LMFDB - Embedded newform 4010.2.a.n.1.12

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			1.12
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.470815 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.470815 q^{6} +2.26316 q^{7} +1.00000 q^{8} -2.77833 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.470815 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.470815 q^{6} +2.26316 q^{7} +1.00000 q^{8} -2.77833 q^{9} +1.00000 q^{10} +2.65457 q^{11} +0.470815 q^{12} -5.41634 q^{13} +2.26316 q^{14} +0.470815 q^{15} +1.00000 q^{16} +2.57005 q^{17} -2.77833 q^{18} -5.28267 q^{19} +1.00000 q^{20} +1.06553 q^{21} +2.65457 q^{22} +6.93371 q^{23} +0.470815 q^{24} +1.00000 q^{25} -5.41634 q^{26} -2.72053 q^{27} +2.26316 q^{28} +3.41645 q^{29} +0.470815 q^{30} -0.582895 q^{31} +1.00000 q^{32} +1.24981 q^{33} +2.57005 q^{34} +2.26316 q^{35} -2.77833 q^{36} +9.97815 q^{37} -5.28267 q^{38} -2.55009 q^{39} +1.00000 q^{40} +3.63306 q^{41} +1.06553 q^{42} +9.99110 q^{43} +2.65457 q^{44} -2.77833 q^{45} +6.93371 q^{46} +13.2118 q^{47} +0.470815 q^{48} -1.87812 q^{49} +1.00000 q^{50} +1.21002 q^{51} -5.41634 q^{52} +2.42794 q^{53} -2.72053 q^{54} +2.65457 q^{55} +2.26316 q^{56} -2.48716 q^{57} +3.41645 q^{58} +14.1629 q^{59} +0.470815 q^{60} -5.55694 q^{61} -0.582895 q^{62} -6.28780 q^{63} +1.00000 q^{64} -5.41634 q^{65} +1.24981 q^{66} +7.81080 q^{67} +2.57005 q^{68} +3.26449 q^{69} +2.26316 q^{70} -7.81146 q^{71} -2.77833 q^{72} -7.29724 q^{73} +9.97815 q^{74} +0.470815 q^{75} -5.28267 q^{76} +6.00771 q^{77} -2.55009 q^{78} +11.4614 q^{79} +1.00000 q^{80} +7.05413 q^{81} +3.63306 q^{82} -8.88037 q^{83} +1.06553 q^{84} +2.57005 q^{85} +9.99110 q^{86} +1.60852 q^{87} +2.65457 q^{88} -10.9119 q^{89} -2.77833 q^{90} -12.2580 q^{91} +6.93371 q^{92} -0.274436 q^{93} +13.2118 q^{94} -5.28267 q^{95} +0.470815 q^{96} -5.33845 q^{97} -1.87812 q^{98} -7.37528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.470815	0.271825	0.135913	−	0.990721i	$-0.456603\pi$
$3$	0.470815	0.271825	0.135913	+	0.990721i	$0.456603\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.470815	0.192210
$7$	2.26316	0.855393	0.427696	−	0.903922i	$-0.359325\pi$
$7$	2.26316	0.855393	0.427696	+	0.903922i	$0.359325\pi$
$8$	1.00000	0.353553
$9$	−2.77833	−0.926111
$10$	1.00000	0.316228
$11$	2.65457	0.800384	0.400192	−	0.916431i	$-0.368944\pi$
$11$	2.65457	0.800384	0.400192	+	0.916431i	$0.368944\pi$
$12$	0.470815	0.135913
$13$	−5.41634	−1.50222	−0.751111	−	0.660176i	$-0.770482\pi$
$13$	−5.41634	−1.50222	−0.751111	+	0.660176i	$0.770482\pi$
$14$	2.26316	0.604854
$15$	0.470815	0.121564
$16$	1.00000	0.250000
$17$	2.57005	0.623328	0.311664	−	0.950192i	$-0.399114\pi$
$17$	2.57005	0.623328	0.311664	+	0.950192i	$0.399114\pi$
$18$	−2.77833	−0.654859
$19$	−5.28267	−1.21193	−0.605964	−	0.795492i	$-0.707212\pi$
$19$	−5.28267	−1.21193	−0.605964	+	0.795492i	$0.707212\pi$
$20$	1.00000	0.223607
$21$	1.06553	0.232517
$22$	2.65457	0.565957
$23$	6.93371	1.44578	0.722889	−	0.690964i	$-0.242814\pi$
$23$	6.93371	1.44578	0.722889	+	0.690964i	$0.242814\pi$
$24$	0.470815	0.0961048
$25$	1.00000	0.200000
$26$	−5.41634	−1.06223
$27$	−2.72053	−0.523566
$28$	2.26316	0.427696
$29$	3.41645	0.634419	0.317210	−	0.948355i	$-0.397254\pi$
$29$	3.41645	0.634419	0.317210	+	0.948355i	$0.397254\pi$
$30$	0.470815	0.0859587
$31$	−0.582895	−0.104691	−0.0523455	−	0.998629i	$-0.516670\pi$
$31$	−0.582895	−0.104691	−0.0523455	+	0.998629i	$0.516670\pi$
$32$	1.00000	0.176777
$33$	1.24981	0.217564
$34$	2.57005	0.440760
$35$	2.26316	0.382543
$36$	−2.77833	−0.463056
$37$	9.97815	1.64040	0.820199	−	0.572079i	$-0.193863\pi$
$37$	9.97815	1.64040	0.820199	+	0.572079i	$0.193863\pi$
$38$	−5.28267	−0.856962
$39$	−2.55009	−0.408342
$40$	1.00000	0.158114
$41$	3.63306	0.567389	0.283695	−	0.958915i	$-0.408440\pi$
$41$	3.63306	0.567389	0.283695	+	0.958915i	$0.408440\pi$
$42$	1.06553	0.164415
$43$	9.99110	1.52363	0.761814	−	0.647796i	$-0.224309\pi$
$43$	9.99110	1.52363	0.761814	+	0.647796i	$0.224309\pi$
$44$	2.65457	0.400192
$45$	−2.77833	−0.414169
$46$	6.93371	1.02232
$47$	13.2118	1.92713	0.963566	−	0.267470i	$-0.0861876\pi$
$47$	13.2118	1.92713	0.963566	+	0.267470i	$0.0861876\pi$
$48$	0.470815	0.0679563
$49$	−1.87812	−0.268303
$50$	1.00000	0.141421
$51$	1.21002	0.169436
$52$	−5.41634	−0.751111
$53$	2.42794	0.333503	0.166752	−	0.985999i	$-0.446672\pi$
$53$	2.42794	0.333503	0.166752	+	0.985999i	$0.446672\pi$
$54$	−2.72053	−0.370217
$55$	2.65457	0.357942
$56$	2.26316	0.302427
$57$	−2.48716	−0.329433
$58$	3.41645	0.448602
$59$	14.1629	1.84385	0.921925	−	0.387369i	$-0.126616\pi$
$59$	14.1629	1.84385	0.921925	+	0.387369i	$0.126616\pi$
$60$	0.470815	0.0607820
$61$	−5.55694	−0.711494	−0.355747	−	0.934582i	$-0.615773\pi$
$61$	−5.55694	−0.711494	−0.355747	+	0.934582i	$0.615773\pi$
$62$	−0.582895	−0.0740277
$63$	−6.28780	−0.792189
$64$	1.00000	0.125000
$65$	−5.41634	−0.671814
$66$	1.24981	0.153841
$67$	7.81080	0.954241	0.477121	−	0.878838i	$-0.341680\pi$
$67$	7.81080	0.954241	0.477121	+	0.878838i	$0.341680\pi$
$68$	2.57005	0.311664
$69$	3.26449	0.392999
$70$	2.26316	0.270499
$71$	−7.81146	−0.927050	−0.463525	−	0.886084i	$-0.653416\pi$
$71$	−7.81146	−0.927050	−0.463525	+	0.886084i	$0.653416\pi$
$72$	−2.77833	−0.327430
$73$	−7.29724	−0.854077	−0.427039	−	0.904233i	$-0.640443\pi$
$73$	−7.29724	−0.854077	−0.427039	+	0.904233i	$0.640443\pi$
$74$	9.97815	1.15994
$75$	0.470815	0.0543651
$76$	−5.28267	−0.605964
$77$	6.00771	0.684642
$78$	−2.55009	−0.288741
$79$	11.4614	1.28951	0.644754	−	0.764390i	$-0.276960\pi$
$79$	11.4614	1.28951	0.644754	+	0.764390i	$0.276960\pi$
$80$	1.00000	0.111803
$81$	7.05413	0.783793
$82$	3.63306	0.401205
$83$	−8.88037	−0.974747	−0.487374	−	0.873194i	$-0.662045\pi$
$83$	−8.88037	−0.974747	−0.487374	+	0.873194i	$0.662045\pi$
$84$	1.06553	0.116259
$85$	2.57005	0.278761
$86$	9.99110	1.07737
$87$	1.60852	0.172451
$88$	2.65457	0.282978
$89$	−10.9119	−1.15666	−0.578332	−	0.815802i	$-0.696296\pi$
$89$	−10.9119	−1.15666	−0.578332	+	0.815802i	$0.696296\pi$
$90$	−2.77833	−0.292862
$91$	−12.2580	−1.28499
$92$	6.93371	0.722889
$93$	−0.274436	−0.0284577
$94$	13.2118	1.36269
$95$	−5.28267	−0.541991
$96$	0.470815	0.0480524
$97$	−5.33845	−0.542037	−0.271019	−	0.962574i	$-0.587361\pi$
$97$	−5.33845	−0.542037	−0.271019	+	0.962574i	$0.587361\pi$
$98$	−1.87812	−0.189719
$99$	−7.37528	−0.741244
$100$	1.00000	0.100000
$101$	−0.882330	−0.0877952	−0.0438976	−	0.999036i	$-0.513978\pi$
$101$	−0.882330	−0.0877952	−0.0438976	+	0.999036i	$0.513978\pi$
$102$	1.21002	0.119810
$103$	−15.6382	−1.54088	−0.770438	−	0.637515i	$-0.779963\pi$
$103$	−15.6382	−1.54088	−0.770438	+	0.637515i	$0.779963\pi$
$104$	−5.41634	−0.531116
$105$	1.06553	0.103985
$106$	2.42794	0.235822
$107$	12.3112	1.19016	0.595082	−	0.803665i	$-0.297120\pi$
$107$	12.3112	1.19016	0.595082	+	0.803665i	$0.297120\pi$
$108$	−2.72053	−0.261783
$109$	−6.37713	−0.610818	−0.305409	−	0.952221i	$-0.598793\pi$
$109$	−6.37713	−0.610818	−0.305409	+	0.952221i	$0.598793\pi$
$110$	2.65457	0.253103
$111$	4.69786	0.445902
$112$	2.26316	0.213848
$113$	6.23271	0.586324	0.293162	−	0.956063i	$-0.405292\pi$
$113$	6.23271	0.586324	0.293162	+	0.956063i	$0.405292\pi$
$114$	−2.48716	−0.232944
$115$	6.93371	0.646571
$116$	3.41645	0.317210
$117$	15.0484	1.39122
$118$	14.1629	1.30380
$119$	5.81642	0.533190
$120$	0.470815	0.0429794
$121$	−3.95325	−0.359386
$122$	−5.55694	−0.503102
$123$	1.71050	0.154231
$124$	−0.582895	−0.0523455
$125$	1.00000	0.0894427
$126$	−6.28780	−0.560162
$127$	−15.3550	−1.36253	−0.681266	−	0.732036i	$-0.738570\pi$
$127$	−15.3550	−1.36253	−0.681266	+	0.732036i	$0.738570\pi$
$128$	1.00000	0.0883883
$129$	4.70396	0.414161
$130$	−5.41634	−0.475044
$131$	9.71663	0.848946	0.424473	−	0.905441i	$-0.360459\pi$
$131$	9.71663	0.848946	0.424473	+	0.905441i	$0.360459\pi$
$132$	1.24981	0.108782
$133$	−11.9555	−1.03667
$134$	7.81080	0.674751
$135$	−2.72053	−0.234146
$136$	2.57005	0.220380
$137$	12.4160	1.06077	0.530387	−	0.847756i	$-0.322047\pi$
$137$	12.4160	1.06077	0.530387	+	0.847756i	$0.322047\pi$
$138$	3.26449	0.277892
$139$	−10.2822	−0.872122	−0.436061	−	0.899917i	$-0.643627\pi$
$139$	−10.2822	−0.872122	−0.436061	+	0.899917i	$0.643627\pi$
$140$	2.26316	0.191272
$141$	6.22029	0.523843
$142$	−7.81146	−0.655523
$143$	−14.3781	−1.20235
$144$	−2.77833	−0.231528
$145$	3.41645	0.283721
$146$	−7.29724	−0.603924
$147$	−0.884249	−0.0729316
$148$	9.97815	0.820199
$149$	−17.9071	−1.46701	−0.733503	−	0.679686i	$-0.762116\pi$
$149$	−17.9071	−1.46701	−0.733503	+	0.679686i	$0.762116\pi$
$150$	0.470815	0.0384419
$151$	21.4170	1.74289	0.871445	−	0.490493i	$-0.163183\pi$
$151$	21.4170	1.74289	0.871445	+	0.490493i	$0.163183\pi$
$152$	−5.28267	−0.428481
$153$	−7.14045	−0.577271
$154$	6.00771	0.484115
$155$	−0.582895	−0.0468192
$156$	−2.55009	−0.204171
$157$	−9.10606	−0.726742	−0.363371	−	0.931644i	$-0.618374\pi$
$157$	−9.10606	−0.726742	−0.363371	+	0.931644i	$0.618374\pi$
$158$	11.4614	0.911820
$159$	1.14311	0.0906546
$160$	1.00000	0.0790569
$161$	15.6921	1.23671
$162$	7.05413	0.554225
$163$	−14.5293	−1.13802	−0.569011	−	0.822330i	$-0.692674\pi$
$163$	−14.5293	−1.13802	−0.569011	+	0.822330i	$0.692674\pi$
$164$	3.63306	0.283695
$165$	1.24981	0.0972978
$166$	−8.88037	−0.689250
$167$	−10.2706	−0.794765	−0.397382	−	0.917653i	$-0.630081\pi$
$167$	−10.2706	−0.794765	−0.397382	+	0.917653i	$0.630081\pi$
$168$	1.06553	0.0822073
$169$	16.3367	1.25667
$170$	2.57005	0.197114
$171$	14.6770	1.12238
$172$	9.99110	0.761814
$173$	−6.13763	−0.466635	−0.233318	−	0.972401i	$-0.574958\pi$
$173$	−6.13763	−0.466635	−0.233318	+	0.972401i	$0.574958\pi$
$174$	1.60852	0.121941
$175$	2.26316	0.171079
$176$	2.65457	0.200096
$177$	6.66810	0.501205
$178$	−10.9119	−0.817884
$179$	14.4823	1.08246	0.541228	−	0.840876i	$-0.317960\pi$
$179$	14.4823	1.08246	0.541228	+	0.840876i	$0.317960\pi$
$180$	−2.77833	−0.207085
$181$	−12.9169	−0.960107	−0.480053	−	0.877239i	$-0.659383\pi$
$181$	−12.9169	−0.960107	−0.480053	+	0.877239i	$0.659383\pi$
$182$	−12.2580	−0.908625
$183$	−2.61629	−0.193402
$184$	6.93371	0.511160
$185$	9.97815	0.733608
$186$	−0.274436	−0.0201226
$187$	6.82238	0.498902
$188$	13.2118	0.963566
$189$	−6.15698	−0.447854
$190$	−5.28267	−0.383245
$191$	−5.98275	−0.432896	−0.216448	−	0.976294i	$-0.569447\pi$
$191$	−5.98275	−0.432896	−0.216448	+	0.976294i	$0.569447\pi$
$192$	0.470815	0.0339782
$193$	−15.6193	−1.12431	−0.562153	−	0.827034i	$-0.690027\pi$
$193$	−15.6193	−1.12431	−0.562153	+	0.827034i	$0.690027\pi$
$194$	−5.33845	−0.383278
$195$	−2.55009	−0.182616
$196$	−1.87812	−0.134152
$197$	−13.1289	−0.935394	−0.467697	−	0.883889i	$-0.654916\pi$
$197$	−13.1289	−0.935394	−0.467697	+	0.883889i	$0.654916\pi$
$198$	−7.37528	−0.524139
$199$	−1.93709	−0.137317	−0.0686583	−	0.997640i	$-0.521872\pi$
$199$	−1.93709	−0.137317	−0.0686583	+	0.997640i	$0.521872\pi$
$200$	1.00000	0.0707107
$201$	3.67744	0.259387
$202$	−0.882330	−0.0620806
$203$	7.73196	0.542677
$204$	1.21002	0.0847182
$205$	3.63306	0.253744
$206$	−15.6382	−1.08956
$207$	−19.2641	−1.33895
$208$	−5.41634	−0.375556
$209$	−14.0232	−0.970007
$210$	1.06553	0.0735284
$211$	−21.6327	−1.48925	−0.744627	−	0.667480i	$-0.767373\pi$
$211$	−21.6327	−1.48925	−0.744627	+	0.667480i	$0.767373\pi$
$212$	2.42794	0.166752
$213$	−3.67775	−0.251996
$214$	12.3112	0.841573
$215$	9.99110	0.681387
$216$	−2.72053	−0.185108
$217$	−1.31918	−0.0895519
$218$	−6.37713	−0.431913
$219$	−3.43565	−0.232160
$220$	2.65457	0.178971
$221$	−13.9203	−0.936377
$222$	4.69786	0.315300
$223$	3.04217	0.203719	0.101859	−	0.994799i	$-0.467521\pi$
$223$	3.04217	0.203719	0.101859	+	0.994799i	$0.467521\pi$
$224$	2.26316	0.151213
$225$	−2.77833	−0.185222
$226$	6.23271	0.414594
$227$	19.1646	1.27200	0.635998	−	0.771690i	$-0.280589\pi$
$227$	19.1646	1.27200	0.635998	+	0.771690i	$0.280589\pi$
$228$	−2.48716	−0.164716
$229$	−12.1767	−0.804658	−0.402329	−	0.915495i	$-0.631799\pi$
$229$	−12.1767	−0.804658	−0.402329	+	0.915495i	$0.631799\pi$
$230$	6.93371	0.457195
$231$	2.82852	0.186103
$232$	3.41645	0.224301
$233$	27.2204	1.78327	0.891633	−	0.452758i	$-0.149560\pi$
$233$	27.2204	1.78327	0.891633	+	0.452758i	$0.149560\pi$
$234$	15.0484	0.983744
$235$	13.2118	0.861840
$236$	14.1629	0.921925
$237$	5.39620	0.350521
$238$	5.81642	0.377023
$239$	19.3537	1.25189	0.625943	−	0.779869i	$-0.284714\pi$
$239$	19.3537	1.25189	0.625943	+	0.779869i	$0.284714\pi$
$240$	0.470815	0.0303910
$241$	−21.7537	−1.40128	−0.700641	−	0.713514i	$-0.747102\pi$
$241$	−21.7537	−1.40128	−0.700641	+	0.713514i	$0.747102\pi$
$242$	−3.95325	−0.254124
$243$	11.4828	0.736620
$244$	−5.55694	−0.355747
$245$	−1.87812	−0.119989
$246$	1.71050	0.109058
$247$	28.6127	1.82058
$248$	−0.582895	−0.0370139
$249$	−4.18101	−0.264961
$250$	1.00000	0.0632456
$251$	8.77239	0.553709	0.276854	−	0.960912i	$-0.410708\pi$
$251$	8.77239	0.553709	0.276854	+	0.960912i	$0.410708\pi$
$252$	−6.28780	−0.396094
$253$	18.4060	1.15718
$254$	−15.3550	−0.963456
$255$	1.21002	0.0757742
$256$	1.00000	0.0625000
$257$	−13.6502	−0.851478	−0.425739	−	0.904846i	$-0.639986\pi$
$257$	−13.6502	−0.851478	−0.425739	+	0.904846i	$0.639986\pi$
$258$	4.70396	0.292856
$259$	22.5821	1.40318
$260$	−5.41634	−0.335907
$261$	−9.49204	−0.587543
$262$	9.71663	0.600295
$263$	−2.53606	−0.156380	−0.0781901	−	0.996938i	$-0.524914\pi$
$263$	−2.53606	−0.156380	−0.0781901	+	0.996938i	$0.524914\pi$
$264$	1.24981	0.0769207
$265$	2.42794	0.149147
$266$	−11.9555	−0.733039
$267$	−5.13751	−0.314410
$268$	7.81080	0.477121
$269$	−11.6019	−0.707383	−0.353692	−	0.935362i	$-0.615074\pi$
$269$	−11.6019	−0.707383	−0.353692	+	0.935362i	$0.615074\pi$
$270$	−2.72053	−0.165566
$271$	−17.0407	−1.03515	−0.517573	−	0.855639i	$-0.673164\pi$
$271$	−17.0407	−1.03515	−0.517573	+	0.855639i	$0.673164\pi$
$272$	2.57005	0.155832
$273$	−5.77126	−0.349293
$274$	12.4160	0.750081
$275$	2.65457	0.160077
$276$	3.26449	0.196499
$277$	5.84294	0.351069	0.175534	−	0.984473i	$-0.443835\pi$
$277$	5.84294	0.351069	0.175534	+	0.984473i	$0.443835\pi$
$278$	−10.2822	−0.616684
$279$	1.61948	0.0969555
$280$	2.26316	0.135249
$281$	13.0626	0.779252	0.389626	−	0.920973i	$-0.372604\pi$
$281$	13.0626	0.779252	0.389626	+	0.920973i	$0.372604\pi$
$282$	6.22029	0.370413
$283$	7.59082	0.451227	0.225614	−	0.974217i	$-0.427561\pi$
$283$	7.59082	0.451227	0.225614	+	0.974217i	$0.427561\pi$
$284$	−7.81146	−0.463525
$285$	−2.48716	−0.147327
$286$	−14.3781	−0.850193
$287$	8.22219	0.485340
$288$	−2.77833	−0.163715
$289$	−10.3949	−0.611462
$290$	3.41645	0.200621
$291$	−2.51342	−0.147339
$292$	−7.29724	−0.427039
$293$	20.3097	1.18651	0.593254	−	0.805016i	$-0.297843\pi$
$293$	20.3097	1.18651	0.593254	+	0.805016i	$0.297843\pi$
$294$	−0.884249	−0.0515705
$295$	14.1629	0.824595
$296$	9.97815	0.579968
$297$	−7.22183	−0.419053
$298$	−17.9071	−1.03733
$299$	−37.5553	−2.17188
$300$	0.470815	0.0271825
$301$	22.6114	1.30330
$302$	21.4170	1.23241
$303$	−0.415415	−0.0238649
$304$	−5.28267	−0.302982
$305$	−5.55694	−0.318190
$306$	−7.14045	−0.408192
$307$	−28.0826	−1.60276	−0.801379	−	0.598156i	$-0.795900\pi$
$307$	−28.0826	−1.60276	−0.801379	+	0.598156i	$0.795900\pi$
$308$	6.00771	0.342321
$309$	−7.36270	−0.418849
$310$	−0.582895	−0.0331062
$311$	3.95431	0.224228	0.112114	−	0.993695i	$-0.464238\pi$
$311$	3.95431	0.224228	0.112114	+	0.993695i	$0.464238\pi$
$312$	−2.55009	−0.144371
$313$	5.32088	0.300754	0.150377	−	0.988629i	$-0.451951\pi$
$313$	5.32088	0.300754	0.150377	+	0.988629i	$0.451951\pi$
$314$	−9.10606	−0.513884
$315$	−6.28780	−0.354278
$316$	11.4614	0.644754
$317$	6.27602	0.352497	0.176248	−	0.984346i	$-0.443604\pi$
$317$	6.27602	0.352497	0.176248	+	0.984346i	$0.443604\pi$
$318$	1.14311	0.0641025
$319$	9.06922	0.507779
$320$	1.00000	0.0559017
$321$	5.79628	0.323517
$322$	15.6921	0.874484
$323$	−13.5767	−0.755429
$324$	7.05413	0.391896
$325$	−5.41634	−0.300444
$326$	−14.5293	−0.804703
$327$	−3.00245	−0.166036
$328$	3.63306	0.200602
$329$	29.9003	1.64845
$330$	1.24981	0.0687999
$331$	−5.74071	−0.315538	−0.157769	−	0.987476i	$-0.550430\pi$
$331$	−5.74071	−0.315538	−0.157769	+	0.987476i	$0.550430\pi$
$332$	−8.88037	−0.487374
$333$	−27.7226	−1.51919
$334$	−10.2706	−0.561984
$335$	7.81080	0.426750
$336$	1.06553	0.0581293
$337$	−1.34480	−0.0732560	−0.0366280	−	0.999329i	$-0.511662\pi$
$337$	−1.34480	−0.0732560	−0.0366280	+	0.999329i	$0.511662\pi$
$338$	16.3367	0.888601
$339$	2.93445	0.159378
$340$	2.57005	0.139380
$341$	−1.54734	−0.0837929
$342$	14.6770	0.793642
$343$	−20.0926	−1.08490
$344$	9.99110	0.538684
$345$	3.26449	0.175754
$346$	−6.13763	−0.329961
$347$	−25.3681	−1.36183	−0.680914	−	0.732363i	$-0.738417\pi$
$347$	−25.3681	−1.36183	−0.680914	+	0.732363i	$0.738417\pi$
$348$	1.60852	0.0862256
$349$	−28.8306	−1.54327	−0.771633	−	0.636068i	$-0.780560\pi$
$349$	−28.8306	−1.54327	−0.771633	+	0.636068i	$0.780560\pi$
$350$	2.26316	0.120971
$351$	14.7353	0.786512
$352$	2.65457	0.141489
$353$	−1.57261	−0.0837014	−0.0418507	−	0.999124i	$-0.513325\pi$
$353$	−1.57261	−0.0837014	−0.0418507	+	0.999124i	$0.513325\pi$
$354$	6.66810	0.354405
$355$	−7.81146	−0.414589
$356$	−10.9119	−0.578332
$357$	2.73846	0.144935
$358$	14.4823	0.765412
$359$	18.9322	0.999202	0.499601	−	0.866256i	$-0.333480\pi$
$359$	18.9322	0.999202	0.499601	+	0.866256i	$0.333480\pi$
$360$	−2.77833	−0.146431
$361$	8.90661	0.468769
$362$	−12.9169	−0.678898
$363$	−1.86125	−0.0976903
$364$	−12.2580	−0.642495
$365$	−7.29724	−0.381955
$366$	−2.61629	−0.136756
$367$	31.3314	1.63549	0.817743	−	0.575583i	$-0.195225\pi$
$367$	31.3314	1.63549	0.817743	+	0.575583i	$0.195225\pi$
$368$	6.93371	0.361444
$369$	−10.0939	−0.525465
$370$	9.97815	0.518739
$371$	5.49481	0.285276
$372$	−0.274436	−0.0142288
$373$	12.3471	0.639306	0.319653	−	0.947535i	$-0.396434\pi$
$373$	12.3471	0.639306	0.319653	+	0.947535i	$0.396434\pi$
$374$	6.82238	0.352777
$375$	0.470815	0.0243128
$376$	13.2118	0.681344
$377$	−18.5047	−0.953038
$378$	−6.15698	−0.316681
$379$	33.5572	1.72372	0.861858	−	0.507150i	$-0.169301\pi$
$379$	33.5572	1.72372	0.861858	+	0.507150i	$0.169301\pi$
$380$	−5.28267	−0.270995
$381$	−7.22935	−0.370371
$382$	−5.98275	−0.306104
$383$	8.24556	0.421329	0.210664	−	0.977558i	$-0.432437\pi$
$383$	8.24556	0.421329	0.210664	+	0.977558i	$0.432437\pi$
$384$	0.470815	0.0240262
$385$	6.00771	0.306181
$386$	−15.6193	−0.795004
$387$	−27.7586	−1.41105
$388$	−5.33845	−0.271019
$389$	−15.7449	−0.798297	−0.399149	−	0.916886i	$-0.630694\pi$
$389$	−15.7449	−0.798297	−0.399149	+	0.916886i	$0.630694\pi$
$390$	−2.55009	−0.129129
$391$	17.8200	0.901194
$392$	−1.87812	−0.0948596
$393$	4.57474	0.230765
$394$	−13.1289	−0.661423
$395$	11.4614	0.576686
$396$	−7.37528	−0.370622
$397$	−1.85725	−0.0932129	−0.0466064	−	0.998913i	$-0.514841\pi$
$397$	−1.85725	−0.0932129	−0.0466064	+	0.998913i	$0.514841\pi$
$398$	−1.93709	−0.0970974
$399$	−5.62884	−0.281794
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	3.67744	0.183414
$403$	3.15716	0.157269
$404$	−0.882330	−0.0438976
$405$	7.05413	0.350523
$406$	7.73196	0.383731
$407$	26.4877	1.31295
$408$	1.21002	0.0599048
$409$	−3.51474	−0.173793	−0.0868963	−	0.996217i	$-0.527695\pi$
$409$	−3.51474	−0.173793	−0.0868963	+	0.996217i	$0.527695\pi$
$410$	3.63306	0.179424
$411$	5.84566	0.288345
$412$	−15.6382	−0.770438
$413$	32.0528	1.57722
$414$	−19.2641	−0.946781
$415$	−8.88037	−0.435920
$416$	−5.41634	−0.265558
$417$	−4.84100	−0.237065
$418$	−14.0232	−0.685899
$419$	−29.1984	−1.42643	−0.713217	−	0.700943i	$-0.752763\pi$
$419$	−29.1984	−1.42643	−0.713217	+	0.700943i	$0.752763\pi$
$420$	1.06553	0.0519925
$421$	24.7048	1.20404	0.602020	−	0.798481i	$-0.294363\pi$
$421$	24.7048	1.20404	0.602020	+	0.798481i	$0.294363\pi$
$422$	−21.6327	−1.05306
$423$	−36.7067	−1.78474
$424$	2.42794	0.117911
$425$	2.57005	0.124666
$426$	−3.67775	−0.178188
$427$	−12.5762	−0.608607
$428$	12.3112	0.595082
$429$	−6.76941	−0.326830
$430$	9.99110	0.481813
$431$	−23.1994	−1.11748	−0.558738	−	0.829344i	$-0.688714\pi$
$431$	−23.1994	−1.11748	−0.558738	+	0.829344i	$0.688714\pi$
$432$	−2.72053	−0.130891
$433$	21.5310	1.03471	0.517357	−	0.855770i	$-0.326916\pi$
$433$	21.5310	1.03471	0.517357	+	0.855770i	$0.326916\pi$
$434$	−1.31918	−0.0633228
$435$	1.60852	0.0771225
$436$	−6.37713	−0.305409
$437$	−36.6285	−1.75218
$438$	−3.43565	−0.164162
$439$	26.6742	1.27309	0.636546	−	0.771239i	$-0.280363\pi$
$439$	26.6742	1.27309	0.636546	+	0.771239i	$0.280363\pi$
$440$	2.65457	0.126552
$441$	5.21805	0.248479
$442$	−13.9203	−0.662119
$443$	−13.7015	−0.650976	−0.325488	−	0.945546i	$-0.605529\pi$
$443$	−13.7015	−0.650976	−0.325488	+	0.945546i	$0.605529\pi$
$444$	4.69786	0.222951
$445$	−10.9119	−0.517276
$446$	3.04217	0.144051
$447$	−8.43093	−0.398769
$448$	2.26316	0.106924
$449$	−16.7835	−0.792060	−0.396030	−	0.918238i	$-0.629612\pi$
$449$	−16.7835	−0.792060	−0.396030	+	0.918238i	$0.629612\pi$
$450$	−2.77833	−0.130972
$451$	9.64423	0.454129
$452$	6.23271	0.293162
$453$	10.0834	0.473762
$454$	19.1646	0.899437
$455$	−12.2580	−0.574665
$456$	−2.48716	−0.116472
$457$	40.5791	1.89821	0.949104	−	0.314962i	$-0.101992\pi$
$457$	40.5791	1.89821	0.949104	+	0.314962i	$0.101992\pi$
$458$	−12.1767	−0.568979
$459$	−6.99188	−0.326353
$460$	6.93371	0.323286
$461$	18.4435	0.858999	0.429500	−	0.903067i	$-0.358690\pi$
$461$	18.4435	0.858999	0.429500	+	0.903067i	$0.358690\pi$
$462$	2.82852	0.131595
$463$	−21.0836	−0.979837	−0.489919	−	0.871768i	$-0.662973\pi$
$463$	−21.0836	−0.979837	−0.489919	+	0.871768i	$0.662973\pi$
$464$	3.41645	0.158605
$465$	−0.274436	−0.0127267
$466$	27.2204	1.26096
$467$	4.99114	0.230962	0.115481	−	0.993310i	$-0.463159\pi$
$467$	4.99114	0.230962	0.115481	+	0.993310i	$0.463159\pi$
$468$	15.0484	0.695612
$469$	17.6771	0.816251
$470$	13.2118	0.609413
$471$	−4.28727	−0.197547
$472$	14.1629	0.651899
$473$	26.5221	1.21949
$474$	5.39620	0.247856
$475$	−5.28267	−0.242386
$476$	5.81642	0.266595
$477$	−6.74562	−0.308861
$478$	19.3537	0.885216
$479$	−13.1544	−0.601038	−0.300519	−	0.953776i	$-0.597160\pi$
$479$	−13.1544	−0.601038	−0.300519	+	0.953776i	$0.597160\pi$
$480$	0.470815	0.0214897
$481$	−54.0450	−2.46424
$482$	−21.7537	−0.990856
$483$	7.38806	0.336168
$484$	−3.95325	−0.179693
$485$	−5.33845	−0.242407
$486$	11.4828	0.520869
$487$	10.7796	0.488470	0.244235	−	0.969716i	$-0.421463\pi$
$487$	10.7796	0.488470	0.244235	+	0.969716i	$0.421463\pi$
$488$	−5.55694	−0.251551
$489$	−6.84061	−0.309343
$490$	−1.87812	−0.0848450
$491$	−26.7576	−1.20755	−0.603777	−	0.797153i	$-0.706338\pi$
$491$	−26.7576	−1.20755	−0.603777	+	0.797153i	$0.706338\pi$
$492$	1.71050	0.0771154
$493$	8.78044	0.395451
$494$	28.6127	1.28735
$495$	−7.37528	−0.331494
$496$	−0.582895	−0.0261727
$497$	−17.6786	−0.792991
$498$	−4.18101	−0.187356
$499$	−10.2293	−0.457926	−0.228963	−	0.973435i	$-0.573534\pi$
$499$	−10.2293	−0.457926	−0.228963	+	0.973435i	$0.573534\pi$
$500$	1.00000	0.0447214
$501$	−4.83557	−0.216037
$502$	8.77239	0.391531
$503$	−14.9158	−0.665062	−0.332531	−	0.943092i	$-0.607903\pi$
$503$	−14.9158	−0.665062	−0.332531	+	0.943092i	$0.607903\pi$
$504$	−6.28780	−0.280081
$505$	−0.882330	−0.0392632
$506$	18.4060	0.818247
$507$	7.69158	0.341595
$508$	−15.3550	−0.681266
$509$	38.6450	1.71291	0.856455	−	0.516222i	$-0.172662\pi$
$509$	38.6450	1.71291	0.856455	+	0.516222i	$0.172662\pi$
$510$	1.21002	0.0535805
$511$	−16.5148	−0.730571
$512$	1.00000	0.0441942
$513$	14.3716	0.634524
$514$	−13.6502	−0.602086
$515$	−15.6382	−0.689101
$516$	4.70396	0.207080
$517$	35.0715	1.54244
$518$	22.5821	0.992201
$519$	−2.88969	−0.126843
$520$	−5.41634	−0.237522
$521$	20.1351	0.882133	0.441067	−	0.897474i	$-0.354600\pi$
$521$	20.1351	0.882133	0.441067	+	0.897474i	$0.354600\pi$
$522$	−9.49204	−0.415455
$523$	−33.5464	−1.46688	−0.733440	−	0.679754i	$-0.762086\pi$
$523$	−33.5464	−1.46688	−0.733440	+	0.679754i	$0.762086\pi$
$524$	9.71663	0.424473
$525$	1.06553	0.0465035
$526$	−2.53606	−0.110577
$527$	−1.49807	−0.0652568
$528$	1.24981	0.0543911
$529$	25.0763	1.09027
$530$	2.42794	0.105463
$531$	−39.3492	−1.70761
$532$	−11.9555	−0.518337
$533$	−19.6779	−0.852344
$534$	−5.13751	−0.222322
$535$	12.3112	0.532257
$536$	7.81080	0.337375
$537$	6.81847	0.294239
$538$	−11.6019	−0.500195
$539$	−4.98561	−0.214746
$540$	−2.72053	−0.117073
$541$	2.38219	0.102418	0.0512091	−	0.998688i	$-0.483693\pi$
$541$	2.38219	0.102418	0.0512091	+	0.998688i	$0.483693\pi$
$542$	−17.0407	−0.731959
$543$	−6.08148	−0.260981
$544$	2.57005	0.110190
$545$	−6.37713	−0.273166
$546$	−5.77126	−0.246987
$547$	−40.2584	−1.72133	−0.860663	−	0.509176i	$-0.829950\pi$
$547$	−40.2584	−1.72133	−0.860663	+	0.509176i	$0.829950\pi$
$548$	12.4160	0.530387
$549$	15.4390	0.658922
$550$	2.65457	0.113191
$551$	−18.0480	−0.768870
$552$	3.26449	0.138946
$553$	25.9389	1.10304
$554$	5.84294	0.248243
$555$	4.69786	0.199413
$556$	−10.2822	−0.436061
$557$	−36.5338	−1.54799	−0.773994	−	0.633193i	$-0.781744\pi$
$557$	−36.5338	−1.54799	−0.773994	+	0.633193i	$0.781744\pi$
$558$	1.61948	0.0685579
$559$	−54.1152	−2.28883
$560$	2.26316	0.0956358
$561$	3.21208	0.135614
$562$	13.0626	0.551015
$563$	−17.6657	−0.744522	−0.372261	−	0.928128i	$-0.621417\pi$
$563$	−17.6657	−0.744522	−0.372261	+	0.928128i	$0.621417\pi$
$564$	6.22029	0.261922
$565$	6.23271	0.262212
$566$	7.59082	0.319066
$567$	15.9646	0.670450
$568$	−7.81146	−0.327762
$569$	−11.0336	−0.462553	−0.231276	−	0.972888i	$-0.574290\pi$
$569$	−11.0336	−0.462553	−0.231276	+	0.972888i	$0.574290\pi$
$570$	−2.48716	−0.104176
$571$	12.9216	0.540754	0.270377	−	0.962755i	$-0.412852\pi$
$571$	12.9216	0.540754	0.270377	+	0.962755i	$0.412852\pi$
$572$	−14.3781	−0.601177
$573$	−2.81677	−0.117672
$574$	8.22219	0.343188
$575$	6.93371	0.289155
$576$	−2.77833	−0.115764
$577$	30.2130	1.25779	0.628893	−	0.777492i	$-0.283508\pi$
$577$	30.2130	1.25779	0.628893	+	0.777492i	$0.283508\pi$
$578$	−10.3949	−0.432369
$579$	−7.35382	−0.305615
$580$	3.41645	0.141860
$581$	−20.0977	−0.833792
$582$	−2.51342	−0.104185
$583$	6.44514	0.266930
$584$	−7.29724	−0.301962
$585$	15.0484	0.622174
$586$	20.3097	0.838987
$587$	−12.2180	−0.504292	−0.252146	−	0.967689i	$-0.581136\pi$
$587$	−12.2180	−0.504292	−0.252146	+	0.967689i	$0.581136\pi$
$588$	−0.884249	−0.0364658
$589$	3.07924	0.126878
$590$	14.1629	0.583076
$591$	−6.18128	−0.254264
$592$	9.97815	0.410099
$593$	−17.9775	−0.738248	−0.369124	−	0.929380i	$-0.620342\pi$
$593$	−17.9775	−0.738248	−0.369124	+	0.929380i	$0.620342\pi$
$594$	−7.22183	−0.296315
$595$	5.81642	0.238450
$596$	−17.9071	−0.733503
$597$	−0.912010	−0.0373261
$598$	−37.5553	−1.53575
$599$	2.97277	0.121464	0.0607320	−	0.998154i	$-0.480656\pi$
$599$	2.97277	0.121464	0.0607320	+	0.998154i	$0.480656\pi$
$600$	0.470815	0.0192210
$601$	30.7286	1.25345	0.626723	−	0.779242i	$-0.284396\pi$
$601$	30.7286	1.25345	0.626723	+	0.779242i	$0.284396\pi$
$602$	22.6114	0.921572
$603$	−21.7010	−0.883733
$604$	21.4170	0.871445
$605$	−3.95325	−0.160722
$606$	−0.415415	−0.0168751
$607$	43.0965	1.74923	0.874616	−	0.484817i	$-0.161114\pi$
$607$	43.0965	1.74923	0.874616	+	0.484817i	$0.161114\pi$
$608$	−5.28267	−0.214241
$609$	3.64033	0.147513
$610$	−5.55694	−0.224994
$611$	−71.5593	−2.89498
$612$	−7.14045	−0.288636
$613$	−30.9227	−1.24895	−0.624477	−	0.781043i	$-0.714688\pi$
$613$	−30.9227	−1.24895	−0.624477	+	0.781043i	$0.714688\pi$
$614$	−28.0826	−1.13332
$615$	1.71050	0.0689741
$616$	6.00771	0.242058
$617$	−14.2308	−0.572909	−0.286454	−	0.958094i	$-0.592477\pi$
$617$	−14.2308	−0.572909	−0.286454	+	0.958094i	$0.592477\pi$
$618$	−7.36270	−0.296171
$619$	25.1053	1.00907	0.504534	−	0.863392i	$-0.331664\pi$
$619$	25.1053	1.00907	0.504534	+	0.863392i	$0.331664\pi$
$620$	−0.582895	−0.0234096
$621$	−18.8633	−0.756959
$622$	3.95431	0.158553
$623$	−24.6954	−0.989401
$624$	−2.55009	−0.102085
$625$	1.00000	0.0400000
$626$	5.32088	0.212665
$627$	−6.60235	−0.263672
$628$	−9.10606	−0.363371
$629$	25.6443	1.02251
$630$	−6.28780	−0.250512
$631$	−14.0751	−0.560320	−0.280160	−	0.959953i	$-0.590387\pi$
$631$	−14.0751	−0.560320	−0.280160	+	0.959953i	$0.590387\pi$
$632$	11.4614	0.455910
$633$	−10.1850	−0.404817
$634$	6.27602	0.249253
$635$	−15.3550	−0.609343
$636$	1.14311	0.0453273
$637$	10.1726	0.403051
$638$	9.06922	0.359054
$639$	21.7028	0.858551
$640$	1.00000	0.0395285
$641$	40.4499	1.59767	0.798837	−	0.601547i	$-0.205449\pi$
$641$	40.4499	1.59767	0.798837	+	0.601547i	$0.205449\pi$
$642$	5.79628	0.228761
$643$	21.8080	0.860022	0.430011	−	0.902824i	$-0.358510\pi$
$643$	21.8080	0.860022	0.430011	+	0.902824i	$0.358510\pi$
$644$	15.6921	0.618354
$645$	4.70396	0.185218
$646$	−13.5767	−0.534169
$647$	3.61151	0.141983	0.0709916	−	0.997477i	$-0.477384\pi$
$647$	3.61151	0.141983	0.0709916	+	0.997477i	$0.477384\pi$
$648$	7.05413	0.277113
$649$	37.5964	1.47579
$650$	−5.41634	−0.212446
$651$	−0.621091	−0.0243425
$652$	−14.5293	−0.569011
$653$	−37.8280	−1.48032	−0.740161	−	0.672429i	$-0.765251\pi$
$653$	−37.8280	−1.48032	−0.740161	+	0.672429i	$0.765251\pi$
$654$	−3.00245	−0.117405
$655$	9.71663	0.379660
$656$	3.63306	0.141847
$657$	20.2742	0.790970
$658$	29.9003	1.16563
$659$	43.1715	1.68172	0.840861	−	0.541251i	$-0.182049\pi$
$659$	43.1715	1.68172	0.840861	+	0.541251i	$0.182049\pi$
$660$	1.24981	0.0486489
$661$	−9.57775	−0.372531	−0.186266	−	0.982499i	$-0.559639\pi$
$661$	−9.57775	−0.372531	−0.186266	+	0.982499i	$0.559639\pi$
$662$	−5.74071	−0.223119
$663$	−6.55387	−0.254531
$664$	−8.88037	−0.344625
$665$	−11.9555	−0.463615
$666$	−27.7226	−1.07423
$667$	23.6887	0.917229
$668$	−10.2706	−0.397382
$669$	1.43230	0.0553759
$670$	7.81080	0.301758
$671$	−14.7513	−0.569468
$672$	1.06553	0.0411037
$673$	−21.6995	−0.836454	−0.418227	−	0.908342i	$-0.637348\pi$
$673$	−21.6995	−0.836454	−0.418227	+	0.908342i	$0.637348\pi$
$674$	−1.34480	−0.0517998
$675$	−2.72053	−0.104713
$676$	16.3367	0.628336
$677$	−28.2107	−1.08423	−0.542113	−	0.840306i	$-0.682375\pi$
$677$	−28.2107	−1.08423	−0.542113	+	0.840306i	$0.682375\pi$
$678$	2.93445	0.112697
$679$	−12.0817	−0.463655
$680$	2.57005	0.0985568
$681$	9.02297	0.345761
$682$	−1.54734	−0.0592506
$683$	−24.4171	−0.934295	−0.467147	−	0.884180i	$-0.654718\pi$
$683$	−24.4171	−0.934295	−0.467147	+	0.884180i	$0.654718\pi$
$684$	14.6770	0.561190
$685$	12.4160	0.474393
$686$	−20.0926	−0.767138
$687$	−5.73297	−0.218726
$688$	9.99110	0.380907
$689$	−13.1505	−0.500996
$690$	3.26449	0.124277
$691$	5.79569	0.220478	0.110239	−	0.993905i	$-0.464838\pi$
$691$	5.79569	0.220478	0.110239	+	0.993905i	$0.464838\pi$
$692$	−6.13763	−0.233318
$693$	−16.6914	−0.634055
$694$	−25.3681	−0.962958
$695$	−10.2822	−0.390025
$696$	1.60852	0.0609707
$697$	9.33715	0.353670
$698$	−28.8306	−1.09125
$699$	12.8158	0.484737
$700$	2.26316	0.0855393
$701$	−3.79995	−0.143522	−0.0717611	−	0.997422i	$-0.522862\pi$
$701$	−3.79995	−0.143522	−0.0717611	+	0.997422i	$0.522862\pi$
$702$	14.7353	0.556148
$703$	−52.7113	−1.98804
$704$	2.65457	0.100048
$705$	6.22029	0.234270
$706$	−1.57261	−0.0591858
$707$	−1.99685	−0.0750993
$708$	6.66810	0.250602
$709$	31.6669	1.18927	0.594637	−	0.803994i	$-0.297296\pi$
$709$	31.6669	1.18927	0.594637	+	0.803994i	$0.297296\pi$
$710$	−7.81146	−0.293159
$711$	−31.8436	−1.19423
$712$	−10.9119	−0.408942
$713$	−4.04162	−0.151360
$714$	2.73846	0.102484
$715$	−14.3781	−0.537709
$716$	14.4823	0.541228
$717$	9.11200	0.340294
$718$	18.9322	0.706543
$719$	−32.3425	−1.20617	−0.603085	−	0.797677i	$-0.706062\pi$
$719$	−32.3425	−1.20617	−0.603085	+	0.797677i	$0.706062\pi$
$720$	−2.77833	−0.103542
$721$	−35.3917	−1.31805
$722$	8.90661	0.331470
$723$	−10.2420	−0.380904
$724$	−12.9169	−0.480053
$725$	3.41645	0.126884
$726$	−1.86125	−0.0690774
$727$	−2.26957	−0.0841735	−0.0420868	−	0.999114i	$-0.513401\pi$
$727$	−2.26957	−0.0841735	−0.0420868	+	0.999114i	$0.513401\pi$
$728$	−12.2580	−0.454312
$729$	−15.7561	−0.583561
$730$	−7.29724	−0.270083
$731$	25.6776	0.949720
$732$	−2.61629	−0.0967010
$733$	−23.8930	−0.882507	−0.441253	−	0.897383i	$-0.645466\pi$
$733$	−23.8930	−0.882507	−0.441253	+	0.897383i	$0.645466\pi$
$734$	31.3314	1.15646
$735$	−0.884249	−0.0326160
$736$	6.93371	0.255580
$737$	20.7343	0.763759
$738$	−10.0939	−0.371560
$739$	7.66001	0.281778	0.140889	−	0.990025i	$-0.455004\pi$
$739$	7.66001	0.281778	0.140889	+	0.990025i	$0.455004\pi$
$740$	9.97815	0.366804
$741$	13.4713	0.494881
$742$	5.49481	0.201721
$743$	−42.2165	−1.54877	−0.774387	−	0.632712i	$-0.781942\pi$
$743$	−42.2165	−1.54877	−0.774387	+	0.632712i	$0.781942\pi$
$744$	−0.274436	−0.0100613
$745$	−17.9071	−0.656065
$746$	12.3471	0.452058
$747$	24.6726	0.902724
$748$	6.82238	0.249451
$749$	27.8621	1.01806
$750$	0.470815	0.0171917
$751$	0.0335117	0.00122286	0.000611429	−	1.00000i	$-0.499805\pi$
$751$	0.0335117	0.00122286	0.000611429		1.00000i	$0.499805\pi$
$752$	13.2118	0.481783
$753$	4.13018	0.150512
$754$	−18.5047	−0.673900
$755$	21.4170	0.779444
$756$	−6.15698	−0.223927
$757$	42.5088	1.54501	0.772504	−	0.635010i	$-0.219004\pi$
$757$	42.5088	1.54501	0.772504	+	0.635010i	$0.219004\pi$
$758$	33.5572	1.21885
$759$	8.66583	0.314550
$760$	−5.28267	−0.191623
$761$	10.9069	0.395374	0.197687	−	0.980265i	$-0.436657\pi$
$761$	10.9069	0.395374	0.197687	+	0.980265i	$0.436657\pi$
$762$	−7.22935	−0.261892
$763$	−14.4324	−0.522489
$764$	−5.98275	−0.216448
$765$	−7.14045	−0.258163
$766$	8.24556	0.297924
$767$	−76.7109	−2.76987
$768$	0.470815	0.0169891
$769$	−51.6467	−1.86243	−0.931213	−	0.364475i	$-0.881248\pi$
$769$	−51.6467	−1.86243	−0.931213	+	0.364475i	$0.881248\pi$
$770$	6.00771	0.216503
$771$	−6.42673	−0.231453
$772$	−15.6193	−0.562153
$773$	−7.18703	−0.258500	−0.129250	−	0.991612i	$-0.541257\pi$
$773$	−7.18703	−0.258500	−0.129250	+	0.991612i	$0.541257\pi$
$774$	−27.7586	−0.997762
$775$	−0.582895	−0.0209382
$776$	−5.33845	−0.191639
$777$	10.6320	0.381421
$778$	−15.7449	−0.564482
$779$	−19.1923	−0.687635
$780$	−2.55009	−0.0913080
$781$	−20.7361	−0.741995
$782$	17.8200	0.637240
$783$	−9.29455	−0.332160
$784$	−1.87812	−0.0670758
$785$	−9.10606	−0.325009
$786$	4.57474	0.163175
$787$	−0.540201	−0.0192561	−0.00962805	−	0.999954i	$-0.503065\pi$
$787$	−0.540201	−0.0192561	−0.00962805	+	0.999954i	$0.503065\pi$
$788$	−13.1289	−0.467697
$789$	−1.19402	−0.0425081
$790$	11.4614	0.407778
$791$	14.1056	0.501537
$792$	−7.37528	−0.262069
$793$	30.0983	1.06882
$794$	−1.85725	−0.0659115
$795$	1.14311	0.0405420
$796$	−1.93709	−0.0686583
$797$	0.982608	0.0348058	0.0174029	−	0.999849i	$-0.494460\pi$
$797$	0.982608	0.0348058	0.0174029	+	0.999849i	$0.494460\pi$
$798$	−5.62884	−0.199259
$799$	33.9548	1.20124
$800$	1.00000	0.0353553
$801$	30.3170	1.07120
$802$	1.00000	0.0353112
$803$	−19.3710	−0.683589
$804$	3.67744	0.129693
$805$	15.6921	0.553072
$806$	3.15716	0.111206
$807$	−5.46237	−0.192285
$808$	−0.882330	−0.0310403
$809$	14.2503	0.501015	0.250508	−	0.968115i	$-0.419403\pi$
$809$	14.2503	0.501015	0.250508	+	0.968115i	$0.419403\pi$
$810$	7.05413	0.247857
$811$	16.9105	0.593807	0.296904	−	0.954907i	$-0.404046\pi$
$811$	16.9105	0.593807	0.296904	+	0.954907i	$0.404046\pi$
$812$	7.73196	0.271339
$813$	−8.02300	−0.281379
$814$	26.4877	0.928394
$815$	−14.5293	−0.508939
$816$	1.21002	0.0423591
$817$	−52.7797	−1.84653
$818$	−3.51474	−0.122890
$819$	34.0569	1.19004
$820$	3.63306	0.126872
$821$	39.7053	1.38573	0.692863	−	0.721070i	$-0.256349\pi$
$821$	39.7053	1.38573	0.692863	+	0.721070i	$0.256349\pi$
$822$	5.84566	0.203891
$823$	−8.44082	−0.294228	−0.147114	−	0.989120i	$-0.546998\pi$
$823$	−8.44082	−0.294228	−0.147114	+	0.989120i	$0.546998\pi$
$824$	−15.6382	−0.544782
$825$	1.24981	0.0435129
$826$	32.0528	1.11526
$827$	−42.1509	−1.46573	−0.732865	−	0.680374i	$-0.761817\pi$
$827$	−42.1509	−1.46573	−0.732865	+	0.680374i	$0.761817\pi$
$828$	−19.2641	−0.669475
$829$	7.19539	0.249906	0.124953	−	0.992163i	$-0.460122\pi$
$829$	7.19539	0.249906	0.124953	+	0.992163i	$0.460122\pi$
$830$	−8.88037	−0.308242
$831$	2.75095	0.0954293
$832$	−5.41634	−0.187778
$833$	−4.82687	−0.167241
$834$	−4.84100	−0.167630
$835$	−10.2706	−0.355430
$836$	−14.0232	−0.485004
$837$	1.58578	0.0548126
$838$	−29.1984	−1.00864
$839$	−17.9131	−0.618427	−0.309214	−	0.950993i	$-0.600066\pi$
$839$	−17.9131	−0.618427	−0.309214	+	0.950993i	$0.600066\pi$
$840$	1.06553	0.0367642
$841$	−17.3279	−0.597512
$842$	24.7048	0.851384
$843$	6.15009	0.211820
$844$	−21.6327	−0.744627
$845$	16.3367	0.562000
$846$	−36.7067	−1.26200
$847$	−8.94682	−0.307416
$848$	2.42794	0.0833758
$849$	3.57387	0.122655
$850$	2.57005	0.0881519
$851$	69.1855	2.37165
$852$	−3.67775	−0.125998
$853$	−6.25709	−0.214239	−0.107119	−	0.994246i	$-0.534163\pi$
$853$	−6.25709	−0.214239	−0.107119	+	0.994246i	$0.534163\pi$
$854$	−12.5762	−0.430350
$855$	14.6770	0.501943
$856$	12.3112	0.420786
$857$	23.1716	0.791526	0.395763	−	0.918353i	$-0.370480\pi$
$857$	23.1716	0.791526	0.395763	+	0.918353i	$0.370480\pi$
$858$	−6.76941	−0.231104
$859$	−6.63876	−0.226512	−0.113256	−	0.993566i	$-0.536128\pi$
$859$	−6.63876	−0.226512	−0.113256	+	0.993566i	$0.536128\pi$
$860$	9.99110	0.340694
$861$	3.87113	0.131928
$862$	−23.1994	−0.790175
$863$	8.83824	0.300857	0.150429	−	0.988621i	$-0.451935\pi$
$863$	8.83824	0.300857	0.150429	+	0.988621i	$0.451935\pi$
$864$	−2.72053	−0.0925542
$865$	−6.13763	−0.208686
$866$	21.5310	0.731653
$867$	−4.89406	−0.166211
$868$	−1.31918	−0.0447760
$869$	30.4251	1.03210
$870$	1.60852	0.0545338
$871$	−42.3059	−1.43348
$872$	−6.37713	−0.215957
$873$	14.8320	0.501987
$874$	−36.6285	−1.23898
$875$	2.26316	0.0765086
$876$	−3.43565	−0.116080
$877$	48.0958	1.62408	0.812040	−	0.583602i	$-0.198357\pi$
$877$	48.0958	1.62408	0.812040	+	0.583602i	$0.198357\pi$
$878$	26.6742	0.900212
$879$	9.56213	0.322523
$880$	2.65457	0.0894856
$881$	3.26809	0.110105	0.0550524	−	0.998483i	$-0.482467\pi$
$881$	3.26809	0.110105	0.0550524	+	0.998483i	$0.482467\pi$
$882$	5.21805	0.175701
$883$	4.39221	0.147809	0.0739047	−	0.997265i	$-0.476454\pi$
$883$	4.39221	0.147809	0.0739047	+	0.997265i	$0.476454\pi$
$884$	−13.9203	−0.468189
$885$	6.66810	0.224146
$886$	−13.7015	−0.460310
$887$	32.3687	1.08684	0.543418	−	0.839462i	$-0.317130\pi$
$887$	32.3687	1.08684	0.543418	+	0.839462i	$0.317130\pi$
$888$	4.69786	0.157650
$889$	−34.7507	−1.16550
$890$	−10.9119	−0.365769
$891$	18.7257	0.627335
$892$	3.04217	0.101859
$893$	−69.7933	−2.33555
$894$	−8.43093	−0.281973
$895$	14.4823	0.484089
$896$	2.26316	0.0756067
$897$	−17.6816	−0.590372
$898$	−16.7835	−0.560071
$899$	−1.99143	−0.0664180
$900$	−2.77833	−0.0926111
$901$	6.23992	0.207882
$902$	9.64423	0.321118
$903$	10.6458	0.354270
$904$	6.23271	0.207297
$905$	−12.9169	−0.429373
$906$	10.0834	0.335000
$907$	−27.5536	−0.914903	−0.457452	−	0.889235i	$-0.651238\pi$
$907$	−27.5536	−0.914903	−0.457452	+	0.889235i	$0.651238\pi$
$908$	19.1646	0.635998
$909$	2.45141	0.0813081
$910$	−12.2580	−0.406349
$911$	6.37452	0.211197	0.105599	−	0.994409i	$-0.466324\pi$
$911$	6.37452	0.211197	0.105599	+	0.994409i	$0.466324\pi$
$912$	−2.48716	−0.0823582
$913$	−23.5736	−0.780172
$914$	40.5791	1.34224
$915$	−2.61629	−0.0864920
$916$	−12.1767	−0.402329
$917$	21.9903	0.726182
$918$	−6.99188	−0.230767
$919$	44.5178	1.46851	0.734253	−	0.678876i	$-0.237532\pi$
$919$	44.5178	1.46851	0.734253	+	0.678876i	$0.237532\pi$
$920$	6.93371	0.228597
$921$	−13.2217	−0.435670
$922$	18.4435	0.607404
$923$	42.3095	1.39263
$924$	2.82852	0.0930515
$925$	9.97815	0.328080
$926$	−21.0836	−0.692849
$927$	43.4481	1.42702
$928$	3.41645	0.112151
$929$	19.1683	0.628893	0.314446	−	0.949275i	$-0.398181\pi$
$929$	19.1683	0.628893	0.314446	+	0.949275i	$0.398181\pi$
$930$	−0.274436	−0.00899910
$931$	9.92151	0.325164
$932$	27.2204	0.891633
$933$	1.86175	0.0609509
$934$	4.99114	0.163315
$935$	6.82238	0.223116
$936$	15.0484	0.491872
$937$	−15.9974	−0.522612	−0.261306	−	0.965256i	$-0.584153\pi$
$937$	−15.9974	−0.522612	−0.261306	+	0.965256i	$0.584153\pi$
$938$	17.6771	0.577177
$939$	2.50515	0.0817526
$940$	13.2118	0.430920
$941$	−30.4556	−0.992823	−0.496411	−	0.868087i	$-0.665349\pi$
$941$	−30.4556	−0.992823	−0.496411	+	0.868087i	$0.665349\pi$
$942$	−4.28727	−0.139687
$943$	25.1906	0.820318
$944$	14.1629	0.460962
$945$	−6.15698	−0.200287
$946$	26.5221	0.862307
$947$	7.77337	0.252601	0.126300	−	0.991992i	$-0.459690\pi$
$947$	7.77337	0.252601	0.126300	+	0.991992i	$0.459690\pi$
$948$	5.39620	0.175261
$949$	39.5243	1.28301
$950$	−5.28267	−0.171392
$951$	2.95485	0.0958175
$952$	5.81642	0.188511
$953$	−25.4886	−0.825656	−0.412828	−	0.910809i	$-0.635459\pi$
$953$	−25.4886	−0.825656	−0.412828	+	0.910809i	$0.635459\pi$
$954$	−6.74562	−0.218398
$955$	−5.98275	−0.193597
$956$	19.3537	0.625943
$957$	4.26992	0.138027
$958$	−13.1544	−0.424998
$959$	28.0994	0.907378
$960$	0.470815	0.0151955
$961$	−30.6602	−0.989040
$962$	−54.0450	−1.74248
$963$	−34.2045	−1.10222
$964$	−21.7537	−0.700641
$965$	−15.6193	−0.502804
$966$	7.38806	0.237707
$967$	−40.9283	−1.31617	−0.658083	−	0.752945i	$-0.728632\pi$
$967$	−40.9283	−1.31617	−0.658083	+	0.752945i	$0.728632\pi$
$968$	−3.95325	−0.127062
$969$	−6.39212	−0.205345
$970$	−5.33845	−0.171407
$971$	−2.39439	−0.0768397	−0.0384199	−	0.999262i	$-0.512232\pi$
$971$	−2.39439	−0.0768397	−0.0384199	+	0.999262i	$0.512232\pi$
$972$	11.4828	0.368310
$973$	−23.2702	−0.746007
$974$	10.7796	0.345400
$975$	−2.55009	−0.0816684
$976$	−5.55694	−0.177873
$977$	22.1122	0.707433	0.353717	−	0.935353i	$-0.384918\pi$
$977$	22.1122	0.707433	0.353717	+	0.935353i	$0.384918\pi$
$978$	−6.84061	−0.218739
$979$	−28.9665	−0.925774
$980$	−1.87812	−0.0599945
$981$	17.7178	0.565685
$982$	−26.7576	−0.853870
$983$	34.7895	1.10961	0.554806	−	0.831980i	$-0.312793\pi$
$983$	34.7895	1.10961	0.554806	+	0.831980i	$0.312793\pi$
$984$	1.71050	0.0545288
$985$	−13.1289	−0.418321
$986$	8.78044	0.279626
$987$	14.0775	0.448092
$988$	28.6127	0.910292
$989$	69.2753	2.20283
$990$	−7.37528	−0.234402
$991$	4.32419	0.137363	0.0686813	−	0.997639i	$-0.478121\pi$
$991$	4.32419	0.137363	0.0686813	+	0.997639i	$0.478121\pi$
$992$	−0.582895	−0.0185069
$993$	−2.70281	−0.0857712
$994$	−17.6786	−0.560730
$995$	−1.93709	−0.0614098
$996$	−4.18101	−0.132480
$997$	−2.20643	−0.0698783	−0.0349392	−	0.999389i	$-0.511124\pi$
$997$	−2.20643	−0.0698783	−0.0349392	+	0.999389i	$0.511124\pi$
$998$	−10.2293	−0.323803
$999$	−27.1458	−0.858856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.n.1.12	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.n.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.470815 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.470815 q^{6} +2.26316 q^{7} +1.00000 q^{8} -2.77833 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.470815 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.470815 q^{6} +2.26316 q^{7} +1.00000 q^{8} -2.77833 q^{9} +1.00000 q^{10} +2.65457 q^{11} +0.470815 q^{12} -5.41634 q^{13} +2.26316 q^{14} +0.470815 q^{15} +1.00000 q^{16} +2.57005 q^{17} -2.77833 q^{18} -5.28267 q^{19} +1.00000 q^{20} +1.06553 q^{21} +2.65457 q^{22} +6.93371 q^{23} +0.470815 q^{24} +1.00000 q^{25} -5.41634 q^{26} -2.72053 q^{27} +2.26316 q^{28} +3.41645 q^{29} +0.470815 q^{30} -0.582895 q^{31} +1.00000 q^{32} +1.24981 q^{33} +2.57005 q^{34} +2.26316 q^{35} -2.77833 q^{36} +9.97815 q^{37} -5.28267 q^{38} -2.55009 q^{39} +1.00000 q^{40} +3.63306 q^{41} +1.06553 q^{42} +9.99110 q^{43} +2.65457 q^{44} -2.77833 q^{45} +6.93371 q^{46} +13.2118 q^{47} +0.470815 q^{48} -1.87812 q^{49} +1.00000 q^{50} +1.21002 q^{51} -5.41634 q^{52} +2.42794 q^{53} -2.72053 q^{54} +2.65457 q^{55} +2.26316 q^{56} -2.48716 q^{57} +3.41645 q^{58} +14.1629 q^{59} +0.470815 q^{60} -5.55694 q^{61} -0.582895 q^{62} -6.28780 q^{63} +1.00000 q^{64} -5.41634 q^{65} +1.24981 q^{66} +7.81080 q^{67} +2.57005 q^{68} +3.26449 q^{69} +2.26316 q^{70} -7.81146 q^{71} -2.77833 q^{72} -7.29724 q^{73} +9.97815 q^{74} +0.470815 q^{75} -5.28267 q^{76} +6.00771 q^{77} -2.55009 q^{78} +11.4614 q^{79} +1.00000 q^{80} +7.05413 q^{81} +3.63306 q^{82} -8.88037 q^{83} +1.06553 q^{84} +2.57005 q^{85} +9.99110 q^{86} +1.60852 q^{87} +2.65457 q^{88} -10.9119 q^{89} -2.77833 q^{90} -12.2580 q^{91} +6.93371 q^{92} -0.274436 q^{93} +13.2118 q^{94} -5.28267 q^{95} +0.470815 q^{96} -5.33845 q^{97} -1.87812 q^{98} -7.37528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) 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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