LMFDB - Embedded newform 799.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(1,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("799.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.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:	$6.38004712150$
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} - 4 x^{19} - 24 x^{18} + 108 x^{17} + 221 x^{16} - 1200 x^{15} - 931 x^{14} + 7128 x^{13} + \cdots + 63 $ x^20 - 4x^19 - 24x^18 + 108x^17 + 221x^16 - 1200x^15 - 931x^14 + 7128x^13 + 1280x^12 - 24559x^11 + 3411x^10 + 49829x^9 - 15132x^8 - 58070x^7 + 20659x^6 + 36738x^5 - 11129x^4 - 11299x^3 + 1589x^2 + 1289*x + 63
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.89867$ of defining polynomial
Character	$\chi$	$=$	799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.89867 q^{2} +2.39331 q^{3} +1.60496 q^{4} +2.00968 q^{5} -4.54411 q^{6} +2.01850 q^{7} +0.750053 q^{8} +2.72793 q^{9} +O(q^{10})$	\(q-1.89867 q^{2} +2.39331 q^{3} +1.60496 q^{4} +2.00968 q^{5} -4.54411 q^{6} +2.01850 q^{7} +0.750053 q^{8} +2.72793 q^{9} -3.81573 q^{10} +0.737632 q^{11} +3.84117 q^{12} +4.77929 q^{13} -3.83247 q^{14} +4.80979 q^{15} -4.63402 q^{16} -1.00000 q^{17} -5.17945 q^{18} -3.77399 q^{19} +3.22546 q^{20} +4.83090 q^{21} -1.40052 q^{22} +7.57161 q^{23} +1.79511 q^{24} -0.961174 q^{25} -9.07432 q^{26} -0.651139 q^{27} +3.23961 q^{28} -2.66479 q^{29} -9.13223 q^{30} -1.23940 q^{31} +7.29839 q^{32} +1.76538 q^{33} +1.89867 q^{34} +4.05654 q^{35} +4.37822 q^{36} +1.27992 q^{37} +7.16558 q^{38} +11.4383 q^{39} +1.50737 q^{40} -9.76379 q^{41} -9.17229 q^{42} -3.38595 q^{43} +1.18387 q^{44} +5.48228 q^{45} -14.3760 q^{46} +1.00000 q^{47} -11.0907 q^{48} -2.92566 q^{49} +1.82496 q^{50} -2.39331 q^{51} +7.67057 q^{52} +8.28764 q^{53} +1.23630 q^{54} +1.48241 q^{55} +1.51398 q^{56} -9.03233 q^{57} +5.05957 q^{58} -13.6983 q^{59} +7.71953 q^{60} -2.00763 q^{61} +2.35322 q^{62} +5.50633 q^{63} -4.58921 q^{64} +9.60487 q^{65} -3.35188 q^{66} -6.97349 q^{67} -1.60496 q^{68} +18.1212 q^{69} -7.70205 q^{70} +11.4103 q^{71} +2.04609 q^{72} +7.51842 q^{73} -2.43016 q^{74} -2.30039 q^{75} -6.05710 q^{76} +1.48891 q^{77} -21.7177 q^{78} -13.7668 q^{79} -9.31292 q^{80} -9.74218 q^{81} +18.5382 q^{82} +3.28563 q^{83} +7.75339 q^{84} -2.00968 q^{85} +6.42882 q^{86} -6.37768 q^{87} +0.553263 q^{88} +12.6555 q^{89} -10.4091 q^{90} +9.64700 q^{91} +12.1521 q^{92} -2.96628 q^{93} -1.89867 q^{94} -7.58453 q^{95} +17.4673 q^{96} -7.22793 q^{97} +5.55487 q^{98} +2.01221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9}+O(q^{10}) $ 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9} - 2 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} + 13 q^{14} + q^{15} + 28 q^{16} - 20 q^{17} + 15 q^{18} + 5 q^{19} + 37 q^{20} + 6 q^{21} - 19 q^{22} + 4 q^{23} + 30 q^{24} + 41 q^{25} - 9 q^{26} + 6 q^{27} - 25 q^{28} + 26 q^{29} - 25 q^{30} + 6 q^{31} + 28 q^{32} + 29 q^{33} - 4 q^{34} + 21 q^{35} - 5 q^{36} - 8 q^{37} - 21 q^{38} - 19 q^{39} - 25 q^{40} + 69 q^{41} + 3 q^{42} - 7 q^{43} + 16 q^{44} + 39 q^{45} - 24 q^{46} + 20 q^{47} + 26 q^{48} + 53 q^{49} + 16 q^{50} - 3 q^{51} + 18 q^{52} + 29 q^{53} + 23 q^{54} + 5 q^{55} - 22 q^{56} - 36 q^{57} - q^{58} + 55 q^{59} - 103 q^{60} - 17 q^{61} - 7 q^{62} - 9 q^{63} + 58 q^{64} + 40 q^{65} + 50 q^{66} - 6 q^{67} - 24 q^{68} + 17 q^{69} - 15 q^{70} + 47 q^{71} + 7 q^{72} - 32 q^{73} - 67 q^{74} - 22 q^{75} - 5 q^{76} + 4 q^{77} - 60 q^{78} - 26 q^{79} + 108 q^{80} + 68 q^{81} + 25 q^{82} + 3 q^{83} + 24 q^{84} - 13 q^{85} + 8 q^{86} - 41 q^{87} - 47 q^{88} + 119 q^{89} - 54 q^{90} - 35 q^{91} - 15 q^{93} + 4 q^{94} - 48 q^{95} - 84 q^{96} - 13 q^{97} + q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9 - 2 * q^10 + 10 * q^11 + 8 * q^12 + q^13 + 13 * q^14 + q^15 + 28 * q^16 - 20 * q^17 + 15 * q^18 + 5 * q^19 + 37 * q^20 + 6 * q^21 - 19 * q^22 + 4 * q^23 + 30 * q^24 + 41 * q^25 - 9 * q^26 + 6 * q^27 - 25 * q^28 + 26 * q^29 - 25 * q^30 + 6 * q^31 + 28 * q^32 + 29 * q^33 - 4 * q^34 + 21 * q^35 - 5 * q^36 - 8 * q^37 - 21 * q^38 - 19 * q^39 - 25 * q^40 + 69 * q^41 + 3 * q^42 - 7 * q^43 + 16 * q^44 + 39 * q^45 - 24 * q^46 + 20 * q^47 + 26 * q^48 + 53 * q^49 + 16 * q^50 - 3 * q^51 + 18 * q^52 + 29 * q^53 + 23 * q^54 + 5 * q^55 - 22 * q^56 - 36 * q^57 - q^58 + 55 * q^59 - 103 * q^60 - 17 * q^61 - 7 * q^62 - 9 * q^63 + 58 * q^64 + 40 * q^65 + 50 * q^66 - 6 * q^67 - 24 * q^68 + 17 * q^69 - 15 * q^70 + 47 * q^71 + 7 * q^72 - 32 * q^73 - 67 * q^74 - 22 * q^75 - 5 * q^76 + 4 * q^77 - 60 * q^78 - 26 * q^79 + 108 * q^80 + 68 * q^81 + 25 * q^82 + 3 * q^83 + 24 * q^84 - 13 * q^85 + 8 * q^86 - 41 * q^87 - 47 * q^88 + 119 * q^89 - 54 * q^90 - 35 * q^91 - 15 * q^93 + 4 * q^94 - 48 * q^95 - 84 * q^96 - 13 * q^97 + q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.89867	−1.34256	−0.671282	−	0.741202i	$-0.734256\pi$
$2$	−1.89867	−1.34256	−0.671282	+	0.741202i	$0.734256\pi$
$3$	2.39331	1.38178	0.690889	−	0.722961i	$-0.257219\pi$
$3$	2.39331	1.38178	0.690889	+	0.722961i	$0.257219\pi$
$4$	1.60496	0.802480
$5$	2.00968	0.898758	0.449379	−	0.893341i	$-0.351645\pi$
$5$	2.00968	0.898758	0.449379	+	0.893341i	$0.351645\pi$
$6$	−4.54411	−1.85513
$7$	2.01850	0.762921	0.381461	−	0.924385i	$-0.375421\pi$
$7$	2.01850	0.762921	0.381461	+	0.924385i	$0.375421\pi$
$8$	0.750053	0.265184
$9$	2.72793	0.909311
$10$	−3.81573	−1.20664
$11$	0.737632	0.222404	0.111202	−	0.993798i	$-0.464530\pi$
$11$	0.737632	0.222404	0.111202	+	0.993798i	$0.464530\pi$
$12$	3.84117	1.10885
$13$	4.77929	1.32554	0.662769	−	0.748824i	$-0.269381\pi$
$13$	4.77929	1.32554	0.662769	+	0.748824i	$0.269381\pi$
$14$	−3.83247	−1.02427
$15$	4.80979	1.24188
$16$	−4.63402	−1.15851
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−5.17945	−1.22081
$19$	−3.77399	−0.865813	−0.432906	−	0.901439i	$-0.642512\pi$
$19$	−3.77399	−0.865813	−0.432906	+	0.901439i	$0.642512\pi$
$20$	3.22546	0.721235
$21$	4.83090	1.05419
$22$	−1.40052	−0.298592
$23$	7.57161	1.57879	0.789395	−	0.613886i	$-0.210395\pi$
$23$	7.57161	1.57879	0.789395	+	0.613886i	$0.210395\pi$
$24$	1.79511	0.366425
$25$	−0.961174	−0.192235
$26$	−9.07432	−1.77962
$27$	−0.651139	−0.125312
$28$	3.23961	0.612229
$29$	−2.66479	−0.494840	−0.247420	−	0.968908i	$-0.579583\pi$
$29$	−2.66479	−0.494840	−0.247420	+	0.968908i	$0.579583\pi$
$30$	−9.13223	−1.66731
$31$	−1.23940	−0.222604	−0.111302	−	0.993787i	$-0.535502\pi$
$31$	−1.23940	−0.222604	−0.111302	+	0.993787i	$0.535502\pi$
$32$	7.29839	1.29019
$33$	1.76538	0.307314
$34$	1.89867	0.325620
$35$	4.05654	0.685681
$36$	4.37822	0.729704
$37$	1.27992	0.210418	0.105209	−	0.994450i	$-0.466449\pi$
$37$	1.27992	0.210418	0.105209	+	0.994450i	$0.466449\pi$
$38$	7.16558	1.16241
$39$	11.4383	1.83160
$40$	1.50737	0.238336
$41$	−9.76379	−1.52485	−0.762424	−	0.647078i	$-0.775991\pi$
$41$	−9.76379	−1.52485	−0.762424	+	0.647078i	$0.775991\pi$
$42$	−9.17229	−1.41532
$43$	−3.38595	−0.516353	−0.258176	−	0.966098i	$-0.583122\pi$
$43$	−3.38595	−0.516353	−0.258176	+	0.966098i	$0.583122\pi$
$44$	1.18387	0.178475
$45$	5.48228	0.817250
$46$	−14.3760	−2.11963
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−11.0907	−1.60080
$49$	−2.92566	−0.417951
$50$	1.82496	0.258088
$51$	−2.39331	−0.335130
$52$	7.67057	1.06372
$53$	8.28764	1.13839	0.569197	−	0.822201i	$-0.307254\pi$
$53$	8.28764	1.13839	0.569197	+	0.822201i	$0.307254\pi$
$54$	1.23630	0.168239
$55$	1.48241	0.199888
$56$	1.51398	0.202314
$57$	−9.03233	−1.19636
$58$	5.05957	0.664355
$59$	−13.6983	−1.78337	−0.891684	−	0.452659i	$-0.850476\pi$
$59$	−13.6983	−1.78337	−0.891684	+	0.452659i	$0.850476\pi$
$60$	7.71953	0.996587
$61$	−2.00763	−0.257051	−0.128526	−	0.991706i	$-0.541024\pi$
$61$	−2.00763	−0.257051	−0.128526	+	0.991706i	$0.541024\pi$
$62$	2.35322	0.298860
$63$	5.50633	0.693733
$64$	−4.58921	−0.573651
$65$	9.60487	1.19134
$66$	−3.35188	−0.412588
$67$	−6.97349	−0.851947	−0.425973	−	0.904736i	$-0.640068\pi$
$67$	−6.97349	−0.851947	−0.425973	+	0.904736i	$0.640068\pi$
$68$	−1.60496	−0.194630
$69$	18.1212	2.18154
$70$	−7.70205	−0.920571
$71$	11.4103	1.35416	0.677079	−	0.735911i	$-0.263246\pi$
$71$	11.4103	1.35416	0.677079	+	0.735911i	$0.263246\pi$
$72$	2.04609	0.241134
$73$	7.51842	0.879965	0.439982	−	0.898006i	$-0.354985\pi$
$73$	7.51842	0.879965	0.439982	+	0.898006i	$0.354985\pi$
$74$	−2.43016	−0.282500
$75$	−2.30039	−0.265626
$76$	−6.05710	−0.694797
$77$	1.48891	0.169677
$78$	−21.7177	−2.45904
$79$	−13.7668	−1.54889	−0.774444	−	0.632642i	$-0.781970\pi$
$79$	−13.7668	−1.54889	−0.774444	+	0.632642i	$0.781970\pi$
$80$	−9.31292	−1.04122
$81$	−9.74218	−1.08246
$82$	18.5382	2.04721
$83$	3.28563	0.360645	0.180322	−	0.983608i	$-0.442286\pi$
$83$	3.28563	0.360645	0.180322	+	0.983608i	$0.442286\pi$
$84$	7.75339	0.845964
$85$	−2.00968	−0.217981
$86$	6.42882	0.693237
$87$	−6.37768	−0.683759
$88$	0.553263	0.0589780
$89$	12.6555	1.34148	0.670741	−	0.741692i	$-0.265976\pi$
$89$	12.6555	1.34148	0.670741	+	0.741692i	$0.265976\pi$
$90$	−10.4091	−1.09721
$91$	9.64700	1.01128
$92$	12.1521	1.26695
$93$	−2.96628	−0.307589
$94$	−1.89867	−0.195833
$95$	−7.58453	−0.778156
$96$	17.4673	1.78275
$97$	−7.22793	−0.733885	−0.366943	−	0.930244i	$-0.619595\pi$
$97$	−7.22793	−0.733885	−0.366943	+	0.930244i	$0.619595\pi$
$98$	5.55487	0.561127
$99$	2.01221	0.202235
$100$	−1.54265	−0.154265
$101$	14.5104	1.44383	0.721917	−	0.691979i	$-0.243261\pi$
$101$	14.5104	1.44383	0.721917	+	0.691979i	$0.243261\pi$
$102$	4.54411	0.449934
$103$	18.3307	1.80618	0.903090	−	0.429452i	$-0.141293\pi$
$103$	18.3307	1.80618	0.903090	+	0.429452i	$0.141293\pi$
$104$	3.58472	0.351511
$105$	9.70857	0.947459
$106$	−15.7355	−1.52837
$107$	9.47925	0.916394	0.458197	−	0.888851i	$-0.348495\pi$
$107$	9.47925	0.916394	0.458197	+	0.888851i	$0.348495\pi$
$108$	−1.04505	−0.100560
$109$	1.70813	0.163609	0.0818046	−	0.996648i	$-0.473932\pi$
$109$	1.70813	0.163609	0.0818046	+	0.996648i	$0.473932\pi$
$110$	−2.81461	−0.268362
$111$	3.06325	0.290751
$112$	−9.35378	−0.883849
$113$	13.9375	1.31113	0.655566	−	0.755138i	$-0.272430\pi$
$113$	13.9375	1.31113	0.655566	+	0.755138i	$0.272430\pi$
$114$	17.1494	1.60619
$115$	15.2165	1.41895
$116$	−4.27689	−0.397099
$117$	13.0376	1.20533
$118$	26.0086	2.39429
$119$	−2.01850	−0.185036
$120$	3.60760	0.329327
$121$	−10.4559	−0.950536
$122$	3.81184	0.345108
$123$	−23.3678	−2.10700
$124$	−1.98919	−0.178635
$125$	−11.9801	−1.07153
$126$	−10.4547	−0.931381
$127$	1.19177	0.105752	0.0528762	−	0.998601i	$-0.483161\pi$
$127$	1.19177	0.105752	0.0528762	+	0.998601i	$0.483161\pi$
$128$	−5.88337	−0.520021
$129$	−8.10363	−0.713485
$130$	−18.2365	−1.59945
$131$	0.927944	0.0810748	0.0405374	−	0.999178i	$-0.487093\pi$
$131$	0.927944	0.0810748	0.0405374	+	0.999178i	$0.487093\pi$
$132$	2.83337	0.246613
$133$	−7.61780	−0.660547
$134$	13.2404	1.14379
$135$	−1.30858	−0.112625
$136$	−0.750053	−0.0643165
$137$	8.32979	0.711662	0.355831	−	0.934550i	$-0.384198\pi$
$137$	8.32979	0.711662	0.355831	+	0.934550i	$0.384198\pi$
$138$	−34.4062	−2.92885
$139$	−9.02437	−0.765437	−0.382718	−	0.923865i	$-0.625012\pi$
$139$	−9.02437	−0.765437	−0.382718	+	0.923865i	$0.625012\pi$
$140$	6.51059	0.550245
$141$	2.39331	0.201553
$142$	−21.6645	−1.81804
$143$	3.52536	0.294806
$144$	−12.6413	−1.05344
$145$	−5.35539	−0.444741
$146$	−14.2750	−1.18141
$147$	−7.00201	−0.577516
$148$	2.05423	0.168856
$149$	−10.2422	−0.839076	−0.419538	−	0.907738i	$-0.637808\pi$
$149$	−10.2422	−0.839076	−0.419538	+	0.907738i	$0.637808\pi$
$150$	4.36768	0.356620
$151$	4.52372	0.368135	0.184067	−	0.982914i	$-0.441074\pi$
$151$	4.52372	0.368135	0.184067	+	0.982914i	$0.441074\pi$
$152$	−2.83069	−0.229599
$153$	−2.72793	−0.220540
$154$	−2.82695	−0.227802
$155$	−2.49081	−0.200067
$156$	18.3581	1.46982
$157$	−8.51922	−0.679908	−0.339954	−	0.940442i	$-0.610411\pi$
$157$	−8.51922	−0.679908	−0.339954	+	0.940442i	$0.610411\pi$
$158$	26.1387	2.07948
$159$	19.8349	1.57301
$160$	14.6675	1.15956
$161$	15.2833	1.20449
$162$	18.4972	1.45328
$163$	7.45539	0.583951	0.291976	−	0.956426i	$-0.405687\pi$
$163$	7.45539	0.583951	0.291976	+	0.956426i	$0.405687\pi$
$164$	−15.6705	−1.22366
$165$	3.54786	0.276200
$166$	−6.23834	−0.484189
$167$	−10.0073	−0.774385	−0.387193	−	0.921999i	$-0.626555\pi$
$167$	−10.0073	−0.774385	−0.387193	+	0.921999i	$0.626555\pi$
$168$	3.62343	0.279553
$169$	9.84166	0.757051
$170$	3.81573	0.292653
$171$	−10.2952	−0.787293
$172$	−5.43432	−0.414363
$173$	−8.47952	−0.644686	−0.322343	−	0.946623i	$-0.604470\pi$
$173$	−8.47952	−0.644686	−0.322343	+	0.946623i	$0.604470\pi$
$174$	12.1091	0.917991
$175$	−1.94013	−0.146660
$176$	−3.41820	−0.257657
$177$	−32.7843	−2.46422
$178$	−24.0287	−1.80103
$179$	1.46984	0.109861	0.0549307	−	0.998490i	$-0.482506\pi$
$179$	1.46984	0.109861	0.0549307	+	0.998490i	$0.482506\pi$
$180$	8.79884	0.655827
$181$	−19.5613	−1.45398	−0.726991	−	0.686647i	$-0.759082\pi$
$181$	−19.5613	−1.45398	−0.726991	+	0.686647i	$0.759082\pi$
$182$	−18.3165	−1.35771
$183$	−4.80489	−0.355188
$184$	5.67910	0.418669
$185$	2.57224	0.189115
$186$	5.63199	0.412958
$187$	−0.737632	−0.0539410
$188$	1.60496	0.117054
$189$	−1.31432	−0.0956031
$190$	14.4005	1.04472
$191$	−16.8687	−1.22057	−0.610286	−	0.792181i	$-0.708946\pi$
$191$	−16.8687	−1.22057	−0.610286	+	0.792181i	$0.708946\pi$
$192$	−10.9834	−0.792659
$193$	−17.9529	−1.29228	−0.646141	−	0.763218i	$-0.723618\pi$
$193$	−17.9529	−1.29228	−0.646141	+	0.763218i	$0.723618\pi$
$194$	13.7235	0.985288
$195$	22.9874	1.64616
$196$	−4.69556	−0.335397
$197$	7.94768	0.566249	0.283125	−	0.959083i	$-0.408629\pi$
$197$	7.94768	0.566249	0.283125	+	0.959083i	$0.408629\pi$
$198$	−3.82053	−0.271513
$199$	6.61066	0.468617	0.234309	−	0.972162i	$-0.424717\pi$
$199$	6.61066	0.468617	0.234309	+	0.972162i	$0.424717\pi$
$200$	−0.720931	−0.0509775
$201$	−16.6897	−1.17720
$202$	−27.5504	−1.93844
$203$	−5.37889	−0.377524
$204$	−3.84117	−0.268935
$205$	−19.6221	−1.37047
$206$	−34.8040	−2.42491
$207$	20.6548	1.43561
$208$	−22.1474	−1.53564
$209$	−2.78382	−0.192561
$210$	−18.4334	−1.27203
$211$	−11.3114	−0.778709	−0.389354	−	0.921088i	$-0.627302\pi$
$211$	−11.3114	−0.778709	−0.389354	+	0.921088i	$0.627302\pi$
$212$	13.3013	0.913539
$213$	27.3085	1.87115
$214$	−17.9980	−1.23032
$215$	−6.80469	−0.464076
$216$	−0.488389	−0.0332307
$217$	−2.50174	−0.169829
$218$	−3.24318	−0.219656
$219$	17.9939	1.21592
$220$	2.37920	0.160406
$221$	−4.77929	−0.321490
$222$	−5.81612	−0.390352
$223$	−7.71746	−0.516800	−0.258400	−	0.966038i	$-0.583195\pi$
$223$	−7.71746	−0.516800	−0.258400	+	0.966038i	$0.583195\pi$
$224$	14.7318	0.984310
$225$	−2.62202	−0.174801
$226$	−26.4628	−1.76028
$227$	7.13564	0.473609	0.236804	−	0.971557i	$-0.423900\pi$
$227$	7.13564	0.473609	0.236804	+	0.971557i	$0.423900\pi$
$228$	−14.4965	−0.960056
$229$	−3.63892	−0.240467	−0.120233	−	0.992746i	$-0.538364\pi$
$229$	−3.63892	−0.240467	−0.120233	+	0.992746i	$0.538364\pi$
$230$	−28.8912	−1.90503
$231$	3.56342	0.234456
$232$	−1.99874	−0.131223
$233$	12.0502	0.789432	0.394716	−	0.918803i	$-0.370843\pi$
$233$	12.0502	0.789432	0.394716	+	0.918803i	$0.370843\pi$
$234$	−24.7541	−1.61823
$235$	2.00968	0.131097
$236$	−21.9852	−1.43112
$237$	−32.9483	−2.14022
$238$	3.83247	0.248422
$239$	−12.8369	−0.830347	−0.415174	−	0.909742i	$-0.636279\pi$
$239$	−12.8369	−0.830347	−0.415174	+	0.909742i	$0.636279\pi$
$240$	−22.2887	−1.43873
$241$	15.0115	0.966977	0.483489	−	0.875351i	$-0.339369\pi$
$241$	15.0115	0.966977	0.483489	+	0.875351i	$0.339369\pi$
$242$	19.8523	1.27616
$243$	−21.3626	−1.37041
$244$	−3.22217	−0.206278
$245$	−5.87965	−0.375637
$246$	44.3678	2.82879
$247$	−18.0370	−1.14767
$248$	−0.929618	−0.0590308
$249$	7.86353	0.498331
$250$	22.7462	1.43860
$251$	−24.5069	−1.54686	−0.773431	−	0.633880i	$-0.781461\pi$
$251$	−24.5069	−1.54686	−0.773431	+	0.633880i	$0.781461\pi$
$252$	8.83744	0.556707
$253$	5.58506	0.351130
$254$	−2.26278	−0.141980
$255$	−4.80979	−0.301201
$256$	20.3490	1.27181
$257$	−3.01195	−0.187880	−0.0939400	−	0.995578i	$-0.529946\pi$
$257$	−3.01195	−0.187880	−0.0939400	+	0.995578i	$0.529946\pi$
$258$	15.3862	0.957900
$259$	2.58352	0.160532
$260$	15.4154	0.956024
$261$	−7.26938	−0.449963
$262$	−1.76186	−0.108848
$263$	−24.1699	−1.49038	−0.745191	−	0.666851i	$-0.767642\pi$
$263$	−24.1699	−1.49038	−0.745191	+	0.666851i	$0.767642\pi$
$264$	1.32413	0.0814945
$265$	16.6555	1.02314
$266$	14.4637	0.886827
$267$	30.2886	1.85363
$268$	−11.1922	−0.683670
$269$	32.0139	1.95192	0.975960	−	0.217948i	$-0.0699365\pi$
$269$	32.0139	1.95192	0.975960	+	0.217948i	$0.0699365\pi$
$270$	2.48457	0.151206
$271$	−10.0051	−0.607768	−0.303884	−	0.952709i	$-0.598284\pi$
$271$	−10.0051	−0.607768	−0.303884	+	0.952709i	$0.598284\pi$
$272$	4.63402	0.280979
$273$	23.0883	1.39737
$274$	−15.8155	−0.955452
$275$	−0.708993	−0.0427539
$276$	29.0838	1.75064
$277$	−30.3734	−1.82496	−0.912479	−	0.409123i	$-0.865835\pi$
$277$	−30.3734	−1.82496	−0.912479	+	0.409123i	$0.865835\pi$
$278$	17.1343	1.02765
$279$	−3.38101	−0.202416
$280$	3.04262	0.181831
$281$	−15.1044	−0.901055	−0.450527	−	0.892763i	$-0.648764\pi$
$281$	−15.1044	−0.901055	−0.450527	+	0.892763i	$0.648764\pi$
$282$	−4.54411	−0.270598
$283$	14.0307	0.834039	0.417020	−	0.908898i	$-0.363075\pi$
$283$	14.0307	0.834039	0.417020	+	0.908898i	$0.363075\pi$
$284$	18.3131	1.08668
$285$	−18.1521	−1.07524
$286$	−6.69351	−0.395795
$287$	−19.7082	−1.16334
$288$	19.9095	1.17318
$289$	1.00000	0.0588235
$290$	10.1681	0.597094
$291$	−17.2987	−1.01407
$292$	12.0668	0.706154
$293$	9.13893	0.533902	0.266951	−	0.963710i	$-0.413984\pi$
$293$	9.13893	0.533902	0.266951	+	0.963710i	$0.413984\pi$
$294$	13.2945	0.775353
$295$	−27.5293	−1.60282
$296$	0.960010	0.0557994
$297$	−0.480301	−0.0278699
$298$	19.4466	1.12651
$299$	36.1869	2.09275
$300$	−3.69203	−0.213159
$301$	−6.83454	−0.393937
$302$	−8.58906	−0.494245
$303$	34.7278	1.99506
$304$	17.4888	1.00305
$305$	−4.03471	−0.231027
$306$	5.17945	0.296090
$307$	4.58836	0.261872	0.130936	−	0.991391i	$-0.458202\pi$
$307$	4.58836	0.261872	0.130936	+	0.991391i	$0.458202\pi$
$308$	2.38964	0.136162
$309$	43.8711	2.49574
$310$	4.72923	0.268602
$311$	32.1496	1.82304	0.911518	−	0.411260i	$-0.134911\pi$
$311$	32.1496	1.82304	0.911518	+	0.411260i	$0.134911\pi$
$312$	8.57935	0.485710
$313$	0.773530	0.0437225	0.0218613	−	0.999761i	$-0.493041\pi$
$313$	0.773530	0.0437225	0.0218613	+	0.999761i	$0.493041\pi$
$314$	16.1752	0.912820
$315$	11.0660	0.623498
$316$	−22.0952	−1.24295
$317$	19.7232	1.10777	0.553883	−	0.832594i	$-0.313145\pi$
$317$	19.7232	1.10777	0.553883	+	0.832594i	$0.313145\pi$
$318$	−37.6600	−2.11187
$319$	−1.96564	−0.110055
$320$	−9.22286	−0.515574
$321$	22.6868	1.26625
$322$	−29.0180	−1.61711
$323$	3.77399	0.209990
$324$	−15.6358	−0.868656
$325$	−4.59373	−0.254814
$326$	−14.1554	−0.783992
$327$	4.08808	0.226072
$328$	−7.32336	−0.404365
$329$	2.01850	0.111283
$330$	−6.73622	−0.370817
$331$	−7.80550	−0.429029	−0.214514	−	0.976721i	$-0.568817\pi$
$331$	−7.80550	−0.429029	−0.214514	+	0.976721i	$0.568817\pi$
$332$	5.27330	0.289410
$333$	3.49155	0.191336
$334$	19.0005	1.03966
$335$	−14.0145	−0.765694
$336$	−22.3865	−1.22128
$337$	5.93289	0.323185	0.161593	−	0.986858i	$-0.448337\pi$
$337$	5.93289	0.323185	0.161593	+	0.986858i	$0.448337\pi$
$338$	−18.6861	−1.01639
$339$	33.3568	1.81169
$340$	−3.22546	−0.174925
$341$	−0.914224	−0.0495080
$342$	19.5472	1.05699
$343$	−20.0349	−1.08179
$344$	−2.53964	−0.136928
$345$	36.4179	1.96067
$346$	16.0998	0.865533
$347$	−13.5360	−0.726651	−0.363325	−	0.931662i	$-0.618359\pi$
$347$	−13.5360	−0.726651	−0.363325	+	0.931662i	$0.618359\pi$
$348$	−10.2359	−0.548703
$349$	−13.3138	−0.712672	−0.356336	−	0.934358i	$-0.615974\pi$
$349$	−13.3138	−0.712672	−0.356336	+	0.934358i	$0.615974\pi$
$350$	3.68367	0.196901
$351$	−3.11199	−0.166106
$352$	5.38353	0.286943
$353$	−6.20207	−0.330103	−0.165052	−	0.986285i	$-0.552779\pi$
$353$	−6.20207	−0.330103	−0.165052	+	0.986285i	$0.552779\pi$
$354$	62.2467	3.30837
$355$	22.9312	1.21706
$356$	20.3116	1.07651
$357$	−4.83090	−0.255678
$358$	−2.79075	−0.147496
$359$	−4.18054	−0.220640	−0.110320	−	0.993896i	$-0.535188\pi$
$359$	−4.18054	−0.220640	−0.110320	+	0.993896i	$0.535188\pi$
$360$	4.11200	0.216721
$361$	−4.75699	−0.250368
$362$	37.1406	1.95207
$363$	−25.0242	−1.31343
$364$	15.4831	0.811532
$365$	15.1096	0.790875
$366$	9.12292	0.476863
$367$	22.8396	1.19222	0.596109	−	0.802903i	$-0.296712\pi$
$367$	22.8396	1.19222	0.596109	+	0.802903i	$0.296712\pi$
$368$	−35.0870	−1.82904
$369$	−26.6350	−1.38656
$370$	−4.88384	−0.253899
$371$	16.7286	0.868506
$372$	−4.76076	−0.246834
$373$	−7.27841	−0.376862	−0.188431	−	0.982086i	$-0.560340\pi$
$373$	−7.27841	−0.376862	−0.188431	+	0.982086i	$0.560340\pi$
$374$	1.40052	0.0724193
$375$	−28.6720	−1.48062
$376$	0.750053	0.0386810
$377$	−12.7358	−0.655929
$378$	2.49547	0.128353
$379$	−12.1026	−0.621667	−0.310834	−	0.950464i	$-0.600608\pi$
$379$	−12.1026	−0.621667	−0.310834	+	0.950464i	$0.600608\pi$
$380$	−12.1729	−0.624454
$381$	2.85227	0.146126
$382$	32.0281	1.63870
$383$	17.2026	0.879012	0.439506	−	0.898240i	$-0.355153\pi$
$383$	17.2026	0.879012	0.439506	+	0.898240i	$0.355153\pi$
$384$	−14.0807	−0.718554
$385$	2.99224	0.152499
$386$	34.0868	1.73497
$387$	−9.23665	−0.469526
$388$	−11.6005	−0.588928
$389$	33.8412	1.71582	0.857908	−	0.513803i	$-0.171764\pi$
$389$	33.8412	1.71582	0.857908	+	0.513803i	$0.171764\pi$
$390$	−43.6456	−2.21008
$391$	−7.57161	−0.382913
$392$	−2.19440	−0.110834
$393$	2.22086	0.112027
$394$	−15.0901	−0.760226
$395$	−27.6669	−1.39207
$396$	3.22952	0.162289
$397$	22.7770	1.14314	0.571572	−	0.820552i	$-0.306334\pi$
$397$	22.7770	1.14314	0.571572	+	0.820552i	$0.306334\pi$
$398$	−12.5515	−0.629149
$399$	−18.2318	−0.912729
$400$	4.45410	0.222705
$401$	14.4371	0.720954	0.360477	−	0.932768i	$-0.382614\pi$
$401$	14.4371	0.720954	0.360477	+	0.932768i	$0.382614\pi$
$402$	31.6883	1.58047
$403$	−5.92348	−0.295069
$404$	23.2885	1.15865
$405$	−19.5787	−0.972873
$406$	10.2127	0.506850
$407$	0.944113	0.0467979
$408$	−1.79511	−0.0888711
$409$	−12.1781	−0.602169	−0.301084	−	0.953598i	$-0.597349\pi$
$409$	−12.1781	−0.602169	−0.301084	+	0.953598i	$0.597349\pi$
$410$	37.2560	1.83994
$411$	19.9358	0.983359
$412$	29.4201	1.44942
$413$	−27.6500	−1.36057
$414$	−39.2168	−1.92740
$415$	6.60307	0.324132
$416$	34.8812	1.71019
$417$	−21.5981	−1.05766
$418$	5.28556	0.258525
$419$	10.8501	0.530064	0.265032	−	0.964240i	$-0.414617\pi$
$419$	10.8501	0.530064	0.265032	+	0.964240i	$0.414617\pi$
$420$	15.5819	0.760317
$421$	7.14140	0.348051	0.174025	−	0.984741i	$-0.444323\pi$
$421$	7.14140	0.348051	0.174025	+	0.984741i	$0.444323\pi$
$422$	21.4766	1.04547
$423$	2.72793	0.132637
$424$	6.21617	0.301884
$425$	0.961174	0.0466238
$426$	−51.8498	−2.51213
$427$	−4.05241	−0.196110
$428$	15.2138	0.735387
$429$	8.43728	0.407356
$430$	12.9199	0.623052
$431$	10.8551	0.522873	0.261437	−	0.965221i	$-0.415804\pi$
$431$	10.8551	0.522873	0.261437	+	0.965221i	$0.415804\pi$
$432$	3.01740	0.145175
$433$	−12.9778	−0.623675	−0.311837	−	0.950136i	$-0.600944\pi$
$433$	−12.9778	−0.623675	−0.311837	+	0.950136i	$0.600944\pi$
$434$	4.74998	0.228006
$435$	−12.8171	−0.614534
$436$	2.74148	0.131293
$437$	−28.5752	−1.36694
$438$	−34.1646	−1.63245
$439$	24.7616	1.18181	0.590904	−	0.806742i	$-0.298771\pi$
$439$	24.7616	1.18181	0.590904	+	0.806742i	$0.298771\pi$
$440$	1.11188	0.0530069
$441$	−7.98100	−0.380048
$442$	9.07432	0.431621
$443$	−23.4619	−1.11471	−0.557354	−	0.830275i	$-0.688183\pi$
$443$	−23.4619	−1.11471	−0.557354	+	0.830275i	$0.688183\pi$
$444$	4.91640	0.233322
$445$	25.4336	1.20567
$446$	14.6529	0.693837
$447$	−24.5128	−1.15942
$448$	−9.26332	−0.437651
$449$	−22.2585	−1.05045	−0.525223	−	0.850965i	$-0.676018\pi$
$449$	−22.2585	−1.05045	−0.525223	+	0.850965i	$0.676018\pi$
$450$	4.97836	0.234682
$451$	−7.20208	−0.339133
$452$	22.3692	1.05216
$453$	10.8267	0.508681
$454$	−13.5482	−0.635850
$455$	19.3874	0.908896
$456$	−6.77472	−0.317256
$457$	16.9237	0.791658	0.395829	−	0.918324i	$-0.370457\pi$
$457$	16.9237	0.791658	0.395829	+	0.918324i	$0.370457\pi$
$458$	6.90913	0.322842
$459$	0.651139	0.0303926
$460$	24.4219	1.13868
$461$	−13.8472	−0.644930	−0.322465	−	0.946581i	$-0.604511\pi$
$461$	−13.8472	−0.644930	−0.322465	+	0.946581i	$0.604511\pi$
$462$	−6.76578	−0.314772
$463$	−3.76540	−0.174993	−0.0874966	−	0.996165i	$-0.527887\pi$
$463$	−3.76540	−0.174993	−0.0874966	+	0.996165i	$0.527887\pi$
$464$	12.3487	0.573275
$465$	−5.96128	−0.276448
$466$	−22.8793	−1.05986
$467$	12.6612	0.585890	0.292945	−	0.956129i	$-0.405365\pi$
$467$	12.6612	0.585890	0.292945	+	0.956129i	$0.405365\pi$
$468$	20.9248	0.967250
$469$	−14.0760	−0.649968
$470$	−3.81573	−0.176007
$471$	−20.3891	−0.939482
$472$	−10.2745	−0.472920
$473$	−2.49759	−0.114839
$474$	62.5580	2.87338
$475$	3.62746	0.166439
$476$	−3.23961	−0.148487
$477$	22.6081	1.03516
$478$	24.3730	1.11479
$479$	−19.4910	−0.890565	−0.445283	−	0.895390i	$-0.646897\pi$
$479$	−19.4910	−0.890565	−0.445283	+	0.895390i	$0.646897\pi$
$480$	35.1038	1.60226
$481$	6.11713	0.278917
$482$	−28.5020	−1.29823
$483$	36.5776	1.66434
$484$	−16.7813	−0.762786
$485$	−14.5258	−0.659585
$486$	40.5607	1.83987
$487$	34.3124	1.55484	0.777421	−	0.628981i	$-0.216528\pi$
$487$	34.3124	1.55484	0.777421	+	0.628981i	$0.216528\pi$
$488$	−1.50583	−0.0681658
$489$	17.8431	0.806891
$490$	11.1635	0.504317
$491$	−26.4340	−1.19295	−0.596475	−	0.802632i	$-0.703432\pi$
$491$	−26.4340	−1.19295	−0.596475	+	0.802632i	$0.703432\pi$
$492$	−37.5043	−1.69083
$493$	2.66479	0.120016
$494$	34.2464	1.54082
$495$	4.04391	0.181760
$496$	5.74343	0.257888
$497$	23.0318	1.03312
$498$	−14.9303	−0.669042
$499$	−25.5412	−1.14338	−0.571689	−	0.820470i	$-0.693712\pi$
$499$	−25.5412	−1.14338	−0.571689	+	0.820470i	$0.693712\pi$
$500$	−19.2275	−0.859881
$501$	−23.9505	−1.07003
$502$	46.5306	2.07676
$503$	−36.4599	−1.62567	−0.812833	−	0.582497i	$-0.802076\pi$
$503$	−36.4599	−1.62567	−0.812833	+	0.582497i	$0.802076\pi$
$504$	4.13004	0.183967
$505$	29.1612	1.29766
$506$	−10.6042	−0.471414
$507$	23.5541	1.04608
$508$	1.91274	0.0848642
$509$	44.0289	1.95155	0.975773	−	0.218785i	$-0.0702094\pi$
$509$	44.0289	1.95155	0.975773	+	0.218785i	$0.0702094\pi$
$510$	9.13223	0.404382
$511$	15.1759	0.671344
$512$	−26.8694	−1.18747
$513$	2.45739	0.108497
$514$	5.71870	0.252241
$515$	36.8389	1.62332
$516$	−13.0060	−0.572558
$517$	0.737632	0.0324410
$518$	−4.90527	−0.215525
$519$	−20.2941	−0.890813
$520$	7.20416	0.315923
$521$	−11.2794	−0.494160	−0.247080	−	0.968995i	$-0.579471\pi$
$521$	−11.2794	−0.494160	−0.247080	+	0.968995i	$0.579471\pi$
$522$	13.8022	0.604105
$523$	16.3534	0.715085	0.357542	−	0.933897i	$-0.383615\pi$
$523$	16.3534	0.715085	0.357542	+	0.933897i	$0.383615\pi$
$524$	1.48931	0.0650609
$525$	−4.64333	−0.202652
$526$	45.8908	2.00094
$527$	1.23940	0.0539893
$528$	−8.18082	−0.356025
$529$	34.3292	1.49258
$530$	−31.6234	−1.37363
$531$	−37.3681	−1.62164
$532$	−12.2263	−0.530076
$533$	−46.6640	−2.02124
$534$	−57.5081	−2.48862
$535$	19.0503	0.823616
$536$	−5.23048	−0.225922
$537$	3.51779	0.151804
$538$	−60.7839	−2.62058
$539$	−2.15806	−0.0929542
$540$	−2.10022	−0.0903793
$541$	21.9161	0.942246	0.471123	−	0.882067i	$-0.343849\pi$
$541$	21.9161	0.942246	0.471123	+	0.882067i	$0.343849\pi$
$542$	18.9965	0.815968
$543$	−46.8163	−2.00908
$544$	−7.29839	−0.312916
$545$	3.43280	0.147045
$546$	−43.8371	−1.87605
$547$	−37.0852	−1.58565	−0.792825	−	0.609449i	$-0.791391\pi$
$547$	−37.0852	−1.58565	−0.792825	+	0.609449i	$0.791391\pi$
$548$	13.3690	0.571094
$549$	−5.47669	−0.233740
$550$	1.34615	0.0573998
$551$	10.0569	0.428439
$552$	13.5919	0.578508
$553$	−27.7883	−1.18168
$554$	57.6691	2.45012
$555$	6.15617	0.261315
$556$	−14.4837	−0.614247
$557$	−25.3527	−1.07423	−0.537113	−	0.843510i	$-0.680485\pi$
$557$	−25.3527	−1.07423	−0.537113	+	0.843510i	$0.680485\pi$
$558$	6.41944	0.271756
$559$	−16.1825	−0.684445
$560$	−18.7981	−0.794366
$561$	−1.76538	−0.0745345
$562$	28.6784	1.20972
$563$	−26.1870	−1.10365	−0.551826	−	0.833959i	$-0.686069\pi$
$563$	−26.1870	−1.10365	−0.551826	+	0.833959i	$0.686069\pi$
$564$	3.84117	0.161742
$565$	28.0100	1.17839
$566$	−26.6397	−1.11975
$567$	−19.6646	−0.825835
$568$	8.55835	0.359100
$569$	−31.2833	−1.31146	−0.655732	−	0.754994i	$-0.727640\pi$
$569$	−31.2833	−1.31146	−0.655732	+	0.754994i	$0.727640\pi$
$570$	34.4649	1.44358
$571$	32.2725	1.35056	0.675282	−	0.737560i	$-0.264022\pi$
$571$	32.2725	1.35056	0.675282	+	0.737560i	$0.264022\pi$
$572$	5.65806	0.236575
$573$	−40.3719	−1.68656
$574$	37.4194	1.56186
$575$	−7.27763	−0.303498
$576$	−12.5191	−0.521628
$577$	15.3664	0.639710	0.319855	−	0.947466i	$-0.396366\pi$
$577$	15.3664	0.639710	0.319855	+	0.947466i	$0.396366\pi$
$578$	−1.89867	−0.0789744
$579$	−42.9670	−1.78565
$580$	−8.59519	−0.356896
$581$	6.63204	0.275143
$582$	32.8445	1.36145
$583$	6.11323	0.253184
$584$	5.63921	0.233352
$585$	26.2014	1.08330
$586$	−17.3518	−0.716798
$587$	−20.5590	−0.848561	−0.424280	−	0.905531i	$-0.639473\pi$
$587$	−20.5590	−0.848561	−0.424280	+	0.905531i	$0.639473\pi$
$588$	−11.2379	−0.463445
$589$	4.67750	0.192733
$590$	52.2691	2.15188
$591$	19.0213	0.782431
$592$	−5.93120	−0.243771
$593$	−28.4549	−1.16850	−0.584252	−	0.811572i	$-0.698612\pi$
$593$	−28.4549	−1.16850	−0.584252	+	0.811572i	$0.698612\pi$
$594$	0.911935	0.0374172
$595$	−4.05654	−0.166302
$596$	−16.4384	−0.673342
$597$	15.8214	0.647525
$598$	−68.7072	−2.80965
$599$	−29.4885	−1.20487	−0.602434	−	0.798169i	$-0.705802\pi$
$599$	−29.4885	−1.20487	−0.602434	+	0.798169i	$0.705802\pi$
$600$	−1.72541	−0.0704396
$601$	−3.77840	−0.154124	−0.0770621	−	0.997026i	$-0.524554\pi$
$601$	−3.77840	−0.154124	−0.0770621	+	0.997026i	$0.524554\pi$
$602$	12.9766	0.528885
$603$	−19.0232	−0.774685
$604$	7.26038	0.295421
$605$	−21.0130	−0.854302
$606$	−65.9367	−2.67850
$607$	−34.8558	−1.41475	−0.707376	−	0.706838i	$-0.750121\pi$
$607$	−34.8558	−1.41475	−0.707376	+	0.706838i	$0.750121\pi$
$608$	−27.5441	−1.11706
$609$	−12.8733	−0.521654
$610$	7.66060	0.310168
$611$	4.77929	0.193350
$612$	−4.37822	−0.176979
$613$	34.7556	1.40376	0.701882	−	0.712293i	$-0.252343\pi$
$613$	34.7556	1.40376	0.701882	+	0.712293i	$0.252343\pi$
$614$	−8.71180	−0.351580
$615$	−46.9618	−1.89368
$616$	1.11676	0.0449956
$617$	29.0266	1.16857	0.584283	−	0.811550i	$-0.301376\pi$
$617$	29.0266	1.16857	0.584283	+	0.811550i	$0.301376\pi$
$618$	−83.2969	−3.35069
$619$	37.4427	1.50495	0.752474	−	0.658622i	$-0.228860\pi$
$619$	37.4427	1.50495	0.752474	+	0.658622i	$0.228860\pi$
$620$	−3.99765	−0.160549
$621$	−4.93017	−0.197841
$622$	−61.0416	−2.44754
$623$	25.5452	1.02344
$624$	−53.0055	−2.12192
$625$	−19.2703	−0.770811
$626$	−1.46868	−0.0587003
$627$	−6.66254	−0.266076
$628$	−13.6730	−0.545612
$629$	−1.27992	−0.0510339
$630$	−21.0107	−0.837086
$631$	17.4741	0.695635	0.347817	−	0.937562i	$-0.386923\pi$
$631$	17.4741	0.695635	0.347817	+	0.937562i	$0.386923\pi$
$632$	−10.3258	−0.410740
$633$	−27.0717	−1.07600
$634$	−37.4480	−1.48725
$635$	2.39508	0.0950458
$636$	31.8342	1.26231
$637$	−13.9826	−0.554010
$638$	3.73210	0.147755
$639$	31.1266	1.23135
$640$	−11.8237	−0.467373
$641$	42.9936	1.69814	0.849072	−	0.528276i	$-0.177162\pi$
$641$	42.9936	1.69814	0.849072	+	0.528276i	$0.177162\pi$
$642$	−43.0748	−1.70003
$643$	20.9522	0.826273	0.413137	−	0.910669i	$-0.364433\pi$
$643$	20.9522	0.826273	0.413137	+	0.910669i	$0.364433\pi$
$644$	24.5291	0.966580
$645$	−16.2857	−0.641250
$646$	−7.16558	−0.281926
$647$	27.1201	1.06620	0.533100	−	0.846052i	$-0.321027\pi$
$647$	27.1201	1.06620	0.533100	+	0.846052i	$0.321027\pi$
$648$	−7.30715	−0.287052
$649$	−10.1043	−0.396629
$650$	8.72200	0.342105
$651$	−5.98743	−0.234666
$652$	11.9656	0.468609
$653$	3.92255	0.153501	0.0767507	−	0.997050i	$-0.475545\pi$
$653$	3.92255	0.153501	0.0767507	+	0.997050i	$0.475545\pi$
$654$	−7.76194	−0.303516
$655$	1.86487	0.0728666
$656$	45.2456	1.76655
$657$	20.5098	0.800162
$658$	−3.83247	−0.149405
$659$	−16.9832	−0.661570	−0.330785	−	0.943706i	$-0.607313\pi$
$659$	−16.9832	−0.661570	−0.330785	+	0.943706i	$0.607313\pi$
$660$	5.69417	0.221645
$661$	13.4127	0.521695	0.260847	−	0.965380i	$-0.415998\pi$
$661$	13.4127	0.521695	0.260847	+	0.965380i	$0.415998\pi$
$662$	14.8201	0.575999
$663$	−11.4383	−0.444228
$664$	2.46439	0.0956371
$665$	−15.3094	−0.593672
$666$	−6.62930	−0.256880
$667$	−20.1768	−0.781248
$668$	−16.0613	−0.621429
$669$	−18.4703	−0.714102
$670$	26.6089	1.02799
$671$	−1.48090	−0.0571694
$672$	35.2578	1.36010
$673$	14.2211	0.548183	0.274092	−	0.961704i	$-0.411623\pi$
$673$	14.2211	0.548183	0.274092	+	0.961704i	$0.411623\pi$
$674$	−11.2646	−0.433897
$675$	0.625858	0.0240893
$676$	15.7955	0.607518
$677$	21.3221	0.819475	0.409738	−	0.912203i	$-0.365620\pi$
$677$	21.3221	0.819475	0.409738	+	0.912203i	$0.365620\pi$
$678$	−63.3337	−2.43232
$679$	−14.5896	−0.559896
$680$	−1.50737	−0.0578049
$681$	17.0778	0.654422
$682$	1.73581	0.0664677
$683$	20.7632	0.794480	0.397240	−	0.917715i	$-0.369968\pi$
$683$	20.7632	0.794480	0.397240	+	0.917715i	$0.369968\pi$
$684$	−16.5234	−0.631787
$685$	16.7402	0.639611
$686$	38.0398	1.45237
$687$	−8.70907	−0.332272
$688$	15.6906	0.598198
$689$	39.6091	1.50899
$690$	−69.1457	−2.63233
$691$	−20.3432	−0.773894	−0.386947	−	0.922102i	$-0.626470\pi$
$691$	−20.3432	−0.773894	−0.386947	+	0.922102i	$0.626470\pi$
$692$	−13.6093	−0.517347
$693$	4.06165	0.154289
$694$	25.7004	0.975576
$695$	−18.1361	−0.687942
$696$	−4.78360	−0.181322
$697$	9.76379	0.369830
$698$	25.2786	0.956809
$699$	28.8398	1.09082
$700$	−3.11383	−0.117692
$701$	−22.3317	−0.843457	−0.421729	−	0.906722i	$-0.638577\pi$
$701$	−22.3317	−0.843457	−0.421729	+	0.906722i	$0.638577\pi$
$702$	5.90865	0.223007
$703$	−4.83042	−0.182183
$704$	−3.38515	−0.127583
$705$	4.80979	0.181147
$706$	11.7757	0.443185
$707$	29.2892	1.10153
$708$	−52.6175	−1.97749
$709$	41.3386	1.55251	0.776253	−	0.630422i	$-0.217118\pi$
$709$	41.3386	1.55251	0.776253	+	0.630422i	$0.217118\pi$
$710$	−43.5388	−1.63398
$711$	−37.5550	−1.40842
$712$	9.49230	0.355739
$713$	−9.38428	−0.351444
$714$	9.17229	0.343264
$715$	7.08486	0.264959
$716$	2.35904	0.0881615
$717$	−30.7226	−1.14736
$718$	7.93748	0.296224
$719$	−49.1618	−1.83343	−0.916714	−	0.399545i	$-0.869168\pi$
$719$	−49.1618	−1.83343	−0.916714	+	0.399545i	$0.869168\pi$
$720$	−25.4050	−0.946789
$721$	37.0005	1.37797
$722$	9.03197	0.336135
$723$	35.9272	1.33615
$724$	−31.3951	−1.16679
$725$	2.56133	0.0951254
$726$	47.5128	1.76337
$727$	−26.4999	−0.982825	−0.491413	−	0.870927i	$-0.663519\pi$
$727$	−26.4999	−0.982825	−0.491413	+	0.870927i	$0.663519\pi$
$728$	7.23576	0.268175
$729$	−21.9009	−0.811144
$730$	−28.6883	−1.06180
$731$	3.38595	0.125234
$732$	−7.71166	−0.285031
$733$	40.6366	1.50095	0.750473	−	0.660901i	$-0.229826\pi$
$733$	40.6366	1.50095	0.750473	+	0.660901i	$0.229826\pi$
$734$	−43.3650	−1.60063
$735$	−14.0718	−0.519047
$736$	55.2606	2.03693
$737$	−5.14387	−0.189477
$738$	50.5711	1.86155
$739$	5.19372	0.191054	0.0955270	−	0.995427i	$-0.469546\pi$
$739$	5.19372	0.191054	0.0955270	+	0.995427i	$0.469546\pi$
$740$	4.12834	0.151761
$741$	−43.1682	−1.58582
$742$	−31.7621	−1.16602
$743$	−18.6557	−0.684411	−0.342206	−	0.939625i	$-0.611174\pi$
$743$	−18.6557	−0.684411	−0.342206	+	0.939625i	$0.611174\pi$
$744$	−2.22487	−0.0815675
$745$	−20.5836	−0.754126
$746$	13.8193	0.505961
$747$	8.96298	0.327938
$748$	−1.18387	−0.0432866
$749$	19.1339	0.699136
$750$	54.4388	1.98782
$751$	−9.88671	−0.360771	−0.180386	−	0.983596i	$-0.557735\pi$
$751$	−9.88671	−0.360771	−0.180386	+	0.983596i	$0.557735\pi$
$752$	−4.63402	−0.168985
$753$	−58.6527	−2.13742
$754$	24.1812	0.880627
$755$	9.09123	0.330864
$756$	−2.10944	−0.0767195
$757$	39.0022	1.41756	0.708779	−	0.705431i	$-0.249246\pi$
$757$	39.0022	1.41756	0.708779	+	0.705431i	$0.249246\pi$
$758$	22.9788	0.834629
$759$	13.3668	0.485184
$760$	−5.68879	−0.206354
$761$	43.5832	1.57989	0.789945	−	0.613178i	$-0.210109\pi$
$761$	43.5832	1.57989	0.789945	+	0.613178i	$0.210109\pi$
$762$	−5.41554	−0.196184
$763$	3.44786	0.124821
$764$	−27.0735	−0.979485
$765$	−5.48228	−0.198212
$766$	−32.6621	−1.18013
$767$	−65.4682	−2.36392
$768$	48.7015	1.75736
$769$	35.1034	1.26586	0.632931	−	0.774208i	$-0.281852\pi$
$769$	35.1034	1.26586	0.632931	+	0.774208i	$0.281852\pi$
$770$	−5.68128	−0.204739
$771$	−7.20852	−0.259609
$772$	−28.8137	−1.03703
$773$	−6.90554	−0.248375	−0.124188	−	0.992259i	$-0.539632\pi$
$773$	−6.90554	−0.248375	−0.124188	+	0.992259i	$0.539632\pi$
$774$	17.5374	0.630368
$775$	1.19128	0.0427922
$776$	−5.42133	−0.194614
$777$	6.18318	0.221820
$778$	−64.2533	−2.30359
$779$	36.8485	1.32023
$780$	36.8939	1.32101
$781$	8.41663	0.301171
$782$	14.3760	0.514085
$783$	1.73515	0.0620093
$784$	13.5576	0.484199
$785$	−17.1209	−0.611072
$786$	−4.21668	−0.150404
$787$	−47.3824	−1.68900	−0.844500	−	0.535556i	$-0.820102\pi$
$787$	−47.3824	−1.68900	−0.844500	+	0.535556i	$0.820102\pi$
$788$	12.7557	0.454403
$789$	−57.8462	−2.05938
$790$	52.5305	1.86895
$791$	28.1329	1.00029
$792$	1.50926	0.0536294
$793$	−9.59508	−0.340731
$794$	−43.2460	−1.53474
$795$	39.8618	1.41375
$796$	10.6098	0.376056
$797$	14.5956	0.517001	0.258501	−	0.966011i	$-0.416772\pi$
$797$	14.5956	0.517001	0.258501	+	0.966011i	$0.416772\pi$
$798$	34.6161	1.22540
$799$	−1.00000	−0.0353775
$800$	−7.01502	−0.248019
$801$	34.5234	1.21982
$802$	−27.4113	−0.967927
$803$	5.54583	0.195708
$804$	−26.7863	−0.944680
$805$	30.7146	1.08255
$806$	11.2467	0.396150
$807$	76.6191	2.69712
$808$	10.8835	0.382881
$809$	21.4214	0.753135	0.376567	−	0.926389i	$-0.377104\pi$
$809$	21.4214	0.753135	0.376567	+	0.926389i	$0.377104\pi$
$810$	37.1735	1.30614
$811$	34.5283	1.21245	0.606227	−	0.795292i	$-0.292682\pi$
$811$	34.5283	1.21245	0.606227	+	0.795292i	$0.292682\pi$
$812$	−8.63290	−0.302955
$813$	−23.9454	−0.839801
$814$	−1.79256	−0.0628292
$815$	14.9830	0.524831
$816$	11.0907	0.388251
$817$	12.7786	0.447065
$818$	23.1222	0.808450
$819$	26.3164	0.919569
$820$	−31.4927	−1.09977
$821$	48.7752	1.70227	0.851133	−	0.524950i	$-0.175916\pi$
$821$	48.7752	1.70227	0.851133	+	0.524950i	$0.175916\pi$
$822$	−37.8515	−1.32022
$823$	−40.0935	−1.39757	−0.698786	−	0.715331i	$-0.746276\pi$
$823$	−40.0935	−1.39757	−0.698786	+	0.715331i	$0.746276\pi$
$824$	13.7490	0.478969
$825$	−1.69684	−0.0590764
$826$	52.4984	1.82665
$827$	7.15705	0.248875	0.124438	−	0.992227i	$-0.460287\pi$
$827$	7.15705	0.248875	0.124438	+	0.992227i	$0.460287\pi$
$828$	33.1502	1.15205
$829$	−1.33528	−0.0463760	−0.0231880	−	0.999731i	$-0.507382\pi$
$829$	−1.33528	−0.0463760	−0.0231880	+	0.999731i	$0.507382\pi$
$830$	−12.5371	−0.435168
$831$	−72.6929	−2.52169
$832$	−21.9332	−0.760397
$833$	2.92566	0.101368
$834$	41.0077	1.41998
$835$	−20.1114	−0.695985
$836$	−4.46791	−0.154526
$837$	0.807025	0.0278949
$838$	−20.6009	−0.711645
$839$	−36.1728	−1.24882	−0.624412	−	0.781095i	$-0.714661\pi$
$839$	−36.1728	−1.24882	−0.624412	+	0.781095i	$0.714661\pi$
$840$	7.28194	0.251251
$841$	−21.8989	−0.755133
$842$	−13.5592	−0.467281
$843$	−36.1496	−1.24506
$844$	−18.1543	−0.624898
$845$	19.7786	0.680405
$846$	−5.17945	−0.178073
$847$	−21.1052	−0.725184
$848$	−38.4051	−1.31884
$849$	33.5798	1.15246
$850$	−1.82496	−0.0625954
$851$	9.69108	0.332206
$852$	43.8290	1.50156
$853$	−1.59402	−0.0545783	−0.0272892	−	0.999628i	$-0.508687\pi$
$853$	−1.59402	−0.0545783	−0.0272892	+	0.999628i	$0.508687\pi$
$854$	7.69420	0.263290
$855$	−20.6901	−0.707586
$856$	7.10994	0.243013
$857$	33.0133	1.12771	0.563857	−	0.825872i	$-0.309317\pi$
$857$	33.0133	1.12771	0.563857	+	0.825872i	$0.309317\pi$
$858$	−16.0196	−0.546902
$859$	−10.2780	−0.350681	−0.175340	−	0.984508i	$-0.556103\pi$
$859$	−10.2780	−0.350681	−0.175340	+	0.984508i	$0.556103\pi$
$860$	−10.9213	−0.372412
$861$	−47.1679	−1.60748
$862$	−20.6103	−0.701991
$863$	43.9238	1.49518	0.747591	−	0.664159i	$-0.231210\pi$
$863$	43.9238	1.49518	0.747591	+	0.664159i	$0.231210\pi$
$864$	−4.75227	−0.161676
$865$	−17.0411	−0.579416
$866$	24.6407	0.837324
$867$	2.39331	0.0812811
$868$	−4.01519	−0.136284
$869$	−10.1548	−0.344480
$870$	24.3355	0.825051
$871$	−33.3283	−1.12929
$872$	1.28119	0.0433865
$873$	−19.7173	−0.667330
$874$	54.2549	1.83520
$875$	−24.1818	−0.817493
$876$	28.8795	0.975748
$877$	19.4549	0.656944	0.328472	−	0.944514i	$-0.393466\pi$
$877$	19.4549	0.656944	0.328472	+	0.944514i	$0.393466\pi$
$878$	−47.0142	−1.58665
$879$	21.8723	0.737734
$880$	−6.86951	−0.231571
$881$	33.8780	1.14138	0.570689	−	0.821166i	$-0.306676\pi$
$881$	33.8780	1.14138	0.570689	+	0.821166i	$0.306676\pi$
$882$	15.1533	0.510239
$883$	25.6036	0.861630	0.430815	−	0.902440i	$-0.358226\pi$
$883$	25.6036	0.861630	0.430815	+	0.902440i	$0.358226\pi$
$884$	−7.67057	−0.257989
$885$	−65.8860	−2.21474
$886$	44.5465	1.49657
$887$	21.1868	0.711382	0.355691	−	0.934604i	$-0.384246\pi$
$887$	21.1868	0.711382	0.355691	+	0.934604i	$0.384246\pi$
$888$	2.29760	0.0771024
$889$	2.40559	0.0806808
$890$	−48.2900	−1.61869
$891$	−7.18614	−0.240745
$892$	−12.3862	−0.414721
$893$	−3.77399	−0.126292
$894$	46.5419	1.55659
$895$	2.95392	0.0987387
$896$	−11.8756	−0.396735
$897$	86.6066	2.89171
$898$	42.2617	1.41029
$899$	3.30276	0.110153
$900$	−4.20823	−0.140274
$901$	−8.28764	−0.276101
$902$	13.6744	0.455308
$903$	−16.3572	−0.544333
$904$	10.4539	0.347691
$905$	−39.3121	−1.30678
$906$	−20.5563	−0.682937
$907$	45.5246	1.51162	0.755810	−	0.654791i	$-0.227243\pi$
$907$	45.5246	1.51162	0.755810	+	0.654791i	$0.227243\pi$
$908$	11.4524	0.380061
$909$	39.5833	1.31290
$910$	−36.8104	−1.22025
$911$	−40.0705	−1.32760	−0.663798	−	0.747912i	$-0.731056\pi$
$911$	−40.0705	−1.32760	−0.663798	+	0.747912i	$0.731056\pi$
$912$	41.8560	1.38599
$913$	2.42359	0.0802090
$914$	−32.1326	−1.06285
$915$	−9.65631	−0.319228
$916$	−5.84032	−0.192970
$917$	1.87305	0.0618537
$918$	−1.23630	−0.0408040
$919$	−21.6664	−0.714707	−0.357354	−	0.933969i	$-0.616321\pi$
$919$	−21.6664	−0.714707	−0.357354	+	0.933969i	$0.616321\pi$
$920$	11.4132	0.376282
$921$	10.9814	0.361849
$922$	26.2914	0.865860
$923$	54.5333	1.79499
$924$	5.71915	0.188146
$925$	−1.23023	−0.0404497
$926$	7.14927	0.234940
$927$	50.0050	1.64238
$928$	−19.4487	−0.638435
$929$	32.8054	1.07631	0.538155	−	0.842846i	$-0.319121\pi$
$929$	32.8054	1.07631	0.538155	+	0.842846i	$0.319121\pi$
$930$	11.3185	0.371149
$931$	11.0414	0.361868
$932$	19.3400	0.633503
$933$	76.9439	2.51903
$934$	−24.0394	−0.786595
$935$	−1.48241	−0.0484799
$936$	9.77888	0.319633
$937$	1.80043	0.0588175	0.0294087	−	0.999567i	$-0.490638\pi$
$937$	1.80043	0.0588175	0.0294087	+	0.999567i	$0.490638\pi$
$938$	26.7257	0.872624
$939$	1.85130	0.0604148
$940$	3.22546	0.105203
$941$	−17.8441	−0.581701	−0.290850	−	0.956769i	$-0.593938\pi$
$941$	−17.8441	−0.581701	−0.290850	+	0.956769i	$0.593938\pi$
$942$	38.7123	1.26132
$943$	−73.9276	−2.40741
$944$	63.4783	2.06604
$945$	−2.64138	−0.0859240
$946$	4.74210	0.154179
$947$	1.53536	0.0498925	0.0249462	−	0.999689i	$-0.492059\pi$
$947$	1.53536	0.0498925	0.0249462	+	0.999689i	$0.492059\pi$
$948$	−52.8806	−1.71748
$949$	35.9328	1.16643
$950$	−6.88736	−0.223456
$951$	47.2038	1.53069
$952$	−1.51398	−0.0490684
$953$	−15.5407	−0.503412	−0.251706	−	0.967804i	$-0.580992\pi$
$953$	−15.5407	−0.503412	−0.251706	+	0.967804i	$0.580992\pi$
$954$	−42.9255	−1.38976
$955$	−33.9006	−1.09700
$956$	−20.6026	−0.666337
$957$	−4.70438	−0.152071
$958$	37.0070	1.19564
$959$	16.8137	0.542942
$960$	−22.0732	−0.712408
$961$	−29.4639	−0.950448
$962$	−11.6144	−0.374464
$963$	25.8588	0.833287
$964$	24.0929	0.775980
$965$	−36.0797	−1.16145
$966$	−69.4490	−2.23448
$967$	57.5797	1.85164	0.925819	−	0.377967i	$-0.123377\pi$
$967$	57.5797	1.85164	0.925819	+	0.377967i	$0.123377\pi$
$968$	−7.84247	−0.252067
$969$	9.03233	0.290160
$970$	27.5798	0.885535
$971$	−29.0772	−0.933133	−0.466566	−	0.884486i	$-0.654509\pi$
$971$	−29.0772	−0.933133	−0.466566	+	0.884486i	$0.654509\pi$
$972$	−34.2862	−1.09973
$973$	−18.2157	−0.583968
$974$	−65.1479	−2.08747
$975$	−10.9942	−0.352097
$976$	9.30343	0.297795
$977$	−20.4699	−0.654890	−0.327445	−	0.944870i	$-0.606188\pi$
$977$	−20.4699	−0.654890	−0.327445	+	0.944870i	$0.606188\pi$
$978$	−33.8781	−1.08330
$979$	9.33511	0.298352
$980$	−9.43660	−0.301441
$981$	4.65966	0.148772
$982$	50.1895	1.60161
$983$	−24.4480	−0.779771	−0.389886	−	0.920863i	$-0.627485\pi$
$983$	−24.4480	−0.779771	−0.389886	+	0.920863i	$0.627485\pi$
$984$	−17.5271	−0.558742
$985$	15.9723	0.508921
$986$	−5.05957	−0.161130
$987$	4.83090	0.153769
$988$	−28.9487	−0.920980
$989$	−25.6371	−0.815213
$990$	−7.67806	−0.244025
$991$	−34.0553	−1.08180	−0.540901	−	0.841086i	$-0.681917\pi$
$991$	−34.0553	−1.08180	−0.540901	+	0.841086i	$0.681917\pi$
$992$	−9.04566	−0.287200
$993$	−18.6810	−0.592823
$994$	−43.7298	−1.38702
$995$	13.2853	0.421173
$996$	12.6206	0.399901
$997$	−47.5345	−1.50543	−0.752716	−	0.658345i	$-0.771257\pi$
$997$	−47.5345	−1.50543	−0.752716	+	0.658345i	$0.771257\pi$
$998$	48.4943	1.53506
$999$	−0.833409	−0.0263679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.g.1.4	✓	20
3.2	odd	2		7191.2.a.bb.1.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.g.1.4	✓	20	1.1	even	1	trivial
7191.2.a.bb.1.17		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:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.a (trivial)

\(f(q)\)	\(=\)	\(q-1.89867 q^{2} +2.39331 q^{3} +1.60496 q^{4} +2.00968 q^{5} -4.54411 q^{6} +2.01850 q^{7} +0.750053 q^{8} +2.72793 q^{9} +O(q^{10})\)	\(q-1.89867 q^{2} +2.39331 q^{3} +1.60496 q^{4} +2.00968 q^{5} -4.54411 q^{6} +2.01850 q^{7} +0.750053 q^{8} +2.72793 q^{9} -3.81573 q^{10} +0.737632 q^{11} +3.84117 q^{12} +4.77929 q^{13} -3.83247 q^{14} +4.80979 q^{15} -4.63402 q^{16} -1.00000 q^{17} -5.17945 q^{18} -3.77399 q^{19} +3.22546 q^{20} +4.83090 q^{21} -1.40052 q^{22} +7.57161 q^{23} +1.79511 q^{24} -0.961174 q^{25} -9.07432 q^{26} -0.651139 q^{27} +3.23961 q^{28} -2.66479 q^{29} -9.13223 q^{30} -1.23940 q^{31} +7.29839 q^{32} +1.76538 q^{33} +1.89867 q^{34} +4.05654 q^{35} +4.37822 q^{36} +1.27992 q^{37} +7.16558 q^{38} +11.4383 q^{39} +1.50737 q^{40} -9.76379 q^{41} -9.17229 q^{42} -3.38595 q^{43} +1.18387 q^{44} +5.48228 q^{45} -14.3760 q^{46} +1.00000 q^{47} -11.0907 q^{48} -2.92566 q^{49} +1.82496 q^{50} -2.39331 q^{51} +7.67057 q^{52} +8.28764 q^{53} +1.23630 q^{54} +1.48241 q^{55} +1.51398 q^{56} -9.03233 q^{57} +5.05957 q^{58} -13.6983 q^{59} +7.71953 q^{60} -2.00763 q^{61} +2.35322 q^{62} +5.50633 q^{63} -4.58921 q^{64} +9.60487 q^{65} -3.35188 q^{66} -6.97349 q^{67} -1.60496 q^{68} +18.1212 q^{69} -7.70205 q^{70} +11.4103 q^{71} +2.04609 q^{72} +7.51842 q^{73} -2.43016 q^{74} -2.30039 q^{75} -6.05710 q^{76} +1.48891 q^{77} -21.7177 q^{78} -13.7668 q^{79} -9.31292 q^{80} -9.74218 q^{81} +18.5382 q^{82} +3.28563 q^{83} +7.75339 q^{84} -2.00968 q^{85} +6.42882 q^{86} -6.37768 q^{87} +0.553263 q^{88} +12.6555 q^{89} -10.4091 q^{90} +9.64700 q^{91} +12.1521 q^{92} -2.96628 q^{93} -1.89867 q^{94} -7.58453 q^{95} +17.4673 q^{96} -7.22793 q^{97} +5.55487 q^{98} +2.01221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9}+O(q^{10}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9} - 2 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} + 13 q^{14} + q^{15} + 28 q^{16} - 20 q^{17} + 15 q^{18} + 5 q^{19} + 37 q^{20} + 6 q^{21} - 19 q^{22} + 4 q^{23} + 30 q^{24} + 41 q^{25} - 9 q^{26} + 6 q^{27} - 25 q^{28} + 26 q^{29} - 25 q^{30} + 6 q^{31} + 28 q^{32} + 29 q^{33} - 4 q^{34} + 21 q^{35} - 5 q^{36} - 8 q^{37} - 21 q^{38} - 19 q^{39} - 25 q^{40} + 69 q^{41} + 3 q^{42} - 7 q^{43} + 16 q^{44} + 39 q^{45} - 24 q^{46} + 20 q^{47} + 26 q^{48} + 53 q^{49} + 16 q^{50} - 3 q^{51} + 18 q^{52} + 29 q^{53} + 23 q^{54} + 5 q^{55} - 22 q^{56} - 36 q^{57} - q^{58} + 55 q^{59} - 103 q^{60} - 17 q^{61} - 7 q^{62} - 9 q^{63} + 58 q^{64} + 40 q^{65} + 50 q^{66} - 6 q^{67} - 24 q^{68} + 17 q^{69} - 15 q^{70} + 47 q^{71} + 7 q^{72} - 32 q^{73} - 67 q^{74} - 22 q^{75} - 5 q^{76} + 4 q^{77} - 60 q^{78} - 26 q^{79} + 108 q^{80} + 68 q^{81} + 25 q^{82} + 3 q^{83} + 24 q^{84} - 13 q^{85} + 8 q^{86} - 41 q^{87} - 47 q^{88} + 119 q^{89} - 54 q^{90} - 35 q^{91} - 15 q^{93} + 4 q^{94} - 48 q^{95} - 84 q^{96} - 13 q^{97} + q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9 - 2 * q^10 + 10 * q^11 + 8 * q^12 + q^13 + 13 * q^14 + q^15 + 28 * q^16 - 20 * q^17 + 15 * q^18 + 5 * q^19 + 37 * q^20 + 6 * q^21 - 19 * q^22 + 4 * q^23 + 30 * q^24 + 41 * q^25 - 9 * q^26 + 6 * q^27 - 25 * q^28 + 26 * q^29 - 25 * q^30 + 6 * q^31 + 28 * q^32 + 29 * q^33 - 4 * q^34 + 21 * q^35 - 5 * q^36 - 8 * q^37 - 21 * q^38 - 19 * q^39 - 25 * q^40 + 69 * q^41 + 3 * q^42 - 7 * q^43 + 16 * q^44 + 39 * q^45 - 24 * q^46 + 20 * q^47 + 26 * q^48 + 53 * q^49 + 16 * q^50 - 3 * q^51 + 18 * q^52 + 29 * q^53 + 23 * q^54 + 5 * q^55 - 22 * q^56 - 36 * q^57 - q^58 + 55 * q^59 - 103 * q^60 - 17 * q^61 - 7 * q^62 - 9 * q^63 + 58 * q^64 + 40 * q^65 + 50 * q^66 - 6 * q^67 - 24 * q^68 + 17 * q^69 - 15 * q^70 + 47 * q^71 + 7 * q^72 - 32 * q^73 - 67 * q^74 - 22 * q^75 - 5 * q^76 + 4 * q^77 - 60 * q^78 - 26 * q^79 + 108 * q^80 + 68 * q^81 + 25 * q^82 + 3 * q^83 + 24 * q^84 - 13 * q^85 + 8 * q^86 - 41 * q^87 - 47 * q^88 + 119 * q^89 - 54 * q^90 - 35 * q^91 - 15 * q^93 + 4 * q^94 - 48 * q^95 - 84 * q^96 - 13 * q^97 + q^98 - 5 * q^99

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