LMFDB - Embedded newform 6013.2.a.f.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09677 q^{2} -1.04747 q^{3} +2.39646 q^{4} -2.55395 q^{5} +2.19632 q^{6} -1.00000 q^{7} -0.831292 q^{8} -1.90280 q^{9} +O(q^{10})$	\(q-2.09677 q^{2} -1.04747 q^{3} +2.39646 q^{4} -2.55395 q^{5} +2.19632 q^{6} -1.00000 q^{7} -0.831292 q^{8} -1.90280 q^{9} +5.35506 q^{10} +1.88656 q^{11} -2.51023 q^{12} +5.49219 q^{13} +2.09677 q^{14} +2.67520 q^{15} -3.04989 q^{16} +0.721010 q^{17} +3.98974 q^{18} +0.786479 q^{19} -6.12045 q^{20} +1.04747 q^{21} -3.95569 q^{22} +5.34471 q^{23} +0.870757 q^{24} +1.52266 q^{25} -11.5159 q^{26} +5.13556 q^{27} -2.39646 q^{28} +2.98527 q^{29} -5.60929 q^{30} +6.72786 q^{31} +8.05752 q^{32} -1.97612 q^{33} -1.51180 q^{34} +2.55395 q^{35} -4.55998 q^{36} +1.70771 q^{37} -1.64907 q^{38} -5.75293 q^{39} +2.12308 q^{40} +12.2169 q^{41} -2.19632 q^{42} -6.38633 q^{43} +4.52107 q^{44} +4.85965 q^{45} -11.2066 q^{46} -7.19218 q^{47} +3.19469 q^{48} +1.00000 q^{49} -3.19268 q^{50} -0.755240 q^{51} +13.1618 q^{52} +4.78220 q^{53} -10.7681 q^{54} -4.81818 q^{55} +0.831292 q^{56} -0.823817 q^{57} -6.25944 q^{58} +4.23016 q^{59} +6.41101 q^{60} -0.608969 q^{61} -14.1068 q^{62} +1.90280 q^{63} -10.7950 q^{64} -14.0268 q^{65} +4.14349 q^{66} +14.7406 q^{67} +1.72787 q^{68} -5.59845 q^{69} -5.35506 q^{70} -1.42316 q^{71} +1.58178 q^{72} -3.73150 q^{73} -3.58068 q^{74} -1.59495 q^{75} +1.88477 q^{76} -1.88656 q^{77} +12.0626 q^{78} +9.28985 q^{79} +7.78928 q^{80} +0.329027 q^{81} -25.6160 q^{82} -0.304575 q^{83} +2.51023 q^{84} -1.84142 q^{85} +13.3907 q^{86} -3.12699 q^{87} -1.56828 q^{88} +10.7676 q^{89} -10.1896 q^{90} -5.49219 q^{91} +12.8084 q^{92} -7.04726 q^{93} +15.0804 q^{94} -2.00863 q^{95} -8.44005 q^{96} -16.7172 q^{97} -2.09677 q^{98} -3.58974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.09677	−1.48264	−0.741322	−	0.671150i	$-0.765801\pi$
$2$	−2.09677	−1.48264	−0.741322	+	0.671150i	$0.765801\pi$
$3$	−1.04747	−0.604760	−0.302380	−	0.953188i	$-0.597781\pi$
$3$	−1.04747	−0.604760	−0.302380	+	0.953188i	$0.597781\pi$
$4$	2.39646	1.19823
$5$	−2.55395	−1.14216	−0.571081	−	0.820894i	$-0.693476\pi$
$5$	−2.55395	−1.14216	−0.571081	+	0.820894i	$0.693476\pi$
$6$	2.19632	0.896643
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.831292	−0.293906
$9$	−1.90280	−0.634266
$10$	5.35506	1.69342
$11$	1.88656	0.568819	0.284410	−	0.958703i	$-0.408202\pi$
$11$	1.88656	0.568819	0.284410	+	0.958703i	$0.408202\pi$
$12$	−2.51023	−0.724642
$13$	5.49219	1.52326	0.761630	−	0.648012i	$-0.224399\pi$
$13$	5.49219	1.52326	0.761630	+	0.648012i	$0.224399\pi$
$14$	2.09677	0.560386
$15$	2.67520	0.690733
$16$	−3.04989	−0.762473
$17$	0.721010	0.174871	0.0874354	−	0.996170i	$-0.472133\pi$
$17$	0.721010	0.174871	0.0874354	+	0.996170i	$0.472133\pi$
$18$	3.98974	0.940390
$19$	0.786479	0.180431	0.0902153	−	0.995922i	$-0.471244\pi$
$19$	0.786479	0.180431	0.0902153	+	0.995922i	$0.471244\pi$
$20$	−6.12045	−1.36857
$21$	1.04747	0.228578
$22$	−3.95569	−0.843356
$23$	5.34471	1.11445	0.557224	−	0.830362i	$-0.311866\pi$
$23$	5.34471	1.11445	0.557224	+	0.830362i	$0.311866\pi$
$24$	0.870757	0.177743
$25$	1.52266	0.304532
$26$	−11.5159	−2.25845
$27$	5.13556	0.988338
$28$	−2.39646	−0.452889
$29$	2.98527	0.554351	0.277175	−	0.960819i	$-0.410602\pi$
$29$	2.98527	0.554351	0.277175	+	0.960819i	$0.410602\pi$
$30$	−5.60929	−1.02411
$31$	6.72786	1.20836	0.604180	−	0.796848i	$-0.293501\pi$
$31$	6.72786	1.20836	0.604180	+	0.796848i	$0.293501\pi$
$32$	8.05752	1.42438
$33$	−1.97612	−0.343999
$34$	−1.51180	−0.259271
$35$	2.55395	0.431696
$36$	−4.55998	−0.759997
$37$	1.70771	0.280746	0.140373	−	0.990099i	$-0.455170\pi$
$37$	1.70771	0.280746	0.140373	+	0.990099i	$0.455170\pi$
$38$	−1.64907	−0.267514
$39$	−5.75293	−0.921206
$40$	2.12308	0.335688
$41$	12.2169	1.90796	0.953978	−	0.299876i	$-0.0969452\pi$
$41$	12.2169	1.90796	0.953978	+	0.299876i	$0.0969452\pi$
$42$	−2.19632	−0.338899
$43$	−6.38633	−0.973906	−0.486953	−	0.873428i	$-0.661892\pi$
$43$	−6.38633	−0.973906	−0.486953	+	0.873428i	$0.661892\pi$
$44$	4.52107	0.681577
$45$	4.85965	0.724434
$46$	−11.2066	−1.65233
$47$	−7.19218	−1.04909	−0.524543	−	0.851384i	$-0.675764\pi$
$47$	−7.19218	−1.04909	−0.524543	+	0.851384i	$0.675764\pi$
$48$	3.19469	0.461113
$49$	1.00000	0.142857
$50$	−3.19268	−0.451513
$51$	−0.755240	−0.105755
$52$	13.1618	1.82522
$53$	4.78220	0.656886	0.328443	−	0.944524i	$-0.393476\pi$
$53$	4.78220	0.656886	0.328443	+	0.944524i	$0.393476\pi$
$54$	−10.7681	−1.46535
$55$	−4.81818	−0.649684
$56$	0.831292	0.111086
$57$	−0.823817	−0.109117
$58$	−6.25944	−0.821904
$59$	4.23016	0.550719	0.275360	−	0.961341i	$-0.411203\pi$
$59$	4.23016	0.550719	0.275360	+	0.961341i	$0.411203\pi$
$60$	6.41101	0.827658
$61$	−0.608969	−0.0779705	−0.0389853	−	0.999240i	$-0.512413\pi$
$61$	−0.608969	−0.0779705	−0.0389853	+	0.999240i	$0.512413\pi$
$62$	−14.1068	−1.79157
$63$	1.90280	0.239730
$64$	−10.7950	−1.34938
$65$	−14.0268	−1.73981
$66$	4.14349	0.510028
$67$	14.7406	1.80085	0.900426	−	0.435010i	$-0.143255\pi$
$67$	14.7406	1.80085	0.900426	+	0.435010i	$0.143255\pi$
$68$	1.72787	0.209536
$69$	−5.59845	−0.673974
$70$	−5.35506	−0.640052
$71$	−1.42316	−0.168898	−0.0844488	−	0.996428i	$-0.526913\pi$
$71$	−1.42316	−0.168898	−0.0844488	+	0.996428i	$0.526913\pi$
$72$	1.58178	0.186415
$73$	−3.73150	−0.436739	−0.218370	−	0.975866i	$-0.570074\pi$
$73$	−3.73150	−0.436739	−0.218370	+	0.975866i	$0.570074\pi$
$74$	−3.58068	−0.416246
$75$	−1.59495	−0.184169
$76$	1.88477	0.216198
$77$	−1.88656	−0.214994
$78$	12.0626	1.36582
$79$	9.28985	1.04519	0.522595	−	0.852581i	$-0.324964\pi$
$79$	9.28985	1.04519	0.522595	+	0.852581i	$0.324964\pi$
$80$	7.78928	0.870867
$81$	0.329027	0.0365586
$82$	−25.6160	−2.82882
$83$	−0.304575	−0.0334314	−0.0167157	−	0.999860i	$-0.505321\pi$
$83$	−0.304575	−0.0334314	−0.0167157	+	0.999860i	$0.505321\pi$
$84$	2.51023	0.273889
$85$	−1.84142	−0.199731
$86$	13.3907	1.44396
$87$	−3.12699	−0.335249
$88$	−1.56828	−0.167179
$89$	10.7676	1.14136	0.570680	−	0.821173i	$-0.306680\pi$
$89$	10.7676	1.14136	0.570680	+	0.821173i	$0.306680\pi$
$90$	−10.1896	−1.07408
$91$	−5.49219	−0.575738
$92$	12.8084	1.33537
$93$	−7.04726	−0.730767
$94$	15.0804	1.55542
$95$	−2.00863	−0.206081
$96$	−8.44005	−0.861409
$97$	−16.7172	−1.69737	−0.848687	−	0.528895i	$-0.822606\pi$
$97$	−16.7172	−1.69737	−0.848687	+	0.528895i	$0.822606\pi$
$98$	−2.09677	−0.211806
$99$	−3.58974	−0.360783
$100$	3.64900	0.364900
$101$	−0.940913	−0.0936243	−0.0468122	−	0.998904i	$-0.514906\pi$
$101$	−0.940913	−0.0936243	−0.0468122	+	0.998904i	$0.514906\pi$
$102$	1.58357	0.156797
$103$	6.81080	0.671088	0.335544	−	0.942025i	$-0.391080\pi$
$103$	6.81080	0.671088	0.335544	+	0.942025i	$0.391080\pi$
$104$	−4.56562	−0.447695
$105$	−2.67520	−0.261073
$106$	−10.0272	−0.973928
$107$	−1.14174	−0.110376	−0.0551879	−	0.998476i	$-0.517576\pi$
$107$	−1.14174	−0.110376	−0.0551879	+	0.998476i	$0.517576\pi$
$108$	12.3072	1.18426
$109$	−16.6653	−1.59624	−0.798122	−	0.602495i	$-0.794173\pi$
$109$	−16.6653	−1.59624	−0.798122	+	0.602495i	$0.794173\pi$
$110$	10.1026	0.963249
$111$	−1.78878	−0.169784
$112$	3.04989	0.288188
$113$	11.4770	1.07967	0.539833	−	0.841772i	$-0.318487\pi$
$113$	11.4770	1.07967	0.539833	+	0.841772i	$0.318487\pi$
$114$	1.72736	0.161782
$115$	−13.6501	−1.27288
$116$	7.15409	0.664240
$117$	−10.4505	−0.966152
$118$	−8.86968	−0.816521
$119$	−0.721010	−0.0660949
$120$	−2.22387	−0.203011
$121$	−7.44089	−0.676444
$122$	1.27687	0.115602
$123$	−12.7969	−1.15386
$124$	16.1231	1.44789
$125$	8.88095	0.794336
$126$	−3.98974	−0.355434
$127$	−18.5049	−1.64205	−0.821023	−	0.570894i	$-0.806597\pi$
$127$	−18.5049	−1.64205	−0.821023	+	0.570894i	$0.806597\pi$
$128$	6.51967	0.576263
$129$	6.68952	0.588979
$130$	29.4110	2.57952
$131$	−2.75796	−0.240964	−0.120482	−	0.992716i	$-0.538444\pi$
$131$	−2.75796	−0.240964	−0.120482	+	0.992716i	$0.538444\pi$
$132$	−4.73571	−0.412190
$133$	−0.786479	−0.0681964
$134$	−30.9077	−2.67002
$135$	−13.1160	−1.12884
$136$	−0.599370	−0.0513956
$137$	−5.22415	−0.446330	−0.223165	−	0.974781i	$-0.571639\pi$
$137$	−5.22415	−0.446330	−0.223165	+	0.974781i	$0.571639\pi$
$138$	11.7387	0.999262
$139$	−9.84320	−0.834889	−0.417445	−	0.908702i	$-0.637074\pi$
$139$	−9.84320	−0.834889	−0.417445	+	0.908702i	$0.637074\pi$
$140$	6.12045	0.517272
$141$	7.53362	0.634445
$142$	2.98404	0.250415
$143$	10.3614	0.866460
$144$	5.80333	0.483611
$145$	−7.62423	−0.633158
$146$	7.82412	0.647529
$147$	−1.04747	−0.0863943
$148$	4.09247	0.336399
$149$	−18.1378	−1.48591	−0.742954	−	0.669342i	$-0.766576\pi$
$149$	−18.1378	−1.48591	−0.742954	+	0.669342i	$0.766576\pi$
$150$	3.34425	0.273057
$151$	5.96821	0.485686	0.242843	−	0.970066i	$-0.421920\pi$
$151$	5.96821	0.485686	0.242843	+	0.970066i	$0.421920\pi$
$152$	−0.653793	−0.0530297
$153$	−1.37194	−0.110914
$154$	3.95569	0.318759
$155$	−17.1826	−1.38014
$156$	−13.7867	−1.10382
$157$	17.7497	1.41658	0.708289	−	0.705922i	$-0.249467\pi$
$157$	17.7497	1.41658	0.708289	+	0.705922i	$0.249467\pi$
$158$	−19.4787	−1.54964
$159$	−5.00924	−0.397258
$160$	−20.5785	−1.62687
$161$	−5.34471	−0.421222
$162$	−0.689895	−0.0542033
$163$	−3.67049	−0.287495	−0.143747	−	0.989614i	$-0.545915\pi$
$163$	−3.67049	−0.287495	−0.143747	+	0.989614i	$0.545915\pi$
$164$	29.2773	2.28617
$165$	5.04692	0.392902
$166$	0.638625	0.0495669
$167$	−2.55663	−0.197838	−0.0989189	−	0.995095i	$-0.531538\pi$
$167$	−2.55663	−0.197838	−0.0989189	+	0.995095i	$0.531538\pi$
$168$	−0.870757	−0.0671804
$169$	17.1642	1.32032
$170$	3.86105	0.296129
$171$	−1.49651	−0.114441
$172$	−15.3046	−1.16696
$173$	−14.5272	−1.10448	−0.552239	−	0.833686i	$-0.686227\pi$
$173$	−14.5272	−1.10448	−0.552239	+	0.833686i	$0.686227\pi$
$174$	6.55660	0.497055
$175$	−1.52266	−0.115102
$176$	−5.75381	−0.433710
$177$	−4.43098	−0.333053
$178$	−22.5772	−1.69223
$179$	4.42595	0.330811	0.165406	−	0.986226i	$-0.447107\pi$
$179$	4.42595	0.330811	0.165406	+	0.986226i	$0.447107\pi$
$180$	11.6460	0.868039
$181$	9.97456	0.741403	0.370702	−	0.928752i	$-0.379117\pi$
$181$	9.97456	0.741403	0.370702	+	0.928752i	$0.379117\pi$
$182$	11.5159	0.853614
$183$	0.637880	0.0471534
$184$	−4.44301	−0.327543
$185$	−4.36141	−0.320657
$186$	14.7765	1.08347
$187$	1.36023	0.0994699
$188$	−17.2358	−1.25705
$189$	−5.13556	−0.373557
$190$	4.21164	0.305544
$191$	14.7941	1.07046	0.535232	−	0.844705i	$-0.320224\pi$
$191$	14.7941	1.07046	0.535232	+	0.844705i	$0.320224\pi$
$192$	11.3075	0.816049
$193$	15.7149	1.13119	0.565593	−	0.824685i	$-0.308647\pi$
$193$	15.7149	1.13119	0.565593	+	0.824685i	$0.308647\pi$
$194$	35.0522	2.51660
$195$	14.6927	1.05217
$196$	2.39646	0.171176
$197$	25.2782	1.80100	0.900500	−	0.434856i	$-0.143201\pi$
$197$	25.2782	1.80100	0.900500	+	0.434856i	$0.143201\pi$
$198$	7.52688	0.534912
$199$	−17.2209	−1.22075	−0.610377	−	0.792111i	$-0.708982\pi$
$199$	−17.2209	−1.22075	−0.610377	+	0.792111i	$0.708982\pi$
$200$	−1.26578	−0.0895039
$201$	−15.4404	−1.08908
$202$	1.97288	0.138811
$203$	−2.98527	−0.209525
$204$	−1.80990	−0.126719
$205$	−31.2013	−2.17919
$206$	−14.2807	−0.994984
$207$	−10.1699	−0.706856
$208$	−16.7506	−1.16145
$209$	1.48374	0.102632
$210$	5.60929	0.387078
$211$	8.67765	0.597394	0.298697	−	0.954348i	$-0.403448\pi$
$211$	8.67765	0.597394	0.298697	+	0.954348i	$0.403448\pi$
$212$	11.4604	0.787102
$213$	1.49072	0.102143
$214$	2.39396	0.163648
$215$	16.3104	1.11236
$216$	−4.26915	−0.290479
$217$	−6.72786	−0.456717
$218$	34.9433	2.36666
$219$	3.90866	0.264122
$220$	−11.5466	−0.778471
$221$	3.95993	0.266374
$222$	3.75068	0.251729
$223$	−7.29742	−0.488671	−0.244336	−	0.969691i	$-0.578570\pi$
$223$	−7.29742	−0.488671	−0.244336	+	0.969691i	$0.578570\pi$
$224$	−8.05752	−0.538366
$225$	−2.89732	−0.193154
$226$	−24.0647	−1.60076
$227$	−0.424814	−0.0281959	−0.0140980	−	0.999901i	$-0.504488\pi$
$227$	−0.424814	−0.0281959	−0.0140980	+	0.999901i	$0.504488\pi$
$228$	−1.97425	−0.130748
$229$	−5.91229	−0.390695	−0.195347	−	0.980734i	$-0.562583\pi$
$229$	−5.91229	−0.390695	−0.195347	+	0.980734i	$0.562583\pi$
$230$	28.6212	1.88723
$231$	1.97612	0.130019
$232$	−2.48163	−0.162927
$233$	13.4705	0.882484	0.441242	−	0.897388i	$-0.354538\pi$
$233$	13.4705	0.882484	0.441242	+	0.897388i	$0.354538\pi$
$234$	21.9124	1.43246
$235$	18.3685	1.19823
$236$	10.1374	0.659889
$237$	−9.73088	−0.632089
$238$	1.51180	0.0979952
$239$	15.3472	0.992729	0.496365	−	0.868114i	$-0.334668\pi$
$239$	15.3472	0.992729	0.496365	+	0.868114i	$0.334668\pi$
$240$	−8.15907	−0.526666
$241$	2.94399	0.189639	0.0948195	−	0.995494i	$-0.469773\pi$
$241$	2.94399	0.189639	0.0948195	+	0.995494i	$0.469773\pi$
$242$	15.6019	1.00293
$243$	−15.7513	−1.01045
$244$	−1.45937	−0.0934267
$245$	−2.55395	−0.163166
$246$	26.8322	1.71076
$247$	4.31949	0.274843
$248$	−5.59282	−0.355144
$249$	0.319034	0.0202180
$250$	−18.6213	−1.17772
$251$	17.1401	1.08187	0.540937	−	0.841063i	$-0.318070\pi$
$251$	17.1401	1.08187	0.540937	+	0.841063i	$0.318070\pi$
$252$	4.55998	0.287252
$253$	10.0831	0.633920
$254$	38.8007	2.43457
$255$	1.92885	0.120789
$256$	7.91976	0.494985
$257$	−1.63812	−0.102183	−0.0510914	−	0.998694i	$-0.516270\pi$
$257$	−1.63812	−0.102183	−0.0510914	+	0.998694i	$0.516270\pi$
$258$	−14.0264	−0.873246
$259$	−1.70771	−0.106112
$260$	−33.6147	−2.08469
$261$	−5.68036	−0.351606
$262$	5.78281	0.357263
$263$	8.31682	0.512837	0.256419	−	0.966566i	$-0.417457\pi$
$263$	8.31682	0.512837	0.256419	+	0.966566i	$0.417457\pi$
$264$	1.64274	0.101103
$265$	−12.2135	−0.750270
$266$	1.64907	0.101111
$267$	−11.2788	−0.690248
$268$	35.3253	2.15784
$269$	5.75999	0.351193	0.175596	−	0.984462i	$-0.443815\pi$
$269$	5.75999	0.351193	0.175596	+	0.984462i	$0.443815\pi$
$270$	27.5012	1.67367
$271$	−20.3309	−1.23501	−0.617506	−	0.786566i	$-0.711857\pi$
$271$	−20.3309	−1.23501	−0.617506	+	0.786566i	$0.711857\pi$
$272$	−2.19900	−0.133334
$273$	5.75293	0.348183
$274$	10.9539	0.661747
$275$	2.87259	0.173224
$276$	−13.4165	−0.807576
$277$	−6.88473	−0.413664	−0.206832	−	0.978377i	$-0.566315\pi$
$277$	−6.88473	−0.413664	−0.206832	+	0.978377i	$0.566315\pi$
$278$	20.6390	1.23784
$279$	−12.8018	−0.766421
$280$	−2.12308	−0.126878
$281$	−30.0710	−1.79389	−0.896944	−	0.442145i	$-0.854218\pi$
$281$	−30.0710	−1.79389	−0.896944	+	0.442145i	$0.854218\pi$
$282$	−15.7963	−0.940656
$283$	−12.3643	−0.734983	−0.367491	−	0.930027i	$-0.619783\pi$
$283$	−12.3643	−0.734983	−0.367491	+	0.930027i	$0.619783\pi$
$284$	−3.41054	−0.202378
$285$	2.10399	0.124629
$286$	−21.7254	−1.28465
$287$	−12.2169	−0.721140
$288$	−15.3318	−0.903437
$289$	−16.4801	−0.969420
$290$	15.9863	0.938747
$291$	17.5108	1.02650
$292$	−8.94241	−0.523315
$293$	−6.32928	−0.369760	−0.184880	−	0.982761i	$-0.559190\pi$
$293$	−6.32928	−0.369760	−0.184880	+	0.982761i	$0.559190\pi$
$294$	2.19632	0.128092
$295$	−10.8036	−0.629010
$296$	−1.41961	−0.0825129
$297$	9.68854	0.562186
$298$	38.0309	2.20307
$299$	29.3542	1.69759
$300$	−3.82224	−0.220677
$301$	6.38633	0.368102
$302$	−12.5140	−0.720099
$303$	0.985582	0.0566202
$304$	−2.39868	−0.137574
$305$	1.55528	0.0890549
$306$	2.87664	0.164447
$307$	−22.0847	−1.26044	−0.630221	−	0.776416i	$-0.717036\pi$
$307$	−22.0847	−1.26044	−0.630221	+	0.776416i	$0.717036\pi$
$308$	−4.52107	−0.257612
$309$	−7.13414	−0.405847
$310$	36.0281	2.04626
$311$	19.2094	1.08926	0.544632	−	0.838675i	$-0.316669\pi$
$311$	19.2094	1.08926	0.544632	+	0.838675i	$0.316669\pi$
$312$	4.78237	0.270748
$313$	1.37227	0.0775651	0.0387826	−	0.999248i	$-0.487652\pi$
$313$	1.37227	0.0775651	0.0387826	+	0.999248i	$0.487652\pi$
$314$	−37.2171	−2.10028
$315$	−4.85965	−0.273810
$316$	22.2628	1.25238
$317$	−10.5573	−0.592957	−0.296478	−	0.955040i	$-0.595812\pi$
$317$	−10.5573	−0.592957	−0.296478	+	0.955040i	$0.595812\pi$
$318$	10.5032	0.588992
$319$	5.63189	0.315325
$320$	27.5699	1.54121
$321$	1.19594	0.0667508
$322$	11.2066	0.624522
$323$	0.567059	0.0315520
$324$	0.788501	0.0438056
$325$	8.36275	0.463882
$326$	7.69618	0.426252
$327$	17.4565	0.965345
$328$	−10.1558	−0.560760
$329$	7.19218	0.396517
$330$	−10.5823	−0.582534
$331$	−26.3287	−1.44716	−0.723578	−	0.690243i	$-0.757504\pi$
$331$	−26.3287	−1.44716	−0.723578	+	0.690243i	$0.757504\pi$
$332$	−0.729902	−0.0400586
$333$	−3.24943	−0.178068
$334$	5.36067	0.293323
$335$	−37.6468	−2.05686
$336$	−3.19469	−0.174284
$337$	27.7020	1.50902	0.754512	−	0.656286i	$-0.227873\pi$
$337$	27.7020	1.50902	0.754512	+	0.656286i	$0.227873\pi$
$338$	−35.9894	−1.95757
$339$	−12.0219	−0.652939
$340$	−4.41290	−0.239323
$341$	12.6925	0.687338
$342$	3.13784	0.169675
$343$	−1.00000	−0.0539949
$344$	5.30890	0.286237
$345$	14.2982	0.769787
$346$	30.4602	1.63755
$347$	6.99710	0.375624	0.187812	−	0.982205i	$-0.439860\pi$
$347$	6.99710	0.375624	0.187812	+	0.982205i	$0.439860\pi$
$348$	−7.49372	−0.401706
$349$	14.3718	0.769306	0.384653	−	0.923061i	$-0.374321\pi$
$349$	14.3718	0.769306	0.384653	+	0.923061i	$0.374321\pi$
$350$	3.19268	0.170656
$351$	28.2055	1.50550
$352$	15.2010	0.810216
$353$	14.8017	0.787814	0.393907	−	0.919150i	$-0.371123\pi$
$353$	14.8017	0.787814	0.393907	+	0.919150i	$0.371123\pi$
$354$	9.29077	0.493799
$355$	3.63467	0.192908
$356$	25.8041	1.36761
$357$	0.755240	0.0399715
$358$	−9.28022	−0.490475
$359$	−25.9056	−1.36725	−0.683623	−	0.729835i	$-0.739597\pi$
$359$	−25.9056	−1.36725	−0.683623	+	0.729835i	$0.739597\pi$
$360$	−4.03979	−0.212915
$361$	−18.3815	−0.967445
$362$	−20.9144	−1.09924
$363$	7.79414	0.409086
$364$	−13.1618	−0.689867
$365$	9.53007	0.498827
$366$	−1.33749	−0.0699117
$367$	24.1681	1.26156	0.630782	−	0.775960i	$-0.282734\pi$
$367$	24.1681	1.26156	0.630782	+	0.775960i	$0.282734\pi$
$368$	−16.3008	−0.849737
$369$	−23.2462	−1.21015
$370$	9.14489	0.475420
$371$	−4.78220	−0.248280
$372$	−16.8885	−0.875628
$373$	32.9362	1.70537	0.852687	−	0.522422i	$-0.174971\pi$
$373$	32.9362	1.70537	0.852687	+	0.522422i	$0.174971\pi$
$374$	−2.85209	−0.147478
$375$	−9.30257	−0.480383
$376$	5.97880	0.308333
$377$	16.3957	0.844420
$378$	10.7681	0.553851
$379$	−27.3526	−1.40501	−0.702504	−	0.711680i	$-0.747935\pi$
$379$	−27.3526	−1.40501	−0.702504	+	0.711680i	$0.747935\pi$
$380$	−4.81360	−0.246933
$381$	19.3834	0.993044
$382$	−31.0199	−1.58712
$383$	33.8638	1.73036	0.865180	−	0.501462i	$-0.167204\pi$
$383$	33.8638	1.73036	0.865180	+	0.501462i	$0.167204\pi$
$384$	−6.82919	−0.348501
$385$	4.81818	0.245557
$386$	−32.9507	−1.67714
$387$	12.1519	0.617715
$388$	−40.0621	−2.03385
$389$	−24.0589	−1.21984	−0.609918	−	0.792464i	$-0.708798\pi$
$389$	−24.0589	−1.21984	−0.609918	+	0.792464i	$0.708798\pi$
$390$	−30.8073	−1.55999
$391$	3.85359	0.194884
$392$	−0.831292	−0.0419866
$393$	2.88889	0.145725
$394$	−53.0028	−2.67024
$395$	−23.7258	−1.19378
$396$	−8.60268	−0.432301
$397$	−2.54490	−0.127725	−0.0638623	−	0.997959i	$-0.520342\pi$
$397$	−2.54490	−0.127725	−0.0638623	+	0.997959i	$0.520342\pi$
$398$	36.1082	1.80994
$399$	0.823817	0.0412424
$400$	−4.64396	−0.232198
$401$	−26.1538	−1.30606	−0.653029	−	0.757333i	$-0.726502\pi$
$401$	−26.1538	−1.30606	−0.653029	+	0.757333i	$0.726502\pi$
$402$	32.3750	1.61472
$403$	36.9507	1.84065
$404$	−2.25486	−0.112184
$405$	−0.840319	−0.0417558
$406$	6.25944	0.310651
$407$	3.22170	0.159694
$408$	0.627825	0.0310820
$409$	−26.0080	−1.28602	−0.643008	−	0.765860i	$-0.722314\pi$
$409$	−26.0080	−1.28602	−0.643008	+	0.765860i	$0.722314\pi$
$410$	65.4221	3.23097
$411$	5.47217	0.269922
$412$	16.3218	0.804119
$413$	−4.23016	−0.208152
$414$	21.3240	1.04802
$415$	0.777869	0.0381841
$416$	44.2535	2.16970
$417$	10.3105	0.504907
$418$	−3.11107	−0.152167
$419$	−16.4527	−0.803766	−0.401883	−	0.915691i	$-0.631644\pi$
$419$	−16.4527	−0.803766	−0.401883	+	0.915691i	$0.631644\pi$
$420$	−6.41101	−0.312825
$421$	−3.29729	−0.160700	−0.0803500	−	0.996767i	$-0.525604\pi$
$421$	−3.29729	−0.160700	−0.0803500	+	0.996767i	$0.525604\pi$
$422$	−18.1951	−0.885723
$423$	13.6852	0.665400
$424$	−3.97541	−0.193063
$425$	1.09786	0.0532538
$426$	−3.12571	−0.151441
$427$	0.608969	0.0294701
$428$	−2.73613	−0.132256
$429$	−10.8533	−0.524000
$430$	−34.1992	−1.64923
$431$	−13.8127	−0.665333	−0.332667	−	0.943045i	$-0.607948\pi$
$431$	−13.8127	−0.665333	−0.332667	+	0.943045i	$0.607948\pi$
$432$	−15.6629	−0.753581
$433$	−8.23972	−0.395975	−0.197988	−	0.980205i	$-0.563441\pi$
$433$	−8.23972	−0.395975	−0.197988	+	0.980205i	$0.563441\pi$
$434$	14.1068	0.677148
$435$	7.98619	0.382908
$436$	−39.9377	−1.91267
$437$	4.20350	0.201081
$438$	−8.19557	−0.391599
$439$	−11.6003	−0.553653	−0.276827	−	0.960920i	$-0.589283\pi$
$439$	−11.6003	−0.553653	−0.276827	+	0.960920i	$0.589283\pi$
$440$	4.00532	0.190946
$441$	−1.90280	−0.0906094
$442$	−8.30307	−0.394937
$443$	22.8333	1.08484	0.542422	−	0.840106i	$-0.317507\pi$
$443$	22.8333	1.08484	0.542422	+	0.840106i	$0.317507\pi$
$444$	−4.28675	−0.203440
$445$	−27.4998	−1.30362
$446$	15.3010	0.724525
$447$	18.9989	0.898618
$448$	10.7950	0.510017
$449$	37.2269	1.75685	0.878424	−	0.477882i	$-0.158595\pi$
$449$	37.2269	1.75685	0.878424	+	0.477882i	$0.158595\pi$
$450$	6.07502	0.286379
$451$	23.0479	1.08528
$452$	27.5042	1.29369
$453$	−6.25155	−0.293723
$454$	0.890740	0.0418045
$455$	14.0268	0.657586
$456$	0.684832	0.0320702
$457$	12.4875	0.584142	0.292071	−	0.956397i	$-0.405656\pi$
$457$	12.4875	0.584142	0.292071	+	0.956397i	$0.405656\pi$
$458$	12.3967	0.579261
$459$	3.70279	0.172831
$460$	−32.7120	−1.52520
$461$	−13.3365	−0.621142	−0.310571	−	0.950550i	$-0.600520\pi$
$461$	−13.3365	−0.621142	−0.310571	+	0.950550i	$0.600520\pi$
$462$	−4.14349	−0.192772
$463$	32.6887	1.51917	0.759587	−	0.650406i	$-0.225401\pi$
$463$	32.6887	1.51917	0.759587	+	0.650406i	$0.225401\pi$
$464$	−9.10475	−0.422678
$465$	17.9984	0.834654
$466$	−28.2447	−1.30841
$467$	18.5403	0.857942	0.428971	−	0.903318i	$-0.358876\pi$
$467$	18.5403	0.857942	0.428971	+	0.903318i	$0.358876\pi$
$468$	−25.0443	−1.15767
$469$	−14.7406	−0.680658
$470$	−38.5145	−1.77654
$471$	−18.5923	−0.856690
$472$	−3.51649	−0.161860
$473$	−12.0482	−0.553977
$474$	20.4035	0.937162
$475$	1.19754	0.0549470
$476$	−1.72787	−0.0791970
$477$	−9.09956	−0.416640
$478$	−32.1797	−1.47186
$479$	22.1645	1.01272	0.506360	−	0.862322i	$-0.330991\pi$
$479$	22.1645	1.01272	0.506360	+	0.862322i	$0.330991\pi$
$480$	21.5555	0.983868
$481$	9.37908	0.427649
$482$	−6.17288	−0.281167
$483$	5.59845	0.254738
$484$	−17.8318	−0.810537
$485$	42.6949	1.93868
$486$	33.0269	1.49813
$487$	−18.8657	−0.854887	−0.427444	−	0.904042i	$-0.640586\pi$
$487$	−18.8657	−0.854887	−0.427444	+	0.904042i	$0.640586\pi$
$488$	0.506231	0.0229160
$489$	3.84474	0.173865
$490$	5.35506	0.241917
$491$	2.00368	0.0904246	0.0452123	−	0.998977i	$-0.485604\pi$
$491$	2.00368	0.0904246	0.0452123	+	0.998977i	$0.485604\pi$
$492$	−30.6672	−1.38259
$493$	2.15241	0.0969397
$494$	−9.05700	−0.407494
$495$	9.16802	0.412072
$496$	−20.5193	−0.921342
$497$	1.42316	0.0638373
$498$	−0.668943	−0.0299761
$499$	26.0290	1.16522	0.582608	−	0.812753i	$-0.302032\pi$
$499$	26.0290	1.16522	0.582608	+	0.812753i	$0.302032\pi$
$500$	21.2829	0.951798
$501$	2.67800	0.119644
$502$	−35.9389	−1.60403
$503$	8.32927	0.371384	0.185692	−	0.982608i	$-0.440547\pi$
$503$	8.32927	0.371384	0.185692	+	0.982608i	$0.440547\pi$
$504$	−1.58178	−0.0704581
$505$	2.40304	0.106934
$506$	−21.1420	−0.939877
$507$	−17.9790	−0.798477
$508$	−44.3464	−1.96755
$509$	6.01605	0.266657	0.133328	−	0.991072i	$-0.457433\pi$
$509$	6.01605	0.266657	0.133328	+	0.991072i	$0.457433\pi$
$510$	−4.04435	−0.179087
$511$	3.73150	0.165072
$512$	−29.6453	−1.31015
$513$	4.03901	0.178326
$514$	3.43476	0.151501
$515$	−17.3944	−0.766491
$516$	16.0312	0.705733
$517$	−13.5685	−0.596741
$518$	3.58068	0.157326
$519$	15.2168	0.667944
$520$	11.6604	0.511340
$521$	24.3779	1.06801	0.534007	−	0.845480i	$-0.320686\pi$
$521$	24.3779	1.06801	0.534007	+	0.845480i	$0.320686\pi$
$522$	11.9104	0.521306
$523$	15.4513	0.675636	0.337818	−	0.941211i	$-0.390311\pi$
$523$	15.4513	0.675636	0.337818	+	0.941211i	$0.390311\pi$
$524$	−6.60934	−0.288730
$525$	1.59495	0.0696093
$526$	−17.4385	−0.760355
$527$	4.85086	0.211307
$528$	6.02697	0.262290
$529$	5.56590	0.241996
$530$	25.6090	1.11238
$531$	−8.04913	−0.349302
$532$	−1.88477	−0.0817150
$533$	67.0975	2.90631
$534$	23.6490	1.02339
$535$	2.91594	0.126067
$536$	−12.2537	−0.529281
$537$	−4.63607	−0.200061
$538$	−12.0774	−0.520694
$539$	1.88656	0.0812599
$540$	−31.4319	−1.35261
$541$	25.9391	1.11521	0.557605	−	0.830106i	$-0.311720\pi$
$541$	25.9391	1.11521	0.557605	+	0.830106i	$0.311720\pi$
$542$	42.6293	1.83108
$543$	−10.4481	−0.448371
$544$	5.80956	0.249083
$545$	42.5623	1.82317
$546$	−12.0626	−0.516232
$547$	12.9117	0.552065	0.276032	−	0.961148i	$-0.410980\pi$
$547$	12.9117	0.552065	0.276032	+	0.961148i	$0.410980\pi$
$548$	−12.5195	−0.534806
$549$	1.15875	0.0494540
$550$	−6.02318	−0.256829
$551$	2.34785	0.100022
$552$	4.65394	0.198085
$553$	−9.28985	−0.395045
$554$	14.4357	0.613316
$555$	4.56847	0.193921
$556$	−23.5889	−1.00039
$557$	7.82647	0.331618	0.165809	−	0.986158i	$-0.446976\pi$
$557$	7.82647	0.331618	0.165809	+	0.986158i	$0.446976\pi$
$558$	26.8424	1.13633
$559$	−35.0750	−1.48351
$560$	−7.78928	−0.329157
$561$	−1.42481	−0.0601554
$562$	63.0522	2.65970
$563$	−17.2300	−0.726158	−0.363079	−	0.931758i	$-0.618274\pi$
$563$	−17.2300	−0.726158	−0.363079	+	0.931758i	$0.618274\pi$
$564$	18.0540	0.760212
$565$	−29.3117	−1.23315
$566$	25.9252	1.08972
$567$	−0.329027	−0.0138178
$568$	1.18306	0.0496401
$569$	44.5479	1.86755	0.933773	−	0.357867i	$-0.116496\pi$
$569$	44.5479	1.86755	0.933773	+	0.357867i	$0.116496\pi$
$570$	−4.41158	−0.184781
$571$	−20.8331	−0.871837	−0.435918	−	0.899986i	$-0.643576\pi$
$571$	−20.8331	−0.871837	−0.435918	+	0.899986i	$0.643576\pi$
$572$	24.8306	1.03822
$573$	−15.4964	−0.647373
$574$	25.6160	1.06919
$575$	8.13819	0.339386
$576$	20.5407	0.855864
$577$	40.4488	1.68391	0.841953	−	0.539550i	$-0.181406\pi$
$577$	40.4488	1.68391	0.841953	+	0.539550i	$0.181406\pi$
$578$	34.5551	1.43730
$579$	−16.4610	−0.684095
$580$	−18.2712	−0.758670
$581$	0.304575	0.0126359
$582$	−36.7163	−1.52194
$583$	9.02192	0.373650
$584$	3.10197	0.128360
$585$	26.6901	1.10350
$586$	13.2711	0.548223
$587$	−5.40393	−0.223044	−0.111522	−	0.993762i	$-0.535573\pi$
$587$	−5.40393	−0.223044	−0.111522	+	0.993762i	$0.535573\pi$
$588$	−2.51023	−0.103520
$589$	5.29132	0.218025
$590$	22.6527	0.932598
$591$	−26.4783	−1.08917
$592$	−5.20834	−0.214061
$593$	40.5854	1.66664	0.833321	−	0.552790i	$-0.186437\pi$
$593$	40.5854	1.66664	0.833321	+	0.552790i	$0.186437\pi$
$594$	−20.3147	−0.833521
$595$	1.84142	0.0754911
$596$	−43.4666	−1.78046
$597$	18.0384	0.738263
$598$	−61.5490	−2.51693
$599$	32.4962	1.32776	0.663880	−	0.747839i	$-0.268909\pi$
$599$	32.4962	1.32776	0.663880	+	0.747839i	$0.268909\pi$
$600$	1.32587	0.0541284
$601$	5.08561	0.207446	0.103723	−	0.994606i	$-0.466924\pi$
$601$	5.08561	0.207446	0.103723	+	0.994606i	$0.466924\pi$
$602$	−13.3907	−0.545764
$603$	−28.0484	−1.14222
$604$	14.3026	0.581964
$605$	19.0037	0.772609
$606$	−2.06654	−0.0839476
$607$	−42.0919	−1.70846	−0.854229	−	0.519898i	$-0.825970\pi$
$607$	−42.0919	−1.70846	−0.854229	+	0.519898i	$0.825970\pi$
$608$	6.33707	0.257002
$609$	3.12699	0.126712
$610$	−3.26107	−0.132037
$611$	−39.5008	−1.59803
$612$	−3.28779	−0.132901
$613$	45.6829	1.84512	0.922558	−	0.385860i	$-0.126095\pi$
$613$	45.6829	1.84512	0.922558	+	0.385860i	$0.126095\pi$
$614$	46.3067	1.86879
$615$	32.6826	1.31789
$616$	1.56828	0.0631879
$617$	−36.7901	−1.48111	−0.740556	−	0.671994i	$-0.765438\pi$
$617$	−36.7901	−1.48111	−0.740556	+	0.671994i	$0.765438\pi$
$618$	14.9587	0.601726
$619$	3.67120	0.147558	0.0737790	−	0.997275i	$-0.476494\pi$
$619$	3.67120	0.147558	0.0737790	+	0.997275i	$0.476494\pi$
$620$	−41.1775	−1.65373
$621$	27.4480	1.10145
$622$	−40.2777	−1.61499
$623$	−10.7676	−0.431393
$624$	17.5458	0.702395
$625$	−30.2948	−1.21179
$626$	−2.87733	−0.115001
$627$	−1.55418	−0.0620680
$628$	42.5364	1.69739
$629$	1.23128	0.0490942
$630$	10.1896	0.405963
$631$	39.8801	1.58760	0.793801	−	0.608178i	$-0.208099\pi$
$631$	39.8801	1.58760	0.793801	+	0.608178i	$0.208099\pi$
$632$	−7.72258	−0.307188
$633$	−9.08962	−0.361280
$634$	22.1363	0.879143
$635$	47.2607	1.87548
$636$	−12.0044	−0.476007
$637$	5.49219	0.217609
$638$	−11.8088	−0.467515
$639$	2.70798	0.107126
$640$	−16.6509	−0.658185
$641$	−9.11864	−0.360165	−0.180082	−	0.983652i	$-0.557636\pi$
$641$	−9.11864	−0.360165	−0.180082	+	0.983652i	$0.557636\pi$
$642$	−2.50761	−0.0989676
$643$	15.9863	0.630437	0.315219	−	0.949019i	$-0.397922\pi$
$643$	15.9863	0.630437	0.315219	+	0.949019i	$0.397922\pi$
$644$	−12.8084	−0.504721
$645$	−17.0847	−0.672709
$646$	−1.18900	−0.0467804
$647$	−35.3487	−1.38970	−0.694850	−	0.719154i	$-0.744529\pi$
$647$	−35.3487	−1.38970	−0.694850	+	0.719154i	$0.744529\pi$
$648$	−0.273517	−0.0107448
$649$	7.98045	0.313260
$650$	−17.5348	−0.687772
$651$	7.04726	0.276204
$652$	−8.79618	−0.344485
$653$	−11.7965	−0.461634	−0.230817	−	0.972997i	$-0.574140\pi$
$653$	−11.7965	−0.461634	−0.230817	+	0.972997i	$0.574140\pi$
$654$	−36.6023	−1.43126
$655$	7.04368	0.275219
$656$	−37.2602	−1.45477
$657$	7.10029	0.277009
$658$	−15.0804	−0.587894
$659$	34.9903	1.36303	0.681514	−	0.731805i	$-0.261322\pi$
$659$	34.9903	1.36303	0.681514	+	0.731805i	$0.261322\pi$
$660$	12.0948	0.470788
$661$	−3.50854	−0.136467	−0.0682333	−	0.997669i	$-0.521736\pi$
$661$	−3.50854	−0.136467	−0.0682333	+	0.997669i	$0.521736\pi$
$662$	55.2053	2.14562
$663$	−4.14792	−0.161092
$664$	0.253191	0.00982570
$665$	2.00863	0.0778912
$666$	6.81332	0.264011
$667$	15.9554	0.617795
$668$	−6.12686	−0.237055
$669$	7.64386	0.295529
$670$	78.9368	3.04959
$671$	−1.14886	−0.0443512
$672$	8.44005	0.325582
$673$	21.7964	0.840189	0.420094	−	0.907480i	$-0.361997\pi$
$673$	21.7964	0.840189	0.420094	+	0.907480i	$0.361997\pi$
$674$	−58.0849	−2.23735
$675$	7.81972	0.300981
$676$	41.1333	1.58205
$677$	27.9820	1.07544	0.537719	−	0.843124i	$-0.319286\pi$
$677$	27.9820	1.07544	0.537719	+	0.843124i	$0.319286\pi$
$678$	25.2072	0.968076
$679$	16.7172	0.641547
$680$	1.53076	0.0587020
$681$	0.444982	0.0170518
$682$	−26.6133	−1.01908
$683$	−20.1593	−0.771375	−0.385688	−	0.922629i	$-0.626036\pi$
$683$	−20.1593	−0.771375	−0.385688	+	0.922629i	$0.626036\pi$
$684$	−3.58633	−0.137127
$685$	13.3422	0.509780
$686$	2.09677	0.0800552
$687$	6.19297	0.236277
$688$	19.4776	0.742577
$689$	26.2648	1.00061
$690$	−29.9800	−1.14132
$691$	−40.6475	−1.54631	−0.773153	−	0.634220i	$-0.781321\pi$
$691$	−40.6475	−1.54631	−0.773153	+	0.634220i	$0.781321\pi$
$692$	−34.8138	−1.32342
$693$	3.58974	0.136363
$694$	−14.6713	−0.556916
$695$	25.1390	0.953578
$696$	2.59945	0.0985317
$697$	8.80850	0.333646
$698$	−30.1345	−1.14061
$699$	−14.1100	−0.533691
$700$	−3.64900	−0.137919
$701$	48.5078	1.83211	0.916057	−	0.401047i	$-0.131354\pi$
$701$	48.5078	1.83211	0.916057	+	0.401047i	$0.131354\pi$
$702$	−59.1405	−2.23211
$703$	1.34308	0.0506552
$704$	−20.3655	−0.767552
$705$	−19.2405	−0.724639
$706$	−31.0358	−1.16805
$707$	0.940913	0.0353867
$708$	−10.6187	−0.399074
$709$	8.81292	0.330976	0.165488	−	0.986212i	$-0.447080\pi$
$709$	8.81292	0.330976	0.165488	+	0.986212i	$0.447080\pi$
$710$	−7.62109	−0.286014
$711$	−17.6767	−0.662928
$712$	−8.95099	−0.335453
$713$	35.9584	1.34665
$714$	−1.58357	−0.0592635
$715$	−26.4624	−0.989637
$716$	10.6066	0.396388
$717$	−16.0758	−0.600363
$718$	54.3182	2.02714
$719$	−11.0052	−0.410423	−0.205212	−	0.978718i	$-0.565788\pi$
$719$	−11.0052	−0.410423	−0.205212	+	0.978718i	$0.565788\pi$
$720$	−14.8214	−0.552361
$721$	−6.81080	−0.253647
$722$	38.5418	1.43438
$723$	−3.08376	−0.114686
$724$	23.9037	0.888373
$725$	4.54556	0.168818
$726$	−16.3426	−0.606529
$727$	−14.8077	−0.549188	−0.274594	−	0.961560i	$-0.588543\pi$
$727$	−14.8077	−0.549188	−0.274594	+	0.961560i	$0.588543\pi$
$728$	4.56562	0.169213
$729$	15.5120	0.574519
$730$	−19.9824	−0.739582
$731$	−4.60461	−0.170308
$732$	1.52866	0.0565007
$733$	21.4473	0.792174	0.396087	−	0.918213i	$-0.370368\pi$
$733$	21.4473	0.792174	0.396087	+	0.918213i	$0.370368\pi$
$734$	−50.6750	−1.87045
$735$	2.67520	0.0986762
$736$	43.0651	1.58740
$737$	27.8090	1.02436
$738$	48.7421	1.79422
$739$	39.7349	1.46167	0.730836	−	0.682554i	$-0.239131\pi$
$739$	39.7349	1.46167	0.730836	+	0.682554i	$0.239131\pi$
$740$	−10.4520	−0.384221
$741$	−4.52456	−0.166214
$742$	10.0272	0.368110
$743$	38.9069	1.42736	0.713679	−	0.700473i	$-0.247028\pi$
$743$	38.9069	1.42736	0.713679	+	0.700473i	$0.247028\pi$
$744$	5.85833	0.214777
$745$	46.3231	1.69715
$746$	−69.0599	−2.52846
$747$	0.579544	0.0212044
$748$	3.25974	0.119188
$749$	1.14174	0.0417181
$750$	19.5054	0.712236
$751$	24.8296	0.906044	0.453022	−	0.891499i	$-0.350346\pi$
$751$	24.8296	0.906044	0.453022	+	0.891499i	$0.350346\pi$
$752$	21.9354	0.799900
$753$	−17.9538	−0.654274
$754$	−34.3780	−1.25197
$755$	−15.2425	−0.554732
$756$	−12.3072	−0.447607
$757$	−20.0667	−0.729338	−0.364669	−	0.931137i	$-0.618818\pi$
$757$	−20.0667	−0.729338	−0.364669	+	0.931137i	$0.618818\pi$
$758$	57.3522	2.08313
$759$	−10.5618	−0.383369
$760$	1.66976	0.0605684
$761$	−5.82788	−0.211260	−0.105630	−	0.994405i	$-0.533686\pi$
$761$	−5.82788	−0.211260	−0.105630	+	0.994405i	$0.533686\pi$
$762$	−40.6427	−1.47233
$763$	16.6653	0.603324
$764$	35.4535	1.28266
$765$	3.50386	0.126682
$766$	−71.0048	−2.56551
$767$	23.2328	0.838889
$768$	−8.29574	−0.299347
$769$	−5.84323	−0.210712	−0.105356	−	0.994435i	$-0.533598\pi$
$769$	−5.84323	−0.210712	−0.105356	+	0.994435i	$0.533598\pi$
$770$	−10.1026	−0.364074
$771$	1.71588	0.0617961
$772$	37.6602	1.35542
$773$	−32.6119	−1.17297	−0.586484	−	0.809961i	$-0.699488\pi$
$773$	−32.6119	−1.17297	−0.586484	+	0.809961i	$0.699488\pi$
$774$	−25.4798	−0.915851
$775$	10.2443	0.367985
$776$	13.8969	0.498869
$777$	1.78878	0.0641723
$778$	50.4462	1.80858
$779$	9.60832	0.344254
$780$	35.2105	1.26074
$781$	−2.68487	−0.0960723
$782$	−8.08011	−0.288944
$783$	15.3310	0.547886
$784$	−3.04989	−0.108925
$785$	−45.3318	−1.61796
$786$	−6.05735	−0.216058
$787$	−20.1149	−0.717017	−0.358508	−	0.933526i	$-0.616715\pi$
$787$	−20.1149	−0.717017	−0.358508	+	0.933526i	$0.616715\pi$
$788$	60.5784	2.15801
$789$	−8.71166	−0.310143
$790$	49.7477	1.76994
$791$	−11.4770	−0.408076
$792$	2.98412	0.106036
$793$	−3.34458	−0.118769
$794$	5.33607	0.189370
$795$	12.7933	0.453733
$796$	−41.2691	−1.46275
$797$	23.0842	0.817684	0.408842	−	0.912605i	$-0.365933\pi$
$797$	23.0842	0.817684	0.408842	+	0.912605i	$0.365933\pi$
$798$	−1.72736	−0.0611478
$799$	−5.18563	−0.183455
$800$	12.2689	0.433771
$801$	−20.4885	−0.723925
$802$	54.8386	1.93642
$803$	−7.03971	−0.248426
$804$	−37.0024	−1.30497
$805$	13.6501	0.481103
$806$	−77.4773	−2.72902
$807$	−6.03345	−0.212387
$808$	0.782173	0.0275168
$809$	−21.4663	−0.754714	−0.377357	−	0.926068i	$-0.623167\pi$
$809$	−21.4663	−0.754714	−0.377357	+	0.926068i	$0.623167\pi$
$810$	1.76196	0.0619089
$811$	21.7819	0.764864	0.382432	−	0.923984i	$-0.375087\pi$
$811$	21.7819	0.764864	0.382432	+	0.923984i	$0.375087\pi$
$812$	−7.15409	−0.251059
$813$	21.2961	0.746886
$814$	−6.75518	−0.236769
$815$	9.37424	0.328365
$816$	2.30340	0.0806352
$817$	−5.02271	−0.175722
$818$	54.5330	1.90670
$819$	10.4505	0.365171
$820$	−74.7728	−2.61118
$821$	−33.4583	−1.16770	−0.583851	−	0.811861i	$-0.698455\pi$
$821$	−33.4583	−1.16770	−0.583851	+	0.811861i	$0.698455\pi$
$822$	−11.4739	−0.400198
$823$	20.5964	0.717946	0.358973	−	0.933348i	$-0.383127\pi$
$823$	20.5964	0.717946	0.358973	+	0.933348i	$0.383127\pi$
$824$	−5.66176	−0.197237
$825$	−3.00897	−0.104759
$826$	8.86968	0.308616
$827$	14.0794	0.489590	0.244795	−	0.969575i	$-0.421279\pi$
$827$	14.0794	0.489590	0.244795	+	0.969575i	$0.421279\pi$
$828$	−24.3718	−0.846977
$829$	−41.0636	−1.42620	−0.713098	−	0.701064i	$-0.752709\pi$
$829$	−41.0636	−1.42620	−0.713098	+	0.701064i	$0.752709\pi$
$830$	−1.63102	−0.0566134
$831$	7.21158	0.250167
$832$	−59.2883	−2.05545
$833$	0.721010	0.0249815
$834$	−21.6188	−0.748598
$835$	6.52950	0.225963
$836$	3.55573	0.122977
$837$	34.5513	1.19427
$838$	34.4975	1.19170
$839$	−38.8952	−1.34281	−0.671406	−	0.741090i	$-0.734309\pi$
$839$	−38.8952	−1.34281	−0.671406	+	0.741090i	$0.734309\pi$
$840$	2.22387	0.0767308
$841$	−20.0882	−0.692695
$842$	6.91367	0.238261
$843$	31.4986	1.08487
$844$	20.7957	0.715816
$845$	−43.8365	−1.50802
$846$	−28.6949	−0.986550
$847$	7.44089	0.255672
$848$	−14.5852	−0.500858
$849$	12.9513	0.444488
$850$	−2.30195	−0.0789564
$851$	9.12722	0.312877
$852$	3.57246	0.122390
$853$	−32.4263	−1.11025	−0.555127	−	0.831766i	$-0.687330\pi$
$853$	−32.4263	−1.11025	−0.555127	+	0.831766i	$0.687330\pi$
$854$	−1.27687	−0.0436936
$855$	3.82201	0.130710
$856$	0.949115	0.0324401
$857$	−47.5676	−1.62488	−0.812439	−	0.583046i	$-0.801861\pi$
$857$	−47.5676	−1.62488	−0.812439	+	0.583046i	$0.801861\pi$
$858$	22.7568	0.776905
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	39.0872	1.33286
$861$	12.7969	0.436116
$862$	28.9621	0.986452
$863$	39.9980	1.36155	0.680774	−	0.732493i	$-0.261643\pi$
$863$	39.9980	1.36155	0.680774	+	0.732493i	$0.261643\pi$
$864$	41.3798	1.40777
$865$	37.1016	1.26149
$866$	17.2768	0.587090
$867$	17.2625	0.586266
$868$	−16.1231	−0.547252
$869$	17.5259	0.594524
$870$	−16.7452	−0.567717
$871$	80.9582	2.74316
$872$	13.8537	0.469146
$873$	31.8094	1.07659
$874$	−8.81379	−0.298131
$875$	−8.88095	−0.300231
$876$	9.36694	0.316480
$877$	−37.6716	−1.27208	−0.636041	−	0.771656i	$-0.719429\pi$
$877$	−37.6716	−1.27208	−0.636041	+	0.771656i	$0.719429\pi$
$878$	24.3233	0.820870
$879$	6.62976	0.223616
$880$	14.6949	0.495366
$881$	20.4894	0.690305	0.345152	−	0.938547i	$-0.387827\pi$
$881$	20.4894	0.690305	0.345152	+	0.938547i	$0.387827\pi$
$882$	3.98974	0.134341
$883$	31.7572	1.06872	0.534358	−	0.845258i	$-0.320553\pi$
$883$	31.7572	1.06872	0.534358	+	0.845258i	$0.320553\pi$
$884$	9.48982	0.319177
$885$	11.3165	0.380400
$886$	−47.8764	−1.60844
$887$	5.49638	0.184550	0.0922752	−	0.995734i	$-0.470586\pi$
$887$	5.49638	0.184550	0.0922752	+	0.995734i	$0.470586\pi$
$888$	1.48700	0.0499005
$889$	18.5049	0.620635
$890$	57.6609	1.93280
$891$	0.620729	0.0207952
$892$	−17.4880	−0.585541
$893$	−5.65649	−0.189287
$894$	−39.8364	−1.33233
$895$	−11.3037	−0.377840
$896$	−6.51967	−0.217807
$897$	−30.7477	−1.02664
$898$	−78.0565	−2.60478
$899$	20.0845	0.669855
$900$	−6.94331	−0.231444
$901$	3.44802	0.114870
$902$	−48.3262	−1.60909
$903$	−6.68952	−0.222613
$904$	−9.54075	−0.317321
$905$	−25.4745	−0.846802
$906$	13.1081	0.435487
$907$	−25.7044	−0.853502	−0.426751	−	0.904369i	$-0.640342\pi$
$907$	−25.7044	−0.853502	−0.426751	+	0.904369i	$0.640342\pi$
$908$	−1.01805	−0.0337852
$909$	1.79037	0.0593827
$910$	−29.4110	−0.974965
$911$	28.6331	0.948656	0.474328	−	0.880348i	$-0.342691\pi$
$911$	28.6331	0.948656	0.474328	+	0.880348i	$0.342691\pi$
$912$	2.51255	0.0831989
$913$	−0.574599	−0.0190164
$914$	−26.1835	−0.866075
$915$	−1.62911	−0.0538568
$916$	−14.1686	−0.468143
$917$	2.75796	0.0910757
$918$	−7.76391	−0.256247
$919$	−24.3178	−0.802171	−0.401086	−	0.916041i	$-0.631367\pi$
$919$	−24.3178	−0.802171	−0.401086	+	0.916041i	$0.631367\pi$
$920$	11.3472	0.374107
$921$	23.1332	0.762265
$922$	27.9636	0.920932
$923$	−7.81625	−0.257275
$924$	4.73571	0.155793
$925$	2.60027	0.0854963
$926$	−68.5408	−2.25239
$927$	−12.9596	−0.425648
$928$	24.0539	0.789607
$929$	−13.4169	−0.440195	−0.220097	−	0.975478i	$-0.570638\pi$
$929$	−13.4169	−0.440195	−0.220097	+	0.975478i	$0.570638\pi$
$930$	−37.7385	−1.23749
$931$	0.786479	0.0257758
$932$	32.2816	1.05742
$933$	−20.1213	−0.658743
$934$	−38.8748	−1.27202
$935$	−3.47396	−0.113611
$936$	8.68744	0.283958
$937$	−34.0701	−1.11302	−0.556511	−	0.830840i	$-0.687860\pi$
$937$	−34.0701	−1.11302	−0.556511	+	0.830840i	$0.687860\pi$
$938$	30.9077	1.00917
$939$	−1.43741	−0.0469083
$940$	44.0193	1.43575
$941$	−20.6889	−0.674439	−0.337219	−	0.941426i	$-0.609486\pi$
$941$	−20.6889	−0.674439	−0.337219	+	0.941426i	$0.609486\pi$
$942$	38.9839	1.27017
$943$	65.2957	2.12632
$944$	−12.9015	−0.419909
$945$	13.1160	0.426662
$946$	25.2624	0.821350
$947$	−35.4327	−1.15141	−0.575704	−	0.817658i	$-0.695272\pi$
$947$	−35.4327	−1.15141	−0.575704	+	0.817658i	$0.695272\pi$
$948$	−23.3197	−0.757388
$949$	−20.4941	−0.665268
$950$	−2.51097	−0.0814668
$951$	11.0585	0.358596
$952$	0.599370	0.0194257
$953$	−0.213955	−0.00693070	−0.00346535	−	0.999994i	$-0.501103\pi$
$953$	−0.213955	−0.00693070	−0.00346535	+	0.999994i	$0.501103\pi$
$954$	19.0797	0.617729
$955$	−37.7834	−1.22264
$956$	36.7790	1.18952
$957$	−5.89926	−0.190696
$958$	−46.4739	−1.50150
$959$	5.22415	0.168697
$960$	−28.8788	−0.932060
$961$	14.2641	0.460132
$962$	−19.6658	−0.634051
$963$	2.17249	0.0700075
$964$	7.05516	0.227231
$965$	−40.1351	−1.29200
$966$	−11.7387	−0.377686
$967$	17.7303	0.570168	0.285084	−	0.958503i	$-0.407978\pi$
$967$	17.7303	0.570168	0.285084	+	0.958503i	$0.407978\pi$
$968$	6.18555	0.198811
$969$	−0.593980	−0.0190814
$970$	−89.5216	−2.87436
$971$	−33.1984	−1.06539	−0.532694	−	0.846308i	$-0.678820\pi$
$971$	−33.1984	−1.06539	−0.532694	+	0.846308i	$0.678820\pi$
$972$	−37.7474	−1.21075
$973$	9.84320	0.315558
$974$	39.5571	1.26749
$975$	−8.75977	−0.280537
$976$	1.85729	0.0594505
$977$	33.7408	1.07946	0.539732	−	0.841837i	$-0.318526\pi$
$977$	33.7408	1.07946	0.539732	+	0.841837i	$0.318526\pi$
$978$	−8.06155	−0.257780
$979$	20.3137	0.649228
$980$	−6.12045	−0.195510
$981$	31.7107	1.01244
$982$	−4.20126	−0.134067
$983$	23.2167	0.740498	0.370249	−	0.928933i	$-0.379272\pi$
$983$	23.2167	0.740498	0.370249	+	0.928933i	$0.379272\pi$
$984$	10.6379	0.339125
$985$	−64.5594	−2.05703
$986$	−4.51312	−0.143727
$987$	−7.53362	−0.239798
$988$	10.3515	0.329325
$989$	−34.1331	−1.08537
$990$	−19.2233	−0.610956
$991$	23.9844	0.761889	0.380944	−	0.924598i	$-0.375599\pi$
$991$	23.9844	0.761889	0.380944	+	0.924598i	$0.375599\pi$
$992$	54.2099	1.72117
$993$	27.5786	0.875182
$994$	−2.98404	−0.0946480
$995$	43.9812	1.39430
$996$	0.764554	0.0242258
$997$	−58.0434	−1.83825	−0.919126	−	0.393963i	$-0.871104\pi$
$997$	−58.0434	−1.83825	−0.919126	+	0.393963i	$0.871104\pi$
$998$	−54.5769	−1.72760
$999$	8.77004	0.277472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.15	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.15	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.09677 q^{2} -1.04747 q^{3} +2.39646 q^{4} -2.55395 q^{5} +2.19632 q^{6} -1.00000 q^{7} -0.831292 q^{8} -1.90280 q^{9} +O(q^{10})\)	\(q-2.09677 q^{2} -1.04747 q^{3} +2.39646 q^{4} -2.55395 q^{5} +2.19632 q^{6} -1.00000 q^{7} -0.831292 q^{8} -1.90280 q^{9} +5.35506 q^{10} +1.88656 q^{11} -2.51023 q^{12} +5.49219 q^{13} +2.09677 q^{14} +2.67520 q^{15} -3.04989 q^{16} +0.721010 q^{17} +3.98974 q^{18} +0.786479 q^{19} -6.12045 q^{20} +1.04747 q^{21} -3.95569 q^{22} +5.34471 q^{23} +0.870757 q^{24} +1.52266 q^{25} -11.5159 q^{26} +5.13556 q^{27} -2.39646 q^{28} +2.98527 q^{29} -5.60929 q^{30} +6.72786 q^{31} +8.05752 q^{32} -1.97612 q^{33} -1.51180 q^{34} +2.55395 q^{35} -4.55998 q^{36} +1.70771 q^{37} -1.64907 q^{38} -5.75293 q^{39} +2.12308 q^{40} +12.2169 q^{41} -2.19632 q^{42} -6.38633 q^{43} +4.52107 q^{44} +4.85965 q^{45} -11.2066 q^{46} -7.19218 q^{47} +3.19469 q^{48} +1.00000 q^{49} -3.19268 q^{50} -0.755240 q^{51} +13.1618 q^{52} +4.78220 q^{53} -10.7681 q^{54} -4.81818 q^{55} +0.831292 q^{56} -0.823817 q^{57} -6.25944 q^{58} +4.23016 q^{59} +6.41101 q^{60} -0.608969 q^{61} -14.1068 q^{62} +1.90280 q^{63} -10.7950 q^{64} -14.0268 q^{65} +4.14349 q^{66} +14.7406 q^{67} +1.72787 q^{68} -5.59845 q^{69} -5.35506 q^{70} -1.42316 q^{71} +1.58178 q^{72} -3.73150 q^{73} -3.58068 q^{74} -1.59495 q^{75} +1.88477 q^{76} -1.88656 q^{77} +12.0626 q^{78} +9.28985 q^{79} +7.78928 q^{80} +0.329027 q^{81} -25.6160 q^{82} -0.304575 q^{83} +2.51023 q^{84} -1.84142 q^{85} +13.3907 q^{86} -3.12699 q^{87} -1.56828 q^{88} +10.7676 q^{89} -10.1896 q^{90} -5.49219 q^{91} +12.8084 q^{92} -7.04726 q^{93} +15.0804 q^{94} -2.00863 q^{95} -8.44005 q^{96} -16.7172 q^{97} -2.09677 q^{98} -3.58974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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