LMFDB - Embedded newform 8015.2.a.l.1.59

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			1.59
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)

$f(q)$	$=$	$q+2.62755 q^{2} -1.18883 q^{3} +4.90404 q^{4} -1.00000 q^{5} -3.12370 q^{6} -1.00000 q^{7} +7.63051 q^{8} -1.58669 q^{9} +O(q^{10})$	\(q+2.62755 q^{2} -1.18883 q^{3} +4.90404 q^{4} -1.00000 q^{5} -3.12370 q^{6} -1.00000 q^{7} +7.63051 q^{8} -1.58669 q^{9} -2.62755 q^{10} -5.79150 q^{11} -5.83004 q^{12} -6.84400 q^{13} -2.62755 q^{14} +1.18883 q^{15} +10.2415 q^{16} +6.86984 q^{17} -4.16912 q^{18} +6.33777 q^{19} -4.90404 q^{20} +1.18883 q^{21} -15.2175 q^{22} +7.14073 q^{23} -9.07135 q^{24} +1.00000 q^{25} -17.9830 q^{26} +5.45278 q^{27} -4.90404 q^{28} -2.28122 q^{29} +3.12370 q^{30} +3.85963 q^{31} +11.6491 q^{32} +6.88508 q^{33} +18.0509 q^{34} +1.00000 q^{35} -7.78120 q^{36} -0.186449 q^{37} +16.6528 q^{38} +8.13632 q^{39} -7.63051 q^{40} +1.16571 q^{41} +3.12370 q^{42} +3.17391 q^{43} -28.4017 q^{44} +1.58669 q^{45} +18.7626 q^{46} +0.258848 q^{47} -12.1754 q^{48} +1.00000 q^{49} +2.62755 q^{50} -8.16704 q^{51} -33.5632 q^{52} -8.96737 q^{53} +14.3275 q^{54} +5.79150 q^{55} -7.63051 q^{56} -7.53451 q^{57} -5.99402 q^{58} +2.12258 q^{59} +5.83004 q^{60} -5.73197 q^{61} +10.1414 q^{62} +1.58669 q^{63} +10.1255 q^{64} +6.84400 q^{65} +18.0909 q^{66} +0.485444 q^{67} +33.6899 q^{68} -8.48908 q^{69} +2.62755 q^{70} +12.9055 q^{71} -12.1073 q^{72} +0.306248 q^{73} -0.489904 q^{74} -1.18883 q^{75} +31.0807 q^{76} +5.79150 q^{77} +21.3786 q^{78} -4.98220 q^{79} -10.2415 q^{80} -1.72233 q^{81} +3.06297 q^{82} +12.3172 q^{83} +5.83004 q^{84} -6.86984 q^{85} +8.33963 q^{86} +2.71197 q^{87} -44.1921 q^{88} +12.0055 q^{89} +4.16912 q^{90} +6.84400 q^{91} +35.0184 q^{92} -4.58843 q^{93} +0.680136 q^{94} -6.33777 q^{95} -13.8487 q^{96} +12.7617 q^{97} +2.62755 q^{98} +9.18933 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.62755	1.85796	0.928980	−	0.370129i	$-0.120687\pi$
$2$	2.62755	1.85796	0.928980	+	0.370129i	$0.120687\pi$
$3$	−1.18883	−0.686369	−0.343184	−	0.939268i	$-0.611506\pi$
$3$	−1.18883	−0.686369	−0.343184	+	0.939268i	$0.611506\pi$
$4$	4.90404	2.45202
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.12370	−1.27525
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	7.63051	2.69779
$9$	−1.58669	−0.528898
$10$	−2.62755	−0.830905
$11$	−5.79150	−1.74620	−0.873101	−	0.487539i	$-0.837895\pi$
$11$	−5.79150	−1.74620	−0.873101	+	0.487539i	$0.837895\pi$
$12$	−5.83004	−1.68299
$13$	−6.84400	−1.89818	−0.949092	−	0.314999i	$-0.897996\pi$
$13$	−6.84400	−1.89818	−0.949092	+	0.314999i	$0.897996\pi$
$14$	−2.62755	−0.702243
$15$	1.18883	0.306954
$16$	10.2415	2.56037
$17$	6.86984	1.66618	0.833090	−	0.553138i	$-0.186570\pi$
$17$	6.86984	1.66618	0.833090	+	0.553138i	$0.186570\pi$
$18$	−4.16912	−0.982671
$19$	6.33777	1.45398	0.726992	−	0.686646i	$-0.240918\pi$
$19$	6.33777	1.45398	0.726992	+	0.686646i	$0.240918\pi$
$20$	−4.90404	−1.09658
$21$	1.18883	0.259423
$22$	−15.2175	−3.24437
$23$	7.14073	1.48894	0.744472	−	0.667654i	$-0.232701\pi$
$23$	7.14073	1.48894	0.744472	+	0.667654i	$0.232701\pi$
$24$	−9.07135	−1.85168
$25$	1.00000	0.200000
$26$	−17.9830	−3.52675
$27$	5.45278	1.04939
$28$	−4.90404	−0.926776
$29$	−2.28122	−0.423611	−0.211806	−	0.977312i	$-0.567934\pi$
$29$	−2.28122	−0.423611	−0.211806	+	0.977312i	$0.567934\pi$
$30$	3.12370	0.570308
$31$	3.85963	0.693211	0.346605	−	0.938011i	$-0.387334\pi$
$31$	3.85963	0.693211	0.346605	+	0.938011i	$0.387334\pi$
$32$	11.6491	2.05928
$33$	6.88508	1.19854
$34$	18.0509	3.09570
$35$	1.00000	0.169031
$36$	−7.78120	−1.29687
$37$	−0.186449	−0.0306520	−0.0153260	−	0.999883i	$-0.504879\pi$
$37$	−0.186449	−0.0306520	−0.0153260	+	0.999883i	$0.504879\pi$
$38$	16.6528	2.70145
$39$	8.13632	1.30285
$40$	−7.63051	−1.20649
$41$	1.16571	0.182053	0.0910267	−	0.995848i	$-0.470985\pi$
$41$	1.16571	0.182053	0.0910267	+	0.995848i	$0.470985\pi$
$42$	3.12370	0.481998
$43$	3.17391	0.484017	0.242009	−	0.970274i	$-0.422194\pi$
$43$	3.17391	0.484017	0.242009	+	0.970274i	$0.422194\pi$
$44$	−28.4017	−4.28172
$45$	1.58669	0.236530
$46$	18.7626	2.76640
$47$	0.258848	0.0377568	0.0188784	−	0.999822i	$-0.493990\pi$
$47$	0.258848	0.0377568	0.0188784	+	0.999822i	$0.493990\pi$
$48$	−12.1754	−1.75736
$49$	1.00000	0.142857
$50$	2.62755	0.371592
$51$	−8.16704	−1.14361
$52$	−33.5632	−4.65438
$53$	−8.96737	−1.23176	−0.615881	−	0.787839i	$-0.711200\pi$
$53$	−8.96737	−1.23176	−0.615881	+	0.787839i	$0.711200\pi$
$54$	14.3275	1.94972
$55$	5.79150	0.780925
$56$	−7.63051	−1.01967
$57$	−7.53451	−0.997970
$58$	−5.99402	−0.787053
$59$	2.12258	0.276336	0.138168	−	0.990409i	$-0.455879\pi$
$59$	2.12258	0.276336	0.138168	+	0.990409i	$0.455879\pi$
$60$	5.83004	0.752656
$61$	−5.73197	−0.733903	−0.366952	−	0.930240i	$-0.619599\pi$
$61$	−5.73197	−0.733903	−0.366952	+	0.930240i	$0.619599\pi$
$62$	10.1414	1.28796
$63$	1.58669	0.199905
$64$	10.1255	1.26569
$65$	6.84400	0.848894
$66$	18.0909	2.22684
$67$	0.485444	0.0593064	0.0296532	−	0.999560i	$-0.490560\pi$
$67$	0.485444	0.0593064	0.0296532	+	0.999560i	$0.490560\pi$
$68$	33.6899	4.08550
$69$	−8.48908	−1.02197
$70$	2.62755	0.314053
$71$	12.9055	1.53160	0.765802	−	0.643076i	$-0.222342\pi$
$71$	12.9055	1.53160	0.765802	+	0.643076i	$0.222342\pi$
$72$	−12.1073	−1.42686
$73$	0.306248	0.0358436	0.0179218	−	0.999839i	$-0.494295\pi$
$73$	0.306248	0.0358436	0.0179218	+	0.999839i	$0.494295\pi$
$74$	−0.489904	−0.0569502
$75$	−1.18883	−0.137274
$76$	31.0807	3.56520
$77$	5.79150	0.660002
$78$	21.3786	2.42065
$79$	−4.98220	−0.560541	−0.280270	−	0.959921i	$-0.590424\pi$
$79$	−4.98220	−0.560541	−0.280270	+	0.959921i	$0.590424\pi$
$80$	−10.2415	−1.14503
$81$	−1.72233	−0.191370
$82$	3.06297	0.338248
$83$	12.3172	1.35199	0.675993	−	0.736908i	$-0.263715\pi$
$83$	12.3172	1.35199	0.675993	+	0.736908i	$0.263715\pi$
$84$	5.83004	0.636110
$85$	−6.86984	−0.745138
$86$	8.33963	0.899285
$87$	2.71197	0.290754
$88$	−44.1921	−4.71089
$89$	12.0055	1.27258	0.636288	−	0.771452i	$-0.280469\pi$
$89$	12.0055	1.27258	0.636288	+	0.771452i	$0.280469\pi$
$90$	4.16912	0.439464
$91$	6.84400	0.717446
$92$	35.0184	3.65092
$93$	−4.58843	−0.475798
$94$	0.680136	0.0701507
$95$	−6.33777	−0.650242
$96$	−13.8487	−1.41343
$97$	12.7617	1.29576	0.647879	−	0.761743i	$-0.275656\pi$
$97$	12.7617	1.29576	0.647879	+	0.761743i	$0.275656\pi$
$98$	2.62755	0.265423
$99$	9.18933	0.923562
$100$	4.90404	0.490404
$101$	18.3388	1.82478	0.912391	−	0.409319i	$-0.134234\pi$
$101$	18.3388	1.82478	0.912391	+	0.409319i	$0.134234\pi$
$102$	−21.4593	−2.12479
$103$	0.620124	0.0611027	0.0305513	−	0.999533i	$-0.490274\pi$
$103$	0.620124	0.0611027	0.0305513	+	0.999533i	$0.490274\pi$
$104$	−52.2232	−5.12091
$105$	−1.18883	−0.116018
$106$	−23.5622	−2.28857
$107$	−2.87994	−0.278414	−0.139207	−	0.990263i	$-0.544455\pi$
$107$	−2.87994	−0.278414	−0.139207	+	0.990263i	$0.544455\pi$
$108$	26.7406	2.57312
$109$	−17.2756	−1.65470	−0.827350	−	0.561686i	$-0.810153\pi$
$109$	−17.2756	−1.65470	−0.827350	+	0.561686i	$0.810153\pi$
$110$	15.2175	1.45093
$111$	0.221655	0.0210386
$112$	−10.2415	−0.967731
$113$	17.7719	1.67184	0.835920	−	0.548851i	$-0.184935\pi$
$113$	17.7719	1.67184	0.835920	+	0.548851i	$0.184935\pi$
$114$	−19.7973	−1.85419
$115$	−7.14073	−0.665876
$116$	−11.1872	−1.03870
$117$	10.8593	1.00395
$118$	5.57719	0.513422
$119$	−6.86984	−0.629757
$120$	9.07135	0.828097
$121$	22.5414	2.04922
$122$	−15.0610	−1.36356
$123$	−1.38583	−0.124956
$124$	18.9278	1.69976
$125$	−1.00000	−0.0894427
$126$	4.16912	0.371415
$127$	−18.1704	−1.61236	−0.806180	−	0.591670i	$-0.798469\pi$
$127$	−18.1704	−1.61236	−0.806180	+	0.591670i	$0.798469\pi$
$128$	3.30725	0.292323
$129$	−3.77323	−0.332214
$130$	17.9830	1.57721
$131$	19.2511	1.68198	0.840990	−	0.541051i	$-0.181973\pi$
$131$	19.2511	1.68198	0.840990	+	0.541051i	$0.181973\pi$
$132$	33.7647	2.93884
$133$	−6.33777	−0.549555
$134$	1.27553	0.110189
$135$	−5.45278	−0.469301
$136$	52.4203	4.49501
$137$	−15.3632	−1.31257	−0.656283	−	0.754515i	$-0.727872\pi$
$137$	−15.3632	−1.31257	−0.656283	+	0.754515i	$0.727872\pi$
$138$	−22.3055	−1.89877
$139$	12.6073	1.06934	0.534668	−	0.845062i	$-0.320436\pi$
$139$	12.6073	1.06934	0.534668	+	0.845062i	$0.320436\pi$
$140$	4.90404	0.414467
$141$	−0.307725	−0.0259151
$142$	33.9100	2.84566
$143$	39.6370	3.31461
$144$	−16.2501	−1.35418
$145$	2.28122	0.189445
$146$	0.804683	0.0665961
$147$	−1.18883	−0.0980527
$148$	−0.914351	−0.0751592
$149$	20.3870	1.67017	0.835085	−	0.550121i	$-0.185419\pi$
$149$	20.3870	1.67017	0.835085	+	0.550121i	$0.185419\pi$
$150$	−3.12370	−0.255049
$151$	0.314224	0.0255712	0.0127856	−	0.999918i	$-0.495930\pi$
$151$	0.314224	0.0255712	0.0127856	+	0.999918i	$0.495930\pi$
$152$	48.3604	3.92255
$153$	−10.9003	−0.881239
$154$	15.2175	1.22626
$155$	−3.85963	−0.310013
$156$	39.9008	3.19462
$157$	−7.24442	−0.578168	−0.289084	−	0.957304i	$-0.593351\pi$
$157$	−7.24442	−0.578168	−0.289084	+	0.957304i	$0.593351\pi$
$158$	−13.0910	−1.04146
$159$	10.6606	0.845444
$160$	−11.6491	−0.920939
$161$	−7.14073	−0.562768
$162$	−4.52550	−0.355557
$163$	14.9142	1.16817	0.584083	−	0.811694i	$-0.301454\pi$
$163$	14.9142	1.16817	0.584083	+	0.811694i	$0.301454\pi$
$164$	5.71668	0.446398
$165$	−6.88508	−0.536003
$166$	32.3640	2.51194
$167$	−4.61121	−0.356826	−0.178413	−	0.983956i	$-0.557096\pi$
$167$	−4.61121	−0.356826	−0.178413	+	0.983956i	$0.557096\pi$
$168$	9.07135	0.699870
$169$	33.8403	2.60310
$170$	−18.0509	−1.38444
$171$	−10.0561	−0.769009
$172$	15.5650	1.18682
$173$	−10.3015	−0.783205	−0.391602	−	0.920135i	$-0.628079\pi$
$173$	−10.3015	−0.783205	−0.391602	+	0.920135i	$0.628079\pi$
$174$	7.12584	0.540209
$175$	−1.00000	−0.0755929
$176$	−59.3136	−4.47093
$177$	−2.52338	−0.189669
$178$	31.5450	2.36440
$179$	18.8850	1.41153	0.705764	−	0.708447i	$-0.250604\pi$
$179$	18.8850	1.41153	0.705764	+	0.708447i	$0.250604\pi$
$180$	7.78120	0.579976
$181$	−11.5182	−0.856140	−0.428070	−	0.903745i	$-0.640806\pi$
$181$	−11.5182	−0.856140	−0.428070	+	0.903745i	$0.640806\pi$
$182$	17.9830	1.33299
$183$	6.81431	0.503728
$184$	54.4874	4.01686
$185$	0.186449	0.0137080
$186$	−12.0563	−0.884014
$187$	−39.7866	−2.90949
$188$	1.26940	0.0925804
$189$	−5.45278	−0.396631
$190$	−16.6528	−1.20812
$191$	−17.7914	−1.28734	−0.643669	−	0.765304i	$-0.722588\pi$
$191$	−17.7914	−1.28734	−0.643669	+	0.765304i	$0.722588\pi$
$192$	−12.0375	−0.868731
$193$	8.44371	0.607791	0.303896	−	0.952705i	$-0.401713\pi$
$193$	8.44371	0.607791	0.303896	+	0.952705i	$0.401713\pi$
$194$	33.5321	2.40747
$195$	−8.13632	−0.582654
$196$	4.90404	0.350288
$197$	−10.1837	−0.725558	−0.362779	−	0.931875i	$-0.618172\pi$
$197$	−10.1837	−0.725558	−0.362779	+	0.931875i	$0.618172\pi$
$198$	24.1454	1.71594
$199$	2.88689	0.204646	0.102323	−	0.994751i	$-0.467372\pi$
$199$	2.88689	0.204646	0.102323	+	0.994751i	$0.467372\pi$
$200$	7.63051	0.539558
$201$	−0.577108	−0.0407060
$202$	48.1863	3.39037
$203$	2.28122	0.160110
$204$	−40.0514	−2.80416
$205$	−1.16571	−0.0814167
$206$	1.62941	0.113526
$207$	−11.3301	−0.787499
$208$	−70.0928	−4.86006
$209$	−36.7052	−2.53895
$210$	−3.12370	−0.215556
$211$	0.598480	0.0412011	0.0206005	−	0.999788i	$-0.493442\pi$
$211$	0.598480	0.0412011	0.0206005	+	0.999788i	$0.493442\pi$
$212$	−43.9763	−3.02030
$213$	−15.3424	−1.05125
$214$	−7.56719	−0.517282
$215$	−3.17391	−0.216459
$216$	41.6075	2.83103
$217$	−3.85963	−0.262009
$218$	−45.3925	−3.07437
$219$	−0.364076	−0.0246020
$220$	28.4017	1.91484
$221$	−47.0172	−3.16272
$222$	0.582410	0.0390888
$223$	24.7467	1.65716	0.828580	−	0.559871i	$-0.189149\pi$
$223$	24.7467	1.65716	0.828580	+	0.559871i	$0.189149\pi$
$224$	−11.6491	−0.778336
$225$	−1.58669	−0.105780
$226$	46.6966	3.10621
$227$	3.30995	0.219689	0.109845	−	0.993949i	$-0.464965\pi$
$227$	3.30995	0.219689	0.109845	+	0.993949i	$0.464965\pi$
$228$	−36.9495	−2.44704
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−18.7626	−1.23717
$231$	−6.88508	−0.453005
$232$	−17.4068	−1.14282
$233$	27.8189	1.82248	0.911240	−	0.411876i	$-0.135126\pi$
$233$	27.8189	1.82248	0.911240	+	0.411876i	$0.135126\pi$
$234$	28.5335	1.86529
$235$	−0.258848	−0.0168854
$236$	10.4092	0.677581
$237$	5.92296	0.384738
$238$	−18.0509	−1.17006
$239$	−18.9879	−1.22822	−0.614111	−	0.789219i	$-0.710485\pi$
$239$	−18.9879	−1.22822	−0.614111	+	0.789219i	$0.710485\pi$
$240$	12.1754	0.785916
$241$	−8.52555	−0.549179	−0.274590	−	0.961562i	$-0.588542\pi$
$241$	−8.52555	−0.549179	−0.274590	+	0.961562i	$0.588542\pi$
$242$	59.2288	3.80737
$243$	−14.3108	−0.918038
$244$	−28.1098	−1.79954
$245$	−1.00000	−0.0638877
$246$	−3.64133	−0.232163
$247$	−43.3757	−2.75993
$248$	29.4510	1.87014
$249$	−14.6430	−0.927961
$250$	−2.62755	−0.166181
$251$	7.55193	0.476674	0.238337	−	0.971183i	$-0.423398\pi$
$251$	7.55193	0.476674	0.238337	+	0.971183i	$0.423398\pi$
$252$	7.78120	0.490170
$253$	−41.3555	−2.60000
$254$	−47.7437	−2.99570
$255$	8.16704	0.511440
$256$	−11.5611	−0.722567
$257$	−20.9456	−1.30655	−0.653275	−	0.757121i	$-0.726605\pi$
$257$	−20.9456	−1.30655	−0.653275	+	0.757121i	$0.726605\pi$
$258$	−9.91437	−0.617241
$259$	0.186449	0.0115854
$260$	33.5632	2.08150
$261$	3.61959	0.224047
$262$	50.5834	3.12505
$263$	7.08415	0.436827	0.218414	−	0.975856i	$-0.429912\pi$
$263$	7.08415	0.436827	0.218414	+	0.975856i	$0.429912\pi$
$264$	52.5367	3.23341
$265$	8.96737	0.550861
$266$	−16.6528	−1.02105
$267$	−14.2724	−0.873457
$268$	2.38063	0.145420
$269$	−25.1463	−1.53320	−0.766598	−	0.642128i	$-0.778052\pi$
$269$	−25.1463	−1.53320	−0.766598	+	0.642128i	$0.778052\pi$
$270$	−14.3275	−0.871942
$271$	−1.88111	−0.114269	−0.0571347	−	0.998366i	$-0.518196\pi$
$271$	−1.88111	−0.114269	−0.0571347	+	0.998366i	$0.518196\pi$
$272$	70.3574	4.26604
$273$	−8.13632	−0.492433
$274$	−40.3676	−2.43869
$275$	−5.79150	−0.349240
$276$	−41.6307	−2.50588
$277$	−13.7162	−0.824126	−0.412063	−	0.911155i	$-0.635192\pi$
$277$	−13.7162	−0.824126	−0.412063	+	0.911155i	$0.635192\pi$
$278$	33.1263	1.98679
$279$	−6.12405	−0.366637
$280$	7.63051	0.456010
$281$	−13.3574	−0.796834	−0.398417	−	0.917204i	$-0.630440\pi$
$281$	−13.3574	−0.796834	−0.398417	+	0.917204i	$0.630440\pi$
$282$	−0.808563	−0.0481493
$283$	14.1780	0.842797	0.421398	−	0.906876i	$-0.361539\pi$
$283$	14.1780	0.842797	0.421398	+	0.906876i	$0.361539\pi$
$284$	63.2892	3.75552
$285$	7.53451	0.446306
$286$	104.148	6.15842
$287$	−1.16571	−0.0688097
$288$	−18.4835	−1.08915
$289$	30.1946	1.77616
$290$	5.99402	0.351981
$291$	−15.1715	−0.889368
$292$	1.50185	0.0878892
$293$	14.3343	0.837419	0.418709	−	0.908120i	$-0.362483\pi$
$293$	14.3343	0.837419	0.418709	+	0.908120i	$0.362483\pi$
$294$	−3.12370	−0.182178
$295$	−2.12258	−0.123581
$296$	−1.42270	−0.0826927
$297$	−31.5798	−1.83244
$298$	53.5680	3.10311
$299$	−48.8711	−2.82629
$300$	−5.83004	−0.336598
$301$	−3.17391	−0.182941
$302$	0.825640	0.0475103
$303$	−21.8017	−1.25247
$304$	64.9083	3.72275
$305$	5.73197	0.328211
$306$	−28.6412	−1.63731
$307$	4.82370	0.275303	0.137651	−	0.990481i	$-0.456045\pi$
$307$	4.82370	0.275303	0.137651	+	0.990481i	$0.456045\pi$
$308$	28.4017	1.61834
$309$	−0.737220	−0.0419390
$310$	−10.1414	−0.575992
$311$	8.50918	0.482512	0.241256	−	0.970462i	$-0.422441\pi$
$311$	8.50918	0.482512	0.241256	+	0.970462i	$0.422441\pi$
$312$	62.0843	3.51483
$313$	−4.71402	−0.266452	−0.133226	−	0.991086i	$-0.542534\pi$
$313$	−4.71402	−0.266452	−0.133226	+	0.991086i	$0.542534\pi$
$314$	−19.0351	−1.07421
$315$	−1.58669	−0.0894000
$316$	−24.4329	−1.37446
$317$	12.8147	0.719744	0.359872	−	0.933002i	$-0.382820\pi$
$317$	12.8147	0.719744	0.359872	+	0.933002i	$0.382820\pi$
$318$	28.0114	1.57080
$319$	13.2117	0.739711
$320$	−10.1255	−0.566034
$321$	3.42374	0.191095
$322$	−18.7626	−1.04560
$323$	43.5395	2.42260
$324$	−8.44635	−0.469242
$325$	−6.84400	−0.379637
$326$	39.1877	2.17041
$327$	20.5377	1.13573
$328$	8.89496	0.491142
$329$	−0.258848	−0.0142707
$330$	−18.0909	−0.995872
$331$	11.1087	0.610587	0.305294	−	0.952258i	$-0.401245\pi$
$331$	11.1087	0.610587	0.305294	+	0.952258i	$0.401245\pi$
$332$	60.4039	3.31509
$333$	0.295837	0.0162118
$334$	−12.1162	−0.662969
$335$	−0.485444	−0.0265226
$336$	12.1754	0.664220
$337$	10.3858	0.565752	0.282876	−	0.959156i	$-0.408711\pi$
$337$	10.3858	0.565752	0.282876	+	0.959156i	$0.408711\pi$
$338$	88.9173	4.83646
$339$	−21.1277	−1.14750
$340$	−33.6899	−1.82709
$341$	−22.3531	−1.21049
$342$	−26.4229	−1.42879
$343$	−1.00000	−0.0539949
$344$	24.2186	1.30578
$345$	8.48908	0.457037
$346$	−27.0676	−1.45516
$347$	−11.3891	−0.611401	−0.305701	−	0.952128i	$-0.598891\pi$
$347$	−11.3891	−0.611401	−0.305701	+	0.952128i	$0.598891\pi$
$348$	13.2996	0.712933
$349$	−24.9331	−1.33464	−0.667318	−	0.744773i	$-0.732558\pi$
$349$	−24.9331	−1.33464	−0.667318	+	0.744773i	$0.732558\pi$
$350$	−2.62755	−0.140449
$351$	−37.3188	−1.99193
$352$	−67.4655	−3.59592
$353$	−26.4654	−1.40861	−0.704305	−	0.709898i	$-0.748741\pi$
$353$	−26.4654	−1.40861	−0.704305	+	0.709898i	$0.748741\pi$
$354$	−6.63031	−0.352397
$355$	−12.9055	−0.684954
$356$	58.8752	3.12038
$357$	8.16704	0.432246
$358$	49.6212	2.62256
$359$	13.0631	0.689446	0.344723	−	0.938704i	$-0.387973\pi$
$359$	13.0631	0.689446	0.344723	+	0.938704i	$0.387973\pi$
$360$	12.1073	0.638109
$361$	21.1674	1.11407
$362$	−30.2647	−1.59068
$363$	−26.7978	−1.40652
$364$	33.5632	1.75919
$365$	−0.306248	−0.0160298
$366$	17.9050	0.935907
$367$	13.0031	0.678757	0.339379	−	0.940650i	$-0.389783\pi$
$367$	13.0031	0.678757	0.339379	+	0.940650i	$0.389783\pi$
$368$	73.1317	3.81225
$369$	−1.84962	−0.0962876
$370$	0.489904	0.0254689
$371$	8.96737	0.465563
$372$	−22.5018	−1.16667
$373$	−8.17554	−0.423313	−0.211657	−	0.977344i	$-0.567886\pi$
$373$	−8.17554	−0.423313	−0.211657	+	0.977344i	$0.567886\pi$
$374$	−104.541	−5.40571
$375$	1.18883	0.0613907
$376$	1.97514	0.101860
$377$	15.6126	0.804092
$378$	−14.3275	−0.736925
$379$	−13.3000	−0.683176	−0.341588	−	0.939850i	$-0.610965\pi$
$379$	−13.3000	−0.683176	−0.341588	+	0.939850i	$0.610965\pi$
$380$	−31.0807	−1.59440
$381$	21.6014	1.10667
$382$	−46.7477	−2.39182
$383$	−11.6799	−0.596816	−0.298408	−	0.954438i	$-0.596456\pi$
$383$	−11.6799	−0.596816	−0.298408	+	0.954438i	$0.596456\pi$
$384$	−3.93175	−0.200641
$385$	−5.79150	−0.295162
$386$	22.1863	1.12925
$387$	−5.03603	−0.255996
$388$	62.5840	3.17722
$389$	−1.82009	−0.0922823	−0.0461411	−	0.998935i	$-0.514692\pi$
$389$	−1.82009	−0.0922823	−0.0461411	+	0.998935i	$0.514692\pi$
$390$	−21.3786	−1.08255
$391$	49.0556	2.48085
$392$	7.63051	0.385399
$393$	−22.8863	−1.15446
$394$	−26.7582	−1.34806
$395$	4.98220	0.250681
$396$	45.0648	2.26459
$397$	−5.10154	−0.256039	−0.128020	−	0.991772i	$-0.540862\pi$
$397$	−5.10154	−0.256039	−0.128020	+	0.991772i	$0.540862\pi$
$398$	7.58546	0.380225
$399$	7.53451	0.377197
$400$	10.2415	0.512075
$401$	−5.52804	−0.276057	−0.138029	−	0.990428i	$-0.544077\pi$
$401$	−5.52804	−0.276057	−0.138029	+	0.990428i	$0.544077\pi$
$402$	−1.51638	−0.0756302
$403$	−26.4153	−1.31584
$404$	89.9343	4.47440
$405$	1.72233	0.0855831
$406$	5.99402	0.297478
$407$	1.07982	0.0535245
$408$	−62.3187	−3.08523
$409$	35.0555	1.73338	0.866691	−	0.498846i	$-0.166243\pi$
$409$	35.0555	1.73338	0.866691	+	0.498846i	$0.166243\pi$
$410$	−3.06297	−0.151269
$411$	18.2641	0.900904
$412$	3.04111	0.149825
$413$	−2.12258	−0.104445
$414$	−29.7705	−1.46314
$415$	−12.3172	−0.604626
$416$	−79.7262	−3.90890
$417$	−14.9879	−0.733960
$418$	−96.4448	−4.71727
$419$	−24.4471	−1.19432	−0.597159	−	0.802123i	$-0.703704\pi$
$419$	−24.4471	−1.19432	−0.597159	+	0.802123i	$0.703704\pi$
$420$	−5.83004	−0.284477
$421$	−1.20577	−0.0587657	−0.0293828	−	0.999568i	$-0.509354\pi$
$421$	−1.20577	−0.0587657	−0.0293828	+	0.999568i	$0.509354\pi$
$422$	1.57254	0.0765500
$423$	−0.410712	−0.0199695
$424$	−68.4256	−3.32304
$425$	6.86984	0.333236
$426$	−40.3130	−1.95317
$427$	5.73197	0.277389
$428$	−14.1233	−0.682676
$429$	−47.1215	−2.27505
$430$	−8.33963	−0.402173
$431$	−10.5721	−0.509239	−0.254619	−	0.967041i	$-0.581950\pi$
$431$	−10.5721	−0.509239	−0.254619	+	0.967041i	$0.581950\pi$
$432$	55.8446	2.68683
$433$	22.4565	1.07919	0.539596	−	0.841924i	$-0.318577\pi$
$433$	22.4565	1.07919	0.539596	+	0.841924i	$0.318577\pi$
$434$	−10.1414	−0.486802
$435$	−2.71197	−0.130029
$436$	−84.7201	−4.05736
$437$	45.2563	2.16490
$438$	−0.956628	−0.0457095
$439$	11.1113	0.530312	0.265156	−	0.964206i	$-0.414577\pi$
$439$	11.1113	0.530312	0.265156	+	0.964206i	$0.414577\pi$
$440$	44.1921	2.10677
$441$	−1.58669	−0.0755568
$442$	−123.540	−5.87620
$443$	−5.79272	−0.275221	−0.137610	−	0.990486i	$-0.543942\pi$
$443$	−5.79272	−0.275221	−0.137610	+	0.990486i	$0.543942\pi$
$444$	1.08700	0.0515869
$445$	−12.0055	−0.569113
$446$	65.0232	3.07894
$447$	−24.2366	−1.14635
$448$	−10.1255	−0.478386
$449$	−31.0356	−1.46466	−0.732331	−	0.680949i	$-0.761568\pi$
$449$	−31.0356	−1.46466	−0.732331	+	0.680949i	$0.761568\pi$
$450$	−4.16912	−0.196534
$451$	−6.75121	−0.317902
$452$	87.1541	4.09938
$453$	−0.373558	−0.0175513
$454$	8.69708	0.408174
$455$	−6.84400	−0.320852
$456$	−57.4921	−2.69232
$457$	34.4713	1.61250	0.806250	−	0.591574i	$-0.201493\pi$
$457$	34.4713	1.61250	0.806250	+	0.591574i	$0.201493\pi$
$458$	2.62755	0.122777
$459$	37.4597	1.74847
$460$	−35.0184	−1.63274
$461$	−10.6385	−0.495486	−0.247743	−	0.968826i	$-0.579689\pi$
$461$	−10.6385	−0.495486	−0.247743	+	0.968826i	$0.579689\pi$
$462$	−18.0909	−0.841666
$463$	−5.24396	−0.243707	−0.121854	−	0.992548i	$-0.538884\pi$
$463$	−5.24396	−0.243707	−0.121854	+	0.992548i	$0.538884\pi$
$464$	−23.3631	−1.08460
$465$	4.58843	0.212783
$466$	73.0958	3.38610
$467$	19.1867	0.887856	0.443928	−	0.896063i	$-0.353585\pi$
$467$	19.1867	0.887856	0.443928	+	0.896063i	$0.353585\pi$
$468$	53.2545	2.46169
$469$	−0.485444	−0.0224157
$470$	−0.680136	−0.0313723
$471$	8.61236	0.396836
$472$	16.1964	0.745498
$473$	−18.3817	−0.845192
$474$	15.5629	0.714828
$475$	6.33777	0.290797
$476$	−33.6899	−1.54418
$477$	14.2285	0.651476
$478$	−49.8916	−2.28199
$479$	−31.9983	−1.46204	−0.731019	−	0.682357i	$-0.760955\pi$
$479$	−31.9983	−1.46204	−0.731019	+	0.682357i	$0.760955\pi$
$480$	13.8487	0.632104
$481$	1.27605	0.0581831
$482$	−22.4013	−1.02035
$483$	8.48908	0.386266
$484$	110.544	5.02473
$485$	−12.7617	−0.579481
$486$	−37.6024	−1.70568
$487$	−41.0140	−1.85852	−0.929262	−	0.369423i	$-0.879555\pi$
$487$	−41.0140	−1.85852	−0.929262	+	0.369423i	$0.879555\pi$
$488$	−43.7378	−1.97992
$489$	−17.7303	−0.801793
$490$	−2.62755	−0.118701
$491$	7.58060	0.342108	0.171054	−	0.985262i	$-0.445283\pi$
$491$	7.58060	0.342108	0.171054	+	0.985262i	$0.445283\pi$
$492$	−6.79614	−0.306394
$493$	−15.6716	−0.705813
$494$	−113.972	−5.12784
$495$	−9.18933	−0.413030
$496$	39.5284	1.77488
$497$	−12.9055	−0.578892
$498$	−38.4752	−1.72411
$499$	−24.2316	−1.08476	−0.542378	−	0.840135i	$-0.682476\pi$
$499$	−24.2316	−1.08476	−0.542378	+	0.840135i	$0.682476\pi$
$500$	−4.90404	−0.219315
$501$	5.48193	0.244915
$502$	19.8431	0.885641
$503$	−37.6231	−1.67753	−0.838765	−	0.544493i	$-0.816722\pi$
$503$	−37.6231	−1.67753	−0.838765	+	0.544493i	$0.816722\pi$
$504$	12.1073	0.539301
$505$	−18.3388	−0.816068
$506$	−108.664	−4.83069
$507$	−40.2303	−1.78669
$508$	−89.1082	−3.95354
$509$	26.2876	1.16518	0.582588	−	0.812768i	$-0.302040\pi$
$509$	26.2876	1.16518	0.582588	+	0.812768i	$0.302040\pi$
$510$	21.4593	0.950235
$511$	−0.306248	−0.0135476
$512$	−36.9919	−1.63482
$513$	34.5585	1.52579
$514$	−55.0356	−2.42752
$515$	−0.620124	−0.0273259
$516$	−18.5041	−0.814596
$517$	−1.49912	−0.0659310
$518$	0.489904	0.0215251
$519$	12.2466	0.537568
$520$	52.2232	2.29014
$521$	10.4956	0.459822	0.229911	−	0.973212i	$-0.426157\pi$
$521$	10.4956	0.459822	0.229911	+	0.973212i	$0.426157\pi$
$522$	9.51067	0.416271
$523$	−21.1160	−0.923340	−0.461670	−	0.887052i	$-0.652750\pi$
$523$	−21.1160	−0.923340	−0.461670	+	0.887052i	$0.652750\pi$
$524$	94.4083	4.12424
$525$	1.18883	0.0518846
$526$	18.6140	0.811608
$527$	26.5150	1.15501
$528$	70.5135	3.06871
$529$	27.9900	1.21695
$530$	23.5622	1.02348
$531$	−3.36788	−0.146154
$532$	−31.0807	−1.34752
$533$	−7.97812	−0.345571
$534$	−37.5015	−1.62285
$535$	2.87994	0.124511
$536$	3.70418	0.159996
$537$	−22.4509	−0.968829
$538$	−66.0732	−2.84862
$539$	−5.79150	−0.249457
$540$	−26.7406	−1.15073
$541$	−24.1894	−1.03998	−0.519992	−	0.854171i	$-0.674065\pi$
$541$	−24.1894	−1.03998	−0.519992	+	0.854171i	$0.674065\pi$
$542$	−4.94273	−0.212308
$543$	13.6931	0.587628
$544$	80.0271	3.43113
$545$	17.2756	0.740004
$546$	−21.3786	−0.914921
$547$	−39.8056	−1.70197	−0.850983	−	0.525194i	$-0.823993\pi$
$547$	−39.8056	−1.70197	−0.850983	+	0.525194i	$0.823993\pi$
$548$	−75.3416	−3.21843
$549$	9.09487	0.388160
$550$	−15.2175	−0.648875
$551$	−14.4578	−0.615924
$552$	−64.7760	−2.75705
$553$	4.98220	0.211864
$554$	−36.0400	−1.53119
$555$	−0.221655	−0.00940873
$556$	61.8266	2.62203
$557$	29.2654	1.24002	0.620008	−	0.784596i	$-0.287130\pi$
$557$	29.2654	1.24002	0.620008	+	0.784596i	$0.287130\pi$
$558$	−16.0913	−0.681198
$559$	−21.7223	−0.918754
$560$	10.2415	0.432782
$561$	47.2994	1.99698
$562$	−35.0972	−1.48049
$563$	−24.6297	−1.03802	−0.519010	−	0.854768i	$-0.673699\pi$
$563$	−24.6297	−1.03802	−0.519010	+	0.854768i	$0.673699\pi$
$564$	−1.50909	−0.0635443
$565$	−17.7719	−0.747670
$566$	37.2536	1.56588
$567$	1.72233	0.0723309
$568$	98.4757	4.13195
$569$	37.1633	1.55797	0.778984	−	0.627043i	$-0.215735\pi$
$569$	37.1633	1.55797	0.778984	+	0.627043i	$0.215735\pi$
$570$	19.7973	0.829219
$571$	5.05955	0.211736	0.105868	−	0.994380i	$-0.466238\pi$
$571$	5.05955	0.211736	0.105868	+	0.994380i	$0.466238\pi$
$572$	194.381	8.12749
$573$	21.1508	0.883588
$574$	−3.06297	−0.127846
$575$	7.14073	0.297789
$576$	−16.0661	−0.669421
$577$	−8.43986	−0.351356	−0.175678	−	0.984448i	$-0.556212\pi$
$577$	−8.43986	−0.351356	−0.175678	+	0.984448i	$0.556212\pi$
$578$	79.3380	3.30003
$579$	−10.0381	−0.417169
$580$	11.1872	0.464522
$581$	−12.3172	−0.511003
$582$	−39.8639	−1.65241
$583$	51.9345	2.15091
$584$	2.33683	0.0966987
$585$	−10.8593	−0.448978
$586$	37.6641	1.55589
$587$	9.62193	0.397140	0.198570	−	0.980087i	$-0.436370\pi$
$587$	9.62193	0.397140	0.198570	+	0.980087i	$0.436370\pi$
$588$	−5.83004	−0.240427
$589$	24.4615	1.00792
$590$	−5.57719	−0.229609
$591$	12.1066	0.498001
$592$	−1.90951	−0.0784805
$593$	41.5647	1.70686	0.853429	−	0.521209i	$-0.174519\pi$
$593$	41.5647	1.70686	0.853429	+	0.521209i	$0.174519\pi$
$594$	−82.9775	−3.40461
$595$	6.86984	0.281636
$596$	99.9787	4.09529
$597$	−3.43201	−0.140463
$598$	−128.411	−5.25114
$599$	6.04850	0.247135	0.123568	−	0.992336i	$-0.460566\pi$
$599$	6.04850	0.247135	0.123568	+	0.992336i	$0.460566\pi$
$600$	−9.07135	−0.370336
$601$	2.44556	0.0997566	0.0498783	−	0.998755i	$-0.484117\pi$
$601$	2.44556	0.0997566	0.0498783	+	0.998755i	$0.484117\pi$
$602$	−8.33963	−0.339898
$603$	−0.770250	−0.0313670
$604$	1.54097	0.0627010
$605$	−22.5414	−0.916440
$606$	−57.2851	−2.32705
$607$	46.2642	1.87781	0.938903	−	0.344183i	$-0.111844\pi$
$607$	46.2642	1.87781	0.938903	+	0.344183i	$0.111844\pi$
$608$	73.8291	2.99417
$609$	−2.71197	−0.109895
$610$	15.0610	0.609804
$611$	−1.77155	−0.0716694
$612$	−53.4556	−2.16081
$613$	−24.9488	−1.00767	−0.503837	−	0.863799i	$-0.668079\pi$
$613$	−24.9488	−1.00767	−0.503837	+	0.863799i	$0.668079\pi$
$614$	12.6745	0.511502
$615$	1.38583	0.0558819
$616$	44.1921	1.78055
$617$	−17.2331	−0.693777	−0.346889	−	0.937906i	$-0.612762\pi$
$617$	−17.2331	−0.693777	−0.346889	+	0.937906i	$0.612762\pi$
$618$	−1.93708	−0.0779210
$619$	0.861823	0.0346396	0.0173198	−	0.999850i	$-0.494487\pi$
$619$	0.861823	0.0346396	0.0173198	+	0.999850i	$0.494487\pi$
$620$	−18.9278	−0.760158
$621$	38.9368	1.56248
$622$	22.3583	0.896488
$623$	−12.0055	−0.480988
$624$	83.3281	3.33580
$625$	1.00000	0.0400000
$626$	−12.3863	−0.495058
$627$	43.6361	1.74266
$628$	−35.5269	−1.41768
$629$	−1.28087	−0.0510717
$630$	−4.16912	−0.166102
$631$	22.8181	0.908373	0.454187	−	0.890907i	$-0.349930\pi$
$631$	22.8181	0.908373	0.454187	+	0.890907i	$0.349930\pi$
$632$	−38.0167	−1.51222
$633$	−0.711489	−0.0282791
$634$	33.6713	1.33726
$635$	18.1704	0.721070
$636$	52.2802	2.07304
$637$	−6.84400	−0.271169
$638$	34.7143	1.37435
$639$	−20.4771	−0.810062
$640$	−3.30725	−0.130731
$641$	−5.11840	−0.202165	−0.101082	−	0.994878i	$-0.532231\pi$
$641$	−5.11840	−0.202165	−0.101082	+	0.994878i	$0.532231\pi$
$642$	8.99607	0.355046
$643$	44.7953	1.76656	0.883278	−	0.468850i	$-0.155332\pi$
$643$	44.7953	1.76656	0.883278	+	0.468850i	$0.155332\pi$
$644$	−35.0184	−1.37992
$645$	3.77323	0.148571
$646$	114.402	4.50110
$647$	−14.6779	−0.577049	−0.288525	−	0.957472i	$-0.593165\pi$
$647$	−14.6779	−0.577049	−0.288525	+	0.957472i	$0.593165\pi$
$648$	−13.1422	−0.516275
$649$	−12.2929	−0.482539
$650$	−17.9830	−0.705350
$651$	4.58843	0.179835
$652$	73.1396	2.86437
$653$	10.9428	0.428226	0.214113	−	0.976809i	$-0.431314\pi$
$653$	10.9428	0.428226	0.214113	+	0.976809i	$0.431314\pi$
$654$	53.9638	2.11015
$655$	−19.2511	−0.752204
$656$	11.9386	0.466125
$657$	−0.485922	−0.0189576
$658$	−0.680136	−0.0265145
$659$	−46.7360	−1.82058	−0.910288	−	0.413975i	$-0.864140\pi$
$659$	−46.7360	−1.82058	−0.910288	+	0.413975i	$0.864140\pi$
$660$	−33.7647	−1.31429
$661$	43.9986	1.71135	0.855674	−	0.517515i	$-0.173143\pi$
$661$	43.9986	1.71135	0.855674	+	0.517515i	$0.173143\pi$
$662$	29.1886	1.13445
$663$	55.8952	2.17079
$664$	93.9863	3.64738
$665$	6.33777	0.245768
$666$	0.777327	0.0301208
$667$	−16.2895	−0.630734
$668$	−22.6136	−0.874945
$669$	−29.4195	−1.13742
$670$	−1.27553	−0.0492780
$671$	33.1967	1.28154
$672$	13.8487	0.534225
$673$	48.7221	1.87810	0.939049	−	0.343784i	$-0.111709\pi$
$673$	48.7221	1.87810	0.939049	+	0.343784i	$0.111709\pi$
$674$	27.2893	1.05115
$675$	5.45278	0.209878
$676$	165.954	6.38285
$677$	8.84502	0.339942	0.169971	−	0.985449i	$-0.445633\pi$
$677$	8.84502	0.339942	0.169971	+	0.985449i	$0.445633\pi$
$678$	−55.5142	−2.13201
$679$	−12.7617	−0.489751
$680$	−52.4203	−2.01023
$681$	−3.93496	−0.150788
$682$	−58.7338	−2.24903
$683$	−25.2971	−0.967968	−0.483984	−	0.875077i	$-0.660811\pi$
$683$	−25.2971	−0.967968	−0.483984	+	0.875077i	$0.660811\pi$
$684$	−49.3155	−1.88562
$685$	15.3632	0.586997
$686$	−2.62755	−0.100320
$687$	−1.18883	−0.0453565
$688$	32.5056	1.23927
$689$	61.3727	2.33811
$690$	22.3055	0.849156
$691$	−0.122930	−0.00467648	−0.00233824	−	0.999997i	$-0.500744\pi$
$691$	−0.122930	−0.00467648	−0.00233824	+	0.999997i	$0.500744\pi$
$692$	−50.5187	−1.92043
$693$	−9.18933	−0.349074
$694$	−29.9256	−1.13596
$695$	−12.6073	−0.478222
$696$	20.6937	0.784393
$697$	8.00824	0.303334
$698$	−65.5129	−2.47970
$699$	−33.0719	−1.25089
$700$	−4.90404	−0.185355
$701$	47.3854	1.78972	0.894861	−	0.446344i	$-0.147274\pi$
$701$	47.3854	1.78972	0.894861	+	0.446344i	$0.147274\pi$
$702$	−98.0572	−3.70093
$703$	−1.18167	−0.0445675
$704$	−58.6420	−2.21015
$705$	0.307725	0.0115896
$706$	−69.5392	−2.61714
$707$	−18.3388	−0.689703
$708$	−12.3747	−0.465071
$709$	−39.5547	−1.48551	−0.742753	−	0.669565i	$-0.766480\pi$
$709$	−39.5547	−1.48551	−0.742753	+	0.669565i	$0.766480\pi$
$710$	−33.9100	−1.27262
$711$	7.90521	0.296469
$712$	91.6078	3.43315
$713$	27.5606	1.03215
$714$	21.4593	0.803095
$715$	−39.6370	−1.48234
$716$	92.6125	3.46109
$717$	22.5733	0.843014
$718$	34.3241	1.28096
$719$	−32.6521	−1.21772	−0.608859	−	0.793279i	$-0.708372\pi$
$719$	−32.6521	−1.21772	−0.608859	+	0.793279i	$0.708372\pi$
$720$	16.2501	0.605606
$721$	−0.620124	−0.0230946
$722$	55.6184	2.06990
$723$	10.1354	0.376940
$724$	−56.4856	−2.09927
$725$	−2.28122	−0.0847223
$726$	−70.4127	−2.61326
$727$	27.6870	1.02685	0.513427	−	0.858134i	$-0.328376\pi$
$727$	27.6870	1.02685	0.513427	+	0.858134i	$0.328376\pi$
$728$	52.2232	1.93552
$729$	22.1800	0.821482
$730$	−0.804683	−0.0297827
$731$	21.8043	0.806460
$732$	33.4176	1.23515
$733$	−26.3705	−0.974018	−0.487009	−	0.873397i	$-0.661912\pi$
$733$	−26.3705	−0.974018	−0.487009	+	0.873397i	$0.661912\pi$
$734$	34.1664	1.26110
$735$	1.18883	0.0438505
$736$	83.1827	3.06616
$737$	−2.81144	−0.103561
$738$	−4.85999	−0.178899
$739$	16.6013	0.610690	0.305345	−	0.952242i	$-0.401228\pi$
$739$	16.6013	0.610690	0.305345	+	0.952242i	$0.401228\pi$
$740$	0.914351	0.0336122
$741$	51.5662	1.89433
$742$	23.5622	0.864997
$743$	2.68069	0.0983451	0.0491726	−	0.998790i	$-0.484342\pi$
$743$	2.68069	0.0983451	0.0491726	+	0.998790i	$0.484342\pi$
$744$	−35.0121	−1.28360
$745$	−20.3870	−0.746922
$746$	−21.4817	−0.786499
$747$	−19.5436	−0.715062
$748$	−195.115	−7.13411
$749$	2.87994	0.105231
$750$	3.12370	0.114062
$751$	−14.6552	−0.534777	−0.267389	−	0.963589i	$-0.586161\pi$
$751$	−14.6552	−0.534777	−0.267389	+	0.963589i	$0.586161\pi$
$752$	2.65099	0.0966716
$753$	−8.97793	−0.327174
$754$	41.0231	1.49397
$755$	−0.314224	−0.0114358
$756$	−26.7406	−0.972547
$757$	0.542768	0.0197272	0.00986362	−	0.999951i	$-0.496860\pi$
$757$	0.542768	0.0197272	0.00986362	+	0.999951i	$0.496860\pi$
$758$	−34.9465	−1.26931
$759$	49.1645	1.78456
$760$	−48.3604	−1.75422
$761$	−27.3323	−0.990796	−0.495398	−	0.868666i	$-0.664978\pi$
$761$	−27.3323	−0.990796	−0.495398	+	0.868666i	$0.664978\pi$
$762$	56.7589	2.05616
$763$	17.2756	0.625418
$764$	−87.2494	−3.15657
$765$	10.9003	0.394102
$766$	−30.6896	−1.10886
$767$	−14.5269	−0.524537
$768$	13.7441	0.495948
$769$	40.9702	1.47742	0.738711	−	0.674023i	$-0.235435\pi$
$769$	40.9702	1.47742	0.738711	+	0.674023i	$0.235435\pi$
$770$	−15.2175	−0.548399
$771$	24.9007	0.896775
$772$	41.4082	1.49032
$773$	17.9717	0.646398	0.323199	−	0.946331i	$-0.395242\pi$
$773$	17.9717	0.646398	0.323199	+	0.946331i	$0.395242\pi$
$774$	−13.2324	−0.475630
$775$	3.85963	0.138642
$776$	97.3785	3.49569
$777$	−0.221655	−0.00795183
$778$	−4.78239	−0.171457
$779$	7.38801	0.264703
$780$	−39.9008	−1.42868
$781$	−74.7423	−2.67449
$782$	128.896	4.60932
$783$	−12.4390	−0.444533
$784$	10.2415	0.365768
$785$	7.24442	0.258565
$786$	−60.1348	−2.14494
$787$	−1.49512	−0.0532953	−0.0266476	−	0.999645i	$-0.508483\pi$
$787$	−1.49512	−0.0532953	−0.0266476	+	0.999645i	$0.508483\pi$
$788$	−49.9412	−1.77908
$789$	−8.42182	−0.299825
$790$	13.0910	0.465756
$791$	−17.7719	−0.631896
$792$	70.1192	2.49158
$793$	39.2296	1.39308
$794$	−13.4046	−0.475711
$795$	−10.6606	−0.378094
$796$	14.1574	0.501796
$797$	14.7465	0.522348	0.261174	−	0.965292i	$-0.415890\pi$
$797$	14.7465	0.522348	0.261174	+	0.965292i	$0.415890\pi$
$798$	19.7973	0.700818
$799$	1.77824	0.0629097
$800$	11.6491	0.411856
$801$	−19.0490	−0.673062
$802$	−14.5252	−0.512903
$803$	−1.77363	−0.0625902
$804$	−2.83016	−0.0998120
$805$	7.14073	0.251678
$806$	−69.4077	−2.44478
$807$	29.8945	1.05234
$808$	139.935	4.92288
$809$	−20.9984	−0.738266	−0.369133	−	0.929377i	$-0.620345\pi$
$809$	−20.9984	−0.738266	−0.369133	+	0.929377i	$0.620345\pi$
$810$	4.52550	0.159010
$811$	−37.2560	−1.30823	−0.654117	−	0.756394i	$-0.726960\pi$
$811$	−37.2560	−1.30823	−0.654117	+	0.756394i	$0.726960\pi$
$812$	11.1872	0.392593
$813$	2.23632	0.0784310
$814$	2.83728	0.0994465
$815$	−14.9142	−0.522420
$816$	−83.6427	−2.92808
$817$	20.1155	0.703754
$818$	92.1101	3.22056
$819$	−10.8593	−0.379456
$820$	−5.71668	−0.199635
$821$	27.1081	0.946078	0.473039	−	0.881042i	$-0.343157\pi$
$821$	27.1081	0.946078	0.473039	+	0.881042i	$0.343157\pi$
$822$	47.9900	1.67384
$823$	−8.90373	−0.310365	−0.155182	−	0.987886i	$-0.549597\pi$
$823$	−8.90373	−0.310365	−0.155182	+	0.987886i	$0.549597\pi$
$824$	4.73186	0.164842
$825$	6.88508	0.239708
$826$	−5.57719	−0.194055
$827$	10.7227	0.372865	0.186433	−	0.982468i	$-0.440307\pi$
$827$	10.7227	0.372865	0.186433	+	0.982468i	$0.440307\pi$
$828$	−55.5634	−1.93096
$829$	28.0878	0.975531	0.487766	−	0.872975i	$-0.337812\pi$
$829$	28.0878	0.975531	0.487766	+	0.872975i	$0.337812\pi$
$830$	−32.3640	−1.12337
$831$	16.3062	0.565655
$832$	−69.2991	−2.40252
$833$	6.86984	0.238026
$834$	−39.3815	−1.36367
$835$	4.61121	0.159578
$836$	−180.004	−6.22555
$837$	21.0457	0.727447
$838$	−64.2360	−2.21900
$839$	0.419278	0.0144751	0.00723754	−	0.999974i	$-0.497696\pi$
$839$	0.419278	0.0144751	0.00723754	+	0.999974i	$0.497696\pi$
$840$	−9.07135	−0.312991
$841$	−23.7960	−0.820553
$842$	−3.16823	−0.109184
$843$	15.8796	0.546922
$844$	2.93497	0.101026
$845$	−33.8403	−1.16414
$846$	−1.07917	−0.0371025
$847$	−22.5414	−0.774533
$848$	−91.8393	−3.15377
$849$	−16.8552	−0.578470
$850$	18.0509	0.619139
$851$	−1.33138	−0.0456391
$852$	−75.2398	−2.57767
$853$	29.8683	1.02267	0.511335	−	0.859382i	$-0.329151\pi$
$853$	29.8683	1.02267	0.511335	+	0.859382i	$0.329151\pi$
$854$	15.0610	0.515378
$855$	10.0561	0.343911
$856$	−21.9754	−0.751103
$857$	27.7454	0.947765	0.473883	−	0.880588i	$-0.342852\pi$
$857$	27.7454	0.947765	0.473883	+	0.880588i	$0.342852\pi$
$858$	−123.814	−4.22695
$859$	−40.0095	−1.36511	−0.682554	−	0.730835i	$-0.739131\pi$
$859$	−40.0095	−1.36511	−0.682554	+	0.730835i	$0.739131\pi$
$860$	−15.5650	−0.530762
$861$	1.38583	0.0472288
$862$	−27.7787	−0.946145
$863$	37.9907	1.29322	0.646609	−	0.762822i	$-0.276187\pi$
$863$	37.9907	1.29322	0.646609	+	0.762822i	$0.276187\pi$
$864$	63.5198	2.16099
$865$	10.3015	0.350260
$866$	59.0058	2.00510
$867$	−35.8962	−1.21910
$868$	−18.9278	−0.642451
$869$	28.8544	0.978817
$870$	−7.12584	−0.241589
$871$	−3.32238	−0.112574
$872$	−131.821	−4.46404
$873$	−20.2490	−0.685323
$874$	118.913	4.02230
$875$	1.00000	0.0338062
$876$	−1.78544	−0.0603244
$877$	21.3492	0.720913	0.360456	−	0.932776i	$-0.382621\pi$
$877$	21.3492	0.720913	0.360456	+	0.932776i	$0.382621\pi$
$878$	29.1955	0.985299
$879$	−17.0410	−0.574778
$880$	59.3136	1.99946
$881$	6.33071	0.213287	0.106644	−	0.994297i	$-0.465990\pi$
$881$	6.33071	0.213287	0.106644	+	0.994297i	$0.465990\pi$
$882$	−4.16912	−0.140382
$883$	22.9572	0.772573	0.386286	−	0.922379i	$-0.373758\pi$
$883$	22.9572	0.772573	0.386286	+	0.922379i	$0.373758\pi$
$884$	−230.574	−7.75504
$885$	2.52338	0.0848224
$886$	−15.2207	−0.511349
$887$	30.6220	1.02819	0.514093	−	0.857734i	$-0.328129\pi$
$887$	30.6220	1.02819	0.514093	+	0.857734i	$0.328129\pi$
$888$	1.69134	0.0567577
$889$	18.1704	0.609415
$890$	−31.5450	−1.05739
$891$	9.97485	0.334170
$892$	121.359	4.06338
$893$	1.64052	0.0548978
$894$	−63.6830	−2.12988
$895$	−18.8850	−0.631255
$896$	−3.30725	−0.110488
$897$	58.0993	1.93988
$898$	−81.5478	−2.72128
$899$	−8.80466	−0.293652
$900$	−7.78120	−0.259373
$901$	−61.6043	−2.05234
$902$	−17.7392	−0.590649
$903$	3.77323	0.125565
$904$	135.609	4.51028
$905$	11.5182	0.382878
$906$	−0.981543	−0.0326096
$907$	41.9465	1.39281	0.696405	−	0.717649i	$-0.254782\pi$
$907$	41.9465	1.39281	0.696405	+	0.717649i	$0.254782\pi$
$908$	16.2321	0.538682
$909$	−29.0981	−0.965123
$910$	−17.9830	−0.596130
$911$	20.7130	0.686252	0.343126	−	0.939289i	$-0.388514\pi$
$911$	20.7130	0.686252	0.343126	+	0.939289i	$0.388514\pi$
$912$	−77.1646	−2.55518
$913$	−71.3349	−2.36084
$914$	90.5753	2.99596
$915$	−6.81431	−0.225274
$916$	4.90404	0.162034
$917$	−19.2511	−0.635729
$918$	98.4274	3.24859
$919$	−16.2776	−0.536948	−0.268474	−	0.963287i	$-0.586519\pi$
$919$	−16.2776	−0.536948	−0.268474	+	0.963287i	$0.586519\pi$
$920$	−54.4874	−1.79640
$921$	−5.73453	−0.188959
$922$	−27.9533	−0.920594
$923$	−88.3254	−2.90727
$924$	−33.7647	−1.11078
$925$	−0.186449	−0.00613040
$926$	−13.7788	−0.452799
$927$	−0.983947	−0.0323171
$928$	−26.5740	−0.872335
$929$	−11.9753	−0.392896	−0.196448	−	0.980514i	$-0.562941\pi$
$929$	−11.9753	−0.392896	−0.196448	+	0.980514i	$0.562941\pi$
$930$	12.0563	0.395343
$931$	6.33777	0.207712
$932$	136.425	4.46875
$933$	−10.1159	−0.331181
$934$	50.4141	1.64960
$935$	39.7866	1.30116
$936$	82.8622	2.70844
$937$	−14.1989	−0.463856	−0.231928	−	0.972733i	$-0.574503\pi$
$937$	−14.1989	−0.463856	−0.231928	+	0.972733i	$0.574503\pi$
$938$	−1.27553	−0.0416475
$939$	5.60415	0.182884
$940$	−1.26940	−0.0414032
$941$	−28.5715	−0.931405	−0.465703	−	0.884941i	$-0.654198\pi$
$941$	−28.5715	−0.931405	−0.465703	+	0.884941i	$0.654198\pi$
$942$	22.6294	0.737307
$943$	8.32402	0.271067
$944$	21.7384	0.707524
$945$	5.45278	0.177379
$946$	−48.2989	−1.57033
$947$	54.1215	1.75871	0.879356	−	0.476164i	$-0.157973\pi$
$947$	54.1215	1.75871	0.879356	+	0.476164i	$0.157973\pi$
$948$	29.0464	0.943384
$949$	−2.09596	−0.0680378
$950$	16.6528	0.540289
$951$	−15.2344	−0.494010
$952$	−52.4203	−1.69895
$953$	37.0139	1.19900	0.599499	−	0.800375i	$-0.295366\pi$
$953$	37.0139	1.19900	0.599499	+	0.800375i	$0.295366\pi$
$954$	37.3860	1.21042
$955$	17.7914	0.575715
$956$	−93.1172	−3.01162
$957$	−15.7064	−0.507715
$958$	−84.0772	−2.71641
$959$	15.3632	0.496103
$960$	12.0375	0.388508
$961$	−16.1032	−0.519459
$962$	3.35290	0.108102
$963$	4.56958	0.147253
$964$	−41.8096	−1.34660
$965$	−8.44371	−0.271813
$966$	22.3055	0.717668
$967$	−15.1097	−0.485896	−0.242948	−	0.970039i	$-0.578114\pi$
$967$	−15.1097	−0.485896	−0.242948	+	0.970039i	$0.578114\pi$
$968$	172.003	5.52837
$969$	−51.7608	−1.66280
$970$	−33.5321	−1.07665
$971$	33.9003	1.08791	0.543956	−	0.839114i	$-0.316926\pi$
$971$	33.9003	1.08791	0.543956	+	0.839114i	$0.316926\pi$
$972$	−70.1806	−2.25105
$973$	−12.6073	−0.404171
$974$	−107.767	−3.45306
$975$	8.13632	0.260571
$976$	−58.7039	−1.87907
$977$	40.5575	1.29755	0.648774	−	0.760981i	$-0.275282\pi$
$977$	40.5575	1.29755	0.648774	+	0.760981i	$0.275282\pi$
$978$	−46.5874	−1.48970
$979$	−69.5296	−2.22217
$980$	−4.90404	−0.156654
$981$	27.4110	0.875167
$982$	19.9184	0.635623
$983$	−33.5434	−1.06987	−0.534934	−	0.844894i	$-0.679664\pi$
$983$	−33.5434	−1.06987	−0.534934	+	0.844894i	$0.679664\pi$
$984$	−10.5746	−0.337105
$985$	10.1837	0.324479
$986$	−41.1779	−1.31137
$987$	0.307725	0.00979499
$988$	−212.716	−6.76740
$989$	22.6640	0.720675
$990$	−24.1454	−0.767393
$991$	40.6860	1.29243	0.646217	−	0.763154i	$-0.276350\pi$
$991$	40.6860	1.29243	0.646217	+	0.763154i	$0.276350\pi$
$992$	44.9611	1.42752
$993$	−13.2063	−0.419088
$994$	−33.9100	−1.07556
$995$	−2.88689	−0.0915206
$996$	−71.8097	−2.27538
$997$	17.4231	0.551795	0.275898	−	0.961187i	$-0.411025\pi$
$997$	17.4231	0.551795	0.275898	+	0.961187i	$0.411025\pi$
$998$	−63.6698	−2.01543
$999$	−1.01666	−0.0321658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.59	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.59	✓	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)

\(f(q)\)	\(=\)	\(q+2.62755 q^{2} -1.18883 q^{3} +4.90404 q^{4} -1.00000 q^{5} -3.12370 q^{6} -1.00000 q^{7} +7.63051 q^{8} -1.58669 q^{9} +O(q^{10})\)	\(q+2.62755 q^{2} -1.18883 q^{3} +4.90404 q^{4} -1.00000 q^{5} -3.12370 q^{6} -1.00000 q^{7} +7.63051 q^{8} -1.58669 q^{9} -2.62755 q^{10} -5.79150 q^{11} -5.83004 q^{12} -6.84400 q^{13} -2.62755 q^{14} +1.18883 q^{15} +10.2415 q^{16} +6.86984 q^{17} -4.16912 q^{18} +6.33777 q^{19} -4.90404 q^{20} +1.18883 q^{21} -15.2175 q^{22} +7.14073 q^{23} -9.07135 q^{24} +1.00000 q^{25} -17.9830 q^{26} +5.45278 q^{27} -4.90404 q^{28} -2.28122 q^{29} +3.12370 q^{30} +3.85963 q^{31} +11.6491 q^{32} +6.88508 q^{33} +18.0509 q^{34} +1.00000 q^{35} -7.78120 q^{36} -0.186449 q^{37} +16.6528 q^{38} +8.13632 q^{39} -7.63051 q^{40} +1.16571 q^{41} +3.12370 q^{42} +3.17391 q^{43} -28.4017 q^{44} +1.58669 q^{45} +18.7626 q^{46} +0.258848 q^{47} -12.1754 q^{48} +1.00000 q^{49} +2.62755 q^{50} -8.16704 q^{51} -33.5632 q^{52} -8.96737 q^{53} +14.3275 q^{54} +5.79150 q^{55} -7.63051 q^{56} -7.53451 q^{57} -5.99402 q^{58} +2.12258 q^{59} +5.83004 q^{60} -5.73197 q^{61} +10.1414 q^{62} +1.58669 q^{63} +10.1255 q^{64} +6.84400 q^{65} +18.0909 q^{66} +0.485444 q^{67} +33.6899 q^{68} -8.48908 q^{69} +2.62755 q^{70} +12.9055 q^{71} -12.1073 q^{72} +0.306248 q^{73} -0.489904 q^{74} -1.18883 q^{75} +31.0807 q^{76} +5.79150 q^{77} +21.3786 q^{78} -4.98220 q^{79} -10.2415 q^{80} -1.72233 q^{81} +3.06297 q^{82} +12.3172 q^{83} +5.83004 q^{84} -6.86984 q^{85} +8.33963 q^{86} +2.71197 q^{87} -44.1921 q^{88} +12.0055 q^{89} +4.16912 q^{90} +6.84400 q^{91} +35.0184 q^{92} -4.58843 q^{93} +0.680136 q^{94} -6.33777 q^{95} -13.8487 q^{96} +12.7617 q^{97} +2.62755 q^{98} +9.18933 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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