LMFDB - Embedded newform 6010.2.a.g.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.83794 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.83794 q^{6} +2.63564 q^{7} -1.00000 q^{8} +0.378009 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.83794 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.83794 q^{6} +2.63564 q^{7} -1.00000 q^{8} +0.378009 q^{9} -1.00000 q^{10} +4.43940 q^{11} +1.83794 q^{12} +4.15571 q^{13} -2.63564 q^{14} +1.83794 q^{15} +1.00000 q^{16} -4.34515 q^{17} -0.378009 q^{18} -1.11047 q^{19} +1.00000 q^{20} +4.84415 q^{21} -4.43940 q^{22} +8.02748 q^{23} -1.83794 q^{24} +1.00000 q^{25} -4.15571 q^{26} -4.81905 q^{27} +2.63564 q^{28} -4.07623 q^{29} -1.83794 q^{30} +2.41883 q^{31} -1.00000 q^{32} +8.15933 q^{33} +4.34515 q^{34} +2.63564 q^{35} +0.378009 q^{36} -9.88181 q^{37} +1.11047 q^{38} +7.63792 q^{39} -1.00000 q^{40} +3.85175 q^{41} -4.84415 q^{42} +2.73022 q^{43} +4.43940 q^{44} +0.378009 q^{45} -8.02748 q^{46} +5.82883 q^{47} +1.83794 q^{48} -0.0533786 q^{49} -1.00000 q^{50} -7.98612 q^{51} +4.15571 q^{52} +8.37589 q^{53} +4.81905 q^{54} +4.43940 q^{55} -2.63564 q^{56} -2.04097 q^{57} +4.07623 q^{58} +10.4585 q^{59} +1.83794 q^{60} +9.87660 q^{61} -2.41883 q^{62} +0.996297 q^{63} +1.00000 q^{64} +4.15571 q^{65} -8.15933 q^{66} +3.01266 q^{67} -4.34515 q^{68} +14.7540 q^{69} -2.63564 q^{70} -15.6358 q^{71} -0.378009 q^{72} +5.69971 q^{73} +9.88181 q^{74} +1.83794 q^{75} -1.11047 q^{76} +11.7007 q^{77} -7.63792 q^{78} -9.03702 q^{79} +1.00000 q^{80} -9.99114 q^{81} -3.85175 q^{82} -15.8303 q^{83} +4.84415 q^{84} -4.34515 q^{85} -2.73022 q^{86} -7.49186 q^{87} -4.43940 q^{88} +10.3696 q^{89} -0.378009 q^{90} +10.9530 q^{91} +8.02748 q^{92} +4.44565 q^{93} -5.82883 q^{94} -1.11047 q^{95} -1.83794 q^{96} -4.51594 q^{97} +0.0533786 q^{98} +1.67813 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.83794	1.06113	0.530566	−	0.847643i	$-0.321979\pi$
$3$	1.83794	1.06113	0.530566	+	0.847643i	$0.321979\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.83794	−0.750334
$7$	2.63564	0.996180	0.498090	−	0.867125i	$-0.334035\pi$
$7$	2.63564	0.996180	0.498090	+	0.867125i	$0.334035\pi$
$8$	−1.00000	−0.353553
$9$	0.378009	0.126003
$10$	−1.00000	−0.316228
$11$	4.43940	1.33853	0.669264	−	0.743024i	$-0.266609\pi$
$11$	4.43940	1.33853	0.669264	+	0.743024i	$0.266609\pi$
$12$	1.83794	0.530566
$13$	4.15571	1.15259	0.576293	−	0.817243i	$-0.304499\pi$
$13$	4.15571	1.15259	0.576293	+	0.817243i	$0.304499\pi$
$14$	−2.63564	−0.704406
$15$	1.83794	0.474553
$16$	1.00000	0.250000
$17$	−4.34515	−1.05385	−0.526927	−	0.849910i	$-0.676656\pi$
$17$	−4.34515	−1.05385	−0.526927	+	0.849910i	$0.676656\pi$
$18$	−0.378009	−0.0890975
$19$	−1.11047	−0.254759	−0.127379	−	0.991854i	$-0.540657\pi$
$19$	−1.11047	−0.254759	−0.127379	+	0.991854i	$0.540657\pi$
$20$	1.00000	0.223607
$21$	4.84415	1.05708
$22$	−4.43940	−0.946483
$23$	8.02748	1.67384	0.836922	−	0.547322i	$-0.184353\pi$
$23$	8.02748	1.67384	0.836922	+	0.547322i	$0.184353\pi$
$24$	−1.83794	−0.375167
$25$	1.00000	0.200000
$26$	−4.15571	−0.815001
$27$	−4.81905	−0.927427
$28$	2.63564	0.498090
$29$	−4.07623	−0.756938	−0.378469	−	0.925614i	$-0.623549\pi$
$29$	−4.07623	−0.756938	−0.378469	+	0.925614i	$0.623549\pi$
$30$	−1.83794	−0.335560
$31$	2.41883	0.434434	0.217217	−	0.976123i	$-0.430302\pi$
$31$	2.41883	0.434434	0.217217	+	0.976123i	$0.430302\pi$
$32$	−1.00000	−0.176777
$33$	8.15933	1.42036
$34$	4.34515	0.745188
$35$	2.63564	0.445505
$36$	0.378009	0.0630015
$37$	−9.88181	−1.62456	−0.812280	−	0.583268i	$-0.801774\pi$
$37$	−9.88181	−1.62456	−0.812280	+	0.583268i	$0.801774\pi$
$38$	1.11047	0.180142
$39$	7.63792	1.22305
$40$	−1.00000	−0.158114
$41$	3.85175	0.601543	0.300771	−	0.953696i	$-0.402756\pi$
$41$	3.85175	0.601543	0.300771	+	0.953696i	$0.402756\pi$
$42$	−4.84415	−0.747468
$43$	2.73022	0.416355	0.208177	−	0.978091i	$-0.433247\pi$
$43$	2.73022	0.416355	0.208177	+	0.978091i	$0.433247\pi$
$44$	4.43940	0.669264
$45$	0.378009	0.0563502
$46$	−8.02748	−1.18359
$47$	5.82883	0.850222	0.425111	−	0.905141i	$-0.360235\pi$
$47$	5.82883	0.850222	0.425111	+	0.905141i	$0.360235\pi$
$48$	1.83794	0.265283
$49$	−0.0533786	−0.00762551
$50$	−1.00000	−0.141421
$51$	−7.98612	−1.11828
$52$	4.15571	0.576293
$53$	8.37589	1.15052	0.575258	−	0.817972i	$-0.304901\pi$
$53$	8.37589	1.15052	0.575258	+	0.817972i	$0.304901\pi$
$54$	4.81905	0.655790
$55$	4.43940	0.598608
$56$	−2.63564	−0.352203
$57$	−2.04097	−0.270333
$58$	4.07623	0.535236
$59$	10.4585	1.36158	0.680789	−	0.732479i	$-0.261637\pi$
$59$	10.4585	1.36158	0.680789	+	0.732479i	$0.261637\pi$
$60$	1.83794	0.237277
$61$	9.87660	1.26457	0.632284	−	0.774736i	$-0.282117\pi$
$61$	9.87660	1.26457	0.632284	+	0.774736i	$0.282117\pi$
$62$	−2.41883	−0.307191
$63$	0.996297	0.125522
$64$	1.00000	0.125000
$65$	4.15571	0.515452
$66$	−8.15933	−1.00434
$67$	3.01266	0.368055	0.184027	−	0.982921i	$-0.441087\pi$
$67$	3.01266	0.368055	0.184027	+	0.982921i	$0.441087\pi$
$68$	−4.34515	−0.526927
$69$	14.7540	1.77617
$70$	−2.63564	−0.315020
$71$	−15.6358	−1.85563	−0.927814	−	0.373043i	$-0.878314\pi$
$71$	−15.6358	−1.85563	−0.927814	+	0.373043i	$0.878314\pi$
$72$	−0.378009	−0.0445488
$73$	5.69971	0.667101	0.333551	−	0.942732i	$-0.391753\pi$
$73$	5.69971	0.667101	0.333551	+	0.942732i	$0.391753\pi$
$74$	9.88181	1.14874
$75$	1.83794	0.212227
$76$	−1.11047	−0.127379
$77$	11.7007	1.33342
$78$	−7.63792	−0.864824
$79$	−9.03702	−1.01674	−0.508372	−	0.861138i	$-0.669752\pi$
$79$	−9.03702	−1.01674	−0.508372	+	0.861138i	$0.669752\pi$
$80$	1.00000	0.111803
$81$	−9.99114	−1.11013
$82$	−3.85175	−0.425355
$83$	−15.8303	−1.73761	−0.868803	−	0.495157i	$-0.835110\pi$
$83$	−15.8303	−1.73761	−0.868803	+	0.495157i	$0.835110\pi$
$84$	4.84415	0.528540
$85$	−4.34515	−0.471298
$86$	−2.73022	−0.294407
$87$	−7.49186	−0.803211
$88$	−4.43940	−0.473241
$89$	10.3696	1.09917	0.549586	−	0.835437i	$-0.314785\pi$
$89$	10.3696	1.09917	0.549586	+	0.835437i	$0.314785\pi$
$90$	−0.378009	−0.0398456
$91$	10.9530	1.14818
$92$	8.02748	0.836922
$93$	4.44565	0.460992
$94$	−5.82883	−0.601198
$95$	−1.11047	−0.113932
$96$	−1.83794	−0.187584
$97$	−4.51594	−0.458524	−0.229262	−	0.973365i	$-0.573631\pi$
$97$	−4.51594	−0.458524	−0.229262	+	0.973365i	$0.573631\pi$
$98$	0.0533786	0.00539205
$99$	1.67813	0.168659
$100$	1.00000	0.100000
$101$	−4.72013	−0.469670	−0.234835	−	0.972035i	$-0.575455\pi$
$101$	−4.72013	−0.469670	−0.234835	+	0.972035i	$0.575455\pi$
$102$	7.98612	0.790743
$103$	8.09034	0.797165	0.398582	−	0.917133i	$-0.369502\pi$
$103$	8.09034	0.797165	0.398582	+	0.917133i	$0.369502\pi$
$104$	−4.15571	−0.407500
$105$	4.84415	0.472740
$106$	−8.37589	−0.813538
$107$	6.96747	0.673570	0.336785	−	0.941582i	$-0.390660\pi$
$107$	6.96747	0.673570	0.336785	+	0.941582i	$0.390660\pi$
$108$	−4.81905	−0.463713
$109$	17.7030	1.69564	0.847820	−	0.530285i	$-0.177915\pi$
$109$	17.7030	1.69564	0.847820	+	0.530285i	$0.177915\pi$
$110$	−4.43940	−0.423280
$111$	−18.1621	−1.72387
$112$	2.63564	0.249045
$113$	7.24411	0.681468	0.340734	−	0.940160i	$-0.389324\pi$
$113$	7.24411	0.681468	0.340734	+	0.940160i	$0.389324\pi$
$114$	2.04097	0.191154
$115$	8.02748	0.748566
$116$	−4.07623	−0.378469
$117$	1.57089	0.145229
$118$	−10.4585	−0.962782
$119$	−11.4523	−1.04983
$120$	−1.83794	−0.167780
$121$	8.70826	0.791660
$122$	−9.87660	−0.894185
$123$	7.07927	0.638317
$124$	2.41883	0.217217
$125$	1.00000	0.0894427
$126$	−0.996297	−0.0887572
$127$	−7.06437	−0.626862	−0.313431	−	0.949611i	$-0.601478\pi$
$127$	−7.06437	−0.626862	−0.313431	+	0.949611i	$0.601478\pi$
$128$	−1.00000	−0.0883883
$129$	5.01797	0.441808
$130$	−4.15571	−0.364479
$131$	−10.8951	−0.951906	−0.475953	−	0.879471i	$-0.657897\pi$
$131$	−10.8951	−0.951906	−0.475953	+	0.879471i	$0.657897\pi$
$132$	8.15933	0.710179
$133$	−2.92680	−0.253785
$134$	−3.01266	−0.260254
$135$	−4.81905	−0.414758
$136$	4.34515	0.372594
$137$	−5.04157	−0.430730	−0.215365	−	0.976534i	$-0.569094\pi$
$137$	−5.04157	−0.430730	−0.215365	+	0.976534i	$0.569094\pi$
$138$	−14.7540	−1.25594
$139$	−14.4798	−1.22816	−0.614080	−	0.789243i	$-0.710473\pi$
$139$	−14.4798	−1.22816	−0.614080	+	0.789243i	$0.710473\pi$
$140$	2.63564	0.222753
$141$	10.7130	0.902199
$142$	15.6358	1.31213
$143$	18.4488	1.54277
$144$	0.378009	0.0315007
$145$	−4.07623	−0.338513
$146$	−5.69971	−0.471712
$147$	−0.0981064	−0.00809168
$148$	−9.88181	−0.812280
$149$	−1.00039	−0.0819549	−0.0409774	−	0.999160i	$-0.513047\pi$
$149$	−1.00039	−0.0819549	−0.0409774	+	0.999160i	$0.513047\pi$
$150$	−1.83794	−0.150067
$151$	−6.49906	−0.528886	−0.264443	−	0.964401i	$-0.585188\pi$
$151$	−6.49906	−0.528886	−0.264443	+	0.964401i	$0.585188\pi$
$152$	1.11047	0.0900708
$153$	−1.64251	−0.132789
$154$	−11.7007	−0.942867
$155$	2.41883	0.194285
$156$	7.63792	0.611523
$157$	−13.1321	−1.04806	−0.524029	−	0.851700i	$-0.675572\pi$
$157$	−13.1321	−1.04806	−0.524029	+	0.851700i	$0.675572\pi$
$158$	9.03702	0.718947
$159$	15.3943	1.22085
$160$	−1.00000	−0.0790569
$161$	21.1576	1.66745
$162$	9.99114	0.784978
$163$	−11.4961	−0.900447	−0.450223	−	0.892916i	$-0.648656\pi$
$163$	−11.4961	−0.900447	−0.450223	+	0.892916i	$0.648656\pi$
$164$	3.85175	0.300771
$165$	8.15933	0.635203
$166$	15.8303	1.22867
$167$	11.1394	0.861996	0.430998	−	0.902353i	$-0.358162\pi$
$167$	11.1394	0.861996	0.430998	+	0.902353i	$0.358162\pi$
$168$	−4.84415	−0.373734
$169$	4.26989	0.328453
$170$	4.34515	0.333258
$171$	−0.419766	−0.0321003
$172$	2.73022	0.208177
$173$	25.9863	1.97570	0.987852	−	0.155399i	$-0.0496663\pi$
$173$	25.9863	1.97570	0.987852	+	0.155399i	$0.0496663\pi$
$174$	7.49186	0.567956
$175$	2.63564	0.199236
$176$	4.43940	0.334632
$177$	19.2220	1.44482
$178$	−10.3696	−0.777232
$179$	−20.4757	−1.53042	−0.765211	−	0.643779i	$-0.777365\pi$
$179$	−20.4757	−1.53042	−0.765211	+	0.643779i	$0.777365\pi$
$180$	0.378009	0.0281751
$181$	−13.0356	−0.968931	−0.484465	−	0.874810i	$-0.660986\pi$
$181$	−13.0356	−0.968931	−0.484465	+	0.874810i	$0.660986\pi$
$182$	−10.9530	−0.811888
$183$	18.1526	1.34188
$184$	−8.02748	−0.591793
$185$	−9.88181	−0.726525
$186$	−4.44565	−0.325971
$187$	−19.2899	−1.41062
$188$	5.82883	0.425111
$189$	−12.7013	−0.923884
$190$	1.11047	0.0805618
$191$	7.86565	0.569138	0.284569	−	0.958656i	$-0.408149\pi$
$191$	7.86565	0.569138	0.284569	+	0.958656i	$0.408149\pi$
$192$	1.83794	0.132642
$193$	−17.4724	−1.25769	−0.628846	−	0.777530i	$-0.716473\pi$
$193$	−17.4724	−1.25769	−0.628846	+	0.777530i	$0.716473\pi$
$194$	4.51594	0.324226
$195$	7.63792	0.546963
$196$	−0.0533786	−0.00381275
$197$	17.5902	1.25325	0.626623	−	0.779322i	$-0.284436\pi$
$197$	17.5902	1.25325	0.626623	+	0.779322i	$0.284436\pi$
$198$	−1.67813	−0.119260
$199$	9.81954	0.696089	0.348044	−	0.937478i	$-0.386846\pi$
$199$	9.81954	0.696089	0.348044	+	0.937478i	$0.386846\pi$
$200$	−1.00000	−0.0707107
$201$	5.53707	0.390555
$202$	4.72013	0.332107
$203$	−10.7435	−0.754046
$204$	−7.98612	−0.559140
$205$	3.85175	0.269018
$206$	−8.09034	−0.563680
$207$	3.03446	0.210909
$208$	4.15571	0.288146
$209$	−4.92981	−0.341002
$210$	−4.84415	−0.334278
$211$	20.6344	1.42053	0.710267	−	0.703932i	$-0.248574\pi$
$211$	20.6344	1.42053	0.710267	+	0.703932i	$0.248574\pi$
$212$	8.37589	0.575258
$213$	−28.7376	−1.96907
$214$	−6.96747	−0.476286
$215$	2.73022	0.186199
$216$	4.81905	0.327895
$217$	6.37516	0.432774
$218$	−17.7030	−1.19900
$219$	10.4757	0.707883
$220$	4.43940	0.299304
$221$	−18.0572	−1.21466
$222$	18.1621	1.21896
$223$	−19.4740	−1.30408	−0.652038	−	0.758186i	$-0.726086\pi$
$223$	−19.4740	−1.30408	−0.652038	+	0.758186i	$0.726086\pi$
$224$	−2.63564	−0.176101
$225$	0.378009	0.0252006
$226$	−7.24411	−0.481871
$227$	0.346663	0.0230088	0.0115044	−	0.999934i	$-0.496338\pi$
$227$	0.346663	0.0230088	0.0115044	+	0.999934i	$0.496338\pi$
$228$	−2.04097	−0.135166
$229$	−11.8096	−0.780400	−0.390200	−	0.920730i	$-0.627594\pi$
$229$	−11.8096	−0.780400	−0.390200	+	0.920730i	$0.627594\pi$
$230$	−8.02748	−0.529316
$231$	21.5051	1.41493
$232$	4.07623	0.267618
$233$	−24.3623	−1.59603	−0.798015	−	0.602637i	$-0.794117\pi$
$233$	−24.3623	−1.59603	−0.798015	+	0.602637i	$0.794117\pi$
$234$	−1.57089	−0.102693
$235$	5.82883	0.380231
$236$	10.4585	0.680789
$237$	−16.6095	−1.07890
$238$	11.4523	0.742341
$239$	10.5172	0.680300	0.340150	−	0.940371i	$-0.389522\pi$
$239$	10.5172	0.680300	0.340150	+	0.940371i	$0.389522\pi$
$240$	1.83794	0.118638
$241$	27.9456	1.80014	0.900068	−	0.435750i	$-0.143517\pi$
$241$	27.9456	1.80014	0.900068	+	0.435750i	$0.143517\pi$
$242$	−8.70826	−0.559788
$243$	−3.90591	−0.250564
$244$	9.87660	0.632284
$245$	−0.0533786	−0.00341023
$246$	−7.07927	−0.451358
$247$	−4.61477	−0.293631
$248$	−2.41883	−0.153596
$249$	−29.0952	−1.84383
$250$	−1.00000	−0.0632456
$251$	8.49354	0.536108	0.268054	−	0.963404i	$-0.413620\pi$
$251$	8.49354	0.536108	0.268054	+	0.963404i	$0.413620\pi$
$252$	0.996297	0.0627608
$253$	35.6372	2.24049
$254$	7.06437	0.443258
$255$	−7.98612	−0.500110
$256$	1.00000	0.0625000
$257$	−7.56962	−0.472180	−0.236090	−	0.971731i	$-0.575866\pi$
$257$	−7.56962	−0.472180	−0.236090	+	0.971731i	$0.575866\pi$
$258$	−5.01797	−0.312405
$259$	−26.0449	−1.61835
$260$	4.15571	0.257726
$261$	−1.54085	−0.0953764
$262$	10.8951	0.673099
$263$	23.3485	1.43973	0.719865	−	0.694114i	$-0.244204\pi$
$263$	23.3485	1.43973	0.719865	+	0.694114i	$0.244204\pi$
$264$	−8.15933	−0.502172
$265$	8.37589	0.514527
$266$	2.92680	0.179453
$267$	19.0586	1.16637
$268$	3.01266	0.184027
$269$	−6.31706	−0.385158	−0.192579	−	0.981281i	$-0.561685\pi$
$269$	−6.31706	−0.385158	−0.192579	+	0.981281i	$0.561685\pi$
$270$	4.81905	0.293278
$271$	5.38773	0.327281	0.163641	−	0.986520i	$-0.447676\pi$
$271$	5.38773	0.327281	0.163641	+	0.986520i	$0.447676\pi$
$272$	−4.34515	−0.263464
$273$	20.1308	1.21837
$274$	5.04157	0.304572
$275$	4.43940	0.267706
$276$	14.7540	0.888086
$277$	0.973293	0.0584795	0.0292398	−	0.999572i	$-0.490691\pi$
$277$	0.973293	0.0584795	0.0292398	+	0.999572i	$0.490691\pi$
$278$	14.4798	0.868441
$279$	0.914338	0.0547400
$280$	−2.63564	−0.157510
$281$	15.2509	0.909794	0.454897	−	0.890544i	$-0.349676\pi$
$281$	15.2509	0.909794	0.454897	+	0.890544i	$0.349676\pi$
$282$	−10.7130	−0.637951
$283$	−9.19154	−0.546380	−0.273190	−	0.961960i	$-0.588079\pi$
$283$	−9.19154	−0.546380	−0.273190	+	0.961960i	$0.588079\pi$
$284$	−15.6358	−0.927814
$285$	−2.04097	−0.120897
$286$	−18.4488	−1.09090
$287$	10.1518	0.599245
$288$	−0.378009	−0.0222744
$289$	1.88037	0.110610
$290$	4.07623	0.239365
$291$	−8.30001	−0.486555
$292$	5.69971	0.333551
$293$	32.0441	1.87203	0.936017	−	0.351956i	$-0.114483\pi$
$293$	32.0441	1.87203	0.936017	+	0.351956i	$0.114483\pi$
$294$	0.0981064	0.00572168
$295$	10.4585	0.608917
$296$	9.88181	0.574369
$297$	−21.3937	−1.24139
$298$	1.00039	0.0579508
$299$	33.3598	1.92925
$300$	1.83794	0.106113
$301$	7.19589	0.414764
$302$	6.49906	0.373979
$303$	−8.67529	−0.498382
$304$	−1.11047	−0.0636897
$305$	9.87660	0.565532
$306$	1.64251	0.0938959
$307$	−27.9871	−1.59731	−0.798653	−	0.601792i	$-0.794454\pi$
$307$	−27.9871	−1.59731	−0.798653	+	0.601792i	$0.794454\pi$
$308$	11.7007	0.666708
$309$	14.8695	0.845898
$310$	−2.41883	−0.137380
$311$	−8.15519	−0.462438	−0.231219	−	0.972902i	$-0.574271\pi$
$311$	−8.15519	−0.462438	−0.231219	+	0.972902i	$0.574271\pi$
$312$	−7.63792	−0.432412
$313$	7.12505	0.402732	0.201366	−	0.979516i	$-0.435462\pi$
$313$	7.12505	0.402732	0.201366	+	0.979516i	$0.435462\pi$
$314$	13.1321	0.741089
$315$	0.996297	0.0561350
$316$	−9.03702	−0.508372
$317$	−7.08969	−0.398197	−0.199098	−	0.979979i	$-0.563801\pi$
$317$	−7.08969	−0.398197	−0.199098	+	0.979979i	$0.563801\pi$
$318$	−15.3943	−0.863272
$319$	−18.0960	−1.01318
$320$	1.00000	0.0559017
$321$	12.8058	0.714748
$322$	−21.1576	−1.17907
$323$	4.82515	0.268479
$324$	−9.99114	−0.555063
$325$	4.15571	0.230517
$326$	11.4961	0.636712
$327$	32.5370	1.79930
$328$	−3.85175	−0.212677
$329$	15.3627	0.846974
$330$	−8.15933	−0.449156
$331$	−27.6659	−1.52066	−0.760328	−	0.649539i	$-0.774962\pi$
$331$	−27.6659	−1.52066	−0.760328	+	0.649539i	$0.774962\pi$
$332$	−15.8303	−0.868803
$333$	−3.73541	−0.204699
$334$	−11.1394	−0.609523
$335$	3.01266	0.164599
$336$	4.84415	0.264270
$337$	−30.3628	−1.65397	−0.826984	−	0.562225i	$-0.809946\pi$
$337$	−30.3628	−1.65397	−0.826984	+	0.562225i	$0.809946\pi$
$338$	−4.26989	−0.232251
$339$	13.3142	0.723128
$340$	−4.34515	−0.235649
$341$	10.7381	0.581502
$342$	0.419766	0.0226984
$343$	−18.5902	−1.00378
$344$	−2.73022	−0.147204
$345$	14.7540	0.794328
$346$	−25.9863	−1.39703
$347$	21.4098	1.14934	0.574669	−	0.818386i	$-0.305131\pi$
$347$	21.4098	1.14934	0.574669	+	0.818386i	$0.305131\pi$
$348$	−7.49186	−0.401606
$349$	−19.8387	−1.06194	−0.530970	−	0.847390i	$-0.678172\pi$
$349$	−19.8387	−1.06194	−0.530970	+	0.847390i	$0.678172\pi$
$350$	−2.63564	−0.140881
$351$	−20.0266	−1.06894
$352$	−4.43940	−0.236621
$353$	−18.9356	−1.00784	−0.503920	−	0.863750i	$-0.668109\pi$
$353$	−18.9356	−1.00784	−0.503920	+	0.863750i	$0.668109\pi$
$354$	−19.2220	−1.02164
$355$	−15.6358	−0.829862
$356$	10.3696	0.549586
$357$	−21.0486	−1.11401
$358$	20.4757	1.08217
$359$	10.0056	0.528075	0.264037	−	0.964512i	$-0.414946\pi$
$359$	10.0056	0.528075	0.264037	+	0.964512i	$0.414946\pi$
$360$	−0.378009	−0.0199228
$361$	−17.7669	−0.935098
$362$	13.0356	0.685137
$363$	16.0052	0.840056
$364$	10.9530	0.574091
$365$	5.69971	0.298337
$366$	−18.1526	−0.948849
$367$	30.4556	1.58977	0.794884	−	0.606762i	$-0.207532\pi$
$367$	30.4556	1.58977	0.794884	+	0.606762i	$0.207532\pi$
$368$	8.02748	0.418461
$369$	1.45600	0.0757961
$370$	9.88181	0.513731
$371$	22.0759	1.14612
$372$	4.44565	0.230496
$373$	27.5947	1.42880	0.714398	−	0.699739i	$-0.246700\pi$
$373$	27.5947	1.42880	0.714398	+	0.699739i	$0.246700\pi$
$374$	19.2899	0.997455
$375$	1.83794	0.0949106
$376$	−5.82883	−0.300599
$377$	−16.9396	−0.872435
$378$	12.7013	0.653285
$379$	19.3976	0.996385	0.498193	−	0.867066i	$-0.333997\pi$
$379$	19.3976	0.996385	0.498193	+	0.867066i	$0.333997\pi$
$380$	−1.11047	−0.0569658
$381$	−12.9839	−0.665183
$382$	−7.86565	−0.402442
$383$	−30.4828	−1.55760	−0.778799	−	0.627273i	$-0.784171\pi$
$383$	−30.4828	−1.55760	−0.778799	+	0.627273i	$0.784171\pi$
$384$	−1.83794	−0.0937918
$385$	11.7007	0.596322
$386$	17.4724	0.889323
$387$	1.03205	0.0524619
$388$	−4.51594	−0.229262
$389$	3.31068	0.167858	0.0839291	−	0.996472i	$-0.473253\pi$
$389$	3.31068	0.167858	0.0839291	+	0.996472i	$0.473253\pi$
$390$	−7.63792	−0.386761
$391$	−34.8806	−1.76399
$392$	0.0533786	0.00269602
$393$	−20.0244	−1.01010
$394$	−17.5902	−0.886179
$395$	−9.03702	−0.454702
$396$	1.67813	0.0843293
$397$	18.5006	0.928518	0.464259	−	0.885700i	$-0.346321\pi$
$397$	18.5006	0.928518	0.464259	+	0.885700i	$0.346321\pi$
$398$	−9.81954	−0.492209
$399$	−5.37927	−0.269300
$400$	1.00000	0.0500000
$401$	16.6099	0.829461	0.414730	−	0.909944i	$-0.363876\pi$
$401$	16.6099	0.829461	0.414730	+	0.909944i	$0.363876\pi$
$402$	−5.53707	−0.276164
$403$	10.0519	0.500722
$404$	−4.72013	−0.234835
$405$	−9.99114	−0.496464
$406$	10.7435	0.533191
$407$	−43.8693	−2.17452
$408$	7.98612	0.395372
$409$	−37.5775	−1.85809	−0.929045	−	0.369968i	$-0.879369\pi$
$409$	−37.5775	−1.85809	−0.929045	+	0.369968i	$0.879369\pi$
$410$	−3.85175	−0.190224
$411$	−9.26608	−0.457062
$412$	8.09034	0.398582
$413$	27.5648	1.35638
$414$	−3.03446	−0.149135
$415$	−15.8303	−0.777081
$416$	−4.15571	−0.203750
$417$	−26.6130	−1.30324
$418$	4.92981	0.241125
$419$	−21.7069	−1.06045	−0.530225	−	0.847857i	$-0.677892\pi$
$419$	−21.7069	−1.06045	−0.530225	+	0.847857i	$0.677892\pi$
$420$	4.84415	0.236370
$421$	20.0781	0.978549	0.489274	−	0.872130i	$-0.337262\pi$
$421$	20.0781	0.978549	0.489274	+	0.872130i	$0.337262\pi$
$422$	−20.6344	−1.00447
$423$	2.20335	0.107130
$424$	−8.37589	−0.406769
$425$	−4.34515	−0.210771
$426$	28.7376	1.39234
$427$	26.0312	1.25974
$428$	6.96747	0.336785
$429$	33.9078	1.63708
$430$	−2.73022	−0.131663
$431$	30.1560	1.45256	0.726282	−	0.687397i	$-0.241247\pi$
$431$	30.1560	1.45256	0.726282	+	0.687397i	$0.241247\pi$
$432$	−4.81905	−0.231857
$433$	−20.6590	−0.992808	−0.496404	−	0.868092i	$-0.665346\pi$
$433$	−20.6590	−0.992808	−0.496404	+	0.868092i	$0.665346\pi$
$434$	−6.37516	−0.306018
$435$	−7.49186	−0.359207
$436$	17.7030	0.847820
$437$	−8.91425	−0.426426
$438$	−10.4757	−0.500549
$439$	18.1658	0.867008	0.433504	−	0.901152i	$-0.357277\pi$
$439$	18.1658	0.867008	0.433504	+	0.901152i	$0.357277\pi$
$440$	−4.43940	−0.211640
$441$	−0.0201776	−0.000960836 0
$442$	18.0572	0.858893
$443$	0.479218	0.0227683	0.0113842	−	0.999935i	$-0.496376\pi$
$443$	0.479218	0.0227683	0.0113842	+	0.999935i	$0.496376\pi$
$444$	−18.1621	−0.861937
$445$	10.3696	0.491565
$446$	19.4740	0.922121
$447$	−1.83865	−0.0869650
$448$	2.63564	0.124522
$449$	−3.68510	−0.173911	−0.0869553	−	0.996212i	$-0.527714\pi$
$449$	−3.68510	−0.173911	−0.0869553	+	0.996212i	$0.527714\pi$
$450$	−0.378009	−0.0178195
$451$	17.0995	0.805182
$452$	7.24411	0.340734
$453$	−11.9449	−0.561218
$454$	−0.346663	−0.0162697
$455$	10.9530	0.513483
$456$	2.04097	0.0955771
$457$	−1.26473	−0.0591618	−0.0295809	−	0.999562i	$-0.509417\pi$
$457$	−1.26473	−0.0591618	−0.0295809	+	0.999562i	$0.509417\pi$
$458$	11.8096	0.551826
$459$	20.9395	0.977373
$460$	8.02748	0.374283
$461$	−39.2833	−1.82961	−0.914803	−	0.403900i	$-0.867654\pi$
$461$	−39.2833	−1.82961	−0.914803	+	0.403900i	$0.867654\pi$
$462$	−21.5051	−1.00051
$463$	−10.4829	−0.487180	−0.243590	−	0.969878i	$-0.578325\pi$
$463$	−10.4829	−0.487180	−0.243590	+	0.969878i	$0.578325\pi$
$464$	−4.07623	−0.189234
$465$	4.44565	0.206162
$466$	24.3623	1.12856
$467$	13.8132	0.639198	0.319599	−	0.947553i	$-0.396452\pi$
$467$	13.8132	0.639198	0.319599	+	0.947553i	$0.396452\pi$
$468$	1.57089	0.0726146
$469$	7.94029	0.366649
$470$	−5.82883	−0.268864
$471$	−24.1360	−1.11213
$472$	−10.4585	−0.481391
$473$	12.1205	0.557303
$474$	16.6095	0.762898
$475$	−1.11047	−0.0509517
$476$	−11.4523	−0.524914
$477$	3.16616	0.144969
$478$	−10.5172	−0.481045
$479$	−13.1304	−0.599944	−0.299972	−	0.953948i	$-0.596977\pi$
$479$	−13.1304	−0.599944	−0.299972	+	0.953948i	$0.596977\pi$
$480$	−1.83794	−0.0838899
$481$	−41.0659	−1.87244
$482$	−27.9456	−1.27289
$483$	38.8863	1.76939
$484$	8.70826	0.395830
$485$	−4.51594	−0.205058
$486$	3.90591	0.177176
$487$	4.33312	0.196352	0.0981762	−	0.995169i	$-0.468699\pi$
$487$	4.33312	0.196352	0.0981762	+	0.995169i	$0.468699\pi$
$488$	−9.87660	−0.447093
$489$	−21.1292	−0.955494
$490$	0.0533786	0.00241140
$491$	−25.2309	−1.13865	−0.569327	−	0.822111i	$-0.692796\pi$
$491$	−25.2309	−1.13865	−0.569327	+	0.822111i	$0.692796\pi$
$492$	7.07927	0.319158
$493$	17.7119	0.797702
$494$	4.61477	0.207629
$495$	1.67813	0.0754264
$496$	2.41883	0.108608
$497$	−41.2104	−1.84854
$498$	29.0952	1.30379
$499$	23.0875	1.03354	0.516770	−	0.856125i	$-0.327134\pi$
$499$	23.0875	1.03354	0.516770	+	0.856125i	$0.327134\pi$
$500$	1.00000	0.0447214
$501$	20.4736	0.914692
$502$	−8.49354	−0.379085
$503$	−29.5387	−1.31706	−0.658532	−	0.752552i	$-0.728822\pi$
$503$	−29.5387	−1.31706	−0.658532	+	0.752552i	$0.728822\pi$
$504$	−0.996297	−0.0443786
$505$	−4.72013	−0.210043
$506$	−35.6372	−1.58427
$507$	7.84778	0.348532
$508$	−7.06437	−0.313431
$509$	40.2041	1.78201	0.891007	−	0.453989i	$-0.150000\pi$
$509$	40.2041	1.78201	0.891007	+	0.453989i	$0.150000\pi$
$510$	7.98612	0.353631
$511$	15.0224	0.664553
$512$	−1.00000	−0.0441942
$513$	5.35140	0.236270
$514$	7.56962	0.333882
$515$	8.09034	0.356503
$516$	5.01797	0.220904
$517$	25.8765	1.13805
$518$	26.0449	1.14435
$519$	47.7612	2.09648
$520$	−4.15571	−0.182240
$521$	25.5524	1.11947	0.559736	−	0.828671i	$-0.310903\pi$
$521$	25.5524	1.11947	0.559736	+	0.828671i	$0.310903\pi$
$522$	1.54085	0.0674413
$523$	−0.494207	−0.0216102	−0.0108051	−	0.999942i	$-0.503439\pi$
$523$	−0.494207	−0.0216102	−0.0108051	+	0.999942i	$0.503439\pi$
$524$	−10.8951	−0.475953
$525$	4.84415	0.211416
$526$	−23.3485	−1.01804
$527$	−10.5102	−0.457830
$528$	8.15933	0.355089
$529$	41.4404	1.80176
$530$	−8.37589	−0.363825
$531$	3.95340	0.171563
$532$	−2.92680	−0.126893
$533$	16.0067	0.693329
$534$	−19.0586	−0.824747
$535$	6.96747	0.301230
$536$	−3.01266	−0.130127
$537$	−37.6329	−1.62398
$538$	6.31706	0.272348
$539$	−0.236969	−0.0102070
$540$	−4.81905	−0.207379
$541$	12.7929	0.550009	0.275005	−	0.961443i	$-0.411321\pi$
$541$	12.7929	0.550009	0.275005	+	0.961443i	$0.411321\pi$
$542$	−5.38773	−0.231423
$543$	−23.9587	−1.02816
$544$	4.34515	0.186297
$545$	17.7030	0.758313
$546$	−20.1308	−0.861521
$547$	−30.0397	−1.28441	−0.642203	−	0.766535i	$-0.721979\pi$
$547$	−30.0397	−1.28441	−0.642203	+	0.766535i	$0.721979\pi$
$548$	−5.04157	−0.215365
$549$	3.73344	0.159339
$550$	−4.43940	−0.189297
$551$	4.52652	0.192836
$552$	−14.7540	−0.627971
$553$	−23.8184	−1.01286
$554$	−0.973293	−0.0413513
$555$	−18.1621	−0.770940
$556$	−14.4798	−0.614080
$557$	43.0056	1.82221	0.911103	−	0.412179i	$-0.135232\pi$
$557$	43.0056	1.82221	0.911103	+	0.412179i	$0.135232\pi$
$558$	−0.914338	−0.0387070
$559$	11.3460	0.479884
$560$	2.63564	0.111376
$561$	−35.4535	−1.49685
$562$	−15.2509	−0.643321
$563$	−28.4955	−1.20094	−0.600472	−	0.799646i	$-0.705020\pi$
$563$	−28.4955	−1.20094	−0.600472	+	0.799646i	$0.705020\pi$
$564$	10.7130	0.451099
$565$	7.24411	0.304762
$566$	9.19154	0.386349
$567$	−26.3331	−1.10589
$568$	15.6358	0.656064
$569$	−31.4313	−1.31767	−0.658833	−	0.752289i	$-0.728950\pi$
$569$	−31.4313	−1.31767	−0.658833	+	0.752289i	$0.728950\pi$
$570$	2.04097	0.0854867
$571$	−9.24802	−0.387018	−0.193509	−	0.981099i	$-0.561987\pi$
$571$	−9.24802	−0.387018	−0.193509	+	0.981099i	$0.561987\pi$
$572$	18.4488	0.771384
$573$	14.4566	0.603931
$574$	−10.1518	−0.423730
$575$	8.02748	0.334769
$576$	0.378009	0.0157504
$577$	34.3491	1.42997	0.714986	−	0.699139i	$-0.246433\pi$
$577$	34.3491	1.42997	0.714986	+	0.699139i	$0.246433\pi$
$578$	−1.88037	−0.0782129
$579$	−32.1132	−1.33458
$580$	−4.07623	−0.169256
$581$	−41.7232	−1.73097
$582$	8.30001	0.344047
$583$	37.1839	1.54000
$584$	−5.69971	−0.235856
$585$	1.57089	0.0649485
$586$	−32.0441	−1.32373
$587$	−40.5307	−1.67288	−0.836441	−	0.548057i	$-0.815368\pi$
$587$	−40.5307	−1.67288	−0.836441	+	0.548057i	$0.815368\pi$
$588$	−0.0981064	−0.00404584
$589$	−2.68603	−0.110676
$590$	−10.4585	−0.430569
$591$	32.3296	1.32986
$592$	−9.88181	−0.406140
$593$	2.13981	0.0878713	0.0439357	−	0.999034i	$-0.486010\pi$
$593$	2.13981	0.0878713	0.0439357	+	0.999034i	$0.486010\pi$
$594$	21.3937	0.877794
$595$	−11.4523	−0.469498
$596$	−1.00039	−0.0409774
$597$	18.0477	0.738643
$598$	−33.3598	−1.36418
$599$	10.4242	0.425920	0.212960	−	0.977061i	$-0.431690\pi$
$599$	10.4242	0.425920	0.212960	+	0.977061i	$0.431690\pi$
$600$	−1.83794	−0.0750334
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−7.19589	−0.293283
$603$	1.13881	0.0463760
$604$	−6.49906	−0.264443
$605$	8.70826	0.354041
$606$	8.67529	0.352410
$607$	−17.0420	−0.691713	−0.345856	−	0.938287i	$-0.612412\pi$
$607$	−17.0420	−0.691713	−0.345856	+	0.938287i	$0.612412\pi$
$608$	1.11047	0.0450354
$609$	−19.7459	−0.800143
$610$	−9.87660	−0.399892
$611$	24.2229	0.979953
$612$	−1.64251	−0.0663944
$613$	−13.9412	−0.563081	−0.281540	−	0.959549i	$-0.590845\pi$
$613$	−13.9412	−0.563081	−0.281540	+	0.959549i	$0.590845\pi$
$614$	27.9871	1.12947
$615$	7.07927	0.285464
$616$	−11.7007	−0.471434
$617$	26.5290	1.06802	0.534009	−	0.845479i	$-0.320685\pi$
$617$	26.5290	1.06802	0.534009	+	0.845479i	$0.320685\pi$
$618$	−14.8695	−0.598140
$619$	40.0363	1.60919	0.804597	−	0.593821i	$-0.202381\pi$
$619$	40.0363	1.60919	0.804597	+	0.593821i	$0.202381\pi$
$620$	2.41883	0.0971424
$621$	−38.6848	−1.55237
$622$	8.15519	0.326993
$623$	27.3305	1.09497
$624$	7.63792	0.305762
$625$	1.00000	0.0400000
$626$	−7.12505	−0.284774
$627$	−9.06067	−0.361848
$628$	−13.1321	−0.524029
$629$	42.9380	1.71205
$630$	−0.996297	−0.0396934
$631$	24.6383	0.980837	0.490419	−	0.871487i	$-0.336844\pi$
$631$	24.6383	0.980837	0.490419	+	0.871487i	$0.336844\pi$
$632$	9.03702	0.359473
$633$	37.9248	1.50738
$634$	7.08969	0.281568
$635$	−7.06437	−0.280341
$636$	15.3943	0.610426
$637$	−0.221826	−0.00878905
$638$	18.0960	0.716428
$639$	−5.91047	−0.233815
$640$	−1.00000	−0.0395285
$641$	32.4033	1.27985	0.639927	−	0.768436i	$-0.278965\pi$
$641$	32.4033	1.27985	0.639927	+	0.768436i	$0.278965\pi$
$642$	−12.8058	−0.505403
$643$	2.21003	0.0871550	0.0435775	−	0.999050i	$-0.486124\pi$
$643$	2.21003	0.0871550	0.0435775	+	0.999050i	$0.486124\pi$
$644$	21.1576	0.833725
$645$	5.01797	0.197582
$646$	−4.82515	−0.189843
$647$	−31.9471	−1.25597	−0.627986	−	0.778225i	$-0.716120\pi$
$647$	−31.9471	−1.25597	−0.627986	+	0.778225i	$0.716120\pi$
$648$	9.99114	0.392489
$649$	46.4294	1.82251
$650$	−4.15571	−0.163000
$651$	11.7171	0.459231
$652$	−11.4961	−0.450223
$653$	−25.1100	−0.982632	−0.491316	−	0.870981i	$-0.663484\pi$
$653$	−25.1100	−0.982632	−0.491316	+	0.870981i	$0.663484\pi$
$654$	−32.5370	−1.27230
$655$	−10.8951	−0.425705
$656$	3.85175	0.150386
$657$	2.15454	0.0840567
$658$	−15.3627	−0.598901
$659$	−6.37168	−0.248205	−0.124103	−	0.992269i	$-0.539605\pi$
$659$	−6.37168	−0.248205	−0.124103	+	0.992269i	$0.539605\pi$
$660$	8.15933	0.317601
$661$	−14.9366	−0.580968	−0.290484	−	0.956880i	$-0.593816\pi$
$661$	−14.9366	−0.580968	−0.290484	+	0.956880i	$0.593816\pi$
$662$	27.6659	1.07527
$663$	−33.1879	−1.28891
$664$	15.8303	0.614337
$665$	−2.92680	−0.113496
$666$	3.73541	0.144744
$667$	−32.7219	−1.26700
$668$	11.1394	0.430998
$669$	−35.7920	−1.38380
$670$	−3.01266	−0.116389
$671$	43.8462	1.69266
$672$	−4.84415	−0.186867
$673$	−7.89316	−0.304259	−0.152129	−	0.988361i	$-0.548613\pi$
$673$	−7.89316	−0.304259	−0.152129	+	0.988361i	$0.548613\pi$
$674$	30.3628	1.16953
$675$	−4.81905	−0.185485
$676$	4.26989	0.164226
$677$	5.75069	0.221017	0.110508	−	0.993875i	$-0.464752\pi$
$677$	5.75069	0.221017	0.110508	+	0.993875i	$0.464752\pi$
$678$	−13.3142	−0.511329
$679$	−11.9024	−0.456773
$680$	4.34515	0.166629
$681$	0.637145	0.0244154
$682$	−10.7381	−0.411184
$683$	−12.7147	−0.486515	−0.243258	−	0.969962i	$-0.578216\pi$
$683$	−12.7147	−0.486515	−0.243258	+	0.969962i	$0.578216\pi$
$684$	−0.419766	−0.0160502
$685$	−5.04157	−0.192628
$686$	18.5902	0.709777
$687$	−21.7053	−0.828108
$688$	2.73022	0.104089
$689$	34.8077	1.32607
$690$	−14.7540	−0.561675
$691$	−43.3621	−1.64957	−0.824786	−	0.565446i	$-0.808704\pi$
$691$	−43.3621	−1.64957	−0.824786	+	0.565446i	$0.808704\pi$
$692$	25.9863	0.987852
$693$	4.42296	0.168014
$694$	−21.4098	−0.812704
$695$	−14.4798	−0.549250
$696$	7.49186	0.283978
$697$	−16.7365	−0.633939
$698$	19.8387	0.750906
$699$	−44.7764	−1.69360
$700$	2.63564	0.0996180
$701$	40.5221	1.53050	0.765249	−	0.643734i	$-0.222616\pi$
$701$	40.5221	1.53050	0.765249	+	0.643734i	$0.222616\pi$
$702$	20.0266	0.755854
$703$	10.9734	0.413871
$704$	4.43940	0.167316
$705$	10.7130	0.403475
$706$	18.9356	0.712651
$707$	−12.4406	−0.467876
$708$	19.2220	0.722408
$709$	−2.21226	−0.0830831	−0.0415415	−	0.999137i	$-0.513227\pi$
$709$	−2.21226	−0.0830831	−0.0415415	+	0.999137i	$0.513227\pi$
$710$	15.6358	0.586801
$711$	−3.41607	−0.128113
$712$	−10.3696	−0.388616
$713$	19.4171	0.727175
$714$	21.0486	0.787723
$715$	18.4488	0.689947
$716$	−20.4757	−0.765211
$717$	19.3299	0.721889
$718$	−10.0056	−0.373405
$719$	−37.9244	−1.41434	−0.707170	−	0.707043i	$-0.750029\pi$
$719$	−37.9244	−1.41434	−0.707170	+	0.707043i	$0.750029\pi$
$720$	0.378009	0.0140876
$721$	21.3233	0.794119
$722$	17.7669	0.661214
$723$	51.3623	1.91018
$724$	−13.0356	−0.484465
$725$	−4.07623	−0.151388
$726$	−16.0052	−0.594009
$727$	14.1715	0.525592	0.262796	−	0.964851i	$-0.415355\pi$
$727$	14.1715	0.525592	0.262796	+	0.964851i	$0.415355\pi$
$728$	−10.9530	−0.405944
$729$	22.7946	0.844244
$730$	−5.69971	−0.210956
$731$	−11.8632	−0.438777
$732$	18.1526	0.670938
$733$	−50.4033	−1.86169	−0.930844	−	0.365417i	$-0.880926\pi$
$733$	−50.4033	−1.86169	−0.930844	+	0.365417i	$0.880926\pi$
$734$	−30.4556	−1.12414
$735$	−0.0981064	−0.00361871
$736$	−8.02748	−0.295897
$737$	13.3744	0.492652
$738$	−1.45600	−0.0535960
$739$	53.8784	1.98195	0.990974	−	0.134054i	$-0.0427997\pi$
$739$	53.8784	1.98195	0.990974	+	0.134054i	$0.0427997\pi$
$740$	−9.88181	−0.363263
$741$	−8.48166	−0.311582
$742$	−22.0759	−0.810431
$743$	−1.99111	−0.0730467	−0.0365233	−	0.999333i	$-0.511628\pi$
$743$	−1.99111	−0.0730467	−0.0365233	+	0.999333i	$0.511628\pi$
$744$	−4.44565	−0.162985
$745$	−1.00039	−0.0366513
$746$	−27.5947	−1.01031
$747$	−5.98401	−0.218944
$748$	−19.2899	−0.705308
$749$	18.3638	0.670997
$750$	−1.83794	−0.0671119
$751$	−14.7576	−0.538513	−0.269256	−	0.963069i	$-0.586778\pi$
$751$	−14.7576	−0.538513	−0.269256	+	0.963069i	$0.586778\pi$
$752$	5.82883	0.212556
$753$	15.6106	0.568881
$754$	16.9396	0.616905
$755$	−6.49906	−0.236525
$756$	−12.7013	−0.461942
$757$	−45.9717	−1.67087	−0.835435	−	0.549589i	$-0.814784\pi$
$757$	−45.9717	−1.67087	−0.835435	+	0.549589i	$0.814784\pi$
$758$	−19.3976	−0.704551
$759$	65.4988	2.37746
$760$	1.11047	0.0402809
$761$	−18.0348	−0.653763	−0.326881	−	0.945065i	$-0.605998\pi$
$761$	−18.0348	−0.653763	−0.326881	+	0.945065i	$0.605998\pi$
$762$	12.9839	0.470356
$763$	46.6588	1.68916
$764$	7.86565	0.284569
$765$	−1.64251	−0.0593850
$766$	30.4828	1.10139
$767$	43.4624	1.56934
$768$	1.83794	0.0663208
$769$	40.6658	1.46645	0.733223	−	0.679988i	$-0.238015\pi$
$769$	40.6658	1.46645	0.733223	+	0.679988i	$0.238015\pi$
$770$	−11.7007	−0.421663
$771$	−13.9125	−0.501046
$772$	−17.4724	−0.628846
$773$	−0.839117	−0.0301809	−0.0150905	−	0.999886i	$-0.504804\pi$
$773$	−0.839117	−0.0301809	−0.0150905	+	0.999886i	$0.504804\pi$
$774$	−1.03205	−0.0370962
$775$	2.41883	0.0868868
$776$	4.51594	0.162113
$777$	−47.8689	−1.71729
$778$	−3.31068	−0.118694
$779$	−4.27724	−0.153248
$780$	7.63792	0.273481
$781$	−69.4135	−2.48381
$782$	34.8806	1.24733
$783$	19.6436	0.702004
$784$	−0.0533786	−0.00190638
$785$	−13.1321	−0.468706
$786$	20.0244	0.714248
$787$	22.9061	0.816516	0.408258	−	0.912867i	$-0.366136\pi$
$787$	22.9061	0.816516	0.408258	+	0.912867i	$0.366136\pi$
$788$	17.5902	0.626623
$789$	42.9130	1.52774
$790$	9.03702	0.321523
$791$	19.0929	0.678865
$792$	−1.67813	−0.0596298
$793$	41.0442	1.45752
$794$	−18.5006	−0.656561
$795$	15.3943	0.545981
$796$	9.81954	0.348044
$797$	−26.7689	−0.948202	−0.474101	−	0.880470i	$-0.657227\pi$
$797$	−26.7689	−0.948202	−0.474101	+	0.880470i	$0.657227\pi$
$798$	5.37927	0.190424
$799$	−25.3272	−0.896011
$800$	−1.00000	−0.0353553
$801$	3.91979	0.138499
$802$	−16.6099	−0.586517
$803$	25.3033	0.892934
$804$	5.53707	0.195277
$805$	21.1576	0.745707
$806$	−10.0519	−0.354064
$807$	−11.6104	−0.408704
$808$	4.72013	0.166053
$809$	11.8028	0.414964	0.207482	−	0.978239i	$-0.433473\pi$
$809$	11.8028	0.414964	0.207482	+	0.978239i	$0.433473\pi$
$810$	9.99114	0.351053
$811$	11.9707	0.420350	0.210175	−	0.977664i	$-0.432597\pi$
$811$	11.9707	0.420350	0.210175	+	0.977664i	$0.432597\pi$
$812$	−10.7435	−0.377023
$813$	9.90231	0.347289
$814$	43.8693	1.53762
$815$	−11.4961	−0.402692
$816$	−7.98612	−0.279570
$817$	−3.03182	−0.106070
$818$	37.5775	1.31387
$819$	4.14032	0.144674
$820$	3.85175	0.134509
$821$	48.7533	1.70150	0.850751	−	0.525569i	$-0.176147\pi$
$821$	48.7533	1.70150	0.850751	+	0.525569i	$0.176147\pi$
$822$	9.26608	0.323192
$823$	22.5740	0.786881	0.393441	−	0.919350i	$-0.371285\pi$
$823$	22.5740	0.786881	0.393441	+	0.919350i	$0.371285\pi$
$824$	−8.09034	−0.281840
$825$	8.15933	0.284071
$826$	−27.5648	−0.959104
$827$	53.8774	1.87350	0.936750	−	0.349999i	$-0.113818\pi$
$827$	53.8774	1.87350	0.936750	+	0.349999i	$0.113818\pi$
$828$	3.03446	0.105455
$829$	−22.4364	−0.779248	−0.389624	−	0.920974i	$-0.627395\pi$
$829$	−22.4364	−0.779248	−0.389624	+	0.920974i	$0.627395\pi$
$830$	15.8303	0.549479
$831$	1.78885	0.0620545
$832$	4.15571	0.144073
$833$	0.231938	0.00803618
$834$	26.6130	0.921531
$835$	11.1394	0.385496
$836$	−4.92981	−0.170501
$837$	−11.6564	−0.402906
$838$	21.7069	0.749851
$839$	−32.0287	−1.10575	−0.552876	−	0.833263i	$-0.686470\pi$
$839$	−32.0287	−1.10575	−0.552876	+	0.833263i	$0.686470\pi$
$840$	−4.84415	−0.167139
$841$	−12.3843	−0.427046
$842$	−20.0781	−0.691938
$843$	28.0302	0.965412
$844$	20.6344	0.710267
$845$	4.26989	0.146889
$846$	−2.20335	−0.0757527
$847$	22.9519	0.788636
$848$	8.37589	0.287629
$849$	−16.8935	−0.579782
$850$	4.34515	0.149038
$851$	−79.3260	−2.71926
$852$	−28.7376	−0.984534
$853$	46.2855	1.58479	0.792393	−	0.610011i	$-0.208835\pi$
$853$	46.2855	1.58479	0.792393	+	0.610011i	$0.208835\pi$
$854$	−26.0312	−0.890769
$855$	−0.419766	−0.0143557
$856$	−6.96747	−0.238143
$857$	12.0955	0.413174	0.206587	−	0.978428i	$-0.433764\pi$
$857$	12.0955	0.413174	0.206587	+	0.978428i	$0.433764\pi$
$858$	−33.9078	−1.15759
$859$	31.2432	1.06601	0.533003	−	0.846114i	$-0.321064\pi$
$859$	31.2432	1.06601	0.533003	+	0.846114i	$0.321064\pi$
$860$	2.73022	0.0930997
$861$	18.6584	0.635878
$862$	−30.1560	−1.02712
$863$	−17.0081	−0.578961	−0.289481	−	0.957184i	$-0.593483\pi$
$863$	−17.0081	−0.578961	−0.289481	+	0.957184i	$0.593483\pi$
$864$	4.81905	0.163947
$865$	25.9863	0.883562
$866$	20.6590	0.702021
$867$	3.45599	0.117372
$868$	6.37516	0.216387
$869$	−40.1189	−1.36094
$870$	7.49186	0.253998
$871$	12.5197	0.424214
$872$	−17.7030	−0.599499
$873$	−1.70707	−0.0577754
$874$	8.91425	0.301529
$875$	2.63564	0.0891010
$876$	10.4757	0.353941
$877$	−27.1949	−0.918306	−0.459153	−	0.888357i	$-0.651847\pi$
$877$	−27.1949	−0.918306	−0.459153	+	0.888357i	$0.651847\pi$
$878$	−18.1658	−0.613067
$879$	58.8949	1.98648
$880$	4.43940	0.149652
$881$	31.0825	1.04720	0.523598	−	0.851966i	$-0.324590\pi$
$881$	31.0825	1.04720	0.523598	+	0.851966i	$0.324590\pi$
$882$	0.0201776	0.000679414 0
$883$	12.9431	0.435571	0.217786	−	0.975997i	$-0.430117\pi$
$883$	12.9431	0.435571	0.217786	+	0.975997i	$0.430117\pi$
$884$	−18.0572	−0.607329
$885$	19.2220	0.646141
$886$	−0.479218	−0.0160997
$887$	19.6161	0.658643	0.329322	−	0.944218i	$-0.393180\pi$
$887$	19.6161	0.658643	0.329322	+	0.944218i	$0.393180\pi$
$888$	18.1621	0.609481
$889$	−18.6192	−0.624467
$890$	−10.3696	−0.347589
$891$	−44.3546	−1.48594
$892$	−19.4740	−0.652038
$893$	−6.47272	−0.216601
$894$	1.83865	0.0614935
$895$	−20.4757	−0.684426
$896$	−2.63564	−0.0880507
$897$	61.3132	2.04719
$898$	3.68510	0.122973
$899$	−9.85970	−0.328839
$900$	0.378009	0.0126003
$901$	−36.3945	−1.21248
$902$	−17.0995	−0.569350
$903$	13.2256	0.440120
$904$	−7.24411	−0.240935
$905$	−13.0356	−0.433319
$906$	11.9449	0.396841
$907$	13.9486	0.463157	0.231578	−	0.972816i	$-0.425611\pi$
$907$	13.9486	0.463157	0.231578	+	0.972816i	$0.425611\pi$
$908$	0.346663	0.0115044
$909$	−1.78425	−0.0591798
$910$	−10.9530	−0.363087
$911$	4.90737	0.162588	0.0812942	−	0.996690i	$-0.474095\pi$
$911$	4.90737	0.162588	0.0812942	+	0.996690i	$0.474095\pi$
$912$	−2.04097	−0.0675832
$913$	−70.2772	−2.32584
$914$	1.26473	0.0418337
$915$	18.1526	0.600105
$916$	−11.8096	−0.390200
$917$	−28.7155	−0.948270
$918$	−20.9395	−0.691107
$919$	31.9742	1.05473	0.527366	−	0.849638i	$-0.323180\pi$
$919$	31.9742	1.05473	0.527366	+	0.849638i	$0.323180\pi$
$920$	−8.02748	−0.264658
$921$	−51.4384	−1.69495
$922$	39.2833	1.29373
$923$	−64.9778	−2.13877
$924$	21.5051	0.707466
$925$	−9.88181	−0.324912
$926$	10.4829	0.344488
$927$	3.05822	0.100445
$928$	4.07623	0.133809
$929$	56.2604	1.84584	0.922921	−	0.384989i	$-0.125795\pi$
$929$	56.2604	1.84584	0.922921	+	0.384989i	$0.125795\pi$
$930$	−4.44565	−0.145779
$931$	0.0592751	0.00194266
$932$	−24.3623	−0.798015
$933$	−14.9887	−0.490708
$934$	−13.8132	−0.451982
$935$	−19.2899	−0.630846
$936$	−1.57089	−0.0513463
$937$	14.9989	0.489994	0.244997	−	0.969524i	$-0.421213\pi$
$937$	14.9989	0.489994	0.244997	+	0.969524i	$0.421213\pi$
$938$	−7.94029	−0.259260
$939$	13.0954	0.427352
$940$	5.82883	0.190115
$941$	30.7006	1.00081	0.500405	−	0.865791i	$-0.333184\pi$
$941$	30.7006	1.00081	0.500405	+	0.865791i	$0.333184\pi$
$942$	24.1360	0.786394
$943$	30.9198	1.00689
$944$	10.4585	0.340395
$945$	−12.7013	−0.413174
$946$	−12.1205	−0.394073
$947$	−0.270714	−0.00879703	−0.00439851	−	0.999990i	$-0.501400\pi$
$947$	−0.270714	−0.00879703	−0.00439851	+	0.999990i	$0.501400\pi$
$948$	−16.6095	−0.539450
$949$	23.6863	0.768891
$950$	1.11047	0.0360283
$951$	−13.0304	−0.422540
$952$	11.4523	0.371171
$953$	−44.9972	−1.45760	−0.728801	−	0.684726i	$-0.759922\pi$
$953$	−44.9972	−1.45760	−0.728801	+	0.684726i	$0.759922\pi$
$954$	−3.16616	−0.102508
$955$	7.86565	0.254526
$956$	10.5172	0.340150
$957$	−33.2593	−1.07512
$958$	13.1304	0.424224
$959$	−13.2878	−0.429085
$960$	1.83794	0.0593191
$961$	−25.1493	−0.811267
$962$	41.0659	1.32402
$963$	2.63376	0.0848719
$964$	27.9456	0.900068
$965$	−17.4724	−0.562457
$966$	−38.8863	−1.25115
$967$	−40.9296	−1.31621	−0.658103	−	0.752928i	$-0.728641\pi$
$967$	−40.9296	−1.31621	−0.658103	+	0.752928i	$0.728641\pi$
$968$	−8.70826	−0.279894
$969$	8.86832	0.284891
$970$	4.51594	0.144998
$971$	50.5423	1.62198	0.810989	−	0.585061i	$-0.198930\pi$
$971$	50.5423	1.62198	0.810989	+	0.585061i	$0.198930\pi$
$972$	−3.90591	−0.125282
$973$	−38.1636	−1.22347
$974$	−4.33312	−0.138842
$975$	7.63792	0.244609
$976$	9.87660	0.316142
$977$	−19.4248	−0.621455	−0.310728	−	0.950499i	$-0.600573\pi$
$977$	−19.4248	−0.621455	−0.310728	+	0.950499i	$0.600573\pi$
$978$	21.1292	0.675636
$979$	46.0347	1.47127
$980$	−0.0533786	−0.00170512
$981$	6.69189	0.213656
$982$	25.2309	0.805149
$983$	47.3156	1.50913	0.754566	−	0.656224i	$-0.227847\pi$
$983$	47.3156	1.50913	0.754566	+	0.656224i	$0.227847\pi$
$984$	−7.07927	−0.225679
$985$	17.5902	0.560469
$986$	−17.7119	−0.564061
$987$	28.2357	0.898752
$988$	−4.61477	−0.146816
$989$	21.9168	0.696913
$990$	−1.67813	−0.0533345
$991$	−11.4356	−0.363264	−0.181632	−	0.983367i	$-0.558138\pi$
$991$	−11.4356	−0.363264	−0.181632	+	0.983367i	$0.558138\pi$
$992$	−2.41883	−0.0767978
$993$	−50.8482	−1.61362
$994$	41.2104	1.30711
$995$	9.81954	0.311300
$996$	−29.0952	−0.921916
$997$	−42.8260	−1.35631	−0.678157	−	0.734917i	$-0.737221\pi$
$997$	−42.8260	−1.35631	−0.678157	+	0.734917i	$0.737221\pi$
$998$	−23.0875	−0.730822
$999$	47.6210	1.50666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.g.1.20	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.g.1.20	✓	27	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.83794 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.83794 q^{6} +2.63564 q^{7} -1.00000 q^{8} +0.378009 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.83794 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.83794 q^{6} +2.63564 q^{7} -1.00000 q^{8} +0.378009 q^{9} -1.00000 q^{10} +4.43940 q^{11} +1.83794 q^{12} +4.15571 q^{13} -2.63564 q^{14} +1.83794 q^{15} +1.00000 q^{16} -4.34515 q^{17} -0.378009 q^{18} -1.11047 q^{19} +1.00000 q^{20} +4.84415 q^{21} -4.43940 q^{22} +8.02748 q^{23} -1.83794 q^{24} +1.00000 q^{25} -4.15571 q^{26} -4.81905 q^{27} +2.63564 q^{28} -4.07623 q^{29} -1.83794 q^{30} +2.41883 q^{31} -1.00000 q^{32} +8.15933 q^{33} +4.34515 q^{34} +2.63564 q^{35} +0.378009 q^{36} -9.88181 q^{37} +1.11047 q^{38} +7.63792 q^{39} -1.00000 q^{40} +3.85175 q^{41} -4.84415 q^{42} +2.73022 q^{43} +4.43940 q^{44} +0.378009 q^{45} -8.02748 q^{46} +5.82883 q^{47} +1.83794 q^{48} -0.0533786 q^{49} -1.00000 q^{50} -7.98612 q^{51} +4.15571 q^{52} +8.37589 q^{53} +4.81905 q^{54} +4.43940 q^{55} -2.63564 q^{56} -2.04097 q^{57} +4.07623 q^{58} +10.4585 q^{59} +1.83794 q^{60} +9.87660 q^{61} -2.41883 q^{62} +0.996297 q^{63} +1.00000 q^{64} +4.15571 q^{65} -8.15933 q^{66} +3.01266 q^{67} -4.34515 q^{68} +14.7540 q^{69} -2.63564 q^{70} -15.6358 q^{71} -0.378009 q^{72} +5.69971 q^{73} +9.88181 q^{74} +1.83794 q^{75} -1.11047 q^{76} +11.7007 q^{77} -7.63792 q^{78} -9.03702 q^{79} +1.00000 q^{80} -9.99114 q^{81} -3.85175 q^{82} -15.8303 q^{83} +4.84415 q^{84} -4.34515 q^{85} -2.73022 q^{86} -7.49186 q^{87} -4.43940 q^{88} +10.3696 q^{89} -0.378009 q^{90} +10.9530 q^{91} +8.02748 q^{92} +4.44565 q^{93} -5.82883 q^{94} -1.11047 q^{95} -1.83794 q^{96} -4.51594 q^{97} +0.0533786 q^{98} +1.67813 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * q^99

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