LMFDB - Embedded newform 8006.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$1$
Dimension:	$75$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.22415 q^{3} +1.00000 q^{4} +2.52556 q^{5} +2.22415 q^{6} +1.21093 q^{7} -1.00000 q^{8} +1.94686 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.22415 q^{3} +1.00000 q^{4} +2.52556 q^{5} +2.22415 q^{6} +1.21093 q^{7} -1.00000 q^{8} +1.94686 q^{9} -2.52556 q^{10} -2.30333 q^{11} -2.22415 q^{12} -0.324255 q^{13} -1.21093 q^{14} -5.61723 q^{15} +1.00000 q^{16} -4.41632 q^{17} -1.94686 q^{18} +3.14931 q^{19} +2.52556 q^{20} -2.69328 q^{21} +2.30333 q^{22} -9.13817 q^{23} +2.22415 q^{24} +1.37845 q^{25} +0.324255 q^{26} +2.34235 q^{27} +1.21093 q^{28} +4.75605 q^{29} +5.61723 q^{30} +3.20643 q^{31} -1.00000 q^{32} +5.12297 q^{33} +4.41632 q^{34} +3.05827 q^{35} +1.94686 q^{36} +1.53005 q^{37} -3.14931 q^{38} +0.721193 q^{39} -2.52556 q^{40} -0.941951 q^{41} +2.69328 q^{42} +2.39887 q^{43} -2.30333 q^{44} +4.91691 q^{45} +9.13817 q^{46} +7.51475 q^{47} -2.22415 q^{48} -5.53366 q^{49} -1.37845 q^{50} +9.82257 q^{51} -0.324255 q^{52} +8.94149 q^{53} -2.34235 q^{54} -5.81721 q^{55} -1.21093 q^{56} -7.00455 q^{57} -4.75605 q^{58} +8.68407 q^{59} -5.61723 q^{60} -13.5395 q^{61} -3.20643 q^{62} +2.35750 q^{63} +1.00000 q^{64} -0.818925 q^{65} -5.12297 q^{66} +5.38665 q^{67} -4.41632 q^{68} +20.3247 q^{69} -3.05827 q^{70} +8.82408 q^{71} -1.94686 q^{72} -6.11778 q^{73} -1.53005 q^{74} -3.06589 q^{75} +3.14931 q^{76} -2.78917 q^{77} -0.721193 q^{78} -7.47161 q^{79} +2.52556 q^{80} -11.0503 q^{81} +0.941951 q^{82} +3.74612 q^{83} -2.69328 q^{84} -11.1537 q^{85} -2.39887 q^{86} -10.5782 q^{87} +2.30333 q^{88} -7.04532 q^{89} -4.91691 q^{90} -0.392649 q^{91} -9.13817 q^{92} -7.13159 q^{93} -7.51475 q^{94} +7.95377 q^{95} +2.22415 q^{96} +8.77499 q^{97} +5.53366 q^{98} -4.48427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) $ 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.22415	−1.28412	−0.642058	−	0.766656i	$-0.721919\pi$
$3$	−2.22415	−1.28412	−0.642058	+	0.766656i	$0.721919\pi$
$4$	1.00000	0.500000
$5$	2.52556	1.12946	0.564732	−	0.825274i	$-0.308979\pi$
$5$	2.52556	1.12946	0.564732	+	0.825274i	$0.308979\pi$
$6$	2.22415	0.908007
$7$	1.21093	0.457687	0.228843	−	0.973463i	$-0.426506\pi$
$7$	1.21093	0.457687	0.228843	+	0.973463i	$0.426506\pi$
$8$	−1.00000	−0.353553
$9$	1.94686	0.648953
$10$	−2.52556	−0.798652
$11$	−2.30333	−0.694481	−0.347241	−	0.937776i	$-0.612881\pi$
$11$	−2.30333	−0.694481	−0.347241	+	0.937776i	$0.612881\pi$
$12$	−2.22415	−0.642058
$13$	−0.324255	−0.0899321	−0.0449661	−	0.998989i	$-0.514318\pi$
$13$	−0.324255	−0.0899321	−0.0449661	+	0.998989i	$0.514318\pi$
$14$	−1.21093	−0.323634
$15$	−5.61723	−1.45036
$16$	1.00000	0.250000
$17$	−4.41632	−1.07111	−0.535557	−	0.844499i	$-0.679898\pi$
$17$	−4.41632	−1.07111	−0.535557	+	0.844499i	$0.679898\pi$
$18$	−1.94686	−0.458879
$19$	3.14931	0.722501	0.361251	−	0.932469i	$-0.382350\pi$
$19$	3.14931	0.722501	0.361251	+	0.932469i	$0.382350\pi$
$20$	2.52556	0.564732
$21$	−2.69328	−0.587723
$22$	2.30333	0.491073
$23$	−9.13817	−1.90544	−0.952720	−	0.303849i	$-0.901728\pi$
$23$	−9.13817	−1.90544	−0.952720	+	0.303849i	$0.901728\pi$
$24$	2.22415	0.454003
$25$	1.37845	0.275690
$26$	0.324255	0.0635916
$27$	2.34235	0.450785
$28$	1.21093	0.228843
$29$	4.75605	0.883176	0.441588	−	0.897218i	$-0.354415\pi$
$29$	4.75605	0.883176	0.441588	+	0.897218i	$0.354415\pi$
$30$	5.61723	1.02556
$31$	3.20643	0.575892	0.287946	−	0.957647i	$-0.407028\pi$
$31$	3.20643	0.575892	0.287946	+	0.957647i	$0.407028\pi$
$32$	−1.00000	−0.176777
$33$	5.12297	0.891794
$34$	4.41632	0.757392
$35$	3.05827	0.516941
$36$	1.94686	0.324476
$37$	1.53005	0.251538	0.125769	−	0.992060i	$-0.459860\pi$
$37$	1.53005	0.251538	0.125769	+	0.992060i	$0.459860\pi$
$38$	−3.14931	−0.510885
$39$	0.721193	0.115483
$40$	−2.52556	−0.399326
$41$	−0.941951	−0.147108	−0.0735540	−	0.997291i	$-0.523434\pi$
$41$	−0.941951	−0.147108	−0.0735540	+	0.997291i	$0.523434\pi$
$42$	2.69328	0.415583
$43$	2.39887	0.365825	0.182912	−	0.983129i	$-0.441447\pi$
$43$	2.39887	0.365825	0.182912	+	0.983129i	$0.441447\pi$
$44$	−2.30333	−0.347241
$45$	4.91691	0.732969
$46$	9.13817	1.34735
$47$	7.51475	1.09614	0.548069	−	0.836433i	$-0.315363\pi$
$47$	7.51475	1.09614	0.548069	+	0.836433i	$0.315363\pi$
$48$	−2.22415	−0.321029
$49$	−5.53366	−0.790523
$50$	−1.37845	−0.194943
$51$	9.82257	1.37543
$52$	−0.324255	−0.0449661
$53$	8.94149	1.22821	0.614104	−	0.789225i	$-0.289518\pi$
$53$	8.94149	1.22821	0.614104	+	0.789225i	$0.289518\pi$
$54$	−2.34235	−0.318753
$55$	−5.81721	−0.784392
$56$	−1.21093	−0.161817
$57$	−7.00455	−0.927775
$58$	−4.75605	−0.624500
$59$	8.68407	1.13057	0.565285	−	0.824896i	$-0.308766\pi$
$59$	8.68407	1.13057	0.565285	+	0.824896i	$0.308766\pi$
$60$	−5.61723	−0.725182
$61$	−13.5395	−1.73355	−0.866775	−	0.498699i	$-0.833811\pi$
$61$	−13.5395	−1.73355	−0.866775	+	0.498699i	$0.833811\pi$
$62$	−3.20643	−0.407217
$63$	2.35750	0.297017
$64$	1.00000	0.125000
$65$	−0.818925	−0.101575
$66$	−5.12297	−0.630594
$67$	5.38665	0.658084	0.329042	−	0.944315i	$-0.393274\pi$
$67$	5.38665	0.658084	0.329042	+	0.944315i	$0.393274\pi$
$68$	−4.41632	−0.535557
$69$	20.3247	2.44681
$70$	−3.05827	−0.365533
$71$	8.82408	1.04723	0.523613	−	0.851956i	$-0.324584\pi$
$71$	8.82408	1.04723	0.523613	+	0.851956i	$0.324584\pi$
$72$	−1.94686	−0.229440
$73$	−6.11778	−0.716032	−0.358016	−	0.933716i	$-0.616547\pi$
$73$	−6.11778	−0.716032	−0.358016	+	0.933716i	$0.616547\pi$
$74$	−1.53005	−0.177864
$75$	−3.06589	−0.354018
$76$	3.14931	0.361251
$77$	−2.78917	−0.317855
$78$	−0.721193	−0.0816590
$79$	−7.47161	−0.840622	−0.420311	−	0.907380i	$-0.638079\pi$
$79$	−7.47161	−0.840622	−0.420311	+	0.907380i	$0.638079\pi$
$80$	2.52556	0.282366
$81$	−11.0503	−1.22781
$82$	0.941951	0.104021
$83$	3.74612	0.411190	0.205595	−	0.978637i	$-0.434087\pi$
$83$	3.74612	0.411190	0.205595	+	0.978637i	$0.434087\pi$
$84$	−2.69328	−0.293861
$85$	−11.1537	−1.20979
$86$	−2.39887	−0.258677
$87$	−10.5782	−1.13410
$88$	2.30333	0.245536
$89$	−7.04532	−0.746803	−0.373401	−	0.927670i	$-0.621809\pi$
$89$	−7.04532	−0.746803	−0.373401	+	0.927670i	$0.621809\pi$
$90$	−4.91691	−0.518288
$91$	−0.392649	−0.0411608
$92$	−9.13817	−0.952720
$93$	−7.13159	−0.739511
$94$	−7.51475	−0.775087
$95$	7.95377	0.816039
$96$	2.22415	0.227002
$97$	8.77499	0.890965	0.445483	−	0.895291i	$-0.353032\pi$
$97$	8.77499	0.890965	0.445483	+	0.895291i	$0.353032\pi$
$98$	5.53366	0.558984
$99$	−4.48427	−0.450686
$100$	1.37845	0.137845
$101$	−5.84626	−0.581725	−0.290862	−	0.956765i	$-0.593942\pi$
$101$	−5.84626	−0.581725	−0.290862	+	0.956765i	$0.593942\pi$
$102$	−9.82257	−0.972579
$103$	5.88799	0.580160	0.290080	−	0.957002i	$-0.406318\pi$
$103$	5.88799	0.580160	0.290080	+	0.957002i	$0.406318\pi$
$104$	0.324255	0.0317958
$105$	−6.80205	−0.663812
$106$	−8.94149	−0.868474
$107$	−4.46560	−0.431706	−0.215853	−	0.976426i	$-0.569253\pi$
$107$	−4.46560	−0.431706	−0.215853	+	0.976426i	$0.569253\pi$
$108$	2.34235	0.225392
$109$	−6.26913	−0.600474	−0.300237	−	0.953865i	$-0.597066\pi$
$109$	−6.26913	−0.600474	−0.300237	+	0.953865i	$0.597066\pi$
$110$	5.81721	0.554649
$111$	−3.40306	−0.323004
$112$	1.21093	0.114422
$113$	14.3403	1.34902	0.674509	−	0.738267i	$-0.264355\pi$
$113$	14.3403	1.34902	0.674509	+	0.738267i	$0.264355\pi$
$114$	7.00455	0.656036
$115$	−23.0790	−2.15213
$116$	4.75605	0.441588
$117$	−0.631278	−0.0583617
$118$	−8.68407	−0.799434
$119$	−5.34783	−0.490235
$120$	5.61723	0.512781
$121$	−5.69465	−0.517696
$122$	13.5395	1.22581
$123$	2.09504	0.188904
$124$	3.20643	0.287946
$125$	−9.14644	−0.818082
$126$	−2.35750	−0.210023
$127$	−12.6805	−1.12522	−0.562608	−	0.826724i	$-0.690202\pi$
$127$	−12.6805	−1.12522	−0.562608	+	0.826724i	$0.690202\pi$
$128$	−1.00000	−0.0883883
$129$	−5.33547	−0.469762
$130$	0.818925	0.0718245
$131$	−6.86946	−0.600188	−0.300094	−	0.953910i	$-0.597018\pi$
$131$	−6.86946	−0.600188	−0.300094	+	0.953910i	$0.597018\pi$
$132$	5.12297	0.445897
$133$	3.81358	0.330679
$134$	−5.38665	−0.465336
$135$	5.91574	0.509146
$136$	4.41632	0.378696
$137$	7.95409	0.679564	0.339782	−	0.940504i	$-0.389647\pi$
$137$	7.95409	0.679564	0.339782	+	0.940504i	$0.389647\pi$
$138$	−20.3247	−1.73015
$139$	−21.2751	−1.80453	−0.902267	−	0.431178i	$-0.858098\pi$
$139$	−21.2751	−1.80453	−0.902267	+	0.431178i	$0.858098\pi$
$140$	3.05827	0.258471
$141$	−16.7139	−1.40757
$142$	−8.82408	−0.740501
$143$	0.746867	0.0624562
$144$	1.94686	0.162238
$145$	12.0117	0.997516
$146$	6.11778	0.506311
$147$	12.3077	1.01512
$148$	1.53005	0.125769
$149$	−8.47550	−0.694340	−0.347170	−	0.937802i	$-0.612857\pi$
$149$	−8.47550	−0.694340	−0.347170	+	0.937802i	$0.612857\pi$
$150$	3.06589	0.250329
$151$	−17.7617	−1.44543	−0.722714	−	0.691148i	$-0.757105\pi$
$151$	−17.7617	−1.44543	−0.722714	+	0.691148i	$0.757105\pi$
$152$	−3.14931	−0.255443
$153$	−8.59795	−0.695103
$154$	2.78917	0.224757
$155$	8.09803	0.650449
$156$	0.721193	0.0577416
$157$	13.4779	1.07566	0.537828	−	0.843054i	$-0.319245\pi$
$157$	13.4779	1.07566	0.537828	+	0.843054i	$0.319245\pi$
$158$	7.47161	0.594409
$159$	−19.8872	−1.57716
$160$	−2.52556	−0.199663
$161$	−11.0656	−0.872095
$162$	11.0503	0.868195
$163$	6.59170	0.516302	0.258151	−	0.966105i	$-0.416887\pi$
$163$	6.59170	0.516302	0.258151	+	0.966105i	$0.416887\pi$
$164$	−0.941951	−0.0735540
$165$	12.9384	1.00725
$166$	−3.74612	−0.290755
$167$	−21.1318	−1.63523	−0.817615	−	0.575765i	$-0.804704\pi$
$167$	−21.1318	−1.63523	−0.817615	+	0.575765i	$0.804704\pi$
$168$	2.69328	0.207791
$169$	−12.8949	−0.991912
$170$	11.1537	0.855448
$171$	6.13126	0.468869
$172$	2.39887	0.182912
$173$	20.3041	1.54370	0.771848	−	0.635808i	$-0.219333\pi$
$173$	20.3041	1.54370	0.771848	+	0.635808i	$0.219333\pi$
$174$	10.5782	0.801930
$175$	1.66920	0.126180
$176$	−2.30333	−0.173620
$177$	−19.3147	−1.45178
$178$	7.04532	0.528069
$179$	23.2243	1.73587	0.867933	−	0.496682i	$-0.165449\pi$
$179$	23.2243	1.73587	0.867933	+	0.496682i	$0.165449\pi$
$180$	4.91691	0.366485
$181$	−1.93354	−0.143719	−0.0718594	−	0.997415i	$-0.522893\pi$
$181$	−1.93354	−0.143719	−0.0718594	+	0.997415i	$0.522893\pi$
$182$	0.392649	0.0291050
$183$	30.1138	2.22608
$184$	9.13817	0.673675
$185$	3.86422	0.284103
$186$	7.13159	0.522914
$187$	10.1723	0.743869
$188$	7.51475	0.548069
$189$	2.83641	0.206318
$190$	−7.95377	−0.577027
$191$	22.2672	1.61120	0.805598	−	0.592462i	$-0.201844\pi$
$191$	22.2672	1.61120	0.805598	+	0.592462i	$0.201844\pi$
$192$	−2.22415	−0.160514
$193$	−9.33722	−0.672108	−0.336054	−	0.941843i	$-0.609092\pi$
$193$	−9.33722	−0.672108	−0.336054	+	0.941843i	$0.609092\pi$
$194$	−8.77499	−0.630007
$195$	1.82142	0.130434
$196$	−5.53366	−0.395261
$197$	−15.2685	−1.08783	−0.543917	−	0.839139i	$-0.683059\pi$
$197$	−15.2685	−1.08783	−0.543917	+	0.839139i	$0.683059\pi$
$198$	4.48427	0.318683
$199$	−20.3913	−1.44550	−0.722751	−	0.691108i	$-0.757123\pi$
$199$	−20.3913	−1.44550	−0.722751	+	0.691108i	$0.757123\pi$
$200$	−1.37845	−0.0974713
$201$	−11.9807	−0.845056
$202$	5.84626	0.411342
$203$	5.75922	0.404218
$204$	9.82257	0.687717
$205$	−2.37895	−0.166153
$206$	−5.88799	−0.410235
$207$	−17.7907	−1.23654
$208$	−0.324255	−0.0224830
$209$	−7.25391	−0.501764
$210$	6.80205	0.469386
$211$	14.7181	1.01324	0.506620	−	0.862170i	$-0.330895\pi$
$211$	14.7181	1.01324	0.506620	+	0.862170i	$0.330895\pi$
$212$	8.94149	0.614104
$213$	−19.6261	−1.34476
$214$	4.46560	0.305262
$215$	6.05850	0.413186
$216$	−2.34235	−0.159377
$217$	3.88275	0.263578
$218$	6.26913	0.424599
$219$	13.6069	0.919467
$220$	−5.81721	−0.392196
$221$	1.43201	0.0963276
$222$	3.40306	0.228398
$223$	11.4620	0.767554	0.383777	−	0.923426i	$-0.374623\pi$
$223$	11.4620	0.767554	0.383777	+	0.923426i	$0.374623\pi$
$224$	−1.21093	−0.0809084
$225$	2.68365	0.178910
$226$	−14.3403	−0.953900
$227$	19.9468	1.32391	0.661957	−	0.749541i	$-0.269726\pi$
$227$	19.9468	1.32391	0.661957	+	0.749541i	$0.269726\pi$
$228$	−7.00455	−0.463887
$229$	−26.1832	−1.73023	−0.865117	−	0.501571i	$-0.832756\pi$
$229$	−26.1832	−1.73023	−0.865117	+	0.501571i	$0.832756\pi$
$230$	23.0790	1.52178
$231$	6.20354	0.408163
$232$	−4.75605	−0.312250
$233$	−19.9327	−1.30584	−0.652918	−	0.757428i	$-0.726456\pi$
$233$	−19.9327	−1.30584	−0.652918	+	0.757428i	$0.726456\pi$
$234$	0.631278	0.0412680
$235$	18.9789	1.23805
$236$	8.68407	0.565285
$237$	16.6180	1.07946
$238$	5.34783	0.346648
$239$	−11.3440	−0.733783	−0.366892	−	0.930264i	$-0.619578\pi$
$239$	−11.3440	−0.733783	−0.366892	+	0.930264i	$0.619578\pi$
$240$	−5.61723	−0.362591
$241$	−28.0778	−1.80865	−0.904326	−	0.426842i	$-0.859626\pi$
$241$	−28.0778	−1.80865	−0.904326	+	0.426842i	$0.859626\pi$
$242$	5.69465	0.366066
$243$	17.5506	1.12587
$244$	−13.5395	−0.866775
$245$	−13.9756	−0.892867
$246$	−2.09504	−0.133575
$247$	−1.02118	−0.0649761
$248$	−3.20643	−0.203608
$249$	−8.33195	−0.528016
$250$	9.14644	0.578471
$251$	17.8166	1.12457	0.562286	−	0.826943i	$-0.309922\pi$
$251$	17.8166	1.12457	0.562286	+	0.826943i	$0.309922\pi$
$252$	2.35750	0.148509
$253$	21.0483	1.32329
$254$	12.6805	0.795647
$255$	24.8075	1.55350
$256$	1.00000	0.0625000
$257$	14.0513	0.876498	0.438249	−	0.898854i	$-0.355599\pi$
$257$	14.0513	0.876498	0.438249	+	0.898854i	$0.355599\pi$
$258$	5.33547	0.332172
$259$	1.85277	0.115126
$260$	−0.818925	−0.0507876
$261$	9.25936	0.573140
$262$	6.86946	0.424397
$263$	8.25180	0.508828	0.254414	−	0.967095i	$-0.418117\pi$
$263$	8.25180	0.508828	0.254414	+	0.967095i	$0.418117\pi$
$264$	−5.12297	−0.315297
$265$	22.5823	1.38722
$266$	−3.81358	−0.233826
$267$	15.6699	0.958981
$268$	5.38665	0.329042
$269$	−5.53134	−0.337252	−0.168626	−	0.985680i	$-0.553933\pi$
$269$	−5.53134	−0.337252	−0.168626	+	0.985680i	$0.553933\pi$
$270$	−5.91574	−0.360020
$271$	17.5560	1.06645	0.533226	−	0.845973i	$-0.320980\pi$
$271$	17.5560	1.06645	0.533226	+	0.845973i	$0.320980\pi$
$272$	−4.41632	−0.267779
$273$	0.873311	0.0528552
$274$	−7.95409	−0.480524
$275$	−3.17504	−0.191462
$276$	20.3247	1.22340
$277$	−5.20217	−0.312568	−0.156284	−	0.987712i	$-0.549952\pi$
$277$	−5.20217	−0.312568	−0.156284	+	0.987712i	$0.549952\pi$
$278$	21.2751	1.27600
$279$	6.24246	0.373727
$280$	−3.05827	−0.182766
$281$	−12.0811	−0.720699	−0.360350	−	0.932817i	$-0.617343\pi$
$281$	−12.0811	−0.720699	−0.360350	+	0.932817i	$0.617343\pi$
$282$	16.7139	0.995301
$283$	3.16178	0.187948	0.0939742	−	0.995575i	$-0.470043\pi$
$283$	3.16178	0.187948	0.0939742	+	0.995575i	$0.470043\pi$
$284$	8.82408	0.523613
$285$	−17.6904	−1.04789
$286$	−0.746867	−0.0441632
$287$	−1.14063	−0.0673294
$288$	−1.94686	−0.114720
$289$	2.50386	0.147286
$290$	−12.0117	−0.705351
$291$	−19.5169	−1.14410
$292$	−6.11778	−0.358016
$293$	30.4190	1.77710	0.888548	−	0.458784i	$-0.151715\pi$
$293$	30.4190	1.77710	0.888548	+	0.458784i	$0.151715\pi$
$294$	−12.3077	−0.717800
$295$	21.9321	1.27694
$296$	−1.53005	−0.0889322
$297$	−5.39521	−0.313062
$298$	8.47550	0.490972
$299$	2.96310	0.171360
$300$	−3.06589	−0.177009
$301$	2.90486	0.167433
$302$	17.7617	1.02207
$303$	13.0030	0.747002
$304$	3.14931	0.180625
$305$	−34.1947	−1.95798
$306$	8.59795	0.491512
$307$	−23.9275	−1.36561	−0.682807	−	0.730599i	$-0.739241\pi$
$307$	−23.9275	−1.36561	−0.682807	+	0.730599i	$0.739241\pi$
$308$	−2.78917	−0.158928
$309$	−13.0958	−0.744993
$310$	−8.09803	−0.459937
$311$	21.3943	1.21316	0.606581	−	0.795022i	$-0.292541\pi$
$311$	21.3943	1.21316	0.606581	+	0.795022i	$0.292541\pi$
$312$	−0.721193	−0.0408295
$313$	9.87787	0.558330	0.279165	−	0.960243i	$-0.409942\pi$
$313$	9.87787	0.558330	0.279165	+	0.960243i	$0.409942\pi$
$314$	−13.4779	−0.760604
$315$	5.95401	0.335471
$316$	−7.47161	−0.420311
$317$	−13.4547	−0.755694	−0.377847	−	0.925868i	$-0.623335\pi$
$317$	−13.4547	−0.755694	−0.377847	+	0.925868i	$0.623335\pi$
$318$	19.8872	1.11522
$319$	−10.9548	−0.613349
$320$	2.52556	0.141183
$321$	9.93219	0.554361
$322$	11.0656	0.616664
$323$	−13.9083	−0.773881
$324$	−11.0503	−0.613907
$325$	−0.446970	−0.0247934
$326$	−6.59170	−0.365081
$327$	13.9435	0.771078
$328$	0.941951	0.0520105
$329$	9.09980	0.501688
$330$	−12.9384	−0.712234
$331$	−21.2041	−1.16548	−0.582740	−	0.812658i	$-0.698020\pi$
$331$	−21.2041	−1.16548	−0.582740	+	0.812658i	$0.698020\pi$
$332$	3.74612	0.205595
$333$	2.97879	0.163236
$334$	21.1318	1.15628
$335$	13.6043	0.743283
$336$	−2.69328	−0.146931
$337$	−31.3578	−1.70817	−0.854085	−	0.520133i	$-0.825882\pi$
$337$	−31.3578	−1.70817	−0.854085	+	0.520133i	$0.825882\pi$
$338$	12.8949	0.701388
$339$	−31.8949	−1.73229
$340$	−11.1537	−0.604893
$341$	−7.38548	−0.399946
$342$	−6.13126	−0.331541
$343$	−15.1773	−0.819499
$344$	−2.39887	−0.129339
$345$	51.3312	2.76358
$346$	−20.3041	−1.09156
$347$	16.9262	0.908646	0.454323	−	0.890837i	$-0.349881\pi$
$347$	16.9262	0.908646	0.454323	+	0.890837i	$0.349881\pi$
$348$	−10.5782	−0.567050
$349$	5.95574	0.318803	0.159402	−	0.987214i	$-0.449044\pi$
$349$	5.95574	0.318803	0.159402	+	0.987214i	$0.449044\pi$
$350$	−1.66920	−0.0892227
$351$	−0.759518	−0.0405400
$352$	2.30333	0.122768
$353$	−14.8421	−0.789964	−0.394982	−	0.918689i	$-0.629249\pi$
$353$	−14.8421	−0.789964	−0.394982	+	0.918689i	$0.629249\pi$
$354$	19.3147	1.02657
$355$	22.2857	1.18280
$356$	−7.04532	−0.373401
$357$	11.8944	0.629518
$358$	−23.2243	−1.22744
$359$	−15.7385	−0.830645	−0.415322	−	0.909674i	$-0.636331\pi$
$359$	−15.7385	−0.830645	−0.415322	+	0.909674i	$0.636331\pi$
$360$	−4.91691	−0.259144
$361$	−9.08185	−0.477992
$362$	1.93354	0.101625
$363$	12.6658	0.664781
$364$	−0.392649	−0.0205804
$365$	−15.4508	−0.808732
$366$	−30.1138	−1.57408
$367$	7.37004	0.384713	0.192356	−	0.981325i	$-0.438387\pi$
$367$	7.37004	0.384713	0.192356	+	0.981325i	$0.438387\pi$
$368$	−9.13817	−0.476360
$369$	−1.83385	−0.0954662
$370$	−3.86422	−0.200891
$371$	10.8275	0.562135
$372$	−7.13159	−0.369756
$373$	−31.6084	−1.63662	−0.818310	−	0.574777i	$-0.805089\pi$
$373$	−31.6084	−1.63662	−0.818310	+	0.574777i	$0.805089\pi$
$374$	−10.1723	−0.525995
$375$	20.3431	1.05051
$376$	−7.51475	−0.387543
$377$	−1.54217	−0.0794259
$378$	−2.83641	−0.145889
$379$	21.1097	1.08433	0.542166	−	0.840272i	$-0.317605\pi$
$379$	21.1097	1.08433	0.542166	+	0.840272i	$0.317605\pi$
$380$	7.95377	0.408020
$381$	28.2034	1.44491
$382$	−22.2672	−1.13929
$383$	−19.2563	−0.983949	−0.491975	−	0.870610i	$-0.663725\pi$
$383$	−19.2563	−0.983949	−0.491975	+	0.870610i	$0.663725\pi$
$384$	2.22415	0.113501
$385$	−7.04421	−0.359006
$386$	9.33722	0.475252
$387$	4.67027	0.237403
$388$	8.77499	0.445483
$389$	−6.39032	−0.324002	−0.162001	−	0.986791i	$-0.551795\pi$
$389$	−6.39032	−0.324002	−0.162001	+	0.986791i	$0.551795\pi$
$390$	−1.82142	−0.0922309
$391$	40.3571	2.04094
$392$	5.53366	0.279492
$393$	15.2787	0.770711
$394$	15.2685	0.769214
$395$	−18.8700	−0.949452
$396$	−4.48427	−0.225343
$397$	10.9109	0.547605	0.273802	−	0.961786i	$-0.411719\pi$
$397$	10.9109	0.547605	0.273802	+	0.961786i	$0.411719\pi$
$398$	20.3913	1.02212
$399$	−8.48199	−0.424630
$400$	1.37845	0.0689226
$401$	16.5455	0.826242	0.413121	−	0.910676i	$-0.364439\pi$
$401$	16.5455	0.826242	0.413121	+	0.910676i	$0.364439\pi$
$402$	11.9807	0.597545
$403$	−1.03970	−0.0517912
$404$	−5.84626	−0.290862
$405$	−27.9082	−1.38677
$406$	−5.75922	−0.285825
$407$	−3.52421	−0.174689
$408$	−9.82257	−0.486290
$409$	−4.59203	−0.227061	−0.113531	−	0.993534i	$-0.536216\pi$
$409$	−4.59203	−0.227061	−0.113531	+	0.993534i	$0.536216\pi$
$410$	2.37895	0.117488
$411$	−17.6911	−0.872639
$412$	5.88799	0.290080
$413$	10.5158	0.517447
$414$	17.7907	0.874367
$415$	9.46105	0.464425
$416$	0.324255	0.0158979
$417$	47.3192	2.31723
$418$	7.25391	0.354800
$419$	−15.5614	−0.760225	−0.380112	−	0.924940i	$-0.624115\pi$
$419$	−15.5614	−0.760225	−0.380112	+	0.924940i	$0.624115\pi$
$420$	−6.80205	−0.331906
$421$	16.4199	0.800256	0.400128	−	0.916459i	$-0.368966\pi$
$421$	16.4199	0.800256	0.400128	+	0.916459i	$0.368966\pi$
$422$	−14.7181	−0.716468
$423$	14.6302	0.711342
$424$	−8.94149	−0.434237
$425$	−6.08768	−0.295296
$426$	19.6261	0.950888
$427$	−16.3953	−0.793423
$428$	−4.46560	−0.215853
$429$	−1.66115	−0.0802010
$430$	−6.05850	−0.292167
$431$	−17.4412	−0.840112	−0.420056	−	0.907498i	$-0.637990\pi$
$431$	−17.4412	−0.840112	−0.420056	+	0.907498i	$0.637990\pi$
$432$	2.34235	0.112696
$433$	−11.5143	−0.553341	−0.276671	−	0.960965i	$-0.589231\pi$
$433$	−11.5143	−0.553341	−0.276671	+	0.960965i	$0.589231\pi$
$434$	−3.88275	−0.186378
$435$	−26.7158	−1.28093
$436$	−6.26913	−0.300237
$437$	−28.7789	−1.37668
$438$	−13.6069	−0.650162
$439$	−8.69333	−0.414910	−0.207455	−	0.978245i	$-0.566518\pi$
$439$	−8.69333	−0.414910	−0.207455	+	0.978245i	$0.566518\pi$
$440$	5.81721	0.277325
$441$	−10.7733	−0.513012
$442$	−1.43201	−0.0681139
$443$	−13.3192	−0.632813	−0.316406	−	0.948624i	$-0.602476\pi$
$443$	−13.3192	−0.632813	−0.316406	+	0.948624i	$0.602476\pi$
$444$	−3.40306	−0.161502
$445$	−17.7934	−0.843487
$446$	−11.4620	−0.542743
$447$	18.8508	0.891613
$448$	1.21093	0.0572109
$449$	20.4496	0.965075	0.482538	−	0.875875i	$-0.339715\pi$
$449$	20.4496	0.965075	0.482538	+	0.875875i	$0.339715\pi$
$450$	−2.68365	−0.126509
$451$	2.16963	0.102164
$452$	14.3403	0.674509
$453$	39.5048	1.85610
$454$	−19.9468	−0.936149
$455$	−0.991657	−0.0464896
$456$	7.00455	0.328018
$457$	−11.2832	−0.527804	−0.263902	−	0.964550i	$-0.585010\pi$
$457$	−11.2832	−0.527804	−0.263902	+	0.964550i	$0.585010\pi$
$458$	26.1832	1.22346
$459$	−10.3445	−0.482842
$460$	−23.0790	−1.07606
$461$	−2.42314	−0.112857	−0.0564284	−	0.998407i	$-0.517971\pi$
$461$	−2.42314	−0.112857	−0.0564284	+	0.998407i	$0.517971\pi$
$462$	−6.20354	−0.288615
$463$	0.687200	0.0319369	0.0159684	−	0.999872i	$-0.494917\pi$
$463$	0.687200	0.0319369	0.0159684	+	0.999872i	$0.494917\pi$
$464$	4.75605	0.220794
$465$	−18.0113	−0.835252
$466$	19.9327	0.923366
$467$	−28.8332	−1.33424	−0.667122	−	0.744949i	$-0.732474\pi$
$467$	−28.8332	−1.33424	−0.667122	+	0.744949i	$0.732474\pi$
$468$	−0.631278	−0.0291809
$469$	6.52284	0.301197
$470$	−18.9789	−0.875433
$471$	−29.9770	−1.38127
$472$	−8.68407	−0.399717
$473$	−5.52541	−0.254059
$474$	−16.6180	−0.763290
$475$	4.34117	0.199187
$476$	−5.34783	−0.245118
$477$	17.4078	0.797049
$478$	11.3440	0.518863
$479$	−19.0977	−0.872596	−0.436298	−	0.899802i	$-0.643711\pi$
$479$	−19.0977	−0.872596	−0.436298	+	0.899802i	$0.643711\pi$
$480$	5.61723	0.256390
$481$	−0.496125	−0.0226214
$482$	28.0778	1.27891
$483$	24.6117	1.11987
$484$	−5.69465	−0.258848
$485$	22.1618	1.00631
$486$	−17.5506	−0.796110
$487$	1.43798	0.0651609	0.0325804	−	0.999469i	$-0.489627\pi$
$487$	1.43798	0.0651609	0.0325804	+	0.999469i	$0.489627\pi$
$488$	13.5395	0.612903
$489$	−14.6610	−0.662992
$490$	13.9756	0.631353
$491$	−34.2325	−1.54489	−0.772446	−	0.635080i	$-0.780967\pi$
$491$	−34.2325	−1.54489	−0.772446	+	0.635080i	$0.780967\pi$
$492$	2.09504	0.0944519
$493$	−21.0042	−0.945983
$494$	1.02118	0.0459450
$495$	−11.3253	−0.509034
$496$	3.20643	0.143973
$497$	10.6853	0.479302
$498$	8.33195	0.373363
$499$	29.4326	1.31758	0.658791	−	0.752326i	$-0.271068\pi$
$499$	29.4326	1.31758	0.658791	+	0.752326i	$0.271068\pi$
$500$	−9.14644	−0.409041
$501$	47.0005	2.09983
$502$	−17.8166	−0.795192
$503$	0.00992528	0.000442546 0	0.000221273	−	1.00000i	$-0.499930\pi$
$503$	0.00992528	0.000442546 0	0.000221273		1.00000i	$0.499930\pi$
$504$	−2.35750	−0.105011
$505$	−14.7651	−0.657038
$506$	−21.0483	−0.935709
$507$	28.6801	1.27373
$508$	−12.6805	−0.562608
$509$	−34.1429	−1.51336	−0.756679	−	0.653786i	$-0.773180\pi$
$509$	−34.1429	−1.51336	−0.756679	+	0.653786i	$0.773180\pi$
$510$	−24.8075	−1.09849
$511$	−7.40817	−0.327718
$512$	−1.00000	−0.0441942
$513$	7.37678	0.325693
$514$	−14.0513	−0.619777
$515$	14.8705	0.655271
$516$	−5.33547	−0.234881
$517$	−17.3090	−0.761248
$518$	−1.85277	−0.0814062
$519$	−45.1595	−1.98228
$520$	0.818925	0.0359122
$521$	8.60001	0.376773	0.188387	−	0.982095i	$-0.439674\pi$
$521$	8.60001	0.376773	0.188387	+	0.982095i	$0.439674\pi$
$522$	−9.25936	−0.405271
$523$	−18.0415	−0.788901	−0.394451	−	0.918917i	$-0.629065\pi$
$523$	−18.0415	−0.788901	−0.394451	+	0.918917i	$0.629065\pi$
$524$	−6.86946	−0.300094
$525$	−3.71256	−0.162030
$526$	−8.25180	−0.359795
$527$	−14.1606	−0.616846
$528$	5.12297	0.222949
$529$	60.5062	2.63070
$530$	−22.5823	−0.980911
$531$	16.9067	0.733687
$532$	3.81358	0.165340
$533$	0.305432	0.0132297
$534$	−15.6699	−0.678102
$535$	−11.2781	−0.487597
$536$	−5.38665	−0.232668
$537$	−51.6544	−2.22905
$538$	5.53134	0.238473
$539$	12.7459	0.549003
$540$	5.91574	0.254573
$541$	−33.0518	−1.42101	−0.710503	−	0.703694i	$-0.751532\pi$
$541$	−33.0518	−1.42101	−0.710503	+	0.703694i	$0.751532\pi$
$542$	−17.5560	−0.754095
$543$	4.30049	0.184552
$544$	4.41632	0.189348
$545$	−15.8331	−0.678214
$546$	−0.873311	−0.0373742
$547$	34.8755	1.49117	0.745584	−	0.666411i	$-0.232171\pi$
$547$	34.8755	1.49117	0.745584	+	0.666411i	$0.232171\pi$
$548$	7.95409	0.339782
$549$	−26.3594	−1.12499
$550$	3.17504	0.135384
$551$	14.9783	0.638096
$552$	−20.3247	−0.865077
$553$	−9.04756	−0.384742
$554$	5.20217	0.221019
$555$	−8.59463	−0.364822
$556$	−21.2751	−0.902267
$557$	9.99685	0.423580	0.211790	−	0.977315i	$-0.432071\pi$
$557$	9.99685	0.423580	0.211790	+	0.977315i	$0.432071\pi$
$558$	−6.24246	−0.264265
$559$	−0.777847	−0.0328994
$560$	3.05827	0.129235
$561$	−22.6247	−0.955214
$562$	12.0811	0.509611
$563$	−6.85915	−0.289079	−0.144539	−	0.989499i	$-0.546170\pi$
$563$	−6.85915	−0.289079	−0.144539	+	0.989499i	$0.546170\pi$
$564$	−16.7139	−0.703784
$565$	36.2172	1.52367
$566$	−3.16178	−0.132900
$567$	−13.3811	−0.561954
$568$	−8.82408	−0.370250
$569$	−28.4412	−1.19232	−0.596159	−	0.802866i	$-0.703307\pi$
$569$	−28.4412	−1.19232	−0.596159	+	0.802866i	$0.703307\pi$
$570$	17.6904	0.740969
$571$	42.6179	1.78351	0.891753	−	0.452523i	$-0.149476\pi$
$571$	42.6179	1.78351	0.891753	+	0.452523i	$0.149476\pi$
$572$	0.746867	0.0312281
$573$	−49.5256	−2.06896
$574$	1.14063	0.0476091
$575$	−12.5965	−0.525312
$576$	1.94686	0.0811191
$577$	−26.6748	−1.11048	−0.555242	−	0.831689i	$-0.687375\pi$
$577$	−26.6748	−1.11048	−0.555242	+	0.831689i	$0.687375\pi$
$578$	−2.50386	−0.104147
$579$	20.7674	0.863064
$580$	12.0117	0.498758
$581$	4.53627	0.188196
$582$	19.5169	0.809002
$583$	−20.5952	−0.852968
$584$	6.11778	0.253155
$585$	−1.59433	−0.0659175
$586$	−30.4190	−1.25660
$587$	−16.7717	−0.692244	−0.346122	−	0.938190i	$-0.612502\pi$
$587$	−16.7717	−0.692244	−0.346122	+	0.938190i	$0.612502\pi$
$588$	12.3077	0.507561
$589$	10.0980	0.416082
$590$	−21.9321	−0.902932
$591$	33.9594	1.39690
$592$	1.53005	0.0628845
$593$	22.9337	0.941773	0.470887	−	0.882194i	$-0.343934\pi$
$593$	22.9337	0.941773	0.470887	+	0.882194i	$0.343934\pi$
$594$	5.39521	0.221368
$595$	−13.5063	−0.553703
$596$	−8.47550	−0.347170
$597$	45.3534	1.85619
$598$	−2.96310	−0.121170
$599$	−47.7545	−1.95120	−0.975598	−	0.219566i	$-0.929536\pi$
$599$	−47.7545	−1.95120	−0.975598	+	0.219566i	$0.929536\pi$
$600$	3.06589	0.125164
$601$	−6.82526	−0.278408	−0.139204	−	0.990264i	$-0.544454\pi$
$601$	−6.82526	−0.278408	−0.139204	+	0.990264i	$0.544454\pi$
$602$	−2.90486	−0.118393
$603$	10.4871	0.427066
$604$	−17.7617	−0.722714
$605$	−14.3822	−0.584719
$606$	−13.0030	−0.528210
$607$	−48.0869	−1.95179	−0.975893	−	0.218249i	$-0.929966\pi$
$607$	−48.0869	−1.95179	−0.975893	+	0.218249i	$0.929966\pi$
$608$	−3.14931	−0.127721
$609$	−12.8094	−0.519063
$610$	34.1947	1.38450
$611$	−2.43669	−0.0985780
$612$	−8.59795	−0.347551
$613$	15.0669	0.608546	0.304273	−	0.952585i	$-0.401586\pi$
$613$	15.0669	0.608546	0.304273	+	0.952585i	$0.401586\pi$
$614$	23.9275	0.965635
$615$	5.29116	0.213360
$616$	2.78917	0.112379
$617$	27.1917	1.09470	0.547349	−	0.836904i	$-0.315637\pi$
$617$	27.1917	1.09470	0.547349	+	0.836904i	$0.315637\pi$
$618$	13.0958	0.526790
$619$	33.0341	1.32775	0.663877	−	0.747842i	$-0.268910\pi$
$619$	33.0341	1.32775	0.663877	+	0.747842i	$0.268910\pi$
$620$	8.09803	0.325225
$621$	−21.4048	−0.858944
$622$	−21.3943	−0.857835
$623$	−8.53136	−0.341802
$624$	0.721193	0.0288708
$625$	−29.9921	−1.19969
$626$	−9.87787	−0.394799
$627$	16.1338	0.644322
$628$	13.4779	0.537828
$629$	−6.75717	−0.269426
$630$	−5.95401	−0.237213
$631$	21.0800	0.839180	0.419590	−	0.907714i	$-0.362174\pi$
$631$	21.0800	0.839180	0.419590	+	0.907714i	$0.362174\pi$
$632$	7.47161	0.297205
$633$	−32.7354	−1.30112
$634$	13.4547	0.534356
$635$	−32.0254	−1.27089
$636$	−19.8872	−0.788581
$637$	1.79432	0.0710934
$638$	10.9548	0.433704
$639$	17.1792	0.679600
$640$	−2.52556	−0.0998315
$641$	−23.5797	−0.931342	−0.465671	−	0.884958i	$-0.654187\pi$
$641$	−23.5797	−0.931342	−0.465671	+	0.884958i	$0.654187\pi$
$642$	−9.93219	−0.391992
$643$	−5.86235	−0.231189	−0.115594	−	0.993297i	$-0.536877\pi$
$643$	−5.86235	−0.231189	−0.115594	+	0.993297i	$0.536877\pi$
$644$	−11.0656	−0.436048
$645$	−13.4750	−0.530579
$646$	13.9083	0.547217
$647$	−37.4130	−1.47086	−0.735429	−	0.677602i	$-0.763019\pi$
$647$	−37.4130	−1.47086	−0.735429	+	0.677602i	$0.763019\pi$
$648$	11.0503	0.434097
$649$	−20.0023	−0.785160
$650$	0.446970	0.0175316
$651$	−8.63583	−0.338465
$652$	6.59170	0.258151
$653$	3.37220	0.131964	0.0659822	−	0.997821i	$-0.478982\pi$
$653$	3.37220	0.131964	0.0659822	+	0.997821i	$0.478982\pi$
$654$	−13.9435	−0.545235
$655$	−17.3492	−0.677891
$656$	−0.941951	−0.0367770
$657$	−11.9104	−0.464671
$658$	−9.09980	−0.354747
$659$	0.557512	0.0217176	0.0108588	−	0.999941i	$-0.496543\pi$
$659$	0.557512	0.0217176	0.0108588	+	0.999941i	$0.496543\pi$
$660$	12.9384	0.503625
$661$	13.8597	0.539080	0.269540	−	0.962989i	$-0.413128\pi$
$661$	13.8597	0.539080	0.269540	+	0.962989i	$0.413128\pi$
$662$	21.2041	0.824120
$663$	−3.18502	−0.123696
$664$	−3.74612	−0.145378
$665$	9.63142	0.373491
$666$	−2.97879	−0.115426
$667$	−43.4616	−1.68284
$668$	−21.1318	−0.817615
$669$	−25.4933	−0.985628
$670$	−13.6043	−0.525580
$671$	31.1859	1.20392
$672$	2.69328	0.103896
$673$	−17.3996	−0.670703	−0.335352	−	0.942093i	$-0.608855\pi$
$673$	−17.3996	−0.670703	−0.335352	+	0.942093i	$0.608855\pi$
$674$	31.3578	1.20786
$675$	3.22881	0.124277
$676$	−12.8949	−0.495956
$677$	12.7801	0.491178	0.245589	−	0.969374i	$-0.421019\pi$
$677$	12.7801	0.491178	0.245589	+	0.969374i	$0.421019\pi$
$678$	31.8949	1.22492
$679$	10.6259	0.407783
$680$	11.1537	0.427724
$681$	−44.3647	−1.70006
$682$	7.38548	0.282805
$683$	33.0427	1.26434	0.632172	−	0.774828i	$-0.282164\pi$
$683$	33.0427	1.26434	0.632172	+	0.774828i	$0.282164\pi$
$684$	6.13126	0.234435
$685$	20.0885	0.767544
$686$	15.1773	0.579473
$687$	58.2354	2.22182
$688$	2.39887	0.0914562
$689$	−2.89932	−0.110455
$690$	−51.3312	−1.95415
$691$	22.3849	0.851563	0.425781	−	0.904826i	$-0.359999\pi$
$691$	22.3849	0.851563	0.425781	+	0.904826i	$0.359999\pi$
$692$	20.3041	0.771848
$693$	−5.43011	−0.206273
$694$	−16.9262	−0.642510
$695$	−53.7316	−2.03816
$696$	10.5782	0.400965
$697$	4.15995	0.157570
$698$	−5.95574	−0.225428
$699$	44.3335	1.67685
$700$	1.66920	0.0630900
$701$	−31.4354	−1.18730	−0.593650	−	0.804724i	$-0.702314\pi$
$701$	−31.4354	−1.18730	−0.593650	+	0.804724i	$0.702314\pi$
$702$	0.759518	0.0286661
$703$	4.81859	0.181737
$704$	−2.30333	−0.0868102
$705$	−42.2121	−1.58980
$706$	14.8421	0.558589
$707$	−7.07939	−0.266248
$708$	−19.3147	−0.725891
$709$	2.63624	0.0990062	0.0495031	−	0.998774i	$-0.484236\pi$
$709$	2.63624	0.0990062	0.0495031	+	0.998774i	$0.484236\pi$
$710$	−22.2857	−0.836369
$711$	−14.5462	−0.545524
$712$	7.04532	0.264035
$713$	−29.3009	−1.09733
$714$	−11.8944	−0.445137
$715$	1.88626	0.0705421
$716$	23.2243	0.867933
$717$	25.2308	0.942263
$718$	15.7385	0.587354
$719$	−18.6151	−0.694225	−0.347112	−	0.937824i	$-0.612838\pi$
$719$	−18.6151	−0.694225	−0.347112	+	0.937824i	$0.612838\pi$
$720$	4.91691	0.183242
$721$	7.12991	0.265532
$722$	9.08185	0.337992
$723$	62.4494	2.32252
$724$	−1.93354	−0.0718594
$725$	6.55599	0.243483
$726$	−12.6658	−0.470071
$727$	−48.3457	−1.79304	−0.896521	−	0.443002i	$-0.853913\pi$
$727$	−48.3457	−1.79304	−0.896521	+	0.443002i	$0.853913\pi$
$728$	0.392649	0.0145525
$729$	−5.88419	−0.217933
$730$	15.4508	0.571860
$731$	−10.5942	−0.391840
$732$	30.1138	1.11304
$733$	−44.2748	−1.63533	−0.817663	−	0.575697i	$-0.804731\pi$
$733$	−44.2748	−1.63533	−0.817663	+	0.575697i	$0.804731\pi$
$734$	−7.37004	−0.272033
$735$	31.0838	1.14655
$736$	9.13817	0.336837
$737$	−12.4073	−0.457027
$738$	1.83385	0.0675048
$739$	38.7293	1.42468	0.712340	−	0.701835i	$-0.247635\pi$
$739$	38.7293	1.42468	0.712340	+	0.701835i	$0.247635\pi$
$740$	3.86422	0.142052
$741$	2.27126	0.0834368
$742$	−10.8275	−0.397489
$743$	−9.29475	−0.340991	−0.170496	−	0.985358i	$-0.554537\pi$
$743$	−9.29475	−0.340991	−0.170496	+	0.985358i	$0.554537\pi$
$744$	7.13159	0.261457
$745$	−21.4054	−0.784232
$746$	31.6084	1.15727
$747$	7.29317	0.266843
$748$	10.1723	0.371934
$749$	−5.40751	−0.197586
$750$	−20.3431	−0.742824
$751$	18.2103	0.664502	0.332251	−	0.943191i	$-0.392192\pi$
$751$	18.2103	0.664502	0.332251	+	0.943191i	$0.392192\pi$
$752$	7.51475	0.274035
$753$	−39.6268	−1.44408
$754$	1.54217	0.0561626
$755$	−44.8583	−1.63256
$756$	2.83641	0.103159
$757$	−1.59718	−0.0580503	−0.0290252	−	0.999579i	$-0.509240\pi$
$757$	−1.59718	−0.0580503	−0.0290252	+	0.999579i	$0.509240\pi$
$758$	−21.1097	−0.766738
$759$	−46.8146	−1.69926
$760$	−7.95377	−0.288513
$761$	−26.8991	−0.975090	−0.487545	−	0.873098i	$-0.662108\pi$
$761$	−26.8991	−0.975090	−0.487545	+	0.873098i	$0.662108\pi$
$762$	−28.2034	−1.02170
$763$	−7.59146	−0.274829
$764$	22.2672	0.805598
$765$	−21.7146	−0.785094
$766$	19.2563	0.695757
$767$	−2.81585	−0.101675
$768$	−2.22415	−0.0802572
$769$	−6.56075	−0.236587	−0.118293	−	0.992979i	$-0.537742\pi$
$769$	−6.56075	−0.236587	−0.118293	+	0.992979i	$0.537742\pi$
$770$	7.04421	0.253856
$771$	−31.2523	−1.12552
$772$	−9.33722	−0.336054
$773$	2.77380	0.0997666	0.0498833	−	0.998755i	$-0.484115\pi$
$773$	2.77380	0.0997666	0.0498833	+	0.998755i	$0.484115\pi$
$774$	−4.67027	−0.167869
$775$	4.41991	0.158768
$776$	−8.77499	−0.315004
$777$	−4.12085	−0.147835
$778$	6.39032	0.229104
$779$	−2.96650	−0.106286
$780$	1.82142	0.0652171
$781$	−20.3248	−0.727279
$782$	−40.3571	−1.44317
$783$	11.1403	0.398123
$784$	−5.53366	−0.197631
$785$	34.0393	1.21492
$786$	−15.2787	−0.544975
$787$	2.33576	0.0832610	0.0416305	−	0.999133i	$-0.486745\pi$
$787$	2.33576	0.0832610	0.0416305	+	0.999133i	$0.486745\pi$
$788$	−15.2685	−0.543917
$789$	−18.3533	−0.653393
$790$	18.8700	0.671364
$791$	17.3650	0.617428
$792$	4.48427	0.159341
$793$	4.39024	0.155902
$794$	−10.9109	−0.387215
$795$	−50.2264	−1.78135
$796$	−20.3913	−0.722751
$797$	−50.7698	−1.79836	−0.899180	−	0.437580i	$-0.855836\pi$
$797$	−50.7698	−1.79836	−0.899180	+	0.437580i	$0.855836\pi$
$798$	8.48199	0.300259
$799$	−33.1875	−1.17409
$800$	−1.37845	−0.0487356
$801$	−13.7162	−0.484640
$802$	−16.5455	−0.584242
$803$	14.0913	0.497271
$804$	−11.9807	−0.422528
$805$	−27.9470	−0.985001
$806$	1.03970	0.0366219
$807$	12.3025	0.433070
$808$	5.84626	0.205671
$809$	19.7385	0.693968	0.346984	−	0.937871i	$-0.387206\pi$
$809$	19.7385	0.693968	0.346984	+	0.937871i	$0.387206\pi$
$810$	27.9082	0.980595
$811$	−5.86821	−0.206061	−0.103030	−	0.994678i	$-0.532854\pi$
$811$	−5.86821	−0.206061	−0.103030	+	0.994678i	$0.532854\pi$
$812$	5.75922	0.202109
$813$	−39.0473	−1.36945
$814$	3.52421	0.123523
$815$	16.6477	0.583145
$816$	9.82257	0.343859
$817$	7.55480	0.264309
$818$	4.59203	0.160557
$819$	−0.764431	−0.0267114
$820$	−2.37895	−0.0830767
$821$	−16.0353	−0.559634	−0.279817	−	0.960053i	$-0.590274\pi$
$821$	−16.0353	−0.559634	−0.279817	+	0.960053i	$0.590274\pi$
$822$	17.6911	0.617049
$823$	−29.7872	−1.03832	−0.519158	−	0.854678i	$-0.673754\pi$
$823$	−29.7872	−1.03832	−0.519158	+	0.854678i	$0.673754\pi$
$824$	−5.88799	−0.205118
$825$	7.06177	0.245859
$826$	−10.5158	−0.365890
$827$	−26.1701	−0.910025	−0.455012	−	0.890485i	$-0.650365\pi$
$827$	−26.1701	−0.910025	−0.455012	+	0.890485i	$0.650365\pi$
$828$	−17.7907	−0.618271
$829$	−25.7189	−0.893253	−0.446627	−	0.894720i	$-0.647375\pi$
$829$	−25.7189	−0.893253	−0.446627	+	0.894720i	$0.647375\pi$
$830$	−9.46105	−0.328398
$831$	11.5704	0.401374
$832$	−0.324255	−0.0112415
$833$	24.4384	0.846740
$834$	−47.3192	−1.63853
$835$	−53.3697	−1.84694
$836$	−7.25391	−0.250882
$837$	7.51057	0.259603
$838$	15.5614	0.537560
$839$	−50.6233	−1.74771	−0.873856	−	0.486185i	$-0.838388\pi$
$839$	−50.6233	−1.74771	−0.873856	+	0.486185i	$0.838388\pi$
$840$	6.80205	0.234693
$841$	−6.37999	−0.220000
$842$	−16.4199	−0.565867
$843$	26.8703	0.925461
$844$	14.7181	0.506620
$845$	−32.5667	−1.12033
$846$	−14.6302	−0.502995
$847$	−6.89580	−0.236942
$848$	8.94149	0.307052
$849$	−7.03229	−0.241348
$850$	6.08768	0.208806
$851$	−13.9818	−0.479291
$852$	−19.6261	−0.672380
$853$	32.0319	1.09675	0.548376	−	0.836232i	$-0.315246\pi$
$853$	32.0319	1.09675	0.548376	+	0.836232i	$0.315246\pi$
$854$	16.3953	0.561035
$855$	15.4849	0.529571
$856$	4.46560	0.152631
$857$	51.5180	1.75982	0.879910	−	0.475140i	$-0.157603\pi$
$857$	51.5180	1.75982	0.879910	+	0.475140i	$0.157603\pi$
$858$	1.66115	0.0567106
$859$	−11.8054	−0.402795	−0.201398	−	0.979510i	$-0.564548\pi$
$859$	−11.8054	−0.402795	−0.201398	+	0.979510i	$0.564548\pi$
$860$	6.05850	0.206593
$861$	2.53694	0.0864588
$862$	17.4412	0.594049
$863$	1.05028	0.0357518	0.0178759	−	0.999840i	$-0.494310\pi$
$863$	1.05028	0.0357518	0.0178759	+	0.999840i	$0.494310\pi$
$864$	−2.34235	−0.0796883
$865$	51.2793	1.74355
$866$	11.5143	0.391272
$867$	−5.56896	−0.189132
$868$	3.88275	0.131789
$869$	17.2096	0.583796
$870$	26.7158	0.905752
$871$	−1.74665	−0.0591829
$872$	6.26913	0.212300
$873$	17.0837	0.578194
$874$	28.7789	0.973462
$875$	−11.0757	−0.374425
$876$	13.6069	0.459734
$877$	−29.4099	−0.993103	−0.496551	−	0.868007i	$-0.665401\pi$
$877$	−29.4099	−0.993103	−0.496551	+	0.868007i	$0.665401\pi$
$878$	8.69333	0.293386
$879$	−67.6565	−2.28200
$880$	−5.81721	−0.196098
$881$	−38.6990	−1.30380	−0.651901	−	0.758304i	$-0.726028\pi$
$881$	−38.6990	−1.30380	−0.651901	+	0.758304i	$0.726028\pi$
$882$	10.7733	0.362754
$883$	−7.16819	−0.241229	−0.120614	−	0.992699i	$-0.538486\pi$
$883$	−7.16819	−0.241229	−0.120614	+	0.992699i	$0.538486\pi$
$884$	1.43201	0.0481638
$885$	−48.7804	−1.63974
$886$	13.3192	0.447466
$887$	−52.4416	−1.76082	−0.880408	−	0.474217i	$-0.842731\pi$
$887$	−52.4416	−1.76082	−0.880408	+	0.474217i	$0.842731\pi$
$888$	3.40306	0.114199
$889$	−15.3552	−0.514996
$890$	17.7934	0.596436
$891$	25.4526	0.852693
$892$	11.4620	0.383777
$893$	23.6663	0.791961
$894$	−18.8508	−0.630465
$895$	58.6543	1.96060
$896$	−1.21093	−0.0404542
$897$	−6.59038	−0.220046
$898$	−20.4496	−0.682411
$899$	15.2499	0.508614
$900$	2.68365	0.0894551
$901$	−39.4885	−1.31555
$902$	−2.16963	−0.0722407
$903$	−6.46085	−0.215004
$904$	−14.3403	−0.476950
$905$	−4.88327	−0.162325
$906$	−39.5048	−1.31246
$907$	−15.0822	−0.500796	−0.250398	−	0.968143i	$-0.580562\pi$
$907$	−15.0822	−0.500796	−0.250398	+	0.968143i	$0.580562\pi$
$908$	19.9468	0.661957
$909$	−11.3819	−0.377512
$910$	0.991657	0.0328731
$911$	33.4711	1.10895	0.554473	−	0.832202i	$-0.312920\pi$
$911$	33.4711	1.10895	0.554473	+	0.832202i	$0.312920\pi$
$912$	−7.00455	−0.231944
$913$	−8.62857	−0.285564
$914$	11.2832	0.373214
$915$	76.0543	2.51428
$916$	−26.1832	−0.865117
$917$	−8.31841	−0.274698
$918$	10.3445	0.341421
$919$	20.7482	0.684420	0.342210	−	0.939624i	$-0.388825\pi$
$919$	20.7482	0.684420	0.342210	+	0.939624i	$0.388825\pi$
$920$	23.0790	0.760892
$921$	53.2184	1.75361
$922$	2.42314	0.0798018
$923$	−2.86125	−0.0941792
$924$	6.20354	0.204081
$925$	2.10910	0.0693467
$926$	−0.687200	−0.0225828
$927$	11.4631	0.376497
$928$	−4.75605	−0.156125
$929$	4.45993	0.146326	0.0731628	−	0.997320i	$-0.476691\pi$
$929$	4.45993	0.146326	0.0731628	+	0.997320i	$0.476691\pi$
$930$	18.0113	0.590612
$931$	−17.4272	−0.571153
$932$	−19.9327	−0.652918
$933$	−47.5843	−1.55784
$934$	28.8332	0.943452
$935$	25.6906	0.840174
$936$	0.631278	0.0206340
$937$	24.7032	0.807019	0.403509	−	0.914976i	$-0.367790\pi$
$937$	24.7032	0.807019	0.403509	+	0.914976i	$0.367790\pi$
$938$	−6.52284	−0.212978
$939$	−21.9699	−0.716960
$940$	18.9789	0.619025
$941$	26.1655	0.852972	0.426486	−	0.904494i	$-0.359751\pi$
$941$	26.1655	0.852972	0.426486	+	0.904494i	$0.359751\pi$
$942$	29.9770	0.976703
$943$	8.60771	0.280306
$944$	8.68407	0.282642
$945$	7.16352	0.233029
$946$	5.52541	0.179647
$947$	−8.12301	−0.263962	−0.131981	−	0.991252i	$-0.542134\pi$
$947$	−8.12301	−0.263962	−0.131981	+	0.991252i	$0.542134\pi$
$948$	16.6180	0.539728
$949$	1.98372	0.0643942
$950$	−4.34117	−0.140846
$951$	29.9254	0.970398
$952$	5.34783	0.173324
$953$	51.7625	1.67675	0.838376	−	0.545093i	$-0.183506\pi$
$953$	51.7625	1.67675	0.838376	+	0.545093i	$0.183506\pi$
$954$	−17.4078	−0.563599
$955$	56.2371	1.81979
$956$	−11.3440	−0.366892
$957$	24.3651	0.787612
$958$	19.0977	0.617018
$959$	9.63182	0.311028
$960$	−5.61723	−0.181295
$961$	−20.7188	−0.668349
$962$	0.496125	0.0159957
$963$	−8.69390	−0.280157
$964$	−28.0778	−0.904326
$965$	−23.5817	−0.759122
$966$	−24.6117	−0.791868
$967$	11.7642	0.378313	0.189156	−	0.981947i	$-0.439425\pi$
$967$	11.7642	0.378313	0.189156	+	0.981947i	$0.439425\pi$
$968$	5.69465	0.183033
$969$	30.9343	0.993753
$970$	−22.1618	−0.711571
$971$	−54.7250	−1.75621	−0.878104	−	0.478469i	$-0.841192\pi$
$971$	−54.7250	−1.75621	−0.878104	+	0.478469i	$0.841192\pi$
$972$	17.5506	0.562934
$973$	−25.7626	−0.825911
$974$	−1.43798	−0.0460757
$975$	0.994129	0.0318376
$976$	−13.5395	−0.433388
$977$	38.0344	1.21683	0.608414	−	0.793620i	$-0.291806\pi$
$977$	38.0344	1.21683	0.608414	+	0.793620i	$0.291806\pi$
$978$	14.6610	0.468806
$979$	16.2277	0.518641
$980$	−13.9756	−0.446434
$981$	−12.2051	−0.389679
$982$	34.2325	1.09240
$983$	18.9382	0.604034	0.302017	−	0.953302i	$-0.402340\pi$
$983$	18.9382	0.604034	0.302017	+	0.953302i	$0.402340\pi$
$984$	−2.09504	−0.0667876
$985$	−38.5614	−1.22867
$986$	21.0042	0.668911
$987$	−20.2394	−0.644226
$988$	−1.02118	−0.0324880
$989$	−21.9213	−0.697058
$990$	11.3253	0.359941
$991$	39.1709	1.24430	0.622152	−	0.782896i	$-0.286259\pi$
$991$	39.1709	1.24430	0.622152	+	0.782896i	$0.286259\pi$
$992$	−3.20643	−0.101804
$993$	47.1611	1.49661
$994$	−10.6853	−0.338917
$995$	−51.4995	−1.63264
$996$	−8.33195	−0.264008
$997$	−48.9188	−1.54927	−0.774637	−	0.632406i	$-0.782067\pi$
$997$	−48.9188	−1.54927	−0.774637	+	0.632406i	$0.782067\pi$
$998$	−29.4326	−0.931672
$999$	3.58390	0.113390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.b.1.14	✓	75

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.b.1.14	✓	75	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.22415 q^{3} +1.00000 q^{4} +2.52556 q^{5} +2.22415 q^{6} +1.21093 q^{7} -1.00000 q^{8} +1.94686 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.22415 q^{3} +1.00000 q^{4} +2.52556 q^{5} +2.22415 q^{6} +1.21093 q^{7} -1.00000 q^{8} +1.94686 q^{9} -2.52556 q^{10} -2.30333 q^{11} -2.22415 q^{12} -0.324255 q^{13} -1.21093 q^{14} -5.61723 q^{15} +1.00000 q^{16} -4.41632 q^{17} -1.94686 q^{18} +3.14931 q^{19} +2.52556 q^{20} -2.69328 q^{21} +2.30333 q^{22} -9.13817 q^{23} +2.22415 q^{24} +1.37845 q^{25} +0.324255 q^{26} +2.34235 q^{27} +1.21093 q^{28} +4.75605 q^{29} +5.61723 q^{30} +3.20643 q^{31} -1.00000 q^{32} +5.12297 q^{33} +4.41632 q^{34} +3.05827 q^{35} +1.94686 q^{36} +1.53005 q^{37} -3.14931 q^{38} +0.721193 q^{39} -2.52556 q^{40} -0.941951 q^{41} +2.69328 q^{42} +2.39887 q^{43} -2.30333 q^{44} +4.91691 q^{45} +9.13817 q^{46} +7.51475 q^{47} -2.22415 q^{48} -5.53366 q^{49} -1.37845 q^{50} +9.82257 q^{51} -0.324255 q^{52} +8.94149 q^{53} -2.34235 q^{54} -5.81721 q^{55} -1.21093 q^{56} -7.00455 q^{57} -4.75605 q^{58} +8.68407 q^{59} -5.61723 q^{60} -13.5395 q^{61} -3.20643 q^{62} +2.35750 q^{63} +1.00000 q^{64} -0.818925 q^{65} -5.12297 q^{66} +5.38665 q^{67} -4.41632 q^{68} +20.3247 q^{69} -3.05827 q^{70} +8.82408 q^{71} -1.94686 q^{72} -6.11778 q^{73} -1.53005 q^{74} -3.06589 q^{75} +3.14931 q^{76} -2.78917 q^{77} -0.721193 q^{78} -7.47161 q^{79} +2.52556 q^{80} -11.0503 q^{81} +0.941951 q^{82} +3.74612 q^{83} -2.69328 q^{84} -11.1537 q^{85} -2.39887 q^{86} -10.5782 q^{87} +2.30333 q^{88} -7.04532 q^{89} -4.91691 q^{90} -0.392649 q^{91} -9.13817 q^{92} -7.13159 q^{93} -7.51475 q^{94} +7.95377 q^{95} +2.22415 q^{96} +8.77499 q^{97} +5.53366 q^{98} -4.48427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * q^99

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