LMFDB - Embedded newform 4013.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$1$
Dimension:	$157$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42617 q^{2} +1.73131 q^{3} +3.88629 q^{4} -0.987697 q^{5} -4.20045 q^{6} +1.01261 q^{7} -4.57644 q^{8} -0.00256059 q^{9} +O(q^{10})$	\(q-2.42617 q^{2} +1.73131 q^{3} +3.88629 q^{4} -0.987697 q^{5} -4.20045 q^{6} +1.01261 q^{7} -4.57644 q^{8} -0.00256059 q^{9} +2.39632 q^{10} +1.41811 q^{11} +6.72837 q^{12} +5.19274 q^{13} -2.45676 q^{14} -1.71001 q^{15} +3.33064 q^{16} +1.56335 q^{17} +0.00621241 q^{18} -5.69351 q^{19} -3.83847 q^{20} +1.75315 q^{21} -3.44058 q^{22} +8.36861 q^{23} -7.92325 q^{24} -4.02445 q^{25} -12.5984 q^{26} -5.19837 q^{27} +3.93530 q^{28} -6.55507 q^{29} +4.14877 q^{30} -7.49466 q^{31} +1.07219 q^{32} +2.45519 q^{33} -3.79296 q^{34} -1.00015 q^{35} -0.00995117 q^{36} -6.37271 q^{37} +13.8134 q^{38} +8.99024 q^{39} +4.52014 q^{40} -5.70590 q^{41} -4.25342 q^{42} -6.41235 q^{43} +5.51119 q^{44} +0.00252908 q^{45} -20.3036 q^{46} -11.4579 q^{47} +5.76638 q^{48} -5.97462 q^{49} +9.76400 q^{50} +2.70665 q^{51} +20.1805 q^{52} +6.49023 q^{53} +12.6121 q^{54} -1.40067 q^{55} -4.63416 q^{56} -9.85724 q^{57} +15.9037 q^{58} +2.63909 q^{59} -6.64559 q^{60} -8.12170 q^{61} +18.1833 q^{62} -0.00259288 q^{63} -9.26260 q^{64} -5.12885 q^{65} -5.95671 q^{66} +14.2901 q^{67} +6.07564 q^{68} +14.4887 q^{69} +2.42654 q^{70} -1.06498 q^{71} +0.0117184 q^{72} -3.87335 q^{73} +15.4613 q^{74} -6.96758 q^{75} -22.1266 q^{76} +1.43600 q^{77} -21.8118 q^{78} +2.83875 q^{79} -3.28967 q^{80} -8.99231 q^{81} +13.8435 q^{82} +4.75580 q^{83} +6.81322 q^{84} -1.54412 q^{85} +15.5574 q^{86} -11.3489 q^{87} -6.48991 q^{88} -2.47806 q^{89} -0.00613598 q^{90} +5.25822 q^{91} +32.5228 q^{92} -12.9756 q^{93} +27.7987 q^{94} +5.62347 q^{95} +1.85629 q^{96} +19.4339 q^{97} +14.4954 q^{98} -0.00363120 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) $ 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * 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 $

$2$	−2.42617	−1.71556	−0.857780	−	0.514018i	$-0.828157\pi$
$2$	−2.42617	−1.71556	−0.857780	+	0.514018i	$0.828157\pi$
$3$	1.73131	0.999573	0.499787	−	0.866149i	$-0.333412\pi$
$3$	1.73131	0.999573	0.499787	+	0.866149i	$0.333412\pi$
$4$	3.88629	1.94314
$5$	−0.987697	−0.441712	−0.220856	−	0.975306i	$-0.570885\pi$
$5$	−0.987697	−0.441712	−0.220856	+	0.975306i	$0.570885\pi$
$6$	−4.20045	−1.71483
$7$	1.01261	0.382731	0.191366	−	0.981519i	$-0.438708\pi$
$7$	1.01261	0.382731	0.191366	+	0.981519i	$0.438708\pi$
$8$	−4.57644	−1.61802
$9$	−0.00256059	−0.000853529 0
$10$	2.39632	0.757782
$11$	1.41811	0.427577	0.213789	−	0.976880i	$-0.431420\pi$
$11$	1.41811	0.427577	0.213789	+	0.976880i	$0.431420\pi$
$12$	6.72837	1.94231
$13$	5.19274	1.44021	0.720103	−	0.693867i	$-0.244095\pi$
$13$	5.19274	1.44021	0.720103	+	0.693867i	$0.244095\pi$
$14$	−2.45676	−0.656598
$15$	−1.71001	−0.441523
$16$	3.33064	0.832661
$17$	1.56335	0.379169	0.189585	−	0.981864i	$-0.439286\pi$
$17$	1.56335	0.379169	0.189585	+	0.981864i	$0.439286\pi$
$18$	0.00621241	0.00146428
$19$	−5.69351	−1.30618	−0.653091	−	0.757280i	$-0.726528\pi$
$19$	−5.69351	−1.30618	−0.653091	+	0.757280i	$0.726528\pi$
$20$	−3.83847	−0.858309
$21$	1.75315	0.382568
$22$	−3.44058	−0.733534
$23$	8.36861	1.74498	0.872488	−	0.488636i	$-0.162505\pi$
$23$	8.36861	1.74498	0.872488	+	0.488636i	$0.162505\pi$
$24$	−7.92325	−1.61733
$25$	−4.02445	−0.804891
$26$	−12.5984	−2.47076
$27$	−5.19837	−1.00043
$28$	3.93530	0.743701
$29$	−6.55507	−1.21725	−0.608623	−	0.793459i	$-0.708278\pi$
$29$	−6.55507	−1.21725	−0.608623	+	0.793459i	$0.708278\pi$
$30$	4.14877	0.757459
$31$	−7.49466	−1.34608	−0.673040	−	0.739606i	$-0.735012\pi$
$31$	−7.49466	−1.34608	−0.673040	+	0.739606i	$0.735012\pi$
$32$	1.07219	0.189538
$33$	2.45519	0.427395
$34$	−3.79296	−0.650487
$35$	−1.00015	−0.169057
$36$	−0.00995117	−0.00165853
$37$	−6.37271	−1.04767	−0.523834	−	0.851821i	$-0.675499\pi$
$37$	−6.37271	−1.04767	−0.523834	+	0.851821i	$0.675499\pi$
$38$	13.8134	2.24083
$39$	8.99024	1.43959
$40$	4.52014	0.714697
$41$	−5.70590	−0.891111	−0.445556	−	0.895254i	$-0.646994\pi$
$41$	−5.70590	−0.891111	−0.445556	+	0.895254i	$0.646994\pi$
$42$	−4.25342	−0.656318
$43$	−6.41235	−0.977874	−0.488937	−	0.872319i	$-0.662615\pi$
$43$	−6.41235	−0.977874	−0.488937	+	0.872319i	$0.662615\pi$
$44$	5.51119	0.830843
$45$	0.00252908	0.000377013 0
$46$	−20.3036	−2.99361
$47$	−11.4579	−1.67130	−0.835651	−	0.549261i	$-0.814909\pi$
$47$	−11.4579	−1.67130	−0.835651	+	0.549261i	$0.814909\pi$
$48$	5.76638	0.832305
$49$	−5.97462	−0.853517
$50$	9.76400	1.38084
$51$	2.70665	0.379007
$52$	20.1805	2.79853
$53$	6.49023	0.891501	0.445751	−	0.895157i	$-0.352937\pi$
$53$	6.49023	0.891501	0.445751	+	0.895157i	$0.352937\pi$
$54$	12.6121	1.71629
$55$	−1.40067	−0.188866
$56$	−4.63416	−0.619265
$57$	−9.85724	−1.30562
$58$	15.9037	2.08826
$59$	2.63909	0.343580	0.171790	−	0.985134i	$-0.445045\pi$
$59$	2.63909	0.343580	0.171790	+	0.985134i	$0.445045\pi$
$60$	−6.64559	−0.857942
$61$	−8.12170	−1.03988	−0.519939	−	0.854203i	$-0.674045\pi$
$61$	−8.12170	−1.03988	−0.519939	+	0.854203i	$0.674045\pi$
$62$	18.1833	2.30928
$63$	−0.00259288	−0.000326672 0
$64$	−9.26260	−1.15782
$65$	−5.12885	−0.636156
$66$	−5.95671	−0.733221
$67$	14.2901	1.74581	0.872904	−	0.487892i	$-0.162234\pi$
$67$	14.2901	1.74581	0.872904	+	0.487892i	$0.162234\pi$
$68$	6.07564	0.736780
$69$	14.4887	1.74423
$70$	2.42654	0.290027
$71$	−1.06498	−0.126390	−0.0631948	−	0.998001i	$-0.520129\pi$
$71$	−1.06498	−0.126390	−0.0631948	+	0.998001i	$0.520129\pi$
$72$	0.0117184	0.00138102
$73$	−3.87335	−0.453341	−0.226671	−	0.973971i	$-0.572784\pi$
$73$	−3.87335	−0.453341	−0.226671	+	0.973971i	$0.572784\pi$
$74$	15.4613	1.79733
$75$	−6.96758	−0.804547
$76$	−22.1266	−2.53810
$77$	1.43600	0.163647
$78$	−21.8118	−2.46970
$79$	2.83875	0.319384	0.159692	−	0.987167i	$-0.448950\pi$
$79$	2.83875	0.319384	0.159692	+	0.987167i	$0.448950\pi$
$80$	−3.28967	−0.367796
$81$	−8.99231	−0.999146
$82$	13.8435	1.52875
$83$	4.75580	0.522017	0.261009	−	0.965336i	$-0.415945\pi$
$83$	4.75580	0.522017	0.261009	+	0.965336i	$0.415945\pi$
$84$	6.81322	0.743384
$85$	−1.54412	−0.167483
$86$	15.5574	1.67760
$87$	−11.3489	−1.21673
$88$	−6.48991	−0.691827
$89$	−2.47806	−0.262674	−0.131337	−	0.991338i	$-0.541927\pi$
$89$	−2.47806	−0.262674	−0.131337	+	0.991338i	$0.541927\pi$
$90$	−0.00613598	−0.000646789 0
$91$	5.25822	0.551211
$92$	32.5228	3.39074
$93$	−12.9756	−1.34551
$94$	27.7987	2.86722
$95$	5.62347	0.576955
$96$	1.85629	0.189457
$97$	19.4339	1.97322	0.986609	−	0.163103i	$-0.0521504\pi$
$97$	19.4339	1.97322	0.986609	+	0.163103i	$0.0521504\pi$
$98$	14.4954	1.46426
$99$	−0.00363120	−0.000364949 0
$100$	−15.6402	−1.56402
$101$	9.44203	0.939517	0.469759	−	0.882795i	$-0.344341\pi$
$101$	9.44203	0.939517	0.469759	+	0.882795i	$0.344341\pi$
$102$	−6.56679	−0.650209
$103$	−15.6089	−1.53799	−0.768995	−	0.639255i	$-0.779243\pi$
$103$	−15.6089	−1.53799	−0.768995	+	0.639255i	$0.779243\pi$
$104$	−23.7643	−2.33028
$105$	−1.73158	−0.168985
$106$	−15.7464	−1.52942
$107$	14.5789	1.40940	0.704699	−	0.709506i	$-0.251082\pi$
$107$	14.5789	1.40940	0.704699	+	0.709506i	$0.251082\pi$
$108$	−20.2023	−1.94397
$109$	−4.18346	−0.400703	−0.200352	−	0.979724i	$-0.564208\pi$
$109$	−4.18346	−0.400703	−0.200352	+	0.979724i	$0.564208\pi$
$110$	3.39825	0.324010
$111$	−11.0331	−1.04722
$112$	3.37265	0.318685
$113$	−10.4959	−0.987376	−0.493688	−	0.869639i	$-0.664351\pi$
$113$	−10.4959	−0.987376	−0.493688	+	0.869639i	$0.664351\pi$
$114$	23.9153	2.23987
$115$	−8.26565	−0.770776
$116$	−25.4749	−2.36528
$117$	−0.0132964	−0.00122926
$118$	−6.40287	−0.589432
$119$	1.58307	0.145120
$120$	7.82577	0.714392
$121$	−8.98896	−0.817178
$122$	19.7046	1.78397
$123$	−9.87868	−0.890731
$124$	−29.1264	−2.61563
$125$	8.91343	0.797241
$126$	0.00629075	0.000560425 0
$127$	−1.25163	−0.111064	−0.0555322	−	0.998457i	$-0.517686\pi$
$127$	−1.25163	−0.111064	−0.0555322	+	0.998457i	$0.517686\pi$
$128$	20.3282	1.79678
$129$	−11.1018	−0.977457
$130$	12.4434	1.09136
$131$	−13.5554	−1.18434	−0.592169	−	0.805814i	$-0.701728\pi$
$131$	−13.5554	−1.18434	−0.592169	+	0.805814i	$0.701728\pi$
$132$	9.54159	0.830489
$133$	−5.76531	−0.499916
$134$	−34.6701	−2.99504
$135$	5.13441	0.441900
$136$	−7.15460	−0.613502
$137$	6.47627	0.553305	0.276652	−	0.960970i	$-0.410775\pi$
$137$	6.47627	0.553305	0.276652	+	0.960970i	$0.410775\pi$
$138$	−35.1519	−2.99233
$139$	−18.7538	−1.59068	−0.795338	−	0.606166i	$-0.792707\pi$
$139$	−18.7538	−1.59068	−0.795338	+	0.606166i	$0.792707\pi$
$140$	−3.88688	−0.328501
$141$	−19.8371	−1.67059
$142$	2.58382	0.216829
$143$	7.36388	0.615799
$144$	−0.00852840	−0.000710700 0
$145$	6.47443	0.537672
$146$	9.39740	0.777734
$147$	−10.3439	−0.853153
$148$	−24.7662	−2.03577
$149$	−2.43223	−0.199256	−0.0996281	−	0.995025i	$-0.531765\pi$
$149$	−2.43223	−0.199256	−0.0996281	+	0.995025i	$0.531765\pi$
$150$	16.9045	1.38025
$151$	−0.529357	−0.0430785	−0.0215392	−	0.999768i	$-0.506857\pi$
$151$	−0.529357	−0.0430785	−0.0215392	+	0.999768i	$0.506857\pi$
$152$	26.0560	2.11342
$153$	−0.00400310	−0.000323632 0
$154$	−3.48397	−0.280746
$155$	7.40246	0.594580
$156$	34.9386	2.79733
$157$	−15.4912	−1.23633	−0.618167	−	0.786046i	$-0.712125\pi$
$157$	−15.4912	−1.23633	−0.618167	+	0.786046i	$0.712125\pi$
$158$	−6.88727	−0.547922
$159$	11.2366	0.891121
$160$	−1.05900	−0.0837212
$161$	8.47415	0.667857
$162$	21.8168	1.71409
$163$	5.15750	0.403967	0.201983	−	0.979389i	$-0.435261\pi$
$163$	5.15750	0.403967	0.201983	+	0.979389i	$0.435261\pi$
$164$	−22.1747	−1.73156
$165$	−2.42499	−0.188785
$166$	−11.5384	−0.895551
$167$	−5.30157	−0.410248	−0.205124	−	0.978736i	$-0.565760\pi$
$167$	−5.30157	−0.410248	−0.205124	+	0.978736i	$0.565760\pi$
$168$	−8.02317	−0.619001
$169$	13.9645	1.07419
$170$	3.74629	0.287328
$171$	0.0145787	0.00111486
$172$	−24.9202	−1.90015
$173$	9.93720	0.755512	0.377756	−	0.925905i	$-0.376696\pi$
$173$	9.93720	0.755512	0.377756	+	0.925905i	$0.376696\pi$
$174$	27.5343	2.08737
$175$	−4.07521	−0.308057
$176$	4.72323	0.356027
$177$	4.56908	0.343433
$178$	6.01219	0.450633
$179$	14.3186	1.07022	0.535111	−	0.844781i	$-0.320270\pi$
$179$	14.3186	1.07022	0.535111	+	0.844781i	$0.320270\pi$
$180$	0.00982874	0.000732591 0
$181$	−7.27767	−0.540945	−0.270473	−	0.962728i	$-0.587180\pi$
$181$	−7.27767	−0.540945	−0.270473	+	0.962728i	$0.587180\pi$
$182$	−12.7573	−0.945636
$183$	−14.0612	−1.03943
$184$	−38.2985	−2.82340
$185$	6.29431	0.462767
$186$	31.4810	2.30830
$187$	2.21701	0.162124
$188$	−44.5285	−3.24758
$189$	−5.26393	−0.382894
$190$	−13.6435	−0.989801
$191$	−23.2720	−1.68391	−0.841953	−	0.539551i	$-0.818594\pi$
$191$	−23.2720	−1.68391	−0.841953	+	0.539551i	$0.818594\pi$
$192$	−16.0364	−1.15733
$193$	18.4319	1.32676	0.663378	−	0.748285i	$-0.269122\pi$
$193$	18.4319	1.32676	0.663378	+	0.748285i	$0.269122\pi$
$194$	−47.1500	−3.38517
$195$	−8.87964	−0.635884
$196$	−23.2191	−1.65851
$197$	3.99076	0.284330	0.142165	−	0.989843i	$-0.454594\pi$
$197$	3.99076	0.284330	0.142165	+	0.989843i	$0.454594\pi$
$198$	0.00880989	0.000626092 0
$199$	−7.72612	−0.547690	−0.273845	−	0.961774i	$-0.588296\pi$
$199$	−7.72612	−0.547690	−0.273845	+	0.961774i	$0.588296\pi$
$200$	18.4177	1.30233
$201$	24.7405	1.74506
$202$	−22.9079	−1.61180
$203$	−6.63774	−0.465878
$204$	10.5188	0.736465
$205$	5.63570	0.393614
$206$	37.8698	2.63851
$207$	−0.0214285	−0.00148939
$208$	17.2952	1.19920
$209$	−8.07404	−0.558493
$210$	4.20109	0.289903
$211$	−5.09832	−0.350983	−0.175492	−	0.984481i	$-0.556151\pi$
$211$	−5.09832	−0.350983	−0.175492	+	0.984481i	$0.556151\pi$
$212$	25.2229	1.73231
$213$	−1.84381	−0.126336
$214$	−35.3709	−2.41791
$215$	6.33346	0.431938
$216$	23.7900	1.61871
$217$	−7.58918	−0.515187
$218$	10.1498	0.687430
$219$	−6.70598	−0.453148
$220$	−5.44339	−0.366993
$221$	8.11808	0.546081
$222$	26.7683	1.79657
$223$	19.2534	1.28931	0.644653	−	0.764476i	$-0.277002\pi$
$223$	19.2534	1.28931	0.644653	+	0.764476i	$0.277002\pi$
$224$	1.08571	0.0725421
$225$	0.0103050	0.000686997 0
$226$	25.4649	1.69390
$227$	9.97028	0.661750	0.330875	−	0.943675i	$-0.392656\pi$
$227$	9.97028	0.661750	0.330875	+	0.943675i	$0.392656\pi$
$228$	−38.3081	−2.53701
$229$	−3.02412	−0.199840	−0.0999199	−	0.994995i	$-0.531859\pi$
$229$	−3.02412	−0.199840	−0.0999199	+	0.994995i	$0.531859\pi$
$230$	20.0539	1.32231
$231$	2.48616	0.163577
$232$	29.9989	1.96953
$233$	−13.5772	−0.889474	−0.444737	−	0.895661i	$-0.646703\pi$
$233$	−13.5772	−0.889474	−0.444737	+	0.895661i	$0.646703\pi$
$234$	0.0322594	0.00210886
$235$	11.3169	0.738233
$236$	10.2563	0.667625
$237$	4.91476	0.319248
$238$	−3.84079	−0.248962
$239$	3.70368	0.239571	0.119786	−	0.992800i	$-0.461779\pi$
$239$	3.70368	0.239571	0.119786	+	0.992800i	$0.461779\pi$
$240$	−5.69544	−0.367639
$241$	−10.4421	−0.672636	−0.336318	−	0.941748i	$-0.609182\pi$
$241$	−10.4421	−0.672636	−0.336318	+	0.941748i	$0.609182\pi$
$242$	21.8087	1.40192
$243$	0.0266104	0.00170706
$244$	−31.5633	−2.02063
$245$	5.90111	0.377008
$246$	23.9673	1.52810
$247$	−29.5649	−1.88117
$248$	34.2989	2.17798
$249$	8.23377	0.521794
$250$	−21.6255	−1.36771
$251$	3.26843	0.206301	0.103151	−	0.994666i	$-0.467108\pi$
$251$	3.26843	0.206301	0.103151	+	0.994666i	$0.467108\pi$
$252$	−0.0100767	−0.000634770 0
$253$	11.8676	0.746112
$254$	3.03667	0.190538
$255$	−2.67335	−0.167412
$256$	−30.7945	−1.92465
$257$	−6.23322	−0.388818	−0.194409	−	0.980921i	$-0.562279\pi$
$257$	−6.23322	−0.388818	−0.194409	+	0.980921i	$0.562279\pi$
$258$	26.9348	1.67688
$259$	−6.45308	−0.400975
$260$	−19.9322	−1.23614
$261$	0.0167848	0.00103895
$262$	32.8876	2.03180
$263$	−19.5427	−1.20505	−0.602527	−	0.798099i	$-0.705839\pi$
$263$	−19.5427	−1.20505	−0.602527	+	0.798099i	$0.705839\pi$
$264$	−11.2361	−0.691532
$265$	−6.41038	−0.393786
$266$	13.9876	0.857636
$267$	−4.29030	−0.262562
$268$	55.5352	3.39235
$269$	13.4916	0.822600	0.411300	−	0.911500i	$-0.365075\pi$
$269$	13.4916	0.822600	0.411300	+	0.911500i	$0.365075\pi$
$270$	−12.4569	−0.758105
$271$	10.7112	0.650657	0.325328	−	0.945601i	$-0.394525\pi$
$271$	10.7112	0.650657	0.325328	+	0.945601i	$0.394525\pi$
$272$	5.20698	0.315719
$273$	9.10362	0.550976
$274$	−15.7125	−0.949227
$275$	−5.70713	−0.344153
$276$	56.3071	3.38929
$277$	5.69215	0.342008	0.171004	−	0.985270i	$-0.445299\pi$
$277$	5.69215	0.342008	0.171004	+	0.985270i	$0.445299\pi$
$278$	45.4998	2.72890
$279$	0.0191907	0.00114892
$280$	4.57715	0.273537
$281$	12.6523	0.754775	0.377387	−	0.926056i	$-0.376823\pi$
$281$	12.6523	0.754775	0.377387	+	0.926056i	$0.376823\pi$
$282$	48.1282	2.86599
$283$	20.2062	1.20114	0.600568	−	0.799574i	$-0.294941\pi$
$283$	20.2062	1.20114	0.600568	+	0.799574i	$0.294941\pi$
$284$	−4.13881	−0.245593
$285$	9.73597	0.576709
$286$	−17.8660	−1.05644
$287$	−5.77785	−0.341056
$288$	−0.00274543	−0.000161776 0
$289$	−14.5559	−0.856231
$290$	−15.7080	−0.922408
$291$	33.6462	1.97238
$292$	−15.0529	−0.880907
$293$	−29.5068	−1.72380	−0.861902	−	0.507075i	$-0.830727\pi$
$293$	−29.5068	−1.72380	−0.861902	+	0.507075i	$0.830727\pi$
$294$	25.0961	1.46363
$295$	−2.60662	−0.151763
$296$	29.1643	1.69514
$297$	−7.37187	−0.427759
$298$	5.90100	0.341836
$299$	43.4560	2.51312
$300$	−27.0780	−1.56335
$301$	−6.49322	−0.374263
$302$	1.28431	0.0739037
$303$	16.3471	0.939116
$304$	−18.9631	−1.08761
$305$	8.02179	0.459326
$306$	0.00971219	0.000555209 0
$307$	−2.69232	−0.153659	−0.0768294	−	0.997044i	$-0.524480\pi$
$307$	−2.69232	−0.153659	−0.0768294	+	0.997044i	$0.524480\pi$
$308$	5.58069	0.317990
$309$	−27.0238	−1.53733
$310$	−17.9596	−1.02004
$311$	−28.4549	−1.61353	−0.806765	−	0.590873i	$-0.798784\pi$
$311$	−28.4549	−1.61353	−0.806765	+	0.590873i	$0.798784\pi$
$312$	−41.1433	−2.32928
$313$	−10.3239	−0.583540	−0.291770	−	0.956489i	$-0.594244\pi$
$313$	−10.3239	−0.583540	−0.291770	+	0.956489i	$0.594244\pi$
$314$	37.5843	2.12101
$315$	0.00256098	0.000144295 0
$316$	11.0322	0.620609
$317$	12.1630	0.683142	0.341571	−	0.939856i	$-0.389041\pi$
$317$	12.1630	0.683142	0.341571	+	0.939856i	$0.389041\pi$
$318$	−27.2619	−1.52877
$319$	−9.29583	−0.520467
$320$	9.14864	0.511425
$321$	25.2407	1.40880
$322$	−20.5597	−1.14575
$323$	−8.90097	−0.495263
$324$	−34.9467	−1.94148
$325$	−20.8979	−1.15921
$326$	−12.5130	−0.693029
$327$	−7.24288	−0.400532
$328$	26.1127	1.44183
$329$	−11.6024	−0.639659
$330$	5.88343	0.323872
$331$	−17.8072	−0.978773	−0.489387	−	0.872067i	$-0.662779\pi$
$331$	−17.8072	−0.978773	−0.489387	+	0.872067i	$0.662779\pi$
$332$	18.4824	1.01435
$333$	0.0163179	0.000894214 0
$334$	12.8625	0.703804
$335$	−14.1142	−0.771144
$336$	5.83910	0.318549
$337$	2.57185	0.140098	0.0700489	−	0.997544i	$-0.477684\pi$
$337$	2.57185	0.140098	0.0700489	+	0.997544i	$0.477684\pi$
$338$	−33.8802	−1.84284
$339$	−18.1718	−0.986954
$340$	−6.00089	−0.325444
$341$	−10.6283	−0.575553
$342$	−0.0353704	−0.00191261
$343$	−13.1382	−0.709399
$344$	29.3457	1.58222
$345$	−14.3104	−0.770447
$346$	−24.1093	−1.29612
$347$	10.9176	0.586086	0.293043	−	0.956099i	$-0.405332\pi$
$347$	10.9176	0.586086	0.293043	+	0.956099i	$0.405332\pi$
$348$	−44.1050	−2.36427
$349$	−9.22932	−0.494034	−0.247017	−	0.969011i	$-0.579450\pi$
$349$	−9.22932	−0.494034	−0.247017	+	0.969011i	$0.579450\pi$
$350$	9.88713	0.528490
$351$	−26.9937	−1.44082
$352$	1.52049	0.0810421
$353$	7.70837	0.410275	0.205137	−	0.978733i	$-0.434236\pi$
$353$	7.70837	0.410275	0.205137	+	0.978733i	$0.434236\pi$
$354$	−11.0854	−0.589180
$355$	1.05188	0.0558278
$356$	−9.63046	−0.510413
$357$	2.74079	0.145058
$358$	−34.7393	−1.83603
$359$	29.7417	1.56970	0.784852	−	0.619683i	$-0.212739\pi$
$359$	29.7417	1.56970	0.784852	+	0.619683i	$0.212739\pi$
$360$	−0.0115742	−0.000610014 0
$361$	13.4161	0.706109
$362$	17.6569	0.928023
$363$	−15.5627	−0.816829
$364$	20.4350	1.07108
$365$	3.82570	0.200246
$366$	34.1148	1.78321
$367$	26.5972	1.38836	0.694182	−	0.719799i	$-0.255766\pi$
$367$	26.5972	1.38836	0.694182	+	0.719799i	$0.255766\pi$
$368$	27.8729	1.45297
$369$	0.0146104	0.000760589 0
$370$	−15.2710	−0.793904
$371$	6.57208	0.341205
$372$	−50.4269	−2.61451
$373$	9.25164	0.479032	0.239516	−	0.970892i	$-0.423011\pi$
$373$	9.25164	0.479032	0.239516	+	0.970892i	$0.423011\pi$
$374$	−5.37884	−0.278133
$375$	15.4319	0.796901
$376$	52.4363	2.70419
$377$	−34.0388	−1.75309
$378$	12.7712	0.656878
$379$	−22.3982	−1.15052	−0.575258	−	0.817972i	$-0.695098\pi$
$379$	−22.3982	−1.15052	−0.575258	+	0.817972i	$0.695098\pi$
$380$	21.8544	1.12111
$381$	−2.16697	−0.111017
$382$	56.4619	2.88884
$383$	−33.9325	−1.73387	−0.866935	−	0.498421i	$-0.833913\pi$
$383$	−33.9325	−1.73387	−0.866935	+	0.498421i	$0.833913\pi$
$384$	35.1945	1.79601
$385$	−1.41833	−0.0722848
$386$	−44.7188	−2.27613
$387$	0.0164194	0.000834643 0
$388$	75.5258	3.83424
$389$	30.3573	1.53918	0.769589	−	0.638540i	$-0.220461\pi$
$389$	30.3573	1.53918	0.769589	+	0.638540i	$0.220461\pi$
$390$	21.5435	1.09090
$391$	13.0831	0.661641
$392$	27.3425	1.38100
$393$	−23.4685	−1.18383
$394$	−9.68225	−0.487785
$395$	−2.80382	−0.141076
$396$	−0.0141119	−0.000709148 0
$397$	−14.7639	−0.740976	−0.370488	−	0.928837i	$-0.620810\pi$
$397$	−14.7639	−0.740976	−0.370488	+	0.928837i	$0.620810\pi$
$398$	18.7449	0.939595
$399$	−9.98155	−0.499703
$400$	−13.4040	−0.670201
$401$	−27.6463	−1.38059	−0.690296	−	0.723527i	$-0.742520\pi$
$401$	−27.6463	−1.38059	−0.690296	+	0.723527i	$0.742520\pi$
$402$	−60.0247	−2.99376
$403$	−38.9178	−1.93863
$404$	36.6944	1.82562
$405$	8.88168	0.441334
$406$	16.1043	0.799242
$407$	−9.03722	−0.447958
$408$	−12.3868	−0.613240
$409$	17.2996	0.855411	0.427705	−	0.903918i	$-0.359322\pi$
$409$	17.2996	0.855411	0.427705	+	0.903918i	$0.359322\pi$
$410$	−13.6731	−0.675268
$411$	11.2124	0.553069
$412$	−60.6606	−2.98853
$413$	2.67237	0.131499
$414$	0.0519892	0.00255513
$415$	−4.69729	−0.230581
$416$	5.56759	0.272974
$417$	−32.4687	−1.59000
$418$	19.5890	0.958128
$419$	−0.622197	−0.0303963	−0.0151982	−	0.999885i	$-0.504838\pi$
$419$	−0.622197	−0.0303963	−0.0151982	+	0.999885i	$0.504838\pi$
$420$	−6.72940	−0.328361
$421$	−11.9499	−0.582404	−0.291202	−	0.956662i	$-0.594055\pi$
$421$	−11.9499	−0.582404	−0.291202	+	0.956662i	$0.594055\pi$
$422$	12.3694	0.602132
$423$	0.0293389	0.00142650
$424$	−29.7022	−1.44246
$425$	−6.29165	−0.305190
$426$	4.47339	0.216736
$427$	−8.22413	−0.397994
$428$	56.6579	2.73866
$429$	12.7492	0.615536
$430$	−15.3660	−0.741016
$431$	19.5886	0.943550	0.471775	−	0.881719i	$-0.343613\pi$
$431$	19.5886	0.943550	0.471775	+	0.881719i	$0.343613\pi$
$432$	−17.3139	−0.833016
$433$	8.44457	0.405820	0.202910	−	0.979197i	$-0.434960\pi$
$433$	8.44457	0.405820	0.202910	+	0.979197i	$0.434960\pi$
$434$	18.4126	0.883834
$435$	11.2093	0.537443
$436$	−16.2581	−0.778623
$437$	−47.6468	−2.27925
$438$	16.2698	0.777402
$439$	18.2369	0.870397	0.435199	−	0.900334i	$-0.356678\pi$
$439$	18.2369	0.870397	0.435199	+	0.900334i	$0.356678\pi$
$440$	6.41007	0.305588
$441$	0.0152985	0.000728501 0
$442$	−19.6958	−0.936835
$443$	17.5734	0.834936	0.417468	−	0.908692i	$-0.362918\pi$
$443$	17.5734	0.834936	0.417468	+	0.908692i	$0.362918\pi$
$444$	−42.8780	−2.03490
$445$	2.44758	0.116026
$446$	−46.7120	−2.21188
$447$	−4.21095	−0.199171
$448$	−9.37941	−0.443136
$449$	27.5971	1.30239	0.651194	−	0.758911i	$-0.274268\pi$
$449$	27.5971	1.30239	0.651194	+	0.758911i	$0.274268\pi$
$450$	−0.0250015	−0.00117858
$451$	−8.09160	−0.381019
$452$	−40.7902	−1.91861
$453$	−0.916482	−0.0430601
$454$	−24.1896	−1.13527
$455$	−5.19353	−0.243477
$456$	45.1111	2.11252
$457$	9.49639	0.444222	0.222111	−	0.975021i	$-0.428705\pi$
$457$	9.49639	0.444222	0.222111	+	0.975021i	$0.428705\pi$
$458$	7.33703	0.342837
$459$	−8.12689	−0.379331
$460$	−32.1227	−1.49773
$461$	−35.8132	−1.66799	−0.833994	−	0.551774i	$-0.813951\pi$
$461$	−35.8132	−1.66799	−0.833994	+	0.551774i	$0.813951\pi$
$462$	−6.03183	−0.280626
$463$	3.12552	0.145255	0.0726276	−	0.997359i	$-0.476862\pi$
$463$	3.12552	0.145255	0.0726276	+	0.997359i	$0.476862\pi$
$464$	−21.8326	−1.01355
$465$	12.8160	0.594326
$466$	32.9406	1.52594
$467$	−41.6424	−1.92698	−0.963491	−	0.267742i	$-0.913723\pi$
$467$	−41.6424	−1.92698	−0.963491	+	0.267742i	$0.913723\pi$
$468$	−0.0516738	−0.00238862
$469$	14.4703	0.668175
$470$	−27.4567	−1.26648
$471$	−26.8201	−1.23581
$472$	−12.0776	−0.555918
$473$	−9.09343	−0.418116
$474$	−11.9240	−0.547688
$475$	22.9133	1.05133
$476$	6.15226	0.281988
$477$	−0.0166188	−0.000760922 0
$478$	−8.98575	−0.410999
$479$	−34.9782	−1.59819	−0.799097	−	0.601203i	$-0.794688\pi$
$479$	−34.9782	−1.59819	−0.799097	+	0.601203i	$0.794688\pi$
$480$	−1.83346	−0.0836854
$481$	−33.0918	−1.50886
$482$	25.3343	1.15395
$483$	14.6714	0.667572
$484$	−34.9336	−1.58789
$485$	−19.1949	−0.871593
$486$	−0.0645612	−0.00292856
$487$	−2.52191	−0.114279	−0.0571393	−	0.998366i	$-0.518198\pi$
$487$	−2.52191	−0.114279	−0.0571393	+	0.998366i	$0.518198\pi$
$488$	37.1685	1.68254
$489$	8.92924	0.403794
$490$	−14.3171	−0.646780
$491$	−4.35304	−0.196450	−0.0982249	−	0.995164i	$-0.531316\pi$
$491$	−4.35304	−0.196450	−0.0982249	+	0.995164i	$0.531316\pi$
$492$	−38.3914	−1.73082
$493$	−10.2479	−0.461542
$494$	71.7294	3.22726
$495$	0.00358653	0.000161202 0
$496$	−24.9620	−1.12083
$497$	−1.07841	−0.0483733
$498$	−19.9765	−0.895169
$499$	−13.1011	−0.586484	−0.293242	−	0.956038i	$-0.594734\pi$
$499$	−13.1011	−0.586484	−0.293242	+	0.956038i	$0.594734\pi$
$500$	34.6401	1.54915
$501$	−9.17867	−0.410073
$502$	−7.92975	−0.353922
$503$	14.8976	0.664252	0.332126	−	0.943235i	$-0.392234\pi$
$503$	14.8976	0.664252	0.332126	+	0.943235i	$0.392234\pi$
$504$	0.0118662	0.000528561 0
$505$	−9.32587	−0.414996
$506$	−28.7929	−1.28000
$507$	24.1769	1.07373
$508$	−4.86420	−0.215814
$509$	23.9188	1.06018	0.530092	−	0.847940i	$-0.322158\pi$
$509$	23.9188	1.06018	0.530092	+	0.847940i	$0.322158\pi$
$510$	6.48600	0.287205
$511$	−3.92220	−0.173508
$512$	34.0561	1.50508
$513$	29.5970	1.30674
$514$	15.1228	0.667040
$515$	15.4169	0.679348
$516$	−43.1447	−1.89934
$517$	−16.2485	−0.714610
$518$	15.6562	0.687896
$519$	17.2044	0.755189
$520$	23.4719	1.02931
$521$	−40.2819	−1.76478	−0.882391	−	0.470516i	$-0.844068\pi$
$521$	−40.2819	−1.76478	−0.882391	+	0.470516i	$0.844068\pi$
$522$	−0.0407228	−0.00178239
$523$	−38.2985	−1.67468	−0.837338	−	0.546686i	$-0.815889\pi$
$523$	−38.2985	−1.67468	−0.837338	+	0.546686i	$0.815889\pi$
$524$	−52.6800	−2.30134
$525$	−7.05545	−0.307925
$526$	47.4138	2.06734
$527$	−11.7168	−0.510392
$528$	8.17738	0.355875
$529$	47.0336	2.04494
$530$	15.5527	0.675564
$531$	−0.00675761	−0.000293255 0
$532$	−22.4057	−0.971408
$533$	−29.6292	−1.28338
$534$	10.4090	0.450440
$535$	−14.3996	−0.622548
$536$	−65.3976	−2.82475
$537$	24.7900	1.06977
$538$	−32.7330	−1.41122
$539$	−8.47268	−0.364944
$540$	19.9538	0.858675
$541$	−8.26958	−0.355537	−0.177769	−	0.984072i	$-0.556888\pi$
$541$	−8.26958	−0.355537	−0.177769	+	0.984072i	$0.556888\pi$
$542$	−25.9871	−1.11624
$543$	−12.5999	−0.540714
$544$	1.67621	0.0718670
$545$	4.13200	0.176995
$546$	−22.0869	−0.945232
$547$	28.0000	1.19719	0.598596	−	0.801051i	$-0.295726\pi$
$547$	28.0000	1.19719	0.598596	+	0.801051i	$0.295726\pi$
$548$	25.1686	1.07515
$549$	0.0207963	0.000887565 0
$550$	13.8464	0.590415
$551$	37.3214	1.58994
$552$	−66.3066	−2.82220
$553$	2.87455	0.122238
$554$	−13.8101	−0.586735
$555$	10.8974	0.462569
$556$	−72.8826	−3.09091
$557$	−29.7148	−1.25906	−0.629528	−	0.776978i	$-0.716752\pi$
$557$	−29.7148	−1.25906	−0.629528	+	0.776978i	$0.716752\pi$
$558$	−0.0465599	−0.00197104
$559$	−33.2976	−1.40834
$560$	−3.33115	−0.140767
$561$	3.83834	0.162055
$562$	−30.6967	−1.29486
$563$	−7.37992	−0.311026	−0.155513	−	0.987834i	$-0.549703\pi$
$563$	−7.37992	−0.311026	−0.155513	+	0.987834i	$0.549703\pi$
$564$	−77.0928	−3.24619
$565$	10.3668	0.436135
$566$	−49.0237	−2.06062
$567$	−9.10572	−0.382404
$568$	4.87381	0.204501
$569$	−14.9628	−0.627271	−0.313636	−	0.949543i	$-0.601547\pi$
$569$	−14.9628	−0.627271	−0.313636	+	0.949543i	$0.601547\pi$
$570$	−23.6211	−0.989379
$571$	−36.2684	−1.51778	−0.758892	−	0.651216i	$-0.774259\pi$
$571$	−36.2684	−1.51778	−0.758892	+	0.651216i	$0.774259\pi$
$572$	28.6182	1.19659
$573$	−40.2911	−1.68319
$574$	14.0180	0.585102
$575$	−33.6791	−1.40452
$576$	0.0237177	0.000988236 0
$577$	10.5777	0.440356	0.220178	−	0.975460i	$-0.429336\pi$
$577$	10.5777	0.440356	0.220178	+	0.975460i	$0.429336\pi$
$578$	35.3151	1.46891
$579$	31.9113	1.32619
$580$	25.1615	1.04477
$581$	4.81578	0.199792
$582$	−81.6313	−3.38373
$583$	9.20387	0.381186
$584$	17.7262	0.733514
$585$	0.0131329	0.000542977 0
$586$	71.5883	2.95729
$587$	26.6736	1.10094	0.550469	−	0.834855i	$-0.314449\pi$
$587$	26.6736	1.10094	0.550469	+	0.834855i	$0.314449\pi$
$588$	−40.1994	−1.65780
$589$	42.6709	1.75823
$590$	6.32410	0.260359
$591$	6.90925	0.284208
$592$	−21.2252	−0.872351
$593$	−44.3812	−1.82252	−0.911260	−	0.411832i	$-0.864889\pi$
$593$	−44.3812	−1.82252	−0.911260	+	0.411832i	$0.864889\pi$
$594$	17.8854	0.733846
$595$	−1.56359	−0.0641011
$596$	−9.45235	−0.387183
$597$	−13.3763	−0.547456
$598$	−105.431	−4.31141
$599$	−13.9344	−0.569343	−0.284671	−	0.958625i	$-0.591885\pi$
$599$	−13.9344	−0.569343	−0.284671	+	0.958625i	$0.591885\pi$
$600$	31.8868	1.30177
$601$	−33.2895	−1.35791	−0.678954	−	0.734181i	$-0.737566\pi$
$601$	−33.2895	−1.35791	−0.678954	+	0.734181i	$0.737566\pi$
$602$	15.7536	0.642070
$603$	−0.0365909	−0.00149010
$604$	−2.05723	−0.0837076
$605$	8.87837	0.360957
$606$	−39.6608	−1.61111
$607$	7.53585	0.305871	0.152935	−	0.988236i	$-0.451127\pi$
$607$	7.53585	0.305871	0.152935	+	0.988236i	$0.451127\pi$
$608$	−6.10452	−0.247571
$609$	−11.4920	−0.465679
$610$	−19.4622	−0.788001
$611$	−59.4977	−2.40702
$612$	−0.0155572	−0.000628862 0
$613$	0.828381	0.0334580	0.0167290	−	0.999860i	$-0.494675\pi$
$613$	0.828381	0.0334580	0.0167290	+	0.999860i	$0.494675\pi$
$614$	6.53202	0.263611
$615$	9.75715	0.393446
$616$	−6.57176	−0.264784
$617$	−19.1679	−0.771669	−0.385834	−	0.922568i	$-0.626086\pi$
$617$	−19.1679	−0.771669	−0.385834	+	0.922568i	$0.626086\pi$
$618$	65.5644	2.63739
$619$	−0.907454	−0.0364737	−0.0182368	−	0.999834i	$-0.505805\pi$
$619$	−0.907454	−0.0364737	−0.0182368	+	0.999834i	$0.505805\pi$
$620$	28.7681	1.15535
$621$	−43.5031	−1.74572
$622$	69.0363	2.76811
$623$	−2.50931	−0.100534
$624$	29.9433	1.19869
$625$	11.3185	0.452740
$626$	25.0474	1.00110
$627$	−13.9787	−0.558255
$628$	−60.2033	−2.40238
$629$	−9.96280	−0.397243
$630$	−0.00621336	−0.000247546 0
$631$	27.3994	1.09075	0.545377	−	0.838191i	$-0.316387\pi$
$631$	27.3994	1.09075	0.545377	+	0.838191i	$0.316387\pi$
$632$	−12.9914	−0.516769
$633$	−8.82679	−0.350833
$634$	−29.5095	−1.17197
$635$	1.23623	0.0490585
$636$	43.6687	1.73157
$637$	−31.0246	−1.22924
$638$	22.5532	0.892892
$639$	0.00272697	0.000107877 0
$640$	−20.0781	−0.793658
$641$	−13.9853	−0.552387	−0.276193	−	0.961102i	$-0.589073\pi$
$641$	−13.9853	−0.552387	−0.276193	+	0.961102i	$0.589073\pi$
$642$	−61.2381	−2.41687
$643$	24.4122	0.962723	0.481361	−	0.876522i	$-0.340142\pi$
$643$	24.4122	0.962723	0.481361	+	0.876522i	$0.340142\pi$
$644$	32.9330	1.29774
$645$	10.9652	0.431754
$646$	21.5952	0.849654
$647$	25.7736	1.01327	0.506633	−	0.862162i	$-0.330890\pi$
$647$	25.7736	1.01327	0.506633	+	0.862162i	$0.330890\pi$
$648$	41.1528	1.61663
$649$	3.74253	0.146907
$650$	50.7019	1.98869
$651$	−13.1392	−0.514967
$652$	20.0435	0.784965
$653$	1.34705	0.0527143	0.0263571	−	0.999653i	$-0.491609\pi$
$653$	1.34705	0.0527143	0.0263571	+	0.999653i	$0.491609\pi$
$654$	17.5724	0.687137
$655$	13.3886	0.523136
$656$	−19.0043	−0.741993
$657$	0.00991805	0.000386940 0
$658$	28.1493	1.09737
$659$	44.9522	1.75109	0.875544	−	0.483138i	$-0.160503\pi$
$659$	44.9522	1.75109	0.875544	+	0.483138i	$0.160503\pi$
$660$	−9.42420	−0.366837
$661$	23.7829	0.925049	0.462524	−	0.886607i	$-0.346944\pi$
$661$	23.7829	0.925049	0.462524	+	0.886607i	$0.346944\pi$
$662$	43.2033	1.67914
$663$	14.0549	0.545848
$664$	−21.7647	−0.844632
$665$	5.69438	0.220819
$666$	−0.0395899	−0.00153408
$667$	−54.8569	−2.12407
$668$	−20.6034	−0.797170
$669$	33.3337	1.28875
$670$	34.2435	1.32294
$671$	−11.5175	−0.444628
$672$	1.87970	0.0725111
$673$	−15.6718	−0.604103	−0.302052	−	0.953292i	$-0.597672\pi$
$673$	−15.6718	−0.604103	−0.302052	+	0.953292i	$0.597672\pi$
$674$	−6.23974	−0.240346
$675$	20.9206	0.805234
$676$	54.2700	2.08731
$677$	−22.1647	−0.851858	−0.425929	−	0.904757i	$-0.640053\pi$
$677$	−22.1647	−0.851858	−0.425929	+	0.904757i	$0.640053\pi$
$678$	44.0877	1.69318
$679$	19.6790	0.755212
$680$	7.06658	0.270991
$681$	17.2617	0.661468
$682$	25.7860	0.987396
$683$	29.2365	1.11870	0.559351	−	0.828931i	$-0.311050\pi$
$683$	29.2365	1.11870	0.559351	+	0.828931i	$0.311050\pi$
$684$	0.0566571	0.00216634
$685$	−6.39659	−0.244401
$686$	31.8756	1.21702
$687$	−5.23570	−0.199754
$688$	−21.3572	−0.814237
$689$	33.7020	1.28395
$690$	34.7195	1.32175
$691$	42.2612	1.60769	0.803845	−	0.594839i	$-0.202784\pi$
$691$	42.2612	1.60769	0.803845	+	0.594839i	$0.202784\pi$
$692$	38.6188	1.46807
$693$	−0.00367699	−0.000139677 0
$694$	−26.4879	−1.00547
$695$	18.5231	0.702620
$696$	51.9375	1.96869
$697$	−8.92034	−0.337882
$698$	22.3919	0.847545
$699$	−23.5064	−0.889094
$700$	−15.8374	−0.598598
$701$	20.2870	0.766230	0.383115	−	0.923701i	$-0.374851\pi$
$701$	20.2870	0.766230	0.383115	+	0.923701i	$0.374851\pi$
$702$	65.4913	2.47181
$703$	36.2831	1.36844
$704$	−13.1354	−0.495059
$705$	19.5931	0.737918
$706$	−18.7018	−0.703851
$707$	9.56111	0.359583
$708$	17.7568	0.667340
$709$	32.5423	1.22215	0.611077	−	0.791571i	$-0.290737\pi$
$709$	32.5423	1.22215	0.611077	+	0.791571i	$0.290737\pi$
$710$	−2.55203	−0.0957759
$711$	−0.00726885	−0.000272603 0
$712$	11.3407	0.425011
$713$	−62.7199	−2.34888
$714$	−6.64961	−0.248855
$715$	−7.27329	−0.272006
$716$	55.6462	2.07960
$717$	6.41223	0.239469
$718$	−72.1582	−2.69292
$719$	−29.2038	−1.08912	−0.544558	−	0.838723i	$-0.683303\pi$
$719$	−29.2038	−1.08912	−0.544558	+	0.838723i	$0.683303\pi$
$720$	0.00842348	0.000313924 0
$721$	−15.8057	−0.588636
$722$	−32.5496	−1.21137
$723$	−18.0786	−0.672349
$724$	−28.2831	−1.05113
$725$	26.3806	0.979751
$726$	37.7577	1.40132
$727$	−40.2981	−1.49457	−0.747287	−	0.664502i	$-0.768644\pi$
$727$	−40.2981	−1.49457	−0.747287	+	0.664502i	$0.768644\pi$
$728$	−24.0640	−0.891870
$729$	27.0230	1.00085
$730$	−9.28178	−0.343534
$731$	−10.0248	−0.370780
$732$	−54.6458	−2.01977
$733$	−43.6048	−1.61058	−0.805290	−	0.592881i	$-0.797990\pi$
$733$	−43.6048	−1.61058	−0.805290	+	0.592881i	$0.797990\pi$
$734$	−64.5293	−2.38182
$735$	10.2167	0.376847
$736$	8.97273	0.330739
$737$	20.2649	0.746467
$738$	−0.0354474	−0.00130483
$739$	−0.967603	−0.0355939	−0.0177969	−	0.999842i	$-0.505665\pi$
$739$	−0.967603	−0.0355939	−0.0177969	+	0.999842i	$0.505665\pi$
$740$	24.4615	0.899222
$741$	−51.1860	−1.88037
$742$	−15.9450	−0.585358
$743$	29.1148	1.06812	0.534060	−	0.845447i	$-0.320666\pi$
$743$	29.1148	1.06812	0.534060	+	0.845447i	$0.320666\pi$
$744$	59.3821	2.17705
$745$	2.40231	0.0880138
$746$	−22.4460	−0.821807
$747$	−0.0121776	−0.000445556 0
$748$	8.61594	0.315030
$749$	14.7628	0.539421
$750$	−37.4404	−1.36713
$751$	37.2584	1.35958	0.679790	−	0.733407i	$-0.262071\pi$
$751$	37.2584	1.35958	0.679790	+	0.733407i	$0.262071\pi$
$752$	−38.1621	−1.39163
$753$	5.65867	0.206213
$754$	82.5837	3.00752
$755$	0.522845	0.0190283
$756$	−20.4571	−0.744018
$757$	17.7645	0.645664	0.322832	−	0.946456i	$-0.395365\pi$
$757$	17.7645	0.645664	0.322832	+	0.946456i	$0.395365\pi$
$758$	54.3417	1.97378
$759$	20.5466	0.745793
$760$	−25.7355	−0.933524
$761$	5.68307	0.206011	0.103006	−	0.994681i	$-0.467154\pi$
$761$	5.68307	0.206011	0.103006	+	0.994681i	$0.467154\pi$
$762$	5.25742	0.190456
$763$	−4.23622	−0.153362
$764$	−90.4418	−3.27207
$765$	0.00395385	0.000142952 0
$766$	82.3259	2.97456
$767$	13.7041	0.494826
$768$	−53.3148	−1.92383
$769$	−0.186191	−0.00671421	−0.00335711	−	0.999994i	$-0.501069\pi$
$769$	−0.186191	−0.00671421	−0.00335711	+	0.999994i	$0.501069\pi$
$770$	3.44111	0.124009
$771$	−10.7917	−0.388652
$772$	71.6315	2.57808
$773$	−30.8995	−1.11138	−0.555688	−	0.831391i	$-0.687545\pi$
$773$	−30.8995	−1.11138	−0.555688	+	0.831391i	$0.687545\pi$
$774$	−0.0398361	−0.00143188
$775$	30.1619	1.08345
$776$	−88.9383	−3.19270
$777$	−11.1723	−0.400804
$778$	−73.6519	−2.64055
$779$	32.4866	1.16395
$780$	−34.5088	−1.23561
$781$	−1.51026	−0.0540413
$782$	−31.7418	−1.13508
$783$	34.0757	1.21777
$784$	−19.8993	−0.710690
$785$	15.3006	0.546103
$786$	56.9386	2.03093
$787$	−33.2069	−1.18370	−0.591850	−	0.806048i	$-0.701602\pi$
$787$	−33.2069	−1.18370	−0.591850	+	0.806048i	$0.701602\pi$
$788$	15.5092	0.552493
$789$	−33.8345	−1.20454
$790$	6.80254	0.242024
$791$	−10.6283	−0.377899
$792$	0.0166180	0.000590494 0
$793$	−42.1739	−1.49764
$794$	35.8196	1.27119
$795$	−11.0984	−0.393618
$796$	−30.0259	−1.06424
$797$	−31.4109	−1.11263	−0.556316	−	0.830971i	$-0.687786\pi$
$797$	−31.4109	−1.11263	−0.556316	+	0.830971i	$0.687786\pi$
$798$	24.2169	0.857270
$799$	−17.9127	−0.633706
$800$	−4.31498	−0.152557
$801$	0.00634529	0.000224200 0
$802$	67.0746	2.36849
$803$	−5.49285	−0.193838
$804$	96.1488	3.39091
$805$	−8.36990	−0.295000
$806$	94.4210	3.32584
$807$	23.3582	0.822249
$808$	−43.2109	−1.52016
$809$	43.2808	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$809$	43.2808	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$810$	−21.5484	−0.757135
$811$	−44.2585	−1.55413	−0.777063	−	0.629422i	$-0.783292\pi$
$811$	−44.2585	−1.55413	−0.777063	+	0.629422i	$0.783292\pi$
$812$	−25.7962	−0.905268
$813$	18.5444	0.650379
$814$	21.9258	0.768499
$815$	−5.09405	−0.178437
$816$	9.01490	0.315584
$817$	36.5088	1.27728
$818$	−41.9718	−1.46751
$819$	−0.0134641	−0.000470475 0
$820$	21.9019	0.764849
$821$	−15.1564	−0.528962	−0.264481	−	0.964391i	$-0.585201\pi$
$821$	−15.1564	−0.528962	−0.264481	+	0.964391i	$0.585201\pi$
$822$	−27.2032	−0.948822
$823$	40.8293	1.42322	0.711609	−	0.702575i	$-0.247967\pi$
$823$	40.8293	1.42322	0.711609	+	0.702575i	$0.247967\pi$
$824$	71.4332	2.48849
$825$	−9.88082	−0.344006
$826$	−6.48362	−0.225594
$827$	−19.0578	−0.662704	−0.331352	−	0.943507i	$-0.607505\pi$
$827$	−19.0578	−0.662704	−0.331352	+	0.943507i	$0.607505\pi$
$828$	−0.0832774	−0.00289409
$829$	55.7939	1.93780	0.968901	−	0.247450i	$-0.0795927\pi$
$829$	55.7939	1.93780	0.968901	+	0.247450i	$0.0795927\pi$
$830$	11.3964	0.395575
$831$	9.85489	0.341862
$832$	−48.0982	−1.66751
$833$	−9.34044	−0.323627
$834$	78.7744	2.72773
$835$	5.23635	0.181211
$836$	−31.3780	−1.08523
$837$	38.9600	1.34665
$838$	1.50955	0.0521467
$839$	39.8315	1.37514	0.687569	−	0.726119i	$-0.258678\pi$
$839$	39.8315	1.37514	0.687569	+	0.726119i	$0.258678\pi$
$840$	7.92446	0.273420
$841$	13.9690	0.481690
$842$	28.9925	0.999149
$843$	21.9051	0.754452
$844$	−19.8135	−0.682010
$845$	−13.7927	−0.474483
$846$	−0.0711809	−0.00244725
$847$	−9.10232	−0.312759
$848$	21.6166	0.742318
$849$	34.9833	1.20062
$850$	15.2646	0.523571
$851$	−53.3307	−1.82815
$852$	−7.16557	−0.245488
$853$	−8.68013	−0.297202	−0.148601	−	0.988897i	$-0.547477\pi$
$853$	−8.68013	−0.297202	−0.148601	+	0.988897i	$0.547477\pi$
$854$	19.9531	0.682781
$855$	−0.0143994	−0.000492448 0
$856$	−66.7197	−2.28043
$857$	−5.23060	−0.178674	−0.0893370	−	0.996001i	$-0.528475\pi$
$857$	−5.23060	−0.178674	−0.0893370	+	0.996001i	$0.528475\pi$
$858$	−30.9316	−1.05599
$859$	0.539846	0.0184193	0.00920966	−	0.999958i	$-0.497068\pi$
$859$	0.539846	0.0184193	0.00920966	+	0.999958i	$0.497068\pi$
$860$	24.6136	0.839318
$861$	−10.0033	−0.340910
$862$	−47.5252	−1.61872
$863$	41.0900	1.39872	0.699360	−	0.714770i	$-0.253468\pi$
$863$	41.0900	1.39872	0.699360	+	0.714770i	$0.253468\pi$
$864$	−5.57363	−0.189619
$865$	−9.81495	−0.333718
$866$	−20.4879	−0.696209
$867$	−25.2008	−0.855865
$868$	−29.4937	−1.00108
$869$	4.02566	0.136561
$870$	−27.1955	−0.922014
$871$	74.2045	2.51432
$872$	19.1454	0.648345
$873$	−0.0497623	−0.00168420
$874$	115.599	3.91020
$875$	9.02584	0.305129
$876$	−26.0613	−0.880531
$877$	−24.6419	−0.832098	−0.416049	−	0.909342i	$-0.636586\pi$
$877$	−24.6419	−0.832098	−0.416049	+	0.909342i	$0.636586\pi$
$878$	−44.2456	−1.49322
$879$	−51.0854	−1.72307
$880$	−4.66512	−0.157261
$881$	33.7368	1.13662	0.568310	−	0.822814i	$-0.307597\pi$
$881$	33.7368	1.13662	0.568310	+	0.822814i	$0.307597\pi$
$882$	−0.0371168	−0.00124979
$883$	−14.4918	−0.487688	−0.243844	−	0.969814i	$-0.578409\pi$
$883$	−14.4918	−0.487688	−0.243844	+	0.969814i	$0.578409\pi$
$884$	31.5492	1.06111
$885$	−4.51287	−0.151699
$886$	−42.6359	−1.43238
$887$	33.5778	1.12743	0.563715	−	0.825969i	$-0.309371\pi$
$887$	33.5778	1.12743	0.563715	+	0.825969i	$0.309371\pi$
$888$	50.4926	1.69442
$889$	−1.26742	−0.0425078
$890$	−5.93823	−0.199050
$891$	−12.7521	−0.427212
$892$	74.8243	2.50530
$893$	65.2355	2.18302
$894$	10.2165	0.341690
$895$	−14.1424	−0.472730
$896$	20.5846	0.687683
$897$	75.2358	2.51205
$898$	−66.9552	−2.23433
$899$	49.1281	1.63851
$900$	0.0400480	0.00133493
$901$	10.1465	0.338030
$902$	19.6316	0.653660
$903$	−11.2418	−0.374103
$904$	48.0341	1.59759
$905$	7.18814	0.238942
$906$	2.22354	0.0738721
$907$	−48.8360	−1.62157	−0.810786	−	0.585342i	$-0.800960\pi$
$907$	−48.8360	−1.62157	−0.810786	+	0.585342i	$0.800960\pi$
$908$	38.7473	1.28588
$909$	−0.0241771	−0.000801905 0
$910$	12.6004	0.417698
$911$	42.9142	1.42181	0.710905	−	0.703288i	$-0.248286\pi$
$911$	42.9142	1.42181	0.710905	+	0.703288i	$0.248286\pi$
$912$	−32.8310	−1.08714
$913$	6.74426	0.223203
$914$	−23.0398	−0.762090
$915$	13.8882	0.459130
$916$	−11.7526	−0.388317
$917$	−13.7263	−0.453283
$918$	19.7172	0.650764
$919$	13.3204	0.439399	0.219699	−	0.975568i	$-0.429492\pi$
$919$	13.3204	0.439399	0.219699	+	0.975568i	$0.429492\pi$
$920$	37.8273	1.24713
$921$	−4.66124	−0.153593
$922$	86.8888	2.86153
$923$	−5.53015	−0.182027
$924$	9.66192	0.317854
$925$	25.6467	0.843258
$926$	−7.58304	−0.249194
$927$	0.0399679	0.00131272
$928$	−7.02828	−0.230715
$929$	10.4686	0.343462	0.171731	−	0.985144i	$-0.445064\pi$
$929$	10.4686	0.343462	0.171731	+	0.985144i	$0.445064\pi$
$930$	−31.0936	−1.01960
$931$	34.0166	1.11485
$932$	−52.7650	−1.72837
$933$	−49.2643	−1.61284
$934$	101.031	3.30585
$935$	−2.18974	−0.0716121
$936$	0.0608504	0.00198896
$937$	48.8907	1.59719	0.798595	−	0.601869i	$-0.205577\pi$
$937$	48.8907	1.59719	0.798595	+	0.601869i	$0.205577\pi$
$938$	−35.1073	−1.14629
$939$	−17.8738	−0.583291
$940$	43.9807	1.43449
$941$	40.0606	1.30594	0.652970	−	0.757384i	$-0.273523\pi$
$941$	40.0606	1.30594	0.652970	+	0.757384i	$0.273523\pi$
$942$	65.0701	2.12010
$943$	−47.7504	−1.55497
$944$	8.78986	0.286086
$945$	5.19917	0.169129
$946$	22.0622	0.717304
$947$	25.2357	0.820050	0.410025	−	0.912074i	$-0.365520\pi$
$947$	25.2357	0.820050	0.410025	+	0.912074i	$0.365520\pi$
$948$	19.1001	0.620344
$949$	−20.1133	−0.652905
$950$	−55.5914	−1.80362
$951$	21.0579	0.682850
$952$	−7.24483	−0.234806
$953$	32.5129	1.05320	0.526598	−	0.850115i	$-0.323467\pi$
$953$	32.5129	1.05320	0.526598	+	0.850115i	$0.323467\pi$
$954$	0.0403199	0.00130541
$955$	22.9857	0.743801
$956$	14.3936	0.465521
$957$	−16.0940	−0.520245
$958$	84.8629	2.74179
$959$	6.55794	0.211767
$960$	15.8391	0.511206
$961$	25.1699	0.811934
$962$	80.2862	2.58853
$963$	−0.0373306	−0.00120296
$964$	−40.5811	−1.30703
$965$	−18.2051	−0.586043
$966$	−35.5952	−1.14526
$967$	6.64076	0.213553	0.106776	−	0.994283i	$-0.465947\pi$
$967$	6.64076	0.213553	0.106776	+	0.994283i	$0.465947\pi$
$968$	41.1374	1.32221
$969$	−15.4104	−0.495052
$970$	46.5699	1.49527
$971$	36.9906	1.18708	0.593542	−	0.804803i	$-0.297729\pi$
$971$	36.9906	1.18708	0.593542	+	0.804803i	$0.297729\pi$
$972$	0.103416	0.00331705
$973$	−18.9903	−0.608801
$974$	6.11858	0.196052
$975$	−36.1808	−1.15871
$976$	−27.0505	−0.865866
$977$	12.4930	0.399688	0.199844	−	0.979828i	$-0.435956\pi$
$977$	12.4930	0.399688	0.199844	+	0.979828i	$0.435956\pi$
$978$	−21.6638	−0.692733
$979$	−3.51417	−0.112313
$980$	22.9334	0.732581
$981$	0.0107121	0.000342012 0
$982$	10.5612	0.337021
$983$	−5.94244	−0.189534	−0.0947672	−	0.995499i	$-0.530211\pi$
$983$	−5.94244	−0.189534	−0.0947672	+	0.995499i	$0.530211\pi$
$984$	45.2092	1.44122
$985$	−3.94166	−0.125592
$986$	24.8631	0.791803
$987$	−20.0873	−0.639386
$988$	−114.898	−3.65538
$989$	−53.6624	−1.70637
$990$	−0.00870151	−0.000276552 0
$991$	−36.8594	−1.17088	−0.585438	−	0.810717i	$-0.699077\pi$
$991$	−36.8594	−1.17088	−0.585438	+	0.810717i	$0.699077\pi$
$992$	−8.03569	−0.255134
$993$	−30.8298	−0.978355
$994$	2.61640	0.0829872
$995$	7.63107	0.241921
$996$	31.9988	1.01392
$997$	−41.9169	−1.32752	−0.663761	−	0.747945i	$-0.731041\pi$
$997$	−41.9169	−1.32752	−0.663761	+	0.747945i	$0.731041\pi$
$998$	31.7853	1.00615
$999$	33.1277	1.04811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.b.1.15	✓	157

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.b.1.15	✓	157	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42617 q^{2} +1.73131 q^{3} +3.88629 q^{4} -0.987697 q^{5} -4.20045 q^{6} +1.01261 q^{7} -4.57644 q^{8} -0.00256059 q^{9} +O(q^{10})\)	\(q-2.42617 q^{2} +1.73131 q^{3} +3.88629 q^{4} -0.987697 q^{5} -4.20045 q^{6} +1.01261 q^{7} -4.57644 q^{8} -0.00256059 q^{9} +2.39632 q^{10} +1.41811 q^{11} +6.72837 q^{12} +5.19274 q^{13} -2.45676 q^{14} -1.71001 q^{15} +3.33064 q^{16} +1.56335 q^{17} +0.00621241 q^{18} -5.69351 q^{19} -3.83847 q^{20} +1.75315 q^{21} -3.44058 q^{22} +8.36861 q^{23} -7.92325 q^{24} -4.02445 q^{25} -12.5984 q^{26} -5.19837 q^{27} +3.93530 q^{28} -6.55507 q^{29} +4.14877 q^{30} -7.49466 q^{31} +1.07219 q^{32} +2.45519 q^{33} -3.79296 q^{34} -1.00015 q^{35} -0.00995117 q^{36} -6.37271 q^{37} +13.8134 q^{38} +8.99024 q^{39} +4.52014 q^{40} -5.70590 q^{41} -4.25342 q^{42} -6.41235 q^{43} +5.51119 q^{44} +0.00252908 q^{45} -20.3036 q^{46} -11.4579 q^{47} +5.76638 q^{48} -5.97462 q^{49} +9.76400 q^{50} +2.70665 q^{51} +20.1805 q^{52} +6.49023 q^{53} +12.6121 q^{54} -1.40067 q^{55} -4.63416 q^{56} -9.85724 q^{57} +15.9037 q^{58} +2.63909 q^{59} -6.64559 q^{60} -8.12170 q^{61} +18.1833 q^{62} -0.00259288 q^{63} -9.26260 q^{64} -5.12885 q^{65} -5.95671 q^{66} +14.2901 q^{67} +6.07564 q^{68} +14.4887 q^{69} +2.42654 q^{70} -1.06498 q^{71} +0.0117184 q^{72} -3.87335 q^{73} +15.4613 q^{74} -6.96758 q^{75} -22.1266 q^{76} +1.43600 q^{77} -21.8118 q^{78} +2.83875 q^{79} -3.28967 q^{80} -8.99231 q^{81} +13.8435 q^{82} +4.75580 q^{83} +6.81322 q^{84} -1.54412 q^{85} +15.5574 q^{86} -11.3489 q^{87} -6.48991 q^{88} -2.47806 q^{89} -0.00613598 q^{90} +5.25822 q^{91} +32.5228 q^{92} -12.9756 q^{93} +27.7987 q^{94} +5.62347 q^{95} +1.85629 q^{96} +19.4339 q^{97} +14.4954 q^{98} -0.00363120 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * q^99

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