LMFDB - Embedded newform 4029.2.a.l.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.937640 q^{2} -1.00000 q^{3} -1.12083 q^{4} +0.347083 q^{5} -0.937640 q^{6} +4.09662 q^{7} -2.92622 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.937640 q^{2} -1.00000 q^{3} -1.12083 q^{4} +0.347083 q^{5} -0.937640 q^{6} +4.09662 q^{7} -2.92622 q^{8} +1.00000 q^{9} +0.325439 q^{10} +5.59970 q^{11} +1.12083 q^{12} +4.86991 q^{13} +3.84115 q^{14} -0.347083 q^{15} -0.502078 q^{16} -1.00000 q^{17} +0.937640 q^{18} +2.01626 q^{19} -0.389021 q^{20} -4.09662 q^{21} +5.25050 q^{22} +7.46088 q^{23} +2.92622 q^{24} -4.87953 q^{25} +4.56623 q^{26} -1.00000 q^{27} -4.59161 q^{28} -1.16192 q^{29} -0.325439 q^{30} -7.75406 q^{31} +5.38166 q^{32} -5.59970 q^{33} -0.937640 q^{34} +1.42186 q^{35} -1.12083 q^{36} +5.13012 q^{37} +1.89053 q^{38} -4.86991 q^{39} -1.01564 q^{40} +12.4998 q^{41} -3.84115 q^{42} -3.07115 q^{43} -6.27631 q^{44} +0.347083 q^{45} +6.99562 q^{46} -9.52721 q^{47} +0.502078 q^{48} +9.78227 q^{49} -4.57525 q^{50} +1.00000 q^{51} -5.45835 q^{52} -12.4919 q^{53} -0.937640 q^{54} +1.94356 q^{55} -11.9876 q^{56} -2.01626 q^{57} -1.08946 q^{58} +4.14723 q^{59} +0.389021 q^{60} -4.30079 q^{61} -7.27052 q^{62} +4.09662 q^{63} +6.05022 q^{64} +1.69026 q^{65} -5.25050 q^{66} -1.33601 q^{67} +1.12083 q^{68} -7.46088 q^{69} +1.33320 q^{70} +5.13907 q^{71} -2.92622 q^{72} +8.49373 q^{73} +4.81021 q^{74} +4.87953 q^{75} -2.25988 q^{76} +22.9398 q^{77} -4.56623 q^{78} +1.00000 q^{79} -0.174263 q^{80} +1.00000 q^{81} +11.7203 q^{82} -11.4290 q^{83} +4.59161 q^{84} -0.347083 q^{85} -2.87963 q^{86} +1.16192 q^{87} -16.3859 q^{88} -12.2948 q^{89} +0.325439 q^{90} +19.9502 q^{91} -8.36238 q^{92} +7.75406 q^{93} -8.93310 q^{94} +0.699808 q^{95} -5.38166 q^{96} -14.1233 q^{97} +9.17225 q^{98} +5.59970 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * 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 $

$2$	0.937640	0.663012	0.331506	−	0.943453i	$-0.392443\pi$
$2$	0.937640	0.663012	0.331506	+	0.943453i	$0.392443\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.12083	−0.560415
$5$	0.347083	0.155220	0.0776100	−	0.996984i	$-0.475271\pi$
$5$	0.347083	0.155220	0.0776100	+	0.996984i	$0.475271\pi$
$6$	−0.937640	−0.382790
$7$	4.09662	1.54838	0.774188	−	0.632956i	$-0.218159\pi$
$7$	4.09662	1.54838	0.774188	+	0.632956i	$0.218159\pi$
$8$	−2.92622	−1.03457
$9$	1.00000	0.333333
$10$	0.325439	0.102913
$11$	5.59970	1.68837	0.844186	−	0.536050i	$-0.180084\pi$
$11$	5.59970	1.68837	0.844186	+	0.536050i	$0.180084\pi$
$12$	1.12083	0.323556
$13$	4.86991	1.35067	0.675336	−	0.737511i	$-0.263999\pi$
$13$	4.86991	1.35067	0.675336	+	0.737511i	$0.263999\pi$
$14$	3.84115	1.02659
$15$	−0.347083	−0.0896163
$16$	−0.502078	−0.125519
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.937640	0.221004
$19$	2.01626	0.462562	0.231281	−	0.972887i	$-0.425708\pi$
$19$	2.01626	0.462562	0.231281	+	0.972887i	$0.425708\pi$
$20$	−0.389021	−0.0869877
$21$	−4.09662	−0.893955
$22$	5.25050	1.11941
$23$	7.46088	1.55570	0.777851	−	0.628449i	$-0.216310\pi$
$23$	7.46088	1.55570	0.777851	+	0.628449i	$0.216310\pi$
$24$	2.92622	0.597311
$25$	−4.87953	−0.975907
$26$	4.56623	0.895511
$27$	−1.00000	−0.192450
$28$	−4.59161	−0.867733
$29$	−1.16192	−0.215763	−0.107882	−	0.994164i	$-0.534407\pi$
$29$	−1.16192	−0.215763	−0.107882	+	0.994164i	$0.534407\pi$
$30$	−0.325439	−0.0594167
$31$	−7.75406	−1.39267	−0.696335	−	0.717717i	$-0.745187\pi$
$31$	−7.75406	−1.39267	−0.696335	+	0.717717i	$0.745187\pi$
$32$	5.38166	0.951353
$33$	−5.59970	−0.974782
$34$	−0.937640	−0.160804
$35$	1.42186	0.240339
$36$	−1.12083	−0.186805
$37$	5.13012	0.843386	0.421693	−	0.906739i	$-0.361436\pi$
$37$	5.13012	0.843386	0.421693	+	0.906739i	$0.361436\pi$
$38$	1.89053	0.306684
$39$	−4.86991	−0.779810
$40$	−1.01564	−0.160587
$41$	12.4998	1.95214	0.976071	−	0.217453i	$-0.0697750\pi$
$41$	12.4998	1.95214	0.976071	+	0.217453i	$0.0697750\pi$
$42$	−3.84115	−0.592703
$43$	−3.07115	−0.468346	−0.234173	−	0.972195i	$-0.575238\pi$
$43$	−3.07115	−0.468346	−0.234173	+	0.972195i	$0.575238\pi$
$44$	−6.27631	−0.946190
$45$	0.347083	0.0517400
$46$	6.99562	1.03145
$47$	−9.52721	−1.38969	−0.694843	−	0.719161i	$-0.744526\pi$
$47$	−9.52721	−1.38969	−0.694843	+	0.719161i	$0.744526\pi$
$48$	0.502078	0.0724687
$49$	9.78227	1.39747
$50$	−4.57525	−0.647038
$51$	1.00000	0.140028
$52$	−5.45835	−0.756937
$53$	−12.4919	−1.71589	−0.857944	−	0.513744i	$-0.828258\pi$
$53$	−12.4919	−1.71589	−0.857944	+	0.513744i	$0.828258\pi$
$54$	−0.937640	−0.127597
$55$	1.94356	0.262069
$56$	−11.9876	−1.60191
$57$	−2.01626	−0.267060
$58$	−1.08946	−0.143054
$59$	4.14723	0.539923	0.269961	−	0.962871i	$-0.412989\pi$
$59$	4.14723	0.539923	0.269961	+	0.962871i	$0.412989\pi$
$60$	0.389021	0.0502224
$61$	−4.30079	−0.550660	−0.275330	−	0.961350i	$-0.588787\pi$
$61$	−4.30079	−0.550660	−0.275330	+	0.961350i	$0.588787\pi$
$62$	−7.27052	−0.923357
$63$	4.09662	0.516125
$64$	6.05022	0.756278
$65$	1.69026	0.209651
$66$	−5.25050	−0.646292
$67$	−1.33601	−0.163220	−0.0816099	−	0.996664i	$-0.526006\pi$
$67$	−1.33601	−0.163220	−0.0816099	+	0.996664i	$0.526006\pi$
$68$	1.12083	0.135921
$69$	−7.46088	−0.898185
$70$	1.33320	0.159348
$71$	5.13907	0.609895	0.304947	−	0.952369i	$-0.401361\pi$
$71$	5.13907	0.609895	0.304947	+	0.952369i	$0.401361\pi$
$72$	−2.92622	−0.344858
$73$	8.49373	0.994116	0.497058	−	0.867717i	$-0.334414\pi$
$73$	8.49373	0.994116	0.497058	+	0.867717i	$0.334414\pi$
$74$	4.81021	0.559175
$75$	4.87953	0.563440
$76$	−2.25988	−0.259227
$77$	22.9398	2.61424
$78$	−4.56623	−0.517023
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−0.174263	−0.0194831
$81$	1.00000	0.111111
$82$	11.7203	1.29429
$83$	−11.4290	−1.25450	−0.627249	−	0.778819i	$-0.715819\pi$
$83$	−11.4290	−1.25450	−0.627249	+	0.778819i	$0.715819\pi$
$84$	4.59161	0.500986
$85$	−0.347083	−0.0376464
$86$	−2.87963	−0.310519
$87$	1.16192	0.124571
$88$	−16.3859	−1.74675
$89$	−12.2948	−1.30325	−0.651624	−	0.758542i	$-0.725912\pi$
$89$	−12.2948	−1.30325	−0.651624	+	0.758542i	$0.725912\pi$
$90$	0.325439	0.0343042
$91$	19.9502	2.09135
$92$	−8.36238	−0.871839
$93$	7.75406	0.804059
$94$	−8.93310	−0.921379
$95$	0.699808	0.0717988
$96$	−5.38166	−0.549264
$97$	−14.1233	−1.43400	−0.717002	−	0.697071i	$-0.754486\pi$
$97$	−14.1233	−1.43400	−0.717002	+	0.697071i	$0.754486\pi$
$98$	9.17225	0.926537
$99$	5.59970	0.562791
$100$	5.46913	0.546913
$101$	13.1639	1.30985	0.654926	−	0.755693i	$-0.272700\pi$
$101$	13.1639	1.30985	0.654926	+	0.755693i	$0.272700\pi$
$102$	0.937640	0.0928402
$103$	9.89370	0.974855	0.487427	−	0.873163i	$-0.337935\pi$
$103$	9.89370	0.974855	0.487427	+	0.873163i	$0.337935\pi$
$104$	−14.2504	−1.39737
$105$	−1.42186	−0.138760
$106$	−11.7129	−1.13765
$107$	−17.5125	−1.69300	−0.846499	−	0.532390i	$-0.821294\pi$
$107$	−17.5125	−1.69300	−0.846499	+	0.532390i	$0.821294\pi$
$108$	1.12083	0.107852
$109$	15.6835	1.50221	0.751104	−	0.660184i	$-0.229522\pi$
$109$	15.6835	1.50221	0.751104	+	0.660184i	$0.229522\pi$
$110$	1.82236	0.173755
$111$	−5.13012	−0.486929
$112$	−2.05682	−0.194351
$113$	9.54304	0.897734	0.448867	−	0.893599i	$-0.351828\pi$
$113$	9.54304	0.897734	0.448867	+	0.893599i	$0.351828\pi$
$114$	−1.89053	−0.177064
$115$	2.58954	0.241476
$116$	1.30232	0.120917
$117$	4.86991	0.450224
$118$	3.88861	0.357975
$119$	−4.09662	−0.375536
$120$	1.01564	0.0927147
$121$	20.3566	1.85060
$122$	−4.03260	−0.365094
$123$	−12.4998	−1.12707
$124$	8.69099	0.780474
$125$	−3.42901	−0.306700
$126$	3.84115	0.342197
$127$	−2.21854	−0.196863	−0.0984317	−	0.995144i	$-0.531383\pi$
$127$	−2.21854	−0.196863	−0.0984317	+	0.995144i	$0.531383\pi$
$128$	−5.09040	−0.449932
$129$	3.07115	0.270400
$130$	1.58486	0.139001
$131$	10.5499	0.921752	0.460876	−	0.887465i	$-0.347535\pi$
$131$	10.5499	0.921752	0.460876	+	0.887465i	$0.347535\pi$
$132$	6.27631	0.546283
$133$	8.25984	0.716219
$134$	−1.25270	−0.108217
$135$	−0.347083	−0.0298721
$136$	2.92622	0.250921
$137$	−13.9317	−1.19026	−0.595132	−	0.803628i	$-0.702900\pi$
$137$	−13.9317	−1.19026	−0.595132	+	0.803628i	$0.702900\pi$
$138$	−6.99562	−0.595507
$139$	11.2444	0.953735	0.476867	−	0.878975i	$-0.341772\pi$
$139$	11.2444	0.953735	0.476867	+	0.878975i	$0.341772\pi$
$140$	−1.59367	−0.134690
$141$	9.52721	0.802336
$142$	4.81860	0.404368
$143$	27.2700	2.28044
$144$	−0.502078	−0.0418398
$145$	−0.403283	−0.0334908
$146$	7.96406	0.659110
$147$	−9.78227	−0.806828
$148$	−5.74999	−0.472647
$149$	−19.7794	−1.62039	−0.810196	−	0.586159i	$-0.800639\pi$
$149$	−19.7794	−1.62039	−0.810196	+	0.586159i	$0.800639\pi$
$150$	4.57525	0.373567
$151$	−0.247160	−0.0201136	−0.0100568	−	0.999949i	$-0.503201\pi$
$151$	−0.247160	−0.0201136	−0.0100568	+	0.999949i	$0.503201\pi$
$152$	−5.90001	−0.478554
$153$	−1.00000	−0.0808452
$154$	21.5093	1.73327
$155$	−2.69130	−0.216170
$156$	5.45835	0.437018
$157$	9.04620	0.721966	0.360983	−	0.932572i	$-0.382441\pi$
$157$	9.04620	0.721966	0.360983	+	0.932572i	$0.382441\pi$
$158$	0.937640	0.0745947
$159$	12.4919	0.990668
$160$	1.86788	0.147669
$161$	30.5644	2.40881
$162$	0.937640	0.0736680
$163$	19.8776	1.55694	0.778469	−	0.627684i	$-0.215997\pi$
$163$	19.8776	1.55694	0.778469	+	0.627684i	$0.215997\pi$
$164$	−14.0102	−1.09401
$165$	−1.94356	−0.151306
$166$	−10.7163	−0.831747
$167$	23.2387	1.79826	0.899132	−	0.437677i	$-0.144199\pi$
$167$	23.2387	1.79826	0.899132	+	0.437677i	$0.144199\pi$
$168$	11.9876	0.924863
$169$	10.7161	0.824312
$170$	−0.325439	−0.0249600
$171$	2.01626	0.154187
$172$	3.44224	0.262468
$173$	23.6309	1.79662	0.898310	−	0.439362i	$-0.144795\pi$
$173$	23.6309	1.79662	0.898310	+	0.439362i	$0.144795\pi$
$174$	1.08946	0.0825921
$175$	−19.9896	−1.51107
$176$	−2.81149	−0.211924
$177$	−4.14723	−0.311725
$178$	−11.5281	−0.864069
$179$	−5.63786	−0.421393	−0.210697	−	0.977552i	$-0.567573\pi$
$179$	−5.63786	−0.421393	−0.210697	+	0.977552i	$0.567573\pi$
$180$	−0.389021	−0.0289959
$181$	−14.1392	−1.05096	−0.525479	−	0.850806i	$-0.676114\pi$
$181$	−14.1392	−1.05096	−0.525479	+	0.850806i	$0.676114\pi$
$182$	18.7061	1.38659
$183$	4.30079	0.317924
$184$	−21.8322	−1.60949
$185$	1.78057	0.130910
$186$	7.27052	0.533101
$187$	−5.59970	−0.409491
$188$	10.6784	0.778802
$189$	−4.09662	−0.297985
$190$	0.656169	0.0476035
$191$	14.4235	1.04365	0.521824	−	0.853053i	$-0.325252\pi$
$191$	14.4235	1.04365	0.521824	+	0.853053i	$0.325252\pi$
$192$	−6.05022	−0.436637
$193$	23.1697	1.66779	0.833894	−	0.551924i	$-0.186106\pi$
$193$	23.1697	1.66779	0.833894	+	0.551924i	$0.186106\pi$
$194$	−13.2426	−0.950762
$195$	−1.69026	−0.121042
$196$	−10.9643	−0.783162
$197$	−19.0246	−1.35545	−0.677724	−	0.735316i	$-0.737034\pi$
$197$	−19.0246	−1.35545	−0.677724	+	0.735316i	$0.737034\pi$
$198$	5.25050	0.373137
$199$	−12.5654	−0.890735	−0.445368	−	0.895348i	$-0.646927\pi$
$199$	−12.5654	−0.890735	−0.445368	+	0.895348i	$0.646927\pi$
$200$	14.2786	1.00965
$201$	1.33601	0.0942350
$202$	12.3430	0.868448
$203$	−4.75995	−0.334083
$204$	−1.12083	−0.0784738
$205$	4.33846	0.303011
$206$	9.27673	0.646340
$207$	7.46088	0.518567
$208$	−2.44508	−0.169536
$209$	11.2904	0.780976
$210$	−1.33320	−0.0919994
$211$	−6.71501	−0.462280	−0.231140	−	0.972920i	$-0.574246\pi$
$211$	−6.71501	−0.462280	−0.231140	+	0.972920i	$0.574246\pi$
$212$	14.0012	0.961610
$213$	−5.13907	−0.352123
$214$	−16.4204	−1.12248
$215$	−1.06594	−0.0726967
$216$	2.92622	0.199104
$217$	−31.7654	−2.15638
$218$	14.7055	0.995982
$219$	−8.49373	−0.573953
$220$	−2.17840	−0.146868
$221$	−4.86991	−0.327586
$222$	−4.81021	−0.322840
$223$	−9.14970	−0.612709	−0.306355	−	0.951917i	$-0.599109\pi$
$223$	−9.14970	−0.612709	−0.306355	+	0.951917i	$0.599109\pi$
$224$	22.0466	1.47305
$225$	−4.87953	−0.325302
$226$	8.94794	0.595208
$227$	−4.22399	−0.280356	−0.140178	−	0.990126i	$-0.544768\pi$
$227$	−4.22399	−0.280356	−0.140178	+	0.990126i	$0.544768\pi$
$228$	2.25988	0.149665
$229$	−2.37348	−0.156844	−0.0784219	−	0.996920i	$-0.524988\pi$
$229$	−2.37348	−0.156844	−0.0784219	+	0.996920i	$0.524988\pi$
$230$	2.42806	0.160101
$231$	−22.9398	−1.50933
$232$	3.40003	0.223223
$233$	10.7498	0.704240	0.352120	−	0.935955i	$-0.385461\pi$
$233$	10.7498	0.704240	0.352120	+	0.935955i	$0.385461\pi$
$234$	4.56623	0.298504
$235$	−3.30673	−0.215707
$236$	−4.64834	−0.302581
$237$	−1.00000	−0.0649570
$238$	−3.84115	−0.248985
$239$	−27.1869	−1.75858	−0.879288	−	0.476290i	$-0.841981\pi$
$239$	−27.1869	−1.75858	−0.879288	+	0.476290i	$0.841981\pi$
$240$	0.174263	0.0112486
$241$	15.8635	1.02186	0.510928	−	0.859623i	$-0.329302\pi$
$241$	15.8635	1.02186	0.510928	+	0.859623i	$0.329302\pi$
$242$	19.0872	1.22697
$243$	−1.00000	−0.0641500
$244$	4.82046	0.308598
$245$	3.39526	0.216915
$246$	−11.7203	−0.747260
$247$	9.81901	0.624769
$248$	22.6901	1.44082
$249$	11.4290	0.724284
$250$	−3.21518	−0.203346
$251$	−1.56038	−0.0984902	−0.0492451	−	0.998787i	$-0.515682\pi$
$251$	−1.56038	−0.0984902	−0.0492451	+	0.998787i	$0.515682\pi$
$252$	−4.59161	−0.289244
$253$	41.7787	2.62660
$254$	−2.08019	−0.130523
$255$	0.347083	0.0217352
$256$	−16.8734	−1.05459
$257$	12.8005	0.798476	0.399238	−	0.916847i	$-0.369275\pi$
$257$	12.8005	0.798476	0.399238	+	0.916847i	$0.369275\pi$
$258$	2.87963	0.179278
$259$	21.0161	1.30588
$260$	−1.89450	−0.117492
$261$	−1.16192	−0.0719211
$262$	9.89204	0.611132
$263$	−17.2751	−1.06523	−0.532614	−	0.846358i	$-0.678790\pi$
$263$	−17.2751	−1.06523	−0.532614	+	0.846358i	$0.678790\pi$
$264$	16.3859	1.00848
$265$	−4.33570	−0.266340
$266$	7.74476	0.474862
$267$	12.2948	0.752431
$268$	1.49744	0.0914708
$269$	13.5428	0.825722	0.412861	−	0.910794i	$-0.364530\pi$
$269$	13.5428	0.825722	0.412861	+	0.910794i	$0.364530\pi$
$270$	−0.325439	−0.0198056
$271$	−5.09831	−0.309700	−0.154850	−	0.987938i	$-0.549489\pi$
$271$	−5.09831	−0.309700	−0.154850	+	0.987938i	$0.549489\pi$
$272$	0.502078	0.0304429
$273$	−19.9502	−1.20744
$274$	−13.0629	−0.789159
$275$	−27.3239	−1.64769
$276$	8.36238	0.503356
$277$	6.00075	0.360550	0.180275	−	0.983616i	$-0.442301\pi$
$277$	6.00075	0.360550	0.180275	+	0.983616i	$0.442301\pi$
$278$	10.5432	0.632337
$279$	−7.75406	−0.464224
$280$	−4.16068	−0.248648
$281$	7.17807	0.428208	0.214104	−	0.976811i	$-0.431317\pi$
$281$	7.17807	0.428208	0.214104	+	0.976811i	$0.431317\pi$
$282$	8.93310	0.531958
$283$	20.0080	1.18935	0.594675	−	0.803966i	$-0.297281\pi$
$283$	20.0080	1.18935	0.594675	+	0.803966i	$0.297281\pi$
$284$	−5.76002	−0.341794
$285$	−0.699808	−0.0414531
$286$	25.5695	1.51196
$287$	51.2069	3.02265
$288$	5.38166	0.317118
$289$	1.00000	0.0588235
$290$	−0.378134	−0.0222048
$291$	14.1233	0.827923
$292$	−9.52003	−0.557118
$293$	−28.3559	−1.65657	−0.828285	−	0.560308i	$-0.810683\pi$
$293$	−28.3559	−1.65657	−0.828285	+	0.560308i	$0.810683\pi$
$294$	−9.17225	−0.534937
$295$	1.43943	0.0838068
$296$	−15.0118	−0.872545
$297$	−5.59970	−0.324927
$298$	−18.5460	−1.07434
$299$	36.3338	2.10124
$300$	−5.46913	−0.315760
$301$	−12.5813	−0.725176
$302$	−0.231747	−0.0133355
$303$	−13.1639	−0.756244
$304$	−1.01232	−0.0580605
$305$	−1.49273	−0.0854734
$306$	−0.937640	−0.0536013
$307$	−23.4856	−1.34039	−0.670196	−	0.742184i	$-0.733790\pi$
$307$	−23.4856	−1.34039	−0.670196	+	0.742184i	$0.733790\pi$
$308$	−25.7117	−1.46506
$309$	−9.89370	−0.562833
$310$	−2.52347	−0.143324
$311$	−9.82176	−0.556941	−0.278470	−	0.960445i	$-0.589827\pi$
$311$	−9.82176	−0.556941	−0.278470	+	0.960445i	$0.589827\pi$
$312$	14.2504	0.806771
$313$	11.7000	0.661323	0.330662	−	0.943749i	$-0.392728\pi$
$313$	11.7000	0.661323	0.330662	+	0.943749i	$0.392728\pi$
$314$	8.48209	0.478672
$315$	1.42186	0.0801130
$316$	−1.12083	−0.0630516
$317$	−20.3892	−1.14517	−0.572586	−	0.819845i	$-0.694060\pi$
$317$	−20.3892	−1.14517	−0.572586	+	0.819845i	$0.694060\pi$
$318$	11.7129	0.656825
$319$	−6.50641	−0.364289
$320$	2.09993	0.117389
$321$	17.5125	0.977453
$322$	28.6584	1.59707
$323$	−2.01626	−0.112188
$324$	−1.12083	−0.0622684
$325$	−23.7629	−1.31813
$326$	18.6381	1.03227
$327$	−15.6835	−0.867300
$328$	−36.5771	−2.01963
$329$	−39.0293	−2.15176
$330$	−1.82236	−0.100318
$331$	−15.2254	−0.836863	−0.418431	−	0.908248i	$-0.637420\pi$
$331$	−15.2254	−0.836863	−0.418431	+	0.908248i	$0.637420\pi$
$332$	12.8100	0.703039
$333$	5.13012	0.281129
$334$	21.7895	1.19227
$335$	−0.463706	−0.0253350
$336$	2.05682	0.112209
$337$	13.5123	0.736062	0.368031	−	0.929814i	$-0.380032\pi$
$337$	13.5123	0.736062	0.368031	+	0.929814i	$0.380032\pi$
$338$	10.0478	0.546529
$339$	−9.54304	−0.518307
$340$	0.389021	0.0210976
$341$	−43.4204	−2.35135
$342$	1.89053	0.102228
$343$	11.3979	0.615429
$344$	8.98685	0.484539
$345$	−2.58954	−0.139416
$346$	22.1572	1.19118
$347$	−3.83122	−0.205671	−0.102835	−	0.994698i	$-0.532791\pi$
$347$	−3.83122	−0.205671	−0.102835	+	0.994698i	$0.532791\pi$
$348$	−1.30232	−0.0698115
$349$	30.8043	1.64891	0.824457	−	0.565924i	$-0.191481\pi$
$349$	30.8043	1.64891	0.824457	+	0.565924i	$0.191481\pi$
$350$	−18.7430	−1.00186
$351$	−4.86991	−0.259937
$352$	30.1357	1.60624
$353$	−17.2001	−0.915471	−0.457735	−	0.889088i	$-0.651339\pi$
$353$	−17.2001	−0.915471	−0.457735	+	0.889088i	$0.651339\pi$
$354$	−3.88861	−0.206677
$355$	1.78368	0.0946679
$356$	13.7804	0.730360
$357$	4.09662	0.216816
$358$	−5.28628	−0.279389
$359$	−22.4491	−1.18482	−0.592410	−	0.805637i	$-0.701823\pi$
$359$	−22.4491	−1.18482	−0.592410	+	0.805637i	$0.701823\pi$
$360$	−1.01564	−0.0535289
$361$	−14.9347	−0.786037
$362$	−13.2575	−0.696798
$363$	−20.3566	−1.06845
$364$	−22.3608	−1.17202
$365$	2.94802	0.154307
$366$	4.03260	0.210787
$367$	−25.8969	−1.35181	−0.675903	−	0.736990i	$-0.736246\pi$
$367$	−25.8969	−1.35181	−0.675903	+	0.736990i	$0.736246\pi$
$368$	−3.74594	−0.195271
$369$	12.4998	0.650714
$370$	1.66954	0.0867952
$371$	−51.1743	−2.65684
$372$	−8.69099	−0.450607
$373$	15.4291	0.798890	0.399445	−	0.916757i	$-0.369203\pi$
$373$	15.4291	0.798890	0.399445	+	0.916757i	$0.369203\pi$
$374$	−5.25050	−0.271497
$375$	3.42901	0.177074
$376$	27.8787	1.43773
$377$	−5.65845	−0.291425
$378$	−3.84115	−0.197568
$379$	−2.04604	−0.105098	−0.0525489	−	0.998618i	$-0.516735\pi$
$379$	−2.04604	−0.105098	−0.0525489	+	0.998618i	$0.516735\pi$
$380$	−0.784367	−0.0402372
$381$	2.21854	0.113659
$382$	13.5241	0.691952
$383$	−0.154093	−0.00787380	−0.00393690	−	0.999992i	$-0.501253\pi$
$383$	−0.154093	−0.00787380	−0.00393690	+	0.999992i	$0.501253\pi$
$384$	5.09040	0.259768
$385$	7.96201	0.405782
$386$	21.7248	1.10576
$387$	−3.07115	−0.156115
$388$	15.8298	0.803638
$389$	18.0285	0.914083	0.457041	−	0.889445i	$-0.348909\pi$
$389$	18.0285	0.914083	0.457041	+	0.889445i	$0.348909\pi$
$390$	−1.58486	−0.0802524
$391$	−7.46088	−0.377313
$392$	−28.6250	−1.44578
$393$	−10.5499	−0.532174
$394$	−17.8383	−0.898678
$395$	0.347083	0.0174636
$396$	−6.27631	−0.315397
$397$	−5.83195	−0.292697	−0.146348	−	0.989233i	$-0.546752\pi$
$397$	−5.83195	−0.292697	−0.146348	+	0.989233i	$0.546752\pi$
$398$	−11.7818	−0.590568
$399$	−8.25984	−0.413509
$400$	2.44991	0.122495
$401$	−4.36405	−0.217930	−0.108965	−	0.994046i	$-0.534754\pi$
$401$	−4.36405	−0.217930	−0.108965	+	0.994046i	$0.534754\pi$
$402$	1.25270	0.0624789
$403$	−37.7616	−1.88104
$404$	−14.7545	−0.734061
$405$	0.347083	0.0172467
$406$	−4.46312	−0.221501
$407$	28.7271	1.42395
$408$	−2.92622	−0.144869
$409$	−19.4906	−0.963747	−0.481873	−	0.876241i	$-0.660043\pi$
$409$	−19.4906	−0.963747	−0.481873	+	0.876241i	$0.660043\pi$
$410$	4.06792	0.200900
$411$	13.9317	0.687199
$412$	−11.0892	−0.546324
$413$	16.9896	0.836003
$414$	6.99562	0.343816
$415$	−3.96681	−0.194723
$416$	26.2082	1.28496
$417$	−11.2444	−0.550639
$418$	10.5864	0.517797
$419$	12.9774	0.633987	0.316993	−	0.948428i	$-0.397327\pi$
$419$	12.9774	0.633987	0.316993	+	0.948428i	$0.397327\pi$
$420$	1.59367	0.0777631
$421$	22.8680	1.11452	0.557258	−	0.830339i	$-0.311853\pi$
$421$	22.8680	1.11452	0.557258	+	0.830339i	$0.311853\pi$
$422$	−6.29626	−0.306497
$423$	−9.52721	−0.463229
$424$	36.5539	1.77521
$425$	4.87953	0.236692
$426$	−4.81860	−0.233462
$427$	−17.6187	−0.852628
$428$	19.6286	0.948782
$429$	−27.2700	−1.31661
$430$	−0.999471	−0.0481988
$431$	−4.19097	−0.201872	−0.100936	−	0.994893i	$-0.532184\pi$
$431$	−4.19097	−0.201872	−0.100936	+	0.994893i	$0.532184\pi$
$432$	0.502078	0.0241562
$433$	−26.4514	−1.27117	−0.635586	−	0.772030i	$-0.719242\pi$
$433$	−26.4514	−1.27117	−0.635586	+	0.772030i	$0.719242\pi$
$434$	−29.7845	−1.42970
$435$	0.403283	0.0193359
$436$	−17.5786	−0.841860
$437$	15.0431	0.719608
$438$	−7.96406	−0.380538
$439$	12.3154	0.587784	0.293892	−	0.955839i	$-0.405049\pi$
$439$	12.3154	0.587784	0.293892	+	0.955839i	$0.405049\pi$
$440$	−5.68727	−0.271130
$441$	9.78227	0.465822
$442$	−4.56623	−0.217193
$443$	18.7289	0.889837	0.444918	−	0.895571i	$-0.353233\pi$
$443$	18.7289	0.889837	0.444918	+	0.895571i	$0.353233\pi$
$444$	5.74999	0.272883
$445$	−4.26732	−0.202290
$446$	−8.57913	−0.406233
$447$	19.7794	0.935534
$448$	24.7854	1.17100
$449$	11.6254	0.548636	0.274318	−	0.961639i	$-0.411548\pi$
$449$	11.6254	0.548636	0.274318	+	0.961639i	$0.411548\pi$
$450$	−4.57525	−0.215679
$451$	69.9951	3.29594
$452$	−10.6961	−0.503104
$453$	0.247160	0.0116126
$454$	−3.96059	−0.185880
$455$	6.92436	0.324619
$456$	5.90001	0.276293
$457$	17.8919	0.836945	0.418473	−	0.908229i	$-0.362566\pi$
$457$	17.8919	0.836945	0.418473	+	0.908229i	$0.362566\pi$
$458$	−2.22547	−0.103989
$459$	1.00000	0.0466760
$460$	−2.90244	−0.135327
$461$	−30.5920	−1.42481	−0.712405	−	0.701769i	$-0.752394\pi$
$461$	−30.5920	−1.42481	−0.712405	+	0.701769i	$0.752394\pi$
$462$	−21.5093	−1.00070
$463$	32.2386	1.49825	0.749126	−	0.662427i	$-0.230474\pi$
$463$	32.2386	1.49825	0.749126	+	0.662427i	$0.230474\pi$
$464$	0.583375	0.0270825
$465$	2.69130	0.124806
$466$	10.0794	0.466920
$467$	15.9870	0.739791	0.369896	−	0.929073i	$-0.379393\pi$
$467$	15.9870	0.739791	0.369896	+	0.929073i	$0.379393\pi$
$468$	−5.45835	−0.252312
$469$	−5.47313	−0.252726
$470$	−3.10052	−0.143016
$471$	−9.04620	−0.416827
$472$	−12.1357	−0.558590
$473$	−17.1975	−0.790743
$474$	−0.937640	−0.0430672
$475$	−9.83841	−0.451417
$476$	4.59161	0.210456
$477$	−12.4919	−0.571963
$478$	−25.4916	−1.16596
$479$	13.0677	0.597079	0.298540	−	0.954397i	$-0.403501\pi$
$479$	13.0677	0.597079	0.298540	+	0.954397i	$0.403501\pi$
$480$	−1.86788	−0.0852568
$481$	24.9832	1.13914
$482$	14.8742	0.677503
$483$	−30.5644	−1.39073
$484$	−22.8163	−1.03711
$485$	−4.90195	−0.222586
$486$	−0.937640	−0.0425322
$487$	−22.1941	−1.00571	−0.502854	−	0.864371i	$-0.667717\pi$
$487$	−22.1941	−1.00571	−0.502854	+	0.864371i	$0.667717\pi$
$488$	12.5850	0.569698
$489$	−19.8776	−0.898898
$490$	3.18353	0.143817
$491$	−10.0490	−0.453503	−0.226752	−	0.973953i	$-0.572811\pi$
$491$	−10.0490	−0.453503	−0.226752	+	0.973953i	$0.572811\pi$
$492$	14.0102	0.631627
$493$	1.16192	0.0523303
$494$	9.20670	0.414229
$495$	1.94356	0.0873564
$496$	3.89314	0.174807
$497$	21.0528	0.944346
$498$	10.7163	0.480209
$499$	−17.5225	−0.784414	−0.392207	−	0.919877i	$-0.628288\pi$
$499$	−17.5225	−0.784414	−0.392207	+	0.919877i	$0.628288\pi$
$500$	3.84334	0.171880
$501$	−23.2387	−1.03823
$502$	−1.46307	−0.0653002
$503$	2.04147	0.0910247	0.0455123	−	0.998964i	$-0.485508\pi$
$503$	2.04147	0.0910247	0.0455123	+	0.998964i	$0.485508\pi$
$504$	−11.9876	−0.533970
$505$	4.56895	0.203315
$506$	39.1734	1.74147
$507$	−10.7161	−0.475917
$508$	2.48661	0.110325
$509$	−39.9557	−1.77101	−0.885504	−	0.464633i	$-0.846186\pi$
$509$	−39.9557	−1.77101	−0.885504	+	0.464633i	$0.846186\pi$
$510$	0.325439	0.0144107
$511$	34.7955	1.53926
$512$	−5.64039	−0.249273
$513$	−2.01626	−0.0890200
$514$	12.0023	0.529399
$515$	3.43393	0.151317
$516$	−3.44224	−0.151536
$517$	−53.3495	−2.34631
$518$	19.7056	0.865813
$519$	−23.6309	−1.03728
$520$	−4.94607	−0.216900
$521$	10.3033	0.451397	0.225699	−	0.974197i	$-0.427534\pi$
$521$	10.3033	0.451397	0.225699	+	0.974197i	$0.427534\pi$
$522$	−1.08946	−0.0476845
$523$	6.43225	0.281263	0.140631	−	0.990062i	$-0.455087\pi$
$523$	6.43225	0.281263	0.140631	+	0.990062i	$0.455087\pi$
$524$	−11.8247	−0.516564
$525$	19.9896	0.872417
$526$	−16.1978	−0.706259
$527$	7.75406	0.337772
$528$	2.81149	0.122354
$529$	32.6647	1.42021
$530$	−4.06533	−0.176587
$531$	4.14723	0.179974
$532$	−9.25788	−0.401380
$533$	60.8730	2.63670
$534$	11.5281	0.498871
$535$	−6.07829	−0.262787
$536$	3.90946	0.168863
$537$	5.63786	0.243291
$538$	12.6983	0.547463
$539$	54.7778	2.35945
$540$	0.389021	0.0167408
$541$	23.1879	0.996927	0.498463	−	0.866911i	$-0.333898\pi$
$541$	23.1879	0.996927	0.498463	+	0.866911i	$0.333898\pi$
$542$	−4.78038	−0.205335
$543$	14.1392	0.606771
$544$	−5.38166	−0.230737
$545$	5.44347	0.233173
$546$	−18.7061	−0.800547
$547$	−11.2899	−0.482721	−0.241361	−	0.970435i	$-0.577594\pi$
$547$	−11.2899	−0.482721	−0.241361	+	0.970435i	$0.577594\pi$
$548$	15.6151	0.667042
$549$	−4.30079	−0.183553
$550$	−25.6200	−1.09244
$551$	−2.34273	−0.0998038
$552$	21.8322	0.929238
$553$	4.09662	0.174206
$554$	5.62654	0.239049
$555$	−1.78057	−0.0755812
$556$	−12.6030	−0.534487
$557$	−24.3062	−1.02989	−0.514943	−	0.857224i	$-0.672187\pi$
$557$	−24.3062	−1.02989	−0.514943	+	0.857224i	$0.672187\pi$
$558$	−7.27052	−0.307786
$559$	−14.9562	−0.632581
$560$	−0.713887	−0.0301672
$561$	5.59970	0.236419
$562$	6.73045	0.283907
$563$	36.5673	1.54113	0.770563	−	0.637364i	$-0.219975\pi$
$563$	36.5673	1.54113	0.770563	+	0.637364i	$0.219975\pi$
$564$	−10.6784	−0.449641
$565$	3.31222	0.139346
$566$	18.7603	0.788553
$567$	4.09662	0.172042
$568$	−15.0380	−0.630981
$569$	−17.3740	−0.728354	−0.364177	−	0.931330i	$-0.618650\pi$
$569$	−17.3740	−0.728354	−0.364177	+	0.931330i	$0.618650\pi$
$570$	−0.656169	−0.0274839
$571$	18.8824	0.790204	0.395102	−	0.918637i	$-0.370709\pi$
$571$	18.8824	0.790204	0.395102	+	0.918637i	$0.370709\pi$
$572$	−30.5651	−1.27799
$573$	−14.4235	−0.602551
$574$	48.0137	2.00405
$575$	−36.4056	−1.51822
$576$	6.05022	0.252093
$577$	8.23163	0.342687	0.171344	−	0.985211i	$-0.445189\pi$
$577$	8.23163	0.342687	0.171344	+	0.985211i	$0.445189\pi$
$578$	0.937640	0.0390007
$579$	−23.1697	−0.962898
$580$	0.452011	0.0187687
$581$	−46.8203	−1.94243
$582$	13.2426	0.548923
$583$	−69.9506	−2.89706
$584$	−24.8545	−1.02849
$585$	1.69026	0.0698837
$586$	−26.5876	−1.09832
$587$	6.53172	0.269593	0.134796	−	0.990873i	$-0.456962\pi$
$587$	6.53172	0.269593	0.134796	+	0.990873i	$0.456962\pi$
$588$	10.9643	0.452159
$589$	−15.6342	−0.644196
$590$	1.34967	0.0555649
$591$	19.0246	0.782568
$592$	−2.57572	−0.105861
$593$	−11.1777	−0.459013	−0.229506	−	0.973307i	$-0.573711\pi$
$593$	−11.1777	−0.459013	−0.229506	+	0.973307i	$0.573711\pi$
$594$	−5.25050	−0.215431
$595$	−1.42186	−0.0582908
$596$	22.1694	0.908092
$597$	12.5654	0.514266
$598$	34.0681	1.39315
$599$	14.5485	0.594435	0.297217	−	0.954810i	$-0.403941\pi$
$599$	14.5485	0.594435	0.297217	+	0.954810i	$0.403941\pi$
$600$	−14.2786	−0.582920
$601$	−14.4650	−0.590040	−0.295020	−	0.955491i	$-0.595326\pi$
$601$	−14.4650	−0.590040	−0.295020	+	0.955491i	$0.595326\pi$
$602$	−11.7968	−0.480800
$603$	−1.33601	−0.0544066
$604$	0.277024	0.0112720
$605$	7.06543	0.287251
$606$	−12.3430	−0.501399
$607$	10.7009	0.434336	0.217168	−	0.976134i	$-0.430318\pi$
$607$	10.7009	0.434336	0.217168	+	0.976134i	$0.430318\pi$
$608$	10.8508	0.440059
$609$	4.75995	0.192883
$610$	−1.39964	−0.0566699
$611$	−46.3967	−1.87701
$612$	1.12083	0.0453069
$613$	−20.8403	−0.841731	−0.420865	−	0.907123i	$-0.638273\pi$
$613$	−20.8403	−0.841731	−0.420865	+	0.907123i	$0.638273\pi$
$614$	−22.0210	−0.888695
$615$	−4.33846	−0.174944
$616$	−67.1269	−2.70462
$617$	−17.3444	−0.698260	−0.349130	−	0.937074i	$-0.613523\pi$
$617$	−17.3444	−0.698260	−0.349130	+	0.937074i	$0.613523\pi$
$618$	−9.27673	−0.373165
$619$	3.24893	0.130585	0.0652927	−	0.997866i	$-0.479202\pi$
$619$	3.24893	0.130585	0.0652927	+	0.997866i	$0.479202\pi$
$620$	3.01649	0.121145
$621$	−7.46088	−0.299395
$622$	−9.20928	−0.369258
$623$	−50.3672	−2.01792
$624$	2.44508	0.0978814
$625$	23.2075	0.928301
$626$	10.9704	0.438465
$627$	−11.2904	−0.450897
$628$	−10.1393	−0.404601
$629$	−5.13012	−0.204551
$630$	1.33320	0.0531159
$631$	33.4493	1.33159	0.665797	−	0.746133i	$-0.268092\pi$
$631$	33.4493	1.33159	0.665797	+	0.746133i	$0.268092\pi$
$632$	−2.92622	−0.116399
$633$	6.71501	0.266898
$634$	−19.1177	−0.759263
$635$	−0.770016	−0.0305571
$636$	−14.0012	−0.555186
$637$	47.6388	1.88752
$638$	−6.10067	−0.241528
$639$	5.13907	0.203298
$640$	−1.76679	−0.0698384
$641$	−17.3263	−0.684348	−0.342174	−	0.939637i	$-0.611163\pi$
$641$	−17.3263	−0.684348	−0.342174	+	0.939637i	$0.611163\pi$
$642$	16.4204	0.648063
$643$	12.7906	0.504414	0.252207	−	0.967673i	$-0.418844\pi$
$643$	12.7906	0.504414	0.252207	+	0.967673i	$0.418844\pi$
$644$	−34.2575	−1.34993
$645$	1.06594	0.0419715
$646$	−1.89053	−0.0743818
$647$	−20.2770	−0.797170	−0.398585	−	0.917131i	$-0.630499\pi$
$647$	−20.2770	−0.797170	−0.398585	+	0.917131i	$0.630499\pi$
$648$	−2.92622	−0.114953
$649$	23.2232	0.911591
$650$	−22.2811	−0.873935
$651$	31.7654	1.24499
$652$	−22.2795	−0.872531
$653$	−7.45780	−0.291846	−0.145923	−	0.989296i	$-0.546615\pi$
$653$	−7.45780	−0.291846	−0.145923	+	0.989296i	$0.546615\pi$
$654$	−14.7055	−0.575030
$655$	3.66170	0.143074
$656$	−6.27588	−0.245032
$657$	8.49373	0.331372
$658$	−36.5955	−1.42664
$659$	−13.1328	−0.511583	−0.255791	−	0.966732i	$-0.582336\pi$
$659$	−13.1328	−0.511583	−0.255791	+	0.966732i	$0.582336\pi$
$660$	2.17840	0.0847941
$661$	−17.9357	−0.697616	−0.348808	−	0.937194i	$-0.613413\pi$
$661$	−17.9357	−0.697616	−0.348808	+	0.937194i	$0.613413\pi$
$662$	−14.2759	−0.554850
$663$	4.86991	0.189132
$664$	33.4438	1.29787
$665$	2.86685	0.111172
$666$	4.81021	0.186392
$667$	−8.66895	−0.335663
$668$	−26.0466	−1.00778
$669$	9.14970	0.353748
$670$	−0.434790	−0.0167974
$671$	−24.0831	−0.929719
$672$	−22.0466	−0.850467
$673$	−7.09535	−0.273506	−0.136753	−	0.990605i	$-0.543667\pi$
$673$	−7.09535	−0.273506	−0.136753	+	0.990605i	$0.543667\pi$
$674$	12.6697	0.488018
$675$	4.87953	0.187813
$676$	−12.0109	−0.461957
$677$	36.6573	1.40885	0.704426	−	0.709777i	$-0.251204\pi$
$677$	36.6573	1.40885	0.704426	+	0.709777i	$0.251204\pi$
$678$	−8.94794	−0.343644
$679$	−57.8578	−2.22038
$680$	1.01564	0.0389480
$681$	4.22399	0.161864
$682$	−40.7127	−1.55897
$683$	−8.43662	−0.322818	−0.161409	−	0.986888i	$-0.551604\pi$
$683$	−8.43662	−0.322818	−0.161409	+	0.986888i	$0.551604\pi$
$684$	−2.25988	−0.0864089
$685$	−4.83544	−0.184753
$686$	10.6871	0.408037
$687$	2.37348	0.0905538
$688$	1.54196	0.0587866
$689$	−60.8342	−2.31760
$690$	−2.42806	−0.0924346
$691$	12.5285	0.476606	0.238303	−	0.971191i	$-0.423409\pi$
$691$	12.5285	0.476606	0.238303	+	0.971191i	$0.423409\pi$
$692$	−26.4862	−1.00685
$693$	22.9398	0.871412
$694$	−3.59231	−0.136362
$695$	3.90272	0.148039
$696$	−3.40003	−0.128878
$697$	−12.4998	−0.473464
$698$	28.8833	1.09325
$699$	−10.7498	−0.406593
$700$	22.4049	0.846827
$701$	−31.0482	−1.17268	−0.586338	−	0.810066i	$-0.699431\pi$
$701$	−31.0482	−1.17268	−0.586338	+	0.810066i	$0.699431\pi$
$702$	−4.56623	−0.172341
$703$	10.3436	0.390118
$704$	33.8794	1.27688
$705$	3.30673	0.124539
$706$	−16.1275	−0.606968
$707$	53.9273	2.02814
$708$	4.64834	0.174695
$709$	−45.1159	−1.69436	−0.847182	−	0.531303i	$-0.821702\pi$
$709$	−45.1159	−1.69436	−0.847182	+	0.531303i	$0.821702\pi$
$710$	1.67245	0.0627659
$711$	1.00000	0.0375029
$712$	35.9773	1.34831
$713$	−57.8521	−2.16658
$714$	3.84115	0.143752
$715$	9.46496	0.353969
$716$	6.31908	0.236155
$717$	27.1869	1.01531
$718$	−21.0492	−0.785550
$719$	−30.1870	−1.12578	−0.562892	−	0.826530i	$-0.690311\pi$
$719$	−30.1870	−1.12578	−0.562892	+	0.826530i	$0.690311\pi$
$720$	−0.174263	−0.00649438
$721$	40.5307	1.50944
$722$	−14.0034	−0.521152
$723$	−15.8635	−0.589969
$724$	15.8476	0.588973
$725$	5.66963	0.210565
$726$	−19.0872	−0.708392
$727$	39.6179	1.46934	0.734672	−	0.678422i	$-0.237336\pi$
$727$	39.6179	1.46934	0.734672	+	0.678422i	$0.237336\pi$
$728$	−58.3785	−2.16365
$729$	1.00000	0.0370370
$730$	2.76419	0.102307
$731$	3.07115	0.113591
$732$	−4.82046	−0.178169
$733$	−0.841789	−0.0310922	−0.0155461	−	0.999879i	$-0.504949\pi$
$733$	−0.841789	−0.0310922	−0.0155461	+	0.999879i	$0.504949\pi$
$734$	−24.2820	−0.896264
$735$	−3.39526	−0.125236
$736$	40.1520	1.48002
$737$	−7.48126	−0.275576
$738$	11.7203	0.431431
$739$	42.6030	1.56718	0.783589	−	0.621280i	$-0.213387\pi$
$739$	42.6030	1.56718	0.783589	+	0.621280i	$0.213387\pi$
$740$	−1.99572	−0.0733642
$741$	−9.81901	−0.360710
$742$	−47.9831	−1.76152
$743$	12.7733	0.468609	0.234304	−	0.972163i	$-0.424719\pi$
$743$	12.7733	0.468609	0.234304	+	0.972163i	$0.424719\pi$
$744$	−22.6901	−0.831858
$745$	−6.86509	−0.251517
$746$	14.4670	0.529673
$747$	−11.4290	−0.418166
$748$	6.27631	0.229485
$749$	−71.7420	−2.62140
$750$	3.21518	0.117402
$751$	26.1462	0.954090	0.477045	−	0.878879i	$-0.341708\pi$
$751$	26.1462	0.954090	0.477045	+	0.878879i	$0.341708\pi$
$752$	4.78340	0.174433
$753$	1.56038	0.0568634
$754$	−5.30560	−0.193218
$755$	−0.0857849	−0.00312203
$756$	4.59161	0.166995
$757$	−22.6111	−0.821816	−0.410908	−	0.911677i	$-0.634788\pi$
$757$	−22.6111	−0.821816	−0.410908	+	0.911677i	$0.634788\pi$
$758$	−1.91845	−0.0696811
$759$	−41.7787	−1.51647
$760$	−2.04779	−0.0742812
$761$	−41.3831	−1.50013	−0.750067	−	0.661362i	$-0.769979\pi$
$761$	−41.3831	−1.50013	−0.750067	+	0.661362i	$0.769979\pi$
$762$	2.08019	0.0753574
$763$	64.2493	2.32598
$764$	−16.1663	−0.584877
$765$	−0.347083	−0.0125488
$766$	−0.144484	−0.00522043
$767$	20.1966	0.729258
$768$	16.8734	0.608867
$769$	−16.6357	−0.599898	−0.299949	−	0.953955i	$-0.596970\pi$
$769$	−16.6357	−0.599898	−0.299949	+	0.953955i	$0.596970\pi$
$770$	7.46550	0.269038
$771$	−12.8005	−0.461000
$772$	−25.9693	−0.934654
$773$	23.6869	0.851959	0.425980	−	0.904733i	$-0.359930\pi$
$773$	23.6869	0.851959	0.425980	+	0.904733i	$0.359930\pi$
$774$	−2.87963	−0.103506
$775$	37.8362	1.35912
$776$	41.3278	1.48358
$777$	−21.0161	−0.753950
$778$	16.9043	0.606048
$779$	25.2028	0.902986
$780$	1.89450	0.0678339
$781$	28.7772	1.02973
$782$	−6.99562	−0.250163
$783$	1.16192	0.0415237
$784$	−4.91146	−0.175409
$785$	3.13978	0.112064
$786$	−9.89204	−0.352837
$787$	−45.5145	−1.62242	−0.811208	−	0.584758i	$-0.801190\pi$
$787$	−45.5145	−1.62242	−0.811208	+	0.584758i	$0.801190\pi$
$788$	21.3234	0.759614
$789$	17.2751	0.615009
$790$	0.325439	0.0115786
$791$	39.0942	1.39003
$792$	−16.3859	−0.582249
$793$	−20.9445	−0.743760
$794$	−5.46827	−0.194062
$795$	4.33570	0.153772
$796$	14.0836	0.499182
$797$	−28.6934	−1.01637	−0.508186	−	0.861247i	$-0.669684\pi$
$797$	−28.6934	−1.01637	−0.508186	+	0.861247i	$0.669684\pi$
$798$	−7.74476	−0.274162
$799$	9.52721	0.337049
$800$	−26.2600	−0.928432
$801$	−12.2948	−0.434416
$802$	−4.09191	−0.144490
$803$	47.5623	1.67844
$804$	−1.49744	−0.0528107
$805$	10.6084	0.373896
$806$	−35.4068	−1.24715
$807$	−13.5428	−0.476731
$808$	−38.5203	−1.35514
$809$	−16.1541	−0.567947	−0.283973	−	0.958832i	$-0.591653\pi$
$809$	−16.1541	−0.567947	−0.283973	+	0.958832i	$0.591653\pi$
$810$	0.325439	0.0114347
$811$	−21.7220	−0.762763	−0.381381	−	0.924418i	$-0.624552\pi$
$811$	−21.7220	−0.762763	−0.381381	+	0.924418i	$0.624552\pi$
$812$	5.33509	0.187225
$813$	5.09831	0.178805
$814$	26.9357	0.944096
$815$	6.89918	0.241668
$816$	−0.502078	−0.0175762
$817$	−6.19224	−0.216639
$818$	−18.2751	−0.638975
$819$	19.9502	0.697115
$820$	−4.86268	−0.169812
$821$	3.79658	0.132502	0.0662508	−	0.997803i	$-0.478896\pi$
$821$	3.79658	0.132502	0.0662508	+	0.997803i	$0.478896\pi$
$822$	13.0629	0.455621
$823$	15.3534	0.535185	0.267592	−	0.963532i	$-0.413772\pi$
$823$	15.3534	0.535185	0.267592	+	0.963532i	$0.413772\pi$
$824$	−28.9511	−1.00856
$825$	27.3239	0.951297
$826$	15.9301	0.554280
$827$	−7.28594	−0.253357	−0.126679	−	0.991944i	$-0.540432\pi$
$827$	−7.28594	−0.253357	−0.126679	+	0.991944i	$0.540432\pi$
$828$	−8.36238	−0.290613
$829$	37.4118	1.29937	0.649683	−	0.760205i	$-0.274902\pi$
$829$	37.4118	1.29937	0.649683	+	0.760205i	$0.274902\pi$
$830$	−3.71944	−0.129104
$831$	−6.00075	−0.208164
$832$	29.4641	1.02148
$833$	−9.78227	−0.338936
$834$	−10.5432	−0.365080
$835$	8.06575	0.279127
$836$	−12.6547	−0.437671
$837$	7.75406	0.268020
$838$	12.1681	0.420341
$839$	7.15124	0.246888	0.123444	−	0.992352i	$-0.460606\pi$
$839$	7.15124	0.246888	0.123444	+	0.992352i	$0.460606\pi$
$840$	4.16068	0.143557
$841$	−27.6499	−0.953446
$842$	21.4419	0.738938
$843$	−7.17807	−0.247226
$844$	7.52638	0.259069
$845$	3.71936	0.127950
$846$	−8.93310	−0.307126
$847$	83.3933	2.86543
$848$	6.27188	0.215377
$849$	−20.0080	−0.686671
$850$	4.57525	0.156930
$851$	38.2752	1.31206
$852$	5.76002	0.197335
$853$	−17.0402	−0.583444	−0.291722	−	0.956503i	$-0.594228\pi$
$853$	−17.0402	−0.583444	−0.291722	+	0.956503i	$0.594228\pi$
$854$	−16.5200	−0.565303
$855$	0.699808	0.0239329
$856$	51.2454	1.75153
$857$	−31.6694	−1.08181	−0.540904	−	0.841085i	$-0.681918\pi$
$857$	−31.6694	−1.08181	−0.540904	+	0.841085i	$0.681918\pi$
$858$	−25.5695	−0.872928
$859$	11.0215	0.376050	0.188025	−	0.982164i	$-0.439791\pi$
$859$	11.0215	0.376050	0.188025	+	0.982164i	$0.439791\pi$
$860$	1.19474	0.0407403
$861$	−51.2069	−1.74513
$862$	−3.92962	−0.133844
$863$	10.8817	0.370416	0.185208	−	0.982699i	$-0.440704\pi$
$863$	10.8817	0.370416	0.185208	+	0.982699i	$0.440704\pi$
$864$	−5.38166	−0.183088
$865$	8.20186	0.278871
$866$	−24.8019	−0.842803
$867$	−1.00000	−0.0339618
$868$	35.6037	1.20847
$869$	5.59970	0.189957
$870$	0.378134	0.0128199
$871$	−6.50626	−0.220456
$872$	−45.8934	−1.55415
$873$	−14.1233	−0.478001
$874$	14.1050	0.477108
$875$	−14.0474	−0.474887
$876$	9.52003	0.321652
$877$	−23.8840	−0.806504	−0.403252	−	0.915089i	$-0.632120\pi$
$877$	−23.8840	−0.806504	−0.403252	+	0.915089i	$0.632120\pi$
$878$	11.5475	0.389708
$879$	28.3559	0.956421
$880$	−0.975818	−0.0328948
$881$	−33.5982	−1.13195	−0.565976	−	0.824422i	$-0.691500\pi$
$881$	−33.5982	−1.13195	−0.565976	+	0.824422i	$0.691500\pi$
$882$	9.17225	0.308846
$883$	−22.1669	−0.745976	−0.372988	−	0.927836i	$-0.621667\pi$
$883$	−22.1669	−0.745976	−0.372988	+	0.927836i	$0.621667\pi$
$884$	5.45835	0.183584
$885$	−1.43943	−0.0483859
$886$	17.5610	0.589972
$887$	25.1366	0.844005	0.422002	−	0.906595i	$-0.361327\pi$
$887$	25.1366	0.844005	0.422002	+	0.906595i	$0.361327\pi$
$888$	15.0118	0.503764
$889$	−9.08850	−0.304819
$890$	−4.00121	−0.134121
$891$	5.59970	0.187597
$892$	10.2553	0.343372
$893$	−19.2093	−0.642816
$894$	18.5460	0.620270
$895$	−1.95680	−0.0654087
$896$	−20.8534	−0.696663
$897$	−36.3338	−1.21315
$898$	10.9004	0.363752
$899$	9.00961	0.300487
$900$	5.46913	0.182304
$901$	12.4919	0.416164
$902$	65.6303	2.18525
$903$	12.5813	0.418680
$904$	−27.9250	−0.928772
$905$	−4.90747	−0.163130
$906$	0.231747	0.00769928
$907$	40.2360	1.33601	0.668006	−	0.744155i	$-0.267148\pi$
$907$	40.2360	1.33601	0.668006	+	0.744155i	$0.267148\pi$
$908$	4.73438	0.157116
$909$	13.1639	0.436618
$910$	6.49256	0.215226
$911$	28.3165	0.938166	0.469083	−	0.883154i	$-0.344584\pi$
$911$	28.3165	0.938166	0.469083	+	0.883154i	$0.344584\pi$
$912$	1.01232	0.0335212
$913$	−63.9990	−2.11806
$914$	16.7761	0.554905
$915$	1.49273	0.0493481
$916$	2.66027	0.0878977
$917$	43.2190	1.42722
$918$	0.937640	0.0309467
$919$	22.4403	0.740238	0.370119	−	0.928984i	$-0.379317\pi$
$919$	22.4403	0.740238	0.370119	+	0.928984i	$0.379317\pi$
$920$	−7.57756	−0.249825
$921$	23.4856	0.773875
$922$	−28.6843	−0.944666
$923$	25.0268	0.823767
$924$	25.7117	0.845851
$925$	−25.0326	−0.823066
$926$	30.2282	0.993359
$927$	9.89370	0.324952
$928$	−6.25307	−0.205267
$929$	12.5436	0.411541	0.205770	−	0.978600i	$-0.434030\pi$
$929$	12.5436	0.411541	0.205770	+	0.978600i	$0.434030\pi$
$930$	2.52347	0.0827479
$931$	19.7236	0.646415
$932$	−12.0487	−0.394667
$933$	9.82176	0.321550
$934$	14.9901	0.490490
$935$	−1.94356	−0.0635611
$936$	−14.2504	−0.465790
$937$	−0.969152	−0.0316608	−0.0158304	−	0.999875i	$-0.505039\pi$
$937$	−0.969152	−0.0316608	−0.0158304	+	0.999875i	$0.505039\pi$
$938$	−5.13182	−0.167560
$939$	−11.7000	−0.381815
$940$	3.70628	0.120886
$941$	23.9777	0.781651	0.390825	−	0.920465i	$-0.372190\pi$
$941$	23.9777	0.781651	0.390825	+	0.920465i	$0.372190\pi$
$942$	−8.48209	−0.276361
$943$	93.2596	3.03695
$944$	−2.08223	−0.0677708
$945$	−1.42186	−0.0462533
$946$	−16.1251	−0.524272
$947$	−21.7920	−0.708146	−0.354073	−	0.935218i	$-0.615204\pi$
$947$	−21.7920	−0.708146	−0.354073	+	0.935218i	$0.615204\pi$
$948$	1.12083	0.0364029
$949$	41.3637	1.34272
$950$	−9.22489	−0.299295
$951$	20.3892	0.661165
$952$	11.9876	0.388520
$953$	39.6953	1.28586	0.642928	−	0.765927i	$-0.277720\pi$
$953$	39.6953	1.28586	0.642928	+	0.765927i	$0.277720\pi$
$954$	−11.7129	−0.379218
$955$	5.00615	0.161995
$956$	30.4719	0.985533
$957$	6.50641	0.210322
$958$	12.2528	0.395871
$959$	−57.0728	−1.84298
$960$	−2.09993	−0.0677748
$961$	29.1255	0.939532
$962$	23.4253	0.755262
$963$	−17.5125	−0.564333
$964$	−17.7803	−0.572664
$965$	8.04179	0.258874
$966$	−28.6584	−0.922069
$967$	−31.3976	−1.00968	−0.504840	−	0.863213i	$-0.668449\pi$
$967$	−31.3976	−1.00968	−0.504840	+	0.863213i	$0.668449\pi$
$968$	−59.5679	−1.91458
$969$	2.01626	0.0647716
$970$	−4.59627	−0.147577
$971$	55.6249	1.78509	0.892545	−	0.450959i	$-0.148918\pi$
$971$	55.6249	1.78509	0.892545	+	0.450959i	$0.148918\pi$
$972$	1.12083	0.0359507
$973$	46.0639	1.47674
$974$	−20.8100	−0.666797
$975$	23.7629	0.761022
$976$	2.15933	0.0691185
$977$	−46.3798	−1.48382	−0.741910	−	0.670499i	$-0.766080\pi$
$977$	−46.3798	−1.48382	−0.741910	+	0.670499i	$0.766080\pi$
$978$	−18.6381	−0.595980
$979$	−68.8473	−2.20037
$980$	−3.80551	−0.121562
$981$	15.6835	0.500736
$982$	−9.42231	−0.300678
$983$	−2.24807	−0.0717024	−0.0358512	−	0.999357i	$-0.511414\pi$
$983$	−2.24807	−0.0717024	−0.0358512	+	0.999357i	$0.511414\pi$
$984$	36.5771	1.16604
$985$	−6.60312	−0.210393
$986$	1.08946	0.0346956
$987$	39.0293	1.24232
$988$	−11.0054	−0.350130
$989$	−22.9135	−0.728606
$990$	1.82236	0.0579183
$991$	−5.02645	−0.159670	−0.0798351	−	0.996808i	$-0.525439\pi$
$991$	−5.02645	−0.159670	−0.0798351	+	0.996808i	$0.525439\pi$
$992$	−41.7298	−1.32492
$993$	15.2254	0.483163
$994$	19.7399	0.626113
$995$	−4.36122	−0.138260
$996$	−12.8100	−0.405900
$997$	40.7833	1.29162	0.645810	−	0.763498i	$-0.276520\pi$
$997$	40.7833	1.29162	0.645810	+	0.763498i	$0.276520\pi$
$998$	−16.4298	−0.520076
$999$	−5.13012	−0.162310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.20	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.20	✓	32	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+0.937640 q^{2} -1.00000 q^{3} -1.12083 q^{4} +0.347083 q^{5} -0.937640 q^{6} +4.09662 q^{7} -2.92622 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.937640 q^{2} -1.00000 q^{3} -1.12083 q^{4} +0.347083 q^{5} -0.937640 q^{6} +4.09662 q^{7} -2.92622 q^{8} +1.00000 q^{9} +0.325439 q^{10} +5.59970 q^{11} +1.12083 q^{12} +4.86991 q^{13} +3.84115 q^{14} -0.347083 q^{15} -0.502078 q^{16} -1.00000 q^{17} +0.937640 q^{18} +2.01626 q^{19} -0.389021 q^{20} -4.09662 q^{21} +5.25050 q^{22} +7.46088 q^{23} +2.92622 q^{24} -4.87953 q^{25} +4.56623 q^{26} -1.00000 q^{27} -4.59161 q^{28} -1.16192 q^{29} -0.325439 q^{30} -7.75406 q^{31} +5.38166 q^{32} -5.59970 q^{33} -0.937640 q^{34} +1.42186 q^{35} -1.12083 q^{36} +5.13012 q^{37} +1.89053 q^{38} -4.86991 q^{39} -1.01564 q^{40} +12.4998 q^{41} -3.84115 q^{42} -3.07115 q^{43} -6.27631 q^{44} +0.347083 q^{45} +6.99562 q^{46} -9.52721 q^{47} +0.502078 q^{48} +9.78227 q^{49} -4.57525 q^{50} +1.00000 q^{51} -5.45835 q^{52} -12.4919 q^{53} -0.937640 q^{54} +1.94356 q^{55} -11.9876 q^{56} -2.01626 q^{57} -1.08946 q^{58} +4.14723 q^{59} +0.389021 q^{60} -4.30079 q^{61} -7.27052 q^{62} +4.09662 q^{63} +6.05022 q^{64} +1.69026 q^{65} -5.25050 q^{66} -1.33601 q^{67} +1.12083 q^{68} -7.46088 q^{69} +1.33320 q^{70} +5.13907 q^{71} -2.92622 q^{72} +8.49373 q^{73} +4.81021 q^{74} +4.87953 q^{75} -2.25988 q^{76} +22.9398 q^{77} -4.56623 q^{78} +1.00000 q^{79} -0.174263 q^{80} +1.00000 q^{81} +11.7203 q^{82} -11.4290 q^{83} +4.59161 q^{84} -0.347083 q^{85} -2.87963 q^{86} +1.16192 q^{87} -16.3859 q^{88} -12.2948 q^{89} +0.325439 q^{90} +19.9502 q^{91} -8.36238 q^{92} +7.75406 q^{93} -8.93310 q^{94} +0.699808 q^{95} -5.38166 q^{96} -14.1233 q^{97} +9.17225 q^{98} +5.59970 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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