LMFDB - Embedded newform 8013.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08790 q^{2} +1.00000 q^{3} +2.35934 q^{4} +0.999516 q^{5} -2.08790 q^{6} -2.01365 q^{7} -0.750272 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.08790 q^{2} +1.00000 q^{3} +2.35934 q^{4} +0.999516 q^{5} -2.08790 q^{6} -2.01365 q^{7} -0.750272 q^{8} +1.00000 q^{9} -2.08689 q^{10} -2.08706 q^{11} +2.35934 q^{12} -3.80897 q^{13} +4.20430 q^{14} +0.999516 q^{15} -3.15219 q^{16} -1.14562 q^{17} -2.08790 q^{18} -7.01905 q^{19} +2.35820 q^{20} -2.01365 q^{21} +4.35759 q^{22} +5.35009 q^{23} -0.750272 q^{24} -4.00097 q^{25} +7.95276 q^{26} +1.00000 q^{27} -4.75089 q^{28} +1.71873 q^{29} -2.08689 q^{30} +2.60484 q^{31} +8.08201 q^{32} -2.08706 q^{33} +2.39194 q^{34} -2.01267 q^{35} +2.35934 q^{36} -0.899584 q^{37} +14.6551 q^{38} -3.80897 q^{39} -0.749909 q^{40} +11.4481 q^{41} +4.20430 q^{42} -3.59734 q^{43} -4.92410 q^{44} +0.999516 q^{45} -11.1705 q^{46} -5.79377 q^{47} -3.15219 q^{48} -2.94522 q^{49} +8.35364 q^{50} -1.14562 q^{51} -8.98666 q^{52} -13.1743 q^{53} -2.08790 q^{54} -2.08605 q^{55} +1.51078 q^{56} -7.01905 q^{57} -3.58854 q^{58} -6.79416 q^{59} +2.35820 q^{60} +11.5720 q^{61} -5.43867 q^{62} -2.01365 q^{63} -10.5701 q^{64} -3.80712 q^{65} +4.35759 q^{66} +14.2860 q^{67} -2.70291 q^{68} +5.35009 q^{69} +4.20227 q^{70} -15.1350 q^{71} -0.750272 q^{72} -1.41883 q^{73} +1.87824 q^{74} -4.00097 q^{75} -16.5603 q^{76} +4.20261 q^{77} +7.95276 q^{78} +0.661519 q^{79} -3.15066 q^{80} +1.00000 q^{81} -23.9025 q^{82} -5.04774 q^{83} -4.75089 q^{84} -1.14506 q^{85} +7.51089 q^{86} +1.71873 q^{87} +1.56587 q^{88} +17.6190 q^{89} -2.08689 q^{90} +7.66992 q^{91} +12.6227 q^{92} +2.60484 q^{93} +12.0968 q^{94} -7.01565 q^{95} +8.08201 q^{96} -12.5482 q^{97} +6.14934 q^{98} -2.08706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * 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 $

$2$	−2.08790	−1.47637	−0.738185	−	0.674598i	$-0.764317\pi$
$2$	−2.08790	−1.47637	−0.738185	+	0.674598i	$0.764317\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.35934	1.17967
$5$	0.999516	0.446997	0.223498	−	0.974704i	$-0.428252\pi$
$5$	0.999516	0.446997	0.223498	+	0.974704i	$0.428252\pi$
$6$	−2.08790	−0.852383
$7$	−2.01365	−0.761087	−0.380544	−	0.924763i	$-0.624263\pi$
$7$	−2.01365	−0.761087	−0.380544	+	0.924763i	$0.624263\pi$
$8$	−0.750272	−0.265261
$9$	1.00000	0.333333
$10$	−2.08689	−0.659933
$11$	−2.08706	−0.629273	−0.314637	−	0.949212i	$-0.601883\pi$
$11$	−2.08706	−0.629273	−0.314637	+	0.949212i	$0.601883\pi$
$12$	2.35934	0.681083
$13$	−3.80897	−1.05642	−0.528209	−	0.849115i	$-0.677136\pi$
$13$	−3.80897	−1.05642	−0.528209	+	0.849115i	$0.677136\pi$
$14$	4.20430	1.12365
$15$	0.999516	0.258074
$16$	−3.15219	−0.788047
$17$	−1.14562	−0.277854	−0.138927	−	0.990303i	$-0.544365\pi$
$17$	−1.14562	−0.277854	−0.138927	+	0.990303i	$0.544365\pi$
$18$	−2.08790	−0.492124
$19$	−7.01905	−1.61028	−0.805141	−	0.593084i	$-0.797910\pi$
$19$	−7.01905	−1.61028	−0.805141	+	0.593084i	$0.797910\pi$
$20$	2.35820	0.527309
$21$	−2.01365	−0.439414
$22$	4.35759	0.929041
$23$	5.35009	1.11557	0.557785	−	0.829985i	$-0.311651\pi$
$23$	5.35009	1.11557	0.557785	+	0.829985i	$0.311651\pi$
$24$	−0.750272	−0.153149
$25$	−4.00097	−0.800194
$26$	7.95276	1.55966
$27$	1.00000	0.192450
$28$	−4.75089	−0.897833
$29$	1.71873	0.319160	0.159580	−	0.987185i	$-0.448986\pi$
$29$	1.71873	0.319160	0.159580	+	0.987185i	$0.448986\pi$
$30$	−2.08689	−0.381013
$31$	2.60484	0.467844	0.233922	−	0.972255i	$-0.424844\pi$
$31$	2.60484	0.467844	0.233922	+	0.972255i	$0.424844\pi$
$32$	8.08201	1.42871
$33$	−2.08706	−0.363311
$34$	2.39194	0.410215
$35$	−2.01267	−0.340204
$36$	2.35934	0.393224
$37$	−0.899584	−0.147891	−0.0739453	−	0.997262i	$-0.523559\pi$
$37$	−0.899584	−0.147891	−0.0739453	+	0.997262i	$0.523559\pi$
$38$	14.6551	2.37737
$39$	−3.80897	−0.609923
$40$	−0.749909	−0.118571
$41$	11.4481	1.78789	0.893945	−	0.448177i	$-0.147926\pi$
$41$	11.4481	1.78789	0.893945	+	0.448177i	$0.147926\pi$
$42$	4.20430	0.648738
$43$	−3.59734	−0.548589	−0.274294	−	0.961646i	$-0.588444\pi$
$43$	−3.59734	−0.548589	−0.274294	+	0.961646i	$0.588444\pi$
$44$	−4.92410	−0.742336
$45$	0.999516	0.148999
$46$	−11.1705	−1.64700
$47$	−5.79377	−0.845108	−0.422554	−	0.906338i	$-0.638866\pi$
$47$	−5.79377	−0.845108	−0.422554	+	0.906338i	$0.638866\pi$
$48$	−3.15219	−0.454979
$49$	−2.94522	−0.420746
$50$	8.35364	1.18138
$51$	−1.14562	−0.160419
$52$	−8.98666	−1.24623
$53$	−13.1743	−1.80963	−0.904815	−	0.425804i	$-0.859991\pi$
$53$	−13.1743	−1.80963	−0.904815	+	0.425804i	$0.859991\pi$
$54$	−2.08790	−0.284128
$55$	−2.08605	−0.281283
$56$	1.51078	0.201887
$57$	−7.01905	−0.929696
$58$	−3.58854	−0.471198
$59$	−6.79416	−0.884524	−0.442262	−	0.896886i	$-0.645824\pi$
$59$	−6.79416	−0.884524	−0.442262	+	0.896886i	$0.645824\pi$
$60$	2.35820	0.304442
$61$	11.5720	1.48164	0.740822	−	0.671701i	$-0.234436\pi$
$61$	11.5720	1.48164	0.740822	+	0.671701i	$0.234436\pi$
$62$	−5.43867	−0.690711
$63$	−2.01365	−0.253696
$64$	−10.5701	−1.32126
$65$	−3.80712	−0.472215
$66$	4.35759	0.536382
$67$	14.2860	1.74531	0.872657	−	0.488334i	$-0.162395\pi$
$67$	14.2860	1.74531	0.872657	+	0.488334i	$0.162395\pi$
$68$	−2.70291	−0.327776
$69$	5.35009	0.644075
$70$	4.20227	0.502267
$71$	−15.1350	−1.79620	−0.898098	−	0.439796i	$-0.855051\pi$
$71$	−15.1350	−1.79620	−0.898098	+	0.439796i	$0.855051\pi$
$72$	−0.750272	−0.0884204
$73$	−1.41883	−0.166062	−0.0830309	−	0.996547i	$-0.526460\pi$
$73$	−1.41883	−0.166062	−0.0830309	+	0.996547i	$0.526460\pi$
$74$	1.87824	0.218341
$75$	−4.00097	−0.461992
$76$	−16.5603	−1.89960
$77$	4.20261	0.478932
$78$	7.95276	0.900472
$79$	0.661519	0.0744267	0.0372133	−	0.999307i	$-0.488152\pi$
$79$	0.661519	0.0744267	0.0372133	+	0.999307i	$0.488152\pi$
$80$	−3.15066	−0.352255
$81$	1.00000	0.111111
$82$	−23.9025	−2.63959
$83$	−5.04774	−0.554062	−0.277031	−	0.960861i	$-0.589350\pi$
$83$	−5.04774	−0.554062	−0.277031	+	0.960861i	$0.589350\pi$
$84$	−4.75089	−0.518364
$85$	−1.14506	−0.124200
$86$	7.51089	0.809920
$87$	1.71873	0.184267
$88$	1.56587	0.166922
$89$	17.6190	1.86761	0.933805	−	0.357782i	$-0.116467\pi$
$89$	17.6190	1.86761	0.933805	+	0.357782i	$0.116467\pi$
$90$	−2.08689	−0.219978
$91$	7.66992	0.804026
$92$	12.6227	1.31601
$93$	2.60484	0.270110
$94$	12.0968	1.24769
$95$	−7.01565	−0.719791
$96$	8.08201	0.824867
$97$	−12.5482	−1.27408	−0.637041	−	0.770830i	$-0.719842\pi$
$97$	−12.5482	−1.27408	−0.637041	+	0.770830i	$0.719842\pi$
$98$	6.14934	0.621177
$99$	−2.08706	−0.209758
$100$	−9.43965	−0.943965
$101$	−15.9567	−1.58776	−0.793878	−	0.608077i	$-0.791941\pi$
$101$	−15.9567	−1.58776	−0.793878	+	0.608077i	$0.791941\pi$
$102$	2.39194	0.236838
$103$	15.4800	1.52529	0.762643	−	0.646820i	$-0.223902\pi$
$103$	15.4800	1.52529	0.762643	+	0.646820i	$0.223902\pi$
$104$	2.85776	0.280227
$105$	−2.01267	−0.196417
$106$	27.5067	2.67169
$107$	10.2250	0.988491	0.494246	−	0.869322i	$-0.335444\pi$
$107$	10.2250	0.988491	0.494246	+	0.869322i	$0.335444\pi$
$108$	2.35934	0.227028
$109$	11.2361	1.07622	0.538111	−	0.842874i	$-0.319138\pi$
$109$	11.2361	1.07622	0.538111	+	0.842874i	$0.319138\pi$
$110$	4.35548	0.415278
$111$	−0.899584	−0.0853847
$112$	6.34740	0.599773
$113$	3.75603	0.353337	0.176669	−	0.984270i	$-0.443468\pi$
$113$	3.75603	0.353337	0.176669	+	0.984270i	$0.443468\pi$
$114$	14.6551	1.37258
$115$	5.34750	0.498657
$116$	4.05507	0.376503
$117$	−3.80897	−0.352139
$118$	14.1855	1.30589
$119$	2.30688	0.211471
$120$	−0.749909	−0.0684570
$121$	−6.64416	−0.604015
$122$	−24.1613	−2.18746
$123$	11.4481	1.03224
$124$	6.14572	0.551902
$125$	−8.99661	−0.804681
$126$	4.20430	0.374549
$127$	12.1830	1.08107	0.540533	−	0.841323i	$-0.318223\pi$
$127$	12.1830	1.08107	0.540533	+	0.841323i	$0.318223\pi$
$128$	5.90530	0.521959
$129$	−3.59734	−0.316728
$130$	7.94890	0.697165
$131$	−0.278300	−0.0243152	−0.0121576	−	0.999926i	$-0.503870\pi$
$131$	−0.278300	−0.0243152	−0.0121576	+	0.999926i	$0.503870\pi$
$132$	−4.92410	−0.428588
$133$	14.1339	1.22556
$134$	−29.8278	−2.57673
$135$	0.999516	0.0860246
$136$	0.859527	0.0737038
$137$	6.98356	0.596645	0.298323	−	0.954465i	$-0.403573\pi$
$137$	6.98356	0.596645	0.298323	+	0.954465i	$0.403573\pi$
$138$	−11.1705	−0.950894
$139$	20.5088	1.73953	0.869767	−	0.493463i	$-0.164269\pi$
$139$	20.5088	1.73953	0.869767	+	0.493463i	$0.164269\pi$
$140$	−4.74858	−0.401329
$141$	−5.79377	−0.487923
$142$	31.6004	2.65185
$143$	7.94956	0.664775
$144$	−3.15219	−0.262682
$145$	1.71789	0.142663
$146$	2.96239	0.245169
$147$	−2.94522	−0.242918
$148$	−2.12243	−0.174462
$149$	−13.9341	−1.14153	−0.570764	−	0.821114i	$-0.693353\pi$
$149$	−13.9341	−1.14153	−0.570764	+	0.821114i	$0.693353\pi$
$150$	8.35364	0.682072
$151$	3.09314	0.251716	0.125858	−	0.992048i	$-0.459832\pi$
$151$	3.09314	0.251716	0.125858	+	0.992048i	$0.459832\pi$
$152$	5.26620	0.427145
$153$	−1.14562	−0.0926179
$154$	−8.77465	−0.707081
$155$	2.60358	0.209125
$156$	−8.98666	−0.719508
$157$	5.43945	0.434115	0.217058	−	0.976159i	$-0.430354\pi$
$157$	5.43945	0.434115	0.217058	+	0.976159i	$0.430354\pi$
$158$	−1.38119	−0.109881
$159$	−13.1743	−1.04479
$160$	8.07810	0.638629
$161$	−10.7732	−0.849047
$162$	−2.08790	−0.164041
$163$	−5.02474	−0.393568	−0.196784	−	0.980447i	$-0.563050\pi$
$163$	−5.02474	−0.393568	−0.196784	+	0.980447i	$0.563050\pi$
$164$	27.0099	2.10912
$165$	−2.08605	−0.162399
$166$	10.5392	0.818001
$167$	0.462761	0.0358096	0.0179048	−	0.999840i	$-0.494300\pi$
$167$	0.462761	0.0358096	0.0179048	+	0.999840i	$0.494300\pi$
$168$	1.51078	0.116560
$169$	1.50823	0.116018
$170$	2.39079	0.183365
$171$	−7.01905	−0.536760
$172$	−8.48735	−0.647154
$173$	14.9951	1.14005	0.570027	−	0.821626i	$-0.306933\pi$
$173$	14.9951	1.14005	0.570027	+	0.821626i	$0.306933\pi$
$174$	−3.58854	−0.272046
$175$	8.05654	0.609017
$176$	6.57882	0.495897
$177$	−6.79416	−0.510680
$178$	−36.7868	−2.75729
$179$	2.25917	0.168858	0.0844290	−	0.996429i	$-0.473093\pi$
$179$	2.25917	0.168858	0.0844290	+	0.996429i	$0.473093\pi$
$180$	2.35820	0.175770
$181$	−15.1992	−1.12975	−0.564876	−	0.825176i	$-0.691076\pi$
$181$	−15.1992	−1.12975	−0.564876	+	0.825176i	$0.691076\pi$
$182$	−16.0141	−1.18704
$183$	11.5720	0.855428
$184$	−4.01402	−0.295918
$185$	−0.899148	−0.0661067
$186$	−5.43867	−0.398782
$187$	2.39098	0.174846
$188$	−13.6695	−0.996949
$189$	−2.01365	−0.146471
$190$	14.6480	1.06268
$191$	7.02323	0.508183	0.254092	−	0.967180i	$-0.418223\pi$
$191$	7.02323	0.508183	0.254092	+	0.967180i	$0.418223\pi$
$192$	−10.5701	−0.762830
$193$	3.31169	0.238380	0.119190	−	0.992871i	$-0.461970\pi$
$193$	3.31169	0.238380	0.119190	+	0.992871i	$0.461970\pi$
$194$	26.1995	1.88102
$195$	−3.80712	−0.272634
$196$	−6.94879	−0.496342
$197$	16.4857	1.17455	0.587277	−	0.809386i	$-0.300200\pi$
$197$	16.4857	1.17455	0.587277	+	0.809386i	$0.300200\pi$
$198$	4.35759	0.309680
$199$	−6.61629	−0.469016	−0.234508	−	0.972114i	$-0.575348\pi$
$199$	−6.61629	−0.469016	−0.234508	+	0.972114i	$0.575348\pi$
$200$	3.00182	0.212260
$201$	14.2860	1.00766
$202$	33.3161	2.34412
$203$	−3.46091	−0.242908
$204$	−2.70291	−0.189242
$205$	11.4425	0.799181
$206$	−32.3207	−2.25189
$207$	5.35009	0.371857
$208$	12.0066	0.832507
$209$	14.6492	1.01331
$210$	4.20227	0.289984
$211$	−15.1031	−1.03974	−0.519869	−	0.854246i	$-0.674019\pi$
$211$	−15.1031	−1.03974	−0.519869	+	0.854246i	$0.674019\pi$
$212$	−31.0827	−2.13477
$213$	−15.1350	−1.03703
$214$	−21.3489	−1.45938
$215$	−3.59559	−0.245217
$216$	−0.750272	−0.0510496
$217$	−5.24524	−0.356070
$218$	−23.4599	−1.58890
$219$	−1.41883	−0.0958759
$220$	−4.92171	−0.331822
$221$	4.36363	0.293529
$222$	1.87824	0.126059
$223$	18.0409	1.20811	0.604054	−	0.796944i	$-0.293551\pi$
$223$	18.0409	1.20811	0.604054	+	0.796944i	$0.293551\pi$
$224$	−16.2743	−1.08737
$225$	−4.00097	−0.266731
$226$	−7.84222	−0.521657
$227$	18.9997	1.26106	0.630528	−	0.776167i	$-0.282838\pi$
$227$	18.9997	1.26106	0.630528	+	0.776167i	$0.282838\pi$
$228$	−16.5603	−1.09674
$229$	15.8562	1.04781	0.523903	−	0.851778i	$-0.324475\pi$
$229$	15.8562	1.04781	0.523903	+	0.851778i	$0.324475\pi$
$230$	−11.1651	−0.736202
$231$	4.20261	0.276512
$232$	−1.28951	−0.0846607
$233$	−7.80994	−0.511646	−0.255823	−	0.966724i	$-0.582346\pi$
$233$	−7.80994	−0.511646	−0.255823	+	0.966724i	$0.582346\pi$
$234$	7.95276	0.519888
$235$	−5.79096	−0.377761
$236$	−16.0297	−1.04345
$237$	0.661519	0.0429703
$238$	−4.81653	−0.312210
$239$	27.7193	1.79301	0.896505	−	0.443033i	$-0.146097\pi$
$239$	27.7193	1.79301	0.896505	+	0.443033i	$0.146097\pi$
$240$	−3.15066	−0.203374
$241$	24.9905	1.60978	0.804890	−	0.593424i	$-0.202224\pi$
$241$	24.9905	1.60978	0.804890	+	0.593424i	$0.202224\pi$
$242$	13.8724	0.891750
$243$	1.00000	0.0641500
$244$	27.3023	1.74785
$245$	−2.94379	−0.188072
$246$	−23.9025	−1.52397
$247$	26.7353	1.70113
$248$	−1.95434	−0.124101
$249$	−5.04774	−0.319888
$250$	18.7841	1.18801
$251$	−13.9240	−0.878874	−0.439437	−	0.898273i	$-0.644822\pi$
$251$	−13.9240	−0.878874	−0.439437	+	0.898273i	$0.644822\pi$
$252$	−4.75089	−0.299278
$253$	−11.1660	−0.701999
$254$	−25.4369	−1.59605
$255$	−1.14506	−0.0717068
$256$	8.81048	0.550655
$257$	−5.18862	−0.323657	−0.161829	−	0.986819i	$-0.551739\pi$
$257$	−5.18862	−0.323657	−0.161829	+	0.986819i	$0.551739\pi$
$258$	7.51089	0.467608
$259$	1.81144	0.112558
$260$	−8.98230	−0.557059
$261$	1.71873	0.106387
$262$	0.581064	0.0358982
$263$	−12.1369	−0.748394	−0.374197	−	0.927349i	$-0.622082\pi$
$263$	−12.1369	−0.748394	−0.374197	+	0.927349i	$0.622082\pi$
$264$	1.56587	0.0963724
$265$	−13.1679	−0.808899
$266$	−29.5102	−1.80939
$267$	17.6190	1.07827
$268$	33.7056	2.05890
$269$	6.67485	0.406973	0.203486	−	0.979078i	$-0.434773\pi$
$269$	6.67485	0.406973	0.203486	+	0.979078i	$0.434773\pi$
$270$	−2.08689	−0.127004
$271$	4.79175	0.291078	0.145539	−	0.989353i	$-0.453508\pi$
$271$	4.79175	0.291078	0.145539	+	0.989353i	$0.453508\pi$
$272$	3.61121	0.218962
$273$	7.66992	0.464205
$274$	−14.5810	−0.880870
$275$	8.35028	0.503541
$276$	12.6227	0.759797
$277$	6.84461	0.411253	0.205626	−	0.978631i	$-0.434077\pi$
$277$	6.84461	0.411253	0.205626	+	0.978631i	$0.434077\pi$
$278$	−42.8204	−2.56820
$279$	2.60484	0.155948
$280$	1.51005	0.0902429
$281$	−6.53725	−0.389980	−0.194990	−	0.980805i	$-0.562467\pi$
$281$	−6.53725	−0.389980	−0.194990	+	0.980805i	$0.562467\pi$
$282$	12.0968	0.720356
$283$	28.2024	1.67646	0.838230	−	0.545317i	$-0.183591\pi$
$283$	28.2024	1.67646	0.838230	+	0.545317i	$0.183591\pi$
$284$	−35.7087	−2.11892
$285$	−7.01565	−0.415571
$286$	−16.5979	−0.981455
$287$	−23.0524	−1.36074
$288$	8.08201	0.476237
$289$	−15.6876	−0.922797
$290$	−3.58680	−0.210624
$291$	−12.5482	−0.735591
$292$	−3.34751	−0.195898
$293$	−5.75477	−0.336198	−0.168099	−	0.985770i	$-0.553763\pi$
$293$	−5.75477	−0.336198	−0.168099	+	0.985770i	$0.553763\pi$
$294$	6.14934	0.358637
$295$	−6.79086	−0.395379
$296$	0.674933	0.0392297
$297$	−2.08706	−0.121104
$298$	29.0931	1.68532
$299$	−20.3783	−1.17851
$300$	−9.43965	−0.544999
$301$	7.24377	0.417524
$302$	−6.45817	−0.371626
$303$	−15.9567	−0.916691
$304$	22.1254	1.26898
$305$	11.5664	0.662291
$306$	2.39194	0.136738
$307$	−8.30892	−0.474215	−0.237108	−	0.971483i	$-0.576199\pi$
$307$	−8.30892	−0.474215	−0.237108	+	0.971483i	$0.576199\pi$
$308$	9.91540	0.564982
$309$	15.4800	0.880624
$310$	−5.43603	−0.308746
$311$	7.60851	0.431439	0.215720	−	0.976455i	$-0.430790\pi$
$311$	7.60851	0.431439	0.215720	+	0.976455i	$0.430790\pi$
$312$	2.85776	0.161789
$313$	−31.5023	−1.78062	−0.890308	−	0.455359i	$-0.849511\pi$
$313$	−31.5023	−1.78062	−0.890308	+	0.455359i	$0.849511\pi$
$314$	−11.3570	−0.640915
$315$	−2.01267	−0.113401
$316$	1.56075	0.0877990
$317$	9.66632	0.542915	0.271457	−	0.962450i	$-0.412494\pi$
$317$	9.66632	0.542915	0.271457	+	0.962450i	$0.412494\pi$
$318$	27.5067	1.54250
$319$	−3.58709	−0.200839
$320$	−10.5650	−0.590599
$321$	10.2250	0.570706
$322$	22.4934	1.25351
$323$	8.04117	0.447423
$324$	2.35934	0.131075
$325$	15.2396	0.845339
$326$	10.4912	0.581052
$327$	11.2361	0.621357
$328$	−8.58918	−0.474258
$329$	11.6666	0.643201
$330$	4.35548	0.239761
$331$	22.2653	1.22381	0.611906	−	0.790930i	$-0.290403\pi$
$331$	22.2653	1.22381	0.611906	+	0.790930i	$0.290403\pi$
$332$	−11.9094	−0.653611
$333$	−0.899584	−0.0492969
$334$	−0.966201	−0.0528682
$335$	14.2791	0.780150
$336$	6.34740	0.346279
$337$	−1.70613	−0.0929387	−0.0464694	−	0.998920i	$-0.514797\pi$
$337$	−1.70613	−0.0929387	−0.0464694	+	0.998920i	$0.514797\pi$
$338$	−3.14903	−0.171285
$339$	3.75603	0.203999
$340$	−2.70160	−0.146515
$341$	−5.43648	−0.294402
$342$	14.6551	0.792457
$343$	20.0262	1.08131
$344$	2.69898	0.145519
$345$	5.34750	0.287900
$346$	−31.3083	−1.68314
$347$	19.4312	1.04312	0.521559	−	0.853215i	$-0.325350\pi$
$347$	19.4312	1.04312	0.521559	+	0.853215i	$0.325350\pi$
$348$	4.05507	0.217374
$349$	−23.1312	−1.23819	−0.619093	−	0.785318i	$-0.712500\pi$
$349$	−23.1312	−1.23819	−0.619093	+	0.785318i	$0.712500\pi$
$350$	−16.8213	−0.899136
$351$	−3.80897	−0.203308
$352$	−16.8677	−0.899050
$353$	15.7988	0.840884	0.420442	−	0.907319i	$-0.361875\pi$
$353$	15.7988	0.840884	0.420442	+	0.907319i	$0.361875\pi$
$354$	14.1855	0.753953
$355$	−15.1277	−0.802894
$356$	41.5693	2.20317
$357$	2.30688	0.122093
$358$	−4.71692	−0.249297
$359$	−16.8896	−0.891398	−0.445699	−	0.895183i	$-0.647045\pi$
$359$	−16.8896	−0.891398	−0.445699	+	0.895183i	$0.647045\pi$
$360$	−0.749909	−0.0395237
$361$	30.2671	1.59301
$362$	31.7346	1.66793
$363$	−6.64416	−0.348728
$364$	18.0960	0.948486
$365$	−1.41815	−0.0742291
$366$	−24.1613	−1.26293
$367$	−22.0324	−1.15008	−0.575042	−	0.818124i	$-0.695014\pi$
$367$	−22.0324	−1.15008	−0.575042	+	0.818124i	$0.695014\pi$
$368$	−16.8645	−0.879122
$369$	11.4481	0.595963
$370$	1.87733	0.0975980
$371$	26.5284	1.37729
$372$	6.14572	0.318641
$373$	−13.3789	−0.692735	−0.346368	−	0.938099i	$-0.612585\pi$
$373$	−13.3789	−0.692735	−0.346368	+	0.938099i	$0.612585\pi$
$374$	−4.99214	−0.258137
$375$	−8.99661	−0.464583
$376$	4.34690	0.224174
$377$	−6.54657	−0.337166
$378$	4.20430	0.216246
$379$	10.0797	0.517758	0.258879	−	0.965910i	$-0.416647\pi$
$379$	10.0797	0.517758	0.258879	+	0.965910i	$0.416647\pi$
$380$	−16.5523	−0.849116
$381$	12.1830	0.624154
$382$	−14.6638	−0.750267
$383$	−8.12285	−0.415058	−0.207529	−	0.978229i	$-0.566542\pi$
$383$	−8.12285	−0.415058	−0.207529	+	0.978229i	$0.566542\pi$
$384$	5.90530	0.301353
$385$	4.20058	0.214081
$386$	−6.91448	−0.351938
$387$	−3.59734	−0.182863
$388$	−29.6056	−1.50300
$389$	36.1450	1.83263	0.916313	−	0.400463i	$-0.131151\pi$
$389$	36.1450	1.83263	0.916313	+	0.400463i	$0.131151\pi$
$390$	7.94890	0.402508
$391$	−6.12917	−0.309965
$392$	2.20972	0.111608
$393$	−0.278300	−0.0140384
$394$	−34.4205	−1.73408
$395$	0.661198	0.0332685
$396$	−4.92410	−0.247445
$397$	14.6817	0.736854	0.368427	−	0.929657i	$-0.379897\pi$
$397$	14.6817	0.736854	0.368427	+	0.929657i	$0.379897\pi$
$398$	13.8142	0.692442
$399$	14.1339	0.707580
$400$	12.6118	0.630590
$401$	9.20173	0.459512	0.229756	−	0.973248i	$-0.426207\pi$
$401$	9.20173	0.459512	0.229756	+	0.973248i	$0.426207\pi$
$402$	−29.8278	−1.48768
$403$	−9.92177	−0.494238
$404$	−37.6474	−1.87303
$405$	0.999516	0.0496663
$406$	7.22605	0.358623
$407$	1.87749	0.0930636
$408$	0.859527	0.0425529
$409$	−11.2093	−0.554265	−0.277132	−	0.960832i	$-0.589384\pi$
$409$	−11.2093	−0.554265	−0.277132	+	0.960832i	$0.589384\pi$
$410$	−23.8909	−1.17989
$411$	6.98356	0.344473
$412$	36.5225	1.79934
$413$	13.6810	0.673200
$414$	−11.1705	−0.548999
$415$	−5.04530	−0.247664
$416$	−30.7841	−1.50932
$417$	20.5088	1.00432
$418$	−30.5861	−1.49602
$419$	−7.33142	−0.358163	−0.179082	−	0.983834i	$-0.557313\pi$
$419$	−7.33142	−0.358163	−0.179082	+	0.983834i	$0.557313\pi$
$420$	−4.74858	−0.231707
$421$	16.6015	0.809107	0.404553	−	0.914514i	$-0.367427\pi$
$421$	16.6015	0.809107	0.404553	+	0.914514i	$0.367427\pi$
$422$	31.5337	1.53504
$423$	−5.79377	−0.281703
$424$	9.88432	0.480025
$425$	4.58359	0.222337
$426$	31.6004	1.53105
$427$	−23.3020	−1.12766
$428$	24.1243	1.16609
$429$	7.94956	0.383808
$430$	7.50725	0.362032
$431$	37.3416	1.79868	0.899341	−	0.437247i	$-0.144047\pi$
$431$	37.3416	1.79868	0.899341	+	0.437247i	$0.144047\pi$
$432$	−3.15219	−0.151660
$433$	6.82529	0.328003	0.164001	−	0.986460i	$-0.447560\pi$
$433$	6.82529	0.328003	0.164001	+	0.986460i	$0.447560\pi$
$434$	10.9516	0.525692
$435$	1.71789	0.0823667
$436$	26.5098	1.26959
$437$	−37.5526	−1.79638
$438$	2.96239	0.141548
$439$	30.2157	1.44212	0.721059	−	0.692874i	$-0.243656\pi$
$439$	30.2157	1.44212	0.721059	+	0.692874i	$0.243656\pi$
$440$	1.56511	0.0746136
$441$	−2.94522	−0.140249
$442$	−9.11084	−0.433358
$443$	−19.7631	−0.938972	−0.469486	−	0.882940i	$-0.655561\pi$
$443$	−19.7631	−0.938972	−0.469486	+	0.882940i	$0.655561\pi$
$444$	−2.12243	−0.100726
$445$	17.6105	0.834816
$446$	−37.6676	−1.78361
$447$	−13.9341	−0.659061
$448$	21.2844	1.00559
$449$	4.49889	0.212316	0.106158	−	0.994349i	$-0.466145\pi$
$449$	4.49889	0.212316	0.106158	+	0.994349i	$0.466145\pi$
$450$	8.35364	0.393794
$451$	−23.8929	−1.12507
$452$	8.86175	0.416822
$453$	3.09314	0.145328
$454$	−39.6696	−1.86179
$455$	7.66620	0.359397
$456$	5.26620	0.246612
$457$	−31.4088	−1.46924	−0.734622	−	0.678477i	$-0.762640\pi$
$457$	−31.4088	−1.46924	−0.734622	+	0.678477i	$0.762640\pi$
$458$	−33.1062	−1.54695
$459$	−1.14562	−0.0534730
$460$	12.6166	0.588251
$461$	−13.4092	−0.624527	−0.312264	−	0.949996i	$-0.601087\pi$
$461$	−13.4092	−0.624527	−0.312264	+	0.949996i	$0.601087\pi$
$462$	−8.77465	−0.408234
$463$	−32.4070	−1.50608	−0.753042	−	0.657973i	$-0.771414\pi$
$463$	−32.4070	−1.50608	−0.753042	+	0.657973i	$0.771414\pi$
$464$	−5.41775	−0.251513
$465$	2.60358	0.120738
$466$	16.3064	0.755379
$467$	−13.7165	−0.634725	−0.317363	−	0.948304i	$-0.602797\pi$
$467$	−13.7165	−0.634725	−0.317363	+	0.948304i	$0.602797\pi$
$468$	−8.98666	−0.415408
$469$	−28.7670	−1.32834
$470$	12.0910	0.557715
$471$	5.43945	0.250636
$472$	5.09747	0.234630
$473$	7.50787	0.345212
$474$	−1.38119	−0.0634400
$475$	28.0830	1.28854
$476$	5.44271	0.249466
$477$	−13.1743	−0.603210
$478$	−57.8752	−2.64715
$479$	−14.9543	−0.683281	−0.341641	−	0.939831i	$-0.610983\pi$
$479$	−14.9543	−0.683281	−0.341641	+	0.939831i	$0.610983\pi$
$480$	8.07810	0.368713
$481$	3.42648	0.156234
$482$	−52.1778	−2.37663
$483$	−10.7732	−0.490197
$484$	−15.6759	−0.712539
$485$	−12.5422	−0.569510
$486$	−2.08790	−0.0947092
$487$	−27.7656	−1.25818	−0.629090	−	0.777332i	$-0.716572\pi$
$487$	−27.7656	−1.25818	−0.629090	+	0.777332i	$0.716572\pi$
$488$	−8.68216	−0.393023
$489$	−5.02474	−0.227227
$490$	6.14636	0.277664
$491$	−11.1613	−0.503702	−0.251851	−	0.967766i	$-0.581039\pi$
$491$	−11.1613	−0.503702	−0.251851	+	0.967766i	$0.581039\pi$
$492$	27.0099	1.21770
$493$	−1.96901	−0.0886797
$494$	−55.8208	−2.51150
$495$	−2.08605	−0.0937611
$496$	−8.21096	−0.368683
$497$	30.4766	1.36706
$498$	10.5392	0.472273
$499$	42.2277	1.89037	0.945186	−	0.326532i	$-0.105880\pi$
$499$	42.2277	1.89037	0.945186	+	0.326532i	$0.105880\pi$
$500$	−21.2261	−0.949259
$501$	0.462761	0.0206747
$502$	29.0719	1.29754
$503$	−12.3933	−0.552592	−0.276296	−	0.961073i	$-0.589107\pi$
$503$	−12.3933	−0.552592	−0.276296	+	0.961073i	$0.589107\pi$
$504$	1.51078	0.0672957
$505$	−15.9490	−0.709722
$506$	23.3135	1.03641
$507$	1.50823	0.0669827
$508$	28.7439	1.27530
$509$	−35.6903	−1.58194	−0.790971	−	0.611853i	$-0.790424\pi$
$509$	−35.6903	−1.58194	−0.790971	+	0.611853i	$0.790424\pi$
$510$	2.39079	0.105866
$511$	2.85703	0.126388
$512$	−30.2060	−1.33493
$513$	−7.01905	−0.309899
$514$	10.8333	0.477838
$515$	15.4725	0.681798
$516$	−8.48735	−0.373635
$517$	12.0920	0.531804
$518$	−3.78212	−0.166177
$519$	14.9951	0.658211
$520$	2.85638	0.125260
$521$	8.36612	0.366526	0.183263	−	0.983064i	$-0.441334\pi$
$521$	8.36612	0.366526	0.183263	+	0.983064i	$0.441334\pi$
$522$	−3.58854	−0.157066
$523$	37.4987	1.63970	0.819851	−	0.572577i	$-0.194056\pi$
$523$	37.4987	1.63970	0.819851	+	0.572577i	$0.194056\pi$
$524$	−0.656605	−0.0286839
$525$	8.05654	0.351616
$526$	25.3407	1.10491
$527$	−2.98416	−0.129992
$528$	6.57882	0.286306
$529$	5.62345	0.244498
$530$	27.4934	1.19424
$531$	−6.79416	−0.294841
$532$	33.3467	1.44576
$533$	−43.6054	−1.88876
$534$	−36.7868	−1.59192
$535$	10.2201	0.441852
$536$	−10.7184	−0.462964
$537$	2.25917	0.0974902
$538$	−13.9364	−0.600843
$539$	6.14686	0.264764
$540$	2.35820	0.101481
$541$	17.9603	0.772175	0.386088	−	0.922462i	$-0.373826\pi$
$541$	17.9603	0.772175	0.386088	+	0.922462i	$0.373826\pi$
$542$	−10.0047	−0.429739
$543$	−15.1992	−0.652262
$544$	−9.25891	−0.396973
$545$	11.2306	0.481068
$546$	−16.0141	−0.685338
$547$	−24.3729	−1.04211	−0.521056	−	0.853523i	$-0.674462\pi$
$547$	−24.3729	−1.04211	−0.521056	+	0.853523i	$0.674462\pi$
$548$	16.4766	0.703845
$549$	11.5720	0.493882
$550$	−17.4346	−0.743413
$551$	−12.0638	−0.513937
$552$	−4.01402	−0.170848
$553$	−1.33207	−0.0566452
$554$	−14.2909	−0.607161
$555$	−0.899148	−0.0381667
$556$	48.3873	2.05208
$557$	−5.51859	−0.233830	−0.116915	−	0.993142i	$-0.537301\pi$
$557$	−5.51859	−0.233830	−0.116915	+	0.993142i	$0.537301\pi$
$558$	−5.43867	−0.230237
$559$	13.7021	0.579539
$560$	6.34432	0.268097
$561$	2.39098	0.100947
$562$	13.6491	0.575754
$563$	2.76655	0.116596	0.0582982	−	0.998299i	$-0.481433\pi$
$563$	2.76655	0.116596	0.0582982	+	0.998299i	$0.481433\pi$
$564$	−13.6695	−0.575589
$565$	3.75421	0.157941
$566$	−58.8839	−2.47508
$567$	−2.01365	−0.0845653
$568$	11.3554	0.476461
$569$	9.85186	0.413012	0.206506	−	0.978445i	$-0.433791\pi$
$569$	9.85186	0.413012	0.206506	+	0.978445i	$0.433791\pi$
$570$	14.6480	0.613537
$571$	−26.2457	−1.09835	−0.549175	−	0.835707i	$-0.685058\pi$
$571$	−26.2457	−1.09835	−0.549175	+	0.835707i	$0.685058\pi$
$572$	18.7557	0.784216
$573$	7.02323	0.293400
$574$	48.1312	2.00896
$575$	−21.4055	−0.892673
$576$	−10.5701	−0.440420
$577$	2.14883	0.0894570	0.0447285	−	0.998999i	$-0.485758\pi$
$577$	2.14883	0.0894570	0.0447285	+	0.998999i	$0.485758\pi$
$578$	32.7541	1.36239
$579$	3.31169	0.137629
$580$	4.05310	0.168296
$581$	10.1644	0.421689
$582$	26.1995	1.08601
$583$	27.4956	1.13875
$584$	1.06451	0.0440498
$585$	−3.80712	−0.157405
$586$	12.0154	0.496352
$587$	35.9289	1.48294	0.741471	−	0.670985i	$-0.234128\pi$
$587$	35.9289	1.48294	0.741471	+	0.670985i	$0.234128\pi$
$588$	−6.94879	−0.286563
$589$	−18.2835	−0.753360
$590$	14.1787	0.583727
$591$	16.4857	0.678129
$592$	2.83566	0.116545
$593$	0.855164	0.0351174	0.0175587	−	0.999846i	$-0.494411\pi$
$593$	0.855164	0.0351174	0.0175587	+	0.999846i	$0.494411\pi$
$594$	4.35759	0.178794
$595$	2.30576	0.0945269
$596$	−32.8754	−1.34663
$597$	−6.61629	−0.270787
$598$	42.5479	1.73992
$599$	−19.3012	−0.788627	−0.394314	−	0.918976i	$-0.629018\pi$
$599$	−19.3012	−0.788627	−0.394314	+	0.918976i	$0.629018\pi$
$600$	3.00182	0.122549
$601$	40.7292	1.66138	0.830690	−	0.556736i	$-0.187946\pi$
$601$	40.7292	1.66138	0.830690	+	0.556736i	$0.187946\pi$
$602$	−15.1243	−0.616420
$603$	14.2860	0.581771
$604$	7.29777	0.296942
$605$	−6.64095	−0.269993
$606$	33.3161	1.35338
$607$	6.75833	0.274312	0.137156	−	0.990549i	$-0.456204\pi$
$607$	6.75833	0.274312	0.137156	+	0.990549i	$0.456204\pi$
$608$	−56.7281	−2.30063
$609$	−3.46091	−0.140243
$610$	−24.1495	−0.977787
$611$	22.0683	0.892787
$612$	−2.70291	−0.109259
$613$	42.8050	1.72888	0.864439	−	0.502738i	$-0.167674\pi$
$613$	42.8050	1.72888	0.864439	+	0.502738i	$0.167674\pi$
$614$	17.3482	0.700117
$615$	11.4425	0.461408
$616$	−3.15310	−0.127042
$617$	−13.6177	−0.548228	−0.274114	−	0.961697i	$-0.588385\pi$
$617$	−13.6177	−0.548228	−0.274114	+	0.961697i	$0.588385\pi$
$618$	−32.3207	−1.30013
$619$	−18.0650	−0.726093	−0.363046	−	0.931771i	$-0.618263\pi$
$619$	−18.0650	−0.726093	−0.363046	+	0.931771i	$0.618263\pi$
$620$	6.14274	0.246699
$621$	5.35009	0.214692
$622$	−15.8858	−0.636964
$623$	−35.4785	−1.42141
$624$	12.0066	0.480648
$625$	11.0126	0.440504
$626$	65.7738	2.62885
$627$	14.6492	0.585033
$628$	12.8335	0.512113
$629$	1.03058	0.0410920
$630$	4.20227	0.167422
$631$	−19.2493	−0.766302	−0.383151	−	0.923686i	$-0.625161\pi$
$631$	−19.2493	−0.766302	−0.383151	+	0.923686i	$0.625161\pi$
$632$	−0.496319	−0.0197425
$633$	−15.1031	−0.600292
$634$	−20.1823	−0.801543
$635$	12.1771	0.483233
$636$	−31.0827	−1.23251
$637$	11.2182	0.444483
$638$	7.48951	0.296512
$639$	−15.1350	−0.598732
$640$	5.90244	0.233314
$641$	−18.5854	−0.734078	−0.367039	−	0.930206i	$-0.619628\pi$
$641$	−18.5854	−0.734078	−0.367039	+	0.930206i	$0.619628\pi$
$642$	−21.3489	−0.842573
$643$	22.8451	0.900923	0.450462	−	0.892796i	$-0.351259\pi$
$643$	22.8451	0.900923	0.450462	+	0.892796i	$0.351259\pi$
$644$	−25.4177	−1.00160
$645$	−3.59559	−0.141576
$646$	−16.7892	−0.660562
$647$	20.1908	0.793784	0.396892	−	0.917865i	$-0.370089\pi$
$647$	20.1908	0.793784	0.396892	+	0.917865i	$0.370089\pi$
$648$	−0.750272	−0.0294735
$649$	14.1798	0.556607
$650$	−31.8187	−1.24803
$651$	−5.24524	−0.205577
$652$	−11.8551	−0.464281
$653$	15.6444	0.612213	0.306107	−	0.951997i	$-0.400974\pi$
$653$	15.6444	0.612213	0.306107	+	0.951997i	$0.400974\pi$
$654$	−23.4599	−0.917353
$655$	−0.278165	−0.0108688
$656$	−36.0865	−1.40894
$657$	−1.41883	−0.0553539
$658$	−24.3588	−0.949603
$659$	−22.0939	−0.860655	−0.430328	−	0.902673i	$-0.641602\pi$
$659$	−22.0939	−0.860655	−0.430328	+	0.902673i	$0.641602\pi$
$660$	−4.92171	−0.191577
$661$	29.8830	1.16231	0.581157	−	0.813791i	$-0.302600\pi$
$661$	29.8830	1.16231	0.581157	+	0.813791i	$0.302600\pi$
$662$	−46.4878	−1.80680
$663$	4.36363	0.169469
$664$	3.78718	0.146971
$665$	14.1271	0.547824
$666$	1.87824	0.0727805
$667$	9.19534	0.356045
$668$	1.09181	0.0422435
$669$	18.0409	0.697501
$670$	−29.8134	−1.15179
$671$	−24.1515	−0.932360
$672$	−16.2743	−0.627796
$673$	43.2201	1.66601	0.833007	−	0.553263i	$-0.186618\pi$
$673$	43.2201	1.66601	0.833007	+	0.553263i	$0.186618\pi$
$674$	3.56223	0.137212
$675$	−4.00097	−0.153997
$676$	3.55843	0.136863
$677$	13.4132	0.515510	0.257755	−	0.966210i	$-0.417017\pi$
$677$	13.4132	0.515510	0.257755	+	0.966210i	$0.417017\pi$
$678$	−7.84222	−0.301179
$679$	25.2678	0.969687
$680$	0.859110	0.0329454
$681$	18.9997	0.728071
$682$	11.3508	0.434646
$683$	0.183155	0.00700825	0.00350412	−	0.999994i	$-0.498885\pi$
$683$	0.183155	0.00700825	0.00350412	+	0.999994i	$0.498885\pi$
$684$	−16.5603	−0.633201
$685$	6.98017	0.266699
$686$	−41.8127	−1.59642
$687$	15.8562	0.604951
$688$	11.3395	0.432314
$689$	50.1805	1.91173
$690$	−11.1651	−0.425047
$691$	−6.13113	−0.233239	−0.116620	−	0.993177i	$-0.537206\pi$
$691$	−6.13113	−0.233239	−0.116620	+	0.993177i	$0.537206\pi$
$692$	35.3785	1.34489
$693$	4.20261	0.159644
$694$	−40.5704	−1.54003
$695$	20.4989	0.777566
$696$	−1.28951	−0.0488789
$697$	−13.1152	−0.496772
$698$	48.2958	1.82802
$699$	−7.80994	−0.295399
$700$	19.0081	0.718440
$701$	14.4799	0.546897	0.273448	−	0.961887i	$-0.411836\pi$
$701$	14.4799	0.546897	0.273448	+	0.961887i	$0.411836\pi$
$702$	7.95276	0.300157
$703$	6.31423	0.238146
$704$	22.0604	0.831434
$705$	−5.79096	−0.218100
$706$	−32.9863	−1.24146
$707$	32.1313	1.20842
$708$	−16.0297	−0.602434
$709$	−24.1894	−0.908453	−0.454227	−	0.890886i	$-0.650084\pi$
$709$	−24.1894	−0.908453	−0.454227	+	0.890886i	$0.650084\pi$
$710$	31.5851	1.18537
$711$	0.661519	0.0248089
$712$	−13.2190	−0.495405
$713$	13.9362	0.521913
$714$	−4.81653	−0.180254
$715$	7.94570	0.297153
$716$	5.33015	0.199197
$717$	27.7193	1.03520
$718$	35.2638	1.31603
$719$	2.85437	0.106450	0.0532251	−	0.998583i	$-0.483050\pi$
$719$	2.85437	0.106450	0.0532251	+	0.998583i	$0.483050\pi$
$720$	−3.15066	−0.117418
$721$	−31.1712	−1.16088
$722$	−63.1948	−2.35187
$723$	24.9905	0.929407
$724$	−35.8602	−1.33273
$725$	−6.87657	−0.255390
$726$	13.8724	0.514852
$727$	−24.6037	−0.912500	−0.456250	−	0.889852i	$-0.650808\pi$
$727$	−24.6037	−0.912500	−0.456250	+	0.889852i	$0.650808\pi$
$728$	−5.75453	−0.213277
$729$	1.00000	0.0370370
$730$	2.96095	0.109590
$731$	4.12118	0.152427
$732$	27.3023	1.00912
$733$	−6.47028	−0.238985	−0.119493	−	0.992835i	$-0.538127\pi$
$733$	−6.47028	−0.238985	−0.119493	+	0.992835i	$0.538127\pi$
$734$	46.0016	1.69795
$735$	−2.94379	−0.108583
$736$	43.2395	1.59383
$737$	−29.8158	−1.09828
$738$	−23.9025	−0.879863
$739$	12.0154	0.441994	0.220997	−	0.975275i	$-0.429069\pi$
$739$	12.0154	0.441994	0.220997	+	0.975275i	$0.429069\pi$
$740$	−2.12140	−0.0779841
$741$	26.7353	0.982147
$742$	−55.3888	−2.03339
$743$	12.3768	0.454062	0.227031	−	0.973888i	$-0.427098\pi$
$743$	12.3768	0.454062	0.227031	+	0.973888i	$0.427098\pi$
$744$	−1.95434	−0.0716497
$745$	−13.9274	−0.510259
$746$	27.9339	1.02273
$747$	−5.04774	−0.184687
$748$	5.64115	0.206261
$749$	−20.5896	−0.752328
$750$	18.7841	0.685897
$751$	9.76033	0.356159	0.178080	−	0.984016i	$-0.443012\pi$
$751$	9.76033	0.356159	0.178080	+	0.984016i	$0.443012\pi$
$752$	18.2630	0.665985
$753$	−13.9240	−0.507418
$754$	13.6686	0.497782
$755$	3.09164	0.112516
$756$	−4.75089	−0.172788
$757$	−23.0769	−0.838743	−0.419371	−	0.907815i	$-0.637750\pi$
$757$	−23.0769	−0.838743	−0.419371	+	0.907815i	$0.637750\pi$
$758$	−21.0454	−0.764403
$759$	−11.1660	−0.405299
$760$	5.26365	0.190933
$761$	−35.8092	−1.29808	−0.649042	−	0.760753i	$-0.724830\pi$
$761$	−35.8092	−1.29808	−0.649042	+	0.760753i	$0.724830\pi$
$762$	−25.4369	−0.921483
$763$	−22.6255	−0.819099
$764$	16.5702	0.599489
$765$	−1.14506	−0.0413999
$766$	16.9597	0.612780
$767$	25.8787	0.934426
$768$	8.81048	0.317921
$769$	−18.0824	−0.652069	−0.326034	−	0.945358i	$-0.605713\pi$
$769$	−18.0824	−0.652069	−0.326034	+	0.945358i	$0.605713\pi$
$770$	−8.77040	−0.316063
$771$	−5.18862	−0.186864
$772$	7.81340	0.281210
$773$	36.2646	1.30435	0.652174	−	0.758069i	$-0.273857\pi$
$773$	36.2646	1.30435	0.652174	+	0.758069i	$0.273857\pi$
$774$	7.51089	0.269973
$775$	−10.4219	−0.374366
$776$	9.41460	0.337964
$777$	1.81144	0.0649852
$778$	−75.4673	−2.70564
$779$	−80.3547	−2.87901
$780$	−8.98230	−0.321618
$781$	31.5877	1.13030
$782$	12.7971	0.457624
$783$	1.71873	0.0614223
$784$	9.28389	0.331568
$785$	5.43681	0.194048
$786$	0.581064	0.0207259
$787$	31.0695	1.10751	0.553754	−	0.832680i	$-0.313195\pi$
$787$	31.0695	1.10751	0.553754	+	0.832680i	$0.313195\pi$
$788$	38.8953	1.38559
$789$	−12.1369	−0.432086
$790$	−1.38052	−0.0491166
$791$	−7.56331	−0.268921
$792$	1.56587	0.0556406
$793$	−44.0774	−1.56524
$794$	−30.6540	−1.08787
$795$	−13.1679	−0.467018
$796$	−15.6101	−0.553285
$797$	0.639795	0.0226627	0.0113314	−	0.999936i	$-0.496393\pi$
$797$	0.639795	0.0226627	0.0113314	+	0.999936i	$0.496393\pi$
$798$	−29.5102	−1.04465
$799$	6.63746	0.234816
$800$	−32.3359	−1.14325
$801$	17.6190	0.622537
$802$	−19.2123	−0.678411
$803$	2.96119	0.104498
$804$	33.7056	1.18870
$805$	−10.7680	−0.379521
$806$	20.7157	0.729679
$807$	6.67485	0.234966
$808$	11.9719	0.421170
$809$	−12.5367	−0.440769	−0.220384	−	0.975413i	$-0.570731\pi$
$809$	−12.5367	−0.440769	−0.220384	+	0.975413i	$0.570731\pi$
$810$	−2.08689	−0.0733259
$811$	28.8175	1.01192	0.505959	−	0.862557i	$-0.331139\pi$
$811$	28.8175	1.01192	0.505959	+	0.862557i	$0.331139\pi$
$812$	−8.16548	−0.286552
$813$	4.79175	0.168054
$814$	−3.92002	−0.137396
$815$	−5.02231	−0.175924
$816$	3.61121	0.126418
$817$	25.2499	0.883382
$818$	23.4040	0.818300
$819$	7.66992	0.268009
$820$	26.9969	0.942771
$821$	−44.0308	−1.53668	−0.768342	−	0.640039i	$-0.778918\pi$
$821$	−44.0308	−1.53668	−0.768342	+	0.640039i	$0.778918\pi$
$822$	−14.5810	−0.508571
$823$	37.0674	1.29209	0.646044	−	0.763300i	$-0.276422\pi$
$823$	37.0674	1.29209	0.646044	+	0.763300i	$0.276422\pi$
$824$	−11.6142	−0.404599
$825$	8.35028	0.290719
$826$	−28.5647	−0.993893
$827$	23.7913	0.827305	0.413653	−	0.910435i	$-0.364253\pi$
$827$	23.7913	0.827305	0.413653	+	0.910435i	$0.364253\pi$
$828$	12.6227	0.438669
$829$	11.7372	0.407650	0.203825	−	0.979007i	$-0.434663\pi$
$829$	11.7372	0.407650	0.203825	+	0.979007i	$0.434663\pi$
$830$	10.5341	0.365644
$831$	6.84461	0.237437
$832$	40.2611	1.39580
$833$	3.37410	0.116906
$834$	−42.8204	−1.48275
$835$	0.462537	0.0160068
$836$	34.5625	1.19537
$837$	2.60484	0.0900366
$838$	15.3073	0.528782
$839$	15.6897	0.541670	0.270835	−	0.962626i	$-0.412700\pi$
$839$	15.6897	0.541670	0.270835	+	0.962626i	$0.412700\pi$
$840$	1.51005	0.0521018
$841$	−26.0460	−0.898137
$842$	−34.6623	−1.19454
$843$	−6.53725	−0.225155
$844$	−35.6333	−1.22655
$845$	1.50750	0.0518595
$846$	12.0968	0.415898
$847$	13.3790	0.459708
$848$	41.5279	1.42607
$849$	28.2024	0.967905
$850$	−9.57009	−0.328252
$851$	−4.81285	−0.164982
$852$	−35.7087	−1.22336
$853$	46.1827	1.58126	0.790632	−	0.612292i	$-0.209752\pi$
$853$	46.1827	1.58126	0.790632	+	0.612292i	$0.209752\pi$
$854$	48.6523	1.66485
$855$	−7.01565	−0.239930
$856$	−7.67156	−0.262208
$857$	8.44028	0.288315	0.144157	−	0.989555i	$-0.453953\pi$
$857$	8.44028	0.288315	0.144157	+	0.989555i	$0.453953\pi$
$858$	−16.5979	−0.566643
$859$	41.5744	1.41850	0.709251	−	0.704956i	$-0.249033\pi$
$859$	41.5744	1.41850	0.709251	+	0.704956i	$0.249033\pi$
$860$	−8.48324	−0.289276
$861$	−23.0524	−0.785624
$862$	−77.9657	−2.65552
$863$	3.92882	0.133739	0.0668693	−	0.997762i	$-0.478699\pi$
$863$	3.92882	0.133739	0.0668693	+	0.997762i	$0.478699\pi$
$864$	8.08201	0.274956
$865$	14.9878	0.509601
$866$	−14.2506	−0.484254
$867$	−15.6876	−0.532777
$868$	−12.3753	−0.420046
$869$	−1.38063	−0.0468347
$870$	−3.58680	−0.121604
$871$	−54.4149	−1.84378
$872$	−8.43012	−0.285480
$873$	−12.5482	−0.424694
$874$	78.4061	2.65213
$875$	18.1160	0.612433
$876$	−3.34751	−0.113102
$877$	32.0100	1.08090	0.540450	−	0.841376i	$-0.318254\pi$
$877$	32.0100	1.08090	0.540450	+	0.841376i	$0.318254\pi$
$878$	−63.0875	−2.12910
$879$	−5.75477	−0.194104
$880$	6.57563	0.221664
$881$	−7.60441	−0.256199	−0.128099	−	0.991761i	$-0.540888\pi$
$881$	−7.60441	−0.256199	−0.128099	+	0.991761i	$0.540888\pi$
$882$	6.14934	0.207059
$883$	52.5015	1.76682	0.883408	−	0.468604i	$-0.155243\pi$
$883$	52.5015	1.76682	0.883408	+	0.468604i	$0.155243\pi$
$884$	10.2953	0.346268
$885$	−6.79086	−0.228272
$886$	41.2634	1.38627
$887$	25.0388	0.840719	0.420360	−	0.907358i	$-0.361904\pi$
$887$	25.0388	0.840719	0.420360	+	0.907358i	$0.361904\pi$
$888$	0.674933	0.0226493
$889$	−24.5323	−0.822786
$890$	−36.7690	−1.23250
$891$	−2.08706	−0.0699193
$892$	42.5646	1.42517
$893$	40.6668	1.36086
$894$	29.0931	0.973019
$895$	2.25807	0.0754790
$896$	−11.8912	−0.397257
$897$	−20.3783	−0.680412
$898$	−9.39325	−0.313457
$899$	4.47702	0.149317
$900$	−9.43965	−0.314655
$901$	15.0928	0.502813
$902$	49.8860	1.66102
$903$	7.24377	0.241058
$904$	−2.81804	−0.0937267
$905$	−15.1919	−0.504995
$906$	−6.45817	−0.214558
$907$	−41.1145	−1.36518	−0.682592	−	0.730800i	$-0.739147\pi$
$907$	−41.1145	−1.36518	−0.682592	+	0.730800i	$0.739147\pi$
$908$	44.8269	1.48763
$909$	−15.9567	−0.529252
$910$	−16.0063	−0.530603
$911$	29.2966	0.970641	0.485320	−	0.874336i	$-0.338703\pi$
$911$	29.2966	0.970641	0.485320	+	0.874336i	$0.338703\pi$
$912$	22.1254	0.732644
$913$	10.5350	0.348656
$914$	65.5786	2.16915
$915$	11.5664	0.382374
$916$	37.4102	1.23607
$917$	0.560398	0.0185060
$918$	2.39194	0.0789459
$919$	0.611800	0.0201814	0.0100907	−	0.999949i	$-0.496788\pi$
$919$	0.611800	0.0201814	0.0100907	+	0.999949i	$0.496788\pi$
$920$	−4.01208	−0.132274
$921$	−8.30892	−0.273788
$922$	27.9970	0.922034
$923$	57.6487	1.89753
$924$	9.91540	0.326193
$925$	3.59921	0.118341
$926$	67.6628	2.22354
$927$	15.4800	0.508428
$928$	13.8908	0.455987
$929$	−27.8253	−0.912919	−0.456460	−	0.889744i	$-0.650883\pi$
$929$	−27.8253	−0.912919	−0.456460	+	0.889744i	$0.650883\pi$
$930$	−5.43603	−0.178254
$931$	20.6727	0.677519
$932$	−18.4263	−0.603574
$933$	7.60851	0.249091
$934$	28.6388	0.937090
$935$	2.38982	0.0781556
$936$	2.85776	0.0934089
$937$	−12.8123	−0.418558	−0.209279	−	0.977856i	$-0.567112\pi$
$937$	−12.8123	−0.418558	−0.209279	+	0.977856i	$0.567112\pi$
$938$	60.0627	1.96112
$939$	−31.5023	−1.02804
$940$	−13.6629	−0.445633
$941$	−15.0918	−0.491978	−0.245989	−	0.969273i	$-0.579113\pi$
$941$	−15.0918	−0.491978	−0.245989	+	0.969273i	$0.579113\pi$
$942$	−11.3570	−0.370032
$943$	61.2482	1.99452
$944$	21.4165	0.697046
$945$	−2.01267	−0.0654722
$946$	−15.6757	−0.509661
$947$	−56.0711	−1.82207	−0.911033	−	0.412333i	$-0.864714\pi$
$947$	−56.0711	−1.82207	−0.911033	+	0.412333i	$0.864714\pi$
$948$	1.56075	0.0506908
$949$	5.40429	0.175431
$950$	−58.6346	−1.90236
$951$	9.66632	0.313452
$952$	−1.73078	−0.0560951
$953$	−31.3330	−1.01497	−0.507487	−	0.861659i	$-0.669426\pi$
$953$	−31.3330	−1.01497	−0.507487	+	0.861659i	$0.669426\pi$
$954$	27.5067	0.890562
$955$	7.01983	0.227156
$956$	65.3993	2.11516
$957$	−3.58709	−0.115954
$958$	31.2232	1.00878
$959$	−14.0624	−0.454099
$960$	−10.5650	−0.340983
$961$	−24.2148	−0.781122
$962$	−7.15417	−0.230660
$963$	10.2250	0.329497
$964$	58.9611	1.89901
$965$	3.31008	0.106555
$966$	22.4934	0.723713
$967$	21.8772	0.703523	0.351762	−	0.936090i	$-0.385583\pi$
$967$	21.8772	0.703523	0.351762	+	0.936090i	$0.385583\pi$
$968$	4.98493	0.160222
$969$	8.04117	0.258320
$970$	26.1868	0.840809
$971$	32.0158	1.02743	0.513717	−	0.857959i	$-0.328268\pi$
$971$	32.0158	1.02743	0.513717	+	0.857959i	$0.328268\pi$
$972$	2.35934	0.0756759
$973$	−41.2975	−1.32394
$974$	57.9719	1.85754
$975$	15.2396	0.488056
$976$	−36.4772	−1.16761
$977$	−38.0026	−1.21581	−0.607906	−	0.794009i	$-0.707990\pi$
$977$	−38.0026	−1.21581	−0.607906	+	0.794009i	$0.707990\pi$
$978$	10.4912	0.335471
$979$	−36.7720	−1.17524
$980$	−6.94542	−0.221863
$981$	11.2361	0.358740
$982$	23.3037	0.743651
$983$	50.6805	1.61646	0.808228	−	0.588869i	$-0.200427\pi$
$983$	50.6805	1.61646	0.808228	+	0.588869i	$0.200427\pi$
$984$	−8.58918	−0.273813
$985$	16.4777	0.525022
$986$	4.11110	0.130924
$987$	11.6666	0.371352
$988$	63.0778	2.00677
$989$	−19.2461	−0.611989
$990$	4.35548	0.138426
$991$	−6.53080	−0.207458	−0.103729	−	0.994606i	$-0.533077\pi$
$991$	−6.53080	−0.207458	−0.103729	+	0.994606i	$0.533077\pi$
$992$	21.0524	0.668414
$993$	22.2653	0.706569
$994$	−63.6322	−2.01829
$995$	−6.61308	−0.209649
$996$	−11.9094	−0.377362
$997$	−21.1550	−0.669986	−0.334993	−	0.942221i	$-0.608734\pi$
$997$	−21.1550	−0.669986	−0.334993	+	0.942221i	$0.608734\pi$
$998$	−88.1674	−2.79089
$999$	−0.899584	−0.0284616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.19	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.d.1.19	✓	129	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08790 q^{2} +1.00000 q^{3} +2.35934 q^{4} +0.999516 q^{5} -2.08790 q^{6} -2.01365 q^{7} -0.750272 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.08790 q^{2} +1.00000 q^{3} +2.35934 q^{4} +0.999516 q^{5} -2.08790 q^{6} -2.01365 q^{7} -0.750272 q^{8} +1.00000 q^{9} -2.08689 q^{10} -2.08706 q^{11} +2.35934 q^{12} -3.80897 q^{13} +4.20430 q^{14} +0.999516 q^{15} -3.15219 q^{16} -1.14562 q^{17} -2.08790 q^{18} -7.01905 q^{19} +2.35820 q^{20} -2.01365 q^{21} +4.35759 q^{22} +5.35009 q^{23} -0.750272 q^{24} -4.00097 q^{25} +7.95276 q^{26} +1.00000 q^{27} -4.75089 q^{28} +1.71873 q^{29} -2.08689 q^{30} +2.60484 q^{31} +8.08201 q^{32} -2.08706 q^{33} +2.39194 q^{34} -2.01267 q^{35} +2.35934 q^{36} -0.899584 q^{37} +14.6551 q^{38} -3.80897 q^{39} -0.749909 q^{40} +11.4481 q^{41} +4.20430 q^{42} -3.59734 q^{43} -4.92410 q^{44} +0.999516 q^{45} -11.1705 q^{46} -5.79377 q^{47} -3.15219 q^{48} -2.94522 q^{49} +8.35364 q^{50} -1.14562 q^{51} -8.98666 q^{52} -13.1743 q^{53} -2.08790 q^{54} -2.08605 q^{55} +1.51078 q^{56} -7.01905 q^{57} -3.58854 q^{58} -6.79416 q^{59} +2.35820 q^{60} +11.5720 q^{61} -5.43867 q^{62} -2.01365 q^{63} -10.5701 q^{64} -3.80712 q^{65} +4.35759 q^{66} +14.2860 q^{67} -2.70291 q^{68} +5.35009 q^{69} +4.20227 q^{70} -15.1350 q^{71} -0.750272 q^{72} -1.41883 q^{73} +1.87824 q^{74} -4.00097 q^{75} -16.5603 q^{76} +4.20261 q^{77} +7.95276 q^{78} +0.661519 q^{79} -3.15066 q^{80} +1.00000 q^{81} -23.9025 q^{82} -5.04774 q^{83} -4.75089 q^{84} -1.14506 q^{85} +7.51089 q^{86} +1.71873 q^{87} +1.56587 q^{88} +17.6190 q^{89} -2.08689 q^{90} +7.66992 q^{91} +12.6227 q^{92} +2.60484 q^{93} +12.0968 q^{94} -7.01565 q^{95} +8.08201 q^{96} -12.5482 q^{97} +6.14934 q^{98} -2.08706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

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