LMFDB - Embedded newform 4011.2.a.m.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00218 q^{2} +1.00000 q^{3} +2.00873 q^{4} -0.971545 q^{5} -2.00218 q^{6} -1.00000 q^{7} -0.0174879 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.00218 q^{2} +1.00000 q^{3} +2.00873 q^{4} -0.971545 q^{5} -2.00218 q^{6} -1.00000 q^{7} -0.0174879 q^{8} +1.00000 q^{9} +1.94521 q^{10} -6.11020 q^{11} +2.00873 q^{12} -4.30835 q^{13} +2.00218 q^{14} -0.971545 q^{15} -3.98245 q^{16} -6.26647 q^{17} -2.00218 q^{18} -4.02551 q^{19} -1.95158 q^{20} -1.00000 q^{21} +12.2337 q^{22} +8.85972 q^{23} -0.0174879 q^{24} -4.05610 q^{25} +8.62610 q^{26} +1.00000 q^{27} -2.00873 q^{28} -7.48648 q^{29} +1.94521 q^{30} -8.46326 q^{31} +8.00858 q^{32} -6.11020 q^{33} +12.5466 q^{34} +0.971545 q^{35} +2.00873 q^{36} -1.00057 q^{37} +8.05981 q^{38} -4.30835 q^{39} +0.0169903 q^{40} +1.92787 q^{41} +2.00218 q^{42} -7.78086 q^{43} -12.2738 q^{44} -0.971545 q^{45} -17.7388 q^{46} +2.39366 q^{47} -3.98245 q^{48} +1.00000 q^{49} +8.12105 q^{50} -6.26647 q^{51} -8.65433 q^{52} +10.0815 q^{53} -2.00218 q^{54} +5.93633 q^{55} +0.0174879 q^{56} -4.02551 q^{57} +14.9893 q^{58} +9.50280 q^{59} -1.95158 q^{60} -0.162794 q^{61} +16.9450 q^{62} -1.00000 q^{63} -8.06972 q^{64} +4.18575 q^{65} +12.2337 q^{66} +8.30971 q^{67} -12.5877 q^{68} +8.85972 q^{69} -1.94521 q^{70} -1.39625 q^{71} -0.0174879 q^{72} +7.09368 q^{73} +2.00333 q^{74} -4.05610 q^{75} -8.08618 q^{76} +6.11020 q^{77} +8.62610 q^{78} -0.145936 q^{79} +3.86913 q^{80} +1.00000 q^{81} -3.85994 q^{82} +9.20865 q^{83} -2.00873 q^{84} +6.08816 q^{85} +15.5787 q^{86} -7.48648 q^{87} +0.106855 q^{88} -5.43499 q^{89} +1.94521 q^{90} +4.30835 q^{91} +17.7968 q^{92} -8.46326 q^{93} -4.79255 q^{94} +3.91096 q^{95} +8.00858 q^{96} +1.17196 q^{97} -2.00218 q^{98} -6.11020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.00218	−1.41576	−0.707878	−	0.706334i	$-0.750348\pi$
$2$	−2.00218	−1.41576	−0.707878	+	0.706334i	$0.750348\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.00873	1.00437
$5$	−0.971545	−0.434488	−0.217244	−	0.976117i	$-0.569707\pi$
$5$	−0.971545	−0.434488	−0.217244	+	0.976117i	$0.569707\pi$
$6$	−2.00218	−0.817388
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.0174879	−0.00618291
$9$	1.00000	0.333333
$10$	1.94521	0.615129
$11$	−6.11020	−1.84229	−0.921147	−	0.389215i	$-0.872746\pi$
$11$	−6.11020	−1.84229	−0.921147	+	0.389215i	$0.872746\pi$
$12$	2.00873	0.579872
$13$	−4.30835	−1.19492	−0.597461	−	0.801898i	$-0.703824\pi$
$13$	−4.30835	−1.19492	−0.597461	+	0.801898i	$0.703824\pi$
$14$	2.00218	0.535106
$15$	−0.971545	−0.250852
$16$	−3.98245	−0.995614
$17$	−6.26647	−1.51984	−0.759921	−	0.650015i	$-0.774762\pi$
$17$	−6.26647	−1.51984	−0.759921	+	0.650015i	$0.774762\pi$
$18$	−2.00218	−0.471919
$19$	−4.02551	−0.923515	−0.461758	−	0.887006i	$-0.652781\pi$
$19$	−4.02551	−0.923515	−0.461758	+	0.887006i	$0.652781\pi$
$20$	−1.95158	−0.436386
$21$	−1.00000	−0.218218
$22$	12.2337	2.60824
$23$	8.85972	1.84738	0.923690	−	0.383142i	$-0.125158\pi$
$23$	8.85972	1.84738	0.923690	+	0.383142i	$0.125158\pi$
$24$	−0.0174879	−0.00356970
$25$	−4.05610	−0.811220
$26$	8.62610	1.69172
$27$	1.00000	0.192450
$28$	−2.00873	−0.379615
$29$	−7.48648	−1.39020	−0.695102	−	0.718911i	$-0.744641\pi$
$29$	−7.48648	−1.39020	−0.695102	+	0.718911i	$0.744641\pi$
$30$	1.94521	0.355145
$31$	−8.46326	−1.52005	−0.760024	−	0.649896i	$-0.774813\pi$
$31$	−8.46326	−1.52005	−0.760024	+	0.649896i	$0.774813\pi$
$32$	8.00858	1.41573
$33$	−6.11020	−1.06365
$34$	12.5466	2.15173
$35$	0.971545	0.164221
$36$	2.00873	0.334789
$37$	−1.00057	−0.164493	−0.0822466	−	0.996612i	$-0.526209\pi$
$37$	−1.00057	−0.164493	−0.0822466	+	0.996612i	$0.526209\pi$
$38$	8.05981	1.30747
$39$	−4.30835	−0.689888
$40$	0.0169903	0.00268640
$41$	1.92787	0.301082	0.150541	−	0.988604i	$-0.451898\pi$
$41$	1.92787	0.301082	0.150541	+	0.988604i	$0.451898\pi$
$42$	2.00218	0.308943
$43$	−7.78086	−1.18657	−0.593285	−	0.804992i	$-0.702169\pi$
$43$	−7.78086	−1.18657	−0.593285	+	0.804992i	$0.702169\pi$
$44$	−12.2738	−1.85034
$45$	−0.971545	−0.144829
$46$	−17.7388	−2.61544
$47$	2.39366	0.349151	0.174576	−	0.984644i	$-0.444145\pi$
$47$	2.39366	0.349151	0.174576	+	0.984644i	$0.444145\pi$
$48$	−3.98245	−0.574818
$49$	1.00000	0.142857
$50$	8.12105	1.14849
$51$	−6.26647	−0.877481
$52$	−8.65433	−1.20014
$53$	10.0815	1.38480	0.692401	−	0.721512i	$-0.256553\pi$
$53$	10.0815	1.38480	0.692401	+	0.721512i	$0.256553\pi$
$54$	−2.00218	−0.272463
$55$	5.93633	0.800455
$56$	0.0174879	0.00233692
$57$	−4.02551	−0.533192
$58$	14.9893	1.96819
$59$	9.50280	1.23716	0.618580	−	0.785722i	$-0.287708\pi$
$59$	9.50280	1.23716	0.618580	+	0.785722i	$0.287708\pi$
$60$	−1.95158	−0.251947
$61$	−0.162794	−0.0208437	−0.0104218	−	0.999946i	$-0.503317\pi$
$61$	−0.162794	−0.0208437	−0.0104218	+	0.999946i	$0.503317\pi$
$62$	16.9450	2.15202
$63$	−1.00000	−0.125988
$64$	−8.06972	−1.00872
$65$	4.18575	0.519179
$66$	12.2337	1.50587
$67$	8.30971	1.01519	0.507596	−	0.861595i	$-0.330534\pi$
$67$	8.30971	1.01519	0.507596	+	0.861595i	$0.330534\pi$
$68$	−12.5877	−1.52648
$69$	8.85972	1.06658
$70$	−1.94521	−0.232497
$71$	−1.39625	−0.165704	−0.0828521	−	0.996562i	$-0.526403\pi$
$71$	−1.39625	−0.165704	−0.0828521	+	0.996562i	$0.526403\pi$
$72$	−0.0174879	−0.00206097
$73$	7.09368	0.830253	0.415126	−	0.909764i	$-0.363737\pi$
$73$	7.09368	0.830253	0.415126	+	0.909764i	$0.363737\pi$
$74$	2.00333	0.232882
$75$	−4.05610	−0.468358
$76$	−8.08618	−0.927549
$77$	6.11020	0.696322
$78$	8.62610	0.976714
$79$	−0.145936	−0.0164191	−0.00820956	−	0.999966i	$-0.502613\pi$
$79$	−0.145936	−0.0164191	−0.00820956	+	0.999966i	$0.502613\pi$
$80$	3.86913	0.432582
$81$	1.00000	0.111111
$82$	−3.85994	−0.426259
$83$	9.20865	1.01078	0.505390	−	0.862891i	$-0.331349\pi$
$83$	9.20865	1.01078	0.505390	+	0.862891i	$0.331349\pi$
$84$	−2.00873	−0.219171
$85$	6.08816	0.660353
$86$	15.5787	1.67990
$87$	−7.48648	−0.802635
$88$	0.106855	0.0113907
$89$	−5.43499	−0.576108	−0.288054	−	0.957614i	$-0.593008\pi$
$89$	−5.43499	−0.576108	−0.288054	+	0.957614i	$0.593008\pi$
$90$	1.94521	0.205043
$91$	4.30835	0.451638
$92$	17.7968	1.85545
$93$	−8.46326	−0.877600
$94$	−4.79255	−0.494313
$95$	3.91096	0.401256
$96$	8.00858	0.817372
$97$	1.17196	0.118995	0.0594974	−	0.998228i	$-0.481050\pi$
$97$	1.17196	0.118995	0.0594974	+	0.998228i	$0.481050\pi$
$98$	−2.00218	−0.202251
$99$	−6.11020	−0.614098
$100$	−8.14763	−0.814763
$101$	−8.59049	−0.854786	−0.427393	−	0.904066i	$-0.640568\pi$
$101$	−8.59049	−0.854786	−0.427393	+	0.904066i	$0.640568\pi$
$102$	12.5466	1.24230
$103$	0.536591	0.0528719	0.0264359	−	0.999651i	$-0.491584\pi$
$103$	0.536591	0.0528719	0.0264359	+	0.999651i	$0.491584\pi$
$104$	0.0753440	0.00738809
$105$	0.971545	0.0948131
$106$	−20.1850	−1.96054
$107$	18.4105	1.77981	0.889906	−	0.456145i	$-0.150770\pi$
$107$	18.4105	1.77981	0.889906	+	0.456145i	$0.150770\pi$
$108$	2.00873	0.193291
$109$	12.5394	1.20106	0.600531	−	0.799602i	$-0.294956\pi$
$109$	12.5394	1.20106	0.600531	+	0.799602i	$0.294956\pi$
$110$	−11.8856	−1.13325
$111$	−1.00057	−0.0949701
$112$	3.98245	0.376307
$113$	−7.53403	−0.708742	−0.354371	−	0.935105i	$-0.615305\pi$
$113$	−7.53403	−0.708742	−0.354371	+	0.935105i	$0.615305\pi$
$114$	8.05981	0.754870
$115$	−8.60761	−0.802664
$116$	−15.0383	−1.39628
$117$	−4.30835	−0.398307
$118$	−19.0263	−1.75152
$119$	6.26647	0.574446
$120$	0.0169903	0.00155099
$121$	26.3345	2.39405
$122$	0.325944	0.0295096
$123$	1.92787	0.173830
$124$	−17.0004	−1.52669
$125$	8.79841	0.786953
$126$	2.00218	0.178369
$127$	−10.1677	−0.902235	−0.451118	−	0.892464i	$-0.648975\pi$
$127$	−10.1677	−0.902235	−0.451118	+	0.892464i	$0.648975\pi$
$128$	0.139902	0.0123657
$129$	−7.78086	−0.685067
$130$	−8.38064	−0.735031
$131$	−3.37147	−0.294567	−0.147283	−	0.989094i	$-0.547053\pi$
$131$	−3.37147	−0.294567	−0.147283	+	0.989094i	$0.547053\pi$
$132$	−12.2738	−1.06829
$133$	4.02551	0.349056
$134$	−16.6375	−1.43727
$135$	−0.971545	−0.0836173
$136$	0.109587	0.00939704
$137$	−3.51467	−0.300278	−0.150139	−	0.988665i	$-0.547972\pi$
$137$	−3.51467	−0.300278	−0.150139	+	0.988665i	$0.547972\pi$
$138$	−17.7388	−1.51002
$139$	−17.0577	−1.44681	−0.723407	−	0.690422i	$-0.757425\pi$
$139$	−17.0577	−1.44681	−0.723407	+	0.690422i	$0.757425\pi$
$140$	1.95158	0.164938
$141$	2.39366	0.201583
$142$	2.79554	0.234597
$143$	26.3249	2.20140
$144$	−3.98245	−0.331871
$145$	7.27345	0.604027
$146$	−14.2028	−1.17544
$147$	1.00000	0.0824786
$148$	−2.00988	−0.165211
$149$	−5.76671	−0.472428	−0.236214	−	0.971701i	$-0.575907\pi$
$149$	−5.76671	−0.472428	−0.236214	+	0.971701i	$0.575907\pi$
$150$	8.12105	0.663081
$151$	11.1916	0.910759	0.455379	−	0.890298i	$-0.349504\pi$
$151$	11.1916	0.910759	0.455379	+	0.890298i	$0.349504\pi$
$152$	0.0703977	0.00571001
$153$	−6.26647	−0.506614
$154$	−12.2337	−0.985822
$155$	8.22244	0.660442
$156$	−8.65433	−0.692901
$157$	−4.91205	−0.392024	−0.196012	−	0.980601i	$-0.562799\pi$
$157$	−4.91205	−0.392024	−0.196012	+	0.980601i	$0.562799\pi$
$158$	0.292191	0.0232455
$159$	10.0815	0.799516
$160$	−7.78069	−0.615118
$161$	−8.85972	−0.698244
$162$	−2.00218	−0.157306
$163$	2.41787	0.189382	0.0946909	−	0.995507i	$-0.469814\pi$
$163$	2.41787	0.189382	0.0946909	+	0.995507i	$0.469814\pi$
$164$	3.87257	0.302397
$165$	5.93633	0.462143
$166$	−18.4374	−1.43102
$167$	12.1432	0.939670	0.469835	−	0.882754i	$-0.344313\pi$
$167$	12.1432	0.939670	0.469835	+	0.882754i	$0.344313\pi$
$168$	0.0174879	0.00134922
$169$	5.56187	0.427836
$170$	−12.1896	−0.934899
$171$	−4.02551	−0.307838
$172$	−15.6297	−1.19175
$173$	−14.3858	−1.09373	−0.546866	−	0.837220i	$-0.684179\pi$
$173$	−14.3858	−1.09373	−0.546866	+	0.837220i	$0.684179\pi$
$174$	14.9893	1.13634
$175$	4.05610	0.306612
$176$	24.3336	1.83421
$177$	9.50280	0.714274
$178$	10.8818	0.815629
$179$	19.0453	1.42351	0.711755	−	0.702428i	$-0.247901\pi$
$179$	19.0453	1.42351	0.711755	+	0.702428i	$0.247901\pi$
$180$	−1.95158	−0.145462
$181$	−14.9185	−1.10888	−0.554441	−	0.832223i	$-0.687068\pi$
$181$	−14.9185	−1.10888	−0.554441	+	0.832223i	$0.687068\pi$
$182$	−8.62610	−0.639409
$183$	−0.162794	−0.0120341
$184$	−0.154938	−0.0114222
$185$	0.972101	0.0714703
$186$	16.9450	1.24247
$187$	38.2894	2.80000
$188$	4.80823	0.350676
$189$	−1.00000	−0.0727393
$190$	−7.83046	−0.568081
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−8.06972	−0.582382
$193$	−10.3610	−0.745798	−0.372899	−	0.927872i	$-0.621636\pi$
$193$	−10.3610	−0.745798	−0.372899	+	0.927872i	$0.621636\pi$
$194$	−2.34648	−0.168468
$195$	4.18575	0.299748
$196$	2.00873	0.143481
$197$	−6.13910	−0.437393	−0.218696	−	0.975793i	$-0.570180\pi$
$197$	−6.13910	−0.437393	−0.218696	+	0.975793i	$0.570180\pi$
$198$	12.2337	0.869413
$199$	−19.9264	−1.41254	−0.706272	−	0.707941i	$-0.749624\pi$
$199$	−19.9264	−1.41254	−0.706272	+	0.707941i	$0.749624\pi$
$200$	0.0709327	0.00501570
$201$	8.30971	0.586122
$202$	17.1997	1.21017
$203$	7.48648	0.525448
$204$	−12.5877	−0.881313
$205$	−1.87301	−0.130817
$206$	−1.07435	−0.0748537
$207$	8.85972	0.615793
$208$	17.1578	1.18968
$209$	24.5967	1.70139
$210$	−1.94521	−0.134232
$211$	15.0878	1.03869	0.519345	−	0.854565i	$-0.326176\pi$
$211$	15.0878	1.03869	0.519345	+	0.854565i	$0.326176\pi$
$212$	20.2511	1.39085
$213$	−1.39625	−0.0956693
$214$	−36.8612	−2.51978
$215$	7.55946	0.515551
$216$	−0.0174879	−0.00118990
$217$	8.46326	0.574524
$218$	−25.1063	−1.70041
$219$	7.09368	0.479347
$220$	11.9245	0.803950
$221$	26.9981	1.81609
$222$	2.00333	0.134455
$223$	−23.3351	−1.56264	−0.781318	−	0.624133i	$-0.785452\pi$
$223$	−23.3351	−1.56264	−0.781318	+	0.624133i	$0.785452\pi$
$224$	−8.00858	−0.535096
$225$	−4.05610	−0.270407
$226$	15.0845	1.00341
$227$	−2.92314	−0.194016	−0.0970079	−	0.995284i	$-0.530927\pi$
$227$	−2.92314	−0.194016	−0.0970079	+	0.995284i	$0.530927\pi$
$228$	−8.08618	−0.535520
$229$	30.1482	1.99225	0.996125	−	0.0879528i	$-0.0280325\pi$
$229$	30.1482	1.99225	0.996125	+	0.0879528i	$0.0280325\pi$
$230$	17.2340	1.13638
$231$	6.11020	0.402022
$232$	0.130923	0.00859550
$233$	−8.51917	−0.558109	−0.279055	−	0.960275i	$-0.590021\pi$
$233$	−8.51917	−0.558109	−0.279055	+	0.960275i	$0.590021\pi$
$234$	8.62610	0.563906
$235$	−2.32555	−0.151702
$236$	19.0886	1.24256
$237$	−0.145936	−0.00947958
$238$	−12.5466	−0.813276
$239$	−26.5586	−1.71793	−0.858965	−	0.512034i	$-0.828892\pi$
$239$	−26.5586	−1.71793	−0.858965	+	0.512034i	$0.828892\pi$
$240$	3.86913	0.249751
$241$	−16.9465	−1.09162	−0.545808	−	0.837910i	$-0.683777\pi$
$241$	−16.9465	−1.09162	−0.545808	+	0.837910i	$0.683777\pi$
$242$	−52.7265	−3.38939
$243$	1.00000	0.0641500
$244$	−0.327011	−0.0209347
$245$	−0.971545	−0.0620697
$246$	−3.85994	−0.246101
$247$	17.3433	1.10353
$248$	0.148005	0.00939831
$249$	9.20865	0.583574
$250$	−17.6160	−1.11413
$251$	−7.91026	−0.499291	−0.249646	−	0.968337i	$-0.580314\pi$
$251$	−7.91026	−0.499291	−0.249646	+	0.968337i	$0.580314\pi$
$252$	−2.00873	−0.126538
$253$	−54.1346	−3.40342
$254$	20.3575	1.27735
$255$	6.08816	0.381255
$256$	15.8593	0.991208
$257$	20.2140	1.26092	0.630458	−	0.776223i	$-0.282867\pi$
$257$	20.2140	1.26092	0.630458	+	0.776223i	$0.282867\pi$
$258$	15.5787	0.969888
$259$	1.00057	0.0621726
$260$	8.40807	0.521446
$261$	−7.48648	−0.463401
$262$	6.75030	0.417035
$263$	3.79058	0.233737	0.116868	−	0.993147i	$-0.462714\pi$
$263$	3.79058	0.233737	0.116868	+	0.993147i	$0.462714\pi$
$264$	0.106855	0.00657644
$265$	−9.79464	−0.601680
$266$	−8.05981	−0.494178
$267$	−5.43499	−0.332616
$268$	16.6920	1.01963
$269$	15.0654	0.918551	0.459275	−	0.888294i	$-0.348109\pi$
$269$	15.0654	0.918551	0.459275	+	0.888294i	$0.348109\pi$
$270$	1.94521	0.118382
$271$	−23.9672	−1.45591	−0.727953	−	0.685627i	$-0.759528\pi$
$271$	−23.9672	−1.45591	−0.727953	+	0.685627i	$0.759528\pi$
$272$	24.9559	1.51318
$273$	4.30835	0.260753
$274$	7.03700	0.425121
$275$	24.7836	1.49451
$276$	17.7968	1.07124
$277$	−31.4993	−1.89261	−0.946304	−	0.323277i	$-0.895215\pi$
$277$	−31.4993	−1.89261	−0.946304	+	0.323277i	$0.895215\pi$
$278$	34.1526	2.04834
$279$	−8.46326	−0.506682
$280$	−0.0169903	−0.00101536
$281$	4.90214	0.292437	0.146218	−	0.989252i	$-0.453290\pi$
$281$	4.90214	0.292437	0.146218	+	0.989252i	$0.453290\pi$
$282$	−4.79255	−0.285392
$283$	5.53086	0.328775	0.164388	−	0.986396i	$-0.447435\pi$
$283$	5.53086	0.328775	0.164388	+	0.986396i	$0.447435\pi$
$284$	−2.80469	−0.166428
$285$	3.91096	0.231665
$286$	−52.7072	−3.11664
$287$	−1.92787	−0.113798
$288$	8.00858	0.471910
$289$	22.2686	1.30992
$290$	−14.5628	−0.855155
$291$	1.17196	0.0687017
$292$	14.2493	0.833879
$293$	−26.1013	−1.52485	−0.762427	−	0.647074i	$-0.775992\pi$
$293$	−26.1013	−1.52485	−0.762427	+	0.647074i	$0.775992\pi$
$294$	−2.00218	−0.116770
$295$	−9.23240	−0.537531
$296$	0.0174979	0.00101705
$297$	−6.11020	−0.354550
$298$	11.5460	0.668843
$299$	−38.1708	−2.20747
$300$	−8.14763	−0.470404
$301$	7.78086	0.448481
$302$	−22.4076	−1.28941
$303$	−8.59049	−0.493511
$304$	16.0314	0.919465
$305$	0.158162	0.00905633
$306$	12.5466	0.717242
$307$	−14.2671	−0.814266	−0.407133	−	0.913369i	$-0.633471\pi$
$307$	−14.2671	−0.814266	−0.407133	+	0.913369i	$0.633471\pi$
$308$	12.2738	0.699363
$309$	0.536591	0.0305256
$310$	−16.4628	−0.935026
$311$	3.66584	0.207871	0.103935	−	0.994584i	$-0.466857\pi$
$311$	3.66584	0.207871	0.103935	+	0.994584i	$0.466857\pi$
$312$	0.0753440	0.00426551
$313$	−9.15846	−0.517667	−0.258833	−	0.965922i	$-0.583338\pi$
$313$	−9.15846	−0.517667	−0.258833	+	0.965922i	$0.583338\pi$
$314$	9.83482	0.555011
$315$	0.971545	0.0547403
$316$	−0.293147	−0.0164908
$317$	21.5082	1.20802	0.604011	−	0.796976i	$-0.293568\pi$
$317$	21.5082	1.20802	0.604011	+	0.796976i	$0.293568\pi$
$318$	−20.1850	−1.13192
$319$	45.7439	2.56116
$320$	7.84010	0.438275
$321$	18.4105	1.02757
$322$	17.7388	0.988543
$323$	25.2257	1.40360
$324$	2.00873	0.111596
$325$	17.4751	0.969344
$326$	−4.84101	−0.268119
$327$	12.5394	0.693433
$328$	−0.0337143	−0.00186156
$329$	−2.39366	−0.131967
$330$	−11.8856	−0.654282
$331$	−0.357008	−0.0196229	−0.00981146	−	0.999952i	$-0.503123\pi$
$331$	−0.357008	−0.0196229	−0.00981146	+	0.999952i	$0.503123\pi$
$332$	18.4977	1.01519
$333$	−1.00057	−0.0548310
$334$	−24.3129	−1.33034
$335$	−8.07325	−0.441089
$336$	3.98245	0.217261
$337$	0.0747362	0.00407114	0.00203557	−	0.999998i	$-0.499352\pi$
$337$	0.0747362	0.00407114	0.00203557	+	0.999998i	$0.499352\pi$
$338$	−11.1359	−0.605712
$339$	−7.53403	−0.409192
$340$	12.2295	0.663237
$341$	51.7122	2.80037
$342$	8.05981	0.435824
$343$	−1.00000	−0.0539949
$344$	0.136071	0.00733646
$345$	−8.60761	−0.463418
$346$	28.8030	1.54846
$347$	−2.73418	−0.146778	−0.0733892	−	0.997303i	$-0.523382\pi$
$347$	−2.73418	−0.146778	−0.0733892	+	0.997303i	$0.523382\pi$
$348$	−15.0383	−0.806140
$349$	24.4230	1.30733	0.653667	−	0.756782i	$-0.273230\pi$
$349$	24.4230	1.30733	0.653667	+	0.756782i	$0.273230\pi$
$350$	−8.12105	−0.434089
$351$	−4.30835	−0.229963
$352$	−48.9340	−2.60819
$353$	19.5957	1.04298	0.521488	−	0.853259i	$-0.325377\pi$
$353$	19.5957	1.04298	0.521488	+	0.853259i	$0.325377\pi$
$354$	−19.0263	−1.01124
$355$	1.35652	0.0719965
$356$	−10.9175	−0.578624
$357$	6.26647	0.331657
$358$	−38.1321	−2.01534
$359$	−26.1709	−1.38125	−0.690624	−	0.723214i	$-0.742664\pi$
$359$	−26.1709	−1.38125	−0.690624	+	0.723214i	$0.742664\pi$
$360$	0.0169903	0.000895467 0
$361$	−2.79526	−0.147119
$362$	29.8695	1.56991
$363$	26.3345	1.38220
$364$	8.65433	0.453610
$365$	−6.89183	−0.360735
$366$	0.325944	0.0170374
$367$	−2.93498	−0.153205	−0.0766023	−	0.997062i	$-0.524407\pi$
$367$	−2.93498	−0.153205	−0.0766023	+	0.997062i	$0.524407\pi$
$368$	−35.2834	−1.83928
$369$	1.92787	0.100361
$370$	−1.94632	−0.101185
$371$	−10.0815	−0.523406
$372$	−17.0004	−0.881432
$373$	6.57060	0.340213	0.170106	−	0.985426i	$-0.445589\pi$
$373$	6.57060	0.340213	0.170106	+	0.985426i	$0.445589\pi$
$374$	−76.6623	−3.96411
$375$	8.79841	0.454348
$376$	−0.0418601	−0.00215877
$377$	32.2544	1.66118
$378$	2.00218	0.102981
$379$	5.63642	0.289523	0.144762	−	0.989467i	$-0.453758\pi$
$379$	5.63642	0.289523	0.144762	+	0.989467i	$0.453758\pi$
$380$	7.85609	0.403009
$381$	−10.1677	−0.520906
$382$	2.00218	0.102441
$383$	4.56870	0.233449	0.116725	−	0.993164i	$-0.462760\pi$
$383$	4.56870	0.233449	0.116725	+	0.993164i	$0.462760\pi$
$384$	0.139902	0.00713934
$385$	−5.93633	−0.302543
$386$	20.7445	1.05587
$387$	−7.78086	−0.395523
$388$	2.35416	0.119514
$389$	0.477610	0.0242158	0.0121079	−	0.999927i	$-0.496146\pi$
$389$	0.477610	0.0242158	0.0121079	+	0.999927i	$0.496146\pi$
$390$	−8.38064	−0.424370
$391$	−55.5192	−2.80772
$392$	−0.0174879	−0.000883273 0
$393$	−3.37147	−0.170068
$394$	12.2916	0.619242
$395$	0.141784	0.00713391
$396$	−12.2738	−0.616780
$397$	28.8064	1.44575	0.722875	−	0.690979i	$-0.242820\pi$
$397$	28.8064	1.44575	0.722875	+	0.690979i	$0.242820\pi$
$398$	39.8963	1.99982
$399$	4.02551	0.201528
$400$	16.1532	0.807662
$401$	−7.21212	−0.360156	−0.180078	−	0.983652i	$-0.557635\pi$
$401$	−7.21212	−0.360156	−0.180078	+	0.983652i	$0.557635\pi$
$402$	−16.6375	−0.829806
$403$	36.4627	1.81634
$404$	−17.2560	−0.858519
$405$	−0.971545	−0.0482764
$406$	−14.9893	−0.743906
$407$	6.11370	0.303045
$408$	0.109587	0.00542539
$409$	5.48948	0.271437	0.135719	−	0.990747i	$-0.456666\pi$
$409$	5.48948	0.271437	0.135719	+	0.990747i	$0.456666\pi$
$410$	3.75010	0.185204
$411$	−3.51467	−0.173366
$412$	1.07787	0.0531028
$413$	−9.50280	−0.467602
$414$	−17.7388	−0.871813
$415$	−8.94661	−0.439172
$416$	−34.5037	−1.69169
$417$	−17.0577	−0.835318
$418$	−49.2470	−2.40875
$419$	−18.3881	−0.898318	−0.449159	−	0.893452i	$-0.648276\pi$
$419$	−18.3881	−0.898318	−0.449159	+	0.893452i	$0.648276\pi$
$420$	1.95158	0.0952271
$421$	−17.4898	−0.852402	−0.426201	−	0.904628i	$-0.640148\pi$
$421$	−17.4898	−0.852402	−0.426201	+	0.904628i	$0.640148\pi$
$422$	−30.2086	−1.47053
$423$	2.39366	0.116384
$424$	−0.176305	−0.00856211
$425$	25.4174	1.23293
$426$	2.79554	0.135444
$427$	0.162794	0.00787817
$428$	36.9818	1.78758
$429$	26.3249	1.27098
$430$	−15.1354	−0.729894
$431$	40.2765	1.94005	0.970026	−	0.242999i	$-0.0781312\pi$
$431$	40.2765	1.94005	0.970026	+	0.242999i	$0.0781312\pi$
$432$	−3.98245	−0.191606
$433$	−33.2525	−1.59801	−0.799007	−	0.601322i	$-0.794641\pi$
$433$	−33.2525	−1.59801	−0.799007	+	0.601322i	$0.794641\pi$
$434$	−16.9450	−0.813386
$435$	7.27345	0.348735
$436$	25.1884	1.20631
$437$	−35.6649	−1.70608
$438$	−14.2028	−0.678638
$439$	19.0758	0.910437	0.455218	−	0.890380i	$-0.349561\pi$
$439$	19.0758	0.910437	0.455218	+	0.890380i	$0.349561\pi$
$440$	−0.103814	−0.00494914
$441$	1.00000	0.0476190
$442$	−54.0552	−2.57114
$443$	−20.9611	−0.995892	−0.497946	−	0.867208i	$-0.665912\pi$
$443$	−20.9611	−0.995892	−0.497946	+	0.867208i	$0.665912\pi$
$444$	−2.00988	−0.0953849
$445$	5.28034	0.250312
$446$	46.7212	2.21231
$447$	−5.76671	−0.272756
$448$	8.06972	0.381259
$449$	−8.97940	−0.423764	−0.211882	−	0.977295i	$-0.567959\pi$
$449$	−8.97940	−0.423764	−0.211882	+	0.977295i	$0.567959\pi$
$450$	8.12105	0.382830
$451$	−11.7796	−0.554682
$452$	−15.1339	−0.711837
$453$	11.1916	0.525827
$454$	5.85267	0.274679
$455$	−4.18575	−0.196231
$456$	0.0703977	0.00329668
$457$	−8.10968	−0.379355	−0.189677	−	0.981846i	$-0.560744\pi$
$457$	−8.10968	−0.379355	−0.189677	+	0.981846i	$0.560744\pi$
$458$	−60.3622	−2.82054
$459$	−6.26647	−0.292494
$460$	−17.2904	−0.806170
$461$	32.1538	1.49755	0.748776	−	0.662823i	$-0.230642\pi$
$461$	32.1538	1.49755	0.748776	+	0.662823i	$0.230642\pi$
$462$	−12.2337	−0.569165
$463$	−9.17856	−0.426564	−0.213282	−	0.976991i	$-0.568415\pi$
$463$	−9.17856	−0.426564	−0.213282	+	0.976991i	$0.568415\pi$
$464$	29.8146	1.38411
$465$	8.22244	0.381306
$466$	17.0569	0.790147
$467$	38.3837	1.77619	0.888094	−	0.459662i	$-0.152029\pi$
$467$	38.3837	1.77619	0.888094	+	0.459662i	$0.152029\pi$
$468$	−8.65433	−0.400047
$469$	−8.30971	−0.383707
$470$	4.65617	0.214773
$471$	−4.91205	−0.226335
$472$	−0.166184	−0.00764924
$473$	47.5426	2.18601
$474$	0.292191	0.0134208
$475$	16.3279	0.749174
$476$	12.5877	0.576955
$477$	10.0815	0.461601
$478$	53.1751	2.43217
$479$	−5.03181	−0.229909	−0.114955	−	0.993371i	$-0.536672\pi$
$479$	−5.03181	−0.229909	−0.114955	+	0.993371i	$0.536672\pi$
$480$	−7.78069	−0.355138
$481$	4.31082	0.196556
$482$	33.9299	1.54546
$483$	−8.85972	−0.403131
$484$	52.8991	2.40450
$485$	−1.13861	−0.0517018
$486$	−2.00218	−0.0908208
$487$	37.8819	1.71659	0.858296	−	0.513155i	$-0.171523\pi$
$487$	37.8819	1.71659	0.858296	+	0.513155i	$0.171523\pi$
$488$	0.00284693	0.000128875 0
$489$	2.41787	0.109340
$490$	1.94521	0.0878756
$491$	9.37301	0.422998	0.211499	−	0.977378i	$-0.432165\pi$
$491$	9.37301	0.422998	0.211499	+	0.977378i	$0.432165\pi$
$492$	3.87257	0.174589
$493$	46.9138	2.11289
$494$	−34.7245	−1.56233
$495$	5.93633	0.266818
$496$	33.7046	1.51338
$497$	1.39625	0.0626303
$498$	−18.4374	−0.826199
$499$	31.1748	1.39557	0.697787	−	0.716305i	$-0.254168\pi$
$499$	31.1748	1.39557	0.697787	+	0.716305i	$0.254168\pi$
$500$	17.6737	0.790390
$501$	12.1432	0.542519
$502$	15.8378	0.706875
$503$	33.6429	1.50006	0.750031	−	0.661403i	$-0.230039\pi$
$503$	33.6429	1.50006	0.750031	+	0.661403i	$0.230039\pi$
$504$	0.0174879	0.000778973 0
$505$	8.34605	0.371394
$506$	108.387	4.81841
$507$	5.56187	0.247011
$508$	−20.4242	−0.906176
$509$	−7.14542	−0.316715	−0.158358	−	0.987382i	$-0.550620\pi$
$509$	−7.14542	−0.316715	−0.158358	+	0.987382i	$0.550620\pi$
$510$	−12.1896	−0.539764
$511$	−7.09368	−0.313806
$512$	−32.0331	−1.41568
$513$	−4.02551	−0.177731
$514$	−40.4722	−1.78515
$515$	−0.521322	−0.0229722
$516$	−15.6297	−0.688059
$517$	−14.6257	−0.643239
$518$	−2.00333	−0.0880212
$519$	−14.3858	−0.631466
$520$	−0.0732001	−0.00321004
$521$	−19.7597	−0.865690	−0.432845	−	0.901468i	$-0.642490\pi$
$521$	−19.7597	−0.865690	−0.432845	+	0.901468i	$0.642490\pi$
$522$	14.9893	0.656064
$523$	−23.4967	−1.02744	−0.513719	−	0.857958i	$-0.671733\pi$
$523$	−23.4967	−1.02744	−0.513719	+	0.857958i	$0.671733\pi$
$524$	−6.77239	−0.295853
$525$	4.05610	0.177023
$526$	−7.58942	−0.330915
$527$	53.0348	2.31023
$528$	24.3336	1.05898
$529$	55.4946	2.41281
$530$	19.6107	0.851833
$531$	9.50280	0.412386
$532$	8.08618	0.350580
$533$	−8.30592	−0.359769
$534$	10.8818	0.470903
$535$	−17.8866	−0.773307
$536$	−0.145319	−0.00627684
$537$	19.0453	0.821864
$538$	−30.1636	−1.30044
$539$	−6.11020	−0.263185
$540$	−1.95158	−0.0839824
$541$	4.02840	0.173195	0.0865973	−	0.996243i	$-0.472401\pi$
$541$	4.02840	0.173195	0.0865973	+	0.996243i	$0.472401\pi$
$542$	47.9868	2.06121
$543$	−14.9185	−0.640214
$544$	−50.1855	−2.15169
$545$	−12.1826	−0.521847
$546$	−8.62610	−0.369163
$547$	43.8803	1.87619	0.938093	−	0.346384i	$-0.112591\pi$
$547$	43.8803	1.87619	0.938093	+	0.346384i	$0.112591\pi$
$548$	−7.06003	−0.301590
$549$	−0.162794	−0.00694790
$550$	−49.6212	−2.11586
$551$	30.1369	1.28387
$552$	−0.154938	−0.00659460
$553$	0.145936	0.00620584
$554$	63.0673	2.67947
$555$	0.972101	0.0412634
$556$	−34.2643	−1.45313
$557$	45.0672	1.90956	0.954778	−	0.297319i	$-0.0960924\pi$
$557$	45.0672	1.90956	0.954778	+	0.297319i	$0.0960924\pi$
$558$	16.9450	0.717339
$559$	33.5227	1.41786
$560$	−3.86913	−0.163501
$561$	38.2894	1.61658
$562$	−9.81497	−0.414020
$563$	−11.0734	−0.466686	−0.233343	−	0.972394i	$-0.574967\pi$
$563$	−11.0734	−0.466686	−0.233343	+	0.972394i	$0.574967\pi$
$564$	4.80823	0.202463
$565$	7.31964	0.307940
$566$	−11.0738	−0.465466
$567$	−1.00000	−0.0419961
$568$	0.0244175	0.00102453
$569$	39.4548	1.65403	0.827017	−	0.562177i	$-0.190036\pi$
$569$	39.4548	1.65403	0.827017	+	0.562177i	$0.190036\pi$
$570$	−7.83046	−0.327982
$571$	−18.9547	−0.793230	−0.396615	−	0.917985i	$-0.629815\pi$
$571$	−18.9547	−0.793230	−0.396615	+	0.917985i	$0.629815\pi$
$572$	52.8797	2.21101
$573$	−1.00000	−0.0417756
$574$	3.85994	0.161111
$575$	−35.9359	−1.49863
$576$	−8.06972	−0.336238
$577$	20.2477	0.842922	0.421461	−	0.906847i	$-0.361518\pi$
$577$	20.2477	0.842922	0.421461	+	0.906847i	$0.361518\pi$
$578$	−44.5859	−1.85453
$579$	−10.3610	−0.430587
$580$	14.6104	0.606665
$581$	−9.20865	−0.382039
$582$	−2.34648	−0.0972648
$583$	−61.6001	−2.55121
$584$	−0.124054	−0.00513338
$585$	4.18575	0.173060
$586$	52.2596	2.15882
$587$	−29.8869	−1.23356	−0.616781	−	0.787135i	$-0.711564\pi$
$587$	−29.8869	−1.23356	−0.616781	+	0.787135i	$0.711564\pi$
$588$	2.00873	0.0828388
$589$	34.0690	1.40379
$590$	18.4849	0.761013
$591$	−6.13910	−0.252529
$592$	3.98473	0.163772
$593$	−21.2337	−0.871963	−0.435981	−	0.899956i	$-0.643599\pi$
$593$	−21.2337	−0.871963	−0.435981	+	0.899956i	$0.643599\pi$
$594$	12.2337	0.501956
$595$	−6.08816	−0.249590
$596$	−11.5838	−0.474491
$597$	−19.9264	−0.815533
$598$	76.4248	3.12524
$599$	−23.4048	−0.956295	−0.478148	−	0.878280i	$-0.658692\pi$
$599$	−23.4048	−0.956295	−0.478148	+	0.878280i	$0.658692\pi$
$600$	0.0709327	0.00289582
$601$	−7.73422	−0.315485	−0.157743	−	0.987480i	$-0.550422\pi$
$601$	−7.73422	−0.315485	−0.157743	+	0.987480i	$0.550422\pi$
$602$	−15.5787	−0.634941
$603$	8.30971	0.338397
$604$	22.4809	0.914736
$605$	−25.5852	−1.04018
$606$	17.1997	0.698691
$607$	−24.0751	−0.977179	−0.488589	−	0.872514i	$-0.662488\pi$
$607$	−24.0751	−0.977179	−0.488589	+	0.872514i	$0.662488\pi$
$608$	−32.2386	−1.30745
$609$	7.48648	0.303367
$610$	−0.316669	−0.0128216
$611$	−10.3127	−0.417208
$612$	−12.5877	−0.508827
$613$	12.0965	0.488571	0.244286	−	0.969703i	$-0.421447\pi$
$613$	12.0965	0.488571	0.244286	+	0.969703i	$0.421447\pi$
$614$	28.5653	1.15280
$615$	−1.87301	−0.0755270
$616$	−0.106855	−0.00430529
$617$	−38.3581	−1.54424	−0.772119	−	0.635478i	$-0.780803\pi$
$617$	−38.3581	−1.54424	−0.772119	+	0.635478i	$0.780803\pi$
$618$	−1.07435	−0.0432168
$619$	12.5685	0.505172	0.252586	−	0.967574i	$-0.418719\pi$
$619$	12.5685	0.505172	0.252586	+	0.967574i	$0.418719\pi$
$620$	16.5167	0.663326
$621$	8.85972	0.355528
$622$	−7.33967	−0.294294
$623$	5.43499	0.217748
$624$	17.1578	0.686862
$625$	11.7325	0.469298
$626$	18.3369	0.732890
$627$	24.5967	0.982296
$628$	−9.86700	−0.393736
$629$	6.27006	0.250004
$630$	−1.94521	−0.0774990
$631$	−23.2917	−0.927229	−0.463615	−	0.886037i	$-0.653448\pi$
$631$	−23.2917	−0.927229	−0.463615	+	0.886037i	$0.653448\pi$
$632$	0.00255212	0.000101518 0
$633$	15.0878	0.599688
$634$	−43.0634	−1.71027
$635$	9.87835	0.392010
$636$	20.2511	0.803008
$637$	−4.30835	−0.170703
$638$	−91.5876	−3.62599
$639$	−1.39625	−0.0552347
$640$	−0.135921	−0.00537275
$641$	−24.1841	−0.955213	−0.477607	−	0.878574i	$-0.658496\pi$
$641$	−24.1841	−0.955213	−0.477607	+	0.878574i	$0.658496\pi$
$642$	−36.8612	−1.45480
$643$	24.1477	0.952294	0.476147	−	0.879366i	$-0.342033\pi$
$643$	24.1477	0.952294	0.476147	+	0.879366i	$0.342033\pi$
$644$	−17.7968	−0.701293
$645$	7.55946	0.297653
$646$	−50.5065	−1.98715
$647$	−36.3287	−1.42823	−0.714115	−	0.700029i	$-0.753170\pi$
$647$	−36.3287	−1.42823	−0.714115	+	0.700029i	$0.753170\pi$
$648$	−0.0174879	−0.000686990 0
$649$	−58.0640	−2.27921
$650$	−34.9883	−1.37236
$651$	8.46326	0.331701
$652$	4.85685	0.190209
$653$	15.5541	0.608680	0.304340	−	0.952563i	$-0.401564\pi$
$653$	15.5541	0.608680	0.304340	+	0.952563i	$0.401564\pi$
$654$	−25.1063	−0.981733
$655$	3.27554	0.127986
$656$	−7.67764	−0.299761
$657$	7.09368	0.276751
$658$	4.79255	0.186833
$659$	37.6439	1.46640	0.733200	−	0.680013i	$-0.238026\pi$
$659$	37.6439	1.46640	0.733200	+	0.680013i	$0.238026\pi$
$660$	11.9245	0.464161
$661$	15.6065	0.607024	0.303512	−	0.952828i	$-0.401841\pi$
$661$	15.6065	0.607024	0.303512	+	0.952828i	$0.401841\pi$
$662$	0.714795	0.0277813
$663$	26.9981	1.04852
$664$	−0.161040	−0.00624956
$665$	−3.91096	−0.151661
$666$	2.00333	0.0776274
$667$	−66.3281	−2.56823
$668$	24.3925	0.943773
$669$	−23.3351	−0.902188
$670$	16.1641	0.624475
$671$	0.994706	0.0384002
$672$	−8.00858	−0.308938
$673$	−23.8584	−0.919672	−0.459836	−	0.888004i	$-0.652092\pi$
$673$	−23.8584	−0.919672	−0.459836	+	0.888004i	$0.652092\pi$
$674$	−0.149635	−0.00576374
$675$	−4.05610	−0.156119
$676$	11.1723	0.429705
$677$	−25.8708	−0.994296	−0.497148	−	0.867666i	$-0.665619\pi$
$677$	−25.8708	−0.994296	−0.497148	+	0.867666i	$0.665619\pi$
$678$	15.0845	0.579317
$679$	−1.17196	−0.0449758
$680$	−0.106469	−0.00408290
$681$	−2.92314	−0.112015
$682$	−103.537	−3.96465
$683$	−19.4325	−0.743564	−0.371782	−	0.928320i	$-0.621253\pi$
$683$	−19.4325	−0.743564	−0.371782	+	0.928320i	$0.621253\pi$
$684$	−8.08618	−0.309183
$685$	3.41465	0.130467
$686$	2.00218	0.0764437
$687$	30.1482	1.15023
$688$	30.9869	1.18137
$689$	−43.4347	−1.65473
$690$	17.2340	0.656088
$691$	14.8979	0.566744	0.283372	−	0.959010i	$-0.408547\pi$
$691$	14.8979	0.566744	0.283372	+	0.959010i	$0.408547\pi$
$692$	−28.8972	−1.09851
$693$	6.11020	0.232107
$694$	5.47433	0.207803
$695$	16.5723	0.628623
$696$	0.130923	0.00496262
$697$	−12.0809	−0.457597
$698$	−48.8993	−1.85087
$699$	−8.51917	−0.322225
$700$	8.14763	0.307951
$701$	15.5015	0.585483	0.292742	−	0.956192i	$-0.405432\pi$
$701$	15.5015	0.585483	0.292742	+	0.956192i	$0.405432\pi$
$702$	8.62610	0.325571
$703$	4.02782	0.151912
$704$	49.3076	1.85835
$705$	−2.32555	−0.0875852
$706$	−39.2342	−1.47660
$707$	8.59049	0.323079
$708$	19.0886	0.717394
$709$	42.2559	1.58695	0.793476	−	0.608601i	$-0.208269\pi$
$709$	42.2559	1.58695	0.793476	+	0.608601i	$0.208269\pi$
$710$	−2.71600	−0.101929
$711$	−0.145936	−0.00547304
$712$	0.0950466	0.00356202
$713$	−74.9821	−2.80810
$714$	−12.5466	−0.469545
$715$	−25.5758	−0.956480
$716$	38.2569	1.42973
$717$	−26.5586	−0.991848
$718$	52.3989	1.95551
$719$	−26.3984	−0.984494	−0.492247	−	0.870456i	$-0.663824\pi$
$719$	−26.3984	−0.984494	−0.492247	+	0.870456i	$0.663824\pi$
$720$	3.86913	0.144194
$721$	−0.536591	−0.0199837
$722$	5.59663	0.208285
$723$	−16.9465	−0.630245
$724$	−29.9673	−1.11373
$725$	30.3659	1.12776
$726$	−52.7265	−1.95686
$727$	−17.4057	−0.645540	−0.322770	−	0.946477i	$-0.604614\pi$
$727$	−17.4057	−0.645540	−0.322770	+	0.946477i	$0.604614\pi$
$728$	−0.0753440	−0.00279243
$729$	1.00000	0.0370370
$730$	13.7987	0.510713
$731$	48.7585	1.80340
$732$	−0.327011	−0.0120867
$733$	−28.7453	−1.06173	−0.530866	−	0.847455i	$-0.678133\pi$
$733$	−28.7453	−1.06173	−0.530866	+	0.847455i	$0.678133\pi$
$734$	5.87636	0.216900
$735$	−0.971545	−0.0358360
$736$	70.9537	2.61539
$737$	−50.7740	−1.87028
$738$	−3.85994	−0.142086
$739$	−51.4351	−1.89207	−0.946035	−	0.324063i	$-0.894951\pi$
$739$	−51.4351	−1.89207	−0.946035	+	0.324063i	$0.894951\pi$
$740$	1.95269	0.0717824
$741$	17.3433	0.637122
$742$	20.1850	0.741016
$743$	−6.19073	−0.227116	−0.113558	−	0.993531i	$-0.536225\pi$
$743$	−6.19073	−0.227116	−0.113558	+	0.993531i	$0.536225\pi$
$744$	0.148005	0.00542612
$745$	5.60262	0.205264
$746$	−13.1555	−0.481658
$747$	9.20865	0.336927
$748$	76.9132	2.81222
$749$	−18.4105	−0.672705
$750$	−17.6160	−0.643246
$751$	31.6704	1.15567	0.577835	−	0.816154i	$-0.303898\pi$
$751$	31.6704	1.15567	0.577835	+	0.816154i	$0.303898\pi$
$752$	−9.53265	−0.347620
$753$	−7.91026	−0.288266
$754$	−64.5791	−2.35183
$755$	−10.8731	−0.395714
$756$	−2.00873	−0.0730570
$757$	13.9017	0.505265	0.252633	−	0.967562i	$-0.418704\pi$
$757$	13.9017	0.505265	0.252633	+	0.967562i	$0.418704\pi$
$758$	−11.2851	−0.409895
$759$	−54.1346	−1.96496
$760$	−0.0683946	−0.00248093
$761$	41.7556	1.51364	0.756819	−	0.653625i	$-0.226752\pi$
$761$	41.7556	1.51364	0.756819	+	0.653625i	$0.226752\pi$
$762$	20.3575	0.737476
$763$	−12.5394	−0.453959
$764$	−2.00873	−0.0726735
$765$	6.08816	0.220118
$766$	−9.14736	−0.330508
$767$	−40.9414	−1.47831
$768$	15.8593	0.572274
$769$	44.1644	1.59261	0.796305	−	0.604896i	$-0.206785\pi$
$769$	44.1644	1.59261	0.796305	+	0.604896i	$0.206785\pi$
$770$	11.8856	0.428328
$771$	20.2140	0.727990
$772$	−20.8124	−0.749055
$773$	52.8024	1.89917	0.949585	−	0.313508i	$-0.101504\pi$
$773$	52.8024	1.89917	0.949585	+	0.313508i	$0.101504\pi$
$774$	15.5787	0.559965
$775$	34.3279	1.23309
$776$	−0.0204952	−0.000735734 0
$777$	1.00057	0.0358953
$778$	−0.956262	−0.0342837
$779$	−7.76064	−0.278054
$780$	8.40807	0.301057
$781$	8.53135	0.305276
$782$	111.159	3.97506
$783$	−7.48648	−0.267545
$784$	−3.98245	−0.142231
$785$	4.77227	0.170330
$786$	6.75030	0.240775
$787$	−3.36123	−0.119815	−0.0599075	−	0.998204i	$-0.519081\pi$
$787$	−3.36123	−0.119815	−0.0599075	+	0.998204i	$0.519081\pi$
$788$	−12.3318	−0.439303
$789$	3.79058	0.134948
$790$	−0.283877	−0.0100999
$791$	7.53403	0.267879
$792$	0.106855	0.00379691
$793$	0.701375	0.0249066
$794$	−57.6756	−2.04683
$795$	−9.79464	−0.347380
$796$	−40.0268	−1.41871
$797$	23.6479	0.837651	0.418826	−	0.908067i	$-0.362442\pi$
$797$	23.6479	0.837651	0.418826	+	0.908067i	$0.362442\pi$
$798$	−8.05981	−0.285314
$799$	−14.9998	−0.530655
$800$	−32.4836	−1.14847
$801$	−5.43499	−0.192036
$802$	14.4400	0.509893
$803$	−43.3438	−1.52957
$804$	16.6920	0.588681
$805$	8.60761	0.303379
$806$	−73.0050	−2.57149
$807$	15.0654	0.530326
$808$	0.150230	0.00528506
$809$	−40.4166	−1.42097	−0.710486	−	0.703711i	$-0.751525\pi$
$809$	−40.4166	−1.42097	−0.710486	+	0.703711i	$0.751525\pi$
$810$	1.94521	0.0683477
$811$	−7.76145	−0.272541	−0.136271	−	0.990672i	$-0.543512\pi$
$811$	−7.76145	−0.272541	−0.136271	+	0.990672i	$0.543512\pi$
$812$	15.0383	0.527742
$813$	−23.9672	−0.840567
$814$	−12.2407	−0.429038
$815$	−2.34907	−0.0822842
$816$	24.9559	0.873632
$817$	31.3219	1.09582
$818$	−10.9909	−0.384289
$819$	4.30835	0.150546
$820$	−3.76238	−0.131388
$821$	27.4859	0.959265	0.479632	−	0.877470i	$-0.340770\pi$
$821$	27.4859	0.959265	0.479632	+	0.877470i	$0.340770\pi$
$822$	7.03700	0.245444
$823$	−51.7498	−1.80388	−0.901941	−	0.431858i	$-0.857858\pi$
$823$	−51.7498	−1.80388	−0.901941	+	0.431858i	$0.857858\pi$
$824$	−0.00938385	−0.000326902 0
$825$	24.7836	0.862853
$826$	19.0263	0.662011
$827$	−12.0291	−0.418293	−0.209146	−	0.977884i	$-0.567068\pi$
$827$	−12.0291	−0.418293	−0.209146	+	0.977884i	$0.567068\pi$
$828$	17.7968	0.618482
$829$	−48.5756	−1.68710	−0.843550	−	0.537051i	$-0.819538\pi$
$829$	−48.5756	−1.68710	−0.843550	+	0.537051i	$0.819538\pi$
$830$	17.9127	0.621761
$831$	−31.4993	−1.09270
$832$	34.7672	1.20534
$833$	−6.26647	−0.217120
$834$	34.1526	1.18261
$835$	−11.7977	−0.408275
$836$	49.4082	1.70882
$837$	−8.46326	−0.292533
$838$	36.8164	1.27180
$839$	12.5104	0.431907	0.215954	−	0.976404i	$-0.430714\pi$
$839$	12.5104	0.431907	0.215954	+	0.976404i	$0.430714\pi$
$840$	−0.0169903	−0.000586220 0
$841$	27.0474	0.932667
$842$	35.0178	1.20679
$843$	4.90214	0.168839
$844$	30.3075	1.04323
$845$	−5.40361	−0.185890
$846$	−4.79255	−0.164771
$847$	−26.3345	−0.904865
$848$	−40.1492	−1.37873
$849$	5.53086	0.189819
$850$	−50.8903	−1.74552
$851$	−8.86479	−0.303881
$852$	−2.80469	−0.0960871
$853$	52.2636	1.78947	0.894736	−	0.446596i	$-0.147364\pi$
$853$	52.2636	1.78947	0.894736	+	0.446596i	$0.147364\pi$
$854$	−0.325944	−0.0111536
$855$	3.91096	0.133752
$856$	−0.321961	−0.0110044
$857$	42.0830	1.43753	0.718765	−	0.695253i	$-0.244708\pi$
$857$	42.0830	1.43753	0.718765	+	0.695253i	$0.244708\pi$
$858$	−52.7072	−1.79939
$859$	−19.6065	−0.668965	−0.334483	−	0.942402i	$-0.608562\pi$
$859$	−19.6065	−0.668965	−0.334483	+	0.942402i	$0.608562\pi$
$860$	15.1849	0.517802
$861$	−1.92787	−0.0657015
$862$	−80.6410	−2.74664
$863$	1.62275	0.0552392	0.0276196	−	0.999619i	$-0.491207\pi$
$863$	1.62275	0.0552392	0.0276196	+	0.999619i	$0.491207\pi$
$864$	8.00858	0.272457
$865$	13.9764	0.475213
$866$	66.5776	2.26240
$867$	22.2686	0.756283
$868$	17.0004	0.577033
$869$	0.891700	0.0302488
$870$	−14.5628	−0.493724
$871$	−35.8011	−1.21307
$872$	−0.219289	−0.00742605
$873$	1.17196	0.0396649
$874$	71.4076	2.41540
$875$	−8.79841	−0.297440
$876$	14.2493	0.481440
$877$	25.9522	0.876345	0.438172	−	0.898891i	$-0.355626\pi$
$877$	25.9522	0.876345	0.438172	+	0.898891i	$0.355626\pi$
$878$	−38.1932	−1.28896
$879$	−26.1013	−0.880375
$880$	−23.6412	−0.796944
$881$	11.8985	0.400870	0.200435	−	0.979707i	$-0.435764\pi$
$881$	11.8985	0.400870	0.200435	+	0.979707i	$0.435764\pi$
$882$	−2.00218	−0.0674170
$883$	−0.230768	−0.00776597	−0.00388298	−	0.999992i	$-0.501236\pi$
$883$	−0.230768	−0.00776597	−0.00388298	+	0.999992i	$0.501236\pi$
$884$	54.2321	1.82402
$885$	−9.23240	−0.310344
$886$	41.9679	1.40994
$887$	−25.6347	−0.860731	−0.430365	−	0.902655i	$-0.641615\pi$
$887$	−25.6347	−0.860731	−0.430365	+	0.902655i	$0.641615\pi$
$888$	0.0174979	0.000587192 0
$889$	10.1677	0.341013
$890$	−10.5722	−0.354381
$891$	−6.11020	−0.204699
$892$	−46.8741	−1.56946
$893$	−9.63571	−0.322447
$894$	11.5460	0.386156
$895$	−18.5033	−0.618498
$896$	−0.139902	−0.00467379
$897$	−38.1708	−1.27448
$898$	17.9784	0.599947
$899$	63.3600	2.11318
$900$	−8.14763	−0.271588
$901$	−63.1755	−2.10468
$902$	23.5850	0.785294
$903$	7.78086	0.258931
$904$	0.131754	0.00438208
$905$	14.4940	0.481796
$906$	−22.4076	−0.744443
$907$	28.4386	0.944287	0.472143	−	0.881522i	$-0.343480\pi$
$907$	28.4386	0.944287	0.472143	+	0.881522i	$0.343480\pi$
$908$	−5.87182	−0.194863
$909$	−8.59049	−0.284929
$910$	8.38064	0.277816
$911$	−38.4073	−1.27249	−0.636245	−	0.771487i	$-0.719513\pi$
$911$	−38.4073	−1.27249	−0.636245	+	0.771487i	$0.719513\pi$
$912$	16.0314	0.530853
$913$	−56.2667	−1.86215
$914$	16.2371	0.537074
$915$	0.158162	0.00522868
$916$	60.5597	2.00095
$917$	3.37147	0.111336
$918$	12.5466	0.414100
$919$	−8.39735	−0.277003	−0.138502	−	0.990362i	$-0.544229\pi$
$919$	−8.39735	−0.277003	−0.138502	+	0.990362i	$0.544229\pi$
$920$	0.150529	0.00496280
$921$	−14.2671	−0.470116
$922$	−64.3778	−2.12017
$923$	6.01552	0.198003
$924$	12.2738	0.403777
$925$	4.05842	0.133440
$926$	18.3772	0.603911
$927$	0.536591	0.0176240
$928$	−59.9560	−1.96815
$929$	−50.4866	−1.65641	−0.828206	−	0.560424i	$-0.810638\pi$
$929$	−50.4866	−1.65641	−0.828206	+	0.560424i	$0.810638\pi$
$930$	−16.4628	−0.539837
$931$	−4.02551	−0.131931
$932$	−17.1127	−0.560547
$933$	3.66584	0.120014
$934$	−76.8513	−2.51465
$935$	−37.1998	−1.21656
$936$	0.0753440	0.00246270
$937$	−22.1941	−0.725048	−0.362524	−	0.931974i	$-0.618085\pi$
$937$	−22.1941	−0.725048	−0.362524	+	0.931974i	$0.618085\pi$
$938$	16.6375	0.543235
$939$	−9.15846	−0.298875
$940$	−4.67141	−0.152365
$941$	0.302066	0.00984707	0.00492354	−	0.999988i	$-0.498433\pi$
$941$	0.302066	0.00984707	0.00492354	+	0.999988i	$0.498433\pi$
$942$	9.83482	0.320436
$943$	17.0803	0.556213
$944$	−37.8445	−1.23173
$945$	0.971545	0.0316044
$946$	−95.1890	−3.09486
$947$	16.9392	0.550448	0.275224	−	0.961380i	$-0.411248\pi$
$947$	16.9392	0.550448	0.275224	+	0.961380i	$0.411248\pi$
$948$	−0.293147	−0.00952098
$949$	−30.5621	−0.992087
$950$	−32.6914	−1.06065
$951$	21.5082	0.697452
$952$	−0.109587	−0.00355175
$953$	−34.3593	−1.11301	−0.556503	−	0.830845i	$-0.687857\pi$
$953$	−34.3593	−1.11301	−0.556503	+	0.830845i	$0.687857\pi$
$954$	−20.1850	−0.653515
$955$	0.971545	0.0314384
$956$	−53.3491	−1.72543
$957$	45.7439	1.47869
$958$	10.0746	0.325496
$959$	3.51467	0.113494
$960$	7.84010	0.253038
$961$	40.6268	1.31054
$962$	−8.63104	−0.278276
$963$	18.4105	0.593270
$964$	−34.0409	−1.09638
$965$	10.0661	0.324040
$966$	17.7388	0.570736
$967$	9.23056	0.296835	0.148417	−	0.988925i	$-0.452582\pi$
$967$	9.23056	0.296835	0.148417	+	0.988925i	$0.452582\pi$
$968$	−0.460536	−0.0148022
$969$	25.2257	0.810367
$970$	2.27971	0.0731972
$971$	25.7385	0.825988	0.412994	−	0.910734i	$-0.364483\pi$
$971$	25.7385	0.825988	0.412994	+	0.910734i	$0.364483\pi$
$972$	2.00873	0.0644302
$973$	17.0577	0.546844
$974$	−75.8465	−2.43028
$975$	17.4751	0.559651
$976$	0.648321	0.0207523
$977$	−31.2949	−1.00121	−0.500606	−	0.865675i	$-0.666889\pi$
$977$	−31.2949	−1.00121	−0.500606	+	0.865675i	$0.666889\pi$
$978$	−4.84101	−0.154798
$979$	33.2089	1.06136
$980$	−1.95158	−0.0623408
$981$	12.5394	0.400354
$982$	−18.7665	−0.598862
$983$	9.68883	0.309026	0.154513	−	0.987991i	$-0.450619\pi$
$983$	9.68883	0.309026	0.154513	+	0.987991i	$0.450619\pi$
$984$	−0.0337143	−0.00107477
$985$	5.96441	0.190042
$986$	−93.9300	−2.99134
$987$	−2.39366	−0.0761911
$988$	34.8381	1.10835
$989$	−68.9363	−2.19205
$990$	−11.8856	−0.377750
$991$	52.5350	1.66883	0.834415	−	0.551137i	$-0.185806\pi$
$991$	52.5350	1.66883	0.834415	+	0.551137i	$0.185806\pi$
$992$	−67.7787	−2.15198
$993$	−0.357008	−0.0113293
$994$	−2.79554	−0.0886692
$995$	19.3594	0.613733
$996$	18.4977	0.586123
$997$	−21.3676	−0.676719	−0.338360	−	0.941017i	$-0.609872\pi$
$997$	−21.3676	−0.676719	−0.338360	+	0.941017i	$0.609872\pi$
$998$	−62.4175	−1.97579
$999$	−1.00057	−0.0316567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.6	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.6	✓	29	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00218 q^{2} +1.00000 q^{3} +2.00873 q^{4} -0.971545 q^{5} -2.00218 q^{6} -1.00000 q^{7} -0.0174879 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.00218 q^{2} +1.00000 q^{3} +2.00873 q^{4} -0.971545 q^{5} -2.00218 q^{6} -1.00000 q^{7} -0.0174879 q^{8} +1.00000 q^{9} +1.94521 q^{10} -6.11020 q^{11} +2.00873 q^{12} -4.30835 q^{13} +2.00218 q^{14} -0.971545 q^{15} -3.98245 q^{16} -6.26647 q^{17} -2.00218 q^{18} -4.02551 q^{19} -1.95158 q^{20} -1.00000 q^{21} +12.2337 q^{22} +8.85972 q^{23} -0.0174879 q^{24} -4.05610 q^{25} +8.62610 q^{26} +1.00000 q^{27} -2.00873 q^{28} -7.48648 q^{29} +1.94521 q^{30} -8.46326 q^{31} +8.00858 q^{32} -6.11020 q^{33} +12.5466 q^{34} +0.971545 q^{35} +2.00873 q^{36} -1.00057 q^{37} +8.05981 q^{38} -4.30835 q^{39} +0.0169903 q^{40} +1.92787 q^{41} +2.00218 q^{42} -7.78086 q^{43} -12.2738 q^{44} -0.971545 q^{45} -17.7388 q^{46} +2.39366 q^{47} -3.98245 q^{48} +1.00000 q^{49} +8.12105 q^{50} -6.26647 q^{51} -8.65433 q^{52} +10.0815 q^{53} -2.00218 q^{54} +5.93633 q^{55} +0.0174879 q^{56} -4.02551 q^{57} +14.9893 q^{58} +9.50280 q^{59} -1.95158 q^{60} -0.162794 q^{61} +16.9450 q^{62} -1.00000 q^{63} -8.06972 q^{64} +4.18575 q^{65} +12.2337 q^{66} +8.30971 q^{67} -12.5877 q^{68} +8.85972 q^{69} -1.94521 q^{70} -1.39625 q^{71} -0.0174879 q^{72} +7.09368 q^{73} +2.00333 q^{74} -4.05610 q^{75} -8.08618 q^{76} +6.11020 q^{77} +8.62610 q^{78} -0.145936 q^{79} +3.86913 q^{80} +1.00000 q^{81} -3.85994 q^{82} +9.20865 q^{83} -2.00873 q^{84} +6.08816 q^{85} +15.5787 q^{86} -7.48648 q^{87} +0.106855 q^{88} -5.43499 q^{89} +1.94521 q^{90} +4.30835 q^{91} +17.7968 q^{92} -8.46326 q^{93} -4.79255 q^{94} +3.91096 q^{95} +8.00858 q^{96} +1.17196 q^{97} -2.00218 q^{98} -6.11020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

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