LMFDB - Embedded newform 4010.2.a.o.1.2

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			1.2
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.90289 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.90289 q^{6} +4.43766 q^{7} +1.00000 q^{8} +5.42676 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.90289 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.90289 q^{6} +4.43766 q^{7} +1.00000 q^{8} +5.42676 q^{9} -1.00000 q^{10} +4.85477 q^{11} -2.90289 q^{12} +1.74292 q^{13} +4.43766 q^{14} +2.90289 q^{15} +1.00000 q^{16} +0.344637 q^{17} +5.42676 q^{18} +2.92164 q^{19} -1.00000 q^{20} -12.8820 q^{21} +4.85477 q^{22} +8.04963 q^{23} -2.90289 q^{24} +1.00000 q^{25} +1.74292 q^{26} -7.04462 q^{27} +4.43766 q^{28} -1.84274 q^{29} +2.90289 q^{30} +8.68492 q^{31} +1.00000 q^{32} -14.0929 q^{33} +0.344637 q^{34} -4.43766 q^{35} +5.42676 q^{36} +8.18638 q^{37} +2.92164 q^{38} -5.05950 q^{39} -1.00000 q^{40} -10.5203 q^{41} -12.8820 q^{42} -12.7763 q^{43} +4.85477 q^{44} -5.42676 q^{45} +8.04963 q^{46} +4.01252 q^{47} -2.90289 q^{48} +12.6929 q^{49} +1.00000 q^{50} -1.00044 q^{51} +1.74292 q^{52} -3.27687 q^{53} -7.04462 q^{54} -4.85477 q^{55} +4.43766 q^{56} -8.48120 q^{57} -1.84274 q^{58} -5.69640 q^{59} +2.90289 q^{60} -9.09176 q^{61} +8.68492 q^{62} +24.0821 q^{63} +1.00000 q^{64} -1.74292 q^{65} -14.0929 q^{66} +2.58967 q^{67} +0.344637 q^{68} -23.3672 q^{69} -4.43766 q^{70} -12.7310 q^{71} +5.42676 q^{72} -1.11072 q^{73} +8.18638 q^{74} -2.90289 q^{75} +2.92164 q^{76} +21.5438 q^{77} -5.05950 q^{78} +2.17237 q^{79} -1.00000 q^{80} +4.16946 q^{81} -10.5203 q^{82} +0.0749572 q^{83} -12.8820 q^{84} -0.344637 q^{85} -12.7763 q^{86} +5.34926 q^{87} +4.85477 q^{88} +10.0242 q^{89} -5.42676 q^{90} +7.73450 q^{91} +8.04963 q^{92} -25.2113 q^{93} +4.01252 q^{94} -2.92164 q^{95} -2.90289 q^{96} -1.03231 q^{97} +12.6929 q^{98} +26.3457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.90289	−1.67598	−0.837992	−	0.545683i	$-0.816270\pi$
$3$	−2.90289	−1.67598	−0.837992	+	0.545683i	$0.816270\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.90289	−1.18510
$7$	4.43766	1.67728	0.838640	−	0.544687i	$-0.183351\pi$
$7$	4.43766	1.67728	0.838640	+	0.544687i	$0.183351\pi$
$8$	1.00000	0.353553
$9$	5.42676	1.80892
$10$	−1.00000	−0.316228
$11$	4.85477	1.46377	0.731884	−	0.681429i	$-0.238641\pi$
$11$	4.85477	1.46377	0.731884	+	0.681429i	$0.238641\pi$
$12$	−2.90289	−0.837992
$13$	1.74292	0.483399	0.241700	−	0.970351i	$-0.422295\pi$
$13$	1.74292	0.483399	0.241700	+	0.970351i	$0.422295\pi$
$14$	4.43766	1.18602
$15$	2.90289	0.749523
$16$	1.00000	0.250000
$17$	0.344637	0.0835868	0.0417934	−	0.999126i	$-0.486693\pi$
$17$	0.344637	0.0835868	0.0417934	+	0.999126i	$0.486693\pi$
$18$	5.42676	1.27910
$19$	2.92164	0.670270	0.335135	−	0.942170i	$-0.391218\pi$
$19$	2.92164	0.670270	0.335135	+	0.942170i	$0.391218\pi$
$20$	−1.00000	−0.223607
$21$	−12.8820	−2.81109
$22$	4.85477	1.03504
$23$	8.04963	1.67846	0.839232	−	0.543773i	$-0.183005\pi$
$23$	8.04963	1.67846	0.839232	+	0.543773i	$0.183005\pi$
$24$	−2.90289	−0.592550
$25$	1.00000	0.200000
$26$	1.74292	0.341815
$27$	−7.04462	−1.35574
$28$	4.43766	0.838640
$29$	−1.84274	−0.342188	−0.171094	−	0.985255i	$-0.554730\pi$
$29$	−1.84274	−0.342188	−0.171094	+	0.985255i	$0.554730\pi$
$30$	2.90289	0.529992
$31$	8.68492	1.55986	0.779928	−	0.625869i	$-0.215255\pi$
$31$	8.68492	1.55986	0.779928	+	0.625869i	$0.215255\pi$
$32$	1.00000	0.176777
$33$	−14.0929	−2.45325
$34$	0.344637	0.0591048
$35$	−4.43766	−0.750102
$36$	5.42676	0.904460
$37$	8.18638	1.34583	0.672916	−	0.739718i	$-0.265041\pi$
$37$	8.18638	1.34583	0.672916	+	0.739718i	$0.265041\pi$
$38$	2.92164	0.473953
$39$	−5.05950	−0.810169
$40$	−1.00000	−0.158114
$41$	−10.5203	−1.64299	−0.821497	−	0.570213i	$-0.806861\pi$
$41$	−10.5203	−1.64299	−0.821497	+	0.570213i	$0.806861\pi$
$42$	−12.8820	−1.98774
$43$	−12.7763	−1.94837	−0.974187	−	0.225743i	$-0.927519\pi$
$43$	−12.7763	−1.94837	−0.974187	+	0.225743i	$0.927519\pi$
$44$	4.85477	0.731884
$45$	−5.42676	−0.808974
$46$	8.04963	1.18685
$47$	4.01252	0.585286	0.292643	−	0.956222i	$-0.405465\pi$
$47$	4.01252	0.585286	0.292643	+	0.956222i	$0.405465\pi$
$48$	−2.90289	−0.418996
$49$	12.6929	1.81327
$50$	1.00000	0.141421
$51$	−1.00044	−0.140090
$52$	1.74292	0.241700
$53$	−3.27687	−0.450113	−0.225056	−	0.974346i	$-0.572257\pi$
$53$	−3.27687	−0.450113	−0.225056	+	0.974346i	$0.572257\pi$
$54$	−7.04462	−0.958651
$55$	−4.85477	−0.654617
$56$	4.43766	0.593008
$57$	−8.48120	−1.12336
$58$	−1.84274	−0.241963
$59$	−5.69640	−0.741608	−0.370804	−	0.928711i	$-0.620918\pi$
$59$	−5.69640	−0.741608	−0.370804	+	0.928711i	$0.620918\pi$
$60$	2.90289	0.374761
$61$	−9.09176	−1.16408	−0.582040	−	0.813160i	$-0.697745\pi$
$61$	−9.09176	−1.16408	−0.582040	+	0.813160i	$0.697745\pi$
$62$	8.68492	1.10299
$63$	24.0821	3.03407
$64$	1.00000	0.125000
$65$	−1.74292	−0.216183
$66$	−14.0929	−1.73471
$67$	2.58967	0.316378	0.158189	−	0.987409i	$-0.449434\pi$
$67$	2.58967	0.316378	0.158189	+	0.987409i	$0.449434\pi$
$68$	0.344637	0.0417934
$69$	−23.3672	−2.81308
$70$	−4.43766	−0.530402
$71$	−12.7310	−1.51090	−0.755448	−	0.655209i	$-0.772581\pi$
$71$	−12.7310	−1.51090	−0.755448	+	0.655209i	$0.772581\pi$
$72$	5.42676	0.639550
$73$	−1.11072	−0.130000	−0.0650000	−	0.997885i	$-0.520705\pi$
$73$	−1.11072	−0.130000	−0.0650000	+	0.997885i	$0.520705\pi$
$74$	8.18638	0.951648
$75$	−2.90289	−0.335197
$76$	2.92164	0.335135
$77$	21.5438	2.45515
$78$	−5.05950	−0.572876
$79$	2.17237	0.244411	0.122205	−	0.992505i	$-0.461003\pi$
$79$	2.17237	0.244411	0.122205	+	0.992505i	$0.461003\pi$
$80$	−1.00000	−0.111803
$81$	4.16946	0.463273
$82$	−10.5203	−1.16177
$83$	0.0749572	0.00822762	0.00411381	−	0.999992i	$-0.498691\pi$
$83$	0.0749572	0.00822762	0.00411381	+	0.999992i	$0.498691\pi$
$84$	−12.8820	−1.40555
$85$	−0.344637	−0.0373812
$86$	−12.7763	−1.37771
$87$	5.34926	0.573501
$88$	4.85477	0.517520
$89$	10.0242	1.06256	0.531281	−	0.847196i	$-0.321711\pi$
$89$	10.0242	1.06256	0.531281	+	0.847196i	$0.321711\pi$
$90$	−5.42676	−0.572031
$91$	7.73450	0.810795
$92$	8.04963	0.839232
$93$	−25.2113	−2.61429
$94$	4.01252	0.413860
$95$	−2.92164	−0.299754
$96$	−2.90289	−0.296275
$97$	−1.03231	−0.104816	−0.0524078	−	0.998626i	$-0.516690\pi$
$97$	−1.03231	−0.104816	−0.0524078	+	0.998626i	$0.516690\pi$
$98$	12.6929	1.28217
$99$	26.3457	2.64784
$100$	1.00000	0.100000
$101$	−12.5574	−1.24951	−0.624755	−	0.780821i	$-0.714801\pi$
$101$	−12.5574	−1.24951	−0.624755	+	0.780821i	$0.714801\pi$
$102$	−1.00044	−0.0990587
$103$	7.47944	0.736971	0.368486	−	0.929633i	$-0.379876\pi$
$103$	7.47944	0.736971	0.368486	+	0.929633i	$0.379876\pi$
$104$	1.74292	0.170907
$105$	12.8820	1.25716
$106$	−3.27687	−0.318278
$107$	−2.64462	−0.255665	−0.127832	−	0.991796i	$-0.540802\pi$
$107$	−2.64462	−0.255665	−0.127832	+	0.991796i	$0.540802\pi$
$108$	−7.04462	−0.677869
$109$	16.6557	1.59533	0.797664	−	0.603102i	$-0.206069\pi$
$109$	16.6557	1.59533	0.797664	+	0.603102i	$0.206069\pi$
$110$	−4.85477	−0.462884
$111$	−23.7642	−2.25559
$112$	4.43766	0.419320
$113$	−4.30548	−0.405025	−0.202513	−	0.979280i	$-0.564911\pi$
$113$	−4.30548	−0.405025	−0.202513	+	0.979280i	$0.564911\pi$
$114$	−8.48120	−0.794337
$115$	−8.04963	−0.750632
$116$	−1.84274	−0.171094
$117$	9.45841	0.874431
$118$	−5.69640	−0.524396
$119$	1.52939	0.140198
$120$	2.90289	0.264996
$121$	12.5688	1.14262
$122$	−9.09176	−0.823129
$123$	30.5392	2.75363
$124$	8.68492	0.779928
$125$	−1.00000	−0.0894427
$126$	24.0821	2.14541
$127$	−15.3702	−1.36389	−0.681944	−	0.731404i	$-0.738865\pi$
$127$	−15.3702	−1.36389	−0.681944	+	0.731404i	$0.738865\pi$
$128$	1.00000	0.0883883
$129$	37.0883	3.26544
$130$	−1.74292	−0.152864
$131$	−12.5718	−1.09841	−0.549203	−	0.835689i	$-0.685069\pi$
$131$	−12.5718	−1.09841	−0.549203	+	0.835689i	$0.685069\pi$
$132$	−14.0929	−1.22663
$133$	12.9653	1.12423
$134$	2.58967	0.223713
$135$	7.04462	0.606304
$136$	0.344637	0.0295524
$137$	3.77832	0.322803	0.161402	−	0.986889i	$-0.448399\pi$
$137$	3.77832	0.322803	0.161402	+	0.986889i	$0.448399\pi$
$138$	−23.3672	−1.98915
$139$	−5.70360	−0.483773	−0.241887	−	0.970305i	$-0.577766\pi$
$139$	−5.70360	−0.483773	−0.241887	+	0.970305i	$0.577766\pi$
$140$	−4.43766	−0.375051
$141$	−11.6479	−0.980930
$142$	−12.7310	−1.06836
$143$	8.46148	0.707585
$144$	5.42676	0.452230
$145$	1.84274	0.153031
$146$	−1.11072	−0.0919238
$147$	−36.8460	−3.03900
$148$	8.18638	0.672916
$149$	−4.84510	−0.396926	−0.198463	−	0.980108i	$-0.563595\pi$
$149$	−4.84510	−0.396926	−0.198463	+	0.980108i	$0.563595\pi$
$150$	−2.90289	−0.237020
$151$	19.0773	1.55249	0.776243	−	0.630434i	$-0.217123\pi$
$151$	19.0773	1.55249	0.776243	+	0.630434i	$0.217123\pi$
$152$	2.92164	0.236976
$153$	1.87026	0.151202
$154$	21.5438	1.73605
$155$	−8.68492	−0.697589
$156$	−5.05950	−0.405084
$157$	−2.51299	−0.200558	−0.100279	−	0.994959i	$-0.531974\pi$
$157$	−2.51299	−0.200558	−0.100279	+	0.994959i	$0.531974\pi$
$158$	2.17237	0.172824
$159$	9.51239	0.754382
$160$	−1.00000	−0.0790569
$161$	35.7216	2.81525
$162$	4.16946	0.327583
$163$	23.8843	1.87076	0.935380	−	0.353644i	$-0.115058\pi$
$163$	23.8843	1.87076	0.935380	+	0.353644i	$0.115058\pi$
$164$	−10.5203	−0.821497
$165$	14.0929	1.09713
$166$	0.0749572	0.00581780
$167$	6.06172	0.469070	0.234535	−	0.972108i	$-0.424643\pi$
$167$	6.06172	0.469070	0.234535	+	0.972108i	$0.424643\pi$
$168$	−12.8820	−0.993871
$169$	−9.96223	−0.766325
$170$	−0.344637	−0.0264325
$171$	15.8550	1.21247
$172$	−12.7763	−0.974187
$173$	6.87310	0.522552	0.261276	−	0.965264i	$-0.415857\pi$
$173$	6.87310	0.522552	0.261276	+	0.965264i	$0.415857\pi$
$174$	5.34926	0.405526
$175$	4.43766	0.335456
$176$	4.85477	0.365942
$177$	16.5360	1.24292
$178$	10.0242	0.751345
$179$	6.46091	0.482911	0.241455	−	0.970412i	$-0.422375\pi$
$179$	6.46091	0.482911	0.241455	+	0.970412i	$0.422375\pi$
$180$	−5.42676	−0.404487
$181$	−18.0260	−1.33986	−0.669931	−	0.742423i	$-0.733676\pi$
$181$	−18.0260	−1.33986	−0.669931	+	0.742423i	$0.733676\pi$
$182$	7.73450	0.573319
$183$	26.3924	1.95098
$184$	8.04963	0.593427
$185$	−8.18638	−0.601875
$186$	−25.2113	−1.84859
$187$	1.67314	0.122352
$188$	4.01252	0.292643
$189$	−31.2616	−2.27395
$190$	−2.92164	−0.211958
$191$	2.17189	0.157153	0.0785764	−	0.996908i	$-0.474963\pi$
$191$	2.17189	0.157153	0.0785764	+	0.996908i	$0.474963\pi$
$192$	−2.90289	−0.209498
$193$	1.72544	0.124200	0.0621000	−	0.998070i	$-0.480220\pi$
$193$	1.72544	0.124200	0.0621000	+	0.998070i	$0.480220\pi$
$194$	−1.03231	−0.0741158
$195$	5.05950	0.362319
$196$	12.6929	0.906633
$197$	3.45339	0.246044	0.123022	−	0.992404i	$-0.460741\pi$
$197$	3.45339	0.246044	0.123022	+	0.992404i	$0.460741\pi$
$198$	26.3457	1.87231
$199$	−23.7092	−1.68070	−0.840349	−	0.542045i	$-0.817650\pi$
$199$	−23.7092	−1.68070	−0.840349	+	0.542045i	$0.817650\pi$
$200$	1.00000	0.0707107
$201$	−7.51751	−0.530244
$202$	−12.5574	−0.883537
$203$	−8.17745	−0.573944
$204$	−1.00044	−0.0700451
$205$	10.5203	0.734769
$206$	7.47944	0.521117
$207$	43.6834	3.03621
$208$	1.74292	0.120850
$209$	14.1839	0.981121
$210$	12.8820	0.888945
$211$	14.3385	0.987105	0.493553	−	0.869716i	$-0.335698\pi$
$211$	14.3385	0.987105	0.493553	+	0.869716i	$0.335698\pi$
$212$	−3.27687	−0.225056
$213$	36.9568	2.53224
$214$	−2.64462	−0.180782
$215$	12.7763	0.871339
$216$	−7.04462	−0.479326
$217$	38.5407	2.61632
$218$	16.6557	1.12807
$219$	3.22430	0.217878
$220$	−4.85477	−0.327309
$221$	0.600676	0.0404058
$222$	−23.7642	−1.59495
$223$	−14.0079	−0.938040	−0.469020	−	0.883188i	$-0.655393\pi$
$223$	−14.0079	−0.938040	−0.469020	+	0.883188i	$0.655393\pi$
$224$	4.43766	0.296504
$225$	5.42676	0.361784
$226$	−4.30548	−0.286396
$227$	10.6115	0.704308	0.352154	−	0.935942i	$-0.385449\pi$
$227$	10.6115	0.704308	0.352154	+	0.935942i	$0.385449\pi$
$228$	−8.48120	−0.561681
$229$	−9.76864	−0.645530	−0.322765	−	0.946479i	$-0.604612\pi$
$229$	−9.76864	−0.645530	−0.322765	+	0.946479i	$0.604612\pi$
$230$	−8.04963	−0.530777
$231$	−62.5394	−4.11479
$232$	−1.84274	−0.120982
$233$	26.9109	1.76299	0.881494	−	0.472195i	$-0.156538\pi$
$233$	26.9109	1.76299	0.881494	+	0.472195i	$0.156538\pi$
$234$	9.45841	0.618316
$235$	−4.01252	−0.261748
$236$	−5.69640	−0.370804
$237$	−6.30614	−0.409628
$238$	1.52939	0.0991353
$239$	−12.6796	−0.820177	−0.410089	−	0.912046i	$-0.634502\pi$
$239$	−12.6796	−0.820177	−0.410089	+	0.912046i	$0.634502\pi$
$240$	2.90289	0.187381
$241$	−13.7979	−0.888799	−0.444400	−	0.895829i	$-0.646583\pi$
$241$	−13.7979	−0.888799	−0.444400	+	0.895829i	$0.646583\pi$
$242$	12.5688	0.807953
$243$	9.03039	0.579300
$244$	−9.09176	−0.582040
$245$	−12.6929	−0.810917
$246$	30.5392	1.94711
$247$	5.09219	0.324008
$248$	8.68492	0.551493
$249$	−0.217592	−0.0137893
$250$	−1.00000	−0.0632456
$251$	−13.5315	−0.854101	−0.427050	−	0.904228i	$-0.640447\pi$
$251$	−13.5315	−0.854101	−0.427050	+	0.904228i	$0.640447\pi$
$252$	24.0821	1.51703
$253$	39.0791	2.45688
$254$	−15.3702	−0.964415
$255$	1.00044	0.0626502
$256$	1.00000	0.0625000
$257$	12.3881	0.772747	0.386374	−	0.922342i	$-0.373728\pi$
$257$	12.3881	0.772747	0.386374	+	0.922342i	$0.373728\pi$
$258$	37.0883	2.30902
$259$	36.3284	2.25734
$260$	−1.74292	−0.108091
$261$	−10.0001	−0.618990
$262$	−12.5718	−0.776690
$263$	2.35019	0.144919	0.0724595	−	0.997371i	$-0.476915\pi$
$263$	2.35019	0.144919	0.0724595	+	0.997371i	$0.476915\pi$
$264$	−14.0929	−0.867356
$265$	3.27687	0.201297
$266$	12.9653	0.794951
$267$	−29.0991	−1.78084
$268$	2.58967	0.158189
$269$	20.8366	1.27043	0.635214	−	0.772336i	$-0.280912\pi$
$269$	20.8366	1.27043	0.635214	+	0.772336i	$0.280912\pi$
$270$	7.04462	0.428722
$271$	3.47959	0.211370	0.105685	−	0.994400i	$-0.466297\pi$
$271$	3.47959	0.211370	0.105685	+	0.994400i	$0.466297\pi$
$272$	0.344637	0.0208967
$273$	−22.4524	−1.35888
$274$	3.77832	0.228256
$275$	4.85477	0.292754
$276$	−23.3672	−1.40654
$277$	−28.3767	−1.70499	−0.852494	−	0.522737i	$-0.824911\pi$
$277$	−28.3767	−1.70499	−0.852494	+	0.522737i	$0.824911\pi$
$278$	−5.70360	−0.342079
$279$	47.1310	2.82166
$280$	−4.43766	−0.265201
$281$	27.7148	1.65332	0.826662	−	0.562698i	$-0.190237\pi$
$281$	27.7148	1.65332	0.826662	+	0.562698i	$0.190237\pi$
$282$	−11.6479	−0.693622
$283$	−3.73263	−0.221882	−0.110941	−	0.993827i	$-0.535386\pi$
$283$	−3.73263	−0.221882	−0.110941	+	0.993827i	$0.535386\pi$
$284$	−12.7310	−0.755448
$285$	8.48120	0.502383
$286$	8.46148	0.500338
$287$	−46.6855	−2.75576
$288$	5.42676	0.319775
$289$	−16.8812	−0.993013
$290$	1.84274	0.108209
$291$	2.99669	0.175669
$292$	−1.11072	−0.0650000
$293$	−26.8620	−1.56930	−0.784648	−	0.619942i	$-0.787156\pi$
$293$	−26.8620	−1.56930	−0.784648	+	0.619942i	$0.787156\pi$
$294$	−36.8460	−2.14890
$295$	5.69640	0.331657
$296$	8.18638	0.475824
$297$	−34.2000	−1.98449
$298$	−4.84510	−0.280669
$299$	14.0299	0.811368
$300$	−2.90289	−0.167598
$301$	−56.6971	−3.26797
$302$	19.0773	1.09777
$303$	36.4528	2.09416
$304$	2.92164	0.167568
$305$	9.09176	0.520593
$306$	1.87026	0.106916
$307$	−26.2846	−1.50014	−0.750071	−	0.661357i	$-0.769981\pi$
$307$	−26.2846	−1.50014	−0.750071	+	0.661357i	$0.769981\pi$
$308$	21.5438	1.22757
$309$	−21.7120	−1.23515
$310$	−8.68492	−0.493270
$311$	−23.1540	−1.31294	−0.656470	−	0.754352i	$-0.727951\pi$
$311$	−23.1540	−1.31294	−0.656470	+	0.754352i	$0.727951\pi$
$312$	−5.05950	−0.286438
$313$	30.7256	1.73671	0.868357	−	0.495939i	$-0.165176\pi$
$313$	30.7256	1.73671	0.868357	+	0.495939i	$0.165176\pi$
$314$	−2.51299	−0.141816
$315$	−24.0821	−1.35688
$316$	2.17237	0.122205
$317$	26.1549	1.46900	0.734502	−	0.678606i	$-0.237416\pi$
$317$	26.1549	1.46900	0.734502	+	0.678606i	$0.237416\pi$
$318$	9.51239	0.533429
$319$	−8.94607	−0.500884
$320$	−1.00000	−0.0559017
$321$	7.67702	0.428490
$322$	35.7216	1.99069
$323$	1.00691	0.0560258
$324$	4.16946	0.231636
$325$	1.74292	0.0966798
$326$	23.8843	1.32283
$327$	−48.3497	−2.67374
$328$	−10.5203	−0.580886
$329$	17.8062	0.981689
$330$	14.0929	0.775786
$331$	−18.2960	−1.00564	−0.502821	−	0.864391i	$-0.667704\pi$
$331$	−18.2960	−1.00564	−0.502821	+	0.864391i	$0.667704\pi$
$332$	0.0749572	0.00411381
$333$	44.4255	2.43450
$334$	6.06172	0.331683
$335$	−2.58967	−0.141489
$336$	−12.8820	−0.702773
$337$	36.3321	1.97913	0.989567	−	0.144072i	$-0.0460197\pi$
$337$	36.3321	1.97913	0.989567	+	0.144072i	$0.0460197\pi$
$338$	−9.96223	−0.541874
$339$	12.4983	0.678816
$340$	−0.344637	−0.0186906
$341$	42.1633	2.28327
$342$	15.8550	0.857343
$343$	25.2630	1.36407
$344$	−12.7763	−0.688854
$345$	23.3672	1.25805
$346$	6.87310	0.369500
$347$	−36.6419	−1.96704	−0.983520	−	0.180799i	$-0.942132\pi$
$347$	−36.6419	−1.96704	−0.983520	+	0.180799i	$0.942132\pi$
$348$	5.34926	0.286751
$349$	7.04125	0.376909	0.188455	−	0.982082i	$-0.439652\pi$
$349$	7.04125	0.376909	0.188455	+	0.982082i	$0.439652\pi$
$350$	4.43766	0.237203
$351$	−12.2782	−0.655362
$352$	4.85477	0.258760
$353$	−6.08177	−0.323700	−0.161850	−	0.986815i	$-0.551746\pi$
$353$	−6.08177	−0.323700	−0.161850	+	0.986815i	$0.551746\pi$
$354$	16.5360	0.878879
$355$	12.7310	0.675693
$356$	10.0242	0.531281
$357$	−4.43963	−0.234970
$358$	6.46091	0.341470
$359$	−17.7493	−0.936772	−0.468386	−	0.883524i	$-0.655164\pi$
$359$	−17.7493	−0.936772	−0.468386	+	0.883524i	$0.655164\pi$
$360$	−5.42676	−0.286015
$361$	−10.4640	−0.550738
$362$	−18.0260	−0.947425
$363$	−36.4858	−1.91501
$364$	7.73450	0.405398
$365$	1.11072	0.0581377
$366$	26.3924	1.37955
$367$	5.47176	0.285624	0.142812	−	0.989750i	$-0.454386\pi$
$367$	5.47176	0.285624	0.142812	+	0.989750i	$0.454386\pi$
$368$	8.04963	0.419616
$369$	−57.0911	−2.97204
$370$	−8.18638	−0.425590
$371$	−14.5417	−0.754965
$372$	−25.2113	−1.30715
$373$	−1.11877	−0.0579279	−0.0289639	−	0.999580i	$-0.509221\pi$
$373$	−1.11877	−0.0579279	−0.0289639	+	0.999580i	$0.509221\pi$
$374$	1.67314	0.0865158
$375$	2.90289	0.149905
$376$	4.01252	0.206930
$377$	−3.21174	−0.165413
$378$	−31.2616	−1.60793
$379$	25.5542	1.31263	0.656317	−	0.754486i	$-0.272114\pi$
$379$	25.5542	1.31263	0.656317	+	0.754486i	$0.272114\pi$
$380$	−2.92164	−0.149877
$381$	44.6181	2.28585
$382$	2.17189	0.111124
$383$	−24.6230	−1.25818	−0.629089	−	0.777334i	$-0.716572\pi$
$383$	−24.6230	−1.25818	−0.629089	+	0.777334i	$0.716572\pi$
$384$	−2.90289	−0.148137
$385$	−21.5438	−1.09798
$386$	1.72544	0.0878226
$387$	−69.3342	−3.52445
$388$	−1.03231	−0.0524078
$389$	−12.3596	−0.626658	−0.313329	−	0.949645i	$-0.601444\pi$
$389$	−12.3596	−0.626658	−0.313329	+	0.949645i	$0.601444\pi$
$390$	5.05950	0.256198
$391$	2.77420	0.140298
$392$	12.6929	0.641086
$393$	36.4946	1.84091
$394$	3.45339	0.173979
$395$	−2.17237	−0.109304
$396$	26.3457	1.32392
$397$	−7.46428	−0.374622	−0.187311	−	0.982301i	$-0.559977\pi$
$397$	−7.46428	−0.374622	−0.187311	+	0.982301i	$0.559977\pi$
$398$	−23.7092	−1.18843
$399$	−37.6367	−1.88419
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−7.51751	−0.374939
$403$	15.1371	0.754034
$404$	−12.5574	−0.624755
$405$	−4.16946	−0.207182
$406$	−8.17745	−0.405840
$407$	39.7430	1.96999
$408$	−1.00044	−0.0495294
$409$	9.97064	0.493017	0.246508	−	0.969141i	$-0.420717\pi$
$409$	9.97064	0.493017	0.246508	+	0.969141i	$0.420717\pi$
$410$	10.5203	0.519560
$411$	−10.9680	−0.541013
$412$	7.47944	0.368486
$413$	−25.2787	−1.24388
$414$	43.6834	2.14692
$415$	−0.0749572	−0.00367950
$416$	1.74292	0.0854537
$417$	16.5569	0.810796
$418$	14.1839	0.693757
$419$	−15.6549	−0.764794	−0.382397	−	0.923998i	$-0.624901\pi$
$419$	−15.6549	−0.764794	−0.382397	+	0.923998i	$0.624901\pi$
$420$	12.8820	0.628579
$421$	2.69691	0.131439	0.0657197	−	0.997838i	$-0.479066\pi$
$421$	2.69691	0.131439	0.0657197	+	0.997838i	$0.479066\pi$
$422$	14.3385	0.697989
$423$	21.7750	1.05874
$424$	−3.27687	−0.159139
$425$	0.344637	0.0167174
$426$	36.9568	1.79056
$427$	−40.3462	−1.95249
$428$	−2.64462	−0.127832
$429$	−24.5627	−1.18590
$430$	12.7763	0.616130
$431$	−34.2218	−1.64841	−0.824204	−	0.566294i	$-0.808377\pi$
$431$	−34.2218	−1.64841	−0.824204	+	0.566294i	$0.808377\pi$
$432$	−7.04462	−0.338934
$433$	33.9474	1.63141	0.815705	−	0.578468i	$-0.196349\pi$
$433$	33.9474	1.63141	0.815705	+	0.578468i	$0.196349\pi$
$434$	38.5407	1.85001
$435$	−5.34926	−0.256477
$436$	16.6557	0.797664
$437$	23.5181	1.12502
$438$	3.22430	0.154063
$439$	8.74755	0.417498	0.208749	−	0.977969i	$-0.433061\pi$
$439$	8.74755	0.417498	0.208749	+	0.977969i	$0.433061\pi$
$440$	−4.85477	−0.231442
$441$	68.8811	3.28005
$442$	0.600676	0.0285712
$443$	−39.4809	−1.87580	−0.937898	−	0.346911i	$-0.887230\pi$
$443$	−39.4809	−1.87580	−0.937898	+	0.346911i	$0.887230\pi$
$444$	−23.7642	−1.12780
$445$	−10.0242	−0.475192
$446$	−14.0079	−0.663295
$447$	14.0648	0.665241
$448$	4.43766	0.209660
$449$	29.3637	1.38576	0.692879	−	0.721053i	$-0.256342\pi$
$449$	29.3637	1.38576	0.692879	+	0.721053i	$0.256342\pi$
$450$	5.42676	0.255820
$451$	−51.0736	−2.40496
$452$	−4.30548	−0.202513
$453$	−55.3791	−2.60194
$454$	10.6115	0.498021
$455$	−7.73450	−0.362599
$456$	−8.48120	−0.397168
$457$	3.47455	0.162533	0.0812663	−	0.996692i	$-0.474104\pi$
$457$	3.47455	0.162533	0.0812663	+	0.996692i	$0.474104\pi$
$458$	−9.76864	−0.456458
$459$	−2.42784	−0.113322
$460$	−8.04963	−0.375316
$461$	−31.8683	−1.48425	−0.742127	−	0.670259i	$-0.766183\pi$
$461$	−31.8683	−1.48425	−0.742127	+	0.670259i	$0.766183\pi$
$462$	−62.5394	−2.90960
$463$	6.16481	0.286503	0.143252	−	0.989686i	$-0.454244\pi$
$463$	6.16481	0.286503	0.143252	+	0.989686i	$0.454244\pi$
$464$	−1.84274	−0.0855469
$465$	25.2113	1.16915
$466$	26.9109	1.24662
$467$	−20.5244	−0.949757	−0.474879	−	0.880051i	$-0.657508\pi$
$467$	−20.5244	−0.949757	−0.474879	+	0.880051i	$0.657508\pi$
$468$	9.45841	0.437215
$469$	11.4921	0.530654
$470$	−4.01252	−0.185084
$471$	7.29493	0.336133
$472$	−5.69640	−0.262198
$473$	−62.0262	−2.85197
$474$	−6.30614	−0.289651
$475$	2.92164	0.134054
$476$	1.52939	0.0700992
$477$	−17.7828	−0.814219
$478$	−12.6796	−0.579953
$479$	−14.7127	−0.672241	−0.336121	−	0.941819i	$-0.609115\pi$
$479$	−14.7127	−0.672241	−0.336121	+	0.941819i	$0.609115\pi$
$480$	2.90289	0.132498
$481$	14.2682	0.650575
$482$	−13.7979	−0.628476
$483$	−103.696	−4.71832
$484$	12.5688	0.571309
$485$	1.03231	0.0468749
$486$	9.03039	0.409627
$487$	−4.52638	−0.205110	−0.102555	−	0.994727i	$-0.532702\pi$
$487$	−4.52638	−0.205110	−0.102555	+	0.994727i	$0.532702\pi$
$488$	−9.09176	−0.411565
$489$	−69.3334	−3.13536
$490$	−12.6929	−0.573405
$491$	18.7949	0.848203	0.424101	−	0.905615i	$-0.360590\pi$
$491$	18.7949	0.848203	0.424101	+	0.905615i	$0.360590\pi$
$492$	30.5392	1.37682
$493$	−0.635076	−0.0286024
$494$	5.09219	0.229108
$495$	−26.3457	−1.18415
$496$	8.68492	0.389964
$497$	−56.4961	−2.53419
$498$	−0.217592	−0.00975054
$499$	5.99805	0.268510	0.134255	−	0.990947i	$-0.457136\pi$
$499$	5.99805	0.268510	0.134255	+	0.990947i	$0.457136\pi$
$500$	−1.00000	−0.0447214
$501$	−17.5965	−0.786154
$502$	−13.5315	−0.603941
$503$	−13.9637	−0.622610	−0.311305	−	0.950310i	$-0.600766\pi$
$503$	−13.9637	−0.622610	−0.311305	+	0.950310i	$0.600766\pi$
$504$	24.0821	1.07270
$505$	12.5574	0.558798
$506$	39.0791	1.73728
$507$	28.9192	1.28435
$508$	−15.3702	−0.681944
$509$	−13.4691	−0.597007	−0.298503	−	0.954409i	$-0.596487\pi$
$509$	−13.4691	−0.597007	−0.298503	+	0.954409i	$0.596487\pi$
$510$	1.00044	0.0443004
$511$	−4.92900	−0.218046
$512$	1.00000	0.0441942
$513$	−20.5818	−0.908710
$514$	12.3881	0.546415
$515$	−7.47944	−0.329584
$516$	37.0883	1.63272
$517$	19.4799	0.856724
$518$	36.3284	1.59618
$519$	−19.9518	−0.875789
$520$	−1.74292	−0.0764321
$521$	−34.5253	−1.51258	−0.756291	−	0.654235i	$-0.772991\pi$
$521$	−34.5253	−1.51258	−0.756291	+	0.654235i	$0.772991\pi$
$522$	−10.0001	−0.437692
$523$	−26.7459	−1.16952	−0.584759	−	0.811207i	$-0.698811\pi$
$523$	−26.7459	−1.16952	−0.584759	+	0.811207i	$0.698811\pi$
$524$	−12.5718	−0.549203
$525$	−12.8820	−0.562218
$526$	2.35019	0.102473
$527$	2.99315	0.130384
$528$	−14.0929	−0.613313
$529$	41.7966	1.81724
$530$	3.27687	0.142338
$531$	−30.9130	−1.34151
$532$	12.9653	0.562115
$533$	−18.3360	−0.794222
$534$	−29.0991	−1.25924
$535$	2.64462	0.114337
$536$	2.58967	0.111857
$537$	−18.7553	−0.809351
$538$	20.8366	0.898328
$539$	61.6209	2.65420
$540$	7.04462	0.303152
$541$	−3.77346	−0.162234	−0.0811169	−	0.996705i	$-0.525849\pi$
$541$	−3.77346	−0.162234	−0.0811169	+	0.996705i	$0.525849\pi$
$542$	3.47959	0.149461
$543$	52.3275	2.24559
$544$	0.344637	0.0147762
$545$	−16.6557	−0.713453
$546$	−22.4524	−0.960873
$547$	37.9659	1.62330	0.811652	−	0.584141i	$-0.198569\pi$
$547$	37.9659	1.62330	0.811652	+	0.584141i	$0.198569\pi$
$548$	3.77832	0.161402
$549$	−49.3388	−2.10573
$550$	4.85477	0.207008
$551$	−5.38382	−0.229358
$552$	−23.3672	−0.994574
$553$	9.64024	0.409945
$554$	−28.3767	−1.20561
$555$	23.7642	1.00873
$556$	−5.70360	−0.241887
$557$	18.6096	0.788513	0.394256	−	0.919001i	$-0.371002\pi$
$557$	18.6096	0.788513	0.394256	+	0.919001i	$0.371002\pi$
$558$	47.1310	1.99521
$559$	−22.2681	−0.941842
$560$	−4.43766	−0.187526
$561$	−4.85693	−0.205060
$562$	27.7148	1.16908
$563$	32.0820	1.35210	0.676048	−	0.736857i	$-0.263691\pi$
$563$	32.0820	1.35210	0.676048	+	0.736857i	$0.263691\pi$
$564$	−11.6479	−0.490465
$565$	4.30548	0.181133
$566$	−3.73263	−0.156894
$567$	18.5026	0.777038
$568$	−12.7310	−0.534182
$569$	−10.4688	−0.438875	−0.219437	−	0.975627i	$-0.570422\pi$
$569$	−10.4688	−0.438875	−0.219437	+	0.975627i	$0.570422\pi$
$570$	8.48120	0.355238
$571$	−28.8469	−1.20720	−0.603602	−	0.797286i	$-0.706268\pi$
$571$	−28.8469	−1.20720	−0.603602	+	0.797286i	$0.706268\pi$
$572$	8.46148	0.353792
$573$	−6.30477	−0.263385
$574$	−46.6855	−1.94862
$575$	8.04963	0.335693
$576$	5.42676	0.226115
$577$	−15.2859	−0.636360	−0.318180	−	0.948030i	$-0.603072\pi$
$577$	−15.2859	−0.636360	−0.318180	+	0.948030i	$0.603072\pi$
$578$	−16.8812	−0.702166
$579$	−5.00876	−0.208157
$580$	1.84274	0.0765155
$581$	0.332635	0.0138000
$582$	2.99669	0.124217
$583$	−15.9085	−0.658861
$584$	−1.11072	−0.0459619
$585$	−9.45841	−0.391057
$586$	−26.8620	−1.10966
$587$	4.38036	0.180797	0.0903984	−	0.995906i	$-0.471186\pi$
$587$	4.38036	0.180797	0.0903984	+	0.995906i	$0.471186\pi$
$588$	−36.8460	−1.51950
$589$	25.3742	1.04553
$590$	5.69640	0.234517
$591$	−10.0248	−0.412365
$592$	8.18638	0.336458
$593$	18.7821	0.771290	0.385645	−	0.922647i	$-0.373979\pi$
$593$	18.7821	0.771290	0.385645	+	0.922647i	$0.373979\pi$
$594$	−34.2000	−1.40324
$595$	−1.52939	−0.0626987
$596$	−4.84510	−0.198463
$597$	68.8251	2.81682
$598$	14.0299	0.573724
$599$	45.7644	1.86988	0.934940	−	0.354805i	$-0.115453\pi$
$599$	45.7644	1.86988	0.934940	+	0.354805i	$0.115453\pi$
$600$	−2.90289	−0.118510
$601$	−13.3705	−0.545394	−0.272697	−	0.962100i	$-0.587916\pi$
$601$	−13.3705	−0.545394	−0.272697	+	0.962100i	$0.587916\pi$
$602$	−56.6971	−2.31080
$603$	14.0535	0.572303
$604$	19.0773	0.776243
$605$	−12.5688	−0.510995
$606$	36.4528	1.48079
$607$	−5.67710	−0.230426	−0.115213	−	0.993341i	$-0.536755\pi$
$607$	−5.67710	−0.230426	−0.115213	+	0.993341i	$0.536755\pi$
$608$	2.92164	0.118488
$609$	23.7382	0.961921
$610$	9.09176	0.368115
$611$	6.99350	0.282927
$612$	1.87026	0.0756010
$613$	12.5250	0.505880	0.252940	−	0.967482i	$-0.418602\pi$
$613$	12.5250	0.505880	0.252940	+	0.967482i	$0.418602\pi$
$614$	−26.2846	−1.06076
$615$	−30.5392	−1.23146
$616$	21.5438	0.868026
$617$	0.259950	0.0104652	0.00523259	−	0.999986i	$-0.498334\pi$
$617$	0.259950	0.0104652	0.00523259	+	0.999986i	$0.498334\pi$
$618$	−21.7120	−0.873384
$619$	28.3588	1.13983	0.569917	−	0.821702i	$-0.306975\pi$
$619$	28.3588	1.13983	0.569917	+	0.821702i	$0.306975\pi$
$620$	−8.68492	−0.348795
$621$	−56.7066	−2.27556
$622$	−23.1540	−0.928389
$623$	44.4840	1.78221
$624$	−5.05950	−0.202542
$625$	1.00000	0.0400000
$626$	30.7256	1.22804
$627$	−41.1743	−1.64434
$628$	−2.51299	−0.100279
$629$	2.82133	0.112494
$630$	−24.0821	−0.959456
$631$	34.1450	1.35929	0.679646	−	0.733540i	$-0.262133\pi$
$631$	34.1450	1.35929	0.679646	+	0.733540i	$0.262133\pi$
$632$	2.17237	0.0864122
$633$	−41.6232	−1.65437
$634$	26.1549	1.03874
$635$	15.3702	0.609950
$636$	9.51239	0.377191
$637$	22.1227	0.876531
$638$	−8.94607	−0.354178
$639$	−69.0883	−2.73309
$640$	−1.00000	−0.0395285
$641$	−4.01932	−0.158754	−0.0793768	−	0.996845i	$-0.525293\pi$
$641$	−4.01932	−0.158754	−0.0793768	+	0.996845i	$0.525293\pi$
$642$	7.67702	0.302988
$643$	30.0358	1.18449	0.592247	−	0.805756i	$-0.298241\pi$
$643$	30.0358	1.18449	0.592247	+	0.805756i	$0.298241\pi$
$644$	35.7216	1.40763
$645$	−37.0883	−1.46035
$646$	1.00691	0.0396162
$647$	20.8296	0.818894	0.409447	−	0.912334i	$-0.365722\pi$
$647$	20.8296	0.818894	0.409447	+	0.912334i	$0.365722\pi$
$648$	4.16946	0.163792
$649$	−27.6547	−1.08554
$650$	1.74292	0.0683630
$651$	−111.879	−4.38490
$652$	23.8843	0.935380
$653$	0.356359	0.0139454	0.00697271	−	0.999976i	$-0.497780\pi$
$653$	0.356359	0.0139454	0.00697271	+	0.999976i	$0.497780\pi$
$654$	−48.3497	−1.89062
$655$	12.5718	0.491222
$656$	−10.5203	−0.410748
$657$	−6.02761	−0.235159
$658$	17.8062	0.694159
$659$	−28.6638	−1.11658	−0.558291	−	0.829645i	$-0.688543\pi$
$659$	−28.6638	−1.11658	−0.558291	+	0.829645i	$0.688543\pi$
$660$	14.0929	0.548564
$661$	−17.8882	−0.695769	−0.347885	−	0.937537i	$-0.613100\pi$
$661$	−17.8882	−0.695769	−0.347885	+	0.937537i	$0.613100\pi$
$662$	−18.2960	−0.711096
$663$	−1.74369	−0.0677195
$664$	0.0749572	0.00290890
$665$	−12.9653	−0.502771
$666$	44.4255	1.72145
$667$	−14.8334	−0.574350
$668$	6.06172	0.234535
$669$	40.6634	1.57214
$670$	−2.58967	−0.100047
$671$	−44.1384	−1.70394
$672$	−12.8820	−0.496936
$673$	−29.3617	−1.13181	−0.565906	−	0.824470i	$-0.691473\pi$
$673$	−29.3617	−1.13181	−0.565906	+	0.824470i	$0.691473\pi$
$674$	36.3321	1.39946
$675$	−7.04462	−0.271147
$676$	−9.96223	−0.383163
$677$	33.8525	1.30106	0.650529	−	0.759481i	$-0.274547\pi$
$677$	33.8525	1.30106	0.650529	+	0.759481i	$0.274547\pi$
$678$	12.4983	0.479995
$679$	−4.58106	−0.175805
$680$	−0.344637	−0.0132162
$681$	−30.8039	−1.18041
$682$	42.1633	1.61452
$683$	−42.7935	−1.63745	−0.818723	−	0.574188i	$-0.805318\pi$
$683$	−42.7935	−1.63745	−0.818723	+	0.574188i	$0.805318\pi$
$684$	15.8550	0.606233
$685$	−3.77832	−0.144362
$686$	25.2630	0.964546
$687$	28.3573	1.08190
$688$	−12.7763	−0.487093
$689$	−5.71133	−0.217584
$690$	23.3672	0.889574
$691$	4.91968	0.187153	0.0935767	−	0.995612i	$-0.470170\pi$
$691$	4.91968	0.187153	0.0935767	+	0.995612i	$0.470170\pi$
$692$	6.87310	0.261276
$693$	116.913	4.44117
$694$	−36.6419	−1.39091
$695$	5.70360	0.216350
$696$	5.34926	0.202763
$697$	−3.62569	−0.137333
$698$	7.04125	0.266515
$699$	−78.1192	−2.95474
$700$	4.43766	0.167728
$701$	26.6488	1.00651	0.503256	−	0.864137i	$-0.332135\pi$
$701$	26.6488	1.00651	0.503256	+	0.864137i	$0.332135\pi$
$702$	−12.2782	−0.463411
$703$	23.9177	0.902072
$704$	4.85477	0.182971
$705$	11.6479	0.438685
$706$	−6.08177	−0.228891
$707$	−55.7256	−2.09578
$708$	16.5360	0.621461
$709$	−1.90796	−0.0716550	−0.0358275	−	0.999358i	$-0.511407\pi$
$709$	−1.90796	−0.0716550	−0.0358275	+	0.999358i	$0.511407\pi$
$710$	12.7310	0.477787
$711$	11.7889	0.442119
$712$	10.0242	0.375672
$713$	69.9104	2.61816
$714$	−4.43963	−0.166149
$715$	−8.46148	−0.316441
$716$	6.46091	0.241455
$717$	36.8076	1.37460
$718$	−17.7493	−0.662398
$719$	−4.94554	−0.184437	−0.0922187	−	0.995739i	$-0.529396\pi$
$719$	−4.94554	−0.184437	−0.0922187	+	0.995739i	$0.529396\pi$
$720$	−5.42676	−0.202243
$721$	33.1912	1.23611
$722$	−10.4640	−0.389430
$723$	40.0537	1.48961
$724$	−18.0260	−0.669931
$725$	−1.84274	−0.0684376
$726$	−36.4858	−1.35412
$727$	36.3489	1.34811	0.674053	−	0.738683i	$-0.264552\pi$
$727$	36.3489	1.34811	0.674053	+	0.738683i	$0.264552\pi$
$728$	7.73450	0.286659
$729$	−38.7226	−1.43417
$730$	1.11072	0.0411096
$731$	−4.40321	−0.162858
$732$	26.3924	0.975490
$733$	32.6176	1.20476	0.602379	−	0.798210i	$-0.294220\pi$
$733$	32.6176	1.20476	0.602379	+	0.798210i	$0.294220\pi$
$734$	5.47176	0.201966
$735$	36.8460	1.35908
$736$	8.04963	0.296713
$737$	12.5722	0.463104
$738$	−57.0911	−2.10155
$739$	17.9860	0.661624	0.330812	−	0.943697i	$-0.392677\pi$
$739$	17.9860	0.661624	0.330812	+	0.943697i	$0.392677\pi$
$740$	−8.18638	−0.300937
$741$	−14.7820	−0.543032
$742$	−14.5417	−0.533841
$743$	−18.6261	−0.683325	−0.341662	−	0.939823i	$-0.610990\pi$
$743$	−18.6261	−0.683325	−0.341662	+	0.939823i	$0.610990\pi$
$744$	−25.2113	−0.924293
$745$	4.84510	0.177511
$746$	−1.11877	−0.0409612
$747$	0.406775	0.0148831
$748$	1.67314	0.0611759
$749$	−11.7359	−0.428821
$750$	2.90289	0.105998
$751$	50.3576	1.83757	0.918787	−	0.394753i	$-0.129170\pi$
$751$	50.3576	1.83757	0.918787	+	0.394753i	$0.129170\pi$
$752$	4.01252	0.146322
$753$	39.2804	1.43146
$754$	−3.21174	−0.116965
$755$	−19.0773	−0.694292
$756$	−31.2616	−1.13698
$757$	28.2842	1.02801	0.514003	−	0.857788i	$-0.328162\pi$
$757$	28.2842	1.02801	0.514003	+	0.857788i	$0.328162\pi$
$758$	25.5542	0.928172
$759$	−113.442	−4.11770
$760$	−2.92164	−0.105979
$761$	3.70140	0.134176	0.0670878	−	0.997747i	$-0.478629\pi$
$761$	3.70140	0.134176	0.0670878	+	0.997747i	$0.478629\pi$
$762$	44.6181	1.61634
$763$	73.9125	2.67581
$764$	2.17189	0.0785764
$765$	−1.87026	−0.0676196
$766$	−24.6230	−0.889666
$767$	−9.92836	−0.358492
$768$	−2.90289	−0.104749
$769$	−22.8736	−0.824844	−0.412422	−	0.910993i	$-0.635317\pi$
$769$	−22.8736	−0.824844	−0.412422	+	0.910993i	$0.635317\pi$
$770$	−21.5438	−0.776386
$771$	−35.9612	−1.29511
$772$	1.72544	0.0621000
$773$	−3.41387	−0.122789	−0.0613943	−	0.998114i	$-0.519555\pi$
$773$	−3.41387	−0.122789	−0.0613943	+	0.998114i	$0.519555\pi$
$774$	−69.3342	−2.49216
$775$	8.68492	0.311971
$776$	−1.03231	−0.0370579
$777$	−105.457	−3.78326
$778$	−12.3596	−0.443114
$779$	−30.7365	−1.10125
$780$	5.05950	0.181159
$781$	−61.8063	−2.21160
$782$	2.77420	0.0992054
$783$	12.9814	0.463917
$784$	12.6929	0.453317
$785$	2.51299	0.0896925
$786$	36.4946	1.30172
$787$	6.96848	0.248399	0.124200	−	0.992257i	$-0.460364\pi$
$787$	6.96848	0.248399	0.124200	+	0.992257i	$0.460364\pi$
$788$	3.45339	0.123022
$789$	−6.82234	−0.242882
$790$	−2.17237	−0.0772894
$791$	−19.1063	−0.679340
$792$	26.3457	0.936153
$793$	−15.8462	−0.562715
$794$	−7.46428	−0.264898
$795$	−9.51239	−0.337370
$796$	−23.7092	−0.840349
$797$	17.3683	0.615217	0.307609	−	0.951513i	$-0.400471\pi$
$797$	17.3683	0.615217	0.307609	+	0.951513i	$0.400471\pi$
$798$	−37.6367	−1.33232
$799$	1.38286	0.0489222
$800$	1.00000	0.0353553
$801$	54.3989	1.92209
$802$	−1.00000	−0.0353112
$803$	−5.39229	−0.190290
$804$	−7.51751	−0.265122
$805$	−35.7216	−1.25902
$806$	15.1371	0.533182
$807$	−60.4862	−2.12922
$808$	−12.5574	−0.441769
$809$	19.3461	0.680172	0.340086	−	0.940394i	$-0.389544\pi$
$809$	19.3461	0.680172	0.340086	+	0.940394i	$0.389544\pi$
$810$	−4.16946	−0.146500
$811$	30.2097	1.06081	0.530404	−	0.847745i	$-0.322040\pi$
$811$	30.2097	1.06081	0.530404	+	0.847745i	$0.322040\pi$
$812$	−8.17745	−0.286972
$813$	−10.1009	−0.354252
$814$	39.7430	1.39299
$815$	−23.8843	−0.836629
$816$	−1.00044	−0.0350225
$817$	−37.3279	−1.30594
$818$	9.97064	0.348615
$819$	41.9733	1.46666
$820$	10.5203	0.367385
$821$	−34.5690	−1.20647	−0.603233	−	0.797565i	$-0.706121\pi$
$821$	−34.5690	−1.20647	−0.603233	+	0.797565i	$0.706121\pi$
$822$	−10.9680	−0.382554
$823$	34.4641	1.20134	0.600672	−	0.799495i	$-0.294900\pi$
$823$	34.4641	1.20134	0.600672	+	0.799495i	$0.294900\pi$
$824$	7.47944	0.260559
$825$	−14.0929	−0.490650
$826$	−25.2787	−0.879558
$827$	18.7713	0.652744	0.326372	−	0.945241i	$-0.394174\pi$
$827$	18.7713	0.652744	0.326372	+	0.945241i	$0.394174\pi$
$828$	43.6834	1.51810
$829$	15.9711	0.554698	0.277349	−	0.960769i	$-0.410544\pi$
$829$	15.9711	0.554698	0.277349	+	0.960769i	$0.410544\pi$
$830$	−0.0749572	−0.00260180
$831$	82.3743	2.85753
$832$	1.74292	0.0604249
$833$	4.37444	0.151565
$834$	16.5569	0.573319
$835$	−6.06172	−0.209775
$836$	14.1839	0.490560
$837$	−61.1819	−2.11476
$838$	−15.6549	−0.540791
$839$	44.4803	1.53563	0.767815	−	0.640672i	$-0.221344\pi$
$839$	44.4803	1.53563	0.767815	+	0.640672i	$0.221344\pi$
$840$	12.8820	0.444473
$841$	−25.6043	−0.882908
$842$	2.69691	0.0929417
$843$	−80.4529	−2.77095
$844$	14.3385	0.493553
$845$	9.96223	0.342711
$846$	21.7750	0.748640
$847$	55.7761	1.91649
$848$	−3.27687	−0.112528
$849$	10.8354	0.371871
$850$	0.344637	0.0118210
$851$	65.8974	2.25893
$852$	36.9568	1.26612
$853$	0.981806	0.0336164	0.0168082	−	0.999859i	$-0.494650\pi$
$853$	0.981806	0.0336164	0.0168082	+	0.999859i	$0.494650\pi$
$854$	−40.3462	−1.38062
$855$	−15.8550	−0.542231
$856$	−2.64462	−0.0903911
$857$	5.84507	0.199664	0.0998319	−	0.995004i	$-0.468170\pi$
$857$	5.84507	0.199664	0.0998319	+	0.995004i	$0.468170\pi$
$858$	−24.5627	−0.838558
$859$	−41.4458	−1.41411	−0.707055	−	0.707158i	$-0.749977\pi$
$859$	−41.4458	−1.41411	−0.707055	+	0.707158i	$0.749977\pi$
$860$	12.7763	0.435670
$861$	135.523	4.61861
$862$	−34.2218	−1.16560
$863$	−39.4834	−1.34403	−0.672015	−	0.740537i	$-0.734571\pi$
$863$	−39.4834	−1.34403	−0.672015	+	0.740537i	$0.734571\pi$
$864$	−7.04462	−0.239663
$865$	−6.87310	−0.233692
$866$	33.9474	1.15358
$867$	49.0043	1.66427
$868$	38.5407	1.30816
$869$	10.5464	0.357760
$870$	−5.34926	−0.181357
$871$	4.51358	0.152937
$872$	16.6557	0.564034
$873$	−5.60212	−0.189603
$874$	23.5181	0.795513
$875$	−4.43766	−0.150020
$876$	3.22430	0.108939
$877$	−31.2005	−1.05357	−0.526783	−	0.850000i	$-0.676602\pi$
$877$	−31.2005	−1.05357	−0.526783	+	0.850000i	$0.676602\pi$
$878$	8.74755	0.295215
$879$	77.9774	2.63011
$880$	−4.85477	−0.163654
$881$	12.5541	0.422957	0.211479	−	0.977383i	$-0.432172\pi$
$881$	12.5541	0.422957	0.211479	+	0.977383i	$0.432172\pi$
$882$	68.8811	2.31935
$883$	−5.68043	−0.191162	−0.0955809	−	0.995422i	$-0.530471\pi$
$883$	−5.68043	−0.191162	−0.0955809	+	0.995422i	$0.530471\pi$
$884$	0.600676	0.0202029
$885$	−16.5360	−0.555852
$886$	−39.4809	−1.32639
$887$	2.37548	0.0797609	0.0398804	−	0.999204i	$-0.487302\pi$
$887$	2.37548	0.0797609	0.0398804	+	0.999204i	$0.487302\pi$
$888$	−23.7642	−0.797473
$889$	−68.2080	−2.28762
$890$	−10.0242	−0.336012
$891$	20.2418	0.678124
$892$	−14.0079	−0.469020
$893$	11.7231	0.392300
$894$	14.0648	0.470396
$895$	−6.46091	−0.215964
$896$	4.43766	0.148252
$897$	−40.7272	−1.35984
$898$	29.3637	0.979880
$899$	−16.0040	−0.533764
$900$	5.42676	0.180892
$901$	−1.12933	−0.0376235
$902$	−51.0736	−1.70057
$903$	164.585	5.47706
$904$	−4.30548	−0.143198
$905$	18.0260	0.599204
$906$	−55.3791	−1.83985
$907$	−3.43204	−0.113959	−0.0569795	−	0.998375i	$-0.518147\pi$
$907$	−3.43204	−0.113959	−0.0569795	+	0.998375i	$0.518147\pi$
$908$	10.6115	0.352154
$909$	−68.1461	−2.26026
$910$	−7.73450	−0.256396
$911$	−31.3587	−1.03896	−0.519480	−	0.854483i	$-0.673874\pi$
$911$	−31.3587	−1.03896	−0.519480	+	0.854483i	$0.673874\pi$
$912$	−8.48120	−0.280840
$913$	0.363900	0.0120433
$914$	3.47455	0.114928
$915$	−26.3924	−0.872505
$916$	−9.76864	−0.322765
$917$	−55.7896	−1.84233
$918$	−2.42784	−0.0801306
$919$	−9.48490	−0.312878	−0.156439	−	0.987688i	$-0.550001\pi$
$919$	−9.48490	−0.312878	−0.156439	+	0.987688i	$0.550001\pi$
$920$	−8.04963	−0.265389
$921$	76.3013	2.51421
$922$	−31.8683	−1.04953
$923$	−22.1892	−0.730366
$924$	−62.5394	−2.05739
$925$	8.18638	0.269167
$926$	6.16481	0.202588
$927$	40.5891	1.33312
$928$	−1.84274	−0.0604908
$929$	−11.3598	−0.372703	−0.186351	−	0.982483i	$-0.559666\pi$
$929$	−11.3598	−0.372703	−0.186351	+	0.982483i	$0.559666\pi$
$930$	25.2113	0.826712
$931$	37.0840	1.21538
$932$	26.9109	0.881494
$933$	67.2133	2.20047
$934$	−20.5244	−0.671580
$935$	−1.67314	−0.0547174
$936$	9.45841	0.309158
$937$	−27.4424	−0.896504	−0.448252	−	0.893907i	$-0.647953\pi$
$937$	−27.4424	−0.896504	−0.448252	+	0.893907i	$0.647953\pi$
$938$	11.4921	0.375229
$939$	−89.1930	−2.91070
$940$	−4.01252	−0.130874
$941$	−35.5183	−1.15786	−0.578931	−	0.815376i	$-0.696530\pi$
$941$	−35.5183	−1.15786	−0.578931	+	0.815376i	$0.696530\pi$
$942$	7.29493	0.237682
$943$	−84.6845	−2.75771
$944$	−5.69640	−0.185402
$945$	31.2616	1.01694
$946$	−62.0262	−2.01665
$947$	5.15024	0.167360	0.0836802	−	0.996493i	$-0.473333\pi$
$947$	5.15024	0.167360	0.0836802	+	0.996493i	$0.473333\pi$
$948$	−6.30614	−0.204814
$949$	−1.93590	−0.0628418
$950$	2.92164	0.0947905
$951$	−75.9247	−2.46203
$952$	1.52939	0.0495677
$953$	−37.0328	−1.19961	−0.599805	−	0.800146i	$-0.704755\pi$
$953$	−37.0328	−1.19961	−0.599805	+	0.800146i	$0.704755\pi$
$954$	−17.7828	−0.575739
$955$	−2.17189	−0.0702809
$956$	−12.6796	−0.410089
$957$	25.9694	0.839473
$958$	−14.7127	−0.475346
$959$	16.7669	0.541432
$960$	2.90289	0.0936903
$961$	44.4278	1.43315
$962$	14.2682	0.460026
$963$	−14.3517	−0.462477
$964$	−13.7979	−0.444400
$965$	−1.72544	−0.0555439
$966$	−103.696	−3.33636
$967$	10.4304	0.335418	0.167709	−	0.985837i	$-0.446363\pi$
$967$	10.4304	0.335418	0.167709	+	0.985837i	$0.446363\pi$
$968$	12.5688	0.403977
$969$	−2.92294	−0.0938983
$970$	1.03231	0.0331456
$971$	−11.3597	−0.364551	−0.182275	−	0.983248i	$-0.558346\pi$
$971$	−11.3597	−0.364551	−0.182275	+	0.983248i	$0.558346\pi$
$972$	9.03039	0.289650
$973$	−25.3107	−0.811423
$974$	−4.52638	−0.145035
$975$	−5.05950	−0.162034
$976$	−9.09176	−0.291020
$977$	16.0561	0.513681	0.256841	−	0.966454i	$-0.417318\pi$
$977$	16.0561	0.513681	0.256841	+	0.966454i	$0.417318\pi$
$978$	−69.3334	−2.21704
$979$	48.6652	1.55535
$980$	−12.6929	−0.405459
$981$	90.3866	2.88582
$982$	18.7949	0.599770
$983$	0.694814	0.0221611	0.0110806	−	0.999939i	$-0.496473\pi$
$983$	0.694814	0.0221611	0.0110806	+	0.999939i	$0.496473\pi$
$984$	30.5392	0.973555
$985$	−3.45339	−0.110034
$986$	−0.635076	−0.0202249
$987$	−51.6895	−1.64529
$988$	5.09219	0.162004
$989$	−102.845	−3.27028
$990$	−26.3457	−0.837321
$991$	46.2882	1.47039	0.735197	−	0.677854i	$-0.237090\pi$
$991$	46.2882	1.47039	0.735197	+	0.677854i	$0.237090\pi$
$992$	8.68492	0.275746
$993$	53.1114	1.68544
$994$	−56.4961	−1.79195
$995$	23.7092	0.751631
$996$	−0.217592	−0.00689467
$997$	−16.2902	−0.515915	−0.257958	−	0.966156i	$-0.583049\pi$
$997$	−16.2902	−0.515915	−0.257958	+	0.966156i	$0.583049\pi$
$998$	5.99805	0.189865
$999$	−57.6699	−1.82460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.o.1.2	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.o.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.90289 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.90289 q^{6} +4.43766 q^{7} +1.00000 q^{8} +5.42676 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.90289 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.90289 q^{6} +4.43766 q^{7} +1.00000 q^{8} +5.42676 q^{9} -1.00000 q^{10} +4.85477 q^{11} -2.90289 q^{12} +1.74292 q^{13} +4.43766 q^{14} +2.90289 q^{15} +1.00000 q^{16} +0.344637 q^{17} +5.42676 q^{18} +2.92164 q^{19} -1.00000 q^{20} -12.8820 q^{21} +4.85477 q^{22} +8.04963 q^{23} -2.90289 q^{24} +1.00000 q^{25} +1.74292 q^{26} -7.04462 q^{27} +4.43766 q^{28} -1.84274 q^{29} +2.90289 q^{30} +8.68492 q^{31} +1.00000 q^{32} -14.0929 q^{33} +0.344637 q^{34} -4.43766 q^{35} +5.42676 q^{36} +8.18638 q^{37} +2.92164 q^{38} -5.05950 q^{39} -1.00000 q^{40} -10.5203 q^{41} -12.8820 q^{42} -12.7763 q^{43} +4.85477 q^{44} -5.42676 q^{45} +8.04963 q^{46} +4.01252 q^{47} -2.90289 q^{48} +12.6929 q^{49} +1.00000 q^{50} -1.00044 q^{51} +1.74292 q^{52} -3.27687 q^{53} -7.04462 q^{54} -4.85477 q^{55} +4.43766 q^{56} -8.48120 q^{57} -1.84274 q^{58} -5.69640 q^{59} +2.90289 q^{60} -9.09176 q^{61} +8.68492 q^{62} +24.0821 q^{63} +1.00000 q^{64} -1.74292 q^{65} -14.0929 q^{66} +2.58967 q^{67} +0.344637 q^{68} -23.3672 q^{69} -4.43766 q^{70} -12.7310 q^{71} +5.42676 q^{72} -1.11072 q^{73} +8.18638 q^{74} -2.90289 q^{75} +2.92164 q^{76} +21.5438 q^{77} -5.05950 q^{78} +2.17237 q^{79} -1.00000 q^{80} +4.16946 q^{81} -10.5203 q^{82} +0.0749572 q^{83} -12.8820 q^{84} -0.344637 q^{85} -12.7763 q^{86} +5.34926 q^{87} +4.85477 q^{88} +10.0242 q^{89} -5.42676 q^{90} +7.73450 q^{91} +8.04963 q^{92} -25.2113 q^{93} +4.01252 q^{94} -2.92164 q^{95} -2.90289 q^{96} -1.03231 q^{97} +12.6929 q^{98} +26.3457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) \) 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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