LMFDB - Embedded newform 2001.2.a.o.1.19

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			1.19
Root			$2.62822$ 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)

$f(q)$	$=$	$q+2.62822 q^{2} +1.00000 q^{3} +4.90753 q^{4} -4.03060 q^{5} +2.62822 q^{6} -1.30880 q^{7} +7.64164 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.62822 q^{2} +1.00000 q^{3} +4.90753 q^{4} -4.03060 q^{5} +2.62822 q^{6} -1.30880 q^{7} +7.64164 q^{8} +1.00000 q^{9} -10.5933 q^{10} +3.92402 q^{11} +4.90753 q^{12} +4.45983 q^{13} -3.43982 q^{14} -4.03060 q^{15} +10.2688 q^{16} +5.05684 q^{17} +2.62822 q^{18} -4.27409 q^{19} -19.7803 q^{20} -1.30880 q^{21} +10.3132 q^{22} +1.00000 q^{23} +7.64164 q^{24} +11.2457 q^{25} +11.7214 q^{26} +1.00000 q^{27} -6.42299 q^{28} +1.00000 q^{29} -10.5933 q^{30} +3.94960 q^{31} +11.7055 q^{32} +3.92402 q^{33} +13.2905 q^{34} +5.27526 q^{35} +4.90753 q^{36} +10.9136 q^{37} -11.2332 q^{38} +4.45983 q^{39} -30.8004 q^{40} -10.8994 q^{41} -3.43982 q^{42} -4.04647 q^{43} +19.2573 q^{44} -4.03060 q^{45} +2.62822 q^{46} +9.36211 q^{47} +10.2688 q^{48} -5.28704 q^{49} +29.5563 q^{50} +5.05684 q^{51} +21.8868 q^{52} -11.0423 q^{53} +2.62822 q^{54} -15.8162 q^{55} -10.0014 q^{56} -4.27409 q^{57} +2.62822 q^{58} -1.85620 q^{59} -19.7803 q^{60} -6.11452 q^{61} +10.3804 q^{62} -1.30880 q^{63} +10.2268 q^{64} -17.9758 q^{65} +10.3132 q^{66} -10.5649 q^{67} +24.8166 q^{68} +1.00000 q^{69} +13.8645 q^{70} -0.234097 q^{71} +7.64164 q^{72} -9.40763 q^{73} +28.6833 q^{74} +11.2457 q^{75} -20.9752 q^{76} -5.13577 q^{77} +11.7214 q^{78} +5.42650 q^{79} -41.3895 q^{80} +1.00000 q^{81} -28.6459 q^{82} -12.1730 q^{83} -6.42299 q^{84} -20.3821 q^{85} -10.6350 q^{86} +1.00000 q^{87} +29.9860 q^{88} -3.98074 q^{89} -10.5933 q^{90} -5.83704 q^{91} +4.90753 q^{92} +3.94960 q^{93} +24.6057 q^{94} +17.2271 q^{95} +11.7055 q^{96} +17.7045 q^{97} -13.8955 q^{98} +3.92402 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.62822	1.85843	0.929216	−	0.369538i	$-0.120484\pi$
$2$	2.62822	1.85843	0.929216	+	0.369538i	$0.120484\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.90753	2.45377
$5$	−4.03060	−1.80254	−0.901270	−	0.433259i	$-0.857364\pi$
$5$	−4.03060	−1.80254	−0.901270	+	0.433259i	$0.857364\pi$
$6$	2.62822	1.07297
$7$	−1.30880	−0.494681	−0.247340	−	0.968929i	$-0.579557\pi$
$7$	−1.30880	−0.494681	−0.247340	+	0.968929i	$0.579557\pi$
$8$	7.64164	2.70173
$9$	1.00000	0.333333
$10$	−10.5933	−3.34990
$11$	3.92402	1.18314	0.591569	−	0.806255i	$-0.298509\pi$
$11$	3.92402	1.18314	0.591569	+	0.806255i	$0.298509\pi$
$12$	4.90753	1.41668
$13$	4.45983	1.23694	0.618468	−	0.785810i	$-0.287754\pi$
$13$	4.45983	1.23694	0.618468	+	0.785810i	$0.287754\pi$
$14$	−3.43982	−0.919330
$15$	−4.03060	−1.04070
$16$	10.2688	2.56721
$17$	5.05684	1.22646	0.613232	−	0.789903i	$-0.289869\pi$
$17$	5.05684	1.22646	0.613232	+	0.789903i	$0.289869\pi$
$18$	2.62822	0.619477
$19$	−4.27409	−0.980543	−0.490271	−	0.871570i	$-0.663102\pi$
$19$	−4.27409	−0.980543	−0.490271	+	0.871570i	$0.663102\pi$
$20$	−19.7803	−4.42301
$21$	−1.30880	−0.285604
$22$	10.3132	2.19878
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	7.64164	1.55984
$25$	11.2457	2.24915
$26$	11.7214	2.29876
$27$	1.00000	0.192450
$28$	−6.42299	−1.21383
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−10.5933	−1.93406
$31$	3.94960	0.709368	0.354684	−	0.934986i	$-0.384588\pi$
$31$	3.94960	0.709368	0.354684	+	0.934986i	$0.384588\pi$
$32$	11.7055	2.06925
$33$	3.92402	0.683085
$34$	13.2905	2.27930
$35$	5.27526	0.891681
$36$	4.90753	0.817922
$37$	10.9136	1.79418	0.897091	−	0.441845i	$-0.145676\pi$
$37$	10.9136	1.79418	0.897091	+	0.441845i	$0.145676\pi$
$38$	−11.2332	−1.82227
$39$	4.45983	0.714145
$40$	−30.8004	−4.86997
$41$	−10.8994	−1.70219	−0.851097	−	0.525009i	$-0.824062\pi$
$41$	−10.8994	−1.70219	−0.851097	+	0.525009i	$0.824062\pi$
$42$	−3.43982	−0.530775
$43$	−4.04647	−0.617080	−0.308540	−	0.951211i	$-0.599840\pi$
$43$	−4.04647	−0.617080	−0.308540	+	0.951211i	$0.599840\pi$
$44$	19.2573	2.90314
$45$	−4.03060	−0.600846
$46$	2.62822	0.387510
$47$	9.36211	1.36560	0.682802	−	0.730604i	$-0.260761\pi$
$47$	9.36211	1.36560	0.682802	+	0.730604i	$0.260761\pi$
$48$	10.2688	1.48218
$49$	−5.28704	−0.755291
$50$	29.5563	4.17989
$51$	5.05684	0.708099
$52$	21.8868	3.03515
$53$	−11.0423	−1.51678	−0.758388	−	0.651804i	$-0.774013\pi$
$53$	−11.0423	−1.51678	−0.758388	+	0.651804i	$0.774013\pi$
$54$	2.62822	0.357655
$55$	−15.8162	−2.13265
$56$	−10.0014	−1.33649
$57$	−4.27409	−0.566117
$58$	2.62822	0.345102
$59$	−1.85620	−0.241656	−0.120828	−	0.992673i	$-0.538555\pi$
$59$	−1.85620	−0.241656	−0.120828	+	0.992673i	$0.538555\pi$
$60$	−19.7803	−2.55363
$61$	−6.11452	−0.782884	−0.391442	−	0.920203i	$-0.628024\pi$
$61$	−6.11452	−0.782884	−0.391442	+	0.920203i	$0.628024\pi$
$62$	10.3804	1.31831
$63$	−1.30880	−0.164894
$64$	10.2268	1.27835
$65$	−17.9758	−2.22962
$66$	10.3132	1.26947
$67$	−10.5649	−1.29071	−0.645354	−	0.763883i	$-0.723290\pi$
$67$	−10.5649	−1.29071	−0.645354	+	0.763883i	$0.723290\pi$
$68$	24.8166	3.00946
$69$	1.00000	0.120386
$70$	13.8645	1.65713
$71$	−0.234097	−0.0277822	−0.0138911	−	0.999904i	$-0.504422\pi$
$71$	−0.234097	−0.0277822	−0.0138911	+	0.999904i	$0.504422\pi$
$72$	7.64164	0.900576
$73$	−9.40763	−1.10108	−0.550540	−	0.834809i	$-0.685578\pi$
$73$	−9.40763	−1.10108	−0.550540	+	0.834809i	$0.685578\pi$
$74$	28.6833	3.33436
$75$	11.2457	1.29855
$76$	−20.9752	−2.40602
$77$	−5.13577	−0.585275
$78$	11.7214	1.32719
$79$	5.42650	0.610529	0.305264	−	0.952268i	$-0.401255\pi$
$79$	5.42650	0.610529	0.305264	+	0.952268i	$0.401255\pi$
$80$	−41.3895	−4.62749
$81$	1.00000	0.111111
$82$	−28.6459	−3.16341
$83$	−12.1730	−1.33616	−0.668082	−	0.744087i	$-0.732885\pi$
$83$	−12.1730	−1.33616	−0.668082	+	0.744087i	$0.732885\pi$
$84$	−6.42299	−0.700806
$85$	−20.3821	−2.21075
$86$	−10.6350	−1.14680
$87$	1.00000	0.107211
$88$	29.9860	3.19651
$89$	−3.98074	−0.421957	−0.210979	−	0.977491i	$-0.567665\pi$
$89$	−3.98074	−0.421957	−0.210979	+	0.977491i	$0.567665\pi$
$90$	−10.5933	−1.11663
$91$	−5.83704	−0.611888
$92$	4.90753	0.511646
$93$	3.94960	0.409554
$94$	24.6057	2.53788
$95$	17.2271	1.76747
$96$	11.7055	1.19468
$97$	17.7045	1.79761	0.898807	−	0.438344i	$-0.144435\pi$
$97$	17.7045	1.79761	0.898807	+	0.438344i	$0.144435\pi$
$98$	−13.8955	−1.40366
$99$	3.92402	0.394379
$100$	55.1888	5.51888
$101$	−4.47540	−0.445319	−0.222660	−	0.974896i	$-0.571474\pi$
$101$	−4.47540	−0.445319	−0.222660	+	0.974896i	$0.571474\pi$
$102$	13.2905	1.31595
$103$	2.13558	0.210425	0.105212	−	0.994450i	$-0.466448\pi$
$103$	2.13558	0.210425	0.105212	+	0.994450i	$0.466448\pi$
$104$	34.0804	3.34186
$105$	5.27526	0.514812
$106$	−29.0216	−2.81882
$107$	0.364469	0.0352346	0.0176173	−	0.999845i	$-0.494392\pi$
$107$	0.364469	0.0352346	0.0176173	+	0.999845i	$0.494392\pi$
$108$	4.90753	0.472228
$109$	5.86304	0.561578	0.280789	−	0.959770i	$-0.409404\pi$
$109$	5.86304	0.561578	0.280789	+	0.959770i	$0.409404\pi$
$110$	−41.5684	−3.96339
$111$	10.9136	1.03587
$112$	−13.4399	−1.26995
$113$	4.04672	0.380683	0.190341	−	0.981718i	$-0.439040\pi$
$113$	4.04672	0.380683	0.190341	+	0.981718i	$0.439040\pi$
$114$	−11.2332	−1.05209
$115$	−4.03060	−0.375855
$116$	4.90753	0.455653
$117$	4.45983	0.412312
$118$	−4.87849	−0.449101
$119$	−6.61840	−0.606708
$120$	−30.8004	−2.81168
$121$	4.39796	0.399814
$122$	−16.0703	−1.45494
$123$	−10.8994	−0.982762
$124$	19.3828	1.74062
$125$	−25.1741	−2.25164
$126$	−3.43982	−0.306443
$127$	12.1075	1.07437	0.537186	−	0.843464i	$-0.319487\pi$
$127$	12.1075	1.07437	0.537186	+	0.843464i	$0.319487\pi$
$128$	3.46746	0.306483
$129$	−4.04647	−0.356271
$130$	−47.2444	−4.14360
$131$	−2.52075	−0.220239	−0.110119	−	0.993918i	$-0.535123\pi$
$131$	−2.52075	−0.220239	−0.110119	+	0.993918i	$0.535123\pi$
$132$	19.2573	1.67613
$133$	5.59393	0.485055
$134$	−27.7669	−2.39869
$135$	−4.03060	−0.346899
$136$	38.6426	3.31357
$137$	−8.87993	−0.758663	−0.379332	−	0.925261i	$-0.623846\pi$
$137$	−8.87993	−0.758663	−0.379332	+	0.925261i	$0.623846\pi$
$138$	2.62822	0.223729
$139$	−13.0214	−1.10446	−0.552229	−	0.833692i	$-0.686223\pi$
$139$	−13.0214	−1.10446	−0.552229	+	0.833692i	$0.686223\pi$
$140$	25.8885	2.18798
$141$	9.36211	0.788432
$142$	−0.615258	−0.0516313
$143$	17.5005	1.46346
$144$	10.2688	0.855736
$145$	−4.03060	−0.334723
$146$	−24.7253	−2.04628
$147$	−5.28704	−0.436068
$148$	53.5588	4.40251
$149$	2.45763	0.201337	0.100668	−	0.994920i	$-0.467902\pi$
$149$	2.45763	0.201337	0.100668	+	0.994920i	$0.467902\pi$
$150$	29.5563	2.41326
$151$	6.21818	0.506029	0.253014	−	0.967463i	$-0.418578\pi$
$151$	6.21818	0.506029	0.253014	+	0.967463i	$0.418578\pi$
$152$	−32.6610	−2.64916
$153$	5.05684	0.408821
$154$	−13.4979	−1.08769
$155$	−15.9192	−1.27866
$156$	21.8868	1.75235
$157$	−13.6785	−1.09166	−0.545830	−	0.837896i	$-0.683786\pi$
$157$	−13.6785	−1.09166	−0.545830	+	0.837896i	$0.683786\pi$
$158$	14.2620	1.13463
$159$	−11.0423	−0.875711
$160$	−47.1800	−3.72991
$161$	−1.30880	−0.103148
$162$	2.62822	0.206492
$163$	22.3241	1.74856	0.874280	−	0.485422i	$-0.161334\pi$
$163$	22.3241	1.74856	0.874280	+	0.485422i	$0.161334\pi$
$164$	−53.4890	−4.17679
$165$	−15.8162	−1.23129
$166$	−31.9934	−2.48317
$167$	−15.0420	−1.16398	−0.581992	−	0.813195i	$-0.697726\pi$
$167$	−15.0420	−1.16398	−0.581992	+	0.813195i	$0.697726\pi$
$168$	−10.0014	−0.771624
$169$	6.89012	0.530009
$170$	−53.5686	−4.10853
$171$	−4.27409	−0.326848
$172$	−19.8582	−1.51417
$173$	−17.7084	−1.34634	−0.673171	−	0.739487i	$-0.735068\pi$
$173$	−17.7084	−1.34634	−0.673171	+	0.739487i	$0.735068\pi$
$174$	2.62822	0.199245
$175$	−14.7184	−1.11261
$176$	40.2951	3.03736
$177$	−1.85620	−0.139520
$178$	−10.4622	−0.784179
$179$	14.3858	1.07524	0.537622	−	0.843186i	$-0.319323\pi$
$179$	14.3858	1.07524	0.537622	+	0.843186i	$0.319323\pi$
$180$	−19.7803	−1.47434
$181$	17.9508	1.33427	0.667135	−	0.744937i	$-0.267520\pi$
$181$	17.9508	1.33427	0.667135	+	0.744937i	$0.267520\pi$
$182$	−15.3410	−1.13715
$183$	−6.11452	−0.451999
$184$	7.64164	0.563349
$185$	−43.9883	−3.23408
$186$	10.3804	0.761128
$187$	19.8432	1.45108
$188$	45.9449	3.35087
$189$	−1.30880	−0.0952013
$190$	45.2767	3.28472
$191$	−2.96160	−0.214294	−0.107147	−	0.994243i	$-0.534171\pi$
$191$	−2.96160	−0.214294	−0.107147	+	0.994243i	$0.534171\pi$
$192$	10.2268	0.738058
$193$	6.26171	0.450727	0.225364	−	0.974275i	$-0.427643\pi$
$193$	6.26171	0.450727	0.225364	+	0.974275i	$0.427643\pi$
$194$	46.5312	3.34074
$195$	−17.9758	−1.28727
$196$	−25.9463	−1.85331
$197$	−23.1754	−1.65118	−0.825589	−	0.564272i	$-0.809157\pi$
$197$	−23.1754	−1.65118	−0.825589	+	0.564272i	$0.809157\pi$
$198$	10.3132	0.732927
$199$	1.65529	0.117340	0.0586702	−	0.998277i	$-0.481314\pi$
$199$	1.65529	0.117340	0.0586702	+	0.998277i	$0.481314\pi$
$200$	85.9358	6.07658
$201$	−10.5649	−0.745191
$202$	−11.7623	−0.827595
$203$	−1.30880	−0.0918599
$204$	24.8166	1.73751
$205$	43.9309	3.06827
$206$	5.61276	0.391060
$207$	1.00000	0.0695048
$208$	45.7973	3.17547
$209$	−16.7716	−1.16012
$210$	13.8645	0.956743
$211$	−0.335765	−0.0231150	−0.0115575	−	0.999933i	$-0.503679\pi$
$211$	−0.335765	−0.0231150	−0.0115575	+	0.999933i	$0.503679\pi$
$212$	−54.1904	−3.72181
$213$	−0.234097	−0.0160401
$214$	0.957905	0.0654810
$215$	16.3097	1.11231
$216$	7.64164	0.519948
$217$	−5.16924	−0.350911
$218$	15.4094	1.04365
$219$	−9.40763	−0.635709
$220$	−77.6184	−5.23303
$221$	22.5527	1.51706
$222$	28.6833	1.92510
$223$	11.4430	0.766283	0.383142	−	0.923690i	$-0.374842\pi$
$223$	11.4430	0.766283	0.383142	+	0.923690i	$0.374842\pi$
$224$	−15.3201	−1.02362
$225$	11.2457	0.749716
$226$	10.6357	0.707473
$227$	13.0515	0.866259	0.433129	−	0.901332i	$-0.357409\pi$
$227$	13.0515	0.866259	0.433129	+	0.901332i	$0.357409\pi$
$228$	−20.9752	−1.38912
$229$	17.2421	1.13939	0.569695	−	0.821856i	$-0.307061\pi$
$229$	17.2421	1.13939	0.569695	+	0.821856i	$0.307061\pi$
$230$	−10.5933	−0.698501
$231$	−5.13577	−0.337909
$232$	7.64164	0.501698
$233$	23.7833	1.55809	0.779046	−	0.626966i	$-0.215704\pi$
$233$	23.7833	1.55809	0.779046	+	0.626966i	$0.215704\pi$
$234$	11.7214	0.766253
$235$	−37.7349	−2.46155
$236$	−9.10935	−0.592968
$237$	5.42650	0.352489
$238$	−17.3946	−1.12753
$239$	−17.1777	−1.11113	−0.555566	−	0.831472i	$-0.687499\pi$
$239$	−17.1777	−1.11113	−0.555566	+	0.831472i	$0.687499\pi$
$240$	−41.3895	−2.67168
$241$	−26.8413	−1.72900	−0.864501	−	0.502631i	$-0.832365\pi$
$241$	−26.8413	−1.72900	−0.864501	+	0.502631i	$0.832365\pi$
$242$	11.5588	0.743028
$243$	1.00000	0.0641500
$244$	−30.0072	−1.92102
$245$	21.3099	1.36144
$246$	−28.6459	−1.82640
$247$	−19.0617	−1.21287
$248$	30.1814	1.91652
$249$	−12.1730	−0.771435
$250$	−66.1630	−4.18451
$251$	−23.8599	−1.50603	−0.753013	−	0.658006i	$-0.771400\pi$
$251$	−23.8599	−1.50603	−0.753013	+	0.658006i	$0.771400\pi$
$252$	−6.42299	−0.404610
$253$	3.92402	0.246701
$254$	31.8213	1.99665
$255$	−20.3821	−1.27638
$256$	−11.3404	−0.708777
$257$	6.38623	0.398362	0.199181	−	0.979963i	$-0.436172\pi$
$257$	6.38623	0.398362	0.199181	+	0.979963i	$0.436172\pi$
$258$	−10.6350	−0.662106
$259$	−14.2837	−0.887547
$260$	−88.2169	−5.47098
$261$	1.00000	0.0618984
$262$	−6.62507	−0.409298
$263$	−14.5150	−0.895035	−0.447518	−	0.894275i	$-0.647692\pi$
$263$	−14.5150	−0.895035	−0.447518	+	0.894275i	$0.647692\pi$
$264$	29.9860	1.84551
$265$	44.5071	2.73405
$266$	14.7021	0.901442
$267$	−3.98074	−0.243617
$268$	−51.8477	−3.16710
$269$	8.53374	0.520311	0.260156	−	0.965567i	$-0.416226\pi$
$269$	8.53374	0.520311	0.260156	+	0.965567i	$0.416226\pi$
$270$	−10.5933	−0.644688
$271$	−32.1862	−1.95517	−0.977585	−	0.210540i	$-0.932478\pi$
$271$	−32.1862	−1.95517	−0.977585	+	0.210540i	$0.932478\pi$
$272$	51.9278	3.14859
$273$	−5.83704	−0.353274
$274$	−23.3384	−1.40992
$275$	44.1285	2.66105
$276$	4.90753	0.295399
$277$	23.6051	1.41829	0.709147	−	0.705060i	$-0.249080\pi$
$277$	23.6051	1.41829	0.709147	+	0.705060i	$0.249080\pi$
$278$	−34.2230	−2.05256
$279$	3.94960	0.236456
$280$	40.3116	2.40908
$281$	−13.4076	−0.799831	−0.399915	−	0.916552i	$-0.630961\pi$
$281$	−13.4076	−0.799831	−0.399915	+	0.916552i	$0.630961\pi$
$282$	24.6057	1.46525
$283$	9.07775	0.539616	0.269808	−	0.962914i	$-0.413040\pi$
$283$	9.07775	0.539616	0.269808	+	0.962914i	$0.413040\pi$
$284$	−1.14884	−0.0681710
$285$	17.2271	1.02045
$286$	45.9951	2.71975
$287$	14.2651	0.842042
$288$	11.7055	0.689750
$289$	8.57165	0.504215
$290$	−10.5933	−0.622060
$291$	17.7045	1.03785
$292$	−46.1683	−2.70179
$293$	17.4273	1.01811	0.509057	−	0.860733i	$-0.329994\pi$
$293$	17.4273	1.01811	0.509057	+	0.860733i	$0.329994\pi$
$294$	−13.8955	−0.810402
$295$	7.48158	0.435595
$296$	83.3977	4.84739
$297$	3.92402	0.227695
$298$	6.45919	0.374171
$299$	4.45983	0.257919
$300$	55.1888	3.18633
$301$	5.29602	0.305258
$302$	16.3427	0.940419
$303$	−4.47540	−0.257105
$304$	−43.8899	−2.51726
$305$	24.6452	1.41118
$306$	13.2905	0.759767
$307$	−18.3100	−1.04501	−0.522504	−	0.852637i	$-0.675002\pi$
$307$	−18.3100	−1.04501	−0.522504	+	0.852637i	$0.675002\pi$
$308$	−25.2040	−1.43613
$309$	2.13558	0.121489
$310$	−41.8392	−2.37631
$311$	−25.1692	−1.42722	−0.713609	−	0.700545i	$-0.752940\pi$
$311$	−25.1692	−1.42722	−0.713609	+	0.700545i	$0.752940\pi$
$312$	34.0804	1.92942
$313$	5.07476	0.286843	0.143421	−	0.989662i	$-0.454190\pi$
$313$	5.07476	0.286843	0.143421	+	0.989662i	$0.454190\pi$
$314$	−35.9500	−2.02878
$315$	5.27526	0.297227
$316$	26.6307	1.49810
$317$	−9.98799	−0.560981	−0.280491	−	0.959857i	$-0.590497\pi$
$317$	−9.98799	−0.560981	−0.280491	+	0.959857i	$0.590497\pi$
$318$	−29.0216	−1.62745
$319$	3.92402	0.219703
$320$	−41.2203	−2.30428
$321$	0.364469	0.0203427
$322$	−3.43982	−0.191694
$323$	−21.6134	−1.20260
$324$	4.90753	0.272641
$325$	50.1541	2.78205
$326$	58.6727	3.24958
$327$	5.86304	0.324227
$328$	−83.2889	−4.59886
$329$	−12.2531	−0.675538
$330$	−41.5684	−2.28826
$331$	11.8792	0.652941	0.326471	−	0.945207i	$-0.394141\pi$
$331$	11.8792	0.652941	0.326471	+	0.945207i	$0.394141\pi$
$332$	−59.7396	−3.27864
$333$	10.9136	0.598061
$334$	−39.5336	−2.16318
$335$	42.5829	2.32655
$336$	−13.4399	−0.733204
$337$	4.20337	0.228972	0.114486	−	0.993425i	$-0.463478\pi$
$337$	4.20337	0.228972	0.114486	+	0.993425i	$0.463478\pi$
$338$	18.1087	0.984985
$339$	4.04672	0.219787
$340$	−100.026	−5.42467
$341$	15.4983	0.839280
$342$	−11.2332	−0.607424
$343$	16.0813	0.868308
$344$	−30.9216	−1.66718
$345$	−4.03060	−0.217000
$346$	−46.5415	−2.50208
$347$	−13.6858	−0.734691	−0.367346	−	0.930084i	$-0.619733\pi$
$347$	−13.6858	−0.734691	−0.367346	+	0.930084i	$0.619733\pi$
$348$	4.90753	0.263071
$349$	−25.6384	−1.37239	−0.686195	−	0.727418i	$-0.740720\pi$
$349$	−25.6384	−1.37239	−0.686195	+	0.727418i	$0.740720\pi$
$350$	−38.6833	−2.06771
$351$	4.45983	0.238048
$352$	45.9325	2.44821
$353$	24.7065	1.31499	0.657497	−	0.753457i	$-0.271615\pi$
$353$	24.7065	1.31499	0.657497	+	0.753457i	$0.271615\pi$
$354$	−4.87849	−0.259289
$355$	0.943551	0.0500785
$356$	−19.5356	−1.03538
$357$	−6.61840	−0.350283
$358$	37.8090	1.99827
$359$	20.2553	1.06903	0.534517	−	0.845158i	$-0.320493\pi$
$359$	20.2553	1.06903	0.534517	+	0.845158i	$0.320493\pi$
$360$	−30.8004	−1.62332
$361$	−0.732187	−0.0385362
$362$	47.1786	2.47965
$363$	4.39796	0.230833
$364$	−28.6455	−1.50143
$365$	37.9184	1.98474
$366$	−16.0703	−0.840008
$367$	33.6637	1.75723	0.878615	−	0.477530i	$-0.158468\pi$
$367$	33.6637	1.75723	0.878615	+	0.477530i	$0.158468\pi$
$368$	10.2688	0.535300
$369$	−10.8994	−0.567398
$370$	−115.611	−6.01032
$371$	14.4522	0.750319
$372$	19.3828	1.00495
$373$	−18.8819	−0.977667	−0.488833	−	0.872377i	$-0.662577\pi$
$373$	−18.8819	−0.977667	−0.488833	+	0.872377i	$0.662577\pi$
$374$	52.1522	2.69672
$375$	−25.1741	−1.29998
$376$	71.5418	3.68949
$377$	4.45983	0.229693
$378$	−3.43982	−0.176925
$379$	6.30502	0.323867	0.161933	−	0.986802i	$-0.448227\pi$
$379$	6.30502	0.323867	0.161933	+	0.986802i	$0.448227\pi$
$380$	84.5427	4.33695
$381$	12.1075	0.620288
$382$	−7.78373	−0.398250
$383$	−2.87741	−0.147029	−0.0735145	−	0.997294i	$-0.523422\pi$
$383$	−2.87741	−0.147029	−0.0735145	+	0.997294i	$0.523422\pi$
$384$	3.46746	0.176948
$385$	20.7002	1.05498
$386$	16.4571	0.837646
$387$	−4.04647	−0.205693
$388$	86.8852	4.41093
$389$	36.8649	1.86913	0.934563	−	0.355797i	$-0.115791\pi$
$389$	36.8649	1.86913	0.934563	+	0.355797i	$0.115791\pi$
$390$	−47.2444	−2.39231
$391$	5.05684	0.255735
$392$	−40.4016	−2.04059
$393$	−2.52075	−0.127155
$394$	−60.9100	−3.06860
$395$	−21.8720	−1.10050
$396$	19.2573	0.967715
$397$	−0.604130	−0.0303204	−0.0151602	−	0.999885i	$-0.504826\pi$
$397$	−0.604130	−0.0303204	−0.0151602	+	0.999885i	$0.504826\pi$
$398$	4.35047	0.218069
$399$	5.59393	0.280047
$400$	115.481	5.77403
$401$	−28.4282	−1.41964	−0.709818	−	0.704385i	$-0.751223\pi$
$401$	−28.4282	−1.41964	−0.709818	+	0.704385i	$0.751223\pi$
$402$	−27.7669	−1.38489
$403$	17.6145	0.877443
$404$	−21.9632	−1.09271
$405$	−4.03060	−0.200282
$406$	−3.43982	−0.170715
$407$	42.8252	2.12276
$408$	38.6426	1.91309
$409$	−28.2203	−1.39540	−0.697702	−	0.716388i	$-0.745794\pi$
$409$	−28.2203	−1.39540	−0.697702	+	0.716388i	$0.745794\pi$
$410$	115.460	5.70217
$411$	−8.87993	−0.438014
$412$	10.4804	0.516333
$413$	2.42939	0.119543
$414$	2.62822	0.129170
$415$	49.0646	2.40849
$416$	52.2044	2.55953
$417$	−13.0214	−0.637660
$418$	−44.0795	−2.15600
$419$	−7.93616	−0.387707	−0.193853	−	0.981031i	$-0.562099\pi$
$419$	−7.93616	−0.387707	−0.193853	+	0.981031i	$0.562099\pi$
$420$	25.8885	1.26323
$421$	17.1419	0.835445	0.417722	−	0.908575i	$-0.362828\pi$
$421$	17.1419	0.835445	0.417722	+	0.908575i	$0.362828\pi$
$422$	−0.882464	−0.0429577
$423$	9.36211	0.455201
$424$	−84.3812	−4.09791
$425$	56.8679	2.75850
$426$	−0.615258	−0.0298093
$427$	8.00270	0.387278
$428$	1.78865	0.0864574
$429$	17.5005	0.844932
$430$	42.8654	2.06715
$431$	−20.8868	−1.00608	−0.503040	−	0.864263i	$-0.667785\pi$
$431$	−20.8868	−1.00608	−0.503040	+	0.864263i	$0.667785\pi$
$432$	10.2688	0.494059
$433$	17.3374	0.833181	0.416590	−	0.909094i	$-0.363225\pi$
$433$	17.3374	0.833181	0.416590	+	0.909094i	$0.363225\pi$
$434$	−13.5859	−0.652143
$435$	−4.03060	−0.193252
$436$	28.7731	1.37798
$437$	−4.27409	−0.204457
$438$	−24.7253	−1.18142
$439$	3.80024	0.181375	0.0906877	−	0.995879i	$-0.471093\pi$
$439$	3.80024	0.181375	0.0906877	+	0.995879i	$0.471093\pi$
$440$	−120.861	−5.76184
$441$	−5.28704	−0.251764
$442$	59.2734	2.81935
$443$	−28.3193	−1.34549	−0.672745	−	0.739875i	$-0.734885\pi$
$443$	−28.3193	−1.34549	−0.672745	+	0.739875i	$0.734885\pi$
$444$	53.5588	2.54179
$445$	16.0448	0.760594
$446$	30.0748	1.42408
$447$	2.45763	0.116242
$448$	−13.3849	−0.632377
$449$	32.2036	1.51978	0.759892	−	0.650049i	$-0.225252\pi$
$449$	32.2036	1.51978	0.759892	+	0.650049i	$0.225252\pi$
$450$	29.5563	1.39330
$451$	−42.7693	−2.01393
$452$	19.8594	0.934107
$453$	6.21818	0.292156
$454$	34.3022	1.60988
$455$	23.5268	1.10295
$456$	−32.6610	−1.52949
$457$	−20.5248	−0.960110	−0.480055	−	0.877238i	$-0.659383\pi$
$457$	−20.5248	−0.960110	−0.480055	+	0.877238i	$0.659383\pi$
$458$	45.3160	2.11748
$459$	5.05684	0.236033
$460$	−19.7803	−0.922262
$461$	−12.9526	−0.603263	−0.301632	−	0.953425i	$-0.597531\pi$
$461$	−12.9526	−0.603263	−0.301632	+	0.953425i	$0.597531\pi$
$462$	−13.4979	−0.627980
$463$	−3.31491	−0.154057	−0.0770285	−	0.997029i	$-0.524543\pi$
$463$	−3.31491	−0.154057	−0.0770285	+	0.997029i	$0.524543\pi$
$464$	10.2688	0.476718
$465$	−15.9192	−0.738237
$466$	62.5076	2.89561
$467$	−12.3457	−0.571292	−0.285646	−	0.958335i	$-0.592208\pi$
$467$	−12.3457	−0.571292	−0.285646	+	0.958335i	$0.592208\pi$
$468$	21.8868	1.01172
$469$	13.8274	0.638489
$470$	−99.1756	−4.57463
$471$	−13.6785	−0.630270
$472$	−14.1844	−0.652889
$473$	−15.8784	−0.730091
$474$	14.2620	0.655076
$475$	−48.0652	−2.20538
$476$	−32.4800	−1.48872
$477$	−11.0423	−0.505592
$478$	−45.1467	−2.06496
$479$	−34.2771	−1.56616	−0.783081	−	0.621920i	$-0.786353\pi$
$479$	−34.2771	−1.56616	−0.783081	+	0.621920i	$0.786353\pi$
$480$	−47.1800	−2.15346
$481$	48.6728	2.21929
$482$	−70.5449	−3.21323
$483$	−1.30880	−0.0595525
$484$	21.5831	0.981051
$485$	−71.3596	−3.24027
$486$	2.62822	0.119218
$487$	23.2630	1.05415	0.527073	−	0.849820i	$-0.323289\pi$
$487$	23.2630	1.05415	0.527073	+	0.849820i	$0.323289\pi$
$488$	−46.7250	−2.11514
$489$	22.3241	1.00953
$490$	56.0072	2.53015
$491$	9.25429	0.417640	0.208820	−	0.977954i	$-0.433038\pi$
$491$	9.25429	0.417640	0.208820	+	0.977954i	$0.433038\pi$
$492$	−53.4890	−2.41147
$493$	5.05684	0.227749
$494$	−50.0984	−2.25403
$495$	−15.8162	−0.710884
$496$	40.5577	1.82110
$497$	0.306386	0.0137433
$498$	−31.9934	−1.43366
$499$	−9.98925	−0.447180	−0.223590	−	0.974683i	$-0.571778\pi$
$499$	−9.98925	−0.447180	−0.223590	+	0.974683i	$0.571778\pi$
$500$	−123.543	−5.52499
$501$	−15.0420	−0.672026
$502$	−62.7091	−2.79885
$503$	30.4391	1.35721	0.678607	−	0.734502i	$-0.262584\pi$
$503$	30.4391	1.35721	0.678607	+	0.734502i	$0.262584\pi$
$504$	−10.0014	−0.445497
$505$	18.0386	0.802706
$506$	10.3132	0.458477
$507$	6.89012	0.306001
$508$	59.4182	2.63626
$509$	17.7690	0.787599	0.393799	−	0.919196i	$-0.371160\pi$
$509$	17.7690	0.787599	0.393799	+	0.919196i	$0.371160\pi$
$510$	−53.5686	−2.37206
$511$	12.3127	0.544683
$512$	−36.7401	−1.62370
$513$	−4.27409	−0.188706
$514$	16.7844	0.740328
$515$	−8.60766	−0.379299
$516$	−19.8582	−0.874207
$517$	36.7371	1.61570
$518$	−37.5407	−1.64945
$519$	−17.7084	−0.777311
$520$	−137.365	−6.02384
$521$	−26.3429	−1.15410	−0.577052	−	0.816708i	$-0.695797\pi$
$521$	−26.3429	−1.15410	−0.577052	+	0.816708i	$0.695797\pi$
$522$	2.62822	0.115034
$523$	16.3553	0.715169	0.357585	−	0.933881i	$-0.383600\pi$
$523$	16.3553	0.715169	0.357585	+	0.933881i	$0.383600\pi$
$524$	−12.3706	−0.540414
$525$	−14.7184	−0.642365
$526$	−38.1487	−1.66336
$527$	19.9725	0.870015
$528$	40.2951	1.75362
$529$	1.00000	0.0434783
$530$	116.974	5.08104
$531$	−1.85620	−0.0805520
$532$	27.4524	1.19021
$533$	−48.6093	−2.10550
$534$	−10.4622	−0.452746
$535$	−1.46903	−0.0635117
$536$	−80.7332	−3.48714
$537$	14.3858	0.620792
$538$	22.4285	0.966963
$539$	−20.7465	−0.893613
$540$	−19.7803	−0.851209
$541$	−35.8863	−1.54287	−0.771436	−	0.636307i	$-0.780461\pi$
$541$	−35.8863	−1.54287	−0.771436	+	0.636307i	$0.780461\pi$
$542$	−84.5923	−3.63355
$543$	17.9508	0.770341
$544$	59.1926	2.53786
$545$	−23.6316	−1.01227
$546$	−15.3410	−0.656535
$547$	7.69359	0.328954	0.164477	−	0.986381i	$-0.447406\pi$
$547$	7.69359	0.328954	0.164477	+	0.986381i	$0.447406\pi$
$548$	−43.5785	−1.86158
$549$	−6.11452	−0.260961
$550$	115.979	4.94538
$551$	−4.27409	−0.182082
$552$	7.64164	0.325250
$553$	−7.10221	−0.302017
$554$	62.0394	2.63580
$555$	−43.9883	−1.86720
$556$	−63.9029	−2.71009
$557$	9.35667	0.396455	0.198227	−	0.980156i	$-0.436482\pi$
$557$	9.35667	0.396455	0.198227	+	0.980156i	$0.436482\pi$
$558$	10.3804	0.439437
$559$	−18.0466	−0.763288
$560$	54.1707	2.28913
$561$	19.8432	0.837779
$562$	−35.2381	−1.48643
$563$	−36.0938	−1.52117	−0.760587	−	0.649236i	$-0.775089\pi$
$563$	−36.0938	−1.52117	−0.760587	+	0.649236i	$0.775089\pi$
$564$	45.9449	1.93463
$565$	−16.3107	−0.686196
$566$	23.8583	1.00284
$567$	−1.30880	−0.0549645
$568$	−1.78888	−0.0750599
$569$	3.60296	0.151044	0.0755219	−	0.997144i	$-0.475938\pi$
$569$	3.60296	0.151044	0.0755219	+	0.997144i	$0.475938\pi$
$570$	45.2767	1.89643
$571$	8.79729	0.368155	0.184078	−	0.982912i	$-0.441070\pi$
$571$	8.79729	0.368155	0.184078	+	0.982912i	$0.441070\pi$
$572$	85.8843	3.59100
$573$	−2.96160	−0.123723
$574$	37.4918	1.56488
$575$	11.2457	0.468980
$576$	10.2268	0.426118
$577$	8.19811	0.341292	0.170646	−	0.985332i	$-0.445415\pi$
$577$	8.19811	0.341292	0.170646	+	0.985332i	$0.445415\pi$
$578$	22.5282	0.937048
$579$	6.26171	0.260228
$580$	−19.7803	−0.821333
$581$	15.9321	0.660975
$582$	46.5312	1.92878
$583$	−43.3302	−1.79455
$584$	−71.8897	−2.97482
$585$	−17.9758	−0.743208
$586$	45.8028	1.89210
$587$	5.43093	0.224158	0.112079	−	0.993699i	$-0.464249\pi$
$587$	5.43093	0.224158	0.112079	+	0.993699i	$0.464249\pi$
$588$	−25.9463	−1.07001
$589$	−16.8809	−0.695566
$590$	19.6632	0.809523
$591$	−23.1754	−0.953308
$592$	112.070	4.60604
$593$	−13.1806	−0.541263	−0.270631	−	0.962683i	$-0.587232\pi$
$593$	−13.1806	−0.541263	−0.270631	+	0.962683i	$0.587232\pi$
$594$	10.3132	0.423155
$595$	26.6761	1.09361
$596$	12.0609	0.494034
$597$	1.65529	0.0677466
$598$	11.7214	0.479324
$599$	2.52635	0.103224	0.0516119	−	0.998667i	$-0.483564\pi$
$599$	2.52635	0.103224	0.0516119	+	0.998667i	$0.483564\pi$
$600$	85.9358	3.50832
$601$	14.8703	0.606571	0.303285	−	0.952900i	$-0.401916\pi$
$601$	14.8703	0.606571	0.303285	+	0.952900i	$0.401916\pi$
$602$	13.9191	0.567300
$603$	−10.5649	−0.430236
$604$	30.5160	1.24168
$605$	−17.7264	−0.720681
$606$	−11.7623	−0.477812
$607$	34.5555	1.40256	0.701282	−	0.712884i	$-0.252611\pi$
$607$	34.5555	1.40256	0.701282	+	0.712884i	$0.252611\pi$
$608$	−50.0301	−2.02899
$609$	−1.30880	−0.0530353
$610$	64.7730	2.62258
$611$	41.7534	1.68916
$612$	24.8166	1.00315
$613$	6.55533	0.264767	0.132384	−	0.991199i	$-0.457737\pi$
$613$	6.55533	0.264767	0.132384	+	0.991199i	$0.457737\pi$
$614$	−48.1227	−1.94208
$615$	43.9309	1.77147
$616$	−39.2457	−1.58125
$617$	−24.5329	−0.987658	−0.493829	−	0.869559i	$-0.664403\pi$
$617$	−24.5329	−0.987658	−0.493829	+	0.869559i	$0.664403\pi$
$618$	5.61276	0.225778
$619$	25.3807	1.02014	0.510068	−	0.860134i	$-0.329620\pi$
$619$	25.3807	1.02014	0.510068	+	0.860134i	$0.329620\pi$
$620$	−78.1242	−3.13754
$621$	1.00000	0.0401286
$622$	−66.1503	−2.65239
$623$	5.20999	0.208734
$624$	45.7973	1.83336
$625$	45.2379	1.80952
$626$	13.3376	0.533077
$627$	−16.7716	−0.669794
$628$	−67.1275	−2.67868
$629$	55.1883	2.20050
$630$	13.8645	0.552376
$631$	−4.56564	−0.181755	−0.0908776	−	0.995862i	$-0.528967\pi$
$631$	−4.56564	−0.181755	−0.0908776	+	0.995862i	$0.528967\pi$
$632$	41.4673	1.64948
$633$	−0.335765	−0.0133455
$634$	−26.2506	−1.04255
$635$	−48.8007	−1.93660
$636$	−54.1904	−2.14879
$637$	−23.5793	−0.934246
$638$	10.3132	0.408303
$639$	−0.234097	−0.00926073
$640$	−13.9759	−0.552447
$641$	−26.4626	−1.04521	−0.522604	−	0.852575i	$-0.675039\pi$
$641$	−26.4626	−1.04521	−0.522604	+	0.852575i	$0.675039\pi$
$642$	0.957905	0.0378055
$643$	19.6322	0.774220	0.387110	−	0.922034i	$-0.373473\pi$
$643$	19.6322	0.774220	0.387110	+	0.922034i	$0.373473\pi$
$644$	−6.42299	−0.253101
$645$	16.3097	0.642193
$646$	−56.8047	−2.23495
$647$	36.3256	1.42811	0.714054	−	0.700091i	$-0.246857\pi$
$647$	36.3256	1.42811	0.714054	+	0.700091i	$0.246857\pi$
$648$	7.64164	0.300192
$649$	−7.28376	−0.285912
$650$	131.816	5.17025
$651$	−5.16924	−0.202598
$652$	109.556	4.29056
$653$	22.3417	0.874297	0.437149	−	0.899389i	$-0.355988\pi$
$653$	22.3417	0.874297	0.437149	+	0.899389i	$0.355988\pi$
$654$	15.4094	0.602554
$655$	10.1601	0.396989
$656$	−111.924	−4.36988
$657$	−9.40763	−0.367027
$658$	−32.2039	−1.25544
$659$	13.3343	0.519431	0.259716	−	0.965685i	$-0.416371\pi$
$659$	13.3343	0.519431	0.259716	+	0.965685i	$0.416371\pi$
$660$	−77.6184	−3.02129
$661$	−1.80412	−0.0701720	−0.0350860	−	0.999384i	$-0.511171\pi$
$661$	−1.80412	−0.0701720	−0.0350860	+	0.999384i	$0.511171\pi$
$662$	31.2212	1.21345
$663$	22.5527	0.875873
$664$	−93.0219	−3.60995
$665$	−22.5469	−0.874331
$666$	28.6833	1.11145
$667$	1.00000	0.0387202
$668$	−73.8191	−2.85615
$669$	11.4430	0.442414
$670$	111.917	4.32374
$671$	−23.9935	−0.926260
$672$	−15.3201	−0.590986
$673$	−35.3630	−1.36314	−0.681572	−	0.731751i	$-0.738703\pi$
$673$	−35.3630	−1.36314	−0.681572	+	0.731751i	$0.738703\pi$
$674$	11.0474	0.425529
$675$	11.2457	0.432849
$676$	33.8135	1.30052
$677$	−5.78388	−0.222293	−0.111146	−	0.993804i	$-0.535452\pi$
$677$	−5.78388	−0.222293	−0.111146	+	0.993804i	$0.535452\pi$
$678$	10.6357	0.408460
$679$	−23.1716	−0.889245
$680$	−155.753	−5.97284
$681$	13.0515	0.500135
$682$	40.7329	1.55974
$683$	−41.1493	−1.57453	−0.787267	−	0.616612i	$-0.788505\pi$
$683$	−41.1493	−1.57453	−0.787267	+	0.616612i	$0.788505\pi$
$684$	−20.9752	−0.802008
$685$	35.7914	1.36752
$686$	42.2652	1.61369
$687$	17.2421	0.657827
$688$	−41.5525	−1.58417
$689$	−49.2468	−1.87615
$690$	−10.5933	−0.403280
$691$	32.8290	1.24887	0.624436	−	0.781076i	$-0.285329\pi$
$691$	32.8290	1.24887	0.624436	+	0.781076i	$0.285329\pi$
$692$	−86.9044	−3.30361
$693$	−5.13577	−0.195092
$694$	−35.9692	−1.36537
$695$	52.4840	1.99083
$696$	7.64164	0.289656
$697$	−55.1163	−2.08768
$698$	−67.3832	−2.55049
$699$	23.7833	0.899565
$700$	−72.2312	−2.73008
$701$	1.79732	0.0678838	0.0339419	−	0.999424i	$-0.489194\pi$
$701$	1.79732	0.0678838	0.0339419	+	0.999424i	$0.489194\pi$
$702$	11.7214	0.442396
$703$	−46.6456	−1.75927
$704$	40.1303	1.51247
$705$	−37.7349	−1.42118
$706$	64.9341	2.44383
$707$	5.85742	0.220291
$708$	−9.10935	−0.342350
$709$	−6.32493	−0.237538	−0.118769	−	0.992922i	$-0.537895\pi$
$709$	−6.32493	−0.237538	−0.118769	+	0.992922i	$0.537895\pi$
$710$	2.47986	0.0930674
$711$	5.42650	0.203510
$712$	−30.4193	−1.14001
$713$	3.94960	0.147914
$714$	−17.3946	−0.650977
$715$	−70.5375	−2.63795
$716$	70.5987	2.63840
$717$	−17.1777	−0.641513
$718$	53.2354	1.98673
$719$	32.7107	1.21990	0.609952	−	0.792438i	$-0.291189\pi$
$719$	32.7107	1.21990	0.609952	+	0.792438i	$0.291189\pi$
$720$	−41.3895	−1.54250
$721$	−2.79505	−0.104093
$722$	−1.92435	−0.0716168
$723$	−26.8413	−0.998240
$724$	88.0940	3.27399
$725$	11.2457	0.417656
$726$	11.5588	0.428987
$727$	21.3139	0.790489	0.395244	−	0.918576i	$-0.370660\pi$
$727$	21.3139	0.790489	0.395244	+	0.918576i	$0.370660\pi$
$728$	−44.6045	−1.65315
$729$	1.00000	0.0370370
$730$	99.6579	3.68850
$731$	−20.4623	−0.756827
$732$	−30.0072	−1.10910
$733$	−1.91080	−0.0705769	−0.0352884	−	0.999377i	$-0.511235\pi$
$733$	−1.91080	−0.0705769	−0.0352884	+	0.999377i	$0.511235\pi$
$734$	88.4756	3.26569
$735$	21.3099	0.786029
$736$	11.7055	0.431469
$737$	−41.4569	−1.52709
$738$	−28.6459	−1.05447
$739$	−35.8192	−1.31763	−0.658816	−	0.752304i	$-0.728942\pi$
$739$	−35.8192	−1.31763	−0.658816	+	0.752304i	$0.728942\pi$
$740$	−215.874	−7.93569
$741$	−19.0617	−0.700250
$742$	37.9835	1.39442
$743$	44.0312	1.61535	0.807673	−	0.589630i	$-0.200727\pi$
$743$	44.0312	1.61535	0.807673	+	0.589630i	$0.200727\pi$
$744$	30.1814	1.10650
$745$	−9.90573	−0.362918
$746$	−49.6257	−1.81693
$747$	−12.1730	−0.445388
$748$	97.3810	3.56060
$749$	−0.477018	−0.0174299
$750$	−66.1630	−2.41593
$751$	27.3898	0.999467	0.499734	−	0.866179i	$-0.333431\pi$
$751$	27.3898	0.999467	0.499734	+	0.866179i	$0.333431\pi$
$752$	96.1379	3.50579
$753$	−23.8599	−0.869505
$754$	11.7214	0.426869
$755$	−25.0630	−0.912136
$756$	−6.42299	−0.233602
$757$	21.5043	0.781588	0.390794	−	0.920478i	$-0.372200\pi$
$757$	21.5043	0.781588	0.390794	+	0.920478i	$0.372200\pi$
$758$	16.5710	0.601885
$759$	3.92402	0.142433
$760$	131.644	4.77521
$761$	11.1035	0.402503	0.201251	−	0.979540i	$-0.435499\pi$
$761$	11.1035	0.402503	0.201251	+	0.979540i	$0.435499\pi$
$762$	31.8213	1.15276
$763$	−7.67356	−0.277802
$764$	−14.5341	−0.525827
$765$	−20.3821	−0.736917
$766$	−7.56247	−0.273243
$767$	−8.27833	−0.298913
$768$	−11.3404	−0.409213
$769$	25.5509	0.921390	0.460695	−	0.887558i	$-0.347600\pi$
$769$	25.5509	0.921390	0.460695	+	0.887558i	$0.347600\pi$
$770$	54.4047	1.96061
$771$	6.38623	0.229994
$772$	30.7295	1.10598
$773$	−7.81970	−0.281255	−0.140628	−	0.990063i	$-0.544912\pi$
$773$	−7.81970	−0.281255	−0.140628	+	0.990063i	$0.544912\pi$
$774$	−10.6350	−0.382267
$775$	44.4161	1.59547
$776$	135.291	4.85666
$777$	−14.2837	−0.512426
$778$	96.8891	3.47364
$779$	46.5848	1.66907
$780$	−88.2169	−3.15867
$781$	−0.918602	−0.0328702
$782$	13.2905	0.475267
$783$	1.00000	0.0357371
$784$	−54.2917	−1.93899
$785$	55.1324	1.96776
$786$	−6.62507	−0.236309
$787$	−20.8943	−0.744801	−0.372400	−	0.928072i	$-0.621465\pi$
$787$	−20.8943	−0.744801	−0.372400	+	0.928072i	$0.621465\pi$
$788$	−113.734	−4.05161
$789$	−14.5150	−0.516749
$790$	−57.4845	−2.04521
$791$	−5.29635	−0.188316
$792$	29.9860	1.06550
$793$	−27.2698	−0.968377
$794$	−1.58779	−0.0563484
$795$	44.5071	1.57850
$796$	8.12340	0.287926
$797$	17.0846	0.605167	0.302584	−	0.953123i	$-0.402151\pi$
$797$	17.0846	0.605167	0.302584	+	0.953123i	$0.402151\pi$
$798$	14.7021	0.520448
$799$	47.3427	1.67486
$800$	131.636	4.65405
$801$	−3.98074	−0.140652
$802$	−74.7155	−2.63830
$803$	−36.9158	−1.30273
$804$	−51.8477	−1.82853
$805$	5.27526	0.185928
$806$	46.2949	1.63067
$807$	8.53374	0.300402
$808$	−34.1994	−1.20313
$809$	37.5299	1.31948	0.659741	−	0.751493i	$-0.270666\pi$
$809$	37.5299	1.31948	0.659741	+	0.751493i	$0.270666\pi$
$810$	−10.5933	−0.372211
$811$	−44.9728	−1.57921	−0.789604	−	0.613617i	$-0.789714\pi$
$811$	−44.9728	−1.57921	−0.789604	+	0.613617i	$0.789714\pi$
$812$	−6.42299	−0.225403
$813$	−32.1862	−1.12882
$814$	112.554	3.94501
$815$	−89.9796	−3.15185
$816$	51.9278	1.81784
$817$	17.2949	0.605073
$818$	−74.1691	−2.59326
$819$	−5.83704	−0.203963
$820$	215.593	7.52882
$821$	7.99805	0.279134	0.139567	−	0.990213i	$-0.455429\pi$
$821$	7.99805	0.279134	0.139567	+	0.990213i	$0.455429\pi$
$822$	−23.3384	−0.814020
$823$	−8.07635	−0.281524	−0.140762	−	0.990043i	$-0.544955\pi$
$823$	−8.07635	−0.281524	−0.140762	+	0.990043i	$0.544955\pi$
$824$	16.3193	0.568510
$825$	44.1285	1.53636
$826$	6.38498	0.222162
$827$	6.72715	0.233926	0.116963	−	0.993136i	$-0.462684\pi$
$827$	6.72715	0.233926	0.116963	+	0.993136i	$0.462684\pi$
$828$	4.90753	0.170549
$829$	−19.6878	−0.683787	−0.341894	−	0.939739i	$-0.611068\pi$
$829$	−19.6878	−0.683787	−0.341894	+	0.939739i	$0.611068\pi$
$830$	128.953	4.47601
$831$	23.6051	0.818853
$832$	45.6100	1.58124
$833$	−26.7357	−0.926338
$834$	−34.2230	−1.18505
$835$	60.6282	2.09813
$836$	−82.3073	−2.84666
$837$	3.94960	0.136518
$838$	−20.8580	−0.720527
$839$	34.4713	1.19008	0.595041	−	0.803695i	$-0.297136\pi$
$839$	34.4713	1.19008	0.595041	+	0.803695i	$0.297136\pi$
$840$	40.3116	1.39088
$841$	1.00000	0.0344828
$842$	45.0526	1.55262
$843$	−13.4076	−0.461783
$844$	−1.64778	−0.0567189
$845$	−27.7713	−0.955362
$846$	24.6057	0.845960
$847$	−5.75606	−0.197780
$848$	−113.391	−3.89388
$849$	9.07775	0.311548
$850$	149.461	5.12648
$851$	10.9136	0.374113
$852$	−1.14884	−0.0393586
$853$	27.6682	0.947341	0.473670	−	0.880702i	$-0.342929\pi$
$853$	27.6682	0.947341	0.473670	+	0.880702i	$0.342929\pi$
$854$	21.0328	0.719729
$855$	17.2271	0.589155
$856$	2.78514	0.0951942
$857$	−54.9024	−1.87543	−0.937715	−	0.347406i	$-0.887063\pi$
$857$	−54.9024	−1.87543	−0.937715	+	0.347406i	$0.887063\pi$
$858$	45.9951	1.57025
$859$	46.1147	1.57341	0.786706	−	0.617328i	$-0.211785\pi$
$859$	46.1147	1.57341	0.786706	+	0.617328i	$0.211785\pi$
$860$	80.0403	2.72935
$861$	14.2651	0.486153
$862$	−54.8950	−1.86973
$863$	−23.9805	−0.816305	−0.408152	−	0.912914i	$-0.633827\pi$
$863$	−23.9805	−0.816305	−0.408152	+	0.912914i	$0.633827\pi$
$864$	11.7055	0.398228
$865$	71.3754	2.42683
$866$	45.5664	1.54841
$867$	8.57165	0.291108
$868$	−25.3682	−0.861053
$869$	21.2937	0.722339
$870$	−10.5933	−0.359146
$871$	−47.1177	−1.59652
$872$	44.8032	1.51723
$873$	17.7045	0.599205
$874$	−11.2332	−0.379970
$875$	32.9479	1.11384
$876$	−46.1683	−1.55988
$877$	−43.0874	−1.45496	−0.727478	−	0.686131i	$-0.759308\pi$
$877$	−43.0874	−1.45496	−0.727478	+	0.686131i	$0.759308\pi$
$878$	9.98786	0.337074
$879$	17.4273	0.587809
$880$	−162.414	−5.47496
$881$	11.7949	0.397382	0.198691	−	0.980062i	$-0.436331\pi$
$881$	11.7949	0.397382	0.198691	+	0.980062i	$0.436331\pi$
$882$	−13.8955	−0.467886
$883$	−10.4990	−0.353320	−0.176660	−	0.984272i	$-0.556529\pi$
$883$	−10.4990	−0.353320	−0.176660	+	0.984272i	$0.556529\pi$
$884$	110.678	3.72250
$885$	7.48158	0.251491
$886$	−74.4292	−2.50050
$887$	−7.04493	−0.236546	−0.118273	−	0.992981i	$-0.537736\pi$
$887$	−7.04493	−0.236546	−0.118273	+	0.992981i	$0.537736\pi$
$888$	83.3977	2.79864
$889$	−15.8464	−0.531470
$890$	42.1691	1.41351
$891$	3.92402	0.131460
$892$	56.1572	1.88028
$893$	−40.0145	−1.33903
$894$	6.45919	0.216028
$895$	−57.9833	−1.93817
$896$	−4.53821	−0.151611
$897$	4.45983	0.148910
$898$	84.6382	2.82441
$899$	3.94960	0.131726
$900$	55.1888	1.83963
$901$	−55.8391	−1.86027
$902$	−112.407	−3.74275
$903$	5.29602	0.176241
$904$	30.9235	1.02850
$905$	−72.3524	−2.40507
$906$	16.3427	0.542951
$907$	36.2555	1.20384	0.601922	−	0.798555i	$-0.294402\pi$
$907$	36.2555	1.20384	0.601922	+	0.798555i	$0.294402\pi$
$908$	64.0507	2.12560
$909$	−4.47540	−0.148440
$910$	61.8335	2.04976
$911$	20.2954	0.672417	0.336209	−	0.941788i	$-0.390855\pi$
$911$	20.2954	0.672417	0.336209	+	0.941788i	$0.390855\pi$
$912$	−43.8899	−1.45334
$913$	−47.7673	−1.58087
$914$	−53.9437	−1.78430
$915$	24.6452	0.814745
$916$	84.6162	2.79580
$917$	3.29916	0.108948
$918$	13.2905	0.438651
$919$	−49.1613	−1.62168	−0.810841	−	0.585266i	$-0.800990\pi$
$919$	−49.1613	−1.62168	−0.810841	+	0.585266i	$0.800990\pi$
$920$	−30.8004	−1.01546
$921$	−18.3100	−0.603336
$922$	−34.0423	−1.12112
$923$	−1.04403	−0.0343648
$924$	−25.2040	−0.829149
$925$	122.731	4.03538
$926$	−8.71231	−0.286304
$927$	2.13558	0.0701415
$928$	11.7055	0.384250
$929$	39.8349	1.30694	0.653471	−	0.756952i	$-0.273312\pi$
$929$	39.8349	1.30694	0.653471	+	0.756952i	$0.273312\pi$
$930$	−41.8392	−1.37196
$931$	22.5973	0.740595
$932$	116.717	3.82320
$933$	−25.1692	−0.824004
$934$	−32.4473	−1.06171
$935$	−79.9799	−2.61562
$936$	34.0804	1.11395
$937$	−16.1779	−0.528510	−0.264255	−	0.964453i	$-0.585126\pi$
$937$	−16.1779	−0.528510	−0.264255	+	0.964453i	$0.585126\pi$
$938$	36.3414	1.18659
$939$	5.07476	0.165609
$940$	−185.185	−6.04008
$941$	−59.5192	−1.94027	−0.970136	−	0.242562i	$-0.922012\pi$
$941$	−59.5192	−1.94027	−0.970136	+	0.242562i	$0.922012\pi$
$942$	−35.9500	−1.17131
$943$	−10.8994	−0.354932
$944$	−19.0610	−0.620381
$945$	5.27526	0.171604
$946$	−41.7320	−1.35682
$947$	31.7387	1.03137	0.515684	−	0.856779i	$-0.327538\pi$
$947$	31.7387	1.03137	0.515684	+	0.856779i	$0.327538\pi$
$948$	26.6307	0.864926
$949$	−41.9565	−1.36196
$950$	−126.326	−4.09856
$951$	−9.98799	−0.323883
$952$	−50.5754	−1.63916
$953$	−32.5881	−1.05563	−0.527817	−	0.849358i	$-0.676989\pi$
$953$	−32.5881	−1.05563	−0.527817	+	0.849358i	$0.676989\pi$
$954$	−29.0216	−0.939608
$955$	11.9370	0.386273
$956$	−84.3001	−2.72646
$957$	3.92402	0.126846
$958$	−90.0877	−2.91060
$959$	11.6221	0.375296
$960$	−41.2203	−1.33038
$961$	−15.4007	−0.496797
$962$	127.923	4.12439
$963$	0.364469	0.0117449
$964$	−131.725	−4.24257
$965$	−25.2384	−0.812454
$966$	−3.43982	−0.110674
$967$	6.36939	0.204826	0.102413	−	0.994742i	$-0.467344\pi$
$967$	6.36939	0.204826	0.102413	+	0.994742i	$0.467344\pi$
$968$	33.6076	1.08019
$969$	−21.6134	−0.694322
$970$	−187.549	−6.02182
$971$	44.5308	1.42906	0.714530	−	0.699605i	$-0.246640\pi$
$971$	44.5308	1.42906	0.714530	+	0.699605i	$0.246640\pi$
$972$	4.90753	0.157409
$973$	17.0424	0.546354
$974$	61.1402	1.95906
$975$	50.1541	1.60622
$976$	−62.7890	−2.00983
$977$	−52.8522	−1.69089	−0.845445	−	0.534062i	$-0.820665\pi$
$977$	−52.8522	−1.69089	−0.845445	+	0.534062i	$0.820665\pi$
$978$	58.6727	1.87615
$979$	−15.6205	−0.499233
$980$	104.579	3.34066
$981$	5.86304	0.187193
$982$	24.3223	0.776156
$983$	28.6636	0.914228	0.457114	−	0.889408i	$-0.348883\pi$
$983$	28.6636	0.914228	0.457114	+	0.889408i	$0.348883\pi$
$984$	−83.2889	−2.65515
$985$	93.4107	2.97631
$986$	13.2905	0.423255
$987$	−12.2531	−0.390022
$988$	−93.5460	−2.97610
$989$	−4.04647	−0.128670
$990$	−41.5684	−1.32113
$991$	−0.248409	−0.00789096	−0.00394548	−	0.999992i	$-0.501256\pi$
$991$	−0.248409	−0.00789096	−0.00394548	+	0.999992i	$0.501256\pi$
$992$	46.2318	1.46786
$993$	11.8792	0.376976
$994$	0.805251	0.0255410
$995$	−6.67182	−0.211511
$996$	−59.7396	−1.89292
$997$	−11.9581	−0.378716	−0.189358	−	0.981908i	$-0.560641\pi$
$997$	−11.9581	−0.378716	−0.189358	+	0.981908i	$0.560641\pi$
$998$	−26.2539	−0.831054
$999$	10.9136	0.345291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.o.1.19	✓	20
3.2	odd	2		6003.2.a.s.1.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.o.1.19	✓	20	1.1	even	1	trivial
6003.2.a.s.1.2		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)

\(f(q)\)	\(=\)	\(q+2.62822 q^{2} +1.00000 q^{3} +4.90753 q^{4} -4.03060 q^{5} +2.62822 q^{6} -1.30880 q^{7} +7.64164 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.62822 q^{2} +1.00000 q^{3} +4.90753 q^{4} -4.03060 q^{5} +2.62822 q^{6} -1.30880 q^{7} +7.64164 q^{8} +1.00000 q^{9} -10.5933 q^{10} +3.92402 q^{11} +4.90753 q^{12} +4.45983 q^{13} -3.43982 q^{14} -4.03060 q^{15} +10.2688 q^{16} +5.05684 q^{17} +2.62822 q^{18} -4.27409 q^{19} -19.7803 q^{20} -1.30880 q^{21} +10.3132 q^{22} +1.00000 q^{23} +7.64164 q^{24} +11.2457 q^{25} +11.7214 q^{26} +1.00000 q^{27} -6.42299 q^{28} +1.00000 q^{29} -10.5933 q^{30} +3.94960 q^{31} +11.7055 q^{32} +3.92402 q^{33} +13.2905 q^{34} +5.27526 q^{35} +4.90753 q^{36} +10.9136 q^{37} -11.2332 q^{38} +4.45983 q^{39} -30.8004 q^{40} -10.8994 q^{41} -3.43982 q^{42} -4.04647 q^{43} +19.2573 q^{44} -4.03060 q^{45} +2.62822 q^{46} +9.36211 q^{47} +10.2688 q^{48} -5.28704 q^{49} +29.5563 q^{50} +5.05684 q^{51} +21.8868 q^{52} -11.0423 q^{53} +2.62822 q^{54} -15.8162 q^{55} -10.0014 q^{56} -4.27409 q^{57} +2.62822 q^{58} -1.85620 q^{59} -19.7803 q^{60} -6.11452 q^{61} +10.3804 q^{62} -1.30880 q^{63} +10.2268 q^{64} -17.9758 q^{65} +10.3132 q^{66} -10.5649 q^{67} +24.8166 q^{68} +1.00000 q^{69} +13.8645 q^{70} -0.234097 q^{71} +7.64164 q^{72} -9.40763 q^{73} +28.6833 q^{74} +11.2457 q^{75} -20.9752 q^{76} -5.13577 q^{77} +11.7214 q^{78} +5.42650 q^{79} -41.3895 q^{80} +1.00000 q^{81} -28.6459 q^{82} -12.1730 q^{83} -6.42299 q^{84} -20.3821 q^{85} -10.6350 q^{86} +1.00000 q^{87} +29.9860 q^{88} -3.98074 q^{89} -10.5933 q^{90} -5.83704 q^{91} +4.90753 q^{92} +3.94960 q^{93} +24.6057 q^{94} +17.2271 q^{95} +11.7055 q^{96} +17.7045 q^{97} -13.8955 q^{98} +3.92402 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 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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