LMFDB - Embedded newform 8041.2.a.i.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.52440 q^{2} -2.61179 q^{3} +0.323806 q^{4} +2.08851 q^{5} +3.98143 q^{6} +2.52784 q^{7} +2.55520 q^{8} +3.82147 q^{9} +O(q^{10})$	\(q-1.52440 q^{2} -2.61179 q^{3} +0.323806 q^{4} +2.08851 q^{5} +3.98143 q^{6} +2.52784 q^{7} +2.55520 q^{8} +3.82147 q^{9} -3.18374 q^{10} +1.00000 q^{11} -0.845713 q^{12} +4.21148 q^{13} -3.85345 q^{14} -5.45477 q^{15} -4.54276 q^{16} -1.00000 q^{17} -5.82546 q^{18} +4.62200 q^{19} +0.676273 q^{20} -6.60220 q^{21} -1.52440 q^{22} -2.56492 q^{23} -6.67365 q^{24} -0.638107 q^{25} -6.42000 q^{26} -2.14551 q^{27} +0.818528 q^{28} -4.16417 q^{29} +8.31527 q^{30} -10.2776 q^{31} +1.81461 q^{32} -2.61179 q^{33} +1.52440 q^{34} +5.27943 q^{35} +1.23741 q^{36} +3.37372 q^{37} -7.04579 q^{38} -10.9995 q^{39} +5.33656 q^{40} -2.06542 q^{41} +10.0644 q^{42} -1.00000 q^{43} +0.323806 q^{44} +7.98119 q^{45} +3.90998 q^{46} +8.00918 q^{47} +11.8648 q^{48} -0.610027 q^{49} +0.972733 q^{50} +2.61179 q^{51} +1.36370 q^{52} +11.1669 q^{53} +3.27062 q^{54} +2.08851 q^{55} +6.45913 q^{56} -12.0717 q^{57} +6.34788 q^{58} -10.6860 q^{59} -1.76628 q^{60} +0.218045 q^{61} +15.6673 q^{62} +9.66006 q^{63} +6.31933 q^{64} +8.79574 q^{65} +3.98143 q^{66} +11.1241 q^{67} -0.323806 q^{68} +6.69905 q^{69} -8.04798 q^{70} +0.842522 q^{71} +9.76461 q^{72} -7.25499 q^{73} -5.14291 q^{74} +1.66660 q^{75} +1.49663 q^{76} +2.52784 q^{77} +16.7677 q^{78} +16.3831 q^{79} -9.48762 q^{80} -5.86078 q^{81} +3.14854 q^{82} +2.32483 q^{83} -2.13783 q^{84} -2.08851 q^{85} +1.52440 q^{86} +10.8760 q^{87} +2.55520 q^{88} -3.90945 q^{89} -12.1666 q^{90} +10.6460 q^{91} -0.830536 q^{92} +26.8431 q^{93} -12.2092 q^{94} +9.65311 q^{95} -4.73938 q^{96} -9.93107 q^{97} +0.929927 q^{98} +3.82147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * 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 $

$2$	−1.52440	−1.07792	−0.538958	−	0.842333i	$-0.681182\pi$
$2$	−1.52440	−1.07792	−0.538958	+	0.842333i	$0.681182\pi$
$3$	−2.61179	−1.50792	−0.753960	−	0.656920i	$-0.771859\pi$
$3$	−2.61179	−1.50792	−0.753960	+	0.656920i	$0.771859\pi$
$4$	0.323806	0.161903
$5$	2.08851	0.934012	0.467006	−	0.884254i	$-0.345333\pi$
$5$	2.08851	0.934012	0.467006	+	0.884254i	$0.345333\pi$
$6$	3.98143	1.62541
$7$	2.52784	0.955434	0.477717	−	0.878514i	$-0.341465\pi$
$7$	2.52784	0.955434	0.477717	+	0.878514i	$0.341465\pi$
$8$	2.55520	0.903398
$9$	3.82147	1.27382
$10$	−3.18374	−1.00679
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.845713	−0.244136
$13$	4.21148	1.16806	0.584028	−	0.811734i	$-0.301476\pi$
$13$	4.21148	1.16806	0.584028	+	0.811734i	$0.301476\pi$
$14$	−3.85345	−1.02988
$15$	−5.45477	−1.40842
$16$	−4.54276	−1.13569
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−5.82546	−1.37307
$19$	4.62200	1.06036	0.530180	−	0.847885i	$-0.322124\pi$
$19$	4.62200	1.06036	0.530180	+	0.847885i	$0.322124\pi$
$20$	0.676273	0.151219
$21$	−6.60220	−1.44072
$22$	−1.52440	−0.325004
$23$	−2.56492	−0.534823	−0.267412	−	0.963582i	$-0.586168\pi$
$23$	−2.56492	−0.534823	−0.267412	+	0.963582i	$0.586168\pi$
$24$	−6.67365	−1.36225
$25$	−0.638107	−0.127621
$26$	−6.42000	−1.25907
$27$	−2.14551	−0.412903
$28$	0.818528	0.154687
$29$	−4.16417	−0.773267	−0.386634	−	0.922233i	$-0.626362\pi$
$29$	−4.16417	−0.773267	−0.386634	+	0.922233i	$0.626362\pi$
$30$	8.31527	1.51815
$31$	−10.2776	−1.84592	−0.922960	−	0.384896i	$-0.874237\pi$
$31$	−10.2776	−1.84592	−0.922960	+	0.384896i	$0.874237\pi$
$32$	1.81461	0.320780
$33$	−2.61179	−0.454655
$34$	1.52440	0.261433
$35$	5.27943	0.892387
$36$	1.23741	0.206235
$37$	3.37372	0.554636	0.277318	−	0.960778i	$-0.410554\pi$
$37$	3.37372	0.554636	0.277318	+	0.960778i	$0.410554\pi$
$38$	−7.04579	−1.14298
$39$	−10.9995	−1.76133
$40$	5.33656	0.843785
$41$	−2.06542	−0.322565	−0.161282	−	0.986908i	$-0.551563\pi$
$41$	−2.06542	−0.322565	−0.161282	+	0.986908i	$0.551563\pi$
$42$	10.0644	1.55297
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.323806	0.0488155
$45$	7.98119	1.18977
$46$	3.90998	0.576494
$47$	8.00918	1.16826	0.584130	−	0.811660i	$-0.301436\pi$
$47$	8.00918	1.16826	0.584130	+	0.811660i	$0.301436\pi$
$48$	11.8648	1.71253
$49$	−0.610027	−0.0871467
$50$	0.972733	0.137565
$51$	2.61179	0.365724
$52$	1.36370	0.189111
$53$	11.1669	1.53389	0.766946	−	0.641712i	$-0.221776\pi$
$53$	11.1669	1.53389	0.766946	+	0.641712i	$0.221776\pi$
$54$	3.27062	0.445075
$55$	2.08851	0.281615
$56$	6.45913	0.863137
$57$	−12.0717	−1.59894
$58$	6.34788	0.833517
$59$	−10.6860	−1.39120	−0.695602	−	0.718428i	$-0.744862\pi$
$59$	−10.6860	−1.39120	−0.695602	+	0.718428i	$0.744862\pi$
$60$	−1.76628	−0.228026
$61$	0.218045	0.0279178	0.0139589	−	0.999903i	$-0.495557\pi$
$61$	0.218045	0.0279178	0.0139589	+	0.999903i	$0.495557\pi$
$62$	15.6673	1.98975
$63$	9.66006	1.21705
$64$	6.31933	0.789916
$65$	8.79574	1.09098
$66$	3.98143	0.490080
$67$	11.1241	1.35903	0.679515	−	0.733661i	$-0.262190\pi$
$67$	11.1241	1.35903	0.679515	+	0.733661i	$0.262190\pi$
$68$	−0.323806	−0.0392672
$69$	6.69905	0.806471
$70$	−8.04798	−0.961918
$71$	0.842522	0.0999889	0.0499945	−	0.998749i	$-0.484080\pi$
$71$	0.842522	0.0999889	0.0499945	+	0.998749i	$0.484080\pi$
$72$	9.76461	1.15077
$73$	−7.25499	−0.849133	−0.424566	−	0.905397i	$-0.639573\pi$
$73$	−7.25499	−0.849133	−0.424566	+	0.905397i	$0.639573\pi$
$74$	−5.14291	−0.597851
$75$	1.66660	0.192443
$76$	1.49663	0.171675
$77$	2.52784	0.288074
$78$	16.7677	1.89857
$79$	16.3831	1.84324	0.921621	−	0.388090i	$-0.126865\pi$
$79$	16.3831	1.84324	0.921621	+	0.388090i	$0.126865\pi$
$80$	−9.48762	−1.06075
$81$	−5.86078	−0.651198
$82$	3.14854	0.347698
$83$	2.32483	0.255183	0.127591	−	0.991827i	$-0.459275\pi$
$83$	2.32483	0.255183	0.127591	+	0.991827i	$0.459275\pi$
$84$	−2.13783	−0.233256
$85$	−2.08851	−0.226531
$86$	1.52440	0.164381
$87$	10.8760	1.16602
$88$	2.55520	0.272385
$89$	−3.90945	−0.414401	−0.207200	−	0.978299i	$-0.566435\pi$
$89$	−3.90945	−0.414401	−0.207200	+	0.978299i	$0.566435\pi$
$90$	−12.1666	−1.28247
$91$	10.6460	1.11600
$92$	−0.830536	−0.0865894
$93$	26.8431	2.78350
$94$	−12.2092	−1.25929
$95$	9.65311	0.990388
$96$	−4.73938	−0.483711
$97$	−9.93107	−1.00835	−0.504174	−	0.863602i	$-0.668203\pi$
$97$	−9.93107	−1.00835	−0.504174	+	0.863602i	$0.668203\pi$
$98$	0.929927	0.0939368
$99$	3.82147	0.384072
$100$	−0.206623	−0.0206623
$101$	12.4528	1.23910	0.619551	−	0.784956i	$-0.287315\pi$
$101$	12.4528	1.23910	0.619551	+	0.784956i	$0.287315\pi$
$102$	−3.98143	−0.394220
$103$	−9.36852	−0.923108	−0.461554	−	0.887112i	$-0.652708\pi$
$103$	−9.36852	−0.923108	−0.461554	+	0.887112i	$0.652708\pi$
$104$	10.7612	1.05522
$105$	−13.7888	−1.34565
$106$	−17.0229	−1.65341
$107$	15.5898	1.50712	0.753561	−	0.657378i	$-0.228334\pi$
$107$	15.5898	1.50712	0.753561	+	0.657378i	$0.228334\pi$
$108$	−0.694728	−0.0668502
$109$	−11.4522	−1.09692	−0.548462	−	0.836175i	$-0.684787\pi$
$109$	−11.4522	−1.09692	−0.548462	+	0.836175i	$0.684787\pi$
$110$	−3.18374	−0.303558
$111$	−8.81147	−0.836347
$112$	−11.4834	−1.08508
$113$	10.5061	0.988329	0.494164	−	0.869368i	$-0.335474\pi$
$113$	10.5061	0.988329	0.494164	+	0.869368i	$0.335474\pi$
$114$	18.4022	1.72352
$115$	−5.35688	−0.499531
$116$	−1.34838	−0.125194
$117$	16.0941	1.48790
$118$	16.2898	1.49960
$119$	−2.52784	−0.231727
$120$	−13.9380	−1.27236
$121$	1.00000	0.0909091
$122$	−0.332388	−0.0300930
$123$	5.39446	0.486402
$124$	−3.32796	−0.298860
$125$	−11.7753	−1.05321
$126$	−14.7258	−1.31188
$127$	0.0683139	0.00606188	0.00303094	−	0.999995i	$-0.499035\pi$
$127$	0.0683139	0.00606188	0.00303094	+	0.999995i	$0.499035\pi$
$128$	−13.2624	−1.17224
$129$	2.61179	0.229956
$130$	−13.4083	−1.17598
$131$	8.40815	0.734624	0.367312	−	0.930098i	$-0.380278\pi$
$131$	8.40815	0.734624	0.367312	+	0.930098i	$0.380278\pi$
$132$	−0.845713	−0.0736099
$133$	11.6837	1.01310
$134$	−16.9577	−1.46492
$135$	−4.48093	−0.385657
$136$	−2.55520	−0.219106
$137$	−4.79750	−0.409878	−0.204939	−	0.978775i	$-0.565700\pi$
$137$	−4.79750	−0.409878	−0.204939	+	0.978775i	$0.565700\pi$
$138$	−10.2121	−0.869308
$139$	20.4479	1.73437	0.867184	−	0.497988i	$-0.165928\pi$
$139$	20.4479	1.73437	0.867184	+	0.497988i	$0.165928\pi$
$140$	1.70951	0.144480
$141$	−20.9183	−1.76164
$142$	−1.28434	−0.107780
$143$	4.21148	0.352182
$144$	−17.3600	−1.44667
$145$	−8.69693	−0.722241
$146$	11.0595	0.915294
$147$	1.59326	0.131410
$148$	1.09243	0.0897972
$149$	13.8181	1.13202	0.566011	−	0.824398i	$-0.308486\pi$
$149$	13.8181	1.13202	0.566011	+	0.824398i	$0.308486\pi$
$150$	−2.54058	−0.207437
$151$	−9.14676	−0.744353	−0.372176	−	0.928162i	$-0.621388\pi$
$151$	−9.14676	−0.744353	−0.372176	+	0.928162i	$0.621388\pi$
$152$	11.8101	0.957927
$153$	−3.82147	−0.308947
$154$	−3.85345	−0.310520
$155$	−21.4650	−1.72411
$156$	−3.56171	−0.285165
$157$	−6.75842	−0.539381	−0.269690	−	0.962947i	$-0.586921\pi$
$157$	−6.75842	−0.539381	−0.269690	+	0.962947i	$0.586921\pi$
$158$	−24.9745	−1.98686
$159$	−29.1656	−2.31299
$160$	3.78983	0.299613
$161$	−6.48371	−0.510988
$162$	8.93419	0.701936
$163$	18.9536	1.48456	0.742281	−	0.670089i	$-0.233744\pi$
$163$	18.9536	1.48456	0.742281	+	0.670089i	$0.233744\pi$
$164$	−0.668795	−0.0522241
$165$	−5.45477	−0.424653
$166$	−3.54397	−0.275066
$167$	−4.16622	−0.322392	−0.161196	−	0.986922i	$-0.551535\pi$
$167$	−4.16622	−0.322392	−0.161196	+	0.986922i	$0.551535\pi$
$168$	−16.8699	−1.30154
$169$	4.73659	0.364353
$170$	3.18374	0.244182
$171$	17.6628	1.35071
$172$	−0.323806	−0.0246899
$173$	17.2976	1.31511	0.657554	−	0.753407i	$-0.271591\pi$
$173$	17.2976	1.31511	0.657554	+	0.753407i	$0.271591\pi$
$174$	−16.5793	−1.25688
$175$	−1.61303	−0.121934
$176$	−4.54276	−0.342423
$177$	27.9097	2.09782
$178$	5.95957	0.446689
$179$	−22.6720	−1.69458	−0.847292	−	0.531127i	$-0.821769\pi$
$179$	−22.6720	−1.69458	−0.847292	+	0.531127i	$0.821769\pi$
$180$	2.58435	0.192626
$181$	19.5544	1.45347	0.726733	−	0.686920i	$-0.241038\pi$
$181$	19.5544	1.45347	0.726733	+	0.686920i	$0.241038\pi$
$182$	−16.2287	−1.20295
$183$	−0.569488	−0.0420978
$184$	−6.55388	−0.483158
$185$	7.04607	0.518037
$186$	−40.9197	−3.00038
$187$	−1.00000	−0.0731272
$188$	2.59342	0.189144
$189$	−5.42350	−0.394502
$190$	−14.7152	−1.06756
$191$	10.5745	0.765145	0.382573	−	0.923925i	$-0.375038\pi$
$191$	10.5745	0.765145	0.382573	+	0.923925i	$0.375038\pi$
$192$	−16.5048	−1.19113
$193$	−14.9762	−1.07801	−0.539006	−	0.842302i	$-0.681200\pi$
$193$	−14.9762	−1.07801	−0.539006	+	0.842302i	$0.681200\pi$
$194$	15.1390	1.08691
$195$	−22.9727	−1.64511
$196$	−0.197530	−0.0141093
$197$	15.0577	1.07282	0.536408	−	0.843959i	$-0.319781\pi$
$197$	15.0577	1.07282	0.536408	+	0.843959i	$0.319781\pi$
$198$	−5.82546	−0.413997
$199$	−11.2627	−0.798390	−0.399195	−	0.916866i	$-0.630710\pi$
$199$	−11.2627	−0.798390	−0.399195	+	0.916866i	$0.630710\pi$
$200$	−1.63049	−0.115293
$201$	−29.0540	−2.04931
$202$	−18.9831	−1.33565
$203$	−10.5264	−0.738805
$204$	0.845713	0.0592118
$205$	−4.31366	−0.301279
$206$	14.2814	0.995033
$207$	−9.80177	−0.681270
$208$	−19.1318	−1.32655
$209$	4.62200	0.319710
$210$	21.0197	1.45049
$211$	25.5415	1.75835	0.879174	−	0.476501i	$-0.158095\pi$
$211$	25.5415	1.75835	0.879174	+	0.476501i	$0.158095\pi$
$212$	3.61590	0.248341
$213$	−2.20049	−0.150775
$214$	−23.7651	−1.62455
$215$	−2.08851	−0.142436
$216$	−5.48220	−0.373016
$217$	−25.9802	−1.76365
$218$	17.4578	1.18239
$219$	18.9485	1.28042
$220$	0.676273	0.0455943
$221$	−4.21148	−0.283295
$222$	13.4322	0.901512
$223$	−7.14062	−0.478171	−0.239085	−	0.970999i	$-0.576848\pi$
$223$	−7.14062	−0.478171	−0.239085	+	0.970999i	$0.576848\pi$
$224$	4.58704	0.306484
$225$	−2.43851	−0.162567
$226$	−16.0155	−1.06534
$227$	19.8202	1.31551	0.657755	−	0.753232i	$-0.271506\pi$
$227$	19.8202	1.31551	0.657755	+	0.753232i	$0.271506\pi$
$228$	−3.90889	−0.258872
$229$	−11.5225	−0.761430	−0.380715	−	0.924692i	$-0.624322\pi$
$229$	−11.5225	−0.761430	−0.380715	+	0.924692i	$0.624322\pi$
$230$	8.16604	0.538453
$231$	−6.60220	−0.434393
$232$	−10.6403	−0.698568
$233$	−0.684884	−0.0448683	−0.0224341	−	0.999748i	$-0.507142\pi$
$233$	−0.684884	−0.0448683	−0.0224341	+	0.999748i	$0.507142\pi$
$234$	−24.5338	−1.60383
$235$	16.7273	1.09117
$236$	−3.46020	−0.225240
$237$	−42.7893	−2.77946
$238$	3.85345	0.249782
$239$	15.6962	1.01530	0.507650	−	0.861563i	$-0.330514\pi$
$239$	15.6962	1.01530	0.507650	+	0.861563i	$0.330514\pi$
$240$	24.7797	1.59952
$241$	22.3618	1.44045	0.720226	−	0.693740i	$-0.244038\pi$
$241$	22.3618	1.44045	0.720226	+	0.693740i	$0.244038\pi$
$242$	−1.52440	−0.0979924
$243$	21.7437	1.39486
$244$	0.0706041	0.00451997
$245$	−1.27405	−0.0813961
$246$	−8.22333	−0.524300
$247$	19.4655	1.23856
$248$	−26.2614	−1.66760
$249$	−6.07197	−0.384795
$250$	17.9503	1.13527
$251$	−25.1249	−1.58587	−0.792936	−	0.609305i	$-0.791449\pi$
$251$	−25.1249	−1.58587	−0.792936	+	0.609305i	$0.791449\pi$
$252$	3.12798	0.197044
$253$	−2.56492	−0.161255
$254$	−0.104138	−0.00653420
$255$	5.45477	0.341591
$256$	7.57862	0.473664
$257$	−16.0150	−0.998988	−0.499494	−	0.866317i	$-0.666481\pi$
$257$	−16.0150	−0.998988	−0.499494	+	0.866317i	$0.666481\pi$
$258$	−3.98143	−0.247873
$259$	8.52823	0.529918
$260$	2.84811	0.176632
$261$	−15.9133	−0.985005
$262$	−12.8174	−0.791862
$263$	−20.7177	−1.27751	−0.638754	−	0.769411i	$-0.720550\pi$
$263$	−20.7177	−1.27751	−0.638754	+	0.769411i	$0.720550\pi$
$264$	−6.67365	−0.410735
$265$	23.3222	1.43267
$266$	−17.8106	−1.09204
$267$	10.2107	0.624883
$268$	3.60206	0.220031
$269$	18.5811	1.13291	0.566455	−	0.824092i	$-0.308314\pi$
$269$	18.5811	1.13291	0.566455	+	0.824092i	$0.308314\pi$
$270$	6.83074	0.415706
$271$	15.8732	0.964227	0.482114	−	0.876109i	$-0.339869\pi$
$271$	15.8732	0.964227	0.482114	+	0.876109i	$0.339869\pi$
$272$	4.54276	0.275445
$273$	−27.8050	−1.68284
$274$	7.31333	0.441814
$275$	−0.638107	−0.0384793
$276$	2.16919	0.130570
$277$	−9.94758	−0.597692	−0.298846	−	0.954301i	$-0.596602\pi$
$277$	−9.94758	−0.597692	−0.298846	+	0.954301i	$0.596602\pi$
$278$	−31.1708	−1.86950
$279$	−39.2757	−2.35138
$280$	13.4900	0.806181
$281$	−9.31187	−0.555500	−0.277750	−	0.960653i	$-0.589589\pi$
$281$	−9.31187	−0.555500	−0.277750	+	0.960653i	$0.589589\pi$
$282$	31.8880	1.89890
$283$	−1.88517	−0.112062	−0.0560310	−	0.998429i	$-0.517845\pi$
$283$	−1.88517	−0.112062	−0.0560310	+	0.998429i	$0.517845\pi$
$284$	0.272813	0.0161885
$285$	−25.2119	−1.49343
$286$	−6.42000	−0.379622
$287$	−5.22106	−0.308189
$288$	6.93447	0.408617
$289$	1.00000	0.0588235
$290$	13.2576	0.778515
$291$	25.9379	1.52051
$292$	−2.34921	−0.137477
$293$	29.5867	1.72847	0.864237	−	0.503085i	$-0.167802\pi$
$293$	29.5867	1.72847	0.864237	+	0.503085i	$0.167802\pi$
$294$	−2.42878	−0.141649
$295$	−22.3179	−1.29940
$296$	8.62052	0.501058
$297$	−2.14551	−0.124495
$298$	−21.0643	−1.22022
$299$	−10.8021	−0.624703
$300$	0.539656	0.0311570
$301$	−2.52784	−0.145702
$302$	13.9434	0.802350
$303$	−32.5242	−1.86847
$304$	−20.9966	−1.20424
$305$	0.455390	0.0260755
$306$	5.82546	0.333019
$307$	12.4896	0.712818	0.356409	−	0.934330i	$-0.384001\pi$
$307$	12.4896	0.712818	0.356409	+	0.934330i	$0.384001\pi$
$308$	0.818528	0.0466400
$309$	24.4687	1.39197
$310$	32.7213	1.85845
$311$	−32.9977	−1.87113	−0.935564	−	0.353156i	$-0.885109\pi$
$311$	−32.9977	−1.87113	−0.935564	+	0.353156i	$0.885109\pi$
$312$	−28.1060	−1.59119
$313$	−17.5560	−0.992326	−0.496163	−	0.868229i	$-0.665258\pi$
$313$	−17.5560	−0.992326	−0.496163	+	0.868229i	$0.665258\pi$
$314$	10.3026	0.581407
$315$	20.1752	1.13674
$316$	5.30494	0.298426
$317$	−25.5227	−1.43350	−0.716748	−	0.697332i	$-0.754370\pi$
$317$	−25.5227	−1.43350	−0.716748	+	0.697332i	$0.754370\pi$
$318$	44.4602	2.49320
$319$	−4.16417	−0.233149
$320$	13.1980	0.737791
$321$	−40.7173	−2.27262
$322$	9.88379	0.550802
$323$	−4.62200	−0.257175
$324$	−1.89775	−0.105431
$325$	−2.68738	−0.149069
$326$	−28.8930	−1.60023
$327$	29.9109	1.65407
$328$	−5.27756	−0.291404
$329$	20.2459	1.11619
$330$	8.31527	0.457741
$331$	−1.23874	−0.0680873	−0.0340437	−	0.999420i	$-0.510839\pi$
$331$	−1.23874	−0.0680873	−0.0340437	+	0.999420i	$0.510839\pi$
$332$	0.752792	0.0413148
$333$	12.8926	0.706509
$334$	6.35100	0.347511
$335$	23.2329	1.26935
$336$	29.9922	1.63621
$337$	19.7330	1.07492	0.537462	−	0.843288i	$-0.319383\pi$
$337$	19.7330	1.07492	0.537462	+	0.843288i	$0.319383\pi$
$338$	−7.22047	−0.392742
$339$	−27.4397	−1.49032
$340$	−0.676273	−0.0366760
$341$	−10.2776	−0.556566
$342$	−26.9253	−1.45595
$343$	−19.2369	−1.03870
$344$	−2.55520	−0.137767
$345$	13.9911	0.753253
$346$	−26.3684	−1.41758
$347$	24.9505	1.33941	0.669707	−	0.742625i	$-0.266420\pi$
$347$	24.9505	1.33941	0.669707	+	0.742625i	$0.266420\pi$
$348$	3.52169	0.188783
$349$	5.02067	0.268750	0.134375	−	0.990931i	$-0.457097\pi$
$349$	5.02067	0.268750	0.134375	+	0.990931i	$0.457097\pi$
$350$	2.45891	0.131434
$351$	−9.03578	−0.482294
$352$	1.81461	0.0967189
$353$	−2.23938	−0.119190	−0.0595950	−	0.998223i	$-0.518981\pi$
$353$	−2.23938	−0.119190	−0.0595950	+	0.998223i	$0.518981\pi$
$354$	−42.5457	−2.26128
$355$	1.75962	0.0933909
$356$	−1.26590	−0.0670926
$357$	6.60220	0.349425
$358$	34.5613	1.82662
$359$	25.6692	1.35477	0.677383	−	0.735630i	$-0.263114\pi$
$359$	25.6692	1.35477	0.677383	+	0.735630i	$0.263114\pi$
$360$	20.3935	1.07483
$361$	2.36288	0.124362
$362$	−29.8088	−1.56671
$363$	−2.61179	−0.137084
$364$	3.44722	0.180683
$365$	−15.1522	−0.793100
$366$	0.868130	0.0453779
$367$	8.89968	0.464560	0.232280	−	0.972649i	$-0.425381\pi$
$367$	8.89968	0.464560	0.232280	+	0.972649i	$0.425381\pi$
$368$	11.6518	0.607394
$369$	−7.89295	−0.410890
$370$	−10.7410	−0.558400
$371$	28.2281	1.46553
$372$	8.69194	0.450656
$373$	−31.5846	−1.63539	−0.817695	−	0.575652i	$-0.804748\pi$
$373$	−31.5846	−1.63539	−0.817695	+	0.575652i	$0.804748\pi$
$374$	1.52440	0.0788250
$375$	30.7546	1.58816
$376$	20.4650	1.05540
$377$	−17.5373	−0.903219
$378$	8.26761	0.425240
$379$	27.3785	1.40634	0.703168	−	0.711023i	$-0.251768\pi$
$379$	27.3785	1.40634	0.703168	+	0.711023i	$0.251768\pi$
$380$	3.12573	0.160347
$381$	−0.178422	−0.00914083
$382$	−16.1198	−0.824762
$383$	−31.1780	−1.59312	−0.796561	−	0.604558i	$-0.793350\pi$
$383$	−31.1780	−1.59312	−0.796561	+	0.604558i	$0.793350\pi$
$384$	34.6387	1.76765
$385$	5.27943	0.269065
$386$	22.8298	1.16201
$387$	−3.82147	−0.194256
$388$	−3.21573	−0.163254
$389$	6.43830	0.326435	0.163217	−	0.986590i	$-0.447813\pi$
$389$	6.43830	0.326435	0.163217	+	0.986590i	$0.447813\pi$
$390$	35.0196	1.77329
$391$	2.56492	0.129714
$392$	−1.55874	−0.0787282
$393$	−21.9604	−1.10775
$394$	−22.9540	−1.15641
$395$	34.2163	1.72161
$396$	1.23741	0.0621823
$397$	−27.9240	−1.40147	−0.700733	−	0.713424i	$-0.747143\pi$
$397$	−27.9240	−1.40147	−0.700733	+	0.713424i	$0.747143\pi$
$398$	17.1689	0.860598
$399$	−30.5154	−1.52768
$400$	2.89877	0.144938
$401$	−14.1222	−0.705230	−0.352615	−	0.935769i	$-0.614707\pi$
$401$	−14.1222	−0.705230	−0.352615	+	0.935769i	$0.614707\pi$
$402$	44.2900	2.20898
$403$	−43.2841	−2.15614
$404$	4.03229	0.200614
$405$	−12.2403	−0.608227
$406$	16.0464	0.796370
$407$	3.37372	0.167229
$408$	6.67365	0.330395
$409$	−1.78582	−0.0883030	−0.0441515	−	0.999025i	$-0.514058\pi$
$409$	−1.78582	−0.0883030	−0.0441515	+	0.999025i	$0.514058\pi$
$410$	6.57576	0.324754
$411$	12.5301	0.618064
$412$	−3.03358	−0.149454
$413$	−27.0126	−1.32920
$414$	14.9419	0.734352
$415$	4.85543	0.238344
$416$	7.64219	0.374689
$417$	−53.4057	−2.61529
$418$	−7.04579	−0.344621
$419$	−8.42087	−0.411386	−0.205693	−	0.978617i	$-0.565945\pi$
$419$	−8.42087	−0.411386	−0.205693	+	0.978617i	$0.565945\pi$
$420$	−4.46488	−0.217864
$421$	−29.8918	−1.45684	−0.728418	−	0.685133i	$-0.759744\pi$
$421$	−29.8918	−1.45684	−0.728418	+	0.685133i	$0.759744\pi$
$422$	−38.9355	−1.89535
$423$	30.6069	1.48816
$424$	28.5336	1.38572
$425$	0.638107	0.0309527
$426$	3.35444	0.162523
$427$	0.551182	0.0266736
$428$	5.04806	0.244007
$429$	−10.9995	−0.531062
$430$	3.18374	0.153534
$431$	24.5729	1.18363	0.591817	−	0.806072i	$-0.298411\pi$
$431$	24.5729	1.18363	0.591817	+	0.806072i	$0.298411\pi$
$432$	9.74654	0.468930
$433$	15.2346	0.732129	0.366064	−	0.930590i	$-0.380705\pi$
$433$	15.2346	0.732129	0.366064	+	0.930590i	$0.380705\pi$
$434$	39.6044	1.90107
$435$	22.7146	1.08908
$436$	−3.70829	−0.177595
$437$	−11.8551	−0.567105
$438$	−28.8852	−1.38019
$439$	7.51213	0.358534	0.179267	−	0.983800i	$-0.442627\pi$
$439$	7.51213	0.358534	0.179267	+	0.983800i	$0.442627\pi$
$440$	5.33656	0.254411
$441$	−2.33120	−0.111009
$442$	6.42000	0.305368
$443$	−0.549215	−0.0260940	−0.0130470	−	0.999915i	$-0.504153\pi$
$443$	−0.549215	−0.0260940	−0.0130470	+	0.999915i	$0.504153\pi$
$444$	−2.85320	−0.135407
$445$	−8.16494	−0.387055
$446$	10.8852	0.515428
$447$	−36.0900	−1.70700
$448$	15.9743	0.754712
$449$	27.9509	1.31909	0.659543	−	0.751667i	$-0.270750\pi$
$449$	27.9509	1.31909	0.659543	+	0.751667i	$0.270750\pi$
$450$	3.71727	0.175234
$451$	−2.06542	−0.0972569
$452$	3.40193	0.160013
$453$	23.8895	1.12242
$454$	−30.2139	−1.41801
$455$	22.2342	1.04236
$456$	−30.8456	−1.44448
$457$	17.8452	0.834764	0.417382	−	0.908731i	$-0.362948\pi$
$457$	17.8452	0.834764	0.417382	+	0.908731i	$0.362948\pi$
$458$	17.5650	0.820757
$459$	2.14551	0.100144
$460$	−1.73459	−0.0808755
$461$	−24.2712	−1.13042	−0.565211	−	0.824947i	$-0.691205\pi$
$461$	−24.2712	−1.13042	−0.565211	+	0.824947i	$0.691205\pi$
$462$	10.0644	0.468239
$463$	42.1441	1.95860	0.979301	−	0.202410i	$-0.0648774\pi$
$463$	42.1441	1.95860	0.979301	+	0.202410i	$0.0648774\pi$
$464$	18.9168	0.878192
$465$	56.0622	2.59982
$466$	1.04404	0.0483642
$467$	16.7816	0.776560	0.388280	−	0.921541i	$-0.373069\pi$
$467$	16.7816	0.776560	0.388280	+	0.921541i	$0.373069\pi$
$468$	5.21134	0.240894
$469$	28.1201	1.29846
$470$	−25.4992	−1.17619
$471$	17.6516	0.813343
$472$	−27.3049	−1.25681
$473$	−1.00000	−0.0459800
$474$	65.2281	2.99603
$475$	−2.94933	−0.135325
$476$	−0.818528	−0.0375172
$477$	42.6740	1.95391
$478$	−23.9273	−1.09441
$479$	24.7169	1.12934	0.564672	−	0.825315i	$-0.309003\pi$
$479$	24.7169	1.12934	0.564672	+	0.825315i	$0.309003\pi$
$480$	−9.89827	−0.451792
$481$	14.2084	0.647846
$482$	−34.0884	−1.55269
$483$	16.9341	0.770529
$484$	0.323806	0.0147184
$485$	−20.7412	−0.941808
$486$	−33.1461	−1.50354
$487$	19.1843	0.869323	0.434661	−	0.900594i	$-0.356868\pi$
$487$	19.1843	0.869323	0.434661	+	0.900594i	$0.356868\pi$
$488$	0.557147	0.0252209
$489$	−49.5030	−2.23860
$490$	1.94217	0.0877381
$491$	−17.2250	−0.777354	−0.388677	−	0.921374i	$-0.627068\pi$
$491$	−17.2250	−0.777354	−0.388677	+	0.921374i	$0.627068\pi$
$492$	1.74676	0.0787498
$493$	4.16417	0.187545
$494$	−29.6732	−1.33506
$495$	7.98119	0.358728
$496$	46.6889	2.09639
$497$	2.12976	0.0955328
$498$	9.25613	0.414777
$499$	28.1566	1.26046	0.630230	−	0.776408i	$-0.282960\pi$
$499$	28.1566	1.26046	0.630230	+	0.776408i	$0.282960\pi$
$500$	−3.81290	−0.170518
$501$	10.8813	0.486141
$502$	38.3005	1.70944
$503$	33.4928	1.49337	0.746684	−	0.665179i	$-0.231645\pi$
$503$	33.4928	1.49337	0.746684	+	0.665179i	$0.231645\pi$
$504$	24.6834	1.09948
$505$	26.0079	1.15734
$506$	3.90998	0.173820
$507$	−12.3710	−0.549415
$508$	0.0221204	0.000981435 0
$509$	38.2477	1.69530	0.847650	−	0.530556i	$-0.178017\pi$
$509$	38.2477	1.69530	0.847650	+	0.530556i	$0.178017\pi$
$510$	−8.31527	−0.368206
$511$	−18.3395	−0.811290
$512$	14.9720	0.661674
$513$	−9.91654	−0.437826
$514$	24.4133	1.07683
$515$	−19.5663	−0.862194
$516$	0.845713	0.0372305
$517$	8.00918	0.352244
$518$	−13.0005	−0.571207
$519$	−45.1776	−1.98308
$520$	22.4749	0.985587
$521$	5.61957	0.246198	0.123099	−	0.992394i	$-0.460717\pi$
$521$	5.61957	0.246198	0.123099	+	0.992394i	$0.460717\pi$
$522$	24.2582	1.06175
$523$	29.0896	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$523$	29.0896	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$524$	2.72261	0.118938
$525$	4.21291	0.183866
$526$	31.5821	1.37705
$527$	10.2776	0.447701
$528$	11.8648	0.516347
$529$	−16.4212	−0.713964
$530$	−35.5525	−1.54430
$531$	−40.8364	−1.77215
$532$	3.78324	0.164024
$533$	−8.69849	−0.376773
$534$	−15.5652	−0.673571
$535$	32.5595	1.40767
$536$	28.4244	1.22775
$537$	59.2146	2.55530
$538$	−28.3251	−1.22118
$539$	−0.610027	−0.0262757
$540$	−1.45095	−0.0624389
$541$	−21.2457	−0.913423	−0.456711	−	0.889615i	$-0.650973\pi$
$541$	−21.2457	−0.913423	−0.456711	+	0.889615i	$0.650973\pi$
$542$	−24.1971	−1.03936
$543$	−51.0720	−2.19171
$544$	−1.81461	−0.0778006
$545$	−23.9181	−1.02454
$546$	42.3861	1.81396
$547$	−41.3094	−1.76626	−0.883131	−	0.469127i	$-0.844569\pi$
$547$	−41.3094	−1.76626	−0.883131	+	0.469127i	$0.844569\pi$
$548$	−1.55346	−0.0663604
$549$	0.833252	0.0355623
$550$	0.972733	0.0414775
$551$	−19.2468	−0.819941
$552$	17.1174	0.728564
$553$	41.4138	1.76110
$554$	15.1641	0.644262
$555$	−18.4029	−0.781158
$556$	6.62114	0.280799
$557$	31.1040	1.31792	0.658959	−	0.752179i	$-0.270997\pi$
$557$	31.1040	1.31792	0.658959	+	0.752179i	$0.270997\pi$
$558$	59.8720	2.53458
$559$	−4.21148	−0.178127
$560$	−23.9832	−1.01347
$561$	2.61179	0.110270
$562$	14.1951	0.598782
$563$	−10.0863	−0.425088	−0.212544	−	0.977152i	$-0.568175\pi$
$563$	−10.0863	−0.425088	−0.212544	+	0.977152i	$0.568175\pi$
$564$	−6.77348	−0.285215
$565$	21.9421	0.923111
$566$	2.87377	0.120793
$567$	−14.8151	−0.622176
$568$	2.15281	0.0903298
$569$	34.2226	1.43468	0.717342	−	0.696721i	$-0.245359\pi$
$569$	34.2226	1.43468	0.717342	+	0.696721i	$0.245359\pi$
$570$	38.4332	1.60979
$571$	20.3009	0.849566	0.424783	−	0.905295i	$-0.360350\pi$
$571$	20.3009	0.849566	0.424783	+	0.905295i	$0.360350\pi$
$572$	1.36370	0.0570192
$573$	−27.6185	−1.15378
$574$	7.95899	0.332202
$575$	1.63670	0.0682549
$576$	24.1491	1.00621
$577$	37.3636	1.55547	0.777734	−	0.628594i	$-0.216369\pi$
$577$	37.3636	1.55547	0.777734	+	0.628594i	$0.216369\pi$
$578$	−1.52440	−0.0634068
$579$	39.1148	1.62556
$580$	−2.81611	−0.116933
$581$	5.87679	0.243810
$582$	−39.5398	−1.63898
$583$	11.1669	0.462486
$584$	−18.5379	−0.767105
$585$	33.6127	1.38971
$586$	−45.1021	−1.86315
$587$	−7.72624	−0.318896	−0.159448	−	0.987206i	$-0.550971\pi$
$587$	−7.72624	−0.318896	−0.159448	+	0.987206i	$0.550971\pi$
$588$	0.515908	0.0212757
$589$	−47.5033	−1.95734
$590$	34.0215	1.40064
$591$	−39.3276	−1.61772
$592$	−15.3260	−0.629895
$593$	−17.6991	−0.726817	−0.363408	−	0.931630i	$-0.618387\pi$
$593$	−17.6991	−0.726817	−0.363408	+	0.931630i	$0.618387\pi$
$594$	3.27062	0.134195
$595$	−5.27943	−0.216436
$596$	4.47437	0.183278
$597$	29.4158	1.20391
$598$	16.4668	0.673377
$599$	35.4275	1.44753	0.723763	−	0.690048i	$-0.242411\pi$
$599$	35.4275	1.44753	0.723763	+	0.690048i	$0.242411\pi$
$600$	4.25850	0.173853
$601$	−44.0727	−1.79776	−0.898881	−	0.438192i	$-0.855619\pi$
$601$	−44.0727	−1.79776	−0.898881	+	0.438192i	$0.855619\pi$
$602$	3.85345	0.157055
$603$	42.5106	1.73116
$604$	−2.96177	−0.120513
$605$	2.08851	0.0849102
$606$	49.5800	2.01405
$607$	−19.2005	−0.779326	−0.389663	−	0.920958i	$-0.627408\pi$
$607$	−19.2005	−0.779326	−0.389663	+	0.920958i	$0.627408\pi$
$608$	8.38711	0.340142
$609$	27.4927	1.11406
$610$	−0.694198	−0.0281073
$611$	33.7305	1.36459
$612$	−1.23741	−0.0500195
$613$	−26.8182	−1.08318	−0.541588	−	0.840644i	$-0.682177\pi$
$613$	−26.8182	−1.08318	−0.541588	+	0.840644i	$0.682177\pi$
$614$	−19.0392	−0.768358
$615$	11.2664	0.454305
$616$	6.45913	0.260246
$617$	−28.6889	−1.15497	−0.577487	−	0.816400i	$-0.695966\pi$
$617$	−28.6889	−1.15497	−0.577487	+	0.816400i	$0.695966\pi$
$618$	−37.3001	−1.50043
$619$	−2.58005	−0.103701	−0.0518505	−	0.998655i	$-0.516512\pi$
$619$	−2.58005	−0.103701	−0.0518505	+	0.998655i	$0.516512\pi$
$620$	−6.95049	−0.279138
$621$	5.50306	0.220830
$622$	50.3018	2.01692
$623$	−9.88246	−0.395932
$624$	49.9682	2.00033
$625$	−21.4023	−0.856091
$626$	26.7625	1.06964
$627$	−12.0717	−0.482098
$628$	−2.18841	−0.0873272
$629$	−3.37372	−0.134519
$630$	−30.7551	−1.22531
$631$	40.8951	1.62801	0.814004	−	0.580860i	$-0.197284\pi$
$631$	40.8951	1.62801	0.814004	+	0.580860i	$0.197284\pi$
$632$	41.8620	1.66518
$633$	−66.7091	−2.65145
$634$	38.9068	1.54519
$635$	0.142675	0.00566187
$636$	−9.44400	−0.374479
$637$	−2.56912	−0.101792
$638$	6.34788	0.251315
$639$	3.21967	0.127368
$640$	−27.6988	−1.09489
$641$	24.5958	0.971476	0.485738	−	0.874104i	$-0.338551\pi$
$641$	24.5958	0.971476	0.485738	+	0.874104i	$0.338551\pi$
$642$	62.0696	2.44969
$643$	21.7586	0.858074	0.429037	−	0.903287i	$-0.358853\pi$
$643$	21.7586	0.858074	0.429037	+	0.903287i	$0.358853\pi$
$644$	−2.09946	−0.0827304
$645$	5.45477	0.214781
$646$	7.04579	0.277213
$647$	−20.5541	−0.808067	−0.404033	−	0.914744i	$-0.632392\pi$
$647$	−20.5541	−0.808067	−0.404033	+	0.914744i	$0.632392\pi$
$648$	−14.9754	−0.588291
$649$	−10.6860	−0.419464
$650$	4.09665	0.160684
$651$	67.8550	2.65945
$652$	6.13729	0.240355
$653$	29.8061	1.16640	0.583201	−	0.812328i	$-0.301800\pi$
$653$	29.8061	1.16640	0.583201	+	0.812328i	$0.301800\pi$
$654$	−45.5962	−1.78295
$655$	17.5605	0.686147
$656$	9.38272	0.366334
$657$	−27.7247	−1.08164
$658$	−30.8630	−1.20316
$659$	−11.6129	−0.452376	−0.226188	−	0.974084i	$-0.572626\pi$
$659$	−11.6129	−0.452376	−0.226188	+	0.974084i	$0.572626\pi$
$660$	−1.76628	−0.0687525
$661$	1.60659	0.0624890	0.0312445	−	0.999512i	$-0.490053\pi$
$661$	1.60659	0.0624890	0.0312445	+	0.999512i	$0.490053\pi$
$662$	1.88834	0.0733924
$663$	10.9995	0.427186
$664$	5.94039	0.230532
$665$	24.4015	0.946250
$666$	−19.6535	−0.761557
$667$	10.6808	0.413561
$668$	−1.34904	−0.0521961
$669$	18.6498	0.721044
$670$	−35.4164	−1.36825
$671$	0.218045	0.00841753
$672$	−11.9804	−0.462154
$673$	33.1063	1.27615	0.638076	−	0.769973i	$-0.279730\pi$
$673$	33.1063	1.27615	0.638076	+	0.769973i	$0.279730\pi$
$674$	−30.0810	−1.15868
$675$	1.36906	0.0526953
$676$	1.53373	0.0589898
$677$	9.97795	0.383484	0.191742	−	0.981445i	$-0.438586\pi$
$677$	9.97795	0.383484	0.191742	+	0.981445i	$0.438586\pi$
$678$	41.8292	1.60644
$679$	−25.1041	−0.963409
$680$	−5.33656	−0.204648
$681$	−51.7662	−1.98368
$682$	15.6673	0.599931
$683$	9.95038	0.380741	0.190370	−	0.981712i	$-0.439031\pi$
$683$	9.95038	0.380741	0.190370	+	0.981712i	$0.439031\pi$
$684$	5.71932	0.218684
$685$	−10.0197	−0.382831
$686$	29.3248	1.11963
$687$	30.0945	1.14818
$688$	4.54276	0.173191
$689$	47.0292	1.79167
$690$	−21.3280	−0.811944
$691$	−16.8218	−0.639930	−0.319965	−	0.947429i	$-0.603671\pi$
$691$	−16.8218	−0.639930	−0.319965	+	0.947429i	$0.603671\pi$
$692$	5.60104	0.212920
$693$	9.66006	0.366955
$694$	−38.0347	−1.44378
$695$	42.7057	1.61992
$696$	27.7902	1.05339
$697$	2.06542	0.0782334
$698$	−7.65353	−0.289690
$699$	1.78878	0.0676578
$700$	−0.522309	−0.0197414
$701$	28.4495	1.07452	0.537261	−	0.843416i	$-0.319459\pi$
$701$	28.4495	1.07452	0.537261	+	0.843416i	$0.319459\pi$
$702$	13.7742	0.519872
$703$	15.5933	0.588114
$704$	6.31933	0.238169
$705$	−43.6883	−1.64540
$706$	3.41371	0.128477
$707$	31.4787	1.18388
$708$	9.03732	0.339643
$709$	2.01680	0.0757427	0.0378713	−	0.999283i	$-0.487942\pi$
$709$	2.01680	0.0757427	0.0378713	+	0.999283i	$0.487942\pi$
$710$	−2.68237	−0.100668
$711$	62.6075	2.34797
$712$	−9.98941	−0.374369
$713$	26.3614	0.987241
$714$	−10.0644	−0.376651
$715$	8.79574	0.328942
$716$	−7.34132	−0.274358
$717$	−40.9951	−1.53099
$718$	−39.1302	−1.46032
$719$	−2.61111	−0.0973778	−0.0486889	−	0.998814i	$-0.515504\pi$
$719$	−2.61111	−0.0973778	−0.0486889	+	0.998814i	$0.515504\pi$
$720$	−36.2567	−1.35121
$721$	−23.6821	−0.881968
$722$	−3.60198	−0.134052
$723$	−58.4045	−2.17209
$724$	6.33182	0.235320
$725$	2.65719	0.0986854
$726$	3.98143	0.147765
$727$	13.6988	0.508060	0.254030	−	0.967196i	$-0.418244\pi$
$727$	13.6988	0.508060	0.254030	+	0.967196i	$0.418244\pi$
$728$	27.2025	1.00819
$729$	−39.2077	−1.45214
$730$	23.0980	0.854895
$731$	1.00000	0.0369863
$732$	−0.184403	−0.00681575
$733$	−13.8959	−0.513256	−0.256628	−	0.966510i	$-0.582612\pi$
$733$	−13.8959	−0.513256	−0.256628	+	0.966510i	$0.582612\pi$
$734$	−13.5667	−0.500756
$735$	3.32756	0.122739
$736$	−4.65433	−0.171561
$737$	11.1241	0.409763
$738$	12.0320	0.442905
$739$	−47.0982	−1.73254	−0.866268	−	0.499579i	$-0.833488\pi$
$739$	−47.0982	−1.73254	−0.866268	+	0.499579i	$0.833488\pi$
$740$	2.28155	0.0838716
$741$	−50.8398	−1.86765
$742$	−43.0311	−1.57972
$743$	12.2955	0.451078	0.225539	−	0.974234i	$-0.427586\pi$
$743$	12.2955	0.451078	0.225539	+	0.974234i	$0.427586\pi$
$744$	68.5894	2.51461
$745$	28.8593	1.05732
$746$	48.1477	1.76281
$747$	8.88426	0.325058
$748$	−0.323806	−0.0118395
$749$	39.4085	1.43996
$750$	−46.8824	−1.71190
$751$	19.0387	0.694731	0.347366	−	0.937730i	$-0.387076\pi$
$751$	19.0387	0.694731	0.347366	+	0.937730i	$0.387076\pi$
$752$	−36.3838	−1.32678
$753$	65.6212	2.39137
$754$	26.7340	0.973594
$755$	−19.1031	−0.695234
$756$	−1.75616	−0.0638709
$757$	−9.39774	−0.341567	−0.170783	−	0.985309i	$-0.554630\pi$
$757$	−9.39774	−0.341567	−0.170783	+	0.985309i	$0.554630\pi$
$758$	−41.7358	−1.51591
$759$	6.69905	0.243160
$760$	24.6656	0.894715
$761$	0.287453	0.0104202	0.00521009	−	0.999986i	$-0.498342\pi$
$761$	0.287453	0.0104202	0.00521009	+	0.999986i	$0.498342\pi$
$762$	0.271987	0.00985305
$763$	−28.9494	−1.04804
$764$	3.42409	0.123879
$765$	−7.98119	−0.288561
$766$	47.5279	1.71725
$767$	−45.0041	−1.62500
$768$	−19.7938	−0.714247
$769$	−26.6207	−0.959966	−0.479983	−	0.877278i	$-0.659357\pi$
$769$	−26.6207	−0.959966	−0.479983	+	0.877278i	$0.659357\pi$
$770$	−8.04798	−0.290029
$771$	41.8279	1.50639
$772$	−4.84939	−0.174533
$773$	35.4018	1.27331	0.636656	−	0.771148i	$-0.280317\pi$
$773$	35.4018	1.27331	0.636656	+	0.771148i	$0.280317\pi$
$774$	5.82546	0.209392
$775$	6.55824	0.235579
$776$	−25.3758	−0.910939
$777$	−22.2740	−0.799074
$778$	−9.81456	−0.351869
$779$	−9.54638	−0.342035
$780$	−7.43868	−0.266347
$781$	0.842522	0.0301478
$782$	−3.90998	−0.139820
$783$	8.93427	0.319285
$784$	2.77121	0.0989716
$785$	−14.1151	−0.503788
$786$	33.4764	1.19407
$787$	12.0085	0.428056	0.214028	−	0.976827i	$-0.431342\pi$
$787$	12.0085	0.428056	0.214028	+	0.976827i	$0.431342\pi$
$788$	4.87576	0.173692
$789$	54.1103	1.92638
$790$	−52.1595	−1.85575
$791$	26.5577	0.944283
$792$	9.76461	0.346970
$793$	0.918292	0.0326095
$794$	42.5674	1.51066
$795$	−60.9129	−2.16036
$796$	−3.64692	−0.129262
$797$	4.59288	0.162688	0.0813440	−	0.996686i	$-0.474079\pi$
$797$	4.59288	0.162688	0.0813440	+	0.996686i	$0.474079\pi$
$798$	46.5177	1.64671
$799$	−8.00918	−0.283345
$800$	−1.15791	−0.0409384
$801$	−14.9398	−0.527873
$802$	21.5279	0.760178
$803$	−7.25499	−0.256023
$804$	−9.40784	−0.331789
$805$	−13.5413	−0.477269
$806$	65.9825	2.32413
$807$	−48.5301	−1.70834
$808$	31.8194	1.11940
$809$	23.3934	0.822469	0.411234	−	0.911530i	$-0.365098\pi$
$809$	23.3934	0.822469	0.411234	+	0.911530i	$0.365098\pi$
$810$	18.6592	0.655617
$811$	24.9092	0.874679	0.437339	−	0.899297i	$-0.355921\pi$
$811$	24.9092	0.874679	0.437339	+	0.899297i	$0.355921\pi$
$812$	−3.40849	−0.119615
$813$	−41.4575	−1.45398
$814$	−5.14291	−0.180259
$815$	39.5849	1.38660
$816$	−11.8648	−0.415350
$817$	−4.62200	−0.161703
$818$	2.72231	0.0951832
$819$	40.6832	1.42159
$820$	−1.39679	−0.0487780
$821$	13.0771	0.456394	0.228197	−	0.973615i	$-0.426717\pi$
$821$	13.0771	0.456394	0.228197	+	0.973615i	$0.426717\pi$
$822$	−19.1009	−0.666221
$823$	−21.5599	−0.751532	−0.375766	−	0.926715i	$-0.622620\pi$
$823$	−21.5599	−0.751532	−0.375766	+	0.926715i	$0.622620\pi$
$824$	−23.9384	−0.833934
$825$	1.66660	0.0580237
$826$	41.1781	1.43277
$827$	−19.1172	−0.664771	−0.332385	−	0.943144i	$-0.607853\pi$
$827$	−19.1172	−0.664771	−0.332385	+	0.943144i	$0.607853\pi$
$828$	−3.17387	−0.110300
$829$	−47.1892	−1.63895	−0.819474	−	0.573117i	$-0.805734\pi$
$829$	−47.1892	−1.63895	−0.819474	+	0.573117i	$0.805734\pi$
$830$	−7.40164	−0.256915
$831$	25.9810	0.901272
$832$	26.6137	0.922666
$833$	0.610027	0.0211362
$834$	81.4118	2.81906
$835$	−8.70121	−0.301118
$836$	1.49663	0.0517620
$837$	22.0508	0.762187
$838$	12.8368	0.443440
$839$	8.34400	0.288067	0.144033	−	0.989573i	$-0.453993\pi$
$839$	8.34400	0.288067	0.144033	+	0.989573i	$0.453993\pi$
$840$	−35.2331	−1.21566
$841$	−11.6597	−0.402058
$842$	45.5671	1.57035
$843$	24.3207	0.837649
$844$	8.27047	0.284681
$845$	9.89244	0.340310
$846$	−46.6572	−1.60411
$847$	2.52784	0.0868576
$848$	−50.7286	−1.74203
$849$	4.92369	0.168980
$850$	−0.972733	−0.0333645
$851$	−8.65333	−0.296632
$852$	−0.712532	−0.0244109
$853$	7.22404	0.247346	0.123673	−	0.992323i	$-0.460533\pi$
$853$	7.22404	0.247346	0.123673	+	0.992323i	$0.460533\pi$
$854$	−0.840224	−0.0287519
$855$	36.8891	1.26158
$856$	39.8350	1.36153
$857$	21.1422	0.722203	0.361101	−	0.932527i	$-0.382401\pi$
$857$	21.1422	0.722203	0.361101	+	0.932527i	$0.382401\pi$
$858$	16.7677	0.572440
$859$	−8.67517	−0.295993	−0.147997	−	0.988988i	$-0.547282\pi$
$859$	−8.67517	−0.295993	−0.147997	+	0.988988i	$0.547282\pi$
$860$	−0.676273	−0.0230607
$861$	13.6363	0.464725
$862$	−37.4590	−1.27586
$863$	−52.2063	−1.77712	−0.888561	−	0.458758i	$-0.848294\pi$
$863$	−52.2063	−1.77712	−0.888561	+	0.458758i	$0.848294\pi$
$864$	−3.89326	−0.132451
$865$	36.1262	1.22833
$866$	−23.2237	−0.789173
$867$	−2.61179	−0.0887012
$868$	−8.41255	−0.285540
$869$	16.3831	0.555759
$870$	−34.6262	−1.17394
$871$	46.8492	1.58742
$872$	−29.2627	−0.990960
$873$	−37.9513	−1.28446
$874$	18.0719	0.611291
$875$	−29.7660	−1.00627
$876$	6.13564	0.207304
$877$	−22.6792	−0.765824	−0.382912	−	0.923785i	$-0.625079\pi$
$877$	−22.6792	−0.765824	−0.382912	+	0.923785i	$0.625079\pi$
$878$	−11.4515	−0.386470
$879$	−77.2744	−2.60640
$880$	−9.48762	−0.319828
$881$	−6.28693	−0.211812	−0.105906	−	0.994376i	$-0.533774\pi$
$881$	−6.28693	−0.211812	−0.105906	+	0.994376i	$0.533774\pi$
$882$	3.55369	0.119659
$883$	6.94902	0.233853	0.116927	−	0.993141i	$-0.462696\pi$
$883$	6.94902	0.233853	0.116927	+	0.993141i	$0.462696\pi$
$884$	−1.36370	−0.0458662
$885$	58.2899	1.95939
$886$	0.837224	0.0281271
$887$	−23.3869	−0.785254	−0.392627	−	0.919698i	$-0.628434\pi$
$887$	−23.3869	−0.785254	−0.392627	+	0.919698i	$0.628434\pi$
$888$	−22.5150	−0.755555
$889$	0.172687	0.00579172
$890$	12.4467	0.417213
$891$	−5.86078	−0.196343
$892$	−2.31217	−0.0774172
$893$	37.0184	1.23878
$894$	55.0157	1.84000
$895$	−47.3508	−1.58276
$896$	−33.5253	−1.12000
$897$	28.2129	0.942002
$898$	−42.6085	−1.42186
$899$	42.7979	1.42739
$900$	−0.789602	−0.0263201
$901$	−11.1669	−0.372023
$902$	3.14854	0.104835
$903$	6.60220	0.219707
$904$	26.8451	0.892855
$905$	40.8396	1.35755
$906$	−36.4172	−1.20988
$907$	−2.47907	−0.0823163	−0.0411581	−	0.999153i	$-0.513105\pi$
$907$	−2.47907	−0.0823163	−0.0411581	+	0.999153i	$0.513105\pi$
$908$	6.41788	0.212985
$909$	47.5881	1.57840
$910$	−33.8939	−1.12357
$911$	−51.1495	−1.69466	−0.847329	−	0.531068i	$-0.821791\pi$
$911$	−51.1495	−1.69466	−0.847329	+	0.531068i	$0.821791\pi$
$912$	54.8389	1.81590
$913$	2.32483	0.0769405
$914$	−27.2033	−0.899805
$915$	−1.18938	−0.0393198
$916$	−3.73106	−0.123278
$917$	21.2545	0.701884
$918$	−3.27062	−0.107947
$919$	−14.0328	−0.462898	−0.231449	−	0.972847i	$-0.574347\pi$
$919$	−14.0328	−0.462898	−0.231449	+	0.972847i	$0.574347\pi$
$920$	−13.6879	−0.451276
$921$	−32.6202	−1.07487
$922$	36.9991	1.21850
$923$	3.54827	0.116793
$924$	−2.13783	−0.0703294
$925$	−2.15280	−0.0707835
$926$	−64.2446	−2.11121
$927$	−35.8015	−1.17588
$928$	−7.55633	−0.248049
$929$	−1.54785	−0.0507833	−0.0253916	−	0.999678i	$-0.508083\pi$
$929$	−1.54785	−0.0507833	−0.0253916	+	0.999678i	$0.508083\pi$
$930$	−85.4614	−2.80239
$931$	−2.81954	−0.0924068
$932$	−0.221769	−0.00726430
$933$	86.1833	2.82151
$934$	−25.5819	−0.837067
$935$	−2.08851	−0.0683017
$936$	41.1235	1.34416
$937$	47.6356	1.55619	0.778094	−	0.628147i	$-0.216187\pi$
$937$	47.6356	1.55619	0.778094	+	0.628147i	$0.216187\pi$
$938$	−42.8663	−1.39963
$939$	45.8528	1.49635
$940$	5.41639	0.176663
$941$	−2.10861	−0.0687386	−0.0343693	−	0.999409i	$-0.510942\pi$
$941$	−2.10861	−0.0687386	−0.0343693	+	0.999409i	$0.510942\pi$
$942$	−26.9082	−0.876715
$943$	5.29765	0.172515
$944$	48.5441	1.57998
$945$	−11.3271	−0.368469
$946$	1.52440	0.0495626
$947$	−22.8912	−0.743865	−0.371932	−	0.928260i	$-0.621305\pi$
$947$	−22.8912	−0.743865	−0.371932	+	0.928260i	$0.621305\pi$
$948$	−13.8554	−0.450003
$949$	−30.5543	−0.991834
$950$	4.49597	0.145869
$951$	66.6600	2.16160
$952$	−6.45913	−0.209342
$953$	−11.5615	−0.374513	−0.187257	−	0.982311i	$-0.559960\pi$
$953$	−11.5615	−0.374513	−0.187257	+	0.982311i	$0.559960\pi$
$954$	−65.0523	−2.10615
$955$	22.0850	0.714655
$956$	5.08250	0.164380
$957$	10.8760	0.351570
$958$	−37.6785	−1.21734
$959$	−12.1273	−0.391611
$960$	−34.4705	−1.11253
$961$	74.6300	2.40742
$962$	−21.6593	−0.698323
$963$	59.5759	1.91981
$964$	7.24088	0.233213
$965$	−31.2781	−1.00688
$966$	−25.8144	−0.830566
$967$	−9.38119	−0.301679	−0.150839	−	0.988558i	$-0.548198\pi$
$967$	−9.38119	−0.301679	−0.150839	+	0.988558i	$0.548198\pi$
$968$	2.55520	0.0821271
$969$	12.0717	0.387799
$970$	31.6179	1.01519
$971$	−3.31428	−0.106360	−0.0531801	−	0.998585i	$-0.516936\pi$
$971$	−3.31428	−0.106360	−0.0531801	+	0.998585i	$0.516936\pi$
$972$	7.04072	0.225831
$973$	51.6890	1.65707
$974$	−29.2446	−0.937057
$975$	7.01888	0.224784
$976$	−0.990526	−0.0317060
$977$	−16.5523	−0.529553	−0.264777	−	0.964310i	$-0.585298\pi$
$977$	−16.5523	−0.529553	−0.264777	+	0.964310i	$0.585298\pi$
$978$	75.4625	2.41302
$979$	−3.90945	−0.124946
$980$	−0.412544	−0.0131782
$981$	−43.7643	−1.39729
$982$	26.2579	0.837922
$983$	8.68985	0.277163	0.138582	−	0.990351i	$-0.455746\pi$
$983$	8.68985	0.277163	0.138582	+	0.990351i	$0.455746\pi$
$984$	13.7839	0.439415
$985$	31.4482	1.00202
$986$	−6.34788	−0.202158
$987$	−52.8782	−1.68313
$988$	6.30303	0.200526
$989$	2.56492	0.0815598
$990$	−12.1666	−0.386679
$991$	42.9911	1.36566	0.682828	−	0.730579i	$-0.260750\pi$
$991$	42.9911	1.36566	0.682828	+	0.730579i	$0.260750\pi$
$992$	−18.6499	−0.592135
$993$	3.23534	0.102670
$994$	−3.24661	−0.102976
$995$	−23.5223	−0.745706
$996$	−1.96614	−0.0622994
$997$	30.8130	0.975857	0.487928	−	0.872884i	$-0.337753\pi$
$997$	30.8130	0.975857	0.487928	+	0.872884i	$0.337753\pi$
$998$	−42.9219	−1.35867
$999$	−7.23835	−0.229011

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.20	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.20	✓	78	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.52440 q^{2} -2.61179 q^{3} +0.323806 q^{4} +2.08851 q^{5} +3.98143 q^{6} +2.52784 q^{7} +2.55520 q^{8} +3.82147 q^{9} +O(q^{10})\)	\(q-1.52440 q^{2} -2.61179 q^{3} +0.323806 q^{4} +2.08851 q^{5} +3.98143 q^{6} +2.52784 q^{7} +2.55520 q^{8} +3.82147 q^{9} -3.18374 q^{10} +1.00000 q^{11} -0.845713 q^{12} +4.21148 q^{13} -3.85345 q^{14} -5.45477 q^{15} -4.54276 q^{16} -1.00000 q^{17} -5.82546 q^{18} +4.62200 q^{19} +0.676273 q^{20} -6.60220 q^{21} -1.52440 q^{22} -2.56492 q^{23} -6.67365 q^{24} -0.638107 q^{25} -6.42000 q^{26} -2.14551 q^{27} +0.818528 q^{28} -4.16417 q^{29} +8.31527 q^{30} -10.2776 q^{31} +1.81461 q^{32} -2.61179 q^{33} +1.52440 q^{34} +5.27943 q^{35} +1.23741 q^{36} +3.37372 q^{37} -7.04579 q^{38} -10.9995 q^{39} +5.33656 q^{40} -2.06542 q^{41} +10.0644 q^{42} -1.00000 q^{43} +0.323806 q^{44} +7.98119 q^{45} +3.90998 q^{46} +8.00918 q^{47} +11.8648 q^{48} -0.610027 q^{49} +0.972733 q^{50} +2.61179 q^{51} +1.36370 q^{52} +11.1669 q^{53} +3.27062 q^{54} +2.08851 q^{55} +6.45913 q^{56} -12.0717 q^{57} +6.34788 q^{58} -10.6860 q^{59} -1.76628 q^{60} +0.218045 q^{61} +15.6673 q^{62} +9.66006 q^{63} +6.31933 q^{64} +8.79574 q^{65} +3.98143 q^{66} +11.1241 q^{67} -0.323806 q^{68} +6.69905 q^{69} -8.04798 q^{70} +0.842522 q^{71} +9.76461 q^{72} -7.25499 q^{73} -5.14291 q^{74} +1.66660 q^{75} +1.49663 q^{76} +2.52784 q^{77} +16.7677 q^{78} +16.3831 q^{79} -9.48762 q^{80} -5.86078 q^{81} +3.14854 q^{82} +2.32483 q^{83} -2.13783 q^{84} -2.08851 q^{85} +1.52440 q^{86} +10.8760 q^{87} +2.55520 q^{88} -3.90945 q^{89} -12.1666 q^{90} +10.6460 q^{91} -0.830536 q^{92} +26.8431 q^{93} -12.2092 q^{94} +9.65311 q^{95} -4.73938 q^{96} -9.93107 q^{97} +0.929927 q^{98} +3.82147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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