LMFDB - Embedded newform 8013.2.a.d.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.27654 q^{2} +1.00000 q^{3} +3.18262 q^{4} -2.00184 q^{5} -2.27654 q^{6} +2.08885 q^{7} -2.69227 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.27654 q^{2} +1.00000 q^{3} +3.18262 q^{4} -2.00184 q^{5} -2.27654 q^{6} +2.08885 q^{7} -2.69227 q^{8} +1.00000 q^{9} +4.55727 q^{10} -1.88228 q^{11} +3.18262 q^{12} +2.84320 q^{13} -4.75535 q^{14} -2.00184 q^{15} -0.236176 q^{16} -6.19071 q^{17} -2.27654 q^{18} +3.03112 q^{19} -6.37110 q^{20} +2.08885 q^{21} +4.28508 q^{22} +0.0200996 q^{23} -2.69227 q^{24} -0.992628 q^{25} -6.47264 q^{26} +1.00000 q^{27} +6.64802 q^{28} +1.86310 q^{29} +4.55727 q^{30} +2.83716 q^{31} +5.92221 q^{32} -1.88228 q^{33} +14.0934 q^{34} -4.18156 q^{35} +3.18262 q^{36} -0.519885 q^{37} -6.90044 q^{38} +2.84320 q^{39} +5.38951 q^{40} -10.0911 q^{41} -4.75535 q^{42} +6.33966 q^{43} -5.99057 q^{44} -2.00184 q^{45} -0.0457574 q^{46} +7.21759 q^{47} -0.236176 q^{48} -2.63669 q^{49} +2.25975 q^{50} -6.19071 q^{51} +9.04881 q^{52} -4.87026 q^{53} -2.27654 q^{54} +3.76802 q^{55} -5.62377 q^{56} +3.03112 q^{57} -4.24142 q^{58} +2.44093 q^{59} -6.37110 q^{60} +2.77322 q^{61} -6.45891 q^{62} +2.08885 q^{63} -13.0098 q^{64} -5.69163 q^{65} +4.28508 q^{66} -6.84103 q^{67} -19.7027 q^{68} +0.0200996 q^{69} +9.51946 q^{70} +2.19829 q^{71} -2.69227 q^{72} +4.10705 q^{73} +1.18354 q^{74} -0.992628 q^{75} +9.64688 q^{76} -3.93180 q^{77} -6.47264 q^{78} -3.87452 q^{79} +0.472787 q^{80} +1.00000 q^{81} +22.9727 q^{82} -11.4382 q^{83} +6.64802 q^{84} +12.3928 q^{85} -14.4325 q^{86} +1.86310 q^{87} +5.06761 q^{88} +13.7392 q^{89} +4.55727 q^{90} +5.93902 q^{91} +0.0639692 q^{92} +2.83716 q^{93} -16.4311 q^{94} -6.06781 q^{95} +5.92221 q^{96} -13.2404 q^{97} +6.00252 q^{98} -1.88228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.27654	−1.60975	−0.804877	−	0.593441i	$-0.797769\pi$
$2$	−2.27654	−1.60975	−0.804877	+	0.593441i	$0.797769\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.18262	1.59131
$5$	−2.00184	−0.895251	−0.447626	−	0.894221i	$-0.647730\pi$
$5$	−2.00184	−0.895251	−0.447626	+	0.894221i	$0.647730\pi$
$6$	−2.27654	−0.929392
$7$	2.08885	0.789512	0.394756	−	0.918786i	$-0.370829\pi$
$7$	2.08885	0.789512	0.394756	+	0.918786i	$0.370829\pi$
$8$	−2.69227	−0.951863
$9$	1.00000	0.333333
$10$	4.55727	1.44113
$11$	−1.88228	−0.567528	−0.283764	−	0.958894i	$-0.591583\pi$
$11$	−1.88228	−0.567528	−0.283764	+	0.958894i	$0.591583\pi$
$12$	3.18262	0.918743
$13$	2.84320	0.788561	0.394280	−	0.918990i	$-0.370994\pi$
$13$	2.84320	0.788561	0.394280	+	0.918990i	$0.370994\pi$
$14$	−4.75535	−1.27092
$15$	−2.00184	−0.516873
$16$	−0.236176	−0.0590440
$17$	−6.19071	−1.50147	−0.750734	−	0.660605i	$-0.770300\pi$
$17$	−6.19071	−1.50147	−0.750734	+	0.660605i	$0.770300\pi$
$18$	−2.27654	−0.536585
$19$	3.03112	0.695385	0.347693	−	0.937609i	$-0.386965\pi$
$19$	3.03112	0.695385	0.347693	+	0.937609i	$0.386965\pi$
$20$	−6.37110	−1.42462
$21$	2.08885	0.455825
$22$	4.28508	0.913581
$23$	0.0200996	0.00419105	0.00209552	−	0.999998i	$-0.499333\pi$
$23$	0.0200996	0.00419105	0.00209552	+	0.999998i	$0.499333\pi$
$24$	−2.69227	−0.549558
$25$	−0.992628	−0.198526
$26$	−6.47264	−1.26939
$27$	1.00000	0.192450
$28$	6.64802	1.25636
$29$	1.86310	0.345969	0.172985	−	0.984925i	$-0.444659\pi$
$29$	1.86310	0.345969	0.172985	+	0.984925i	$0.444659\pi$
$30$	4.55727	0.832039
$31$	2.83716	0.509570	0.254785	−	0.966998i	$-0.417995\pi$
$31$	2.83716	0.509570	0.254785	+	0.966998i	$0.417995\pi$
$32$	5.92221	1.04691
$33$	−1.88228	−0.327663
$34$	14.0934	2.41699
$35$	−4.18156	−0.706812
$36$	3.18262	0.530436
$37$	−0.519885	−0.0854685	−0.0427343	−	0.999086i	$-0.513607\pi$
$37$	−0.519885	−0.0854685	−0.0427343	+	0.999086i	$0.513607\pi$
$38$	−6.90044	−1.11940
$39$	2.84320	0.455276
$40$	5.38951	0.852156
$41$	−10.0911	−1.57596	−0.787981	−	0.615699i	$-0.788874\pi$
$41$	−10.0911	−1.57596	−0.787981	+	0.615699i	$0.788874\pi$
$42$	−4.75535	−0.733767
$43$	6.33966	0.966789	0.483394	−	0.875403i	$-0.339404\pi$
$43$	6.33966	0.966789	0.483394	+	0.875403i	$0.339404\pi$
$44$	−5.99057	−0.903113
$45$	−2.00184	−0.298417
$46$	−0.0457574	−0.00674656
$47$	7.21759	1.05279	0.526397	−	0.850239i	$-0.323543\pi$
$47$	7.21759	1.05279	0.526397	+	0.850239i	$0.323543\pi$
$48$	−0.236176	−0.0340890
$49$	−2.63669	−0.376670
$50$	2.25975	0.319577
$51$	−6.19071	−0.866873
$52$	9.04881	1.25484
$53$	−4.87026	−0.668982	−0.334491	−	0.942399i	$-0.608564\pi$
$53$	−4.87026	−0.668982	−0.334491	+	0.942399i	$0.608564\pi$
$54$	−2.27654	−0.309797
$55$	3.76802	0.508080
$56$	−5.62377	−0.751507
$57$	3.03112	0.401481
$58$	−4.24142	−0.556926
$59$	2.44093	0.317782	0.158891	−	0.987296i	$-0.449208\pi$
$59$	2.44093	0.317782	0.158891	+	0.987296i	$0.449208\pi$
$60$	−6.37110	−0.822506
$61$	2.77322	0.355075	0.177537	−	0.984114i	$-0.443187\pi$
$61$	2.77322	0.355075	0.177537	+	0.984114i	$0.443187\pi$
$62$	−6.45891	−0.820282
$63$	2.08885	0.263171
$64$	−13.0098	−1.62622
$65$	−5.69163	−0.705960
$66$	4.28508	0.527456
$67$	−6.84103	−0.835765	−0.417882	−	0.908501i	$-0.637228\pi$
$67$	−6.84103	−0.835765	−0.417882	+	0.908501i	$0.637228\pi$
$68$	−19.7027	−2.38930
$69$	0.0200996	0.00241970
$70$	9.51946	1.13779
$71$	2.19829	0.260889	0.130444	−	0.991456i	$-0.458360\pi$
$71$	2.19829	0.260889	0.130444	+	0.991456i	$0.458360\pi$
$72$	−2.69227	−0.317288
$73$	4.10705	0.480694	0.240347	−	0.970687i	$-0.422739\pi$
$73$	4.10705	0.480694	0.240347	+	0.970687i	$0.422739\pi$
$74$	1.18354	0.137583
$75$	−0.992628	−0.114619
$76$	9.64688	1.10657
$77$	−3.93180	−0.448071
$78$	−6.47264	−0.732882
$79$	−3.87452	−0.435918	−0.217959	−	0.975958i	$-0.569940\pi$
$79$	−3.87452	−0.435918	−0.217959	+	0.975958i	$0.569940\pi$
$80$	0.472787	0.0528592
$81$	1.00000	0.111111
$82$	22.9727	2.53691
$83$	−11.4382	−1.25550	−0.627752	−	0.778413i	$-0.716025\pi$
$83$	−11.4382	−1.25550	−0.627752	+	0.778413i	$0.716025\pi$
$84$	6.64802	0.725359
$85$	12.3928	1.34419
$86$	−14.4325	−1.55629
$87$	1.86310	0.199746
$88$	5.06761	0.540209
$89$	13.7392	1.45635	0.728174	−	0.685393i	$-0.240369\pi$
$89$	13.7392	1.45635	0.728174	+	0.685393i	$0.240369\pi$
$90$	4.55727	0.480378
$91$	5.93902	0.622578
$92$	0.0639692	0.00666925
$93$	2.83716	0.294200
$94$	−16.4311	−1.69474
$95$	−6.06781	−0.622545
$96$	5.92221	0.604433
$97$	−13.2404	−1.34436	−0.672181	−	0.740387i	$-0.734642\pi$
$97$	−13.2404	−1.34436	−0.672181	+	0.740387i	$0.734642\pi$
$98$	6.00252	0.606347
$99$	−1.88228	−0.189176
$100$	−3.15916	−0.315916
$101$	15.6887	1.56109	0.780544	−	0.625100i	$-0.214942\pi$
$101$	15.6887	1.56109	0.780544	+	0.625100i	$0.214942\pi$
$102$	14.0934	1.39545
$103$	7.15400	0.704905	0.352452	−	0.935830i	$-0.385348\pi$
$103$	7.15400	0.704905	0.352452	+	0.935830i	$0.385348\pi$
$104$	−7.65466	−0.750601
$105$	−4.18156	−0.408078
$106$	11.0873	1.07690
$107$	−3.69482	−0.357191	−0.178596	−	0.983923i	$-0.557155\pi$
$107$	−3.69482	−0.357191	−0.178596	+	0.983923i	$0.557155\pi$
$108$	3.18262	0.306248
$109$	16.2075	1.55240	0.776199	−	0.630487i	$-0.217145\pi$
$109$	16.2075	1.55240	0.776199	+	0.630487i	$0.217145\pi$
$110$	−8.57805	−0.817885
$111$	−0.519885	−0.0493453
$112$	−0.493337	−0.0466159
$113$	8.17145	0.768706	0.384353	−	0.923186i	$-0.374425\pi$
$113$	8.17145	0.768706	0.384353	+	0.923186i	$0.374425\pi$
$114$	−6.90044	−0.646286
$115$	−0.0402362	−0.00375204
$116$	5.92954	0.550544
$117$	2.84320	0.262854
$118$	−5.55686	−0.511551
$119$	−12.9315	−1.18543
$120$	5.38951	0.491993
$121$	−7.45703	−0.677912
$122$	−6.31335	−0.571583
$123$	−10.0911	−0.909882
$124$	9.02961	0.810883
$125$	11.9963	1.07298
$126$	−4.75535	−0.423640
$127$	14.5201	1.28845	0.644223	−	0.764838i	$-0.277181\pi$
$127$	14.5201	1.28845	0.644223	+	0.764838i	$0.277181\pi$
$128$	17.7728	1.57091
$129$	6.33966	0.558176
$130$	12.9572	1.13642
$131$	9.93534	0.868055	0.434027	−	0.900900i	$-0.357092\pi$
$131$	9.93534	0.868055	0.434027	+	0.900900i	$0.357092\pi$
$132$	−5.99057	−0.521413
$133$	6.33155	0.549015
$134$	15.5739	1.34538
$135$	−2.00184	−0.172291
$136$	16.6671	1.42919
$137$	12.6643	1.08198	0.540991	−	0.841028i	$-0.318049\pi$
$137$	12.6643	1.08198	0.540991	+	0.841028i	$0.318049\pi$
$138$	−0.0457574	−0.00389513
$139$	−3.97464	−0.337125	−0.168562	−	0.985691i	$-0.553912\pi$
$139$	−3.97464	−0.337125	−0.168562	+	0.985691i	$0.553912\pi$
$140$	−13.3083	−1.12476
$141$	7.21759	0.607831
$142$	−5.00448	−0.419967
$143$	−5.35169	−0.447530
$144$	−0.236176	−0.0196813
$145$	−3.72964	−0.309730
$146$	−9.34985	−0.773799
$147$	−2.63669	−0.217471
$148$	−1.65459	−0.136007
$149$	−17.1073	−1.40148	−0.700740	−	0.713416i	$-0.747147\pi$
$149$	−17.1073	−1.40148	−0.700740	+	0.713416i	$0.747147\pi$
$150$	2.25975	0.184508
$151$	−4.73113	−0.385014	−0.192507	−	0.981296i	$-0.561662\pi$
$151$	−4.73113	−0.385014	−0.192507	+	0.981296i	$0.561662\pi$
$152$	−8.16059	−0.661912
$153$	−6.19071	−0.500489
$154$	8.95089	0.721284
$155$	−5.67956	−0.456193
$156$	9.04881	0.724484
$157$	23.2385	1.85464	0.927319	−	0.374272i	$-0.122108\pi$
$157$	23.2385	1.85464	0.927319	+	0.374272i	$0.122108\pi$
$158$	8.82049	0.701721
$159$	−4.87026	−0.386237
$160$	−11.8553	−0.937246
$161$	0.0419850	0.00330888
$162$	−2.27654	−0.178862
$163$	−23.1919	−1.81653	−0.908267	−	0.418392i	$-0.862594\pi$
$163$	−23.1919	−1.81653	−0.908267	+	0.418392i	$0.862594\pi$
$164$	−32.1161	−2.50784
$165$	3.76802	0.293340
$166$	26.0395	2.02105
$167$	16.4185	1.27050	0.635249	−	0.772307i	$-0.280897\pi$
$167$	16.4185	1.27050	0.635249	+	0.772307i	$0.280897\pi$
$168$	−5.62377	−0.433883
$169$	−4.91624	−0.378172
$170$	−28.2127	−2.16382
$171$	3.03112	0.231795
$172$	20.1767	1.53846
$173$	−15.5457	−1.18192	−0.590960	−	0.806701i	$-0.701251\pi$
$173$	−15.5457	−1.18192	−0.590960	+	0.806701i	$0.701251\pi$
$174$	−4.24142	−0.321541
$175$	−2.07345	−0.156738
$176$	0.444549	0.0335091
$177$	2.44093	0.183471
$178$	−31.2777	−2.34436
$179$	−0.352055	−0.0263138	−0.0131569	−	0.999913i	$-0.504188\pi$
$179$	−0.352055	−0.0263138	−0.0131569	+	0.999913i	$0.504188\pi$
$180$	−6.37110	−0.474874
$181$	5.15127	0.382891	0.191445	−	0.981503i	$-0.438682\pi$
$181$	5.15127	0.382891	0.191445	+	0.981503i	$0.438682\pi$
$182$	−13.5204	−1.00220
$183$	2.77322	0.205003
$184$	−0.0541135	−0.00398930
$185$	1.04073	0.0765158
$186$	−6.45891	−0.473590
$187$	11.6526	0.852125
$188$	22.9708	1.67532
$189$	2.08885	0.151942
$190$	13.8136	1.00214
$191$	17.5285	1.26832	0.634159	−	0.773202i	$-0.281346\pi$
$191$	17.5285	1.26832	0.634159	+	0.773202i	$0.281346\pi$
$192$	−13.0098	−0.938900
$193$	16.9953	1.22335	0.611674	−	0.791110i	$-0.290496\pi$
$193$	16.9953	1.22335	0.611674	+	0.791110i	$0.290496\pi$
$194$	30.1423	2.16409
$195$	−5.69163	−0.407586
$196$	−8.39158	−0.599399
$197$	−10.6530	−0.758998	−0.379499	−	0.925192i	$-0.623904\pi$
$197$	−10.6530	−0.758998	−0.379499	+	0.925192i	$0.623904\pi$
$198$	4.28508	0.304527
$199$	1.60011	0.113429	0.0567144	−	0.998390i	$-0.481938\pi$
$199$	1.60011	0.113429	0.0567144	+	0.998390i	$0.481938\pi$
$200$	2.67243	0.188969
$201$	−6.84103	−0.482529
$202$	−35.7160	−2.51297
$203$	3.89175	0.273147
$204$	−19.7027	−1.37946
$205$	20.2008	1.41088
$206$	−16.2863	−1.13472
$207$	0.0200996	0.00139702
$208$	−0.671494	−0.0465597
$209$	−5.70540	−0.394651
$210$	9.51946	0.656905
$211$	8.25886	0.568563	0.284282	−	0.958741i	$-0.408245\pi$
$211$	8.25886	0.568563	0.284282	+	0.958741i	$0.408245\pi$
$212$	−15.5002	−1.06456
$213$	2.19829	0.150624
$214$	8.41139	0.574991
$215$	−12.6910	−0.865519
$216$	−2.69227	−0.183186
$217$	5.92642	0.402312
$218$	−36.8970	−2.49898
$219$	4.10705	0.277529
$220$	11.9922	0.808513
$221$	−17.6014	−1.18400
$222$	1.18354	0.0794338
$223$	−4.75449	−0.318384	−0.159192	−	0.987248i	$-0.550889\pi$
$223$	−4.75449	−0.318384	−0.159192	+	0.987248i	$0.550889\pi$
$224$	12.3706	0.826548
$225$	−0.992628	−0.0661752
$226$	−18.6026	−1.23743
$227$	−17.9008	−1.18812	−0.594058	−	0.804422i	$-0.702475\pi$
$227$	−17.9008	−1.18812	−0.594058	+	0.804422i	$0.702475\pi$
$228$	9.64688	0.638880
$229$	−13.0277	−0.860897	−0.430449	−	0.902615i	$-0.641645\pi$
$229$	−13.0277	−0.860897	−0.430449	+	0.902615i	$0.641645\pi$
$230$	0.0915991	0.00603986
$231$	−3.93180	−0.258694
$232$	−5.01598	−0.329315
$233$	−12.0850	−0.791713	−0.395857	−	0.918312i	$-0.629552\pi$
$233$	−12.0850	−0.791713	−0.395857	+	0.918312i	$0.629552\pi$
$234$	−6.47264	−0.423130
$235$	−14.4485	−0.942515
$236$	7.76854	0.505689
$237$	−3.87452	−0.251677
$238$	29.4390	1.90825
$239$	5.80701	0.375624	0.187812	−	0.982205i	$-0.439860\pi$
$239$	5.80701	0.375624	0.187812	+	0.982205i	$0.439860\pi$
$240$	0.472787	0.0305183
$241$	−9.59210	−0.617881	−0.308941	−	0.951081i	$-0.599974\pi$
$241$	−9.59210	−0.617881	−0.308941	+	0.951081i	$0.599974\pi$
$242$	16.9762	1.09127
$243$	1.00000	0.0641500
$244$	8.82611	0.565034
$245$	5.27824	0.337214
$246$	22.9727	1.46469
$247$	8.61805	0.548354
$248$	−7.63843	−0.485040
$249$	−11.4382	−0.724866
$250$	−27.3100	−1.72724
$251$	−12.3913	−0.782134	−0.391067	−	0.920362i	$-0.627894\pi$
$251$	−12.3913	−0.782134	−0.391067	+	0.920362i	$0.627894\pi$
$252$	6.64802	0.418786
$253$	−0.0378330	−0.00237854
$254$	−33.0554	−2.07408
$255$	12.3928	0.776069
$256$	−14.4409	−0.902557
$257$	10.8895	0.679267	0.339633	−	0.940558i	$-0.389697\pi$
$257$	10.8895	0.679267	0.339633	+	0.940558i	$0.389697\pi$
$258$	−14.4325	−0.898526
$259$	−1.08596	−0.0674785
$260$	−18.1143	−1.12340
$261$	1.86310	0.115323
$262$	−22.6182	−1.39736
$263$	6.62175	0.408315	0.204157	−	0.978938i	$-0.434555\pi$
$263$	6.62175	0.408315	0.204157	+	0.978938i	$0.434555\pi$
$264$	5.06761	0.311890
$265$	9.74949	0.598907
$266$	−14.4140	−0.883780
$267$	13.7392	0.840823
$268$	−21.7724	−1.32996
$269$	18.4347	1.12398	0.561991	−	0.827144i	$-0.310036\pi$
$269$	18.4347	1.12398	0.561991	+	0.827144i	$0.310036\pi$
$270$	4.55727	0.277346
$271$	1.69508	0.102969	0.0514845	−	0.998674i	$-0.483605\pi$
$271$	1.69508	0.102969	0.0514845	+	0.998674i	$0.483605\pi$
$272$	1.46210	0.0886526
$273$	5.93902	0.359446
$274$	−28.8307	−1.74173
$275$	1.86840	0.112669
$276$	0.0639692	0.00385050
$277$	24.0787	1.44675	0.723374	−	0.690457i	$-0.242590\pi$
$277$	24.0787	1.44675	0.723374	+	0.690457i	$0.242590\pi$
$278$	9.04842	0.542688
$279$	2.83716	0.169857
$280$	11.2579	0.672788
$281$	30.0179	1.79072	0.895360	−	0.445343i	$-0.146918\pi$
$281$	30.0179	1.79072	0.895360	+	0.445343i	$0.146918\pi$
$282$	−16.4311	−0.978459
$283$	12.6432	0.751562	0.375781	−	0.926709i	$-0.377375\pi$
$283$	12.6432	0.751562	0.375781	+	0.926709i	$0.377375\pi$
$284$	6.99631	0.415155
$285$	−6.06781	−0.359426
$286$	12.1833	0.720414
$287$	−21.0788	−1.24424
$288$	5.92221	0.348970
$289$	21.3249	1.25440
$290$	8.49066	0.498588
$291$	−13.2404	−0.776167
$292$	13.0712	0.764933
$293$	8.11743	0.474225	0.237113	−	0.971482i	$-0.423799\pi$
$293$	8.11743	0.474225	0.237113	+	0.971482i	$0.423799\pi$
$294$	6.00252	0.350074
$295$	−4.88635	−0.284495
$296$	1.39967	0.0813543
$297$	−1.88228	−0.109221
$298$	38.9453	2.25604
$299$	0.0571470	0.00330490
$300$	−3.15916	−0.182394
$301$	13.2426	0.763292
$302$	10.7706	0.619778
$303$	15.6887	0.901295
$304$	−0.715876	−0.0410583
$305$	−5.55156	−0.317881
$306$	14.0934	0.805665
$307$	−20.2784	−1.15735	−0.578675	−	0.815558i	$-0.696430\pi$
$307$	−20.2784	−1.15735	−0.578675	+	0.815558i	$0.696430\pi$
$308$	−12.5134	−0.713019
$309$	7.15400	0.406977
$310$	12.9297	0.734358
$311$	−0.789591	−0.0447736	−0.0223868	−	0.999749i	$-0.507127\pi$
$311$	−0.789591	−0.0447736	−0.0223868	+	0.999749i	$0.507127\pi$
$312$	−7.65466	−0.433360
$313$	−5.99597	−0.338912	−0.169456	−	0.985538i	$-0.554201\pi$
$313$	−5.99597	−0.338912	−0.169456	+	0.985538i	$0.554201\pi$
$314$	−52.9034	−2.98551
$315$	−4.18156	−0.235604
$316$	−12.3311	−0.693680
$317$	4.34365	0.243964	0.121982	−	0.992532i	$-0.461075\pi$
$317$	4.34365	0.243964	0.121982	+	0.992532i	$0.461075\pi$
$318$	11.0873	0.621746
$319$	−3.50688	−0.196347
$320$	26.0435	1.45588
$321$	−3.69482	−0.206225
$322$	−0.0955805	−0.00532649
$323$	−18.7648	−1.04410
$324$	3.18262	0.176812
$325$	−2.82223	−0.156549
$326$	52.7973	2.92417
$327$	16.2075	0.896278
$328$	27.1680	1.50010
$329$	15.0765	0.831194
$330$	−8.57805	−0.472206
$331$	−14.2108	−0.781095	−0.390547	−	0.920583i	$-0.627714\pi$
$331$	−14.2108	−0.781095	−0.390547	+	0.920583i	$0.627714\pi$
$332$	−36.4034	−1.99790
$333$	−0.519885	−0.0284895
$334$	−37.3772	−2.04519
$335$	13.6947	0.748219
$336$	−0.493337	−0.0269137
$337$	−12.0499	−0.656398	−0.328199	−	0.944609i	$-0.606442\pi$
$337$	−12.0499	−0.656398	−0.328199	+	0.944609i	$0.606442\pi$
$338$	11.1920	0.608765
$339$	8.17145	0.443812
$340$	39.4416	2.13902
$341$	−5.34033	−0.289195
$342$	−6.90044	−0.373133
$343$	−20.1296	−1.08690
$344$	−17.0681	−0.920250
$345$	−0.0402362	−0.00216624
$346$	35.3904	1.90260
$347$	−32.6064	−1.75040	−0.875202	−	0.483757i	$-0.839272\pi$
$347$	−32.6064	−1.75040	−0.875202	+	0.483757i	$0.839272\pi$
$348$	5.92954	0.317857
$349$	21.7208	1.16269	0.581344	−	0.813658i	$-0.302527\pi$
$349$	21.7208	1.16269	0.581344	+	0.813658i	$0.302527\pi$
$350$	4.72029	0.252310
$351$	2.84320	0.151759
$352$	−11.1473	−0.594151
$353$	36.9662	1.96751	0.983757	−	0.179505i	$-0.0574496\pi$
$353$	36.9662	1.96751	0.983757	+	0.179505i	$0.0574496\pi$
$354$	−5.55686	−0.295344
$355$	−4.40063	−0.233561
$356$	43.7265	2.31750
$357$	−12.9315	−0.684407
$358$	0.801467	0.0423588
$359$	−1.88171	−0.0993127	−0.0496563	−	0.998766i	$-0.515813\pi$
$359$	−1.88171	−0.0993127	−0.0496563	+	0.998766i	$0.515813\pi$
$360$	5.38951	0.284052
$361$	−9.81234	−0.516439
$362$	−11.7271	−0.616360
$363$	−7.45703	−0.391392
$364$	18.9016	0.990715
$365$	−8.22167	−0.430342
$366$	−6.31335	−0.330004
$367$	7.38143	0.385308	0.192654	−	0.981267i	$-0.438291\pi$
$367$	7.38143	0.385308	0.192654	+	0.981267i	$0.438291\pi$
$368$	−0.00474703	−0.000247456 0
$369$	−10.0911	−0.525321
$370$	−2.36925	−0.123172
$371$	−10.1733	−0.528169
$372$	9.02961	0.468164
$373$	4.89911	0.253666	0.126833	−	0.991924i	$-0.459519\pi$
$373$	4.89911	0.253666	0.126833	+	0.991924i	$0.459519\pi$
$374$	−26.5277	−1.37171
$375$	11.9963	0.619486
$376$	−19.4317	−1.00212
$377$	5.29716	0.272818
$378$	−4.75535	−0.244589
$379$	0.472635	0.0242776	0.0121388	−	0.999926i	$-0.496136\pi$
$379$	0.472635	0.0242776	0.0121388	+	0.999926i	$0.496136\pi$
$380$	−19.3115	−0.990661
$381$	14.5201	0.743885
$382$	−39.9043	−2.04168
$383$	−3.44047	−0.175800	−0.0878998	−	0.996129i	$-0.528016\pi$
$383$	−3.44047	−0.175800	−0.0878998	+	0.996129i	$0.528016\pi$
$384$	17.7728	0.906965
$385$	7.87085	0.401136
$386$	−38.6904	−1.96929
$387$	6.33966	0.322263
$388$	−42.1392	−2.13929
$389$	−14.1601	−0.717947	−0.358973	−	0.933348i	$-0.616873\pi$
$389$	−14.1601	−0.717947	−0.358973	+	0.933348i	$0.616873\pi$
$390$	12.9572	0.656113
$391$	−0.124431	−0.00629272
$392$	7.09870	0.358538
$393$	9.93534	0.501172
$394$	24.2520	1.22180
$395$	7.75618	0.390256
$396$	−5.99057	−0.301038
$397$	24.4675	1.22799	0.613995	−	0.789310i	$-0.289562\pi$
$397$	24.4675	1.22799	0.613995	+	0.789310i	$0.289562\pi$
$398$	−3.64271	−0.182592
$399$	6.33155	0.316974
$400$	0.234435	0.0117217
$401$	14.9397	0.746051	0.373026	−	0.927821i	$-0.378320\pi$
$401$	14.9397	0.746051	0.373026	+	0.927821i	$0.378320\pi$
$402$	15.5739	0.776753
$403$	8.06661	0.401827
$404$	49.9313	2.48418
$405$	−2.00184	−0.0994723
$406$	−8.85971	−0.439700
$407$	0.978568	0.0485058
$408$	16.6671	0.825144
$409$	−27.6096	−1.36521	−0.682603	−	0.730789i	$-0.739152\pi$
$409$	−27.6096	−1.36521	−0.682603	+	0.730789i	$0.739152\pi$
$410$	−45.9878	−2.27117
$411$	12.6643	0.624683
$412$	22.7685	1.12172
$413$	5.09874	0.250893
$414$	−0.0457574	−0.00224885
$415$	22.8975	1.12399
$416$	16.8380	0.825551
$417$	−3.97464	−0.194639
$418$	12.9886	0.635291
$419$	29.8856	1.46001	0.730003	−	0.683443i	$-0.239518\pi$
$419$	29.8856	1.46001	0.730003	+	0.683443i	$0.239518\pi$
$420$	−13.3083	−0.649378
$421$	33.7353	1.64416	0.822079	−	0.569374i	$-0.192814\pi$
$421$	33.7353	1.64416	0.822079	+	0.569374i	$0.192814\pi$
$422$	−18.8016	−0.915247
$423$	7.21759	0.350931
$424$	13.1121	0.636779
$425$	6.14507	0.298080
$426$	−5.00448	−0.242468
$427$	5.79286	0.280336
$428$	−11.7592	−0.568402
$429$	−5.35169	−0.258382
$430$	28.8915	1.39327
$431$	−20.6917	−0.996686	−0.498343	−	0.866980i	$-0.666058\pi$
$431$	−20.6917	−0.996686	−0.498343	+	0.866980i	$0.666058\pi$
$432$	−0.236176	−0.0113630
$433$	26.1492	1.25665	0.628325	−	0.777951i	$-0.283741\pi$
$433$	26.1492	1.25665	0.628325	+	0.777951i	$0.283741\pi$
$434$	−13.4917	−0.647623
$435$	−3.72964	−0.178822
$436$	51.5824	2.47035
$437$	0.0609241	0.00291439
$438$	−9.34985	−0.446753
$439$	11.9421	0.569967	0.284983	−	0.958532i	$-0.408012\pi$
$439$	11.9421	0.569967	0.284983	+	0.958532i	$0.408012\pi$
$440$	−10.1446	−0.483623
$441$	−2.63669	−0.125557
$442$	40.0702	1.90595
$443$	10.5654	0.501978	0.250989	−	0.967990i	$-0.419244\pi$
$443$	10.5654	0.501978	0.250989	+	0.967990i	$0.419244\pi$
$444$	−1.65459	−0.0785236
$445$	−27.5036	−1.30380
$446$	10.8238	0.512520
$447$	−17.1073	−0.809145
$448$	−27.1755	−1.28392
$449$	−7.47543	−0.352787	−0.176394	−	0.984320i	$-0.556443\pi$
$449$	−7.47543	−0.352787	−0.176394	+	0.984320i	$0.556443\pi$
$450$	2.25975	0.106526
$451$	18.9942	0.894403
$452$	26.0066	1.22325
$453$	−4.73113	−0.222288
$454$	40.7518	1.91258
$455$	−11.8890	−0.557364
$456$	−8.16059	−0.382155
$457$	−4.33594	−0.202827	−0.101413	−	0.994844i	$-0.532336\pi$
$457$	−4.33594	−0.202827	−0.101413	+	0.994844i	$0.532336\pi$
$458$	29.6581	1.38583
$459$	−6.19071	−0.288958
$460$	−0.128056	−0.00597066
$461$	22.1666	1.03240	0.516201	−	0.856468i	$-0.327346\pi$
$461$	22.1666	1.03240	0.516201	+	0.856468i	$0.327346\pi$
$462$	8.95089	0.416433
$463$	−20.5385	−0.954503	−0.477252	−	0.878767i	$-0.658367\pi$
$463$	−20.5385	−0.954503	−0.477252	+	0.878767i	$0.658367\pi$
$464$	−0.440020	−0.0204274
$465$	−5.67956	−0.263383
$466$	27.5119	1.27446
$467$	−32.4992	−1.50388	−0.751941	−	0.659230i	$-0.770882\pi$
$467$	−32.4992	−1.50388	−0.751941	+	0.659230i	$0.770882\pi$
$468$	9.04881	0.418281
$469$	−14.2899	−0.659847
$470$	32.8925	1.51722
$471$	23.2385	1.07078
$472$	−6.57165	−0.302485
$473$	−11.9330	−0.548680
$474$	8.82049	0.405139
$475$	−3.00877	−0.138052
$476$	−41.1560	−1.88638
$477$	−4.87026	−0.222994
$478$	−13.2199	−0.604663
$479$	−8.30660	−0.379538	−0.189769	−	0.981829i	$-0.560774\pi$
$479$	−8.30660	−0.379538	−0.189769	+	0.981829i	$0.560774\pi$
$480$	−11.8553	−0.541120
$481$	−1.47813	−0.0673971
$482$	21.8368	0.994637
$483$	0.0419850	0.00191039
$484$	−23.7329	−1.07877
$485$	26.5052	1.20354
$486$	−2.27654	−0.103266
$487$	23.9835	1.08680	0.543398	−	0.839475i	$-0.317137\pi$
$487$	23.9835	1.08680	0.543398	+	0.839475i	$0.317137\pi$
$488$	−7.46628	−0.337983
$489$	−23.1919	−1.04878
$490$	−12.0161	−0.542832
$491$	19.7496	0.891289	0.445644	−	0.895210i	$-0.352975\pi$
$491$	19.7496	0.891289	0.445644	+	0.895210i	$0.352975\pi$
$492$	−32.1161	−1.44790
$493$	−11.5339	−0.519462
$494$	−19.6193	−0.882715
$495$	3.76802	0.169360
$496$	−0.670070	−0.0300870
$497$	4.59190	0.205975
$498$	26.0395	1.16686
$499$	16.6971	0.747464	0.373732	−	0.927537i	$-0.378078\pi$
$499$	16.6971	0.747464	0.373732	+	0.927537i	$0.378078\pi$
$500$	38.1796	1.70745
$501$	16.4185	0.733523
$502$	28.2093	1.25904
$503$	27.3685	1.22030	0.610150	−	0.792286i	$-0.291109\pi$
$503$	27.3685	1.22030	0.610150	+	0.792286i	$0.291109\pi$
$504$	−5.62377	−0.250502
$505$	−31.4064	−1.39757
$506$	0.0861282	0.00382886
$507$	−4.91624	−0.218338
$508$	46.2118	2.05032
$509$	−25.6214	−1.13565	−0.567824	−	0.823150i	$-0.692215\pi$
$509$	−25.6214	−1.13565	−0.567824	+	0.823150i	$0.692215\pi$
$510$	−28.2127	−1.24928
$511$	8.57903	0.379514
$512$	−2.67038	−0.118015
$513$	3.03112	0.133827
$514$	−24.7903	−1.09345
$515$	−14.3212	−0.631067
$516$	20.1767	0.888230
$517$	−13.5855	−0.597491
$518$	2.47223	0.108624
$519$	−15.5457	−0.682381
$520$	15.3234	0.671977
$521$	−3.94071	−0.172646	−0.0863228	−	0.996267i	$-0.527512\pi$
$521$	−3.94071	−0.172646	−0.0863228	+	0.996267i	$0.527512\pi$
$522$	−4.24142	−0.185642
$523$	11.2202	0.490624	0.245312	−	0.969444i	$-0.421110\pi$
$523$	11.2202	0.490624	0.245312	+	0.969444i	$0.421110\pi$
$524$	31.6204	1.38134
$525$	−2.07345	−0.0904929
$526$	−15.0747	−0.657286
$527$	−17.5641	−0.765102
$528$	0.444549	0.0193465
$529$	−22.9996	−0.999982
$530$	−22.1951	−0.964093
$531$	2.44093	0.105927
$532$	20.1509	0.873653
$533$	−28.6909	−1.24274
$534$	−31.2777	−1.35352
$535$	7.39644	0.319776
$536$	18.4179	0.795533
$537$	−0.352055	−0.0151923
$538$	−41.9672	−1.80933
$539$	4.96299	0.213771
$540$	−6.37110	−0.274169
$541$	10.5730	0.454568	0.227284	−	0.973828i	$-0.427015\pi$
$541$	10.5730	0.454568	0.227284	+	0.973828i	$0.427015\pi$
$542$	−3.85892	−0.165755
$543$	5.15127	0.221062
$544$	−36.6627	−1.57190
$545$	−32.4449	−1.38979
$546$	−13.5204	−0.578619
$547$	8.35560	0.357259	0.178630	−	0.983916i	$-0.442834\pi$
$547$	8.35560	0.357259	0.178630	+	0.983916i	$0.442834\pi$
$548$	40.3056	1.72177
$549$	2.77322	0.118358
$550$	−4.25348	−0.181369
$551$	5.64728	0.240582
$552$	−0.0541135	−0.00230323
$553$	−8.09331	−0.344162
$554$	−54.8160	−2.32891
$555$	1.04073	0.0441764
$556$	−12.6498	−0.536470
$557$	−20.1752	−0.854851	−0.427425	−	0.904051i	$-0.640579\pi$
$557$	−20.1752	−0.854851	−0.427425	+	0.904051i	$0.640579\pi$
$558$	−6.45891	−0.273427
$559$	18.0249	0.762371
$560$	0.987582	0.0417330
$561$	11.6526	0.491975
$562$	−68.3369	−2.88262
$563$	9.58339	0.403892	0.201946	−	0.979397i	$-0.435273\pi$
$563$	9.58339	0.403892	0.201946	+	0.979397i	$0.435273\pi$
$564$	22.9708	0.967247
$565$	−16.3580	−0.688185
$566$	−28.7828	−1.20983
$567$	2.08885	0.0877236
$568$	−5.91840	−0.248330
$569$	−15.4584	−0.648051	−0.324025	−	0.946048i	$-0.605036\pi$
$569$	−15.4584	−0.648051	−0.324025	+	0.946048i	$0.605036\pi$
$570$	13.8136	0.578588
$571$	3.36194	0.140693	0.0703465	−	0.997523i	$-0.477590\pi$
$571$	3.36194	0.140693	0.0703465	+	0.997523i	$0.477590\pi$
$572$	−17.0324	−0.712159
$573$	17.5285	0.732264
$574$	47.9866	2.00292
$575$	−0.0199514	−0.000832030 0
$576$	−13.0098	−0.542074
$577$	29.3415	1.22150	0.610751	−	0.791823i	$-0.290868\pi$
$577$	29.3415	1.22150	0.610751	+	0.791823i	$0.290868\pi$
$578$	−48.5469	−2.01928
$579$	16.9953	0.706300
$580$	−11.8700	−0.492875
$581$	−23.8927	−0.991236
$582$	30.1423	1.24944
$583$	9.16719	0.379666
$584$	−11.0573	−0.457555
$585$	−5.69163	−0.235320
$586$	−18.4796	−0.763386
$587$	26.9791	1.11355	0.556774	−	0.830664i	$-0.312039\pi$
$587$	26.9791	1.11355	0.556774	+	0.830664i	$0.312039\pi$
$588$	−8.39158	−0.346063
$589$	8.59977	0.354347
$590$	11.1240	0.457966
$591$	−10.6530	−0.438208
$592$	0.122784	0.00504640
$593$	−5.78848	−0.237704	−0.118852	−	0.992912i	$-0.537921\pi$
$593$	−5.78848	−0.237704	−0.118852	+	0.992912i	$0.537921\pi$
$594$	4.28508	0.175819
$595$	25.8868	1.06125
$596$	−54.4459	−2.23019
$597$	1.60011	0.0654881
$598$	−0.130097	−0.00532007
$599$	22.5543	0.921543	0.460771	−	0.887519i	$-0.347573\pi$
$599$	22.5543	0.921543	0.460771	+	0.887519i	$0.347573\pi$
$600$	2.67243	0.109101
$601$	4.04594	0.165037	0.0825186	−	0.996590i	$-0.473704\pi$
$601$	4.04594	0.165037	0.0825186	+	0.996590i	$0.473704\pi$
$602$	−30.1473	−1.22871
$603$	−6.84103	−0.278588
$604$	−15.0574	−0.612676
$605$	14.9278	0.606901
$606$	−35.7160	−1.45086
$607$	−8.17869	−0.331963	−0.165981	−	0.986129i	$-0.553079\pi$
$607$	−8.17869	−0.331963	−0.165981	+	0.986129i	$0.553079\pi$
$608$	17.9509	0.728005
$609$	3.89175	0.157702
$610$	12.6383	0.511711
$611$	20.5210	0.830192
$612$	−19.7027	−0.796433
$613$	−24.8265	−1.00273	−0.501366	−	0.865235i	$-0.667169\pi$
$613$	−24.8265	−1.00273	−0.501366	+	0.865235i	$0.667169\pi$
$614$	46.1646	1.86305
$615$	20.2008	0.814573
$616$	10.5855	0.426502
$617$	2.86256	0.115242	0.0576211	−	0.998339i	$-0.481648\pi$
$617$	2.86256	0.115242	0.0576211	+	0.998339i	$0.481648\pi$
$618$	−16.2863	−0.655133
$619$	−34.9486	−1.40470	−0.702351	−	0.711831i	$-0.747866\pi$
$619$	−34.9486	−1.40470	−0.702351	+	0.711831i	$0.747866\pi$
$620$	−18.0759	−0.725944
$621$	0.0200996	0.000806568 0
$622$	1.79753	0.0720745
$623$	28.6991	1.14980
$624$	−0.671494	−0.0268813
$625$	−19.0516	−0.762062
$626$	13.6500	0.545565
$627$	−5.70540	−0.227852
$628$	73.9594	2.95130
$629$	3.21846	0.128328
$630$	9.51946	0.379264
$631$	38.8495	1.54657	0.773286	−	0.634057i	$-0.218611\pi$
$631$	38.8495	1.54657	0.773286	+	0.634057i	$0.218611\pi$
$632$	10.4313	0.414934
$633$	8.25886	0.328260
$634$	−9.88848	−0.392722
$635$	−29.0669	−1.15348
$636$	−15.5002	−0.614622
$637$	−7.49663	−0.297027
$638$	7.98353	0.316071
$639$	2.19829	0.0869630
$640$	−35.5784	−1.40636
$641$	40.9515	1.61749	0.808744	−	0.588161i	$-0.200148\pi$
$641$	40.9515	1.61749	0.808744	+	0.588161i	$0.200148\pi$
$642$	8.41139	0.331971
$643$	−9.22090	−0.363637	−0.181818	−	0.983332i	$-0.558198\pi$
$643$	−9.22090	−0.363637	−0.181818	+	0.983332i	$0.558198\pi$
$644$	0.133622	0.00526546
$645$	−12.6910	−0.499707
$646$	42.7186	1.68074
$647$	−0.365141	−0.0143552	−0.00717758	−	0.999974i	$-0.502285\pi$
$647$	−0.365141	−0.0143552	−0.00717758	+	0.999974i	$0.502285\pi$
$648$	−2.69227	−0.105763
$649$	−4.59451	−0.180350
$650$	6.42492	0.252006
$651$	5.92642	0.232275
$652$	−73.8111	−2.89067
$653$	−26.1813	−1.02455	−0.512277	−	0.858820i	$-0.671198\pi$
$653$	−26.1813	−1.02455	−0.512277	+	0.858820i	$0.671198\pi$
$654$	−36.8970	−1.44279
$655$	−19.8890	−0.777127
$656$	2.38327	0.0930510
$657$	4.10705	0.160231
$658$	−34.3222	−1.33802
$659$	2.10505	0.0820013	0.0410006	−	0.999159i	$-0.486945\pi$
$659$	2.10505	0.0820013	0.0410006	+	0.999159i	$0.486945\pi$
$660$	11.9922	0.466795
$661$	−16.7419	−0.651186	−0.325593	−	0.945510i	$-0.605564\pi$
$661$	−16.7419	−0.651186	−0.325593	+	0.945510i	$0.605564\pi$
$662$	32.3513	1.25737
$663$	−17.6014	−0.683582
$664$	30.7948	1.19507
$665$	−12.6748	−0.491507
$666$	1.18354	0.0458611
$667$	0.0374475	0.00144997
$668$	52.2537	2.02176
$669$	−4.75449	−0.183819
$670$	−31.1764	−1.20445
$671$	−5.21998	−0.201515
$672$	12.3706	0.477208
$673$	−29.0045	−1.11804	−0.559021	−	0.829154i	$-0.688823\pi$
$673$	−29.0045	−1.11804	−0.559021	+	0.829154i	$0.688823\pi$
$674$	27.4320	1.05664
$675$	−0.992628	−0.0382063
$676$	−15.6465	−0.601789
$677$	−13.4929	−0.518575	−0.259288	−	0.965800i	$-0.583488\pi$
$677$	−13.4929	−0.518575	−0.259288	+	0.965800i	$0.583488\pi$
$678$	−18.6026	−0.714429
$679$	−27.6573	−1.06139
$680$	−33.3649	−1.27948
$681$	−17.9008	−0.685959
$682$	12.1575	0.465533
$683$	27.2081	1.04109	0.520545	−	0.853834i	$-0.325729\pi$
$683$	27.2081	1.04109	0.520545	+	0.853834i	$0.325729\pi$
$684$	9.64688	0.368858
$685$	−25.3519	−0.968646
$686$	45.8259	1.74964
$687$	−13.0277	−0.497039
$688$	−1.49727	−0.0570830
$689$	−13.8471	−0.527533
$690$	0.0915991	0.00348712
$691$	−24.9247	−0.948181	−0.474090	−	0.880476i	$-0.657223\pi$
$691$	−24.9247	−0.948181	−0.474090	+	0.880476i	$0.657223\pi$
$692$	−49.4761	−1.88080
$693$	−3.93180	−0.149357
$694$	74.2297	2.81772
$695$	7.95661	0.301811
$696$	−5.01598	−0.190130
$697$	62.4709	2.36626
$698$	−49.4482	−1.87164
$699$	−12.0850	−0.457096
$700$	−6.59901	−0.249419
$701$	−30.6524	−1.15772	−0.578862	−	0.815425i	$-0.696503\pi$
$701$	−30.6524	−1.15772	−0.578862	+	0.815425i	$0.696503\pi$
$702$	−6.47264	−0.244294
$703$	−1.57583	−0.0594336
$704$	24.4880	0.922927
$705$	−14.4485	−0.544161
$706$	−84.1550	−3.16721
$707$	32.7715	1.23250
$708$	7.76854	0.291960
$709$	33.6592	1.26410	0.632049	−	0.774928i	$-0.282214\pi$
$709$	33.6592	1.26410	0.632049	+	0.774928i	$0.282214\pi$
$710$	10.0182	0.375976
$711$	−3.87452	−0.145306
$712$	−36.9896	−1.38624
$713$	0.0570258	0.00213563
$714$	29.4390	1.10173
$715$	10.7132	0.400652
$716$	−1.12046	−0.0418735
$717$	5.80701	0.216867
$718$	4.28377	0.159869
$719$	18.6224	0.694500	0.347250	−	0.937773i	$-0.387116\pi$
$719$	18.6224	0.694500	0.347250	+	0.937773i	$0.387116\pi$
$720$	0.472787	0.0176197
$721$	14.9437	0.556531
$722$	22.3382	0.831340
$723$	−9.59210	−0.356734
$724$	16.3945	0.609298
$725$	−1.84937	−0.0686838
$726$	16.9762	0.630046
$727$	34.6145	1.28378	0.641890	−	0.766797i	$-0.278151\pi$
$727$	34.6145	1.28378	0.641890	+	0.766797i	$0.278151\pi$
$728$	−15.9895	−0.592609
$729$	1.00000	0.0370370
$730$	18.7169	0.692745
$731$	−39.2470	−1.45160
$732$	8.82611	0.326223
$733$	16.9759	0.627019	0.313510	−	0.949585i	$-0.398495\pi$
$733$	16.9759	0.627019	0.313510	+	0.949585i	$0.398495\pi$
$734$	−16.8041	−0.620251
$735$	5.27824	0.194691
$736$	0.119034	0.00438765
$737$	12.8767	0.474320
$738$	22.9727	0.845637
$739$	−14.1309	−0.519813	−0.259906	−	0.965634i	$-0.583692\pi$
$739$	−14.1309	−0.519813	−0.259906	+	0.965634i	$0.583692\pi$
$740$	3.31224	0.121760
$741$	8.61805	0.316592
$742$	23.1598	0.850223
$743$	18.8077	0.689987	0.344993	−	0.938605i	$-0.387881\pi$
$743$	18.8077	0.689987	0.344993	+	0.938605i	$0.387881\pi$
$744$	−7.63843	−0.280038
$745$	34.2460	1.25468
$746$	−11.1530	−0.408340
$747$	−11.4382	−0.418502
$748$	37.0859	1.35599
$749$	−7.71793	−0.282007
$750$	−27.3100	−0.997220
$751$	26.9289	0.982651	0.491326	−	0.870976i	$-0.336513\pi$
$751$	26.9289	0.982651	0.491326	+	0.870976i	$0.336513\pi$
$752$	−1.70462	−0.0621611
$753$	−12.3913	−0.451565
$754$	−12.0592	−0.439170
$755$	9.47097	0.344684
$756$	6.64802	0.241786
$757$	40.6574	1.47772	0.738860	−	0.673859i	$-0.235365\pi$
$757$	40.6574	1.47772	0.738860	+	0.673859i	$0.235365\pi$
$758$	−1.07597	−0.0390810
$759$	−0.0378330	−0.00137325
$760$	16.3362	0.592577
$761$	30.8254	1.11742	0.558710	−	0.829363i	$-0.311296\pi$
$761$	30.8254	1.11742	0.558710	+	0.829363i	$0.311296\pi$
$762$	−33.0554	−1.19747
$763$	33.8551	1.22564
$764$	55.7866	2.01829
$765$	12.3928	0.448063
$766$	7.83235	0.282994
$767$	6.94004	0.250590
$768$	−14.4409	−0.521091
$769$	8.95267	0.322841	0.161421	−	0.986886i	$-0.448392\pi$
$769$	8.95267	0.322841	0.161421	+	0.986886i	$0.448392\pi$
$770$	−17.9183	−0.645730
$771$	10.8895	0.392175
$772$	54.0895	1.94673
$773$	−5.76563	−0.207375	−0.103688	−	0.994610i	$-0.533064\pi$
$773$	−5.76563	−0.207375	−0.103688	+	0.994610i	$0.533064\pi$
$774$	−14.4325	−0.518764
$775$	−2.81625	−0.101163
$776$	35.6468	1.27965
$777$	−1.08596	−0.0389587
$778$	32.2360	1.15572
$779$	−30.5872	−1.09590
$780$	−18.1143	−0.648595
$781$	−4.13779	−0.148062
$782$	0.283271	0.0101297
$783$	1.86310	0.0665818
$784$	0.622723	0.0222401
$785$	−46.5199	−1.66037
$786$	−22.6182	−0.806763
$787$	31.1041	1.10874	0.554371	−	0.832270i	$-0.312959\pi$
$787$	31.1041	1.10874	0.554371	+	0.832270i	$0.312959\pi$
$788$	−33.9046	−1.20780
$789$	6.62175	0.235741
$790$	−17.6572	−0.628216
$791$	17.0690	0.606903
$792$	5.06761	0.180070
$793$	7.88482	0.279998
$794$	−55.7012	−1.97676
$795$	9.74949	0.345779
$796$	5.09254	0.180500
$797$	31.7658	1.12520	0.562601	−	0.826729i	$-0.309801\pi$
$797$	31.7658	1.12520	0.562601	+	0.826729i	$0.309801\pi$
$798$	−14.4140	−0.510251
$799$	−44.6820	−1.58074
$800$	−5.87855	−0.207838
$801$	13.7392	0.485449
$802$	−34.0107	−1.20096
$803$	−7.73061	−0.272807
$804$	−21.7724	−0.767853
$805$	−0.0840474	−0.00296228
$806$	−18.3639	−0.646842
$807$	18.4347	0.648931
$808$	−42.2384	−1.48594
$809$	−18.4158	−0.647463	−0.323732	−	0.946149i	$-0.604938\pi$
$809$	−18.4158	−0.647463	−0.323732	+	0.946149i	$0.604938\pi$
$810$	4.55727	0.160126
$811$	31.7930	1.11640	0.558201	−	0.829706i	$-0.311492\pi$
$811$	31.7930	1.11640	0.558201	+	0.829706i	$0.311492\pi$
$812$	12.3859	0.434662
$813$	1.69508	0.0594492
$814$	−2.22775	−0.0780824
$815$	46.4266	1.62625
$816$	1.46210	0.0511836
$817$	19.2162	0.672291
$818$	62.8543	2.19765
$819$	5.93902	0.207526
$820$	64.2913	2.24515
$821$	34.2396	1.19497	0.597484	−	0.801881i	$-0.296167\pi$
$821$	34.2396	1.19497	0.597484	+	0.801881i	$0.296167\pi$
$822$	−28.8307	−1.00559
$823$	16.0400	0.559118	0.279559	−	0.960129i	$-0.409812\pi$
$823$	16.0400	0.559118	0.279559	+	0.960129i	$0.409812\pi$
$824$	−19.2605	−0.670973
$825$	1.86840	0.0650494
$826$	−11.6075	−0.403876
$827$	38.6322	1.34337	0.671687	−	0.740835i	$-0.265570\pi$
$827$	38.6322	1.34337	0.671687	+	0.740835i	$0.265570\pi$
$828$	0.0639692	0.00222308
$829$	13.6891	0.475441	0.237720	−	0.971334i	$-0.423600\pi$
$829$	13.6891	0.475441	0.237720	+	0.971334i	$0.423600\pi$
$830$	−52.1269	−1.80935
$831$	24.0787	0.835280
$832$	−36.9893	−1.28237
$833$	16.3230	0.565558
$834$	9.04842	0.313321
$835$	−32.8672	−1.13742
$836$	−18.1581	−0.628012
$837$	2.83716	0.0980667
$838$	−68.0356	−2.35025
$839$	−16.3010	−0.562773	−0.281386	−	0.959595i	$-0.590794\pi$
$839$	−16.3010	−0.562773	−0.281386	+	0.959595i	$0.590794\pi$
$840$	11.2579	0.388434
$841$	−25.5288	−0.880305
$842$	−76.7996	−2.64669
$843$	30.0179	1.03387
$844$	26.2848	0.904760
$845$	9.84154	0.338559
$846$	−16.4311	−0.564913
$847$	−15.5766	−0.535220
$848$	1.15024	0.0394993
$849$	12.6432	0.433914
$850$	−13.9895	−0.479835
$851$	−0.0104495	−0.000358203 0
$852$	6.99631	0.239690
$853$	39.0045	1.33549	0.667744	−	0.744391i	$-0.267260\pi$
$853$	39.0045	1.33549	0.667744	+	0.744391i	$0.267260\pi$
$854$	−13.1877	−0.451272
$855$	−6.06781	−0.207515
$856$	9.94746	0.339997
$857$	30.6658	1.04752	0.523761	−	0.851865i	$-0.324528\pi$
$857$	30.6658	1.04752	0.523761	+	0.851865i	$0.324528\pi$
$858$	12.1833	0.415931
$859$	−14.1640	−0.483270	−0.241635	−	0.970367i	$-0.577684\pi$
$859$	−14.1640	−0.483270	−0.241635	+	0.970367i	$0.577684\pi$
$860$	−40.3906	−1.37731
$861$	−21.0788	−0.718363
$862$	47.1055	1.60442
$863$	15.5749	0.530174	0.265087	−	0.964224i	$-0.414599\pi$
$863$	15.5749	0.530174	0.265087	+	0.964224i	$0.414599\pi$
$864$	5.92221	0.201478
$865$	31.1201	1.05811
$866$	−59.5296	−2.02290
$867$	21.3249	0.724231
$868$	18.8615	0.640202
$869$	7.29293	0.247396
$870$	8.49066	0.287860
$871$	−19.4504	−0.659051
$872$	−43.6351	−1.47767
$873$	−13.2404	−0.448120
$874$	−0.138696	−0.00469146
$875$	25.0585	0.847132
$876$	13.0712	0.441634
$877$	8.76628	0.296016	0.148008	−	0.988986i	$-0.452714\pi$
$877$	8.76628	0.296016	0.148008	+	0.988986i	$0.452714\pi$
$878$	−27.1867	−0.917507
$879$	8.11743	0.273794
$880$	−0.889916	−0.0299991
$881$	−34.6399	−1.16705	−0.583525	−	0.812095i	$-0.698327\pi$
$881$	−34.6399	−1.16705	−0.583525	+	0.812095i	$0.698327\pi$
$882$	6.00252	0.202116
$883$	3.35391	0.112868	0.0564340	−	0.998406i	$-0.482027\pi$
$883$	3.35391	0.112868	0.0564340	+	0.998406i	$0.482027\pi$
$884$	−56.0185	−1.88411
$885$	−4.88635	−0.164253
$886$	−24.0526	−0.808061
$887$	47.2528	1.58659	0.793296	−	0.608836i	$-0.208363\pi$
$887$	47.2528	1.58659	0.793296	+	0.608836i	$0.208363\pi$
$888$	1.39967	0.0469699
$889$	30.3303	1.01724
$890$	62.6130	2.09879
$891$	−1.88228	−0.0630587
$892$	−15.1317	−0.506648
$893$	21.8774	0.732098
$894$	38.9453	1.30253
$895$	0.704759	0.0235575
$896$	37.1248	1.24025
$897$	0.0571470	0.00190808
$898$	17.0181	0.567901
$899$	5.28593	0.176296
$900$	−3.15916	−0.105305
$901$	30.1504	1.00445
$902$	−43.2411	−1.43977
$903$	13.2426	0.440687
$904$	−21.9998	−0.731702
$905$	−10.3120	−0.342783
$906$	10.7706	0.357829
$907$	41.8576	1.38986	0.694930	−	0.719078i	$-0.255436\pi$
$907$	41.8576	1.38986	0.694930	+	0.719078i	$0.255436\pi$
$908$	−56.9713	−1.89066
$909$	15.6887	0.520363
$910$	27.0657	0.897219
$911$	−34.1655	−1.13195	−0.565976	−	0.824422i	$-0.691501\pi$
$911$	−34.1655	−1.13195	−0.565976	+	0.824422i	$0.691501\pi$
$912$	−0.715876	−0.0237050
$913$	21.5299	0.712534
$914$	9.87092	0.326501
$915$	−5.55156	−0.183529
$916$	−41.4623	−1.36995
$917$	20.7535	0.685340
$918$	14.0934	0.465151
$919$	16.5383	0.545547	0.272773	−	0.962078i	$-0.412059\pi$
$919$	16.5383	0.545547	0.272773	+	0.962078i	$0.412059\pi$
$920$	0.108327	0.00357143
$921$	−20.2784	−0.668197
$922$	−50.4631	−1.66191
$923$	6.25016	0.205727
$924$	−12.5134	−0.411662
$925$	0.516052	0.0169677
$926$	46.7566	1.53652
$927$	7.15400	0.234968
$928$	11.0337	0.362199
$929$	31.0774	1.01962	0.509808	−	0.860288i	$-0.329717\pi$
$929$	31.0774	1.01962	0.509808	+	0.860288i	$0.329717\pi$
$930$	12.9297	0.423982
$931$	−7.99212	−0.261931
$932$	−38.4619	−1.25986
$933$	−0.789591	−0.0258500
$934$	73.9855	2.42088
$935$	−23.3267	−0.762866
$936$	−7.65466	−0.250200
$937$	−45.2341	−1.47773	−0.738866	−	0.673852i	$-0.764639\pi$
$937$	−45.2341	−1.47773	−0.738866	+	0.673852i	$0.764639\pi$
$938$	32.5315	1.06219
$939$	−5.99597	−0.195671
$940$	−45.9840	−1.49983
$941$	40.5493	1.32187	0.660935	−	0.750443i	$-0.270160\pi$
$941$	40.5493	1.32187	0.660935	+	0.750443i	$0.270160\pi$
$942$	−52.9034	−1.72369
$943$	−0.202826	−0.00660493
$944$	−0.576488	−0.0187631
$945$	−4.18156	−0.136026
$946$	27.1659	0.883240
$947$	−53.3125	−1.73242	−0.866211	−	0.499678i	$-0.833452\pi$
$947$	−53.3125	−1.73242	−0.866211	+	0.499678i	$0.833452\pi$
$948$	−12.3311	−0.400496
$949$	11.6771	0.379056
$950$	6.84957	0.222229
$951$	4.34365	0.140852
$952$	34.8151	1.12836
$953$	−13.9133	−0.450697	−0.225348	−	0.974278i	$-0.572352\pi$
$953$	−13.9133	−0.450697	−0.225348	+	0.974278i	$0.572352\pi$
$954$	11.0873	0.358965
$955$	−35.0893	−1.13546
$956$	18.4815	0.597734
$957$	−3.50688	−0.113361
$958$	18.9103	0.610964
$959$	26.4538	0.854239
$960$	26.0435	0.840551
$961$	−22.9505	−0.740339
$962$	3.36503	0.108493
$963$	−3.69482	−0.119064
$964$	−30.5280	−0.983240
$965$	−34.0219	−1.09520
$966$	−0.0955805	−0.00307525
$967$	25.5656	0.822133	0.411066	−	0.911605i	$-0.365156\pi$
$967$	25.5656	0.822133	0.411066	+	0.911605i	$0.365156\pi$
$968$	20.0764	0.645279
$969$	−18.7648	−0.602811
$970$	−60.3401	−1.93741
$971$	−1.47504	−0.0473364	−0.0236682	−	0.999720i	$-0.507535\pi$
$971$	−1.47504	−0.0473364	−0.0236682	+	0.999720i	$0.507535\pi$
$972$	3.18262	0.102083
$973$	−8.30244	−0.266164
$974$	−54.5993	−1.74947
$975$	−2.82223	−0.0903838
$976$	−0.654968	−0.0209650
$977$	10.3406	0.330825	0.165413	−	0.986224i	$-0.447104\pi$
$977$	10.3406	0.330825	0.165413	+	0.986224i	$0.447104\pi$
$978$	52.7973	1.68827
$979$	−25.8609	−0.826518
$980$	16.7986	0.536612
$981$	16.2075	0.517466
$982$	−44.9608	−1.43476
$983$	−19.3345	−0.616673	−0.308337	−	0.951277i	$-0.599772\pi$
$983$	−19.3345	−0.616673	−0.308337	+	0.951277i	$0.599772\pi$
$984$	27.1680	0.866083
$985$	21.3257	0.679494
$986$	26.2574	0.836206
$987$	15.0765	0.479890
$988$	27.4280	0.872600
$989$	0.127424	0.00405186
$990$	−8.57805	−0.272628
$991$	−45.7936	−1.45468	−0.727342	−	0.686276i	$-0.759244\pi$
$991$	−45.7936	−1.45468	−0.727342	+	0.686276i	$0.759244\pi$
$992$	16.8023	0.533473
$993$	−14.2108	−0.450965
$994$	−10.4536	−0.331569
$995$	−3.20317	−0.101547
$996$	−36.4034	−1.15349
$997$	19.3559	0.613007	0.306503	−	0.951870i	$-0.400841\pi$
$997$	19.3559	0.613007	0.306503	+	0.951870i	$0.400841\pi$
$998$	−38.0115	−1.20323
$999$	−0.519885	−0.0164484

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.15	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.d.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.27654 q^{2} +1.00000 q^{3} +3.18262 q^{4} -2.00184 q^{5} -2.27654 q^{6} +2.08885 q^{7} -2.69227 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.27654 q^{2} +1.00000 q^{3} +3.18262 q^{4} -2.00184 q^{5} -2.27654 q^{6} +2.08885 q^{7} -2.69227 q^{8} +1.00000 q^{9} +4.55727 q^{10} -1.88228 q^{11} +3.18262 q^{12} +2.84320 q^{13} -4.75535 q^{14} -2.00184 q^{15} -0.236176 q^{16} -6.19071 q^{17} -2.27654 q^{18} +3.03112 q^{19} -6.37110 q^{20} +2.08885 q^{21} +4.28508 q^{22} +0.0200996 q^{23} -2.69227 q^{24} -0.992628 q^{25} -6.47264 q^{26} +1.00000 q^{27} +6.64802 q^{28} +1.86310 q^{29} +4.55727 q^{30} +2.83716 q^{31} +5.92221 q^{32} -1.88228 q^{33} +14.0934 q^{34} -4.18156 q^{35} +3.18262 q^{36} -0.519885 q^{37} -6.90044 q^{38} +2.84320 q^{39} +5.38951 q^{40} -10.0911 q^{41} -4.75535 q^{42} +6.33966 q^{43} -5.99057 q^{44} -2.00184 q^{45} -0.0457574 q^{46} +7.21759 q^{47} -0.236176 q^{48} -2.63669 q^{49} +2.25975 q^{50} -6.19071 q^{51} +9.04881 q^{52} -4.87026 q^{53} -2.27654 q^{54} +3.76802 q^{55} -5.62377 q^{56} +3.03112 q^{57} -4.24142 q^{58} +2.44093 q^{59} -6.37110 q^{60} +2.77322 q^{61} -6.45891 q^{62} +2.08885 q^{63} -13.0098 q^{64} -5.69163 q^{65} +4.28508 q^{66} -6.84103 q^{67} -19.7027 q^{68} +0.0200996 q^{69} +9.51946 q^{70} +2.19829 q^{71} -2.69227 q^{72} +4.10705 q^{73} +1.18354 q^{74} -0.992628 q^{75} +9.64688 q^{76} -3.93180 q^{77} -6.47264 q^{78} -3.87452 q^{79} +0.472787 q^{80} +1.00000 q^{81} +22.9727 q^{82} -11.4382 q^{83} +6.64802 q^{84} +12.3928 q^{85} -14.4325 q^{86} +1.86310 q^{87} +5.06761 q^{88} +13.7392 q^{89} +4.55727 q^{90} +5.93902 q^{91} +0.0639692 q^{92} +2.83716 q^{93} -16.4311 q^{94} -6.06781 q^{95} +5.92221 q^{96} -13.2404 q^{97} +6.00252 q^{98} -1.88228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 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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