LMFDB - Embedded newform 6014.2.a.k.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.95043 q^{3} +1.00000 q^{4} -1.96504 q^{5} -1.95043 q^{6} +0.849460 q^{7} +1.00000 q^{8} +0.804176 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.95043 q^{3} +1.00000 q^{4} -1.96504 q^{5} -1.95043 q^{6} +0.849460 q^{7} +1.00000 q^{8} +0.804176 q^{9} -1.96504 q^{10} +5.75702 q^{11} -1.95043 q^{12} +3.96494 q^{13} +0.849460 q^{14} +3.83268 q^{15} +1.00000 q^{16} -3.51206 q^{17} +0.804176 q^{18} -2.82907 q^{19} -1.96504 q^{20} -1.65681 q^{21} +5.75702 q^{22} +3.99048 q^{23} -1.95043 q^{24} -1.13860 q^{25} +3.96494 q^{26} +4.28280 q^{27} +0.849460 q^{28} +1.18154 q^{29} +3.83268 q^{30} +1.00000 q^{31} +1.00000 q^{32} -11.2287 q^{33} -3.51206 q^{34} -1.66923 q^{35} +0.804176 q^{36} -4.35094 q^{37} -2.82907 q^{38} -7.73334 q^{39} -1.96504 q^{40} +11.6730 q^{41} -1.65681 q^{42} -4.22537 q^{43} +5.75702 q^{44} -1.58024 q^{45} +3.99048 q^{46} +4.42955 q^{47} -1.95043 q^{48} -6.27842 q^{49} -1.13860 q^{50} +6.85004 q^{51} +3.96494 q^{52} +6.92121 q^{53} +4.28280 q^{54} -11.3128 q^{55} +0.849460 q^{56} +5.51789 q^{57} +1.18154 q^{58} -11.7376 q^{59} +3.83268 q^{60} +11.3118 q^{61} +1.00000 q^{62} +0.683116 q^{63} +1.00000 q^{64} -7.79129 q^{65} -11.2287 q^{66} -8.58532 q^{67} -3.51206 q^{68} -7.78315 q^{69} -1.66923 q^{70} -2.39681 q^{71} +0.804176 q^{72} +8.81329 q^{73} -4.35094 q^{74} +2.22076 q^{75} -2.82907 q^{76} +4.89036 q^{77} -7.73334 q^{78} -3.96157 q^{79} -1.96504 q^{80} -10.7658 q^{81} +11.6730 q^{82} +0.509626 q^{83} -1.65681 q^{84} +6.90136 q^{85} -4.22537 q^{86} -2.30451 q^{87} +5.75702 q^{88} +7.40231 q^{89} -1.58024 q^{90} +3.36806 q^{91} +3.99048 q^{92} -1.95043 q^{93} +4.42955 q^{94} +5.55924 q^{95} -1.95043 q^{96} +1.00000 q^{97} -6.27842 q^{98} +4.62966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * 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
$3$	−1.95043	−1.12608	−0.563041	−	0.826429i	$-0.690369\pi$
$3$	−1.95043	−1.12608	−0.563041	+	0.826429i	$0.690369\pi$
$4$	1.00000	0.500000
$5$	−1.96504	−0.878795	−0.439397	−	0.898293i	$-0.644808\pi$
$5$	−1.96504	−0.878795	−0.439397	+	0.898293i	$0.644808\pi$
$6$	−1.95043	−0.796260
$7$	0.849460	0.321066	0.160533	−	0.987030i	$-0.448679\pi$
$7$	0.849460	0.321066	0.160533	+	0.987030i	$0.448679\pi$
$8$	1.00000	0.353553
$9$	0.804176	0.268059
$10$	−1.96504	−0.621402
$11$	5.75702	1.73581	0.867903	−	0.496734i	$-0.165467\pi$
$11$	5.75702	1.73581	0.867903	+	0.496734i	$0.165467\pi$
$12$	−1.95043	−0.563041
$13$	3.96494	1.09968	0.549839	−	0.835271i	$-0.314689\pi$
$13$	3.96494	1.09968	0.549839	+	0.835271i	$0.314689\pi$
$14$	0.849460	0.227028
$15$	3.83268	0.989594
$16$	1.00000	0.250000
$17$	−3.51206	−0.851801	−0.425900	−	0.904770i	$-0.640043\pi$
$17$	−3.51206	−0.851801	−0.425900	+	0.904770i	$0.640043\pi$
$18$	0.804176	0.189546
$19$	−2.82907	−0.649032	−0.324516	−	0.945880i	$-0.605201\pi$
$19$	−2.82907	−0.649032	−0.324516	+	0.945880i	$0.605201\pi$
$20$	−1.96504	−0.439397
$21$	−1.65681	−0.361546
$22$	5.75702	1.22740
$23$	3.99048	0.832072	0.416036	−	0.909348i	$-0.363419\pi$
$23$	3.99048	0.832072	0.416036	+	0.909348i	$0.363419\pi$
$24$	−1.95043	−0.398130
$25$	−1.13860	−0.227720
$26$	3.96494	0.777589
$27$	4.28280	0.824225
$28$	0.849460	0.160533
$29$	1.18154	0.219406	0.109703	−	0.993964i	$-0.465010\pi$
$29$	1.18154	0.219406	0.109703	+	0.993964i	$0.465010\pi$
$30$	3.83268	0.699749
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−11.2287	−1.95466
$34$	−3.51206	−0.602314
$35$	−1.66923	−0.282151
$36$	0.804176	0.134029
$37$	−4.35094	−0.715289	−0.357645	−	0.933858i	$-0.616420\pi$
$37$	−4.35094	−0.715289	−0.357645	+	0.933858i	$0.616420\pi$
$38$	−2.82907	−0.458935
$39$	−7.73334	−1.23833
$40$	−1.96504	−0.310701
$41$	11.6730	1.82302	0.911508	−	0.411283i	$-0.134919\pi$
$41$	11.6730	1.82302	0.911508	+	0.411283i	$0.134919\pi$
$42$	−1.65681	−0.255652
$43$	−4.22537	−0.644363	−0.322181	−	0.946678i	$-0.604416\pi$
$43$	−4.22537	−0.644363	−0.322181	+	0.946678i	$0.604416\pi$
$44$	5.75702	0.867903
$45$	−1.58024	−0.235569
$46$	3.99048	0.588364
$47$	4.42955	0.646117	0.323058	−	0.946379i	$-0.395289\pi$
$47$	4.42955	0.646117	0.323058	+	0.946379i	$0.395289\pi$
$48$	−1.95043	−0.281520
$49$	−6.27842	−0.896917
$50$	−1.13860	−0.161022
$51$	6.85004	0.959197
$52$	3.96494	0.549839
$53$	6.92121	0.950701	0.475351	−	0.879797i	$-0.342321\pi$
$53$	6.92121	0.950701	0.475351	+	0.879797i	$0.342321\pi$
$54$	4.28280	0.582815
$55$	−11.3128	−1.52542
$56$	0.849460	0.113514
$57$	5.51789	0.730863
$58$	1.18154	0.155144
$59$	−11.7376	−1.52810	−0.764051	−	0.645156i	$-0.776792\pi$
$59$	−11.7376	−1.52810	−0.764051	+	0.645156i	$0.776792\pi$
$60$	3.83268	0.494797
$61$	11.3118	1.44833	0.724166	−	0.689626i	$-0.242225\pi$
$61$	11.3118	1.44833	0.724166	+	0.689626i	$0.242225\pi$
$62$	1.00000	0.127000
$63$	0.683116	0.0860645
$64$	1.00000	0.125000
$65$	−7.79129	−0.966391
$66$	−11.2287	−1.38215
$67$	−8.58532	−1.04886	−0.524432	−	0.851452i	$-0.675722\pi$
$67$	−8.58532	−1.04886	−0.524432	+	0.851452i	$0.675722\pi$
$68$	−3.51206	−0.425900
$69$	−7.78315	−0.936981
$70$	−1.66923	−0.199511
$71$	−2.39681	−0.284449	−0.142225	−	0.989834i	$-0.545426\pi$
$71$	−2.39681	−0.284449	−0.142225	+	0.989834i	$0.545426\pi$
$72$	0.804176	0.0947731
$73$	8.81329	1.03152	0.515759	−	0.856734i	$-0.327510\pi$
$73$	8.81329	1.03152	0.515759	+	0.856734i	$0.327510\pi$
$74$	−4.35094	−0.505786
$75$	2.22076	0.256431
$76$	−2.82907	−0.324516
$77$	4.89036	0.557308
$78$	−7.73334	−0.875628
$79$	−3.96157	−0.445711	−0.222856	−	0.974851i	$-0.571538\pi$
$79$	−3.96157	−0.445711	−0.222856	+	0.974851i	$0.571538\pi$
$80$	−1.96504	−0.219699
$81$	−10.7658	−1.19620
$82$	11.6730	1.28907
$83$	0.509626	0.0559388	0.0279694	−	0.999609i	$-0.491096\pi$
$83$	0.509626	0.0559388	0.0279694	+	0.999609i	$0.491096\pi$
$84$	−1.65681	−0.180773
$85$	6.90136	0.748558
$86$	−4.22537	−0.455633
$87$	−2.30451	−0.247069
$88$	5.75702	0.613700
$89$	7.40231	0.784643	0.392322	−	0.919828i	$-0.371672\pi$
$89$	7.40231	0.784643	0.392322	+	0.919828i	$0.371672\pi$
$90$	−1.58024	−0.166572
$91$	3.36806	0.353069
$92$	3.99048	0.416036
$93$	−1.95043	−0.202250
$94$	4.42955	0.456874
$95$	5.55924	0.570366
$96$	−1.95043	−0.199065
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−6.27842	−0.634216
$99$	4.62966	0.465298
$100$	−1.13860	−0.113860
$101$	0.259225	0.0257939	0.0128969	−	0.999917i	$-0.495895\pi$
$101$	0.259225	0.0257939	0.0128969	+	0.999917i	$0.495895\pi$
$102$	6.85004	0.678255
$103$	−9.36759	−0.923016	−0.461508	−	0.887136i	$-0.652691\pi$
$103$	−9.36759	−0.923016	−0.461508	+	0.887136i	$0.652691\pi$
$104$	3.96494	0.388795
$105$	3.25571	0.317725
$106$	6.92121	0.672247
$107$	−11.3581	−1.09803	−0.549015	−	0.835812i	$-0.684997\pi$
$107$	−11.3581	−1.09803	−0.549015	+	0.835812i	$0.684997\pi$
$108$	4.28280	0.412113
$109$	−11.9170	−1.14144	−0.570721	−	0.821144i	$-0.693336\pi$
$109$	−11.9170	−1.14144	−0.570721	+	0.821144i	$0.693336\pi$
$110$	−11.3128	−1.07863
$111$	8.48619	0.805474
$112$	0.849460	0.0802664
$113$	−6.64110	−0.624742	−0.312371	−	0.949960i	$-0.601123\pi$
$113$	−6.64110	−0.624742	−0.312371	+	0.949960i	$0.601123\pi$
$114$	5.51789	0.516798
$115$	−7.84147	−0.731221
$116$	1.18154	0.109703
$117$	3.18851	0.294778
$118$	−11.7376	−1.08053
$119$	−2.98336	−0.273484
$120$	3.83268	0.349874
$121$	22.1433	2.01302
$122$	11.3118	1.02413
$123$	−22.7674	−2.05286
$124$	1.00000	0.0898027
$125$	12.0626	1.07891
$126$	0.683116	0.0608568
$127$	−20.1943	−1.79195	−0.895976	−	0.444103i	$-0.853522\pi$
$127$	−20.1943	−1.79195	−0.895976	+	0.444103i	$0.853522\pi$
$128$	1.00000	0.0883883
$129$	8.24128	0.725605
$130$	−7.79129	−0.683341
$131$	17.2669	1.50862	0.754308	−	0.656521i	$-0.227973\pi$
$131$	17.2669	1.50862	0.754308	+	0.656521i	$0.227973\pi$
$132$	−11.2287	−0.977329
$133$	−2.40318	−0.208382
$134$	−8.58532	−0.741659
$135$	−8.41589	−0.724325
$136$	−3.51206	−0.301157
$137$	8.38494	0.716374	0.358187	−	0.933650i	$-0.383395\pi$
$137$	8.38494	0.716374	0.358187	+	0.933650i	$0.383395\pi$
$138$	−7.78315	−0.662546
$139$	16.6928	1.41587	0.707933	−	0.706280i	$-0.249628\pi$
$139$	16.6928	1.41587	0.707933	+	0.706280i	$0.249628\pi$
$140$	−1.66923	−0.141075
$141$	−8.63953	−0.727580
$142$	−2.39681	−0.201136
$143$	22.8262	1.90883
$144$	0.804176	0.0670147
$145$	−2.32178	−0.192813
$146$	8.81329	0.729393
$147$	12.2456	1.01000
$148$	−4.35094	−0.357645
$149$	−12.3433	−1.01120	−0.505600	−	0.862768i	$-0.668729\pi$
$149$	−12.3433	−1.01120	−0.505600	+	0.862768i	$0.668729\pi$
$150$	2.22076	0.181324
$151$	5.60225	0.455905	0.227952	−	0.973672i	$-0.426797\pi$
$151$	5.60225	0.455905	0.227952	+	0.973672i	$0.426797\pi$
$152$	−2.82907	−0.229468
$153$	−2.82432	−0.228333
$154$	4.89036	0.394076
$155$	−1.96504	−0.157836
$156$	−7.73334	−0.619163
$157$	18.3404	1.46372	0.731861	−	0.681454i	$-0.238652\pi$
$157$	18.3404	1.46372	0.731861	+	0.681454i	$0.238652\pi$
$158$	−3.96157	−0.315165
$159$	−13.4993	−1.07057
$160$	−1.96504	−0.155350
$161$	3.38975	0.267150
$162$	−10.7658	−0.845843
$163$	9.77004	0.765249	0.382624	−	0.923904i	$-0.375020\pi$
$163$	9.77004	0.765249	0.382624	+	0.923904i	$0.375020\pi$
$164$	11.6730	0.911508
$165$	22.0648	1.71774
$166$	0.509626	0.0395547
$167$	21.1107	1.63360	0.816798	−	0.576923i	$-0.195747\pi$
$167$	21.1107	1.63360	0.816798	+	0.576923i	$0.195747\pi$
$168$	−1.65681	−0.127826
$169$	2.72077	0.209290
$170$	6.90136	0.529311
$171$	−2.27507	−0.173979
$172$	−4.22537	−0.322181
$173$	−6.88709	−0.523616	−0.261808	−	0.965120i	$-0.584319\pi$
$173$	−6.88709	−0.523616	−0.261808	+	0.965120i	$0.584319\pi$
$174$	−2.30451	−0.174704
$175$	−0.967194	−0.0731130
$176$	5.75702	0.433952
$177$	22.8933	1.72077
$178$	7.40231	0.554827
$179$	5.59978	0.418548	0.209274	−	0.977857i	$-0.432890\pi$
$179$	5.59978	0.418548	0.209274	+	0.977857i	$0.432890\pi$
$180$	−1.58024	−0.117784
$181$	15.5677	1.15714	0.578571	−	0.815632i	$-0.303611\pi$
$181$	15.5677	1.15714	0.578571	+	0.815632i	$0.303611\pi$
$182$	3.36806	0.249657
$183$	−22.0629	−1.63094
$184$	3.99048	0.294182
$185$	8.54978	0.628593
$186$	−1.95043	−0.143012
$187$	−20.2190	−1.47856
$188$	4.42955	0.323058
$189$	3.63807	0.264631
$190$	5.55924	0.403310
$191$	5.27267	0.381517	0.190759	−	0.981637i	$-0.438905\pi$
$191$	5.27267	0.381517	0.190759	+	0.981637i	$0.438905\pi$
$192$	−1.95043	−0.140760
$193$	22.8247	1.64295	0.821477	−	0.570241i	$-0.193150\pi$
$193$	22.8247	1.64295	0.821477	+	0.570241i	$0.193150\pi$
$194$	1.00000	0.0717958
$195$	15.1964	1.08823
$196$	−6.27842	−0.448458
$197$	−0.965049	−0.0687569	−0.0343784	−	0.999409i	$-0.510945\pi$
$197$	−0.965049	−0.0687569	−0.0343784	+	0.999409i	$0.510945\pi$
$198$	4.62966	0.329015
$199$	20.6925	1.46685	0.733426	−	0.679769i	$-0.237920\pi$
$199$	20.6925	1.46685	0.733426	+	0.679769i	$0.237920\pi$
$200$	−1.13860	−0.0805111
$201$	16.7451	1.18111
$202$	0.259225	0.0182390
$203$	1.00367	0.0704439
$204$	6.85004	0.479598
$205$	−22.9380	−1.60206
$206$	−9.36759	−0.652671
$207$	3.20905	0.223044
$208$	3.96494	0.274919
$209$	−16.2870	−1.12659
$210$	3.25571	0.224665
$211$	27.6344	1.90243	0.951214	−	0.308532i	$-0.0998377\pi$
$211$	27.6344	1.90243	0.951214	+	0.308532i	$0.0998377\pi$
$212$	6.92121	0.475351
$213$	4.67481	0.320313
$214$	−11.3581	−0.776425
$215$	8.30304	0.566263
$216$	4.28280	0.291408
$217$	0.849460	0.0576651
$218$	−11.9170	−0.807121
$219$	−17.1897	−1.16157
$220$	−11.3128	−0.762709
$221$	−13.9251	−0.936706
$222$	8.48619	0.569556
$223$	−2.78037	−0.186188	−0.0930938	−	0.995657i	$-0.529676\pi$
$223$	−2.78037	−0.186188	−0.0930938	+	0.995657i	$0.529676\pi$
$224$	0.849460	0.0567570
$225$	−0.915634	−0.0610423
$226$	−6.64110	−0.441760
$227$	−11.2656	−0.747726	−0.373863	−	0.927484i	$-0.621967\pi$
$227$	−11.2656	−0.747726	−0.373863	+	0.927484i	$0.621967\pi$
$228$	5.51789	0.365431
$229$	−13.3464	−0.881953	−0.440977	−	0.897519i	$-0.645368\pi$
$229$	−13.3464	−0.881953	−0.440977	+	0.897519i	$0.645368\pi$
$230$	−7.84147	−0.517051
$231$	−9.53830	−0.627574
$232$	1.18154	0.0775719
$233$	17.5061	1.14687	0.573433	−	0.819253i	$-0.305611\pi$
$233$	17.5061	1.14687	0.573433	+	0.819253i	$0.305611\pi$
$234$	3.18851	0.208440
$235$	−8.70427	−0.567804
$236$	−11.7376	−0.764051
$237$	7.72676	0.501907
$238$	−2.98336	−0.193382
$239$	24.3085	1.57238	0.786192	−	0.617982i	$-0.212050\pi$
$239$	24.3085	1.57238	0.786192	+	0.617982i	$0.212050\pi$
$240$	3.83268	0.247399
$241$	10.0867	0.649740	0.324870	−	0.945759i	$-0.394680\pi$
$241$	10.0867	0.649740	0.324870	+	0.945759i	$0.394680\pi$
$242$	22.1433	1.42342
$243$	8.14959	0.522797
$244$	11.3118	0.724166
$245$	12.3374	0.788206
$246$	−22.7674	−1.45159
$247$	−11.2171	−0.713726
$248$	1.00000	0.0635001
$249$	−0.993990	−0.0629916
$250$	12.0626	0.762907
$251$	9.68064	0.611036	0.305518	−	0.952186i	$-0.401170\pi$
$251$	9.68064	0.611036	0.305518	+	0.952186i	$0.401170\pi$
$252$	0.683116	0.0430322
$253$	22.9733	1.44432
$254$	−20.1943	−1.26710
$255$	−13.4606	−0.842937
$256$	1.00000	0.0625000
$257$	9.18692	0.573065	0.286532	−	0.958071i	$-0.407497\pi$
$257$	9.18692	0.573065	0.286532	+	0.958071i	$0.407497\pi$
$258$	8.24128	0.513080
$259$	−3.69595	−0.229655
$260$	−7.79129	−0.483195
$261$	0.950166	0.0588138
$262$	17.2669	1.06675
$263$	6.14728	0.379058	0.189529	−	0.981875i	$-0.439304\pi$
$263$	6.14728	0.379058	0.189529	+	0.981875i	$0.439304\pi$
$264$	−11.2287	−0.691076
$265$	−13.6005	−0.835471
$266$	−2.40318	−0.147348
$267$	−14.4377	−0.883572
$268$	−8.58532	−0.524432
$269$	−27.1025	−1.65247	−0.826235	−	0.563326i	$-0.809521\pi$
$269$	−27.1025	−1.65247	−0.826235	+	0.563326i	$0.809521\pi$
$270$	−8.41589	−0.512175
$271$	20.2854	1.23225	0.616124	−	0.787649i	$-0.288702\pi$
$271$	20.2854	1.23225	0.616124	+	0.787649i	$0.288702\pi$
$272$	−3.51206	−0.212950
$273$	−6.56917	−0.397584
$274$	8.38494	0.506553
$275$	−6.55493	−0.395277
$276$	−7.78315	−0.468491
$277$	7.30191	0.438729	0.219365	−	0.975643i	$-0.429602\pi$
$277$	7.30191	0.438729	0.219365	+	0.975643i	$0.429602\pi$
$278$	16.6928	1.00117
$279$	0.804176	0.0481448
$280$	−1.66923	−0.0997554
$281$	−11.2279	−0.669799	−0.334900	−	0.942254i	$-0.608702\pi$
$281$	−11.2279	−0.669799	−0.334900	+	0.942254i	$0.608702\pi$
$282$	−8.63953	−0.514477
$283$	32.9309	1.95754	0.978770	−	0.204959i	$-0.0657062\pi$
$283$	32.9309	1.95754	0.978770	+	0.204959i	$0.0657062\pi$
$284$	−2.39681	−0.142225
$285$	−10.8429	−0.642279
$286$	22.8262	1.34974
$287$	9.91575	0.585308
$288$	0.804176	0.0473865
$289$	−4.66540	−0.274435
$290$	−2.32178	−0.136340
$291$	−1.95043	−0.114336
$292$	8.81329	0.515759
$293$	−12.5483	−0.733077	−0.366538	−	0.930403i	$-0.619457\pi$
$293$	−12.5483	−0.733077	−0.366538	+	0.930403i	$0.619457\pi$
$294$	12.2456	0.714179
$295$	23.0648	1.34289
$296$	−4.35094	−0.252893
$297$	24.6562	1.43070
$298$	−12.3433	−0.715026
$299$	15.8220	0.915011
$300$	2.22076	0.128215
$301$	−3.58928	−0.206883
$302$	5.60225	0.322373
$303$	−0.505601	−0.0290460
$304$	−2.82907	−0.162258
$305$	−22.2283	−1.27279
$306$	−2.82432	−0.161456
$307$	20.0179	1.14248	0.571242	−	0.820782i	$-0.306462\pi$
$307$	20.0179	1.14248	0.571242	+	0.820782i	$0.306462\pi$
$308$	4.89036	0.278654
$309$	18.2708	1.03939
$310$	−1.96504	−0.111607
$311$	−29.9092	−1.69599	−0.847997	−	0.530001i	$-0.822191\pi$
$311$	−29.9092	−1.69599	−0.847997	+	0.530001i	$0.822191\pi$
$312$	−7.73334	−0.437814
$313$	15.8336	0.894968	0.447484	−	0.894292i	$-0.352320\pi$
$313$	15.8336	0.894968	0.447484	+	0.894292i	$0.352320\pi$
$314$	18.3404	1.03501
$315$	−1.34235	−0.0756330
$316$	−3.96157	−0.222856
$317$	17.9522	1.00830	0.504148	−	0.863617i	$-0.331807\pi$
$317$	17.9522	1.00830	0.504148	+	0.863617i	$0.331807\pi$
$318$	−13.4993	−0.757005
$319$	6.80215	0.380847
$320$	−1.96504	−0.109849
$321$	22.1532	1.23647
$322$	3.38975	0.188904
$323$	9.93586	0.552846
$324$	−10.7658	−0.598102
$325$	−4.51448	−0.250418
$326$	9.77004	0.541113
$327$	23.2433	1.28536
$328$	11.6730	0.644533
$329$	3.76273	0.207446
$330$	22.0648	1.21463
$331$	19.9675	1.09751	0.548756	−	0.835983i	$-0.315102\pi$
$331$	19.9675	1.09751	0.548756	+	0.835983i	$0.315102\pi$
$332$	0.509626	0.0279694
$333$	−3.49892	−0.191740
$334$	21.1107	1.15513
$335$	16.8705	0.921736
$336$	−1.65681	−0.0903865
$337$	21.6031	1.17680	0.588399	−	0.808571i	$-0.299759\pi$
$337$	21.6031	1.17680	0.588399	+	0.808571i	$0.299759\pi$
$338$	2.72077	0.147990
$339$	12.9530	0.703511
$340$	6.90136	0.374279
$341$	5.75702	0.311760
$342$	−2.27507	−0.123022
$343$	−11.2795	−0.609035
$344$	−4.22537	−0.227817
$345$	15.2942	0.823414
$346$	−6.88709	−0.370252
$347$	−15.7869	−0.847485	−0.423743	−	0.905783i	$-0.639284\pi$
$347$	−15.7869	−0.847485	−0.423743	+	0.905783i	$0.639284\pi$
$348$	−2.30451	−0.123535
$349$	23.5041	1.25814	0.629072	−	0.777347i	$-0.283435\pi$
$349$	23.5041	1.25814	0.629072	+	0.777347i	$0.283435\pi$
$350$	−0.967194	−0.0516987
$351$	16.9811	0.906382
$352$	5.75702	0.306850
$353$	−14.8432	−0.790024	−0.395012	−	0.918676i	$-0.629260\pi$
$353$	−14.8432	−0.790024	−0.395012	+	0.918676i	$0.629260\pi$
$354$	22.8933	1.21677
$355$	4.70984	0.249972
$356$	7.40231	0.392322
$357$	5.81883	0.307965
$358$	5.59978	0.295958
$359$	4.57793	0.241614	0.120807	−	0.992676i	$-0.461452\pi$
$359$	4.57793	0.241614	0.120807	+	0.992676i	$0.461452\pi$
$360$	−1.58024	−0.0832861
$361$	−10.9964	−0.578757
$362$	15.5677	0.818223
$363$	−43.1889	−2.26683
$364$	3.36806	0.176534
$365$	−17.3185	−0.906492
$366$	−22.0629	−1.15325
$367$	1.58924	0.0829576	0.0414788	−	0.999139i	$-0.486793\pi$
$367$	1.58924	0.0829576	0.0414788	+	0.999139i	$0.486793\pi$
$368$	3.99048	0.208018
$369$	9.38715	0.488675
$370$	8.54978	0.444482
$371$	5.87929	0.305238
$372$	−1.95043	−0.101125
$373$	−10.3206	−0.534379	−0.267189	−	0.963644i	$-0.586095\pi$
$373$	−10.3206	−0.534379	−0.267189	+	0.963644i	$0.586095\pi$
$374$	−20.2190	−1.04550
$375$	−23.5273	−1.21494
$376$	4.42955	0.228437
$377$	4.68474	0.241276
$378$	3.63807	0.187122
$379$	20.6296	1.05967	0.529835	−	0.848101i	$-0.322254\pi$
$379$	20.6296	1.05967	0.529835	+	0.848101i	$0.322254\pi$
$380$	5.55924	0.285183
$381$	39.3875	2.01788
$382$	5.27267	0.269773
$383$	11.7151	0.598614	0.299307	−	0.954157i	$-0.403245\pi$
$383$	11.7151	0.598614	0.299307	+	0.954157i	$0.403245\pi$
$384$	−1.95043	−0.0995325
$385$	−9.60977	−0.489759
$386$	22.8247	1.16174
$387$	−3.39794	−0.172727
$388$	1.00000	0.0507673
$389$	−36.7199	−1.86177	−0.930886	−	0.365309i	$-0.880963\pi$
$389$	−36.7199	−1.86177	−0.930886	+	0.365309i	$0.880963\pi$
$390$	15.1964	0.769498
$391$	−14.0148	−0.708760
$392$	−6.27842	−0.317108
$393$	−33.6779	−1.69882
$394$	−0.965049	−0.0486184
$395$	7.78466	0.391689
$396$	4.62966	0.232649
$397$	0.953912	0.0478755	0.0239377	−	0.999713i	$-0.492380\pi$
$397$	0.953912	0.0478755	0.0239377	+	0.999713i	$0.492380\pi$
$398$	20.6925	1.03722
$399$	4.68723	0.234655
$400$	−1.13860	−0.0569299
$401$	−38.6180	−1.92849	−0.964246	−	0.265010i	$-0.914625\pi$
$401$	−38.6180	−1.92849	−0.964246	+	0.265010i	$0.914625\pi$
$402$	16.7451	0.835168
$403$	3.96494	0.197508
$404$	0.259225	0.0128969
$405$	21.1553	1.05122
$406$	1.00367	0.0498114
$407$	−25.0484	−1.24160
$408$	6.85004	0.339127
$409$	4.85395	0.240012	0.120006	−	0.992773i	$-0.461709\pi$
$409$	4.85395	0.240012	0.120006	+	0.992773i	$0.461709\pi$
$410$	−22.9380	−1.13283
$411$	−16.3542	−0.806695
$412$	−9.36759	−0.461508
$413$	−9.97060	−0.490621
$414$	3.20905	0.157716
$415$	−1.00144	−0.0491587
$416$	3.96494	0.194397
$417$	−32.5581	−1.59438
$418$	−16.2870	−0.796622
$419$	38.5072	1.88120	0.940600	−	0.339517i	$-0.110264\pi$
$419$	38.5072	1.88120	0.940600	+	0.339517i	$0.110264\pi$
$420$	3.25571	0.158862
$421$	−37.5225	−1.82873	−0.914367	−	0.404887i	$-0.867311\pi$
$421$	−37.5225	−1.82873	−0.914367	+	0.404887i	$0.867311\pi$
$422$	27.6344	1.34522
$423$	3.56214	0.173197
$424$	6.92121	0.336124
$425$	3.99883	0.193972
$426$	4.67481	0.226495
$427$	9.60895	0.465010
$428$	−11.3581	−0.549015
$429$	−44.5210	−2.14949
$430$	8.30304	0.400408
$431$	22.0921	1.06414	0.532070	−	0.846700i	$-0.321414\pi$
$431$	22.0921	1.06414	0.532070	+	0.846700i	$0.321414\pi$
$432$	4.28280	0.206056
$433$	6.89269	0.331242	0.165621	−	0.986190i	$-0.447037\pi$
$433$	6.89269	0.331242	0.165621	+	0.986190i	$0.447037\pi$
$434$	0.849460	0.0407754
$435$	4.52847	0.217123
$436$	−11.9170	−0.570721
$437$	−11.2893	−0.540042
$438$	−17.1897	−0.821356
$439$	−32.8212	−1.56647	−0.783235	−	0.621726i	$-0.786432\pi$
$439$	−32.8212	−1.56647	−0.783235	+	0.621726i	$0.786432\pi$
$440$	−11.3128	−0.539316
$441$	−5.04895	−0.240426
$442$	−13.9251	−0.662351
$443$	12.2335	0.581232	0.290616	−	0.956840i	$-0.406140\pi$
$443$	12.2335	0.581232	0.290616	+	0.956840i	$0.406140\pi$
$444$	8.48619	0.402737
$445$	−14.5459	−0.689540
$446$	−2.78037	−0.131655
$447$	24.0747	1.13869
$448$	0.849460	0.0401332
$449$	20.6792	0.975913	0.487956	−	0.872868i	$-0.337743\pi$
$449$	20.6792	0.975913	0.487956	+	0.872868i	$0.337743\pi$
$450$	−0.915634	−0.0431634
$451$	67.2016	3.16440
$452$	−6.64110	−0.312371
$453$	−10.9268	−0.513386
$454$	−11.2656	−0.528722
$455$	−6.61839	−0.310275
$456$	5.51789	0.258399
$457$	−34.0194	−1.59136	−0.795680	−	0.605717i	$-0.792886\pi$
$457$	−34.0194	−1.59136	−0.795680	+	0.605717i	$0.792886\pi$
$458$	−13.3464	−0.623635
$459$	−15.0415	−0.702076
$460$	−7.84147	−0.365610
$461$	−11.4858	−0.534948	−0.267474	−	0.963565i	$-0.586189\pi$
$461$	−11.4858	−0.534948	−0.267474	+	0.963565i	$0.586189\pi$
$462$	−9.53830	−0.443762
$463$	6.49973	0.302068	0.151034	−	0.988529i	$-0.451740\pi$
$463$	6.49973	0.302068	0.151034	+	0.988529i	$0.451740\pi$
$464$	1.18154	0.0548516
$465$	3.83268	0.177736
$466$	17.5061	0.810956
$467$	−25.2960	−1.17056	−0.585279	−	0.810832i	$-0.699015\pi$
$467$	−25.2960	−1.17056	−0.585279	+	0.810832i	$0.699015\pi$
$468$	3.18851	0.147389
$469$	−7.29289	−0.336754
$470$	−8.70427	−0.401498
$471$	−35.7716	−1.64827
$472$	−11.7376	−0.540265
$473$	−24.3255	−1.11849
$474$	7.72676	0.354902
$475$	3.22117	0.147797
$476$	−2.98336	−0.136742
$477$	5.56587	0.254844
$478$	24.3085	1.11184
$479$	−1.90964	−0.0872537	−0.0436269	−	0.999048i	$-0.513891\pi$
$479$	−1.90964	−0.0872537	−0.0436269	+	0.999048i	$0.513891\pi$
$480$	3.83268	0.174937
$481$	−17.2512	−0.786587
$482$	10.0867	0.459435
$483$	−6.61148	−0.300833
$484$	22.1433	1.00651
$485$	−1.96504	−0.0892281
$486$	8.14959	0.369673
$487$	−28.8545	−1.30752	−0.653761	−	0.756701i	$-0.726810\pi$
$487$	−28.8545	−1.30752	−0.653761	+	0.756701i	$0.726810\pi$
$488$	11.3118	0.512063
$489$	−19.0558	−0.861732
$490$	12.3374	0.557346
$491$	−29.0430	−1.31069	−0.655346	−	0.755329i	$-0.727477\pi$
$491$	−29.0430	−1.31069	−0.655346	+	0.755329i	$0.727477\pi$
$492$	−22.7674	−1.02643
$493$	−4.14964	−0.186891
$494$	−11.2171	−0.504680
$495$	−9.09748	−0.408901
$496$	1.00000	0.0449013
$497$	−2.03600	−0.0913269
$498$	−0.993990	−0.0445418
$499$	19.8056	0.886619	0.443310	−	0.896369i	$-0.353804\pi$
$499$	19.8056	0.886619	0.443310	+	0.896369i	$0.353804\pi$
$500$	12.0626	0.539457
$501$	−41.1750	−1.83956
$502$	9.68064	0.432068
$503$	−22.9004	−1.02108	−0.510540	−	0.859854i	$-0.670555\pi$
$503$	−22.9004	−1.02108	−0.510540	+	0.859854i	$0.670555\pi$
$504$	0.683116	0.0304284
$505$	−0.509389	−0.0226675
$506$	22.9733	1.02129
$507$	−5.30667	−0.235677
$508$	−20.1943	−0.895976
$509$	−7.23069	−0.320495	−0.160247	−	0.987077i	$-0.551229\pi$
$509$	−7.23069	−0.320495	−0.160247	+	0.987077i	$0.551229\pi$
$510$	−13.4606	−0.596047
$511$	7.48654	0.331185
$512$	1.00000	0.0441942
$513$	−12.1163	−0.534949
$514$	9.18692	0.405218
$515$	18.4077	0.811141
$516$	8.24128	0.362802
$517$	25.5010	1.12153
$518$	−3.69595	−0.162391
$519$	13.4328	0.589634
$520$	−7.79129	−0.341671
$521$	−16.4935	−0.722592	−0.361296	−	0.932451i	$-0.617666\pi$
$521$	−16.4935	−0.722592	−0.361296	+	0.932451i	$0.617666\pi$
$522$	0.950166	0.0415876
$523$	16.7950	0.734394	0.367197	−	0.930143i	$-0.380318\pi$
$523$	16.7950	0.734394	0.367197	+	0.930143i	$0.380318\pi$
$524$	17.2669	0.754308
$525$	1.88644	0.0823312
$526$	6.14728	0.268034
$527$	−3.51206	−0.152988
$528$	−11.2287	−0.488665
$529$	−7.07607	−0.307655
$530$	−13.6005	−0.590767
$531$	−9.43907	−0.409621
$532$	−2.40318	−0.104191
$533$	46.2828	2.00473
$534$	−14.4377	−0.624780
$535$	22.3192	0.964943
$536$	−8.58532	−0.370829
$537$	−10.9220	−0.471318
$538$	−27.1025	−1.16847
$539$	−36.1450	−1.55687
$540$	−8.41589	−0.362162
$541$	10.6394	0.457425	0.228712	−	0.973494i	$-0.426548\pi$
$541$	10.6394	0.457425	0.228712	+	0.973494i	$0.426548\pi$
$542$	20.2854	0.871331
$543$	−30.3638	−1.30304
$544$	−3.51206	−0.150579
$545$	23.4174	1.00309
$546$	−6.56917	−0.281134
$547$	9.88970	0.422853	0.211427	−	0.977394i	$-0.432189\pi$
$547$	9.88970	0.422853	0.211427	+	0.977394i	$0.432189\pi$
$548$	8.38494	0.358187
$549$	9.09671	0.388238
$550$	−6.55493	−0.279503
$551$	−3.34265	−0.142402
$552$	−7.78315	−0.331273
$553$	−3.36519	−0.143103
$554$	7.30191	0.310228
$555$	−16.6758	−0.707846
$556$	16.6928	0.707933
$557$	4.27507	0.181140	0.0905702	−	0.995890i	$-0.471131\pi$
$557$	4.27507	0.181140	0.0905702	+	0.995890i	$0.471131\pi$
$558$	0.804176	0.0340435
$559$	−16.7533	−0.708591
$560$	−1.66923	−0.0705377
$561$	39.4358	1.66498
$562$	−11.2279	−0.473620
$563$	−4.63496	−0.195340	−0.0976701	−	0.995219i	$-0.531139\pi$
$563$	−4.63496	−0.195340	−0.0976701	+	0.995219i	$0.531139\pi$
$564$	−8.63953	−0.363790
$565$	13.0501	0.549020
$566$	32.9309	1.38419
$567$	−9.14514	−0.384060
$568$	−2.39681	−0.100568
$569$	16.2225	0.680084	0.340042	−	0.940410i	$-0.389559\pi$
$569$	16.2225	0.680084	0.340042	+	0.940410i	$0.389559\pi$
$570$	−10.8429	−0.454159
$571$	−31.7518	−1.32877	−0.664385	−	0.747390i	$-0.731307\pi$
$571$	−31.7518	−1.32877	−0.664385	+	0.747390i	$0.731307\pi$
$572$	22.8262	0.954413
$573$	−10.2840	−0.429619
$574$	9.91575	0.413875
$575$	−4.54355	−0.189479
$576$	0.804176	0.0335073
$577$	−24.4848	−1.01932	−0.509658	−	0.860377i	$-0.670228\pi$
$577$	−24.4848	−1.01932	−0.509658	+	0.860377i	$0.670228\pi$
$578$	−4.66540	−0.194055
$579$	−44.5179	−1.85010
$580$	−2.32178	−0.0964066
$581$	0.432907	0.0179600
$582$	−1.95043	−0.0808479
$583$	39.8455	1.65023
$584$	8.81329	0.364697
$585$	−6.26557	−0.259049
$586$	−12.5483	−0.518364
$587$	−13.5268	−0.558309	−0.279154	−	0.960246i	$-0.590054\pi$
$587$	−13.5268	−0.558309	−0.279154	+	0.960246i	$0.590054\pi$
$588$	12.2456	0.505001
$589$	−2.82907	−0.116570
$590$	23.0648	0.949565
$591$	1.88226	0.0774258
$592$	−4.35094	−0.178822
$593$	−14.8116	−0.608238	−0.304119	−	0.952634i	$-0.598362\pi$
$593$	−14.8116	−0.608238	−0.304119	+	0.952634i	$0.598362\pi$
$594$	24.6562	1.01165
$595$	5.86243	0.240336
$596$	−12.3433	−0.505600
$597$	−40.3593	−1.65179
$598$	15.8220	0.647011
$599$	29.8225	1.21851	0.609257	−	0.792973i	$-0.291468\pi$
$599$	29.8225	1.21851	0.609257	+	0.792973i	$0.291468\pi$
$600$	2.22076	0.0906620
$601$	41.6972	1.70086	0.850432	−	0.526084i	$-0.176340\pi$
$601$	41.6972	1.70086	0.850432	+	0.526084i	$0.176340\pi$
$602$	−3.58928	−0.146288
$603$	−6.90411	−0.281157
$604$	5.60225	0.227952
$605$	−43.5125	−1.76903
$606$	−0.505601	−0.0205386
$607$	−32.5561	−1.32141	−0.660705	−	0.750645i	$-0.729743\pi$
$607$	−32.5561	−1.32141	−0.660705	+	0.750645i	$0.729743\pi$
$608$	−2.82907	−0.114734
$609$	−1.95759	−0.0793256
$610$	−22.2283	−0.899996
$611$	17.5629	0.710520
$612$	−2.82432	−0.114166
$613$	−0.104993	−0.00424061	−0.00212031	−	0.999998i	$-0.500675\pi$
$613$	−0.104993	−0.00424061	−0.00212031	+	0.999998i	$0.500675\pi$
$614$	20.0179	0.807858
$615$	44.7389	1.80405
$616$	4.89036	0.197038
$617$	−42.7219	−1.71992	−0.859959	−	0.510363i	$-0.829511\pi$
$617$	−42.7219	−1.71992	−0.859959	+	0.510363i	$0.829511\pi$
$618$	18.2708	0.734960
$619$	−9.25951	−0.372171	−0.186086	−	0.982534i	$-0.559580\pi$
$619$	−9.25951	−0.372171	−0.186086	+	0.982534i	$0.559580\pi$
$620$	−1.96504	−0.0789181
$621$	17.0904	0.685815
$622$	−29.9092	−1.19925
$623$	6.28797	0.251922
$624$	−7.73334	−0.309581
$625$	−18.0106	−0.720424
$626$	15.8336	0.632838
$627$	31.7666	1.26864
$628$	18.3404	0.731861
$629$	15.2808	0.609284
$630$	−1.34235	−0.0534806
$631$	−0.707439	−0.0281627	−0.0140813	−	0.999901i	$-0.504482\pi$
$631$	−0.707439	−0.0281627	−0.0140813	+	0.999901i	$0.504482\pi$
$632$	−3.96157	−0.157583
$633$	−53.8989	−2.14229
$634$	17.9522	0.712973
$635$	39.6826	1.57476
$636$	−13.4993	−0.535283
$637$	−24.8936	−0.986319
$638$	6.80215	0.269300
$639$	−1.92746	−0.0762491
$640$	−1.96504	−0.0776752
$641$	−33.9762	−1.34198	−0.670990	−	0.741467i	$-0.734130\pi$
$641$	−33.9762	−1.34198	−0.670990	+	0.741467i	$0.734130\pi$
$642$	22.1532	0.874317
$643$	−23.0041	−0.907191	−0.453596	−	0.891208i	$-0.649859\pi$
$643$	−23.0041	−0.907191	−0.453596	+	0.891208i	$0.649859\pi$
$644$	3.38975	0.133575
$645$	−16.1945	−0.637658
$646$	9.93586	0.390921
$647$	6.71815	0.264118	0.132059	−	0.991242i	$-0.457841\pi$
$647$	6.71815	0.264118	0.132059	+	0.991242i	$0.457841\pi$
$648$	−10.7658	−0.422922
$649$	−67.5734	−2.65249
$650$	−4.51448	−0.177072
$651$	−1.65681	−0.0649356
$652$	9.77004	0.382624
$653$	4.84626	0.189649	0.0948244	−	0.995494i	$-0.469771\pi$
$653$	4.84626	0.189649	0.0948244	+	0.995494i	$0.469771\pi$
$654$	23.2433	0.908884
$655$	−33.9302	−1.32576
$656$	11.6730	0.455754
$657$	7.08744	0.276507
$658$	3.76273	0.146686
$659$	33.0804	1.28863	0.644315	−	0.764760i	$-0.277143\pi$
$659$	33.0804	1.28863	0.644315	+	0.764760i	$0.277143\pi$
$660$	22.0648	0.858872
$661$	10.1368	0.394276	0.197138	−	0.980376i	$-0.436835\pi$
$661$	10.1368	0.394276	0.197138	+	0.980376i	$0.436835\pi$
$662$	19.9675	0.776058
$663$	27.1600	1.05481
$664$	0.509626	0.0197773
$665$	4.72235	0.183125
$666$	−3.49892	−0.135580
$667$	4.71491	0.182562
$668$	21.1107	0.816798
$669$	5.42293	0.209662
$670$	16.8705	0.651766
$671$	65.1224	2.51402
$672$	−1.65681	−0.0639129
$673$	−7.35882	−0.283662	−0.141831	−	0.989891i	$-0.545299\pi$
$673$	−7.35882	−0.283662	−0.141831	+	0.989891i	$0.545299\pi$
$674$	21.6031	0.832122
$675$	−4.87639	−0.187692
$676$	2.72077	0.104645
$677$	−18.0767	−0.694745	−0.347372	−	0.937727i	$-0.612926\pi$
$677$	−18.0767	−0.694745	−0.347372	+	0.937727i	$0.612926\pi$
$678$	12.9530	0.497457
$679$	0.849460	0.0325993
$680$	6.90136	0.264655
$681$	21.9728	0.842001
$682$	5.75702	0.220448
$683$	−19.7976	−0.757536	−0.378768	−	0.925492i	$-0.623652\pi$
$683$	−19.7976	−0.757536	−0.378768	+	0.925492i	$0.623652\pi$
$684$	−2.27507	−0.0869894
$685$	−16.4768	−0.629546
$686$	−11.2795	−0.430653
$687$	26.0312	0.993151
$688$	−4.22537	−0.161091
$689$	27.4422	1.04546
$690$	15.2942	0.582242
$691$	45.7073	1.73879	0.869395	−	0.494118i	$-0.164509\pi$
$691$	45.7073	1.73879	0.869395	+	0.494118i	$0.164509\pi$
$692$	−6.88709	−0.261808
$693$	3.93271	0.149391
$694$	−15.7869	−0.599263
$695$	−32.8021	−1.24425
$696$	−2.30451	−0.0873522
$697$	−40.9963	−1.55285
$698$	23.5041	0.889642
$699$	−34.1445	−1.29146
$700$	−0.967194	−0.0365565
$701$	−12.1870	−0.460297	−0.230148	−	0.973156i	$-0.573921\pi$
$701$	−12.1870	−0.460297	−0.230148	+	0.973156i	$0.573921\pi$
$702$	16.9811	0.640909
$703$	12.3091	0.464246
$704$	5.75702	0.216976
$705$	16.9771	0.639393
$706$	−14.8432	−0.558631
$707$	0.220202	0.00828153
$708$	22.8933	0.860383
$709$	34.2670	1.28692	0.643462	−	0.765478i	$-0.277497\pi$
$709$	34.2670	1.28692	0.643462	+	0.765478i	$0.277497\pi$
$710$	4.70984	0.176757
$711$	−3.18580	−0.119477
$712$	7.40231	0.277413
$713$	3.99048	0.149445
$714$	5.81883	0.217764
$715$	−44.8546	−1.67747
$716$	5.59978	0.209274
$717$	−47.4120	−1.77063
$718$	4.57793	0.170847
$719$	46.6512	1.73979	0.869897	−	0.493233i	$-0.164185\pi$
$719$	46.6512	1.73979	0.869897	+	0.493233i	$0.164185\pi$
$720$	−1.58024	−0.0588922
$721$	−7.95739	−0.296349
$722$	−10.9964	−0.409243
$723$	−19.6733	−0.731660
$724$	15.5677	0.578571
$725$	−1.34530	−0.0499632
$726$	−43.1889	−1.60289
$727$	23.9426	0.887981	0.443990	−	0.896032i	$-0.353562\pi$
$727$	23.9426	0.887981	0.443990	+	0.896032i	$0.353562\pi$
$728$	3.36806	0.124829
$729$	16.4023	0.607492
$730$	−17.3185	−0.640987
$731$	14.8398	0.548869
$732$	−22.0629	−0.815470
$733$	12.5960	0.465245	0.232622	−	0.972567i	$-0.425269\pi$
$733$	12.5960	0.465245	0.232622	+	0.972567i	$0.425269\pi$
$734$	1.58924	0.0586599
$735$	−24.0632	−0.887584
$736$	3.99048	0.147091
$737$	−49.4259	−1.82062
$738$	9.38715	0.345546
$739$	6.68545	0.245928	0.122964	−	0.992411i	$-0.460760\pi$
$739$	6.68545	0.245928	0.122964	+	0.992411i	$0.460760\pi$
$740$	8.54978	0.314296
$741$	21.8781	0.803713
$742$	5.87929	0.215836
$743$	−51.4606	−1.88791	−0.943954	−	0.330077i	$-0.892925\pi$
$743$	−51.4606	−1.88791	−0.943954	+	0.330077i	$0.892925\pi$
$744$	−1.95043	−0.0715062
$745$	24.2551	0.888637
$746$	−10.3206	−0.377863
$747$	0.409829	0.0149949
$748$	−20.2190	−0.739281
$749$	−9.64826	−0.352540
$750$	−23.5273	−0.859095
$751$	−30.7737	−1.12295	−0.561474	−	0.827494i	$-0.689766\pi$
$751$	−30.7737	−1.12295	−0.561474	+	0.827494i	$0.689766\pi$
$752$	4.42955	0.161529
$753$	−18.8814	−0.688076
$754$	4.68474	0.170608
$755$	−11.0087	−0.400647
$756$	3.63807	0.132315
$757$	−4.14745	−0.150742	−0.0753708	−	0.997156i	$-0.524014\pi$
$757$	−4.14745	−0.150742	−0.0753708	+	0.997156i	$0.524014\pi$
$758$	20.6296	0.749300
$759$	−44.8077	−1.62642
$760$	5.55924	0.201655
$761$	−11.3917	−0.412947	−0.206474	−	0.978452i	$-0.566199\pi$
$761$	−11.3917	−0.412947	−0.206474	+	0.978452i	$0.566199\pi$
$762$	39.3875	1.42686
$763$	−10.1230	−0.366478
$764$	5.27267	0.190759
$765$	5.54991	0.200658
$766$	11.7151	0.423284
$767$	−46.5388	−1.68042
$768$	−1.95043	−0.0703801
$769$	42.2755	1.52449	0.762247	−	0.647286i	$-0.224096\pi$
$769$	42.2755	1.52449	0.762247	+	0.647286i	$0.224096\pi$
$770$	−9.60977	−0.346312
$771$	−17.9184	−0.645317
$772$	22.8247	0.821477
$773$	54.6634	1.96610	0.983052	−	0.183326i	$-0.0586864\pi$
$773$	54.6634	1.96610	0.983052	+	0.183326i	$0.0586864\pi$
$774$	−3.39794	−0.122136
$775$	−1.13860	−0.0408997
$776$	1.00000	0.0358979
$777$	7.20868	0.258610
$778$	−36.7199	−1.31647
$779$	−33.0237	−1.18320
$780$	15.1964	0.544117
$781$	−13.7985	−0.493749
$782$	−14.0148	−0.501169
$783$	5.06030	0.180840
$784$	−6.27842	−0.224229
$785$	−36.0397	−1.28631
$786$	−33.6779	−1.20125
$787$	21.6870	0.773059	0.386530	−	0.922277i	$-0.373674\pi$
$787$	21.6870	0.773059	0.386530	+	0.922277i	$0.373674\pi$
$788$	−0.965049	−0.0343784
$789$	−11.9898	−0.426850
$790$	7.78466	0.276966
$791$	−5.64135	−0.200583
$792$	4.62966	0.164508
$793$	44.8508	1.59270
$794$	0.953912	0.0338531
$795$	26.5268	0.940808
$796$	20.6925	0.733426
$797$	4.01548	0.142236	0.0711178	−	0.997468i	$-0.477343\pi$
$797$	4.01548	0.142236	0.0711178	+	0.997468i	$0.477343\pi$
$798$	4.68723	0.165926
$799$	−15.5569	−0.550363
$800$	−1.13860	−0.0402555
$801$	5.95276	0.210330
$802$	−38.6180	−1.36365
$803$	50.7383	1.79051
$804$	16.7451	0.590553
$805$	−6.66102	−0.234770
$806$	3.96494	0.139659
$807$	52.8615	1.86081
$808$	0.259225	0.00911951
$809$	43.0202	1.51251	0.756255	−	0.654277i	$-0.227027\pi$
$809$	43.0202	1.51251	0.756255	+	0.654277i	$0.227027\pi$
$810$	21.1553	0.743323
$811$	22.3770	0.785764	0.392882	−	0.919589i	$-0.371478\pi$
$811$	22.3770	0.785764	0.392882	+	0.919589i	$0.371478\pi$
$812$	1.00367	0.0352220
$813$	−39.5652	−1.38761
$814$	−25.0484	−0.877946
$815$	−19.1986	−0.672497
$816$	6.85004	0.239799
$817$	11.9538	0.418212
$818$	4.85395	0.169714
$819$	2.70851	0.0946432
$820$	−22.9380	−0.801028
$821$	29.2194	1.01976	0.509882	−	0.860244i	$-0.329689\pi$
$821$	29.2194	1.01976	0.509882	+	0.860244i	$0.329689\pi$
$822$	−16.3542	−0.570420
$823$	−23.3283	−0.813174	−0.406587	−	0.913612i	$-0.633281\pi$
$823$	−23.3283	−0.813174	−0.406587	+	0.913612i	$0.633281\pi$
$824$	−9.36759	−0.326335
$825$	12.7849	0.445114
$826$	−9.97060	−0.346921
$827$	−32.7489	−1.13879	−0.569396	−	0.822064i	$-0.692823\pi$
$827$	−32.7489	−1.13879	−0.569396	+	0.822064i	$0.692823\pi$
$828$	3.20905	0.111522
$829$	−5.53125	−0.192108	−0.0960541	−	0.995376i	$-0.530622\pi$
$829$	−5.53125	−0.192108	−0.0960541	+	0.995376i	$0.530622\pi$
$830$	−1.00144	−0.0347604
$831$	−14.2419	−0.494045
$832$	3.96494	0.137460
$833$	22.0502	0.763994
$834$	−32.5581	−1.12740
$835$	−41.4835	−1.43560
$836$	−16.2870	−0.563297
$837$	4.28280	0.148035
$838$	38.5072	1.33021
$839$	−22.4608	−0.775433	−0.387717	−	0.921779i	$-0.626736\pi$
$839$	−22.4608	−0.775433	−0.387717	+	0.921779i	$0.626736\pi$
$840$	3.25571	0.112333
$841$	−27.6040	−0.951861
$842$	−37.5225	−1.29311
$843$	21.8992	0.754248
$844$	27.6344	0.951214
$845$	−5.34643	−0.183923
$846$	3.56214	0.122469
$847$	18.8098	0.646313
$848$	6.92121	0.237675
$849$	−64.2295	−2.20435
$850$	3.99883	0.137159
$851$	−17.3623	−0.595173
$852$	4.67481	0.160156
$853$	16.8277	0.576168	0.288084	−	0.957605i	$-0.406982\pi$
$853$	16.8277	0.576168	0.288084	+	0.957605i	$0.406982\pi$
$854$	9.60895	0.328812
$855$	4.47061	0.152892
$856$	−11.3581	−0.388212
$857$	−22.4241	−0.765994	−0.382997	−	0.923750i	$-0.625108\pi$
$857$	−22.4241	−0.765994	−0.382997	+	0.923750i	$0.625108\pi$
$858$	−44.5210	−1.51992
$859$	−33.0110	−1.12632	−0.563160	−	0.826348i	$-0.690414\pi$
$859$	−33.0110	−1.12632	−0.563160	+	0.826348i	$0.690414\pi$
$860$	8.30304	0.283131
$861$	−19.3400	−0.659104
$862$	22.0921	0.752461
$863$	−5.34714	−0.182019	−0.0910093	−	0.995850i	$-0.529009\pi$
$863$	−5.34714	−0.182019	−0.0910093	+	0.995850i	$0.529009\pi$
$864$	4.28280	0.145704
$865$	13.5334	0.460151
$866$	6.89269	0.234223
$867$	9.09954	0.309037
$868$	0.849460	0.0288326
$869$	−22.8068	−0.773668
$870$	4.52847	0.153529
$871$	−34.0403	−1.15341
$872$	−11.9170	−0.403561
$873$	0.804176	0.0272172
$874$	−11.2893	−0.381867
$875$	10.2467	0.346402
$876$	−17.1897	−0.580786
$877$	37.5829	1.26909	0.634543	−	0.772888i	$-0.281189\pi$
$877$	37.5829	1.26909	0.634543	+	0.772888i	$0.281189\pi$
$878$	−32.8212	−1.10766
$879$	24.4745	0.825504
$880$	−11.3128	−0.381354
$881$	−11.5124	−0.387861	−0.193931	−	0.981015i	$-0.562124\pi$
$881$	−11.5124	−0.387861	−0.193931	+	0.981015i	$0.562124\pi$
$882$	−5.04895	−0.170007
$883$	−21.9477	−0.738599	−0.369300	−	0.929310i	$-0.620402\pi$
$883$	−21.9477	−0.738599	−0.369300	+	0.929310i	$0.620402\pi$
$884$	−13.9251	−0.468353
$885$	−44.9864	−1.51220
$886$	12.2335	0.410993
$887$	−22.4611	−0.754169	−0.377084	−	0.926179i	$-0.623073\pi$
$887$	−22.4611	−0.754169	−0.377084	+	0.926179i	$0.623073\pi$
$888$	8.48619	0.284778
$889$	−17.1542	−0.575334
$890$	−14.5459	−0.487579
$891$	−61.9791	−2.07638
$892$	−2.78037	−0.0930938
$893$	−12.5315	−0.419351
$894$	24.0747	0.805177
$895$	−11.0038	−0.367817
$896$	0.849460	0.0283785
$897$	−30.8597	−1.03038
$898$	20.6792	0.690075
$899$	1.18154	0.0394066
$900$	−0.915634	−0.0305211
$901$	−24.3077	−0.809808
$902$	67.2016	2.23757
$903$	7.00064	0.232967
$904$	−6.64110	−0.220880
$905$	−30.5913	−1.01689
$906$	−10.9268	−0.363018
$907$	39.4681	1.31052	0.655258	−	0.755405i	$-0.272560\pi$
$907$	39.4681	1.31052	0.655258	+	0.755405i	$0.272560\pi$
$908$	−11.2656	−0.373863
$909$	0.208463	0.00691427
$910$	−6.61839	−0.219398
$911$	−48.3900	−1.60323	−0.801616	−	0.597839i	$-0.796026\pi$
$911$	−48.3900	−1.60323	−0.801616	+	0.597839i	$0.796026\pi$
$912$	5.51789	0.182716
$913$	2.93393	0.0970988
$914$	−34.0194	−1.12526
$915$	43.3547	1.43326
$916$	−13.3464	−0.440977
$917$	14.6675	0.484365
$918$	−15.0415	−0.496443
$919$	48.8409	1.61111	0.805556	−	0.592520i	$-0.201867\pi$
$919$	48.8409	1.61111	0.805556	+	0.592520i	$0.201867\pi$
$920$	−7.84147	−0.258526
$921$	−39.0436	−1.28653
$922$	−11.4858	−0.378265
$923$	−9.50322	−0.312802
$924$	−9.53830	−0.313787
$925$	4.95397	0.162885
$926$	6.49973	0.213594
$927$	−7.53319	−0.247422
$928$	1.18154	0.0387859
$929$	−24.0029	−0.787508	−0.393754	−	0.919216i	$-0.628824\pi$
$929$	−24.0029	−0.787508	−0.393754	+	0.919216i	$0.628824\pi$
$930$	3.83268	0.125679
$931$	17.7621	0.582128
$932$	17.5061	0.573433
$933$	58.3357	1.90983
$934$	−25.2960	−0.827709
$935$	39.7313	1.29935
$936$	3.18851	0.104220
$937$	35.5441	1.16117	0.580587	−	0.814198i	$-0.302823\pi$
$937$	35.5441	1.16117	0.580587	+	0.814198i	$0.302823\pi$
$938$	−7.29289	−0.238121
$939$	−30.8823	−1.00781
$940$	−8.70427	−0.283902
$941$	40.3462	1.31525	0.657624	−	0.753346i	$-0.271562\pi$
$941$	40.3462	1.31525	0.657624	+	0.753346i	$0.271562\pi$
$942$	−35.7716	−1.16550
$943$	46.5809	1.51688
$944$	−11.7376	−0.382025
$945$	−7.14897	−0.232556
$946$	−24.3255	−0.790891
$947$	49.5835	1.61125	0.805624	−	0.592427i	$-0.201830\pi$
$947$	49.5835	1.61125	0.805624	+	0.592427i	$0.201830\pi$
$948$	7.72676	0.250953
$949$	34.9442	1.13434
$950$	3.22117	0.104509
$951$	−35.0145	−1.13542
$952$	−2.98336	−0.0966912
$953$	34.2771	1.11034	0.555172	−	0.831736i	$-0.312652\pi$
$953$	34.2771	1.11034	0.555172	+	0.831736i	$0.312652\pi$
$954$	5.56587	0.180202
$955$	−10.3610	−0.335275
$956$	24.3085	0.786192
$957$	−13.2671	−0.428865
$958$	−1.90964	−0.0616977
$959$	7.12267	0.230003
$960$	3.83268	0.123699
$961$	1.00000	0.0322581
$962$	−17.2512	−0.556201
$963$	−9.13392	−0.294337
$964$	10.0867	0.324870
$965$	−44.8515	−1.44382
$966$	−6.61148	−0.212721
$967$	59.6287	1.91753	0.958765	−	0.284201i	$-0.0917284\pi$
$967$	59.6287	1.91753	0.958765	+	0.284201i	$0.0917284\pi$
$968$	22.1433	0.711711
$969$	−19.3792	−0.622550
$970$	−1.96504	−0.0630938
$971$	6.96641	0.223563	0.111781	−	0.993733i	$-0.464344\pi$
$971$	6.96641	0.223563	0.111781	+	0.993733i	$0.464344\pi$
$972$	8.14959	0.261398
$973$	14.1799	0.454586
$974$	−28.8545	−0.924558
$975$	8.80517	0.281991
$976$	11.3118	0.362083
$977$	−28.7740	−0.920562	−0.460281	−	0.887773i	$-0.652251\pi$
$977$	−28.7740	−0.920562	−0.460281	+	0.887773i	$0.652251\pi$
$978$	−19.0558	−0.609337
$979$	42.6152	1.36199
$980$	12.3374	0.394103
$981$	−9.58337	−0.305974
$982$	−29.0430	−0.926799
$983$	−14.9234	−0.475983	−0.237991	−	0.971267i	$-0.576489\pi$
$983$	−14.9234	−0.475983	−0.237991	+	0.971267i	$0.576489\pi$
$984$	−22.7674	−0.725797
$985$	1.89636	0.0604232
$986$	−4.14964	−0.132152
$987$	−7.33894	−0.233601
$988$	−11.2171	−0.356863
$989$	−16.8612	−0.536156
$990$	−9.09748	−0.289137
$991$	−56.8426	−1.80567	−0.902833	−	0.429991i	$-0.858517\pi$
$991$	−56.8426	−1.80567	−0.902833	+	0.429991i	$0.858517\pi$
$992$	1.00000	0.0317500
$993$	−38.9451	−1.23589
$994$	−2.03600	−0.0645779
$995$	−40.6617	−1.28906
$996$	−0.993990	−0.0314958
$997$	6.54562	0.207302	0.103651	−	0.994614i	$-0.466948\pi$
$997$	6.54562	0.207302	0.103651	+	0.994614i	$0.466948\pi$
$998$	19.8056	0.626934
$999$	−18.6342	−0.589560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.9	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.9	✓	37	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.95043 q^{3} +1.00000 q^{4} -1.96504 q^{5} -1.95043 q^{6} +0.849460 q^{7} +1.00000 q^{8} +0.804176 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.95043 q^{3} +1.00000 q^{4} -1.96504 q^{5} -1.95043 q^{6} +0.849460 q^{7} +1.00000 q^{8} +0.804176 q^{9} -1.96504 q^{10} +5.75702 q^{11} -1.95043 q^{12} +3.96494 q^{13} +0.849460 q^{14} +3.83268 q^{15} +1.00000 q^{16} -3.51206 q^{17} +0.804176 q^{18} -2.82907 q^{19} -1.96504 q^{20} -1.65681 q^{21} +5.75702 q^{22} +3.99048 q^{23} -1.95043 q^{24} -1.13860 q^{25} +3.96494 q^{26} +4.28280 q^{27} +0.849460 q^{28} +1.18154 q^{29} +3.83268 q^{30} +1.00000 q^{31} +1.00000 q^{32} -11.2287 q^{33} -3.51206 q^{34} -1.66923 q^{35} +0.804176 q^{36} -4.35094 q^{37} -2.82907 q^{38} -7.73334 q^{39} -1.96504 q^{40} +11.6730 q^{41} -1.65681 q^{42} -4.22537 q^{43} +5.75702 q^{44} -1.58024 q^{45} +3.99048 q^{46} +4.42955 q^{47} -1.95043 q^{48} -6.27842 q^{49} -1.13860 q^{50} +6.85004 q^{51} +3.96494 q^{52} +6.92121 q^{53} +4.28280 q^{54} -11.3128 q^{55} +0.849460 q^{56} +5.51789 q^{57} +1.18154 q^{58} -11.7376 q^{59} +3.83268 q^{60} +11.3118 q^{61} +1.00000 q^{62} +0.683116 q^{63} +1.00000 q^{64} -7.79129 q^{65} -11.2287 q^{66} -8.58532 q^{67} -3.51206 q^{68} -7.78315 q^{69} -1.66923 q^{70} -2.39681 q^{71} +0.804176 q^{72} +8.81329 q^{73} -4.35094 q^{74} +2.22076 q^{75} -2.82907 q^{76} +4.89036 q^{77} -7.73334 q^{78} -3.96157 q^{79} -1.96504 q^{80} -10.7658 q^{81} +11.6730 q^{82} +0.509626 q^{83} -1.65681 q^{84} +6.90136 q^{85} -4.22537 q^{86} -2.30451 q^{87} +5.75702 q^{88} +7.40231 q^{89} -1.58024 q^{90} +3.36806 q^{91} +3.99048 q^{92} -1.95043 q^{93} +4.42955 q^{94} +5.55924 q^{95} -1.95043 q^{96} +1.00000 q^{97} -6.27842 q^{98} +4.62966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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