LMFDB - Embedded newform 8018.2.a.k.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.33535 q^{3} +1.00000 q^{4} +0.425182 q^{5} -1.33535 q^{6} -2.10915 q^{7} +1.00000 q^{8} -1.21683 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.33535 q^{3} +1.00000 q^{4} +0.425182 q^{5} -1.33535 q^{6} -2.10915 q^{7} +1.00000 q^{8} -1.21683 q^{9} +0.425182 q^{10} +3.38072 q^{11} -1.33535 q^{12} -3.49845 q^{13} -2.10915 q^{14} -0.567767 q^{15} +1.00000 q^{16} -7.70079 q^{17} -1.21683 q^{18} +1.00000 q^{19} +0.425182 q^{20} +2.81646 q^{21} +3.38072 q^{22} +5.14828 q^{23} -1.33535 q^{24} -4.81922 q^{25} -3.49845 q^{26} +5.63096 q^{27} -2.10915 q^{28} -2.86691 q^{29} -0.567767 q^{30} +1.94230 q^{31} +1.00000 q^{32} -4.51445 q^{33} -7.70079 q^{34} -0.896773 q^{35} -1.21683 q^{36} +5.95362 q^{37} +1.00000 q^{38} +4.67166 q^{39} +0.425182 q^{40} -0.0123240 q^{41} +2.81646 q^{42} +2.25672 q^{43} +3.38072 q^{44} -0.517376 q^{45} +5.14828 q^{46} -3.21044 q^{47} -1.33535 q^{48} -2.55148 q^{49} -4.81922 q^{50} +10.2833 q^{51} -3.49845 q^{52} +5.28393 q^{53} +5.63096 q^{54} +1.43742 q^{55} -2.10915 q^{56} -1.33535 q^{57} -2.86691 q^{58} -7.71638 q^{59} -0.567767 q^{60} -13.9896 q^{61} +1.94230 q^{62} +2.56649 q^{63} +1.00000 q^{64} -1.48748 q^{65} -4.51445 q^{66} +13.6441 q^{67} -7.70079 q^{68} -6.87476 q^{69} -0.896773 q^{70} +14.0484 q^{71} -1.21683 q^{72} -7.81370 q^{73} +5.95362 q^{74} +6.43536 q^{75} +1.00000 q^{76} -7.13045 q^{77} +4.67166 q^{78} -0.972383 q^{79} +0.425182 q^{80} -3.86881 q^{81} -0.0123240 q^{82} -6.08493 q^{83} +2.81646 q^{84} -3.27424 q^{85} +2.25672 q^{86} +3.82834 q^{87} +3.38072 q^{88} +2.97605 q^{89} -0.517376 q^{90} +7.37876 q^{91} +5.14828 q^{92} -2.59366 q^{93} -3.21044 q^{94} +0.425182 q^{95} -1.33535 q^{96} +17.3111 q^{97} -2.55148 q^{98} -4.11378 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) $ 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9 + 17 * q^10 + 21 * q^11 + 13 * q^12 + 13 * q^13 + 22 * q^14 + 8 * q^15 + 49 * q^16 + 24 * q^17 + 66 * q^18 + 49 * q^19 + 17 * q^20 + 6 * q^21 + 21 * q^22 + 22 * q^23 + 13 * q^24 + 96 * q^25 + 13 * q^26 + 31 * q^27 + 22 * q^28 + 33 * q^29 + 8 * q^30 + 21 * q^31 + 49 * q^32 + 20 * q^33 + 24 * q^34 + 18 * q^35 + 66 * q^36 + 48 * q^37 + 49 * q^38 + 4 * q^39 + 17 * q^40 + 37 * q^41 + 6 * q^42 + 43 * q^43 + 21 * q^44 + 47 * q^45 + 22 * q^46 + 7 * q^47 + 13 * q^48 + 87 * q^49 + 96 * q^50 + 12 * q^51 + 13 * q^52 + 23 * q^53 + 31 * q^54 + 31 * q^55 + 22 * q^56 + 13 * q^57 + 33 * q^58 + 37 * q^59 + 8 * q^60 + 61 * q^61 + 21 * q^62 + 45 * q^63 + 49 * q^64 + 36 * q^65 + 20 * q^66 + 43 * q^67 + 24 * q^68 + 18 * q^69 + 18 * q^70 + 14 * q^71 + 66 * q^72 + 90 * q^73 + 48 * q^74 + 53 * q^75 + 49 * q^76 + 46 * q^77 + 4 * q^78 + 16 * q^79 + 17 * q^80 + 97 * q^81 + 37 * q^82 + 11 * q^83 + 6 * q^84 + 88 * q^85 + 43 * q^86 - 35 * q^87 + 21 * q^88 + 46 * q^89 + 47 * q^90 + 27 * q^91 + 22 * q^92 + 9 * q^93 + 7 * q^94 + 17 * q^95 + 13 * q^96 + 34 * q^97 + 87 * q^98 + 84 * 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
$3$	−1.33535	−0.770966	−0.385483	−	0.922715i	$-0.625965\pi$
$3$	−1.33535	−0.770966	−0.385483	+	0.922715i	$0.625965\pi$
$4$	1.00000	0.500000
$5$	0.425182	0.190147	0.0950735	−	0.995470i	$-0.469691\pi$
$5$	0.425182	0.190147	0.0950735	+	0.995470i	$0.469691\pi$
$6$	−1.33535	−0.545155
$7$	−2.10915	−0.797184	−0.398592	−	0.917128i	$-0.630501\pi$
$7$	−2.10915	−0.797184	−0.398592	+	0.917128i	$0.630501\pi$
$8$	1.00000	0.353553
$9$	−1.21683	−0.405612
$10$	0.425182	0.134454
$11$	3.38072	1.01933	0.509663	−	0.860374i	$-0.329770\pi$
$11$	3.38072	1.01933	0.509663	+	0.860374i	$0.329770\pi$
$12$	−1.33535	−0.385483
$13$	−3.49845	−0.970295	−0.485147	−	0.874432i	$-0.661234\pi$
$13$	−3.49845	−0.970295	−0.485147	+	0.874432i	$0.661234\pi$
$14$	−2.10915	−0.563695
$15$	−0.567767	−0.146597
$16$	1.00000	0.250000
$17$	−7.70079	−1.86772	−0.933858	−	0.357643i	$-0.883581\pi$
$17$	−7.70079	−1.86772	−0.933858	+	0.357643i	$0.883581\pi$
$18$	−1.21683	−0.286811
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.425182	0.0950735
$21$	2.81646	0.614602
$22$	3.38072	0.720772
$23$	5.14828	1.07349	0.536745	−	0.843744i	$-0.319654\pi$
$23$	5.14828	1.07349	0.536745	+	0.843744i	$0.319654\pi$
$24$	−1.33535	−0.272578
$25$	−4.81922	−0.963844
$26$	−3.49845	−0.686102
$27$	5.63096	1.08368
$28$	−2.10915	−0.398592
$29$	−2.86691	−0.532372	−0.266186	−	0.963922i	$-0.585764\pi$
$29$	−2.86691	−0.532372	−0.266186	+	0.963922i	$0.585764\pi$
$30$	−0.567767	−0.103660
$31$	1.94230	0.348848	0.174424	−	0.984671i	$-0.444194\pi$
$31$	1.94230	0.348848	0.174424	+	0.984671i	$0.444194\pi$
$32$	1.00000	0.176777
$33$	−4.51445	−0.785865
$34$	−7.70079	−1.32068
$35$	−0.896773	−0.151582
$36$	−1.21683	−0.202806
$37$	5.95362	0.978769	0.489384	−	0.872068i	$-0.337222\pi$
$37$	5.95362	0.978769	0.489384	+	0.872068i	$0.337222\pi$
$38$	1.00000	0.162221
$39$	4.67166	0.748064
$40$	0.425182	0.0672271
$41$	−0.0123240	−0.00192469	−0.000962346	−	1.00000i	$-0.500306\pi$
$41$	−0.0123240	−0.00192469	−0.000962346		1.00000i	$0.500306\pi$
$42$	2.81646	0.434589
$43$	2.25672	0.344147	0.172074	−	0.985084i	$-0.444953\pi$
$43$	2.25672	0.344147	0.172074	+	0.985084i	$0.444953\pi$
$44$	3.38072	0.509663
$45$	−0.517376	−0.0771258
$46$	5.14828	0.759072
$47$	−3.21044	−0.468291	−0.234146	−	0.972202i	$-0.575229\pi$
$47$	−3.21044	−0.468291	−0.234146	+	0.972202i	$0.575229\pi$
$48$	−1.33535	−0.192741
$49$	−2.55148	−0.364497
$50$	−4.81922	−0.681541
$51$	10.2833	1.43995
$52$	−3.49845	−0.485147
$53$	5.28393	0.725804	0.362902	−	0.931827i	$-0.381786\pi$
$53$	5.28393	0.725804	0.362902	+	0.931827i	$0.381786\pi$
$54$	5.63096	0.766276
$55$	1.43742	0.193822
$56$	−2.10915	−0.281847
$57$	−1.33535	−0.176872
$58$	−2.86691	−0.376444
$59$	−7.71638	−1.00459	−0.502294	−	0.864697i	$-0.667510\pi$
$59$	−7.71638	−1.00459	−0.502294	+	0.864697i	$0.667510\pi$
$60$	−0.567767	−0.0732984
$61$	−13.9896	−1.79119	−0.895594	−	0.444871i	$-0.853249\pi$
$61$	−13.9896	−1.79119	−0.895594	+	0.444871i	$0.853249\pi$
$62$	1.94230	0.246673
$63$	2.56649	0.323347
$64$	1.00000	0.125000
$65$	−1.48748	−0.184499
$66$	−4.51445	−0.555691
$67$	13.6441	1.66689	0.833444	−	0.552603i	$-0.186366\pi$
$67$	13.6441	1.66689	0.833444	+	0.552603i	$0.186366\pi$
$68$	−7.70079	−0.933858
$69$	−6.87476	−0.827624
$70$	−0.896773	−0.107185
$71$	14.0484	1.66724	0.833621	−	0.552337i	$-0.186264\pi$
$71$	14.0484	1.66724	0.833621	+	0.552337i	$0.186264\pi$
$72$	−1.21683	−0.143405
$73$	−7.81370	−0.914525	−0.457262	−	0.889332i	$-0.651170\pi$
$73$	−7.81370	−0.914525	−0.457262	+	0.889332i	$0.651170\pi$
$74$	5.95362	0.692094
$75$	6.43536	0.743091
$76$	1.00000	0.114708
$77$	−7.13045	−0.812590
$78$	4.67166	0.528961
$79$	−0.972383	−0.109402	−0.0547008	−	0.998503i	$-0.517421\pi$
$79$	−0.972383	−0.109402	−0.0547008	+	0.998503i	$0.517421\pi$
$80$	0.425182	0.0475368
$81$	−3.86881	−0.429868
$82$	−0.0123240	−0.00136096
$83$	−6.08493	−0.667908	−0.333954	−	0.942589i	$-0.608383\pi$
$83$	−6.08493	−0.667908	−0.333954	+	0.942589i	$0.608383\pi$
$84$	2.81646	0.307301
$85$	−3.27424	−0.355141
$86$	2.25672	0.243349
$87$	3.82834	0.410441
$88$	3.38072	0.360386
$89$	2.97605	0.315461	0.157730	−	0.987482i	$-0.449582\pi$
$89$	2.97605	0.315461	0.157730	+	0.987482i	$0.449582\pi$
$90$	−0.517376	−0.0545362
$91$	7.37876	0.773504
$92$	5.14828	0.536745
$93$	−2.59366	−0.268950
$94$	−3.21044	−0.331132
$95$	0.425182	0.0436227
$96$	−1.33535	−0.136289
$97$	17.3111	1.75768	0.878838	−	0.477120i	$-0.158319\pi$
$97$	17.3111	1.75768	0.878838	+	0.477120i	$0.158319\pi$
$98$	−2.55148	−0.257738
$99$	−4.11378	−0.413450
$100$	−4.81922	−0.481922
$101$	11.8730	1.18141	0.590703	−	0.806889i	$-0.298850\pi$
$101$	11.8730	1.18141	0.590703	+	0.806889i	$0.298850\pi$
$102$	10.2833	1.01820
$103$	−6.16934	−0.607883	−0.303941	−	0.952691i	$-0.598303\pi$
$103$	−6.16934	−0.607883	−0.303941	+	0.952691i	$0.598303\pi$
$104$	−3.49845	−0.343051
$105$	1.19751	0.116865
$106$	5.28393	0.513221
$107$	19.6416	1.89882	0.949411	−	0.314035i	$-0.101681\pi$
$107$	19.6416	1.89882	0.949411	+	0.314035i	$0.101681\pi$
$108$	5.63096	0.541839
$109$	13.2937	1.27330	0.636651	−	0.771152i	$-0.280319\pi$
$109$	13.2937	1.27330	0.636651	+	0.771152i	$0.280319\pi$
$110$	1.43742	0.137053
$111$	−7.95018	−0.754597
$112$	−2.10915	−0.199296
$113$	2.63879	0.248236	0.124118	−	0.992267i	$-0.460390\pi$
$113$	2.63879	0.248236	0.124118	+	0.992267i	$0.460390\pi$
$114$	−1.33535	−0.125067
$115$	2.18895	0.204121
$116$	−2.86691	−0.266186
$117$	4.25703	0.393563
$118$	−7.71638	−0.710351
$119$	16.2421	1.48891
$120$	−0.567767	−0.0518298
$121$	0.429266	0.0390241
$122$	−13.9896	−1.26656
$123$	0.0164569	0.00148387
$124$	1.94230	0.174424
$125$	−4.17495	−0.373419
$126$	2.56649	0.228641
$127$	13.2557	1.17625	0.588126	−	0.808769i	$-0.299866\pi$
$127$	13.2557	1.17625	0.588126	+	0.808769i	$0.299866\pi$
$128$	1.00000	0.0883883
$129$	−3.01352	−0.265326
$130$	−1.48748	−0.130460
$131$	−8.52034	−0.744426	−0.372213	−	0.928147i	$-0.621401\pi$
$131$	−8.52034	−0.744426	−0.372213	+	0.928147i	$0.621401\pi$
$132$	−4.51445	−0.392933
$133$	−2.10915	−0.182887
$134$	13.6441	1.17867
$135$	2.39418	0.206058
$136$	−7.70079	−0.660338
$137$	16.2915	1.39188	0.695940	−	0.718100i	$-0.254988\pi$
$137$	16.2915	1.39188	0.695940	+	0.718100i	$0.254988\pi$
$138$	−6.87476	−0.585219
$139$	0.131931	0.0111902	0.00559511	−	0.999984i	$-0.498219\pi$
$139$	0.131931	0.0111902	0.00559511	+	0.999984i	$0.498219\pi$
$140$	−0.896773	−0.0757911
$141$	4.28707	0.361037
$142$	14.0484	1.17892
$143$	−11.8273	−0.989046
$144$	−1.21683	−0.101403
$145$	−1.21896	−0.101229
$146$	−7.81370	−0.646667
$147$	3.40712	0.281015
$148$	5.95362	0.489384
$149$	−1.58501	−0.129849	−0.0649247	−	0.997890i	$-0.520681\pi$
$149$	−1.58501	−0.129849	−0.0649247	+	0.997890i	$0.520681\pi$
$150$	6.43536	0.525445
$151$	9.18662	0.747597	0.373798	−	0.927510i	$-0.378055\pi$
$151$	9.18662	0.747597	0.373798	+	0.927510i	$0.378055\pi$
$152$	1.00000	0.0811107
$153$	9.37059	0.757568
$154$	−7.13045	−0.574588
$155$	0.825832	0.0663324
$156$	4.67166	0.374032
$157$	0.361511	0.0288517	0.0144259	−	0.999896i	$-0.495408\pi$
$157$	0.361511	0.0288517	0.0144259	+	0.999896i	$0.495408\pi$
$158$	−0.972383	−0.0773586
$159$	−7.05591	−0.559570
$160$	0.425182	0.0336136
$161$	−10.8585	−0.855770
$162$	−3.86881	−0.303962
$163$	−3.97917	−0.311672	−0.155836	−	0.987783i	$-0.549807\pi$
$163$	−3.97917	−0.311672	−0.155836	+	0.987783i	$0.549807\pi$
$164$	−0.0123240	−0.000962346 0
$165$	−1.91946	−0.149430
$166$	−6.08493	−0.472282
$167$	4.67351	0.361647	0.180824	−	0.983516i	$-0.442124\pi$
$167$	4.67351	0.361647	0.180824	+	0.983516i	$0.442124\pi$
$168$	2.81646	0.217295
$169$	−0.760863	−0.0585280
$170$	−3.27424	−0.251123
$171$	−1.21683	−0.0930537
$172$	2.25672	0.172074
$173$	−4.54318	−0.345411	−0.172706	−	0.984973i	$-0.555251\pi$
$173$	−4.54318	−0.345411	−0.172706	+	0.984973i	$0.555251\pi$
$174$	3.82834	0.290226
$175$	10.1645	0.768362
$176$	3.38072	0.254831
$177$	10.3041	0.774503
$178$	2.97605	0.223064
$179$	3.76401	0.281335	0.140668	−	0.990057i	$-0.455075\pi$
$179$	3.76401	0.281335	0.140668	+	0.990057i	$0.455075\pi$
$180$	−0.517376	−0.0385629
$181$	2.08026	0.154624	0.0773121	−	0.997007i	$-0.475366\pi$
$181$	2.08026	0.154624	0.0773121	+	0.997007i	$0.475366\pi$
$182$	7.37876	0.546950
$183$	18.6811	1.38095
$184$	5.14828	0.379536
$185$	2.53137	0.186110
$186$	−2.59366	−0.190176
$187$	−26.0342	−1.90381
$188$	−3.21044	−0.234146
$189$	−11.8765	−0.863892
$190$	0.425182	0.0308459
$191$	−6.55713	−0.474457	−0.237229	−	0.971454i	$-0.576239\pi$
$191$	−6.55713	−0.474457	−0.237229	+	0.971454i	$0.576239\pi$
$192$	−1.33535	−0.0963707
$193$	−16.0487	−1.15521	−0.577604	−	0.816317i	$-0.696012\pi$
$193$	−16.0487	−1.15521	−0.577604	+	0.816317i	$0.696012\pi$
$194$	17.3111	1.24286
$195$	1.98630	0.142242
$196$	−2.55148	−0.182248
$197$	−6.44975	−0.459526	−0.229763	−	0.973247i	$-0.573795\pi$
$197$	−6.44975	−0.459526	−0.229763	+	0.973247i	$0.573795\pi$
$198$	−4.11378	−0.292353
$199$	2.97751	0.211070	0.105535	−	0.994416i	$-0.466345\pi$
$199$	2.97751	0.211070	0.105535	+	0.994416i	$0.466345\pi$
$200$	−4.81922	−0.340770
$201$	−18.2196	−1.28511
$202$	11.8730	0.835380
$203$	6.04675	0.424399
$204$	10.2833	0.719973
$205$	−0.00523996	−0.000365975 0
$206$	−6.16934	−0.429838
$207$	−6.26460	−0.435420
$208$	−3.49845	−0.242574
$209$	3.38072	0.233849
$210$	1.19751	0.0826359
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	5.28393	0.362902
$213$	−18.7596	−1.28539
$214$	19.6416	1.34267
$215$	0.959517	0.0654385
$216$	5.63096	0.383138
$217$	−4.09661	−0.278096
$218$	13.2937	0.900361
$219$	10.4340	0.705068
$220$	1.43742	0.0969109
$221$	26.9408	1.81224
$222$	−7.95018	−0.533581
$223$	−2.11233	−0.141452	−0.0707261	−	0.997496i	$-0.522532\pi$
$223$	−2.11233	−0.141452	−0.0707261	+	0.997496i	$0.522532\pi$
$224$	−2.10915	−0.140924
$225$	5.86419	0.390946
$226$	2.63879	0.175530
$227$	−23.0955	−1.53290	−0.766450	−	0.642304i	$-0.777979\pi$
$227$	−23.0955	−1.53290	−0.766450	+	0.642304i	$0.777979\pi$
$228$	−1.33535	−0.0884359
$229$	−3.75494	−0.248133	−0.124067	−	0.992274i	$-0.539594\pi$
$229$	−3.75494	−0.248133	−0.124067	+	0.992274i	$0.539594\pi$
$230$	2.18895	0.144335
$231$	9.52166	0.626479
$232$	−2.86691	−0.188222
$233$	11.9387	0.782132	0.391066	−	0.920363i	$-0.372106\pi$
$233$	11.9387	0.782132	0.391066	+	0.920363i	$0.372106\pi$
$234$	4.25703	0.278291
$235$	−1.36502	−0.0890442
$236$	−7.71638	−0.502294
$237$	1.29847	0.0843449
$238$	16.2421	1.05282
$239$	5.46707	0.353635	0.176818	−	0.984244i	$-0.443420\pi$
$239$	5.46707	0.353635	0.176818	+	0.984244i	$0.443420\pi$
$240$	−0.567767	−0.0366492
$241$	28.7160	1.84976	0.924881	−	0.380257i	$-0.124165\pi$
$241$	28.7160	1.84976	0.924881	+	0.380257i	$0.124165\pi$
$242$	0.429266	0.0275942
$243$	−11.7267	−0.752265
$244$	−13.9896	−0.895594
$245$	−1.08484	−0.0693080
$246$	0.0164569	0.00104926
$247$	−3.49845	−0.222601
$248$	1.94230	0.123336
$249$	8.12553	0.514934
$250$	−4.17495	−0.264047
$251$	24.7408	1.56163	0.780814	−	0.624763i	$-0.214804\pi$
$251$	24.7408	1.56163	0.780814	+	0.624763i	$0.214804\pi$
$252$	2.56649	0.161674
$253$	17.4049	1.09424
$254$	13.2557	0.831736
$255$	4.37226	0.273802
$256$	1.00000	0.0625000
$257$	24.6682	1.53876	0.769380	−	0.638792i	$-0.220565\pi$
$257$	24.6682	1.53876	0.769380	+	0.638792i	$0.220565\pi$
$258$	−3.01352	−0.187614
$259$	−12.5571	−0.780259
$260$	−1.48748	−0.0922493
$261$	3.48856	0.215936
$262$	−8.52034	−0.526388
$263$	25.5797	1.57731	0.788655	−	0.614836i	$-0.210778\pi$
$263$	25.5797	1.57731	0.788655	+	0.614836i	$0.210778\pi$
$264$	−4.51445	−0.277845
$265$	2.24663	0.138009
$266$	−2.10915	−0.129320
$267$	−3.97407	−0.243209
$268$	13.6441	0.833444
$269$	−26.7838	−1.63304	−0.816518	−	0.577321i	$-0.804098\pi$
$269$	−26.7838	−1.63304	−0.816518	+	0.577321i	$0.804098\pi$
$270$	2.39418	0.145705
$271$	7.74272	0.470337	0.235168	−	0.971955i	$-0.424436\pi$
$271$	7.74272	0.470337	0.235168	+	0.971955i	$0.424436\pi$
$272$	−7.70079	−0.466929
$273$	−9.85324	−0.596345
$274$	16.2915	0.984208
$275$	−16.2924	−0.982471
$276$	−6.87476	−0.413812
$277$	−5.51647	−0.331452	−0.165726	−	0.986172i	$-0.552997\pi$
$277$	−5.51647	−0.331452	−0.165726	+	0.986172i	$0.552997\pi$
$278$	0.131931	0.00791269
$279$	−2.36346	−0.141497
$280$	−0.896773	−0.0535924
$281$	1.11616	0.0665844	0.0332922	−	0.999446i	$-0.489401\pi$
$281$	1.11616	0.0665844	0.0332922	+	0.999446i	$0.489401\pi$
$282$	4.28707	0.255291
$283$	−19.3894	−1.15258	−0.576290	−	0.817246i	$-0.695500\pi$
$283$	−19.3894	−1.15258	−0.576290	+	0.817246i	$0.695500\pi$
$284$	14.0484	0.833621
$285$	−0.567767	−0.0336316
$286$	−11.8273	−0.699361
$287$	0.0259933	0.00153434
$288$	−1.21683	−0.0717027
$289$	42.3022	2.48837
$290$	−1.21896	−0.0715797
$291$	−23.1164	−1.35511
$292$	−7.81370	−0.457262
$293$	−19.0245	−1.11142	−0.555710	−	0.831376i	$-0.687554\pi$
$293$	−19.0245	−1.11142	−0.555710	+	0.831376i	$0.687554\pi$
$294$	3.40712	0.198707
$295$	−3.28087	−0.191019
$296$	5.95362	0.346047
$297$	19.0367	1.10462
$298$	−1.58501	−0.0918173
$299$	−18.0110	−1.04160
$300$	6.43536	0.371545
$301$	−4.75977	−0.274349
$302$	9.18662	0.528631
$303$	−15.8546	−0.910824
$304$	1.00000	0.0573539
$305$	−5.94814	−0.340589
$306$	9.37059	0.535681
$307$	16.0438	0.915666	0.457833	−	0.889038i	$-0.348626\pi$
$307$	16.0438	0.915666	0.457833	+	0.889038i	$0.348626\pi$
$308$	−7.13045	−0.406295
$309$	8.23824	0.468657
$310$	0.825832	0.0469041
$311$	17.8001	1.00935	0.504676	−	0.863309i	$-0.331612\pi$
$311$	17.8001	1.00935	0.504676	+	0.863309i	$0.331612\pi$
$312$	4.67166	0.264481
$313$	19.6422	1.11024	0.555121	−	0.831770i	$-0.312672\pi$
$313$	19.6422	1.11024	0.555121	+	0.831770i	$0.312672\pi$
$314$	0.361511	0.0204012
$315$	1.09122	0.0614835
$316$	−0.972383	−0.0547008
$317$	19.2286	1.07999	0.539993	−	0.841669i	$-0.318427\pi$
$317$	19.2286	1.07999	0.539993	+	0.841669i	$0.318427\pi$
$318$	−7.05591	−0.395676
$319$	−9.69223	−0.542661
$320$	0.425182	0.0237684
$321$	−26.2284	−1.46393
$322$	−10.8585	−0.605120
$323$	−7.70079	−0.428484
$324$	−3.86881	−0.214934
$325$	16.8598	0.935213
$326$	−3.97917	−0.220386
$327$	−17.7517	−0.981673
$328$	−0.0123240	−0.000680482 0
$329$	6.77131	0.373315
$330$	−1.91946	−0.105663
$331$	−7.32026	−0.402358	−0.201179	−	0.979555i	$-0.564477\pi$
$331$	−7.32026	−0.402358	−0.201179	+	0.979555i	$0.564477\pi$
$332$	−6.08493	−0.333954
$333$	−7.24457	−0.397000
$334$	4.67351	0.255723
$335$	5.80121	0.316954
$336$	2.81646	0.153651
$337$	−33.7934	−1.84084	−0.920421	−	0.390929i	$-0.872154\pi$
$337$	−33.7934	−1.84084	−0.920421	+	0.390929i	$0.872154\pi$
$338$	−0.760863	−0.0413855
$339$	−3.52371	−0.191382
$340$	−3.27424	−0.177570
$341$	6.56639	0.355590
$342$	−1.21683	−0.0657989
$343$	20.1455	1.08776
$344$	2.25672	0.121674
$345$	−2.92302	−0.157370
$346$	−4.54318	−0.244243
$347$	29.6191	1.59004	0.795019	−	0.606584i	$-0.207461\pi$
$347$	29.6191	1.59004	0.795019	+	0.606584i	$0.207461\pi$
$348$	3.82834	0.205220
$349$	12.5327	0.670858	0.335429	−	0.942066i	$-0.391119\pi$
$349$	12.5327	0.670858	0.335429	+	0.942066i	$0.391119\pi$
$350$	10.1645	0.543314
$351$	−19.6996	−1.05149
$352$	3.38072	0.180193
$353$	8.51877	0.453408	0.226704	−	0.973964i	$-0.427205\pi$
$353$	8.51877	0.453408	0.226704	+	0.973964i	$0.427205\pi$
$354$	10.3041	0.547656
$355$	5.97314	0.317021
$356$	2.97605	0.157730
$357$	−21.6890	−1.14790
$358$	3.76401	0.198934
$359$	−10.0166	−0.528658	−0.264329	−	0.964433i	$-0.585150\pi$
$359$	−10.0166	−0.528658	−0.264329	+	0.964433i	$0.585150\pi$
$360$	−0.517376	−0.0272681
$361$	1.00000	0.0526316
$362$	2.08026	0.109336
$363$	−0.573221	−0.0300863
$364$	7.37876	0.386752
$365$	−3.32224	−0.173894
$366$	18.6811	0.976476
$367$	23.9538	1.25038	0.625188	−	0.780474i	$-0.285022\pi$
$367$	23.9538	1.25038	0.625188	+	0.780474i	$0.285022\pi$
$368$	5.14828	0.268373
$369$	0.0149963	0.000780678 0
$370$	2.53137	0.131600
$371$	−11.1446	−0.578600
$372$	−2.59366	−0.134475
$373$	33.3367	1.72611	0.863055	−	0.505110i	$-0.168548\pi$
$373$	33.3367	1.72611	0.863055	+	0.505110i	$0.168548\pi$
$374$	−26.0342	−1.34620
$375$	5.57503	0.287893
$376$	−3.21044	−0.165566
$377$	10.0297	0.516558
$378$	−11.8765	−0.610864
$379$	−12.9365	−0.664501	−0.332251	−	0.943191i	$-0.607808\pi$
$379$	−12.9365	−0.664501	−0.332251	+	0.943191i	$0.607808\pi$
$380$	0.425182	0.0218114
$381$	−17.7010	−0.906850
$382$	−6.55713	−0.335492
$383$	−3.13910	−0.160401	−0.0802003	−	0.996779i	$-0.525556\pi$
$383$	−3.13910	−0.160401	−0.0802003	+	0.996779i	$0.525556\pi$
$384$	−1.33535	−0.0681444
$385$	−3.03174	−0.154512
$386$	−16.0487	−0.816855
$387$	−2.74606	−0.139590
$388$	17.3111	0.878838
$389$	0.721942	0.0366039	0.0183020	−	0.999833i	$-0.494174\pi$
$389$	0.721942	0.0366039	0.0183020	+	0.999833i	$0.494174\pi$
$390$	1.98630	0.100580
$391$	−39.6458	−2.00498
$392$	−2.55148	−0.128869
$393$	11.3777	0.573927
$394$	−6.44975	−0.324934
$395$	−0.413440	−0.0208024
$396$	−4.11378	−0.206725
$397$	8.10631	0.406844	0.203422	−	0.979091i	$-0.434794\pi$
$397$	8.10631	0.406844	0.203422	+	0.979091i	$0.434794\pi$
$398$	2.97751	0.149249
$399$	2.81646	0.140999
$400$	−4.81922	−0.240961
$401$	−22.9854	−1.14784	−0.573918	−	0.818913i	$-0.694577\pi$
$401$	−22.9854	−1.14784	−0.573918	+	0.818913i	$0.694577\pi$
$402$	−18.2196	−0.908713
$403$	−6.79505	−0.338486
$404$	11.8730	0.590703
$405$	−1.64495	−0.0817381
$406$	6.04675	0.300095
$407$	20.1275	0.997684
$408$	10.2833	0.509098
$409$	14.0331	0.693893	0.346946	−	0.937885i	$-0.387219\pi$
$409$	14.0331	0.693893	0.346946	+	0.937885i	$0.387219\pi$
$410$	−0.00523996	−0.000258783 0
$411$	−21.7549	−1.07309
$412$	−6.16934	−0.303941
$413$	16.2750	0.800842
$414$	−6.26460	−0.307888
$415$	−2.58720	−0.127001
$416$	−3.49845	−0.171526
$417$	−0.176174	−0.00862728
$418$	3.38072	0.165356
$419$	9.93326	0.485272	0.242636	−	0.970117i	$-0.421988\pi$
$419$	9.93326	0.485272	0.242636	+	0.970117i	$0.421988\pi$
$420$	1.19751	0.0584324
$421$	−35.0125	−1.70640	−0.853201	−	0.521582i	$-0.825342\pi$
$421$	−35.0125	−1.70640	−0.853201	+	0.521582i	$0.825342\pi$
$422$	1.00000	0.0486792
$423$	3.90658	0.189944
$424$	5.28393	0.256610
$425$	37.1118	1.80019
$426$	−18.7596	−0.908906
$427$	29.5063	1.42791
$428$	19.6416	0.949411
$429$	15.7936	0.762521
$430$	0.959517	0.0462720
$431$	−14.3281	−0.690162	−0.345081	−	0.938573i	$-0.612149\pi$
$431$	−14.3281	−0.690162	−0.345081	+	0.938573i	$0.612149\pi$
$432$	5.63096	0.270920
$433$	−3.90638	−0.187729	−0.0938643	−	0.995585i	$-0.529922\pi$
$433$	−3.90638	−0.187729	−0.0938643	+	0.995585i	$0.529922\pi$
$434$	−4.09661	−0.196644
$435$	1.62774	0.0780441
$436$	13.2937	0.636651
$437$	5.14828	0.246276
$438$	10.4340	0.498558
$439$	15.1906	0.725006	0.362503	−	0.931983i	$-0.381922\pi$
$439$	15.1906	0.725006	0.362503	+	0.931983i	$0.381922\pi$
$440$	1.43742	0.0685263
$441$	3.10473	0.147844
$442$	26.9408	1.28144
$443$	9.41748	0.447438	0.223719	−	0.974654i	$-0.428180\pi$
$443$	9.41748	0.447438	0.223719	+	0.974654i	$0.428180\pi$
$444$	−7.95018	−0.377299
$445$	1.26536	0.0599839
$446$	−2.11233	−0.100022
$447$	2.11655	0.100109
$448$	−2.10915	−0.0996481
$449$	−1.05432	−0.0497562	−0.0248781	−	0.999690i	$-0.507920\pi$
$449$	−1.05432	−0.0497562	−0.0248781	+	0.999690i	$0.507920\pi$
$450$	5.86419	0.276441
$451$	−0.0416641	−0.00196189
$452$	2.63879	0.124118
$453$	−12.2674	−0.576372
$454$	−23.0955	−1.08392
$455$	3.13731	0.147079
$456$	−1.33535	−0.0625336
$457$	−33.6213	−1.57274	−0.786368	−	0.617758i	$-0.788041\pi$
$457$	−33.6213	−1.57274	−0.786368	+	0.617758i	$0.788041\pi$
$458$	−3.75494	−0.175457
$459$	−43.3629	−2.02400
$460$	2.18895	0.102060
$461$	22.4758	1.04680	0.523402	−	0.852086i	$-0.324663\pi$
$461$	22.4758	1.04680	0.523402	+	0.852086i	$0.324663\pi$
$462$	9.52166	0.442988
$463$	−24.8805	−1.15630	−0.578148	−	0.815932i	$-0.696224\pi$
$463$	−24.8805	−1.15630	−0.578148	+	0.815932i	$0.696224\pi$
$464$	−2.86691	−0.133093
$465$	−1.10278	−0.0511401
$466$	11.9387	0.553051
$467$	24.0093	1.11102	0.555509	−	0.831511i	$-0.312524\pi$
$467$	24.0093	1.11102	0.555509	+	0.831511i	$0.312524\pi$
$468$	4.25703	0.196781
$469$	−28.7774	−1.32882
$470$	−1.36502	−0.0629638
$471$	−0.482744	−0.0222437
$472$	−7.71638	−0.355175
$473$	7.62935	0.350798
$474$	1.29847	0.0596409
$475$	−4.81922	−0.221121
$476$	16.2421	0.744457
$477$	−6.42967	−0.294394
$478$	5.46707	0.250058
$479$	37.8079	1.72749	0.863743	−	0.503933i	$-0.168114\pi$
$479$	37.8079	1.72749	0.863743	+	0.503933i	$0.168114\pi$
$480$	−0.567767	−0.0259149
$481$	−20.8284	−0.949694
$482$	28.7160	1.30798
$483$	14.4999	0.659769
$484$	0.429266	0.0195121
$485$	7.36036	0.334217
$486$	−11.7267	−0.531932
$487$	−4.73970	−0.214776	−0.107388	−	0.994217i	$-0.534249\pi$
$487$	−4.73970	−0.214776	−0.107388	+	0.994217i	$0.534249\pi$
$488$	−13.9896	−0.633281
$489$	5.31359	0.240289
$490$	−1.08484	−0.0490082
$491$	−29.3737	−1.32562	−0.662809	−	0.748789i	$-0.730636\pi$
$491$	−29.3737	−1.32562	−0.662809	+	0.748789i	$0.730636\pi$
$492$	0.0164569	0.000741936 0
$493$	22.0775	0.994321
$494$	−3.49845	−0.157403
$495$	−1.74910	−0.0786163
$496$	1.94230	0.0872120
$497$	−29.6303	−1.32910
$498$	8.12553	0.364114
$499$	29.6438	1.32704	0.663520	−	0.748159i	$-0.269062\pi$
$499$	29.6438	1.32704	0.663520	+	0.748159i	$0.269062\pi$
$500$	−4.17495	−0.186710
$501$	−6.24078	−0.278818
$502$	24.7408	1.10424
$503$	39.7884	1.77408	0.887038	−	0.461696i	$-0.152759\pi$
$503$	39.7884	1.77408	0.887038	+	0.461696i	$0.152759\pi$
$504$	2.56649	0.114320
$505$	5.04818	0.224641
$506$	17.4049	0.773741
$507$	1.01602	0.0451231
$508$	13.2557	0.588126
$509$	40.4962	1.79496	0.897481	−	0.441054i	$-0.145395\pi$
$509$	40.4962	1.79496	0.897481	+	0.441054i	$0.145395\pi$
$510$	4.37226	0.193607
$511$	16.4803	0.729045
$512$	1.00000	0.0441942
$513$	5.63096	0.248613
$514$	24.6682	1.08807
$515$	−2.62309	−0.115587
$516$	−3.01352	−0.132663
$517$	−10.8536	−0.477341
$518$	−12.5571	−0.551727
$519$	6.06674	0.266300
$520$	−1.48748	−0.0652301
$521$	1.05466	0.0462054	0.0231027	−	0.999733i	$-0.492646\pi$
$521$	1.05466	0.0462054	0.0231027	+	0.999733i	$0.492646\pi$
$522$	3.48856	0.152690
$523$	13.6196	0.595545	0.297772	−	0.954637i	$-0.403756\pi$
$523$	13.6196	0.595545	0.297772	+	0.954637i	$0.403756\pi$
$524$	−8.52034	−0.372213
$525$	−13.5731	−0.592381
$526$	25.5797	1.11533
$527$	−14.9573	−0.651550
$528$	−4.51445	−0.196466
$529$	3.50476	0.152381
$530$	2.24663	0.0975874
$531$	9.38956	0.407472
$532$	−2.10915	−0.0914433
$533$	0.0431150	0.00186752
$534$	−3.97407	−0.171975
$535$	8.35124	0.361056
$536$	13.6441	0.589334
$537$	−5.02628	−0.216900
$538$	−26.7838	−1.15473
$539$	−8.62583	−0.371541
$540$	2.39418	0.103029
$541$	7.82716	0.336516	0.168258	−	0.985743i	$-0.446186\pi$
$541$	7.82716	0.336516	0.168258	+	0.985743i	$0.446186\pi$
$542$	7.74272	0.332578
$543$	−2.77787	−0.119210
$544$	−7.70079	−0.330169
$545$	5.65222	0.242115
$546$	−9.85324	−0.421680
$547$	−22.6177	−0.967065	−0.483533	−	0.875326i	$-0.660647\pi$
$547$	−22.6177	−0.967065	−0.483533	+	0.875326i	$0.660647\pi$
$548$	16.2915	0.695940
$549$	17.0231	0.726527
$550$	−16.2924	−0.694712
$551$	−2.86691	−0.122135
$552$	−6.87476	−0.292609
$553$	2.05090	0.0872133
$554$	−5.51647	−0.234372
$555$	−3.38027	−0.143484
$556$	0.131931	0.00559511
$557$	19.7022	0.834810	0.417405	−	0.908720i	$-0.362940\pi$
$557$	19.7022	0.834810	0.417405	+	0.908720i	$0.362940\pi$
$558$	−2.36346	−0.100053
$559$	−7.89503	−0.333924
$560$	−0.896773	−0.0378956
$561$	34.7649	1.46777
$562$	1.11616	0.0470823
$563$	−29.7588	−1.25419	−0.627093	−	0.778945i	$-0.715755\pi$
$563$	−29.7588	−1.25419	−0.627093	+	0.778945i	$0.715755\pi$
$564$	4.28707	0.180518
$565$	1.12196	0.0472014
$566$	−19.3894	−0.814996
$567$	8.15991	0.342684
$568$	14.0484	0.589459
$569$	7.94307	0.332991	0.166495	−	0.986042i	$-0.446755\pi$
$569$	7.94307	0.332991	0.166495	+	0.986042i	$0.446755\pi$
$570$	−0.567767	−0.0237812
$571$	−6.95255	−0.290955	−0.145477	−	0.989362i	$-0.546472\pi$
$571$	−6.95255	−0.290955	−0.145477	+	0.989362i	$0.546472\pi$
$572$	−11.8273	−0.494523
$573$	8.75608	0.365790
$574$	0.0259933	0.00108494
$575$	−24.8107	−1.03468
$576$	−1.21683	−0.0507014
$577$	19.0859	0.794557	0.397279	−	0.917698i	$-0.369955\pi$
$577$	19.0859	0.794557	0.397279	+	0.917698i	$0.369955\pi$
$578$	42.3022	1.75954
$579$	21.4306	0.890626
$580$	−1.21896	−0.0506145
$581$	12.8340	0.532446
$582$	−23.1164	−0.958206
$583$	17.8635	0.739830
$584$	−7.81370	−0.323333
$585$	1.81001	0.0748348
$586$	−19.0245	−0.785893
$587$	31.2484	1.28976	0.644880	−	0.764283i	$-0.276907\pi$
$587$	31.2484	1.28976	0.644880	+	0.764283i	$0.276907\pi$
$588$	3.40712	0.140507
$589$	1.94230	0.0800313
$590$	−3.28087	−0.135071
$591$	8.61269	0.354279
$592$	5.95362	0.244692
$593$	12.6960	0.521360	0.260680	−	0.965425i	$-0.416053\pi$
$593$	12.6960	0.521360	0.260680	+	0.965425i	$0.416053\pi$
$594$	19.0367	0.781085
$595$	6.90586	0.283113
$596$	−1.58501	−0.0649247
$597$	−3.97602	−0.162728
$598$	−18.0110	−0.736524
$599$	19.5732	0.799739	0.399870	−	0.916572i	$-0.369055\pi$
$599$	19.5732	0.799739	0.399870	+	0.916572i	$0.369055\pi$
$600$	6.43536	0.262722
$601$	9.16715	0.373936	0.186968	−	0.982366i	$-0.440134\pi$
$601$	9.16715	0.373936	0.186968	+	0.982366i	$0.440134\pi$
$602$	−4.75977	−0.193994
$603$	−16.6026	−0.676109
$604$	9.18662	0.373798
$605$	0.182516	0.00742033
$606$	−15.8546	−0.644050
$607$	−14.3860	−0.583910	−0.291955	−	0.956432i	$-0.594306\pi$
$607$	−14.3860	−0.583910	−0.291955	+	0.956432i	$0.594306\pi$
$608$	1.00000	0.0405554
$609$	−8.07455	−0.327197
$610$	−5.94814	−0.240833
$611$	11.2316	0.454381
$612$	9.37059	0.378784
$613$	33.1680	1.33964	0.669820	−	0.742523i	$-0.266371\pi$
$613$	33.1680	1.33964	0.669820	+	0.742523i	$0.266371\pi$
$614$	16.0438	0.647473
$615$	0.00699719	0.000282154 0
$616$	−7.13045	−0.287294
$617$	−19.4511	−0.783071	−0.391536	−	0.920163i	$-0.628056\pi$
$617$	−19.4511	−0.783071	−0.391536	+	0.920163i	$0.628056\pi$
$618$	8.23824	0.331391
$619$	−6.34361	−0.254971	−0.127486	−	0.991840i	$-0.540691\pi$
$619$	−6.34361	−0.254971	−0.127486	+	0.991840i	$0.540691\pi$
$620$	0.825832	0.0331662
$621$	28.9897	1.16332
$622$	17.8001	0.713720
$623$	−6.27694	−0.251480
$624$	4.67166	0.187016
$625$	22.3210	0.892840
$626$	19.6422	0.785059
$627$	−4.51445	−0.180290
$628$	0.361511	0.0144259
$629$	−45.8476	−1.82806
$630$	1.09122	0.0434754
$631$	13.7312	0.546630	0.273315	−	0.961925i	$-0.411880\pi$
$631$	13.7312	0.546630	0.273315	+	0.961925i	$0.411880\pi$
$632$	−0.972383	−0.0386793
$633$	−1.33535	−0.0530755
$634$	19.2286	0.763666
$635$	5.63608	0.223661
$636$	−7.05591	−0.279785
$637$	8.92622	0.353670
$638$	−9.69223	−0.383719
$639$	−17.0946	−0.676253
$640$	0.425182	0.0168068
$641$	−39.8546	−1.57416	−0.787082	−	0.616849i	$-0.788409\pi$
$641$	−39.8546	−1.57416	−0.787082	+	0.616849i	$0.788409\pi$
$642$	−26.2284	−1.03515
$643$	−18.3319	−0.722938	−0.361469	−	0.932384i	$-0.617725\pi$
$643$	−18.3319	−0.722938	−0.361469	+	0.932384i	$0.617725\pi$
$644$	−10.8585	−0.427885
$645$	−1.28129	−0.0504509
$646$	−7.70079	−0.302984
$647$	−23.6433	−0.929512	−0.464756	−	0.885439i	$-0.653858\pi$
$647$	−23.6433	−0.929512	−0.464756	+	0.885439i	$0.653858\pi$
$648$	−3.86881	−0.151981
$649$	−26.0869	−1.02400
$650$	16.8598	0.661295
$651$	5.47042	0.214403
$652$	−3.97917	−0.155836
$653$	−22.6525	−0.886462	−0.443231	−	0.896407i	$-0.646168\pi$
$653$	−22.6525	−0.886462	−0.443231	+	0.896407i	$0.646168\pi$
$654$	−17.7517	−0.694147
$655$	−3.62269	−0.141550
$656$	−0.0123240	−0.000481173 0
$657$	9.50799	0.370942
$658$	6.77131	0.263973
$659$	35.9005	1.39848	0.699242	−	0.714885i	$-0.253521\pi$
$659$	35.9005	1.39848	0.699242	+	0.714885i	$0.253521\pi$
$660$	−1.91946	−0.0747150
$661$	−36.6239	−1.42451	−0.712253	−	0.701923i	$-0.752325\pi$
$661$	−36.6239	−1.42451	−0.712253	+	0.701923i	$0.752325\pi$
$662$	−7.32026	−0.284510
$663$	−35.9755	−1.39717
$664$	−6.08493	−0.236141
$665$	−0.896773	−0.0347754
$666$	−7.24457	−0.280721
$667$	−14.7597	−0.571496
$668$	4.67351	0.180824
$669$	2.82071	0.109055
$670$	5.80121	0.224120
$671$	−47.2950	−1.82580
$672$	2.81646	0.108647
$673$	−13.2616	−0.511198	−0.255599	−	0.966783i	$-0.582273\pi$
$673$	−13.2616	−0.511198	−0.255599	+	0.966783i	$0.582273\pi$
$674$	−33.7934	−1.30167
$675$	−27.1368	−1.04450
$676$	−0.760863	−0.0292640
$677$	39.7100	1.52618	0.763090	−	0.646292i	$-0.223681\pi$
$677$	39.7100	1.52618	0.763090	+	0.646292i	$0.223681\pi$
$678$	−3.52371	−0.135327
$679$	−36.5117	−1.40119
$680$	−3.27424	−0.125561
$681$	30.8406	1.18181
$682$	6.56639	0.251440
$683$	−13.3076	−0.509201	−0.254601	−	0.967046i	$-0.581944\pi$
$683$	−13.3076	−0.509201	−0.254601	+	0.967046i	$0.581944\pi$
$684$	−1.21683	−0.0465268
$685$	6.92687	0.264662
$686$	20.1455	0.769159
$687$	5.01416	0.191302
$688$	2.25672	0.0860368
$689$	−18.4856	−0.704244
$690$	−2.92302	−0.111278
$691$	−23.6701	−0.900451	−0.450226	−	0.892915i	$-0.648656\pi$
$691$	−23.6701	−0.900451	−0.450226	+	0.892915i	$0.648656\pi$
$692$	−4.54318	−0.172706
$693$	8.67658	0.329596
$694$	29.6191	1.12433
$695$	0.0560946	0.00212779
$696$	3.82834	0.145113
$697$	0.0949049	0.00359478
$698$	12.5327	0.474368
$699$	−15.9424	−0.602997
$700$	10.1645	0.384181
$701$	−37.4893	−1.41595	−0.707976	−	0.706237i	$-0.750391\pi$
$701$	−37.4893	−1.41595	−0.707976	+	0.706237i	$0.750391\pi$
$702$	−19.6996	−0.743514
$703$	5.95362	0.224545
$704$	3.38072	0.127416
$705$	1.82279	0.0686501
$706$	8.51877	0.320608
$707$	−25.0419	−0.941799
$708$	10.3041	0.387251
$709$	−12.4260	−0.466668	−0.233334	−	0.972397i	$-0.574964\pi$
$709$	−12.4260	−0.466668	−0.233334	+	0.972397i	$0.574964\pi$
$710$	5.97314	0.224168
$711$	1.18323	0.0443746
$712$	2.97605	0.111532
$713$	9.99952	0.374485
$714$	−21.6890	−0.811690
$715$	−5.02874	−0.188064
$716$	3.76401	0.140668
$717$	−7.30046	−0.272641
$718$	−10.0166	−0.373817
$719$	−34.7415	−1.29564	−0.647820	−	0.761794i	$-0.724319\pi$
$719$	−34.7415	−1.29564	−0.647820	+	0.761794i	$0.724319\pi$
$720$	−0.517376	−0.0192815
$721$	13.0121	0.484595
$722$	1.00000	0.0372161
$723$	−38.3460	−1.42610
$724$	2.08026	0.0773121
$725$	13.8163	0.513124
$726$	−0.573221	−0.0212742
$727$	−15.8037	−0.586127	−0.293064	−	0.956093i	$-0.594675\pi$
$727$	−15.8037	−0.586127	−0.293064	+	0.956093i	$0.594675\pi$
$728$	7.37876	0.273475
$729$	27.2656	1.00984
$730$	−3.32224	−0.122962
$731$	−17.3786	−0.642769
$732$	18.6811	0.690473
$733$	31.6970	1.17075	0.585377	−	0.810761i	$-0.300947\pi$
$733$	31.6970	1.17075	0.585377	+	0.810761i	$0.300947\pi$
$734$	23.9538	0.884149
$735$	1.44865	0.0534341
$736$	5.14828	0.189768
$737$	46.1268	1.69910
$738$	0.0149963	0.000552022 0
$739$	−36.2746	−1.33438	−0.667192	−	0.744886i	$-0.732504\pi$
$739$	−36.2746	−1.33438	−0.667192	+	0.744886i	$0.732504\pi$
$740$	2.53137	0.0930550
$741$	4.67166	0.171618
$742$	−11.1446	−0.409132
$743$	3.32111	0.121840	0.0609199	−	0.998143i	$-0.480597\pi$
$743$	3.32111	0.121840	0.0609199	+	0.998143i	$0.480597\pi$
$744$	−2.59366	−0.0950882
$745$	−0.673919	−0.0246905
$746$	33.3367	1.22054
$747$	7.40436	0.270911
$748$	−26.0342	−0.951906
$749$	−41.4271	−1.51371
$750$	5.57503	0.203571
$751$	23.2551	0.848590	0.424295	−	0.905524i	$-0.360522\pi$
$751$	23.2551	0.848590	0.424295	+	0.905524i	$0.360522\pi$
$752$	−3.21044	−0.117073
$753$	−33.0377	−1.20396
$754$	10.0297	0.365262
$755$	3.90598	0.142153
$756$	−11.8765	−0.431946
$757$	13.4991	0.490633	0.245317	−	0.969443i	$-0.421108\pi$
$757$	13.4991	0.490633	0.245317	+	0.969443i	$0.421108\pi$
$758$	−12.9365	−0.469873
$759$	−23.2416	−0.843618
$760$	0.425182	0.0154230
$761$	−4.84161	−0.175508	−0.0877541	−	0.996142i	$-0.527969\pi$
$761$	−4.84161	−0.175508	−0.0877541	+	0.996142i	$0.527969\pi$
$762$	−17.7010	−0.641240
$763$	−28.0384	−1.01506
$764$	−6.55713	−0.237229
$765$	3.98420	0.144049
$766$	−3.13910	−0.113420
$767$	26.9954	0.974746
$768$	−1.33535	−0.0481854
$769$	−47.3707	−1.70823	−0.854115	−	0.520084i	$-0.825901\pi$
$769$	−47.3707	−1.70823	−0.854115	+	0.520084i	$0.825901\pi$
$770$	−3.03174	−0.109256
$771$	−32.9407	−1.18633
$772$	−16.0487	−0.577604
$773$	−10.4475	−0.375771	−0.187885	−	0.982191i	$-0.560163\pi$
$773$	−10.4475	−0.375771	−0.187885	+	0.982191i	$0.560163\pi$
$774$	−2.74606	−0.0987050
$775$	−9.36039	−0.336235
$776$	17.3111	0.621432
$777$	16.7681	0.601553
$778$	0.721942	0.0258829
$779$	−0.0123240	−0.000441555 0
$780$	1.98630	0.0711211
$781$	47.4938	1.69946
$782$	−39.6458	−1.41773
$783$	−16.1435	−0.576920
$784$	−2.55148	−0.0911242
$785$	0.153708	0.00548607
$786$	11.3777	0.405827
$787$	−43.6165	−1.55476	−0.777381	−	0.629031i	$-0.783452\pi$
$787$	−43.6165	−1.55476	−0.777381	+	0.629031i	$0.783452\pi$
$788$	−6.44975	−0.229763
$789$	−34.1579	−1.21605
$790$	−0.413440	−0.0147095
$791$	−5.56560	−0.197890
$792$	−4.11378	−0.146177
$793$	48.9420	1.73798
$794$	8.10631	0.287682
$795$	−3.00004	−0.106401
$796$	2.97751	0.105535
$797$	1.33962	0.0474518	0.0237259	−	0.999719i	$-0.492447\pi$
$797$	1.33962	0.0474518	0.0237259	+	0.999719i	$0.492447\pi$
$798$	2.81646	0.0997016
$799$	24.7230	0.874636
$800$	−4.81922	−0.170385
$801$	−3.62136	−0.127954
$802$	−22.9854	−0.811642
$803$	−26.4159	−0.932198
$804$	−18.2196	−0.642557
$805$	−4.61684	−0.162722
$806$	−6.79505	−0.239345
$807$	35.7658	1.25901
$808$	11.8730	0.417690
$809$	26.5494	0.933428	0.466714	−	0.884408i	$-0.345438\pi$
$809$	26.5494	0.933428	0.466714	+	0.884408i	$0.345438\pi$
$810$	−1.64495	−0.0577976
$811$	−27.1450	−0.953191	−0.476596	−	0.879123i	$-0.658129\pi$
$811$	−27.1450	−0.953191	−0.476596	+	0.879123i	$0.658129\pi$
$812$	6.04675	0.212199
$813$	−10.3393	−0.362614
$814$	20.1275	0.705469
$815$	−1.69187	−0.0592636
$816$	10.2833	0.359987
$817$	2.25672	0.0789527
$818$	14.0331	0.490656
$819$	−8.97873	−0.313742
$820$	−0.00523996	−0.000182987 0
$821$	16.5035	0.575975	0.287987	−	0.957634i	$-0.407014\pi$
$821$	16.5035	0.575975	0.287987	+	0.957634i	$0.407014\pi$
$822$	−21.7549	−0.758791
$823$	−22.1005	−0.770376	−0.385188	−	0.922838i	$-0.625863\pi$
$823$	−22.1005	−0.770376	−0.385188	+	0.922838i	$0.625863\pi$
$824$	−6.16934	−0.214919
$825$	21.7561	0.757451
$826$	16.2750	0.566281
$827$	−21.8184	−0.758701	−0.379351	−	0.925253i	$-0.623853\pi$
$827$	−21.8184	−0.758701	−0.379351	+	0.925253i	$0.623853\pi$
$828$	−6.26460	−0.217710
$829$	37.9232	1.31713	0.658564	−	0.752524i	$-0.271164\pi$
$829$	37.9232	1.31713	0.658564	+	0.752524i	$0.271164\pi$
$830$	−2.58720	−0.0898031
$831$	7.36643	0.255539
$832$	−3.49845	−0.121287
$833$	19.6484	0.680777
$834$	−0.176174	−0.00610041
$835$	1.98709	0.0687661
$836$	3.38072	0.116925
$837$	10.9370	0.378039
$838$	9.93326	0.343139
$839$	14.3247	0.494544	0.247272	−	0.968946i	$-0.420466\pi$
$839$	14.3247	0.494544	0.247272	+	0.968946i	$0.420466\pi$
$840$	1.19751	0.0413179
$841$	−20.7808	−0.716580
$842$	−35.0125	−1.20661
$843$	−1.49046	−0.0513343
$844$	1.00000	0.0344214
$845$	−0.323505	−0.0111289
$846$	3.90658	0.134311
$847$	−0.905386	−0.0311094
$848$	5.28393	0.181451
$849$	25.8917	0.888599
$850$	37.1118	1.27293
$851$	30.6509	1.05070
$852$	−18.7596	−0.642694
$853$	33.2755	1.13933	0.569666	−	0.821876i	$-0.307072\pi$
$853$	33.2755	1.13933	0.569666	+	0.821876i	$0.307072\pi$
$854$	29.5063	1.00968
$855$	−0.517376	−0.0176939
$856$	19.6416	0.671335
$857$	−7.84486	−0.267975	−0.133988	−	0.990983i	$-0.542778\pi$
$857$	−7.84486	−0.267975	−0.133988	+	0.990983i	$0.542778\pi$
$858$	15.7936	0.539184
$859$	10.5196	0.358923	0.179461	−	0.983765i	$-0.442565\pi$
$859$	10.5196	0.358923	0.179461	+	0.983765i	$0.442565\pi$
$860$	0.959517	0.0327193
$861$	−0.0347102	−0.00118292
$862$	−14.3281	−0.488018
$863$	−49.5403	−1.68637	−0.843187	−	0.537621i	$-0.819323\pi$
$863$	−49.5403	−1.68637	−0.843187	+	0.537621i	$0.819323\pi$
$864$	5.63096	0.191569
$865$	−1.93168	−0.0656789
$866$	−3.90638	−0.132744
$867$	−56.4884	−1.91845
$868$	−4.09661	−0.139048
$869$	−3.28735	−0.111516
$870$	1.62774	0.0551855
$871$	−47.7331	−1.61737
$872$	13.2937	0.450180
$873$	−21.0647	−0.712934
$874$	5.14828	0.174143
$875$	8.80561	0.297684
$876$	10.4340	0.352534
$877$	−5.36479	−0.181156	−0.0905780	−	0.995889i	$-0.528871\pi$
$877$	−5.36479	−0.181156	−0.0905780	+	0.995889i	$0.528871\pi$
$878$	15.1906	0.512657
$879$	25.4043	0.856867
$880$	1.43742	0.0484554
$881$	14.4550	0.487002	0.243501	−	0.969901i	$-0.421704\pi$
$881$	14.4550	0.487002	0.243501	+	0.969901i	$0.421704\pi$
$882$	3.10473	0.104542
$883$	−36.2341	−1.21937	−0.609687	−	0.792643i	$-0.708705\pi$
$883$	−36.2341	−1.21937	−0.609687	+	0.792643i	$0.708705\pi$
$884$	26.9408	0.906118
$885$	4.38111	0.147269
$886$	9.41748	0.316386
$887$	−36.0850	−1.21162	−0.605808	−	0.795611i	$-0.707150\pi$
$887$	−36.0850	−1.21162	−0.605808	+	0.795611i	$0.707150\pi$
$888$	−7.95018	−0.266790
$889$	−27.9583	−0.937690
$890$	1.26536	0.0424150
$891$	−13.0794	−0.438175
$892$	−2.11233	−0.0707261
$893$	−3.21044	−0.107433
$894$	2.11655	0.0707880
$895$	1.60039	0.0534951
$896$	−2.10915	−0.0704618
$897$	24.0510	0.803040
$898$	−1.05432	−0.0351830
$899$	−5.56842	−0.185717
$900$	5.86419	0.195473
$901$	−40.6905	−1.35560
$902$	−0.0416641	−0.00138726
$903$	6.35597	0.211513
$904$	2.63879	0.0877648
$905$	0.884487	0.0294013
$906$	−12.2674	−0.407556
$907$	49.5773	1.64619	0.823094	−	0.567905i	$-0.192246\pi$
$907$	49.5773	1.64619	0.823094	+	0.567905i	$0.192246\pi$
$908$	−23.0955	−0.766450
$909$	−14.4475	−0.479192
$910$	3.13731	0.104001
$911$	22.6759	0.751287	0.375644	−	0.926764i	$-0.377422\pi$
$911$	22.6759	0.751287	0.375644	+	0.926764i	$0.377422\pi$
$912$	−1.33535	−0.0442179
$913$	−20.5715	−0.680816
$914$	−33.6213	−1.11209
$915$	7.94286	0.262583
$916$	−3.75494	−0.124067
$917$	17.9707	0.593444
$918$	−43.3629	−1.43119
$919$	−36.7612	−1.21264	−0.606320	−	0.795221i	$-0.707355\pi$
$919$	−36.7612	−1.21264	−0.606320	+	0.795221i	$0.707355\pi$
$920$	2.18895	0.0721677
$921$	−21.4241	−0.705947
$922$	22.4758	0.740202
$923$	−49.1477	−1.61772
$924$	9.52166	0.313240
$925$	−28.6918	−0.943381
$926$	−24.8805	−0.817625
$927$	7.50706	0.246564
$928$	−2.86691	−0.0941110
$929$	8.22082	0.269716	0.134858	−	0.990865i	$-0.456942\pi$
$929$	8.22082	0.269716	0.134858	+	0.990865i	$0.456942\pi$
$930$	−1.10278	−0.0361615
$931$	−2.55148	−0.0836213
$932$	11.9387	0.391066
$933$	−23.7694	−0.778176
$934$	24.0093	0.785608
$935$	−11.0693	−0.362004
$936$	4.25703	0.139145
$937$	18.9263	0.618297	0.309148	−	0.951014i	$-0.399956\pi$
$937$	18.9263	0.618297	0.309148	+	0.951014i	$0.399956\pi$
$938$	−28.7774	−0.939616
$939$	−26.2292	−0.855958
$940$	−1.36502	−0.0445221
$941$	53.5589	1.74597	0.872985	−	0.487747i	$-0.162181\pi$
$941$	53.5589	1.74597	0.872985	+	0.487747i	$0.162181\pi$
$942$	−0.482744	−0.0157287
$943$	−0.0634476	−0.00206614
$944$	−7.71638	−0.251147
$945$	−5.04969	−0.164266
$946$	7.62935	0.248052
$947$	35.7684	1.16232	0.581159	−	0.813790i	$-0.302599\pi$
$947$	35.7684	1.16232	0.581159	+	0.813790i	$0.302599\pi$
$948$	1.29847	0.0421725
$949$	27.3358	0.887359
$950$	−4.81922	−0.156356
$951$	−25.6770	−0.832633
$952$	16.2421	0.526411
$953$	15.6950	0.508412	0.254206	−	0.967150i	$-0.418186\pi$
$953$	15.6950	0.508412	0.254206	+	0.967150i	$0.418186\pi$
$954$	−6.42967	−0.208168
$955$	−2.78797	−0.0902167
$956$	5.46707	0.176818
$957$	12.9425	0.418373
$958$	37.8079	1.22152
$959$	−34.3613	−1.10959
$960$	−0.567767	−0.0183246
$961$	−27.2275	−0.878305
$962$	−20.8284	−0.671535
$963$	−23.9006	−0.770184
$964$	28.7160	0.924881
$965$	−6.82360	−0.219659
$966$	14.4999	0.466527
$967$	43.7028	1.40539	0.702694	−	0.711492i	$-0.251980\pi$
$967$	43.7028	1.40539	0.702694	+	0.711492i	$0.251980\pi$
$968$	0.429266	0.0137971
$969$	10.2833	0.330346
$970$	7.36036	0.236327
$971$	−34.4863	−1.10672	−0.553360	−	0.832942i	$-0.686655\pi$
$971$	−34.4863	−1.10672	−0.553360	+	0.832942i	$0.686655\pi$
$972$	−11.7267	−0.376133
$973$	−0.278262	−0.00892067
$974$	−4.73970	−0.151870
$975$	−22.5138	−0.721017
$976$	−13.9896	−0.447797
$977$	58.4875	1.87118	0.935591	−	0.353086i	$-0.114868\pi$
$977$	58.4875	1.87118	0.935591	+	0.353086i	$0.114868\pi$
$978$	5.31359	0.169910
$979$	10.0612	0.321557
$980$	−1.08484	−0.0346540
$981$	−16.1762	−0.516466
$982$	−29.3737	−0.937353
$983$	14.0377	0.447733	0.223866	−	0.974620i	$-0.428132\pi$
$983$	14.0377	0.447733	0.223866	+	0.974620i	$0.428132\pi$
$984$	0.0164569	0.000524628 0
$985$	−2.74232	−0.0873775
$986$	22.0775	0.703091
$987$	−9.04209	−0.287813
$988$	−3.49845	−0.111300
$989$	11.6182	0.369438
$990$	−1.74910	−0.0555901
$991$	9.73602	0.309275	0.154637	−	0.987971i	$-0.450579\pi$
$991$	9.73602	0.309275	0.154637	+	0.987971i	$0.450579\pi$
$992$	1.94230	0.0616682
$993$	9.77512	0.310204
$994$	−29.6303	−0.939815
$995$	1.26598	0.0401343
$996$	8.12553	0.257467
$997$	−41.8879	−1.32660	−0.663301	−	0.748353i	$-0.730845\pi$
$997$	−41.8879	−1.32660	−0.663301	+	0.748353i	$0.730845\pi$
$998$	29.6438	0.938358
$999$	33.5246	1.06067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.k.1.14	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.k.1.14	✓	49	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.33535 q^{3} +1.00000 q^{4} +0.425182 q^{5} -1.33535 q^{6} -2.10915 q^{7} +1.00000 q^{8} -1.21683 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.33535 q^{3} +1.00000 q^{4} +0.425182 q^{5} -1.33535 q^{6} -2.10915 q^{7} +1.00000 q^{8} -1.21683 q^{9} +0.425182 q^{10} +3.38072 q^{11} -1.33535 q^{12} -3.49845 q^{13} -2.10915 q^{14} -0.567767 q^{15} +1.00000 q^{16} -7.70079 q^{17} -1.21683 q^{18} +1.00000 q^{19} +0.425182 q^{20} +2.81646 q^{21} +3.38072 q^{22} +5.14828 q^{23} -1.33535 q^{24} -4.81922 q^{25} -3.49845 q^{26} +5.63096 q^{27} -2.10915 q^{28} -2.86691 q^{29} -0.567767 q^{30} +1.94230 q^{31} +1.00000 q^{32} -4.51445 q^{33} -7.70079 q^{34} -0.896773 q^{35} -1.21683 q^{36} +5.95362 q^{37} +1.00000 q^{38} +4.67166 q^{39} +0.425182 q^{40} -0.0123240 q^{41} +2.81646 q^{42} +2.25672 q^{43} +3.38072 q^{44} -0.517376 q^{45} +5.14828 q^{46} -3.21044 q^{47} -1.33535 q^{48} -2.55148 q^{49} -4.81922 q^{50} +10.2833 q^{51} -3.49845 q^{52} +5.28393 q^{53} +5.63096 q^{54} +1.43742 q^{55} -2.10915 q^{56} -1.33535 q^{57} -2.86691 q^{58} -7.71638 q^{59} -0.567767 q^{60} -13.9896 q^{61} +1.94230 q^{62} +2.56649 q^{63} +1.00000 q^{64} -1.48748 q^{65} -4.51445 q^{66} +13.6441 q^{67} -7.70079 q^{68} -6.87476 q^{69} -0.896773 q^{70} +14.0484 q^{71} -1.21683 q^{72} -7.81370 q^{73} +5.95362 q^{74} +6.43536 q^{75} +1.00000 q^{76} -7.13045 q^{77} +4.67166 q^{78} -0.972383 q^{79} +0.425182 q^{80} -3.86881 q^{81} -0.0123240 q^{82} -6.08493 q^{83} +2.81646 q^{84} -3.27424 q^{85} +2.25672 q^{86} +3.82834 q^{87} +3.38072 q^{88} +2.97605 q^{89} -0.517376 q^{90} +7.37876 q^{91} +5.14828 q^{92} -2.59366 q^{93} -3.21044 q^{94} +0.425182 q^{95} -1.33535 q^{96} +17.3111 q^{97} -2.55148 q^{98} -4.11378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9 + 17 * q^10 + 21 * q^11 + 13 * q^12 + 13 * q^13 + 22 * q^14 + 8 * q^15 + 49 * q^16 + 24 * q^17 + 66 * q^18 + 49 * q^19 + 17 * q^20 + 6 * q^21 + 21 * q^22 + 22 * q^23 + 13 * q^24 + 96 * q^25 + 13 * q^26 + 31 * q^27 + 22 * q^28 + 33 * q^29 + 8 * q^30 + 21 * q^31 + 49 * q^32 + 20 * q^33 + 24 * q^34 + 18 * q^35 + 66 * q^36 + 48 * q^37 + 49 * q^38 + 4 * q^39 + 17 * q^40 + 37 * q^41 + 6 * q^42 + 43 * q^43 + 21 * q^44 + 47 * q^45 + 22 * q^46 + 7 * q^47 + 13 * q^48 + 87 * q^49 + 96 * q^50 + 12 * q^51 + 13 * q^52 + 23 * q^53 + 31 * q^54 + 31 * q^55 + 22 * q^56 + 13 * q^57 + 33 * q^58 + 37 * q^59 + 8 * q^60 + 61 * q^61 + 21 * q^62 + 45 * q^63 + 49 * q^64 + 36 * q^65 + 20 * q^66 + 43 * q^67 + 24 * q^68 + 18 * q^69 + 18 * q^70 + 14 * q^71 + 66 * q^72 + 90 * q^73 + 48 * q^74 + 53 * q^75 + 49 * q^76 + 46 * q^77 + 4 * q^78 + 16 * q^79 + 17 * q^80 + 97 * q^81 + 37 * q^82 + 11 * q^83 + 6 * q^84 + 88 * q^85 + 43 * q^86 - 35 * q^87 + 21 * q^88 + 46 * q^89 + 47 * q^90 + 27 * q^91 + 22 * q^92 + 9 * q^93 + 7 * q^94 + 17 * q^95 + 13 * q^96 + 34 * q^97 + 87 * q^98 + 84 * q^99

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