LMFDB - Embedded newform 8003.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72330 q^{2} +1.38182 q^{3} +5.41638 q^{4} +0.695892 q^{5} -3.76310 q^{6} +2.22178 q^{7} -9.30382 q^{8} -1.09059 q^{9} +O(q^{10})$	\(q-2.72330 q^{2} +1.38182 q^{3} +5.41638 q^{4} +0.695892 q^{5} -3.76310 q^{6} +2.22178 q^{7} -9.30382 q^{8} -1.09059 q^{9} -1.89512 q^{10} +5.79477 q^{11} +7.48443 q^{12} +4.76800 q^{13} -6.05057 q^{14} +0.961594 q^{15} +14.5044 q^{16} +3.86720 q^{17} +2.97000 q^{18} +4.05190 q^{19} +3.76921 q^{20} +3.07008 q^{21} -15.7809 q^{22} -4.01996 q^{23} -12.8562 q^{24} -4.51573 q^{25} -12.9847 q^{26} -5.65243 q^{27} +12.0340 q^{28} +0.104372 q^{29} -2.61871 q^{30} -5.52903 q^{31} -20.8921 q^{32} +8.00731 q^{33} -10.5316 q^{34} +1.54612 q^{35} -5.90703 q^{36} +3.67717 q^{37} -11.0346 q^{38} +6.58849 q^{39} -6.47445 q^{40} -7.81619 q^{41} -8.36077 q^{42} +6.96172 q^{43} +31.3867 q^{44} -0.758930 q^{45} +10.9476 q^{46} -10.7582 q^{47} +20.0424 q^{48} -2.06371 q^{49} +12.2977 q^{50} +5.34376 q^{51} +25.8253 q^{52} +1.00000 q^{53} +15.3933 q^{54} +4.03254 q^{55} -20.6710 q^{56} +5.59898 q^{57} -0.284238 q^{58} -0.809716 q^{59} +5.20835 q^{60} +8.24367 q^{61} +15.0572 q^{62} -2.42304 q^{63} +27.8869 q^{64} +3.31801 q^{65} -21.8063 q^{66} +7.38674 q^{67} +20.9462 q^{68} -5.55484 q^{69} -4.21054 q^{70} +14.4465 q^{71} +10.1466 q^{72} +14.4546 q^{73} -10.0141 q^{74} -6.23991 q^{75} +21.9466 q^{76} +12.8747 q^{77} -17.9424 q^{78} +0.624196 q^{79} +10.0935 q^{80} -4.53886 q^{81} +21.2858 q^{82} -4.65202 q^{83} +16.6287 q^{84} +2.69116 q^{85} -18.9589 q^{86} +0.144223 q^{87} -53.9136 q^{88} -0.342282 q^{89} +2.06680 q^{90} +10.5934 q^{91} -21.7736 q^{92} -7.64010 q^{93} +29.2977 q^{94} +2.81969 q^{95} -28.8691 q^{96} +13.4398 q^{97} +5.62012 q^{98} -6.31970 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) $ 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * 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 $

$2$	−2.72330	−1.92567	−0.962833	−	0.270098i	$-0.912944\pi$
$2$	−2.72330	−1.92567	−0.962833	+	0.270098i	$0.912944\pi$
$3$	1.38182	0.797791	0.398896	−	0.916996i	$-0.369394\pi$
$3$	1.38182	0.797791	0.398896	+	0.916996i	$0.369394\pi$
$4$	5.41638	2.70819
$5$	0.695892	0.311212	0.155606	−	0.987819i	$-0.450267\pi$
$5$	0.695892	0.311212	0.155606	+	0.987819i	$0.450267\pi$
$6$	−3.76310	−1.53628
$7$	2.22178	0.839752	0.419876	−	0.907581i	$-0.362074\pi$
$7$	2.22178	0.839752	0.419876	+	0.907581i	$0.362074\pi$
$8$	−9.30382	−3.28940
$9$	−1.09059	−0.363529
$10$	−1.89512	−0.599291
$11$	5.79477	1.74719	0.873595	−	0.486653i	$-0.161783\pi$
$11$	5.79477	1.74719	0.873595	+	0.486653i	$0.161783\pi$
$12$	7.48443	2.16057
$13$	4.76800	1.32240	0.661202	−	0.750208i	$-0.270047\pi$
$13$	4.76800	1.32240	0.661202	+	0.750208i	$0.270047\pi$
$14$	−6.05057	−1.61708
$15$	0.961594	0.248283
$16$	14.5044	3.62609
$17$	3.86720	0.937935	0.468967	−	0.883216i	$-0.344626\pi$
$17$	3.86720	0.937935	0.468967	+	0.883216i	$0.344626\pi$
$18$	2.97000	0.700035
$19$	4.05190	0.929570	0.464785	−	0.885423i	$-0.346132\pi$
$19$	4.05190	0.929570	0.464785	+	0.885423i	$0.346132\pi$
$20$	3.76921	0.842821
$21$	3.07008	0.669947
$22$	−15.7809	−3.36450
$23$	−4.01996	−0.838219	−0.419110	−	0.907936i	$-0.637658\pi$
$23$	−4.01996	−0.838219	−0.419110	+	0.907936i	$0.637658\pi$
$24$	−12.8562	−2.62425
$25$	−4.51573	−0.903147
$26$	−12.9847	−2.54651
$27$	−5.65243	−1.08781
$28$	12.0340	2.27421
$29$	0.104372	0.0193815	0.00969074	−	0.999953i	$-0.496915\pi$
$29$	0.104372	0.0193815	0.00969074	+	0.999953i	$0.496915\pi$
$30$	−2.61871	−0.478109
$31$	−5.52903	−0.993043	−0.496522	−	0.868024i	$-0.665390\pi$
$31$	−5.52903	−0.993043	−0.496522	+	0.868024i	$0.665390\pi$
$32$	−20.8921	−3.69324
$33$	8.00731	1.39389
$34$	−10.5316	−1.80615
$35$	1.54612	0.261341
$36$	−5.90703	−0.984504
$37$	3.67717	0.604523	0.302262	−	0.953225i	$-0.402258\pi$
$37$	3.67717	0.604523	0.302262	+	0.953225i	$0.402258\pi$
$38$	−11.0346	−1.79004
$39$	6.58849	1.05500
$40$	−6.47445	−1.02370
$41$	−7.81619	−1.22068	−0.610342	−	0.792138i	$-0.708968\pi$
$41$	−7.81619	−1.22068	−0.610342	+	0.792138i	$0.708968\pi$
$42$	−8.36077	−1.29009
$43$	6.96172	1.06165	0.530826	−	0.847481i	$-0.321882\pi$
$43$	6.96172	1.06165	0.530826	+	0.847481i	$0.321882\pi$
$44$	31.3867	4.73172
$45$	−0.758930	−0.113135
$46$	10.9476	1.61413
$47$	−10.7582	−1.56924	−0.784619	−	0.619978i	$-0.787141\pi$
$47$	−10.7582	−1.56924	−0.784619	+	0.619978i	$0.787141\pi$
$48$	20.0424	2.89287
$49$	−2.06371	−0.294816
$50$	12.2977	1.73916
$51$	5.34376	0.748276
$52$	25.8253	3.58132
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	15.3933	2.09476
$55$	4.03254	0.543747
$56$	−20.6710	−2.76228
$57$	5.59898	0.741603
$58$	−0.284238	−0.0373222
$59$	−0.809716	−0.105416	−0.0527080	−	0.998610i	$-0.516785\pi$
$59$	−0.809716	−0.105416	−0.0527080	+	0.998610i	$0.516785\pi$
$60$	5.20835	0.672396
$61$	8.24367	1.05549	0.527747	−	0.849402i	$-0.323037\pi$
$61$	8.24367	1.05549	0.527747	+	0.849402i	$0.323037\pi$
$62$	15.0572	1.91227
$63$	−2.42304	−0.305274
$64$	27.8869	3.48586
$65$	3.31801	0.411548
$66$	−21.8063	−2.68417
$67$	7.38674	0.902434	0.451217	−	0.892414i	$-0.350990\pi$
$67$	7.38674	0.902434	0.451217	+	0.892414i	$0.350990\pi$
$68$	20.9462	2.54010
$69$	−5.55484	−0.668724
$70$	−4.21054	−0.503256
$71$	14.4465	1.71448	0.857242	−	0.514914i	$-0.172176\pi$
$71$	14.4465	1.71448	0.857242	+	0.514914i	$0.172176\pi$
$72$	10.1466	1.19579
$73$	14.4546	1.69178	0.845891	−	0.533355i	$-0.179069\pi$
$73$	14.4546	1.69178	0.845891	+	0.533355i	$0.179069\pi$
$74$	−10.0141	−1.16411
$75$	−6.23991	−0.720523
$76$	21.9466	2.51745
$77$	12.8747	1.46721
$78$	−17.9424	−2.03158
$79$	0.624196	0.0702275	0.0351138	−	0.999383i	$-0.488821\pi$
$79$	0.624196	0.0702275	0.0351138	+	0.999383i	$0.488821\pi$
$80$	10.0935	1.12848
$81$	−4.53886	−0.504318
$82$	21.2858	2.35063
$83$	−4.65202	−0.510626	−0.255313	−	0.966858i	$-0.582178\pi$
$83$	−4.65202	−0.510626	−0.255313	+	0.966858i	$0.582178\pi$
$84$	16.6287	1.81434
$85$	2.69116	0.291897
$86$	−18.9589	−2.04439
$87$	0.144223	0.0154624
$88$	−53.9136	−5.74721
$89$	−0.342282	−0.0362818	−0.0181409	−	0.999835i	$-0.505775\pi$
$89$	−0.342282	−0.0362818	−0.0181409	+	0.999835i	$0.505775\pi$
$90$	2.06680	0.217859
$91$	10.5934	1.11049
$92$	−21.7736	−2.27005
$93$	−7.64010	−0.792241
$94$	29.2977	3.02183
$95$	2.81969	0.289294
$96$	−28.8691	−2.94644
$97$	13.4398	1.36461	0.682305	−	0.731068i	$-0.260978\pi$
$97$	13.4398	1.36461	0.682305	+	0.731068i	$0.260978\pi$
$98$	5.62012	0.567717
$99$	−6.31970	−0.635154
$100$	−24.4589	−2.44589
$101$	16.2591	1.61784	0.808922	−	0.587915i	$-0.200051\pi$
$101$	16.2591	1.61784	0.808922	+	0.587915i	$0.200051\pi$
$102$	−14.5527	−1.44093
$103$	−14.9183	−1.46995	−0.734974	−	0.678095i	$-0.762806\pi$
$103$	−14.9183	−1.46995	−0.734974	+	0.678095i	$0.762806\pi$
$104$	−44.3606	−4.34991
$105$	2.13645	0.208496
$106$	−2.72330	−0.264511
$107$	7.49757	0.724818	0.362409	−	0.932019i	$-0.381954\pi$
$107$	7.49757	0.724818	0.362409	+	0.932019i	$0.381954\pi$
$108$	−30.6157	−2.94600
$109$	4.09511	0.392240	0.196120	−	0.980580i	$-0.437166\pi$
$109$	4.09511	0.392240	0.196120	+	0.980580i	$0.437166\pi$
$110$	−10.9818	−1.04708
$111$	5.08117	0.482284
$112$	32.2255	3.04502
$113$	8.31499	0.782209	0.391104	−	0.920346i	$-0.372093\pi$
$113$	8.31499	0.782209	0.391104	+	0.920346i	$0.372093\pi$
$114$	−15.2477	−1.42808
$115$	−2.79746	−0.260864
$116$	0.565320	0.0524887
$117$	−5.19991	−0.480732
$118$	2.20510	0.202996
$119$	8.59206	0.787633
$120$	−8.94650	−0.816700
$121$	22.5794	2.05267
$122$	−22.4500	−2.03253
$123$	−10.8005	−0.973851
$124$	−29.9473	−2.68935
$125$	−6.62192	−0.592283
$126$	6.59867	0.587856
$127$	−0.409204	−0.0363110	−0.0181555	−	0.999835i	$-0.505779\pi$
$127$	−0.409204	−0.0363110	−0.0181555	+	0.999835i	$0.505779\pi$
$128$	−34.1601	−3.01936
$129$	9.61981	0.846977
$130$	−9.03594	−0.792505
$131$	7.86141	0.686855	0.343427	−	0.939179i	$-0.388412\pi$
$131$	7.86141	0.686855	0.343427	+	0.939179i	$0.388412\pi$
$132$	43.3706	3.77493
$133$	9.00242	0.780609
$134$	−20.1163	−1.73779
$135$	−3.93348	−0.338540
$136$	−35.9798	−3.08524
$137$	−20.3848	−1.74159	−0.870795	−	0.491646i	$-0.836396\pi$
$137$	−20.3848	−1.74159	−0.870795	+	0.491646i	$0.836396\pi$
$138$	15.1275	1.28774
$139$	−21.2634	−1.80354	−0.901771	−	0.432215i	$-0.857732\pi$
$139$	−21.2634	−1.80354	−0.901771	+	0.432215i	$0.857732\pi$
$140$	8.37434	0.707761
$141$	−14.8658	−1.25192
$142$	−39.3422	−3.30152
$143$	27.6295	2.31049
$144$	−15.8183	−1.31819
$145$	0.0726319	0.00603175
$146$	−39.3642	−3.25781
$147$	−2.85167	−0.235202
$148$	19.9169	1.63716
$149$	4.98947	0.408753	0.204376	−	0.978892i	$-0.434483\pi$
$149$	4.98947	0.408753	0.204376	+	0.978892i	$0.434483\pi$
$150$	16.9932	1.38749
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−37.6982	−3.05773
$153$	−4.21752	−0.340966
$154$	−35.0617	−2.82535
$155$	−3.84761	−0.309047
$156$	35.6857	2.85715
$157$	14.8928	1.18857	0.594287	−	0.804253i	$-0.297434\pi$
$157$	14.8928	1.18857	0.594287	+	0.804253i	$0.297434\pi$
$158$	−1.69987	−0.135235
$159$	1.38182	0.109585
$160$	−14.5387	−1.14938
$161$	−8.93144	−0.703896
$162$	12.3607	0.971148
$163$	−4.89528	−0.383428	−0.191714	−	0.981451i	$-0.561405\pi$
$163$	−4.89528	−0.383428	−0.191714	+	0.981451i	$0.561405\pi$
$164$	−42.3354	−3.30584
$165$	5.57222	0.433797
$166$	12.6689	0.983294
$167$	5.15758	0.399105	0.199553	−	0.979887i	$-0.436051\pi$
$167$	5.15758	0.399105	0.199553	+	0.979887i	$0.436051\pi$
$168$	−28.5635	−2.20372
$169$	9.73378	0.748752
$170$	−7.32883	−0.562096
$171$	−4.41895	−0.337926
$172$	37.7073	2.87515
$173$	14.3965	1.09455	0.547273	−	0.836954i	$-0.315666\pi$
$173$	14.3965	1.09455	0.547273	+	0.836954i	$0.315666\pi$
$174$	−0.392764	−0.0297754
$175$	−10.0329	−0.758420
$176$	84.0496	6.33548
$177$	−1.11888	−0.0841000
$178$	0.932138	0.0698667
$179$	6.53731	0.488622	0.244311	−	0.969697i	$-0.421438\pi$
$179$	6.53731	0.488622	0.244311	+	0.969697i	$0.421438\pi$
$180$	−4.11065	−0.306390
$181$	−17.4193	−1.29477	−0.647385	−	0.762163i	$-0.724137\pi$
$181$	−17.4193	−1.29477	−0.647385	+	0.762163i	$0.724137\pi$
$182$	−28.8491	−2.13844
$183$	11.3912	0.842064
$184$	37.4010	2.75724
$185$	2.55891	0.188135
$186$	20.8063	1.52559
$187$	22.4096	1.63875
$188$	−58.2702	−4.24979
$189$	−12.5584	−0.913492
$190$	−7.67886	−0.557083
$191$	−2.00287	−0.144922	−0.0724612	−	0.997371i	$-0.523085\pi$
$191$	−2.00287	−0.144922	−0.0724612	+	0.997371i	$0.523085\pi$
$192$	38.5345	2.78099
$193$	3.58438	0.258009	0.129005	−	0.991644i	$-0.458822\pi$
$193$	3.58438	0.258009	0.129005	+	0.991644i	$0.458822\pi$
$194$	−36.6008	−2.62778
$195$	4.58488	0.328330
$196$	−11.1778	−0.798418
$197$	−19.6493	−1.39996	−0.699979	−	0.714164i	$-0.746807\pi$
$197$	−19.6493	−1.39996	−0.699979	+	0.714164i	$0.746807\pi$
$198$	17.2105	1.22309
$199$	9.71465	0.688653	0.344327	−	0.938850i	$-0.388107\pi$
$199$	9.71465	0.688653	0.344327	+	0.938850i	$0.388107\pi$
$200$	42.0136	2.97081
$201$	10.2071	0.719955
$202$	−44.2786	−3.11543
$203$	0.231892	0.0162756
$204$	28.9438	2.02647
$205$	−5.43922	−0.379892
$206$	40.6272	2.83063
$207$	4.38411	0.304717
$208$	69.1568	4.79516
$209$	23.4799	1.62414
$210$	−5.81819	−0.401493
$211$	22.2650	1.53278	0.766392	−	0.642374i	$-0.222050\pi$
$211$	22.2650	1.53278	0.766392	+	0.642374i	$0.222050\pi$
$212$	5.41638	0.371998
$213$	19.9624	1.36780
$214$	−20.4182	−1.39576
$215$	4.84460	0.330399
$216$	52.5893	3.57825
$217$	−12.2843	−0.833910
$218$	−11.1522	−0.755324
$219$	19.9736	1.34969
$220$	21.8417	1.47257
$221$	18.4388	1.24033
$222$	−13.8376	−0.928717
$223$	1.26359	0.0846160	0.0423080	−	0.999105i	$-0.486529\pi$
$223$	1.26359	0.0846160	0.0423080	+	0.999105i	$0.486529\pi$
$224$	−46.4177	−3.10141
$225$	4.92480	0.328320
$226$	−22.6442	−1.50627
$227$	−17.5572	−1.16531	−0.582656	−	0.812719i	$-0.697986\pi$
$227$	−17.5572	−1.16531	−0.582656	+	0.812719i	$0.697986\pi$
$228$	30.3262	2.00840
$229$	20.4328	1.35023	0.675117	−	0.737710i	$-0.264093\pi$
$229$	20.4328	1.35023	0.675117	+	0.737710i	$0.264093\pi$
$230$	7.61832	0.502337
$231$	17.7904	1.17053
$232$	−0.971063	−0.0637534
$233$	3.61323	0.236710	0.118355	−	0.992971i	$-0.462238\pi$
$233$	3.61323	0.236710	0.118355	+	0.992971i	$0.462238\pi$
$234$	14.1609	0.925729
$235$	−7.48651	−0.488366
$236$	−4.38573	−0.285486
$237$	0.862524	0.0560269
$238$	−23.3988	−1.51672
$239$	−17.1132	−1.10696	−0.553479	−	0.832863i	$-0.686700\pi$
$239$	−17.1132	−1.10696	−0.553479	+	0.832863i	$0.686700\pi$
$240$	13.9473	0.900296
$241$	−20.1339	−1.29694	−0.648470	−	0.761240i	$-0.724591\pi$
$241$	−20.1339	−1.29694	−0.648470	+	0.761240i	$0.724591\pi$
$242$	−61.4906	−3.95276
$243$	10.6854	0.685471
$244$	44.6508	2.85848
$245$	−1.43612	−0.0917504
$246$	29.4131	1.87531
$247$	19.3195	1.22927
$248$	51.4411	3.26651
$249$	−6.42823	−0.407373
$250$	18.0335	1.14054
$251$	13.5471	0.855084	0.427542	−	0.903995i	$-0.359380\pi$
$251$	13.5471	0.855084	0.427542	+	0.903995i	$0.359380\pi$
$252$	−13.1241	−0.826740
$253$	−23.2947	−1.46453
$254$	1.11439	0.0699228
$255$	3.71868	0.232873
$256$	37.2546	2.32841
$257$	5.86683	0.365963	0.182981	−	0.983116i	$-0.441425\pi$
$257$	5.86683	0.365963	0.182981	+	0.983116i	$0.441425\pi$
$258$	−26.1976	−1.63099
$259$	8.16985	0.507650
$260$	17.9716	1.11455
$261$	−0.113827	−0.00704573
$262$	−21.4090	−1.32265
$263$	4.47489	0.275933	0.137967	−	0.990437i	$-0.455943\pi$
$263$	4.47489	0.275933	0.137967	+	0.990437i	$0.455943\pi$
$264$	−74.4986	−4.58507
$265$	0.695892	0.0427483
$266$	−24.5163	−1.50319
$267$	−0.472971	−0.0289453
$268$	40.0094	2.44396
$269$	−24.5833	−1.49887	−0.749436	−	0.662077i	$-0.769675\pi$
$269$	−24.5833	−1.49887	−0.749436	+	0.662077i	$0.769675\pi$
$270$	10.7121	0.651915
$271$	−6.78455	−0.412132	−0.206066	−	0.978538i	$-0.566066\pi$
$271$	−6.78455	−0.412132	−0.206066	+	0.978538i	$0.566066\pi$
$272$	56.0914	3.40104
$273$	14.6381	0.885941
$274$	55.5140	3.35372
$275$	−26.1677	−1.57797
$276$	−30.0871	−1.81103
$277$	6.30215	0.378660	0.189330	−	0.981914i	$-0.439368\pi$
$277$	6.30215	0.378660	0.189330	+	0.981914i	$0.439368\pi$
$278$	57.9068	3.47302
$279$	6.02988	0.361000
$280$	−14.3848	−0.859655
$281$	−24.6879	−1.47276	−0.736378	−	0.676571i	$-0.763465\pi$
$281$	−24.6879	−1.47276	−0.736378	+	0.676571i	$0.763465\pi$
$282$	40.4840	2.41079
$283$	−25.6640	−1.52557	−0.762785	−	0.646653i	$-0.776168\pi$
$283$	−25.6640	−1.52557	−0.762785	+	0.646653i	$0.776168\pi$
$284$	78.2477	4.64314
$285$	3.89629	0.230796
$286$	−75.2434	−4.44923
$287$	−17.3658	−1.02507
$288$	22.7847	1.34260
$289$	−2.04474	−0.120279
$290$	−0.197799	−0.0116151
$291$	18.5714	1.08867
$292$	78.2915	4.58167
$293$	32.2435	1.88369	0.941843	−	0.336052i	$-0.109092\pi$
$293$	32.2435	1.88369	0.941843	+	0.336052i	$0.109092\pi$
$294$	7.76596	0.452920
$295$	−0.563475	−0.0328068
$296$	−34.2118	−1.98852
$297$	−32.7546	−1.90061
$298$	−13.5878	−0.787122
$299$	−19.1671	−1.10846
$300$	−33.7977	−1.95131
$301$	15.4674	0.891524
$302$	2.72330	0.156708
$303$	22.4671	1.29070
$304$	58.7703	3.37071
$305$	5.73671	0.328483
$306$	11.4856	0.656587
$307$	34.3594	1.96099	0.980497	−	0.196532i	$-0.0629680\pi$
$307$	34.3594	1.96099	0.980497	+	0.196532i	$0.0629680\pi$
$308$	69.7342	3.97347
$309$	−20.6144	−1.17271
$310$	10.4782	0.595122
$311$	−3.84636	−0.218107	−0.109053	−	0.994036i	$-0.534782\pi$
$311$	−3.84636	−0.218107	−0.109053	+	0.994036i	$0.534782\pi$
$312$	−61.2981	−3.47032
$313$	5.34592	0.302169	0.151085	−	0.988521i	$-0.451723\pi$
$313$	5.34592	0.302169	0.151085	+	0.988521i	$0.451723\pi$
$314$	−40.5576	−2.28880
$315$	−1.68617	−0.0950051
$316$	3.38088	0.190189
$317$	−22.5305	−1.26544	−0.632721	−	0.774380i	$-0.718062\pi$
$317$	−22.5305	−1.26544	−0.632721	+	0.774380i	$0.718062\pi$
$318$	−3.76310	−0.211024
$319$	0.604815	0.0338631
$320$	19.4063	1.08484
$321$	10.3603	0.578253
$322$	24.3230	1.35547
$323$	15.6695	0.871876
$324$	−24.5842	−1.36579
$325$	−21.5310	−1.19433
$326$	13.3313	0.738354
$327$	5.65869	0.312926
$328$	72.7204	4.01532
$329$	−23.9022	−1.31777
$330$	−15.1748	−0.835348
$331$	−6.52681	−0.358746	−0.179373	−	0.983781i	$-0.557407\pi$
$331$	−6.52681	−0.358746	−0.179373	+	0.983781i	$0.557407\pi$
$332$	−25.1971	−1.38287
$333$	−4.01027	−0.219762
$334$	−14.0456	−0.768543
$335$	5.14038	0.280849
$336$	44.5296	2.42929
$337$	14.4647	0.787943	0.393972	−	0.919123i	$-0.371101\pi$
$337$	14.4647	0.787943	0.393972	+	0.919123i	$0.371101\pi$
$338$	−26.5080	−1.44185
$339$	11.4898	0.624039
$340$	14.5763	0.790511
$341$	−32.0395	−1.73504
$342$	12.0341	0.650732
$343$	−20.1375	−1.08732
$344$	−64.7706	−3.49220
$345$	−3.86557	−0.208115
$346$	−39.2061	−2.10773
$347$	8.05061	0.432179	0.216090	−	0.976374i	$-0.430670\pi$
$347$	8.05061	0.432179	0.216090	+	0.976374i	$0.430670\pi$
$348$	0.781168	0.0418750
$349$	28.8200	1.54270	0.771348	−	0.636413i	$-0.219583\pi$
$349$	28.8200	1.54270	0.771348	+	0.636413i	$0.219583\pi$
$350$	27.3228	1.46046
$351$	−26.9508	−1.43853
$352$	−121.065	−6.45280
$353$	−27.7681	−1.47795	−0.738973	−	0.673735i	$-0.764689\pi$
$353$	−27.7681	−1.47795	−0.738973	+	0.673735i	$0.764689\pi$
$354$	3.04704	0.161948
$355$	10.0532	0.533568
$356$	−1.85393	−0.0982580
$357$	11.8726	0.628367
$358$	−17.8031	−0.940922
$359$	14.3914	0.759548	0.379774	−	0.925079i	$-0.376002\pi$
$359$	14.3914	0.759548	0.379774	+	0.925079i	$0.376002\pi$
$360$	7.06095	0.372145
$361$	−2.58208	−0.135899
$362$	47.4381	2.49329
$363$	31.2006	1.63761
$364$	57.3779	3.00742
$365$	10.0588	0.526504
$366$	−31.0218	−1.62153
$367$	−25.5044	−1.33132	−0.665658	−	0.746257i	$-0.731849\pi$
$367$	−25.5044	−1.33132	−0.665658	+	0.746257i	$0.731849\pi$
$368$	−58.3070	−3.03946
$369$	8.52423	0.443754
$370$	−6.96870	−0.362285
$371$	2.22178	0.115349
$372$	−41.3816	−2.14554
$373$	31.2939	1.62033	0.810167	−	0.586199i	$-0.199376\pi$
$373$	31.2939	1.62033	0.810167	+	0.586199i	$0.199376\pi$
$374$	−61.0280	−3.15568
$375$	−9.15027	−0.472518
$376$	100.092	5.16185
$377$	0.497647	0.0256301
$378$	34.2004	1.75908
$379$	−24.2719	−1.24676	−0.623382	−	0.781917i	$-0.714242\pi$
$379$	−24.2719	−1.24676	−0.623382	+	0.781917i	$0.714242\pi$
$380$	15.2725	0.783462
$381$	−0.565444	−0.0289686
$382$	5.45442	0.279072
$383$	8.41367	0.429919	0.214959	−	0.976623i	$-0.431038\pi$
$383$	8.41367	0.429919	0.214959	+	0.976623i	$0.431038\pi$
$384$	−47.2030	−2.40882
$385$	8.95939	0.456613
$386$	−9.76135	−0.496840
$387$	−7.59235	−0.385941
$388$	72.7953	3.69562
$389$	−27.5769	−1.39820	−0.699102	−	0.715022i	$-0.746416\pi$
$389$	−27.5769	−1.39820	−0.699102	+	0.715022i	$0.746416\pi$
$390$	−12.4860	−0.632253
$391$	−15.5460	−0.786195
$392$	19.2004	0.969768
$393$	10.8630	0.547967
$394$	53.5111	2.69585
$395$	0.434373	0.0218557
$396$	−34.2299	−1.72012
$397$	−22.8736	−1.14799	−0.573996	−	0.818858i	$-0.694607\pi$
$397$	−22.8736	−1.14799	−0.573996	+	0.818858i	$0.694607\pi$
$398$	−26.4559	−1.32612
$399$	12.4397	0.622763
$400$	−65.4979	−3.27490
$401$	−22.8512	−1.14114	−0.570568	−	0.821251i	$-0.693277\pi$
$401$	−22.8512	−1.14114	−0.570568	+	0.821251i	$0.693277\pi$
$402$	−27.7971	−1.38639
$403$	−26.3624	−1.31320
$404$	88.0656	4.38143
$405$	−3.15856	−0.156950
$406$	−0.631513	−0.0313414
$407$	21.3084	1.05622
$408$	−49.7174	−2.46138
$409$	−28.1608	−1.39246	−0.696232	−	0.717817i	$-0.745141\pi$
$409$	−28.1608	−1.39246	−0.696232	+	0.717817i	$0.745141\pi$
$410$	14.8126	0.731544
$411$	−28.1680	−1.38943
$412$	−80.8033	−3.98089
$413$	−1.79901	−0.0885233
$414$	−11.9393	−0.586783
$415$	−3.23730	−0.158913
$416$	−99.6137	−4.88396
$417$	−29.3821	−1.43885
$418$	−63.9428	−3.12754
$419$	−1.00377	−0.0490374	−0.0245187	−	0.999699i	$-0.507805\pi$
$419$	−1.00377	−0.0490374	−0.0245187	+	0.999699i	$0.507805\pi$
$420$	11.5718	0.564646
$421$	28.1793	1.37338	0.686689	−	0.726952i	$-0.259064\pi$
$421$	28.1793	1.37338	0.686689	+	0.726952i	$0.259064\pi$
$422$	−60.6342	−2.95163
$423$	11.7327	0.570463
$424$	−9.30382	−0.451834
$425$	−17.4633	−0.847093
$426$	−54.3636	−2.63393
$427$	18.3156	0.886354
$428$	40.6097	1.96294
$429$	38.1788	1.84329
$430$	−13.1933	−0.636238
$431$	22.4719	1.08243	0.541217	−	0.840883i	$-0.317964\pi$
$431$	22.4719	1.08243	0.541217	+	0.840883i	$0.317964\pi$
$432$	−81.9850	−3.94451
$433$	30.3447	1.45828	0.729138	−	0.684367i	$-0.239921\pi$
$433$	30.3447	1.45828	0.729138	+	0.684367i	$0.239921\pi$
$434$	33.4538	1.60583
$435$	0.100364	0.00481208
$436$	22.1807	1.06226
$437$	−16.2885	−0.779184
$438$	−54.3941	−2.59905
$439$	−2.03975	−0.0973521	−0.0486761	−	0.998815i	$-0.515500\pi$
$439$	−2.03975	−0.0973521	−0.0486761	+	0.998815i	$0.515500\pi$
$440$	−37.5180	−1.78860
$441$	2.25066	0.107174
$442$	−50.2145	−2.38846
$443$	−39.9136	−1.89635	−0.948177	−	0.317744i	$-0.897075\pi$
$443$	−39.9136	−1.89635	−0.948177	+	0.317744i	$0.897075\pi$
$444$	27.5215	1.30611
$445$	−0.238191	−0.0112914
$446$	−3.44113	−0.162942
$447$	6.89452	0.326100
$448$	61.9584	2.92726
$449$	13.9005	0.656005	0.328002	−	0.944677i	$-0.393625\pi$
$449$	13.9005	0.656005	0.328002	+	0.944677i	$0.393625\pi$
$450$	−13.4117	−0.632234
$451$	−45.2931	−2.13277
$452$	45.0371	2.11837
$453$	−1.38182	−0.0649233
$454$	47.8135	2.24400
$455$	7.37187	0.345599
$456$	−52.0919	−2.43943
$457$	27.1538	1.27020	0.635101	−	0.772429i	$-0.280958\pi$
$457$	27.1538	1.27020	0.635101	+	0.772429i	$0.280958\pi$
$458$	−55.6446	−2.60010
$459$	−21.8591	−1.02030
$460$	−15.1521	−0.706469
$461$	10.2340	0.476644	0.238322	−	0.971186i	$-0.423403\pi$
$461$	10.2340	0.476644	0.238322	+	0.971186i	$0.423403\pi$
$462$	−48.4488	−2.25404
$463$	27.4132	1.27400	0.637000	−	0.770864i	$-0.280175\pi$
$463$	27.4132	1.27400	0.637000	+	0.770864i	$0.280175\pi$
$464$	1.51386	0.0702791
$465$	−5.31668	−0.246555
$466$	−9.83990	−0.455825
$467$	19.3255	0.894278	0.447139	−	0.894464i	$-0.352443\pi$
$467$	19.3255	0.894278	0.447139	+	0.894464i	$0.352443\pi$
$468$	−28.1647	−1.30191
$469$	16.4117	0.757821
$470$	20.3880	0.940430
$471$	20.5791	0.948234
$472$	7.53345	0.346755
$473$	40.3416	1.85491
$474$	−2.34891	−0.107889
$475$	−18.2973	−0.839539
$476$	46.5378	2.13306
$477$	−1.09059	−0.0499345
$478$	46.6043	2.13163
$479$	−38.5075	−1.75945	−0.879727	−	0.475480i	$-0.842275\pi$
$479$	−38.5075	−1.75945	−0.879727	+	0.475480i	$0.842275\pi$
$480$	−20.0898	−0.916968
$481$	17.5327	0.799424
$482$	54.8308	2.49747
$483$	−12.3416	−0.561563
$484$	122.299	5.55903
$485$	9.35268	0.424683
$486$	−29.0997	−1.31999
$487$	1.34939	0.0611467	0.0305734	−	0.999533i	$-0.490267\pi$
$487$	1.34939	0.0611467	0.0305734	+	0.999533i	$0.490267\pi$
$488$	−76.6977	−3.47194
$489$	−6.76437	−0.305896
$490$	3.91099	0.176681
$491$	7.91053	0.356997	0.178499	−	0.983940i	$-0.442876\pi$
$491$	7.91053	0.356997	0.178499	+	0.983940i	$0.442876\pi$
$492$	−58.4997	−2.63737
$493$	0.403630	0.0181786
$494$	−52.6127	−2.36716
$495$	−4.39783	−0.197668
$496$	−80.1951	−3.60087
$497$	32.0969	1.43974
$498$	17.5060	0.784464
$499$	35.6833	1.59740	0.798701	−	0.601728i	$-0.205521\pi$
$499$	35.6833	1.59740	0.798701	+	0.601728i	$0.205521\pi$
$500$	−35.8668	−1.60401
$501$	7.12682	0.318403
$502$	−36.8928	−1.64661
$503$	−38.7025	−1.72566	−0.862830	−	0.505494i	$-0.831310\pi$
$503$	−38.7025	−1.72566	−0.862830	+	0.505494i	$0.831310\pi$
$504$	22.5435	1.00417
$505$	11.3146	0.503493
$506$	63.4386	2.82019
$507$	13.4503	0.597348
$508$	−2.21640	−0.0983370
$509$	1.72176	0.0763155	0.0381577	−	0.999272i	$-0.487851\pi$
$509$	1.72176	0.0763155	0.0381577	+	0.999272i	$0.487851\pi$
$510$	−10.1271	−0.448435
$511$	32.1149	1.42068
$512$	−33.1352	−1.46438
$513$	−22.9031	−1.01120
$514$	−15.9772	−0.704722
$515$	−10.3816	−0.457466
$516$	52.1045	2.29377
$517$	−62.3411	−2.74176
$518$	−22.2490	−0.977564
$519$	19.8933	0.873220
$520$	−30.8702	−1.35375
$521$	−26.5676	−1.16395	−0.581974	−	0.813207i	$-0.697720\pi$
$521$	−26.5676	−1.16395	−0.581974	+	0.813207i	$0.697720\pi$
$522$	0.309986	0.0135677
$523$	31.1756	1.36321	0.681606	−	0.731719i	$-0.261282\pi$
$523$	31.1756	1.36321	0.681606	+	0.731719i	$0.261282\pi$
$524$	42.5803	1.86013
$525$	−13.8637	−0.605061
$526$	−12.1865	−0.531355
$527$	−21.3819	−0.931409
$528$	116.141	5.05439
$529$	−6.83994	−0.297389
$530$	−1.89512	−0.0823189
$531$	0.883065	0.0383218
$532$	48.7605	2.11404
$533$	−37.2676	−1.61424
$534$	1.28804	0.0557390
$535$	5.21750	0.225572
$536$	−68.7250	−2.96847
$537$	9.03336	0.389818
$538$	66.9478	2.88632
$539$	−11.9588	−0.515100
$540$	−21.3052	−0.916831
$541$	16.6634	0.716417	0.358208	−	0.933642i	$-0.383388\pi$
$541$	16.6634	0.716417	0.358208	+	0.933642i	$0.383388\pi$
$542$	18.4764	0.793628
$543$	−24.0703	−1.03296
$544$	−80.7942	−3.46402
$545$	2.84975	0.122070
$546$	−39.8641	−1.70603
$547$	32.7265	1.39928	0.699642	−	0.714494i	$-0.253343\pi$
$547$	32.7265	1.39928	0.699642	+	0.714494i	$0.253343\pi$
$548$	−110.412	−4.71655
$549$	−8.99044	−0.383703
$550$	71.2625	3.03864
$551$	0.422907	0.0180165
$552$	51.6812	2.19970
$553$	1.38682	0.0589737
$554$	−17.1627	−0.729172
$555$	3.53595	0.150093
$556$	−115.171	−4.88433
$557$	−20.0295	−0.848677	−0.424338	−	0.905504i	$-0.639493\pi$
$557$	−20.0295	−0.848677	−0.424338	+	0.905504i	$0.639493\pi$
$558$	−16.4212	−0.695165
$559$	33.1934	1.40393
$560$	22.4254	0.947648
$561$	30.9659	1.30738
$562$	67.2326	2.83603
$563$	−14.4412	−0.608622	−0.304311	−	0.952573i	$-0.598426\pi$
$563$	−14.4412	−0.608622	−0.304311	+	0.952573i	$0.598426\pi$
$564$	−80.5187	−3.39045
$565$	5.78633	0.243433
$566$	69.8909	2.93774
$567$	−10.0843	−0.423502
$568$	−134.408	−5.63962
$569$	36.1331	1.51478	0.757389	−	0.652964i	$-0.226475\pi$
$569$	36.1331	1.51478	0.757389	+	0.652964i	$0.226475\pi$
$570$	−10.6108	−0.444436
$571$	−15.9322	−0.666742	−0.333371	−	0.942796i	$-0.608186\pi$
$571$	−15.9322	−0.666742	−0.333371	+	0.942796i	$0.608186\pi$
$572$	149.652	6.25725
$573$	−2.76759	−0.115618
$574$	47.2924	1.97395
$575$	18.1531	0.757035
$576$	−30.4131	−1.26721
$577$	38.8031	1.61539	0.807697	−	0.589598i	$-0.200714\pi$
$577$	38.8031	1.61539	0.807697	+	0.589598i	$0.200714\pi$
$578$	5.56844	0.231616
$579$	4.95295	0.205838
$580$	0.393402	0.0163351
$581$	−10.3357	−0.428799
$582$	−50.5755	−2.09642
$583$	5.79477	0.239995
$584$	−134.483	−5.56495
$585$	−3.61858	−0.149610
$586$	−87.8089	−3.62735
$587$	34.0509	1.40543	0.702716	−	0.711471i	$-0.251970\pi$
$587$	34.0509	1.40543	0.702716	+	0.711471i	$0.251970\pi$
$588$	−15.4457	−0.636971
$589$	−22.4031	−0.923103
$590$	1.53451	0.0631749
$591$	−27.1518	−1.11687
$592$	53.3351	2.19206
$593$	−11.0715	−0.454650	−0.227325	−	0.973819i	$-0.572998\pi$
$593$	−11.0715	−0.454650	−0.227325	+	0.973819i	$0.572998\pi$
$594$	89.2006	3.65995
$595$	5.97914	0.245121
$596$	27.0248	1.10698
$597$	13.4238	0.549401
$598$	52.1979	2.13453
$599$	34.1147	1.39389	0.696944	−	0.717126i	$-0.254543\pi$
$599$	34.1147	1.39389	0.696944	+	0.717126i	$0.254543\pi$
$600$	58.0550	2.37009
$601$	−45.4145	−1.85250	−0.926249	−	0.376913i	$-0.876986\pi$
$601$	−45.4145	−1.85250	−0.926249	+	0.376913i	$0.876986\pi$
$602$	−42.1223	−1.71678
$603$	−8.05588	−0.328061
$604$	−5.41638	−0.220389
$605$	15.7128	0.638817
$606$	−61.1848	−2.48546
$607$	8.64512	0.350895	0.175447	−	0.984489i	$-0.443863\pi$
$607$	8.64512	0.350895	0.175447	+	0.984489i	$0.443863\pi$
$608$	−84.6530	−3.43313
$609$	0.320432	0.0129846
$610$	−15.6228	−0.632548
$611$	−51.2948	−2.07517
$612$	−22.8437	−0.923401
$613$	−8.53167	−0.344591	−0.172296	−	0.985045i	$-0.555118\pi$
$613$	−8.53167	−0.344591	−0.172296	+	0.985045i	$0.555118\pi$
$614$	−93.5710	−3.77622
$615$	−7.51600	−0.303074
$616$	−119.784	−4.82623
$617$	−48.4684	−1.95127	−0.975633	−	0.219408i	$-0.929587\pi$
$617$	−48.4684	−1.95127	−0.975633	+	0.219408i	$0.929587\pi$
$618$	56.1392	2.25825
$619$	−42.0119	−1.68860	−0.844300	−	0.535871i	$-0.819983\pi$
$619$	−42.0119	−1.68860	−0.844300	+	0.535871i	$0.819983\pi$
$620$	−20.8401	−0.836958
$621$	22.7225	0.911825
$622$	10.4748	0.420001
$623$	−0.760474	−0.0304677
$624$	95.5619	3.82554
$625$	17.9705	0.718821
$626$	−14.5586	−0.581877
$627$	32.4448	1.29572
$628$	80.6649	3.21888
$629$	14.2204	0.567003
$630$	4.59196	0.182948
$631$	−29.0167	−1.15514	−0.577568	−	0.816343i	$-0.695998\pi$
$631$	−29.0167	−1.15514	−0.577568	+	0.816343i	$0.695998\pi$
$632$	−5.80741	−0.231006
$633$	30.7661	1.22284
$634$	61.3575	2.43682
$635$	−0.284762	−0.0113004
$636$	7.48443	0.296777
$637$	−9.83978	−0.389866
$638$	−1.64709	−0.0652091
$639$	−15.7552	−0.623264
$640$	−23.7718	−0.939661
$641$	10.0258	0.395993	0.197997	−	0.980203i	$-0.436556\pi$
$641$	10.0258	0.395993	0.197997	+	0.980203i	$0.436556\pi$
$642$	−28.2141	−1.11352
$643$	−13.6022	−0.536417	−0.268209	−	0.963361i	$-0.586432\pi$
$643$	−13.6022	−0.536417	−0.268209	+	0.963361i	$0.586432\pi$
$644$	−48.3761	−1.90628
$645$	6.69434	0.263590
$646$	−42.6729	−1.67894
$647$	23.0562	0.906432	0.453216	−	0.891401i	$-0.350277\pi$
$647$	23.0562	0.906432	0.453216	+	0.891401i	$0.350277\pi$
$648$	42.2288	1.65890
$649$	−4.69212	−0.184182
$650$	58.6354	2.29987
$651$	−16.9746	−0.665286
$652$	−26.5147	−1.03840
$653$	6.22692	0.243678	0.121839	−	0.992550i	$-0.461121\pi$
$653$	6.22692	0.243678	0.121839	+	0.992550i	$0.461121\pi$
$654$	−15.4103	−0.602591
$655$	5.47069	0.213758
$656$	−113.369	−4.42631
$657$	−15.7640	−0.615012
$658$	65.0929	2.53759
$659$	−50.3091	−1.95976	−0.979882	−	0.199578i	$-0.936043\pi$
$659$	−50.3091	−1.95976	−0.979882	+	0.199578i	$0.936043\pi$
$660$	30.1812	1.17480
$661$	17.1116	0.665565	0.332782	−	0.943004i	$-0.392013\pi$
$661$	17.1116	0.665565	0.332782	+	0.943004i	$0.392013\pi$
$662$	17.7745	0.690825
$663$	25.4790	0.989523
$664$	43.2816	1.67965
$665$	6.26471	0.242935
$666$	10.9212	0.423187
$667$	−0.419573	−0.0162459
$668$	27.9354	1.08085
$669$	1.74604	0.0675059
$670$	−13.9988	−0.540821
$671$	47.7702	1.84415
$672$	−64.1406	−2.47428
$673$	10.2328	0.394444	0.197222	−	0.980359i	$-0.436808\pi$
$673$	10.2328	0.394444	0.197222	+	0.980359i	$0.436808\pi$
$674$	−39.3918	−1.51732
$675$	25.5249	0.982454
$676$	52.7218	2.02776
$677$	13.6430	0.524345	0.262172	−	0.965021i	$-0.415561\pi$
$677$	13.6430	0.524345	0.262172	+	0.965021i	$0.415561\pi$
$678$	−31.2902	−1.20169
$679$	29.8603	1.14593
$680$	−25.0380	−0.960165
$681$	−24.2608	−0.929675
$682$	87.2532	3.34110
$683$	26.8837	1.02868	0.514338	−	0.857588i	$-0.328038\pi$
$683$	26.8837	1.02868	0.514338	+	0.857588i	$0.328038\pi$
$684$	−23.9347	−0.915166
$685$	−14.1856	−0.542004
$686$	54.8406	2.09382
$687$	28.2343	1.07721
$688$	100.975	3.84965
$689$	4.76800	0.181646
$690$	10.5271	0.400760
$691$	−2.65236	−0.100900	−0.0504502	−	0.998727i	$-0.516066\pi$
$691$	−2.65236	−0.100900	−0.0504502	+	0.998727i	$0.516066\pi$
$692$	77.9769	2.96424
$693$	−14.0410	−0.533372
$694$	−21.9242	−0.832233
$695$	−14.7971	−0.561284
$696$	−1.34183	−0.0508619
$697$	−30.2268	−1.14492
$698$	−78.4854	−2.97072
$699$	4.99281	0.188845
$700$	−54.3422	−2.05394
$701$	−24.6143	−0.929670	−0.464835	−	0.885397i	$-0.653886\pi$
$701$	−24.6143	−0.929670	−0.464835	+	0.885397i	$0.653886\pi$
$702$	73.3951	2.77012
$703$	14.8995	0.561947
$704$	161.598	6.09046
$705$	−10.3450	−0.389614
$706$	75.6209	2.84603
$707$	36.1242	1.35859
$708$	−6.06026	−0.227759
$709$	−9.88667	−0.371302	−0.185651	−	0.982616i	$-0.559439\pi$
$709$	−9.88667	−0.371302	−0.185651	+	0.982616i	$0.559439\pi$
$710$	−27.3779	−1.02747
$711$	−0.680740	−0.0255297
$712$	3.18453	0.119345
$713$	22.2265	0.832388
$714$	−32.3328	−1.21002
$715$	19.2271	0.719053
$716$	35.4085	1.32328
$717$	−23.6472	−0.883122
$718$	−39.1921	−1.46263
$719$	−8.61796	−0.321396	−0.160698	−	0.987004i	$-0.551374\pi$
$719$	−8.61796	−0.321396	−0.160698	+	0.987004i	$0.551374\pi$
$720$	−11.0078	−0.410237
$721$	−33.1452	−1.23439
$722$	7.03177	0.261696
$723$	−27.8214	−1.03469
$724$	−94.3497	−3.50648
$725$	−0.471318	−0.0175043
$726$	−84.9686	−3.15348
$727$	33.4850	1.24189	0.620945	−	0.783854i	$-0.286749\pi$
$727$	33.4850	1.24189	0.620945	+	0.783854i	$0.286749\pi$
$728$	−98.5593	−3.65285
$729$	28.3819	1.05118
$730$	−27.3933	−1.01387
$731$	26.9224	0.995760
$732$	61.6992	2.28047
$733$	30.0087	1.10840	0.554198	−	0.832385i	$-0.313025\pi$
$733$	30.0087	1.10840	0.554198	+	0.832385i	$0.313025\pi$
$734$	69.4561	2.56367
$735$	−1.98445	−0.0731977
$736$	83.9855	3.09575
$737$	42.8045	1.57672
$738$	−23.2141	−0.854521
$739$	−25.5442	−0.939658	−0.469829	−	0.882757i	$-0.655685\pi$
$739$	−25.5442	−0.939658	−0.469829	+	0.882757i	$0.655685\pi$
$740$	13.8600	0.509505
$741$	26.6959	0.980699
$742$	−6.05057	−0.222123
$743$	−5.57785	−0.204632	−0.102316	−	0.994752i	$-0.532625\pi$
$743$	−5.57785	−0.204632	−0.102316	+	0.994752i	$0.532625\pi$
$744$	71.0821	2.60600
$745$	3.47213	0.127209
$746$	−85.2226	−3.12022
$747$	5.07343	0.185627
$748$	121.379	4.43804
$749$	16.6579	0.608667
$750$	24.9190	0.909912
$751$	54.3143	1.98196	0.990978	−	0.134023i	$-0.0427895\pi$
$751$	54.3143	1.98196	0.990978	+	0.134023i	$0.0427895\pi$
$752$	−156.040	−5.69020
$753$	18.7196	0.682179
$754$	−1.35524	−0.0493551
$755$	−0.695892	−0.0253261
$756$	−68.0212	−2.47391
$757$	−9.18253	−0.333745	−0.166872	−	0.985979i	$-0.553367\pi$
$757$	−9.18253	−0.333745	−0.166872	+	0.985979i	$0.553367\pi$
$758$	66.0997	2.40085
$759$	−32.1890	−1.16839
$760$	−26.2339	−0.951602
$761$	36.3709	1.31844	0.659222	−	0.751948i	$-0.270886\pi$
$761$	36.3709	1.31844	0.659222	+	0.751948i	$0.270886\pi$
$762$	1.53988	0.0557838
$763$	9.09841	0.329385
$764$	−10.8483	−0.392477
$765$	−2.93494	−0.106113
$766$	−22.9130	−0.827879
$767$	−3.86072	−0.139403
$768$	51.4789	1.85759
$769$	31.2813	1.12803	0.564016	−	0.825764i	$-0.309256\pi$
$769$	31.2813	1.12803	0.564016	+	0.825764i	$0.309256\pi$
$770$	−24.3991	−0.879284
$771$	8.10688	0.291962
$772$	19.4144	0.698738
$773$	39.4755	1.41983	0.709917	−	0.704285i	$-0.248732\pi$
$773$	39.4755	1.41983	0.709917	+	0.704285i	$0.248732\pi$
$774$	20.6763	0.743193
$775$	24.9676	0.896864
$776$	−125.042	−4.48875
$777$	11.2892	0.404999
$778$	75.1002	2.69247
$779$	−31.6704	−1.13471
$780$	24.8334	0.889179
$781$	83.7142	2.99553
$782$	42.3364	1.51395
$783$	−0.589959	−0.0210834
$784$	−29.9329	−1.06903
$785$	10.3638	0.369899
$786$	−29.5833	−1.05520
$787$	−28.5990	−1.01945	−0.509723	−	0.860339i	$-0.670252\pi$
$787$	−28.5990	−1.01945	−0.509723	+	0.860339i	$0.670252\pi$
$788$	−106.428	−3.79135
$789$	6.18347	0.220137
$790$	−1.18293	−0.0420867
$791$	18.4740	0.656861
$792$	58.7974	2.08927
$793$	39.3058	1.39579
$794$	62.2917	2.21065
$795$	0.961594	0.0341042
$796$	52.6182	1.86500
$797$	−39.2280	−1.38953	−0.694763	−	0.719239i	$-0.744491\pi$
$797$	−39.2280	−1.38953	−0.694763	+	0.719239i	$0.744491\pi$
$798$	−33.8770	−1.19923
$799$	−41.6040	−1.47184
$800$	94.3434	3.33554
$801$	0.373288	0.0131895
$802$	62.2308	2.19744
$803$	83.7611	2.95587
$804$	55.2856	1.94977
$805$	−6.21532	−0.219061
$806$	71.7928	2.52879
$807$	−33.9696	−1.19579
$808$	−151.272	−5.32174
$809$	2.03413	0.0715163	0.0357581	−	0.999360i	$-0.488615\pi$
$809$	2.03413	0.0715163	0.0357581	+	0.999360i	$0.488615\pi$
$810$	8.60171	0.302233
$811$	−15.4076	−0.541034	−0.270517	−	0.962715i	$-0.587195\pi$
$811$	−15.4076	−0.541034	−0.270517	+	0.962715i	$0.587195\pi$
$812$	1.25602	0.0440775
$813$	−9.37499	−0.328795
$814$	−58.0292	−2.03392
$815$	−3.40659	−0.119328
$816$	77.5079	2.71332
$817$	28.2082	0.986880
$818$	76.6904	2.68142
$819$	−11.5530	−0.403696
$820$	−29.4609	−1.02882
$821$	−30.4062	−1.06118	−0.530592	−	0.847627i	$-0.678030\pi$
$821$	−30.4062	−1.06118	−0.530592	+	0.847627i	$0.678030\pi$
$822$	76.7100	2.67557
$823$	5.50211	0.191792	0.0958958	−	0.995391i	$-0.469428\pi$
$823$	5.50211	0.191792	0.0958958	+	0.995391i	$0.469428\pi$
$824$	138.798	4.83524
$825$	−36.1589	−1.25889
$826$	4.89924	0.170466
$827$	4.44665	0.154625	0.0773127	−	0.997007i	$-0.475366\pi$
$827$	4.44665	0.154625	0.0773127	+	0.997007i	$0.475366\pi$
$828$	23.7460	0.825230
$829$	−37.1933	−1.29178	−0.645889	−	0.763431i	$-0.723513\pi$
$829$	−37.1933	−1.29178	−0.645889	+	0.763431i	$0.723513\pi$
$830$	8.81616	0.306013
$831$	8.70841	0.302091
$832$	132.965	4.60972
$833$	−7.98080	−0.276518
$834$	80.0165	2.77074
$835$	3.58911	0.124206
$836$	127.176	4.39847
$837$	31.2525	1.08024
$838$	2.73357	0.0944297
$839$	17.0484	0.588577	0.294288	−	0.955717i	$-0.404917\pi$
$839$	17.0484	0.588577	0.294288	+	0.955717i	$0.404917\pi$
$840$	−19.8771	−0.685826
$841$	−28.9891	−0.999624
$842$	−76.7409	−2.64466
$843$	−34.1141	−1.17495
$844$	120.595	4.15106
$845$	6.77366	0.233021
$846$	−31.9517	−1.09852
$847$	50.1664	1.72374
$848$	14.5044	0.498082
$849$	−35.4630	−1.21709
$850$	47.5577	1.63122
$851$	−14.7821	−0.506723
$852$	108.124	3.70426
$853$	−24.5878	−0.841870	−0.420935	−	0.907091i	$-0.638298\pi$
$853$	−24.5878	−0.841870	−0.420935	+	0.907091i	$0.638298\pi$
$854$	−49.8789	−1.70682
$855$	−3.07511	−0.105167
$856$	−69.7561	−2.38421
$857$	−8.75445	−0.299046	−0.149523	−	0.988758i	$-0.547774\pi$
$857$	−8.75445	−0.299046	−0.149523	+	0.988758i	$0.547774\pi$
$858$	−103.972	−3.54956
$859$	−2.96304	−0.101098	−0.0505488	−	0.998722i	$-0.516097\pi$
$859$	−2.96304	−0.101098	−0.0505488	+	0.998722i	$0.516097\pi$
$860$	26.2402	0.894783
$861$	−23.9964	−0.817794
$862$	−61.1978	−2.08441
$863$	−25.0659	−0.853253	−0.426626	−	0.904428i	$-0.640298\pi$
$863$	−25.0659	−0.853253	−0.426626	+	0.904428i	$0.640298\pi$
$864$	118.092	4.01755
$865$	10.0184	0.340636
$866$	−82.6379	−2.80815
$867$	−2.82545	−0.0959573
$868$	−66.5362	−2.25839
$869$	3.61707	0.122701
$870$	−0.273321	−0.00926646
$871$	35.2200	1.19338
$872$	−38.1002	−1.29023
$873$	−14.6573	−0.496075
$874$	44.3585	1.50045
$875$	−14.7124	−0.497371
$876$	108.184	3.65521
$877$	−42.7884	−1.44486	−0.722431	−	0.691443i	$-0.756975\pi$
$877$	−42.7884	−1.44486	−0.722431	+	0.691443i	$0.756975\pi$
$878$	5.55487	0.187468
$879$	44.5546	1.50279
$880$	58.4894	1.97168
$881$	51.6694	1.74079	0.870393	−	0.492358i	$-0.163865\pi$
$881$	51.6694	1.74079	0.870393	+	0.492358i	$0.163865\pi$
$882$	−6.12922	−0.206382
$883$	−40.7013	−1.36971	−0.684854	−	0.728681i	$-0.740134\pi$
$883$	−40.7013	−1.36971	−0.684854	+	0.728681i	$0.740134\pi$
$884$	99.8715	3.35904
$885$	−0.778618	−0.0261730
$886$	108.697	3.65174
$887$	−41.1982	−1.38330	−0.691650	−	0.722233i	$-0.743116\pi$
$887$	−41.1982	−1.38330	−0.691650	+	0.722233i	$0.743116\pi$
$888$	−47.2743	−1.58642
$889$	−0.909160	−0.0304922
$890$	0.648667	0.0217434
$891$	−26.3017	−0.881140
$892$	6.84405	0.229156
$893$	−43.5910	−1.45872
$894$	−18.7759	−0.627959
$895$	4.54926	0.152065
$896$	−75.8961	−2.53551
$897$	−26.4854	−0.884323
$898$	−37.8552	−1.26325
$899$	−0.577078	−0.0192466
$900$	26.6746	0.889152
$901$	3.86720	0.128835
$902$	123.347	4.10700
$903$	21.3731	0.711251
$904$	−77.3612	−2.57300
$905$	−12.1220	−0.402948
$906$	3.76310	0.125021
$907$	2.45451	0.0815008	0.0407504	−	0.999169i	$-0.487025\pi$
$907$	2.45451	0.0815008	0.0407504	+	0.999169i	$0.487025\pi$
$908$	−95.0963	−3.15588
$909$	−17.7320	−0.588133
$910$	−20.0758	−0.665507
$911$	11.1431	0.369188	0.184594	−	0.982815i	$-0.440903\pi$
$911$	11.1431	0.369188	0.184594	+	0.982815i	$0.440903\pi$
$912$	81.2097	2.68912
$913$	−26.9574	−0.892160
$914$	−73.9481	−2.44599
$915$	7.92707	0.262061
$916$	110.672	3.65669
$917$	17.4663	0.576788
$918$	59.5290	1.96475
$919$	28.8317	0.951068	0.475534	−	0.879697i	$-0.342255\pi$
$919$	28.8317	0.951068	0.475534	+	0.879697i	$0.342255\pi$
$920$	26.0270	0.858086
$921$	47.4784	1.56446
$922$	−27.8702	−0.917857
$923$	68.8808	2.26724
$924$	96.3597	3.17000
$925$	−16.6051	−0.545973
$926$	−74.6544	−2.45330
$927$	16.2697	0.534368
$928$	−2.18056	−0.0715805
$929$	−11.7673	−0.386071	−0.193036	−	0.981192i	$-0.561833\pi$
$929$	−11.7673	−0.386071	−0.193036	+	0.981192i	$0.561833\pi$
$930$	14.4789	0.474783
$931$	−8.36197	−0.274052
$932$	19.5706	0.641056
$933$	−5.31495	−0.174004
$934$	−52.6292	−1.72208
$935$	15.5946	0.509999
$936$	48.3791	1.58132
$937$	11.4258	0.373264	0.186632	−	0.982430i	$-0.440243\pi$
$937$	11.4258	0.373264	0.186632	+	0.982430i	$0.440243\pi$
$938$	−44.6940	−1.45931
$939$	7.38708	0.241068
$940$	−40.5498	−1.32259
$941$	18.4422	0.601199	0.300600	−	0.953750i	$-0.402813\pi$
$941$	18.4422	0.601199	0.300600	+	0.953750i	$0.402813\pi$
$942$	−56.0431	−1.82598
$943$	31.4208	1.02320
$944$	−11.7444	−0.382248
$945$	−8.73932	−0.284290
$946$	−109.862	−3.57193
$947$	−2.08706	−0.0678202	−0.0339101	−	0.999425i	$-0.510796\pi$
$947$	−2.08706	−0.0678202	−0.0339101	+	0.999425i	$0.510796\pi$
$948$	4.67175	0.151731
$949$	68.9195	2.23722
$950$	49.8291	1.61667
$951$	−31.1331	−1.00956
$952$	−79.9390	−2.59084
$953$	20.0962	0.650981	0.325490	−	0.945545i	$-0.394471\pi$
$953$	20.0962	0.650981	0.325490	+	0.945545i	$0.394471\pi$
$954$	2.97000	0.0961572
$955$	−1.39378	−0.0451016
$956$	−92.6913	−2.99785
$957$	0.835743	0.0270157
$958$	104.868	3.38812
$959$	−45.2904	−1.46250
$960$	26.8159	0.865478
$961$	−0.429830	−0.0138655
$962$	−47.7469	−1.53942
$963$	−8.17675	−0.263492
$964$	−109.053	−3.51236
$965$	2.49434	0.0802957
$966$	33.6099	1.08138
$967$	45.8890	1.47569	0.737845	−	0.674970i	$-0.235844\pi$
$967$	45.8890	1.47569	0.737845	+	0.674970i	$0.235844\pi$
$968$	−210.075	−6.75206
$969$	21.6524	0.695575
$970$	−25.4702	−0.817798
$971$	−10.6512	−0.341812	−0.170906	−	0.985287i	$-0.554670\pi$
$971$	−10.6512	−0.341812	−0.170906	+	0.985287i	$0.554670\pi$
$972$	57.8763	1.85638
$973$	−47.2426	−1.51453
$974$	−3.67480	−0.117748
$975$	−29.7519	−0.952822
$976$	119.569	3.82732
$977$	27.6035	0.883115	0.441558	−	0.897233i	$-0.354426\pi$
$977$	27.6035	0.883115	0.441558	+	0.897233i	$0.354426\pi$
$978$	18.4214	0.589053
$979$	−1.98345	−0.0633913
$980$	−7.77857	−0.248477
$981$	−4.46607	−0.142591
$982$	−21.5428	−0.687457
$983$	44.8001	1.42890	0.714450	−	0.699687i	$-0.246677\pi$
$983$	44.8001	1.42890	0.714450	+	0.699687i	$0.246677\pi$
$984$	100.486	3.20338
$985$	−13.6738	−0.435684
$986$	−1.09921	−0.0350058
$987$	−33.0284	−1.05131
$988$	104.641	3.32909
$989$	−27.9858	−0.889897
$990$	11.9766	0.380642
$991$	−10.2898	−0.326867	−0.163433	−	0.986554i	$-0.552257\pi$
$991$	−10.2898	−0.326867	−0.163433	+	0.986554i	$0.552257\pi$
$992$	115.513	3.66755
$993$	−9.01885	−0.286205
$994$	−87.4095	−2.77246
$995$	6.76034	0.214317
$996$	−34.8177	−1.10324
$997$	−2.78154	−0.0880921	−0.0440461	−	0.999030i	$-0.514025\pi$
$997$	−2.78154	−0.0880921	−0.0440461	+	0.999030i	$0.514025\pi$
$998$	−97.1763	−3.07606
$999$	−20.7850	−0.657608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.d.1.5	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.d.1.5	✓	179	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72330 q^{2} +1.38182 q^{3} +5.41638 q^{4} +0.695892 q^{5} -3.76310 q^{6} +2.22178 q^{7} -9.30382 q^{8} -1.09059 q^{9} +O(q^{10})\)	\(q-2.72330 q^{2} +1.38182 q^{3} +5.41638 q^{4} +0.695892 q^{5} -3.76310 q^{6} +2.22178 q^{7} -9.30382 q^{8} -1.09059 q^{9} -1.89512 q^{10} +5.79477 q^{11} +7.48443 q^{12} +4.76800 q^{13} -6.05057 q^{14} +0.961594 q^{15} +14.5044 q^{16} +3.86720 q^{17} +2.97000 q^{18} +4.05190 q^{19} +3.76921 q^{20} +3.07008 q^{21} -15.7809 q^{22} -4.01996 q^{23} -12.8562 q^{24} -4.51573 q^{25} -12.9847 q^{26} -5.65243 q^{27} +12.0340 q^{28} +0.104372 q^{29} -2.61871 q^{30} -5.52903 q^{31} -20.8921 q^{32} +8.00731 q^{33} -10.5316 q^{34} +1.54612 q^{35} -5.90703 q^{36} +3.67717 q^{37} -11.0346 q^{38} +6.58849 q^{39} -6.47445 q^{40} -7.81619 q^{41} -8.36077 q^{42} +6.96172 q^{43} +31.3867 q^{44} -0.758930 q^{45} +10.9476 q^{46} -10.7582 q^{47} +20.0424 q^{48} -2.06371 q^{49} +12.2977 q^{50} +5.34376 q^{51} +25.8253 q^{52} +1.00000 q^{53} +15.3933 q^{54} +4.03254 q^{55} -20.6710 q^{56} +5.59898 q^{57} -0.284238 q^{58} -0.809716 q^{59} +5.20835 q^{60} +8.24367 q^{61} +15.0572 q^{62} -2.42304 q^{63} +27.8869 q^{64} +3.31801 q^{65} -21.8063 q^{66} +7.38674 q^{67} +20.9462 q^{68} -5.55484 q^{69} -4.21054 q^{70} +14.4465 q^{71} +10.1466 q^{72} +14.4546 q^{73} -10.0141 q^{74} -6.23991 q^{75} +21.9466 q^{76} +12.8747 q^{77} -17.9424 q^{78} +0.624196 q^{79} +10.0935 q^{80} -4.53886 q^{81} +21.2858 q^{82} -4.65202 q^{83} +16.6287 q^{84} +2.69116 q^{85} -18.9589 q^{86} +0.144223 q^{87} -53.9136 q^{88} -0.342282 q^{89} +2.06680 q^{90} +10.5934 q^{91} -21.7736 q^{92} -7.64010 q^{93} +29.2977 q^{94} +2.81969 q^{95} -28.8691 q^{96} +13.4398 q^{97} +5.62012 q^{98} -6.31970 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * q^99

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