LMFDB - Embedded newform 6023.2.a.c.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.40954 q^{2} +1.37728 q^{3} +3.80590 q^{4} -2.93809 q^{5} -3.31862 q^{6} -1.98041 q^{7} -4.35139 q^{8} -1.10309 q^{9} +O(q^{10})$	\(q-2.40954 q^{2} +1.37728 q^{3} +3.80590 q^{4} -2.93809 q^{5} -3.31862 q^{6} -1.98041 q^{7} -4.35139 q^{8} -1.10309 q^{9} +7.07945 q^{10} -4.29062 q^{11} +5.24179 q^{12} +4.72605 q^{13} +4.77188 q^{14} -4.04658 q^{15} +2.87306 q^{16} +4.79826 q^{17} +2.65795 q^{18} +1.00000 q^{19} -11.1821 q^{20} -2.72758 q^{21} +10.3384 q^{22} -5.99637 q^{23} -5.99309 q^{24} +3.63237 q^{25} -11.3876 q^{26} -5.65112 q^{27} -7.53724 q^{28} +3.80934 q^{29} +9.75040 q^{30} +4.69864 q^{31} +1.78002 q^{32} -5.90940 q^{33} -11.5616 q^{34} +5.81862 q^{35} -4.19826 q^{36} -0.0921425 q^{37} -2.40954 q^{38} +6.50910 q^{39} +12.7848 q^{40} -12.4315 q^{41} +6.57223 q^{42} -3.48785 q^{43} -16.3297 q^{44} +3.24099 q^{45} +14.4485 q^{46} +1.33900 q^{47} +3.95701 q^{48} -3.07798 q^{49} -8.75235 q^{50} +6.60855 q^{51} +17.9868 q^{52} +1.49986 q^{53} +13.6166 q^{54} +12.6062 q^{55} +8.61753 q^{56} +1.37728 q^{57} -9.17876 q^{58} -3.87403 q^{59} -15.4009 q^{60} +0.385290 q^{61} -11.3216 q^{62} +2.18458 q^{63} -10.0351 q^{64} -13.8855 q^{65} +14.2389 q^{66} -8.43132 q^{67} +18.2617 q^{68} -8.25869 q^{69} -14.0202 q^{70} -5.46241 q^{71} +4.79999 q^{72} +6.83548 q^{73} +0.222021 q^{74} +5.00280 q^{75} +3.80590 q^{76} +8.49719 q^{77} -15.6839 q^{78} +16.5425 q^{79} -8.44130 q^{80} -4.47390 q^{81} +29.9543 q^{82} -17.5415 q^{83} -10.3809 q^{84} -14.0977 q^{85} +8.40413 q^{86} +5.24653 q^{87} +18.6701 q^{88} +9.65012 q^{89} -7.80930 q^{90} -9.35951 q^{91} -22.8216 q^{92} +6.47135 q^{93} -3.22637 q^{94} -2.93809 q^{95} +2.45159 q^{96} -18.2661 q^{97} +7.41652 q^{98} +4.73296 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40954	−1.70380	−0.851902	−	0.523701i	$-0.824551\pi$
$2$	−2.40954	−1.70380	−0.851902	+	0.523701i	$0.824551\pi$
$3$	1.37728	0.795174	0.397587	−	0.917564i	$-0.369848\pi$
$3$	1.37728	0.795174	0.397587	+	0.917564i	$0.369848\pi$
$4$	3.80590	1.90295
$5$	−2.93809	−1.31395	−0.656977	−	0.753911i	$-0.728165\pi$
$5$	−2.93809	−1.31395	−0.656977	+	0.753911i	$0.728165\pi$
$6$	−3.31862	−1.35482
$7$	−1.98041	−0.748525	−0.374262	−	0.927323i	$-0.622104\pi$
$7$	−1.98041	−0.748525	−0.374262	+	0.927323i	$0.622104\pi$
$8$	−4.35139	−1.53845
$9$	−1.10309	−0.367698
$10$	7.07945	2.23872
$11$	−4.29062	−1.29367	−0.646836	−	0.762630i	$-0.723908\pi$
$11$	−4.29062	−1.29367	−0.646836	+	0.762630i	$0.723908\pi$
$12$	5.24179	1.51318
$13$	4.72605	1.31077	0.655385	−	0.755295i	$-0.272507\pi$
$13$	4.72605	1.31077	0.655385	+	0.755295i	$0.272507\pi$
$14$	4.77188	1.27534
$15$	−4.04658	−1.04482
$16$	2.87306	0.718264
$17$	4.79826	1.16375	0.581874	−	0.813279i	$-0.302320\pi$
$17$	4.79826	1.16375	0.581874	+	0.813279i	$0.302320\pi$
$18$	2.65795	0.626485
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−11.1821	−2.50039
$21$	−2.72758	−0.595207
$22$	10.3384	2.20416
$23$	−5.99637	−1.25033	−0.625165	−	0.780493i	$-0.714968\pi$
$23$	−5.99637	−1.25033	−0.625165	+	0.780493i	$0.714968\pi$
$24$	−5.99309	−1.22333
$25$	3.63237	0.726474
$26$	−11.3876	−2.23329
$27$	−5.65112	−1.08756
$28$	−7.53724	−1.42440
$29$	3.80934	0.707376	0.353688	−	0.935363i	$-0.384927\pi$
$29$	3.80934	0.707376	0.353688	+	0.935363i	$0.384927\pi$
$30$	9.75040	1.78017
$31$	4.69864	0.843900	0.421950	−	0.906619i	$-0.361346\pi$
$31$	4.69864	0.843900	0.421950	+	0.906619i	$0.361346\pi$
$32$	1.78002	0.314666
$33$	−5.90940	−1.02869
$34$	−11.5616	−1.98280
$35$	5.81862	0.983527
$36$	−4.19826	−0.699710
$37$	−0.0921425	−0.0151481	−0.00757406	−	0.999971i	$-0.502411\pi$
$37$	−0.0921425	−0.0151481	−0.00757406	+	0.999971i	$0.502411\pi$
$38$	−2.40954	−0.390879
$39$	6.50910	1.04229
$40$	12.7848	2.02145
$41$	−12.4315	−1.94148	−0.970739	−	0.240138i	$-0.922807\pi$
$41$	−12.4315	−1.94148	−0.970739	+	0.240138i	$0.922807\pi$
$42$	6.57223	1.01412
$43$	−3.48785	−0.531893	−0.265946	−	0.963988i	$-0.585684\pi$
$43$	−3.48785	−0.531893	−0.265946	+	0.963988i	$0.585684\pi$
$44$	−16.3297	−2.46179
$45$	3.24099	0.483138
$46$	14.4485	2.13032
$47$	1.33900	0.195313	0.0976563	−	0.995220i	$-0.468865\pi$
$47$	1.33900	0.195313	0.0976563	+	0.995220i	$0.468865\pi$
$48$	3.95701	0.571145
$49$	−3.07798	−0.439711
$50$	−8.75235	−1.23777
$51$	6.60855	0.925383
$52$	17.9868	2.49433
$53$	1.49986	0.206022	0.103011	−	0.994680i	$-0.467152\pi$
$53$	1.49986	0.206022	0.103011	+	0.994680i	$0.467152\pi$
$54$	13.6166	1.85299
$55$	12.6062	1.69982
$56$	8.61753	1.15157
$57$	1.37728	0.182425
$58$	−9.17876	−1.20523
$59$	−3.87403	−0.504356	−0.252178	−	0.967681i	$-0.581147\pi$
$59$	−3.87403	−0.504356	−0.252178	+	0.967681i	$0.581147\pi$
$60$	−15.4009	−1.98824
$61$	0.385290	0.0493313	0.0246656	−	0.999696i	$-0.492148\pi$
$61$	0.385290	0.0493313	0.0246656	+	0.999696i	$0.492148\pi$
$62$	−11.3216	−1.43784
$63$	2.18458	0.275231
$64$	−10.0351	−1.25439
$65$	−13.8855	−1.72229
$66$	14.2389	1.75269
$67$	−8.43132	−1.03005	−0.515025	−	0.857175i	$-0.672217\pi$
$67$	−8.43132	−1.03005	−0.515025	+	0.857175i	$0.672217\pi$
$68$	18.2617	2.21455
$69$	−8.25869	−0.994230
$70$	−14.0202	−1.67574
$71$	−5.46241	−0.648269	−0.324135	−	0.946011i	$-0.605073\pi$
$71$	−5.46241	−0.648269	−0.324135	+	0.946011i	$0.605073\pi$
$72$	4.79999	0.565684
$73$	6.83548	0.800033	0.400016	−	0.916508i	$-0.369004\pi$
$73$	6.83548	0.800033	0.400016	+	0.916508i	$0.369004\pi$
$74$	0.222021	0.0258094
$75$	5.00280	0.577673
$76$	3.80590	0.436566
$77$	8.49719	0.968345
$78$	−15.6839	−1.77586
$79$	16.5425	1.86118	0.930589	−	0.366064i	$-0.119295\pi$
$79$	16.5425	1.86118	0.930589	+	0.366064i	$0.119295\pi$
$80$	−8.44130	−0.943766
$81$	−4.47390	−0.497100
$82$	29.9543	3.30790
$83$	−17.5415	−1.92543	−0.962715	−	0.270517i	$-0.912805\pi$
$83$	−17.5415	−1.92543	−0.962715	+	0.270517i	$0.912805\pi$
$84$	−10.3809	−1.13265
$85$	−14.0977	−1.52911
$86$	8.40413	0.906241
$87$	5.24653	0.562487
$88$	18.6701	1.99024
$89$	9.65012	1.02291	0.511455	−	0.859310i	$-0.329107\pi$
$89$	9.65012	1.02291	0.511455	+	0.859310i	$0.329107\pi$
$90$	−7.80930	−0.823173
$91$	−9.35951	−0.981143
$92$	−22.8216	−2.37931
$93$	6.47135	0.671048
$94$	−3.22637	−0.332775
$95$	−2.93809	−0.301442
$96$	2.45159	0.250214
$97$	−18.2661	−1.85464	−0.927320	−	0.374269i	$-0.877894\pi$
$97$	−18.2661	−1.85464	−0.927320	+	0.374269i	$0.877894\pi$
$98$	7.41652	0.749181
$99$	4.73296	0.475680
$100$	13.8244	1.38244
$101$	−16.3333	−1.62522	−0.812611	−	0.582806i	$-0.801955\pi$
$101$	−16.3333	−1.62522	−0.812611	+	0.582806i	$0.801955\pi$
$102$	−15.9236	−1.57667
$103$	−19.5613	−1.92743	−0.963717	−	0.266925i	$-0.913992\pi$
$103$	−19.5613	−1.92743	−0.963717	+	0.266925i	$0.913992\pi$
$104$	−20.5648	−2.01655
$105$	8.01388	0.782075
$106$	−3.61398	−0.351021
$107$	−1.32026	−0.127634	−0.0638171	−	0.997962i	$-0.520327\pi$
$107$	−1.32026	−0.127634	−0.0638171	+	0.997962i	$0.520327\pi$
$108$	−21.5076	−2.06957
$109$	−6.20284	−0.594124	−0.297062	−	0.954858i	$-0.596007\pi$
$109$	−6.20284	−0.594124	−0.297062	+	0.954858i	$0.596007\pi$
$110$	−30.3752	−2.89617
$111$	−0.126906	−0.0120454
$112$	−5.68983	−0.537638
$113$	−6.63857	−0.624504	−0.312252	−	0.949999i	$-0.601083\pi$
$113$	−6.63857	−0.624504	−0.312252	+	0.949999i	$0.601083\pi$
$114$	−3.31862	−0.310817
$115$	17.6179	1.64287
$116$	14.4979	1.34610
$117$	−5.21327	−0.481967
$118$	9.33464	0.859323
$119$	−9.50252	−0.871094
$120$	17.6082	1.60740
$121$	7.40943	0.673585
$122$	−0.928372	−0.0840508
$123$	−17.1217	−1.54381
$124$	17.8825	1.60590
$125$	4.01822	0.359401
$126$	−5.26384	−0.468940
$127$	9.32571	0.827523	0.413761	−	0.910385i	$-0.364215\pi$
$127$	9.32571	0.827523	0.413761	+	0.910385i	$0.364215\pi$
$128$	20.6201	1.82257
$129$	−4.80376	−0.422947
$130$	33.4578	2.93444
$131$	−0.457275	−0.0399523	−0.0199762	−	0.999800i	$-0.506359\pi$
$131$	−0.457275	−0.0399523	−0.0199762	+	0.999800i	$0.506359\pi$
$132$	−22.4906	−1.95755
$133$	−1.98041	−0.171723
$134$	20.3156	1.75500
$135$	16.6035	1.42900
$136$	−20.8791	−1.79037
$137$	−11.0720	−0.945945	−0.472973	−	0.881077i	$-0.656819\pi$
$137$	−11.0720	−0.945945	−0.472973	+	0.881077i	$0.656819\pi$
$138$	19.8997	1.69397
$139$	19.7581	1.67586	0.837932	−	0.545774i	$-0.183764\pi$
$139$	19.7581	1.67586	0.837932	+	0.545774i	$0.183764\pi$
$140$	22.1451	1.87160
$141$	1.84418	0.155308
$142$	13.1619	1.10452
$143$	−20.2777	−1.69570
$144$	−3.16925	−0.264104
$145$	−11.1922	−0.929459
$146$	−16.4704	−1.36310
$147$	−4.23924	−0.349647
$148$	−0.350685	−0.0288261
$149$	23.9004	1.95800	0.979000	−	0.203858i	$-0.0653481\pi$
$149$	23.9004	1.95800	0.979000	+	0.203858i	$0.0653481\pi$
$150$	−12.0545	−0.984242
$151$	7.89721	0.642666	0.321333	−	0.946966i	$-0.395869\pi$
$151$	7.89721	0.642666	0.321333	+	0.946966i	$0.395869\pi$
$152$	−4.35139	−0.352944
$153$	−5.29293	−0.427908
$154$	−20.4743	−1.64987
$155$	−13.8050	−1.10885
$156$	24.7730	1.98342
$157$	14.5505	1.16126	0.580629	−	0.814168i	$-0.302807\pi$
$157$	14.5505	1.16126	0.580629	+	0.814168i	$0.302807\pi$
$158$	−39.8599	−3.17108
$159$	2.06573	0.163823
$160$	−5.22985	−0.413456
$161$	11.8753	0.935903
$162$	10.7801	0.846961
$163$	2.28403	0.178899	0.0894495	−	0.995991i	$-0.471489\pi$
$163$	2.28403	0.178899	0.0894495	+	0.995991i	$0.471489\pi$
$164$	−47.3131	−3.69453
$165$	17.3623	1.35166
$166$	42.2670	3.28056
$167$	−1.85870	−0.143831	−0.0719154	−	0.997411i	$-0.522911\pi$
$167$	−1.85870	−0.143831	−0.0719154	+	0.997411i	$0.522911\pi$
$168$	11.8688	0.915695
$169$	9.33550	0.718116
$170$	33.9690	2.60531
$171$	−1.10309	−0.0843557
$172$	−13.2744	−1.01216
$173$	−0.951686	−0.0723554	−0.0361777	−	0.999345i	$-0.511518\pi$
$173$	−0.951686	−0.0723554	−0.0361777	+	0.999345i	$0.511518\pi$
$174$	−12.6417	−0.958368
$175$	−7.19358	−0.543784
$176$	−12.3272	−0.929198
$177$	−5.33563	−0.401051
$178$	−23.2524	−1.74284
$179$	−1.09816	−0.0820805	−0.0410403	−	0.999157i	$-0.513067\pi$
$179$	−1.09816	−0.0820805	−0.0410403	+	0.999157i	$0.513067\pi$
$180$	12.3349	0.919387
$181$	−9.63612	−0.716247	−0.358124	−	0.933674i	$-0.616583\pi$
$181$	−9.63612	−0.716247	−0.358124	+	0.933674i	$0.616583\pi$
$182$	22.5521	1.67168
$183$	0.530652	0.0392269
$184$	26.0925	1.92357
$185$	0.270723	0.0199039
$186$	−15.5930	−1.14333
$187$	−20.5875	−1.50551
$188$	5.09608	0.371670
$189$	11.1915	0.814064
$190$	7.07945	0.513597
$191$	14.1213	1.02178	0.510892	−	0.859645i	$-0.329315\pi$
$191$	14.1213	1.02178	0.510892	+	0.859645i	$0.329315\pi$
$192$	−13.8212	−0.997461
$193$	5.82041	0.418962	0.209481	−	0.977813i	$-0.432822\pi$
$193$	5.82041	0.418962	0.209481	+	0.977813i	$0.432822\pi$
$194$	44.0129	3.15994
$195$	−19.1243	−1.36952
$196$	−11.7145	−0.836747
$197$	11.5727	0.824522	0.412261	−	0.911066i	$-0.364739\pi$
$197$	11.5727	0.824522	0.412261	+	0.911066i	$0.364739\pi$
$198$	−11.4043	−0.810466
$199$	−6.45849	−0.457830	−0.228915	−	0.973446i	$-0.573518\pi$
$199$	−6.45849	−0.457830	−0.228915	+	0.973446i	$0.573518\pi$
$200$	−15.8058	−1.11764
$201$	−11.6123	−0.819069
$202$	39.3558	2.76906
$203$	−7.54405	−0.529488
$204$	25.1515	1.76096
$205$	36.5249	2.55101
$206$	47.1338	3.28397
$207$	6.61456	0.459744
$208$	13.5782	0.941479
$209$	−4.29062	−0.296788
$210$	−19.3098	−1.33250
$211$	27.0338	1.86108	0.930542	−	0.366184i	$-0.119336\pi$
$211$	27.0338	1.86108	0.930542	+	0.366184i	$0.119336\pi$
$212$	5.70831	0.392049
$213$	−7.52328	−0.515487
$214$	3.18122	0.217464
$215$	10.2476	0.698882
$216$	24.5902	1.67315
$217$	−9.30523	−0.631680
$218$	14.9460	1.01227
$219$	9.41439	0.636165
$220$	47.9780	3.23468
$221$	22.6768	1.52541
$222$	0.305786	0.0205230
$223$	−11.2492	−0.753301	−0.376651	−	0.926355i	$-0.622924\pi$
$223$	−11.2492	−0.753301	−0.376651	+	0.926355i	$0.622924\pi$
$224$	−3.52516	−0.235535
$225$	−4.00684	−0.267123
$226$	15.9959	1.06403
$227$	−0.161002	−0.0106861	−0.00534304	−	0.999986i	$-0.501701\pi$
$227$	−0.161002	−0.0106861	−0.00534304	+	0.999986i	$0.501701\pi$
$228$	5.24179	0.347146
$229$	18.0496	1.19275	0.596377	−	0.802705i	$-0.296606\pi$
$229$	18.0496	1.19275	0.596377	+	0.802705i	$0.296606\pi$
$230$	−42.4510	−2.79914
$231$	11.7030	0.770003
$232$	−16.5759	−1.08826
$233$	23.4659	1.53730	0.768651	−	0.639668i	$-0.220928\pi$
$233$	23.4659	1.53730	0.768651	+	0.639668i	$0.220928\pi$
$234$	12.5616	0.821178
$235$	−3.93409	−0.256632
$236$	−14.7442	−0.959763
$237$	22.7837	1.47996
$238$	22.8967	1.48417
$239$	−25.0725	−1.62181	−0.810903	−	0.585180i	$-0.801024\pi$
$239$	−25.0725	−1.62181	−0.810903	+	0.585180i	$0.801024\pi$
$240$	−11.6260	−0.750458
$241$	10.8077	0.696188	0.348094	−	0.937460i	$-0.386829\pi$
$241$	10.8077	0.696188	0.348094	+	0.937460i	$0.386829\pi$
$242$	−17.8533	−1.14766
$243$	10.7915	0.692277
$244$	1.46637	0.0938749
$245$	9.04337	0.577760
$246$	41.2555	2.63035
$247$	4.72605	0.300711
$248$	−20.4456	−1.29830
$249$	−24.1596	−1.53105
$250$	−9.68208	−0.612348
$251$	2.44203	0.154140	0.0770699	−	0.997026i	$-0.475444\pi$
$251$	2.44203	0.154140	0.0770699	+	0.997026i	$0.475444\pi$
$252$	8.31428	0.523751
$253$	25.7282	1.61752
$254$	−22.4707	−1.40994
$255$	−19.4165	−1.21591
$256$	−29.6147	−1.85092
$257$	24.4548	1.52545	0.762724	−	0.646724i	$-0.223861\pi$
$257$	24.4548	1.52545	0.762724	+	0.646724i	$0.223861\pi$
$258$	11.5749	0.720619
$259$	0.182480	0.0113387
$260$	−52.8469	−3.27743
$261$	−4.20206	−0.260101
$262$	1.10182	0.0680709
$263$	18.0524	1.11316	0.556578	−	0.830795i	$-0.312114\pi$
$263$	18.0524	1.11316	0.556578	+	0.830795i	$0.312114\pi$
$264$	25.7141	1.58259
$265$	−4.40672	−0.270703
$266$	4.77188	0.292583
$267$	13.2909	0.813392
$268$	−32.0887	−1.96013
$269$	−5.18223	−0.315966	−0.157983	−	0.987442i	$-0.550499\pi$
$269$	−5.18223	−0.315966	−0.157983	+	0.987442i	$0.550499\pi$
$270$	−40.0068	−2.43474
$271$	−2.22720	−0.135293	−0.0676464	−	0.997709i	$-0.521549\pi$
$271$	−2.22720	−0.135293	−0.0676464	+	0.997709i	$0.521549\pi$
$272$	13.7857	0.835879
$273$	−12.8907	−0.780180
$274$	26.6785	1.61171
$275$	−15.5851	−0.939818
$276$	−31.4317	−1.89197
$277$	7.22210	0.433934	0.216967	−	0.976179i	$-0.430384\pi$
$277$	7.22210	0.433934	0.216967	+	0.976179i	$0.430384\pi$
$278$	−47.6081	−2.85534
$279$	−5.18304	−0.310301
$280$	−25.3191	−1.51310
$281$	21.1594	1.26226	0.631132	−	0.775676i	$-0.282591\pi$
$281$	21.1594	1.26226	0.631132	+	0.775676i	$0.282591\pi$
$282$	−4.44362	−0.264614
$283$	−0.277617	−0.0165026	−0.00825131	−	0.999966i	$-0.502627\pi$
$283$	−0.277617	−0.0165026	−0.00825131	+	0.999966i	$0.502627\pi$
$284$	−20.7894	−1.23362
$285$	−4.04658	−0.239699
$286$	48.8599	2.88915
$287$	24.6195	1.45324
$288$	−1.96353	−0.115702
$289$	6.02327	0.354310
$290$	26.9680	1.58362
$291$	−25.1576	−1.47476
$292$	26.0151	1.52242
$293$	−29.5200	−1.72458	−0.862289	−	0.506417i	$-0.830970\pi$
$293$	−29.5200	−1.72458	−0.862289	+	0.506417i	$0.830970\pi$
$294$	10.2146	0.595729
$295$	11.3822	0.662700
$296$	0.400947	0.0233046
$297$	24.2468	1.40694
$298$	−57.5892	−3.33605
$299$	−28.3391	−1.63889
$300$	19.0401	1.09928
$301$	6.90738	0.398135
$302$	−19.0287	−1.09498
$303$	−22.4955	−1.29234
$304$	2.87306	0.164781
$305$	−1.13202	−0.0648190
$306$	12.7535	0.729071
$307$	21.8126	1.24491	0.622455	−	0.782656i	$-0.286136\pi$
$307$	21.8126	1.24491	0.622455	+	0.782656i	$0.286136\pi$
$308$	32.3394	1.84271
$309$	−26.9415	−1.53265
$310$	33.2638	1.88926
$311$	−19.2504	−1.09159	−0.545795	−	0.837919i	$-0.683772\pi$
$311$	−19.2504	−1.09159	−0.545795	+	0.837919i	$0.683772\pi$
$312$	−28.3236	−1.60351
$313$	−3.74668	−0.211775	−0.105887	−	0.994378i	$-0.533768\pi$
$313$	−3.74668	−0.211775	−0.105887	+	0.994378i	$0.533768\pi$
$314$	−35.0601	−1.97856
$315$	−6.41849	−0.361641
$316$	62.9591	3.54173
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−4.97747	−0.279122
$319$	−16.3444	−0.915112
$320$	29.4841	1.64821
$321$	−1.81837	−0.101491
$322$	−28.6140	−1.59459
$323$	4.79826	0.266982
$324$	−17.0272	−0.945956
$325$	17.1667	0.952239
$326$	−5.50347	−0.304809
$327$	−8.54306	−0.472432
$328$	54.0943	2.98686
$329$	−2.65176	−0.146196
$330$	−41.8353	−2.30296
$331$	−10.0884	−0.554509	−0.277254	−	0.960797i	$-0.589425\pi$
$331$	−10.0884	−0.554509	−0.277254	+	0.960797i	$0.589425\pi$
$332$	−66.7612	−3.66399
$333$	0.101642	0.00556994
$334$	4.47863	0.245060
$335$	24.7720	1.35344
$336$	−7.83650	−0.427516
$337$	35.0977	1.91189	0.955947	−	0.293540i	$-0.0948335\pi$
$337$	35.0977	1.91189	0.955947	+	0.293540i	$0.0948335\pi$
$338$	−22.4943	−1.22353
$339$	−9.14318	−0.496589
$340$	−53.6544	−2.90982
$341$	−20.1601	−1.09173
$342$	2.65795	0.143726
$343$	19.9585	1.07766
$344$	15.1770	0.818289
$345$	24.2648	1.30637
$346$	2.29313	0.123279
$347$	14.3271	0.769117	0.384558	−	0.923101i	$-0.374354\pi$
$347$	14.3271	0.769117	0.384558	+	0.923101i	$0.374354\pi$
$348$	19.9677	1.07038
$349$	20.2866	1.08591	0.542957	−	0.839760i	$-0.317304\pi$
$349$	20.2866	1.08591	0.542957	+	0.839760i	$0.317304\pi$
$350$	17.3332	0.926501
$351$	−26.7074	−1.42554
$352$	−7.63738	−0.407074
$353$	31.4772	1.67536	0.837680	−	0.546161i	$-0.183911\pi$
$353$	31.4772	1.67536	0.837680	+	0.546161i	$0.183911\pi$
$354$	12.8564	0.683312
$355$	16.0491	0.851796
$356$	36.7274	1.94655
$357$	−13.0876	−0.692672
$358$	2.64607	0.139849
$359$	26.9387	1.42177	0.710884	−	0.703309i	$-0.248295\pi$
$359$	26.9387	1.42177	0.710884	+	0.703309i	$0.248295\pi$
$360$	−14.1028	−0.743283
$361$	1.00000	0.0526316
$362$	23.2186	1.22034
$363$	10.2049	0.535617
$364$	−35.6213	−1.86706
$365$	−20.0833	−1.05121
$366$	−1.27863	−0.0668350
$367$	15.2911	0.798189	0.399094	−	0.916910i	$-0.369325\pi$
$367$	15.2911	0.798189	0.399094	+	0.916910i	$0.369325\pi$
$368$	−17.2279	−0.898067
$369$	13.7131	0.713877
$370$	−0.652318	−0.0339124
$371$	−2.97034	−0.154212
$372$	24.6293	1.27697
$373$	11.0373	0.571489	0.285744	−	0.958306i	$-0.407759\pi$
$373$	11.0373	0.571489	0.285744	+	0.958306i	$0.407759\pi$
$374$	49.6065	2.56509
$375$	5.53423	0.285786
$376$	−5.82649	−0.300478
$377$	18.0031	0.927206
$378$	−26.9665	−1.38701
$379$	−25.6241	−1.31622	−0.658111	−	0.752921i	$-0.728644\pi$
$379$	−25.6241	−1.31622	−0.658111	+	0.752921i	$0.728644\pi$
$380$	−11.1821	−0.573628
$381$	12.8441	0.658025
$382$	−34.0259	−1.74092
$383$	−12.1692	−0.621816	−0.310908	−	0.950440i	$-0.600633\pi$
$383$	−12.1692	−0.621816	−0.310908	+	0.950440i	$0.600633\pi$
$384$	28.3997	1.44926
$385$	−24.9655	−1.27236
$386$	−14.0245	−0.713830
$387$	3.84743	0.195576
$388$	−69.5188	−3.52928
$389$	−1.20546	−0.0611194	−0.0305597	−	0.999533i	$-0.509729\pi$
$389$	−1.20546	−0.0611194	−0.0305597	+	0.999533i	$0.509729\pi$
$390$	46.0808	2.33339
$391$	−28.7721	−1.45507
$392$	13.3935	0.676472
$393$	−0.629797	−0.0317690
$394$	−27.8850	−1.40482
$395$	−48.6034	−2.44550
$396$	18.0132	0.905195
$397$	−9.84755	−0.494234	−0.247117	−	0.968986i	$-0.579483\pi$
$397$	−9.84755	−0.494234	−0.247117	+	0.968986i	$0.579483\pi$
$398$	15.5620	0.780053
$399$	−2.72758	−0.136550
$400$	10.4360	0.521800
$401$	−12.9757	−0.647977	−0.323988	−	0.946061i	$-0.605024\pi$
$401$	−12.9757	−0.647977	−0.323988	+	0.946061i	$0.605024\pi$
$402$	27.9804	1.39553
$403$	22.2060	1.10616
$404$	−62.1628	−3.09271
$405$	13.1447	0.653166
$406$	18.1777	0.902144
$407$	0.395348	0.0195967
$408$	−28.7564	−1.42365
$409$	−13.7590	−0.680337	−0.340169	−	0.940364i	$-0.610484\pi$
$409$	−13.7590	−0.680337	−0.340169	+	0.940364i	$0.610484\pi$
$410$	−88.0084	−4.34642
$411$	−15.2493	−0.752191
$412$	−74.4484	−3.66781
$413$	7.67217	0.377523
$414$	−15.9381	−0.783313
$415$	51.5385	2.52993
$416$	8.41244	0.412454
$417$	27.2125	1.33260
$418$	10.3384	0.505669
$419$	0.683776	0.0334046	0.0167023	−	0.999861i	$-0.494683\pi$
$419$	0.683776	0.0334046	0.0167023	+	0.999861i	$0.494683\pi$
$420$	30.5000	1.48825
$421$	−21.0685	−1.02682	−0.513408	−	0.858145i	$-0.671617\pi$
$421$	−21.0685	−1.02682	−0.513408	+	0.858145i	$0.671617\pi$
$422$	−65.1391	−3.17092
$423$	−1.47704	−0.0718161
$424$	−6.52647	−0.316953
$425$	17.4290	0.845433
$426$	18.1277	0.878289
$427$	−0.763031	−0.0369257
$428$	−5.02476	−0.242881
$429$	−27.9281	−1.34838
$430$	−24.6921	−1.19076
$431$	−37.4940	−1.80602	−0.903011	−	0.429618i	$-0.858648\pi$
$431$	−37.4940	−1.80602	−0.903011	+	0.429618i	$0.858648\pi$
$432$	−16.2360	−0.781154
$433$	−23.9485	−1.15089	−0.575447	−	0.817839i	$-0.695172\pi$
$433$	−23.9485	−1.15089	−0.575447	+	0.817839i	$0.695172\pi$
$434$	22.4214	1.07626
$435$	−15.4148	−0.739082
$436$	−23.6074	−1.13059
$437$	−5.99637	−0.286845
$438$	−22.6844	−1.08390
$439$	−19.6844	−0.939484	−0.469742	−	0.882804i	$-0.655653\pi$
$439$	−19.6844	−0.939484	−0.469742	+	0.882804i	$0.655653\pi$
$440$	−54.8546	−2.61509
$441$	3.39530	0.161681
$442$	−54.6407	−2.59899
$443$	−33.7860	−1.60522	−0.802610	−	0.596505i	$-0.796556\pi$
$443$	−33.7860	−1.60522	−0.802610	+	0.596505i	$0.796556\pi$
$444$	−0.482992	−0.0229218
$445$	−28.3529	−1.34406
$446$	27.1054	1.28348
$447$	32.9177	1.55695
$448$	19.8737	0.938944
$449$	8.65316	0.408368	0.204184	−	0.978933i	$-0.434546\pi$
$449$	8.65316	0.408368	0.204184	+	0.978933i	$0.434546\pi$
$450$	9.65466	0.455125
$451$	53.3389	2.51163
$452$	−25.2657	−1.18840
$453$	10.8767	0.511031
$454$	0.387941	0.0182070
$455$	27.4991	1.28918
$456$	−5.99309	−0.280652
$457$	12.7982	0.598674	0.299337	−	0.954148i	$-0.403235\pi$
$457$	12.7982	0.598674	0.299337	+	0.954148i	$0.403235\pi$
$458$	−43.4914	−2.03222
$459$	−27.1155	−1.26564
$460$	67.0518	3.12631
$461$	27.1028	1.26230	0.631151	−	0.775660i	$-0.282583\pi$
$461$	27.1028	1.26230	0.631151	+	0.775660i	$0.282583\pi$
$462$	−28.1989	−1.31193
$463$	7.11831	0.330816	0.165408	−	0.986225i	$-0.447106\pi$
$463$	7.11831	0.330816	0.165408	+	0.986225i	$0.447106\pi$
$464$	10.9444	0.508083
$465$	−19.0134	−0.881726
$466$	−56.5421	−2.61926
$467$	11.3623	0.525786	0.262893	−	0.964825i	$-0.415323\pi$
$467$	11.3623	0.525786	0.262893	+	0.964825i	$0.415323\pi$
$468$	−19.8412	−0.917159
$469$	16.6975	0.771018
$470$	9.47936	0.437250
$471$	20.0402	0.923403
$472$	16.8574	0.775925
$473$	14.9651	0.688094
$474$	−54.8983	−2.52156
$475$	3.63237	0.166665
$476$	−36.1656	−1.65765
$477$	−1.65449	−0.0757538
$478$	60.4133	2.76324
$479$	−24.9338	−1.13925	−0.569627	−	0.821903i	$-0.692912\pi$
$479$	−24.9338	−1.13925	−0.569627	+	0.821903i	$0.692912\pi$
$480$	−7.20298	−0.328770
$481$	−0.435469	−0.0198557
$482$	−26.0417	−1.18617
$483$	16.3556	0.744205
$484$	28.1995	1.28180
$485$	53.6674	2.43691
$486$	−26.0027	−1.17950
$487$	−20.1989	−0.915298	−0.457649	−	0.889133i	$-0.651308\pi$
$487$	−20.1989	−0.915298	−0.457649	+	0.889133i	$0.651308\pi$
$488$	−1.67654	−0.0758936
$489$	3.14575	0.142256
$490$	−21.7904	−0.984389
$491$	−5.10644	−0.230451	−0.115225	−	0.993339i	$-0.536759\pi$
$491$	−5.10644	−0.230451	−0.115225	+	0.993339i	$0.536759\pi$
$492$	−65.1635	−2.93780
$493$	18.2782	0.823207
$494$	−11.3876	−0.512353
$495$	−13.9059	−0.625022
$496$	13.4995	0.606143
$497$	10.8178	0.485245
$498$	58.2136	2.60861
$499$	−27.0716	−1.21189	−0.605946	−	0.795506i	$-0.707205\pi$
$499$	−27.0716	−1.21189	−0.605946	+	0.795506i	$0.707205\pi$
$500$	15.2929	0.683921
$501$	−2.55996	−0.114371
$502$	−5.88418	−0.262624
$503$	22.9868	1.02493	0.512465	−	0.858708i	$-0.328732\pi$
$503$	22.9868	1.02493	0.512465	+	0.858708i	$0.328732\pi$
$504$	−9.50595	−0.423428
$505$	47.9887	2.13547
$506$	−61.9931	−2.75593
$507$	12.8576	0.571027
$508$	35.4927	1.57473
$509$	4.95358	0.219564	0.109782	−	0.993956i	$-0.464985\pi$
$509$	4.95358	0.219564	0.109782	+	0.993956i	$0.464985\pi$
$510$	46.7849	2.07167
$511$	−13.5371	−0.598844
$512$	30.1177	1.33102
$513$	−5.65112	−0.249503
$514$	−58.9249	−2.59906
$515$	57.4729	2.53256
$516$	−18.2826	−0.804847
$517$	−5.74513	−0.252670
$518$	−0.439693	−0.0193190
$519$	−1.31074	−0.0575351
$520$	60.4214	2.64965
$521$	39.5870	1.73434	0.867169	−	0.498015i	$-0.165938\pi$
$521$	39.5870	1.73434	0.867169	+	0.498015i	$0.165938\pi$
$522$	10.1250	0.443161
$523$	22.3666	0.978025	0.489013	−	0.872277i	$-0.337357\pi$
$523$	22.3666	0.978025	0.489013	+	0.872277i	$0.337357\pi$
$524$	−1.74034	−0.0760272
$525$	−9.90759	−0.432403
$526$	−43.4980	−1.89660
$527$	22.5453	0.982088
$528$	−16.9780	−0.738874
$529$	12.9565	0.563324
$530$	10.6182	0.461225
$531$	4.27342	0.185451
$532$	−7.53724	−0.326781
$533$	−58.7519	−2.54483
$534$	−32.0251	−1.38586
$535$	3.87903	0.167705
$536$	36.6879	1.58468
$537$	−1.51248	−0.0652683
$538$	12.4868	0.538344
$539$	13.2064	0.568841
$540$	63.1912	2.71931
$541$	−15.8204	−0.680170	−0.340085	−	0.940395i	$-0.610456\pi$
$541$	−15.8204	−0.680170	−0.340085	+	0.940395i	$0.610456\pi$
$542$	5.36654	0.230512
$543$	−13.2717	−0.569541
$544$	8.54098	0.366192
$545$	18.2245	0.780652
$546$	31.0606	1.32927
$547$	31.7761	1.35865	0.679323	−	0.733839i	$-0.262273\pi$
$547$	31.7761	1.35865	0.679323	+	0.733839i	$0.262273\pi$
$548$	−42.1389	−1.80008
$549$	−0.425011	−0.0181390
$550$	37.5530	1.60127
$551$	3.80934	0.162283
$552$	35.9368	1.52957
$553$	−32.7610	−1.39314
$554$	−17.4020	−0.739339
$555$	0.372862	0.0158271
$556$	75.1975	3.18908
$557$	−31.0297	−1.31477	−0.657385	−	0.753555i	$-0.728337\pi$
$557$	−31.0297	−1.31477	−0.657385	+	0.753555i	$0.728337\pi$
$558$	12.4888	0.528691
$559$	−16.4838	−0.697188
$560$	16.7172	0.706432
$561$	−28.3548	−1.19714
$562$	−50.9845	−2.15065
$563$	26.4598	1.11515	0.557574	−	0.830128i	$-0.311732\pi$
$563$	26.4598	1.11515	0.557574	+	0.830128i	$0.311732\pi$
$564$	7.01874	0.295542
$565$	19.5047	0.820569
$566$	0.668931	0.0281172
$567$	8.86016	0.372092
$568$	23.7691	0.997328
$569$	−2.11233	−0.0885535	−0.0442768	−	0.999019i	$-0.514098\pi$
$569$	−2.11233	−0.0885535	−0.0442768	+	0.999019i	$0.514098\pi$
$570$	9.75040	0.408399
$571$	−42.4110	−1.77484	−0.887422	−	0.460958i	$-0.847506\pi$
$571$	−42.4110	−1.77484	−0.887422	+	0.460958i	$0.847506\pi$
$572$	−77.1747	−3.22684
$573$	19.4491	0.812496
$574$	−59.3218	−2.47604
$575$	−21.7810	−0.908332
$576$	11.0697	0.461238
$577$	37.4559	1.55931	0.779655	−	0.626209i	$-0.215394\pi$
$577$	37.4559	1.55931	0.779655	+	0.626209i	$0.215394\pi$
$578$	−14.5133	−0.603675
$579$	8.01635	0.333148
$580$	−42.5962	−1.76871
$581$	34.7394	1.44123
$582$	60.6182	2.51271
$583$	−6.43533	−0.266524
$584$	−29.7438	−1.23081
$585$	15.3171	0.633283
$586$	71.1297	2.93834
$587$	−38.2738	−1.57973	−0.789864	−	0.613282i	$-0.789849\pi$
$587$	−38.2738	−1.57973	−0.789864	+	0.613282i	$0.789849\pi$
$588$	−16.1341	−0.665360
$589$	4.69864	0.193604
$590$	−27.4260	−1.12911
$591$	15.9389	0.655638
$592$	−0.264731	−0.0108804
$593$	−2.99193	−0.122864	−0.0614319	−	0.998111i	$-0.519567\pi$
$593$	−2.99193	−0.122864	−0.0614319	+	0.998111i	$0.519567\pi$
$594$	−58.4237	−2.39715
$595$	27.9192	1.14458
$596$	90.9626	3.72597
$597$	−8.89516	−0.364055
$598$	68.2843	2.79235
$599$	0.122907	0.00502182	0.00251091	−	0.999997i	$-0.499201\pi$
$599$	0.122907	0.00502182	0.00251091	+	0.999997i	$0.499201\pi$
$600$	−21.7691	−0.888720
$601$	2.51237	0.102482	0.0512409	−	0.998686i	$-0.483682\pi$
$601$	2.51237	0.102482	0.0512409	+	0.998686i	$0.483682\pi$
$602$	−16.6436	−0.678344
$603$	9.30054	0.378747
$604$	30.0560	1.22296
$605$	−21.7696	−0.885059
$606$	54.2040	2.20189
$607$	9.60345	0.389792	0.194896	−	0.980824i	$-0.437563\pi$
$607$	9.60345	0.389792	0.194896	+	0.980824i	$0.437563\pi$
$608$	1.78002	0.0721893
$609$	−10.3903	−0.421035
$610$	2.72764	0.110439
$611$	6.32816	0.256010
$612$	−20.1443	−0.814287
$613$	18.4390	0.744744	0.372372	−	0.928084i	$-0.378545\pi$
$613$	18.4390	0.744744	0.372372	+	0.928084i	$0.378545\pi$
$614$	−52.5583	−2.12108
$615$	50.3051	2.02850
$616$	−36.9746	−1.48975
$617$	−7.33549	−0.295316	−0.147658	−	0.989038i	$-0.547173\pi$
$617$	−7.33549	−0.295316	−0.147658	+	0.989038i	$0.547173\pi$
$618$	64.9166	2.61133
$619$	−38.5074	−1.54774	−0.773872	−	0.633342i	$-0.781683\pi$
$619$	−38.5074	−1.54774	−0.773872	+	0.633342i	$0.781683\pi$
$620$	−52.5405	−2.11008
$621$	33.8862	1.35981
$622$	46.3847	1.85986
$623$	−19.1112	−0.765674
$624$	18.7010	0.748639
$625$	−29.9677	−1.19871
$626$	9.02778	0.360823
$627$	−5.90940	−0.235999
$628$	55.3778	2.20982
$629$	−0.442123	−0.0176286
$630$	15.4656	0.616165
$631$	−21.1716	−0.842830	−0.421415	−	0.906868i	$-0.638466\pi$
$631$	−21.1716	−0.842830	−0.421415	+	0.906868i	$0.638466\pi$
$632$	−71.9829	−2.86333
$633$	37.2332	1.47989
$634$	2.40954	0.0956952
$635$	−27.3998	−1.08733
$636$	7.86196	0.311747
$637$	−14.5467	−0.576359
$638$	39.3826	1.55917
$639$	6.02556	0.238367
$640$	−60.5836	−2.39478
$641$	34.1208	1.34769	0.673846	−	0.738872i	$-0.264641\pi$
$641$	34.1208	1.34769	0.673846	+	0.738872i	$0.264641\pi$
$642$	4.38143	0.172921
$643$	28.0012	1.10426	0.552130	−	0.833758i	$-0.313815\pi$
$643$	28.0012	1.10426	0.552130	+	0.833758i	$0.313815\pi$
$644$	45.1961	1.78097
$645$	14.1139	0.555733
$646$	−11.5616	−0.454885
$647$	6.75869	0.265711	0.132856	−	0.991135i	$-0.457585\pi$
$647$	6.75869	0.265711	0.132856	+	0.991135i	$0.457585\pi$
$648$	19.4677	0.764762
$649$	16.6220	0.652470
$650$	−41.3640	−1.62243
$651$	−12.8159	−0.502296
$652$	8.69278	0.340436
$653$	3.51194	0.137433	0.0687164	−	0.997636i	$-0.478110\pi$
$653$	3.51194	0.137433	0.0687164	+	0.997636i	$0.478110\pi$
$654$	20.5849	0.804932
$655$	1.34352	0.0524955
$656$	−35.7165	−1.39449
$657$	−7.54018	−0.294171
$658$	6.38953	0.249090
$659$	11.3491	0.442099	0.221049	−	0.975263i	$-0.429052\pi$
$659$	11.3491	0.442099	0.221049	+	0.975263i	$0.429052\pi$
$660$	66.0792	2.57213
$661$	38.7966	1.50901	0.754505	−	0.656294i	$-0.227877\pi$
$661$	38.7966	1.50901	0.754505	+	0.656294i	$0.227877\pi$
$662$	24.3084	0.944775
$663$	31.2323	1.21296
$664$	76.3299	2.96217
$665$	5.81862	0.225636
$666$	−0.244910	−0.00949008
$667$	−22.8422	−0.884453
$668$	−7.07404	−0.273703
$669$	−15.4933	−0.599006
$670$	−59.6892	−2.30599
$671$	−1.65313	−0.0638184
$672$	−4.85515	−0.187291
$673$	32.8961	1.26805	0.634026	−	0.773312i	$-0.281401\pi$
$673$	32.8961	1.26805	0.634026	+	0.773312i	$0.281401\pi$
$674$	−84.5694	−3.25749
$675$	−20.5269	−0.790082
$676$	35.5300	1.36654
$677$	19.7778	0.760121	0.380061	−	0.924962i	$-0.375903\pi$
$677$	19.7778	0.760121	0.380061	+	0.924962i	$0.375903\pi$
$678$	22.0309	0.846091
$679$	36.1743	1.38824
$680$	61.3446	2.35246
$681$	−0.221745	−0.00849729
$682$	48.5766	1.86009
$683$	17.7096	0.677640	0.338820	−	0.940851i	$-0.389972\pi$
$683$	17.7096	0.677640	0.338820	+	0.940851i	$0.389972\pi$
$684$	−4.19826	−0.160525
$685$	32.5305	1.24293
$686$	−48.0909	−1.83612
$687$	24.8594	0.948447
$688$	−10.0208	−0.382039
$689$	7.08841	0.270047
$690$	−58.4670	−2.22580
$691$	35.3678	1.34546	0.672728	−	0.739890i	$-0.265123\pi$
$691$	35.3678	1.34546	0.672728	+	0.739890i	$0.265123\pi$
$692$	−3.62202	−0.137689
$693$	−9.37320	−0.356058
$694$	−34.5216	−1.31042
$695$	−58.0512	−2.20201
$696$	−22.8297	−0.865356
$697$	−59.6496	−2.25939
$698$	−48.8813	−1.85019
$699$	32.3192	1.22242
$700$	−27.3780	−1.03479
$701$	−33.5428	−1.26689	−0.633447	−	0.773786i	$-0.718360\pi$
$701$	−33.5428	−1.26689	−0.633447	+	0.773786i	$0.718360\pi$
$702$	64.3527	2.42884
$703$	−0.0921425	−0.00347522
$704$	43.0570	1.62277
$705$	−5.41835	−0.204067
$706$	−75.8456	−2.85449
$707$	32.3466	1.21652
$708$	−20.3069	−0.763179
$709$	−7.29013	−0.273787	−0.136893	−	0.990586i	$-0.543712\pi$
$709$	−7.29013	−0.273787	−0.136893	+	0.990586i	$0.543712\pi$
$710$	−38.6709	−1.45129
$711$	−18.2480	−0.684352
$712$	−41.9914	−1.57369
$713$	−28.1748	−1.05515
$714$	31.5352	1.18018
$715$	59.5776	2.22808
$716$	−4.17949	−0.156195
$717$	−34.5319	−1.28962
$718$	−64.9098	−2.42241
$719$	49.5083	1.84635	0.923174	−	0.384383i	$-0.125586\pi$
$719$	49.5083	1.84635	0.923174	+	0.384383i	$0.125586\pi$
$720$	9.31155	0.347021
$721$	38.7394	1.44273
$722$	−2.40954	−0.0896739
$723$	14.8853	0.553590
$724$	−36.6741	−1.36298
$725$	13.8369	0.513890
$726$	−24.5891	−0.912587
$727$	−7.61959	−0.282595	−0.141297	−	0.989967i	$-0.545127\pi$
$727$	−7.61959	−0.282595	−0.141297	+	0.989967i	$0.545127\pi$
$728$	40.7268	1.50944
$729$	28.2847	1.04758
$730$	48.3915	1.79105
$731$	−16.7356	−0.618989
$732$	2.01961	0.0746469
$733$	−8.46646	−0.312716	−0.156358	−	0.987700i	$-0.549975\pi$
$733$	−8.46646	−0.312716	−0.156358	+	0.987700i	$0.549975\pi$
$734$	−36.8446	−1.35996
$735$	12.4553	0.459420
$736$	−10.6736	−0.393436
$737$	36.1756	1.33255
$738$	−33.0424	−1.21631
$739$	−21.3287	−0.784588	−0.392294	−	0.919840i	$-0.628318\pi$
$739$	−21.3287	−0.784588	−0.392294	+	0.919840i	$0.628318\pi$
$740$	1.03034	0.0378762
$741$	6.50910	0.239118
$742$	7.15716	0.262748
$743$	30.6925	1.12600	0.562999	−	0.826458i	$-0.309648\pi$
$743$	30.6925	1.12600	0.562999	+	0.826458i	$0.309648\pi$
$744$	−28.1593	−1.03237
$745$	−70.2216	−2.57272
$746$	−26.5948	−0.973705
$747$	19.3499	0.707977
$748$	−78.3539	−2.86490
$749$	2.61465	0.0955373
$750$	−13.3350	−0.486924
$751$	−8.80435	−0.321275	−0.160638	−	0.987013i	$-0.551355\pi$
$751$	−8.80435	−0.321275	−0.160638	+	0.987013i	$0.551355\pi$
$752$	3.84701	0.140286
$753$	3.36337	0.122568
$754$	−43.3792	−1.57978
$755$	−23.2027	−0.844433
$756$	42.5938	1.54912
$757$	31.4467	1.14295	0.571475	−	0.820620i	$-0.306372\pi$
$757$	31.4467	1.14295	0.571475	+	0.820620i	$0.306372\pi$
$758$	61.7424	2.24259
$759$	35.4349	1.28621
$760$	12.7848	0.463752
$761$	21.7050	0.786806	0.393403	−	0.919366i	$-0.371298\pi$
$761$	21.7050	0.786806	0.393403	+	0.919366i	$0.371298\pi$
$762$	−30.9485	−1.12115
$763$	12.2842	0.444717
$764$	53.7443	1.94440
$765$	15.5511	0.562251
$766$	29.3222	1.05945
$767$	−18.3088	−0.661094
$768$	−40.7877	−1.47180
$769$	37.1947	1.34127	0.670637	−	0.741786i	$-0.266021\pi$
$769$	37.1947	1.34127	0.670637	+	0.741786i	$0.266021\pi$
$770$	60.1554	2.16785
$771$	33.6811	1.21300
$772$	22.1519	0.797264
$773$	15.3733	0.552938	0.276469	−	0.961023i	$-0.410836\pi$
$773$	15.3733	0.552938	0.276469	+	0.961023i	$0.410836\pi$
$774$	−9.27055	−0.333223
$775$	17.0672	0.613071
$776$	79.4828	2.85327
$777$	0.251326	0.00901628
$778$	2.90461	0.104135
$779$	−12.4315	−0.445405
$780$	−72.7851	−2.60613
$781$	23.4371	0.838647
$782$	69.3277	2.47915
$783$	−21.5270	−0.769312
$784$	−8.84320	−0.315829
$785$	−42.7508	−1.52584
$786$	1.51752	0.0541282
$787$	−31.2468	−1.11383	−0.556914	−	0.830570i	$-0.688015\pi$
$787$	−31.2468	−1.11383	−0.556914	+	0.830570i	$0.688015\pi$
$788$	44.0446	1.56902
$789$	24.8632	0.885153
$790$	117.112	4.16666
$791$	13.1471	0.467456
$792$	−20.5949	−0.731809
$793$	1.82090	0.0646619
$794$	23.7281	0.842079
$795$	−6.06930	−0.215256
$796$	−24.5804	−0.871228
$797$	−36.1928	−1.28201	−0.641007	−	0.767535i	$-0.721483\pi$
$797$	−36.1928	−1.28201	−0.641007	+	0.767535i	$0.721483\pi$
$798$	6.57223	0.232654
$799$	6.42485	0.227295
$800$	6.46568	0.228596
$801$	−10.6450	−0.376122
$802$	31.2656	1.10403
$803$	−29.3285	−1.03498
$804$	−44.1953	−1.55865
$805$	−34.8906	−1.22973
$806$	−53.5063	−1.88468
$807$	−7.13739	−0.251248
$808$	71.0724	2.50032
$809$	46.5864	1.63789	0.818945	−	0.573873i	$-0.194560\pi$
$809$	46.5864	1.63789	0.818945	+	0.573873i	$0.194560\pi$
$810$	−31.6728	−1.11287
$811$	−15.7651	−0.553586	−0.276793	−	0.960930i	$-0.589272\pi$
$811$	−15.7651	−0.553586	−0.276793	+	0.960930i	$0.589272\pi$
$812$	−28.7119	−1.00759
$813$	−3.06748	−0.107581
$814$	−0.952609	−0.0333889
$815$	−6.71068	−0.235065
$816$	18.9868	0.664669
$817$	−3.48785	−0.122025
$818$	33.1528	1.15916
$819$	10.3244	0.360764
$820$	139.010	4.85444
$821$	42.9689	1.49962	0.749812	−	0.661651i	$-0.230144\pi$
$821$	42.9689	1.49962	0.749812	+	0.661651i	$0.230144\pi$
$822$	36.7438	1.28159
$823$	17.8189	0.621127	0.310563	−	0.950553i	$-0.399482\pi$
$823$	17.8189	0.621127	0.310563	+	0.950553i	$0.399482\pi$
$824$	85.1189	2.96526
$825$	−21.4651	−0.747319
$826$	−18.4864	−0.643225
$827$	26.5316	0.922595	0.461297	−	0.887246i	$-0.347384\pi$
$827$	26.5316	0.922595	0.461297	+	0.887246i	$0.347384\pi$
$828$	25.1743	0.874869
$829$	42.9826	1.49285	0.746424	−	0.665471i	$-0.231769\pi$
$829$	42.9826	1.49285	0.746424	+	0.665471i	$0.231769\pi$
$830$	−124.184	−4.31050
$831$	9.94687	0.345053
$832$	−47.4265	−1.64422
$833$	−14.7689	−0.511713
$834$	−65.5698	−2.27050
$835$	5.46104	0.188987
$836$	−16.3297	−0.564773
$837$	−26.5526	−0.917791
$838$	−1.64759	−0.0569149
$839$	−35.0020	−1.20840	−0.604201	−	0.796832i	$-0.706508\pi$
$839$	−35.0020	−1.20840	−0.604201	+	0.796832i	$0.706508\pi$
$840$	−34.8715	−1.20318
$841$	−14.4890	−0.499619
$842$	50.7654	1.74949
$843$	29.1425	1.00372
$844$	102.888	3.54155
$845$	−27.4285	−0.943571
$846$	3.55899	0.122361
$847$	−14.6737	−0.504195
$848$	4.30918	0.147978
$849$	−0.382357	−0.0131225
$850$	−41.9960	−1.44045
$851$	0.552520	0.0189402
$852$	−28.6328	−0.980945
$853$	48.4867	1.66015	0.830076	−	0.557650i	$-0.188297\pi$
$853$	48.4867	1.66015	0.830076	+	0.557650i	$0.188297\pi$
$854$	1.83856	0.0629141
$855$	3.24099	0.110839
$856$	5.74495	0.196358
$857$	−49.1518	−1.67899	−0.839497	−	0.543364i	$-0.817150\pi$
$857$	−49.1518	−1.67899	−0.839497	+	0.543364i	$0.817150\pi$
$858$	67.2939	2.29738
$859$	27.1413	0.926048	0.463024	−	0.886346i	$-0.346764\pi$
$859$	27.1413	0.926048	0.463024	+	0.886346i	$0.346764\pi$
$860$	39.0014	1.32994
$861$	33.9080	1.15558
$862$	90.3434	3.07711
$863$	−0.662117	−0.0225387	−0.0112694	−	0.999936i	$-0.503587\pi$
$863$	−0.662117	−0.0225387	−0.0112694	+	0.999936i	$0.503587\pi$
$864$	−10.0591	−0.342217
$865$	2.79614	0.0950716
$866$	57.7051	1.96090
$867$	8.29575	0.281738
$868$	−35.4147	−1.20205
$869$	−70.9777	−2.40775
$870$	37.1426	1.25925
$871$	−39.8468	−1.35016
$872$	26.9910	0.914029
$873$	20.1492	0.681948
$874$	14.4485	0.488728
$875$	−7.95773	−0.269020
$876$	35.8302	1.21059
$877$	−3.56787	−0.120478	−0.0602392	−	0.998184i	$-0.519186\pi$
$877$	−3.56787	−0.120478	−0.0602392	+	0.998184i	$0.519186\pi$
$878$	47.4303	1.60070
$879$	−40.6574	−1.37134
$880$	36.2184	1.22092
$881$	−15.9453	−0.537210	−0.268605	−	0.963250i	$-0.586563\pi$
$881$	−15.9453	−0.537210	−0.268605	+	0.963250i	$0.586563\pi$
$882$	−8.18111	−0.275472
$883$	15.6098	0.525312	0.262656	−	0.964890i	$-0.415402\pi$
$883$	15.6098	0.525312	0.262656	+	0.964890i	$0.415402\pi$
$884$	86.3055	2.90277
$885$	15.6766	0.526962
$886$	81.4087	2.73498
$887$	12.0715	0.405321	0.202660	−	0.979249i	$-0.435041\pi$
$887$	12.0715	0.405321	0.202660	+	0.979249i	$0.435041\pi$
$888$	0.552218	0.0185312
$889$	−18.4687	−0.619421
$890$	68.3176	2.29001
$891$	19.1958	0.643084
$892$	−42.8132	−1.43349
$893$	1.33900	0.0448078
$894$	−79.3165	−2.65274
$895$	3.22650	0.107850
$896$	−40.8362	−1.36424
$897$	−39.0310	−1.30321
$898$	−20.8502	−0.695779
$899$	17.8987	0.596955
$900$	−15.2496	−0.508321
$901$	7.19672	0.239757
$902$	−128.522	−4.27933
$903$	9.51341	0.316586
$904$	28.8870	0.960766
$905$	28.3118	0.941115
$906$	−26.2079	−0.870698
$907$	29.0459	0.964454	0.482227	−	0.876046i	$-0.339828\pi$
$907$	29.0459	0.964454	0.482227	+	0.876046i	$0.339828\pi$
$908$	−0.612757	−0.0203350
$909$	18.0172	0.597591
$910$	−66.2602	−2.19650
$911$	13.8345	0.458357	0.229178	−	0.973384i	$-0.426396\pi$
$911$	13.8345	0.458357	0.229178	+	0.973384i	$0.426396\pi$
$912$	3.95701	0.131030
$913$	75.2640	2.49087
$914$	−30.8378	−1.02002
$915$	−1.55910	−0.0515424
$916$	68.6951	2.26975
$917$	0.905592	0.0299053
$918$	65.3360	2.15641
$919$	−24.9164	−0.821917	−0.410958	−	0.911654i	$-0.634806\pi$
$919$	−24.9164	−0.821917	−0.410958	+	0.911654i	$0.634806\pi$
$920$	−76.6622	−2.52748
$921$	30.0421	0.989920
$922$	−65.3053	−2.15072
$923$	−25.8156	−0.849731
$924$	44.5405	1.46528
$925$	−0.334695	−0.0110047
$926$	−17.1519	−0.563645
$927$	21.5780	0.708714
$928$	6.78068	0.222587
$929$	−51.5207	−1.69034	−0.845169	−	0.534499i	$-0.820500\pi$
$929$	−51.5207	−1.69034	−0.845169	+	0.534499i	$0.820500\pi$
$930$	45.8136	1.50229
$931$	−3.07798	−0.100877
$932$	89.3088	2.92541
$933$	−26.5132	−0.868004
$934$	−27.3780	−0.895836
$935$	60.4879	1.97817
$936$	22.6850	0.741481
$937$	−35.9696	−1.17507	−0.587537	−	0.809197i	$-0.699902\pi$
$937$	−35.9696	−1.17507	−0.587537	+	0.809197i	$0.699902\pi$
$938$	−40.2333	−1.31366
$939$	−5.16023	−0.168398
$940$	−14.9727	−0.488357
$941$	−3.84115	−0.125218	−0.0626090	−	0.998038i	$-0.519942\pi$
$941$	−3.84115	−0.125218	−0.0626090	+	0.998038i	$0.519942\pi$
$942$	−48.2877	−1.57330
$943$	74.5440	2.42749
$944$	−11.1303	−0.362261
$945$	−32.8817	−1.06964
$946$	−36.0589	−1.17238
$947$	54.7827	1.78020	0.890099	−	0.455767i	$-0.150635\pi$
$947$	54.7827	1.78020	0.890099	+	0.455767i	$0.150635\pi$
$948$	86.7125	2.81629
$949$	32.3048	1.04866
$950$	−8.75235	−0.283964
$951$	−1.37728	−0.0446614
$952$	41.3491	1.34013
$953$	−49.7680	−1.61214	−0.806071	−	0.591819i	$-0.798410\pi$
$953$	−49.7680	−1.61214	−0.806071	+	0.591819i	$0.798410\pi$
$954$	3.98656	0.129070
$955$	−41.4897	−1.34258
$956$	−95.4234	−3.08621
$957$	−22.5109	−0.727673
$958$	60.0790	1.94107
$959$	21.9271	0.708063
$960$	40.6080	1.31062
$961$	−8.92280	−0.287832
$962$	1.04928	0.0338302
$963$	1.45637	0.0469308
$964$	41.1331	1.32481
$965$	−17.1009	−0.550497
$966$	−39.4095	−1.26798
$967$	−42.9600	−1.38150	−0.690749	−	0.723094i	$-0.742719\pi$
$967$	−42.9600	−1.38150	−0.690749	+	0.723094i	$0.742719\pi$
$968$	−32.2413	−1.03627
$969$	6.60855	0.212297
$970$	−129.314	−4.15202
$971$	26.1905	0.840492	0.420246	−	0.907410i	$-0.361944\pi$
$971$	26.1905	0.840492	0.420246	+	0.907410i	$0.361944\pi$
$972$	41.0715	1.31737
$973$	−39.1292	−1.25443
$974$	48.6700	1.55949
$975$	23.6434	0.757196
$976$	1.10696	0.0354329
$977$	−32.1235	−1.02772	−0.513861	−	0.857874i	$-0.671785\pi$
$977$	−32.1235	−1.02772	−0.513861	+	0.857874i	$0.671785\pi$
$978$	−7.57982	−0.242376
$979$	−41.4050	−1.32331
$980$	34.4181	1.09945
$981$	6.84232	0.218458
$982$	12.3042	0.392643
$983$	−27.9593	−0.891763	−0.445882	−	0.895092i	$-0.647110\pi$
$983$	−27.9593	−0.891763	−0.445882	+	0.895092i	$0.647110\pi$
$984$	74.5032	2.37507
$985$	−34.0017	−1.08338
$986$	−44.0420	−1.40258
$987$	−3.65222	−0.116252
$988$	17.9868	0.572238
$989$	20.9145	0.665041
$990$	33.5068	1.06491
$991$	30.8132	0.978813	0.489406	−	0.872056i	$-0.337213\pi$
$991$	30.8132	0.978813	0.489406	+	0.872056i	$0.337213\pi$
$992$	8.36366	0.265546
$993$	−13.8946	−0.440931
$994$	−26.0660	−0.826763
$995$	18.9756	0.601568
$996$	−91.9489	−2.91351
$997$	−52.6178	−1.66642	−0.833211	−	0.552955i	$-0.813500\pi$
$997$	−52.6178	−1.66642	−0.833211	+	0.552955i	$0.813500\pi$
$998$	65.2302	2.06483
$999$	0.520708	0.0164745

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.12	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-2.40954 q^{2} +1.37728 q^{3} +3.80590 q^{4} -2.93809 q^{5} -3.31862 q^{6} -1.98041 q^{7} -4.35139 q^{8} -1.10309 q^{9} +O(q^{10})\)	\(q-2.40954 q^{2} +1.37728 q^{3} +3.80590 q^{4} -2.93809 q^{5} -3.31862 q^{6} -1.98041 q^{7} -4.35139 q^{8} -1.10309 q^{9} +7.07945 q^{10} -4.29062 q^{11} +5.24179 q^{12} +4.72605 q^{13} +4.77188 q^{14} -4.04658 q^{15} +2.87306 q^{16} +4.79826 q^{17} +2.65795 q^{18} +1.00000 q^{19} -11.1821 q^{20} -2.72758 q^{21} +10.3384 q^{22} -5.99637 q^{23} -5.99309 q^{24} +3.63237 q^{25} -11.3876 q^{26} -5.65112 q^{27} -7.53724 q^{28} +3.80934 q^{29} +9.75040 q^{30} +4.69864 q^{31} +1.78002 q^{32} -5.90940 q^{33} -11.5616 q^{34} +5.81862 q^{35} -4.19826 q^{36} -0.0921425 q^{37} -2.40954 q^{38} +6.50910 q^{39} +12.7848 q^{40} -12.4315 q^{41} +6.57223 q^{42} -3.48785 q^{43} -16.3297 q^{44} +3.24099 q^{45} +14.4485 q^{46} +1.33900 q^{47} +3.95701 q^{48} -3.07798 q^{49} -8.75235 q^{50} +6.60855 q^{51} +17.9868 q^{52} +1.49986 q^{53} +13.6166 q^{54} +12.6062 q^{55} +8.61753 q^{56} +1.37728 q^{57} -9.17876 q^{58} -3.87403 q^{59} -15.4009 q^{60} +0.385290 q^{61} -11.3216 q^{62} +2.18458 q^{63} -10.0351 q^{64} -13.8855 q^{65} +14.2389 q^{66} -8.43132 q^{67} +18.2617 q^{68} -8.25869 q^{69} -14.0202 q^{70} -5.46241 q^{71} +4.79999 q^{72} +6.83548 q^{73} +0.222021 q^{74} +5.00280 q^{75} +3.80590 q^{76} +8.49719 q^{77} -15.6839 q^{78} +16.5425 q^{79} -8.44130 q^{80} -4.47390 q^{81} +29.9543 q^{82} -17.5415 q^{83} -10.3809 q^{84} -14.0977 q^{85} +8.40413 q^{86} +5.24653 q^{87} +18.6701 q^{88} +9.65012 q^{89} -7.80930 q^{90} -9.35951 q^{91} -22.8216 q^{92} +6.47135 q^{93} -3.22637 q^{94} -2.93809 q^{95} +2.45159 q^{96} -18.2661 q^{97} +7.41652 q^{98} +4.73296 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 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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