 q^{97} -7.11768 q^{98} +0.0950928 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9} + 7 q^{10} + 30 q^{12} + 21 q^{13} - q^{14} - q^{15} + 58 q^{16} - 4 q^{17} + 2 q^{18} + 7 q^{19} - 20 q^{20} + 9 q^{21} + 7 q^{22} + 20 q^{23} + 6 q^{24} + 47 q^{25} + 8 q^{26} + 20 q^{27} + 11 q^{28} + 20 q^{29} + 7 q^{30} + 28 q^{31} + 14 q^{32} + 16 q^{34} + 9 q^{35} + 30 q^{36} + 14 q^{37} - 20 q^{38} + 21 q^{39} + 34 q^{40} + 7 q^{41} - q^{42} + 3 q^{43} - q^{44} - q^{45} + 2 q^{46} + 3 q^{47} + 58 q^{48} + 35 q^{49} - 24 q^{50} - 4 q^{51} + 73 q^{52} - 19 q^{53} + 2 q^{54} + 29 q^{55} - 30 q^{56} + 7 q^{57} + 2 q^{58} + 20 q^{59} - 20 q^{60} + 15 q^{61} + 12 q^{62} + 9 q^{63} + 82 q^{64} - 28 q^{65} + 7 q^{66} + 20 q^{67} - 23 q^{68} + 20 q^{69} - 24 q^{70} + 63 q^{71} + 6 q^{72} + 19 q^{73} + 16 q^{74} + 47 q^{75} - 44 q^{76} - 7 q^{77} + 8 q^{78} + 32 q^{79} - 56 q^{80} + 20 q^{81} - 20 q^{82} - 21 q^{83} + 11 q^{84} + 4 q^{85} - 6 q^{86} + 20 q^{87} + 55 q^{88} - 13 q^{89} + 7 q^{90} + 70 q^{91} + 30 q^{92} + 28 q^{93} - 12 q^{94} + 9 q^{95} + 14 q^{96} - 9 q^{97} + 31 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9 + 7 * q^10 + 30 * q^12 + 21 * q^13 - q^14 - q^15 + 58 * q^16 - 4 * q^17 + 2 * q^18 + 7 * q^19 - 20 * q^20 + 9 * q^21 + 7 * q^22 + 20 * q^23 + 6 * q^24 + 47 * q^25 + 8 * q^26 + 20 * q^27 + 11 * q^28 + 20 * q^29 + 7 * q^30 + 28 * q^31 + 14 * q^32 + 16 * q^34 + 9 * q^35 + 30 * q^36 + 14 * q^37 - 20 * q^38 + 21 * q^39 + 34 * q^40 + 7 * q^41 - q^42 + 3 * q^43 - q^44 - q^45 + 2 * q^46 + 3 * q^47 + 58 * q^48 + 35 * q^49 - 24 * q^50 - 4 * q^51 + 73 * q^52 - 19 * q^53 + 2 * q^54 + 29 * q^55 - 30 * q^56 + 7 * q^57 + 2 * q^58 + 20 * q^59 - 20 * q^60 + 15 * q^61 + 12 * q^62 + 9 * q^63 + 82 * q^64 - 28 * q^65 + 7 * q^66 + 20 * q^67 - 23 * q^68 + 20 * q^69 - 24 * q^70 + 63 * q^71 + 6 * q^72 + 19 * q^73 + 16 * q^74 + 47 * q^75 - 44 * q^76 - 7 * q^77 + 8 * q^78 + 32 * q^79 - 56 * q^80 + 20 * q^81 - 20 * q^82 - 21 * q^83 + 11 * q^84 + 4 * q^85 - 6 * q^86 + 20 * q^87 + 55 * q^88 - 13 * q^89 + 7 * q^90 + 70 * q^91 + 30 * q^92 + 28 * q^93 - 12 * q^94 + 9 * q^95 + 14 * q^96 - 9 * q^97 + 31 * q^98

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