LMFDB - Embedded newform 1003.2.a.j.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.18647 q^{2} +3.36438 q^{3} +2.78064 q^{4} +4.25307 q^{5} -7.35611 q^{6} -0.847258 q^{7} -1.70683 q^{8} +8.31907 q^{9} +O(q^{10})$	\(q-2.18647 q^{2} +3.36438 q^{3} +2.78064 q^{4} +4.25307 q^{5} -7.35611 q^{6} -0.847258 q^{7} -1.70683 q^{8} +8.31907 q^{9} -9.29919 q^{10} -3.70617 q^{11} +9.35512 q^{12} +2.69004 q^{13} +1.85250 q^{14} +14.3090 q^{15} -1.82934 q^{16} -1.00000 q^{17} -18.1894 q^{18} -5.37106 q^{19} +11.8262 q^{20} -2.85050 q^{21} +8.10341 q^{22} -2.86595 q^{23} -5.74244 q^{24} +13.0886 q^{25} -5.88169 q^{26} +17.8954 q^{27} -2.35592 q^{28} -1.44610 q^{29} -31.2860 q^{30} +5.46960 q^{31} +7.41345 q^{32} -12.4690 q^{33} +2.18647 q^{34} -3.60345 q^{35} +23.1323 q^{36} -1.31524 q^{37} +11.7436 q^{38} +9.05033 q^{39} -7.25928 q^{40} +11.1806 q^{41} +6.23252 q^{42} -5.20661 q^{43} -10.3055 q^{44} +35.3816 q^{45} +6.26630 q^{46} -4.41001 q^{47} -6.15459 q^{48} -6.28215 q^{49} -28.6178 q^{50} -3.36438 q^{51} +7.48003 q^{52} -8.78689 q^{53} -39.1276 q^{54} -15.7626 q^{55} +1.44613 q^{56} -18.0703 q^{57} +3.16184 q^{58} +1.00000 q^{59} +39.7880 q^{60} -7.39515 q^{61} -11.9591 q^{62} -7.04840 q^{63} -12.5506 q^{64} +11.4409 q^{65} +27.2630 q^{66} -4.95527 q^{67} -2.78064 q^{68} -9.64215 q^{69} +7.87882 q^{70} +9.06504 q^{71} -14.1993 q^{72} -2.55251 q^{73} +2.87573 q^{74} +44.0351 q^{75} -14.9350 q^{76} +3.14008 q^{77} -19.7882 q^{78} -0.704041 q^{79} -7.78030 q^{80} +35.2497 q^{81} -24.4459 q^{82} -5.58588 q^{83} -7.92620 q^{84} -4.25307 q^{85} +11.3841 q^{86} -4.86522 q^{87} +6.32581 q^{88} -7.67627 q^{89} -77.3606 q^{90} -2.27916 q^{91} -7.96916 q^{92} +18.4018 q^{93} +9.64235 q^{94} -22.8435 q^{95} +24.9417 q^{96} +12.4899 q^{97} +13.7357 q^{98} -30.8319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.18647	−1.54607	−0.773033	−	0.634366i	$-0.781261\pi$
$2$	−2.18647	−1.54607	−0.773033	+	0.634366i	$0.781261\pi$
$3$	3.36438	1.94243	0.971213	−	0.238211i	$-0.0765610\pi$
$3$	3.36438	1.94243	0.971213	+	0.238211i	$0.0765610\pi$
$4$	2.78064	1.39032
$5$	4.25307	1.90203	0.951015	−	0.309144i	$-0.100042\pi$
$5$	4.25307	1.90203	0.951015	+	0.309144i	$0.100042\pi$
$6$	−7.35611	−3.00312
$7$	−0.847258	−0.320233	−0.160117	−	0.987098i	$-0.551187\pi$
$7$	−0.847258	−0.320233	−0.160117	+	0.987098i	$0.551187\pi$
$8$	−1.70683	−0.603457
$9$	8.31907	2.77302
$10$	−9.29919	−2.94066
$11$	−3.70617	−1.11745	−0.558726	−	0.829352i	$-0.688710\pi$
$11$	−3.70617	−1.11745	−0.558726	+	0.829352i	$0.688710\pi$
$12$	9.35512	2.70059
$13$	2.69004	0.746084	0.373042	−	0.927815i	$-0.378315\pi$
$13$	2.69004	0.746084	0.373042	+	0.927815i	$0.378315\pi$
$14$	1.85250	0.495102
$15$	14.3090	3.69456
$16$	−1.82934	−0.457334
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−18.1894	−4.28727
$19$	−5.37106	−1.23221	−0.616103	−	0.787666i	$-0.711289\pi$
$19$	−5.37106	−1.23221	−0.616103	+	0.787666i	$0.711289\pi$
$20$	11.8262	2.64443
$21$	−2.85050	−0.622030
$22$	8.10341	1.72765
$23$	−2.86595	−0.597592	−0.298796	−	0.954317i	$-0.596585\pi$
$23$	−2.86595	−0.597592	−0.298796	+	0.954317i	$0.596585\pi$
$24$	−5.74244	−1.17217
$25$	13.0886	2.61772
$26$	−5.88169	−1.15349
$27$	17.8954	3.44397
$28$	−2.35592	−0.445226
$29$	−1.44610	−0.268534	−0.134267	−	0.990945i	$-0.542868\pi$
$29$	−1.44610	−0.268534	−0.134267	+	0.990945i	$0.542868\pi$
$30$	−31.2860	−5.71202
$31$	5.46960	0.982370	0.491185	−	0.871055i	$-0.336564\pi$
$31$	5.46960	0.982370	0.491185	+	0.871055i	$0.336564\pi$
$32$	7.41345	1.31053
$33$	−12.4690	−2.17057
$34$	2.18647	0.374976
$35$	−3.60345	−0.609094
$36$	23.1323	3.85538
$37$	−1.31524	−0.216224	−0.108112	−	0.994139i	$-0.534481\pi$
$37$	−1.31524	−0.216224	−0.108112	+	0.994139i	$0.534481\pi$
$38$	11.7436	1.90507
$39$	9.05033	1.44921
$40$	−7.25928	−1.14779
$41$	11.1806	1.74611	0.873055	−	0.487622i	$-0.162136\pi$
$41$	11.1806	1.74611	0.873055	+	0.487622i	$0.162136\pi$
$42$	6.23252	0.961699
$43$	−5.20661	−0.794000	−0.397000	−	0.917819i	$-0.629949\pi$
$43$	−5.20661	−0.794000	−0.397000	+	0.917819i	$0.629949\pi$
$44$	−10.3055	−1.55361
$45$	35.3816	5.27437
$46$	6.26630	0.923916
$47$	−4.41001	−0.643267	−0.321633	−	0.946864i	$-0.604232\pi$
$47$	−4.41001	−0.643267	−0.321633	+	0.946864i	$0.604232\pi$
$48$	−6.15459	−0.888339
$49$	−6.28215	−0.897451
$50$	−28.6178	−4.04717
$51$	−3.36438	−0.471108
$52$	7.48003	1.03729
$53$	−8.78689	−1.20697	−0.603486	−	0.797374i	$-0.706222\pi$
$53$	−8.78689	−1.20697	−0.603486	+	0.797374i	$0.706222\pi$
$54$	−39.1276	−5.32460
$55$	−15.7626	−2.12543
$56$	1.44613	0.193247
$57$	−18.0703	−2.39347
$58$	3.16184	0.415170
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	39.7880	5.13661
$61$	−7.39515	−0.946851	−0.473426	−	0.880834i	$-0.656983\pi$
$61$	−7.39515	−0.946851	−0.473426	+	0.880834i	$0.656983\pi$
$62$	−11.9591	−1.51881
$63$	−7.04840	−0.888014
$64$	−12.5506	−1.56882
$65$	11.4409	1.41907
$66$	27.2630	3.35584
$67$	−4.95527	−0.605383	−0.302691	−	0.953089i	$-0.597885\pi$
$67$	−4.95527	−0.605383	−0.302691	+	0.953089i	$0.597885\pi$
$68$	−2.78064	−0.337202
$69$	−9.64215	−1.16078
$70$	7.87882	0.941699
$71$	9.06504	1.07582	0.537911	−	0.843002i	$-0.319214\pi$
$71$	9.06504	1.07582	0.537911	+	0.843002i	$0.319214\pi$
$72$	−14.1993	−1.67340
$73$	−2.55251	−0.298749	−0.149375	−	0.988781i	$-0.547726\pi$
$73$	−2.55251	−0.298749	−0.149375	+	0.988781i	$0.547726\pi$
$74$	2.87573	0.334297
$75$	44.0351	5.08473
$76$	−14.9350	−1.71316
$77$	3.14008	0.357845
$78$	−19.7882	−2.24058
$79$	−0.704041	−0.0792108	−0.0396054	−	0.999215i	$-0.512610\pi$
$79$	−0.704041	−0.0792108	−0.0396054	+	0.999215i	$0.512610\pi$
$80$	−7.78030	−0.869864
$81$	35.2497	3.91663
$82$	−24.4459	−2.69960
$83$	−5.58588	−0.613130	−0.306565	−	0.951850i	$-0.599180\pi$
$83$	−5.58588	−0.613130	−0.306565	+	0.951850i	$0.599180\pi$
$84$	−7.92620	−0.864819
$85$	−4.25307	−0.461310
$86$	11.3841	1.22758
$87$	−4.86522	−0.521607
$88$	6.32581	0.674334
$89$	−7.67627	−0.813683	−0.406841	−	0.913499i	$-0.633370\pi$
$89$	−7.67627	−0.813683	−0.406841	+	0.913499i	$0.633370\pi$
$90$	−77.3606	−8.15453
$91$	−2.27916	−0.238921
$92$	−7.96916	−0.830843
$93$	18.4018	1.90818
$94$	9.64235	0.994532
$95$	−22.8435	−2.34369
$96$	24.9417	2.54560
$97$	12.4899	1.26816	0.634079	−	0.773268i	$-0.281379\pi$
$97$	12.4899	1.26816	0.634079	+	0.773268i	$0.281379\pi$
$98$	13.7357	1.38752
$99$	−30.8319	−3.09872
$100$	36.3946	3.63946
$101$	−1.70861	−0.170013	−0.0850064	−	0.996380i	$-0.527091\pi$
$101$	−1.70861	−0.170013	−0.0850064	+	0.996380i	$0.527091\pi$
$102$	7.35611	0.728363
$103$	−17.2004	−1.69481	−0.847405	−	0.530947i	$-0.821837\pi$
$103$	−17.2004	−1.69481	−0.847405	+	0.530947i	$0.821837\pi$
$104$	−4.59145	−0.450229
$105$	−12.1234	−1.18312
$106$	19.2122	1.86606
$107$	−4.96470	−0.479956	−0.239978	−	0.970778i	$-0.577140\pi$
$107$	−4.96470	−0.479956	−0.239978	+	0.970778i	$0.577140\pi$
$108$	49.7605	4.78821
$109$	−6.19752	−0.593615	−0.296808	−	0.954937i	$-0.595922\pi$
$109$	−6.19752	−0.593615	−0.296808	+	0.954937i	$0.595922\pi$
$110$	34.4644	3.28605
$111$	−4.42497	−0.420000
$112$	1.54992	0.146454
$113$	16.0150	1.50657	0.753283	−	0.657696i	$-0.228469\pi$
$113$	16.0150	1.50657	0.753283	+	0.657696i	$0.228469\pi$
$114$	39.5101	3.70046
$115$	−12.1891	−1.13664
$116$	−4.02107	−0.373347
$117$	22.3786	2.06891
$118$	−2.18647	−0.201281
$119$	0.847258	0.0776680
$120$	−24.4230	−2.22950
$121$	2.73569	0.248699
$122$	16.1692	1.46389
$123$	37.6157	3.39169
$124$	15.2090	1.36581
$125$	34.4014	3.07696
$126$	15.4111	1.37293
$127$	−7.70163	−0.683409	−0.341705	−	0.939807i	$-0.611004\pi$
$127$	−7.70163	−0.683409	−0.341705	+	0.939807i	$0.611004\pi$
$128$	12.6145	1.11498
$129$	−17.5170	−1.54229
$130$	−25.0152	−2.19398
$131$	8.04645	0.703021	0.351511	−	0.936184i	$-0.385668\pi$
$131$	8.04645	0.703021	0.351511	+	0.936184i	$0.385668\pi$
$132$	−34.6716	−3.01778
$133$	4.55067	0.394593
$134$	10.8345	0.935961
$135$	76.1103	6.55053
$136$	1.70683	0.146360
$137$	3.52261	0.300957	0.150478	−	0.988613i	$-0.451919\pi$
$137$	3.52261	0.300957	0.150478	+	0.988613i	$0.451919\pi$
$138$	21.0822	1.79464
$139$	−12.5177	−1.06174	−0.530868	−	0.847454i	$-0.678134\pi$
$139$	−12.5177	−1.06174	−0.530868	+	0.847454i	$0.678134\pi$
$140$	−10.0199	−0.846834
$141$	−14.8370	−1.24950
$142$	−19.8204	−1.66329
$143$	−9.96975	−0.833713
$144$	−15.2184	−1.26820
$145$	−6.15035	−0.510759
$146$	5.58099	0.461886
$147$	−21.1356	−1.74323
$148$	−3.65721	−0.300621
$149$	16.6921	1.36747	0.683733	−	0.729732i	$-0.260355\pi$
$149$	16.6921	1.36747	0.683733	+	0.729732i	$0.260355\pi$
$150$	−96.2812	−7.86133
$151$	11.4952	0.935466	0.467733	−	0.883870i	$-0.345071\pi$
$151$	11.4952	0.935466	0.467733	+	0.883870i	$0.345071\pi$
$152$	9.16750	0.743582
$153$	−8.31907	−0.672557
$154$	−6.86568	−0.553252
$155$	23.2626	1.86850
$156$	25.1657	2.01487
$157$	15.3969	1.22880	0.614402	−	0.788993i	$-0.289397\pi$
$157$	15.3969	1.22880	0.614402	+	0.788993i	$0.289397\pi$
$158$	1.53936	0.122465
$159$	−29.5624	−2.34445
$160$	31.5299	2.49266
$161$	2.42820	0.191369
$162$	−77.0722	−6.05536
$163$	7.99260	0.626029	0.313014	−	0.949748i	$-0.398661\pi$
$163$	7.99260	0.626029	0.313014	+	0.949748i	$0.398661\pi$
$164$	31.0891	2.42765
$165$	−53.0314	−4.12849
$166$	12.2133	0.947939
$167$	22.2532	1.72200	0.861001	−	0.508604i	$-0.169838\pi$
$167$	22.2532	1.72200	0.861001	+	0.508604i	$0.169838\pi$
$168$	4.86533	0.375368
$169$	−5.76367	−0.443359
$170$	9.29919	0.713216
$171$	−44.6822	−3.41693
$172$	−14.4777	−1.10391
$173$	9.37454	0.712733	0.356367	−	0.934346i	$-0.384015\pi$
$173$	9.37454	0.712733	0.356367	+	0.934346i	$0.384015\pi$
$174$	10.6376	0.806438
$175$	−11.0894	−0.838282
$176$	6.77983	0.511049
$177$	3.36438	0.252882
$178$	16.7839	1.25801
$179$	2.02393	0.151276	0.0756380	−	0.997135i	$-0.475901\pi$
$179$	2.02393	0.151276	0.0756380	+	0.997135i	$0.475901\pi$
$180$	98.3833	7.33305
$181$	−3.58049	−0.266135	−0.133068	−	0.991107i	$-0.542483\pi$
$181$	−3.58049	−0.266135	−0.133068	+	0.991107i	$0.542483\pi$
$182$	4.98331	0.369387
$183$	−24.8801	−1.83919
$184$	4.89170	0.360621
$185$	−5.59381	−0.411265
$186$	−40.2350	−2.95017
$187$	3.70617	0.271022
$188$	−12.2626	−0.894345
$189$	−15.1620	−1.10287
$190$	49.9465	3.62350
$191$	−10.6224	−0.768612	−0.384306	−	0.923206i	$-0.625559\pi$
$191$	−10.6224	−0.768612	−0.384306	+	0.923206i	$0.625559\pi$
$192$	−42.2250	−3.04732
$193$	−21.7300	−1.56416	−0.782079	−	0.623179i	$-0.785841\pi$
$193$	−21.7300	−1.56416	−0.782079	+	0.623179i	$0.785841\pi$
$194$	−27.3088	−1.96066
$195$	38.4917	2.75645
$196$	−17.4684	−1.24774
$197$	−10.3620	−0.738259	−0.369129	−	0.929378i	$-0.620344\pi$
$197$	−10.3620	−0.738259	−0.369129	+	0.929378i	$0.620344\pi$
$198$	67.4128	4.79082
$199$	−24.6196	−1.74523	−0.872617	−	0.488405i	$-0.837579\pi$
$199$	−24.6196	−1.74523	−0.872617	+	0.488405i	$0.837579\pi$
$200$	−22.3401	−1.57968
$201$	−16.6714	−1.17591
$202$	3.73581	0.262851
$203$	1.22522	0.0859934
$204$	−9.35512	−0.654989
$205$	47.5517	3.32115
$206$	37.6082	2.62029
$207$	−23.8420	−1.65714
$208$	−4.92100	−0.341210
$209$	19.9060	1.37693
$210$	26.5074	1.82918
$211$	−11.0119	−0.758090	−0.379045	−	0.925378i	$-0.623747\pi$
$211$	−11.0119	−0.758090	−0.379045	+	0.925378i	$0.623747\pi$
$212$	−24.4331	−1.67807
$213$	30.4983	2.08971
$214$	10.8552	0.742043
$215$	−22.1441	−1.51021
$216$	−30.5444	−2.07828
$217$	−4.63417	−0.314588
$218$	13.5507	0.917768
$219$	−8.58763	−0.580298
$220$	−43.8300	−2.95502
$221$	−2.69004	−0.180952
$222$	9.67506	0.649347
$223$	−10.4205	−0.697808	−0.348904	−	0.937158i	$-0.613446\pi$
$223$	−10.4205	−0.697808	−0.348904	+	0.937158i	$0.613446\pi$
$224$	−6.28111	−0.419674
$225$	108.885	7.25900
$226$	−35.0163	−2.32925
$227$	24.2418	1.60898	0.804491	−	0.593965i	$-0.202438\pi$
$227$	24.2418	1.60898	0.804491	+	0.593965i	$0.202438\pi$
$228$	−50.2469	−3.32768
$229$	−5.91911	−0.391146	−0.195573	−	0.980689i	$-0.562657\pi$
$229$	−5.91911	−0.391146	−0.195573	+	0.980689i	$0.562657\pi$
$230$	26.6510	1.75732
$231$	10.5644	0.695089
$232$	2.46825	0.162048
$233$	9.85741	0.645781	0.322890	−	0.946436i	$-0.395346\pi$
$233$	9.85741	0.645781	0.322890	+	0.946436i	$0.395346\pi$
$234$	−48.9302	−3.19866
$235$	−18.7561	−1.22351
$236$	2.78064	0.181004
$237$	−2.36866	−0.153861
$238$	−1.85250	−0.120080
$239$	−3.75320	−0.242774	−0.121387	−	0.992605i	$-0.538734\pi$
$239$	−3.75320	−0.242774	−0.121387	+	0.992605i	$0.538734\pi$
$240$	−26.1759	−1.68965
$241$	−6.17826	−0.397977	−0.198988	−	0.980002i	$-0.563766\pi$
$241$	−6.17826	−0.397977	−0.198988	+	0.980002i	$0.563766\pi$
$242$	−5.98148	−0.384504
$243$	64.9072	4.16380
$244$	−20.5632	−1.31642
$245$	−26.7184	−1.70698
$246$	−82.2454	−5.24377
$247$	−14.4484	−0.919328
$248$	−9.33570	−0.592818
$249$	−18.7930	−1.19096
$250$	−75.2175	−4.75717
$251$	3.04942	0.192478	0.0962388	−	0.995358i	$-0.469319\pi$
$251$	3.04942	0.192478	0.0962388	+	0.995358i	$0.469319\pi$
$252$	−19.5990	−1.23462
$253$	10.6217	0.667780
$254$	16.8394	1.05660
$255$	−14.3090	−0.896061
$256$	−2.48008	−0.155005
$257$	−15.4784	−0.965514	−0.482757	−	0.875754i	$-0.660365\pi$
$257$	−15.4784	−0.965514	−0.482757	+	0.875754i	$0.660365\pi$
$258$	38.3004	2.38448
$259$	1.11435	0.0692423
$260$	31.8131	1.97296
$261$	−12.0302	−0.744649
$262$	−17.5933	−1.08692
$263$	−30.7841	−1.89823	−0.949114	−	0.314934i	$-0.898018\pi$
$263$	−30.7841	−1.89823	−0.949114	+	0.314934i	$0.898018\pi$
$264$	21.2824	1.30984
$265$	−37.3713	−2.29570
$266$	−9.94989	−0.610067
$267$	−25.8259	−1.58052
$268$	−13.7788	−0.841674
$269$	14.4172	0.879031	0.439516	−	0.898235i	$-0.355150\pi$
$269$	14.4172	0.879031	0.439516	+	0.898235i	$0.355150\pi$
$270$	−166.413	−10.1275
$271$	8.63776	0.524707	0.262353	−	0.964972i	$-0.415501\pi$
$271$	8.63776	0.524707	0.262353	+	0.964972i	$0.415501\pi$
$272$	1.82934	0.110920
$273$	−7.66797	−0.464086
$274$	−7.70206	−0.465299
$275$	−48.5086	−2.92518
$276$	−26.8113	−1.61385
$277$	1.17221	0.0704311	0.0352155	−	0.999380i	$-0.488788\pi$
$277$	1.17221	0.0704311	0.0352155	+	0.999380i	$0.488788\pi$
$278$	27.3695	1.64151
$279$	45.5020	2.72413
$280$	6.15048	0.367562
$281$	−7.44411	−0.444079	−0.222039	−	0.975038i	$-0.571271\pi$
$281$	−7.44411	−0.444079	−0.222039	+	0.975038i	$0.571271\pi$
$282$	32.4405	1.93181
$283$	11.1558	0.663144	0.331572	−	0.943430i	$-0.392421\pi$
$283$	11.1558	0.663144	0.331572	+	0.943430i	$0.392421\pi$
$284$	25.2066	1.49573
$285$	−76.8542	−4.55245
$286$	21.7985	1.28897
$287$	−9.47282	−0.559163
$288$	61.6730	3.63412
$289$	1.00000	0.0588235
$290$	13.4475	0.789667
$291$	42.0209	2.46331
$292$	−7.09761	−0.415356
$293$	24.4344	1.42747	0.713737	−	0.700414i	$-0.247001\pi$
$293$	24.4344	1.42747	0.713737	+	0.700414i	$0.247001\pi$
$294$	46.2122	2.69515
$295$	4.25307	0.247623
$296$	2.24490	0.130482
$297$	−66.3233	−3.84847
$298$	−36.4966	−2.11419
$299$	−7.70953	−0.445853
$300$	122.445	7.06939
$301$	4.41134	0.254265
$302$	−25.1339	−1.44629
$303$	−5.74841	−0.330238
$304$	9.82548	0.563530
$305$	−31.4521	−1.80094
$306$	18.1894	1.03982
$307$	−1.66650	−0.0951122	−0.0475561	−	0.998869i	$-0.515143\pi$
$307$	−1.66650	−0.0951122	−0.0475561	+	0.998869i	$0.515143\pi$
$308$	8.73142	0.497519
$309$	−57.8689	−3.29205
$310$	−50.8629	−2.88882
$311$	24.2977	1.37780	0.688899	−	0.724857i	$-0.258094\pi$
$311$	24.2977	1.37780	0.688899	+	0.724857i	$0.258094\pi$
$312$	−15.4474	−0.874537
$313$	−25.7350	−1.45463	−0.727313	−	0.686306i	$-0.759231\pi$
$313$	−25.7350	−1.45463	−0.727313	+	0.686306i	$0.759231\pi$
$314$	−33.6648	−1.89981
$315$	−29.9773	−1.68903
$316$	−1.95768	−0.110128
$317$	21.5355	1.20955	0.604776	−	0.796396i	$-0.293263\pi$
$317$	21.5355	1.20955	0.604776	+	0.796396i	$0.293263\pi$
$318$	64.6373	3.62468
$319$	5.35948	0.300073
$320$	−53.3785	−2.98395
$321$	−16.7032	−0.932280
$322$	−5.30918	−0.295869
$323$	5.37106	0.298854
$324$	98.0165	5.44536
$325$	35.2089	1.95304
$326$	−17.4756	−0.967882
$327$	−20.8508	−1.15305
$328$	−19.0833	−1.05370
$329$	3.73642	0.205995
$330$	115.951	6.38291
$331$	27.5358	1.51350	0.756751	−	0.653703i	$-0.226785\pi$
$331$	27.5358	1.51350	0.756751	+	0.653703i	$0.226785\pi$
$332$	−15.5323	−0.852445
$333$	−10.9416	−0.599595
$334$	−48.6558	−2.66233
$335$	−21.0751	−1.15146
$336$	5.21453	0.284476
$337$	22.6662	1.23471	0.617354	−	0.786686i	$-0.288205\pi$
$337$	22.6662	1.23471	0.617354	+	0.786686i	$0.288205\pi$
$338$	12.6021	0.685462
$339$	53.8807	2.92640
$340$	−11.8262	−0.641368
$341$	−20.2713	−1.09775
$342$	97.6961	5.28280
$343$	11.2534	0.607627
$344$	8.88681	0.479145
$345$	−41.0087	−2.20784
$346$	−20.4971	−1.10193
$347$	−17.2111	−0.923939	−0.461970	−	0.886896i	$-0.652857\pi$
$347$	−17.2111	−0.923939	−0.461970	+	0.886896i	$0.652857\pi$
$348$	−13.5284	−0.725199
$349$	−6.37279	−0.341128	−0.170564	−	0.985347i	$-0.554559\pi$
$349$	−6.37279	−0.341128	−0.170564	+	0.985347i	$0.554559\pi$
$350$	24.2467	1.29604
$351$	48.1393	2.56949
$352$	−27.4755	−1.46445
$353$	−36.3275	−1.93352	−0.966758	−	0.255694i	$-0.917696\pi$
$353$	−36.3275	−1.93352	−0.966758	+	0.255694i	$0.917696\pi$
$354$	−7.35611	−0.390973
$355$	38.5542	2.04625
$356$	−21.3449	−1.13128
$357$	2.85050	0.150864
$358$	−4.42526	−0.233882
$359$	−2.75055	−0.145168	−0.0725841	−	0.997362i	$-0.523125\pi$
$359$	−2.75055	−0.145168	−0.0725841	+	0.997362i	$0.523125\pi$
$360$	−60.3904	−3.18286
$361$	9.84826	0.518329
$362$	7.82861	0.411463
$363$	9.20389	0.483079
$364$	−6.33751	−0.332176
$365$	−10.8560	−0.568230
$366$	54.3995	2.84351
$367$	31.2868	1.63316	0.816578	−	0.577235i	$-0.195868\pi$
$367$	31.2868	1.63316	0.816578	+	0.577235i	$0.195868\pi$
$368$	5.24279	0.273299
$369$	93.0118	4.84200
$370$	12.2307	0.635843
$371$	7.44476	0.386513
$372$	51.1688	2.65298
$373$	16.2184	0.839756	0.419878	−	0.907580i	$-0.362073\pi$
$373$	16.2184	0.839756	0.419878	+	0.907580i	$0.362073\pi$
$374$	−8.10341	−0.419018
$375$	115.739	5.97676
$376$	7.52716	0.388183
$377$	−3.89006	−0.200348
$378$	33.1512	1.70511
$379$	2.13736	0.109789	0.0548944	−	0.998492i	$-0.482518\pi$
$379$	2.13736	0.109789	0.0548944	+	0.998492i	$0.482518\pi$
$380$	−63.5194	−3.25848
$381$	−25.9112	−1.32747
$382$	23.2256	1.18832
$383$	−4.74536	−0.242477	−0.121238	−	0.992623i	$-0.538687\pi$
$383$	−4.74536	−0.242477	−0.121238	+	0.992623i	$0.538687\pi$
$384$	42.4401	2.16576
$385$	13.3550	0.680633
$386$	47.5119	2.41829
$387$	−43.3141	−2.20178
$388$	34.7299	1.76314
$389$	−19.5885	−0.993175	−0.496588	−	0.867987i	$-0.665414\pi$
$389$	−19.5885	−0.993175	−0.496588	+	0.867987i	$0.665414\pi$
$390$	−84.1608	−4.26165
$391$	2.86595	0.144937
$392$	10.7226	0.541572
$393$	27.0713	1.36557
$394$	22.6561	1.14140
$395$	−2.99434	−0.150661
$396$	−85.7322	−4.30820
$397$	−1.13063	−0.0567449	−0.0283724	−	0.999597i	$-0.509032\pi$
$397$	−1.13063	−0.0567449	−0.0283724	+	0.999597i	$0.509032\pi$
$398$	53.8298	2.69825
$399$	15.3102	0.766469
$400$	−23.9435	−1.19717
$401$	−18.9809	−0.947860	−0.473930	−	0.880562i	$-0.657165\pi$
$401$	−18.9809	−0.947860	−0.473930	+	0.880562i	$0.657165\pi$
$402$	36.4515	1.81804
$403$	14.7135	0.732930
$404$	−4.75102	−0.236372
$405$	149.919	7.44955
$406$	−2.67890	−0.132951
$407$	4.87451	0.241620
$408$	5.74244	0.284293
$409$	−19.4609	−0.962280	−0.481140	−	0.876644i	$-0.659777\pi$
$409$	−19.4609	−0.962280	−0.481140	+	0.876644i	$0.659777\pi$
$410$	−103.970	−5.13472
$411$	11.8514	0.584586
$412$	−47.8282	−2.35633
$413$	−0.847258	−0.0416908
$414$	52.1298	2.56204
$415$	−23.7571	−1.16619
$416$	19.9425	0.977762
$417$	−42.1143	−2.06235
$418$	−43.5239	−2.12882
$419$	−16.6670	−0.814236	−0.407118	−	0.913376i	$-0.633466\pi$
$419$	−16.6670	−0.814236	−0.407118	+	0.913376i	$0.633466\pi$
$420$	−33.7107	−1.64491
$421$	−17.2661	−0.841497	−0.420748	−	0.907177i	$-0.638232\pi$
$421$	−17.2661	−0.841497	−0.420748	+	0.907177i	$0.638232\pi$
$422$	24.0771	1.17206
$423$	−36.6872	−1.78379
$424$	14.9978	0.728355
$425$	−13.0886	−0.634891
$426$	−66.6834	−3.23082
$427$	6.26560	0.303213
$428$	−13.8050	−0.667291
$429$	−33.5421	−1.61943
$430$	48.4173	2.33489
$431$	37.7126	1.81655	0.908276	−	0.418372i	$-0.137399\pi$
$431$	37.7126	1.81655	0.908276	+	0.418372i	$0.137399\pi$
$432$	−32.7367	−1.57504
$433$	5.38917	0.258987	0.129493	−	0.991580i	$-0.458665\pi$
$433$	5.38917	0.258987	0.129493	+	0.991580i	$0.458665\pi$
$434$	10.1324	0.486373
$435$	−20.6921	−0.992112
$436$	−17.2331	−0.825314
$437$	15.3932	0.736356
$438$	18.7766	0.897179
$439$	14.0272	0.669484	0.334742	−	0.942310i	$-0.391351\pi$
$439$	14.0272	0.669484	0.334742	+	0.942310i	$0.391351\pi$
$440$	26.9041	1.28260
$441$	−52.2617	−2.48865
$442$	5.88169	0.279763
$443$	−21.9992	−1.04522	−0.522608	−	0.852573i	$-0.675041\pi$
$443$	−21.9992	−1.04522	−0.522608	+	0.852573i	$0.675041\pi$
$444$	−12.3042	−0.583933
$445$	−32.6477	−1.54765
$446$	22.7841	1.07886
$447$	56.1585	2.65620
$448$	10.6336	0.502390
$449$	−24.9884	−1.17928	−0.589638	−	0.807667i	$-0.700730\pi$
$449$	−24.9884	−1.17928	−0.589638	+	0.807667i	$0.700730\pi$
$450$	−238.073	−11.2229
$451$	−41.4370	−1.95119
$452$	44.5319	2.09461
$453$	38.6742	1.81707
$454$	−53.0038	−2.48759
$455$	−9.69343	−0.454435
$456$	30.8430	1.44435
$457$	17.4660	0.817027	0.408513	−	0.912752i	$-0.366047\pi$
$457$	17.4660	0.817027	0.408513	+	0.912752i	$0.366047\pi$
$458$	12.9419	0.604737
$459$	−17.8954	−0.835284
$460$	−33.8934	−1.58029
$461$	29.4799	1.37302	0.686509	−	0.727122i	$-0.259142\pi$
$461$	29.4799	1.37302	0.686509	+	0.727122i	$0.259142\pi$
$462$	−23.0988	−1.07465
$463$	2.31581	0.107625	0.0538125	−	0.998551i	$-0.482863\pi$
$463$	2.31581	0.107625	0.0538125	+	0.998551i	$0.482863\pi$
$464$	2.64540	0.122810
$465$	78.2643	3.62942
$466$	−21.5529	−0.998419
$467$	34.0908	1.57753	0.788766	−	0.614693i	$-0.210720\pi$
$467$	34.0908	1.57753	0.788766	+	0.614693i	$0.210720\pi$
$468$	62.2268	2.87644
$469$	4.19839	0.193864
$470$	41.0096	1.89163
$471$	51.8010	2.38686
$472$	−1.70683	−0.0785634
$473$	19.2966	0.887257
$474$	5.17900	0.237880
$475$	−70.2996	−3.22557
$476$	2.35592	0.107983
$477$	−73.0987	−3.34696
$478$	8.20625	0.375345
$479$	−13.8840	−0.634377	−0.317189	−	0.948362i	$-0.602739\pi$
$479$	−13.8840	−0.634377	−0.317189	+	0.948362i	$0.602739\pi$
$480$	106.079	4.84181
$481$	−3.53805	−0.161321
$482$	13.5086	0.615298
$483$	8.16939	0.371720
$484$	7.60694	0.345770
$485$	53.1205	2.41208
$486$	−141.917	−6.43751
$487$	31.7057	1.43672	0.718360	−	0.695671i	$-0.244893\pi$
$487$	31.7057	1.43672	0.718360	+	0.695671i	$0.244893\pi$
$488$	12.6223	0.571384
$489$	26.8902	1.21602
$490$	58.4190	2.63910
$491$	−18.8253	−0.849572	−0.424786	−	0.905294i	$-0.639651\pi$
$491$	−18.8253	−0.849572	−0.424786	+	0.905294i	$0.639651\pi$
$492$	104.595	4.71553
$493$	1.44610	0.0651289
$494$	31.5909	1.42134
$495$	−131.130	−5.89386
$496$	−10.0058	−0.449272
$497$	−7.68043	−0.344514
$498$	41.0903	1.84130
$499$	−21.9631	−0.983202	−0.491601	−	0.870821i	$-0.663588\pi$
$499$	−21.9631	−0.983202	−0.491601	+	0.870821i	$0.663588\pi$
$500$	95.6578	4.27795
$501$	74.8682	3.34486
$502$	−6.66745	−0.297583
$503$	−0.668140	−0.0297909	−0.0148954	−	0.999889i	$-0.504742\pi$
$503$	−0.668140	−0.0297909	−0.0148954	+	0.999889i	$0.504742\pi$
$504$	12.0304	0.535878
$505$	−7.26683	−0.323370
$506$	−23.2240	−1.03243
$507$	−19.3912	−0.861193
$508$	−21.4154	−0.950156
$509$	7.02289	0.311284	0.155642	−	0.987814i	$-0.450255\pi$
$509$	7.02289	0.311284	0.155642	+	0.987814i	$0.450255\pi$
$510$	31.2860	1.38537
$511$	2.16264	0.0956695
$512$	−19.8065	−0.875330
$513$	−96.1171	−4.24367
$514$	33.8429	1.49275
$515$	−73.1547	−3.22358
$516$	−48.7085	−2.14427
$517$	16.3443	0.718819
$518$	−2.43649	−0.107053
$519$	31.5395	1.38443
$520$	−19.5278	−0.856350
$521$	−4.68201	−0.205122	−0.102561	−	0.994727i	$-0.532704\pi$
$521$	−4.68201	−0.205122	−0.102561	+	0.994727i	$0.532704\pi$
$522$	26.3036	1.15128
$523$	−9.54143	−0.417217	−0.208609	−	0.977999i	$-0.566894\pi$
$523$	−9.54143	−0.417217	−0.208609	+	0.977999i	$0.566894\pi$
$524$	22.3742	0.977423
$525$	−37.3091	−1.62830
$526$	67.3083	2.93478
$527$	−5.46960	−0.238260
$528$	22.8099	0.992676
$529$	−14.7863	−0.642884
$530$	81.7110	3.54930
$531$	8.31907	0.361017
$532$	12.6538	0.548610
$533$	30.0762	1.30274
$534$	56.4675	2.44359
$535$	−21.1152	−0.912891
$536$	8.45782	0.365322
$537$	6.80929	0.293842
$538$	−31.5227	−1.35904
$539$	23.2827	1.00286
$540$	211.635	9.10732
$541$	−32.0890	−1.37961	−0.689806	−	0.723994i	$-0.742304\pi$
$541$	−32.0890	−1.37961	−0.689806	+	0.723994i	$0.742304\pi$
$542$	−18.8862	−0.811231
$543$	−12.0461	−0.516949
$544$	−7.41345	−0.317849
$545$	−26.3585	−1.12907
$546$	16.7657	0.717508
$547$	17.1693	0.734104	0.367052	−	0.930200i	$-0.380367\pi$
$547$	17.1693	0.734104	0.367052	+	0.930200i	$0.380367\pi$
$548$	9.79508	0.418425
$549$	−61.5207	−2.62564
$550$	106.062	4.52251
$551$	7.76707	0.330888
$552$	16.4575	0.700479
$553$	0.596505	0.0253660
$554$	−2.56299	−0.108891
$555$	−18.8197	−0.798853
$556$	−34.8071	−1.47615
$557$	−4.95148	−0.209801	−0.104900	−	0.994483i	$-0.533452\pi$
$557$	−4.95148	−0.209801	−0.104900	+	0.994483i	$0.533452\pi$
$558$	−99.4886	−4.21169
$559$	−14.0060	−0.592391
$560$	6.59192	0.278560
$561$	12.4690	0.526440
$562$	16.2763	0.686574
$563$	8.36861	0.352695	0.176347	−	0.984328i	$-0.443572\pi$
$563$	8.36861	0.352695	0.176347	+	0.984328i	$0.443572\pi$
$564$	−41.2562	−1.73720
$565$	68.1130	2.86554
$566$	−24.3918	−1.02526
$567$	−29.8656	−1.25424
$568$	−15.4725	−0.649212
$569$	−32.1520	−1.34788	−0.673941	−	0.738785i	$-0.735400\pi$
$569$	−32.1520	−1.34788	−0.673941	+	0.738785i	$0.735400\pi$
$570$	168.039	7.03838
$571$	36.8768	1.54325	0.771623	−	0.636080i	$-0.219445\pi$
$571$	36.8768	1.54325	0.771623	+	0.636080i	$0.219445\pi$
$572$	−27.7222	−1.15913
$573$	−35.7379	−1.49297
$574$	20.7120	0.864502
$575$	−37.5113	−1.56433
$576$	−104.409	−4.35038
$577$	26.1817	1.08996	0.544978	−	0.838450i	$-0.316538\pi$
$577$	26.1817	1.08996	0.544978	+	0.838450i	$0.316538\pi$
$578$	−2.18647	−0.0909450
$579$	−73.1079	−3.03826
$580$	−17.1019	−0.710117
$581$	4.73268	0.196345
$582$	−91.8772	−3.80843
$583$	32.5657	1.34873
$584$	4.35672	0.180282
$585$	95.1779	3.93512
$586$	−53.4250	−2.20697
$587$	19.6022	0.809071	0.404535	−	0.914522i	$-0.367433\pi$
$587$	19.6022	0.809071	0.404535	+	0.914522i	$0.367433\pi$
$588$	−58.7703	−2.42365
$589$	−29.3776	−1.21048
$590$	−9.29919	−0.382842
$591$	−34.8616	−1.43401
$592$	2.40602	0.0988868
$593$	25.7639	1.05800	0.528998	−	0.848623i	$-0.322568\pi$
$593$	25.7639	1.05800	0.528998	+	0.848623i	$0.322568\pi$
$594$	145.014	5.94998
$595$	3.60345	0.147727
$596$	46.4145	1.90121
$597$	−82.8296	−3.38999
$598$	16.8566	0.689319
$599$	6.07789	0.248336	0.124168	−	0.992261i	$-0.460374\pi$
$599$	6.07789	0.248336	0.124168	+	0.992261i	$0.460374\pi$
$600$	−75.1605	−3.06842
$601$	−7.62422	−0.310999	−0.155499	−	0.987836i	$-0.549699\pi$
$601$	−7.62422	−0.310999	−0.155499	+	0.987836i	$0.549699\pi$
$602$	−9.64525	−0.393111
$603$	−41.2232	−1.67874
$604$	31.9640	1.30059
$605$	11.6351	0.473032
$606$	12.5687	0.510569
$607$	−32.6230	−1.32413	−0.662063	−	0.749449i	$-0.730319\pi$
$607$	−32.6230	−1.32413	−0.662063	+	0.749449i	$0.730319\pi$
$608$	−39.8181	−1.61484
$609$	4.12210	0.167036
$610$	68.7689	2.78437
$611$	−11.8631	−0.479931
$612$	−23.1323	−0.935067
$613$	−23.3569	−0.943377	−0.471688	−	0.881765i	$-0.656355\pi$
$613$	−23.3569	−0.943377	−0.471688	+	0.881765i	$0.656355\pi$
$614$	3.64375	0.147050
$615$	159.982	6.45110
$616$	−5.35959	−0.215944
$617$	−2.77263	−0.111622	−0.0558109	−	0.998441i	$-0.517774\pi$
$617$	−2.77263	−0.111622	−0.0558109	+	0.998441i	$0.517774\pi$
$618$	126.528	5.08972
$619$	3.02220	0.121472	0.0607362	−	0.998154i	$-0.480655\pi$
$619$	3.02220	0.121472	0.0607362	+	0.998154i	$0.480655\pi$
$620$	64.6848	2.59781
$621$	−51.2872	−2.05809
$622$	−53.1262	−2.13017
$623$	6.50378	0.260568
$624$	−16.5561	−0.662775
$625$	80.8686	3.23474
$626$	56.2686	2.24895
$627$	66.9715	2.67459
$628$	42.8131	1.70843
$629$	1.31524	0.0524421
$630$	65.5444	2.61135
$631$	−13.9379	−0.554858	−0.277429	−	0.960746i	$-0.589482\pi$
$631$	−13.9379	−0.554858	−0.277429	+	0.960746i	$0.589482\pi$
$632$	1.20168	0.0478003
$633$	−37.0482	−1.47253
$634$	−47.0866	−1.87005
$635$	−32.7556	−1.29987
$636$	−82.2024	−3.25954
$637$	−16.8993	−0.669573
$638$	−11.7183	−0.463933
$639$	75.4127	2.98328
$640$	53.6505	2.12072
$641$	−27.8479	−1.09993	−0.549963	−	0.835189i	$-0.685358\pi$
$641$	−27.8479	−1.09993	−0.549963	+	0.835189i	$0.685358\pi$
$642$	36.5209	1.44137
$643$	−27.7761	−1.09538	−0.547691	−	0.836681i	$-0.684493\pi$
$643$	−27.7761	−1.09538	−0.547691	+	0.836681i	$0.684493\pi$
$644$	6.75194	0.266064
$645$	−74.5011	−2.93348
$646$	−11.7436	−0.462047
$647$	23.6383	0.929318	0.464659	−	0.885490i	$-0.346177\pi$
$647$	23.6383	0.929318	0.464659	+	0.885490i	$0.346177\pi$
$648$	−60.1653	−2.36352
$649$	−3.70617	−0.145480
$650$	−76.9831	−3.01953
$651$	−15.5911	−0.611064
$652$	22.2245	0.870379
$653$	−4.27977	−0.167480	−0.0837402	−	0.996488i	$-0.526687\pi$
$653$	−4.27977	−0.167480	−0.0837402	+	0.996488i	$0.526687\pi$
$654$	45.5897	1.78270
$655$	34.2221	1.33717
$656$	−20.4530	−0.798556
$657$	−21.2345	−0.828438
$658$	−8.16955	−0.318482
$659$	23.9331	0.932303	0.466151	−	0.884705i	$-0.345640\pi$
$659$	23.9331	0.932303	0.466151	+	0.884705i	$0.345640\pi$
$660$	−147.461	−5.73991
$661$	29.5982	1.15124	0.575619	−	0.817718i	$-0.304761\pi$
$661$	29.5982	1.15124	0.575619	+	0.817718i	$0.304761\pi$
$662$	−60.2060	−2.33997
$663$	−9.05033	−0.351486
$664$	9.53416	0.369997
$665$	19.3543	0.750528
$666$	23.9234	0.927013
$667$	4.14444	0.160473
$668$	61.8779	2.39413
$669$	−35.0585	−1.35544
$670$	46.0800	1.78023
$671$	27.4077	1.05806
$672$	−21.1320	−0.815186
$673$	27.9525	1.07749	0.538745	−	0.842469i	$-0.318899\pi$
$673$	27.9525	1.07749	0.538745	+	0.842469i	$0.318899\pi$
$674$	−49.5589	−1.90894
$675$	234.225	9.01534
$676$	−16.0267	−0.616410
$677$	44.1238	1.69582	0.847908	−	0.530144i	$-0.177862\pi$
$677$	44.1238	1.69582	0.847908	+	0.530144i	$0.177862\pi$
$678$	−117.808	−4.52440
$679$	−10.5822	−0.406107
$680$	7.25928	0.278381
$681$	81.5585	3.12533
$682$	44.3225	1.69719
$683$	18.9896	0.726618	0.363309	−	0.931669i	$-0.381647\pi$
$683$	18.9896	0.726618	0.363309	+	0.931669i	$0.381647\pi$
$684$	−124.245	−4.75062
$685$	14.9819	0.572429
$686$	−24.6052	−0.939431
$687$	−19.9141	−0.759772
$688$	9.52465	0.363124
$689$	−23.6371	−0.900502
$690$	89.6642	3.41346
$691$	−41.2206	−1.56810	−0.784052	−	0.620695i	$-0.786851\pi$
$691$	−41.2206	−1.56810	−0.784052	+	0.620695i	$0.786851\pi$
$692$	26.0672	0.990925
$693$	26.1225	0.992313
$694$	37.6315	1.42847
$695$	−53.2386	−2.01946
$696$	8.30413	0.314767
$697$	−11.1806	−0.423494
$698$	13.9339	0.527406
$699$	33.1641	1.25438
$700$	−30.8356	−1.16548
$701$	0.444634	0.0167936	0.00839680	−	0.999965i	$-0.497327\pi$
$701$	0.444634	0.0167936	0.00839680	+	0.999965i	$0.497327\pi$
$702$	−105.255	−3.97259
$703$	7.06424	0.266433
$704$	46.5146	1.75308
$705$	−63.1027	−2.37658
$706$	79.4288	2.98934
$707$	1.44763	0.0544438
$708$	9.35512	0.351587
$709$	29.2890	1.09997	0.549986	−	0.835174i	$-0.314633\pi$
$709$	29.2890	1.09997	0.549986	+	0.835174i	$0.314633\pi$
$710$	−84.2976	−3.16363
$711$	−5.85697	−0.219653
$712$	13.1021	0.491022
$713$	−15.6756	−0.587056
$714$	−6.23252	−0.233246
$715$	−42.4021	−1.58575
$716$	5.62782	0.210322
$717$	−12.6272	−0.471572
$718$	6.01398	0.224440
$719$	−0.828425	−0.0308950	−0.0154475	−	0.999881i	$-0.504917\pi$
$719$	−0.828425	−0.0308950	−0.0154475	+	0.999881i	$0.504917\pi$
$720$	−64.7248	−2.41215
$721$	14.5732	0.542735
$722$	−21.5329	−0.801371
$723$	−20.7860	−0.773041
$724$	−9.95603	−0.370013
$725$	−18.9274	−0.702946
$726$	−20.1240	−0.746872
$727$	−2.20479	−0.0817712	−0.0408856	−	0.999164i	$-0.513018\pi$
$727$	−2.20479	−0.0817712	−0.0408856	+	0.999164i	$0.513018\pi$
$728$	3.89015	0.144178
$729$	112.624	4.17125
$730$	23.7363	0.878521
$731$	5.20661	0.192573
$732$	−69.1825	−2.55706
$733$	−2.24667	−0.0829827	−0.0414913	−	0.999139i	$-0.513211\pi$
$733$	−2.24667	−0.0829827	−0.0414913	+	0.999139i	$0.513211\pi$
$734$	−68.4075	−2.52497
$735$	−89.8910	−3.31568
$736$	−21.2466	−0.783159
$737$	18.3651	0.676486
$738$	−203.367	−7.48605
$739$	22.4627	0.826305	0.413153	−	0.910662i	$-0.364428\pi$
$739$	22.4627	0.826305	0.413153	+	0.910662i	$0.364428\pi$
$740$	−15.5544	−0.571789
$741$	−48.6098	−1.78573
$742$	−16.2777	−0.597574
$743$	−37.5821	−1.37875	−0.689377	−	0.724403i	$-0.742116\pi$
$743$	−37.5821	−1.37875	−0.689377	+	0.724403i	$0.742116\pi$
$744$	−31.4089	−1.15150
$745$	70.9925	2.60096
$746$	−35.4610	−1.29832
$747$	−46.4693	−1.70022
$748$	10.3055	0.376807
$749$	4.20639	0.153698
$750$	−253.060	−9.24046
$751$	−15.9517	−0.582084	−0.291042	−	0.956710i	$-0.594002\pi$
$751$	−15.9517	−0.582084	−0.291042	+	0.956710i	$0.594002\pi$
$752$	8.06740	0.294188
$753$	10.2594	0.373874
$754$	8.50549	0.309752
$755$	48.8899	1.77929
$756$	−42.1600	−1.53334
$757$	17.7261	0.644267	0.322134	−	0.946694i	$-0.395600\pi$
$757$	17.7261	0.644267	0.322134	+	0.946694i	$0.395600\pi$
$758$	−4.67326	−0.169741
$759$	35.7354	1.29711
$760$	38.9900	1.41432
$761$	2.06843	0.0749804	0.0374902	−	0.999297i	$-0.488064\pi$
$761$	2.06843	0.0749804	0.0374902	+	0.999297i	$0.488064\pi$
$762$	56.6541	2.05236
$763$	5.25090	0.190095
$764$	−29.5371	−1.06861
$765$	−35.3816	−1.27922
$766$	10.3756	0.374885
$767$	2.69004	0.0971318
$768$	−8.34394	−0.301086
$769$	17.6357	0.635961	0.317981	−	0.948097i	$-0.396995\pi$
$769$	17.6357	0.635961	0.317981	+	0.948097i	$0.396995\pi$
$770$	−29.2002	−1.05230
$771$	−52.0751	−1.87544
$772$	−60.4231	−2.17468
$773$	−52.3131	−1.88157	−0.940785	−	0.339003i	$-0.889910\pi$
$773$	−52.3131	−1.88157	−0.940785	+	0.339003i	$0.889910\pi$
$774$	94.7049	3.40410
$775$	71.5895	2.57157
$776$	−21.3182	−0.765279
$777$	3.74909	0.134498
$778$	42.8296	1.53551
$779$	−60.0514	−2.15157
$780$	107.031	3.83234
$781$	−33.5966	−1.20218
$782$	−6.26630	−0.224083
$783$	−25.8784	−0.924820
$784$	11.4922	0.410435
$785$	65.4840	2.33722
$786$	−59.1905	−2.11126
$787$	13.1503	0.468758	0.234379	−	0.972145i	$-0.424694\pi$
$787$	13.1503	0.468758	0.234379	+	0.972145i	$0.424694\pi$
$788$	−28.8128	−1.02641
$789$	−103.569	−3.68717
$790$	6.54702	0.232932
$791$	−13.5689	−0.482453
$792$	52.6248	1.86994
$793$	−19.8933	−0.706430
$794$	2.47209	0.0877313
$795$	−125.731	−4.45922
$796$	−68.4580	−2.42643
$797$	25.4325	0.900864	0.450432	−	0.892811i	$-0.351270\pi$
$797$	25.4325	0.900864	0.450432	+	0.892811i	$0.351270\pi$
$798$	−33.4752	−1.18501
$799$	4.41001	0.156015
$800$	97.0317	3.43059
$801$	−63.8594	−2.25636
$802$	41.5011	1.46545
$803$	9.46005	0.333838
$804$	−46.3572	−1.63489
$805$	10.3273	0.363990
$806$	−32.1705	−1.13316
$807$	48.5049	1.70745
$808$	2.91631	0.102595
$809$	9.13237	0.321077	0.160539	−	0.987030i	$-0.448677\pi$
$809$	9.13237	0.321077	0.160539	+	0.987030i	$0.448677\pi$
$810$	−327.794	−11.5175
$811$	−47.0421	−1.65187	−0.825935	−	0.563765i	$-0.809352\pi$
$811$	−47.0421	−1.65187	−0.825935	+	0.563765i	$0.809352\pi$
$812$	3.40688	0.119558
$813$	29.0607	1.01920
$814$	−10.6579	−0.373561
$815$	33.9931	1.19073
$816$	6.15459	0.215454
$817$	27.9650	0.978371
$818$	42.5506	1.48775
$819$	−18.9605	−0.662533
$820$	132.224	4.61746
$821$	−13.5305	−0.472217	−0.236108	−	0.971727i	$-0.575872\pi$
$821$	−13.5305	−0.472217	−0.236108	+	0.971727i	$0.575872\pi$
$822$	−25.9127	−0.903808
$823$	−14.8314	−0.516991	−0.258495	−	0.966013i	$-0.583227\pi$
$823$	−14.8314	−0.516991	−0.258495	+	0.966013i	$0.583227\pi$
$824$	29.3583	1.02274
$825$	−163.201	−5.68194
$826$	1.85250	0.0644568
$827$	−32.8667	−1.14289	−0.571443	−	0.820642i	$-0.693616\pi$
$827$	−32.8667	−1.14289	−0.571443	+	0.820642i	$0.693616\pi$
$828$	−66.2960	−2.30394
$829$	30.6855	1.06575	0.532876	−	0.846193i	$-0.321111\pi$
$829$	30.6855	1.06575	0.532876	+	0.846193i	$0.321111\pi$
$830$	51.9442	1.80301
$831$	3.94375	0.136807
$832$	−33.7616	−1.17047
$833$	6.28215	0.217664
$834$	92.0815	3.18852
$835$	94.6443	3.27530
$836$	55.3514	1.91437
$837$	97.8806	3.38325
$838$	36.4418	1.25886
$839$	28.1338	0.971288	0.485644	−	0.874157i	$-0.338585\pi$
$839$	28.1338	0.971288	0.485644	+	0.874157i	$0.338585\pi$
$840$	20.6926	0.713962
$841$	−26.9088	−0.927890
$842$	37.7517	1.30101
$843$	−25.0448	−0.862590
$844$	−30.6201	−1.05399
$845$	−24.5133	−0.843283
$846$	80.2153	2.75786
$847$	−2.31783	−0.0796416
$848$	16.0742	0.551990
$849$	37.5324	1.28811
$850$	28.6178	0.981582
$851$	3.76942	0.129214
$852$	84.8045	2.90535
$853$	3.23590	0.110795	0.0553976	−	0.998464i	$-0.482357\pi$
$853$	3.23590	0.110795	0.0553976	+	0.998464i	$0.482357\pi$
$854$	−13.6995	−0.468788
$855$	−190.036	−6.49911
$856$	8.47392	0.289633
$857$	3.82555	0.130678	0.0653392	−	0.997863i	$-0.479187\pi$
$857$	3.82555	0.130678	0.0653392	+	0.997863i	$0.479187\pi$
$858$	73.3386	2.50374
$859$	31.7355	1.08280	0.541400	−	0.840765i	$-0.317894\pi$
$859$	31.7355	1.08280	0.541400	+	0.840765i	$0.317894\pi$
$860$	−61.5746	−2.09968
$861$	−31.8702	−1.08613
$862$	−82.4573	−2.80851
$863$	40.8730	1.39133	0.695666	−	0.718365i	$-0.255109\pi$
$863$	40.8730	1.39133	0.695666	+	0.718365i	$0.255109\pi$
$864$	132.666	4.51340
$865$	39.8706	1.35564
$866$	−11.7832	−0.400411
$867$	3.36438	0.114260
$868$	−12.8859	−0.437377
$869$	2.60930	0.0885143
$870$	45.2427	1.53387
$871$	−13.3299	−0.451666
$872$	10.5781	0.358221
$873$	103.904	3.51663
$874$	−33.6567	−1.13845
$875$	−29.1469	−0.985344
$876$	−23.8791	−0.806799
$877$	35.5901	1.20179	0.600897	−	0.799327i	$-0.294810\pi$
$877$	35.5901	1.20179	0.600897	+	0.799327i	$0.294810\pi$
$878$	−30.6701	−1.03507
$879$	82.2067	2.77276
$880$	28.8351	0.972031
$881$	−29.2786	−0.986420	−0.493210	−	0.869910i	$-0.664177\pi$
$881$	−29.2786	−0.986420	−0.493210	+	0.869910i	$0.664177\pi$
$882$	114.268	3.84762
$883$	−15.6015	−0.525033	−0.262517	−	0.964927i	$-0.584552\pi$
$883$	−15.6015	−0.525033	−0.262517	+	0.964927i	$0.584552\pi$
$884$	−7.48003	−0.251581
$885$	14.3090	0.480990
$886$	48.1006	1.61597
$887$	24.2744	0.815054	0.407527	−	0.913193i	$-0.366391\pi$
$887$	24.2744	0.815054	0.407527	+	0.913193i	$0.366391\pi$
$888$	7.55269	0.253452
$889$	6.52527	0.218851
$890$	71.3831	2.39277
$891$	−130.641	−4.37664
$892$	−28.9756	−0.970175
$893$	23.6864	0.792636
$894$	−122.789	−4.10666
$895$	8.60793	0.287731
$896$	−10.6878	−0.357053
$897$	−25.9378	−0.866038
$898$	54.6364	1.82324
$899$	−7.90958	−0.263799
$900$	302.769	10.0923
$901$	8.78689	0.292734
$902$	90.6007	3.01667
$903$	14.8414	0.493892
$904$	−27.3350	−0.909148
$905$	−15.2281	−0.506198
$906$	−84.5599	−2.80932
$907$	8.97041	0.297858	0.148929	−	0.988848i	$-0.452417\pi$
$907$	8.97041	0.297858	0.148929	+	0.988848i	$0.452417\pi$
$908$	67.4075	2.23700
$909$	−14.2140	−0.471450
$910$	21.1944	0.702586
$911$	39.2432	1.30019	0.650093	−	0.759855i	$-0.274730\pi$
$911$	39.2432	1.30019	0.650093	+	0.759855i	$0.274730\pi$
$912$	33.0567	1.09462
$913$	20.7022	0.685143
$914$	−38.1889	−1.26318
$915$	−105.817	−3.49820
$916$	−16.4589	−0.543817
$917$	−6.81742	−0.225131
$918$	39.1276	1.29140
$919$	12.1920	0.402177	0.201088	−	0.979573i	$-0.435552\pi$
$919$	12.1920	0.402177	0.201088	+	0.979573i	$0.435552\pi$
$920$	20.8047	0.685912
$921$	−5.60674	−0.184748
$922$	−64.4569	−2.12277
$923$	24.3853	0.802653
$924$	29.3758	0.966394
$925$	−17.2147	−0.566015
$926$	−5.06345	−0.166395
$927$	−143.092	−4.69975
$928$	−10.7206	−0.351920
$929$	−23.2473	−0.762721	−0.381360	−	0.924426i	$-0.624544\pi$
$929$	−23.2473	−0.762721	−0.381360	+	0.924426i	$0.624544\pi$
$930$	−171.122	−5.61132
$931$	33.7418	1.10584
$932$	27.4099	0.897840
$933$	81.7469	2.67627
$934$	−74.5383	−2.43897
$935$	15.7626	0.515492
$936$	−38.1966	−1.24850
$937$	47.6358	1.55619	0.778097	−	0.628144i	$-0.216185\pi$
$937$	47.6358	1.55619	0.778097	+	0.628144i	$0.216185\pi$
$938$	−9.17964	−0.299726
$939$	−86.5822	−2.82550
$940$	−52.1539	−1.70107
$941$	−2.88409	−0.0940186	−0.0470093	−	0.998894i	$-0.514969\pi$
$941$	−2.88409	−0.0940186	−0.0470093	+	0.998894i	$0.514969\pi$
$942$	−113.261	−3.69025
$943$	−32.0429	−1.04346
$944$	−1.82934	−0.0595399
$945$	−64.4850	−2.09770
$946$	−42.1913	−1.37176
$947$	−49.9156	−1.62204	−0.811019	−	0.585019i	$-0.801087\pi$
$947$	−49.9156	−1.62204	−0.811019	+	0.585019i	$0.801087\pi$
$948$	−6.58639	−0.213916
$949$	−6.86637	−0.222892
$950$	153.708	4.98694
$951$	72.4535	2.34947
$952$	−1.44613	−0.0468693
$953$	2.70557	0.0876420	0.0438210	−	0.999039i	$-0.486047\pi$
$953$	2.70557	0.0876420	0.0438210	+	0.999039i	$0.486047\pi$
$954$	159.828	5.17462
$955$	−45.1779	−1.46192
$956$	−10.4363	−0.337534
$957$	18.0313	0.582870
$958$	30.3570	0.980789
$959$	−2.98456	−0.0963764
$960$	−179.586	−5.79611
$961$	−1.08342	−0.0349492
$962$	7.73584	0.249413
$963$	−41.3017	−1.33093
$964$	−17.1795	−0.553314
$965$	−92.4191	−2.97508
$966$	−17.8621	−0.574703
$967$	9.71188	0.312313	0.156156	−	0.987732i	$-0.450090\pi$
$967$	9.71188	0.312313	0.156156	+	0.987732i	$0.450090\pi$
$968$	−4.66936	−0.150079
$969$	18.0703	0.580501
$970$	−116.146	−3.72923
$971$	−55.4528	−1.77956	−0.889782	−	0.456386i	$-0.849144\pi$
$971$	−55.4528	−1.77956	−0.889782	+	0.456386i	$0.849144\pi$
$972$	180.483	5.78901
$973$	10.6057	0.340004
$974$	−69.3234	−2.22126
$975$	118.456	3.79364
$976$	13.5282	0.433028
$977$	20.0458	0.641321	0.320661	−	0.947194i	$-0.396095\pi$
$977$	20.0458	0.641321	0.320661	+	0.947194i	$0.396095\pi$
$978$	−58.7944	−1.88004
$979$	28.4495	0.909251
$980$	−74.2942	−2.37324
$981$	−51.5576	−1.64611
$982$	41.1608	1.31349
$983$	35.6831	1.13811	0.569057	−	0.822298i	$-0.307309\pi$
$983$	35.6831	1.13811	0.569057	+	0.822298i	$0.307309\pi$
$984$	−64.2037	−2.04674
$985$	−44.0701	−1.40419
$986$	−3.16184	−0.100694
$987$	12.5707	0.400131
$988$	−40.1757	−1.27816
$989$	14.9219	0.474488
$990$	286.711	9.11229
$991$	−21.2628	−0.675436	−0.337718	−	0.941247i	$-0.609655\pi$
$991$	−21.2628	−0.675436	−0.337718	+	0.941247i	$0.609655\pi$
$992$	40.5486	1.28742
$993$	92.6409	2.93987
$994$	16.7930	0.532641
$995$	−104.709	−3.31949
$996$	−52.2566	−1.65581
$997$	25.8393	0.818338	0.409169	−	0.912459i	$-0.365819\pi$
$997$	25.8393	0.818338	0.409169	+	0.912459i	$0.365819\pi$
$998$	48.0215	1.52009
$999$	−23.5367	−0.744669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.j.1.3	✓	22
3.2	odd	2		9027.2.a.s.1.20		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.j.1.3	✓	22	1.1	even	1	trivial
9027.2.a.s.1.20		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)

\(f(q)\)	\(=\)	\(q-2.18647 q^{2} +3.36438 q^{3} +2.78064 q^{4} +4.25307 q^{5} -7.35611 q^{6} -0.847258 q^{7} -1.70683 q^{8} +8.31907 q^{9} +O(q^{10})\)	\(q-2.18647 q^{2} +3.36438 q^{3} +2.78064 q^{4} +4.25307 q^{5} -7.35611 q^{6} -0.847258 q^{7} -1.70683 q^{8} +8.31907 q^{9} -9.29919 q^{10} -3.70617 q^{11} +9.35512 q^{12} +2.69004 q^{13} +1.85250 q^{14} +14.3090 q^{15} -1.82934 q^{16} -1.00000 q^{17} -18.1894 q^{18} -5.37106 q^{19} +11.8262 q^{20} -2.85050 q^{21} +8.10341 q^{22} -2.86595 q^{23} -5.74244 q^{24} +13.0886 q^{25} -5.88169 q^{26} +17.8954 q^{27} -2.35592 q^{28} -1.44610 q^{29} -31.2860 q^{30} +5.46960 q^{31} +7.41345 q^{32} -12.4690 q^{33} +2.18647 q^{34} -3.60345 q^{35} +23.1323 q^{36} -1.31524 q^{37} +11.7436 q^{38} +9.05033 q^{39} -7.25928 q^{40} +11.1806 q^{41} +6.23252 q^{42} -5.20661 q^{43} -10.3055 q^{44} +35.3816 q^{45} +6.26630 q^{46} -4.41001 q^{47} -6.15459 q^{48} -6.28215 q^{49} -28.6178 q^{50} -3.36438 q^{51} +7.48003 q^{52} -8.78689 q^{53} -39.1276 q^{54} -15.7626 q^{55} +1.44613 q^{56} -18.0703 q^{57} +3.16184 q^{58} +1.00000 q^{59} +39.7880 q^{60} -7.39515 q^{61} -11.9591 q^{62} -7.04840 q^{63} -12.5506 q^{64} +11.4409 q^{65} +27.2630 q^{66} -4.95527 q^{67} -2.78064 q^{68} -9.64215 q^{69} +7.87882 q^{70} +9.06504 q^{71} -14.1993 q^{72} -2.55251 q^{73} +2.87573 q^{74} +44.0351 q^{75} -14.9350 q^{76} +3.14008 q^{77} -19.7882 q^{78} -0.704041 q^{79} -7.78030 q^{80} +35.2497 q^{81} -24.4459 q^{82} -5.58588 q^{83} -7.92620 q^{84} -4.25307 q^{85} +11.3841 q^{86} -4.86522 q^{87} +6.32581 q^{88} -7.67627 q^{89} -77.3606 q^{90} -2.27916 q^{91} -7.96916 q^{92} +18.4018 q^{93} +9.64235 q^{94} -22.8435 q^{95} +24.9417 q^{96} +12.4899 q^{97} +13.7357 q^{98} -30.8319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 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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