LMFDB - Embedded newform 8013.2.a.a.1.17

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:	$1$
Dimension:	$94$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.05347 q^{2} +1.00000 q^{3} +2.21673 q^{4} -2.14654 q^{5} -2.05347 q^{6} -0.521799 q^{7} -0.445046 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.05347 q^{2} +1.00000 q^{3} +2.21673 q^{4} -2.14654 q^{5} -2.05347 q^{6} -0.521799 q^{7} -0.445046 q^{8} +1.00000 q^{9} +4.40785 q^{10} +3.54058 q^{11} +2.21673 q^{12} +3.68288 q^{13} +1.07150 q^{14} -2.14654 q^{15} -3.51957 q^{16} +0.402277 q^{17} -2.05347 q^{18} +4.52521 q^{19} -4.75830 q^{20} -0.521799 q^{21} -7.27046 q^{22} +3.27230 q^{23} -0.445046 q^{24} -0.392362 q^{25} -7.56267 q^{26} +1.00000 q^{27} -1.15669 q^{28} -7.86254 q^{29} +4.40785 q^{30} -6.40461 q^{31} +8.11742 q^{32} +3.54058 q^{33} -0.826062 q^{34} +1.12006 q^{35} +2.21673 q^{36} -3.39138 q^{37} -9.29236 q^{38} +3.68288 q^{39} +0.955309 q^{40} -0.850189 q^{41} +1.07150 q^{42} -6.58933 q^{43} +7.84850 q^{44} -2.14654 q^{45} -6.71956 q^{46} +10.5963 q^{47} -3.51957 q^{48} -6.72773 q^{49} +0.805702 q^{50} +0.402277 q^{51} +8.16394 q^{52} +2.32164 q^{53} -2.05347 q^{54} -7.60000 q^{55} +0.232224 q^{56} +4.52521 q^{57} +16.1455 q^{58} -11.4691 q^{59} -4.75830 q^{60} -14.9509 q^{61} +13.1517 q^{62} -0.521799 q^{63} -9.62971 q^{64} -7.90545 q^{65} -7.27046 q^{66} +7.26313 q^{67} +0.891738 q^{68} +3.27230 q^{69} -2.30001 q^{70} +6.02557 q^{71} -0.445046 q^{72} -2.15465 q^{73} +6.96408 q^{74} -0.392362 q^{75} +10.0312 q^{76} -1.84747 q^{77} -7.56267 q^{78} -11.9725 q^{79} +7.55490 q^{80} +1.00000 q^{81} +1.74583 q^{82} -9.54343 q^{83} -1.15669 q^{84} -0.863503 q^{85} +13.5310 q^{86} -7.86254 q^{87} -1.57572 q^{88} -4.83824 q^{89} +4.40785 q^{90} -1.92172 q^{91} +7.25380 q^{92} -6.40461 q^{93} -21.7592 q^{94} -9.71354 q^{95} +8.11742 q^{96} -4.39676 q^{97} +13.8152 q^{98} +3.54058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9} - 39 q^{10} - 49 q^{11} + 73 q^{12} - 52 q^{13} - 7 q^{14} - 14 q^{15} + 43 q^{16} - 22 q^{17} - 13 q^{18} - 89 q^{19} - 22 q^{20} - 55 q^{21} - 36 q^{22} - 46 q^{23} - 36 q^{24} + 18 q^{25} + q^{26} + 94 q^{27} - 123 q^{28} - 20 q^{29} - 39 q^{30} - 61 q^{31} - 65 q^{32} - 49 q^{33} - 67 q^{34} - 40 q^{35} + 73 q^{36} - 83 q^{37} - 19 q^{38} - 52 q^{39} - 101 q^{40} - 25 q^{41} - 7 q^{42} - 150 q^{43} - 71 q^{44} - 14 q^{45} - 72 q^{46} - 39 q^{47} + 43 q^{48} - q^{49} - 45 q^{50} - 22 q^{51} - 110 q^{52} - 30 q^{53} - 13 q^{54} - 54 q^{55} - 5 q^{56} - 89 q^{57} - 77 q^{58} - 43 q^{59} - 22 q^{60} - 109 q^{61} - 33 q^{62} - 55 q^{63} + 10 q^{64} - 66 q^{65} - 36 q^{66} - 155 q^{67} - 46 q^{68} - 46 q^{69} - 43 q^{70} - 27 q^{71} - 36 q^{72} - 157 q^{73} - 29 q^{74} + 18 q^{75} - 176 q^{76} - 9 q^{77} + q^{78} - 99 q^{79} - 18 q^{80} + 94 q^{81} - 53 q^{82} - 144 q^{83} - 123 q^{84} - 105 q^{85} + 23 q^{86} - 20 q^{87} - 88 q^{88} - 4 q^{89} - 39 q^{90} - 99 q^{91} - 76 q^{92} - 61 q^{93} - 65 q^{94} - 49 q^{95} - 65 q^{96} - 139 q^{97} - 6 q^{98} - 49 q^{99}+O(q^{100}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9 - 39 * q^10 - 49 * q^11 + 73 * q^12 - 52 * q^13 - 7 * q^14 - 14 * q^15 + 43 * q^16 - 22 * q^17 - 13 * q^18 - 89 * q^19 - 22 * q^20 - 55 * q^21 - 36 * q^22 - 46 * q^23 - 36 * q^24 + 18 * q^25 + q^26 + 94 * q^27 - 123 * q^28 - 20 * q^29 - 39 * q^30 - 61 * q^31 - 65 * q^32 - 49 * q^33 - 67 * q^34 - 40 * q^35 + 73 * q^36 - 83 * q^37 - 19 * q^38 - 52 * q^39 - 101 * q^40 - 25 * q^41 - 7 * q^42 - 150 * q^43 - 71 * q^44 - 14 * q^45 - 72 * q^46 - 39 * q^47 + 43 * q^48 - q^49 - 45 * q^50 - 22 * q^51 - 110 * q^52 - 30 * q^53 - 13 * q^54 - 54 * q^55 - 5 * q^56 - 89 * q^57 - 77 * q^58 - 43 * q^59 - 22 * q^60 - 109 * q^61 - 33 * q^62 - 55 * q^63 + 10 * q^64 - 66 * q^65 - 36 * q^66 - 155 * q^67 - 46 * q^68 - 46 * q^69 - 43 * q^70 - 27 * q^71 - 36 * q^72 - 157 * q^73 - 29 * q^74 + 18 * q^75 - 176 * q^76 - 9 * q^77 + q^78 - 99 * q^79 - 18 * q^80 + 94 * q^81 - 53 * q^82 - 144 * q^83 - 123 * q^84 - 105 * q^85 + 23 * q^86 - 20 * q^87 - 88 * q^88 - 4 * q^89 - 39 * q^90 - 99 * q^91 - 76 * q^92 - 61 * q^93 - 65 * q^94 - 49 * q^95 - 65 * q^96 - 139 * q^97 - 6 * q^98 - 49 * 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 $

$2$	−2.05347	−1.45202	−0.726010	−	0.687684i	$-0.758628\pi$
$2$	−2.05347	−1.45202	−0.726010	+	0.687684i	$0.758628\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.21673	1.10836
$5$	−2.14654	−0.959962	−0.479981	−	0.877279i	$-0.659357\pi$
$5$	−2.14654	−0.959962	−0.479981	+	0.877279i	$0.659357\pi$
$6$	−2.05347	−0.838325
$7$	−0.521799	−0.197221	−0.0986107	−	0.995126i	$-0.531440\pi$
$7$	−0.521799	−0.197221	−0.0986107	+	0.995126i	$0.531440\pi$
$8$	−0.445046	−0.157347
$9$	1.00000	0.333333
$10$	4.40785	1.39389
$11$	3.54058	1.06752	0.533762	−	0.845634i	$-0.320778\pi$
$11$	3.54058	1.06752	0.533762	+	0.845634i	$0.320778\pi$
$12$	2.21673	0.639915
$13$	3.68288	1.02145	0.510723	−	0.859745i	$-0.329378\pi$
$13$	3.68288	1.02145	0.510723	+	0.859745i	$0.329378\pi$
$14$	1.07150	0.286369
$15$	−2.14654	−0.554235
$16$	−3.51957	−0.879893
$17$	0.402277	0.0975664	0.0487832	−	0.998809i	$-0.484466\pi$
$17$	0.402277	0.0975664	0.0487832	+	0.998809i	$0.484466\pi$
$18$	−2.05347	−0.484007
$19$	4.52521	1.03815	0.519077	−	0.854728i	$-0.326276\pi$
$19$	4.52521	1.03815	0.519077	+	0.854728i	$0.326276\pi$
$20$	−4.75830	−1.06399
$21$	−0.521799	−0.113866
$22$	−7.27046	−1.55007
$23$	3.27230	0.682321	0.341161	−	0.940005i	$-0.389180\pi$
$23$	3.27230	0.682321	0.341161	+	0.940005i	$0.389180\pi$
$24$	−0.445046	−0.0908446
$25$	−0.392362	−0.0784723
$26$	−7.56267	−1.48316
$27$	1.00000	0.192450
$28$	−1.15669	−0.218593
$29$	−7.86254	−1.46004	−0.730018	−	0.683428i	$-0.760488\pi$
$29$	−7.86254	−1.46004	−0.730018	+	0.683428i	$0.760488\pi$
$30$	4.40785	0.804760
$31$	−6.40461	−1.15030	−0.575151	−	0.818047i	$-0.695057\pi$
$31$	−6.40461	−1.15030	−0.575151	+	0.818047i	$0.695057\pi$
$32$	8.11742	1.43497
$33$	3.54058	0.616336
$34$	−0.826062	−0.141668
$35$	1.12006	0.189325
$36$	2.21673	0.369455
$37$	−3.39138	−0.557539	−0.278769	−	0.960358i	$-0.589927\pi$
$37$	−3.39138	−0.557539	−0.278769	+	0.960358i	$0.589927\pi$
$38$	−9.29236	−1.50742
$39$	3.68288	0.589732
$40$	0.955309	0.151048
$41$	−0.850189	−0.132777	−0.0663886	−	0.997794i	$-0.521148\pi$
$41$	−0.850189	−0.132777	−0.0663886	+	0.997794i	$0.521148\pi$
$42$	1.07150	0.165335
$43$	−6.58933	−1.00486	−0.502431	−	0.864617i	$-0.667561\pi$
$43$	−6.58933	−1.00486	−0.502431	+	0.864617i	$0.667561\pi$
$44$	7.84850	1.18321
$45$	−2.14654	−0.319987
$46$	−6.71956	−0.990745
$47$	10.5963	1.54563	0.772816	−	0.634630i	$-0.218848\pi$
$47$	10.5963	1.54563	0.772816	+	0.634630i	$0.218848\pi$
$48$	−3.51957	−0.508006
$49$	−6.72773	−0.961104
$50$	0.805702	0.113943
$51$	0.402277	0.0563300
$52$	8.16394	1.13213
$53$	2.32164	0.318901	0.159451	−	0.987206i	$-0.449028\pi$
$53$	2.32164	0.318901	0.159451	+	0.987206i	$0.449028\pi$
$54$	−2.05347	−0.279442
$55$	−7.60000	−1.02478
$56$	0.232224	0.0310323
$57$	4.52521	0.599378
$58$	16.1455	2.12000
$59$	−11.4691	−1.49315	−0.746574	−	0.665302i	$-0.768303\pi$
$59$	−11.4691	−1.49315	−0.746574	+	0.665302i	$0.768303\pi$
$60$	−4.75830	−0.614294
$61$	−14.9509	−1.91426	−0.957131	−	0.289656i	$-0.906459\pi$
$61$	−14.9509	−1.91426	−0.957131	+	0.289656i	$0.906459\pi$
$62$	13.1517	1.67026
$63$	−0.521799	−0.0657404
$64$	−9.62971	−1.20371
$65$	−7.90545	−0.980550
$66$	−7.27046	−0.894932
$67$	7.26313	0.887332	0.443666	−	0.896192i	$-0.353678\pi$
$67$	7.26313	0.887332	0.443666	+	0.896192i	$0.353678\pi$
$68$	0.891738	0.108139
$69$	3.27230	0.393938
$70$	−2.30001	−0.274904
$71$	6.02557	0.715104	0.357552	−	0.933893i	$-0.383611\pi$
$71$	6.02557	0.715104	0.357552	+	0.933893i	$0.383611\pi$
$72$	−0.445046	−0.0524492
$73$	−2.15465	−0.252182	−0.126091	−	0.992019i	$-0.540243\pi$
$73$	−2.15465	−0.252182	−0.126091	+	0.992019i	$0.540243\pi$
$74$	6.96408	0.809558
$75$	−0.392362	−0.0453060
$76$	10.0312	1.15065
$77$	−1.84747	−0.210539
$78$	−7.56267	−0.856303
$79$	−11.9725	−1.34701	−0.673506	−	0.739181i	$-0.735213\pi$
$79$	−11.9725	−1.34701	−0.673506	+	0.739181i	$0.735213\pi$
$80$	7.55490	0.844664
$81$	1.00000	0.111111
$82$	1.74583	0.192795
$83$	−9.54343	−1.04753	−0.523764	−	0.851863i	$-0.675473\pi$
$83$	−9.54343	−1.04753	−0.523764	+	0.851863i	$0.675473\pi$
$84$	−1.15669	−0.126205
$85$	−0.863503	−0.0936601
$86$	13.5310	1.45908
$87$	−7.86254	−0.842952
$88$	−1.57572	−0.167972
$89$	−4.83824	−0.512852	−0.256426	−	0.966564i	$-0.582545\pi$
$89$	−4.83824	−0.512852	−0.256426	+	0.966564i	$0.582545\pi$
$90$	4.40785	0.464628
$91$	−1.92172	−0.201451
$92$	7.25380	0.756261
$93$	−6.40461	−0.664127
$94$	−21.7592	−2.24429
$95$	−9.71354	−0.996588
$96$	8.11742	0.828480
$97$	−4.39676	−0.446423	−0.223211	−	0.974770i	$-0.571654\pi$
$97$	−4.39676	−0.446423	−0.223211	+	0.974770i	$0.571654\pi$
$98$	13.8152	1.39554
$99$	3.54058	0.355842
$100$	−0.869760	−0.0869760
$101$	8.47973	0.843765	0.421883	−	0.906651i	$-0.361369\pi$
$101$	8.47973	0.843765	0.421883	+	0.906651i	$0.361369\pi$
$102$	−0.826062	−0.0817923
$103$	5.84329	0.575756	0.287878	−	0.957667i	$-0.407050\pi$
$103$	5.84329	0.575756	0.287878	+	0.957667i	$0.407050\pi$
$104$	−1.63905	−0.160722
$105$	1.12006	0.109307
$106$	−4.76740	−0.463051
$107$	−6.46737	−0.625225	−0.312612	−	0.949881i	$-0.601204\pi$
$107$	−6.46737	−0.625225	−0.312612	+	0.949881i	$0.601204\pi$
$108$	2.21673	0.213305
$109$	−7.68041	−0.735650	−0.367825	−	0.929895i	$-0.619897\pi$
$109$	−7.68041	−0.735650	−0.367825	+	0.929895i	$0.619897\pi$
$110$	15.6064	1.48801
$111$	−3.39138	−0.321895
$112$	1.83651	0.173534
$113$	16.0942	1.51402	0.757008	−	0.653406i	$-0.226661\pi$
$113$	16.0942	1.51402	0.757008	+	0.653406i	$0.226661\pi$
$114$	−9.29236	−0.870310
$115$	−7.02412	−0.655003
$116$	−17.4291	−1.61825
$117$	3.68288	0.340482
$118$	23.5514	2.16808
$119$	−0.209907	−0.0192422
$120$	0.955309	0.0872074
$121$	1.53570	0.139609
$122$	30.7011	2.77955
$123$	−0.850189	−0.0766589
$124$	−14.1973	−1.27495
$125$	11.5749	1.03529
$126$	1.07150	0.0954565
$127$	−8.71240	−0.773100	−0.386550	−	0.922268i	$-0.626333\pi$
$127$	−8.71240	−0.773100	−0.386550	+	0.922268i	$0.626333\pi$
$128$	3.53946	0.312847
$129$	−6.58933	−0.580158
$130$	16.2336	1.42378
$131$	−5.65039	−0.493677	−0.246838	−	0.969057i	$-0.579392\pi$
$131$	−5.65039	−0.493677	−0.246838	+	0.969057i	$0.579392\pi$
$132$	7.84850	0.683125
$133$	−2.36125	−0.204746
$134$	−14.9146	−1.28842
$135$	−2.14654	−0.184745
$136$	−0.179032	−0.0153518
$137$	−7.93417	−0.677862	−0.338931	−	0.940811i	$-0.610065\pi$
$137$	−7.93417	−0.677862	−0.338931	+	0.940811i	$0.610065\pi$
$138$	−6.71956	−0.572007
$139$	16.4557	1.39575	0.697875	−	0.716219i	$-0.254129\pi$
$139$	16.4557	1.39575	0.697875	+	0.716219i	$0.254129\pi$
$140$	2.48287	0.209841
$141$	10.5963	0.892371
$142$	−12.3733	−1.03835
$143$	13.0395	1.09042
$144$	−3.51957	−0.293298
$145$	16.8773	1.40158
$146$	4.42450	0.366174
$147$	−6.72773	−0.554894
$148$	−7.51776	−0.617956
$149$	2.99358	0.245244	0.122622	−	0.992453i	$-0.460870\pi$
$149$	2.99358	0.245244	0.122622	+	0.992453i	$0.460870\pi$
$150$	0.805702	0.0657853
$151$	16.8918	1.37463	0.687316	−	0.726359i	$-0.258789\pi$
$151$	16.8918	1.37463	0.687316	+	0.726359i	$0.258789\pi$
$152$	−2.01392	−0.163351
$153$	0.402277	0.0325221
$154$	3.79372	0.305706
$155$	13.7478	1.10425
$156$	8.16394	0.653638
$157$	−19.2255	−1.53436	−0.767182	−	0.641429i	$-0.778342\pi$
$157$	−19.2255	−1.53436	−0.767182	+	0.641429i	$0.778342\pi$
$158$	24.5852	1.95589
$159$	2.32164	0.184118
$160$	−17.4244	−1.37752
$161$	−1.70748	−0.134568
$162$	−2.05347	−0.161336
$163$	9.30752	0.729021	0.364511	−	0.931199i	$-0.381236\pi$
$163$	9.30752	0.729021	0.364511	+	0.931199i	$0.381236\pi$
$164$	−1.88464	−0.147166
$165$	−7.60000	−0.591659
$166$	19.5971	1.52103
$167$	6.16830	0.477317	0.238659	−	0.971103i	$-0.423292\pi$
$167$	6.16830	0.477317	0.238659	+	0.971103i	$0.423292\pi$
$168$	0.232224	0.0179165
$169$	0.563578	0.0433522
$170$	1.77318	0.135996
$171$	4.52521	0.346051
$172$	−14.6068	−1.11375
$173$	−11.8646	−0.902051	−0.451025	−	0.892511i	$-0.648942\pi$
$173$	−11.8646	−0.902051	−0.451025	+	0.892511i	$0.648942\pi$
$174$	16.1455	1.22398
$175$	0.204734	0.0154764
$176$	−12.4613	−0.939307
$177$	−11.4691	−0.862069
$178$	9.93517	0.744672
$179$	5.85631	0.437721	0.218861	−	0.975756i	$-0.429766\pi$
$179$	5.85631	0.437721	0.218861	+	0.975756i	$0.429766\pi$
$180$	−4.75830	−0.354663
$181$	−10.3061	−0.766043	−0.383022	−	0.923739i	$-0.625117\pi$
$181$	−10.3061	−0.766043	−0.383022	+	0.923739i	$0.625117\pi$
$182$	3.94619	0.292511
$183$	−14.9509	−1.10520
$184$	−1.45632	−0.107362
$185$	7.27973	0.535216
$186$	13.1517	0.964326
$187$	1.42429	0.104155
$188$	23.4892	1.71312
$189$	−0.521799	−0.0379553
$190$	19.9464	1.44707
$191$	−14.2877	−1.03382	−0.516912	−	0.856039i	$-0.672918\pi$
$191$	−14.2877	−1.03382	−0.516912	+	0.856039i	$0.672918\pi$
$192$	−9.62971	−0.694964
$193$	15.3904	1.10783	0.553913	−	0.832575i	$-0.313134\pi$
$193$	15.3904	1.10783	0.553913	+	0.832575i	$0.313134\pi$
$194$	9.02860	0.648215
$195$	−7.90545	−0.566121
$196$	−14.9135	−1.06525
$197$	−7.97430	−0.568146	−0.284073	−	0.958803i	$-0.591686\pi$
$197$	−7.97430	−0.568146	−0.284073	+	0.958803i	$0.591686\pi$
$198$	−7.27046	−0.516689
$199$	16.2669	1.15313	0.576566	−	0.817051i	$-0.304393\pi$
$199$	16.2669	1.15313	0.576566	+	0.817051i	$0.304393\pi$
$200$	0.174619	0.0123474
$201$	7.26313	0.512302
$202$	−17.4129	−1.22516
$203$	4.10266	0.287950
$204$	0.891738	0.0624342
$205$	1.82496	0.127461
$206$	−11.9990	−0.836010
$207$	3.27230	0.227440
$208$	−12.9621	−0.898763
$209$	16.0219	1.10825
$210$	−2.30001	−0.158716
$211$	−12.7839	−0.880082	−0.440041	−	0.897978i	$-0.645036\pi$
$211$	−12.7839	−0.880082	−0.440041	+	0.897978i	$0.645036\pi$
$212$	5.14644	0.353459
$213$	6.02557	0.412866
$214$	13.2805	0.907839
$215$	14.1443	0.964631
$216$	−0.445046	−0.0302815
$217$	3.34192	0.226864
$218$	15.7715	1.06818
$219$	−2.15465	−0.145598
$220$	−16.8471	−1.13583
$221$	1.48154	0.0996588
$222$	6.96408	0.467399
$223$	9.01306	0.603559	0.301780	−	0.953378i	$-0.402419\pi$
$223$	9.01306	0.603559	0.301780	+	0.953378i	$0.402419\pi$
$224$	−4.23566	−0.283007
$225$	−0.392362	−0.0261574
$226$	−33.0489	−2.19838
$227$	19.7859	1.31324	0.656618	−	0.754223i	$-0.271986\pi$
$227$	19.7859	1.31324	0.656618	+	0.754223i	$0.271986\pi$
$228$	10.0312	0.664330
$229$	−5.42212	−0.358304	−0.179152	−	0.983821i	$-0.557335\pi$
$229$	−5.42212	−0.358304	−0.179152	+	0.983821i	$0.557335\pi$
$230$	14.4238	0.951078
$231$	−1.84747	−0.121555
$232$	3.49919	0.229733
$233$	5.42210	0.355214	0.177607	−	0.984102i	$-0.443164\pi$
$233$	5.42210	0.355214	0.177607	+	0.984102i	$0.443164\pi$
$234$	−7.56267	−0.494387
$235$	−22.7454	−1.48375
$236$	−25.4239	−1.65495
$237$	−11.9725	−0.777698
$238$	0.431038	0.0279400
$239$	26.1799	1.69344	0.846718	−	0.532042i	$-0.178575\pi$
$239$	26.1799	1.69344	0.846718	+	0.532042i	$0.178575\pi$
$240$	7.55490	0.487667
$241$	−30.2021	−1.94549	−0.972745	−	0.231879i	$-0.925513\pi$
$241$	−30.2021	−1.94549	−0.972745	+	0.231879i	$0.925513\pi$
$242$	−3.15351	−0.202716
$243$	1.00000	0.0641500
$244$	−33.1420	−2.12170
$245$	14.4413	0.922623
$246$	1.74583	0.111310
$247$	16.6658	1.06042
$248$	2.85034	0.180997
$249$	−9.54343	−0.604791
$250$	−23.7687	−1.50327
$251$	−17.6044	−1.11118	−0.555589	−	0.831457i	$-0.687507\pi$
$251$	−17.6044	−1.11118	−0.555589	+	0.831457i	$0.687507\pi$
$252$	−1.15669	−0.0728644
$253$	11.5858	0.728395
$254$	17.8906	1.12256
$255$	−0.863503	−0.0540747
$256$	11.9912	0.749453
$257$	−6.14564	−0.383355	−0.191677	−	0.981458i	$-0.561393\pi$
$257$	−6.14564	−0.383355	−0.191677	+	0.981458i	$0.561393\pi$
$258$	13.5310	0.842401
$259$	1.76962	0.109959
$260$	−17.5242	−1.08681
$261$	−7.86254	−0.486679
$262$	11.6029	0.716829
$263$	7.12856	0.439566	0.219783	−	0.975549i	$-0.429465\pi$
$263$	7.12856	0.439566	0.219783	+	0.975549i	$0.429465\pi$
$264$	−1.57572	−0.0969789
$265$	−4.98349	−0.306133
$266$	4.84874	0.297295
$267$	−4.83824	−0.296095
$268$	16.1004	0.983488
$269$	−4.62986	−0.282288	−0.141144	−	0.989989i	$-0.545078\pi$
$269$	−4.62986	−0.282288	−0.141144	+	0.989989i	$0.545078\pi$
$270$	4.40785	0.268253
$271$	19.5831	1.18959	0.594793	−	0.803879i	$-0.297234\pi$
$271$	19.5831	1.18959	0.594793	+	0.803879i	$0.297234\pi$
$272$	−1.41584	−0.0858480
$273$	−1.92172	−0.116308
$274$	16.2926	0.984270
$275$	−1.38919	−0.0837712
$276$	7.25380	0.436627
$277$	24.1876	1.45329	0.726646	−	0.687012i	$-0.241078\pi$
$277$	24.1876	1.45329	0.726646	+	0.687012i	$0.241078\pi$
$278$	−33.7912	−2.02666
$279$	−6.40461	−0.383434
$280$	−0.498479	−0.0297898
$281$	−28.1112	−1.67697	−0.838486	−	0.544923i	$-0.816559\pi$
$281$	−28.1112	−1.67697	−0.838486	+	0.544923i	$0.816559\pi$
$282$	−21.7592	−1.29574
$283$	−11.7571	−0.698890	−0.349445	−	0.936957i	$-0.613630\pi$
$283$	−11.7571	−0.698890	−0.349445	+	0.936957i	$0.613630\pi$
$284$	13.3571	0.792596
$285$	−9.71354	−0.575381
$286$	−26.7762	−1.58331
$287$	0.443627	0.0261865
$288$	8.11742	0.478323
$289$	−16.8382	−0.990481
$290$	−34.6569	−2.03512
$291$	−4.39676	−0.257742
$292$	−4.77627	−0.279510
$293$	−21.0537	−1.22997	−0.614984	−	0.788540i	$-0.710838\pi$
$293$	−21.0537	−1.22997	−0.614984	+	0.788540i	$0.710838\pi$
$294$	13.8152	0.805717
$295$	24.6189	1.43337
$296$	1.50932	0.0877273
$297$	3.54058	0.205445
$298$	−6.14722	−0.356099
$299$	12.0515	0.696955
$300$	−0.869760	−0.0502156
$301$	3.43830	0.198180
$302$	−34.6867	−1.99599
$303$	8.47973	0.487148
$304$	−15.9268	−0.913464
$305$	32.0926	1.83762
$306$	−0.826062	−0.0472228
$307$	−16.7762	−0.957469	−0.478735	−	0.877960i	$-0.658904\pi$
$307$	−16.7762	−0.957469	−0.478735	+	0.877960i	$0.658904\pi$
$308$	−4.09534	−0.233354
$309$	5.84329	0.332413
$310$	−28.2306	−1.60339
$311$	18.1254	1.02780	0.513898	−	0.857851i	$-0.328201\pi$
$311$	18.1254	1.02780	0.513898	+	0.857851i	$0.328201\pi$
$312$	−1.63905	−0.0927929
$313$	−26.4119	−1.49289	−0.746445	−	0.665447i	$-0.768241\pi$
$313$	−26.4119	−1.49289	−0.746445	+	0.665447i	$0.768241\pi$
$314$	39.4790	2.22793
$315$	1.12006	0.0631083
$316$	−26.5398	−1.49298
$317$	16.9909	0.954303	0.477151	−	0.878821i	$-0.341669\pi$
$317$	16.9909	0.954303	0.477151	+	0.878821i	$0.341669\pi$
$318$	−4.76740	−0.267343
$319$	−27.8379	−1.55863
$320$	20.6706	1.15552
$321$	−6.46737	−0.360974
$322$	3.50626	0.195396
$323$	1.82039	0.101289
$324$	2.21673	0.123152
$325$	−1.44502	−0.0801553
$326$	−19.1127	−1.05855
$327$	−7.68041	−0.424728
$328$	0.378373	0.0208921
$329$	−5.52914	−0.304831
$330$	15.6064	0.859101
$331$	−3.04302	−0.167260	−0.0836298	−	0.996497i	$-0.526651\pi$
$331$	−3.04302	−0.167260	−0.0836298	+	0.996497i	$0.526651\pi$
$332$	−21.1552	−1.16104
$333$	−3.39138	−0.185846
$334$	−12.6664	−0.693075
$335$	−15.5906	−0.851806
$336$	1.83651	0.100190
$337$	−21.3337	−1.16212	−0.581061	−	0.813860i	$-0.697362\pi$
$337$	−21.3337	−1.16212	−0.581061	+	0.813860i	$0.697362\pi$
$338$	−1.15729	−0.0629482
$339$	16.0942	0.874117
$340$	−1.91415	−0.103810
$341$	−22.6760	−1.22798
$342$	−9.29236	−0.502474
$343$	7.16311	0.386771
$344$	2.93255	0.158113
$345$	−7.02412	−0.378166
$346$	24.3636	1.30980
$347$	−11.8648	−0.636938	−0.318469	−	0.947933i	$-0.603169\pi$
$347$	−11.8648	−0.636938	−0.318469	+	0.947933i	$0.603169\pi$
$348$	−17.4291	−0.934298
$349$	28.2371	1.51150	0.755749	−	0.654861i	$-0.227273\pi$
$349$	28.2371	1.51150	0.755749	+	0.654861i	$0.227273\pi$
$350$	−0.420414	−0.0224721
$351$	3.68288	0.196577
$352$	28.7404	1.53187
$353$	−33.5110	−1.78361	−0.891804	−	0.452421i	$-0.850560\pi$
$353$	−33.5110	−1.78361	−0.891804	+	0.452421i	$0.850560\pi$
$354$	23.5514	1.25174
$355$	−12.9341	−0.686473
$356$	−10.7251	−0.568427
$357$	−0.209907	−0.0111095
$358$	−12.0258	−0.635581
$359$	−1.33542	−0.0704806	−0.0352403	−	0.999379i	$-0.511220\pi$
$359$	−1.33542	−0.0704806	−0.0352403	+	0.999379i	$0.511220\pi$
$360$	0.955309	0.0503492
$361$	1.47750	0.0777629
$362$	21.1632	1.11231
$363$	1.53570	0.0806035
$364$	−4.25993	−0.223281
$365$	4.62504	0.242086
$366$	30.7011	1.60477
$367$	−25.9769	−1.35598	−0.677991	−	0.735070i	$-0.737149\pi$
$367$	−25.9769	−1.35598	−0.677991	+	0.735070i	$0.737149\pi$
$368$	−11.5171	−0.600370
$369$	−0.850189	−0.0442591
$370$	−14.9487	−0.777145
$371$	−1.21143	−0.0628941
$372$	−14.1973	−0.736095
$373$	−21.6372	−1.12033	−0.560165	−	0.828381i	$-0.689262\pi$
$373$	−21.6372	−1.12033	−0.560165	+	0.828381i	$0.689262\pi$
$374$	−2.92474	−0.151235
$375$	11.5749	0.597727
$376$	−4.71585	−0.243201
$377$	−28.9567	−1.49135
$378$	1.07150	0.0551118
$379$	−37.2883	−1.91537	−0.957685	−	0.287819i	$-0.907070\pi$
$379$	−37.2883	−1.91537	−0.957685	+	0.287819i	$0.907070\pi$
$380$	−21.5323	−1.10458
$381$	−8.71240	−0.446350
$382$	29.3394	1.50113
$383$	16.2261	0.829113	0.414556	−	0.910024i	$-0.363937\pi$
$383$	16.2261	0.829113	0.414556	+	0.910024i	$0.363937\pi$
$384$	3.53946	0.180622
$385$	3.96567	0.202109
$386$	−31.6037	−1.60859
$387$	−6.58933	−0.334954
$388$	−9.74642	−0.494799
$389$	34.6592	1.75729	0.878646	−	0.477474i	$-0.158447\pi$
$389$	34.6592	1.75729	0.878646	+	0.477474i	$0.158447\pi$
$390$	16.2336	0.822019
$391$	1.31637	0.0665717
$392$	2.99415	0.151227
$393$	−5.65039	−0.285024
$394$	16.3750	0.824959
$395$	25.6995	1.29308
$396$	7.84850	0.394402
$397$	2.11890	0.106345	0.0531724	−	0.998585i	$-0.483067\pi$
$397$	2.11890	0.106345	0.0531724	+	0.998585i	$0.483067\pi$
$398$	−33.4036	−1.67437
$399$	−2.36125	−0.118210
$400$	1.38094	0.0690472
$401$	−6.78949	−0.339051	−0.169525	−	0.985526i	$-0.554223\pi$
$401$	−6.78949	−0.339051	−0.169525	+	0.985526i	$0.554223\pi$
$402$	−14.9146	−0.743873
$403$	−23.5874	−1.17497
$404$	18.7973	0.935199
$405$	−2.14654	−0.106662
$406$	−8.42468	−0.418110
$407$	−12.0074	−0.595187
$408$	−0.179032	−0.00886338
$409$	0.543720	0.0268852	0.0134426	−	0.999910i	$-0.495721\pi$
$409$	0.543720	0.0268852	0.0134426	+	0.999910i	$0.495721\pi$
$410$	−3.74751	−0.185076
$411$	−7.93417	−0.391364
$412$	12.9530	0.638148
$413$	5.98455	0.294481
$414$	−6.71956	−0.330248
$415$	20.4854	1.00559
$416$	29.8954	1.46574
$417$	16.4557	0.805837
$418$	−32.9004	−1.60921
$419$	−25.1042	−1.22642	−0.613210	−	0.789920i	$-0.710122\pi$
$419$	−25.1042	−1.22642	−0.613210	+	0.789920i	$0.710122\pi$
$420$	2.48287	0.121152
$421$	−11.3751	−0.554390	−0.277195	−	0.960814i	$-0.589405\pi$
$421$	−11.3751	−0.554390	−0.277195	+	0.960814i	$0.589405\pi$
$422$	26.2514	1.27790
$423$	10.5963	0.515211
$424$	−1.03323	−0.0501783
$425$	−0.157838	−0.00765627
$426$	−12.3733	−0.599489
$427$	7.80134	0.377533
$428$	−14.3364	−0.692977
$429$	13.0395	0.629554
$430$	−29.0448	−1.40066
$431$	−6.07924	−0.292827	−0.146413	−	0.989224i	$-0.546773\pi$
$431$	−6.07924	−0.292827	−0.146413	+	0.989224i	$0.546773\pi$
$432$	−3.51957	−0.169335
$433$	−16.1169	−0.774527	−0.387264	−	0.921969i	$-0.626580\pi$
$433$	−16.1169	−0.774527	−0.387264	+	0.921969i	$0.626580\pi$
$434$	−6.86252	−0.329411
$435$	16.8773	0.809203
$436$	−17.0254	−0.815368
$437$	14.8078	0.708354
$438$	4.42450	0.211411
$439$	37.1205	1.77167	0.885833	−	0.464005i	$-0.153588\pi$
$439$	37.1205	1.77167	0.885833	+	0.464005i	$0.153588\pi$
$440$	3.38235	0.161247
$441$	−6.72773	−0.320368
$442$	−3.04228	−0.144707
$443$	−35.0294	−1.66430	−0.832149	−	0.554551i	$-0.812890\pi$
$443$	−35.0294	−1.66430	−0.832149	+	0.554551i	$0.812890\pi$
$444$	−7.51776	−0.356777
$445$	10.3855	0.492319
$446$	−18.5080	−0.876381
$447$	2.99358	0.141591
$448$	5.02477	0.237398
$449$	34.4006	1.62347	0.811733	−	0.584028i	$-0.198524\pi$
$449$	34.4006	1.62347	0.811733	+	0.584028i	$0.198524\pi$
$450$	0.805702	0.0379812
$451$	−3.01016	−0.141743
$452$	35.6765	1.67808
$453$	16.8918	0.793644
$454$	−40.6297	−1.90685
$455$	4.12505	0.193385
$456$	−2.01392	−0.0943106
$457$	−37.5908	−1.75842	−0.879211	−	0.476433i	$-0.841930\pi$
$457$	−37.5908	−1.75842	−0.879211	+	0.476433i	$0.841930\pi$
$458$	11.1342	0.520265
$459$	0.402277	0.0187767
$460$	−15.5706	−0.725982
$461$	6.06375	0.282417	0.141208	−	0.989980i	$-0.454901\pi$
$461$	6.06375	0.282417	0.141208	+	0.989980i	$0.454901\pi$
$462$	3.79372	0.176500
$463$	−28.9548	−1.34564	−0.672822	−	0.739804i	$-0.734918\pi$
$463$	−28.9548	−1.34564	−0.672822	+	0.739804i	$0.734918\pi$
$464$	27.6728	1.28468
$465$	13.7478	0.637537
$466$	−11.1341	−0.515778
$467$	41.0902	1.90143	0.950715	−	0.310066i	$-0.100351\pi$
$467$	41.0902	1.90143	0.950715	+	0.310066i	$0.100351\pi$
$468$	8.16394	0.377378
$469$	−3.78989	−0.175001
$470$	46.7070	2.15443
$471$	−19.2255	−0.885866
$472$	5.10427	0.234943
$473$	−23.3300	−1.07272
$474$	24.5852	1.12923
$475$	−1.77552	−0.0814663
$476$	−0.465308	−0.0213273
$477$	2.32164	0.106300
$478$	−53.7596	−2.45890
$479$	−6.06917	−0.277308	−0.138654	−	0.990341i	$-0.544278\pi$
$479$	−6.06917	−0.277308	−0.138654	+	0.990341i	$0.544278\pi$
$480$	−17.4244	−0.795310
$481$	−12.4900	−0.569496
$482$	62.0191	2.82489
$483$	−1.70748	−0.0776931
$484$	3.40424	0.154738
$485$	9.43782	0.428549
$486$	−2.05347	−0.0931472
$487$	13.6996	0.620786	0.310393	−	0.950608i	$-0.399539\pi$
$487$	13.6996	0.620786	0.310393	+	0.950608i	$0.399539\pi$
$488$	6.65382	0.301204
$489$	9.30752	0.420901
$490$	−29.6548	−1.33967
$491$	4.83322	0.218120	0.109060	−	0.994035i	$-0.465216\pi$
$491$	4.83322	0.218120	0.109060	+	0.994035i	$0.465216\pi$
$492$	−1.88464	−0.0849660
$493$	−3.16292	−0.142451
$494$	−34.2226	−1.53975
$495$	−7.60000	−0.341595
$496$	22.5415	1.01214
$497$	−3.14414	−0.141034
$498$	19.5971	0.878168
$499$	13.5803	0.607936	0.303968	−	0.952682i	$-0.401688\pi$
$499$	13.5803	0.607936	0.303968	+	0.952682i	$0.401688\pi$
$500$	25.6585	1.14748
$501$	6.16830	0.275579
$502$	36.1500	1.61345
$503$	−25.7024	−1.14602	−0.573008	−	0.819550i	$-0.694223\pi$
$503$	−25.7024	−1.14602	−0.573008	+	0.819550i	$0.694223\pi$
$504$	0.232224	0.0103441
$505$	−18.2021	−0.809983
$506$	−23.7911	−1.05764
$507$	0.563578	0.0250294
$508$	−19.3130	−0.856877
$509$	11.1205	0.492908	0.246454	−	0.969154i	$-0.420735\pi$
$509$	11.1205	0.492908	0.246454	+	0.969154i	$0.420735\pi$
$510$	1.77318	0.0785176
$511$	1.12429	0.0497357
$512$	−31.7026	−1.40107
$513$	4.52521	0.199793
$514$	12.6199	0.556639
$515$	−12.5429	−0.552704
$516$	−14.6068	−0.643026
$517$	37.5171	1.65000
$518$	−3.63385	−0.159662
$519$	−11.8646	−0.520799
$520$	3.51829	0.154287
$521$	21.6559	0.948763	0.474382	−	0.880319i	$-0.342672\pi$
$521$	21.6559	0.948763	0.474382	+	0.880319i	$0.342672\pi$
$522$	16.1455	0.706668
$523$	21.5006	0.940156	0.470078	−	0.882625i	$-0.344226\pi$
$523$	21.5006	0.940156	0.470078	+	0.882625i	$0.344226\pi$
$524$	−12.5254	−0.547174
$525$	0.204734	0.00893531
$526$	−14.6383	−0.638259
$527$	−2.57642	−0.112231
$528$	−12.4613	−0.542309
$529$	−12.2921	−0.534438
$530$	10.2334	0.444512
$531$	−11.4691	−0.497716
$532$	−5.23424	−0.226933
$533$	−3.13114	−0.135625
$534$	9.93517	0.429937
$535$	13.8825	0.600192
$536$	−3.23242	−0.139619
$537$	5.85631	0.252719
$538$	9.50728	0.409888
$539$	−23.8200	−1.02600
$540$	−4.75830	−0.204765
$541$	−10.7539	−0.462345	−0.231172	−	0.972913i	$-0.574256\pi$
$541$	−10.7539	−0.462345	−0.231172	+	0.972913i	$0.574256\pi$
$542$	−40.2132	−1.72730
$543$	−10.3061	−0.442275
$544$	3.26545	0.140005
$545$	16.4863	0.706196
$546$	3.94619	0.168881
$547$	−28.7513	−1.22932	−0.614659	−	0.788793i	$-0.710706\pi$
$547$	−28.7513	−1.22932	−0.614659	+	0.788793i	$0.710706\pi$
$548$	−17.5879	−0.751318
$549$	−14.9509	−0.638087
$550$	2.85265	0.121637
$551$	−35.5796	−1.51574
$552$	−1.45632	−0.0619852
$553$	6.24724	0.265660
$554$	−49.6685	−2.11021
$555$	7.27973	0.309007
$556$	36.4777	1.54700
$557$	30.6476	1.29858	0.649290	−	0.760541i	$-0.275066\pi$
$557$	30.6476	1.29858	0.649290	+	0.760541i	$0.275066\pi$
$558$	13.1517	0.556754
$559$	−24.2677	−1.02641
$560$	−3.94214	−0.166586
$561$	1.42429	0.0601337
$562$	57.7254	2.43500
$563$	−3.30199	−0.139162	−0.0695811	−	0.997576i	$-0.522166\pi$
$563$	−3.30199	−0.139162	−0.0695811	+	0.997576i	$0.522166\pi$
$564$	23.4892	0.989072
$565$	−34.5469	−1.45340
$566$	24.1429	1.01480
$567$	−0.521799	−0.0219135
$568$	−2.68166	−0.112520
$569$	34.6100	1.45093	0.725463	−	0.688261i	$-0.241625\pi$
$569$	34.6100	1.45093	0.725463	+	0.688261i	$0.241625\pi$
$570$	19.9464	0.835465
$571$	10.6717	0.446595	0.223298	−	0.974750i	$-0.428318\pi$
$571$	10.6717	0.446595	0.223298	+	0.974750i	$0.428318\pi$
$572$	28.9051	1.20858
$573$	−14.2877	−0.596878
$574$	−0.910974	−0.0380233
$575$	−1.28392	−0.0535434
$576$	−9.62971	−0.401238
$577$	−29.4790	−1.22723	−0.613614	−	0.789606i	$-0.710285\pi$
$577$	−29.4790	−1.22723	−0.613614	+	0.789606i	$0.710285\pi$
$578$	34.5766	1.43820
$579$	15.3904	0.639604
$580$	37.4123	1.55346
$581$	4.97975	0.206595
$582$	9.02860	0.374247
$583$	8.21993	0.340435
$584$	0.958917	0.0396802
$585$	−7.90545	−0.326850
$586$	43.2330	1.78594
$587$	−23.4063	−0.966083	−0.483042	−	0.875597i	$-0.660468\pi$
$587$	−23.4063	−0.966083	−0.483042	+	0.875597i	$0.660468\pi$
$588$	−14.9135	−0.615024
$589$	−28.9822	−1.19419
$590$	−50.5540	−2.08128
$591$	−7.97430	−0.328019
$592$	11.9362	0.490574
$593$	46.6659	1.91634	0.958170	−	0.286199i	$-0.0923918\pi$
$593$	46.6659	1.91634	0.958170	+	0.286199i	$0.0923918\pi$
$594$	−7.27046	−0.298311
$595$	0.450575	0.0184718
$596$	6.63596	0.271819
$597$	16.2669	0.665760
$598$	−24.7473	−1.01199
$599$	22.4457	0.917107	0.458554	−	0.888667i	$-0.348368\pi$
$599$	22.4457	0.917107	0.458554	+	0.888667i	$0.348368\pi$
$600$	0.174619	0.00712879
$601$	48.6847	1.98589	0.992946	−	0.118571i	$-0.0378312\pi$
$601$	48.6847	1.98589	0.992946	+	0.118571i	$0.0378312\pi$
$602$	−7.06044	−0.287762
$603$	7.26313	0.295777
$604$	37.4444	1.52359
$605$	−3.29645	−0.134020
$606$	−17.4129	−0.707349
$607$	41.1706	1.67106	0.835531	−	0.549443i	$-0.185160\pi$
$607$	41.1706	1.67106	0.835531	+	0.549443i	$0.185160\pi$
$608$	36.7330	1.48972
$609$	4.10266	0.166248
$610$	−65.9012	−2.66826
$611$	39.0249	1.57878
$612$	0.891738	0.0360464
$613$	−32.7224	−1.32164	−0.660822	−	0.750542i	$-0.729792\pi$
$613$	−32.7224	−1.32164	−0.660822	+	0.750542i	$0.729792\pi$
$614$	34.4494	1.39027
$615$	1.82496	0.0735897
$616$	0.822208	0.0331277
$617$	4.32227	0.174008	0.0870039	−	0.996208i	$-0.472271\pi$
$617$	4.32227	0.174008	0.0870039	+	0.996208i	$0.472271\pi$
$618$	−11.9990	−0.482671
$619$	29.4327	1.18300	0.591501	−	0.806304i	$-0.298536\pi$
$619$	29.4327	1.18300	0.591501	+	0.806304i	$0.298536\pi$
$620$	30.4750	1.22391
$621$	3.27230	0.131313
$622$	−37.2199	−1.49238
$623$	2.52459	0.101145
$624$	−12.9621	−0.518901
$625$	−22.8842	−0.915370
$626$	54.2360	2.16771
$627$	16.0219	0.639851
$628$	−42.6178	−1.70063
$629$	−1.36427	−0.0543971
$630$	−2.30001	−0.0916346
$631$	−35.7358	−1.42262	−0.711310	−	0.702879i	$-0.751898\pi$
$631$	−35.7358	−1.42262	−0.711310	+	0.702879i	$0.751898\pi$
$632$	5.32832	0.211949
$633$	−12.7839	−0.508115
$634$	−34.8902	−1.38567
$635$	18.7015	0.742147
$636$	5.14644	0.204069
$637$	−24.7774	−0.981716
$638$	57.1643	2.26316
$639$	6.02557	0.238368
$640$	−7.59760	−0.300322
$641$	0.373113	0.0147371	0.00736854	−	0.999973i	$-0.497654\pi$
$641$	0.373113	0.0147371	0.00736854	+	0.999973i	$0.497654\pi$
$642$	13.2805	0.524141
$643$	5.87009	0.231494	0.115747	−	0.993279i	$-0.463074\pi$
$643$	5.87009	0.231494	0.115747	+	0.993279i	$0.463074\pi$
$644$	−3.78502	−0.149151
$645$	14.1443	0.556930
$646$	−3.73810	−0.147074
$647$	26.1307	1.02730	0.513652	−	0.857999i	$-0.328292\pi$
$647$	26.1307	1.02730	0.513652	+	0.857999i	$0.328292\pi$
$648$	−0.445046	−0.0174831
$649$	−40.6072	−1.59397
$650$	2.96730	0.116387
$651$	3.34192	0.130980
$652$	20.6322	0.808021
$653$	−8.37428	−0.327711	−0.163855	−	0.986484i	$-0.552393\pi$
$653$	−8.37428	−0.327711	−0.163855	+	0.986484i	$0.552393\pi$
$654$	15.7715	0.616713
$655$	12.1288	0.473911
$656$	2.99230	0.116830
$657$	−2.15465	−0.0840608
$658$	11.3539	0.442622
$659$	34.7678	1.35436	0.677180	−	0.735818i	$-0.263202\pi$
$659$	34.7678	1.35436	0.677180	+	0.735818i	$0.263202\pi$
$660$	−16.8471	−0.655774
$661$	−6.38487	−0.248343	−0.124171	−	0.992261i	$-0.539627\pi$
$661$	−6.38487	−0.248343	−0.124171	+	0.992261i	$0.539627\pi$
$662$	6.24875	0.242864
$663$	1.48154	0.0575381
$664$	4.24727	0.164826
$665$	5.06851	0.196548
$666$	6.96408	0.269853
$667$	−25.7286	−0.996214
$668$	13.6735	0.529042
$669$	9.01306	0.348465
$670$	32.0148	1.23684
$671$	−52.9347	−2.04352
$672$	−4.23566	−0.163394
$673$	−4.14979	−0.159963	−0.0799814	−	0.996796i	$-0.525486\pi$
$673$	−4.14979	−0.159963	−0.0799814	+	0.996796i	$0.525486\pi$
$674$	43.8081	1.68743
$675$	−0.392362	−0.0151020
$676$	1.24930	0.0480500
$677$	−28.0584	−1.07837	−0.539186	−	0.842187i	$-0.681268\pi$
$677$	−28.0584	−1.07837	−0.539186	+	0.842187i	$0.681268\pi$
$678$	−33.0489	−1.26924
$679$	2.29422	0.0880441
$680$	0.384299	0.0147372
$681$	19.7859	0.758197
$682$	46.5645	1.78305
$683$	−37.1331	−1.42086	−0.710430	−	0.703768i	$-0.751500\pi$
$683$	−37.1331	−1.42086	−0.710430	+	0.703768i	$0.751500\pi$
$684$	10.0312	0.383551
$685$	17.0310	0.650722
$686$	−14.7092	−0.561600
$687$	−5.42212	−0.206867
$688$	23.1916	0.884172
$689$	8.55030	0.325740
$690$	14.4238	0.549105
$691$	21.4507	0.816022	0.408011	−	0.912977i	$-0.366222\pi$
$691$	21.4507	0.816022	0.408011	+	0.912977i	$0.366222\pi$
$692$	−26.3007	−0.999801
$693$	−1.84747	−0.0701795
$694$	24.3641	0.924847
$695$	−35.3227	−1.33987
$696$	3.49919	0.132636
$697$	−0.342011	−0.0129546
$698$	−57.9840	−2.19473
$699$	5.42210	0.205083
$700$	0.453839	0.0171535
$701$	−11.1081	−0.419548	−0.209774	−	0.977750i	$-0.567273\pi$
$701$	−11.1081	−0.419548	−0.209774	+	0.977750i	$0.567273\pi$
$702$	−7.56267	−0.285434
$703$	−15.3467	−0.578811
$704$	−34.0947	−1.28499
$705$	−22.7454	−0.856642
$706$	68.8137	2.58984
$707$	−4.42471	−0.166408
$708$	−25.4239	−0.955487
$709$	−0.657239	−0.0246831	−0.0123416	−	0.999924i	$-0.503929\pi$
$709$	−0.657239	−0.0246831	−0.0123416	+	0.999924i	$0.503929\pi$
$710$	26.5598	0.996773
$711$	−11.9725	−0.449004
$712$	2.15324	0.0806960
$713$	−20.9578	−0.784875
$714$	0.431038	0.0161312
$715$	−27.9899	−1.04676
$716$	12.9819	0.485155
$717$	26.1799	0.977706
$718$	2.74224	0.102339
$719$	−19.3450	−0.721448	−0.360724	−	0.932673i	$-0.617470\pi$
$719$	−19.3450	−0.721448	−0.360724	+	0.932673i	$0.617470\pi$
$720$	7.55490	0.281555
$721$	−3.04902	−0.113551
$722$	−3.03399	−0.112913
$723$	−30.2021	−1.12323
$724$	−22.8457	−0.849055
$725$	3.08496	0.114572
$726$	−3.15351	−0.117038
$727$	−1.55799	−0.0577828	−0.0288914	−	0.999583i	$-0.509198\pi$
$727$	−1.55799	−0.0577828	−0.0288914	+	0.999583i	$0.509198\pi$
$728$	0.855253	0.0316978
$729$	1.00000	0.0370370
$730$	−9.49736	−0.351513
$731$	−2.65073	−0.0980409
$732$	−33.1420	−1.22496
$733$	36.9526	1.36487	0.682437	−	0.730944i	$-0.260920\pi$
$733$	36.9526	1.36487	0.682437	+	0.730944i	$0.260920\pi$
$734$	53.3427	1.96892
$735$	14.4413	0.532677
$736$	26.5626	0.979111
$737$	25.7157	0.947249
$738$	1.74583	0.0642651
$739$	−45.4518	−1.67197	−0.835986	−	0.548751i	$-0.815104\pi$
$739$	−45.4518	−1.67197	−0.835986	+	0.548751i	$0.815104\pi$
$740$	16.1372	0.593215
$741$	16.6658	0.612233
$742$	2.48762	0.0913235
$743$	−39.1323	−1.43563	−0.717813	−	0.696236i	$-0.754857\pi$
$743$	−39.1323	−1.43563	−0.717813	+	0.696236i	$0.754857\pi$
$744$	2.85034	0.104499
$745$	−6.42584	−0.235425
$746$	44.4312	1.62674
$747$	−9.54343	−0.349176
$748$	3.15727	0.115441
$749$	3.37467	0.123308
$750$	−23.7687	−0.867911
$751$	37.5037	1.36853	0.684265	−	0.729234i	$-0.260123\pi$
$751$	37.5037	1.36853	0.684265	+	0.729234i	$0.260123\pi$
$752$	−37.2945	−1.35999
$753$	−17.6044	−0.641539
$754$	59.4617	2.16547
$755$	−36.2588	−1.31959
$756$	−1.15669	−0.0420683
$757$	−44.5878	−1.62057	−0.810286	−	0.586035i	$-0.800688\pi$
$757$	−44.5878	−1.62057	−0.810286	+	0.586035i	$0.800688\pi$
$758$	76.5703	2.78116
$759$	11.5858	0.420539
$760$	4.32297	0.156811
$761$	−10.8445	−0.393111	−0.196556	−	0.980493i	$-0.562976\pi$
$761$	−10.8445	−0.393111	−0.196556	+	0.980493i	$0.562976\pi$
$762$	17.8906	0.648109
$763$	4.00763	0.145086
$764$	−31.6720	−1.14585
$765$	−0.863503	−0.0312200
$766$	−33.3197	−1.20389
$767$	−42.2392	−1.52517
$768$	11.9912	0.432697
$769$	13.2764	0.478760	0.239380	−	0.970926i	$-0.423056\pi$
$769$	13.2764	0.478760	0.239380	+	0.970926i	$0.423056\pi$
$770$	−8.14337	−0.293467
$771$	−6.14564	−0.221330
$772$	34.1164	1.22787
$773$	−21.3908	−0.769375	−0.384687	−	0.923047i	$-0.625691\pi$
$773$	−21.3908	−0.769375	−0.384687	+	0.923047i	$0.625691\pi$
$774$	13.5310	0.486361
$775$	2.51292	0.0902669
$776$	1.95676	0.0702435
$777$	1.76962	0.0634846
$778$	−71.1716	−2.55162
$779$	−3.84728	−0.137843
$780$	−17.5242	−0.627468
$781$	21.3340	0.763391
$782$	−2.70312	−0.0966634
$783$	−7.86254	−0.280984
$784$	23.6787	0.845668
$785$	41.2684	1.47293
$786$	11.6029	0.413861
$787$	35.4757	1.26457	0.632286	−	0.774735i	$-0.282117\pi$
$787$	35.4757	1.26457	0.632286	+	0.774735i	$0.282117\pi$
$788$	−17.6769	−0.629712
$789$	7.12856	0.253783
$790$	−52.7731	−1.87758
$791$	−8.39793	−0.298596
$792$	−1.57572	−0.0559908
$793$	−55.0622	−1.95532
$794$	−4.35110	−0.154415
$795$	−4.98349	−0.176746
$796$	36.0593	1.27809
$797$	25.9837	0.920388	0.460194	−	0.887818i	$-0.347780\pi$
$797$	25.9837	0.920388	0.460194	+	0.887818i	$0.347780\pi$
$798$	4.84874	0.171644
$799$	4.26265	0.150802
$800$	−3.18496	−0.112605
$801$	−4.83824	−0.170951
$802$	13.9420	0.492309
$803$	−7.62870	−0.269211
$804$	16.1004	0.567817
$805$	3.66518	0.129181
$806$	48.4359	1.70608
$807$	−4.62986	−0.162979
$808$	−3.77387	−0.132764
$809$	−20.5082	−0.721031	−0.360515	−	0.932753i	$-0.617399\pi$
$809$	−20.5082	−0.721031	−0.360515	+	0.932753i	$0.617399\pi$
$810$	4.40785	0.154876
$811$	−38.7796	−1.36174	−0.680868	−	0.732406i	$-0.738397\pi$
$811$	−38.7796	−1.36174	−0.680868	+	0.732406i	$0.738397\pi$
$812$	9.09449	0.319154
$813$	19.5831	0.686808
$814$	24.6569	0.864223
$815$	−19.9790	−0.699833
$816$	−1.41584	−0.0495644
$817$	−29.8181	−1.04320
$818$	−1.11651	−0.0390379
$819$	−1.92172	−0.0671503
$820$	4.04545	0.141273
$821$	−55.2222	−1.92727	−0.963634	−	0.267227i	$-0.913893\pi$
$821$	−55.2222	−1.92727	−0.963634	+	0.267227i	$0.913893\pi$
$822$	16.2926	0.568268
$823$	10.9005	0.379969	0.189984	−	0.981787i	$-0.439156\pi$
$823$	10.9005	0.379969	0.189984	+	0.981787i	$0.439156\pi$
$824$	−2.60053	−0.0905938
$825$	−1.38919	−0.0483653
$826$	−12.2891	−0.427592
$827$	−21.7881	−0.757647	−0.378823	−	0.925469i	$-0.623671\pi$
$827$	−21.7881	−0.757647	−0.378823	+	0.925469i	$0.623671\pi$
$828$	7.25380	0.252087
$829$	8.14420	0.282860	0.141430	−	0.989948i	$-0.454830\pi$
$829$	8.14420	0.282860	0.141430	+	0.989948i	$0.454830\pi$
$830$	−42.0660	−1.46013
$831$	24.1876	0.839059
$832$	−35.4650	−1.22953
$833$	−2.70641	−0.0937715
$834$	−33.7912	−1.17009
$835$	−13.2405	−0.458207
$836$	35.5161	1.22835
$837$	−6.40461	−0.221376
$838$	51.5507	1.78079
$839$	−33.8308	−1.16797	−0.583984	−	0.811765i	$-0.698507\pi$
$839$	−33.8308	−1.16797	−0.583984	+	0.811765i	$0.698507\pi$
$840$	−0.498479	−0.0171992
$841$	32.8195	1.13171
$842$	23.3585	0.804986
$843$	−28.1112	−0.968201
$844$	−28.3385	−0.975451
$845$	−1.20974	−0.0416164
$846$	−21.7592	−0.748096
$847$	−0.801327	−0.0275339
$848$	−8.17116	−0.280599
$849$	−11.7571	−0.403504
$850$	0.324115	0.0111171
$851$	−11.0976	−0.380421
$852$	13.3571	0.457606
$853$	−6.99307	−0.239438	−0.119719	−	0.992808i	$-0.538199\pi$
$853$	−6.99307	−0.239438	−0.119719	+	0.992808i	$0.538199\pi$
$854$	−16.0198	−0.548186
$855$	−9.71354	−0.332196
$856$	2.87828	0.0983775
$857$	26.0713	0.890579	0.445289	−	0.895387i	$-0.353101\pi$
$857$	26.0713	0.890579	0.445289	+	0.895387i	$0.353101\pi$
$858$	−26.7762	−0.914125
$859$	55.1495	1.88168	0.940838	−	0.338857i	$-0.110040\pi$
$859$	55.1495	1.88168	0.940838	+	0.338857i	$0.110040\pi$
$860$	31.3540	1.06916
$861$	0.443627	0.0151188
$862$	12.4835	0.425190
$863$	−18.6937	−0.636342	−0.318171	−	0.948033i	$-0.603069\pi$
$863$	−18.6937	−0.636342	−0.318171	+	0.948033i	$0.603069\pi$
$864$	8.11742	0.276160
$865$	25.4679	0.865935
$866$	33.0955	1.12463
$867$	−16.8382	−0.571854
$868$	7.40812	0.251448
$869$	−42.3896	−1.43797
$870$	−34.6569	−1.17498
$871$	26.7492	0.906362
$872$	3.41813	0.115753
$873$	−4.39676	−0.148808
$874$	−30.4074	−1.02855
$875$	−6.03978	−0.204182
$876$	−4.77627	−0.161375
$877$	−4.07063	−0.137455	−0.0687277	−	0.997635i	$-0.521894\pi$
$877$	−4.07063	−0.137455	−0.0687277	+	0.997635i	$0.521894\pi$
$878$	−76.2258	−2.57249
$879$	−21.0537	−0.710122
$880$	26.7487	0.901700
$881$	14.6664	0.494122	0.247061	−	0.969000i	$-0.420535\pi$
$881$	14.6664	0.494122	0.247061	+	0.969000i	$0.420535\pi$
$882$	13.8152	0.465181
$883$	31.3510	1.05505	0.527523	−	0.849541i	$-0.323121\pi$
$883$	31.3510	1.05505	0.527523	+	0.849541i	$0.323121\pi$
$884$	3.28416	0.110458
$885$	24.6189	0.827554
$886$	71.9318	2.41660
$887$	−20.7150	−0.695542	−0.347771	−	0.937580i	$-0.613061\pi$
$887$	−20.7150	−0.695542	−0.347771	+	0.937580i	$0.613061\pi$
$888$	1.50932	0.0506494
$889$	4.54612	0.152472
$890$	−21.3262	−0.714857
$891$	3.54058	0.118614
$892$	19.9795	0.668964
$893$	47.9505	1.60460
$894$	−6.14722	−0.205594
$895$	−12.5708	−0.420196
$896$	−1.84689	−0.0617001
$897$	12.0515	0.402387
$898$	−70.6406	−2.35731
$899$	50.3565	1.67948
$900$	−0.869760	−0.0289920
$901$	0.933940	0.0311140
$902$	6.18127	0.205814
$903$	3.43830	0.114419
$904$	−7.16266	−0.238226
$905$	22.1224	0.735373
$906$	−34.6867	−1.15239
$907$	−53.0463	−1.76137	−0.880687	−	0.473699i	$-0.842919\pi$
$907$	−53.0463	−1.76137	−0.880687	+	0.473699i	$0.842919\pi$
$908$	43.8600	1.45554
$909$	8.47973	0.281255
$910$	−8.47066	−0.280799
$911$	16.1472	0.534981	0.267491	−	0.963560i	$-0.413806\pi$
$911$	16.1472	0.534981	0.267491	+	0.963560i	$0.413806\pi$
$912$	−15.9268	−0.527389
$913$	−33.7893	−1.11826
$914$	77.1914	2.55327
$915$	32.0926	1.06095
$916$	−12.0194	−0.397131
$917$	2.94836	0.0973635
$918$	−0.826062	−0.0272641
$919$	−0.0752442	−0.00248208	−0.00124104	−	0.999999i	$-0.500395\pi$
$919$	−0.0752442	−0.00248208	−0.00124104	+	0.999999i	$0.500395\pi$
$920$	3.12606	0.103063
$921$	−16.7762	−0.552795
$922$	−12.4517	−0.410075
$923$	22.1914	0.730440
$924$	−4.09534	−0.134727
$925$	1.33065	0.0437514
$926$	59.4578	1.95390
$927$	5.84329	0.191919
$928$	−63.8235	−2.09511
$929$	−23.3660	−0.766614	−0.383307	−	0.923621i	$-0.625215\pi$
$929$	−23.3660	−0.766614	−0.383307	+	0.923621i	$0.625215\pi$
$930$	−28.2306	−0.925717
$931$	−30.4444	−0.997773
$932$	12.0193	0.393706
$933$	18.1254	0.593399
$934$	−84.3775	−2.76092
$935$	−3.05730	−0.0999845
$936$	−1.63905	−0.0535740
$937$	−36.8868	−1.20504	−0.602520	−	0.798104i	$-0.705836\pi$
$937$	−36.8868	−1.20504	−0.602520	+	0.798104i	$0.705836\pi$
$938$	7.78242	0.254105
$939$	−26.4119	−0.861920
$940$	−50.4204	−1.64453
$941$	−25.9040	−0.844448	−0.422224	−	0.906492i	$-0.638750\pi$
$941$	−25.9040	−0.844448	−0.422224	+	0.906492i	$0.638750\pi$
$942$	39.4790	1.28630
$943$	−2.78207	−0.0905967
$944$	40.3663	1.31381
$945$	1.12006	0.0364356
$946$	47.9075	1.55761
$947$	33.9697	1.10387	0.551933	−	0.833888i	$-0.313890\pi$
$947$	33.9697	1.10387	0.551933	+	0.833888i	$0.313890\pi$
$948$	−26.5398	−0.861973
$949$	−7.93530	−0.257591
$950$	3.64597	0.118291
$951$	16.9909	0.550967
$952$	0.0934184	0.00302771
$953$	−24.4408	−0.791715	−0.395857	−	0.918312i	$-0.629553\pi$
$953$	−24.4408	−0.791715	−0.395857	+	0.918312i	$0.629553\pi$
$954$	−4.76740	−0.154350
$955$	30.6692	0.992431
$956$	58.0337	1.87694
$957$	−27.8379	−0.899873
$958$	12.4628	0.402656
$959$	4.14004	0.133689
$960$	20.6706	0.667140
$961$	10.0190	0.323194
$962$	25.6479	0.826920
$963$	−6.46737	−0.208408
$964$	−66.9499	−2.15631
$965$	−33.0361	−1.06347
$966$	3.50626	0.112812
$967$	13.7015	0.440610	0.220305	−	0.975431i	$-0.429295\pi$
$967$	13.7015	0.440610	0.220305	+	0.975431i	$0.429295\pi$
$968$	−0.683458	−0.0219672
$969$	1.82039	0.0584792
$970$	−19.3802	−0.622262
$971$	5.34728	0.171602	0.0858012	−	0.996312i	$-0.472655\pi$
$971$	5.34728	0.171602	0.0858012	+	0.996312i	$0.472655\pi$
$972$	2.21673	0.0711016
$973$	−8.58654	−0.275272
$974$	−28.1316	−0.901395
$975$	−1.44502	−0.0462777
$976$	52.6206	1.68434
$977$	1.61821	0.0517712	0.0258856	−	0.999665i	$-0.491759\pi$
$977$	1.61821	0.0517712	0.0258856	+	0.999665i	$0.491759\pi$
$978$	−19.1127	−0.611156
$979$	−17.1302	−0.547483
$980$	32.0125	1.02260
$981$	−7.68041	−0.245217
$982$	−9.92485	−0.316715
$983$	−31.8979	−1.01738	−0.508692	−	0.860948i	$-0.669871\pi$
$983$	−31.8979	−1.01738	−0.508692	+	0.860948i	$0.669871\pi$
$984$	0.378373	0.0120621
$985$	17.1172	0.545398
$986$	6.49494	0.206841
$987$	−5.52914	−0.175995
$988$	36.9435	1.17533
$989$	−21.5622	−0.685639
$990$	15.6064	0.496002
$991$	11.8792	0.377355	0.188677	−	0.982039i	$-0.439580\pi$
$991$	11.8792	0.377355	0.188677	+	0.982039i	$0.439580\pi$
$992$	−51.9889	−1.65065
$993$	−3.04302	−0.0965674
$994$	6.45638	0.204784
$995$	−34.9176	−1.10696
$996$	−21.1552	−0.670328
$997$	−5.82400	−0.184448	−0.0922239	−	0.995738i	$-0.529398\pi$
$997$	−5.82400	−0.184448	−0.0922239	+	0.995738i	$0.529398\pi$
$998$	−27.8866	−0.882736
$999$	−3.39138	−0.107298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.a.1.17	✓	94

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.a.1.17	✓	94	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)

\(f(q)\)	\(=\)	\(q-2.05347 q^{2} +1.00000 q^{3} +2.21673 q^{4} -2.14654 q^{5} -2.05347 q^{6} -0.521799 q^{7} -0.445046 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.05347 q^{2} +1.00000 q^{3} +2.21673 q^{4} -2.14654 q^{5} -2.05347 q^{6} -0.521799 q^{7} -0.445046 q^{8} +1.00000 q^{9} +4.40785 q^{10} +3.54058 q^{11} +2.21673 q^{12} +3.68288 q^{13} +1.07150 q^{14} -2.14654 q^{15} -3.51957 q^{16} +0.402277 q^{17} -2.05347 q^{18} +4.52521 q^{19} -4.75830 q^{20} -0.521799 q^{21} -7.27046 q^{22} +3.27230 q^{23} -0.445046 q^{24} -0.392362 q^{25} -7.56267 q^{26} +1.00000 q^{27} -1.15669 q^{28} -7.86254 q^{29} +4.40785 q^{30} -6.40461 q^{31} +8.11742 q^{32} +3.54058 q^{33} -0.826062 q^{34} +1.12006 q^{35} +2.21673 q^{36} -3.39138 q^{37} -9.29236 q^{38} +3.68288 q^{39} +0.955309 q^{40} -0.850189 q^{41} +1.07150 q^{42} -6.58933 q^{43} +7.84850 q^{44} -2.14654 q^{45} -6.71956 q^{46} +10.5963 q^{47} -3.51957 q^{48} -6.72773 q^{49} +0.805702 q^{50} +0.402277 q^{51} +8.16394 q^{52} +2.32164 q^{53} -2.05347 q^{54} -7.60000 q^{55} +0.232224 q^{56} +4.52521 q^{57} +16.1455 q^{58} -11.4691 q^{59} -4.75830 q^{60} -14.9509 q^{61} +13.1517 q^{62} -0.521799 q^{63} -9.62971 q^{64} -7.90545 q^{65} -7.27046 q^{66} +7.26313 q^{67} +0.891738 q^{68} +3.27230 q^{69} -2.30001 q^{70} +6.02557 q^{71} -0.445046 q^{72} -2.15465 q^{73} +6.96408 q^{74} -0.392362 q^{75} +10.0312 q^{76} -1.84747 q^{77} -7.56267 q^{78} -11.9725 q^{79} +7.55490 q^{80} +1.00000 q^{81} +1.74583 q^{82} -9.54343 q^{83} -1.15669 q^{84} -0.863503 q^{85} +13.5310 q^{86} -7.86254 q^{87} -1.57572 q^{88} -4.83824 q^{89} +4.40785 q^{90} -1.92172 q^{91} +7.25380 q^{92} -6.40461 q^{93} -21.7592 q^{94} -9.71354 q^{95} +8.11742 q^{96} -4.39676 q^{97} +13.8152 q^{98} +3.54058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9} - 39 q^{10} - 49 q^{11} + 73 q^{12} - 52 q^{13} - 7 q^{14} - 14 q^{15} + 43 q^{16} - 22 q^{17} - 13 q^{18} - 89 q^{19} - 22 q^{20} - 55 q^{21} - 36 q^{22} - 46 q^{23} - 36 q^{24} + 18 q^{25} + q^{26} + 94 q^{27} - 123 q^{28} - 20 q^{29} - 39 q^{30} - 61 q^{31} - 65 q^{32} - 49 q^{33} - 67 q^{34} - 40 q^{35} + 73 q^{36} - 83 q^{37} - 19 q^{38} - 52 q^{39} - 101 q^{40} - 25 q^{41} - 7 q^{42} - 150 q^{43} - 71 q^{44} - 14 q^{45} - 72 q^{46} - 39 q^{47} + 43 q^{48} - q^{49} - 45 q^{50} - 22 q^{51} - 110 q^{52} - 30 q^{53} - 13 q^{54} - 54 q^{55} - 5 q^{56} - 89 q^{57} - 77 q^{58} - 43 q^{59} - 22 q^{60} - 109 q^{61} - 33 q^{62} - 55 q^{63} + 10 q^{64} - 66 q^{65} - 36 q^{66} - 155 q^{67} - 46 q^{68} - 46 q^{69} - 43 q^{70} - 27 q^{71} - 36 q^{72} - 157 q^{73} - 29 q^{74} + 18 q^{75} - 176 q^{76} - 9 q^{77} + q^{78} - 99 q^{79} - 18 q^{80} + 94 q^{81} - 53 q^{82} - 144 q^{83} - 123 q^{84} - 105 q^{85} + 23 q^{86} - 20 q^{87} - 88 q^{88} - 4 q^{89} - 39 q^{90} - 99 q^{91} - 76 q^{92} - 61 q^{93} - 65 q^{94} - 49 q^{95} - 65 q^{96} - 139 q^{97} - 6 q^{98} - 49 q^{99}+O(q^{100}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9 - 39 * q^10 - 49 * q^11 + 73 * q^12 - 52 * q^13 - 7 * q^14 - 14 * q^15 + 43 * q^16 - 22 * q^17 - 13 * q^18 - 89 * q^19 - 22 * q^20 - 55 * q^21 - 36 * q^22 - 46 * q^23 - 36 * q^24 + 18 * q^25 + q^26 + 94 * q^27 - 123 * q^28 - 20 * q^29 - 39 * q^30 - 61 * q^31 - 65 * q^32 - 49 * q^33 - 67 * q^34 - 40 * q^35 + 73 * q^36 - 83 * q^37 - 19 * q^38 - 52 * q^39 - 101 * q^40 - 25 * q^41 - 7 * q^42 - 150 * q^43 - 71 * q^44 - 14 * q^45 - 72 * q^46 - 39 * q^47 + 43 * q^48 - q^49 - 45 * q^50 - 22 * q^51 - 110 * q^52 - 30 * q^53 - 13 * q^54 - 54 * q^55 - 5 * q^56 - 89 * q^57 - 77 * q^58 - 43 * q^59 - 22 * q^60 - 109 * q^61 - 33 * q^62 - 55 * q^63 + 10 * q^64 - 66 * q^65 - 36 * q^66 - 155 * q^67 - 46 * q^68 - 46 * q^69 - 43 * q^70 - 27 * q^71 - 36 * q^72 - 157 * q^73 - 29 * q^74 + 18 * q^75 - 176 * q^76 - 9 * q^77 + q^78 - 99 * q^79 - 18 * q^80 + 94 * q^81 - 53 * q^82 - 144 * q^83 - 123 * q^84 - 105 * q^85 + 23 * q^86 - 20 * q^87 - 88 * q^88 - 4 * q^89 - 39 * q^90 - 99 * q^91 - 76 * q^92 - 61 * q^93 - 65 * q^94 - 49 * q^95 - 65 * q^96 - 139 * q^97 - 6 * q^98 - 49 * q^99

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