LMFDB - Embedded newform 8007.2.a.f.1.35

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:	$1$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.35
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)

$f(q)$	$=$	$q+1.36019 q^{2} -1.00000 q^{3} -0.149892 q^{4} -3.22830 q^{5} -1.36019 q^{6} +2.99593 q^{7} -2.92425 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.36019 q^{2} -1.00000 q^{3} -0.149892 q^{4} -3.22830 q^{5} -1.36019 q^{6} +2.99593 q^{7} -2.92425 q^{8} +1.00000 q^{9} -4.39109 q^{10} -3.10094 q^{11} +0.149892 q^{12} +1.97983 q^{13} +4.07502 q^{14} +3.22830 q^{15} -3.67775 q^{16} -1.00000 q^{17} +1.36019 q^{18} -0.710503 q^{19} +0.483896 q^{20} -2.99593 q^{21} -4.21786 q^{22} +6.91202 q^{23} +2.92425 q^{24} +5.42193 q^{25} +2.69294 q^{26} -1.00000 q^{27} -0.449065 q^{28} +9.35128 q^{29} +4.39109 q^{30} -7.97012 q^{31} +0.846083 q^{32} +3.10094 q^{33} -1.36019 q^{34} -9.67175 q^{35} -0.149892 q^{36} -4.06302 q^{37} -0.966417 q^{38} -1.97983 q^{39} +9.44038 q^{40} -0.959933 q^{41} -4.07502 q^{42} -1.47429 q^{43} +0.464806 q^{44} -3.22830 q^{45} +9.40163 q^{46} +5.23028 q^{47} +3.67775 q^{48} +1.97557 q^{49} +7.37484 q^{50} +1.00000 q^{51} -0.296760 q^{52} +4.09703 q^{53} -1.36019 q^{54} +10.0108 q^{55} -8.76085 q^{56} +0.710503 q^{57} +12.7195 q^{58} +2.47378 q^{59} -0.483896 q^{60} +8.55814 q^{61} -10.8409 q^{62} +2.99593 q^{63} +8.50633 q^{64} -6.39148 q^{65} +4.21786 q^{66} -5.39634 q^{67} +0.149892 q^{68} -6.91202 q^{69} -13.1554 q^{70} -0.392945 q^{71} -2.92425 q^{72} -3.98267 q^{73} -5.52647 q^{74} -5.42193 q^{75} +0.106499 q^{76} -9.29019 q^{77} -2.69294 q^{78} -5.00199 q^{79} +11.8729 q^{80} +1.00000 q^{81} -1.30569 q^{82} +13.6271 q^{83} +0.449065 q^{84} +3.22830 q^{85} -2.00531 q^{86} -9.35128 q^{87} +9.06794 q^{88} +9.10587 q^{89} -4.39109 q^{90} +5.93142 q^{91} -1.03605 q^{92} +7.97012 q^{93} +7.11416 q^{94} +2.29372 q^{95} -0.846083 q^{96} -15.0235 q^{97} +2.68715 q^{98} -3.10094 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.36019	0.961797	0.480899	−	0.876776i	$-0.340310\pi$
$2$	1.36019	0.961797	0.480899	+	0.876776i	$0.340310\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.149892	−0.0749459
$5$	−3.22830	−1.44374	−0.721870	−	0.692028i	$-0.756717\pi$
$5$	−3.22830	−1.44374	−0.721870	+	0.692028i	$0.756717\pi$
$6$	−1.36019	−0.555294
$7$	2.99593	1.13235	0.566177	−	0.824284i	$-0.308422\pi$
$7$	2.99593	1.13235	0.566177	+	0.824284i	$0.308422\pi$
$8$	−2.92425	−1.03388
$9$	1.00000	0.333333
$10$	−4.39109	−1.38859
$11$	−3.10094	−0.934969	−0.467485	−	0.884001i	$-0.654840\pi$
$11$	−3.10094	−0.934969	−0.467485	+	0.884001i	$0.654840\pi$
$12$	0.149892	0.0432700
$13$	1.97983	0.549105	0.274553	−	0.961572i	$-0.411470\pi$
$13$	1.97983	0.549105	0.274553	+	0.961572i	$0.411470\pi$
$14$	4.07502	1.08909
$15$	3.22830	0.833544
$16$	−3.67775	−0.919437
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.36019	0.320599
$19$	−0.710503	−0.163001	−0.0815003	−	0.996673i	$-0.525971\pi$
$19$	−0.710503	−0.163001	−0.0815003	+	0.996673i	$0.525971\pi$
$20$	0.483896	0.108202
$21$	−2.99593	−0.653765
$22$	−4.21786	−0.899251
$23$	6.91202	1.44125	0.720627	−	0.693323i	$-0.243854\pi$
$23$	6.91202	1.44125	0.720627	+	0.693323i	$0.243854\pi$
$24$	2.92425	0.596911
$25$	5.42193	1.08439
$26$	2.69294	0.528128
$27$	−1.00000	−0.192450
$28$	−0.449065	−0.0848652
$29$	9.35128	1.73649	0.868244	−	0.496137i	$-0.165249\pi$
$29$	9.35128	1.73649	0.868244	+	0.496137i	$0.165249\pi$
$30$	4.39109	0.801700
$31$	−7.97012	−1.43148	−0.715738	−	0.698369i	$-0.753909\pi$
$31$	−7.97012	−1.43148	−0.715738	+	0.698369i	$0.753909\pi$
$32$	0.846083	0.149568
$33$	3.10094	0.539805
$34$	−1.36019	−0.233270
$35$	−9.67175	−1.63482
$36$	−0.149892	−0.0249820
$37$	−4.06302	−0.667957	−0.333978	−	0.942581i	$-0.608391\pi$
$37$	−4.06302	−0.667957	−0.333978	+	0.942581i	$0.608391\pi$
$38$	−0.966417	−0.156774
$39$	−1.97983	−0.317026
$40$	9.44038	1.49265
$41$	−0.959933	−0.149916	−0.0749582	−	0.997187i	$-0.523882\pi$
$41$	−0.959933	−0.149916	−0.0749582	+	0.997187i	$0.523882\pi$
$42$	−4.07502	−0.628789
$43$	−1.47429	−0.224828	−0.112414	−	0.993661i	$-0.535858\pi$
$43$	−1.47429	−0.224828	−0.112414	+	0.993661i	$0.535858\pi$
$44$	0.464806	0.0700721
$45$	−3.22830	−0.481247
$46$	9.40163	1.38620
$47$	5.23028	0.762915	0.381457	−	0.924386i	$-0.375422\pi$
$47$	5.23028	0.762915	0.381457	+	0.924386i	$0.375422\pi$
$48$	3.67775	0.530837
$49$	1.97557	0.282225
$50$	7.37484	1.04296
$51$	1.00000	0.140028
$52$	−0.296760	−0.0411532
$53$	4.09703	0.562770	0.281385	−	0.959595i	$-0.409206\pi$
$53$	4.09703	0.562770	0.281385	+	0.959595i	$0.409206\pi$
$54$	−1.36019	−0.185098
$55$	10.0108	1.34985
$56$	−8.76085	−1.17072
$57$	0.710503	0.0941085
$58$	12.7195	1.67015
$59$	2.47378	0.322059	0.161029	−	0.986950i	$-0.448519\pi$
$59$	2.47378	0.322059	0.161029	+	0.986950i	$0.448519\pi$
$60$	−0.483896	−0.0624707
$61$	8.55814	1.09576	0.547879	−	0.836558i	$-0.315435\pi$
$61$	8.55814	1.09576	0.547879	+	0.836558i	$0.315435\pi$
$62$	−10.8409	−1.37679
$63$	2.99593	0.377451
$64$	8.50633	1.06329
$65$	−6.39148	−0.792766
$66$	4.21786	0.519183
$67$	−5.39634	−0.659267	−0.329634	−	0.944109i	$-0.606925\pi$
$67$	−5.39634	−0.659267	−0.329634	+	0.944109i	$0.606925\pi$
$68$	0.149892	0.0181770
$69$	−6.91202	−0.832109
$70$	−13.1554	−1.57237
$71$	−0.392945	−0.0466340	−0.0233170	−	0.999728i	$-0.507423\pi$
$71$	−0.392945	−0.0466340	−0.0233170	+	0.999728i	$0.507423\pi$
$72$	−2.92425	−0.344627
$73$	−3.98267	−0.466136	−0.233068	−	0.972460i	$-0.574876\pi$
$73$	−3.98267	−0.466136	−0.233068	+	0.972460i	$0.574876\pi$
$74$	−5.52647	−0.642439
$75$	−5.42193	−0.626071
$76$	0.106499	0.0122162
$77$	−9.29019	−1.05872
$78$	−2.69294	−0.304915
$79$	−5.00199	−0.562768	−0.281384	−	0.959595i	$-0.590794\pi$
$79$	−5.00199	−0.562768	−0.281384	+	0.959595i	$0.590794\pi$
$80$	11.8729	1.32743
$81$	1.00000	0.111111
$82$	−1.30569	−0.144189
$83$	13.6271	1.49577	0.747884	−	0.663830i	$-0.231070\pi$
$83$	13.6271	1.49577	0.747884	+	0.663830i	$0.231070\pi$
$84$	0.449065	0.0489970
$85$	3.22830	0.350159
$86$	−2.00531	−0.216239
$87$	−9.35128	−1.00256
$88$	9.06794	0.966646
$89$	9.10587	0.965220	0.482610	−	0.875835i	$-0.339689\pi$
$89$	9.10587	0.965220	0.482610	+	0.875835i	$0.339689\pi$
$90$	−4.39109	−0.462862
$91$	5.93142	0.621781
$92$	−1.03605	−0.108016
$93$	7.97012	0.826463
$94$	7.11416	0.733769
$95$	2.29372	0.235331
$96$	−0.846083	−0.0863530
$97$	−15.0235	−1.52541	−0.762704	−	0.646747i	$-0.776129\pi$
$97$	−15.0235	−1.52541	−0.762704	+	0.646747i	$0.776129\pi$
$98$	2.68715	0.271443
$99$	−3.10094	−0.311656
$100$	−0.812703	−0.0812703
$101$	−11.0817	−1.10267	−0.551337	−	0.834283i	$-0.685882\pi$
$101$	−11.0817	−1.10267	−0.551337	+	0.834283i	$0.685882\pi$
$102$	1.36019	0.134679
$103$	0.479670	0.0472633	0.0236317	−	0.999721i	$-0.492477\pi$
$103$	0.479670	0.0472633	0.0236317	+	0.999721i	$0.492477\pi$
$104$	−5.78952	−0.567709
$105$	9.67175	0.943867
$106$	5.57272	0.541271
$107$	−7.15167	−0.691378	−0.345689	−	0.938349i	$-0.612355\pi$
$107$	−7.15167	−0.691378	−0.345689	+	0.938349i	$0.612355\pi$
$108$	0.149892	0.0144233
$109$	13.1173	1.25641	0.628203	−	0.778050i	$-0.283791\pi$
$109$	13.1173	1.25641	0.628203	+	0.778050i	$0.283791\pi$
$110$	13.6165	1.29829
$111$	4.06302	0.385645
$112$	−11.0183	−1.04113
$113$	−17.8656	−1.68066	−0.840328	−	0.542078i	$-0.817638\pi$
$113$	−17.8656	−1.68066	−0.840328	+	0.542078i	$0.817638\pi$
$114$	0.966417	0.0905133
$115$	−22.3141	−2.08080
$116$	−1.40168	−0.130143
$117$	1.97983	0.183035
$118$	3.36480	0.309755
$119$	−2.99593	−0.274636
$120$	−9.44038	−0.861785
$121$	−1.38416	−0.125832
$122$	11.6407	1.05390
$123$	0.959933	0.0865543
$124$	1.19466	0.107283
$125$	−1.36213	−0.121833
$126$	4.07502	0.363032
$127$	−7.44419	−0.660565	−0.330282	−	0.943882i	$-0.607144\pi$
$127$	−7.44419	−0.660565	−0.330282	+	0.943882i	$0.607144\pi$
$128$	9.87803	0.873103
$129$	1.47429	0.129804
$130$	−8.69361	−0.762480
$131$	10.7794	0.941804	0.470902	−	0.882185i	$-0.343928\pi$
$131$	10.7794	0.941804	0.470902	+	0.882185i	$0.343928\pi$
$132$	−0.464806	−0.0404561
$133$	−2.12862	−0.184574
$134$	−7.34003	−0.634082
$135$	3.22830	0.277848
$136$	2.92425	0.250753
$137$	−13.1892	−1.12683	−0.563415	−	0.826174i	$-0.690513\pi$
$137$	−13.1892	−1.12683	−0.563415	+	0.826174i	$0.690513\pi$
$138$	−9.40163	−0.800320
$139$	20.3422	1.72540	0.862701	−	0.505714i	$-0.168771\pi$
$139$	20.3422	1.72540	0.862701	+	0.505714i	$0.168771\pi$
$140$	1.44972	0.122523
$141$	−5.23028	−0.440469
$142$	−0.534479	−0.0448525
$143$	−6.13933	−0.513397
$144$	−3.67775	−0.306479
$145$	−30.1887	−2.50704
$146$	−5.41717	−0.448328
$147$	−1.97557	−0.162942
$148$	0.609014	0.0500606
$149$	20.1066	1.64720	0.823600	−	0.567171i	$-0.191962\pi$
$149$	20.1066	1.64720	0.823600	+	0.567171i	$0.191962\pi$
$150$	−7.37484	−0.602153
$151$	−22.9247	−1.86558	−0.932792	−	0.360416i	$-0.882635\pi$
$151$	−22.9247	−1.86558	−0.932792	+	0.360416i	$0.882635\pi$
$152$	2.07769	0.168523
$153$	−1.00000	−0.0808452
$154$	−12.6364	−1.01827
$155$	25.7300	2.06668
$156$	0.296760	0.0237598
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−6.80365	−0.541269
$159$	−4.09703	−0.324915
$160$	−2.73141	−0.215937
$161$	20.7079	1.63201
$162$	1.36019	0.106866
$163$	7.59890	0.595192	0.297596	−	0.954692i	$-0.403815\pi$
$163$	7.59890	0.595192	0.297596	+	0.954692i	$0.403815\pi$
$164$	0.143886	0.0112356
$165$	−10.0108	−0.779338
$166$	18.5354	1.43862
$167$	1.04495	0.0808609	0.0404305	−	0.999182i	$-0.487127\pi$
$167$	1.04495	0.0808609	0.0404305	+	0.999182i	$0.487127\pi$
$168$	8.76085	0.675914
$169$	−9.08028	−0.698483
$170$	4.39109	0.336782
$171$	−0.710503	−0.0543336
$172$	0.220984	0.0168499
$173$	−16.3423	−1.24248	−0.621242	−	0.783619i	$-0.713372\pi$
$173$	−16.3423	−1.24248	−0.621242	+	0.783619i	$0.713372\pi$
$174$	−12.7195	−0.964261
$175$	16.2437	1.22791
$176$	11.4045	0.859646
$177$	−2.47378	−0.185941
$178$	12.3857	0.928346
$179$	−10.6512	−0.796111	−0.398056	−	0.917361i	$-0.630315\pi$
$179$	−10.6512	−0.796111	−0.398056	+	0.917361i	$0.630315\pi$
$180$	0.483896	0.0360675
$181$	−13.6692	−1.01602	−0.508010	−	0.861351i	$-0.669619\pi$
$181$	−13.6692	−1.01602	−0.508010	+	0.861351i	$0.669619\pi$
$182$	8.06783	0.598028
$183$	−8.55814	−0.632636
$184$	−20.2125	−1.49008
$185$	13.1167	0.964357
$186$	10.8409	0.794890
$187$	3.10094	0.226763
$188$	−0.783976	−0.0571773
$189$	−2.99593	−0.217922
$190$	3.11989	0.226340
$191$	−8.15314	−0.589940	−0.294970	−	0.955506i	$-0.595310\pi$
$191$	−8.15314	−0.589940	−0.294970	+	0.955506i	$0.595310\pi$
$192$	−8.50633	−0.613891
$193$	−23.0830	−1.66155	−0.830776	−	0.556607i	$-0.812103\pi$
$193$	−23.0830	−1.66155	−0.830776	+	0.556607i	$0.812103\pi$
$194$	−20.4348	−1.46713
$195$	6.39148	0.457703
$196$	−0.296122	−0.0211516
$197$	−26.6711	−1.90024	−0.950120	−	0.311885i	$-0.899040\pi$
$197$	−26.6711	−1.90024	−0.950120	+	0.311885i	$0.899040\pi$
$198$	−4.21786	−0.299750
$199$	−0.433103	−0.0307019	−0.0153509	−	0.999882i	$-0.504887\pi$
$199$	−0.433103	−0.0307019	−0.0153509	+	0.999882i	$0.504887\pi$
$200$	−15.8551	−1.12113
$201$	5.39634	0.380628
$202$	−15.0732	−1.06055
$203$	28.0157	1.96632
$204$	−0.149892	−0.0104945
$205$	3.09895	0.216440
$206$	0.652441	0.0454577
$207$	6.91202	0.480418
$208$	−7.28131	−0.504868
$209$	2.20323	0.152401
$210$	13.1554	0.907808
$211$	−23.9319	−1.64754	−0.823771	−	0.566923i	$-0.808134\pi$
$211$	−23.9319	−1.64754	−0.823771	+	0.566923i	$0.808134\pi$
$212$	−0.614110	−0.0421773
$213$	0.392945	0.0269242
$214$	−9.72760	−0.664965
$215$	4.75946	0.324593
$216$	2.92425	0.198970
$217$	−23.8779	−1.62094
$218$	17.8419	1.20841
$219$	3.98267	0.269124
$220$	−1.50053	−0.101166
$221$	−1.97983	−0.133178
$222$	5.52647	0.370912
$223$	−19.9609	−1.33668	−0.668339	−	0.743857i	$-0.732995\pi$
$223$	−19.9609	−1.33668	−0.668339	+	0.743857i	$0.732995\pi$
$224$	2.53480	0.169364
$225$	5.42193	0.361462
$226$	−24.3006	−1.61645
$227$	−5.50929	−0.365665	−0.182832	−	0.983144i	$-0.558527\pi$
$227$	−5.50929	−0.365665	−0.182832	+	0.983144i	$0.558527\pi$
$228$	−0.106499	−0.00705304
$229$	−20.3676	−1.34593	−0.672964	−	0.739675i	$-0.734979\pi$
$229$	−20.3676	−1.34593	−0.672964	+	0.739675i	$0.734979\pi$
$230$	−30.3513	−2.00131
$231$	9.29019	0.611250
$232$	−27.3455	−1.79532
$233$	−11.2941	−0.739900	−0.369950	−	0.929052i	$-0.620625\pi$
$233$	−11.2941	−0.739900	−0.369950	+	0.929052i	$0.620625\pi$
$234$	2.69294	0.176043
$235$	−16.8849	−1.10145
$236$	−0.370799	−0.0241370
$237$	5.00199	0.324914
$238$	−4.07502	−0.264144
$239$	0.941056	0.0608718	0.0304359	−	0.999537i	$-0.490310\pi$
$239$	0.941056	0.0608718	0.0304359	+	0.999537i	$0.490310\pi$
$240$	−11.8729	−0.766391
$241$	11.0760	0.713470	0.356735	−	0.934206i	$-0.383890\pi$
$241$	11.0760	0.713470	0.356735	+	0.934206i	$0.383890\pi$
$242$	−1.88271	−0.121025
$243$	−1.00000	−0.0641500
$244$	−1.28280	−0.0821225
$245$	−6.37775	−0.407459
$246$	1.30569	0.0832477
$247$	−1.40667	−0.0895045
$248$	23.3067	1.47997
$249$	−13.6271	−0.863582
$250$	−1.85275	−0.117178
$251$	−8.17534	−0.516023	−0.258011	−	0.966142i	$-0.583067\pi$
$251$	−8.17534	−0.516023	−0.258011	+	0.966142i	$0.583067\pi$
$252$	−0.449065	−0.0282884
$253$	−21.4338	−1.34753
$254$	−10.1255	−0.635330
$255$	−3.22830	−0.202164
$256$	−3.57669	−0.223543
$257$	18.4333	1.14984	0.574919	−	0.818210i	$-0.305034\pi$
$257$	18.4333	1.14984	0.574919	+	0.818210i	$0.305034\pi$
$258$	2.00531	0.124845
$259$	−12.1725	−0.756364
$260$	0.958030	0.0594145
$261$	9.35128	0.578829
$262$	14.6621	0.905825
$263$	23.5480	1.45203	0.726015	−	0.687679i	$-0.241370\pi$
$263$	23.5480	1.45203	0.726015	+	0.687679i	$0.241370\pi$
$264$	−9.06794	−0.558093
$265$	−13.2264	−0.812494
$266$	−2.89531	−0.177523
$267$	−9.10587	−0.557270
$268$	0.808866	0.0494094
$269$	−1.74484	−0.106385	−0.0531923	−	0.998584i	$-0.516940\pi$
$269$	−1.74484	−0.106385	−0.0531923	+	0.998584i	$0.516940\pi$
$270$	4.39109	0.267233
$271$	−20.1218	−1.22231	−0.611155	−	0.791511i	$-0.709295\pi$
$271$	−20.1218	−1.22231	−0.611155	+	0.791511i	$0.709295\pi$
$272$	3.67775	0.222996
$273$	−5.93142	−0.358986
$274$	−17.9398	−1.08378
$275$	−16.8131	−1.01387
$276$	1.03605	0.0623631
$277$	1.60990	0.0967296	0.0483648	−	0.998830i	$-0.484599\pi$
$277$	1.60990	0.0967296	0.0483648	+	0.998830i	$0.484599\pi$
$278$	27.6692	1.65949
$279$	−7.97012	−0.477159
$280$	28.2827	1.69021
$281$	21.7941	1.30013	0.650064	−	0.759879i	$-0.274742\pi$
$281$	21.7941	1.30013	0.650064	+	0.759879i	$0.274742\pi$
$282$	−7.11416	−0.423642
$283$	2.77076	0.164704	0.0823522	−	0.996603i	$-0.473757\pi$
$283$	2.77076	0.164704	0.0823522	+	0.996603i	$0.473757\pi$
$284$	0.0588993	0.00349503
$285$	−2.29372	−0.135868
$286$	−8.35064	−0.493783
$287$	−2.87589	−0.169758
$288$	0.846083	0.0498559
$289$	1.00000	0.0588235
$290$	−41.0623	−2.41126
$291$	15.0235	0.880695
$292$	0.596969	0.0349350
$293$	0.402509	0.0235148	0.0117574	−	0.999931i	$-0.496257\pi$
$293$	0.402509	0.0235148	0.0117574	+	0.999931i	$0.496257\pi$
$294$	−2.68715	−0.156718
$295$	−7.98611	−0.464969
$296$	11.8813	0.690587
$297$	3.10094	0.179935
$298$	27.3488	1.58427
$299$	13.6846	0.791401
$300$	0.812703	0.0469214
$301$	−4.41687	−0.254584
$302$	−31.1818	−1.79431
$303$	11.0817	0.636629
$304$	2.61305	0.149869
$305$	−27.6283	−1.58199
$306$	−1.36019	−0.0777567
$307$	29.0637	1.65875	0.829376	−	0.558691i	$-0.188696\pi$
$307$	29.0637	1.65875	0.829376	+	0.558691i	$0.188696\pi$
$308$	1.39252	0.0793464
$309$	−0.479670	−0.0272875
$310$	34.9975	1.98773
$311$	1.51575	0.0859502	0.0429751	−	0.999076i	$-0.486316\pi$
$311$	1.51575	0.0859502	0.0429751	+	0.999076i	$0.486316\pi$
$312$	5.78952	0.327767
$313$	14.5943	0.824916	0.412458	−	0.910977i	$-0.364670\pi$
$313$	14.5943	0.824916	0.412458	+	0.910977i	$0.364670\pi$
$314$	−1.36019	−0.0767598
$315$	−9.67175	−0.544942
$316$	0.749758	0.0421772
$317$	4.00663	0.225035	0.112517	−	0.993650i	$-0.464109\pi$
$317$	4.00663	0.225035	0.112517	+	0.993650i	$0.464109\pi$
$318$	−5.57272	−0.312503
$319$	−28.9978	−1.62356
$320$	−27.4610	−1.53512
$321$	7.15167	0.399167
$322$	28.1666	1.56966
$323$	0.710503	0.0395335
$324$	−0.149892	−0.00832732
$325$	10.7345	0.595443
$326$	10.3359	0.572454
$327$	−13.1173	−0.725386
$328$	2.80709	0.154996
$329$	15.6695	0.863889
$330$	−13.6165	−0.749565
$331$	−6.98207	−0.383769	−0.191885	−	0.981418i	$-0.561460\pi$
$331$	−6.98207	−0.383769	−0.191885	+	0.981418i	$0.561460\pi$
$332$	−2.04259	−0.112102
$333$	−4.06302	−0.222652
$334$	1.42133	0.0777718
$335$	17.4210	0.951811
$336$	11.0183	0.601096
$337$	26.8163	1.46078	0.730389	−	0.683031i	$-0.239339\pi$
$337$	26.8163	1.46078	0.730389	+	0.683031i	$0.239339\pi$
$338$	−12.3509	−0.671799
$339$	17.8656	0.970327
$340$	−0.483896	−0.0262429
$341$	24.7149	1.33839
$342$	−0.966417	−0.0522579
$343$	−15.0528	−0.812775
$344$	4.31121	0.232445
$345$	22.3141	1.20135
$346$	−22.2286	−1.19502
$347$	−35.8479	−1.92441	−0.962207	−	0.272317i	$-0.912210\pi$
$347$	−35.8479	−1.92441	−0.962207	+	0.272317i	$0.912210\pi$
$348$	1.40168	0.0751379
$349$	−24.5337	−1.31326	−0.656628	−	0.754214i	$-0.728018\pi$
$349$	−24.5337	−1.31326	−0.656628	+	0.754214i	$0.728018\pi$
$350$	22.0945	1.18100
$351$	−1.97983	−0.105675
$352$	−2.62366	−0.139841
$353$	26.8289	1.42796	0.713979	−	0.700167i	$-0.246891\pi$
$353$	26.8289	1.42796	0.713979	+	0.700167i	$0.246891\pi$
$354$	−3.36480	−0.178837
$355$	1.26855	0.0673274
$356$	−1.36489	−0.0723393
$357$	2.99593	0.158561
$358$	−14.4877	−0.765698
$359$	22.1075	1.16679	0.583396	−	0.812188i	$-0.301724\pi$
$359$	22.1075	1.16679	0.583396	+	0.812188i	$0.301724\pi$
$360$	9.44038	0.497552
$361$	−18.4952	−0.973431
$362$	−18.5926	−0.977206
$363$	1.38416	0.0726494
$364$	−0.889070	−0.0466000
$365$	12.8573	0.672980
$366$	−11.6407	−0.608468
$367$	−23.5498	−1.22929	−0.614646	−	0.788803i	$-0.710701\pi$
$367$	−23.5498	−1.22929	−0.614646	+	0.788803i	$0.710701\pi$
$368$	−25.4207	−1.32514
$369$	−0.959933	−0.0499721
$370$	17.8411	0.927516
$371$	12.2744	0.637254
$372$	−1.19466	−0.0619400
$373$	8.36700	0.433227	0.216614	−	0.976257i	$-0.430499\pi$
$373$	8.36700	0.433227	0.216614	+	0.976257i	$0.430499\pi$
$374$	4.21786	0.218100
$375$	1.36213	0.0703402
$376$	−15.2947	−0.788762
$377$	18.5139	0.953515
$378$	−4.07502	−0.209596
$379$	−0.731209	−0.0375597	−0.0187798	−	0.999824i	$-0.505978\pi$
$379$	−0.731209	−0.0375597	−0.0187798	+	0.999824i	$0.505978\pi$
$380$	−0.343810	−0.0176371
$381$	7.44419	0.381377
$382$	−11.0898	−0.567403
$383$	11.8672	0.606385	0.303192	−	0.952929i	$-0.401947\pi$
$383$	11.8672	0.606385	0.303192	+	0.952929i	$0.401947\pi$
$384$	−9.87803	−0.504086
$385$	29.9916	1.52851
$386$	−31.3972	−1.59808
$387$	−1.47429	−0.0749425
$388$	2.25190	0.114323
$389$	−28.3872	−1.43929	−0.719645	−	0.694342i	$-0.755696\pi$
$389$	−28.3872	−1.43929	−0.719645	+	0.694342i	$0.755696\pi$
$390$	8.69361	0.440218
$391$	−6.91202	−0.349556
$392$	−5.77708	−0.291786
$393$	−10.7794	−0.543751
$394$	−36.2777	−1.82765
$395$	16.1479	0.812491
$396$	0.464806	0.0233574
$397$	23.2632	1.16755	0.583773	−	0.811917i	$-0.301576\pi$
$397$	23.2632	1.16755	0.583773	+	0.811917i	$0.301576\pi$
$398$	−0.589101	−0.0295290
$399$	2.12862	0.106564
$400$	−19.9405	−0.997026
$401$	−34.3264	−1.71418	−0.857090	−	0.515167i	$-0.827730\pi$
$401$	−34.3264	−1.71418	−0.857090	+	0.515167i	$0.827730\pi$
$402$	7.34003	0.366087
$403$	−15.7795	−0.786031
$404$	1.66106	0.0826408
$405$	−3.22830	−0.160416
$406$	38.1066	1.89120
$407$	12.5992	0.624519
$408$	−2.92425	−0.144772
$409$	25.1427	1.24323	0.621614	−	0.783324i	$-0.286477\pi$
$409$	25.1427	1.24323	0.621614	+	0.783324i	$0.286477\pi$
$410$	4.21516	0.208172
$411$	13.1892	0.650576
$412$	−0.0718986	−0.00354219
$413$	7.41126	0.364684
$414$	9.40163	0.462065
$415$	−43.9924	−2.15950
$416$	1.67510	0.0821285
$417$	−20.3422	−0.996161
$418$	2.99680	0.146578
$419$	−36.6041	−1.78823	−0.894114	−	0.447839i	$-0.852194\pi$
$419$	−36.6041	−1.78823	−0.894114	+	0.447839i	$0.852194\pi$
$420$	−1.44972	−0.0707389
$421$	−30.7382	−1.49809	−0.749044	−	0.662520i	$-0.769487\pi$
$421$	−30.7382	−1.49809	−0.749044	+	0.662520i	$0.769487\pi$
$422$	−32.5519	−1.58460
$423$	5.23028	0.254305
$424$	−11.9807	−0.581837
$425$	−5.42193	−0.263002
$426$	0.534479	0.0258956
$427$	25.6396	1.24079
$428$	1.07198	0.0518159
$429$	6.13933	0.296410
$430$	6.47376	0.312192
$431$	3.65106	0.175865	0.0879326	−	0.996126i	$-0.471974\pi$
$431$	3.65106	0.175865	0.0879326	+	0.996126i	$0.471974\pi$
$432$	3.67775	0.176946
$433$	−11.1690	−0.536749	−0.268374	−	0.963315i	$-0.586486\pi$
$433$	−11.1690	−0.536749	−0.268374	+	0.963315i	$0.586486\pi$
$434$	−32.4784	−1.55901
$435$	30.1887	1.44744
$436$	−1.96617	−0.0941624
$437$	−4.91101	−0.234925
$438$	5.41717	0.258843
$439$	−15.9845	−0.762900	−0.381450	−	0.924389i	$-0.624575\pi$
$439$	−15.9845	−0.762900	−0.381450	+	0.924389i	$0.624575\pi$
$440$	−29.2741	−1.39559
$441$	1.97557	0.0940749
$442$	−2.69294	−0.128090
$443$	−20.6925	−0.983131	−0.491566	−	0.870841i	$-0.663575\pi$
$443$	−20.6925	−0.983131	−0.491566	+	0.870841i	$0.663575\pi$
$444$	−0.609014	−0.0289025
$445$	−29.3965	−1.39353
$446$	−27.1505	−1.28561
$447$	−20.1066	−0.951011
$448$	25.4843	1.20402
$449$	10.9512	0.516818	0.258409	−	0.966036i	$-0.416802\pi$
$449$	10.9512	0.516818	0.258409	+	0.966036i	$0.416802\pi$
$450$	7.37484	0.347653
$451$	2.97670	0.140167
$452$	2.67791	0.125958
$453$	22.9247	1.07710
$454$	−7.49367	−0.351695
$455$	−19.1484	−0.897691
$456$	−2.07769	−0.0972969
$457$	20.1929	0.944585	0.472293	−	0.881442i	$-0.343427\pi$
$457$	20.1929	0.944585	0.472293	+	0.881442i	$0.343427\pi$
$458$	−27.7037	−1.29451
$459$	1.00000	0.0466760
$460$	3.34470	0.155947
$461$	−28.0471	−1.30628	−0.653142	−	0.757235i	$-0.726550\pi$
$461$	−28.0471	−1.30628	−0.653142	+	0.757235i	$0.726550\pi$
$462$	12.6364	0.587898
$463$	11.4533	0.532278	0.266139	−	0.963935i	$-0.414252\pi$
$463$	11.4533	0.532278	0.266139	+	0.963935i	$0.414252\pi$
$464$	−34.3916	−1.59659
$465$	−25.7300	−1.19320
$466$	−15.3621	−0.711634
$467$	18.4240	0.852563	0.426281	−	0.904591i	$-0.359823\pi$
$467$	18.4240	0.852563	0.426281	+	0.904591i	$0.359823\pi$
$468$	−0.296760	−0.0137177
$469$	−16.1670	−0.746524
$470$	−22.9667	−1.05937
$471$	1.00000	0.0460776
$472$	−7.23396	−0.332970
$473$	4.57170	0.210207
$474$	6.80365	0.312502
$475$	−3.85230	−0.176756
$476$	0.449065	0.0205828
$477$	4.09703	0.187590
$478$	1.28001	0.0585464
$479$	−35.4383	−1.61922	−0.809609	−	0.586969i	$-0.800321\pi$
$479$	−35.4383	−1.61922	−0.809609	+	0.586969i	$0.800321\pi$
$480$	2.73141	0.124671
$481$	−8.04409	−0.366779
$482$	15.0655	0.686214
$483$	−20.7079	−0.942241
$484$	0.207474	0.00943062
$485$	48.5005	2.20229
$486$	−1.36019	−0.0616993
$487$	17.7572	0.804654	0.402327	−	0.915496i	$-0.368201\pi$
$487$	17.7572	0.804654	0.402327	+	0.915496i	$0.368201\pi$
$488$	−25.0262	−1.13288
$489$	−7.59890	−0.343634
$490$	−8.67493	−0.391893
$491$	27.0554	1.22099	0.610497	−	0.792019i	$-0.290970\pi$
$491$	27.0554	1.22099	0.610497	+	0.792019i	$0.290970\pi$
$492$	−0.143886	−0.00648689
$493$	−9.35128	−0.421160
$494$	−1.91334	−0.0860852
$495$	10.0108	0.449951
$496$	29.3121	1.31615
$497$	−1.17723	−0.0528062
$498$	−18.5354	−0.830590
$499$	34.2567	1.53354	0.766769	−	0.641923i	$-0.221863\pi$
$499$	34.2567	1.53354	0.766769	+	0.641923i	$0.221863\pi$
$500$	0.204172	0.00913087
$501$	−1.04495	−0.0466851
$502$	−11.1200	−0.496310
$503$	−0.407685	−0.0181778	−0.00908888	−	0.999959i	$-0.502893\pi$
$503$	−0.407685	−0.0181778	−0.00908888	+	0.999959i	$0.502893\pi$
$504$	−8.76085	−0.390239
$505$	35.7752	1.59197
$506$	−29.1539	−1.29605
$507$	9.08028	0.403270
$508$	1.11582	0.0495066
$509$	−32.9394	−1.46001	−0.730007	−	0.683439i	$-0.760483\pi$
$509$	−32.9394	−1.46001	−0.730007	+	0.683439i	$0.760483\pi$
$510$	−4.39109	−0.194441
$511$	−11.9318	−0.527831
$512$	−24.6210	−1.08811
$513$	0.710503	0.0313695
$514$	25.0727	1.10591
$515$	−1.54852	−0.0682360
$516$	−0.220984	−0.00972829
$517$	−16.2188	−0.713302
$518$	−16.5569	−0.727468
$519$	16.3423	0.717348
$520$	18.6903	0.819625
$521$	35.0986	1.53770	0.768848	−	0.639431i	$-0.220830\pi$
$521$	35.0986	1.53770	0.768848	+	0.639431i	$0.220830\pi$
$522$	12.7195	0.556717
$523$	−35.8291	−1.56670	−0.783348	−	0.621583i	$-0.786490\pi$
$523$	−35.8291	−1.56670	−0.783348	+	0.621583i	$0.786490\pi$
$524$	−1.61575	−0.0705843
$525$	−16.2437	−0.708934
$526$	32.0296	1.39656
$527$	7.97012	0.347184
$528$	−11.4045	−0.496317
$529$	24.7760	1.07722
$530$	−17.9904	−0.781454
$531$	2.47378	0.107353
$532$	0.319062	0.0138331
$533$	−1.90050	−0.0823199
$534$	−12.3857	−0.535981
$535$	23.0877	0.998170
$536$	15.7803	0.681603
$537$	10.6512	0.459635
$538$	−2.37330	−0.102320
$539$	−6.12614	−0.263871
$540$	−0.483896	−0.0208236
$541$	29.9432	1.28736	0.643679	−	0.765295i	$-0.277407\pi$
$541$	29.9432	1.28736	0.643679	+	0.765295i	$0.277407\pi$
$542$	−27.3694	−1.17562
$543$	13.6692	0.586600
$544$	−0.846083	−0.0362755
$545$	−42.3465	−1.81392
$546$	−8.06783	−0.345271
$547$	−26.9190	−1.15097	−0.575487	−	0.817811i	$-0.695187\pi$
$547$	−26.9190	−1.15097	−0.575487	+	0.817811i	$0.695187\pi$
$548$	1.97695	0.0844513
$549$	8.55814	0.365253
$550$	−22.8690	−0.975136
$551$	−6.64411	−0.283049
$552$	20.2125	0.860301
$553$	−14.9856	−0.637253
$554$	2.18977	0.0930342
$555$	−13.1167	−0.556772
$556$	−3.04913	−0.129312
$557$	25.5205	1.08134	0.540670	−	0.841235i	$-0.318171\pi$
$557$	25.5205	1.08134	0.540670	+	0.841235i	$0.318171\pi$
$558$	−10.8409	−0.458930
$559$	−2.91885	−0.123454
$560$	35.5703	1.50312
$561$	−3.10094	−0.130922
$562$	29.6441	1.25046
$563$	32.5667	1.37252	0.686261	−	0.727355i	$-0.259251\pi$
$563$	32.5667	1.37252	0.686261	+	0.727355i	$0.259251\pi$
$564$	0.783976	0.0330113
$565$	57.6756	2.42643
$566$	3.76875	0.158412
$567$	2.99593	0.125817
$568$	1.14907	0.0482140
$569$	−18.8148	−0.788756	−0.394378	−	0.918948i	$-0.629040\pi$
$569$	−18.8148	−0.788756	−0.394378	+	0.918948i	$0.629040\pi$
$570$	−3.11989	−0.130678
$571$	18.1739	0.760555	0.380278	−	0.924872i	$-0.375828\pi$
$571$	18.1739	0.760555	0.380278	+	0.924872i	$0.375828\pi$
$572$	0.920235	0.0384770
$573$	8.15314	0.340602
$574$	−3.91175	−0.163273
$575$	37.4765	1.56288
$576$	8.50633	0.354430
$577$	−0.495928	−0.0206458	−0.0103229	−	0.999947i	$-0.503286\pi$
$577$	−0.495928	−0.0206458	−0.0103229	+	0.999947i	$0.503286\pi$
$578$	1.36019	0.0565763
$579$	23.0830	0.959297
$580$	4.52504	0.187892
$581$	40.8257	1.69374
$582$	20.4348	0.847050
$583$	−12.7046	−0.526173
$584$	11.6463	0.481929
$585$	−6.39148	−0.264255
$586$	0.547488	0.0226165
$587$	41.3693	1.70749	0.853747	−	0.520688i	$-0.174325\pi$
$587$	41.3693	1.70749	0.853747	+	0.520688i	$0.174325\pi$
$588$	0.296122	0.0122119
$589$	5.66280	0.233331
$590$	−10.8626	−0.447206
$591$	26.6711	1.09710
$592$	14.9428	0.614145
$593$	38.7697	1.59208	0.796041	−	0.605243i	$-0.206924\pi$
$593$	38.7697	1.59208	0.796041	+	0.605243i	$0.206924\pi$
$594$	4.21786	0.173061
$595$	9.67175	0.396503
$596$	−3.01382	−0.123451
$597$	0.433103	0.0177257
$598$	18.6136	0.761167
$599$	−29.3493	−1.19918	−0.599589	−	0.800308i	$-0.704669\pi$
$599$	−29.3493	−1.19918	−0.599589	+	0.800308i	$0.704669\pi$
$600$	15.8551	0.647282
$601$	−40.1888	−1.63934	−0.819668	−	0.572839i	$-0.805842\pi$
$601$	−40.1888	−1.63934	−0.819668	+	0.572839i	$0.805842\pi$
$602$	−6.00777	−0.244859
$603$	−5.39634	−0.219756
$604$	3.43622	0.139818
$605$	4.46848	0.181669
$606$	15.0732	0.612308
$607$	−16.5081	−0.670043	−0.335021	−	0.942211i	$-0.608744\pi$
$607$	−16.5081	−0.670043	−0.335021	+	0.942211i	$0.608744\pi$
$608$	−0.601145	−0.0243796
$609$	−28.0157	−1.13525
$610$	−37.5796	−1.52155
$611$	10.3551	0.418921
$612$	0.149892	0.00605902
$613$	−25.2978	−1.02177	−0.510885	−	0.859649i	$-0.670682\pi$
$613$	−25.2978	−1.02177	−0.510885	+	0.859649i	$0.670682\pi$
$614$	39.5320	1.59538
$615$	−3.09895	−0.124962
$616$	27.1669	1.09459
$617$	−2.50442	−0.100824	−0.0504120	−	0.998729i	$-0.516053\pi$
$617$	−2.50442	−0.100824	−0.0504120	+	0.998729i	$0.516053\pi$
$618$	−0.652441	−0.0262450
$619$	−1.82866	−0.0735000	−0.0367500	−	0.999324i	$-0.511701\pi$
$619$	−1.82866	−0.0735000	−0.0367500	+	0.999324i	$0.511701\pi$
$620$	−3.85671	−0.154889
$621$	−6.91202	−0.277370
$622$	2.06170	0.0826666
$623$	27.2805	1.09297
$624$	7.28131	0.291486
$625$	−22.7123	−0.908492
$626$	19.8509	0.793402
$627$	−2.20323	−0.0879885
$628$	0.149892	0.00598133
$629$	4.06302	0.162003
$630$	−13.1554	−0.524123
$631$	−16.9691	−0.675528	−0.337764	−	0.941231i	$-0.609671\pi$
$631$	−16.9691	−0.675528	−0.337764	+	0.941231i	$0.609671\pi$
$632$	14.6271	0.581835
$633$	23.9319	0.951208
$634$	5.44977	0.216438
$635$	24.0321	0.953684
$636$	0.614110	0.0243511
$637$	3.91129	0.154971
$638$	−39.4424	−1.56154
$639$	−0.392945	−0.0155447
$640$	−31.8893	−1.26053
$641$	−15.1783	−0.599506	−0.299753	−	0.954017i	$-0.596904\pi$
$641$	−15.1783	−0.599506	−0.299753	+	0.954017i	$0.596904\pi$
$642$	9.72760	0.383918
$643$	−26.8376	−1.05837	−0.529186	−	0.848506i	$-0.677503\pi$
$643$	−26.8376	−1.05837	−0.529186	+	0.848506i	$0.677503\pi$
$644$	−3.10394	−0.122312
$645$	−4.75946	−0.187404
$646$	0.966417	0.0380232
$647$	−14.3159	−0.562817	−0.281409	−	0.959588i	$-0.590802\pi$
$647$	−14.3159	−0.562817	−0.281409	+	0.959588i	$0.590802\pi$
$648$	−2.92425	−0.114876
$649$	−7.67105	−0.301115
$650$	14.6009	0.572695
$651$	23.8779	0.935848
$652$	−1.13901	−0.0446072
$653$	−30.5029	−1.19367	−0.596836	−	0.802364i	$-0.703576\pi$
$653$	−30.5029	−1.19367	−0.596836	+	0.802364i	$0.703576\pi$
$654$	−17.8419	−0.697675
$655$	−34.7993	−1.35972
$656$	3.53039	0.137839
$657$	−3.98267	−0.155379
$658$	21.3135	0.830886
$659$	1.12394	0.0437824	0.0218912	−	0.999760i	$-0.493031\pi$
$659$	1.12394	0.0437824	0.0218912	+	0.999760i	$0.493031\pi$
$660$	1.50053	0.0584082
$661$	19.5244	0.759411	0.379706	−	0.925107i	$-0.376025\pi$
$661$	19.5244	0.759411	0.379706	+	0.925107i	$0.376025\pi$
$662$	−9.49692	−0.369108
$663$	1.97983	0.0768901
$664$	−39.8491	−1.54644
$665$	6.87181	0.266478
$666$	−5.52647	−0.214146
$667$	64.6362	2.50272
$668$	−0.156630	−0.00606019
$669$	19.9609	0.771732
$670$	23.6958	0.915449
$671$	−26.5383	−1.02450
$672$	−2.53480	−0.0977821
$673$	−40.8207	−1.57352	−0.786762	−	0.617257i	$-0.788244\pi$
$673$	−40.8207	−1.57352	−0.786762	+	0.617257i	$0.788244\pi$
$674$	36.4752	1.40497
$675$	−5.42193	−0.208690
$676$	1.36106	0.0523484
$677$	−14.5913	−0.560790	−0.280395	−	0.959885i	$-0.590465\pi$
$677$	−14.5913	−0.560790	−0.280395	+	0.959885i	$0.590465\pi$
$678$	24.3006	0.933258
$679$	−45.0094	−1.72730
$680$	−9.44038	−0.362022
$681$	5.50929	0.211117
$682$	33.6169	1.28726
$683$	4.41012	0.168749	0.0843744	−	0.996434i	$-0.473111\pi$
$683$	4.41012	0.168749	0.0843744	+	0.996434i	$0.473111\pi$
$684$	0.106499	0.00407208
$685$	42.5787	1.62685
$686$	−20.4746	−0.781725
$687$	20.3676	0.777072
$688$	5.42208	0.206715
$689$	8.11141	0.309020
$690$	30.3513	1.15545
$691$	−21.1419	−0.804277	−0.402138	−	0.915579i	$-0.631733\pi$
$691$	−21.1419	−0.804277	−0.402138	+	0.915579i	$0.631733\pi$
$692$	2.44958	0.0931190
$693$	−9.29019	−0.352905
$694$	−48.7598	−1.85090
$695$	−65.6707	−2.49103
$696$	27.3455	1.03653
$697$	0.959933	0.0363601
$698$	−33.3704	−1.26309
$699$	11.2941	0.427181
$700$	−2.43480	−0.0920267
$701$	12.4713	0.471034	0.235517	−	0.971870i	$-0.424322\pi$
$701$	12.4713	0.471034	0.235517	+	0.971870i	$0.424322\pi$
$702$	−2.69294	−0.101638
$703$	2.88679	0.108877
$704$	−26.3776	−0.994145
$705$	16.8849	0.635923
$706$	36.4923	1.37341
$707$	−33.2000	−1.24862
$708$	0.370799	0.0139355
$709$	−11.4412	−0.429682	−0.214841	−	0.976649i	$-0.568923\pi$
$709$	−11.4412	−0.429682	−0.214841	+	0.976649i	$0.568923\pi$
$710$	1.72546	0.0647553
$711$	−5.00199	−0.187589
$712$	−26.6279	−0.997922
$713$	−55.0896	−2.06312
$714$	4.07502	0.152504
$715$	19.8196	0.741212
$716$	1.59653	0.0596653
$717$	−0.941056	−0.0351444
$718$	30.0704	1.12222
$719$	−34.4197	−1.28364	−0.641819	−	0.766856i	$-0.721820\pi$
$719$	−34.4197	−1.28364	−0.641819	+	0.766856i	$0.721820\pi$
$720$	11.8729	0.442476
$721$	1.43706	0.0535188
$722$	−25.1569	−0.936243
$723$	−11.0760	−0.411922
$724$	2.04889	0.0761465
$725$	50.7020	1.88303
$726$	1.88271	0.0698740
$727$	−0.566545	−0.0210120	−0.0105060	−	0.999945i	$-0.503344\pi$
$727$	−0.566545	−0.0210120	−0.0105060	+	0.999945i	$0.503344\pi$
$728$	−17.3450	−0.642847
$729$	1.00000	0.0370370
$730$	17.4883	0.647270
$731$	1.47429	0.0545287
$732$	1.28280	0.0474135
$733$	16.6202	0.613881	0.306940	−	0.951729i	$-0.400695\pi$
$733$	16.6202	0.613881	0.306940	+	0.951729i	$0.400695\pi$
$734$	−32.0322	−1.18233
$735$	6.37775	0.235247
$736$	5.84814	0.215565
$737$	16.7337	0.616395
$738$	−1.30569	−0.0480631
$739$	0.659089	0.0242450	0.0121225	−	0.999927i	$-0.496141\pi$
$739$	0.659089	0.0242450	0.0121225	+	0.999927i	$0.496141\pi$
$740$	−1.96608	−0.0722746
$741$	1.40667	0.0516755
$742$	16.6955	0.612910
$743$	20.6658	0.758154	0.379077	−	0.925365i	$-0.376241\pi$
$743$	20.6658	0.758154	0.379077	+	0.925365i	$0.376241\pi$
$744$	−23.3067	−0.854464
$745$	−64.9103	−2.37813
$746$	11.3807	0.416677
$747$	13.6271	0.498589
$748$	−0.464806	−0.0169950
$749$	−21.4259	−0.782884
$750$	1.85275	0.0676530
$751$	27.6699	1.00969	0.504845	−	0.863210i	$-0.331550\pi$
$751$	27.6699	1.00969	0.504845	+	0.863210i	$0.331550\pi$
$752$	−19.2357	−0.701452
$753$	8.17534	0.297926
$754$	25.1824	0.917088
$755$	74.0078	2.69342
$756$	0.449065	0.0163323
$757$	34.9709	1.27104	0.635519	−	0.772085i	$-0.280786\pi$
$757$	34.9709	1.27104	0.635519	+	0.772085i	$0.280786\pi$
$758$	−0.994580	−0.0361248
$759$	21.4338	0.777996
$760$	−6.70742	−0.243304
$761$	40.2156	1.45781	0.728907	−	0.684613i	$-0.240029\pi$
$761$	40.2156	1.45781	0.728907	+	0.684613i	$0.240029\pi$
$762$	10.1255	0.366808
$763$	39.2983	1.42270
$764$	1.22209	0.0442136
$765$	3.22830	0.116720
$766$	16.1416	0.583219
$767$	4.89766	0.176844
$768$	3.57669	0.129063
$769$	−29.1027	−1.04947	−0.524735	−	0.851266i	$-0.675836\pi$
$769$	−29.1027	−1.04947	−0.524735	+	0.851266i	$0.675836\pi$
$770$	40.7941	1.47012
$771$	−18.4333	−0.663859
$772$	3.45995	0.124526
$773$	15.4068	0.554144	0.277072	−	0.960849i	$-0.410636\pi$
$773$	15.4068	0.554144	0.277072	+	0.960849i	$0.410636\pi$
$774$	−2.00531	−0.0720795
$775$	−43.2135	−1.55227
$776$	43.9326	1.57709
$777$	12.1725	0.436687
$778$	−38.6120	−1.38431
$779$	0.682036	0.0244365
$780$	−0.958030	−0.0343030
$781$	1.21850	0.0436014
$782$	−9.40163	−0.336202
$783$	−9.35128	−0.334187
$784$	−7.26566	−0.259488
$785$	3.22830	0.115223
$786$	−14.6621	−0.522978
$787$	−23.8310	−0.849482	−0.424741	−	0.905315i	$-0.639635\pi$
$787$	−23.8310	−0.849482	−0.424741	+	0.905315i	$0.639635\pi$
$788$	3.99778	0.142415
$789$	−23.5480	−0.838330
$790$	21.9642	0.781452
$791$	−53.5241	−1.90310
$792$	9.06794	0.322215
$793$	16.9436	0.601686
$794$	31.6423	1.12294
$795$	13.2264	0.469093
$796$	0.0649186	0.00230098
$797$	20.1569	0.713993	0.356997	−	0.934106i	$-0.383801\pi$
$797$	20.1569	0.713993	0.356997	+	0.934106i	$0.383801\pi$
$798$	2.89531	0.102493
$799$	−5.23028	−0.185034
$800$	4.58741	0.162189
$801$	9.10587	0.321740
$802$	−46.6903	−1.64869
$803$	12.3500	0.435823
$804$	−0.808866	−0.0285265
$805$	−66.8513	−2.35620
$806$	−21.4630	−0.756003
$807$	1.74484	0.0614211
$808$	32.4058	1.14003
$809$	−2.16465	−0.0761049	−0.0380525	−	0.999276i	$-0.512115\pi$
$809$	−2.16465	−0.0761049	−0.0380525	+	0.999276i	$0.512115\pi$
$810$	−4.39109	−0.154287
$811$	27.5859	0.968673	0.484336	−	0.874882i	$-0.339061\pi$
$811$	27.5859	0.968673	0.484336	+	0.874882i	$0.339061\pi$
$812$	−4.19933	−0.147367
$813$	20.1218	0.705701
$814$	17.1373	0.600661
$815$	−24.5315	−0.859303
$816$	−3.67775	−0.128747
$817$	1.04749	0.0366470
$818$	34.1988	1.19573
$819$	5.93142	0.207260
$820$	−0.464508	−0.0162213
$821$	−25.3863	−0.885987	−0.442994	−	0.896525i	$-0.646084\pi$
$821$	−25.3863	−0.885987	−0.442994	+	0.896525i	$0.646084\pi$
$822$	17.9398	0.625722
$823$	−36.1110	−1.25875	−0.629374	−	0.777102i	$-0.716689\pi$
$823$	−36.1110	−1.25875	−0.629374	+	0.777102i	$0.716689\pi$
$824$	−1.40268	−0.0488646
$825$	16.8131	0.585357
$826$	10.0807	0.350752
$827$	−10.6867	−0.371614	−0.185807	−	0.982586i	$-0.559490\pi$
$827$	−10.6867	−0.371614	−0.185807	+	0.982586i	$0.559490\pi$
$828$	−1.03605	−0.0360054
$829$	13.1639	0.457200	0.228600	−	0.973520i	$-0.426585\pi$
$829$	13.1639	0.457200	0.228600	+	0.973520i	$0.426585\pi$
$830$	−59.8378	−2.07700
$831$	−1.60990	−0.0558468
$832$	16.8411	0.583859
$833$	−1.97557	−0.0684495
$834$	−27.6692	−0.958105
$835$	−3.37343	−0.116742
$836$	−0.330246	−0.0114218
$837$	7.97012	0.275488
$838$	−49.7885	−1.71991
$839$	−35.1891	−1.21486	−0.607431	−	0.794372i	$-0.707800\pi$
$839$	−35.1891	−1.21486	−0.607431	+	0.794372i	$0.707800\pi$
$840$	−28.2827	−0.975845
$841$	58.4464	2.01539
$842$	−41.8097	−1.44086
$843$	−21.7941	−0.750629
$844$	3.58720	0.123476
$845$	29.3139	1.00843
$846$	7.11416	0.244590
$847$	−4.14683	−0.142487
$848$	−15.0678	−0.517432
$849$	−2.77076	−0.0950921
$850$	−7.37484	−0.252955
$851$	−28.0837	−0.962696
$852$	−0.0588993	−0.00201786
$853$	39.5498	1.35416	0.677080	−	0.735910i	$-0.263245\pi$
$853$	39.5498	1.35416	0.677080	+	0.735910i	$0.263245\pi$
$854$	34.8746	1.19338
$855$	2.29372	0.0784436
$856$	20.9133	0.714802
$857$	−41.9770	−1.43391	−0.716953	−	0.697122i	$-0.754464\pi$
$857$	−41.9770	−1.43391	−0.716953	+	0.697122i	$0.754464\pi$
$858$	8.35064	0.285086
$859$	25.7663	0.879134	0.439567	−	0.898210i	$-0.355132\pi$
$859$	25.7663	0.879134	0.439567	+	0.898210i	$0.355132\pi$
$860$	−0.713404	−0.0243269
$861$	2.87589	0.0980100
$862$	4.96612	0.169147
$863$	−27.6036	−0.939639	−0.469819	−	0.882763i	$-0.655681\pi$
$863$	−27.6036	−0.939639	−0.469819	+	0.882763i	$0.655681\pi$
$864$	−0.846083	−0.0287843
$865$	52.7580	1.79382
$866$	−15.1920	−0.516244
$867$	−1.00000	−0.0339618
$868$	3.57910	0.121483
$869$	15.5109	0.526171
$870$	41.0623	1.39214
$871$	−10.6838	−0.362007
$872$	−38.3582	−1.29897
$873$	−15.0235	−0.508470
$874$	−6.67989	−0.225951
$875$	−4.08085	−0.137958
$876$	−0.596969	−0.0201697
$877$	−13.5592	−0.457862	−0.228931	−	0.973443i	$-0.573523\pi$
$877$	−13.5592	−0.457862	−0.228931	+	0.973443i	$0.573523\pi$
$878$	−21.7420	−0.733755
$879$	−0.402509	−0.0135763
$880$	−36.8171	−1.24111
$881$	−42.9425	−1.44677	−0.723384	−	0.690446i	$-0.757415\pi$
$881$	−42.9425	−1.44677	−0.723384	+	0.690446i	$0.757415\pi$
$882$	2.68715	0.0904810
$883$	−6.54972	−0.220416	−0.110208	−	0.993909i	$-0.535152\pi$
$883$	−6.54972	−0.220416	−0.110208	+	0.993909i	$0.535152\pi$
$884$	0.296760	0.00998111
$885$	7.98611	0.268450
$886$	−28.1457	−0.945573
$887$	39.1733	1.31531	0.657656	−	0.753318i	$-0.271548\pi$
$887$	39.1733	1.31531	0.657656	+	0.753318i	$0.271548\pi$
$888$	−11.8813	−0.398711
$889$	−22.3022	−0.747993
$890$	−39.9847	−1.34029
$891$	−3.10094	−0.103885
$892$	2.99197	0.100179
$893$	−3.71613	−0.124356
$894$	−27.3488	−0.914680
$895$	34.3854	1.14938
$896$	29.5938	0.988661
$897$	−13.6846	−0.456915
$898$	14.8957	0.497075
$899$	−74.5308	−2.48574
$900$	−0.812703	−0.0270901
$901$	−4.09703	−0.136492
$902$	4.04886	0.134812
$903$	4.41687	0.146984
$904$	52.2436	1.73760
$905$	44.1282	1.46687
$906$	31.1818	1.03595
$907$	57.7416	1.91728	0.958639	−	0.284625i	$-0.0918690\pi$
$907$	57.7416	1.91728	0.958639	+	0.284625i	$0.0918690\pi$
$908$	0.825798	0.0274051
$909$	−11.0817	−0.367558
$910$	−26.0454	−0.863397
$911$	23.3402	0.773296	0.386648	−	0.922227i	$-0.373633\pi$
$911$	23.3402	0.773296	0.386648	+	0.922227i	$0.373633\pi$
$912$	−2.61305	−0.0865268
$913$	−42.2568	−1.39850
$914$	27.4662	0.908500
$915$	27.6283	0.913362
$916$	3.05293	0.100872
$917$	32.2944	1.06646
$918$	1.36019	0.0448929
$919$	−9.27010	−0.305792	−0.152896	−	0.988242i	$-0.548860\pi$
$919$	−9.27010	−0.305792	−0.152896	+	0.988242i	$0.548860\pi$
$920$	65.2520	2.15130
$921$	−29.0637	−0.957681
$922$	−38.1493	−1.25638
$923$	−0.777964	−0.0256070
$924$	−1.39252	−0.0458107
$925$	−22.0294	−0.724324
$926$	15.5786	0.511944
$927$	0.479670	0.0157544
$928$	7.91196	0.259723
$929$	0.753499	0.0247215	0.0123608	−	0.999924i	$-0.496065\pi$
$929$	0.753499	0.0247215	0.0123608	+	0.999924i	$0.496065\pi$
$930$	−34.9975	−1.14761
$931$	−1.40365	−0.0460028
$932$	1.69289	0.0554524
$933$	−1.51575	−0.0496233
$934$	25.0601	0.819993
$935$	−10.0108	−0.327387
$936$	−5.78952	−0.189236
$937$	−35.2077	−1.15019	−0.575094	−	0.818088i	$-0.695034\pi$
$937$	−35.2077	−1.15019	−0.575094	+	0.818088i	$0.695034\pi$
$938$	−21.9902	−0.718005
$939$	−14.5943	−0.476265
$940$	2.53091	0.0825492
$941$	14.2112	0.463271	0.231636	−	0.972803i	$-0.425592\pi$
$941$	14.2112	0.463271	0.231636	+	0.972803i	$0.425592\pi$
$942$	1.36019	0.0443173
$943$	−6.63507	−0.216068
$944$	−9.09794	−0.296113
$945$	9.67175	0.314622
$946$	6.21836	0.202176
$947$	11.8458	0.384935	0.192468	−	0.981303i	$-0.438351\pi$
$947$	11.8458	0.384935	0.192468	+	0.981303i	$0.438351\pi$
$948$	−0.749758	−0.0243510
$949$	−7.88500	−0.255958
$950$	−5.23985	−0.170003
$951$	−4.00663	−0.129924
$952$	8.76085	0.283941
$953$	−30.4435	−0.986162	−0.493081	−	0.869983i	$-0.664129\pi$
$953$	−30.4435	−0.986162	−0.493081	+	0.869983i	$0.664129\pi$
$954$	5.57272	0.180424
$955$	26.3208	0.851721
$956$	−0.141056	−0.00456209
$957$	28.9978	0.937365
$958$	−48.2027	−1.55736
$959$	−39.5139	−1.27597
$960$	27.4610	0.886300
$961$	32.5228	1.04912
$962$	−10.9415	−0.352767
$963$	−7.15167	−0.230459
$964$	−1.66021	−0.0534717
$965$	74.5189	2.39885
$966$	−28.1666	−0.906245
$967$	−32.6784	−1.05087	−0.525433	−	0.850835i	$-0.676097\pi$
$967$	−32.6784	−1.05087	−0.525433	+	0.850835i	$0.676097\pi$
$968$	4.04763	0.130096
$969$	−0.710503	−0.0228247
$970$	65.9697	2.11816
$971$	−3.81520	−0.122436	−0.0612179	−	0.998124i	$-0.519498\pi$
$971$	−3.81520	−0.122436	−0.0612179	+	0.998124i	$0.519498\pi$
$972$	0.149892	0.00480778
$973$	60.9437	1.95377
$974$	24.1531	0.773914
$975$	−10.7345	−0.343779
$976$	−31.4747	−1.00748
$977$	−3.06867	−0.0981753	−0.0490877	−	0.998794i	$-0.515631\pi$
$977$	−3.06867	−0.0981753	−0.0490877	+	0.998794i	$0.515631\pi$
$978$	−10.3359	−0.330506
$979$	−28.2368	−0.902451
$980$	0.955971	0.0305374
$981$	13.1173	0.418802
$982$	36.8004	1.17435
$983$	20.1766	0.643533	0.321766	−	0.946819i	$-0.395723\pi$
$983$	20.1766	0.643533	0.321766	+	0.946819i	$0.395723\pi$
$984$	−2.80709	−0.0894867
$985$	86.1025	2.74345
$986$	−12.7195	−0.405071
$987$	−15.6695	−0.498767
$988$	0.210849	0.00670800
$989$	−10.1903	−0.324034
$990$	13.6165	0.432762
$991$	31.3412	0.995586	0.497793	−	0.867296i	$-0.334144\pi$
$991$	31.3412	0.995586	0.497793	+	0.867296i	$0.334144\pi$
$992$	−6.74338	−0.214103
$993$	6.98207	0.221569
$994$	−1.60126	−0.0507889
$995$	1.39819	0.0443255
$996$	2.04259	0.0647219
$997$	22.3368	0.707414	0.353707	−	0.935356i	$-0.384921\pi$
$997$	22.3368	0.707414	0.353707	+	0.935356i	$0.384921\pi$
$998$	46.5954	1.47495
$999$	4.06302	0.128548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.35	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.35	✓	48	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)

\(f(q)\)	\(=\)	\(q+1.36019 q^{2} -1.00000 q^{3} -0.149892 q^{4} -3.22830 q^{5} -1.36019 q^{6} +2.99593 q^{7} -2.92425 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.36019 q^{2} -1.00000 q^{3} -0.149892 q^{4} -3.22830 q^{5} -1.36019 q^{6} +2.99593 q^{7} -2.92425 q^{8} +1.00000 q^{9} -4.39109 q^{10} -3.10094 q^{11} +0.149892 q^{12} +1.97983 q^{13} +4.07502 q^{14} +3.22830 q^{15} -3.67775 q^{16} -1.00000 q^{17} +1.36019 q^{18} -0.710503 q^{19} +0.483896 q^{20} -2.99593 q^{21} -4.21786 q^{22} +6.91202 q^{23} +2.92425 q^{24} +5.42193 q^{25} +2.69294 q^{26} -1.00000 q^{27} -0.449065 q^{28} +9.35128 q^{29} +4.39109 q^{30} -7.97012 q^{31} +0.846083 q^{32} +3.10094 q^{33} -1.36019 q^{34} -9.67175 q^{35} -0.149892 q^{36} -4.06302 q^{37} -0.966417 q^{38} -1.97983 q^{39} +9.44038 q^{40} -0.959933 q^{41} -4.07502 q^{42} -1.47429 q^{43} +0.464806 q^{44} -3.22830 q^{45} +9.40163 q^{46} +5.23028 q^{47} +3.67775 q^{48} +1.97557 q^{49} +7.37484 q^{50} +1.00000 q^{51} -0.296760 q^{52} +4.09703 q^{53} -1.36019 q^{54} +10.0108 q^{55} -8.76085 q^{56} +0.710503 q^{57} +12.7195 q^{58} +2.47378 q^{59} -0.483896 q^{60} +8.55814 q^{61} -10.8409 q^{62} +2.99593 q^{63} +8.50633 q^{64} -6.39148 q^{65} +4.21786 q^{66} -5.39634 q^{67} +0.149892 q^{68} -6.91202 q^{69} -13.1554 q^{70} -0.392945 q^{71} -2.92425 q^{72} -3.98267 q^{73} -5.52647 q^{74} -5.42193 q^{75} +0.106499 q^{76} -9.29019 q^{77} -2.69294 q^{78} -5.00199 q^{79} +11.8729 q^{80} +1.00000 q^{81} -1.30569 q^{82} +13.6271 q^{83} +0.449065 q^{84} +3.22830 q^{85} -2.00531 q^{86} -9.35128 q^{87} +9.06794 q^{88} +9.10587 q^{89} -4.39109 q^{90} +5.93142 q^{91} -1.03605 q^{92} +7.97012 q^{93} +7.11416 q^{94} +2.29372 q^{95} -0.846083 q^{96} -15.0235 q^{97} +2.68715 q^{98} -3.10094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

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