LMFDB - Embedded newform 8015.2.a.l.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.17211 q^{2} +3.11306 q^{3} +2.71804 q^{4} -1.00000 q^{5} -6.76191 q^{6} -1.00000 q^{7} -1.55967 q^{8} +6.69117 q^{9} +O(q^{10})$	\(q-2.17211 q^{2} +3.11306 q^{3} +2.71804 q^{4} -1.00000 q^{5} -6.76191 q^{6} -1.00000 q^{7} -1.55967 q^{8} +6.69117 q^{9} +2.17211 q^{10} -0.102826 q^{11} +8.46145 q^{12} +3.05479 q^{13} +2.17211 q^{14} -3.11306 q^{15} -2.04832 q^{16} +6.79945 q^{17} -14.5339 q^{18} +7.10673 q^{19} -2.71804 q^{20} -3.11306 q^{21} +0.223349 q^{22} -6.34050 q^{23} -4.85535 q^{24} +1.00000 q^{25} -6.63532 q^{26} +11.4909 q^{27} -2.71804 q^{28} +3.49304 q^{29} +6.76191 q^{30} -6.66081 q^{31} +7.56851 q^{32} -0.320104 q^{33} -14.7691 q^{34} +1.00000 q^{35} +18.1869 q^{36} +3.36922 q^{37} -15.4366 q^{38} +9.50975 q^{39} +1.55967 q^{40} +0.870493 q^{41} +6.76191 q^{42} -6.76435 q^{43} -0.279485 q^{44} -6.69117 q^{45} +13.7722 q^{46} -2.90931 q^{47} -6.37657 q^{48} +1.00000 q^{49} -2.17211 q^{50} +21.1671 q^{51} +8.30304 q^{52} +1.10328 q^{53} -24.9594 q^{54} +0.102826 q^{55} +1.55967 q^{56} +22.1237 q^{57} -7.58726 q^{58} -5.23203 q^{59} -8.46145 q^{60} +8.37943 q^{61} +14.4680 q^{62} -6.69117 q^{63} -12.3430 q^{64} -3.05479 q^{65} +0.695300 q^{66} +7.08104 q^{67} +18.4812 q^{68} -19.7384 q^{69} -2.17211 q^{70} -7.78159 q^{71} -10.4360 q^{72} +7.59574 q^{73} -7.31830 q^{74} +3.11306 q^{75} +19.3164 q^{76} +0.102826 q^{77} -20.6562 q^{78} +14.4279 q^{79} +2.04832 q^{80} +15.6983 q^{81} -1.89080 q^{82} +11.2735 q^{83} -8.46145 q^{84} -6.79945 q^{85} +14.6929 q^{86} +10.8741 q^{87} +0.160374 q^{88} +2.05982 q^{89} +14.5339 q^{90} -3.05479 q^{91} -17.2338 q^{92} -20.7355 q^{93} +6.31933 q^{94} -7.10673 q^{95} +23.5613 q^{96} +1.16378 q^{97} -2.17211 q^{98} -0.688026 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.17211	−1.53591	−0.767955	−	0.640503i	$-0.778726\pi$
$2$	−2.17211	−1.53591	−0.767955	+	0.640503i	$0.778726\pi$
$3$	3.11306	1.79733	0.898664	−	0.438637i	$-0.144539\pi$
$3$	3.11306	1.79733	0.898664	+	0.438637i	$0.144539\pi$
$4$	2.71804	1.35902
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−6.76191	−2.76054
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.55967	−0.551426
$9$	6.69117	2.23039
$10$	2.17211	0.686880
$11$	−0.102826	−0.0310032	−0.0155016	−	0.999880i	$-0.504935\pi$
$11$	−0.102826	−0.0310032	−0.0155016	+	0.999880i	$0.504935\pi$
$12$	8.46145	2.44261
$13$	3.05479	0.847245	0.423623	−	0.905839i	$-0.360758\pi$
$13$	3.05479	0.847245	0.423623	+	0.905839i	$0.360758\pi$
$14$	2.17211	0.580520
$15$	−3.11306	−0.803790
$16$	−2.04832	−0.512081
$17$	6.79945	1.64911	0.824555	−	0.565782i	$-0.191426\pi$
$17$	6.79945	1.64911	0.824555	+	0.565782i	$0.191426\pi$
$18$	−14.5339	−3.42568
$19$	7.10673	1.63039	0.815197	−	0.579183i	$-0.196628\pi$
$19$	7.10673	1.63039	0.815197	+	0.579183i	$0.196628\pi$
$20$	−2.71804	−0.607773
$21$	−3.11306	−0.679326
$22$	0.223349	0.0476181
$23$	−6.34050	−1.32209	−0.661043	−	0.750348i	$-0.729886\pi$
$23$	−6.34050	−1.32209	−0.661043	+	0.750348i	$0.729886\pi$
$24$	−4.85535	−0.991094
$25$	1.00000	0.200000
$26$	−6.63532	−1.30129
$27$	11.4909	2.21142
$28$	−2.71804	−0.513662
$29$	3.49304	0.648641	0.324321	−	0.945947i	$-0.394864\pi$
$29$	3.49304	0.648641	0.324321	+	0.945947i	$0.394864\pi$
$30$	6.76191	1.23455
$31$	−6.66081	−1.19632	−0.598159	−	0.801378i	$-0.704101\pi$
$31$	−6.66081	−1.19632	−0.598159	+	0.801378i	$0.704101\pi$
$32$	7.56851	1.33794
$33$	−0.320104	−0.0557229
$34$	−14.7691	−2.53288
$35$	1.00000	0.169031
$36$	18.1869	3.03115
$37$	3.36922	0.553896	0.276948	−	0.960885i	$-0.410677\pi$
$37$	3.36922	0.553896	0.276948	+	0.960885i	$0.410677\pi$
$38$	−15.4366	−2.50414
$39$	9.50975	1.52278
$40$	1.55967	0.246605
$41$	0.870493	0.135948	0.0679741	−	0.997687i	$-0.478346\pi$
$41$	0.870493	0.135948	0.0679741	+	0.997687i	$0.478346\pi$
$42$	6.76191	1.04338
$43$	−6.76435	−1.03155	−0.515777	−	0.856723i	$-0.672497\pi$
$43$	−6.76435	−1.03155	−0.515777	+	0.856723i	$0.672497\pi$
$44$	−0.279485	−0.0421340
$45$	−6.69117	−0.997461
$46$	13.7722	2.03061
$47$	−2.90931	−0.424366	−0.212183	−	0.977230i	$-0.568057\pi$
$47$	−2.90931	−0.424366	−0.212183	+	0.977230i	$0.568057\pi$
$48$	−6.37657	−0.920378
$49$	1.00000	0.142857
$50$	−2.17211	−0.307182
$51$	21.1671	2.96399
$52$	8.30304	1.15143
$53$	1.10328	0.151548	0.0757738	−	0.997125i	$-0.475857\pi$
$53$	1.10328	0.151548	0.0757738	+	0.997125i	$0.475857\pi$
$54$	−24.9594	−3.39654
$55$	0.102826	0.0138650
$56$	1.55967	0.208419
$57$	22.1237	2.93036
$58$	−7.58726	−0.996255
$59$	−5.23203	−0.681152	−0.340576	−	0.940217i	$-0.610622\pi$
$59$	−5.23203	−0.681152	−0.340576	+	0.940217i	$0.610622\pi$
$60$	−8.46145	−1.09237
$61$	8.37943	1.07288	0.536438	−	0.843940i	$-0.319769\pi$
$61$	8.37943	1.07288	0.536438	+	0.843940i	$0.319769\pi$
$62$	14.4680	1.83744
$63$	−6.69117	−0.843009
$64$	−12.3430	−1.54287
$65$	−3.05479	−0.378900
$66$	0.695300	0.0855855
$67$	7.08104	0.865087	0.432544	−	0.901613i	$-0.357616\pi$
$67$	7.08104	0.865087	0.432544	+	0.901613i	$0.357616\pi$
$68$	18.4812	2.24118
$69$	−19.7384	−2.37622
$70$	−2.17211	−0.259616
$71$	−7.78159	−0.923505	−0.461753	−	0.887009i	$-0.652779\pi$
$71$	−7.78159	−0.923505	−0.461753	+	0.887009i	$0.652779\pi$
$72$	−10.4360	−1.22990
$73$	7.59574	0.889014	0.444507	−	0.895775i	$-0.353379\pi$
$73$	7.59574	0.889014	0.444507	+	0.895775i	$0.353379\pi$
$74$	−7.31830	−0.850735
$75$	3.11306	0.359466
$76$	19.3164	2.21574
$77$	0.102826	0.0117181
$78$	−20.6562	−2.33885
$79$	14.4279	1.62326	0.811631	−	0.584170i	$-0.198580\pi$
$79$	14.4279	1.62326	0.811631	+	0.584170i	$0.198580\pi$
$80$	2.04832	0.229010
$81$	15.6983	1.74425
$82$	−1.89080	−0.208804
$83$	11.2735	1.23742	0.618712	−	0.785618i	$-0.287655\pi$
$83$	11.2735	1.23742	0.618712	+	0.785618i	$0.287655\pi$
$84$	−8.46145	−0.923220
$85$	−6.79945	−0.737504
$86$	14.6929	1.58437
$87$	10.8741	1.16582
$88$	0.160374	0.0170960
$89$	2.05982	0.218341	0.109170	−	0.994023i	$-0.465181\pi$
$89$	2.05982	0.218341	0.109170	+	0.994023i	$0.465181\pi$
$90$	14.5339	1.53201
$91$	−3.05479	−0.320229
$92$	−17.2338	−1.79674
$93$	−20.7355	−2.15018
$94$	6.31933	0.651789
$95$	−7.10673	−0.729135
$96$	23.5613	2.40471
$97$	1.16378	0.118164	0.0590820	−	0.998253i	$-0.481183\pi$
$97$	1.16378	0.118164	0.0590820	+	0.998253i	$0.481183\pi$
$98$	−2.17211	−0.219416
$99$	−0.688026	−0.0691492
$100$	2.71804	0.271804
$101$	13.6692	1.36014	0.680069	−	0.733148i	$-0.261950\pi$
$101$	13.6692	1.36014	0.680069	+	0.733148i	$0.261950\pi$
$102$	−45.9773	−4.55243
$103$	4.87115	0.479968	0.239984	−	0.970777i	$-0.422858\pi$
$103$	4.87115	0.479968	0.239984	+	0.970777i	$0.422858\pi$
$104$	−4.76445	−0.467193
$105$	3.11306	0.303804
$106$	−2.39645	−0.232764
$107$	−6.00710	−0.580729	−0.290364	−	0.956916i	$-0.593776\pi$
$107$	−6.00710	−0.580729	−0.290364	+	0.956916i	$0.593776\pi$
$108$	31.2327	3.00537
$109$	13.0643	1.25134	0.625669	−	0.780089i	$-0.284826\pi$
$109$	13.0643	1.25134	0.625669	+	0.780089i	$0.284826\pi$
$110$	−0.223349	−0.0212955
$111$	10.4886	0.995534
$112$	2.04832	0.193548
$113$	−7.16338	−0.673875	−0.336937	−	0.941527i	$-0.609391\pi$
$113$	−7.16338	−0.673875	−0.336937	+	0.941527i	$0.609391\pi$
$114$	−48.0550	−4.50076
$115$	6.34050	0.591255
$116$	9.49424	0.881518
$117$	20.4401	1.88969
$118$	11.3645	1.04619
$119$	−6.79945	−0.623305
$120$	4.85535	0.443231
$121$	−10.9894	−0.999039
$122$	−18.2010	−1.64784
$123$	2.70990	0.244343
$124$	−18.1044	−1.62582
$125$	−1.00000	−0.0894427
$126$	14.5339	1.29479
$127$	−18.1476	−1.61034	−0.805170	−	0.593044i	$-0.797926\pi$
$127$	−18.1476	−1.61034	−0.805170	+	0.593044i	$0.797926\pi$
$128$	11.6732	1.03177
$129$	−21.0578	−1.85404
$130$	6.63532	0.581956
$131$	−12.3798	−1.08163	−0.540815	−	0.841141i	$-0.681884\pi$
$131$	−12.3798	−1.08163	−0.540815	+	0.841141i	$0.681884\pi$
$132$	−0.870056	−0.0757287
$133$	−7.10673	−0.616231
$134$	−15.3808	−1.32870
$135$	−11.4909	−0.988976
$136$	−10.6049	−0.909362
$137$	19.7491	1.68728	0.843638	−	0.536912i	$-0.180409\pi$
$137$	19.7491	1.68728	0.843638	+	0.536912i	$0.180409\pi$
$138$	42.8739	3.64967
$139$	0.155070	0.0131529	0.00657644	−	0.999978i	$-0.497907\pi$
$139$	0.155070	0.0131529	0.00657644	+	0.999978i	$0.497907\pi$
$140$	2.71804	0.229717
$141$	−9.05687	−0.762726
$142$	16.9024	1.41842
$143$	−0.314111	−0.0262673
$144$	−13.7057	−1.14214
$145$	−3.49304	−0.290081
$146$	−16.4988	−1.36545
$147$	3.11306	0.256761
$148$	9.15769	0.752757
$149$	20.7529	1.70014	0.850070	−	0.526669i	$-0.176559\pi$
$149$	20.7529	1.70014	0.850070	+	0.526669i	$0.176559\pi$
$150$	−6.76191	−0.552107
$151$	−0.865117	−0.0704022	−0.0352011	−	0.999380i	$-0.511207\pi$
$151$	−0.865117	−0.0704022	−0.0352011	+	0.999380i	$0.511207\pi$
$152$	−11.0841	−0.899042
$153$	45.4963	3.67816
$154$	−0.223349	−0.0179980
$155$	6.66081	0.535009
$156$	25.8479	2.06949
$157$	−6.35164	−0.506916	−0.253458	−	0.967346i	$-0.581568\pi$
$157$	−6.35164	−0.506916	−0.253458	+	0.967346i	$0.581568\pi$
$158$	−31.3389	−2.49319
$159$	3.43459	0.272381
$160$	−7.56851	−0.598343
$161$	6.34050	0.499701
$162$	−34.0983	−2.67902
$163$	12.5084	0.979733	0.489867	−	0.871797i	$-0.337045\pi$
$163$	12.5084	0.979733	0.489867	+	0.871797i	$0.337045\pi$
$164$	2.36604	0.184756
$165$	0.320104	0.0249201
$166$	−24.4872	−1.90057
$167$	−6.02749	−0.466421	−0.233210	−	0.972426i	$-0.574923\pi$
$167$	−6.02749	−0.466421	−0.233210	+	0.972426i	$0.574923\pi$
$168$	4.85535	0.374598
$169$	−3.66828	−0.282175
$170$	14.7691	1.13274
$171$	47.5523	3.63642
$172$	−18.3858	−1.40190
$173$	−16.2595	−1.23619	−0.618093	−	0.786105i	$-0.712095\pi$
$173$	−16.2595	−1.23619	−0.618093	+	0.786105i	$0.712095\pi$
$174$	−23.6196	−1.79060
$175$	−1.00000	−0.0755929
$176$	0.210621	0.0158761
$177$	−16.2876	−1.22425
$178$	−4.47416	−0.335352
$179$	−4.56853	−0.341468	−0.170734	−	0.985317i	$-0.554614\pi$
$179$	−4.56853	−0.341468	−0.170734	+	0.985317i	$0.554614\pi$
$180$	−18.1869	−1.35557
$181$	−6.49969	−0.483118	−0.241559	−	0.970386i	$-0.577659\pi$
$181$	−6.49969	−0.483118	−0.241559	+	0.970386i	$0.577659\pi$
$182$	6.63532	0.491843
$183$	26.0857	1.92831
$184$	9.88907	0.729032
$185$	−3.36922	−0.247710
$186$	45.0398	3.30248
$187$	−0.699160	−0.0511277
$188$	−7.90763	−0.576723
$189$	−11.4909	−0.835837
$190$	15.4366	1.11989
$191$	−15.4783	−1.11997	−0.559985	−	0.828503i	$-0.689193\pi$
$191$	−15.4783	−1.11997	−0.559985	+	0.828503i	$0.689193\pi$
$192$	−38.4244	−2.77305
$193$	−2.52612	−0.181834	−0.0909169	−	0.995858i	$-0.528980\pi$
$193$	−2.52612	−0.181834	−0.0909169	+	0.995858i	$0.528980\pi$
$194$	−2.52785	−0.181489
$195$	−9.50975	−0.681007
$196$	2.71804	0.194146
$197$	−25.4728	−1.81486	−0.907430	−	0.420203i	$-0.861959\pi$
$197$	−25.4728	−1.81486	−0.907430	+	0.420203i	$0.861959\pi$
$198$	1.49447	0.106207
$199$	−18.7698	−1.33056	−0.665278	−	0.746596i	$-0.731687\pi$
$199$	−18.7698	−1.33056	−0.665278	+	0.746596i	$0.731687\pi$
$200$	−1.55967	−0.110285
$201$	22.0437	1.55485
$202$	−29.6910	−2.08905
$203$	−3.49304	−0.245163
$204$	57.5332	4.02813
$205$	−0.870493	−0.0607978
$206$	−10.5806	−0.737188
$207$	−42.4254	−2.94877
$208$	−6.25719	−0.433858
$209$	−0.730756	−0.0505474
$210$	−6.76191	−0.466616
$211$	−22.9860	−1.58242	−0.791210	−	0.611545i	$-0.790548\pi$
$211$	−22.9860	−1.58242	−0.791210	+	0.611545i	$0.790548\pi$
$212$	2.99877	0.205957
$213$	−24.2246	−1.65984
$214$	13.0481	0.891947
$215$	6.76435	0.461325
$216$	−17.9219	−1.21943
$217$	6.66081	0.452165
$218$	−28.3771	−1.92194
$219$	23.6460	1.59785
$220$	0.279485	0.0188429
$221$	20.7709	1.39720
$222$	−22.7823	−1.52905
$223$	9.69459	0.649198	0.324599	−	0.945852i	$-0.394771\pi$
$223$	9.69459	0.649198	0.324599	+	0.945852i	$0.394771\pi$
$224$	−7.56851	−0.505693
$225$	6.69117	0.446078
$226$	15.5596	1.03501
$227$	−14.7518	−0.979112	−0.489556	−	0.871972i	$-0.662841\pi$
$227$	−14.7518	−0.979112	−0.489556	+	0.871972i	$0.662841\pi$
$228$	60.1332	3.98242
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−13.7722	−0.908114
$231$	0.320104	0.0210613
$232$	−5.44799	−0.357678
$233$	−1.68649	−0.110486	−0.0552428	−	0.998473i	$-0.517593\pi$
$233$	−1.68649	−0.110486	−0.0552428	+	0.998473i	$0.517593\pi$
$234$	−44.3981	−2.90239
$235$	2.90931	0.189782
$236$	−14.2209	−0.925700
$237$	44.9149	2.91754
$238$	14.7691	0.957340
$239$	−8.41214	−0.544136	−0.272068	−	0.962278i	$-0.587708\pi$
$239$	−8.41214	−0.544136	−0.272068	+	0.962278i	$0.587708\pi$
$240$	6.37657	0.411606
$241$	−0.905279	−0.0583142	−0.0291571	−	0.999575i	$-0.509282\pi$
$241$	−0.905279	−0.0583142	−0.0291571	+	0.999575i	$0.509282\pi$
$242$	23.8702	1.53443
$243$	14.3972	0.923580
$244$	22.7757	1.45806
$245$	−1.00000	−0.0638877
$246$	−5.88619	−0.375290
$247$	21.7095	1.38134
$248$	10.3887	0.659680
$249$	35.0950	2.22406
$250$	2.17211	0.137376
$251$	2.81828	0.177888	0.0889441	−	0.996037i	$-0.471651\pi$
$251$	2.81828	0.177888	0.0889441	+	0.996037i	$0.471651\pi$
$252$	−18.1869	−1.14567
$253$	0.651968	0.0409889
$254$	39.4185	2.47334
$255$	−21.1671	−1.32554
$256$	−0.669499	−0.0418437
$257$	−2.69672	−0.168217	−0.0841084	−	0.996457i	$-0.526804\pi$
$257$	−2.69672	−0.168217	−0.0841084	+	0.996457i	$0.526804\pi$
$258$	45.7399	2.84764
$259$	−3.36922	−0.209353
$260$	−8.30304	−0.514933
$261$	23.3725	1.44672
$262$	26.8903	1.66129
$263$	6.66574	0.411027	0.205514	−	0.978654i	$-0.434114\pi$
$263$	6.66574	0.411027	0.205514	+	0.978654i	$0.434114\pi$
$264$	0.499256	0.0307271
$265$	−1.10328	−0.0677742
$266$	15.4366	0.946476
$267$	6.41236	0.392430
$268$	19.2466	1.17567
$269$	−19.7870	−1.20644	−0.603218	−	0.797576i	$-0.706115\pi$
$269$	−19.7870	−1.20644	−0.603218	+	0.797576i	$0.706115\pi$
$270$	24.9594	1.51898
$271$	0.884167	0.0537093	0.0268547	−	0.999639i	$-0.491451\pi$
$271$	0.884167	0.0537093	0.0268547	+	0.999639i	$0.491451\pi$
$272$	−13.9275	−0.844478
$273$	−9.50975	−0.575556
$274$	−42.8971	−2.59151
$275$	−0.102826	−0.00620064
$276$	−53.6498	−3.22934
$277$	5.24972	0.315425	0.157712	−	0.987485i	$-0.449588\pi$
$277$	5.24972	0.315425	0.157712	+	0.987485i	$0.449588\pi$
$278$	−0.336829	−0.0202017
$279$	−44.5687	−2.66826
$280$	−1.55967	−0.0932080
$281$	23.7773	1.41844	0.709218	−	0.704990i	$-0.249048\pi$
$281$	23.7773	1.41844	0.709218	+	0.704990i	$0.249048\pi$
$282$	19.6725	1.17148
$283$	9.39880	0.558700	0.279350	−	0.960189i	$-0.409881\pi$
$283$	9.39880	0.558700	0.279350	+	0.960189i	$0.409881\pi$
$284$	−21.1507	−1.25506
$285$	−22.1237	−1.31049
$286$	0.682283	0.0403442
$287$	−0.870493	−0.0513836
$288$	50.6422	2.98412
$289$	29.2325	1.71956
$290$	7.58726	0.445539
$291$	3.62292	0.212380
$292$	20.6456	1.20819
$293$	26.8567	1.56898	0.784492	−	0.620138i	$-0.212924\pi$
$293$	26.8567	1.56898	0.784492	+	0.620138i	$0.212924\pi$
$294$	−6.76191	−0.394362
$295$	5.23203	0.304620
$296$	−5.25486	−0.305433
$297$	−1.18156	−0.0685610
$298$	−45.0774	−2.61126
$299$	−19.3689	−1.12013
$300$	8.46145	0.488522
$301$	6.76435	0.389890
$302$	1.87913	0.108132
$303$	42.5532	2.44462
$304$	−14.5569	−0.834894
$305$	−8.37943	−0.479805
$306$	−98.8228	−5.64932
$307$	10.1752	0.580728	0.290364	−	0.956916i	$-0.406224\pi$
$307$	10.1752	0.580728	0.290364	+	0.956916i	$0.406224\pi$
$308$	0.279485	0.0159252
$309$	15.1642	0.862661
$310$	−14.4680	−0.821727
$311$	0.908506	0.0515167	0.0257583	−	0.999668i	$-0.491800\pi$
$311$	0.908506	0.0515167	0.0257583	+	0.999668i	$0.491800\pi$
$312$	−14.8321	−0.839700
$313$	13.8325	0.781862	0.390931	−	0.920420i	$-0.372153\pi$
$313$	13.8325	0.781862	0.390931	+	0.920420i	$0.372153\pi$
$314$	13.7964	0.778578
$315$	6.69117	0.377005
$316$	39.2156	2.20605
$317$	26.4053	1.48307	0.741536	−	0.670913i	$-0.234098\pi$
$317$	26.4053	1.48307	0.741536	+	0.670913i	$0.234098\pi$
$318$	−7.46030	−0.418353
$319$	−0.359175	−0.0201100
$320$	12.3430	0.689993
$321$	−18.7005	−1.04376
$322$	−13.7722	−0.767497
$323$	48.3218	2.68870
$324$	42.6686	2.37048
$325$	3.05479	0.169449
$326$	−27.1696	−1.50478
$327$	40.6702	2.24907
$328$	−1.35768	−0.0749653
$329$	2.90931	0.160395
$330$	−0.695300	−0.0382750
$331$	26.2852	1.44476	0.722381	−	0.691495i	$-0.243047\pi$
$331$	26.2852	1.44476	0.722381	+	0.691495i	$0.243047\pi$
$332$	30.6418	1.68169
$333$	22.5440	1.23541
$334$	13.0923	0.716381
$335$	−7.08104	−0.386879
$336$	6.37657	0.347870
$337$	21.5380	1.17325	0.586625	−	0.809858i	$-0.300456\pi$
$337$	21.5380	1.17325	0.586625	+	0.809858i	$0.300456\pi$
$338$	7.96790	0.433396
$339$	−22.3001	−1.21117
$340$	−18.4812	−1.00228
$341$	0.684904	0.0370897
$342$	−103.289	−5.58521
$343$	−1.00000	−0.0539949
$344$	10.5501	0.568825
$345$	19.7384	1.06268
$346$	35.3174	1.89867
$347$	−5.63445	−0.302473	−0.151237	−	0.988498i	$-0.548326\pi$
$347$	−5.63445	−0.302473	−0.151237	+	0.988498i	$0.548326\pi$
$348$	29.5562	1.58438
$349$	18.0715	0.967343	0.483671	−	0.875250i	$-0.339303\pi$
$349$	18.0715	0.967343	0.483671	+	0.875250i	$0.339303\pi$
$350$	2.17211	0.116104
$351$	35.1021	1.87361
$352$	−0.778240	−0.0414803
$353$	−16.8473	−0.896689	−0.448345	−	0.893861i	$-0.647986\pi$
$353$	−16.8473	−0.896689	−0.448345	+	0.893861i	$0.647986\pi$
$354$	35.3785	1.88034
$355$	7.78159	0.413004
$356$	5.59869	0.296730
$357$	−21.1671	−1.12028
$358$	9.92333	0.524464
$359$	1.86585	0.0984756	0.0492378	−	0.998787i	$-0.484321\pi$
$359$	1.86585	0.0984756	0.0492378	+	0.998787i	$0.484321\pi$
$360$	10.4360	0.550026
$361$	31.5055	1.65819
$362$	14.1180	0.742027
$363$	−34.2108	−1.79560
$364$	−8.30304	−0.435198
$365$	−7.59574	−0.397579
$366$	−56.6609	−2.96171
$367$	9.71776	0.507263	0.253632	−	0.967301i	$-0.418375\pi$
$367$	9.71776	0.507263	0.253632	+	0.967301i	$0.418375\pi$
$368$	12.9874	0.677015
$369$	5.82462	0.303217
$370$	7.31830	0.380460
$371$	−1.10328	−0.0572796
$372$	−56.3601	−2.92214
$373$	31.9200	1.65275	0.826376	−	0.563118i	$-0.190398\pi$
$373$	31.9200	1.65275	0.826376	+	0.563118i	$0.190398\pi$
$374$	1.51865	0.0785275
$375$	−3.11306	−0.160758
$376$	4.53756	0.234007
$377$	10.6705	0.549558
$378$	24.9594	1.28377
$379$	20.4226	1.04904	0.524520	−	0.851398i	$-0.324245\pi$
$379$	20.4226	1.04904	0.524520	+	0.851398i	$0.324245\pi$
$380$	−19.3164	−0.990910
$381$	−56.4947	−2.89431
$382$	33.6205	1.72017
$383$	−29.1053	−1.48721	−0.743606	−	0.668618i	$-0.766886\pi$
$383$	−29.1053	−1.48721	−0.743606	+	0.668618i	$0.766886\pi$
$384$	36.3394	1.85444
$385$	−0.102826	−0.00524050
$386$	5.48699	0.279281
$387$	−45.2614	−2.30077
$388$	3.16321	0.160587
$389$	−27.8679	−1.41296	−0.706480	−	0.707733i	$-0.749718\pi$
$389$	−27.8679	−1.41296	−0.706480	+	0.707733i	$0.749718\pi$
$390$	20.6562	1.04597
$391$	−43.1119	−2.18026
$392$	−1.55967	−0.0787751
$393$	−38.5392	−1.94405
$394$	55.3296	2.78746
$395$	−14.4279	−0.725945
$396$	−1.87009	−0.0939754
$397$	14.4731	0.726382	0.363191	−	0.931715i	$-0.381687\pi$
$397$	14.4731	0.726382	0.363191	+	0.931715i	$0.381687\pi$
$398$	40.7700	2.04362
$399$	−22.1237	−1.10757
$400$	−2.04832	−0.102416
$401$	26.6313	1.32990	0.664952	−	0.746886i	$-0.268452\pi$
$401$	26.6313	1.32990	0.664952	+	0.746886i	$0.268452\pi$
$402$	−47.8814	−2.38810
$403$	−20.3474	−1.01357
$404$	37.1535	1.84846
$405$	−15.6983	−0.780054
$406$	7.58726	0.376549
$407$	−0.346443	−0.0171726
$408$	−33.0137	−1.63442
$409$	9.38514	0.464065	0.232033	−	0.972708i	$-0.425462\pi$
$409$	9.38514	0.464065	0.232033	+	0.972708i	$0.425462\pi$
$410$	1.89080	0.0933801
$411$	61.4801	3.03259
$412$	13.2400	0.652288
$413$	5.23203	0.257451
$414$	92.1524	4.52904
$415$	−11.2735	−0.553393
$416$	23.1202	1.13356
$417$	0.482744	0.0236401
$418$	1.58728	0.0776364
$419$	1.30305	0.0636582	0.0318291	−	0.999493i	$-0.489867\pi$
$419$	1.30305	0.0636582	0.0318291	+	0.999493i	$0.489867\pi$
$420$	8.46145	0.412876
$421$	10.5958	0.516406	0.258203	−	0.966091i	$-0.416870\pi$
$421$	10.5958	0.516406	0.258203	+	0.966091i	$0.416870\pi$
$422$	49.9280	2.43046
$423$	−19.4667	−0.946503
$424$	−1.72076	−0.0835673
$425$	6.79945	0.329822
$426$	52.6184	2.54937
$427$	−8.37943	−0.405509
$428$	−16.3276	−0.789223
$429$	−0.977849	−0.0472110
$430$	−14.6929	−0.708553
$431$	−36.0449	−1.73622	−0.868110	−	0.496372i	$-0.834665\pi$
$431$	−36.0449	−1.73622	−0.868110	+	0.496372i	$0.834665\pi$
$432$	−23.5370	−1.13242
$433$	−17.6845	−0.849862	−0.424931	−	0.905226i	$-0.639702\pi$
$433$	−17.6845	−0.849862	−0.424931	+	0.905226i	$0.639702\pi$
$434$	−14.4680	−0.694486
$435$	−10.8741	−0.521371
$436$	35.5095	1.70060
$437$	−45.0602	−2.15552
$438$	−51.3617	−2.45416
$439$	31.1139	1.48498	0.742492	−	0.669855i	$-0.233644\pi$
$439$	31.1139	1.48498	0.742492	+	0.669855i	$0.233644\pi$
$440$	−0.160374	−0.00764555
$441$	6.69117	0.318627
$442$	−45.1165	−2.14597
$443$	−0.415957	−0.0197627	−0.00988136	−	0.999951i	$-0.503145\pi$
$443$	−0.415957	−0.0197627	−0.00988136	+	0.999951i	$0.503145\pi$
$444$	28.5085	1.35295
$445$	−2.05982	−0.0976450
$446$	−21.0577	−0.997110
$447$	64.6050	3.05571
$448$	12.3430	0.583150
$449$	−0.304179	−0.0143551	−0.00717754	−	0.999974i	$-0.502285\pi$
$449$	−0.304179	−0.0143551	−0.00717754	+	0.999974i	$0.502285\pi$
$450$	−14.5339	−0.685136
$451$	−0.0895092	−0.00421483
$452$	−19.4704	−0.915810
$453$	−2.69317	−0.126536
$454$	32.0425	1.50383
$455$	3.05479	0.143211
$456$	−34.5056	−1.61587
$457$	−28.6458	−1.33999	−0.669996	−	0.742365i	$-0.733704\pi$
$457$	−28.6458	−1.33999	−0.669996	+	0.742365i	$0.733704\pi$
$458$	−2.17211	−0.101496
$459$	78.1316	3.64687
$460$	17.2338	0.803528
$461$	6.42458	0.299223	0.149611	−	0.988745i	$-0.452198\pi$
$461$	6.42458	0.299223	0.149611	+	0.988745i	$0.452198\pi$
$462$	−0.695300	−0.0323483
$463$	−5.70188	−0.264989	−0.132494	−	0.991184i	$-0.542299\pi$
$463$	−5.70188	−0.264989	−0.132494	+	0.991184i	$0.542299\pi$
$464$	−7.15488	−0.332157
$465$	20.7355	0.961588
$466$	3.66323	0.169696
$467$	36.1469	1.67268	0.836340	−	0.548212i	$-0.184691\pi$
$467$	36.1469	1.67268	0.836340	+	0.548212i	$0.184691\pi$
$468$	55.5571	2.56813
$469$	−7.08104	−0.326972
$470$	−6.31933	−0.291489
$471$	−19.7731	−0.911095
$472$	8.16023	0.375605
$473$	0.695550	0.0319814
$474$	−97.5599	−4.48108
$475$	7.10673	0.326079
$476$	−18.4812	−0.847085
$477$	7.38226	0.338010
$478$	18.2720	0.835744
$479$	−30.4520	−1.39139	−0.695694	−	0.718338i	$-0.744903\pi$
$479$	−30.4520	−1.39139	−0.695694	+	0.718338i	$0.744903\pi$
$480$	−23.5613	−1.07542
$481$	10.2922	0.469286
$482$	1.96636	0.0895654
$483$	19.7384	0.898128
$484$	−29.8697	−1.35772
$485$	−1.16378	−0.0528445
$486$	−31.2722	−1.41854
$487$	14.7751	0.669524	0.334762	−	0.942303i	$-0.391344\pi$
$487$	14.7751	0.669524	0.334762	+	0.942303i	$0.391344\pi$
$488$	−13.0691	−0.591612
$489$	38.9395	1.76090
$490$	2.17211	0.0981257
$491$	−8.63189	−0.389552	−0.194776	−	0.980848i	$-0.562398\pi$
$491$	−8.63189	−0.389552	−0.194776	+	0.980848i	$0.562398\pi$
$492$	7.36563	0.332068
$493$	23.7508	1.06968
$494$	−47.1554	−2.12162
$495$	0.688026	0.0309245
$496$	13.6435	0.612611
$497$	7.78159	0.349052
$498$	−76.2301	−3.41595
$499$	12.8633	0.575840	0.287920	−	0.957655i	$-0.407036\pi$
$499$	12.8633	0.575840	0.287920	+	0.957655i	$0.407036\pi$
$500$	−2.71804	−0.121555
$501$	−18.7640	−0.838312
$502$	−6.12160	−0.273221
$503$	14.7692	0.658525	0.329262	−	0.944238i	$-0.393200\pi$
$503$	14.7692	0.658525	0.329262	+	0.944238i	$0.393200\pi$
$504$	10.4360	0.464857
$505$	−13.6692	−0.608272
$506$	−1.41614	−0.0629552
$507$	−11.4196	−0.507162
$508$	−49.3260	−2.18849
$509$	−28.1750	−1.24883	−0.624417	−	0.781091i	$-0.714663\pi$
$509$	−28.1750	−1.24883	−0.624417	+	0.781091i	$0.714663\pi$
$510$	45.9773	2.03591
$511$	−7.59574	−0.336016
$512$	−21.8922	−0.967507
$513$	81.6624	3.60548
$514$	5.85756	0.258366
$515$	−4.87115	−0.214648
$516$	−57.2362	−2.51968
$517$	0.299153	0.0131567
$518$	7.31830	0.321548
$519$	−50.6169	−2.22183
$520$	4.76445	0.208935
$521$	−1.92597	−0.0843782	−0.0421891	−	0.999110i	$-0.513433\pi$
$521$	−1.92597	−0.0843782	−0.0421891	+	0.999110i	$0.513433\pi$
$522$	−50.7676	−2.22204
$523$	30.7122	1.34295	0.671476	−	0.741026i	$-0.265661\pi$
$523$	30.7122	1.34295	0.671476	+	0.741026i	$0.265661\pi$
$524$	−33.6489	−1.46996
$525$	−3.11306	−0.135865
$526$	−14.4787	−0.631301
$527$	−45.2899	−1.97286
$528$	0.655676	0.0285347
$529$	17.2019	0.747910
$530$	2.39645	0.104095
$531$	−35.0084	−1.51923
$532$	−19.3164	−0.837472
$533$	2.65917	0.115181
$534$	−13.9283	−0.602738
$535$	6.00710	0.259710
$536$	−11.0441	−0.477031
$537$	−14.2221	−0.613730
$538$	42.9795	1.85298
$539$	−0.102826	−0.00442903
$540$	−31.2327	−1.34404
$541$	11.6957	0.502839	0.251420	−	0.967878i	$-0.419103\pi$
$541$	11.6957	0.502839	0.251420	+	0.967878i	$0.419103\pi$
$542$	−1.92050	−0.0824927
$543$	−20.2340	−0.868323
$544$	51.4617	2.20640
$545$	−13.0643	−0.559615
$546$	20.6562	0.884003
$547$	17.7354	0.758312	0.379156	−	0.925333i	$-0.376214\pi$
$547$	17.7354	0.758312	0.379156	+	0.925333i	$0.376214\pi$
$548$	53.6788	2.29305
$549$	56.0682	2.39293
$550$	0.223349	0.00952363
$551$	24.8241	1.05754
$552$	30.7853	1.31031
$553$	−14.4279	−0.613535
$554$	−11.4029	−0.484464
$555$	−10.4886	−0.445216
$556$	0.421488	0.0178751
$557$	−21.6871	−0.918910	−0.459455	−	0.888201i	$-0.651955\pi$
$557$	−21.6871	−0.918910	−0.459455	+	0.888201i	$0.651955\pi$
$558$	96.8078	4.09820
$559$	−20.6636	−0.873978
$560$	−2.04832	−0.0865575
$561$	−2.17653	−0.0918932
$562$	−51.6468	−2.17859
$563$	0.814825	0.0343408	0.0171704	−	0.999853i	$-0.494534\pi$
$563$	0.814825	0.0343408	0.0171704	+	0.999853i	$0.494534\pi$
$564$	−24.6170	−1.03656
$565$	7.16338	0.301366
$566$	−20.4152	−0.858114
$567$	−15.6983	−0.659266
$568$	12.1367	0.509245
$569$	11.5836	0.485610	0.242805	−	0.970075i	$-0.421933\pi$
$569$	11.5836	0.485610	0.242805	+	0.970075i	$0.421933\pi$
$570$	48.0550	2.01280
$571$	−15.6604	−0.655366	−0.327683	−	0.944788i	$-0.606268\pi$
$571$	−15.6604	−0.655366	−0.327683	+	0.944788i	$0.606268\pi$
$572$	−0.853768	−0.0356979
$573$	−48.1849	−2.01295
$574$	1.89080	0.0789206
$575$	−6.34050	−0.264417
$576$	−82.5889	−3.44120
$577$	24.9148	1.03722	0.518609	−	0.855012i	$-0.326450\pi$
$577$	24.9148	1.03722	0.518609	+	0.855012i	$0.326450\pi$
$578$	−63.4962	−2.64109
$579$	−7.86397	−0.326815
$580$	−9.49424	−0.394227
$581$	−11.2735	−0.467702
$582$	−7.86937	−0.326196
$583$	−0.113446	−0.00469846
$584$	−11.8468	−0.490226
$585$	−20.4401	−0.845094
$586$	−58.3356	−2.40982
$587$	17.2353	0.711377	0.355689	−	0.934605i	$-0.384246\pi$
$587$	17.2353	0.711377	0.355689	+	0.934605i	$0.384246\pi$
$588$	8.46145	0.348944
$589$	−47.3366	−1.95047
$590$	−11.3645	−0.467870
$591$	−79.2984	−3.26190
$592$	−6.90125	−0.283640
$593$	38.7192	1.59001	0.795003	−	0.606606i	$-0.207469\pi$
$593$	38.7192	1.59001	0.795003	+	0.606606i	$0.207469\pi$
$594$	2.56647	0.105304
$595$	6.79945	0.278750
$596$	56.4072	2.31053
$597$	−58.4316	−2.39145
$598$	42.0712	1.72042
$599$	−15.3411	−0.626819	−0.313410	−	0.949618i	$-0.601471\pi$
$599$	−15.3411	−0.626819	−0.313410	+	0.949618i	$0.601471\pi$
$600$	−4.85535	−0.198219
$601$	−14.0883	−0.574675	−0.287337	−	0.957829i	$-0.592770\pi$
$601$	−14.0883	−0.574675	−0.287337	+	0.957829i	$0.592770\pi$
$602$	−14.6929	−0.598837
$603$	47.3805	1.92948
$604$	−2.35143	−0.0956782
$605$	10.9894	0.446784
$606$	−92.4300	−3.75471
$607$	−40.8918	−1.65975	−0.829874	−	0.557951i	$-0.811588\pi$
$607$	−40.8918	−1.65975	−0.829874	+	0.557951i	$0.811588\pi$
$608$	53.7873	2.18136
$609$	−10.8741	−0.440639
$610$	18.2010	0.736937
$611$	−8.88732	−0.359542
$612$	123.661	4.99870
$613$	20.4871	0.827465	0.413733	−	0.910398i	$-0.364225\pi$
$613$	20.4871	0.827465	0.413733	+	0.910398i	$0.364225\pi$
$614$	−22.1015	−0.891946
$615$	−2.70990	−0.109274
$616$	−0.160374	−0.00646167
$617$	−0.665042	−0.0267736	−0.0133868	−	0.999910i	$-0.504261\pi$
$617$	−0.665042	−0.0267736	−0.0133868	+	0.999910i	$0.504261\pi$
$618$	−32.9382	−1.32497
$619$	18.5476	0.745491	0.372745	−	0.927934i	$-0.378417\pi$
$619$	18.5476	0.745491	0.372745	+	0.927934i	$0.378417\pi$
$620$	18.1044	0.727090
$621$	−72.8578	−2.92368
$622$	−1.97337	−0.0791250
$623$	−2.05982	−0.0825251
$624$	−19.4790	−0.779786
$625$	1.00000	0.0400000
$626$	−30.0457	−1.20087
$627$	−2.27489	−0.0908504
$628$	−17.2640	−0.688910
$629$	22.9088	0.913436
$630$	−14.5339	−0.579046
$631$	46.8659	1.86570	0.932851	−	0.360262i	$-0.117313\pi$
$631$	46.8659	1.86570	0.932851	+	0.360262i	$0.117313\pi$
$632$	−22.5027	−0.895109
$633$	−71.5568	−2.84413
$634$	−57.3552	−2.27787
$635$	18.1476	0.720166
$636$	9.33538	0.370172
$637$	3.05479	0.121035
$638$	0.780167	0.0308871
$639$	−52.0680	−2.05978
$640$	−11.6732	−0.461424
$641$	42.7847	1.68989	0.844947	−	0.534850i	$-0.179632\pi$
$641$	42.7847	1.68989	0.844947	+	0.534850i	$0.179632\pi$
$642$	40.6195	1.60312
$643$	−25.2775	−0.996846	−0.498423	−	0.866934i	$-0.666087\pi$
$643$	−25.2775	−0.996846	−0.498423	+	0.866934i	$0.666087\pi$
$644$	17.2338	0.679105
$645$	21.0578	0.829152
$646$	−104.960	−4.12960
$647$	−38.8002	−1.52539	−0.762696	−	0.646757i	$-0.776125\pi$
$647$	−38.8002	−1.52539	−0.762696	+	0.646757i	$0.776125\pi$
$648$	−24.4841	−0.961827
$649$	0.537988	0.0211179
$650$	−6.63532	−0.260259
$651$	20.7355	0.812690
$652$	33.9984	1.33148
$653$	10.7403	0.420299	0.210149	−	0.977669i	$-0.432605\pi$
$653$	10.7403	0.420299	0.210149	+	0.977669i	$0.432605\pi$
$654$	−88.3399	−3.45436
$655$	12.3798	0.483720
$656$	−1.78305	−0.0696164
$657$	50.8244	1.98285
$658$	−6.31933	−0.246353
$659$	−39.6316	−1.54383	−0.771914	−	0.635727i	$-0.780700\pi$
$659$	−39.6316	−1.54383	−0.771914	+	0.635727i	$0.780700\pi$
$660$	0.870056	0.0338669
$661$	−4.50623	−0.175272	−0.0876361	−	0.996153i	$-0.527931\pi$
$661$	−4.50623	−0.175272	−0.0876361	+	0.996153i	$0.527931\pi$
$662$	−57.0941	−2.21903
$663$	64.6611	2.51123
$664$	−17.5829	−0.682347
$665$	7.10673	0.275587
$666$	−48.9680	−1.89747
$667$	−22.1476	−0.857559
$668$	−16.3830	−0.633876
$669$	30.1799	1.16682
$670$	15.3808	0.594211
$671$	−0.861623	−0.0332626
$672$	−23.5613	−0.908896
$673$	36.4948	1.40677	0.703386	−	0.710808i	$-0.251670\pi$
$673$	36.4948	1.40677	0.703386	+	0.710808i	$0.251670\pi$
$674$	−46.7829	−1.80201
$675$	11.4909	0.442284
$676$	−9.97055	−0.383483
$677$	31.0800	1.19450	0.597251	−	0.802054i	$-0.296259\pi$
$677$	31.0800	1.19450	0.597251	+	0.802054i	$0.296259\pi$
$678$	48.4381	1.86026
$679$	−1.16378	−0.0446618
$680$	10.6049	0.406679
$681$	−45.9233	−1.75979
$682$	−1.48768	−0.0569664
$683$	−16.2894	−0.623296	−0.311648	−	0.950198i	$-0.600881\pi$
$683$	−16.2894	−0.623296	−0.311648	+	0.950198i	$0.600881\pi$
$684$	129.249	4.94197
$685$	−19.7491	−0.754573
$686$	2.17211	0.0829314
$687$	3.11306	0.118771
$688$	13.8556	0.528239
$689$	3.37029	0.128398
$690$	−42.8739	−1.63218
$691$	−18.6256	−0.708550	−0.354275	−	0.935141i	$-0.615272\pi$
$691$	−18.6256	−0.708550	−0.354275	+	0.935141i	$0.615272\pi$
$692$	−44.1940	−1.68001
$693$	0.688026	0.0261360
$694$	12.2386	0.464572
$695$	−0.155070	−0.00588215
$696$	−16.9599	−0.642865
$697$	5.91887	0.224193
$698$	−39.2531	−1.48575
$699$	−5.25015	−0.198579
$700$	−2.71804	−0.102732
$701$	11.3230	0.427663	0.213832	−	0.976871i	$-0.431406\pi$
$701$	11.3230	0.427663	0.213832	+	0.976871i	$0.431406\pi$
$702$	−76.2455	−2.87770
$703$	23.9441	0.903070
$704$	1.26918	0.0478339
$705$	9.05687	0.341101
$706$	36.5940	1.37723
$707$	−13.6692	−0.514084
$708$	−44.2705	−1.66379
$709$	10.8956	0.409191	0.204595	−	0.978847i	$-0.434412\pi$
$709$	10.8956	0.409191	0.204595	+	0.978847i	$0.434412\pi$
$710$	−16.9024	−0.634337
$711$	96.5394	3.62051
$712$	−3.21264	−0.120399
$713$	42.2329	1.58163
$714$	45.9773	1.72066
$715$	0.314111	0.0117471
$716$	−12.4175	−0.464062
$717$	−26.1875	−0.977991
$718$	−4.05281	−0.151250
$719$	−27.6644	−1.03171	−0.515854	−	0.856677i	$-0.672525\pi$
$719$	−27.6644	−1.03171	−0.515854	+	0.856677i	$0.672525\pi$
$720$	13.7057	0.510781
$721$	−4.87115	−0.181411
$722$	−68.4334	−2.54683
$723$	−2.81819	−0.104810
$724$	−17.6665	−0.656569
$725$	3.49304	0.129728
$726$	74.3095	2.75788
$727$	−19.8207	−0.735110	−0.367555	−	0.930002i	$-0.619805\pi$
$727$	−19.8207	−0.735110	−0.367555	+	0.930002i	$0.619805\pi$
$728$	4.76445	0.176582
$729$	−2.27548	−0.0842770
$730$	16.4988	0.610646
$731$	−45.9938	−1.70114
$732$	70.9021	2.62062
$733$	15.8034	0.583712	0.291856	−	0.956462i	$-0.405727\pi$
$733$	15.8034	0.583712	0.291856	+	0.956462i	$0.405727\pi$
$734$	−21.1080	−0.779111
$735$	−3.11306	−0.114827
$736$	−47.9881	−1.76887
$737$	−0.728115	−0.0268205
$738$	−12.6517	−0.465715
$739$	21.7168	0.798866	0.399433	−	0.916762i	$-0.369207\pi$
$739$	21.7168	0.798866	0.399433	+	0.916762i	$0.369207\pi$
$740$	−9.15769	−0.336643
$741$	67.5832	2.48273
$742$	2.39645	0.0879764
$743$	32.0473	1.17570	0.587850	−	0.808970i	$-0.299975\pi$
$743$	32.0473	1.17570	0.587850	+	0.808970i	$0.299975\pi$
$744$	32.3406	1.18566
$745$	−20.7529	−0.760326
$746$	−69.3335	−2.53848
$747$	75.4327	2.75994
$748$	−1.90035	−0.0694836
$749$	6.00710	0.219495
$750$	6.76191	0.246910
$751$	−9.55970	−0.348838	−0.174419	−	0.984671i	$-0.555805\pi$
$751$	−9.55970	−0.348838	−0.174419	+	0.984671i	$0.555805\pi$
$752$	5.95921	0.217310
$753$	8.77349	0.319724
$754$	−23.1774	−0.844073
$755$	0.865117	0.0314848
$756$	−31.2327	−1.13592
$757$	31.5331	1.14609	0.573044	−	0.819525i	$-0.305762\pi$
$757$	31.5331	1.14609	0.573044	+	0.819525i	$0.305762\pi$
$758$	−44.3601	−1.61123
$759$	2.02962	0.0736705
$760$	11.0841	0.402064
$761$	−13.8681	−0.502718	−0.251359	−	0.967894i	$-0.580877\pi$
$761$	−13.8681	−0.502718	−0.251359	+	0.967894i	$0.580877\pi$
$762$	122.712	4.44540
$763$	−13.0643	−0.472961
$764$	−42.0706	−1.52206
$765$	−45.4963	−1.64492
$766$	63.2198	2.28423
$767$	−15.9827	−0.577103
$768$	−2.08419	−0.0752068
$769$	−2.12500	−0.0766293	−0.0383146	−	0.999266i	$-0.512199\pi$
$769$	−2.12500	−0.0766293	−0.0383146	+	0.999266i	$0.512199\pi$
$770$	0.223349	0.00804893
$771$	−8.39507	−0.302341
$772$	−6.86610	−0.247116
$773$	33.5625	1.20716	0.603580	−	0.797302i	$-0.293740\pi$
$773$	33.5625	1.20716	0.603580	+	0.797302i	$0.293740\pi$
$774$	98.3126	3.53377
$775$	−6.66081	−0.239263
$776$	−1.81511	−0.0651587
$777$	−10.4886	−0.376276
$778$	60.5321	2.17018
$779$	6.18635	0.221649
$780$	−25.8479	−0.925504
$781$	0.800150	0.0286316
$782$	93.6436	3.34869
$783$	40.1381	1.43442
$784$	−2.04832	−0.0731544
$785$	6.35164	0.226700
$786$	83.7112	2.98588
$787$	−43.0409	−1.53424	−0.767121	−	0.641502i	$-0.778312\pi$
$787$	−43.0409	−1.53424	−0.767121	+	0.641502i	$0.778312\pi$
$788$	−69.2361	−2.46644
$789$	20.7509	0.738751
$790$	31.3389	1.11499
$791$	7.16338	0.254701
$792$	1.07309	0.0381307
$793$	25.5974	0.908989
$794$	−31.4370	−1.11566
$795$	−3.43459	−0.121812
$796$	−51.0172	−1.80826
$797$	7.88948	0.279460	0.139730	−	0.990190i	$-0.455377\pi$
$797$	7.88948	0.279460	0.139730	+	0.990190i	$0.455377\pi$
$798$	48.0550	1.70113
$799$	−19.7817	−0.699827
$800$	7.56851	0.267587
$801$	13.7826	0.486986
$802$	−57.8460	−2.04261
$803$	−0.781039	−0.0275623
$804$	59.9159	2.11307
$805$	−6.34050	−0.223473
$806$	44.1966	1.55676
$807$	−61.5983	−2.16836
$808$	−21.3195	−0.750016
$809$	10.5509	0.370949	0.185474	−	0.982649i	$-0.440618\pi$
$809$	10.5509	0.370949	0.185474	+	0.982649i	$0.440618\pi$
$810$	34.0983	1.19809
$811$	−0.824190	−0.0289412	−0.0144706	−	0.999895i	$-0.504606\pi$
$811$	−0.824190	−0.0289412	−0.0144706	+	0.999895i	$0.504606\pi$
$812$	−9.49424	−0.333183
$813$	2.75247	0.0965333
$814$	0.752511	0.0263755
$815$	−12.5084	−0.438150
$816$	−43.3571	−1.51780
$817$	−48.0723	−1.68184
$818$	−20.3855	−0.712763
$819$	−20.4401	−0.714235
$820$	−2.36604	−0.0826256
$821$	26.5713	0.927345	0.463673	−	0.886007i	$-0.346531\pi$
$821$	26.5713	0.927345	0.463673	+	0.886007i	$0.346531\pi$
$822$	−133.541	−4.65779
$823$	−0.216709	−0.00755401	−0.00377701	−	0.999993i	$-0.501202\pi$
$823$	−0.216709	−0.00755401	−0.00377701	+	0.999993i	$0.501202\pi$
$824$	−7.59737	−0.264667
$825$	−0.320104	−0.0111446
$826$	−11.3645	−0.395422
$827$	30.6375	1.06537	0.532686	−	0.846313i	$-0.321183\pi$
$827$	30.6375	1.06537	0.532686	+	0.846313i	$0.321183\pi$
$828$	−115.314	−4.00744
$829$	−39.5044	−1.37204	−0.686022	−	0.727581i	$-0.740645\pi$
$829$	−39.5044	−1.37204	−0.686022	+	0.727581i	$0.740645\pi$
$830$	24.4872	0.849962
$831$	16.3427	0.566922
$832$	−37.7051	−1.30719
$833$	6.79945	0.235587
$834$	−1.04857	−0.0363090
$835$	6.02749	0.208590
$836$	−1.98623	−0.0686951
$837$	−76.5385	−2.64556
$838$	−2.83037	−0.0977734
$839$	−31.3649	−1.08284	−0.541419	−	0.840753i	$-0.682113\pi$
$839$	−31.3649	−1.08284	−0.541419	+	0.840753i	$0.682113\pi$
$840$	−4.85535	−0.167525
$841$	−16.7987	−0.579264
$842$	−23.0151	−0.793154
$843$	74.0203	2.54939
$844$	−62.4769	−2.15054
$845$	3.66828	0.126193
$846$	42.2837	1.45374
$847$	10.9894	0.377601
$848$	−2.25988	−0.0776047
$849$	29.2591	1.00417
$850$	−14.7691	−0.506577
$851$	−21.3625	−0.732298
$852$	−65.8436	−2.25576
$853$	−25.5673	−0.875406	−0.437703	−	0.899120i	$-0.644208\pi$
$853$	−25.5673	−0.875406	−0.437703	+	0.899120i	$0.644208\pi$
$854$	18.2010	0.622826
$855$	−47.5523	−1.62626
$856$	9.36909	0.320229
$857$	−31.7674	−1.08515	−0.542576	−	0.840007i	$-0.682551\pi$
$857$	−31.7674	−1.08515	−0.542576	+	0.840007i	$0.682551\pi$
$858$	2.12399	0.0725119
$859$	46.8125	1.59722	0.798611	−	0.601847i	$-0.205568\pi$
$859$	46.8125	1.59722	0.798611	+	0.601847i	$0.205568\pi$
$860$	18.3858	0.626950
$861$	−2.70990	−0.0923532
$862$	78.2932	2.66668
$863$	−24.8390	−0.845530	−0.422765	−	0.906239i	$-0.638940\pi$
$863$	−24.8390	−0.845530	−0.422765	+	0.906239i	$0.638940\pi$
$864$	86.9687	2.95874
$865$	16.2595	0.552840
$866$	38.4126	1.30531
$867$	91.0028	3.09062
$868$	18.1044	0.614503
$869$	−1.48356	−0.0503263
$870$	23.6196	0.800780
$871$	21.6311	0.732941
$872$	−20.3760	−0.690020
$873$	7.78706	0.263552
$874$	97.8755	3.31069
$875$	1.00000	0.0338062
$876$	64.2710	2.17151
$877$	−35.1169	−1.18581	−0.592907	−	0.805271i	$-0.702020\pi$
$877$	−35.1169	−1.18581	−0.592907	+	0.805271i	$0.702020\pi$
$878$	−67.5826	−2.28080
$879$	83.6066	2.81998
$880$	−0.210621	−0.00710003
$881$	7.06882	0.238155	0.119077	−	0.992885i	$-0.462006\pi$
$881$	7.06882	0.238155	0.119077	+	0.992885i	$0.462006\pi$
$882$	−14.5339	−0.489383
$883$	−1.32433	−0.0445673	−0.0222836	−	0.999752i	$-0.507094\pi$
$883$	−1.32433	−0.0445673	−0.0222836	+	0.999752i	$0.507094\pi$
$884$	56.4561	1.89883
$885$	16.2876	0.547503
$886$	0.903503	0.0303538
$887$	40.2163	1.35033	0.675166	−	0.737666i	$-0.264072\pi$
$887$	40.2163	1.35033	0.675166	+	0.737666i	$0.264072\pi$
$888$	−16.3587	−0.548963
$889$	18.1476	0.608652
$890$	4.47416	0.149974
$891$	−1.61419	−0.0540774
$892$	26.3503	0.882274
$893$	−20.6757	−0.691885
$894$	−140.329	−4.69330
$895$	4.56853	0.152709
$896$	−11.6732	−0.389974
$897$	−60.2965	−2.01324
$898$	0.660709	0.0220481
$899$	−23.2665	−0.775981
$900$	18.1869	0.606230
$901$	7.50172	0.249919
$902$	0.194424	0.00647360
$903$	21.0578	0.700761
$904$	11.1725	0.371592
$905$	6.49969	0.216057
$906$	5.84984	0.194348
$907$	56.1213	1.86348	0.931738	−	0.363132i	$-0.118292\pi$
$907$	56.1213	1.86348	0.931738	+	0.363132i	$0.118292\pi$
$908$	−40.0961	−1.33063
$909$	91.4631	3.03364
$910$	−6.63532	−0.219959
$911$	−40.2959	−1.33506	−0.667531	−	0.744582i	$-0.732649\pi$
$911$	−40.2959	−1.33506	−0.667531	+	0.744582i	$0.732649\pi$
$912$	−45.3165	−1.50058
$913$	−1.15920	−0.0383641
$914$	62.2216	2.05811
$915$	−26.0857	−0.862367
$916$	2.71804	0.0898067
$917$	12.3798	0.408818
$918$	−169.710	−5.60127
$919$	−52.3469	−1.72676	−0.863382	−	0.504550i	$-0.831658\pi$
$919$	−52.3469	−1.72676	−0.863382	+	0.504550i	$0.831658\pi$
$920$	−9.88907	−0.326033
$921$	31.6760	1.04376
$922$	−13.9549	−0.459579
$923$	−23.7711	−0.782435
$924$	0.870056	0.0286228
$925$	3.36922	0.110779
$926$	12.3851	0.406999
$927$	32.5937	1.07052
$928$	26.4371	0.867841
$929$	−41.1491	−1.35006	−0.675029	−	0.737791i	$-0.735869\pi$
$929$	−41.1491	−1.35006	−0.675029	+	0.737791i	$0.735869\pi$
$930$	−45.0398	−1.47691
$931$	7.10673	0.232914
$932$	−4.58395	−0.150152
$933$	2.82824	0.0925924
$934$	−78.5149	−2.56909
$935$	0.699160	0.0228650
$936$	−31.8798	−1.04202
$937$	3.79567	0.123999	0.0619996	−	0.998076i	$-0.480252\pi$
$937$	3.79567	0.123999	0.0619996	+	0.998076i	$0.480252\pi$
$938$	15.3808	0.502200
$939$	43.0616	1.40526
$940$	7.90763	0.257919
$941$	7.14817	0.233024	0.116512	−	0.993189i	$-0.462829\pi$
$941$	7.14817	0.233024	0.116512	+	0.993189i	$0.462829\pi$
$942$	42.9492	1.39936
$943$	−5.51936	−0.179735
$944$	10.7169	0.348805
$945$	11.4909	0.373798
$946$	−1.51081	−0.0491206
$947$	−16.1204	−0.523841	−0.261921	−	0.965089i	$-0.584356\pi$
$947$	−16.1204	−0.523841	−0.261921	+	0.965089i	$0.584356\pi$
$948$	122.081	3.96500
$949$	23.2034	0.753213
$950$	−15.4366	−0.500828
$951$	82.2015	2.66557
$952$	10.6049	0.343706
$953$	25.3401	0.820848	0.410424	−	0.911895i	$-0.365381\pi$
$953$	25.3401	0.820848	0.410424	+	0.911895i	$0.365381\pi$
$954$	−16.0351	−0.519154
$955$	15.4783	0.500865
$956$	−22.8646	−0.739493
$957$	−1.11814	−0.0361442
$958$	66.1450	2.13705
$959$	−19.7491	−0.637731
$960$	38.4244	1.24014
$961$	13.3664	0.431175
$962$	−22.3558	−0.720781
$963$	−40.1946	−1.29525
$964$	−2.46059	−0.0792502
$965$	2.52612	0.0813186
$966$	−42.8739	−1.37944
$967$	32.9138	1.05844	0.529218	−	0.848486i	$-0.322485\pi$
$967$	32.9138	1.05844	0.529218	+	0.848486i	$0.322485\pi$
$968$	17.1399	0.550896
$969$	150.429	4.83248
$970$	2.52785	0.0811645
$971$	52.1076	1.67221	0.836106	−	0.548567i	$-0.184827\pi$
$971$	52.1076	1.67221	0.836106	+	0.548567i	$0.184827\pi$
$972$	39.1322	1.25517
$973$	−0.155070	−0.00497132
$974$	−32.0931	−1.02833
$975$	9.50975	0.304556
$976$	−17.1638	−0.549399
$977$	45.8499	1.46687	0.733435	−	0.679760i	$-0.237916\pi$
$977$	45.8499	1.46687	0.733435	+	0.679760i	$0.237916\pi$
$978$	−84.5806	−2.70459
$979$	−0.211803	−0.00676926
$980$	−2.71804	−0.0868247
$981$	87.4158	2.79097
$982$	18.7494	0.598317
$983$	−31.5397	−1.00596	−0.502980	−	0.864298i	$-0.667763\pi$
$983$	−31.5397	−1.00596	−0.502980	+	0.864298i	$0.667763\pi$
$984$	−4.22655	−0.134737
$985$	25.4728	0.811630
$986$	−51.5892	−1.64293
$987$	9.05687	0.288283
$988$	59.0075	1.87728
$989$	42.8893	1.36380
$990$	−1.49447	−0.0474972
$991$	32.0784	1.01900	0.509502	−	0.860469i	$-0.329829\pi$
$991$	32.0784	1.01900	0.509502	+	0.860469i	$0.329829\pi$
$992$	−50.4124	−1.60060
$993$	81.8274	2.59671
$994$	−16.9024	−0.536113
$995$	18.7698	0.595043
$996$	95.3898	3.02254
$997$	−30.6817	−0.971699	−0.485849	−	0.874043i	$-0.661490\pi$
$997$	−30.6817	−0.971699	−0.485849	+	0.874043i	$0.661490\pi$
$998$	−27.9404	−0.884438
$999$	38.7152	1.22490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.10	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.17211 q^{2} +3.11306 q^{3} +2.71804 q^{4} -1.00000 q^{5} -6.76191 q^{6} -1.00000 q^{7} -1.55967 q^{8} +6.69117 q^{9} +O(q^{10})\)	\(q-2.17211 q^{2} +3.11306 q^{3} +2.71804 q^{4} -1.00000 q^{5} -6.76191 q^{6} -1.00000 q^{7} -1.55967 q^{8} +6.69117 q^{9} +2.17211 q^{10} -0.102826 q^{11} +8.46145 q^{12} +3.05479 q^{13} +2.17211 q^{14} -3.11306 q^{15} -2.04832 q^{16} +6.79945 q^{17} -14.5339 q^{18} +7.10673 q^{19} -2.71804 q^{20} -3.11306 q^{21} +0.223349 q^{22} -6.34050 q^{23} -4.85535 q^{24} +1.00000 q^{25} -6.63532 q^{26} +11.4909 q^{27} -2.71804 q^{28} +3.49304 q^{29} +6.76191 q^{30} -6.66081 q^{31} +7.56851 q^{32} -0.320104 q^{33} -14.7691 q^{34} +1.00000 q^{35} +18.1869 q^{36} +3.36922 q^{37} -15.4366 q^{38} +9.50975 q^{39} +1.55967 q^{40} +0.870493 q^{41} +6.76191 q^{42} -6.76435 q^{43} -0.279485 q^{44} -6.69117 q^{45} +13.7722 q^{46} -2.90931 q^{47} -6.37657 q^{48} +1.00000 q^{49} -2.17211 q^{50} +21.1671 q^{51} +8.30304 q^{52} +1.10328 q^{53} -24.9594 q^{54} +0.102826 q^{55} +1.55967 q^{56} +22.1237 q^{57} -7.58726 q^{58} -5.23203 q^{59} -8.46145 q^{60} +8.37943 q^{61} +14.4680 q^{62} -6.69117 q^{63} -12.3430 q^{64} -3.05479 q^{65} +0.695300 q^{66} +7.08104 q^{67} +18.4812 q^{68} -19.7384 q^{69} -2.17211 q^{70} -7.78159 q^{71} -10.4360 q^{72} +7.59574 q^{73} -7.31830 q^{74} +3.11306 q^{75} +19.3164 q^{76} +0.102826 q^{77} -20.6562 q^{78} +14.4279 q^{79} +2.04832 q^{80} +15.6983 q^{81} -1.89080 q^{82} +11.2735 q^{83} -8.46145 q^{84} -6.79945 q^{85} +14.6929 q^{86} +10.8741 q^{87} +0.160374 q^{88} +2.05982 q^{89} +14.5339 q^{90} -3.05479 q^{91} -17.2338 q^{92} -20.7355 q^{93} +6.31933 q^{94} -7.10673 q^{95} +23.5613 q^{96} +1.16378 q^{97} -2.17211 q^{98} -0.688026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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