LMFDB - Embedded newform 6014.2.a.j.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.284664 q^{3} +1.00000 q^{4} -2.60924 q^{5} -0.284664 q^{6} -1.90185 q^{7} -1.00000 q^{8} -2.91897 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.284664 q^{3} +1.00000 q^{4} -2.60924 q^{5} -0.284664 q^{6} -1.90185 q^{7} -1.00000 q^{8} -2.91897 q^{9} +2.60924 q^{10} +2.56595 q^{11} +0.284664 q^{12} -6.63830 q^{13} +1.90185 q^{14} -0.742756 q^{15} +1.00000 q^{16} +1.20401 q^{17} +2.91897 q^{18} -5.88359 q^{19} -2.60924 q^{20} -0.541389 q^{21} -2.56595 q^{22} -9.03898 q^{23} -0.284664 q^{24} +1.80812 q^{25} +6.63830 q^{26} -1.68492 q^{27} -1.90185 q^{28} +3.80721 q^{29} +0.742756 q^{30} -1.00000 q^{31} -1.00000 q^{32} +0.730432 q^{33} -1.20401 q^{34} +4.96239 q^{35} -2.91897 q^{36} -3.65430 q^{37} +5.88359 q^{38} -1.88968 q^{39} +2.60924 q^{40} -3.99029 q^{41} +0.541389 q^{42} -4.29734 q^{43} +2.56595 q^{44} +7.61628 q^{45} +9.03898 q^{46} -9.02713 q^{47} +0.284664 q^{48} -3.38295 q^{49} -1.80812 q^{50} +0.342738 q^{51} -6.63830 q^{52} -5.85842 q^{53} +1.68492 q^{54} -6.69516 q^{55} +1.90185 q^{56} -1.67484 q^{57} -3.80721 q^{58} +4.74654 q^{59} -0.742756 q^{60} +4.90663 q^{61} +1.00000 q^{62} +5.55145 q^{63} +1.00000 q^{64} +17.3209 q^{65} -0.730432 q^{66} +9.04385 q^{67} +1.20401 q^{68} -2.57307 q^{69} -4.96239 q^{70} -4.53573 q^{71} +2.91897 q^{72} -8.68142 q^{73} +3.65430 q^{74} +0.514708 q^{75} -5.88359 q^{76} -4.88005 q^{77} +1.88968 q^{78} -3.80526 q^{79} -2.60924 q^{80} +8.27726 q^{81} +3.99029 q^{82} +4.53197 q^{83} -0.541389 q^{84} -3.14155 q^{85} +4.29734 q^{86} +1.08377 q^{87} -2.56595 q^{88} -10.2511 q^{89} -7.61628 q^{90} +12.6251 q^{91} -9.03898 q^{92} -0.284664 q^{93} +9.02713 q^{94} +15.3517 q^{95} -0.284664 q^{96} +1.00000 q^{97} +3.38295 q^{98} -7.48991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * 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
$3$	0.284664	0.164351	0.0821754	−	0.996618i	$-0.473813\pi$
$3$	0.284664	0.164351	0.0821754	+	0.996618i	$0.473813\pi$
$4$	1.00000	0.500000
$5$	−2.60924	−1.16689	−0.583443	−	0.812154i	$-0.698295\pi$
$5$	−2.60924	−1.16689	−0.583443	+	0.812154i	$0.698295\pi$
$6$	−0.284664	−0.116214
$7$	−1.90185	−0.718833	−0.359417	−	0.933177i	$-0.617024\pi$
$7$	−1.90185	−0.718833	−0.359417	+	0.933177i	$0.617024\pi$
$8$	−1.00000	−0.353553
$9$	−2.91897	−0.972989
$10$	2.60924	0.825114
$11$	2.56595	0.773662	0.386831	−	0.922151i	$-0.373570\pi$
$11$	2.56595	0.773662	0.386831	+	0.922151i	$0.373570\pi$
$12$	0.284664	0.0821754
$13$	−6.63830	−1.84113	−0.920566	−	0.390586i	$-0.872272\pi$
$13$	−6.63830	−1.84113	−0.920566	+	0.390586i	$0.872272\pi$
$14$	1.90185	0.508292
$15$	−0.742756	−0.191779
$16$	1.00000	0.250000
$17$	1.20401	0.292015	0.146008	−	0.989283i	$-0.453358\pi$
$17$	1.20401	0.292015	0.146008	+	0.989283i	$0.453358\pi$
$18$	2.91897	0.688007
$19$	−5.88359	−1.34979	−0.674894	−	0.737915i	$-0.735810\pi$
$19$	−5.88359	−1.34979	−0.674894	+	0.737915i	$0.735810\pi$
$20$	−2.60924	−0.583443
$21$	−0.541389	−0.118141
$22$	−2.56595	−0.547061
$23$	−9.03898	−1.88476	−0.942379	−	0.334546i	$-0.891417\pi$
$23$	−9.03898	−1.88476	−0.942379	+	0.334546i	$0.891417\pi$
$24$	−0.284664	−0.0581068
$25$	1.80812	0.361625
$26$	6.63830	1.30188
$27$	−1.68492	−0.324262
$28$	−1.90185	−0.359417
$29$	3.80721	0.706980	0.353490	−	0.935438i	$-0.384995\pi$
$29$	3.80721	0.706980	0.353490	+	0.935438i	$0.384995\pi$
$30$	0.742756	0.135608
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	0.730432	0.127152
$34$	−1.20401	−0.206486
$35$	4.96239	0.838797
$36$	−2.91897	−0.486494
$37$	−3.65430	−0.600763	−0.300381	−	0.953819i	$-0.597114\pi$
$37$	−3.65430	−0.600763	−0.300381	+	0.953819i	$0.597114\pi$
$38$	5.88359	0.954444
$39$	−1.88968	−0.302592
$40$	2.60924	0.412557
$41$	−3.99029	−0.623179	−0.311590	−	0.950217i	$-0.600861\pi$
$41$	−3.99029	−0.623179	−0.311590	+	0.950217i	$0.600861\pi$
$42$	0.541389	0.0835382
$43$	−4.29734	−0.655338	−0.327669	−	0.944793i	$-0.606263\pi$
$43$	−4.29734	−0.655338	−0.327669	+	0.944793i	$0.606263\pi$
$44$	2.56595	0.386831
$45$	7.61628	1.13537
$46$	9.03898	1.33273
$47$	−9.02713	−1.31674	−0.658371	−	0.752693i	$-0.728754\pi$
$47$	−9.02713	−1.31674	−0.658371	+	0.752693i	$0.728754\pi$
$48$	0.284664	0.0410877
$49$	−3.38295	−0.483279
$50$	−1.80812	−0.255707
$51$	0.342738	0.0479929
$52$	−6.63830	−0.920566
$53$	−5.85842	−0.804716	−0.402358	−	0.915482i	$-0.631809\pi$
$53$	−5.85842	−0.804716	−0.402358	+	0.915482i	$0.631809\pi$
$54$	1.68492	0.229288
$55$	−6.69516	−0.902776
$56$	1.90185	0.254146
$57$	−1.67484	−0.221839
$58$	−3.80721	−0.499911
$59$	4.74654	0.617947	0.308974	−	0.951071i	$-0.400014\pi$
$59$	4.74654	0.617947	0.308974	+	0.951071i	$0.400014\pi$
$60$	−0.742756	−0.0958894
$61$	4.90663	0.628230	0.314115	−	0.949385i	$-0.398292\pi$
$61$	4.90663	0.628230	0.314115	+	0.949385i	$0.398292\pi$
$62$	1.00000	0.127000
$63$	5.55145	0.699417
$64$	1.00000	0.125000
$65$	17.3209	2.14839
$66$	−0.730432	−0.0899100
$67$	9.04385	1.10488	0.552441	−	0.833552i	$-0.313697\pi$
$67$	9.04385	1.10488	0.552441	+	0.833552i	$0.313697\pi$
$68$	1.20401	0.146008
$69$	−2.57307	−0.309762
$70$	−4.96239	−0.593119
$71$	−4.53573	−0.538292	−0.269146	−	0.963099i	$-0.586741\pi$
$71$	−4.53573	−0.538292	−0.269146	+	0.963099i	$0.586741\pi$
$72$	2.91897	0.344003
$73$	−8.68142	−1.01608	−0.508042	−	0.861332i	$-0.669630\pi$
$73$	−8.68142	−1.01608	−0.508042	+	0.861332i	$0.669630\pi$
$74$	3.65430	0.424803
$75$	0.514708	0.0594333
$76$	−5.88359	−0.674894
$77$	−4.88005	−0.556134
$78$	1.88968	0.213965
$79$	−3.80526	−0.428126	−0.214063	−	0.976820i	$-0.568670\pi$
$79$	−3.80526	−0.428126	−0.214063	+	0.976820i	$0.568670\pi$
$80$	−2.60924	−0.291722
$81$	8.27726	0.919696
$82$	3.99029	0.440654
$83$	4.53197	0.497448	0.248724	−	0.968574i	$-0.419989\pi$
$83$	4.53197	0.497448	0.248724	+	0.968574i	$0.419989\pi$
$84$	−0.541389	−0.0590704
$85$	−3.14155	−0.340749
$86$	4.29734	0.463394
$87$	1.08377	0.116193
$88$	−2.56595	−0.273531
$89$	−10.2511	−1.08662	−0.543309	−	0.839533i	$-0.682829\pi$
$89$	−10.2511	−1.08662	−0.543309	+	0.839533i	$0.682829\pi$
$90$	−7.61628	−0.802826
$91$	12.6251	1.32347
$92$	−9.03898	−0.942379
$93$	−0.284664	−0.0295183
$94$	9.02713	0.931078
$95$	15.3517	1.57505
$96$	−0.284664	−0.0290534
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	3.38295	0.341730
$99$	−7.48991	−0.752764
$100$	1.80812	0.180812
$101$	−5.31725	−0.529086	−0.264543	−	0.964374i	$-0.585221\pi$
$101$	−5.31725	−0.529086	−0.264543	+	0.964374i	$0.585221\pi$
$102$	−0.342738	−0.0339361
$103$	−16.6503	−1.64060	−0.820300	−	0.571934i	$-0.806193\pi$
$103$	−16.6503	−1.64060	−0.820300	+	0.571934i	$0.806193\pi$
$104$	6.63830	0.650939
$105$	1.41261	0.137857
$106$	5.85842	0.569020
$107$	8.35761	0.807961	0.403980	−	0.914768i	$-0.367626\pi$
$107$	8.35761	0.807961	0.403980	+	0.914768i	$0.367626\pi$
$108$	−1.68492	−0.162131
$109$	−0.0560917	−0.00537261	−0.00268630	−	0.999996i	$-0.500855\pi$
$109$	−0.0560917	−0.00537261	−0.00268630	+	0.999996i	$0.500855\pi$
$110$	6.69516	0.638359
$111$	−1.04025	−0.0987358
$112$	−1.90185	−0.179708
$113$	−4.30647	−0.405119	−0.202559	−	0.979270i	$-0.564926\pi$
$113$	−4.30647	−0.405119	−0.202559	+	0.979270i	$0.564926\pi$
$114$	1.67484	0.156864
$115$	23.5849	2.19930
$116$	3.80721	0.353490
$117$	19.3770	1.79140
$118$	−4.74654	−0.436955
$119$	−2.28985	−0.209910
$120$	0.742756	0.0678040
$121$	−4.41592	−0.401447
$122$	−4.90663	−0.444226
$123$	−1.13589	−0.102420
$124$	−1.00000	−0.0898027
$125$	8.32837	0.744912
$126$	−5.55145	−0.494562
$127$	−18.0650	−1.60301	−0.801506	−	0.597987i	$-0.795967\pi$
$127$	−18.0650	−1.60301	−0.801506	+	0.597987i	$0.795967\pi$
$128$	−1.00000	−0.0883883
$129$	−1.22330	−0.107705
$130$	−17.3209	−1.51914
$131$	−10.4195	−0.910358	−0.455179	−	0.890400i	$-0.650425\pi$
$131$	−10.4195	−0.910358	−0.455179	+	0.890400i	$0.650425\pi$
$132$	0.730432	0.0635760
$133$	11.1897	0.970272
$134$	−9.04385	−0.781269
$135$	4.39635	0.378377
$136$	−1.20401	−0.103243
$137$	9.28588	0.793346	0.396673	−	0.917960i	$-0.370165\pi$
$137$	9.28588	0.793346	0.396673	+	0.917960i	$0.370165\pi$
$138$	2.57307	0.219034
$139$	21.3223	1.80854	0.904268	−	0.426965i	$-0.140417\pi$
$139$	21.3223	1.80854	0.904268	+	0.426965i	$0.140417\pi$
$140$	4.96239	0.419399
$141$	−2.56970	−0.216408
$142$	4.53573	0.380630
$143$	−17.0335	−1.42441
$144$	−2.91897	−0.243247
$145$	−9.93391	−0.824966
$146$	8.68142	0.718480
$147$	−0.963004	−0.0794272
$148$	−3.65430	−0.300381
$149$	−10.8984	−0.892834	−0.446417	−	0.894825i	$-0.647300\pi$
$149$	−10.8984	−0.892834	−0.446417	+	0.894825i	$0.647300\pi$
$150$	−0.514708	−0.0420257
$151$	−3.25948	−0.265253	−0.132626	−	0.991166i	$-0.542341\pi$
$151$	−3.25948	−0.265253	−0.132626	+	0.991166i	$0.542341\pi$
$152$	5.88359	0.477222
$153$	−3.51446	−0.284128
$154$	4.88005	0.393246
$155$	2.60924	0.209579
$156$	−1.88968	−0.151296
$157$	4.46419	0.356281	0.178140	−	0.984005i	$-0.442992\pi$
$157$	4.46419	0.356281	0.178140	+	0.984005i	$0.442992\pi$
$158$	3.80526	0.302731
$159$	−1.66768	−0.132256
$160$	2.60924	0.206278
$161$	17.1908	1.35483
$162$	−8.27726	−0.650323
$163$	4.29344	0.336288	0.168144	−	0.985762i	$-0.446223\pi$
$163$	4.29344	0.336288	0.168144	+	0.985762i	$0.446223\pi$
$164$	−3.99029	−0.311590
$165$	−1.90587	−0.148372
$166$	−4.53197	−0.351749
$167$	−6.86757	−0.531428	−0.265714	−	0.964052i	$-0.585608\pi$
$167$	−6.86757	−0.531428	−0.265714	+	0.964052i	$0.585608\pi$
$168$	0.541389	0.0417691
$169$	31.0670	2.38977
$170$	3.14155	0.240946
$171$	17.1740	1.31333
$172$	−4.29734	−0.327669
$173$	−4.91014	−0.373311	−0.186656	−	0.982425i	$-0.559765\pi$
$173$	−4.91014	−0.373311	−0.186656	+	0.982425i	$0.559765\pi$
$174$	−1.08377	−0.0821607
$175$	−3.43879	−0.259948
$176$	2.56595	0.193415
$177$	1.35117	0.101560
$178$	10.2511	0.768355
$179$	−11.4497	−0.855789	−0.427894	−	0.903829i	$-0.640744\pi$
$179$	−11.4497	−0.855789	−0.427894	+	0.903829i	$0.640744\pi$
$180$	7.61628	0.567684
$181$	11.7863	0.876066	0.438033	−	0.898959i	$-0.355675\pi$
$181$	11.7863	0.876066	0.438033	+	0.898959i	$0.355675\pi$
$182$	−12.6251	−0.935833
$183$	1.39674	0.103250
$184$	9.03898	0.666363
$185$	9.53493	0.701022
$186$	0.284664	0.0208726
$187$	3.08942	0.225921
$188$	−9.02713	−0.658371
$189$	3.20446	0.233091
$190$	−15.3517	−1.11373
$191$	−10.9665	−0.793509	−0.396754	−	0.917925i	$-0.629864\pi$
$191$	−10.9665	−0.793509	−0.396754	+	0.917925i	$0.629864\pi$
$192$	0.284664	0.0205438
$193$	−13.1665	−0.947746	−0.473873	−	0.880593i	$-0.657144\pi$
$193$	−13.1665	−0.947746	−0.473873	+	0.880593i	$0.657144\pi$
$194$	−1.00000	−0.0717958
$195$	4.93064	0.353090
$196$	−3.38295	−0.241639
$197$	−19.1849	−1.36687	−0.683435	−	0.730011i	$-0.739515\pi$
$197$	−19.1849	−1.36687	−0.683435	+	0.730011i	$0.739515\pi$
$198$	7.48991	0.532285
$199$	7.50605	0.532090	0.266045	−	0.963961i	$-0.414283\pi$
$199$	7.50605	0.532090	0.266045	+	0.963961i	$0.414283\pi$
$200$	−1.80812	−0.127854
$201$	2.57446	0.181588
$202$	5.31725	0.374120
$203$	−7.24075	−0.508201
$204$	0.342738	0.0239965
$205$	10.4116	0.727180
$206$	16.6503	1.16008
$207$	26.3845	1.83385
$208$	−6.63830	−0.460283
$209$	−15.0970	−1.04428
$210$	−1.41261	−0.0974796
$211$	−4.43383	−0.305237	−0.152619	−	0.988285i	$-0.548771\pi$
$211$	−4.43383	−0.305237	−0.152619	+	0.988285i	$0.548771\pi$
$212$	−5.85842	−0.402358
$213$	−1.29116	−0.0884687
$214$	−8.35761	−0.571314
$215$	11.2128	0.764706
$216$	1.68492	0.114644
$217$	1.90185	0.129106
$218$	0.0560917	0.00379901
$219$	−2.47129	−0.166994
$220$	−6.69516	−0.451388
$221$	−7.99258	−0.537639
$222$	1.04025	0.0698168
$223$	−13.4882	−0.903234	−0.451617	−	0.892212i	$-0.649153\pi$
$223$	−13.4882	−0.903234	−0.451617	+	0.892212i	$0.649153\pi$
$224$	1.90185	0.127073
$225$	−5.27785	−0.351857
$226$	4.30647	0.286462
$227$	22.6750	1.50499	0.752495	−	0.658598i	$-0.228850\pi$
$227$	22.6750	1.50499	0.752495	+	0.658598i	$0.228850\pi$
$228$	−1.67484	−0.110919
$229$	9.38517	0.620190	0.310095	−	0.950706i	$-0.399639\pi$
$229$	9.38517	0.620190	0.310095	+	0.950706i	$0.399639\pi$
$230$	−23.5849	−1.55514
$231$	−1.38918	−0.0914010
$232$	−3.80721	−0.249955
$233$	3.50632	0.229706	0.114853	−	0.993382i	$-0.463360\pi$
$233$	3.50632	0.229706	0.114853	+	0.993382i	$0.463360\pi$
$234$	−19.3770	−1.26671
$235$	23.5539	1.53649
$236$	4.74654	0.308974
$237$	−1.08322	−0.0703628
$238$	2.28985	0.148429
$239$	27.1800	1.75813	0.879063	−	0.476706i	$-0.158169\pi$
$239$	27.1800	1.75813	0.879063	+	0.476706i	$0.158169\pi$
$240$	−0.742756	−0.0479447
$241$	7.69685	0.495797	0.247899	−	0.968786i	$-0.420260\pi$
$241$	7.69685	0.495797	0.247899	+	0.968786i	$0.420260\pi$
$242$	4.41592	0.283866
$243$	7.41099	0.475415
$244$	4.90663	0.314115
$245$	8.82692	0.563931
$246$	1.13589	0.0724219
$247$	39.0570	2.48514
$248$	1.00000	0.0635001
$249$	1.29009	0.0817560
$250$	−8.32837	−0.526732
$251$	−4.95918	−0.313021	−0.156510	−	0.987676i	$-0.550024\pi$
$251$	−4.95918	−0.313021	−0.156510	+	0.987676i	$0.550024\pi$
$252$	5.55145	0.349708
$253$	−23.1935	−1.45817
$254$	18.0650	1.13350
$255$	−0.894285	−0.0560023
$256$	1.00000	0.0625000
$257$	0.120632	0.00752485	0.00376242	−	0.999993i	$-0.498802\pi$
$257$	0.120632	0.00752485	0.00376242	+	0.999993i	$0.498802\pi$
$258$	1.22330	0.0761592
$259$	6.94994	0.431848
$260$	17.3209	1.07420
$261$	−11.1131	−0.687884
$262$	10.4195	0.643720
$263$	10.4627	0.645155	0.322578	−	0.946543i	$-0.395451\pi$
$263$	10.4627	0.645155	0.322578	+	0.946543i	$0.395451\pi$
$264$	−0.730432	−0.0449550
$265$	15.2860	0.939013
$266$	−11.1897	−0.686086
$267$	−2.91813	−0.178586
$268$	9.04385	0.552441
$269$	11.3576	0.692484	0.346242	−	0.938145i	$-0.387458\pi$
$269$	11.3576	0.692484	0.346242	+	0.938145i	$0.387458\pi$
$270$	−4.39635	−0.267553
$271$	25.5120	1.54975	0.774873	−	0.632117i	$-0.217814\pi$
$271$	25.5120	1.54975	0.774873	+	0.632117i	$0.217814\pi$
$272$	1.20401	0.0730038
$273$	3.59390	0.217513
$274$	−9.28588	−0.560980
$275$	4.63955	0.279775
$276$	−2.57307	−0.154881
$277$	−1.38993	−0.0835128	−0.0417564	−	0.999128i	$-0.513295\pi$
$277$	−1.38993	−0.0835128	−0.0417564	+	0.999128i	$0.513295\pi$
$278$	−21.3223	−1.27883
$279$	2.91897	0.174754
$280$	−4.96239	−0.296560
$281$	12.7407	0.760044	0.380022	−	0.924978i	$-0.375916\pi$
$281$	12.7407	0.760044	0.380022	+	0.924978i	$0.375916\pi$
$282$	2.56970	0.153023
$283$	8.10998	0.482088	0.241044	−	0.970514i	$-0.422510\pi$
$283$	8.10998	0.482088	0.241044	+	0.970514i	$0.422510\pi$
$284$	−4.53573	−0.269146
$285$	4.37007	0.258860
$286$	17.0335	1.00721
$287$	7.58896	0.447962
$288$	2.91897	0.172002
$289$	−15.5504	−0.914727
$290$	9.93391	0.583339
$291$	0.284664	0.0166873
$292$	−8.68142	−0.508042
$293$	−0.587574	−0.0343264	−0.0171632	−	0.999853i	$-0.505463\pi$
$293$	−0.587574	−0.0343264	−0.0171632	+	0.999853i	$0.505463\pi$
$294$	0.963004	0.0561635
$295$	−12.3849	−0.721075
$296$	3.65430	0.212402
$297$	−4.32340	−0.250869
$298$	10.8984	0.631329
$299$	60.0035	3.47009
$300$	0.514708	0.0297167
$301$	8.17292	0.471079
$302$	3.25948	0.187562
$303$	−1.51363	−0.0869557
$304$	−5.88359	−0.337447
$305$	−12.8026	−0.733073
$306$	3.51446	0.200908
$307$	−18.4104	−1.05074	−0.525368	−	0.850875i	$-0.676072\pi$
$307$	−18.4104	−1.05074	−0.525368	+	0.850875i	$0.676072\pi$
$308$	−4.88005	−0.278067
$309$	−4.73973	−0.269634
$310$	−2.60924	−0.148195
$311$	28.6665	1.62553	0.812763	−	0.582594i	$-0.197962\pi$
$311$	28.6665	1.62553	0.812763	+	0.582594i	$0.197962\pi$
$312$	1.88968	0.106982
$313$	5.71371	0.322958	0.161479	−	0.986876i	$-0.448374\pi$
$313$	5.71371	0.322958	0.161479	+	0.986876i	$0.448374\pi$
$314$	−4.46419	−0.251929
$315$	−14.4851	−0.816140
$316$	−3.80526	−0.214063
$317$	−30.7719	−1.72832	−0.864162	−	0.503213i	$-0.832151\pi$
$317$	−30.7719	−1.72832	−0.864162	+	0.503213i	$0.832151\pi$
$318$	1.66768	0.0935189
$319$	9.76908	0.546964
$320$	−2.60924	−0.145861
$321$	2.37911	0.132789
$322$	−17.1908	−0.958008
$323$	−7.08389	−0.394158
$324$	8.27726	0.459848
$325$	−12.0029	−0.665799
$326$	−4.29344	−0.237792
$327$	−0.0159673	−0.000882993 0
$328$	3.99029	0.220327
$329$	17.1683	0.946519
$330$	1.90587	0.104915
$331$	−16.4893	−0.906334	−0.453167	−	0.891426i	$-0.649706\pi$
$331$	−16.4893	−0.906334	−0.453167	+	0.891426i	$0.649706\pi$
$332$	4.53197	0.248724
$333$	10.6668	0.584535
$334$	6.86757	0.375777
$335$	−23.5975	−1.28927
$336$	−0.541389	−0.0295352
$337$	−7.44703	−0.405665	−0.202833	−	0.979213i	$-0.565015\pi$
$337$	−7.44703	−0.405665	−0.202833	+	0.979213i	$0.565015\pi$
$338$	−31.0670	−1.68982
$339$	−1.22590	−0.0665816
$340$	−3.14155	−0.170374
$341$	−2.56595	−0.138954
$342$	−17.1740	−0.928663
$343$	19.7469	1.06623
$344$	4.29734	0.231697
$345$	6.71376	0.361457
$346$	4.91014	0.263971
$347$	−20.9512	−1.12472	−0.562358	−	0.826894i	$-0.690106\pi$
$347$	−20.9512	−1.12472	−0.562358	+	0.826894i	$0.690106\pi$
$348$	1.08377	0.0580964
$349$	−5.83358	−0.312264	−0.156132	−	0.987736i	$-0.549903\pi$
$349$	−5.83358	−0.312264	−0.156132	+	0.987736i	$0.549903\pi$
$350$	3.43879	0.183811
$351$	11.1850	0.597010
$352$	−2.56595	−0.136765
$353$	−20.2619	−1.07843	−0.539215	−	0.842168i	$-0.681279\pi$
$353$	−20.2619	−1.07843	−0.539215	+	0.842168i	$0.681279\pi$
$354$	−1.35117	−0.0718139
$355$	11.8348	0.628126
$356$	−10.2511	−0.543309
$357$	−0.651838	−0.0344989
$358$	11.4497	0.605134
$359$	−15.1259	−0.798315	−0.399157	−	0.916882i	$-0.630697\pi$
$359$	−15.1259	−0.798315	−0.399157	+	0.916882i	$0.630697\pi$
$360$	−7.61628	−0.401413
$361$	15.6166	0.821925
$362$	−11.7863	−0.619472
$363$	−1.25705	−0.0659782
$364$	12.6251	0.661734
$365$	22.6519	1.18565
$366$	−1.39674	−0.0730088
$367$	30.0627	1.56926	0.784631	−	0.619963i	$-0.212852\pi$
$367$	30.0627	1.56926	0.784631	+	0.619963i	$0.212852\pi$
$368$	−9.03898	−0.471190
$369$	11.6475	0.606346
$370$	−9.53493	−0.495697
$371$	11.1419	0.578457
$372$	−0.284664	−0.0147591
$373$	−31.1345	−1.61208	−0.806041	−	0.591859i	$-0.798394\pi$
$373$	−31.1345	−1.61208	−0.806041	+	0.591859i	$0.798394\pi$
$374$	−3.08942	−0.159750
$375$	2.37079	0.122427
$376$	9.02713	0.465539
$377$	−25.2734	−1.30164
$378$	−3.20446	−0.164820
$379$	−14.9896	−0.769964	−0.384982	−	0.922924i	$-0.625792\pi$
$379$	−14.9896	−0.769964	−0.384982	+	0.922924i	$0.625792\pi$
$380$	15.3517	0.787524
$381$	−5.14246	−0.263456
$382$	10.9665	0.561096
$383$	1.28488	0.0656545	0.0328272	−	0.999461i	$-0.489549\pi$
$383$	1.28488	0.0656545	0.0328272	+	0.999461i	$0.489549\pi$
$384$	−0.284664	−0.0145267
$385$	12.7332	0.648945
$386$	13.1665	0.670157
$387$	12.5438	0.637637
$388$	1.00000	0.0507673
$389$	−28.6293	−1.45156	−0.725781	−	0.687926i	$-0.758521\pi$
$389$	−28.6293	−1.45156	−0.725781	+	0.687926i	$0.758521\pi$
$390$	−4.93064	−0.249672
$391$	−10.8830	−0.550378
$392$	3.38295	0.170865
$393$	−2.96606	−0.149618
$394$	19.1849	0.966524
$395$	9.92884	0.499574
$396$	−7.48991	−0.376382
$397$	−7.41758	−0.372277	−0.186139	−	0.982523i	$-0.559597\pi$
$397$	−7.41758	−0.372277	−0.186139	+	0.982523i	$0.559597\pi$
$398$	−7.50605	−0.376244
$399$	3.18531	0.159465
$400$	1.80812	0.0904062
$401$	−23.0403	−1.15058	−0.575288	−	0.817951i	$-0.695110\pi$
$401$	−23.0403	−1.15058	−0.575288	+	0.817951i	$0.695110\pi$
$402$	−2.57446	−0.128402
$403$	6.63830	0.330677
$404$	−5.31725	−0.264543
$405$	−21.5974	−1.07318
$406$	7.24075	0.359352
$407$	−9.37673	−0.464787
$408$	−0.342738	−0.0169681
$409$	−5.92783	−0.293113	−0.146556	−	0.989202i	$-0.546819\pi$
$409$	−5.92783	−0.293113	−0.146556	+	0.989202i	$0.546819\pi$
$410$	−10.4116	−0.514194
$411$	2.64335	0.130387
$412$	−16.6503	−0.820300
$413$	−9.02724	−0.444201
$414$	−26.3845	−1.29673
$415$	−11.8250	−0.580465
$416$	6.63830	0.325469
$417$	6.06970	0.297234
$418$	15.0970	0.738416
$419$	−22.3412	−1.09144	−0.545720	−	0.837968i	$-0.683744\pi$
$419$	−22.3412	−1.09144	−0.545720	+	0.837968i	$0.683744\pi$
$420$	1.41261	0.0689285
$421$	0.506186	0.0246700	0.0123350	−	0.999924i	$-0.496074\pi$
$421$	0.506186	0.0246700	0.0123350	+	0.999924i	$0.496074\pi$
$422$	4.43383	0.215835
$423$	26.3499	1.28118
$424$	5.85842	0.284510
$425$	2.17700	0.105600
$426$	1.29116	0.0625568
$427$	−9.33170	−0.451593
$428$	8.35761	0.403980
$429$	−4.84883	−0.234104
$430$	−11.2128	−0.540729
$431$	13.3244	0.641814	0.320907	−	0.947111i	$-0.396012\pi$
$431$	13.3244	0.641814	0.320907	+	0.947111i	$0.396012\pi$
$432$	−1.68492	−0.0810656
$433$	36.9624	1.77630	0.888150	−	0.459554i	$-0.151991\pi$
$433$	36.9624	1.77630	0.888150	+	0.459554i	$0.151991\pi$
$434$	−1.90185	−0.0912919
$435$	−2.82782	−0.135584
$436$	−0.0560917	−0.00268630
$437$	53.1816	2.54402
$438$	2.47129	0.118083
$439$	1.42562	0.0680411	0.0340206	−	0.999421i	$-0.489169\pi$
$439$	1.42562	0.0680411	0.0340206	+	0.999421i	$0.489169\pi$
$440$	6.69516	0.319179
$441$	9.87472	0.470225
$442$	7.99258	0.380168
$443$	−22.4139	−1.06492	−0.532458	−	0.846456i	$-0.678732\pi$
$443$	−22.4139	−1.06492	−0.532458	+	0.846456i	$0.678732\pi$
$444$	−1.04025	−0.0493679
$445$	26.7476	1.26796
$446$	13.4882	0.638683
$447$	−3.10239	−0.146738
$448$	−1.90185	−0.0898542
$449$	−26.2959	−1.24098	−0.620491	−	0.784213i	$-0.713067\pi$
$449$	−26.2959	−1.24098	−0.620491	+	0.784213i	$0.713067\pi$
$450$	5.27785	0.248800
$451$	−10.2389	−0.482130
$452$	−4.30647	−0.202559
$453$	−0.927857	−0.0435945
$454$	−22.6750	−1.06419
$455$	−32.9418	−1.54434
$456$	1.67484	0.0784318
$457$	21.7674	1.01824	0.509119	−	0.860696i	$-0.329971\pi$
$457$	21.7674	1.01824	0.509119	+	0.860696i	$0.329971\pi$
$458$	−9.38517	−0.438540
$459$	−2.02865	−0.0946895
$460$	23.5849	1.09965
$461$	−2.23008	−0.103865	−0.0519325	−	0.998651i	$-0.516538\pi$
$461$	−2.23008	−0.103865	−0.0519325	+	0.998651i	$0.516538\pi$
$462$	1.38918	0.0646303
$463$	−1.58156	−0.0735012	−0.0367506	−	0.999324i	$-0.511701\pi$
$463$	−1.58156	−0.0735012	−0.0367506	+	0.999324i	$0.511701\pi$
$464$	3.80721	0.176745
$465$	0.742756	0.0344445
$466$	−3.50632	−0.162427
$467$	14.3604	0.664519	0.332260	−	0.943188i	$-0.392189\pi$
$467$	14.3604	0.664519	0.332260	+	0.943188i	$0.392189\pi$
$468$	19.3770	0.895701
$469$	−17.2001	−0.794226
$470$	−23.5539	−1.08646
$471$	1.27079	0.0585550
$472$	−4.74654	−0.218477
$473$	−11.0267	−0.507010
$474$	1.08322	0.0497540
$475$	−10.6382	−0.488116
$476$	−2.28985	−0.104955
$477$	17.1005	0.782980
$478$	−27.1800	−1.24318
$479$	18.0722	0.825740	0.412870	−	0.910790i	$-0.364526\pi$
$479$	18.0722	0.825740	0.412870	+	0.910790i	$0.364526\pi$
$480$	0.742756	0.0339020
$481$	24.2583	1.10608
$482$	−7.69685	−0.350582
$483$	4.89361	0.222667
$484$	−4.41592	−0.200724
$485$	−2.60924	−0.118479
$486$	−7.41099	−0.336169
$487$	−7.09355	−0.321439	−0.160720	−	0.987000i	$-0.551381\pi$
$487$	−7.09355	−0.321439	−0.160720	+	0.987000i	$0.551381\pi$
$488$	−4.90663	−0.222113
$489$	1.22219	0.0552692
$490$	−8.82692	−0.398760
$491$	−26.5366	−1.19758	−0.598789	−	0.800907i	$-0.704351\pi$
$491$	−26.5366	−1.19758	−0.598789	+	0.800907i	$0.704351\pi$
$492$	−1.13589	−0.0512100
$493$	4.58391	0.206449
$494$	−39.0570	−1.75726
$495$	19.5430	0.878391
$496$	−1.00000	−0.0449013
$497$	8.62630	0.386942
$498$	−1.29009	−0.0578102
$499$	33.5266	1.50086	0.750429	−	0.660951i	$-0.229847\pi$
$499$	33.5266	1.50086	0.750429	+	0.660951i	$0.229847\pi$
$500$	8.32837	0.372456
$501$	−1.95495	−0.0873407
$502$	4.95918	0.221339
$503$	−38.3000	−1.70771	−0.853856	−	0.520509i	$-0.825742\pi$
$503$	−38.3000	−1.70771	−0.853856	+	0.520509i	$0.825742\pi$
$504$	−5.55145	−0.247281
$505$	13.8740	0.617384
$506$	23.1935	1.03108
$507$	8.84366	0.392761
$508$	−18.0650	−0.801506
$509$	−6.54944	−0.290299	−0.145149	−	0.989410i	$-0.546366\pi$
$509$	−6.54944	−0.290299	−0.145149	+	0.989410i	$0.546366\pi$
$510$	0.894285	0.0395996
$511$	16.5108	0.730395
$512$	−1.00000	−0.0441942
$513$	9.91335	0.437685
$514$	−0.120632	−0.00532087
$515$	43.4445	1.91439
$516$	−1.22330	−0.0538527
$517$	−23.1631	−1.01871
$518$	−6.94994	−0.305363
$519$	−1.39774	−0.0613540
$520$	−17.3209	−0.759572
$521$	−4.93694	−0.216291	−0.108146	−	0.994135i	$-0.534491\pi$
$521$	−4.93694	−0.216291	−0.108146	+	0.994135i	$0.534491\pi$
$522$	11.1131	0.486407
$523$	−7.45147	−0.325830	−0.162915	−	0.986640i	$-0.552090\pi$
$523$	−7.45147	−0.325830	−0.162915	+	0.986640i	$0.552090\pi$
$524$	−10.4195	−0.455179
$525$	−0.978899	−0.0427226
$526$	−10.4627	−0.456194
$527$	−1.20401	−0.0524475
$528$	0.730432	0.0317880
$529$	58.7032	2.55231
$530$	−15.2860	−0.663982
$531$	−13.8550	−0.601256
$532$	11.1897	0.485136
$533$	26.4888	1.14736
$534$	2.91813	0.126280
$535$	−21.8070	−0.942799
$536$	−9.04385	−0.390635
$537$	−3.25931	−0.140650
$538$	−11.3576	−0.489660
$539$	−8.68047	−0.373894
$540$	4.39635	0.189189
$541$	15.6713	0.673760	0.336880	−	0.941548i	$-0.390628\pi$
$541$	15.6713	0.673760	0.336880	+	0.941548i	$0.390628\pi$
$542$	−25.5120	−1.09584
$543$	3.35512	0.143982
$544$	−1.20401	−0.0516215
$545$	0.146357	0.00626923
$546$	−3.59390	−0.153805
$547$	29.6569	1.26804	0.634019	−	0.773318i	$-0.281404\pi$
$547$	29.6569	1.26804	0.634019	+	0.773318i	$0.281404\pi$
$548$	9.28588	0.396673
$549$	−14.3223	−0.611261
$550$	−4.63955	−0.197831
$551$	−22.4000	−0.954273
$552$	2.57307	0.109517
$553$	7.23706	0.307751
$554$	1.38993	0.0590525
$555$	2.71425	0.115214
$556$	21.3223	0.904268
$557$	−7.77847	−0.329584	−0.164792	−	0.986328i	$-0.552695\pi$
$557$	−7.77847	−0.329584	−0.164792	+	0.986328i	$0.552695\pi$
$558$	−2.91897	−0.123570
$559$	28.5270	1.20657
$560$	4.96239	0.209699
$561$	0.879447	0.0371303
$562$	−12.7407	−0.537432
$563$	15.6043	0.657645	0.328822	−	0.944392i	$-0.393348\pi$
$563$	15.6043	0.657645	0.328822	+	0.944392i	$0.393348\pi$
$564$	−2.56970	−0.108204
$565$	11.2366	0.472728
$566$	−8.10998	−0.340888
$567$	−15.7422	−0.661108
$568$	4.53573	0.190315
$569$	−8.01468	−0.335993	−0.167996	−	0.985788i	$-0.553730\pi$
$569$	−8.01468	−0.335993	−0.167996	+	0.985788i	$0.553730\pi$
$570$	−4.37007	−0.183042
$571$	34.7469	1.45411	0.727056	−	0.686578i	$-0.240888\pi$
$571$	34.7469	1.45411	0.727056	+	0.686578i	$0.240888\pi$
$572$	−17.0335	−0.712207
$573$	−3.12177	−0.130414
$574$	−7.58896	−0.316757
$575$	−16.3436	−0.681575
$576$	−2.91897	−0.121624
$577$	20.3189	0.845887	0.422944	−	0.906156i	$-0.360997\pi$
$577$	20.3189	0.845887	0.422944	+	0.906156i	$0.360997\pi$
$578$	15.5504	0.646810
$579$	−3.74803	−0.155763
$580$	−9.93391	−0.412483
$581$	−8.61914	−0.357582
$582$	−0.284664	−0.0117997
$583$	−15.0324	−0.622578
$584$	8.68142	0.359240
$585$	−50.5591	−2.09036
$586$	0.587574	0.0242724
$587$	−20.7316	−0.855686	−0.427843	−	0.903853i	$-0.640726\pi$
$587$	−20.7316	−0.855686	−0.427843	+	0.903853i	$0.640726\pi$
$588$	−0.963004	−0.0397136
$589$	5.88359	0.242429
$590$	12.3849	0.509877
$591$	−5.46126	−0.224646
$592$	−3.65430	−0.150191
$593$	28.8724	1.18565	0.592823	−	0.805333i	$-0.298013\pi$
$593$	28.8724	1.18565	0.592823	+	0.805333i	$0.298013\pi$
$594$	4.32340	0.177391
$595$	5.97477	0.244942
$596$	−10.8984	−0.446417
$597$	2.13670	0.0874494
$598$	−60.0035	−2.45372
$599$	−21.6603	−0.885016	−0.442508	−	0.896765i	$-0.645911\pi$
$599$	−21.6603	−0.885016	−0.442508	+	0.896765i	$0.645911\pi$
$600$	−0.514708	−0.0210128
$601$	−40.6845	−1.65955	−0.829777	−	0.558095i	$-0.811532\pi$
$601$	−40.6845	−1.65955	−0.829777	+	0.558095i	$0.811532\pi$
$602$	−8.17292	−0.333103
$603$	−26.3987	−1.07504
$604$	−3.25948	−0.132626
$605$	11.5222	0.468444
$606$	1.51363	0.0614870
$607$	43.3865	1.76100	0.880501	−	0.474044i	$-0.157206\pi$
$607$	43.3865	1.76100	0.880501	+	0.474044i	$0.157206\pi$
$608$	5.88359	0.238611
$609$	−2.06118	−0.0835232
$610$	12.8026	0.518361
$611$	59.9248	2.42430
$612$	−3.51446	−0.142064
$613$	−41.4854	−1.67558	−0.837790	−	0.545993i	$-0.816153\pi$
$613$	−41.4854	−1.67558	−0.837790	+	0.545993i	$0.816153\pi$
$614$	18.4104	0.742982
$615$	2.96381	0.119513
$616$	4.88005	0.196623
$617$	24.3150	0.978885	0.489442	−	0.872036i	$-0.337200\pi$
$617$	24.3150	0.978885	0.489442	+	0.872036i	$0.337200\pi$
$618$	4.73973	0.190660
$619$	2.34549	0.0942731	0.0471366	−	0.998888i	$-0.484990\pi$
$619$	2.34549	0.0942731	0.0471366	+	0.998888i	$0.484990\pi$
$620$	2.60924	0.104790
$621$	15.2299	0.611156
$622$	−28.6665	−1.14942
$623$	19.4962	0.781097
$624$	−1.88968	−0.0756479
$625$	−30.7713	−1.23085
$626$	−5.71371	−0.228366
$627$	−4.29756	−0.171628
$628$	4.46419	0.178140
$629$	−4.39981	−0.175432
$630$	14.4851	0.577098
$631$	4.77118	0.189938	0.0949689	−	0.995480i	$-0.469725\pi$
$631$	4.77118	0.189938	0.0949689	+	0.995480i	$0.469725\pi$
$632$	3.80526	0.151365
$633$	−1.26215	−0.0501660
$634$	30.7719	1.22211
$635$	47.1360	1.87053
$636$	−1.66768	−0.0661279
$637$	22.4570	0.889780
$638$	−9.76908	−0.386762
$639$	13.2396	0.523752
$640$	2.60924	0.103139
$641$	−16.4366	−0.649205	−0.324602	−	0.945851i	$-0.605231\pi$
$641$	−16.4366	−0.649205	−0.324602	+	0.945851i	$0.605231\pi$
$642$	−2.37911	−0.0938960
$643$	28.3719	1.11888	0.559438	−	0.828872i	$-0.311017\pi$
$643$	28.3719	1.11888	0.559438	+	0.828872i	$0.311017\pi$
$644$	17.1908	0.677414
$645$	3.19188	0.125680
$646$	7.08389	0.278712
$647$	−26.5432	−1.04352	−0.521761	−	0.853091i	$-0.674725\pi$
$647$	−26.5432	−1.04352	−0.521761	+	0.853091i	$0.674725\pi$
$648$	−8.27726	−0.325162
$649$	12.1794	0.478082
$650$	12.0029	0.470791
$651$	0.541389	0.0212187
$652$	4.29344	0.168144
$653$	4.21343	0.164884	0.0824421	−	0.996596i	$-0.473728\pi$
$653$	4.21343	0.164884	0.0824421	+	0.996596i	$0.473728\pi$
$654$	0.0159673	0.000624370 0
$655$	27.1870	1.06228
$656$	−3.99029	−0.155795
$657$	25.3408	0.988638
$658$	−17.1683	−0.669290
$659$	−29.4767	−1.14825	−0.574124	−	0.818768i	$-0.694657\pi$
$659$	−29.4767	−1.14825	−0.574124	+	0.818768i	$0.694657\pi$
$660$	−1.90587	−0.0741859
$661$	−0.856784	−0.0333251	−0.0166625	−	0.999861i	$-0.505304\pi$
$661$	−0.856784	−0.0333251	−0.0166625	+	0.999861i	$0.505304\pi$
$662$	16.4893	0.640875
$663$	−2.27520	−0.0883614
$664$	−4.53197	−0.175874
$665$	−29.1966	−1.13220
$666$	−10.6668	−0.413329
$667$	−34.4133	−1.33249
$668$	−6.86757	−0.265714
$669$	−3.83959	−0.148447
$670$	23.5975	0.911653
$671$	12.5902	0.486037
$672$	0.541389	0.0208845
$673$	34.5712	1.33262	0.666312	−	0.745673i	$-0.267872\pi$
$673$	34.5712	1.33262	0.666312	+	0.745673i	$0.267872\pi$
$674$	7.44703	0.286849
$675$	−3.04654	−0.117261
$676$	31.0670	1.19489
$677$	6.26825	0.240908	0.120454	−	0.992719i	$-0.461565\pi$
$677$	6.26825	0.240908	0.120454	+	0.992719i	$0.461565\pi$
$678$	1.22590	0.0470803
$679$	−1.90185	−0.0729865
$680$	3.14155	0.120473
$681$	6.45474	0.247346
$682$	2.56595	0.0982551
$683$	−31.3974	−1.20139	−0.600694	−	0.799479i	$-0.705109\pi$
$683$	−31.3974	−1.20139	−0.600694	+	0.799479i	$0.705109\pi$
$684$	17.1740	0.656664
$685$	−24.2291	−0.925745
$686$	−19.7469	−0.753939
$687$	2.67162	0.101929
$688$	−4.29734	−0.163835
$689$	38.8900	1.48159
$690$	−6.71376	−0.255588
$691$	−6.04022	−0.229781	−0.114890	−	0.993378i	$-0.536652\pi$
$691$	−6.04022	−0.229781	−0.114890	+	0.993378i	$0.536652\pi$
$692$	−4.91014	−0.186656
$693$	14.2447	0.541112
$694$	20.9512	0.795295
$695$	−55.6350	−2.11036
$696$	−1.08377	−0.0410804
$697$	−4.80435	−0.181978
$698$	5.83358	0.220804
$699$	0.998121	0.0377524
$700$	−3.43879	−0.129974
$701$	27.2689	1.02993	0.514967	−	0.857210i	$-0.327804\pi$
$701$	27.2689	1.02993	0.514967	+	0.857210i	$0.327804\pi$
$702$	−11.1850	−0.422150
$703$	21.5004	0.810902
$704$	2.56595	0.0967077
$705$	6.70496	0.252523
$706$	20.2619	0.762565
$707$	10.1126	0.380325
$708$	1.35117	0.0507801
$709$	17.8716	0.671183	0.335591	−	0.942008i	$-0.391064\pi$
$709$	17.8716	0.671183	0.335591	+	0.942008i	$0.391064\pi$
$710$	−11.8348	−0.444152
$711$	11.1074	0.416561
$712$	10.2511	0.384177
$713$	9.03898	0.338513
$714$	0.651838	0.0243944
$715$	44.4445	1.66213
$716$	−11.4497	−0.427894
$717$	7.73715	0.288949
$718$	15.1259	0.564494
$719$	−32.1714	−1.19979	−0.599895	−	0.800079i	$-0.704791\pi$
$719$	−32.1714	−1.19979	−0.599895	+	0.800079i	$0.704791\pi$
$720$	7.61628	0.283842
$721$	31.6664	1.17932
$722$	−15.6166	−0.581189
$723$	2.19101	0.0814847
$724$	11.7863	0.438033
$725$	6.88390	0.255662
$726$	1.25705	0.0466536
$727$	30.7116	1.13903	0.569515	−	0.821981i	$-0.307131\pi$
$727$	30.7116	1.13903	0.569515	+	0.821981i	$0.307131\pi$
$728$	−12.6251	−0.467917
$729$	−22.7222	−0.841561
$730$	−22.6519	−0.838384
$731$	−5.17404	−0.191369
$732$	1.39674	0.0516250
$733$	−13.8961	−0.513265	−0.256632	−	0.966509i	$-0.582613\pi$
$733$	−13.8961	−0.513265	−0.256632	+	0.966509i	$0.582613\pi$
$734$	−30.0627	−1.10964
$735$	2.51271	0.0926826
$736$	9.03898	0.333181
$737$	23.2060	0.854805
$738$	−11.6475	−0.428752
$739$	−14.0899	−0.518307	−0.259154	−	0.965836i	$-0.583444\pi$
$739$	−14.0899	−0.518307	−0.259154	+	0.965836i	$0.583444\pi$
$740$	9.53493	0.350511
$741$	11.1181	0.408434
$742$	−11.1419	−0.409031
$743$	−6.98768	−0.256353	−0.128177	−	0.991751i	$-0.540912\pi$
$743$	−6.98768	−0.256353	−0.128177	+	0.991751i	$0.540912\pi$
$744$	0.284664	0.0104363
$745$	28.4366	1.04184
$746$	31.1345	1.13991
$747$	−13.2287	−0.484011
$748$	3.08942	0.112960
$749$	−15.8950	−0.580789
$750$	−2.37079	−0.0865688
$751$	15.9172	0.580827	0.290414	−	0.956901i	$-0.406207\pi$
$751$	15.9172	0.580827	0.290414	+	0.956901i	$0.406207\pi$
$752$	−9.02713	−0.329186
$753$	−1.41170	−0.0514452
$754$	25.2734	0.920402
$755$	8.50477	0.309520
$756$	3.20446	0.116545
$757$	−10.2399	−0.372174	−0.186087	−	0.982533i	$-0.559581\pi$
$757$	−10.2399	−0.372174	−0.186087	+	0.982533i	$0.559581\pi$
$758$	14.9896	0.544447
$759$	−6.60236	−0.239651
$760$	−15.3517	−0.556864
$761$	−10.7865	−0.391009	−0.195504	−	0.980703i	$-0.562634\pi$
$761$	−10.7865	−0.391009	−0.195504	+	0.980703i	$0.562634\pi$
$762$	5.14246	0.186292
$763$	0.106678	0.00386201
$764$	−10.9665	−0.396754
$765$	9.17007	0.331545
$766$	−1.28488	−0.0464247
$767$	−31.5090	−1.13772
$768$	0.284664	0.0102719
$769$	12.1258	0.437269	0.218635	−	0.975807i	$-0.429840\pi$
$769$	12.1258	0.437269	0.218635	+	0.975807i	$0.429840\pi$
$770$	−12.7332	−0.458874
$771$	0.0343397	0.00123671
$772$	−13.1665	−0.473873
$773$	−2.01439	−0.0724525	−0.0362263	−	0.999344i	$-0.511534\pi$
$773$	−2.01439	−0.0724525	−0.0362263	+	0.999344i	$0.511534\pi$
$774$	−12.5438	−0.450877
$775$	−1.80812	−0.0649497
$776$	−1.00000	−0.0358979
$777$	1.97840	0.0709746
$778$	28.6293	1.02641
$779$	23.4772	0.841159
$780$	4.93064	0.176545
$781$	−11.6384	−0.416456
$782$	10.8830	0.389176
$783$	−6.41482	−0.229247
$784$	−3.38295	−0.120820
$785$	−11.6481	−0.415739
$786$	2.96606	0.105796
$787$	−21.0370	−0.749888	−0.374944	−	0.927048i	$-0.622338\pi$
$787$	−21.0370	−0.749888	−0.374944	+	0.927048i	$0.622338\pi$
$788$	−19.1849	−0.683435
$789$	2.97834	0.106032
$790$	−9.92884	−0.353252
$791$	8.19028	0.291213
$792$	7.48991	0.266142
$793$	−32.5717	−1.15665
$794$	7.41758	0.263240
$795$	4.35138	0.154327
$796$	7.50605	0.266045
$797$	−13.0333	−0.461664	−0.230832	−	0.972994i	$-0.574145\pi$
$797$	−13.0333	−0.461664	−0.230832	+	0.972994i	$0.574145\pi$
$798$	−3.18531	−0.112759
$799$	−10.8688	−0.384509
$800$	−1.80812	−0.0639268
$801$	29.9227	1.05727
$802$	23.0403	0.813580
$803$	−22.2761	−0.786105
$804$	2.57446	0.0907941
$805$	−44.8550	−1.58093
$806$	−6.63830	−0.233824
$807$	3.23309	0.113810
$808$	5.31725	0.187060
$809$	19.3471	0.680207	0.340104	−	0.940388i	$-0.389538\pi$
$809$	19.3471	0.680207	0.340104	+	0.940388i	$0.389538\pi$
$810$	21.5974	0.758854
$811$	−27.8927	−0.979447	−0.489723	−	0.871878i	$-0.662902\pi$
$811$	−27.8927	−0.979447	−0.489723	+	0.871878i	$0.662902\pi$
$812$	−7.24075	−0.254101
$813$	7.26236	0.254702
$814$	9.37673	0.328654
$815$	−11.2026	−0.392410
$816$	0.342738	0.0119982
$817$	25.2838	0.884567
$818$	5.92783	0.207262
$819$	−36.8522	−1.28772
$820$	10.4116	0.363590
$821$	−45.3965	−1.58435	−0.792175	−	0.610294i	$-0.791051\pi$
$821$	−45.3965	−1.58435	−0.792175	+	0.610294i	$0.791051\pi$
$822$	−2.64335	−0.0921975
$823$	−22.2541	−0.775730	−0.387865	−	0.921716i	$-0.626787\pi$
$823$	−22.2541	−0.775730	−0.387865	+	0.921716i	$0.626787\pi$
$824$	16.6503	0.580039
$825$	1.32071	0.0459813
$826$	9.02724	0.314098
$827$	−30.3855	−1.05661	−0.528304	−	0.849055i	$-0.677172\pi$
$827$	−30.3855	−1.05661	−0.528304	+	0.849055i	$0.677172\pi$
$828$	26.3845	0.916925
$829$	14.8996	0.517484	0.258742	−	0.965946i	$-0.416692\pi$
$829$	14.8996	0.517484	0.258742	+	0.965946i	$0.416692\pi$
$830$	11.8250	0.410451
$831$	−0.395663	−0.0137254
$832$	−6.63830	−0.230142
$833$	−4.07310	−0.141125
$834$	−6.06970	−0.210176
$835$	17.9191	0.620117
$836$	−15.0970	−0.522139
$837$	1.68492	0.0582392
$838$	22.3412	0.771764
$839$	−24.4119	−0.842793	−0.421396	−	0.906877i	$-0.638460\pi$
$839$	−24.4119	−0.842793	−0.421396	+	0.906877i	$0.638460\pi$
$840$	−1.41261	−0.0487398
$841$	−14.5052	−0.500179
$842$	−0.506186	−0.0174443
$843$	3.62680	0.124914
$844$	−4.43383	−0.152619
$845$	−81.0612	−2.78859
$846$	−26.3499	−0.905928
$847$	8.39844	0.288574
$848$	−5.85842	−0.201179
$849$	2.30862	0.0792316
$850$	−2.17700	−0.0746704
$851$	33.0311	1.13229
$852$	−1.29116	−0.0442344
$853$	9.01117	0.308537	0.154268	−	0.988029i	$-0.450698\pi$
$853$	9.01117	0.308537	0.154268	+	0.988029i	$0.450698\pi$
$854$	9.33170	0.319324
$855$	−44.8110	−1.53250
$856$	−8.35761	−0.285657
$857$	−49.1389	−1.67855	−0.839276	−	0.543705i	$-0.817021\pi$
$857$	−49.1389	−1.67855	−0.839276	+	0.543705i	$0.817021\pi$
$858$	4.84883	0.165536
$859$	−15.4759	−0.528029	−0.264015	−	0.964519i	$-0.585047\pi$
$859$	−15.4759	−0.528029	−0.264015	+	0.964519i	$0.585047\pi$
$860$	11.2128	0.382353
$861$	2.16030	0.0736229
$862$	−13.3244	−0.453831
$863$	−35.1231	−1.19561	−0.597803	−	0.801643i	$-0.703959\pi$
$863$	−35.1231	−1.19561	−0.597803	+	0.801643i	$0.703959\pi$
$864$	1.68492	0.0573220
$865$	12.8117	0.435612
$866$	−36.9624	−1.25603
$867$	−4.42663	−0.150336
$868$	1.90185	0.0645531
$869$	−9.76410	−0.331224
$870$	2.82782	0.0958722
$871$	−60.0358	−2.03423
$872$	0.0560917	0.00189950
$873$	−2.91897	−0.0987920
$874$	−53.1816	−1.79890
$875$	−15.8393	−0.535467
$876$	−2.47129	−0.0834971
$877$	14.8415	0.501162	0.250581	−	0.968096i	$-0.419378\pi$
$877$	14.8415	0.501162	0.250581	+	0.968096i	$0.419378\pi$
$878$	−1.42562	−0.0481123
$879$	−0.167261	−0.00564157
$880$	−6.69516	−0.225694
$881$	4.63857	0.156277	0.0781387	−	0.996942i	$-0.475102\pi$
$881$	4.63857	0.156277	0.0781387	+	0.996942i	$0.475102\pi$
$882$	−9.87472	−0.332499
$883$	−26.3153	−0.885582	−0.442791	−	0.896625i	$-0.646012\pi$
$883$	−26.3153	−0.885582	−0.442791	+	0.896625i	$0.646012\pi$
$884$	−7.99258	−0.268819
$885$	−3.52552	−0.118509
$886$	22.4139	0.753009
$887$	1.68479	0.0565696	0.0282848	−	0.999600i	$-0.490995\pi$
$887$	1.68479	0.0565696	0.0282848	+	0.999600i	$0.490995\pi$
$888$	1.04025	0.0349084
$889$	34.3570	1.15230
$890$	−26.7476	−0.896583
$891$	21.2390	0.711534
$892$	−13.4882	−0.451617
$893$	53.1119	1.77732
$894$	3.10239	0.103759
$895$	29.8749	0.998609
$896$	1.90185	0.0635365
$897$	17.0808	0.570312
$898$	26.2959	0.877507
$899$	−3.80721	−0.126977
$900$	−5.27785	−0.175928
$901$	−7.05360	−0.234989
$902$	10.2389	0.340917
$903$	2.32653	0.0774222
$904$	4.30647	0.143231
$905$	−30.7532	−1.02227
$906$	0.927857	0.0308260
$907$	8.31733	0.276172	0.138086	−	0.990420i	$-0.455905\pi$
$907$	8.31733	0.276172	0.138086	+	0.990420i	$0.455905\pi$
$908$	22.6750	0.752495
$909$	15.5209	0.514795
$910$	32.9418	1.09201
$911$	21.4828	0.711758	0.355879	−	0.934532i	$-0.384181\pi$
$911$	21.4828	0.711758	0.355879	+	0.934532i	$0.384181\pi$
$912$	−1.67484	−0.0554596
$913$	11.6288	0.384856
$914$	−21.7674	−0.720002
$915$	−3.64443	−0.120481
$916$	9.38517	0.310095
$917$	19.8164	0.654396
$918$	2.02865	0.0669556
$919$	−24.3743	−0.804032	−0.402016	−	0.915633i	$-0.631690\pi$
$919$	−24.3743	−0.804032	−0.402016	+	0.915633i	$0.631690\pi$
$920$	−23.5849	−0.777570
$921$	−5.24077	−0.172689
$922$	2.23008	0.0734437
$923$	30.1095	0.991067
$924$	−1.38918	−0.0457005
$925$	−6.60742	−0.217251
$926$	1.58156	0.0519732
$927$	48.6016	1.59628
$928$	−3.80721	−0.124978
$929$	−8.87216	−0.291086	−0.145543	−	0.989352i	$-0.546493\pi$
$929$	−8.87216	−0.291086	−0.145543	+	0.989352i	$0.546493\pi$
$930$	−0.742756	−0.0243559
$931$	19.9039	0.652323
$932$	3.50632	0.114853
$933$	8.16031	0.267157
$934$	−14.3604	−0.469886
$935$	−8.06104	−0.263624
$936$	−19.3770	−0.633356
$937$	−30.2299	−0.987567	−0.493783	−	0.869585i	$-0.664386\pi$
$937$	−30.2299	−0.987567	−0.493783	+	0.869585i	$0.664386\pi$
$938$	17.2001	0.561602
$939$	1.62649	0.0530784
$940$	23.5539	0.768245
$941$	51.7171	1.68593	0.842964	−	0.537969i	$-0.180808\pi$
$941$	51.7171	1.68593	0.842964	+	0.537969i	$0.180808\pi$
$942$	−1.27079	−0.0414047
$943$	36.0682	1.17454
$944$	4.74654	0.154487
$945$	−8.36121	−0.271990
$946$	11.0267	0.358510
$947$	53.7152	1.74551	0.872755	−	0.488158i	$-0.162331\pi$
$947$	53.7152	1.74551	0.872755	+	0.488158i	$0.162331\pi$
$948$	−1.08322	−0.0351814
$949$	57.6299	1.87075
$950$	10.6382	0.345150
$951$	−8.75966	−0.284051
$952$	2.28985	0.0742145
$953$	31.7661	1.02901	0.514503	−	0.857489i	$-0.327977\pi$
$953$	31.7661	1.02901	0.514503	+	0.857489i	$0.327977\pi$
$954$	−17.1005	−0.553650
$955$	28.6142	0.925935
$956$	27.1800	0.879063
$957$	2.78091	0.0898939
$958$	−18.0722	−0.583886
$959$	−17.6604	−0.570283
$960$	−0.742756	−0.0239723
$961$	1.00000	0.0322581
$962$	−24.2583	−0.782120
$963$	−24.3956	−0.786137
$964$	7.69685	0.247899
$965$	34.3545	1.10591
$966$	−4.89361	−0.157449
$967$	15.5580	0.500311	0.250155	−	0.968206i	$-0.419518\pi$
$967$	15.5580	0.500311	0.250155	+	0.968206i	$0.419518\pi$
$968$	4.41592	0.141933
$969$	−2.01653	−0.0647802
$970$	2.60924	0.0837776
$971$	14.8551	0.476722	0.238361	−	0.971177i	$-0.423390\pi$
$971$	14.8551	0.476722	0.238361	+	0.971177i	$0.423390\pi$
$972$	7.41099	0.237708
$973$	−40.5520	−1.30004
$974$	7.09355	0.227292
$975$	−3.41678	−0.109425
$976$	4.90663	0.157057
$977$	25.1521	0.804688	0.402344	−	0.915489i	$-0.368196\pi$
$977$	25.1521	0.804688	0.402344	+	0.915489i	$0.368196\pi$
$978$	−1.22219	−0.0390812
$979$	−26.3038	−0.840674
$980$	8.82692	0.281966
$981$	0.163730	0.00522749
$982$	26.5366	0.846815
$983$	−6.04285	−0.192737	−0.0963685	−	0.995346i	$-0.530723\pi$
$983$	−6.04285	−0.192737	−0.0963685	+	0.995346i	$0.530723\pi$
$984$	1.13589	0.0362109
$985$	50.0581	1.59498
$986$	−4.58391	−0.145982
$987$	4.88719	0.155561
$988$	39.0570	1.24257
$989$	38.8436	1.23515
$990$	−19.5430	−0.621116
$991$	−2.18446	−0.0693916	−0.0346958	−	0.999398i	$-0.511046\pi$
$991$	−2.18446	−0.0693916	−0.0346958	+	0.999398i	$0.511046\pi$
$992$	1.00000	0.0317500
$993$	−4.69391	−0.148957
$994$	−8.62630	−0.273609
$995$	−19.5851	−0.620888
$996$	1.29009	0.0408780
$997$	−4.43212	−0.140367	−0.0701833	−	0.997534i	$-0.522358\pi$
$997$	−4.43212	−0.140367	−0.0701833	+	0.997534i	$0.522358\pi$
$998$	−33.5266	−1.06127
$999$	6.15718	0.194805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.18	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.18	✓	32	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.284664 q^{3} +1.00000 q^{4} -2.60924 q^{5} -0.284664 q^{6} -1.90185 q^{7} -1.00000 q^{8} -2.91897 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.284664 q^{3} +1.00000 q^{4} -2.60924 q^{5} -0.284664 q^{6} -1.90185 q^{7} -1.00000 q^{8} -2.91897 q^{9} +2.60924 q^{10} +2.56595 q^{11} +0.284664 q^{12} -6.63830 q^{13} +1.90185 q^{14} -0.742756 q^{15} +1.00000 q^{16} +1.20401 q^{17} +2.91897 q^{18} -5.88359 q^{19} -2.60924 q^{20} -0.541389 q^{21} -2.56595 q^{22} -9.03898 q^{23} -0.284664 q^{24} +1.80812 q^{25} +6.63830 q^{26} -1.68492 q^{27} -1.90185 q^{28} +3.80721 q^{29} +0.742756 q^{30} -1.00000 q^{31} -1.00000 q^{32} +0.730432 q^{33} -1.20401 q^{34} +4.96239 q^{35} -2.91897 q^{36} -3.65430 q^{37} +5.88359 q^{38} -1.88968 q^{39} +2.60924 q^{40} -3.99029 q^{41} +0.541389 q^{42} -4.29734 q^{43} +2.56595 q^{44} +7.61628 q^{45} +9.03898 q^{46} -9.02713 q^{47} +0.284664 q^{48} -3.38295 q^{49} -1.80812 q^{50} +0.342738 q^{51} -6.63830 q^{52} -5.85842 q^{53} +1.68492 q^{54} -6.69516 q^{55} +1.90185 q^{56} -1.67484 q^{57} -3.80721 q^{58} +4.74654 q^{59} -0.742756 q^{60} +4.90663 q^{61} +1.00000 q^{62} +5.55145 q^{63} +1.00000 q^{64} +17.3209 q^{65} -0.730432 q^{66} +9.04385 q^{67} +1.20401 q^{68} -2.57307 q^{69} -4.96239 q^{70} -4.53573 q^{71} +2.91897 q^{72} -8.68142 q^{73} +3.65430 q^{74} +0.514708 q^{75} -5.88359 q^{76} -4.88005 q^{77} +1.88968 q^{78} -3.80526 q^{79} -2.60924 q^{80} +8.27726 q^{81} +3.99029 q^{82} +4.53197 q^{83} -0.541389 q^{84} -3.14155 q^{85} +4.29734 q^{86} +1.08377 q^{87} -2.56595 q^{88} -10.2511 q^{89} -7.61628 q^{90} +12.6251 q^{91} -9.03898 q^{92} -0.284664 q^{93} +9.02713 q^{94} +15.3517 q^{95} -0.284664 q^{96} +1.00000 q^{97} +3.38295 q^{98} -7.48991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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