LMFDB - Embedded newform 4010.2.a.n.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.38202 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.38202 q^{6} +3.56623 q^{7} +1.00000 q^{8} -1.09003 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.38202 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.38202 q^{6} +3.56623 q^{7} +1.00000 q^{8} -1.09003 q^{9} +1.00000 q^{10} +1.62456 q^{11} -1.38202 q^{12} +4.83658 q^{13} +3.56623 q^{14} -1.38202 q^{15} +1.00000 q^{16} +5.91946 q^{17} -1.09003 q^{18} -6.58913 q^{19} +1.00000 q^{20} -4.92858 q^{21} +1.62456 q^{22} +2.76297 q^{23} -1.38202 q^{24} +1.00000 q^{25} +4.83658 q^{26} +5.65249 q^{27} +3.56623 q^{28} -1.79507 q^{29} -1.38202 q^{30} -0.670964 q^{31} +1.00000 q^{32} -2.24517 q^{33} +5.91946 q^{34} +3.56623 q^{35} -1.09003 q^{36} +1.30284 q^{37} -6.58913 q^{38} -6.68422 q^{39} +1.00000 q^{40} +1.23942 q^{41} -4.92858 q^{42} -1.10859 q^{43} +1.62456 q^{44} -1.09003 q^{45} +2.76297 q^{46} +2.28159 q^{47} -1.38202 q^{48} +5.71799 q^{49} +1.00000 q^{50} -8.18079 q^{51} +4.83658 q^{52} +0.0390912 q^{53} +5.65249 q^{54} +1.62456 q^{55} +3.56623 q^{56} +9.10628 q^{57} -1.79507 q^{58} -5.91619 q^{59} -1.38202 q^{60} -0.962509 q^{61} -0.670964 q^{62} -3.88731 q^{63} +1.00000 q^{64} +4.83658 q^{65} -2.24517 q^{66} -8.94636 q^{67} +5.91946 q^{68} -3.81847 q^{69} +3.56623 q^{70} +4.11926 q^{71} -1.09003 q^{72} +11.6530 q^{73} +1.30284 q^{74} -1.38202 q^{75} -6.58913 q^{76} +5.79357 q^{77} -6.68422 q^{78} -10.9960 q^{79} +1.00000 q^{80} -4.54172 q^{81} +1.23942 q^{82} -8.89461 q^{83} -4.92858 q^{84} +5.91946 q^{85} -1.10859 q^{86} +2.48082 q^{87} +1.62456 q^{88} -7.12545 q^{89} -1.09003 q^{90} +17.2483 q^{91} +2.76297 q^{92} +0.927282 q^{93} +2.28159 q^{94} -6.58913 q^{95} -1.38202 q^{96} -2.46579 q^{97} +5.71799 q^{98} -1.77083 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * 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
$3$	−1.38202	−0.797907	−0.398953	−	0.916971i	$-0.630626\pi$
$3$	−1.38202	−0.797907	−0.398953	+	0.916971i	$0.630626\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.38202	−0.564205
$7$	3.56623	1.34791	0.673954	−	0.738773i	$-0.264595\pi$
$7$	3.56623	1.34791	0.673954	+	0.738773i	$0.264595\pi$
$8$	1.00000	0.353553
$9$	−1.09003	−0.363345
$10$	1.00000	0.316228
$11$	1.62456	0.489825	0.244912	−	0.969545i	$-0.421241\pi$
$11$	1.62456	0.489825	0.244912	+	0.969545i	$0.421241\pi$
$12$	−1.38202	−0.398953
$13$	4.83658	1.34142	0.670712	−	0.741718i	$-0.265989\pi$
$13$	4.83658	1.34142	0.670712	+	0.741718i	$0.265989\pi$
$14$	3.56623	0.953115
$15$	−1.38202	−0.356835
$16$	1.00000	0.250000
$17$	5.91946	1.43568	0.717840	−	0.696208i	$-0.245131\pi$
$17$	5.91946	1.43568	0.717840	+	0.696208i	$0.245131\pi$
$18$	−1.09003	−0.256924
$19$	−6.58913	−1.51165	−0.755825	−	0.654774i	$-0.772764\pi$
$19$	−6.58913	−1.51165	−0.755825	+	0.654774i	$0.772764\pi$
$20$	1.00000	0.223607
$21$	−4.92858	−1.07550
$22$	1.62456	0.346358
$23$	2.76297	0.576119	0.288060	−	0.957612i	$-0.406990\pi$
$23$	2.76297	0.576119	0.288060	+	0.957612i	$0.406990\pi$
$24$	−1.38202	−0.282103
$25$	1.00000	0.200000
$26$	4.83658	0.948530
$27$	5.65249	1.08782
$28$	3.56623	0.673954
$29$	−1.79507	−0.333337	−0.166668	−	0.986013i	$-0.553301\pi$
$29$	−1.79507	−0.333337	−0.166668	+	0.986013i	$0.553301\pi$
$30$	−1.38202	−0.252320
$31$	−0.670964	−0.120509	−0.0602543	−	0.998183i	$-0.519191\pi$
$31$	−0.670964	−0.120509	−0.0602543	+	0.998183i	$0.519191\pi$
$32$	1.00000	0.176777
$33$	−2.24517	−0.390834
$34$	5.91946	1.01518
$35$	3.56623	0.602803
$36$	−1.09003	−0.181672
$37$	1.30284	0.214186	0.107093	−	0.994249i	$-0.465846\pi$
$37$	1.30284	0.214186	0.107093	+	0.994249i	$0.465846\pi$
$38$	−6.58913	−1.06890
$39$	−6.68422	−1.07033
$40$	1.00000	0.158114
$41$	1.23942	0.193564	0.0967822	−	0.995306i	$-0.469145\pi$
$41$	1.23942	0.193564	0.0967822	+	0.995306i	$0.469145\pi$
$42$	−4.92858	−0.760497
$43$	−1.10859	−0.169058	−0.0845292	−	0.996421i	$-0.526939\pi$
$43$	−1.10859	−0.169058	−0.0845292	+	0.996421i	$0.526939\pi$
$44$	1.62456	0.244912
$45$	−1.09003	−0.162493
$46$	2.76297	0.407378
$47$	2.28159	0.332804	0.166402	−	0.986058i	$-0.446785\pi$
$47$	2.28159	0.332804	0.166402	+	0.986058i	$0.446785\pi$
$48$	−1.38202	−0.199477
$49$	5.71799	0.816855
$50$	1.00000	0.141421
$51$	−8.18079	−1.14554
$52$	4.83658	0.670712
$53$	0.0390912	0.00536959	0.00268479	−	0.999996i	$-0.499145\pi$
$53$	0.0390912	0.00536959	0.00268479	+	0.999996i	$0.499145\pi$
$54$	5.65249	0.769206
$55$	1.62456	0.219056
$56$	3.56623	0.476557
$57$	9.10628	1.20616
$58$	−1.79507	−0.235705
$59$	−5.91619	−0.770222	−0.385111	−	0.922870i	$-0.625837\pi$
$59$	−5.91619	−0.770222	−0.385111	+	0.922870i	$0.625837\pi$
$60$	−1.38202	−0.178417
$61$	−0.962509	−0.123237	−0.0616183	−	0.998100i	$-0.519626\pi$
$61$	−0.962509	−0.123237	−0.0616183	+	0.998100i	$0.519626\pi$
$62$	−0.670964	−0.0852125
$63$	−3.88731	−0.489755
$64$	1.00000	0.125000
$65$	4.83658	0.599903
$66$	−2.24517	−0.276362
$67$	−8.94636	−1.09297	−0.546486	−	0.837468i	$-0.684035\pi$
$67$	−8.94636	−1.09297	−0.546486	+	0.837468i	$0.684035\pi$
$68$	5.91946	0.717840
$69$	−3.81847	−0.459689
$70$	3.56623	0.426246
$71$	4.11926	0.488867	0.244433	−	0.969666i	$-0.421398\pi$
$71$	4.11926	0.488867	0.244433	+	0.969666i	$0.421398\pi$
$72$	−1.09003	−0.128462
$73$	11.6530	1.36388	0.681938	−	0.731410i	$-0.261137\pi$
$73$	11.6530	1.36388	0.681938	+	0.731410i	$0.261137\pi$
$74$	1.30284	0.151453
$75$	−1.38202	−0.159581
$76$	−6.58913	−0.755825
$77$	5.79357	0.660238
$78$	−6.68422	−0.756839
$79$	−10.9960	−1.23715	−0.618576	−	0.785725i	$-0.712290\pi$
$79$	−10.9960	−1.23715	−0.618576	+	0.785725i	$0.712290\pi$
$80$	1.00000	0.111803
$81$	−4.54172	−0.504636
$82$	1.23942	0.136871
$83$	−8.89461	−0.976310	−0.488155	−	0.872757i	$-0.662330\pi$
$83$	−8.89461	−0.976310	−0.488155	+	0.872757i	$0.662330\pi$
$84$	−4.92858	−0.537752
$85$	5.91946	0.642056
$86$	−1.10859	−0.119542
$87$	2.48082	0.265972
$88$	1.62456	0.173179
$89$	−7.12545	−0.755296	−0.377648	−	0.925949i	$-0.623267\pi$
$89$	−7.12545	−0.755296	−0.377648	+	0.925949i	$0.623267\pi$
$90$	−1.09003	−0.114900
$91$	17.2483	1.80812
$92$	2.76297	0.288060
$93$	0.927282	0.0961547
$94$	2.28159	0.235328
$95$	−6.58913	−0.676031
$96$	−1.38202	−0.141051
$97$	−2.46579	−0.250363	−0.125182	−	0.992134i	$-0.539951\pi$
$97$	−2.46579	−0.250363	−0.125182	+	0.992134i	$0.539951\pi$
$98$	5.71799	0.577604
$99$	−1.77083	−0.177975
$100$	1.00000	0.100000
$101$	1.85549	0.184628	0.0923140	−	0.995730i	$-0.470574\pi$
$101$	1.85549	0.184628	0.0923140	+	0.995730i	$0.470574\pi$
$102$	−8.18079	−0.810018
$103$	12.6667	1.24809	0.624044	−	0.781389i	$-0.285489\pi$
$103$	12.6667	1.24809	0.624044	+	0.781389i	$0.285489\pi$
$104$	4.83658	0.474265
$105$	−4.92858	−0.480980
$106$	0.0390912	0.00379687
$107$	18.2486	1.76415	0.882077	−	0.471105i	$-0.156145\pi$
$107$	18.2486	1.76415	0.882077	+	0.471105i	$0.156145\pi$
$108$	5.65249	0.543911
$109$	−10.4537	−1.00128	−0.500640	−	0.865656i	$-0.666902\pi$
$109$	−10.4537	−1.00128	−0.500640	+	0.865656i	$0.666902\pi$
$110$	1.62456	0.154896
$111$	−1.80055	−0.170901
$112$	3.56623	0.336977
$113$	10.5822	0.995490	0.497745	−	0.867323i	$-0.334162\pi$
$113$	10.5822	0.995490	0.497745	+	0.867323i	$0.334162\pi$
$114$	9.10628	0.852881
$115$	2.76297	0.257648
$116$	−1.79507	−0.166668
$117$	−5.27203	−0.487400
$118$	−5.91619	−0.544629
$119$	21.1102	1.93516
$120$	−1.38202	−0.126160
$121$	−8.36079	−0.760072
$122$	−0.962509	−0.0871414
$123$	−1.71289	−0.154446
$124$	−0.670964	−0.0602543
$125$	1.00000	0.0894427
$126$	−3.88731	−0.346309
$127$	10.7389	0.952921	0.476460	−	0.879196i	$-0.341920\pi$
$127$	10.7389	0.952921	0.476460	+	0.879196i	$0.341920\pi$
$128$	1.00000	0.0883883
$129$	1.53209	0.134893
$130$	4.83658	0.424196
$131$	−15.2661	−1.33381	−0.666904	−	0.745144i	$-0.732381\pi$
$131$	−15.2661	−1.33381	−0.666904	+	0.745144i	$0.732381\pi$
$132$	−2.24517	−0.195417
$133$	−23.4983	−2.03756
$134$	−8.94636	−0.772848
$135$	5.65249	0.486489
$136$	5.91946	0.507590
$137$	−8.52606	−0.728431	−0.364215	−	0.931315i	$-0.618663\pi$
$137$	−8.52606	−0.728431	−0.364215	+	0.931315i	$0.618663\pi$
$138$	−3.81847	−0.325049
$139$	5.02066	0.425847	0.212923	−	0.977069i	$-0.431701\pi$
$139$	5.02066	0.425847	0.212923	+	0.977069i	$0.431701\pi$
$140$	3.56623	0.301401
$141$	−3.15319	−0.265547
$142$	4.11926	0.345681
$143$	7.85733	0.657063
$144$	−1.09003	−0.0908362
$145$	−1.79507	−0.149073
$146$	11.6530	0.964406
$147$	−7.90234	−0.651774
$148$	1.30284	0.107093
$149$	1.47742	0.121035	0.0605176	−	0.998167i	$-0.480725\pi$
$149$	1.47742	0.121035	0.0605176	+	0.998167i	$0.480725\pi$
$150$	−1.38202	−0.112841
$151$	6.73973	0.548471	0.274236	−	0.961663i	$-0.411575\pi$
$151$	6.73973	0.548471	0.274236	+	0.961663i	$0.411575\pi$
$152$	−6.58913	−0.534449
$153$	−6.45241	−0.521647
$154$	5.79357	0.466859
$155$	−0.670964	−0.0538931
$156$	−6.68422	−0.535166
$157$	−3.95872	−0.315940	−0.157970	−	0.987444i	$-0.550495\pi$
$157$	−3.95872	−0.315940	−0.157970	+	0.987444i	$0.550495\pi$
$158$	−10.9960	−0.874799
$159$	−0.0540246	−0.00428443
$160$	1.00000	0.0790569
$161$	9.85338	0.776555
$162$	−4.54172	−0.356831
$163$	1.24862	0.0977996	0.0488998	−	0.998804i	$-0.484428\pi$
$163$	1.24862	0.0977996	0.0488998	+	0.998804i	$0.484428\pi$
$164$	1.23942	0.0967822
$165$	−2.24517	−0.174786
$166$	−8.89461	−0.690355
$167$	23.7956	1.84136	0.920681	−	0.390317i	$-0.127635\pi$
$167$	23.7956	1.84136	0.920681	+	0.390317i	$0.127635\pi$
$168$	−4.92858	−0.380248
$169$	10.3925	0.799420
$170$	5.91946	0.454002
$171$	7.18238	0.549250
$172$	−1.10859	−0.0845292
$173$	9.42061	0.716235	0.358118	−	0.933676i	$-0.383419\pi$
$173$	9.42061	0.716235	0.358118	+	0.933676i	$0.383419\pi$
$174$	2.48082	0.188070
$175$	3.56623	0.269582
$176$	1.62456	0.122456
$177$	8.17626	0.614565
$178$	−7.12545	−0.534075
$179$	−24.1011	−1.80140	−0.900700	−	0.434442i	$-0.856945\pi$
$179$	−24.1011	−1.80140	−0.900700	+	0.434442i	$0.856945\pi$
$180$	−1.09003	−0.0812463
$181$	16.4565	1.22320	0.611600	−	0.791167i	$-0.290526\pi$
$181$	16.4565	1.22320	0.611600	+	0.791167i	$0.290526\pi$
$182$	17.2483	1.27853
$183$	1.33020	0.0983313
$184$	2.76297	0.203689
$185$	1.30284	0.0957870
$186$	0.927282	0.0679916
$187$	9.61655	0.703232
$188$	2.28159	0.166402
$189$	20.1581	1.46628
$190$	−6.58913	−0.478026
$191$	7.29447	0.527809	0.263905	−	0.964549i	$-0.414990\pi$
$191$	7.29447	0.527809	0.263905	+	0.964549i	$0.414990\pi$
$192$	−1.38202	−0.0997384
$193$	6.92850	0.498724	0.249362	−	0.968410i	$-0.419779\pi$
$193$	6.92850	0.498724	0.249362	+	0.968410i	$0.419779\pi$
$194$	−2.46579	−0.177033
$195$	−6.68422	−0.478667
$196$	5.71799	0.408428
$197$	10.3858	0.739960	0.369980	−	0.929040i	$-0.379365\pi$
$197$	10.3858	0.739960	0.369980	+	0.929040i	$0.379365\pi$
$198$	−1.77083	−0.125847
$199$	−7.01356	−0.497178	−0.248589	−	0.968609i	$-0.579967\pi$
$199$	−7.01356	−0.497178	−0.248589	+	0.968609i	$0.579967\pi$
$200$	1.00000	0.0707107
$201$	12.3640	0.872090
$202$	1.85549	0.130552
$203$	−6.40164	−0.449307
$204$	−8.18079	−0.572770
$205$	1.23942	0.0865647
$206$	12.6667	0.882531
$207$	−3.01173	−0.209330
$208$	4.83658	0.335356
$209$	−10.7045	−0.740443
$210$	−4.92858	−0.340104
$211$	17.3548	1.19475	0.597377	−	0.801961i	$-0.296210\pi$
$211$	17.3548	1.19475	0.597377	+	0.801961i	$0.296210\pi$
$212$	0.0390912	0.00268479
$213$	−5.69288	−0.390070
$214$	18.2486	1.24745
$215$	−1.10859	−0.0756052
$216$	5.65249	0.384603
$217$	−2.39281	−0.162435
$218$	−10.4537	−0.708011
$219$	−16.1046	−1.08825
$220$	1.62456	0.109528
$221$	28.6299	1.92586
$222$	−1.80055	−0.120845
$223$	−20.1171	−1.34714	−0.673572	−	0.739122i	$-0.735241\pi$
$223$	−20.1171	−1.34714	−0.673572	+	0.739122i	$0.735241\pi$
$224$	3.56623	0.238279
$225$	−1.09003	−0.0726689
$226$	10.5822	0.703918
$227$	−17.7556	−1.17848	−0.589240	−	0.807958i	$-0.700573\pi$
$227$	−17.7556	−1.17848	−0.589240	+	0.807958i	$0.700573\pi$
$228$	9.10628	0.603078
$229$	15.5960	1.03061	0.515305	−	0.857007i	$-0.327679\pi$
$229$	15.5960	1.03061	0.515305	+	0.857007i	$0.327679\pi$
$230$	2.76297	0.182185
$231$	−8.00680	−0.526809
$232$	−1.79507	−0.117852
$233$	10.6552	0.698045	0.349022	−	0.937114i	$-0.386514\pi$
$233$	10.6552	0.698045	0.349022	+	0.937114i	$0.386514\pi$
$234$	−5.27203	−0.344644
$235$	2.28159	0.148835
$236$	−5.91619	−0.385111
$237$	15.1967	0.987132
$238$	21.1102	1.36837
$239$	−0.234350	−0.0151589	−0.00757943	−	0.999971i	$-0.502413\pi$
$239$	−0.234350	−0.0151589	−0.00757943	+	0.999971i	$0.502413\pi$
$240$	−1.38202	−0.0892087
$241$	15.6591	1.00869	0.504347	−	0.863501i	$-0.331733\pi$
$241$	15.6591	1.00869	0.504347	+	0.863501i	$0.331733\pi$
$242$	−8.36079	−0.537452
$243$	−10.6807	−0.685170
$244$	−0.962509	−0.0616183
$245$	5.71799	0.365309
$246$	−1.71289	−0.109210
$247$	−31.8688	−2.02776
$248$	−0.670964	−0.0426062
$249$	12.2925	0.779004
$250$	1.00000	0.0632456
$251$	27.9247	1.76259	0.881295	−	0.472566i	$-0.156672\pi$
$251$	27.9247	1.76259	0.881295	+	0.472566i	$0.156672\pi$
$252$	−3.88731	−0.244878
$253$	4.48862	0.282197
$254$	10.7389	0.673817
$255$	−8.18079	−0.512301
$256$	1.00000	0.0625000
$257$	−0.108037	−0.00673919	−0.00336959	−	0.999994i	$-0.501073\pi$
$257$	−0.108037	−0.00673919	−0.00336959	+	0.999994i	$0.501073\pi$
$258$	1.53209	0.0953837
$259$	4.64624	0.288703
$260$	4.83658	0.299952
$261$	1.95669	0.121116
$262$	−15.2661	−0.943145
$263$	−29.9333	−1.84577	−0.922884	−	0.385077i	$-0.874175\pi$
$263$	−29.9333	−1.84577	−0.922884	+	0.385077i	$0.874175\pi$
$264$	−2.24517	−0.138181
$265$	0.0390912	0.00240135
$266$	−23.4983	−1.44078
$267$	9.84747	0.602656
$268$	−8.94636	−0.546486
$269$	−5.37042	−0.327440	−0.163720	−	0.986507i	$-0.552349\pi$
$269$	−5.37042	−0.327440	−0.163720	+	0.986507i	$0.552349\pi$
$270$	5.65249	0.344000
$271$	2.26309	0.137473	0.0687363	−	0.997635i	$-0.478103\pi$
$271$	2.26309	0.137473	0.0687363	+	0.997635i	$0.478103\pi$
$272$	5.91946	0.358920
$273$	−23.8375	−1.44271
$274$	−8.52606	−0.515078
$275$	1.62456	0.0979649
$276$	−3.81847	−0.229845
$277$	6.37995	0.383334	0.191667	−	0.981460i	$-0.438611\pi$
$277$	6.37995	0.383334	0.191667	+	0.981460i	$0.438611\pi$
$278$	5.02066	0.301119
$279$	0.731373	0.0437862
$280$	3.56623	0.213123
$281$	−17.4594	−1.04154	−0.520771	−	0.853697i	$-0.674355\pi$
$281$	−17.4594	−1.04154	−0.520771	+	0.853697i	$0.674355\pi$
$282$	−3.15319	−0.187770
$283$	−1.70877	−0.101576	−0.0507880	−	0.998709i	$-0.516173\pi$
$283$	−1.70877	−0.101576	−0.0507880	+	0.998709i	$0.516173\pi$
$284$	4.11926	0.244433
$285$	9.10628	0.539409
$286$	7.85733	0.464614
$287$	4.42005	0.260907
$288$	−1.09003	−0.0642309
$289$	18.0400	1.06118
$290$	−1.79507	−0.105410
$291$	3.40776	0.199766
$292$	11.6530	0.681938
$293$	−19.6861	−1.15007	−0.575037	−	0.818128i	$-0.695012\pi$
$293$	−19.6861	−1.15007	−0.575037	+	0.818128i	$0.695012\pi$
$294$	−7.90234	−0.460874
$295$	−5.91619	−0.344454
$296$	1.30284	0.0757263
$297$	9.18283	0.532842
$298$	1.47742	0.0855849
$299$	13.3633	0.772820
$300$	−1.38202	−0.0797907
$301$	−3.95349	−0.227875
$302$	6.73973	0.387828
$303$	−2.56431	−0.147316
$304$	−6.58913	−0.377913
$305$	−0.962509	−0.0551131
$306$	−6.45241	−0.368860
$307$	10.1053	0.576743	0.288371	−	0.957519i	$-0.406886\pi$
$307$	10.1053	0.576743	0.288371	+	0.957519i	$0.406886\pi$
$308$	5.79357	0.330119
$309$	−17.5056	−0.995858
$310$	−0.670964	−0.0381082
$311$	−10.5544	−0.598484	−0.299242	−	0.954177i	$-0.596734\pi$
$311$	−10.5544	−0.598484	−0.299242	+	0.954177i	$0.596734\pi$
$312$	−6.68422	−0.378419
$313$	4.67127	0.264036	0.132018	−	0.991247i	$-0.457854\pi$
$313$	4.67127	0.264036	0.132018	+	0.991247i	$0.457854\pi$
$314$	−3.95872	−0.223403
$315$	−3.88731	−0.219025
$316$	−10.9960	−0.618576
$317$	4.57895	0.257180	0.128590	−	0.991698i	$-0.458955\pi$
$317$	4.57895	0.257180	0.128590	+	0.991698i	$0.458955\pi$
$318$	−0.0540246	−0.00302955
$319$	−2.91621	−0.163277
$320$	1.00000	0.0559017
$321$	−25.2198	−1.40763
$322$	9.85338	0.549108
$323$	−39.0041	−2.17025
$324$	−4.54172	−0.252318
$325$	4.83658	0.268285
$326$	1.24862	0.0691548
$327$	14.4471	0.798927
$328$	1.23942	0.0684354
$329$	8.13667	0.448589
$330$	−2.24517	−0.123593
$331$	−15.4509	−0.849260	−0.424630	−	0.905367i	$-0.639596\pi$
$331$	−15.4509	−0.849260	−0.424630	+	0.905367i	$0.639596\pi$
$332$	−8.89461	−0.488155
$333$	−1.42014	−0.0778234
$334$	23.7956	1.30204
$335$	−8.94636	−0.488792
$336$	−4.92858	−0.268876
$337$	2.70114	0.147141	0.0735703	−	0.997290i	$-0.476561\pi$
$337$	2.70114	0.147141	0.0735703	+	0.997290i	$0.476561\pi$
$338$	10.3925	0.565275
$339$	−14.6248	−0.794308
$340$	5.91946	0.321028
$341$	−1.09002	−0.0590281
$342$	7.18238	0.388378
$343$	−4.57196	−0.246862
$344$	−1.10859	−0.0597712
$345$	−3.81847	−0.205579
$346$	9.42061	0.506455
$347$	18.4002	0.987773	0.493886	−	0.869526i	$-0.335576\pi$
$347$	18.4002	0.987773	0.493886	+	0.869526i	$0.335576\pi$
$348$	2.48082	0.132986
$349$	−21.5853	−1.15543	−0.577717	−	0.816237i	$-0.696056\pi$
$349$	−21.5853	−1.15543	−0.577717	+	0.816237i	$0.696056\pi$
$350$	3.56623	0.190623
$351$	27.3387	1.45923
$352$	1.62456	0.0865896
$353$	−13.0243	−0.693214	−0.346607	−	0.938010i	$-0.612666\pi$
$353$	−13.0243	−0.693214	−0.346607	+	0.938010i	$0.612666\pi$
$354$	8.17626	0.434563
$355$	4.11926	0.218628
$356$	−7.12545	−0.377648
$357$	−29.1745	−1.54408
$358$	−24.1011	−1.27378
$359$	−32.8364	−1.73304	−0.866520	−	0.499142i	$-0.833648\pi$
$359$	−32.8364	−1.73304	−0.866520	+	0.499142i	$0.833648\pi$
$360$	−1.09003	−0.0574498
$361$	24.4166	1.28509
$362$	16.4565	0.864933
$363$	11.5547	0.606467
$364$	17.2483	0.904058
$365$	11.6530	0.609944
$366$	1.33020	0.0695307
$367$	8.54820	0.446212	0.223106	−	0.974794i	$-0.428380\pi$
$367$	8.54820	0.446212	0.223106	+	0.974794i	$0.428380\pi$
$368$	2.76297	0.144030
$369$	−1.35101	−0.0703306
$370$	1.30284	0.0677316
$371$	0.139408	0.00723771
$372$	0.927282	0.0480773
$373$	−9.93468	−0.514398	−0.257199	−	0.966358i	$-0.582800\pi$
$373$	−9.93468	−0.514398	−0.257199	+	0.966358i	$0.582800\pi$
$374$	9.61655	0.497260
$375$	−1.38202	−0.0713670
$376$	2.28159	0.117664
$377$	−8.68201	−0.447146
$378$	20.1581	1.03682
$379$	26.2574	1.34875	0.674376	−	0.738388i	$-0.264413\pi$
$379$	26.2574	1.34875	0.674376	+	0.738388i	$0.264413\pi$
$380$	−6.58913	−0.338015
$381$	−14.8413	−0.760342
$382$	7.29447	0.373217
$383$	6.42596	0.328351	0.164176	−	0.986431i	$-0.447504\pi$
$383$	6.42596	0.328351	0.164176	+	0.986431i	$0.447504\pi$
$384$	−1.38202	−0.0705257
$385$	5.79357	0.295268
$386$	6.92850	0.352651
$387$	1.20840	0.0614265
$388$	−2.46579	−0.125182
$389$	29.7206	1.50690	0.753448	−	0.657507i	$-0.228389\pi$
$389$	29.7206	1.50690	0.753448	+	0.657507i	$0.228389\pi$
$390$	−6.68422	−0.338469
$391$	16.3553	0.827123
$392$	5.71799	0.288802
$393$	21.0980	1.06425
$394$	10.3858	0.523231
$395$	−10.9960	−0.553271
$396$	−1.77083	−0.0889876
$397$	−16.0212	−0.804082	−0.402041	−	0.915622i	$-0.631699\pi$
$397$	−16.0212	−0.804082	−0.402041	+	0.915622i	$0.631699\pi$
$398$	−7.01356	−0.351558
$399$	32.4751	1.62579
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	12.3640	0.616661
$403$	−3.24517	−0.161653
$404$	1.85549	0.0923140
$405$	−4.54172	−0.225680
$406$	−6.40164	−0.317708
$407$	2.11655	0.104914
$408$	−8.18079	−0.405009
$409$	5.43480	0.268733	0.134367	−	0.990932i	$-0.457100\pi$
$409$	5.43480	0.268733	0.134367	+	0.990932i	$0.457100\pi$
$410$	1.23942	0.0612105
$411$	11.7832	0.581220
$412$	12.6667	0.624044
$413$	−21.0985	−1.03819
$414$	−3.01173	−0.148019
$415$	−8.89461	−0.436619
$416$	4.83658	0.237133
$417$	−6.93863	−0.339786
$418$	−10.7045	−0.523573
$419$	−6.29592	−0.307576	−0.153788	−	0.988104i	$-0.549147\pi$
$419$	−6.29592	−0.307576	−0.153788	+	0.988104i	$0.549147\pi$
$420$	−4.92858	−0.240490
$421$	4.29394	0.209274	0.104637	−	0.994510i	$-0.466632\pi$
$421$	4.29394	0.209274	0.104637	+	0.994510i	$0.466632\pi$
$422$	17.3548	0.844818
$423$	−2.48701	−0.120923
$424$	0.0390912	0.00189844
$425$	5.91946	0.287136
$426$	−5.69288	−0.275821
$427$	−3.43253	−0.166112
$428$	18.2486	0.882077
$429$	−10.8589	−0.524275
$430$	−1.10859	−0.0534610
$431$	−25.6298	−1.23454	−0.617271	−	0.786750i	$-0.711762\pi$
$431$	−25.6298	−1.23454	−0.617271	+	0.786750i	$0.711762\pi$
$432$	5.65249	0.271956
$433$	22.4053	1.07673	0.538366	−	0.842711i	$-0.319042\pi$
$433$	22.4053	1.07673	0.538366	+	0.842711i	$0.319042\pi$
$434$	−2.39281	−0.114859
$435$	2.48082	0.118946
$436$	−10.4537	−0.500640
$437$	−18.2056	−0.870891
$438$	−16.1046	−0.769506
$439$	25.9024	1.23625	0.618127	−	0.786078i	$-0.287892\pi$
$439$	25.9024	1.23625	0.618127	+	0.786078i	$0.287892\pi$
$440$	1.62456	0.0774481
$441$	−6.23280	−0.296800
$442$	28.6299	1.36179
$443$	−4.82334	−0.229164	−0.114582	−	0.993414i	$-0.536553\pi$
$443$	−4.82334	−0.229164	−0.114582	+	0.993414i	$0.536553\pi$
$444$	−1.80055	−0.0854503
$445$	−7.12545	−0.337779
$446$	−20.1171	−0.952575
$447$	−2.04182	−0.0965749
$448$	3.56623	0.168488
$449$	24.1515	1.13978	0.569890	−	0.821721i	$-0.306986\pi$
$449$	24.1515	1.13978	0.569890	+	0.821721i	$0.306986\pi$
$450$	−1.09003	−0.0513847
$451$	2.01351	0.0948127
$452$	10.5822	0.497745
$453$	−9.31441	−0.437629
$454$	−17.7556	−0.833311
$455$	17.2483	0.808614
$456$	9.10628	0.426441
$457$	4.84573	0.226674	0.113337	−	0.993557i	$-0.463846\pi$
$457$	4.84573	0.226674	0.113337	+	0.993557i	$0.463846\pi$
$458$	15.5960	0.728752
$459$	33.4597	1.56176
$460$	2.76297	0.128824
$461$	8.60203	0.400636	0.200318	−	0.979731i	$-0.435802\pi$
$461$	8.60203	0.400636	0.200318	+	0.979731i	$0.435802\pi$
$462$	−8.00680	−0.372510
$463$	10.0689	0.467939	0.233970	−	0.972244i	$-0.424828\pi$
$463$	10.0689	0.467939	0.233970	+	0.972244i	$0.424828\pi$
$464$	−1.79507	−0.0833342
$465$	0.927282	0.0430017
$466$	10.6552	0.493592
$467$	−26.3827	−1.22085	−0.610424	−	0.792075i	$-0.709001\pi$
$467$	−26.3827	−1.22085	−0.610424	+	0.792075i	$0.709001\pi$
$468$	−5.27203	−0.243700
$469$	−31.9048	−1.47323
$470$	2.28159	0.105242
$471$	5.47101	0.252091
$472$	−5.91619	−0.272315
$473$	−1.80098	−0.0828090
$474$	15.1967	0.698008
$475$	−6.58913	−0.302330
$476$	21.1102	0.967582
$477$	−0.0426107	−0.00195101
$478$	−0.234350	−0.0107189
$479$	−41.4402	−1.89345	−0.946725	−	0.322042i	$-0.895631\pi$
$479$	−41.4402	−1.89345	−0.946725	+	0.322042i	$0.895631\pi$
$480$	−1.38202	−0.0630801
$481$	6.30130	0.287315
$482$	15.6591	0.713255
$483$	−13.6175	−0.619619
$484$	−8.36079	−0.380036
$485$	−2.46579	−0.111966
$486$	−10.6807	−0.484488
$487$	−5.06588	−0.229557	−0.114778	−	0.993391i	$-0.536616\pi$
$487$	−5.06588	−0.229557	−0.114778	+	0.993391i	$0.536616\pi$
$488$	−0.962509	−0.0435707
$489$	−1.72561	−0.0780350
$490$	5.71799	0.258312
$491$	−28.8094	−1.30015	−0.650075	−	0.759870i	$-0.725263\pi$
$491$	−28.8094	−1.30015	−0.650075	+	0.759870i	$0.725263\pi$
$492$	−1.71289	−0.0772232
$493$	−10.6259	−0.478565
$494$	−31.8688	−1.43385
$495$	−1.77083	−0.0795929
$496$	−0.670964	−0.0301272
$497$	14.6902	0.658947
$498$	12.2925	0.550839
$499$	−9.44574	−0.422849	−0.211425	−	0.977394i	$-0.567810\pi$
$499$	−9.44574	−0.422849	−0.211425	+	0.977394i	$0.567810\pi$
$500$	1.00000	0.0447214
$501$	−32.8859	−1.46923
$502$	27.9247	1.24634
$503$	−29.6189	−1.32064	−0.660321	−	0.750984i	$-0.729580\pi$
$503$	−29.6189	−1.32064	−0.660321	+	0.750984i	$0.729580\pi$
$504$	−3.88731	−0.173155
$505$	1.85549	0.0825681
$506$	4.48862	0.199544
$507$	−14.3625	−0.637863
$508$	10.7389	0.476460
$509$	−14.0257	−0.621677	−0.310838	−	0.950463i	$-0.600610\pi$
$509$	−14.0257	−0.621677	−0.310838	+	0.950463i	$0.600610\pi$
$510$	−8.18079	−0.362251
$511$	41.5571	1.83838
$512$	1.00000	0.0441942
$513$	−37.2450	−1.64441
$514$	−0.108037	−0.00476533
$515$	12.6667	0.558162
$516$	1.53209	0.0674464
$517$	3.70659	0.163016
$518$	4.64624	0.204144
$519$	−13.0194	−0.571489
$520$	4.83658	0.212098
$521$	0.151511	0.00663782	0.00331891	−	0.999994i	$-0.498944\pi$
$521$	0.151511	0.00663782	0.00331891	+	0.999994i	$0.498944\pi$
$522$	1.95669	0.0856421
$523$	36.4244	1.59273	0.796365	−	0.604817i	$-0.206754\pi$
$523$	36.4244	1.59273	0.796365	+	0.604817i	$0.206754\pi$
$524$	−15.2661	−0.666904
$525$	−4.92858	−0.215101
$526$	−29.9333	−1.30516
$527$	−3.97174	−0.173012
$528$	−2.24517	−0.0977086
$529$	−15.3660	−0.668087
$530$	0.0390912	0.00169801
$531$	6.44884	0.279856
$532$	−23.4983	−1.01878
$533$	5.99454	0.259652
$534$	9.84747	0.426142
$535$	18.2486	0.788954
$536$	−8.94636	−0.386424
$537$	33.3081	1.43735
$538$	−5.37042	−0.231535
$539$	9.28924	0.400116
$540$	5.65249	0.243244
$541$	8.50998	0.365873	0.182936	−	0.983125i	$-0.441440\pi$
$541$	8.50998	0.365873	0.182936	+	0.983125i	$0.441440\pi$
$542$	2.26309	0.0972079
$543$	−22.7431	−0.976000
$544$	5.91946	0.253795
$545$	−10.4537	−0.447786
$546$	−23.8375	−1.02015
$547$	−24.2236	−1.03573	−0.517863	−	0.855464i	$-0.673272\pi$
$547$	−24.2236	−1.03573	−0.517863	+	0.855464i	$0.673272\pi$
$548$	−8.52606	−0.364215
$549$	1.04917	0.0447774
$550$	1.62456	0.0692717
$551$	11.8280	0.503889
$552$	−3.81847	−0.162525
$553$	−39.2144	−1.66757
$554$	6.37995	0.271058
$555$	−1.80055	−0.0764291
$556$	5.02066	0.212923
$557$	−25.2542	−1.07005	−0.535027	−	0.844835i	$-0.679699\pi$
$557$	−25.2542	−1.07005	−0.535027	+	0.844835i	$0.679699\pi$
$558$	0.731373	0.0309615
$559$	−5.36178	−0.226779
$560$	3.56623	0.150701
$561$	−13.2902	−0.561113
$562$	−17.4594	−0.736481
$563$	−32.4026	−1.36561	−0.682804	−	0.730602i	$-0.739240\pi$
$563$	−32.4026	−1.36561	−0.682804	+	0.730602i	$0.739240\pi$
$564$	−3.15319	−0.132773
$565$	10.5822	0.445197
$566$	−1.70877	−0.0718250
$567$	−16.1968	−0.680203
$568$	4.11926	0.172840
$569$	1.17117	0.0490980	0.0245490	−	0.999699i	$-0.492185\pi$
$569$	1.17117	0.0490980	0.0245490	+	0.999699i	$0.492185\pi$
$570$	9.10628	0.381420
$571$	−19.3733	−0.810746	−0.405373	−	0.914151i	$-0.632858\pi$
$571$	−19.3733	−0.810746	−0.405373	+	0.914151i	$0.632858\pi$
$572$	7.85733	0.328531
$573$	−10.0811	−0.421143
$574$	4.42005	0.184489
$575$	2.76297	0.115224
$576$	−1.09003	−0.0454181
$577$	28.1382	1.17141	0.585704	−	0.810525i	$-0.300818\pi$
$577$	28.1382	1.17141	0.585704	+	0.810525i	$0.300818\pi$
$578$	18.0400	0.750366
$579$	−9.57529	−0.397935
$580$	−1.79507	−0.0745364
$581$	−31.7202	−1.31598
$582$	3.40776	0.141256
$583$	0.0635062	0.00263016
$584$	11.6530	0.482203
$585$	−5.27203	−0.217972
$586$	−19.6861	−0.813225
$587$	−32.3928	−1.33699	−0.668497	−	0.743715i	$-0.733062\pi$
$587$	−32.3928	−1.33699	−0.668497	+	0.743715i	$0.733062\pi$
$588$	−7.90234	−0.325887
$589$	4.42107	0.182167
$590$	−5.91619	−0.243565
$591$	−14.3534	−0.590419
$592$	1.30284	0.0535466
$593$	24.6934	1.01404	0.507018	−	0.861936i	$-0.330748\pi$
$593$	24.6934	1.01404	0.507018	+	0.861936i	$0.330748\pi$
$594$	9.18283	0.376776
$595$	21.1102	0.865432
$596$	1.47742	0.0605176
$597$	9.69284	0.396702
$598$	13.3633	0.546467
$599$	−18.3962	−0.751649	−0.375825	−	0.926691i	$-0.622641\pi$
$599$	−18.3962	−0.751649	−0.375825	+	0.926691i	$0.622641\pi$
$600$	−1.38202	−0.0564205
$601$	−12.8405	−0.523776	−0.261888	−	0.965098i	$-0.584345\pi$
$601$	−12.8405	−0.523776	−0.261888	+	0.965098i	$0.584345\pi$
$602$	−3.95349	−0.161132
$603$	9.75184	0.397126
$604$	6.73973	0.274236
$605$	−8.36079	−0.339914
$606$	−2.56431	−0.104168
$607$	−7.09563	−0.288003	−0.144001	−	0.989577i	$-0.545997\pi$
$607$	−7.09563	−0.288003	−0.144001	+	0.989577i	$0.545997\pi$
$608$	−6.58913	−0.267225
$609$	8.84717	0.358505
$610$	−0.962509	−0.0389708
$611$	11.0351	0.446432
$612$	−6.45241	−0.260823
$613$	−12.6890	−0.512503	−0.256252	−	0.966610i	$-0.582488\pi$
$613$	−12.6890	−0.512503	−0.256252	+	0.966610i	$0.582488\pi$
$614$	10.1053	0.407819
$615$	−1.71289	−0.0690705
$616$	5.79357	0.233430
$617$	0.221575	0.00892026	0.00446013	−	0.999990i	$-0.498580\pi$
$617$	0.221575	0.00892026	0.00446013	+	0.999990i	$0.498580\pi$
$618$	−17.5056	−0.704178
$619$	7.62857	0.306618	0.153309	−	0.988178i	$-0.451007\pi$
$619$	7.62857	0.306618	0.153309	+	0.988178i	$0.451007\pi$
$620$	−0.670964	−0.0269466
$621$	15.6177	0.626715
$622$	−10.5544	−0.423192
$623$	−25.4110	−1.01807
$624$	−6.68422	−0.267583
$625$	1.00000	0.0400000
$626$	4.67127	0.186702
$627$	14.7937	0.590805
$628$	−3.95872	−0.157970
$629$	7.71213	0.307503
$630$	−3.88731	−0.154874
$631$	32.2585	1.28419	0.642095	−	0.766625i	$-0.278065\pi$
$631$	32.2585	1.28419	0.642095	+	0.766625i	$0.278065\pi$
$632$	−10.9960	−0.437399
$633$	−23.9846	−0.953302
$634$	4.57895	0.181853
$635$	10.7389	0.426159
$636$	−0.0540246	−0.00214222
$637$	27.6555	1.09575
$638$	−2.91621	−0.115454
$639$	−4.49014	−0.177627
$640$	1.00000	0.0395285
$641$	14.9889	0.592028	0.296014	−	0.955184i	$-0.404343\pi$
$641$	14.9889	0.592028	0.296014	+	0.955184i	$0.404343\pi$
$642$	−25.2198	−0.995345
$643$	0.733000	0.0289067	0.0144534	−	0.999896i	$-0.495399\pi$
$643$	0.733000	0.0289067	0.0144534	+	0.999896i	$0.495399\pi$
$644$	9.85338	0.388278
$645$	1.53209	0.0603259
$646$	−39.0041	−1.53460
$647$	−46.4686	−1.82687	−0.913434	−	0.406987i	$-0.866579\pi$
$647$	−46.4686	−1.82687	−0.913434	+	0.406987i	$0.866579\pi$
$648$	−4.54172	−0.178416
$649$	−9.61122	−0.377274
$650$	4.83658	0.189706
$651$	3.30690	0.129608
$652$	1.24862	0.0488998
$653$	26.4712	1.03590	0.517949	−	0.855411i	$-0.326696\pi$
$653$	26.4712	1.03590	0.517949	+	0.855411i	$0.326696\pi$
$654$	14.4471	0.564927
$655$	−15.2661	−0.596497
$656$	1.23942	0.0483911
$657$	−12.7021	−0.495557
$658$	8.13667	0.317201
$659$	−6.30863	−0.245749	−0.122875	−	0.992422i	$-0.539211\pi$
$659$	−6.30863	−0.245749	−0.122875	+	0.992422i	$0.539211\pi$
$660$	−2.24517	−0.0873932
$661$	−51.0464	−1.98548	−0.992738	−	0.120299i	$-0.961615\pi$
$661$	−51.0464	−1.98548	−0.992738	+	0.120299i	$0.961615\pi$
$662$	−15.4509	−0.600517
$663$	−39.5670	−1.53665
$664$	−8.89461	−0.345178
$665$	−23.4983	−0.911227
$666$	−1.42014	−0.0550295
$667$	−4.95974	−0.192042
$668$	23.7956	0.920681
$669$	27.8022	1.07490
$670$	−8.94636	−0.345628
$671$	−1.56366	−0.0603643
$672$	−4.92858	−0.190124
$673$	−26.7088	−1.02955	−0.514775	−	0.857325i	$-0.672125\pi$
$673$	−26.7088	−1.02955	−0.514775	+	0.857325i	$0.672125\pi$
$674$	2.70114	0.104044
$675$	5.65249	0.217564
$676$	10.3925	0.399710
$677$	−10.3938	−0.399467	−0.199733	−	0.979850i	$-0.564008\pi$
$677$	−10.3938	−0.399467	−0.199733	+	0.979850i	$0.564008\pi$
$678$	−14.6248	−0.561661
$679$	−8.79357	−0.337466
$680$	5.91946	0.227001
$681$	24.5385	0.940317
$682$	−1.09002	−0.0417392
$683$	−22.9944	−0.879857	−0.439928	−	0.898033i	$-0.644996\pi$
$683$	−22.9944	−0.879857	−0.439928	+	0.898033i	$0.644996\pi$
$684$	7.18238	0.274625
$685$	−8.52606	−0.325764
$686$	−4.57196	−0.174558
$687$	−21.5539	−0.822331
$688$	−1.10859	−0.0422646
$689$	0.189067	0.00720290
$690$	−3.81847	−0.145367
$691$	−43.0936	−1.63936	−0.819679	−	0.572823i	$-0.805848\pi$
$691$	−43.0936	−1.63936	−0.819679	+	0.572823i	$0.805848\pi$
$692$	9.42061	0.358118
$693$	−6.31519	−0.239894
$694$	18.4002	0.698461
$695$	5.02066	0.190445
$696$	2.48082	0.0940352
$697$	7.33668	0.277897
$698$	−21.5853	−0.817015
$699$	−14.7256	−0.556975
$700$	3.56623	0.134791
$701$	−36.5360	−1.37995	−0.689974	−	0.723835i	$-0.742378\pi$
$701$	−36.5360	−1.37995	−0.689974	+	0.723835i	$0.742378\pi$
$702$	27.3387	1.03183
$703$	−8.58461	−0.323775
$704$	1.62456	0.0612281
$705$	−3.15319	−0.118756
$706$	−13.0243	−0.490176
$707$	6.61709	0.248861
$708$	8.17626	0.307283
$709$	37.0300	1.39069	0.695345	−	0.718676i	$-0.255252\pi$
$709$	37.0300	1.39069	0.695345	+	0.718676i	$0.255252\pi$
$710$	4.11926	0.154593
$711$	11.9861	0.449513
$712$	−7.12545	−0.267037
$713$	−1.85385	−0.0694273
$714$	−29.1745	−1.09183
$715$	7.85733	0.293847
$716$	−24.1011	−0.900700
$717$	0.323875	0.0120954
$718$	−32.8364	−1.22544
$719$	−15.3656	−0.573039	−0.286519	−	0.958074i	$-0.592498\pi$
$719$	−15.3656	−0.573039	−0.286519	+	0.958074i	$0.592498\pi$
$720$	−1.09003	−0.0406232
$721$	45.1724	1.68231
$722$	24.4166	0.908693
$723$	−21.6412	−0.804844
$724$	16.4565	0.611600
$725$	−1.79507	−0.0666674
$726$	11.5547	0.428837
$727$	−28.3264	−1.05057	−0.525283	−	0.850927i	$-0.676041\pi$
$727$	−28.3264	−1.05057	−0.525283	+	0.850927i	$0.676041\pi$
$728$	17.2483	0.639266
$729$	28.3861	1.05134
$730$	11.6530	0.431295
$731$	−6.56226	−0.242714
$732$	1.33020	0.0491657
$733$	−29.5644	−1.09199	−0.545993	−	0.837790i	$-0.683847\pi$
$733$	−29.5644	−1.09199	−0.545993	+	0.837790i	$0.683847\pi$
$734$	8.54820	0.315520
$735$	−7.90234	−0.291482
$736$	2.76297	0.101844
$737$	−14.5339	−0.535365
$738$	−1.35101	−0.0497313
$739$	1.22485	0.0450570	0.0225285	−	0.999746i	$-0.492828\pi$
$739$	1.22485	0.0450570	0.0225285	+	0.999746i	$0.492828\pi$
$740$	1.30284	0.0478935
$741$	44.0432	1.61797
$742$	0.139408	0.00511783
$743$	44.5225	1.63337	0.816686	−	0.577082i	$-0.195809\pi$
$743$	44.5225	1.63337	0.816686	+	0.577082i	$0.195809\pi$
$744$	0.927282	0.0339958
$745$	1.47742	0.0541286
$746$	−9.93468	−0.363734
$747$	9.69543	0.354737
$748$	9.61655	0.351616
$749$	65.0785	2.37792
$750$	−1.38202	−0.0504641
$751$	−21.3248	−0.778154	−0.389077	−	0.921205i	$-0.627206\pi$
$751$	−21.3248	−0.778154	−0.389077	+	0.921205i	$0.627206\pi$
$752$	2.28159	0.0832010
$753$	−38.5923	−1.40638
$754$	−8.68201	−0.316180
$755$	6.73973	0.245284
$756$	20.1581	0.733142
$757$	22.1599	0.805414	0.402707	−	0.915329i	$-0.368069\pi$
$757$	22.1599	0.805414	0.402707	+	0.915329i	$0.368069\pi$
$758$	26.2574	0.953712
$759$	−6.20335	−0.225167
$760$	−6.58913	−0.239013
$761$	−21.5481	−0.781119	−0.390560	−	0.920578i	$-0.627718\pi$
$761$	−21.5481	−0.781119	−0.390560	+	0.920578i	$0.627718\pi$
$762$	−14.8413	−0.537643
$763$	−37.2801	−1.34963
$764$	7.29447	0.263905
$765$	−6.45241	−0.233288
$766$	6.42596	0.232179
$767$	−28.6141	−1.03319
$768$	−1.38202	−0.0498692
$769$	18.7422	0.675860	0.337930	−	0.941171i	$-0.390273\pi$
$769$	18.7422	0.675860	0.337930	+	0.941171i	$0.390273\pi$
$770$	5.79357	0.208786
$771$	0.149309	0.00537724
$772$	6.92850	0.249362
$773$	−0.936573	−0.0336862	−0.0168431	−	0.999858i	$-0.505362\pi$
$773$	−0.936573	−0.0336862	−0.0168431	+	0.999858i	$0.505362\pi$
$774$	1.20840	0.0434351
$775$	−0.670964	−0.0241017
$776$	−2.46579	−0.0885167
$777$	−6.42117	−0.230358
$778$	29.7206	1.06554
$779$	−8.16668	−0.292602
$780$	−6.68422	−0.239333
$781$	6.69201	0.239459
$782$	16.3553	0.584864
$783$	−10.1466	−0.362611
$784$	5.71799	0.204214
$785$	−3.95872	−0.141293
$786$	21.0980	0.752542
$787$	25.9499	0.925015	0.462507	−	0.886615i	$-0.346950\pi$
$787$	25.9499	0.925015	0.462507	+	0.886615i	$0.346950\pi$
$788$	10.3858	0.369980
$789$	41.3683	1.47275
$790$	−10.9960	−0.391222
$791$	37.7386	1.34183
$792$	−1.77083	−0.0629237
$793$	−4.65525	−0.165313
$794$	−16.0212	−0.568572
$795$	−0.0540246	−0.00191606
$796$	−7.01356	−0.248589
$797$	−21.1783	−0.750174	−0.375087	−	0.926990i	$-0.622387\pi$
$797$	−21.1783	−0.750174	−0.375087	+	0.926990i	$0.622387\pi$
$798$	32.4751	1.14960
$799$	13.5058	0.477800
$800$	1.00000	0.0353553
$801$	7.76698	0.274433
$802$	1.00000	0.0353112
$803$	18.9310	0.668060
$804$	12.3640	0.436045
$805$	9.85338	0.347286
$806$	−3.24517	−0.114306
$807$	7.42200	0.261267
$808$	1.85549	0.0652758
$809$	−12.8758	−0.452690	−0.226345	−	0.974047i	$-0.572678\pi$
$809$	−12.8758	−0.452690	−0.226345	+	0.974047i	$0.572678\pi$
$810$	−4.54172	−0.159580
$811$	−30.8919	−1.08476	−0.542381	−	0.840133i	$-0.682477\pi$
$811$	−30.8919	−1.08476	−0.542381	+	0.840133i	$0.682477\pi$
$812$	−6.40164	−0.224654
$813$	−3.12762	−0.109690
$814$	2.11655	0.0741852
$815$	1.24862	0.0437373
$816$	−8.18079	−0.286385
$817$	7.30465	0.255557
$818$	5.43480	0.190023
$819$	−18.8013	−0.656970
$820$	1.23942	0.0432823
$821$	51.0745	1.78251	0.891257	−	0.453499i	$-0.149824\pi$
$821$	51.0745	1.78251	0.891257	+	0.453499i	$0.149824\pi$
$822$	11.7832	0.410985
$823$	1.31005	0.0456654	0.0228327	−	0.999739i	$-0.492731\pi$
$823$	1.31005	0.0456654	0.0228327	+	0.999739i	$0.492731\pi$
$824$	12.6667	0.441266
$825$	−2.24517	−0.0781669
$826$	−21.0985	−0.734110
$827$	−5.55206	−0.193064	−0.0965320	−	0.995330i	$-0.530775\pi$
$827$	−5.55206	−0.193064	−0.0965320	+	0.995330i	$0.530775\pi$
$828$	−3.01173	−0.104665
$829$	−27.6965	−0.961939	−0.480969	−	0.876737i	$-0.659715\pi$
$829$	−27.6965	−0.961939	−0.480969	+	0.876737i	$0.659715\pi$
$830$	−8.89461	−0.308736
$831$	−8.81719	−0.305865
$832$	4.83658	0.167678
$833$	33.8474	1.17274
$834$	−6.93863	−0.240265
$835$	23.7956	0.823482
$836$	−10.7045	−0.370222
$837$	−3.79262	−0.131092
$838$	−6.29592	−0.217489
$839$	−32.8768	−1.13503	−0.567517	−	0.823362i	$-0.692096\pi$
$839$	−32.8768	−1.13503	−0.567517	+	0.823362i	$0.692096\pi$
$840$	−4.92858	−0.170052
$841$	−25.7777	−0.888887
$842$	4.29394	0.147979
$843$	24.1292	0.831053
$844$	17.3548	0.597377
$845$	10.3925	0.357512
$846$	−2.48701	−0.0855052
$847$	−29.8165	−1.02451
$848$	0.0390912	0.00134240
$849$	2.36155	0.0810482
$850$	5.91946	0.203036
$851$	3.59972	0.123397
$852$	−5.69288	−0.195035
$853$	−42.1551	−1.44336	−0.721682	−	0.692225i	$-0.756631\pi$
$853$	−42.1551	−1.44336	−0.721682	+	0.692225i	$0.756631\pi$
$854$	−3.43253	−0.117459
$855$	7.18238	0.245632
$856$	18.2486	0.623723
$857$	19.1152	0.652962	0.326481	−	0.945204i	$-0.394137\pi$
$857$	19.1152	0.652962	0.326481	+	0.945204i	$0.394137\pi$
$858$	−10.8589	−0.370718
$859$	14.6572	0.500097	0.250048	−	0.968233i	$-0.419553\pi$
$859$	14.6572	0.500097	0.250048	+	0.968233i	$0.419553\pi$
$860$	−1.10859	−0.0378026
$861$	−6.10857	−0.208180
$862$	−25.6298	−0.872953
$863$	−23.8577	−0.812127	−0.406063	−	0.913845i	$-0.633099\pi$
$863$	−23.8577	−0.812127	−0.406063	+	0.913845i	$0.633099\pi$
$864$	5.65249	0.192302
$865$	9.42061	0.320310
$866$	22.4053	0.761364
$867$	−24.9316	−0.846721
$868$	−2.39281	−0.0812173
$869$	−17.8638	−0.605988
$870$	2.48082	0.0841077
$871$	−43.2697	−1.46614
$872$	−10.4537	−0.354006
$873$	2.68780	0.0909681
$874$	−18.2056	−0.615813
$875$	3.56623	0.120561
$876$	−16.1046	−0.544123
$877$	−31.3672	−1.05919	−0.529597	−	0.848250i	$-0.677657\pi$
$877$	−31.3672	−1.05919	−0.529597	+	0.848250i	$0.677657\pi$
$878$	25.9024	0.874164
$879$	27.2065	0.917652
$880$	1.62456	0.0547641
$881$	9.47340	0.319167	0.159584	−	0.987184i	$-0.448985\pi$
$881$	9.47340	0.319167	0.159584	+	0.987184i	$0.448985\pi$
$882$	−6.23280	−0.209869
$883$	15.5053	0.521796	0.260898	−	0.965366i	$-0.415981\pi$
$883$	15.5053	0.521796	0.260898	+	0.965366i	$0.415981\pi$
$884$	28.6299	0.962928
$885$	8.17626	0.274842
$886$	−4.82334	−0.162043
$887$	−5.49742	−0.184585	−0.0922927	−	0.995732i	$-0.529420\pi$
$887$	−5.49742	−0.184585	−0.0922927	+	0.995732i	$0.529420\pi$
$888$	−1.80055	−0.0604225
$889$	38.2973	1.28445
$890$	−7.12545	−0.238846
$891$	−7.37832	−0.247183
$892$	−20.1171	−0.673572
$893$	−15.0337	−0.503084
$894$	−2.04182	−0.0682887
$895$	−24.1011	−0.805610
$896$	3.56623	0.119139
$897$	−18.4683	−0.616639
$898$	24.1515	0.805947
$899$	1.20443	0.0401700
$900$	−1.09003	−0.0363345
$901$	0.231399	0.00770901
$902$	2.01351	0.0670427
$903$	5.46378	0.181823
$904$	10.5822	0.351959
$905$	16.4565	0.547032
$906$	−9.31441	−0.309450
$907$	−6.78269	−0.225216	−0.112608	−	0.993640i	$-0.535920\pi$
$907$	−6.78269	−0.225216	−0.112608	+	0.993640i	$0.535920\pi$
$908$	−17.7556	−0.589240
$909$	−2.02254	−0.0670836
$910$	17.2483	0.571777
$911$	−21.1393	−0.700377	−0.350188	−	0.936679i	$-0.613882\pi$
$911$	−21.1393	−0.700377	−0.350188	+	0.936679i	$0.613882\pi$
$912$	9.10628	0.301539
$913$	−14.4499	−0.478221
$914$	4.84573	0.160282
$915$	1.33020	0.0439751
$916$	15.5960	0.515305
$917$	−54.4425	−1.79785
$918$	33.4597	1.10433
$919$	−44.6701	−1.47353	−0.736765	−	0.676149i	$-0.763647\pi$
$919$	−44.6701	−1.47353	−0.736765	+	0.676149i	$0.763647\pi$
$920$	2.76297	0.0910924
$921$	−13.9657	−0.460187
$922$	8.60203	0.283293
$923$	19.9231	0.655778
$924$	−8.00680	−0.263404
$925$	1.30284	0.0428372
$926$	10.0689	0.330883
$927$	−13.8071	−0.453486
$928$	−1.79507	−0.0589262
$929$	30.6212	1.00465	0.502325	−	0.864679i	$-0.332478\pi$
$929$	30.6212	1.00465	0.502325	+	0.864679i	$0.332478\pi$
$930$	0.927282	0.0304068
$931$	−37.6766	−1.23480
$932$	10.6552	0.349022
$933$	14.5863	0.477534
$934$	−26.3827	−0.863270
$935$	9.61655	0.314495
$936$	−5.27203	−0.172322
$937$	−10.6325	−0.347348	−0.173674	−	0.984803i	$-0.555564\pi$
$937$	−10.6325	−0.347348	−0.173674	+	0.984803i	$0.555564\pi$
$938$	−31.9048	−1.04173
$939$	−6.45577	−0.210676
$940$	2.28159	0.0744173
$941$	22.9248	0.747326	0.373663	−	0.927565i	$-0.378102\pi$
$941$	22.9248	0.747326	0.373663	+	0.927565i	$0.378102\pi$
$942$	5.47101	0.178255
$943$	3.42447	0.111516
$944$	−5.91619	−0.192555
$945$	20.1581	0.655742
$946$	−1.80098	−0.0585548
$947$	37.7852	1.22785	0.613927	−	0.789363i	$-0.289589\pi$
$947$	37.7852	1.22785	0.613927	+	0.789363i	$0.289589\pi$
$948$	15.1967	0.493566
$949$	56.3604	1.82954
$950$	−6.58913	−0.213780
$951$	−6.32818	−0.205205
$952$	21.1102	0.684184
$953$	1.91009	0.0618739	0.0309369	−	0.999521i	$-0.490151\pi$
$953$	1.91009	0.0618739	0.0309369	+	0.999521i	$0.490151\pi$
$954$	−0.0426107	−0.00137957
$955$	7.29447	0.236043
$956$	−0.234350	−0.00757943
$957$	4.03025	0.130280
$958$	−41.4402	−1.33887
$959$	−30.4059	−0.981858
$960$	−1.38202	−0.0446043
$961$	−30.5498	−0.985478
$962$	6.30130	0.203162
$963$	−19.8915	−0.640996
$964$	15.6591	0.504347
$965$	6.92850	0.223036
$966$	−13.6175	−0.438137
$967$	−48.8059	−1.56949	−0.784746	−	0.619817i	$-0.787207\pi$
$967$	−48.8059	−1.56949	−0.784746	+	0.619817i	$0.787207\pi$
$968$	−8.36079	−0.268726
$969$	53.9043	1.73165
$970$	−2.46579	−0.0791718
$971$	−53.8606	−1.72847	−0.864234	−	0.503091i	$-0.832196\pi$
$971$	−53.8606	−1.72847	−0.864234	+	0.503091i	$0.832196\pi$
$972$	−10.6807	−0.342585
$973$	17.9048	0.574002
$974$	−5.06588	−0.162321
$975$	−6.68422	−0.214066
$976$	−0.962509	−0.0308091
$977$	26.7481	0.855748	0.427874	−	0.903838i	$-0.359263\pi$
$977$	26.7481	0.855748	0.427874	+	0.903838i	$0.359263\pi$
$978$	−1.72561	−0.0551791
$979$	−11.5757	−0.369962
$980$	5.71799	0.182654
$981$	11.3948	0.363809
$982$	−28.8094	−0.919346
$983$	44.7650	1.42778	0.713890	−	0.700258i	$-0.246931\pi$
$983$	44.7650	1.42778	0.713890	+	0.700258i	$0.246931\pi$
$984$	−1.71289	−0.0546051
$985$	10.3858	0.330920
$986$	−10.6259	−0.338397
$987$	−11.2450	−0.357932
$988$	−31.8688	−1.01388
$989$	−3.06300	−0.0973978
$990$	−1.77083	−0.0562807
$991$	−17.6130	−0.559495	−0.279747	−	0.960074i	$-0.590251\pi$
$991$	−17.6130	−0.559495	−0.279747	+	0.960074i	$0.590251\pi$
$992$	−0.670964	−0.0213031
$993$	21.3534	0.677630
$994$	14.6902	0.465946
$995$	−7.01356	−0.222345
$996$	12.2925	0.389502
$997$	−26.2518	−0.831403	−0.415701	−	0.909501i	$-0.636464\pi$
$997$	−26.2518	−0.831403	−0.415701	+	0.909501i	$0.636464\pi$
$998$	−9.44574	−0.299000
$999$	7.36431	0.232997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.n.1.8	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.n.1.8	✓	22	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.38202 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.38202 q^{6} +3.56623 q^{7} +1.00000 q^{8} -1.09003 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.38202 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.38202 q^{6} +3.56623 q^{7} +1.00000 q^{8} -1.09003 q^{9} +1.00000 q^{10} +1.62456 q^{11} -1.38202 q^{12} +4.83658 q^{13} +3.56623 q^{14} -1.38202 q^{15} +1.00000 q^{16} +5.91946 q^{17} -1.09003 q^{18} -6.58913 q^{19} +1.00000 q^{20} -4.92858 q^{21} +1.62456 q^{22} +2.76297 q^{23} -1.38202 q^{24} +1.00000 q^{25} +4.83658 q^{26} +5.65249 q^{27} +3.56623 q^{28} -1.79507 q^{29} -1.38202 q^{30} -0.670964 q^{31} +1.00000 q^{32} -2.24517 q^{33} +5.91946 q^{34} +3.56623 q^{35} -1.09003 q^{36} +1.30284 q^{37} -6.58913 q^{38} -6.68422 q^{39} +1.00000 q^{40} +1.23942 q^{41} -4.92858 q^{42} -1.10859 q^{43} +1.62456 q^{44} -1.09003 q^{45} +2.76297 q^{46} +2.28159 q^{47} -1.38202 q^{48} +5.71799 q^{49} +1.00000 q^{50} -8.18079 q^{51} +4.83658 q^{52} +0.0390912 q^{53} +5.65249 q^{54} +1.62456 q^{55} +3.56623 q^{56} +9.10628 q^{57} -1.79507 q^{58} -5.91619 q^{59} -1.38202 q^{60} -0.962509 q^{61} -0.670964 q^{62} -3.88731 q^{63} +1.00000 q^{64} +4.83658 q^{65} -2.24517 q^{66} -8.94636 q^{67} +5.91946 q^{68} -3.81847 q^{69} +3.56623 q^{70} +4.11926 q^{71} -1.09003 q^{72} +11.6530 q^{73} +1.30284 q^{74} -1.38202 q^{75} -6.58913 q^{76} +5.79357 q^{77} -6.68422 q^{78} -10.9960 q^{79} +1.00000 q^{80} -4.54172 q^{81} +1.23942 q^{82} -8.89461 q^{83} -4.92858 q^{84} +5.91946 q^{85} -1.10859 q^{86} +2.48082 q^{87} +1.62456 q^{88} -7.12545 q^{89} -1.09003 q^{90} +17.2483 q^{91} +2.76297 q^{92} +0.927282 q^{93} +2.28159 q^{94} -6.58913 q^{95} -1.38202 q^{96} -2.46579 q^{97} +5.71799 q^{98} -1.77083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * q^99

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