LMFDB - Embedded newform 8015.2.a.l.1.28

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			1.28
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)

$f(q)$	$=$	$q-0.431324 q^{2} +3.18734 q^{3} -1.81396 q^{4} -1.00000 q^{5} -1.37477 q^{6} -1.00000 q^{7} +1.64505 q^{8} +7.15913 q^{9} +O(q^{10})$	\(q-0.431324 q^{2} +3.18734 q^{3} -1.81396 q^{4} -1.00000 q^{5} -1.37477 q^{6} -1.00000 q^{7} +1.64505 q^{8} +7.15913 q^{9} +0.431324 q^{10} +3.80287 q^{11} -5.78170 q^{12} -2.66079 q^{13} +0.431324 q^{14} -3.18734 q^{15} +2.91837 q^{16} +4.14418 q^{17} -3.08790 q^{18} +0.188739 q^{19} +1.81396 q^{20} -3.18734 q^{21} -1.64027 q^{22} -5.11240 q^{23} +5.24334 q^{24} +1.00000 q^{25} +1.14766 q^{26} +13.2565 q^{27} +1.81396 q^{28} +6.66693 q^{29} +1.37477 q^{30} -3.15228 q^{31} -4.54887 q^{32} +12.1210 q^{33} -1.78748 q^{34} +1.00000 q^{35} -12.9864 q^{36} -5.04444 q^{37} -0.0814076 q^{38} -8.48084 q^{39} -1.64505 q^{40} +11.6032 q^{41} +1.37477 q^{42} +8.17712 q^{43} -6.89826 q^{44} -7.15913 q^{45} +2.20510 q^{46} -0.591708 q^{47} +9.30183 q^{48} +1.00000 q^{49} -0.431324 q^{50} +13.2089 q^{51} +4.82657 q^{52} -4.28908 q^{53} -5.71786 q^{54} -3.80287 q^{55} -1.64505 q^{56} +0.601575 q^{57} -2.87560 q^{58} +8.59415 q^{59} +5.78170 q^{60} -12.1270 q^{61} +1.35965 q^{62} -7.15913 q^{63} -3.87471 q^{64} +2.66079 q^{65} -5.22810 q^{66} -11.5559 q^{67} -7.51737 q^{68} -16.2949 q^{69} -0.431324 q^{70} +7.44658 q^{71} +11.7771 q^{72} +2.33383 q^{73} +2.17579 q^{74} +3.18734 q^{75} -0.342365 q^{76} -3.80287 q^{77} +3.65799 q^{78} +7.64931 q^{79} -2.91837 q^{80} +20.7757 q^{81} -5.00474 q^{82} +5.54696 q^{83} +5.78170 q^{84} -4.14418 q^{85} -3.52699 q^{86} +21.2498 q^{87} +6.25592 q^{88} -12.3112 q^{89} +3.08790 q^{90} +2.66079 q^{91} +9.27369 q^{92} -10.0474 q^{93} +0.255218 q^{94} -0.188739 q^{95} -14.4988 q^{96} -10.2903 q^{97} -0.431324 q^{98} +27.2253 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.431324	−0.304992	−0.152496	−	0.988304i	$-0.548731\pi$
$2$	−0.431324	−0.304992	−0.152496	+	0.988304i	$0.548731\pi$
$3$	3.18734	1.84021	0.920105	−	0.391671i	$-0.128103\pi$
$3$	3.18734	1.84021	0.920105	+	0.391671i	$0.128103\pi$
$4$	−1.81396	−0.906980
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.37477	−0.561249
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.64505	0.581614
$9$	7.15913	2.38638
$10$	0.431324	0.136397
$11$	3.80287	1.14661	0.573305	−	0.819342i	$-0.305661\pi$
$11$	3.80287	1.14661	0.573305	+	0.819342i	$0.305661\pi$
$12$	−5.78170	−1.66903
$13$	−2.66079	−0.737970	−0.368985	−	0.929435i	$-0.620295\pi$
$13$	−2.66079	−0.737970	−0.368985	+	0.929435i	$0.620295\pi$
$14$	0.431324	0.115276
$15$	−3.18734	−0.822967
$16$	2.91837	0.729592
$17$	4.14418	1.00511	0.502555	−	0.864545i	$-0.332393\pi$
$17$	4.14418	1.00511	0.502555	+	0.864545i	$0.332393\pi$
$18$	−3.08790	−0.727825
$19$	0.188739	0.0432997	0.0216498	−	0.999766i	$-0.493108\pi$
$19$	0.188739	0.0432997	0.0216498	+	0.999766i	$0.493108\pi$
$20$	1.81396	0.405614
$21$	−3.18734	−0.695534
$22$	−1.64027	−0.349707
$23$	−5.11240	−1.06601	−0.533004	−	0.846112i	$-0.678937\pi$
$23$	−5.11240	−1.06601	−0.533004	+	0.846112i	$0.678937\pi$
$24$	5.24334	1.07029
$25$	1.00000	0.200000
$26$	1.14766	0.225075
$27$	13.2565	2.55122
$28$	1.81396	0.342806
$29$	6.66693	1.23802	0.619009	−	0.785384i	$-0.287535\pi$
$29$	6.66693	1.23802	0.619009	+	0.785384i	$0.287535\pi$
$30$	1.37477	0.250998
$31$	−3.15228	−0.566165	−0.283083	−	0.959096i	$-0.591357\pi$
$31$	−3.15228	−0.566165	−0.283083	+	0.959096i	$0.591357\pi$
$32$	−4.54887	−0.804133
$33$	12.1210	2.11000
$34$	−1.78748	−0.306551
$35$	1.00000	0.169031
$36$	−12.9864	−2.16439
$37$	−5.04444	−0.829300	−0.414650	−	0.909981i	$-0.636096\pi$
$37$	−5.04444	−0.829300	−0.414650	+	0.909981i	$0.636096\pi$
$38$	−0.0814076	−0.0132061
$39$	−8.48084	−1.35802
$40$	−1.64505	−0.260105
$41$	11.6032	1.81212	0.906058	−	0.423154i	$-0.139077\pi$
$41$	11.6032	1.81212	0.906058	+	0.423154i	$0.139077\pi$
$42$	1.37477	0.212132
$43$	8.17712	1.24700	0.623500	−	0.781824i	$-0.285710\pi$
$43$	8.17712	1.24700	0.623500	+	0.781824i	$0.285710\pi$
$44$	−6.89826	−1.03995
$45$	−7.15913	−1.06722
$46$	2.20510	0.325124
$47$	−0.591708	−0.0863095	−0.0431548	−	0.999068i	$-0.513741\pi$
$47$	−0.591708	−0.0863095	−0.0431548	+	0.999068i	$0.513741\pi$
$48$	9.30183	1.34260
$49$	1.00000	0.142857
$50$	−0.431324	−0.0609984
$51$	13.2089	1.84961
$52$	4.82657	0.669324
$53$	−4.28908	−0.589150	−0.294575	−	0.955628i	$-0.595178\pi$
$53$	−4.28908	−0.589150	−0.294575	+	0.955628i	$0.595178\pi$
$54$	−5.71786	−0.778103
$55$	−3.80287	−0.512780
$56$	−1.64505	−0.219829
$57$	0.601575	0.0796806
$58$	−2.87560	−0.377585
$59$	8.59415	1.11886	0.559432	−	0.828877i	$-0.311019\pi$
$59$	8.59415	1.11886	0.559432	+	0.828877i	$0.311019\pi$
$60$	5.78170	0.746415
$61$	−12.1270	−1.55271	−0.776353	−	0.630299i	$-0.782932\pi$
$61$	−12.1270	−1.55271	−0.776353	+	0.630299i	$0.782932\pi$
$62$	1.35965	0.172676
$63$	−7.15913	−0.901965
$64$	−3.87471	−0.484338
$65$	2.66079	0.330030
$66$	−5.22810	−0.643534
$67$	−11.5559	−1.41178	−0.705890	−	0.708322i	$-0.749453\pi$
$67$	−11.5559	−1.41178	−0.705890	+	0.708322i	$0.749453\pi$
$68$	−7.51737	−0.911615
$69$	−16.2949	−1.96168
$70$	−0.431324	−0.0515530
$71$	7.44658	0.883746	0.441873	−	0.897078i	$-0.354314\pi$
$71$	7.44658	0.883746	0.441873	+	0.897078i	$0.354314\pi$
$72$	11.7771	1.38795
$73$	2.33383	0.273154	0.136577	−	0.990629i	$-0.456390\pi$
$73$	2.33383	0.273154	0.136577	+	0.990629i	$0.456390\pi$
$74$	2.17579	0.252930
$75$	3.18734	0.368042
$76$	−0.342365	−0.0392720
$77$	−3.80287	−0.433378
$78$	3.65799	0.414185
$79$	7.64931	0.860615	0.430307	−	0.902682i	$-0.358405\pi$
$79$	7.64931	0.860615	0.430307	+	0.902682i	$0.358405\pi$
$80$	−2.91837	−0.326284
$81$	20.7757	2.30841
$82$	−5.00474	−0.552681
$83$	5.54696	0.608858	0.304429	−	0.952535i	$-0.401534\pi$
$83$	5.54696	0.608858	0.304429	+	0.952535i	$0.401534\pi$
$84$	5.78170	0.630836
$85$	−4.14418	−0.449499
$86$	−3.52699	−0.380325
$87$	21.2498	2.27821
$88$	6.25592	0.666884
$89$	−12.3112	−1.30498	−0.652490	−	0.757798i	$-0.726275\pi$
$89$	−12.3112	−1.30498	−0.652490	+	0.757798i	$0.726275\pi$
$90$	3.08790	0.325493
$91$	2.66079	0.278927
$92$	9.27369	0.966849
$93$	−10.0474	−1.04186
$94$	0.255218	0.0263237
$95$	−0.188739	−0.0193642
$96$	−14.4988	−1.47977
$97$	−10.2903	−1.04483	−0.522413	−	0.852693i	$-0.674968\pi$
$97$	−10.2903	−1.04483	−0.522413	+	0.852693i	$0.674968\pi$
$98$	−0.431324	−0.0435703
$99$	27.2253	2.73624
$100$	−1.81396	−0.181396
$101$	−4.91978	−0.489536	−0.244768	−	0.969582i	$-0.578712\pi$
$101$	−4.91978	−0.489536	−0.244768	+	0.969582i	$0.578712\pi$
$102$	−5.69731	−0.564118
$103$	10.6717	1.05151	0.525757	−	0.850635i	$-0.323782\pi$
$103$	10.6717	1.05151	0.525757	+	0.850635i	$0.323782\pi$
$104$	−4.37714	−0.429214
$105$	3.18734	0.311052
$106$	1.84998	0.179686
$107$	16.6958	1.61404	0.807020	−	0.590524i	$-0.201079\pi$
$107$	16.6958	1.61404	0.807020	+	0.590524i	$0.201079\pi$
$108$	−24.0468	−2.31391
$109$	−10.2366	−0.980488	−0.490244	−	0.871585i	$-0.663092\pi$
$109$	−10.2366	−0.980488	−0.490244	+	0.871585i	$0.663092\pi$
$110$	1.64027	0.156394
$111$	−16.0783	−1.52609
$112$	−2.91837	−0.275760
$113$	14.7513	1.38768	0.693841	−	0.720128i	$-0.255917\pi$
$113$	14.7513	1.38768	0.693841	+	0.720128i	$0.255917\pi$
$114$	−0.259474	−0.0243019
$115$	5.11240	0.476734
$116$	−12.0935	−1.12286
$117$	−19.0489	−1.76107
$118$	−3.70686	−0.341244
$119$	−4.14418	−0.379896
$120$	−5.24334	−0.478649
$121$	3.46186	0.314714
$122$	5.23067	0.473563
$123$	36.9833	3.33468
$124$	5.71810	0.513501
$125$	−1.00000	−0.0894427
$126$	3.08790	0.275092
$127$	−2.10873	−0.187120	−0.0935599	−	0.995614i	$-0.529825\pi$
$127$	−2.10873	−0.187120	−0.0935599	+	0.995614i	$0.529825\pi$
$128$	10.7690	0.951853
$129$	26.0633	2.29474
$130$	−1.14766	−0.100657
$131$	17.5819	1.53614	0.768068	−	0.640368i	$-0.221218\pi$
$131$	17.5819	1.53614	0.768068	+	0.640368i	$0.221218\pi$
$132$	−21.9871	−1.91373
$133$	−0.188739	−0.0163657
$134$	4.98434	0.430581
$135$	−13.2565	−1.14094
$136$	6.81738	0.584586
$137$	−14.0926	−1.20402	−0.602008	−	0.798490i	$-0.705632\pi$
$137$	−14.0926	−1.20402	−0.602008	+	0.798490i	$0.705632\pi$
$138$	7.02840	0.598297
$139$	−22.6086	−1.91764	−0.958820	−	0.284014i	$-0.908334\pi$
$139$	−22.6086	−1.91764	−0.958820	+	0.284014i	$0.908334\pi$
$140$	−1.81396	−0.153308
$141$	−1.88597	−0.158828
$142$	−3.21189	−0.269535
$143$	−10.1186	−0.846164
$144$	20.8930	1.74108
$145$	−6.66693	−0.553658
$146$	−1.00664	−0.0833097
$147$	3.18734	0.262887
$148$	9.15041	0.752159
$149$	17.8672	1.46374	0.731870	−	0.681444i	$-0.238648\pi$
$149$	17.8672	1.46374	0.731870	+	0.681444i	$0.238648\pi$
$150$	−1.37477	−0.112250
$151$	10.5400	0.857732	0.428866	−	0.903368i	$-0.358913\pi$
$151$	10.5400	0.857732	0.428866	+	0.903368i	$0.358913\pi$
$152$	0.310485	0.0251837
$153$	29.6687	2.39857
$154$	1.64027	0.132177
$155$	3.15228	0.253197
$156$	15.3839	1.23170
$157$	18.3982	1.46834	0.734168	−	0.678968i	$-0.237573\pi$
$157$	18.3982	1.46834	0.734168	+	0.678968i	$0.237573\pi$
$158$	−3.29933	−0.262481
$159$	−13.6708	−1.08416
$160$	4.54887	0.359619
$161$	5.11240	0.402914
$162$	−8.96106	−0.704048
$163$	23.9768	1.87801	0.939003	−	0.343909i	$-0.111751\pi$
$163$	23.9768	1.87801	0.939003	+	0.343909i	$0.111751\pi$
$164$	−21.0477	−1.64355
$165$	−12.1210	−0.943622
$166$	−2.39253	−0.185697
$167$	23.7618	1.83875	0.919373	−	0.393387i	$-0.128697\pi$
$167$	23.7618	1.83875	0.919373	+	0.393387i	$0.128697\pi$
$168$	−5.24334	−0.404532
$169$	−5.92020	−0.455400
$170$	1.78748	0.137094
$171$	1.35121	0.103329
$172$	−14.8330	−1.13100
$173$	21.0548	1.60077	0.800385	−	0.599487i	$-0.204629\pi$
$173$	21.0548	1.60077	0.800385	+	0.599487i	$0.204629\pi$
$174$	−9.16553	−0.694837
$175$	−1.00000	−0.0755929
$176$	11.0982	0.836558
$177$	27.3925	2.05894
$178$	5.31009	0.398008
$179$	−17.6887	−1.32211	−0.661057	−	0.750336i	$-0.729892\pi$
$179$	−17.6887	−1.32211	−0.661057	+	0.750336i	$0.729892\pi$
$180$	12.9864	0.967947
$181$	−11.7329	−0.872099	−0.436049	−	0.899923i	$-0.643623\pi$
$181$	−11.7329	−0.872099	−0.436049	+	0.899923i	$0.643623\pi$
$182$	−1.14766	−0.0850704
$183$	−38.6529	−2.85730
$184$	−8.41016	−0.620005
$185$	5.04444	0.370874
$186$	4.33367	0.317760
$187$	15.7598	1.15247
$188$	1.07334	0.0782810
$189$	−13.2565	−0.964272
$190$	0.0814076	0.00590593
$191$	−13.0233	−0.942331	−0.471165	−	0.882045i	$-0.656166\pi$
$191$	−13.0233	−0.942331	−0.471165	+	0.882045i	$0.656166\pi$
$192$	−12.3500	−0.891284
$193$	18.0577	1.29982	0.649912	−	0.760009i	$-0.274806\pi$
$193$	18.0577	1.29982	0.649912	+	0.760009i	$0.274806\pi$
$194$	4.43847	0.318663
$195$	8.48084	0.607325
$196$	−1.81396	−0.129569
$197$	9.89014	0.704644	0.352322	−	0.935879i	$-0.385392\pi$
$197$	9.89014	0.704644	0.352322	+	0.935879i	$0.385392\pi$
$198$	−11.7429	−0.834532
$199$	−1.37522	−0.0974868	−0.0487434	−	0.998811i	$-0.515522\pi$
$199$	−1.37522	−0.0974868	−0.0487434	+	0.998811i	$0.515522\pi$
$200$	1.64505	0.116323
$201$	−36.8326	−2.59797
$202$	2.12202	0.149305
$203$	−6.66693	−0.467927
$204$	−23.9604	−1.67756
$205$	−11.6032	−0.810403
$206$	−4.60295	−0.320703
$207$	−36.6003	−2.54390
$208$	−7.76517	−0.538418
$209$	0.717751	0.0496479
$210$	−1.37477	−0.0948685
$211$	−11.3366	−0.780443	−0.390222	−	0.920721i	$-0.627602\pi$
$211$	−11.3366	−0.780443	−0.390222	+	0.920721i	$0.627602\pi$
$212$	7.78022	0.534348
$213$	23.7348	1.62628
$214$	−7.20128	−0.492269
$215$	−8.17712	−0.557675
$216$	21.8077	1.48383
$217$	3.15228	0.213990
$218$	4.41529	0.299041
$219$	7.43870	0.502661
$220$	6.89826	0.465081
$221$	−11.0268	−0.741741
$222$	6.93497	0.465444
$223$	24.8557	1.66446	0.832230	−	0.554430i	$-0.187064\pi$
$223$	24.8557	1.66446	0.832230	+	0.554430i	$0.187064\pi$
$224$	4.54887	0.303934
$225$	7.15913	0.477275
$226$	−6.36257	−0.423232
$227$	−16.4839	−1.09407	−0.547036	−	0.837109i	$-0.684244\pi$
$227$	−16.4839	−1.09407	−0.547036	+	0.837109i	$0.684244\pi$
$228$	−1.09123	−0.0722687
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−2.20510	−0.145400
$231$	−12.1210	−0.797506
$232$	10.9674	0.720048
$233$	14.6913	0.962461	0.481231	−	0.876594i	$-0.340190\pi$
$233$	14.6913	0.962461	0.481231	+	0.876594i	$0.340190\pi$
$234$	8.21626	0.537114
$235$	0.591708	0.0385988
$236$	−15.5894	−1.01479
$237$	24.3810	1.58371
$238$	1.78748	0.115865
$239$	−3.65923	−0.236696	−0.118348	−	0.992972i	$-0.537760\pi$
$239$	−3.65923	−0.236696	−0.118348	+	0.992972i	$0.537760\pi$
$240$	−9.30183	−0.600431
$241$	−15.3783	−0.990606	−0.495303	−	0.868720i	$-0.664943\pi$
$241$	−15.3783	−0.990606	−0.495303	+	0.868720i	$0.664943\pi$
$242$	−1.49318	−0.0959853
$243$	26.4496	1.69674
$244$	21.9979	1.40827
$245$	−1.00000	−0.0638877
$246$	−15.9518	−1.01705
$247$	−0.502195	−0.0319539
$248$	−5.18566	−0.329289
$249$	17.6800	1.12043
$250$	0.431324	0.0272793
$251$	18.6118	1.17477	0.587383	−	0.809309i	$-0.300158\pi$
$251$	18.6118	1.17477	0.587383	+	0.809309i	$0.300158\pi$
$252$	12.9864	0.818064
$253$	−19.4418	−1.22230
$254$	0.909547	0.0570700
$255$	−13.2089	−0.827173
$256$	3.10449	0.194031
$257$	11.4758	0.715839	0.357919	−	0.933753i	$-0.383486\pi$
$257$	11.4758	0.715839	0.357919	+	0.933753i	$0.383486\pi$
$258$	−11.2417	−0.699878
$259$	5.04444	0.313446
$260$	−4.82657	−0.299331
$261$	47.7294	2.95438
$262$	−7.58349	−0.468509
$263$	−19.2988	−1.19002	−0.595008	−	0.803720i	$-0.702851\pi$
$263$	−19.2988	−1.19002	−0.595008	+	0.803720i	$0.702851\pi$
$264$	19.9398	1.22721
$265$	4.28908	0.263476
$266$	0.0814076	0.00499142
$267$	−39.2398	−2.40144
$268$	20.9620	1.28046
$269$	−14.8908	−0.907907	−0.453953	−	0.891025i	$-0.649987\pi$
$269$	−14.8908	−0.907907	−0.453953	+	0.891025i	$0.649987\pi$
$270$	5.71786	0.347978
$271$	13.9433	0.846993	0.423496	−	0.905898i	$-0.360803\pi$
$271$	13.9433	0.846993	0.423496	+	0.905898i	$0.360803\pi$
$272$	12.0942	0.733321
$273$	8.48084	0.513284
$274$	6.07849	0.367215
$275$	3.80287	0.229322
$276$	29.5584	1.77921
$277$	−17.9895	−1.08089	−0.540444	−	0.841380i	$-0.681744\pi$
$277$	−17.9895	−1.08089	−0.540444	+	0.841380i	$0.681744\pi$
$278$	9.75165	0.584865
$279$	−22.5675	−1.35108
$280$	1.64505	0.0983106
$281$	22.1310	1.32023	0.660113	−	0.751166i	$-0.270508\pi$
$281$	22.1310	1.32023	0.660113	+	0.751166i	$0.270508\pi$
$282$	0.813466	0.0484412
$283$	−30.3258	−1.80268	−0.901341	−	0.433109i	$-0.857416\pi$
$283$	−30.3258	−1.80268	−0.901341	+	0.433109i	$0.857416\pi$
$284$	−13.5078	−0.801540
$285$	−0.601575	−0.0356342
$286$	4.36441	0.258073
$287$	−11.6032	−0.684915
$288$	−32.5659	−1.91896
$289$	0.174190	0.0102465
$290$	2.87560	0.168861
$291$	−32.7988	−1.92270
$292$	−4.23347	−0.247745
$293$	19.3863	1.13256	0.566280	−	0.824213i	$-0.308382\pi$
$293$	19.3863	1.13256	0.566280	+	0.824213i	$0.308382\pi$
$294$	−1.37477	−0.0801785
$295$	−8.59415	−0.500371
$296$	−8.29836	−0.482332
$297$	50.4130	2.92526
$298$	−7.70656	−0.446429
$299$	13.6030	0.786683
$300$	−5.78170	−0.333807
$301$	−8.17712	−0.471321
$302$	−4.54615	−0.261602
$303$	−15.6810	−0.900850
$304$	0.550810	0.0315911
$305$	12.1270	0.694391
$306$	−12.7968	−0.731545
$307$	28.8830	1.64844	0.824219	−	0.566271i	$-0.191615\pi$
$307$	28.8830	1.64844	0.824219	+	0.566271i	$0.191615\pi$
$308$	6.89826	0.393065
$309$	34.0143	1.93501
$310$	−1.35965	−0.0772230
$311$	0.982883	0.0557342	0.0278671	−	0.999612i	$-0.491128\pi$
$311$	0.982883	0.0557342	0.0278671	+	0.999612i	$0.491128\pi$
$312$	−13.9514	−0.789843
$313$	3.23297	0.182738	0.0913692	−	0.995817i	$-0.470876\pi$
$313$	3.23297	0.182738	0.0913692	+	0.995817i	$0.470876\pi$
$314$	−7.93557	−0.447830
$315$	7.15913	0.403371
$316$	−13.8755	−0.780560
$317$	14.4678	0.812592	0.406296	−	0.913741i	$-0.366820\pi$
$317$	14.4678	0.812592	0.406296	+	0.913741i	$0.366820\pi$
$318$	5.89652	0.330660
$319$	25.3535	1.41952
$320$	3.87471	0.216603
$321$	53.2150	2.97017
$322$	−2.20510	−0.122885
$323$	0.782167	0.0435210
$324$	−37.6863	−2.09369
$325$	−2.66079	−0.147594
$326$	−10.3418	−0.572777
$327$	−32.6275	−1.80430
$328$	19.0879	1.05395
$329$	0.591708	0.0326219
$330$	5.22810	0.287797
$331$	−30.5538	−1.67939	−0.839693	−	0.543061i	$-0.817265\pi$
$331$	−30.5538	−1.67939	−0.839693	+	0.543061i	$0.817265\pi$
$332$	−10.0620	−0.552222
$333$	−36.1138	−1.97902
$334$	−10.2490	−0.560803
$335$	11.5559	0.631367
$336$	−9.30183	−0.507457
$337$	−31.4380	−1.71254	−0.856268	−	0.516533i	$-0.827222\pi$
$337$	−31.4380	−1.71254	−0.856268	+	0.516533i	$0.827222\pi$
$338$	2.55352	0.138893
$339$	47.0173	2.55363
$340$	7.51737	0.407687
$341$	−11.9877	−0.649171
$342$	−0.582807	−0.0315146
$343$	−1.00000	−0.0539949
$344$	13.4518	0.725272
$345$	16.2949	0.877291
$346$	−9.08145	−0.488222
$347$	6.81509	0.365853	0.182927	−	0.983127i	$-0.441443\pi$
$347$	6.81509	0.365853	0.182927	+	0.983127i	$0.441443\pi$
$348$	−38.5462	−2.06629
$349$	−1.51865	−0.0812914	−0.0406457	−	0.999174i	$-0.512941\pi$
$349$	−1.51865	−0.0812914	−0.0406457	+	0.999174i	$0.512941\pi$
$350$	0.431324	0.0230552
$351$	−35.2729	−1.88273
$352$	−17.2988	−0.922027
$353$	19.4322	1.03427	0.517136	−	0.855903i	$-0.326998\pi$
$353$	19.4322	1.03427	0.517136	+	0.855903i	$0.326998\pi$
$354$	−11.8150	−0.627961
$355$	−7.44658	−0.395223
$356$	22.3319	1.18359
$357$	−13.2089	−0.699089
$358$	7.62955	0.403234
$359$	16.9024	0.892074	0.446037	−	0.895015i	$-0.352835\pi$
$359$	16.9024	0.892074	0.446037	+	0.895015i	$0.352835\pi$
$360$	−11.7771	−0.620709
$361$	−18.9644	−0.998125
$362$	5.06067	0.265983
$363$	11.0341	0.579140
$364$	−4.82657	−0.252981
$365$	−2.33383	−0.122158
$366$	16.6719	0.871455
$367$	−17.8773	−0.933186	−0.466593	−	0.884472i	$-0.654519\pi$
$367$	−17.8773	−0.933186	−0.466593	+	0.884472i	$0.654519\pi$
$368$	−14.9199	−0.777752
$369$	83.0688	4.32439
$370$	−2.17579	−0.113114
$371$	4.28908	0.222678
$372$	18.2255	0.944949
$373$	0.860712	0.0445660	0.0222830	−	0.999752i	$-0.492907\pi$
$373$	0.860712	0.0445660	0.0222830	+	0.999752i	$0.492907\pi$
$374$	−6.79757	−0.351494
$375$	−3.18734	−0.164593
$376$	−0.973391	−0.0501988
$377$	−17.7393	−0.913620
$378$	5.71786	0.294095
$379$	7.68378	0.394689	0.197345	−	0.980334i	$-0.436768\pi$
$379$	7.68378	0.394689	0.197345	+	0.980334i	$0.436768\pi$
$380$	0.342365	0.0175630
$381$	−6.72125	−0.344340
$382$	5.61724	0.287403
$383$	−2.46551	−0.125982	−0.0629909	−	0.998014i	$-0.520064\pi$
$383$	−2.46551	−0.125982	−0.0629909	+	0.998014i	$0.520064\pi$
$384$	34.3244	1.75161
$385$	3.80287	0.193812
$386$	−7.78873	−0.396436
$387$	58.5411	2.97581
$388$	18.6663	0.947636
$389$	23.8264	1.20805	0.604023	−	0.796967i	$-0.293563\pi$
$389$	23.8264	1.20805	0.604023	+	0.796967i	$0.293563\pi$
$390$	−3.65799	−0.185229
$391$	−21.1867	−1.07146
$392$	1.64505	0.0830876
$393$	56.0394	2.82682
$394$	−4.26585	−0.214911
$395$	−7.64931	−0.384879
$396$	−49.3855	−2.48172
$397$	9.21387	0.462431	0.231215	−	0.972903i	$-0.425730\pi$
$397$	9.21387	0.462431	0.231215	+	0.972903i	$0.425730\pi$
$398$	0.593165	0.0297327
$399$	−0.601575	−0.0301164
$400$	2.91837	0.145918
$401$	−8.71805	−0.435359	−0.217679	−	0.976020i	$-0.569849\pi$
$401$	−8.71805	−0.435359	−0.217679	+	0.976020i	$0.569849\pi$
$402$	15.8868	0.792361
$403$	8.38754	0.417813
$404$	8.92428	0.444000
$405$	−20.7757	−1.03235
$406$	2.87560	0.142714
$407$	−19.1834	−0.950884
$408$	21.7293	1.07576
$409$	−0.578684	−0.0286141	−0.0143070	−	0.999898i	$-0.504554\pi$
$409$	−0.578684	−0.0286141	−0.0143070	+	0.999898i	$0.504554\pi$
$410$	5.00474	0.247166
$411$	−44.9180	−2.21564
$412$	−19.3580	−0.953701
$413$	−8.59415	−0.422890
$414$	15.7866	0.775868
$415$	−5.54696	−0.272289
$416$	12.1036	0.593427
$417$	−72.0614	−3.52886
$418$	−0.309583	−0.0151422
$419$	17.2738	0.843880	0.421940	−	0.906624i	$-0.361349\pi$
$419$	17.2738	0.843880	0.421940	+	0.906624i	$0.361349\pi$
$420$	−5.78170	−0.282118
$421$	−15.7648	−0.768329	−0.384165	−	0.923265i	$-0.625511\pi$
$421$	−15.7648	−0.768329	−0.384165	+	0.923265i	$0.625511\pi$
$422$	4.88974	0.238029
$423$	−4.23612	−0.205967
$424$	−7.05576	−0.342658
$425$	4.14418	0.201022
$426$	−10.2374	−0.496002
$427$	12.1270	0.586867
$428$	−30.2854	−1.46390
$429$	−32.2516	−1.55712
$430$	3.52699	0.170086
$431$	15.6648	0.754549	0.377275	−	0.926101i	$-0.376861\pi$
$431$	15.6648	0.754549	0.377275	+	0.926101i	$0.376861\pi$
$432$	38.6875	1.86135
$433$	21.7596	1.04570	0.522850	−	0.852425i	$-0.324869\pi$
$433$	21.7596	1.04570	0.522850	+	0.852425i	$0.324869\pi$
$434$	−1.35965	−0.0652653
$435$	−21.2498	−1.01885
$436$	18.5688	0.889283
$437$	−0.964909	−0.0461579
$438$	−3.20849	−0.153307
$439$	12.3074	0.587399	0.293700	−	0.955898i	$-0.405113\pi$
$439$	12.3074	0.587399	0.293700	+	0.955898i	$0.405113\pi$
$440$	−6.25592	−0.298240
$441$	7.15913	0.340911
$442$	4.75611	0.226225
$443$	19.7789	0.939722	0.469861	−	0.882740i	$-0.344304\pi$
$443$	19.7789	0.939722	0.469861	+	0.882740i	$0.344304\pi$
$444$	29.1654	1.38413
$445$	12.3112	0.583604
$446$	−10.7209	−0.507647
$447$	56.9489	2.69359
$448$	3.87471	0.183063
$449$	0.916740	0.0432636	0.0216318	−	0.999766i	$-0.493114\pi$
$449$	0.916740	0.0432636	0.0216318	+	0.999766i	$0.493114\pi$
$450$	−3.08790	−0.145565
$451$	44.1255	2.07779
$452$	−26.7582	−1.25860
$453$	33.5945	1.57841
$454$	7.10988	0.333683
$455$	−2.66079	−0.124740
$456$	0.989622	0.0463433
$457$	39.4881	1.84718	0.923588	−	0.383386i	$-0.125242\pi$
$457$	39.4881	1.84718	0.923588	+	0.383386i	$0.125242\pi$
$458$	−0.431324	−0.0201544
$459$	54.9375	2.56426
$460$	−9.27369	−0.432388
$461$	−15.2780	−0.711566	−0.355783	−	0.934569i	$-0.615786\pi$
$461$	−15.2780	−0.711566	−0.355783	+	0.934569i	$0.615786\pi$
$462$	5.22810	0.243233
$463$	41.0319	1.90691	0.953456	−	0.301531i	$-0.0974978\pi$
$463$	41.0319	1.90691	0.953456	+	0.301531i	$0.0974978\pi$
$464$	19.4566	0.903248
$465$	10.0474	0.465936
$466$	−6.33672	−0.293543
$467$	−11.5529	−0.534603	−0.267302	−	0.963613i	$-0.586132\pi$
$467$	−11.5529	−0.534603	−0.267302	+	0.963613i	$0.586132\pi$
$468$	34.5540	1.59726
$469$	11.5559	0.533603
$470$	−0.255218	−0.0117723
$471$	58.6412	2.70205
$472$	14.1378	0.650746
$473$	31.0966	1.42982
$474$	−10.5161	−0.483020
$475$	0.188739	0.00865994
$476$	7.51737	0.344558
$477$	−30.7061	−1.40593
$478$	1.57831	0.0721904
$479$	23.1406	1.05732	0.528661	−	0.848833i	$-0.322694\pi$
$479$	23.1406	1.05732	0.528661	+	0.848833i	$0.322694\pi$
$480$	14.4988	0.661775
$481$	13.4222	0.611999
$482$	6.63304	0.302127
$483$	16.2949	0.741446
$484$	−6.27967	−0.285439
$485$	10.2903	0.467260
$486$	−11.4084	−0.517493
$487$	−12.3142	−0.558009	−0.279005	−	0.960290i	$-0.590005\pi$
$487$	−12.3142	−0.558009	−0.279005	+	0.960290i	$0.590005\pi$
$488$	−19.9496	−0.903074
$489$	76.4221	3.45593
$490$	0.431324	0.0194852
$491$	6.07097	0.273979	0.136989	−	0.990573i	$-0.456257\pi$
$491$	6.07097	0.273979	0.136989	+	0.990573i	$0.456257\pi$
$492$	−67.0863	−3.02448
$493$	27.6289	1.24434
$494$	0.216609	0.00974568
$495$	−27.2253	−1.22368
$496$	−9.19951	−0.413070
$497$	−7.44658	−0.334025
$498$	−7.62582	−0.341721
$499$	1.10464	0.0494504	0.0247252	−	0.999694i	$-0.492129\pi$
$499$	1.10464	0.0494504	0.0247252	+	0.999694i	$0.492129\pi$
$500$	1.81396	0.0811227
$501$	75.7370	3.38368
$502$	−8.02770	−0.358294
$503$	−25.8473	−1.15248	−0.576238	−	0.817282i	$-0.695480\pi$
$503$	−25.8473	−1.15248	−0.576238	+	0.817282i	$0.695480\pi$
$504$	−11.7771	−0.524595
$505$	4.91978	0.218927
$506$	8.38572	0.372791
$507$	−18.8697	−0.838032
$508$	3.82516	0.169714
$509$	16.9051	0.749306	0.374653	−	0.927165i	$-0.377762\pi$
$509$	16.9051	0.749306	0.374653	+	0.927165i	$0.377762\pi$
$510$	5.69731	0.252281
$511$	−2.33383	−0.103242
$512$	−22.8770	−1.01103
$513$	2.50203	0.110467
$514$	−4.94977	−0.218325
$515$	−10.6717	−0.470251
$516$	−47.2777	−2.08128
$517$	−2.25019	−0.0989633
$518$	−2.17579	−0.0955985
$519$	67.1089	2.94575
$520$	4.37714	0.191950
$521$	−3.68794	−0.161571	−0.0807857	−	0.996731i	$-0.525743\pi$
$521$	−3.68794	−0.161571	−0.0807857	+	0.996731i	$0.525743\pi$
$522$	−20.5868	−0.901061
$523$	26.3095	1.15043	0.575216	−	0.818001i	$-0.304918\pi$
$523$	26.3095	1.15043	0.575216	+	0.818001i	$0.304918\pi$
$524$	−31.8928	−1.39324
$525$	−3.18734	−0.139107
$526$	8.32404	0.362945
$527$	−13.0636	−0.569059
$528$	35.3737	1.53944
$529$	3.13663	0.136375
$530$	−1.84998	−0.0803581
$531$	61.5266	2.67003
$532$	0.342365	0.0148434
$533$	−30.8737	−1.33729
$534$	16.9251	0.732419
$535$	−16.6958	−0.721821
$536$	−19.0101	−0.821110
$537$	−56.3798	−2.43297
$538$	6.42275	0.276904
$539$	3.80287	0.163801
$540$	24.0468	1.03481
$541$	−29.9342	−1.28697	−0.643486	−	0.765458i	$-0.722513\pi$
$541$	−29.9342	−1.28697	−0.643486	+	0.765458i	$0.722513\pi$
$542$	−6.01406	−0.258326
$543$	−37.3967	−1.60485
$544$	−18.8513	−0.808243
$545$	10.2366	0.438488
$546$	−3.65799	−0.156547
$547$	−25.5394	−1.09199	−0.545993	−	0.837790i	$-0.683847\pi$
$547$	−25.5394	−1.09199	−0.545993	+	0.837790i	$0.683847\pi$
$548$	25.5635	1.09202
$549$	−86.8188	−3.70534
$550$	−1.64027	−0.0699414
$551$	1.25831	0.0536058
$552$	−26.8060	−1.14094
$553$	−7.64931	−0.325282
$554$	7.75932	0.329662
$555$	16.0783	0.682487
$556$	41.0112	1.73926
$557$	2.12199	0.0899116	0.0449558	−	0.998989i	$-0.485685\pi$
$557$	2.12199	0.0899116	0.0449558	+	0.998989i	$0.485685\pi$
$558$	9.73392	0.412070
$559$	−21.7576	−0.920248
$560$	2.91837	0.123324
$561$	50.2318	2.12079
$562$	−9.54564	−0.402658
$563$	25.4240	1.07149	0.535747	−	0.844379i	$-0.320030\pi$
$563$	25.4240	1.07149	0.535747	+	0.844379i	$0.320030\pi$
$564$	3.42108	0.144054
$565$	−14.7513	−0.620590
$566$	13.0802	0.549804
$567$	−20.7757	−0.872498
$568$	12.2500	0.513999
$569$	34.2223	1.43467	0.717337	−	0.696726i	$-0.245361\pi$
$569$	34.2223	1.43467	0.717337	+	0.696726i	$0.245361\pi$
$570$	0.259474	0.0108682
$571$	−37.6687	−1.57638	−0.788192	−	0.615429i	$-0.788983\pi$
$571$	−37.6687	−1.57638	−0.788192	+	0.615429i	$0.788983\pi$
$572$	18.3548	0.767454
$573$	−41.5096	−1.73409
$574$	5.00474	0.208894
$575$	−5.11240	−0.213202
$576$	−27.7395	−1.15581
$577$	−32.1430	−1.33813	−0.669066	−	0.743203i	$-0.733306\pi$
$577$	−32.1430	−1.33813	−0.669066	+	0.743203i	$0.733306\pi$
$578$	−0.0751323	−0.00312509
$579$	57.5561	2.39195
$580$	12.0935	0.502157
$581$	−5.54696	−0.230127
$582$	14.1469	0.586408
$583$	−16.3108	−0.675526
$584$	3.83927	0.158870
$585$	19.0489	0.787576
$586$	−8.36177	−0.345421
$587$	−28.5355	−1.17779	−0.588893	−	0.808211i	$-0.700436\pi$
$587$	−28.5355	−1.17779	−0.588893	+	0.808211i	$0.700436\pi$
$588$	−5.78170	−0.238433
$589$	−0.594957	−0.0245148
$590$	3.70686	0.152609
$591$	31.5232	1.29669
$592$	−14.7215	−0.605051
$593$	37.2555	1.52990	0.764951	−	0.644089i	$-0.222763\pi$
$593$	37.2555	1.52990	0.764951	+	0.644089i	$0.222763\pi$
$594$	−21.7443	−0.892180
$595$	4.14418	0.169895
$596$	−32.4104	−1.32758
$597$	−4.38329	−0.179396
$598$	−5.86731	−0.239932
$599$	−10.5346	−0.430432	−0.215216	−	0.976566i	$-0.569046\pi$
$599$	−10.5346	−0.430432	−0.215216	+	0.976566i	$0.569046\pi$
$600$	5.24334	0.214058
$601$	−8.77443	−0.357916	−0.178958	−	0.983857i	$-0.557273\pi$
$601$	−8.77443	−0.357916	−0.178958	+	0.983857i	$0.557273\pi$
$602$	3.52699	0.143749
$603$	−82.7303	−3.36904
$604$	−19.1191	−0.777946
$605$	−3.46186	−0.140744
$606$	6.76359	0.274752
$607$	36.5587	1.48387	0.741935	−	0.670471i	$-0.233908\pi$
$607$	36.5587	1.48387	0.741935	+	0.670471i	$0.233908\pi$
$608$	−0.858548	−0.0348187
$609$	−21.2498	−0.861084
$610$	−5.23067	−0.211784
$611$	1.57441	0.0636939
$612$	−53.8178	−2.17546
$613$	−43.1191	−1.74156	−0.870781	−	0.491670i	$-0.836386\pi$
$613$	−43.1191	−1.74156	−0.870781	+	0.491670i	$0.836386\pi$
$614$	−12.4579	−0.502760
$615$	−36.9833	−1.49131
$616$	−6.25592	−0.252058
$617$	29.9756	1.20677	0.603386	−	0.797449i	$-0.293818\pi$
$617$	29.9756	1.20677	0.603386	+	0.797449i	$0.293818\pi$
$618$	−14.6712	−0.590161
$619$	−46.9897	−1.88868	−0.944339	−	0.328975i	$-0.893297\pi$
$619$	−46.9897	−1.88868	−0.944339	+	0.328975i	$0.893297\pi$
$620$	−5.71810	−0.229644
$621$	−67.7728	−2.71963
$622$	−0.423941	−0.0169985
$623$	12.3112	0.493236
$624$	−24.7502	−0.990802
$625$	1.00000	0.0400000
$626$	−1.39446	−0.0557337
$627$	2.28771	0.0913625
$628$	−33.3736	−1.33175
$629$	−20.9050	−0.833538
$630$	−3.08790	−0.123025
$631$	−4.43882	−0.176707	−0.0883534	−	0.996089i	$-0.528160\pi$
$631$	−4.43882	−0.176707	−0.0883534	+	0.996089i	$0.528160\pi$
$632$	12.5835	0.500545
$633$	−36.1336	−1.43618
$634$	−6.24030	−0.247834
$635$	2.10873	0.0836825
$636$	24.7982	0.983312
$637$	−2.66079	−0.105424
$638$	−10.9356	−0.432943
$639$	53.3110	2.10895
$640$	−10.7690	−0.425681
$641$	−2.17254	−0.0858104	−0.0429052	−	0.999079i	$-0.513661\pi$
$641$	−2.17254	−0.0858104	−0.0429052	+	0.999079i	$0.513661\pi$
$642$	−22.9529	−0.905879
$643$	13.2621	0.523004	0.261502	−	0.965203i	$-0.415782\pi$
$643$	13.2621	0.523004	0.261502	+	0.965203i	$0.415782\pi$
$644$	−9.27369	−0.365434
$645$	−26.0633	−1.02624
$646$	−0.337367	−0.0132735
$647$	2.15262	0.0846283	0.0423141	−	0.999104i	$-0.486527\pi$
$647$	2.15262	0.0846283	0.0423141	+	0.999104i	$0.486527\pi$
$648$	34.1771	1.34260
$649$	32.6825	1.28290
$650$	1.14766	0.0450150
$651$	10.0474	0.393787
$652$	−43.4929	−1.70331
$653$	−8.59362	−0.336294	−0.168147	−	0.985762i	$-0.553778\pi$
$653$	−8.59362	−0.336294	−0.168147	+	0.985762i	$0.553778\pi$
$654$	14.0730	0.550298
$655$	−17.5819	−0.686981
$656$	33.8624	1.32211
$657$	16.7082	0.651848
$658$	−0.255218	−0.00994943
$659$	−0.271480	−0.0105753	−0.00528767	−	0.999986i	$-0.501683\pi$
$659$	−0.271480	−0.0105753	−0.00528767	+	0.999986i	$0.501683\pi$
$660$	21.9871	0.855847
$661$	36.6340	1.42490	0.712449	−	0.701724i	$-0.247586\pi$
$661$	36.6340	1.42490	0.712449	+	0.701724i	$0.247586\pi$
$662$	13.1786	0.512199
$663$	−35.1461	−1.36496
$664$	9.12503	0.354120
$665$	0.188739	0.00731898
$666$	15.5767	0.603586
$667$	−34.0840	−1.31974
$668$	−43.1030	−1.66771
$669$	79.2235	3.06296
$670$	−4.98434	−0.192562
$671$	−46.1175	−1.78035
$672$	14.4988	0.559302
$673$	−25.2255	−0.972372	−0.486186	−	0.873855i	$-0.661612\pi$
$673$	−25.2255	−0.972372	−0.486186	+	0.873855i	$0.661612\pi$
$674$	13.5599	0.522309
$675$	13.2565	0.510245
$676$	10.7390	0.413039
$677$	−39.5064	−1.51835	−0.759177	−	0.650884i	$-0.774398\pi$
$677$	−39.5064	−1.51835	−0.759177	+	0.650884i	$0.774398\pi$
$678$	−20.2797	−0.778836
$679$	10.2903	0.394907
$680$	−6.81738	−0.261435
$681$	−52.5396	−2.01332
$682$	5.17058	0.197992
$683$	4.74035	0.181385	0.0906923	−	0.995879i	$-0.471092\pi$
$683$	4.74035	0.181385	0.0906923	+	0.995879i	$0.471092\pi$
$684$	−2.45103	−0.0937176
$685$	14.0926	0.538452
$686$	0.431324	0.0164680
$687$	3.18734	0.121605
$688$	23.8639	0.909801
$689$	11.4123	0.434776
$690$	−7.02840	−0.267567
$691$	−3.87633	−0.147463	−0.0737313	−	0.997278i	$-0.523491\pi$
$691$	−3.87633	−0.147463	−0.0737313	+	0.997278i	$0.523491\pi$
$692$	−38.1926	−1.45187
$693$	−27.2253	−1.03420
$694$	−2.93951	−0.111582
$695$	22.6086	0.857595
$696$	34.9569	1.32504
$697$	48.0857	1.82138
$698$	0.655029	0.0247932
$699$	46.8262	1.77113
$700$	1.81396	0.0685612
$701$	−40.6005	−1.53346	−0.766729	−	0.641971i	$-0.778117\pi$
$701$	−40.6005	−1.53346	−0.766729	+	0.641971i	$0.778117\pi$
$702$	15.2140	0.574217
$703$	−0.952082	−0.0359085
$704$	−14.7350	−0.555347
$705$	1.88597	0.0710299
$706$	−8.38157	−0.315444
$707$	4.91978	0.185027
$708$	−49.6888	−1.86742
$709$	−5.15024	−0.193421	−0.0967107	−	0.995313i	$-0.530832\pi$
$709$	−5.15024	−0.193421	−0.0967107	+	0.995313i	$0.530832\pi$
$710$	3.21189	0.120540
$711$	54.7624	2.05375
$712$	−20.2525	−0.758994
$713$	16.1157	0.603537
$714$	5.69731	0.213216
$715$	10.1186	0.378416
$716$	32.0865	1.19913
$717$	−11.6632	−0.435571
$718$	−7.29040	−0.272075
$719$	−12.2737	−0.457730	−0.228865	−	0.973458i	$-0.573501\pi$
$719$	−12.2737	−0.457730	−0.228865	+	0.973458i	$0.573501\pi$
$720$	−20.8930	−0.778635
$721$	−10.6717	−0.397435
$722$	8.17979	0.304420
$723$	−49.0160	−1.82292
$724$	21.2830	0.790976
$725$	6.66693	0.247604
$726$	−4.75927	−0.176633
$727$	22.5932	0.837936	0.418968	−	0.908001i	$-0.362392\pi$
$727$	22.5932	0.837936	0.418968	+	0.908001i	$0.362392\pi$
$728$	4.37714	0.162227
$729$	21.9767	0.813954
$730$	1.00664	0.0372572
$731$	33.8874	1.25337
$732$	70.1148	2.59152
$733$	−41.6416	−1.53807	−0.769034	−	0.639208i	$-0.779262\pi$
$733$	−41.6416	−1.53807	−0.769034	+	0.639208i	$0.779262\pi$
$734$	7.71090	0.284614
$735$	−3.18734	−0.117567
$736$	23.2556	0.857213
$737$	−43.9457	−1.61876
$738$	−35.8296	−1.31890
$739$	13.0710	0.480826	0.240413	−	0.970671i	$-0.422717\pi$
$739$	13.0710	0.480826	0.240413	+	0.970671i	$0.422717\pi$
$740$	−9.15041	−0.336376
$741$	−1.60066	−0.0588019
$742$	−1.84998	−0.0679150
$743$	−50.9362	−1.86867	−0.934335	−	0.356397i	$-0.884005\pi$
$743$	−50.9362	−1.86867	−0.934335	+	0.356397i	$0.884005\pi$
$744$	−16.5284	−0.605962
$745$	−17.8672	−0.654604
$746$	−0.371246	−0.0135923
$747$	39.7114	1.45296
$748$	−28.5876	−1.04527
$749$	−16.6958	−0.610050
$750$	1.37477	0.0501997
$751$	−44.5613	−1.62607	−0.813033	−	0.582218i	$-0.802185\pi$
$751$	−44.5613	−1.62607	−0.813033	+	0.582218i	$0.802185\pi$
$752$	−1.72682	−0.0629708
$753$	59.3221	2.16182
$754$	7.65138	0.278647
$755$	−10.5400	−0.383590
$756$	24.0468	0.874575
$757$	−1.26477	−0.0459689	−0.0229844	−	0.999736i	$-0.507317\pi$
$757$	−1.26477	−0.0459689	−0.0229844	+	0.999736i	$0.507317\pi$
$758$	−3.31420	−0.120377
$759$	−61.9676	−2.24928
$760$	−0.310485	−0.0112625
$761$	−50.3101	−1.82374	−0.911870	−	0.410478i	$-0.865362\pi$
$761$	−50.3101	−1.82374	−0.911870	+	0.410478i	$0.865362\pi$
$762$	2.89903	0.105021
$763$	10.2366	0.370590
$764$	23.6237	0.854675
$765$	−29.6687	−1.07267
$766$	1.06343	0.0384234
$767$	−22.8672	−0.825688
$768$	9.89507	0.357058
$769$	−1.10149	−0.0397208	−0.0198604	−	0.999803i	$-0.506322\pi$
$769$	−1.10149	−0.0397208	−0.0198604	+	0.999803i	$0.506322\pi$
$770$	−1.64027	−0.0591112
$771$	36.5772	1.31729
$772$	−32.7560	−1.17891
$773$	−0.461182	−0.0165876	−0.00829378	−	0.999966i	$-0.502640\pi$
$773$	−0.461182	−0.0165876	−0.00829378	+	0.999966i	$0.502640\pi$
$774$	−25.2501	−0.907598
$775$	−3.15228	−0.113233
$776$	−16.9281	−0.607685
$777$	16.0783	0.576807
$778$	−10.2769	−0.368444
$779$	2.18998	0.0784641
$780$	−15.3839	−0.550832
$781$	28.3184	1.01331
$782$	9.13832	0.326786
$783$	88.3805	3.15846
$784$	2.91837	0.104227
$785$	−18.3982	−0.656659
$786$	−24.1711	−0.862156
$787$	10.8517	0.386820	0.193410	−	0.981118i	$-0.438045\pi$
$787$	10.8517	0.386820	0.193410	+	0.981118i	$0.438045\pi$
$788$	−17.9403	−0.639098
$789$	−61.5119	−2.18988
$790$	3.29933	0.117385
$791$	−14.7513	−0.524495
$792$	44.7870	1.59144
$793$	32.2674	1.14585
$794$	−3.97416	−0.141038
$795$	13.6708	0.484852
$796$	2.49460	0.0884186
$797$	15.2348	0.539644	0.269822	−	0.962910i	$-0.413035\pi$
$797$	15.2348	0.539644	0.269822	+	0.962910i	$0.413035\pi$
$798$	0.259474	0.00918527
$799$	−2.45214	−0.0867506
$800$	−4.54887	−0.160827
$801$	−88.1371	−3.11417
$802$	3.76030	0.132781
$803$	8.87525	0.313201
$804$	66.8129	2.35631
$805$	−5.11240	−0.180188
$806$	−3.61775	−0.127430
$807$	−47.4619	−1.67074
$808$	−8.09329	−0.284721
$809$	−7.09334	−0.249389	−0.124694	−	0.992195i	$-0.539795\pi$
$809$	−7.09334	−0.249389	−0.124694	+	0.992195i	$0.539795\pi$
$810$	8.96106	0.314860
$811$	−11.1450	−0.391354	−0.195677	−	0.980668i	$-0.562690\pi$
$811$	−11.1450	−0.391354	−0.195677	+	0.980668i	$0.562690\pi$
$812$	12.0935	0.424400
$813$	44.4419	1.55864
$814$	8.27424	0.290012
$815$	−23.9768	−0.839870
$816$	38.5484	1.34946
$817$	1.54334	0.0539947
$818$	0.249600	0.00872707
$819$	19.0489	0.665624
$820$	21.0477	0.735019
$821$	−8.02219	−0.279976	−0.139988	−	0.990153i	$-0.544706\pi$
$821$	−8.02219	−0.279976	−0.139988	+	0.990153i	$0.544706\pi$
$822$	19.3742	0.675753
$823$	28.3107	0.986850	0.493425	−	0.869788i	$-0.335745\pi$
$823$	28.3107	0.986850	0.493425	+	0.869788i	$0.335745\pi$
$824$	17.5555	0.611574
$825$	12.1210	0.422001
$826$	3.70686	0.128978
$827$	52.5170	1.82620	0.913098	−	0.407739i	$-0.133683\pi$
$827$	52.5170	1.82620	0.913098	+	0.407739i	$0.133683\pi$
$828$	66.3915	2.30726
$829$	0.127034	0.00441208	0.00220604	−	0.999998i	$-0.499298\pi$
$829$	0.127034	0.00441208	0.00220604	+	0.999998i	$0.499298\pi$
$830$	2.39253	0.0830461
$831$	−57.3388	−1.98906
$832$	10.3098	0.357427
$833$	4.14418	0.143587
$834$	31.0818	1.07627
$835$	−23.7618	−0.822312
$836$	−1.30197	−0.0450296
$837$	−41.7883	−1.44441
$838$	−7.45060	−0.257377
$839$	−37.2003	−1.28430	−0.642148	−	0.766580i	$-0.721957\pi$
$839$	−37.2003	−1.28430	−0.642148	+	0.766580i	$0.721957\pi$
$840$	5.24334	0.180912
$841$	15.4479	0.532688
$842$	6.79973	0.234334
$843$	70.5391	2.42950
$844$	20.5641	0.707847
$845$	5.92020	0.203661
$846$	1.82714	0.0628183
$847$	−3.46186	−0.118951
$848$	−12.5171	−0.429840
$849$	−96.6587	−3.31732
$850$	−1.78748	−0.0613101
$851$	25.7892	0.884042
$852$	−43.0539	−1.47500
$853$	28.5784	0.978505	0.489253	−	0.872142i	$-0.337270\pi$
$853$	28.5784	0.978505	0.489253	+	0.872142i	$0.337270\pi$
$854$	−5.23067	−0.178990
$855$	−1.35121	−0.0462103
$856$	27.4654	0.938748
$857$	−49.2472	−1.68225	−0.841127	−	0.540838i	$-0.818107\pi$
$857$	−49.2472	−1.68225	−0.841127	+	0.540838i	$0.818107\pi$
$858$	13.9109	0.474909
$859$	−45.0012	−1.53542	−0.767711	−	0.640796i	$-0.778604\pi$
$859$	−45.0012	−1.53542	−0.767711	+	0.640796i	$0.778604\pi$
$860$	14.8330	0.505800
$861$	−36.9833	−1.26039
$862$	−6.75662	−0.230131
$863$	−5.75485	−0.195897	−0.0979486	−	0.995191i	$-0.531228\pi$
$863$	−5.75485	−0.195897	−0.0979486	+	0.995191i	$0.531228\pi$
$864$	−60.3023	−2.05152
$865$	−21.0548	−0.715886
$866$	−9.38543	−0.318930
$867$	0.555203	0.0188557
$868$	−5.71810	−0.194085
$869$	29.0894	0.986790
$870$	9.16553	0.310740
$871$	30.7479	1.04185
$872$	−16.8397	−0.570265
$873$	−73.6699	−2.49335
$874$	0.416188	0.0140778
$875$	1.00000	0.0338062
$876$	−13.4935	−0.455903
$877$	26.8334	0.906101	0.453051	−	0.891485i	$-0.350336\pi$
$877$	26.8334	0.906101	0.453051	+	0.891485i	$0.350336\pi$
$878$	−5.30846	−0.179152
$879$	61.7907	2.08415
$880$	−11.0982	−0.374120
$881$	−37.0951	−1.24977	−0.624883	−	0.780718i	$-0.714853\pi$
$881$	−37.0951	−1.24977	−0.624883	+	0.780718i	$0.714853\pi$
$882$	−3.08790	−0.103975
$883$	−48.8596	−1.64426	−0.822129	−	0.569301i	$-0.807214\pi$
$883$	−48.8596	−1.64426	−0.822129	+	0.569301i	$0.807214\pi$
$884$	20.0021	0.672745
$885$	−27.3925	−0.920788
$886$	−8.53110	−0.286608
$887$	−16.8207	−0.564783	−0.282392	−	0.959299i	$-0.591128\pi$
$887$	−16.8207	−0.564783	−0.282392	+	0.959299i	$0.591128\pi$
$888$	−26.4497	−0.887593
$889$	2.10873	0.0707247
$890$	−5.31009	−0.177995
$891$	79.0075	2.64685
$892$	−45.0872	−1.50963
$893$	−0.111678	−0.00373718
$894$	−24.5634	−0.821523
$895$	17.6887	0.591267
$896$	−10.7690	−0.359766
$897$	43.3574	1.44766
$898$	−0.395412	−0.0131951
$899$	−21.0160	−0.700923
$900$	−12.9864	−0.432879
$901$	−17.7747	−0.592161
$902$	−19.0324	−0.633709
$903$	−26.0633	−0.867331
$904$	24.2666	0.807095
$905$	11.7329	0.390014
$906$	−14.4901	−0.481402
$907$	−34.1951	−1.13543	−0.567715	−	0.823225i	$-0.692172\pi$
$907$	−34.1951	−1.13543	−0.567715	+	0.823225i	$0.692172\pi$
$908$	29.9010	0.992301
$909$	−35.2213	−1.16822
$910$	1.14766	0.0380446
$911$	52.0548	1.72465	0.862327	−	0.506352i	$-0.169006\pi$
$911$	52.0548	1.72465	0.862327	+	0.506352i	$0.169006\pi$
$912$	1.75562	0.0581343
$913$	21.0944	0.698122
$914$	−17.0322	−0.563374
$915$	38.6529	1.27783
$916$	−1.81396	−0.0599349
$917$	−17.5819	−0.580605
$918$	−23.6958	−0.782079
$919$	−31.3659	−1.03467	−0.517333	−	0.855784i	$-0.673075\pi$
$919$	−31.3659	−1.03467	−0.517333	+	0.855784i	$0.673075\pi$
$920$	8.41016	0.277275
$921$	92.0598	3.03347
$922$	6.58976	0.217022
$923$	−19.8138	−0.652178
$924$	21.9871	0.723322
$925$	−5.04444	−0.165860
$926$	−17.6980	−0.581593
$927$	76.4000	2.50931
$928$	−30.3270	−0.995531
$929$	−11.4975	−0.377220	−0.188610	−	0.982052i	$-0.560398\pi$
$929$	−11.4975	−0.377220	−0.188610	+	0.982052i	$0.560398\pi$
$930$	−4.33367	−0.142107
$931$	0.188739	0.00618567
$932$	−26.6495	−0.872933
$933$	3.13278	0.102563
$934$	4.98303	0.163050
$935$	−15.7598	−0.515400
$936$	−31.3365	−1.02426
$937$	23.7500	0.775879	0.387939	−	0.921685i	$-0.373187\pi$
$937$	23.7500	0.775879	0.387939	+	0.921685i	$0.373187\pi$
$938$	−4.98434	−0.162745
$939$	10.3046	0.336277
$940$	−1.07334	−0.0350083
$941$	27.0664	0.882339	0.441170	−	0.897424i	$-0.354564\pi$
$941$	27.0664	0.882339	0.441170	+	0.897424i	$0.354564\pi$
$942$	−25.2934	−0.824102
$943$	−59.3202	−1.93173
$944$	25.0809	0.816314
$945$	13.2565	0.431236
$946$	−13.4127	−0.436084
$947$	−56.4179	−1.83334	−0.916668	−	0.399651i	$-0.869131\pi$
$947$	−56.4179	−1.83334	−0.916668	+	0.399651i	$0.869131\pi$
$948$	−44.2261	−1.43640
$949$	−6.20982	−0.201579
$950$	−0.0814076	−0.00264121
$951$	46.1138	1.49534
$952$	−6.81738	−0.220953
$953$	18.1390	0.587580	0.293790	−	0.955870i	$-0.405083\pi$
$953$	18.1390	0.587580	0.293790	+	0.955870i	$0.405083\pi$
$954$	13.2443	0.428799
$955$	13.0233	0.421423
$956$	6.63770	0.214679
$957$	80.8102	2.61222
$958$	−9.98110	−0.322475
$959$	14.0926	0.455075
$960$	12.3500	0.398595
$961$	−21.0632	−0.679457
$962$	−5.78931	−0.186655
$963$	119.527	3.85171
$964$	27.8957	0.898460
$965$	−18.0577	−0.581299
$966$	−7.02840	−0.226135
$967$	56.4223	1.81442	0.907209	−	0.420681i	$-0.138209\pi$
$967$	56.4223	1.81442	0.907209	+	0.420681i	$0.138209\pi$
$968$	5.69493	0.183042
$969$	2.49303	0.0800877
$970$	−4.43847	−0.142511
$971$	−17.5102	−0.561929	−0.280965	−	0.959718i	$-0.590654\pi$
$971$	−17.5102	−0.561929	−0.280965	+	0.959718i	$0.590654\pi$
$972$	−47.9786	−1.53891
$973$	22.6086	0.724800
$974$	5.31141	0.170188
$975$	−8.48084	−0.271604
$976$	−35.3911	−1.13284
$977$	16.3052	0.521650	0.260825	−	0.965386i	$-0.416005\pi$
$977$	16.3052	0.521650	0.260825	+	0.965386i	$0.416005\pi$
$978$	−32.9627	−1.05403
$979$	−46.8178	−1.49630
$980$	1.81396	0.0579448
$981$	−73.2851	−2.33981
$982$	−2.61855	−0.0835613
$983$	−38.7562	−1.23613	−0.618066	−	0.786127i	$-0.712083\pi$
$983$	−38.7562	−1.23613	−0.618066	+	0.786127i	$0.712083\pi$
$984$	60.8395	1.93949
$985$	−9.89014	−0.315126
$986$	−11.9170	−0.379515
$987$	1.88597	0.0600312
$988$	0.910961	0.0289815
$989$	−41.8047	−1.32931
$990$	11.7429	0.373214
$991$	−29.2154	−0.928057	−0.464028	−	0.885820i	$-0.653596\pi$
$991$	−29.2154	−0.928057	−0.464028	+	0.885820i	$0.653596\pi$
$992$	14.3393	0.455272
$993$	−97.3852	−3.09042
$994$	3.21189	0.101875
$995$	1.37522	0.0435974
$996$	−32.0709	−1.01620
$997$	−25.9415	−0.821574	−0.410787	−	0.911731i	$-0.634746\pi$
$997$	−25.9415	−0.821574	−0.410787	+	0.911731i	$0.634746\pi$
$998$	−0.476456	−0.0150820
$999$	−66.8718	−2.11573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.28	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.28	✓	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)

\(f(q)\)	\(=\)	\(q-0.431324 q^{2} +3.18734 q^{3} -1.81396 q^{4} -1.00000 q^{5} -1.37477 q^{6} -1.00000 q^{7} +1.64505 q^{8} +7.15913 q^{9} +O(q^{10})\)	\(q-0.431324 q^{2} +3.18734 q^{3} -1.81396 q^{4} -1.00000 q^{5} -1.37477 q^{6} -1.00000 q^{7} +1.64505 q^{8} +7.15913 q^{9} +0.431324 q^{10} +3.80287 q^{11} -5.78170 q^{12} -2.66079 q^{13} +0.431324 q^{14} -3.18734 q^{15} +2.91837 q^{16} +4.14418 q^{17} -3.08790 q^{18} +0.188739 q^{19} +1.81396 q^{20} -3.18734 q^{21} -1.64027 q^{22} -5.11240 q^{23} +5.24334 q^{24} +1.00000 q^{25} +1.14766 q^{26} +13.2565 q^{27} +1.81396 q^{28} +6.66693 q^{29} +1.37477 q^{30} -3.15228 q^{31} -4.54887 q^{32} +12.1210 q^{33} -1.78748 q^{34} +1.00000 q^{35} -12.9864 q^{36} -5.04444 q^{37} -0.0814076 q^{38} -8.48084 q^{39} -1.64505 q^{40} +11.6032 q^{41} +1.37477 q^{42} +8.17712 q^{43} -6.89826 q^{44} -7.15913 q^{45} +2.20510 q^{46} -0.591708 q^{47} +9.30183 q^{48} +1.00000 q^{49} -0.431324 q^{50} +13.2089 q^{51} +4.82657 q^{52} -4.28908 q^{53} -5.71786 q^{54} -3.80287 q^{55} -1.64505 q^{56} +0.601575 q^{57} -2.87560 q^{58} +8.59415 q^{59} +5.78170 q^{60} -12.1270 q^{61} +1.35965 q^{62} -7.15913 q^{63} -3.87471 q^{64} +2.66079 q^{65} -5.22810 q^{66} -11.5559 q^{67} -7.51737 q^{68} -16.2949 q^{69} -0.431324 q^{70} +7.44658 q^{71} +11.7771 q^{72} +2.33383 q^{73} +2.17579 q^{74} +3.18734 q^{75} -0.342365 q^{76} -3.80287 q^{77} +3.65799 q^{78} +7.64931 q^{79} -2.91837 q^{80} +20.7757 q^{81} -5.00474 q^{82} +5.54696 q^{83} +5.78170 q^{84} -4.14418 q^{85} -3.52699 q^{86} +21.2498 q^{87} +6.25592 q^{88} -12.3112 q^{89} +3.08790 q^{90} +2.66079 q^{91} +9.27369 q^{92} -10.0474 q^{93} +0.255218 q^{94} -0.188739 q^{95} -14.4988 q^{96} -10.2903 q^{97} -0.431324 q^{98} +27.2253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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