LMFDB - Embedded newform 4022.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.79779 q^{3} +1.00000 q^{4} +3.03526 q^{5} +1.79779 q^{6} -2.51987 q^{7} -1.00000 q^{8} +0.232040 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.79779 q^{3} +1.00000 q^{4} +3.03526 q^{5} +1.79779 q^{6} -2.51987 q^{7} -1.00000 q^{8} +0.232040 q^{9} -3.03526 q^{10} -4.37943 q^{11} -1.79779 q^{12} +4.32402 q^{13} +2.51987 q^{14} -5.45675 q^{15} +1.00000 q^{16} +4.54447 q^{17} -0.232040 q^{18} +3.86021 q^{19} +3.03526 q^{20} +4.53020 q^{21} +4.37943 q^{22} -7.19977 q^{23} +1.79779 q^{24} +4.21280 q^{25} -4.32402 q^{26} +4.97620 q^{27} -2.51987 q^{28} -7.60153 q^{29} +5.45675 q^{30} +5.99300 q^{31} -1.00000 q^{32} +7.87329 q^{33} -4.54447 q^{34} -7.64847 q^{35} +0.232040 q^{36} -8.12883 q^{37} -3.86021 q^{38} -7.77366 q^{39} -3.03526 q^{40} +3.02432 q^{41} -4.53020 q^{42} +3.21388 q^{43} -4.37943 q^{44} +0.704303 q^{45} +7.19977 q^{46} -4.44563 q^{47} -1.79779 q^{48} -0.650236 q^{49} -4.21280 q^{50} -8.17000 q^{51} +4.32402 q^{52} +2.61881 q^{53} -4.97620 q^{54} -13.2927 q^{55} +2.51987 q^{56} -6.93983 q^{57} +7.60153 q^{58} -2.50986 q^{59} -5.45675 q^{60} +10.7777 q^{61} -5.99300 q^{62} -0.584712 q^{63} +1.00000 q^{64} +13.1245 q^{65} -7.87329 q^{66} +5.35342 q^{67} +4.54447 q^{68} +12.9437 q^{69} +7.64847 q^{70} -2.33516 q^{71} -0.232040 q^{72} +10.8306 q^{73} +8.12883 q^{74} -7.57372 q^{75} +3.86021 q^{76} +11.0356 q^{77} +7.77366 q^{78} +6.84070 q^{79} +3.03526 q^{80} -9.64228 q^{81} -3.02432 q^{82} -9.19625 q^{83} +4.53020 q^{84} +13.7937 q^{85} -3.21388 q^{86} +13.6659 q^{87} +4.37943 q^{88} +0.403267 q^{89} -0.704303 q^{90} -10.8960 q^{91} -7.19977 q^{92} -10.7741 q^{93} +4.44563 q^{94} +11.7167 q^{95} +1.79779 q^{96} -5.55537 q^{97} +0.650236 q^{98} -1.01621 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) $ 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.79779	−1.03795	−0.518977	−	0.854788i	$-0.673687\pi$
$3$	−1.79779	−1.03795	−0.518977	+	0.854788i	$0.673687\pi$
$4$	1.00000	0.500000
$5$	3.03526	1.35741	0.678705	−	0.734411i	$-0.262542\pi$
$5$	3.03526	1.35741	0.678705	+	0.734411i	$0.262542\pi$
$6$	1.79779	0.733944
$7$	−2.51987	−0.952423	−0.476211	−	0.879331i	$-0.657990\pi$
$7$	−2.51987	−0.952423	−0.476211	+	0.879331i	$0.657990\pi$
$8$	−1.00000	−0.353553
$9$	0.232040	0.0773468
$10$	−3.03526	−0.959833
$11$	−4.37943	−1.32045	−0.660224	−	0.751068i	$-0.729539\pi$
$11$	−4.37943	−1.32045	−0.660224	+	0.751068i	$0.729539\pi$
$12$	−1.79779	−0.518977
$13$	4.32402	1.19927	0.599633	−	0.800275i	$-0.295313\pi$
$13$	4.32402	1.19927	0.599633	+	0.800275i	$0.295313\pi$
$14$	2.51987	0.673465
$15$	−5.45675	−1.40893
$16$	1.00000	0.250000
$17$	4.54447	1.10220	0.551098	−	0.834440i	$-0.314209\pi$
$17$	4.54447	1.10220	0.551098	+	0.834440i	$0.314209\pi$
$18$	−0.232040	−0.0546924
$19$	3.86021	0.885592	0.442796	−	0.896622i	$-0.353987\pi$
$19$	3.86021	0.885592	0.442796	+	0.896622i	$0.353987\pi$
$20$	3.03526	0.678705
$21$	4.53020	0.988570
$22$	4.37943	0.933698
$23$	−7.19977	−1.50126	−0.750628	−	0.660725i	$-0.770249\pi$
$23$	−7.19977	−1.50126	−0.750628	+	0.660725i	$0.770249\pi$
$24$	1.79779	0.366972
$25$	4.21280	0.842560
$26$	−4.32402	−0.848009
$27$	4.97620	0.957671
$28$	−2.51987	−0.476211
$29$	−7.60153	−1.41157	−0.705784	−	0.708427i	$-0.749405\pi$
$29$	−7.60153	−1.41157	−0.705784	+	0.708427i	$0.749405\pi$
$30$	5.45675	0.996262
$31$	5.99300	1.07638	0.538188	−	0.842825i	$-0.319109\pi$
$31$	5.99300	1.07638	0.538188	+	0.842825i	$0.319109\pi$
$32$	−1.00000	−0.176777
$33$	7.87329	1.37056
$34$	−4.54447	−0.779371
$35$	−7.64847	−1.29283
$36$	0.232040	0.0386734
$37$	−8.12883	−1.33637	−0.668185	−	0.743995i	$-0.732929\pi$
$37$	−8.12883	−1.33637	−0.668185	+	0.743995i	$0.732929\pi$
$38$	−3.86021	−0.626208
$39$	−7.77366	−1.24478
$40$	−3.03526	−0.479917
$41$	3.02432	0.472319	0.236159	−	0.971714i	$-0.424111\pi$
$41$	3.02432	0.472319	0.236159	+	0.971714i	$0.424111\pi$
$42$	−4.53020	−0.699025
$43$	3.21388	0.490112	0.245056	−	0.969509i	$-0.421194\pi$
$43$	3.21388	0.490112	0.245056	+	0.969509i	$0.421194\pi$
$44$	−4.37943	−0.660224
$45$	0.704303	0.104991
$46$	7.19977	1.06155
$47$	−4.44563	−0.648462	−0.324231	−	0.945978i	$-0.605105\pi$
$47$	−4.44563	−0.648462	−0.324231	+	0.945978i	$0.605105\pi$
$48$	−1.79779	−0.259488
$49$	−0.650236	−0.0928909
$50$	−4.21280	−0.595780
$51$	−8.17000	−1.14403
$52$	4.32402	0.599633
$53$	2.61881	0.359721	0.179860	−	0.983692i	$-0.442435\pi$
$53$	2.61881	0.359721	0.179860	+	0.983692i	$0.442435\pi$
$54$	−4.97620	−0.677176
$55$	−13.2927	−1.79239
$56$	2.51987	0.336732
$57$	−6.93983	−0.919203
$58$	7.60153	0.998130
$59$	−2.50986	−0.326756	−0.163378	−	0.986564i	$-0.552239\pi$
$59$	−2.50986	−0.326756	−0.163378	+	0.986564i	$0.552239\pi$
$60$	−5.45675	−0.704464
$61$	10.7777	1.37994	0.689972	−	0.723836i	$-0.257623\pi$
$61$	10.7777	1.37994	0.689972	+	0.723836i	$0.257623\pi$
$62$	−5.99300	−0.761112
$63$	−0.584712	−0.0736669
$64$	1.00000	0.125000
$65$	13.1245	1.62790
$66$	−7.87329	−0.969135
$67$	5.35342	0.654025	0.327012	−	0.945020i	$-0.393958\pi$
$67$	5.35342	0.654025	0.327012	+	0.945020i	$0.393958\pi$
$68$	4.54447	0.551098
$69$	12.9437	1.55823
$70$	7.64847	0.914167
$71$	−2.33516	−0.277133	−0.138566	−	0.990353i	$-0.544249\pi$
$71$	−2.33516	−0.277133	−0.138566	+	0.990353i	$0.544249\pi$
$72$	−0.232040	−0.0273462
$73$	10.8306	1.26762	0.633812	−	0.773487i	$-0.281489\pi$
$73$	10.8306	1.26762	0.633812	+	0.773487i	$0.281489\pi$
$74$	8.12883	0.944957
$75$	−7.57372	−0.874538
$76$	3.86021	0.442796
$77$	11.0356	1.25763
$78$	7.77366	0.880194
$79$	6.84070	0.769639	0.384820	−	0.922992i	$-0.374264\pi$
$79$	6.84070	0.769639	0.384820	+	0.922992i	$0.374264\pi$
$80$	3.03526	0.339352
$81$	−9.64228	−1.07136
$82$	−3.02432	−0.333980
$83$	−9.19625	−1.00942	−0.504710	−	0.863289i	$-0.668400\pi$
$83$	−9.19625	−1.00942	−0.504710	+	0.863289i	$0.668400\pi$
$84$	4.53020	0.494285
$85$	13.7937	1.49613
$86$	−3.21388	−0.346561
$87$	13.6659	1.46514
$88$	4.37943	0.466849
$89$	0.403267	0.0427462	0.0213731	−	0.999772i	$-0.493196\pi$
$89$	0.403267	0.0427462	0.0213731	+	0.999772i	$0.493196\pi$
$90$	−0.704303	−0.0742400
$91$	−10.8960	−1.14221
$92$	−7.19977	−0.750628
$93$	−10.7741	−1.11723
$94$	4.44563	0.458532
$95$	11.7167	1.20211
$96$	1.79779	0.183486
$97$	−5.55537	−0.564062	−0.282031	−	0.959405i	$-0.591008\pi$
$97$	−5.55537	−0.564062	−0.282031	+	0.959405i	$0.591008\pi$
$98$	0.650236	0.0656838
$99$	−1.01621	−0.102132
$100$	4.21280	0.421280
$101$	2.23873	0.222762	0.111381	−	0.993778i	$-0.464473\pi$
$101$	2.23873	0.222762	0.111381	+	0.993778i	$0.464473\pi$
$102$	8.17000	0.808950
$103$	−4.19080	−0.412932	−0.206466	−	0.978454i	$-0.566196\pi$
$103$	−4.19080	−0.412932	−0.206466	+	0.978454i	$0.566196\pi$
$104$	−4.32402	−0.424005
$105$	13.7503	1.34189
$106$	−2.61881	−0.254361
$107$	5.82241	0.562874	0.281437	−	0.959580i	$-0.409189\pi$
$107$	5.82241	0.562874	0.281437	+	0.959580i	$0.409189\pi$
$108$	4.97620	0.478835
$109$	−3.27565	−0.313751	−0.156875	−	0.987618i	$-0.550142\pi$
$109$	−3.27565	−0.313751	−0.156875	+	0.987618i	$0.550142\pi$
$110$	13.2927	1.26741
$111$	14.6139	1.38709
$112$	−2.51987	−0.238106
$113$	7.30676	0.687362	0.343681	−	0.939086i	$-0.388326\pi$
$113$	7.30676	0.687362	0.343681	+	0.939086i	$0.388326\pi$
$114$	6.93983	0.649975
$115$	−21.8532	−2.03782
$116$	−7.60153	−0.705784
$117$	1.00335	0.0927594
$118$	2.50986	0.231051
$119$	−11.4515	−1.04976
$120$	5.45675	0.498131
$121$	8.17943	0.743585
$122$	−10.7777	−0.975768
$123$	−5.43708	−0.490245
$124$	5.99300	0.538188
$125$	−2.38936	−0.213711
$126$	0.584712	0.0520903
$127$	9.56803	0.849025	0.424513	−	0.905422i	$-0.360445\pi$
$127$	9.56803	0.849025	0.424513	+	0.905422i	$0.360445\pi$
$128$	−1.00000	−0.0883883
$129$	−5.77787	−0.508713
$130$	−13.1245	−1.15110
$131$	12.8207	1.12015	0.560076	−	0.828441i	$-0.310772\pi$
$131$	12.8207	1.12015	0.560076	+	0.828441i	$0.310772\pi$
$132$	7.87329	0.685282
$133$	−9.72723	−0.843458
$134$	−5.35342	−0.462465
$135$	15.1041	1.29995
$136$	−4.54447	−0.389685
$137$	−4.40722	−0.376534	−0.188267	−	0.982118i	$-0.560287\pi$
$137$	−4.40722	−0.376534	−0.188267	+	0.982118i	$0.560287\pi$
$138$	−12.9437	−1.10184
$139$	−12.7090	−1.07796	−0.538981	−	0.842318i	$-0.681191\pi$
$139$	−12.7090	−1.07796	−0.538981	+	0.842318i	$0.681191\pi$
$140$	−7.64847	−0.646414
$141$	7.99230	0.673073
$142$	2.33516	0.195962
$143$	−18.9367	−1.58357
$144$	0.232040	0.0193367
$145$	−23.0726	−1.91608
$146$	−10.8306	−0.896346
$147$	1.16899	0.0964164
$148$	−8.12883	−0.668185
$149$	6.60738	0.541298	0.270649	−	0.962678i	$-0.412762\pi$
$149$	6.60738	0.541298	0.270649	+	0.962678i	$0.412762\pi$
$150$	7.57372	0.618392
$151$	−20.1477	−1.63959	−0.819797	−	0.572654i	$-0.805914\pi$
$151$	−20.1477	−1.63959	−0.819797	+	0.572654i	$0.805914\pi$
$152$	−3.86021	−0.313104
$153$	1.05450	0.0852514
$154$	−11.0356	−0.889275
$155$	18.1903	1.46108
$156$	−7.77366	−0.622391
$157$	5.94841	0.474735	0.237367	−	0.971420i	$-0.423715\pi$
$157$	5.94841	0.474735	0.237367	+	0.971420i	$0.423715\pi$
$158$	−6.84070	−0.544217
$159$	−4.70806	−0.373373
$160$	−3.03526	−0.239958
$161$	18.1425	1.42983
$162$	9.64228	0.757569
$163$	21.2404	1.66367	0.831836	−	0.555021i	$-0.187290\pi$
$163$	21.2404	1.66367	0.831836	+	0.555021i	$0.187290\pi$
$164$	3.02432	0.236159
$165$	23.8975	1.86042
$166$	9.19625	0.713767
$167$	12.5662	0.972404	0.486202	−	0.873846i	$-0.338382\pi$
$167$	12.5662	0.972404	0.486202	+	0.873846i	$0.338382\pi$
$168$	−4.53020	−0.349512
$169$	5.69711	0.438239
$170$	−13.7937	−1.05792
$171$	0.895724	0.0684977
$172$	3.21388	0.245056
$173$	1.48088	0.112589	0.0562945	−	0.998414i	$-0.482071\pi$
$173$	1.48088	0.112589	0.0562945	+	0.998414i	$0.482071\pi$
$174$	−13.6659	−1.03601
$175$	−10.6157	−0.802473
$176$	−4.37943	−0.330112
$177$	4.51219	0.339157
$178$	−0.403267	−0.0302261
$179$	−6.81046	−0.509037	−0.254519	−	0.967068i	$-0.581917\pi$
$179$	−6.81046	−0.509037	−0.254519	+	0.967068i	$0.581917\pi$
$180$	0.704303	0.0524956
$181$	22.3641	1.66231	0.831156	−	0.556040i	$-0.187680\pi$
$181$	22.3641	1.66231	0.831156	+	0.556040i	$0.187680\pi$
$182$	10.8960	0.807663
$183$	−19.3760	−1.43232
$184$	7.19977	0.530774
$185$	−24.6731	−1.81400
$186$	10.7741	0.789999
$187$	−19.9022	−1.45539
$188$	−4.44563	−0.324231
$189$	−12.5394	−0.912108
$190$	−11.7167	−0.850021
$191$	−1.98514	−0.143640	−0.0718200	−	0.997418i	$-0.522881\pi$
$191$	−1.98514	−0.143640	−0.0718200	+	0.997418i	$0.522881\pi$
$192$	−1.79779	−0.129744
$193$	23.2860	1.67616	0.838081	−	0.545546i	$-0.183678\pi$
$193$	23.2860	1.67616	0.838081	+	0.545546i	$0.183678\pi$
$194$	5.55537	0.398852
$195$	−23.5951	−1.68968
$196$	−0.650236	−0.0464454
$197$	13.1535	0.937146	0.468573	−	0.883425i	$-0.344768\pi$
$197$	13.1535	0.937146	0.468573	+	0.883425i	$0.344768\pi$
$198$	1.01621	0.0722186
$199$	−0.838188	−0.0594175	−0.0297088	−	0.999559i	$-0.509458\pi$
$199$	−0.838188	−0.0594175	−0.0297088	+	0.999559i	$0.509458\pi$
$200$	−4.21280	−0.297890
$201$	−9.62432	−0.678847
$202$	−2.23873	−0.157517
$203$	19.1549	1.34441
$204$	−8.17000	−0.572014
$205$	9.17959	0.641130
$206$	4.19080	0.291987
$207$	−1.67064	−0.116117
$208$	4.32402	0.299817
$209$	−16.9055	−1.16938
$210$	−13.7503	−0.948863
$211$	−23.5644	−1.62224	−0.811119	−	0.584882i	$-0.801141\pi$
$211$	−23.5644	−1.62224	−0.811119	+	0.584882i	$0.801141\pi$
$212$	2.61881	0.179860
$213$	4.19813	0.287651
$214$	−5.82241	−0.398012
$215$	9.75495	0.665282
$216$	−4.97620	−0.338588
$217$	−15.1016	−1.02516
$218$	3.27565	0.221855
$219$	−19.4711	−1.31573
$220$	−13.2927	−0.896195
$221$	19.6504	1.32183
$222$	−14.6139	−0.980821
$223$	−14.0350	−0.939851	−0.469925	−	0.882706i	$-0.655719\pi$
$223$	−14.0350	−0.939851	−0.469925	+	0.882706i	$0.655719\pi$
$224$	2.51987	0.168366
$225$	0.977540	0.0651693
$226$	−7.30676	−0.486039
$227$	4.55816	0.302536	0.151268	−	0.988493i	$-0.451664\pi$
$227$	4.55816	0.302536	0.151268	+	0.988493i	$0.451664\pi$
$228$	−6.93983	−0.459602
$229$	14.1312	0.933815	0.466908	−	0.884306i	$-0.345368\pi$
$229$	14.1312	0.933815	0.466908	+	0.884306i	$0.345368\pi$
$230$	21.8532	1.44096
$231$	−19.8397	−1.30536
$232$	7.60153	0.499065
$233$	−10.5731	−0.692665	−0.346333	−	0.938112i	$-0.612573\pi$
$233$	−10.5731	−0.692665	−0.346333	+	0.938112i	$0.612573\pi$
$234$	−1.00335	−0.0655908
$235$	−13.4936	−0.880228
$236$	−2.50986	−0.163378
$237$	−12.2981	−0.798850
$238$	11.4515	0.742290
$239$	20.4067	1.32000	0.659998	−	0.751267i	$-0.270557\pi$
$239$	20.4067	1.32000	0.659998	+	0.751267i	$0.270557\pi$
$240$	−5.45675	−0.352232
$241$	21.1038	1.35942	0.679709	−	0.733482i	$-0.262106\pi$
$241$	21.1038	1.35942	0.679709	+	0.733482i	$0.262106\pi$
$242$	−8.17943	−0.525794
$243$	2.40616	0.154355
$244$	10.7777	0.689972
$245$	−1.97363	−0.126091
$246$	5.43708	0.346656
$247$	16.6916	1.06206
$248$	−5.99300	−0.380556
$249$	16.5329	1.04773
$250$	2.38936	0.151116
$251$	−20.5850	−1.29931	−0.649655	−	0.760229i	$-0.725087\pi$
$251$	−20.5850	−1.29931	−0.649655	+	0.760229i	$0.725087\pi$
$252$	−0.584712	−0.0368334
$253$	31.5309	1.98233
$254$	−9.56803	−0.600351
$255$	−24.7981	−1.55291
$256$	1.00000	0.0625000
$257$	23.2887	1.45271	0.726354	−	0.687320i	$-0.241213\pi$
$257$	23.2887	1.45271	0.726354	+	0.687320i	$0.241213\pi$
$258$	5.77787	0.359714
$259$	20.4836	1.27279
$260$	13.1245	0.813948
$261$	−1.76386	−0.109180
$262$	−12.8207	−0.792067
$263$	26.4203	1.62915	0.814574	−	0.580060i	$-0.196971\pi$
$263$	26.4203	1.62915	0.814574	+	0.580060i	$0.196971\pi$
$264$	−7.87329	−0.484567
$265$	7.94875	0.488288
$266$	9.72723	0.596415
$267$	−0.724988	−0.0443686
$268$	5.35342	0.327012
$269$	14.2407	0.868270	0.434135	−	0.900848i	$-0.357054\pi$
$269$	14.2407	0.868270	0.434135	+	0.900848i	$0.357054\pi$
$270$	−15.1041	−0.919204
$271$	1.71921	0.104435	0.0522173	−	0.998636i	$-0.483371\pi$
$271$	1.71921	0.104435	0.0522173	+	0.998636i	$0.483371\pi$
$272$	4.54447	0.275549
$273$	19.5886	1.18556
$274$	4.40722	0.266250
$275$	−18.4497	−1.11256
$276$	12.9437	0.779117
$277$	−5.70900	−0.343020	−0.171510	−	0.985182i	$-0.554865\pi$
$277$	−5.70900	−0.343020	−0.171510	+	0.985182i	$0.554865\pi$
$278$	12.7090	0.762235
$279$	1.39062	0.0832542
$280$	7.64847	0.457084
$281$	11.4601	0.683651	0.341825	−	0.939764i	$-0.388955\pi$
$281$	11.4601	0.683651	0.341825	+	0.939764i	$0.388955\pi$
$282$	−7.99230	−0.475934
$283$	−8.47145	−0.503575	−0.251788	−	0.967782i	$-0.581018\pi$
$283$	−8.47145	−0.503575	−0.251788	+	0.967782i	$0.581018\pi$
$284$	−2.33516	−0.138566
$285$	−21.0642	−1.24773
$286$	18.9367	1.11975
$287$	−7.62090	−0.449847
$288$	−0.232040	−0.0136731
$289$	3.65223	0.214837
$290$	23.0726	1.35487
$291$	9.98737	0.585470
$292$	10.8306	0.633812
$293$	9.05221	0.528836	0.264418	−	0.964408i	$-0.414820\pi$
$293$	9.05221	0.528836	0.264418	+	0.964408i	$0.414820\pi$
$294$	−1.16899	−0.0681767
$295$	−7.61808	−0.443541
$296$	8.12883	0.472478
$297$	−21.7929	−1.26456
$298$	−6.60738	−0.382755
$299$	−31.1319	−1.80041
$300$	−7.57372	−0.437269
$301$	−8.09857	−0.466794
$302$	20.1477	1.15937
$303$	−4.02477	−0.231217
$304$	3.86021	0.221398
$305$	32.7131	1.87315
$306$	−1.05450	−0.0602818
$307$	13.0357	0.743986	0.371993	−	0.928235i	$-0.378674\pi$
$307$	13.0357	0.743986	0.371993	+	0.928235i	$0.378674\pi$
$308$	11.0356	0.628813
$309$	7.53417	0.428604
$310$	−18.1903	−1.03314
$311$	3.98698	0.226081	0.113040	−	0.993590i	$-0.463941\pi$
$311$	3.98698	0.226081	0.113040	+	0.993590i	$0.463941\pi$
$312$	7.77366	0.440097
$313$	3.85594	0.217951	0.108975	−	0.994044i	$-0.465243\pi$
$313$	3.85594	0.217951	0.108975	+	0.994044i	$0.465243\pi$
$314$	−5.94841	−0.335688
$315$	−1.77475	−0.0999961
$316$	6.84070	0.384820
$317$	1.13673	0.0638451	0.0319226	−	0.999490i	$-0.489837\pi$
$317$	1.13673	0.0638451	0.0319226	+	0.999490i	$0.489837\pi$
$318$	4.70806	0.264015
$319$	33.2904	1.86390
$320$	3.03526	0.169676
$321$	−10.4675	−0.584236
$322$	−18.1425	−1.01104
$323$	17.5426	0.976096
$324$	−9.64228	−0.535682
$325$	18.2162	1.01045
$326$	−21.2404	−1.17639
$327$	5.88893	0.325658
$328$	−3.02432	−0.166990
$329$	11.2024	0.617610
$330$	−23.8975	−1.31551
$331$	−7.88280	−0.433278	−0.216639	−	0.976252i	$-0.569509\pi$
$331$	−7.88280	−0.433278	−0.216639	+	0.976252i	$0.569509\pi$
$332$	−9.19625	−0.504710
$333$	−1.88622	−0.103364
$334$	−12.5662	−0.687594
$335$	16.2490	0.887779
$336$	4.53020	0.247143
$337$	15.4467	0.841435	0.420718	−	0.907192i	$-0.361778\pi$
$337$	15.4467	0.841435	0.420718	+	0.907192i	$0.361778\pi$
$338$	−5.69711	−0.309882
$339$	−13.1360	−0.713450
$340$	13.7937	0.748066
$341$	−26.2460	−1.42130
$342$	−0.895724	−0.0484352
$343$	19.2776	1.04089
$344$	−3.21388	−0.173281
$345$	39.2874	2.11516
$346$	−1.48088	−0.0796125
$347$	7.37954	0.396155	0.198077	−	0.980186i	$-0.436530\pi$
$347$	7.37954	0.396155	0.198077	+	0.980186i	$0.436530\pi$
$348$	13.6659	0.732571
$349$	6.25649	0.334902	0.167451	−	0.985880i	$-0.446446\pi$
$349$	6.25649	0.334902	0.167451	+	0.985880i	$0.446446\pi$
$350$	10.6157	0.567434
$351$	21.5172	1.14850
$352$	4.37943	0.233425
$353$	−16.6429	−0.885812	−0.442906	−	0.896568i	$-0.646052\pi$
$353$	−16.6429	−0.885812	−0.442906	+	0.896568i	$0.646052\pi$
$354$	−4.51219	−0.239820
$355$	−7.08782	−0.376183
$356$	0.403267	0.0213731
$357$	20.5874	1.08960
$358$	6.81046	0.359944
$359$	29.0195	1.53159	0.765796	−	0.643083i	$-0.222345\pi$
$359$	29.0195	1.53159	0.765796	+	0.643083i	$0.222345\pi$
$360$	−0.704303	−0.0371200
$361$	−4.09881	−0.215727
$362$	−22.3641	−1.17543
$363$	−14.7049	−0.771806
$364$	−10.8960	−0.571104
$365$	32.8736	1.72068
$366$	19.3760	1.01280
$367$	15.3130	0.799331	0.399666	−	0.916661i	$-0.369126\pi$
$367$	15.3130	0.799331	0.399666	+	0.916661i	$0.369126\pi$
$368$	−7.19977	−0.375314
$369$	0.701764	0.0365324
$370$	24.6731	1.28269
$371$	−6.59906	−0.342606
$372$	−10.7741	−0.558614
$373$	22.4775	1.16384	0.581922	−	0.813245i	$-0.302301\pi$
$373$	22.4775	1.16384	0.581922	+	0.813245i	$0.302301\pi$
$374$	19.9022	1.02912
$375$	4.29556	0.221822
$376$	4.44563	0.229266
$377$	−32.8691	−1.69285
$378$	12.5394	0.644957
$379$	−24.0974	−1.23780	−0.618900	−	0.785470i	$-0.712421\pi$
$379$	−24.0974	−1.23780	−0.618900	+	0.785470i	$0.712421\pi$
$380$	11.7167	0.601055
$381$	−17.2013	−0.881248
$382$	1.98514	0.101569
$383$	20.0064	1.02228	0.511139	−	0.859498i	$-0.329224\pi$
$383$	20.0064	1.02228	0.511139	+	0.859498i	$0.329224\pi$
$384$	1.79779	0.0917430
$385$	33.4960	1.70711
$386$	−23.2860	−1.18523
$387$	0.745749	0.0379086
$388$	−5.55537	−0.282031
$389$	−34.7980	−1.76433	−0.882166	−	0.470939i	$-0.843915\pi$
$389$	−34.7980	−1.76433	−0.882166	+	0.470939i	$0.843915\pi$
$390$	23.5951	1.19478
$391$	−32.7192	−1.65468
$392$	0.650236	0.0328419
$393$	−23.0489	−1.16266
$394$	−13.1535	−0.662662
$395$	20.7633	1.04472
$396$	−1.01621	−0.0510662
$397$	7.81914	0.392431	0.196216	−	0.980561i	$-0.437135\pi$
$397$	7.81914	0.392431	0.196216	+	0.980561i	$0.437135\pi$
$398$	0.838188	0.0420146
$399$	17.4875	0.875470
$400$	4.21280	0.210640
$401$	27.7744	1.38699	0.693495	−	0.720462i	$-0.256070\pi$
$401$	27.7744	1.38699	0.693495	+	0.720462i	$0.256070\pi$
$402$	9.62432	0.480017
$403$	25.9138	1.29086
$404$	2.23873	0.111381
$405$	−29.2668	−1.45428
$406$	−19.1549	−0.950641
$407$	35.5996	1.76461
$408$	8.17000	0.404475
$409$	−5.26663	−0.260418	−0.130209	−	0.991487i	$-0.541565\pi$
$409$	−5.26663	−0.260418	−0.130209	+	0.991487i	$0.541565\pi$
$410$	−9.17959	−0.453347
$411$	7.92325	0.390825
$412$	−4.19080	−0.206466
$413$	6.32453	0.311210
$414$	1.67064	0.0821074
$415$	−27.9130	−1.37020
$416$	−4.32402	−0.212002
$417$	22.8481	1.11887
$418$	16.9055	0.826876
$419$	26.3340	1.28650	0.643251	−	0.765656i	$-0.277585\pi$
$419$	26.3340	1.28650	0.643251	+	0.765656i	$0.277585\pi$
$420$	13.7503	0.670947
$421$	14.0499	0.684749	0.342374	−	0.939564i	$-0.388769\pi$
$421$	14.0499	0.684749	0.342374	+	0.939564i	$0.388769\pi$
$422$	23.5644	1.14710
$423$	−1.03157	−0.0501564
$424$	−2.61881	−0.127180
$425$	19.1449	0.928666
$426$	−4.19813	−0.203400
$427$	−27.1585	−1.31429
$428$	5.82241	0.281437
$429$	34.0442	1.64367
$430$	−9.75495	−0.470426
$431$	5.70625	0.274860	0.137430	−	0.990511i	$-0.456116\pi$
$431$	5.70625	0.274860	0.137430	+	0.990511i	$0.456116\pi$
$432$	4.97620	0.239418
$433$	38.4908	1.84975	0.924876	−	0.380269i	$-0.124169\pi$
$433$	38.4908	1.84975	0.924876	+	0.380269i	$0.124169\pi$
$434$	15.1016	0.724901
$435$	41.4797	1.98880
$436$	−3.27565	−0.156875
$437$	−27.7926	−1.32950
$438$	19.4711	0.930365
$439$	5.69623	0.271866	0.135933	−	0.990718i	$-0.456597\pi$
$439$	5.69623	0.271866	0.135933	+	0.990718i	$0.456597\pi$
$440$	13.2927	0.633705
$441$	−0.150881	−0.00718481
$442$	−19.6504	−0.934673
$443$	−24.0885	−1.14448	−0.572240	−	0.820086i	$-0.693926\pi$
$443$	−24.0885	−1.14448	−0.572240	+	0.820086i	$0.693926\pi$
$444$	14.6139	0.693545
$445$	1.22402	0.0580241
$446$	14.0350	0.664575
$447$	−11.8787	−0.561842
$448$	−2.51987	−0.119053
$449$	4.82545	0.227727	0.113864	−	0.993496i	$-0.463677\pi$
$449$	4.82545	0.227727	0.113864	+	0.993496i	$0.463677\pi$
$450$	−0.977540	−0.0460817
$451$	−13.2448	−0.623673
$452$	7.30676	0.343681
$453$	36.2212	1.70182
$454$	−4.55816	−0.213925
$455$	−33.0721	−1.55044
$456$	6.93983	0.324987
$457$	−24.5664	−1.14917	−0.574585	−	0.818445i	$-0.694836\pi$
$457$	−24.5664	−1.14917	−0.574585	+	0.818445i	$0.694836\pi$
$458$	−14.1312	−0.660307
$459$	22.6142	1.05554
$460$	−21.8532	−1.01891
$461$	−12.2443	−0.570273	−0.285137	−	0.958487i	$-0.592039\pi$
$461$	−12.2443	−0.570273	−0.285137	+	0.958487i	$0.592039\pi$
$462$	19.8397	0.923026
$463$	39.7969	1.84952	0.924759	−	0.380553i	$-0.124266\pi$
$463$	39.7969	1.84952	0.924759	+	0.380553i	$0.124266\pi$
$464$	−7.60153	−0.352892
$465$	−32.7023	−1.51653
$466$	10.5731	0.489788
$467$	−15.0333	−0.695658	−0.347829	−	0.937558i	$-0.613081\pi$
$467$	−15.0333	−0.695658	−0.347829	+	0.937558i	$0.613081\pi$
$468$	1.00335	0.0463797
$469$	−13.4900	−0.622908
$470$	13.4936	0.622415
$471$	−10.6940	−0.492752
$472$	2.50986	0.115526
$473$	−14.0750	−0.647167
$474$	12.2981	0.564872
$475$	16.2623	0.746164
$476$	−11.4515	−0.524878
$477$	0.607669	0.0278232
$478$	−20.4067	−0.933379
$479$	2.90578	0.132769	0.0663843	−	0.997794i	$-0.478854\pi$
$479$	2.90578	0.132769	0.0663843	+	0.997794i	$0.478854\pi$
$480$	5.45675	0.249066
$481$	−35.1492	−1.60266
$482$	−21.1038	−0.961253
$483$	−32.6164	−1.48410
$484$	8.17943	0.371792
$485$	−16.8620	−0.765663
$486$	−2.40616	−0.109146
$487$	22.9181	1.03852	0.519259	−	0.854617i	$-0.326208\pi$
$487$	22.9181	1.03852	0.519259	+	0.854617i	$0.326208\pi$
$488$	−10.7777	−0.487884
$489$	−38.1856	−1.72681
$490$	1.97363	0.0891597
$491$	38.0512	1.71723	0.858613	−	0.512624i	$-0.171326\pi$
$491$	38.0512	1.71723	0.858613	+	0.512624i	$0.171326\pi$
$492$	−5.43708	−0.245122
$493$	−34.5449	−1.55583
$494$	−16.6916	−0.750990
$495$	−3.08445	−0.138636
$496$	5.99300	0.269094
$497$	5.88432	0.263948
$498$	−16.5329	−0.740857
$499$	33.9034	1.51773	0.758863	−	0.651250i	$-0.225755\pi$
$499$	33.9034	1.51773	0.758863	+	0.651250i	$0.225755\pi$
$500$	−2.38936	−0.106855
$501$	−22.5914	−1.00931
$502$	20.5850	0.918751
$503$	15.7995	0.704465	0.352233	−	0.935912i	$-0.385423\pi$
$503$	15.7995	0.704465	0.352233	+	0.935912i	$0.385423\pi$
$504$	0.584712	0.0260452
$505$	6.79514	0.302380
$506$	−31.5309	−1.40172
$507$	−10.2422	−0.454872
$508$	9.56803	0.424513
$509$	−33.4469	−1.48251	−0.741255	−	0.671224i	$-0.765769\pi$
$509$	−33.4469	−1.48251	−0.741255	+	0.671224i	$0.765769\pi$
$510$	24.7981	1.09808
$511$	−27.2917	−1.20731
$512$	−1.00000	−0.0441942
$513$	19.2092	0.848106
$514$	−23.2887	−1.02722
$515$	−12.7202	−0.560518
$516$	−5.77787	−0.254356
$517$	19.4693	0.856260
$518$	−20.4836	−0.899998
$519$	−2.66230	−0.116862
$520$	−13.1245	−0.575548
$521$	−1.26876	−0.0555852	−0.0277926	−	0.999614i	$-0.508848\pi$
$521$	−1.26876	−0.0555852	−0.0277926	+	0.999614i	$0.508848\pi$
$522$	1.76386	0.0772021
$523$	−1.19656	−0.0523220	−0.0261610	−	0.999658i	$-0.508328\pi$
$523$	−1.19656	−0.0523220	−0.0261610	+	0.999658i	$0.508328\pi$
$524$	12.8207	0.560076
$525$	19.0848	0.832930
$526$	−26.4203	−1.15198
$527$	27.2350	1.18638
$528$	7.87329	0.342641
$529$	28.8367	1.25377
$530$	−7.94875	−0.345272
$531$	−0.582389	−0.0252735
$532$	−9.72723	−0.421729
$533$	13.0772	0.566436
$534$	0.724988	0.0313733
$535$	17.6725	0.764050
$536$	−5.35342	−0.231233
$537$	12.2438	0.528357
$538$	−14.2407	−0.613960
$539$	2.84766	0.122658
$540$	15.1041	0.649976
$541$	−36.1785	−1.55543	−0.777717	−	0.628614i	$-0.783622\pi$
$541$	−36.1785	−1.55543	−0.777717	+	0.628614i	$0.783622\pi$
$542$	−1.71921	−0.0738464
$543$	−40.2059	−1.72540
$544$	−4.54447	−0.194843
$545$	−9.94245	−0.425888
$546$	−19.5886	−0.838317
$547$	16.1859	0.692060	0.346030	−	0.938223i	$-0.387530\pi$
$547$	16.1859	0.692060	0.346030	+	0.938223i	$0.387530\pi$
$548$	−4.40722	−0.188267
$549$	2.50086	0.106734
$550$	18.4497	0.786697
$551$	−29.3435	−1.25007
$552$	−12.9437	−0.550919
$553$	−17.2377	−0.733022
$554$	5.70900	0.242552
$555$	44.3570	1.88285
$556$	−12.7090	−0.538981
$557$	9.04068	0.383066	0.191533	−	0.981486i	$-0.438654\pi$
$557$	9.04068	0.383066	0.191533	+	0.981486i	$0.438654\pi$
$558$	−1.39062	−0.0588696
$559$	13.8969	0.587774
$560$	−7.64847	−0.323207
$561$	35.7799	1.51063
$562$	−11.4601	−0.483414
$563$	10.2846	0.433445	0.216723	−	0.976233i	$-0.430463\pi$
$563$	10.2846	0.433445	0.216723	+	0.976233i	$0.430463\pi$
$564$	7.99230	0.336536
$565$	22.1779	0.933032
$566$	8.47145	0.356082
$567$	24.2973	1.02039
$568$	2.33516	0.0979812
$569$	−19.5280	−0.818658	−0.409329	−	0.912387i	$-0.634237\pi$
$569$	−19.5280	−0.818658	−0.409329	+	0.912387i	$0.634237\pi$
$570$	21.0642	0.882282
$571$	−11.9282	−0.499178	−0.249589	−	0.968352i	$-0.580296\pi$
$571$	−11.9282	−0.499178	−0.249589	+	0.968352i	$0.580296\pi$
$572$	−18.9367	−0.791785
$573$	3.56887	0.149092
$574$	7.62090	0.318090
$575$	−30.3312	−1.26490
$576$	0.232040	0.00966835
$577$	38.6121	1.60744	0.803722	−	0.595005i	$-0.202850\pi$
$577$	38.6121	1.60744	0.803722	+	0.595005i	$0.202850\pi$
$578$	−3.65223	−0.151913
$579$	−41.8632	−1.73978
$580$	−23.0726	−0.958038
$581$	23.1734	0.961394
$582$	−9.98737	−0.413990
$583$	−11.4689	−0.474993
$584$	−10.8306	−0.448173
$585$	3.04542	0.125912
$586$	−9.05221	−0.373943
$587$	−33.8767	−1.39824	−0.699121	−	0.715003i	$-0.746425\pi$
$587$	−33.8767	−1.39824	−0.699121	+	0.715003i	$0.746425\pi$
$588$	1.16899	0.0482082
$589$	23.1342	0.953229
$590$	7.61808	0.313631
$591$	−23.6471	−0.972713
$592$	−8.12883	−0.334093
$593$	−46.7586	−1.92014	−0.960072	−	0.279753i	$-0.909748\pi$
$593$	−46.7586	−1.92014	−0.960072	+	0.279753i	$0.909748\pi$
$594$	21.7929	0.894175
$595$	−34.7583	−1.42495
$596$	6.60738	0.270649
$597$	1.50688	0.0616726
$598$	31.1319	1.27308
$599$	−22.4518	−0.917357	−0.458679	−	0.888602i	$-0.651677\pi$
$599$	−22.4518	−0.917357	−0.458679	+	0.888602i	$0.651677\pi$
$600$	7.57372	0.309196
$601$	−1.65638	−0.0675651	−0.0337825	−	0.999429i	$-0.510755\pi$
$601$	−1.65638	−0.0675651	−0.0337825	+	0.999429i	$0.510755\pi$
$602$	8.09857	0.330073
$603$	1.24221	0.0505867
$604$	−20.1477	−0.819797
$605$	24.8267	1.00935
$606$	4.02477	0.163495
$607$	27.7776	1.12746	0.563728	−	0.825960i	$-0.309367\pi$
$607$	27.7776	1.12746	0.563728	+	0.825960i	$0.309367\pi$
$608$	−3.86021	−0.156552
$609$	−34.4364	−1.39543
$610$	−32.7131	−1.32452
$611$	−19.2230	−0.777678
$612$	1.05450	0.0426257
$613$	14.5163	0.586309	0.293155	−	0.956065i	$-0.405295\pi$
$613$	14.5163	0.586309	0.293155	+	0.956065i	$0.405295\pi$
$614$	−13.0357	−0.526078
$615$	−16.5029	−0.665463
$616$	−11.0356	−0.444638
$617$	4.30187	0.173187	0.0865934	−	0.996244i	$-0.472402\pi$
$617$	4.30187	0.173187	0.0865934	+	0.996244i	$0.472402\pi$
$618$	−7.53417	−0.303069
$619$	36.8329	1.48044	0.740220	−	0.672364i	$-0.234721\pi$
$619$	36.8329	1.48044	0.740220	+	0.672364i	$0.234721\pi$
$620$	18.1903	0.730541
$621$	−35.8275	−1.43771
$622$	−3.98698	−0.159863
$623$	−1.01618	−0.0407125
$624$	−7.77366	−0.311196
$625$	−28.3163	−1.13265
$626$	−3.85594	−0.154114
$627$	30.3925	1.21376
$628$	5.94841	0.237367
$629$	−36.9412	−1.47294
$630$	1.77475	0.0707079
$631$	−35.2970	−1.40515	−0.702575	−	0.711610i	$-0.747966\pi$
$631$	−35.2970	−1.40515	−0.702575	+	0.711610i	$0.747966\pi$
$632$	−6.84070	−0.272109
$633$	42.3637	1.68381
$634$	−1.13673	−0.0451453
$635$	29.0414	1.15247
$636$	−4.70806	−0.186687
$637$	−2.81163	−0.111401
$638$	−33.2904	−1.31798
$639$	−0.541852	−0.0214353
$640$	−3.03526	−0.119979
$641$	12.6796	0.500814	0.250407	−	0.968141i	$-0.419436\pi$
$641$	12.6796	0.500814	0.250407	+	0.968141i	$0.419436\pi$
$642$	10.4675	0.413117
$643$	−27.8411	−1.09794	−0.548972	−	0.835841i	$-0.684981\pi$
$643$	−27.8411	−1.09794	−0.548972	+	0.835841i	$0.684981\pi$
$644$	18.1425	0.714916
$645$	−17.5373	−0.690532
$646$	−17.5426	−0.690204
$647$	42.3175	1.66367	0.831836	−	0.555021i	$-0.187290\pi$
$647$	42.3175	1.66367	0.831836	+	0.555021i	$0.187290\pi$
$648$	9.64228	0.378784
$649$	10.9918	0.431464
$650$	−18.2162	−0.714499
$651$	27.1495	1.06407
$652$	21.2404	0.831836
$653$	−34.9891	−1.36923	−0.684614	−	0.728906i	$-0.740029\pi$
$653$	−34.9891	−1.36923	−0.684614	+	0.728906i	$0.740029\pi$
$654$	−5.88893	−0.230275
$655$	38.9142	1.52050
$656$	3.02432	0.118080
$657$	2.51313	0.0980467
$658$	−11.2024	−0.436716
$659$	25.0452	0.975622	0.487811	−	0.872949i	$-0.337796\pi$
$659$	25.0452	0.975622	0.487811	+	0.872949i	$0.337796\pi$
$660$	23.8975	0.930208
$661$	34.2999	1.33411	0.667055	−	0.745008i	$-0.267554\pi$
$661$	34.2999	1.33411	0.667055	+	0.745008i	$0.267554\pi$
$662$	7.88280	0.306374
$663$	−35.3272	−1.37199
$664$	9.19625	0.356884
$665$	−29.5247	−1.14492
$666$	1.88622	0.0730894
$667$	54.7293	2.11913
$668$	12.5662	0.486202
$669$	25.2319	0.975521
$670$	−16.2490	−0.627755
$671$	−47.2002	−1.82215
$672$	−4.53020	−0.174756
$673$	−16.0364	−0.618159	−0.309080	−	0.951036i	$-0.600021\pi$
$673$	−16.0364	−0.618159	−0.309080	+	0.951036i	$0.600021\pi$
$674$	−15.4467	−0.594985
$675$	20.9637	0.806895
$676$	5.69711	0.219120
$677$	26.2195	1.00770	0.503848	−	0.863792i	$-0.331917\pi$
$677$	26.2195	1.00770	0.503848	+	0.863792i	$0.331917\pi$
$678$	13.1360	0.504485
$679$	13.9988	0.537226
$680$	−13.7937	−0.528962
$681$	−8.19461	−0.314018
$682$	26.2460	1.00501
$683$	40.3928	1.54559	0.772795	−	0.634656i	$-0.218858\pi$
$683$	40.3928	1.54559	0.772795	+	0.634656i	$0.218858\pi$
$684$	0.895724	0.0342489
$685$	−13.3771	−0.511111
$686$	−19.2776	−0.736023
$687$	−25.4049	−0.969256
$688$	3.21388	0.122528
$689$	11.3238	0.431401
$690$	−39.2874	−1.49564
$691$	33.8367	1.28721	0.643604	−	0.765359i	$-0.277439\pi$
$691$	33.8367	1.28721	0.643604	+	0.765359i	$0.277439\pi$
$692$	1.48088	0.0562945
$693$	2.56071	0.0972733
$694$	−7.37954	−0.280124
$695$	−38.5751	−1.46324
$696$	−13.6659	−0.518006
$697$	13.7439	0.520588
$698$	−6.25649	−0.236812
$699$	19.0081	0.718954
$700$	−10.6157	−0.401237
$701$	−25.5368	−0.964513	−0.482257	−	0.876030i	$-0.660183\pi$
$701$	−25.5368	−0.964513	−0.482257	+	0.876030i	$0.660183\pi$
$702$	−21.5172	−0.812114
$703$	−31.3789	−1.18348
$704$	−4.37943	−0.165056
$705$	24.2587	0.913635
$706$	16.6429	0.626364
$707$	−5.64133	−0.212164
$708$	4.51219	0.169579
$709$	4.00682	0.150479	0.0752396	−	0.997165i	$-0.476028\pi$
$709$	4.00682	0.150479	0.0752396	+	0.997165i	$0.476028\pi$
$710$	7.08782	0.266001
$711$	1.58732	0.0595291
$712$	−0.403267	−0.0151131
$713$	−43.1483	−1.61592
$714$	−20.5874	−0.770463
$715$	−57.4779	−2.14955
$716$	−6.81046	−0.254519
$717$	−36.6868	−1.37009
$718$	−29.0195	−1.08300
$719$	−23.7751	−0.886663	−0.443332	−	0.896358i	$-0.646204\pi$
$719$	−23.7751	−0.886663	−0.443332	+	0.896358i	$0.646204\pi$
$720$	0.704303	0.0262478
$721$	10.5603	0.393286
$722$	4.09881	0.152542
$723$	−37.9402	−1.41101
$724$	22.3641	0.831156
$725$	−32.0237	−1.18933
$726$	14.7049	0.545749
$727$	17.4203	0.646082	0.323041	−	0.946385i	$-0.395295\pi$
$727$	17.4203	0.646082	0.323041	+	0.946385i	$0.395295\pi$
$728$	10.8960	0.403832
$729$	24.6011	0.911151
$730$	−32.8736	−1.21671
$731$	14.6054	0.540199
$732$	−19.3760	−0.716159
$733$	−28.7619	−1.06234	−0.531172	−	0.847264i	$-0.678248\pi$
$733$	−28.7619	−1.06234	−0.531172	+	0.847264i	$0.678248\pi$
$734$	−15.3130	−0.565212
$735$	3.54818	0.130876
$736$	7.19977	0.265387
$737$	−23.4450	−0.863606
$738$	−0.701764	−0.0258323
$739$	−8.34513	−0.306980	−0.153490	−	0.988150i	$-0.549051\pi$
$739$	−8.34513	−0.306980	−0.153490	+	0.988150i	$0.549051\pi$
$740$	−24.6731	−0.907001
$741$	−30.0079	−1.10237
$742$	6.59906	0.242259
$743$	−50.0996	−1.83798	−0.918988	−	0.394286i	$-0.870992\pi$
$743$	−50.0996	−1.83798	−0.918988	+	0.394286i	$0.870992\pi$
$744$	10.7741	0.394999
$745$	20.0551	0.734763
$746$	−22.4775	−0.822961
$747$	−2.13390	−0.0780754
$748$	−19.9022	−0.727697
$749$	−14.6717	−0.536094
$750$	−4.29556	−0.156852
$751$	−24.2908	−0.886386	−0.443193	−	0.896426i	$-0.646154\pi$
$751$	−24.2908	−0.886386	−0.443193	+	0.896426i	$0.646154\pi$
$752$	−4.44563	−0.162115
$753$	37.0074	1.34862
$754$	32.8691	1.19702
$755$	−61.1534	−2.22560
$756$	−12.5394	−0.456054
$757$	15.4364	0.561046	0.280523	−	0.959847i	$-0.409492\pi$
$757$	15.4364	0.561046	0.280523	+	0.959847i	$0.409492\pi$
$758$	24.0974	0.875256
$759$	−56.6859	−2.05757
$760$	−11.7167	−0.425010
$761$	−6.41323	−0.232479	−0.116240	−	0.993221i	$-0.537084\pi$
$761$	−6.41323	−0.232479	−0.116240	+	0.993221i	$0.537084\pi$
$762$	17.2013	0.623137
$763$	8.25423	0.298823
$764$	−1.98514	−0.0718200
$765$	3.20068	0.115721
$766$	−20.0064	−0.722859
$767$	−10.8527	−0.391867
$768$	−1.79779	−0.0648721
$769$	−52.4454	−1.89123	−0.945614	−	0.325291i	$-0.894538\pi$
$769$	−52.4454	−1.89123	−0.945614	+	0.325291i	$0.894538\pi$
$770$	−33.4960	−1.20711
$771$	−41.8681	−1.50784
$772$	23.2860	0.838081
$773$	8.26911	0.297419	0.148710	−	0.988881i	$-0.452488\pi$
$773$	8.26911	0.297419	0.148710	+	0.988881i	$0.452488\pi$
$774$	−0.745749	−0.0268054
$775$	25.2473	0.906911
$776$	5.55537	0.199426
$777$	−36.8252	−1.32110
$778$	34.7980	1.24757
$779$	11.6745	0.418282
$780$	−23.5951	−0.844839
$781$	10.2267	0.365940
$782$	32.7192	1.17004
$783$	−37.8268	−1.35182
$784$	−0.650236	−0.0232227
$785$	18.0550	0.644409
$786$	23.0489	0.822128
$787$	9.46844	0.337514	0.168757	−	0.985658i	$-0.446025\pi$
$787$	9.46844	0.337514	0.168757	+	0.985658i	$0.446025\pi$
$788$	13.1535	0.468573
$789$	−47.4982	−1.69098
$790$	−20.7633	−0.738725
$791$	−18.4121	−0.654659
$792$	1.01621	0.0361093
$793$	46.6030	1.65492
$794$	−7.81914	−0.277491
$795$	−14.2902	−0.506820
$796$	−0.838188	−0.0297088
$797$	−24.4831	−0.867235	−0.433618	−	0.901097i	$-0.642763\pi$
$797$	−24.4831	−0.867235	−0.433618	+	0.901097i	$0.642763\pi$
$798$	−17.4875	−0.619051
$799$	−20.2030	−0.714732
$800$	−4.21280	−0.148945
$801$	0.0935742	0.00330628
$802$	−27.7744	−0.980750
$803$	−47.4318	−1.67383
$804$	−9.62432	−0.339424
$805$	55.0673	1.94087
$806$	−25.9138	−0.912776
$807$	−25.6017	−0.901224
$808$	−2.23873	−0.0787584
$809$	18.6617	0.656109	0.328055	−	0.944659i	$-0.393607\pi$
$809$	18.6617	0.656109	0.328055	+	0.944659i	$0.393607\pi$
$810$	29.2668	1.02833
$811$	7.75517	0.272321	0.136160	−	0.990687i	$-0.456524\pi$
$811$	7.75517	0.272321	0.136160	+	0.990687i	$0.456524\pi$
$812$	19.1549	0.672205
$813$	−3.09077	−0.108398
$814$	−35.5996	−1.24777
$815$	64.4700	2.25828
$816$	−8.17000	−0.286007
$817$	12.4062	0.434039
$818$	5.26663	0.184144
$819$	−2.52831	−0.0883462
$820$	9.17959	0.320565
$821$	−21.1885	−0.739483	−0.369742	−	0.929135i	$-0.620554\pi$
$821$	−21.1885	−0.739483	−0.369742	+	0.929135i	$0.620554\pi$
$822$	−7.92325	−0.276355
$823$	−30.5995	−1.06663	−0.533315	−	0.845917i	$-0.679054\pi$
$823$	−30.5995	−1.06663	−0.533315	+	0.845917i	$0.679054\pi$
$824$	4.19080	0.145993
$825$	33.1686	1.15478
$826$	−6.32453	−0.220059
$827$	−38.1826	−1.32774	−0.663870	−	0.747848i	$-0.731087\pi$
$827$	−38.1826	−1.32774	−0.663870	+	0.747848i	$0.731087\pi$
$828$	−1.67064	−0.0580587
$829$	−32.6781	−1.13496	−0.567478	−	0.823388i	$-0.692081\pi$
$829$	−32.6781	−1.13496	−0.567478	+	0.823388i	$0.692081\pi$
$830$	27.9130	0.968874
$831$	10.2636	0.356039
$832$	4.32402	0.149908
$833$	−2.95498	−0.102384
$834$	−22.8481	−0.791164
$835$	38.1418	1.31995
$836$	−16.9055	−0.584689
$837$	29.8224	1.03081
$838$	−26.3340	−0.909694
$839$	−31.7421	−1.09586	−0.547930	−	0.836524i	$-0.684584\pi$
$839$	−31.7421	−1.09586	−0.547930	+	0.836524i	$0.684584\pi$
$840$	−13.7503	−0.474431
$841$	28.7832	0.992525
$842$	−14.0499	−0.484191
$843$	−20.6028	−0.709597
$844$	−23.5644	−0.811119
$845$	17.2922	0.594870
$846$	1.03157	0.0354660
$847$	−20.6111	−0.708207
$848$	2.61881	0.0899301
$849$	15.2299	0.522688
$850$	−19.1449	−0.656666
$851$	58.5257	2.00624
$852$	4.19813	0.143825
$853$	−14.8537	−0.508581	−0.254290	−	0.967128i	$-0.581842\pi$
$853$	−14.8537	−0.508581	−0.254290	+	0.967128i	$0.581842\pi$
$854$	27.1585	0.929344
$855$	2.71875	0.0929794
$856$	−5.82241	−0.199006
$857$	8.82608	0.301493	0.150747	−	0.988572i	$-0.451832\pi$
$857$	8.82608	0.301493	0.150747	+	0.988572i	$0.451832\pi$
$858$	−34.0442	−1.16225
$859$	16.0606	0.547980	0.273990	−	0.961733i	$-0.411656\pi$
$859$	16.0606	0.547980	0.273990	+	0.961733i	$0.411656\pi$
$860$	9.75495	0.332641
$861$	13.7008	0.466920
$862$	−5.70625	−0.194356
$863$	37.7506	1.28504	0.642522	−	0.766267i	$-0.277888\pi$
$863$	37.7506	1.28504	0.642522	+	0.766267i	$0.277888\pi$
$864$	−4.97620	−0.169294
$865$	4.49485	0.152829
$866$	−38.4908	−1.30797
$867$	−6.56593	−0.222991
$868$	−15.1016	−0.512582
$869$	−29.9584	−1.01627
$870$	−41.4797	−1.40629
$871$	23.1483	0.784350
$872$	3.27565	0.110928
$873$	−1.28907	−0.0436284
$874$	27.7926	0.940099
$875$	6.02088	0.203543
$876$	−19.4711	−0.657867
$877$	−15.4687	−0.522342	−0.261171	−	0.965293i	$-0.584109\pi$
$877$	−15.4687	−0.522342	−0.261171	+	0.965293i	$0.584109\pi$
$878$	−5.69623	−0.192239
$879$	−16.2740	−0.548907
$880$	−13.2927	−0.448097
$881$	−50.5891	−1.70439	−0.852195	−	0.523224i	$-0.824729\pi$
$881$	−50.5891	−1.70439	−0.852195	+	0.523224i	$0.824729\pi$
$882$	0.150881	0.00508043
$883$	56.5469	1.90295	0.951477	−	0.307719i	$-0.0995657\pi$
$883$	56.5469	1.90295	0.951477	+	0.307719i	$0.0995657\pi$
$884$	19.6504	0.660913
$885$	13.6957	0.460375
$886$	24.0885	0.809270
$887$	−21.9633	−0.737456	−0.368728	−	0.929537i	$-0.620207\pi$
$887$	−21.9633	−0.737456	−0.368728	+	0.929537i	$0.620207\pi$
$888$	−14.6139	−0.490410
$889$	−24.1102	−0.808631
$890$	−1.22402	−0.0410292
$891$	42.2277	1.41468
$892$	−14.0350	−0.469925
$893$	−17.1610	−0.574273
$894$	11.8787	0.397282
$895$	−20.6715	−0.690972
$896$	2.51987	0.0841831
$897$	55.9686	1.86874
$898$	−4.82545	−0.161028
$899$	−45.5560	−1.51938
$900$	0.977540	0.0325847
$901$	11.9011	0.396483
$902$	13.2448	0.441003
$903$	14.5595	0.484510
$904$	−7.30676	−0.243019
$905$	67.8809	2.25644
$906$	−36.2212	−1.20337
$907$	19.1032	0.634312	0.317156	−	0.948373i	$-0.397272\pi$
$907$	19.1032	0.634312	0.317156	+	0.948373i	$0.397272\pi$
$908$	4.55816	0.151268
$909$	0.519477	0.0172299
$910$	33.0721	1.09633
$911$	26.7483	0.886212	0.443106	−	0.896469i	$-0.353877\pi$
$911$	26.7483	0.886212	0.443106	+	0.896469i	$0.353877\pi$
$912$	−6.93983	−0.229801
$913$	40.2743	1.33289
$914$	24.5664	0.812586
$915$	−58.8113	−1.94424
$916$	14.1312	0.466908
$917$	−32.3066	−1.06686
$918$	−22.6142	−0.746380
$919$	11.4933	0.379129	0.189565	−	0.981868i	$-0.439292\pi$
$919$	11.4933	0.379129	0.189565	+	0.981868i	$0.439292\pi$
$920$	21.8532	0.720478
$921$	−23.4354	−0.772223
$922$	12.2443	0.403244
$923$	−10.0973	−0.332356
$924$	−19.8397	−0.652678
$925$	−34.2451	−1.12597
$926$	−39.7969	−1.30781
$927$	−0.972435	−0.0319390
$928$	7.60153	0.249532
$929$	−11.8841	−0.389904	−0.194952	−	0.980813i	$-0.562455\pi$
$929$	−11.8841	−0.389904	−0.194952	+	0.980813i	$0.562455\pi$
$930$	32.7023	1.07235
$931$	−2.51005	−0.0822634
$932$	−10.5731	−0.346333
$933$	−7.16774	−0.234661
$934$	15.0333	0.491904
$935$	−60.4084	−1.97556
$936$	−1.00335	−0.0327954
$937$	−8.38392	−0.273891	−0.136945	−	0.990579i	$-0.543728\pi$
$937$	−8.38392	−0.273891	−0.136945	+	0.990579i	$0.543728\pi$
$938$	13.4900	0.440463
$939$	−6.93216	−0.226223
$940$	−13.4936	−0.440114
$941$	36.0864	1.17638	0.588192	−	0.808721i	$-0.299840\pi$
$941$	36.0864	1.17638	0.588192	+	0.808721i	$0.299840\pi$
$942$	10.6940	0.348429
$943$	−21.7744	−0.709072
$944$	−2.50986	−0.0816890
$945$	−38.0603	−1.23810
$946$	14.0750	0.457616
$947$	5.96062	0.193694	0.0968470	−	0.995299i	$-0.469124\pi$
$947$	5.96062	0.193694	0.0968470	+	0.995299i	$0.469124\pi$
$948$	−12.2981	−0.399425
$949$	46.8316	1.52022
$950$	−16.2623	−0.527618
$951$	−2.04360	−0.0662682
$952$	11.4515	0.371145
$953$	51.8525	1.67967	0.839834	−	0.542843i	$-0.182652\pi$
$953$	51.8525	1.67967	0.839834	+	0.542843i	$0.182652\pi$
$954$	−0.607669	−0.0196740
$955$	−6.02543	−0.194978
$956$	20.4067	0.659998
$957$	−59.8490	−1.93464
$958$	−2.90578	−0.0938815
$959$	11.1056	0.358620
$960$	−5.45675	−0.176116
$961$	4.91610	0.158584
$962$	35.1492	1.13325
$963$	1.35103	0.0435365
$964$	21.1038	0.679709
$965$	70.6790	2.27524
$966$	32.6164	1.04942
$967$	5.07549	0.163217	0.0816083	−	0.996664i	$-0.473994\pi$
$967$	5.07549	0.163217	0.0816083	+	0.996664i	$0.473994\pi$
$968$	−8.17943	−0.262897
$969$	−31.5379	−1.01314
$970$	16.8620	0.541406
$971$	−5.97310	−0.191686	−0.0958430	−	0.995396i	$-0.530555\pi$
$971$	−5.97310	−0.191686	−0.0958430	+	0.995396i	$0.530555\pi$
$972$	2.40616	0.0771776
$973$	32.0251	1.02668
$974$	−22.9181	−0.734343
$975$	−32.7489	−1.04880
$976$	10.7777	0.344986
$977$	12.2562	0.392111	0.196055	−	0.980593i	$-0.437187\pi$
$977$	12.2562	0.392111	0.196055	+	0.980593i	$0.437187\pi$
$978$	38.1856	1.22104
$979$	−1.76608	−0.0564442
$980$	−1.97363	−0.0630455
$981$	−0.760083	−0.0242676
$982$	−38.0512	−1.21426
$983$	54.3551	1.73366	0.866829	−	0.498605i	$-0.166154\pi$
$983$	54.3551	1.73366	0.866829	+	0.498605i	$0.166154\pi$
$984$	5.43708	0.173328
$985$	39.9242	1.27209
$986$	34.5449	1.10013
$987$	−20.1396	−0.641050
$988$	16.6916	0.531030
$989$	−23.1392	−0.735783
$990$	3.08445	0.0980301
$991$	0.522399	0.0165946	0.00829728	−	0.999966i	$-0.497359\pi$
$991$	0.522399	0.0165946	0.00829728	+	0.999966i	$0.497359\pi$
$992$	−5.99300	−0.190278
$993$	14.1716	0.449722
$994$	−5.88432	−0.186639
$995$	−2.54412	−0.0806539
$996$	16.5329	0.523865
$997$	−19.7610	−0.625838	−0.312919	−	0.949780i	$-0.601307\pi$
$997$	−19.7610	−0.625838	−0.312919	+	0.949780i	$0.601307\pi$
$998$	−33.9034	−1.07319
$999$	−40.4507	−1.27980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.e.1.12	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.e.1.12	✓	46	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.79779 q^{3} +1.00000 q^{4} +3.03526 q^{5} +1.79779 q^{6} -2.51987 q^{7} -1.00000 q^{8} +0.232040 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.79779 q^{3} +1.00000 q^{4} +3.03526 q^{5} +1.79779 q^{6} -2.51987 q^{7} -1.00000 q^{8} +0.232040 q^{9} -3.03526 q^{10} -4.37943 q^{11} -1.79779 q^{12} +4.32402 q^{13} +2.51987 q^{14} -5.45675 q^{15} +1.00000 q^{16} +4.54447 q^{17} -0.232040 q^{18} +3.86021 q^{19} +3.03526 q^{20} +4.53020 q^{21} +4.37943 q^{22} -7.19977 q^{23} +1.79779 q^{24} +4.21280 q^{25} -4.32402 q^{26} +4.97620 q^{27} -2.51987 q^{28} -7.60153 q^{29} +5.45675 q^{30} +5.99300 q^{31} -1.00000 q^{32} +7.87329 q^{33} -4.54447 q^{34} -7.64847 q^{35} +0.232040 q^{36} -8.12883 q^{37} -3.86021 q^{38} -7.77366 q^{39} -3.03526 q^{40} +3.02432 q^{41} -4.53020 q^{42} +3.21388 q^{43} -4.37943 q^{44} +0.704303 q^{45} +7.19977 q^{46} -4.44563 q^{47} -1.79779 q^{48} -0.650236 q^{49} -4.21280 q^{50} -8.17000 q^{51} +4.32402 q^{52} +2.61881 q^{53} -4.97620 q^{54} -13.2927 q^{55} +2.51987 q^{56} -6.93983 q^{57} +7.60153 q^{58} -2.50986 q^{59} -5.45675 q^{60} +10.7777 q^{61} -5.99300 q^{62} -0.584712 q^{63} +1.00000 q^{64} +13.1245 q^{65} -7.87329 q^{66} +5.35342 q^{67} +4.54447 q^{68} +12.9437 q^{69} +7.64847 q^{70} -2.33516 q^{71} -0.232040 q^{72} +10.8306 q^{73} +8.12883 q^{74} -7.57372 q^{75} +3.86021 q^{76} +11.0356 q^{77} +7.77366 q^{78} +6.84070 q^{79} +3.03526 q^{80} -9.64228 q^{81} -3.02432 q^{82} -9.19625 q^{83} +4.53020 q^{84} +13.7937 q^{85} -3.21388 q^{86} +13.6659 q^{87} +4.37943 q^{88} +0.403267 q^{89} -0.704303 q^{90} -10.8960 q^{91} -7.19977 q^{92} -10.7741 q^{93} +4.44563 q^{94} +11.7167 q^{95} +1.79779 q^{96} -5.55537 q^{97} +0.650236 q^{98} -1.01621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

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