LMFDB - Embedded newform 8013.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, 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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$1$
Dimension:	$116$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77241 q^{2} -1.00000 q^{3} +5.68625 q^{4} +1.80856 q^{5} +2.77241 q^{6} -1.74273 q^{7} -10.2198 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.77241 q^{2} -1.00000 q^{3} +5.68625 q^{4} +1.80856 q^{5} +2.77241 q^{6} -1.74273 q^{7} -10.2198 q^{8} +1.00000 q^{9} -5.01408 q^{10} +6.05260 q^{11} -5.68625 q^{12} -2.06905 q^{13} +4.83156 q^{14} -1.80856 q^{15} +16.9609 q^{16} -4.84760 q^{17} -2.77241 q^{18} -2.15275 q^{19} +10.2840 q^{20} +1.74273 q^{21} -16.7803 q^{22} +0.906101 q^{23} +10.2198 q^{24} -1.72909 q^{25} +5.73624 q^{26} -1.00000 q^{27} -9.90959 q^{28} +0.253515 q^{29} +5.01408 q^{30} +4.84625 q^{31} -26.5831 q^{32} -6.05260 q^{33} +13.4395 q^{34} -3.15184 q^{35} +5.68625 q^{36} +6.38729 q^{37} +5.96830 q^{38} +2.06905 q^{39} -18.4832 q^{40} +0.563910 q^{41} -4.83156 q^{42} +1.36456 q^{43} +34.4166 q^{44} +1.80856 q^{45} -2.51208 q^{46} -7.10291 q^{47} -16.9609 q^{48} -3.96290 q^{49} +4.79375 q^{50} +4.84760 q^{51} -11.7651 q^{52} -7.20499 q^{53} +2.77241 q^{54} +10.9465 q^{55} +17.8103 q^{56} +2.15275 q^{57} -0.702849 q^{58} +1.09328 q^{59} -10.2840 q^{60} -1.83056 q^{61} -13.4358 q^{62} -1.74273 q^{63} +39.7773 q^{64} -3.74200 q^{65} +16.7803 q^{66} +3.42619 q^{67} -27.5647 q^{68} -0.906101 q^{69} +8.73819 q^{70} -7.36120 q^{71} -10.2198 q^{72} +6.85163 q^{73} -17.7082 q^{74} +1.72909 q^{75} -12.2411 q^{76} -10.5480 q^{77} -5.73624 q^{78} +2.34085 q^{79} +30.6750 q^{80} +1.00000 q^{81} -1.56339 q^{82} +8.91361 q^{83} +9.90959 q^{84} -8.76720 q^{85} -3.78311 q^{86} -0.253515 q^{87} -61.8563 q^{88} +4.52553 q^{89} -5.01408 q^{90} +3.60579 q^{91} +5.15232 q^{92} -4.84625 q^{93} +19.6922 q^{94} -3.89339 q^{95} +26.5831 q^{96} -2.42178 q^{97} +10.9868 q^{98} +6.05260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) $ 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9 + 3 * q^10 - 57 * q^11 - 116 * q^12 + 6 * q^13 - 9 * q^14 + 20 * q^15 + 112 * q^16 - 30 * q^17 - 16 * q^18 + 3 * q^19 - 54 * q^20 + 33 * q^21 - 22 * q^22 - 58 * q^23 + 45 * q^24 + 126 * q^25 - 21 * q^26 - 116 * q^27 - 77 * q^28 - 38 * q^29 - 3 * q^30 + 17 * q^31 - 106 * q^32 + 57 * q^33 + 35 * q^34 - 72 * q^35 + 116 * q^36 - 41 * q^37 - 45 * q^38 - 6 * q^39 + 5 * q^40 - 39 * q^41 + 9 * q^42 - 118 * q^43 - 103 * q^44 - 20 * q^45 - 8 * q^46 - 65 * q^47 - 112 * q^48 + 165 * q^49 - 72 * q^50 + 30 * q^51 - 10 * q^52 - 58 * q^53 + 16 * q^54 + 14 * q^55 - 23 * q^56 - 3 * q^57 - 27 * q^58 - 75 * q^59 + 54 * q^60 + 45 * q^61 - 73 * q^62 - 33 * q^63 + 111 * q^64 - 86 * q^65 + 22 * q^66 - 127 * q^67 - 94 * q^68 + 58 * q^69 - 7 * q^70 - 61 * q^71 - 45 * q^72 + 15 * q^73 - 51 * q^74 - 126 * q^75 + 96 * q^76 - 57 * q^77 + 21 * q^78 + 7 * q^79 - 144 * q^80 + 116 * q^81 - 37 * q^82 - 194 * q^83 + 77 * q^84 + 3 * q^85 - 57 * q^86 + 38 * q^87 - 42 * q^88 - 56 * q^89 + 3 * q^90 - 39 * q^91 - 138 * q^92 - 17 * q^93 + 51 * q^94 - 127 * q^95 + 106 * q^96 + 57 * q^97 - 105 * q^98 - 57 * 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 $

$2$	−2.77241	−1.96039	−0.980195	−	0.198037i	$-0.936543\pi$
$2$	−2.77241	−1.96039	−0.980195	+	0.198037i	$0.936543\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.68625	2.84313
$5$	1.80856	0.808815	0.404407	−	0.914579i	$-0.367478\pi$
$5$	1.80856	0.808815	0.404407	+	0.914579i	$0.367478\pi$
$6$	2.77241	1.13183
$7$	−1.74273	−0.658690	−0.329345	−	0.944210i	$-0.606828\pi$
$7$	−1.74273	−0.658690	−0.329345	+	0.944210i	$0.606828\pi$
$8$	−10.2198	−3.61324
$9$	1.00000	0.333333
$10$	−5.01408	−1.58559
$11$	6.05260	1.82493	0.912464	−	0.409158i	$-0.134177\pi$
$11$	6.05260	1.82493	0.912464	+	0.409158i	$0.134177\pi$
$12$	−5.68625	−1.64148
$13$	−2.06905	−0.573850	−0.286925	−	0.957953i	$-0.592633\pi$
$13$	−2.06905	−0.573850	−0.286925	+	0.957953i	$0.592633\pi$
$14$	4.83156	1.29129
$15$	−1.80856	−0.466969
$16$	16.9609	4.24024
$17$	−4.84760	−1.17572	−0.587858	−	0.808964i	$-0.700029\pi$
$17$	−4.84760	−1.17572	−0.587858	+	0.808964i	$0.700029\pi$
$18$	−2.77241	−0.653463
$19$	−2.15275	−0.493874	−0.246937	−	0.969031i	$-0.579424\pi$
$19$	−2.15275	−0.493874	−0.246937	+	0.969031i	$0.579424\pi$
$20$	10.2840	2.29956
$21$	1.74273	0.380295
$22$	−16.7803	−3.57757
$23$	0.906101	0.188935	0.0944676	−	0.995528i	$-0.469885\pi$
$23$	0.906101	0.188935	0.0944676	+	0.995528i	$0.469885\pi$
$24$	10.2198	2.08611
$25$	−1.72909	−0.345819
$26$	5.73624	1.12497
$27$	−1.00000	−0.192450
$28$	−9.90959	−1.87274
$29$	0.253515	0.0470766	0.0235383	−	0.999723i	$-0.492507\pi$
$29$	0.253515	0.0470766	0.0235383	+	0.999723i	$0.492507\pi$
$30$	5.01408	0.915442
$31$	4.84625	0.870413	0.435206	−	0.900331i	$-0.356675\pi$
$31$	4.84625	0.870413	0.435206	+	0.900331i	$0.356675\pi$
$32$	−26.5831	−4.69927
$33$	−6.05260	−1.05362
$34$	13.4395	2.30486
$35$	−3.15184	−0.532758
$36$	5.68625	0.947709
$37$	6.38729	1.05006	0.525032	−	0.851083i	$-0.324053\pi$
$37$	6.38729	1.05006	0.525032	+	0.851083i	$0.324053\pi$
$38$	5.96830	0.968186
$39$	2.06905	0.331313
$40$	−18.4832	−2.92244
$41$	0.563910	0.0880679	0.0440340	−	0.999030i	$-0.485979\pi$
$41$	0.563910	0.0880679	0.0440340	+	0.999030i	$0.485979\pi$
$42$	−4.83156	−0.745525
$43$	1.36456	0.208093	0.104047	−	0.994572i	$-0.466821\pi$
$43$	1.36456	0.208093	0.104047	+	0.994572i	$0.466821\pi$
$44$	34.4166	5.18850
$45$	1.80856	0.269605
$46$	−2.51208	−0.370386
$47$	−7.10291	−1.03607	−0.518033	−	0.855361i	$-0.673336\pi$
$47$	−7.10291	−1.03607	−0.518033	+	0.855361i	$0.673336\pi$
$48$	−16.9609	−2.44810
$49$	−3.96290	−0.566128
$50$	4.79375	0.677939
$51$	4.84760	0.678800
$52$	−11.7651	−1.63153
$53$	−7.20499	−0.989682	−0.494841	−	0.868983i	$-0.664774\pi$
$53$	−7.20499	−0.989682	−0.494841	+	0.868983i	$0.664774\pi$
$54$	2.77241	0.377277
$55$	10.9465	1.47603
$56$	17.8103	2.38001
$57$	2.15275	0.285138
$58$	−0.702849	−0.0922885
$59$	1.09328	0.142333	0.0711664	−	0.997464i	$-0.477328\pi$
$59$	1.09328	0.142333	0.0711664	+	0.997464i	$0.477328\pi$
$60$	−10.2840	−1.32765
$61$	−1.83056	−0.234380	−0.117190	−	0.993110i	$-0.537389\pi$
$61$	−1.83056	−0.234380	−0.117190	+	0.993110i	$0.537389\pi$
$62$	−13.4358	−1.70635
$63$	−1.74273	−0.219563
$64$	39.7773	4.97216
$65$	−3.74200	−0.464139
$66$	16.7803	2.06551
$67$	3.42619	0.418576	0.209288	−	0.977854i	$-0.432885\pi$
$67$	3.42619	0.418576	0.209288	+	0.977854i	$0.432885\pi$
$68$	−27.5647	−3.34271
$69$	−0.906101	−0.109082
$70$	8.73819	1.04441
$71$	−7.36120	−0.873614	−0.436807	−	0.899555i	$-0.643891\pi$
$71$	−7.36120	−0.873614	−0.436807	+	0.899555i	$0.643891\pi$
$72$	−10.2198	−1.20441
$73$	6.85163	0.801923	0.400961	−	0.916095i	$-0.368676\pi$
$73$	6.85163	0.801923	0.400961	+	0.916095i	$0.368676\pi$
$74$	−17.7082	−2.05853
$75$	1.72909	0.199658
$76$	−12.2411	−1.40415
$77$	−10.5480	−1.20206
$78$	−5.73624	−0.649502
$79$	2.34085	0.263367	0.131683	−	0.991292i	$-0.457962\pi$
$79$	2.34085	0.263367	0.131683	+	0.991292i	$0.457962\pi$
$80$	30.6750	3.42957
$81$	1.00000	0.111111
$82$	−1.56339	−0.172647
$83$	8.91361	0.978396	0.489198	−	0.872173i	$-0.337290\pi$
$83$	8.91361	0.978396	0.489198	+	0.872173i	$0.337290\pi$
$84$	9.90959	1.08123
$85$	−8.76720	−0.950936
$86$	−3.78311	−0.407944
$87$	−0.253515	−0.0271797
$88$	−61.8563	−6.59391
$89$	4.52553	0.479705	0.239853	−	0.970809i	$-0.422901\pi$
$89$	4.52553	0.479705	0.239853	+	0.970809i	$0.422901\pi$
$90$	−5.01408	−0.528531
$91$	3.60579	0.377989
$92$	5.15232	0.537166
$93$	−4.84625	−0.502533
$94$	19.6922	2.03109
$95$	−3.89339	−0.399453
$96$	26.5831	2.71313
$97$	−2.42178	−0.245894	−0.122947	−	0.992413i	$-0.539235\pi$
$97$	−2.42178	−0.245894	−0.122947	+	0.992413i	$0.539235\pi$
$98$	10.9868	1.10983
$99$	6.05260	0.608309
$100$	−9.83205	−0.983205
$101$	−10.1794	−1.01289	−0.506446	−	0.862272i	$-0.669041\pi$
$101$	−10.1794	−1.01289	−0.506446	+	0.862272i	$0.669041\pi$
$102$	−13.4395	−1.33071
$103$	9.35853	0.922124	0.461062	−	0.887368i	$-0.347469\pi$
$103$	9.35853	0.922124	0.461062	+	0.887368i	$0.347469\pi$
$104$	21.1452	2.07346
$105$	3.15184	0.307588
$106$	19.9752	1.94016
$107$	6.72754	0.650376	0.325188	−	0.945649i	$-0.394572\pi$
$107$	6.72754	0.650376	0.325188	+	0.945649i	$0.394572\pi$
$108$	−5.68625	−0.547160
$109$	8.96657	0.858841	0.429421	−	0.903105i	$-0.358718\pi$
$109$	8.96657	0.858841	0.429421	+	0.903105i	$0.358718\pi$
$110$	−30.3482	−2.89359
$111$	−6.38729	−0.606255
$112$	−29.5583	−2.79300
$113$	−0.0813277	−0.00765066	−0.00382533	−	0.999993i	$-0.501218\pi$
$113$	−0.0813277	−0.00765066	−0.00382533	+	0.999993i	$0.501218\pi$
$114$	−5.96830	−0.558982
$115$	1.63874	0.152814
$116$	1.44155	0.133845
$117$	−2.06905	−0.191283
$118$	−3.03101	−0.279028
$119$	8.44805	0.774432
$120$	18.4832	1.68727
$121$	25.6340	2.33036
$122$	5.07507	0.459475
$123$	−0.563910	−0.0508460
$124$	27.5570	2.47469
$125$	−12.1700	−1.08852
$126$	4.83156	0.430429
$127$	6.47881	0.574901	0.287451	−	0.957795i	$-0.407192\pi$
$127$	6.47881	0.574901	0.287451	+	0.957795i	$0.407192\pi$
$128$	−57.1128	−5.04810
$129$	−1.36456	−0.120143
$130$	10.3744	0.909892
$131$	−14.1053	−1.23239	−0.616194	−	0.787594i	$-0.711326\pi$
$131$	−14.1053	−1.23239	−0.616194	+	0.787594i	$0.711326\pi$
$132$	−34.4166	−2.99558
$133$	3.75166	0.325310
$134$	−9.49881	−0.820572
$135$	−1.80856	−0.155656
$136$	49.5415	4.24815
$137$	−6.23546	−0.532732	−0.266366	−	0.963872i	$-0.585823\pi$
$137$	−6.23546	−0.532732	−0.266366	+	0.963872i	$0.585823\pi$
$138$	2.51208	0.213843
$139$	−4.27442	−0.362552	−0.181276	−	0.983432i	$-0.558023\pi$
$139$	−4.27442	−0.362552	−0.181276	+	0.983432i	$0.558023\pi$
$140$	−17.9221	−1.51470
$141$	7.10291	0.598173
$142$	20.4083	1.71262
$143$	−12.5231	−1.04723
$144$	16.9609	1.41341
$145$	0.458499	0.0380763
$146$	−18.9955	−1.57208
$147$	3.96290	0.326854
$148$	36.3197	2.98546
$149$	−21.5340	−1.76414	−0.882068	−	0.471122i	$-0.843849\pi$
$149$	−21.5340	−1.76414	−0.882068	+	0.471122i	$0.843849\pi$
$150$	−4.79375	−0.391408
$151$	−9.64356	−0.784782	−0.392391	−	0.919799i	$-0.628352\pi$
$151$	−9.64356	−0.784782	−0.392391	+	0.919799i	$0.628352\pi$
$152$	22.0006	1.78449
$153$	−4.84760	−0.391905
$154$	29.2435	2.35651
$155$	8.76476	0.704003
$156$	11.7651	0.941963
$157$	4.91929	0.392602	0.196301	−	0.980544i	$-0.437107\pi$
$157$	4.91929	0.392602	0.196301	+	0.980544i	$0.437107\pi$
$158$	−6.48980	−0.516301
$159$	7.20499	0.571393
$160$	−48.0773	−3.80084
$161$	−1.57909	−0.124450
$162$	−2.77241	−0.217821
$163$	−18.7246	−1.46663	−0.733313	−	0.679891i	$-0.762027\pi$
$163$	−18.7246	−1.46663	−0.733313	+	0.679891i	$0.762027\pi$
$164$	3.20653	0.250388
$165$	−10.9465	−0.852185
$166$	−24.7122	−1.91804
$167$	−6.01328	−0.465321	−0.232661	−	0.972558i	$-0.574743\pi$
$167$	−6.01328	−0.465321	−0.232661	+	0.972558i	$0.574743\pi$
$168$	−17.8103	−1.37410
$169$	−8.71905	−0.670696
$170$	24.3063	1.86421
$171$	−2.15275	−0.164625
$172$	7.75922	0.591635
$173$	−17.6869	−1.34471	−0.672355	−	0.740229i	$-0.734717\pi$
$173$	−17.6869	−1.34471	−0.672355	+	0.740229i	$0.734717\pi$
$174$	0.702849	0.0532828
$175$	3.01334	0.227787
$176$	102.658	7.73812
$177$	−1.09328	−0.0821758
$178$	−12.5466	−0.940409
$179$	20.9189	1.56355	0.781775	−	0.623561i	$-0.214315\pi$
$179$	20.9189	1.56355	0.781775	+	0.623561i	$0.214315\pi$
$180$	10.2840	0.766521
$181$	0.695740	0.0517140	0.0258570	−	0.999666i	$-0.491769\pi$
$181$	0.695740	0.0517140	0.0258570	+	0.999666i	$0.491769\pi$
$182$	−9.99672	−0.741006
$183$	1.83056	0.135319
$184$	−9.26017	−0.682669
$185$	11.5518	0.849307
$186$	13.4358	0.985160
$187$	−29.3406	−2.14560
$188$	−40.3889	−2.94567
$189$	1.74273	0.126765
$190$	10.7941	0.783083
$191$	−25.5089	−1.84576	−0.922879	−	0.385090i	$-0.874170\pi$
$191$	−25.5089	−1.84576	−0.922879	+	0.385090i	$0.874170\pi$
$192$	−39.7773	−2.87068
$193$	−18.4261	−1.32634	−0.663169	−	0.748469i	$-0.730789\pi$
$193$	−18.4261	−1.32634	−0.663169	+	0.748469i	$0.730789\pi$
$194$	6.71416	0.482048
$195$	3.74200	0.267971
$196$	−22.5340	−1.60957
$197$	10.3868	0.740028	0.370014	−	0.929026i	$-0.379353\pi$
$197$	10.3868	0.740028	0.370014	+	0.929026i	$0.379353\pi$
$198$	−16.7803	−1.19252
$199$	3.87864	0.274949	0.137475	−	0.990505i	$-0.456101\pi$
$199$	3.87864	0.274949	0.137475	+	0.990505i	$0.456101\pi$
$200$	17.6710	1.24953
$201$	−3.42619	−0.241665
$202$	28.2216	1.98566
$203$	−0.441809	−0.0310089
$204$	27.5647	1.92991
$205$	1.01987	0.0712306
$206$	−25.9457	−1.80772
$207$	0.906101	0.0629784
$208$	−35.0930	−2.43326
$209$	−13.0297	−0.901285
$210$	−8.73819	−0.602992
$211$	−0.880365	−0.0606069	−0.0303034	−	0.999541i	$-0.509647\pi$
$211$	−0.880365	−0.0606069	−0.0303034	+	0.999541i	$0.509647\pi$
$212$	−40.9694	−2.81379
$213$	7.36120	0.504381
$214$	−18.6515	−1.27499
$215$	2.46789	0.168309
$216$	10.2198	0.695369
$217$	−8.44570	−0.573332
$218$	−24.8590	−1.68366
$219$	−6.85163	−0.462990
$220$	62.2447	4.19653
$221$	10.0299	0.674685
$222$	17.7082	1.18850
$223$	3.53281	0.236574	0.118287	−	0.992979i	$-0.462260\pi$
$223$	3.53281	0.236574	0.118287	+	0.992979i	$0.462260\pi$
$224$	46.3271	3.09536
$225$	−1.72909	−0.115273
$226$	0.225474	0.0149983
$227$	−10.8963	−0.723212	−0.361606	−	0.932331i	$-0.617771\pi$
$227$	−10.8963	−0.723212	−0.361606	+	0.932331i	$0.617771\pi$
$228$	12.2411	0.810684
$229$	17.4075	1.15032	0.575161	−	0.818040i	$-0.304939\pi$
$229$	17.4075	1.15032	0.575161	+	0.818040i	$0.304939\pi$
$230$	−4.54326	−0.299574
$231$	10.5480	0.694010
$232$	−2.59088	−0.170099
$233$	−24.2687	−1.58990	−0.794948	−	0.606678i	$-0.792502\pi$
$233$	−24.2687	−1.58990	−0.794948	+	0.606678i	$0.792502\pi$
$234$	5.73624	0.374990
$235$	−12.8461	−0.837986
$236$	6.21666	0.404670
$237$	−2.34085	−0.152055
$238$	−23.4215	−1.51819
$239$	−5.69984	−0.368692	−0.184346	−	0.982861i	$-0.559017\pi$
$239$	−5.69984	−0.368692	−0.184346	+	0.982861i	$0.559017\pi$
$240$	−30.6750	−1.98006
$241$	−2.83794	−0.182808	−0.0914038	−	0.995814i	$-0.529135\pi$
$241$	−2.83794	−0.182808	−0.0914038	+	0.995814i	$0.529135\pi$
$242$	−71.0678	−4.56841
$243$	−1.00000	−0.0641500
$244$	−10.4090	−0.666371
$245$	−7.16715	−0.457893
$246$	1.56339	0.0996780
$247$	4.45414	0.283410
$248$	−49.5277	−3.14501
$249$	−8.91361	−0.564877
$250$	33.7402	2.13392
$251$	−18.0096	−1.13675	−0.568376	−	0.822769i	$-0.692428\pi$
$251$	−18.0096	−1.13675	−0.568376	+	0.822769i	$0.692428\pi$
$252$	−9.90959	−0.624246
$253$	5.48427	0.344793
$254$	−17.9619	−1.12703
$255$	8.76720	0.549023
$256$	78.7854	4.92409
$257$	20.2583	1.26368	0.631839	−	0.775100i	$-0.282301\pi$
$257$	20.2583	1.26368	0.631839	+	0.775100i	$0.282301\pi$
$258$	3.78311	0.235526
$259$	−11.1313	−0.691666
$260$	−21.2780	−1.31960
$261$	0.253515	0.0156922
$262$	39.1057	2.41596
$263$	−14.8233	−0.914046	−0.457023	−	0.889455i	$-0.651084\pi$
$263$	−14.8233	−0.914046	−0.457023	+	0.889455i	$0.651084\pi$
$264$	61.8563	3.80699
$265$	−13.0307	−0.800470
$266$	−10.4011	−0.637734
$267$	−4.52553	−0.276958
$268$	19.4822	1.19006
$269$	3.98012	0.242672	0.121336	−	0.992611i	$-0.461282\pi$
$269$	3.98012	0.242672	0.121336	+	0.992611i	$0.461282\pi$
$270$	5.01408	0.305147
$271$	−7.01043	−0.425854	−0.212927	−	0.977068i	$-0.568300\pi$
$271$	−7.01043	−0.425854	−0.212927	+	0.977068i	$0.568300\pi$
$272$	−82.2199	−4.98531
$273$	−3.60579	−0.218232
$274$	17.2873	1.04436
$275$	−10.4655	−0.631094
$276$	−5.15232	−0.310133
$277$	−0.260345	−0.0156426	−0.00782129	−	0.999969i	$-0.502490\pi$
$277$	−0.260345	−0.0156426	−0.00782129	+	0.999969i	$0.502490\pi$
$278$	11.8504	0.710742
$279$	4.84625	0.290138
$280$	32.2111	1.92498
$281$	5.48732	0.327346	0.163673	−	0.986515i	$-0.447666\pi$
$281$	5.48732	0.327346	0.163673	+	0.986515i	$0.447666\pi$
$282$	−19.6922	−1.17265
$283$	14.5978	0.867747	0.433874	−	0.900974i	$-0.357146\pi$
$283$	14.5978	0.867747	0.433874	+	0.900974i	$0.357146\pi$
$284$	−41.8576	−2.48379
$285$	3.89339	0.230624
$286$	34.7192	2.05299
$287$	−0.982742	−0.0580094
$288$	−26.5831	−1.56642
$289$	6.49922	0.382307
$290$	−1.27115	−0.0746443
$291$	2.42178	0.141967
$292$	38.9601	2.27997
$293$	18.0787	1.05617	0.528083	−	0.849193i	$-0.322911\pi$
$293$	18.0787	1.05617	0.528083	+	0.849193i	$0.322911\pi$
$294$	−10.9868	−0.640761
$295$	1.97727	0.115121
$296$	−65.2768	−3.79414
$297$	−6.05260	−0.351207
$298$	59.7011	3.45839
$299$	−1.87477	−0.108420
$300$	9.83205	0.567654
$301$	−2.37805	−0.137069
$302$	26.7359	1.53848
$303$	10.1794	0.584794
$304$	−36.5127	−2.09414
$305$	−3.31069	−0.189570
$306$	13.4395	0.768287
$307$	23.5650	1.34492	0.672462	−	0.740132i	$-0.265237\pi$
$307$	23.5650	1.34492	0.672462	+	0.740132i	$0.265237\pi$
$308$	−59.9788	−3.41761
$309$	−9.35853	−0.532388
$310$	−24.2995	−1.38012
$311$	30.3891	1.72321	0.861603	−	0.507583i	$-0.169461\pi$
$311$	30.3891	1.72321	0.861603	+	0.507583i	$0.169461\pi$
$312$	−21.1452	−1.19711
$313$	7.07389	0.399840	0.199920	−	0.979812i	$-0.435932\pi$
$313$	7.07389	0.399840	0.199920	+	0.979812i	$0.435932\pi$
$314$	−13.6383	−0.769653
$315$	−3.15184	−0.177586
$316$	13.3107	0.748784
$317$	26.5860	1.49322	0.746608	−	0.665264i	$-0.231681\pi$
$317$	26.5860	1.49322	0.746608	+	0.665264i	$0.231681\pi$
$318$	−19.9752	−1.12015
$319$	1.53443	0.0859114
$320$	71.9399	4.02156
$321$	−6.72754	−0.375494
$322$	4.37788	0.243970
$323$	10.4357	0.580656
$324$	5.68625	0.315903
$325$	3.57757	0.198448
$326$	51.9123	2.87516
$327$	−8.96657	−0.495852
$328$	−5.76304	−0.318211
$329$	12.3785	0.682446
$330$	30.3482	1.67061
$331$	−1.27797	−0.0702437	−0.0351218	−	0.999383i	$-0.511182\pi$
$331$	−1.27797	−0.0702437	−0.0351218	+	0.999383i	$0.511182\pi$
$332$	50.6850	2.78170
$333$	6.38729	0.350021
$334$	16.6713	0.912211
$335$	6.19649	0.338551
$336$	29.5583	1.61254
$337$	−6.33371	−0.345019	−0.172510	−	0.985008i	$-0.555188\pi$
$337$	−6.33371	−0.345019	−0.172510	+	0.985008i	$0.555188\pi$
$338$	24.1728	1.31482
$339$	0.0813277	0.00441711
$340$	−49.8525	−2.70363
$341$	29.3324	1.58844
$342$	5.96830	0.322729
$343$	19.1054	1.03159
$344$	−13.9455	−0.751891
$345$	−1.63874	−0.0882269
$346$	49.0353	2.63616
$347$	−22.6313	−1.21491	−0.607455	−	0.794354i	$-0.707809\pi$
$347$	−22.6313	−1.21491	−0.607455	+	0.794354i	$0.707809\pi$
$348$	−1.44155	−0.0772753
$349$	8.19136	0.438473	0.219237	−	0.975672i	$-0.429643\pi$
$349$	8.19136	0.438473	0.219237	+	0.975672i	$0.429643\pi$
$350$	−8.35421	−0.446551
$351$	2.06905	0.110438
$352$	−160.897	−8.57583
$353$	−19.3536	−1.03009	−0.515044	−	0.857164i	$-0.672224\pi$
$353$	−19.3536	−1.03009	−0.515044	+	0.857164i	$0.672224\pi$
$354$	3.03101	0.161097
$355$	−13.3132	−0.706592
$356$	25.7333	1.36386
$357$	−8.44805	−0.447118
$358$	−57.9956	−3.06516
$359$	−1.39620	−0.0736884	−0.0368442	−	0.999321i	$-0.511731\pi$
$359$	−1.39620	−0.0736884	−0.0368442	+	0.999321i	$0.511731\pi$
$360$	−18.4832	−0.974148
$361$	−14.3657	−0.756088
$362$	−1.92888	−0.101379
$363$	−25.6340	−1.34543
$364$	20.5034	1.07467
$365$	12.3916	0.648607
$366$	−5.07507	−0.265278
$367$	−22.5325	−1.17619	−0.588094	−	0.808793i	$-0.700121\pi$
$367$	−22.5325	−1.17619	−0.588094	+	0.808793i	$0.700121\pi$
$368$	15.3683	0.801130
$369$	0.563910	0.0293560
$370$	−32.0264	−1.66497
$371$	12.5564	0.651893
$372$	−27.5570	−1.42876
$373$	−1.61342	−0.0835395	−0.0417697	−	0.999127i	$-0.513300\pi$
$373$	−1.61342	−0.0835395	−0.0417697	+	0.999127i	$0.513300\pi$
$374$	81.3441	4.20620
$375$	12.1700	0.628456
$376$	72.5903	3.74356
$377$	−0.524535	−0.0270149
$378$	−4.83156	−0.248508
$379$	−26.3322	−1.35259	−0.676297	−	0.736629i	$-0.736416\pi$
$379$	−26.3322	−1.35259	−0.676297	+	0.736629i	$0.736416\pi$
$380$	−22.1388	−1.13569
$381$	−6.47881	−0.331919
$382$	70.7210	3.61840
$383$	−10.8072	−0.552222	−0.276111	−	0.961126i	$-0.589046\pi$
$383$	−10.8072	−0.552222	−0.276111	+	0.961126i	$0.589046\pi$
$384$	57.1128	2.91452
$385$	−19.0768	−0.972245
$386$	51.0846	2.60014
$387$	1.36456	0.0693644
$388$	−13.7708	−0.699108
$389$	6.16320	0.312486	0.156243	−	0.987719i	$-0.450062\pi$
$389$	6.16320	0.312486	0.156243	+	0.987719i	$0.450062\pi$
$390$	−10.3744	−0.525327
$391$	−4.39242	−0.222134
$392$	40.5000	2.04556
$393$	14.1053	0.711519
$394$	−28.7964	−1.45074
$395$	4.23358	0.213015
$396$	34.4166	1.72950
$397$	29.7744	1.49433	0.747166	−	0.664637i	$-0.231414\pi$
$397$	29.7744	1.49433	0.747166	+	0.664637i	$0.231414\pi$
$398$	−10.7532	−0.539008
$399$	−3.75166	−0.187818
$400$	−29.3271	−1.46635
$401$	−24.7617	−1.23654	−0.618270	−	0.785966i	$-0.712166\pi$
$401$	−24.7617	−1.23654	−0.618270	+	0.785966i	$0.712166\pi$
$402$	9.49881	0.473758
$403$	−10.0271	−0.499486
$404$	−57.8829	−2.87978
$405$	1.80856	0.0898683
$406$	1.22487	0.0607895
$407$	38.6597	1.91629
$408$	−49.5415	−2.45267
$409$	28.9547	1.43172	0.715858	−	0.698246i	$-0.246036\pi$
$409$	28.9547	1.43172	0.715858	+	0.698246i	$0.246036\pi$
$410$	−2.82749	−0.139640
$411$	6.23546	0.307573
$412$	53.2150	2.62171
$413$	−1.90529	−0.0937531
$414$	−2.51208	−0.123462
$415$	16.1208	0.791341
$416$	55.0017	2.69668
$417$	4.27442	0.209319
$418$	36.1237	1.76687
$419$	−19.5261	−0.953913	−0.476956	−	0.878927i	$-0.658260\pi$
$419$	−19.5261	−0.953913	−0.476956	+	0.878927i	$0.658260\pi$
$420$	17.9221	0.874511
$421$	13.2394	0.645251	0.322625	−	0.946527i	$-0.395435\pi$
$421$	13.2394	0.645251	0.322625	+	0.946527i	$0.395435\pi$
$422$	2.44073	0.118813
$423$	−7.10291	−0.345355
$424$	73.6336	3.57596
$425$	8.38195	0.406584
$426$	−20.4083	−0.988783
$427$	3.19018	0.154383
$428$	38.2545	1.84910
$429$	12.5231	0.604621
$430$	−6.84201	−0.329951
$431$	−15.1248	−0.728535	−0.364268	−	0.931294i	$-0.618681\pi$
$431$	−15.1248	−0.728535	−0.364268	+	0.931294i	$0.618681\pi$
$432$	−16.9609	−0.816034
$433$	−2.34420	−0.112655	−0.0563274	−	0.998412i	$-0.517939\pi$
$433$	−2.34420	−0.112655	−0.0563274	+	0.998412i	$0.517939\pi$
$434$	23.4149	1.12395
$435$	−0.458499	−0.0219834
$436$	50.9861	2.44179
$437$	−1.95061	−0.0933102
$438$	18.9955	0.907641
$439$	−22.7367	−1.08516	−0.542582	−	0.840003i	$-0.682553\pi$
$439$	−22.7367	−1.08516	−0.542582	+	0.840003i	$0.682553\pi$
$440$	−111.871	−5.33325
$441$	−3.96290	−0.188709
$442$	−27.8070	−1.32264
$443$	−13.4450	−0.638791	−0.319395	−	0.947622i	$-0.603480\pi$
$443$	−13.4450	−0.638791	−0.319395	+	0.947622i	$0.603480\pi$
$444$	−36.3197	−1.72366
$445$	8.18471	0.387993
$446$	−9.79439	−0.463778
$447$	21.5340	1.01852
$448$	−69.3211	−3.27511
$449$	−19.4455	−0.917690	−0.458845	−	0.888516i	$-0.651737\pi$
$449$	−19.4455	−0.917690	−0.458845	+	0.888516i	$0.651737\pi$
$450$	4.79375	0.225980
$451$	3.41312	0.160718
$452$	−0.462450	−0.0217518
$453$	9.64356	0.453094
$454$	30.2089	1.41778
$455$	6.52130	0.305723
$456$	−22.0006	−1.03027
$457$	39.7290	1.85845	0.929223	−	0.369520i	$-0.120478\pi$
$457$	39.7290	1.85845	0.929223	+	0.369520i	$0.120478\pi$
$458$	−48.2608	−2.25508
$459$	4.84760	0.226267
$460$	9.31830	0.434468
$461$	−23.4897	−1.09402	−0.547011	−	0.837125i	$-0.684234\pi$
$461$	−23.4897	−1.09402	−0.547011	+	0.837125i	$0.684234\pi$
$462$	−29.2435	−1.36053
$463$	19.0496	0.885309	0.442654	−	0.896692i	$-0.354037\pi$
$463$	19.0496	0.885309	0.442654	+	0.896692i	$0.354037\pi$
$464$	4.29986	0.199616
$465$	−8.76476	−0.406456
$466$	67.2828	3.11681
$467$	35.8055	1.65688	0.828440	−	0.560078i	$-0.189229\pi$
$467$	35.8055	1.65688	0.828440	+	0.560078i	$0.189229\pi$
$468$	−11.7651	−0.543843
$469$	−5.97093	−0.275712
$470$	35.6146	1.64278
$471$	−4.91929	−0.226669
$472$	−11.1731	−0.514283
$473$	8.25912	0.379755
$474$	6.48980	0.298086
$475$	3.72230	0.170791
$476$	48.0377	2.20181
$477$	−7.20499	−0.329894
$478$	15.8023	0.722780
$479$	10.5109	0.480256	0.240128	−	0.970741i	$-0.422811\pi$
$479$	10.5109	0.480256	0.240128	+	0.970741i	$0.422811\pi$
$480$	48.0773	2.19442
$481$	−13.2156	−0.602579
$482$	7.86792	0.358374
$483$	1.57909	0.0718510
$484$	145.761	6.62550
$485$	−4.37994	−0.198883
$486$	2.77241	0.125759
$487$	1.19285	0.0540530	0.0270265	−	0.999635i	$-0.491396\pi$
$487$	1.19285	0.0540530	0.0270265	+	0.999635i	$0.491396\pi$
$488$	18.7080	0.846870
$489$	18.7246	0.846757
$490$	19.8703	0.897648
$491$	9.83261	0.443739	0.221870	−	0.975076i	$-0.428784\pi$
$491$	9.83261	0.443739	0.221870	+	0.975076i	$0.428784\pi$
$492$	−3.20653	−0.144562
$493$	−1.22894	−0.0553487
$494$	−12.3487	−0.555594
$495$	10.9465	0.492009
$496$	82.1970	3.69076
$497$	12.8286	0.575440
$498$	24.7122	1.10738
$499$	−27.5056	−1.23132	−0.615660	−	0.788012i	$-0.711110\pi$
$499$	−27.5056	−1.23132	−0.615660	+	0.788012i	$0.711110\pi$
$500$	−69.2017	−3.09479
$501$	6.01328	0.268653
$502$	49.9298	2.22848
$503$	−8.81453	−0.393020	−0.196510	−	0.980502i	$-0.562961\pi$
$503$	−8.81453	−0.393020	−0.196510	+	0.980502i	$0.562961\pi$
$504$	17.8103	0.793335
$505$	−18.4102	−0.819242
$506$	−15.2046	−0.675928
$507$	8.71905	0.387226
$508$	36.8401	1.63452
$509$	41.4691	1.83808	0.919042	−	0.394159i	$-0.128964\pi$
$509$	41.4691	1.83808	0.919042	+	0.394159i	$0.128964\pi$
$510$	−24.3063	−1.07630
$511$	−11.9405	−0.528218
$512$	−104.200	−4.60502
$513$	2.15275	0.0950462
$514$	−56.1643	−2.47730
$515$	16.9255	0.745827
$516$	−7.75922	−0.341581
$517$	−42.9911	−1.89075
$518$	30.8606	1.35593
$519$	17.6869	0.776369
$520$	38.2425	1.67705
$521$	19.6246	0.859769	0.429884	−	0.902884i	$-0.358554\pi$
$521$	19.6246	0.859769	0.429884	+	0.902884i	$0.358554\pi$
$522$	−0.702849	−0.0307628
$523$	−26.0028	−1.13702	−0.568510	−	0.822676i	$-0.692480\pi$
$523$	−26.0028	−1.13702	−0.568510	+	0.822676i	$0.692480\pi$
$524$	−80.2064	−3.50383
$525$	−3.01334	−0.131513
$526$	41.0963	1.79189
$527$	−23.4927	−1.02336
$528$	−102.658	−4.46761
$529$	−22.1790	−0.964304
$530$	36.1264	1.56923
$531$	1.09328	0.0474442
$532$	21.3329	0.924897
$533$	−1.16676	−0.0505378
$534$	12.5466	0.542945
$535$	12.1672	0.526033
$536$	−35.0150	−1.51242
$537$	−20.9189	−0.902716
$538$	−11.0345	−0.475732
$539$	−23.9858	−1.03314
$540$	−10.2840	−0.442551
$541$	−22.4100	−0.963483	−0.481742	−	0.876313i	$-0.659996\pi$
$541$	−22.4100	−0.963483	−0.481742	+	0.876313i	$0.659996\pi$
$542$	19.4358	0.834839
$543$	−0.695740	−0.0298571
$544$	128.864	5.52501
$545$	16.2166	0.694644
$546$	9.99672	0.427820
$547$	−42.0532	−1.79806	−0.899032	−	0.437883i	$-0.855728\pi$
$547$	−42.0532	−1.79806	−0.899032	+	0.437883i	$0.855728\pi$
$548$	−35.4564	−1.51462
$549$	−1.83056	−0.0781265
$550$	29.0147	1.23719
$551$	−0.545755	−0.0232499
$552$	9.26017	0.394139
$553$	−4.07947	−0.173477
$554$	0.721782	0.0306656
$555$	−11.5518	−0.490348
$556$	−24.3054	−1.03078
$557$	2.85600	0.121013	0.0605064	−	0.998168i	$-0.480728\pi$
$557$	2.85600	0.121013	0.0605064	+	0.998168i	$0.480728\pi$
$558$	−13.4358	−0.568782
$559$	−2.82333	−0.119414
$560$	−53.4582	−2.25902
$561$	29.3406	1.23876
$562$	−15.2131	−0.641726
$563$	−23.0639	−0.972030	−0.486015	−	0.873951i	$-0.661550\pi$
$563$	−23.0639	−0.972030	−0.486015	+	0.873951i	$0.661550\pi$
$564$	40.3889	1.70068
$565$	−0.147086	−0.00618797
$566$	−40.4710	−1.70112
$567$	−1.74273	−0.0731877
$568$	75.2299	3.15658
$569$	28.0560	1.17617	0.588083	−	0.808800i	$-0.299883\pi$
$569$	28.0560	1.17617	0.588083	+	0.808800i	$0.299883\pi$
$570$	−10.7941	−0.452113
$571$	46.0441	1.92689	0.963443	−	0.267915i	$-0.0863345\pi$
$571$	46.0441	1.92689	0.963443	+	0.267915i	$0.0863345\pi$
$572$	−71.2095	−2.97742
$573$	25.5089	1.06565
$574$	2.72456	0.113721
$575$	−1.56673	−0.0653373
$576$	39.7773	1.65739
$577$	27.1694	1.13108	0.565538	−	0.824722i	$-0.308668\pi$
$577$	27.1694	1.13108	0.565538	+	0.824722i	$0.308668\pi$
$578$	−18.0185	−0.749471
$579$	18.4261	0.765762
$580$	2.60714	0.108256
$581$	−15.5340	−0.644459
$582$	−6.71416	−0.278311
$583$	−43.6089	−1.80610
$584$	−70.0223	−2.89754
$585$	−3.74200	−0.154713
$586$	−50.1214	−2.07050
$587$	47.7895	1.97248	0.986242	−	0.165309i	$-0.0528622\pi$
$587$	47.7895	1.97248	0.986242	+	0.165309i	$0.0528622\pi$
$588$	22.5340	0.929287
$589$	−10.4328	−0.429874
$590$	−5.48179	−0.225682
$591$	−10.3868	−0.427256
$592$	108.334	4.45252
$593$	−13.4343	−0.551679	−0.275840	−	0.961204i	$-0.588956\pi$
$593$	−13.4343	−0.551679	−0.275840	+	0.961204i	$0.588956\pi$
$594$	16.7803	0.688503
$595$	15.2789	0.626372
$596$	−122.448	−5.01566
$597$	−3.87864	−0.158742
$598$	5.19762	0.212546
$599$	5.05554	0.206564	0.103282	−	0.994652i	$-0.467066\pi$
$599$	5.05554	0.206564	0.103282	+	0.994652i	$0.467066\pi$
$600$	−17.6710	−0.721414
$601$	−40.3347	−1.64529	−0.822643	−	0.568558i	$-0.807502\pi$
$601$	−40.3347	−1.64529	−0.822643	+	0.568558i	$0.807502\pi$
$602$	6.59294	0.268708
$603$	3.42619	0.139525
$604$	−54.8357	−2.23123
$605$	46.3607	1.88483
$606$	−28.2216	−1.14642
$607$	−42.4968	−1.72489	−0.862447	−	0.506147i	$-0.831069\pi$
$607$	−42.4968	−1.72489	−0.862447	+	0.506147i	$0.831069\pi$
$608$	57.2267	2.32085
$609$	0.441809	0.0179030
$610$	9.17859	0.371630
$611$	14.6963	0.594547
$612$	−27.5647	−1.11424
$613$	14.4389	0.583180	0.291590	−	0.956543i	$-0.405816\pi$
$613$	14.4389	0.583180	0.291590	+	0.956543i	$0.405816\pi$
$614$	−65.3317	−2.63657
$615$	−1.01987	−0.0411250
$616$	107.799	4.34334
$617$	0.757081	0.0304789	0.0152395	−	0.999884i	$-0.495149\pi$
$617$	0.757081	0.0304789	0.0152395	+	0.999884i	$0.495149\pi$
$618$	25.9457	1.04369
$619$	6.64991	0.267282	0.133641	−	0.991030i	$-0.457333\pi$
$619$	6.64991	0.267282	0.133641	+	0.991030i	$0.457333\pi$
$620$	49.8386	2.00157
$621$	−0.906101	−0.0363606
$622$	−84.2509	−3.37815
$623$	−7.88677	−0.315977
$624$	35.0930	1.40484
$625$	−13.3648	−0.534591
$626$	−19.6117	−0.783842
$627$	13.0297	0.520357
$628$	27.9723	1.11622
$629$	−30.9630	−1.23458
$630$	8.73819	0.348138
$631$	34.1537	1.35964	0.679819	−	0.733380i	$-0.262058\pi$
$631$	34.1537	1.35964	0.679819	+	0.733380i	$0.262058\pi$
$632$	−23.9230	−0.951607
$633$	0.880365	0.0349914
$634$	−73.7072	−2.92729
$635$	11.7173	0.464989
$636$	40.9694	1.62454
$637$	8.19942	0.324873
$638$	−4.25406	−0.168420
$639$	−7.36120	−0.291205
$640$	−103.292	−4.08298
$641$	9.89010	0.390636	0.195318	−	0.980740i	$-0.437426\pi$
$641$	9.89010	0.390636	0.195318	+	0.980740i	$0.437426\pi$
$642$	18.6515	0.736115
$643$	−7.17903	−0.283113	−0.141557	−	0.989930i	$-0.545211\pi$
$643$	−7.17903	−0.283113	−0.141557	+	0.989930i	$0.545211\pi$
$644$	−8.97909	−0.353826
$645$	−2.46789	−0.0971731
$646$	−28.9319	−1.13831
$647$	−26.9321	−1.05881	−0.529405	−	0.848369i	$-0.677585\pi$
$647$	−26.9321	−1.05881	−0.529405	+	0.848369i	$0.677585\pi$
$648$	−10.2198	−0.401471
$649$	6.61718	0.259747
$650$	−9.91850	−0.389035
$651$	8.44570	0.331013
$652$	−106.473	−4.16980
$653$	−27.5257	−1.07716	−0.538582	−	0.842573i	$-0.681040\pi$
$653$	−27.5257	−1.07716	−0.538582	+	0.842573i	$0.681040\pi$
$654$	24.8590	0.972063
$655$	−25.5104	−0.996774
$656$	9.56445	0.373429
$657$	6.85163	0.267308
$658$	−34.3181	−1.33786
$659$	−26.9544	−1.04999	−0.524997	−	0.851104i	$-0.675934\pi$
$659$	−26.9544	−1.04999	−0.524997	+	0.851104i	$0.675934\pi$
$660$	−62.2447	−2.42287
$661$	48.3098	1.87903	0.939516	−	0.342505i	$-0.111275\pi$
$661$	48.3098	1.87903	0.939516	+	0.342505i	$0.111275\pi$
$662$	3.54306	0.137705
$663$	−10.0299	−0.389529
$664$	−91.0953	−3.53518
$665$	6.78511	0.263115
$666$	−17.7082	−0.686178
$667$	0.229711	0.00889443
$668$	−34.1930	−1.32297
$669$	−3.53281	−0.136586
$670$	−17.1792	−0.663691
$671$	−11.0797	−0.427726
$672$	−46.3271	−1.78711
$673$	−37.6922	−1.45293	−0.726464	−	0.687205i	$-0.758837\pi$
$673$	−37.6922	−1.45293	−0.726464	+	0.687205i	$0.758837\pi$
$674$	17.5596	0.676372
$675$	1.72909	0.0665528
$676$	−49.5787	−1.90687
$677$	7.95521	0.305743	0.152872	−	0.988246i	$-0.451148\pi$
$677$	7.95521	0.305743	0.152872	+	0.988246i	$0.451148\pi$
$678$	−0.225474	−0.00865926
$679$	4.22050	0.161968
$680$	89.5990	3.43596
$681$	10.8963	0.417546
$682$	−81.3215	−3.11396
$683$	36.7257	1.40527	0.702634	−	0.711551i	$-0.252007\pi$
$683$	36.7257	1.40527	0.702634	+	0.711551i	$0.252007\pi$
$684$	−12.2411	−0.468049
$685$	−11.2772	−0.430881
$686$	−52.9679	−2.02232
$687$	−17.4075	−0.664138
$688$	23.1442	0.882364
$689$	14.9075	0.567929
$690$	4.54326	0.172959
$691$	−16.5178	−0.628368	−0.314184	−	0.949362i	$-0.601731\pi$
$691$	−16.5178	−0.628368	−0.314184	+	0.949362i	$0.601731\pi$
$692$	−100.572	−3.82318
$693$	−10.5480	−0.400687
$694$	62.7431	2.38169
$695$	−7.73057	−0.293237
$696$	2.59088	0.0982069
$697$	−2.73361	−0.103543
$698$	−22.7098	−0.859578
$699$	24.2687	0.917927
$700$	17.1346	0.647627
$701$	4.88666	0.184567	0.0922833	−	0.995733i	$-0.470583\pi$
$701$	4.88666	0.184567	0.0922833	+	0.995733i	$0.470583\pi$
$702$	−5.73624	−0.216501
$703$	−13.7502	−0.518600
$704$	240.756	9.07384
$705$	12.8461	0.483811
$706$	53.6560	2.01937
$707$	17.7400	0.667182
$708$	−6.21666	−0.233636
$709$	−37.8680	−1.42216	−0.711081	−	0.703110i	$-0.751794\pi$
$709$	−37.8680	−1.42216	−0.711081	+	0.703110i	$0.751794\pi$
$710$	36.9096	1.38519
$711$	2.34085	0.0877888
$712$	−46.2500	−1.73329
$713$	4.39119	0.164452
$714$	23.4215	0.876526
$715$	−22.6489	−0.847019
$716$	118.950	4.44537
$717$	5.69984	0.212865
$718$	3.87082	0.144458
$719$	−48.8334	−1.82118	−0.910589	−	0.413312i	$-0.864372\pi$
$719$	−48.8334	−1.82118	−0.910589	+	0.413312i	$0.864372\pi$
$720$	30.6750	1.14319
$721$	−16.3094	−0.607393
$722$	39.8275	1.48223
$723$	2.83794	0.105544
$724$	3.95615	0.147029
$725$	−0.438352	−0.0162800
$726$	71.0678	2.63757
$727$	0.362619	0.0134488	0.00672439	−	0.999977i	$-0.497860\pi$
$727$	0.362619	0.0134488	0.00672439	+	0.999977i	$0.497860\pi$
$728$	−36.8504	−1.36577
$729$	1.00000	0.0370370
$730$	−34.3546	−1.27152
$731$	−6.61483	−0.244658
$732$	10.4090	0.384729
$733$	16.5921	0.612841	0.306421	−	0.951896i	$-0.400869\pi$
$733$	16.5921	0.612841	0.306421	+	0.951896i	$0.400869\pi$
$734$	62.4693	2.30579
$735$	7.16715	0.264364
$736$	−24.0870	−0.887858
$737$	20.7374	0.763871
$738$	−1.56339	−0.0575491
$739$	−34.7426	−1.27803	−0.639013	−	0.769196i	$-0.720657\pi$
$739$	−34.7426	−1.27803	−0.639013	+	0.769196i	$0.720657\pi$
$740$	65.6866	2.41469
$741$	−4.45414	−0.163627
$742$	−34.8113	−1.27796
$743$	−24.4318	−0.896317	−0.448158	−	0.893954i	$-0.647920\pi$
$743$	−24.4318	−0.896317	−0.448158	+	0.893954i	$0.647920\pi$
$744$	49.5277	1.81577
$745$	−38.9457	−1.42686
$746$	4.47305	0.163770
$747$	8.91361	0.326132
$748$	−166.838	−6.10020
$749$	−11.7243	−0.428396
$750$	−33.7402	−1.23202
$751$	10.5864	0.386304	0.193152	−	0.981169i	$-0.438129\pi$
$751$	10.5864	0.386304	0.193152	+	0.981169i	$0.438129\pi$
$752$	−120.472	−4.39317
$753$	18.0096	0.656305
$754$	1.45423	0.0529598
$755$	−17.4410	−0.634743
$756$	9.90959	0.360408
$757$	−33.1527	−1.20496	−0.602478	−	0.798136i	$-0.705820\pi$
$757$	−33.1527	−1.20496	−0.602478	+	0.798136i	$0.705820\pi$
$758$	73.0036	2.65161
$759$	−5.48427	−0.199066
$760$	39.7896	1.44332
$761$	−34.8700	−1.26404	−0.632019	−	0.774953i	$-0.717774\pi$
$761$	−34.8700	−1.26404	−0.632019	+	0.774953i	$0.717774\pi$
$762$	17.9619	0.650691
$763$	−15.6263	−0.565710
$764$	−145.050	−5.24772
$765$	−8.76720	−0.316979
$766$	29.9620	1.08257
$767$	−2.26204	−0.0816777
$768$	−78.7854	−2.84292
$769$	−38.2419	−1.37904	−0.689519	−	0.724267i	$-0.742178\pi$
$769$	−38.2419	−1.37904	−0.689519	+	0.724267i	$0.742178\pi$
$770$	52.8887	1.90598
$771$	−20.2583	−0.729584
$772$	−104.775	−3.77095
$773$	−36.3373	−1.30696	−0.653480	−	0.756944i	$-0.726692\pi$
$773$	−36.3373	−1.30696	−0.653480	+	0.756944i	$0.726692\pi$
$774$	−3.78311	−0.135981
$775$	−8.37962	−0.301005
$776$	24.7501	0.888476
$777$	11.1313	0.399334
$778$	−17.0869	−0.612595
$779$	−1.21396	−0.0434945
$780$	21.2780	0.761874
$781$	−44.5544	−1.59428
$782$	12.1776	0.435469
$783$	−0.253515	−0.00905990
$784$	−67.2145	−2.40052
$785$	8.89685	0.317542
$786$	−39.1057	−1.39485
$787$	28.1855	1.00471	0.502353	−	0.864663i	$-0.332468\pi$
$787$	28.1855	1.00471	0.502353	+	0.864663i	$0.332468\pi$
$788$	59.0619	2.10399
$789$	14.8233	0.527725
$790$	−11.7372	−0.417592
$791$	0.141732	0.00503941
$792$	−61.8563	−2.19797
$793$	3.78752	0.134499
$794$	−82.5467	−2.92947
$795$	13.0307	0.462151
$796$	22.0549	0.781716
$797$	5.51674	0.195413	0.0977065	−	0.995215i	$-0.468849\pi$
$797$	5.51674	0.195413	0.0977065	+	0.995215i	$0.468849\pi$
$798$	10.4011	0.368196
$799$	34.4321	1.21812
$800$	45.9646	1.62510
$801$	4.52553	0.159902
$802$	68.6495	2.42410
$803$	41.4702	1.46345
$804$	−19.4822	−0.687084
$805$	−2.85588	−0.100657
$806$	27.7993	0.979188
$807$	−3.98012	−0.140107
$808$	104.032	3.65983
$809$	18.6456	0.655545	0.327772	−	0.944757i	$-0.393702\pi$
$809$	18.6456	0.655545	0.327772	+	0.944757i	$0.393702\pi$
$810$	−5.01408	−0.176177
$811$	−48.1976	−1.69245	−0.846224	−	0.532828i	$-0.821129\pi$
$811$	−48.1976	−1.69245	−0.846224	+	0.532828i	$0.821129\pi$
$812$	−2.51224	−0.0881622
$813$	7.01043	0.245867
$814$	−107.181	−3.75667
$815$	−33.8647	−1.18623
$816$	82.2199	2.87827
$817$	−2.93755	−0.102772
$818$	−80.2741	−2.80672
$819$	3.60579	0.125996
$820$	5.79922	0.202518
$821$	−2.51904	−0.0879153	−0.0439576	−	0.999033i	$-0.513997\pi$
$821$	−2.51904	−0.0879153	−0.0439576	+	0.999033i	$0.513997\pi$
$822$	−17.2873	−0.602962
$823$	21.0611	0.734143	0.367072	−	0.930193i	$-0.380360\pi$
$823$	21.0611	0.734143	0.367072	+	0.930193i	$0.380360\pi$
$824$	−95.6423	−3.33186
$825$	10.4655	0.364362
$826$	5.28224	0.183793
$827$	7.54617	0.262406	0.131203	−	0.991356i	$-0.458116\pi$
$827$	7.54617	0.262406	0.131203	+	0.991356i	$0.458116\pi$
$828$	5.15232	0.179055
$829$	18.1326	0.629772	0.314886	−	0.949130i	$-0.398034\pi$
$829$	18.1326	0.629772	0.314886	+	0.949130i	$0.398034\pi$
$830$	−44.6936	−1.55134
$831$	0.260345	0.00903125
$832$	−82.3011	−2.85328
$833$	19.2105	0.665605
$834$	−11.8504	−0.410347
$835$	−10.8754	−0.376359
$836$	−74.0903	−2.56247
$837$	−4.84625	−0.167511
$838$	54.1343	1.87004
$839$	6.43737	0.222243	0.111121	−	0.993807i	$-0.464556\pi$
$839$	6.43737	0.222243	0.111121	+	0.993807i	$0.464556\pi$
$840$	−32.2111	−1.11139
$841$	−28.9357	−0.997784
$842$	−36.7051	−1.26494
$843$	−5.48732	−0.188993
$844$	−5.00598	−0.172313
$845$	−15.7690	−0.542469
$846$	19.6922	0.677031
$847$	−44.6730	−1.53498
$848$	−122.204	−4.19649
$849$	−14.5978	−0.500994
$850$	−23.2382	−0.797063
$851$	5.78753	0.198394
$852$	41.8576	1.43402
$853$	−48.9759	−1.67690	−0.838452	−	0.544976i	$-0.816539\pi$
$853$	−48.9759	−1.67690	−0.838452	+	0.544976i	$0.816539\pi$
$854$	−8.84447	−0.302652
$855$	−3.89339	−0.133151
$856$	−68.7541	−2.34997
$857$	37.5715	1.28342	0.641710	−	0.766948i	$-0.278225\pi$
$857$	37.5715	1.28342	0.641710	+	0.766948i	$0.278225\pi$
$858$	−34.7192	−1.18529
$859$	40.6528	1.38706	0.693528	−	0.720429i	$-0.256055\pi$
$859$	40.6528	1.38706	0.693528	+	0.720429i	$0.256055\pi$
$860$	14.0331	0.478523
$861$	0.982742	0.0334918
$862$	41.9321	1.42821
$863$	−18.6320	−0.634242	−0.317121	−	0.948385i	$-0.602716\pi$
$863$	−18.6320	−0.634242	−0.317121	+	0.948385i	$0.602716\pi$
$864$	26.5831	0.904375
$865$	−31.9879	−1.08762
$866$	6.49907	0.220847
$867$	−6.49922	−0.220725
$868$	−48.0244	−1.63005
$869$	14.1682	0.480625
$870$	1.27115	0.0430959
$871$	−7.08895	−0.240200
$872$	−91.6365	−3.10320
$873$	−2.42178	−0.0819647
$874$	5.40788	0.182924
$875$	21.2090	0.716996
$876$	−38.9601	−1.31634
$877$	−14.1176	−0.476719	−0.238359	−	0.971177i	$-0.576610\pi$
$877$	−14.1176	−0.476719	−0.238359	+	0.971177i	$0.576610\pi$
$878$	63.0354	2.12734
$879$	−18.0787	−0.609778
$880$	185.663	6.25871
$881$	−39.2110	−1.32105	−0.660525	−	0.750804i	$-0.729666\pi$
$881$	−39.2110	−1.32105	−0.660525	+	0.750804i	$0.729666\pi$
$882$	10.9868	0.369944
$883$	−30.5762	−1.02897	−0.514486	−	0.857499i	$-0.672017\pi$
$883$	−30.5762	−1.02897	−0.514486	+	0.857499i	$0.672017\pi$
$884$	57.0326	1.91821
$885$	−1.97727	−0.0664650
$886$	37.2750	1.25228
$887$	−23.7506	−0.797467	−0.398734	−	0.917067i	$-0.630550\pi$
$887$	−23.7506	−0.797467	−0.398734	+	0.917067i	$0.630550\pi$
$888$	65.2768	2.19055
$889$	−11.2908	−0.378681
$890$	−22.6914	−0.760616
$891$	6.05260	0.202770
$892$	20.0884	0.672611
$893$	15.2908	0.511686
$894$	−59.7011	−1.99670
$895$	37.8331	1.26462
$896$	99.5321	3.32513
$897$	1.87477	0.0625966
$898$	53.9109	1.79903
$899$	1.22860	0.0409761
$900$	−9.83205	−0.327735
$901$	34.9269	1.16358
$902$	−9.46256	−0.315069
$903$	2.37805	0.0791367
$904$	0.831152	0.0276437
$905$	1.25829	0.0418270
$906$	−26.7359	−0.888240
$907$	−17.1199	−0.568456	−0.284228	−	0.958757i	$-0.591737\pi$
$907$	−17.1199	−0.568456	−0.284228	+	0.958757i	$0.591737\pi$
$908$	−61.9590	−2.05618
$909$	−10.1794	−0.337631
$910$	−18.0797	−0.599337
$911$	3.93748	0.130455	0.0652273	−	0.997870i	$-0.479223\pi$
$911$	3.93748	0.130455	0.0652273	+	0.997870i	$0.479223\pi$
$912$	36.5127	1.20905
$913$	53.9505	1.78550
$914$	−110.145	−3.64328
$915$	3.31069	0.109448
$916$	98.9835	3.27051
$917$	24.5818	0.811761
$918$	−13.4395	−0.443571
$919$	−36.7220	−1.21135	−0.605673	−	0.795713i	$-0.707096\pi$
$919$	−36.7220	−1.21135	−0.605673	+	0.795713i	$0.707096\pi$
$920$	−16.7476	−0.552153
$921$	−23.5650	−0.776492
$922$	65.1229	2.14471
$923$	15.2307	0.501323
$924$	59.9788	1.97316
$925$	−11.0442	−0.363132
$926$	−52.8132	−1.73555
$927$	9.35853	0.307375
$928$	−6.73923	−0.221226
$929$	7.14042	0.234270	0.117135	−	0.993116i	$-0.462629\pi$
$929$	7.14042	0.234270	0.117135	+	0.993116i	$0.462629\pi$
$930$	24.2995	0.796812
$931$	8.53112	0.279596
$932$	−137.998	−4.52027
$933$	−30.3891	−0.994894
$934$	−99.2675	−3.24813
$935$	−53.0643	−1.73539
$936$	21.1452	0.691153
$937$	57.1285	1.86631	0.933153	−	0.359479i	$-0.117046\pi$
$937$	57.1285	1.86631	0.933153	+	0.359479i	$0.117046\pi$
$938$	16.5539	0.540502
$939$	−7.07389	−0.230848
$940$	−73.0460	−2.38250
$941$	30.4597	0.992959	0.496479	−	0.868049i	$-0.334626\pi$
$941$	30.4597	0.992959	0.496479	+	0.868049i	$0.334626\pi$
$942$	13.6383	0.444359
$943$	0.510959	0.0166391
$944$	18.5430	0.603525
$945$	3.15184	0.102529
$946$	−22.8977	−0.744467
$947$	3.32077	0.107910	0.0539552	−	0.998543i	$-0.482817\pi$
$947$	3.32077	0.107910	0.0539552	+	0.998543i	$0.482817\pi$
$948$	−13.3107	−0.432311
$949$	−14.1763	−0.460183
$950$	−10.3197	−0.334817
$951$	−26.5860	−0.862109
$952$	−86.3374	−2.79821
$953$	−50.6121	−1.63949	−0.819743	−	0.572731i	$-0.805884\pi$
$953$	−50.6121	−1.63949	−0.819743	+	0.572731i	$0.805884\pi$
$954$	19.9752	0.646721
$955$	−46.1345	−1.49288
$956$	−32.4107	−1.04824
$957$	−1.53443	−0.0496010
$958$	−29.1406	−0.941490
$959$	10.8667	0.350905
$960$	−71.9399	−2.32185
$961$	−7.51384	−0.242382
$962$	36.6390	1.18129
$963$	6.72754	0.216792
$964$	−16.1372	−0.519745
$965$	−33.3248	−1.07276
$966$	−4.37788	−0.140856
$967$	−11.1860	−0.359718	−0.179859	−	0.983692i	$-0.557564\pi$
$967$	−11.1860	−0.359718	−0.179859	+	0.983692i	$0.557564\pi$
$968$	−261.974	−8.42016
$969$	−10.4357	−0.335242
$970$	12.1430	0.389888
$971$	33.4718	1.07416	0.537080	−	0.843531i	$-0.319527\pi$
$971$	33.4718	1.07416	0.537080	+	0.843531i	$0.319527\pi$
$972$	−5.68625	−0.182387
$973$	7.44916	0.238809
$974$	−3.30706	−0.105965
$975$	−3.57757	−0.114574
$976$	−31.0481	−0.993825
$977$	−1.58016	−0.0505539	−0.0252769	−	0.999680i	$-0.508047\pi$
$977$	−1.58016	−0.0505539	−0.0252769	+	0.999680i	$0.508047\pi$
$978$	−51.9123	−1.65997
$979$	27.3912	0.875427
$980$	−40.7542	−1.30185
$981$	8.96657	0.286280
$982$	−27.2600	−0.869902
$983$	−21.8309	−0.696297	−0.348148	−	0.937439i	$-0.613189\pi$
$983$	−21.8309	−0.696297	−0.348148	+	0.937439i	$0.613189\pi$
$984$	5.76304	0.183719
$985$	18.7852	0.598546
$986$	3.40713	0.108505
$987$	−12.3785	−0.394010
$988$	25.3273	0.805770
$989$	1.23643	0.0393161
$990$	−30.3482	−0.964530
$991$	−52.2007	−1.65821	−0.829105	−	0.559092i	$-0.811150\pi$
$991$	−52.2007	−1.65821	−0.829105	+	0.559092i	$0.811150\pi$
$992$	−128.828	−4.09031
$993$	1.27797	0.0405552
$994$	−35.5661	−1.12809
$995$	7.01477	0.222383
$996$	−50.6850	−1.60602
$997$	30.4114	0.963138	0.481569	−	0.876408i	$-0.340067\pi$
$997$	30.4114	0.963138	0.481569	+	0.876408i	$0.340067\pi$
$998$	76.2568	2.41387
$999$	−6.38729	−0.202085

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.c.1.2	✓	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.c.1.2	✓	116	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77241 q^{2} -1.00000 q^{3} +5.68625 q^{4} +1.80856 q^{5} +2.77241 q^{6} -1.74273 q^{7} -10.2198 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.77241 q^{2} -1.00000 q^{3} +5.68625 q^{4} +1.80856 q^{5} +2.77241 q^{6} -1.74273 q^{7} -10.2198 q^{8} +1.00000 q^{9} -5.01408 q^{10} +6.05260 q^{11} -5.68625 q^{12} -2.06905 q^{13} +4.83156 q^{14} -1.80856 q^{15} +16.9609 q^{16} -4.84760 q^{17} -2.77241 q^{18} -2.15275 q^{19} +10.2840 q^{20} +1.74273 q^{21} -16.7803 q^{22} +0.906101 q^{23} +10.2198 q^{24} -1.72909 q^{25} +5.73624 q^{26} -1.00000 q^{27} -9.90959 q^{28} +0.253515 q^{29} +5.01408 q^{30} +4.84625 q^{31} -26.5831 q^{32} -6.05260 q^{33} +13.4395 q^{34} -3.15184 q^{35} +5.68625 q^{36} +6.38729 q^{37} +5.96830 q^{38} +2.06905 q^{39} -18.4832 q^{40} +0.563910 q^{41} -4.83156 q^{42} +1.36456 q^{43} +34.4166 q^{44} +1.80856 q^{45} -2.51208 q^{46} -7.10291 q^{47} -16.9609 q^{48} -3.96290 q^{49} +4.79375 q^{50} +4.84760 q^{51} -11.7651 q^{52} -7.20499 q^{53} +2.77241 q^{54} +10.9465 q^{55} +17.8103 q^{56} +2.15275 q^{57} -0.702849 q^{58} +1.09328 q^{59} -10.2840 q^{60} -1.83056 q^{61} -13.4358 q^{62} -1.74273 q^{63} +39.7773 q^{64} -3.74200 q^{65} +16.7803 q^{66} +3.42619 q^{67} -27.5647 q^{68} -0.906101 q^{69} +8.73819 q^{70} -7.36120 q^{71} -10.2198 q^{72} +6.85163 q^{73} -17.7082 q^{74} +1.72909 q^{75} -12.2411 q^{76} -10.5480 q^{77} -5.73624 q^{78} +2.34085 q^{79} +30.6750 q^{80} +1.00000 q^{81} -1.56339 q^{82} +8.91361 q^{83} +9.90959 q^{84} -8.76720 q^{85} -3.78311 q^{86} -0.253515 q^{87} -61.8563 q^{88} +4.52553 q^{89} -5.01408 q^{90} +3.60579 q^{91} +5.15232 q^{92} -4.84625 q^{93} +19.6922 q^{94} -3.89339 q^{95} +26.5831 q^{96} -2.42178 q^{97} +10.9868 q^{98} +6.05260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9 + 3 * q^10 - 57 * q^11 - 116 * q^12 + 6 * q^13 - 9 * q^14 + 20 * q^15 + 112 * q^16 - 30 * q^17 - 16 * q^18 + 3 * q^19 - 54 * q^20 + 33 * q^21 - 22 * q^22 - 58 * q^23 + 45 * q^24 + 126 * q^25 - 21 * q^26 - 116 * q^27 - 77 * q^28 - 38 * q^29 - 3 * q^30 + 17 * q^31 - 106 * q^32 + 57 * q^33 + 35 * q^34 - 72 * q^35 + 116 * q^36 - 41 * q^37 - 45 * q^38 - 6 * q^39 + 5 * q^40 - 39 * q^41 + 9 * q^42 - 118 * q^43 - 103 * q^44 - 20 * q^45 - 8 * q^46 - 65 * q^47 - 112 * q^48 + 165 * q^49 - 72 * q^50 + 30 * q^51 - 10 * q^52 - 58 * q^53 + 16 * q^54 + 14 * q^55 - 23 * q^56 - 3 * q^57 - 27 * q^58 - 75 * q^59 + 54 * q^60 + 45 * q^61 - 73 * q^62 - 33 * q^63 + 111 * q^64 - 86 * q^65 + 22 * q^66 - 127 * q^67 - 94 * q^68 + 58 * q^69 - 7 * q^70 - 61 * q^71 - 45 * q^72 + 15 * q^73 - 51 * q^74 - 126 * q^75 + 96 * q^76 - 57 * q^77 + 21 * q^78 + 7 * q^79 - 144 * q^80 + 116 * q^81 - 37 * q^82 - 194 * q^83 + 77 * q^84 + 3 * q^85 - 57 * q^86 + 38 * q^87 - 42 * q^88 - 56 * q^89 + 3 * q^90 - 39 * q^91 - 138 * q^92 - 17 * q^93 + 51 * q^94 - 127 * q^95 + 106 * q^96 + 57 * q^97 - 105 * q^98 - 57 * q^99

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