LMFDB - Embedded newform 6013.2.a.f.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.67470 q^{2} +1.47568 q^{3} +5.15405 q^{4} -1.35988 q^{5} -3.94701 q^{6} -1.00000 q^{7} -8.43614 q^{8} -0.822364 q^{9} +O(q^{10})$	\(q-2.67470 q^{2} +1.47568 q^{3} +5.15405 q^{4} -1.35988 q^{5} -3.94701 q^{6} -1.00000 q^{7} -8.43614 q^{8} -0.822364 q^{9} +3.63728 q^{10} +2.79662 q^{11} +7.60573 q^{12} +4.88498 q^{13} +2.67470 q^{14} -2.00675 q^{15} +12.2561 q^{16} +5.34042 q^{17} +2.19958 q^{18} +7.33305 q^{19} -7.00888 q^{20} -1.47568 q^{21} -7.48013 q^{22} +5.39884 q^{23} -12.4491 q^{24} -3.15073 q^{25} -13.0659 q^{26} -5.64059 q^{27} -5.15405 q^{28} +9.84171 q^{29} +5.36746 q^{30} -6.54000 q^{31} -15.9091 q^{32} +4.12692 q^{33} -14.2840 q^{34} +1.35988 q^{35} -4.23850 q^{36} +2.43400 q^{37} -19.6137 q^{38} +7.20868 q^{39} +11.4721 q^{40} +11.1774 q^{41} +3.94701 q^{42} +6.41063 q^{43} +14.4139 q^{44} +1.11832 q^{45} -14.4403 q^{46} +8.21730 q^{47} +18.0861 q^{48} +1.00000 q^{49} +8.42727 q^{50} +7.88076 q^{51} +25.1774 q^{52} -3.57205 q^{53} +15.0869 q^{54} -3.80306 q^{55} +8.43614 q^{56} +10.8212 q^{57} -26.3237 q^{58} -0.265972 q^{59} -10.3429 q^{60} -7.51350 q^{61} +17.4926 q^{62} +0.822364 q^{63} +18.0401 q^{64} -6.64299 q^{65} -11.0383 q^{66} -8.68547 q^{67} +27.5248 q^{68} +7.96697 q^{69} -3.63728 q^{70} +0.0105531 q^{71} +6.93758 q^{72} -5.17862 q^{73} -6.51022 q^{74} -4.64947 q^{75} +37.7949 q^{76} -2.79662 q^{77} -19.2811 q^{78} -9.06772 q^{79} -16.6668 q^{80} -5.85663 q^{81} -29.8963 q^{82} -0.954026 q^{83} -7.60573 q^{84} -7.26233 q^{85} -17.1465 q^{86} +14.5232 q^{87} -23.5927 q^{88} -1.81219 q^{89} -2.99116 q^{90} -4.88498 q^{91} +27.8259 q^{92} -9.65096 q^{93} -21.9788 q^{94} -9.97206 q^{95} -23.4768 q^{96} +3.68643 q^{97} -2.67470 q^{98} -2.29984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67470	−1.89130	−0.945651	−	0.325184i	$-0.894574\pi$
$2$	−2.67470	−1.89130	−0.945651	+	0.325184i	$0.894574\pi$
$3$	1.47568	0.851985	0.425993	−	0.904727i	$-0.359925\pi$
$3$	1.47568	0.851985	0.425993	+	0.904727i	$0.359925\pi$
$4$	5.15405	2.57702
$5$	−1.35988	−0.608157	−0.304078	−	0.952647i	$-0.598348\pi$
$5$	−1.35988	−0.608157	−0.304078	+	0.952647i	$0.598348\pi$
$6$	−3.94701	−1.61136
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−8.43614	−2.98263
$9$	−0.822364	−0.274121
$10$	3.63728	1.15021
$11$	2.79662	0.843212	0.421606	−	0.906779i	$-0.361467\pi$
$11$	2.79662	0.843212	0.421606	+	0.906779i	$0.361467\pi$
$12$	7.60573	2.19558
$13$	4.88498	1.35485	0.677425	−	0.735591i	$-0.263096\pi$
$13$	4.88498	1.35485	0.677425	+	0.735591i	$0.263096\pi$
$14$	2.67470	0.714845
$15$	−2.00675	−0.518140
$16$	12.2561	3.06402
$17$	5.34042	1.29524	0.647621	−	0.761963i	$-0.275764\pi$
$17$	5.34042	1.29524	0.647621	+	0.761963i	$0.275764\pi$
$18$	2.19958	0.518446
$19$	7.33305	1.68232	0.841159	−	0.540789i	$-0.181874\pi$
$19$	7.33305	1.68232	0.841159	+	0.540789i	$0.181874\pi$
$20$	−7.00888	−1.56723
$21$	−1.47568	−0.322020
$22$	−7.48013	−1.59477
$23$	5.39884	1.12574	0.562868	−	0.826547i	$-0.309698\pi$
$23$	5.39884	1.12574	0.562868	+	0.826547i	$0.309698\pi$
$24$	−12.4491	−2.54115
$25$	−3.15073	−0.630146
$26$	−13.0659	−2.56243
$27$	−5.64059	−1.08553
$28$	−5.15405	−0.974023
$29$	9.84171	1.82756	0.913780	−	0.406210i	$-0.133150\pi$
$29$	9.84171	1.82756	0.913780	+	0.406210i	$0.133150\pi$
$30$	5.36746	0.979960
$31$	−6.54000	−1.17462	−0.587309	−	0.809363i	$-0.699813\pi$
$31$	−6.54000	−1.17462	−0.587309	+	0.809363i	$0.699813\pi$
$32$	−15.9091	−2.81237
$33$	4.12692	0.718404
$34$	−14.2840	−2.44969
$35$	1.35988	0.229862
$36$	−4.23850	−0.706417
$37$	2.43400	0.400147	0.200073	−	0.979781i	$-0.435882\pi$
$37$	2.43400	0.400147	0.200073	+	0.979781i	$0.435882\pi$
$38$	−19.6137	−3.18177
$39$	7.20868	1.15431
$40$	11.4721	1.81390
$41$	11.1774	1.74562	0.872809	−	0.488062i	$-0.162296\pi$
$41$	11.1774	1.74562	0.872809	+	0.488062i	$0.162296\pi$
$42$	3.94701	0.609037
$43$	6.41063	0.977612	0.488806	−	0.872393i	$-0.337433\pi$
$43$	6.41063	0.977612	0.488806	+	0.872393i	$0.337433\pi$
$44$	14.4139	2.17298
$45$	1.11832	0.166709
$46$	−14.4403	−2.12911
$47$	8.21730	1.19862	0.599308	−	0.800519i	$-0.295443\pi$
$47$	8.21730	1.19862	0.599308	+	0.800519i	$0.295443\pi$
$48$	18.0861	2.61050
$49$	1.00000	0.142857
$50$	8.42727	1.19180
$51$	7.88076	1.10353
$52$	25.1774	3.49148
$53$	−3.57205	−0.490659	−0.245330	−	0.969440i	$-0.578896\pi$
$53$	−3.57205	−0.490659	−0.245330	+	0.969440i	$0.578896\pi$
$54$	15.0869	2.05307
$55$	−3.80306	−0.512805
$56$	8.43614	1.12733
$57$	10.8212	1.43331
$58$	−26.3237	−3.45647
$59$	−0.265972	−0.0346266	−0.0173133	−	0.999850i	$-0.505511\pi$
$59$	−0.265972	−0.0346266	−0.0173133	+	0.999850i	$0.505511\pi$
$60$	−10.3429	−1.33526
$61$	−7.51350	−0.962005	−0.481002	−	0.876719i	$-0.659727\pi$
$61$	−7.51350	−0.962005	−0.481002	+	0.876719i	$0.659727\pi$
$62$	17.4926	2.22156
$63$	0.822364	0.103608
$64$	18.0401	2.25501
$65$	−6.64299	−0.823961
$66$	−11.0383	−1.35872
$67$	−8.68547	−1.06110	−0.530550	−	0.847654i	$-0.678014\pi$
$67$	−8.68547	−1.06110	−0.530550	+	0.847654i	$0.678014\pi$
$68$	27.5248	3.33787
$69$	7.96697	0.959110
$70$	−3.63728	−0.434738
$71$	0.0105531	0.00125242	0.000626209	−	1.00000i	$-0.499801\pi$
$71$	0.0105531	0.00125242	0.000626209		1.00000i	$0.499801\pi$
$72$	6.93758	0.817601
$73$	−5.17862	−0.606112	−0.303056	−	0.952973i	$-0.598007\pi$
$73$	−5.17862	−0.606112	−0.303056	+	0.952973i	$0.598007\pi$
$74$	−6.51022	−0.756798
$75$	−4.64947	−0.536875
$76$	37.7949	4.33537
$77$	−2.79662	−0.318704
$78$	−19.2811	−2.18315
$79$	−9.06772	−1.02020	−0.510099	−	0.860116i	$-0.670391\pi$
$79$	−9.06772	−1.02020	−0.510099	+	0.860116i	$0.670391\pi$
$80$	−16.6668	−1.86341
$81$	−5.85663	−0.650736
$82$	−29.8963	−3.30149
$83$	−0.954026	−0.104718	−0.0523590	−	0.998628i	$-0.516674\pi$
$83$	−0.954026	−0.104718	−0.0523590	+	0.998628i	$0.516674\pi$
$84$	−7.60573	−0.829853
$85$	−7.26233	−0.787710
$86$	−17.1465	−1.84896
$87$	14.5232	1.55705
$88$	−23.5927	−2.51499
$89$	−1.81219	−0.192092	−0.0960459	−	0.995377i	$-0.530620\pi$
$89$	−1.81219	−0.192092	−0.0960459	+	0.995377i	$0.530620\pi$
$90$	−2.99116	−0.315296
$91$	−4.88498	−0.512086
$92$	27.8259	2.90105
$93$	−9.65096	−1.00076
$94$	−21.9788	−2.26694
$95$	−9.97206	−1.02311
$96$	−23.4768	−2.39609
$97$	3.68643	0.374301	0.187150	−	0.982331i	$-0.440075\pi$
$97$	3.68643	0.374301	0.187150	+	0.982331i	$0.440075\pi$
$98$	−2.67470	−0.270186
$99$	−2.29984	−0.231142
$100$	−16.2390	−1.62390
$101$	0.548959	0.0546234	0.0273117	−	0.999627i	$-0.491305\pi$
$101$	0.548959	0.0546234	0.0273117	+	0.999627i	$0.491305\pi$
$102$	−21.0787	−2.08710
$103$	−17.3643	−1.71095	−0.855477	−	0.517841i	$-0.826736\pi$
$103$	−17.3643	−1.71095	−0.855477	+	0.517841i	$0.826736\pi$
$104$	−41.2104	−4.04101
$105$	2.00675	0.195839
$106$	9.55419	0.927985
$107$	18.8388	1.82121	0.910607	−	0.413274i	$-0.135615\pi$
$107$	18.8388	1.82121	0.910607	+	0.413274i	$0.135615\pi$
$108$	−29.0719	−2.79744
$109$	−9.79517	−0.938207	−0.469103	−	0.883143i	$-0.655423\pi$
$109$	−9.79517	−0.938207	−0.469103	+	0.883143i	$0.655423\pi$
$110$	10.1721	0.969869
$111$	3.59181	0.340919
$112$	−12.2561	−1.15809
$113$	−7.44328	−0.700205	−0.350102	−	0.936711i	$-0.613853\pi$
$113$	−7.44328	−0.700205	−0.350102	+	0.936711i	$0.613853\pi$
$114$	−28.9436	−2.71082
$115$	−7.34177	−0.684624
$116$	50.7246	4.70966
$117$	−4.01723	−0.371394
$118$	0.711397	0.0654894
$119$	−5.34042	−0.489555
$120$	16.9292	1.54542
$121$	−3.17893	−0.288993
$122$	20.0964	1.81944
$123$	16.4943	1.48724
$124$	−33.7075	−3.02702
$125$	11.0840	0.991384
$126$	−2.19958	−0.195954
$127$	11.3737	1.00925	0.504625	−	0.863339i	$-0.331631\pi$
$127$	11.3737	1.00925	0.504625	+	0.863339i	$0.331631\pi$
$128$	−16.4336	−1.45254
$129$	9.46004	0.832910
$130$	17.7680	1.55836
$131$	−2.54745	−0.222572	−0.111286	−	0.993788i	$-0.535497\pi$
$131$	−2.54745	−0.222572	−0.111286	+	0.993788i	$0.535497\pi$
$132$	21.2703	1.85134
$133$	−7.33305	−0.635856
$134$	23.2311	2.00686
$135$	7.67052	0.660174
$136$	−45.0525	−3.86322
$137$	−14.5006	−1.23887	−0.619434	−	0.785049i	$-0.712638\pi$
$137$	−14.5006	−1.23887	−0.619434	+	0.785049i	$0.712638\pi$
$138$	−21.3093	−1.81397
$139$	−11.7944	−1.00038	−0.500192	−	0.865914i	$-0.666737\pi$
$139$	−11.7944	−1.00038	−0.500192	+	0.865914i	$0.666737\pi$
$140$	7.00888	0.592358
$141$	12.1261	1.02120
$142$	−0.0282263	−0.00236870
$143$	13.6614	1.14243
$144$	−10.0790	−0.839914
$145$	−13.3835	−1.11144
$146$	13.8513	1.14634
$147$	1.47568	0.121712
$148$	12.5449	1.03119
$149$	13.3055	1.09003	0.545014	−	0.838427i	$-0.316524\pi$
$149$	13.3055	1.09003	0.545014	+	0.838427i	$0.316524\pi$
$150$	12.4360	1.01539
$151$	20.3814	1.65861	0.829307	−	0.558794i	$-0.188736\pi$
$151$	20.3814	1.65861	0.829307	+	0.558794i	$0.188736\pi$
$152$	−61.8626	−5.01772
$153$	−4.39177	−0.355053
$154$	7.48013	0.602766
$155$	8.89361	0.714352
$156$	37.1539	2.97469
$157$	13.5611	1.08229	0.541145	−	0.840929i	$-0.317991\pi$
$157$	13.5611	1.08229	0.541145	+	0.840929i	$0.317991\pi$
$158$	24.2535	1.92950
$159$	−5.27121	−0.418034
$160$	21.6345	1.71036
$161$	−5.39884	−0.425488
$162$	15.6647	1.23074
$163$	18.1753	1.42360	0.711801	−	0.702382i	$-0.247880\pi$
$163$	18.1753	1.42360	0.711801	+	0.702382i	$0.247880\pi$
$164$	57.6089	4.49850
$165$	−5.61211	−0.436902
$166$	2.55174	0.198053
$167$	0.497002	0.0384592	0.0192296	−	0.999815i	$-0.493879\pi$
$167$	0.497002	0.0384592	0.0192296	+	0.999815i	$0.493879\pi$
$168$	12.4491	0.960465
$169$	10.8631	0.835621
$170$	19.4246	1.48980
$171$	−6.03044	−0.461159
$172$	33.0407	2.51933
$173$	3.60952	0.274427	0.137213	−	0.990542i	$-0.456185\pi$
$173$	3.60952	0.274427	0.137213	+	0.990542i	$0.456185\pi$
$174$	−38.8454	−2.94486
$175$	3.15073	0.238173
$176$	34.2756	2.58362
$177$	−0.392490	−0.0295014
$178$	4.84707	0.363303
$179$	−21.9902	−1.64362	−0.821812	−	0.569759i	$-0.807037\pi$
$179$	−21.9902	−1.64362	−0.821812	+	0.569759i	$0.807037\pi$
$180$	5.76385	0.429612
$181$	−25.4703	−1.89319	−0.946597	−	0.322419i	$-0.895504\pi$
$181$	−25.4703	−1.89319	−0.946597	+	0.322419i	$0.895504\pi$
$182$	13.0659	0.968508
$183$	−11.0875	−0.819614
$184$	−45.5454	−3.35765
$185$	−3.30994	−0.243352
$186$	25.8135	1.89273
$187$	14.9351	1.09216
$188$	42.3523	3.08886
$189$	5.64059	0.410293
$190$	26.6723	1.93501
$191$	−21.4853	−1.55462	−0.777310	−	0.629118i	$-0.783416\pi$
$191$	−21.4853	−1.55462	−0.777310	+	0.629118i	$0.783416\pi$
$192$	26.6214	1.92124
$193$	−0.788380	−0.0567488	−0.0283744	−	0.999597i	$-0.509033\pi$
$193$	−0.788380	−0.0567488	−0.0283744	+	0.999597i	$0.509033\pi$
$194$	−9.86012	−0.707916
$195$	−9.80294	−0.702003
$196$	5.15405	0.368146
$197$	−2.80052	−0.199528	−0.0997642	−	0.995011i	$-0.531809\pi$
$197$	−2.80052	−0.199528	−0.0997642	+	0.995011i	$0.531809\pi$
$198$	6.15139	0.437160
$199$	−15.8658	−1.12469	−0.562347	−	0.826902i	$-0.690101\pi$
$199$	−15.8658	−1.12469	−0.562347	+	0.826902i	$0.690101\pi$
$200$	26.5800	1.87949
$201$	−12.8170	−0.904041
$202$	−1.46830	−0.103309
$203$	−9.84171	−0.690753
$204$	40.6178	2.84381
$205$	−15.1999	−1.06161
$206$	46.4443	3.23593
$207$	−4.43981	−0.308588
$208$	59.8708	4.15129
$209$	20.5077	1.41855
$210$	−5.36746	−0.370390
$211$	−0.722082	−0.0497102	−0.0248551	−	0.999691i	$-0.507912\pi$
$211$	−0.722082	−0.0497102	−0.0248551	+	0.999691i	$0.507912\pi$
$212$	−18.4105	−1.26444
$213$	0.0155729	0.00106704
$214$	−50.3882	−3.44446
$215$	−8.71768	−0.594541
$216$	47.5848	3.23774
$217$	6.54000	0.443964
$218$	26.1992	1.77443
$219$	−7.64200	−0.516399
$220$	−19.6012	−1.32151
$221$	26.0879	1.75486
$222$	−9.60702	−0.644781
$223$	26.9541	1.80498	0.902491	−	0.430709i	$-0.141736\pi$
$223$	26.9541	1.80498	0.902491	+	0.430709i	$0.141736\pi$
$224$	15.9091	1.06297
$225$	2.59105	0.172736
$226$	19.9086	1.32430
$227$	4.69802	0.311818	0.155909	−	0.987771i	$-0.450169\pi$
$227$	4.69802	0.311818	0.155909	+	0.987771i	$0.450169\pi$
$228$	55.7732	3.69367
$229$	27.0804	1.78952	0.894761	−	0.446546i	$-0.147346\pi$
$229$	27.0804	1.78952	0.894761	+	0.446546i	$0.147346\pi$
$230$	19.6371	1.29483
$231$	−4.12692	−0.271531
$232$	−83.0260	−5.45093
$233$	−22.5447	−1.47695	−0.738476	−	0.674280i	$-0.764454\pi$
$233$	−22.5447	−1.47695	−0.738476	+	0.674280i	$0.764454\pi$
$234$	10.7449	0.702417
$235$	−11.1745	−0.728946
$236$	−1.37083	−0.0892336
$237$	−13.3811	−0.869193
$238$	14.2840	0.925897
$239$	28.3321	1.83265	0.916324	−	0.400437i	$-0.131142\pi$
$239$	28.3321	1.83265	0.916324	+	0.400437i	$0.131142\pi$
$240$	−24.5949	−1.58759
$241$	14.1754	0.913121	0.456560	−	0.889692i	$-0.349081\pi$
$241$	14.1754	0.913121	0.456560	+	0.889692i	$0.349081\pi$
$242$	8.50269	0.546574
$243$	8.27926	0.531115
$244$	−38.7249	−2.47911
$245$	−1.35988	−0.0868795
$246$	−44.1174	−2.81282
$247$	35.8218	2.27929
$248$	55.1724	3.50345
$249$	−1.40784	−0.0892182
$250$	−29.6464	−1.87501
$251$	22.9296	1.44731	0.723653	−	0.690164i	$-0.242461\pi$
$251$	22.9296	1.44731	0.723653	+	0.690164i	$0.242461\pi$
$252$	4.23850	0.267000
$253$	15.0985	0.949234
$254$	−30.4212	−1.90880
$255$	−10.7169	−0.671117
$256$	7.87486	0.492179
$257$	16.6120	1.03623	0.518115	−	0.855311i	$-0.326634\pi$
$257$	16.6120	1.03623	0.518115	+	0.855311i	$0.326634\pi$
$258$	−25.3028	−1.57529
$259$	−2.43400	−0.151241
$260$	−34.2383	−2.12337
$261$	−8.09347	−0.500973
$262$	6.81368	0.420951
$263$	−11.2253	−0.692182	−0.346091	−	0.938201i	$-0.612491\pi$
$263$	−11.2253	−0.692182	−0.346091	+	0.938201i	$0.612491\pi$
$264$	−34.8153	−2.14273
$265$	4.85756	0.298398
$266$	19.6137	1.20260
$267$	−2.67422	−0.163659
$268$	−44.7653	−2.73448
$269$	4.47137	0.272624	0.136312	−	0.990666i	$-0.456475\pi$
$269$	4.47137	0.272624	0.136312	+	0.990666i	$0.456475\pi$
$270$	−20.5164	−1.24859
$271$	−0.199202	−0.0121006	−0.00605032	−	0.999982i	$-0.501926\pi$
$271$	−0.199202	−0.0121006	−0.00605032	+	0.999982i	$0.501926\pi$
$272$	65.4527	3.96865
$273$	−7.20868	−0.436289
$274$	38.7848	2.34307
$275$	−8.81138	−0.531346
$276$	41.0621	2.47165
$277$	−12.2026	−0.733185	−0.366592	−	0.930382i	$-0.619476\pi$
$277$	−12.2026	−0.733185	−0.366592	+	0.930382i	$0.619476\pi$
$278$	31.5464	1.89203
$279$	5.37826	0.321988
$280$	−11.4721	−0.685591
$281$	12.1192	0.722969	0.361484	−	0.932378i	$-0.382270\pi$
$281$	12.1192	0.722969	0.361484	+	0.932378i	$0.382270\pi$
$282$	−32.4338	−1.93140
$283$	23.6225	1.40421	0.702105	−	0.712073i	$-0.252244\pi$
$283$	23.6225	1.40421	0.702105	+	0.712073i	$0.252244\pi$
$284$	0.0543909	0.00322751
$285$	−14.7156	−0.871676
$286$	−36.5403	−2.16067
$287$	−11.1774	−0.659782
$288$	13.0831	0.770929
$289$	11.5201	0.677651
$290$	35.7970	2.10207
$291$	5.44000	0.318899
$292$	−26.6909	−1.56196
$293$	−22.9643	−1.34159	−0.670794	−	0.741643i	$-0.734047\pi$
$293$	−22.9643	−1.34159	−0.670794	+	0.741643i	$0.734047\pi$
$294$	−3.94701	−0.230194
$295$	0.361690	0.0210584
$296$	−20.5335	−1.19349
$297$	−15.7746	−0.915334
$298$	−35.5882	−2.06157
$299$	26.3732	1.52520
$300$	−23.9636	−1.38354
$301$	−6.41063	−0.369502
$302$	−54.5142	−3.13694
$303$	0.810088	0.0465383
$304$	89.8745	5.15466
$305$	10.2174	0.585049
$306$	11.7467	0.671513
$307$	−11.8358	−0.675507	−0.337754	−	0.941235i	$-0.609667\pi$
$307$	−11.8358	−0.675507	−0.337754	+	0.941235i	$0.609667\pi$
$308$	−14.4139	−0.821308
$309$	−25.6242	−1.45771
$310$	−23.7878	−1.35106
$311$	−30.3096	−1.71870	−0.859351	−	0.511387i	$-0.829132\pi$
$311$	−30.3096	−1.71870	−0.859351	+	0.511387i	$0.829132\pi$
$312$	−60.8134	−3.44288
$313$	19.6745	1.11207	0.556035	−	0.831159i	$-0.312322\pi$
$313$	19.6745	1.11207	0.556035	+	0.831159i	$0.312322\pi$
$314$	−36.2718	−2.04694
$315$	−1.11832	−0.0630099
$316$	−46.7354	−2.62907
$317$	−12.2919	−0.690382	−0.345191	−	0.938533i	$-0.612186\pi$
$317$	−12.2919	−0.690382	−0.345191	+	0.938533i	$0.612186\pi$
$318$	14.0989	0.790629
$319$	27.5235	1.54102
$320$	−24.5323	−1.37140
$321$	27.8000	1.55165
$322$	14.4403	0.804726
$323$	39.1616	2.17901
$324$	−30.1853	−1.67696
$325$	−15.3913	−0.853753
$326$	−48.6136	−2.69246
$327$	−14.4545	−0.799338
$328$	−94.2942	−5.20653
$329$	−8.21730	−0.453034
$330$	15.0107	0.826314
$331$	1.36769	0.0751751	0.0375876	−	0.999293i	$-0.488033\pi$
$331$	1.36769	0.0751751	0.0375876	+	0.999293i	$0.488033\pi$
$332$	−4.91710	−0.269861
$333$	−2.00163	−0.109689
$334$	−1.32933	−0.0727380
$335$	11.8112	0.645314
$336$	−18.0861	−0.986677
$337$	14.3739	0.782994	0.391497	−	0.920179i	$-0.371957\pi$
$337$	14.3739	0.782994	0.391497	+	0.920179i	$0.371957\pi$
$338$	−29.0555	−1.58041
$339$	−10.9839	−0.596564
$340$	−37.4304	−2.02995
$341$	−18.2899	−0.990453
$342$	16.1296	0.872191
$343$	−1.00000	−0.0539949
$344$	−54.0809	−2.91585
$345$	−10.8341	−0.583289
$346$	−9.65441	−0.519024
$347$	3.62807	0.194765	0.0973826	−	0.995247i	$-0.468953\pi$
$347$	3.62807	0.194765	0.0973826	+	0.995247i	$0.468953\pi$
$348$	74.8534	4.01256
$349$	12.1945	0.652758	0.326379	−	0.945239i	$-0.394171\pi$
$349$	12.1945	0.652758	0.326379	+	0.945239i	$0.394171\pi$
$350$	−8.42727	−0.450456
$351$	−27.5542	−1.47073
$352$	−44.4918	−2.37142
$353$	−17.9032	−0.952894	−0.476447	−	0.879203i	$-0.658075\pi$
$353$	−17.9032	−0.952894	−0.476447	+	0.879203i	$0.658075\pi$
$354$	1.04980	0.0557960
$355$	−0.0143509	−0.000761666 0
$356$	−9.34011	−0.495025
$357$	−7.88076	−0.417094
$358$	58.8173	3.10859
$359$	23.3764	1.23376	0.616880	−	0.787057i	$-0.288396\pi$
$359$	23.3764	1.23376	0.616880	+	0.787057i	$0.288396\pi$
$360$	−9.43427	−0.497229
$361$	34.7736	1.83019
$362$	68.1256	3.58060
$363$	−4.69108	−0.246218
$364$	−25.1774	−1.31966
$365$	7.04230	0.368611
$366$	29.6559	1.55014
$367$	−5.35767	−0.279668	−0.139834	−	0.990175i	$-0.544657\pi$
$367$	−5.35767	−0.279668	−0.139834	+	0.990175i	$0.544657\pi$
$368$	66.1687	3.44928
$369$	−9.19190	−0.478511
$370$	8.85312	0.460252
$371$	3.57205	0.185452
$372$	−49.7415	−2.57898
$373$	−20.7782	−1.07585	−0.537927	−	0.842991i	$-0.680792\pi$
$373$	−20.7782	−1.07585	−0.537927	+	0.842991i	$0.680792\pi$
$374$	−39.9470	−2.06561
$375$	16.3565	0.844644
$376$	−69.3222	−3.57502
$377$	48.0766	2.47607
$378$	−15.0869	−0.775987
$379$	−7.34247	−0.377157	−0.188579	−	0.982058i	$-0.560388\pi$
$379$	−7.34247	−0.377157	−0.188579	+	0.982058i	$0.560388\pi$
$380$	−51.3965	−2.63658
$381$	16.7839	0.859866
$382$	57.4667	2.94025
$383$	34.8722	1.78189	0.890944	−	0.454113i	$-0.150044\pi$
$383$	34.8722	1.78189	0.890944	+	0.454113i	$0.150044\pi$
$384$	−24.2508	−1.23754
$385$	3.80306	0.193822
$386$	2.10868	0.107329
$387$	−5.27187	−0.267984
$388$	19.0000	0.964581
$389$	17.7754	0.901248	0.450624	−	0.892714i	$-0.351201\pi$
$389$	17.7754	0.901248	0.450624	+	0.892714i	$0.351201\pi$
$390$	26.2200	1.32770
$391$	28.8321	1.45810
$392$	−8.43614	−0.426089
$393$	−3.75923	−0.189628
$394$	7.49055	0.377368
$395$	12.3310	0.620440
$396$	−11.8535	−0.595659
$397$	20.0799	1.00778	0.503891	−	0.863767i	$-0.331901\pi$
$397$	20.0799	1.00778	0.503891	+	0.863767i	$0.331901\pi$
$398$	42.4362	2.12713
$399$	−10.8212	−0.541740
$400$	−38.6156	−1.93078
$401$	−3.40406	−0.169991	−0.0849953	−	0.996381i	$-0.527088\pi$
$401$	−3.40406	−0.169991	−0.0849953	+	0.996381i	$0.527088\pi$
$402$	34.2817	1.70981
$403$	−31.9478	−1.59143
$404$	2.82936	0.140766
$405$	7.96430	0.395749
$406$	26.3237	1.30642
$407$	6.80696	0.337409
$408$	−66.4832	−3.29141
$409$	−6.65887	−0.329260	−0.164630	−	0.986355i	$-0.552643\pi$
$409$	−6.65887	−0.329260	−0.164630	+	0.986355i	$0.552643\pi$
$410$	40.6553	2.00782
$411$	−21.3982	−1.05550
$412$	−89.4963	−4.40917
$413$	0.265972	0.0130876
$414$	11.8752	0.583633
$415$	1.29736	0.0636849
$416$	−77.7159	−3.81034
$417$	−17.4047	−0.852313
$418$	−54.8522	−2.68291
$419$	−34.9917	−1.70946	−0.854729	−	0.519075i	$-0.826276\pi$
$419$	−34.9917	−1.70946	−0.854729	+	0.519075i	$0.826276\pi$
$420$	10.3429	0.504681
$421$	−18.6430	−0.908603	−0.454301	−	0.890848i	$-0.650111\pi$
$421$	−18.6430	−0.908603	−0.454301	+	0.890848i	$0.650111\pi$
$422$	1.93136	0.0940170
$423$	−6.75761	−0.328566
$424$	30.1343	1.46345
$425$	−16.8262	−0.816191
$426$	−0.0416530	−0.00201810
$427$	7.51350	0.363604
$428$	97.0959	4.69331
$429$	20.1599	0.973331
$430$	23.3172	1.12446
$431$	−18.7580	−0.903543	−0.451771	−	0.892134i	$-0.649208\pi$
$431$	−18.7580	−0.903543	−0.451771	+	0.892134i	$0.649208\pi$
$432$	−69.1316	−3.32610
$433$	29.1278	1.39979	0.699896	−	0.714244i	$-0.253229\pi$
$433$	29.1278	1.39979	0.699896	+	0.714244i	$0.253229\pi$
$434$	−17.4926	−0.839670
$435$	−19.7498	−0.946932
$436$	−50.4847	−2.41778
$437$	39.5900	1.89384
$438$	20.4401	0.976666
$439$	−15.5705	−0.743138	−0.371569	−	0.928405i	$-0.621180\pi$
$439$	−15.5705	−0.743138	−0.371569	+	0.928405i	$0.621180\pi$
$440$	32.0832	1.52951
$441$	−0.822364	−0.0391602
$442$	−69.7773	−3.31897
$443$	−2.72522	−0.129479	−0.0647396	−	0.997902i	$-0.520622\pi$
$443$	−2.72522	−0.129479	−0.0647396	+	0.997902i	$0.520622\pi$
$444$	18.5123	0.878556
$445$	2.46436	0.116822
$446$	−72.0943	−3.41377
$447$	19.6347	0.928688
$448$	−18.0401	−0.852314
$449$	5.31518	0.250839	0.125420	−	0.992104i	$-0.459972\pi$
$449$	5.31518	0.250839	0.125420	+	0.992104i	$0.459972\pi$
$450$	−6.93028	−0.326697
$451$	31.2589	1.47193
$452$	−38.3630	−1.80444
$453$	30.0764	1.41311
$454$	−12.5658	−0.589743
$455$	6.64299	0.311428
$456$	−91.2895	−4.27502
$457$	−32.8516	−1.53673	−0.768366	−	0.640011i	$-0.778930\pi$
$457$	−32.8516	−1.53673	−0.768366	+	0.640011i	$0.778930\pi$
$458$	−72.4320	−3.38453
$459$	−30.1231	−1.40603
$460$	−37.8398	−1.76429
$461$	5.75293	0.267941	0.133970	−	0.990985i	$-0.457227\pi$
$461$	5.75293	0.267941	0.133970	+	0.990985i	$0.457227\pi$
$462$	11.0383	0.513548
$463$	−23.9979	−1.11528	−0.557638	−	0.830084i	$-0.688292\pi$
$463$	−23.9979	−1.11528	−0.557638	+	0.830084i	$0.688292\pi$
$464$	120.621	5.59968
$465$	13.1241	0.608617
$466$	60.3004	2.79336
$467$	11.7633	0.544341	0.272171	−	0.962249i	$-0.412259\pi$
$467$	11.7633	0.544341	0.272171	+	0.962249i	$0.412259\pi$
$468$	−20.7050	−0.957089
$469$	8.68547	0.401058
$470$	29.8886	1.37866
$471$	20.0118	0.922096
$472$	2.24378	0.103278
$473$	17.9281	0.824334
$474$	35.7904	1.64391
$475$	−23.1044	−1.06010
$476$	−27.5248	−1.26160
$477$	2.93753	0.134500
$478$	−75.7799	−3.46609
$479$	−33.6853	−1.53912	−0.769560	−	0.638574i	$-0.779524\pi$
$479$	−33.6853	−1.53912	−0.769560	+	0.638574i	$0.779524\pi$
$480$	31.9257	1.45720
$481$	11.8900	0.542139
$482$	−37.9151	−1.72699
$483$	−7.96697	−0.362510
$484$	−16.3843	−0.744742
$485$	−5.01311	−0.227633
$486$	−22.1446	−1.00450
$487$	13.0225	0.590105	0.295053	−	0.955481i	$-0.404663\pi$
$487$	13.0225	0.590105	0.295053	+	0.955481i	$0.404663\pi$
$488$	63.3849	2.86930
$489$	26.8210	1.21289
$490$	3.63728	0.164315
$491$	26.1566	1.18043	0.590215	−	0.807246i	$-0.299043\pi$
$491$	26.1566	1.18043	0.590215	+	0.807246i	$0.299043\pi$
$492$	85.0124	3.83265
$493$	52.5589	2.36713
$494$	−95.8128	−4.31082
$495$	3.12750	0.140571
$496$	−80.1548	−3.59906
$497$	−0.0105531	−0.000473369 0
$498$	3.76555	0.168739
$499$	−9.98015	−0.446773	−0.223387	−	0.974730i	$-0.571711\pi$
$499$	−9.98015	−0.446773	−0.223387	+	0.974730i	$0.571711\pi$
$500$	57.1275	2.55482
$501$	0.733417	0.0327667
$502$	−61.3300	−2.73729
$503$	−40.6923	−1.81438	−0.907190	−	0.420722i	$-0.861777\pi$
$503$	−40.6923	−1.81438	−0.907190	+	0.420722i	$0.861777\pi$
$504$	−6.93758	−0.309024
$505$	−0.746517	−0.0332196
$506$	−40.3840	−1.79529
$507$	16.0304	0.711937
$508$	58.6204	2.60086
$509$	−0.293790	−0.0130220	−0.00651100	−	0.999979i	$-0.502073\pi$
$509$	−0.293790	−0.0130220	−0.00651100	+	0.999979i	$0.502073\pi$
$510$	28.6645	1.26928
$511$	5.17862	0.229089
$512$	11.8043	0.521680
$513$	−41.3627	−1.82621
$514$	−44.4323	−1.95983
$515$	23.6133	1.04053
$516$	48.7575	2.14643
$517$	22.9806	1.01069
$518$	6.51022	0.286043
$519$	5.32651	0.233808
$520$	56.0412	2.45757
$521$	19.4475	0.852012	0.426006	−	0.904720i	$-0.359920\pi$
$521$	19.4475	0.852012	0.426006	+	0.904720i	$0.359920\pi$
$522$	21.6476	0.947491
$523$	−12.7033	−0.555476	−0.277738	−	0.960657i	$-0.589585\pi$
$523$	−12.7033	−0.555476	−0.277738	+	0.960657i	$0.589585\pi$
$524$	−13.1297	−0.573573
$525$	4.64947	0.202920
$526$	30.0244	1.30913
$527$	−34.9263	−1.52142
$528$	50.5799	2.20121
$529$	6.14746	0.267281
$530$	−12.9925	−0.564360
$531$	0.218726	0.00949190
$532$	−37.7949	−1.63862
$533$	54.6015	2.36505
$534$	7.15274	0.309529
$535$	−25.6185	−1.10758
$536$	73.2718	3.16486
$537$	−32.4505	−1.40034
$538$	−11.9596	−0.515614
$539$	2.79662	0.120459
$540$	39.5342	1.70128
$541$	−5.24301	−0.225415	−0.112707	−	0.993628i	$-0.535952\pi$
$541$	−5.24301	−0.225415	−0.112707	+	0.993628i	$0.535952\pi$
$542$	0.532806	0.0228860
$543$	−37.5861	−1.61297
$544$	−84.9615	−3.64269
$545$	13.3202	0.570577
$546$	19.2811	0.825155
$547$	37.3826	1.59836	0.799181	−	0.601090i	$-0.205267\pi$
$547$	37.3826	1.59836	0.799181	+	0.601090i	$0.205267\pi$
$548$	−74.7366	−3.19259
$549$	6.17883	0.263706
$550$	23.5678	1.00494
$551$	72.1698	3.07453
$552$	−67.2104	−2.86067
$553$	9.06772	0.385599
$554$	32.6384	1.38667
$555$	−4.88442	−0.207332
$556$	−60.7887	−2.57801
$557$	−41.9512	−1.77753	−0.888765	−	0.458363i	$-0.848436\pi$
$557$	−41.9512	−1.77753	−0.888765	+	0.458363i	$0.848436\pi$
$558$	−14.3853	−0.608977
$559$	31.3158	1.32452
$560$	16.6668	0.704301
$561$	22.0395	0.930507
$562$	−32.4152	−1.36735
$563$	19.2853	0.812779	0.406389	−	0.913700i	$-0.366788\pi$
$563$	19.2853	0.812779	0.406389	+	0.913700i	$0.366788\pi$
$564$	62.4985	2.63166
$565$	10.1220	0.425834
$566$	−63.1831	−2.65579
$567$	5.85663	0.245955
$568$	−0.0890270	−0.00373549
$569$	−17.6869	−0.741472	−0.370736	−	0.928738i	$-0.620895\pi$
$569$	−17.6869	−0.741472	−0.370736	+	0.928738i	$0.620895\pi$
$570$	39.3599	1.64860
$571$	−1.49998	−0.0627724	−0.0313862	−	0.999507i	$-0.509992\pi$
$571$	−1.49998	−0.0627724	−0.0313862	+	0.999507i	$0.509992\pi$
$572$	70.4117	2.94406
$573$	−31.7054	−1.32451
$574$	29.8963	1.24785
$575$	−17.0103	−0.709377
$576$	−14.8355	−0.618146
$577$	−2.91558	−0.121377	−0.0606887	−	0.998157i	$-0.519330\pi$
$577$	−2.91558	−0.121377	−0.0606887	+	0.998157i	$0.519330\pi$
$578$	−30.8128	−1.28164
$579$	−1.16340	−0.0483492
$580$	−68.9794	−2.86421
$581$	0.954026	0.0395797
$582$	−14.5504	−0.603134
$583$	−9.98967	−0.413730
$584$	43.6876	1.80781
$585$	5.46295	0.225865
$586$	61.4227	2.53735
$587$	19.7841	0.816578	0.408289	−	0.912853i	$-0.366125\pi$
$587$	19.7841	0.816578	0.408289	+	0.912853i	$0.366125\pi$
$588$	7.60573	0.313655
$589$	−47.9582	−1.97608
$590$	−0.967415	−0.0398278
$591$	−4.13267	−0.169995
$592$	29.8313	1.22606
$593$	4.15905	0.170792	0.0853958	−	0.996347i	$-0.472785\pi$
$593$	4.15905	0.170792	0.0853958	+	0.996347i	$0.472785\pi$
$594$	42.1923	1.73117
$595$	7.26233	0.297726
$596$	68.5771	2.80903
$597$	−23.4128	−0.958222
$598$	−70.5406	−2.88462
$599$	−12.4191	−0.507429	−0.253715	−	0.967279i	$-0.581652\pi$
$599$	−12.4191	−0.507429	−0.253715	+	0.967279i	$0.581652\pi$
$600$	39.2236	1.60130
$601$	−1.14880	−0.0468606	−0.0234303	−	0.999725i	$-0.507459\pi$
$601$	−1.14880	−0.0468606	−0.0234303	+	0.999725i	$0.507459\pi$
$602$	17.1465	0.698841
$603$	7.14262	0.290870
$604$	105.047	4.27428
$605$	4.32296	0.175753
$606$	−2.16675	−0.0880180
$607$	19.9227	0.808638	0.404319	−	0.914618i	$-0.367509\pi$
$607$	19.9227	0.808638	0.404319	+	0.914618i	$0.367509\pi$
$608$	−116.663	−4.73129
$609$	−14.5232	−0.588511
$610$	−27.3287	−1.10651
$611$	40.1414	1.62395
$612$	−22.6354	−0.914981
$613$	−37.3011	−1.50658	−0.753289	−	0.657690i	$-0.771534\pi$
$613$	−37.3011	−1.50658	−0.753289	+	0.657690i	$0.771534\pi$
$614$	31.6574	1.27759
$615$	−22.4303	−0.904475
$616$	23.5927	0.950575
$617$	10.0269	0.403670	0.201835	−	0.979420i	$-0.435310\pi$
$617$	10.0269	0.403670	0.201835	+	0.979420i	$0.435310\pi$
$618$	68.5370	2.75696
$619$	−5.20266	−0.209112	−0.104556	−	0.994519i	$-0.533342\pi$
$619$	−5.20266	−0.209112	−0.104556	+	0.994519i	$0.533342\pi$
$620$	45.8381	1.84090
$621$	−30.4526	−1.22202
$622$	81.0693	3.25058
$623$	1.81219	0.0726039
$624$	88.3503	3.53684
$625$	0.680729	0.0272292
$626$	−52.6236	−2.10326
$627$	30.2629	1.20858
$628$	69.8943	2.78909
$629$	12.9986	0.518287
$630$	2.99116	0.119171
$631$	−13.7130	−0.545905	−0.272952	−	0.962028i	$-0.588000\pi$
$631$	−13.7130	−0.545905	−0.272952	+	0.962028i	$0.588000\pi$
$632$	76.4965	3.04287
$633$	−1.06556	−0.0423523
$634$	32.8772	1.30572
$635$	−15.4668	−0.613782
$636$	−27.1681	−1.07728
$637$	4.88498	0.193550
$638$	−73.6172	−2.91453
$639$	−0.00867845	−0.000343314 0
$640$	22.3477	0.883371
$641$	22.7333	0.897912	0.448956	−	0.893554i	$-0.351796\pi$
$641$	22.7333	0.897912	0.448956	+	0.893554i	$0.351796\pi$
$642$	−74.3569	−2.93463
$643$	46.9583	1.85185	0.925927	−	0.377701i	$-0.123285\pi$
$643$	46.9583	1.85185	0.925927	+	0.377701i	$0.123285\pi$
$644$	−27.8259	−1.09649
$645$	−12.8645	−0.506540
$646$	−104.746	−4.12116
$647$	−16.9147	−0.664985	−0.332493	−	0.943106i	$-0.607890\pi$
$647$	−16.9147	−0.664985	−0.332493	+	0.943106i	$0.607890\pi$
$648$	49.4073	1.94090
$649$	−0.743823	−0.0291976
$650$	41.1671	1.61471
$651$	9.65096	0.378251
$652$	93.6764	3.66865
$653$	−14.5563	−0.569631	−0.284815	−	0.958582i	$-0.591932\pi$
$653$	−14.5563	−0.569631	−0.284815	+	0.958582i	$0.591932\pi$
$654$	38.6617	1.51179
$655$	3.46423	0.135359
$656$	136.991	5.34861
$657$	4.25871	0.166148
$658$	21.9788	0.856824
$659$	−49.7278	−1.93712	−0.968560	−	0.248778i	$-0.919971\pi$
$659$	−49.7278	−1.93712	−0.968560	+	0.248778i	$0.919971\pi$
$660$	−28.9251	−1.12591
$661$	−20.2076	−0.785986	−0.392993	−	0.919541i	$-0.628560\pi$
$661$	−20.2076	−0.785986	−0.392993	+	0.919541i	$0.628560\pi$
$662$	−3.65817	−0.142179
$663$	38.4974	1.49511
$664$	8.04830	0.312335
$665$	9.97206	0.386700
$666$	5.35377	0.207455
$667$	53.1338	2.05735
$668$	2.56157	0.0991102
$669$	39.7757	1.53782
$670$	−31.5915	−1.22048
$671$	−21.0124	−0.811174
$672$	23.4768	0.905638
$673$	24.3491	0.938587	0.469293	−	0.883042i	$-0.344509\pi$
$673$	24.3491	0.938587	0.469293	+	0.883042i	$0.344509\pi$
$674$	−38.4458	−1.48088
$675$	17.7720	0.684044
$676$	55.9888	2.15341
$677$	−1.51962	−0.0584039	−0.0292019	−	0.999574i	$-0.509297\pi$
$677$	−1.51962	−0.0584039	−0.0292019	+	0.999574i	$0.509297\pi$
$678$	29.3787	1.12828
$679$	−3.68643	−0.141472
$680$	61.2660	2.34944
$681$	6.93278	0.265665
$682$	48.9200	1.87325
$683$	18.9316	0.724397	0.362198	−	0.932101i	$-0.382026\pi$
$683$	18.9316	0.724397	0.362198	+	0.932101i	$0.382026\pi$
$684$	−31.0811	−1.18842
$685$	19.7190	0.753426
$686$	2.67470	0.102121
$687$	39.9620	1.52465
$688$	78.5692	2.99542
$689$	−17.4494	−0.664770
$690$	28.9781	1.10318
$691$	−4.54952	−0.173072	−0.0865360	−	0.996249i	$-0.527580\pi$
$691$	−4.54952	−0.173072	−0.0865360	+	0.996249i	$0.527580\pi$
$692$	18.6036	0.707204
$693$	2.29984	0.0873636
$694$	−9.70402	−0.368360
$695$	16.0389	0.608390
$696$	−122.520	−4.64411
$697$	59.6920	2.26100
$698$	−32.6168	−1.23456
$699$	−33.2688	−1.25834
$700$	16.2390	0.613776
$701$	40.9274	1.54581	0.772904	−	0.634524i	$-0.218804\pi$
$701$	40.9274	1.54581	0.772904	+	0.634524i	$0.218804\pi$
$702$	73.6994	2.78160
$703$	17.8486	0.673174
$704$	50.4512	1.90145
$705$	−16.4900	−0.621051
$706$	47.8859	1.80221
$707$	−0.548959	−0.0206457
$708$	−2.02291	−0.0760257
$709$	−24.5025	−0.920212	−0.460106	−	0.887864i	$-0.652189\pi$
$709$	−24.5025	−0.920212	−0.460106	+	0.887864i	$0.652189\pi$
$710$	0.0383844	0.00144054
$711$	7.45696	0.279658
$712$	15.2879	0.572938
$713$	−35.3084	−1.32231
$714$	21.0787	0.788850
$715$	−18.5779	−0.694774
$716$	−113.338	−4.23566
$717$	41.8091	1.56139
$718$	−62.5250	−2.33341
$719$	−17.2094	−0.641801	−0.320901	−	0.947113i	$-0.603986\pi$
$719$	−17.2094	−0.641801	−0.320901	+	0.947113i	$0.603986\pi$
$720$	13.7062	0.510799
$721$	17.3643	0.646680
$722$	−93.0092	−3.46144
$723$	20.9184	0.777965
$724$	−131.275	−4.87880
$725$	−31.0086	−1.15163
$726$	12.5473	0.465673
$727$	−39.7849	−1.47554	−0.737771	−	0.675051i	$-0.764121\pi$
$727$	−39.7849	−1.47554	−0.737771	+	0.675051i	$0.764121\pi$
$728$	41.2104	1.52736
$729$	29.7874	1.10324
$730$	−18.8361	−0.697155
$731$	34.2354	1.26624
$732$	−57.1456	−2.11216
$733$	17.5946	0.649872	0.324936	−	0.945736i	$-0.394657\pi$
$733$	17.5946	0.649872	0.324936	+	0.945736i	$0.394657\pi$
$734$	14.3302	0.528937
$735$	−2.00675	−0.0740200
$736$	−85.8909	−3.16598
$737$	−24.2899	−0.894732
$738$	24.5856	0.905009
$739$	−24.6162	−0.905521	−0.452761	−	0.891632i	$-0.649561\pi$
$739$	−24.6162	−0.905521	−0.452761	+	0.891632i	$0.649561\pi$
$740$	−17.0596	−0.627123
$741$	52.8616	1.94192
$742$	−9.55419	−0.350745
$743$	7.29935	0.267787	0.133894	−	0.990996i	$-0.457252\pi$
$743$	7.29935	0.267787	0.133894	+	0.990996i	$0.457252\pi$
$744$	81.4168	2.98489
$745$	−18.0939	−0.662908
$746$	55.5755	2.03476
$747$	0.784557	0.0287054
$748$	76.9762	2.81453
$749$	−18.8388	−0.688354
$750$	−43.7487	−1.59748
$751$	11.6293	0.424358	0.212179	−	0.977231i	$-0.431944\pi$
$751$	11.6293	0.424358	0.212179	+	0.977231i	$0.431944\pi$
$752$	100.712	3.67259
$753$	33.8369	1.23308
$754$	−128.591	−4.68300
$755$	−27.7162	−1.00870
$756$	29.0719	1.05733
$757$	28.9973	1.05392	0.526962	−	0.849889i	$-0.323331\pi$
$757$	28.9973	1.05392	0.526962	+	0.849889i	$0.323331\pi$
$758$	19.6389	0.713319
$759$	22.2806	0.808733
$760$	84.1257	3.05156
$761$	19.1447	0.693995	0.346998	−	0.937866i	$-0.387201\pi$
$761$	19.1447	0.693995	0.346998	+	0.937866i	$0.387201\pi$
$762$	−44.8920	−1.62627
$763$	9.79517	0.354609
$764$	−110.736	−4.00629
$765$	5.97227	0.215928
$766$	−93.2729	−3.37009
$767$	−1.29927	−0.0469139
$768$	11.6208	0.419329
$769$	9.81638	0.353988	0.176994	−	0.984212i	$-0.443363\pi$
$769$	9.81638	0.353988	0.176994	+	0.984212i	$0.443363\pi$
$770$	−10.1721	−0.366576
$771$	24.5141	0.882853
$772$	−4.06335	−0.146243
$773$	−9.49769	−0.341608	−0.170804	−	0.985305i	$-0.554637\pi$
$773$	−9.49769	−0.341608	−0.170804	+	0.985305i	$0.554637\pi$
$774$	14.1007	0.506839
$775$	20.6058	0.740181
$776$	−31.0993	−1.11640
$777$	−3.59181	−0.128855
$778$	−47.5439	−1.70453
$779$	81.9645	2.93668
$780$	−50.5248	−1.80908
$781$	0.0295129	0.00105605
$782$	−77.1172	−2.75771
$783$	−55.5131	−1.98388
$784$	12.2561	0.437718
$785$	−18.4414	−0.658202
$786$	10.0548	0.358644
$787$	38.4486	1.37055	0.685273	−	0.728286i	$-0.259683\pi$
$787$	38.4486	1.37055	0.685273	+	0.728286i	$0.259683\pi$
$788$	−14.4340	−0.514189
$789$	−16.5650	−0.589729
$790$	−32.9818	−1.17344
$791$	7.44328	0.264653
$792$	19.4018	0.689411
$793$	−36.7033	−1.30337
$794$	−53.7079	−1.90602
$795$	7.16821	0.254230
$796$	−81.7728	−2.89836
$797$	−44.3921	−1.57245	−0.786225	−	0.617941i	$-0.787967\pi$
$797$	−44.3921	−1.57245	−0.786225	+	0.617941i	$0.787967\pi$
$798$	28.9436	1.02459
$799$	43.8838	1.55250
$800$	50.1254	1.77220
$801$	1.49028	0.0526564
$802$	9.10485	0.321503
$803$	−14.4826	−0.511081
$804$	−66.0593	−2.32973
$805$	7.34177	0.258763
$806$	85.4509	3.00988
$807$	6.59831	0.232272
$808$	−4.63109	−0.162921
$809$	0.481633	0.0169333	0.00846666	−	0.999964i	$-0.497305\pi$
$809$	0.481633	0.0169333	0.00846666	+	0.999964i	$0.497305\pi$
$810$	−21.3022	−0.748482
$811$	−34.0438	−1.19544	−0.597720	−	0.801705i	$-0.703926\pi$
$811$	−34.0438	−1.19544	−0.597720	+	0.801705i	$0.703926\pi$
$812$	−50.7246	−1.78009
$813$	−0.293958	−0.0103096
$814$	−18.2066	−0.638141
$815$	−24.7162	−0.865772
$816$	96.5873	3.38123
$817$	47.0095	1.64465
$818$	17.8105	0.622730
$819$	4.01723	0.140374
$820$	−78.3411	−2.73579
$821$	8.97502	0.313230	0.156615	−	0.987660i	$-0.449942\pi$
$821$	8.97502	0.313230	0.156615	+	0.987660i	$0.449942\pi$
$822$	57.2340	1.99626
$823$	−34.9631	−1.21874	−0.609368	−	0.792887i	$-0.708577\pi$
$823$	−34.9631	−1.21874	−0.609368	+	0.792887i	$0.708577\pi$
$824$	146.487	5.10313
$825$	−13.0028	−0.452699
$826$	−0.711397	−0.0247527
$827$	6.66846	0.231885	0.115943	−	0.993256i	$-0.463011\pi$
$827$	6.66846	0.231885	0.115943	+	0.993256i	$0.463011\pi$
$828$	−22.8830	−0.795239
$829$	−2.10670	−0.0731687	−0.0365843	−	0.999331i	$-0.511648\pi$
$829$	−2.10670	−0.0731687	−0.0365843	+	0.999331i	$0.511648\pi$
$830$	−3.47006	−0.120447
$831$	−18.0072	−0.624663
$832$	88.1255	3.05520
$833$	5.34042	0.185035
$834$	46.5525	1.61198
$835$	−0.675863	−0.0233892
$836$	105.698	3.65564
$837$	36.8895	1.27509
$838$	93.5925	3.23310
$839$	−22.4816	−0.776151	−0.388076	−	0.921628i	$-0.626860\pi$
$839$	−22.4816	−0.776151	−0.388076	+	0.921628i	$0.626860\pi$
$840$	−16.9292	−0.584113
$841$	67.8593	2.33997
$842$	49.8644	1.71844
$843$	17.8840	0.615959
$844$	−3.72164	−0.128104
$845$	−14.7725	−0.508188
$846$	18.0746	0.621418
$847$	3.17893	0.109229
$848$	−43.7794	−1.50339
$849$	34.8592	1.19637
$850$	45.0051	1.54366
$851$	13.1408	0.450459
$852$	0.0802637	0.00274979
$853$	19.3954	0.664086	0.332043	−	0.943264i	$-0.392262\pi$
$853$	19.3954	0.664086	0.332043	+	0.943264i	$0.392262\pi$
$854$	−20.0964	−0.687684
$855$	8.20066	0.280457
$856$	−158.927	−5.43200
$857$	45.6803	1.56041	0.780205	−	0.625524i	$-0.215115\pi$
$857$	45.6803	1.56041	0.780205	+	0.625524i	$0.215115\pi$
$858$	−53.9219	−1.84086
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−44.9313	−1.53215
$861$	−16.4943	−0.562124
$862$	50.1722	1.70887
$863$	26.0542	0.886895	0.443447	−	0.896300i	$-0.353755\pi$
$863$	26.0542	0.886895	0.443447	+	0.896300i	$0.353755\pi$
$864$	89.7370	3.05291
$865$	−4.90851	−0.166895
$866$	−77.9083	−2.64743
$867$	17.0000	0.577349
$868$	33.7075	1.14411
$869$	−25.3589	−0.860243
$870$	52.8250	1.79093
$871$	−42.4284	−1.43763
$872$	82.6334	2.79832
$873$	−3.03159	−0.102604
$874$	−105.891	−3.58183
$875$	−11.0840	−0.374708
$876$	−39.3872	−1.33077
$877$	−18.0442	−0.609308	−0.304654	−	0.952463i	$-0.598541\pi$
$877$	−18.0442	−0.609308	−0.304654	+	0.952463i	$0.598541\pi$
$878$	41.6464	1.40550
$879$	−33.8880	−1.14301
$880$	−46.6107	−1.57125
$881$	23.3201	0.785674	0.392837	−	0.919608i	$-0.371494\pi$
$881$	23.3201	0.785674	0.392837	+	0.919608i	$0.371494\pi$
$882$	2.19958	0.0740637
$883$	−40.1218	−1.35021	−0.675104	−	0.737723i	$-0.735901\pi$
$883$	−40.1218	−1.35021	−0.675104	+	0.737723i	$0.735901\pi$
$884$	134.458	4.52231
$885$	0.533740	0.0179415
$886$	7.28917	0.244884
$887$	28.3999	0.953575	0.476788	−	0.879019i	$-0.341801\pi$
$887$	28.3999	0.953575	0.476788	+	0.879019i	$0.341801\pi$
$888$	−30.3010	−1.01683
$889$	−11.3737	−0.381461
$890$	−6.59143	−0.220945
$891$	−16.3787	−0.548709
$892$	138.923	4.65148
$893$	60.2578	2.01645
$894$	−52.5169	−1.75643
$895$	29.9040	0.999580
$896$	16.4336	0.549008
$897$	38.9185	1.29945
$898$	−14.2165	−0.474412
$899$	−64.3648	−2.14669
$900$	13.3544	0.445145
$901$	−19.0763	−0.635522
$902$	−83.6085	−2.78386
$903$	−9.46004	−0.314811
$904$	62.7926	2.08845
$905$	34.6366	1.15136
$906$	−80.4456	−2.67263
$907$	−11.2136	−0.372341	−0.186170	−	0.982517i	$-0.559608\pi$
$907$	−11.2136	−0.372341	−0.186170	+	0.982517i	$0.559608\pi$
$908$	24.2138	0.803563
$909$	−0.451444	−0.0149734
$910$	−17.7680	−0.589005
$911$	44.7154	1.48149	0.740744	−	0.671787i	$-0.234473\pi$
$911$	44.7154	1.48149	0.740744	+	0.671787i	$0.234473\pi$
$912$	132.626	4.39169
$913$	−2.66805	−0.0882995
$914$	87.8683	2.90642
$915$	15.0777	0.498453
$916$	139.573	4.61164
$917$	2.54745	0.0841243
$918$	80.5705	2.65922
$919$	−40.0966	−1.32267	−0.661333	−	0.750093i	$-0.730009\pi$
$919$	−40.0966	−1.32267	−0.661333	+	0.750093i	$0.730009\pi$
$920$	61.9362	2.04198
$921$	−17.4659	−0.575522
$922$	−15.3874	−0.506757
$923$	0.0515515	0.00169684
$924$	−21.2703	−0.699742
$925$	−7.66886	−0.252151
$926$	64.1872	2.10932
$927$	14.2798	0.469009
$928$	−156.573	−5.13977
$929$	33.3906	1.09551	0.547754	−	0.836639i	$-0.315483\pi$
$929$	33.3906	1.09551	0.547754	+	0.836639i	$0.315483\pi$
$930$	−35.1032	−1.15108
$931$	7.33305	0.240331
$932$	−116.196	−3.80614
$933$	−44.7274	−1.46431
$934$	−31.4634	−1.02951
$935$	−20.3100	−0.664206
$936$	33.8900	1.10773
$937$	−34.3968	−1.12369	−0.561847	−	0.827241i	$-0.689909\pi$
$937$	−34.3968	−1.12369	−0.561847	+	0.827241i	$0.689909\pi$
$938$	−23.2311	−0.758521
$939$	29.0333	0.947467
$940$	−57.5940	−1.87851
$941$	−46.6445	−1.52057	−0.760284	−	0.649591i	$-0.774940\pi$
$941$	−46.6445	−1.52057	−0.760284	+	0.649591i	$0.774940\pi$
$942$	−53.5257	−1.74396
$943$	60.3450	1.96510
$944$	−3.25978	−0.106097
$945$	−7.67052	−0.249522
$946$	−47.9523	−1.55906
$947$	−10.1758	−0.330671	−0.165335	−	0.986237i	$-0.552871\pi$
$947$	−10.1758	−0.330671	−0.165335	+	0.986237i	$0.552871\pi$
$948$	−68.9666	−2.23993
$949$	−25.2975	−0.821192
$950$	61.7976	2.00498
$951$	−18.1389	−0.588195
$952$	45.0525	1.46016
$953$	−35.0359	−1.13492	−0.567462	−	0.823399i	$-0.692075\pi$
$953$	−35.0359	−1.13492	−0.567462	+	0.823399i	$0.692075\pi$
$954$	−7.85702	−0.254380
$955$	29.2174	0.945452
$956$	146.025	4.72278
$957$	40.6159	1.31293
$958$	90.0982	2.91094
$959$	14.5006	0.468248
$960$	−36.2019	−1.16841
$961$	11.7716	0.379729
$962$	−31.8023	−1.02535
$963$	−15.4923	−0.499233
$964$	73.0609	2.35313
$965$	1.07210	0.0345122
$966$	21.3093	0.685615
$967$	11.2904	0.363074	0.181537	−	0.983384i	$-0.441893\pi$
$967$	11.2904	0.363074	0.181537	+	0.983384i	$0.441893\pi$
$968$	26.8179	0.861959
$969$	57.7900	1.85648
$970$	13.4086	0.430523
$971$	−59.2926	−1.90279	−0.951396	−	0.307971i	$-0.900350\pi$
$971$	−59.2926	−1.90279	−0.951396	+	0.307971i	$0.900350\pi$
$972$	42.6717	1.36869
$973$	11.7944	0.378110
$974$	−34.8313	−1.11607
$975$	−22.7126	−0.727385
$976$	−92.0861	−2.94760
$977$	−4.83375	−0.154645	−0.0773227	−	0.997006i	$-0.524637\pi$
$977$	−4.83375	−0.154645	−0.0773227	+	0.997006i	$0.524637\pi$
$978$	−71.7382	−2.29394
$979$	−5.06800	−0.161974
$980$	−7.00888	−0.223890
$981$	8.05519	0.257183
$982$	−69.9611	−2.23255
$983$	3.43004	0.109401	0.0547006	−	0.998503i	$-0.482580\pi$
$983$	3.43004	0.109401	0.0547006	+	0.998503i	$0.482580\pi$
$984$	−139.148	−4.43588
$985$	3.80836	0.121345
$986$	−140.579	−4.47696
$987$	−12.1261	−0.385978
$988$	184.627	5.87378
$989$	34.6099	1.10053
$990$	−8.36514	−0.265862
$991$	11.1448	0.354027	0.177014	−	0.984208i	$-0.443356\pi$
$991$	11.1448	0.354027	0.177014	+	0.984208i	$0.443356\pi$
$992$	104.046	3.30346
$993$	2.01828	0.0640481
$994$	0.0282263	0.000895284 0
$995$	21.5755	0.683990
$996$	−7.25607	−0.229917
$997$	1.20129	0.0380453	0.0190227	−	0.999819i	$-0.493945\pi$
$997$	1.20129	0.0380453	0.0190227	+	0.999819i	$0.493945\pi$
$998$	26.6940	0.844983
$999$	−13.7292	−0.434372

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.2	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.67470 q^{2} +1.47568 q^{3} +5.15405 q^{4} -1.35988 q^{5} -3.94701 q^{6} -1.00000 q^{7} -8.43614 q^{8} -0.822364 q^{9} +O(q^{10})\)	\(q-2.67470 q^{2} +1.47568 q^{3} +5.15405 q^{4} -1.35988 q^{5} -3.94701 q^{6} -1.00000 q^{7} -8.43614 q^{8} -0.822364 q^{9} +3.63728 q^{10} +2.79662 q^{11} +7.60573 q^{12} +4.88498 q^{13} +2.67470 q^{14} -2.00675 q^{15} +12.2561 q^{16} +5.34042 q^{17} +2.19958 q^{18} +7.33305 q^{19} -7.00888 q^{20} -1.47568 q^{21} -7.48013 q^{22} +5.39884 q^{23} -12.4491 q^{24} -3.15073 q^{25} -13.0659 q^{26} -5.64059 q^{27} -5.15405 q^{28} +9.84171 q^{29} +5.36746 q^{30} -6.54000 q^{31} -15.9091 q^{32} +4.12692 q^{33} -14.2840 q^{34} +1.35988 q^{35} -4.23850 q^{36} +2.43400 q^{37} -19.6137 q^{38} +7.20868 q^{39} +11.4721 q^{40} +11.1774 q^{41} +3.94701 q^{42} +6.41063 q^{43} +14.4139 q^{44} +1.11832 q^{45} -14.4403 q^{46} +8.21730 q^{47} +18.0861 q^{48} +1.00000 q^{49} +8.42727 q^{50} +7.88076 q^{51} +25.1774 q^{52} -3.57205 q^{53} +15.0869 q^{54} -3.80306 q^{55} +8.43614 q^{56} +10.8212 q^{57} -26.3237 q^{58} -0.265972 q^{59} -10.3429 q^{60} -7.51350 q^{61} +17.4926 q^{62} +0.822364 q^{63} +18.0401 q^{64} -6.64299 q^{65} -11.0383 q^{66} -8.68547 q^{67} +27.5248 q^{68} +7.96697 q^{69} -3.63728 q^{70} +0.0105531 q^{71} +6.93758 q^{72} -5.17862 q^{73} -6.51022 q^{74} -4.64947 q^{75} +37.7949 q^{76} -2.79662 q^{77} -19.2811 q^{78} -9.06772 q^{79} -16.6668 q^{80} -5.85663 q^{81} -29.8963 q^{82} -0.954026 q^{83} -7.60573 q^{84} -7.26233 q^{85} -17.1465 q^{86} +14.5232 q^{87} -23.5927 q^{88} -1.81219 q^{89} -2.99116 q^{90} -4.88498 q^{91} +27.8259 q^{92} -9.65096 q^{93} -21.9788 q^{94} -9.97206 q^{95} -23.4768 q^{96} +3.68643 q^{97} -2.67470 q^{98} -2.29984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 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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