LMFDB - Embedded newform 8003.2.a.b.1.3

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:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.72579 q^{2} +2.89515 q^{3} +5.42994 q^{4} -2.27822 q^{5} -7.89157 q^{6} -3.84210 q^{7} -9.34930 q^{8} +5.38188 q^{9} +O(q^{10})$	\(q-2.72579 q^{2} +2.89515 q^{3} +5.42994 q^{4} -2.27822 q^{5} -7.89157 q^{6} -3.84210 q^{7} -9.34930 q^{8} +5.38188 q^{9} +6.20996 q^{10} +2.32327 q^{11} +15.7205 q^{12} +0.203934 q^{13} +10.4728 q^{14} -6.59579 q^{15} +14.6244 q^{16} +1.55678 q^{17} -14.6699 q^{18} -0.522326 q^{19} -12.3706 q^{20} -11.1235 q^{21} -6.33275 q^{22} -2.89946 q^{23} -27.0676 q^{24} +0.190298 q^{25} -0.555881 q^{26} +6.89591 q^{27} -20.8624 q^{28} +1.67183 q^{29} +17.9788 q^{30} -6.73048 q^{31} -21.1643 q^{32} +6.72621 q^{33} -4.24346 q^{34} +8.75317 q^{35} +29.2233 q^{36} +2.76054 q^{37} +1.42375 q^{38} +0.590418 q^{39} +21.2998 q^{40} +10.0381 q^{41} +30.3202 q^{42} +3.67885 q^{43} +12.6152 q^{44} -12.2611 q^{45} +7.90332 q^{46} -0.655415 q^{47} +42.3397 q^{48} +7.76177 q^{49} -0.518712 q^{50} +4.50711 q^{51} +1.10735 q^{52} -1.00000 q^{53} -18.7968 q^{54} -5.29293 q^{55} +35.9210 q^{56} -1.51221 q^{57} -4.55707 q^{58} -0.383772 q^{59} -35.8147 q^{60} +5.23951 q^{61} +18.3459 q^{62} -20.6778 q^{63} +28.4409 q^{64} -0.464606 q^{65} -18.3343 q^{66} -5.10346 q^{67} +8.45322 q^{68} -8.39437 q^{69} -23.8593 q^{70} -6.43413 q^{71} -50.3168 q^{72} +0.0435738 q^{73} -7.52465 q^{74} +0.550941 q^{75} -2.83620 q^{76} -8.92625 q^{77} -1.60936 q^{78} +6.92112 q^{79} -33.3175 q^{80} +3.81903 q^{81} -27.3619 q^{82} -3.05720 q^{83} -60.3997 q^{84} -3.54669 q^{85} -10.0278 q^{86} +4.84020 q^{87} -21.7209 q^{88} +15.0824 q^{89} +33.4213 q^{90} -0.783534 q^{91} -15.7439 q^{92} -19.4857 q^{93} +1.78653 q^{94} +1.18997 q^{95} -61.2739 q^{96} -7.18425 q^{97} -21.1570 q^{98} +12.5036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) $ 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * 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 $

$2$	−2.72579	−1.92743	−0.963713	−	0.266941i	$-0.913987\pi$
$2$	−2.72579	−1.92743	−0.963713	+	0.266941i	$0.913987\pi$
$3$	2.89515	1.67151	0.835757	−	0.549099i	$-0.185029\pi$
$3$	2.89515	1.67151	0.835757	+	0.549099i	$0.185029\pi$
$4$	5.42994	2.71497
$5$	−2.27822	−1.01885	−0.509426	−	0.860514i	$-0.670142\pi$
$5$	−2.27822	−1.01885	−0.509426	+	0.860514i	$0.670142\pi$
$6$	−7.89157	−3.22172
$7$	−3.84210	−1.45218	−0.726089	−	0.687600i	$-0.758664\pi$
$7$	−3.84210	−1.45218	−0.726089	+	0.687600i	$0.758664\pi$
$8$	−9.34930	−3.30547
$9$	5.38188	1.79396
$10$	6.20996	1.96376
$11$	2.32327	0.700493	0.350246	−	0.936658i	$-0.386098\pi$
$11$	2.32327	0.700493	0.350246	+	0.936658i	$0.386098\pi$
$12$	15.7205	4.53811
$13$	0.203934	0.0565610	0.0282805	−	0.999600i	$-0.490997\pi$
$13$	0.203934	0.0565610	0.0282805	+	0.999600i	$0.490997\pi$
$14$	10.4728	2.79897
$15$	−6.59579	−1.70303
$16$	14.6244	3.65609
$17$	1.55678	0.377575	0.188787	−	0.982018i	$-0.439544\pi$
$17$	1.55678	0.377575	0.188787	+	0.982018i	$0.439544\pi$
$18$	−14.6699	−3.45773
$19$	−0.522326	−0.119830	−0.0599149	−	0.998203i	$-0.519083\pi$
$19$	−0.522326	−0.119830	−0.0599149	+	0.998203i	$0.519083\pi$
$20$	−12.3706	−2.76615
$21$	−11.1235	−2.42734
$22$	−6.33275	−1.35015
$23$	−2.89946	−0.604579	−0.302290	−	0.953216i	$-0.597751\pi$
$23$	−2.89946	−0.604579	−0.302290	+	0.953216i	$0.597751\pi$
$24$	−27.0676	−5.52515
$25$	0.190298	0.0380596
$26$	−0.555881	−0.109017
$27$	6.89591	1.32712
$28$	−20.8624	−3.94262
$29$	1.67183	0.310452	0.155226	−	0.987879i	$-0.450389\pi$
$29$	1.67183	0.310452	0.155226	+	0.987879i	$0.450389\pi$
$30$	17.9788	3.28246
$31$	−6.73048	−1.20883	−0.604415	−	0.796670i	$-0.706593\pi$
$31$	−6.73048	−1.20883	−0.604415	+	0.796670i	$0.706593\pi$
$32$	−21.1643	−3.74136
$33$	6.72621	1.17088
$34$	−4.24346	−0.727747
$35$	8.75317	1.47956
$36$	29.2233	4.87055
$37$	2.76054	0.453829	0.226915	−	0.973915i	$-0.427136\pi$
$37$	2.76054	0.453829	0.226915	+	0.973915i	$0.427136\pi$
$38$	1.42375	0.230963
$39$	0.590418	0.0945426
$40$	21.2998	3.36779
$41$	10.0381	1.56769	0.783846	−	0.620955i	$-0.213255\pi$
$41$	10.0381	1.56769	0.783846	+	0.620955i	$0.213255\pi$
$42$	30.3202	4.67851
$43$	3.67885	0.561020	0.280510	−	0.959851i	$-0.409496\pi$
$43$	3.67885	0.561020	0.280510	+	0.959851i	$0.409496\pi$
$44$	12.6152	1.90182
$45$	−12.2611	−1.82778
$46$	7.90332	1.16528
$47$	−0.655415	−0.0956022	−0.0478011	−	0.998857i	$-0.515221\pi$
$47$	−0.655415	−0.0956022	−0.0478011	+	0.998857i	$0.515221\pi$
$48$	42.3397	6.11120
$49$	7.76177	1.10882
$50$	−0.518712	−0.0733570
$51$	4.50711	0.631122
$52$	1.10735	0.153561
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−18.7968	−2.55792
$55$	−5.29293	−0.713698
$56$	35.9210	4.80014
$57$	−1.51221	−0.200297
$58$	−4.55707	−0.598372
$59$	−0.383772	−0.0499629	−0.0249815	−	0.999688i	$-0.507953\pi$
$59$	−0.383772	−0.0499629	−0.0249815	+	0.999688i	$0.507953\pi$
$60$	−35.8147	−4.62366
$61$	5.23951	0.670850	0.335425	−	0.942067i	$-0.391120\pi$
$61$	5.23951	0.670850	0.335425	+	0.942067i	$0.391120\pi$
$62$	18.3459	2.32993
$63$	−20.6778	−2.60515
$64$	28.4409	3.55511
$65$	−0.464606	−0.0576273
$66$	−18.3343	−2.25679
$67$	−5.10346	−0.623487	−0.311744	−	0.950166i	$-0.600913\pi$
$67$	−5.10346	−0.623487	−0.311744	+	0.950166i	$0.600913\pi$
$68$	8.45322	1.02510
$69$	−8.39437	−1.01056
$70$	−23.8593	−2.85173
$71$	−6.43413	−0.763591	−0.381795	−	0.924247i	$-0.624694\pi$
$71$	−6.43413	−0.763591	−0.381795	+	0.924247i	$0.624694\pi$
$72$	−50.3168	−5.92990
$73$	0.0435738	0.00509993	0.00254996	−	0.999997i	$-0.499188\pi$
$73$	0.0435738	0.00509993	0.00254996	+	0.999997i	$0.499188\pi$
$74$	−7.52465	−0.874722
$75$	0.550941	0.0636172
$76$	−2.83620	−0.325334
$77$	−8.92625	−1.01724
$78$	−1.60936	−0.182224
$79$	6.92112	0.778687	0.389343	−	0.921093i	$-0.372702\pi$
$79$	6.92112	0.778687	0.389343	+	0.921093i	$0.372702\pi$
$80$	−33.3175	−3.72501
$81$	3.81903	0.424337
$82$	−27.3619	−3.02161
$83$	−3.05720	−0.335571	−0.167786	−	0.985824i	$-0.553662\pi$
$83$	−3.05720	−0.335571	−0.167786	+	0.985824i	$0.553662\pi$
$84$	−60.3997	−6.59015
$85$	−3.54669	−0.384693
$86$	−10.0278	−1.08132
$87$	4.84020	0.518924
$88$	−21.7209	−2.31546
$89$	15.0824	1.59873	0.799366	−	0.600845i	$-0.205169\pi$
$89$	15.0824	1.59873	0.799366	+	0.600845i	$0.205169\pi$
$90$	33.4213	3.52291
$91$	−0.783534	−0.0821367
$92$	−15.7439	−1.64141
$93$	−19.4857	−2.02058
$94$	1.78653	0.184266
$95$	1.18997	0.122089
$96$	−61.2739	−6.25374
$97$	−7.18425	−0.729450	−0.364725	−	0.931115i	$-0.618837\pi$
$97$	−7.18425	−0.729450	−0.364725	+	0.931115i	$0.618837\pi$
$98$	−21.1570	−2.13718
$99$	12.5036	1.25666
$100$	1.03331	0.103331
$101$	6.26842	0.623731	0.311866	−	0.950126i	$-0.399046\pi$
$101$	6.26842	0.623731	0.311866	+	0.950126i	$0.399046\pi$
$102$	−12.2854	−1.21644
$103$	−13.2590	−1.30645	−0.653226	−	0.757163i	$-0.726585\pi$
$103$	−13.2590	−1.30645	−0.653226	+	0.757163i	$0.726585\pi$
$104$	−1.90664	−0.186961
$105$	25.3417	2.47310
$106$	2.72579	0.264752
$107$	7.75951	0.750140	0.375070	−	0.926996i	$-0.377619\pi$
$107$	7.75951	0.750140	0.375070	+	0.926996i	$0.377619\pi$
$108$	37.4444	3.60309
$109$	−17.7031	−1.69565	−0.847824	−	0.530278i	$-0.822088\pi$
$109$	−17.7031	−1.69565	−0.847824	+	0.530278i	$0.822088\pi$
$110$	14.4274	1.37560
$111$	7.99216	0.758582
$112$	−56.1883	−5.30929
$113$	−4.72616	−0.444599	−0.222300	−	0.974978i	$-0.571356\pi$
$113$	−4.72616	−0.444599	−0.222300	+	0.974978i	$0.571356\pi$
$114$	4.12197	0.386058
$115$	6.60562	0.615977
$116$	9.07795	0.842866
$117$	1.09755	0.101468
$118$	1.04608	0.0962998
$119$	−5.98131	−0.548306
$120$	61.6660	5.62931
$121$	−5.60241	−0.509310
$122$	−14.2818	−1.29301
$123$	29.0619	2.62042
$124$	−36.5461	−3.28194
$125$	10.9576	0.980075
$126$	56.3633	5.02124
$127$	3.57719	0.317424	0.158712	−	0.987325i	$-0.449266\pi$
$127$	3.57719	0.317424	0.158712	+	0.987325i	$0.449266\pi$
$128$	−35.1952	−3.11084
$129$	10.6508	0.937752
$130$	1.26642	0.111072
$131$	17.8001	1.55520	0.777602	−	0.628756i	$-0.216436\pi$
$131$	17.8001	1.55520	0.777602	+	0.628756i	$0.216436\pi$
$132$	36.5229	3.17891
$133$	2.00683	0.174014
$134$	13.9110	1.20172
$135$	−15.7104	−1.35214
$136$	−14.5548	−1.24806
$137$	−10.9461	−0.935185	−0.467592	−	0.883944i	$-0.654878\pi$
$137$	−10.9461	−0.935185	−0.467592	+	0.883944i	$0.654878\pi$
$138$	22.8813	1.94779
$139$	−14.9371	−1.26695	−0.633473	−	0.773765i	$-0.718371\pi$
$139$	−14.9371	−1.26695	−0.633473	+	0.773765i	$0.718371\pi$
$140$	47.5292	4.01695
$141$	−1.89753	−0.159800
$142$	17.5381	1.47176
$143$	0.473793	0.0396206
$144$	78.7066	6.55888
$145$	−3.80881	−0.316304
$146$	−0.118773	−0.00982973
$147$	22.4715	1.85342
$148$	14.9895	1.23213
$149$	−7.65613	−0.627215	−0.313607	−	0.949553i	$-0.601538\pi$
$149$	−7.65613	−0.627215	−0.313607	+	0.949553i	$0.601538\pi$
$150$	−1.50175	−0.122617
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	4.88338	0.396094
$153$	8.37841	0.677354
$154$	24.3311	1.96066
$155$	15.3335	1.23162
$156$	3.20593	0.256680
$157$	−18.0028	−1.43678	−0.718391	−	0.695639i	$-0.755121\pi$
$157$	−18.0028	−1.43678	−0.718391	+	0.695639i	$0.755121\pi$
$158$	−18.8655	−1.50086
$159$	−2.89515	−0.229600
$160$	48.2171	3.81189
$161$	11.1400	0.877957
$162$	−10.4099	−0.817877
$163$	−4.85204	−0.380041	−0.190021	−	0.981780i	$-0.560855\pi$
$163$	−4.85204	−0.380041	−0.190021	+	0.981780i	$0.560855\pi$
$164$	54.5064	4.25624
$165$	−15.3238	−1.19296
$166$	8.33328	0.646788
$167$	0.117714	0.00910897	0.00455448	−	0.999990i	$-0.498550\pi$
$167$	0.117714	0.00910897	0.00455448	+	0.999990i	$0.498550\pi$
$168$	103.997	8.02351
$169$	−12.9584	−0.996801
$170$	9.66754	0.741466
$171$	−2.81110	−0.214970
$172$	19.9759	1.52315
$173$	−1.68091	−0.127797	−0.0638985	−	0.997956i	$-0.520353\pi$
$173$	−1.68091	−0.127797	−0.0638985	+	0.997956i	$0.520353\pi$
$174$	−13.1934	−1.00019
$175$	−0.731145	−0.0552693
$176$	33.9763	2.56106
$177$	−1.11108	−0.0835137
$178$	−41.1115	−3.08144
$179$	−9.90153	−0.740075	−0.370038	−	0.929017i	$-0.620655\pi$
$179$	−9.90153	−0.740075	−0.370038	+	0.929017i	$0.620655\pi$
$180$	−66.5772	−4.96237
$181$	19.2260	1.42906	0.714530	−	0.699605i	$-0.246640\pi$
$181$	19.2260	1.42906	0.714530	+	0.699605i	$0.246640\pi$
$182$	2.13575	0.158312
$183$	15.1691	1.12134
$184$	27.1079	1.99842
$185$	−6.28912	−0.462385
$186$	53.1141	3.89451
$187$	3.61682	0.264488
$188$	−3.55887	−0.259557
$189$	−26.4948	−1.92721
$190$	−3.24362	−0.235317
$191$	8.67772	0.627898	0.313949	−	0.949440i	$-0.398348\pi$
$191$	8.67772	0.627898	0.313949	+	0.949440i	$0.398348\pi$
$192$	82.3405	5.94242
$193$	6.44883	0.464197	0.232099	−	0.972692i	$-0.425441\pi$
$193$	6.44883	0.464197	0.232099	+	0.972692i	$0.425441\pi$
$194$	19.5828	1.40596
$195$	−1.34510	−0.0963249
$196$	42.1459	3.01042
$197$	−11.4335	−0.814605	−0.407303	−	0.913293i	$-0.633531\pi$
$197$	−11.4335	−0.814605	−0.407303	+	0.913293i	$0.633531\pi$
$198$	−34.0821	−2.42211
$199$	−12.3363	−0.874498	−0.437249	−	0.899340i	$-0.644047\pi$
$199$	−12.3363	−0.874498	−0.437249	+	0.899340i	$0.644047\pi$
$200$	−1.77915	−0.125805
$201$	−14.7753	−1.04217
$202$	−17.0864	−1.20220
$203$	−6.42336	−0.450831
$204$	24.4733	1.71348
$205$	−22.8691	−1.59725
$206$	36.1414	2.51809
$207$	−15.6046	−1.08459
$208$	2.98240	0.206792
$209$	−1.21350	−0.0839398
$210$	−69.0762	−4.76671
$211$	−17.0729	−1.17535	−0.587674	−	0.809097i	$-0.699956\pi$
$211$	−17.0729	−1.17535	−0.587674	+	0.809097i	$0.699956\pi$
$212$	−5.42994	−0.372930
$213$	−18.6278	−1.27635
$214$	−21.1508	−1.44584
$215$	−8.38124	−0.571596
$216$	−64.4719	−4.38676
$217$	25.8592	1.75544
$218$	48.2549	3.26823
$219$	0.126153	0.00852461
$220$	−28.7403	−1.93767
$221$	0.317480	0.0213560
$222$	−21.7850	−1.46211
$223$	25.9887	1.74033	0.870167	−	0.492756i	$-0.164011\pi$
$223$	25.9887	1.74033	0.870167	+	0.492756i	$0.164011\pi$
$224$	81.3156	5.43313
$225$	1.02416	0.0682774
$226$	12.8825	0.856932
$227$	−9.63109	−0.639238	−0.319619	−	0.947546i	$-0.603555\pi$
$227$	−9.63109	−0.639238	−0.319619	+	0.947546i	$0.603555\pi$
$228$	−8.21121	−0.543801
$229$	−1.92835	−0.127429	−0.0637144	−	0.997968i	$-0.520295\pi$
$229$	−1.92835	−0.127429	−0.0637144	+	0.997968i	$0.520295\pi$
$230$	−18.0055	−1.18725
$231$	−25.8428	−1.70033
$232$	−15.6305	−1.02619
$233$	−28.5746	−1.87199	−0.935993	−	0.352020i	$-0.885495\pi$
$233$	−28.5746	−1.87199	−0.935993	+	0.352020i	$0.885495\pi$
$234$	−2.99169	−0.195573
$235$	1.49318	0.0974045
$236$	−2.08386	−0.135648
$237$	20.0377	1.30159
$238$	16.3038	1.05682
$239$	−11.0854	−0.717054	−0.358527	−	0.933519i	$-0.616721\pi$
$239$	−11.0854	−0.717054	−0.358527	+	0.933519i	$0.616721\pi$
$240$	−96.4592	−6.22641
$241$	3.11433	0.200611	0.100306	−	0.994957i	$-0.468018\pi$
$241$	3.11433	0.200611	0.100306	+	0.994957i	$0.468018\pi$
$242$	15.2710	0.981657
$243$	−9.63107	−0.617834
$244$	28.4502	1.82134
$245$	−17.6830	−1.12973
$246$	−79.2166	−5.05067
$247$	−0.106520	−0.00677769
$248$	62.9253	3.99576
$249$	−8.85104	−0.560912
$250$	−29.8681	−1.88902
$251$	9.29619	0.586770	0.293385	−	0.955994i	$-0.405218\pi$
$251$	9.29619	0.586770	0.293385	+	0.955994i	$0.405218\pi$
$252$	−112.279	−7.07291
$253$	−6.73623	−0.423503
$254$	−9.75066	−0.611811
$255$	−10.2682	−0.643020
$256$	39.0530	2.44081
$257$	−9.16503	−0.571699	−0.285849	−	0.958275i	$-0.592276\pi$
$257$	−9.16503	−0.571699	−0.285849	+	0.958275i	$0.592276\pi$
$258$	−29.0319	−1.80745
$259$	−10.6063	−0.659041
$260$	−2.52278	−0.156456
$261$	8.99761	0.556938
$262$	−48.5194	−2.99754
$263$	3.19827	0.197214	0.0986068	−	0.995126i	$-0.468561\pi$
$263$	3.19827	0.197214	0.0986068	+	0.995126i	$0.468561\pi$
$264$	−62.8854	−3.87033
$265$	2.27822	0.139950
$266$	−5.47020	−0.335399
$267$	43.6658	2.67230
$268$	−27.7115	−1.69275
$269$	16.7559	1.02162	0.510812	−	0.859692i	$-0.329345\pi$
$269$	16.7559	1.02162	0.510812	+	0.859692i	$0.329345\pi$
$270$	42.8233	2.60614
$271$	−17.7458	−1.07798	−0.538990	−	0.842312i	$-0.681194\pi$
$271$	−17.7458	−1.07798	−0.538990	+	0.842312i	$0.681194\pi$
$272$	22.7669	1.38045
$273$	−2.26845	−0.137293
$274$	29.8367	1.80250
$275$	0.442114	0.0266605
$276$	−45.5809	−2.74365
$277$	13.9595	0.838748	0.419374	−	0.907814i	$-0.362250\pi$
$277$	13.9595	0.838748	0.419374	+	0.907814i	$0.362250\pi$
$278$	40.7153	2.44194
$279$	−36.2227	−2.16859
$280$	−81.8360	−4.89063
$281$	3.39667	0.202628	0.101314	−	0.994854i	$-0.467695\pi$
$281$	3.39667	0.202628	0.101314	+	0.994854i	$0.467695\pi$
$282$	5.17226	0.308003
$283$	23.8686	1.41884	0.709420	−	0.704786i	$-0.248957\pi$
$283$	23.8686	1.41884	0.709420	+	0.704786i	$0.248957\pi$
$284$	−34.9369	−2.07313
$285$	3.44515	0.204073
$286$	−1.29146	−0.0763657
$287$	−38.5676	−2.27657
$288$	−113.904	−6.71186
$289$	−14.5764	−0.857437
$290$	10.3820	0.609653
$291$	−20.7995	−1.21929
$292$	0.236603	0.0138461
$293$	−4.81108	−0.281066	−0.140533	−	0.990076i	$-0.544882\pi$
$293$	−4.81108	−0.281066	−0.140533	+	0.990076i	$0.544882\pi$
$294$	−61.2525	−3.57232
$295$	0.874319	0.0509048
$296$	−25.8091	−1.50012
$297$	16.0211	0.929637
$298$	20.8690	1.20891
$299$	−0.591298	−0.0341956
$300$	2.99157	0.172719
$301$	−14.1345	−0.814701
$302$	2.72579	0.156852
$303$	18.1480	1.04258
$304$	−7.63867	−0.438108
$305$	−11.9368	−0.683497
$306$	−22.8378	−1.30555
$307$	2.90468	0.165779	0.0828893	−	0.996559i	$-0.473585\pi$
$307$	2.90468	0.165779	0.0828893	+	0.996559i	$0.473585\pi$
$308$	−48.4690	−2.76178
$309$	−38.3869	−2.18375
$310$	−41.7960	−2.37385
$311$	16.7201	0.948111	0.474055	−	0.880495i	$-0.342790\pi$
$311$	16.7201	0.948111	0.474055	+	0.880495i	$0.342790\pi$
$312$	−5.51999	−0.312508
$313$	−16.6733	−0.942432	−0.471216	−	0.882018i	$-0.656185\pi$
$313$	−16.6733	−0.942432	−0.471216	+	0.882018i	$0.656185\pi$
$314$	49.0720	2.76929
$315$	47.1085	2.65427
$316$	37.5812	2.11411
$317$	−24.1799	−1.35808	−0.679041	−	0.734101i	$-0.737604\pi$
$317$	−24.1799	−1.35808	−0.679041	+	0.734101i	$0.737604\pi$
$318$	7.89157	0.442537
$319$	3.88412	0.217469
$320$	−64.7946	−3.62213
$321$	22.4649	1.25387
$322$	−30.3654	−1.69220
$323$	−0.813146	−0.0452447
$324$	20.7371	1.15206
$325$	0.0388082	0.00215269
$326$	13.2257	0.732501
$327$	−51.2530	−2.83430
$328$	−93.8495	−5.18197
$329$	2.51817	0.138831
$330$	41.7695	2.29934
$331$	1.51180	0.0830959	0.0415480	−	0.999137i	$-0.486771\pi$
$331$	1.51180	0.0830959	0.0415480	+	0.999137i	$0.486771\pi$
$332$	−16.6004	−0.911065
$333$	14.8569	0.814152
$334$	−0.320863	−0.0175569
$335$	11.6268	0.635241
$336$	−162.673	−8.87456
$337$	−5.85763	−0.319085	−0.159543	−	0.987191i	$-0.551002\pi$
$337$	−5.85763	−0.319085	−0.159543	+	0.987191i	$0.551002\pi$
$338$	35.3219	1.92126
$339$	−13.6829	−0.743155
$340$	−19.2583	−1.04443
$341$	−15.6367	−0.846776
$342$	7.66246	0.414339
$343$	−2.92679	−0.158032
$344$	−34.3947	−1.85444
$345$	19.1242	1.02961
$346$	4.58180	0.246319
$347$	13.8115	0.741438	0.370719	−	0.928745i	$-0.379111\pi$
$347$	13.8115	0.741438	0.370719	+	0.928745i	$0.379111\pi$
$348$	26.2820	1.40886
$349$	−26.2982	−1.40771	−0.703855	−	0.710343i	$-0.748540\pi$
$349$	−26.2982	−1.40771	−0.703855	+	0.710343i	$0.748540\pi$
$350$	1.99295	0.106528
$351$	1.40631	0.0750632
$352$	−49.1705	−2.62080
$353$	12.5272	0.666754	0.333377	−	0.942794i	$-0.391812\pi$
$353$	12.5272	0.666754	0.333377	+	0.942794i	$0.391812\pi$
$354$	3.02857	0.160966
$355$	14.6584	0.777986
$356$	81.8965	4.34051
$357$	−17.3168	−0.916501
$358$	26.9895	1.42644
$359$	−15.1845	−0.801407	−0.400704	−	0.916208i	$-0.631234\pi$
$359$	−15.1845	−0.801407	−0.400704	+	0.916208i	$0.631234\pi$
$360$	114.633	6.04169
$361$	−18.7272	−0.985641
$362$	−52.4062	−2.75441
$363$	−16.2198	−0.851319
$364$	−4.25454	−0.222999
$365$	−0.0992708	−0.00519607
$366$	−41.3479	−2.16129
$367$	−10.9649	−0.572364	−0.286182	−	0.958175i	$-0.592386\pi$
$367$	−10.9649	−0.572364	−0.286182	+	0.958175i	$0.592386\pi$
$368$	−42.4027	−2.21039
$369$	54.0241	2.81238
$370$	17.1428	0.891213
$371$	3.84210	0.199472
$372$	−105.806	−5.48580
$373$	−16.3216	−0.845100	−0.422550	−	0.906340i	$-0.638865\pi$
$373$	−16.3216	−0.845100	−0.422550	+	0.906340i	$0.638865\pi$
$374$	−9.85870	−0.509781
$375$	31.7238	1.63821
$376$	6.12767	0.316011
$377$	0.340943	0.0175595
$378$	72.2193	3.71456
$379$	−1.64087	−0.0842861	−0.0421430	−	0.999112i	$-0.513419\pi$
$379$	−1.64087	−0.0842861	−0.0421430	+	0.999112i	$0.513419\pi$
$380$	6.46149	0.331467
$381$	10.3565	0.530579
$382$	−23.6537	−1.21023
$383$	−18.4499	−0.942745	−0.471372	−	0.881934i	$-0.656241\pi$
$383$	−18.4499	−0.942745	−0.471372	+	0.881934i	$0.656241\pi$
$384$	−101.895	−5.19982
$385$	20.3360	1.03642
$386$	−17.5782	−0.894705
$387$	19.7992	1.00645
$388$	−39.0100	−1.98043
$389$	5.00166	0.253594	0.126797	−	0.991929i	$-0.459530\pi$
$389$	5.00166	0.253594	0.126797	+	0.991929i	$0.459530\pi$
$390$	3.66647	0.185659
$391$	−4.51382	−0.228274
$392$	−72.5670	−3.66519
$393$	51.5340	2.59955
$394$	31.1654	1.57009
$395$	−15.7678	−0.793366
$396$	67.8936	3.41178
$397$	−34.0309	−1.70796	−0.853980	−	0.520306i	$-0.825818\pi$
$397$	−34.0309	−1.70796	−0.853980	+	0.520306i	$0.825818\pi$
$398$	33.6262	1.68553
$399$	5.81007	0.290867
$400$	2.78298	0.139149
$401$	−8.42042	−0.420496	−0.210248	−	0.977648i	$-0.567427\pi$
$401$	−8.42042	−0.420496	−0.210248	+	0.977648i	$0.567427\pi$
$402$	40.2743	2.00870
$403$	−1.37257	−0.0683727
$404$	34.0371	1.69341
$405$	−8.70060	−0.432336
$406$	17.5087	0.868944
$407$	6.41347	0.317904
$408$	−42.1383	−2.08616
$409$	29.2362	1.44564	0.722818	−	0.691039i	$-0.242847\pi$
$409$	29.2362	1.44564	0.722818	+	0.691039i	$0.242847\pi$
$410$	62.3364	3.07858
$411$	−31.6905	−1.56318
$412$	−71.9958	−3.54698
$413$	1.47449	0.0725551
$414$	42.5348	2.09047
$415$	6.96498	0.341897
$416$	−4.31612	−0.211615
$417$	−43.2450	−2.11772
$418$	3.30776	0.161788
$419$	15.1511	0.740181	0.370091	−	0.928996i	$-0.379327\pi$
$419$	15.1511	0.740181	0.370091	+	0.928996i	$0.379327\pi$
$420$	137.604	6.71439
$421$	−31.8504	−1.55229	−0.776146	−	0.630553i	$-0.782828\pi$
$421$	−31.8504	−1.55229	−0.776146	+	0.630553i	$0.782828\pi$
$422$	46.5372	2.26540
$423$	−3.52737	−0.171507
$424$	9.34930	0.454042
$425$	0.296252	0.0143703
$426$	50.7754	2.46008
$427$	−20.1307	−0.974194
$428$	42.1337	2.03661
$429$	1.37170	0.0662264
$430$	22.8455	1.10171
$431$	−8.11994	−0.391124	−0.195562	−	0.980691i	$-0.562653\pi$
$431$	−8.11994	−0.391124	−0.195562	+	0.980691i	$0.562653\pi$
$432$	100.848	4.85206
$433$	−4.30676	−0.206970	−0.103485	−	0.994631i	$-0.532999\pi$
$433$	−4.30676	−0.206970	−0.103485	+	0.994631i	$0.532999\pi$
$434$	−70.4868	−3.38348
$435$	−11.0271	−0.528707
$436$	−96.1266	−4.60363
$437$	1.51446	0.0724466
$438$	−0.343866	−0.0164305
$439$	19.7306	0.941690	0.470845	−	0.882216i	$-0.343949\pi$
$439$	19.7306	0.941690	0.470845	+	0.882216i	$0.343949\pi$
$440$	49.4851	2.35911
$441$	41.7729	1.98919
$442$	−0.865384	−0.0411621
$443$	−3.01218	−0.143113	−0.0715565	−	0.997437i	$-0.522797\pi$
$443$	−3.01218	−0.143113	−0.0715565	+	0.997437i	$0.522797\pi$
$444$	43.3969	2.05953
$445$	−34.3611	−1.62887
$446$	−70.8399	−3.35437
$447$	−22.1656	−1.04840
$448$	−109.273	−5.16265
$449$	−1.05075	−0.0495878	−0.0247939	−	0.999693i	$-0.507893\pi$
$449$	−1.05075	−0.0495878	−0.0247939	+	0.999693i	$0.507893\pi$
$450$	−2.79165	−0.131600
$451$	23.3213	1.09816
$452$	−25.6627	−1.20707
$453$	−2.89515	−0.136026
$454$	26.2523	1.23208
$455$	1.78507	0.0836852
$456$	14.1381	0.662077
$457$	−10.4105	−0.486981	−0.243490	−	0.969903i	$-0.578292\pi$
$457$	−10.4105	−0.486981	−0.243490	+	0.969903i	$0.578292\pi$
$458$	5.25627	0.245609
$459$	10.7354	0.501086
$460$	35.8681	1.67236
$461$	26.0201	1.21188	0.605938	−	0.795512i	$-0.292798\pi$
$461$	26.0201	1.21188	0.605938	+	0.795512i	$0.292798\pi$
$462$	70.4421	3.27726
$463$	16.6583	0.774177	0.387089	−	0.922043i	$-0.373481\pi$
$463$	16.6583	0.774177	0.387089	+	0.922043i	$0.373481\pi$
$464$	24.4495	1.13504
$465$	44.3929	2.05867
$466$	77.8884	3.60811
$467$	30.8844	1.42916	0.714580	−	0.699554i	$-0.246618\pi$
$467$	30.8844	1.42916	0.714580	+	0.699554i	$0.246618\pi$
$468$	5.95962	0.275483
$469$	19.6080	0.905415
$470$	−4.07010	−0.187740
$471$	−52.1209	−2.40160
$472$	3.58800	0.165151
$473$	8.54697	0.392990
$474$	−54.6185	−2.50871
$475$	−0.0993975	−0.00456067
$476$	−32.4782	−1.48863
$477$	−5.38188	−0.246420
$478$	30.2164	1.38207
$479$	−3.25271	−0.148620	−0.0743099	−	0.997235i	$-0.523675\pi$
$479$	−3.25271	−0.148620	−0.0743099	+	0.997235i	$0.523675\pi$
$480$	139.596	6.37164
$481$	0.562966	0.0256691
$482$	−8.48900	−0.386664
$483$	32.2520	1.46752
$484$	−30.4207	−1.38276
$485$	16.3673	0.743202
$486$	26.2523	1.19083
$487$	−7.91375	−0.358606	−0.179303	−	0.983794i	$-0.557384\pi$
$487$	−7.91375	−0.358606	−0.179303	+	0.983794i	$0.557384\pi$
$488$	−48.9857	−2.21748
$489$	−14.0474	−0.635245
$490$	48.2003	2.17747
$491$	−38.7922	−1.75067	−0.875333	−	0.483521i	$-0.839358\pi$
$491$	−38.7922	−1.75067	−0.875333	+	0.483521i	$0.839358\pi$
$492$	157.804	7.11436
$493$	2.60268	0.117219
$494$	0.290351	0.0130635
$495$	−28.4859	−1.28035
$496$	−98.4289	−4.41959
$497$	24.7206	1.10887
$498$	24.1261	1.08112
$499$	21.1361	0.946184	0.473092	−	0.881013i	$-0.343138\pi$
$499$	21.1361	0.946184	0.473092	+	0.881013i	$0.343138\pi$
$500$	59.4989	2.66087
$501$	0.340799	0.0152258
$502$	−25.3395	−1.13096
$503$	−12.2665	−0.546937	−0.273469	−	0.961881i	$-0.588171\pi$
$503$	−12.2665	−0.546937	−0.273469	+	0.961881i	$0.588171\pi$
$504$	193.323	8.61127
$505$	−14.2809	−0.635490
$506$	18.3616	0.816271
$507$	−37.5165	−1.66617
$508$	19.4239	0.861796
$509$	3.97730	0.176291	0.0881453	−	0.996108i	$-0.471906\pi$
$509$	3.97730	0.176291	0.0881453	+	0.996108i	$0.471906\pi$
$510$	27.9890	1.23937
$511$	−0.167415	−0.00740601
$512$	−36.0600	−1.59364
$513$	−3.60191	−0.159028
$514$	24.9819	1.10191
$515$	30.2071	1.33108
$516$	57.8333	2.54597
$517$	−1.52271	−0.0669686
$518$	28.9105	1.27025
$519$	−4.86648	−0.213615
$520$	4.34374	0.190486
$521$	−31.6494	−1.38659	−0.693293	−	0.720656i	$-0.743841\pi$
$521$	−31.6494	−1.38659	−0.693293	+	0.720656i	$0.743841\pi$
$522$	−24.5256	−1.07346
$523$	−40.7785	−1.78312	−0.891559	−	0.452904i	$-0.850388\pi$
$523$	−40.7785	−1.78312	−0.891559	+	0.452904i	$0.850388\pi$
$524$	96.6536	4.22233
$525$	−2.11677	−0.0923835
$526$	−8.71780	−0.380114
$527$	−10.4779	−0.456424
$528$	98.3665	4.28085
$529$	−14.5931	−0.634484
$530$	−6.20996	−0.269743
$531$	−2.06542	−0.0896315
$532$	10.8970	0.472443
$533$	2.04711	0.0886703
$534$	−119.024	−5.15067
$535$	−17.6779	−0.764282
$536$	47.7138	2.06092
$537$	−28.6664	−1.23705
$538$	−45.6730	−1.96910
$539$	18.0327	0.776723
$540$	−85.3066	−3.67101
$541$	−40.8766	−1.75742	−0.878711	−	0.477355i	$-0.841596\pi$
$541$	−40.8766	−1.75742	−0.878711	+	0.477355i	$0.841596\pi$
$542$	48.3713	2.07773
$543$	55.6623	2.38870
$544$	−32.9482	−1.41264
$545$	40.3316	1.72761
$546$	6.18332	0.264622
$547$	−13.2169	−0.565114	−0.282557	−	0.959250i	$-0.591183\pi$
$547$	−13.2169	−0.565114	−0.282557	+	0.959250i	$0.591183\pi$
$548$	−59.4364	−2.53900
$549$	28.1984	1.20348
$550$	−1.20511	−0.0513860
$551$	−0.873241	−0.0372013
$552$	78.4814	3.34039
$553$	−26.5917	−1.13079
$554$	−38.0508	−1.61662
$555$	−18.2079	−0.772883
$556$	−81.1073	−3.43972
$557$	−40.9754	−1.73618	−0.868091	−	0.496405i	$-0.834653\pi$
$557$	−40.9754	−1.73618	−0.868091	+	0.496405i	$0.834653\pi$
$558$	98.7354	4.17980
$559$	0.750242	0.0317318
$560$	128.009	5.40938
$561$	10.4712	0.442096
$562$	−9.25862	−0.390551
$563$	44.7913	1.88773	0.943863	−	0.330336i	$-0.107162\pi$
$563$	44.7913	1.88773	0.943863	+	0.330336i	$0.107162\pi$
$564$	−10.3034	−0.433853
$565$	10.7672	0.452981
$566$	−65.0608	−2.73471
$567$	−14.6731	−0.616213
$568$	60.1546	2.52403
$569$	43.7045	1.83219	0.916093	−	0.400966i	$-0.131325\pi$
$569$	43.7045	1.83219	0.916093	+	0.400966i	$0.131325\pi$
$570$	−9.39076	−0.393336
$571$	6.86801	0.287417	0.143709	−	0.989620i	$-0.454097\pi$
$571$	6.86801	0.287417	0.143709	+	0.989620i	$0.454097\pi$
$572$	2.57267	0.107569
$573$	25.1233	1.04954
$574$	105.127	4.38792
$575$	−0.551761	−0.0230100
$576$	153.065	6.37773
$577$	−8.72931	−0.363406	−0.181703	−	0.983353i	$-0.558161\pi$
$577$	−8.72931	−0.363406	−0.181703	+	0.983353i	$0.558161\pi$
$578$	39.7323	1.65265
$579$	18.6703	0.775912
$580$	−20.6816	−0.858756
$581$	11.7461	0.487309
$582$	56.6950	2.35008
$583$	−2.32327	−0.0962201
$584$	−0.407384	−0.0168577
$585$	−2.50046	−0.103381
$586$	13.1140	0.541735
$587$	−22.2323	−0.917627	−0.458813	−	0.888533i	$-0.651725\pi$
$587$	−22.2323	−0.917627	−0.458813	+	0.888533i	$0.651725\pi$
$588$	122.019	5.03196
$589$	3.51550	0.144854
$590$	−2.38321	−0.0981152
$591$	−33.1018	−1.36162
$592$	40.3711	1.65924
$593$	33.1822	1.36263	0.681315	−	0.731990i	$-0.261408\pi$
$593$	33.1822	1.36263	0.681315	+	0.731990i	$0.261408\pi$
$594$	−43.6701	−1.79181
$595$	13.6268	0.558643
$596$	−41.5723	−1.70287
$597$	−35.7155	−1.46174
$598$	1.61175	0.0659095
$599$	−18.6892	−0.763622	−0.381811	−	0.924241i	$-0.624699\pi$
$599$	−18.6892	−0.763622	−0.381811	+	0.924241i	$0.624699\pi$
$600$	−5.15091	−0.210285
$601$	−1.58501	−0.0646540	−0.0323270	−	0.999477i	$-0.510292\pi$
$601$	−1.58501	−0.0646540	−0.0323270	+	0.999477i	$0.510292\pi$
$602$	38.5278	1.57027
$603$	−27.4662	−1.11851
$604$	−5.42994	−0.220941
$605$	12.7635	0.518912
$606$	−49.4677	−2.00949
$607$	−37.1175	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$607$	−37.1175	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$608$	11.0547	0.448326
$609$	−18.5966	−0.753571
$610$	32.5371	1.31739
$611$	−0.133661	−0.00540736
$612$	45.4943	1.83900
$613$	−6.02541	−0.243364	−0.121682	−	0.992569i	$-0.538829\pi$
$613$	−6.02541	−0.243364	−0.121682	+	0.992569i	$0.538829\pi$
$614$	−7.91754	−0.319526
$615$	−66.2094	−2.66982
$616$	83.4541	3.36246
$617$	−47.4335	−1.90960	−0.954801	−	0.297245i	$-0.903932\pi$
$617$	−47.4335	−1.90960	−0.954801	+	0.297245i	$0.903932\pi$
$618$	104.635	4.20902
$619$	3.47340	0.139608	0.0698039	−	0.997561i	$-0.477763\pi$
$619$	3.47340	0.139608	0.0698039	+	0.997561i	$0.477763\pi$
$620$	83.2601	3.34381
$621$	−19.9944	−0.802348
$622$	−45.5755	−1.82741
$623$	−57.9482	−2.32164
$624$	8.63448	0.345656
$625$	−25.9153	−1.03661
$626$	45.4480	1.81647
$627$	−3.51327	−0.140307
$628$	−97.7542	−3.90082
$629$	4.29755	0.171354
$630$	−128.408	−5.11590
$631$	−6.94325	−0.276407	−0.138203	−	0.990404i	$-0.544133\pi$
$631$	−6.94325	−0.276407	−0.138203	+	0.990404i	$0.544133\pi$
$632$	−64.7076	−2.57393
$633$	−49.4287	−1.96461
$634$	65.9095	2.61760
$635$	−8.14963	−0.323408
$636$	−15.7205	−0.623357
$637$	1.58289	0.0627162
$638$	−10.5873	−0.419155
$639$	−34.6277	−1.36985
$640$	80.1825	3.16949
$641$	−1.81266	−0.0715956	−0.0357978	−	0.999359i	$-0.511397\pi$
$641$	−1.81266	−0.0715956	−0.0357978	+	0.999359i	$0.511397\pi$
$642$	−61.2347	−2.41674
$643$	36.4934	1.43916	0.719580	−	0.694409i	$-0.244334\pi$
$643$	36.4934	1.43916	0.719580	+	0.694409i	$0.244334\pi$
$644$	60.4897	2.38363
$645$	−24.2649	−0.955431
$646$	2.21647	0.0872057
$647$	32.8803	1.29266	0.646329	−	0.763059i	$-0.276303\pi$
$647$	32.8803	1.29266	0.646329	+	0.763059i	$0.276303\pi$
$648$	−35.7052	−1.40263
$649$	−0.891607	−0.0349986
$650$	−0.105783	−0.00414915
$651$	74.8663	2.93424
$652$	−26.3463	−1.03180
$653$	−5.76635	−0.225655	−0.112827	−	0.993615i	$-0.535991\pi$
$653$	−5.76635	−0.225655	−0.112827	+	0.993615i	$0.535991\pi$
$654$	139.705	5.46290
$655$	−40.5527	−1.58452
$656$	146.801	5.73162
$657$	0.234509	0.00914908
$658$	−6.86402	−0.267587
$659$	44.4810	1.73273	0.866366	−	0.499410i	$-0.166450\pi$
$659$	44.4810	1.73273	0.866366	+	0.499410i	$0.166450\pi$
$660$	−83.2074	−3.23884
$661$	11.2993	0.439493	0.219746	−	0.975557i	$-0.429477\pi$
$661$	11.2993	0.439493	0.219746	+	0.975557i	$0.429477\pi$
$662$	−4.12085	−0.160161
$663$	0.919151	0.0356969
$664$	28.5826	1.10922
$665$	−4.57200	−0.177295
$666$	−40.4968	−1.56922
$667$	−4.84741	−0.187693
$668$	0.639179	0.0247306
$669$	75.2413	2.90899
$670$	−31.6923	−1.22438
$671$	12.1728	0.469926
$672$	235.421	9.08155
$673$	13.8835	0.535169	0.267584	−	0.963534i	$-0.413775\pi$
$673$	13.8835	0.535169	0.267584	+	0.963534i	$0.413775\pi$
$674$	15.9667	0.615013
$675$	1.31228	0.0505096
$676$	−70.3634	−2.70628
$677$	−16.4266	−0.631325	−0.315663	−	0.948871i	$-0.602227\pi$
$677$	−16.4266	−0.631325	−0.315663	+	0.948871i	$0.602227\pi$
$678$	37.2968	1.43237
$679$	27.6026	1.05929
$680$	33.1591	1.27159
$681$	−27.8834	−1.06850
$682$	42.6225	1.63210
$683$	21.7647	0.832802	0.416401	−	0.909181i	$-0.363291\pi$
$683$	21.7647	0.832802	0.416401	+	0.909181i	$0.363291\pi$
$684$	−15.2641	−0.583637
$685$	24.9376	0.952815
$686$	7.97781	0.304594
$687$	−5.58285	−0.212999
$688$	53.8008	2.05114
$689$	−0.203934	−0.00776925
$690$	−52.1287	−1.98450
$691$	2.54294	0.0967378	0.0483689	−	0.998830i	$-0.484598\pi$
$691$	2.54294	0.0967378	0.0483689	+	0.998830i	$0.484598\pi$
$692$	−9.12722	−0.346965
$693$	−48.0400	−1.82489
$694$	−37.6472	−1.42907
$695$	34.0300	1.29083
$696$	−45.2525	−1.71529
$697$	15.6272	0.591921
$698$	71.6834	2.71326
$699$	−82.7277	−3.12905
$700$	−3.97007	−0.150055
$701$	5.17645	0.195512	0.0977560	−	0.995210i	$-0.468834\pi$
$701$	5.17645	0.195512	0.0977560	+	0.995210i	$0.468834\pi$
$702$	−3.83330	−0.144679
$703$	−1.44190	−0.0543822
$704$	66.0758	2.49033
$705$	4.32298	0.162813
$706$	−34.1465	−1.28512
$707$	−24.0839	−0.905769
$708$	−6.03308	−0.226737
$709$	−27.5605	−1.03506	−0.517529	−	0.855666i	$-0.673148\pi$
$709$	−27.5605	−1.03506	−0.517529	+	0.855666i	$0.673148\pi$
$710$	−39.9557	−1.49951
$711$	37.2487	1.39693
$712$	−141.010	−5.28457
$713$	19.5148	0.730834
$714$	47.2019	1.76649
$715$	−1.07941	−0.0403675
$716$	−53.7647	−2.00928
$717$	−32.0938	−1.19857
$718$	41.3898	1.54465
$719$	−28.1653	−1.05039	−0.525194	−	0.850982i	$-0.676007\pi$
$719$	−28.1653	−1.05039	−0.525194	+	0.850982i	$0.676007\pi$
$720$	−179.311	−6.68253
$721$	50.9426	1.89720
$722$	51.0464	1.89975
$723$	9.01644	0.335325
$724$	104.396	3.87986
$725$	0.318146	0.0118157
$726$	44.2118	1.64085
$727$	7.65975	0.284085	0.142042	−	0.989861i	$-0.454633\pi$
$727$	7.65975	0.284085	0.142042	+	0.989861i	$0.454633\pi$
$728$	7.32550	0.271501
$729$	−39.3405	−1.45705
$730$	0.270592	0.0100150
$731$	5.72716	0.211827
$732$	82.3675	3.04439
$733$	−34.7970	−1.28526	−0.642629	−	0.766178i	$-0.722156\pi$
$733$	−34.7970	−1.28526	−0.642629	+	0.766178i	$0.722156\pi$
$734$	29.8881	1.10319
$735$	−51.1950	−1.88836
$736$	61.3652	2.26195
$737$	−11.8567	−0.436748
$738$	−147.258	−5.42065
$739$	19.1345	0.703874	0.351937	−	0.936024i	$-0.385523\pi$
$739$	19.1345	0.703874	0.351937	+	0.936024i	$0.385523\pi$
$740$	−34.1495	−1.25536
$741$	−0.308391	−0.0113290
$742$	−10.4728	−0.384468
$743$	−36.9082	−1.35403	−0.677016	−	0.735968i	$-0.736727\pi$
$743$	−36.9082	−1.35403	−0.677016	+	0.735968i	$0.736727\pi$
$744$	182.178	6.67897
$745$	17.4424	0.639039
$746$	44.4893	1.62887
$747$	−16.4535	−0.602002
$748$	19.6391	0.718077
$749$	−29.8129	−1.08934
$750$	−86.4724	−3.15753
$751$	−15.4281	−0.562978	−0.281489	−	0.959564i	$-0.590828\pi$
$751$	−15.4281	−0.562978	−0.281489	+	0.959564i	$0.590828\pi$
$752$	−9.58503	−0.349530
$753$	26.9138	0.980795
$754$	−0.929340	−0.0338446
$755$	2.27822	0.0829130
$756$	−143.865	−5.23232
$757$	−17.1093	−0.621849	−0.310925	−	0.950435i	$-0.600639\pi$
$757$	−17.1093	−0.621849	−0.310925	+	0.950435i	$0.600639\pi$
$758$	4.47268	0.162455
$759$	−19.5024	−0.707892
$760$	−11.1254	−0.403561
$761$	54.0508	1.95934	0.979669	−	0.200619i	$-0.0642953\pi$
$761$	54.0508	1.95934	0.979669	+	0.200619i	$0.0642953\pi$
$762$	−28.2296	−1.02265
$763$	68.0171	2.46238
$764$	47.1195	1.70472
$765$	−19.0879	−0.690124
$766$	50.2905	1.81707
$767$	−0.0782641	−0.00282595
$768$	113.064	4.07985
$769$	−16.8159	−0.606396	−0.303198	−	0.952928i	$-0.598054\pi$
$769$	−16.8159	−0.606396	−0.303198	+	0.952928i	$0.598054\pi$
$770$	−55.4316	−1.99762
$771$	−26.5341	−0.955603
$772$	35.0168	1.26028
$773$	−39.3482	−1.41526	−0.707628	−	0.706585i	$-0.750235\pi$
$773$	−39.3482	−1.41526	−0.707628	+	0.706585i	$0.750235\pi$
$774$	−53.9684	−1.93985
$775$	−1.28080	−0.0460076
$776$	67.1677	2.41118
$777$	−30.7067	−1.10160
$778$	−13.6335	−0.488784
$779$	−5.24317	−0.187856
$780$	−7.30383	−0.261519
$781$	−14.9482	−0.534890
$782$	12.3037	0.439981
$783$	11.5288	0.412006
$784$	113.511	4.05396
$785$	41.0145	1.46387
$786$	−140.471	−5.01043
$787$	0.00184276	6.56873e−5 0	3.28437e−5	−	1.00000i	$-0.499990\pi$
$787$	0.00184276	6.56873e−5 0	3.28437e−5		1.00000i	$0.499990\pi$
$788$	−62.0834	−2.21163
$789$	9.25945	0.329645
$790$	42.9799	1.52915
$791$	18.1584	0.645638
$792$	−116.900	−4.15385
$793$	1.06851	0.0379440
$794$	92.7610	3.29197
$795$	6.59579	0.233929
$796$	−66.9854	−2.37424
$797$	−34.7510	−1.23094	−0.615472	−	0.788159i	$-0.711035\pi$
$797$	−34.7510	−1.23094	−0.615472	+	0.788159i	$0.711035\pi$
$798$	−15.8370	−0.560625
$799$	−1.02034	−0.0360970
$800$	−4.02753	−0.142395
$801$	81.1717	2.86806
$802$	22.9523	0.810474
$803$	0.101234	0.00357246
$804$	−80.2289	−2.82945
$805$	−25.3795	−0.894509
$806$	3.74134	0.131783
$807$	48.5108	1.70766
$808$	−58.6053	−2.06173
$809$	−9.01460	−0.316936	−0.158468	−	0.987364i	$-0.550656\pi$
$809$	−9.01460	−0.316936	−0.158468	+	0.987364i	$0.550656\pi$
$810$	23.7160	0.833296
$811$	−9.05066	−0.317812	−0.158906	−	0.987294i	$-0.550797\pi$
$811$	−9.05066	−0.317812	−0.158906	+	0.987294i	$0.550797\pi$
$812$	−34.8784	−1.22399
$813$	−51.3767	−1.80186
$814$	−17.4818	−0.612736
$815$	11.0540	0.387206
$816$	65.9135	2.30744
$817$	−1.92156	−0.0672268
$818$	−79.6917	−2.78635
$819$	−4.21689	−0.147350
$820$	−124.178	−4.33648
$821$	−6.82623	−0.238237	−0.119119	−	0.992880i	$-0.538007\pi$
$821$	−6.82623	−0.238237	−0.119119	+	0.992880i	$0.538007\pi$
$822$	86.3816	3.01290
$823$	12.2202	0.425969	0.212984	−	0.977056i	$-0.431682\pi$
$823$	12.2202	0.425969	0.212984	+	0.977056i	$0.431682\pi$
$824$	123.963	4.31845
$825$	1.27998	0.0445634
$826$	−4.01916	−0.139844
$827$	19.4915	0.677785	0.338893	−	0.940825i	$-0.389948\pi$
$827$	19.4915	0.677785	0.338893	+	0.940825i	$0.389948\pi$
$828$	−84.7318	−2.94463
$829$	−43.3048	−1.50404	−0.752019	−	0.659141i	$-0.770920\pi$
$829$	−43.3048	−1.50404	−0.752019	+	0.659141i	$0.770920\pi$
$830$	−18.9851	−0.658982
$831$	40.4150	1.40198
$832$	5.80005	0.201081
$833$	12.0834	0.418664
$834$	117.877	4.08174
$835$	−0.268178	−0.00928069
$836$	−6.58925	−0.227894
$837$	−46.4128	−1.60426
$838$	−41.2988	−1.42664
$839$	−15.4619	−0.533805	−0.266902	−	0.963724i	$-0.586000\pi$
$839$	−15.4619	−0.533805	−0.266902	+	0.963724i	$0.586000\pi$
$840$	−236.927	−8.17477
$841$	−26.2050	−0.903620
$842$	86.8174	2.99193
$843$	9.83387	0.338697
$844$	−92.7049	−3.19104
$845$	29.5221	1.01559
$846$	9.61488	0.330566
$847$	21.5251	0.739610
$848$	−14.6244	−0.502202
$849$	69.1031	2.37161
$850$	−0.807521	−0.0276978
$851$	−8.00406	−0.274376
$852$	−101.148	−3.46526
$853$	−5.46365	−0.187072	−0.0935358	−	0.995616i	$-0.529817\pi$
$853$	−5.46365	−0.187072	−0.0935358	+	0.995616i	$0.529817\pi$
$854$	54.8722	1.87769
$855$	6.40430	0.219023
$856$	−72.5460	−2.47957
$857$	−15.1580	−0.517789	−0.258894	−	0.965906i	$-0.583358\pi$
$857$	−15.1580	−0.517789	−0.258894	+	0.965906i	$0.583358\pi$
$858$	−3.73897	−0.127646
$859$	35.7423	1.21951	0.609755	−	0.792590i	$-0.291268\pi$
$859$	35.7423	1.21951	0.609755	+	0.792590i	$0.291268\pi$
$860$	−45.5096	−1.55187
$861$	−111.659	−3.80532
$862$	22.1332	0.753861
$863$	−54.6459	−1.86017	−0.930084	−	0.367348i	$-0.880266\pi$
$863$	−54.6459	−1.86017	−0.930084	+	0.367348i	$0.880266\pi$
$864$	−145.947	−4.96523
$865$	3.82948	0.130206
$866$	11.7393	0.398919
$867$	−42.2009	−1.43322
$868$	140.414	4.76596
$869$	16.0796	0.545464
$870$	30.0575	1.01904
$871$	−1.04077	−0.0352651
$872$	165.511	5.60492
$873$	−38.6648	−1.30861
$874$	−4.12811	−0.139635
$875$	−42.1001	−1.42324
$876$	0.685001	0.0231440
$877$	44.0614	1.48785	0.743924	−	0.668265i	$-0.232963\pi$
$877$	44.0614	1.48785	0.743924	+	0.668265i	$0.232963\pi$
$878$	−53.7815	−1.81504
$879$	−13.9288	−0.469807
$880$	−77.4056	−2.60934
$881$	−38.2241	−1.28780	−0.643901	−	0.765109i	$-0.722685\pi$
$881$	−38.2241	−1.28780	−0.643901	+	0.765109i	$0.722685\pi$
$882$	−113.864	−3.83401
$883$	−5.84288	−0.196629	−0.0983143	−	0.995155i	$-0.531345\pi$
$883$	−5.84288	−0.196629	−0.0983143	+	0.995155i	$0.531345\pi$
$884$	1.72390	0.0579809
$885$	2.53128	0.0850881
$886$	8.21057	0.275840
$887$	25.0989	0.842737	0.421369	−	0.906889i	$-0.361550\pi$
$887$	25.0989	0.842737	0.421369	+	0.906889i	$0.361550\pi$
$888$	−74.7211	−2.50748
$889$	−13.7439	−0.460956
$890$	93.6611	3.13953
$891$	8.87264	0.297245
$892$	141.117	4.72495
$893$	0.342340	0.0114560
$894$	60.4189	2.02071
$895$	22.5579	0.754027
$896$	135.224	4.51750
$897$	−1.71189	−0.0571585
$898$	2.86411	0.0955767
$899$	−11.2522	−0.375283
$900$	5.56113	0.185371
$901$	−1.55678	−0.0518639
$902$	−63.5690	−2.11662
$903$	−40.9216	−1.36178
$904$	44.1862	1.46961
$905$	−43.8012	−1.45600
$906$	7.89157	0.262180
$907$	−17.8735	−0.593480	−0.296740	−	0.954958i	$-0.595899\pi$
$907$	−17.8735	−0.593480	−0.296740	+	0.954958i	$0.595899\pi$
$908$	−52.2962	−1.73551
$909$	33.7359	1.11895
$910$	−4.86572	−0.161297
$911$	28.7282	0.951807	0.475904	−	0.879497i	$-0.342121\pi$
$911$	28.7282	0.951807	0.475904	+	0.879497i	$0.342121\pi$
$912$	−22.1151	−0.732304
$913$	−7.10270	−0.235065
$914$	28.3767	0.938619
$915$	−34.5587	−1.14248
$916$	−10.4708	−0.345965
$917$	−68.3900	−2.25844
$918$	−29.2625	−0.965806
$919$	23.8901	0.788062	0.394031	−	0.919097i	$-0.371080\pi$
$919$	23.8901	0.788062	0.394031	+	0.919097i	$0.371080\pi$
$920$	−61.7578	−2.03610
$921$	8.40947	0.277101
$922$	−70.9254	−2.33580
$923$	−1.31214	−0.0431895
$924$	−140.325	−4.61635
$925$	0.525324	0.0172726
$926$	−45.4071	−1.49217
$927$	−71.3587	−2.34373
$928$	−35.3832	−1.16151
$929$	−19.1197	−0.627297	−0.313648	−	0.949539i	$-0.601551\pi$
$929$	−19.1197	−0.627297	−0.313648	+	0.949539i	$0.601551\pi$
$930$	−121.006	−3.96793
$931$	−4.05417	−0.132870
$932$	−155.158	−5.08238
$933$	48.4072	1.58478
$934$	−84.1845	−2.75460
$935$	−8.23993	−0.269474
$936$	−10.2613	−0.335401
$937$	28.4572	0.929655	0.464827	−	0.885401i	$-0.346116\pi$
$937$	28.4572	0.929655	0.464827	+	0.885401i	$0.346116\pi$
$938$	−53.4474	−1.74512
$939$	−48.2718	−1.57529
$940$	8.10789	0.264450
$941$	−1.55702	−0.0507573	−0.0253787	−	0.999678i	$-0.508079\pi$
$941$	−1.55702	−0.0507573	−0.0253787	+	0.999678i	$0.508079\pi$
$942$	142.071	4.62891
$943$	−29.1052	−0.947795
$944$	−5.61242	−0.182669
$945$	60.3611	1.96355
$946$	−23.2973	−0.757459
$947$	−58.2130	−1.89167	−0.945834	−	0.324649i	$-0.894754\pi$
$947$	−58.2130	−1.89167	−0.945834	+	0.324649i	$0.894754\pi$
$948$	108.803	3.53377
$949$	0.00888617	0.000288457 0
$950$	0.270937	0.00879035
$951$	−70.0045	−2.27005
$952$	55.9210	1.81241
$953$	−43.2609	−1.40136	−0.700678	−	0.713477i	$-0.747119\pi$
$953$	−43.2609	−1.40136	−0.700678	+	0.713477i	$0.747119\pi$
$954$	14.6699	0.474955
$955$	−19.7698	−0.639735
$956$	−60.1930	−1.94678
$957$	11.2451	0.363503
$958$	8.86620	0.286454
$959$	42.0559	1.35806
$960$	−187.590	−6.05444
$961$	14.2994	0.461270
$962$	−1.53453	−0.0494752
$963$	41.7608	1.34572
$964$	16.9106	0.544654
$965$	−14.6919	−0.472948
$966$	−87.9123	−2.82853
$967$	6.90444	0.222032	0.111016	−	0.993819i	$-0.464590\pi$
$967$	6.90444	0.222032	0.111016	+	0.993819i	$0.464590\pi$
$968$	52.3786	1.68351
$969$	−2.35418	−0.0756271
$970$	−44.6139	−1.43247
$971$	2.38279	0.0764672	0.0382336	−	0.999269i	$-0.487827\pi$
$971$	2.38279	0.0764672	0.0382336	+	0.999269i	$0.487827\pi$
$972$	−52.2961	−1.67740
$973$	57.3898	1.83983
$974$	21.5712	0.691186
$975$	0.112355	0.00359825
$976$	76.6244	2.45269
$977$	−4.46821	−0.142951	−0.0714754	−	0.997442i	$-0.522771\pi$
$977$	−4.46821	−0.142951	−0.0714754	+	0.997442i	$0.522771\pi$
$978$	38.2902	1.22439
$979$	35.0405	1.11990
$980$	−96.0178	−3.06717
$981$	−95.2759	−3.04193
$982$	105.739	3.37428
$983$	9.87718	0.315033	0.157517	−	0.987516i	$-0.449651\pi$
$983$	9.87718	0.315033	0.157517	+	0.987516i	$0.449651\pi$
$984$	−271.708	−8.66174
$985$	26.0481	0.829962
$986$	−7.09435	−0.225930
$987$	7.29049	0.232059
$988$	−0.578396	−0.0184012
$989$	−10.6667	−0.339181
$990$	77.6467	2.46777
$991$	60.2048	1.91247	0.956234	−	0.292604i	$-0.0945218\pi$
$991$	60.2048	1.91247	0.956234	+	0.292604i	$0.0945218\pi$
$992$	142.446	4.52267
$993$	4.37688	0.138896
$994$	−67.3832	−2.13727
$995$	28.1049	0.890984
$996$	−48.0606	−1.52286
$997$	−27.8113	−0.880792	−0.440396	−	0.897804i	$-0.645162\pi$
$997$	−27.8113	−0.880792	−0.440396	+	0.897804i	$0.645162\pi$
$998$	−57.6127	−1.82370
$999$	19.0364	0.602285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.3	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.3	✓	153	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)

\(f(q)\)	\(=\)	\(q-2.72579 q^{2} +2.89515 q^{3} +5.42994 q^{4} -2.27822 q^{5} -7.89157 q^{6} -3.84210 q^{7} -9.34930 q^{8} +5.38188 q^{9} +O(q^{10})\)	\(q-2.72579 q^{2} +2.89515 q^{3} +5.42994 q^{4} -2.27822 q^{5} -7.89157 q^{6} -3.84210 q^{7} -9.34930 q^{8} +5.38188 q^{9} +6.20996 q^{10} +2.32327 q^{11} +15.7205 q^{12} +0.203934 q^{13} +10.4728 q^{14} -6.59579 q^{15} +14.6244 q^{16} +1.55678 q^{17} -14.6699 q^{18} -0.522326 q^{19} -12.3706 q^{20} -11.1235 q^{21} -6.33275 q^{22} -2.89946 q^{23} -27.0676 q^{24} +0.190298 q^{25} -0.555881 q^{26} +6.89591 q^{27} -20.8624 q^{28} +1.67183 q^{29} +17.9788 q^{30} -6.73048 q^{31} -21.1643 q^{32} +6.72621 q^{33} -4.24346 q^{34} +8.75317 q^{35} +29.2233 q^{36} +2.76054 q^{37} +1.42375 q^{38} +0.590418 q^{39} +21.2998 q^{40} +10.0381 q^{41} +30.3202 q^{42} +3.67885 q^{43} +12.6152 q^{44} -12.2611 q^{45} +7.90332 q^{46} -0.655415 q^{47} +42.3397 q^{48} +7.76177 q^{49} -0.518712 q^{50} +4.50711 q^{51} +1.10735 q^{52} -1.00000 q^{53} -18.7968 q^{54} -5.29293 q^{55} +35.9210 q^{56} -1.51221 q^{57} -4.55707 q^{58} -0.383772 q^{59} -35.8147 q^{60} +5.23951 q^{61} +18.3459 q^{62} -20.6778 q^{63} +28.4409 q^{64} -0.464606 q^{65} -18.3343 q^{66} -5.10346 q^{67} +8.45322 q^{68} -8.39437 q^{69} -23.8593 q^{70} -6.43413 q^{71} -50.3168 q^{72} +0.0435738 q^{73} -7.52465 q^{74} +0.550941 q^{75} -2.83620 q^{76} -8.92625 q^{77} -1.60936 q^{78} +6.92112 q^{79} -33.3175 q^{80} +3.81903 q^{81} -27.3619 q^{82} -3.05720 q^{83} -60.3997 q^{84} -3.54669 q^{85} -10.0278 q^{86} +4.84020 q^{87} -21.7209 q^{88} +15.0824 q^{89} +33.4213 q^{90} -0.783534 q^{91} -15.7439 q^{92} -19.4857 q^{93} +1.78653 q^{94} +1.18997 q^{95} -61.2739 q^{96} -7.18425 q^{97} -21.1570 q^{98} +12.5036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * q^99

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