LMFDB - Embedded newform 6023.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39507 q^{2} +3.00458 q^{3} +3.73634 q^{4} -1.01813 q^{5} -7.19617 q^{6} -4.72960 q^{7} -4.15865 q^{8} +6.02752 q^{9} +O(q^{10})$	\(q-2.39507 q^{2} +3.00458 q^{3} +3.73634 q^{4} -1.01813 q^{5} -7.19617 q^{6} -4.72960 q^{7} -4.15865 q^{8} +6.02752 q^{9} +2.43848 q^{10} +0.589200 q^{11} +11.2261 q^{12} -6.17224 q^{13} +11.3277 q^{14} -3.05904 q^{15} +2.48757 q^{16} +2.09909 q^{17} -14.4363 q^{18} +1.00000 q^{19} -3.80407 q^{20} -14.2105 q^{21} -1.41117 q^{22} +5.81257 q^{23} -12.4950 q^{24} -3.96342 q^{25} +14.7829 q^{26} +9.09643 q^{27} -17.6714 q^{28} +1.13107 q^{29} +7.32661 q^{30} -7.55520 q^{31} +2.35942 q^{32} +1.77030 q^{33} -5.02746 q^{34} +4.81533 q^{35} +22.5209 q^{36} -3.19545 q^{37} -2.39507 q^{38} -18.5450 q^{39} +4.23403 q^{40} -8.50920 q^{41} +34.0350 q^{42} +11.8294 q^{43} +2.20145 q^{44} -6.13677 q^{45} -13.9215 q^{46} -9.12944 q^{47} +7.47410 q^{48} +15.3691 q^{49} +9.49265 q^{50} +6.30689 q^{51} -23.0616 q^{52} +7.56474 q^{53} -21.7866 q^{54} -0.599880 q^{55} +19.6688 q^{56} +3.00458 q^{57} -2.70900 q^{58} -1.97358 q^{59} -11.4296 q^{60} -6.88396 q^{61} +18.0952 q^{62} -28.5078 q^{63} -10.6261 q^{64} +6.28412 q^{65} -4.23999 q^{66} +11.9074 q^{67} +7.84291 q^{68} +17.4643 q^{69} -11.5330 q^{70} +16.3376 q^{71} -25.0664 q^{72} +13.1663 q^{73} +7.65333 q^{74} -11.9084 q^{75} +3.73634 q^{76} -2.78668 q^{77} +44.4165 q^{78} +6.17848 q^{79} -2.53266 q^{80} +9.24843 q^{81} +20.3801 q^{82} -10.2291 q^{83} -53.0952 q^{84} -2.13714 q^{85} -28.3322 q^{86} +3.39841 q^{87} -2.45028 q^{88} +8.27659 q^{89} +14.6980 q^{90} +29.1922 q^{91} +21.7177 q^{92} -22.7002 q^{93} +21.8656 q^{94} -1.01813 q^{95} +7.08908 q^{96} -3.03293 q^{97} -36.8101 q^{98} +3.55141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	−2.39507	−1.69357	−0.846784	−	0.531937i	$-0.821464\pi$
$2$	−2.39507	−1.69357	−0.846784	+	0.531937i	$0.821464\pi$
$3$	3.00458	1.73470	0.867348	−	0.497701i	$-0.165822\pi$
$3$	3.00458	1.73470	0.867348	+	0.497701i	$0.165822\pi$
$4$	3.73634	1.86817
$5$	−1.01813	−0.455320	−0.227660	−	0.973741i	$-0.573107\pi$
$5$	−1.01813	−0.455320	−0.227660	+	0.973741i	$0.573107\pi$
$6$	−7.19617	−2.93783
$7$	−4.72960	−1.78762	−0.893811	−	0.448445i	$-0.851978\pi$
$7$	−4.72960	−1.78762	−0.893811	+	0.448445i	$0.851978\pi$
$8$	−4.15865	−1.47031
$9$	6.02752	2.00917
$10$	2.43848	0.771115
$11$	0.589200	0.177650	0.0888252	−	0.996047i	$-0.471689\pi$
$11$	0.589200	0.177650	0.0888252	+	0.996047i	$0.471689\pi$
$12$	11.2261	3.24071
$13$	−6.17224	−1.71187	−0.855935	−	0.517083i	$-0.827018\pi$
$13$	−6.17224	−1.71187	−0.855935	+	0.517083i	$0.827018\pi$
$14$	11.3277	3.02746
$15$	−3.05904	−0.789842
$16$	2.48757	0.621892
$17$	2.09909	0.509104	0.254552	−	0.967059i	$-0.418072\pi$
$17$	2.09909	0.509104	0.254552	+	0.967059i	$0.418072\pi$
$18$	−14.4363	−3.40267
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.80407	−0.850615
$21$	−14.2105	−3.10098
$22$	−1.41117	−0.300863
$23$	5.81257	1.21200	0.606002	−	0.795463i	$-0.292772\pi$
$23$	5.81257	1.21200	0.606002	+	0.795463i	$0.292772\pi$
$24$	−12.4950	−2.55054
$25$	−3.96342	−0.792684
$26$	14.7829	2.89917
$27$	9.09643	1.75061
$28$	−17.6714	−3.33958
$29$	1.13107	0.210035	0.105018	−	0.994470i	$-0.466510\pi$
$29$	1.13107	0.210035	0.105018	+	0.994470i	$0.466510\pi$
$30$	7.32661	1.33765
$31$	−7.55520	−1.35695	−0.678477	−	0.734622i	$-0.737360\pi$
$31$	−7.55520	−1.35695	−0.678477	+	0.734622i	$0.737360\pi$
$32$	2.35942	0.417091
$33$	1.77030	0.308170
$34$	−5.02746	−0.862202
$35$	4.81533	0.813939
$36$	22.5209	3.75348
$37$	−3.19545	−0.525330	−0.262665	−	0.964887i	$-0.584601\pi$
$37$	−3.19545	−0.525330	−0.262665	+	0.964887i	$0.584601\pi$
$38$	−2.39507	−0.388531
$39$	−18.5450	−2.96958
$40$	4.23403	0.669459
$41$	−8.50920	−1.32891	−0.664457	−	0.747326i	$-0.731337\pi$
$41$	−8.50920	−1.32891	−0.664457	+	0.747326i	$0.731337\pi$
$42$	34.0350	5.25172
$43$	11.8294	1.80397	0.901983	−	0.431771i	$-0.142111\pi$
$43$	11.8294	1.80397	0.901983	+	0.431771i	$0.142111\pi$
$44$	2.20145	0.331881
$45$	−6.13677	−0.914816
$46$	−13.9215	−2.05261
$47$	−9.12944	−1.33167	−0.665833	−	0.746101i	$-0.731924\pi$
$47$	−9.12944	−1.33167	−0.665833	+	0.746101i	$0.731924\pi$
$48$	7.47410	1.07879
$49$	15.3691	2.19559
$50$	9.49265	1.34246
$51$	6.30689	0.883141
$52$	−23.0616	−3.19807
$53$	7.56474	1.03910	0.519549	−	0.854441i	$-0.326100\pi$
$53$	7.56474	1.03910	0.519549	+	0.854441i	$0.326100\pi$
$54$	−21.7866	−2.96477
$55$	−0.599880	−0.0808878
$56$	19.6688	2.62835
$57$	3.00458	0.397967
$58$	−2.70900	−0.355709
$59$	−1.97358	−0.256939	−0.128469	−	0.991713i	$-0.541006\pi$
$59$	−1.97358	−0.256939	−0.128469	+	0.991713i	$0.541006\pi$
$60$	−11.4296	−1.47556
$61$	−6.88396	−0.881401	−0.440700	−	0.897654i	$-0.645270\pi$
$61$	−6.88396	−0.881401	−0.440700	+	0.897654i	$0.645270\pi$
$62$	18.0952	2.29809
$63$	−28.5078	−3.59164
$64$	−10.6261	−1.32826
$65$	6.28412	0.779449
$66$	−4.23999	−0.521906
$67$	11.9074	1.45472	0.727359	−	0.686257i	$-0.240748\pi$
$67$	11.9074	1.45472	0.727359	+	0.686257i	$0.240748\pi$
$68$	7.84291	0.951093
$69$	17.4643	2.10246
$70$	−11.5330	−1.37846
$71$	16.3376	1.93892	0.969460	−	0.245250i	$-0.0788700\pi$
$71$	16.3376	1.93892	0.969460	+	0.245250i	$0.0788700\pi$
$72$	−25.0664	−2.95410
$73$	13.1663	1.54100	0.770499	−	0.637442i	$-0.220007\pi$
$73$	13.1663	1.54100	0.770499	+	0.637442i	$0.220007\pi$
$74$	7.65333	0.889681
$75$	−11.9084	−1.37507
$76$	3.73634	0.428588
$77$	−2.78668	−0.317572
$78$	44.4165	5.02918
$79$	6.17848	0.695134	0.347567	−	0.937655i	$-0.387008\pi$
$79$	6.17848	0.695134	0.347567	+	0.937655i	$0.387008\pi$
$80$	−2.53266	−0.283160
$81$	9.24843	1.02760
$82$	20.3801	2.25061
$83$	−10.2291	−1.12279	−0.561395	−	0.827548i	$-0.689735\pi$
$83$	−10.2291	−1.12279	−0.561395	+	0.827548i	$0.689735\pi$
$84$	−53.0952	−5.79316
$85$	−2.13714	−0.231805
$86$	−28.3322	−3.05514
$87$	3.39841	0.364348
$88$	−2.45028	−0.261201
$89$	8.27659	0.877317	0.438658	−	0.898654i	$-0.355454\pi$
$89$	8.27659	0.877317	0.438658	+	0.898654i	$0.355454\pi$
$90$	14.6980	1.54930
$91$	29.1922	3.06018
$92$	21.7177	2.26423
$93$	−22.7002	−2.35390
$94$	21.8656	2.25527
$95$	−1.01813	−0.104458
$96$	7.08908	0.723526
$97$	−3.03293	−0.307947	−0.153974	−	0.988075i	$-0.549207\pi$
$97$	−3.03293	−0.307947	−0.153974	+	0.988075i	$0.549207\pi$
$98$	−36.8101	−3.71838
$99$	3.55141	0.356931
$100$	−14.8087	−1.48087
$101$	−4.80855	−0.478468	−0.239234	−	0.970962i	$-0.576896\pi$
$101$	−4.80855	−0.478468	−0.239234	+	0.970962i	$0.576896\pi$
$102$	−15.1054	−1.49566
$103$	−4.89068	−0.481893	−0.240947	−	0.970538i	$-0.577458\pi$
$103$	−4.89068	−0.481893	−0.240947	+	0.970538i	$0.577458\pi$
$104$	25.6682	2.51697
$105$	14.4681	1.41194
$106$	−18.1181	−1.75978
$107$	−0.0309404	−0.00299112	−0.00149556	−	0.999999i	$-0.500476\pi$
$107$	−0.0309404	−0.00299112	−0.00149556	+	0.999999i	$0.500476\pi$
$108$	33.9874	3.27044
$109$	−8.44365	−0.808755	−0.404378	−	0.914592i	$-0.632512\pi$
$109$	−8.44365	−0.808755	−0.404378	+	0.914592i	$0.632512\pi$
$110$	1.43675	0.136989
$111$	−9.60101	−0.911287
$112$	−11.7652	−1.11171
$113$	5.99693	0.564144	0.282072	−	0.959393i	$-0.408978\pi$
$113$	5.99693	0.564144	0.282072	+	0.959393i	$0.408978\pi$
$114$	−7.19617	−0.673984
$115$	−5.91793	−0.551849
$116$	4.22608	0.392382
$117$	−37.2033	−3.43944
$118$	4.72686	0.435143
$119$	−9.92785	−0.910085
$120$	12.7215	1.16131
$121$	−10.6528	−0.968440
$122$	16.4875	1.49271
$123$	−25.5666	−2.30526
$124$	−28.2288	−2.53502
$125$	9.12589	0.816244
$126$	68.2780	6.08269
$127$	1.49946	0.133055	0.0665277	−	0.997785i	$-0.478808\pi$
$127$	1.49946	0.133055	0.0665277	+	0.997785i	$0.478808\pi$
$128$	20.7314	1.83241
$129$	35.5424	3.12934
$130$	−15.0509	−1.32005
$131$	−16.1613	−1.41202	−0.706009	−	0.708203i	$-0.749506\pi$
$131$	−16.1613	−1.41202	−0.706009	+	0.708203i	$0.749506\pi$
$132$	6.61445	0.575714
$133$	−4.72960	−0.410108
$134$	−28.5190	−2.46366
$135$	−9.26131	−0.797087
$136$	−8.72938	−0.748538
$137$	19.9060	1.70069	0.850343	−	0.526228i	$-0.176394\pi$
$137$	19.9060	1.70069	0.850343	+	0.526228i	$0.176394\pi$
$138$	−41.8282	−3.56066
$139$	−1.66455	−0.141185	−0.0705927	−	0.997505i	$-0.522489\pi$
$139$	−1.66455	−0.141185	−0.0705927	+	0.997505i	$0.522489\pi$
$140$	17.9917	1.52058
$141$	−27.4302	−2.31004
$142$	−39.1297	−3.28369
$143$	−3.63668	−0.304115
$144$	14.9939	1.24949
$145$	−1.15158	−0.0956332
$146$	−31.5341	−2.60978
$147$	46.1778	3.80868
$148$	−11.9393	−0.981405
$149$	13.7195	1.12395	0.561973	−	0.827156i	$-0.310042\pi$
$149$	13.7195	1.12395	0.561973	+	0.827156i	$0.310042\pi$
$150$	28.5215	2.32877
$151$	1.30634	0.106308	0.0531540	−	0.998586i	$-0.483073\pi$
$151$	1.30634	0.106308	0.0531540	+	0.998586i	$0.483073\pi$
$152$	−4.15865	−0.337311
$153$	12.6523	1.02288
$154$	6.67429	0.537829
$155$	7.69215	0.617848
$156$	−69.2905	−5.54768
$157$	7.41210	0.591550	0.295775	−	0.955258i	$-0.404422\pi$
$157$	7.41210	0.591550	0.295775	+	0.955258i	$0.404422\pi$
$158$	−14.7979	−1.17726
$159$	22.7289	1.80252
$160$	−2.40219	−0.189910
$161$	−27.4911	−2.16660
$162$	−22.1506	−1.74032
$163$	−8.64547	−0.677166	−0.338583	−	0.940937i	$-0.609948\pi$
$163$	−8.64547	−0.677166	−0.338583	+	0.940937i	$0.609948\pi$
$164$	−31.7933	−2.48264
$165$	−1.80239	−0.140316
$166$	24.4994	1.90152
$167$	10.9368	0.846315	0.423158	−	0.906056i	$-0.360922\pi$
$167$	10.9368	0.846315	0.423158	+	0.906056i	$0.360922\pi$
$168$	59.0965	4.55939
$169$	25.0965	1.93050
$170$	5.11858	0.392578
$171$	6.02752	0.460936
$172$	44.1987	3.37012
$173$	−7.48000	−0.568694	−0.284347	−	0.958721i	$-0.591777\pi$
$173$	−7.48000	−0.568694	−0.284347	+	0.958721i	$0.591777\pi$
$174$	−8.13941	−0.617047
$175$	18.7454	1.41702
$176$	1.46567	0.110479
$177$	−5.92979	−0.445711
$178$	−19.8230	−1.48579
$179$	12.9278	0.966268	0.483134	−	0.875546i	$-0.339498\pi$
$179$	12.9278	0.966268	0.483134	+	0.875546i	$0.339498\pi$
$180$	−22.9291	−1.70903
$181$	17.8870	1.32953	0.664767	−	0.747051i	$-0.268531\pi$
$181$	17.8870	1.32953	0.664767	+	0.747051i	$0.268531\pi$
$182$	−69.9173	−5.18261
$183$	−20.6834	−1.52896
$184$	−24.1725	−1.78202
$185$	3.25338	0.239193
$186$	54.3685	3.98649
$187$	1.23678	0.0904425
$188$	−34.1107	−2.48778
$189$	−43.0225	−3.12943
$190$	2.43848	0.176906
$191$	16.1413	1.16794	0.583970	−	0.811775i	$-0.301499\pi$
$191$	16.1413	1.16794	0.583970	+	0.811775i	$0.301499\pi$
$192$	−31.9270	−2.30413
$193$	−11.6189	−0.836346	−0.418173	−	0.908368i	$-0.637329\pi$
$193$	−11.6189	−0.836346	−0.418173	+	0.908368i	$0.637329\pi$
$194$	7.26406	0.521529
$195$	18.8811	1.35211
$196$	57.4243	4.10174
$197$	−4.41738	−0.314726	−0.157363	−	0.987541i	$-0.550299\pi$
$197$	−4.41738	−0.314726	−0.157363	+	0.987541i	$0.550299\pi$
$198$	−8.50587	−0.604486
$199$	4.54096	0.321900	0.160950	−	0.986963i	$-0.448544\pi$
$199$	4.54096	0.321900	0.160950	+	0.986963i	$0.448544\pi$
$200$	16.4825	1.16549
$201$	35.7767	2.52349
$202$	11.5168	0.810318
$203$	−5.34953	−0.375464
$204$	23.5647	1.64986
$205$	8.66344	0.605081
$206$	11.7135	0.816118
$207$	35.0354	2.43513
$208$	−15.3538	−1.06460
$209$	0.589200	0.0407558
$210$	−34.6520	−2.39121
$211$	21.9635	1.51203	0.756015	−	0.654554i	$-0.227143\pi$
$211$	21.9635	1.51203	0.756015	+	0.654554i	$0.227143\pi$
$212$	28.2645	1.94121
$213$	49.0878	3.36344
$214$	0.0741043	0.00506567
$215$	−12.0438	−0.821382
$216$	−37.8289	−2.57393
$217$	35.7331	2.42572
$218$	20.2231	1.36968
$219$	39.5592	2.67316
$220$	−2.24136	−0.151112
$221$	−12.9561	−0.871520
$222$	22.9951	1.54333
$223$	15.0700	1.00916	0.504582	−	0.863364i	$-0.331647\pi$
$223$	15.0700	1.00916	0.504582	+	0.863364i	$0.331647\pi$
$224$	−11.1591	−0.745600
$225$	−23.8896	−1.59264
$226$	−14.3630	−0.955416
$227$	27.5355	1.82760	0.913798	−	0.406170i	$-0.133136\pi$
$227$	27.5355	1.82760	0.913798	+	0.406170i	$0.133136\pi$
$228$	11.2261	0.743470
$229$	3.71761	0.245666	0.122833	−	0.992427i	$-0.460802\pi$
$229$	3.71761	0.245666	0.122833	+	0.992427i	$0.460802\pi$
$230$	14.1738	0.934594
$231$	−8.37282	−0.550891
$232$	−4.70375	−0.308816
$233$	−21.5433	−1.41135	−0.705675	−	0.708535i	$-0.749356\pi$
$233$	−21.5433	−1.41135	−0.705675	+	0.708535i	$0.749356\pi$
$234$	89.1043	5.82493
$235$	9.29492	0.606334
$236$	−7.37398	−0.480005
$237$	18.5638	1.20585
$238$	23.7779	1.54129
$239$	5.16580	0.334148	0.167074	−	0.985944i	$-0.446568\pi$
$239$	5.16580	0.334148	0.167074	+	0.985944i	$0.446568\pi$
$240$	−7.60958	−0.491196
$241$	4.16454	0.268262	0.134131	−	0.990964i	$-0.457176\pi$
$241$	4.16454	0.268262	0.134131	+	0.990964i	$0.457176\pi$
$242$	25.5143	1.64012
$243$	0.498374	0.0319707
$244$	−25.7208	−1.64661
$245$	−15.6477	−0.999696
$246$	61.2337	3.90412
$247$	−6.17224	−0.392730
$248$	31.4195	1.99514
$249$	−30.7342	−1.94770
$250$	−21.8571	−1.38237
$251$	11.7893	0.744132	0.372066	−	0.928206i	$-0.378649\pi$
$251$	11.7893	0.744132	0.372066	+	0.928206i	$0.378649\pi$
$252$	−106.515	−6.70980
$253$	3.42476	0.215313
$254$	−3.59130	−0.225338
$255$	−6.42121	−0.402112
$256$	−28.4008	−1.77505
$257$	−0.789208	−0.0492294	−0.0246147	−	0.999697i	$-0.507836\pi$
$257$	−0.789208	−0.0492294	−0.0246147	+	0.999697i	$0.507836\pi$
$258$	−85.1264	−5.29974
$259$	15.1132	0.939090
$260$	23.4796	1.45614
$261$	6.81757	0.421997
$262$	38.7073	2.39135
$263$	−3.34852	−0.206478	−0.103239	−	0.994657i	$-0.532921\pi$
$263$	−3.34852	−0.206478	−0.103239	+	0.994657i	$0.532921\pi$
$264$	−7.36207	−0.453104
$265$	−7.70186	−0.473122
$266$	11.3277	0.694546
$267$	24.8677	1.52188
$268$	44.4900	2.71766
$269$	8.83235	0.538518	0.269259	−	0.963068i	$-0.413221\pi$
$269$	8.83235	0.538518	0.269259	+	0.963068i	$0.413221\pi$
$270$	22.1815	1.34992
$271$	30.8776	1.87568	0.937841	−	0.347066i	$-0.112822\pi$
$271$	30.8776	1.87568	0.937841	+	0.347066i	$0.112822\pi$
$272$	5.22162	0.316607
$273$	87.7104	5.30848
$274$	−47.6763	−2.88023
$275$	−2.33525	−0.140821
$276$	65.2527	3.92775
$277$	−5.19006	−0.311841	−0.155920	−	0.987770i	$-0.549834\pi$
$277$	−5.19006	−0.311841	−0.155920	+	0.987770i	$0.549834\pi$
$278$	3.98671	0.239107
$279$	−45.5391	−2.72636
$280$	−20.0253	−1.19674
$281$	−16.8870	−1.00739	−0.503697	−	0.863880i	$-0.668027\pi$
$281$	−16.8870	−1.00739	−0.503697	+	0.863880i	$0.668027\pi$
$282$	65.6971	3.91220
$283$	32.6531	1.94103	0.970514	−	0.241045i	$-0.0774902\pi$
$283$	32.6531	1.94103	0.970514	+	0.241045i	$0.0774902\pi$
$284$	61.0430	3.62223
$285$	−3.05904	−0.181202
$286$	8.71009	0.515039
$287$	40.2451	2.37560
$288$	14.2215	0.838007
$289$	−12.5938	−0.740813
$290$	2.75810	0.161961
$291$	−9.11269	−0.534195
$292$	49.1937	2.87885
$293$	−28.1439	−1.64418	−0.822091	−	0.569356i	$-0.807192\pi$
$293$	−28.1439	−1.64418	−0.822091	+	0.569356i	$0.807192\pi$
$294$	−110.599	−6.45026
$295$	2.00936	0.116989
$296$	13.2888	0.772395
$297$	5.35962	0.310997
$298$	−32.8591	−1.90348
$299$	−35.8765	−2.07479
$300$	−44.4939	−2.56886
$301$	−55.9484	−3.22481
$302$	−3.12876	−0.180040
$303$	−14.4477	−0.829997
$304$	2.48757	0.142672
$305$	7.00874	0.401319
$306$	−30.3031	−1.73231
$307$	−19.4815	−1.11187	−0.555933	−	0.831227i	$-0.687639\pi$
$307$	−19.4815	−1.11187	−0.555933	+	0.831227i	$0.687639\pi$
$308$	−10.4120	−0.593278
$309$	−14.6945	−0.835938
$310$	−18.4232	−1.04637
$311$	−16.5883	−0.940636	−0.470318	−	0.882497i	$-0.655861\pi$
$311$	−16.5883	−0.940636	−0.470318	+	0.882497i	$0.655861\pi$
$312$	77.1222	4.36619
$313$	28.1487	1.59106	0.795529	−	0.605916i	$-0.207193\pi$
$313$	28.1487	1.59106	0.795529	+	0.605916i	$0.207193\pi$
$314$	−17.7525	−1.00183
$315$	29.0245	1.63535
$316$	23.0849	1.29863
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−54.4372	−3.05269
$319$	0.666429	0.0373129
$320$	10.8187	0.604784
$321$	−0.0929630	−0.00518869
$322$	65.8431	3.66929
$323$	2.09909	0.116796
$324$	34.5553	1.91974
$325$	24.4632	1.35697
$326$	20.7065	1.14683
$327$	−25.3697	−1.40294
$328$	35.3868	1.95391
$329$	43.1786	2.38051
$330$	4.31684	0.237634
$331$	−10.2911	−0.565652	−0.282826	−	0.959171i	$-0.591272\pi$
$331$	−10.2911	−0.565652	−0.282826	+	0.959171i	$0.591272\pi$
$332$	−38.2194	−2.09756
$333$	−19.2607	−1.05548
$334$	−26.1944	−1.43329
$335$	−12.1232	−0.662362
$336$	−35.3495	−1.92847
$337$	8.05278	0.438663	0.219331	−	0.975650i	$-0.429612\pi$
$337$	8.05278	0.438663	0.219331	+	0.975650i	$0.429612\pi$
$338$	−60.1078	−3.26943
$339$	18.0183	0.978619
$340$	−7.98507	−0.433051
$341$	−4.45152	−0.241064
$342$	−14.4363	−0.780626
$343$	−39.5826	−2.13726
$344$	−49.1944	−2.65238
$345$	−17.7809	−0.957291
$346$	17.9151	0.963122
$347$	19.1177	1.02629	0.513146	−	0.858301i	$-0.328480\pi$
$347$	19.1177	1.02629	0.513146	+	0.858301i	$0.328480\pi$
$348$	12.6976	0.680663
$349$	−1.52944	−0.0818689	−0.0409344	−	0.999162i	$-0.513033\pi$
$349$	−1.52944	−0.0818689	−0.0409344	+	0.999162i	$0.513033\pi$
$350$	−44.8965	−2.39982
$351$	−56.1453	−2.99682
$352$	1.39017	0.0740964
$353$	−10.5043	−0.559090	−0.279545	−	0.960133i	$-0.590184\pi$
$353$	−10.5043	−0.559090	−0.279545	+	0.960133i	$0.590184\pi$
$354$	14.2022	0.754841
$355$	−16.6338	−0.882829
$356$	30.9242	1.63898
$357$	−29.8291	−1.57872
$358$	−30.9629	−1.63644
$359$	7.01081	0.370016	0.185008	−	0.982737i	$-0.440769\pi$
$359$	7.01081	0.370016	0.185008	+	0.982737i	$0.440769\pi$
$360$	25.5207	1.34506
$361$	1.00000	0.0526316
$362$	−42.8406	−2.25165
$363$	−32.0074	−1.67995
$364$	109.072	5.71693
$365$	−13.4049	−0.701647
$366$	49.5382	2.58940
$367$	17.7693	0.927548	0.463774	−	0.885953i	$-0.346495\pi$
$367$	17.7693	0.927548	0.463774	+	0.885953i	$0.346495\pi$
$368$	14.4591	0.753735
$369$	−51.2894	−2.67002
$370$	−7.79205	−0.405089
$371$	−35.7782	−1.85751
$372$	−84.8158	−4.39749
$373$	24.3782	1.26225	0.631127	−	0.775680i	$-0.282593\pi$
$373$	24.3782	1.26225	0.631127	+	0.775680i	$0.282593\pi$
$374$	−2.96218	−0.153171
$375$	27.4195	1.41594
$376$	37.9662	1.95796
$377$	−6.98126	−0.359553
$378$	103.042	5.29989
$379$	15.0096	0.770994	0.385497	−	0.922709i	$-0.374030\pi$
$379$	15.0096	0.770994	0.385497	+	0.922709i	$0.374030\pi$
$380$	−3.80407	−0.195145
$381$	4.50524	0.230811
$382$	−38.6594	−1.97799
$383$	33.5248	1.71304	0.856518	−	0.516116i	$-0.172623\pi$
$383$	33.5248	1.71304	0.856518	+	0.516116i	$0.172623\pi$
$384$	62.2891	3.17868
$385$	2.83719	0.144597
$386$	27.8280	1.41641
$387$	71.3019	3.62448
$388$	−11.3321	−0.575298
$389$	−2.99217	−0.151709	−0.0758545	−	0.997119i	$-0.524168\pi$
$389$	−2.99217	−0.151709	−0.0758545	+	0.997119i	$0.524168\pi$
$390$	−45.2216	−2.28988
$391$	12.2011	0.617036
$392$	−63.9149	−3.22819
$393$	−48.5579	−2.44942
$394$	10.5799	0.533009
$395$	−6.29048	−0.316508
$396$	13.2693	0.666807
$397$	−14.2418	−0.714773	−0.357387	−	0.933957i	$-0.616332\pi$
$397$	−14.2418	−0.714773	−0.357387	+	0.933957i	$0.616332\pi$
$398$	−10.8759	−0.545159
$399$	−14.2105	−0.711414
$400$	−9.85927	−0.492963
$401$	28.7792	1.43717	0.718583	−	0.695441i	$-0.244791\pi$
$401$	28.7792	1.43717	0.718583	+	0.695441i	$0.244791\pi$
$402$	−85.6876	−4.27371
$403$	46.6325	2.32293
$404$	−17.9664	−0.893860
$405$	−9.41607	−0.467888
$406$	12.8125	0.635873
$407$	−1.88276	−0.0933250
$408$	−26.2282	−1.29849
$409$	29.2176	1.44472	0.722358	−	0.691520i	$-0.243059\pi$
$409$	29.2176	1.44472	0.722358	+	0.691520i	$0.243059\pi$
$410$	−20.7495	−1.02475
$411$	59.8093	2.95018
$412$	−18.2733	−0.900259
$413$	9.33426	0.459309
$414$	−83.9120	−4.12405
$415$	10.4145	0.511229
$416$	−14.5629	−0.714005
$417$	−5.00128	−0.244914
$418$	−1.41117	−0.0690227
$419$	−30.6549	−1.49759	−0.748794	−	0.662803i	$-0.769367\pi$
$419$	−30.6549	−1.49759	−0.748794	+	0.662803i	$0.769367\pi$
$420$	54.0576	2.63774
$421$	5.10046	0.248581	0.124291	−	0.992246i	$-0.460334\pi$
$421$	5.10046	0.248581	0.124291	+	0.992246i	$0.460334\pi$
$422$	−52.6041	−2.56073
$423$	−55.0279	−2.67555
$424$	−31.4591	−1.52779
$425$	−8.31957	−0.403558
$426$	−117.568	−5.69621
$427$	32.5584	1.57561
$428$	−0.115604	−0.00558793
$429$	−10.9267	−0.527547
$430$	28.8457	1.39107
$431$	−35.6999	−1.71960	−0.859802	−	0.510628i	$-0.829413\pi$
$431$	−35.6999	−1.71960	−0.859802	+	0.510628i	$0.829413\pi$
$432$	22.6280	1.08869
$433$	30.5061	1.46603	0.733015	−	0.680212i	$-0.238112\pi$
$433$	30.5061	1.46603	0.733015	+	0.680212i	$0.238112\pi$
$434$	−85.5831	−4.10812
$435$	−3.46001	−0.165895
$436$	−31.5484	−1.51089
$437$	5.81257	0.278053
$438$	−94.7469	−4.52718
$439$	−10.5786	−0.504889	−0.252444	−	0.967611i	$-0.581235\pi$
$439$	−10.5786	−0.504889	−0.252444	+	0.967611i	$0.581235\pi$
$440$	2.49469	0.118930
$441$	92.6377	4.41132
$442$	31.0307	1.47598
$443$	−4.72928	−0.224695	−0.112348	−	0.993669i	$-0.535837\pi$
$443$	−4.72928	−0.224695	−0.112348	+	0.993669i	$0.535837\pi$
$444$	−35.8727	−1.70244
$445$	−8.42661	−0.399460
$446$	−36.0937	−1.70909
$447$	41.2214	1.94971
$448$	50.2572	2.37443
$449$	−30.2070	−1.42556	−0.712778	−	0.701390i	$-0.752563\pi$
$449$	−30.2070	−1.42556	−0.712778	+	0.701390i	$0.752563\pi$
$450$	57.2171	2.69724
$451$	−5.01362	−0.236082
$452$	22.4066	1.05392
$453$	3.92499	0.184412
$454$	−65.9493	−3.09516
$455$	−29.7214	−1.39336
$456$	−12.4950	−0.585133
$457$	17.0765	0.798803	0.399402	−	0.916776i	$-0.369218\pi$
$457$	17.0765	0.798803	0.399402	+	0.916776i	$0.369218\pi$
$458$	−8.90391	−0.416053
$459$	19.0942	0.891242
$460$	−22.1114	−1.03095
$461$	−30.7892	−1.43400	−0.716999	−	0.697074i	$-0.754485\pi$
$461$	−30.7892	−1.43400	−0.716999	+	0.697074i	$0.754485\pi$
$462$	20.0534	0.932971
$463$	−21.9123	−1.01835	−0.509175	−	0.860663i	$-0.670049\pi$
$463$	−21.9123	−1.01835	−0.509175	+	0.860663i	$0.670049\pi$
$464$	2.81362	0.130619
$465$	23.1117	1.07178
$466$	51.5977	2.39022
$467$	6.47387	0.299575	0.149788	−	0.988718i	$-0.452141\pi$
$467$	6.47387	0.299575	0.149788	+	0.988718i	$0.452141\pi$
$468$	−139.004	−6.42547
$469$	−56.3172	−2.60048
$470$	−22.2620	−1.02687
$471$	22.2703	1.02616
$472$	8.20745	0.377778
$473$	6.96988	0.320476
$474$	−44.4615	−2.04218
$475$	−3.96342	−0.181854
$476$	−37.0939	−1.70019
$477$	45.5966	2.08773
$478$	−12.3724	−0.565902
$479$	−16.1941	−0.739926	−0.369963	−	0.929047i	$-0.620630\pi$
$479$	−16.1941	−0.739926	−0.369963	+	0.929047i	$0.620630\pi$
$480$	−7.21757	−0.329436
$481$	19.7231	0.899296
$482$	−9.97436	−0.454320
$483$	−82.5994	−3.75840
$484$	−39.8027	−1.80921
$485$	3.08790	0.140214
$486$	−1.19364	−0.0541446
$487$	26.9300	1.22031	0.610156	−	0.792281i	$-0.291107\pi$
$487$	26.9300	1.22031	0.610156	+	0.792281i	$0.291107\pi$
$488$	28.6280	1.29593
$489$	−25.9760	−1.17468
$490$	37.4773	1.69305
$491$	−13.0677	−0.589738	−0.294869	−	0.955538i	$-0.595276\pi$
$491$	−13.0677	−0.589738	−0.294869	+	0.955538i	$0.595276\pi$
$492$	−95.5256	−4.30663
$493$	2.37423	0.106930
$494$	14.7829	0.665115
$495$	−3.61579	−0.162518
$496$	−18.7941	−0.843878
$497$	−77.2705	−3.46605
$498$	73.6104	3.29856
$499$	10.9024	0.488060	0.244030	−	0.969768i	$-0.421531\pi$
$499$	10.9024	0.488060	0.244030	+	0.969768i	$0.421531\pi$
$500$	34.0974	1.52488
$501$	32.8605	1.46810
$502$	−28.2361	−1.26024
$503$	−12.2113	−0.544474	−0.272237	−	0.962230i	$-0.587764\pi$
$503$	−12.2113	−0.544474	−0.272237	+	0.962230i	$0.587764\pi$
$504$	118.554	5.28081
$505$	4.89571	0.217856
$506$	−8.20254	−0.364647
$507$	75.4045	3.34883
$508$	5.60249	0.248570
$509$	5.12331	0.227087	0.113543	−	0.993533i	$-0.463780\pi$
$509$	5.12331	0.227087	0.113543	+	0.993533i	$0.463780\pi$
$510$	15.3792	0.681003
$511$	−62.2713	−2.75472
$512$	26.5591	1.17376
$513$	9.09643	0.401617
$514$	1.89021	0.0833734
$515$	4.97933	0.219415
$516$	132.799	5.84613
$517$	−5.37907	−0.236571
$518$	−36.1972	−1.59041
$519$	−22.4743	−0.986512
$520$	−26.1335	−1.14603
$521$	−10.4076	−0.455965	−0.227983	−	0.973665i	$-0.573213\pi$
$521$	−10.4076	−0.455965	−0.227983	+	0.973665i	$0.573213\pi$
$522$	−16.3285	−0.714681
$523$	7.09420	0.310208	0.155104	−	0.987898i	$-0.450429\pi$
$523$	7.09420	0.310208	0.155104	+	0.987898i	$0.450429\pi$
$524$	−60.3841	−2.63789
$525$	56.3221	2.45810
$526$	8.01992	0.349685
$527$	−15.8590	−0.690830
$528$	4.40374	0.191648
$529$	10.7859	0.468954
$530$	18.4465	0.801263
$531$	−11.8958	−0.516234
$532$	−17.6714	−0.766153
$533$	52.5208	2.27493
$534$	−59.5598	−2.57740
$535$	0.0315012	0.00136192
$536$	−49.5187	−2.13888
$537$	38.8426	1.67618
$538$	−21.1541	−0.912016
$539$	9.05549	0.390048
$540$	−34.6034	−1.48909
$541$	16.9982	0.730809	0.365405	−	0.930849i	$-0.380931\pi$
$541$	16.9982	0.730809	0.365405	+	0.930849i	$0.380931\pi$
$542$	−73.9539	−3.17659
$543$	53.7431	2.30634
$544$	4.95263	0.212342
$545$	8.59670	0.368242
$546$	−210.072	−8.99027
$547$	27.0950	1.15850	0.579250	−	0.815150i	$-0.303346\pi$
$547$	27.0950	1.15850	0.579250	+	0.815150i	$0.303346\pi$
$548$	74.3757	3.17717
$549$	−41.4932	−1.77089
$550$	5.59307	0.238489
$551$	1.13107	0.0481854
$552$	−72.6281	−3.09126
$553$	−29.2218	−1.24264
$554$	12.4305	0.528123
$555$	9.77504	0.414927
$556$	−6.21933	−0.263758
$557$	14.6003	0.618634	0.309317	−	0.950959i	$-0.399900\pi$
$557$	14.6003	0.618634	0.309317	+	0.950959i	$0.399900\pi$
$558$	109.069	4.61727
$559$	−73.0139	−3.08816
$560$	11.9785	0.506182
$561$	3.71602	0.156890
$562$	40.4455	1.70609
$563$	−29.7252	−1.25277	−0.626383	−	0.779515i	$-0.715466\pi$
$563$	−29.7252	−1.25277	−0.626383	+	0.779515i	$0.715466\pi$
$564$	−102.488	−4.31554
$565$	−6.10563	−0.256866
$566$	−78.2064	−3.28726
$567$	−43.7414	−1.83697
$568$	−67.9425	−2.85081
$569$	−26.4817	−1.11017	−0.555086	−	0.831793i	$-0.687315\pi$
$569$	−26.4817	−1.11017	−0.555086	+	0.831793i	$0.687315\pi$
$570$	7.32661	0.306878
$571$	29.2970	1.22604	0.613020	−	0.790067i	$-0.289954\pi$
$571$	29.2970	1.22604	0.613020	+	0.790067i	$0.289954\pi$
$572$	−13.5879	−0.568138
$573$	48.4977	2.02602
$574$	−96.3898	−4.02323
$575$	−23.0376	−0.960736
$576$	−64.0490	−2.66871
$577$	−23.7568	−0.989010	−0.494505	−	0.869175i	$-0.664651\pi$
$577$	−23.7568	−0.989010	−0.494505	+	0.869175i	$0.664651\pi$
$578$	30.1630	1.25462
$579$	−34.9099	−1.45081
$580$	−4.30268	−0.178659
$581$	48.3796	2.00712
$582$	21.8255	0.904695
$583$	4.45715	0.184596
$584$	−54.7540	−2.26574
$585$	37.8776	1.56605
$586$	67.4064	2.78453
$587$	29.6092	1.22210	0.611051	−	0.791592i	$-0.290747\pi$
$587$	29.6092	1.22210	0.611051	+	0.791592i	$0.290747\pi$
$588$	172.536	7.11527
$589$	−7.55520	−0.311307
$590$	−4.81254	−0.198129
$591$	−13.2724	−0.545953
$592$	−7.94891	−0.326698
$593$	41.2347	1.69330	0.846652	−	0.532146i	$-0.178614\pi$
$593$	41.2347	1.69330	0.846652	+	0.532146i	$0.178614\pi$
$594$	−12.8366	−0.526694
$595$	10.1078	0.414380
$596$	51.2608	2.09972
$597$	13.6437	0.558399
$598$	85.9267	3.51380
$599$	−43.2716	−1.76803	−0.884015	−	0.467459i	$-0.845170\pi$
$599$	−43.2716	−1.76803	−0.884015	+	0.467459i	$0.845170\pi$
$600$	49.5230	2.02177
$601$	−13.2000	−0.538437	−0.269219	−	0.963079i	$-0.586765\pi$
$601$	−13.2000	−0.538437	−0.269219	+	0.963079i	$0.586765\pi$
$602$	134.000	5.46143
$603$	71.7720	2.92278
$604$	4.88092	0.198602
$605$	10.8459	0.440950
$606$	34.6031	1.40566
$607$	−3.89524	−0.158103	−0.0790515	−	0.996871i	$-0.525189\pi$
$607$	−3.89524	−0.158103	−0.0790515	+	0.996871i	$0.525189\pi$
$608$	2.35942	0.0956872
$609$	−16.0731	−0.651315
$610$	−16.7864	−0.679661
$611$	56.3491	2.27964
$612$	47.2733	1.91091
$613$	2.90037	0.117145	0.0585724	−	0.998283i	$-0.481345\pi$
$613$	2.90037	0.117145	0.0585724	+	0.998283i	$0.481345\pi$
$614$	46.6594	1.88302
$615$	26.0300	1.04963
$616$	11.5888	0.466928
$617$	12.5465	0.505103	0.252551	−	0.967584i	$-0.418730\pi$
$617$	12.5465	0.505103	0.252551	+	0.967584i	$0.418730\pi$
$618$	35.1942	1.41572
$619$	−39.9272	−1.60481	−0.802406	−	0.596779i	$-0.796447\pi$
$619$	−39.9272	−1.60481	−0.802406	+	0.596779i	$0.796447\pi$
$620$	28.7405	1.15425
$621$	52.8736	2.12175
$622$	39.7300	1.59303
$623$	−39.1450	−1.56831
$624$	−46.1319	−1.84675
$625$	10.5258	0.421032
$626$	−67.4179	−2.69456
$627$	1.77030	0.0706990
$628$	27.6941	1.10512
$629$	−6.70754	−0.267447
$630$	−69.5156	−2.76957
$631$	17.5667	0.699320	0.349660	−	0.936877i	$-0.386297\pi$
$631$	17.5667	0.699320	0.349660	+	0.936877i	$0.386297\pi$
$632$	−25.6942	−1.02206
$633$	65.9912	2.62292
$634$	2.39507	0.0951202
$635$	−1.52664	−0.0605827
$636$	84.9229	3.36741
$637$	−94.8619	−3.75857
$638$	−1.59614	−0.0631919
$639$	98.4754	3.89563
$640$	−21.1072	−0.834333
$641$	3.49267	0.137952	0.0689761	−	0.997618i	$-0.478027\pi$
$641$	3.49267	0.137952	0.0689761	+	0.997618i	$0.478027\pi$
$642$	0.222653	0.00878739
$643$	3.30764	0.130441	0.0652203	−	0.997871i	$-0.479225\pi$
$643$	3.30764	0.130441	0.0652203	+	0.997871i	$0.479225\pi$
$644$	−102.716	−4.04759
$645$	−36.1867	−1.42485
$646$	−5.02746	−0.197803
$647$	5.80277	0.228130	0.114065	−	0.993473i	$-0.463613\pi$
$647$	5.80277	0.228130	0.114065	+	0.993473i	$0.463613\pi$
$648$	−38.4610	−1.51089
$649$	−1.16284	−0.0456453
$650$	−58.5909	−2.29812
$651$	107.363	4.20789
$652$	−32.3024	−1.26506
$653$	−6.99359	−0.273680	−0.136840	−	0.990593i	$-0.543695\pi$
$653$	−6.99359	−0.273680	−0.136840	+	0.990593i	$0.543695\pi$
$654$	60.7620	2.37598
$655$	16.4542	0.642919
$656$	−21.1672	−0.826441
$657$	79.3600	3.09613
$658$	−103.416	−4.03156
$659$	−7.22235	−0.281343	−0.140671	−	0.990056i	$-0.544926\pi$
$659$	−7.22235	−0.281343	−0.140671	+	0.990056i	$0.544926\pi$
$660$	−6.73434	−0.262134
$661$	−42.4562	−1.65136	−0.825678	−	0.564142i	$-0.809207\pi$
$661$	−42.4562	−1.65136	−0.825678	+	0.564142i	$0.809207\pi$
$662$	24.6479	0.957969
$663$	−38.9276	−1.51182
$664$	42.5393	1.65084
$665$	4.81533	0.186731
$666$	46.1306	1.78752
$667$	6.57445	0.254564
$668$	40.8636	1.58106
$669$	45.2791	1.75059
$670$	29.0359	1.12175
$671$	−4.05603	−0.156581
$672$	−33.5285	−1.29339
$673$	−23.1288	−0.891549	−0.445775	−	0.895145i	$-0.647072\pi$
$673$	−23.1288	−0.891549	−0.445775	+	0.895145i	$0.647072\pi$
$674$	−19.2869	−0.742905
$675$	−36.0530	−1.38768
$676$	93.7691	3.60650
$677$	−6.31118	−0.242558	−0.121279	−	0.992618i	$-0.538700\pi$
$677$	−6.31118	−0.242558	−0.121279	+	0.992618i	$0.538700\pi$
$678$	−43.1550	−1.65736
$679$	14.3445	0.550493
$680$	8.88761	0.340824
$681$	82.7327	3.17032
$682$	10.6617	0.408257
$683$	43.5548	1.66658	0.833289	−	0.552838i	$-0.186455\pi$
$683$	43.5548	1.66658	0.833289	+	0.552838i	$0.186455\pi$
$684$	22.5209	0.861107
$685$	−20.2668	−0.774356
$686$	94.8031	3.61960
$687$	11.1699	0.426157
$688$	29.4264	1.12187
$689$	−46.6914	−1.77880
$690$	42.5864	1.62124
$691$	−30.4117	−1.15691	−0.578457	−	0.815713i	$-0.696345\pi$
$691$	−30.4117	−1.15691	−0.578457	+	0.815713i	$0.696345\pi$
$692$	−27.9478	−1.06242
$693$	−16.7968	−0.638057
$694$	−45.7882	−1.73809
$695$	1.69472	0.0642845
$696$	−14.1328	−0.535702
$697$	−17.8616	−0.676555
$698$	3.66310	0.138650
$699$	−64.7287	−2.44827
$700$	70.0392	2.64723
$701$	10.6193	0.401086	0.200543	−	0.979685i	$-0.435729\pi$
$701$	10.6193	0.401086	0.200543	+	0.979685i	$0.435729\pi$
$702$	134.472	5.07531
$703$	−3.19545	−0.120519
$704$	−6.26090	−0.235967
$705$	27.9274	1.05181
$706$	25.1586	0.946856
$707$	22.7425	0.855320
$708$	−22.1557	−0.832664
$709$	6.07485	0.228146	0.114073	−	0.993472i	$-0.463610\pi$
$709$	6.07485	0.228146	0.114073	+	0.993472i	$0.463610\pi$
$710$	39.8390	1.49513
$711$	37.2409	1.39664
$712$	−34.4195	−1.28992
$713$	−43.9151	−1.64463
$714$	71.4426	2.67367
$715$	3.70260	0.138469
$716$	48.3026	1.80515
$717$	15.5211	0.579645
$718$	−16.7913	−0.626647
$719$	35.7313	1.33255	0.666276	−	0.745705i	$-0.267887\pi$
$719$	35.7313	1.33255	0.666276	+	0.745705i	$0.267887\pi$
$720$	−15.2656	−0.568917
$721$	23.1310	0.861442
$722$	−2.39507	−0.0891351
$723$	12.5127	0.465353
$724$	66.8321	2.48380
$725$	−4.48292	−0.166492
$726$	76.6597	2.84511
$727$	20.9709	0.777766	0.388883	−	0.921287i	$-0.372861\pi$
$727$	20.9709	0.777766	0.388883	+	0.921287i	$0.372861\pi$
$728$	−121.400	−4.49940
$729$	−26.2479	−0.972144
$730$	32.1057	1.18829
$731$	24.8310	0.918406
$732$	−77.2803	−2.85636
$733$	−28.9570	−1.06955	−0.534775	−	0.844994i	$-0.679604\pi$
$733$	−28.9570	−1.06955	−0.534775	+	0.844994i	$0.679604\pi$
$734$	−42.5586	−1.57087
$735$	−47.0148	−1.73417
$736$	13.7143	0.505516
$737$	7.01583	0.258431
$738$	122.841	4.52186
$739$	−0.303958	−0.0111813	−0.00559064	−	0.999984i	$-0.501780\pi$
$739$	−0.303958	−0.0111813	−0.00559064	+	0.999984i	$0.501780\pi$
$740$	12.1557	0.446853
$741$	−18.5450	−0.681268
$742$	85.6912	3.14582
$743$	45.2536	1.66019	0.830096	−	0.557620i	$-0.188285\pi$
$743$	45.2536	1.66019	0.830096	+	0.557620i	$0.188285\pi$
$744$	94.4024	3.46096
$745$	−13.9682	−0.511755
$746$	−58.3873	−2.13771
$747$	−61.6561	−2.25588
$748$	4.62104	0.168962
$749$	0.146336	0.00534699
$750$	−65.6715	−2.39798
$751$	−37.7690	−1.37821	−0.689106	−	0.724661i	$-0.741996\pi$
$751$	−37.7690	−1.37821	−0.689106	+	0.724661i	$0.741996\pi$
$752$	−22.7101	−0.828152
$753$	35.4219	1.29084
$754$	16.7206	0.608928
$755$	−1.33001	−0.0484042
$756$	−160.747	−5.84630
$757$	12.2399	0.444869	0.222434	−	0.974948i	$-0.428600\pi$
$757$	12.2399	0.444869	0.222434	+	0.974948i	$0.428600\pi$
$758$	−35.9491	−1.30573
$759$	10.2900	0.373503
$760$	4.23403	0.153585
$761$	39.6653	1.43787	0.718933	−	0.695079i	$-0.244631\pi$
$761$	39.6653	1.43787	0.718933	+	0.695079i	$0.244631\pi$
$762$	−10.7904	−0.390893
$763$	39.9351	1.44575
$764$	60.3092	2.18191
$765$	−12.8816	−0.465736
$766$	−80.2941	−2.90114
$767$	12.1814	0.439846
$768$	−85.3326	−3.07917
$769$	−35.4238	−1.27741	−0.638707	−	0.769450i	$-0.720530\pi$
$769$	−35.4238	−1.27741	−0.638707	+	0.769450i	$0.720530\pi$
$770$	−6.79526	−0.244884
$771$	−2.37124	−0.0853982
$772$	−43.4121	−1.56244
$773$	39.6927	1.42765	0.713823	−	0.700326i	$-0.246962\pi$
$773$	39.6927	1.42765	0.713823	+	0.700326i	$0.246962\pi$
$774$	−170.773	−6.13830
$775$	29.9444	1.07564
$776$	12.6129	0.452777
$777$	45.4089	1.62904
$778$	7.16644	0.256929
$779$	−8.50920	−0.304874
$780$	70.5464	2.52597
$781$	9.62613	0.344450
$782$	−29.2224	−1.04499
$783$	10.2887	0.367690
$784$	38.2317	1.36542
$785$	−7.54645	−0.269344
$786$	116.299	4.14826
$787$	49.9656	1.78108	0.890541	−	0.454904i	$-0.150326\pi$
$787$	49.9656	1.78108	0.890541	+	0.454904i	$0.150326\pi$
$788$	−16.5049	−0.587961
$789$	−10.0609	−0.358178
$790$	15.0661	0.536028
$791$	−28.3631	−1.00848
$792$	−14.7691	−0.524797
$793$	42.4894	1.50884
$794$	34.1099	1.21052
$795$	−23.1409	−0.820723
$796$	16.9666	0.601364
$797$	−14.1368	−0.500752	−0.250376	−	0.968149i	$-0.580554\pi$
$797$	−14.1368	−0.500752	−0.250376	+	0.968149i	$0.580554\pi$
$798$	34.0350	1.20483
$799$	−19.1635	−0.677956
$800$	−9.35137	−0.330621
$801$	49.8873	1.76268
$802$	−68.9281	−2.43394
$803$	7.75758	0.273759
$804$	133.674	4.71432
$805$	27.9894	0.986498
$806$	−111.688	−3.93404
$807$	26.5375	0.934165
$808$	19.9971	0.703495
$809$	26.4539	0.930071	0.465035	−	0.885292i	$-0.346042\pi$
$809$	26.4539	0.930071	0.465035	+	0.885292i	$0.346042\pi$
$810$	22.5521	0.792400
$811$	−35.6817	−1.25295	−0.626477	−	0.779440i	$-0.715504\pi$
$811$	−35.6817	−1.25295	−0.626477	+	0.779440i	$0.715504\pi$
$812$	−19.9877	−0.701430
$813$	92.7744	3.25374
$814$	4.50934	0.158052
$815$	8.80218	0.308327
$816$	15.6888	0.549218
$817$	11.8294	0.413858
$818$	−69.9780	−2.44672
$819$	175.957	6.14842
$820$	32.3696	1.13039
$821$	6.49854	0.226800	0.113400	−	0.993549i	$-0.463826\pi$
$821$	6.49854	0.226800	0.113400	+	0.993549i	$0.463826\pi$
$822$	−143.247	−4.99632
$823$	−12.9418	−0.451123	−0.225561	−	0.974229i	$-0.572422\pi$
$823$	−12.9418	−0.451123	−0.225561	+	0.974229i	$0.572422\pi$
$824$	20.3386	0.708530
$825$	−7.01644	−0.244281
$826$	−22.3562	−0.777871
$827$	−13.6953	−0.476232	−0.238116	−	0.971237i	$-0.576530\pi$
$827$	−13.6953	−0.476232	−0.238116	+	0.971237i	$0.576530\pi$
$828$	130.904	4.54923
$829$	50.6391	1.75877	0.879384	−	0.476113i	$-0.157955\pi$
$829$	50.6391	1.75877	0.879384	+	0.476113i	$0.157955\pi$
$830$	−24.9435	−0.865800
$831$	−15.5940	−0.540949
$832$	65.5868	2.27381
$833$	32.2612	1.11778
$834$	11.9784	0.414778
$835$	−11.1350	−0.385344
$836$	2.20145	0.0761388
$837$	−68.7254	−2.37550
$838$	73.4204	2.53627
$839$	51.0695	1.76312	0.881558	−	0.472076i	$-0.156495\pi$
$839$	51.0695	1.76312	0.881558	+	0.472076i	$0.156495\pi$
$840$	−60.1676	−2.07598
$841$	−27.7207	−0.955885
$842$	−12.2160	−0.420989
$843$	−50.7384	−1.74752
$844$	82.0632	2.82473
$845$	−25.5514	−0.878995
$846$	131.795	4.53122
$847$	50.3837	1.73120
$848$	18.8178	0.646206
$849$	98.1091	3.36709
$850$	19.9259	0.683453
$851$	−18.5738	−0.636702
$852$	183.409	6.28348
$853$	−11.1345	−0.381237	−0.190618	−	0.981664i	$-0.561049\pi$
$853$	−11.1345	−0.381237	−0.190618	+	0.981664i	$0.561049\pi$
$854$	−77.9795	−2.66840
$855$	−6.13677	−0.209873
$856$	0.128670	0.00439786
$857$	7.41904	0.253429	0.126715	−	0.991939i	$-0.459557\pi$
$857$	7.41904	0.253429	0.126715	+	0.991939i	$0.459557\pi$
$858$	26.1702	0.893436
$859$	−48.2201	−1.64525	−0.822624	−	0.568586i	$-0.807491\pi$
$859$	−48.2201	−1.64525	−0.822624	+	0.568586i	$0.807491\pi$
$860$	−44.9998	−1.53448
$861$	120.920	4.12094
$862$	85.5036	2.91226
$863$	−34.3971	−1.17089	−0.585446	−	0.810711i	$-0.699081\pi$
$863$	−34.3971	−1.17089	−0.585446	+	0.810711i	$0.699081\pi$
$864$	21.4623	0.730163
$865$	7.61559	0.258938
$866$	−73.0642	−2.48282
$867$	−37.8392	−1.28509
$868$	133.511	4.53166
$869$	3.64036	0.123491
$870$	8.28695	0.280954
$871$	−73.4952	−2.49029
$872$	35.1142	1.18912
$873$	−18.2810	−0.618719
$874$	−13.9215	−0.470901
$875$	−43.1618	−1.45914
$876$	147.807	4.99393
$877$	39.2156	1.32422	0.662109	−	0.749408i	$-0.269662\pi$
$877$	39.2156	1.32422	0.662109	+	0.749408i	$0.269662\pi$
$878$	25.3364	0.855064
$879$	−84.5606	−2.85216
$880$	−1.49224	−0.0503034
$881$	−4.54632	−0.153169	−0.0765847	−	0.997063i	$-0.524402\pi$
$881$	−4.54632	−0.153169	−0.0765847	+	0.997063i	$0.524402\pi$
$882$	−221.873	−7.47087
$883$	50.2702	1.69173	0.845863	−	0.533400i	$-0.179086\pi$
$883$	50.2702	1.69173	0.845863	+	0.533400i	$0.179086\pi$
$884$	−48.4083	−1.62815
$885$	6.03728	0.202941
$886$	11.3269	0.380536
$887$	−57.8965	−1.94397	−0.971986	−	0.235037i	$-0.924479\pi$
$887$	−57.8965	−1.94397	−0.971986	+	0.235037i	$0.924479\pi$
$888$	39.9273	1.33987
$889$	−7.09184	−0.237853
$890$	20.1823	0.676512
$891$	5.44917	0.182554
$892$	56.3068	1.88529
$893$	−9.12944	−0.305505
$894$	−98.7280	−3.30196
$895$	−13.1621	−0.439961
$896$	−98.0511	−3.27566
$897$	−107.794	−3.59914
$898$	72.3478	2.41428
$899$	−8.54550	−0.285008
$900$	−89.2597	−2.97532
$901$	15.8791	0.529008
$902$	12.0080	0.399821
$903$	−168.101	−5.59407
$904$	−24.9392	−0.829464
$905$	−18.2113	−0.605363
$906$	−9.40062	−0.312315
$907$	−36.1734	−1.20112	−0.600560	−	0.799580i	$-0.705056\pi$
$907$	−36.1734	−1.20112	−0.600560	+	0.799580i	$0.705056\pi$
$908$	102.882	3.41426
$909$	−28.9836	−0.961326
$910$	71.1846	2.35975
$911$	2.95244	0.0978187	0.0489093	−	0.998803i	$-0.484425\pi$
$911$	2.95244	0.0978187	0.0489093	+	0.998803i	$0.484425\pi$
$912$	7.47410	0.247492
$913$	−6.02699	−0.199464
$914$	−40.8993	−1.35283
$915$	21.0583	0.696167
$916$	13.8902	0.458947
$917$	76.4364	2.52415
$918$	−45.7319	−1.50938
$919$	−26.1144	−0.861434	−0.430717	−	0.902487i	$-0.641739\pi$
$919$	−26.1144	−0.861434	−0.430717	+	0.902487i	$0.641739\pi$
$920$	24.6106	0.811388
$921$	−58.5337	−1.92875
$922$	73.7423	2.42857
$923$	−100.840	−3.31918
$924$	−31.2837	−1.02916
$925$	12.6649	0.416420
$926$	52.4814	1.72464
$927$	−29.4787	−0.968207
$928$	2.66868	0.0876038
$929$	14.4249	0.473266	0.236633	−	0.971599i	$-0.423956\pi$
$929$	14.4249	0.473266	0.236633	+	0.971599i	$0.423956\pi$
$930$	−55.3540	−1.81513
$931$	15.3691	0.503703
$932$	−80.4932	−2.63664
$933$	−49.8409	−1.63172
$934$	−15.5054	−0.507351
$935$	−1.25920	−0.0411803
$936$	154.716	5.05704
$937$	−43.3788	−1.41712	−0.708562	−	0.705648i	$-0.750656\pi$
$937$	−43.3788	−1.41712	−0.708562	+	0.705648i	$0.750656\pi$
$938$	134.883	4.40410
$939$	84.5750	2.76000
$940$	34.7290	1.13274
$941$	14.2186	0.463514	0.231757	−	0.972774i	$-0.425553\pi$
$941$	14.2186	0.463514	0.231757	+	0.972774i	$0.425553\pi$
$942$	−53.3388	−1.73787
$943$	−49.4603	−1.61065
$944$	−4.90942	−0.159788
$945$	43.8023	1.42489
$946$	−16.6933	−0.542747
$947$	−36.0066	−1.17006	−0.585028	−	0.811013i	$-0.698916\pi$
$947$	−36.0066	−1.17006	−0.585028	+	0.811013i	$0.698916\pi$
$948$	69.3606	2.25273
$949$	−81.2654	−2.63799
$950$	9.49265	0.307982
$951$	−3.00458	−0.0974303
$952$	41.2865	1.33810
$953$	37.1609	1.20376	0.601880	−	0.798586i	$-0.294418\pi$
$953$	37.1609	1.20376	0.601880	+	0.798586i	$0.294418\pi$
$954$	−109.207	−3.53571
$955$	−16.4338	−0.531786
$956$	19.3012	0.624245
$957$	2.00234	0.0647265
$958$	38.7858	1.25311
$959$	−94.1476	−3.04018
$960$	32.5057	1.04912
$961$	26.0810	0.841324
$962$	−47.2381	−1.52302
$963$	−0.186494	−0.00600968
$964$	15.5602	0.501159
$965$	11.8295	0.380805
$966$	197.831	6.36511
$967$	−16.2332	−0.522024	−0.261012	−	0.965336i	$-0.584056\pi$
$967$	−16.2332	−0.522024	−0.261012	+	0.965336i	$0.584056\pi$
$968$	44.3015	1.42390
$969$	6.30689	0.202606
$970$	−7.39573	−0.237463
$971$	−1.13243	−0.0363413	−0.0181706	−	0.999835i	$-0.505784\pi$
$971$	−1.13243	−0.0363413	−0.0181706	+	0.999835i	$0.505784\pi$
$972$	1.86210	0.0597268
$973$	7.87267	0.252386
$974$	−64.4990	−2.06668
$975$	73.5016	2.35394
$976$	−17.1243	−0.548136
$977$	−8.12614	−0.259978	−0.129989	−	0.991515i	$-0.541494\pi$
$977$	−8.12614	−0.259978	−0.129989	+	0.991515i	$0.541494\pi$
$978$	62.2143	1.98939
$979$	4.87657	0.155856
$980$	−58.4652	−1.86760
$981$	−50.8943	−1.62493
$982$	31.2980	0.998761
$983$	36.0787	1.15073	0.575366	−	0.817896i	$-0.304860\pi$
$983$	36.0787	1.15073	0.575366	+	0.817896i	$0.304860\pi$
$984$	106.323	3.38944
$985$	4.49745	0.143301
$986$	−5.68643	−0.181093
$987$	129.734	4.12947
$988$	−23.0616	−0.733687
$989$	68.7592	2.18641
$990$	8.66005	0.275234
$991$	30.2572	0.961151	0.480576	−	0.876953i	$-0.340428\pi$
$991$	30.2572	0.961151	0.480576	+	0.876953i	$0.340428\pi$
$992$	−17.8259	−0.565973
$993$	−30.9206	−0.981234
$994$	185.068	5.87000
$995$	−4.62327	−0.146567
$996$	−114.833	−3.63864
$997$	53.4854	1.69390	0.846950	−	0.531672i	$-0.178436\pi$
$997$	53.4854	1.69390	0.846950	+	0.531672i	$0.178436\pi$
$998$	−26.1120	−0.826562
$999$	−29.0672	−0.919647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.14	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.14	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.39507 q^{2} +3.00458 q^{3} +3.73634 q^{4} -1.01813 q^{5} -7.19617 q^{6} -4.72960 q^{7} -4.15865 q^{8} +6.02752 q^{9} +O(q^{10})\)	\(q-2.39507 q^{2} +3.00458 q^{3} +3.73634 q^{4} -1.01813 q^{5} -7.19617 q^{6} -4.72960 q^{7} -4.15865 q^{8} +6.02752 q^{9} +2.43848 q^{10} +0.589200 q^{11} +11.2261 q^{12} -6.17224 q^{13} +11.3277 q^{14} -3.05904 q^{15} +2.48757 q^{16} +2.09909 q^{17} -14.4363 q^{18} +1.00000 q^{19} -3.80407 q^{20} -14.2105 q^{21} -1.41117 q^{22} +5.81257 q^{23} -12.4950 q^{24} -3.96342 q^{25} +14.7829 q^{26} +9.09643 q^{27} -17.6714 q^{28} +1.13107 q^{29} +7.32661 q^{30} -7.55520 q^{31} +2.35942 q^{32} +1.77030 q^{33} -5.02746 q^{34} +4.81533 q^{35} +22.5209 q^{36} -3.19545 q^{37} -2.39507 q^{38} -18.5450 q^{39} +4.23403 q^{40} -8.50920 q^{41} +34.0350 q^{42} +11.8294 q^{43} +2.20145 q^{44} -6.13677 q^{45} -13.9215 q^{46} -9.12944 q^{47} +7.47410 q^{48} +15.3691 q^{49} +9.49265 q^{50} +6.30689 q^{51} -23.0616 q^{52} +7.56474 q^{53} -21.7866 q^{54} -0.599880 q^{55} +19.6688 q^{56} +3.00458 q^{57} -2.70900 q^{58} -1.97358 q^{59} -11.4296 q^{60} -6.88396 q^{61} +18.0952 q^{62} -28.5078 q^{63} -10.6261 q^{64} +6.28412 q^{65} -4.23999 q^{66} +11.9074 q^{67} +7.84291 q^{68} +17.4643 q^{69} -11.5330 q^{70} +16.3376 q^{71} -25.0664 q^{72} +13.1663 q^{73} +7.65333 q^{74} -11.9084 q^{75} +3.73634 q^{76} -2.78668 q^{77} +44.4165 q^{78} +6.17848 q^{79} -2.53266 q^{80} +9.24843 q^{81} +20.3801 q^{82} -10.2291 q^{83} -53.0952 q^{84} -2.13714 q^{85} -28.3322 q^{86} +3.39841 q^{87} -2.45028 q^{88} +8.27659 q^{89} +14.6980 q^{90} +29.1922 q^{91} +21.7177 q^{92} -22.7002 q^{93} +21.8656 q^{94} -1.01813 q^{95} +7.08908 q^{96} -3.03293 q^{97} -36.8101 q^{98} +3.55141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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