LMFDB - Embedded newform 8015.2.a.l.1.60

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.60
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.63990 q^{2} +2.23988 q^{3} +4.96906 q^{4} -1.00000 q^{5} +5.91306 q^{6} -1.00000 q^{7} +7.83803 q^{8} +2.01707 q^{9} +O(q^{10})$	\(q+2.63990 q^{2} +2.23988 q^{3} +4.96906 q^{4} -1.00000 q^{5} +5.91306 q^{6} -1.00000 q^{7} +7.83803 q^{8} +2.01707 q^{9} -2.63990 q^{10} +2.72136 q^{11} +11.1301 q^{12} +1.32703 q^{13} -2.63990 q^{14} -2.23988 q^{15} +10.7535 q^{16} +5.16286 q^{17} +5.32485 q^{18} +4.00409 q^{19} -4.96906 q^{20} -2.23988 q^{21} +7.18411 q^{22} +3.31628 q^{23} +17.5562 q^{24} +1.00000 q^{25} +3.50322 q^{26} -2.20166 q^{27} -4.96906 q^{28} -3.92085 q^{29} -5.91306 q^{30} -6.66906 q^{31} +12.7120 q^{32} +6.09552 q^{33} +13.6294 q^{34} +1.00000 q^{35} +10.0229 q^{36} -11.3033 q^{37} +10.5704 q^{38} +2.97238 q^{39} -7.83803 q^{40} +3.99615 q^{41} -5.91306 q^{42} -5.70472 q^{43} +13.5226 q^{44} -2.01707 q^{45} +8.75465 q^{46} +0.309767 q^{47} +24.0865 q^{48} +1.00000 q^{49} +2.63990 q^{50} +11.5642 q^{51} +6.59408 q^{52} -0.760981 q^{53} -5.81215 q^{54} -2.72136 q^{55} -7.83803 q^{56} +8.96869 q^{57} -10.3506 q^{58} +3.18259 q^{59} -11.1301 q^{60} -11.5545 q^{61} -17.6056 q^{62} -2.01707 q^{63} +12.0515 q^{64} -1.32703 q^{65} +16.0915 q^{66} +12.6942 q^{67} +25.6546 q^{68} +7.42808 q^{69} +2.63990 q^{70} +8.73450 q^{71} +15.8098 q^{72} -1.07664 q^{73} -29.8396 q^{74} +2.23988 q^{75} +19.8966 q^{76} -2.72136 q^{77} +7.84679 q^{78} +7.12680 q^{79} -10.7535 q^{80} -10.9826 q^{81} +10.5494 q^{82} +17.4892 q^{83} -11.1301 q^{84} -5.16286 q^{85} -15.0599 q^{86} -8.78223 q^{87} +21.3301 q^{88} -0.252692 q^{89} -5.32485 q^{90} -1.32703 q^{91} +16.4788 q^{92} -14.9379 q^{93} +0.817754 q^{94} -4.00409 q^{95} +28.4734 q^{96} -5.71617 q^{97} +2.63990 q^{98} +5.48916 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	2.63990	1.86669	0.933345	−	0.358981i	$-0.116876\pi$
$2$	2.63990	1.86669	0.933345	+	0.358981i	$0.116876\pi$
$3$	2.23988	1.29320	0.646598	−	0.762831i	$-0.276191\pi$
$3$	2.23988	1.29320	0.646598	+	0.762831i	$0.276191\pi$
$4$	4.96906	2.48453
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.91306	2.41400
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	7.83803	2.77116
$9$	2.01707	0.672355
$10$	−2.63990	−0.834809
$11$	2.72136	0.820520	0.410260	−	0.911969i	$-0.365438\pi$
$11$	2.72136	0.820520	0.410260	+	0.911969i	$0.365438\pi$
$12$	11.1301	3.21299
$13$	1.32703	0.368051	0.184026	−	0.982921i	$-0.441087\pi$
$13$	1.32703	0.368051	0.184026	+	0.982921i	$0.441087\pi$
$14$	−2.63990	−0.705543
$15$	−2.23988	−0.578335
$16$	10.7535	2.68837
$17$	5.16286	1.25218	0.626088	−	0.779752i	$-0.284655\pi$
$17$	5.16286	1.25218	0.626088	+	0.779752i	$0.284655\pi$
$18$	5.32485	1.25508
$19$	4.00409	0.918602	0.459301	−	0.888281i	$-0.348100\pi$
$19$	4.00409	0.918602	0.459301	+	0.888281i	$0.348100\pi$
$20$	−4.96906	−1.11112
$21$	−2.23988	−0.488782
$22$	7.18411	1.53166
$23$	3.31628	0.691493	0.345746	−	0.938328i	$-0.387626\pi$
$23$	3.31628	0.691493	0.345746	+	0.938328i	$0.387626\pi$
$24$	17.5562	3.58365
$25$	1.00000	0.200000
$26$	3.50322	0.687037
$27$	−2.20166	−0.423709
$28$	−4.96906	−0.939065
$29$	−3.92085	−0.728083	−0.364041	−	0.931383i	$-0.618603\pi$
$29$	−3.92085	−0.728083	−0.364041	+	0.931383i	$0.618603\pi$
$30$	−5.91306	−1.07957
$31$	−6.66906	−1.19780	−0.598899	−	0.800824i	$-0.704395\pi$
$31$	−6.66906	−1.19780	−0.598899	+	0.800824i	$0.704395\pi$
$32$	12.7120	2.24719
$33$	6.09552	1.06109
$34$	13.6294	2.33743
$35$	1.00000	0.169031
$36$	10.0229	1.67049
$37$	−11.3033	−1.85826	−0.929128	−	0.369759i	$-0.879440\pi$
$37$	−11.3033	−1.85826	−0.929128	+	0.369759i	$0.879440\pi$
$38$	10.5704	1.71475
$39$	2.97238	0.475962
$40$	−7.83803	−1.23930
$41$	3.99615	0.624093	0.312047	−	0.950067i	$-0.398985\pi$
$41$	3.99615	0.624093	0.312047	+	0.950067i	$0.398985\pi$
$42$	−5.91306	−0.912405
$43$	−5.70472	−0.869961	−0.434981	−	0.900440i	$-0.643245\pi$
$43$	−5.70472	−0.869961	−0.434981	+	0.900440i	$0.643245\pi$
$44$	13.5226	2.03861
$45$	−2.01707	−0.300686
$46$	8.75465	1.29080
$47$	0.309767	0.0451842	0.0225921	−	0.999745i	$-0.492808\pi$
$47$	0.309767	0.0451842	0.0225921	+	0.999745i	$0.492808\pi$
$48$	24.0865	3.47658
$49$	1.00000	0.142857
$50$	2.63990	0.373338
$51$	11.5642	1.61931
$52$	6.59408	0.914435
$53$	−0.760981	−0.104529	−0.0522644	−	0.998633i	$-0.516644\pi$
$53$	−0.760981	−0.104529	−0.0522644	+	0.998633i	$0.516644\pi$
$54$	−5.81215	−0.790933
$55$	−2.72136	−0.366948
$56$	−7.83803	−1.04740
$57$	8.96869	1.18793
$58$	−10.3506	−1.35910
$59$	3.18259	0.414338	0.207169	−	0.978305i	$-0.433575\pi$
$59$	3.18259	0.414338	0.207169	+	0.978305i	$0.433575\pi$
$60$	−11.1301	−1.43689
$61$	−11.5545	−1.47941	−0.739703	−	0.672933i	$-0.765034\pi$
$61$	−11.5545	−1.47941	−0.739703	+	0.672933i	$0.765034\pi$
$62$	−17.6056	−2.23592
$63$	−2.01707	−0.254126
$64$	12.0515	1.50643
$65$	−1.32703	−0.164597
$66$	16.0915	1.98073
$67$	12.6942	1.55085	0.775424	−	0.631440i	$-0.217536\pi$
$67$	12.6942	1.55085	0.775424	+	0.631440i	$0.217536\pi$
$68$	25.6546	3.11107
$69$	7.42808	0.894236
$70$	2.63990	0.315528
$71$	8.73450	1.03659	0.518297	−	0.855201i	$-0.326566\pi$
$71$	8.73450	1.03659	0.518297	+	0.855201i	$0.326566\pi$
$72$	15.8098	1.86320
$73$	−1.07664	−0.126011	−0.0630055	−	0.998013i	$-0.520069\pi$
$73$	−1.07664	−0.126011	−0.0630055	+	0.998013i	$0.520069\pi$
$74$	−29.8396	−3.46879
$75$	2.23988	0.258639
$76$	19.8966	2.28230
$77$	−2.72136	−0.310128
$78$	7.84679	0.888474
$79$	7.12680	0.801828	0.400914	−	0.916116i	$-0.368693\pi$
$79$	7.12680	0.801828	0.400914	+	0.916116i	$0.368693\pi$
$80$	−10.7535	−1.20227
$81$	−10.9826	−1.22029
$82$	10.5494	1.16499
$83$	17.4892	1.91969	0.959847	−	0.280523i	$-0.0905080\pi$
$83$	17.4892	1.91969	0.959847	+	0.280523i	$0.0905080\pi$
$84$	−11.1301	−1.21439
$85$	−5.16286	−0.559990
$86$	−15.0599	−1.62395
$87$	−8.78223	−0.941553
$88$	21.3301	2.27379
$89$	−0.252692	−0.0267853	−0.0133927	−	0.999910i	$-0.504263\pi$
$89$	−0.252692	−0.0267853	−0.0133927	+	0.999910i	$0.504263\pi$
$90$	−5.32485	−0.561288
$91$	−1.32703	−0.139110
$92$	16.4788	1.71804
$93$	−14.9379	−1.54899
$94$	0.817754	0.0843448
$95$	−4.00409	−0.410811
$96$	28.4734	2.90605
$97$	−5.71617	−0.580389	−0.290194	−	0.956968i	$-0.593720\pi$
$97$	−5.71617	−0.580389	−0.290194	+	0.956968i	$0.593720\pi$
$98$	2.63990	0.266670
$99$	5.48916	0.551681
$100$	4.96906	0.496906
$101$	1.25145	0.124524	0.0622622	−	0.998060i	$-0.480169\pi$
$101$	1.25145	0.124524	0.0622622	+	0.998060i	$0.480169\pi$
$102$	30.5283	3.02275
$103$	−8.30099	−0.817921	−0.408961	−	0.912552i	$-0.634109\pi$
$103$	−8.30099	−0.817921	−0.408961	+	0.912552i	$0.634109\pi$
$104$	10.4013	1.01993
$105$	2.23988	0.218590
$106$	−2.00891	−0.195123
$107$	6.74619	0.652179	0.326089	−	0.945339i	$-0.394269\pi$
$107$	6.74619	0.652179	0.326089	+	0.945339i	$0.394269\pi$
$108$	−10.9402	−1.05272
$109$	3.69105	0.353539	0.176769	−	0.984252i	$-0.443435\pi$
$109$	3.69105	0.353539	0.176769	+	0.984252i	$0.443435\pi$
$110$	−7.18411	−0.684978
$111$	−25.3181	−2.40309
$112$	−10.7535	−1.01611
$113$	−5.11147	−0.480847	−0.240423	−	0.970668i	$-0.577286\pi$
$113$	−5.11147	−0.480847	−0.240423	+	0.970668i	$0.577286\pi$
$114$	23.6764	2.21750
$115$	−3.31628	−0.309245
$116$	−19.4829	−1.80894
$117$	2.67670	0.247461
$118$	8.40171	0.773440
$119$	−5.16286	−0.473278
$120$	−17.5562	−1.60266
$121$	−3.59421	−0.326746
$122$	−30.5028	−2.76159
$123$	8.95089	0.807075
$124$	−33.1390	−2.97597
$125$	−1.00000	−0.0894427
$126$	−5.32485	−0.474375
$127$	4.33688	0.384836	0.192418	−	0.981313i	$-0.438367\pi$
$127$	4.33688	0.384836	0.192418	+	0.981313i	$0.438367\pi$
$128$	6.39066	0.564860
$129$	−12.7779	−1.12503
$130$	−3.50322	−0.307252
$131$	6.76692	0.591228	0.295614	−	0.955307i	$-0.404476\pi$
$131$	6.76692	0.591228	0.295614	+	0.955307i	$0.404476\pi$
$132$	30.2890	2.63632
$133$	−4.00409	−0.347199
$134$	33.5115	2.89495
$135$	2.20166	0.189488
$136$	40.4666	3.46998
$137$	0.0291688	0.00249206	0.00124603	−	0.999999i	$-0.499603\pi$
$137$	0.0291688	0.00249206	0.00124603	+	0.999999i	$0.499603\pi$
$138$	19.6094	1.66926
$139$	16.5953	1.40760	0.703798	−	0.710401i	$-0.251486\pi$
$139$	16.5953	1.40760	0.703798	+	0.710401i	$0.251486\pi$
$140$	4.96906	0.419963
$141$	0.693841	0.0584320
$142$	23.0582	1.93500
$143$	3.61132	0.301993
$144$	21.6905	1.80754
$145$	3.92085	0.325608
$146$	−2.84222	−0.235223
$147$	2.23988	0.184742
$148$	−56.1669	−4.61689
$149$	−14.2460	−1.16708	−0.583540	−	0.812085i	$-0.698333\pi$
$149$	−14.2460	−1.16708	−0.583540	+	0.812085i	$0.698333\pi$
$150$	5.91306	0.482799
$151$	−16.7246	−1.36103	−0.680515	−	0.732734i	$-0.738244\pi$
$151$	−16.7246	−1.36103	−0.680515	+	0.732734i	$0.738244\pi$
$152$	31.3842	2.54559
$153$	10.4138	0.841908
$154$	−7.18411	−0.578912
$155$	6.66906	0.535672
$156$	14.7700	1.18254
$157$	1.44668	0.115458	0.0577288	−	0.998332i	$-0.481614\pi$
$157$	1.44668	0.115458	0.0577288	+	0.998332i	$0.481614\pi$
$158$	18.8140	1.49676
$159$	−1.70451	−0.135176
$160$	−12.7120	−1.00497
$161$	−3.31628	−0.261360
$162$	−28.9931	−2.27791
$163$	−13.2714	−1.03950	−0.519748	−	0.854319i	$-0.673974\pi$
$163$	−13.2714	−1.03950	−0.519748	+	0.854319i	$0.673974\pi$
$164$	19.8571	1.55058
$165$	−6.09552	−0.474535
$166$	46.1698	3.58347
$167$	8.80456	0.681318	0.340659	−	0.940187i	$-0.389350\pi$
$167$	8.80456	0.681318	0.340659	+	0.940187i	$0.389350\pi$
$168$	−17.5562	−1.35449
$169$	−11.2390	−0.864538
$170$	−13.6294	−1.04533
$171$	8.07652	0.617627
$172$	−28.3471	−2.16145
$173$	−0.574156	−0.0436523	−0.0218261	−	0.999762i	$-0.506948\pi$
$173$	−0.574156	−0.0436523	−0.0218261	+	0.999762i	$0.506948\pi$
$174$	−23.1842	−1.75759
$175$	−1.00000	−0.0755929
$176$	29.2640	2.20586
$177$	7.12862	0.535820
$178$	−0.667082	−0.0499999
$179$	−7.41062	−0.553896	−0.276948	−	0.960885i	$-0.589323\pi$
$179$	−7.41062	−0.553896	−0.276948	+	0.960885i	$0.589323\pi$
$180$	−10.0229	−0.747065
$181$	−3.65740	−0.271852	−0.135926	−	0.990719i	$-0.543401\pi$
$181$	−3.65740	−0.271852	−0.135926	+	0.990719i	$0.543401\pi$
$182$	−3.50322	−0.259676
$183$	−25.8808	−1.91316
$184$	25.9931	1.91624
$185$	11.3033	0.831037
$186$	−39.4345	−2.89148
$187$	14.0500	1.02744
$188$	1.53925	0.112262
$189$	2.20166	0.160147
$190$	−10.5704	−0.766857
$191$	8.12688	0.588041	0.294020	−	0.955799i	$-0.405007\pi$
$191$	8.12688	0.588041	0.294020	+	0.955799i	$0.405007\pi$
$192$	26.9939	1.94812
$193$	−25.7690	−1.85489	−0.927446	−	0.373956i	$-0.878001\pi$
$193$	−25.7690	−1.85489	−0.927446	+	0.373956i	$0.878001\pi$
$194$	−15.0901	−1.08341
$195$	−2.97238	−0.212857
$196$	4.96906	0.354933
$197$	6.30826	0.449445	0.224722	−	0.974423i	$-0.427852\pi$
$197$	6.30826	0.449445	0.224722	+	0.974423i	$0.427852\pi$
$198$	14.4908	1.02982
$199$	−11.7117	−0.830222	−0.415111	−	0.909771i	$-0.636257\pi$
$199$	−11.7117	−0.830222	−0.415111	+	0.909771i	$0.636257\pi$
$200$	7.83803	0.554232
$201$	28.4336	2.00555
$202$	3.30371	0.232448
$203$	3.92085	0.275189
$204$	57.4632	4.02323
$205$	−3.99615	−0.279103
$206$	−21.9138	−1.52681
$207$	6.68916	0.464929
$208$	14.2701	0.989457
$209$	10.8966	0.753732
$210$	5.91306	0.408040
$211$	1.19240	0.0820879	0.0410440	−	0.999157i	$-0.486932\pi$
$211$	1.19240	0.0820879	0.0410440	+	0.999157i	$0.486932\pi$
$212$	−3.78136	−0.259705
$213$	19.5642	1.34052
$214$	17.8093	1.21742
$215$	5.70472	0.389059
$216$	−17.2566	−1.17417
$217$	6.66906	0.452725
$218$	9.74400	0.659947
$219$	−2.41154	−0.162957
$220$	−13.5226	−0.911694
$221$	6.85125	0.460865
$222$	−66.8372	−4.48582
$223$	−12.0722	−0.808412	−0.404206	−	0.914668i	$-0.632452\pi$
$223$	−12.0722	−0.808412	−0.404206	+	0.914668i	$0.632452\pi$
$224$	−12.7120	−0.849357
$225$	2.01707	0.134471
$226$	−13.4938	−0.897592
$227$	−10.8524	−0.720302	−0.360151	−	0.932894i	$-0.617275\pi$
$227$	−10.8524	−0.720302	−0.360151	+	0.932894i	$0.617275\pi$
$228$	44.5660	2.95146
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−8.75465	−0.577265
$231$	−6.09552	−0.401056
$232$	−30.7317	−2.01763
$233$	−5.87257	−0.384725	−0.192362	−	0.981324i	$-0.561615\pi$
$233$	−5.87257	−0.384725	−0.192362	+	0.981324i	$0.561615\pi$
$234$	7.06622	0.461933
$235$	−0.309767	−0.0202070
$236$	15.8145	1.02944
$237$	15.9632	1.03692
$238$	−13.6294	−0.883464
$239$	9.94340	0.643185	0.321593	−	0.946878i	$-0.395782\pi$
$239$	9.94340	0.643185	0.321593	+	0.946878i	$0.395782\pi$
$240$	−24.0865	−1.55478
$241$	2.73831	0.176390	0.0881951	−	0.996103i	$-0.471890\pi$
$241$	2.73831	0.176390	0.0881951	+	0.996103i	$0.471890\pi$
$242$	−9.48835	−0.609934
$243$	−17.9948	−1.15437
$244$	−57.4152	−3.67563
$245$	−1.00000	−0.0638877
$246$	23.6294	1.50656
$247$	5.31354	0.338093
$248$	−52.2723	−3.31929
$249$	39.1738	2.48254
$250$	−2.63990	−0.166962
$251$	−7.79993	−0.492327	−0.246164	−	0.969228i	$-0.579170\pi$
$251$	−7.79993	−0.492327	−0.246164	+	0.969228i	$0.579170\pi$
$252$	−10.0229	−0.631385
$253$	9.02479	0.567384
$254$	11.4489	0.718370
$255$	−11.5642	−0.724177
$256$	−7.23226	−0.452016
$257$	13.3254	0.831215	0.415607	−	0.909544i	$-0.363569\pi$
$257$	13.3254	0.831215	0.415607	+	0.909544i	$0.363569\pi$
$258$	−33.7323	−2.10008
$259$	11.3033	0.702354
$260$	−6.59408	−0.408948
$261$	−7.90860	−0.489530
$262$	17.8640	1.10364
$263$	0.640300	0.0394826	0.0197413	−	0.999805i	$-0.493716\pi$
$263$	0.640300	0.0394826	0.0197413	+	0.999805i	$0.493716\pi$
$264$	47.7768	2.94046
$265$	0.760981	0.0467467
$266$	−10.5704	−0.648113
$267$	−0.566001	−0.0346387
$268$	63.0785	3.85313
$269$	15.4945	0.944715	0.472357	−	0.881407i	$-0.343403\pi$
$269$	15.4945	0.944715	0.472357	+	0.881407i	$0.343403\pi$
$270$	5.81215	0.353716
$271$	14.7223	0.894316	0.447158	−	0.894455i	$-0.352436\pi$
$271$	14.7223	0.894316	0.447158	+	0.894455i	$0.352436\pi$
$272$	55.5186	3.36631
$273$	−2.97238	−0.179897
$274$	0.0770027	0.00465190
$275$	2.72136	0.164104
$276$	36.9106	2.22176
$277$	−4.23530	−0.254475	−0.127237	−	0.991872i	$-0.540611\pi$
$277$	−4.23530	−0.254475	−0.127237	+	0.991872i	$0.540611\pi$
$278$	43.8099	2.62754
$279$	−13.4519	−0.805346
$280$	7.83803	0.468412
$281$	−1.75422	−0.104648	−0.0523241	−	0.998630i	$-0.516663\pi$
$281$	−1.75422	−0.104648	−0.0523241	+	0.998630i	$0.516663\pi$
$282$	1.83167	0.109074
$283$	−2.72124	−0.161761	−0.0808806	−	0.996724i	$-0.525773\pi$
$283$	−2.72124	−0.161761	−0.0808806	+	0.996724i	$0.525773\pi$
$284$	43.4023	2.57545
$285$	−8.96869	−0.531259
$286$	9.53351	0.563728
$287$	−3.99615	−0.235885
$288$	25.6410	1.51091
$289$	9.65509	0.567947
$290$	10.3506	0.607810
$291$	−12.8035	−0.750556
$292$	−5.34988	−0.313078
$293$	20.0547	1.17161	0.585803	−	0.810453i	$-0.300779\pi$
$293$	20.0547	1.17161	0.585803	+	0.810453i	$0.300779\pi$
$294$	5.91306	0.344857
$295$	−3.18259	−0.185298
$296$	−88.5958	−5.14952
$297$	−5.99149	−0.347662
$298$	−37.6080	−2.17858
$299$	4.40080	0.254505
$300$	11.1301	0.642597
$301$	5.70472	0.328814
$302$	−44.1513	−2.54062
$303$	2.80311	0.161034
$304$	43.0579	2.46954
$305$	11.5545	0.661611
$306$	27.4914	1.57158
$307$	−6.17627	−0.352498	−0.176249	−	0.984346i	$-0.556396\pi$
$307$	−6.17627	−0.352498	−0.176249	+	0.984346i	$0.556396\pi$
$308$	−13.5226	−0.770522
$309$	−18.5932	−1.05773
$310$	17.6056	0.999933
$311$	−13.0898	−0.742254	−0.371127	−	0.928582i	$-0.621029\pi$
$311$	−13.0898	−0.742254	−0.371127	+	0.928582i	$0.621029\pi$
$312$	23.2976	1.31897
$313$	−9.21662	−0.520954	−0.260477	−	0.965480i	$-0.583880\pi$
$313$	−9.21662	−0.520954	−0.260477	+	0.965480i	$0.583880\pi$
$314$	3.81909	0.215524
$315$	2.01707	0.113649
$316$	35.4135	1.99217
$317$	−31.8480	−1.78876	−0.894382	−	0.447304i	$-0.852384\pi$
$317$	−31.8480	−1.78876	−0.894382	+	0.447304i	$0.852384\pi$
$318$	−4.49973	−0.252332
$319$	−10.6700	−0.597407
$320$	−12.0515	−0.673698
$321$	15.1107	0.843395
$322$	−8.75465	−0.487878
$323$	20.6726	1.15025
$324$	−54.5735	−3.03186
$325$	1.32703	0.0736102
$326$	−35.0352	−1.94042
$327$	8.26752	0.457195
$328$	31.3219	1.72946
$329$	−0.309767	−0.0170780
$330$	−16.0915	−0.885810
$331$	6.01438	0.330580	0.165290	−	0.986245i	$-0.447144\pi$
$331$	6.01438	0.330580	0.165290	+	0.986245i	$0.447144\pi$
$332$	86.9052	4.76954
$333$	−22.7995	−1.24941
$334$	23.2432	1.27181
$335$	−12.6942	−0.693561
$336$	−24.0865	−1.31403
$337$	−27.7321	−1.51067	−0.755333	−	0.655342i	$-0.772525\pi$
$337$	−27.7321	−1.51067	−0.755333	+	0.655342i	$0.772525\pi$
$338$	−29.6698	−1.61383
$339$	−11.4491	−0.621829
$340$	−25.6546	−1.39131
$341$	−18.1489	−0.982818
$342$	21.3212	1.15292
$343$	−1.00000	−0.0539949
$344$	−44.7137	−2.41080
$345$	−7.42808	−0.399914
$346$	−1.51571	−0.0814853
$347$	10.9230	0.586378	0.293189	−	0.956054i	$-0.405283\pi$
$347$	10.9230	0.586378	0.293189	+	0.956054i	$0.405283\pi$
$348$	−43.6394	−2.33932
$349$	17.8963	0.957965	0.478983	−	0.877824i	$-0.341006\pi$
$349$	17.8963	0.957965	0.478983	+	0.877824i	$0.341006\pi$
$350$	−2.63990	−0.141109
$351$	−2.92166	−0.155947
$352$	34.5939	1.84386
$353$	−5.67409	−0.302001	−0.151001	−	0.988534i	$-0.548250\pi$
$353$	−5.67409	−0.302001	−0.151001	+	0.988534i	$0.548250\pi$
$354$	18.8188	1.00021
$355$	−8.73450	−0.463579
$356$	−1.25564	−0.0665490
$357$	−11.5642	−0.612042
$358$	−19.5633	−1.03395
$359$	−34.0656	−1.79791	−0.898957	−	0.438036i	$-0.855674\pi$
$359$	−34.0656	−1.79791	−0.898957	+	0.438036i	$0.855674\pi$
$360$	−15.8098	−0.833250
$361$	−2.96723	−0.156170
$362$	−9.65515	−0.507464
$363$	−8.05060	−0.422547
$364$	−6.59408	−0.345624
$365$	1.07664	0.0563538
$366$	−68.3226	−3.57128
$367$	−18.3678	−0.958791	−0.479395	−	0.877599i	$-0.659144\pi$
$367$	−18.3678	−0.958791	−0.479395	+	0.877599i	$0.659144\pi$
$368$	35.6616	1.85899
$369$	8.06049	0.419612
$370$	29.8396	1.55129
$371$	0.760981	0.0395082
$372$	−74.2274	−3.84851
$373$	−14.4234	−0.746814	−0.373407	−	0.927668i	$-0.621811\pi$
$373$	−14.4234	−0.746814	−0.373407	+	0.927668i	$0.621811\pi$
$374$	37.0905	1.91791
$375$	−2.23988	−0.115667
$376$	2.42796	0.125213
$377$	−5.20307	−0.267972
$378$	5.81215	0.298945
$379$	12.1242	0.622777	0.311389	−	0.950283i	$-0.399206\pi$
$379$	12.1242	0.622777	0.311389	+	0.950283i	$0.399206\pi$
$380$	−19.8966	−1.02067
$381$	9.71410	0.497669
$382$	21.4542	1.09769
$383$	31.6405	1.61675	0.808377	−	0.588665i	$-0.200346\pi$
$383$	31.6405	1.61675	0.808377	+	0.588665i	$0.200346\pi$
$384$	14.3143	0.730474
$385$	2.72136	0.138693
$386$	−68.0275	−3.46251
$387$	−11.5068	−0.584923
$388$	−28.4040	−1.44199
$389$	−1.22977	−0.0623518	−0.0311759	−	0.999514i	$-0.509925\pi$
$389$	−1.22977	−0.0623518	−0.0311759	+	0.999514i	$0.509925\pi$
$390$	−7.84679	−0.397338
$391$	17.1215	0.865871
$392$	7.83803	0.395880
$393$	15.1571	0.764574
$394$	16.6532	0.838974
$395$	−7.12680	−0.358588
$396$	27.2760	1.37067
$397$	0.302888	0.0152015	0.00760075	−	0.999971i	$-0.497581\pi$
$397$	0.302888	0.0152015	0.00760075	+	0.999971i	$0.497581\pi$
$398$	−30.9178	−1.54977
$399$	−8.96869	−0.448996
$400$	10.7535	0.537673
$401$	−5.36444	−0.267887	−0.133944	−	0.990989i	$-0.542764\pi$
$401$	−5.36444	−0.267887	−0.133944	+	0.990989i	$0.542764\pi$
$402$	75.0618	3.74374
$403$	−8.85003	−0.440851
$404$	6.21856	0.309385
$405$	10.9826	0.545732
$406$	10.3506	0.513693
$407$	−30.7604	−1.52474
$408$	90.6404	4.48737
$409$	22.8874	1.13171	0.565856	−	0.824504i	$-0.308546\pi$
$409$	22.8874	1.13171	0.565856	+	0.824504i	$0.308546\pi$
$410$	−10.5494	−0.520999
$411$	0.0653347	0.00322272
$412$	−41.2482	−2.03215
$413$	−3.18259	−0.156605
$414$	17.6587	0.867878
$415$	−17.4892	−0.858513
$416$	16.8692	0.827080
$417$	37.1715	1.82030
$418$	28.7658	1.40698
$419$	−4.65847	−0.227581	−0.113790	−	0.993505i	$-0.536299\pi$
$419$	−4.65847	−0.227581	−0.113790	+	0.993505i	$0.536299\pi$
$420$	11.1301	0.543094
$421$	−32.3430	−1.57630	−0.788151	−	0.615482i	$-0.788961\pi$
$421$	−32.3430	−1.57630	−0.788151	+	0.615482i	$0.788961\pi$
$422$	3.14780	0.153233
$423$	0.624821	0.0303798
$424$	−5.96459	−0.289666
$425$	5.16286	0.250435
$426$	51.6476	2.50233
$427$	11.5545	0.559163
$428$	33.5222	1.62036
$429$	8.08892	0.390537
$430$	15.0599	0.726252
$431$	−27.6088	−1.32987	−0.664936	−	0.746901i	$-0.731541\pi$
$431$	−27.6088	−1.32987	−0.664936	+	0.746901i	$0.731541\pi$
$432$	−23.6754	−1.13908
$433$	32.3761	1.55589	0.777947	−	0.628330i	$-0.216261\pi$
$433$	32.3761	1.55589	0.777947	+	0.628330i	$0.216261\pi$
$434$	17.6056	0.845098
$435$	8.78223	0.421075
$436$	18.3411	0.878378
$437$	13.2787	0.635207
$438$	−6.36622	−0.304190
$439$	−26.4892	−1.26426	−0.632131	−	0.774861i	$-0.717820\pi$
$439$	−26.4892	−1.26426	−0.632131	+	0.774861i	$0.717820\pi$
$440$	−21.3301	−1.01687
$441$	2.01707	0.0960507
$442$	18.0866	0.860292
$443$	7.19720	0.341949	0.170975	−	0.985275i	$-0.445308\pi$
$443$	7.19720	0.341949	0.170975	+	0.985275i	$0.445308\pi$
$444$	−125.807	−5.97055
$445$	0.252692	0.0119788
$446$	−31.8693	−1.50905
$447$	−31.9094	−1.50926
$448$	−12.0515	−0.569379
$449$	−5.04917	−0.238285	−0.119143	−	0.992877i	$-0.538015\pi$
$449$	−5.04917	−0.238285	−0.119143	+	0.992877i	$0.538015\pi$
$450$	5.32485	0.251016
$451$	10.8749	0.512081
$452$	−25.3992	−1.19468
$453$	−37.4612	−1.76008
$454$	−28.6494	−1.34458
$455$	1.32703	0.0622120
$456$	70.2969	3.29195
$457$	−4.26410	−0.199466	−0.0997332	−	0.995014i	$-0.531799\pi$
$457$	−4.26410	−0.199466	−0.0997332	+	0.995014i	$0.531799\pi$
$458$	2.63990	0.123354
$459$	−11.3668	−0.530558
$460$	−16.4788	−0.768329
$461$	−37.7111	−1.75638	−0.878191	−	0.478309i	$-0.841250\pi$
$461$	−37.7111	−1.75638	−0.878191	+	0.478309i	$0.841250\pi$
$462$	−16.0915	−0.748646
$463$	−14.1039	−0.655462	−0.327731	−	0.944771i	$-0.606284\pi$
$463$	−14.1039	−0.655462	−0.327731	+	0.944771i	$0.606284\pi$
$464$	−42.1627	−1.95735
$465$	14.9379	0.692729
$466$	−15.5030	−0.718162
$467$	−23.9737	−1.10937	−0.554686	−	0.832060i	$-0.687162\pi$
$467$	−23.9737	−1.10937	−0.554686	+	0.832060i	$0.687162\pi$
$468$	13.3007	0.614825
$469$	−12.6942	−0.586166
$470$	−0.817754	−0.0377202
$471$	3.24039	0.149309
$472$	24.9452	1.14820
$473$	−15.5246	−0.713821
$474$	42.1412	1.93561
$475$	4.00409	0.183720
$476$	−25.6546	−1.17588
$477$	−1.53495	−0.0702805
$478$	26.2496	1.20063
$479$	−9.96924	−0.455506	−0.227753	−	0.973719i	$-0.573138\pi$
$479$	−9.96924	−0.455506	−0.227753	+	0.973719i	$0.573138\pi$
$480$	−28.4734	−1.29963
$481$	−14.9998	−0.683933
$482$	7.22887	0.329266
$483$	−7.42808	−0.337989
$484$	−17.8599	−0.811812
$485$	5.71617	0.259558
$486$	−47.5046	−2.15485
$487$	13.2821	0.601870	0.300935	−	0.953645i	$-0.402701\pi$
$487$	13.2821	0.601870	0.300935	+	0.953645i	$0.402701\pi$
$488$	−90.5648	−4.09968
$489$	−29.7264	−1.34427
$490$	−2.63990	−0.119258
$491$	37.0532	1.67219	0.836094	−	0.548586i	$-0.184834\pi$
$491$	37.0532	1.67219	0.836094	+	0.548586i	$0.184834\pi$
$492$	44.4776	2.00520
$493$	−20.2428	−0.911688
$494$	14.0272	0.631114
$495$	−5.48916	−0.246719
$496$	−71.7155	−3.22012
$497$	−8.73450	−0.391796
$498$	103.415	4.63413
$499$	−5.06473	−0.226728	−0.113364	−	0.993554i	$-0.536163\pi$
$499$	−5.06473	−0.226728	−0.113364	+	0.993554i	$0.536163\pi$
$500$	−4.96906	−0.222223
$501$	19.7212	0.881077
$502$	−20.5910	−0.919023
$503$	27.8765	1.24295	0.621476	−	0.783433i	$-0.286533\pi$
$503$	27.8765	1.24295	0.621476	+	0.783433i	$0.286533\pi$
$504$	−15.8098	−0.704225
$505$	−1.25145	−0.0556890
$506$	23.8245	1.05913
$507$	−25.1740	−1.11802
$508$	21.5503	0.956138
$509$	−2.66097	−0.117945	−0.0589727	−	0.998260i	$-0.518782\pi$
$509$	−2.66097	−0.117945	−0.0589727	+	0.998260i	$0.518782\pi$
$510$	−30.5283	−1.35181
$511$	1.07664	0.0476277
$512$	−31.8738	−1.40863
$513$	−8.81564	−0.389220
$514$	35.1777	1.55162
$515$	8.30099	0.365785
$516$	−63.4941	−2.79517
$517$	0.842987	0.0370745
$518$	29.8396	1.31108
$519$	−1.28604	−0.0564509
$520$	−10.4013	−0.456126
$521$	1.70664	0.0747691	0.0373845	−	0.999301i	$-0.488097\pi$
$521$	1.70664	0.0747691	0.0373845	+	0.999301i	$0.488097\pi$
$522$	−20.8779	−0.913801
$523$	12.1750	0.532375	0.266187	−	0.963921i	$-0.414236\pi$
$523$	12.1750	0.532375	0.266187	+	0.963921i	$0.414236\pi$
$524$	33.6252	1.46893
$525$	−2.23988	−0.0977564
$526$	1.69033	0.0737017
$527$	−34.4314	−1.49986
$528$	65.5480	2.85261
$529$	−12.0023	−0.521838
$530$	2.00891	0.0872616
$531$	6.41949	0.278582
$532$	−19.8966	−0.862627
$533$	5.30300	0.229698
$534$	−1.49418	−0.0646597
$535$	−6.74619	−0.291663
$536$	99.4978	4.29765
$537$	−16.5989	−0.716295
$538$	40.9038	1.76349
$539$	2.72136	0.117217
$540$	10.9402	0.470790
$541$	21.2246	0.912515	0.456258	−	0.889848i	$-0.349190\pi$
$541$	21.2246	0.912515	0.456258	+	0.889848i	$0.349190\pi$
$542$	38.8654	1.66941
$543$	−8.19213	−0.351558
$544$	65.6303	2.81388
$545$	−3.69105	−0.158107
$546$	−7.84679	−0.335812
$547$	19.7095	0.842716	0.421358	−	0.906894i	$-0.361554\pi$
$547$	19.7095	0.842716	0.421358	+	0.906894i	$0.361554\pi$
$548$	0.144942	0.00619160
$549$	−23.3063	−0.994687
$550$	7.18411	0.306331
$551$	−15.6994	−0.668818
$552$	58.2215	2.47807
$553$	−7.12680	−0.303062
$554$	−11.1808	−0.475025
$555$	25.3181	1.07469
$556$	82.4631	3.49722
$557$	−36.6572	−1.55322	−0.776608	−	0.629984i	$-0.783062\pi$
$557$	−36.6572	−1.55322	−0.776608	+	0.629984i	$0.783062\pi$
$558$	−35.5117	−1.50333
$559$	−7.57032	−0.320190
$560$	10.7535	0.454417
$561$	31.4703	1.32868
$562$	−4.63098	−0.195346
$563$	−8.96692	−0.377911	−0.188955	−	0.981986i	$-0.560510\pi$
$563$	−8.96692	−0.377911	−0.188955	+	0.981986i	$0.560510\pi$
$564$	3.44774	0.145176
$565$	5.11147	0.215041
$566$	−7.18381	−0.301958
$567$	10.9826	0.461228
$568$	68.4612	2.87257
$569$	13.0873	0.548647	0.274324	−	0.961637i	$-0.411546\pi$
$569$	13.0873	0.548647	0.274324	+	0.961637i	$0.411546\pi$
$570$	−23.6764	−0.991697
$571$	−27.0306	−1.13120	−0.565598	−	0.824681i	$-0.691355\pi$
$571$	−27.0306	−1.13120	−0.565598	+	0.824681i	$0.691355\pi$
$572$	17.9449	0.750312
$573$	18.2033	0.760452
$574$	−10.5494	−0.440324
$575$	3.31628	0.138299
$576$	24.3086	1.01286
$577$	18.3851	0.765384	0.382692	−	0.923876i	$-0.374997\pi$
$577$	18.3851	0.765384	0.382692	+	0.923876i	$0.374997\pi$
$578$	25.4885	1.06018
$579$	−57.7195	−2.39874
$580$	19.4829	0.808985
$581$	−17.4892	−0.725576
$582$	−33.8000	−1.40106
$583$	−2.07090	−0.0857680
$584$	−8.43872	−0.349197
$585$	−2.67670	−0.110668
$586$	52.9423	2.18703
$587$	23.9544	0.988702	0.494351	−	0.869262i	$-0.335406\pi$
$587$	23.9544	0.988702	0.494351	+	0.869262i	$0.335406\pi$
$588$	11.1301	0.458998
$589$	−26.7035	−1.10030
$590$	−8.40171	−0.345893
$591$	14.1298	0.581220
$592$	−121.550	−4.99567
$593$	−5.42859	−0.222926	−0.111463	−	0.993769i	$-0.535554\pi$
$593$	−5.42859	−0.222926	−0.111463	+	0.993769i	$0.535554\pi$
$594$	−15.8169	−0.648977
$595$	5.16286	0.211657
$596$	−70.7894	−2.89965
$597$	−26.2329	−1.07364
$598$	11.6177	0.475082
$599$	8.33216	0.340443	0.170221	−	0.985406i	$-0.445552\pi$
$599$	8.33216	0.340443	0.170221	+	0.985406i	$0.445552\pi$
$600$	17.5562	0.716731
$601$	7.66900	0.312825	0.156412	−	0.987692i	$-0.450007\pi$
$601$	7.66900	0.312825	0.156412	+	0.987692i	$0.450007\pi$
$602$	15.0599	0.613795
$603$	25.6051	1.04272
$604$	−83.1057	−3.38152
$605$	3.59421	0.146125
$606$	7.39992	0.300601
$607$	27.8683	1.13114	0.565571	−	0.824700i	$-0.308656\pi$
$607$	27.8683	1.13114	0.565571	+	0.824700i	$0.308656\pi$
$608$	50.9001	2.06427
$609$	8.78223	0.355874
$610$	30.5028	1.23502
$611$	0.411069	0.0166301
$612$	51.7469	2.09175
$613$	−38.5679	−1.55774	−0.778871	−	0.627184i	$-0.784207\pi$
$613$	−38.5679	−1.55774	−0.778871	+	0.627184i	$0.784207\pi$
$614$	−16.3047	−0.658005
$615$	−8.95089	−0.360935
$616$	−21.3301	−0.859413
$617$	14.6163	0.588430	0.294215	−	0.955739i	$-0.404942\pi$
$617$	14.6163	0.588430	0.294215	+	0.955739i	$0.404942\pi$
$618$	−49.0843	−1.97446
$619$	27.9837	1.12476	0.562379	−	0.826879i	$-0.309886\pi$
$619$	27.9837	1.12476	0.562379	+	0.826879i	$0.309886\pi$
$620$	33.1390	1.33089
$621$	−7.30131	−0.292992
$622$	−34.5557	−1.38556
$623$	0.252692	0.0101239
$624$	31.9634	1.27956
$625$	1.00000	0.0400000
$626$	−24.3309	−0.972460
$627$	24.4070	0.974723
$628$	7.18864	0.286858
$629$	−58.3575	−2.32686
$630$	5.32485	0.212147
$631$	38.9894	1.55214	0.776072	−	0.630644i	$-0.217209\pi$
$631$	38.9894	1.55214	0.776072	+	0.630644i	$0.217209\pi$
$632$	55.8601	2.22199
$633$	2.67083	0.106156
$634$	−84.0756	−3.33907
$635$	−4.33688	−0.172104
$636$	−8.46980	−0.335850
$637$	1.32703	0.0525787
$638$	−28.1678	−1.11517
$639$	17.6181	0.696960
$640$	−6.39066	−0.252613
$641$	45.6963	1.80490	0.902448	−	0.430800i	$-0.141768\pi$
$641$	45.6963	1.80490	0.902448	+	0.430800i	$0.141768\pi$
$642$	39.8906	1.57436
$643$	−38.9906	−1.53764	−0.768820	−	0.639465i	$-0.779156\pi$
$643$	−38.9906	−1.53764	−0.768820	+	0.639465i	$0.779156\pi$
$644$	−16.4788	−0.649357
$645$	12.7779	0.503129
$646$	54.5735	2.14716
$647$	44.6786	1.75650	0.878248	−	0.478205i	$-0.158712\pi$
$647$	44.6786	1.75650	0.878248	+	0.478205i	$0.158712\pi$
$648$	−86.0823	−3.38163
$649$	8.66096	0.339973
$650$	3.50322	0.137407
$651$	14.9379	0.585463
$652$	−65.9465	−2.58266
$653$	−17.1963	−0.672944	−0.336472	−	0.941694i	$-0.609234\pi$
$653$	−17.1963	−0.672944	−0.336472	+	0.941694i	$0.609234\pi$
$654$	21.8254	0.853441
$655$	−6.76692	−0.264405
$656$	42.9724	1.67779
$657$	−2.17165	−0.0847241
$658$	−0.817754	−0.0318794
$659$	43.0517	1.67706	0.838529	−	0.544857i	$-0.183416\pi$
$659$	43.0517	1.67706	0.838529	+	0.544857i	$0.183416\pi$
$660$	−30.2890	−1.17900
$661$	2.24574	0.0873492	0.0436746	−	0.999046i	$-0.486094\pi$
$661$	2.24574	0.0873492	0.0436746	+	0.999046i	$0.486094\pi$
$662$	15.8773	0.617090
$663$	15.3460	0.595989
$664$	137.081	5.31978
$665$	4.00409	0.155272
$666$	−60.1885	−2.33226
$667$	−13.0026	−0.503464
$668$	43.7504	1.69276
$669$	−27.0402	−1.04543
$670$	−33.5115	−1.29466
$671$	−31.4440	−1.21388
$672$	−28.4734	−1.09838
$673$	42.1677	1.62545	0.812724	−	0.582649i	$-0.197984\pi$
$673$	42.1677	1.62545	0.812724	+	0.582649i	$0.197984\pi$
$674$	−73.2100	−2.81994
$675$	−2.20166	−0.0847418
$676$	−55.8473	−2.14797
$677$	−28.6806	−1.10228	−0.551142	−	0.834411i	$-0.685808\pi$
$677$	−28.6806	−1.10228	−0.551142	+	0.834411i	$0.685808\pi$
$678$	−30.2244	−1.16076
$679$	5.71617	0.219366
$680$	−40.4666	−1.55182
$681$	−24.3082	−0.931492
$682$	−47.9113	−1.83462
$683$	−23.9411	−0.916080	−0.458040	−	0.888932i	$-0.651448\pi$
$683$	−23.9411	−0.916080	−0.458040	+	0.888932i	$0.651448\pi$
$684$	40.1327	1.53451
$685$	−0.0291688	−0.00111448
$686$	−2.63990	−0.100792
$687$	2.23988	0.0854568
$688$	−61.3455	−2.33878
$689$	−1.00984	−0.0384719
$690$	−19.6094	−0.746516
$691$	−17.7237	−0.674241	−0.337120	−	0.941462i	$-0.609453\pi$
$691$	−17.7237	−0.674241	−0.337120	+	0.941462i	$0.609453\pi$
$692$	−2.85302	−0.108455
$693$	−5.48916	−0.208516
$694$	28.8357	1.09459
$695$	−16.5953	−0.629496
$696$	−68.8353	−2.60920
$697$	20.6315	0.781475
$698$	47.2443	1.78822
$699$	−13.1539	−0.497524
$700$	−4.96906	−0.187813
$701$	24.2050	0.914212	0.457106	−	0.889412i	$-0.348886\pi$
$701$	24.2050	0.914212	0.457106	+	0.889412i	$0.348886\pi$
$702$	−7.71288	−0.291104
$703$	−45.2596	−1.70700
$704$	32.7964	1.23606
$705$	−0.693841	−0.0261316
$706$	−14.9790	−0.563743
$707$	−1.25145	−0.0470658
$708$	35.4226	1.33126
$709$	2.52998	0.0950155	0.0475077	−	0.998871i	$-0.484872\pi$
$709$	2.52998	0.0950155	0.0475077	+	0.998871i	$0.484872\pi$
$710$	−23.0582	−0.865358
$711$	14.3752	0.539113
$712$	−1.98061	−0.0742265
$713$	−22.1165	−0.828269
$714$	−30.5283	−1.14249
$715$	−3.61132	−0.135056
$716$	−36.8238	−1.37617
$717$	22.2720	0.831765
$718$	−89.9298	−3.35615
$719$	−34.1503	−1.27359	−0.636796	−	0.771033i	$-0.719741\pi$
$719$	−34.1503	−1.27359	−0.636796	+	0.771033i	$0.719741\pi$
$720$	−21.6905	−0.808355
$721$	8.30099	0.309145
$722$	−7.83320	−0.291521
$723$	6.13349	0.228107
$724$	−18.1738	−0.675425
$725$	−3.92085	−0.145617
$726$	−21.2528	−0.788765
$727$	32.8998	1.22018	0.610092	−	0.792330i	$-0.291132\pi$
$727$	32.8998	1.22018	0.610092	+	0.792330i	$0.291132\pi$
$728$	−10.4013	−0.385497
$729$	−7.35838	−0.272532
$730$	2.84222	0.105195
$731$	−29.4526	−1.08935
$732$	−128.603	−4.75331
$733$	−40.2033	−1.48494	−0.742471	−	0.669878i	$-0.766346\pi$
$733$	−40.2033	−1.48494	−0.742471	+	0.669878i	$0.766346\pi$
$734$	−48.4891	−1.78977
$735$	−2.23988	−0.0826192
$736$	42.1566	1.55391
$737$	34.5456	1.27250
$738$	21.2789	0.783286
$739$	−2.29644	−0.0844758	−0.0422379	−	0.999108i	$-0.513449\pi$
$739$	−2.29644	−0.0844758	−0.0422379	+	0.999108i	$0.513449\pi$
$740$	56.1669	2.06474
$741$	11.9017	0.437220
$742$	2.00891	0.0737495
$743$	31.0508	1.13914	0.569571	−	0.821942i	$-0.307109\pi$
$743$	31.0508	1.13914	0.569571	+	0.821942i	$0.307109\pi$
$744$	−117.084	−4.29250
$745$	14.2460	0.521934
$746$	−38.0763	−1.39407
$747$	35.2770	1.29072
$748$	69.8153	2.55270
$749$	−6.74619	−0.246500
$750$	−5.91306	−0.215914
$751$	−43.9562	−1.60399	−0.801993	−	0.597334i	$-0.796227\pi$
$751$	−43.9562	−1.60399	−0.801993	+	0.597334i	$0.796227\pi$
$752$	3.33107	0.121472
$753$	−17.4709	−0.636676
$754$	−13.7356	−0.500220
$755$	16.7246	0.608671
$756$	10.9402	0.397890
$757$	41.5254	1.50927	0.754633	−	0.656147i	$-0.227815\pi$
$757$	41.5254	1.50927	0.754633	+	0.656147i	$0.227815\pi$
$758$	32.0066	1.16253
$759$	20.2145	0.733739
$760$	−31.3842	−1.13842
$761$	26.8469	0.973198	0.486599	−	0.873625i	$-0.338237\pi$
$761$	26.8469	0.973198	0.486599	+	0.873625i	$0.338237\pi$
$762$	25.6442	0.928993
$763$	−3.69105	−0.133625
$764$	40.3830	1.46101
$765$	−10.4138	−0.376513
$766$	83.5277	3.01798
$767$	4.22338	0.152498
$768$	−16.1994	−0.584546
$769$	20.1833	0.727829	0.363915	−	0.931432i	$-0.381440\pi$
$769$	20.1833	0.727829	0.363915	+	0.931432i	$0.381440\pi$
$770$	7.18411	0.258897
$771$	29.8473	1.07492
$772$	−128.048	−4.60854
$773$	−10.5727	−0.380272	−0.190136	−	0.981758i	$-0.560893\pi$
$773$	−10.5727	−0.380272	−0.190136	+	0.981758i	$0.560893\pi$
$774$	−30.3768	−1.09187
$775$	−6.66906	−0.239560
$776$	−44.8035	−1.60835
$777$	25.3181	0.908282
$778$	−3.24647	−0.116392
$779$	16.0009	0.573293
$780$	−14.7700	−0.528849
$781$	23.7697	0.850547
$782$	45.1990	1.61631
$783$	8.63235	0.308495
$784$	10.7535	0.384052
$785$	−1.44668	−0.0516342
$786$	40.0132	1.42722
$787$	25.1544	0.896657	0.448329	−	0.893869i	$-0.352019\pi$
$787$	25.1544	0.896657	0.448329	+	0.893869i	$0.352019\pi$
$788$	31.3462	1.11666
$789$	1.43420	0.0510587
$790$	−18.8140	−0.669373
$791$	5.11147	0.181743
$792$	43.0242	1.52880
$793$	−15.3332	−0.544497
$794$	0.799593	0.0283765
$795$	1.70451	0.0604526
$796$	−58.1963	−2.06271
$797$	9.99175	0.353926	0.176963	−	0.984218i	$-0.443373\pi$
$797$	9.99175	0.353926	0.176963	+	0.984218i	$0.443373\pi$
$798$	−23.6764	−0.838137
$799$	1.59928	0.0565786
$800$	12.7120	0.449437
$801$	−0.509697	−0.0180093
$802$	−14.1616	−0.500063
$803$	−2.92992	−0.103395
$804$	141.288	4.98286
$805$	3.31628	0.116884
$806$	−23.3632	−0.822933
$807$	34.7058	1.22170
$808$	9.80893	0.345077
$809$	−24.5109	−0.861758	−0.430879	−	0.902410i	$-0.641796\pi$
$809$	−24.5109	−0.861758	−0.430879	+	0.902410i	$0.641796\pi$
$810$	28.9931	1.01871
$811$	13.4607	0.472668	0.236334	−	0.971672i	$-0.424054\pi$
$811$	13.4607	0.472668	0.236334	+	0.971672i	$0.424054\pi$
$812$	19.4829	0.683717
$813$	32.9762	1.15653
$814$	−81.2043	−2.84621
$815$	13.2714	0.464877
$816$	124.355	4.35330
$817$	−22.8422	−0.799148
$818$	60.4205	2.11255
$819$	−2.67670	−0.0935315
$820$	−19.8571	−0.693440
$821$	42.9090	1.49753	0.748767	−	0.662833i	$-0.230646\pi$
$821$	42.9090	1.49753	0.748767	+	0.662833i	$0.230646\pi$
$822$	0.172477	0.00601582
$823$	−24.1142	−0.840567	−0.420283	−	0.907393i	$-0.638069\pi$
$823$	−24.1142	−0.840567	−0.420283	+	0.907393i	$0.638069\pi$
$824$	−65.0634	−2.26659
$825$	6.09552	0.212219
$826$	−8.40171	−0.292333
$827$	40.1335	1.39558	0.697789	−	0.716303i	$-0.254167\pi$
$827$	40.1335	1.39558	0.697789	+	0.716303i	$0.254167\pi$
$828$	33.2389	1.15513
$829$	−32.8041	−1.13933	−0.569667	−	0.821875i	$-0.692928\pi$
$829$	−32.8041	−1.13933	−0.569667	+	0.821875i	$0.692928\pi$
$830$	−46.1698	−1.60258
$831$	−9.48657	−0.329086
$832$	15.9926	0.554445
$833$	5.16286	0.178882
$834$	98.1290	3.39793
$835$	−8.80456	−0.304694
$836$	54.1458	1.87267
$837$	14.6830	0.507518
$838$	−12.2979	−0.424823
$839$	−45.4206	−1.56809	−0.784046	−	0.620703i	$-0.786847\pi$
$839$	−45.4206	−1.56809	−0.784046	+	0.620703i	$0.786847\pi$
$840$	17.5562	0.605748
$841$	−13.6270	−0.469896
$842$	−85.3823	−2.94247
$843$	−3.92925	−0.135331
$844$	5.92509	0.203950
$845$	11.2390	0.386633
$846$	1.64946	0.0567097
$847$	3.59421	0.123499
$848$	−8.18319	−0.281012
$849$	−6.09526	−0.209189
$850$	13.6294	0.467485
$851$	−37.4850	−1.28497
$852$	97.2159	3.33056
$853$	31.2210	1.06899	0.534494	−	0.845172i	$-0.320502\pi$
$853$	31.2210	1.06899	0.534494	+	0.845172i	$0.320502\pi$
$854$	30.5028	1.04378
$855$	−8.07652	−0.276211
$856$	52.8768	1.80729
$857$	42.7198	1.45928	0.729640	−	0.683832i	$-0.239688\pi$
$857$	42.7198	1.45928	0.729640	+	0.683832i	$0.239688\pi$
$858$	21.3539	0.729011
$859$	0.868425	0.0296303	0.0148151	−	0.999890i	$-0.495284\pi$
$859$	0.868425	0.0296303	0.0148151	+	0.999890i	$0.495284\pi$
$860$	28.3471	0.966628
$861$	−8.95089	−0.305046
$862$	−72.8845	−2.48246
$863$	−16.9656	−0.577516	−0.288758	−	0.957402i	$-0.593242\pi$
$863$	−16.9656	−0.577516	−0.288758	+	0.957402i	$0.593242\pi$
$864$	−27.9875	−0.952153
$865$	0.574156	0.0195219
$866$	85.4695	2.90437
$867$	21.6263	0.734466
$868$	33.1390	1.12481
$869$	19.3946	0.657916
$870$	23.1842	0.786017
$871$	16.8456	0.570792
$872$	28.9306	0.979712
$873$	−11.5299	−0.390227
$874$	35.0544	1.18573
$875$	1.00000	0.0338062
$876$	−11.9831	−0.404872
$877$	−3.96249	−0.133804	−0.0669019	−	0.997760i	$-0.521311\pi$
$877$	−3.96249	−0.133804	−0.0669019	+	0.997760i	$0.521311\pi$
$878$	−69.9289	−2.35999
$879$	44.9201	1.51512
$880$	−29.2640	−0.986490
$881$	−11.4958	−0.387302	−0.193651	−	0.981070i	$-0.562033\pi$
$881$	−11.4958	−0.387302	−0.193651	+	0.981070i	$0.562033\pi$
$882$	5.32485	0.179297
$883$	−5.30517	−0.178533	−0.0892666	−	0.996008i	$-0.528452\pi$
$883$	−5.30517	−0.178533	−0.0892666	+	0.996008i	$0.528452\pi$
$884$	34.0443	1.14503
$885$	−7.12862	−0.239626
$886$	18.9999	0.638313
$887$	26.9010	0.903249	0.451624	−	0.892208i	$-0.350845\pi$
$887$	26.9010	0.903249	0.451624	+	0.892208i	$0.350845\pi$
$888$	−198.444	−6.65934
$889$	−4.33688	−0.145454
$890$	0.667082	0.0223606
$891$	−29.8877	−1.00128
$892$	−59.9873	−2.00852
$893$	1.24034	0.0415063
$894$	−84.2375	−2.81732
$895$	7.41062	0.247710
$896$	−6.39066	−0.213497
$897$	9.85726	0.329124
$898$	−13.3293	−0.444804
$899$	26.1484	0.872097
$900$	10.0229	0.334098
$901$	−3.92884	−0.130889
$902$	28.7087	0.955897
$903$	12.7779	0.425221
$904$	−40.0638	−1.33250
$905$	3.65740	0.121576
$906$	−98.8937	−3.28552
$907$	−48.6319	−1.61480	−0.807398	−	0.590007i	$-0.799125\pi$
$907$	−48.6319	−1.61480	−0.807398	+	0.590007i	$0.799125\pi$
$908$	−53.9265	−1.78961
$909$	2.52427	0.0837246
$910$	3.50322	0.116131
$911$	44.0064	1.45800	0.728998	−	0.684515i	$-0.239986\pi$
$911$	44.0064	1.45800	0.728998	+	0.684515i	$0.239986\pi$
$912$	96.4445	3.19360
$913$	47.5945	1.57515
$914$	−11.2568	−0.372342
$915$	25.8808	0.855592
$916$	4.96906	0.164182
$917$	−6.76692	−0.223463
$918$	−30.0073	−0.990388
$919$	13.1260	0.432988	0.216494	−	0.976284i	$-0.430538\pi$
$919$	13.1260	0.432988	0.216494	+	0.976284i	$0.430538\pi$
$920$	−25.9931	−0.856968
$921$	−13.8341	−0.455850
$922$	−99.5536	−3.27862
$923$	11.5909	0.381520
$924$	−30.2890	−0.996435
$925$	−11.3033	−0.371651
$926$	−37.2328	−1.22354
$927$	−16.7436	−0.549934
$928$	−49.8418	−1.63614
$929$	−7.03062	−0.230667	−0.115334	−	0.993327i	$-0.536794\pi$
$929$	−7.03062	−0.230667	−0.115334	+	0.993327i	$0.536794\pi$
$930$	39.4345	1.29311
$931$	4.00409	0.131229
$932$	−29.1812	−0.955861
$933$	−29.3196	−0.959879
$934$	−63.2882	−2.07085
$935$	−14.0500	−0.459484
$936$	20.9801	0.685755
$937$	27.6516	0.903340	0.451670	−	0.892185i	$-0.350828\pi$
$937$	27.6516	0.903340	0.451670	+	0.892185i	$0.350828\pi$
$938$	−33.5115	−1.09419
$939$	−20.6441	−0.673696
$940$	−1.53925	−0.0502049
$941$	37.8872	1.23509	0.617543	−	0.786537i	$-0.288128\pi$
$941$	37.8872	1.23509	0.617543	+	0.786537i	$0.288128\pi$
$942$	8.55430	0.278714
$943$	13.2524	0.431556
$944$	34.2239	1.11389
$945$	−2.20166	−0.0716199
$946$	−40.9833	−1.33248
$947$	−37.0379	−1.20357	−0.601785	−	0.798658i	$-0.705544\pi$
$947$	−37.0379	−1.20357	−0.601785	+	0.798658i	$0.705544\pi$
$948$	79.3221	2.57626
$949$	−1.42873	−0.0463785
$950$	10.5704	0.342949
$951$	−71.3358	−2.31322
$952$	−40.4666	−1.31153
$953$	−32.2407	−1.04438	−0.522189	−	0.852830i	$-0.674884\pi$
$953$	−32.2407	−1.04438	−0.522189	+	0.852830i	$0.674884\pi$
$954$	−4.05211	−0.131192
$955$	−8.12688	−0.262980
$956$	49.4094	1.59801
$957$	−23.8996	−0.772564
$958$	−26.3178	−0.850289
$959$	−0.0291688	−0.000941910 0
$960$	−26.9939	−0.871224
$961$	13.4764	0.434722
$962$	−39.5980	−1.27669
$963$	13.6075	0.438496
$964$	13.6069	0.438247
$965$	25.7690	0.829533
$966$	−19.6094	−0.630921
$967$	−52.9043	−1.70129	−0.850644	−	0.525742i	$-0.823788\pi$
$967$	−52.9043	−1.70129	−0.850644	+	0.525742i	$0.823788\pi$
$968$	−28.1715	−0.905467
$969$	46.3041	1.48750
$970$	15.0901	0.484514
$971$	−46.7245	−1.49946	−0.749730	−	0.661744i	$-0.769816\pi$
$971$	−46.7245	−1.49946	−0.749730	+	0.661744i	$0.769816\pi$
$972$	−89.4175	−2.86807
$973$	−16.5953	−0.532021
$974$	35.0634	1.12351
$975$	2.97238	0.0951924
$976$	−124.251	−3.97719
$977$	35.0174	1.12031	0.560153	−	0.828389i	$-0.310742\pi$
$977$	35.0174	1.12031	0.560153	+	0.828389i	$0.310742\pi$
$978$	−78.4746	−2.50934
$979$	−0.687666	−0.0219779
$980$	−4.96906	−0.158731
$981$	7.44509	0.237704
$982$	97.8167	3.12146
$983$	37.3695	1.19190	0.595951	−	0.803021i	$-0.296775\pi$
$983$	37.3695	1.19190	0.595951	+	0.803021i	$0.296775\pi$
$984$	70.1573	2.23653
$985$	−6.30826	−0.200998
$986$	−53.4388	−1.70184
$987$	−0.693841	−0.0220852
$988$	26.4033	0.840002
$989$	−18.9185	−0.601572
$990$	−14.4908	−0.460548
$991$	33.9287	1.07778	0.538890	−	0.842376i	$-0.318844\pi$
$991$	33.9287	1.07778	0.538890	+	0.842376i	$0.318844\pi$
$992$	−84.7772	−2.69168
$993$	13.4715	0.427505
$994$	−23.0582	−0.731361
$995$	11.7117	0.371287
$996$	194.657	6.16795
$997$	7.56393	0.239552	0.119776	−	0.992801i	$-0.461782\pi$
$997$	7.56393	0.239552	0.119776	+	0.992801i	$0.461782\pi$
$998$	−13.3704	−0.423231
$999$	24.8860	0.787359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.60	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.60	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+2.63990 q^{2} +2.23988 q^{3} +4.96906 q^{4} -1.00000 q^{5} +5.91306 q^{6} -1.00000 q^{7} +7.83803 q^{8} +2.01707 q^{9} +O(q^{10})\)	\(q+2.63990 q^{2} +2.23988 q^{3} +4.96906 q^{4} -1.00000 q^{5} +5.91306 q^{6} -1.00000 q^{7} +7.83803 q^{8} +2.01707 q^{9} -2.63990 q^{10} +2.72136 q^{11} +11.1301 q^{12} +1.32703 q^{13} -2.63990 q^{14} -2.23988 q^{15} +10.7535 q^{16} +5.16286 q^{17} +5.32485 q^{18} +4.00409 q^{19} -4.96906 q^{20} -2.23988 q^{21} +7.18411 q^{22} +3.31628 q^{23} +17.5562 q^{24} +1.00000 q^{25} +3.50322 q^{26} -2.20166 q^{27} -4.96906 q^{28} -3.92085 q^{29} -5.91306 q^{30} -6.66906 q^{31} +12.7120 q^{32} +6.09552 q^{33} +13.6294 q^{34} +1.00000 q^{35} +10.0229 q^{36} -11.3033 q^{37} +10.5704 q^{38} +2.97238 q^{39} -7.83803 q^{40} +3.99615 q^{41} -5.91306 q^{42} -5.70472 q^{43} +13.5226 q^{44} -2.01707 q^{45} +8.75465 q^{46} +0.309767 q^{47} +24.0865 q^{48} +1.00000 q^{49} +2.63990 q^{50} +11.5642 q^{51} +6.59408 q^{52} -0.760981 q^{53} -5.81215 q^{54} -2.72136 q^{55} -7.83803 q^{56} +8.96869 q^{57} -10.3506 q^{58} +3.18259 q^{59} -11.1301 q^{60} -11.5545 q^{61} -17.6056 q^{62} -2.01707 q^{63} +12.0515 q^{64} -1.32703 q^{65} +16.0915 q^{66} +12.6942 q^{67} +25.6546 q^{68} +7.42808 q^{69} +2.63990 q^{70} +8.73450 q^{71} +15.8098 q^{72} -1.07664 q^{73} -29.8396 q^{74} +2.23988 q^{75} +19.8966 q^{76} -2.72136 q^{77} +7.84679 q^{78} +7.12680 q^{79} -10.7535 q^{80} -10.9826 q^{81} +10.5494 q^{82} +17.4892 q^{83} -11.1301 q^{84} -5.16286 q^{85} -15.0599 q^{86} -8.78223 q^{87} +21.3301 q^{88} -0.252692 q^{89} -5.32485 q^{90} -1.32703 q^{91} +16.4788 q^{92} -14.9379 q^{93} +0.817754 q^{94} -4.00409 q^{95} +28.4734 q^{96} -5.71617 q^{97} +2.63990 q^{98} +5.48916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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