LMFDB - Embedded newform 6019.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52129 q^{2} +0.498790 q^{3} +4.35689 q^{4} -0.537697 q^{5} -1.25759 q^{6} -2.34122 q^{7} -5.94240 q^{8} -2.75121 q^{9} +O(q^{10})$	\(q-2.52129 q^{2} +0.498790 q^{3} +4.35689 q^{4} -0.537697 q^{5} -1.25759 q^{6} -2.34122 q^{7} -5.94240 q^{8} -2.75121 q^{9} +1.35569 q^{10} +0.0314280 q^{11} +2.17318 q^{12} -1.00000 q^{13} +5.90288 q^{14} -0.268198 q^{15} +6.26873 q^{16} -4.25323 q^{17} +6.93659 q^{18} -1.37753 q^{19} -2.34269 q^{20} -1.16778 q^{21} -0.0792390 q^{22} -4.98217 q^{23} -2.96401 q^{24} -4.71088 q^{25} +2.52129 q^{26} -2.86865 q^{27} -10.2004 q^{28} +6.67889 q^{29} +0.676204 q^{30} +3.42160 q^{31} -3.92045 q^{32} +0.0156760 q^{33} +10.7236 q^{34} +1.25886 q^{35} -11.9867 q^{36} -9.67275 q^{37} +3.47315 q^{38} -0.498790 q^{39} +3.19521 q^{40} -6.24444 q^{41} +2.94430 q^{42} -2.65510 q^{43} +0.136928 q^{44} +1.47932 q^{45} +12.5615 q^{46} +8.10622 q^{47} +3.12678 q^{48} -1.51871 q^{49} +11.8775 q^{50} -2.12147 q^{51} -4.35689 q^{52} -12.6375 q^{53} +7.23268 q^{54} -0.0168987 q^{55} +13.9124 q^{56} -0.687100 q^{57} -16.8394 q^{58} +0.496912 q^{59} -1.16851 q^{60} +10.3973 q^{61} -8.62684 q^{62} +6.44117 q^{63} -2.65286 q^{64} +0.537697 q^{65} -0.0395237 q^{66} +6.97823 q^{67} -18.5308 q^{68} -2.48506 q^{69} -3.17396 q^{70} -5.98342 q^{71} +16.3488 q^{72} -11.4367 q^{73} +24.3878 q^{74} -2.34974 q^{75} -6.00176 q^{76} -0.0735797 q^{77} +1.25759 q^{78} -15.4889 q^{79} -3.37067 q^{80} +6.82277 q^{81} +15.7440 q^{82} +2.00663 q^{83} -5.08787 q^{84} +2.28694 q^{85} +6.69427 q^{86} +3.33137 q^{87} -0.186758 q^{88} +6.71943 q^{89} -3.72978 q^{90} +2.34122 q^{91} -21.7068 q^{92} +1.70666 q^{93} -20.4381 q^{94} +0.740694 q^{95} -1.95548 q^{96} -2.53684 q^{97} +3.82910 q^{98} -0.0864650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * 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 $

$2$	−2.52129	−1.78282	−0.891410	−	0.453198i	$-0.850283\pi$
$2$	−2.52129	−1.78282	−0.891410	+	0.453198i	$0.850283\pi$
$3$	0.498790	0.287977	0.143988	−	0.989579i	$-0.454007\pi$
$3$	0.498790	0.287977	0.143988	+	0.989579i	$0.454007\pi$
$4$	4.35689	2.17845
$5$	−0.537697	−0.240465	−0.120233	−	0.992746i	$-0.538364\pi$
$5$	−0.537697	−0.240465	−0.120233	+	0.992746i	$0.538364\pi$
$6$	−1.25759	−0.513411
$7$	−2.34122	−0.884896	−0.442448	−	0.896794i	$-0.645890\pi$
$7$	−2.34122	−0.884896	−0.442448	+	0.896794i	$0.645890\pi$
$8$	−5.94240	−2.10096
$9$	−2.75121	−0.917069
$10$	1.35569	0.428706
$11$	0.0314280	0.00947590	0.00473795	−	0.999989i	$-0.498492\pi$
$11$	0.0314280	0.00947590	0.00473795	+	0.999989i	$0.498492\pi$
$12$	2.17318	0.627342
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.90288	1.57761
$15$	−0.268198	−0.0692484
$16$	6.26873	1.56718
$17$	−4.25323	−1.03156	−0.515779	−	0.856721i	$-0.672498\pi$
$17$	−4.25323	−1.03156	−0.515779	+	0.856721i	$0.672498\pi$
$18$	6.93659	1.63497
$19$	−1.37753	−0.316028	−0.158014	−	0.987437i	$-0.550509\pi$
$19$	−1.37753	−0.316028	−0.158014	+	0.987437i	$0.550509\pi$
$20$	−2.34269	−0.523841
$21$	−1.16778	−0.254830
$22$	−0.0792390	−0.0168938
$23$	−4.98217	−1.03885	−0.519427	−	0.854515i	$-0.673855\pi$
$23$	−4.98217	−1.03885	−0.519427	+	0.854515i	$0.673855\pi$
$24$	−2.96401	−0.605027
$25$	−4.71088	−0.942176
$26$	2.52129	0.494465
$27$	−2.86865	−0.552071
$28$	−10.2004	−1.92770
$29$	6.67889	1.24024	0.620120	−	0.784507i	$-0.287084\pi$
$29$	6.67889	1.24024	0.620120	+	0.784507i	$0.287084\pi$
$30$	0.676204	0.123457
$31$	3.42160	0.614537	0.307269	−	0.951623i	$-0.400585\pi$
$31$	3.42160	0.614537	0.307269	+	0.951623i	$0.400585\pi$
$32$	−3.92045	−0.693045
$33$	0.0156760	0.00272884
$34$	10.7236	1.83908
$35$	1.25886	0.212787
$36$	−11.9867	−1.99779
$37$	−9.67275	−1.59019	−0.795095	−	0.606484i	$-0.792579\pi$
$37$	−9.67275	−1.59019	−0.795095	+	0.606484i	$0.792579\pi$
$38$	3.47315	0.563420
$39$	−0.498790	−0.0798704
$40$	3.19521	0.505207
$41$	−6.24444	−0.975218	−0.487609	−	0.873062i	$-0.662131\pi$
$41$	−6.24444	−0.975218	−0.487609	+	0.873062i	$0.662131\pi$
$42$	2.94430	0.454315
$43$	−2.65510	−0.404899	−0.202450	−	0.979293i	$-0.564890\pi$
$43$	−2.65510	−0.404899	−0.202450	+	0.979293i	$0.564890\pi$
$44$	0.136928	0.0206427
$45$	1.47932	0.220523
$46$	12.5615	1.85209
$47$	8.10622	1.18241	0.591207	−	0.806520i	$-0.298652\pi$
$47$	8.10622	1.18241	0.591207	+	0.806520i	$0.298652\pi$
$48$	3.12678	0.451312
$49$	−1.51871	−0.216959
$50$	11.8775	1.67973
$51$	−2.12147	−0.297065
$52$	−4.35689	−0.604192
$53$	−12.6375	−1.73589	−0.867944	−	0.496663i	$-0.834559\pi$
$53$	−12.6375	−1.73589	−0.867944	+	0.496663i	$0.834559\pi$
$54$	7.23268	0.984244
$55$	−0.0168987	−0.00227862
$56$	13.9124	1.85913
$57$	−0.687100	−0.0910086
$58$	−16.8394	−2.21112
$59$	0.496912	0.0646925	0.0323462	−	0.999477i	$-0.489702\pi$
$59$	0.496912	0.0646925	0.0323462	+	0.999477i	$0.489702\pi$
$60$	−1.16851	−0.150854
$61$	10.3973	1.33124	0.665619	−	0.746292i	$-0.268168\pi$
$61$	10.3973	1.33124	0.665619	+	0.746292i	$0.268168\pi$
$62$	−8.62684	−1.09561
$63$	6.44117	0.811511
$64$	−2.65286	−0.331607
$65$	0.537697	0.0666931
$66$	−0.0395237	−0.00486503
$67$	6.97823	0.852526	0.426263	−	0.904599i	$-0.359830\pi$
$67$	6.97823	0.852526	0.426263	+	0.904599i	$0.359830\pi$
$68$	−18.5308	−2.24719
$69$	−2.48506	−0.299166
$70$	−3.17396	−0.379361
$71$	−5.98342	−0.710101	−0.355050	−	0.934847i	$-0.615536\pi$
$71$	−5.98342	−0.710101	−0.355050	+	0.934847i	$0.615536\pi$
$72$	16.3488	1.92672
$73$	−11.4367	−1.33857	−0.669283	−	0.743008i	$-0.733399\pi$
$73$	−11.4367	−1.33857	−0.669283	+	0.743008i	$0.733399\pi$
$74$	24.3878	2.83502
$75$	−2.34974	−0.271325
$76$	−6.00176	−0.688449
$77$	−0.0735797	−0.00838519
$78$	1.25759	0.142394
$79$	−15.4889	−1.74264	−0.871319	−	0.490716i	$-0.836735\pi$
$79$	−15.4889	−1.74264	−0.871319	+	0.490716i	$0.836735\pi$
$80$	−3.37067	−0.376853
$81$	6.82277	0.758086
$82$	15.7440	1.73864
$83$	2.00663	0.220257	0.110128	−	0.993917i	$-0.464874\pi$
$83$	2.00663	0.220257	0.110128	+	0.993917i	$0.464874\pi$
$84$	−5.08787	−0.555132
$85$	2.28694	0.248054
$86$	6.69427	0.721862
$87$	3.33137	0.357160
$88$	−0.186758	−0.0199085
$89$	6.71943	0.712259	0.356129	−	0.934437i	$-0.384096\pi$
$89$	6.71943	0.712259	0.356129	+	0.934437i	$0.384096\pi$
$90$	−3.72978	−0.393153
$91$	2.34122	0.245426
$92$	−21.7068	−2.26309
$93$	1.70666	0.176972
$94$	−20.4381	−2.10803
$95$	0.740694	0.0759936
$96$	−1.95548	−0.199581
$97$	−2.53684	−0.257577	−0.128789	−	0.991672i	$-0.541109\pi$
$97$	−2.53684	−0.257577	−0.128789	+	0.991672i	$0.541109\pi$
$98$	3.82910	0.386798
$99$	−0.0864650	−0.00869006
$100$	−20.5248	−2.05248
$101$	0.264104	0.0262793	0.0131397	−	0.999914i	$-0.495817\pi$
$101$	0.264104	0.0262793	0.0131397	+	0.999914i	$0.495817\pi$
$102$	5.34883	0.529613
$103$	−9.18368	−0.904894	−0.452447	−	0.891791i	$-0.649449\pi$
$103$	−9.18368	−0.904894	−0.452447	+	0.891791i	$0.649449\pi$
$104$	5.94240	0.582701
$105$	0.627909	0.0612777
$106$	31.8627	3.09477
$107$	−8.98166	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$107$	−8.98166	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$108$	−12.4984	−1.20266
$109$	−13.0564	−1.25058	−0.625289	−	0.780393i	$-0.715019\pi$
$109$	−13.0564	−1.25058	−0.625289	+	0.780393i	$0.715019\pi$
$110$	0.0426066	0.00406238
$111$	−4.82468	−0.457938
$112$	−14.6764	−1.38679
$113$	0.513179	0.0482758	0.0241379	−	0.999709i	$-0.492316\pi$
$113$	0.513179	0.0482758	0.0241379	+	0.999709i	$0.492316\pi$
$114$	1.73238	0.162252
$115$	2.67890	0.249808
$116$	29.0992	2.70179
$117$	2.75121	0.254349
$118$	−1.25286	−0.115335
$119$	9.95772	0.912822
$120$	1.59374	0.145488
$121$	−10.9990	−0.999910
$122$	−26.2146	−2.37336
$123$	−3.11467	−0.280840
$124$	14.9075	1.33874
$125$	5.22151	0.467026
$126$	−16.2400	−1.44678
$127$	−6.61847	−0.587294	−0.293647	−	0.955914i	$-0.594869\pi$
$127$	−6.61847	−0.587294	−0.293647	+	0.955914i	$0.594869\pi$
$128$	14.5295	1.28424
$129$	−1.32434	−0.116602
$130$	−1.35569	−0.118902
$131$	13.3797	1.16899	0.584496	−	0.811397i	$-0.301292\pi$
$131$	13.3797	1.16899	0.584496	+	0.811397i	$0.301292\pi$
$132$	0.0682986	0.00594463
$133$	3.22510	0.279652
$134$	−17.5941	−1.51990
$135$	1.54246	0.132754
$136$	25.2744	2.16726
$137$	3.18150	0.271814	0.135907	−	0.990722i	$-0.456605\pi$
$137$	3.18150	0.271814	0.135907	+	0.990722i	$0.456605\pi$
$138$	6.26555	0.533359
$139$	17.7097	1.50211	0.751057	−	0.660238i	$-0.229545\pi$
$139$	17.7097	1.50211	0.751057	+	0.660238i	$0.229545\pi$
$140$	5.48473	0.463545
$141$	4.04330	0.340508
$142$	15.0859	1.26598
$143$	−0.0314280	−0.00262814
$144$	−17.2466	−1.43721
$145$	−3.59122	−0.298234
$146$	28.8352	2.38642
$147$	−0.757518	−0.0624790
$148$	−42.1431	−3.46414
$149$	−13.1900	−1.08057	−0.540283	−	0.841483i	$-0.681683\pi$
$149$	−13.1900	−1.08057	−0.540283	+	0.841483i	$0.681683\pi$
$150$	5.92438	0.483723
$151$	7.67623	0.624683	0.312341	−	0.949970i	$-0.398887\pi$
$151$	7.67623	0.624683	0.312341	+	0.949970i	$0.398887\pi$
$152$	8.18585	0.663960
$153$	11.7015	0.946011
$154$	0.185516	0.0149493
$155$	−1.83978	−0.147775
$156$	−2.17318	−0.173993
$157$	−14.5425	−1.16062	−0.580311	−	0.814395i	$-0.697069\pi$
$157$	−14.5425	−1.16062	−0.580311	+	0.814395i	$0.697069\pi$
$158$	39.0520	3.10681
$159$	−6.30344	−0.499895
$160$	2.10801	0.166653
$161$	11.6643	0.919279
$162$	−17.2022	−1.35153
$163$	14.8976	1.16687	0.583434	−	0.812160i	$-0.301709\pi$
$163$	14.8976	1.16687	0.583434	+	0.812160i	$0.301709\pi$
$164$	−27.2064	−2.12446
$165$	−0.00842892	−0.000656191 0
$166$	−5.05930	−0.392678
$167$	8.15036	0.630694	0.315347	−	0.948976i	$-0.397879\pi$
$167$	8.15036	0.630694	0.315347	+	0.948976i	$0.397879\pi$
$168$	6.93939	0.535386
$169$	1.00000	0.0769231
$170$	−5.76605	−0.442236
$171$	3.78988	0.289819
$172$	−11.5680	−0.882051
$173$	2.25580	0.171505	0.0857525	−	0.996316i	$-0.472671\pi$
$173$	2.25580	0.171505	0.0857525	+	0.996316i	$0.472671\pi$
$174$	−8.39934	−0.636752
$175$	11.0292	0.833728
$176$	0.197013	0.0148505
$177$	0.247855	0.0186299
$178$	−16.9416	−1.26983
$179$	−1.25402	−0.0937296	−0.0468648	−	0.998901i	$-0.514923\pi$
$179$	−1.25402	−0.0937296	−0.0468648	+	0.998901i	$0.514923\pi$
$180$	6.44522	0.480398
$181$	−6.40169	−0.475834	−0.237917	−	0.971285i	$-0.576465\pi$
$181$	−6.40169	−0.475834	−0.237917	+	0.971285i	$0.576465\pi$
$182$	−5.90288	−0.437550
$183$	5.18607	0.383366
$184$	29.6061	2.18259
$185$	5.20101	0.382386
$186$	−4.30298	−0.315510
$187$	−0.133670	−0.00977494
$188$	35.3179	2.57583
$189$	6.71612	0.488526
$190$	−1.86750	−0.135483
$191$	7.86371	0.568998	0.284499	−	0.958676i	$-0.408173\pi$
$191$	7.86371	0.568998	0.284499	+	0.958676i	$0.408173\pi$
$192$	−1.32322	−0.0954952
$193$	17.2718	1.24325	0.621627	−	0.783313i	$-0.286472\pi$
$193$	17.2718	1.24325	0.621627	+	0.783313i	$0.286472\pi$
$194$	6.39611	0.459214
$195$	0.268198	0.0192060
$196$	−6.61685	−0.472632
$197$	12.0808	0.860721	0.430361	−	0.902657i	$-0.358386\pi$
$197$	12.0808	0.860721	0.430361	+	0.902657i	$0.358386\pi$
$198$	0.218003	0.0154928
$199$	19.2690	1.36594	0.682972	−	0.730445i	$-0.260687\pi$
$199$	19.2690	1.36594	0.682972	+	0.730445i	$0.260687\pi$
$200$	27.9940	1.97947
$201$	3.48067	0.245508
$202$	−0.665882	−0.0468513
$203$	−15.6367	−1.09748
$204$	−9.24301	−0.647140
$205$	3.35762	0.234506
$206$	23.1547	1.61326
$207$	13.7070	0.952702
$208$	−6.26873	−0.434658
$209$	−0.0432931	−0.00299464
$210$	−1.58314	−0.109247
$211$	−22.7599	−1.56685	−0.783427	−	0.621484i	$-0.786530\pi$
$211$	−22.7599	−1.56685	−0.783427	+	0.621484i	$0.786530\pi$
$212$	−55.0600	−3.78154
$213$	−2.98447	−0.204493
$214$	22.6453	1.54800
$215$	1.42764	0.0973642
$216$	17.0467	1.15988
$217$	−8.01070	−0.543802
$218$	32.9190	2.22955
$219$	−5.70452	−0.385476
$220$	−0.0736259	−0.00496386
$221$	4.25323	0.286103
$222$	12.1644	0.816421
$223$	−5.95481	−0.398764	−0.199382	−	0.979922i	$-0.563893\pi$
$223$	−5.95481	−0.398764	−0.199382	+	0.979922i	$0.563893\pi$
$224$	9.17863	0.613273
$225$	12.9606	0.864041
$226$	−1.29387	−0.0860671
$227$	15.9663	1.05972	0.529860	−	0.848085i	$-0.322244\pi$
$227$	15.9663	1.05972	0.529860	+	0.848085i	$0.322244\pi$
$228$	−2.99362	−0.198257
$229$	18.1454	1.19908	0.599541	−	0.800344i	$-0.295350\pi$
$229$	18.1454	1.19908	0.599541	+	0.800344i	$0.295350\pi$
$230$	−6.75427	−0.445363
$231$	−0.0367009	−0.00241474
$232$	−39.6887	−2.60569
$233$	−6.08385	−0.398566	−0.199283	−	0.979942i	$-0.563861\pi$
$233$	−6.08385	−0.398566	−0.199283	+	0.979942i	$0.563861\pi$
$234$	−6.93659	−0.453459
$235$	−4.35869	−0.284329
$236$	2.16499	0.140929
$237$	−7.72572	−0.501839
$238$	−25.1063	−1.62740
$239$	21.9647	1.42078	0.710388	−	0.703810i	$-0.248519\pi$
$239$	21.9647	1.42078	0.710388	+	0.703810i	$0.248519\pi$
$240$	−1.68126	−0.108525
$241$	21.6059	1.39176	0.695878	−	0.718160i	$-0.255015\pi$
$241$	21.6059	1.39176	0.695878	+	0.718160i	$0.255015\pi$
$242$	27.7317	1.78266
$243$	12.0091	0.770382
$244$	45.2999	2.90003
$245$	0.816605	0.0521710
$246$	7.85297	0.500687
$247$	1.37753	0.0876503
$248$	−20.3325	−1.29112
$249$	1.00089	0.0634288
$250$	−13.1649	−0.832623
$251$	−13.9521	−0.880651	−0.440325	−	0.897838i	$-0.645137\pi$
$251$	−13.9521	−0.880651	−0.440325	+	0.897838i	$0.645137\pi$
$252$	28.0635	1.76783
$253$	−0.156580	−0.00984408
$254$	16.6871	1.04704
$255$	1.14071	0.0714338
$256$	−31.3274	−1.95796
$257$	9.58796	0.598080	0.299040	−	0.954241i	$-0.403334\pi$
$257$	9.58796	0.598080	0.299040	+	0.954241i	$0.403334\pi$
$258$	3.33904	0.207880
$259$	22.6460	1.40715
$260$	2.34269	0.145287
$261$	−18.3750	−1.13739
$262$	−33.7341	−2.08410
$263$	−9.55183	−0.588991	−0.294496	−	0.955653i	$-0.595152\pi$
$263$	−9.55183	−0.588991	−0.294496	+	0.955653i	$0.595152\pi$
$264$	−0.0931530	−0.00573317
$265$	6.79512	0.417421
$266$	−8.13140	−0.498568
$267$	3.35159	0.205114
$268$	30.4034	1.85718
$269$	20.8420	1.27076	0.635380	−	0.772199i	$-0.280843\pi$
$269$	20.8420	1.27076	0.635380	+	0.772199i	$0.280843\pi$
$270$	−3.88899	−0.236676
$271$	−31.4149	−1.90832	−0.954160	−	0.299298i	$-0.903247\pi$
$271$	−31.4149	−1.90832	−0.954160	+	0.299298i	$0.903247\pi$
$272$	−26.6623	−1.61664
$273$	1.16778	0.0706770
$274$	−8.02148	−0.484595
$275$	−0.148054	−0.00892797
$276$	−10.8271	−0.651717
$277$	−8.34815	−0.501592	−0.250796	−	0.968040i	$-0.580692\pi$
$277$	−8.34815	−0.501592	−0.250796	+	0.968040i	$0.580692\pi$
$278$	−44.6511	−2.67800
$279$	−9.41353	−0.563573
$280$	−7.48068	−0.447056
$281$	−19.8398	−1.18354	−0.591772	−	0.806105i	$-0.701571\pi$
$281$	−19.8398	−1.18354	−0.591772	+	0.806105i	$0.701571\pi$
$282$	−10.1943	−0.607064
$283$	−20.5617	−1.22227	−0.611133	−	0.791528i	$-0.709286\pi$
$283$	−20.5617	−1.22227	−0.611133	+	0.791528i	$0.709286\pi$
$284$	−26.0691	−1.54692
$285$	0.369451	0.0218844
$286$	0.0792390	0.00468550
$287$	14.6196	0.862967
$288$	10.7860	0.635570
$289$	1.08992	0.0641132
$290$	9.05449	0.531698
$291$	−1.26535	−0.0741763
$292$	−49.8285	−2.91599
$293$	−9.46625	−0.553024	−0.276512	−	0.961010i	$-0.589179\pi$
$293$	−9.46625	−0.553024	−0.276512	+	0.961010i	$0.589179\pi$
$294$	1.90992	0.111389
$295$	−0.267188	−0.0155563
$296$	57.4794	3.34092
$297$	−0.0901558	−0.00523137
$298$	33.2558	1.92646
$299$	4.98217	0.288126
$300$	−10.2376	−0.591067
$301$	6.21616	0.358294
$302$	−19.3540	−1.11370
$303$	0.131732	0.00756783
$304$	−8.63537	−0.495272
$305$	−5.59059	−0.320116
$306$	−29.5029	−1.68657
$307$	−12.1323	−0.692429	−0.346215	−	0.938155i	$-0.612533\pi$
$307$	−12.1323	−0.692429	−0.346215	+	0.938155i	$0.612533\pi$
$308$	−0.320579	−0.0182667
$309$	−4.58073	−0.260589
$310$	4.63862	0.263456
$311$	25.1350	1.42527	0.712637	−	0.701533i	$-0.247501\pi$
$311$	25.1350	1.42527	0.712637	+	0.701533i	$0.247501\pi$
$312$	2.96401	0.167804
$313$	−0.523928	−0.0296142	−0.0148071	−	0.999890i	$-0.504713\pi$
$313$	−0.523928	−0.0296142	−0.0148071	+	0.999890i	$0.504713\pi$
$314$	36.6659	2.06918
$315$	−3.46340	−0.195140
$316$	−67.4835	−3.79624
$317$	−5.74571	−0.322711	−0.161356	−	0.986896i	$-0.551587\pi$
$317$	−5.74571	−0.322711	−0.161356	+	0.986896i	$0.551587\pi$
$318$	15.8928	0.891223
$319$	0.209904	0.0117524
$320$	1.42643	0.0797400
$321$	−4.47996	−0.250047
$322$	−29.4092	−1.63891
$323$	5.85895	0.326001
$324$	29.7261	1.65145
$325$	4.71088	0.261313
$326$	−37.5611	−2.08032
$327$	−6.51241	−0.360137
$328$	37.1070	2.04889
$329$	−18.9784	−1.04631
$330$	0.0212517	0.00116987
$331$	2.81337	0.154637	0.0773185	−	0.997006i	$-0.475364\pi$
$331$	2.81337	0.154637	0.0773185	+	0.997006i	$0.475364\pi$
$332$	8.74269	0.479817
$333$	26.6118	1.45832
$334$	−20.5494	−1.12441
$335$	−3.75217	−0.205003
$336$	−7.32047	−0.399364
$337$	−15.9085	−0.866593	−0.433297	−	0.901251i	$-0.642650\pi$
$337$	−15.9085	−0.866593	−0.433297	+	0.901251i	$0.642650\pi$
$338$	−2.52129	−0.137140
$339$	0.255969	0.0139023
$340$	9.96397	0.540372
$341$	0.107534	0.00582329
$342$	−9.55537	−0.516695
$343$	19.9441	1.07688
$344$	15.7777	0.850676
$345$	1.33621	0.0719390
$346$	−5.68751	−0.305763
$347$	−22.1137	−1.18712	−0.593562	−	0.804788i	$-0.702279\pi$
$347$	−22.1137	−1.18712	−0.593562	+	0.804788i	$0.702279\pi$
$348$	14.5144	0.778054
$349$	−13.6568	−0.731029	−0.365515	−	0.930806i	$-0.619107\pi$
$349$	−13.6568	−0.731029	−0.365515	+	0.930806i	$0.619107\pi$
$350$	−27.8078	−1.48639
$351$	2.86865	0.153117
$352$	−0.123212	−0.00656722
$353$	3.12097	0.166113	0.0830563	−	0.996545i	$-0.473532\pi$
$353$	3.12097	0.166113	0.0830563	+	0.996545i	$0.473532\pi$
$354$	−0.624914	−0.0332138
$355$	3.21726	0.170755
$356$	29.2759	1.55162
$357$	4.96681	0.262872
$358$	3.16174	0.167103
$359$	−3.45253	−0.182217	−0.0911087	−	0.995841i	$-0.529041\pi$
$359$	−3.45253	−0.182217	−0.0911087	+	0.995841i	$0.529041\pi$
$360$	−8.79069	−0.463310
$361$	−17.1024	−0.900127
$362$	16.1405	0.848326
$363$	−5.48620	−0.287951
$364$	10.2004	0.534647
$365$	6.14948	0.321879
$366$	−13.0756	−0.683472
$367$	−6.55515	−0.342176	−0.171088	−	0.985256i	$-0.554728\pi$
$367$	−6.55515	−0.342176	−0.171088	+	0.985256i	$0.554728\pi$
$368$	−31.2319	−1.62807
$369$	17.1798	0.894343
$370$	−13.1132	−0.681725
$371$	29.5870	1.53608
$372$	7.43574	0.385525
$373$	−17.6395	−0.913336	−0.456668	−	0.889637i	$-0.650957\pi$
$373$	−17.6395	−0.913336	−0.456668	+	0.889637i	$0.650957\pi$
$374$	0.337021	0.0174270
$375$	2.60444	0.134493
$376$	−48.1704	−2.48420
$377$	−6.67889	−0.343980
$378$	−16.9333	−0.870954
$379$	−10.7557	−0.552482	−0.276241	−	0.961088i	$-0.589089\pi$
$379$	−10.7557	−0.552482	−0.276241	+	0.961088i	$0.589089\pi$
$380$	3.22713	0.165548
$381$	−3.30123	−0.169127
$382$	−19.8267	−1.01442
$383$	9.38932	0.479772	0.239886	−	0.970801i	$-0.422890\pi$
$383$	9.38932	0.479772	0.239886	+	0.970801i	$0.422890\pi$
$384$	7.24719	0.369832
$385$	0.0395636	0.00201635
$386$	−43.5473	−2.21650
$387$	7.30474	0.371321
$388$	−11.0528	−0.561119
$389$	0.738525	0.0374447	0.0187223	−	0.999825i	$-0.494040\pi$
$389$	0.738525	0.0374447	0.0187223	+	0.999825i	$0.494040\pi$
$390$	−0.676204	−0.0342409
$391$	21.1903	1.07164
$392$	9.02478	0.455820
$393$	6.67368	0.336642
$394$	−30.4592	−1.53451
$395$	8.32834	0.419044
$396$	−0.376719	−0.0189308
$397$	5.25986	0.263985	0.131992	−	0.991251i	$-0.457863\pi$
$397$	5.25986	0.263985	0.131992	+	0.991251i	$0.457863\pi$
$398$	−48.5827	−2.43523
$399$	1.60865	0.0805332
$400$	−29.5312	−1.47656
$401$	−17.8668	−0.892227	−0.446113	−	0.894976i	$-0.647192\pi$
$401$	−17.8668	−0.892227	−0.446113	+	0.894976i	$0.647192\pi$
$402$	−8.77578	−0.437696
$403$	−3.42160	−0.170442
$404$	1.15067	0.0572481
$405$	−3.66858	−0.182293
$406$	39.4247	1.95661
$407$	−0.303995	−0.0150685
$408$	12.6066	0.624121
$409$	22.2742	1.10139	0.550693	−	0.834708i	$-0.314364\pi$
$409$	22.2742	1.10139	0.550693	+	0.834708i	$0.314364\pi$
$410$	−8.46552	−0.418082
$411$	1.58690	0.0782761
$412$	−40.0123	−1.97126
$413$	−1.16338	−0.0572461
$414$	−34.5593	−1.69850
$415$	−1.07896	−0.0529641
$416$	3.92045	0.192216
$417$	8.83340	0.432574
$418$	0.109154	0.00533891
$419$	−3.91635	−0.191326	−0.0956631	−	0.995414i	$-0.530497\pi$
$419$	−3.91635	−0.191326	−0.0956631	+	0.995414i	$0.530497\pi$
$420$	2.73573	0.133490
$421$	11.2625	0.548899	0.274450	−	0.961602i	$-0.411504\pi$
$421$	11.2625	0.548899	0.274450	+	0.961602i	$0.411504\pi$
$422$	57.3842	2.79342
$423$	−22.3019	−1.08436
$424$	75.0968	3.64702
$425$	20.0364	0.971910
$426$	7.52471	0.364573
$427$	−24.3423	−1.17801
$428$	−39.1321	−1.89152
$429$	−0.0156760	−0.000756844 0
$430$	−3.59949	−0.173583
$431$	25.2762	1.21751	0.608756	−	0.793357i	$-0.291669\pi$
$431$	25.2762	1.21751	0.608756	+	0.793357i	$0.291669\pi$
$432$	−17.9828	−0.865196
$433$	−4.02471	−0.193415	−0.0967076	−	0.995313i	$-0.530831\pi$
$433$	−4.02471	−0.193415	−0.0967076	+	0.995313i	$0.530831\pi$
$434$	20.1973	0.969501
$435$	−1.79126	−0.0858846
$436$	−56.8854	−2.72432
$437$	6.86310	0.328307
$438$	14.3827	0.687234
$439$	−21.3991	−1.02132	−0.510661	−	0.859782i	$-0.670599\pi$
$439$	−21.3991	−1.02132	−0.510661	+	0.859782i	$0.670599\pi$
$440$	0.100419	0.00478729
$441$	4.17829	0.198966
$442$	−10.7236	−0.510070
$443$	4.80176	0.228139	0.114069	−	0.993473i	$-0.463611\pi$
$443$	4.80176	0.228139	0.114069	+	0.993473i	$0.463611\pi$
$444$	−21.0206	−0.997593
$445$	−3.61302	−0.171273
$446$	15.0138	0.710924
$447$	−6.57904	−0.311178
$448$	6.21091	0.293438
$449$	11.7697	0.555446	0.277723	−	0.960661i	$-0.410420\pi$
$449$	11.7697	0.555446	0.277723	+	0.960661i	$0.410420\pi$
$450$	−32.6774	−1.54043
$451$	−0.196250	−0.00924107
$452$	2.23587	0.105166
$453$	3.82883	0.179894
$454$	−40.2556	−1.88929
$455$	−1.25886	−0.0590164
$456$	4.08302	0.191205
$457$	30.5383	1.42852	0.714260	−	0.699880i	$-0.246763\pi$
$457$	30.5383	1.42852	0.714260	+	0.699880i	$0.246763\pi$
$458$	−45.7498	−2.13775
$459$	12.2010	0.569494
$460$	11.6717	0.544194
$461$	−20.6887	−0.963570	−0.481785	−	0.876290i	$-0.660011\pi$
$461$	−20.6887	−0.963570	−0.481785	+	0.876290i	$0.660011\pi$
$462$	0.0925334	0.00430504
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	41.8681	1.94368
$465$	−0.917666	−0.0425557
$466$	15.3391	0.710572
$467$	3.60116	0.166642	0.0833209	−	0.996523i	$-0.473447\pi$
$467$	3.60116	0.166642	0.0833209	+	0.996523i	$0.473447\pi$
$468$	11.9867	0.554086
$469$	−16.3375	−0.754397
$470$	10.9895	0.506908
$471$	−7.25368	−0.334232
$472$	−2.95285	−0.135916
$473$	−0.0834445	−0.00383678
$474$	19.4788	0.894689
$475$	6.48939	0.297754
$476$	43.3847	1.98853
$477$	34.7683	1.59193
$478$	−55.3793	−2.53299
$479$	12.6193	0.576592	0.288296	−	0.957541i	$-0.406911\pi$
$479$	12.6193	0.576592	0.288296	+	0.957541i	$0.406911\pi$
$480$	1.05146	0.0479922
$481$	9.67275	0.441040
$482$	−54.4746	−2.48125
$483$	5.81806	0.264731
$484$	−47.9215	−2.17825
$485$	1.36405	0.0619384
$486$	−30.2783	−1.37345
$487$	−24.1961	−1.09643	−0.548216	−	0.836337i	$-0.684693\pi$
$487$	−24.1961	−1.09643	−0.548216	+	0.836337i	$0.684693\pi$
$488$	−61.7850	−2.79687
$489$	7.43077	0.336031
$490$	−2.05890	−0.0930115
$491$	−19.9292	−0.899393	−0.449697	−	0.893181i	$-0.648468\pi$
$491$	−19.9292	−0.899393	−0.449697	+	0.893181i	$0.648468\pi$
$492$	−13.5703	−0.611795
$493$	−28.4068	−1.27938
$494$	−3.47315	−0.156265
$495$	0.0464919	0.00208966
$496$	21.4491	0.963091
$497$	14.0085	0.628366
$498$	−2.52353	−0.113082
$499$	−12.5714	−0.562775	−0.281387	−	0.959594i	$-0.590795\pi$
$499$	−12.5714	−0.562775	−0.281387	+	0.959594i	$0.590795\pi$
$500$	22.7496	1.01739
$501$	4.06532	0.181625
$502$	35.1773	1.57004
$503$	23.6461	1.05433	0.527165	−	0.849763i	$-0.323255\pi$
$503$	23.6461	1.05433	0.527165	+	0.849763i	$0.323255\pi$
$504$	−38.2760	−1.70495
$505$	−0.142008	−0.00631926
$506$	0.394783	0.0175502
$507$	0.498790	0.0221521
$508$	−28.8359	−1.27939
$509$	31.5265	1.39739	0.698694	−	0.715421i	$-0.253765\pi$
$509$	31.5265	1.39739	0.698694	+	0.715421i	$0.253765\pi$
$510$	−2.87605	−0.127354
$511$	26.7758	1.18449
$512$	49.9263	2.20645
$513$	3.95165	0.174470
$514$	−24.1740	−1.06627
$515$	4.93803	0.217596
$516$	−5.77000	−0.254010
$517$	0.254762	0.0112044
$518$	−57.0971	−2.50870
$519$	1.12517	0.0493895
$520$	−3.19521	−0.140119
$521$	21.1480	0.926513	0.463256	−	0.886224i	$-0.346681\pi$
$521$	21.1480	0.926513	0.463256	+	0.886224i	$0.346681\pi$
$522$	46.3287	2.02775
$523$	33.8563	1.48043	0.740217	−	0.672368i	$-0.234723\pi$
$523$	33.8563	1.48043	0.740217	+	0.672368i	$0.234723\pi$
$524$	58.2940	2.54659
$525$	5.50125	0.240094
$526$	24.0829	1.05006
$527$	−14.5528	−0.633931
$528$	0.0982684	0.00427658
$529$	1.82204	0.0792192
$530$	−17.1324	−0.744186
$531$	−1.36711	−0.0593275
$532$	14.0514	0.609206
$533$	6.24444	0.270477
$534$	−8.45032	−0.365681
$535$	4.82941	0.208793
$536$	−41.4675	−1.79112
$537$	−0.625491	−0.0269919
$538$	−52.5487	−2.26554
$539$	−0.0477300	−0.00205588
$540$	6.72034	0.289197
$541$	−6.23342	−0.267996	−0.133998	−	0.990982i	$-0.542781\pi$
$541$	−6.23342	−0.267996	−0.133998	+	0.990982i	$0.542781\pi$
$542$	79.2060	3.40219
$543$	−3.19310	−0.137029
$544$	16.6746	0.714916
$545$	7.02039	0.300720
$546$	−2.94430	−0.126004
$547$	15.8263	0.676686	0.338343	−	0.941023i	$-0.390134\pi$
$547$	15.8263	0.676686	0.338343	+	0.941023i	$0.390134\pi$
$548$	13.8615	0.592132
$549$	−28.6051	−1.22084
$550$	0.373286	0.0159170
$551$	−9.20039	−0.391950
$552$	14.7672	0.628535
$553$	36.2629	1.54205
$554$	21.0481	0.894247
$555$	2.59421	0.110118
$556$	77.1590	3.27227
$557$	−2.50821	−0.106276	−0.0531381	−	0.998587i	$-0.516922\pi$
$557$	−2.50821	−0.106276	−0.0531381	+	0.998587i	$0.516922\pi$
$558$	23.7342	1.00475
$559$	2.65510	0.112299
$560$	7.89147	0.333476
$561$	−0.0666735	−0.00281496
$562$	50.0219	2.11005
$563$	36.5607	1.54085	0.770425	−	0.637531i	$-0.220044\pi$
$563$	36.5607	1.54085	0.770425	+	0.637531i	$0.220044\pi$
$564$	17.6162	0.741778
$565$	−0.275935	−0.0116087
$566$	51.8419	2.17908
$567$	−15.9736	−0.670827
$568$	35.5559	1.49189
$569$	12.7865	0.536038	0.268019	−	0.963414i	$-0.413631\pi$
$569$	12.7865	0.536038	0.268019	+	0.963414i	$0.413631\pi$
$570$	−0.931493	−0.0390159
$571$	16.1393	0.675407	0.337704	−	0.941252i	$-0.390350\pi$
$571$	16.1393	0.675407	0.337704	+	0.941252i	$0.390350\pi$
$572$	−0.136928	−0.00572526
$573$	3.92234	0.163858
$574$	−36.8602	−1.53851
$575$	23.4704	0.978784
$576$	7.29857	0.304107
$577$	3.86339	0.160835	0.0804175	−	0.996761i	$-0.474375\pi$
$577$	3.86339	0.160835	0.0804175	+	0.996761i	$0.474375\pi$
$578$	−2.74801	−0.114302
$579$	8.61502	0.358028
$580$	−15.6466	−0.649688
$581$	−4.69796	−0.194904
$582$	3.19032	0.132243
$583$	−0.397170	−0.0164491
$584$	67.9615	2.81227
$585$	−1.47932	−0.0611622
$586$	23.8671	0.985942
$587$	−14.4568	−0.596696	−0.298348	−	0.954457i	$-0.596436\pi$
$587$	−14.4568	−0.596696	−0.298348	+	0.954457i	$0.596436\pi$
$588$	−3.30042	−0.136107
$589$	−4.71336	−0.194211
$590$	0.673658	0.0277341
$591$	6.02578	0.247868
$592$	−60.6358	−2.49212
$593$	40.9769	1.68272	0.841360	−	0.540475i	$-0.181755\pi$
$593$	40.9769	1.68272	0.841360	+	0.540475i	$0.181755\pi$
$594$	0.227309	0.00932659
$595$	−5.35423	−0.219502
$596$	−57.4674	−2.35396
$597$	9.61120	0.393360
$598$	−12.5615	−0.513678
$599$	−29.1221	−1.18990	−0.594948	−	0.803764i	$-0.702827\pi$
$599$	−29.1221	−1.18990	−0.594948	+	0.803764i	$0.702827\pi$
$600$	13.9631	0.570042
$601$	15.7974	0.644390	0.322195	−	0.946673i	$-0.395579\pi$
$601$	15.7974	0.644390	0.322195	+	0.946673i	$0.395579\pi$
$602$	−15.6727	−0.638773
$603$	−19.1986	−0.781826
$604$	33.4445	1.36084
$605$	5.91413	0.240444
$606$	−0.332135	−0.0134921
$607$	−5.19474	−0.210848	−0.105424	−	0.994427i	$-0.533620\pi$
$607$	−5.19474	−0.210848	−0.105424	+	0.994427i	$0.533620\pi$
$608$	5.40055	0.219021
$609$	−7.79945	−0.316050
$610$	14.0955	0.570710
$611$	−8.10622	−0.327943
$612$	50.9822	2.06083
$613$	14.9251	0.602821	0.301410	−	0.953495i	$-0.402543\pi$
$613$	14.9251	0.602821	0.301410	+	0.953495i	$0.402543\pi$
$614$	30.5891	1.23448
$615$	1.67475	0.0675323
$616$	0.437240	0.0176169
$617$	13.0246	0.524351	0.262176	−	0.965020i	$-0.415560\pi$
$617$	13.0246	0.524351	0.262176	+	0.965020i	$0.415560\pi$
$618$	11.5493	0.464582
$619$	−6.20785	−0.249514	−0.124757	−	0.992187i	$-0.539815\pi$
$619$	−6.20785	−0.249514	−0.124757	+	0.992187i	$0.539815\pi$
$620$	−8.01573	−0.321920
$621$	14.2921	0.573522
$622$	−63.3725	−2.54101
$623$	−15.7316	−0.630275
$624$	−3.12678	−0.125171
$625$	20.7468	0.829873
$626$	1.32097	0.0527967
$627$	−0.0215942	−0.000862388 0
$628$	−63.3603	−2.52835
$629$	41.1404	1.64037
$630$	8.73222	0.347900
$631$	19.4140	0.772860	0.386430	−	0.922319i	$-0.373708\pi$
$631$	19.4140	0.772860	0.386430	+	0.922319i	$0.373708\pi$
$632$	92.0414	3.66121
$633$	−11.3524	−0.451218
$634$	14.4866	0.575336
$635$	3.55873	0.141224
$636$	−27.4634	−1.08899
$637$	1.51871	0.0601735
$638$	−0.529229	−0.0209524
$639$	16.4616	0.651212
$640$	−7.81248	−0.308815
$641$	29.6837	1.17244	0.586218	−	0.810153i	$-0.300616\pi$
$641$	29.6837	1.17244	0.586218	+	0.810153i	$0.300616\pi$
$642$	11.2953	0.445789
$643$	30.2387	1.19250	0.596249	−	0.802800i	$-0.296657\pi$
$643$	30.2387	1.19250	0.596249	+	0.802800i	$0.296657\pi$
$644$	50.8203	2.00260
$645$	0.712093	0.0280386
$646$	−14.7721	−0.581201
$647$	−6.19714	−0.243635	−0.121817	−	0.992553i	$-0.538872\pi$
$647$	−6.19714	−0.243635	−0.121817	+	0.992553i	$0.538872\pi$
$648$	−40.5437	−1.59271
$649$	0.0156170	0.000613019 0
$650$	−11.8775	−0.465873
$651$	−3.99566	−0.156602
$652$	64.9071	2.54196
$653$	21.4386	0.838956	0.419478	−	0.907766i	$-0.362213\pi$
$653$	21.4386	0.838956	0.419478	+	0.907766i	$0.362213\pi$
$654$	16.4197	0.642060
$655$	−7.19423	−0.281102
$656$	−39.1447	−1.52834
$657$	31.4648	1.22756
$658$	47.8500	1.86539
$659$	36.9464	1.43923	0.719615	−	0.694374i	$-0.244319\pi$
$659$	36.9464	1.43923	0.719615	+	0.694374i	$0.244319\pi$
$660$	−0.0367239	−0.00142948
$661$	7.73669	0.300922	0.150461	−	0.988616i	$-0.451924\pi$
$661$	7.73669	0.300922	0.150461	+	0.988616i	$0.451924\pi$
$662$	−7.09332	−0.275690
$663$	2.12147	0.0823910
$664$	−11.9242	−0.462750
$665$	−1.73413	−0.0672465
$666$	−67.0959	−2.59991
$667$	−33.2754	−1.28843
$668$	35.5103	1.37393
$669$	−2.97020	−0.114835
$670$	9.46030	0.365483
$671$	0.326766	0.0126147
$672$	4.57821	0.176608
$673$	−11.3893	−0.439026	−0.219513	−	0.975610i	$-0.570447\pi$
$673$	−11.3893	−0.439026	−0.219513	+	0.975610i	$0.570447\pi$
$674$	40.1100	1.54498
$675$	13.5139	0.520149
$676$	4.35689	0.167573
$677$	−8.77316	−0.337180	−0.168590	−	0.985686i	$-0.553921\pi$
$677$	−8.77316	−0.337180	−0.168590	+	0.985686i	$0.553921\pi$
$678$	−0.645371	−0.0247853
$679$	5.93930	0.227929
$680$	−13.5899	−0.521151
$681$	7.96383	0.305175
$682$	−0.271124	−0.0103819
$683$	−1.69049	−0.0646849	−0.0323425	−	0.999477i	$-0.510297\pi$
$683$	−1.69049	−0.0646849	−0.0323425	+	0.999477i	$0.510297\pi$
$684$	16.5121	0.631355
$685$	−1.71068	−0.0653618
$686$	−50.2849	−1.91989
$687$	9.05075	0.345307
$688$	−16.6441	−0.634550
$689$	12.6375	0.481449
$690$	−3.36897	−0.128254
$691$	−23.4391	−0.891667	−0.445834	−	0.895116i	$-0.647093\pi$
$691$	−23.4391	−0.891667	−0.445834	+	0.895116i	$0.647093\pi$
$692$	9.82826	0.373614
$693$	0.202433	0.00768980
$694$	55.7550	2.11643
$695$	−9.52242	−0.361206
$696$	−19.7963	−0.750378
$697$	26.5590	1.00599
$698$	34.4326	1.30329
$699$	−3.03457	−0.114778
$700$	48.0530	1.81623
$701$	−18.5318	−0.699935	−0.349967	−	0.936762i	$-0.613807\pi$
$701$	−18.5318	−0.699935	−0.349967	+	0.936762i	$0.613807\pi$
$702$	−7.23268	−0.272980
$703$	13.3245	0.502544
$704$	−0.0833740	−0.00314228
$705$	−2.17407	−0.0818803
$706$	−7.86887	−0.296149
$707$	−0.618324	−0.0232545
$708$	1.07988	0.0405843
$709$	10.5949	0.397902	0.198951	−	0.980009i	$-0.436247\pi$
$709$	10.5949	0.397902	0.198951	+	0.980009i	$0.436247\pi$
$710$	−8.11164	−0.304425
$711$	42.6132	1.59812
$712$	−39.9296	−1.49642
$713$	−17.0470	−0.638415
$714$	−12.5228	−0.468653
$715$	0.0168987	0.000631977 0
$716$	−5.46361	−0.204185
$717$	10.9558	0.409151
$718$	8.70481	0.324861
$719$	0.0503627	0.00187821	0.000939106	−	1.00000i	$-0.499701\pi$
$719$	0.0503627	0.00187821	0.000939106		1.00000i	$0.499701\pi$
$720$	9.27342	0.345600
$721$	21.5010	0.800738
$722$	43.1201	1.60476
$723$	10.7768	0.400793
$724$	−27.8915	−1.03658
$725$	−31.4635	−1.16852
$726$	13.8323	0.513364
$727$	−14.7123	−0.545650	−0.272825	−	0.962064i	$-0.587958\pi$
$727$	−14.7123	−0.545650	−0.272825	+	0.962064i	$0.587958\pi$
$728$	−13.9124	−0.515630
$729$	−14.4783	−0.536233
$730$	−15.5046	−0.573851
$731$	11.2927	0.417677
$732$	22.5952	0.835141
$733$	8.52355	0.314824	0.157412	−	0.987533i	$-0.449685\pi$
$733$	8.52355	0.314824	0.157412	+	0.987533i	$0.449685\pi$
$734$	16.5274	0.610039
$735$	0.407315	0.0150240
$736$	19.5324	0.719973
$737$	0.219312	0.00807845
$738$	−43.3151	−1.59445
$739$	−40.4718	−1.48878	−0.744390	−	0.667745i	$-0.767260\pi$
$739$	−40.4718	−1.48878	−0.744390	+	0.667745i	$0.767260\pi$
$740$	22.6602	0.833006
$741$	0.687100	0.0252412
$742$	−74.5973	−2.73855
$743$	7.25375	0.266114	0.133057	−	0.991108i	$-0.457521\pi$
$743$	7.25375	0.266114	0.133057	+	0.991108i	$0.457521\pi$
$744$	−10.1417	−0.371811
$745$	7.09222	0.259839
$746$	44.4741	1.62831
$747$	−5.52067	−0.201991
$748$	−0.582387	−0.0212942
$749$	21.0280	0.768346
$750$	−6.56654	−0.239776
$751$	−20.9560	−0.764694	−0.382347	−	0.924019i	$-0.624884\pi$
$751$	−20.9560	−0.764694	−0.382347	+	0.924019i	$0.624884\pi$
$752$	50.8157	1.85306
$753$	−6.95919	−0.253607
$754$	16.8394	0.613255
$755$	−4.12748	−0.150214
$756$	29.2614	1.06423
$757$	−19.9898	−0.726541	−0.363270	−	0.931684i	$-0.618340\pi$
$757$	−19.9898	−0.726541	−0.363270	+	0.931684i	$0.618340\pi$
$758$	27.1182	0.984976
$759$	−0.0781004	−0.00283487
$760$	−4.40150	−0.159659
$761$	−10.1416	−0.367631	−0.183816	−	0.982961i	$-0.558845\pi$
$761$	−10.1416	−0.367631	−0.183816	+	0.982961i	$0.558845\pi$
$762$	8.32334	0.301523
$763$	30.5679	1.10663
$764$	34.2614	1.23953
$765$	−6.29186	−0.227483
$766$	−23.6732	−0.855346
$767$	−0.496912	−0.0179425
$768$	−15.6258	−0.563848
$769$	−13.8266	−0.498599	−0.249300	−	0.968426i	$-0.580200\pi$
$769$	−13.8266	−0.498599	−0.249300	+	0.968426i	$0.580200\pi$
$770$	−0.0997511	−0.00359478
$771$	4.78238	0.172233
$772$	75.2515	2.70836
$773$	23.6963	0.852297	0.426148	−	0.904653i	$-0.359870\pi$
$773$	23.6963	0.852297	0.426148	+	0.904653i	$0.359870\pi$
$774$	−18.4173	−0.661998
$775$	−16.1187	−0.579003
$776$	15.0750	0.541159
$777$	11.2956	0.405228
$778$	−1.86203	−0.0667571
$779$	8.60192	0.308196
$780$	1.16851	0.0418393
$781$	−0.188047	−0.00672884
$782$	−53.4268	−1.91054
$783$	−19.1594	−0.684701
$784$	−9.52037	−0.340013
$785$	7.81947	0.279089
$786$	−16.8263	−0.600173
$787$	23.6011	0.841287	0.420644	−	0.907226i	$-0.361804\pi$
$787$	23.6011	0.841287	0.420644	+	0.907226i	$0.361804\pi$
$788$	52.6347	1.87503
$789$	−4.76436	−0.169616
$790$	−20.9981	−0.747080
$791$	−1.20146	−0.0427191
$792$	0.513810	0.0182574
$793$	−10.3973	−0.369219
$794$	−13.2616	−0.470637
$795$	3.38934	0.120207
$796$	83.9530	2.97564
$797$	−29.6442	−1.05005	−0.525026	−	0.851086i	$-0.675944\pi$
$797$	−29.6442	−1.05005	−0.525026	+	0.851086i	$0.675944\pi$
$798$	−4.05587	−0.143576
$799$	−34.4776	−1.21973
$800$	18.4688	0.652971
$801$	−18.4866	−0.653191
$802$	45.0474	1.59068
$803$	−0.359433	−0.0126841
$804$	15.1649	0.534825
$805$	−6.27188	−0.221055
$806$	8.62684	0.303867
$807$	10.3958	0.365949
$808$	−1.56941	−0.0552117
$809$	−0.741098	−0.0260556	−0.0130278	−	0.999915i	$-0.504147\pi$
$809$	−0.741098	−0.0260556	−0.0130278	+	0.999915i	$0.504147\pi$
$810$	9.24955	0.324996
$811$	27.0294	0.949130	0.474565	−	0.880221i	$-0.342605\pi$
$811$	27.0294	0.949130	0.474565	+	0.880221i	$0.342605\pi$
$812$	−68.1275	−2.39081
$813$	−15.6694	−0.549552
$814$	0.766460	0.0268644
$815$	−8.01038	−0.280591
$816$	−13.2989	−0.465555
$817$	3.65749	0.127959
$818$	−56.1595	−1.96357
$819$	−6.44117	−0.225073
$820$	14.6288	0.510859
$821$	−56.2675	−1.96375	−0.981875	−	0.189532i	$-0.939303\pi$
$821$	−56.2675	−1.96375	−0.981875	+	0.189532i	$0.939303\pi$
$822$	−4.00104	−0.139552
$823$	5.03113	0.175374	0.0876871	−	0.996148i	$-0.472052\pi$
$823$	5.03113	0.175374	0.0876871	+	0.996148i	$0.472052\pi$
$824$	54.5731	1.90114
$825$	−0.0738477	−0.00257105
$826$	2.93321	0.102060
$827$	−16.0626	−0.558552	−0.279276	−	0.960211i	$-0.590094\pi$
$827$	−16.0626	−0.558552	−0.279276	+	0.960211i	$0.590094\pi$
$828$	59.7199	2.07541
$829$	31.8197	1.10514	0.552572	−	0.833465i	$-0.313647\pi$
$829$	31.8197	1.10514	0.552572	+	0.833465i	$0.313647\pi$
$830$	2.72037	0.0944254
$831$	−4.16398	−0.144447
$832$	2.65286	0.0919713
$833$	6.45941	0.223805
$834$	−22.2716	−0.771201
$835$	−4.38242	−0.151660
$836$	−0.188623	−0.00652367
$837$	−9.81536	−0.339268
$838$	9.87425	0.341100
$839$	43.6345	1.50643	0.753215	−	0.657775i	$-0.228502\pi$
$839$	43.6345	1.50643	0.753215	+	0.657775i	$0.228502\pi$
$840$	−3.73129	−0.128742
$841$	15.6076	0.538193
$842$	−28.3959	−0.978588
$843$	−9.89591	−0.340833
$844$	−99.1623	−3.41331
$845$	−0.537697	−0.0184973
$846$	56.2295	1.93321
$847$	25.7511	0.884817
$848$	−79.2207	−2.72045
$849$	−10.2560	−0.351984
$850$	−50.5176	−1.73274
$851$	48.1913	1.65198
$852$	−13.0030	−0.445476
$853$	−15.6943	−0.537362	−0.268681	−	0.963229i	$-0.586588\pi$
$853$	−15.6943	−0.537362	−0.268681	+	0.963229i	$0.586588\pi$
$854$	61.3740	2.10018
$855$	−2.03780	−0.0696914
$856$	53.3726	1.82424
$857$	−50.0112	−1.70835	−0.854174	−	0.519987i	$-0.825937\pi$
$857$	−50.0112	−1.70835	−0.854174	+	0.519987i	$0.825937\pi$
$858$	0.0395237	0.00134932
$859$	25.2312	0.860879	0.430439	−	0.902619i	$-0.358359\pi$
$859$	25.2312	0.860879	0.430439	+	0.902619i	$0.358359\pi$
$860$	6.22007	0.212103
$861$	7.29211	0.248514
$862$	−63.7286	−2.17060
$863$	−43.2659	−1.47279	−0.736394	−	0.676553i	$-0.763473\pi$
$863$	−43.2659	−1.47279	−0.736394	+	0.676553i	$0.763473\pi$
$864$	11.2464	0.382610
$865$	−1.21293	−0.0412410
$866$	10.1475	0.344825
$867$	0.543643	0.0184631
$868$	−34.9018	−1.18464
$869$	−0.486785	−0.0165131
$870$	4.51629	0.153117
$871$	−6.97823	−0.236448
$872$	77.5865	2.62741
$873$	6.97939	0.236216
$874$	−17.3039	−0.585312
$875$	−12.2247	−0.413270
$876$	−24.8540	−0.839738
$877$	−48.4383	−1.63565	−0.817823	−	0.575470i	$-0.804819\pi$
$877$	−48.4383	−1.63565	−0.817823	+	0.575470i	$0.804819\pi$
$878$	53.9532	1.82083
$879$	−4.72167	−0.159258
$880$	−0.105933	−0.00357102
$881$	35.6341	1.20054	0.600272	−	0.799796i	$-0.295059\pi$
$881$	35.6341	1.20054	0.600272	+	0.799796i	$0.295059\pi$
$882$	−10.5347	−0.354721
$883$	17.3988	0.585517	0.292759	−	0.956186i	$-0.405427\pi$
$883$	17.3988	0.585517	0.292759	+	0.956186i	$0.405427\pi$
$884$	18.5308	0.623260
$885$	−0.133271	−0.00447985
$886$	−12.1066	−0.406730
$887$	12.9080	0.433407	0.216703	−	0.976237i	$-0.430470\pi$
$887$	12.9080	0.433407	0.216703	+	0.976237i	$0.430470\pi$
$888$	28.6702	0.962108
$889$	15.4953	0.519694
$890$	9.10946	0.305350
$891$	0.214426	0.00718354
$892$	−25.9445	−0.868686
$893$	−11.1666	−0.373675
$894$	16.5877	0.554774
$895$	0.674280	0.0225387
$896$	−34.0168	−1.13642
$897$	2.48506	0.0829737
$898$	−29.6748	−0.990260
$899$	22.8525	0.762173
$900$	56.4680	1.88227
$901$	53.7499	1.79067
$902$	0.494804	0.0164752
$903$	3.10056	0.103180
$904$	−3.04952	−0.101425
$905$	3.44217	0.114422
$906$	−9.65358	−0.320719
$907$	39.7345	1.31936	0.659681	−	0.751545i	$-0.270691\pi$
$907$	39.7345	1.31936	0.659681	+	0.751545i	$0.270691\pi$
$908$	69.5634	2.30854
$909$	−0.726605	−0.0241000
$910$	3.17396	0.105216
$911$	−3.41597	−0.113176	−0.0565880	−	0.998398i	$-0.518022\pi$
$911$	−3.41597	−0.113176	−0.0565880	+	0.998398i	$0.518022\pi$
$912$	−4.30724	−0.142627
$913$	0.0630645	0.00208713
$914$	−76.9958	−2.54679
$915$	−2.78853	−0.0921861
$916$	79.0575	2.61213
$917$	−31.3248	−1.03444
$918$	−30.7622	−1.01531
$919$	−39.8468	−1.31443	−0.657213	−	0.753705i	$-0.728265\pi$
$919$	−39.8468	−1.31443	−0.657213	+	0.753705i	$0.728265\pi$
$920$	−15.9191	−0.524837
$921$	−6.05149	−0.199403
$922$	52.1622	1.71787
$923$	5.98342	0.196947
$924$	−0.159902	−0.00526038
$925$	45.5672	1.49824
$926$	−2.52129	−0.0828547
$927$	25.2662	0.829851
$928$	−26.1843	−0.859541
$929$	4.12558	0.135356	0.0676780	−	0.997707i	$-0.478441\pi$
$929$	4.12558	0.135356	0.0676780	+	0.997707i	$0.478441\pi$
$930$	2.31370	0.0758692
$931$	2.09207	0.0685649
$932$	−26.5067	−0.868255
$933$	12.5371	0.410446
$934$	−9.07956	−0.297092
$935$	0.0718741	0.00235053
$936$	−16.3488	−0.534377
$937$	−45.7322	−1.49401	−0.747004	−	0.664820i	$-0.768508\pi$
$937$	−45.7322	−1.49401	−0.747004	+	0.664820i	$0.768508\pi$
$938$	41.1916	1.34495
$939$	−0.261330	−0.00852819
$940$	−18.9903	−0.619396
$941$	−25.2542	−0.823264	−0.411632	−	0.911350i	$-0.635041\pi$
$941$	−25.2542	−0.823264	−0.411632	+	0.911350i	$0.635041\pi$
$942$	18.2886	0.595875
$943$	31.1109	1.01311
$944$	3.11501	0.101385
$945$	−3.61124	−0.117474
$946$	0.210388	0.00684029
$947$	−17.5083	−0.568944	−0.284472	−	0.958684i	$-0.591818\pi$
$947$	−17.5083	−0.568944	−0.284472	+	0.958684i	$0.591818\pi$
$948$	−33.6601	−1.09323
$949$	11.4367	0.371251
$950$	−16.3616	−0.530841
$951$	−2.86591	−0.0929334
$952$	−59.1728	−1.91780
$953$	−37.2540	−1.20677	−0.603387	−	0.797448i	$-0.706183\pi$
$953$	−37.2540	−1.20677	−0.603387	+	0.797448i	$0.706183\pi$
$954$	−87.6608	−2.83812
$955$	−4.22829	−0.136824
$956$	95.6977	3.09509
$957$	0.104698	0.00338441
$958$	−31.8170	−1.02796
$959$	−7.44858	−0.240527
$960$	0.711491	0.0229633
$961$	−19.2927	−0.622344
$962$	−24.3878	−0.786294
$963$	24.7104	0.796282
$964$	94.1344	3.03187
$965$	−9.28701	−0.298959
$966$	−14.6690	−0.471967
$967$	−37.6475	−1.21066	−0.605330	−	0.795974i	$-0.706959\pi$
$967$	−37.6475	−1.21066	−0.605330	+	0.795974i	$0.706959\pi$
$968$	65.3606	2.10077
$969$	2.92239	0.0938807
$970$	−3.43917	−0.110425
$971$	−35.6079	−1.14271	−0.571355	−	0.820703i	$-0.693582\pi$
$971$	−35.6079	−1.14271	−0.571355	+	0.820703i	$0.693582\pi$
$972$	52.3222	1.67824
$973$	−41.4621	−1.32921
$974$	61.0054	1.95474
$975$	2.34974	0.0752520
$976$	65.1778	2.08629
$977$	−55.0505	−1.76122	−0.880610	−	0.473841i	$-0.842867\pi$
$977$	−55.0505	−1.76122	−0.880610	+	0.473841i	$0.842867\pi$
$978$	−18.7351	−0.599083
$979$	0.211178	0.00674929
$980$	3.55786	0.113652
$981$	35.9209	1.14687
$982$	50.2473	1.60346
$983$	45.1991	1.44163	0.720814	−	0.693128i	$-0.243768\pi$
$983$	45.1991	1.44163	0.720814	+	0.693128i	$0.243768\pi$
$984$	18.5086	0.590033
$985$	−6.49580	−0.206974
$986$	71.6218	2.28090
$987$	−9.46625	−0.301314
$988$	6.00176	0.190941
$989$	13.2282	0.420631
$990$	−0.117220	−0.00372548
$991$	49.0372	1.55772	0.778859	−	0.627199i	$-0.215799\pi$
$991$	49.0372	1.55772	0.778859	+	0.627199i	$0.215799\pi$
$992$	−13.4142	−0.425902
$993$	1.40328	0.0445318
$994$	−35.3194	−1.12026
$995$	−10.3609	−0.328462
$996$	4.36077	0.138176
$997$	30.2328	0.957482	0.478741	−	0.877956i	$-0.341093\pi$
$997$	30.2328	0.957482	0.478741	+	0.877956i	$0.341093\pi$
$998$	31.6962	1.00333
$999$	27.7477	0.877899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.8	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.8	✓	123	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52129 q^{2} +0.498790 q^{3} +4.35689 q^{4} -0.537697 q^{5} -1.25759 q^{6} -2.34122 q^{7} -5.94240 q^{8} -2.75121 q^{9} +O(q^{10})\)	\(q-2.52129 q^{2} +0.498790 q^{3} +4.35689 q^{4} -0.537697 q^{5} -1.25759 q^{6} -2.34122 q^{7} -5.94240 q^{8} -2.75121 q^{9} +1.35569 q^{10} +0.0314280 q^{11} +2.17318 q^{12} -1.00000 q^{13} +5.90288 q^{14} -0.268198 q^{15} +6.26873 q^{16} -4.25323 q^{17} +6.93659 q^{18} -1.37753 q^{19} -2.34269 q^{20} -1.16778 q^{21} -0.0792390 q^{22} -4.98217 q^{23} -2.96401 q^{24} -4.71088 q^{25} +2.52129 q^{26} -2.86865 q^{27} -10.2004 q^{28} +6.67889 q^{29} +0.676204 q^{30} +3.42160 q^{31} -3.92045 q^{32} +0.0156760 q^{33} +10.7236 q^{34} +1.25886 q^{35} -11.9867 q^{36} -9.67275 q^{37} +3.47315 q^{38} -0.498790 q^{39} +3.19521 q^{40} -6.24444 q^{41} +2.94430 q^{42} -2.65510 q^{43} +0.136928 q^{44} +1.47932 q^{45} +12.5615 q^{46} +8.10622 q^{47} +3.12678 q^{48} -1.51871 q^{49} +11.8775 q^{50} -2.12147 q^{51} -4.35689 q^{52} -12.6375 q^{53} +7.23268 q^{54} -0.0168987 q^{55} +13.9124 q^{56} -0.687100 q^{57} -16.8394 q^{58} +0.496912 q^{59} -1.16851 q^{60} +10.3973 q^{61} -8.62684 q^{62} +6.44117 q^{63} -2.65286 q^{64} +0.537697 q^{65} -0.0395237 q^{66} +6.97823 q^{67} -18.5308 q^{68} -2.48506 q^{69} -3.17396 q^{70} -5.98342 q^{71} +16.3488 q^{72} -11.4367 q^{73} +24.3878 q^{74} -2.34974 q^{75} -6.00176 q^{76} -0.0735797 q^{77} +1.25759 q^{78} -15.4889 q^{79} -3.37067 q^{80} +6.82277 q^{81} +15.7440 q^{82} +2.00663 q^{83} -5.08787 q^{84} +2.28694 q^{85} +6.69427 q^{86} +3.33137 q^{87} -0.186758 q^{88} +6.71943 q^{89} -3.72978 q^{90} +2.34122 q^{91} -21.7068 q^{92} +1.70666 q^{93} -20.4381 q^{94} +0.740694 q^{95} -1.95548 q^{96} -2.53684 q^{97} +3.82910 q^{98} -0.0864650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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