LMFDB - Embedded newform 8018.2.a.d.1.19

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:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.677734 q^{3} +1.00000 q^{4} -4.37664 q^{5} +0.677734 q^{6} -1.03965 q^{7} +1.00000 q^{8} -2.54068 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.677734 q^{3} +1.00000 q^{4} -4.37664 q^{5} +0.677734 q^{6} -1.03965 q^{7} +1.00000 q^{8} -2.54068 q^{9} -4.37664 q^{10} +1.08793 q^{11} +0.677734 q^{12} +1.73790 q^{13} -1.03965 q^{14} -2.96620 q^{15} +1.00000 q^{16} +3.23599 q^{17} -2.54068 q^{18} +1.00000 q^{19} -4.37664 q^{20} -0.704609 q^{21} +1.08793 q^{22} +0.112769 q^{23} +0.677734 q^{24} +14.1550 q^{25} +1.73790 q^{26} -3.75510 q^{27} -1.03965 q^{28} +3.19669 q^{29} -2.96620 q^{30} -0.880743 q^{31} +1.00000 q^{32} +0.737328 q^{33} +3.23599 q^{34} +4.55020 q^{35} -2.54068 q^{36} -5.39162 q^{37} +1.00000 q^{38} +1.17783 q^{39} -4.37664 q^{40} -3.58857 q^{41} -0.704609 q^{42} +4.67245 q^{43} +1.08793 q^{44} +11.1196 q^{45} +0.112769 q^{46} +11.3703 q^{47} +0.677734 q^{48} -5.91912 q^{49} +14.1550 q^{50} +2.19314 q^{51} +1.73790 q^{52} +6.66703 q^{53} -3.75510 q^{54} -4.76149 q^{55} -1.03965 q^{56} +0.677734 q^{57} +3.19669 q^{58} -6.07647 q^{59} -2.96620 q^{60} -3.81434 q^{61} -0.880743 q^{62} +2.64142 q^{63} +1.00000 q^{64} -7.60617 q^{65} +0.737328 q^{66} -11.5399 q^{67} +3.23599 q^{68} +0.0764274 q^{69} +4.55020 q^{70} -8.52973 q^{71} -2.54068 q^{72} -3.18541 q^{73} -5.39162 q^{74} +9.59333 q^{75} +1.00000 q^{76} -1.13107 q^{77} +1.17783 q^{78} -9.57466 q^{79} -4.37664 q^{80} +5.07707 q^{81} -3.58857 q^{82} +12.4902 q^{83} -0.704609 q^{84} -14.1628 q^{85} +4.67245 q^{86} +2.16650 q^{87} +1.08793 q^{88} -12.6888 q^{89} +11.1196 q^{90} -1.80681 q^{91} +0.112769 q^{92} -0.596909 q^{93} +11.3703 q^{94} -4.37664 q^{95} +0.677734 q^{96} +9.17511 q^{97} -5.91912 q^{98} -2.76408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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
$3$	0.677734	0.391290	0.195645	−	0.980675i	$-0.437320\pi$
$3$	0.677734	0.391290	0.195645	+	0.980675i	$0.437320\pi$
$4$	1.00000	0.500000
$5$	−4.37664	−1.95729	−0.978647	−	0.205546i	$-0.934103\pi$
$5$	−4.37664	−1.95729	−0.978647	+	0.205546i	$0.934103\pi$
$6$	0.677734	0.276684
$7$	−1.03965	−0.392952	−0.196476	−	0.980509i	$-0.562950\pi$
$7$	−1.03965	−0.392952	−0.196476	+	0.980509i	$0.562950\pi$
$8$	1.00000	0.353553
$9$	−2.54068	−0.846892
$10$	−4.37664	−1.38402
$11$	1.08793	0.328024	0.164012	−	0.986458i	$-0.447556\pi$
$11$	1.08793	0.328024	0.164012	+	0.986458i	$0.447556\pi$
$12$	0.677734	0.195645
$13$	1.73790	0.482007	0.241003	−	0.970524i	$-0.422524\pi$
$13$	1.73790	0.482007	0.241003	+	0.970524i	$0.422524\pi$
$14$	−1.03965	−0.277859
$15$	−2.96620	−0.765869
$16$	1.00000	0.250000
$17$	3.23599	0.784844	0.392422	−	0.919785i	$-0.371637\pi$
$17$	3.23599	0.784844	0.392422	+	0.919785i	$0.371637\pi$
$18$	−2.54068	−0.598843
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−4.37664	−0.978647
$21$	−0.704609	−0.153758
$22$	1.08793	0.231948
$23$	0.112769	0.0235140	0.0117570	−	0.999931i	$-0.496258\pi$
$23$	0.112769	0.0235140	0.0117570	+	0.999931i	$0.496258\pi$
$24$	0.677734	0.138342
$25$	14.1550	2.83100
$26$	1.73790	0.340830
$27$	−3.75510	−0.722670
$28$	−1.03965	−0.196476
$29$	3.19669	0.593610	0.296805	−	0.954938i	$-0.404079\pi$
$29$	3.19669	0.593610	0.296805	+	0.954938i	$0.404079\pi$
$30$	−2.96620	−0.541551
$31$	−0.880743	−0.158186	−0.0790930	−	0.996867i	$-0.525202\pi$
$31$	−0.880743	−0.158186	−0.0790930	+	0.996867i	$0.525202\pi$
$32$	1.00000	0.176777
$33$	0.737328	0.128352
$34$	3.23599	0.554969
$35$	4.55020	0.769123
$36$	−2.54068	−0.423446
$37$	−5.39162	−0.886376	−0.443188	−	0.896429i	$-0.646153\pi$
$37$	−5.39162	−0.886376	−0.443188	+	0.896429i	$0.646153\pi$
$38$	1.00000	0.162221
$39$	1.17783	0.188604
$40$	−4.37664	−0.692008
$41$	−3.58857	−0.560440	−0.280220	−	0.959936i	$-0.590407\pi$
$41$	−3.58857	−0.560440	−0.280220	+	0.959936i	$0.590407\pi$
$42$	−0.704609	−0.108723
$43$	4.67245	0.712542	0.356271	−	0.934383i	$-0.384048\pi$
$43$	4.67245	0.712542	0.356271	+	0.934383i	$0.384048\pi$
$44$	1.08793	0.164012
$45$	11.1196	1.65762
$46$	0.112769	0.0166269
$47$	11.3703	1.65853	0.829264	−	0.558856i	$-0.188760\pi$
$47$	11.3703	1.65853	0.829264	+	0.558856i	$0.188760\pi$
$48$	0.677734	0.0978225
$49$	−5.91912	−0.845589
$50$	14.1550	2.00182
$51$	2.19314	0.307101
$52$	1.73790	0.241003
$53$	6.66703	0.915786	0.457893	−	0.889007i	$-0.348604\pi$
$53$	6.66703	0.915786	0.457893	+	0.889007i	$0.348604\pi$
$54$	−3.75510	−0.511005
$55$	−4.76149	−0.642039
$56$	−1.03965	−0.138930
$57$	0.677734	0.0897680
$58$	3.19669	0.419745
$59$	−6.07647	−0.791090	−0.395545	−	0.918447i	$-0.629444\pi$
$59$	−6.07647	−0.791090	−0.395545	+	0.918447i	$0.629444\pi$
$60$	−2.96620	−0.382935
$61$	−3.81434	−0.488376	−0.244188	−	0.969728i	$-0.578521\pi$
$61$	−3.81434	−0.488376	−0.244188	+	0.969728i	$0.578521\pi$
$62$	−0.880743	−0.111854
$63$	2.64142	0.332788
$64$	1.00000	0.125000
$65$	−7.60617	−0.943429
$66$	0.737328	0.0907588
$67$	−11.5399	−1.40982	−0.704909	−	0.709298i	$-0.749012\pi$
$67$	−11.5399	−1.40982	−0.704909	+	0.709298i	$0.749012\pi$
$68$	3.23599	0.392422
$69$	0.0764274	0.00920077
$70$	4.55020	0.543852
$71$	−8.52973	−1.01229	−0.506146	−	0.862448i	$-0.668930\pi$
$71$	−8.52973	−1.01229	−0.506146	+	0.862448i	$0.668930\pi$
$72$	−2.54068	−0.299422
$73$	−3.18541	−0.372824	−0.186412	−	0.982472i	$-0.559686\pi$
$73$	−3.18541	−0.372824	−0.186412	+	0.982472i	$0.559686\pi$
$74$	−5.39162	−0.626763
$75$	9.59333	1.10774
$76$	1.00000	0.114708
$77$	−1.13107	−0.128898
$78$	1.17783	0.133363
$79$	−9.57466	−1.07723	−0.538616	−	0.842551i	$-0.681053\pi$
$79$	−9.57466	−1.07723	−0.538616	+	0.842551i	$0.681053\pi$
$80$	−4.37664	−0.489324
$81$	5.07707	0.564119
$82$	−3.58857	−0.396291
$83$	12.4902	1.37098	0.685489	−	0.728083i	$-0.259589\pi$
$83$	12.4902	1.37098	0.685489	+	0.728083i	$0.259589\pi$
$84$	−0.704609	−0.0768791
$85$	−14.1628	−1.53617
$86$	4.67245	0.503843
$87$	2.16650	0.232273
$88$	1.08793	0.115974
$89$	−12.6888	−1.34501	−0.672503	−	0.740094i	$-0.734781\pi$
$89$	−12.6888	−1.34501	−0.672503	+	0.740094i	$0.734781\pi$
$90$	11.1196	1.17211
$91$	−1.80681	−0.189406
$92$	0.112769	0.0117570
$93$	−0.596909	−0.0618966
$94$	11.3703	1.17276
$95$	−4.37664	−0.449034
$96$	0.677734	0.0691709
$97$	9.17511	0.931591	0.465796	−	0.884892i	$-0.345768\pi$
$97$	9.17511	0.931591	0.465796	+	0.884892i	$0.345768\pi$
$98$	−5.91912	−0.597921
$99$	−2.76408	−0.277801
$100$	14.1550	1.41550
$101$	−14.1641	−1.40938	−0.704691	−	0.709514i	$-0.748914\pi$
$101$	−14.1641	−1.40938	−0.704691	+	0.709514i	$0.748914\pi$
$102$	2.19314	0.217154
$103$	−3.16377	−0.311736	−0.155868	−	0.987778i	$-0.549817\pi$
$103$	−3.16377	−0.311736	−0.155868	+	0.987778i	$0.549817\pi$
$104$	1.73790	0.170415
$105$	3.08382	0.300950
$106$	6.66703	0.647559
$107$	2.48968	0.240686	0.120343	−	0.992732i	$-0.461601\pi$
$107$	2.48968	0.240686	0.120343	+	0.992732i	$0.461601\pi$
$108$	−3.75510	−0.361335
$109$	7.05283	0.675539	0.337769	−	0.941229i	$-0.390328\pi$
$109$	7.05283	0.675539	0.337769	+	0.941229i	$0.390328\pi$
$110$	−4.76149	−0.453990
$111$	−3.65408	−0.346830
$112$	−1.03965	−0.0982381
$113$	−16.5892	−1.56058	−0.780291	−	0.625416i	$-0.784929\pi$
$113$	−16.5892	−1.56058	−0.780291	+	0.625416i	$0.784929\pi$
$114$	0.677734	0.0634756
$115$	−0.493550	−0.0460237
$116$	3.19669	0.296805
$117$	−4.41544	−0.408208
$118$	−6.07647	−0.559385
$119$	−3.36431	−0.308406
$120$	−2.96620	−0.270776
$121$	−9.81641	−0.892401
$122$	−3.81434	−0.345334
$123$	−2.43209	−0.219295
$124$	−0.880743	−0.0790930
$125$	−40.0682	−3.58381
$126$	2.64142	0.235317
$127$	−3.51464	−0.311874	−0.155937	−	0.987767i	$-0.549840\pi$
$127$	−3.51464	−0.311874	−0.155937	+	0.987767i	$0.549840\pi$
$128$	1.00000	0.0883883
$129$	3.16668	0.278810
$130$	−7.60617	−0.667105
$131$	−12.9808	−1.13414	−0.567070	−	0.823669i	$-0.691923\pi$
$131$	−12.9808	−1.13414	−0.567070	+	0.823669i	$0.691923\pi$
$132$	0.737328	0.0641761
$133$	−1.03965	−0.0901494
$134$	−11.5399	−0.996892
$135$	16.4348	1.41448
$136$	3.23599	0.277484
$137$	8.38749	0.716592	0.358296	−	0.933608i	$-0.383358\pi$
$137$	8.38749	0.716592	0.358296	+	0.933608i	$0.383358\pi$
$138$	0.0764274	0.00650593
$139$	−18.9541	−1.60767	−0.803834	−	0.594854i	$-0.797210\pi$
$139$	−18.9541	−1.60767	−0.803834	+	0.594854i	$0.797210\pi$
$140$	4.55020	0.384562
$141$	7.70604	0.648965
$142$	−8.52973	−0.715799
$143$	1.89072	0.158110
$144$	−2.54068	−0.211723
$145$	−13.9908	−1.16187
$146$	−3.18541	−0.263626
$147$	−4.01159	−0.330870
$148$	−5.39162	−0.443188
$149$	−15.3632	−1.25860	−0.629302	−	0.777161i	$-0.716659\pi$
$149$	−15.3632	−1.25860	−0.629302	+	0.777161i	$0.716659\pi$
$150$	9.59333	0.783292
$151$	16.1717	1.31603	0.658016	−	0.753004i	$-0.271396\pi$
$151$	16.1717	1.31603	0.658016	+	0.753004i	$0.271396\pi$
$152$	1.00000	0.0811107
$153$	−8.22162	−0.664678
$154$	−1.13107	−0.0911444
$155$	3.85470	0.309617
$156$	1.17783	0.0943021
$157$	20.0070	1.59673	0.798365	−	0.602174i	$-0.205699\pi$
$157$	20.0070	1.59673	0.798365	+	0.602174i	$0.205699\pi$
$158$	−9.57466	−0.761719
$159$	4.51847	0.358338
$160$	−4.37664	−0.346004
$161$	−0.117241	−0.00923986
$162$	5.07707	0.398892
$163$	7.50860	0.588119	0.294060	−	0.955787i	$-0.404994\pi$
$163$	7.50860	0.588119	0.294060	+	0.955787i	$0.404994\pi$
$164$	−3.58857	−0.280220
$165$	−3.22702	−0.251223
$166$	12.4902	0.969427
$167$	10.5744	0.818270	0.409135	−	0.912474i	$-0.365831\pi$
$167$	10.5744	0.818270	0.409135	+	0.912474i	$0.365831\pi$
$168$	−0.704609	−0.0543617
$169$	−9.97971	−0.767670
$170$	−14.1628	−1.08624
$171$	−2.54068	−0.194290
$172$	4.67245	0.356271
$173$	17.9144	1.36201	0.681004	−	0.732279i	$-0.261543\pi$
$173$	17.9144	1.36201	0.681004	+	0.732279i	$0.261543\pi$
$174$	2.16650	0.164242
$175$	−14.7163	−1.11245
$176$	1.08793	0.0820059
$177$	−4.11823	−0.309545
$178$	−12.6888	−0.951063
$179$	−22.4848	−1.68060	−0.840298	−	0.542124i	$-0.817620\pi$
$179$	−22.4848	−1.68060	−0.840298	+	0.542124i	$0.817620\pi$
$180$	11.1196	0.828809
$181$	1.63017	0.121169	0.0605847	−	0.998163i	$-0.480703\pi$
$181$	1.63017	0.121169	0.0605847	+	0.998163i	$0.480703\pi$
$182$	−1.80681	−0.133930
$183$	−2.58511	−0.191097
$184$	0.112769	0.00831344
$185$	23.5972	1.73490
$186$	−0.596909	−0.0437675
$187$	3.52054	0.257447
$188$	11.3703	0.829264
$189$	3.90401	0.283975
$190$	−4.37664	−0.317515
$191$	−3.20936	−0.232221	−0.116111	−	0.993236i	$-0.537043\pi$
$191$	−3.20936	−0.232221	−0.116111	+	0.993236i	$0.537043\pi$
$192$	0.677734	0.0489112
$193$	−13.6373	−0.981636	−0.490818	−	0.871262i	$-0.663302\pi$
$193$	−13.6373	−0.981636	−0.490818	+	0.871262i	$0.663302\pi$
$194$	9.17511	0.658734
$195$	−5.15496	−0.369154
$196$	−5.91912	−0.422794
$197$	−24.4141	−1.73944	−0.869718	−	0.493549i	$-0.835699\pi$
$197$	−24.4141	−1.73944	−0.869718	+	0.493549i	$0.835699\pi$
$198$	−2.76408	−0.196435
$199$	4.83687	0.342877	0.171438	−	0.985195i	$-0.445159\pi$
$199$	4.83687	0.342877	0.171438	+	0.985195i	$0.445159\pi$
$200$	14.1550	1.00091
$201$	−7.82095	−0.551647
$202$	−14.1641	−0.996584
$203$	−3.32345	−0.233260
$204$	2.19314	0.153551
$205$	15.7059	1.09695
$206$	−3.16377	−0.220430
$207$	−0.286510	−0.0199138
$208$	1.73790	0.120502
$209$	1.08793	0.0752538
$210$	3.08382	0.212804
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	6.66703	0.457893
$213$	−5.78088	−0.396100
$214$	2.48968	0.170191
$215$	−20.4496	−1.39465
$216$	−3.75510	−0.255502
$217$	0.915668	0.0621596
$218$	7.05283	0.477678
$219$	−2.15886	−0.145882
$220$	−4.76149	−0.321019
$221$	5.62383	0.378300
$222$	−3.65408	−0.245246
$223$	3.93852	0.263743	0.131871	−	0.991267i	$-0.457901\pi$
$223$	3.93852	0.263743	0.131871	+	0.991267i	$0.457901\pi$
$224$	−1.03965	−0.0694648
$225$	−35.9633	−2.39755
$226$	−16.5892	−1.10350
$227$	2.97691	0.197585	0.0987923	−	0.995108i	$-0.468502\pi$
$227$	2.97691	0.197585	0.0987923	+	0.995108i	$0.468502\pi$
$228$	0.677734	0.0448840
$229$	−24.6325	−1.62776	−0.813882	−	0.581030i	$-0.802650\pi$
$229$	−24.6325	−1.62776	−0.813882	+	0.581030i	$0.802650\pi$
$230$	−0.493550	−0.0325437
$231$	−0.766566	−0.0504363
$232$	3.19669	0.209873
$233$	3.21421	0.210570	0.105285	−	0.994442i	$-0.466424\pi$
$233$	3.21421	0.210570	0.105285	+	0.994442i	$0.466424\pi$
$234$	−4.41544	−0.288646
$235$	−49.7638	−3.24623
$236$	−6.07647	−0.395545
$237$	−6.48907	−0.421510
$238$	−3.36431	−0.218076
$239$	1.83792	0.118885	0.0594427	−	0.998232i	$-0.481068\pi$
$239$	1.83792	0.118885	0.0594427	+	0.998232i	$0.481068\pi$
$240$	−2.96620	−0.191467
$241$	2.01575	0.129846	0.0649228	−	0.997890i	$-0.479320\pi$
$241$	2.01575	0.129846	0.0649228	+	0.997890i	$0.479320\pi$
$242$	−9.81641	−0.631022
$243$	14.7062	0.943404
$244$	−3.81434	−0.244188
$245$	25.9059	1.65507
$246$	−2.43209	−0.155065
$247$	1.73790	0.110580
$248$	−0.880743	−0.0559272
$249$	8.46503	0.536449
$250$	−40.0682	−2.53414
$251$	1.53715	0.0970240	0.0485120	−	0.998823i	$-0.484552\pi$
$251$	1.53715	0.0970240	0.0485120	+	0.998823i	$0.484552\pi$
$252$	2.64142	0.166394
$253$	0.122685	0.00771313
$254$	−3.51464	−0.220528
$255$	−9.59861	−0.601088
$256$	1.00000	0.0625000
$257$	−13.8071	−0.861264	−0.430632	−	0.902528i	$-0.641709\pi$
$257$	−13.8071	−0.861264	−0.430632	+	0.902528i	$0.641709\pi$
$258$	3.16668	0.197149
$259$	5.60542	0.348304
$260$	−7.60617	−0.471714
$261$	−8.12174	−0.502723
$262$	−12.9808	−0.801958
$263$	−10.5628	−0.651330	−0.325665	−	0.945485i	$-0.605588\pi$
$263$	−10.5628	−0.651330	−0.325665	+	0.945485i	$0.605588\pi$
$264$	0.737328	0.0453794
$265$	−29.1792	−1.79246
$266$	−1.03965	−0.0637453
$267$	−8.59961	−0.526287
$268$	−11.5399	−0.704909
$269$	16.6982	1.01811	0.509055	−	0.860734i	$-0.329995\pi$
$269$	16.6982	1.01811	0.509055	+	0.860734i	$0.329995\pi$
$270$	16.4348	1.00019
$271$	−2.72534	−0.165553	−0.0827763	−	0.996568i	$-0.526379\pi$
$271$	−2.72534	−0.165553	−0.0827763	+	0.996568i	$0.526379\pi$
$272$	3.23599	0.196211
$273$	−1.22454	−0.0741125
$274$	8.38749	0.506707
$275$	15.3997	0.928636
$276$	0.0764274	0.00460039
$277$	29.0179	1.74352	0.871759	−	0.489935i	$-0.162980\pi$
$277$	29.0179	1.74352	0.871759	+	0.489935i	$0.162980\pi$
$278$	−18.9541	−1.13679
$279$	2.23768	0.133967
$280$	4.55020	0.271926
$281$	1.00727	0.0600888	0.0300444	−	0.999549i	$-0.490435\pi$
$281$	1.00727	0.0600888	0.0300444	+	0.999549i	$0.490435\pi$
$282$	7.70604	0.458888
$283$	−33.1531	−1.97075	−0.985373	−	0.170414i	$-0.945490\pi$
$283$	−33.1531	−1.97075	−0.985373	+	0.170414i	$0.945490\pi$
$284$	−8.52973	−0.506146
$285$	−2.96620	−0.175703
$286$	1.89072	0.111800
$287$	3.73087	0.220226
$288$	−2.54068	−0.149711
$289$	−6.52834	−0.384020
$290$	−13.9908	−0.821565
$291$	6.21828	0.364522
$292$	−3.18541	−0.186412
$293$	11.2238	0.655701	0.327850	−	0.944730i	$-0.393676\pi$
$293$	11.2238	0.655701	0.327850	+	0.944730i	$0.393676\pi$
$294$	−4.01159	−0.233961
$295$	26.5946	1.54840
$296$	−5.39162	−0.313381
$297$	−4.08530	−0.237053
$298$	−15.3632	−0.889967
$299$	0.195981	0.0113339
$300$	9.59333	0.553871
$301$	−4.85773	−0.279995
$302$	16.1717	0.930575
$303$	−9.59950	−0.551477
$304$	1.00000	0.0573539
$305$	16.6940	0.955896
$306$	−8.22162	−0.469999
$307$	−1.17249	−0.0669175	−0.0334588	−	0.999440i	$-0.510652\pi$
$307$	−1.17249	−0.0669175	−0.0334588	+	0.999440i	$0.510652\pi$
$308$	−1.13107	−0.0644488
$309$	−2.14419	−0.121979
$310$	3.85470	0.218932
$311$	−12.4924	−0.708377	−0.354188	−	0.935174i	$-0.615243\pi$
$311$	−12.4924	−0.708377	−0.354188	+	0.935174i	$0.615243\pi$
$312$	1.17783	0.0666817
$313$	6.41799	0.362766	0.181383	−	0.983412i	$-0.441943\pi$
$313$	6.41799	0.362766	0.181383	+	0.983412i	$0.441943\pi$
$314$	20.0070	1.12906
$315$	−11.5606	−0.651365
$316$	−9.57466	−0.538616
$317$	16.0619	0.902129	0.451064	−	0.892491i	$-0.351044\pi$
$317$	16.0619	0.902129	0.451064	+	0.892491i	$0.351044\pi$
$318$	4.51847	0.253383
$319$	3.47777	0.194718
$320$	−4.37664	−0.244662
$321$	1.68734	0.0941780
$322$	−0.117241	−0.00653357
$323$	3.23599	0.180056
$324$	5.07707	0.282059
$325$	24.6000	1.36456
$326$	7.50860	0.415863
$327$	4.77994	0.264331
$328$	−3.58857	−0.198146
$329$	−11.8212	−0.651723
$330$	−3.22702	−0.177642
$331$	−29.6379	−1.62905	−0.814524	−	0.580130i	$-0.803002\pi$
$331$	−29.6379	−1.62905	−0.814524	+	0.580130i	$0.803002\pi$
$332$	12.4902	0.685489
$333$	13.6984	0.750665
$334$	10.5744	0.578604
$335$	50.5058	2.75943
$336$	−0.704609	−0.0384396
$337$	−4.45504	−0.242682	−0.121341	−	0.992611i	$-0.538719\pi$
$337$	−4.45504	−0.242682	−0.121341	+	0.992611i	$0.538719\pi$
$338$	−9.97971	−0.542824
$339$	−11.2431	−0.610640
$340$	−14.1628	−0.768086
$341$	−0.958188	−0.0518888
$342$	−2.54068	−0.137384
$343$	13.4314	0.725228
$344$	4.67245	0.251922
$345$	−0.334495	−0.0180086
$346$	17.9144	0.963086
$347$	2.94754	0.158232	0.0791162	−	0.996865i	$-0.474790\pi$
$347$	2.94754	0.158232	0.0791162	+	0.996865i	$0.474790\pi$
$348$	2.16650	0.116137
$349$	12.1898	0.652504	0.326252	−	0.945283i	$-0.394214\pi$
$349$	12.1898	0.652504	0.326252	+	0.945283i	$0.394214\pi$
$350$	−14.7163	−0.786620
$351$	−6.52599	−0.348332
$352$	1.08793	0.0579869
$353$	1.80519	0.0960807	0.0480403	−	0.998845i	$-0.484702\pi$
$353$	1.80519	0.0960807	0.0480403	+	0.998845i	$0.484702\pi$
$354$	−4.11823	−0.218882
$355$	37.3316	1.98135
$356$	−12.6888	−0.672503
$357$	−2.28011	−0.120676
$358$	−22.4848	−1.18836
$359$	3.38306	0.178551	0.0892754	−	0.996007i	$-0.471545\pi$
$359$	3.38306	0.178551	0.0892754	+	0.996007i	$0.471545\pi$
$360$	11.1196	0.586056
$361$	1.00000	0.0526316
$362$	1.63017	0.0856798
$363$	−6.65291	−0.349187
$364$	−1.80681	−0.0947028
$365$	13.9414	0.729726
$366$	−2.58511	−0.135126
$367$	−30.5652	−1.59549	−0.797746	−	0.602993i	$-0.793975\pi$
$367$	−30.5652	−1.59549	−0.797746	+	0.602993i	$0.793975\pi$
$368$	0.112769	0.00587849
$369$	9.11739	0.474632
$370$	23.5972	1.22676
$371$	−6.93140	−0.359860
$372$	−0.596909	−0.0309483
$373$	−19.5072	−1.01004	−0.505022	−	0.863106i	$-0.668516\pi$
$373$	−19.5072	−1.01004	−0.505022	+	0.863106i	$0.668516\pi$
$374$	3.52054	0.182043
$375$	−27.1556	−1.40231
$376$	11.3703	0.586378
$377$	5.55552	0.286124
$378$	3.90401	0.200801
$379$	−25.9549	−1.33321	−0.666607	−	0.745409i	$-0.732254\pi$
$379$	−25.9549	−1.33321	−0.666607	+	0.745409i	$0.732254\pi$
$380$	−4.37664	−0.224517
$381$	−2.38199	−0.122033
$382$	−3.20936	−0.164205
$383$	30.3912	1.55292	0.776460	−	0.630167i	$-0.217013\pi$
$383$	30.3912	1.55292	0.776460	+	0.630167i	$0.217013\pi$
$384$	0.677734	0.0345855
$385$	4.95030	0.252291
$386$	−13.6373	−0.694122
$387$	−11.8712	−0.603446
$388$	9.17511	0.465796
$389$	10.7419	0.544636	0.272318	−	0.962207i	$-0.412210\pi$
$389$	10.7419	0.544636	0.272318	+	0.962207i	$0.412210\pi$
$390$	−5.15496	−0.261031
$391$	0.364920	0.0184548
$392$	−5.91912	−0.298961
$393$	−8.79755	−0.443778
$394$	−24.4141	−1.22997
$395$	41.9049	2.10846
$396$	−2.76408	−0.138900
$397$	−9.73475	−0.488573	−0.244287	−	0.969703i	$-0.578554\pi$
$397$	−9.73475	−0.488573	−0.244287	+	0.969703i	$0.578554\pi$
$398$	4.83687	0.242451
$399$	−0.704609	−0.0352746
$400$	14.1550	0.707751
$401$	8.63370	0.431146	0.215573	−	0.976488i	$-0.430838\pi$
$401$	8.63370	0.431146	0.215573	+	0.976488i	$0.430838\pi$
$402$	−7.82095	−0.390074
$403$	−1.53064	−0.0762467
$404$	−14.1641	−0.704691
$405$	−22.2205	−1.10415
$406$	−3.32345	−0.164940
$407$	−5.86571	−0.290752
$408$	2.19314	0.108577
$409$	0.907335	0.0448648	0.0224324	−	0.999748i	$-0.492859\pi$
$409$	0.907335	0.0448648	0.0224324	+	0.999748i	$0.492859\pi$
$410$	15.7059	0.775658
$411$	5.68449	0.280395
$412$	−3.16377	−0.155868
$413$	6.31743	0.310860
$414$	−0.286510	−0.0140812
$415$	−54.6651	−2.68341
$416$	1.73790	0.0852075
$417$	−12.8459	−0.629064
$418$	1.08793	0.0532125
$419$	−19.6319	−0.959080	−0.479540	−	0.877520i	$-0.659196\pi$
$419$	−19.6319	−0.959080	−0.479540	+	0.877520i	$0.659196\pi$
$420$	3.08382	0.150475
$421$	−27.2987	−1.33046	−0.665229	−	0.746640i	$-0.731666\pi$
$421$	−27.2987	−1.33046	−0.665229	+	0.746640i	$0.731666\pi$
$422$	−1.00000	−0.0486792
$423$	−28.8883	−1.40460
$424$	6.66703	0.323779
$425$	45.8055	2.22190
$426$	−5.78088	−0.280085
$427$	3.96559	0.191908
$428$	2.48968	0.120343
$429$	1.28140	0.0618667
$430$	−20.4496	−0.986169
$431$	6.94829	0.334687	0.167344	−	0.985899i	$-0.446481\pi$
$431$	6.94829	0.334687	0.167344	+	0.985899i	$0.446481\pi$
$432$	−3.75510	−0.180668
$433$	−28.7277	−1.38056	−0.690282	−	0.723540i	$-0.742514\pi$
$433$	−28.7277	−1.38056	−0.690282	+	0.723540i	$0.742514\pi$
$434$	0.915668	0.0439535
$435$	−9.48201	−0.454627
$436$	7.05283	0.337769
$437$	0.112769	0.00539447
$438$	−2.15886	−0.103154
$439$	22.0835	1.05399	0.526993	−	0.849870i	$-0.323319\pi$
$439$	22.0835	1.05399	0.526993	+	0.849870i	$0.323319\pi$
$440$	−4.76149	−0.226995
$441$	15.0386	0.716122
$442$	5.62383	0.267498
$443$	3.42410	0.162684	0.0813420	−	0.996686i	$-0.474079\pi$
$443$	3.42410	0.162684	0.0813420	+	0.996686i	$0.474079\pi$
$444$	−3.65408	−0.173415
$445$	55.5342	2.63257
$446$	3.93852	0.186494
$447$	−10.4122	−0.492479
$448$	−1.03965	−0.0491190
$449$	−6.45014	−0.304401	−0.152200	−	0.988350i	$-0.548636\pi$
$449$	−6.45014	−0.304401	−0.152200	+	0.988350i	$0.548636\pi$
$450$	−35.9633	−1.69533
$451$	−3.90412	−0.183838
$452$	−16.5892	−0.780291
$453$	10.9601	0.514950
$454$	2.97691	0.139713
$455$	7.90778	0.370723
$456$	0.677734	0.0317378
$457$	17.0170	0.796023	0.398012	−	0.917380i	$-0.369700\pi$
$457$	17.0170	0.796023	0.398012	+	0.917380i	$0.369700\pi$
$458$	−24.6325	−1.15100
$459$	−12.1515	−0.567183
$460$	−0.493550	−0.0230119
$461$	−6.85354	−0.319201	−0.159601	−	0.987182i	$-0.551021\pi$
$461$	−6.85354	−0.319201	−0.159601	+	0.987182i	$0.551021\pi$
$462$	−0.766566	−0.0356639
$463$	−13.7414	−0.638615	−0.319308	−	0.947651i	$-0.603450\pi$
$463$	−13.7414	−0.638615	−0.319308	+	0.947651i	$0.603450\pi$
$464$	3.19669	0.148402
$465$	2.61246	0.121150
$466$	3.21421	0.148896
$467$	33.1199	1.53261	0.766303	−	0.642480i	$-0.222094\pi$
$467$	33.1199	1.53261	0.766303	+	0.642480i	$0.222094\pi$
$468$	−4.41544	−0.204104
$469$	11.9975	0.553991
$470$	−49.7638	−2.29543
$471$	13.5594	0.624784
$472$	−6.07647	−0.279692
$473$	5.08330	0.233731
$474$	−6.48907	−0.298053
$475$	14.1550	0.649477
$476$	−3.36431	−0.154203
$477$	−16.9388	−0.775572
$478$	1.83792	0.0840646
$479$	10.3502	0.472913	0.236456	−	0.971642i	$-0.424014\pi$
$479$	10.3502	0.472913	0.236456	+	0.971642i	$0.424014\pi$
$480$	−2.96620	−0.135388
$481$	−9.37009	−0.427239
$482$	2.01575	0.0918147
$483$	−0.0794580	−0.00361546
$484$	−9.81641	−0.446200
$485$	−40.1562	−1.82340
$486$	14.7062	0.667087
$487$	−8.92066	−0.404234	−0.202117	−	0.979361i	$-0.564782\pi$
$487$	−8.92066	−0.404234	−0.202117	+	0.979361i	$0.564782\pi$
$488$	−3.81434	−0.172667
$489$	5.08883	0.230125
$490$	25.9059	1.17031
$491$	26.0318	1.17480	0.587400	−	0.809297i	$-0.300152\pi$
$491$	26.0318	1.17480	0.587400	+	0.809297i	$0.300152\pi$
$492$	−2.43209	−0.109647
$493$	10.3445	0.465891
$494$	1.73790	0.0781918
$495$	12.0974	0.543738
$496$	−0.880743	−0.0395465
$497$	8.86796	0.397783
$498$	8.46503	0.379327
$499$	−4.96533	−0.222279	−0.111139	−	0.993805i	$-0.535450\pi$
$499$	−4.96533	−0.222279	−0.111139	+	0.993805i	$0.535450\pi$
$500$	−40.0682	−1.79191
$501$	7.16661	0.320181
$502$	1.53715	0.0686063
$503$	−15.5829	−0.694808	−0.347404	−	0.937716i	$-0.612937\pi$
$503$	−15.5829	−0.694808	−0.347404	+	0.937716i	$0.612937\pi$
$504$	2.64142	0.117658
$505$	61.9913	2.75858
$506$	0.122685	0.00545401
$507$	−6.76358	−0.300381
$508$	−3.51464	−0.155937
$509$	−18.7446	−0.830842	−0.415421	−	0.909629i	$-0.636366\pi$
$509$	−18.7446	−0.830842	−0.415421	+	0.909629i	$0.636366\pi$
$510$	−9.59861	−0.425033
$511$	3.31172	0.146502
$512$	1.00000	0.0441942
$513$	−3.75510	−0.165792
$514$	−13.8071	−0.609005
$515$	13.8467	0.610159
$516$	3.16668	0.139405
$517$	12.3701	0.544037
$518$	5.60542	0.246288
$519$	12.1412	0.532940
$520$	−7.60617	−0.333553
$521$	4.43158	0.194151	0.0970755	−	0.995277i	$-0.469051\pi$
$521$	4.43158	0.194151	0.0970755	+	0.995277i	$0.469051\pi$
$522$	−8.12174	−0.355479
$523$	−0.307784	−0.0134585	−0.00672923	−	0.999977i	$-0.502142\pi$
$523$	−0.307784	−0.0134585	−0.00672923	+	0.999977i	$0.502142\pi$
$524$	−12.9808	−0.567070
$525$	−9.97374	−0.435290
$526$	−10.5628	−0.460560
$527$	−2.85008	−0.124151
$528$	0.737328	0.0320881
$529$	−22.9873	−0.999447
$530$	−29.1792	−1.26746
$531$	15.4384	0.669968
$532$	−1.03965	−0.0450747
$533$	−6.23657	−0.270136
$534$	−8.59961	−0.372141
$535$	−10.8964	−0.471094
$536$	−11.5399	−0.498446
$537$	−15.2387	−0.657600
$538$	16.6982	0.719912
$539$	−6.43960	−0.277373
$540$	16.4348	0.707239
$541$	4.14272	0.178109	0.0890546	−	0.996027i	$-0.471615\pi$
$541$	4.14272	0.178109	0.0890546	+	0.996027i	$0.471615\pi$
$542$	−2.72534	−0.117063
$543$	1.10482	0.0474124
$544$	3.23599	0.138742
$545$	−30.8677	−1.32223
$546$	−1.22454	−0.0524054
$547$	−29.3319	−1.25414	−0.627070	−	0.778963i	$-0.715746\pi$
$547$	−29.3319	−1.25414	−0.627070	+	0.778963i	$0.715746\pi$
$548$	8.38749	0.358296
$549$	9.69100	0.413602
$550$	15.3997	0.656645
$551$	3.19669	0.136183
$552$	0.0764274	0.00325296
$553$	9.95433	0.423301
$554$	29.0179	1.23285
$555$	15.9926	0.678849
$556$	−18.9541	−0.803834
$557$	11.4328	0.484422	0.242211	−	0.970224i	$-0.422127\pi$
$557$	11.4328	0.484422	0.242211	+	0.970224i	$0.422127\pi$
$558$	2.23768	0.0947287
$559$	8.12025	0.343450
$560$	4.55020	0.192281
$561$	2.38599	0.100737
$562$	1.00727	0.0424892
$563$	−43.2521	−1.82286	−0.911430	−	0.411455i	$-0.865021\pi$
$563$	−43.2521	−1.82286	−0.911430	+	0.411455i	$0.865021\pi$
$564$	7.70604	0.324483
$565$	72.6051	3.05452
$566$	−33.1531	−1.39353
$567$	−5.27840	−0.221672
$568$	−8.52973	−0.357899
$569$	−24.0639	−1.00881	−0.504406	−	0.863466i	$-0.668289\pi$
$569$	−24.0639	−1.00881	−0.504406	+	0.863466i	$0.668289\pi$
$570$	−2.96620	−0.124240
$571$	8.73645	0.365609	0.182805	−	0.983149i	$-0.441482\pi$
$571$	8.73645	0.365609	0.182805	+	0.983149i	$0.441482\pi$
$572$	1.89072	0.0790548
$573$	−2.17509	−0.0908658
$574$	3.73087	0.155723
$575$	1.59625	0.0665681
$576$	−2.54068	−0.105862
$577$	34.3770	1.43113	0.715567	−	0.698544i	$-0.246169\pi$
$577$	34.3770	1.43113	0.715567	+	0.698544i	$0.246169\pi$
$578$	−6.52834	−0.271543
$579$	−9.24248	−0.384104
$580$	−13.9908	−0.580934
$581$	−12.9855	−0.538729
$582$	6.21828	0.257756
$583$	7.25327	0.300400
$584$	−3.18541	−0.131813
$585$	19.3248	0.798983
$586$	11.2238	0.463650
$587$	22.1454	0.914039	0.457020	−	0.889457i	$-0.348917\pi$
$587$	22.1454	0.914039	0.457020	+	0.889457i	$0.348917\pi$
$588$	−4.01159	−0.165435
$589$	−0.880743	−0.0362904
$590$	26.5946	1.09488
$591$	−16.5463	−0.680624
$592$	−5.39162	−0.221594
$593$	27.9209	1.14657	0.573287	−	0.819355i	$-0.305668\pi$
$593$	27.9209	1.14657	0.573287	+	0.819355i	$0.305668\pi$
$594$	−4.08530	−0.167622
$595$	14.7244	0.603642
$596$	−15.3632	−0.629302
$597$	3.27811	0.134164
$598$	0.195981	0.00801427
$599$	1.89628	0.0774798	0.0387399	−	0.999249i	$-0.487666\pi$
$599$	1.89628	0.0774798	0.0387399	+	0.999249i	$0.487666\pi$
$600$	9.59333	0.391646
$601$	−20.6199	−0.841102	−0.420551	−	0.907269i	$-0.638163\pi$
$601$	−20.6199	−0.841102	−0.420551	+	0.907269i	$0.638163\pi$
$602$	−4.85773	−0.197986
$603$	29.3190	1.19396
$604$	16.1717	0.658016
$605$	42.9629	1.74669
$606$	−9.59950	−0.389953
$607$	−28.1411	−1.14221	−0.571107	−	0.820876i	$-0.693486\pi$
$607$	−28.1411	−1.14221	−0.571107	+	0.820876i	$0.693486\pi$
$608$	1.00000	0.0405554
$609$	−2.25241	−0.0912723
$610$	16.6940	0.675920
$611$	19.7604	0.799422
$612$	−8.22162	−0.332339
$613$	1.60168	0.0646911	0.0323455	−	0.999477i	$-0.489702\pi$
$613$	1.60168	0.0646911	0.0323455	+	0.999477i	$0.489702\pi$
$614$	−1.17249	−0.0473178
$615$	10.6444	0.429224
$616$	−1.13107	−0.0455722
$617$	−22.0485	−0.887640	−0.443820	−	0.896116i	$-0.646377\pi$
$617$	−22.0485	−0.887640	−0.443820	+	0.896116i	$0.646377\pi$
$618$	−2.14419	−0.0862522
$619$	−29.7628	−1.19627	−0.598135	−	0.801396i	$-0.704091\pi$
$619$	−29.7628	−1.19627	−0.598135	+	0.801396i	$0.704091\pi$
$620$	3.85470	0.154808
$621$	−0.423459	−0.0169928
$622$	−12.4924	−0.500898
$623$	13.1919	0.528523
$624$	1.17783	0.0471511
$625$	104.589	4.18357
$626$	6.41799	0.256515
$627$	0.737328	0.0294460
$628$	20.0070	0.798365
$629$	−17.4472	−0.695667
$630$	−11.5606	−0.460584
$631$	−9.89467	−0.393901	−0.196950	−	0.980413i	$-0.563104\pi$
$631$	−9.89467	−0.393901	−0.196950	+	0.980413i	$0.563104\pi$
$632$	−9.57466	−0.380859
$633$	−0.677734	−0.0269375
$634$	16.0619	0.637901
$635$	15.3823	0.610429
$636$	4.51847	0.179169
$637$	−10.2868	−0.407579
$638$	3.47777	0.137686
$639$	21.6713	0.857303
$640$	−4.37664	−0.173002
$641$	37.3617	1.47570	0.737849	−	0.674965i	$-0.235841\pi$
$641$	37.3617	1.47570	0.737849	+	0.674965i	$0.235841\pi$
$642$	1.68734	0.0665939
$643$	−27.7726	−1.09524	−0.547622	−	0.836726i	$-0.684467\pi$
$643$	−27.7726	−1.09524	−0.547622	+	0.836726i	$0.684467\pi$
$644$	−0.117241	−0.00461993
$645$	−13.8594	−0.545714
$646$	3.23599	0.127319
$647$	−29.6180	−1.16440	−0.582202	−	0.813044i	$-0.697809\pi$
$647$	−29.6180	−1.16440	−0.582202	+	0.813044i	$0.697809\pi$
$648$	5.07707	0.199446
$649$	−6.61079	−0.259496
$650$	24.6000	0.964891
$651$	0.620579	0.0243224
$652$	7.50860	0.294060
$653$	17.4693	0.683626	0.341813	−	0.939768i	$-0.388959\pi$
$653$	17.4693	0.683626	0.341813	+	0.939768i	$0.388959\pi$
$654$	4.77994	0.186911
$655$	56.8125	2.21985
$656$	−3.58857	−0.140110
$657$	8.09309	0.315741
$658$	−11.8212	−0.460838
$659$	13.7271	0.534733	0.267367	−	0.963595i	$-0.413847\pi$
$659$	13.7271	0.534733	0.267367	+	0.963595i	$0.413847\pi$
$660$	−3.22702	−0.125612
$661$	31.9960	1.24450	0.622249	−	0.782819i	$-0.286219\pi$
$661$	31.9960	1.24450	0.622249	+	0.782819i	$0.286219\pi$
$662$	−29.6379	−1.15191
$663$	3.81146	0.148025
$664$	12.4902	0.484714
$665$	4.55020	0.176449
$666$	13.6984	0.530800
$667$	0.360487	0.0139581
$668$	10.5744	0.409135
$669$	2.66927	0.103200
$670$	50.5058	1.95121
$671$	−4.14974	−0.160199
$672$	−0.704609	−0.0271809
$673$	4.33516	0.167108	0.0835541	−	0.996503i	$-0.473373\pi$
$673$	4.33516	0.167108	0.0835541	+	0.996503i	$0.473373\pi$
$674$	−4.45504	−0.171602
$675$	−53.1535	−2.04588
$676$	−9.97971	−0.383835
$677$	30.9367	1.18899	0.594497	−	0.804098i	$-0.297351\pi$
$677$	30.9367	1.18899	0.594497	+	0.804098i	$0.297351\pi$
$678$	−11.2431	−0.431788
$679$	−9.53894	−0.366071
$680$	−14.1628	−0.543118
$681$	2.01755	0.0773128
$682$	−0.958188	−0.0366909
$683$	14.5295	0.555957	0.277978	−	0.960587i	$-0.410336\pi$
$683$	14.5295	0.555957	0.277978	+	0.960587i	$0.410336\pi$
$684$	−2.54068	−0.0971452
$685$	−36.7091	−1.40258
$686$	13.4314	0.512814
$687$	−16.6943	−0.636927
$688$	4.67245	0.178135
$689$	11.5866	0.441415
$690$	−0.334495	−0.0127340
$691$	−14.3955	−0.547632	−0.273816	−	0.961782i	$-0.588286\pi$
$691$	−14.3955	−0.547632	−0.273816	+	0.961782i	$0.588286\pi$
$692$	17.9144	0.681004
$693$	2.87369	0.109162
$694$	2.94754	0.111887
$695$	82.9554	3.14668
$696$	2.16650	0.0821210
$697$	−11.6126	−0.439858
$698$	12.1898	0.461390
$699$	2.17838	0.0823940
$700$	−14.7163	−0.556224
$701$	5.95449	0.224898	0.112449	−	0.993657i	$-0.464131\pi$
$701$	5.95449	0.224898	0.112449	+	0.993657i	$0.464131\pi$
$702$	−6.52599	−0.246308
$703$	−5.39162	−0.203349
$704$	1.08793	0.0410030
$705$	−33.7266	−1.27022
$706$	1.80519	0.0679393
$707$	14.7258	0.553820
$708$	−4.11823	−0.154773
$709$	−18.9234	−0.710682	−0.355341	−	0.934737i	$-0.615635\pi$
$709$	−18.9234	−0.710682	−0.355341	+	0.934737i	$0.615635\pi$
$710$	37.3316	1.40103
$711$	24.3261	0.912300
$712$	−12.6888	−0.475532
$713$	−0.0993205	−0.00371958
$714$	−2.28011	−0.0853310
$715$	−8.27499	−0.309467
$716$	−22.4848	−0.840298
$717$	1.24562	0.0465186
$718$	3.38306	0.126255
$719$	−9.62073	−0.358793	−0.179396	−	0.983777i	$-0.557414\pi$
$719$	−9.62073	−0.358793	−0.179396	+	0.983777i	$0.557414\pi$
$720$	11.1196	0.414404
$721$	3.28923	0.122497
$722$	1.00000	0.0372161
$723$	1.36614	0.0508073
$724$	1.63017	0.0605847
$725$	45.2491	1.68051
$726$	−6.65291	−0.246913
$727$	−43.6033	−1.61716	−0.808579	−	0.588387i	$-0.799763\pi$
$727$	−43.6033	−1.61716	−0.808579	+	0.588387i	$0.799763\pi$
$728$	−1.80681	−0.0669650
$729$	−5.26431	−0.194974
$730$	13.9414	0.515994
$731$	15.1200	0.559234
$732$	−2.58511	−0.0955483
$733$	26.9647	0.995964	0.497982	−	0.867187i	$-0.334075\pi$
$733$	26.9647	0.995964	0.497982	+	0.867187i	$0.334075\pi$
$734$	−30.5652	−1.12818
$735$	17.5573	0.647610
$736$	0.112769	0.00415672
$737$	−12.5546	−0.462454
$738$	9.11739	0.335616
$739$	−13.8465	−0.509353	−0.254677	−	0.967026i	$-0.581969\pi$
$739$	−13.8465	−0.509353	−0.254677	+	0.967026i	$0.581969\pi$
$740$	23.5972	0.867450
$741$	1.17783	0.0432688
$742$	−6.93140	−0.254460
$743$	17.1248	0.628248	0.314124	−	0.949382i	$-0.398289\pi$
$743$	17.1248	0.628248	0.314124	+	0.949382i	$0.398289\pi$
$744$	−0.596909	−0.0218838
$745$	67.2393	2.46346
$746$	−19.5072	−0.714210
$747$	−31.7336	−1.16107
$748$	3.52054	0.128724
$749$	−2.58840	−0.0945782
$750$	−27.1556	−0.991582
$751$	32.5624	1.18822	0.594109	−	0.804384i	$-0.297505\pi$
$751$	32.5624	1.18822	0.594109	+	0.804384i	$0.297505\pi$
$752$	11.3703	0.414632
$753$	1.04178	0.0379645
$754$	5.55552	0.202320
$755$	−70.7776	−2.57586
$756$	3.90401	0.141987
$757$	−25.7400	−0.935535	−0.467767	−	0.883852i	$-0.654942\pi$
$757$	−25.7400	−0.935535	−0.467767	+	0.883852i	$0.654942\pi$
$758$	−25.9549	−0.942725
$759$	0.0831477	0.00301807
$760$	−4.37664	−0.158758
$761$	11.3198	0.410344	0.205172	−	0.978726i	$-0.434225\pi$
$761$	11.3198	0.410344	0.205172	+	0.978726i	$0.434225\pi$
$762$	−2.38199	−0.0862904
$763$	−7.33250	−0.265454
$764$	−3.20936	−0.116111
$765$	35.9831	1.30097
$766$	30.3912	1.09808
$767$	−10.5603	−0.381310
$768$	0.677734	0.0244556
$769$	35.1897	1.26897	0.634487	−	0.772933i	$-0.281211\pi$
$769$	35.1897	1.26897	0.634487	+	0.772933i	$0.281211\pi$
$770$	4.95030	0.178396
$771$	−9.35754	−0.337004
$772$	−13.6373	−0.490818
$773$	15.8358	0.569576	0.284788	−	0.958591i	$-0.408077\pi$
$773$	15.8358	0.569576	0.284788	+	0.958591i	$0.408077\pi$
$774$	−11.8712	−0.426701
$775$	−12.4669	−0.447825
$776$	9.17511	0.329367
$777$	3.79898	0.136288
$778$	10.7419	0.385116
$779$	−3.58857	−0.128574
$780$	−5.15496	−0.184577
$781$	−9.27976	−0.332056
$782$	0.364920	0.0130495
$783$	−12.0039	−0.428984
$784$	−5.91912	−0.211397
$785$	−87.5634	−3.12527
$786$	−8.79755	−0.313798
$787$	−34.6096	−1.23370	−0.616849	−	0.787081i	$-0.711591\pi$
$787$	−34.6096	−1.23370	−0.616849	+	0.787081i	$0.711591\pi$
$788$	−24.4141	−0.869718
$789$	−7.15876	−0.254859
$790$	41.9049	1.49091
$791$	17.2470	0.613234
$792$	−2.76408	−0.0982174
$793$	−6.62894	−0.235400
$794$	−9.73475	−0.345473
$795$	−19.7757	−0.701373
$796$	4.83687	0.171438
$797$	22.2230	0.787179	0.393589	−	0.919286i	$-0.371233\pi$
$797$	22.2230	0.787179	0.393589	+	0.919286i	$0.371233\pi$
$798$	−0.704609	−0.0249429
$799$	36.7942	1.30169
$800$	14.1550	0.500455
$801$	32.2381	1.13908
$802$	8.63370	0.304867
$803$	−3.46550	−0.122295
$804$	−7.82095	−0.275824
$805$	0.513121	0.0180851
$806$	−1.53064	−0.0539146
$807$	11.3170	0.398376
$808$	−14.1641	−0.498292
$809$	14.4195	0.506962	0.253481	−	0.967340i	$-0.418424\pi$
$809$	14.4195	0.506962	0.253481	+	0.967340i	$0.418424\pi$
$810$	−22.2205	−0.780750
$811$	55.7753	1.95854	0.979268	−	0.202569i	$-0.0649291\pi$
$811$	55.7753	1.95854	0.979268	+	0.202569i	$0.0649291\pi$
$812$	−3.32345	−0.116630
$813$	−1.84706	−0.0647791
$814$	−5.86571	−0.205593
$815$	−32.8625	−1.15112
$816$	2.19314	0.0767754
$817$	4.67245	0.163468
$818$	0.907335	0.0317242
$819$	4.59053	0.160406
$820$	15.7059	0.548473
$821$	−52.6843	−1.83870	−0.919348	−	0.393446i	$-0.871283\pi$
$821$	−52.6843	−1.83870	−0.919348	+	0.393446i	$0.871283\pi$
$822$	5.68449	0.198269
$823$	−10.9292	−0.380969	−0.190484	−	0.981690i	$-0.561006\pi$
$823$	−10.9292	−0.380969	−0.190484	+	0.981690i	$0.561006\pi$
$824$	−3.16377	−0.110215
$825$	10.4369	0.363366
$826$	6.31743	0.219812
$827$	−28.5567	−0.993012	−0.496506	−	0.868033i	$-0.665384\pi$
$827$	−28.5567	−0.993012	−0.496506	+	0.868033i	$0.665384\pi$
$828$	−0.286510	−0.00995690
$829$	31.2443	1.08516	0.542580	−	0.840004i	$-0.317448\pi$
$829$	31.2443	1.08516	0.542580	+	0.840004i	$0.317448\pi$
$830$	−54.6651	−1.89745
$831$	19.6664	0.682221
$832$	1.73790	0.0602508
$833$	−19.1542	−0.663655
$834$	−12.8459	−0.444815
$835$	−46.2803	−1.60159
$836$	1.08793	0.0376269
$837$	3.30728	0.114316
$838$	−19.6319	−0.678172
$839$	−25.6234	−0.884616	−0.442308	−	0.896863i	$-0.645840\pi$
$839$	−25.6234	−0.884616	−0.442308	+	0.896863i	$0.645840\pi$
$840$	3.08382	0.106402
$841$	−18.7812	−0.647628
$842$	−27.2987	−0.940775
$843$	0.682662	0.0235121
$844$	−1.00000	−0.0344214
$845$	43.6776	1.50256
$846$	−28.8883	−0.993199
$847$	10.2057	0.350671
$848$	6.66703	0.228947
$849$	−22.4690	−0.771132
$850$	45.8055	1.57112
$851$	−0.608007	−0.0208422
$852$	−5.78088	−0.198050
$853$	22.0570	0.755219	0.377609	−	0.925965i	$-0.376746\pi$
$853$	22.0570	0.755219	0.377609	+	0.925965i	$0.376746\pi$
$854$	3.96559	0.135700
$855$	11.1196	0.380284
$856$	2.48968	0.0850954
$857$	24.5272	0.837834	0.418917	−	0.908024i	$-0.362410\pi$
$857$	24.5272	0.837834	0.418917	+	0.908024i	$0.362410\pi$
$858$	1.28140	0.0437463
$859$	−28.2679	−0.964489	−0.482244	−	0.876037i	$-0.660178\pi$
$859$	−28.2679	−0.964489	−0.482244	+	0.876037i	$0.660178\pi$
$860$	−20.4496	−0.697327
$861$	2.52854	0.0861723
$862$	6.94829	0.236660
$863$	28.0607	0.955198	0.477599	−	0.878578i	$-0.341507\pi$
$863$	28.0607	0.955198	0.477599	+	0.878578i	$0.341507\pi$
$864$	−3.75510	−0.127751
$865$	−78.4051	−2.66585
$866$	−28.7277	−0.976207
$867$	−4.42448	−0.150263
$868$	0.915668	0.0310798
$869$	−10.4166	−0.353358
$870$	−9.48201	−0.321470
$871$	−20.0551	−0.679541
$872$	7.05283	0.238839
$873$	−23.3110	−0.788957
$874$	0.112769	0.00381447
$875$	41.6571	1.40827
$876$	−2.15886	−0.0729410
$877$	−25.9774	−0.877195	−0.438597	−	0.898684i	$-0.644525\pi$
$877$	−25.9774	−0.877195	−0.438597	+	0.898684i	$0.644525\pi$
$878$	22.0835	0.745281
$879$	7.60674	0.256569
$880$	−4.76149	−0.160510
$881$	50.2449	1.69279	0.846397	−	0.532553i	$-0.178767\pi$
$881$	50.2449	1.69279	0.846397	+	0.532553i	$0.178767\pi$
$882$	15.0386	0.506375
$883$	11.2831	0.379707	0.189854	−	0.981812i	$-0.439199\pi$
$883$	11.2831	0.379707	0.189854	+	0.981812i	$0.439199\pi$
$884$	5.62383	0.189150
$885$	18.0240	0.605871
$886$	3.42410	0.115035
$887$	−44.7976	−1.50416	−0.752078	−	0.659074i	$-0.770948\pi$
$887$	−44.7976	−1.50416	−0.752078	+	0.659074i	$0.770948\pi$
$888$	−3.65408	−0.122623
$889$	3.65401	0.122552
$890$	55.5342	1.86151
$891$	5.52350	0.185044
$892$	3.93852	0.131871
$893$	11.3703	0.380493
$894$	−10.4122	−0.348235
$895$	98.4082	3.28942
$896$	−1.03965	−0.0347324
$897$	0.132823	0.00443483
$898$	−6.45014	−0.215244
$899$	−2.81546	−0.0939008
$900$	−35.9633	−1.19878
$901$	21.5745	0.718749
$902$	−3.90412	−0.129993
$903$	−3.29225	−0.109559
$904$	−16.5892	−0.551749
$905$	−7.13467	−0.237164
$906$	10.9601	0.364124
$907$	5.01363	0.166475	0.0832374	−	0.996530i	$-0.473474\pi$
$907$	5.01363	0.166475	0.0832374	+	0.996530i	$0.473474\pi$
$908$	2.97691	0.0987923
$909$	35.9864	1.19359
$910$	7.90778	0.262140
$911$	−55.3502	−1.83384	−0.916918	−	0.399077i	$-0.869331\pi$
$911$	−55.3502	−1.83384	−0.916918	+	0.399077i	$0.869331\pi$
$912$	0.677734	0.0224420
$913$	13.5885	0.449713
$914$	17.0170	0.562873
$915$	11.3141	0.374032
$916$	−24.6325	−0.813882
$917$	13.4956	0.445663
$918$	−12.1515	−0.401059
$919$	−15.0345	−0.495943	−0.247971	−	0.968767i	$-0.579764\pi$
$919$	−15.0345	−0.495943	−0.247971	+	0.968767i	$0.579764\pi$
$920$	−0.493550	−0.0162719
$921$	−0.794636	−0.0261841
$922$	−6.85354	−0.225709
$923$	−14.8238	−0.487932
$924$	−0.766566	−0.0252182
$925$	−76.3184	−2.50933
$926$	−13.7414	−0.451569
$927$	8.03812	0.264007
$928$	3.19669	0.104936
$929$	56.2773	1.84640	0.923198	−	0.384324i	$-0.125565\pi$
$929$	56.2773	1.84640	0.923198	+	0.384324i	$0.125565\pi$
$930$	2.61246	0.0856659
$931$	−5.91912	−0.193991
$932$	3.21421	0.105285
$933$	−8.46650	−0.277181
$934$	33.1199	1.08372
$935$	−15.4081	−0.503900
$936$	−4.41544	−0.144323
$937$	−28.8804	−0.943481	−0.471740	−	0.881737i	$-0.656374\pi$
$937$	−28.8804	−0.943481	−0.471740	+	0.881737i	$0.656374\pi$
$938$	11.9975	0.391731
$939$	4.34969	0.141947
$940$	−49.7638	−1.62311
$941$	−0.483464	−0.0157605	−0.00788024	−	0.999969i	$-0.502508\pi$
$941$	−0.483464	−0.0157605	−0.00788024	+	0.999969i	$0.502508\pi$
$942$	13.5594	0.441789
$943$	−0.404679	−0.0131782
$944$	−6.07647	−0.197772
$945$	−17.0865	−0.555823
$946$	5.08330	0.165272
$947$	4.38320	0.142435	0.0712174	−	0.997461i	$-0.477312\pi$
$947$	4.38320	0.142435	0.0712174	+	0.997461i	$0.477312\pi$
$948$	−6.48907	−0.210755
$949$	−5.53592	−0.179703
$950$	14.1550	0.459249
$951$	10.8857	0.352994
$952$	−3.36431	−0.109038
$953$	40.0977	1.29889	0.649446	−	0.760408i	$-0.275001\pi$
$953$	40.0977	1.29889	0.649446	+	0.760408i	$0.275001\pi$
$954$	−16.9388	−0.548413
$955$	14.0462	0.454525
$956$	1.83792	0.0594427
$957$	2.35700	0.0761911
$958$	10.3502	0.334400
$959$	−8.72009	−0.281586
$960$	−2.96620	−0.0957337
$961$	−30.2243	−0.974977
$962$	−9.37009	−0.302104
$963$	−6.32546	−0.203835
$964$	2.01575	0.0649228
$965$	59.6857	1.92135
$966$	−0.0794580	−0.00255652
$967$	33.0590	1.06311	0.531553	−	0.847025i	$-0.321608\pi$
$967$	33.0590	1.06311	0.531553	+	0.847025i	$0.321608\pi$
$968$	−9.81641	−0.315511
$969$	2.19314	0.0704539
$970$	−40.1562	−1.28934
$971$	−0.210526	−0.00675609	−0.00337804	−	0.999994i	$-0.501075\pi$
$971$	−0.210526	−0.00675609	−0.00337804	+	0.999994i	$0.501075\pi$
$972$	14.7062	0.471702
$973$	19.7057	0.631737
$974$	−8.92066	−0.285836
$975$	16.6722	0.533939
$976$	−3.81434	−0.122094
$977$	5.30124	0.169602	0.0848009	−	0.996398i	$-0.472975\pi$
$977$	5.30124	0.169602	0.0848009	+	0.996398i	$0.472975\pi$
$978$	5.08883	0.162723
$979$	−13.8045	−0.441194
$980$	25.9059	0.827533
$981$	−17.9190	−0.572109
$982$	26.0318	0.830709
$983$	39.0136	1.24434	0.622170	−	0.782882i	$-0.286251\pi$
$983$	39.0136	1.24434	0.622170	+	0.782882i	$0.286251\pi$
$984$	−2.43209	−0.0775323
$985$	106.852	3.40459
$986$	10.3445	0.329435
$987$	−8.01161	−0.255012
$988$	1.73790	0.0552899
$989$	0.526907	0.0167547
$990$	12.0974	0.384481
$991$	7.95223	0.252611	0.126305	−	0.991991i	$-0.459688\pi$
$991$	7.95223	0.252611	0.126305	+	0.991991i	$0.459688\pi$
$992$	−0.880743	−0.0279636
$993$	−20.0866	−0.637430
$994$	8.86796	0.281275
$995$	−21.1693	−0.671111
$996$	8.46503	0.268225
$997$	−43.0933	−1.36478	−0.682389	−	0.730989i	$-0.739059\pi$
$997$	−43.0933	−1.36478	−0.682389	+	0.730989i	$0.739059\pi$
$998$	−4.96533	−0.157175
$999$	20.2461	0.640558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.19	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.19	✓	30	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.677734 q^{3} +1.00000 q^{4} -4.37664 q^{5} +0.677734 q^{6} -1.03965 q^{7} +1.00000 q^{8} -2.54068 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.677734 q^{3} +1.00000 q^{4} -4.37664 q^{5} +0.677734 q^{6} -1.03965 q^{7} +1.00000 q^{8} -2.54068 q^{9} -4.37664 q^{10} +1.08793 q^{11} +0.677734 q^{12} +1.73790 q^{13} -1.03965 q^{14} -2.96620 q^{15} +1.00000 q^{16} +3.23599 q^{17} -2.54068 q^{18} +1.00000 q^{19} -4.37664 q^{20} -0.704609 q^{21} +1.08793 q^{22} +0.112769 q^{23} +0.677734 q^{24} +14.1550 q^{25} +1.73790 q^{26} -3.75510 q^{27} -1.03965 q^{28} +3.19669 q^{29} -2.96620 q^{30} -0.880743 q^{31} +1.00000 q^{32} +0.737328 q^{33} +3.23599 q^{34} +4.55020 q^{35} -2.54068 q^{36} -5.39162 q^{37} +1.00000 q^{38} +1.17783 q^{39} -4.37664 q^{40} -3.58857 q^{41} -0.704609 q^{42} +4.67245 q^{43} +1.08793 q^{44} +11.1196 q^{45} +0.112769 q^{46} +11.3703 q^{47} +0.677734 q^{48} -5.91912 q^{49} +14.1550 q^{50} +2.19314 q^{51} +1.73790 q^{52} +6.66703 q^{53} -3.75510 q^{54} -4.76149 q^{55} -1.03965 q^{56} +0.677734 q^{57} +3.19669 q^{58} -6.07647 q^{59} -2.96620 q^{60} -3.81434 q^{61} -0.880743 q^{62} +2.64142 q^{63} +1.00000 q^{64} -7.60617 q^{65} +0.737328 q^{66} -11.5399 q^{67} +3.23599 q^{68} +0.0764274 q^{69} +4.55020 q^{70} -8.52973 q^{71} -2.54068 q^{72} -3.18541 q^{73} -5.39162 q^{74} +9.59333 q^{75} +1.00000 q^{76} -1.13107 q^{77} +1.17783 q^{78} -9.57466 q^{79} -4.37664 q^{80} +5.07707 q^{81} -3.58857 q^{82} +12.4902 q^{83} -0.704609 q^{84} -14.1628 q^{85} +4.67245 q^{86} +2.16650 q^{87} +1.08793 q^{88} -12.6888 q^{89} +11.1196 q^{90} -1.80681 q^{91} +0.112769 q^{92} -0.596909 q^{93} +11.3703 q^{94} -4.37664 q^{95} +0.677734 q^{96} +9.17511 q^{97} -5.91912 q^{98} -2.76408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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