LMFDB - Embedded newform 8007.2.a.h.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.30269 q^{2} +1.00000 q^{3} -0.302986 q^{4} +1.77397 q^{5} -1.30269 q^{6} +4.96759 q^{7} +3.00009 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.30269 q^{2} +1.00000 q^{3} -0.302986 q^{4} +1.77397 q^{5} -1.30269 q^{6} +4.96759 q^{7} +3.00009 q^{8} +1.00000 q^{9} -2.31094 q^{10} +3.26508 q^{11} -0.302986 q^{12} +5.32809 q^{13} -6.47126 q^{14} +1.77397 q^{15} -3.30223 q^{16} -1.00000 q^{17} -1.30269 q^{18} -1.23221 q^{19} -0.537487 q^{20} +4.96759 q^{21} -4.25341 q^{22} -3.28460 q^{23} +3.00009 q^{24} -1.85305 q^{25} -6.94087 q^{26} +1.00000 q^{27} -1.50511 q^{28} -1.38745 q^{29} -2.31094 q^{30} -4.09785 q^{31} -1.69838 q^{32} +3.26508 q^{33} +1.30269 q^{34} +8.81234 q^{35} -0.302986 q^{36} -6.42384 q^{37} +1.60519 q^{38} +5.32809 q^{39} +5.32205 q^{40} -7.82428 q^{41} -6.47126 q^{42} -7.22926 q^{43} -0.989275 q^{44} +1.77397 q^{45} +4.27883 q^{46} +6.67261 q^{47} -3.30223 q^{48} +17.6770 q^{49} +2.41395 q^{50} -1.00000 q^{51} -1.61434 q^{52} +12.6211 q^{53} -1.30269 q^{54} +5.79214 q^{55} +14.9032 q^{56} -1.23221 q^{57} +1.80742 q^{58} +12.8065 q^{59} -0.537487 q^{60} +7.56095 q^{61} +5.33825 q^{62} +4.96759 q^{63} +8.81693 q^{64} +9.45184 q^{65} -4.25341 q^{66} +0.416044 q^{67} +0.302986 q^{68} -3.28460 q^{69} -11.4798 q^{70} -13.4932 q^{71} +3.00009 q^{72} +9.52385 q^{73} +8.36831 q^{74} -1.85305 q^{75} +0.373342 q^{76} +16.2196 q^{77} -6.94087 q^{78} -5.08995 q^{79} -5.85804 q^{80} +1.00000 q^{81} +10.1927 q^{82} +12.6258 q^{83} -1.50511 q^{84} -1.77397 q^{85} +9.41752 q^{86} -1.38745 q^{87} +9.79553 q^{88} +6.96248 q^{89} -2.31094 q^{90} +26.4678 q^{91} +0.995187 q^{92} -4.09785 q^{93} -8.69238 q^{94} -2.18590 q^{95} -1.69838 q^{96} +9.44439 q^{97} -23.0277 q^{98} +3.26508 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.30269	−0.921144	−0.460572	−	0.887622i	$-0.652356\pi$
$2$	−1.30269	−0.921144	−0.460572	+	0.887622i	$0.652356\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.302986	−0.151493
$5$	1.77397	0.793341	0.396671	−	0.917961i	$-0.370165\pi$
$5$	1.77397	0.793341	0.396671	+	0.917961i	$0.370165\pi$
$6$	−1.30269	−0.531823
$7$	4.96759	1.87757	0.938787	−	0.344499i	$-0.111951\pi$
$7$	4.96759	1.87757	0.938787	+	0.344499i	$0.111951\pi$
$8$	3.00009	1.06069
$9$	1.00000	0.333333
$10$	−2.31094	−0.730782
$11$	3.26508	0.984459	0.492230	−	0.870465i	$-0.336182\pi$
$11$	3.26508	0.984459	0.492230	+	0.870465i	$0.336182\pi$
$12$	−0.302986	−0.0874646
$13$	5.32809	1.47775	0.738873	−	0.673845i	$-0.235358\pi$
$13$	5.32809	1.47775	0.738873	+	0.673845i	$0.235358\pi$
$14$	−6.47126	−1.72952
$15$	1.77397	0.458036
$16$	−3.30223	−0.825557
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.30269	−0.307048
$19$	−1.23221	−0.282688	−0.141344	−	0.989961i	$-0.545142\pi$
$19$	−1.23221	−0.282688	−0.141344	+	0.989961i	$0.545142\pi$
$20$	−0.537487	−0.120186
$21$	4.96759	1.08402
$22$	−4.25341	−0.906829
$23$	−3.28460	−0.684885	−0.342443	−	0.939539i	$-0.611254\pi$
$23$	−3.28460	−0.684885	−0.342443	+	0.939539i	$0.611254\pi$
$24$	3.00009	0.612390
$25$	−1.85305	−0.370609
$26$	−6.94087	−1.36122
$27$	1.00000	0.192450
$28$	−1.50511	−0.284439
$29$	−1.38745	−0.257642	−0.128821	−	0.991668i	$-0.541119\pi$
$29$	−1.38745	−0.257642	−0.128821	+	0.991668i	$0.541119\pi$
$30$	−2.31094	−0.421917
$31$	−4.09785	−0.735996	−0.367998	−	0.929827i	$-0.619957\pi$
$31$	−4.09785	−0.735996	−0.367998	+	0.929827i	$0.619957\pi$
$32$	−1.69838	−0.300234
$33$	3.26508	0.568378
$34$	1.30269	0.223410
$35$	8.81234	1.48956
$36$	−0.302986	−0.0504977
$37$	−6.42384	−1.05607	−0.528037	−	0.849222i	$-0.677072\pi$
$37$	−6.42384	−1.05607	−0.528037	+	0.849222i	$0.677072\pi$
$38$	1.60519	0.260397
$39$	5.32809	0.853177
$40$	5.32205	0.841490
$41$	−7.82428	−1.22195	−0.610974	−	0.791651i	$-0.709222\pi$
$41$	−7.82428	−1.22195	−0.610974	+	0.791651i	$0.709222\pi$
$42$	−6.47126	−0.998537
$43$	−7.22926	−1.10245	−0.551226	−	0.834356i	$-0.685840\pi$
$43$	−7.22926	−1.10245	−0.551226	+	0.834356i	$0.685840\pi$
$44$	−0.989275	−0.149139
$45$	1.77397	0.264447
$46$	4.27883	0.630878
$47$	6.67261	0.973301	0.486650	−	0.873597i	$-0.338219\pi$
$47$	6.67261	0.973301	0.486650	+	0.873597i	$0.338219\pi$
$48$	−3.30223	−0.476635
$49$	17.6770	2.52528
$50$	2.41395	0.341385
$51$	−1.00000	−0.140028
$52$	−1.61434	−0.223868
$53$	12.6211	1.73365	0.866824	−	0.498614i	$-0.166158\pi$
$53$	12.6211	1.73365	0.866824	+	0.498614i	$0.166158\pi$
$54$	−1.30269	−0.177274
$55$	5.79214	0.781012
$56$	14.9032	1.99153
$57$	−1.23221	−0.163210
$58$	1.80742	0.237326
$59$	12.8065	1.66727	0.833634	−	0.552318i	$-0.186257\pi$
$59$	12.8065	1.66727	0.833634	+	0.552318i	$0.186257\pi$
$60$	−0.537487	−0.0693893
$61$	7.56095	0.968081	0.484040	−	0.875046i	$-0.339169\pi$
$61$	7.56095	0.968081	0.484040	+	0.875046i	$0.339169\pi$
$62$	5.33825	0.677958
$63$	4.96759	0.625858
$64$	8.81693	1.10212
$65$	9.45184	1.17236
$66$	−4.25341	−0.523558
$67$	0.416044	0.0508279	0.0254139	−	0.999677i	$-0.491910\pi$
$67$	0.416044	0.0508279	0.0254139	+	0.999677i	$0.491910\pi$
$68$	0.302986	0.0367425
$69$	−3.28460	−0.395419
$70$	−11.4798	−1.37210
$71$	−13.4932	−1.60135	−0.800673	−	0.599102i	$-0.795524\pi$
$71$	−13.4932	−1.60135	−0.800673	+	0.599102i	$0.795524\pi$
$72$	3.00009	0.353564
$73$	9.52385	1.11468	0.557341	−	0.830283i	$-0.311821\pi$
$73$	9.52385	1.11468	0.557341	+	0.830283i	$0.311821\pi$
$74$	8.36831	0.972796
$75$	−1.85305	−0.213971
$76$	0.373342	0.0428253
$77$	16.2196	1.84839
$78$	−6.94087	−0.785899
$79$	−5.08995	−0.572665	−0.286332	−	0.958130i	$-0.592436\pi$
$79$	−5.08995	−0.572665	−0.286332	+	0.958130i	$0.592436\pi$
$80$	−5.85804	−0.654948
$81$	1.00000	0.111111
$82$	10.1927	1.12559
$83$	12.6258	1.38586	0.692932	−	0.721003i	$-0.256319\pi$
$83$	12.6258	1.38586	0.692932	+	0.721003i	$0.256319\pi$
$84$	−1.50511	−0.164221
$85$	−1.77397	−0.192414
$86$	9.41752	1.01552
$87$	−1.38745	−0.148750
$88$	9.79553	1.04421
$89$	6.96248	0.738022	0.369011	−	0.929425i	$-0.379697\pi$
$89$	6.96248	0.738022	0.369011	+	0.929425i	$0.379697\pi$
$90$	−2.31094	−0.243594
$91$	26.4678	2.77458
$92$	0.995187	0.103755
$93$	−4.09785	−0.424927
$94$	−8.69238	−0.896551
$95$	−2.18590	−0.224268
$96$	−1.69838	−0.173340
$97$	9.44439	0.958933	0.479466	−	0.877560i	$-0.340830\pi$
$97$	9.44439	0.958933	0.479466	+	0.877560i	$0.340830\pi$
$98$	−23.0277	−2.32615
$99$	3.26508	0.328153
$100$	0.561448	0.0561448
$101$	−15.5846	−1.55073	−0.775364	−	0.631515i	$-0.782433\pi$
$101$	−15.5846	−1.55073	−0.775364	+	0.631515i	$0.782433\pi$
$102$	1.30269	0.128986
$103$	−11.5694	−1.13997	−0.569983	−	0.821656i	$-0.693050\pi$
$103$	−11.5694	−1.13997	−0.569983	+	0.821656i	$0.693050\pi$
$104$	15.9847	1.56743
$105$	8.81234	0.859996
$106$	−16.4415	−1.59694
$107$	0.232264	0.0224538	0.0112269	−	0.999937i	$-0.496426\pi$
$107$	0.232264	0.0224538	0.0112269	+	0.999937i	$0.496426\pi$
$108$	−0.302986	−0.0291549
$109$	−0.681004	−0.0652284	−0.0326142	−	0.999468i	$-0.510383\pi$
$109$	−0.681004	−0.0652284	−0.0326142	+	0.999468i	$0.510383\pi$
$110$	−7.54539	−0.719425
$111$	−6.42384	−0.609724
$112$	−16.4041	−1.55004
$113$	10.2157	0.961015	0.480508	−	0.876990i	$-0.340452\pi$
$113$	10.2157	0.961015	0.480508	+	0.876990i	$0.340452\pi$
$114$	1.60519	0.150340
$115$	−5.82676	−0.543348
$116$	0.420377	0.0390310
$117$	5.32809	0.492582
$118$	−16.6830	−1.53579
$119$	−4.96759	−0.455378
$120$	5.32205	0.485835
$121$	−0.339238	−0.0308399
$122$	−9.84961	−0.891742
$123$	−7.82428	−0.705492
$124$	1.24159	0.111498
$125$	−12.1571	−1.08736
$126$	−6.47126	−0.576505
$127$	5.28103	0.468615	0.234308	−	0.972162i	$-0.424718\pi$
$127$	5.28103	0.468615	0.234308	+	0.972162i	$0.424718\pi$
$128$	−8.08900	−0.714973
$129$	−7.22926	−0.636501
$130$	−12.3129	−1.07991
$131$	7.75853	0.677866	0.338933	−	0.940810i	$-0.389934\pi$
$131$	7.75853	0.677866	0.338933	+	0.940810i	$0.389934\pi$
$132$	−0.989275	−0.0861053
$133$	−6.12111	−0.530768
$134$	−0.541978	−0.0468198
$135$	1.77397	0.152679
$136$	−3.00009	−0.257255
$137$	13.9736	1.19385	0.596923	−	0.802298i	$-0.296390\pi$
$137$	13.9736	1.19385	0.596923	+	0.802298i	$0.296390\pi$
$138$	4.27883	0.364238
$139$	0.454198	0.0385246	0.0192623	−	0.999814i	$-0.493868\pi$
$139$	0.454198	0.0385246	0.0192623	+	0.999814i	$0.493868\pi$
$140$	−2.67002	−0.225658
$141$	6.67261	0.561936
$142$	17.5775	1.47507
$143$	17.3966	1.45478
$144$	−3.30223	−0.275186
$145$	−2.46128	−0.204398
$146$	−12.4067	−1.02678
$147$	17.6770	1.45797
$148$	1.94634	0.159988
$149$	16.1136	1.32008	0.660040	−	0.751231i	$-0.270539\pi$
$149$	16.1136	1.32008	0.660040	+	0.751231i	$0.270539\pi$
$150$	2.41395	0.197099
$151$	−14.8953	−1.21217	−0.606083	−	0.795402i	$-0.707260\pi$
$151$	−14.8953	−1.21217	−0.606083	+	0.795402i	$0.707260\pi$
$152$	−3.69674	−0.299845
$153$	−1.00000	−0.0808452
$154$	−21.1292	−1.70264
$155$	−7.26944	−0.583896
$156$	−1.61434	−0.129250
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	6.63066	0.527507
$159$	12.6211	1.00092
$160$	−3.01287	−0.238188
$161$	−16.3165	−1.28592
$162$	−1.30269	−0.102349
$163$	3.49079	0.273420	0.136710	−	0.990611i	$-0.456347\pi$
$163$	3.49079	0.273420	0.136710	+	0.990611i	$0.456347\pi$
$164$	2.37065	0.185117
$165$	5.79214	0.450918
$166$	−16.4476	−1.27658
$167$	−22.5151	−1.74227	−0.871135	−	0.491043i	$-0.836616\pi$
$167$	−22.5151	−1.74227	−0.871135	+	0.491043i	$0.836616\pi$
$168$	14.9032	1.14981
$169$	15.3885	1.18373
$170$	2.31094	0.177241
$171$	−1.23221	−0.0942294
$172$	2.19037	0.167014
$173$	−5.59665	−0.425505	−0.212753	−	0.977106i	$-0.568243\pi$
$173$	−5.59665	−0.425505	−0.212753	+	0.977106i	$0.568243\pi$
$174$	1.80742	0.137020
$175$	−9.20518	−0.695846
$176$	−10.7820	−0.812727
$177$	12.8065	0.962597
$178$	−9.06999	−0.679824
$179$	11.3283	0.846716	0.423358	−	0.905963i	$-0.360851\pi$
$179$	11.3283	0.846716	0.423358	+	0.905963i	$0.360851\pi$
$180$	−0.537487	−0.0400619
$181$	10.0485	0.746899	0.373450	−	0.927650i	$-0.378175\pi$
$181$	10.0485	0.746899	0.373450	+	0.927650i	$0.378175\pi$
$182$	−34.4794	−2.55579
$183$	7.56095	0.558922
$184$	−9.85408	−0.726452
$185$	−11.3957	−0.837827
$186$	5.33825	0.391419
$187$	−3.26508	−0.238766
$188$	−2.02171	−0.147448
$189$	4.96759	0.361339
$190$	2.84756	0.206583
$191$	24.6837	1.78605	0.893025	−	0.450007i	$-0.148578\pi$
$191$	24.6837	1.78605	0.893025	+	0.450007i	$0.148578\pi$
$192$	8.81693	0.636307
$193$	−13.7761	−0.991627	−0.495814	−	0.868429i	$-0.665130\pi$
$193$	−13.7761	−0.991627	−0.495814	+	0.868429i	$0.665130\pi$
$194$	−12.3032	−0.883315
$195$	9.45184	0.676861
$196$	−5.35588	−0.382563
$197$	5.20459	0.370812	0.185406	−	0.982662i	$-0.440640\pi$
$197$	5.20459	0.370812	0.185406	+	0.982662i	$0.440640\pi$
$198$	−4.25341	−0.302276
$199$	−13.8953	−0.985010	−0.492505	−	0.870310i	$-0.663919\pi$
$199$	−13.8953	−0.985010	−0.492505	+	0.870310i	$0.663919\pi$
$200$	−5.55930	−0.393102
$201$	0.416044	0.0293455
$202$	20.3020	1.42844
$203$	−6.89227	−0.483742
$204$	0.302986	0.0212133
$205$	−13.8800	−0.969422
$206$	15.0714	1.05007
$207$	−3.28460	−0.228295
$208$	−17.5946	−1.21996
$209$	−4.02326	−0.278295
$210$	−11.4798	−0.792181
$211$	15.3415	1.05615	0.528077	−	0.849196i	$-0.322913\pi$
$211$	15.3415	1.05615	0.528077	+	0.849196i	$0.322913\pi$
$212$	−3.82403	−0.262636
$213$	−13.4932	−0.924537
$214$	−0.302569	−0.0206832
$215$	−12.8245	−0.874621
$216$	3.00009	0.204130
$217$	−20.3565	−1.38189
$218$	0.887141	0.0600848
$219$	9.52385	0.643562
$220$	−1.75494	−0.118318
$221$	−5.32809	−0.358406
$222$	8.36831	0.561644
$223$	0.787249	0.0527181	0.0263590	−	0.999653i	$-0.491609\pi$
$223$	0.787249	0.0527181	0.0263590	+	0.999653i	$0.491609\pi$
$224$	−8.43687	−0.563712
$225$	−1.85305	−0.123536
$226$	−13.3080	−0.885234
$227$	28.9435	1.92105	0.960524	−	0.278197i	$-0.0897366\pi$
$227$	28.9435	1.92105	0.960524	+	0.278197i	$0.0897366\pi$
$228$	0.373342	0.0247252
$229$	11.1856	0.739166	0.369583	−	0.929198i	$-0.379501\pi$
$229$	11.1856	0.739166	0.369583	+	0.929198i	$0.379501\pi$
$230$	7.59049	0.500502
$231$	16.2196	1.06717
$232$	−4.16246	−0.273279
$233$	−26.7364	−1.75156	−0.875781	−	0.482709i	$-0.839653\pi$
$233$	−26.7364	−1.75156	−0.875781	+	0.482709i	$0.839653\pi$
$234$	−6.94087	−0.453739
$235$	11.8370	0.772160
$236$	−3.88020	−0.252579
$237$	−5.08995	−0.330628
$238$	6.47126	0.419469
$239$	−28.0902	−1.81701	−0.908503	−	0.417878i	$-0.862774\pi$
$239$	−28.0902	−1.81701	−0.908503	+	0.417878i	$0.862774\pi$
$240$	−5.85804	−0.378135
$241$	20.2748	1.30601	0.653007	−	0.757352i	$-0.273507\pi$
$241$	20.2748	1.30601	0.653007	+	0.757352i	$0.273507\pi$
$242$	0.441924	0.0284080
$243$	1.00000	0.0641500
$244$	−2.29086	−0.146658
$245$	31.3583	2.00341
$246$	10.1927	0.649860
$247$	−6.56532	−0.417741
$248$	−12.2939	−0.780664
$249$	12.6258	0.800129
$250$	15.8369	1.00162
$251$	7.43695	0.469416	0.234708	−	0.972066i	$-0.424587\pi$
$251$	7.43695	0.469416	0.234708	+	0.972066i	$0.424587\pi$
$252$	−1.50511	−0.0948132
$253$	−10.7245	−0.674242
$254$	−6.87957	−0.431662
$255$	−1.77397	−0.111090
$256$	−7.09636	−0.443522
$257$	16.2944	1.01642	0.508210	−	0.861233i	$-0.330308\pi$
$257$	16.2944	1.01642	0.508210	+	0.861233i	$0.330308\pi$
$258$	9.41752	0.586309
$259$	−31.9110	−1.98286
$260$	−2.86378	−0.177604
$261$	−1.38745	−0.0858807
$262$	−10.1070	−0.624413
$263$	20.8873	1.28797	0.643983	−	0.765040i	$-0.277281\pi$
$263$	20.8873	1.28797	0.643983	+	0.765040i	$0.277281\pi$
$264$	9.79553	0.602873
$265$	22.3895	1.37537
$266$	7.97394	0.488914
$267$	6.96248	0.426097
$268$	−0.126056	−0.00770007
$269$	14.1751	0.864269	0.432135	−	0.901809i	$-0.357761\pi$
$269$	14.1751	0.864269	0.432135	+	0.901809i	$0.357761\pi$
$270$	−2.31094	−0.140639
$271$	5.90867	0.358926	0.179463	−	0.983765i	$-0.442564\pi$
$271$	5.90867	0.358926	0.179463	+	0.983765i	$0.442564\pi$
$272$	3.30223	0.200227
$273$	26.4678	1.60190
$274$	−18.2034	−1.09971
$275$	−6.05035	−0.364850
$276$	0.995187	0.0599032
$277$	13.5599	0.814736	0.407368	−	0.913264i	$-0.366447\pi$
$277$	13.5599	0.814736	0.407368	+	0.913264i	$0.366447\pi$
$278$	−0.591682	−0.0354867
$279$	−4.09785	−0.245332
$280$	26.4378	1.57996
$281$	−20.0114	−1.19378	−0.596889	−	0.802324i	$-0.703597\pi$
$281$	−20.0114	−1.19378	−0.596889	+	0.802324i	$0.703597\pi$
$282$	−8.69238	−0.517624
$283$	2.47756	0.147275	0.0736377	−	0.997285i	$-0.476539\pi$
$283$	2.47756	0.147275	0.0736377	+	0.997285i	$0.476539\pi$
$284$	4.08825	0.242593
$285$	−2.18590	−0.129481
$286$	−22.6625	−1.34006
$287$	−38.8679	−2.29430
$288$	−1.69838	−0.100078
$289$	1.00000	0.0588235
$290$	3.20630	0.188280
$291$	9.44439	0.553640
$292$	−2.88560	−0.168867
$293$	−23.9104	−1.39686	−0.698430	−	0.715678i	$-0.746118\pi$
$293$	−23.9104	−1.39686	−0.698430	+	0.715678i	$0.746118\pi$
$294$	−23.0277	−1.34300
$295$	22.7183	1.32271
$296$	−19.2721	−1.12017
$297$	3.26508	0.189459
$298$	−20.9911	−1.21598
$299$	−17.5006	−1.01209
$300$	0.561448	0.0324152
$301$	−35.9120	−2.06994
$302$	19.4041	1.11658
$303$	−15.5846	−0.895313
$304$	4.06903	0.233375
$305$	13.4129	0.768019
$306$	1.30269	0.0744701
$307$	−0.944796	−0.0539224	−0.0269612	−	0.999636i	$-0.508583\pi$
$307$	−0.944796	−0.0539224	−0.0269612	+	0.999636i	$0.508583\pi$
$308$	−4.91431	−0.280019
$309$	−11.5694	−0.658160
$310$	9.46987	0.537852
$311$	23.4674	1.33071	0.665357	−	0.746526i	$-0.268279\pi$
$311$	23.4674	1.33071	0.665357	+	0.746526i	$0.268279\pi$
$312$	15.9847	0.904957
$313$	21.7472	1.22922	0.614612	−	0.788830i	$-0.289313\pi$
$313$	21.7472	1.22922	0.614612	+	0.788830i	$0.289313\pi$
$314$	1.30269	0.0735153
$315$	8.81234	0.496519
$316$	1.54219	0.0867547
$317$	−15.7934	−0.887044	−0.443522	−	0.896264i	$-0.646271\pi$
$317$	−15.7934	−0.887044	−0.443522	+	0.896264i	$0.646271\pi$
$318$	−16.4415	−0.921994
$319$	−4.53012	−0.253638
$320$	15.6409	0.874354
$321$	0.232264	0.0129637
$322$	21.2555	1.18452
$323$	1.23221	0.0685620
$324$	−0.302986	−0.0168326
$325$	−9.87320	−0.547666
$326$	−4.54744	−0.251859
$327$	−0.681004	−0.0376596
$328$	−23.4735	−1.29611
$329$	33.1468	1.82744
$330$	−7.54539	−0.415360
$331$	−13.5193	−0.743089	−0.371545	−	0.928415i	$-0.621172\pi$
$331$	−13.5193	−0.743089	−0.371545	+	0.928415i	$0.621172\pi$
$332$	−3.82545	−0.209949
$333$	−6.42384	−0.352024
$334$	29.3303	1.60488
$335$	0.738048	0.0403238
$336$	−16.4041	−0.894918
$337$	4.63099	0.252266	0.126133	−	0.992013i	$-0.459743\pi$
$337$	4.63099	0.252266	0.126133	+	0.992013i	$0.459743\pi$
$338$	−20.0465	−1.09039
$339$	10.2157	0.554843
$340$	0.537487	0.0291493
$341$	−13.3798	−0.724558
$342$	1.60519	0.0867989
$343$	53.0389	2.86383
$344$	−21.6884	−1.16936
$345$	−5.82676	−0.313702
$346$	7.29072	0.391952
$347$	27.5240	1.47756	0.738782	−	0.673944i	$-0.235401\pi$
$347$	27.5240	1.47756	0.738782	+	0.673944i	$0.235401\pi$
$348$	0.420377	0.0225346
$349$	−25.4640	−1.36306	−0.681530	−	0.731791i	$-0.738685\pi$
$349$	−25.4640	−1.36306	−0.681530	+	0.731791i	$0.738685\pi$
$350$	11.9915	0.640975
$351$	5.32809	0.284392
$352$	−5.54536	−0.295569
$353$	−36.8316	−1.96035	−0.980174	−	0.198138i	$-0.936510\pi$
$353$	−36.8316	−1.96035	−0.980174	+	0.198138i	$0.936510\pi$
$354$	−16.6830	−0.886691
$355$	−23.9364	−1.27041
$356$	−2.10954	−0.111805
$357$	−4.96759	−0.262913
$358$	−14.7573	−0.779947
$359$	13.1347	0.693221	0.346611	−	0.938009i	$-0.387333\pi$
$359$	13.1347	0.693221	0.346611	+	0.938009i	$0.387333\pi$
$360$	5.32205	0.280497
$361$	−17.4817	−0.920087
$362$	−13.0901	−0.688002
$363$	−0.339238	−0.0178054
$364$	−8.01937	−0.420329
$365$	16.8950	0.884324
$366$	−9.84961	−0.514848
$367$	−23.3698	−1.21989	−0.609947	−	0.792442i	$-0.708809\pi$
$367$	−23.3698	−1.21989	−0.609947	+	0.792442i	$0.708809\pi$
$368$	10.8465	0.565412
$369$	−7.82428	−0.407316
$370$	14.8451	0.771759
$371$	62.6967	3.25505
$372$	1.24159	0.0643736
$373$	−2.88162	−0.149205	−0.0746024	−	0.997213i	$-0.523769\pi$
$373$	−2.88162	−0.149205	−0.0746024	+	0.997213i	$0.523769\pi$
$374$	4.25341	0.219938
$375$	−12.1571	−0.627788
$376$	20.0184	1.03237
$377$	−7.39243	−0.380730
$378$	−6.47126	−0.332846
$379$	−22.5943	−1.16059	−0.580297	−	0.814405i	$-0.697063\pi$
$379$	−22.5943	−1.16059	−0.580297	+	0.814405i	$0.697063\pi$
$380$	0.662297	0.0339751
$381$	5.28103	0.270555
$382$	−32.1553	−1.64521
$383$	−8.35914	−0.427132	−0.213566	−	0.976929i	$-0.568508\pi$
$383$	−8.35914	−0.427132	−0.213566	+	0.976929i	$0.568508\pi$
$384$	−8.08900	−0.412790
$385$	28.7730	1.46641
$386$	17.9461	0.913432
$387$	−7.22926	−0.367484
$388$	−2.86152	−0.145272
$389$	9.78601	0.496170	0.248085	−	0.968738i	$-0.420199\pi$
$389$	9.78601	0.496170	0.248085	+	0.968738i	$0.420199\pi$
$390$	−12.3129	−0.623486
$391$	3.28460	0.166109
$392$	53.0325	2.67855
$393$	7.75853	0.391366
$394$	−6.78000	−0.341571
$395$	−9.02940	−0.454319
$396$	−0.989275	−0.0497129
$397$	−4.30987	−0.216306	−0.108153	−	0.994134i	$-0.534494\pi$
$397$	−4.30987	−0.216306	−0.108153	+	0.994134i	$0.534494\pi$
$398$	18.1013	0.907337
$399$	−6.12111	−0.306439
$400$	6.11918	0.305959
$401$	−10.2150	−0.510113	−0.255057	−	0.966926i	$-0.582094\pi$
$401$	−10.2150	−0.510113	−0.255057	+	0.966926i	$0.582094\pi$
$402$	−0.541978	−0.0270314
$403$	−21.8337	−1.08761
$404$	4.72192	0.234924
$405$	1.77397	0.0881491
$406$	8.97852	0.445596
$407$	−20.9744	−1.03966
$408$	−3.00009	−0.148526
$409$	−12.6539	−0.625697	−0.312849	−	0.949803i	$-0.601283\pi$
$409$	−12.6539	−0.625697	−0.312849	+	0.949803i	$0.601283\pi$
$410$	18.0814	0.892978
$411$	13.9736	0.689268
$412$	3.50537	0.172697
$413$	63.6176	3.13042
$414$	4.27883	0.210293
$415$	22.3978	1.09946
$416$	−9.04913	−0.443670
$417$	0.454198	0.0222422
$418$	5.24109	0.256350
$419$	7.97379	0.389545	0.194773	−	0.980848i	$-0.437603\pi$
$419$	7.97379	0.389545	0.194773	+	0.980848i	$0.437603\pi$
$420$	−2.67002	−0.130283
$421$	13.4161	0.653860	0.326930	−	0.945049i	$-0.393986\pi$
$421$	13.4161	0.653860	0.326930	+	0.945049i	$0.393986\pi$
$422$	−19.9853	−0.972871
$423$	6.67261	0.324434
$424$	37.8646	1.83887
$425$	1.85305	0.0898860
$426$	17.5775	0.851632
$427$	37.5597	1.81764
$428$	−0.0703728	−0.00340160
$429$	17.3966	0.839918
$430$	16.7064	0.805652
$431$	22.8212	1.09926	0.549629	−	0.835409i	$-0.314769\pi$
$431$	22.8212	1.09926	0.549629	+	0.835409i	$0.314769\pi$
$432$	−3.30223	−0.158878
$433$	2.61206	0.125527	0.0627637	−	0.998028i	$-0.480009\pi$
$433$	2.61206	0.125527	0.0627637	+	0.998028i	$0.480009\pi$
$434$	26.5182	1.27292
$435$	−2.46128	−0.118009
$436$	0.206335	0.00988165
$437$	4.04731	0.193609
$438$	−12.4067	−0.592814
$439$	14.5131	0.692675	0.346337	−	0.938110i	$-0.387425\pi$
$439$	14.5131	0.692675	0.346337	+	0.938110i	$0.387425\pi$
$440$	17.3769	0.828413
$441$	17.6770	0.841761
$442$	6.94087	0.330144
$443$	−10.0972	−0.479732	−0.239866	−	0.970806i	$-0.577103\pi$
$443$	−10.0972	−0.479732	−0.239866	+	0.970806i	$0.577103\pi$
$444$	1.94634	0.0923690
$445$	12.3512	0.585503
$446$	−1.02555	−0.0485610
$447$	16.1136	0.762148
$448$	43.7989	2.06930
$449$	12.3200	0.581416	0.290708	−	0.956812i	$-0.406109\pi$
$449$	12.3200	0.581416	0.290708	+	0.956812i	$0.406109\pi$
$450$	2.41395	0.113795
$451$	−25.5469	−1.20296
$452$	−3.09523	−0.145587
$453$	−14.8953	−0.699844
$454$	−37.7046	−1.76956
$455$	46.9529	2.20119
$456$	−3.69674	−0.173116
$457$	−8.46200	−0.395836	−0.197918	−	0.980219i	$-0.563418\pi$
$457$	−8.46200	−0.395836	−0.197918	+	0.980219i	$0.563418\pi$
$458$	−14.5714	−0.680878
$459$	−1.00000	−0.0466760
$460$	1.76543	0.0823135
$461$	3.90762	0.181996	0.0909981	−	0.995851i	$-0.470994\pi$
$461$	3.90762	0.181996	0.0909981	+	0.995851i	$0.470994\pi$
$462$	−21.1292	−0.983019
$463$	−34.7059	−1.61292	−0.806460	−	0.591289i	$-0.798619\pi$
$463$	−34.7059	−1.61292	−0.806460	+	0.591289i	$0.798619\pi$
$464$	4.58166	0.212698
$465$	−7.26944	−0.337112
$466$	34.8294	1.61344
$467$	19.0139	0.879857	0.439928	−	0.898033i	$-0.355004\pi$
$467$	19.0139	0.879857	0.439928	+	0.898033i	$0.355004\pi$
$468$	−1.61434	−0.0746228
$469$	2.06674	0.0954330
$470$	−15.4200	−0.711271
$471$	−1.00000	−0.0460776
$472$	38.4207	1.76846
$473$	−23.6041	−1.08532
$474$	6.63066	0.304556
$475$	2.28334	0.104767
$476$	1.50511	0.0689867
$477$	12.6211	0.577883
$478$	36.5930	1.67373
$479$	−33.8900	−1.54847	−0.774237	−	0.632896i	$-0.781866\pi$
$479$	−33.8900	−1.54847	−0.774237	+	0.632896i	$0.781866\pi$
$480$	−3.01287	−0.137518
$481$	−34.2268	−1.56061
$482$	−26.4119	−1.20303
$483$	−16.3165	−0.742428
$484$	0.102785	0.00467203
$485$	16.7540	0.760761
$486$	−1.30269	−0.0590914
$487$	−15.9586	−0.723151	−0.361576	−	0.932343i	$-0.617761\pi$
$487$	−15.9586	−0.723151	−0.361576	+	0.932343i	$0.617761\pi$
$488$	22.6835	1.02683
$489$	3.49079	0.157859
$490$	−40.8504	−1.84543
$491$	18.0682	0.815406	0.407703	−	0.913115i	$-0.366330\pi$
$491$	18.0682	0.815406	0.407703	+	0.913115i	$0.366330\pi$
$492$	2.37065	0.106877
$493$	1.38745	0.0624874
$494$	8.55261	0.384800
$495$	5.79214	0.260337
$496$	13.5320	0.607606
$497$	−67.0286	−3.00664
$498$	−16.4476	−0.737034
$499$	−38.6643	−1.73085	−0.865426	−	0.501037i	$-0.832952\pi$
$499$	−38.6643	−1.73085	−0.865426	+	0.501037i	$0.832952\pi$
$500$	3.68342	0.164728
$501$	−22.5151	−1.00590
$502$	−9.68807	−0.432400
$503$	7.21846	0.321855	0.160928	−	0.986966i	$-0.448551\pi$
$503$	7.21846	0.321855	0.160928	+	0.986966i	$0.448551\pi$
$504$	14.9032	0.663842
$505$	−27.6466	−1.23026
$506$	13.9707	0.621074
$507$	15.3885	0.683428
$508$	−1.60008	−0.0709920
$509$	−1.15353	−0.0511292	−0.0255646	−	0.999673i	$-0.508138\pi$
$509$	−1.15353	−0.0511292	−0.0255646	+	0.999673i	$0.508138\pi$
$510$	2.31094	0.102330
$511$	47.3106	2.09290
$512$	25.4224	1.12352
$513$	−1.23221	−0.0544034
$514$	−21.2267	−0.936269
$515$	−20.5237	−0.904383
$516$	2.19037	0.0964255
$517$	21.7866	0.958175
$518$	41.5703	1.82650
$519$	−5.59665	−0.245666
$520$	28.3564	1.24351
$521$	11.4002	0.499450	0.249725	−	0.968317i	$-0.419660\pi$
$521$	11.4002	0.499450	0.249725	+	0.968317i	$0.419660\pi$
$522$	1.80742	0.0791086
$523$	44.3343	1.93860	0.969302	−	0.245871i	$-0.0790741\pi$
$523$	44.3343	1.93860	0.969302	+	0.245871i	$0.0790741\pi$
$524$	−2.35073	−0.102692
$525$	−9.20518	−0.401747
$526$	−27.2098	−1.18640
$527$	4.09785	0.178505
$528$	−10.7820	−0.469228
$529$	−12.2114	−0.530932
$530$	−29.1667	−1.26692
$531$	12.8065	0.555756
$532$	1.85461	0.0804077
$533$	−41.6885	−1.80573
$534$	−9.06999	−0.392497
$535$	0.412028	0.0178135
$536$	1.24817	0.0539127
$537$	11.3283	0.488852
$538$	−18.4658	−0.796117
$539$	57.7168	2.48604
$540$	−0.537487	−0.0231298
$541$	41.6837	1.79212	0.896062	−	0.443929i	$-0.146416\pi$
$541$	41.6837	1.79212	0.896062	+	0.443929i	$0.146416\pi$
$542$	−7.69719	−0.330623
$543$	10.0485	0.431223
$544$	1.69838	0.0728175
$545$	−1.20808	−0.0517484
$546$	−34.4794	−1.47558
$547$	−31.0214	−1.32638	−0.663189	−	0.748452i	$-0.730798\pi$
$547$	−31.0214	−1.32638	−0.663189	+	0.748452i	$0.730798\pi$
$548$	−4.23381	−0.180860
$549$	7.56095	0.322694
$550$	7.88176	0.336079
$551$	1.70962	0.0728324
$552$	−9.85408	−0.419417
$553$	−25.2848	−1.07522
$554$	−17.6644	−0.750489
$555$	−11.3957	−0.483720
$556$	−0.137616	−0.00583621
$557$	7.21950	0.305900	0.152950	−	0.988234i	$-0.451123\pi$
$557$	7.21950	0.305900	0.152950	+	0.988234i	$0.451123\pi$
$558$	5.33825	0.225986
$559$	−38.5182	−1.62914
$560$	−29.1003	−1.22971
$561$	−3.26508	−0.137852
$562$	26.0687	1.09964
$563$	−31.5342	−1.32901	−0.664503	−	0.747285i	$-0.731357\pi$
$563$	−31.5342	−1.32901	−0.664503	+	0.747285i	$0.731357\pi$
$564$	−2.02171	−0.0851294
$565$	18.1224	0.762413
$566$	−3.22750	−0.135662
$567$	4.96759	0.208619
$568$	−40.4807	−1.69853
$569$	−9.30798	−0.390211	−0.195105	−	0.980782i	$-0.562505\pi$
$569$	−9.30798	−0.390211	−0.195105	+	0.980782i	$0.562505\pi$
$570$	2.84756	0.119271
$571$	−27.7687	−1.16208	−0.581042	−	0.813873i	$-0.697355\pi$
$571$	−27.7687	−1.16208	−0.581042	+	0.813873i	$0.697355\pi$
$572$	−5.27094	−0.220389
$573$	24.6837	1.03118
$574$	50.6330	2.11338
$575$	6.08651	0.253825
$576$	8.81693	0.367372
$577$	−24.1302	−1.00455	−0.502276	−	0.864707i	$-0.667504\pi$
$577$	−24.1302	−1.00455	−0.502276	+	0.864707i	$0.667504\pi$
$578$	−1.30269	−0.0541850
$579$	−13.7761	−0.572516
$580$	0.745734	0.0309649
$581$	62.7200	2.60206
$582$	−12.3032	−0.509982
$583$	41.2091	1.70671
$584$	28.5724	1.18233
$585$	9.45184	0.390786
$586$	31.1479	1.28671
$587$	39.8336	1.64411	0.822053	−	0.569410i	$-0.192828\pi$
$587$	39.8336	1.64411	0.822053	+	0.569410i	$0.192828\pi$
$588$	−5.35588	−0.220873
$589$	5.04941	0.208057
$590$	−29.5950	−1.21841
$591$	5.20459	0.214088
$592$	21.2130	0.871849
$593$	−5.62079	−0.230818	−0.115409	−	0.993318i	$-0.536818\pi$
$593$	−5.62079	−0.230818	−0.115409	+	0.993318i	$0.536818\pi$
$594$	−4.25341	−0.174519
$595$	−8.81234	−0.361271
$596$	−4.88221	−0.199983
$597$	−13.8953	−0.568696
$598$	22.7980	0.932278
$599$	−35.4804	−1.44969	−0.724844	−	0.688913i	$-0.758088\pi$
$599$	−35.4804	−1.44969	−0.724844	+	0.688913i	$0.758088\pi$
$600$	−5.55930	−0.226958
$601$	−1.62491	−0.0662815	−0.0331407	−	0.999451i	$-0.510551\pi$
$601$	−1.62491	−0.0662815	−0.0331407	+	0.999451i	$0.510551\pi$
$602$	46.7824	1.90671
$603$	0.416044	0.0169426
$604$	4.51308	0.183635
$605$	−0.601797	−0.0244665
$606$	20.3020	0.824712
$607$	−47.1657	−1.91440	−0.957199	−	0.289432i	$-0.906534\pi$
$607$	−47.1657	−1.91440	−0.957199	+	0.289432i	$0.906534\pi$
$608$	2.09276	0.0848727
$609$	−6.89227	−0.279289
$610$	−17.4729	−0.707456
$611$	35.5523	1.43829
$612$	0.302986	0.0122475
$613$	−44.7847	−1.80884	−0.904419	−	0.426645i	$-0.859695\pi$
$613$	−44.7847	−1.80884	−0.904419	+	0.426645i	$0.859695\pi$
$614$	1.23078	0.0496703
$615$	−13.8800	−0.559696
$616$	48.6602	1.96058
$617$	35.9955	1.44912	0.724562	−	0.689209i	$-0.242042\pi$
$617$	35.9955	1.44912	0.724562	+	0.689209i	$0.242042\pi$
$618$	15.0714	0.606260
$619$	−19.6427	−0.789507	−0.394754	−	0.918787i	$-0.629170\pi$
$619$	−19.6427	−0.789507	−0.394754	+	0.918787i	$0.629170\pi$
$620$	2.20254	0.0884562
$621$	−3.28460	−0.131806
$622$	−30.5708	−1.22578
$623$	34.5868	1.38569
$624$	−17.5946	−0.704346
$625$	−12.3010	−0.492039
$626$	−28.3299	−1.13229
$627$	−4.02326	−0.160674
$628$	0.302986	0.0120905
$629$	6.42384	0.256135
$630$	−11.4798	−0.457366
$631$	−28.6652	−1.14114	−0.570572	−	0.821247i	$-0.693279\pi$
$631$	−28.6652	−1.14114	−0.570572	+	0.821247i	$0.693279\pi$
$632$	−15.2703	−0.607420
$633$	15.3415	0.609771
$634$	20.5739	0.817095
$635$	9.36836	0.371772
$636$	−3.82403	−0.151633
$637$	94.1845	3.73173
$638$	5.90137	0.233637
$639$	−13.4932	−0.533782
$640$	−14.3496	−0.567218
$641$	−11.6313	−0.459407	−0.229704	−	0.973261i	$-0.573776\pi$
$641$	−11.6313	−0.459407	−0.229704	+	0.973261i	$0.573776\pi$
$642$	−0.302569	−0.0119414
$643$	−16.0350	−0.632360	−0.316180	−	0.948699i	$-0.602400\pi$
$643$	−16.0350	−0.632360	−0.316180	+	0.948699i	$0.602400\pi$
$644$	4.94368	0.194808
$645$	−12.8245	−0.504963
$646$	−1.60519	−0.0631555
$647$	−7.37388	−0.289897	−0.144949	−	0.989439i	$-0.546302\pi$
$647$	−7.37388	−0.289897	−0.144949	+	0.989439i	$0.546302\pi$
$648$	3.00009	0.117855
$649$	41.8143	1.64136
$650$	12.8618	0.504480
$651$	−20.3565	−0.797832
$652$	−1.05766	−0.0414212
$653$	0.934430	0.0365671	0.0182835	−	0.999833i	$-0.494180\pi$
$653$	0.934430	0.0365671	0.0182835	+	0.999833i	$0.494180\pi$
$654$	0.887141	0.0346900
$655$	13.7634	0.537779
$656$	25.8376	1.00879
$657$	9.52385	0.371561
$658$	−43.1802	−1.68334
$659$	−0.669035	−0.0260619	−0.0130309	−	0.999915i	$-0.504148\pi$
$659$	−0.669035	−0.0260619	−0.0130309	+	0.999915i	$0.504148\pi$
$660$	−1.75494	−0.0683109
$661$	−17.6113	−0.685000	−0.342500	−	0.939518i	$-0.611274\pi$
$661$	−17.6113	−0.685000	−0.342500	+	0.939518i	$0.611274\pi$
$662$	17.6116	0.684492
$663$	−5.32809	−0.206926
$664$	37.8786	1.46997
$665$	−10.8586	−0.421080
$666$	8.36831	0.324265
$667$	4.55720	0.176455
$668$	6.82176	0.263942
$669$	0.787249	0.0304368
$670$	−0.961451	−0.0371441
$671$	24.6871	0.953036
$672$	−8.43687	−0.325459
$673$	−32.3599	−1.24738	−0.623692	−	0.781670i	$-0.714368\pi$
$673$	−32.3599	−1.24738	−0.623692	+	0.781670i	$0.714368\pi$
$674$	−6.03276	−0.232373
$675$	−1.85305	−0.0713238
$676$	−4.66251	−0.179327
$677$	13.8708	0.533099	0.266550	−	0.963821i	$-0.414116\pi$
$677$	13.8708	0.533099	0.266550	+	0.963821i	$0.414116\pi$
$678$	−13.3080	−0.511090
$679$	46.9159	1.80047
$680$	−5.32205	−0.204091
$681$	28.9435	1.10912
$682$	17.4298	0.667422
$683$	−8.84993	−0.338633	−0.169317	−	0.985562i	$-0.554156\pi$
$683$	−8.84993	−0.338633	−0.169317	+	0.985562i	$0.554156\pi$
$684$	0.373342	0.0142751
$685$	24.7887	0.947128
$686$	−69.0935	−2.63800
$687$	11.1856	0.426757
$688$	23.8727	0.910137
$689$	67.2466	2.56189
$690$	7.59049	0.288965
$691$	21.8116	0.829754	0.414877	−	0.909877i	$-0.363825\pi$
$691$	21.8116	0.829754	0.414877	+	0.909877i	$0.363825\pi$
$692$	1.69571	0.0644611
$693$	16.2196	0.616132
$694$	−35.8553	−1.36105
$695$	0.805732	0.0305632
$696$	−4.16246	−0.157778
$697$	7.82428	0.296366
$698$	33.1719	1.25557
$699$	−26.7364	−1.01126
$700$	2.78904	0.105416
$701$	33.7742	1.27563	0.637817	−	0.770188i	$-0.279838\pi$
$701$	33.7742	1.27563	0.637817	+	0.770188i	$0.279838\pi$
$702$	−6.94087	−0.261966
$703$	7.91552	0.298539
$704$	28.7880	1.08499
$705$	11.8370	0.445807
$706$	47.9803	1.80576
$707$	−77.4180	−2.91160
$708$	−3.88020	−0.145827
$709$	−19.3878	−0.728123	−0.364062	−	0.931375i	$-0.618610\pi$
$709$	−19.3878	−0.728123	−0.364062	+	0.931375i	$0.618610\pi$
$710$	31.1819	1.17023
$711$	−5.08995	−0.190888
$712$	20.8881	0.782813
$713$	13.4598	0.504073
$714$	6.47126	0.242181
$715$	30.8610	1.15414
$716$	−3.43231	−0.128272
$717$	−28.0902	−1.04905
$718$	−17.1105	−0.638557
$719$	−1.17433	−0.0437951	−0.0218975	−	0.999760i	$-0.506971\pi$
$719$	−1.17433	−0.0437951	−0.0218975	+	0.999760i	$0.506971\pi$
$720$	−5.85804	−0.218316
$721$	−57.4720	−2.14037
$722$	22.7733	0.847533
$723$	20.2748	0.754027
$724$	−3.04456	−0.113150
$725$	2.57100	0.0954846
$726$	0.441924	0.0164013
$727$	−4.15321	−0.154034	−0.0770170	−	0.997030i	$-0.524540\pi$
$727$	−4.15321	−0.154034	−0.0770170	+	0.997030i	$0.524540\pi$
$728$	79.4057	2.94297
$729$	1.00000	0.0370370
$730$	−22.0090	−0.814590
$731$	7.22926	0.267384
$732$	−2.29086	−0.0846728
$733$	−12.4746	−0.460759	−0.230379	−	0.973101i	$-0.573997\pi$
$733$	−12.4746	−0.460759	−0.230379	+	0.973101i	$0.573997\pi$
$734$	30.4437	1.12370
$735$	31.3583	1.15667
$736$	5.57850	0.205626
$737$	1.35842	0.0500380
$738$	10.1927	0.375197
$739$	−27.0658	−0.995632	−0.497816	−	0.867283i	$-0.665864\pi$
$739$	−27.0658	−0.995632	−0.497816	+	0.867283i	$0.665864\pi$
$740$	3.45273	0.126925
$741$	−6.56532	−0.241183
$742$	−81.6747	−2.99837
$743$	−44.8671	−1.64601	−0.823006	−	0.568032i	$-0.807705\pi$
$743$	−44.8671	−1.64601	−0.823006	+	0.568032i	$0.807705\pi$
$744$	−12.2939	−0.450717
$745$	28.5850	1.04727
$746$	3.75388	0.137439
$747$	12.6258	0.461955
$748$	0.989275	0.0361715
$749$	1.15379	0.0421587
$750$	15.8369	0.578284
$751$	−16.1177	−0.588144	−0.294072	−	0.955783i	$-0.595011\pi$
$751$	−16.1177	−0.588144	−0.294072	+	0.955783i	$0.595011\pi$
$752$	−22.0345	−0.803515
$753$	7.43695	0.271017
$754$	9.63008	0.350707
$755$	−26.4238	−0.961661
$756$	−1.50511	−0.0547404
$757$	−31.3076	−1.13790	−0.568948	−	0.822374i	$-0.692649\pi$
$757$	−31.3076	−1.13790	−0.568948	+	0.822374i	$0.692649\pi$
$758$	29.4335	1.06907
$759$	−10.7245	−0.389274
$760$	−6.55788	−0.237879
$761$	36.8375	1.33536	0.667679	−	0.744449i	$-0.267288\pi$
$761$	36.8375	1.33536	0.667679	+	0.744449i	$0.267288\pi$
$762$	−6.87957	−0.249220
$763$	−3.38295	−0.122471
$764$	−7.47882	−0.270574
$765$	−1.77397	−0.0641379
$766$	10.8894	0.393450
$767$	68.2343	2.46380
$768$	−7.09636	−0.256068
$769$	1.71275	0.0617635	0.0308817	−	0.999523i	$-0.490168\pi$
$769$	1.71275	0.0617635	0.0308817	+	0.999523i	$0.490168\pi$
$770$	−37.4824	−1.35077
$771$	16.2944	0.586830
$772$	4.17398	0.150225
$773$	−52.3319	−1.88225	−0.941124	−	0.338061i	$-0.890229\pi$
$773$	−52.3319	−1.88225	−0.941124	+	0.338061i	$0.890229\pi$
$774$	9.41752	0.338506
$775$	7.59351	0.272767
$776$	28.3340	1.01713
$777$	−31.9110	−1.14480
$778$	−12.7482	−0.457045
$779$	9.64116	0.345430
$780$	−2.86378	−0.102540
$781$	−44.0563	−1.57646
$782$	−4.27883	−0.153010
$783$	−1.38745	−0.0495833
$784$	−58.3734	−2.08476
$785$	−1.77397	−0.0633155
$786$	−10.1070	−0.360505
$787$	−19.4209	−0.692281	−0.346140	−	0.938183i	$-0.612508\pi$
$787$	−19.4209	−0.692281	−0.346140	+	0.938183i	$0.612508\pi$
$788$	−1.57692	−0.0561755
$789$	20.8873	0.743607
$790$	11.7626	0.418493
$791$	50.7476	1.80438
$792$	9.79553	0.348069
$793$	40.2854	1.43058
$794$	5.61444	0.199249
$795$	22.3895	0.794073
$796$	4.21008	0.149222
$797$	−44.7635	−1.58561	−0.792803	−	0.609478i	$-0.791379\pi$
$797$	−44.7635	−1.58561	−0.792803	+	0.609478i	$0.791379\pi$
$798$	7.97394	0.282275
$799$	−6.67261	−0.236060
$800$	3.14718	0.111270
$801$	6.96248	0.246007
$802$	13.3070	0.469888
$803$	31.0962	1.09736
$804$	−0.126056	−0.00444564
$805$	−28.9450	−1.02018
$806$	28.4427	1.00185
$807$	14.1751	0.498986
$808$	−46.7552	−1.64484
$809$	−16.4217	−0.577357	−0.288678	−	0.957426i	$-0.593216\pi$
$809$	−16.4217	−0.577357	−0.288678	+	0.957426i	$0.593216\pi$
$810$	−2.31094	−0.0811980
$811$	38.8018	1.36252	0.681259	−	0.732043i	$-0.261433\pi$
$811$	38.8018	1.36252	0.681259	+	0.732043i	$0.261433\pi$
$812$	2.08826	0.0732836
$813$	5.90867	0.207226
$814$	27.3232	0.957678
$815$	6.19254	0.216915
$816$	3.30223	0.115601
$817$	8.90796	0.311650
$818$	16.4842	0.576357
$819$	26.4678	0.924859
$820$	4.20545	0.146861
$821$	29.0979	1.01552	0.507762	−	0.861497i	$-0.330473\pi$
$821$	29.0979	1.01552	0.507762	+	0.861497i	$0.330473\pi$
$822$	−18.2034	−0.634915
$823$	−19.2470	−0.670908	−0.335454	−	0.942057i	$-0.608890\pi$
$823$	−19.2470	−0.670908	−0.335454	+	0.942057i	$0.608890\pi$
$824$	−34.7092	−1.20915
$825$	−6.05035	−0.210646
$826$	−82.8743	−2.88357
$827$	−8.41938	−0.292771	−0.146385	−	0.989228i	$-0.546764\pi$
$827$	−8.41938	−0.292771	−0.146385	+	0.989228i	$0.546764\pi$
$828$	0.995187	0.0345851
$829$	2.83859	0.0985885	0.0492942	−	0.998784i	$-0.484303\pi$
$829$	2.83859	0.0985885	0.0492942	+	0.998784i	$0.484303\pi$
$830$	−29.1775	−1.01276
$831$	13.5599	0.470388
$832$	46.9774	1.62865
$833$	−17.6770	−0.612471
$834$	−0.591682	−0.0204883
$835$	−39.9410	−1.38222
$836$	1.21899	0.0421598
$837$	−4.09785	−0.141642
$838$	−10.3874	−0.358828
$839$	38.2226	1.31959	0.659795	−	0.751445i	$-0.270643\pi$
$839$	38.2226	1.31959	0.659795	+	0.751445i	$0.270643\pi$
$840$	26.4378	0.912190
$841$	−27.0750	−0.933620
$842$	−17.4771	−0.602299
$843$	−20.0114	−0.689229
$844$	−4.64827	−0.160000
$845$	27.2987	0.939104
$846$	−8.69238	−0.298850
$847$	−1.68520	−0.0579041
$848$	−41.6779	−1.43122
$849$	2.47756	0.0850295
$850$	−2.41395	−0.0827979
$851$	21.0997	0.723289
$852$	4.08825	0.140061
$853$	11.8698	0.406414	0.203207	−	0.979136i	$-0.434864\pi$
$853$	11.8698	0.406414	0.203207	+	0.979136i	$0.434864\pi$
$854$	−48.9289	−1.67431
$855$	−2.18590	−0.0747561
$856$	0.696812	0.0238165
$857$	−19.7870	−0.675911	−0.337956	−	0.941162i	$-0.609735\pi$
$857$	−19.7870	−0.675911	−0.337956	+	0.941162i	$0.609735\pi$
$858$	−22.6625	−0.773686
$859$	14.4354	0.492530	0.246265	−	0.969203i	$-0.420797\pi$
$859$	14.4354	0.492530	0.246265	+	0.969203i	$0.420797\pi$
$860$	3.88564	0.132499
$861$	−38.8679	−1.32461
$862$	−29.7291	−1.01258
$863$	−40.8679	−1.39116	−0.695580	−	0.718448i	$-0.744853\pi$
$863$	−40.8679	−1.39116	−0.695580	+	0.718448i	$0.744853\pi$
$864$	−1.69838	−0.0577801
$865$	−9.92826	−0.337571
$866$	−3.40271	−0.115629
$867$	1.00000	0.0339618
$868$	6.16772	0.209346
$869$	−16.6191	−0.563765
$870$	3.20630	0.108704
$871$	2.21672	0.0751107
$872$	−2.04307	−0.0691872
$873$	9.44439	0.319644
$874$	−5.27241	−0.178342
$875$	−60.3914	−2.04160
$876$	−2.88560	−0.0974953
$877$	−2.63801	−0.0890794	−0.0445397	−	0.999008i	$-0.514182\pi$
$877$	−2.63801	−0.0890794	−0.0445397	+	0.999008i	$0.514182\pi$
$878$	−18.9062	−0.638053
$879$	−23.9104	−0.806478
$880$	−19.1270	−0.644770
$881$	33.1920	1.11827	0.559133	−	0.829078i	$-0.311134\pi$
$881$	33.1920	1.11827	0.559133	+	0.829078i	$0.311134\pi$
$882$	−23.0277	−0.775383
$883$	−51.6721	−1.73891	−0.869453	−	0.494016i	$-0.835529\pi$
$883$	−51.6721	−1.73891	−0.869453	+	0.494016i	$0.835529\pi$
$884$	1.61434	0.0542960
$885$	22.7183	0.763668
$886$	13.1535	0.441902
$887$	−4.47304	−0.150190	−0.0750950	−	0.997176i	$-0.523926\pi$
$887$	−4.47304	−0.150190	−0.0750950	+	0.997176i	$0.523926\pi$
$888$	−19.2721	−0.646729
$889$	26.2340	0.879860
$890$	−16.0898	−0.539333
$891$	3.26508	0.109384
$892$	−0.238526	−0.00798643
$893$	−8.22206	−0.275141
$894$	−20.9911	−0.702048
$895$	20.0960	0.671735
$896$	−40.1829	−1.34242
$897$	−17.5006	−0.584328
$898$	−16.0492	−0.535568
$899$	5.68555	0.189624
$900$	0.561448	0.0187149
$901$	−12.6211	−0.420471
$902$	33.2799	1.10810
$903$	−35.9120	−1.19508
$904$	30.6481	1.01934
$905$	17.8257	0.592546
$906$	19.4041	0.644657
$907$	−29.6154	−0.983362	−0.491681	−	0.870775i	$-0.663617\pi$
$907$	−29.6154	−0.983362	−0.491681	+	0.870775i	$0.663617\pi$
$908$	−8.76949	−0.291026
$909$	−15.5846	−0.516909
$910$	−61.1653	−2.02761
$911$	−5.67515	−0.188026	−0.0940130	−	0.995571i	$-0.529970\pi$
$911$	−5.67515	−0.188026	−0.0940130	+	0.995571i	$0.529970\pi$
$912$	4.06903	0.134739
$913$	41.2244	1.36433
$914$	11.0234	0.364622
$915$	13.4129	0.443416
$916$	−3.38908	−0.111979
$917$	38.5412	1.27274
$918$	1.30269	0.0429953
$919$	18.7545	0.618654	0.309327	−	0.950956i	$-0.399896\pi$
$919$	18.7545	0.618654	0.309327	+	0.950956i	$0.399896\pi$
$920$	−17.4808	−0.576325
$921$	−0.944796	−0.0311321
$922$	−5.09044	−0.167645
$923$	−71.8928	−2.36638
$924$	−4.91431	−0.161669
$925$	11.9037	0.391391
$926$	45.2112	1.48573
$927$	−11.5694	−0.379989
$928$	2.35641	0.0773531
$929$	5.84329	0.191712	0.0958561	−	0.995395i	$-0.469441\pi$
$929$	5.84329	0.191712	0.0958561	+	0.995395i	$0.469441\pi$
$930$	9.46987	0.310529
$931$	−21.7817	−0.713868
$932$	8.10077	0.265350
$933$	23.4674	0.768288
$934$	−24.7693	−0.810475
$935$	−5.79214	−0.189423
$936$	15.9847	0.522477
$937$	−20.5032	−0.669810	−0.334905	−	0.942252i	$-0.608704\pi$
$937$	−20.5032	−0.669810	−0.334905	+	0.942252i	$0.608704\pi$
$938$	−2.69233	−0.0879076
$939$	21.7472	0.709692
$940$	−3.58644	−0.116977
$941$	9.89433	0.322546	0.161273	−	0.986910i	$-0.448440\pi$
$941$	9.89433	0.322546	0.161273	+	0.986910i	$0.448440\pi$
$942$	1.30269	0.0424441
$943$	25.6996	0.836894
$944$	−42.2900	−1.37642
$945$	8.81234	0.286665
$946$	30.7490	0.999736
$947$	49.2712	1.60110	0.800550	−	0.599266i	$-0.204541\pi$
$947$	49.2712	1.60110	0.800550	+	0.599266i	$0.204541\pi$
$948$	1.54219	0.0500879
$949$	50.7439	1.64722
$950$	−2.97450	−0.0965054
$951$	−15.7934	−0.512135
$952$	−14.9032	−0.483016
$953$	−23.5307	−0.762233	−0.381117	−	0.924527i	$-0.624460\pi$
$953$	−23.5307	−0.762233	−0.381117	+	0.924527i	$0.624460\pi$
$954$	−16.4415	−0.532313
$955$	43.7880	1.41695
$956$	8.51096	0.275264
$957$	−4.53012	−0.146438
$958$	44.1483	1.42637
$959$	69.4152	2.24154
$960$	15.6409	0.504809
$961$	−14.2076	−0.458310
$962$	44.5871	1.43755
$963$	0.232264	0.00748460
$964$	−6.14298	−0.197852
$965$	−24.4384	−0.786699
$966$	21.2555	0.683883
$967$	−40.8669	−1.31419	−0.657096	−	0.753807i	$-0.728215\pi$
$967$	−40.8669	−1.31419	−0.657096	+	0.753807i	$0.728215\pi$
$968$	−1.01775	−0.0327116
$969$	1.23221	0.0395843
$970$	−21.8254	−0.700771
$971$	−16.0406	−0.514767	−0.257383	−	0.966309i	$-0.582860\pi$
$971$	−16.0406	−0.514767	−0.257383	+	0.966309i	$0.582860\pi$
$972$	−0.302986	−0.00971829
$973$	2.25627	0.0723328
$974$	20.7891	0.666127
$975$	−9.87320	−0.316195
$976$	−24.9680	−0.799206
$977$	7.24755	0.231870	0.115935	−	0.993257i	$-0.463014\pi$
$977$	7.24755	0.231870	0.115935	+	0.993257i	$0.463014\pi$
$978$	−4.54744	−0.145411
$979$	22.7331	0.726552
$980$	−9.50115	−0.303503
$981$	−0.681004	−0.0217428
$982$	−23.5373	−0.751106
$983$	42.1136	1.34321	0.671607	−	0.740907i	$-0.265604\pi$
$983$	42.1136	1.34321	0.671607	+	0.740907i	$0.265604\pi$
$984$	−23.4735	−0.748309
$985$	9.23277	0.294180
$986$	−1.80742	−0.0575599
$987$	33.1468	1.05508
$988$	1.98920	0.0632849
$989$	23.7452	0.755054
$990$	−7.54539	−0.239808
$991$	−59.6797	−1.89579	−0.947894	−	0.318585i	$-0.896792\pi$
$991$	−59.6797	−1.89579	−0.947894	+	0.318585i	$0.896792\pi$
$992$	6.95972	0.220971
$993$	−13.5193	−0.429023
$994$	87.3178	2.76955
$995$	−24.6497	−0.781449
$996$	−3.82545	−0.121214
$997$	19.5738	0.619907	0.309954	−	0.950752i	$-0.399686\pi$
$997$	19.5738	0.619907	0.309954	+	0.950752i	$0.399686\pi$
$998$	50.3678	1.59436
$999$	−6.42384	−0.203241

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.16	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.16	✓	56	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.30269 q^{2} +1.00000 q^{3} -0.302986 q^{4} +1.77397 q^{5} -1.30269 q^{6} +4.96759 q^{7} +3.00009 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.30269 q^{2} +1.00000 q^{3} -0.302986 q^{4} +1.77397 q^{5} -1.30269 q^{6} +4.96759 q^{7} +3.00009 q^{8} +1.00000 q^{9} -2.31094 q^{10} +3.26508 q^{11} -0.302986 q^{12} +5.32809 q^{13} -6.47126 q^{14} +1.77397 q^{15} -3.30223 q^{16} -1.00000 q^{17} -1.30269 q^{18} -1.23221 q^{19} -0.537487 q^{20} +4.96759 q^{21} -4.25341 q^{22} -3.28460 q^{23} +3.00009 q^{24} -1.85305 q^{25} -6.94087 q^{26} +1.00000 q^{27} -1.50511 q^{28} -1.38745 q^{29} -2.31094 q^{30} -4.09785 q^{31} -1.69838 q^{32} +3.26508 q^{33} +1.30269 q^{34} +8.81234 q^{35} -0.302986 q^{36} -6.42384 q^{37} +1.60519 q^{38} +5.32809 q^{39} +5.32205 q^{40} -7.82428 q^{41} -6.47126 q^{42} -7.22926 q^{43} -0.989275 q^{44} +1.77397 q^{45} +4.27883 q^{46} +6.67261 q^{47} -3.30223 q^{48} +17.6770 q^{49} +2.41395 q^{50} -1.00000 q^{51} -1.61434 q^{52} +12.6211 q^{53} -1.30269 q^{54} +5.79214 q^{55} +14.9032 q^{56} -1.23221 q^{57} +1.80742 q^{58} +12.8065 q^{59} -0.537487 q^{60} +7.56095 q^{61} +5.33825 q^{62} +4.96759 q^{63} +8.81693 q^{64} +9.45184 q^{65} -4.25341 q^{66} +0.416044 q^{67} +0.302986 q^{68} -3.28460 q^{69} -11.4798 q^{70} -13.4932 q^{71} +3.00009 q^{72} +9.52385 q^{73} +8.36831 q^{74} -1.85305 q^{75} +0.373342 q^{76} +16.2196 q^{77} -6.94087 q^{78} -5.08995 q^{79} -5.85804 q^{80} +1.00000 q^{81} +10.1927 q^{82} +12.6258 q^{83} -1.50511 q^{84} -1.77397 q^{85} +9.41752 q^{86} -1.38745 q^{87} +9.79553 q^{88} +6.96248 q^{89} -2.31094 q^{90} +26.4678 q^{91} +0.995187 q^{92} -4.09785 q^{93} -8.69238 q^{94} -2.18590 q^{95} -1.69838 q^{96} +9.44439 q^{97} -23.0277 q^{98} +3.26508 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

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