LMFDB - Embedded newform 2001.2.a.o.1.5

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			1.5
Root			$-1.94926$ 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)

$f(q)$	$=$	$q-1.94926 q^{2} +1.00000 q^{3} +1.79960 q^{4} +3.69296 q^{5} -1.94926 q^{6} -2.45473 q^{7} +0.390627 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.94926 q^{2} +1.00000 q^{3} +1.79960 q^{4} +3.69296 q^{5} -1.94926 q^{6} -2.45473 q^{7} +0.390627 q^{8} +1.00000 q^{9} -7.19852 q^{10} +4.43817 q^{11} +1.79960 q^{12} -4.28535 q^{13} +4.78490 q^{14} +3.69296 q^{15} -4.36064 q^{16} -1.49875 q^{17} -1.94926 q^{18} +1.06731 q^{19} +6.64585 q^{20} -2.45473 q^{21} -8.65112 q^{22} +1.00000 q^{23} +0.390627 q^{24} +8.63793 q^{25} +8.35324 q^{26} +1.00000 q^{27} -4.41754 q^{28} +1.00000 q^{29} -7.19852 q^{30} +2.48186 q^{31} +7.71875 q^{32} +4.43817 q^{33} +2.92144 q^{34} -9.06522 q^{35} +1.79960 q^{36} +3.20872 q^{37} -2.08047 q^{38} -4.28535 q^{39} +1.44257 q^{40} +4.57310 q^{41} +4.78490 q^{42} +5.98441 q^{43} +7.98693 q^{44} +3.69296 q^{45} -1.94926 q^{46} -4.84278 q^{47} -4.36064 q^{48} -0.974292 q^{49} -16.8375 q^{50} -1.49875 q^{51} -7.71192 q^{52} +4.65981 q^{53} -1.94926 q^{54} +16.3900 q^{55} -0.958884 q^{56} +1.06731 q^{57} -1.94926 q^{58} +0.167254 q^{59} +6.64585 q^{60} +13.1401 q^{61} -4.83778 q^{62} -2.45473 q^{63} -6.32455 q^{64} -15.8256 q^{65} -8.65112 q^{66} +11.9525 q^{67} -2.69715 q^{68} +1.00000 q^{69} +17.6704 q^{70} +8.22431 q^{71} +0.390627 q^{72} -10.4723 q^{73} -6.25462 q^{74} +8.63793 q^{75} +1.92074 q^{76} -10.8945 q^{77} +8.35324 q^{78} +0.909584 q^{79} -16.1036 q^{80} +1.00000 q^{81} -8.91415 q^{82} -4.61155 q^{83} -4.41754 q^{84} -5.53480 q^{85} -11.6652 q^{86} +1.00000 q^{87} +1.73367 q^{88} +12.8616 q^{89} -7.19852 q^{90} +10.5194 q^{91} +1.79960 q^{92} +2.48186 q^{93} +9.43982 q^{94} +3.94154 q^{95} +7.71875 q^{96} +1.88580 q^{97} +1.89915 q^{98} +4.43817 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.94926	−1.37833	−0.689166	−	0.724603i	$-0.742023\pi$
$2$	−1.94926	−1.37833	−0.689166	+	0.724603i	$0.742023\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.79960	0.899801
$5$	3.69296	1.65154	0.825770	−	0.564007i	$-0.190741\pi$
$5$	3.69296	1.65154	0.825770	+	0.564007i	$0.190741\pi$
$6$	−1.94926	−0.795781
$7$	−2.45473	−0.927801	−0.463901	−	0.885887i	$-0.653551\pi$
$7$	−2.45473	−0.927801	−0.463901	+	0.885887i	$0.653551\pi$
$8$	0.390627	0.138107
$9$	1.00000	0.333333
$10$	−7.19852	−2.27637
$11$	4.43817	1.33816	0.669079	−	0.743192i	$-0.266689\pi$
$11$	4.43817	1.33816	0.669079	+	0.743192i	$0.266689\pi$
$12$	1.79960	0.519500
$13$	−4.28535	−1.18854	−0.594271	−	0.804265i	$-0.702559\pi$
$13$	−4.28535	−1.18854	−0.594271	+	0.804265i	$0.702559\pi$
$14$	4.78490	1.27882
$15$	3.69296	0.953517
$16$	−4.36064	−1.09016
$17$	−1.49875	−0.363499	−0.181750	−	0.983345i	$-0.558176\pi$
$17$	−1.49875	−0.363499	−0.181750	+	0.983345i	$0.558176\pi$
$18$	−1.94926	−0.459444
$19$	1.06731	0.244858	0.122429	−	0.992477i	$-0.460932\pi$
$19$	1.06731	0.244858	0.122429	+	0.992477i	$0.460932\pi$
$20$	6.64585	1.48606
$21$	−2.45473	−0.535666
$22$	−8.65112	−1.84443
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.390627	0.0797364
$25$	8.63793	1.72759
$26$	8.35324	1.63821
$27$	1.00000	0.192450
$28$	−4.41754	−0.834837
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−7.19852	−1.31426
$31$	2.48186	0.445755	0.222878	−	0.974846i	$-0.428455\pi$
$31$	2.48186	0.445755	0.222878	+	0.974846i	$0.428455\pi$
$32$	7.71875	1.36449
$33$	4.43817	0.772585
$34$	2.92144	0.501023
$35$	−9.06522	−1.53230
$36$	1.79960	0.299934
$37$	3.20872	0.527510	0.263755	−	0.964590i	$-0.415039\pi$
$37$	3.20872	0.527510	0.263755	+	0.964590i	$0.415039\pi$
$38$	−2.08047	−0.337496
$39$	−4.28535	−0.686205
$40$	1.44257	0.228090
$41$	4.57310	0.714199	0.357099	−	0.934066i	$-0.383766\pi$
$41$	4.57310	0.714199	0.357099	+	0.934066i	$0.383766\pi$
$42$	4.78490	0.738327
$43$	5.98441	0.912614	0.456307	−	0.889822i	$-0.349172\pi$
$43$	5.98441	0.912614	0.456307	+	0.889822i	$0.349172\pi$
$44$	7.98693	1.20408
$45$	3.69296	0.550514
$46$	−1.94926	−0.287402
$47$	−4.84278	−0.706392	−0.353196	−	0.935549i	$-0.614905\pi$
$47$	−4.84278	−0.706392	−0.353196	+	0.935549i	$0.614905\pi$
$48$	−4.36064	−0.629404
$49$	−0.974292	−0.139185
$50$	−16.8375	−2.38119
$51$	−1.49875	−0.209866
$52$	−7.71192	−1.06945
$53$	4.65981	0.640074	0.320037	−	0.947405i	$-0.396305\pi$
$53$	4.65981	0.640074	0.320037	+	0.947405i	$0.396305\pi$
$54$	−1.94926	−0.265260
$55$	16.3900	2.21002
$56$	−0.958884	−0.128136
$57$	1.06731	0.141369
$58$	−1.94926	−0.255950
$59$	0.167254	0.0217746	0.0108873	−	0.999941i	$-0.496534\pi$
$59$	0.167254	0.0217746	0.0108873	+	0.999941i	$0.496534\pi$
$60$	6.64585	0.857976
$61$	13.1401	1.68242	0.841212	−	0.540706i	$-0.181843\pi$
$61$	13.1401	1.68242	0.841212	+	0.540706i	$0.181843\pi$
$62$	−4.83778	−0.614399
$63$	−2.45473	−0.309267
$64$	−6.32455	−0.790568
$65$	−15.8256	−1.96292
$66$	−8.65112	−1.06488
$67$	11.9525	1.46023	0.730113	−	0.683327i	$-0.239467\pi$
$67$	11.9525	1.46023	0.730113	+	0.683327i	$0.239467\pi$
$68$	−2.69715	−0.327077
$69$	1.00000	0.120386
$70$	17.6704	2.11202
$71$	8.22431	0.976046	0.488023	−	0.872831i	$-0.337718\pi$
$71$	8.22431	0.976046	0.488023	+	0.872831i	$0.337718\pi$
$72$	0.390627	0.0460358
$73$	−10.4723	−1.22569	−0.612845	−	0.790203i	$-0.709975\pi$
$73$	−10.4723	−1.22569	−0.612845	+	0.790203i	$0.709975\pi$
$74$	−6.25462	−0.727084
$75$	8.63793	0.997422
$76$	1.92074	0.220324
$77$	−10.8945	−1.24154
$78$	8.35324	0.945818
$79$	0.909584	0.102336	0.0511681	−	0.998690i	$-0.483706\pi$
$79$	0.909584	0.102336	0.0511681	+	0.998690i	$0.483706\pi$
$80$	−16.1036	−1.80044
$81$	1.00000	0.111111
$82$	−8.91415	−0.984403
$83$	−4.61155	−0.506183	−0.253092	−	0.967442i	$-0.581447\pi$
$83$	−4.61155	−0.506183	−0.253092	+	0.967442i	$0.581447\pi$
$84$	−4.41754	−0.481993
$85$	−5.53480	−0.600334
$86$	−11.6652	−1.25789
$87$	1.00000	0.107211
$88$	1.73367	0.184809
$89$	12.8616	1.36333	0.681664	−	0.731665i	$-0.261256\pi$
$89$	12.8616	1.36333	0.681664	+	0.731665i	$0.261256\pi$
$90$	−7.19852	−0.758791
$91$	10.5194	1.10273
$92$	1.79960	0.187622
$93$	2.48186	0.257357
$94$	9.43982	0.973643
$95$	3.94154	0.404394
$96$	7.71875	0.787791
$97$	1.88580	0.191474	0.0957372	−	0.995407i	$-0.469479\pi$
$97$	1.88580	0.191474	0.0957372	+	0.995407i	$0.469479\pi$
$98$	1.89915	0.191843
$99$	4.43817	0.446052
$100$	15.5448	1.55448
$101$	5.40314	0.537633	0.268816	−	0.963191i	$-0.413368\pi$
$101$	5.40314	0.537633	0.268816	+	0.963191i	$0.413368\pi$
$102$	2.92144	0.289266
$103$	−6.14017	−0.605009	−0.302505	−	0.953148i	$-0.597823\pi$
$103$	−6.14017	−0.605009	−0.302505	+	0.953148i	$0.597823\pi$
$104$	−1.67397	−0.164146
$105$	−9.06522	−0.884675
$106$	−9.08316	−0.882234
$107$	−3.00788	−0.290783	−0.145391	−	0.989374i	$-0.546444\pi$
$107$	−3.00788	−0.290783	−0.145391	+	0.989374i	$0.546444\pi$
$108$	1.79960	0.173167
$109$	−13.3033	−1.27423	−0.637113	−	0.770771i	$-0.719871\pi$
$109$	−13.3033	−1.27423	−0.637113	+	0.770771i	$0.719871\pi$
$110$	−31.9482	−3.04614
$111$	3.20872	0.304558
$112$	10.7042	1.01145
$113$	−18.0625	−1.69918	−0.849590	−	0.527443i	$-0.823151\pi$
$113$	−18.0625	−1.69918	−0.849590	+	0.527443i	$0.823151\pi$
$114$	−2.08047	−0.194854
$115$	3.69296	0.344370
$116$	1.79960	0.167089
$117$	−4.28535	−0.396181
$118$	−0.326020	−0.0300126
$119$	3.67902	0.337255
$120$	1.44257	0.131688
$121$	8.69731	0.790665
$122$	−25.6135	−2.31894
$123$	4.57310	0.412343
$124$	4.46636	0.401091
$125$	13.4347	1.20164
$126$	4.78490	0.426273
$127$	−6.61372	−0.586873	−0.293436	−	0.955979i	$-0.594799\pi$
$127$	−6.61372	−0.586873	−0.293436	+	0.955979i	$0.594799\pi$
$128$	−3.10933	−0.274828
$129$	5.98441	0.526898
$130$	30.8482	2.70556
$131$	−10.8669	−0.949448	−0.474724	−	0.880135i	$-0.657452\pi$
$131$	−10.8669	−0.949448	−0.474724	+	0.880135i	$0.657452\pi$
$132$	7.98693	0.695173
$133$	−2.61997	−0.227180
$134$	−23.2984	−2.01268
$135$	3.69296	0.317839
$136$	−0.585450	−0.0502019
$137$	19.4409	1.66095	0.830474	−	0.557057i	$-0.188070\pi$
$137$	19.4409	1.66095	0.830474	+	0.557057i	$0.188070\pi$
$138$	−1.94926	−0.165932
$139$	−14.9146	−1.26504	−0.632520	−	0.774544i	$-0.717979\pi$
$139$	−14.9146	−1.26504	−0.632520	+	0.774544i	$0.717979\pi$
$140$	−16.3138	−1.37877
$141$	−4.84278	−0.407836
$142$	−16.0313	−1.34532
$143$	−19.0191	−1.59046
$144$	−4.36064	−0.363386
$145$	3.69296	0.306683
$146$	20.4132	1.68941
$147$	−0.974292	−0.0803583
$148$	5.77442	0.474654
$149$	−7.73831	−0.633947	−0.316974	−	0.948434i	$-0.602667\pi$
$149$	−7.73831	−0.633947	−0.316974	+	0.948434i	$0.602667\pi$
$150$	−16.8375	−1.37478
$151$	12.8699	1.04733	0.523667	−	0.851923i	$-0.324564\pi$
$151$	12.8699	1.04733	0.523667	+	0.851923i	$0.324564\pi$
$152$	0.416921	0.0338168
$153$	−1.49875	−0.121166
$154$	21.2362	1.71126
$155$	9.16540	0.736183
$156$	−7.71192	−0.617448
$157$	12.6332	1.00824	0.504120	−	0.863634i	$-0.331817\pi$
$157$	12.6332	1.00824	0.504120	+	0.863634i	$0.331817\pi$
$158$	−1.77301	−0.141053
$159$	4.65981	0.369547
$160$	28.5050	2.25352
$161$	−2.45473	−0.193460
$162$	−1.94926	−0.153148
$163$	−8.96876	−0.702488	−0.351244	−	0.936284i	$-0.614241\pi$
$163$	−8.96876	−0.702488	−0.351244	+	0.936284i	$0.614241\pi$
$164$	8.22977	0.642637
$165$	16.3900	1.27596
$166$	8.98909	0.697689
$167$	12.9614	1.00298	0.501492	−	0.865162i	$-0.332785\pi$
$167$	12.9614	1.00298	0.501492	+	0.865162i	$0.332785\pi$
$168$	−0.958884	−0.0739795
$169$	5.36420	0.412631
$170$	10.7888	0.827460
$171$	1.06731	0.0816195
$172$	10.7696	0.821171
$173$	−4.02670	−0.306144	−0.153072	−	0.988215i	$-0.548917\pi$
$173$	−4.02670	−0.306144	−0.153072	+	0.988215i	$0.548917\pi$
$174$	−1.94926	−0.147773
$175$	−21.2038	−1.60286
$176$	−19.3532	−1.45880
$177$	0.167254	0.0125715
$178$	−25.0706	−1.87912
$179$	−0.565219	−0.0422464	−0.0211232	−	0.999777i	$-0.506724\pi$
$179$	−0.565219	−0.0422464	−0.0211232	+	0.999777i	$0.506724\pi$
$180$	6.64585	0.495353
$181$	14.4322	1.07274	0.536368	−	0.843984i	$-0.319796\pi$
$181$	14.4322	1.07274	0.536368	+	0.843984i	$0.319796\pi$
$182$	−20.5050	−1.51993
$183$	13.1401	0.971348
$184$	0.390627	0.0287974
$185$	11.8497	0.871204
$186$	−4.83778	−0.354723
$187$	−6.65168	−0.486419
$188$	−8.71508	−0.635612
$189$	−2.45473	−0.178555
$190$	−7.68308	−0.557389
$191$	−11.1284	−0.805223	−0.402612	−	0.915371i	$-0.631897\pi$
$191$	−11.1284	−0.805223	−0.402612	+	0.915371i	$0.631897\pi$
$192$	−6.32455	−0.456435
$193$	−18.0097	−1.29637	−0.648183	−	0.761485i	$-0.724471\pi$
$193$	−18.0097	−1.29637	−0.648183	+	0.761485i	$0.724471\pi$
$194$	−3.67591	−0.263915
$195$	−15.8256	−1.13329
$196$	−1.75334	−0.125238
$197$	22.4270	1.59786	0.798930	−	0.601424i	$-0.205400\pi$
$197$	22.4270	1.59786	0.798930	+	0.601424i	$0.205400\pi$
$198$	−8.65112	−0.614809
$199$	26.8224	1.90139	0.950694	−	0.310129i	$-0.100372\pi$
$199$	26.8224	1.90139	0.950694	+	0.310129i	$0.100372\pi$
$200$	3.37421	0.238592
$201$	11.9525	0.843062
$202$	−10.5321	−0.741037
$203$	−2.45473	−0.172288
$204$	−2.69715	−0.188838
$205$	16.8883	1.17953
$206$	11.9688	0.833904
$207$	1.00000	0.0695048
$208$	18.6868	1.29570
$209$	4.73691	0.327659
$210$	17.6704	1.21938
$211$	9.39698	0.646915	0.323457	−	0.946243i	$-0.395155\pi$
$211$	9.39698	0.646915	0.323457	+	0.946243i	$0.395155\pi$
$212$	8.38580	0.575939
$213$	8.22431	0.563521
$214$	5.86313	0.400795
$215$	22.1002	1.50722
$216$	0.390627	0.0265788
$217$	−6.09230	−0.413572
$218$	25.9316	1.75631
$219$	−10.4723	−0.707652
$220$	29.4954	1.98858
$221$	6.42265	0.432034
$222$	−6.25462	−0.419782
$223$	14.7193	0.985681	0.492840	−	0.870120i	$-0.335959\pi$
$223$	14.7193	0.985681	0.492840	+	0.870120i	$0.335959\pi$
$224$	−18.9475	−1.26598
$225$	8.63793	0.575862
$226$	35.2085	2.34204
$227$	25.3440	1.68214	0.841070	−	0.540927i	$-0.181926\pi$
$227$	25.3440	1.68214	0.841070	+	0.540927i	$0.181926\pi$
$228$	1.92074	0.127204
$229$	22.2652	1.47133	0.735664	−	0.677347i	$-0.236870\pi$
$229$	22.2652	1.47133	0.735664	+	0.677347i	$0.236870\pi$
$230$	−7.19852	−0.474656
$231$	−10.8945	−0.716806
$232$	0.390627	0.0256459
$233$	5.91632	0.387591	0.193796	−	0.981042i	$-0.437920\pi$
$233$	5.91632	0.387591	0.193796	+	0.981042i	$0.437920\pi$
$234$	8.35324	0.546069
$235$	−17.8842	−1.16664
$236$	0.300990	0.0195928
$237$	0.909584	0.0590838
$238$	−7.17135	−0.464850
$239$	15.1516	0.980072	0.490036	−	0.871702i	$-0.336984\pi$
$239$	15.1516	0.980072	0.490036	+	0.871702i	$0.336984\pi$
$240$	−16.1036	−1.03949
$241$	−1.07716	−0.0693858	−0.0346929	−	0.999398i	$-0.511045\pi$
$241$	−1.07716	−0.0693858	−0.0346929	+	0.999398i	$0.511045\pi$
$242$	−16.9533	−1.08980
$243$	1.00000	0.0641500
$244$	23.6470	1.51385
$245$	−3.59802	−0.229869
$246$	−8.91415	−0.568346
$247$	−4.57381	−0.291024
$248$	0.969481	0.0615621
$249$	−4.61155	−0.292245
$250$	−26.1877	−1.65626
$251$	26.7693	1.68966	0.844832	−	0.535032i	$-0.179701\pi$
$251$	26.7693	1.68966	0.844832	+	0.535032i	$0.179701\pi$
$252$	−4.41754	−0.278279
$253$	4.43817	0.279025
$254$	12.8918	0.808906
$255$	−5.53480	−0.346603
$256$	18.7100	1.16937
$257$	−19.8433	−1.23779	−0.618897	−	0.785472i	$-0.712420\pi$
$257$	−19.8433	−1.23779	−0.618897	+	0.785472i	$0.712420\pi$
$258$	−11.6652	−0.726241
$259$	−7.87654	−0.489425
$260$	−28.4798	−1.76624
$261$	1.00000	0.0618984
$262$	21.1824	1.30866
$263$	−16.6065	−1.02400	−0.512002	−	0.858984i	$-0.671096\pi$
$263$	−16.6065	−1.02400	−0.512002	+	0.858984i	$0.671096\pi$
$264$	1.73367	0.106700
$265$	17.2085	1.05711
$266$	5.10699	0.313130
$267$	12.8616	0.787118
$268$	21.5097	1.31391
$269$	−17.7138	−1.08003	−0.540015	−	0.841655i	$-0.681582\pi$
$269$	−17.7138	−1.08003	−0.540015	+	0.841655i	$0.681582\pi$
$270$	−7.19852	−0.438088
$271$	14.0182	0.851544	0.425772	−	0.904830i	$-0.360003\pi$
$271$	14.0182	0.851544	0.425772	+	0.904830i	$0.360003\pi$
$272$	6.53548	0.396272
$273$	10.5194	0.636662
$274$	−37.8953	−2.28934
$275$	38.3366	2.31178
$276$	1.79960	0.108323
$277$	10.0263	0.602425	0.301212	−	0.953557i	$-0.402609\pi$
$277$	10.0263	0.602425	0.301212	+	0.953557i	$0.402609\pi$
$278$	29.0724	1.74364
$279$	2.48186	0.148585
$280$	−3.54112	−0.211622
$281$	−18.4255	−1.09917	−0.549587	−	0.835437i	$-0.685215\pi$
$281$	−18.4255	−1.09917	−0.549587	+	0.835437i	$0.685215\pi$
$282$	9.43982	0.562133
$283$	−25.7278	−1.52936	−0.764680	−	0.644411i	$-0.777103\pi$
$283$	−25.7278	−1.52936	−0.764680	+	0.644411i	$0.777103\pi$
$284$	14.8005	0.878248
$285$	3.94154	0.233477
$286$	37.0731	2.19218
$287$	−11.2257	−0.662635
$288$	7.71875	0.454832
$289$	−14.7538	−0.867868
$290$	−7.19852	−0.422712
$291$	1.88580	0.110548
$292$	−18.8460	−1.10288
$293$	−24.2334	−1.41573	−0.707865	−	0.706348i	$-0.750341\pi$
$293$	−24.2334	−1.41573	−0.707865	+	0.706348i	$0.750341\pi$
$294$	1.89915	0.110760
$295$	0.617660	0.0359616
$296$	1.25341	0.0728531
$297$	4.43817	0.257528
$298$	15.0840	0.873790
$299$	−4.28535	−0.247828
$300$	15.5448	0.897482
$301$	−14.6901	−0.846725
$302$	−25.0867	−1.44357
$303$	5.40314	0.310402
$304$	−4.65416	−0.266935
$305$	48.5260	2.77859
$306$	2.92144	0.167008
$307$	−7.93632	−0.452950	−0.226475	−	0.974017i	$-0.572720\pi$
$307$	−7.93632	−0.452950	−0.226475	+	0.974017i	$0.572720\pi$
$308$	−19.6058	−1.11714
$309$	−6.14017	−0.349302
$310$	−17.8657	−1.01470
$311$	−10.8054	−0.612717	−0.306358	−	0.951916i	$-0.599111\pi$
$311$	−10.8054	−0.612717	−0.306358	+	0.951916i	$0.599111\pi$
$312$	−1.67397	−0.0947700
$313$	−25.0705	−1.41707	−0.708535	−	0.705675i	$-0.750644\pi$
$313$	−25.0705	−1.41707	−0.708535	+	0.705675i	$0.750644\pi$
$314$	−24.6254	−1.38969
$315$	−9.06522	−0.510767
$316$	1.63689	0.0920822
$317$	−14.5292	−0.816041	−0.408021	−	0.912973i	$-0.633781\pi$
$317$	−14.5292	−0.816041	−0.408021	+	0.912973i	$0.633781\pi$
$318$	−9.08316	−0.509358
$319$	4.43817	0.248490
$320$	−23.3563	−1.30566
$321$	−3.00788	−0.167883
$322$	4.78490	0.266652
$323$	−1.59963	−0.0890058
$324$	1.79960	0.0999779
$325$	−37.0165	−2.05331
$326$	17.4824	0.968262
$327$	−13.3033	−0.735674
$328$	1.78638	0.0986361
$329$	11.8877	0.655392
$330$	−31.9482	−1.75869
$331$	−2.56900	−0.141205	−0.0706026	−	0.997505i	$-0.522492\pi$
$331$	−2.56900	−0.141205	−0.0706026	+	0.997505i	$0.522492\pi$
$332$	−8.29895	−0.455464
$333$	3.20872	0.175837
$334$	−25.2651	−1.38245
$335$	44.1399	2.41162
$336$	10.7042	0.583962
$337$	−27.1666	−1.47986	−0.739930	−	0.672683i	$-0.765142\pi$
$337$	−27.1666	−1.47986	−0.739930	+	0.672683i	$0.765142\pi$
$338$	−10.4562	−0.568743
$339$	−18.0625	−0.981022
$340$	−9.96044	−0.540181
$341$	11.0149	0.596490
$342$	−2.08047	−0.112499
$343$	19.5747	1.05694
$344$	2.33767	0.126039
$345$	3.69296	0.198822
$346$	7.84907	0.421968
$347$	24.3805	1.30881	0.654406	−	0.756143i	$-0.272919\pi$
$347$	24.3805	1.30881	0.654406	+	0.756143i	$0.272919\pi$
$348$	1.79960	0.0964688
$349$	−25.6829	−1.37478	−0.687388	−	0.726290i	$-0.741243\pi$
$349$	−25.6829	−1.37478	−0.687388	+	0.726290i	$0.741243\pi$
$350$	41.3317	2.20927
$351$	−4.28535	−0.228735
$352$	34.2571	1.82591
$353$	−27.0213	−1.43820	−0.719100	−	0.694907i	$-0.755445\pi$
$353$	−27.0213	−1.43820	−0.719100	+	0.694907i	$0.755445\pi$
$354$	−0.326020	−0.0173278
$355$	30.3720	1.61198
$356$	23.1458	1.22672
$357$	3.67902	0.194714
$358$	1.10176	0.0582296
$359$	14.3872	0.759326	0.379663	−	0.925125i	$-0.376040\pi$
$359$	14.3872	0.759326	0.379663	+	0.925125i	$0.376040\pi$
$360$	1.44257	0.0760300
$361$	−17.8608	−0.940044
$362$	−28.1320	−1.47859
$363$	8.69731	0.456491
$364$	18.9307	0.992238
$365$	−38.6738	−2.02428
$366$	−25.6135	−1.33884
$367$	13.3059	0.694564	0.347282	−	0.937761i	$-0.387105\pi$
$367$	13.3059	0.694564	0.347282	+	0.937761i	$0.387105\pi$
$368$	−4.36064	−0.227314
$369$	4.57310	0.238066
$370$	−23.0980	−1.20081
$371$	−11.4386	−0.593861
$372$	4.46636	0.231570
$373$	20.9296	1.08370	0.541848	−	0.840477i	$-0.317725\pi$
$373$	20.9296	1.08370	0.541848	+	0.840477i	$0.317725\pi$
$374$	12.9658	0.670447
$375$	13.4347	0.693766
$376$	−1.89172	−0.0975580
$377$	−4.28535	−0.220707
$378$	4.78490	0.246109
$379$	17.6614	0.907206	0.453603	−	0.891204i	$-0.350138\pi$
$379$	17.6614	0.907206	0.453603	+	0.891204i	$0.350138\pi$
$380$	7.09321	0.363874
$381$	−6.61372	−0.338831
$382$	21.6921	1.10987
$383$	−24.2702	−1.24015	−0.620076	−	0.784542i	$-0.712898\pi$
$383$	−24.2702	−1.24015	−0.620076	+	0.784542i	$0.712898\pi$
$384$	−3.10933	−0.158672
$385$	−40.2329	−2.05046
$386$	35.1055	1.78682
$387$	5.98441	0.304205
$388$	3.39370	0.172289
$389$	−17.6760	−0.896208	−0.448104	−	0.893981i	$-0.647901\pi$
$389$	−17.6760	−0.896208	−0.448104	+	0.893981i	$0.647901\pi$
$390$	30.8482	1.56206
$391$	−1.49875	−0.0757948
$392$	−0.380585	−0.0192224
$393$	−10.8669	−0.548164
$394$	−43.7161	−2.20238
$395$	3.35905	0.169012
$396$	7.98693	0.401358
$397$	−1.88374	−0.0945421	−0.0472711	−	0.998882i	$-0.515052\pi$
$397$	−1.88374	−0.0945421	−0.0472711	+	0.998882i	$0.515052\pi$
$398$	−52.2837	−2.62075
$399$	−2.61997	−0.131162
$400$	−37.6669	−1.88334
$401$	21.3807	1.06770	0.533849	−	0.845580i	$-0.320745\pi$
$401$	21.3807	1.06770	0.533849	+	0.845580i	$0.320745\pi$
$402$	−23.2984	−1.16202
$403$	−10.6356	−0.529798
$404$	9.72351	0.483763
$405$	3.69296	0.183505
$406$	4.78490	0.237471
$407$	14.2408	0.705891
$408$	−0.585450	−0.0289841
$409$	−23.6232	−1.16809	−0.584045	−	0.811721i	$-0.698531\pi$
$409$	−23.6232	−1.16809	−0.584045	+	0.811721i	$0.698531\pi$
$410$	−32.9196	−1.62578
$411$	19.4409	0.958949
$412$	−11.0499	−0.544388
$413$	−0.410563	−0.0202025
$414$	−1.94926	−0.0958007
$415$	−17.0302	−0.835982
$416$	−33.0775	−1.62176
$417$	−14.9146	−0.730371
$418$	−9.23346	−0.451623
$419$	8.32610	0.406757	0.203378	−	0.979100i	$-0.434808\pi$
$419$	8.32610	0.406757	0.203378	+	0.979100i	$0.434808\pi$
$420$	−16.3138	−0.796031
$421$	12.2050	0.594835	0.297417	−	0.954748i	$-0.403875\pi$
$421$	12.2050	0.594835	0.297417	+	0.954748i	$0.403875\pi$
$422$	−18.3171	−0.891663
$423$	−4.84278	−0.235464
$424$	1.82024	0.0883989
$425$	−12.9461	−0.627976
$426$	−16.0313	−0.776719
$427$	−32.2555	−1.56095
$428$	−5.41299	−0.261647
$429$	−19.0191	−0.918250
$430$	−43.0789	−2.07745
$431$	−0.126584	−0.00609733	−0.00304867	−	0.999995i	$-0.500970\pi$
$431$	−0.126584	−0.00609733	−0.00304867	+	0.999995i	$0.500970\pi$
$432$	−4.36064	−0.209801
$433$	32.4809	1.56093	0.780467	−	0.625197i	$-0.214981\pi$
$433$	32.4809	1.56093	0.780467	+	0.625197i	$0.214981\pi$
$434$	11.8755	0.570040
$435$	3.69296	0.177064
$436$	−23.9407	−1.14655
$437$	1.06731	0.0510565
$438$	20.4132	0.975381
$439$	28.2416	1.34790	0.673950	−	0.738777i	$-0.264596\pi$
$439$	28.2416	1.34790	0.673950	+	0.738777i	$0.264596\pi$
$440$	6.40235	0.305220
$441$	−0.974292	−0.0463949
$442$	−12.5194	−0.595486
$443$	−7.98359	−0.379312	−0.189656	−	0.981851i	$-0.560737\pi$
$443$	−7.98359	−0.379312	−0.189656	+	0.981851i	$0.560737\pi$
$444$	5.77442	0.274042
$445$	47.4974	2.25159
$446$	−28.6918	−1.35860
$447$	−7.73831	−0.366010
$448$	15.5251	0.733490
$449$	−21.4781	−1.01361	−0.506807	−	0.862059i	$-0.669174\pi$
$449$	−21.4781	−1.01361	−0.506807	+	0.862059i	$0.669174\pi$
$450$	−16.8375	−0.793730
$451$	20.2962	0.955710
$452$	−32.5054	−1.52892
$453$	12.8699	0.604679
$454$	−49.4019	−2.31855
$455$	38.8476	1.82120
$456$	0.416921	0.0195241
$457$	−15.5058	−0.725332	−0.362666	−	0.931919i	$-0.618133\pi$
$457$	−15.5058	−0.725332	−0.362666	+	0.931919i	$0.618133\pi$
$458$	−43.4006	−2.02798
$459$	−1.49875	−0.0699555
$460$	6.64585	0.309865
$461$	−39.6350	−1.84599	−0.922993	−	0.384817i	$-0.874265\pi$
$461$	−39.6350	−1.84599	−0.922993	+	0.384817i	$0.874265\pi$
$462$	21.2362	0.987997
$463$	−0.779361	−0.0362200	−0.0181100	−	0.999836i	$-0.505765\pi$
$463$	−0.779361	−0.0362200	−0.0181100	+	0.999836i	$0.505765\pi$
$464$	−4.36064	−0.202437
$465$	9.16540	0.425035
$466$	−11.5324	−0.534230
$467$	26.1858	1.21173	0.605867	−	0.795566i	$-0.292826\pi$
$467$	26.1858	1.21173	0.605867	+	0.795566i	$0.292826\pi$
$468$	−7.71192	−0.356484
$469$	−29.3401	−1.35480
$470$	34.8609	1.60801
$471$	12.6332	0.582108
$472$	0.0653337	0.00300723
$473$	26.5598	1.22122
$474$	−1.77301	−0.0814372
$475$	9.21938	0.423014
$476$	6.62077	0.303462
$477$	4.65981	0.213358
$478$	−29.5343	−1.35087
$479$	15.1362	0.691589	0.345794	−	0.938310i	$-0.387610\pi$
$479$	15.1362	0.691589	0.345794	+	0.938310i	$0.387610\pi$
$480$	28.5050	1.30107
$481$	−13.7505	−0.626968
$482$	2.09966	0.0956367
$483$	−2.45473	−0.111694
$484$	15.6517	0.711441
$485$	6.96419	0.316228
$486$	−1.94926	−0.0884201
$487$	27.2117	1.23308	0.616540	−	0.787323i	$-0.288534\pi$
$487$	27.2117	1.23308	0.616540	+	0.787323i	$0.288534\pi$
$488$	5.13289	0.232355
$489$	−8.96876	−0.405581
$490$	7.01346	0.316836
$491$	−35.7369	−1.61279	−0.806393	−	0.591380i	$-0.798583\pi$
$491$	−35.7369	−1.61279	−0.806393	+	0.591380i	$0.798583\pi$
$492$	8.22977	0.371027
$493$	−1.49875	−0.0675001
$494$	8.91552	0.401128
$495$	16.3900	0.736674
$496$	−10.8225	−0.485944
$497$	−20.1885	−0.905577
$498$	8.98909	0.402811
$499$	−2.79653	−0.125190	−0.0625950	−	0.998039i	$-0.519938\pi$
$499$	−2.79653	−0.125190	−0.0625950	+	0.998039i	$0.519938\pi$
$500$	24.1772	1.08124
$501$	12.9614	0.579074
$502$	−52.1802	−2.32892
$503$	−1.52256	−0.0678877	−0.0339438	−	0.999424i	$-0.510807\pi$
$503$	−1.52256	−0.0678877	−0.0339438	+	0.999424i	$0.510807\pi$
$504$	−0.958884	−0.0427121
$505$	19.9536	0.887922
$506$	−8.65112	−0.384589
$507$	5.36420	0.238233
$508$	−11.9021	−0.528069
$509$	−20.7212	−0.918449	−0.459225	−	0.888320i	$-0.651873\pi$
$509$	−20.7212	−0.918449	−0.459225	+	0.888320i	$0.651873\pi$
$510$	10.7888	0.477734
$511$	25.7067	1.13720
$512$	−30.2519	−1.33696
$513$	1.06731	0.0471230
$514$	38.6798	1.70609
$515$	−22.6754	−0.999197
$516$	10.7696	0.474104
$517$	−21.4931	−0.945264
$518$	15.3534	0.674590
$519$	−4.02670	−0.176752
$520$	−6.18190	−0.271094
$521$	−38.9143	−1.70486	−0.852432	−	0.522837i	$-0.824873\pi$
$521$	−38.9143	−1.70486	−0.852432	+	0.522837i	$0.824873\pi$
$522$	−1.94926	−0.0853167
$523$	−23.1164	−1.01081	−0.505405	−	0.862882i	$-0.668657\pi$
$523$	−23.1164	−1.01081	−0.505405	+	0.862882i	$0.668657\pi$
$524$	−19.5562	−0.854314
$525$	−21.2038	−0.925410
$526$	32.3704	1.41142
$527$	−3.71968	−0.162032
$528$	−19.3532	−0.842241
$529$	1.00000	0.0434783
$530$	−33.5437	−1.45705
$531$	0.167254	0.00725819
$532$	−4.71490	−0.204417
$533$	−19.5973	−0.848855
$534$	−25.0706	−1.08491
$535$	−11.1080	−0.480239
$536$	4.66895	0.201668
$537$	−0.565219	−0.0243910
$538$	34.5288	1.48864
$539$	−4.32407	−0.186251
$540$	6.64585	0.285992
$541$	−1.05558	−0.0453827	−0.0226914	−	0.999743i	$-0.507224\pi$
$541$	−1.05558	−0.0453827	−0.0226914	+	0.999743i	$0.507224\pi$
$542$	−27.3250	−1.17371
$543$	14.4322	0.619344
$544$	−11.5684	−0.495993
$545$	−49.1285	−2.10444
$546$	−20.5050	−0.877532
$547$	12.3543	0.528231	0.264115	−	0.964491i	$-0.414920\pi$
$547$	12.3543	0.528231	0.264115	+	0.964491i	$0.414920\pi$
$548$	34.9859	1.49452
$549$	13.1401	0.560808
$550$	−74.7278	−3.18640
$551$	1.06731	0.0454691
$552$	0.390627	0.0166262
$553$	−2.23278	−0.0949477
$554$	−19.5439	−0.830342
$555$	11.8497	0.502990
$556$	−26.8403	−1.13828
$557$	37.8043	1.60182	0.800909	−	0.598786i	$-0.204350\pi$
$557$	37.8043	1.60182	0.800909	+	0.598786i	$0.204350\pi$
$558$	−4.83778	−0.204800
$559$	−25.6453	−1.08468
$560$	39.5301	1.67045
$561$	−6.65168	−0.280834
$562$	35.9161	1.51503
$563$	−5.16163	−0.217537	−0.108768	−	0.994067i	$-0.534691\pi$
$563$	−5.16163	−0.217537	−0.108768	+	0.994067i	$0.534691\pi$
$564$	−8.71508	−0.366971
$565$	−66.7042	−2.80627
$566$	50.1501	2.10797
$567$	−2.45473	−0.103089
$568$	3.21264	0.134799
$569$	−3.91406	−0.164086	−0.0820429	−	0.996629i	$-0.526144\pi$
$569$	−3.91406	−0.164086	−0.0820429	+	0.996629i	$0.526144\pi$
$570$	−7.68308	−0.321809
$571$	−30.6511	−1.28271	−0.641355	−	0.767245i	$-0.721627\pi$
$571$	−30.6511	−1.28271	−0.641355	+	0.767245i	$0.721627\pi$
$572$	−34.2268	−1.43109
$573$	−11.1284	−0.464896
$574$	21.8819	0.913331
$575$	8.63793	0.360227
$576$	−6.32455	−0.263523
$577$	−39.4740	−1.64333	−0.821663	−	0.569974i	$-0.806953\pi$
$577$	−39.4740	−1.64333	−0.821663	+	0.569974i	$0.806953\pi$
$578$	28.7589	1.19621
$579$	−18.0097	−0.748457
$580$	6.64585	0.275954
$581$	11.3201	0.469637
$582$	−3.67591	−0.152372
$583$	20.6810	0.856519
$584$	−4.09076	−0.169277
$585$	−15.8256	−0.654308
$586$	47.2371	1.95135
$587$	3.03610	0.125313	0.0626567	−	0.998035i	$-0.480043\pi$
$587$	3.03610	0.125313	0.0626567	+	0.998035i	$0.480043\pi$
$588$	−1.75334	−0.0723064
$589$	2.64892	0.109147
$590$	−1.20398	−0.0495670
$591$	22.4270	0.922525
$592$	−13.9921	−0.575070
$593$	−18.8795	−0.775289	−0.387644	−	0.921809i	$-0.626711\pi$
$593$	−18.8795	−0.775289	−0.387644	+	0.921809i	$0.626711\pi$
$594$	−8.65112	−0.354960
$595$	13.5865	0.556990
$596$	−13.9259	−0.570426
$597$	26.8224	1.09777
$598$	8.35324	0.341589
$599$	−12.7183	−0.519657	−0.259828	−	0.965655i	$-0.583666\pi$
$599$	−12.7183	−0.519657	−0.259828	+	0.965655i	$0.583666\pi$
$600$	3.37421	0.137751
$601$	13.5436	0.552456	0.276228	−	0.961092i	$-0.410916\pi$
$601$	13.5436	0.552456	0.276228	+	0.961092i	$0.410916\pi$
$602$	28.6348	1.16707
$603$	11.9525	0.486742
$604$	23.1606	0.942392
$605$	32.1188	1.30581
$606$	−10.5321	−0.427838
$607$	−24.2819	−0.985573	−0.492786	−	0.870150i	$-0.664022\pi$
$607$	−24.2819	−0.985573	−0.492786	+	0.870150i	$0.664022\pi$
$608$	8.23832	0.334108
$609$	−2.45473	−0.0994708
$610$	−94.5896	−3.82982
$611$	20.7530	0.839576
$612$	−2.69715	−0.109026
$613$	39.0334	1.57654	0.788272	−	0.615327i	$-0.210976\pi$
$613$	39.0334	1.57654	0.788272	+	0.615327i	$0.210976\pi$
$614$	15.4699	0.624315
$615$	16.8883	0.681001
$616$	−4.25569	−0.171466
$617$	0.677906	0.0272915	0.0136457	−	0.999907i	$-0.495656\pi$
$617$	0.677906	0.0272915	0.0136457	+	0.999907i	$0.495656\pi$
$618$	11.9688	0.481455
$619$	−14.0270	−0.563794	−0.281897	−	0.959445i	$-0.590964\pi$
$619$	−14.0270	−0.563794	−0.281897	+	0.959445i	$0.590964\pi$
$620$	16.4941	0.662418
$621$	1.00000	0.0401286
$622$	21.0625	0.844527
$623$	−31.5718	−1.26490
$624$	18.6868	0.748072
$625$	6.42419	0.256968
$626$	48.8689	1.95319
$627$	4.73691	0.189174
$628$	22.7348	0.907216
$629$	−4.80905	−0.191749
$630$	17.6704	0.704007
$631$	−3.52595	−0.140366	−0.0701829	−	0.997534i	$-0.522358\pi$
$631$	−3.52595	−0.140366	−0.0701829	+	0.997534i	$0.522358\pi$
$632$	0.355308	0.0141334
$633$	9.39698	0.373496
$634$	28.3211	1.12478
$635$	−24.4242	−0.969245
$636$	8.38580	0.332518
$637$	4.17518	0.165427
$638$	−8.65112	−0.342501
$639$	8.22431	0.325349
$640$	−11.4826	−0.453890
$641$	−32.2414	−1.27346	−0.636729	−	0.771088i	$-0.719713\pi$
$641$	−32.2414	−1.27346	−0.636729	+	0.771088i	$0.719713\pi$
$642$	5.86313	0.231399
$643$	15.2087	0.599772	0.299886	−	0.953975i	$-0.403051\pi$
$643$	15.2087	0.599772	0.299886	+	0.953975i	$0.403051\pi$
$644$	−4.41754	−0.174075
$645$	22.1002	0.870194
$646$	3.11809	0.122680
$647$	−8.38839	−0.329781	−0.164891	−	0.986312i	$-0.552727\pi$
$647$	−8.38839	−0.329781	−0.164891	+	0.986312i	$0.552727\pi$
$648$	0.390627	0.0153453
$649$	0.742299	0.0291378
$650$	72.1547	2.83014
$651$	−6.09230	−0.238776
$652$	−16.1402	−0.632099
$653$	3.35936	0.131462	0.0657309	−	0.997837i	$-0.479062\pi$
$653$	3.35936	0.131462	0.0657309	+	0.997837i	$0.479062\pi$
$654$	25.9316	1.01400
$655$	−40.1311	−1.56805
$656$	−19.9416	−0.778590
$657$	−10.4723	−0.408563
$658$	−23.1722	−0.903348
$659$	−21.5018	−0.837591	−0.418796	−	0.908080i	$-0.637548\pi$
$659$	−21.5018	−0.837591	−0.418796	+	0.908080i	$0.637548\pi$
$660$	29.4954	1.14811
$661$	20.8099	0.809412	0.404706	−	0.914447i	$-0.367374\pi$
$661$	20.8099	0.809412	0.404706	+	0.914447i	$0.367374\pi$
$662$	5.00764	0.194628
$663$	6.42265	0.249435
$664$	−1.80139	−0.0699076
$665$	−9.67543	−0.375197
$666$	−6.25462	−0.242361
$667$	1.00000	0.0387202
$668$	23.3254	0.902487
$669$	14.7193	0.569083
$670$	−86.0401	−3.32402
$671$	58.3181	2.25135
$672$	−18.9475	−0.730914
$673$	−11.9922	−0.462267	−0.231133	−	0.972922i	$-0.574243\pi$
$673$	−11.9922	−0.462267	−0.231133	+	0.972922i	$0.574243\pi$
$674$	52.9547	2.03974
$675$	8.63793	0.332474
$676$	9.65343	0.371286
$677$	−40.8268	−1.56910	−0.784551	−	0.620064i	$-0.787107\pi$
$677$	−40.8268	−1.56910	−0.784551	+	0.620064i	$0.787107\pi$
$678$	35.2085	1.35218
$679$	−4.62914	−0.177650
$680$	−2.16204	−0.0829105
$681$	25.3440	0.971184
$682$	−21.4709	−0.822162
$683$	23.2310	0.888909	0.444454	−	0.895801i	$-0.353398\pi$
$683$	23.2310	0.888909	0.444454	+	0.895801i	$0.353398\pi$
$684$	1.92074	0.0734413
$685$	71.7944	2.74312
$686$	−38.1562	−1.45681
$687$	22.2652	0.849471
$688$	−26.0958	−0.994895
$689$	−19.9689	−0.760754
$690$	−7.19852	−0.274043
$691$	−5.77244	−0.219594	−0.109797	−	0.993954i	$-0.535020\pi$
$691$	−5.77244	−0.219594	−0.109797	+	0.993954i	$0.535020\pi$
$692$	−7.24645	−0.275469
$693$	−10.8945	−0.413848
$694$	−47.5238	−1.80398
$695$	−55.0789	−2.08926
$696$	0.390627	0.0148067
$697$	−6.85392	−0.259611
$698$	50.0627	1.89490
$699$	5.91632	0.223776
$700$	−38.1584	−1.44225
$701$	0.668564	0.0252513	0.0126256	−	0.999920i	$-0.495981\pi$
$701$	0.668564	0.0252513	0.0126256	+	0.999920i	$0.495981\pi$
$702$	8.35324	0.315273
$703$	3.42471	0.129165
$704$	−28.0694	−1.05790
$705$	−17.8842	−0.673557
$706$	52.6715	1.98232
$707$	−13.2633	−0.498816
$708$	0.300990	0.0113119
$709$	−8.21463	−0.308507	−0.154253	−	0.988031i	$-0.549297\pi$
$709$	−8.21463	−0.308507	−0.154253	+	0.988031i	$0.549297\pi$
$710$	−59.2029	−2.22185
$711$	0.909584	0.0341121
$712$	5.02409	0.188286
$713$	2.48186	0.0929464
$714$	−7.17135	−0.268381
$715$	−70.2366	−2.62670
$716$	−1.01717	−0.0380134
$717$	15.1516	0.565845
$718$	−28.0443	−1.04660
$719$	21.6313	0.806710	0.403355	−	0.915044i	$-0.367844\pi$
$719$	21.6313	0.806710	0.403355	+	0.915044i	$0.367844\pi$
$720$	−16.1036	−0.600147
$721$	15.0725	0.561329
$722$	34.8154	1.29569
$723$	−1.07716	−0.0400599
$724$	25.9722	0.965249
$725$	8.63793	0.320805
$726$	−16.9533	−0.629196
$727$	−19.4681	−0.722031	−0.361016	−	0.932560i	$-0.617570\pi$
$727$	−19.4681	−0.722031	−0.361016	+	0.932560i	$0.617570\pi$
$728$	4.10915	0.152295
$729$	1.00000	0.0370370
$730$	75.3851	2.79013
$731$	−8.96911	−0.331735
$732$	23.6470	0.874020
$733$	−43.4969	−1.60659	−0.803297	−	0.595578i	$-0.796923\pi$
$733$	−43.4969	−1.60659	−0.803297	+	0.595578i	$0.796923\pi$
$734$	−25.9367	−0.957340
$735$	−3.59802	−0.132715
$736$	7.71875	0.284517
$737$	53.0470	1.95401
$738$	−8.91415	−0.328134
$739$	6.06700	0.223178	0.111589	−	0.993754i	$-0.464406\pi$
$739$	6.06700	0.223178	0.111589	+	0.993754i	$0.464406\pi$
$740$	21.3247	0.783911
$741$	−4.57381	−0.168023
$742$	22.2967	0.818538
$743$	9.80597	0.359746	0.179873	−	0.983690i	$-0.442431\pi$
$743$	9.80597	0.359746	0.179873	+	0.983690i	$0.442431\pi$
$744$	0.969481	0.0355429
$745$	−28.5773	−1.04699
$746$	−40.7972	−1.49369
$747$	−4.61155	−0.168728
$748$	−11.9704	−0.437680
$749$	7.38354	0.269789
$750$	−26.1877	−0.956240
$751$	−17.4182	−0.635599	−0.317799	−	0.948158i	$-0.602944\pi$
$751$	−17.4182	−0.635599	−0.317799	+	0.948158i	$0.602944\pi$
$752$	21.1176	0.770080
$753$	26.7693	0.975528
$754$	8.35324	0.304207
$755$	47.5278	1.72971
$756$	−4.41754	−0.160664
$757$	6.99421	0.254209	0.127104	−	0.991889i	$-0.459432\pi$
$757$	6.99421	0.254209	0.127104	+	0.991889i	$0.459432\pi$
$758$	−34.4266	−1.25043
$759$	4.43817	0.161095
$760$	1.53967	0.0558498
$761$	−22.9466	−0.831813	−0.415906	−	0.909407i	$-0.636536\pi$
$761$	−22.9466	−0.831813	−0.415906	+	0.909407i	$0.636536\pi$
$762$	12.8918	0.467022
$763$	32.6560	1.18223
$764$	−20.0267	−0.724541
$765$	−5.53480	−0.200111
$766$	47.3089	1.70934
$767$	−0.716740	−0.0258800
$768$	18.7100	0.675138
$769$	−12.9447	−0.466798	−0.233399	−	0.972381i	$-0.574985\pi$
$769$	−12.9447	−0.466798	−0.233399	+	0.972381i	$0.574985\pi$
$770$	78.4243	2.82622
$771$	−19.8433	−0.714641
$772$	−32.4103	−1.16647
$773$	25.9962	0.935020	0.467510	−	0.883988i	$-0.345151\pi$
$773$	25.9962	0.935020	0.467510	+	0.883988i	$0.345151\pi$
$774$	−11.6652	−0.419295
$775$	21.4381	0.770080
$776$	0.736645	0.0264440
$777$	−7.87654	−0.282569
$778$	34.4550	1.23527
$779$	4.88093	0.174878
$780$	−28.4798	−1.01974
$781$	36.5009	1.30610
$782$	2.92144	0.104470
$783$	1.00000	0.0357371
$784$	4.24853	0.151733
$785$	46.6539	1.66515
$786$	21.1824	0.755553
$787$	55.5880	1.98150	0.990750	−	0.135701i	$-0.0433286\pi$
$787$	55.5880	1.98150	0.990750	+	0.135701i	$0.0433286\pi$
$788$	40.3597	1.43776
$789$	−16.6065	−0.591209
$790$	−6.54766	−0.232955
$791$	44.3387	1.57650
$792$	1.73367	0.0616031
$793$	−56.3101	−1.99963
$794$	3.67189	0.130311
$795$	17.2085	0.610321
$796$	48.2696	1.71087
$797$	−4.13366	−0.146422	−0.0732110	−	0.997316i	$-0.523325\pi$
$797$	−4.13366	−0.146422	−0.0732110	+	0.997316i	$0.523325\pi$
$798$	5.10699	0.180785
$799$	7.25810	0.256773
$800$	66.6740	2.35728
$801$	12.8616	0.454443
$802$	−41.6764	−1.47164
$803$	−46.4778	−1.64017
$804$	21.5097	0.758588
$805$	−9.06522	−0.319507
$806$	20.7316	0.730239
$807$	−17.7138	−0.623556
$808$	2.11061	0.0742511
$809$	27.6896	0.973514	0.486757	−	0.873537i	$-0.338180\pi$
$809$	27.6896	0.973514	0.486757	+	0.873537i	$0.338180\pi$
$810$	−7.19852	−0.252930
$811$	−1.07695	−0.0378168	−0.0189084	−	0.999821i	$-0.506019\pi$
$811$	−1.07695	−0.0378168	−0.0189084	+	0.999821i	$0.506019\pi$
$812$	−4.41754	−0.155025
$813$	14.0182	0.491639
$814$	−27.7590	−0.972953
$815$	−33.1213	−1.16019
$816$	6.53548	0.228788
$817$	6.38724	0.223461
$818$	46.0476	1.61002
$819$	10.5194	0.367577
$820$	30.3922	1.06134
$821$	41.8221	1.45960	0.729800	−	0.683660i	$-0.239613\pi$
$821$	41.8221	1.45960	0.729800	+	0.683660i	$0.239613\pi$
$822$	−37.8953	−1.32175
$823$	−16.1258	−0.562109	−0.281055	−	0.959692i	$-0.590684\pi$
$823$	−16.1258	−0.562109	−0.281055	+	0.959692i	$0.590684\pi$
$824$	−2.39852	−0.0835563
$825$	38.3366	1.33471
$826$	0.800292	0.0278457
$827$	−19.5277	−0.679046	−0.339523	−	0.940598i	$-0.610266\pi$
$827$	−19.5277	−0.679046	−0.339523	+	0.940598i	$0.610266\pi$
$828$	1.79960	0.0625405
$829$	−21.6037	−0.750327	−0.375163	−	0.926959i	$-0.622413\pi$
$829$	−21.6037	−0.750327	−0.375163	+	0.926959i	$0.622413\pi$
$830$	33.1963	1.15226
$831$	10.0263	0.347810
$832$	27.1029	0.939623
$833$	1.46022	0.0505935
$834$	29.0724	1.00669
$835$	47.8660	1.65647
$836$	8.52456	0.294828
$837$	2.48186	0.0857856
$838$	−16.2297	−0.560646
$839$	−41.4413	−1.43071	−0.715357	−	0.698759i	$-0.753736\pi$
$839$	−41.4413	−1.43071	−0.715357	+	0.698759i	$0.753736\pi$
$840$	−3.54112	−0.122180
$841$	1.00000	0.0344828
$842$	−23.7907	−0.819880
$843$	−18.4255	−0.634608
$844$	16.9108	0.582094
$845$	19.8098	0.681477
$846$	9.43982	0.324548
$847$	−21.3496	−0.733580
$848$	−20.3197	−0.697782
$849$	−25.7278	−0.882976
$850$	25.2352	0.865560
$851$	3.20872	0.109993
$852$	14.8005	0.507057
$853$	−6.19307	−0.212047	−0.106023	−	0.994364i	$-0.533812\pi$
$853$	−6.19307	−0.212047	−0.106023	+	0.994364i	$0.533812\pi$
$854$	62.8743	2.15152
$855$	3.94154	0.134798
$856$	−1.17496	−0.0401592
$857$	−46.6836	−1.59468	−0.797340	−	0.603530i	$-0.793760\pi$
$857$	−46.6836	−1.59468	−0.797340	+	0.603530i	$0.793760\pi$
$858$	37.0731	1.26565
$859$	34.7061	1.18416	0.592079	−	0.805880i	$-0.298307\pi$
$859$	34.7061	1.18416	0.592079	+	0.805880i	$0.298307\pi$
$860$	39.7715	1.35620
$861$	−11.2257	−0.382572
$862$	0.246745	0.00840416
$863$	11.5543	0.393312	0.196656	−	0.980473i	$-0.436992\pi$
$863$	11.5543	0.393312	0.196656	+	0.980473i	$0.436992\pi$
$864$	7.71875	0.262597
$865$	−14.8704	−0.505609
$866$	−63.3137	−2.15149
$867$	−14.7538	−0.501064
$868$	−10.9637	−0.372133
$869$	4.03688	0.136942
$870$	−7.19852	−0.244053
$871$	−51.2205	−1.73554
$872$	−5.19663	−0.175980
$873$	1.88580	0.0638248
$874$	−2.08047	−0.0703729
$875$	−32.9786	−1.11488
$876$	−18.8460	−0.636746
$877$	29.6949	1.00273	0.501363	−	0.865237i	$-0.332832\pi$
$877$	29.6949	1.00273	0.501363	+	0.865237i	$0.332832\pi$
$878$	−55.0502	−1.85785
$879$	−24.2334	−0.817372
$880$	−71.4706	−2.40927
$881$	−2.14823	−0.0723756	−0.0361878	−	0.999345i	$-0.511521\pi$
$881$	−2.14823	−0.0723756	−0.0361878	+	0.999345i	$0.511521\pi$
$882$	1.89915	0.0639476
$883$	12.0264	0.404720	0.202360	−	0.979311i	$-0.435139\pi$
$883$	12.0264	0.404720	0.202360	+	0.979311i	$0.435139\pi$
$884$	11.5582	0.388745
$885$	0.617660	0.0207624
$886$	15.5621	0.522818
$887$	−47.0278	−1.57904	−0.789520	−	0.613725i	$-0.789671\pi$
$887$	−47.0278	−1.57904	−0.789520	+	0.613725i	$0.789671\pi$
$888$	1.25341	0.0420617
$889$	16.2349	0.544502
$890$	−92.5846	−3.10344
$891$	4.43817	0.148684
$892$	26.4890	0.886916
$893$	−5.16876	−0.172966
$894$	15.0840	0.504483
$895$	−2.08733	−0.0697717
$896$	7.63256	0.254986
$897$	−4.28535	−0.143084
$898$	41.8663	1.39710
$899$	2.48186	0.0827747
$900$	15.5448	0.518161
$901$	−6.98386	−0.232666
$902$	−39.5625	−1.31729
$903$	−14.6901	−0.488857
$904$	−7.05571	−0.234669
$905$	53.2974	1.77167
$906$	−25.0867	−0.833448
$907$	35.1405	1.16682	0.583411	−	0.812177i	$-0.301718\pi$
$907$	35.1405	1.16682	0.583411	+	0.812177i	$0.301718\pi$
$908$	45.6091	1.51359
$909$	5.40314	0.179211
$910$	−75.7240	−2.51023
$911$	43.8758	1.45367	0.726835	−	0.686812i	$-0.240990\pi$
$911$	43.8758	1.45367	0.726835	+	0.686812i	$0.240990\pi$
$912$	−4.65416	−0.154115
$913$	−20.4668	−0.677353
$914$	30.2249	0.999749
$915$	48.5260	1.60422
$916$	40.0685	1.32390
$917$	26.6754	0.880899
$918$	2.92144	0.0964219
$919$	−45.6219	−1.50493	−0.752463	−	0.658634i	$-0.771135\pi$
$919$	−45.6219	−1.50493	−0.752463	+	0.658634i	$0.771135\pi$
$920$	1.44257	0.0475600
$921$	−7.93632	−0.261511
$922$	77.2588	2.54438
$923$	−35.2440	−1.16007
$924$	−19.6058	−0.644983
$925$	27.7167	0.911319
$926$	1.51918	0.0499232
$927$	−6.14017	−0.201670
$928$	7.71875	0.253380
$929$	30.1167	0.988096	0.494048	−	0.869435i	$-0.335517\pi$
$929$	30.1167	0.988096	0.494048	+	0.869435i	$0.335517\pi$
$930$	−17.8657	−0.585840
$931$	−1.03987	−0.0340805
$932$	10.6470	0.348755
$933$	−10.8054	−0.353752
$934$	−51.0428	−1.67017
$935$	−24.5644	−0.803341
$936$	−1.67397	−0.0547155
$937$	−57.7787	−1.88755	−0.943773	−	0.330594i	$-0.892751\pi$
$937$	−57.7787	−1.88755	−0.943773	+	0.330594i	$0.892751\pi$
$938$	57.1914	1.86736
$939$	−25.0705	−0.818146
$940$	−32.1844	−1.04974
$941$	4.84815	0.158045	0.0790226	−	0.996873i	$-0.474820\pi$
$941$	4.84815	0.158045	0.0790226	+	0.996873i	$0.474820\pi$
$942$	−24.6254	−0.802338
$943$	4.57310	0.148921
$944$	−0.729332	−0.0237377
$945$	−9.06522	−0.294892
$946$	−51.7719	−1.68325
$947$	−24.7151	−0.803134	−0.401567	−	0.915830i	$-0.631534\pi$
$947$	−24.7151	−0.803134	−0.401567	+	0.915830i	$0.631534\pi$
$948$	1.63689	0.0531637
$949$	44.8774	1.45678
$950$	−17.9709	−0.583054
$951$	−14.5292	−0.471142
$952$	1.43712	0.0465774
$953$	32.7211	1.05994	0.529970	−	0.848016i	$-0.322203\pi$
$953$	32.7211	1.05994	0.529970	+	0.848016i	$0.322203\pi$
$954$	−9.08316	−0.294078
$955$	−41.0967	−1.32986
$956$	27.2668	0.881870
$957$	4.43817	0.143466
$958$	−29.5043	−0.953239
$959$	−47.7222	−1.54103
$960$	−23.3563	−0.753821
$961$	−24.8404	−0.801302
$962$	26.8032	0.864170
$963$	−3.00788	−0.0969275
$964$	−1.93845	−0.0624334
$965$	−66.5090	−2.14100
$966$	4.78490	0.153952
$967$	−37.3079	−1.19974	−0.599870	−	0.800097i	$-0.704781\pi$
$967$	−37.3079	−1.19974	−0.599870	+	0.800097i	$0.704781\pi$
$968$	3.39740	0.109197
$969$	−1.59963	−0.0513875
$970$	−13.5750	−0.435867
$971$	27.8228	0.892876	0.446438	−	0.894815i	$-0.352692\pi$
$971$	27.8228	0.892876	0.446438	+	0.894815i	$0.352692\pi$
$972$	1.79960	0.0577223
$973$	36.6113	1.17371
$974$	−53.0426	−1.69960
$975$	−37.0165	−1.18548
$976$	−57.2994	−1.83411
$977$	−54.0284	−1.72852	−0.864260	−	0.503045i	$-0.832213\pi$
$977$	−54.0284	−1.72852	−0.864260	+	0.503045i	$0.832213\pi$
$978$	17.4824	0.559026
$979$	57.0820	1.82435
$980$	−6.47500	−0.206836
$981$	−13.3033	−0.424742
$982$	69.6605	2.22296
$983$	−15.2109	−0.485154	−0.242577	−	0.970132i	$-0.577993\pi$
$983$	−15.2109	−0.485154	−0.242577	+	0.970132i	$0.577993\pi$
$984$	1.78638	0.0569476
$985$	82.8221	2.63893
$986$	2.92144	0.0930376
$987$	11.8877	0.378391
$988$	−8.23103	−0.261864
$989$	5.98441	0.190293
$990$	−31.9482	−1.01538
$991$	1.74186	0.0553321	0.0276660	−	0.999617i	$-0.491193\pi$
$991$	1.74186	0.0553321	0.0276660	+	0.999617i	$0.491193\pi$
$992$	19.1568	0.608230
$993$	−2.56900	−0.0815248
$994$	39.3525	1.24819
$995$	99.0539	3.14022
$996$	−8.29895	−0.262962
$997$	−16.9495	−0.536797	−0.268398	−	0.963308i	$-0.586494\pi$
$997$	−16.9495	−0.536797	−0.268398	+	0.963308i	$0.586494\pi$
$998$	5.45116	0.172553
$999$	3.20872	0.101519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.o.1.5	✓	20
3.2	odd	2		6003.2.a.s.1.16		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.o.1.5	✓	20	1.1	even	1	trivial
6003.2.a.s.1.16		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)

\(f(q)\)	\(=\)	\(q-1.94926 q^{2} +1.00000 q^{3} +1.79960 q^{4} +3.69296 q^{5} -1.94926 q^{6} -2.45473 q^{7} +0.390627 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.94926 q^{2} +1.00000 q^{3} +1.79960 q^{4} +3.69296 q^{5} -1.94926 q^{6} -2.45473 q^{7} +0.390627 q^{8} +1.00000 q^{9} -7.19852 q^{10} +4.43817 q^{11} +1.79960 q^{12} -4.28535 q^{13} +4.78490 q^{14} +3.69296 q^{15} -4.36064 q^{16} -1.49875 q^{17} -1.94926 q^{18} +1.06731 q^{19} +6.64585 q^{20} -2.45473 q^{21} -8.65112 q^{22} +1.00000 q^{23} +0.390627 q^{24} +8.63793 q^{25} +8.35324 q^{26} +1.00000 q^{27} -4.41754 q^{28} +1.00000 q^{29} -7.19852 q^{30} +2.48186 q^{31} +7.71875 q^{32} +4.43817 q^{33} +2.92144 q^{34} -9.06522 q^{35} +1.79960 q^{36} +3.20872 q^{37} -2.08047 q^{38} -4.28535 q^{39} +1.44257 q^{40} +4.57310 q^{41} +4.78490 q^{42} +5.98441 q^{43} +7.98693 q^{44} +3.69296 q^{45} -1.94926 q^{46} -4.84278 q^{47} -4.36064 q^{48} -0.974292 q^{49} -16.8375 q^{50} -1.49875 q^{51} -7.71192 q^{52} +4.65981 q^{53} -1.94926 q^{54} +16.3900 q^{55} -0.958884 q^{56} +1.06731 q^{57} -1.94926 q^{58} +0.167254 q^{59} +6.64585 q^{60} +13.1401 q^{61} -4.83778 q^{62} -2.45473 q^{63} -6.32455 q^{64} -15.8256 q^{65} -8.65112 q^{66} +11.9525 q^{67} -2.69715 q^{68} +1.00000 q^{69} +17.6704 q^{70} +8.22431 q^{71} +0.390627 q^{72} -10.4723 q^{73} -6.25462 q^{74} +8.63793 q^{75} +1.92074 q^{76} -10.8945 q^{77} +8.35324 q^{78} +0.909584 q^{79} -16.1036 q^{80} +1.00000 q^{81} -8.91415 q^{82} -4.61155 q^{83} -4.41754 q^{84} -5.53480 q^{85} -11.6652 q^{86} +1.00000 q^{87} +1.73367 q^{88} +12.8616 q^{89} -7.19852 q^{90} +10.5194 q^{91} +1.79960 q^{92} +2.48186 q^{93} +9.43982 q^{94} +3.94154 q^{95} +7.71875 q^{96} +1.88580 q^{97} +1.89915 q^{98} +4.43817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 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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