LMFDB - Embedded newform 4029.2.a.k.1.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.68083 q^{2} +1.00000 q^{3} +0.825202 q^{4} +0.800308 q^{5} +1.68083 q^{6} +3.61045 q^{7} -1.97464 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.68083 q^{2} +1.00000 q^{3} +0.825202 q^{4} +0.800308 q^{5} +1.68083 q^{6} +3.61045 q^{7} -1.97464 q^{8} +1.00000 q^{9} +1.34519 q^{10} +4.82141 q^{11} +0.825202 q^{12} +0.00709615 q^{13} +6.06856 q^{14} +0.800308 q^{15} -4.96945 q^{16} +1.00000 q^{17} +1.68083 q^{18} +4.13639 q^{19} +0.660416 q^{20} +3.61045 q^{21} +8.10399 q^{22} -0.768981 q^{23} -1.97464 q^{24} -4.35951 q^{25} +0.0119275 q^{26} +1.00000 q^{27} +2.97935 q^{28} +6.53041 q^{29} +1.34519 q^{30} +1.44813 q^{31} -4.40353 q^{32} +4.82141 q^{33} +1.68083 q^{34} +2.88947 q^{35} +0.825202 q^{36} -8.76200 q^{37} +6.95258 q^{38} +0.00709615 q^{39} -1.58032 q^{40} -3.87228 q^{41} +6.06856 q^{42} +6.04268 q^{43} +3.97864 q^{44} +0.800308 q^{45} -1.29253 q^{46} -8.36103 q^{47} -4.96945 q^{48} +6.03532 q^{49} -7.32761 q^{50} +1.00000 q^{51} +0.00585576 q^{52} -7.19030 q^{53} +1.68083 q^{54} +3.85862 q^{55} -7.12933 q^{56} +4.13639 q^{57} +10.9765 q^{58} -7.87966 q^{59} +0.660416 q^{60} -6.09187 q^{61} +2.43407 q^{62} +3.61045 q^{63} +2.53728 q^{64} +0.00567911 q^{65} +8.10399 q^{66} +4.26443 q^{67} +0.825202 q^{68} -0.768981 q^{69} +4.85672 q^{70} +3.62745 q^{71} -1.97464 q^{72} +15.6135 q^{73} -14.7275 q^{74} -4.35951 q^{75} +3.41336 q^{76} +17.4074 q^{77} +0.0119275 q^{78} +1.00000 q^{79} -3.97709 q^{80} +1.00000 q^{81} -6.50866 q^{82} +12.1008 q^{83} +2.97935 q^{84} +0.800308 q^{85} +10.1567 q^{86} +6.53041 q^{87} -9.52055 q^{88} +13.7917 q^{89} +1.34519 q^{90} +0.0256203 q^{91} -0.634565 q^{92} +1.44813 q^{93} -14.0535 q^{94} +3.31039 q^{95} -4.40353 q^{96} +2.78872 q^{97} +10.1444 q^{98} +4.82141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	1.68083	1.18853	0.594264	−	0.804270i	$-0.297443\pi$
$2$	1.68083	1.18853	0.594264	+	0.804270i	$0.297443\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.825202	0.412601
$5$	0.800308	0.357909	0.178954	−	0.983857i	$-0.442729\pi$
$5$	0.800308	0.357909	0.178954	+	0.983857i	$0.442729\pi$
$6$	1.68083	0.686198
$7$	3.61045	1.36462	0.682310	−	0.731063i	$-0.260975\pi$
$7$	3.61045	1.36462	0.682310	+	0.731063i	$0.260975\pi$
$8$	−1.97464	−0.698141
$9$	1.00000	0.333333
$10$	1.34519	0.425385
$11$	4.82141	1.45371	0.726855	−	0.686791i	$-0.240981\pi$
$11$	4.82141	1.45371	0.726855	+	0.686791i	$0.240981\pi$
$12$	0.825202	0.238215
$13$	0.00709615	0.00196812	0.000984059	−	1.00000i	$-0.499687\pi$
$13$	0.00709615	0.00196812	0.000984059		1.00000i	$0.499687\pi$
$14$	6.06856	1.62189
$15$	0.800308	0.206639
$16$	−4.96945	−1.24236
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.68083	0.396176
$19$	4.13639	0.948953	0.474476	−	0.880268i	$-0.342637\pi$
$19$	4.13639	0.948953	0.474476	+	0.880268i	$0.342637\pi$
$20$	0.660416	0.147674
$21$	3.61045	0.787864
$22$	8.10399	1.72778
$23$	−0.768981	−0.160344	−0.0801718	−	0.996781i	$-0.525547\pi$
$23$	−0.768981	−0.160344	−0.0801718	+	0.996781i	$0.525547\pi$
$24$	−1.97464	−0.403072
$25$	−4.35951	−0.871901
$26$	0.0119275	0.00233917
$27$	1.00000	0.192450
$28$	2.97935	0.563044
$29$	6.53041	1.21267	0.606333	−	0.795211i	$-0.292640\pi$
$29$	6.53041	1.21267	0.606333	+	0.795211i	$0.292640\pi$
$30$	1.34519	0.245596
$31$	1.44813	0.260092	0.130046	−	0.991508i	$-0.458487\pi$
$31$	1.44813	0.260092	0.130046	+	0.991508i	$0.458487\pi$
$32$	−4.40353	−0.778442
$33$	4.82141	0.839300
$34$	1.68083	0.288261
$35$	2.88947	0.488410
$36$	0.825202	0.137534
$37$	−8.76200	−1.44046	−0.720232	−	0.693733i	$-0.755965\pi$
$37$	−8.76200	−1.44046	−0.720232	+	0.693733i	$0.755965\pi$
$38$	6.95258	1.12786
$39$	0.00709615	0.00113629
$40$	−1.58032	−0.249871
$41$	−3.87228	−0.604749	−0.302374	−	0.953189i	$-0.597779\pi$
$41$	−3.87228	−0.604749	−0.302374	+	0.953189i	$0.597779\pi$
$42$	6.06856	0.936399
$43$	6.04268	0.921501	0.460750	−	0.887530i	$-0.347580\pi$
$43$	6.04268	0.921501	0.460750	+	0.887530i	$0.347580\pi$
$44$	3.97864	0.599803
$45$	0.800308	0.119303
$46$	−1.29253	−0.190573
$47$	−8.36103	−1.21958	−0.609791	−	0.792562i	$-0.708747\pi$
$47$	−8.36103	−1.21958	−0.609791	+	0.792562i	$0.708747\pi$
$48$	−4.96945	−0.717278
$49$	6.03532	0.862189
$50$	−7.32761	−1.03628
$51$	1.00000	0.140028
$52$	0.00585576	0.000812048 0
$53$	−7.19030	−0.987663	−0.493832	−	0.869558i	$-0.664404\pi$
$53$	−7.19030	−0.987663	−0.493832	+	0.869558i	$0.664404\pi$
$54$	1.68083	0.228733
$55$	3.85862	0.520296
$56$	−7.12933	−0.952697
$57$	4.13639	0.547878
$58$	10.9765	1.44129
$59$	−7.87966	−1.02584	−0.512922	−	0.858435i	$-0.671437\pi$
$59$	−7.87966	−1.02584	−0.512922	+	0.858435i	$0.671437\pi$
$60$	0.660416	0.0852594
$61$	−6.09187	−0.779984	−0.389992	−	0.920818i	$-0.627522\pi$
$61$	−6.09187	−0.779984	−0.389992	+	0.920818i	$0.627522\pi$
$62$	2.43407	0.309127
$63$	3.61045	0.454873
$64$	2.53728	0.317160
$65$	0.00567911	0.000704407 0
$66$	8.10399	0.997533
$67$	4.26443	0.520983	0.260491	−	0.965476i	$-0.416115\pi$
$67$	4.26443	0.520983	0.260491	+	0.965476i	$0.416115\pi$
$68$	0.825202	0.100070
$69$	−0.768981	−0.0925745
$70$	4.85672	0.580489
$71$	3.62745	0.430499	0.215250	−	0.976559i	$-0.430944\pi$
$71$	3.62745	0.430499	0.215250	+	0.976559i	$0.430944\pi$
$72$	−1.97464	−0.232714
$73$	15.6135	1.82742	0.913711	−	0.406364i	$-0.133204\pi$
$73$	15.6135	1.82742	0.913711	+	0.406364i	$0.133204\pi$
$74$	−14.7275	−1.71203
$75$	−4.35951	−0.503392
$76$	3.41336	0.391539
$77$	17.4074	1.98376
$78$	0.0119275	0.00135052
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−3.97709	−0.444652
$81$	1.00000	0.111111
$82$	−6.50866	−0.718761
$83$	12.1008	1.32823	0.664115	−	0.747630i	$-0.268808\pi$
$83$	12.1008	1.32823	0.664115	+	0.747630i	$0.268808\pi$
$84$	2.97935	0.325074
$85$	0.800308	0.0868056
$86$	10.1567	1.09523
$87$	6.53041	0.700133
$88$	−9.52055	−1.01489
$89$	13.7917	1.46192	0.730960	−	0.682420i	$-0.239073\pi$
$89$	13.7917	1.46192	0.730960	+	0.682420i	$0.239073\pi$
$90$	1.34519	0.141795
$91$	0.0256203	0.00268574
$92$	−0.634565	−0.0661580
$93$	1.44813	0.150164
$94$	−14.0535	−1.44951
$95$	3.31039	0.339638
$96$	−4.40353	−0.449434
$97$	2.78872	0.283152	0.141576	−	0.989927i	$-0.454783\pi$
$97$	2.78872	0.283152	0.141576	+	0.989927i	$0.454783\pi$
$98$	10.1444	1.02474
$99$	4.82141	0.484570
$100$	−3.59748	−0.359748
$101$	3.62805	0.361004	0.180502	−	0.983575i	$-0.442228\pi$
$101$	3.62805	0.361004	0.180502	+	0.983575i	$0.442228\pi$
$102$	1.68083	0.166427
$103$	−17.5539	−1.72964	−0.864819	−	0.502084i	$-0.832567\pi$
$103$	−17.5539	−1.72964	−0.864819	+	0.502084i	$0.832567\pi$
$104$	−0.0140123	−0.00137402
$105$	2.88947	0.281983
$106$	−12.0857	−1.17387
$107$	−7.48986	−0.724072	−0.362036	−	0.932164i	$-0.617918\pi$
$107$	−7.48986	−0.724072	−0.362036	+	0.932164i	$0.617918\pi$
$108$	0.825202	0.0794051
$109$	4.12658	0.395254	0.197627	−	0.980277i	$-0.436676\pi$
$109$	4.12658	0.395254	0.197627	+	0.980277i	$0.436676\pi$
$110$	6.48569	0.618386
$111$	−8.76200	−0.831652
$112$	−17.9419	−1.69535
$113$	4.87245	0.458361	0.229181	−	0.973384i	$-0.426395\pi$
$113$	4.87245	0.458361	0.229181	+	0.973384i	$0.426395\pi$
$114$	6.95258	0.651169
$115$	−0.615422	−0.0573884
$116$	5.38891	0.500348
$117$	0.00709615	0.000656040 0
$118$	−13.2444	−1.21925
$119$	3.61045	0.330969
$120$	−1.58032	−0.144263
$121$	12.2460	1.11327
$122$	−10.2394	−0.927034
$123$	−3.87228	−0.349152
$124$	1.19500	0.107314
$125$	−7.49049	−0.669970
$126$	6.06856	0.540630
$127$	−13.2192	−1.17302	−0.586509	−	0.809942i	$-0.699498\pi$
$127$	−13.2192	−1.17302	−0.586509	+	0.809942i	$0.699498\pi$
$128$	13.0718	1.15540
$129$	6.04268	0.532029
$130$	0.00954564	0.000837208 0
$131$	−9.27464	−0.810329	−0.405165	−	0.914244i	$-0.632786\pi$
$131$	−9.27464	−0.810329	−0.405165	+	0.914244i	$0.632786\pi$
$132$	3.97864	0.346296
$133$	14.9342	1.29496
$134$	7.16779	0.619203
$135$	0.800308	0.0688796
$136$	−1.97464	−0.169324
$137$	16.2974	1.39238	0.696189	−	0.717859i	$-0.254878\pi$
$137$	16.2974	1.39238	0.696189	+	0.717859i	$0.254878\pi$
$138$	−1.29253	−0.110027
$139$	−4.02326	−0.341249	−0.170624	−	0.985336i	$-0.554578\pi$
$139$	−4.02326	−0.341249	−0.170624	+	0.985336i	$0.554578\pi$
$140$	2.38440	0.201518
$141$	−8.36103	−0.704126
$142$	6.09714	0.511661
$143$	0.0342135	0.00286107
$144$	−4.96945	−0.414120
$145$	5.22634	0.434024
$146$	26.2437	2.17194
$147$	6.03532	0.497785
$148$	−7.23042	−0.594337
$149$	−5.87752	−0.481505	−0.240753	−	0.970586i	$-0.577394\pi$
$149$	−5.87752	−0.481505	−0.240753	+	0.970586i	$0.577394\pi$
$150$	−7.32761	−0.598297
$151$	−2.63570	−0.214491	−0.107245	−	0.994233i	$-0.534203\pi$
$151$	−2.63570	−0.214491	−0.107245	+	0.994233i	$0.534203\pi$
$152$	−8.16788	−0.662502
$153$	1.00000	0.0808452
$154$	29.2590	2.35776
$155$	1.15895	0.0930893
$156$	0.00585576	0.000468836 0
$157$	22.1610	1.76864	0.884319	−	0.466883i	$-0.154623\pi$
$157$	22.1610	1.76864	0.884319	+	0.466883i	$0.154623\pi$
$158$	1.68083	0.133720
$159$	−7.19030	−0.570228
$160$	−3.52418	−0.278611
$161$	−2.77637	−0.218808
$162$	1.68083	0.132059
$163$	−9.03546	−0.707712	−0.353856	−	0.935300i	$-0.615130\pi$
$163$	−9.03546	−0.707712	−0.353856	+	0.935300i	$0.615130\pi$
$164$	−3.19541	−0.249520
$165$	3.85862	0.300393
$166$	20.3394	1.57864
$167$	−2.81925	−0.218160	−0.109080	−	0.994033i	$-0.534790\pi$
$167$	−2.81925	−0.218160	−0.109080	+	0.994033i	$0.534790\pi$
$168$	−7.12933	−0.550040
$169$	−12.9999	−0.999996
$170$	1.34519	0.103171
$171$	4.13639	0.316318
$172$	4.98644	0.380212
$173$	−20.0327	−1.52306	−0.761530	−	0.648130i	$-0.775552\pi$
$173$	−20.0327	−1.52306	−0.761530	+	0.648130i	$0.775552\pi$
$174$	10.9765	0.832129
$175$	−15.7398	−1.18981
$176$	−23.9597	−1.80603
$177$	−7.87966	−0.592272
$178$	23.1816	1.73753
$179$	15.3999	1.15104	0.575521	−	0.817787i	$-0.304799\pi$
$179$	15.3999	1.15104	0.575521	+	0.817787i	$0.304799\pi$
$180$	0.660416	0.0492245
$181$	4.31558	0.320774	0.160387	−	0.987054i	$-0.448726\pi$
$181$	4.31558	0.320774	0.160387	+	0.987054i	$0.448726\pi$
$182$	0.0430634	0.00319207
$183$	−6.09187	−0.450324
$184$	1.51846	0.111942
$185$	−7.01230	−0.515555
$186$	2.43407	0.178475
$187$	4.82141	0.352577
$188$	−6.89954	−0.503201
$189$	3.61045	0.262621
$190$	5.56421	0.403670
$191$	−0.240788	−0.0174228	−0.00871139	−	0.999962i	$-0.502773\pi$
$191$	−0.240788	−0.0174228	−0.00871139	+	0.999962i	$0.502773\pi$
$192$	2.53728	0.183113
$193$	10.6442	0.766190	0.383095	−	0.923709i	$-0.374858\pi$
$193$	10.6442	0.766190	0.383095	+	0.923709i	$0.374858\pi$
$194$	4.68738	0.336534
$195$	0.00567911	0.000406690 0
$196$	4.98036	0.355740
$197$	−15.3640	−1.09464	−0.547319	−	0.836924i	$-0.684352\pi$
$197$	−15.3640	−1.09464	−0.547319	+	0.836924i	$0.684352\pi$
$198$	8.10399	0.575926
$199$	−27.1318	−1.92332	−0.961662	−	0.274238i	$-0.911575\pi$
$199$	−27.1318	−1.92332	−0.961662	+	0.274238i	$0.911575\pi$
$200$	8.60845	0.608710
$201$	4.26443	0.300789
$202$	6.09815	0.429064
$203$	23.5777	1.65483
$204$	0.825202	0.0577757
$205$	−3.09902	−0.216445
$206$	−29.5052	−2.05573
$207$	−0.768981	−0.0534479
$208$	−0.0352639	−0.00244511
$209$	19.9432	1.37950
$210$	4.85672	0.335145
$211$	−10.2740	−0.707292	−0.353646	−	0.935379i	$-0.615058\pi$
$211$	−10.2740	−0.707292	−0.353646	+	0.935379i	$0.615058\pi$
$212$	−5.93345	−0.407511
$213$	3.62745	0.248549
$214$	−12.5892	−0.860580
$215$	4.83601	0.329813
$216$	−1.97464	−0.134357
$217$	5.22841	0.354927
$218$	6.93609	0.469771
$219$	15.6135	1.05506
$220$	3.18414	0.214675
$221$	0.00709615	0.000477339 0
$222$	−14.7275	−0.988443
$223$	11.5412	0.772856	0.386428	−	0.922320i	$-0.373709\pi$
$223$	11.5412	0.772856	0.386428	+	0.922320i	$0.373709\pi$
$224$	−15.8987	−1.06228
$225$	−4.35951	−0.290634
$226$	8.18978	0.544776
$227$	8.60197	0.570933	0.285466	−	0.958389i	$-0.407851\pi$
$227$	8.60197	0.570933	0.285466	+	0.958389i	$0.407851\pi$
$228$	3.41336	0.226055
$229$	−11.5091	−0.760542	−0.380271	−	0.924875i	$-0.624169\pi$
$229$	−11.5091	−0.760542	−0.380271	+	0.924875i	$0.624169\pi$
$230$	−1.03442	−0.0682078
$231$	17.4074	1.14533
$232$	−12.8952	−0.846612
$233$	−16.7940	−1.10021	−0.550107	−	0.835094i	$-0.685413\pi$
$233$	−16.7940	−1.10021	−0.550107	+	0.835094i	$0.685413\pi$
$234$	0.0119275	0.000779722 0
$235$	−6.69140	−0.436499
$236$	−6.50232	−0.423265
$237$	1.00000	0.0649570
$238$	6.06856	0.393366
$239$	0.371744	0.0240461	0.0120231	−	0.999928i	$-0.496173\pi$
$239$	0.371744	0.0240461	0.0120231	+	0.999928i	$0.496173\pi$
$240$	−3.97709	−0.256720
$241$	0.0229532	0.00147855	0.000739273	−	1.00000i	$-0.499765\pi$
$241$	0.0229532	0.00147855	0.000739273		1.00000i	$0.499765\pi$
$242$	20.5835	1.32316
$243$	1.00000	0.0641500
$244$	−5.02702	−0.321822
$245$	4.83012	0.308585
$246$	−6.50866	−0.414977
$247$	0.0293524	0.00186765
$248$	−2.85954	−0.181581
$249$	12.1008	0.766854
$250$	−12.5903	−0.796279
$251$	14.0560	0.887206	0.443603	−	0.896223i	$-0.353700\pi$
$251$	14.0560	0.887206	0.443603	+	0.896223i	$0.353700\pi$
$252$	2.97935	0.187681
$253$	−3.70758	−0.233093
$254$	−22.2194	−1.39417
$255$	0.800308	0.0501172
$256$	16.8970	1.05606
$257$	−20.2155	−1.26101	−0.630504	−	0.776186i	$-0.717152\pi$
$257$	−20.2155	−1.26101	−0.630504	+	0.776186i	$0.717152\pi$
$258$	10.1567	0.632331
$259$	−31.6347	−1.96569
$260$	0.00468641	0.000290639 0
$261$	6.53041	0.404222
$262$	−15.5891	−0.963100
$263$	10.6398	0.656080	0.328040	−	0.944664i	$-0.393612\pi$
$263$	10.6398	0.656080	0.328040	+	0.944664i	$0.393612\pi$
$264$	−9.52055	−0.585949
$265$	−5.75445	−0.353493
$266$	25.1019	1.53910
$267$	13.7917	0.844040
$268$	3.51901	0.214958
$269$	3.95832	0.241343	0.120672	−	0.992692i	$-0.461495\pi$
$269$	3.95832	0.241343	0.120672	+	0.992692i	$0.461495\pi$
$270$	1.34519	0.0818654
$271$	−7.37830	−0.448200	−0.224100	−	0.974566i	$-0.571944\pi$
$271$	−7.37830	−0.448200	−0.224100	+	0.974566i	$0.571944\pi$
$272$	−4.96945	−0.301317
$273$	0.0256203	0.00155061
$274$	27.3932	1.65488
$275$	−21.0190	−1.26749
$276$	−0.634565	−0.0381963
$277$	−10.8218	−0.650222	−0.325111	−	0.945676i	$-0.605402\pi$
$277$	−10.8218	−0.650222	−0.325111	+	0.945676i	$0.605402\pi$
$278$	−6.76244	−0.405584
$279$	1.44813	0.0866975
$280$	−5.70566	−0.340978
$281$	9.19579	0.548575	0.274288	−	0.961648i	$-0.411558\pi$
$281$	9.19579	0.548575	0.274288	+	0.961648i	$0.411558\pi$
$282$	−14.0535	−0.836874
$283$	4.00602	0.238133	0.119066	−	0.992886i	$-0.462010\pi$
$283$	4.00602	0.238133	0.119066	+	0.992886i	$0.462010\pi$
$284$	2.99338	0.177624
$285$	3.31039	0.196090
$286$	0.0575072	0.00340047
$287$	−13.9807	−0.825252
$288$	−4.40353	−0.259481
$289$	1.00000	0.0588235
$290$	8.78461	0.515850
$291$	2.78872	0.163478
$292$	12.8843	0.753997
$293$	9.29992	0.543307	0.271654	−	0.962395i	$-0.412429\pi$
$293$	9.29992	0.543307	0.271654	+	0.962395i	$0.412429\pi$
$294$	10.1444	0.591632
$295$	−6.30616	−0.367159
$296$	17.3018	1.00565
$297$	4.82141	0.279767
$298$	−9.87914	−0.572283
$299$	−0.00545681	−0.000315575 0
$300$	−3.59748	−0.207700
$301$	21.8168	1.25750
$302$	−4.43018	−0.254928
$303$	3.62805	0.208426
$304$	−20.5556	−1.17894
$305$	−4.87537	−0.279163
$306$	1.68083	0.0960869
$307$	−20.2010	−1.15293	−0.576466	−	0.817121i	$-0.695569\pi$
$307$	−20.2010	−1.15293	−0.576466	+	0.817121i	$0.695569\pi$
$308$	14.3647	0.818503
$309$	−17.5539	−0.998607
$310$	1.94801	0.110639
$311$	19.9709	1.13245	0.566223	−	0.824252i	$-0.308404\pi$
$311$	19.9709	1.13245	0.566223	+	0.824252i	$0.308404\pi$
$312$	−0.0140123	−0.000793293 0
$313$	−26.9665	−1.52423	−0.762117	−	0.647439i	$-0.775840\pi$
$313$	−26.9665	−1.52423	−0.762117	+	0.647439i	$0.775840\pi$
$314$	37.2489	2.10208
$315$	2.88947	0.162803
$316$	0.825202	0.0464213
$317$	−5.89179	−0.330916	−0.165458	−	0.986217i	$-0.552910\pi$
$317$	−5.89179	−0.330916	−0.165458	+	0.986217i	$0.552910\pi$
$318$	−12.0857	−0.677732
$319$	31.4858	1.76287
$320$	2.03061	0.113514
$321$	−7.48986	−0.418043
$322$	−4.66661	−0.260060
$323$	4.13639	0.230155
$324$	0.825202	0.0458446
$325$	−0.0309357	−0.00171601
$326$	−15.1871	−0.841136
$327$	4.12658	0.228200
$328$	7.64636	0.422200
$329$	−30.1870	−1.66427
$330$	6.48569	0.357026
$331$	9.49535	0.521912	0.260956	−	0.965351i	$-0.415962\pi$
$331$	9.49535	0.521912	0.260956	+	0.965351i	$0.415962\pi$
$332$	9.98557	0.548029
$333$	−8.76200	−0.480155
$334$	−4.73868	−0.259289
$335$	3.41286	0.186464
$336$	−17.9419	−0.978812
$337$	13.0999	0.713595	0.356797	−	0.934182i	$-0.383869\pi$
$337$	13.0999	0.713595	0.356797	+	0.934182i	$0.383869\pi$
$338$	−21.8508	−1.18852
$339$	4.87245	0.264635
$340$	0.660416	0.0358161
$341$	6.98205	0.378099
$342$	6.95258	0.375953
$343$	−3.48292	−0.188060
$344$	−11.9321	−0.643337
$345$	−0.615422	−0.0331332
$346$	−33.6717	−1.81020
$347$	6.33450	0.340054	0.170027	−	0.985439i	$-0.445615\pi$
$347$	6.33450	0.340054	0.170027	+	0.985439i	$0.445615\pi$
$348$	5.38891	0.288876
$349$	27.0156	1.44611	0.723057	−	0.690788i	$-0.242736\pi$
$349$	27.0156	1.44611	0.723057	+	0.690788i	$0.242736\pi$
$350$	−26.4559	−1.41413
$351$	0.00709615	0.000378765 0
$352$	−21.2312	−1.13163
$353$	7.94784	0.423021	0.211510	−	0.977376i	$-0.432162\pi$
$353$	7.94784	0.423021	0.211510	+	0.977376i	$0.432162\pi$
$354$	−13.2444	−0.703932
$355$	2.90308	0.154079
$356$	11.3810	0.603190
$357$	3.61045	0.191085
$358$	25.8846	1.36805
$359$	4.49378	0.237173	0.118586	−	0.992944i	$-0.462164\pi$
$359$	4.49378	0.237173	0.118586	+	0.992944i	$0.462164\pi$
$360$	−1.58032	−0.0832902
$361$	−1.89029	−0.0994890
$362$	7.25377	0.381250
$363$	12.2460	0.642749
$364$	0.0211419	0.00110814
$365$	12.4956	0.654050
$366$	−10.2394	−0.535223
$367$	−15.1194	−0.789227	−0.394613	−	0.918847i	$-0.629121\pi$
$367$	−15.1194	−0.789227	−0.394613	+	0.918847i	$0.629121\pi$
$368$	3.82141	0.199205
$369$	−3.87228	−0.201583
$370$	−11.7865	−0.612752
$371$	−25.9602	−1.34779
$372$	1.19500	0.0619580
$373$	14.6396	0.758008	0.379004	−	0.925395i	$-0.376267\pi$
$373$	14.6396	0.758008	0.379004	+	0.925395i	$0.376267\pi$
$374$	8.10399	0.419047
$375$	−7.49049	−0.386807
$376$	16.5100	0.851439
$377$	0.0463408	0.00238667
$378$	6.06856	0.312133
$379$	−20.5840	−1.05733	−0.528665	−	0.848831i	$-0.677307\pi$
$379$	−20.5840	−1.05733	−0.528665	+	0.848831i	$0.677307\pi$
$380$	2.73174	0.140135
$381$	−13.2192	−0.677243
$382$	−0.404724	−0.0207075
$383$	−28.7867	−1.47093	−0.735466	−	0.677561i	$-0.763037\pi$
$383$	−28.7867	−1.47093	−0.735466	+	0.677561i	$0.763037\pi$
$384$	13.0718	0.667068
$385$	13.9313	0.710006
$386$	17.8912	0.910639
$387$	6.04268	0.307167
$388$	2.30126	0.116829
$389$	−18.6908	−0.947660	−0.473830	−	0.880616i	$-0.657129\pi$
$389$	−18.6908	−0.947660	−0.473830	+	0.880616i	$0.657129\pi$
$390$	0.00954564	0.000483362 0
$391$	−0.768981	−0.0388890
$392$	−11.9176	−0.601929
$393$	−9.27464	−0.467844
$394$	−25.8243	−1.30101
$395$	0.800308	0.0402679
$396$	3.97864	0.199934
$397$	−25.0007	−1.25475	−0.627376	−	0.778717i	$-0.715871\pi$
$397$	−25.0007	−1.25475	−0.627376	+	0.778717i	$0.715871\pi$
$398$	−45.6041	−2.28593
$399$	14.9342	0.747646
$400$	21.6643	1.08322
$401$	6.30617	0.314915	0.157457	−	0.987526i	$-0.449670\pi$
$401$	6.30617	0.314915	0.157457	+	0.987526i	$0.449670\pi$
$402$	7.16779	0.357497
$403$	0.0102762	0.000511893 0
$404$	2.99388	0.148951
$405$	0.800308	0.0397676
$406$	39.6302	1.96681
$407$	−42.2452	−2.09402
$408$	−1.97464	−0.0977592
$409$	−30.2063	−1.49361	−0.746803	−	0.665045i	$-0.768412\pi$
$409$	−30.2063	−1.49361	−0.746803	+	0.665045i	$0.768412\pi$
$410$	−5.20893	−0.257251
$411$	16.2974	0.803890
$412$	−14.4855	−0.713651
$413$	−28.4491	−1.39989
$414$	−1.29253	−0.0635244
$415$	9.68433	0.475385
$416$	−0.0312481	−0.00153207
$417$	−4.02326	−0.197020
$418$	33.5213	1.63958
$419$	−9.38530	−0.458502	−0.229251	−	0.973367i	$-0.573628\pi$
$419$	−9.38530	−0.458502	−0.229251	+	0.973367i	$0.573628\pi$
$420$	2.38440	0.116347
$421$	16.1251	0.785892	0.392946	−	0.919562i	$-0.371456\pi$
$421$	16.1251	0.785892	0.392946	+	0.919562i	$0.371456\pi$
$422$	−17.2689	−0.840638
$423$	−8.36103	−0.406527
$424$	14.1982	0.689528
$425$	−4.35951	−0.211467
$426$	6.09714	0.295407
$427$	−21.9944	−1.06438
$428$	−6.18065	−0.298753
$429$	0.0342135	0.00165184
$430$	8.12853	0.391992
$431$	30.0215	1.44609	0.723043	−	0.690803i	$-0.242743\pi$
$431$	30.0215	1.44609	0.723043	+	0.690803i	$0.242743\pi$
$432$	−4.96945	−0.239093
$433$	25.3076	1.21621	0.608103	−	0.793858i	$-0.291931\pi$
$433$	25.3076	1.21621	0.608103	+	0.793858i	$0.291931\pi$
$434$	8.78808	0.421841
$435$	5.22634	0.250584
$436$	3.40526	0.163082
$437$	−3.18080	−0.152159
$438$	26.2437	1.25397
$439$	−26.9454	−1.28603	−0.643016	−	0.765853i	$-0.722317\pi$
$439$	−26.9454	−1.28603	−0.643016	+	0.765853i	$0.722317\pi$
$440$	−7.61938	−0.363239
$441$	6.03532	0.287396
$442$	0.0119275	0.000567331 0
$443$	−29.0759	−1.38144	−0.690719	−	0.723123i	$-0.742706\pi$
$443$	−29.0759	−1.38144	−0.690719	+	0.723123i	$0.742706\pi$
$444$	−7.23042	−0.343141
$445$	11.0376	0.523234
$446$	19.3988	0.918562
$447$	−5.87752	−0.277997
$448$	9.16073	0.432804
$449$	−8.25745	−0.389693	−0.194847	−	0.980834i	$-0.562421\pi$
$449$	−8.25745	−0.389693	−0.194847	+	0.980834i	$0.562421\pi$
$450$	−7.32761	−0.345427
$451$	−18.6699	−0.879129
$452$	4.02076	0.189120
$453$	−2.63570	−0.123836
$454$	14.4585	0.678570
$455$	0.0205041	0.000961248 0
$456$	−8.16788	−0.382496
$457$	−5.33948	−0.249770	−0.124885	−	0.992171i	$-0.539856\pi$
$457$	−5.33948	−0.249770	−0.124885	+	0.992171i	$0.539856\pi$
$458$	−19.3449	−0.903927
$459$	1.00000	0.0466760
$460$	−0.507848	−0.0236785
$461$	−12.4128	−0.578123	−0.289061	−	0.957311i	$-0.593343\pi$
$461$	−12.4128	−0.578123	−0.289061	+	0.957311i	$0.593343\pi$
$462$	29.2590	1.36125
$463$	28.6863	1.33317	0.666583	−	0.745431i	$-0.267756\pi$
$463$	28.6863	1.33317	0.666583	+	0.745431i	$0.267756\pi$
$464$	−32.4525	−1.50657
$465$	1.15895	0.0537452
$466$	−28.2280	−1.30764
$467$	−20.3744	−0.942815	−0.471407	−	0.881916i	$-0.656254\pi$
$467$	−20.3744	−0.942815	−0.471407	+	0.881916i	$0.656254\pi$
$468$	0.00585576	0.000270683 0
$469$	15.3965	0.710943
$470$	−11.2471	−0.518792
$471$	22.1610	1.02112
$472$	15.5595	0.716184
$473$	29.1343	1.33960
$474$	1.68083	0.0772033
$475$	−18.0326	−0.827393
$476$	2.97935	0.136558
$477$	−7.19030	−0.329221
$478$	0.624840	0.0285795
$479$	21.9055	1.00089	0.500445	−	0.865768i	$-0.333170\pi$
$479$	21.9055	1.00089	0.500445	+	0.865768i	$0.333170\pi$
$480$	−3.52418	−0.160856
$481$	−0.0621765	−0.00283500
$482$	0.0385805	0.00175729
$483$	−2.77637	−0.126329
$484$	10.1054	0.459338
$485$	2.23184	0.101342
$486$	1.68083	0.0762442
$487$	−9.40854	−0.426342	−0.213171	−	0.977015i	$-0.568379\pi$
$487$	−9.40854	−0.426342	−0.213171	+	0.977015i	$0.568379\pi$
$488$	12.0292	0.544538
$489$	−9.03546	−0.408598
$490$	8.11862	0.366762
$491$	−1.19719	−0.0540282	−0.0270141	−	0.999635i	$-0.508600\pi$
$491$	−1.19719	−0.0540282	−0.0270141	+	0.999635i	$0.508600\pi$
$492$	−3.19541	−0.144060
$493$	6.53041	0.294115
$494$	0.0493366	0.00221976
$495$	3.85862	0.173432
$496$	−7.19642	−0.323129
$497$	13.0967	0.587468
$498$	20.3394	0.911428
$499$	−7.66272	−0.343031	−0.171515	−	0.985181i	$-0.554866\pi$
$499$	−7.66272	−0.343031	−0.171515	+	0.985181i	$0.554866\pi$
$500$	−6.18117	−0.276430
$501$	−2.81925	−0.125955
$502$	23.6258	1.05447
$503$	−21.3583	−0.952320	−0.476160	−	0.879359i	$-0.657972\pi$
$503$	−21.3583	−0.952320	−0.476160	+	0.879359i	$0.657972\pi$
$504$	−7.12933	−0.317566
$505$	2.90356	0.129207
$506$	−6.23182	−0.277038
$507$	−12.9999	−0.577348
$508$	−10.9086	−0.483989
$509$	32.2107	1.42771	0.713857	−	0.700291i	$-0.246947\pi$
$509$	32.2107	1.42771	0.713857	+	0.700291i	$0.246947\pi$
$510$	1.34519	0.0595658
$511$	56.3717	2.49374
$512$	2.25739	0.0997635
$513$	4.13639	0.182626
$514$	−33.9789	−1.49875
$515$	−14.0485	−0.619053
$516$	4.98644	0.219516
$517$	−40.3120	−1.77292
$518$	−53.1727	−2.33628
$519$	−20.0327	−0.879339
$520$	−0.0112142	−0.000491775 0
$521$	22.6855	0.993870	0.496935	−	0.867788i	$-0.334459\pi$
$521$	22.6855	0.993870	0.496935	+	0.867788i	$0.334459\pi$
$522$	10.9765	0.480430
$523$	−11.1541	−0.487733	−0.243866	−	0.969809i	$-0.578416\pi$
$523$	−11.1541	−0.487733	−0.243866	+	0.969809i	$0.578416\pi$
$524$	−7.65346	−0.334343
$525$	−15.7398	−0.686940
$526$	17.8838	0.779771
$527$	1.44813	0.0630817
$528$	−23.9597	−1.04271
$529$	−22.4087	−0.974290
$530$	−9.67228	−0.420137
$531$	−7.87966	−0.341948
$532$	12.3237	0.534302
$533$	−0.0274783	−0.00119022
$534$	23.1816	1.00317
$535$	−5.99419	−0.259152
$536$	−8.42070	−0.363719
$537$	15.3999	0.664554
$538$	6.65328	0.286843
$539$	29.0988	1.25337
$540$	0.660416	0.0284198
$541$	−2.43689	−0.104770	−0.0523850	−	0.998627i	$-0.516682\pi$
$541$	−2.43689	−0.104770	−0.0523850	+	0.998627i	$0.516682\pi$
$542$	−12.4017	−0.532699
$543$	4.31558	0.185199
$544$	−4.40353	−0.188800
$545$	3.30253	0.141465
$546$	0.0430634	0.00184294
$547$	14.9414	0.638847	0.319424	−	0.947612i	$-0.396511\pi$
$547$	14.9414	0.638847	0.319424	+	0.947612i	$0.396511\pi$
$548$	13.4486	0.574497
$549$	−6.09187	−0.259995
$550$	−35.3294	−1.50645
$551$	27.0123	1.15076
$552$	1.51846	0.0646300
$553$	3.61045	0.153532
$554$	−18.1897	−0.772807
$555$	−7.01230	−0.297656
$556$	−3.32001	−0.140800
$557$	−16.1106	−0.682626	−0.341313	−	0.939950i	$-0.610872\pi$
$557$	−16.1106	−0.682626	−0.341313	+	0.939950i	$0.610872\pi$
$558$	2.43407	0.103042
$559$	0.0428798	0.00181362
$560$	−14.3591	−0.606781
$561$	4.82141	0.203560
$562$	15.4566	0.651997
$563$	−0.284584	−0.0119938	−0.00599689	−	0.999982i	$-0.501909\pi$
$563$	−0.284584	−0.0119938	−0.00599689	+	0.999982i	$0.501909\pi$
$564$	−6.89954	−0.290523
$565$	3.89946	0.164052
$566$	6.73345	0.283028
$567$	3.61045	0.151624
$568$	−7.16291	−0.300549
$569$	1.60417	0.0672505	0.0336252	−	0.999435i	$-0.489295\pi$
$569$	1.60417	0.0672505	0.0336252	+	0.999435i	$0.489295\pi$
$570$	5.56421	0.233059
$571$	−8.09373	−0.338712	−0.169356	−	0.985555i	$-0.554169\pi$
$571$	−8.09373	−0.338712	−0.169356	+	0.985555i	$0.554169\pi$
$572$	0.0282330	0.00118048
$573$	−0.240788	−0.0100591
$574$	−23.4992	−0.980836
$575$	3.35238	0.139804
$576$	2.53728	0.105720
$577$	20.6992	0.861717	0.430859	−	0.902419i	$-0.358211\pi$
$577$	20.6992	0.861717	0.430859	+	0.902419i	$0.358211\pi$
$578$	1.68083	0.0699135
$579$	10.6442	0.442360
$580$	4.31279	0.179079
$581$	43.6891	1.81253
$582$	4.68738	0.194298
$583$	−34.6674	−1.43578
$584$	−30.8310	−1.27580
$585$	0.00567911	0.000234802 0
$586$	15.6316	0.645736
$587$	−21.1626	−0.873473	−0.436737	−	0.899589i	$-0.643866\pi$
$587$	−21.1626	−0.873473	−0.436737	+	0.899589i	$0.643866\pi$
$588$	4.98036	0.205387
$589$	5.99004	0.246815
$590$	−10.5996	−0.436379
$591$	−15.3640	−0.631990
$592$	43.5423	1.78958
$593$	−20.1449	−0.827252	−0.413626	−	0.910447i	$-0.635738\pi$
$593$	−20.1449	−0.827252	−0.413626	+	0.910447i	$0.635738\pi$
$594$	8.10399	0.332511
$595$	2.88947	0.118457
$596$	−4.85015	−0.198670
$597$	−27.1318	−1.11043
$598$	−0.00917199	−0.000375070 0
$599$	−22.6988	−0.927446	−0.463723	−	0.885980i	$-0.653487\pi$
$599$	−22.6988	−0.927446	−0.463723	+	0.885980i	$0.653487\pi$
$600$	8.60845	0.351439
$601$	15.1316	0.617229	0.308615	−	0.951187i	$-0.400135\pi$
$601$	15.1316	0.617229	0.308615	+	0.951187i	$0.400135\pi$
$602$	36.6704	1.49457
$603$	4.26443	0.173661
$604$	−2.17499	−0.0884991
$605$	9.80059	0.398451
$606$	6.09815	0.247720
$607$	8.42545	0.341979	0.170989	−	0.985273i	$-0.445304\pi$
$607$	8.42545	0.341979	0.170989	+	0.985273i	$0.445304\pi$
$608$	−18.2147	−0.738705
$609$	23.5777	0.955416
$610$	−8.19469	−0.331793
$611$	−0.0593311	−0.00240028
$612$	0.825202	0.0333568
$613$	−40.3990	−1.63170	−0.815850	−	0.578264i	$-0.803730\pi$
$613$	−40.3990	−1.63170	−0.815850	+	0.578264i	$0.803730\pi$
$614$	−33.9545	−1.37029
$615$	−3.09902	−0.124964
$616$	−34.3734	−1.38495
$617$	19.4678	0.783744	0.391872	−	0.920020i	$-0.371828\pi$
$617$	19.4678	0.783744	0.391872	+	0.920020i	$0.371828\pi$
$618$	−29.5052	−1.18687
$619$	−26.6505	−1.07118	−0.535588	−	0.844480i	$-0.679910\pi$
$619$	−26.6505	−1.07118	−0.535588	+	0.844480i	$0.679910\pi$
$620$	0.956371	0.0384088
$621$	−0.768981	−0.0308582
$622$	33.5678	1.34595
$623$	49.7943	1.99497
$624$	−0.0352639	−0.00141169
$625$	15.8028	0.632113
$626$	−45.3261	−1.81160
$627$	19.9432	0.796456
$628$	18.2873	0.729742
$629$	−8.76200	−0.349364
$630$	4.85672	0.193496
$631$	−25.1202	−1.00002	−0.500009	−	0.866020i	$-0.666670\pi$
$631$	−25.1202	−1.00002	−0.500009	+	0.866020i	$0.666670\pi$
$632$	−1.97464	−0.0785469
$633$	−10.2740	−0.408355
$634$	−9.90312	−0.393303
$635$	−10.5795	−0.419834
$636$	−5.93345	−0.235277
$637$	0.0428276	0.00169689
$638$	52.9224	2.09522
$639$	3.62745	0.143500
$640$	10.4615	0.413526
$641$	21.2783	0.840441	0.420221	−	0.907422i	$-0.361953\pi$
$641$	21.2783	0.840441	0.420221	+	0.907422i	$0.361953\pi$
$642$	−12.5892	−0.496856
$643$	35.0794	1.38340	0.691699	−	0.722186i	$-0.256862\pi$
$643$	35.0794	1.38340	0.691699	+	0.722186i	$0.256862\pi$
$644$	−2.29106	−0.0902805
$645$	4.83601	0.190418
$646$	6.95258	0.273546
$647$	−4.81679	−0.189368	−0.0946838	−	0.995507i	$-0.530184\pi$
$647$	−4.81679	−0.189368	−0.0946838	+	0.995507i	$0.530184\pi$
$648$	−1.97464	−0.0775712
$649$	−37.9911	−1.49128
$650$	−0.0519978	−0.00203952
$651$	5.22841	0.204917
$652$	−7.45608	−0.292003
$653$	8.92750	0.349360	0.174680	−	0.984625i	$-0.444111\pi$
$653$	8.92750	0.349360	0.174680	+	0.984625i	$0.444111\pi$
$654$	6.93609	0.271223
$655$	−7.42257	−0.290024
$656$	19.2431	0.751316
$657$	15.6135	0.609141
$658$	−50.7394	−1.97803
$659$	−1.19480	−0.0465429	−0.0232714	−	0.999729i	$-0.507408\pi$
$659$	−1.19480	−0.0465429	−0.0232714	+	0.999729i	$0.507408\pi$
$660$	3.18414	0.123942
$661$	−6.91105	−0.268809	−0.134404	−	0.990927i	$-0.542912\pi$
$661$	−6.91105	−0.268809	−0.134404	+	0.990927i	$0.542912\pi$
$662$	15.9601	0.620307
$663$	0.00709615	0.000275592 0
$664$	−23.8946	−0.927291
$665$	11.9520	0.463477
$666$	−14.7275	−0.570678
$667$	−5.02176	−0.194443
$668$	−2.32645	−0.0900130
$669$	11.5412	0.446209
$670$	5.73644	0.221618
$671$	−29.3714	−1.13387
$672$	−15.8987	−0.613306
$673$	−30.3780	−1.17099	−0.585493	−	0.810678i	$-0.699099\pi$
$673$	−30.3780	−1.17099	−0.585493	+	0.810678i	$0.699099\pi$
$674$	22.0187	0.848128
$675$	−4.35951	−0.167797
$676$	−10.7276	−0.412600
$677$	−10.5098	−0.403923	−0.201961	−	0.979393i	$-0.564732\pi$
$677$	−10.5098	−0.403923	−0.201961	+	0.979393i	$0.564732\pi$
$678$	8.18978	0.314526
$679$	10.0685	0.386395
$680$	−1.58032	−0.0606025
$681$	8.60197	0.329628
$682$	11.7357	0.449382
$683$	5.42743	0.207675	0.103837	−	0.994594i	$-0.466888\pi$
$683$	5.42743	0.207675	0.103837	+	0.994594i	$0.466888\pi$
$684$	3.41336	0.130513
$685$	13.0429	0.498344
$686$	−5.85421	−0.223515
$687$	−11.5091	−0.439099
$688$	−30.0288	−1.14484
$689$	−0.0510234	−0.00194384
$690$	−1.03442	−0.0393798
$691$	45.1736	1.71848	0.859242	−	0.511569i	$-0.170935\pi$
$691$	45.1736	1.71848	0.859242	+	0.511569i	$0.170935\pi$
$692$	−16.5311	−0.628416
$693$	17.4074	0.661254
$694$	10.6472	0.404164
$695$	−3.21985	−0.122136
$696$	−12.8952	−0.488791
$697$	−3.87228	−0.146673
$698$	45.4088	1.71875
$699$	−16.7940	−0.635208
$700$	−12.9885	−0.490919
$701$	−15.7042	−0.593141	−0.296570	−	0.955011i	$-0.595843\pi$
$701$	−15.7042	−0.593141	−0.296570	+	0.955011i	$0.595843\pi$
$702$	0.0119275	0.000450173 0
$703$	−36.2430	−1.36693
$704$	12.2333	0.461059
$705$	−6.69140	−0.252013
$706$	13.3590	0.502773
$707$	13.0989	0.492634
$708$	−6.50232	−0.244372
$709$	−5.71431	−0.214606	−0.107303	−	0.994226i	$-0.534221\pi$
$709$	−5.71431	−0.214606	−0.107303	+	0.994226i	$0.534221\pi$
$710$	4.87959	0.183128
$711$	1.00000	0.0375029
$712$	−27.2337	−1.02063
$713$	−1.11359	−0.0417042
$714$	6.06856	0.227110
$715$	0.0273813	0.00102400
$716$	12.7080	0.474921
$717$	0.371744	0.0138830
$718$	7.55330	0.281886
$719$	35.5654	1.32637	0.663183	−	0.748457i	$-0.269205\pi$
$719$	35.5654	1.32637	0.663183	+	0.748457i	$0.269205\pi$
$720$	−3.97709	−0.148217
$721$	−63.3774	−2.36030
$722$	−3.17727	−0.118246
$723$	0.0229532	0.000853639 0
$724$	3.56123	0.132352
$725$	−28.4694	−1.05733
$726$	20.5835	0.763926
$727$	27.9879	1.03801	0.519006	−	0.854770i	$-0.326302\pi$
$727$	27.9879	1.03801	0.519006	+	0.854770i	$0.326302\pi$
$728$	−0.0505908	−0.00187502
$729$	1.00000	0.0370370
$730$	21.0031	0.777358
$731$	6.04268	0.223497
$732$	−5.02702	−0.185804
$733$	−49.1228	−1.81439	−0.907195	−	0.420710i	$-0.861781\pi$
$733$	−49.1228	−1.81439	−0.907195	+	0.420710i	$0.861781\pi$
$734$	−25.4132	−0.938019
$735$	4.83012	0.178162
$736$	3.38623	0.124818
$737$	20.5606	0.757358
$738$	−6.50866	−0.239587
$739$	−44.0142	−1.61909	−0.809545	−	0.587058i	$-0.800286\pi$
$739$	−44.0142	−1.61909	−0.809545	+	0.587058i	$0.800286\pi$
$740$	−5.78657	−0.212718
$741$	0.0293524	0.00107829
$742$	−43.6347	−1.60188
$743$	−8.63057	−0.316625	−0.158312	−	0.987389i	$-0.550605\pi$
$743$	−8.63057	−0.316625	−0.158312	+	0.987389i	$0.550605\pi$
$744$	−2.85954	−0.104836
$745$	−4.70383	−0.172335
$746$	24.6067	0.900915
$747$	12.1008	0.442743
$748$	3.97864	0.145474
$749$	−27.0417	−0.988083
$750$	−12.5903	−0.459732
$751$	−11.9340	−0.435479	−0.217739	−	0.976007i	$-0.569868\pi$
$751$	−11.9340	−0.435479	−0.217739	+	0.976007i	$0.569868\pi$
$752$	41.5497	1.51516
$753$	14.0560	0.512229
$754$	0.0778912	0.00283663
$755$	−2.10938	−0.0767681
$756$	2.97935	0.108358
$757$	−41.8027	−1.51935	−0.759673	−	0.650305i	$-0.774641\pi$
$757$	−41.8027	−1.51935	−0.759673	+	0.650305i	$0.774641\pi$
$758$	−34.5983	−1.25667
$759$	−3.70758	−0.134576
$760$	−6.53682	−0.237115
$761$	41.4739	1.50343	0.751713	−	0.659490i	$-0.229228\pi$
$761$	41.4739	1.50343	0.751713	+	0.659490i	$0.229228\pi$
$762$	−22.2194	−0.804923
$763$	14.8988	0.539372
$764$	−0.198699	−0.00718866
$765$	0.800308	0.0289352
$766$	−48.3857	−1.74825
$767$	−0.0559153	−0.00201898
$768$	16.8970	0.609718
$769$	−27.5569	−0.993726	−0.496863	−	0.867829i	$-0.665515\pi$
$769$	−27.5569	−0.993726	−0.496863	+	0.867829i	$0.665515\pi$
$770$	23.4162	0.843863
$771$	−20.2155	−0.728044
$772$	8.78366	0.316131
$773$	17.4289	0.626872	0.313436	−	0.949609i	$-0.398520\pi$
$773$	17.4289	0.626872	0.313436	+	0.949609i	$0.398520\pi$
$774$	10.1567	0.365077
$775$	−6.31315	−0.226775
$776$	−5.50672	−0.197680
$777$	−31.6347	−1.13489
$778$	−31.4161	−1.12632
$779$	−16.0173	−0.573878
$780$	0.00468641	0.000167801 0
$781$	17.4894	0.625821
$782$	−1.29253	−0.0462208
$783$	6.53041	0.233378
$784$	−29.9922	−1.07115
$785$	17.7356	0.633011
$786$	−15.5891	−0.556046
$787$	8.41279	0.299884	0.149942	−	0.988695i	$-0.452091\pi$
$787$	8.41279	0.299884	0.149942	+	0.988695i	$0.452091\pi$
$788$	−12.6784	−0.451649
$789$	10.6398	0.378788
$790$	1.34519	0.0478595
$791$	17.5917	0.625489
$792$	−9.52055	−0.338298
$793$	−0.0432288	−0.00153510
$794$	−42.0221	−1.49131
$795$	−5.75445	−0.204089
$796$	−22.3892	−0.793566
$797$	−2.36995	−0.0839480	−0.0419740	−	0.999119i	$-0.513365\pi$
$797$	−2.36995	−0.0839480	−0.0419740	+	0.999119i	$0.513365\pi$
$798$	25.1019	0.888598
$799$	−8.36103	−0.295792
$800$	19.1972	0.678725
$801$	13.7917	0.487307
$802$	10.5996	0.374286
$803$	75.2791	2.65654
$804$	3.51901	0.124106
$805$	−2.22195	−0.0783134
$806$	0.0172725	0.000608399 0
$807$	3.95832	0.139340
$808$	−7.16409	−0.252032
$809$	3.94308	0.138631	0.0693156	−	0.997595i	$-0.477918\pi$
$809$	3.94308	0.138631	0.0693156	+	0.997595i	$0.477918\pi$
$810$	1.34519	0.0472650
$811$	−33.3719	−1.17185	−0.585923	−	0.810367i	$-0.699268\pi$
$811$	−33.3719	−1.17185	−0.585923	+	0.810367i	$0.699268\pi$
$812$	19.4564	0.682785
$813$	−7.37830	−0.258768
$814$	−71.0072	−2.48880
$815$	−7.23115	−0.253296
$816$	−4.96945	−0.173965
$817$	24.9949	0.874460
$818$	−50.7718	−1.77519
$819$	0.0256203	0.000895245 0
$820$	−2.55732	−0.0893054
$821$	−9.19145	−0.320784	−0.160392	−	0.987053i	$-0.551276\pi$
$821$	−9.19145	−0.320784	−0.160392	+	0.987053i	$0.551276\pi$
$822$	27.3932	0.955446
$823$	−0.319114	−0.0111236	−0.00556181	−	0.999985i	$-0.501770\pi$
$823$	−0.319114	−0.0111236	−0.00556181	+	0.999985i	$0.501770\pi$
$824$	34.6626	1.20753
$825$	−21.0190	−0.731787
$826$	−47.8182	−1.66381
$827$	0.666766	0.0231857	0.0115929	−	0.999933i	$-0.496310\pi$
$827$	0.666766	0.0231857	0.0115929	+	0.999933i	$0.496310\pi$
$828$	−0.634565	−0.0220527
$829$	24.1141	0.837517	0.418758	−	0.908098i	$-0.362465\pi$
$829$	24.1141	0.837517	0.418758	+	0.908098i	$0.362465\pi$
$830$	16.2778	0.565009
$831$	−10.8218	−0.375406
$832$	0.0180050	0.000624209 0
$833$	6.03532	0.209111
$834$	−6.76244	−0.234164
$835$	−2.25627	−0.0780813
$836$	16.4572	0.569184
$837$	1.44813	0.0500548
$838$	−15.7751	−0.544943
$839$	−29.2594	−1.01015	−0.505074	−	0.863076i	$-0.668535\pi$
$839$	−29.2594	−1.01015	−0.505074	+	0.863076i	$0.668535\pi$
$840$	−5.70566	−0.196864
$841$	13.6462	0.470560
$842$	27.1037	0.934055
$843$	9.19579	0.316720
$844$	−8.47814	−0.291830
$845$	−10.4040	−0.357907
$846$	−14.0535	−0.483169
$847$	44.2136	1.51920
$848$	35.7318	1.22703
$849$	4.00602	0.137486
$850$	−7.32761	−0.251335
$851$	6.73781	0.230969
$852$	2.99338	0.102552
$853$	7.52480	0.257644	0.128822	−	0.991668i	$-0.458880\pi$
$853$	7.52480	0.257644	0.128822	+	0.991668i	$0.458880\pi$
$854$	−36.9689	−1.26505
$855$	3.31039	0.113213
$856$	14.7898	0.505504
$857$	−42.3298	−1.44596	−0.722980	−	0.690869i	$-0.757228\pi$
$857$	−42.3298	−1.44596	−0.722980	+	0.690869i	$0.757228\pi$
$858$	0.0575072	0.00196326
$859$	−18.7513	−0.639787	−0.319894	−	0.947453i	$-0.603647\pi$
$859$	−18.7513	−0.639787	−0.319894	+	0.947453i	$0.603647\pi$
$860$	3.99069	0.136081
$861$	−13.9807	−0.476460
$862$	50.4612	1.71872
$863$	24.9941	0.850809	0.425405	−	0.905003i	$-0.360132\pi$
$863$	24.9941	0.850809	0.425405	+	0.905003i	$0.360132\pi$
$864$	−4.40353	−0.149811
$865$	−16.0324	−0.545117
$866$	42.5379	1.44550
$867$	1.00000	0.0339618
$868$	4.31449	0.146443
$869$	4.82141	0.163555
$870$	8.78461	0.297826
$871$	0.0302610	0.00102536
$872$	−8.14850	−0.275943
$873$	2.78872	0.0943839
$874$	−5.34640	−0.180845
$875$	−27.0440	−0.914254
$876$	12.8843	0.435320
$877$	51.9565	1.75445	0.877223	−	0.480082i	$-0.159393\pi$
$877$	51.9565	1.75445	0.877223	+	0.480082i	$0.159393\pi$
$878$	−45.2907	−1.52849
$879$	9.29992	0.313679
$880$	−19.1752	−0.646395
$881$	20.8441	0.702255	0.351128	−	0.936328i	$-0.385798\pi$
$881$	20.8441	0.702255	0.351128	+	0.936328i	$0.385798\pi$
$882$	10.1444	0.341579
$883$	40.9728	1.37885	0.689423	−	0.724359i	$-0.257864\pi$
$883$	40.9728	1.37885	0.689423	+	0.724359i	$0.257864\pi$
$884$	0.00585576	0.000196951 0
$885$	−6.30616	−0.211979
$886$	−48.8718	−1.64188
$887$	−37.5756	−1.26167	−0.630833	−	0.775918i	$-0.717287\pi$
$887$	−37.5756	−1.26167	−0.630833	+	0.775918i	$0.717287\pi$
$888$	17.3018	0.580610
$889$	−47.7274	−1.60073
$890$	18.5524	0.621879
$891$	4.82141	0.161523
$892$	9.52383	0.318881
$893$	−34.5845	−1.15733
$894$	−9.87914	−0.330408
$895$	12.3247	0.411968
$896$	47.1951	1.57668
$897$	−0.00545681	−0.000182198 0
$898$	−13.8794	−0.463161
$899$	9.45690	0.315405
$900$	−3.59748	−0.119916
$901$	−7.19030	−0.239543
$902$	−31.3809	−1.04487
$903$	21.8168	0.726017
$904$	−9.62133	−0.320001
$905$	3.45379	0.114808
$906$	−4.43018	−0.147183
$907$	−44.3641	−1.47309	−0.736543	−	0.676391i	$-0.763543\pi$
$907$	−44.3641	−1.47309	−0.736543	+	0.676391i	$0.763543\pi$
$908$	7.09837	0.235568
$909$	3.62805	0.120335
$910$	0.0344640	0.00114247
$911$	53.8626	1.78455	0.892273	−	0.451496i	$-0.149109\pi$
$911$	53.8626	1.78455	0.892273	+	0.451496i	$0.149109\pi$
$912$	−20.5556	−0.680663
$913$	58.3427	1.93086
$914$	−8.97478	−0.296859
$915$	−4.87537	−0.161175
$916$	−9.49733	−0.313801
$917$	−33.4856	−1.10579
$918$	1.68083	0.0554758
$919$	12.3123	0.406146	0.203073	−	0.979164i	$-0.434907\pi$
$919$	12.3123	0.406146	0.203073	+	0.979164i	$0.434907\pi$
$920$	1.21524	0.0400652
$921$	−20.2010	−0.665646
$922$	−20.8639	−0.687116
$923$	0.0257409	0.000847273 0
$924$	14.3647	0.472563
$925$	38.1980	1.25594
$926$	48.2169	1.58451
$927$	−17.5539	−0.576546
$928$	−28.7569	−0.943991
$929$	41.2536	1.35349	0.676743	−	0.736219i	$-0.263391\pi$
$929$	41.2536	1.35349	0.676743	+	0.736219i	$0.263391\pi$
$930$	1.94801	0.0638777
$931$	24.9644	0.818176
$932$	−13.8585	−0.453949
$933$	19.9709	0.653818
$934$	−34.2460	−1.12056
$935$	3.85862	0.126190
$936$	−0.0140123	−0.000458008 0
$937$	−1.71830	−0.0561344	−0.0280672	−	0.999606i	$-0.508935\pi$
$937$	−1.71830	−0.0561344	−0.0280672	+	0.999606i	$0.508935\pi$
$938$	25.8789	0.844977
$939$	−26.9665	−0.880017
$940$	−5.52176	−0.180100
$941$	24.5421	0.800051	0.400025	−	0.916504i	$-0.369001\pi$
$941$	24.5421	0.800051	0.400025	+	0.916504i	$0.369001\pi$
$942$	37.2489	1.21364
$943$	2.97771	0.0969676
$944$	39.1576	1.27447
$945$	2.88947	0.0939945
$946$	48.9699	1.59215
$947$	0.572898	0.0186167	0.00930834	−	0.999957i	$-0.497037\pi$
$947$	0.572898	0.0186167	0.00930834	+	0.999957i	$0.497037\pi$
$948$	0.825202	0.0268013
$949$	0.110796	0.00359658
$950$	−30.3098	−0.983381
$951$	−5.89179	−0.191054
$952$	−7.12933	−0.231063
$953$	24.1017	0.780730	0.390365	−	0.920660i	$-0.372349\pi$
$953$	24.1017	0.780730	0.390365	+	0.920660i	$0.372349\pi$
$954$	−12.0857	−0.391289
$955$	−0.192704	−0.00623577
$956$	0.306764	0.00992146
$957$	31.4858	1.01779
$958$	36.8196	1.18959
$959$	58.8408	1.90007
$960$	2.03061	0.0655376
$961$	−28.9029	−0.932352
$962$	−0.104508	−0.00336948
$963$	−7.48986	−0.241357
$964$	0.0189410	0.000610050 0
$965$	8.51868	0.274226
$966$	−4.66661	−0.150146
$967$	−2.41662	−0.0777132	−0.0388566	−	0.999245i	$-0.512372\pi$
$967$	−2.41662	−0.0777132	−0.0388566	+	0.999245i	$0.512372\pi$
$968$	−24.1815	−0.777222
$969$	4.13639	0.132880
$970$	3.75135	0.120448
$971$	0.655845	0.0210471	0.0105235	−	0.999945i	$-0.496650\pi$
$971$	0.655845	0.0210471	0.0105235	+	0.999945i	$0.496650\pi$
$972$	0.825202	0.0264684
$973$	−14.5258	−0.465675
$974$	−15.8142	−0.506720
$975$	−0.0309357	−0.000990736 0
$976$	30.2732	0.969022
$977$	57.0935	1.82658	0.913291	−	0.407307i	$-0.133532\pi$
$977$	57.0935	1.82658	0.913291	+	0.407307i	$0.133532\pi$
$978$	−15.1871	−0.485630
$979$	66.4956	2.12521
$980$	3.98582	0.127322
$981$	4.12658	0.131751
$982$	−2.01227	−0.0642141
$983$	42.7606	1.36385	0.681925	−	0.731422i	$-0.261143\pi$
$983$	42.7606	1.36385	0.681925	+	0.731422i	$0.261143\pi$
$984$	7.64636	0.243757
$985$	−12.2959	−0.391781
$986$	10.9765	0.349564
$987$	−30.1870	−0.960864
$988$	0.0242217	0.000770595 0
$989$	−4.64671	−0.147757
$990$	6.48569	0.206129
$991$	31.3295	0.995213	0.497607	−	0.867403i	$-0.334212\pi$
$991$	31.3295	0.995213	0.497607	+	0.867403i	$0.334212\pi$
$992$	−6.37690	−0.202467
$993$	9.49535	0.301326
$994$	22.0134	0.698222
$995$	−21.7138	−0.688374
$996$	9.98557	0.316405
$997$	−0.608436	−0.0192694	−0.00963469	−	0.999954i	$-0.503067\pi$
$997$	−0.608436	−0.0192694	−0.00963469	+	0.999954i	$0.503067\pi$
$998$	−12.8798	−0.407702
$999$	−8.76200	−0.277217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.24	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.24	✓	31	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+1.68083 q^{2} +1.00000 q^{3} +0.825202 q^{4} +0.800308 q^{5} +1.68083 q^{6} +3.61045 q^{7} -1.97464 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.68083 q^{2} +1.00000 q^{3} +0.825202 q^{4} +0.800308 q^{5} +1.68083 q^{6} +3.61045 q^{7} -1.97464 q^{8} +1.00000 q^{9} +1.34519 q^{10} +4.82141 q^{11} +0.825202 q^{12} +0.00709615 q^{13} +6.06856 q^{14} +0.800308 q^{15} -4.96945 q^{16} +1.00000 q^{17} +1.68083 q^{18} +4.13639 q^{19} +0.660416 q^{20} +3.61045 q^{21} +8.10399 q^{22} -0.768981 q^{23} -1.97464 q^{24} -4.35951 q^{25} +0.0119275 q^{26} +1.00000 q^{27} +2.97935 q^{28} +6.53041 q^{29} +1.34519 q^{30} +1.44813 q^{31} -4.40353 q^{32} +4.82141 q^{33} +1.68083 q^{34} +2.88947 q^{35} +0.825202 q^{36} -8.76200 q^{37} +6.95258 q^{38} +0.00709615 q^{39} -1.58032 q^{40} -3.87228 q^{41} +6.06856 q^{42} +6.04268 q^{43} +3.97864 q^{44} +0.800308 q^{45} -1.29253 q^{46} -8.36103 q^{47} -4.96945 q^{48} +6.03532 q^{49} -7.32761 q^{50} +1.00000 q^{51} +0.00585576 q^{52} -7.19030 q^{53} +1.68083 q^{54} +3.85862 q^{55} -7.12933 q^{56} +4.13639 q^{57} +10.9765 q^{58} -7.87966 q^{59} +0.660416 q^{60} -6.09187 q^{61} +2.43407 q^{62} +3.61045 q^{63} +2.53728 q^{64} +0.00567911 q^{65} +8.10399 q^{66} +4.26443 q^{67} +0.825202 q^{68} -0.768981 q^{69} +4.85672 q^{70} +3.62745 q^{71} -1.97464 q^{72} +15.6135 q^{73} -14.7275 q^{74} -4.35951 q^{75} +3.41336 q^{76} +17.4074 q^{77} +0.0119275 q^{78} +1.00000 q^{79} -3.97709 q^{80} +1.00000 q^{81} -6.50866 q^{82} +12.1008 q^{83} +2.97935 q^{84} +0.800308 q^{85} +10.1567 q^{86} +6.53041 q^{87} -9.52055 q^{88} +13.7917 q^{89} +1.34519 q^{90} +0.0256203 q^{91} -0.634565 q^{92} +1.44813 q^{93} -14.0535 q^{94} +3.31039 q^{95} -4.40353 q^{96} +2.78872 q^{97} +10.1444 q^{98} +4.82141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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