LMFDB - Embedded newform 8015.2.a.l.1.55

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			1.55
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)

$f(q)$	$=$	$q+2.36805 q^{2} -2.00963 q^{3} +3.60764 q^{4} -1.00000 q^{5} -4.75889 q^{6} -1.00000 q^{7} +3.80696 q^{8} +1.03861 q^{9} +O(q^{10})$	\(q+2.36805 q^{2} -2.00963 q^{3} +3.60764 q^{4} -1.00000 q^{5} -4.75889 q^{6} -1.00000 q^{7} +3.80696 q^{8} +1.03861 q^{9} -2.36805 q^{10} -4.69124 q^{11} -7.25001 q^{12} -0.376745 q^{13} -2.36805 q^{14} +2.00963 q^{15} +1.79977 q^{16} -6.64858 q^{17} +2.45947 q^{18} +6.10646 q^{19} -3.60764 q^{20} +2.00963 q^{21} -11.1091 q^{22} -7.22433 q^{23} -7.65057 q^{24} +1.00000 q^{25} -0.892148 q^{26} +3.94167 q^{27} -3.60764 q^{28} +4.12509 q^{29} +4.75889 q^{30} -5.11724 q^{31} -3.35197 q^{32} +9.42765 q^{33} -15.7441 q^{34} +1.00000 q^{35} +3.74692 q^{36} +6.31706 q^{37} +14.4604 q^{38} +0.757117 q^{39} -3.80696 q^{40} +1.38450 q^{41} +4.75889 q^{42} +3.57663 q^{43} -16.9243 q^{44} -1.03861 q^{45} -17.1075 q^{46} +9.57906 q^{47} -3.61687 q^{48} +1.00000 q^{49} +2.36805 q^{50} +13.3612 q^{51} -1.35916 q^{52} -2.34354 q^{53} +9.33406 q^{54} +4.69124 q^{55} -3.80696 q^{56} -12.2717 q^{57} +9.76840 q^{58} +10.2410 q^{59} +7.25001 q^{60} +1.00073 q^{61} -12.1179 q^{62} -1.03861 q^{63} -11.5372 q^{64} +0.376745 q^{65} +22.3251 q^{66} +0.542699 q^{67} -23.9857 q^{68} +14.5182 q^{69} +2.36805 q^{70} -14.9311 q^{71} +3.95393 q^{72} +15.6290 q^{73} +14.9591 q^{74} -2.00963 q^{75} +22.0299 q^{76} +4.69124 q^{77} +1.79289 q^{78} -6.35712 q^{79} -1.79977 q^{80} -11.0371 q^{81} +3.27855 q^{82} +14.3897 q^{83} +7.25001 q^{84} +6.64858 q^{85} +8.46961 q^{86} -8.28990 q^{87} -17.8594 q^{88} +6.09510 q^{89} -2.45947 q^{90} +0.376745 q^{91} -26.0628 q^{92} +10.2838 q^{93} +22.6836 q^{94} -6.10646 q^{95} +6.73622 q^{96} -15.5793 q^{97} +2.36805 q^{98} -4.87235 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.36805	1.67446	0.837230	−	0.546850i	$-0.184173\pi$
$2$	2.36805	1.67446	0.837230	+	0.546850i	$0.184173\pi$
$3$	−2.00963	−1.16026	−0.580130	−	0.814524i	$-0.696998\pi$
$3$	−2.00963	−1.16026	−0.580130	+	0.814524i	$0.696998\pi$
$4$	3.60764	1.80382
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.75889	−1.94281
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.80696	1.34596
$9$	1.03861	0.346202
$10$	−2.36805	−0.748842
$11$	−4.69124	−1.41446	−0.707231	−	0.706982i	$-0.750056\pi$
$11$	−4.69124	−1.41446	−0.707231	+	0.706982i	$0.750056\pi$
$12$	−7.25001	−2.09290
$13$	−0.376745	−0.104490	−0.0522451	−	0.998634i	$-0.516638\pi$
$13$	−0.376745	−0.104490	−0.0522451	+	0.998634i	$0.516638\pi$
$14$	−2.36805	−0.632887
$15$	2.00963	0.518884
$16$	1.79977	0.449943
$17$	−6.64858	−1.61252	−0.806259	−	0.591563i	$-0.798511\pi$
$17$	−6.64858	−1.61252	−0.806259	+	0.591563i	$0.798511\pi$
$18$	2.45947	0.579702
$19$	6.10646	1.40092	0.700458	−	0.713693i	$-0.252979\pi$
$19$	6.10646	1.40092	0.700458	+	0.713693i	$0.252979\pi$
$20$	−3.60764	−0.806692
$21$	2.00963	0.438537
$22$	−11.1091	−2.36846
$23$	−7.22433	−1.50638	−0.753189	−	0.657804i	$-0.771485\pi$
$23$	−7.22433	−1.50638	−0.753189	+	0.657804i	$0.771485\pi$
$24$	−7.65057	−1.56167
$25$	1.00000	0.200000
$26$	−0.892148	−0.174965
$27$	3.94167	0.758575
$28$	−3.60764	−0.681779
$29$	4.12509	0.766010	0.383005	−	0.923746i	$-0.374889\pi$
$29$	4.12509	0.766010	0.383005	+	0.923746i	$0.374889\pi$
$30$	4.75889	0.868851
$31$	−5.11724	−0.919084	−0.459542	−	0.888156i	$-0.651986\pi$
$31$	−5.11724	−0.919084	−0.459542	+	0.888156i	$0.651986\pi$
$32$	−3.35197	−0.592551
$33$	9.42765	1.64114
$34$	−15.7441	−2.70010
$35$	1.00000	0.169031
$36$	3.74692	0.624486
$37$	6.31706	1.03852	0.519259	−	0.854617i	$-0.326208\pi$
$37$	6.31706	1.03852	0.519259	+	0.854617i	$0.326208\pi$
$38$	14.4604	2.34578
$39$	0.757117	0.121236
$40$	−3.80696	−0.601933
$41$	1.38450	0.216222	0.108111	−	0.994139i	$-0.465520\pi$
$41$	1.38450	0.216222	0.108111	+	0.994139i	$0.465520\pi$
$42$	4.75889	0.734313
$43$	3.57663	0.545430	0.272715	−	0.962095i	$-0.412078\pi$
$43$	3.57663	0.545430	0.272715	+	0.962095i	$0.412078\pi$
$44$	−16.9243	−2.55143
$45$	−1.03861	−0.154826
$46$	−17.1075	−2.52237
$47$	9.57906	1.39725	0.698625	−	0.715488i	$-0.253796\pi$
$47$	9.57906	1.39725	0.698625	+	0.715488i	$0.253796\pi$
$48$	−3.61687	−0.522051
$49$	1.00000	0.142857
$50$	2.36805	0.334892
$51$	13.3612	1.87094
$52$	−1.35916	−0.188481
$53$	−2.34354	−0.321909	−0.160955	−	0.986962i	$-0.551457\pi$
$53$	−2.34354	−0.321909	−0.160955	+	0.986962i	$0.551457\pi$
$54$	9.33406	1.27020
$55$	4.69124	0.632567
$56$	−3.80696	−0.508726
$57$	−12.2717	−1.62543
$58$	9.76840	1.28265
$59$	10.2410	1.33326	0.666632	−	0.745387i	$-0.267735\pi$
$59$	10.2410	1.33326	0.666632	+	0.745387i	$0.267735\pi$
$60$	7.25001	0.935972
$61$	1.00073	0.128130	0.0640649	−	0.997946i	$-0.479594\pi$
$61$	1.00073	0.128130	0.0640649	+	0.997946i	$0.479594\pi$
$62$	−12.1179	−1.53897
$63$	−1.03861	−0.130852
$64$	−11.5372	−1.44215
$65$	0.376745	0.0467294
$66$	22.3251	2.74803
$67$	0.542699	0.0663012	0.0331506	−	0.999450i	$-0.489446\pi$
$67$	0.542699	0.0663012	0.0331506	+	0.999450i	$0.489446\pi$
$68$	−23.9857	−2.90869
$69$	14.5182	1.74779
$70$	2.36805	0.283036
$71$	−14.9311	−1.77200	−0.886000	−	0.463686i	$-0.846527\pi$
$71$	−14.9311	−1.77200	−0.886000	+	0.463686i	$0.846527\pi$
$72$	3.95393	0.465975
$73$	15.6290	1.82923	0.914615	−	0.404325i	$-0.132493\pi$
$73$	15.6290	1.82923	0.914615	+	0.404325i	$0.132493\pi$
$74$	14.9591	1.73896
$75$	−2.00963	−0.232052
$76$	22.0299	2.52700
$77$	4.69124	0.534616
$78$	1.79289	0.203004
$79$	−6.35712	−0.715232	−0.357616	−	0.933869i	$-0.616410\pi$
$79$	−6.35712	−0.715232	−0.357616	+	0.933869i	$0.616410\pi$
$80$	−1.79977	−0.201221
$81$	−11.0371	−1.22635
$82$	3.27855	0.362056
$83$	14.3897	1.57948	0.789738	−	0.613444i	$-0.210216\pi$
$83$	14.3897	1.57948	0.789738	+	0.613444i	$0.210216\pi$
$84$	7.25001	0.791041
$85$	6.64858	0.721140
$86$	8.46961	0.913302
$87$	−8.28990	−0.888771
$88$	−17.8594	−1.90381
$89$	6.09510	0.646080	0.323040	−	0.946385i	$-0.395295\pi$
$89$	6.09510	0.646080	0.323040	+	0.946385i	$0.395295\pi$
$90$	−2.45947	−0.259251
$91$	0.376745	0.0394936
$92$	−26.0628	−2.71723
$93$	10.2838	1.06638
$94$	22.6836	2.33964
$95$	−6.10646	−0.626509
$96$	6.73622	0.687513
$97$	−15.5793	−1.58184	−0.790921	−	0.611918i	$-0.790398\pi$
$97$	−15.5793	−1.58184	−0.790921	+	0.611918i	$0.790398\pi$
$98$	2.36805	0.239209
$99$	−4.87235	−0.489690
$100$	3.60764	0.360764
$101$	−17.4321	−1.73455	−0.867277	−	0.497826i	$-0.834132\pi$
$101$	−17.4321	−1.73455	−0.867277	+	0.497826i	$0.834132\pi$
$102$	31.6399	3.13281
$103$	11.3428	1.11764	0.558818	−	0.829290i	$-0.311255\pi$
$103$	11.3428	1.11764	0.558818	+	0.829290i	$0.311255\pi$
$104$	−1.43425	−0.140640
$105$	−2.00963	−0.196120
$106$	−5.54960	−0.539025
$107$	15.5472	1.50301	0.751504	−	0.659729i	$-0.229329\pi$
$107$	15.5472	1.50301	0.751504	+	0.659729i	$0.229329\pi$
$108$	14.2201	1.36833
$109$	18.2251	1.74565	0.872826	−	0.488032i	$-0.162285\pi$
$109$	18.2251	1.74565	0.872826	+	0.488032i	$0.162285\pi$
$110$	11.1091	1.05921
$111$	−12.6949	−1.20495
$112$	−1.79977	−0.170063
$113$	−5.14934	−0.484410	−0.242205	−	0.970225i	$-0.577871\pi$
$113$	−5.14934	−0.484410	−0.242205	+	0.970225i	$0.577871\pi$
$114$	−29.0600	−2.72171
$115$	7.22433	0.673672
$116$	14.8818	1.38174
$117$	−0.391289	−0.0361747
$118$	24.2511	2.23250
$119$	6.64858	0.609474
$120$	7.65057	0.698398
$121$	11.0077	1.00070
$122$	2.36976	0.214548
$123$	−2.78233	−0.250874
$124$	−18.4612	−1.65786
$125$	−1.00000	−0.0894427
$126$	−2.45947	−0.219107
$127$	−4.02935	−0.357547	−0.178774	−	0.983890i	$-0.557213\pi$
$127$	−4.02935	−0.357547	−0.178774	+	0.983890i	$0.557213\pi$
$128$	−20.6166	−1.82227
$129$	−7.18769	−0.632841
$130$	0.892148	0.0782466
$131$	3.16807	0.276796	0.138398	−	0.990377i	$-0.455805\pi$
$131$	3.16807	0.276796	0.138398	+	0.990377i	$0.455805\pi$
$132$	34.0115	2.96032
$133$	−6.10646	−0.529497
$134$	1.28514	0.111019
$135$	−3.94167	−0.339245
$136$	−25.3109	−2.17039
$137$	6.48851	0.554351	0.277175	−	0.960819i	$-0.410602\pi$
$137$	6.48851	0.554351	0.277175	+	0.960819i	$0.410602\pi$
$138$	34.3798	2.92660
$139$	11.1111	0.942431	0.471216	−	0.882018i	$-0.343815\pi$
$139$	11.1111	0.942431	0.471216	+	0.882018i	$0.343815\pi$
$140$	3.60764	0.304901
$141$	−19.2503	−1.62117
$142$	−35.3576	−2.96714
$143$	1.76740	0.147797
$144$	1.86926	0.155771
$145$	−4.12509	−0.342570
$146$	37.0101	3.06298
$147$	−2.00963	−0.165751
$148$	22.7897	1.87330
$149$	8.01375	0.656512	0.328256	−	0.944589i	$-0.393539\pi$
$149$	8.01375	0.656512	0.328256	+	0.944589i	$0.393539\pi$
$150$	−4.75889	−0.388562
$151$	4.61444	0.375518	0.187759	−	0.982215i	$-0.439878\pi$
$151$	4.61444	0.375518	0.187759	+	0.982215i	$0.439878\pi$
$152$	23.2470	1.88558
$153$	−6.90526	−0.558257
$154$	11.1091	0.895194
$155$	5.11724	0.411027
$156$	2.73140	0.218687
$157$	13.5849	1.08419	0.542096	−	0.840317i	$-0.317631\pi$
$157$	13.5849	1.08419	0.542096	+	0.840317i	$0.317631\pi$
$158$	−15.0540	−1.19763
$159$	4.70964	0.373498
$160$	3.35197	0.264997
$161$	7.22433	0.569357
$162$	−26.1364	−2.05347
$163$	−22.7320	−1.78051	−0.890255	−	0.455462i	$-0.849474\pi$
$163$	−22.7320	−1.78051	−0.890255	+	0.455462i	$0.849474\pi$
$164$	4.99476	0.390026
$165$	−9.42765	−0.733942
$166$	34.0755	2.64477
$167$	−8.75142	−0.677205	−0.338602	−	0.940930i	$-0.609954\pi$
$167$	−8.75142	−0.677205	−0.338602	+	0.940930i	$0.609954\pi$
$168$	7.65057	0.590254
$169$	−12.8581	−0.989082
$170$	15.7441	1.20752
$171$	6.34220	0.485000
$172$	12.9032	0.983857
$173$	2.35809	0.179282	0.0896410	−	0.995974i	$-0.471428\pi$
$173$	2.35809	0.179282	0.0896410	+	0.995974i	$0.471428\pi$
$174$	−19.6309	−1.48821
$175$	−1.00000	−0.0755929
$176$	−8.44316	−0.636427
$177$	−20.5806	−1.54693
$178$	14.4335	1.08184
$179$	1.74198	0.130202	0.0651009	−	0.997879i	$-0.479263\pi$
$179$	1.74198	0.130202	0.0651009	+	0.997879i	$0.479263\pi$
$180$	−3.74692	−0.279279
$181$	17.1861	1.27743	0.638716	−	0.769442i	$-0.279466\pi$
$181$	17.1861	1.27743	0.638716	+	0.769442i	$0.279466\pi$
$182$	0.892148	0.0661304
$183$	−2.01109	−0.148664
$184$	−27.5027	−2.02753
$185$	−6.31706	−0.464439
$186$	24.3524	1.78560
$187$	31.1901	2.28085
$188$	34.5578	2.52038
$189$	−3.94167	−0.286714
$190$	−14.4604	−1.04906
$191$	2.55093	0.184579	0.0922894	−	0.995732i	$-0.470581\pi$
$191$	2.55093	0.184579	0.0922894	+	0.995732i	$0.470581\pi$
$192$	23.1854	1.67326
$193$	6.15597	0.443117	0.221558	−	0.975147i	$-0.428886\pi$
$193$	6.15597	0.443117	0.221558	+	0.975147i	$0.428886\pi$
$194$	−36.8926	−2.64873
$195$	−0.757117	−0.0542182
$196$	3.60764	0.257688
$197$	−1.00610	−0.0716814	−0.0358407	−	0.999358i	$-0.511411\pi$
$197$	−1.00610	−0.0716814	−0.0358407	+	0.999358i	$0.511411\pi$
$198$	−11.5379	−0.819966
$199$	−23.3335	−1.65407	−0.827033	−	0.562153i	$-0.809973\pi$
$199$	−23.3335	−1.65407	−0.827033	+	0.562153i	$0.809973\pi$
$200$	3.80696	0.269193
$201$	−1.09062	−0.0769266
$202$	−41.2799	−2.90444
$203$	−4.12509	−0.289525
$204$	48.2023	3.37484
$205$	−1.38450	−0.0966975
$206$	26.8602	1.87144
$207$	−7.50324	−0.521511
$208$	−0.678054	−0.0470146
$209$	−28.6468	−1.98154
$210$	−4.75889	−0.328395
$211$	−19.4796	−1.34103	−0.670515	−	0.741896i	$-0.733927\pi$
$211$	−19.4796	−1.34103	−0.670515	+	0.741896i	$0.733927\pi$
$212$	−8.45463	−0.580666
$213$	30.0060	2.05598
$214$	36.8165	2.51673
$215$	−3.57663	−0.243924
$216$	15.0058	1.02101
$217$	5.11724	0.347381
$218$	43.1579	2.92302
$219$	−31.4084	−2.12238
$220$	16.9243	1.14104
$221$	2.50482	0.168492
$222$	−30.0622	−2.01764
$223$	−7.44201	−0.498354	−0.249177	−	0.968458i	$-0.580160\pi$
$223$	−7.44201	−0.498354	−0.249177	+	0.968458i	$0.580160\pi$
$224$	3.35197	0.223963
$225$	1.03861	0.0692404
$226$	−12.1939	−0.811125
$227$	−4.15200	−0.275578	−0.137789	−	0.990462i	$-0.544000\pi$
$227$	−4.15200	−0.275578	−0.137789	+	0.990462i	$0.544000\pi$
$228$	−44.2719	−2.93198
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	17.1075	1.12804
$231$	−9.42765	−0.620294
$232$	15.7040	1.03102
$233$	13.3866	0.876986	0.438493	−	0.898735i	$-0.355512\pi$
$233$	13.3866	0.876986	0.438493	+	0.898735i	$0.355512\pi$
$234$	−0.926591	−0.0605731
$235$	−9.57906	−0.624869
$236$	36.9458	2.40497
$237$	12.7755	0.829855
$238$	15.7441	1.02054
$239$	−14.8815	−0.962603	−0.481301	−	0.876555i	$-0.659836\pi$
$239$	−14.8815	−0.962603	−0.481301	+	0.876555i	$0.659836\pi$
$240$	3.61687	0.233468
$241$	2.16867	0.139696	0.0698482	−	0.997558i	$-0.477749\pi$
$241$	2.16867	0.139696	0.0698482	+	0.997558i	$0.477749\pi$
$242$	26.0668	1.67564
$243$	10.3555	0.664305
$244$	3.61026	0.231123
$245$	−1.00000	−0.0638877
$246$	−6.58867	−0.420078
$247$	−2.30057	−0.146382
$248$	−19.4811	−1.23705
$249$	−28.9180	−1.83260
$250$	−2.36805	−0.149768
$251$	9.83789	0.620962	0.310481	−	0.950580i	$-0.399510\pi$
$251$	9.83789	0.620962	0.310481	+	0.950580i	$0.399510\pi$
$252$	−3.74692	−0.236033
$253$	33.8911	2.13071
$254$	−9.54169	−0.598699
$255$	−13.3612	−0.836709
$256$	−25.7467	−1.60917
$257$	24.6991	1.54069	0.770345	−	0.637627i	$-0.220084\pi$
$257$	24.6991	1.54069	0.770345	+	0.637627i	$0.220084\pi$
$258$	−17.0208	−1.05967
$259$	−6.31706	−0.392523
$260$	1.35916	0.0842914
$261$	4.28435	0.265194
$262$	7.50214	0.463484
$263$	13.8033	0.851148	0.425574	−	0.904924i	$-0.360072\pi$
$263$	13.8033	0.851148	0.425574	+	0.904924i	$0.360072\pi$
$264$	35.8907	2.20892
$265$	2.34354	0.143962
$266$	−14.4604	−0.886622
$267$	−12.2489	−0.749620
$268$	1.95786	0.119595
$269$	−22.4237	−1.36719	−0.683597	−	0.729859i	$-0.739586\pi$
$269$	−22.4237	−1.36719	−0.683597	+	0.729859i	$0.739586\pi$
$270$	−9.33406	−0.568053
$271$	−30.1213	−1.82974	−0.914869	−	0.403750i	$-0.867706\pi$
$271$	−30.1213	−1.82974	−0.914869	+	0.403750i	$0.867706\pi$
$272$	−11.9659	−0.725541
$273$	−0.757117	−0.0458228
$274$	15.3651	0.928239
$275$	−4.69124	−0.282892
$276$	52.3765	3.15269
$277$	7.18602	0.431766	0.215883	−	0.976419i	$-0.430737\pi$
$277$	7.18602	0.431766	0.215883	+	0.976419i	$0.430737\pi$
$278$	26.3116	1.57806
$279$	−5.31480	−0.318189
$280$	3.80696	0.227509
$281$	−16.8806	−1.00701	−0.503507	−	0.863991i	$-0.667957\pi$
$281$	−16.8806	−1.00701	−0.503507	+	0.863991i	$0.667957\pi$
$282$	−45.5857	−2.71459
$283$	22.7190	1.35050	0.675252	−	0.737587i	$-0.264035\pi$
$283$	22.7190	1.35050	0.675252	+	0.737587i	$0.264035\pi$
$284$	−53.8661	−3.19637
$285$	12.2717	0.726913
$286$	4.18528	0.247481
$287$	−1.38450	−0.0817243
$288$	−3.48138	−0.205142
$289$	27.2036	1.60021
$290$	−9.76840	−0.573620
$291$	31.3087	1.83535
$292$	56.3836	3.29960
$293$	−3.31644	−0.193749	−0.0968743	−	0.995297i	$-0.530884\pi$
$293$	−3.31644	−0.193749	−0.0968743	+	0.995297i	$0.530884\pi$
$294$	−4.75889	−0.277544
$295$	−10.2410	−0.596254
$296$	24.0488	1.39781
$297$	−18.4913	−1.07298
$298$	18.9769	1.09930
$299$	2.72173	0.157402
$300$	−7.25001	−0.418580
$301$	−3.57663	−0.206153
$302$	10.9272	0.628790
$303$	35.0320	2.01253
$304$	10.9902	0.630333
$305$	−1.00073	−0.0573014
$306$	−16.3520	−0.934780
$307$	23.5246	1.34262	0.671309	−	0.741178i	$-0.265733\pi$
$307$	23.5246	1.34262	0.671309	+	0.741178i	$0.265733\pi$
$308$	16.9243	0.964351
$309$	−22.7947	−1.29675
$310$	12.1179	0.688248
$311$	15.1484	0.858986	0.429493	−	0.903070i	$-0.358692\pi$
$311$	15.1484	0.858986	0.429493	+	0.903070i	$0.358692\pi$
$312$	2.88231	0.163179
$313$	−8.61928	−0.487191	−0.243595	−	0.969877i	$-0.578327\pi$
$313$	−8.61928	−0.487191	−0.243595	+	0.969877i	$0.578327\pi$
$314$	32.1696	1.81544
$315$	1.03861	0.0585188
$316$	−22.9342	−1.29015
$317$	14.5008	0.814446	0.407223	−	0.913329i	$-0.366497\pi$
$317$	14.5008	0.814446	0.407223	+	0.913329i	$0.366497\pi$
$318$	11.1526	0.625409
$319$	−19.3518	−1.08349
$320$	11.5372	0.644947
$321$	−31.2441	−1.74388
$322$	17.1075	0.953366
$323$	−40.5993	−2.25900
$324$	−39.8179	−2.21211
$325$	−0.376745	−0.0208980
$326$	−53.8305	−2.98139
$327$	−36.6257	−2.02541
$328$	5.27072	0.291027
$329$	−9.57906	−0.528111
$330$	−22.3251	−1.22896
$331$	25.7306	1.41428	0.707140	−	0.707073i	$-0.249985\pi$
$331$	25.7306	1.41428	0.707140	+	0.707073i	$0.249985\pi$
$332$	51.9129	2.84909
$333$	6.56094	0.359537
$334$	−20.7237	−1.13395
$335$	−0.542699	−0.0296508
$336$	3.61687	0.197317
$337$	24.0813	1.31179	0.655896	−	0.754851i	$-0.272291\pi$
$337$	24.0813	1.31179	0.655896	+	0.754851i	$0.272291\pi$
$338$	−30.4485	−1.65618
$339$	10.3483	0.562041
$340$	23.9857	1.30081
$341$	24.0062	1.30001
$342$	15.0186	0.812114
$343$	−1.00000	−0.0539949
$344$	13.6161	0.734129
$345$	−14.5182	−0.781635
$346$	5.58405	0.300201
$347$	−4.03005	−0.216344	−0.108172	−	0.994132i	$-0.534500\pi$
$347$	−4.03005	−0.216344	−0.108172	+	0.994132i	$0.534500\pi$
$348$	−29.9070	−1.60318
$349$	27.1577	1.45372	0.726860	−	0.686786i	$-0.240979\pi$
$349$	27.1577	1.45372	0.726860	+	0.686786i	$0.240979\pi$
$350$	−2.36805	−0.126577
$351$	−1.48500	−0.0792636
$352$	15.7249	0.838141
$353$	34.4127	1.83160	0.915802	−	0.401631i	$-0.131556\pi$
$353$	34.4127	1.83160	0.915802	+	0.401631i	$0.131556\pi$
$354$	−48.7358	−2.59028
$355$	14.9311	0.792462
$356$	21.9889	1.16541
$357$	−13.3612	−0.707149
$358$	4.12509	0.218018
$359$	14.8877	0.785743	0.392871	−	0.919593i	$-0.371482\pi$
$359$	14.8877	0.785743	0.392871	+	0.919593i	$0.371482\pi$
$360$	−3.95393	−0.208390
$361$	18.2888	0.962568
$362$	40.6974	2.13901
$363$	−22.1215	−1.16108
$364$	1.35916	0.0712392
$365$	−15.6290	−0.818057
$366$	−4.76235	−0.248932
$367$	−20.0982	−1.04912	−0.524559	−	0.851374i	$-0.675770\pi$
$367$	−20.0982	−1.04912	−0.524559	+	0.851374i	$0.675770\pi$
$368$	−13.0022	−0.677784
$369$	1.43795	0.0748566
$370$	−14.9591	−0.777686
$371$	2.34354	0.121670
$372$	37.1001	1.92355
$373$	18.0717	0.935719	0.467860	−	0.883803i	$-0.345025\pi$
$373$	18.0717	0.935719	0.467860	+	0.883803i	$0.345025\pi$
$374$	73.8595	3.81919
$375$	2.00963	0.103777
$376$	36.4671	1.88065
$377$	−1.55411	−0.0800405
$378$	−9.33406	−0.480092
$379$	−2.04815	−0.105206	−0.0526031	−	0.998615i	$-0.516752\pi$
$379$	−2.04815	−0.105206	−0.0526031	+	0.998615i	$0.516752\pi$
$380$	−22.0299	−1.13011
$381$	8.09750	0.414848
$382$	6.04072	0.309070
$383$	14.0790	0.719404	0.359702	−	0.933067i	$-0.382878\pi$
$383$	14.0790	0.719404	0.359702	+	0.933067i	$0.382878\pi$
$384$	41.4317	2.11430
$385$	−4.69124	−0.239088
$386$	14.5776	0.741982
$387$	3.71471	0.188829
$388$	−56.2046	−2.85336
$389$	−16.5297	−0.838087	−0.419043	−	0.907966i	$-0.637634\pi$
$389$	−16.5297	−0.838087	−0.419043	+	0.907966i	$0.637634\pi$
$390$	−1.79289	−0.0907863
$391$	48.0316	2.42906
$392$	3.80696	0.192280
$393$	−6.36665	−0.321155
$394$	−2.38248	−0.120028
$395$	6.35712	0.319862
$396$	−17.5777	−0.883312
$397$	−15.7218	−0.789053	−0.394527	−	0.918884i	$-0.629091\pi$
$397$	−15.7218	−0.789053	−0.394527	+	0.918884i	$0.629091\pi$
$398$	−55.2547	−2.76967
$399$	12.2717	0.614354
$400$	1.79977	0.0899886
$401$	−25.8659	−1.29168	−0.645842	−	0.763471i	$-0.723493\pi$
$401$	−25.8659	−1.29168	−0.645842	+	0.763471i	$0.723493\pi$
$402$	−2.58264	−0.128811
$403$	1.92789	0.0960352
$404$	−62.8885	−3.12882
$405$	11.0371	0.548439
$406$	−9.76840	−0.484798
$407$	−29.6348	−1.46894
$408$	50.8654	2.51821
$409$	29.8263	1.47482	0.737408	−	0.675448i	$-0.236050\pi$
$409$	29.8263	1.47482	0.737408	+	0.675448i	$0.236050\pi$
$410$	−3.27855	−0.161916
$411$	−13.0395	−0.643191
$412$	40.9206	2.01601
$413$	−10.2410	−0.503927
$414$	−17.7680	−0.873250
$415$	−14.3897	−0.706363
$416$	1.26284	0.0619157
$417$	−22.3292	−1.09346
$418$	−67.8370	−3.31802
$419$	−20.1673	−0.985236	−0.492618	−	0.870246i	$-0.663960\pi$
$419$	−20.1673	−0.985236	−0.492618	+	0.870246i	$0.663960\pi$
$420$	−7.25001	−0.353764
$421$	25.1716	1.22679	0.613394	−	0.789777i	$-0.289804\pi$
$421$	25.1716	1.22679	0.613394	+	0.789777i	$0.289804\pi$
$422$	−46.1285	−2.24550
$423$	9.94887	0.483731
$424$	−8.92174	−0.433278
$425$	−6.64858	−0.322504
$426$	71.0556	3.44266
$427$	−1.00073	−0.0484285
$428$	56.0888	2.71115
$429$	−3.55182	−0.171483
$430$	−8.46961	−0.408441
$431$	8.74040	0.421010	0.210505	−	0.977593i	$-0.432489\pi$
$431$	8.74040	0.421010	0.210505	+	0.977593i	$0.432489\pi$
$432$	7.09411	0.341316
$433$	34.9109	1.67771	0.838855	−	0.544354i	$-0.183225\pi$
$433$	34.9109	1.67771	0.838855	+	0.544354i	$0.183225\pi$
$434$	12.1179	0.581676
$435$	8.28990	0.397470
$436$	65.7497	3.14884
$437$	−44.1151	−2.11031
$438$	−74.3765	−3.55385
$439$	−16.8518	−0.804292	−0.402146	−	0.915575i	$-0.631736\pi$
$439$	−16.8518	−0.804292	−0.402146	+	0.915575i	$0.631736\pi$
$440$	17.8594	0.851411
$441$	1.03861	0.0494574
$442$	5.93152	0.282134
$443$	−4.51871	−0.214690	−0.107345	−	0.994222i	$-0.534235\pi$
$443$	−4.51871	−0.214690	−0.107345	+	0.994222i	$0.534235\pi$
$444$	−45.7987	−2.17351
$445$	−6.09510	−0.288936
$446$	−17.6230	−0.834473
$447$	−16.1047	−0.761725
$448$	11.5372	0.545080
$449$	20.1871	0.952687	0.476344	−	0.879259i	$-0.341962\pi$
$449$	20.1871	0.952687	0.476344	+	0.879259i	$0.341962\pi$
$450$	2.45947	0.115940
$451$	−6.49501	−0.305838
$452$	−18.5770	−0.873787
$453$	−9.27331	−0.435698
$454$	−9.83211	−0.461444
$455$	−0.376745	−0.0176621
$456$	−46.7179	−2.18776
$457$	−6.24911	−0.292321	−0.146161	−	0.989261i	$-0.546692\pi$
$457$	−6.24911	−0.292321	−0.146161	+	0.989261i	$0.546692\pi$
$458$	2.36805	0.110651
$459$	−26.2065	−1.22322
$460$	26.0628	1.21518
$461$	−36.9391	−1.72042	−0.860212	−	0.509936i	$-0.829669\pi$
$461$	−36.9391	−1.72042	−0.860212	+	0.509936i	$0.829669\pi$
$462$	−22.3251	−1.03866
$463$	−20.7951	−0.966432	−0.483216	−	0.875501i	$-0.660531\pi$
$463$	−20.7951	−0.966432	−0.483216	+	0.875501i	$0.660531\pi$
$464$	7.42423	0.344661
$465$	−10.2838	−0.476898
$466$	31.7001	1.46848
$467$	15.7121	0.727068	0.363534	−	0.931581i	$-0.381570\pi$
$467$	15.7121	0.727068	0.363534	+	0.931581i	$0.381570\pi$
$468$	−1.41163	−0.0652526
$469$	−0.542699	−0.0250595
$470$	−22.6836	−1.04632
$471$	−27.3006	−1.25794
$472$	38.9870	1.79452
$473$	−16.7788	−0.771490
$474$	30.2529	1.38956
$475$	6.10646	0.280183
$476$	23.9857	1.09938
$477$	−2.43401	−0.111446
$478$	−35.2400	−1.61184
$479$	−4.79325	−0.219009	−0.109505	−	0.993986i	$-0.534926\pi$
$479$	−4.79325	−0.219009	−0.109505	+	0.993986i	$0.534926\pi$
$480$	−6.73622	−0.307465
$481$	−2.37992	−0.108515
$482$	5.13551	0.233916
$483$	−14.5182	−0.660602
$484$	39.7119	1.80509
$485$	15.5793	0.707421
$486$	24.5223	1.11235
$487$	13.6442	0.618277	0.309138	−	0.951017i	$-0.399959\pi$
$487$	13.6442	0.618277	0.309138	+	0.951017i	$0.399959\pi$
$488$	3.80972	0.172458
$489$	45.6829	2.06585
$490$	−2.36805	−0.106977
$491$	−5.82875	−0.263048	−0.131524	−	0.991313i	$-0.541987\pi$
$491$	−5.82875	−0.263048	−0.131524	+	0.991313i	$0.541987\pi$
$492$	−10.0376	−0.452531
$493$	−27.4260	−1.23521
$494$	−5.44786	−0.245111
$495$	4.87235	0.218996
$496$	−9.20987	−0.413535
$497$	14.9311	0.669753
$498$	−68.4791	−3.06862
$499$	16.3292	0.730994	0.365497	−	0.930812i	$-0.380899\pi$
$499$	16.3292	0.730994	0.365497	+	0.930812i	$0.380899\pi$
$500$	−3.60764	−0.161338
$501$	17.5871	0.785733
$502$	23.2966	1.03978
$503$	−16.8141	−0.749704	−0.374852	−	0.927085i	$-0.622307\pi$
$503$	−16.8141	−0.749704	−0.374852	+	0.927085i	$0.622307\pi$
$504$	−3.95393	−0.176122
$505$	17.4321	0.775716
$506$	80.2556	3.56780
$507$	25.8399	1.14759
$508$	−14.5364	−0.644951
$509$	−18.5008	−0.820035	−0.410017	−	0.912078i	$-0.634477\pi$
$509$	−18.5008	−0.820035	−0.410017	+	0.912078i	$0.634477\pi$
$510$	−31.6399	−1.40104
$511$	−15.6290	−0.691384
$512$	−19.7361	−0.872221
$513$	24.0696	1.06270
$514$	58.4887	2.57982
$515$	−11.3428	−0.499822
$516$	−25.9306	−1.14153
$517$	−44.9377	−1.97636
$518$	−14.9591	−0.657264
$519$	−4.73888	−0.208014
$520$	1.43425	0.0628960
$521$	−26.6985	−1.16968	−0.584842	−	0.811147i	$-0.698843\pi$
$521$	−26.6985	−1.16968	−0.584842	+	0.811147i	$0.698843\pi$
$522$	10.1455	0.444058
$523$	6.24610	0.273123	0.136561	−	0.990632i	$-0.456395\pi$
$523$	6.24610	0.273123	0.136561	+	0.990632i	$0.456395\pi$
$524$	11.4293	0.499289
$525$	2.00963	0.0877074
$526$	32.6868	1.42521
$527$	34.0224	1.48204
$528$	16.9676	0.738421
$529$	29.1910	1.26917
$530$	5.54960	0.241059
$531$	10.6364	0.461579
$532$	−22.0299	−0.955116
$533$	−0.521602	−0.0225931
$534$	−29.0059	−1.25521
$535$	−15.5472	−0.672165
$536$	2.06603	0.0892390
$537$	−3.50073	−0.151068
$538$	−53.1002	−2.28931
$539$	−4.69124	−0.202066
$540$	−14.2201	−0.611937
$541$	24.4866	1.05276	0.526381	−	0.850249i	$-0.323548\pi$
$541$	24.4866	1.05276	0.526381	+	0.850249i	$0.323548\pi$
$542$	−71.3286	−3.06383
$543$	−34.5377	−1.48215
$544$	22.2859	0.955499
$545$	−18.2251	−0.780679
$546$	−1.79289	−0.0767284
$547$	21.1362	0.903717	0.451859	−	0.892090i	$-0.350761\pi$
$547$	21.1362	0.903717	0.451859	+	0.892090i	$0.350761\pi$
$548$	23.4082	0.999948
$549$	1.03936	0.0443588
$550$	−11.1091	−0.473692
$551$	25.1897	1.07312
$552$	55.2703	2.35246
$553$	6.35712	0.270332
$554$	17.0168	0.722975
$555$	12.6949	0.538870
$556$	40.0848	1.69997
$557$	−11.3102	−0.479228	−0.239614	−	0.970868i	$-0.577021\pi$
$557$	−11.3102	−0.479228	−0.239614	+	0.970868i	$0.577021\pi$
$558$	−12.5857	−0.532795
$559$	−1.34747	−0.0569921
$560$	1.79977	0.0760543
$561$	−62.6805	−2.64637
$562$	−39.9741	−1.68621
$563$	−37.6529	−1.58688	−0.793440	−	0.608649i	$-0.791712\pi$
$563$	−37.6529	−1.58688	−0.793440	+	0.608649i	$0.791712\pi$
$564$	−69.4483	−2.92430
$565$	5.14934	0.216635
$566$	53.7996	2.26137
$567$	11.0371	0.463515
$568$	−56.8422	−2.38505
$569$	−3.26326	−0.136803	−0.0684015	−	0.997658i	$-0.521790\pi$
$569$	−3.26326	−0.136803	−0.0684015	+	0.997658i	$0.521790\pi$
$570$	29.0600	1.21719
$571$	39.9899	1.67353	0.836763	−	0.547566i	$-0.184445\pi$
$571$	39.9899	1.67353	0.836763	+	0.547566i	$0.184445\pi$
$572$	6.37614	0.266600
$573$	−5.12642	−0.214159
$574$	−3.27855	−0.136844
$575$	−7.22433	−0.301275
$576$	−11.9826	−0.499274
$577$	−12.5128	−0.520916	−0.260458	−	0.965485i	$-0.583874\pi$
$577$	−12.5128	−0.520916	−0.260458	+	0.965485i	$0.583874\pi$
$578$	64.4194	2.67950
$579$	−12.3712	−0.514130
$580$	−14.8818	−0.617934
$581$	−14.3897	−0.596986
$582$	74.1404	3.07322
$583$	10.9941	0.455329
$584$	59.4988	2.46208
$585$	0.391289	0.0161778
$586$	−7.85348	−0.324424
$587$	−32.8279	−1.35495	−0.677477	−	0.735544i	$-0.736927\pi$
$587$	−32.8279	−1.35495	−0.677477	+	0.735544i	$0.736927\pi$
$588$	−7.25001	−0.298985
$589$	−31.2482	−1.28756
$590$	−24.2511	−0.998404
$591$	2.02188	0.0831690
$592$	11.3693	0.467274
$593$	16.6581	0.684068	0.342034	−	0.939688i	$-0.388884\pi$
$593$	16.6581	0.684068	0.342034	+	0.939688i	$0.388884\pi$
$594$	−43.7883	−1.79666
$595$	−6.64858	−0.272565
$596$	28.9107	1.18423
$597$	46.8916	1.91915
$598$	6.44517	0.263563
$599$	−13.7946	−0.563631	−0.281815	−	0.959469i	$-0.590937\pi$
$599$	−13.7946	−0.563631	−0.281815	+	0.959469i	$0.590937\pi$
$600$	−7.65057	−0.312333
$601$	36.4800	1.48805	0.744026	−	0.668151i	$-0.232914\pi$
$601$	36.4800	1.48805	0.744026	+	0.668151i	$0.232914\pi$
$602$	−8.46961	−0.345196
$603$	0.563651	0.0229536
$604$	16.6472	0.677366
$605$	−11.0077	−0.447528
$606$	82.9572	3.36991
$607$	−17.8226	−0.723395	−0.361698	−	0.932295i	$-0.617803\pi$
$607$	−17.8226	−0.723395	−0.361698	+	0.932295i	$0.617803\pi$
$608$	−20.4687	−0.830114
$609$	8.28990	0.335924
$610$	−2.36976	−0.0959489
$611$	−3.60886	−0.145999
$612$	−24.9117	−1.00699
$613$	−31.6961	−1.28019	−0.640096	−	0.768295i	$-0.721105\pi$
$613$	−31.6961	−1.28019	−0.640096	+	0.768295i	$0.721105\pi$
$614$	55.7072	2.24816
$615$	2.78233	0.112194
$616$	17.8594	0.719574
$617$	24.2049	0.974453	0.487227	−	0.873276i	$-0.338009\pi$
$617$	24.2049	0.974453	0.487227	+	0.873276i	$0.338009\pi$
$618$	−53.9790	−2.17135
$619$	47.4595	1.90756	0.953779	−	0.300508i	$-0.0971561\pi$
$619$	47.4595	1.90756	0.953779	+	0.300508i	$0.0971561\pi$
$620$	18.4612	0.741418
$621$	−28.4760	−1.14270
$622$	35.8721	1.43834
$623$	−6.09510	−0.244195
$624$	1.36264	0.0545492
$625$	1.00000	0.0400000
$626$	−20.4109	−0.815782
$627$	57.5695	2.29911
$628$	49.0093	1.95568
$629$	−41.9995	−1.67463
$630$	2.45947	0.0979875
$631$	−31.9477	−1.27182	−0.635909	−	0.771764i	$-0.719375\pi$
$631$	−31.9477	−1.27182	−0.635909	+	0.771764i	$0.719375\pi$
$632$	−24.2013	−0.962676
$633$	39.1467	1.55594
$634$	34.3386	1.36376
$635$	4.02935	0.159900
$636$	16.9907	0.673724
$637$	−0.376745	−0.0149272
$638$	−45.8259	−1.81427
$639$	−15.5076	−0.613470
$640$	20.6166	0.814942
$641$	26.5351	1.04807	0.524037	−	0.851695i	$-0.324425\pi$
$641$	26.5351	1.04807	0.524037	+	0.851695i	$0.324425\pi$
$642$	−73.9876	−2.92006
$643$	6.20130	0.244555	0.122278	−	0.992496i	$-0.460980\pi$
$643$	6.20130	0.244555	0.122278	+	0.992496i	$0.460980\pi$
$644$	26.0628	1.02702
$645$	7.18769	0.283015
$646$	−96.1409	−3.78261
$647$	−5.07861	−0.199661	−0.0998304	−	0.995004i	$-0.531830\pi$
$647$	−5.07861	−0.199661	−0.0998304	+	0.995004i	$0.531830\pi$
$648$	−42.0178	−1.65062
$649$	−48.0430	−1.88585
$650$	−0.892148	−0.0349929
$651$	−10.2838	−0.403052
$652$	−82.0089	−3.21172
$653$	−14.9145	−0.583650	−0.291825	−	0.956472i	$-0.594262\pi$
$653$	−14.9145	−0.583650	−0.291825	+	0.956472i	$0.594262\pi$
$654$	−86.7314	−3.39147
$655$	−3.16807	−0.123787
$656$	2.49178	0.0972877
$657$	16.2323	0.633284
$658$	−22.6836	−0.884300
$659$	−0.233973	−0.00911431	−0.00455716	−	0.999990i	$-0.501451\pi$
$659$	−0.233973	−0.00911431	−0.00455716	+	0.999990i	$0.501451\pi$
$660$	−34.0115	−1.32390
$661$	−12.3365	−0.479833	−0.239916	−	0.970794i	$-0.577120\pi$
$661$	−12.3365	−0.479833	−0.239916	+	0.970794i	$0.577120\pi$
$662$	60.9312	2.36816
$663$	−5.03375	−0.195495
$664$	54.7810	2.12592
$665$	6.10646	0.236798
$666$	15.5366	0.602031
$667$	−29.8010	−1.15390
$668$	−31.5719	−1.22155
$669$	14.9557	0.578219
$670$	−1.28514	−0.0496491
$671$	−4.69465	−0.181235
$672$	−6.73622	−0.259855
$673$	−17.5703	−0.677284	−0.338642	−	0.940915i	$-0.609967\pi$
$673$	−17.5703	−0.677284	−0.338642	+	0.940915i	$0.609967\pi$
$674$	57.0256	2.19654
$675$	3.94167	0.151715
$676$	−46.3872	−1.78412
$677$	40.2015	1.54507	0.772535	−	0.634972i	$-0.218988\pi$
$677$	40.2015	1.54507	0.772535	+	0.634972i	$0.218988\pi$
$678$	24.5052	0.941115
$679$	15.5793	0.597880
$680$	25.3109	0.970628
$681$	8.34397	0.319742
$682$	56.8478	2.17681
$683$	−48.7564	−1.86561	−0.932805	−	0.360381i	$-0.882647\pi$
$683$	−48.7564	−1.86561	−0.932805	+	0.360381i	$0.882647\pi$
$684$	22.8804	0.874853
$685$	−6.48851	−0.247913
$686$	−2.36805	−0.0904124
$687$	−2.00963	−0.0766721
$688$	6.43711	0.245413
$689$	0.882914	0.0336364
$690$	−34.3798	−1.30882
$691$	2.37863	0.0904873	0.0452437	−	0.998976i	$-0.485594\pi$
$691$	2.37863	0.0904873	0.0452437	+	0.998976i	$0.485594\pi$
$692$	8.50712	0.323392
$693$	4.87235	0.185085
$694$	−9.54334	−0.362260
$695$	−11.1111	−0.421468
$696$	−31.5593	−1.19625
$697$	−9.20494	−0.348662
$698$	64.3107	2.43420
$699$	−26.9021	−1.01753
$700$	−3.60764	−0.136356
$701$	−32.5555	−1.22960	−0.614802	−	0.788682i	$-0.710764\pi$
$701$	−32.5555	−1.22960	−0.614802	+	0.788682i	$0.710764\pi$
$702$	−3.51656	−0.132724
$703$	38.5748	1.45488
$704$	54.1236	2.03986
$705$	19.2503	0.725010
$706$	81.4908	3.06695
$707$	17.4321	0.655600
$708$	−74.2473	−2.79039
$709$	−17.5172	−0.657873	−0.328937	−	0.944352i	$-0.606690\pi$
$709$	−17.5172	−0.657873	−0.328937	+	0.944352i	$0.606690\pi$
$710$	35.3576	1.32695
$711$	−6.60255	−0.247615
$712$	23.2038	0.869599
$713$	36.9687	1.38449
$714$	−31.6399	−1.18409
$715$	−1.76740	−0.0660970
$716$	6.28443	0.234860
$717$	29.9062	1.11687
$718$	35.2547	1.31570
$719$	19.8162	0.739020	0.369510	−	0.929227i	$-0.379526\pi$
$719$	19.8162	0.739020	0.369510	+	0.929227i	$0.379526\pi$
$720$	−1.86926	−0.0696630
$721$	−11.3428	−0.422427
$722$	43.3087	1.61178
$723$	−4.35822	−0.162084
$724$	62.0012	2.30426
$725$	4.12509	0.153202
$726$	−52.3846	−1.94417
$727$	31.0854	1.15289	0.576447	−	0.817135i	$-0.304439\pi$
$727$	31.0854	1.15289	0.576447	+	0.817135i	$0.304439\pi$
$728$	1.43425	0.0531569
$729$	12.3007	0.455580
$730$	−37.0101	−1.36980
$731$	−23.7795	−0.879516
$732$	−7.25527	−0.268163
$733$	41.7165	1.54083	0.770417	−	0.637540i	$-0.220048\pi$
$733$	41.7165	1.54083	0.770417	+	0.637540i	$0.220048\pi$
$734$	−47.5935	−1.75671
$735$	2.00963	0.0741263
$736$	24.2158	0.892605
$737$	−2.54593	−0.0937806
$738$	3.40513	0.125344
$739$	−9.63419	−0.354399	−0.177200	−	0.984175i	$-0.556704\pi$
$739$	−9.63419	−0.354399	−0.177200	+	0.984175i	$0.556704\pi$
$740$	−22.7897	−0.837764
$741$	4.62330	0.169841
$742$	5.54960	0.203732
$743$	−9.17856	−0.336729	−0.168364	−	0.985725i	$-0.553849\pi$
$743$	−9.17856	−0.336729	−0.168364	+	0.985725i	$0.553849\pi$
$744$	39.1498	1.43530
$745$	−8.01375	−0.293601
$746$	42.7947	1.56683
$747$	14.9452	0.546818
$748$	112.523	4.11423
$749$	−15.5472	−0.568083
$750$	4.75889	0.173770
$751$	31.3039	1.14230	0.571149	−	0.820847i	$-0.306498\pi$
$751$	31.3039	1.14230	0.571149	+	0.820847i	$0.306498\pi$
$752$	17.2401	0.628683
$753$	−19.7705	−0.720477
$754$	−3.68019	−0.134025
$755$	−4.61444	−0.167937
$756$	−14.2201	−0.517181
$757$	18.8826	0.686300	0.343150	−	0.939281i	$-0.388506\pi$
$757$	18.8826	0.686300	0.343150	+	0.939281i	$0.388506\pi$
$758$	−4.85010	−0.176164
$759$	−68.1085	−2.47218
$760$	−23.2470	−0.843258
$761$	−1.40659	−0.0509889	−0.0254945	−	0.999675i	$-0.508116\pi$
$761$	−1.40659	−0.0509889	−0.0254945	+	0.999675i	$0.508116\pi$
$762$	19.1753	0.694646
$763$	−18.2251	−0.659794
$764$	9.20283	0.332947
$765$	6.90526	0.249660
$766$	33.3397	1.20461
$767$	−3.85824	−0.139313
$768$	51.7412	1.86705
$769$	−7.04453	−0.254032	−0.127016	−	0.991901i	$-0.540540\pi$
$769$	−7.04453	−0.254032	−0.127016	+	0.991901i	$0.540540\pi$
$770$	−11.1091	−0.400343
$771$	−49.6361	−1.78760
$772$	22.2085	0.799302
$773$	19.4599	0.699923	0.349961	−	0.936764i	$-0.386195\pi$
$773$	19.4599	0.699923	0.349961	+	0.936764i	$0.386195\pi$
$774$	8.79659	0.316187
$775$	−5.11724	−0.183817
$776$	−59.3099	−2.12910
$777$	12.6949	0.455428
$778$	−39.1430	−1.40334
$779$	8.45437	0.302909
$780$	−2.73140	−0.0977999
$781$	70.0455	2.50643
$782$	113.741	4.06737
$783$	16.2598	0.581076
$784$	1.79977	0.0642776
$785$	−13.5849	−0.484865
$786$	−15.0765	−0.537761
$787$	45.5140	1.62240	0.811199	−	0.584770i	$-0.198815\pi$
$787$	45.5140	1.62240	0.811199	+	0.584770i	$0.198815\pi$
$788$	−3.62963	−0.129300
$789$	−27.7395	−0.987553
$790$	15.0540	0.535596
$791$	5.14934	0.183090
$792$	−18.5488	−0.659104
$793$	−0.377018	−0.0133883
$794$	−37.2299	−1.32124
$795$	−4.70964	−0.167034
$796$	−84.1787	−2.98364
$797$	24.4638	0.866553	0.433277	−	0.901261i	$-0.357357\pi$
$797$	24.4638	0.866553	0.433277	+	0.901261i	$0.357357\pi$
$798$	29.0600	1.02871
$799$	−63.6872	−2.25309
$800$	−3.35197	−0.118510
$801$	6.33041	0.223674
$802$	−61.2517	−2.16287
$803$	−73.3192	−2.58738
$804$	−3.93457	−0.138762
$805$	−7.22433	−0.254624
$806$	4.56534	0.160807
$807$	45.0632	1.58630
$808$	−66.3631	−2.33465
$809$	−0.911420	−0.0320438	−0.0160219	−	0.999872i	$-0.505100\pi$
$809$	−0.911420	−0.0320438	−0.0160219	+	0.999872i	$0.505100\pi$
$810$	26.1364	0.918339
$811$	40.0862	1.40762	0.703808	−	0.710390i	$-0.251482\pi$
$811$	40.0862	1.40762	0.703808	+	0.710390i	$0.251482\pi$
$812$	−14.8818	−0.522250
$813$	60.5326	2.12297
$814$	−70.1766	−2.45969
$815$	22.7320	0.796268
$816$	24.0471	0.841816
$817$	21.8405	0.764103
$818$	70.6300	2.46952
$819$	0.391289	0.0136728
$820$	−4.99476	−0.174425
$821$	3.19163	0.111389	0.0556944	−	0.998448i	$-0.482263\pi$
$821$	3.19163	0.111389	0.0556944	+	0.998448i	$0.482263\pi$
$822$	−30.8781	−1.07700
$823$	−44.8559	−1.56358	−0.781790	−	0.623542i	$-0.785693\pi$
$823$	−44.8559	−1.56358	−0.781790	+	0.623542i	$0.785693\pi$
$824$	43.1814	1.50430
$825$	9.42765	0.328229
$826$	−24.2511	−0.843805
$827$	−15.2603	−0.530653	−0.265327	−	0.964159i	$-0.585480\pi$
$827$	−15.2603	−0.530653	−0.265327	+	0.964159i	$0.585480\pi$
$828$	−27.0690	−0.940711
$829$	−16.3321	−0.567239	−0.283619	−	0.958937i	$-0.591535\pi$
$829$	−16.3321	−0.567239	−0.283619	+	0.958937i	$0.591535\pi$
$830$	−34.0755	−1.18278
$831$	−14.4412	−0.500961
$832$	4.34657	0.150690
$833$	−6.64858	−0.230360
$834$	−52.8765	−1.83096
$835$	8.75142	0.302855
$836$	−103.347	−3.57435
$837$	−20.1705	−0.697194
$838$	−47.7570	−1.64974
$839$	13.4052	0.462800	0.231400	−	0.972859i	$-0.425669\pi$
$839$	13.4052	0.462800	0.231400	+	0.972859i	$0.425669\pi$
$840$	−7.65057	−0.263970
$841$	−11.9836	−0.413228
$842$	59.6075	2.05421
$843$	33.9238	1.16840
$844$	−70.2752	−2.41897
$845$	12.8581	0.442331
$846$	23.5594	0.809988
$847$	−11.0077	−0.378230
$848$	−4.21783	−0.144841
$849$	−45.6567	−1.56693
$850$	−15.7441	−0.540020
$851$	−45.6365	−1.56440
$852$	108.251	3.70861
$853$	−18.1022	−0.619806	−0.309903	−	0.950768i	$-0.600297\pi$
$853$	−18.1022	−0.619806	−0.309903	+	0.950768i	$0.600297\pi$
$854$	−2.36976	−0.0810917
$855$	−6.34220	−0.216899
$856$	59.1876	2.02299
$857$	22.8699	0.781220	0.390610	−	0.920556i	$-0.372264\pi$
$857$	22.8699	0.781220	0.390610	+	0.920556i	$0.372264\pi$
$858$	−8.41086	−0.287142
$859$	−21.6994	−0.740374	−0.370187	−	0.928957i	$-0.620706\pi$
$859$	−21.6994	−0.740374	−0.370187	+	0.928957i	$0.620706\pi$
$860$	−12.9032	−0.439994
$861$	2.78233	0.0948214
$862$	20.6977	0.704965
$863$	−46.1103	−1.56961	−0.784806	−	0.619742i	$-0.787237\pi$
$863$	−46.1103	−1.56961	−0.784806	+	0.619742i	$0.787237\pi$
$864$	−13.2124	−0.449494
$865$	−2.35809	−0.0801773
$866$	82.6706	2.80926
$867$	−54.6692	−1.85666
$868$	18.4612	0.626612
$869$	29.8228	1.01167
$870$	19.6309	0.665548
$871$	−0.204459	−0.00692782
$872$	69.3823	2.34958
$873$	−16.1808	−0.547637
$874$	−104.466	−3.53363
$875$	1.00000	0.0338062
$876$	−113.310	−3.82839
$877$	17.2910	0.583875	0.291937	−	0.956437i	$-0.405700\pi$
$877$	17.2910	0.583875	0.291937	+	0.956437i	$0.405700\pi$
$878$	−39.9058	−1.34676
$879$	6.66481	0.224799
$880$	8.44316	0.284619
$881$	−33.6305	−1.13304	−0.566520	−	0.824048i	$-0.691711\pi$
$881$	−33.6305	−1.13304	−0.566520	+	0.824048i	$0.691711\pi$
$882$	2.45947	0.0828146
$883$	−20.1033	−0.676531	−0.338266	−	0.941051i	$-0.609840\pi$
$883$	−20.1033	−0.676531	−0.338266	+	0.941051i	$0.609840\pi$
$884$	9.03647	0.303929
$885$	20.5806	0.691809
$886$	−10.7005	−0.359490
$887$	17.3102	0.581219	0.290610	−	0.956842i	$-0.406142\pi$
$887$	17.3102	0.581219	0.290610	+	0.956842i	$0.406142\pi$
$888$	−48.3291	−1.62182
$889$	4.02935	0.135140
$890$	−14.4335	−0.483811
$891$	51.7778	1.73462
$892$	−26.8481	−0.898939
$893$	58.4941	1.95743
$894$	−38.1366	−1.27548
$895$	−1.74198	−0.0582280
$896$	20.6166	0.688752
$897$	−5.46966	−0.182627
$898$	47.8039	1.59524
$899$	−21.1091	−0.704027
$900$	3.74692	0.124897
$901$	15.5812	0.519085
$902$	−15.3805	−0.512114
$903$	7.18769	0.239191
$904$	−19.6033	−0.651997
$905$	−17.1861	−0.571285
$906$	−21.9596	−0.729560
$907$	−48.7931	−1.62015	−0.810075	−	0.586327i	$-0.800573\pi$
$907$	−48.7931	−1.62015	−0.810075	+	0.586327i	$0.800573\pi$
$908$	−14.9789	−0.497092
$909$	−18.1050	−0.600506
$910$	−0.892148	−0.0295744
$911$	9.01521	0.298687	0.149344	−	0.988785i	$-0.452284\pi$
$911$	9.01521	0.298687	0.149344	+	0.988785i	$0.452284\pi$
$912$	−22.0863	−0.731350
$913$	−67.5056	−2.23411
$914$	−14.7982	−0.489480
$915$	2.01109	0.0664845
$916$	3.60764	0.119200
$917$	−3.16807	−0.104619
$918$	−62.0582	−2.04823
$919$	−34.2171	−1.12872	−0.564358	−	0.825530i	$-0.690876\pi$
$919$	−34.2171	−1.12872	−0.564358	+	0.825530i	$0.690876\pi$
$920$	27.5027	0.906738
$921$	−47.2756	−1.55778
$922$	−87.4734	−2.88078
$923$	5.62522	0.185156
$924$	−34.0115	−1.11890
$925$	6.31706	0.207704
$926$	−49.2438	−1.61825
$927$	11.7807	0.386928
$928$	−13.8272	−0.453900
$929$	41.1258	1.34930	0.674648	−	0.738140i	$-0.264296\pi$
$929$	41.1258	1.34930	0.674648	+	0.738140i	$0.264296\pi$
$930$	−24.3524	−0.798546
$931$	6.10646	0.200131
$932$	48.2940	1.58192
$933$	−30.4426	−0.996647
$934$	37.2069	1.21745
$935$	−31.1901	−1.02003
$936$	−1.48962	−0.0486898
$937$	−10.8224	−0.353551	−0.176776	−	0.984251i	$-0.556567\pi$
$937$	−10.8224	−0.353551	−0.176776	+	0.984251i	$0.556567\pi$
$938$	−1.28514	−0.0419612
$939$	17.3216	0.565268
$940$	−34.5578	−1.12715
$941$	1.16687	0.0380387	0.0190194	−	0.999819i	$-0.493946\pi$
$941$	1.16687	0.0380387	0.0190194	+	0.999819i	$0.493946\pi$
$942$	−64.6489	−2.10638
$943$	−10.0021	−0.325712
$944$	18.4315	0.599893
$945$	3.94167	0.128223
$946$	−39.7330	−1.29183
$947$	5.05122	0.164143	0.0820713	−	0.996626i	$-0.473846\pi$
$947$	5.05122	0.164143	0.0820713	+	0.996626i	$0.473846\pi$
$948$	46.0892	1.49691
$949$	−5.88812	−0.191137
$950$	14.4604	0.469156
$951$	−29.1412	−0.944969
$952$	25.3109	0.820330
$953$	9.55535	0.309528	0.154764	−	0.987951i	$-0.450538\pi$
$953$	9.55535	0.309528	0.154764	+	0.987951i	$0.450538\pi$
$954$	−5.76385	−0.186612
$955$	−2.55093	−0.0825462
$956$	−53.6870	−1.73636
$957$	38.8899	1.25713
$958$	−11.3506	−0.366722
$959$	−6.48851	−0.209525
$960$	−23.1854	−0.748306
$961$	−4.81384	−0.155285
$962$	−5.63575	−0.181704
$963$	16.1474	0.520344
$964$	7.82377	0.251987
$965$	−6.15597	−0.198168
$966$	−34.3798	−1.10615
$967$	−7.81947	−0.251457	−0.125729	−	0.992065i	$-0.540127\pi$
$967$	−7.81947	−0.251457	−0.125729	+	0.992065i	$0.540127\pi$
$968$	41.9060	1.34691
$969$	81.5894	2.62103
$970$	36.8926	1.18455
$971$	7.19810	0.230998	0.115499	−	0.993308i	$-0.463153\pi$
$971$	7.19810	0.230998	0.115499	+	0.993308i	$0.463153\pi$
$972$	37.3588	1.19829
$973$	−11.1111	−0.356205
$974$	32.3100	1.03528
$975$	0.757117	0.0242471
$976$	1.80108	0.0576511
$977$	−46.7002	−1.49407	−0.747036	−	0.664784i	$-0.768524\pi$
$977$	−46.7002	−1.49407	−0.747036	+	0.664784i	$0.768524\pi$
$978$	108.179	3.45919
$979$	−28.5936	−0.913855
$980$	−3.60764	−0.115242
$981$	18.9287	0.604348
$982$	−13.8027	−0.440463
$983$	−56.9979	−1.81795	−0.908976	−	0.416849i	$-0.863134\pi$
$983$	−56.9979	−1.81795	−0.908976	+	0.416849i	$0.863134\pi$
$984$	−10.5922	−0.337667
$985$	1.00610	0.0320569
$986$	−64.9460	−2.06830
$987$	19.2503	0.612745
$988$	−8.29964	−0.264047
$989$	−25.8387	−0.821624
$990$	11.5379	0.366700
$991$	3.29027	0.104519	0.0522594	−	0.998634i	$-0.483358\pi$
$991$	3.29027	0.104519	0.0522594	+	0.998634i	$0.483358\pi$
$992$	17.1529	0.544604
$993$	−51.7089	−1.64093
$994$	35.3576	1.12147
$995$	23.3335	0.739721
$996$	−104.326	−3.30568
$997$	25.3405	0.802542	0.401271	−	0.915959i	$-0.368569\pi$
$997$	25.3405	0.802542	0.401271	+	0.915959i	$0.368569\pi$
$998$	38.6682	1.22402
$999$	24.8998	0.787794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.55	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.55	✓	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)

\(f(q)\)	\(=\)	\(q+2.36805 q^{2} -2.00963 q^{3} +3.60764 q^{4} -1.00000 q^{5} -4.75889 q^{6} -1.00000 q^{7} +3.80696 q^{8} +1.03861 q^{9} +O(q^{10})\)	\(q+2.36805 q^{2} -2.00963 q^{3} +3.60764 q^{4} -1.00000 q^{5} -4.75889 q^{6} -1.00000 q^{7} +3.80696 q^{8} +1.03861 q^{9} -2.36805 q^{10} -4.69124 q^{11} -7.25001 q^{12} -0.376745 q^{13} -2.36805 q^{14} +2.00963 q^{15} +1.79977 q^{16} -6.64858 q^{17} +2.45947 q^{18} +6.10646 q^{19} -3.60764 q^{20} +2.00963 q^{21} -11.1091 q^{22} -7.22433 q^{23} -7.65057 q^{24} +1.00000 q^{25} -0.892148 q^{26} +3.94167 q^{27} -3.60764 q^{28} +4.12509 q^{29} +4.75889 q^{30} -5.11724 q^{31} -3.35197 q^{32} +9.42765 q^{33} -15.7441 q^{34} +1.00000 q^{35} +3.74692 q^{36} +6.31706 q^{37} +14.4604 q^{38} +0.757117 q^{39} -3.80696 q^{40} +1.38450 q^{41} +4.75889 q^{42} +3.57663 q^{43} -16.9243 q^{44} -1.03861 q^{45} -17.1075 q^{46} +9.57906 q^{47} -3.61687 q^{48} +1.00000 q^{49} +2.36805 q^{50} +13.3612 q^{51} -1.35916 q^{52} -2.34354 q^{53} +9.33406 q^{54} +4.69124 q^{55} -3.80696 q^{56} -12.2717 q^{57} +9.76840 q^{58} +10.2410 q^{59} +7.25001 q^{60} +1.00073 q^{61} -12.1179 q^{62} -1.03861 q^{63} -11.5372 q^{64} +0.376745 q^{65} +22.3251 q^{66} +0.542699 q^{67} -23.9857 q^{68} +14.5182 q^{69} +2.36805 q^{70} -14.9311 q^{71} +3.95393 q^{72} +15.6290 q^{73} +14.9591 q^{74} -2.00963 q^{75} +22.0299 q^{76} +4.69124 q^{77} +1.79289 q^{78} -6.35712 q^{79} -1.79977 q^{80} -11.0371 q^{81} +3.27855 q^{82} +14.3897 q^{83} +7.25001 q^{84} +6.64858 q^{85} +8.46961 q^{86} -8.28990 q^{87} -17.8594 q^{88} +6.09510 q^{89} -2.45947 q^{90} +0.376745 q^{91} -26.0628 q^{92} +10.2838 q^{93} +22.6836 q^{94} -6.10646 q^{95} +6.73622 q^{96} -15.5793 q^{97} +2.36805 q^{98} -4.87235 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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