LMFDB - Embedded newform 8015.2.a.l.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.12264 q^{2} -2.04208 q^{3} +2.50559 q^{4} -1.00000 q^{5} +4.33460 q^{6} -1.00000 q^{7} -1.07319 q^{8} +1.17010 q^{9} +O(q^{10})$	\(q-2.12264 q^{2} -2.04208 q^{3} +2.50559 q^{4} -1.00000 q^{5} +4.33460 q^{6} -1.00000 q^{7} -1.07319 q^{8} +1.17010 q^{9} +2.12264 q^{10} +3.06648 q^{11} -5.11662 q^{12} +4.61144 q^{13} +2.12264 q^{14} +2.04208 q^{15} -2.73319 q^{16} -5.63379 q^{17} -2.48369 q^{18} -3.26056 q^{19} -2.50559 q^{20} +2.04208 q^{21} -6.50903 q^{22} +4.76193 q^{23} +2.19154 q^{24} +1.00000 q^{25} -9.78843 q^{26} +3.73681 q^{27} -2.50559 q^{28} -3.51013 q^{29} -4.33460 q^{30} -2.15089 q^{31} +7.94796 q^{32} -6.26201 q^{33} +11.9585 q^{34} +1.00000 q^{35} +2.93178 q^{36} +5.31424 q^{37} +6.92099 q^{38} -9.41694 q^{39} +1.07319 q^{40} -9.14281 q^{41} -4.33460 q^{42} +2.94660 q^{43} +7.68335 q^{44} -1.17010 q^{45} -10.1079 q^{46} +1.74188 q^{47} +5.58140 q^{48} +1.00000 q^{49} -2.12264 q^{50} +11.5046 q^{51} +11.5544 q^{52} -10.4360 q^{53} -7.93190 q^{54} -3.06648 q^{55} +1.07319 q^{56} +6.65833 q^{57} +7.45073 q^{58} +12.7186 q^{59} +5.11662 q^{60} +6.25110 q^{61} +4.56556 q^{62} -1.17010 q^{63} -11.4042 q^{64} -4.61144 q^{65} +13.2920 q^{66} -2.70719 q^{67} -14.1160 q^{68} -9.72424 q^{69} -2.12264 q^{70} +11.6344 q^{71} -1.25573 q^{72} +7.59479 q^{73} -11.2802 q^{74} -2.04208 q^{75} -8.16964 q^{76} -3.06648 q^{77} +19.9888 q^{78} -4.26352 q^{79} +2.73319 q^{80} -11.1412 q^{81} +19.4069 q^{82} +13.3150 q^{83} +5.11662 q^{84} +5.63379 q^{85} -6.25456 q^{86} +7.16797 q^{87} -3.29091 q^{88} -3.77914 q^{89} +2.48369 q^{90} -4.61144 q^{91} +11.9314 q^{92} +4.39229 q^{93} -3.69739 q^{94} +3.26056 q^{95} -16.2304 q^{96} +6.32500 q^{97} -2.12264 q^{98} +3.58808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.12264	−1.50093	−0.750466	−	0.660909i	$-0.770171\pi$
$2$	−2.12264	−1.50093	−0.750466	+	0.660909i	$0.770171\pi$
$3$	−2.04208	−1.17900	−0.589498	−	0.807770i	$-0.700674\pi$
$3$	−2.04208	−1.17900	−0.589498	+	0.807770i	$0.700674\pi$
$4$	2.50559	1.25280
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.33460	1.76959
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.07319	−0.379429
$9$	1.17010	0.390032
$10$	2.12264	0.671237
$11$	3.06648	0.924579	0.462290	−	0.886729i	$-0.347028\pi$
$11$	3.06648	0.924579	0.462290	+	0.886729i	$0.347028\pi$
$12$	−5.11662	−1.47704
$13$	4.61144	1.27898	0.639492	−	0.768798i	$-0.279145\pi$
$13$	4.61144	1.27898	0.639492	+	0.768798i	$0.279145\pi$
$14$	2.12264	0.567299
$15$	2.04208	0.527263
$16$	−2.73319	−0.683299
$17$	−5.63379	−1.36639	−0.683197	−	0.730234i	$-0.739411\pi$
$17$	−5.63379	−1.36639	−0.683197	+	0.730234i	$0.739411\pi$
$18$	−2.48369	−0.585411
$19$	−3.26056	−0.748024	−0.374012	−	0.927424i	$-0.622018\pi$
$19$	−3.26056	−0.748024	−0.374012	+	0.927424i	$0.622018\pi$
$20$	−2.50559	−0.560267
$21$	2.04208	0.445619
$22$	−6.50903	−1.38773
$23$	4.76193	0.992931	0.496465	−	0.868057i	$-0.334631\pi$
$23$	4.76193	0.992931	0.496465	+	0.868057i	$0.334631\pi$
$24$	2.19154	0.447345
$25$	1.00000	0.200000
$26$	−9.78843	−1.91967
$27$	3.73681	0.719150
$28$	−2.50559	−0.473512
$29$	−3.51013	−0.651815	−0.325907	−	0.945402i	$-0.605670\pi$
$29$	−3.51013	−0.651815	−0.325907	+	0.945402i	$0.605670\pi$
$30$	−4.33460	−0.791386
$31$	−2.15089	−0.386311	−0.193156	−	0.981168i	$-0.561872\pi$
$31$	−2.15089	−0.386311	−0.193156	+	0.981168i	$0.561872\pi$
$32$	7.94796	1.40501
$33$	−6.26201	−1.09008
$34$	11.9585	2.05086
$35$	1.00000	0.169031
$36$	2.93178	0.488630
$37$	5.31424	0.873656	0.436828	−	0.899545i	$-0.356102\pi$
$37$	5.31424	0.873656	0.436828	+	0.899545i	$0.356102\pi$
$38$	6.92099	1.12273
$39$	−9.41694	−1.50792
$40$	1.07319	0.169686
$41$	−9.14281	−1.42787	−0.713933	−	0.700214i	$-0.753088\pi$
$41$	−9.14281	−1.42787	−0.713933	+	0.700214i	$0.753088\pi$
$42$	−4.33460	−0.668843
$43$	2.94660	0.449352	0.224676	−	0.974434i	$-0.427868\pi$
$43$	2.94660	0.449352	0.224676	+	0.974434i	$0.427868\pi$
$44$	7.68335	1.15831
$45$	−1.17010	−0.174427
$46$	−10.1079	−1.49032
$47$	1.74188	0.254080	0.127040	−	0.991898i	$-0.459452\pi$
$47$	1.74188	0.254080	0.127040	+	0.991898i	$0.459452\pi$
$48$	5.58140	0.805606
$49$	1.00000	0.142857
$50$	−2.12264	−0.300186
$51$	11.5046	1.61097
$52$	11.5544	1.60231
$53$	−10.4360	−1.43350	−0.716750	−	0.697330i	$-0.754371\pi$
$53$	−10.4360	−1.43350	−0.716750	+	0.697330i	$0.754371\pi$
$54$	−7.93190	−1.07940
$55$	−3.06648	−0.413484
$56$	1.07319	0.143411
$57$	6.65833	0.881918
$58$	7.45073	0.978329
$59$	12.7186	1.65582	0.827909	−	0.560862i	$-0.189530\pi$
$59$	12.7186	1.65582	0.827909	+	0.560862i	$0.189530\pi$
$60$	5.11662	0.660553
$61$	6.25110	0.800371	0.400185	−	0.916434i	$-0.368946\pi$
$61$	6.25110	0.800371	0.400185	+	0.916434i	$0.368946\pi$
$62$	4.56556	0.579826
$63$	−1.17010	−0.147418
$64$	−11.4042	−1.42553
$65$	−4.61144	−0.571979
$66$	13.2920	1.63613
$67$	−2.70719	−0.330736	−0.165368	−	0.986232i	$-0.552881\pi$
$67$	−2.70719	−0.330736	−0.165368	+	0.986232i	$0.552881\pi$
$68$	−14.1160	−1.71181
$69$	−9.72424	−1.17066
$70$	−2.12264	−0.253704
$71$	11.6344	1.38075	0.690374	−	0.723453i	$-0.257446\pi$
$71$	11.6344	1.38075	0.690374	+	0.723453i	$0.257446\pi$
$72$	−1.25573	−0.147989
$73$	7.59479	0.888903	0.444452	−	0.895803i	$-0.353399\pi$
$73$	7.59479	0.888903	0.444452	+	0.895803i	$0.353399\pi$
$74$	−11.2802	−1.31130
$75$	−2.04208	−0.235799
$76$	−8.16964	−0.937122
$77$	−3.06648	−0.349458
$78$	19.9888	2.26328
$79$	−4.26352	−0.479683	−0.239842	−	0.970812i	$-0.577096\pi$
$79$	−4.26352	−0.479683	−0.239842	+	0.970812i	$0.577096\pi$
$80$	2.73319	0.305580
$81$	−11.1412	−1.23791
$82$	19.4069	2.14313
$83$	13.3150	1.46151	0.730756	−	0.682638i	$-0.239168\pi$
$83$	13.3150	1.46151	0.730756	+	0.682638i	$0.239168\pi$
$84$	5.11662	0.558269
$85$	5.63379	0.611070
$86$	−6.25456	−0.674446
$87$	7.16797	0.768487
$88$	−3.29091	−0.350812
$89$	−3.77914	−0.400588	−0.200294	−	0.979736i	$-0.564190\pi$
$89$	−3.77914	−0.400588	−0.200294	+	0.979736i	$0.564190\pi$
$90$	2.48369	0.261804
$91$	−4.61144	−0.483411
$92$	11.9314	1.24394
$93$	4.39229	0.455459
$94$	−3.69739	−0.381357
$95$	3.26056	0.334527
$96$	−16.2304	−1.65651
$97$	6.32500	0.642206	0.321103	−	0.947044i	$-0.395946\pi$
$97$	6.32500	0.642206	0.321103	+	0.947044i	$0.395946\pi$
$98$	−2.12264	−0.214419
$99$	3.58808	0.360615
$100$	2.50559	0.250559
$101$	0.223535	0.0222425	0.0111213	−	0.999938i	$-0.496460\pi$
$101$	0.223535	0.0222425	0.0111213	+	0.999938i	$0.496460\pi$
$102$	−24.4202	−2.41796
$103$	8.72842	0.860037	0.430019	−	0.902820i	$-0.358507\pi$
$103$	8.72842	0.860037	0.430019	+	0.902820i	$0.358507\pi$
$104$	−4.94894	−0.485284
$105$	−2.04208	−0.199287
$106$	22.1519	2.15159
$107$	−12.2087	−1.18026	−0.590128	−	0.807310i	$-0.700923\pi$
$107$	−12.2087	−1.18026	−0.590128	+	0.807310i	$0.700923\pi$
$108$	9.36293	0.900948
$109$	−6.81227	−0.652497	−0.326249	−	0.945284i	$-0.605785\pi$
$109$	−6.81227	−0.652497	−0.326249	+	0.945284i	$0.605785\pi$
$110$	6.50903	0.620612
$111$	−10.8521	−1.03004
$112$	2.73319	0.258263
$113$	11.5652	1.08796	0.543979	−	0.839099i	$-0.316917\pi$
$113$	11.5652	1.08796	0.543979	+	0.839099i	$0.316917\pi$
$114$	−14.1332	−1.32370
$115$	−4.76193	−0.444052
$116$	−8.79495	−0.816591
$117$	5.39583	0.498845
$118$	−26.9969	−2.48527
$119$	5.63379	0.516448
$120$	−2.19154	−0.200059
$121$	−1.59669	−0.145153
$122$	−13.2688	−1.20130
$123$	18.6704	1.68345
$124$	−5.38925	−0.483969
$125$	−1.00000	−0.0894427
$126$	2.48369	0.221265
$127$	−9.82591	−0.871909	−0.435954	−	0.899969i	$-0.643589\pi$
$127$	−9.82591	−0.871909	−0.435954	+	0.899969i	$0.643589\pi$
$128$	8.31117	0.734610
$129$	−6.01719	−0.529784
$130$	9.78843	0.858502
$131$	−6.88741	−0.601756	−0.300878	−	0.953663i	$-0.597280\pi$
$131$	−6.88741	−0.601756	−0.300878	+	0.953663i	$0.597280\pi$
$132$	−15.6900	−1.36564
$133$	3.26056	0.282727
$134$	5.74639	0.496412
$135$	−3.73681	−0.321614
$136$	6.04611	0.518450
$137$	−8.90601	−0.760892	−0.380446	−	0.924803i	$-0.624229\pi$
$137$	−8.90601	−0.760892	−0.380446	+	0.924803i	$0.624229\pi$
$138$	20.6410	1.75708
$139$	13.2483	1.12370	0.561851	−	0.827238i	$-0.310089\pi$
$139$	13.2483	1.12370	0.561851	+	0.827238i	$0.310089\pi$
$140$	2.50559	0.211761
$141$	−3.55707	−0.299559
$142$	−24.6956	−2.07241
$143$	14.1409	1.18252
$144$	−3.19810	−0.266508
$145$	3.51013	0.291500
$146$	−16.1210	−1.33418
$147$	−2.04208	−0.168428
$148$	13.3153	1.09451
$149$	−8.98809	−0.736333	−0.368167	−	0.929760i	$-0.620014\pi$
$149$	−8.98809	−0.736333	−0.368167	+	0.929760i	$0.620014\pi$
$150$	4.33460	0.353918
$151$	−13.3460	−1.08609	−0.543043	−	0.839705i	$-0.682728\pi$
$151$	−13.3460	−1.08609	−0.543043	+	0.839705i	$0.682728\pi$
$152$	3.49919	0.283822
$153$	−6.59207	−0.532937
$154$	6.50903	0.524513
$155$	2.15089	0.172764
$156$	−23.5950	−1.88911
$157$	3.65570	0.291756	0.145878	−	0.989303i	$-0.453399\pi$
$157$	3.65570	0.291756	0.145878	+	0.989303i	$0.453399\pi$
$158$	9.04991	0.719972
$159$	21.3112	1.69009
$160$	−7.94796	−0.628341
$161$	−4.76193	−0.375293
$162$	23.6487	1.85801
$163$	9.04593	0.708532	0.354266	−	0.935145i	$-0.384731\pi$
$163$	9.04593	0.708532	0.354266	+	0.935145i	$0.384731\pi$
$164$	−22.9081	−1.78882
$165$	6.26201	0.487496
$166$	−28.2630	−2.19363
$167$	17.0657	1.32058	0.660291	−	0.751010i	$-0.270433\pi$
$167$	17.0657	1.32058	0.660291	+	0.751010i	$0.270433\pi$
$168$	−2.19154	−0.169081
$169$	8.26542	0.635801
$170$	−11.9585	−0.917174
$171$	−3.81517	−0.291753
$172$	7.38297	0.562946
$173$	17.0726	1.29800	0.649002	−	0.760787i	$-0.275187\pi$
$173$	17.0726	1.29800	0.649002	+	0.760787i	$0.275187\pi$
$174$	−15.2150	−1.15345
$175$	−1.00000	−0.0755929
$176$	−8.38129	−0.631764
$177$	−25.9724	−1.95220
$178$	8.02175	0.601255
$179$	−17.0019	−1.27078	−0.635392	−	0.772190i	$-0.719162\pi$
$179$	−17.0019	−1.27078	−0.635392	+	0.772190i	$0.719162\pi$
$180$	−2.93178	−0.218522
$181$	3.54374	0.263404	0.131702	−	0.991289i	$-0.457956\pi$
$181$	3.54374	0.263404	0.131702	+	0.991289i	$0.457956\pi$
$182$	9.78843	0.725566
$183$	−12.7652	−0.943634
$184$	−5.11044	−0.376747
$185$	−5.31424	−0.390711
$186$	−9.32324	−0.683613
$187$	−17.2759	−1.26334
$188$	4.36445	0.318310
$189$	−3.73681	−0.271813
$190$	−6.92099	−0.502102
$191$	−25.1507	−1.81984	−0.909922	−	0.414779i	$-0.863859\pi$
$191$	−25.1507	−1.81984	−0.909922	+	0.414779i	$0.863859\pi$
$192$	23.2884	1.68070
$193$	−11.2607	−0.810566	−0.405283	−	0.914191i	$-0.632827\pi$
$193$	−11.2607	−0.810566	−0.405283	+	0.914191i	$0.632827\pi$
$194$	−13.4257	−0.963908
$195$	9.41694	0.674361
$196$	2.50559	0.178971
$197$	−5.77791	−0.411659	−0.205829	−	0.978588i	$-0.565989\pi$
$197$	−5.77791	−0.411659	−0.205829	+	0.978588i	$0.565989\pi$
$198$	−7.61619	−0.541259
$199$	−10.1673	−0.720739	−0.360370	−	0.932810i	$-0.617349\pi$
$199$	−10.1673	−0.720739	−0.360370	+	0.932810i	$0.617349\pi$
$200$	−1.07319	−0.0758858
$201$	5.52831	0.389937
$202$	−0.474483	−0.0333845
$203$	3.51013	0.246363
$204$	28.8259	2.01822
$205$	9.14281	0.638561
$206$	−18.5273	−1.29086
$207$	5.57191	0.387275
$208$	−12.6040	−0.873928
$209$	−9.99846	−0.691608
$210$	4.33460	0.299116
$211$	25.3243	1.74340	0.871698	−	0.490043i	$-0.163019\pi$
$211$	25.3243	1.74340	0.871698	+	0.490043i	$0.163019\pi$
$212$	−26.1485	−1.79588
$213$	−23.7584	−1.62790
$214$	25.9146	1.77148
$215$	−2.94660	−0.200956
$216$	−4.01030	−0.272866
$217$	2.15089	0.146012
$218$	14.4600	0.979354
$219$	−15.5092	−1.04801
$220$	−7.68335	−0.518011
$221$	−25.9799	−1.74760
$222$	23.0351	1.54602
$223$	14.7787	0.989652	0.494826	−	0.868992i	$-0.335232\pi$
$223$	14.7787	0.989652	0.494826	+	0.868992i	$0.335232\pi$
$224$	−7.94796	−0.531045
$225$	1.17010	0.0780063
$226$	−24.5486	−1.63295
$227$	−26.0088	−1.72627	−0.863134	−	0.504975i	$-0.831502\pi$
$227$	−26.0088	−1.72627	−0.863134	+	0.504975i	$0.831502\pi$
$228$	16.6831	1.10486
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	10.1079	0.666492
$231$	6.26201	0.412010
$232$	3.76703	0.247317
$233$	2.54395	0.166660	0.0833299	−	0.996522i	$-0.473444\pi$
$233$	2.54395	0.166660	0.0833299	+	0.996522i	$0.473444\pi$
$234$	−11.4534	−0.748732
$235$	−1.74188	−0.113628
$236$	31.8676	2.07440
$237$	8.70645	0.565545
$238$	−11.9585	−0.775154
$239$	−25.9383	−1.67781	−0.838904	−	0.544279i	$-0.816803\pi$
$239$	−25.9383	−1.67781	−0.838904	+	0.544279i	$0.816803\pi$
$240$	−5.58140	−0.360278
$241$	10.9253	0.703757	0.351879	−	0.936046i	$-0.385543\pi$
$241$	10.9253	0.703757	0.351879	+	0.936046i	$0.385543\pi$
$242$	3.38919	0.217865
$243$	11.5407	0.740337
$244$	15.6627	1.00270
$245$	−1.00000	−0.0638877
$246$	−39.6304	−2.52674
$247$	−15.0359	−0.956712
$248$	2.30831	0.146578
$249$	−27.1903	−1.72312
$250$	2.12264	0.134247
$251$	−10.8962	−0.687760	−0.343880	−	0.939014i	$-0.611741\pi$
$251$	−10.8962	−0.687760	−0.343880	+	0.939014i	$0.611741\pi$
$252$	−2.93178	−0.184685
$253$	14.6024	0.918043
$254$	20.8568	1.30868
$255$	−11.5046	−0.720449
$256$	5.16689	0.322931
$257$	8.55327	0.533538	0.266769	−	0.963760i	$-0.414044\pi$
$257$	8.55327	0.533538	0.266769	+	0.963760i	$0.414044\pi$
$258$	12.7723	0.795170
$259$	−5.31424	−0.330211
$260$	−11.5544	−0.716573
$261$	−4.10719	−0.254228
$262$	14.6195	0.903194
$263$	−26.8373	−1.65486	−0.827429	−	0.561570i	$-0.810197\pi$
$263$	−26.8373	−1.65486	−0.827429	+	0.561570i	$0.810197\pi$
$264$	6.72031	0.413606
$265$	10.4360	0.641081
$266$	−6.92099	−0.424353
$267$	7.71731	0.472292
$268$	−6.78312	−0.414345
$269$	23.1962	1.41430	0.707150	−	0.707064i	$-0.249981\pi$
$269$	23.1962	1.41430	0.707150	+	0.707064i	$0.249981\pi$
$270$	7.93190	0.482720
$271$	−16.5502	−1.00535	−0.502675	−	0.864475i	$-0.667651\pi$
$271$	−16.5502	−1.00535	−0.502675	+	0.864475i	$0.667651\pi$
$272$	15.3982	0.933655
$273$	9.41694	0.569939
$274$	18.9042	1.14205
$275$	3.06648	0.184916
$276$	−24.3650	−1.46660
$277$	23.6464	1.42077	0.710387	−	0.703812i	$-0.248520\pi$
$277$	23.6464	1.42077	0.710387	+	0.703812i	$0.248520\pi$
$278$	−28.1213	−1.68660
$279$	−2.51674	−0.150674
$280$	−1.07319	−0.0641352
$281$	−11.1360	−0.664319	−0.332159	−	0.943223i	$-0.607777\pi$
$281$	−11.1360	−0.664319	−0.332159	+	0.943223i	$0.607777\pi$
$282$	7.55037	0.449618
$283$	16.2753	0.967467	0.483733	−	0.875215i	$-0.339280\pi$
$283$	16.2753	0.967467	0.483733	+	0.875215i	$0.339280\pi$
$284$	29.1510	1.72980
$285$	−6.65833	−0.394406
$286$	−30.0160	−1.77489
$287$	9.14281	0.539683
$288$	9.29987	0.548000
$289$	14.7395	0.867032
$290$	−7.45073	−0.437522
$291$	−12.9162	−0.757159
$292$	19.0295	1.11361
$293$	21.0407	1.22921	0.614605	−	0.788835i	$-0.289315\pi$
$293$	21.0407	1.22921	0.614605	+	0.788835i	$0.289315\pi$
$294$	4.33460	0.252799
$295$	−12.7186	−0.740504
$296$	−5.70318	−0.331490
$297$	11.4589	0.664911
$298$	19.0785	1.10519
$299$	21.9594	1.26994
$300$	−5.11662	−0.295408
$301$	−2.94660	−0.169839
$302$	28.3288	1.63014
$303$	−0.456476	−0.0262239
$304$	8.91175	0.511124
$305$	−6.25110	−0.357937
$306$	13.9926	0.799902
$307$	−29.7346	−1.69704	−0.848522	−	0.529161i	$-0.822507\pi$
$307$	−29.7346	−1.69704	−0.848522	+	0.529161i	$0.822507\pi$
$308$	−7.68335	−0.437800
$309$	−17.8242	−1.01398
$310$	−4.56556	−0.259306
$311$	29.5926	1.67804	0.839022	−	0.544098i	$-0.183128\pi$
$311$	29.5926	1.67804	0.839022	+	0.544098i	$0.183128\pi$
$312$	10.1061	0.572148
$313$	−34.4107	−1.94501	−0.972504	−	0.232885i	$-0.925184\pi$
$313$	−34.4107	−1.94501	−0.972504	+	0.232885i	$0.925184\pi$
$314$	−7.75972	−0.437906
$315$	1.17010	0.0659274
$316$	−10.6826	−0.600945
$317$	−1.77424	−0.0996513	−0.0498257	−	0.998758i	$-0.515867\pi$
$317$	−1.77424	−0.0996513	−0.0498257	+	0.998758i	$0.515867\pi$
$318$	−45.2361	−2.53671
$319$	−10.7638	−0.602654
$320$	11.4042	0.637517
$321$	24.9311	1.39152
$322$	10.1079	0.563288
$323$	18.3693	1.02210
$324$	−27.9152	−1.55084
$325$	4.61144	0.255797
$326$	−19.2012	−1.06346
$327$	13.9112	0.769292
$328$	9.81195	0.541774
$329$	−1.74188	−0.0960332
$330$	−13.2920	−0.731699
$331$	−24.1241	−1.32598	−0.662989	−	0.748629i	$-0.730712\pi$
$331$	−24.1241	−1.32598	−0.662989	+	0.748629i	$0.730712\pi$
$332$	33.3620	1.83098
$333$	6.21817	0.340754
$334$	−36.2242	−1.98210
$335$	2.70719	0.147910
$336$	−5.58140	−0.304491
$337$	−10.5005	−0.571997	−0.285998	−	0.958230i	$-0.592325\pi$
$337$	−10.5005	−0.571997	−0.285998	+	0.958230i	$0.592325\pi$
$338$	−17.5445	−0.954294
$339$	−23.6170	−1.28270
$340$	14.1160	0.765546
$341$	−6.59566	−0.357175
$342$	8.09822	0.437902
$343$	−1.00000	−0.0539949
$344$	−3.16225	−0.170497
$345$	9.72424	0.523536
$346$	−36.2389	−1.94821
$347$	2.78571	0.149545	0.0747723	−	0.997201i	$-0.476177\pi$
$347$	2.78571	0.149545	0.0747723	+	0.997201i	$0.476177\pi$
$348$	17.9600	0.962757
$349$	−18.0677	−0.967143	−0.483571	−	0.875305i	$-0.660661\pi$
$349$	−18.0677	−0.967143	−0.483571	+	0.875305i	$0.660661\pi$
$350$	2.12264	0.113460
$351$	17.2321	0.919782
$352$	24.3723	1.29905
$353$	−26.8713	−1.43021	−0.715106	−	0.699016i	$-0.753622\pi$
$353$	−26.8713	−1.43021	−0.715106	+	0.699016i	$0.753622\pi$
$354$	55.1299	2.93012
$355$	−11.6344	−0.617489
$356$	−9.46898	−0.501855
$357$	−11.5046	−0.608891
$358$	36.0890	1.90736
$359$	−29.2865	−1.54568	−0.772842	−	0.634599i	$-0.781165\pi$
$359$	−29.2865	−1.54568	−0.772842	+	0.634599i	$0.781165\pi$
$360$	1.25573	0.0661829
$361$	−8.36873	−0.440460
$362$	−7.52208	−0.395352
$363$	3.26056	0.171135
$364$	−11.5544	−0.605615
$365$	−7.59479	−0.397530
$366$	27.0960	1.41633
$367$	23.1745	1.20970	0.604850	−	0.796339i	$-0.293233\pi$
$367$	23.1745	1.20970	0.604850	+	0.796339i	$0.293233\pi$
$368$	−13.0153	−0.678468
$369$	−10.6980	−0.556913
$370$	11.2802	0.586430
$371$	10.4360	0.541812
$372$	11.0053	0.570597
$373$	−16.7267	−0.866074	−0.433037	−	0.901376i	$-0.642558\pi$
$373$	−16.7267	−0.866074	−0.433037	+	0.901376i	$0.642558\pi$
$374$	36.6705	1.89619
$375$	2.04208	0.105453
$376$	−1.86937	−0.0964053
$377$	−16.1868	−0.833661
$378$	7.93190	0.407973
$379$	29.6413	1.52257	0.761287	−	0.648415i	$-0.224568\pi$
$379$	29.6413	1.52257	0.761287	+	0.648415i	$0.224568\pi$
$380$	8.16964	0.419094
$381$	20.0653	1.02798
$382$	53.3859	2.73146
$383$	−9.28910	−0.474651	−0.237325	−	0.971430i	$-0.576271\pi$
$383$	−9.28910	−0.474651	−0.237325	+	0.971430i	$0.576271\pi$
$384$	−16.9721	−0.866103
$385$	3.06648	0.156282
$386$	23.9025	1.21660
$387$	3.44780	0.175261
$388$	15.8479	0.804553
$389$	33.5409	1.70059	0.850296	−	0.526305i	$-0.176423\pi$
$389$	33.5409	1.70059	0.850296	+	0.526305i	$0.176423\pi$
$390$	−19.9888	−1.01217
$391$	−26.8277	−1.35673
$392$	−1.07319	−0.0542042
$393$	14.0647	0.709468
$394$	12.2644	0.617872
$395$	4.26352	0.214521
$396$	8.99025	0.451777
$397$	11.5278	0.578566	0.289283	−	0.957244i	$-0.406583\pi$
$397$	11.5278	0.578566	0.289283	+	0.957244i	$0.406583\pi$
$398$	21.5815	1.08178
$399$	−6.65833	−0.333334
$400$	−2.73319	−0.136660
$401$	26.0596	1.30135	0.650677	−	0.759355i	$-0.274485\pi$
$401$	26.0596	1.30135	0.650677	+	0.759355i	$0.274485\pi$
$402$	−11.7346	−0.585268
$403$	−9.91870	−0.494086
$404$	0.560087	0.0278654
$405$	11.1412	0.553609
$406$	−7.45073	−0.369774
$407$	16.2960	0.807764
$408$	−12.3466	−0.611250
$409$	7.62205	0.376886	0.188443	−	0.982084i	$-0.439656\pi$
$409$	7.62205	0.376886	0.188443	+	0.982084i	$0.439656\pi$
$410$	−19.4069	−0.958437
$411$	18.1868	0.897089
$412$	21.8699	1.07745
$413$	−12.7186	−0.625840
$414$	−11.8271	−0.581273
$415$	−13.3150	−0.653608
$416$	36.6516	1.79699
$417$	−27.0540	−1.32484
$418$	21.2231	1.03806
$419$	1.50873	0.0737061	0.0368531	−	0.999321i	$-0.488267\pi$
$419$	1.50873	0.0737061	0.0368531	+	0.999321i	$0.488267\pi$
$420$	−5.11662	−0.249666
$421$	2.85527	0.139158	0.0695788	−	0.997576i	$-0.477834\pi$
$421$	2.85527	0.139158	0.0695788	+	0.997576i	$0.477834\pi$
$422$	−53.7543	−2.61672
$423$	2.03817	0.0990992
$424$	11.1998	0.543912
$425$	−5.63379	−0.273279
$426$	50.4304	2.44336
$427$	−6.25110	−0.302512
$428$	−30.5899	−1.47862
$429$	−28.8769	−1.39419
$430$	6.25456	0.301622
$431$	−18.7728	−0.904256	−0.452128	−	0.891953i	$-0.649335\pi$
$431$	−18.7728	−0.904256	−0.452128	+	0.891953i	$0.649335\pi$
$432$	−10.2134	−0.491394
$433$	25.3428	1.21790	0.608948	−	0.793210i	$-0.291592\pi$
$433$	25.3428	1.21790	0.608948	+	0.793210i	$0.291592\pi$
$434$	−4.56556	−0.219154
$435$	−7.16797	−0.343678
$436$	−17.0688	−0.817446
$437$	−15.5266	−0.742736
$438$	32.9204	1.57300
$439$	−21.2610	−1.01473	−0.507367	−	0.861730i	$-0.669381\pi$
$439$	−21.2610	−1.01473	−0.507367	+	0.861730i	$0.669381\pi$
$440$	3.29091	0.156888
$441$	1.17010	0.0557188
$442$	55.1459	2.62302
$443$	4.89366	0.232505	0.116252	−	0.993220i	$-0.462912\pi$
$443$	4.89366	0.232505	0.116252	+	0.993220i	$0.462912\pi$
$444$	−27.1910	−1.29043
$445$	3.77914	0.179148
$446$	−31.3697	−1.48540
$447$	18.3544	0.868134
$448$	11.4042	0.538800
$449$	−13.3205	−0.628635	−0.314318	−	0.949318i	$-0.601776\pi$
$449$	−13.3205	−0.628635	−0.314318	+	0.949318i	$0.601776\pi$
$450$	−2.48369	−0.117082
$451$	−28.0363	−1.32018
$452$	28.9776	1.36299
$453$	27.2537	1.28049
$454$	55.2074	2.59101
$455$	4.61144	0.216188
$456$	−7.14564	−0.334625
$457$	39.9404	1.86833	0.934167	−	0.356835i	$-0.116144\pi$
$457$	39.9404	1.86833	0.934167	+	0.356835i	$0.116144\pi$
$458$	−2.12264	−0.0991844
$459$	−21.0524	−0.982642
$460$	−11.9314	−0.556307
$461$	5.78241	0.269314	0.134657	−	0.990892i	$-0.457007\pi$
$461$	5.78241	0.269314	0.134657	+	0.990892i	$0.457007\pi$
$462$	−13.2920	−0.618398
$463$	25.0507	1.16420	0.582102	−	0.813115i	$-0.302230\pi$
$463$	25.0507	1.16420	0.582102	+	0.813115i	$0.302230\pi$
$464$	9.59387	0.445384
$465$	−4.39229	−0.203688
$466$	−5.39989	−0.250145
$467$	18.8812	0.873718	0.436859	−	0.899530i	$-0.356091\pi$
$467$	18.8812	0.873718	0.436859	+	0.899530i	$0.356091\pi$
$468$	13.5197	0.624950
$469$	2.70719	0.125007
$470$	3.69739	0.170548
$471$	−7.46523	−0.343980
$472$	−13.6494	−0.628266
$473$	9.03569	0.415461
$474$	−18.4806	−0.848844
$475$	−3.26056	−0.149605
$476$	14.1160	0.647004
$477$	−12.2112	−0.559111
$478$	55.0576	2.51828
$479$	−5.35204	−0.244541	−0.122271	−	0.992497i	$-0.539018\pi$
$479$	−5.35204	−0.244541	−0.122271	+	0.992497i	$0.539018\pi$
$480$	16.2304	0.740812
$481$	24.5063	1.11739
$482$	−23.1904	−1.05629
$483$	9.72424	0.442468
$484$	−4.00065	−0.181848
$485$	−6.32500	−0.287203
$486$	−24.4968	−1.11120
$487$	−18.9679	−0.859517	−0.429759	−	0.902944i	$-0.641401\pi$
$487$	−18.9679	−0.859517	−0.429759	+	0.902944i	$0.641401\pi$
$488$	−6.70860	−0.303684
$489$	−18.4725	−0.835356
$490$	2.12264	0.0958910
$491$	−26.3558	−1.18942	−0.594710	−	0.803940i	$-0.702733\pi$
$491$	−26.3558	−1.18942	−0.594710	+	0.803940i	$0.702733\pi$
$492$	46.7803	2.10902
$493$	19.7753	0.890636
$494$	31.9158	1.43596
$495$	−3.58808	−0.161272
$496$	5.87880	0.263966
$497$	−11.6344	−0.521874
$498$	57.7152	2.58628
$499$	2.51107	0.112411	0.0562054	−	0.998419i	$-0.482100\pi$
$499$	2.51107	0.112411	0.0562054	+	0.998419i	$0.482100\pi$
$500$	−2.50559	−0.112053
$501$	−34.8495	−1.55696
$502$	23.1286	1.03228
$503$	−14.0204	−0.625138	−0.312569	−	0.949895i	$-0.601190\pi$
$503$	−14.0204	−0.625138	−0.312569	+	0.949895i	$0.601190\pi$
$504$	1.25573	0.0559347
$505$	−0.223535	−0.00994717
$506$	−30.9955	−1.37792
$507$	−16.8787	−0.749607
$508$	−24.6197	−1.09232
$509$	17.3762	0.770189	0.385094	−	0.922877i	$-0.374169\pi$
$509$	17.3762	0.770189	0.385094	+	0.922877i	$0.374169\pi$
$510$	24.4202	1.08134
$511$	−7.59479	−0.335974
$512$	−27.5898	−1.21931
$513$	−12.1841	−0.537942
$514$	−18.1555	−0.800804
$515$	−8.72842	−0.384620
$516$	−15.0766	−0.663711
$517$	5.34146	0.234917
$518$	11.2802	0.495624
$519$	−34.8636	−1.53034
$520$	4.94894	0.217026
$521$	−34.0736	−1.49279	−0.746395	−	0.665503i	$-0.768217\pi$
$521$	−34.0736	−1.49279	−0.746395	+	0.665503i	$0.768217\pi$
$522$	8.71807	0.381580
$523$	23.6750	1.03523	0.517617	−	0.855612i	$-0.326819\pi$
$523$	23.6750	1.03523	0.517617	+	0.855612i	$0.326819\pi$
$524$	−17.2570	−0.753877
$525$	2.04208	0.0891237
$526$	56.9658	2.48383
$527$	12.1176	0.527853
$528$	17.1153	0.744847
$529$	−0.324034	−0.0140885
$530$	−22.1519	−0.962219
$531$	14.8820	0.645822
$532$	8.16964	0.354199
$533$	−42.1615	−1.82622
$534$	−16.3811	−0.708878
$535$	12.2087	0.527827
$536$	2.90532	0.125491
$537$	34.7193	1.49825
$538$	−49.2372	−2.12277
$539$	3.06648	0.132083
$540$	−9.36293	−0.402916
$541$	−0.272589	−0.0117195	−0.00585976	−	0.999983i	$-0.501865\pi$
$541$	−0.272589	−0.0117195	−0.00585976	+	0.999983i	$0.501865\pi$
$542$	35.1300	1.50896
$543$	−7.23661	−0.310553
$544$	−44.7771	−1.91980
$545$	6.81227	0.291806
$546$	−19.9888	−0.855440
$547$	2.18910	0.0935991	0.0467995	−	0.998904i	$-0.485098\pi$
$547$	2.18910	0.0935991	0.0467995	+	0.998904i	$0.485098\pi$
$548$	−22.3148	−0.953242
$549$	7.31438	0.312170
$550$	−6.50903	−0.277546
$551$	11.4450	0.487573
$552$	10.4359	0.444183
$553$	4.26352	0.181303
$554$	−50.1927	−2.13248
$555$	10.8521	0.460647
$556$	33.1947	1.40777
$557$	−10.6716	−0.452169	−0.226085	−	0.974108i	$-0.572593\pi$
$557$	−10.6716	−0.452169	−0.226085	+	0.974108i	$0.572593\pi$
$558$	5.34214	0.226151
$559$	13.5881	0.574714
$560$	−2.73319	−0.115499
$561$	35.2788	1.48947
$562$	23.6377	0.997097
$563$	−42.5192	−1.79197	−0.895986	−	0.444083i	$-0.853529\pi$
$563$	−42.5192	−1.79197	−0.895986	+	0.444083i	$0.853529\pi$
$564$	−8.91256	−0.375286
$565$	−11.5652	−0.486550
$566$	−34.5466	−1.45210
$567$	11.1412	0.467885
$568$	−12.4859	−0.523896
$569$	39.2890	1.64708	0.823541	−	0.567256i	$-0.191995\pi$
$569$	39.2890	1.64708	0.823541	+	0.567256i	$0.191995\pi$
$570$	14.1332	0.591976
$571$	31.3362	1.31138	0.655689	−	0.755031i	$-0.272378\pi$
$571$	31.3362	1.31138	0.655689	+	0.755031i	$0.272378\pi$
$572$	35.4313	1.48146
$573$	51.3599	2.14559
$574$	−19.4069	−0.810027
$575$	4.76193	0.198586
$576$	−13.3441	−0.556002
$577$	9.38736	0.390801	0.195400	−	0.980724i	$-0.437399\pi$
$577$	9.38736	0.390801	0.195400	+	0.980724i	$0.437399\pi$
$578$	−31.2867	−1.30136
$579$	22.9954	0.955654
$580$	8.79495	0.365190
$581$	−13.3150	−0.552400
$582$	27.4163	1.13644
$583$	−32.0019	−1.32538
$584$	−8.15064	−0.337276
$585$	−5.39583	−0.223090
$586$	−44.6618	−1.84496
$587$	−22.9190	−0.945968	−0.472984	−	0.881071i	$-0.656823\pi$
$587$	−22.9190	−0.945968	−0.472984	+	0.881071i	$0.656823\pi$
$588$	−5.11662	−0.211006
$589$	7.01311	0.288970
$590$	26.9969	1.11145
$591$	11.7990	0.485344
$592$	−14.5249	−0.596968
$593$	−7.94890	−0.326422	−0.163211	−	0.986591i	$-0.552185\pi$
$593$	−7.94890	−0.326422	−0.163211	+	0.986591i	$0.552185\pi$
$594$	−24.3230	−0.997986
$595$	−5.63379	−0.230963
$596$	−22.5205	−0.922475
$597$	20.7624	0.849749
$598$	−46.6118	−1.90610
$599$	37.2515	1.52205	0.761027	−	0.648720i	$-0.224695\pi$
$599$	37.2515	1.52205	0.761027	+	0.648720i	$0.224695\pi$
$600$	2.19154	0.0894691
$601$	−7.57068	−0.308814	−0.154407	−	0.988007i	$-0.549347\pi$
$601$	−7.57068	−0.308814	−0.154407	+	0.988007i	$0.549347\pi$
$602$	6.25456	0.254917
$603$	−3.16767	−0.128998
$604$	−33.4397	−1.36064
$605$	1.59669	0.0649146
$606$	0.968934	0.0393602
$607$	−34.3256	−1.39323	−0.696617	−	0.717443i	$-0.745312\pi$
$607$	−34.3256	−1.39323	−0.696617	+	0.717443i	$0.745312\pi$
$608$	−25.9148	−1.05098
$609$	−7.16797	−0.290461
$610$	13.2688	0.537239
$611$	8.03260	0.324964
$612$	−16.5170	−0.667661
$613$	29.1949	1.17917	0.589585	−	0.807707i	$-0.299292\pi$
$613$	29.1949	1.17917	0.589585	+	0.807707i	$0.299292\pi$
$614$	63.1158	2.54715
$615$	−18.6704	−0.752861
$616$	3.29091	0.132595
$617$	−30.7230	−1.23686	−0.618430	−	0.785840i	$-0.712231\pi$
$617$	−30.7230	−1.23686	−0.618430	+	0.785840i	$0.712231\pi$
$618$	37.8342	1.52192
$619$	24.3738	0.979666	0.489833	−	0.871816i	$-0.337058\pi$
$619$	24.3738	0.979666	0.489833	+	0.871816i	$0.337058\pi$
$620$	5.38925	0.216437
$621$	17.7944	0.714066
$622$	−62.8144	−2.51863
$623$	3.77914	0.151408
$624$	25.7383	1.03036
$625$	1.00000	0.0400000
$626$	73.0415	2.91933
$627$	20.4177	0.815403
$628$	9.15968	0.365511
$629$	−29.9393	−1.19376
$630$	−2.48369	−0.0989525
$631$	−1.75619	−0.0699129	−0.0349564	−	0.999389i	$-0.511129\pi$
$631$	−1.75619	−0.0699129	−0.0349564	+	0.999389i	$0.511129\pi$
$632$	4.57556	0.182006
$633$	−51.7143	−2.05546
$634$	3.76607	0.149570
$635$	9.82591	0.389929
$636$	53.3973	2.11734
$637$	4.61144	0.182712
$638$	22.8475	0.904543
$639$	13.6133	0.538536
$640$	−8.31117	−0.328528
$641$	18.8825	0.745816	0.372908	−	0.927868i	$-0.378361\pi$
$641$	18.8825	0.745816	0.372908	+	0.927868i	$0.378361\pi$
$642$	−52.9197	−2.08857
$643$	2.69666	0.106346	0.0531730	−	0.998585i	$-0.483067\pi$
$643$	2.69666	0.106346	0.0531730	+	0.998585i	$0.483067\pi$
$644$	−11.9314	−0.470165
$645$	6.01719	0.236927
$646$	−38.9914	−1.53410
$647$	−10.7195	−0.421426	−0.210713	−	0.977548i	$-0.567579\pi$
$647$	−10.7195	−0.421426	−0.210713	+	0.977548i	$0.567579\pi$
$648$	11.9566	0.469698
$649$	39.0013	1.53093
$650$	−9.78843	−0.383934
$651$	−4.39229	−0.172147
$652$	22.6654	0.887646
$653$	−34.9606	−1.36811	−0.684057	−	0.729429i	$-0.739786\pi$
$653$	−34.9606	−1.36811	−0.684057	+	0.729429i	$0.739786\pi$
$654$	−29.5285	−1.15465
$655$	6.88741	0.269113
$656$	24.9891	0.975659
$657$	8.88663	0.346701
$658$	3.69739	0.144139
$659$	21.1440	0.823653	0.411826	−	0.911262i	$-0.364891\pi$
$659$	21.1440	0.823653	0.411826	+	0.911262i	$0.364891\pi$
$660$	15.6900	0.610733
$661$	18.2657	0.710455	0.355227	−	0.934780i	$-0.384403\pi$
$661$	18.2657	0.710455	0.355227	+	0.934780i	$0.384403\pi$
$662$	51.2066	1.99020
$663$	53.0530	2.06041
$664$	−14.2895	−0.554540
$665$	−3.26056	−0.126439
$666$	−13.1989	−0.511448
$667$	−16.7150	−0.647207
$668$	42.7596	1.65442
$669$	−30.1792	−1.16680
$670$	−5.74639	−0.222002
$671$	19.1689	0.740006
$672$	16.2304	0.626100
$673$	25.0722	0.966464	0.483232	−	0.875492i	$-0.339463\pi$
$673$	25.0722	0.966464	0.483232	+	0.875492i	$0.339463\pi$
$674$	22.2887	0.858528
$675$	3.73681	0.143830
$676$	20.7098	0.796529
$677$	−42.5619	−1.63579	−0.817893	−	0.575371i	$-0.804858\pi$
$677$	−42.5619	−1.63579	−0.817893	+	0.575371i	$0.804858\pi$
$678$	50.1303	1.92524
$679$	−6.32500	−0.242731
$680$	−6.04611	−0.231858
$681$	53.1122	2.03526
$682$	14.0002	0.536095
$683$	−40.4792	−1.54890	−0.774448	−	0.632638i	$-0.781972\pi$
$683$	−40.4792	−1.54890	−0.774448	+	0.632638i	$0.781972\pi$
$684$	−9.55925	−0.365507
$685$	8.90601	0.340281
$686$	2.12264	0.0810427
$687$	−2.04208	−0.0779103
$688$	−8.05362	−0.307042
$689$	−48.1252	−1.83343
$690$	−20.6410	−0.785791
$691$	25.5214	0.970881	0.485440	−	0.874270i	$-0.338659\pi$
$691$	25.5214	0.970881	0.485440	+	0.874270i	$0.338659\pi$
$692$	42.7769	1.62613
$693$	−3.58808	−0.136300
$694$	−5.91305	−0.224456
$695$	−13.2483	−0.502535
$696$	−7.69258	−0.291586
$697$	51.5086	1.95103
$698$	38.3512	1.45162
$699$	−5.19495	−0.196491
$700$	−2.50559	−0.0947025
$701$	36.6153	1.38294	0.691470	−	0.722405i	$-0.256963\pi$
$701$	36.6153	1.38294	0.691470	+	0.722405i	$0.256963\pi$
$702$	−36.5775	−1.38053
$703$	−17.3274	−0.653516
$704$	−34.9709	−1.31802
$705$	3.55707	0.133967
$706$	57.0380	2.14665
$707$	−0.223535	−0.00840689
$708$	−65.0762	−2.44571
$709$	39.2437	1.47383	0.736915	−	0.675986i	$-0.236282\pi$
$709$	39.2437	1.47383	0.736915	+	0.675986i	$0.236282\pi$
$710$	24.6956	0.926809
$711$	−4.98872	−0.187092
$712$	4.05573	0.151995
$713$	−10.2424	−0.383580
$714$	24.4202	0.913903
$715$	−14.1409	−0.528840
$716$	−42.5999	−1.59203
$717$	52.9681	1.97813
$718$	62.1647	2.31997
$719$	1.23151	0.0459274	0.0229637	−	0.999736i	$-0.492690\pi$
$719$	1.23151	0.0459274	0.0229637	+	0.999736i	$0.492690\pi$
$720$	3.19810	0.119186
$721$	−8.72842	−0.325064
$722$	17.7638	0.661100
$723$	−22.3103	−0.829727
$724$	8.87917	0.329992
$725$	−3.51013	−0.130363
$726$	−6.92100	−0.256862
$727$	34.6280	1.28428	0.642140	−	0.766587i	$-0.278047\pi$
$727$	34.6280	1.28428	0.642140	+	0.766587i	$0.278047\pi$
$728$	4.94894	0.183420
$729$	9.85641	0.365052
$730$	16.1210	0.596665
$731$	−16.6005	−0.613992
$732$	−31.9845	−1.18218
$733$	4.30702	0.159083	0.0795416	−	0.996832i	$-0.474654\pi$
$733$	4.30702	0.159083	0.0795416	+	0.996832i	$0.474654\pi$
$734$	−49.1911	−1.81568
$735$	2.04208	0.0753233
$736$	37.8476	1.39508
$737$	−8.30156	−0.305792
$738$	22.7079	0.835889
$739$	−15.0350	−0.553072	−0.276536	−	0.961004i	$-0.589187\pi$
$739$	−15.0350	−0.553072	−0.276536	+	0.961004i	$0.589187\pi$
$740$	−13.3153	−0.489481
$741$	30.7045	1.12796
$742$	−22.1519	−0.813223
$743$	−14.3180	−0.525278	−0.262639	−	0.964894i	$-0.584593\pi$
$743$	−14.3180	−0.525278	−0.262639	+	0.964894i	$0.584593\pi$
$744$	−4.71375	−0.172814
$745$	8.98809	0.329298
$746$	35.5046	1.29992
$747$	15.5798	0.570036
$748$	−43.2864	−1.58271
$749$	12.2087	0.446095
$750$	−4.33460	−0.158277
$751$	44.7372	1.63248	0.816242	−	0.577710i	$-0.196054\pi$
$751$	44.7372	1.63248	0.816242	+	0.577710i	$0.196054\pi$
$752$	−4.76091	−0.173612
$753$	22.2509	0.810866
$754$	34.3586	1.25127
$755$	13.3460	0.485712
$756$	−9.36293	−0.340526
$757$	42.4048	1.54123	0.770614	−	0.637302i	$-0.219950\pi$
$757$	42.4048	1.54123	0.770614	+	0.637302i	$0.219950\pi$
$758$	−62.9178	−2.28528
$759$	−29.8192	−1.08237
$760$	−3.49919	−0.126929
$761$	−5.37407	−0.194810	−0.0974050	−	0.995245i	$-0.531054\pi$
$761$	−5.37407	−0.194810	−0.0974050	+	0.995245i	$0.531054\pi$
$762$	−42.5914	−1.54292
$763$	6.81227	0.246621
$764$	−63.0175	−2.27989
$765$	6.59207	0.238337
$766$	19.7174	0.712418
$767$	58.6510	2.11777
$768$	−10.5512	−0.380734
$769$	45.2364	1.63127	0.815633	−	0.578570i	$-0.196389\pi$
$769$	45.2364	1.63127	0.815633	+	0.578570i	$0.196389\pi$
$770$	−6.50903	−0.234569
$771$	−17.4665	−0.629039
$772$	−28.2148	−1.01547
$773$	42.2415	1.51932	0.759660	−	0.650320i	$-0.225365\pi$
$773$	42.2415	1.51932	0.759660	+	0.650320i	$0.225365\pi$
$774$	−7.31843	−0.263056
$775$	−2.15089	−0.0772622
$776$	−6.78791	−0.243672
$777$	10.8521	0.389317
$778$	−71.1952	−2.55247
$779$	29.8107	1.06808
$780$	23.5950	0.844837
$781$	35.6766	1.27661
$782$	56.9455	2.03637
$783$	−13.1167	−0.468753
$784$	−2.73319	−0.0976141
$785$	−3.65570	−0.130477
$786$	−29.8542	−1.06486
$787$	8.00191	0.285237	0.142619	−	0.989778i	$-0.454448\pi$
$787$	8.00191	0.285237	0.142619	+	0.989778i	$0.454448\pi$
$788$	−14.4771	−0.515724
$789$	54.8039	1.95107
$790$	−9.04991	−0.321981
$791$	−11.5652	−0.411210
$792$	−3.85068	−0.136828
$793$	28.8266	1.02366
$794$	−24.4694	−0.868388
$795$	−21.3112	−0.755832
$796$	−25.4751	−0.902939
$797$	25.2981	0.896105	0.448053	−	0.894007i	$-0.352118\pi$
$797$	25.2981	0.896105	0.448053	+	0.894007i	$0.352118\pi$
$798$	14.1332	0.500311
$799$	−9.81340	−0.347173
$800$	7.94796	0.281003
$801$	−4.42195	−0.156242
$802$	−55.3151	−1.95324
$803$	23.2893	0.821862
$804$	13.8517	0.488511
$805$	4.76193	0.167836
$806$	21.0538	0.741589
$807$	−47.3686	−1.66745
$808$	−0.239895	−0.00843947
$809$	55.1741	1.93982	0.969908	−	0.243470i	$-0.0782858\pi$
$809$	55.1741	1.93982	0.969908	+	0.243470i	$0.0782858\pi$
$810$	−23.6487	−0.830929
$811$	7.02071	0.246531	0.123265	−	0.992374i	$-0.460663\pi$
$811$	7.02071	0.246531	0.123265	+	0.992374i	$0.460663\pi$
$812$	8.79495	0.308642
$813$	33.7968	1.18530
$814$	−34.5906	−1.21240
$815$	−9.04593	−0.316865
$816$	−31.4444	−1.10078
$817$	−9.60756	−0.336126
$818$	−16.1789	−0.565680
$819$	−5.39583	−0.188546
$820$	22.9081	0.799987
$821$	−19.9345	−0.695719	−0.347860	−	0.937547i	$-0.613091\pi$
$821$	−19.9345	−0.695719	−0.347860	+	0.937547i	$0.613091\pi$
$822$	−38.6040	−1.34647
$823$	12.8969	0.449559	0.224780	−	0.974410i	$-0.427834\pi$
$823$	12.8969	0.449559	0.224780	+	0.974410i	$0.427834\pi$
$824$	−9.36724	−0.326323
$825$	−6.26201	−0.218015
$826$	26.9969	0.939344
$827$	17.2107	0.598476	0.299238	−	0.954178i	$-0.403268\pi$
$827$	17.2107	0.598476	0.299238	+	0.954178i	$0.403268\pi$
$828$	13.9609	0.485176
$829$	−16.0537	−0.557569	−0.278785	−	0.960354i	$-0.589932\pi$
$829$	−16.0537	−0.557569	−0.278785	+	0.960354i	$0.589932\pi$
$830$	28.2630	0.981022
$831$	−48.2878	−1.67509
$832$	−52.5900	−1.82323
$833$	−5.63379	−0.195199
$834$	57.4259	1.98850
$835$	−17.0657	−0.590582
$836$	−25.0520	−0.866443
$837$	−8.03747	−0.277816
$838$	−3.20248	−0.110628
$839$	41.4646	1.43152	0.715758	−	0.698348i	$-0.246081\pi$
$839$	41.4646	1.43152	0.715758	+	0.698348i	$0.246081\pi$
$840$	2.19154	0.0756152
$841$	−16.6790	−0.575137
$842$	−6.06071	−0.208866
$843$	22.7406	0.783229
$844$	63.4523	2.18412
$845$	−8.26542	−0.284339
$846$	−4.32630	−0.148741
$847$	1.59669	0.0548628
$848$	28.5237	0.979509
$849$	−33.2355	−1.14064
$850$	11.9585	0.410173
$851$	25.3060	0.867480
$852$	−59.5288	−2.03942
$853$	11.1093	0.380377	0.190188	−	0.981748i	$-0.439090\pi$
$853$	11.1093	0.380377	0.190188	+	0.981748i	$0.439090\pi$
$854$	13.2688	0.454049
$855$	3.81517	0.130476
$856$	13.1022	0.447824
$857$	−21.6269	−0.738760	−0.369380	−	0.929278i	$-0.620430\pi$
$857$	−21.6269	−0.738760	−0.369380	+	0.929278i	$0.620430\pi$
$858$	61.2952	2.09258
$859$	38.1861	1.30289	0.651446	−	0.758695i	$-0.274163\pi$
$859$	38.1861	1.30289	0.651446	+	0.758695i	$0.274163\pi$
$860$	−7.38297	−0.251757
$861$	−18.6704	−0.636284
$862$	39.8479	1.35723
$863$	−55.7673	−1.89834	−0.949171	−	0.314760i	$-0.898076\pi$
$863$	−55.7673	−1.89834	−0.949171	+	0.314760i	$0.898076\pi$
$864$	29.7000	1.01042
$865$	−17.0726	−0.580485
$866$	−53.7935	−1.82798
$867$	−30.0994	−1.02223
$868$	5.38925	0.182923
$869$	−13.0740	−0.443505
$870$	15.2150	0.515837
$871$	−12.4841	−0.423006
$872$	7.31085	0.247576
$873$	7.40085	0.250481
$874$	32.9573	1.11480
$875$	1.00000	0.0338062
$876$	−38.8597	−1.31295
$877$	−8.33568	−0.281476	−0.140738	−	0.990047i	$-0.544948\pi$
$877$	−8.33568	−0.281476	−0.140738	+	0.990047i	$0.544948\pi$
$878$	45.1295	1.52305
$879$	−42.9668	−1.44923
$880$	8.38129	0.282533
$881$	−15.6621	−0.527669	−0.263834	−	0.964568i	$-0.584987\pi$
$881$	−15.6621	−0.527669	−0.263834	+	0.964568i	$0.584987\pi$
$882$	−2.48369	−0.0836301
$883$	12.1951	0.410398	0.205199	−	0.978720i	$-0.434216\pi$
$883$	12.1951	0.410398	0.205199	+	0.978720i	$0.434216\pi$
$884$	−65.0950	−2.18938
$885$	25.9724	0.873052
$886$	−10.3875	−0.348973
$887$	43.0680	1.44608	0.723040	−	0.690806i	$-0.242744\pi$
$887$	43.0680	1.44608	0.723040	+	0.690806i	$0.242744\pi$
$888$	11.6464	0.390826
$889$	9.82591	0.329550
$890$	−8.02175	−0.268890
$891$	−34.1642	−1.14454
$892$	37.0293	1.23983
$893$	−5.67952	−0.190058
$894$	−38.9598	−1.30301
$895$	17.0019	0.568312
$896$	−8.31117	−0.277657
$897$	−44.8428	−1.49726
$898$	28.2747	0.943539
$899$	7.54990	0.251803
$900$	2.93178	0.0977260
$901$	58.7944	1.95873
$902$	59.5108	1.98149
$903$	6.01719	0.200240
$904$	−12.4116	−0.412803
$905$	−3.54374	−0.117798
$906$	−57.8497	−1.92193
$907$	51.2419	1.70146	0.850729	−	0.525604i	$-0.176161\pi$
$907$	51.2419	1.70146	0.850729	+	0.525604i	$0.176161\pi$
$908$	−65.1675	−2.16266
$909$	0.261557	0.00867530
$910$	−9.78843	−0.324483
$911$	−8.94013	−0.296200	−0.148100	−	0.988972i	$-0.547316\pi$
$911$	−8.94013	−0.296200	−0.148100	+	0.988972i	$0.547316\pi$
$912$	−18.1985	−0.602613
$913$	40.8303	1.35128
$914$	−84.7791	−2.80424
$915$	12.7652	0.422006
$916$	2.50559	0.0827871
$917$	6.88741	0.227442
$918$	44.6866	1.47488
$919$	22.2120	0.732707	0.366354	−	0.930476i	$-0.380606\pi$
$919$	22.2120	0.732707	0.366354	+	0.930476i	$0.380606\pi$
$920$	5.11044	0.168486
$921$	60.7205	2.00081
$922$	−12.2740	−0.404221
$923$	53.6513	1.76596
$924$	15.6900	0.516164
$925$	5.31424	0.174731
$926$	−53.1736	−1.74739
$927$	10.2131	0.335442
$928$	−27.8984	−0.915809
$929$	15.5265	0.509408	0.254704	−	0.967019i	$-0.418022\pi$
$929$	15.5265	0.509408	0.254704	+	0.967019i	$0.418022\pi$
$930$	9.32324	0.305721
$931$	−3.26056	−0.106861
$932$	6.37410	0.208791
$933$	−60.4305	−1.97841
$934$	−40.0780	−1.31139
$935$	17.2759	0.564983
$936$	−5.79074	−0.189276
$937$	7.01098	0.229039	0.114519	−	0.993421i	$-0.463467\pi$
$937$	7.01098	0.229039	0.114519	+	0.993421i	$0.463467\pi$
$938$	−5.74639	−0.187626
$939$	70.2695	2.29316
$940$	−4.36445	−0.142353
$941$	26.1510	0.852499	0.426250	−	0.904606i	$-0.359835\pi$
$941$	26.1510	0.852499	0.426250	+	0.904606i	$0.359835\pi$
$942$	15.8460	0.516290
$943$	−43.5374	−1.41777
$944$	−34.7624	−1.13142
$945$	3.73681	0.121559
$946$	−19.1795	−0.623579
$947$	39.6232	1.28758	0.643791	−	0.765202i	$-0.277361\pi$
$947$	39.6232	1.28758	0.643791	+	0.765202i	$0.277361\pi$
$948$	21.8148	0.708512
$949$	35.0230	1.13689
$950$	6.92099	0.224547
$951$	3.62314	0.117488
$952$	−6.04611	−0.195956
$953$	42.3360	1.37140	0.685699	−	0.727886i	$-0.259497\pi$
$953$	42.3360	1.37140	0.685699	+	0.727886i	$0.259497\pi$
$954$	25.9199	0.839187
$955$	25.1507	0.813859
$956$	−64.9908	−2.10195
$957$	21.9805	0.710527
$958$	11.3605	0.367040
$959$	8.90601	0.287590
$960$	−23.2884	−0.751630
$961$	−26.3737	−0.850764
$962$	−52.0181	−1.67713
$963$	−14.2853	−0.460337
$964$	27.3742	0.881664
$965$	11.2607	0.362496
$966$	−20.6410	−0.664115
$967$	−23.7374	−0.763342	−0.381671	−	0.924298i	$-0.624651\pi$
$967$	−23.7374	−0.763342	−0.381671	+	0.924298i	$0.624651\pi$
$968$	1.71354	0.0550754
$969$	−37.5116	−1.20505
$970$	13.4257	0.431073
$971$	−15.0226	−0.482097	−0.241049	−	0.970513i	$-0.577491\pi$
$971$	−15.0226	−0.482097	−0.241049	+	0.970513i	$0.577491\pi$
$972$	28.9163	0.927491
$973$	−13.2483	−0.424720
$974$	40.2620	1.29008
$975$	−9.41694	−0.301584
$976$	−17.0855	−0.546892
$977$	10.2097	0.326637	0.163319	−	0.986573i	$-0.447780\pi$
$977$	10.2097	0.326637	0.163319	+	0.986573i	$0.447780\pi$
$978$	39.2105	1.25381
$979$	−11.5887	−0.370375
$980$	−2.50559	−0.0800382
$981$	−7.97101	−0.254495
$982$	55.9438	1.78524
$983$	9.38284	0.299266	0.149633	−	0.988742i	$-0.452191\pi$
$983$	9.38284	0.299266	0.149633	+	0.988742i	$0.452191\pi$
$984$	−20.0368	−0.638749
$985$	5.77791	0.184099
$986$	−41.9758	−1.33678
$987$	3.55707	0.113223
$988$	−37.6738	−1.19856
$989$	14.0315	0.446175
$990$	7.61619	0.242058
$991$	2.18631	0.0694503	0.0347251	−	0.999397i	$-0.488944\pi$
$991$	2.18631	0.0694503	0.0347251	+	0.999397i	$0.488944\pi$
$992$	−17.0952	−0.542772
$993$	49.2633	1.56332
$994$	24.6956	0.783297
$995$	10.1673	0.322324
$996$	−68.1279	−2.15871
$997$	58.6579	1.85772	0.928858	−	0.370436i	$-0.120792\pi$
$997$	58.6579	1.85772	0.928858	+	0.370436i	$0.120792\pi$
$998$	−5.33008	−0.168721
$999$	19.8583	0.628290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.11	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.12264 q^{2} -2.04208 q^{3} +2.50559 q^{4} -1.00000 q^{5} +4.33460 q^{6} -1.00000 q^{7} -1.07319 q^{8} +1.17010 q^{9} +O(q^{10})\)	\(q-2.12264 q^{2} -2.04208 q^{3} +2.50559 q^{4} -1.00000 q^{5} +4.33460 q^{6} -1.00000 q^{7} -1.07319 q^{8} +1.17010 q^{9} +2.12264 q^{10} +3.06648 q^{11} -5.11662 q^{12} +4.61144 q^{13} +2.12264 q^{14} +2.04208 q^{15} -2.73319 q^{16} -5.63379 q^{17} -2.48369 q^{18} -3.26056 q^{19} -2.50559 q^{20} +2.04208 q^{21} -6.50903 q^{22} +4.76193 q^{23} +2.19154 q^{24} +1.00000 q^{25} -9.78843 q^{26} +3.73681 q^{27} -2.50559 q^{28} -3.51013 q^{29} -4.33460 q^{30} -2.15089 q^{31} +7.94796 q^{32} -6.26201 q^{33} +11.9585 q^{34} +1.00000 q^{35} +2.93178 q^{36} +5.31424 q^{37} +6.92099 q^{38} -9.41694 q^{39} +1.07319 q^{40} -9.14281 q^{41} -4.33460 q^{42} +2.94660 q^{43} +7.68335 q^{44} -1.17010 q^{45} -10.1079 q^{46} +1.74188 q^{47} +5.58140 q^{48} +1.00000 q^{49} -2.12264 q^{50} +11.5046 q^{51} +11.5544 q^{52} -10.4360 q^{53} -7.93190 q^{54} -3.06648 q^{55} +1.07319 q^{56} +6.65833 q^{57} +7.45073 q^{58} +12.7186 q^{59} +5.11662 q^{60} +6.25110 q^{61} +4.56556 q^{62} -1.17010 q^{63} -11.4042 q^{64} -4.61144 q^{65} +13.2920 q^{66} -2.70719 q^{67} -14.1160 q^{68} -9.72424 q^{69} -2.12264 q^{70} +11.6344 q^{71} -1.25573 q^{72} +7.59479 q^{73} -11.2802 q^{74} -2.04208 q^{75} -8.16964 q^{76} -3.06648 q^{77} +19.9888 q^{78} -4.26352 q^{79} +2.73319 q^{80} -11.1412 q^{81} +19.4069 q^{82} +13.3150 q^{83} +5.11662 q^{84} +5.63379 q^{85} -6.25456 q^{86} +7.16797 q^{87} -3.29091 q^{88} -3.77914 q^{89} +2.48369 q^{90} -4.61144 q^{91} +11.9314 q^{92} +4.39229 q^{93} -3.69739 q^{94} +3.26056 q^{95} -16.2304 q^{96} +6.32500 q^{97} -2.12264 q^{98} +3.58808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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