LMFDB - Embedded newform 4010.2.a.o.1.20

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			1.20
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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.00389 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.00389 q^{6} -1.21989 q^{7} +1.00000 q^{8} +6.02333 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.00389 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.00389 q^{6} -1.21989 q^{7} +1.00000 q^{8} +6.02333 q^{9} -1.00000 q^{10} +1.59965 q^{11} +3.00389 q^{12} -3.00564 q^{13} -1.21989 q^{14} -3.00389 q^{15} +1.00000 q^{16} -1.84866 q^{17} +6.02333 q^{18} +1.34008 q^{19} -1.00000 q^{20} -3.66442 q^{21} +1.59965 q^{22} +5.95325 q^{23} +3.00389 q^{24} +1.00000 q^{25} -3.00564 q^{26} +9.08175 q^{27} -1.21989 q^{28} +7.71371 q^{29} -3.00389 q^{30} +3.88312 q^{31} +1.00000 q^{32} +4.80516 q^{33} -1.84866 q^{34} +1.21989 q^{35} +6.02333 q^{36} +2.28307 q^{37} +1.34008 q^{38} -9.02861 q^{39} -1.00000 q^{40} +7.95958 q^{41} -3.66442 q^{42} -10.8527 q^{43} +1.59965 q^{44} -6.02333 q^{45} +5.95325 q^{46} +9.85130 q^{47} +3.00389 q^{48} -5.51186 q^{49} +1.00000 q^{50} -5.55318 q^{51} -3.00564 q^{52} +12.6285 q^{53} +9.08175 q^{54} -1.59965 q^{55} -1.21989 q^{56} +4.02544 q^{57} +7.71371 q^{58} +4.74021 q^{59} -3.00389 q^{60} +7.05909 q^{61} +3.88312 q^{62} -7.34783 q^{63} +1.00000 q^{64} +3.00564 q^{65} +4.80516 q^{66} +7.76453 q^{67} -1.84866 q^{68} +17.8829 q^{69} +1.21989 q^{70} -4.11149 q^{71} +6.02333 q^{72} -16.0806 q^{73} +2.28307 q^{74} +3.00389 q^{75} +1.34008 q^{76} -1.95140 q^{77} -9.02861 q^{78} -6.95866 q^{79} -1.00000 q^{80} +9.21056 q^{81} +7.95958 q^{82} -1.11438 q^{83} -3.66442 q^{84} +1.84866 q^{85} -10.8527 q^{86} +23.1711 q^{87} +1.59965 q^{88} -10.3092 q^{89} -6.02333 q^{90} +3.66657 q^{91} +5.95325 q^{92} +11.6644 q^{93} +9.85130 q^{94} -1.34008 q^{95} +3.00389 q^{96} -8.73328 q^{97} -5.51186 q^{98} +9.63521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - 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
$3$	3.00389	1.73429	0.867147	−	0.498052i	$-0.165951\pi$
$3$	3.00389	1.73429	0.867147	+	0.498052i	$0.165951\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.00389	1.22633
$7$	−1.21989	−0.461077	−0.230538	−	0.973063i	$-0.574049\pi$
$7$	−1.21989	−0.461077	−0.230538	+	0.973063i	$0.574049\pi$
$8$	1.00000	0.353553
$9$	6.02333	2.00778
$10$	−1.00000	−0.316228
$11$	1.59965	0.482312	0.241156	−	0.970486i	$-0.422473\pi$
$11$	1.59965	0.482312	0.241156	+	0.970486i	$0.422473\pi$
$12$	3.00389	0.867147
$13$	−3.00564	−0.833615	−0.416807	−	0.908995i	$-0.636851\pi$
$13$	−3.00564	−0.833615	−0.416807	+	0.908995i	$0.636851\pi$
$14$	−1.21989	−0.326031
$15$	−3.00389	−0.775600
$16$	1.00000	0.250000
$17$	−1.84866	−0.448367	−0.224183	−	0.974547i	$-0.571971\pi$
$17$	−1.84866	−0.448367	−0.224183	+	0.974547i	$0.571971\pi$
$18$	6.02333	1.41971
$19$	1.34008	0.307435	0.153717	−	0.988115i	$-0.450875\pi$
$19$	1.34008	0.307435	0.153717	+	0.988115i	$0.450875\pi$
$20$	−1.00000	−0.223607
$21$	−3.66442	−0.799643
$22$	1.59965	0.341046
$23$	5.95325	1.24134	0.620669	−	0.784073i	$-0.286861\pi$
$23$	5.95325	1.24134	0.620669	+	0.784073i	$0.286861\pi$
$24$	3.00389	0.613166
$25$	1.00000	0.200000
$26$	−3.00564	−0.589455
$27$	9.08175	1.74778
$28$	−1.21989	−0.230538
$29$	7.71371	1.43240	0.716200	−	0.697895i	$-0.245880\pi$
$29$	7.71371	1.43240	0.716200	+	0.697895i	$0.245880\pi$
$30$	−3.00389	−0.548432
$31$	3.88312	0.697429	0.348714	−	0.937229i	$-0.386618\pi$
$31$	3.88312	0.697429	0.348714	+	0.937229i	$0.386618\pi$
$32$	1.00000	0.176777
$33$	4.80516	0.836471
$34$	−1.84866	−0.317043
$35$	1.21989	0.206200
$36$	6.02333	1.00389
$37$	2.28307	0.375334	0.187667	−	0.982233i	$-0.439907\pi$
$37$	2.28307	0.375334	0.187667	+	0.982233i	$0.439907\pi$
$38$	1.34008	0.217389
$39$	−9.02861	−1.44573
$40$	−1.00000	−0.158114
$41$	7.95958	1.24308	0.621538	−	0.783384i	$-0.286508\pi$
$41$	7.95958	1.24308	0.621538	+	0.783384i	$0.286508\pi$
$42$	−3.66442	−0.565433
$43$	−10.8527	−1.65502	−0.827509	−	0.561452i	$-0.810243\pi$
$43$	−10.8527	−1.65502	−0.827509	+	0.561452i	$0.810243\pi$
$44$	1.59965	0.241156
$45$	−6.02333	−0.897906
$46$	5.95325	0.877759
$47$	9.85130	1.43696	0.718480	−	0.695548i	$-0.244838\pi$
$47$	9.85130	1.43696	0.718480	+	0.695548i	$0.244838\pi$
$48$	3.00389	0.433574
$49$	−5.51186	−0.787408
$50$	1.00000	0.141421
$51$	−5.55318	−0.777600
$52$	−3.00564	−0.416807
$53$	12.6285	1.73466	0.867330	−	0.497734i	$-0.165835\pi$
$53$	12.6285	1.73466	0.867330	+	0.497734i	$0.165835\pi$
$54$	9.08175	1.23587
$55$	−1.59965	−0.215696
$56$	−1.21989	−0.163015
$57$	4.02544	0.533182
$58$	7.71371	1.01286
$59$	4.74021	0.617122	0.308561	−	0.951205i	$-0.400153\pi$
$59$	4.74021	0.617122	0.308561	+	0.951205i	$0.400153\pi$
$60$	−3.00389	−0.387800
$61$	7.05909	0.903824	0.451912	−	0.892062i	$-0.350742\pi$
$61$	7.05909	0.903824	0.451912	+	0.892062i	$0.350742\pi$
$62$	3.88312	0.493157
$63$	−7.34783	−0.925740
$64$	1.00000	0.125000
$65$	3.00564	0.372804
$66$	4.80516	0.591474
$67$	7.76453	0.948588	0.474294	−	0.880367i	$-0.342703\pi$
$67$	7.76453	0.948588	0.474294	+	0.880367i	$0.342703\pi$
$68$	−1.84866	−0.224183
$69$	17.8829	2.15285
$70$	1.21989	0.145805
$71$	−4.11149	−0.487945	−0.243972	−	0.969782i	$-0.578451\pi$
$71$	−4.11149	−0.487945	−0.243972	+	0.969782i	$0.578451\pi$
$72$	6.02333	0.709857
$73$	−16.0806	−1.88209	−0.941047	−	0.338275i	$-0.890157\pi$
$73$	−16.0806	−1.88209	−0.941047	+	0.338275i	$0.890157\pi$
$74$	2.28307	0.265401
$75$	3.00389	0.346859
$76$	1.34008	0.153717
$77$	−1.95140	−0.222383
$78$	−9.02861	−1.02229
$79$	−6.95866	−0.782910	−0.391455	−	0.920197i	$-0.628028\pi$
$79$	−6.95866	−0.782910	−0.391455	+	0.920197i	$0.628028\pi$
$80$	−1.00000	−0.111803
$81$	9.21056	1.02340
$82$	7.95958	0.878988
$83$	−1.11438	−0.122319	−0.0611597	−	0.998128i	$-0.519480\pi$
$83$	−1.11438	−0.122319	−0.0611597	+	0.998128i	$0.519480\pi$
$84$	−3.66442	−0.399822
$85$	1.84866	0.200516
$86$	−10.8527	−1.17027
$87$	23.1711	2.48420
$88$	1.59965	0.170523
$89$	−10.3092	−1.09277	−0.546386	−	0.837534i	$-0.683997\pi$
$89$	−10.3092	−1.09277	−0.546386	+	0.837534i	$0.683997\pi$
$90$	−6.02333	−0.634915
$91$	3.66657	0.384360
$92$	5.95325	0.620669
$93$	11.6644	1.20955
$94$	9.85130	1.01608
$95$	−1.34008	−0.137489
$96$	3.00389	0.306583
$97$	−8.73328	−0.886730	−0.443365	−	0.896341i	$-0.646215\pi$
$97$	−8.73328	−0.886730	−0.443365	+	0.896341i	$0.646215\pi$
$98$	−5.51186	−0.556782
$99$	9.63521	0.968375
$100$	1.00000	0.100000
$101$	−7.77922	−0.774061	−0.387031	−	0.922067i	$-0.626499\pi$
$101$	−7.77922	−0.774061	−0.387031	+	0.922067i	$0.626499\pi$
$102$	−5.55318	−0.549847
$103$	5.21784	0.514129	0.257065	−	0.966394i	$-0.417245\pi$
$103$	5.21784	0.514129	0.257065	+	0.966394i	$0.417245\pi$
$104$	−3.00564	−0.294727
$105$	3.66442	0.357611
$106$	12.6285	1.22659
$107$	15.9302	1.54003	0.770017	−	0.638023i	$-0.220248\pi$
$107$	15.9302	1.54003	0.770017	+	0.638023i	$0.220248\pi$
$108$	9.08175	0.873892
$109$	−6.16963	−0.590943	−0.295472	−	0.955352i	$-0.595477\pi$
$109$	−6.16963	−0.590943	−0.295472	+	0.955352i	$0.595477\pi$
$110$	−1.59965	−0.152520
$111$	6.85808	0.650940
$112$	−1.21989	−0.115269
$113$	−11.0536	−1.03984	−0.519919	−	0.854216i	$-0.674038\pi$
$113$	−11.0536	−1.03984	−0.519919	+	0.854216i	$0.674038\pi$
$114$	4.02544	0.377017
$115$	−5.95325	−0.555143
$116$	7.71371	0.716200
$117$	−18.1040	−1.67371
$118$	4.74021	0.436371
$119$	2.25518	0.206732
$120$	−3.00389	−0.274216
$121$	−8.44113	−0.767375
$122$	7.05909	0.639100
$123$	23.9097	2.15586
$124$	3.88312	0.348714
$125$	−1.00000	−0.0894427
$126$	−7.34783	−0.654597
$127$	−20.5673	−1.82506	−0.912528	−	0.409014i	$-0.865873\pi$
$127$	−20.5673	−1.82506	−0.912528	+	0.409014i	$0.865873\pi$
$128$	1.00000	0.0883883
$129$	−32.6002	−2.87029
$130$	3.00564	0.263612
$131$	−18.2294	−1.59271	−0.796356	−	0.604828i	$-0.793242\pi$
$131$	−18.2294	−1.59271	−0.796356	+	0.604828i	$0.793242\pi$
$132$	4.80516	0.418235
$133$	−1.63475	−0.141751
$134$	7.76453	0.670753
$135$	−9.08175	−0.781633
$136$	−1.84866	−0.158522
$137$	9.68157	0.827153	0.413576	−	0.910469i	$-0.364280\pi$
$137$	9.68157	0.827153	0.413576	+	0.910469i	$0.364280\pi$
$138$	17.8829	1.52229
$139$	−18.5897	−1.57676	−0.788379	−	0.615189i	$-0.789080\pi$
$139$	−18.5897	−1.57676	−0.788379	+	0.615189i	$0.789080\pi$
$140$	1.21989	0.103100
$141$	29.5922	2.49211
$142$	−4.11149	−0.345029
$143$	−4.80797	−0.402062
$144$	6.02333	0.501945
$145$	−7.71371	−0.640588
$146$	−16.0806	−1.33084
$147$	−16.5570	−1.36560
$148$	2.28307	0.187667
$149$	−20.5109	−1.68032	−0.840159	−	0.542341i	$-0.817538\pi$
$149$	−20.5109	−1.68032	−0.840159	+	0.542341i	$0.817538\pi$
$150$	3.00389	0.245266
$151$	−17.2501	−1.40380	−0.701898	−	0.712277i	$-0.747664\pi$
$151$	−17.2501	−1.40380	−0.701898	+	0.712277i	$0.747664\pi$
$152$	1.34008	0.108695
$153$	−11.1351	−0.900221
$154$	−1.95140	−0.157248
$155$	−3.88312	−0.311900
$156$	−9.02861	−0.722867
$157$	18.6296	1.48680	0.743401	−	0.668846i	$-0.233211\pi$
$157$	18.6296	1.48680	0.743401	+	0.668846i	$0.233211\pi$
$158$	−6.95866	−0.553601
$159$	37.9346	3.00841
$160$	−1.00000	−0.0790569
$161$	−7.26233	−0.572352
$162$	9.21056	0.723650
$163$	18.4813	1.44757	0.723783	−	0.690028i	$-0.242402\pi$
$163$	18.4813	1.44757	0.723783	+	0.690028i	$0.242402\pi$
$164$	7.95958	0.621538
$165$	−4.80516	−0.374081
$166$	−1.11438	−0.0864928
$167$	−13.4290	−1.03917	−0.519584	−	0.854419i	$-0.673913\pi$
$167$	−13.4290	−1.03917	−0.519584	+	0.854419i	$0.673913\pi$
$168$	−3.66442	−0.282716
$169$	−3.96612	−0.305086
$170$	1.84866	0.141786
$171$	8.07173	0.617261
$172$	−10.8527	−0.827509
$173$	−19.9690	−1.51821	−0.759107	−	0.650966i	$-0.774364\pi$
$173$	−19.9690	−1.51821	−0.759107	+	0.650966i	$0.774364\pi$
$174$	23.1711	1.75660
$175$	−1.21989	−0.0922154
$176$	1.59965	0.120578
$177$	14.2390	1.07027
$178$	−10.3092	−0.772706
$179$	−16.8053	−1.25609	−0.628044	−	0.778178i	$-0.716144\pi$
$179$	−16.8053	−1.25609	−0.628044	+	0.778178i	$0.716144\pi$
$180$	−6.02333	−0.448953
$181$	5.69061	0.422980	0.211490	−	0.977380i	$-0.432168\pi$
$181$	5.69061	0.422980	0.211490	+	0.977380i	$0.432168\pi$
$182$	3.66657	0.271784
$183$	21.2047	1.56750
$184$	5.95325	0.438879
$185$	−2.28307	−0.167855
$186$	11.6644	0.855279
$187$	−2.95721	−0.216253
$188$	9.85130	0.718480
$189$	−11.0788	−0.805863
$190$	−1.34008	−0.0972194
$191$	−15.8074	−1.14379	−0.571893	−	0.820328i	$-0.693791\pi$
$191$	−15.8074	−1.14379	−0.571893	+	0.820328i	$0.693791\pi$
$192$	3.00389	0.216787
$193$	15.0906	1.08625	0.543124	−	0.839652i	$-0.317241\pi$
$193$	15.0906	1.08625	0.543124	+	0.839652i	$0.317241\pi$
$194$	−8.73328	−0.627013
$195$	9.02861	0.646552
$196$	−5.51186	−0.393704
$197$	14.1991	1.01165	0.505823	−	0.862637i	$-0.331189\pi$
$197$	14.1991	1.01165	0.505823	+	0.862637i	$0.331189\pi$
$198$	9.63521	0.684745
$199$	21.4201	1.51843	0.759214	−	0.650841i	$-0.225584\pi$
$199$	21.4201	1.51843	0.759214	+	0.650841i	$0.225584\pi$
$200$	1.00000	0.0707107
$201$	23.3238	1.64513
$202$	−7.77922	−0.547344
$203$	−9.40991	−0.660446
$204$	−5.55318	−0.388800
$205$	−7.95958	−0.555921
$206$	5.21784	0.363544
$207$	35.8584	2.49233
$208$	−3.00564	−0.208404
$209$	2.14365	0.148279
$210$	3.66442	0.252869
$211$	20.6394	1.42087	0.710436	−	0.703762i	$-0.248498\pi$
$211$	20.6394	1.42087	0.710436	+	0.703762i	$0.248498\pi$
$212$	12.6285	0.867330
$213$	−12.3505	−0.846240
$214$	15.9302	1.08897
$215$	10.8527	0.740147
$216$	9.08175	0.617935
$217$	−4.73699	−0.321568
$218$	−6.16963	−0.417860
$219$	−48.3044	−3.26411
$220$	−1.59965	−0.107848
$221$	5.55642	0.373765
$222$	6.85808	0.460284
$223$	29.5140	1.97641	0.988203	−	0.153150i	$-0.0489418\pi$
$223$	29.5140	1.97641	0.988203	+	0.153150i	$0.0489418\pi$
$224$	−1.21989	−0.0815076
$225$	6.02333	0.401556
$226$	−11.0536	−0.735277
$227$	18.7839	1.24673	0.623366	−	0.781930i	$-0.285765\pi$
$227$	18.7839	1.24673	0.623366	+	0.781930i	$0.285765\pi$
$228$	4.02544	0.266591
$229$	−14.1578	−0.935574	−0.467787	−	0.883841i	$-0.654949\pi$
$229$	−14.1578	−0.935574	−0.467787	+	0.883841i	$0.654949\pi$
$230$	−5.95325	−0.392546
$231$	−5.86179	−0.385677
$232$	7.71371	0.506430
$233$	−18.1788	−1.19093	−0.595466	−	0.803381i	$-0.703032\pi$
$233$	−18.1788	−1.19093	−0.595466	+	0.803381i	$0.703032\pi$
$234$	−18.1040	−1.18349
$235$	−9.85130	−0.642628
$236$	4.74021	0.308561
$237$	−20.9030	−1.35780
$238$	2.25518	0.146181
$239$	−22.6002	−1.46188	−0.730942	−	0.682440i	$-0.760919\pi$
$239$	−22.6002	−1.46188	−0.730942	+	0.682440i	$0.760919\pi$
$240$	−3.00389	−0.193900
$241$	3.91756	0.252352	0.126176	−	0.992008i	$-0.459730\pi$
$241$	3.91756	0.252352	0.126176	+	0.992008i	$0.459730\pi$
$242$	−8.44113	−0.542616
$243$	0.422206	0.0270845
$244$	7.05909	0.451912
$245$	5.51186	0.352140
$246$	23.9097	1.52442
$247$	−4.02779	−0.256282
$248$	3.88312	0.246578
$249$	−3.34748	−0.212138
$250$	−1.00000	−0.0632456
$251$	4.58994	0.289715	0.144857	−	0.989453i	$-0.453728\pi$
$251$	4.58994	0.289715	0.144857	+	0.989453i	$0.453728\pi$
$252$	−7.34783	−0.462870
$253$	9.52310	0.598712
$254$	−20.5673	−1.29051
$255$	5.55318	0.347753
$256$	1.00000	0.0625000
$257$	15.2215	0.949494	0.474747	−	0.880122i	$-0.342540\pi$
$257$	15.2215	0.949494	0.474747	+	0.880122i	$0.342540\pi$
$258$	−32.6002	−2.02960
$259$	−2.78510	−0.173058
$260$	3.00564	0.186402
$261$	46.4622	2.87594
$262$	−18.2294	−1.12622
$263$	0.106323	0.00655617	0.00327808	−	0.999995i	$-0.498957\pi$
$263$	0.106323	0.00655617	0.00327808	+	0.999995i	$0.498957\pi$
$264$	4.80516	0.295737
$265$	−12.6285	−0.775763
$266$	−1.63475	−0.100233
$267$	−30.9676	−1.89519
$268$	7.76453	0.474294
$269$	11.9395	0.727965	0.363982	−	0.931406i	$-0.381417\pi$
$269$	11.9395	0.727965	0.363982	+	0.931406i	$0.381417\pi$
$270$	−9.08175	−0.552698
$271$	13.7975	0.838139	0.419069	−	0.907954i	$-0.362356\pi$
$271$	13.7975	0.838139	0.419069	+	0.907954i	$0.362356\pi$
$272$	−1.84866	−0.112092
$273$	11.0139	0.666594
$274$	9.68157	0.584885
$275$	1.59965	0.0964624
$276$	17.8829	1.07642
$277$	10.2299	0.614654	0.307327	−	0.951604i	$-0.400565\pi$
$277$	10.2299	0.614654	0.307327	+	0.951604i	$0.400565\pi$
$278$	−18.5897	−1.11494
$279$	23.3893	1.40028
$280$	1.21989	0.0729026
$281$	2.23561	0.133365	0.0666827	−	0.997774i	$-0.478758\pi$
$281$	2.23561	0.133365	0.0666827	+	0.997774i	$0.478758\pi$
$282$	29.5922	1.76219
$283$	−18.4400	−1.09614	−0.548071	−	0.836432i	$-0.684638\pi$
$283$	−18.4400	−1.09614	−0.548071	+	0.836432i	$0.684638\pi$
$284$	−4.11149	−0.243972
$285$	−4.02544	−0.238446
$286$	−4.80797	−0.284301
$287$	−9.70984	−0.573154
$288$	6.02333	0.354928
$289$	−13.5824	−0.798967
$290$	−7.71371	−0.452964
$291$	−26.2338	−1.53785
$292$	−16.0806	−0.941047
$293$	−0.340587	−0.0198973	−0.00994865	−	0.999951i	$-0.503167\pi$
$293$	−0.340587	−0.0198973	−0.00994865	+	0.999951i	$0.503167\pi$
$294$	−16.5570	−0.965624
$295$	−4.74021	−0.275985
$296$	2.28307	0.132701
$297$	14.5276	0.842977
$298$	−20.5109	−1.18816
$299$	−17.8933	−1.03480
$300$	3.00389	0.173429
$301$	13.2391	0.763090
$302$	−17.2501	−0.992634
$303$	−23.3679	−1.34245
$304$	1.34008	0.0768587
$305$	−7.05909	−0.404203
$306$	−11.1351	−0.636553
$307$	−13.7942	−0.787278	−0.393639	−	0.919265i	$-0.628784\pi$
$307$	−13.7942	−0.787278	−0.393639	+	0.919265i	$0.628784\pi$
$308$	−1.95140	−0.111191
$309$	15.6738	0.891652
$310$	−3.88312	−0.220546
$311$	−6.54776	−0.371289	−0.185645	−	0.982617i	$-0.559437\pi$
$311$	−6.54776	−0.371289	−0.185645	+	0.982617i	$0.559437\pi$
$312$	−9.02861	−0.511144
$313$	15.5529	0.879101	0.439550	−	0.898218i	$-0.355138\pi$
$313$	15.5529	0.879101	0.439550	+	0.898218i	$0.355138\pi$
$314$	18.6296	1.05133
$315$	7.34783	0.414003
$316$	−6.95866	−0.391455
$317$	−16.5737	−0.930874	−0.465437	−	0.885081i	$-0.654103\pi$
$317$	−16.5737	−0.930874	−0.465437	+	0.885081i	$0.654103\pi$
$318$	37.9346	2.12727
$319$	12.3392	0.690863
$320$	−1.00000	−0.0559017
$321$	47.8526	2.67087
$322$	−7.26233	−0.404714
$323$	−2.47735	−0.137844
$324$	9.21056	0.511698
$325$	−3.00564	−0.166723
$326$	18.4813	1.02358
$327$	−18.5329	−1.02487
$328$	7.95958	0.439494
$329$	−12.0175	−0.662549
$330$	−4.80516	−0.264515
$331$	−21.9122	−1.20440	−0.602201	−	0.798345i	$-0.705709\pi$
$331$	−21.9122	−1.20440	−0.602201	+	0.798345i	$0.705709\pi$
$332$	−1.11438	−0.0611597
$333$	13.7517	0.753588
$334$	−13.4290	−0.734803
$335$	−7.76453	−0.424221
$336$	−3.66442	−0.199911
$337$	3.43292	0.187003	0.0935015	−	0.995619i	$-0.470194\pi$
$337$	3.43292	0.187003	0.0935015	+	0.995619i	$0.470194\pi$
$338$	−3.96612	−0.215728
$339$	−33.2039	−1.80339
$340$	1.84866	0.100258
$341$	6.21162	0.336378
$342$	8.07173	0.436469
$343$	15.2631	0.824132
$344$	−10.8527	−0.585137
$345$	−17.8829	−0.962782
$346$	−19.9690	−1.07354
$347$	34.1509	1.83332	0.916658	−	0.399673i	$-0.130876\pi$
$347$	34.1509	1.83332	0.916658	+	0.399673i	$0.130876\pi$
$348$	23.1711	1.24210
$349$	−12.9754	−0.694558	−0.347279	−	0.937762i	$-0.612894\pi$
$349$	−12.9754	−0.694558	−0.347279	+	0.937762i	$0.612894\pi$
$350$	−1.21989	−0.0652061
$351$	−27.2965	−1.45698
$352$	1.59965	0.0852615
$353$	−1.68851	−0.0898703	−0.0449352	−	0.998990i	$-0.514308\pi$
$353$	−1.68851	−0.0898703	−0.0449352	+	0.998990i	$0.514308\pi$
$354$	14.2390	0.756796
$355$	4.11149	0.218215
$356$	−10.3092	−0.546386
$357$	6.77429	0.358533
$358$	−16.8053	−0.888188
$359$	0.845620	0.0446301	0.0223150	−	0.999751i	$-0.492896\pi$
$359$	0.845620	0.0446301	0.0223150	+	0.999751i	$0.492896\pi$
$360$	−6.02333	−0.317458
$361$	−17.2042	−0.905484
$362$	5.69061	0.299092
$363$	−25.3562	−1.33085
$364$	3.66657	0.192180
$365$	16.0806	0.841698
$366$	21.2047	1.10839
$367$	27.2095	1.42032	0.710162	−	0.704039i	$-0.248622\pi$
$367$	27.2095	1.42032	0.710162	+	0.704039i	$0.248622\pi$
$368$	5.95325	0.310335
$369$	47.9432	2.49582
$370$	−2.28307	−0.118691
$371$	−15.4054	−0.799811
$372$	11.6644	0.604773
$373$	−9.66514	−0.500442	−0.250221	−	0.968189i	$-0.580503\pi$
$373$	−9.66514	−0.500442	−0.250221	+	0.968189i	$0.580503\pi$
$374$	−2.95721	−0.152914
$375$	−3.00389	−0.155120
$376$	9.85130	0.508042
$377$	−23.1846	−1.19407
$378$	−11.0788	−0.569831
$379$	−14.3728	−0.738281	−0.369140	−	0.929374i	$-0.620348\pi$
$379$	−14.3728	−0.738281	−0.369140	+	0.929374i	$0.620348\pi$
$380$	−1.34008	−0.0687445
$381$	−61.7819	−3.16518
$382$	−15.8074	−0.808779
$383$	5.27028	0.269299	0.134649	−	0.990893i	$-0.457009\pi$
$383$	5.27028	0.269299	0.134649	+	0.990893i	$0.457009\pi$
$384$	3.00389	0.153291
$385$	1.95140	0.0994526
$386$	15.0906	0.768094
$387$	−65.3693	−3.32291
$388$	−8.73328	−0.443365
$389$	29.4368	1.49251	0.746253	−	0.665663i	$-0.231851\pi$
$389$	29.4368	1.49251	0.746253	+	0.665663i	$0.231851\pi$
$390$	9.02861	0.457181
$391$	−11.0056	−0.556575
$392$	−5.51186	−0.278391
$393$	−54.7591	−2.76223
$394$	14.1991	0.715342
$395$	6.95866	0.350128
$396$	9.63521	0.484188
$397$	−19.5966	−0.983524	−0.491762	−	0.870730i	$-0.663647\pi$
$397$	−19.5966	−0.983524	−0.491762	+	0.870730i	$0.663647\pi$
$398$	21.4201	1.07369
$399$	−4.91061	−0.245838
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	23.3238	1.16328
$403$	−11.6713	−0.581387
$404$	−7.77922	−0.387031
$405$	−9.21056	−0.457676
$406$	−9.40991	−0.467006
$407$	3.65211	0.181028
$408$	−5.55318	−0.274923
$409$	−28.3085	−1.39976	−0.699882	−	0.714259i	$-0.746764\pi$
$409$	−28.3085	−1.39976	−0.699882	+	0.714259i	$0.746764\pi$
$410$	−7.95958	−0.393095
$411$	29.0823	1.43453
$412$	5.21784	0.257065
$413$	−5.78255	−0.284541
$414$	35.8584	1.76234
$415$	1.11438	0.0547029
$416$	−3.00564	−0.147364
$417$	−55.8414	−2.73456
$418$	2.14365	0.104849
$419$	−10.1526	−0.495988	−0.247994	−	0.968762i	$-0.579771\pi$
$419$	−10.1526	−0.495988	−0.247994	+	0.968762i	$0.579771\pi$
$420$	3.66442	0.178806
$421$	31.9438	1.55684	0.778422	−	0.627741i	$-0.216020\pi$
$421$	31.9438	1.55684	0.778422	+	0.627741i	$0.216020\pi$
$422$	20.6394	1.00471
$423$	59.3377	2.88510
$424$	12.6285	0.613295
$425$	−1.84866	−0.0896734
$426$	−12.3505	−0.598382
$427$	−8.61135	−0.416732
$428$	15.9302	0.770017
$429$	−14.4426	−0.697295
$430$	10.8527	0.523363
$431$	31.5054	1.51756	0.758780	−	0.651347i	$-0.225796\pi$
$431$	31.5054	1.51756	0.758780	+	0.651347i	$0.225796\pi$
$432$	9.08175	0.436946
$433$	−12.5768	−0.604400	−0.302200	−	0.953244i	$-0.597721\pi$
$433$	−12.5768	−0.604400	−0.302200	+	0.953244i	$0.597721\pi$
$434$	−4.73699	−0.227383
$435$	−23.1711	−1.11097
$436$	−6.16963	−0.295472
$437$	7.97781	0.381630
$438$	−48.3044	−2.30807
$439$	−4.28805	−0.204657	−0.102329	−	0.994751i	$-0.532629\pi$
$439$	−4.28805	−0.204657	−0.102329	+	0.994751i	$0.532629\pi$
$440$	−1.59965	−0.0762602
$441$	−33.1998	−1.58094
$442$	5.55642	0.264292
$443$	24.9377	1.18482	0.592412	−	0.805635i	$-0.298176\pi$
$443$	24.9377	1.18482	0.592412	+	0.805635i	$0.298176\pi$
$444$	6.85808	0.325470
$445$	10.3092	0.488702
$446$	29.5140	1.39753
$447$	−61.6124	−2.91417
$448$	−1.21989	−0.0576346
$449$	14.1902	0.669678	0.334839	−	0.942275i	$-0.391318\pi$
$449$	14.1902	0.669678	0.334839	+	0.942275i	$0.391318\pi$
$450$	6.02333	0.283943
$451$	12.7325	0.599551
$452$	−11.0536	−0.519919
$453$	−51.8174	−2.43460
$454$	18.7839	0.881573
$455$	−3.66657	−0.171891
$456$	4.02544	0.188508
$457$	−5.83494	−0.272947	−0.136473	−	0.990644i	$-0.543577\pi$
$457$	−5.83494	−0.272947	−0.136473	+	0.990644i	$0.543577\pi$
$458$	−14.1578	−0.661551
$459$	−16.7891	−0.783649
$460$	−5.95325	−0.277572
$461$	−21.2093	−0.987816	−0.493908	−	0.869514i	$-0.664432\pi$
$461$	−21.2093	−0.987816	−0.493908	+	0.869514i	$0.664432\pi$
$462$	−5.86179	−0.272715
$463$	−14.1355	−0.656934	−0.328467	−	0.944515i	$-0.606532\pi$
$463$	−14.1355	−0.656934	−0.328467	+	0.944515i	$0.606532\pi$
$464$	7.71371	0.358100
$465$	−11.6644	−0.540926
$466$	−18.1788	−0.842116
$467$	−27.9822	−1.29486	−0.647431	−	0.762124i	$-0.724157\pi$
$467$	−27.9822	−1.29486	−0.647431	+	0.762124i	$0.724157\pi$
$468$	−18.1040	−0.836857
$469$	−9.47190	−0.437372
$470$	−9.85130	−0.454407
$471$	55.9612	2.57855
$472$	4.74021	0.218186
$473$	−17.3605	−0.798235
$474$	−20.9030	−0.960108
$475$	1.34008	0.0614869
$476$	2.25518	0.103366
$477$	76.0657	3.48281
$478$	−22.6002	−1.03371
$479$	14.9356	0.682426	0.341213	−	0.939986i	$-0.389162\pi$
$479$	14.9356	0.682426	0.341213	+	0.939986i	$0.389162\pi$
$480$	−3.00389	−0.137108
$481$	−6.86209	−0.312884
$482$	3.91756	0.178440
$483$	−21.8152	−0.992627
$484$	−8.44113	−0.383688
$485$	8.73328	0.396558
$486$	0.422206	0.0191516
$487$	2.23478	0.101267	0.0506337	−	0.998717i	$-0.483876\pi$
$487$	2.23478	0.101267	0.0506337	+	0.998717i	$0.483876\pi$
$488$	7.05909	0.319550
$489$	55.5157	2.51051
$490$	5.51186	0.249000
$491$	38.9067	1.75584	0.877918	−	0.478810i	$-0.158932\pi$
$491$	38.9067	1.75584	0.877918	+	0.478810i	$0.158932\pi$
$492$	23.9097	1.07793
$493$	−14.2601	−0.642240
$494$	−4.02779	−0.181219
$495$	−9.63521	−0.433071
$496$	3.88312	0.174357
$497$	5.01559	0.224980
$498$	−3.34748	−0.150004
$499$	12.9992	0.581923	0.290961	−	0.956735i	$-0.406025\pi$
$499$	12.9992	0.581923	0.290961	+	0.956735i	$0.406025\pi$
$500$	−1.00000	−0.0447214
$501$	−40.3392	−1.80222
$502$	4.58994	0.204859
$503$	36.2876	1.61799	0.808993	−	0.587818i	$-0.200013\pi$
$503$	36.2876	1.61799	0.808993	+	0.587818i	$0.200013\pi$
$504$	−7.34783	−0.327298
$505$	7.77922	0.346171
$506$	9.52310	0.423353
$507$	−11.9138	−0.529109
$508$	−20.5673	−0.912528
$509$	−23.9013	−1.05941	−0.529704	−	0.848183i	$-0.677697\pi$
$509$	−23.9013	−1.05941	−0.529704	+	0.848183i	$0.677697\pi$
$510$	5.55318	0.245899
$511$	19.6167	0.867790
$512$	1.00000	0.0441942
$513$	12.1702	0.537330
$514$	15.2215	0.671393
$515$	−5.21784	−0.229926
$516$	−32.6002	−1.43514
$517$	15.7586	0.693063
$518$	−2.78510	−0.122370
$519$	−59.9845	−2.63303
$520$	3.00564	0.131806
$521$	−42.3983	−1.85750	−0.928751	−	0.370704i	$-0.879116\pi$
$521$	−42.3983	−1.85750	−0.928751	+	0.370704i	$0.879116\pi$
$522$	46.4622	2.03360
$523$	0.406715	0.0177844	0.00889220	−	0.999960i	$-0.497169\pi$
$523$	0.406715	0.0177844	0.00889220	+	0.999960i	$0.497169\pi$
$524$	−18.2294	−0.796356
$525$	−3.66442	−0.159929
$526$	0.106323	0.00463591
$527$	−7.17858	−0.312704
$528$	4.80516	0.209118
$529$	12.4412	0.540920
$530$	−12.6285	−0.548547
$531$	28.5518	1.23904
$532$	−1.63475	−0.0708755
$533$	−23.9236	−1.03625
$534$	−30.9676	−1.34010
$535$	−15.9302	−0.688724
$536$	7.76453	0.335376
$537$	−50.4812	−2.17843
$538$	11.9395	0.514749
$539$	−8.81703	−0.379776
$540$	−9.08175	−0.390817
$541$	13.8233	0.594312	0.297156	−	0.954829i	$-0.403962\pi$
$541$	13.8233	0.594312	0.297156	+	0.954829i	$0.403962\pi$
$542$	13.7975	0.592653
$543$	17.0940	0.733572
$544$	−1.84866	−0.0792608
$545$	6.16963	0.264278
$546$	11.0139	0.471353
$547$	10.6660	0.456046	0.228023	−	0.973656i	$-0.426774\pi$
$547$	10.6660	0.456046	0.228023	+	0.973656i	$0.426774\pi$
$548$	9.68157	0.413576
$549$	42.5193	1.81468
$550$	1.59965	0.0682092
$551$	10.3370	0.440369
$552$	17.8829	0.761146
$553$	8.48883	0.360982
$554$	10.2299	0.434626
$555$	−6.85808	−0.291109
$556$	−18.5897	−0.788379
$557$	33.5511	1.42161	0.710803	−	0.703391i	$-0.248332\pi$
$557$	33.5511	1.42161	0.710803	+	0.703391i	$0.248332\pi$
$558$	23.3893	0.990149
$559$	32.6193	1.37965
$560$	1.21989	0.0515499
$561$	−8.88313	−0.375046
$562$	2.23561	0.0943035
$563$	−15.8983	−0.670035	−0.335017	−	0.942212i	$-0.608742\pi$
$563$	−15.8983	−0.670035	−0.335017	+	0.942212i	$0.608742\pi$
$564$	29.5922	1.24606
$565$	11.0536	0.465030
$566$	−18.4400	−0.775090
$567$	−11.2359	−0.471864
$568$	−4.11149	−0.172514
$569$	18.3242	0.768188	0.384094	−	0.923294i	$-0.374514\pi$
$569$	18.3242	0.768188	0.384094	+	0.923294i	$0.374514\pi$
$570$	−4.02544	−0.168607
$571$	34.7793	1.45547	0.727735	−	0.685858i	$-0.240573\pi$
$571$	34.7793	1.45547	0.727735	+	0.685858i	$0.240573\pi$
$572$	−4.80797	−0.201031
$573$	−47.4838	−1.98366
$574$	−9.70984	−0.405281
$575$	5.95325	0.248268
$576$	6.02333	0.250972
$577$	−26.5100	−1.10363	−0.551814	−	0.833967i	$-0.686064\pi$
$577$	−26.5100	−1.10363	−0.551814	+	0.833967i	$0.686064\pi$
$578$	−13.5824	−0.564955
$579$	45.3306	1.88387
$580$	−7.71371	−0.320294
$581$	1.35943	0.0563986
$582$	−26.2338	−1.08742
$583$	20.2012	0.836647
$584$	−16.0806	−0.665421
$585$	18.1040	0.748508
$586$	−0.340587	−0.0140695
$587$	−25.0292	−1.03307	−0.516533	−	0.856267i	$-0.672778\pi$
$587$	−25.0292	−1.03307	−0.516533	+	0.856267i	$0.672778\pi$
$588$	−16.5570	−0.682799
$589$	5.20368	0.214414
$590$	−4.74021	−0.195151
$591$	42.6526	1.75449
$592$	2.28307	0.0938336
$593$	−45.7572	−1.87902	−0.939512	−	0.342515i	$-0.888721\pi$
$593$	−45.7572	−1.87902	−0.939512	+	0.342515i	$0.888721\pi$
$594$	14.5276	0.596075
$595$	−2.25518	−0.0924532
$596$	−20.5109	−0.840159
$597$	64.3434	2.63340
$598$	−17.8933	−0.731713
$599$	−13.2241	−0.540324	−0.270162	−	0.962815i	$-0.587077\pi$
$599$	−13.2241	−0.540324	−0.270162	+	0.962815i	$0.587077\pi$
$600$	3.00389	0.122633
$601$	17.3970	0.709640	0.354820	−	0.934935i	$-0.384542\pi$
$601$	17.3970	0.709640	0.354820	+	0.934935i	$0.384542\pi$
$602$	13.2391	0.539586
$603$	46.7683	1.90455
$604$	−17.2501	−0.701898
$605$	8.44113	0.343181
$606$	−23.3679	−0.949256
$607$	−2.93632	−0.119182	−0.0595908	−	0.998223i	$-0.518980\pi$
$607$	−2.93632	−0.119182	−0.0595908	+	0.998223i	$0.518980\pi$
$608$	1.34008	0.0543473
$609$	−28.2663	−1.14541
$610$	−7.05909	−0.285814
$611$	−29.6095	−1.19787
$612$	−11.1351	−0.450111
$613$	10.0617	0.406388	0.203194	−	0.979139i	$-0.434868\pi$
$613$	10.0617	0.406388	0.203194	+	0.979139i	$0.434868\pi$
$614$	−13.7942	−0.556689
$615$	−23.9097	−0.964131
$616$	−1.95140	−0.0786242
$617$	−26.5009	−1.06689	−0.533443	−	0.845836i	$-0.679102\pi$
$617$	−26.5009	−1.06689	−0.533443	+	0.845836i	$0.679102\pi$
$618$	15.6738	0.630493
$619$	5.01154	0.201431	0.100715	−	0.994915i	$-0.467887\pi$
$619$	5.01154	0.201431	0.100715	+	0.994915i	$0.467887\pi$
$620$	−3.88312	−0.155950
$621$	54.0659	2.16959
$622$	−6.54776	−0.262541
$623$	12.5761	0.503852
$624$	−9.02861	−0.361434
$625$	1.00000	0.0400000
$626$	15.5529	0.621618
$627$	6.43928	0.257160
$628$	18.6296	0.743401
$629$	−4.22063	−0.168287
$630$	7.34783	0.292745
$631$	43.1604	1.71819	0.859095	−	0.511816i	$-0.171027\pi$
$631$	43.1604	1.71819	0.859095	+	0.511816i	$0.171027\pi$
$632$	−6.95866	−0.276801
$633$	61.9983	2.46421
$634$	−16.5737	−0.658227
$635$	20.5673	0.816190
$636$	37.9346	1.50421
$637$	16.5667	0.656395
$638$	12.3392	0.488514
$639$	−24.7649	−0.979684
$640$	−1.00000	−0.0395285
$641$	−13.4437	−0.530995	−0.265498	−	0.964112i	$-0.585536\pi$
$641$	−13.4437	−0.530995	−0.265498	+	0.964112i	$0.585536\pi$
$642$	47.8526	1.88859
$643$	−24.0962	−0.950262	−0.475131	−	0.879915i	$-0.657599\pi$
$643$	−24.0962	−0.950262	−0.475131	+	0.879915i	$0.657599\pi$
$644$	−7.26233	−0.286176
$645$	32.6002	1.28363
$646$	−2.47735	−0.0974701
$647$	9.29409	0.365389	0.182694	−	0.983170i	$-0.441518\pi$
$647$	9.29409	0.365389	0.182694	+	0.983170i	$0.441518\pi$
$648$	9.21056	0.361825
$649$	7.58266	0.297645
$650$	−3.00564	−0.117891
$651$	−14.2294	−0.557694
$652$	18.4813	0.723783
$653$	−21.0237	−0.822722	−0.411361	−	0.911472i	$-0.634947\pi$
$653$	−21.0237	−0.822722	−0.411361	+	0.911472i	$0.634947\pi$
$654$	−18.5329	−0.724692
$655$	18.2294	0.712283
$656$	7.95958	0.310769
$657$	−96.8590	−3.77883
$658$	−12.0175	−0.468493
$659$	11.6843	0.455154	0.227577	−	0.973760i	$-0.426920\pi$
$659$	11.6843	0.455154	0.227577	+	0.973760i	$0.426920\pi$
$660$	−4.80516	−0.187041
$661$	12.9447	0.503489	0.251744	−	0.967794i	$-0.418996\pi$
$661$	12.9447	0.503489	0.251744	+	0.967794i	$0.418996\pi$
$662$	−21.9122	−0.851640
$663$	16.6909	0.648219
$664$	−1.11438	−0.0432464
$665$	1.63475	0.0633930
$666$	13.7517	0.532867
$667$	45.9216	1.77809
$668$	−13.4290	−0.519584
$669$	88.6568	3.42767
$670$	−7.76453	−0.299970
$671$	11.2921	0.435925
$672$	−3.66442	−0.141358
$673$	44.5842	1.71859	0.859296	−	0.511478i	$-0.170902\pi$
$673$	44.5842	1.71859	0.859296	+	0.511478i	$0.170902\pi$
$674$	3.43292	0.132231
$675$	9.08175	0.349557
$676$	−3.96612	−0.152543
$677$	−23.9908	−0.922040	−0.461020	−	0.887390i	$-0.652516\pi$
$677$	−23.9908	−0.922040	−0.461020	+	0.887390i	$0.652516\pi$
$678$	−33.2039	−1.27519
$679$	10.6537	0.408851
$680$	1.84866	0.0708930
$681$	56.4247	2.16220
$682$	6.21162	0.237855
$683$	−14.1303	−0.540680	−0.270340	−	0.962765i	$-0.587136\pi$
$683$	−14.1303	−0.540680	−0.270340	+	0.962765i	$0.587136\pi$
$684$	8.07173	0.308630
$685$	−9.68157	−0.369914
$686$	15.2631	0.582750
$687$	−42.5285	−1.62256
$688$	−10.8527	−0.413755
$689$	−37.9568	−1.44604
$690$	−17.8829	−0.680790
$691$	−11.7783	−0.448066	−0.224033	−	0.974582i	$-0.571922\pi$
$691$	−11.7783	−0.448066	−0.224033	+	0.974582i	$0.571922\pi$
$692$	−19.9690	−0.759107
$693$	−11.7539	−0.446495
$694$	34.1509	1.29635
$695$	18.5897	0.705148
$696$	23.1711	0.878298
$697$	−14.7146	−0.557355
$698$	−12.9754	−0.491127
$699$	−54.6070	−2.06543
$700$	−1.21989	−0.0461077
$701$	26.6090	1.00501	0.502504	−	0.864575i	$-0.332412\pi$
$701$	26.6090	1.00501	0.502504	+	0.864575i	$0.332412\pi$
$702$	−27.2965	−1.03024
$703$	3.05949	0.115391
$704$	1.59965	0.0602890
$705$	−29.5922	−1.11451
$706$	−1.68851	−0.0635479
$707$	9.48983	0.356902
$708$	14.2390	0.535136
$709$	−15.9021	−0.597217	−0.298609	−	0.954376i	$-0.596523\pi$
$709$	−15.9021	−0.597217	−0.298609	+	0.954376i	$0.596523\pi$
$710$	4.11149	0.154302
$711$	−41.9143	−1.57191
$712$	−10.3092	−0.386353
$713$	23.1172	0.865745
$714$	6.77429	0.253521
$715$	4.80797	0.179808
$716$	−16.8053	−0.628044
$717$	−67.8884	−2.53534
$718$	0.845620	0.0315582
$719$	−45.2838	−1.68880	−0.844401	−	0.535712i	$-0.820043\pi$
$719$	−45.2838	−1.68880	−0.844401	+	0.535712i	$0.820043\pi$
$720$	−6.02333	−0.224476
$721$	−6.36522	−0.237053
$722$	−17.2042	−0.640274
$723$	11.7679	0.437653
$724$	5.69061	0.211490
$725$	7.71371	0.286480
$726$	−25.3562	−0.941056
$727$	17.7643	0.658843	0.329421	−	0.944183i	$-0.393146\pi$
$727$	17.7643	0.658843	0.329421	+	0.944183i	$0.393146\pi$
$728$	3.66657	0.135892
$729$	−26.3634	−0.976423
$730$	16.0806	0.595171
$731$	20.0630	0.742055
$732$	21.2047	0.783749
$733$	14.1969	0.524376	0.262188	−	0.965017i	$-0.415556\pi$
$733$	14.1969	0.524376	0.262188	+	0.965017i	$0.415556\pi$
$734$	27.2095	1.00432
$735$	16.5570	0.610714
$736$	5.95325	0.219440
$737$	12.4205	0.457515
$738$	47.9432	1.76481
$739$	−18.6226	−0.685042	−0.342521	−	0.939510i	$-0.611281\pi$
$739$	−18.6226	−0.685042	−0.342521	+	0.939510i	$0.611281\pi$
$740$	−2.28307	−0.0839273
$741$	−12.0990	−0.444469
$742$	−15.4054	−0.565552
$743$	25.8140	0.947022	0.473511	−	0.880788i	$-0.342986\pi$
$743$	25.8140	0.947022	0.473511	+	0.880788i	$0.342986\pi$
$744$	11.6644	0.427639
$745$	20.5109	0.751461
$746$	−9.66514	−0.353866
$747$	−6.71230	−0.245590
$748$	−2.95721	−0.108126
$749$	−19.4332	−0.710074
$750$	−3.00389	−0.109686
$751$	−1.33024	−0.0485411	−0.0242706	−	0.999705i	$-0.507726\pi$
$751$	−1.33024	−0.0485411	−0.0242706	+	0.999705i	$0.507726\pi$
$752$	9.85130	0.359240
$753$	13.7877	0.502451
$754$	−23.1846	−0.844335
$755$	17.2501	0.627797
$756$	−11.0788	−0.402931
$757$	−31.0961	−1.13021	−0.565103	−	0.825020i	$-0.691164\pi$
$757$	−31.0961	−1.13021	−0.565103	+	0.825020i	$0.691164\pi$
$758$	−14.3728	−0.522043
$759$	28.6063	1.03834
$760$	−1.34008	−0.0486097
$761$	4.51611	0.163709	0.0818544	−	0.996644i	$-0.473916\pi$
$761$	4.51611	0.163709	0.0818544	+	0.996644i	$0.473916\pi$
$762$	−61.7819	−2.23812
$763$	7.52630	0.272470
$764$	−15.8074	−0.571893
$765$	11.1351	0.402591
$766$	5.27028	0.190423
$767$	−14.2474	−0.514442
$768$	3.00389	0.108393
$769$	30.2556	1.09104	0.545522	−	0.838097i	$-0.316332\pi$
$769$	30.2556	1.09104	0.545522	+	0.838097i	$0.316332\pi$
$770$	1.95140	0.0703236
$771$	45.7238	1.64670
$772$	15.0906	0.543124
$773$	44.9619	1.61717	0.808583	−	0.588382i	$-0.200235\pi$
$773$	44.9619	1.61717	0.808583	+	0.588382i	$0.200235\pi$
$774$	−65.3693	−2.34965
$775$	3.88312	0.139486
$776$	−8.73328	−0.313506
$777$	−8.36613	−0.300133
$778$	29.4368	1.05536
$779$	10.6664	0.382165
$780$	9.02861	0.323276
$781$	−6.57694	−0.235341
$782$	−11.0056	−0.393558
$783$	70.0540	2.50353
$784$	−5.51186	−0.196852
$785$	−18.6296	−0.664918
$786$	−54.7591	−1.95319
$787$	25.8919	0.922947	0.461474	−	0.887154i	$-0.347321\pi$
$787$	25.8919	0.922947	0.461474	+	0.887154i	$0.347321\pi$
$788$	14.1991	0.505823
$789$	0.319383	0.0113703
$790$	6.95866	0.247578
$791$	13.4843	0.479445
$792$	9.63521	0.342372
$793$	−21.2171	−0.753441
$794$	−19.5966	−0.695456
$795$	−37.9346	−1.34540
$796$	21.4201	0.759214
$797$	−5.24972	−0.185955	−0.0929774	−	0.995668i	$-0.529638\pi$
$797$	−5.24972	−0.185955	−0.0929774	+	0.995668i	$0.529638\pi$
$798$	−4.91061	−0.173834
$799$	−18.2117	−0.644285
$800$	1.00000	0.0353553
$801$	−62.0957	−2.19404
$802$	−1.00000	−0.0353112
$803$	−25.7233	−0.907757
$804$	23.3238	0.822566
$805$	7.26233	0.255964
$806$	−11.6713	−0.411103
$807$	35.8649	1.26251
$808$	−7.77922	−0.273672
$809$	20.2633	0.712420	0.356210	−	0.934406i	$-0.384069\pi$
$809$	20.2633	0.712420	0.356210	+	0.934406i	$0.384069\pi$
$810$	−9.21056	−0.323626
$811$	0.213850	0.00750929	0.00375464	−	0.999993i	$-0.498805\pi$
$811$	0.213850	0.00750929	0.00375464	+	0.999993i	$0.498805\pi$
$812$	−9.40991	−0.330223
$813$	41.4461	1.45358
$814$	3.65211	0.128006
$815$	−18.4813	−0.647371
$816$	−5.55318	−0.194400
$817$	−14.5434	−0.508810
$818$	−28.3085	−0.989782
$819$	22.0850	0.771711
$820$	−7.95958	−0.277960
$821$	15.9607	0.557033	0.278517	−	0.960431i	$-0.410157\pi$
$821$	15.9607	0.557033	0.278517	+	0.960431i	$0.410157\pi$
$822$	29.0823	1.01436
$823$	23.3668	0.814516	0.407258	−	0.913313i	$-0.366485\pi$
$823$	23.3668	0.814516	0.407258	+	0.913313i	$0.366485\pi$
$824$	5.21784	0.181772
$825$	4.80516	0.167294
$826$	−5.78255	−0.201201
$827$	−12.0667	−0.419602	−0.209801	−	0.977744i	$-0.567282\pi$
$827$	−12.0667	−0.419602	−0.209801	+	0.977744i	$0.567282\pi$
$828$	35.8584	1.24617
$829$	−39.7569	−1.38081	−0.690406	−	0.723422i	$-0.742568\pi$
$829$	−39.7569	−1.38081	−0.690406	+	0.723422i	$0.742568\pi$
$830$	1.11438	0.0386808
$831$	30.7294	1.06599
$832$	−3.00564	−0.104202
$833$	10.1896	0.353048
$834$	−55.8414	−1.93363
$835$	13.4290	0.464730
$836$	2.14365	0.0741397
$837$	35.2655	1.21896
$838$	−10.1526	−0.350717
$839$	−26.4358	−0.912664	−0.456332	−	0.889809i	$-0.650837\pi$
$839$	−26.4358	−0.912664	−0.456332	+	0.889809i	$0.650837\pi$
$840$	3.66442	0.126435
$841$	30.5013	1.05177
$842$	31.9438	1.10086
$843$	6.71552	0.231295
$844$	20.6394	0.710436
$845$	3.96612	0.136439
$846$	59.3377	2.04007
$847$	10.2973	0.353819
$848$	12.6285	0.433665
$849$	−55.3916	−1.90103
$850$	−1.84866	−0.0634087
$851$	13.5917	0.465917
$852$	−12.3505	−0.423120
$853$	−15.0463	−0.515174	−0.257587	−	0.966255i	$-0.582927\pi$
$853$	−15.0463	−0.515174	−0.257587	+	0.966255i	$0.582927\pi$
$854$	−8.61135	−0.294674
$855$	−8.07173	−0.276047
$856$	15.9302	0.544484
$857$	15.2407	0.520611	0.260306	−	0.965526i	$-0.416177\pi$
$857$	15.2407	0.520611	0.260306	+	0.965526i	$0.416177\pi$
$858$	−14.4426	−0.493062
$859$	−45.2319	−1.54329	−0.771645	−	0.636053i	$-0.780566\pi$
$859$	−45.2319	−1.54329	−0.771645	+	0.636053i	$0.780566\pi$
$860$	10.8527	0.370073
$861$	−29.1673	−0.994018
$862$	31.5054	1.07308
$863$	55.4620	1.88795	0.943974	−	0.330020i	$-0.107056\pi$
$863$	55.4620	1.88795	0.943974	+	0.330020i	$0.107056\pi$
$864$	9.08175	0.308968
$865$	19.9690	0.678966
$866$	−12.5768	−0.427376
$867$	−40.8001	−1.38564
$868$	−4.73699	−0.160784
$869$	−11.1314	−0.377607
$870$	−23.1711	−0.785574
$871$	−23.3374	−0.790757
$872$	−6.16963	−0.208930
$873$	−52.6034	−1.78036
$874$	7.97781	0.269853
$875$	1.21989	0.0412400
$876$	−48.3044	−1.63205
$877$	−10.3560	−0.349697	−0.174849	−	0.984595i	$-0.555944\pi$
$877$	−10.3560	−0.349697	−0.174849	+	0.984595i	$0.555944\pi$
$878$	−4.28805	−0.144715
$879$	−1.02308	−0.0345078
$880$	−1.59965	−0.0539241
$881$	−27.6235	−0.930660	−0.465330	−	0.885137i	$-0.654064\pi$
$881$	−27.6235	−0.930660	−0.465330	+	0.885137i	$0.654064\pi$
$882$	−33.1998	−1.11789
$883$	−29.7846	−1.00233	−0.501166	−	0.865351i	$-0.667095\pi$
$883$	−29.7846	−1.00233	−0.501166	+	0.865351i	$0.667095\pi$
$884$	5.55642	0.186883
$885$	−14.2390	−0.478640
$886$	24.9377	0.837797
$887$	−25.4775	−0.855449	−0.427725	−	0.903909i	$-0.640685\pi$
$887$	−25.4775	−0.855449	−0.427725	+	0.903909i	$0.640685\pi$
$888$	6.85808	0.230142
$889$	25.0900	0.841491
$890$	10.3092	0.345565
$891$	14.7336	0.493596
$892$	29.5140	0.988203
$893$	13.2015	0.441771
$894$	−61.6124	−2.06063
$895$	16.8053	0.561739
$896$	−1.21989	−0.0407538
$897$	−53.7495	−1.79464
$898$	14.1902	0.473534
$899$	29.9532	0.998996
$900$	6.02333	0.200778
$901$	−23.3459	−0.777764
$902$	12.7325	0.423946
$903$	39.7688	1.32342
$904$	−11.0536	−0.367638
$905$	−5.69061	−0.189162
$906$	−51.8174	−1.72152
$907$	−23.1441	−0.768487	−0.384244	−	0.923232i	$-0.625538\pi$
$907$	−23.1441	−0.768487	−0.384244	+	0.923232i	$0.625538\pi$
$908$	18.7839	0.623366
$909$	−46.8568	−1.55414
$910$	−3.66657	−0.121545
$911$	−38.8591	−1.28746	−0.643730	−	0.765253i	$-0.722614\pi$
$911$	−38.8591	−1.28746	−0.643730	+	0.765253i	$0.722614\pi$
$912$	4.02544	0.133296
$913$	−1.78262	−0.0589961
$914$	−5.83494	−0.193002
$915$	−21.2047	−0.701006
$916$	−14.1578	−0.467787
$917$	22.2380	0.734363
$918$	−16.7891	−0.554123
$919$	−13.3116	−0.439109	−0.219554	−	0.975600i	$-0.570460\pi$
$919$	−13.3116	−0.439109	−0.219554	+	0.975600i	$0.570460\pi$
$920$	−5.95325	−0.196273
$921$	−41.4363	−1.36537
$922$	−21.2093	−0.698491
$923$	12.3577	0.406758
$924$	−5.86179	−0.192839
$925$	2.28307	0.0750669
$926$	−14.1355	−0.464523
$927$	31.4288	1.03226
$928$	7.71371	0.253215
$929$	37.7792	1.23949	0.619747	−	0.784801i	$-0.287235\pi$
$929$	37.7792	1.23949	0.619747	+	0.784801i	$0.287235\pi$
$930$	−11.6644	−0.382492
$931$	−7.38631	−0.242077
$932$	−18.1788	−0.595466
$933$	−19.6687	−0.643925
$934$	−27.9822	−0.915606
$935$	2.95721	0.0967111
$936$	−18.1040	−0.591747
$937$	−2.19197	−0.0716085	−0.0358043	−	0.999359i	$-0.511399\pi$
$937$	−2.19197	−0.0716085	−0.0358043	+	0.999359i	$0.511399\pi$
$938$	−9.47190	−0.309269
$939$	46.7191	1.52462
$940$	−9.85130	−0.321314
$941$	12.5473	0.409029	0.204514	−	0.978864i	$-0.434438\pi$
$941$	12.5473	0.409029	0.204514	+	0.978864i	$0.434438\pi$
$942$	55.9612	1.82331
$943$	47.3853	1.54308
$944$	4.74021	0.154281
$945$	11.0788	0.360393
$946$	−17.3605	−0.564437
$947$	−38.6776	−1.25685	−0.628426	−	0.777869i	$-0.716300\pi$
$947$	−38.6776	−1.25685	−0.628426	+	0.777869i	$0.716300\pi$
$948$	−20.9030	−0.678899
$949$	48.3326	1.56894
$950$	1.34008	0.0434778
$951$	−49.7856	−1.61441
$952$	2.25518	0.0730906
$953$	40.8939	1.32468	0.662342	−	0.749202i	$-0.269563\pi$
$953$	40.8939	1.32468	0.662342	+	0.749202i	$0.269563\pi$
$954$	76.0657	2.46272
$955$	15.8074	0.511517
$956$	−22.6002	−0.730942
$957$	37.0656	1.19816
$958$	14.9356	0.482548
$959$	−11.8105	−0.381381
$960$	−3.00389	−0.0969500
$961$	−15.9214	−0.513593
$962$	−6.86209	−0.221243
$963$	95.9531	3.09205
$964$	3.91756	0.126176
$965$	−15.0906	−0.485785
$966$	−21.8152	−0.701893
$967$	−26.6591	−0.857300	−0.428650	−	0.903471i	$-0.641011\pi$
$967$	−26.6591	−0.857300	−0.428650	+	0.903471i	$0.641011\pi$
$968$	−8.44113	−0.271308
$969$	−7.44169	−0.239061
$970$	8.73328	0.280409
$971$	−47.3319	−1.51895	−0.759477	−	0.650534i	$-0.774545\pi$
$971$	−47.3319	−1.51895	−0.759477	+	0.650534i	$0.774545\pi$
$972$	0.422206	0.0135423
$973$	22.6775	0.727007
$974$	2.23478	0.0716069
$975$	−9.02861	−0.289147
$976$	7.05909	0.225956
$977$	37.7553	1.20790	0.603950	−	0.797022i	$-0.293593\pi$
$977$	37.7553	1.20790	0.603950	+	0.797022i	$0.293593\pi$
$978$	55.5157	1.77520
$979$	−16.4911	−0.527057
$980$	5.51186	0.176070
$981$	−37.1617	−1.18648
$982$	38.9067	1.24156
$983$	6.56546	0.209406	0.104703	−	0.994504i	$-0.466611\pi$
$983$	6.56546	0.209406	0.104703	+	0.994504i	$0.466611\pi$
$984$	23.9097	0.762212
$985$	−14.1991	−0.452422
$986$	−14.2601	−0.454133
$987$	−36.0994	−1.14906
$988$	−4.02779	−0.128141
$989$	−64.6087	−2.05444
$990$	−9.63521	−0.306227
$991$	−16.4217	−0.521653	−0.260827	−	0.965386i	$-0.583995\pi$
$991$	−16.4217	−0.521653	−0.260827	+	0.965386i	$0.583995\pi$
$992$	3.88312	0.123289
$993$	−65.8216	−2.08879
$994$	5.01559	0.159085
$995$	−21.4201	−0.679061
$996$	−3.34748	−0.106069
$997$	11.1292	0.352466	0.176233	−	0.984348i	$-0.443609\pi$
$997$	11.1292	0.352466	0.176233	+	0.984348i	$0.443609\pi$
$998$	12.9992	0.411482
$999$	20.7343	0.656003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.o.1.20	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.o.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.00389 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.00389 q^{6} -1.21989 q^{7} +1.00000 q^{8} +6.02333 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.00389 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.00389 q^{6} -1.21989 q^{7} +1.00000 q^{8} +6.02333 q^{9} -1.00000 q^{10} +1.59965 q^{11} +3.00389 q^{12} -3.00564 q^{13} -1.21989 q^{14} -3.00389 q^{15} +1.00000 q^{16} -1.84866 q^{17} +6.02333 q^{18} +1.34008 q^{19} -1.00000 q^{20} -3.66442 q^{21} +1.59965 q^{22} +5.95325 q^{23} +3.00389 q^{24} +1.00000 q^{25} -3.00564 q^{26} +9.08175 q^{27} -1.21989 q^{28} +7.71371 q^{29} -3.00389 q^{30} +3.88312 q^{31} +1.00000 q^{32} +4.80516 q^{33} -1.84866 q^{34} +1.21989 q^{35} +6.02333 q^{36} +2.28307 q^{37} +1.34008 q^{38} -9.02861 q^{39} -1.00000 q^{40} +7.95958 q^{41} -3.66442 q^{42} -10.8527 q^{43} +1.59965 q^{44} -6.02333 q^{45} +5.95325 q^{46} +9.85130 q^{47} +3.00389 q^{48} -5.51186 q^{49} +1.00000 q^{50} -5.55318 q^{51} -3.00564 q^{52} +12.6285 q^{53} +9.08175 q^{54} -1.59965 q^{55} -1.21989 q^{56} +4.02544 q^{57} +7.71371 q^{58} +4.74021 q^{59} -3.00389 q^{60} +7.05909 q^{61} +3.88312 q^{62} -7.34783 q^{63} +1.00000 q^{64} +3.00564 q^{65} +4.80516 q^{66} +7.76453 q^{67} -1.84866 q^{68} +17.8829 q^{69} +1.21989 q^{70} -4.11149 q^{71} +6.02333 q^{72} -16.0806 q^{73} +2.28307 q^{74} +3.00389 q^{75} +1.34008 q^{76} -1.95140 q^{77} -9.02861 q^{78} -6.95866 q^{79} -1.00000 q^{80} +9.21056 q^{81} +7.95958 q^{82} -1.11438 q^{83} -3.66442 q^{84} +1.84866 q^{85} -10.8527 q^{86} +23.1711 q^{87} +1.59965 q^{88} -10.3092 q^{89} -6.02333 q^{90} +3.66657 q^{91} +5.95325 q^{92} +11.6644 q^{93} +9.85130 q^{94} -1.34008 q^{95} +3.00389 q^{96} -8.73328 q^{97} -5.51186 q^{98} +9.63521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - q^99

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