LMFDB - Embedded newform 8015.2.a.l.1.40

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			1.40
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)

$f(q)$	$=$	$q+0.970097 q^{2} -0.396968 q^{3} -1.05891 q^{4} -1.00000 q^{5} -0.385098 q^{6} -1.00000 q^{7} -2.96744 q^{8} -2.84242 q^{9} +O(q^{10})$	\(q+0.970097 q^{2} -0.396968 q^{3} -1.05891 q^{4} -1.00000 q^{5} -0.385098 q^{6} -1.00000 q^{7} -2.96744 q^{8} -2.84242 q^{9} -0.970097 q^{10} -2.20338 q^{11} +0.420355 q^{12} +4.66808 q^{13} -0.970097 q^{14} +0.396968 q^{15} -0.760881 q^{16} -3.82317 q^{17} -2.75742 q^{18} -5.08764 q^{19} +1.05891 q^{20} +0.396968 q^{21} -2.13749 q^{22} -8.61116 q^{23} +1.17798 q^{24} +1.00000 q^{25} +4.52849 q^{26} +2.31925 q^{27} +1.05891 q^{28} -6.53813 q^{29} +0.385098 q^{30} -3.90594 q^{31} +5.19675 q^{32} +0.874671 q^{33} -3.70885 q^{34} +1.00000 q^{35} +3.00987 q^{36} +1.56682 q^{37} -4.93550 q^{38} -1.85308 q^{39} +2.96744 q^{40} -10.3901 q^{41} +0.385098 q^{42} -5.42344 q^{43} +2.33318 q^{44} +2.84242 q^{45} -8.35365 q^{46} +4.14775 q^{47} +0.302046 q^{48} +1.00000 q^{49} +0.970097 q^{50} +1.51768 q^{51} -4.94309 q^{52} -1.57645 q^{53} +2.24990 q^{54} +2.20338 q^{55} +2.96744 q^{56} +2.01963 q^{57} -6.34262 q^{58} +8.65116 q^{59} -0.420355 q^{60} +1.84183 q^{61} -3.78914 q^{62} +2.84242 q^{63} +6.56312 q^{64} -4.66808 q^{65} +0.848516 q^{66} +10.0744 q^{67} +4.04840 q^{68} +3.41836 q^{69} +0.970097 q^{70} +2.25770 q^{71} +8.43470 q^{72} -10.5309 q^{73} +1.51997 q^{74} -0.396968 q^{75} +5.38736 q^{76} +2.20338 q^{77} -1.79767 q^{78} +8.74949 q^{79} +0.760881 q^{80} +7.60658 q^{81} -10.0794 q^{82} -13.9029 q^{83} -0.420355 q^{84} +3.82317 q^{85} -5.26126 q^{86} +2.59543 q^{87} +6.53839 q^{88} -8.53761 q^{89} +2.75742 q^{90} -4.66808 q^{91} +9.11846 q^{92} +1.55053 q^{93} +4.02372 q^{94} +5.08764 q^{95} -2.06295 q^{96} -14.8303 q^{97} +0.970097 q^{98} +6.26291 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.970097	0.685962	0.342981	−	0.939342i	$-0.388563\pi$
$2$	0.970097	0.685962	0.342981	+	0.939342i	$0.388563\pi$
$3$	−0.396968	−0.229190	−0.114595	−	0.993412i	$-0.536557\pi$
$3$	−0.396968	−0.229190	−0.114595	+	0.993412i	$0.536557\pi$
$4$	−1.05891	−0.529456
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.385098	−0.157216
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.96744	−1.04915
$9$	−2.84242	−0.947472
$10$	−0.970097	−0.306772
$11$	−2.20338	−0.664343	−0.332172	−	0.943219i	$-0.607781\pi$
$11$	−2.20338	−0.664343	−0.332172	+	0.943219i	$0.607781\pi$
$12$	0.420355	0.121346
$13$	4.66808	1.29469	0.647347	−	0.762196i	$-0.275879\pi$
$13$	4.66808	1.29469	0.647347	+	0.762196i	$0.275879\pi$
$14$	−0.970097	−0.259269
$15$	0.396968	0.102497
$16$	−0.760881	−0.190220
$17$	−3.82317	−0.927255	−0.463628	−	0.886030i	$-0.653452\pi$
$17$	−3.82317	−0.927255	−0.463628	+	0.886030i	$0.653452\pi$
$18$	−2.75742	−0.649930
$19$	−5.08764	−1.16718	−0.583592	−	0.812047i	$-0.698353\pi$
$19$	−5.08764	−1.16718	−0.583592	+	0.812047i	$0.698353\pi$
$20$	1.05891	0.236780
$21$	0.396968	0.0866256
$22$	−2.13749	−0.455714
$23$	−8.61116	−1.79555	−0.897775	−	0.440454i	$-0.854817\pi$
$23$	−8.61116	−1.79555	−0.897775	+	0.440454i	$0.854817\pi$
$24$	1.17798	0.240454
$25$	1.00000	0.200000
$26$	4.52849	0.888110
$27$	2.31925	0.446341
$28$	1.05891	0.200116
$29$	−6.53813	−1.21410	−0.607050	−	0.794664i	$-0.707647\pi$
$29$	−6.53813	−1.21410	−0.607050	+	0.794664i	$0.707647\pi$
$30$	0.385098	0.0703089
$31$	−3.90594	−0.701527	−0.350764	−	0.936464i	$-0.614078\pi$
$31$	−3.90594	−0.701527	−0.350764	+	0.936464i	$0.614078\pi$
$32$	5.19675	0.918665
$33$	0.874671	0.152261
$34$	−3.70885	−0.636062
$35$	1.00000	0.169031
$36$	3.00987	0.501645
$37$	1.56682	0.257584	0.128792	−	0.991672i	$-0.458890\pi$
$37$	1.56682	0.257584	0.128792	+	0.991672i	$0.458890\pi$
$38$	−4.93550	−0.800644
$39$	−1.85308	−0.296731
$40$	2.96744	0.469194
$41$	−10.3901	−1.62265	−0.811327	−	0.584592i	$-0.801254\pi$
$41$	−10.3901	−1.62265	−0.811327	+	0.584592i	$0.801254\pi$
$42$	0.385098	0.0594219
$43$	−5.42344	−0.827067	−0.413533	−	0.910489i	$-0.635705\pi$
$43$	−5.42344	−0.827067	−0.413533	+	0.910489i	$0.635705\pi$
$44$	2.33318	0.351740
$45$	2.84242	0.423722
$46$	−8.35365	−1.23168
$47$	4.14775	0.605011	0.302505	−	0.953148i	$-0.402177\pi$
$47$	4.14775	0.605011	0.302505	+	0.953148i	$0.402177\pi$
$48$	0.302046	0.0435966
$49$	1.00000	0.142857
$50$	0.970097	0.137192
$51$	1.51768	0.212517
$52$	−4.94309	−0.685483
$53$	−1.57645	−0.216541	−0.108271	−	0.994121i	$-0.534531\pi$
$53$	−1.57645	−0.216541	−0.108271	+	0.994121i	$0.534531\pi$
$54$	2.24990	0.306173
$55$	2.20338	0.297103
$56$	2.96744	0.396541
$57$	2.01963	0.267507
$58$	−6.34262	−0.832827
$59$	8.65116	1.12628	0.563142	−	0.826360i	$-0.309592\pi$
$59$	8.65116	1.12628	0.563142	+	0.826360i	$0.309592\pi$
$60$	−0.420355	−0.0542675
$61$	1.84183	0.235822	0.117911	−	0.993024i	$-0.462380\pi$
$61$	1.84183	0.235822	0.117911	+	0.993024i	$0.462380\pi$
$62$	−3.78914	−0.481221
$63$	2.84242	0.358111
$64$	6.56312	0.820390
$65$	−4.66808	−0.579004
$66$	0.848516	0.104445
$67$	10.0744	1.23078	0.615392	−	0.788222i	$-0.288998\pi$
$67$	10.0744	1.23078	0.615392	+	0.788222i	$0.288998\pi$
$68$	4.04840	0.490941
$69$	3.41836	0.411522
$70$	0.970097	0.115949
$71$	2.25770	0.267939	0.133970	−	0.990985i	$-0.457228\pi$
$71$	2.25770	0.267939	0.133970	+	0.990985i	$0.457228\pi$
$72$	8.43470	0.994039
$73$	−10.5309	−1.23255	−0.616275	−	0.787531i	$-0.711359\pi$
$73$	−10.5309	−1.23255	−0.616275	+	0.787531i	$0.711359\pi$
$74$	1.51997	0.176693
$75$	−0.396968	−0.0458380
$76$	5.38736	0.617973
$77$	2.20338	0.251098
$78$	−1.79767	−0.203546
$79$	8.74949	0.984394	0.492197	−	0.870484i	$-0.336194\pi$
$79$	8.74949	0.984394	0.492197	+	0.870484i	$0.336194\pi$
$80$	0.760881	0.0850691
$81$	7.60658	0.845175
$82$	−10.0794	−1.11308
$83$	−13.9029	−1.52604	−0.763022	−	0.646373i	$-0.776285\pi$
$83$	−13.9029	−1.52604	−0.763022	+	0.646373i	$0.776285\pi$
$84$	−0.420355	−0.0458645
$85$	3.82317	0.414681
$86$	−5.26126	−0.567336
$87$	2.59543	0.278259
$88$	6.53839	0.696995
$89$	−8.53761	−0.904985	−0.452492	−	0.891768i	$-0.649465\pi$
$89$	−8.53761	−0.904985	−0.452492	+	0.891768i	$0.649465\pi$
$90$	2.75742	0.290657
$91$	−4.66808	−0.489348
$92$	9.11846	0.950665
$93$	1.55053	0.160783
$94$	4.02372	0.415015
$95$	5.08764	0.521981
$96$	−2.06295	−0.210549
$97$	−14.8303	−1.50578	−0.752892	−	0.658144i	$-0.771342\pi$
$97$	−14.8303	−1.50578	−0.752892	+	0.658144i	$0.771342\pi$
$98$	0.970097	0.0979946
$99$	6.26291	0.629446
$100$	−1.05891	−0.105891
$101$	3.96350	0.394383	0.197191	−	0.980365i	$-0.436818\pi$
$101$	3.96350	0.394383	0.197191	+	0.980365i	$0.436818\pi$
$102$	1.47229	0.145779
$103$	−8.14891	−0.802936	−0.401468	−	0.915873i	$-0.631500\pi$
$103$	−8.14891	−0.802936	−0.401468	+	0.915873i	$0.631500\pi$
$104$	−13.8523	−1.35833
$105$	−0.396968	−0.0387402
$106$	−1.52931	−0.148539
$107$	−9.09956	−0.879688	−0.439844	−	0.898074i	$-0.644966\pi$
$107$	−9.09956	−0.879688	−0.439844	+	0.898074i	$0.644966\pi$
$108$	−2.45589	−0.236318
$109$	11.2079	1.07352	0.536760	−	0.843735i	$-0.319648\pi$
$109$	11.2079	1.07352	0.536760	+	0.843735i	$0.319648\pi$
$110$	2.13749	0.203802
$111$	−0.621979	−0.0590356
$112$	0.760881	0.0718965
$113$	0.420027	0.0395129	0.0197564	−	0.999805i	$-0.493711\pi$
$113$	0.420027	0.0395129	0.0197564	+	0.999805i	$0.493711\pi$
$114$	1.95924	0.183499
$115$	8.61116	0.802994
$116$	6.92330	0.642813
$117$	−13.2686	−1.22669
$118$	8.39246	0.772589
$119$	3.82317	0.350470
$120$	−1.17798	−0.107534
$121$	−6.14513	−0.558648
$122$	1.78675	0.161765
$123$	4.12452	0.371896
$124$	4.13605	0.371428
$125$	−1.00000	−0.0894427
$126$	2.75742	0.245650
$127$	4.25797	0.377834	0.188917	−	0.981993i	$-0.439502\pi$
$127$	4.25797	0.377834	0.188917	+	0.981993i	$0.439502\pi$
$128$	−4.02665	−0.355909
$129$	2.15293	0.189555
$130$	−4.52849	−0.397175
$131$	−8.77509	−0.766683	−0.383342	−	0.923607i	$-0.625227\pi$
$131$	−8.77509	−0.766683	−0.383342	+	0.923607i	$0.625227\pi$
$132$	−0.926200	−0.0806153
$133$	5.08764	0.441154
$134$	9.77314	0.844271
$135$	−2.31925	−0.199610
$136$	11.3450	0.972829
$137$	−0.00613626	−0.000524256 0	−0.000262128	−	1.00000i	$-0.500083\pi$
$137$	−0.00613626	−0.000524256 0	−0.000262128		1.00000i	$0.500083\pi$
$138$	3.31614	0.282288
$139$	−9.63822	−0.817503	−0.408752	−	0.912646i	$-0.634036\pi$
$139$	−9.63822	−0.817503	−0.408752	+	0.912646i	$0.634036\pi$
$140$	−1.05891	−0.0894944
$141$	−1.64652	−0.138662
$142$	2.19018	0.183796
$143$	−10.2855	−0.860120
$144$	2.16274	0.180228
$145$	6.53813	0.542962
$146$	−10.2160	−0.845483
$147$	−0.396968	−0.0327414
$148$	−1.65913	−0.136379
$149$	13.3212	1.09131	0.545657	−	0.838009i	$-0.316280\pi$
$149$	13.3212	1.09131	0.545657	+	0.838009i	$0.316280\pi$
$150$	−0.385098	−0.0314431
$151$	−5.14788	−0.418929	−0.209464	−	0.977816i	$-0.567172\pi$
$151$	−5.14788	−0.418929	−0.209464	+	0.977816i	$0.567172\pi$
$152$	15.0973	1.22455
$153$	10.8670	0.878548
$154$	2.13749	0.172244
$155$	3.90594	0.313733
$156$	1.96225	0.157106
$157$	9.06063	0.723117	0.361558	−	0.932349i	$-0.382245\pi$
$157$	9.06063	0.723117	0.361558	+	0.932349i	$0.382245\pi$
$158$	8.48785	0.675257
$159$	0.625799	0.0496291
$160$	−5.19675	−0.410839
$161$	8.61116	0.678654
$162$	7.37912	0.579758
$163$	−0.996155	−0.0780249	−0.0390124	−	0.999239i	$-0.512421\pi$
$163$	−0.996155	−0.0780249	−0.0390124	+	0.999239i	$0.512421\pi$
$164$	11.0022	0.859124
$165$	−0.874671	−0.0680930
$166$	−13.4872	−1.04681
$167$	−12.3079	−0.952412	−0.476206	−	0.879334i	$-0.657988\pi$
$167$	−12.3079	−0.952412	−0.476206	+	0.879334i	$0.657988\pi$
$168$	−1.17798	−0.0908832
$169$	8.79100	0.676231
$170$	3.70885	0.284456
$171$	14.4612	1.10587
$172$	5.74294	0.437895
$173$	16.4452	1.25031	0.625154	−	0.780501i	$-0.285036\pi$
$173$	16.4452	1.25031	0.625154	+	0.780501i	$0.285036\pi$
$174$	2.51782	0.190875
$175$	−1.00000	−0.0755929
$176$	1.67651	0.126372
$177$	−3.43424	−0.258133
$178$	−8.28231	−0.620785
$179$	5.29031	0.395416	0.197708	−	0.980261i	$-0.436650\pi$
$179$	5.29031	0.395416	0.197708	+	0.980261i	$0.436650\pi$
$180$	−3.00987	−0.224342
$181$	11.0371	0.820378	0.410189	−	0.912001i	$-0.365463\pi$
$181$	11.0371	0.820378	0.410189	+	0.912001i	$0.365463\pi$
$182$	−4.52849	−0.335674
$183$	−0.731149	−0.0540481
$184$	25.5531	1.88380
$185$	−1.56682	−0.115195
$186$	1.50417	0.110291
$187$	8.42389	0.616016
$188$	−4.39210	−0.320327
$189$	−2.31925	−0.168701
$190$	4.93550	0.358059
$191$	−11.7995	−0.853782	−0.426891	−	0.904303i	$-0.640391\pi$
$191$	−11.7995	−0.853782	−0.426891	+	0.904303i	$0.640391\pi$
$192$	−2.60535	−0.188025
$193$	6.22737	0.448256	0.224128	−	0.974560i	$-0.428047\pi$
$193$	6.22737	0.448256	0.224128	+	0.974560i	$0.428047\pi$
$194$	−14.3868	−1.03291
$195$	1.85308	0.132702
$196$	−1.05891	−0.0756366
$197$	−6.52208	−0.464679	−0.232339	−	0.972635i	$-0.574638\pi$
$197$	−6.52208	−0.464679	−0.232339	+	0.972635i	$0.574638\pi$
$198$	6.07563	0.431776
$199$	−0.945655	−0.0670357	−0.0335179	−	0.999438i	$-0.510671\pi$
$199$	−0.945655	−0.0670357	−0.0335179	+	0.999438i	$0.510671\pi$
$200$	−2.96744	−0.209830
$201$	−3.99922	−0.282083
$202$	3.84497	0.270531
$203$	6.53813	0.458887
$204$	−1.60709	−0.112519
$205$	10.3901	0.725673
$206$	−7.90524	−0.550784
$207$	24.4765	1.70123
$208$	−3.55186	−0.246277
$209$	11.2100	0.775410
$210$	−0.385098	−0.0265743
$211$	−2.49474	−0.171745	−0.0858725	−	0.996306i	$-0.527368\pi$
$211$	−2.49474	−0.171745	−0.0858725	+	0.996306i	$0.527368\pi$
$212$	1.66932	0.114649
$213$	−0.896234	−0.0614089
$214$	−8.82746	−0.603433
$215$	5.42344	0.369875
$216$	−6.88225	−0.468278
$217$	3.90594	0.265152
$218$	10.8727	0.736394
$219$	4.18044	0.282488
$220$	−2.33318	−0.157303
$221$	−17.8469	−1.20051
$222$	−0.603380	−0.0404962
$223$	23.9274	1.60230	0.801149	−	0.598465i	$-0.204222\pi$
$223$	23.9274	1.60230	0.801149	+	0.598465i	$0.204222\pi$
$224$	−5.19675	−0.347223
$225$	−2.84242	−0.189494
$226$	0.407467	0.0271043
$227$	12.3622	0.820510	0.410255	−	0.911971i	$-0.365440\pi$
$227$	12.3622	0.820510	0.410255	+	0.911971i	$0.365440\pi$
$228$	−2.13861	−0.141633
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	8.35365	0.550824
$231$	−0.874671	−0.0575491
$232$	19.4015	1.27377
$233$	−21.9933	−1.44083	−0.720414	−	0.693544i	$-0.756048\pi$
$233$	−21.9933	−1.44083	−0.720414	+	0.693544i	$0.756048\pi$
$234$	−12.8719	−0.841460
$235$	−4.14775	−0.270569
$236$	−9.16081	−0.596318
$237$	−3.47327	−0.225613
$238$	3.70885	0.240409
$239$	16.6728	1.07847	0.539236	−	0.842155i	$-0.318713\pi$
$239$	16.6728	1.07847	0.539236	+	0.842155i	$0.318713\pi$
$240$	−0.302046	−0.0194970
$241$	5.79359	0.373198	0.186599	−	0.982436i	$-0.440254\pi$
$241$	5.79359	0.373198	0.186599	+	0.982436i	$0.440254\pi$
$242$	−5.96137	−0.383212
$243$	−9.97733	−0.640046
$244$	−1.95034	−0.124858
$245$	−1.00000	−0.0638877
$246$	4.00119	0.255106
$247$	−23.7495	−1.51115
$248$	11.5906	0.736007
$249$	5.51902	0.349754
$250$	−0.970097	−0.0613543
$251$	22.9827	1.45066	0.725328	−	0.688404i	$-0.241688\pi$
$251$	22.9827	1.45066	0.725328	+	0.688404i	$0.241688\pi$
$252$	−3.00987	−0.189604
$253$	18.9736	1.19286
$254$	4.13065	0.259180
$255$	−1.51768	−0.0950407
$256$	−17.0325	−1.06453
$257$	9.03120	0.563351	0.281675	−	0.959510i	$-0.409110\pi$
$257$	9.03120	0.563351	0.281675	+	0.959510i	$0.409110\pi$
$258$	2.08855	0.130028
$259$	−1.56682	−0.0973576
$260$	4.94309	0.306557
$261$	18.5841	1.15033
$262$	−8.51269	−0.525915
$263$	−7.40733	−0.456755	−0.228378	−	0.973573i	$-0.573342\pi$
$263$	−7.40733	−0.456755	−0.228378	+	0.973573i	$0.573342\pi$
$264$	−2.59553	−0.159744
$265$	1.57645	0.0968403
$266$	4.93550	0.302615
$267$	3.38916	0.207413
$268$	−10.6679	−0.651646
$269$	16.2546	0.991063	0.495531	−	0.868590i	$-0.334973\pi$
$269$	16.2546	0.991063	0.495531	+	0.868590i	$0.334973\pi$
$270$	−2.24990	−0.136925
$271$	25.9362	1.57551	0.787757	−	0.615986i	$-0.211242\pi$
$271$	25.9362	1.57551	0.787757	+	0.615986i	$0.211242\pi$
$272$	2.90898	0.176383
$273$	1.85308	0.112154
$274$	−0.00595277	−0.000359620 0
$275$	−2.20338	−0.132869
$276$	−3.61974	−0.217883
$277$	−7.44191	−0.447141	−0.223570	−	0.974688i	$-0.571771\pi$
$277$	−7.44191	−0.447141	−0.223570	+	0.974688i	$0.571771\pi$
$278$	−9.35001	−0.560776
$279$	11.1023	0.664678
$280$	−2.96744	−0.177339
$281$	−17.8273	−1.06349	−0.531743	−	0.846906i	$-0.678463\pi$
$281$	−17.8273	−1.06349	−0.531743	+	0.846906i	$0.678463\pi$
$282$	−1.59729	−0.0951171
$283$	11.3850	0.676768	0.338384	−	0.941008i	$-0.390120\pi$
$283$	11.3850	0.676768	0.338384	+	0.941008i	$0.390120\pi$
$284$	−2.39070	−0.141862
$285$	−2.01963	−0.119633
$286$	−9.97797	−0.590010
$287$	10.3901	0.613306
$288$	−14.7713	−0.870409
$289$	−2.38336	−0.140198
$290$	6.34262	0.372451
$291$	5.88715	0.345111
$292$	11.1513	0.652581
$293$	−14.6010	−0.852997	−0.426498	−	0.904488i	$-0.640253\pi$
$293$	−14.6010	−0.852997	−0.426498	+	0.904488i	$0.640253\pi$
$294$	−0.385098	−0.0224594
$295$	−8.65116	−0.503690
$296$	−4.64945	−0.270244
$297$	−5.11019	−0.296523
$298$	12.9228	0.748600
$299$	−40.1976	−2.32469
$300$	0.420355	0.0242692
$301$	5.42344	0.312602
$302$	−4.99394	−0.287369
$303$	−1.57338	−0.0903885
$304$	3.87109	0.222022
$305$	−1.84183	−0.105463
$306$	10.5421	0.602651
$307$	4.07326	0.232473	0.116237	−	0.993222i	$-0.462917\pi$
$307$	4.07326	0.232473	0.116237	+	0.993222i	$0.462917\pi$
$308$	−2.33318	−0.132945
$309$	3.23486	0.184025
$310$	3.78914	0.215209
$311$	6.74219	0.382314	0.191157	−	0.981559i	$-0.438776\pi$
$311$	6.74219	0.382314	0.191157	+	0.981559i	$0.438776\pi$
$312$	5.49891	0.311314
$313$	4.88163	0.275926	0.137963	−	0.990437i	$-0.455944\pi$
$313$	4.88163	0.275926	0.137963	+	0.990437i	$0.455944\pi$
$314$	8.78969	0.496031
$315$	−2.84242	−0.160152
$316$	−9.26494	−0.521193
$317$	26.1274	1.46746	0.733729	−	0.679442i	$-0.237778\pi$
$317$	26.1274	1.46746	0.733729	+	0.679442i	$0.237778\pi$
$318$	0.607086	0.0340437
$319$	14.4060	0.806579
$320$	−6.56312	−0.366889
$321$	3.61224	0.201616
$322$	8.35365	0.465531
$323$	19.4509	1.08228
$324$	−8.05470	−0.447483
$325$	4.66808	0.258939
$326$	−0.966367	−0.0535221
$327$	−4.44917	−0.246040
$328$	30.8319	1.70241
$329$	−4.14775	−0.228673
$330$	−0.848516	−0.0467092
$331$	24.1488	1.32734	0.663669	−	0.748026i	$-0.268998\pi$
$331$	24.1488	1.32734	0.663669	+	0.748026i	$0.268998\pi$
$332$	14.7220	0.807973
$333$	−4.45356	−0.244054
$334$	−11.9398	−0.653318
$335$	−10.0744	−0.550423
$336$	−0.302046	−0.0164779
$337$	31.0135	1.68941	0.844707	−	0.535230i	$-0.179775\pi$
$337$	31.0135	1.68941	0.844707	+	0.535230i	$0.179775\pi$
$338$	8.52812	0.463869
$339$	−0.166738	−0.00905594
$340$	−4.04840	−0.219555
$341$	8.60626	0.466055
$342$	14.0287	0.758588
$343$	−1.00000	−0.0539949
$344$	16.0937	0.867716
$345$	−3.41836	−0.184038
$346$	15.9535	0.857664
$347$	0.0306680	0.00164634	0.000823172	−	1.00000i	$-0.499738\pi$
$347$	0.0306680	0.00164634	0.000823172		1.00000i	$0.499738\pi$
$348$	−2.74833	−0.147326
$349$	21.6364	1.15817	0.579085	−	0.815267i	$-0.303410\pi$
$349$	21.6364	1.15817	0.579085	+	0.815267i	$0.303410\pi$
$350$	−0.970097	−0.0518539
$351$	10.8265	0.577874
$352$	−11.4504	−0.610309
$353$	2.83747	0.151023	0.0755117	−	0.997145i	$-0.475941\pi$
$353$	2.83747	0.151023	0.0755117	+	0.997145i	$0.475941\pi$
$354$	−3.33154	−0.177069
$355$	−2.25770	−0.119826
$356$	9.04058	0.479150
$357$	−1.51768	−0.0803241
$358$	5.13211	0.271241
$359$	−33.7911	−1.78342	−0.891712	−	0.452603i	$-0.850495\pi$
$359$	−33.7911	−1.78342	−0.891712	+	0.452603i	$0.850495\pi$
$360$	−8.43470	−0.444548
$361$	6.88405	0.362318
$362$	10.7070	0.562748
$363$	2.43942	0.128037
$364$	4.94309	0.259088
$365$	10.5309	0.551213
$366$	−0.709285	−0.0370749
$367$	6.12803	0.319881	0.159940	−	0.987127i	$-0.448870\pi$
$367$	6.12803	0.319881	0.159940	+	0.987127i	$0.448870\pi$
$368$	6.55207	0.341550
$369$	29.5329	1.53742
$370$	−1.51997	−0.0790194
$371$	1.57645	0.0818450
$372$	−1.64188	−0.0851275
$373$	11.3406	0.587195	0.293597	−	0.955929i	$-0.405148\pi$
$373$	11.3406	0.587195	0.293597	+	0.955929i	$0.405148\pi$
$374$	8.17199	0.422563
$375$	0.396968	0.0204994
$376$	−12.3082	−0.634746
$377$	−30.5205	−1.57189
$378$	−2.24990	−0.115722
$379$	−34.4420	−1.76917	−0.884583	−	0.466383i	$-0.845557\pi$
$379$	−34.4420	−1.76917	−0.884583	+	0.466383i	$0.845557\pi$
$380$	−5.38736	−0.276366
$381$	−1.69028	−0.0865957
$382$	−11.4467	−0.585662
$383$	−36.0412	−1.84162	−0.920810	−	0.390010i	$-0.872471\pi$
$383$	−36.0412	−1.84162	−0.920810	+	0.390010i	$0.872471\pi$
$384$	1.59845	0.0815707
$385$	−2.20338	−0.112294
$386$	6.04115	0.307487
$387$	15.4157	0.783623
$388$	15.7039	0.797247
$389$	30.7369	1.55842	0.779211	−	0.626762i	$-0.215620\pi$
$389$	30.7369	1.55842	0.779211	+	0.626762i	$0.215620\pi$
$390$	1.79767	0.0910285
$391$	32.9219	1.66493
$392$	−2.96744	−0.149878
$393$	3.48343	0.175716
$394$	−6.32705	−0.318752
$395$	−8.74949	−0.440234
$396$	−6.63187	−0.333264
$397$	25.6295	1.28631	0.643153	−	0.765737i	$-0.277626\pi$
$397$	25.6295	1.28631	0.643153	+	0.765737i	$0.277626\pi$
$398$	−0.917377	−0.0459839
$399$	−2.01963	−0.101108
$400$	−0.760881	−0.0380441
$401$	1.76129	0.0879547	0.0439773	−	0.999033i	$-0.485997\pi$
$401$	1.76129	0.0879547	0.0439773	+	0.999033i	$0.485997\pi$
$402$	−3.87963	−0.193498
$403$	−18.2333	−0.908263
$404$	−4.19699	−0.208808
$405$	−7.60658	−0.377974
$406$	6.34262	0.314779
$407$	−3.45230	−0.171124
$408$	−4.50362	−0.222962
$409$	22.9828	1.13643	0.568214	−	0.822881i	$-0.307635\pi$
$409$	22.9828	1.13643	0.568214	+	0.822881i	$0.307635\pi$
$410$	10.0794	0.497784
$411$	0.00243590	0.000120154 0
$412$	8.62898	0.425119
$413$	−8.65116	−0.425696
$414$	23.7446	1.16698
$415$	13.9029	0.682467
$416$	24.2589	1.18939
$417$	3.82607	0.187363
$418$	10.8748	0.531902
$419$	−12.9493	−0.632614	−0.316307	−	0.948657i	$-0.602443\pi$
$419$	−12.9493	−0.632614	−0.316307	+	0.948657i	$0.602443\pi$
$420$	0.420355	0.0205112
$421$	−29.2841	−1.42722	−0.713610	−	0.700543i	$-0.752941\pi$
$421$	−29.2841	−1.42722	−0.713610	+	0.700543i	$0.752941\pi$
$422$	−2.42014	−0.117811
$423$	−11.7896	−0.573231
$424$	4.67801	0.227184
$425$	−3.82317	−0.185451
$426$	−0.869434	−0.0421242
$427$	−1.84183	−0.0891324
$428$	9.63564	0.465756
$429$	4.08304	0.197131
$430$	5.26126	0.253721
$431$	14.3388	0.690675	0.345337	−	0.938479i	$-0.387765\pi$
$431$	14.3388	0.690675	0.345337	+	0.938479i	$0.387765\pi$
$432$	−1.76468	−0.0849031
$433$	5.82467	0.279916	0.139958	−	0.990157i	$-0.455303\pi$
$433$	5.82467	0.279916	0.139958	+	0.990157i	$0.455303\pi$
$434$	3.78914	0.181885
$435$	−2.59543	−0.124441
$436$	−11.8682	−0.568382
$437$	43.8104	2.09574
$438$	4.05543	0.193776
$439$	−33.2124	−1.58514	−0.792570	−	0.609780i	$-0.791258\pi$
$439$	−33.2124	−1.58514	−0.792570	+	0.609780i	$0.791258\pi$
$440$	−6.53839	−0.311706
$441$	−2.84242	−0.135353
$442$	−17.3132	−0.823505
$443$	−16.1169	−0.765738	−0.382869	−	0.923803i	$-0.625064\pi$
$443$	−16.1169	−0.765738	−0.382869	+	0.923803i	$0.625064\pi$
$444$	0.658621	0.0312568
$445$	8.53761	0.404721
$446$	23.2119	1.09912
$447$	−5.28809	−0.250118
$448$	−6.56312	−0.310078
$449$	0.840226	0.0396527	0.0198264	−	0.999803i	$-0.493689\pi$
$449$	0.840226	0.0396527	0.0198264	+	0.999803i	$0.493689\pi$
$450$	−2.75742	−0.129986
$451$	22.8932	1.07800
$452$	−0.444772	−0.0209203
$453$	2.04355	0.0960142
$454$	11.9926	0.562839
$455$	4.66808	0.218843
$456$	−5.99314	−0.280654
$457$	−9.74058	−0.455645	−0.227823	−	0.973703i	$-0.573161\pi$
$457$	−9.74058	−0.455645	−0.227823	+	0.973703i	$0.573161\pi$
$458$	0.970097	0.0453297
$459$	−8.86691	−0.413872
$460$	−9.11846	−0.425150
$461$	−14.7555	−0.687231	−0.343615	−	0.939110i	$-0.611652\pi$
$461$	−14.7555	−0.687231	−0.343615	+	0.939110i	$0.611652\pi$
$462$	−0.848516	−0.0394765
$463$	−17.7643	−0.825577	−0.412788	−	0.910827i	$-0.635445\pi$
$463$	−17.7643	−0.825577	−0.412788	+	0.910827i	$0.635445\pi$
$464$	4.97474	0.230946
$465$	−1.55053	−0.0719043
$466$	−21.3356	−0.988353
$467$	11.1165	0.514410	0.257205	−	0.966357i	$-0.417198\pi$
$467$	11.1165	0.514410	0.257205	+	0.966357i	$0.417198\pi$
$468$	14.0503	0.649476
$469$	−10.0744	−0.465192
$470$	−4.02372	−0.185600
$471$	−3.59678	−0.165731
$472$	−25.6718	−1.18164
$473$	11.9499	0.549456
$474$	−3.36941	−0.154762
$475$	−5.08764	−0.233437
$476$	−4.04840	−0.185558
$477$	4.48092	0.205167
$478$	16.1742	0.739790
$479$	−40.0322	−1.82912	−0.914559	−	0.404452i	$-0.867462\pi$
$479$	−40.0322	−1.82912	−0.914559	+	0.404452i	$0.867462\pi$
$480$	2.06295	0.0941602
$481$	7.31406	0.333492
$482$	5.62034	0.255999
$483$	−3.41836	−0.155541
$484$	6.50715	0.295780
$485$	14.8303	0.673408
$486$	−9.67898	−0.439048
$487$	−16.2358	−0.735716	−0.367858	−	0.929882i	$-0.619909\pi$
$487$	−16.2358	−0.735716	−0.367858	+	0.929882i	$0.619909\pi$
$488$	−5.46552	−0.247413
$489$	0.395442	0.0178825
$490$	−0.970097	−0.0438245
$491$	−22.9333	−1.03497	−0.517483	−	0.855694i	$-0.673131\pi$
$491$	−22.9333	−1.03497	−0.517483	+	0.855694i	$0.673131\pi$
$492$	−4.36751	−0.196903
$493$	24.9964	1.12578
$494$	−23.0393	−1.03659
$495$	−6.26291	−0.281497
$496$	2.97196	0.133445
$497$	−2.25770	−0.101271
$498$	5.35398	0.239918
$499$	17.0699	0.764154	0.382077	−	0.924131i	$-0.375209\pi$
$499$	17.0699	0.764154	0.382077	+	0.924131i	$0.375209\pi$
$500$	1.05891	0.0473560
$501$	4.88584	0.218283
$502$	22.2954	0.995094
$503$	−15.3081	−0.682554	−0.341277	−	0.939963i	$-0.610859\pi$
$503$	−15.3081	−0.682554	−0.341277	+	0.939963i	$0.610859\pi$
$504$	−8.43470	−0.375711
$505$	−3.96350	−0.176373
$506$	18.4062	0.818257
$507$	−3.48975	−0.154985
$508$	−4.50882	−0.200046
$509$	−9.62930	−0.426811	−0.213406	−	0.976964i	$-0.568456\pi$
$509$	−9.62930	−0.426811	−0.213406	+	0.976964i	$0.568456\pi$
$510$	−1.47229	−0.0651943
$511$	10.5309	0.465860
$512$	−8.46985	−0.374318
$513$	−11.7995	−0.520962
$514$	8.76114	0.386437
$515$	8.14891	0.359084
$516$	−2.27977	−0.100361
$517$	−9.13905	−0.401935
$518$	−1.51997	−0.0667836
$519$	−6.52824	−0.286558
$520$	13.8523	0.607462
$521$	3.33359	0.146047	0.0730237	−	0.997330i	$-0.476735\pi$
$521$	3.33359	0.146047	0.0730237	+	0.997330i	$0.476735\pi$
$522$	18.0284	0.789080
$523$	−10.8231	−0.473262	−0.236631	−	0.971600i	$-0.576043\pi$
$523$	−10.8231	−0.473262	−0.236631	+	0.971600i	$0.576043\pi$
$524$	9.29205	0.405925
$525$	0.396968	0.0173251
$526$	−7.18583	−0.313317
$527$	14.9331	0.650495
$528$	−0.665521	−0.0289631
$529$	51.1520	2.22400
$530$	1.52931	0.0664288
$531$	−24.5902	−1.06712
$532$	−5.38736	−0.233572
$533$	−48.5017	−2.10084
$534$	3.28781	0.142278
$535$	9.09956	0.393408
$536$	−29.8952	−1.29127
$537$	−2.10009	−0.0906254
$538$	15.7686	0.679832
$539$	−2.20338	−0.0949061
$540$	2.45589	0.105685
$541$	30.1401	1.29582	0.647911	−	0.761716i	$-0.275643\pi$
$541$	30.1401	1.29582	0.647911	+	0.761716i	$0.275643\pi$
$542$	25.1607	1.08074
$543$	−4.38136	−0.188022
$544$	−19.8681	−0.851837
$545$	−11.2079	−0.480093
$546$	1.79767	0.0769331
$547$	−22.9241	−0.980166	−0.490083	−	0.871676i	$-0.663033\pi$
$547$	−22.9241	−0.980166	−0.490083	+	0.871676i	$0.663033\pi$
$548$	0.00649776	0.000277571 0
$549$	−5.23525	−0.223435
$550$	−2.13749	−0.0911428
$551$	33.2636	1.41708
$552$	−10.1438	−0.431748
$553$	−8.74949	−0.372066
$554$	−7.21937	−0.306722
$555$	0.621979	0.0264015
$556$	10.2060	0.432832
$557$	9.20116	0.389866	0.194933	−	0.980817i	$-0.437551\pi$
$557$	9.20116	0.389866	0.194933	+	0.980817i	$0.437551\pi$
$558$	10.7703	0.455944
$559$	−25.3171	−1.07080
$560$	−0.760881	−0.0321531
$561$	−3.34402	−0.141184
$562$	−17.2942	−0.729511
$563$	−21.4310	−0.903207	−0.451604	−	0.892219i	$-0.649148\pi$
$563$	−21.4310	−0.903207	−0.451604	+	0.892219i	$0.649148\pi$
$564$	1.74352	0.0734156
$565$	−0.420027	−0.0176707
$566$	11.0446	0.464237
$567$	−7.60658	−0.319446
$568$	−6.69958	−0.281108
$569$	4.44920	0.186520	0.0932600	−	0.995642i	$-0.470271\pi$
$569$	4.44920	0.186520	0.0932600	+	0.995642i	$0.470271\pi$
$570$	−1.95924	−0.0820634
$571$	−42.8836	−1.79462	−0.897312	−	0.441397i	$-0.854483\pi$
$571$	−42.8836	−1.79462	−0.897312	+	0.441397i	$0.854483\pi$
$572$	10.8915	0.455396
$573$	4.68403	0.195678
$574$	10.0794	0.420704
$575$	−8.61116	−0.359110
$576$	−18.6551	−0.777296
$577$	−35.9822	−1.49796	−0.748979	−	0.662594i	$-0.769455\pi$
$577$	−35.9822	−1.49796	−0.748979	+	0.662594i	$0.769455\pi$
$578$	−2.31209	−0.0961703
$579$	−2.47207	−0.102736
$580$	−6.92330	−0.287474
$581$	13.9029	0.576790
$582$	5.71110	0.236733
$583$	3.47350	0.143858
$584$	31.2499	1.29313
$585$	13.2686	0.548590
$586$	−14.1643	−0.585124
$587$	−3.77637	−0.155867	−0.0779337	−	0.996959i	$-0.524832\pi$
$587$	−3.77637	−0.155867	−0.0779337	+	0.996959i	$0.524832\pi$
$588$	0.420355	0.0173351
$589$	19.8720	0.818812
$590$	−8.39246	−0.345512
$591$	2.58906	0.106500
$592$	−1.19217	−0.0489977
$593$	−47.9537	−1.96922	−0.984612	−	0.174755i	$-0.944087\pi$
$593$	−47.9537	−1.96922	−0.984612	+	0.174755i	$0.944087\pi$
$594$	−4.95738	−0.203404
$595$	−3.82317	−0.156735
$596$	−14.1060	−0.577803
$597$	0.375395	0.0153639
$598$	−38.9956	−1.59465
$599$	8.62497	0.352407	0.176203	−	0.984354i	$-0.443618\pi$
$599$	8.62497	0.352407	0.176203	+	0.984354i	$0.443618\pi$
$600$	1.17798	0.0480908
$601$	−25.0778	−1.02294	−0.511471	−	0.859300i	$-0.670899\pi$
$601$	−25.0778	−1.02294	−0.511471	+	0.859300i	$0.670899\pi$
$602$	5.26126	0.214433
$603$	−28.6356	−1.16613
$604$	5.45115	0.221804
$605$	6.14513	0.249835
$606$	−1.52633	−0.0620031
$607$	22.0772	0.896088	0.448044	−	0.894012i	$-0.352121\pi$
$607$	22.0772	0.896088	0.448044	+	0.894012i	$0.352121\pi$
$608$	−26.4392	−1.07225
$609$	−2.59543	−0.105172
$610$	−1.78675	−0.0723436
$611$	19.3620	0.783304
$612$	−11.5072	−0.465153
$613$	22.9679	0.927664	0.463832	−	0.885923i	$-0.346474\pi$
$613$	22.9679	0.927664	0.463832	+	0.885923i	$0.346474\pi$
$614$	3.95146	0.159468
$615$	−4.12452	−0.166317
$616$	−6.53839	−0.263439
$617$	−42.8701	−1.72589	−0.862943	−	0.505301i	$-0.831381\pi$
$617$	−42.8701	−1.72589	−0.862943	+	0.505301i	$0.831381\pi$
$618$	3.13813	0.126234
$619$	−8.22940	−0.330767	−0.165384	−	0.986229i	$-0.552886\pi$
$619$	−8.22940	−0.330767	−0.165384	+	0.986229i	$0.552886\pi$
$620$	−4.13605	−0.166108
$621$	−19.9715	−0.801427
$622$	6.54058	0.262253
$623$	8.53761	0.342052
$624$	1.40997	0.0564442
$625$	1.00000	0.0400000
$626$	4.73566	0.189275
$627$	−4.45001	−0.177716
$628$	−9.59441	−0.382859
$629$	−5.99023	−0.238846
$630$	−2.75742	−0.109858
$631$	6.97229	0.277562	0.138781	−	0.990323i	$-0.455682\pi$
$631$	6.97229	0.277562	0.138781	+	0.990323i	$0.455682\pi$
$632$	−25.9636	−1.03278
$633$	0.990333	0.0393622
$634$	25.3461	1.00662
$635$	−4.25797	−0.168972
$636$	−0.662666	−0.0262764
$637$	4.66808	0.184956
$638$	13.9752	0.553282
$639$	−6.41731	−0.253865
$640$	4.02665	0.159167
$641$	20.5071	0.809980	0.404990	−	0.914321i	$-0.367275\pi$
$641$	20.5071	0.809980	0.404990	+	0.914321i	$0.367275\pi$
$642$	3.50422	0.138301
$643$	8.28256	0.326632	0.163316	−	0.986574i	$-0.447781\pi$
$643$	8.28256	0.326632	0.163316	+	0.986574i	$0.447781\pi$
$644$	−9.11846	−0.359317
$645$	−2.15293	−0.0847717
$646$	18.8693	0.742401
$647$	13.7628	0.541073	0.270536	−	0.962710i	$-0.412799\pi$
$647$	13.7628	0.541073	0.270536	+	0.962710i	$0.412799\pi$
$648$	−22.5721	−0.886715
$649$	−19.0618	−0.748239
$650$	4.52849	0.177622
$651$	−1.55053	−0.0607702
$652$	1.05484	0.0413107
$653$	−15.1249	−0.591882	−0.295941	−	0.955206i	$-0.595633\pi$
$653$	−15.1249	−0.591882	−0.295941	+	0.955206i	$0.595633\pi$
$654$	−4.31613	−0.168774
$655$	8.77509	0.342871
$656$	7.90560	0.308662
$657$	29.9333	1.16781
$658$	−4.02372	−0.156861
$659$	−13.4571	−0.524216	−0.262108	−	0.965039i	$-0.584418\pi$
$659$	−13.4571	−0.524216	−0.262108	+	0.965039i	$0.584418\pi$
$660$	0.926200	0.0360523
$661$	−36.1753	−1.40706	−0.703528	−	0.710667i	$-0.748393\pi$
$661$	−36.1753	−1.40706	−0.703528	+	0.710667i	$0.748393\pi$
$662$	23.4267	0.910504
$663$	7.08465	0.275145
$664$	41.2561	1.60105
$665$	−5.08764	−0.197290
$666$	−4.32039	−0.167412
$667$	56.3008	2.17998
$668$	13.0330	0.504260
$669$	−9.49843	−0.367230
$670$	−9.77314	−0.377569
$671$	−4.05825	−0.156667
$672$	2.06295	0.0795799
$673$	−33.6626	−1.29760	−0.648799	−	0.760959i	$-0.724729\pi$
$673$	−33.6626	−1.29760	−0.648799	+	0.760959i	$0.724729\pi$
$674$	30.0861	1.15887
$675$	2.31925	0.0892682
$676$	−9.30889	−0.358034
$677$	−11.3713	−0.437033	−0.218517	−	0.975833i	$-0.570122\pi$
$677$	−11.3713	−0.437033	−0.218517	+	0.975833i	$0.570122\pi$
$678$	−0.161752	−0.00621203
$679$	14.8303	0.569133
$680$	−11.3450	−0.435062
$681$	−4.90741	−0.188052
$682$	8.34890	0.319696
$683$	−11.6951	−0.447502	−0.223751	−	0.974646i	$-0.571830\pi$
$683$	−11.6951	−0.447502	−0.223751	+	0.974646i	$0.571830\pi$
$684$	−15.3131	−0.585512
$685$	0.00613626	0.000234455 0
$686$	−0.970097	−0.0370385
$687$	−0.396968	−0.0151453
$688$	4.12659	0.157325
$689$	−7.35898	−0.280355
$690$	−3.31614	−0.126243
$691$	−27.1242	−1.03185	−0.515927	−	0.856632i	$-0.672552\pi$
$691$	−27.1242	−1.03185	−0.515927	+	0.856632i	$0.672552\pi$
$692$	−17.4141	−0.661983
$693$	−6.26291	−0.237908
$694$	0.0297509	0.00112933
$695$	9.63822	0.365599
$696$	−7.70179	−0.291935
$697$	39.7230	1.50461
$698$	20.9894	0.794461
$699$	8.73064	0.330223
$700$	1.05891	0.0400231
$701$	28.6667	1.08272	0.541362	−	0.840789i	$-0.317909\pi$
$701$	28.6667	1.08272	0.541362	+	0.840789i	$0.317909\pi$
$702$	10.5027	0.396400
$703$	−7.97142	−0.300648
$704$	−14.4610	−0.545020
$705$	1.64652	0.0620117
$706$	2.75262	0.103596
$707$	−3.96350	−0.149063
$708$	3.63655	0.136670
$709$	−28.2128	−1.05955	−0.529776	−	0.848137i	$-0.677724\pi$
$709$	−28.2128	−1.05955	−0.529776	+	0.848137i	$0.677724\pi$
$710$	−2.19018	−0.0821961
$711$	−24.8697	−0.932686
$712$	25.3349	0.949464
$713$	33.6347	1.25963
$714$	−1.47229	−0.0550993
$715$	10.2855	0.384658
$716$	−5.60197	−0.209356
$717$	−6.61856	−0.247175
$718$	−32.7806	−1.22336
$719$	−9.99293	−0.372674	−0.186337	−	0.982486i	$-0.559662\pi$
$719$	−9.99293	−0.372674	−0.186337	+	0.982486i	$0.559662\pi$
$720$	−2.16274	−0.0806006
$721$	8.14891	0.303481
$722$	6.67819	0.248537
$723$	−2.29987	−0.0855331
$724$	−11.6873	−0.434354
$725$	−6.53813	−0.242820
$726$	2.36648	0.0878282
$727$	20.9421	0.776699	0.388350	−	0.921512i	$-0.373045\pi$
$727$	20.9421	0.776699	0.388350	+	0.921512i	$0.373045\pi$
$728$	13.8523	0.513399
$729$	−18.8590	−0.698483
$730$	10.2160	0.378112
$731$	20.7347	0.766902
$732$	0.774222	0.0286161
$733$	21.0024	0.775740	0.387870	−	0.921714i	$-0.373211\pi$
$733$	21.0024	0.775740	0.387870	+	0.921714i	$0.373211\pi$
$734$	5.94478	0.219426
$735$	0.396968	0.0146424
$736$	−44.7501	−1.64951
$737$	−22.1977	−0.817662
$738$	28.6497	1.05461
$739$	14.8485	0.546210	0.273105	−	0.961984i	$-0.411949\pi$
$739$	14.8485	0.546210	0.273105	+	0.961984i	$0.411949\pi$
$740$	1.65913	0.0609907
$741$	9.42781	0.346339
$742$	1.52931	0.0561426
$743$	−33.9274	−1.24468	−0.622338	−	0.782749i	$-0.713817\pi$
$743$	−33.9274	−1.24468	−0.622338	+	0.782749i	$0.713817\pi$
$744$	−4.60112	−0.168685
$745$	−13.3212	−0.488050
$746$	11.0015	0.402793
$747$	39.5179	1.44588
$748$	−8.92015	−0.326153
$749$	9.09956	0.332491
$750$	0.385098	0.0140618
$751$	−43.6902	−1.59428	−0.797139	−	0.603795i	$-0.793654\pi$
$751$	−43.6902	−1.59428	−0.797139	+	0.603795i	$0.793654\pi$
$752$	−3.15594	−0.115085
$753$	−9.12341	−0.332475
$754$	−29.6079	−1.07825
$755$	5.14788	0.187351
$756$	2.45589	0.0893197
$757$	15.9082	0.578194	0.289097	−	0.957300i	$-0.406645\pi$
$757$	15.9082	0.578194	0.289097	+	0.957300i	$0.406645\pi$
$758$	−33.4121	−1.21358
$759$	−7.53193	−0.273392
$760$	−15.0973	−0.547635
$761$	−16.0488	−0.581768	−0.290884	−	0.956758i	$-0.593949\pi$
$761$	−16.0488	−0.581768	−0.290884	+	0.956758i	$0.593949\pi$
$762$	−1.63974	−0.0594014
$763$	−11.2079	−0.405752
$764$	12.4946	0.452040
$765$	−10.8670	−0.392899
$766$	−34.9635	−1.26328
$767$	40.3843	1.45819
$768$	6.76135	0.243979
$769$	−43.2353	−1.55911	−0.779553	−	0.626337i	$-0.784554\pi$
$769$	−43.2353	−1.55911	−0.779553	+	0.626337i	$0.784554\pi$
$770$	−2.13749	−0.0770297
$771$	−3.58510	−0.129114
$772$	−6.59424	−0.237332
$773$	−4.00538	−0.144064	−0.0720318	−	0.997402i	$-0.522948\pi$
$773$	−4.00538	−0.144064	−0.0720318	+	0.997402i	$0.522948\pi$
$774$	14.9547	0.537535
$775$	−3.90594	−0.140305
$776$	44.0079	1.57979
$777$	0.621979	0.0223134
$778$	29.8177	1.06902
$779$	52.8608	1.89394
$780$	−1.96225	−0.0702598
$781$	−4.97455	−0.178004
$782$	31.9375	1.14208
$783$	−15.1636	−0.541902
$784$	−0.760881	−0.0271743
$785$	−9.06063	−0.323388
$786$	3.37927	0.120534
$787$	38.6808	1.37882	0.689411	−	0.724370i	$-0.257869\pi$
$787$	38.6808	1.37882	0.689411	+	0.724370i	$0.257869\pi$
$788$	6.90631	0.246027
$789$	2.94048	0.104684
$790$	−8.48785	−0.301984
$791$	−0.420027	−0.0149345
$792$	−18.5848	−0.660383
$793$	8.59782	0.305318
$794$	24.8631	0.882358
$795$	−0.625799	−0.0221948
$796$	1.00137	0.0354925
$797$	0.586778	0.0207847	0.0103924	−	0.999946i	$-0.496692\pi$
$797$	0.586778	0.0207847	0.0103924	+	0.999946i	$0.496692\pi$
$798$	−1.95924	−0.0693563
$799$	−15.8575	−0.561000
$800$	5.19675	0.183733
$801$	24.2674	0.857448
$802$	1.70862	0.0603336
$803$	23.2036	0.818837
$804$	4.23482	0.149351
$805$	−8.61116	−0.303503
$806$	−17.6880	−0.623034
$807$	−6.45258	−0.227142
$808$	−11.7614	−0.413766
$809$	−43.0287	−1.51281	−0.756404	−	0.654104i	$-0.773046\pi$
$809$	−43.0287	−1.51281	−0.756404	+	0.654104i	$0.773046\pi$
$810$	−7.37912	−0.259276
$811$	−42.8131	−1.50337	−0.751686	−	0.659521i	$-0.770759\pi$
$811$	−42.8131	−1.50337	−0.751686	+	0.659521i	$0.770759\pi$
$812$	−6.92330	−0.242960
$813$	−10.2959	−0.361092
$814$	−3.34906	−0.117385
$815$	0.996155	0.0348938
$816$	−1.15477	−0.0404251
$817$	27.5925	0.965339
$818$	22.2956	0.779546
$819$	13.2686	0.463644
$820$	−11.0022	−0.384212
$821$	35.5694	1.24138	0.620690	−	0.784056i	$-0.286852\pi$
$821$	35.5694	1.24138	0.620690	+	0.784056i	$0.286852\pi$
$822$	0.00236306	8.24213e−5 0
$823$	−9.24595	−0.322293	−0.161147	−	0.986930i	$-0.551519\pi$
$823$	−9.24595	−0.322293	−0.161147	+	0.986930i	$0.551519\pi$
$824$	24.1814	0.842400
$825$	0.874671	0.0304521
$826$	−8.39246	−0.292011
$827$	21.7702	0.757025	0.378513	−	0.925596i	$-0.376436\pi$
$827$	21.7702	0.757025	0.378513	+	0.925596i	$0.376436\pi$
$828$	−25.9184	−0.900728
$829$	32.8043	1.13934	0.569671	−	0.821873i	$-0.307071\pi$
$829$	32.8043	1.13934	0.569671	+	0.821873i	$0.307071\pi$
$830$	13.4872	0.468147
$831$	2.95420	0.102480
$832$	30.6372	1.06215
$833$	−3.82317	−0.132465
$834$	3.71166	0.128524
$835$	12.3079	0.425932
$836$	−11.8704	−0.410546
$837$	−9.05887	−0.313120
$838$	−12.5621	−0.433949
$839$	21.9111	0.756456	0.378228	−	0.925712i	$-0.376534\pi$
$839$	21.9111	0.756456	0.378228	+	0.925712i	$0.376534\pi$
$840$	1.17798	0.0406442
$841$	13.7471	0.474039
$842$	−28.4084	−0.979019
$843$	7.07687	0.243740
$844$	2.64171	0.0909314
$845$	−8.79100	−0.302420
$846$	−11.4371	−0.393215
$847$	6.14513	0.211149
$848$	1.19949	0.0411906
$849$	−4.51949	−0.155108
$850$	−3.70885	−0.127212
$851$	−13.4921	−0.462505
$852$	0.949033	0.0325133
$853$	27.1671	0.930183	0.465091	−	0.885263i	$-0.346021\pi$
$853$	27.1671	0.930183	0.465091	+	0.885263i	$0.346021\pi$
$854$	−1.78675	−0.0611415
$855$	−14.4612	−0.494562
$856$	27.0024	0.922924
$857$	46.1986	1.57812	0.789058	−	0.614319i	$-0.210569\pi$
$857$	46.1986	1.57812	0.789058	+	0.614319i	$0.210569\pi$
$858$	3.96094	0.135224
$859$	−11.6704	−0.398190	−0.199095	−	0.979980i	$-0.563800\pi$
$859$	−11.6704	−0.398190	−0.199095	+	0.979980i	$0.563800\pi$
$860$	−5.74294	−0.195833
$861$	−4.12452	−0.140563
$862$	13.9100	0.473777
$863$	15.2359	0.518635	0.259317	−	0.965792i	$-0.416502\pi$
$863$	15.2359	0.518635	0.259317	+	0.965792i	$0.416502\pi$
$864$	12.0526	0.410038
$865$	−16.4452	−0.559155
$866$	5.65050	0.192012
$867$	0.946119	0.0321319
$868$	−4.13605	−0.140387
$869$	−19.2784	−0.653975
$870$	−2.51782	−0.0853621
$871$	47.0281	1.59349
$872$	−33.2587	−1.12628
$873$	42.1538	1.42669
$874$	42.5004	1.43760
$875$	1.00000	0.0338062
$876$	−4.42672	−0.149565
$877$	−7.57101	−0.255655	−0.127827	−	0.991796i	$-0.540800\pi$
$877$	−7.57101	−0.255655	−0.127827	+	0.991796i	$0.540800\pi$
$878$	−32.2192	−1.08735
$879$	5.79612	0.195498
$880$	−1.67651	−0.0565151
$881$	−2.47954	−0.0835379	−0.0417689	−	0.999127i	$-0.513299\pi$
$881$	−2.47954	−0.0835379	−0.0417689	+	0.999127i	$0.513299\pi$
$882$	−2.75742	−0.0928471
$883$	−31.3125	−1.05375	−0.526874	−	0.849943i	$-0.676636\pi$
$883$	−31.3125	−1.05375	−0.526874	+	0.849943i	$0.676636\pi$
$884$	18.8983	0.635618
$885$	3.43424	0.115441
$886$	−15.6350	−0.525267
$887$	2.61870	0.0879272	0.0439636	−	0.999033i	$-0.486001\pi$
$887$	2.61870	0.0879272	0.0439636	+	0.999033i	$0.486001\pi$
$888$	1.84569	0.0619372
$889$	−4.25797	−0.142808
$890$	8.28231	0.277624
$891$	−16.7602	−0.561486
$892$	−25.3370	−0.848346
$893$	−21.1022	−0.706159
$894$	−5.12996	−0.171571
$895$	−5.29031	−0.176836
$896$	4.02665	0.134521
$897$	15.9572	0.532794
$898$	0.815101	0.0272003
$899$	25.5375	0.851724
$900$	3.00987	0.100329
$901$	6.02702	0.200789
$902$	22.2086	0.739467
$903$	−2.15293	−0.0716452
$904$	−1.24641	−0.0414549
$905$	−11.0371	−0.366884
$906$	1.98244	0.0658621
$907$	−2.40941	−0.0800032	−0.0400016	−	0.999200i	$-0.512736\pi$
$907$	−2.40941	−0.0800032	−0.0400016	+	0.999200i	$0.512736\pi$
$908$	−13.0905	−0.434424
$909$	−11.2659	−0.373666
$910$	4.52849	0.150118
$911$	12.5161	0.414676	0.207338	−	0.978269i	$-0.433520\pi$
$911$	12.5161	0.414676	0.207338	+	0.978269i	$0.433520\pi$
$912$	−1.53670	−0.0508852
$913$	30.6334	1.01382
$914$	−9.44931	−0.312555
$915$	0.731149	0.0241710
$916$	−1.05891	−0.0349874
$917$	8.77509	0.289779
$918$	−8.60176	−0.283900
$919$	−5.20958	−0.171848	−0.0859242	−	0.996302i	$-0.527384\pi$
$919$	−5.20958	−0.171848	−0.0859242	+	0.996302i	$0.527384\pi$
$920$	−25.5531	−0.842461
$921$	−1.61696	−0.0532805
$922$	−14.3142	−0.471414
$923$	10.5391	0.346899
$924$	0.926200	0.0304697
$925$	1.56682	0.0515168
$926$	−17.2331	−0.566314
$927$	23.1626	0.760760
$928$	−33.9770	−1.11535
$929$	41.4038	1.35841	0.679207	−	0.733947i	$-0.262324\pi$
$929$	41.4038	1.35841	0.679207	+	0.733947i	$0.262324\pi$
$930$	−1.50417	−0.0493236
$931$	−5.08764	−0.166741
$932$	23.2890	0.762855
$933$	−2.67644	−0.0876226
$934$	10.7841	0.352866
$935$	−8.42389	−0.275491
$936$	39.3739	1.28698
$937$	13.0517	0.426379	0.213190	−	0.977011i	$-0.431615\pi$
$937$	13.0517	0.426379	0.213190	+	0.977011i	$0.431615\pi$
$938$	−9.77314	−0.319104
$939$	−1.93785	−0.0632395
$940$	4.39210	0.143254
$941$	−43.4066	−1.41501	−0.707507	−	0.706706i	$-0.750180\pi$
$941$	−43.4066	−1.41501	−0.707507	+	0.706706i	$0.750180\pi$
$942$	−3.48923	−0.113685
$943$	89.4704	2.91356
$944$	−6.58250	−0.214242
$945$	2.31925	0.0754454
$946$	11.5925	0.376906
$947$	45.7348	1.48618	0.743091	−	0.669191i	$-0.233359\pi$
$947$	45.7348	1.48618	0.743091	+	0.669191i	$0.233359\pi$
$948$	3.67789	0.119452
$949$	−49.1592	−1.59578
$950$	−4.93550	−0.160129
$951$	−10.3717	−0.336326
$952$	−11.3450	−0.367695
$953$	−36.0278	−1.16706	−0.583528	−	0.812093i	$-0.698328\pi$
$953$	−36.0278	−1.16706	−0.583528	+	0.812093i	$0.698328\pi$
$954$	4.34692	0.140737
$955$	11.7995	0.381823
$956$	−17.6550	−0.571003
$957$	−5.71871	−0.184860
$958$	−38.8351	−1.25471
$959$	0.00613626	0.000198150 0
$960$	2.60535	0.0840873
$961$	−15.7436	−0.507859
$962$	7.09534	0.228763
$963$	25.8647	0.833480
$964$	−6.13490	−0.197592
$965$	−6.22737	−0.200466
$966$	−3.31614	−0.106695
$967$	−31.8922	−1.02558	−0.512792	−	0.858513i	$-0.671389\pi$
$967$	−31.8922	−1.02558	−0.512792	+	0.858513i	$0.671389\pi$
$968$	18.2353	0.586105
$969$	−7.72140	−0.248047
$970$	14.3868	0.461932
$971$	39.9911	1.28338	0.641688	−	0.766966i	$-0.278234\pi$
$971$	39.9911	1.28338	0.641688	+	0.766966i	$0.278234\pi$
$972$	10.5651	0.338876
$973$	9.63822	0.308987
$974$	−15.7503	−0.504674
$975$	−1.85308	−0.0593461
$976$	−1.40141	−0.0448582
$977$	26.3668	0.843549	0.421774	−	0.906701i	$-0.361407\pi$
$977$	26.3668	0.843549	0.421774	+	0.906701i	$0.361407\pi$
$978$	0.383617	0.0122667
$979$	18.8116	0.601220
$980$	1.05891	0.0338257
$981$	−31.8574	−1.01713
$982$	−22.2475	−0.709947
$983$	6.84062	0.218182	0.109091	−	0.994032i	$-0.465206\pi$
$983$	6.84062	0.218182	0.109091	+	0.994032i	$0.465206\pi$
$984$	−12.2393	−0.390174
$985$	6.52208	0.207811
$986$	24.2489	0.772243
$987$	1.64652	0.0524094
$988$	25.1486	0.800085
$989$	46.7021	1.48504
$990$	−6.07563	−0.193096
$991$	−10.4466	−0.331847	−0.165924	−	0.986139i	$-0.553061\pi$
$991$	−10.4466	−0.331847	−0.165924	+	0.986139i	$0.553061\pi$
$992$	−20.2982	−0.644469
$993$	−9.58632	−0.304213
$994$	−2.19018	−0.0694684
$995$	0.945655	0.0299793
$996$	−5.84415	−0.185179
$997$	−33.4358	−1.05892	−0.529461	−	0.848334i	$-0.677606\pi$
$997$	−33.4358	−1.05892	−0.529461	+	0.848334i	$0.677606\pi$
$998$	16.5595	0.524180
$999$	3.63386	0.114970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.40	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.40	✓	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)

\(f(q)\)	\(=\)	\(q+0.970097 q^{2} -0.396968 q^{3} -1.05891 q^{4} -1.00000 q^{5} -0.385098 q^{6} -1.00000 q^{7} -2.96744 q^{8} -2.84242 q^{9} +O(q^{10})\)	\(q+0.970097 q^{2} -0.396968 q^{3} -1.05891 q^{4} -1.00000 q^{5} -0.385098 q^{6} -1.00000 q^{7} -2.96744 q^{8} -2.84242 q^{9} -0.970097 q^{10} -2.20338 q^{11} +0.420355 q^{12} +4.66808 q^{13} -0.970097 q^{14} +0.396968 q^{15} -0.760881 q^{16} -3.82317 q^{17} -2.75742 q^{18} -5.08764 q^{19} +1.05891 q^{20} +0.396968 q^{21} -2.13749 q^{22} -8.61116 q^{23} +1.17798 q^{24} +1.00000 q^{25} +4.52849 q^{26} +2.31925 q^{27} +1.05891 q^{28} -6.53813 q^{29} +0.385098 q^{30} -3.90594 q^{31} +5.19675 q^{32} +0.874671 q^{33} -3.70885 q^{34} +1.00000 q^{35} +3.00987 q^{36} +1.56682 q^{37} -4.93550 q^{38} -1.85308 q^{39} +2.96744 q^{40} -10.3901 q^{41} +0.385098 q^{42} -5.42344 q^{43} +2.33318 q^{44} +2.84242 q^{45} -8.35365 q^{46} +4.14775 q^{47} +0.302046 q^{48} +1.00000 q^{49} +0.970097 q^{50} +1.51768 q^{51} -4.94309 q^{52} -1.57645 q^{53} +2.24990 q^{54} +2.20338 q^{55} +2.96744 q^{56} +2.01963 q^{57} -6.34262 q^{58} +8.65116 q^{59} -0.420355 q^{60} +1.84183 q^{61} -3.78914 q^{62} +2.84242 q^{63} +6.56312 q^{64} -4.66808 q^{65} +0.848516 q^{66} +10.0744 q^{67} +4.04840 q^{68} +3.41836 q^{69} +0.970097 q^{70} +2.25770 q^{71} +8.43470 q^{72} -10.5309 q^{73} +1.51997 q^{74} -0.396968 q^{75} +5.38736 q^{76} +2.20338 q^{77} -1.79767 q^{78} +8.74949 q^{79} +0.760881 q^{80} +7.60658 q^{81} -10.0794 q^{82} -13.9029 q^{83} -0.420355 q^{84} +3.82317 q^{85} -5.26126 q^{86} +2.59543 q^{87} +6.53839 q^{88} -8.53761 q^{89} +2.75742 q^{90} -4.66808 q^{91} +9.11846 q^{92} +1.55053 q^{93} +4.02372 q^{94} +5.08764 q^{95} -2.06295 q^{96} -14.8303 q^{97} +0.970097 q^{98} +6.26291 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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