LMFDB - Embedded newform 4010.2.a.n.1.15

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			1.15
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.38303 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.38303 q^{6} +3.80913 q^{7} +1.00000 q^{8} -1.08722 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.38303 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.38303 q^{6} +3.80913 q^{7} +1.00000 q^{8} -1.08722 q^{9} +1.00000 q^{10} +4.83406 q^{11} +1.38303 q^{12} +2.94727 q^{13} +3.80913 q^{14} +1.38303 q^{15} +1.00000 q^{16} -1.01937 q^{17} -1.08722 q^{18} -0.201637 q^{19} +1.00000 q^{20} +5.26815 q^{21} +4.83406 q^{22} -3.04202 q^{23} +1.38303 q^{24} +1.00000 q^{25} +2.94727 q^{26} -5.65276 q^{27} +3.80913 q^{28} +6.21607 q^{29} +1.38303 q^{30} -3.17340 q^{31} +1.00000 q^{32} +6.68566 q^{33} -1.01937 q^{34} +3.80913 q^{35} -1.08722 q^{36} -2.22794 q^{37} -0.201637 q^{38} +4.07617 q^{39} +1.00000 q^{40} -7.65712 q^{41} +5.26815 q^{42} -0.0875362 q^{43} +4.83406 q^{44} -1.08722 q^{45} -3.04202 q^{46} -4.17899 q^{47} +1.38303 q^{48} +7.50947 q^{49} +1.00000 q^{50} -1.40982 q^{51} +2.94727 q^{52} -4.55795 q^{53} -5.65276 q^{54} +4.83406 q^{55} +3.80913 q^{56} -0.278871 q^{57} +6.21607 q^{58} -4.45161 q^{59} +1.38303 q^{60} -4.77645 q^{61} -3.17340 q^{62} -4.14136 q^{63} +1.00000 q^{64} +2.94727 q^{65} +6.68566 q^{66} +5.20804 q^{67} -1.01937 q^{68} -4.20721 q^{69} +3.80913 q^{70} +1.60125 q^{71} -1.08722 q^{72} -7.86753 q^{73} -2.22794 q^{74} +1.38303 q^{75} -0.201637 q^{76} +18.4135 q^{77} +4.07617 q^{78} +6.02174 q^{79} +1.00000 q^{80} -4.55630 q^{81} -7.65712 q^{82} -3.93000 q^{83} +5.26815 q^{84} -1.01937 q^{85} -0.0875362 q^{86} +8.59703 q^{87} +4.83406 q^{88} +5.94071 q^{89} -1.08722 q^{90} +11.2265 q^{91} -3.04202 q^{92} -4.38892 q^{93} -4.17899 q^{94} -0.201637 q^{95} +1.38303 q^{96} -7.88048 q^{97} +7.50947 q^{98} -5.25568 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.38303	0.798495	0.399247	−	0.916843i	$-0.369271\pi$
$3$	1.38303	0.798495	0.399247	+	0.916843i	$0.369271\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.38303	0.564621
$7$	3.80913	1.43972	0.719858	−	0.694121i	$-0.244207\pi$
$7$	3.80913	1.43972	0.719858	+	0.694121i	$0.244207\pi$
$8$	1.00000	0.353553
$9$	−1.08722	−0.362406
$10$	1.00000	0.316228
$11$	4.83406	1.45752	0.728761	−	0.684768i	$-0.240096\pi$
$11$	4.83406	1.45752	0.728761	+	0.684768i	$0.240096\pi$
$12$	1.38303	0.399247
$13$	2.94727	0.817426	0.408713	−	0.912663i	$-0.365978\pi$
$13$	2.94727	0.817426	0.408713	+	0.912663i	$0.365978\pi$
$14$	3.80913	1.01803
$15$	1.38303	0.357098
$16$	1.00000	0.250000
$17$	−1.01937	−0.247234	−0.123617	−	0.992330i	$-0.539449\pi$
$17$	−1.01937	−0.247234	−0.123617	+	0.992330i	$0.539449\pi$
$18$	−1.08722	−0.256260
$19$	−0.201637	−0.0462587	−0.0231294	−	0.999732i	$-0.507363\pi$
$19$	−0.201637	−0.0462587	−0.0231294	+	0.999732i	$0.507363\pi$
$20$	1.00000	0.223607
$21$	5.26815	1.14961
$22$	4.83406	1.03062
$23$	−3.04202	−0.634305	−0.317152	−	0.948375i	$-0.602727\pi$
$23$	−3.04202	−0.634305	−0.317152	+	0.948375i	$0.602727\pi$
$24$	1.38303	0.282310
$25$	1.00000	0.200000
$26$	2.94727	0.578007
$27$	−5.65276	−1.08787
$28$	3.80913	0.719858
$29$	6.21607	1.15430	0.577148	−	0.816640i	$-0.304166\pi$
$29$	6.21607	1.15430	0.577148	+	0.816640i	$0.304166\pi$
$30$	1.38303	0.252506
$31$	−3.17340	−0.569960	−0.284980	−	0.958533i	$-0.591987\pi$
$31$	−3.17340	−0.569960	−0.284980	+	0.958533i	$0.591987\pi$
$32$	1.00000	0.176777
$33$	6.68566	1.16382
$34$	−1.01937	−0.174820
$35$	3.80913	0.643860
$36$	−1.08722	−0.181203
$37$	−2.22794	−0.366271	−0.183135	−	0.983088i	$-0.558625\pi$
$37$	−2.22794	−0.366271	−0.183135	+	0.983088i	$0.558625\pi$
$38$	−0.201637	−0.0327099
$39$	4.07617	0.652710
$40$	1.00000	0.158114
$41$	−7.65712	−1.19584	−0.597920	−	0.801556i	$-0.704006\pi$
$41$	−7.65712	−1.19584	−0.597920	+	0.801556i	$0.704006\pi$
$42$	5.26815	0.812894
$43$	−0.0875362	−0.0133491	−0.00667457	−	0.999978i	$-0.502125\pi$
$43$	−0.0875362	−0.0133491	−0.00667457	+	0.999978i	$0.502125\pi$
$44$	4.83406	0.728761
$45$	−1.08722	−0.162073
$46$	−3.04202	−0.448521
$47$	−4.17899	−0.609568	−0.304784	−	0.952421i	$-0.598584\pi$
$47$	−4.17899	−0.609568	−0.304784	+	0.952421i	$0.598584\pi$
$48$	1.38303	0.199624
$49$	7.50947	1.07278
$50$	1.00000	0.141421
$51$	−1.40982	−0.197415
$52$	2.94727	0.408713
$53$	−4.55795	−0.626082	−0.313041	−	0.949740i	$-0.601348\pi$
$53$	−4.55795	−0.626082	−0.313041	+	0.949740i	$0.601348\pi$
$54$	−5.65276	−0.769243
$55$	4.83406	0.651824
$56$	3.80913	0.509016
$57$	−0.278871	−0.0369373
$58$	6.21607	0.816210
$59$	−4.45161	−0.579551	−0.289775	−	0.957095i	$-0.593581\pi$
$59$	−4.45161	−0.579551	−0.289775	+	0.957095i	$0.593581\pi$
$60$	1.38303	0.178549
$61$	−4.77645	−0.611562	−0.305781	−	0.952102i	$-0.598918\pi$
$61$	−4.77645	−0.611562	−0.305781	+	0.952102i	$0.598918\pi$
$62$	−3.17340	−0.403023
$63$	−4.14136	−0.521762
$64$	1.00000	0.125000
$65$	2.94727	0.365564
$66$	6.68566	0.822948
$67$	5.20804	0.636263	0.318131	−	0.948047i	$-0.396945\pi$
$67$	5.20804	0.636263	0.318131	+	0.948047i	$0.396945\pi$
$68$	−1.01937	−0.123617
$69$	−4.20721	−0.506489
$70$	3.80913	0.455278
$71$	1.60125	0.190033	0.0950165	−	0.995476i	$-0.469710\pi$
$71$	1.60125	0.190033	0.0950165	+	0.995476i	$0.469710\pi$
$72$	−1.08722	−0.128130
$73$	−7.86753	−0.920825	−0.460412	−	0.887705i	$-0.652298\pi$
$73$	−7.86753	−0.920825	−0.460412	+	0.887705i	$0.652298\pi$
$74$	−2.22794	−0.258993
$75$	1.38303	0.159699
$76$	−0.201637	−0.0231294
$77$	18.4135	2.09842
$78$	4.07617	0.461536
$79$	6.02174	0.677499	0.338749	−	0.940877i	$-0.389996\pi$
$79$	6.02174	0.677499	0.338749	+	0.940877i	$0.389996\pi$
$80$	1.00000	0.111803
$81$	−4.55630	−0.506255
$82$	−7.65712	−0.845587
$83$	−3.93000	−0.431374	−0.215687	−	0.976463i	$-0.569199\pi$
$83$	−3.93000	−0.431374	−0.215687	+	0.976463i	$0.569199\pi$
$84$	5.26815	0.574803
$85$	−1.01937	−0.110566
$86$	−0.0875362	−0.00943927
$87$	8.59703	0.921698
$88$	4.83406	0.515312
$89$	5.94071	0.629714	0.314857	−	0.949139i	$-0.398044\pi$
$89$	5.94071	0.629714	0.314857	+	0.949139i	$0.398044\pi$
$90$	−1.08722	−0.114603
$91$	11.2265	1.17686
$92$	−3.04202	−0.317152
$93$	−4.38892	−0.455110
$94$	−4.17899	−0.431030
$95$	−0.201637	−0.0206875
$96$	1.38303	0.141155
$97$	−7.88048	−0.800142	−0.400071	−	0.916484i	$-0.631015\pi$
$97$	−7.88048	−0.800142	−0.400071	+	0.916484i	$0.631015\pi$
$98$	7.50947	0.758571
$99$	−5.25568	−0.528215
$100$	1.00000	0.100000
$101$	−17.0937	−1.70089	−0.850443	−	0.526068i	$-0.823666\pi$
$101$	−17.0937	−1.70089	−0.850443	+	0.526068i	$0.823666\pi$
$102$	−1.40982	−0.139593
$103$	−20.0060	−1.97125	−0.985625	−	0.168948i	$-0.945963\pi$
$103$	−20.0060	−1.97125	−0.985625	+	0.168948i	$0.945963\pi$
$104$	2.94727	0.289004
$105$	5.26815	0.514119
$106$	−4.55795	−0.442707
$107$	11.4969	1.11145	0.555723	−	0.831368i	$-0.312442\pi$
$107$	11.4969	1.11145	0.555723	+	0.831368i	$0.312442\pi$
$108$	−5.65276	−0.543937
$109$	14.8135	1.41888	0.709439	−	0.704767i	$-0.248948\pi$
$109$	14.8135	1.41888	0.709439	+	0.704767i	$0.248948\pi$
$110$	4.83406	0.460909
$111$	−3.08131	−0.292465
$112$	3.80913	0.359929
$113$	−5.52582	−0.519825	−0.259913	−	0.965632i	$-0.583694\pi$
$113$	−5.52582	−0.519825	−0.259913	+	0.965632i	$0.583694\pi$
$114$	−0.278871	−0.0261186
$115$	−3.04202	−0.283670
$116$	6.21607	0.577148
$117$	−3.20433	−0.296240
$118$	−4.45161	−0.409804
$119$	−3.88291	−0.355946
$120$	1.38303	0.126253
$121$	12.3681	1.12437
$122$	−4.77645	−0.432440
$123$	−10.5900	−0.954872
$124$	−3.17340	−0.284980
$125$	1.00000	0.0894427
$126$	−4.14136	−0.368942
$127$	12.3399	1.09499	0.547493	−	0.836810i	$-0.315582\pi$
$127$	12.3399	1.09499	0.547493	+	0.836810i	$0.315582\pi$
$128$	1.00000	0.0883883
$129$	−0.121066	−0.0106592
$130$	2.94727	0.258493
$131$	−3.37769	−0.295111	−0.147555	−	0.989054i	$-0.547140\pi$
$131$	−3.37769	−0.295111	−0.147555	+	0.989054i	$0.547140\pi$
$132$	6.68566	0.581912
$133$	−0.768062	−0.0665994
$134$	5.20804	0.449906
$135$	−5.65276	−0.486512
$136$	−1.01937	−0.0874102
$137$	3.70041	0.316147	0.158073	−	0.987427i	$-0.449472\pi$
$137$	3.70041	0.316147	0.158073	+	0.987427i	$0.449472\pi$
$138$	−4.20721	−0.358142
$139$	5.50696	0.467094	0.233547	−	0.972345i	$-0.424967\pi$
$139$	5.50696	0.467094	0.233547	+	0.972345i	$0.424967\pi$
$140$	3.80913	0.321930
$141$	−5.77968	−0.486737
$142$	1.60125	0.134374
$143$	14.2473	1.19142
$144$	−1.08722	−0.0906016
$145$	6.21607	0.516216
$146$	−7.86753	−0.651121
$147$	10.3858	0.856610
$148$	−2.22794	−0.183135
$149$	1.32527	0.108570	0.0542851	−	0.998525i	$-0.482712\pi$
$149$	1.32527	0.108570	0.0542851	+	0.998525i	$0.482712\pi$
$150$	1.38303	0.112924
$151$	−19.9193	−1.62101	−0.810505	−	0.585732i	$-0.800807\pi$
$151$	−19.9193	−1.62101	−0.810505	+	0.585732i	$0.800807\pi$
$152$	−0.201637	−0.0163549
$153$	1.10828	0.0895990
$154$	18.4135	1.48381
$155$	−3.17340	−0.254894
$156$	4.07617	0.326355
$157$	5.19122	0.414304	0.207152	−	0.978309i	$-0.433581\pi$
$157$	5.19122	0.414304	0.207152	+	0.978309i	$0.433581\pi$
$158$	6.02174	0.479064
$159$	−6.30379	−0.499923
$160$	1.00000	0.0790569
$161$	−11.5874	−0.913219
$162$	−4.55630	−0.357977
$163$	17.8781	1.40032	0.700160	−	0.713986i	$-0.253112\pi$
$163$	17.8781	1.40032	0.700160	+	0.713986i	$0.253112\pi$
$164$	−7.65712	−0.597920
$165$	6.68566	0.520478
$166$	−3.93000	−0.305027
$167$	12.8572	0.994921	0.497461	−	0.867487i	$-0.334266\pi$
$167$	12.8572	0.994921	0.497461	+	0.867487i	$0.334266\pi$
$168$	5.26815	0.406447
$169$	−4.31359	−0.331815
$170$	−1.01937	−0.0781821
$171$	0.219224	0.0167645
$172$	−0.0875362	−0.00667457
$173$	−12.9695	−0.986056	−0.493028	−	0.870013i	$-0.664110\pi$
$173$	−12.9695	−0.986056	−0.493028	+	0.870013i	$0.664110\pi$
$174$	8.59703	0.651739
$175$	3.80913	0.287943
$176$	4.83406	0.364381
$177$	−6.15673	−0.462768
$178$	5.94071	0.445275
$179$	−0.720213	−0.0538312	−0.0269156	−	0.999638i	$-0.508569\pi$
$179$	−0.720213	−0.0538312	−0.0269156	+	0.999638i	$0.508569\pi$
$180$	−1.08722	−0.0810365
$181$	2.58041	0.191800	0.0959001	−	0.995391i	$-0.469427\pi$
$181$	2.58041	0.191800	0.0959001	+	0.995391i	$0.469427\pi$
$182$	11.2265	0.832166
$183$	−6.60599	−0.488329
$184$	−3.04202	−0.224261
$185$	−2.22794	−0.163801
$186$	−4.38892	−0.321811
$187$	−4.92769	−0.360348
$188$	−4.17899	−0.304784
$189$	−21.5321	−1.56623
$190$	−0.201637	−0.0146283
$191$	12.2337	0.885202	0.442601	−	0.896719i	$-0.354056\pi$
$191$	12.2337	0.885202	0.442601	+	0.896719i	$0.354056\pi$
$192$	1.38303	0.0998118
$193$	−0.976078	−0.0702596	−0.0351298	−	0.999383i	$-0.511184\pi$
$193$	−0.976078	−0.0702596	−0.0351298	+	0.999383i	$0.511184\pi$
$194$	−7.88048	−0.565786
$195$	4.07617	0.291901
$196$	7.50947	0.536391
$197$	13.9489	0.993817	0.496909	−	0.867803i	$-0.334468\pi$
$197$	13.9489	0.993817	0.496909	+	0.867803i	$0.334468\pi$
$198$	−5.25568	−0.373505
$199$	6.24894	0.442976	0.221488	−	0.975163i	$-0.428909\pi$
$199$	6.24894	0.442976	0.221488	+	0.975163i	$0.428909\pi$
$200$	1.00000	0.0707107
$201$	7.20289	0.508053
$202$	−17.0937	−1.20271
$203$	23.6778	1.66186
$204$	−1.40982	−0.0987073
$205$	−7.65712	−0.534796
$206$	−20.0060	−1.39388
$207$	3.30734	0.229876
$208$	2.94727	0.204356
$209$	−0.974725	−0.0674231
$210$	5.26815	0.363537
$211$	16.2075	1.11577	0.557885	−	0.829919i	$-0.311613\pi$
$211$	16.2075	1.11577	0.557885	+	0.829919i	$0.311613\pi$
$212$	−4.55795	−0.313041
$213$	2.21458	0.151740
$214$	11.4969	0.785911
$215$	−0.0875362	−0.00596992
$216$	−5.65276	−0.384622
$217$	−12.0879	−0.820581
$218$	14.8135	1.00330
$219$	−10.8811	−0.735274
$220$	4.83406	0.325912
$221$	−3.00436	−0.202095
$222$	−3.08131	−0.206804
$223$	−2.85254	−0.191020	−0.0955101	−	0.995428i	$-0.530448\pi$
$223$	−2.85254	−0.191020	−0.0955101	+	0.995428i	$0.530448\pi$
$224$	3.80913	0.254508
$225$	−1.08722	−0.0724813
$226$	−5.52582	−0.367572
$227$	12.9298	0.858183	0.429091	−	0.903261i	$-0.358834\pi$
$227$	12.9298	0.858183	0.429091	+	0.903261i	$0.358834\pi$
$228$	−0.278871	−0.0184687
$229$	−12.1221	−0.801052	−0.400526	−	0.916285i	$-0.631173\pi$
$229$	−12.1221	−0.801052	−0.400526	+	0.916285i	$0.631173\pi$
$230$	−3.04202	−0.200585
$231$	25.4665	1.67558
$232$	6.21607	0.408105
$233$	−1.07877	−0.0706724	−0.0353362	−	0.999375i	$-0.511250\pi$
$233$	−1.07877	−0.0706724	−0.0353362	+	0.999375i	$0.511250\pi$
$234$	−3.20433	−0.209474
$235$	−4.17899	−0.272607
$236$	−4.45161	−0.289775
$237$	8.32826	0.540979
$238$	−3.88291	−0.251692
$239$	−11.4892	−0.743176	−0.371588	−	0.928398i	$-0.621187\pi$
$239$	−11.4892	−0.743176	−0.371588	+	0.928398i	$0.621187\pi$
$240$	1.38303	0.0892744
$241$	4.38725	0.282607	0.141304	−	0.989966i	$-0.454871\pi$
$241$	4.38725	0.282607	0.141304	+	0.989966i	$0.454871\pi$
$242$	12.3681	0.795051
$243$	10.6568	0.683632
$244$	−4.77645	−0.305781
$245$	7.50947	0.479763
$246$	−10.5900	−0.675197
$247$	−0.594279	−0.0378131
$248$	−3.17340	−0.201511
$249$	−5.43533	−0.344450
$250$	1.00000	0.0632456
$251$	−1.12866	−0.0712401	−0.0356201	−	0.999365i	$-0.511341\pi$
$251$	−1.12866	−0.0712401	−0.0356201	+	0.999365i	$0.511341\pi$
$252$	−4.14136	−0.260881
$253$	−14.7053	−0.924514
$254$	12.3399	0.774272
$255$	−1.40982	−0.0882865
$256$	1.00000	0.0625000
$257$	−7.52265	−0.469250	−0.234625	−	0.972086i	$-0.575386\pi$
$257$	−7.52265	−0.469250	−0.234625	+	0.972086i	$0.575386\pi$
$258$	−0.121066	−0.00753721
$259$	−8.48651	−0.527326
$260$	2.94727	0.182782
$261$	−6.75823	−0.418324
$262$	−3.37769	−0.208675
$263$	4.03116	0.248572	0.124286	−	0.992246i	$-0.460336\pi$
$263$	4.03116	0.248572	0.124286	+	0.992246i	$0.460336\pi$
$264$	6.68566	0.411474
$265$	−4.55795	−0.279992
$266$	−0.768062	−0.0470929
$267$	8.21619	0.502823
$268$	5.20804	0.318131
$269$	2.84563	0.173501	0.0867507	−	0.996230i	$-0.472352\pi$
$269$	2.84563	0.173501	0.0867507	+	0.996230i	$0.472352\pi$
$270$	−5.65276	−0.344016
$271$	13.9100	0.844971	0.422486	−	0.906370i	$-0.361158\pi$
$271$	13.9100	0.844971	0.422486	+	0.906370i	$0.361158\pi$
$272$	−1.01937	−0.0618084
$273$	15.5267	0.939717
$274$	3.70041	0.223550
$275$	4.83406	0.291504
$276$	−4.20721	−0.253245
$277$	5.62976	0.338259	0.169130	−	0.985594i	$-0.445904\pi$
$277$	5.62976	0.338259	0.169130	+	0.985594i	$0.445904\pi$
$278$	5.50696	0.330286
$279$	3.45019	0.206557
$280$	3.80913	0.227639
$281$	−7.06513	−0.421470	−0.210735	−	0.977543i	$-0.567586\pi$
$281$	−7.06513	−0.421470	−0.210735	+	0.977543i	$0.567586\pi$
$282$	−5.77968	−0.344175
$283$	5.83591	0.346909	0.173454	−	0.984842i	$-0.444507\pi$
$283$	5.83591	0.346909	0.173454	+	0.984842i	$0.444507\pi$
$284$	1.60125	0.0950165
$285$	−0.278871	−0.0165189
$286$	14.2473	0.842459
$287$	−29.1670	−1.72167
$288$	−1.08722	−0.0640650
$289$	−15.9609	−0.938876
$290$	6.21607	0.365020
$291$	−10.8990	−0.638909
$292$	−7.86753	−0.460412
$293$	−17.5372	−1.02453	−0.512267	−	0.858826i	$-0.671194\pi$
$293$	−17.5372	−1.02453	−0.512267	+	0.858826i	$0.671194\pi$
$294$	10.3858	0.605715
$295$	−4.45161	−0.259183
$296$	−2.22794	−0.129496
$297$	−27.3258	−1.58560
$298$	1.32527	0.0767708
$299$	−8.96566	−0.518497
$300$	1.38303	0.0798495
$301$	−0.333437	−0.0192190
$302$	−19.9193	−1.14623
$303$	−23.6411	−1.35815
$304$	−0.201637	−0.0115647
$305$	−4.77645	−0.273499
$306$	1.10828	0.0633561
$307$	27.6317	1.57702	0.788511	−	0.615021i	$-0.210852\pi$
$307$	27.6317	1.57702	0.788511	+	0.615021i	$0.210852\pi$
$308$	18.4135	1.04921
$309$	−27.6690	−1.57403
$310$	−3.17340	−0.180237
$311$	−26.6526	−1.51133	−0.755665	−	0.654958i	$-0.772686\pi$
$311$	−26.6526	−1.51133	−0.755665	+	0.654958i	$0.772686\pi$
$312$	4.07617	0.230768
$313$	−9.90655	−0.559951	−0.279976	−	0.960007i	$-0.590326\pi$
$313$	−9.90655	−0.559951	−0.279976	+	0.960007i	$0.590326\pi$
$314$	5.19122	0.292957
$315$	−4.14136	−0.233339
$316$	6.02174	0.338749
$317$	4.84944	0.272372	0.136186	−	0.990683i	$-0.456516\pi$
$317$	4.84944	0.272372	0.136186	+	0.990683i	$0.456516\pi$
$318$	−6.30379	−0.353499
$319$	30.0488	1.68241
$320$	1.00000	0.0559017
$321$	15.9006	0.887484
$322$	−11.5874	−0.645743
$323$	0.205543	0.0114367
$324$	−4.55630	−0.253128
$325$	2.94727	0.163485
$326$	17.8781	0.990175
$327$	20.4876	1.13297
$328$	−7.65712	−0.422794
$329$	−15.9183	−0.877605
$330$	6.68566	0.368033
$331$	26.2640	1.44360	0.721800	−	0.692102i	$-0.243315\pi$
$331$	26.2640	1.44360	0.721800	+	0.692102i	$0.243315\pi$
$332$	−3.93000	−0.215687
$333$	2.42226	0.132739
$334$	12.8572	0.703516
$335$	5.20804	0.284545
$336$	5.26815	0.287401
$337$	−0.213773	−0.0116450	−0.00582248	−	0.999983i	$-0.501853\pi$
$337$	−0.213773	−0.0116450	−0.00582248	+	0.999983i	$0.501853\pi$
$338$	−4.31359	−0.234629
$339$	−7.64239	−0.415078
$340$	−1.01937	−0.0552831
$341$	−15.3404	−0.830730
$342$	0.219224	0.0118543
$343$	1.94064	0.104785
$344$	−0.0875362	−0.00471964
$345$	−4.20721	−0.226509
$346$	−12.9695	−0.697247
$347$	−13.7466	−0.737957	−0.368978	−	0.929438i	$-0.620292\pi$
$347$	−13.7466	−0.737957	−0.368978	+	0.929438i	$0.620292\pi$
$348$	8.59703	0.460849
$349$	25.5460	1.36745	0.683723	−	0.729742i	$-0.260360\pi$
$349$	25.5460	1.36745	0.683723	+	0.729742i	$0.260360\pi$
$350$	3.80913	0.203607
$351$	−16.6602	−0.889256
$352$	4.83406	0.257656
$353$	15.2804	0.813294	0.406647	−	0.913585i	$-0.366698\pi$
$353$	15.2804	0.813294	0.406647	+	0.913585i	$0.366698\pi$
$354$	−6.15673	−0.327226
$355$	1.60125	0.0849854
$356$	5.94071	0.314857
$357$	−5.37020	−0.284221
$358$	−0.720213	−0.0380644
$359$	−21.1184	−1.11459	−0.557294	−	0.830315i	$-0.688160\pi$
$359$	−21.1184	−1.11459	−0.557294	+	0.830315i	$0.688160\pi$
$360$	−1.08722	−0.0573015
$361$	−18.9593	−0.997860
$362$	2.58041	0.135623
$363$	17.1055	0.897805
$364$	11.2265	0.588430
$365$	−7.86753	−0.411805
$366$	−6.60599	−0.345301
$367$	−24.4320	−1.27534	−0.637669	−	0.770311i	$-0.720101\pi$
$367$	−24.4320	−1.27534	−0.637669	+	0.770311i	$0.720101\pi$
$368$	−3.04202	−0.158576
$369$	8.32496	0.433380
$370$	−2.22794	−0.115825
$371$	−17.3618	−0.901380
$372$	−4.38892	−0.227555
$373$	19.9825	1.03465	0.517327	−	0.855788i	$-0.326927\pi$
$373$	19.9825	1.03465	0.517327	+	0.855788i	$0.326927\pi$
$374$	−4.92769	−0.254805
$375$	1.38303	0.0714195
$376$	−4.17899	−0.215515
$377$	18.3204	0.943551
$378$	−21.5321	−1.10749
$379$	−14.0482	−0.721606	−0.360803	−	0.932642i	$-0.617497\pi$
$379$	−14.0482	−0.721606	−0.360803	+	0.932642i	$0.617497\pi$
$380$	−0.201637	−0.0103438
$381$	17.0664	0.874340
$382$	12.2337	0.625932
$383$	15.7917	0.806920	0.403460	−	0.914997i	$-0.367807\pi$
$383$	15.7917	0.806920	0.403460	+	0.914997i	$0.367807\pi$
$384$	1.38303	0.0705776
$385$	18.4135	0.938441
$386$	−0.976078	−0.0496811
$387$	0.0951711	0.00483782
$388$	−7.88048	−0.400071
$389$	3.96716	0.201143	0.100571	−	0.994930i	$-0.467933\pi$
$389$	3.96716	0.201143	0.100571	+	0.994930i	$0.467933\pi$
$390$	4.07617	0.206405
$391$	3.10094	0.156821
$392$	7.50947	0.379286
$393$	−4.67146	−0.235644
$394$	13.9489	0.702735
$395$	6.02174	0.302987
$396$	−5.25568	−0.264108
$397$	1.05981	0.0531904	0.0265952	−	0.999646i	$-0.491533\pi$
$397$	1.05981	0.0531904	0.0265952	+	0.999646i	$0.491533\pi$
$398$	6.24894	0.313231
$399$	−1.06226	−0.0531793
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	7.20289	0.359247
$403$	−9.35288	−0.465900
$404$	−17.0937	−0.850443
$405$	−4.55630	−0.226404
$406$	23.6778	1.17511
$407$	−10.7700	−0.533848
$408$	−1.40982	−0.0697966
$409$	9.49775	0.469634	0.234817	−	0.972040i	$-0.424551\pi$
$409$	9.49775	0.469634	0.234817	+	0.972040i	$0.424551\pi$
$410$	−7.65712	−0.378158
$411$	5.11778	0.252442
$412$	−20.0060	−0.985625
$413$	−16.9568	−0.834388
$414$	3.30734	0.162547
$415$	−3.93000	−0.192916
$416$	2.94727	0.144502
$417$	7.61631	0.372972
$418$	−0.974725	−0.0476754
$419$	−8.75561	−0.427740	−0.213870	−	0.976862i	$-0.568607\pi$
$419$	−8.75561	−0.427740	−0.213870	+	0.976862i	$0.568607\pi$
$420$	5.26815	0.257060
$421$	−12.9056	−0.628978	−0.314489	−	0.949261i	$-0.601833\pi$
$421$	−12.9056	−0.628978	−0.314489	+	0.949261i	$0.601833\pi$
$422$	16.2075	0.788968
$423$	4.54348	0.220911
$424$	−4.55795	−0.221353
$425$	−1.01937	−0.0494467
$426$	2.21458	0.107297
$427$	−18.1941	−0.880476
$428$	11.4969	0.555723
$429$	19.7044	0.951340
$430$	−0.0875362	−0.00422137
$431$	−13.1664	−0.634205	−0.317102	−	0.948391i	$-0.602710\pi$
$431$	−13.1664	−0.634205	−0.317102	+	0.948391i	$0.602710\pi$
$432$	−5.65276	−0.271969
$433$	−10.0661	−0.483746	−0.241873	−	0.970308i	$-0.577762\pi$
$433$	−10.0661	−0.483746	−0.241873	+	0.970308i	$0.577762\pi$
$434$	−12.0879	−0.580238
$435$	8.59703	0.412196
$436$	14.8135	0.709439
$437$	0.613384	0.0293421
$438$	−10.8811	−0.519917
$439$	1.10118	0.0525565	0.0262783	−	0.999655i	$-0.491634\pi$
$439$	1.10118	0.0525565	0.0262783	+	0.999655i	$0.491634\pi$
$440$	4.83406	0.230455
$441$	−8.16444	−0.388783
$442$	−3.00436	−0.142903
$443$	21.6030	1.02639	0.513196	−	0.858272i	$-0.328462\pi$
$443$	21.6030	1.02639	0.513196	+	0.858272i	$0.328462\pi$
$444$	−3.08131	−0.146233
$445$	5.94071	0.281616
$446$	−2.85254	−0.135072
$447$	1.83289	0.0866928
$448$	3.80913	0.179964
$449$	−31.4417	−1.48382	−0.741912	−	0.670497i	$-0.766081\pi$
$449$	−31.4417	−1.48382	−0.741912	+	0.670497i	$0.766081\pi$
$450$	−1.08722	−0.0512520
$451$	−37.0149	−1.74296
$452$	−5.52582	−0.259913
$453$	−27.5491	−1.29437
$454$	12.9298	0.606827
$455$	11.2265	0.526308
$456$	−0.278871	−0.0130593
$457$	38.5907	1.80520	0.902598	−	0.430485i	$-0.141658\pi$
$457$	38.5907	1.80520	0.902598	+	0.430485i	$0.141658\pi$
$458$	−12.1221	−0.566429
$459$	5.76225	0.268959
$460$	−3.04202	−0.141835
$461$	4.54428	0.211648	0.105824	−	0.994385i	$-0.466252\pi$
$461$	4.54428	0.211648	0.105824	+	0.994385i	$0.466252\pi$
$462$	25.4665	1.18481
$463$	−25.1437	−1.16853	−0.584264	−	0.811564i	$-0.698617\pi$
$463$	−25.1437	−1.16853	−0.584264	+	0.811564i	$0.698617\pi$
$464$	6.21607	0.288574
$465$	−4.38892	−0.203531
$466$	−1.07877	−0.0499729
$467$	6.01767	0.278465	0.139232	−	0.990260i	$-0.455537\pi$
$467$	6.01767	0.278465	0.139232	+	0.990260i	$0.455537\pi$
$468$	−3.20433	−0.148120
$469$	19.8381	0.916038
$470$	−4.17899	−0.192762
$471$	7.17962	0.330820
$472$	−4.45161	−0.204902
$473$	−0.423155	−0.0194567
$474$	8.32826	0.382530
$475$	−0.201637	−0.00925175
$476$	−3.88291	−0.177973
$477$	4.95549	0.226896
$478$	−11.4892	−0.525505
$479$	27.2777	1.24635	0.623176	−	0.782082i	$-0.285842\pi$
$479$	27.2777	1.24635	0.623176	+	0.782082i	$0.285842\pi$
$480$	1.38303	0.0631265
$481$	−6.56634	−0.299399
$482$	4.38725	0.199834
$483$	−16.0258	−0.729200
$484$	12.3681	0.562186
$485$	−7.88048	−0.357834
$486$	10.6568	0.483401
$487$	−15.9097	−0.720935	−0.360468	−	0.932772i	$-0.617383\pi$
$487$	−15.9097	−0.720935	−0.360468	+	0.932772i	$0.617383\pi$
$488$	−4.77645	−0.216220
$489$	24.7260	1.11815
$490$	7.50947	0.339243
$491$	29.3659	1.32526	0.662632	−	0.748945i	$-0.269439\pi$
$491$	29.3659	1.32526	0.662632	+	0.748945i	$0.269439\pi$
$492$	−10.5900	−0.477436
$493$	−6.33647	−0.285380
$494$	−0.594279	−0.0267379
$495$	−5.25568	−0.236225
$496$	−3.17340	−0.142490
$497$	6.09936	0.273594
$498$	−5.43533	−0.243563
$499$	43.2346	1.93545	0.967724	−	0.252013i	$-0.0810925\pi$
$499$	43.2346	1.93545	0.967724	+	0.252013i	$0.0810925\pi$
$500$	1.00000	0.0447214
$501$	17.7820	0.794439
$502$	−1.12866	−0.0503744
$503$	4.48934	0.200170	0.100085	−	0.994979i	$-0.468089\pi$
$503$	4.48934	0.200170	0.100085	+	0.994979i	$0.468089\pi$
$504$	−4.14136	−0.184471
$505$	−17.0937	−0.760659
$506$	−14.7053	−0.653730
$507$	−5.96584	−0.264952
$508$	12.3399	0.547493
$509$	36.2141	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$509$	36.2141	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$510$	−1.40982	−0.0624280
$511$	−29.9684	−1.32573
$512$	1.00000	0.0441942
$513$	1.13981	0.0503237
$514$	−7.52265	−0.331810
$515$	−20.0060	−0.881570
$516$	−0.121066	−0.00532961
$517$	−20.2015	−0.888460
$518$	−8.48651	−0.372876
$519$	−17.9373	−0.787360
$520$	2.94727	0.129246
$521$	−30.3279	−1.32869	−0.664344	−	0.747427i	$-0.731289\pi$
$521$	−30.3279	−1.32869	−0.664344	+	0.747427i	$0.731289\pi$
$522$	−6.75823	−0.295800
$523$	−41.5691	−1.81769	−0.908845	−	0.417134i	$-0.863035\pi$
$523$	−41.5691	−1.81769	−0.908845	+	0.417134i	$0.863035\pi$
$524$	−3.37769	−0.147555
$525$	5.26815	0.229921
$526$	4.03116	0.175767
$527$	3.23487	0.140913
$528$	6.68566	0.290956
$529$	−13.7461	−0.597657
$530$	−4.55795	−0.197985
$531$	4.83988	0.210033
$532$	−0.768062	−0.0332997
$533$	−22.5676	−0.977511
$534$	8.21619	0.355550
$535$	11.4969	0.497054
$536$	5.20804	0.224953
$537$	−0.996078	−0.0429839
$538$	2.84563	0.122684
$539$	36.3012	1.56360
$540$	−5.65276	−0.243256
$541$	4.50449	0.193663	0.0968317	−	0.995301i	$-0.469129\pi$
$541$	4.50449	0.193663	0.0968317	+	0.995301i	$0.469129\pi$
$542$	13.9100	0.597485
$543$	3.56879	0.153151
$544$	−1.01937	−0.0437051
$545$	14.8135	0.634541
$546$	15.5267	0.664480
$547$	−7.10021	−0.303583	−0.151792	−	0.988413i	$-0.548504\pi$
$547$	−7.10021	−0.303583	−0.151792	+	0.988413i	$0.548504\pi$
$548$	3.70041	0.158073
$549$	5.19305	0.221634
$550$	4.83406	0.206125
$551$	−1.25339	−0.0533962
$552$	−4.20721	−0.179071
$553$	22.9376	0.975405
$554$	5.62976	0.239185
$555$	−3.08131	−0.130794
$556$	5.50696	0.233547
$557$	13.7824	0.583978	0.291989	−	0.956422i	$-0.405683\pi$
$557$	13.7824	0.583978	0.291989	+	0.956422i	$0.405683\pi$
$558$	3.45019	0.146058
$559$	−0.257993	−0.0109119
$560$	3.80913	0.160965
$561$	−6.81516	−0.287736
$562$	−7.06513	−0.298024
$563$	−28.5388	−1.20277	−0.601383	−	0.798961i	$-0.705383\pi$
$563$	−28.5388	−1.20277	−0.601383	+	0.798961i	$0.705383\pi$
$564$	−5.77968	−0.243369
$565$	−5.52582	−0.232473
$566$	5.83591	0.245302
$567$	−17.3555	−0.728864
$568$	1.60125	0.0671868
$569$	−9.68225	−0.405901	−0.202951	−	0.979189i	$-0.565053\pi$
$569$	−9.68225	−0.405901	−0.202951	+	0.979189i	$0.565053\pi$
$570$	−0.278871	−0.0116806
$571$	28.8301	1.20650	0.603251	−	0.797551i	$-0.293872\pi$
$571$	28.8301	1.20650	0.603251	+	0.797551i	$0.293872\pi$
$572$	14.2473	0.595708
$573$	16.9197	0.706829
$574$	−29.1670	−1.21740
$575$	−3.04202	−0.126861
$576$	−1.08722	−0.0453008
$577$	−2.54698	−0.106032	−0.0530161	−	0.998594i	$-0.516883\pi$
$577$	−2.54698	−0.106032	−0.0530161	+	0.998594i	$0.516883\pi$
$578$	−15.9609	−0.663885
$579$	−1.34995	−0.0561019
$580$	6.21607	0.258108
$581$	−14.9699	−0.621056
$582$	−10.8990	−0.451777
$583$	−22.0334	−0.912529
$584$	−7.86753	−0.325561
$585$	−3.20433	−0.132483
$586$	−17.5372	−0.724455
$587$	−22.6294	−0.934017	−0.467008	−	0.884253i	$-0.654668\pi$
$587$	−22.6294	−0.934017	−0.467008	+	0.884253i	$0.654668\pi$
$588$	10.3858	0.428305
$589$	0.639876	0.0263656
$590$	−4.45161	−0.183270
$591$	19.2918	0.793558
$592$	−2.22794	−0.0915677
$593$	−16.8455	−0.691761	−0.345881	−	0.938278i	$-0.612420\pi$
$593$	−16.8455	−0.691761	−0.345881	+	0.938278i	$0.612420\pi$
$594$	−27.3258	−1.12119
$595$	−3.88291	−0.159184
$596$	1.32527	0.0542851
$597$	8.64250	0.353714
$598$	−8.96566	−0.366633
$599$	−26.2839	−1.07393	−0.536965	−	0.843604i	$-0.680429\pi$
$599$	−26.2839	−1.07393	−0.536965	+	0.843604i	$0.680429\pi$
$600$	1.38303	0.0564621
$601$	22.6001	0.921878	0.460939	−	0.887432i	$-0.347513\pi$
$601$	22.6001	0.921878	0.460939	+	0.887432i	$0.347513\pi$
$602$	−0.333437	−0.0135899
$603$	−5.66228	−0.230586
$604$	−19.9193	−0.810505
$605$	12.3681	0.502834
$606$	−23.6411	−0.960355
$607$	10.1201	0.410762	0.205381	−	0.978682i	$-0.434157\pi$
$607$	10.1201	0.410762	0.205381	+	0.978682i	$0.434157\pi$
$608$	−0.201637	−0.00817747
$609$	32.7472	1.32698
$610$	−4.77645	−0.193393
$611$	−12.3166	−0.498277
$612$	1.10828	0.0447995
$613$	26.3062	1.06250	0.531248	−	0.847216i	$-0.321723\pi$
$613$	26.3062	1.06250	0.531248	+	0.847216i	$0.321723\pi$
$614$	27.6317	1.11512
$615$	−10.5900	−0.427032
$616$	18.4135	0.741903
$617$	−18.3916	−0.740417	−0.370208	−	0.928949i	$-0.620714\pi$
$617$	−18.3916	−0.740417	−0.370208	+	0.928949i	$0.620714\pi$
$618$	−27.6690	−1.11301
$619$	−3.23679	−0.130098	−0.0650488	−	0.997882i	$-0.520720\pi$
$619$	−3.23679	−0.130098	−0.0650488	+	0.997882i	$0.520720\pi$
$620$	−3.17340	−0.127447
$621$	17.1958	0.690044
$622$	−26.6526	−1.06867
$623$	22.6289	0.906609
$624$	4.07617	0.163178
$625$	1.00000	0.0400000
$626$	−9.90655	−0.395945
$627$	−1.34808	−0.0538370
$628$	5.19122	0.207152
$629$	2.27109	0.0905544
$630$	−4.14136	−0.164996
$631$	−11.7824	−0.469050	−0.234525	−	0.972110i	$-0.575353\pi$
$631$	−11.7824	−0.469050	−0.234525	+	0.972110i	$0.575353\pi$
$632$	6.02174	0.239532
$633$	22.4155	0.890936
$634$	4.84944	0.192596
$635$	12.3399	0.489692
$636$	−6.30379	−0.249962
$637$	22.1324	0.876919
$638$	30.0488	1.18964
$639$	−1.74091	−0.0688692
$640$	1.00000	0.0395285
$641$	−5.90491	−0.233230	−0.116615	−	0.993177i	$-0.537204\pi$
$641$	−5.90491	−0.233230	−0.116615	+	0.993177i	$0.537204\pi$
$642$	15.9006	0.627546
$643$	−20.7851	−0.819684	−0.409842	−	0.912156i	$-0.634416\pi$
$643$	−20.7851	−0.819684	−0.409842	+	0.912156i	$0.634416\pi$
$644$	−11.5874	−0.456609
$645$	−0.121066	−0.00476695
$646$	0.205543	0.00808697
$647$	−41.9035	−1.64740	−0.823699	−	0.567028i	$-0.808093\pi$
$647$	−41.9035	−1.64740	−0.823699	+	0.567028i	$0.808093\pi$
$648$	−4.55630	−0.178988
$649$	−21.5193	−0.844708
$650$	2.94727	0.115601
$651$	−16.7180	−0.655229
$652$	17.8781	0.700160
$653$	−7.44210	−0.291232	−0.145616	−	0.989341i	$-0.546516\pi$
$653$	−7.44210	−0.291232	−0.145616	+	0.989341i	$0.546516\pi$
$654$	20.4876	0.801128
$655$	−3.37769	−0.131977
$656$	−7.65712	−0.298960
$657$	8.55373	0.333713
$658$	−15.9183	−0.620561
$659$	25.3942	0.989219	0.494610	−	0.869115i	$-0.335311\pi$
$659$	25.3942	0.989219	0.494610	+	0.869115i	$0.335311\pi$
$660$	6.68566	0.260239
$661$	−9.94158	−0.386683	−0.193341	−	0.981132i	$-0.561932\pi$
$661$	−9.94158	−0.386683	−0.193341	+	0.981132i	$0.561932\pi$
$662$	26.2640	1.02078
$663$	−4.15513	−0.161372
$664$	−3.93000	−0.152514
$665$	−0.768062	−0.0297842
$666$	2.42226	0.0938605
$667$	−18.9094	−0.732175
$668$	12.8572	0.497461
$669$	−3.94516	−0.152529
$670$	5.20804	0.201204
$671$	−23.0896	−0.891365
$672$	5.26815	0.203223
$673$	24.3419	0.938310	0.469155	−	0.883116i	$-0.344559\pi$
$673$	24.3419	0.938310	0.469155	+	0.883116i	$0.344559\pi$
$674$	−0.213773	−0.00823424
$675$	−5.65276	−0.217575
$676$	−4.31359	−0.165907
$677$	2.99288	0.115026	0.0575129	−	0.998345i	$-0.481683\pi$
$677$	2.99288	0.115026	0.0575129	+	0.998345i	$0.481683\pi$
$678$	−7.64239	−0.293504
$679$	−30.0178	−1.15198
$680$	−1.01937	−0.0390910
$681$	17.8824	0.685254
$682$	−15.3404	−0.587415
$683$	−48.8317	−1.86849	−0.934246	−	0.356629i	$-0.883926\pi$
$683$	−48.8317	−1.86849	−0.934246	+	0.356629i	$0.883926\pi$
$684$	0.219224	0.00838223
$685$	3.70041	0.141385
$686$	1.94064	0.0740941
$687$	−16.7653	−0.639636
$688$	−0.0875362	−0.00333729
$689$	−13.4335	−0.511776
$690$	−4.20721	−0.160166
$691$	26.5868	1.01141	0.505705	−	0.862707i	$-0.331233\pi$
$691$	26.5868	1.01141	0.505705	+	0.862707i	$0.331233\pi$
$692$	−12.9695	−0.493028
$693$	−20.0196	−0.760480
$694$	−13.7466	−0.521814
$695$	5.50696	0.208891
$696$	8.59703	0.325870
$697$	7.80543	0.295652
$698$	25.5460	0.966930
$699$	−1.49197	−0.0564315
$700$	3.80913	0.143972
$701$	13.2561	0.500675	0.250337	−	0.968159i	$-0.419458\pi$
$701$	13.2561	0.500675	0.250337	+	0.968159i	$0.419458\pi$
$702$	−16.6602	−0.628799
$703$	0.449235	0.0169432
$704$	4.83406	0.182190
$705$	−5.77968	−0.217675
$706$	15.2804	0.575085
$707$	−65.1121	−2.44879
$708$	−6.15673	−0.231384
$709$	−30.8563	−1.15883	−0.579417	−	0.815032i	$-0.696720\pi$
$709$	−30.8563	−1.15883	−0.579417	+	0.815032i	$0.696720\pi$
$710$	1.60125	0.0600937
$711$	−6.54695	−0.245530
$712$	5.94071	0.222637
$713$	9.65356	0.361529
$714$	−5.37020	−0.200975
$715$	14.2473	0.532818
$716$	−0.720213	−0.0269156
$717$	−15.8900	−0.593422
$718$	−21.1184	−0.788133
$719$	−28.2375	−1.05308	−0.526540	−	0.850150i	$-0.676511\pi$
$719$	−28.2375	−1.05308	−0.526540	+	0.850150i	$0.676511\pi$
$720$	−1.08722	−0.0405183
$721$	−76.2055	−2.83804
$722$	−18.9593	−0.705594
$723$	6.06771	0.225660
$724$	2.58041	0.0959001
$725$	6.21607	0.230859
$726$	17.1055	0.634844
$727$	−30.5047	−1.13136	−0.565679	−	0.824626i	$-0.691386\pi$
$727$	−30.5047	−1.13136	−0.565679	+	0.824626i	$0.691386\pi$
$728$	11.2265	0.416083
$729$	28.4076	1.05213
$730$	−7.86753	−0.291190
$731$	0.0892318	0.00330036
$732$	−6.60599	−0.244165
$733$	−26.0647	−0.962720	−0.481360	−	0.876523i	$-0.659857\pi$
$733$	−26.0647	−0.962720	−0.481360	+	0.876523i	$0.659857\pi$
$734$	−24.4320	−0.901800
$735$	10.3858	0.383088
$736$	−3.04202	−0.112130
$737$	25.1759	0.927368
$738$	8.32496	0.306446
$739$	−34.6625	−1.27508	−0.637540	−	0.770418i	$-0.720048\pi$
$739$	−34.6625	−1.27508	−0.637540	+	0.770418i	$0.720048\pi$
$740$	−2.22794	−0.0819006
$741$	−0.821908	−0.0301935
$742$	−17.3618	−0.637372
$743$	28.9277	1.06125	0.530627	−	0.847606i	$-0.321957\pi$
$743$	28.9277	1.06125	0.530627	+	0.847606i	$0.321957\pi$
$744$	−4.38892	−0.160906
$745$	1.32527	0.0485541
$746$	19.9825	0.731611
$747$	4.27278	0.156333
$748$	−4.92769	−0.180174
$749$	43.7931	1.60017
$750$	1.38303	0.0505012
$751$	6.45168	0.235425	0.117713	−	0.993048i	$-0.462444\pi$
$751$	6.45168	0.235425	0.117713	+	0.993048i	$0.462444\pi$
$752$	−4.17899	−0.152392
$753$	−1.56097	−0.0568849
$754$	18.3204	0.667191
$755$	−19.9193	−0.724938
$756$	−21.5321	−0.783115
$757$	7.90731	0.287396	0.143698	−	0.989622i	$-0.454101\pi$
$757$	7.90731	0.287396	0.143698	+	0.989622i	$0.454101\pi$
$758$	−14.0482	−0.510253
$759$	−20.3379	−0.738219
$760$	−0.201637	−0.00731415
$761$	−20.6365	−0.748073	−0.374036	−	0.927414i	$-0.622026\pi$
$761$	−20.6365	−0.748073	−0.374036	+	0.927414i	$0.622026\pi$
$762$	17.0664	0.618252
$763$	56.4266	2.04278
$764$	12.2337	0.442601
$765$	1.10828	0.0400699
$766$	15.7917	0.570579
$767$	−13.1201	−0.473740
$768$	1.38303	0.0499059
$769$	52.7156	1.90097	0.950486	−	0.310767i	$-0.100586\pi$
$769$	52.7156	1.90097	0.950486	+	0.310767i	$0.100586\pi$
$770$	18.4135	0.663578
$771$	−10.4041	−0.374694
$772$	−0.976078	−0.0351298
$773$	−34.1281	−1.22750	−0.613752	−	0.789499i	$-0.710341\pi$
$773$	−34.1281	−1.22750	−0.613752	+	0.789499i	$0.710341\pi$
$774$	0.0951711	0.00342085
$775$	−3.17340	−0.113992
$776$	−7.88048	−0.282893
$777$	−11.7371	−0.421067
$778$	3.96716	0.142229
$779$	1.54396	0.0553181
$780$	4.07617	0.145950
$781$	7.74052	0.276977
$782$	3.10094	0.110890
$783$	−35.1379	−1.25573
$784$	7.50947	0.268195
$785$	5.19122	0.185282
$786$	−4.67146	−0.166626
$787$	42.7882	1.52523	0.762617	−	0.646850i	$-0.223914\pi$
$787$	42.7882	1.52523	0.762617	+	0.646850i	$0.223914\pi$
$788$	13.9489	0.496909
$789$	5.57522	0.198483
$790$	6.02174	0.214244
$791$	−21.0486	−0.748401
$792$	−5.25568	−0.186752
$793$	−14.0775	−0.499907
$794$	1.05981	0.0376113
$795$	−6.30379	−0.223572
$796$	6.24894	0.221488
$797$	37.9577	1.34453	0.672265	−	0.740311i	$-0.265322\pi$
$797$	37.9577	1.34453	0.672265	+	0.740311i	$0.265322\pi$
$798$	−1.06226	−0.0376034
$799$	4.25994	0.150706
$800$	1.00000	0.0353553
$801$	−6.45885	−0.228212
$802$	1.00000	0.0353112
$803$	−38.0321	−1.34212
$804$	7.20289	0.254026
$805$	−11.5874	−0.408404
$806$	−9.35288	−0.329441
$807$	3.93561	0.138540
$808$	−17.0937	−0.601354
$809$	10.7667	0.378539	0.189269	−	0.981925i	$-0.439388\pi$
$809$	10.7667	0.378539	0.189269	+	0.981925i	$0.439388\pi$
$810$	−4.55630	−0.160092
$811$	3.60302	0.126519	0.0632596	−	0.997997i	$-0.479850\pi$
$811$	3.60302	0.126519	0.0632596	+	0.997997i	$0.479850\pi$
$812$	23.6778	0.830928
$813$	19.2380	0.674705
$814$	−10.7700	−0.377487
$815$	17.8781	0.626242
$816$	−1.40982	−0.0493537
$817$	0.0176506	0.000617515 0
$818$	9.49775	0.332081
$819$	−12.2057	−0.426502
$820$	−7.65712	−0.267398
$821$	20.4831	0.714866	0.357433	−	0.933939i	$-0.383652\pi$
$821$	20.4831	0.714866	0.357433	+	0.933939i	$0.383652\pi$
$822$	5.11778	0.178503
$823$	−16.3454	−0.569763	−0.284882	−	0.958563i	$-0.591954\pi$
$823$	−16.3454	−0.569763	−0.284882	+	0.958563i	$0.591954\pi$
$824$	−20.0060	−0.696942
$825$	6.68566	0.232765
$826$	−16.9568	−0.590002
$827$	−15.3895	−0.535146	−0.267573	−	0.963538i	$-0.586222\pi$
$827$	−15.3895	−0.535146	−0.267573	+	0.963538i	$0.586222\pi$
$828$	3.30734	0.114938
$829$	6.80169	0.236233	0.118116	−	0.993000i	$-0.462314\pi$
$829$	6.80169	0.236233	0.118116	+	0.993000i	$0.462314\pi$
$830$	−3.93000	−0.136412
$831$	7.78614	0.270098
$832$	2.94727	0.102178
$833$	−7.65493	−0.265228
$834$	7.61631	0.263731
$835$	12.8572	0.444942
$836$	−0.974725	−0.0337116
$837$	17.9385	0.620045
$838$	−8.75561	−0.302458
$839$	−25.0706	−0.865533	−0.432767	−	0.901506i	$-0.642463\pi$
$839$	−25.0706	−0.865533	−0.432767	+	0.901506i	$0.642463\pi$
$840$	5.26815	0.181769
$841$	9.63952	0.332397
$842$	−12.9056	−0.444755
$843$	−9.77131	−0.336542
$844$	16.2075	0.557885
$845$	−4.31359	−0.148392
$846$	4.54348	0.156208
$847$	47.1117	1.61878
$848$	−4.55795	−0.156521
$849$	8.07126	0.277005
$850$	−1.01937	−0.0349641
$851$	6.77743	0.232327
$852$	2.21458	0.0758702
$853$	25.4901	0.872764	0.436382	−	0.899762i	$-0.356260\pi$
$853$	25.4901	0.872764	0.436382	+	0.899762i	$0.356260\pi$
$854$	−18.1941	−0.622590
$855$	0.219224	0.00749729
$856$	11.4969	0.392955
$857$	−10.5263	−0.359573	−0.179787	−	0.983706i	$-0.557541\pi$
$857$	−10.5263	−0.359573	−0.179787	+	0.983706i	$0.557541\pi$
$858$	19.7044	0.672699
$859$	41.6523	1.42116	0.710579	−	0.703617i	$-0.248433\pi$
$859$	41.6523	1.42116	0.710579	+	0.703617i	$0.248433\pi$
$860$	−0.0875362	−0.00298496
$861$	−40.3389	−1.37474
$862$	−13.1664	−0.448451
$863$	9.67342	0.329287	0.164643	−	0.986353i	$-0.447353\pi$
$863$	9.67342	0.329287	0.164643	+	0.986353i	$0.447353\pi$
$864$	−5.65276	−0.192311
$865$	−12.9695	−0.440978
$866$	−10.0661	−0.342060
$867$	−22.0744	−0.749687
$868$	−12.0879	−0.410290
$869$	29.1094	0.987469
$870$	8.59703	0.291467
$871$	15.3495	0.520098
$872$	14.8135	0.501649
$873$	8.56781	0.289977
$874$	0.613384	0.0207480
$875$	3.80913	0.128772
$876$	−10.8811	−0.367637
$877$	40.3743	1.36334	0.681672	−	0.731658i	$-0.261253\pi$
$877$	40.3743	1.36334	0.681672	+	0.731658i	$0.261253\pi$
$878$	1.10118	0.0371631
$879$	−24.2545	−0.818085
$880$	4.83406	0.162956
$881$	40.6509	1.36956	0.684781	−	0.728748i	$-0.259898\pi$
$881$	40.6509	1.36956	0.684781	+	0.728748i	$0.259898\pi$
$882$	−8.16444	−0.274911
$883$	−24.3955	−0.820973	−0.410487	−	0.911867i	$-0.634641\pi$
$883$	−24.3955	−0.820973	−0.410487	+	0.911867i	$0.634641\pi$
$884$	−3.00436	−0.101048
$885$	−6.15673	−0.206956
$886$	21.6030	0.725768
$887$	−4.20835	−0.141303	−0.0706513	−	0.997501i	$-0.522508\pi$
$887$	−4.20835	−0.141303	−0.0706513	+	0.997501i	$0.522508\pi$
$888$	−3.08131	−0.103402
$889$	47.0041	1.57647
$890$	5.94071	0.199133
$891$	−22.0254	−0.737878
$892$	−2.85254	−0.0955101
$893$	0.842640	0.0281979
$894$	1.83289	0.0613010
$895$	−0.720213	−0.0240741
$896$	3.80913	0.127254
$897$	−12.3998	−0.414017
$898$	−31.4417	−1.04922
$899$	−19.7261	−0.657902
$900$	−1.08722	−0.0362406
$901$	4.64623	0.154788
$902$	−37.0149	−1.23246
$903$	−0.461154	−0.0153463
$904$	−5.52582	−0.183786
$905$	2.58041	0.0857757
$906$	−27.5491	−0.915256
$907$	23.9405	0.794930	0.397465	−	0.917617i	$-0.369890\pi$
$907$	23.9405	0.794930	0.397465	+	0.917617i	$0.369890\pi$
$908$	12.9298	0.429091
$909$	18.5846	0.616412
$910$	11.2265	0.372156
$911$	−24.5308	−0.812740	−0.406370	−	0.913709i	$-0.633206\pi$
$911$	−24.5308	−0.812740	−0.406370	+	0.913709i	$0.633206\pi$
$912$	−0.278871	−0.00923434
$913$	−18.9979	−0.628737
$914$	38.5907	1.27647
$915$	−6.60599	−0.218387
$916$	−12.1221	−0.400526
$917$	−12.8661	−0.424875
$918$	5.76225	0.190183
$919$	17.2064	0.567588	0.283794	−	0.958885i	$-0.408407\pi$
$919$	17.2064	0.567588	0.283794	+	0.958885i	$0.408407\pi$
$920$	−3.04202	−0.100292
$921$	38.2155	1.25924
$922$	4.54428	0.149658
$923$	4.71931	0.155338
$924$	25.4665	0.837788
$925$	−2.22794	−0.0732542
$926$	−25.1437	−0.826273
$927$	21.7509	0.714394
$928$	6.21607	0.204052
$929$	29.9897	0.983931	0.491965	−	0.870615i	$-0.336279\pi$
$929$	29.9897	0.983931	0.491965	+	0.870615i	$0.336279\pi$
$930$	−4.38892	−0.143918
$931$	−1.51419	−0.0496255
$932$	−1.07877	−0.0353362
$933$	−36.8614	−1.20679
$934$	6.01767	0.196904
$935$	−4.92769	−0.161153
$936$	−3.20433	−0.104737
$937$	32.8297	1.07250	0.536250	−	0.844059i	$-0.319841\pi$
$937$	32.8297	1.07250	0.536250	+	0.844059i	$0.319841\pi$
$938$	19.8381	0.647737
$939$	−13.7011	−0.447118
$940$	−4.17899	−0.136304
$941$	−20.3214	−0.662457	−0.331229	−	0.943550i	$-0.607463\pi$
$941$	−20.3214	−0.662457	−0.331229	+	0.943550i	$0.607463\pi$
$942$	7.17962	0.233925
$943$	23.2931	0.758528
$944$	−4.45161	−0.144888
$945$	−21.5321	−0.700439
$946$	−0.423155	−0.0137580
$947$	−32.8290	−1.06680	−0.533400	−	0.845863i	$-0.679086\pi$
$947$	−32.8290	−1.06680	−0.533400	+	0.845863i	$0.679086\pi$
$948$	8.32826	0.270489
$949$	−23.1877	−0.752706
$950$	−0.201637	−0.00654197
$951$	6.70693	0.217487
$952$	−3.88291	−0.125846
$953$	29.7624	0.964099	0.482049	−	0.876144i	$-0.339893\pi$
$953$	29.7624	0.964099	0.482049	+	0.876144i	$0.339893\pi$
$954$	4.95549	0.160440
$955$	12.2337	0.395874
$956$	−11.4892	−0.371588
$957$	41.5585	1.34340
$958$	27.2777	0.881304
$959$	14.0953	0.455162
$960$	1.38303	0.0446372
$961$	−20.9295	−0.675145
$962$	−6.56634	−0.211707
$963$	−12.4996	−0.402795
$964$	4.38725	0.141304
$965$	−0.976078	−0.0314211
$966$	−16.0258	−0.515623
$967$	−14.0726	−0.452546	−0.226273	−	0.974064i	$-0.572654\pi$
$967$	−14.0726	−0.452546	−0.226273	+	0.974064i	$0.572654\pi$
$968$	12.3681	0.397525
$969$	0.284273	0.00913215
$970$	−7.88048	−0.253027
$971$	34.0314	1.09212	0.546060	−	0.837746i	$-0.316127\pi$
$971$	34.0314	1.09212	0.546060	+	0.837746i	$0.316127\pi$
$972$	10.6568	0.341816
$973$	20.9767	0.672483
$974$	−15.9097	−0.509778
$975$	4.07617	0.130542
$976$	−4.77645	−0.152891
$977$	−40.9934	−1.31150	−0.655748	−	0.754980i	$-0.727647\pi$
$977$	−40.9934	−1.31150	−0.655748	+	0.754980i	$0.727647\pi$
$978$	24.7260	0.790649
$979$	28.7177	0.917822
$980$	7.50947	0.239881
$981$	−16.1055	−0.514210
$982$	29.3659	0.937103
$983$	−17.5424	−0.559515	−0.279758	−	0.960071i	$-0.590254\pi$
$983$	−17.5424	−0.559515	−0.279758	+	0.960071i	$0.590254\pi$
$984$	−10.5900	−0.337598
$985$	13.9489	0.444449
$986$	−6.33647	−0.201794
$987$	−22.0156	−0.700763
$988$	−0.594279	−0.0189065
$989$	0.266287	0.00846743
$990$	−5.25568	−0.167036
$991$	34.6289	1.10002	0.550011	−	0.835157i	$-0.314623\pi$
$991$	34.6289	1.10002	0.550011	+	0.835157i	$0.314623\pi$
$992$	−3.17340	−0.100756
$993$	36.3240	1.15271
$994$	6.09936	0.193460
$995$	6.24894	0.198105
$996$	−5.43533	−0.172225
$997$	−10.5972	−0.335617	−0.167808	−	0.985820i	$-0.553669\pi$
$997$	−10.5972	−0.335617	−0.167808	+	0.985820i	$0.553669\pi$
$998$	43.2346	1.36857
$999$	12.5940	0.398456

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.n.1.15	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.n.1.15	✓	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.38303 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.38303 q^{6} +3.80913 q^{7} +1.00000 q^{8} -1.08722 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.38303 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.38303 q^{6} +3.80913 q^{7} +1.00000 q^{8} -1.08722 q^{9} +1.00000 q^{10} +4.83406 q^{11} +1.38303 q^{12} +2.94727 q^{13} +3.80913 q^{14} +1.38303 q^{15} +1.00000 q^{16} -1.01937 q^{17} -1.08722 q^{18} -0.201637 q^{19} +1.00000 q^{20} +5.26815 q^{21} +4.83406 q^{22} -3.04202 q^{23} +1.38303 q^{24} +1.00000 q^{25} +2.94727 q^{26} -5.65276 q^{27} +3.80913 q^{28} +6.21607 q^{29} +1.38303 q^{30} -3.17340 q^{31} +1.00000 q^{32} +6.68566 q^{33} -1.01937 q^{34} +3.80913 q^{35} -1.08722 q^{36} -2.22794 q^{37} -0.201637 q^{38} +4.07617 q^{39} +1.00000 q^{40} -7.65712 q^{41} +5.26815 q^{42} -0.0875362 q^{43} +4.83406 q^{44} -1.08722 q^{45} -3.04202 q^{46} -4.17899 q^{47} +1.38303 q^{48} +7.50947 q^{49} +1.00000 q^{50} -1.40982 q^{51} +2.94727 q^{52} -4.55795 q^{53} -5.65276 q^{54} +4.83406 q^{55} +3.80913 q^{56} -0.278871 q^{57} +6.21607 q^{58} -4.45161 q^{59} +1.38303 q^{60} -4.77645 q^{61} -3.17340 q^{62} -4.14136 q^{63} +1.00000 q^{64} +2.94727 q^{65} +6.68566 q^{66} +5.20804 q^{67} -1.01937 q^{68} -4.20721 q^{69} +3.80913 q^{70} +1.60125 q^{71} -1.08722 q^{72} -7.86753 q^{73} -2.22794 q^{74} +1.38303 q^{75} -0.201637 q^{76} +18.4135 q^{77} +4.07617 q^{78} +6.02174 q^{79} +1.00000 q^{80} -4.55630 q^{81} -7.65712 q^{82} -3.93000 q^{83} +5.26815 q^{84} -1.01937 q^{85} -0.0875362 q^{86} +8.59703 q^{87} +4.83406 q^{88} +5.94071 q^{89} -1.08722 q^{90} +11.2265 q^{91} -3.04202 q^{92} -4.38892 q^{93} -4.17899 q^{94} -0.201637 q^{95} +1.38303 q^{96} -7.88048 q^{97} +7.50947 q^{98} -5.25568 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) 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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