LMFDB - Embedded newform 6014.2.a.i.1.9

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:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.17506 q^{3} +1.00000 q^{4} -0.398275 q^{5} -1.17506 q^{6} -4.80253 q^{7} +1.00000 q^{8} -1.61923 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.17506 q^{3} +1.00000 q^{4} -0.398275 q^{5} -1.17506 q^{6} -4.80253 q^{7} +1.00000 q^{8} -1.61923 q^{9} -0.398275 q^{10} +6.36546 q^{11} -1.17506 q^{12} +5.33213 q^{13} -4.80253 q^{14} +0.467997 q^{15} +1.00000 q^{16} -0.335563 q^{17} -1.61923 q^{18} +2.59046 q^{19} -0.398275 q^{20} +5.64326 q^{21} +6.36546 q^{22} -6.07976 q^{23} -1.17506 q^{24} -4.84138 q^{25} +5.33213 q^{26} +5.42788 q^{27} -4.80253 q^{28} -8.23126 q^{29} +0.467997 q^{30} -1.00000 q^{31} +1.00000 q^{32} -7.47979 q^{33} -0.335563 q^{34} +1.91273 q^{35} -1.61923 q^{36} +8.30202 q^{37} +2.59046 q^{38} -6.26557 q^{39} -0.398275 q^{40} -6.69850 q^{41} +5.64326 q^{42} -1.90451 q^{43} +6.36546 q^{44} +0.644900 q^{45} -6.07976 q^{46} -3.40968 q^{47} -1.17506 q^{48} +16.0643 q^{49} -4.84138 q^{50} +0.394307 q^{51} +5.33213 q^{52} +2.05027 q^{53} +5.42788 q^{54} -2.53520 q^{55} -4.80253 q^{56} -3.04395 q^{57} -8.23126 q^{58} -0.494905 q^{59} +0.467997 q^{60} +8.99436 q^{61} -1.00000 q^{62} +7.77642 q^{63} +1.00000 q^{64} -2.12365 q^{65} -7.47979 q^{66} +3.04653 q^{67} -0.335563 q^{68} +7.14408 q^{69} +1.91273 q^{70} +5.29926 q^{71} -1.61923 q^{72} +2.07932 q^{73} +8.30202 q^{74} +5.68891 q^{75} +2.59046 q^{76} -30.5703 q^{77} -6.26557 q^{78} +13.3938 q^{79} -0.398275 q^{80} -1.52038 q^{81} -6.69850 q^{82} -8.86757 q^{83} +5.64326 q^{84} +0.133646 q^{85} -1.90451 q^{86} +9.67223 q^{87} +6.36546 q^{88} -12.2168 q^{89} +0.644900 q^{90} -25.6077 q^{91} -6.07976 q^{92} +1.17506 q^{93} -3.40968 q^{94} -1.03172 q^{95} -1.17506 q^{96} -1.00000 q^{97} +16.0643 q^{98} -10.3072 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * 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
$3$	−1.17506	−0.678421	−0.339211	−	0.940710i	$-0.610160\pi$
$3$	−1.17506	−0.678421	−0.339211	+	0.940710i	$0.610160\pi$
$4$	1.00000	0.500000
$5$	−0.398275	−0.178114	−0.0890570	−	0.996027i	$-0.528385\pi$
$5$	−0.398275	−0.178114	−0.0890570	+	0.996027i	$0.528385\pi$
$6$	−1.17506	−0.479716
$7$	−4.80253	−1.81519	−0.907593	−	0.419852i	$-0.862082\pi$
$7$	−4.80253	−1.81519	−0.907593	+	0.419852i	$0.862082\pi$
$8$	1.00000	0.353553
$9$	−1.61923	−0.539745
$10$	−0.398275	−0.125946
$11$	6.36546	1.91926	0.959629	−	0.281270i	$-0.0907556\pi$
$11$	6.36546	1.91926	0.959629	+	0.281270i	$0.0907556\pi$
$12$	−1.17506	−0.339211
$13$	5.33213	1.47887	0.739433	−	0.673230i	$-0.235094\pi$
$13$	5.33213	1.47887	0.739433	+	0.673230i	$0.235094\pi$
$14$	−4.80253	−1.28353
$15$	0.467997	0.120836
$16$	1.00000	0.250000
$17$	−0.335563	−0.0813860	−0.0406930	−	0.999172i	$-0.512957\pi$
$17$	−0.335563	−0.0813860	−0.0406930	+	0.999172i	$0.512957\pi$
$18$	−1.61923	−0.381657
$19$	2.59046	0.594293	0.297146	−	0.954832i	$-0.403965\pi$
$19$	2.59046	0.594293	0.297146	+	0.954832i	$0.403965\pi$
$20$	−0.398275	−0.0890570
$21$	5.64326	1.23146
$22$	6.36546	1.35712
$23$	−6.07976	−1.26772	−0.633859	−	0.773449i	$-0.718530\pi$
$23$	−6.07976	−1.26772	−0.633859	+	0.773449i	$0.718530\pi$
$24$	−1.17506	−0.239858
$25$	−4.84138	−0.968275
$26$	5.33213	1.04572
$27$	5.42788	1.04460
$28$	−4.80253	−0.907593
$29$	−8.23126	−1.52851	−0.764253	−	0.644916i	$-0.776892\pi$
$29$	−8.23126	−1.52851	−0.764253	+	0.644916i	$0.776892\pi$
$30$	0.467997	0.0854442
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−7.47979	−1.30207
$34$	−0.335563	−0.0575486
$35$	1.91273	0.323310
$36$	−1.61923	−0.269872
$37$	8.30202	1.36484	0.682422	−	0.730959i	$-0.260927\pi$
$37$	8.30202	1.36484	0.682422	+	0.730959i	$0.260927\pi$
$38$	2.59046	0.420228
$39$	−6.26557	−1.00329
$40$	−0.398275	−0.0629728
$41$	−6.69850	−1.04613	−0.523065	−	0.852293i	$-0.675211\pi$
$41$	−6.69850	−1.04613	−0.523065	+	0.852293i	$0.675211\pi$
$42$	5.64326	0.870774
$43$	−1.90451	−0.290435	−0.145217	−	0.989400i	$-0.546388\pi$
$43$	−1.90451	−0.290435	−0.145217	+	0.989400i	$0.546388\pi$
$44$	6.36546	0.959629
$45$	0.644900	0.0961360
$46$	−6.07976	−0.896412
$47$	−3.40968	−0.497353	−0.248677	−	0.968587i	$-0.579996\pi$
$47$	−3.40968	−0.497353	−0.248677	+	0.968587i	$0.579996\pi$
$48$	−1.17506	−0.169605
$49$	16.0643	2.29490
$50$	−4.84138	−0.684674
$51$	0.394307	0.0552140
$52$	5.33213	0.739433
$53$	2.05027	0.281626	0.140813	−	0.990036i	$-0.455028\pi$
$53$	2.05027	0.281626	0.140813	+	0.990036i	$0.455028\pi$
$54$	5.42788	0.738641
$55$	−2.53520	−0.341847
$56$	−4.80253	−0.641765
$57$	−3.04395	−0.403181
$58$	−8.23126	−1.08082
$59$	−0.494905	−0.0644312	−0.0322156	−	0.999481i	$-0.510256\pi$
$59$	−0.494905	−0.0644312	−0.0322156	+	0.999481i	$0.510256\pi$
$60$	0.467997	0.0604181
$61$	8.99436	1.15161	0.575805	−	0.817587i	$-0.304689\pi$
$61$	8.99436	1.15161	0.575805	+	0.817587i	$0.304689\pi$
$62$	−1.00000	−0.127000
$63$	7.77642	0.979736
$64$	1.00000	0.125000
$65$	−2.12365	−0.263407
$66$	−7.47979	−0.920699
$67$	3.04653	0.372193	0.186097	−	0.982531i	$-0.440416\pi$
$67$	3.04653	0.372193	0.186097	+	0.982531i	$0.440416\pi$
$68$	−0.335563	−0.0406930
$69$	7.14408	0.860047
$70$	1.91273	0.228615
$71$	5.29926	0.628907	0.314453	−	0.949273i	$-0.398179\pi$
$71$	5.29926	0.628907	0.314453	+	0.949273i	$0.398179\pi$
$72$	−1.61923	−0.190829
$73$	2.07932	0.243365	0.121683	−	0.992569i	$-0.461171\pi$
$73$	2.07932	0.243365	0.121683	+	0.992569i	$0.461171\pi$
$74$	8.30202	0.965090
$75$	5.68891	0.656899
$76$	2.59046	0.297146
$77$	−30.5703	−3.48381
$78$	−6.26557	−0.709436
$79$	13.3938	1.50692	0.753460	−	0.657494i	$-0.228383\pi$
$79$	13.3938	1.50692	0.753460	+	0.657494i	$0.228383\pi$
$80$	−0.398275	−0.0445285
$81$	−1.52038	−0.168931
$82$	−6.69850	−0.739725
$83$	−8.86757	−0.973342	−0.486671	−	0.873585i	$-0.661789\pi$
$83$	−8.86757	−0.973342	−0.486671	+	0.873585i	$0.661789\pi$
$84$	5.64326	0.615730
$85$	0.133646	0.0144960
$86$	−1.90451	−0.205368
$87$	9.67223	1.03697
$88$	6.36546	0.678560
$89$	−12.2168	−1.29498	−0.647489	−	0.762074i	$-0.724181\pi$
$89$	−12.2168	−1.29498	−0.647489	+	0.762074i	$0.724181\pi$
$90$	0.644900	0.0679784
$91$	−25.6077	−2.68442
$92$	−6.07976	−0.633859
$93$	1.17506	0.121848
$94$	−3.40968	−0.351682
$95$	−1.03172	−0.105852
$96$	−1.17506	−0.119929
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	16.0643	1.62274
$99$	−10.3072	−1.03591
$100$	−4.84138	−0.484138
$101$	2.50710	0.249466	0.124733	−	0.992190i	$-0.460193\pi$
$101$	2.50710	0.249466	0.124733	+	0.992190i	$0.460193\pi$
$102$	0.394307	0.0390422
$103$	11.9113	1.17366	0.586830	−	0.809710i	$-0.300376\pi$
$103$	11.9113	1.17366	0.586830	+	0.809710i	$0.300376\pi$
$104$	5.33213	0.522858
$105$	−2.24757	−0.219340
$106$	2.05027	0.199140
$107$	16.4063	1.58606	0.793029	−	0.609184i	$-0.208503\pi$
$107$	16.4063	1.58606	0.793029	+	0.609184i	$0.208503\pi$
$108$	5.42788	0.522298
$109$	1.37460	0.131663	0.0658315	−	0.997831i	$-0.479030\pi$
$109$	1.37460	0.131663	0.0658315	+	0.997831i	$0.479030\pi$
$110$	−2.53520	−0.241722
$111$	−9.75537	−0.925939
$112$	−4.80253	−0.453796
$113$	−12.5176	−1.17755	−0.588777	−	0.808295i	$-0.700391\pi$
$113$	−12.5176	−1.17755	−0.588777	+	0.808295i	$0.700391\pi$
$114$	−3.04395	−0.285092
$115$	2.42142	0.225798
$116$	−8.23126	−0.764253
$117$	−8.63396	−0.798210
$118$	−0.494905	−0.0455597
$119$	1.61155	0.147731
$120$	0.467997	0.0427221
$121$	29.5190	2.68355
$122$	8.99436	0.814311
$123$	7.87114	0.709716
$124$	−1.00000	−0.0898027
$125$	3.91957	0.350577
$126$	7.77642	0.692778
$127$	−18.9773	−1.68396	−0.841982	−	0.539506i	$-0.818611\pi$
$127$	−18.9773	−1.68396	−0.841982	+	0.539506i	$0.818611\pi$
$128$	1.00000	0.0883883
$129$	2.23791	0.197037
$130$	−2.12365	−0.186257
$131$	−0.324388	−0.0283419	−0.0141709	−	0.999900i	$-0.504511\pi$
$131$	−0.324388	−0.0283419	−0.0141709	+	0.999900i	$0.504511\pi$
$132$	−7.47979	−0.651033
$133$	−12.4408	−1.07875
$134$	3.04653	0.263180
$135$	−2.16179	−0.186057
$136$	−0.335563	−0.0287743
$137$	11.7394	1.00297	0.501484	−	0.865167i	$-0.332788\pi$
$137$	11.7394	1.00297	0.501484	+	0.865167i	$0.332788\pi$
$138$	7.14408	0.608145
$139$	13.2380	1.12283	0.561415	−	0.827534i	$-0.310257\pi$
$139$	13.2380	1.12283	0.561415	+	0.827534i	$0.310257\pi$
$140$	1.91273	0.161655
$141$	4.00658	0.337415
$142$	5.29926	0.444704
$143$	33.9414	2.83833
$144$	−1.61923	−0.134936
$145$	3.27830	0.272248
$146$	2.07932	0.172085
$147$	−18.8765	−1.55691
$148$	8.30202	0.682422
$149$	14.8200	1.21410	0.607052	−	0.794662i	$-0.292352\pi$
$149$	14.8200	1.21410	0.607052	+	0.794662i	$0.292352\pi$
$150$	5.68891	0.464497
$151$	17.1763	1.39779	0.698895	−	0.715225i	$-0.253676\pi$
$151$	17.1763	1.39779	0.698895	+	0.715225i	$0.253676\pi$
$152$	2.59046	0.210114
$153$	0.543355	0.0439276
$154$	−30.5703	−2.46342
$155$	0.398275	0.0319902
$156$	−6.26557	−0.501647
$157$	2.70384	0.215790	0.107895	−	0.994162i	$-0.465589\pi$
$157$	2.70384	0.215790	0.107895	+	0.994162i	$0.465589\pi$
$158$	13.3938	1.06555
$159$	−2.40919	−0.191061
$160$	−0.398275	−0.0314864
$161$	29.1982	2.30114
$162$	−1.52038	−0.119452
$163$	2.04591	0.160248	0.0801239	−	0.996785i	$-0.474468\pi$
$163$	2.04591	0.160248	0.0801239	+	0.996785i	$0.474468\pi$
$164$	−6.69850	−0.523065
$165$	2.97901	0.231916
$166$	−8.86757	−0.688257
$167$	11.2011	0.866767	0.433384	−	0.901210i	$-0.357320\pi$
$167$	11.2011	0.866767	0.433384	+	0.901210i	$0.357320\pi$
$168$	5.64326	0.435387
$169$	15.4316	1.18705
$170$	0.133646	0.0102502
$171$	−4.19456	−0.320766
$172$	−1.90451	−0.145217
$173$	−11.5282	−0.876472	−0.438236	−	0.898860i	$-0.644397\pi$
$173$	−11.5282	−0.876472	−0.438236	+	0.898860i	$0.644397\pi$
$174$	9.67223	0.733250
$175$	23.2509	1.75760
$176$	6.36546	0.479814
$177$	0.581544	0.0437115
$178$	−12.2168	−0.915688
$179$	10.2721	0.767771	0.383886	−	0.923381i	$-0.374586\pi$
$179$	10.2721	0.767771	0.383886	+	0.923381i	$0.374586\pi$
$180$	0.644900	0.0480680
$181$	−2.37168	−0.176286	−0.0881428	−	0.996108i	$-0.528093\pi$
$181$	−2.37168	−0.176286	−0.0881428	+	0.996108i	$0.528093\pi$
$182$	−25.6077	−1.89817
$183$	−10.5689	−0.781276
$184$	−6.07976	−0.448206
$185$	−3.30649	−0.243098
$186$	1.17506	0.0861596
$187$	−2.13601	−0.156201
$188$	−3.40968	−0.248677
$189$	−26.0675	−1.89613
$190$	−1.03172	−0.0748485
$191$	22.9068	1.65748	0.828741	−	0.559633i	$-0.189058\pi$
$191$	22.9068	1.65748	0.828741	+	0.559633i	$0.189058\pi$
$192$	−1.17506	−0.0848027
$193$	27.6816	1.99257	0.996283	−	0.0861358i	$-0.0274519\pi$
$193$	27.6816	1.99257	0.996283	+	0.0861358i	$0.0274519\pi$
$194$	−1.00000	−0.0717958
$195$	2.49542	0.178701
$196$	16.0643	1.14745
$197$	13.1177	0.934600	0.467300	−	0.884099i	$-0.345227\pi$
$197$	13.1177	0.934600	0.467300	+	0.884099i	$0.345227\pi$
$198$	−10.3072	−0.732498
$199$	−0.0603103	−0.00427529	−0.00213764	−	0.999998i	$-0.500680\pi$
$199$	−0.0603103	−0.00427529	−0.00213764	+	0.999998i	$0.500680\pi$
$200$	−4.84138	−0.342337
$201$	−3.57986	−0.252504
$202$	2.50710	0.176399
$203$	39.5309	2.77452
$204$	0.394307	0.0276070
$205$	2.66784	0.186330
$206$	11.9113	0.829903
$207$	9.84455	0.684244
$208$	5.33213	0.369717
$209$	16.4895	1.14060
$210$	−2.24757	−0.155097
$211$	−12.9359	−0.890544	−0.445272	−	0.895395i	$-0.646893\pi$
$211$	−12.9359	−0.890544	−0.445272	+	0.895395i	$0.646893\pi$
$212$	2.05027	0.140813
$213$	−6.22695	−0.426664
$214$	16.4063	1.12151
$215$	0.758518	0.0517305
$216$	5.42788	0.369320
$217$	4.80253	0.326017
$218$	1.37460	0.0930998
$219$	−2.44332	−0.165104
$220$	−2.53520	−0.170923
$221$	−1.78927	−0.120359
$222$	−9.75537	−0.654738
$223$	5.68460	0.380669	0.190334	−	0.981719i	$-0.439043\pi$
$223$	5.68460	0.380669	0.190334	+	0.981719i	$0.439043\pi$
$224$	−4.80253	−0.320882
$225$	7.83932	0.522621
$226$	−12.5176	−0.832657
$227$	13.9353	0.924915	0.462458	−	0.886641i	$-0.346968\pi$
$227$	13.9353	0.924915	0.462458	+	0.886641i	$0.346968\pi$
$228$	−3.04395	−0.201590
$229$	4.57381	0.302246	0.151123	−	0.988515i	$-0.451711\pi$
$229$	4.57381	0.302246	0.151123	+	0.988515i	$0.451711\pi$
$230$	2.42142	0.159663
$231$	35.9219	2.36349
$232$	−8.23126	−0.540409
$233$	−3.06494	−0.200791	−0.100396	−	0.994948i	$-0.532011\pi$
$233$	−3.06494	−0.200791	−0.100396	+	0.994948i	$0.532011\pi$
$234$	−8.63396	−0.564420
$235$	1.35799	0.0885855
$236$	−0.494905	−0.0322156
$237$	−15.7385	−1.02233
$238$	1.61155	0.104461
$239$	−21.0181	−1.35955	−0.679774	−	0.733422i	$-0.737922\pi$
$239$	−21.0181	−1.35955	−0.679774	+	0.733422i	$0.737922\pi$
$240$	0.467997	0.0302091
$241$	0.248703	0.0160204	0.00801019	−	0.999968i	$-0.497450\pi$
$241$	0.248703	0.0160204	0.00801019	+	0.999968i	$0.497450\pi$
$242$	29.5190	1.89756
$243$	−14.4971	−0.929989
$244$	8.99436	0.575805
$245$	−6.39800	−0.408753
$246$	7.87114	0.501845
$247$	13.8127	0.878880
$248$	−1.00000	−0.0635001
$249$	10.4199	0.660336
$250$	3.91957	0.247896
$251$	15.6293	0.986510	0.493255	−	0.869885i	$-0.335807\pi$
$251$	15.6293	0.986510	0.493255	+	0.869885i	$0.335807\pi$
$252$	7.77642	0.489868
$253$	−38.7004	−2.43308
$254$	−18.9773	−1.19074
$255$	−0.157042	−0.00983438
$256$	1.00000	0.0625000
$257$	−5.70608	−0.355935	−0.177968	−	0.984036i	$-0.556952\pi$
$257$	−5.70608	−0.355935	−0.177968	+	0.984036i	$0.556952\pi$
$258$	2.23791	0.139326
$259$	−39.8707	−2.47744
$260$	−2.12365	−0.131703
$261$	13.3283	0.825003
$262$	−0.324388	−0.0200407
$263$	−15.8351	−0.976436	−0.488218	−	0.872722i	$-0.662353\pi$
$263$	−15.8351	−0.976436	−0.488218	+	0.872722i	$0.662353\pi$
$264$	−7.47979	−0.460350
$265$	−0.816571	−0.0501615
$266$	−12.4408	−0.762792
$267$	14.3555	0.878541
$268$	3.04653	0.186097
$269$	2.28126	0.139091	0.0695455	−	0.997579i	$-0.477845\pi$
$269$	2.28126	0.139091	0.0695455	+	0.997579i	$0.477845\pi$
$270$	−2.16179	−0.131562
$271$	29.8828	1.81525	0.907627	−	0.419778i	$-0.137892\pi$
$271$	29.8828	1.81525	0.907627	+	0.419778i	$0.137892\pi$
$272$	−0.335563	−0.0203465
$273$	30.0906	1.82117
$274$	11.7394	0.709206
$275$	−30.8176	−1.85837
$276$	7.14408	0.430023
$277$	−18.0434	−1.08412	−0.542061	−	0.840339i	$-0.682356\pi$
$277$	−18.0434	−1.08412	−0.542061	+	0.840339i	$0.682356\pi$
$278$	13.2380	0.793961
$279$	1.61923	0.0969410
$280$	1.91273	0.114307
$281$	28.5233	1.70156	0.850779	−	0.525524i	$-0.176131\pi$
$281$	28.5233	1.70156	0.850779	+	0.525524i	$0.176131\pi$
$282$	4.00658	0.238588
$283$	−10.2819	−0.611195	−0.305597	−	0.952161i	$-0.598856\pi$
$283$	−10.2819	−0.611195	−0.305597	+	0.952161i	$0.598856\pi$
$284$	5.29926	0.314453
$285$	1.21233	0.0718121
$286$	33.9414	2.00700
$287$	32.1697	1.89892
$288$	−1.61923	−0.0954143
$289$	−16.8874	−0.993376
$290$	3.27830	0.192509
$291$	1.17506	0.0688832
$292$	2.07932	0.121683
$293$	8.01839	0.468439	0.234220	−	0.972184i	$-0.424747\pi$
$293$	8.01839	0.468439	0.234220	+	0.972184i	$0.424747\pi$
$294$	−18.8765	−1.10090
$295$	0.197108	0.0114761
$296$	8.30202	0.482545
$297$	34.5509	2.00485
$298$	14.8200	0.858501
$299$	−32.4181	−1.87479
$300$	5.68891	0.328449
$301$	9.14646	0.527193
$302$	17.1763	0.988386
$303$	−2.94599	−0.169243
$304$	2.59046	0.148573
$305$	−3.58223	−0.205118
$306$	0.543355	0.0310615
$307$	11.0291	0.629465	0.314732	−	0.949180i	$-0.398085\pi$
$307$	11.0291	0.629465	0.314732	+	0.949180i	$0.398085\pi$
$308$	−30.5703	−1.74190
$309$	−13.9965	−0.796236
$310$	0.398275	0.0226205
$311$	19.2010	1.08879	0.544394	−	0.838830i	$-0.316760\pi$
$311$	19.2010	1.08879	0.544394	+	0.838830i	$0.316760\pi$
$312$	−6.26557	−0.354718
$313$	−14.6653	−0.828934	−0.414467	−	0.910064i	$-0.636032\pi$
$313$	−14.6653	−0.828934	−0.414467	+	0.910064i	$0.636032\pi$
$314$	2.70384	0.152587
$315$	−3.09715	−0.174505
$316$	13.3938	0.753460
$317$	−26.0725	−1.46438	−0.732189	−	0.681102i	$-0.761501\pi$
$317$	−26.0725	−1.46438	−0.732189	+	0.681102i	$0.761501\pi$
$318$	−2.40919	−0.135101
$319$	−52.3957	−2.93360
$320$	−0.398275	−0.0222642
$321$	−19.2784	−1.07602
$322$	29.1982	1.62715
$323$	−0.869263	−0.0483671
$324$	−1.52038	−0.0844656
$325$	−25.8148	−1.43195
$326$	2.04591	0.113312
$327$	−1.61524	−0.0893230
$328$	−6.69850	−0.369863
$329$	16.3751	0.902788
$330$	2.97901	0.163989
$331$	−8.51857	−0.468223	−0.234111	−	0.972210i	$-0.575218\pi$
$331$	−8.51857	−0.468223	−0.234111	+	0.972210i	$0.575218\pi$
$332$	−8.86757	−0.486671
$333$	−13.4429	−0.736667
$334$	11.2011	0.612897
$335$	−1.21336	−0.0662928
$336$	5.64326	0.307865
$337$	20.5324	1.11847	0.559234	−	0.829010i	$-0.311095\pi$
$337$	20.5324	1.11847	0.559234	+	0.829010i	$0.311095\pi$
$338$	15.4316	0.839368
$339$	14.7089	0.798878
$340$	0.133646	0.00724799
$341$	−6.36546	−0.344709
$342$	−4.19456	−0.226816
$343$	−43.5315	−2.35048
$344$	−1.90451	−0.102684
$345$	−2.84531	−0.153186
$346$	−11.5282	−0.619760
$347$	−3.13286	−0.168181	−0.0840904	−	0.996458i	$-0.526798\pi$
$347$	−3.13286	−0.168181	−0.0840904	+	0.996458i	$0.526798\pi$
$348$	9.67223	0.518486
$349$	25.5851	1.36954	0.684770	−	0.728759i	$-0.259903\pi$
$349$	25.5851	1.36954	0.684770	+	0.728759i	$0.259903\pi$
$350$	23.2509	1.24281
$351$	28.9421	1.54482
$352$	6.36546	0.339280
$353$	−21.5063	−1.14466	−0.572332	−	0.820022i	$-0.693961\pi$
$353$	−21.5063	−1.14466	−0.572332	+	0.820022i	$0.693961\pi$
$354$	0.581544	0.0309087
$355$	−2.11056	−0.112017
$356$	−12.2168	−0.647489
$357$	−1.89367	−0.100224
$358$	10.2721	0.542896
$359$	−17.9281	−0.946211	−0.473106	−	0.881006i	$-0.656867\pi$
$359$	−17.9281	−0.946211	−0.473106	+	0.881006i	$0.656867\pi$
$360$	0.644900	0.0339892
$361$	−12.2895	−0.646816
$362$	−2.37168	−0.124653
$363$	−34.6866	−1.82058
$364$	−25.6077	−1.34221
$365$	−0.828139	−0.0433468
$366$	−10.5689	−0.552446
$367$	28.3286	1.47874	0.739372	−	0.673298i	$-0.235123\pi$
$367$	28.3286	1.47874	0.739372	+	0.673298i	$0.235123\pi$
$368$	−6.07976	−0.316929
$369$	10.8464	0.564643
$370$	−3.30649	−0.171896
$371$	−9.84648	−0.511204
$372$	1.17506	0.0609240
$373$	11.0302	0.571120	0.285560	−	0.958361i	$-0.407820\pi$
$373$	11.0302	0.571120	0.285560	+	0.958361i	$0.407820\pi$
$374$	−2.13601	−0.110451
$375$	−4.60573	−0.237839
$376$	−3.40968	−0.175841
$377$	−43.8901	−2.26046
$378$	−26.0675	−1.34077
$379$	5.50368	0.282705	0.141353	−	0.989959i	$-0.454855\pi$
$379$	5.50368	0.282705	0.141353	+	0.989959i	$0.454855\pi$
$380$	−1.03172	−0.0529259
$381$	22.2995	1.14244
$382$	22.9068	1.17202
$383$	16.9592	0.866577	0.433288	−	0.901255i	$-0.357353\pi$
$383$	16.9592	0.866577	0.433288	+	0.901255i	$0.357353\pi$
$384$	−1.17506	−0.0599645
$385$	12.1754	0.620515
$386$	27.6816	1.40896
$387$	3.08384	0.156761
$388$	−1.00000	−0.0507673
$389$	6.98190	0.353996	0.176998	−	0.984211i	$-0.443361\pi$
$389$	6.98190	0.353996	0.176998	+	0.984211i	$0.443361\pi$
$390$	2.49542	0.126361
$391$	2.04014	0.103174
$392$	16.0643	0.811369
$393$	0.381175	0.0192277
$394$	13.1177	0.660862
$395$	−5.33441	−0.268403
$396$	−10.3072	−0.517954
$397$	11.9080	0.597644	0.298822	−	0.954309i	$-0.403406\pi$
$397$	11.9080	0.597644	0.298822	+	0.954309i	$0.403406\pi$
$398$	−0.0603103	−0.00302308
$399$	14.6187	0.731848
$400$	−4.84138	−0.242069
$401$	−26.1879	−1.30776	−0.653882	−	0.756597i	$-0.726861\pi$
$401$	−26.1879	−1.30776	−0.653882	+	0.756597i	$0.726861\pi$
$402$	−3.57986	−0.178547
$403$	−5.33213	−0.265612
$404$	2.50710	0.124733
$405$	0.605530	0.0300890
$406$	39.5309	1.96188
$407$	52.8461	2.61949
$408$	0.394307	0.0195211
$409$	−25.6716	−1.26938	−0.634689	−	0.772767i	$-0.718872\pi$
$409$	−25.6716	−1.26938	−0.634689	+	0.772767i	$0.718872\pi$
$410$	2.66784	0.131755
$411$	−13.7946	−0.680435
$412$	11.9113	0.586830
$413$	2.37680	0.116955
$414$	9.84455	0.483833
$415$	3.53173	0.173366
$416$	5.33213	0.261429
$417$	−15.5554	−0.761752
$418$	16.4895	0.806527
$419$	14.4584	0.706338	0.353169	−	0.935560i	$-0.385104\pi$
$419$	14.4584	0.706338	0.353169	+	0.935560i	$0.385104\pi$
$420$	−2.24757	−0.109670
$421$	20.5166	0.999918	0.499959	−	0.866049i	$-0.333348\pi$
$421$	20.5166	0.999918	0.499959	+	0.866049i	$0.333348\pi$
$422$	−12.9359	−0.629710
$423$	5.52107	0.268444
$424$	2.05027	0.0995699
$425$	1.62459	0.0788040
$426$	−6.22695	−0.301697
$427$	−43.1957	−2.09038
$428$	16.4063	0.793029
$429$	−39.8832	−1.92558
$430$	0.758518	0.0365790
$431$	12.8793	0.620375	0.310187	−	0.950675i	$-0.399608\pi$
$431$	12.8793	0.620375	0.310187	+	0.950675i	$0.399608\pi$
$432$	5.42788	0.261149
$433$	−24.1157	−1.15893	−0.579464	−	0.814998i	$-0.696738\pi$
$433$	−24.1157	−1.15893	−0.579464	+	0.814998i	$0.696738\pi$
$434$	4.80253	0.230529
$435$	−3.85220	−0.184699
$436$	1.37460	0.0658315
$437$	−15.7494	−0.753395
$438$	−2.44332	−0.116746
$439$	24.4764	1.16819	0.584097	−	0.811684i	$-0.301449\pi$
$439$	24.4764	1.16819	0.584097	+	0.811684i	$0.301449\pi$
$440$	−2.53520	−0.120861
$441$	−26.0118	−1.23866
$442$	−1.78927	−0.0851067
$443$	35.5689	1.68993	0.844966	−	0.534820i	$-0.179621\pi$
$443$	35.5689	1.68993	0.844966	+	0.534820i	$0.179621\pi$
$444$	−9.75537	−0.462969
$445$	4.86565	0.230654
$446$	5.68460	0.269174
$447$	−17.4144	−0.823674
$448$	−4.80253	−0.226898
$449$	−28.0511	−1.32381	−0.661906	−	0.749587i	$-0.730252\pi$
$449$	−28.0511	−1.32381	−0.661906	+	0.749587i	$0.730252\pi$
$450$	7.83932	0.369549
$451$	−42.6390	−2.00779
$452$	−12.5176	−0.588777
$453$	−20.1832	−0.948290
$454$	13.9353	0.654014
$455$	10.1989	0.478132
$456$	−3.04395	−0.142546
$457$	20.0959	0.940047	0.470024	−	0.882654i	$-0.344245\pi$
$457$	20.0959	0.940047	0.470024	+	0.882654i	$0.344245\pi$
$458$	4.57381	0.213720
$459$	−1.82139	−0.0850154
$460$	2.42142	0.112899
$461$	1.31220	0.0611151	0.0305576	−	0.999533i	$-0.490272\pi$
$461$	1.31220	0.0611151	0.0305576	+	0.999533i	$0.490272\pi$
$462$	35.9219	1.67124
$463$	10.2838	0.477928	0.238964	−	0.971028i	$-0.423192\pi$
$463$	10.2838	0.477928	0.238964	+	0.971028i	$0.423192\pi$
$464$	−8.23126	−0.382127
$465$	−0.467997	−0.0217028
$466$	−3.06494	−0.141981
$467$	17.0424	0.788630	0.394315	−	0.918975i	$-0.370982\pi$
$467$	17.0424	0.788630	0.394315	+	0.918975i	$0.370982\pi$
$468$	−8.63396	−0.399105
$469$	−14.6311	−0.675599
$470$	1.35799	0.0626394
$471$	−3.17718	−0.146397
$472$	−0.494905	−0.0227799
$473$	−12.1231	−0.557419
$474$	−15.7385	−0.722894
$475$	−12.5414	−0.575439
$476$	1.61155	0.0738653
$477$	−3.31986	−0.152006
$478$	−21.0181	−0.961346
$479$	22.1225	1.01080	0.505402	−	0.862884i	$-0.331344\pi$
$479$	22.1225	1.01080	0.505402	+	0.862884i	$0.331344\pi$
$480$	0.467997	0.0213610
$481$	44.2674	2.01842
$482$	0.248703	0.0113281
$483$	−34.3097	−1.56114
$484$	29.5190	1.34177
$485$	0.398275	0.0180847
$486$	−14.4971	−0.657601
$487$	16.0666	0.728047	0.364023	−	0.931390i	$-0.381403\pi$
$487$	16.0666	0.728047	0.364023	+	0.931390i	$0.381403\pi$
$488$	8.99436	0.407155
$489$	−2.40406	−0.108716
$490$	−6.39800	−0.289032
$491$	9.85952	0.444954	0.222477	−	0.974938i	$-0.428586\pi$
$491$	9.85952	0.444954	0.222477	+	0.974938i	$0.428586\pi$
$492$	7.87114	0.354858
$493$	2.76211	0.124399
$494$	13.8127	0.621462
$495$	4.10508	0.184510
$496$	−1.00000	−0.0449013
$497$	−25.4499	−1.14158
$498$	10.4199	0.466928
$499$	−18.3547	−0.821669	−0.410834	−	0.911710i	$-0.634763\pi$
$499$	−18.3547	−0.821669	−0.410834	+	0.911710i	$0.634763\pi$
$500$	3.91957	0.175289
$501$	−13.1620	−0.588033
$502$	15.6293	0.697568
$503$	1.86340	0.0830849	0.0415425	−	0.999137i	$-0.486773\pi$
$503$	1.86340	0.0830849	0.0415425	+	0.999137i	$0.486773\pi$
$504$	7.77642	0.346389
$505$	−0.998515	−0.0444333
$506$	−38.7004	−1.72044
$507$	−18.1331	−0.805317
$508$	−18.9773	−0.841982
$509$	−27.0641	−1.19960	−0.599798	−	0.800152i	$-0.704752\pi$
$509$	−27.0641	−1.19960	−0.599798	+	0.800152i	$0.704752\pi$
$510$	−0.157042	−0.00695396
$511$	−9.98597	−0.441753
$512$	1.00000	0.0441942
$513$	14.0607	0.620796
$514$	−5.70608	−0.251684
$515$	−4.74399	−0.209045
$516$	2.23791	0.0985186
$517$	−21.7042	−0.954549
$518$	−39.8707	−1.75182
$519$	13.5463	0.594618
$520$	−2.12365	−0.0931283
$521$	−44.4632	−1.94797	−0.973985	−	0.226613i	$-0.927235\pi$
$521$	−44.4632	−1.94797	−0.973985	+	0.226613i	$0.927235\pi$
$522$	13.3283	0.583365
$523$	−31.3852	−1.37238	−0.686189	−	0.727423i	$-0.740718\pi$
$523$	−31.3852	−1.37238	−0.686189	+	0.727423i	$0.740718\pi$
$524$	−0.324388	−0.0141709
$525$	−27.3212	−1.19239
$526$	−15.8351	−0.690445
$527$	0.335563	0.0146174
$528$	−7.47979	−0.325516
$529$	13.9635	0.607108
$530$	−0.816571	−0.0354696
$531$	0.801368	0.0347764
$532$	−12.4408	−0.539376
$533$	−35.7172	−1.54709
$534$	14.3555	0.621222
$535$	−6.53422	−0.282499
$536$	3.04653	0.131590
$537$	−12.0703	−0.520872
$538$	2.28126	0.0983522
$539$	102.256	4.40450
$540$	−2.16179	−0.0930285
$541$	−1.87276	−0.0805163	−0.0402582	−	0.999189i	$-0.512818\pi$
$541$	−1.87276	−0.0805163	−0.0402582	+	0.999189i	$0.512818\pi$
$542$	29.8828	1.28358
$543$	2.78687	0.119596
$544$	−0.335563	−0.0143871
$545$	−0.547470	−0.0234510
$546$	30.0906	1.28776
$547$	−24.1717	−1.03351	−0.516753	−	0.856135i	$-0.672859\pi$
$547$	−24.1717	−1.03351	−0.516753	+	0.856135i	$0.672859\pi$
$548$	11.7394	0.501484
$549$	−14.5640	−0.621575
$550$	−30.8176	−1.31407
$551$	−21.3228	−0.908380
$552$	7.14408	0.304072
$553$	−64.3241	−2.73534
$554$	−18.0434	−0.766591
$555$	3.88532	0.164923
$556$	13.2380	0.561415
$557$	−37.7404	−1.59911	−0.799556	−	0.600591i	$-0.794932\pi$
$557$	−37.7404	−1.59911	−0.799556	+	0.600591i	$0.794932\pi$
$558$	1.61923	0.0685476
$559$	−10.1551	−0.429514
$560$	1.91273	0.0808275
$561$	2.50994	0.105970
$562$	28.5233	1.20318
$563$	−2.71467	−0.114410	−0.0572048	−	0.998362i	$-0.518219\pi$
$563$	−2.71467	−0.114410	−0.0572048	+	0.998362i	$0.518219\pi$
$564$	4.00658	0.168707
$565$	4.98544	0.209739
$566$	−10.2819	−0.432180
$567$	7.30168	0.306642
$568$	5.29926	0.222352
$569$	39.6296	1.66136	0.830679	−	0.556751i	$-0.187952\pi$
$569$	39.6296	1.66136	0.830679	+	0.556751i	$0.187952\pi$
$570$	1.21233	0.0507788
$571$	1.46922	0.0614848	0.0307424	−	0.999527i	$-0.490213\pi$
$571$	1.46922	0.0614848	0.0307424	+	0.999527i	$0.490213\pi$
$572$	33.9414	1.41916
$573$	−26.9169	−1.12447
$574$	32.1697	1.34274
$575$	29.4344	1.22750
$576$	−1.61923	−0.0674681
$577$	−10.0065	−0.416574	−0.208287	−	0.978068i	$-0.566789\pi$
$577$	−10.0065	−0.416574	−0.208287	+	0.978068i	$0.566789\pi$
$578$	−16.8874	−0.702423
$579$	−32.5276	−1.35180
$580$	3.27830	0.136124
$581$	42.5868	1.76680
$582$	1.17506	0.0487078
$583$	13.0509	0.540513
$584$	2.07932	0.0860427
$585$	3.43869	0.142172
$586$	8.01839	0.331237
$587$	33.5048	1.38289	0.691445	−	0.722429i	$-0.256974\pi$
$587$	33.5048	1.38289	0.691445	+	0.722429i	$0.256974\pi$
$588$	−18.8765	−0.778454
$589$	−2.59046	−0.106738
$590$	0.197108	0.00811482
$591$	−15.4141	−0.634052
$592$	8.30202	0.341211
$593$	4.11234	0.168874	0.0844368	−	0.996429i	$-0.473091\pi$
$593$	4.11234	0.168874	0.0844368	+	0.996429i	$0.473091\pi$
$594$	34.5509	1.41764
$595$	−0.641840	−0.0263129
$596$	14.8200	0.607052
$597$	0.0708683	0.00290044
$598$	−32.4181	−1.32567
$599$	−41.0723	−1.67817	−0.839085	−	0.544000i	$-0.816909\pi$
$599$	−41.0723	−1.67817	−0.839085	+	0.544000i	$0.816909\pi$
$600$	5.68891	0.232249
$601$	−29.1637	−1.18961	−0.594806	−	0.803869i	$-0.702771\pi$
$601$	−29.1637	−1.18961	−0.594806	+	0.803869i	$0.702771\pi$
$602$	9.14646	0.372782
$603$	−4.93305	−0.200889
$604$	17.1763	0.698895
$605$	−11.7567	−0.477977
$606$	−2.94599	−0.119673
$607$	−8.80736	−0.357480	−0.178740	−	0.983896i	$-0.557202\pi$
$607$	−8.80736	−0.357480	−0.178740	+	0.983896i	$0.557202\pi$
$608$	2.59046	0.105057
$609$	−46.4511	−1.88230
$610$	−3.58223	−0.145040
$611$	−18.1809	−0.735519
$612$	0.543355	0.0219638
$613$	−39.6200	−1.60023	−0.800117	−	0.599843i	$-0.795230\pi$
$613$	−39.6200	−1.60023	−0.800117	+	0.599843i	$0.795230\pi$
$614$	11.0291	0.445099
$615$	−3.13488	−0.126410
$616$	−30.5703	−1.23171
$617$	5.26550	0.211981	0.105990	−	0.994367i	$-0.466199\pi$
$617$	5.26550	0.211981	0.105990	+	0.994367i	$0.466199\pi$
$618$	−13.9965	−0.563024
$619$	−27.8707	−1.12022	−0.560109	−	0.828419i	$-0.689241\pi$
$619$	−27.8707	−1.12022	−0.560109	+	0.828419i	$0.689241\pi$
$620$	0.398275	0.0159951
$621$	−33.0002	−1.32425
$622$	19.2010	0.769889
$623$	58.6716	2.35063
$624$	−6.26557	−0.250824
$625$	22.6458	0.905833
$626$	−14.6653	−0.586145
$627$	−19.3761	−0.773808
$628$	2.70384	0.107895
$629$	−2.78585	−0.111079
$630$	−3.09715	−0.123393
$631$	28.8332	1.14783	0.573916	−	0.818914i	$-0.305424\pi$
$631$	28.8332	1.14783	0.573916	+	0.818914i	$0.305424\pi$
$632$	13.3938	0.532777
$633$	15.2005	0.604164
$634$	−26.0725	−1.03547
$635$	7.55819	0.299937
$636$	−2.40919	−0.0955306
$637$	85.6568	3.39385
$638$	−52.3957	−2.07437
$639$	−8.58074	−0.339449
$640$	−0.398275	−0.0157432
$641$	40.5313	1.60089	0.800445	−	0.599407i	$-0.204597\pi$
$641$	40.5313	1.60089	0.800445	+	0.599407i	$0.204597\pi$
$642$	−19.2784	−0.760858
$643$	40.7705	1.60783	0.803916	−	0.594743i	$-0.202746\pi$
$643$	40.7705	1.60783	0.803916	+	0.594743i	$0.202746\pi$
$644$	29.1982	1.15057
$645$	−0.891304	−0.0350951
$646$	−0.869263	−0.0342007
$647$	−30.0963	−1.18321	−0.591603	−	0.806229i	$-0.701505\pi$
$647$	−30.0963	−1.18321	−0.591603	+	0.806229i	$0.701505\pi$
$648$	−1.52038	−0.0597262
$649$	−3.15030	−0.123660
$650$	−25.8148	−1.01254
$651$	−5.64326	−0.221177
$652$	2.04591	0.0801239
$653$	−9.48255	−0.371081	−0.185540	−	0.982637i	$-0.559404\pi$
$653$	−9.48255	−0.371081	−0.185540	+	0.982637i	$0.559404\pi$
$654$	−1.61524	−0.0631609
$655$	0.129195	0.00504808
$656$	−6.69850	−0.261532
$657$	−3.36690	−0.131355
$658$	16.3751	0.638368
$659$	−23.0633	−0.898417	−0.449209	−	0.893427i	$-0.648294\pi$
$659$	−23.0633	−0.898417	−0.449209	+	0.893427i	$0.648294\pi$
$660$	2.97901	0.115958
$661$	33.1702	1.29017	0.645086	−	0.764110i	$-0.276821\pi$
$661$	33.1702	1.29017	0.645086	+	0.764110i	$0.276821\pi$
$662$	−8.51857	−0.331084
$663$	2.10249	0.0816541
$664$	−8.86757	−0.344128
$665$	4.95485	0.192141
$666$	−13.4429	−0.520902
$667$	50.0441	1.93771
$668$	11.2011	0.433384
$669$	−6.67975	−0.258254
$670$	−1.21336	−0.0468761
$671$	57.2532	2.21024
$672$	5.64326	0.217693
$673$	−26.5577	−1.02373	−0.511863	−	0.859067i	$-0.671044\pi$
$673$	−26.5577	−1.02373	−0.511863	+	0.859067i	$0.671044\pi$
$674$	20.5324	0.790877
$675$	−26.2784	−1.01146
$676$	15.4316	0.593523
$677$	25.2852	0.971789	0.485894	−	0.874018i	$-0.338494\pi$
$677$	25.2852	0.971789	0.485894	+	0.874018i	$0.338494\pi$
$678$	14.7089	0.564892
$679$	4.80253	0.184304
$680$	0.133646	0.00512510
$681$	−16.3748	−0.627482
$682$	−6.36546	−0.243746
$683$	−32.7148	−1.25180	−0.625898	−	0.779905i	$-0.715267\pi$
$683$	−32.7148	−1.25180	−0.625898	+	0.779905i	$0.715267\pi$
$684$	−4.19456	−0.160383
$685$	−4.67553	−0.178643
$686$	−43.5315	−1.66204
$687$	−5.37450	−0.205050
$688$	−1.90451	−0.0726087
$689$	10.9323	0.416487
$690$	−2.84531	−0.108319
$691$	−31.8761	−1.21262	−0.606312	−	0.795227i	$-0.707352\pi$
$691$	−31.8761	−1.21262	−0.606312	+	0.795227i	$0.707352\pi$
$692$	−11.5282	−0.438236
$693$	49.5004	1.88037
$694$	−3.13286	−0.118922
$695$	−5.27235	−0.199992
$696$	9.67223	0.366625
$697$	2.24777	0.0851403
$698$	25.5851	0.968411
$699$	3.60149	0.136221
$700$	23.2509	0.878800
$701$	25.9185	0.978929	0.489465	−	0.872023i	$-0.337192\pi$
$701$	25.9185	0.978929	0.489465	+	0.872023i	$0.337192\pi$
$702$	28.9421	1.09235
$703$	21.5061	0.811117
$704$	6.36546	0.239907
$705$	−1.59572	−0.0600983
$706$	−21.5063	−0.809399
$707$	−12.0404	−0.452827
$708$	0.581544	0.0218557
$709$	−24.8714	−0.934065	−0.467033	−	0.884240i	$-0.654677\pi$
$709$	−24.8714	−0.934065	−0.467033	+	0.884240i	$0.654677\pi$
$710$	−2.11056	−0.0792080
$711$	−21.6877	−0.813352
$712$	−12.2168	−0.457844
$713$	6.07976	0.227689
$714$	−1.89367	−0.0708688
$715$	−13.5180	−0.505545
$716$	10.2721	0.383886
$717$	24.6975	0.922346
$718$	−17.9281	−0.669072
$719$	0.509297	0.0189936	0.00949679	−	0.999955i	$-0.496977\pi$
$719$	0.509297	0.0189936	0.00949679	+	0.999955i	$0.496977\pi$
$720$	0.644900	0.0240340
$721$	−57.2046	−2.13041
$722$	−12.2895	−0.457368
$723$	−0.292241	−0.0108686
$724$	−2.37168	−0.0881428
$725$	39.8506	1.48002
$726$	−34.6866	−1.28734
$727$	39.8257	1.47705	0.738526	−	0.674225i	$-0.235522\pi$
$727$	39.8257	1.47705	0.738526	+	0.674225i	$0.235522\pi$
$728$	−25.6077	−0.949085
$729$	21.5961	0.799856
$730$	−0.828139	−0.0306508
$731$	0.639083	0.0236373
$732$	−10.5689	−0.390638
$733$	−45.1484	−1.66759	−0.833797	−	0.552071i	$-0.813838\pi$
$733$	−45.1484	−1.66759	−0.833797	+	0.552071i	$0.813838\pi$
$734$	28.3286	1.04563
$735$	7.51804	0.277307
$736$	−6.07976	−0.224103
$737$	19.3926	0.714334
$738$	10.8464	0.399263
$739$	−6.06506	−0.223107	−0.111553	−	0.993758i	$-0.535583\pi$
$739$	−6.06506	−0.223107	−0.111553	+	0.993758i	$0.535583\pi$
$740$	−3.30649	−0.121549
$741$	−16.2307	−0.596251
$742$	−9.84648	−0.361476
$743$	−7.17594	−0.263260	−0.131630	−	0.991299i	$-0.542021\pi$
$743$	−7.17594	−0.263260	−0.131630	+	0.991299i	$0.542021\pi$
$744$	1.17506	0.0430798
$745$	−5.90244	−0.216249
$746$	11.0302	0.403843
$747$	14.3587	0.525356
$748$	−2.13601	−0.0781003
$749$	−78.7918	−2.87899
$750$	−4.60573	−0.168178
$751$	17.5413	0.640090	0.320045	−	0.947402i	$-0.396302\pi$
$751$	17.5413	0.640090	0.320045	+	0.947402i	$0.396302\pi$
$752$	−3.40968	−0.124338
$753$	−18.3653	−0.669270
$754$	−43.8901	−1.59838
$755$	−6.84090	−0.248966
$756$	−26.0675	−0.948067
$757$	−52.6425	−1.91332	−0.956662	−	0.291202i	$-0.905945\pi$
$757$	−52.6425	−1.91332	−0.956662	+	0.291202i	$0.905945\pi$
$758$	5.50368	0.199903
$759$	45.4754	1.65065
$760$	−1.03172	−0.0374243
$761$	26.4963	0.960490	0.480245	−	0.877134i	$-0.340548\pi$
$761$	26.4963	0.960490	0.480245	+	0.877134i	$0.340548\pi$
$762$	22.2995	0.807825
$763$	−6.60157	−0.238993
$764$	22.9068	0.828741
$765$	−0.216405	−0.00782413
$766$	16.9592	0.612762
$767$	−2.63890	−0.0952851
$768$	−1.17506	−0.0424013
$769$	3.09513	0.111613	0.0558066	−	0.998442i	$-0.482227\pi$
$769$	3.09513	0.111613	0.0558066	+	0.998442i	$0.482227\pi$
$770$	12.1754	0.438770
$771$	6.70498	0.241474
$772$	27.6816	0.996283
$773$	−4.12080	−0.148215	−0.0741074	−	0.997250i	$-0.523611\pi$
$773$	−4.12080	−0.148215	−0.0741074	+	0.997250i	$0.523611\pi$
$774$	3.08384	0.110846
$775$	4.84138	0.173907
$776$	−1.00000	−0.0358979
$777$	46.8505	1.68075
$778$	6.98190	0.250313
$779$	−17.3522	−0.621707
$780$	2.49542	0.0893504
$781$	33.7322	1.20703
$782$	2.04014	0.0729553
$783$	−44.6783	−1.59667
$784$	16.0643	0.573724
$785$	−1.07687	−0.0384353
$786$	0.381175	0.0135961
$787$	31.4215	1.12006	0.560029	−	0.828473i	$-0.310790\pi$
$787$	31.4215	1.12006	0.560029	+	0.828473i	$0.310790\pi$
$788$	13.1177	0.467300
$789$	18.6072	0.662435
$790$	−5.33441	−0.189790
$791$	60.1160	2.13748
$792$	−10.3072	−0.366249
$793$	47.9591	1.70308
$794$	11.9080	0.422598
$795$	0.959520	0.0340307
$796$	−0.0603103	−0.00213764
$797$	7.63192	0.270336	0.135168	−	0.990823i	$-0.456843\pi$
$797$	7.63192	0.270336	0.135168	+	0.990823i	$0.456843\pi$
$798$	14.6187	0.517495
$799$	1.14416	0.0404776
$800$	−4.84138	−0.171169
$801$	19.7819	0.698958
$802$	−26.1879	−0.924729
$803$	13.2358	0.467081
$804$	−3.57986	−0.126252
$805$	−11.6289	−0.409866
$806$	−5.33213	−0.187816
$807$	−2.68062	−0.0943623
$808$	2.50710	0.0881995
$809$	−20.4519	−0.719050	−0.359525	−	0.933136i	$-0.617061\pi$
$809$	−20.4519	−0.719050	−0.359525	+	0.933136i	$0.617061\pi$
$810$	0.605530	0.0212761
$811$	37.7420	1.32530	0.662650	−	0.748929i	$-0.269432\pi$
$811$	37.7420	1.32530	0.662650	+	0.748929i	$0.269432\pi$
$812$	39.5309	1.38726
$813$	−35.1141	−1.23151
$814$	52.8461	1.85226
$815$	−0.814834	−0.0285424
$816$	0.394307	0.0138035
$817$	−4.93356	−0.172603
$818$	−25.6716	−0.897586
$819$	41.4649	1.44890
$820$	2.66784	0.0931651
$821$	−19.2654	−0.672368	−0.336184	−	0.941796i	$-0.609136\pi$
$821$	−19.2654	−0.672368	−0.336184	+	0.941796i	$0.609136\pi$
$822$	−13.7946	−0.481140
$823$	1.36862	0.0477071	0.0238535	−	0.999715i	$-0.492406\pi$
$823$	1.36862	0.0477071	0.0238535	+	0.999715i	$0.492406\pi$
$824$	11.9113	0.414951
$825$	36.2125	1.26076
$826$	2.37680	0.0826994
$827$	−16.1357	−0.561093	−0.280547	−	0.959840i	$-0.590516\pi$
$827$	−16.1357	−0.561093	−0.280547	+	0.959840i	$0.590516\pi$
$828$	9.84455	0.342122
$829$	46.3736	1.61062	0.805311	−	0.592852i	$-0.201998\pi$
$829$	46.3736	1.61062	0.805311	+	0.592852i	$0.201998\pi$
$830$	3.53173	0.122588
$831$	21.2021	0.735492
$832$	5.33213	0.184858
$833$	−5.39058	−0.186772
$834$	−15.5554	−0.538640
$835$	−4.46112	−0.154383
$836$	16.4895	0.570300
$837$	−5.42788	−0.187615
$838$	14.4584	0.499456
$839$	20.2806	0.700163	0.350081	−	0.936719i	$-0.386154\pi$
$839$	20.2806	0.700163	0.350081	+	0.936719i	$0.386154\pi$
$840$	−2.24757	−0.0775485
$841$	38.7537	1.33633
$842$	20.5166	0.707049
$843$	−33.5166	−1.15437
$844$	−12.9359	−0.445272
$845$	−6.14602	−0.211429
$846$	5.52107	0.189818
$847$	−141.766	−4.87114
$848$	2.05027	0.0704065
$849$	12.0818	0.414647
$850$	1.62459	0.0557229
$851$	−50.4743	−1.73024
$852$	−6.22695	−0.213332
$853$	33.2000	1.13675	0.568373	−	0.822771i	$-0.307573\pi$
$853$	33.2000	1.13675	0.568373	+	0.822771i	$0.307573\pi$
$854$	−43.1957	−1.47813
$855$	1.67059	0.0571329
$856$	16.4063	0.560756
$857$	15.9972	0.546455	0.273228	−	0.961949i	$-0.411909\pi$
$857$	15.9972	0.546455	0.273228	+	0.961949i	$0.411909\pi$
$858$	−39.8832	−1.36159
$859$	50.2310	1.71386	0.856930	−	0.515433i	$-0.172369\pi$
$859$	50.2310	1.71386	0.856930	+	0.515433i	$0.172369\pi$
$860$	0.758518	0.0258652
$861$	−37.8014	−1.28827
$862$	12.8793	0.438671
$863$	−38.7766	−1.31997	−0.659985	−	0.751278i	$-0.729438\pi$
$863$	−38.7766	−1.31997	−0.659985	+	0.751278i	$0.729438\pi$
$864$	5.42788	0.184660
$865$	4.59139	0.156112
$866$	−24.1157	−0.819486
$867$	19.8437	0.673928
$868$	4.80253	0.163008
$869$	85.2576	2.89217
$870$	−3.85220	−0.130602
$871$	16.2445	0.550424
$872$	1.37460	0.0465499
$873$	1.61923	0.0548028
$874$	−15.7494	−0.532731
$875$	−18.8239	−0.636363
$876$	−2.44332	−0.0825522
$877$	−26.4571	−0.893394	−0.446697	−	0.894685i	$-0.647400\pi$
$877$	−26.4571	−0.893394	−0.446697	+	0.894685i	$0.647400\pi$
$878$	24.4764	0.826038
$879$	−9.42209	−0.317799
$880$	−2.53520	−0.0854616
$881$	−24.9281	−0.839847	−0.419924	−	0.907559i	$-0.637943\pi$
$881$	−24.9281	−0.839847	−0.419924	+	0.907559i	$0.637943\pi$
$882$	−26.0118	−0.875864
$883$	13.8772	0.467006	0.233503	−	0.972356i	$-0.424981\pi$
$883$	13.8772	0.467006	0.233503	+	0.972356i	$0.424981\pi$
$884$	−1.78927	−0.0601795
$885$	−0.231614	−0.00778563
$886$	35.5689	1.19496
$887$	7.32025	0.245790	0.122895	−	0.992420i	$-0.460782\pi$
$887$	7.32025	0.245790	0.122895	+	0.992420i	$0.460782\pi$
$888$	−9.75537	−0.327369
$889$	91.1391	3.05671
$890$	4.86565	0.163097
$891$	−9.67792	−0.324223
$892$	5.68460	0.190334
$893$	−8.83265	−0.295573
$894$	−17.4144	−0.582425
$895$	−4.09111	−0.136751
$896$	−4.80253	−0.160441
$897$	38.0932	1.27189
$898$	−28.0511	−0.936076
$899$	8.23126	0.274528
$900$	7.83932	0.261311
$901$	−0.687994	−0.0229204
$902$	−42.6390	−1.41972
$903$	−10.7476	−0.357659
$904$	−12.5176	−0.416328
$905$	0.944581	0.0313989
$906$	−20.1832	−0.670542
$907$	−29.2082	−0.969841	−0.484920	−	0.874558i	$-0.661151\pi$
$907$	−29.2082	−0.969841	−0.484920	+	0.874558i	$0.661151\pi$
$908$	13.9353	0.462458
$909$	−4.05958	−0.134648
$910$	10.1989	0.338090
$911$	9.74967	0.323021	0.161511	−	0.986871i	$-0.448363\pi$
$911$	9.74967	0.323021	0.161511	+	0.986871i	$0.448363\pi$
$912$	−3.04395	−0.100795
$913$	−56.4461	−1.86809
$914$	20.0959	0.664714
$915$	4.20933	0.139156
$916$	4.57381	0.151123
$917$	1.55788	0.0514458
$918$	−1.82139	−0.0601150
$919$	−32.4277	−1.06969	−0.534846	−	0.844949i	$-0.679630\pi$
$919$	−32.4277	−1.06969	−0.534846	+	0.844949i	$0.679630\pi$
$920$	2.42142	0.0798317
$921$	−12.9599	−0.427042
$922$	1.31220	0.0432149
$923$	28.2563	0.930069
$924$	35.9219	1.18174
$925$	−40.1932	−1.32154
$926$	10.2838	0.337946
$927$	−19.2872	−0.633476
$928$	−8.23126	−0.270204
$929$	−17.0318	−0.558794	−0.279397	−	0.960176i	$-0.590135\pi$
$929$	−17.0318	−0.558794	−0.279397	+	0.960176i	$0.590135\pi$
$930$	−0.467997	−0.0153462
$931$	41.6139	1.36384
$932$	−3.06494	−0.100396
$933$	−22.5623	−0.738657
$934$	17.0424	0.557646
$935$	0.850720	0.0278215
$936$	−8.63396	−0.282210
$937$	1.61998	0.0529225	0.0264612	−	0.999650i	$-0.491576\pi$
$937$	1.61998	0.0529225	0.0264612	+	0.999650i	$0.491576\pi$
$938$	−14.6311	−0.477721
$939$	17.2326	0.562366
$940$	1.35799	0.0442928
$941$	57.7433	1.88238	0.941188	−	0.337883i	$-0.109711\pi$
$941$	57.7433	1.88238	0.941188	+	0.337883i	$0.109711\pi$
$942$	−3.17718	−0.103518
$943$	40.7253	1.32620
$944$	−0.494905	−0.0161078
$945$	10.3820	0.337728
$946$	−12.1231	−0.394155
$947$	0.403886	0.0131245	0.00656227	−	0.999978i	$-0.497911\pi$
$947$	0.403886	0.0131245	0.00656227	+	0.999978i	$0.497911\pi$
$948$	−15.7385	−0.511163
$949$	11.0872	0.359905
$950$	−12.5414	−0.406897
$951$	30.6367	0.993465
$952$	1.61155	0.0522307
$953$	9.58979	0.310644	0.155322	−	0.987864i	$-0.450359\pi$
$953$	9.58979	0.310644	0.155322	+	0.987864i	$0.450359\pi$
$954$	−3.31986	−0.107485
$955$	−9.12322	−0.295221
$956$	−21.0181	−0.679774
$957$	61.5681	1.99022
$958$	22.1225	0.714747
$959$	−56.3790	−1.82057
$960$	0.467997	0.0151045
$961$	1.00000	0.0322581
$962$	44.2674	1.42724
$963$	−26.5656	−0.856066
$964$	0.248703	0.00801019
$965$	−11.0249	−0.354904
$966$	−34.3097	−1.10390
$967$	57.2012	1.83947	0.919733	−	0.392544i	$-0.128405\pi$
$967$	57.2012	1.83947	0.919733	+	0.392544i	$0.128405\pi$
$968$	29.5190	0.948778
$969$	1.02144	0.0328133
$970$	0.398275	0.0127878
$971$	−1.57383	−0.0505066	−0.0252533	−	0.999681i	$-0.508039\pi$
$971$	−1.57383	−0.0505066	−0.0252533	+	0.999681i	$0.508039\pi$
$972$	−14.4971	−0.464994
$973$	−63.5758	−2.03815
$974$	16.0666	0.514807
$975$	30.3340	0.971465
$976$	8.99436	0.287902
$977$	−9.66925	−0.309347	−0.154673	−	0.987966i	$-0.549432\pi$
$977$	−9.66925	−0.309347	−0.154673	+	0.987966i	$0.549432\pi$
$978$	−2.40406	−0.0768735
$979$	−77.7655	−2.48540
$980$	−6.39800	−0.204377
$981$	−2.22580	−0.0710644
$982$	9.85952	0.314630
$983$	7.49377	0.239014	0.119507	−	0.992833i	$-0.461869\pi$
$983$	7.49377	0.239014	0.119507	+	0.992833i	$0.461869\pi$
$984$	7.87114	0.250923
$985$	−5.22446	−0.166465
$986$	2.76211	0.0879634
$987$	−19.2417	−0.612471
$988$	13.8127	0.439440
$989$	11.5790	0.368189
$990$	4.10508	0.130468
$991$	−19.3935	−0.616055	−0.308027	−	0.951377i	$-0.599669\pi$
$991$	−19.3935	−0.616055	−0.308027	+	0.951377i	$0.599669\pi$
$992$	−1.00000	−0.0317500
$993$	10.0098	0.317652
$994$	−25.4499	−0.807221
$995$	0.0240201	0.000761488 0
$996$	10.4199	0.330168
$997$	−2.09582	−0.0663751	−0.0331876	−	0.999449i	$-0.510566\pi$
$997$	−2.09582	−0.0663751	−0.0331876	+	0.999449i	$0.510566\pi$
$998$	−18.3547	−0.581007
$999$	45.0623	1.42571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.i.1.9	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.i.1.9	✓	28	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.17506 q^{3} +1.00000 q^{4} -0.398275 q^{5} -1.17506 q^{6} -4.80253 q^{7} +1.00000 q^{8} -1.61923 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.17506 q^{3} +1.00000 q^{4} -0.398275 q^{5} -1.17506 q^{6} -4.80253 q^{7} +1.00000 q^{8} -1.61923 q^{9} -0.398275 q^{10} +6.36546 q^{11} -1.17506 q^{12} +5.33213 q^{13} -4.80253 q^{14} +0.467997 q^{15} +1.00000 q^{16} -0.335563 q^{17} -1.61923 q^{18} +2.59046 q^{19} -0.398275 q^{20} +5.64326 q^{21} +6.36546 q^{22} -6.07976 q^{23} -1.17506 q^{24} -4.84138 q^{25} +5.33213 q^{26} +5.42788 q^{27} -4.80253 q^{28} -8.23126 q^{29} +0.467997 q^{30} -1.00000 q^{31} +1.00000 q^{32} -7.47979 q^{33} -0.335563 q^{34} +1.91273 q^{35} -1.61923 q^{36} +8.30202 q^{37} +2.59046 q^{38} -6.26557 q^{39} -0.398275 q^{40} -6.69850 q^{41} +5.64326 q^{42} -1.90451 q^{43} +6.36546 q^{44} +0.644900 q^{45} -6.07976 q^{46} -3.40968 q^{47} -1.17506 q^{48} +16.0643 q^{49} -4.84138 q^{50} +0.394307 q^{51} +5.33213 q^{52} +2.05027 q^{53} +5.42788 q^{54} -2.53520 q^{55} -4.80253 q^{56} -3.04395 q^{57} -8.23126 q^{58} -0.494905 q^{59} +0.467997 q^{60} +8.99436 q^{61} -1.00000 q^{62} +7.77642 q^{63} +1.00000 q^{64} -2.12365 q^{65} -7.47979 q^{66} +3.04653 q^{67} -0.335563 q^{68} +7.14408 q^{69} +1.91273 q^{70} +5.29926 q^{71} -1.61923 q^{72} +2.07932 q^{73} +8.30202 q^{74} +5.68891 q^{75} +2.59046 q^{76} -30.5703 q^{77} -6.26557 q^{78} +13.3938 q^{79} -0.398275 q^{80} -1.52038 q^{81} -6.69850 q^{82} -8.86757 q^{83} +5.64326 q^{84} +0.133646 q^{85} -1.90451 q^{86} +9.67223 q^{87} +6.36546 q^{88} -12.2168 q^{89} +0.644900 q^{90} -25.6077 q^{91} -6.07976 q^{92} +1.17506 q^{93} -3.40968 q^{94} -1.03172 q^{95} -1.17506 q^{96} -1.00000 q^{97} +16.0643 q^{98} -10.3072 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * q^99

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