LMFDB - Embedded newform 4017.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36961 q^{2} -1.00000 q^{3} +3.61506 q^{4} -2.39998 q^{5} +2.36961 q^{6} -0.116274 q^{7} -3.82707 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.36961 q^{2} -1.00000 q^{3} +3.61506 q^{4} -2.39998 q^{5} +2.36961 q^{6} -0.116274 q^{7} -3.82707 q^{8} +1.00000 q^{9} +5.68703 q^{10} +6.13402 q^{11} -3.61506 q^{12} +1.00000 q^{13} +0.275524 q^{14} +2.39998 q^{15} +1.83856 q^{16} +2.09587 q^{17} -2.36961 q^{18} -7.41857 q^{19} -8.67609 q^{20} +0.116274 q^{21} -14.5353 q^{22} -1.40898 q^{23} +3.82707 q^{24} +0.759917 q^{25} -2.36961 q^{26} -1.00000 q^{27} -0.420338 q^{28} +7.01793 q^{29} -5.68703 q^{30} +0.944662 q^{31} +3.29748 q^{32} -6.13402 q^{33} -4.96640 q^{34} +0.279056 q^{35} +3.61506 q^{36} +6.01036 q^{37} +17.5791 q^{38} -1.00000 q^{39} +9.18491 q^{40} +7.72190 q^{41} -0.275524 q^{42} +10.3949 q^{43} +22.1749 q^{44} -2.39998 q^{45} +3.33874 q^{46} +11.7311 q^{47} -1.83856 q^{48} -6.98648 q^{49} -1.80071 q^{50} -2.09587 q^{51} +3.61506 q^{52} +2.14660 q^{53} +2.36961 q^{54} -14.7215 q^{55} +0.444989 q^{56} +7.41857 q^{57} -16.6298 q^{58} +5.08541 q^{59} +8.67609 q^{60} -11.4265 q^{61} -2.23848 q^{62} -0.116274 q^{63} -11.4909 q^{64} -2.39998 q^{65} +14.5353 q^{66} +8.27795 q^{67} +7.57671 q^{68} +1.40898 q^{69} -0.661254 q^{70} -13.4824 q^{71} -3.82707 q^{72} -1.99101 q^{73} -14.2422 q^{74} -0.759917 q^{75} -26.8186 q^{76} -0.713228 q^{77} +2.36961 q^{78} +1.94350 q^{79} -4.41251 q^{80} +1.00000 q^{81} -18.2979 q^{82} -3.21526 q^{83} +0.420338 q^{84} -5.03005 q^{85} -24.6319 q^{86} -7.01793 q^{87} -23.4754 q^{88} -6.25664 q^{89} +5.68703 q^{90} -0.116274 q^{91} -5.09356 q^{92} -0.944662 q^{93} -27.7982 q^{94} +17.8044 q^{95} -3.29748 q^{96} -6.94282 q^{97} +16.5553 q^{98} +6.13402 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	−2.36961	−1.67557	−0.837785	−	0.546001i	$-0.816149\pi$
$2$	−2.36961	−1.67557	−0.837785	+	0.546001i	$0.816149\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.61506	1.80753
$5$	−2.39998	−1.07330	−0.536652	−	0.843803i	$-0.680311\pi$
$5$	−2.39998	−1.07330	−0.536652	+	0.843803i	$0.680311\pi$
$6$	2.36961	0.967390
$7$	−0.116274	−0.0439474	−0.0219737	−	0.999759i	$-0.506995\pi$
$7$	−0.116274	−0.0439474	−0.0219737	+	0.999759i	$0.506995\pi$
$8$	−3.82707	−1.35308
$9$	1.00000	0.333333
$10$	5.68703	1.79840
$11$	6.13402	1.84948	0.924739	−	0.380602i	$-0.124283\pi$
$11$	6.13402	1.84948	0.924739	+	0.380602i	$0.124283\pi$
$12$	−3.61506	−1.04358
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.275524	0.0736370
$15$	2.39998	0.619673
$16$	1.83856	0.459639
$17$	2.09587	0.508323	0.254162	−	0.967162i	$-0.418200\pi$
$17$	2.09587	0.508323	0.254162	+	0.967162i	$0.418200\pi$
$18$	−2.36961	−0.558523
$19$	−7.41857	−1.70194	−0.850969	−	0.525216i	$-0.823984\pi$
$19$	−7.41857	−1.70194	−0.850969	+	0.525216i	$0.823984\pi$
$20$	−8.67609	−1.94003
$21$	0.116274	0.0253731
$22$	−14.5353	−3.09893
$23$	−1.40898	−0.293793	−0.146897	−	0.989152i	$-0.546928\pi$
$23$	−1.40898	−0.293793	−0.146897	+	0.989152i	$0.546928\pi$
$24$	3.82707	0.781198
$25$	0.759917	0.151983
$26$	−2.36961	−0.464719
$27$	−1.00000	−0.192450
$28$	−0.420338	−0.0794364
$29$	7.01793	1.30320	0.651599	−	0.758564i	$-0.274099\pi$
$29$	7.01793	1.30320	0.651599	+	0.758564i	$0.274099\pi$
$30$	−5.68703	−1.03830
$31$	0.944662	0.169666	0.0848332	−	0.996395i	$-0.472964\pi$
$31$	0.944662	0.169666	0.0848332	+	0.996395i	$0.472964\pi$
$32$	3.29748	0.582918
$33$	−6.13402	−1.06780
$34$	−4.96640	−0.851731
$35$	0.279056	0.0471690
$36$	3.61506	0.602511
$37$	6.01036	0.988096	0.494048	−	0.869435i	$-0.335517\pi$
$37$	6.01036	0.988096	0.494048	+	0.869435i	$0.335517\pi$
$38$	17.5791	2.85171
$39$	−1.00000	−0.160128
$40$	9.18491	1.45226
$41$	7.72190	1.20596	0.602979	−	0.797757i	$-0.293980\pi$
$41$	7.72190	1.20596	0.602979	+	0.797757i	$0.293980\pi$
$42$	−0.275524	−0.0425143
$43$	10.3949	1.58521	0.792605	−	0.609736i	$-0.208724\pi$
$43$	10.3949	1.58521	0.792605	+	0.609736i	$0.208724\pi$
$44$	22.1749	3.34299
$45$	−2.39998	−0.357768
$46$	3.33874	0.492271
$47$	11.7311	1.71116	0.855580	−	0.517671i	$-0.173201\pi$
$47$	11.7311	1.71116	0.855580	+	0.517671i	$0.173201\pi$
$48$	−1.83856	−0.265373
$49$	−6.98648	−0.998069
$50$	−1.80071	−0.254659
$51$	−2.09587	−0.293481
$52$	3.61506	0.501319
$53$	2.14660	0.294858	0.147429	−	0.989073i	$-0.452900\pi$
$53$	2.14660	0.294858	0.147429	+	0.989073i	$0.452900\pi$
$54$	2.36961	0.322463
$55$	−14.7215	−1.98505
$56$	0.444989	0.0594642
$57$	7.41857	0.982614
$58$	−16.6298	−2.18360
$59$	5.08541	0.662064	0.331032	−	0.943619i	$-0.392603\pi$
$59$	5.08541	0.662064	0.331032	+	0.943619i	$0.392603\pi$
$60$	8.67609	1.12008
$61$	−11.4265	−1.46302	−0.731509	−	0.681832i	$-0.761183\pi$
$61$	−11.4265	−1.46302	−0.731509	+	0.681832i	$0.761183\pi$
$62$	−2.23848	−0.284288
$63$	−0.116274	−0.0146491
$64$	−11.4909	−1.43636
$65$	−2.39998	−0.297681
$66$	14.5353	1.78917
$67$	8.27795	1.01131	0.505656	−	0.862735i	$-0.331250\pi$
$67$	8.27795	1.01131	0.505656	+	0.862735i	$0.331250\pi$
$68$	7.57671	0.918811
$69$	1.40898	0.169621
$70$	−0.661254	−0.0790349
$71$	−13.4824	−1.60007	−0.800035	−	0.599953i	$-0.795186\pi$
$71$	−13.4824	−1.60007	−0.800035	+	0.599953i	$0.795186\pi$
$72$	−3.82707	−0.451025
$73$	−1.99101	−0.233030	−0.116515	−	0.993189i	$-0.537172\pi$
$73$	−1.99101	−0.233030	−0.116515	+	0.993189i	$0.537172\pi$
$74$	−14.2422	−1.65562
$75$	−0.759917	−0.0877477
$76$	−26.8186	−3.07631
$77$	−0.713228	−0.0812798
$78$	2.36961	0.268306
$79$	1.94350	0.218661	0.109331	−	0.994005i	$-0.465129\pi$
$79$	1.94350	0.218661	0.109331	+	0.994005i	$0.465129\pi$
$80$	−4.41251	−0.493333
$81$	1.00000	0.111111
$82$	−18.2979	−2.02067
$83$	−3.21526	−0.352921	−0.176460	−	0.984308i	$-0.556465\pi$
$83$	−3.21526	−0.352921	−0.176460	+	0.984308i	$0.556465\pi$
$84$	0.420338	0.0458626
$85$	−5.03005	−0.545586
$86$	−24.6319	−2.65613
$87$	−7.01793	−0.752401
$88$	−23.4754	−2.50248
$89$	−6.25664	−0.663203	−0.331601	−	0.943420i	$-0.607589\pi$
$89$	−6.25664	−0.663203	−0.331601	+	0.943420i	$0.607589\pi$
$90$	5.68703	0.599466
$91$	−0.116274	−0.0121888
$92$	−5.09356	−0.531040
$93$	−0.944662	−0.0979569
$94$	−27.7982	−2.86717
$95$	17.8044	1.82670
$96$	−3.29748	−0.336548
$97$	−6.94282	−0.704936	−0.352468	−	0.935824i	$-0.614658\pi$
$97$	−6.94282	−0.704936	−0.352468	+	0.935824i	$0.614658\pi$
$98$	16.5553	1.67233
$99$	6.13402	0.616493
$100$	2.74715	0.274715
$101$	−10.2226	−1.01719	−0.508593	−	0.861007i	$-0.669834\pi$
$101$	−10.2226	−1.01719	−0.508593	+	0.861007i	$0.669834\pi$
$102$	4.96640	0.491747
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−3.82707	−0.375276
$105$	−0.279056	−0.0272330
$106$	−5.08660	−0.494054
$107$	−4.67454	−0.451905	−0.225952	−	0.974138i	$-0.572549\pi$
$107$	−4.67454	−0.451905	−0.225952	+	0.974138i	$0.572549\pi$
$108$	−3.61506	−0.347860
$109$	3.41075	0.326691	0.163346	−	0.986569i	$-0.447771\pi$
$109$	3.41075	0.326691	0.163346	+	0.986569i	$0.447771\pi$
$110$	34.8844	3.32609
$111$	−6.01036	−0.570478
$112$	−0.213776	−0.0202000
$113$	−5.88948	−0.554036	−0.277018	−	0.960865i	$-0.589346\pi$
$113$	−5.88948	−0.554036	−0.277018	+	0.960865i	$0.589346\pi$
$114$	−17.5791	−1.64644
$115$	3.38153	0.315330
$116$	25.3703	2.35557
$117$	1.00000	0.0924500
$118$	−12.0505	−1.10933
$119$	−0.243695	−0.0223395
$120$	−9.18491	−0.838464
$121$	26.6262	2.42057
$122$	27.0765	2.45139
$123$	−7.72190	−0.696261
$124$	3.41501	0.306677
$125$	10.1761	0.910180
$126$	0.275524	0.0245457
$127$	−6.02610	−0.534730	−0.267365	−	0.963595i	$-0.586153\pi$
$127$	−6.02610	−0.534730	−0.267365	+	0.963595i	$0.586153\pi$
$128$	20.6339	1.82380
$129$	−10.3949	−0.915221
$130$	5.68703	0.498785
$131$	−15.5972	−1.36273	−0.681365	−	0.731944i	$-0.738613\pi$
$131$	−15.5972	−1.36273	−0.681365	+	0.731944i	$0.738613\pi$
$132$	−22.1749	−1.93008
$133$	0.862587	0.0747958
$134$	−19.6155	−1.69452
$135$	2.39998	0.206558
$136$	−8.02105	−0.687800
$137$	1.52562	0.130342	0.0651710	−	0.997874i	$-0.479241\pi$
$137$	1.52562	0.130342	0.0651710	+	0.997874i	$0.479241\pi$
$138$	−3.33874	−0.284213
$139$	−9.77054	−0.828726	−0.414363	−	0.910112i	$-0.635996\pi$
$139$	−9.77054	−0.828726	−0.414363	+	0.910112i	$0.635996\pi$
$140$	1.00880	0.0852595
$141$	−11.7311	−0.987939
$142$	31.9481	2.68103
$143$	6.13402	0.512953
$144$	1.83856	0.153213
$145$	−16.8429	−1.39873
$146$	4.71792	0.390458
$147$	6.98648	0.576235
$148$	21.7278	1.78602
$149$	11.5754	0.948293	0.474146	−	0.880446i	$-0.342757\pi$
$149$	11.5754	0.948293	0.474146	+	0.880446i	$0.342757\pi$
$150$	1.80071	0.147027
$151$	−2.15749	−0.175574	−0.0877870	−	0.996139i	$-0.527979\pi$
$151$	−2.15749	−0.175574	−0.0877870	+	0.996139i	$0.527979\pi$
$152$	28.3914	2.30285
$153$	2.09587	0.169441
$154$	1.69007	0.136190
$155$	−2.26717	−0.182104
$156$	−3.61506	−0.289437
$157$	−2.58005	−0.205911	−0.102955	−	0.994686i	$-0.532830\pi$
$157$	−2.58005	−0.205911	−0.102955	+	0.994686i	$0.532830\pi$
$158$	−4.60535	−0.366382
$159$	−2.14660	−0.170236
$160$	−7.91390	−0.625648
$161$	0.163828	0.0129115
$162$	−2.36961	−0.186174
$163$	16.0762	1.25919	0.629593	−	0.776925i	$-0.283222\pi$
$163$	16.0762	1.25919	0.629593	+	0.776925i	$0.283222\pi$
$164$	27.9152	2.17981
$165$	14.7215	1.14607
$166$	7.61892	0.591343
$167$	−0.398337	−0.0308242	−0.0154121	−	0.999881i	$-0.504906\pi$
$167$	−0.398337	−0.0308242	−0.0154121	+	0.999881i	$0.504906\pi$
$168$	−0.444989	−0.0343317
$169$	1.00000	0.0769231
$170$	11.9193	0.914167
$171$	−7.41857	−0.567312
$172$	37.5783	2.86532
$173$	0.645860	0.0491038	0.0245519	−	0.999699i	$-0.492184\pi$
$173$	0.645860	0.0491038	0.0245519	+	0.999699i	$0.492184\pi$
$174$	16.6298	1.26070
$175$	−0.0883586	−0.00667929
$176$	11.2778	0.850093
$177$	−5.08541	−0.382243
$178$	14.8258	1.11124
$179$	−13.3349	−0.996696	−0.498348	−	0.866977i	$-0.666060\pi$
$179$	−13.3349	−0.996696	−0.498348	+	0.866977i	$0.666060\pi$
$180$	−8.67609	−0.646678
$181$	−7.65395	−0.568914	−0.284457	−	0.958689i	$-0.591813\pi$
$181$	−7.65395	−0.568914	−0.284457	+	0.958689i	$0.591813\pi$
$182$	0.275524	0.0204232
$183$	11.4265	0.844674
$184$	5.39228	0.397524
$185$	−14.4248	−1.06053
$186$	2.23848	0.164134
$187$	12.8561	0.940133
$188$	42.4087	3.09298
$189$	0.116274	0.00845769
$190$	−42.1896	−3.06076
$191$	20.8707	1.51015	0.755076	−	0.655638i	$-0.227600\pi$
$191$	20.8707	1.51015	0.755076	+	0.655638i	$0.227600\pi$
$192$	11.4909	0.829282
$193$	−2.98729	−0.215030	−0.107515	−	0.994203i	$-0.534289\pi$
$193$	−2.98729	−0.215030	−0.107515	+	0.994203i	$0.534289\pi$
$194$	16.4518	1.18117
$195$	2.39998	0.171866
$196$	−25.2566	−1.80404
$197$	14.1735	1.00982	0.504911	−	0.863171i	$-0.331525\pi$
$197$	14.1735	1.00982	0.504911	+	0.863171i	$0.331525\pi$
$198$	−14.5353	−1.03298
$199$	−16.2594	−1.15260	−0.576300	−	0.817238i	$-0.695504\pi$
$199$	−16.2594	−1.15260	−0.576300	+	0.817238i	$0.695504\pi$
$200$	−2.90826	−0.205645
$201$	−8.27795	−0.583882
$202$	24.2236	1.70437
$203$	−0.816003	−0.0572722
$204$	−7.57671	−0.530476
$205$	−18.5324	−1.29436
$206$	2.36961	0.165099
$207$	−1.40898	−0.0979310
$208$	1.83856	0.127481
$209$	−45.5057	−3.14770
$210$	0.661254	0.0456308
$211$	15.7417	1.08370	0.541850	−	0.840475i	$-0.317724\pi$
$211$	15.7417	1.08370	0.541850	+	0.840475i	$0.317724\pi$
$212$	7.76008	0.532965
$213$	13.4824	0.923801
$214$	11.0768	0.757198
$215$	−24.9476	−1.70141
$216$	3.82707	0.260399
$217$	−0.109840	−0.00745640
$218$	−8.08217	−0.547393
$219$	1.99101	0.134540
$220$	−53.2193	−3.58805
$221$	2.09587	0.140984
$222$	14.2422	0.955875
$223$	−2.35632	−0.157791	−0.0788954	−	0.996883i	$-0.525139\pi$
$223$	−2.35632	−0.157791	−0.0788954	+	0.996883i	$0.525139\pi$
$224$	−0.383411	−0.0256177
$225$	0.759917	0.0506612
$226$	13.9558	0.928326
$227$	0.0550758	0.00365551	0.00182775	−	0.999998i	$-0.499418\pi$
$227$	0.0550758	0.00365551	0.00182775	+	0.999998i	$0.499418\pi$
$228$	26.8186	1.77611
$229$	−17.8185	−1.17748	−0.588741	−	0.808322i	$-0.700376\pi$
$229$	−17.8185	−1.17748	−0.588741	+	0.808322i	$0.700376\pi$
$230$	−8.01292	−0.528356
$231$	0.713228	0.0469269
$232$	−26.8581	−1.76332
$233$	18.3560	1.20254	0.601271	−	0.799045i	$-0.294661\pi$
$233$	18.3560	1.20254	0.601271	+	0.799045i	$0.294661\pi$
$234$	−2.36961	−0.154906
$235$	−28.1545	−1.83660
$236$	18.3841	1.19670
$237$	−1.94350	−0.126244
$238$	0.577463	0.0374314
$239$	6.73765	0.435822	0.217911	−	0.975969i	$-0.430076\pi$
$239$	6.73765	0.435822	0.217911	+	0.975969i	$0.430076\pi$
$240$	4.41251	0.284826
$241$	14.4248	0.929180	0.464590	−	0.885526i	$-0.346202\pi$
$241$	14.4248	0.929180	0.464590	+	0.885526i	$0.346202\pi$
$242$	−63.0939	−4.05583
$243$	−1.00000	−0.0641500
$244$	−41.3076	−2.64445
$245$	16.7674	1.07123
$246$	18.2979	1.16663
$247$	−7.41857	−0.472033
$248$	−3.61529	−0.229571
$249$	3.21526	0.203759
$250$	−24.1135	−1.52507
$251$	−3.33272	−0.210360	−0.105180	−	0.994453i	$-0.533542\pi$
$251$	−3.33272	−0.210360	−0.105180	+	0.994453i	$0.533542\pi$
$252$	−0.420338	−0.0264788
$253$	−8.64273	−0.543364
$254$	14.2795	0.895977
$255$	5.03005	0.314994
$256$	−25.9127	−1.61954
$257$	17.1817	1.07177	0.535883	−	0.844292i	$-0.319979\pi$
$257$	17.1817	1.07177	0.535883	+	0.844292i	$0.319979\pi$
$258$	24.6319	1.53352
$259$	−0.698848	−0.0434243
$260$	−8.67609	−0.538068
$261$	7.01793	0.434399
$262$	36.9592	2.28335
$263$	4.03724	0.248947	0.124473	−	0.992223i	$-0.460276\pi$
$263$	4.03724	0.248947	0.124473	+	0.992223i	$0.460276\pi$
$264$	23.4754	1.44481
$265$	−5.15179	−0.316472
$266$	−2.04400	−0.125326
$267$	6.25664	0.382900
$268$	29.9253	1.82798
$269$	23.3134	1.42144	0.710721	−	0.703474i	$-0.248369\pi$
$269$	23.3134	1.42144	0.710721	+	0.703474i	$0.248369\pi$
$270$	−5.68703	−0.346102
$271$	26.0550	1.58273	0.791364	−	0.611345i	$-0.209371\pi$
$271$	26.0550	1.58273	0.791364	+	0.611345i	$0.209371\pi$
$272$	3.85338	0.233645
$273$	0.116274	0.00703722
$274$	−3.61512	−0.218397
$275$	4.66135	0.281090
$276$	5.09356	0.306596
$277$	30.8306	1.85243	0.926215	−	0.376995i	$-0.123043\pi$
$277$	30.8306	1.85243	0.926215	+	0.376995i	$0.123043\pi$
$278$	23.1524	1.38859
$279$	0.944662	0.0565554
$280$	−1.06797	−0.0638232
$281$	−25.8182	−1.54018	−0.770092	−	0.637933i	$-0.779790\pi$
$281$	−25.8182	−1.54018	−0.770092	+	0.637933i	$0.779790\pi$
$282$	27.7982	1.65536
$283$	6.88462	0.409248	0.204624	−	0.978841i	$-0.434403\pi$
$283$	6.88462	0.409248	0.204624	+	0.978841i	$0.434403\pi$
$284$	−48.7398	−2.89218
$285$	−17.8044	−1.05464
$286$	−14.5353	−0.859488
$287$	−0.897857	−0.0529988
$288$	3.29748	0.194306
$289$	−12.6073	−0.741607
$290$	39.9112	2.34367
$291$	6.94282	0.406995
$292$	−7.19763	−0.421209
$293$	−28.1257	−1.64312	−0.821561	−	0.570121i	$-0.806896\pi$
$293$	−28.1257	−1.64312	−0.821561	+	0.570121i	$0.806896\pi$
$294$	−16.5553	−0.965522
$295$	−12.2049	−0.710597
$296$	−23.0021	−1.33697
$297$	−6.13402	−0.355932
$298$	−27.4292	−1.58893
$299$	−1.40898	−0.0814835
$300$	−2.74715	−0.158607
$301$	−1.20866	−0.0696659
$302$	5.11241	0.294186
$303$	10.2226	0.587273
$304$	−13.6395	−0.782278
$305$	27.4235	1.57026
$306$	−4.96640	−0.283910
$307$	18.1931	1.03833	0.519166	−	0.854673i	$-0.326243\pi$
$307$	18.1931	1.03833	0.519166	+	0.854673i	$0.326243\pi$
$308$	−2.57836	−0.146916
$309$	1.00000	0.0568880
$310$	5.37232	0.305127
$311$	24.1152	1.36745	0.683725	−	0.729740i	$-0.260359\pi$
$311$	24.1152	1.36745	0.683725	+	0.729740i	$0.260359\pi$
$312$	3.82707	0.216665
$313$	5.78369	0.326913	0.163457	−	0.986551i	$-0.447736\pi$
$313$	5.78369	0.326913	0.163457	+	0.986551i	$0.447736\pi$
$314$	6.11373	0.345018
$315$	0.279056	0.0157230
$316$	7.02589	0.395237
$317$	7.27734	0.408736	0.204368	−	0.978894i	$-0.434486\pi$
$317$	7.27734	0.408736	0.204368	+	0.978894i	$0.434486\pi$
$318$	5.08660	0.285242
$319$	43.0481	2.41023
$320$	27.5779	1.54165
$321$	4.67454	0.260907
$322$	−0.388209	−0.0216340
$323$	−15.5484	−0.865134
$324$	3.61506	0.200837
$325$	0.759917	0.0421526
$326$	−38.0944	−2.10985
$327$	−3.41075	−0.188615
$328$	−29.5523	−1.63175
$329$	−1.36402	−0.0752011
$330$	−34.8844	−1.92032
$331$	−0.00818240	−0.000449745 0	−0.000224873	−	1.00000i	$-0.500072\pi$
$331$	−0.00818240	−0.000449745 0	−0.000224873		1.00000i	$0.500072\pi$
$332$	−11.6234	−0.637916
$333$	6.01036	0.329365
$334$	0.943904	0.0516481
$335$	−19.8669	−1.08545
$336$	0.213776	0.0116625
$337$	14.9787	0.815942	0.407971	−	0.912995i	$-0.366237\pi$
$337$	14.9787	0.815942	0.407971	+	0.912995i	$0.366237\pi$
$338$	−2.36961	−0.128890
$339$	5.88948	0.319873
$340$	−18.1840	−0.986164
$341$	5.79458	0.313794
$342$	17.5791	0.950571
$343$	1.62626	0.0878100
$344$	−39.7821	−2.14491
$345$	−3.38153	−0.182056
$346$	−1.53044	−0.0822769
$347$	−15.0237	−0.806512	−0.403256	−	0.915087i	$-0.632122\pi$
$347$	−15.0237	−0.806512	−0.403256	+	0.915087i	$0.632122\pi$
$348$	−25.3703	−1.35999
$349$	−11.8939	−0.636668	−0.318334	−	0.947979i	$-0.603123\pi$
$349$	−11.8939	−0.636668	−0.318334	+	0.947979i	$0.603123\pi$
$350$	0.209376	0.0111916
$351$	−1.00000	−0.0533761
$352$	20.2268	1.07809
$353$	4.60173	0.244926	0.122463	−	0.992473i	$-0.460921\pi$
$353$	4.60173	0.244926	0.122463	+	0.992473i	$0.460921\pi$
$354$	12.0505	0.640475
$355$	32.3576	1.71736
$356$	−22.6182	−1.19876
$357$	0.243695	0.0128977
$358$	31.5985	1.67003
$359$	−2.12663	−0.112239	−0.0561195	−	0.998424i	$-0.517873\pi$
$359$	−2.12663	−0.112239	−0.0561195	+	0.998424i	$0.517873\pi$
$360$	9.18491	0.484087
$361$	36.0352	1.89659
$362$	18.1369	0.953254
$363$	−26.6262	−1.39752
$364$	−0.420338	−0.0220317
$365$	4.77839	0.250112
$366$	−27.0765	−1.41531
$367$	−18.7710	−0.979838	−0.489919	−	0.871768i	$-0.662974\pi$
$367$	−18.7710	−0.979838	−0.489919	+	0.871768i	$0.662974\pi$
$368$	−2.59049	−0.135039
$369$	7.72190	0.401986
$370$	34.1811	1.77699
$371$	−0.249593	−0.0129582
$372$	−3.41501	−0.177060
$373$	2.94927	0.152707	0.0763536	−	0.997081i	$-0.475672\pi$
$373$	2.94927	0.152707	0.0763536	+	0.997081i	$0.475672\pi$
$374$	−30.4640	−1.57526
$375$	−10.1761	−0.525493
$376$	−44.8959	−2.31533
$377$	7.01793	0.361442
$378$	−0.275524	−0.0141714
$379$	−29.8273	−1.53213	−0.766064	−	0.642764i	$-0.777787\pi$
$379$	−29.8273	−1.53213	−0.766064	+	0.642764i	$0.777787\pi$
$380$	64.3642	3.30181
$381$	6.02610	0.308726
$382$	−49.4555	−2.53036
$383$	−3.24483	−0.165803	−0.0829014	−	0.996558i	$-0.526419\pi$
$383$	−3.24483	−0.165803	−0.0829014	+	0.996558i	$0.526419\pi$
$384$	−20.6339	−1.05297
$385$	1.71173	0.0872380
$386$	7.07871	0.360297
$387$	10.3949	0.528403
$388$	−25.0987	−1.27420
$389$	−33.9431	−1.72098	−0.860491	−	0.509466i	$-0.829843\pi$
$389$	−33.9431	−1.72098	−0.860491	+	0.509466i	$0.829843\pi$
$390$	−5.68703	−0.287974
$391$	−2.95304	−0.149342
$392$	26.7378	1.35046
$393$	15.5972	0.786772
$394$	−33.5858	−1.69203
$395$	−4.66437	−0.234690
$396$	22.1749	1.11433
$397$	22.9989	1.15428	0.577142	−	0.816644i	$-0.304168\pi$
$397$	22.9989	1.15428	0.577142	+	0.816644i	$0.304168\pi$
$398$	38.5286	1.93126
$399$	−0.862587	−0.0431834
$400$	1.39715	0.0698576
$401$	−3.15596	−0.157601	−0.0788006	−	0.996890i	$-0.525109\pi$
$401$	−3.15596	−0.157601	−0.0788006	+	0.996890i	$0.525109\pi$
$402$	19.6155	0.978334
$403$	0.944662	0.0470570
$404$	−36.9553	−1.83860
$405$	−2.39998	−0.119256
$406$	1.93361	0.0959635
$407$	36.8677	1.82746
$408$	8.02105	0.397101
$409$	28.6686	1.41757	0.708785	−	0.705425i	$-0.249244\pi$
$409$	28.6686	1.41757	0.708785	+	0.705425i	$0.249244\pi$
$410$	43.9147	2.16879
$411$	−1.52562	−0.0752530
$412$	−3.61506	−0.178101
$413$	−0.591301	−0.0290960
$414$	3.33874	0.164090
$415$	7.71657	0.378792
$416$	3.29748	0.161672
$417$	9.77054	0.478465
$418$	107.831	5.27418
$419$	9.68642	0.473212	0.236606	−	0.971606i	$-0.423965\pi$
$419$	9.68642	0.473212	0.236606	+	0.971606i	$0.423965\pi$
$420$	−1.00880	−0.0492246
$421$	6.86042	0.334356	0.167178	−	0.985927i	$-0.446534\pi$
$421$	6.86042	0.334356	0.167178	+	0.985927i	$0.446534\pi$
$422$	−37.3016	−1.81582
$423$	11.7311	0.570387
$424$	−8.21518	−0.398965
$425$	1.59269	0.0772567
$426$	−31.9481	−1.54789
$427$	1.32861	0.0642959
$428$	−16.8988	−0.816832
$429$	−6.13402	−0.296153
$430$	59.1162	2.85084
$431$	34.0110	1.63825	0.819127	−	0.573613i	$-0.194459\pi$
$431$	34.0110	1.63825	0.819127	+	0.573613i	$0.194459\pi$
$432$	−1.83856	−0.0884576
$433$	−17.7135	−0.851256	−0.425628	−	0.904898i	$-0.639947\pi$
$433$	−17.7135	−0.851256	−0.425628	+	0.904898i	$0.639947\pi$
$434$	0.260277	0.0124937
$435$	16.8429	0.807556
$436$	12.3301	0.590504
$437$	10.4526	0.500017
$438$	−4.71792	−0.225431
$439$	4.41143	0.210546	0.105273	−	0.994443i	$-0.466428\pi$
$439$	4.41143	0.210546	0.105273	+	0.994443i	$0.466428\pi$
$440$	56.3405	2.68593
$441$	−6.98648	−0.332690
$442$	−4.96640	−0.236228
$443$	−16.1742	−0.768460	−0.384230	−	0.923237i	$-0.625533\pi$
$443$	−16.1742	−0.768460	−0.384230	+	0.923237i	$0.625533\pi$
$444$	−21.7278	−1.03116
$445$	15.0158	0.711819
$446$	5.58356	0.264389
$447$	−11.5754	−0.547497
$448$	1.33609	0.0631243
$449$	15.8538	0.748187	0.374093	−	0.927391i	$-0.377954\pi$
$449$	15.8538	0.748187	0.374093	+	0.927391i	$0.377954\pi$
$450$	−1.80071	−0.0848863
$451$	47.3663	2.23039
$452$	−21.2909	−1.00144
$453$	2.15749	0.101368
$454$	−0.130508	−0.00612506
$455$	0.279056	0.0130823
$456$	−28.3914	−1.32955
$457$	−21.8320	−1.02126	−0.510629	−	0.859801i	$-0.670588\pi$
$457$	−21.8320	−1.02126	−0.510629	+	0.859801i	$0.670588\pi$
$458$	42.2230	1.97295
$459$	−2.09587	−0.0978269
$460$	12.2245	0.569968
$461$	22.9270	1.06782	0.533908	−	0.845543i	$-0.320723\pi$
$461$	22.9270	1.06782	0.533908	+	0.845543i	$0.320723\pi$
$462$	−1.69007	−0.0786293
$463$	21.4577	0.997223	0.498611	−	0.866826i	$-0.333843\pi$
$463$	21.4577	0.997223	0.498611	+	0.866826i	$0.333843\pi$
$464$	12.9029	0.599001
$465$	2.26717	0.105138
$466$	−43.4966	−2.01494
$467$	−18.3118	−0.847368	−0.423684	−	0.905810i	$-0.639263\pi$
$467$	−18.3118	−0.847368	−0.423684	+	0.905810i	$0.639263\pi$
$468$	3.61506	0.167106
$469$	−0.962510	−0.0444446
$470$	66.7152	3.07734
$471$	2.58005	0.118883
$472$	−19.4623	−0.895823
$473$	63.7627	2.93181
$474$	4.60535	0.211531
$475$	−5.63750	−0.258666
$476$	−0.880974	−0.0403794
$477$	2.14660	0.0982859
$478$	−15.9656	−0.730250
$479$	6.66562	0.304560	0.152280	−	0.988337i	$-0.451338\pi$
$479$	6.66562	0.304560	0.152280	+	0.988337i	$0.451338\pi$
$480$	7.91390	0.361218
$481$	6.01036	0.274049
$482$	−34.1811	−1.55691
$483$	−0.163828	−0.00745443
$484$	96.2555	4.37525
$485$	16.6626	0.756612
$486$	2.36961	0.107488
$487$	39.6562	1.79699	0.898496	−	0.438981i	$-0.144660\pi$
$487$	39.6562	1.79699	0.898496	+	0.438981i	$0.144660\pi$
$488$	43.7302	1.97957
$489$	−16.0762	−0.726992
$490$	−39.7323	−1.79492
$491$	2.41411	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$491$	2.41411	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$492$	−27.9152	−1.25851
$493$	14.7087	0.662445
$494$	17.5791	0.790923
$495$	−14.7215	−0.661684
$496$	1.73682	0.0779853
$497$	1.56766	0.0703190
$498$	−7.61892	−0.341412
$499$	10.4716	0.468775	0.234388	−	0.972143i	$-0.424692\pi$
$499$	10.4716	0.468775	0.234388	+	0.972143i	$0.424692\pi$
$500$	36.7873	1.64518
$501$	0.398337	0.0177964
$502$	7.89726	0.352472
$503$	−20.7218	−0.923937	−0.461969	−	0.886896i	$-0.652857\pi$
$503$	−20.7218	−0.923937	−0.461969	+	0.886896i	$0.652857\pi$
$504$	0.444989	0.0198214
$505$	24.5341	1.09175
$506$	20.4799	0.910443
$507$	−1.00000	−0.0444116
$508$	−21.7847	−0.966541
$509$	29.3660	1.30163	0.650813	−	0.759238i	$-0.274428\pi$
$509$	29.3660	1.30163	0.650813	+	0.759238i	$0.274428\pi$
$510$	−11.9193	−0.527794
$511$	0.231503	0.0102411
$512$	20.1352	0.889859
$513$	7.41857	0.327538
$514$	−40.7140	−1.79582
$515$	2.39998	0.105756
$516$	−37.5783	−1.65429
$517$	71.9590	3.16475
$518$	1.65600	0.0727604
$519$	−0.645860	−0.0283501
$520$	9.18491	0.402785
$521$	−15.6956	−0.687635	−0.343817	−	0.939037i	$-0.611720\pi$
$521$	−15.6956	−0.687635	−0.343817	+	0.939037i	$0.611720\pi$
$522$	−16.6298	−0.727866
$523$	−37.7153	−1.64917	−0.824587	−	0.565735i	$-0.808593\pi$
$523$	−37.7153	−1.64917	−0.824587	+	0.565735i	$0.808593\pi$
$524$	−56.3847	−2.46318
$525$	0.0883586	0.00385629
$526$	−9.56670	−0.417128
$527$	1.97989	0.0862453
$528$	−11.2778	−0.490801
$529$	−21.0148	−0.913686
$530$	12.2078	0.530271
$531$	5.08541	0.220688
$532$	3.11831	0.135196
$533$	7.72190	0.334473
$534$	−14.8258	−0.641576
$535$	11.2188	0.485032
$536$	−31.6803	−1.36838
$537$	13.3349	0.575443
$538$	−55.2437	−2.38172
$539$	−42.8552	−1.84591
$540$	8.67609	0.373359
$541$	−28.6810	−1.23309	−0.616546	−	0.787319i	$-0.711469\pi$
$541$	−28.6810	−1.23309	−0.616546	+	0.787319i	$0.711469\pi$
$542$	−61.7402	−2.65197
$543$	7.65395	0.328462
$544$	6.91109	0.296311
$545$	−8.18575	−0.350639
$546$	−0.275524	−0.0117914
$547$	18.8589	0.806346	0.403173	−	0.915124i	$-0.367907\pi$
$547$	18.8589	0.806346	0.403173	+	0.915124i	$0.367907\pi$
$548$	5.51520	0.235597
$549$	−11.4265	−0.487673
$550$	−11.0456	−0.470986
$551$	−52.0630	−2.21796
$552$	−5.39228	−0.229511
$553$	−0.225979	−0.00960960
$554$	−73.0565	−3.10387
$555$	14.4248	0.612297
$556$	−35.3211	−1.49795
$557$	32.3709	1.37160	0.685799	−	0.727791i	$-0.259453\pi$
$557$	32.3709	1.37160	0.685799	+	0.727791i	$0.259453\pi$
$558$	−2.23848	−0.0947625
$559$	10.3949	0.439658
$560$	0.513060	0.0216807
$561$	−12.8561	−0.542786
$562$	61.1791	2.58068
$563$	36.1358	1.52294	0.761472	−	0.648198i	$-0.224477\pi$
$563$	36.1358	1.52294	0.761472	+	0.648198i	$0.224477\pi$
$564$	−42.4087	−1.78573
$565$	14.1347	0.594650
$566$	−16.3139	−0.685724
$567$	−0.116274	−0.00488305
$568$	51.5983	2.16502
$569$	25.5231	1.06998	0.534992	−	0.844857i	$-0.320315\pi$
$569$	25.5231	1.06998	0.534992	+	0.844857i	$0.320315\pi$
$570$	42.1896	1.76713
$571$	−13.9219	−0.582612	−0.291306	−	0.956630i	$-0.594090\pi$
$571$	−13.9219	−0.582612	−0.291306	+	0.956630i	$0.594090\pi$
$572$	22.1749	0.927178
$573$	−20.8707	−0.871886
$574$	2.12757	0.0888032
$575$	−1.07071	−0.0446517
$576$	−11.4909	−0.478786
$577$	−17.7906	−0.740633	−0.370316	−	0.928906i	$-0.620751\pi$
$577$	−17.7906	−0.740633	−0.370316	+	0.928906i	$0.620751\pi$
$578$	29.8745	1.24261
$579$	2.98729	0.124147
$580$	−60.8882	−2.52824
$581$	0.373851	0.0155100
$582$	−16.4518	−0.681949
$583$	13.1673	0.545333
$584$	7.61974	0.315307
$585$	−2.39998	−0.0992271
$586$	66.6470	2.75316
$587$	20.7514	0.856503	0.428251	−	0.903660i	$-0.359130\pi$
$587$	20.7514	0.856503	0.428251	+	0.903660i	$0.359130\pi$
$588$	25.2566	1.04156
$589$	−7.00804	−0.288761
$590$	28.9209	1.19065
$591$	−14.1735	−0.583022
$592$	11.0504	0.454168
$593$	8.47324	0.347954	0.173977	−	0.984750i	$-0.444338\pi$
$593$	8.47324	0.347954	0.173977	+	0.984750i	$0.444338\pi$
$594$	14.5353	0.596389
$595$	0.584865	0.0239771
$596$	41.8458	1.71407
$597$	16.2594	0.665454
$598$	3.33874	0.136531
$599$	−18.8081	−0.768479	−0.384239	−	0.923234i	$-0.625536\pi$
$599$	−18.8081	−0.768479	−0.384239	+	0.923234i	$0.625536\pi$
$600$	2.90826	0.118729
$601$	25.0414	1.02146	0.510729	−	0.859742i	$-0.329375\pi$
$601$	25.0414	1.02146	0.510729	+	0.859742i	$0.329375\pi$
$602$	2.86405	0.116730
$603$	8.27795	0.337104
$604$	−7.79946	−0.317356
$605$	−63.9025	−2.59801
$606$	−24.2236	−0.984017
$607$	−15.6860	−0.636673	−0.318337	−	0.947978i	$-0.603124\pi$
$607$	−15.6860	−0.636673	−0.318337	+	0.947978i	$0.603124\pi$
$608$	−24.4626	−0.992090
$609$	0.816003	0.0330661
$610$	−64.9830	−2.63109
$611$	11.7311	0.474590
$612$	7.57671	0.306270
$613$	−21.7968	−0.880364	−0.440182	−	0.897909i	$-0.645086\pi$
$613$	−21.7968	−0.880364	−0.440182	+	0.897909i	$0.645086\pi$
$614$	−43.1105	−1.73980
$615$	18.5324	0.747300
$616$	2.72958	0.109978
$617$	11.1706	0.449710	0.224855	−	0.974392i	$-0.427809\pi$
$617$	11.1706	0.449710	0.224855	+	0.974392i	$0.427809\pi$
$618$	−2.36961	−0.0953198
$619$	3.13589	0.126042	0.0630211	−	0.998012i	$-0.479926\pi$
$619$	3.13589	0.126042	0.0630211	+	0.998012i	$0.479926\pi$
$620$	−8.19597	−0.329158
$621$	1.40898	0.0565405
$622$	−57.1438	−2.29126
$623$	0.727485	0.0291461
$624$	−1.83856	−0.0736012
$625$	−28.2221	−1.12888
$626$	−13.7051	−0.547766
$627$	45.5057	1.81732
$628$	−9.32706	−0.372190
$629$	12.5969	0.502272
$630$	−0.661254	−0.0263450
$631$	−46.2876	−1.84268	−0.921340	−	0.388758i	$-0.872904\pi$
$631$	−46.2876	−1.84268	−0.921340	+	0.388758i	$0.872904\pi$
$632$	−7.43793	−0.295865
$633$	−15.7417	−0.625675
$634$	−17.2445	−0.684865
$635$	14.4625	0.573928
$636$	−7.76008	−0.307707
$637$	−6.98648	−0.276814
$638$	−102.007	−4.03851
$639$	−13.4824	−0.533357
$640$	−49.5211	−1.95749
$641$	17.7990	0.703020	0.351510	−	0.936184i	$-0.385668\pi$
$641$	17.7990	0.703020	0.351510	+	0.936184i	$0.385668\pi$
$642$	−11.0768	−0.437168
$643$	−25.9758	−1.02438	−0.512192	−	0.858871i	$-0.671166\pi$
$643$	−25.9758	−1.02438	−0.512192	+	0.858871i	$0.671166\pi$
$644$	0.592249	0.0233379
$645$	24.9476	0.982312
$646$	36.8436	1.44959
$647$	32.8205	1.29031	0.645153	−	0.764053i	$-0.276794\pi$
$647$	32.8205	1.29031	0.645153	+	0.764053i	$0.276794\pi$
$648$	−3.82707	−0.150342
$649$	31.1940	1.22447
$650$	−1.80071	−0.0706296
$651$	0.109840	0.00430496
$652$	58.1165	2.27602
$653$	−15.8081	−0.618619	−0.309309	−	0.950961i	$-0.600098\pi$
$653$	−15.8081	−0.618619	−0.309309	+	0.950961i	$0.600098\pi$
$654$	8.08217	0.316038
$655$	37.4329	1.46262
$656$	14.1972	0.554306
$657$	−1.99101	−0.0776767
$658$	3.23221	0.126005
$659$	−5.78413	−0.225318	−0.112659	−	0.993634i	$-0.535937\pi$
$659$	−5.78413	−0.225318	−0.112659	+	0.993634i	$0.535937\pi$
$660$	53.2193	2.07156
$661$	34.7299	1.35084	0.675418	−	0.737435i	$-0.263963\pi$
$661$	34.7299	1.35084	0.675418	+	0.737435i	$0.263963\pi$
$662$	0.0193891	0.000753579 0
$663$	−2.09587	−0.0813969
$664$	12.3050	0.477528
$665$	−2.07019	−0.0802787
$666$	−14.2422	−0.551875
$667$	−9.88814	−0.382870
$668$	−1.44001	−0.0557158
$669$	2.35632	0.0911005
$670$	47.0769	1.81874
$671$	−70.0906	−2.70582
$672$	0.383411	0.0147904
$673$	−42.3818	−1.63370	−0.816849	−	0.576852i	$-0.804281\pi$
$673$	−42.3818	−1.63370	−0.816849	+	0.576852i	$0.804281\pi$
$674$	−35.4937	−1.36717
$675$	−0.759917	−0.0292492
$676$	3.61506	0.139041
$677$	−1.48246	−0.0569754	−0.0284877	−	0.999594i	$-0.509069\pi$
$677$	−1.48246	−0.0569754	−0.0284877	+	0.999594i	$0.509069\pi$
$678$	−13.9558	−0.535969
$679$	0.807270	0.0309802
$680$	19.2504	0.738219
$681$	−0.0550758	−0.00211051
$682$	−13.7309	−0.525784
$683$	41.9200	1.60403	0.802013	−	0.597307i	$-0.203762\pi$
$683$	41.9200	1.60403	0.802013	+	0.597307i	$0.203762\pi$
$684$	−26.8186	−1.02544
$685$	−3.66145	−0.139897
$686$	−3.85362	−0.147132
$687$	17.8185	0.679820
$688$	19.1117	0.728625
$689$	2.14660	0.0817788
$690$	8.01292	0.305047
$691$	46.4261	1.76613	0.883066	−	0.469249i	$-0.155475\pi$
$691$	46.4261	1.76613	0.883066	+	0.469249i	$0.155475\pi$
$692$	2.33483	0.0887568
$693$	−0.713228	−0.0270933
$694$	35.6003	1.35137
$695$	23.4491	0.889476
$696$	26.8581	1.01806
$697$	16.1841	0.613017
$698$	28.1840	1.06678
$699$	−18.3560	−0.694288
$700$	−0.319422	−0.0120730
$701$	16.6390	0.628445	0.314222	−	0.949349i	$-0.398256\pi$
$701$	16.6390	0.628445	0.314222	+	0.949349i	$0.398256\pi$
$702$	2.36961	0.0894353
$703$	−44.5883	−1.68168
$704$	−70.4852	−2.65651
$705$	28.1545	1.06036
$706$	−10.9043	−0.410390
$707$	1.18862	0.0447028
$708$	−18.3841	−0.690917
$709$	−14.9418	−0.561149	−0.280575	−	0.959832i	$-0.590525\pi$
$709$	−14.9418	−0.561149	−0.280575	+	0.959832i	$0.590525\pi$
$710$	−76.6750	−2.87756
$711$	1.94350	0.0728871
$712$	23.9446	0.897363
$713$	−1.33101	−0.0498468
$714$	−0.577463	−0.0216110
$715$	−14.7215	−0.550555
$716$	−48.2064	−1.80156
$717$	−6.73765	−0.251622
$718$	5.03928	0.188064
$719$	32.1728	1.19984	0.599922	−	0.800058i	$-0.295198\pi$
$719$	32.1728	1.19984	0.599922	+	0.800058i	$0.295198\pi$
$720$	−4.41251	−0.164444
$721$	0.116274	0.00433027
$722$	−85.3895	−3.17787
$723$	−14.4248	−0.536463
$724$	−27.6695	−1.02833
$725$	5.33305	0.198064
$726$	63.0939	2.34163
$727$	4.20568	0.155980	0.0779900	−	0.996954i	$-0.475150\pi$
$727$	4.20568	0.155980	0.0779900	+	0.996954i	$0.475150\pi$
$728$	0.444989	0.0164924
$729$	1.00000	0.0370370
$730$	−11.3229	−0.419081
$731$	21.7864	0.805799
$732$	41.3076	1.52677
$733$	9.58797	0.354140	0.177070	−	0.984198i	$-0.443338\pi$
$733$	9.58797	0.354140	0.177070	+	0.984198i	$0.443338\pi$
$734$	44.4800	1.64179
$735$	−16.7674	−0.618476
$736$	−4.64609	−0.171257
$737$	50.7771	1.87040
$738$	−18.2979	−0.673556
$739$	31.4808	1.15804	0.579020	−	0.815313i	$-0.303435\pi$
$739$	31.4808	1.15804	0.579020	+	0.815313i	$0.303435\pi$
$740$	−52.1464	−1.91694
$741$	7.41857	0.272528
$742$	0.591440	0.0217124
$743$	29.9663	1.09936	0.549678	−	0.835377i	$-0.314750\pi$
$743$	29.9663	1.09936	0.549678	+	0.835377i	$0.314750\pi$
$744$	3.61529	0.132543
$745$	−27.7807	−1.01781
$746$	−6.98862	−0.255871
$747$	−3.21526	−0.117640
$748$	46.4757	1.69932
$749$	0.543528	0.0198601
$750$	24.1135	0.880500
$751$	−3.48987	−0.127347	−0.0636735	−	0.997971i	$-0.520282\pi$
$751$	−3.48987	−0.127347	−0.0636735	+	0.997971i	$0.520282\pi$
$752$	21.5683	0.786516
$753$	3.33272	0.121451
$754$	−16.6298	−0.605621
$755$	5.17794	0.188444
$756$	0.420338	0.0152875
$757$	−44.1066	−1.60308	−0.801542	−	0.597939i	$-0.795986\pi$
$757$	−44.1066	−1.60308	−0.801542	+	0.597939i	$0.795986\pi$
$758$	70.6793	2.56719
$759$	8.64273	0.313711
$760$	−68.1390	−2.47166
$761$	24.1692	0.876134	0.438067	−	0.898942i	$-0.355663\pi$
$761$	24.1692	0.876134	0.438067	+	0.898942i	$0.355663\pi$
$762$	−14.2795	−0.517292
$763$	−0.396582	−0.0143572
$764$	75.4489	2.72965
$765$	−5.03005	−0.181862
$766$	7.68898	0.277814
$767$	5.08541	0.183624
$768$	25.9127	0.935044
$769$	−8.22778	−0.296701	−0.148351	−	0.988935i	$-0.547396\pi$
$769$	−8.22778	−0.296701	−0.148351	+	0.988935i	$0.547396\pi$
$770$	−4.05615	−0.146173
$771$	−17.1817	−0.618785
$772$	−10.7992	−0.388673
$773$	14.0889	0.506742	0.253371	−	0.967369i	$-0.418461\pi$
$773$	14.0889	0.506742	0.253371	+	0.967369i	$0.418461\pi$
$774$	−24.6319	−0.885376
$775$	0.717865	0.0257865
$776$	26.5707	0.953832
$777$	0.698848	0.0250710
$778$	80.4319	2.88362
$779$	−57.2855	−2.05247
$780$	8.67609	0.310654
$781$	−82.7015	−2.95929
$782$	6.99757	0.250233
$783$	−7.01793	−0.250800
$784$	−12.8450	−0.458752
$785$	6.19208	0.221005
$786$	−36.9592	−1.31829
$787$	4.07590	0.145290	0.0726451	−	0.997358i	$-0.476856\pi$
$787$	4.07590	0.145290	0.0726451	+	0.997358i	$0.476856\pi$
$788$	51.2382	1.82529
$789$	−4.03724	−0.143730
$790$	11.0528	0.393239
$791$	0.684794	0.0243485
$792$	−23.4754	−0.834161
$793$	−11.4265	−0.405768
$794$	−54.4985	−1.93408
$795$	5.15179	0.182715
$796$	−58.7789	−2.08336
$797$	11.6042	0.411043	0.205521	−	0.978653i	$-0.434111\pi$
$797$	11.6042	0.411043	0.205521	+	0.978653i	$0.434111\pi$
$798$	2.04400	0.0723567
$799$	24.5869	0.869822
$800$	2.50581	0.0885939
$801$	−6.25664	−0.221068
$802$	7.47840	0.264072
$803$	−12.2129	−0.430984
$804$	−29.9253	−1.05538
$805$	−0.393184	−0.0138579
$806$	−2.23848	−0.0788472
$807$	−23.3134	−0.820670
$808$	39.1227	1.37633
$809$	33.0718	1.16274	0.581372	−	0.813638i	$-0.302516\pi$
$809$	33.0718	1.16274	0.581372	+	0.813638i	$0.302516\pi$
$810$	5.68703	0.199822
$811$	−3.75191	−0.131747	−0.0658737	−	0.997828i	$-0.520983\pi$
$811$	−3.75191	−0.131747	−0.0658737	+	0.997828i	$0.520983\pi$
$812$	−2.94990	−0.103521
$813$	−26.0550	−0.913788
$814$	−87.3621	−3.06204
$815$	−38.5826	−1.35149
$816$	−3.85338	−0.134895
$817$	−77.1154	−2.69793
$818$	−67.9334	−2.37524
$819$	−0.116274	−0.00406294
$820$	−66.9959	−2.33960
$821$	−2.24654	−0.0784046	−0.0392023	−	0.999231i	$-0.512482\pi$
$821$	−2.24654	−0.0784046	−0.0392023	+	0.999231i	$0.512482\pi$
$822$	3.61512	0.126092
$823$	52.2548	1.82149	0.910743	−	0.412973i	$-0.135510\pi$
$823$	52.2548	1.82149	0.910743	+	0.412973i	$0.135510\pi$
$824$	3.82707	0.133322
$825$	−4.66135	−0.162287
$826$	1.40116	0.0487524
$827$	18.9886	0.660298	0.330149	−	0.943929i	$-0.392901\pi$
$827$	18.9886	0.660298	0.330149	+	0.943929i	$0.392901\pi$
$828$	−5.09356	−0.177013
$829$	51.3792	1.78447	0.892236	−	0.451569i	$-0.149135\pi$
$829$	51.3792	1.78447	0.892236	+	0.451569i	$0.149135\pi$
$830$	−18.2853	−0.634692
$831$	−30.8306	−1.06950
$832$	−11.4909	−0.398374
$833$	−14.6428	−0.507342
$834$	−23.1524	−0.801702
$835$	0.956002	0.0330838
$836$	−164.506	−5.68956
$837$	−0.944662	−0.0326523
$838$	−22.9531	−0.792900
$839$	−2.44169	−0.0842965	−0.0421483	−	0.999111i	$-0.513420\pi$
$839$	−2.44169	−0.0842965	−0.0421483	+	0.999111i	$0.513420\pi$
$840$	1.06797	0.0368484
$841$	20.2514	0.698322
$842$	−16.2565	−0.560237
$843$	25.8182	0.889225
$844$	56.9071	1.95882
$845$	−2.39998	−0.0825619
$846$	−27.7982	−0.955722
$847$	−3.09594	−0.106378
$848$	3.94664	0.135528
$849$	−6.88462	−0.236280
$850$	−3.77405	−0.129449
$851$	−8.46848	−0.290296
$852$	48.7398	1.66980
$853$	−48.1007	−1.64694	−0.823469	−	0.567361i	$-0.807964\pi$
$853$	−48.1007	−1.64694	−0.823469	+	0.567361i	$0.807964\pi$
$854$	−3.14829	−0.107732
$855$	17.8044	0.608899
$856$	17.8898	0.611461
$857$	4.66589	0.159384	0.0796920	−	0.996820i	$-0.474606\pi$
$857$	4.66589	0.159384	0.0796920	+	0.996820i	$0.474606\pi$
$858$	14.5353	0.496226
$859$	54.9984	1.87652	0.938261	−	0.345928i	$-0.112436\pi$
$859$	54.9984	1.87652	0.938261	+	0.345928i	$0.112436\pi$
$860$	−90.1872	−3.07536
$861$	0.897857	0.0305989
$862$	−80.5929	−2.74501
$863$	8.41035	0.286292	0.143146	−	0.989702i	$-0.454278\pi$
$863$	8.41035	0.286292	0.143146	+	0.989702i	$0.454278\pi$
$864$	−3.29748	−0.112183
$865$	−1.55005	−0.0527034
$866$	41.9741	1.42634
$867$	12.6073	0.428167
$868$	−0.397077	−0.0134777
$869$	11.9215	0.404409
$870$	−39.9112	−1.35312
$871$	8.27795	0.280488
$872$	−13.0532	−0.442038
$873$	−6.94282	−0.234979
$874$	−24.7687	−0.837814
$875$	−1.18322	−0.0400001
$876$	7.19763	0.243185
$877$	8.40319	0.283756	0.141878	−	0.989884i	$-0.454686\pi$
$877$	8.40319	0.283756	0.141878	+	0.989884i	$0.454686\pi$
$878$	−10.4534	−0.352784
$879$	28.1257	0.948656
$880$	−27.0664	−0.912409
$881$	10.1955	0.343496	0.171748	−	0.985141i	$-0.445059\pi$
$881$	10.1955	0.343496	0.171748	+	0.985141i	$0.445059\pi$
$882$	16.5553	0.557444
$883$	2.57833	0.0867677	0.0433838	−	0.999058i	$-0.486186\pi$
$883$	2.57833	0.0867677	0.0433838	+	0.999058i	$0.486186\pi$
$884$	7.57671	0.254832
$885$	12.2049	0.410263
$886$	38.3266	1.28761
$887$	4.83824	0.162452	0.0812261	−	0.996696i	$-0.474116\pi$
$887$	4.83824	0.162452	0.0812261	+	0.996696i	$0.474116\pi$
$888$	23.0021	0.771899
$889$	0.700679	0.0235000
$890$	−35.5817	−1.19270
$891$	6.13402	0.205498
$892$	−8.51824	−0.285212
$893$	−87.0282	−2.91229
$894$	27.4292	0.917369
$895$	32.0035	1.06976
$896$	−2.39919	−0.0801514
$897$	1.40898	0.0470445
$898$	−37.5673	−1.25364
$899$	6.62957	0.221109
$900$	2.74715	0.0915717
$901$	4.49899	0.149883
$902$	−112.240	−3.73718
$903$	1.20866	0.0402216
$904$	22.5395	0.749653
$905$	18.3694	0.610618
$906$	−5.11241	−0.169849
$907$	−31.3535	−1.04108	−0.520538	−	0.853839i	$-0.674268\pi$
$907$	−31.3535	−1.04108	−0.520538	+	0.853839i	$0.674268\pi$
$908$	0.199102	0.00660745
$909$	−10.2226	−0.339062
$910$	−0.661254	−0.0219203
$911$	−48.9811	−1.62282	−0.811408	−	0.584480i	$-0.801299\pi$
$911$	−48.9811	−1.62282	−0.811408	+	0.584480i	$0.801299\pi$
$912$	13.6395	0.451648
$913$	−19.7225	−0.652719
$914$	51.7334	1.71119
$915$	−27.4235	−0.906592
$916$	−64.4151	−2.12834
$917$	1.81354	0.0598885
$918$	4.96640	0.163916
$919$	27.6423	0.911836	0.455918	−	0.890022i	$-0.349311\pi$
$919$	27.6423	0.911836	0.455918	+	0.890022i	$0.349311\pi$
$920$	−12.9414	−0.426665
$921$	−18.1931	−0.599482
$922$	−54.3280	−1.78920
$923$	−13.4824	−0.443780
$924$	2.57836	0.0848219
$925$	4.56737	0.150174
$926$	−50.8464	−1.67092
$927$	−1.00000	−0.0328443
$928$	23.1415	0.759657
$929$	56.6574	1.85887	0.929435	−	0.368986i	$-0.120295\pi$
$929$	56.6574	1.85887	0.929435	+	0.368986i	$0.120295\pi$
$930$	−5.37232	−0.176165
$931$	51.8297	1.69865
$932$	66.3582	2.17363
$933$	−24.1152	−0.789498
$934$	43.3918	1.41982
$935$	−30.8545	−1.00905
$936$	−3.82707	−0.125092
$937$	32.6711	1.06732	0.533658	−	0.845700i	$-0.320817\pi$
$937$	32.6711	1.06732	0.533658	+	0.845700i	$0.320817\pi$
$938$	2.28078	0.0744700
$939$	−5.78369	−0.188744
$940$	−101.780	−3.31971
$941$	20.9401	0.682628	0.341314	−	0.939949i	$-0.389128\pi$
$941$	20.9401	0.682628	0.341314	+	0.939949i	$0.389128\pi$
$942$	−6.11373	−0.199196
$943$	−10.8800	−0.354302
$944$	9.34983	0.304311
$945$	−0.279056	−0.00907768
$946$	−151.093	−4.91245
$947$	19.8558	0.645228	0.322614	−	0.946531i	$-0.395438\pi$
$947$	19.8558	0.645228	0.322614	+	0.946531i	$0.395438\pi$
$948$	−7.02589	−0.228190
$949$	−1.99101	−0.0646309
$950$	13.3587	0.433413
$951$	−7.27734	−0.235984
$952$	0.932640	0.0302270
$953$	34.3986	1.11428	0.557140	−	0.830418i	$-0.311898\pi$
$953$	34.3986	1.11428	0.557140	+	0.830418i	$0.311898\pi$
$954$	−5.08660	−0.164685
$955$	−50.0893	−1.62085
$956$	24.3570	0.787763
$957$	−43.0481	−1.39155
$958$	−15.7949	−0.510311
$959$	−0.177389	−0.00572820
$960$	−27.5779	−0.890072
$961$	−30.1076	−0.971213
$962$	−14.2422	−0.459187
$963$	−4.67454	−0.150635
$964$	52.1464	1.67952
$965$	7.16944	0.230792
$966$	0.388209	0.0124904
$967$	25.3380	0.814814	0.407407	−	0.913247i	$-0.366433\pi$
$967$	25.3380	0.814814	0.407407	+	0.913247i	$0.366433\pi$
$968$	−101.901	−3.27521
$969$	15.5484	0.499486
$970$	−39.4840	−1.26776
$971$	−21.0796	−0.676476	−0.338238	−	0.941061i	$-0.609831\pi$
$971$	−21.0796	−0.676476	−0.338238	+	0.941061i	$0.609831\pi$
$972$	−3.61506	−0.115953
$973$	1.13606	0.0364204
$974$	−93.9698	−3.01099
$975$	−0.759917	−0.0243368
$976$	−21.0083	−0.672461
$977$	−46.4442	−1.48588	−0.742941	−	0.669357i	$-0.766570\pi$
$977$	−46.4442	−1.48588	−0.742941	+	0.669357i	$0.766570\pi$
$978$	38.0944	1.21812
$979$	−38.3784	−1.22658
$980$	60.6153	1.93629
$981$	3.41075	0.108897
$982$	−5.72050	−0.182548
$983$	4.77287	0.152231	0.0761155	−	0.997099i	$-0.475748\pi$
$983$	4.77287	0.152231	0.0761155	+	0.997099i	$0.475748\pi$
$984$	29.5523	0.942093
$985$	−34.0163	−1.08385
$986$	−34.8539	−1.10997
$987$	1.36402	0.0434174
$988$	−26.8186	−0.853214
$989$	−14.6462	−0.465724
$990$	34.8844	1.10870
$991$	16.1603	0.513348	0.256674	−	0.966498i	$-0.417373\pi$
$991$	16.1603	0.513348	0.256674	+	0.966498i	$0.417373\pi$
$992$	3.11500	0.0989015
$993$	0.00818240	0.000259660 0
$994$	−3.71474	−0.117824
$995$	39.0224	1.23709
$996$	11.6234	0.368301
$997$	−53.0022	−1.67860	−0.839298	−	0.543672i	$-0.817033\pi$
$997$	−53.0022	−1.67860	−0.839298	+	0.543672i	$0.817033\pi$
$998$	−24.8137	−0.785465
$999$	−6.01036	−0.190159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.2	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.2	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36961 q^{2} -1.00000 q^{3} +3.61506 q^{4} -2.39998 q^{5} +2.36961 q^{6} -0.116274 q^{7} -3.82707 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.36961 q^{2} -1.00000 q^{3} +3.61506 q^{4} -2.39998 q^{5} +2.36961 q^{6} -0.116274 q^{7} -3.82707 q^{8} +1.00000 q^{9} +5.68703 q^{10} +6.13402 q^{11} -3.61506 q^{12} +1.00000 q^{13} +0.275524 q^{14} +2.39998 q^{15} +1.83856 q^{16} +2.09587 q^{17} -2.36961 q^{18} -7.41857 q^{19} -8.67609 q^{20} +0.116274 q^{21} -14.5353 q^{22} -1.40898 q^{23} +3.82707 q^{24} +0.759917 q^{25} -2.36961 q^{26} -1.00000 q^{27} -0.420338 q^{28} +7.01793 q^{29} -5.68703 q^{30} +0.944662 q^{31} +3.29748 q^{32} -6.13402 q^{33} -4.96640 q^{34} +0.279056 q^{35} +3.61506 q^{36} +6.01036 q^{37} +17.5791 q^{38} -1.00000 q^{39} +9.18491 q^{40} +7.72190 q^{41} -0.275524 q^{42} +10.3949 q^{43} +22.1749 q^{44} -2.39998 q^{45} +3.33874 q^{46} +11.7311 q^{47} -1.83856 q^{48} -6.98648 q^{49} -1.80071 q^{50} -2.09587 q^{51} +3.61506 q^{52} +2.14660 q^{53} +2.36961 q^{54} -14.7215 q^{55} +0.444989 q^{56} +7.41857 q^{57} -16.6298 q^{58} +5.08541 q^{59} +8.67609 q^{60} -11.4265 q^{61} -2.23848 q^{62} -0.116274 q^{63} -11.4909 q^{64} -2.39998 q^{65} +14.5353 q^{66} +8.27795 q^{67} +7.57671 q^{68} +1.40898 q^{69} -0.661254 q^{70} -13.4824 q^{71} -3.82707 q^{72} -1.99101 q^{73} -14.2422 q^{74} -0.759917 q^{75} -26.8186 q^{76} -0.713228 q^{77} +2.36961 q^{78} +1.94350 q^{79} -4.41251 q^{80} +1.00000 q^{81} -18.2979 q^{82} -3.21526 q^{83} +0.420338 q^{84} -5.03005 q^{85} -24.6319 q^{86} -7.01793 q^{87} -23.4754 q^{88} -6.25664 q^{89} +5.68703 q^{90} -0.116274 q^{91} -5.09356 q^{92} -0.944662 q^{93} -27.7982 q^{94} +17.8044 q^{95} -3.29748 q^{96} -6.94282 q^{97} +16.5553 q^{98} +6.13402 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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