LMFDB - Embedded newform 8007.2.a.j.1.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.37
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.541058 q^{2} -1.00000 q^{3} -1.70726 q^{4} -2.26573 q^{5} -0.541058 q^{6} +3.33057 q^{7} -2.00584 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.541058 q^{2} -1.00000 q^{3} -1.70726 q^{4} -2.26573 q^{5} -0.541058 q^{6} +3.33057 q^{7} -2.00584 q^{8} +1.00000 q^{9} -1.22589 q^{10} -0.254429 q^{11} +1.70726 q^{12} -6.68543 q^{13} +1.80203 q^{14} +2.26573 q^{15} +2.32924 q^{16} +1.00000 q^{17} +0.541058 q^{18} -5.63505 q^{19} +3.86818 q^{20} -3.33057 q^{21} -0.137661 q^{22} -1.40410 q^{23} +2.00584 q^{24} +0.133518 q^{25} -3.61721 q^{26} -1.00000 q^{27} -5.68613 q^{28} +3.12689 q^{29} +1.22589 q^{30} -3.20027 q^{31} +5.27193 q^{32} +0.254429 q^{33} +0.541058 q^{34} -7.54615 q^{35} -1.70726 q^{36} -2.27331 q^{37} -3.04889 q^{38} +6.68543 q^{39} +4.54469 q^{40} -12.5850 q^{41} -1.80203 q^{42} +5.38322 q^{43} +0.434376 q^{44} -2.26573 q^{45} -0.759700 q^{46} +13.3341 q^{47} -2.32924 q^{48} +4.09267 q^{49} +0.0722412 q^{50} -1.00000 q^{51} +11.4138 q^{52} -4.33609 q^{53} -0.541058 q^{54} +0.576467 q^{55} -6.68058 q^{56} +5.63505 q^{57} +1.69183 q^{58} -8.07694 q^{59} -3.86818 q^{60} -9.06644 q^{61} -1.73153 q^{62} +3.33057 q^{63} -1.80606 q^{64} +15.1474 q^{65} +0.137661 q^{66} -9.72002 q^{67} -1.70726 q^{68} +1.40410 q^{69} -4.08291 q^{70} +6.36223 q^{71} -2.00584 q^{72} +4.58099 q^{73} -1.22999 q^{74} -0.133518 q^{75} +9.62047 q^{76} -0.847393 q^{77} +3.61721 q^{78} +13.4061 q^{79} -5.27742 q^{80} +1.00000 q^{81} -6.80919 q^{82} +2.95907 q^{83} +5.68613 q^{84} -2.26573 q^{85} +2.91263 q^{86} -3.12689 q^{87} +0.510344 q^{88} -8.86519 q^{89} -1.22589 q^{90} -22.2663 q^{91} +2.39716 q^{92} +3.20027 q^{93} +7.21453 q^{94} +12.7675 q^{95} -5.27193 q^{96} -10.4669 q^{97} +2.21437 q^{98} -0.254429 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	0.541058	0.382586	0.191293	−	0.981533i	$-0.438732\pi$
$2$	0.541058	0.382586	0.191293	+	0.981533i	$0.438732\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.70726	−0.853628
$5$	−2.26573	−1.01326	−0.506632	−	0.862162i	$-0.669110\pi$
$5$	−2.26573	−1.01326	−0.506632	+	0.862162i	$0.669110\pi$
$6$	−0.541058	−0.220886
$7$	3.33057	1.25884	0.629418	−	0.777067i	$-0.283293\pi$
$7$	3.33057	1.25884	0.629418	+	0.777067i	$0.283293\pi$
$8$	−2.00584	−0.709171
$9$	1.00000	0.333333
$10$	−1.22589	−0.387660
$11$	−0.254429	−0.0767132	−0.0383566	−	0.999264i	$-0.512212\pi$
$11$	−0.254429	−0.0767132	−0.0383566	+	0.999264i	$0.512212\pi$
$12$	1.70726	0.492843
$13$	−6.68543	−1.85421	−0.927103	−	0.374807i	$-0.877709\pi$
$13$	−6.68543	−1.85421	−0.927103	+	0.374807i	$0.877709\pi$
$14$	1.80203	0.481612
$15$	2.26573	0.585008
$16$	2.32924	0.582309
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.541058	0.127529
$19$	−5.63505	−1.29277	−0.646384	−	0.763012i	$-0.723720\pi$
$19$	−5.63505	−1.29277	−0.646384	+	0.763012i	$0.723720\pi$
$20$	3.86818	0.864951
$21$	−3.33057	−0.726789
$22$	−0.137661	−0.0293494
$23$	−1.40410	−0.292775	−0.146388	−	0.989227i	$-0.546765\pi$
$23$	−1.40410	−0.292775	−0.146388	+	0.989227i	$0.546765\pi$
$24$	2.00584	0.409440
$25$	0.133518	0.0267037
$26$	−3.61721	−0.709392
$27$	−1.00000	−0.192450
$28$	−5.68613	−1.07458
$29$	3.12689	0.580648	0.290324	−	0.956928i	$-0.406237\pi$
$29$	3.12689	0.580648	0.290324	+	0.956928i	$0.406237\pi$
$30$	1.22589	0.223816
$31$	−3.20027	−0.574786	−0.287393	−	0.957813i	$-0.592789\pi$
$31$	−3.20027	−0.574786	−0.287393	+	0.957813i	$0.592789\pi$
$32$	5.27193	0.931955
$33$	0.254429	0.0442904
$34$	0.541058	0.0927906
$35$	−7.54615	−1.27553
$36$	−1.70726	−0.284543
$37$	−2.27331	−0.373730	−0.186865	−	0.982386i	$-0.559833\pi$
$37$	−2.27331	−0.373730	−0.186865	+	0.982386i	$0.559833\pi$
$38$	−3.04889	−0.494594
$39$	6.68543	1.07053
$40$	4.54469	0.718578
$41$	−12.5850	−1.96544	−0.982720	−	0.185099i	$-0.940739\pi$
$41$	−12.5850	−1.96544	−0.982720	+	0.185099i	$0.940739\pi$
$42$	−1.80203	−0.278059
$43$	5.38322	0.820933	0.410466	−	0.911876i	$-0.365366\pi$
$43$	5.38322	0.820933	0.410466	+	0.911876i	$0.365366\pi$
$44$	0.434376	0.0654846
$45$	−2.26573	−0.337755
$46$	−0.759700	−0.112012
$47$	13.3341	1.94498	0.972491	−	0.232941i	$-0.0748350\pi$
$47$	13.3341	1.94498	0.972491	+	0.232941i	$0.0748350\pi$
$48$	−2.32924	−0.336197
$49$	4.09267	0.584668
$50$	0.0722412	0.0102164
$51$	−1.00000	−0.140028
$52$	11.4138	1.58280
$53$	−4.33609	−0.595608	−0.297804	−	0.954627i	$-0.596254\pi$
$53$	−4.33609	−0.595608	−0.297804	+	0.954627i	$0.596254\pi$
$54$	−0.541058	−0.0736286
$55$	0.576467	0.0777307
$56$	−6.68058	−0.892730
$57$	5.63505	0.746380
$58$	1.69183	0.222148
$59$	−8.07694	−1.05153	−0.525764	−	0.850630i	$-0.676221\pi$
$59$	−8.07694	−1.05153	−0.525764	+	0.850630i	$0.676221\pi$
$60$	−3.86818	−0.499380
$61$	−9.06644	−1.16084	−0.580420	−	0.814318i	$-0.697111\pi$
$61$	−9.06644	−1.16084	−0.580420	+	0.814318i	$0.697111\pi$
$62$	−1.73153	−0.219905
$63$	3.33057	0.419612
$64$	−1.80606	−0.225757
$65$	15.1474	1.87880
$66$	0.137661	0.0169449
$67$	−9.72002	−1.18749	−0.593745	−	0.804653i	$-0.702351\pi$
$67$	−9.72002	−1.18749	−0.593745	+	0.804653i	$0.702351\pi$
$68$	−1.70726	−0.207035
$69$	1.40410	0.169034
$70$	−4.08291	−0.488001
$71$	6.36223	0.755058	0.377529	−	0.925998i	$-0.376774\pi$
$71$	6.36223	0.755058	0.377529	+	0.925998i	$0.376774\pi$
$72$	−2.00584	−0.236390
$73$	4.58099	0.536165	0.268082	−	0.963396i	$-0.413610\pi$
$73$	4.58099	0.536165	0.268082	+	0.963396i	$0.413610\pi$
$74$	−1.22999	−0.142984
$75$	−0.133518	−0.0154174
$76$	9.62047	1.10354
$77$	−0.847393	−0.0965694
$78$	3.61721	0.409568
$79$	13.4061	1.50830	0.754152	−	0.656700i	$-0.228048\pi$
$79$	13.4061	1.50830	0.754152	+	0.656700i	$0.228048\pi$
$80$	−5.27742	−0.590033
$81$	1.00000	0.111111
$82$	−6.80919	−0.751949
$83$	2.95907	0.324801	0.162400	−	0.986725i	$-0.448076\pi$
$83$	2.95907	0.324801	0.162400	+	0.986725i	$0.448076\pi$
$84$	5.68613	0.620408
$85$	−2.26573	−0.245753
$86$	2.91263	0.314077
$87$	−3.12689	−0.335238
$88$	0.510344	0.0544028
$89$	−8.86519	−0.939708	−0.469854	−	0.882744i	$-0.655693\pi$
$89$	−8.86519	−0.939708	−0.469854	+	0.882744i	$0.655693\pi$
$90$	−1.22589	−0.129220
$91$	−22.2663	−2.33414
$92$	2.39716	0.249921
$93$	3.20027	0.331853
$94$	7.21453	0.744122
$95$	12.7675	1.30992
$96$	−5.27193	−0.538064
$97$	−10.4669	−1.06275	−0.531374	−	0.847137i	$-0.678324\pi$
$97$	−10.4669	−1.06275	−0.531374	+	0.847137i	$0.678324\pi$
$98$	2.21437	0.223685
$99$	−0.254429	−0.0255711
$100$	−0.227950	−0.0227950
$101$	−1.30688	−0.130039	−0.0650197	−	0.997884i	$-0.520711\pi$
$101$	−1.30688	−0.130039	−0.0650197	+	0.997884i	$0.520711\pi$
$102$	−0.541058	−0.0535727
$103$	−15.7744	−1.55430	−0.777149	−	0.629316i	$-0.783335\pi$
$103$	−15.7744	−1.55430	−0.777149	+	0.629316i	$0.783335\pi$
$104$	13.4099	1.31495
$105$	7.54615	0.736429
$106$	−2.34608	−0.227871
$107$	−14.6763	−1.41882	−0.709408	−	0.704798i	$-0.751038\pi$
$107$	−14.6763	−1.41882	−0.709408	+	0.704798i	$0.751038\pi$
$108$	1.70726	0.164281
$109$	−3.01460	−0.288746	−0.144373	−	0.989523i	$-0.546117\pi$
$109$	−3.01460	−0.288746	−0.144373	+	0.989523i	$0.546117\pi$
$110$	0.311902	0.0297387
$111$	2.27331	0.215773
$112$	7.75768	0.733032
$113$	12.0161	1.13038	0.565191	−	0.824960i	$-0.308802\pi$
$113$	12.0161	1.13038	0.565191	+	0.824960i	$0.308802\pi$
$114$	3.04889	0.285554
$115$	3.18131	0.296659
$116$	−5.33840	−0.495658
$117$	−6.68543	−0.618069
$118$	−4.37009	−0.402300
$119$	3.33057	0.305313
$120$	−4.54469	−0.414871
$121$	−10.9353	−0.994115
$122$	−4.90547	−0.444120
$123$	12.5850	1.13475
$124$	5.46369	0.490654
$125$	11.0261	0.986206
$126$	1.80203	0.160537
$127$	7.47761	0.663530	0.331765	−	0.943362i	$-0.392356\pi$
$127$	7.47761	0.663530	0.331765	+	0.943362i	$0.392356\pi$
$128$	−11.5210	−1.01833
$129$	−5.38322	−0.473966
$130$	8.19560	0.718802
$131$	3.03141	0.264856	0.132428	−	0.991193i	$-0.457723\pi$
$131$	3.03141	0.264856	0.132428	+	0.991193i	$0.457723\pi$
$132$	−0.434376	−0.0378075
$133$	−18.7679	−1.62738
$134$	−5.25909	−0.454317
$135$	2.26573	0.195003
$136$	−2.00584	−0.171999
$137$	−20.0337	−1.71159	−0.855796	−	0.517314i	$-0.826932\pi$
$137$	−20.0337	−1.71159	−0.855796	+	0.517314i	$0.826932\pi$
$138$	0.759700	0.0646699
$139$	10.0285	0.850603	0.425302	−	0.905052i	$-0.360168\pi$
$139$	10.0285	0.850603	0.425302	+	0.905052i	$0.360168\pi$
$140$	12.8832	1.08883
$141$	−13.3341	−1.12294
$142$	3.44233	0.288874
$143$	1.70097	0.142242
$144$	2.32924	0.194103
$145$	−7.08467	−0.588350
$146$	2.47858	0.205129
$147$	−4.09267	−0.337558
$148$	3.88112	0.319026
$149$	−2.19950	−0.180190	−0.0900951	−	0.995933i	$-0.528717\pi$
$149$	−2.19950	−0.180190	−0.0900951	+	0.995933i	$0.528717\pi$
$150$	−0.0722412	−0.00589847
$151$	1.33507	0.108646	0.0543232	−	0.998523i	$-0.482700\pi$
$151$	1.33507	0.108646	0.0543232	+	0.998523i	$0.482700\pi$
$152$	11.3030	0.916794
$153$	1.00000	0.0808452
$154$	−0.458488	−0.0369460
$155$	7.25095	0.582410
$156$	−11.4138	−0.913831
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	7.25347	0.577055
$159$	4.33609	0.343875
$160$	−11.9448	−0.944316
$161$	−4.67645	−0.368556
$162$	0.541058	0.0425095
$163$	6.50799	0.509745	0.254873	−	0.966975i	$-0.417966\pi$
$163$	6.50799	0.509745	0.254873	+	0.966975i	$0.417966\pi$
$164$	21.4857	1.67775
$165$	−0.576467	−0.0448779
$166$	1.60103	0.124264
$167$	−18.4006	−1.42388	−0.711941	−	0.702239i	$-0.752184\pi$
$167$	−18.4006	−1.42388	−0.711941	+	0.702239i	$0.752184\pi$
$168$	6.68058	0.515418
$169$	31.6950	2.43808
$170$	−1.22589	−0.0940214
$171$	−5.63505	−0.430923
$172$	−9.19053	−0.700771
$173$	−18.3545	−1.39546	−0.697732	−	0.716359i	$-0.745807\pi$
$173$	−18.3545	−1.39546	−0.697732	+	0.716359i	$0.745807\pi$
$174$	−1.69183	−0.128257
$175$	0.444692	0.0336155
$176$	−0.592626	−0.0446708
$177$	8.07694	0.607100
$178$	−4.79658	−0.359519
$179$	−2.86562	−0.214186	−0.107093	−	0.994249i	$-0.534154\pi$
$179$	−2.86562	−0.214186	−0.107093	+	0.994249i	$0.534154\pi$
$180$	3.86818	0.288317
$181$	9.63226	0.715960	0.357980	−	0.933729i	$-0.383466\pi$
$181$	9.63226	0.715960	0.357980	+	0.933729i	$0.383466\pi$
$182$	−12.0473	−0.893009
$183$	9.06644	0.670211
$184$	2.81640	0.207628
$185$	5.15070	0.378687
$186$	1.73153	0.126962
$187$	−0.254429	−0.0186057
$188$	−22.7648	−1.66029
$189$	−3.33057	−0.242263
$190$	6.90794	0.501155
$191$	0.0594591	0.00430231	0.00215116	−	0.999998i	$-0.499315\pi$
$191$	0.0594591	0.00430231	0.00215116	+	0.999998i	$0.499315\pi$
$192$	1.80606	0.130341
$193$	18.3736	1.32256	0.661280	−	0.750139i	$-0.270013\pi$
$193$	18.3736	1.32256	0.661280	+	0.750139i	$0.270013\pi$
$194$	−5.66318	−0.406592
$195$	−15.1474	−1.08473
$196$	−6.98724	−0.499089
$197$	−3.69839	−0.263499	−0.131750	−	0.991283i	$-0.542059\pi$
$197$	−3.69839	−0.263499	−0.131750	+	0.991283i	$0.542059\pi$
$198$	−0.137661	−0.00978312
$199$	19.0648	1.35147	0.675736	−	0.737144i	$-0.263826\pi$
$199$	19.0648	1.35147	0.675736	+	0.737144i	$0.263826\pi$
$200$	−0.267817	−0.0189375
$201$	9.72002	0.685598
$202$	−0.707097	−0.0497512
$203$	10.4143	0.730941
$204$	1.70726	0.119532
$205$	28.5141	1.99151
$206$	−8.53487	−0.594652
$207$	−1.40410	−0.0975918
$208$	−15.5720	−1.07972
$209$	1.43372	0.0991724
$210$	4.08291	0.281747
$211$	18.4245	1.26840	0.634199	−	0.773170i	$-0.281330\pi$
$211$	18.4245	1.26840	0.634199	+	0.773170i	$0.281330\pi$
$212$	7.40282	0.508428
$213$	−6.36223	−0.435933
$214$	−7.94075	−0.542819
$215$	−12.1969	−0.831821
$216$	2.00584	0.136480
$217$	−10.6587	−0.723561
$218$	−1.63107	−0.110470
$219$	−4.58099	−0.309555
$220$	−0.984176	−0.0663532
$221$	−6.68543	−0.449711
$222$	1.22999	0.0825517
$223$	13.9594	0.934789	0.467394	−	0.884049i	$-0.345193\pi$
$223$	13.9594	0.934789	0.467394	+	0.884049i	$0.345193\pi$
$224$	17.5585	1.17318
$225$	0.133518	0.00890123
$226$	6.50142	0.432468
$227$	9.60857	0.637743	0.318871	−	0.947798i	$-0.396696\pi$
$227$	9.60857	0.637743	0.318871	+	0.947798i	$0.396696\pi$
$228$	−9.62047	−0.637131
$229$	13.3778	0.884027	0.442014	−	0.897008i	$-0.354264\pi$
$229$	13.3778	0.884027	0.442014	+	0.897008i	$0.354264\pi$
$230$	1.72127	0.113497
$231$	0.847393	0.0557543
$232$	−6.27204	−0.411779
$233$	15.6520	1.02540	0.512700	−	0.858568i	$-0.328645\pi$
$233$	15.6520	1.02540	0.512700	+	0.858568i	$0.328645\pi$
$234$	−3.61721	−0.236464
$235$	−30.2115	−1.97078
$236$	13.7894	0.897614
$237$	−13.4061	−0.870819
$238$	1.80203	0.116808
$239$	4.01552	0.259742	0.129871	−	0.991531i	$-0.458544\pi$
$239$	4.01552	0.259742	0.129871	+	0.991531i	$0.458544\pi$
$240$	5.27742	0.340656
$241$	10.1686	0.655015	0.327508	−	0.944849i	$-0.393791\pi$
$241$	10.1686	0.655015	0.327508	+	0.944849i	$0.393791\pi$
$242$	−5.91661	−0.380334
$243$	−1.00000	−0.0641500
$244$	15.4787	0.990925
$245$	−9.27288	−0.592423
$246$	6.80919	0.434138
$247$	37.6727	2.39706
$248$	6.41924	0.407622
$249$	−2.95907	−0.187524
$250$	5.96577	0.377308
$251$	−22.8809	−1.44423	−0.722115	−	0.691773i	$-0.756830\pi$
$251$	−22.8809	−1.44423	−0.722115	+	0.691773i	$0.756830\pi$
$252$	−5.68613	−0.358193
$253$	0.357244	0.0224597
$254$	4.04582	0.253857
$255$	2.26573	0.141885
$256$	−2.62144	−0.163840
$257$	3.77063	0.235205	0.117603	−	0.993061i	$-0.462479\pi$
$257$	3.77063	0.235205	0.117603	+	0.993061i	$0.462479\pi$
$258$	−2.91263	−0.181332
$259$	−7.57141	−0.470465
$260$	−25.8604	−1.60380
$261$	3.12689	0.193549
$262$	1.64017	0.101330
$263$	12.6583	0.780541	0.390271	−	0.920700i	$-0.372381\pi$
$263$	12.6583	0.780541	0.390271	+	0.920700i	$0.372381\pi$
$264$	−0.510344	−0.0314095
$265$	9.82440	0.603508
$266$	−10.1545	−0.622613
$267$	8.86519	0.542541
$268$	16.5946	1.01367
$269$	3.15915	0.192617	0.0963085	−	0.995352i	$-0.469296\pi$
$269$	3.15915	0.192617	0.0963085	+	0.995352i	$0.469296\pi$
$270$	1.22589	0.0746052
$271$	31.9787	1.94257	0.971283	−	0.237927i	$-0.0764679\pi$
$271$	31.9787	1.94257	0.971283	+	0.237927i	$0.0764679\pi$
$272$	2.32924	0.141231
$273$	22.2663	1.34762
$274$	−10.8394	−0.654830
$275$	−0.0339709	−0.00204853
$276$	−2.39716	−0.144292
$277$	17.9452	1.07822	0.539112	−	0.842234i	$-0.318760\pi$
$277$	17.9452	1.07822	0.539112	+	0.842234i	$0.318760\pi$
$278$	5.42598	0.325429
$279$	−3.20027	−0.191595
$280$	15.1364	0.904572
$281$	−5.31471	−0.317049	−0.158524	−	0.987355i	$-0.550674\pi$
$281$	−5.31471	−0.317049	−0.158524	+	0.987355i	$0.550674\pi$
$282$	−7.21453	−0.429619
$283$	22.6414	1.34589	0.672944	−	0.739693i	$-0.265029\pi$
$283$	22.6414	1.34589	0.672944	+	0.739693i	$0.265029\pi$
$284$	−10.8620	−0.644539
$285$	−12.7675	−0.756280
$286$	0.920322	0.0544198
$287$	−41.9150	−2.47417
$288$	5.27193	0.310652
$289$	1.00000	0.0588235
$290$	−3.83322	−0.225094
$291$	10.4669	0.613578
$292$	−7.82093	−0.457685
$293$	−12.7297	−0.743680	−0.371840	−	0.928297i	$-0.621273\pi$
$293$	−12.7297	−0.743680	−0.371840	+	0.928297i	$0.621273\pi$
$294$	−2.21437	−0.129145
$295$	18.3001	1.06548
$296$	4.55990	0.265039
$297$	0.254429	0.0147635
$298$	−1.19006	−0.0689382
$299$	9.38702	0.542866
$300$	0.227950	0.0131607
$301$	17.9292	1.03342
$302$	0.722349	0.0415665
$303$	1.30688	0.0750783
$304$	−13.1254	−0.752791
$305$	20.5421	1.17624
$306$	0.541058	0.0309302
$307$	−5.57938	−0.318432	−0.159216	−	0.987244i	$-0.550897\pi$
$307$	−5.57938	−0.318432	−0.159216	+	0.987244i	$0.550897\pi$
$308$	1.44672	0.0824343
$309$	15.7744	0.897375
$310$	3.92318	0.222822
$311$	−11.5904	−0.657230	−0.328615	−	0.944464i	$-0.606582\pi$
$311$	−11.5904	−0.657230	−0.328615	+	0.944464i	$0.606582\pi$
$312$	−13.4099	−0.759187
$313$	6.14677	0.347436	0.173718	−	0.984795i	$-0.444422\pi$
$313$	6.14677	0.347436	0.173718	+	0.984795i	$0.444422\pi$
$314$	−0.541058	−0.0305337
$315$	−7.54615	−0.425178
$316$	−22.8876	−1.28753
$317$	18.7913	1.05543	0.527713	−	0.849423i	$-0.323050\pi$
$317$	18.7913	1.05543	0.527713	+	0.849423i	$0.323050\pi$
$318$	2.34608	0.131561
$319$	−0.795571	−0.0445434
$320$	4.09203	0.228751
$321$	14.6763	0.819154
$322$	−2.53023	−0.141004
$323$	−5.63505	−0.313542
$324$	−1.70726	−0.0948476
$325$	−0.892628	−0.0495141
$326$	3.52120	0.195021
$327$	3.01460	0.166708
$328$	25.2434	1.39383
$329$	44.4102	2.44841
$330$	−0.311902	−0.0171696
$331$	19.9054	1.09410	0.547051	−	0.837099i	$-0.315750\pi$
$331$	19.9054	1.09410	0.547051	+	0.837099i	$0.315750\pi$
$332$	−5.05190	−0.277259
$333$	−2.27331	−0.124577
$334$	−9.95580	−0.544757
$335$	22.0229	1.20324
$336$	−7.75768	−0.423216
$337$	−21.4534	−1.16864	−0.584322	−	0.811522i	$-0.698639\pi$
$337$	−21.4534	−1.16864	−0.584322	+	0.811522i	$0.698639\pi$
$338$	17.1488	0.932774
$339$	−12.0161	−0.652627
$340$	3.86818	0.209781
$341$	0.814242	0.0440937
$342$	−3.04889	−0.164865
$343$	−9.68304	−0.522835
$344$	−10.7979	−0.582182
$345$	−3.18131	−0.171276
$346$	−9.93082	−0.533884
$347$	16.7140	0.897254	0.448627	−	0.893719i	$-0.351913\pi$
$347$	16.7140	0.897254	0.448627	+	0.893719i	$0.351913\pi$
$348$	5.33840	0.286168
$349$	12.9275	0.691995	0.345998	−	0.938235i	$-0.387541\pi$
$349$	12.9275	0.691995	0.345998	+	0.938235i	$0.387541\pi$
$350$	0.240604	0.0128608
$351$	6.68543	0.356842
$352$	−1.34133	−0.0714932
$353$	−19.6470	−1.04571	−0.522853	−	0.852423i	$-0.675132\pi$
$353$	−19.6470	−1.04571	−0.522853	+	0.852423i	$0.675132\pi$
$354$	4.37009	0.232268
$355$	−14.4151	−0.765073
$356$	15.1352	0.802161
$357$	−3.33057	−0.176272
$358$	−1.55046	−0.0819446
$359$	7.80160	0.411753	0.205876	−	0.978578i	$-0.433996\pi$
$359$	7.80160	0.411753	0.205876	+	0.978578i	$0.433996\pi$
$360$	4.54469	0.239526
$361$	12.7537	0.671249
$362$	5.21161	0.273916
$363$	10.9353	0.573953
$364$	38.0143	1.99249
$365$	−10.3793	−0.543276
$366$	4.90547	0.256413
$367$	−24.1948	−1.26296	−0.631480	−	0.775392i	$-0.717552\pi$
$367$	−24.1948	−1.26296	−0.631480	+	0.775392i	$0.717552\pi$
$368$	−3.27048	−0.170486
$369$	−12.5850	−0.655147
$370$	2.78683	0.144880
$371$	−14.4416	−0.749773
$372$	−5.46369	−0.283279
$373$	8.88169	0.459876	0.229938	−	0.973205i	$-0.426148\pi$
$373$	8.88169	0.459876	0.229938	+	0.973205i	$0.426148\pi$
$374$	−0.137661	−0.00711827
$375$	−11.0261	−0.569386
$376$	−26.7461	−1.37933
$377$	−20.9046	−1.07664
$378$	−1.80203	−0.0926864
$379$	13.9775	0.717978	0.358989	−	0.933342i	$-0.383122\pi$
$379$	13.9775	0.717978	0.358989	+	0.933342i	$0.383122\pi$
$380$	−21.7974	−1.11818
$381$	−7.47761	−0.383089
$382$	0.0321708	0.00164600
$383$	36.1971	1.84959	0.924794	−	0.380468i	$-0.124237\pi$
$383$	36.1971	1.84959	0.924794	+	0.380468i	$0.124237\pi$
$384$	11.5210	0.587931
$385$	1.91996	0.0978502
$386$	9.94118	0.505993
$387$	5.38322	0.273644
$388$	17.8696	0.907192
$389$	1.22339	0.0620282	0.0310141	−	0.999519i	$-0.490126\pi$
$389$	1.22339	0.0620282	0.0310141	+	0.999519i	$0.490126\pi$
$390$	−8.19560	−0.415000
$391$	−1.40410	−0.0710084
$392$	−8.20925	−0.414630
$393$	−3.03141	−0.152915
$394$	−2.00104	−0.100811
$395$	−30.3746	−1.52831
$396$	0.434376	0.0218282
$397$	−18.7418	−0.940622	−0.470311	−	0.882501i	$-0.655858\pi$
$397$	−18.7418	−0.940622	−0.470311	+	0.882501i	$0.655858\pi$
$398$	10.3152	0.517053
$399$	18.7679	0.939570
$400$	0.310996	0.0155498
$401$	−5.41964	−0.270644	−0.135322	−	0.990802i	$-0.543207\pi$
$401$	−5.41964	−0.270644	−0.135322	+	0.990802i	$0.543207\pi$
$402$	5.25909	0.262300
$403$	21.3952	1.06577
$404$	2.23118	0.111005
$405$	−2.26573	−0.112585
$406$	5.63474	0.279648
$407$	0.578396	0.0286700
$408$	2.00584	0.0993039
$409$	29.1424	1.44100	0.720500	−	0.693455i	$-0.243912\pi$
$409$	29.1424	1.44100	0.720500	+	0.693455i	$0.243912\pi$
$410$	15.4278	0.761923
$411$	20.0337	0.988188
$412$	26.9310	1.32679
$413$	−26.9008	−1.32370
$414$	−0.759700	−0.0373372
$415$	−6.70446	−0.329109
$416$	−35.2452	−1.72804
$417$	−10.0285	−0.491096
$418$	0.775725	0.0379419
$419$	−10.8081	−0.528009	−0.264004	−	0.964521i	$-0.585043\pi$
$419$	−10.8081	−0.528009	−0.264004	+	0.964521i	$0.585043\pi$
$420$	−12.8832	−0.628637
$421$	−28.7557	−1.40147	−0.700733	−	0.713424i	$-0.747143\pi$
$421$	−28.7557	−1.40147	−0.700733	+	0.713424i	$0.747143\pi$
$422$	9.96874	0.485270
$423$	13.3341	0.648327
$424$	8.69751	0.422388
$425$	0.133518	0.00647659
$426$	−3.44233	−0.166782
$427$	−30.1964	−1.46131
$428$	25.0563	1.21114
$429$	−1.70097	−0.0821235
$430$	−6.59923	−0.318243
$431$	34.8074	1.67662	0.838308	−	0.545197i	$-0.183545\pi$
$431$	34.8074	1.67662	0.838308	+	0.545197i	$0.183545\pi$
$432$	−2.32924	−0.112066
$433$	−25.4376	−1.22245	−0.611226	−	0.791456i	$-0.709323\pi$
$433$	−25.4376	−1.22245	−0.611226	+	0.791456i	$0.709323\pi$
$434$	−5.76699	−0.276824
$435$	7.08467	0.339684
$436$	5.14669	0.246482
$437$	7.91217	0.378491
$438$	−2.47858	−0.118431
$439$	29.9673	1.43026	0.715131	−	0.698991i	$-0.246367\pi$
$439$	29.9673	1.43026	0.715131	+	0.698991i	$0.246367\pi$
$440$	−1.15630	−0.0551244
$441$	4.09267	0.194889
$442$	−3.61721	−0.172053
$443$	−4.49320	−0.213478	−0.106739	−	0.994287i	$-0.534041\pi$
$443$	−4.49320	−0.213478	−0.106739	+	0.994287i	$0.534041\pi$
$444$	−3.88112	−0.184190
$445$	20.0861	0.952172
$446$	7.55283	0.357637
$447$	2.19950	0.104033
$448$	−6.01519	−0.284191
$449$	−28.6639	−1.35273	−0.676367	−	0.736565i	$-0.736447\pi$
$449$	−28.6639	−1.35273	−0.676367	+	0.736565i	$0.736447\pi$
$450$	0.0722412	0.00340548
$451$	3.20198	0.150775
$452$	−20.5146	−0.964927
$453$	−1.33507	−0.0627270
$454$	5.19879	0.243991
$455$	50.4493	2.36510
$456$	−11.3030	−0.529311
$457$	13.4887	0.630974	0.315487	−	0.948930i	$-0.397832\pi$
$457$	13.4887	0.630974	0.315487	+	0.948930i	$0.397832\pi$
$458$	7.23814	0.338216
$459$	−1.00000	−0.0466760
$460$	−5.43131	−0.253236
$461$	−13.1655	−0.613181	−0.306590	−	0.951842i	$-0.599188\pi$
$461$	−13.1655	−0.613181	−0.306590	+	0.951842i	$0.599188\pi$
$462$	0.458488	0.0213308
$463$	7.33210	0.340752	0.170376	−	0.985379i	$-0.445502\pi$
$463$	7.33210	0.340752	0.170376	+	0.985379i	$0.445502\pi$
$464$	7.28327	0.338117
$465$	−7.25095	−0.336255
$466$	8.46866	0.392303
$467$	−14.9482	−0.691721	−0.345860	−	0.938286i	$-0.612413\pi$
$467$	−14.9482	−0.691721	−0.345860	+	0.938286i	$0.612413\pi$
$468$	11.4138	0.527601
$469$	−32.3732	−1.49485
$470$	−16.3462	−0.753992
$471$	1.00000	0.0460776
$472$	16.2011	0.745714
$473$	−1.36965	−0.0629764
$474$	−7.25347	−0.333163
$475$	−0.752382	−0.0345217
$476$	−5.68613	−0.260623
$477$	−4.33609	−0.198536
$478$	2.17263	0.0993737
$479$	34.5968	1.58077	0.790384	−	0.612611i	$-0.209881\pi$
$479$	34.5968	1.58077	0.790384	+	0.612611i	$0.209881\pi$
$480$	11.9448	0.545201
$481$	15.1981	0.692972
$482$	5.50179	0.250599
$483$	4.67645	0.212786
$484$	18.6693	0.848605
$485$	23.7151	1.07684
$486$	−0.541058	−0.0245429
$487$	1.34779	0.0610742	0.0305371	−	0.999534i	$-0.490278\pi$
$487$	1.34779	0.0610742	0.0305371	+	0.999534i	$0.490278\pi$
$488$	18.1858	0.823234
$489$	−6.50799	−0.294302
$490$	−5.01716	−0.226652
$491$	22.3680	1.00945	0.504727	−	0.863279i	$-0.331593\pi$
$491$	22.3680	1.00945	0.504727	+	0.863279i	$0.331593\pi$
$492$	−21.4857	−0.968652
$493$	3.12689	0.140828
$494$	20.3831	0.917080
$495$	0.576467	0.0259102
$496$	−7.45420	−0.334703
$497$	21.1898	0.950494
$498$	−1.60103	−0.0717439
$499$	−12.0150	−0.537867	−0.268934	−	0.963159i	$-0.586671\pi$
$499$	−12.0150	−0.537867	−0.268934	+	0.963159i	$0.586671\pi$
$500$	−18.8244	−0.841853
$501$	18.4006	0.822079
$502$	−12.3799	−0.552542
$503$	30.0833	1.34135	0.670675	−	0.741752i	$-0.266005\pi$
$503$	30.0833	1.34135	0.670675	+	0.741752i	$0.266005\pi$
$504$	−6.68058	−0.297577
$505$	2.96103	0.131764
$506$	0.193290	0.00859277
$507$	−31.6950	−1.40763
$508$	−12.7662	−0.566408
$509$	−22.6860	−1.00554	−0.502769	−	0.864421i	$-0.667685\pi$
$509$	−22.6860	−1.00554	−0.502769	+	0.864421i	$0.667685\pi$
$510$	1.22589	0.0542833
$511$	15.2573	0.674943
$512$	21.6237	0.955643
$513$	5.63505	0.248793
$514$	2.04013	0.0899862
$515$	35.7405	1.57491
$516$	9.19053	0.404591
$517$	−3.39259	−0.149206
$518$	−4.09657	−0.179993
$519$	18.3545	0.805671
$520$	−30.3832	−1.33239
$521$	−8.16895	−0.357888	−0.178944	−	0.983859i	$-0.557268\pi$
$521$	−8.16895	−0.357888	−0.178944	+	0.983859i	$0.557268\pi$
$522$	1.69183	0.0740492
$523$	3.72928	0.163070	0.0815349	−	0.996670i	$-0.474018\pi$
$523$	3.72928	0.163070	0.0815349	+	0.996670i	$0.474018\pi$
$524$	−5.17540	−0.226088
$525$	−0.444692	−0.0194079
$526$	6.84885	0.298624
$527$	−3.20027	−0.139406
$528$	0.592626	0.0257907
$529$	−21.0285	−0.914283
$530$	5.31557	0.230894
$531$	−8.07694	−0.350509
$532$	32.0416	1.38918
$533$	84.1359	3.64433
$534$	4.79658	0.207568
$535$	33.2526	1.43763
$536$	19.4968	0.842134
$537$	2.86562	0.123660
$538$	1.70928	0.0736925
$539$	−1.04129	−0.0448517
$540$	−3.86818	−0.166460
$541$	−15.3237	−0.658816	−0.329408	−	0.944188i	$-0.606849\pi$
$541$	−15.3237	−0.658816	−0.329408	+	0.944188i	$0.606849\pi$
$542$	17.3023	0.743198
$543$	−9.63226	−0.413360
$544$	5.27193	0.226032
$545$	6.83026	0.292576
$546$	12.0473	0.515579
$547$	32.1288	1.37373	0.686864	−	0.726786i	$-0.258987\pi$
$547$	32.1288	1.37373	0.686864	+	0.726786i	$0.258987\pi$
$548$	34.2026	1.46106
$549$	−9.06644	−0.386946
$550$	−0.0183802	−0.000783736 0
$551$	−17.6202	−0.750644
$552$	−2.81640	−0.119874
$553$	44.6499	1.89871
$554$	9.70941	0.412513
$555$	−5.15070	−0.218635
$556$	−17.1212	−0.726099
$557$	−33.3026	−1.41108	−0.705539	−	0.708671i	$-0.749295\pi$
$557$	−33.3026	−1.41108	−0.705539	+	0.708671i	$0.749295\pi$
$558$	−1.73153	−0.0733016
$559$	−35.9891	−1.52218
$560$	−17.5768	−0.742755
$561$	0.254429	0.0107420
$562$	−2.87556	−0.121298
$563$	0.421937	0.0177825	0.00889126	−	0.999960i	$-0.497170\pi$
$563$	0.421937	0.0177825	0.00889126	+	0.999960i	$0.497170\pi$
$564$	22.7648	0.958570
$565$	−27.2253	−1.14538
$566$	12.2503	0.514918
$567$	3.33057	0.139871
$568$	−12.7616	−0.535465
$569$	2.36894	0.0993112	0.0496556	−	0.998766i	$-0.484188\pi$
$569$	2.36894	0.0993112	0.0496556	+	0.998766i	$0.484188\pi$
$570$	−6.90794	−0.289342
$571$	0.791437	0.0331206	0.0165603	−	0.999863i	$-0.494728\pi$
$571$	0.791437	0.0331206	0.0165603	+	0.999863i	$0.494728\pi$
$572$	−2.90399	−0.121422
$573$	−0.0594591	−0.00248394
$574$	−22.6785	−0.946580
$575$	−0.187473	−0.00781818
$576$	−1.80606	−0.0752523
$577$	−22.7296	−0.946244	−0.473122	−	0.880997i	$-0.656873\pi$
$577$	−22.7296	−0.946244	−0.473122	+	0.880997i	$0.656873\pi$
$578$	0.541058	0.0225050
$579$	−18.3736	−0.763581
$580$	12.0954	0.502232
$581$	9.85540	0.408871
$582$	5.66318	0.234746
$583$	1.10323	0.0456910
$584$	−9.18874	−0.380233
$585$	15.1474	0.626267
$586$	−6.88753	−0.284521
$587$	−22.5006	−0.928699	−0.464350	−	0.885652i	$-0.653712\pi$
$587$	−22.5006	−0.928699	−0.464350	+	0.885652i	$0.653712\pi$
$588$	6.98724	0.288149
$589$	18.0337	0.743065
$590$	9.90143	0.407636
$591$	3.69839	0.152131
$592$	−5.29508	−0.217626
$593$	4.80328	0.197247	0.0986236	−	0.995125i	$-0.468556\pi$
$593$	4.80328	0.197247	0.0986236	+	0.995125i	$0.468556\pi$
$594$	0.137661	0.00564829
$595$	−7.54615	−0.309362
$596$	3.75511	0.153815
$597$	−19.0648	−0.780272
$598$	5.07892	0.207693
$599$	26.0884	1.06594	0.532971	−	0.846134i	$-0.321076\pi$
$599$	26.0884	1.06594	0.532971	+	0.846134i	$0.321076\pi$
$600$	0.267817	0.0109336
$601$	−4.35804	−0.177768	−0.0888842	−	0.996042i	$-0.528330\pi$
$601$	−4.35804	−0.177768	−0.0888842	+	0.996042i	$0.528330\pi$
$602$	9.70071	0.395371
$603$	−9.72002	−0.395830
$604$	−2.27930	−0.0927436
$605$	24.7763	1.00730
$606$	0.707097	0.0287239
$607$	6.13947	0.249193	0.124597	−	0.992207i	$-0.460236\pi$
$607$	6.13947	0.249193	0.124597	+	0.992207i	$0.460236\pi$
$608$	−29.7076	−1.20480
$609$	−10.4143	−0.422009
$610$	11.1145	0.450011
$611$	−89.1444	−3.60640
$612$	−1.70726	−0.0690118
$613$	48.1862	1.94622	0.973111	−	0.230337i	$-0.0739829\pi$
$613$	48.1862	1.94622	0.973111	+	0.230337i	$0.0739829\pi$
$614$	−3.01877	−0.121828
$615$	−28.5141	−1.14980
$616$	1.69973	0.0684842
$617$	−15.9712	−0.642976	−0.321488	−	0.946914i	$-0.604183\pi$
$617$	−15.9712	−0.642976	−0.321488	+	0.946914i	$0.604183\pi$
$618$	8.53487	0.343323
$619$	7.24889	0.291357	0.145679	−	0.989332i	$-0.453463\pi$
$619$	7.24889	0.291357	0.145679	+	0.989332i	$0.453463\pi$
$620$	−12.3792	−0.497162
$621$	1.40410	0.0563446
$622$	−6.27106	−0.251447
$623$	−29.5261	−1.18294
$624$	15.5720	0.623378
$625$	−25.6498	−1.02599
$626$	3.32576	0.132924
$627$	−1.43372	−0.0572572
$628$	1.70726	0.0681270
$629$	−2.27331	−0.0906428
$630$	−4.08291	−0.162667
$631$	30.2140	1.20280	0.601400	−	0.798948i	$-0.294610\pi$
$631$	30.2140	1.20280	0.601400	+	0.798948i	$0.294610\pi$
$632$	−26.8905	−1.06965
$633$	−18.4245	−0.732309
$634$	10.1672	0.403791
$635$	−16.9422	−0.672331
$636$	−7.40282	−0.293541
$637$	−27.3613	−1.08409
$638$	−0.430450	−0.0170417
$639$	6.36223	0.251686
$640$	26.1035	1.03183
$641$	21.5837	0.852506	0.426253	−	0.904604i	$-0.359833\pi$
$641$	21.5837	0.852506	0.426253	+	0.904604i	$0.359833\pi$
$642$	7.94075	0.313396
$643$	−43.0529	−1.69784	−0.848921	−	0.528520i	$-0.822747\pi$
$643$	−43.0529	−1.69784	−0.848921	+	0.528520i	$0.822747\pi$
$644$	7.98390	0.314610
$645$	12.1969	0.480252
$646$	−3.04889	−0.119957
$647$	31.4738	1.23736	0.618681	−	0.785642i	$-0.287667\pi$
$647$	31.4738	1.23736	0.618681	+	0.785642i	$0.287667\pi$
$648$	−2.00584	−0.0787968
$649$	2.05501	0.0806661
$650$	−0.482964	−0.0189434
$651$	10.6587	0.417748
$652$	−11.1108	−0.435133
$653$	−4.16669	−0.163055	−0.0815276	−	0.996671i	$-0.525980\pi$
$653$	−4.16669	−0.163055	−0.0815276	+	0.996671i	$0.525980\pi$
$654$	1.63107	0.0637800
$655$	−6.86835	−0.268369
$656$	−29.3134	−1.14449
$657$	4.58099	0.178722
$658$	24.0285	0.936727
$659$	−15.7417	−0.613211	−0.306605	−	0.951837i	$-0.599193\pi$
$659$	−15.7417	−0.613211	−0.306605	+	0.951837i	$0.599193\pi$
$660$	0.984176	0.0383090
$661$	−1.77176	−0.0689136	−0.0344568	−	0.999406i	$-0.510970\pi$
$661$	−1.77176	−0.0689136	−0.0344568	+	0.999406i	$0.510970\pi$
$662$	10.7700	0.418588
$663$	6.68543	0.259641
$664$	−5.93543	−0.230339
$665$	42.5229	1.64897
$666$	−1.22999	−0.0476612
$667$	−4.39047	−0.169999
$668$	31.4146	1.21547
$669$	−13.9594	−0.539701
$670$	11.9157	0.460343
$671$	2.30677	0.0890517
$672$	−17.5585	−0.677335
$673$	7.62146	0.293786	0.146893	−	0.989152i	$-0.453073\pi$
$673$	7.62146	0.293786	0.146893	+	0.989152i	$0.453073\pi$
$674$	−11.6076	−0.447106
$675$	−0.133518	−0.00513913
$676$	−54.1116	−2.08121
$677$	0.512892	0.0197120	0.00985602	−	0.999951i	$-0.496863\pi$
$677$	0.512892	0.0197120	0.00985602	+	0.999951i	$0.496863\pi$
$678$	−6.50142	−0.249686
$679$	−34.8606	−1.33783
$680$	4.54469	0.174281
$681$	−9.60857	−0.368201
$682$	0.440552	0.0168696
$683$	−22.4997	−0.860928	−0.430464	−	0.902608i	$-0.641650\pi$
$683$	−22.4997	−0.860928	−0.430464	+	0.902608i	$0.641650\pi$
$684$	9.62047	0.367848
$685$	45.3908	1.73429
$686$	−5.23909	−0.200029
$687$	−13.3778	−0.510393
$688$	12.5388	0.478037
$689$	28.9887	1.10438
$690$	−1.72127	−0.0655277
$691$	24.9657	0.949742	0.474871	−	0.880056i	$-0.342495\pi$
$691$	24.9657	0.949742	0.474871	+	0.880056i	$0.342495\pi$
$692$	31.3358	1.19121
$693$	−0.847393	−0.0321898
$694$	9.04323	0.343276
$695$	−22.7218	−0.861885
$696$	6.27204	0.237741
$697$	−12.5850	−0.476689
$698$	6.99454	0.264747
$699$	−15.6520	−0.592014
$700$	−0.759203	−0.0286952
$701$	0.956991	0.0361451	0.0180725	−	0.999837i	$-0.494247\pi$
$701$	0.956991	0.0361451	0.0180725	+	0.999837i	$0.494247\pi$
$702$	3.61721	0.136523
$703$	12.8102	0.483146
$704$	0.459513	0.0173185
$705$	30.2115	1.13783
$706$	−10.6302	−0.400072
$707$	−4.35265	−0.163698
$708$	−13.7894	−0.518238
$709$	39.4157	1.48029	0.740145	−	0.672448i	$-0.234757\pi$
$709$	39.4157	1.48029	0.740145	+	0.672448i	$0.234757\pi$
$710$	−7.79939	−0.292706
$711$	13.4061	0.502768
$712$	17.7821	0.666414
$713$	4.49351	0.168283
$714$	−1.80203	−0.0674392
$715$	−3.85393	−0.144129
$716$	4.89234	0.182835
$717$	−4.01552	−0.149962
$718$	4.22111	0.157531
$719$	−8.66587	−0.323183	−0.161591	−	0.986858i	$-0.551663\pi$
$719$	−8.66587	−0.323183	−0.161591	+	0.986858i	$0.551663\pi$
$720$	−5.27742	−0.196678
$721$	−52.5377	−1.95661
$722$	6.90051	0.256810
$723$	−10.1686	−0.378173
$724$	−16.4447	−0.611164
$725$	0.417497	0.0155055
$726$	5.91661	0.219586
$727$	27.9289	1.03583	0.517913	−	0.855433i	$-0.326709\pi$
$727$	27.9289	1.03583	0.517913	+	0.855433i	$0.326709\pi$
$728$	44.6626	1.65531
$729$	1.00000	0.0370370
$730$	−5.61579	−0.207850
$731$	5.38322	0.199105
$732$	−15.4787	−0.572111
$733$	−25.0016	−0.923455	−0.461727	−	0.887022i	$-0.652770\pi$
$733$	−25.0016	−0.923455	−0.461727	+	0.887022i	$0.652770\pi$
$734$	−13.0908	−0.483191
$735$	9.27288	0.342035
$736$	−7.40232	−0.272853
$737$	2.47306	0.0910962
$738$	−6.80919	−0.250650
$739$	38.8064	1.42752	0.713758	−	0.700392i	$-0.246992\pi$
$739$	38.8064	1.42752	0.713758	+	0.700392i	$0.246992\pi$
$740$	−8.79357	−0.323258
$741$	−37.6727	−1.38394
$742$	−7.81376	−0.286852
$743$	34.4398	1.26347	0.631736	−	0.775184i	$-0.282343\pi$
$743$	34.4398	1.26347	0.631736	+	0.775184i	$0.282343\pi$
$744$	−6.41924	−0.235341
$745$	4.98347	0.182580
$746$	4.80551	0.175942
$747$	2.95907	0.108267
$748$	0.434376	0.0158823
$749$	−48.8806	−1.78606
$750$	−5.96577	−0.217839
$751$	−35.0609	−1.27939	−0.639696	−	0.768628i	$-0.720940\pi$
$751$	−35.0609	−1.27939	−0.639696	+	0.768628i	$0.720940\pi$
$752$	31.0583	1.13258
$753$	22.8809	0.833827
$754$	−11.3106	−0.411908
$755$	−3.02490	−0.110087
$756$	5.68613	0.206803
$757$	−13.0832	−0.475518	−0.237759	−	0.971324i	$-0.576413\pi$
$757$	−13.0832	−0.475518	−0.237759	+	0.971324i	$0.576413\pi$
$758$	7.56266	0.274688
$759$	−0.357244	−0.0129671
$760$	−25.6095	−0.928955
$761$	−17.8204	−0.645987	−0.322994	−	0.946401i	$-0.604689\pi$
$761$	−17.8204	−0.645987	−0.322994	+	0.946401i	$0.604689\pi$
$762$	−4.04582	−0.146564
$763$	−10.0403	−0.363484
$764$	−0.101512	−0.00367257
$765$	−2.26573	−0.0819175
$766$	19.5847	0.707626
$767$	53.9979	1.94975
$768$	2.62144	0.0945930
$769$	43.8584	1.58158	0.790788	−	0.612090i	$-0.209671\pi$
$769$	43.8584	1.58158	0.790788	+	0.612090i	$0.209671\pi$
$770$	1.03881	0.0374361
$771$	−3.77063	−0.135796
$772$	−31.3685	−1.12898
$773$	0.812578	0.0292264	0.0146132	−	0.999893i	$-0.495348\pi$
$773$	0.812578	0.0292264	0.0146132	+	0.999893i	$0.495348\pi$
$774$	2.91263	0.104692
$775$	−0.427295	−0.0153489
$776$	20.9948	0.753671
$777$	7.57141	0.271623
$778$	0.661923	0.0237311
$779$	70.9168	2.54086
$780$	25.8604	0.925952
$781$	−1.61874	−0.0579229
$782$	−0.759700	−0.0271668
$783$	−3.12689	−0.111746
$784$	9.53281	0.340458
$785$	2.26573	0.0808673
$786$	−1.64017	−0.0585029
$787$	−16.1315	−0.575025	−0.287512	−	0.957777i	$-0.592828\pi$
$787$	−16.1315	−0.575025	−0.287512	+	0.957777i	$0.592828\pi$
$788$	6.31410	0.224930
$789$	−12.6583	−0.450646
$790$	−16.4344	−0.584709
$791$	40.0205	1.42297
$792$	0.510344	0.0181343
$793$	60.6131	2.15243
$794$	−10.1404	−0.359869
$795$	−9.82440	−0.348436
$796$	−32.5486	−1.15365
$797$	44.0144	1.55907	0.779534	−	0.626360i	$-0.215456\pi$
$797$	44.0144	1.55907	0.779534	+	0.626360i	$0.215456\pi$
$798$	10.1545	0.359466
$799$	13.3341	0.471727
$800$	0.703900	0.0248866
$801$	−8.86519	−0.313236
$802$	−2.93234	−0.103544
$803$	−1.16554	−0.0411309
$804$	−16.5946	−0.585246
$805$	10.5956	0.373444
$806$	11.5761	0.407749
$807$	−3.15915	−0.111207
$808$	2.62139	0.0922202
$809$	−14.2351	−0.500480	−0.250240	−	0.968184i	$-0.580509\pi$
$809$	−14.2351	−0.500480	−0.250240	+	0.968184i	$0.580509\pi$
$810$	−1.22589	−0.0430734
$811$	28.8456	1.01291	0.506454	−	0.862267i	$-0.330956\pi$
$811$	28.8456	1.01291	0.506454	+	0.862267i	$0.330956\pi$
$812$	−17.7799	−0.623952
$813$	−31.9787	−1.12154
$814$	0.312946	0.0109687
$815$	−14.7453	−0.516506
$816$	−2.32924	−0.0815396
$817$	−30.3347	−1.06128
$818$	15.7677	0.551306
$819$	−22.2663	−0.778047
$820$	−48.6808	−1.70001
$821$	−44.2940	−1.54587	−0.772935	−	0.634485i	$-0.781212\pi$
$821$	−44.2940	−1.54587	−0.772935	+	0.634485i	$0.781212\pi$
$822$	10.8394	0.378067
$823$	−15.0189	−0.523526	−0.261763	−	0.965132i	$-0.584304\pi$
$823$	−15.0189	−0.523526	−0.261763	+	0.965132i	$0.584304\pi$
$824$	31.6409	1.10226
$825$	0.0339709	0.00118272
$826$	−14.5549	−0.506429
$827$	6.08818	0.211707	0.105853	−	0.994382i	$-0.466243\pi$
$827$	6.08818	0.211707	0.105853	+	0.994382i	$0.466243\pi$
$828$	2.39716	0.0833071
$829$	9.87373	0.342929	0.171464	−	0.985190i	$-0.445150\pi$
$829$	9.87373	0.342929	0.171464	+	0.985190i	$0.445150\pi$
$830$	−3.62750	−0.125912
$831$	−17.9452	−0.622513
$832$	12.0743	0.418600
$833$	4.09267	0.141803
$834$	−5.42598	−0.187886
$835$	41.6908	1.44277
$836$	−2.44773	−0.0846564
$837$	3.20027	0.110618
$838$	−5.84779	−0.202009
$839$	3.36064	0.116022	0.0580110	−	0.998316i	$-0.481524\pi$
$839$	3.36064	0.116022	0.0580110	+	0.998316i	$0.481524\pi$
$840$	−15.1364	−0.522255
$841$	−19.2226	−0.662847
$842$	−15.5585	−0.536180
$843$	5.31471	0.183048
$844$	−31.4554	−1.08274
$845$	−71.8123	−2.47042
$846$	7.21453	0.248041
$847$	−36.4206	−1.25143
$848$	−10.0998	−0.346828
$849$	−22.6414	−0.777049
$850$	0.0722412	0.00247785
$851$	3.19196	0.109419
$852$	10.8620	0.372125
$853$	37.2010	1.27374	0.636868	−	0.770973i	$-0.280229\pi$
$853$	37.2010	1.27374	0.636868	+	0.770973i	$0.280229\pi$
$854$	−16.3380	−0.559075
$855$	12.7675	0.436638
$856$	29.4384	1.00618
$857$	8.67921	0.296476	0.148238	−	0.988952i	$-0.452640\pi$
$857$	8.67921	0.296476	0.148238	+	0.988952i	$0.452640\pi$
$858$	−0.920322	−0.0314193
$859$	−52.0809	−1.77698	−0.888489	−	0.458897i	$-0.848245\pi$
$859$	−52.0809	−1.77698	−0.888489	+	0.458897i	$0.848245\pi$
$860$	20.8232	0.710066
$861$	41.9150	1.42846
$862$	18.8328	0.641449
$863$	−47.5919	−1.62005	−0.810023	−	0.586398i	$-0.800546\pi$
$863$	−47.5919	−1.62005	−0.810023	+	0.586398i	$0.800546\pi$
$864$	−5.27193	−0.179355
$865$	41.5862	1.41397
$866$	−13.7632	−0.467693
$867$	−1.00000	−0.0339618
$868$	18.1972	0.617653
$869$	−3.41090	−0.115707
$870$	3.83322	0.129958
$871$	64.9826	2.20185
$872$	6.04680	0.204771
$873$	−10.4669	−0.354250
$874$	4.28094	0.144805
$875$	36.7232	1.24147
$876$	7.82093	0.264245
$877$	8.03151	0.271205	0.135602	−	0.990763i	$-0.456703\pi$
$877$	8.03151	0.271205	0.135602	+	0.990763i	$0.456703\pi$
$878$	16.2140	0.547197
$879$	12.7297	0.429364
$880$	1.34273	0.0452633
$881$	−32.7234	−1.10248	−0.551240	−	0.834347i	$-0.685845\pi$
$881$	−32.7234	−1.10248	−0.551240	+	0.834347i	$0.685845\pi$
$882$	2.21437	0.0745618
$883$	24.4158	0.821657	0.410829	−	0.911713i	$-0.365239\pi$
$883$	24.4158	0.821657	0.410829	+	0.911713i	$0.365239\pi$
$884$	11.4138	0.383886
$885$	−18.3001	−0.615153
$886$	−2.43108	−0.0816737
$887$	−4.89983	−0.164520	−0.0822602	−	0.996611i	$-0.526214\pi$
$887$	−4.89983	−0.164520	−0.0822602	+	0.996611i	$0.526214\pi$
$888$	−4.55990	−0.153020
$889$	24.9047	0.835276
$890$	10.8677	0.364287
$891$	−0.254429	−0.00852369
$892$	−23.8322	−0.797962
$893$	−75.1384	−2.51441
$894$	1.19006	0.0398015
$895$	6.49271	0.217027
$896$	−38.3716	−1.28191
$897$	−9.38702	−0.313424
$898$	−15.5088	−0.517536
$899$	−10.0069	−0.333749
$900$	−0.227950	−0.00759834
$901$	−4.33609	−0.144456
$902$	1.73245	0.0576844
$903$	−17.9292	−0.596645
$904$	−24.1024	−0.801635
$905$	−21.8241	−0.725456
$906$	−0.722349	−0.0239984
$907$	10.3832	0.344768	0.172384	−	0.985030i	$-0.444853\pi$
$907$	10.3832	0.344768	0.172384	+	0.985030i	$0.444853\pi$
$908$	−16.4043	−0.544395
$909$	−1.30688	−0.0433465
$910$	27.2960	0.904853
$911$	−43.2251	−1.43211	−0.716056	−	0.698043i	$-0.754054\pi$
$911$	−43.2251	−1.43211	−0.716056	+	0.698043i	$0.754054\pi$
$912$	13.1254	0.434624
$913$	−0.752874	−0.0249165
$914$	7.29815	0.241402
$915$	−20.5421	−0.679100
$916$	−22.8393	−0.754631
$917$	10.0963	0.333410
$918$	−0.541058	−0.0178576
$919$	−19.0719	−0.629124	−0.314562	−	0.949237i	$-0.601858\pi$
$919$	−19.0719	−0.629124	−0.314562	+	0.949237i	$0.601858\pi$
$920$	−6.38120	−0.210382
$921$	5.57938	0.183847
$922$	−7.12332	−0.234594
$923$	−42.5343	−1.40003
$924$	−1.44672	−0.0475935
$925$	−0.303529	−0.00997996
$926$	3.96709	0.130367
$927$	−15.7744	−0.518100
$928$	16.4847	0.541138
$929$	−21.1209	−0.692956	−0.346478	−	0.938058i	$-0.612622\pi$
$929$	−21.1209	−0.692956	−0.346478	+	0.938058i	$0.612622\pi$
$930$	−3.92318	−0.128646
$931$	−23.0624	−0.755840
$932$	−26.7220	−0.875310
$933$	11.5904	0.379452
$934$	−8.08785	−0.264642
$935$	0.576467	0.0188525
$936$	13.4099	0.438317
$937$	13.5978	0.444221	0.222110	−	0.975022i	$-0.428706\pi$
$937$	13.5978	0.444221	0.222110	+	0.975022i	$0.428706\pi$
$938$	−17.5158	−0.571910
$939$	−6.14677	−0.200592
$940$	51.5787	1.68231
$941$	5.36980	0.175050	0.0875252	−	0.996162i	$-0.472104\pi$
$941$	5.36980	0.175050	0.0875252	+	0.996162i	$0.472104\pi$
$942$	0.541058	0.0176286
$943$	17.6705	0.575432
$944$	−18.8131	−0.612315
$945$	7.54615	0.245476
$946$	−0.741058	−0.0240939
$947$	26.0782	0.847428	0.423714	−	0.905796i	$-0.360726\pi$
$947$	26.0782	0.847428	0.423714	+	0.905796i	$0.360726\pi$
$948$	22.8876	0.743356
$949$	−30.6259	−0.994160
$950$	−0.407082	−0.0132075
$951$	−18.7913	−0.609351
$952$	−6.68058	−0.216519
$953$	36.9591	1.19722	0.598612	−	0.801039i	$-0.295719\pi$
$953$	36.9591	1.19722	0.598612	+	0.801039i	$0.295719\pi$
$954$	−2.34608	−0.0759570
$955$	−0.134718	−0.00435938
$956$	−6.85552	−0.221723
$957$	0.795571	0.0257172
$958$	18.7189	0.604779
$959$	−66.7235	−2.15461
$960$	−4.09203	−0.132070
$961$	−20.7582	−0.669621
$962$	8.22303	0.265121
$963$	−14.6763	−0.472939
$964$	−17.3604	−0.559140
$965$	−41.6296	−1.34010
$966$	2.53023	0.0814088
$967$	−57.7057	−1.85569	−0.927846	−	0.372964i	$-0.878341\pi$
$967$	−57.7057	−1.85569	−0.927846	+	0.372964i	$0.878341\pi$
$968$	21.9344	0.704998
$969$	5.63505	0.181024
$970$	12.8312	0.411985
$971$	35.4244	1.13682	0.568411	−	0.822745i	$-0.307558\pi$
$971$	35.4244	1.13682	0.568411	+	0.822745i	$0.307558\pi$
$972$	1.70726	0.0547603
$973$	33.4005	1.07077
$974$	0.729232	0.0233661
$975$	0.892628	0.0285870
$976$	−21.1179	−0.675968
$977$	17.6595	0.564976	0.282488	−	0.959271i	$-0.408840\pi$
$977$	17.6595	0.564976	0.282488	+	0.959271i	$0.408840\pi$
$978$	−3.52120	−0.112596
$979$	2.25556	0.0720880
$980$	15.8312	0.505709
$981$	−3.01460	−0.0962487
$982$	12.1024	0.386203
$983$	−46.2782	−1.47605	−0.738023	−	0.674776i	$-0.764240\pi$
$983$	−46.2782	−1.47605	−0.738023	+	0.674776i	$0.764240\pi$
$984$	−25.2434	−0.804730
$985$	8.37954	0.266994
$986$	1.69183	0.0538787
$987$	−44.4102	−1.41359
$988$	−64.3170	−2.04620
$989$	−7.55858	−0.240349
$990$	0.311902	0.00991289
$991$	−26.9897	−0.857356	−0.428678	−	0.903457i	$-0.641020\pi$
$991$	−26.9897	−0.857356	−0.428678	+	0.903457i	$0.641020\pi$
$992$	−16.8716	−0.535675
$993$	−19.9054	−0.631680
$994$	11.4649	0.363645
$995$	−43.1957	−1.36940
$996$	5.05190	0.160076
$997$	−4.53595	−0.143655	−0.0718276	−	0.997417i	$-0.522883\pi$
$997$	−4.53595	−0.143655	−0.0718276	+	0.997417i	$0.522883\pi$
$998$	−6.50083	−0.205780
$999$	2.27331	0.0719243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.37	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.37	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+0.541058 q^{2} -1.00000 q^{3} -1.70726 q^{4} -2.26573 q^{5} -0.541058 q^{6} +3.33057 q^{7} -2.00584 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.541058 q^{2} -1.00000 q^{3} -1.70726 q^{4} -2.26573 q^{5} -0.541058 q^{6} +3.33057 q^{7} -2.00584 q^{8} +1.00000 q^{9} -1.22589 q^{10} -0.254429 q^{11} +1.70726 q^{12} -6.68543 q^{13} +1.80203 q^{14} +2.26573 q^{15} +2.32924 q^{16} +1.00000 q^{17} +0.541058 q^{18} -5.63505 q^{19} +3.86818 q^{20} -3.33057 q^{21} -0.137661 q^{22} -1.40410 q^{23} +2.00584 q^{24} +0.133518 q^{25} -3.61721 q^{26} -1.00000 q^{27} -5.68613 q^{28} +3.12689 q^{29} +1.22589 q^{30} -3.20027 q^{31} +5.27193 q^{32} +0.254429 q^{33} +0.541058 q^{34} -7.54615 q^{35} -1.70726 q^{36} -2.27331 q^{37} -3.04889 q^{38} +6.68543 q^{39} +4.54469 q^{40} -12.5850 q^{41} -1.80203 q^{42} +5.38322 q^{43} +0.434376 q^{44} -2.26573 q^{45} -0.759700 q^{46} +13.3341 q^{47} -2.32924 q^{48} +4.09267 q^{49} +0.0722412 q^{50} -1.00000 q^{51} +11.4138 q^{52} -4.33609 q^{53} -0.541058 q^{54} +0.576467 q^{55} -6.68058 q^{56} +5.63505 q^{57} +1.69183 q^{58} -8.07694 q^{59} -3.86818 q^{60} -9.06644 q^{61} -1.73153 q^{62} +3.33057 q^{63} -1.80606 q^{64} +15.1474 q^{65} +0.137661 q^{66} -9.72002 q^{67} -1.70726 q^{68} +1.40410 q^{69} -4.08291 q^{70} +6.36223 q^{71} -2.00584 q^{72} +4.58099 q^{73} -1.22999 q^{74} -0.133518 q^{75} +9.62047 q^{76} -0.847393 q^{77} +3.61721 q^{78} +13.4061 q^{79} -5.27742 q^{80} +1.00000 q^{81} -6.80919 q^{82} +2.95907 q^{83} +5.68613 q^{84} -2.26573 q^{85} +2.91263 q^{86} -3.12689 q^{87} +0.510344 q^{88} -8.86519 q^{89} -1.22589 q^{90} -22.2663 q^{91} +2.39716 q^{92} +3.20027 q^{93} +7.21453 q^{94} +12.7675 q^{95} -5.27193 q^{96} -10.4669 q^{97} +2.21437 q^{98} -0.254429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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