LMFDB - Embedded newform 1003.2.a.j.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.05162 q^{2} +1.73406 q^{3} +2.20914 q^{4} +2.98180 q^{5} +3.55764 q^{6} -0.740180 q^{7} +0.429083 q^{8} +0.00697358 q^{9} +O(q^{10})$	\(q+2.05162 q^{2} +1.73406 q^{3} +2.20914 q^{4} +2.98180 q^{5} +3.55764 q^{6} -0.740180 q^{7} +0.429083 q^{8} +0.00697358 q^{9} +6.11752 q^{10} -5.67094 q^{11} +3.83079 q^{12} +5.82270 q^{13} -1.51857 q^{14} +5.17063 q^{15} -3.53797 q^{16} -1.00000 q^{17} +0.0143071 q^{18} +7.13588 q^{19} +6.58722 q^{20} -1.28352 q^{21} -11.6346 q^{22} +2.83870 q^{23} +0.744057 q^{24} +3.89112 q^{25} +11.9460 q^{26} -5.19010 q^{27} -1.63516 q^{28} +7.10565 q^{29} +10.6082 q^{30} -3.32861 q^{31} -8.11674 q^{32} -9.83377 q^{33} -2.05162 q^{34} -2.20707 q^{35} +0.0154056 q^{36} -9.15944 q^{37} +14.6401 q^{38} +10.0969 q^{39} +1.27944 q^{40} -6.21978 q^{41} -2.63329 q^{42} +3.79386 q^{43} -12.5279 q^{44} +0.0207938 q^{45} +5.82393 q^{46} -5.37187 q^{47} -6.13506 q^{48} -6.45213 q^{49} +7.98311 q^{50} -1.73406 q^{51} +12.8632 q^{52} +1.82941 q^{53} -10.6481 q^{54} -16.9096 q^{55} -0.317599 q^{56} +12.3741 q^{57} +14.5781 q^{58} +1.00000 q^{59} +11.4227 q^{60} -6.74867 q^{61} -6.82905 q^{62} -0.00516170 q^{63} -9.57652 q^{64} +17.3621 q^{65} -20.1752 q^{66} -12.2012 q^{67} -2.20914 q^{68} +4.92248 q^{69} -4.52806 q^{70} -3.54665 q^{71} +0.00299225 q^{72} +4.72707 q^{73} -18.7917 q^{74} +6.74745 q^{75} +15.7642 q^{76} +4.19752 q^{77} +20.7150 q^{78} -15.3122 q^{79} -10.5495 q^{80} -9.02087 q^{81} -12.7606 q^{82} +2.58455 q^{83} -2.83548 q^{84} -2.98180 q^{85} +7.78356 q^{86} +12.3216 q^{87} -2.43331 q^{88} +8.96536 q^{89} +0.0426610 q^{90} -4.30984 q^{91} +6.27109 q^{92} -5.77202 q^{93} -11.0210 q^{94} +21.2777 q^{95} -14.0749 q^{96} +10.4241 q^{97} -13.2373 q^{98} -0.0395468 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) $ 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * 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 $

$2$	2.05162	1.45071	0.725357	−	0.688373i	$-0.241675\pi$
$2$	2.05162	1.45071	0.725357	+	0.688373i	$0.241675\pi$
$3$	1.73406	1.00116	0.500581	−	0.865690i	$-0.333120\pi$
$3$	1.73406	1.00116	0.500581	+	0.865690i	$0.333120\pi$
$4$	2.20914	1.10457
$5$	2.98180	1.33350	0.666750	−	0.745281i	$-0.267685\pi$
$5$	2.98180	1.33350	0.666750	+	0.745281i	$0.267685\pi$
$6$	3.55764	1.45240
$7$	−0.740180	−0.279762	−0.139881	−	0.990168i	$-0.544672\pi$
$7$	−0.740180	−0.279762	−0.139881	+	0.990168i	$0.544672\pi$
$8$	0.429083	0.151704
$9$	0.00697358	0.00232453
$10$	6.11752	1.93453
$11$	−5.67094	−1.70985	−0.854926	−	0.518749i	$-0.826398\pi$
$11$	−5.67094	−1.70985	−0.854926	+	0.518749i	$0.826398\pi$
$12$	3.83079	1.10585
$13$	5.82270	1.61493	0.807463	−	0.589918i	$-0.200840\pi$
$13$	5.82270	1.61493	0.807463	+	0.589918i	$0.200840\pi$
$14$	−1.51857	−0.405854
$15$	5.17063	1.33505
$16$	−3.53797	−0.884493
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.0143071	0.00337222
$19$	7.13588	1.63708	0.818541	−	0.574448i	$-0.194783\pi$
$19$	7.13588	1.63708	0.818541	+	0.574448i	$0.194783\pi$
$20$	6.58722	1.47295
$21$	−1.28352	−0.280087
$22$	−11.6346	−2.48051
$23$	2.83870	0.591910	0.295955	−	0.955202i	$-0.404362\pi$
$23$	2.83870	0.591910	0.295955	+	0.955202i	$0.404362\pi$
$24$	0.744057	0.151880
$25$	3.89112	0.778225
$26$	11.9460	2.34280
$27$	−5.19010	−0.998834
$28$	−1.63516	−0.309017
$29$	7.10565	1.31949	0.659743	−	0.751491i	$-0.270665\pi$
$29$	7.10565	1.31949	0.659743	+	0.751491i	$0.270665\pi$
$30$	10.6082	1.93678
$31$	−3.32861	−0.597837	−0.298918	−	0.954279i	$-0.596626\pi$
$31$	−3.32861	−0.597837	−0.298918	+	0.954279i	$0.596626\pi$
$32$	−8.11674	−1.43485
$33$	−9.83377	−1.71184
$34$	−2.05162	−0.351850
$35$	−2.20707	−0.373062
$36$	0.0154056	0.00256761
$37$	−9.15944	−1.50580	−0.752902	−	0.658133i	$-0.771346\pi$
$37$	−9.15944	−1.50580	−0.752902	+	0.658133i	$0.771346\pi$
$38$	14.6401	2.37494
$39$	10.0969	1.61680
$40$	1.27944	0.202297
$41$	−6.21978	−0.971366	−0.485683	−	0.874135i	$-0.661429\pi$
$41$	−6.21978	−0.971366	−0.485683	+	0.874135i	$0.661429\pi$
$42$	−2.63329	−0.406326
$43$	3.79386	0.578559	0.289279	−	0.957245i	$-0.406584\pi$
$43$	3.79386	0.578559	0.289279	+	0.957245i	$0.406584\pi$
$44$	−12.5279	−1.88866
$45$	0.0207938	0.00309976
$46$	5.82393	0.858692
$47$	−5.37187	−0.783568	−0.391784	−	0.920057i	$-0.628142\pi$
$47$	−5.37187	−0.783568	−0.391784	+	0.920057i	$0.628142\pi$
$48$	−6.13506	−0.885520
$49$	−6.45213	−0.921733
$50$	7.98311	1.12898
$51$	−1.73406	−0.242817
$52$	12.8632	1.78380
$53$	1.82941	0.251289	0.125644	−	0.992075i	$-0.459900\pi$
$53$	1.82941	0.251289	0.125644	+	0.992075i	$0.459900\pi$
$54$	−10.6481	−1.44902
$55$	−16.9096	−2.28009
$56$	−0.317599	−0.0424409
$57$	12.3741	1.63898
$58$	14.5781	1.91420
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	11.4227	1.47466
$61$	−6.74867	−0.864078	−0.432039	−	0.901855i	$-0.642206\pi$
$61$	−6.74867	−0.864078	−0.432039	+	0.901855i	$0.642206\pi$
$62$	−6.82905	−0.867290
$63$	−0.00516170	−0.000650314 0
$64$	−9.57652	−1.19706
$65$	17.3621	2.15351
$66$	−20.1752	−2.48339
$67$	−12.2012	−1.49062	−0.745308	−	0.666720i	$-0.767698\pi$
$67$	−12.2012	−1.49062	−0.745308	+	0.666720i	$0.767698\pi$
$68$	−2.20914	−0.267898
$69$	4.92248	0.592597
$70$	−4.52806	−0.541207
$71$	−3.54665	−0.420910	−0.210455	−	0.977603i	$-0.567495\pi$
$71$	−3.54665	−0.420910	−0.210455	+	0.977603i	$0.567495\pi$
$72$	0.00299225	0.000352640 0
$73$	4.72707	0.553262	0.276631	−	0.960976i	$-0.410782\pi$
$73$	4.72707	0.553262	0.276631	+	0.960976i	$0.410782\pi$
$74$	−18.7917	−2.18449
$75$	6.74745	0.779129
$76$	15.7642	1.80827
$77$	4.19752	0.478351
$78$	20.7150	2.34552
$79$	−15.3122	−1.72276	−0.861379	−	0.507963i	$-0.830399\pi$
$79$	−15.3122	−1.72276	−0.861379	+	0.507963i	$0.830399\pi$
$80$	−10.5495	−1.17947
$81$	−9.02087	−1.00232
$82$	−12.7606	−1.40917
$83$	2.58455	0.283691	0.141845	−	0.989889i	$-0.454696\pi$
$83$	2.58455	0.283691	0.141845	+	0.989889i	$0.454696\pi$
$84$	−2.83548	−0.309376
$85$	−2.98180	−0.323421
$86$	7.78356	0.839323
$87$	12.3216	1.32102
$88$	−2.43331	−0.259391
$89$	8.96536	0.950327	0.475163	−	0.879898i	$-0.342389\pi$
$89$	8.96536	0.950327	0.475163	+	0.879898i	$0.342389\pi$
$90$	0.0426610	0.00449686
$91$	−4.30984	−0.451794
$92$	6.27109	0.653807
$93$	−5.77202	−0.598531
$94$	−11.0210	−1.13673
$95$	21.2777	2.18305
$96$	−14.0749	−1.43652
$97$	10.4241	1.05840	0.529202	−	0.848496i	$-0.322491\pi$
$97$	10.4241	1.05840	0.529202	+	0.848496i	$0.322491\pi$
$98$	−13.2373	−1.33717
$99$	−0.0395468	−0.00397460
$100$	8.59605	0.859605
$101$	2.30139	0.228997	0.114499	−	0.993423i	$-0.463474\pi$
$101$	2.30139	0.228997	0.114499	+	0.993423i	$0.463474\pi$
$102$	−3.55764	−0.352259
$103$	−6.51543	−0.641984	−0.320992	−	0.947082i	$-0.604016\pi$
$103$	−6.51543	−0.641984	−0.320992	+	0.947082i	$0.604016\pi$
$104$	2.49842	0.244990
$105$	−3.82719	−0.373496
$106$	3.75326	0.364548
$107$	15.8561	1.53287	0.766434	−	0.642323i	$-0.222029\pi$
$107$	15.8561	1.53287	0.766434	+	0.642323i	$0.222029\pi$
$108$	−11.4657	−1.10328
$109$	2.29862	0.220167	0.110084	−	0.993922i	$-0.464888\pi$
$109$	2.29862	0.220167	0.110084	+	0.993922i	$0.464888\pi$
$110$	−34.6921	−3.30776
$111$	−15.8831	−1.50755
$112$	2.61874	0.247447
$113$	18.0018	1.69347	0.846736	−	0.532014i	$-0.178565\pi$
$113$	18.0018	1.69347	0.846736	+	0.532014i	$0.178565\pi$
$114$	25.3869	2.37770
$115$	8.46443	0.789312
$116$	15.6974	1.45747
$117$	0.0406051	0.00375394
$118$	2.05162	0.188867
$119$	0.740180	0.0678522
$120$	2.21863	0.202532
$121$	21.1596	1.92360
$122$	−13.8457	−1.25353
$123$	−10.7855	−0.972494
$124$	−7.35338	−0.660353
$125$	−3.30645	−0.295738
$126$	−0.0105899	−0.000943419 0
$127$	8.01231	0.710978	0.355489	−	0.934680i	$-0.384314\pi$
$127$	8.01231	0.710978	0.355489	+	0.934680i	$0.384314\pi$
$128$	−3.41390	−0.301749
$129$	6.57879	0.579231
$130$	35.6205	3.12412
$131$	6.89724	0.602615	0.301307	−	0.953527i	$-0.402577\pi$
$131$	6.89724	0.602615	0.301307	+	0.953527i	$0.402577\pi$
$132$	−21.7242	−1.89085
$133$	−5.28183	−0.457993
$134$	−25.0323	−2.16246
$135$	−15.4758	−1.33195
$136$	−0.429083	−0.0367936
$137$	13.4685	1.15069	0.575345	−	0.817911i	$-0.304868\pi$
$137$	13.4685	1.15069	0.575345	+	0.817911i	$0.304868\pi$
$138$	10.0991	0.859689
$139$	0.312953	0.0265443	0.0132722	−	0.999912i	$-0.495775\pi$
$139$	0.312953	0.0265443	0.0132722	+	0.999912i	$0.495775\pi$
$140$	−4.87573	−0.412074
$141$	−9.31516	−0.784478
$142$	−7.27639	−0.610621
$143$	−33.0202	−2.76129
$144$	−0.0246723	−0.00205603
$145$	21.1876	1.75954
$146$	9.69816	0.802625
$147$	−11.1884	−0.922804
$148$	−20.2345	−1.66327
$149$	6.93601	0.568220	0.284110	−	0.958792i	$-0.408302\pi$
$149$	6.93601	0.568220	0.284110	+	0.958792i	$0.408302\pi$
$150$	13.8432	1.13029
$151$	4.25984	0.346661	0.173331	−	0.984864i	$-0.444547\pi$
$151$	4.25984	0.346661	0.173331	+	0.984864i	$0.444547\pi$
$152$	3.06188	0.248352
$153$	−0.00697358	−0.000563781 0
$154$	8.61171	0.693951
$155$	−9.92525	−0.797216
$156$	22.3056	1.78587
$157$	−12.5328	−1.00023	−0.500115	−	0.865959i	$-0.666709\pi$
$157$	−12.5328	−1.00023	−0.500115	+	0.865959i	$0.666709\pi$
$158$	−31.4148	−2.49923
$159$	3.17231	0.251581
$160$	−24.2025	−1.91337
$161$	−2.10115	−0.165594
$162$	−18.5074	−1.45408
$163$	7.17791	0.562217	0.281109	−	0.959676i	$-0.409298\pi$
$163$	7.17791	0.562217	0.281109	+	0.959676i	$0.409298\pi$
$164$	−13.7404	−1.07294
$165$	−29.3223	−2.28274
$166$	5.30251	0.411554
$167$	−2.46676	−0.190884	−0.0954419	−	0.995435i	$-0.530426\pi$
$167$	−2.46676	−0.190884	−0.0954419	+	0.995435i	$0.530426\pi$
$168$	−0.550736	−0.0424902
$169$	20.9038	1.60799
$170$	−6.11752	−0.469192
$171$	0.0497626	0.00380544
$172$	8.38119	0.639059
$173$	−7.57570	−0.575970	−0.287985	−	0.957635i	$-0.592985\pi$
$173$	−7.57570	−0.575970	−0.287985	+	0.957635i	$0.592985\pi$
$174$	25.2793	1.91642
$175$	−2.88013	−0.217717
$176$	20.0636	1.51235
$177$	1.73406	0.130340
$178$	18.3935	1.37865
$179$	−2.86653	−0.214255	−0.107127	−	0.994245i	$-0.534165\pi$
$179$	−2.86653	−0.214255	−0.107127	+	0.994245i	$0.534165\pi$
$180$	0.0459365	0.00342391
$181$	24.2934	1.80572	0.902858	−	0.429938i	$-0.141465\pi$
$181$	24.2934	1.80572	0.902858	+	0.429938i	$0.141465\pi$
$182$	−8.84216	−0.655425
$183$	−11.7026	−0.865082
$184$	1.21804	0.0897950
$185$	−27.3116	−2.00799
$186$	−11.8420	−0.868297
$187$	5.67094	0.414700
$188$	−11.8672	−0.865507
$189$	3.84160	0.279436
$190$	43.6538	3.16698
$191$	1.94481	0.140722	0.0703608	−	0.997522i	$-0.477585\pi$
$191$	1.94481	0.140722	0.0703608	+	0.997522i	$0.477585\pi$
$192$	−16.6063	−1.19846
$193$	7.79283	0.560941	0.280470	−	0.959863i	$-0.409510\pi$
$193$	7.79283	0.560941	0.280470	+	0.959863i	$0.409510\pi$
$194$	21.3862	1.53544
$195$	30.1070	2.15601
$196$	−14.2537	−1.01812
$197$	16.3685	1.16621	0.583104	−	0.812398i	$-0.301838\pi$
$197$	16.3685	1.16621	0.583104	+	0.812398i	$0.301838\pi$
$198$	−0.0811349	−0.00576601
$199$	−14.5969	−1.03474	−0.517372	−	0.855761i	$-0.673090\pi$
$199$	−14.5969	−1.03474	−0.517372	+	0.855761i	$0.673090\pi$
$200$	1.66962	0.118060
$201$	−21.1577	−1.49235
$202$	4.72159	0.332210
$203$	−5.25946	−0.369142
$204$	−3.83079	−0.268209
$205$	−18.5461	−1.29532
$206$	−13.3672	−0.931335
$207$	0.0197959	0.00137591
$208$	−20.6005	−1.42839
$209$	−40.4671	−2.79917
$210$	−7.85194	−0.541836
$211$	−15.3974	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$211$	−15.3974	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$212$	4.04143	0.277567
$213$	−6.15012	−0.421399
$214$	32.5307	2.22375
$215$	11.3125	0.771508
$216$	−2.22698	−0.151527
$217$	2.46377	0.167252
$218$	4.71589	0.319400
$219$	8.19704	0.553905
$220$	−37.3557	−2.51852
$221$	−5.82270	−0.391677
$222$	−32.5860	−2.18703
$223$	−26.0419	−1.74390	−0.871948	−	0.489599i	$-0.837143\pi$
$223$	−26.0419	−1.74390	−0.871948	+	0.489599i	$0.837143\pi$
$224$	6.00785	0.401416
$225$	0.0271351	0.00180900
$226$	36.9329	2.45674
$227$	−25.3134	−1.68011	−0.840056	−	0.542500i	$-0.817478\pi$
$227$	−25.3134	−1.68011	−0.840056	+	0.542500i	$0.817478\pi$
$228$	27.3361	1.81038
$229$	24.3236	1.60735	0.803675	−	0.595068i	$-0.202875\pi$
$229$	24.3236	1.60735	0.803675	+	0.595068i	$0.202875\pi$
$230$	17.3658	1.14507
$231$	7.27876	0.478907
$232$	3.04892	0.200171
$233$	−13.2509	−0.868092	−0.434046	−	0.900891i	$-0.642915\pi$
$233$	−13.2509	−0.868092	−0.434046	+	0.900891i	$0.642915\pi$
$234$	0.0833061	0.00544589
$235$	−16.0178	−1.04489
$236$	2.20914	0.143803
$237$	−26.5523	−1.72476
$238$	1.51857	0.0984341
$239$	20.6147	1.33346	0.666728	−	0.745301i	$-0.267694\pi$
$239$	20.6147	1.33346	0.666728	+	0.745301i	$0.267694\pi$
$240$	−18.2935	−1.18084
$241$	7.04208	0.453620	0.226810	−	0.973939i	$-0.427170\pi$
$241$	7.04208	0.453620	0.226810	+	0.973939i	$0.427170\pi$
$242$	43.4114	2.79059
$243$	−0.0724714	−0.00464904
$244$	−14.9088	−0.954436
$245$	−19.2390	−1.22913
$246$	−22.1277	−1.41081
$247$	41.5500	2.64377
$248$	−1.42825	−0.0906941
$249$	4.48176	0.284020
$250$	−6.78357	−0.429031
$251$	5.02071	0.316905	0.158452	−	0.987367i	$-0.449350\pi$
$251$	5.02071	0.316905	0.158452	+	0.987367i	$0.449350\pi$
$252$	−0.0114029	−0.000718318 0
$253$	−16.0981	−1.01208
$254$	16.4382	1.03143
$255$	−5.17063	−0.323797
$256$	12.1490	0.759314
$257$	4.31506	0.269166	0.134583	−	0.990902i	$-0.457031\pi$
$257$	4.31506	0.269166	0.134583	+	0.990902i	$0.457031\pi$
$258$	13.4972	0.840298
$259$	6.77964	0.421266
$260$	38.3554	2.37870
$261$	0.0495519	0.00306718
$262$	14.1505	0.874222
$263$	15.0108	0.925607	0.462803	−	0.886461i	$-0.346844\pi$
$263$	15.0108	0.925607	0.462803	+	0.886461i	$0.346844\pi$
$264$	−4.21950	−0.259693
$265$	5.45494	0.335094
$266$	−10.8363	−0.664417
$267$	15.5465	0.951431
$268$	−26.9543	−1.64649
$269$	17.3303	1.05664	0.528322	−	0.849044i	$-0.322821\pi$
$269$	17.3303	1.05664	0.528322	+	0.849044i	$0.322821\pi$
$270$	−31.7505	−1.93227
$271$	30.5858	1.85795	0.928977	−	0.370138i	$-0.120690\pi$
$271$	30.5858	1.85795	0.928977	+	0.370138i	$0.120690\pi$
$272$	3.53797	0.214521
$273$	−7.47354	−0.452319
$274$	27.6322	1.66932
$275$	−22.0663	−1.33065
$276$	10.8745	0.654566
$277$	−5.59732	−0.336310	−0.168155	−	0.985761i	$-0.553781\pi$
$277$	−5.59732	−0.336310	−0.168155	+	0.985761i	$0.553781\pi$
$278$	0.642060	0.0385082
$279$	−0.0232124	−0.00138969
$280$	−0.947015	−0.0565950
$281$	−8.00266	−0.477398	−0.238699	−	0.971094i	$-0.576721\pi$
$281$	−8.00266	−0.477398	−0.238699	+	0.971094i	$0.576721\pi$
$282$	−19.1112	−1.13805
$283$	9.25813	0.550338	0.275169	−	0.961396i	$-0.411266\pi$
$283$	9.25813	0.550338	0.275169	+	0.961396i	$0.411266\pi$
$284$	−7.83507	−0.464926
$285$	36.8969	2.18559
$286$	−67.7448	−4.00584
$287$	4.60375	0.271751
$288$	−0.0566027	−0.00333535
$289$	1.00000	0.0588235
$290$	43.4690	2.55259
$291$	18.0760	1.05963
$292$	10.4428	0.611118
$293$	−13.3573	−0.780340	−0.390170	−	0.920743i	$-0.627584\pi$
$293$	−13.3573	−0.780340	−0.390170	+	0.920743i	$0.627584\pi$
$294$	−22.9544	−1.33873
$295$	2.98180	0.173607
$296$	−3.93016	−0.228436
$297$	29.4327	1.70786
$298$	14.2301	0.824325
$299$	16.5289	0.955890
$300$	14.9061	0.860604
$301$	−2.80814	−0.161858
$302$	8.73958	0.502906
$303$	3.99076	0.229263
$304$	−25.2465	−1.44799
$305$	−20.1232	−1.15225
$306$	−0.0143071	−0.000817885 0
$307$	15.1476	0.864519	0.432260	−	0.901749i	$-0.357716\pi$
$307$	15.1476	0.864519	0.432260	+	0.901749i	$0.357716\pi$
$308$	9.27291	0.528373
$309$	−11.2982	−0.642730
$310$	−20.3628	−1.15653
$311$	−5.12050	−0.290357	−0.145178	−	0.989406i	$-0.546376\pi$
$311$	−5.12050	−0.290357	−0.145178	+	0.989406i	$0.546376\pi$
$312$	4.33242	0.245275
$313$	−23.9205	−1.35207	−0.676033	−	0.736871i	$-0.736303\pi$
$313$	−23.9205	−1.35207	−0.676033	+	0.736871i	$0.736303\pi$
$314$	−25.7126	−1.45105
$315$	−0.0153912	−0.000867194 0
$316$	−33.8269	−1.90291
$317$	20.1545	1.13199	0.565995	−	0.824409i	$-0.308492\pi$
$317$	20.1545	1.13199	0.565995	+	0.824409i	$0.308492\pi$
$318$	6.50838	0.364972
$319$	−40.2957	−2.25613
$320$	−28.5553	−1.59629
$321$	27.4955	1.53465
$322$	−4.31076	−0.240229
$323$	−7.13588	−0.397051
$324$	−19.9284	−1.10713
$325$	22.6568	1.25678
$326$	14.7263	0.815616
$327$	3.98594	0.220423
$328$	−2.66880	−0.147360
$329$	3.97615	0.219212
$330$	−60.1582	−3.31160
$331$	−19.4231	−1.06759	−0.533796	−	0.845614i	$-0.679235\pi$
$331$	−19.4231	−1.06759	−0.533796	+	0.845614i	$0.679235\pi$
$332$	5.70963	0.313357
$333$	−0.0638741	−0.00350028
$334$	−5.06086	−0.276918
$335$	−36.3816	−1.98774
$336$	4.54105	0.247735
$337$	−31.9769	−1.74189	−0.870946	−	0.491378i	$-0.836493\pi$
$337$	−31.9769	−1.74189	−0.870946	+	0.491378i	$0.836493\pi$
$338$	42.8867	2.33273
$339$	31.2163	1.69544
$340$	−6.58722	−0.357242
$341$	18.8764	1.02221
$342$	0.102094	0.00552061
$343$	9.95700	0.537627
$344$	1.62788	0.0877695
$345$	14.6779	0.790229
$346$	−15.5425	−0.835567
$347$	−14.5565	−0.781436	−0.390718	−	0.920510i	$-0.627773\pi$
$347$	−14.5565	−0.781436	−0.390718	+	0.920510i	$0.627773\pi$
$348$	27.2203	1.45916
$349$	15.4346	0.826196	0.413098	−	0.910687i	$-0.364447\pi$
$349$	15.4346	0.826196	0.413098	+	0.910687i	$0.364447\pi$
$350$	−5.90893	−0.315846
$351$	−30.2204	−1.61304
$352$	46.0295	2.45338
$353$	1.35380	0.0720552	0.0360276	−	0.999351i	$-0.488530\pi$
$353$	1.35380	0.0720552	0.0360276	+	0.999351i	$0.488530\pi$
$354$	3.55764	0.189086
$355$	−10.5754	−0.561284
$356$	19.8058	1.04970
$357$	1.28352	0.0679310
$358$	−5.88104	−0.310822
$359$	30.1921	1.59348	0.796739	−	0.604323i	$-0.206557\pi$
$359$	30.1921	1.59348	0.796739	+	0.604323i	$0.206557\pi$
$360$	0.00892228	0.000470245 0
$361$	31.9207	1.68004
$362$	49.8409	2.61958
$363$	36.6920	1.92583
$364$	−9.52106	−0.499039
$365$	14.0952	0.737775
$366$	−24.0093	−1.25499
$367$	−35.5213	−1.85420	−0.927098	−	0.374818i	$-0.877705\pi$
$367$	−35.5213	−1.85420	−0.927098	+	0.374818i	$0.877705\pi$
$368$	−10.0432	−0.523540
$369$	−0.0433741	−0.00225797
$370$	−56.0331	−2.91302
$371$	−1.35409	−0.0703010
$372$	−12.7512	−0.661120
$373$	−28.8427	−1.49342	−0.746710	−	0.665150i	$-0.768368\pi$
$373$	−28.8427	−1.49342	−0.746710	+	0.665150i	$0.768368\pi$
$374$	11.6346	0.601612
$375$	−5.73359	−0.296081
$376$	−2.30498	−0.118870
$377$	41.3741	2.13087
$378$	7.88151	0.405381
$379$	−15.1406	−0.777719	−0.388860	−	0.921297i	$-0.627131\pi$
$379$	−15.1406	−0.777719	−0.388860	+	0.921297i	$0.627131\pi$
$380$	47.0056	2.41134
$381$	13.8939	0.711804
$382$	3.99001	0.204147
$383$	17.2801	0.882972	0.441486	−	0.897268i	$-0.354452\pi$
$383$	17.2801	0.882972	0.441486	+	0.897268i	$0.354452\pi$
$384$	−5.91991	−0.302099
$385$	12.5161	0.637882
$386$	15.9879	0.813764
$387$	0.0264568	0.00134487
$388$	23.0283	1.16908
$389$	0.787347	0.0399201	0.0199600	−	0.999801i	$-0.493646\pi$
$389$	0.787347	0.0399201	0.0199600	+	0.999801i	$0.493646\pi$
$390$	61.7681	3.12775
$391$	−2.83870	−0.143559
$392$	−2.76850	−0.139830
$393$	11.9602	0.603315
$394$	33.5819	1.69183
$395$	−45.6579	−2.29730
$396$	−0.0873645	−0.00439023
$397$	−2.76990	−0.139017	−0.0695087	−	0.997581i	$-0.522143\pi$
$397$	−2.76990	−0.139017	−0.0695087	+	0.997581i	$0.522143\pi$
$398$	−29.9472	−1.50112
$399$	−9.15903	−0.458525
$400$	−13.7667	−0.688334
$401$	−22.5588	−1.12653	−0.563267	−	0.826275i	$-0.690456\pi$
$401$	−22.5588	−1.12653	−0.563267	+	0.826275i	$0.690456\pi$
$402$	−43.4075	−2.16497
$403$	−19.3815	−0.965462
$404$	5.08411	0.252944
$405$	−26.8984	−1.33659
$406$	−10.7904	−0.535519
$407$	51.9427	2.57470
$408$	−0.744057	−0.0368363
$409$	−5.20757	−0.257498	−0.128749	−	0.991677i	$-0.541096\pi$
$409$	−5.20757	−0.257498	−0.128749	+	0.991677i	$0.541096\pi$
$410$	−38.0496	−1.87914
$411$	23.3552	1.15203
$412$	−14.3935	−0.709117
$413$	−0.740180	−0.0364219
$414$	0.0406137	0.00199605
$415$	7.70659	0.378302
$416$	−47.2613	−2.31718
$417$	0.542680	0.0265751
$418$	−83.0232	−4.06080
$419$	−17.2532	−0.842872	−0.421436	−	0.906858i	$-0.638474\pi$
$419$	−17.2532	−0.842872	−0.421436	+	0.906858i	$0.638474\pi$
$420$	−8.45482	−0.412553
$421$	9.11227	0.444105	0.222052	−	0.975035i	$-0.428724\pi$
$421$	9.11227	0.444105	0.222052	+	0.975035i	$0.428724\pi$
$422$	−31.5895	−1.53776
$423$	−0.0374612	−0.00182143
$424$	0.784969	0.0381215
$425$	−3.89112	−0.188747
$426$	−12.6177	−0.611330
$427$	4.99523	0.241736
$428$	35.0284	1.69316
$429$	−57.2591	−2.76449
$430$	23.2090	1.11924
$431$	−9.48204	−0.456734	−0.228367	−	0.973575i	$-0.573339\pi$
$431$	−9.48204	−0.456734	−0.228367	+	0.973575i	$0.573339\pi$
$432$	18.3624	0.883462
$433$	11.6316	0.558977	0.279489	−	0.960149i	$-0.409835\pi$
$433$	11.6316	0.558977	0.279489	+	0.960149i	$0.409835\pi$
$434$	5.05472	0.242634
$435$	36.7407	1.76158
$436$	5.07797	0.243191
$437$	20.2566	0.969005
$438$	16.8172	0.803557
$439$	15.2107	0.725965	0.362982	−	0.931796i	$-0.381759\pi$
$439$	15.2107	0.725965	0.362982	+	0.931796i	$0.381759\pi$
$440$	−7.25563	−0.345898
$441$	−0.0449945	−0.00214259
$442$	−11.9460	−0.568212
$443$	8.12577	0.386067	0.193034	−	0.981192i	$-0.438167\pi$
$443$	8.12577	0.386067	0.193034	+	0.981192i	$0.438167\pi$
$444$	−35.0879	−1.66520
$445$	26.7329	1.26726
$446$	−53.4281	−2.52989
$447$	12.0275	0.568880
$448$	7.08835	0.334893
$449$	41.7860	1.97201	0.986003	−	0.166730i	$-0.0533207\pi$
$449$	41.7860	1.97201	0.986003	+	0.166730i	$0.0533207\pi$
$450$	0.0556708	0.00262435
$451$	35.2720	1.66089
$452$	39.7687	1.87056
$453$	7.38683	0.347064
$454$	−51.9335	−2.43736
$455$	−12.8511	−0.602468
$456$	5.30950	0.248640
$457$	10.3753	0.485335	0.242668	−	0.970109i	$-0.421978\pi$
$457$	10.3753	0.485335	0.242668	+	0.970109i	$0.421978\pi$
$458$	49.9028	2.33181
$459$	5.19010	0.242253
$460$	18.6991	0.871852
$461$	−27.4095	−1.27659	−0.638294	−	0.769793i	$-0.720360\pi$
$461$	−27.4095	−1.27659	−0.638294	+	0.769793i	$0.720360\pi$
$462$	14.9332	0.694757
$463$	8.12617	0.377655	0.188828	−	0.982010i	$-0.439531\pi$
$463$	8.12617	0.377655	0.188828	+	0.982010i	$0.439531\pi$
$464$	−25.1396	−1.16708
$465$	−17.2110	−0.798142
$466$	−27.1857	−1.25935
$467$	−29.4869	−1.36449	−0.682245	−	0.731124i	$-0.738996\pi$
$467$	−29.4869	−1.36449	−0.682245	+	0.731124i	$0.738996\pi$
$468$	0.0897024	0.00414650
$469$	9.03110	0.417017
$470$	−32.8625	−1.51583
$471$	−21.7327	−1.00139
$472$	0.429083	0.0197502
$473$	−21.5148	−0.989250
$474$	−54.4753	−2.50213
$475$	27.7666	1.27402
$476$	1.63516	0.0749476
$477$	0.0127575	0.000584128 0
$478$	42.2936	1.93446
$479$	−2.23453	−0.102098	−0.0510492	−	0.998696i	$-0.516257\pi$
$479$	−2.23453	−0.102098	−0.0510492	+	0.998696i	$0.516257\pi$
$480$	−41.9686	−1.91560
$481$	−53.3327	−2.43176
$482$	14.4477	0.658073
$483$	−3.64352	−0.165786
$484$	46.7445	2.12475
$485$	31.0825	1.41138
$486$	−0.148684	−0.00674444
$487$	−6.03805	−0.273610	−0.136805	−	0.990598i	$-0.543683\pi$
$487$	−6.03805	−0.273610	−0.136805	+	0.990598i	$0.543683\pi$
$488$	−2.89574	−0.131084
$489$	12.4469	0.562870
$490$	−39.4710	−1.78312
$491$	14.6004	0.658905	0.329453	−	0.944172i	$-0.393136\pi$
$491$	14.6004	0.658905	0.329453	+	0.944172i	$0.393136\pi$
$492$	−23.8267	−1.07419
$493$	−7.10565	−0.320023
$494$	85.2449	3.83535
$495$	−0.117920	−0.00530013
$496$	11.7765	0.528782
$497$	2.62516	0.117755
$498$	9.19488	0.412032
$499$	−30.3448	−1.35842	−0.679209	−	0.733945i	$-0.737677\pi$
$499$	−30.3448	−1.35842	−0.679209	+	0.733945i	$0.737677\pi$
$500$	−7.30442	−0.326663
$501$	−4.27752	−0.191105
$502$	10.3006	0.459738
$503$	28.8318	1.28555	0.642774	−	0.766056i	$-0.277784\pi$
$503$	28.8318	1.28555	0.642774	+	0.766056i	$0.277784\pi$
$504$	−0.00221480	−9.86550e−5 0
$505$	6.86230	0.305368
$506$	−33.0272	−1.46824
$507$	36.2485	1.60985
$508$	17.7004	0.785326
$509$	−33.2548	−1.47399	−0.736996	−	0.675897i	$-0.763757\pi$
$509$	−33.2548	−1.47399	−0.736996	+	0.675897i	$0.763757\pi$
$510$	−10.6082	−0.469737
$511$	−3.49888	−0.154782
$512$	31.7530	1.40330
$513$	−37.0359	−1.63517
$514$	8.85286	0.390483
$515$	−19.4277	−0.856086
$516$	14.5335	0.639802
$517$	30.4636	1.33979
$518$	13.9092	0.611137
$519$	−13.1367	−0.576639
$520$	7.44979	0.326695
$521$	1.97123	0.0863613	0.0431807	−	0.999067i	$-0.486251\pi$
$521$	1.97123	0.0863613	0.0431807	+	0.999067i	$0.486251\pi$
$522$	0.101662	0.00444961
$523$	−14.3007	−0.625324	−0.312662	−	0.949864i	$-0.601221\pi$
$523$	−14.3007	−0.625324	−0.312662	+	0.949864i	$0.601221\pi$
$524$	15.2370	0.665631
$525$	−4.99433	−0.217970
$526$	30.7965	1.34279
$527$	3.32861	0.144997
$528$	34.7916	1.51411
$529$	−14.9418	−0.649643
$530$	11.1915	0.486126
$531$	0.00697358	0.000302628 0
$532$	−11.6683	−0.505886
$533$	−36.2159	−1.56868
$534$	31.8955	1.38025
$535$	47.2797	2.04408
$536$	−5.23534	−0.226132
$537$	−4.97075	−0.214504
$538$	35.5551	1.53289
$539$	36.5897	1.57603
$540$	−34.1883	−1.47123
$541$	−29.0736	−1.24997	−0.624986	−	0.780636i	$-0.714895\pi$
$541$	−29.0736	−1.24997	−0.624986	+	0.780636i	$0.714895\pi$
$542$	62.7504	2.69536
$543$	42.1263	1.80781
$544$	8.11674	0.348002
$545$	6.85401	0.293593
$546$	−15.3329	−0.656186
$547$	−38.1327	−1.63044	−0.815219	−	0.579153i	$-0.803383\pi$
$547$	−38.1327	−1.63044	−0.815219	+	0.579153i	$0.803383\pi$
$548$	29.7538	1.27102
$549$	−0.0470624	−0.00200857
$550$	−45.2717	−1.93039
$551$	50.7051	2.16011
$552$	2.11215	0.0898993
$553$	11.3338	0.481962
$554$	−11.4836	−0.487890
$555$	−47.3601	−2.01032
$556$	0.691357	0.0293201
$557$	−27.4331	−1.16238	−0.581188	−	0.813769i	$-0.697412\pi$
$557$	−27.4331	−1.16238	−0.581188	+	0.813769i	$0.697412\pi$
$558$	−0.0476229	−0.00201604
$559$	22.0905	0.934329
$560$	7.80854	0.329971
$561$	9.83377	0.415182
$562$	−16.4184	−0.692569
$563$	22.7611	0.959268	0.479634	−	0.877469i	$-0.340769\pi$
$563$	22.7611	0.959268	0.479634	+	0.877469i	$0.340769\pi$
$564$	−20.5785	−0.866512
$565$	53.6779	2.25825
$566$	18.9942	0.798384
$567$	6.67707	0.280410
$568$	−1.52181	−0.0638537
$569$	−3.13346	−0.131361	−0.0656807	−	0.997841i	$-0.520922\pi$
$569$	−3.13346	−0.131361	−0.0656807	+	0.997841i	$0.520922\pi$
$570$	75.6985	3.17066
$571$	−27.6122	−1.15553	−0.577767	−	0.816201i	$-0.696076\pi$
$571$	−27.6122	−1.15553	−0.577767	+	0.816201i	$0.696076\pi$
$572$	−72.9463	−3.05004
$573$	3.37242	0.140885
$574$	9.44515	0.394233
$575$	11.0457	0.460639
$576$	−0.0667826	−0.00278261
$577$	13.7840	0.573834	0.286917	−	0.957955i	$-0.407370\pi$
$577$	13.7840	0.573834	0.286917	+	0.957955i	$0.407370\pi$
$578$	2.05162	0.0853361
$579$	13.5133	0.561592
$580$	46.8065	1.94353
$581$	−1.91303	−0.0793658
$582$	37.0851	1.53723
$583$	−10.3745	−0.429667
$584$	2.02831	0.0839320
$585$	0.121076	0.00500588
$586$	−27.4040	−1.13205
$587$	16.2493	0.670682	0.335341	−	0.942097i	$-0.391149\pi$
$587$	16.2493	0.670682	0.335341	+	0.942097i	$0.391149\pi$
$588$	−24.7168	−1.01930
$589$	−23.7526	−0.978707
$590$	6.11752	0.251854
$591$	28.3840	1.16756
$592$	32.4059	1.33187
$593$	−14.2400	−0.584768	−0.292384	−	0.956301i	$-0.594449\pi$
$593$	−14.2400	−0.584768	−0.292384	+	0.956301i	$0.594449\pi$
$594$	60.3848	2.47762
$595$	2.20707	0.0904809
$596$	15.3227	0.627640
$597$	−25.3119	−1.03595
$598$	33.9110	1.38672
$599$	−3.21445	−0.131339	−0.0656695	−	0.997841i	$-0.520918\pi$
$599$	−3.21445	−0.131339	−0.0656695	+	0.997841i	$0.520918\pi$
$600$	2.89522	0.118197
$601$	7.07839	0.288734	0.144367	−	0.989524i	$-0.453885\pi$
$601$	7.07839	0.288734	0.144367	+	0.989524i	$0.453885\pi$
$602$	−5.76124	−0.234810
$603$	−0.0850862	−0.00346498
$604$	9.41060	0.382912
$605$	63.0936	2.56512
$606$	8.18753	0.332596
$607$	−37.1455	−1.50769	−0.753844	−	0.657054i	$-0.771803\pi$
$607$	−37.1455	−1.50769	−0.753844	+	0.657054i	$0.771803\pi$
$608$	−57.9200	−2.34897
$609$	−9.12024	−0.369571
$610$	−41.2851	−1.67158
$611$	−31.2788	−1.26540
$612$	−0.0154056	−0.000622736 0
$613$	−18.1480	−0.732991	−0.366496	−	0.930420i	$-0.619443\pi$
$613$	−18.1480	−0.732991	−0.366496	+	0.930420i	$0.619443\pi$
$614$	31.0771	1.25417
$615$	−32.1601	−1.29682
$616$	1.80108	0.0725677
$617$	40.7406	1.64015	0.820077	−	0.572254i	$-0.193931\pi$
$617$	40.7406	1.64015	0.820077	+	0.572254i	$0.193931\pi$
$618$	−23.1795	−0.932417
$619$	−32.6000	−1.31030	−0.655152	−	0.755497i	$-0.727396\pi$
$619$	−32.6000	−1.31030	−0.655152	+	0.755497i	$0.727396\pi$
$620$	−21.9263	−0.880582
$621$	−14.7331	−0.591220
$622$	−10.5053	−0.421225
$623$	−6.63598	−0.265865
$624$	−35.7226	−1.43005
$625$	−29.3148	−1.17259
$626$	−49.0758	−1.96146
$627$	−70.1725	−2.80242
$628$	−27.6868	−1.10483
$629$	9.15944	0.365211
$630$	−0.0315768	−0.00125805
$631$	41.5837	1.65542	0.827711	−	0.561155i	$-0.189643\pi$
$631$	41.5837	1.65542	0.827711	+	0.561155i	$0.189643\pi$
$632$	−6.57021	−0.261349
$633$	−26.7000	−1.06123
$634$	41.3494	1.64219
$635$	23.8911	0.948090
$636$	7.00810	0.277889
$637$	−37.5688	−1.48853
$638$	−82.6715	−3.27300
$639$	−0.0247329	−0.000978418 0
$640$	−10.1796	−0.402382
$641$	−27.2689	−1.07706	−0.538528	−	0.842607i	$-0.681019\pi$
$641$	−27.2689	−1.07706	−0.538528	+	0.842607i	$0.681019\pi$
$642$	56.4103	2.22634
$643$	27.5975	1.08834	0.544169	−	0.838976i	$-0.316845\pi$
$643$	27.5975	1.08834	0.544169	+	0.838976i	$0.316845\pi$
$644$	−4.64174	−0.182910
$645$	19.6166	0.772404
$646$	−14.6401	−0.576007
$647$	−31.5531	−1.24048	−0.620240	−	0.784412i	$-0.712965\pi$
$647$	−31.5531	−1.24048	−0.620240	+	0.784412i	$0.712965\pi$
$648$	−3.87070	−0.152056
$649$	−5.67094	−0.222604
$650$	46.4832	1.82322
$651$	4.27234	0.167446
$652$	15.8570	0.621009
$653$	11.5424	0.451687	0.225844	−	0.974164i	$-0.427486\pi$
$653$	11.5424	0.451687	0.225844	+	0.974164i	$0.427486\pi$
$654$	8.17764	0.319771
$655$	20.5662	0.803587
$656$	22.0054	0.859166
$657$	0.0329646	0.00128607
$658$	8.15755	0.318014
$659$	−13.5820	−0.529081	−0.264541	−	0.964375i	$-0.585220\pi$
$659$	−13.5820	−0.529081	−0.264541	+	0.964375i	$0.585220\pi$
$660$	−64.7772	−2.52145
$661$	48.6257	1.89132	0.945661	−	0.325156i	$-0.105417\pi$
$661$	48.6257	1.89132	0.945661	+	0.325156i	$0.105417\pi$
$662$	−39.8489	−1.54877
$663$	−10.0969	−0.392132
$664$	1.10899	0.0430370
$665$	−15.7494	−0.610734
$666$	−0.131045	−0.00507791
$667$	20.1708	0.781017
$668$	−5.44943	−0.210845
$669$	−45.1583	−1.74592
$670$	−74.6412	−2.88364
$671$	38.2713	1.47745
$672$	10.4180	0.401882
$673$	20.3670	0.785090	0.392545	−	0.919733i	$-0.371595\pi$
$673$	20.3670	0.785090	0.392545	+	0.919733i	$0.371595\pi$
$674$	−65.6044	−2.52699
$675$	−20.1953	−0.777318
$676$	46.1795	1.77614
$677$	21.2616	0.817151	0.408576	−	0.912725i	$-0.366026\pi$
$677$	21.2616	0.817151	0.408576	+	0.912725i	$0.366026\pi$
$678$	64.0440	2.45960
$679$	−7.71569	−0.296101
$680$	−1.27944	−0.0490643
$681$	−43.8951	−1.68206
$682$	38.7271	1.48294
$683$	−35.1020	−1.34314	−0.671570	−	0.740941i	$-0.734380\pi$
$683$	−35.1020	−1.34314	−0.671570	+	0.740941i	$0.734380\pi$
$684$	0.109933	0.00420338
$685$	40.1603	1.53445
$686$	20.4280	0.779944
$687$	42.1787	1.60922
$688$	−13.4226	−0.511731
$689$	10.6521	0.405813
$690$	30.1134	1.14640
$691$	34.1395	1.29873	0.649364	−	0.760478i	$-0.275035\pi$
$691$	34.1395	1.29873	0.649364	+	0.760478i	$0.275035\pi$
$692$	−16.7358	−0.636200
$693$	0.0292717	0.00111194
$694$	−29.8645	−1.13364
$695$	0.933162	0.0353969
$696$	5.28701	0.200404
$697$	6.21978	0.235591
$698$	31.6660	1.19857
$699$	−22.9778	−0.869101
$700$	−6.36262	−0.240485
$701$	4.89724	0.184966	0.0924831	−	0.995714i	$-0.470520\pi$
$701$	4.89724	0.184966	0.0924831	+	0.995714i	$0.470520\pi$
$702$	−62.0007	−2.34007
$703$	−65.3607	−2.46512
$704$	54.3079	2.04680
$705$	−27.7759	−1.04610
$706$	2.77747	0.104532
$707$	−1.70345	−0.0640647
$708$	3.83079	0.143970
$709$	−3.78056	−0.141982	−0.0709909	−	0.997477i	$-0.522616\pi$
$709$	−3.78056	−0.141982	−0.0709909	+	0.997477i	$0.522616\pi$
$710$	−21.6967	−0.814263
$711$	−0.106781	−0.00400460
$712$	3.84689	0.144168
$713$	−9.44893	−0.353865
$714$	2.63329	0.0985485
$715$	−98.4595	−3.68218
$716$	−6.33258	−0.236660
$717$	35.7472	1.33501
$718$	61.9427	2.31168
$719$	37.7730	1.40870	0.704348	−	0.709854i	$-0.251239\pi$
$719$	37.7730	1.40870	0.704348	+	0.709854i	$0.251239\pi$
$720$	−0.0735679	−0.00274171
$721$	4.82259	0.179603
$722$	65.4892	2.43725
$723$	12.2114	0.454147
$724$	53.6677	1.99454
$725$	27.6490	1.02686
$726$	75.2781	2.79383
$727$	−24.6082	−0.912666	−0.456333	−	0.889809i	$-0.650837\pi$
$727$	−24.6082	−0.912666	−0.456333	+	0.889809i	$0.650837\pi$
$728$	−1.84928	−0.0685389
$729$	26.9369	0.997665
$730$	28.9179	1.07030
$731$	−3.79386	−0.140321
$732$	−25.8527	−0.955545
$733$	−10.2882	−0.380005	−0.190003	−	0.981784i	$-0.560850\pi$
$733$	−10.2882	−0.380005	−0.190003	+	0.981784i	$0.560850\pi$
$734$	−72.8762	−2.68991
$735$	−33.3616	−1.23056
$736$	−23.0410	−0.849302
$737$	69.1924	2.54874
$738$	−0.0889872	−0.00327566
$739$	50.2961	1.85017	0.925086	−	0.379757i	$-0.123993\pi$
$739$	50.2961	1.85017	0.925086	+	0.379757i	$0.123993\pi$
$740$	−60.3353	−2.21797
$741$	72.0504	2.64684
$742$	−2.77808	−0.101987
$743$	−21.9384	−0.804843	−0.402421	−	0.915455i	$-0.631831\pi$
$743$	−21.9384	−0.804843	−0.402421	+	0.915455i	$0.631831\pi$
$744$	−2.47668	−0.0907994
$745$	20.6818	0.757722
$746$	−59.1743	−2.16653
$747$	0.0180235	0.000659447 0
$748$	12.5279	0.458066
$749$	−11.7364	−0.428838
$750$	−11.7631	−0.429529
$751$	5.85045	0.213486	0.106743	−	0.994287i	$-0.465958\pi$
$751$	5.85045	0.213486	0.106743	+	0.994287i	$0.465958\pi$
$752$	19.0055	0.693060
$753$	8.70623	0.317273
$754$	84.8839	3.09129
$755$	12.7020	0.462273
$756$	8.48665	0.308657
$757$	3.60829	0.131146	0.0655728	−	0.997848i	$-0.479113\pi$
$757$	3.60829	0.131146	0.0655728	+	0.997848i	$0.479113\pi$
$758$	−31.0627	−1.12825
$759$	−27.9151	−1.01325
$760$	9.12992	0.331177
$761$	45.3381	1.64351	0.821753	−	0.569844i	$-0.192996\pi$
$761$	45.3381	1.64351	0.821753	+	0.569844i	$0.192996\pi$
$762$	28.5049	1.03262
$763$	−1.70139	−0.0615944
$764$	4.29636	0.155437
$765$	−0.0207938	−0.000751802 0
$766$	35.4522	1.28094
$767$	5.82270	0.210245
$768$	21.0672	0.760196
$769$	−6.14020	−0.221421	−0.110711	−	0.993853i	$-0.535313\pi$
$769$	−6.14020	−0.221421	−0.110711	+	0.993853i	$0.535313\pi$
$770$	25.6784	0.925384
$771$	7.48259	0.269479
$772$	17.2155	0.619599
$773$	−14.9765	−0.538669	−0.269334	−	0.963047i	$-0.586804\pi$
$773$	−14.9765	−0.538669	−0.269334	+	0.963047i	$0.586804\pi$
$774$	0.0542793	0.00195103
$775$	−12.9520	−0.465251
$776$	4.47279	0.160564
$777$	11.7563	0.421755
$778$	1.61534	0.0579126
$779$	−44.3836	−1.59021
$780$	66.5107	2.38146
$781$	20.1129	0.719695
$782$	−5.82393	−0.208263
$783$	−36.8790	−1.31795
$784$	22.8275	0.815267
$785$	−37.3704	−1.33381
$786$	24.5379	0.875237
$787$	−24.6835	−0.879873	−0.439936	−	0.898029i	$-0.644999\pi$
$787$	−24.6835	−0.879873	−0.439936	+	0.898029i	$0.644999\pi$
$788$	36.1604	1.28816
$789$	26.0297	0.926682
$790$	−93.6727	−3.33272
$791$	−13.3246	−0.473768
$792$	−0.0169689	−0.000602962 0
$793$	−39.2954	−1.39542
$794$	−5.68278	−0.201674
$795$	9.45920	0.335483
$796$	−32.2465	−1.14295
$797$	−39.1025	−1.38508	−0.692540	−	0.721379i	$-0.743509\pi$
$797$	−39.1025	−1.38508	−0.692540	+	0.721379i	$0.743509\pi$
$798$	−18.7908	−0.665188
$799$	5.37187	0.190043
$800$	−31.5832	−1.11664
$801$	0.0625207	0.00220906
$802$	−46.2821	−1.63428
$803$	−26.8069	−0.945997
$804$	−46.7404	−1.64841
$805$	−6.26520	−0.220819
$806$	−39.7635	−1.40061
$807$	30.0517	1.05787
$808$	0.987490	0.0347398
$809$	−5.69320	−0.200162	−0.100081	−	0.994979i	$-0.531910\pi$
$809$	−5.69320	−0.200162	−0.100081	+	0.994979i	$0.531910\pi$
$810$	−55.1853	−1.93902
$811$	54.7948	1.92410	0.962052	−	0.272866i	$-0.0879715\pi$
$811$	54.7948	1.92410	0.962052	+	0.272866i	$0.0879715\pi$
$812$	−11.6189	−0.407744
$813$	53.0377	1.86011
$814$	106.567	3.73516
$815$	21.4031	0.749717
$816$	6.13506	0.214770
$817$	27.0725	0.947148
$818$	−10.6840	−0.373556
$819$	−0.0300550	−0.00105021
$820$	−40.9711	−1.43077
$821$	11.2806	0.393694	0.196847	−	0.980434i	$-0.436930\pi$
$821$	11.2806	0.393694	0.196847	+	0.980434i	$0.436930\pi$
$822$	47.9159	1.67126
$823$	−14.6565	−0.510893	−0.255446	−	0.966823i	$-0.582222\pi$
$823$	−14.6565	−0.510893	−0.255446	+	0.966823i	$0.582222\pi$
$824$	−2.79566	−0.0973914
$825$	−38.2644	−1.33220
$826$	−1.51857	−0.0528377
$827$	−42.3751	−1.47353	−0.736763	−	0.676151i	$-0.763647\pi$
$827$	−42.3751	−1.47353	−0.736763	+	0.676151i	$0.763647\pi$
$828$	0.0437320	0.00151979
$829$	27.8117	0.965941	0.482970	−	0.875637i	$-0.339558\pi$
$829$	27.8117	0.965941	0.482970	+	0.875637i	$0.339558\pi$
$830$	15.8110	0.548808
$831$	−9.70610	−0.336701
$832$	−55.7612	−1.93317
$833$	6.45213	0.223553
$834$	1.11337	0.0385529
$835$	−7.35539	−0.254544
$836$	−89.3977	−3.09188
$837$	17.2758	0.597140
$838$	−35.3969	−1.22277
$839$	−26.0207	−0.898334	−0.449167	−	0.893448i	$-0.648279\pi$
$839$	−26.0207	−0.898334	−0.449167	+	0.893448i	$0.648279\pi$
$840$	−1.64218	−0.0566607
$841$	21.4903	0.741045
$842$	18.6949	0.644269
$843$	−13.8771	−0.477953
$844$	−34.0150	−1.17084
$845$	62.3310	2.14425
$846$	−0.0768561	−0.00264237
$847$	−15.6619	−0.538149
$848$	−6.47240	−0.222263
$849$	16.0542	0.550978
$850$	−7.98311	−0.273818
$851$	−26.0009	−0.891300
$852$	−13.5865	−0.465466
$853$	−42.6966	−1.46190	−0.730952	−	0.682429i	$-0.760923\pi$
$853$	−42.6966	−1.46190	−0.730952	+	0.682429i	$0.760923\pi$
$854$	10.2483	0.350690
$855$	0.148382	0.00507456
$856$	6.80359	0.232542
$857$	31.8211	1.08699	0.543494	−	0.839413i	$-0.317101\pi$
$857$	31.8211	1.08699	0.543494	+	0.839413i	$0.317101\pi$
$858$	−117.474	−4.01049
$859$	−47.4274	−1.61820	−0.809100	−	0.587671i	$-0.800045\pi$
$859$	−47.4274	−1.61820	−0.809100	+	0.587671i	$0.800045\pi$
$860$	24.9910	0.852186
$861$	7.98320	0.272067
$862$	−19.4535	−0.662590
$863$	−19.6478	−0.668820	−0.334410	−	0.942428i	$-0.608537\pi$
$863$	−19.6478	−0.668820	−0.334410	+	0.942428i	$0.608537\pi$
$864$	42.1267	1.43318
$865$	−22.5892	−0.768056
$866$	23.8635	0.810916
$867$	1.73406	0.0588919
$868$	5.44283	0.184742
$869$	86.8346	2.94566
$870$	75.3779	2.55555
$871$	−71.0441	−2.40724
$872$	0.986297	0.0334002
$873$	0.0726931	0.00246029
$874$	41.5589	1.40575
$875$	2.44737	0.0827360
$876$	18.1084	0.611827
$877$	−45.0618	−1.52163	−0.760815	−	0.648969i	$-0.775200\pi$
$877$	−45.0618	−1.52163	−0.760815	+	0.648969i	$0.775200\pi$
$878$	31.2065	1.05317
$879$	−23.1623	−0.781246
$880$	59.8257	2.01672
$881$	4.35680	0.146784	0.0733921	−	0.997303i	$-0.476618\pi$
$881$	4.35680	0.146784	0.0733921	+	0.997303i	$0.476618\pi$
$882$	−0.0923116	−0.00310829
$883$	48.3953	1.62863	0.814316	−	0.580422i	$-0.197112\pi$
$883$	48.3953	1.62863	0.814316	+	0.580422i	$0.197112\pi$
$884$	−12.8632	−0.432635
$885$	5.17063	0.173809
$886$	16.6710	0.560073
$887$	43.9537	1.47582	0.737910	−	0.674899i	$-0.235813\pi$
$887$	43.9537	1.47582	0.737910	+	0.674899i	$0.235813\pi$
$888$	−6.81515	−0.228701
$889$	−5.93055	−0.198904
$890$	54.8458	1.83843
$891$	51.1568	1.71382
$892$	−57.5303	−1.92626
$893$	−38.3330	−1.28277
$894$	24.6758	0.825283
$895$	−8.54743	−0.285709
$896$	2.52690	0.0844177
$897$	28.6621	0.957001
$898$	85.7291	2.86082
$899$	−23.6520	−0.788837
$900$	0.0599453	0.00199818
$901$	−1.82941	−0.0609465
$902$	72.3647	2.40948
$903$	−4.86949	−0.162047
$904$	7.72429	0.256906
$905$	72.4381	2.40792
$906$	15.1550	0.503490
$907$	44.2530	1.46940	0.734698	−	0.678395i	$-0.237324\pi$
$907$	44.2530	1.46940	0.734698	+	0.678395i	$0.237324\pi$
$908$	−55.9210	−1.85580
$909$	0.0160490	0.000532311 0
$910$	−26.3655	−0.874009
$911$	26.5176	0.878568	0.439284	−	0.898348i	$-0.355232\pi$
$911$	26.5176	0.878568	0.439284	+	0.898348i	$0.355232\pi$
$912$	−43.7791	−1.44967
$913$	−14.6568	−0.485069
$914$	21.2861	0.704083
$915$	−34.8948	−1.15359
$916$	53.7344	1.77543
$917$	−5.10520	−0.168588
$918$	10.6481	0.351440
$919$	−20.3911	−0.672639	−0.336319	−	0.941748i	$-0.609182\pi$
$919$	−20.3911	−0.672639	−0.336319	+	0.941748i	$0.609182\pi$
$920$	3.63194	0.119742
$921$	26.2669	0.865523
$922$	−56.2339	−1.85196
$923$	−20.6511	−0.679739
$924$	16.0798	0.528987
$925$	−35.6405	−1.17185
$926$	16.6718	0.547870
$927$	−0.0454359	−0.00149231
$928$	−57.6747	−1.89327
$929$	−7.09952	−0.232928	−0.116464	−	0.993195i	$-0.537156\pi$
$929$	−7.09952	−0.232928	−0.116464	+	0.993195i	$0.537156\pi$
$930$	−35.3105	−1.15788
$931$	−46.0416	−1.50895
$932$	−29.2730	−0.958870
$933$	−8.87926	−0.290694
$934$	−60.4958	−1.97948
$935$	16.9096	0.553003
$936$	0.0174229	0.000569487 0
$937$	32.6526	1.06671	0.533357	−	0.845890i	$-0.320930\pi$
$937$	32.6526	1.06671	0.533357	+	0.845890i	$0.320930\pi$
$938$	18.5284	0.604973
$939$	−41.4797	−1.35364
$940$	−35.3857	−1.15415
$941$	−58.9992	−1.92332	−0.961659	−	0.274248i	$-0.911571\pi$
$941$	−58.9992	−1.92332	−0.961659	+	0.274248i	$0.911571\pi$
$942$	−44.5873	−1.45273
$943$	−17.6561	−0.574961
$944$	−3.53797	−0.115151
$945$	11.4549	0.372628
$946$	−44.1401	−1.43512
$947$	−15.3650	−0.499295	−0.249647	−	0.968337i	$-0.580315\pi$
$947$	−15.3650	−0.499295	−0.249647	+	0.968337i	$0.580315\pi$
$948$	−58.6579	−1.90512
$949$	27.5243	0.893477
$950$	56.9664	1.84824
$951$	34.9492	1.13330
$952$	0.317599	0.0102934
$953$	46.9620	1.52125	0.760625	−	0.649192i	$-0.224893\pi$
$953$	46.9620	1.52125	0.760625	+	0.649192i	$0.224893\pi$
$954$	0.0261736	0.000847403 0
$955$	5.79903	0.187652
$956$	45.5409	1.47290
$957$	−69.8753	−2.25875
$958$	−4.58441	−0.148116
$959$	−9.96909	−0.321919
$960$	−49.5166	−1.59814
$961$	−19.9203	−0.642591
$962$	−109.418	−3.52779
$963$	0.110574	0.00356319
$964$	15.5570	0.501056
$965$	23.2367	0.748015
$966$	−7.47512	−0.240508
$967$	−57.0033	−1.83310	−0.916552	−	0.399917i	$-0.869039\pi$
$967$	−57.0033	−1.83310	−0.916552	+	0.399917i	$0.869039\pi$
$968$	9.07921	0.291817
$969$	−12.3741	−0.397512
$970$	63.7695	2.04751
$971$	−47.0024	−1.50838	−0.754189	−	0.656657i	$-0.771970\pi$
$971$	−47.0024	−1.50838	−0.754189	+	0.656657i	$0.771970\pi$
$972$	−0.160100	−0.00513520
$973$	−0.231641	−0.00742608
$974$	−12.3878	−0.396930
$975$	39.2884	1.25824
$976$	23.8766	0.764271
$977$	−16.9392	−0.541934	−0.270967	−	0.962589i	$-0.587343\pi$
$977$	−16.9392	−0.541934	−0.270967	+	0.962589i	$0.587343\pi$
$978$	25.5364	0.816564
$979$	−50.8421	−1.62492
$980$	−42.5016	−1.35766
$981$	0.0160296	0.000511785 0
$982$	29.9544	0.955884
$983$	−22.2199	−0.708704	−0.354352	−	0.935112i	$-0.615299\pi$
$983$	−22.2199	−0.708704	−0.354352	+	0.935112i	$0.615299\pi$
$984$	−4.62787	−0.147531
$985$	48.8076	1.55514
$986$	−14.5781	−0.464261
$987$	6.89490	0.219467
$988$	91.7900	2.92023
$989$	10.7696	0.342454
$990$	−0.241928	−0.00768898
$991$	3.95276	0.125564	0.0627819	−	0.998027i	$-0.480003\pi$
$991$	3.95276	0.125564	0.0627819	+	0.998027i	$0.480003\pi$
$992$	27.0175	0.857806
$993$	−33.6809	−1.06883
$994$	5.38583	0.170828
$995$	−43.5249	−1.37983
$996$	9.90086	0.313721
$997$	−47.4803	−1.50372	−0.751858	−	0.659325i	$-0.770842\pi$
$997$	−47.4803	−1.50372	−0.751858	+	0.659325i	$0.770842\pi$
$998$	−62.2559	−1.97068
$999$	47.5384	1.50405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.j.1.17	✓	22
3.2	odd	2		9027.2.a.s.1.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.j.1.17	✓	22	1.1	even	1	trivial
9027.2.a.s.1.6		22	3.2	odd	2

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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+2.05162 q^{2} +1.73406 q^{3} +2.20914 q^{4} +2.98180 q^{5} +3.55764 q^{6} -0.740180 q^{7} +0.429083 q^{8} +0.00697358 q^{9} +O(q^{10})\)	\(q+2.05162 q^{2} +1.73406 q^{3} +2.20914 q^{4} +2.98180 q^{5} +3.55764 q^{6} -0.740180 q^{7} +0.429083 q^{8} +0.00697358 q^{9} +6.11752 q^{10} -5.67094 q^{11} +3.83079 q^{12} +5.82270 q^{13} -1.51857 q^{14} +5.17063 q^{15} -3.53797 q^{16} -1.00000 q^{17} +0.0143071 q^{18} +7.13588 q^{19} +6.58722 q^{20} -1.28352 q^{21} -11.6346 q^{22} +2.83870 q^{23} +0.744057 q^{24} +3.89112 q^{25} +11.9460 q^{26} -5.19010 q^{27} -1.63516 q^{28} +7.10565 q^{29} +10.6082 q^{30} -3.32861 q^{31} -8.11674 q^{32} -9.83377 q^{33} -2.05162 q^{34} -2.20707 q^{35} +0.0154056 q^{36} -9.15944 q^{37} +14.6401 q^{38} +10.0969 q^{39} +1.27944 q^{40} -6.21978 q^{41} -2.63329 q^{42} +3.79386 q^{43} -12.5279 q^{44} +0.0207938 q^{45} +5.82393 q^{46} -5.37187 q^{47} -6.13506 q^{48} -6.45213 q^{49} +7.98311 q^{50} -1.73406 q^{51} +12.8632 q^{52} +1.82941 q^{53} -10.6481 q^{54} -16.9096 q^{55} -0.317599 q^{56} +12.3741 q^{57} +14.5781 q^{58} +1.00000 q^{59} +11.4227 q^{60} -6.74867 q^{61} -6.82905 q^{62} -0.00516170 q^{63} -9.57652 q^{64} +17.3621 q^{65} -20.1752 q^{66} -12.2012 q^{67} -2.20914 q^{68} +4.92248 q^{69} -4.52806 q^{70} -3.54665 q^{71} +0.00299225 q^{72} +4.72707 q^{73} -18.7917 q^{74} +6.74745 q^{75} +15.7642 q^{76} +4.19752 q^{77} +20.7150 q^{78} -15.3122 q^{79} -10.5495 q^{80} -9.02087 q^{81} -12.7606 q^{82} +2.58455 q^{83} -2.83548 q^{84} -2.98180 q^{85} +7.78356 q^{86} +12.3216 q^{87} -2.43331 q^{88} +8.96536 q^{89} +0.0426610 q^{90} -4.30984 q^{91} +6.27109 q^{92} -5.77202 q^{93} -11.0210 q^{94} +21.2777 q^{95} -14.0749 q^{96} +10.4241 q^{97} -13.2373 q^{98} -0.0395468 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * q^99

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