LMFDB - Embedded newform 2001.2.a.o.1.7

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			1.7
Root			$-1.19744$ 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)

$f(q)$	$=$	$q-1.19744 q^{2} +1.00000 q^{3} -0.566132 q^{4} -2.06209 q^{5} -1.19744 q^{6} -5.04192 q^{7} +3.07279 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.19744 q^{2} +1.00000 q^{3} -0.566132 q^{4} -2.06209 q^{5} -1.19744 q^{6} -5.04192 q^{7} +3.07279 q^{8} +1.00000 q^{9} +2.46923 q^{10} -3.25064 q^{11} -0.566132 q^{12} -6.23948 q^{13} +6.03741 q^{14} -2.06209 q^{15} -2.54723 q^{16} -1.68848 q^{17} -1.19744 q^{18} -6.81012 q^{19} +1.16742 q^{20} -5.04192 q^{21} +3.89245 q^{22} +1.00000 q^{23} +3.07279 q^{24} -0.747782 q^{25} +7.47142 q^{26} +1.00000 q^{27} +2.85439 q^{28} +1.00000 q^{29} +2.46923 q^{30} +7.68803 q^{31} -3.09543 q^{32} -3.25064 q^{33} +2.02185 q^{34} +10.3969 q^{35} -0.566132 q^{36} +8.10347 q^{37} +8.15472 q^{38} -6.23948 q^{39} -6.33638 q^{40} -3.55608 q^{41} +6.03741 q^{42} -5.36003 q^{43} +1.84029 q^{44} -2.06209 q^{45} -1.19744 q^{46} -2.48056 q^{47} -2.54723 q^{48} +18.4210 q^{49} +0.895426 q^{50} -1.68848 q^{51} +3.53237 q^{52} -12.9770 q^{53} -1.19744 q^{54} +6.70311 q^{55} -15.4928 q^{56} -6.81012 q^{57} -1.19744 q^{58} -6.25362 q^{59} +1.16742 q^{60} -5.81696 q^{61} -9.20597 q^{62} -5.04192 q^{63} +8.80106 q^{64} +12.8664 q^{65} +3.89245 q^{66} +8.79413 q^{67} +0.955901 q^{68} +1.00000 q^{69} -12.4497 q^{70} +3.86749 q^{71} +3.07279 q^{72} +4.08466 q^{73} -9.70343 q^{74} -0.747782 q^{75} +3.85542 q^{76} +16.3895 q^{77} +7.47142 q^{78} +3.99104 q^{79} +5.25262 q^{80} +1.00000 q^{81} +4.25820 q^{82} -10.7509 q^{83} +2.85439 q^{84} +3.48179 q^{85} +6.41833 q^{86} +1.00000 q^{87} -9.98854 q^{88} -6.20467 q^{89} +2.46923 q^{90} +31.4590 q^{91} -0.566132 q^{92} +7.68803 q^{93} +2.97033 q^{94} +14.0431 q^{95} -3.09543 q^{96} -7.98764 q^{97} -22.0581 q^{98} -3.25064 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.19744	−0.846720	−0.423360	−	0.905962i	$-0.639149\pi$
$2$	−1.19744	−0.846720	−0.423360	+	0.905962i	$0.639149\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.566132	−0.283066
$5$	−2.06209	−0.922195	−0.461098	−	0.887349i	$-0.652544\pi$
$5$	−2.06209	−0.922195	−0.461098	+	0.887349i	$0.652544\pi$
$6$	−1.19744	−0.488854
$7$	−5.04192	−1.90567	−0.952834	−	0.303492i	$-0.901847\pi$
$7$	−5.04192	−1.90567	−0.952834	+	0.303492i	$0.901847\pi$
$8$	3.07279	1.08640
$9$	1.00000	0.333333
$10$	2.46923	0.780841
$11$	−3.25064	−0.980104	−0.490052	−	0.871693i	$-0.663022\pi$
$11$	−3.25064	−0.980104	−0.490052	+	0.871693i	$0.663022\pi$
$12$	−0.566132	−0.163428
$13$	−6.23948	−1.73052	−0.865261	−	0.501323i	$-0.832847\pi$
$13$	−6.23948	−1.73052	−0.865261	+	0.501323i	$0.832847\pi$
$14$	6.03741	1.61357
$15$	−2.06209	−0.532430
$16$	−2.54723	−0.636808
$17$	−1.68848	−0.409516	−0.204758	−	0.978813i	$-0.565641\pi$
$17$	−1.68848	−0.409516	−0.204758	+	0.978813i	$0.565641\pi$
$18$	−1.19744	−0.282240
$19$	−6.81012	−1.56235	−0.781174	−	0.624313i	$-0.785379\pi$
$19$	−6.81012	−1.56235	−0.781174	+	0.624313i	$0.785379\pi$
$20$	1.16742	0.261042
$21$	−5.04192	−1.10024
$22$	3.89245	0.829873
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	3.07279	0.627232
$25$	−0.747782	−0.149556
$26$	7.47142	1.46527
$27$	1.00000	0.192450
$28$	2.85439	0.539430
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	2.46923	0.450819
$31$	7.68803	1.38081	0.690405	−	0.723423i	$-0.257432\pi$
$31$	7.68803	1.38081	0.690405	+	0.723423i	$0.257432\pi$
$32$	−3.09543	−0.547199
$33$	−3.25064	−0.565863
$34$	2.02185	0.346745
$35$	10.3969	1.75740
$36$	−0.566132	−0.0943553
$37$	8.10347	1.33220	0.666101	−	0.745862i	$-0.267962\pi$
$37$	8.10347	1.33220	0.666101	+	0.745862i	$0.267962\pi$
$38$	8.15472	1.32287
$39$	−6.23948	−0.999117
$40$	−6.33638	−1.00187
$41$	−3.55608	−0.555366	−0.277683	−	0.960673i	$-0.589566\pi$
$41$	−3.55608	−0.555366	−0.277683	+	0.960673i	$0.589566\pi$
$42$	6.03741	0.931593
$43$	−5.36003	−0.817397	−0.408699	−	0.912669i	$-0.634017\pi$
$43$	−5.36003	−0.817397	−0.408699	+	0.912669i	$0.634017\pi$
$44$	1.84029	0.277434
$45$	−2.06209	−0.307398
$46$	−1.19744	−0.176553
$47$	−2.48056	−0.361828	−0.180914	−	0.983499i	$-0.557905\pi$
$47$	−2.48056	−0.361828	−0.180914	+	0.983499i	$0.557905\pi$
$48$	−2.54723	−0.367661
$49$	18.4210	2.63157
$50$	0.895426	0.126632
$51$	−1.68848	−0.236434
$52$	3.53237	0.489852
$53$	−12.9770	−1.78252	−0.891261	−	0.453491i	$-0.850178\pi$
$53$	−12.9770	−1.78252	−0.891261	+	0.453491i	$0.850178\pi$
$54$	−1.19744	−0.162951
$55$	6.70311	0.903847
$56$	−15.4928	−2.07031
$57$	−6.81012	−0.902022
$58$	−1.19744	−0.157232
$59$	−6.25362	−0.814152	−0.407076	−	0.913394i	$-0.633452\pi$
$59$	−6.25362	−0.814152	−0.407076	+	0.913394i	$0.633452\pi$
$60$	1.16742	0.150713
$61$	−5.81696	−0.744786	−0.372393	−	0.928075i	$-0.621463\pi$
$61$	−5.81696	−0.744786	−0.372393	+	0.928075i	$0.621463\pi$
$62$	−9.20597	−1.16916
$63$	−5.04192	−0.635223
$64$	8.80106	1.10013
$65$	12.8664	1.59588
$66$	3.89245	0.479128
$67$	8.79413	1.07437	0.537187	−	0.843463i	$-0.319487\pi$
$67$	8.79413	1.07437	0.537187	+	0.843463i	$0.319487\pi$
$68$	0.955901	0.115920
$69$	1.00000	0.120386
$70$	−12.4497	−1.48802
$71$	3.86749	0.458986	0.229493	−	0.973310i	$-0.426293\pi$
$71$	3.86749	0.458986	0.229493	+	0.973310i	$0.426293\pi$
$72$	3.07279	0.362132
$73$	4.08466	0.478073	0.239037	−	0.971011i	$-0.423168\pi$
$73$	4.08466	0.478073	0.239037	+	0.971011i	$0.423168\pi$
$74$	−9.70343	−1.12800
$75$	−0.747782	−0.0863464
$76$	3.85542	0.442248
$77$	16.3895	1.86775
$78$	7.47142	0.845972
$79$	3.99104	0.449027	0.224513	−	0.974471i	$-0.427921\pi$
$79$	3.99104	0.449027	0.224513	+	0.974471i	$0.427921\pi$
$80$	5.25262	0.587261
$81$	1.00000	0.111111
$82$	4.25820	0.470239
$83$	−10.7509	−1.18007	−0.590033	−	0.807379i	$-0.700885\pi$
$83$	−10.7509	−1.18007	−0.590033	+	0.807379i	$0.700885\pi$
$84$	2.85439	0.311440
$85$	3.48179	0.377653
$86$	6.41833	0.692106
$87$	1.00000	0.107211
$88$	−9.98854	−1.06478
$89$	−6.20467	−0.657694	−0.328847	−	0.944383i	$-0.606660\pi$
$89$	−6.20467	−0.657694	−0.328847	+	0.944383i	$0.606660\pi$
$90$	2.46923	0.260280
$91$	31.4590	3.29780
$92$	−0.566132	−0.0590233
$93$	7.68803	0.797211
$94$	2.97033	0.306366
$95$	14.0431	1.44079
$96$	−3.09543	−0.315926
$97$	−7.98764	−0.811022	−0.405511	−	0.914090i	$-0.632906\pi$
$97$	−7.98764	−0.811022	−0.405511	+	0.914090i	$0.632906\pi$
$98$	−22.0581	−2.22820
$99$	−3.25064	−0.326701
$100$	0.423343	0.0423343
$101$	7.07558	0.704047	0.352023	−	0.935991i	$-0.385494\pi$
$101$	7.07558	0.704047	0.352023	+	0.935991i	$0.385494\pi$
$102$	2.02185	0.200193
$103$	0.849617	0.0837153	0.0418576	−	0.999124i	$-0.486672\pi$
$103$	0.849617	0.0837153	0.0418576	+	0.999124i	$0.486672\pi$
$104$	−19.1726	−1.88003
$105$	10.3969	1.01463
$106$	15.5392	1.50930
$107$	5.71817	0.552797	0.276398	−	0.961043i	$-0.410859\pi$
$107$	5.71817	0.552797	0.276398	+	0.961043i	$0.410859\pi$
$108$	−0.566132	−0.0544761
$109$	−10.9139	−1.04536	−0.522679	−	0.852529i	$-0.675068\pi$
$109$	−10.9139	−1.04536	−0.522679	+	0.852529i	$0.675068\pi$
$110$	−8.02659	−0.765305
$111$	8.10347	0.769147
$112$	12.8429	1.21354
$113$	8.32904	0.783530	0.391765	−	0.920065i	$-0.371865\pi$
$113$	8.32904	0.783530	0.391765	+	0.920065i	$0.371865\pi$
$114$	8.15472	0.763760
$115$	−2.06209	−0.192291
$116$	−0.566132	−0.0525640
$117$	−6.23948	−0.576840
$118$	7.48835	0.689359
$119$	8.51317	0.780401
$120$	−6.33638	−0.578430
$121$	−0.433356	−0.0393960
$122$	6.96548	0.630625
$123$	−3.55608	−0.320641
$124$	−4.35244	−0.390860
$125$	11.8524	1.06012
$126$	6.03741	0.537855
$127$	13.5960	1.20645	0.603226	−	0.797570i	$-0.293882\pi$
$127$	13.5960	1.20645	0.603226	+	0.797570i	$0.293882\pi$
$128$	−4.34790	−0.384304
$129$	−5.36003	−0.471924
$130$	−15.4067	−1.35126
$131$	11.8536	1.03566	0.517829	−	0.855484i	$-0.326740\pi$
$131$	11.8536	1.03566	0.517829	+	0.855484i	$0.326740\pi$
$132$	1.84029	0.160177
$133$	34.3361	2.97732
$134$	−10.5305	−0.909693
$135$	−2.06209	−0.177477
$136$	−5.18834	−0.444897
$137$	−19.0233	−1.62527	−0.812633	−	0.582775i	$-0.801967\pi$
$137$	−19.0233	−1.62527	−0.812633	+	0.582775i	$0.801967\pi$
$138$	−1.19744	−0.101933
$139$	−18.9710	−1.60910	−0.804550	−	0.593885i	$-0.797593\pi$
$139$	−18.9710	−1.60910	−0.804550	+	0.593885i	$0.797593\pi$
$140$	−5.88602	−0.497459
$141$	−2.48056	−0.208901
$142$	−4.63109	−0.388633
$143$	20.2823	1.69609
$144$	−2.54723	−0.212269
$145$	−2.06209	−0.171247
$146$	−4.89115	−0.404794
$147$	18.4210	1.51934
$148$	−4.58763	−0.377101
$149$	−2.25885	−0.185052	−0.0925260	−	0.995710i	$-0.529494\pi$
$149$	−2.25885	−0.185052	−0.0925260	+	0.995710i	$0.529494\pi$
$150$	0.895426	0.0731112
$151$	8.59882	0.699762	0.349881	−	0.936794i	$-0.386222\pi$
$151$	8.59882	0.699762	0.349881	+	0.936794i	$0.386222\pi$
$152$	−20.9261	−1.69733
$153$	−1.68848	−0.136505
$154$	−19.6254	−1.58146
$155$	−15.8534	−1.27338
$156$	3.53237	0.282816
$157$	17.7686	1.41809	0.709044	−	0.705164i	$-0.249127\pi$
$157$	17.7686	1.41809	0.709044	+	0.705164i	$0.249127\pi$
$158$	−4.77903	−0.380200
$159$	−12.9770	−1.02914
$160$	6.38305	0.504625
$161$	−5.04192	−0.397359
$162$	−1.19744	−0.0940800
$163$	−19.2559	−1.50824	−0.754120	−	0.656736i	$-0.771936\pi$
$163$	−19.2559	−1.50824	−0.754120	+	0.656736i	$0.771936\pi$
$164$	2.01321	0.157205
$165$	6.70311	0.521836
$166$	12.8736	0.999185
$167$	−13.8503	−1.07176	−0.535882	−	0.844293i	$-0.680021\pi$
$167$	−13.8503	−1.07176	−0.535882	+	0.844293i	$0.680021\pi$
$168$	−15.4928	−1.19530
$169$	25.9311	1.99470
$170$	−4.16925	−0.319767
$171$	−6.81012	−0.520783
$172$	3.03448	0.231377
$173$	−7.38728	−0.561645	−0.280822	−	0.959760i	$-0.590607\pi$
$173$	−7.38728	−0.561645	−0.280822	+	0.959760i	$0.590607\pi$
$174$	−1.19744	−0.0907779
$175$	3.77026	0.285005
$176$	8.28012	0.624138
$177$	−6.25362	−0.470051
$178$	7.42974	0.556883
$179$	10.4050	0.777705	0.388853	−	0.921300i	$-0.372871\pi$
$179$	10.4050	0.777705	0.388853	+	0.921300i	$0.372871\pi$
$180$	1.16742	0.0870140
$181$	6.19248	0.460284	0.230142	−	0.973157i	$-0.426081\pi$
$181$	6.19248	0.460284	0.230142	+	0.973157i	$0.426081\pi$
$182$	−37.6703	−2.79231
$183$	−5.81696	−0.430002
$184$	3.07279	0.226529
$185$	−16.7101	−1.22855
$186$	−9.20597	−0.675015
$187$	5.48863	0.401368
$188$	1.40433	0.102421
$189$	−5.04192	−0.366746
$190$	−16.8158	−1.21994
$191$	16.4242	1.18842	0.594208	−	0.804312i	$-0.297466\pi$
$191$	16.4242	1.18842	0.594208	+	0.804312i	$0.297466\pi$
$192$	8.80106	0.635162
$193$	11.1785	0.804645	0.402323	−	0.915498i	$-0.368203\pi$
$193$	11.1785	0.804645	0.402323	+	0.915498i	$0.368203\pi$
$194$	9.56474	0.686708
$195$	12.8664	0.921380
$196$	−10.4287	−0.744908
$197$	−17.0954	−1.21799	−0.608997	−	0.793173i	$-0.708428\pi$
$197$	−17.0954	−1.21799	−0.608997	+	0.793173i	$0.708428\pi$
$198$	3.89245	0.276624
$199$	−1.17232	−0.0831035	−0.0415517	−	0.999136i	$-0.513230\pi$
$199$	−1.17232	−0.0831035	−0.0415517	+	0.999136i	$0.513230\pi$
$200$	−2.29778	−0.162478
$201$	8.79413	0.620290
$202$	−8.47260	−0.596130
$203$	−5.04192	−0.353874
$204$	0.955901	0.0669264
$205$	7.33295	0.512156
$206$	−1.01737	−0.0708834
$207$	1.00000	0.0695048
$208$	15.8934	1.10201
$209$	22.1372	1.53126
$210$	−12.4497	−0.859110
$211$	−11.7737	−0.810532	−0.405266	−	0.914199i	$-0.632821\pi$
$211$	−11.7737	−0.810532	−0.405266	+	0.914199i	$0.632821\pi$
$212$	7.34667	0.504571
$213$	3.86749	0.264996
$214$	−6.84718	−0.468064
$215$	11.0529	0.753800
$216$	3.07279	0.209077
$217$	−38.7625	−2.63137
$218$	13.0687	0.885126
$219$	4.08466	0.276016
$220$	−3.79484	−0.255848
$221$	10.5352	0.708676
$222$	−9.70343	−0.651252
$223$	4.01214	0.268673	0.134336	−	0.990936i	$-0.457110\pi$
$223$	4.01214	0.268673	0.134336	+	0.990936i	$0.457110\pi$
$224$	15.6069	1.04278
$225$	−0.747782	−0.0498521
$226$	−9.97355	−0.663430
$227$	−15.6398	−1.03805	−0.519024	−	0.854760i	$-0.673704\pi$
$227$	−15.6398	−1.03805	−0.519024	+	0.854760i	$0.673704\pi$
$228$	3.85542	0.255332
$229$	10.1942	0.673652	0.336826	−	0.941567i	$-0.390647\pi$
$229$	10.1942	0.673652	0.336826	+	0.941567i	$0.390647\pi$
$230$	2.46923	0.162817
$231$	16.3895	1.07835
$232$	3.07279	0.201739
$233$	−4.13073	−0.270613	−0.135307	−	0.990804i	$-0.543202\pi$
$233$	−4.13073	−0.270613	−0.135307	+	0.990804i	$0.543202\pi$
$234$	7.47142	0.488422
$235$	5.11515	0.333676
$236$	3.54037	0.230459
$237$	3.99104	0.259246
$238$	−10.1940	−0.660781
$239$	−4.45359	−0.288079	−0.144039	−	0.989572i	$-0.546009\pi$
$239$	−4.45359	−0.288079	−0.144039	+	0.989572i	$0.546009\pi$
$240$	5.25262	0.339055
$241$	−11.9261	−0.768228	−0.384114	−	0.923286i	$-0.625493\pi$
$241$	−11.9261	−0.768228	−0.384114	+	0.923286i	$0.625493\pi$
$242$	0.518919	0.0333574
$243$	1.00000	0.0641500
$244$	3.29317	0.210824
$245$	−37.9858	−2.42682
$246$	4.25820	0.271493
$247$	42.4916	2.70368
$248$	23.6237	1.50011
$249$	−10.7509	−0.681311
$250$	−14.1926	−0.897620
$251$	2.06690	0.130462	0.0652308	−	0.997870i	$-0.479222\pi$
$251$	2.06690	0.130462	0.0652308	+	0.997870i	$0.479222\pi$
$252$	2.85439	0.179810
$253$	−3.25064	−0.204366
$254$	−16.2805	−1.02153
$255$	3.48179	0.218038
$256$	−12.3958	−0.774734
$257$	9.80955	0.611903	0.305951	−	0.952047i	$-0.401026\pi$
$257$	9.80955	0.611903	0.305951	+	0.952047i	$0.401026\pi$
$258$	6.41833	0.399588
$259$	−40.8571	−2.53873
$260$	−7.28407	−0.451739
$261$	1.00000	0.0618984
$262$	−14.1940	−0.876911
$263$	24.1442	1.48879	0.744397	−	0.667738i	$-0.232737\pi$
$263$	24.1442	1.48879	0.744397	+	0.667738i	$0.232737\pi$
$264$	−9.98854	−0.614752
$265$	26.7597	1.64383
$266$	−41.1155	−2.52095
$267$	−6.20467	−0.379720
$268$	−4.97863	−0.304119
$269$	−14.0387	−0.855952	−0.427976	−	0.903790i	$-0.640773\pi$
$269$	−14.0387	−0.855952	−0.427976	+	0.903790i	$0.640773\pi$
$270$	2.46923	0.150273
$271$	26.6094	1.61641	0.808204	−	0.588902i	$-0.200440\pi$
$271$	26.6094	1.61641	0.808204	+	0.588902i	$0.200440\pi$
$272$	4.30094	0.260783
$273$	31.4590	1.90398
$274$	22.7793	1.37615
$275$	2.43077	0.146581
$276$	−0.566132	−0.0340771
$277$	−27.7848	−1.66943	−0.834715	−	0.550683i	$-0.814367\pi$
$277$	−27.7848	−1.66943	−0.834715	+	0.550683i	$0.814367\pi$
$278$	22.7167	1.36246
$279$	7.68803	0.460270
$280$	31.9476	1.90923
$281$	−20.8344	−1.24288	−0.621438	−	0.783463i	$-0.713451\pi$
$281$	−20.8344	−1.24288	−0.621438	+	0.783463i	$0.713451\pi$
$282$	2.97033	0.176881
$283$	2.22869	0.132482	0.0662410	−	0.997804i	$-0.478899\pi$
$283$	2.22869	0.132482	0.0662410	+	0.997804i	$0.478899\pi$
$284$	−2.18951	−0.129923
$285$	14.0431	0.831840
$286$	−24.2869	−1.43611
$287$	17.9295	1.05834
$288$	−3.09543	−0.182400
$289$	−14.1490	−0.832297
$290$	2.46923	0.144998
$291$	−7.98764	−0.468244
$292$	−2.31246	−0.135326
$293$	−25.7063	−1.50178	−0.750889	−	0.660428i	$-0.770375\pi$
$293$	−25.7063	−1.50178	−0.750889	+	0.660428i	$0.770375\pi$
$294$	−22.0581	−1.28645
$295$	12.8955	0.750807
$296$	24.9003	1.44730
$297$	−3.25064	−0.188621
$298$	2.70484	0.156687
$299$	−6.23948	−0.360839
$300$	0.423343	0.0244417
$301$	27.0249	1.55769
$302$	−10.2966	−0.592502
$303$	7.07558	0.406482
$304$	17.3469	0.994915
$305$	11.9951	0.686838
$306$	2.02185	0.115582
$307$	32.2228	1.83905	0.919526	−	0.393029i	$-0.128573\pi$
$307$	32.2228	1.83905	0.919526	+	0.393029i	$0.128573\pi$
$308$	−9.27860	−0.528697
$309$	0.849617	0.0483330
$310$	18.9835	1.07819
$311$	13.1142	0.743636	0.371818	−	0.928306i	$-0.378734\pi$
$311$	13.1142	0.743636	0.371818	+	0.928306i	$0.378734\pi$
$312$	−19.1726	−1.08544
$313$	−13.2453	−0.748668	−0.374334	−	0.927294i	$-0.622129\pi$
$313$	−13.2453	−0.748668	−0.374334	+	0.927294i	$0.622129\pi$
$314$	−21.2769	−1.20072
$315$	10.3969	0.585799
$316$	−2.25945	−0.127104
$317$	−14.4154	−0.809651	−0.404826	−	0.914394i	$-0.632668\pi$
$317$	−14.4154	−0.809651	−0.404826	+	0.914394i	$0.632668\pi$
$318$	15.5392	0.871393
$319$	−3.25064	−0.182001
$320$	−18.1486	−1.01454
$321$	5.71817	0.319157
$322$	6.03741	0.336452
$323$	11.4987	0.639806
$324$	−0.566132	−0.0314518
$325$	4.66577	0.258810
$326$	23.0579	1.27706
$327$	−10.9139	−0.603538
$328$	−10.9271	−0.603348
$329$	12.5068	0.689523
$330$	−8.02659	−0.441849
$331$	24.5366	1.34865	0.674326	−	0.738434i	$-0.264434\pi$
$331$	24.5366	1.34865	0.674326	+	0.738434i	$0.264434\pi$
$332$	6.08643	0.334036
$333$	8.10347	0.444067
$334$	16.5849	0.907484
$335$	−18.1343	−0.990782
$336$	12.8429	0.700640
$337$	29.2378	1.59268	0.796342	−	0.604846i	$-0.206765\pi$
$337$	29.2378	1.59268	0.796342	+	0.604846i	$0.206765\pi$
$338$	−31.0510	−1.68895
$339$	8.32904	0.452371
$340$	−1.97115	−0.106901
$341$	−24.9910	−1.35334
$342$	8.15472	0.440957
$343$	−57.5838	−3.10923
$344$	−16.4703	−0.888018
$345$	−2.06209	−0.111019
$346$	8.84585	0.475556
$347$	−28.3632	−1.52262	−0.761309	−	0.648389i	$-0.775443\pi$
$347$	−28.3632	−1.52262	−0.761309	+	0.648389i	$0.775443\pi$
$348$	−0.566132	−0.0303479
$349$	−1.53730	−0.0822900	−0.0411450	−	0.999153i	$-0.513101\pi$
$349$	−1.53730	−0.0822900	−0.0411450	+	0.999153i	$0.513101\pi$
$350$	−4.51467	−0.241319
$351$	−6.23948	−0.333039
$352$	10.0621	0.536312
$353$	−27.5147	−1.46446	−0.732230	−	0.681057i	$-0.761521\pi$
$353$	−27.5147	−1.46446	−0.732230	+	0.681057i	$0.761521\pi$
$354$	7.48835	0.398001
$355$	−7.97511	−0.423275
$356$	3.51266	0.186171
$357$	8.51317	0.450565
$358$	−12.4594	−0.658498
$359$	9.89302	0.522134	0.261067	−	0.965321i	$-0.415926\pi$
$359$	9.89302	0.522134	0.261067	+	0.965321i	$0.415926\pi$
$360$	−6.33638	−0.333957
$361$	27.3777	1.44093
$362$	−7.41514	−0.389731
$363$	−0.433356	−0.0227453
$364$	−17.8099	−0.933494
$365$	−8.42294	−0.440877
$366$	6.96548	0.364091
$367$	−33.5227	−1.74987	−0.874936	−	0.484239i	$-0.839096\pi$
$367$	−33.5227	−1.74987	−0.874936	+	0.484239i	$0.839096\pi$
$368$	−2.54723	−0.132784
$369$	−3.55608	−0.185122
$370$	20.0094	1.04024
$371$	65.4288	3.39690
$372$	−4.35244	−0.225663
$373$	3.10888	0.160972	0.0804858	−	0.996756i	$-0.474353\pi$
$373$	3.10888	0.160972	0.0804858	+	0.996756i	$0.474353\pi$
$374$	−6.57231	−0.339846
$375$	11.8524	0.612058
$376$	−7.62227	−0.393088
$377$	−6.23948	−0.321350
$378$	6.03741	0.310531
$379$	4.02318	0.206657	0.103328	−	0.994647i	$-0.467051\pi$
$379$	4.02318	0.206657	0.103328	+	0.994647i	$0.467051\pi$
$380$	−7.95023	−0.407838
$381$	13.5960	0.696546
$382$	−19.6671	−1.00625
$383$	24.5468	1.25428	0.627142	−	0.778905i	$-0.284225\pi$
$383$	24.5468	1.25428	0.627142	+	0.778905i	$0.284225\pi$
$384$	−4.34790	−0.221878
$385$	−33.7966	−1.72243
$386$	−13.3856	−0.681309
$387$	−5.36003	−0.272466
$388$	4.52206	0.229573
$389$	−4.99909	−0.253464	−0.126732	−	0.991937i	$-0.540449\pi$
$389$	−4.99909	−0.253464	−0.126732	+	0.991937i	$0.540449\pi$
$390$	−15.4067	−0.780151
$391$	−1.68848	−0.0853899
$392$	56.6039	2.85893
$393$	11.8536	0.597937
$394$	20.4707	1.03130
$395$	−8.22988	−0.414090
$396$	1.84029	0.0924780
$397$	22.3687	1.12265	0.561326	−	0.827595i	$-0.310292\pi$
$397$	22.3687	1.12265	0.561326	+	0.827595i	$0.310292\pi$
$398$	1.40378	0.0703653
$399$	34.3361	1.71895
$400$	1.90477	0.0952387
$401$	23.8839	1.19270	0.596352	−	0.802723i	$-0.296616\pi$
$401$	23.8839	1.19270	0.596352	+	0.802723i	$0.296616\pi$
$402$	−10.5305	−0.525212
$403$	−47.9693	−2.38952
$404$	−4.00571	−0.199292
$405$	−2.06209	−0.102466
$406$	6.03741	0.299632
$407$	−26.3414	−1.30570
$408$	−5.18834	−0.256861
$409$	26.6761	1.31905	0.659523	−	0.751684i	$-0.270758\pi$
$409$	26.6761	1.31905	0.659523	+	0.751684i	$0.270758\pi$
$410$	−8.78079	−0.433652
$411$	−19.0233	−0.938348
$412$	−0.480995	−0.0236969
$413$	31.5303	1.55150
$414$	−1.19744	−0.0588511
$415$	22.1694	1.08825
$416$	19.3139	0.946940
$417$	−18.9710	−0.929014
$418$	−26.5080	−1.29655
$419$	−28.5412	−1.39433	−0.697165	−	0.716911i	$-0.745555\pi$
$419$	−28.5412	−1.39433	−0.697165	+	0.716911i	$0.745555\pi$
$420$	−5.88602	−0.287208
$421$	8.17571	0.398460	0.199230	−	0.979953i	$-0.436156\pi$
$421$	8.17571	0.398460	0.199230	+	0.979953i	$0.436156\pi$
$422$	14.0983	0.686293
$423$	−2.48056	−0.120609
$424$	−39.8755	−1.93653
$425$	1.26261	0.0612457
$426$	−4.63109	−0.224377
$427$	29.3287	1.41931
$428$	−3.23724	−0.156478
$429$	20.2823	0.979238
$430$	−13.2352	−0.638257
$431$	23.2858	1.12164	0.560819	−	0.827939i	$-0.310487\pi$
$431$	23.2858	1.12164	0.560819	+	0.827939i	$0.310487\pi$
$432$	−2.54723	−0.122554
$433$	−32.2493	−1.54980	−0.774901	−	0.632083i	$-0.782200\pi$
$433$	−32.2493	−1.54980	−0.774901	+	0.632083i	$0.782200\pi$
$434$	46.4158	2.22803
$435$	−2.06209	−0.0988697
$436$	6.17869	0.295905
$437$	−6.81012	−0.325772
$438$	−4.89115	−0.233708
$439$	−7.65572	−0.365387	−0.182694	−	0.983170i	$-0.558482\pi$
$439$	−7.65572	−0.365387	−0.182694	+	0.983170i	$0.558482\pi$
$440$	20.5973	0.981937
$441$	18.4210	0.877190
$442$	−12.6153	−0.600050
$443$	13.5058	0.641682	0.320841	−	0.947133i	$-0.396035\pi$
$443$	13.5058	0.641682	0.320841	+	0.947133i	$0.396035\pi$
$444$	−4.58763	−0.217719
$445$	12.7946	0.606522
$446$	−4.80430	−0.227490
$447$	−2.25885	−0.106840
$448$	−44.3743	−2.09649
$449$	−13.4126	−0.632978	−0.316489	−	0.948596i	$-0.602504\pi$
$449$	−13.4126	−0.632978	−0.316489	+	0.948596i	$0.602504\pi$
$450$	0.895426	0.0422108
$451$	11.5595	0.544316
$452$	−4.71534	−0.221791
$453$	8.59882	0.404008
$454$	18.7277	0.878936
$455$	−64.8713	−3.04121
$456$	−20.9261	−0.979954
$457$	−20.5991	−0.963587	−0.481793	−	0.876285i	$-0.660014\pi$
$457$	−20.5991	−0.963587	−0.481793	+	0.876285i	$0.660014\pi$
$458$	−12.2070	−0.570394
$459$	−1.68848	−0.0788114
$460$	1.16742	0.0544310
$461$	−19.4004	−0.903567	−0.451783	−	0.892128i	$-0.649212\pi$
$461$	−19.4004	−0.903567	−0.451783	+	0.892128i	$0.649212\pi$
$462$	−19.6254	−0.913058
$463$	−16.7434	−0.778132	−0.389066	−	0.921210i	$-0.627202\pi$
$463$	−16.7434	−0.778132	−0.389066	+	0.921210i	$0.627202\pi$
$464$	−2.54723	−0.118252
$465$	−15.8534	−0.735184
$466$	4.94631	0.229133
$467$	14.4444	0.668409	0.334205	−	0.942501i	$-0.391532\pi$
$467$	14.4444	0.668409	0.334205	+	0.942501i	$0.391532\pi$
$468$	3.53237	0.163284
$469$	−44.3393	−2.04740
$470$	−6.12510	−0.282530
$471$	17.7686	0.818734
$472$	−19.2161	−0.884492
$473$	17.4235	0.801134
$474$	−4.77903	−0.219508
$475$	5.09248	0.233659
$476$	−4.81958	−0.220905
$477$	−12.9770	−0.594174
$478$	5.33292	0.243922
$479$	−42.0985	−1.92353	−0.961765	−	0.273877i	$-0.911694\pi$
$479$	−42.0985	−1.92353	−0.961765	+	0.273877i	$0.911694\pi$
$480$	6.38305	0.291345
$481$	−50.5614	−2.30540
$482$	14.2808	0.650474
$483$	−5.04192	−0.229415
$484$	0.245337	0.0111517
$485$	16.4712	0.747920
$486$	−1.19744	−0.0543171
$487$	−33.3917	−1.51312	−0.756561	−	0.653923i	$-0.773122\pi$
$487$	−33.3917	−1.51312	−0.756561	+	0.653923i	$0.773122\pi$
$488$	−17.8743	−0.809133
$489$	−19.2559	−0.870783
$490$	45.4858	2.05484
$491$	−18.5636	−0.837765	−0.418883	−	0.908040i	$-0.637578\pi$
$491$	−18.5636	−0.837765	−0.418883	+	0.908040i	$0.637578\pi$
$492$	2.01321	0.0907624
$493$	−1.68848	−0.0760452
$494$	−50.8812	−2.28926
$495$	6.70311	0.301282
$496$	−19.5832	−0.879311
$497$	−19.4996	−0.874675
$498$	12.8736	0.576880
$499$	−40.8090	−1.82686	−0.913431	−	0.406993i	$-0.866577\pi$
$499$	−40.8090	−1.82686	−0.913431	+	0.406993i	$0.866577\pi$
$500$	−6.71005	−0.300082
$501$	−13.8503	−0.618784
$502$	−2.47499	−0.110464
$503$	−19.9372	−0.888955	−0.444478	−	0.895790i	$-0.646611\pi$
$503$	−19.9372	−0.888955	−0.444478	+	0.895790i	$0.646611\pi$
$504$	−15.4928	−0.690104
$505$	−14.5905	−0.649268
$506$	3.89245	0.173041
$507$	25.9311	1.15164
$508$	−7.69714	−0.341506
$509$	−5.56812	−0.246803	−0.123401	−	0.992357i	$-0.539380\pi$
$509$	−5.56812	−0.246803	−0.123401	+	0.992357i	$0.539380\pi$
$510$	−4.16925	−0.184617
$511$	−20.5946	−0.911049
$512$	23.5390	1.04029
$513$	−6.81012	−0.300674
$514$	−11.7464	−0.518110
$515$	−1.75199	−0.0772018
$516$	3.03448	0.133586
$517$	8.06342	0.354629
$518$	48.9240	2.14960
$519$	−7.38728	−0.324266
$520$	39.5357	1.73376
$521$	−14.0001	−0.613353	−0.306677	−	0.951814i	$-0.599217\pi$
$521$	−14.0001	−0.613353	−0.306677	+	0.951814i	$0.599217\pi$
$522$	−1.19744	−0.0524106
$523$	−24.8212	−1.08536	−0.542678	−	0.839941i	$-0.682590\pi$
$523$	−24.8212	−1.08536	−0.542678	+	0.839941i	$0.682590\pi$
$524$	−6.71072	−0.293159
$525$	3.77026	0.164548
$526$	−28.9112	−1.26059
$527$	−12.9811	−0.565464
$528$	8.28012	0.360346
$529$	1.00000	0.0434783
$530$	−32.0431	−1.39187
$531$	−6.25362	−0.271384
$532$	−19.4388	−0.842777
$533$	22.1881	0.961072
$534$	7.42974	0.321516
$535$	−11.7914	−0.509786
$536$	27.0225	1.16720
$537$	10.4050	0.449008
$538$	16.8105	0.724752
$539$	−59.8800	−2.57921
$540$	1.16742	0.0502376
$541$	6.70658	0.288338	0.144169	−	0.989553i	$-0.453949\pi$
$541$	6.70658	0.288338	0.144169	+	0.989553i	$0.453949\pi$
$542$	−31.8633	−1.36865
$543$	6.19248	0.265745
$544$	5.22656	0.224087
$545$	22.5054	0.964025
$546$	−37.6703	−1.61214
$547$	30.7909	1.31653	0.658263	−	0.752788i	$-0.271292\pi$
$547$	30.7909	1.31653	0.658263	+	0.752788i	$0.271292\pi$
$548$	10.7697	0.460058
$549$	−5.81696	−0.248262
$550$	−2.91070	−0.124113
$551$	−6.81012	−0.290121
$552$	3.07279	0.130787
$553$	−20.1225	−0.855695
$554$	33.2707	1.41354
$555$	−16.7101	−0.709304
$556$	10.7401	0.455481
$557$	16.1106	0.682629	0.341315	−	0.939949i	$-0.389128\pi$
$557$	16.1106	0.682629	0.341315	+	0.939949i	$0.389128\pi$
$558$	−9.20597	−0.389720
$559$	33.4438	1.41452
$560$	−26.4833	−1.11912
$561$	5.48863	0.231730
$562$	24.9480	1.05237
$563$	−12.0500	−0.507846	−0.253923	−	0.967224i	$-0.581721\pi$
$563$	−12.0500	−0.507846	−0.253923	+	0.967224i	$0.581721\pi$
$564$	1.40433	0.0591328
$565$	−17.1752	−0.722568
$566$	−2.66873	−0.112175
$567$	−5.04192	−0.211741
$568$	11.8840	0.498641
$569$	−5.73467	−0.240410	−0.120205	−	0.992749i	$-0.538355\pi$
$569$	−5.73467	−0.240410	−0.120205	+	0.992749i	$0.538355\pi$
$570$	−16.8158	−0.704335
$571$	15.9360	0.666900	0.333450	−	0.942768i	$-0.391787\pi$
$571$	15.9360	0.666900	0.333450	+	0.942768i	$0.391787\pi$
$572$	−11.4825	−0.480105
$573$	16.4242	0.686132
$574$	−21.4695	−0.896120
$575$	−0.747782	−0.0311847
$576$	8.80106	0.366711
$577$	25.1482	1.04693	0.523467	−	0.852046i	$-0.324638\pi$
$577$	25.1482	1.04693	0.523467	+	0.852046i	$0.324638\pi$
$578$	16.9427	0.704722
$579$	11.1785	0.464562
$580$	1.16742	0.0484743
$581$	54.2053	2.24881
$582$	9.56474	0.396471
$583$	42.1834	1.74706
$584$	12.5513	0.519378
$585$	12.8664	0.531959
$586$	30.7818	1.27159
$587$	−20.5545	−0.848376	−0.424188	−	0.905574i	$-0.639440\pi$
$587$	−20.5545	−0.848376	−0.424188	+	0.905574i	$0.639440\pi$
$588$	−10.4287	−0.430073
$589$	−52.3564	−2.15731
$590$	−15.4417	−0.635723
$591$	−17.0954	−0.703209
$592$	−20.6414	−0.848356
$593$	−4.65816	−0.191288	−0.0956439	−	0.995416i	$-0.530491\pi$
$593$	−4.65816	−0.191288	−0.0956439	+	0.995416i	$0.530491\pi$
$594$	3.89245	0.159709
$595$	−17.5549	−0.719682
$596$	1.27880	0.0523819
$597$	−1.17232	−0.0479798
$598$	7.47142	0.305529
$599$	16.0992	0.657797	0.328899	−	0.944365i	$-0.393323\pi$
$599$	16.0992	0.657797	0.328899	+	0.944365i	$0.393323\pi$
$600$	−2.29778	−0.0938065
$601$	−25.2142	−1.02851	−0.514254	−	0.857638i	$-0.671931\pi$
$601$	−25.2142	−1.02851	−0.514254	+	0.857638i	$0.671931\pi$
$602$	−32.3607	−1.31892
$603$	8.79413	0.358124
$604$	−4.86807	−0.198079
$605$	0.893620	0.0363308
$606$	−8.47260	−0.344176
$607$	28.0469	1.13839	0.569195	−	0.822203i	$-0.307255\pi$
$607$	28.0469	1.13839	0.569195	+	0.822203i	$0.307255\pi$
$608$	21.0802	0.854916
$609$	−5.04192	−0.204309
$610$	−14.3635	−0.581559
$611$	15.4774	0.626150
$612$	0.955901	0.0386400
$613$	31.0124	1.25258	0.626290	−	0.779590i	$-0.284572\pi$
$613$	31.0124	1.25258	0.626290	+	0.779590i	$0.284572\pi$
$614$	−38.5849	−1.55716
$615$	7.33295	0.295693
$616$	50.3615	2.02912
$617$	30.9966	1.24787	0.623937	−	0.781475i	$-0.285532\pi$
$617$	30.9966	1.24787	0.623937	+	0.781475i	$0.285532\pi$
$618$	−1.01737	−0.0409245
$619$	−0.176704	−0.00710234	−0.00355117	−	0.999994i	$-0.501130\pi$
$619$	−0.176704	−0.00710234	−0.00355117	+	0.999994i	$0.501130\pi$
$620$	8.97512	0.360450
$621$	1.00000	0.0401286
$622$	−15.7035	−0.629652
$623$	31.2835	1.25335
$624$	15.8934	0.636245
$625$	−20.7019	−0.828077
$626$	15.8605	0.633911
$627$	22.1372	0.884076
$628$	−10.0594	−0.401412
$629$	−13.6825	−0.545558
$630$	−12.4497	−0.496008
$631$	−9.35919	−0.372583	−0.186292	−	0.982494i	$-0.559647\pi$
$631$	−9.35919	−0.372583	−0.186292	+	0.982494i	$0.559647\pi$
$632$	12.2636	0.487821
$633$	−11.7737	−0.467961
$634$	17.2617	0.685548
$635$	−28.0362	−1.11258
$636$	7.34667	0.291314
$637$	−114.937	−4.55399
$638$	3.89245	0.154104
$639$	3.86749	0.152995
$640$	8.96577	0.354403
$641$	24.6606	0.974037	0.487019	−	0.873392i	$-0.338084\pi$
$641$	24.6606	0.974037	0.487019	+	0.873392i	$0.338084\pi$
$642$	−6.84718	−0.270237
$643$	7.81464	0.308179	0.154090	−	0.988057i	$-0.450756\pi$
$643$	7.81464	0.308179	0.154090	+	0.988057i	$0.450756\pi$
$644$	2.85439	0.112479
$645$	11.0529	0.435206
$646$	−13.7691	−0.541736
$647$	−13.5259	−0.531757	−0.265878	−	0.964007i	$-0.585662\pi$
$647$	−13.5259	−0.531757	−0.265878	+	0.964007i	$0.585662\pi$
$648$	3.07279	0.120711
$649$	20.3283	0.797954
$650$	−5.58699	−0.219140
$651$	−38.7625	−1.51922
$652$	10.9014	0.426932
$653$	−22.2051	−0.868951	−0.434476	−	0.900684i	$-0.643066\pi$
$653$	−22.2051	−0.868951	−0.434476	+	0.900684i	$0.643066\pi$
$654$	13.0687	0.511028
$655$	−24.4433	−0.955078
$656$	9.05815	0.353661
$657$	4.08466	0.159358
$658$	−14.9762	−0.583833
$659$	2.41065	0.0939057	0.0469529	−	0.998897i	$-0.485049\pi$
$659$	2.41065	0.0939057	0.0469529	+	0.998897i	$0.485049\pi$
$660$	−3.79484	−0.147714
$661$	−30.1307	−1.17195	−0.585975	−	0.810329i	$-0.699288\pi$
$661$	−30.1307	−1.17195	−0.585975	+	0.810329i	$0.699288\pi$
$662$	−29.3811	−1.14193
$663$	10.5352	0.409154
$664$	−33.0353	−1.28202
$665$	−70.8041	−2.74567
$666$	−9.70343	−0.376000
$667$	1.00000	0.0387202
$668$	7.84107	0.303380
$669$	4.01214	0.155118
$670$	21.7148	0.838914
$671$	18.9088	0.729968
$672$	15.6069	0.602050
$673$	48.4182	1.86638	0.933192	−	0.359377i	$-0.117011\pi$
$673$	48.4182	1.86638	0.933192	+	0.359377i	$0.117011\pi$
$674$	−35.0106	−1.34856
$675$	−0.747782	−0.0287821
$676$	−14.6804	−0.564632
$677$	16.8459	0.647442	0.323721	−	0.946153i	$-0.395066\pi$
$677$	16.8459	0.647442	0.323721	+	0.946153i	$0.395066\pi$
$678$	−9.97355	−0.383032
$679$	40.2731	1.54554
$680$	10.6988	0.410282
$681$	−15.6398	−0.599317
$682$	29.9253	1.14590
$683$	28.0812	1.07450	0.537248	−	0.843424i	$-0.319464\pi$
$683$	28.0812	1.07450	0.537248	+	0.843424i	$0.319464\pi$
$684$	3.85542	0.147416
$685$	39.2277	1.49881
$686$	68.9533	2.63265
$687$	10.1942	0.388933
$688$	13.6532	0.520525
$689$	80.9695	3.08469
$690$	2.46923	0.0940022
$691$	−18.2999	−0.696161	−0.348081	−	0.937465i	$-0.613166\pi$
$691$	−18.2999	−0.696161	−0.348081	+	0.937465i	$0.613166\pi$
$692$	4.18218	0.158982
$693$	16.3895	0.622584
$694$	33.9633	1.28923
$695$	39.1199	1.48390
$696$	3.07279	0.116474
$697$	6.00435	0.227431
$698$	1.84083	0.0696766
$699$	−4.13073	−0.156239
$700$	−2.13446	−0.0806751
$701$	34.8853	1.31760	0.658800	−	0.752318i	$-0.271064\pi$
$701$	34.8853	1.31760	0.658800	+	0.752318i	$0.271064\pi$
$702$	7.47142	0.281991
$703$	−55.1856	−2.08136
$704$	−28.6090	−1.07824
$705$	5.11515	0.192648
$706$	32.9473	1.23999
$707$	−35.6745	−1.34168
$708$	3.54037	0.133055
$709$	41.4053	1.55501	0.777503	−	0.628879i	$-0.216486\pi$
$709$	41.4053	1.55501	0.777503	+	0.628879i	$0.216486\pi$
$710$	9.54973	0.358395
$711$	3.99104	0.149676
$712$	−19.0657	−0.714517
$713$	7.68803	0.287919
$714$	−10.1940	−0.381502
$715$	−41.8239	−1.56413
$716$	−5.89060	−0.220142
$717$	−4.45359	−0.166322
$718$	−11.8463	−0.442101
$719$	31.3446	1.16895	0.584477	−	0.811410i	$-0.301300\pi$
$719$	31.3446	1.16895	0.584477	+	0.811410i	$0.301300\pi$
$720$	5.25262	0.195754
$721$	−4.28371	−0.159534
$722$	−32.7832	−1.22007
$723$	−11.9261	−0.443537
$724$	−3.50576	−0.130291
$725$	−0.747782	−0.0277719
$726$	0.518919	0.0192589
$727$	23.6364	0.876627	0.438314	−	0.898822i	$-0.355576\pi$
$727$	23.6364	0.876627	0.438314	+	0.898822i	$0.355576\pi$
$728$	96.6670	3.58272
$729$	1.00000	0.0370370
$730$	10.0860	0.373299
$731$	9.05029	0.334737
$732$	3.29317	0.121719
$733$	22.6643	0.837126	0.418563	−	0.908188i	$-0.362534\pi$
$733$	22.6643	0.837126	0.418563	+	0.908188i	$0.362534\pi$
$734$	40.1415	1.48165
$735$	−37.9858	−1.40113
$736$	−3.09543	−0.114099
$737$	−28.5865	−1.05300
$738$	4.25820	0.156746
$739$	−28.5965	−1.05194	−0.525970	−	0.850503i	$-0.676298\pi$
$739$	−28.5965	−1.05194	−0.525970	+	0.850503i	$0.676298\pi$
$740$	9.46011	0.347761
$741$	42.4916	1.56097
$742$	−78.3472	−2.87622
$743$	−51.2185	−1.87903	−0.939513	−	0.342514i	$-0.888722\pi$
$743$	−51.2185	−1.87903	−0.939513	+	0.342514i	$0.888722\pi$
$744$	23.6237	0.866088
$745$	4.65795	0.170654
$746$	−3.72270	−0.136298
$747$	−10.7509	−0.393355
$748$	−3.10729	−0.113614
$749$	−28.8306	−1.05345
$750$	−14.1926	−0.518241
$751$	31.2908	1.14182	0.570908	−	0.821014i	$-0.306591\pi$
$751$	31.2908	1.14182	0.570908	+	0.821014i	$0.306591\pi$
$752$	6.31857	0.230415
$753$	2.06690	0.0753220
$754$	7.47142	0.272093
$755$	−17.7315	−0.645317
$756$	2.85439	0.103813
$757$	−4.16334	−0.151319	−0.0756596	−	0.997134i	$-0.524106\pi$
$757$	−4.16334	−0.151319	−0.0756596	+	0.997134i	$0.524106\pi$
$758$	−4.81753	−0.174980
$759$	−3.25064	−0.117991
$760$	43.1515	1.56527
$761$	−30.3090	−1.09870	−0.549351	−	0.835592i	$-0.685125\pi$
$761$	−30.3090	−1.09870	−0.549351	+	0.835592i	$0.685125\pi$
$762$	−16.2805	−0.589779
$763$	55.0269	1.99211
$764$	−9.29828	−0.336400
$765$	3.48179	0.125884
$766$	−29.3934	−1.06203
$767$	39.0194	1.40891
$768$	−12.3958	−0.447293
$769$	0.202559	0.00730447	0.00365224	−	0.999993i	$-0.498837\pi$
$769$	0.202559	0.00730447	0.00365224	+	0.999993i	$0.498837\pi$
$770$	40.4694	1.45842
$771$	9.80955	0.353282
$772$	−6.32850	−0.227768
$773$	−50.4003	−1.81277	−0.906386	−	0.422450i	$-0.861170\pi$
$773$	−50.4003	−1.81277	−0.906386	+	0.422450i	$0.861170\pi$
$774$	6.41833	0.230702
$775$	−5.74897	−0.206509
$776$	−24.5444	−0.881092
$777$	−40.8571	−1.46574
$778$	5.98612	0.214613
$779$	24.2173	0.867675
$780$	−7.28407	−0.260811
$781$	−12.5718	−0.449854
$782$	2.02185	0.0723013
$783$	1.00000	0.0357371
$784$	−46.9225	−1.67580
$785$	−36.6405	−1.30775
$786$	−14.1940	−0.506285
$787$	−10.7921	−0.384697	−0.192349	−	0.981327i	$-0.561610\pi$
$787$	−10.7921	−0.384697	−0.192349	+	0.981327i	$0.561610\pi$
$788$	9.67822	0.344772
$789$	24.1442	0.859555
$790$	9.85480	0.350618
$791$	−41.9944	−1.49315
$792$	−9.98854	−0.354927
$793$	36.2948	1.28887
$794$	−26.7852	−0.950571
$795$	26.7597	0.949067
$796$	0.663687	0.0235238
$797$	−52.6370	−1.86450	−0.932249	−	0.361816i	$-0.882157\pi$
$797$	−52.6370	−1.86450	−0.932249	+	0.361816i	$0.882157\pi$
$798$	−41.1155	−1.45547
$799$	4.18838	0.148174
$800$	2.31470	0.0818372
$801$	−6.20467	−0.219231
$802$	−28.5996	−1.00989
$803$	−13.2778	−0.468562
$804$	−4.97863	−0.175583
$805$	10.3969	0.366443
$806$	57.4405	2.02326
$807$	−14.0387	−0.494184
$808$	21.7418	0.764874
$809$	41.3605	1.45416	0.727080	−	0.686553i	$-0.240877\pi$
$809$	41.3605	1.45416	0.727080	+	0.686553i	$0.240877\pi$
$810$	2.46923	0.0867601
$811$	11.8526	0.416203	0.208101	−	0.978107i	$-0.433272\pi$
$811$	11.8526	0.416203	0.208101	+	0.978107i	$0.433272\pi$
$812$	2.85439	0.100170
$813$	26.6094	0.933234
$814$	31.5423	1.10556
$815$	39.7075	1.39089
$816$	4.30094	0.150563
$817$	36.5024	1.27706
$818$	−31.9431	−1.11686
$819$	31.4590	1.09927
$820$	−4.15142	−0.144974
$821$	23.3747	0.815781	0.407891	−	0.913031i	$-0.366264\pi$
$821$	23.3747	0.815781	0.407891	+	0.913031i	$0.366264\pi$
$822$	22.7793	0.794518
$823$	22.8021	0.794832	0.397416	−	0.917638i	$-0.369907\pi$
$823$	22.8021	0.794832	0.397416	+	0.917638i	$0.369907\pi$
$824$	2.61070	0.0909480
$825$	2.43077	0.0846285
$826$	−37.7557	−1.31369
$827$	−33.2724	−1.15699	−0.578497	−	0.815684i	$-0.696361\pi$
$827$	−33.2724	−1.15699	−0.578497	+	0.815684i	$0.696361\pi$
$828$	−0.566132	−0.0196744
$829$	39.2694	1.36388	0.681942	−	0.731407i	$-0.261136\pi$
$829$	39.2694	1.36388	0.681942	+	0.731407i	$0.261136\pi$
$830$	−26.5465	−0.921443
$831$	−27.7848	−0.963846
$832$	−54.9140	−1.90380
$833$	−31.1034	−1.07767
$834$	22.7167	0.786614
$835$	28.5605	0.988376
$836$	−12.5326	−0.433449
$837$	7.68803	0.265737
$838$	34.1765	1.18061
$839$	34.4182	1.18825	0.594124	−	0.804374i	$-0.297499\pi$
$839$	34.4182	1.18825	0.594124	+	0.804374i	$0.297499\pi$
$840$	31.9476	1.10230
$841$	1.00000	0.0344828
$842$	−9.78994	−0.337384
$843$	−20.8344	−0.717575
$844$	6.66544	0.229434
$845$	−53.4724	−1.83951
$846$	2.97033	0.102122
$847$	2.18495	0.0750758
$848$	33.0553	1.13512
$849$	2.22869	0.0764886
$850$	−1.51191	−0.0518579
$851$	8.10347	0.277783
$852$	−2.18951	−0.0750113
$853$	29.4613	1.00873	0.504367	−	0.863489i	$-0.331726\pi$
$853$	29.4613	1.00873	0.504367	+	0.863489i	$0.331726\pi$
$854$	−35.1194	−1.20176
$855$	14.0431	0.480263
$856$	17.5708	0.600557
$857$	18.1437	0.619776	0.309888	−	0.950773i	$-0.399708\pi$
$857$	18.1437	0.619776	0.309888	+	0.950773i	$0.399708\pi$
$858$	−24.2869	−0.829140
$859$	22.3321	0.761960	0.380980	−	0.924583i	$-0.375587\pi$
$859$	22.3321	0.761960	0.380980	+	0.924583i	$0.375587\pi$
$860$	−6.25738	−0.213375
$861$	17.9295	0.611035
$862$	−27.8834	−0.949712
$863$	−1.86768	−0.0635766	−0.0317883	−	0.999495i	$-0.510120\pi$
$863$	−1.86768	−0.0635766	−0.0317883	+	0.999495i	$0.510120\pi$
$864$	−3.09543	−0.105309
$865$	15.2332	0.517946
$866$	38.6167	1.31225
$867$	−14.1490	−0.480527
$868$	21.9447	0.744850
$869$	−12.9734	−0.440093
$870$	2.46923	0.0837149
$871$	−54.8708	−1.85923
$872$	−33.5361	−1.13567
$873$	−7.98764	−0.270341
$874$	8.15472	0.275838
$875$	−59.7591	−2.02023
$876$	−2.31246	−0.0781307
$877$	−13.3782	−0.451749	−0.225875	−	0.974156i	$-0.572524\pi$
$877$	−13.3782	−0.451749	−0.225875	+	0.974156i	$0.572524\pi$
$878$	9.16728	0.309381
$879$	−25.7063	−0.867052
$880$	−17.0744	−0.575577
$881$	−9.97548	−0.336083	−0.168041	−	0.985780i	$-0.553744\pi$
$881$	−9.97548	−0.336083	−0.168041	+	0.985780i	$0.553744\pi$
$882$	−22.0581	−0.742734
$883$	−6.25218	−0.210403	−0.105201	−	0.994451i	$-0.533549\pi$
$883$	−6.25218	−0.210403	−0.105201	+	0.994451i	$0.533549\pi$
$884$	−5.96432	−0.200602
$885$	12.8955	0.433479
$886$	−16.1725	−0.543325
$887$	41.2664	1.38559	0.692795	−	0.721134i	$-0.256379\pi$
$887$	41.2664	1.38559	0.692795	+	0.721134i	$0.256379\pi$
$888$	24.9003	0.835599
$889$	−68.5501	−2.29910
$890$	−15.3208	−0.513554
$891$	−3.25064	−0.108900
$892$	−2.27140	−0.0760521
$893$	16.8929	0.565301
$894$	2.70484	0.0904633
$895$	−21.4560	−0.717196
$896$	21.9218	0.732356
$897$	−6.23948	−0.208330
$898$	16.0608	0.535955
$899$	7.68803	0.256410
$900$	0.423343	0.0141114
$901$	21.9113	0.729971
$902$	−13.8419	−0.460883
$903$	27.0249	0.899331
$904$	25.5934	0.851225
$905$	−12.7695	−0.424471
$906$	−10.2966	−0.342081
$907$	23.6124	0.784038	0.392019	−	0.919957i	$-0.371777\pi$
$907$	23.6124	0.784038	0.392019	+	0.919957i	$0.371777\pi$
$908$	8.85417	0.293836
$909$	7.07558	0.234682
$910$	77.6796	2.57505
$911$	−6.19372	−0.205207	−0.102603	−	0.994722i	$-0.532717\pi$
$911$	−6.19372	−0.205207	−0.102603	+	0.994722i	$0.532717\pi$
$912$	17.3469	0.574415
$913$	34.9473	1.15659
$914$	24.6663	0.815888
$915$	11.9951	0.396546
$916$	−5.77126	−0.190688
$917$	−59.7651	−1.97362
$918$	2.02185	0.0667311
$919$	41.9811	1.38483	0.692414	−	0.721500i	$-0.256547\pi$
$919$	41.9811	1.38483	0.692414	+	0.721500i	$0.256547\pi$
$920$	−6.33638	−0.208904
$921$	32.2228	1.06178
$922$	23.2309	0.765068
$923$	−24.1311	−0.794285
$924$	−9.27860	−0.305243
$925$	−6.05962	−0.199239
$926$	20.0492	0.658859
$927$	0.849617	0.0279051
$928$	−3.09543	−0.101612
$929$	−45.9424	−1.50732	−0.753661	−	0.657264i	$-0.771714\pi$
$929$	−45.9424	−1.50732	−0.753661	+	0.657264i	$0.771714\pi$
$930$	18.9835	0.622495
$931$	−125.449	−4.11143
$932$	2.33854	0.0766014
$933$	13.1142	0.429339
$934$	−17.2964	−0.565955
$935$	−11.3180	−0.370140
$936$	−19.1726	−0.626678
$937$	−26.1173	−0.853215	−0.426608	−	0.904437i	$-0.640291\pi$
$937$	−26.1173	−0.853215	−0.426608	+	0.904437i	$0.640291\pi$
$938$	53.0938	1.73357
$939$	−13.2453	−0.432243
$940$	−2.89585	−0.0944522
$941$	32.5296	1.06044	0.530218	−	0.847861i	$-0.322110\pi$
$941$	32.5296	1.06044	0.530218	+	0.847861i	$0.322110\pi$
$942$	−21.2769	−0.693238
$943$	−3.55608	−0.115802
$944$	15.9294	0.518458
$945$	10.3969	0.338211
$946$	−20.8637	−0.678336
$947$	3.46449	0.112581	0.0562905	−	0.998414i	$-0.482073\pi$
$947$	3.46449	0.112581	0.0562905	+	0.998414i	$0.482073\pi$
$948$	−2.25945	−0.0733836
$949$	−25.4862	−0.827316
$950$	−6.09795	−0.197844
$951$	−14.4154	−0.467452
$952$	26.1592	0.847826
$953$	0.809283	0.0262153	0.0131076	−	0.999914i	$-0.495828\pi$
$953$	0.809283	0.0262153	0.0131076	+	0.999914i	$0.495828\pi$
$954$	15.5392	0.503099
$955$	−33.8683	−1.09595
$956$	2.52132	0.0815453
$957$	−3.25064	−0.105078
$958$	50.4105	1.62869
$959$	95.9138	3.09722
$960$	−18.1486	−0.585743
$961$	28.1058	0.906638
$962$	60.5444	1.95203
$963$	5.71817	0.184266
$964$	6.75175	0.217459
$965$	−23.0511	−0.742040
$966$	6.03741	0.194251
$967$	23.6129	0.759341	0.379671	−	0.925122i	$-0.376037\pi$
$967$	23.6129	0.759341	0.379671	+	0.925122i	$0.376037\pi$
$968$	−1.33162	−0.0427997
$969$	11.4987	0.369392
$970$	−19.7234	−0.633279
$971$	23.4909	0.753859	0.376930	−	0.926242i	$-0.376980\pi$
$971$	23.4909	0.753859	0.376930	+	0.926242i	$0.376980\pi$
$972$	−0.566132	−0.0181587
$973$	95.6504	3.06641
$974$	39.9846	1.28119
$975$	4.66577	0.149424
$976$	14.8172	0.474286
$977$	−49.8145	−1.59371	−0.796854	−	0.604172i	$-0.793504\pi$
$977$	−49.8145	−1.59371	−0.796854	+	0.604172i	$0.793504\pi$
$978$	23.0579	0.737309
$979$	20.1691	0.644609
$980$	21.5049	0.686950
$981$	−10.9139	−0.348453
$982$	22.2289	0.709352
$983$	−38.4490	−1.22633	−0.613167	−	0.789954i	$-0.710105\pi$
$983$	−38.4490	−1.22633	−0.613167	+	0.789954i	$0.710105\pi$
$984$	−10.9271	−0.348343
$985$	35.2522	1.12323
$986$	2.02185	0.0643889
$987$	12.5068	0.398096
$988$	−24.0559	−0.765319
$989$	−5.36003	−0.170439
$990$	−8.02659	−0.255102
$991$	−7.36344	−0.233907	−0.116954	−	0.993137i	$-0.537313\pi$
$991$	−7.36344	−0.233907	−0.116954	+	0.993137i	$0.537313\pi$
$992$	−23.7977	−0.755579
$993$	24.5366	0.778644
$994$	23.3496	0.740605
$995$	2.41743	0.0766376
$996$	6.08643	0.192856
$997$	13.9655	0.442290	0.221145	−	0.975241i	$-0.429021\pi$
$997$	13.9655	0.442290	0.221145	+	0.975241i	$0.429021\pi$
$998$	48.8664	1.54684
$999$	8.10347	0.256382

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.o.1.7	✓	20	1.1	even	1	trivial
6003.2.a.s.1.14		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)

\(f(q)\)	\(=\)	\(q-1.19744 q^{2} +1.00000 q^{3} -0.566132 q^{4} -2.06209 q^{5} -1.19744 q^{6} -5.04192 q^{7} +3.07279 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.19744 q^{2} +1.00000 q^{3} -0.566132 q^{4} -2.06209 q^{5} -1.19744 q^{6} -5.04192 q^{7} +3.07279 q^{8} +1.00000 q^{9} +2.46923 q^{10} -3.25064 q^{11} -0.566132 q^{12} -6.23948 q^{13} +6.03741 q^{14} -2.06209 q^{15} -2.54723 q^{16} -1.68848 q^{17} -1.19744 q^{18} -6.81012 q^{19} +1.16742 q^{20} -5.04192 q^{21} +3.89245 q^{22} +1.00000 q^{23} +3.07279 q^{24} -0.747782 q^{25} +7.47142 q^{26} +1.00000 q^{27} +2.85439 q^{28} +1.00000 q^{29} +2.46923 q^{30} +7.68803 q^{31} -3.09543 q^{32} -3.25064 q^{33} +2.02185 q^{34} +10.3969 q^{35} -0.566132 q^{36} +8.10347 q^{37} +8.15472 q^{38} -6.23948 q^{39} -6.33638 q^{40} -3.55608 q^{41} +6.03741 q^{42} -5.36003 q^{43} +1.84029 q^{44} -2.06209 q^{45} -1.19744 q^{46} -2.48056 q^{47} -2.54723 q^{48} +18.4210 q^{49} +0.895426 q^{50} -1.68848 q^{51} +3.53237 q^{52} -12.9770 q^{53} -1.19744 q^{54} +6.70311 q^{55} -15.4928 q^{56} -6.81012 q^{57} -1.19744 q^{58} -6.25362 q^{59} +1.16742 q^{60} -5.81696 q^{61} -9.20597 q^{62} -5.04192 q^{63} +8.80106 q^{64} +12.8664 q^{65} +3.89245 q^{66} +8.79413 q^{67} +0.955901 q^{68} +1.00000 q^{69} -12.4497 q^{70} +3.86749 q^{71} +3.07279 q^{72} +4.08466 q^{73} -9.70343 q^{74} -0.747782 q^{75} +3.85542 q^{76} +16.3895 q^{77} +7.47142 q^{78} +3.99104 q^{79} +5.25262 q^{80} +1.00000 q^{81} +4.25820 q^{82} -10.7509 q^{83} +2.85439 q^{84} +3.48179 q^{85} +6.41833 q^{86} +1.00000 q^{87} -9.98854 q^{88} -6.20467 q^{89} +2.46923 q^{90} +31.4590 q^{91} -0.566132 q^{92} +7.68803 q^{93} +2.97033 q^{94} +14.0431 q^{95} -3.09543 q^{96} -7.98764 q^{97} -22.0581 q^{98} -3.25064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 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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