LMFDB - Embedded newform 1003.2.a.j.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.25705 q^{2} -2.18501 q^{3} -0.419822 q^{4} +4.45642 q^{5} +2.74667 q^{6} -4.53135 q^{7} +3.04184 q^{8} +1.77428 q^{9} +O(q^{10})$	\(q-1.25705 q^{2} -2.18501 q^{3} -0.419822 q^{4} +4.45642 q^{5} +2.74667 q^{6} -4.53135 q^{7} +3.04184 q^{8} +1.77428 q^{9} -5.60195 q^{10} -0.915633 q^{11} +0.917317 q^{12} +3.82507 q^{13} +5.69614 q^{14} -9.73733 q^{15} -2.98410 q^{16} -1.00000 q^{17} -2.23036 q^{18} +1.42810 q^{19} -1.87090 q^{20} +9.90106 q^{21} +1.15100 q^{22} -0.780221 q^{23} -6.64646 q^{24} +14.8597 q^{25} -4.80830 q^{26} +2.67822 q^{27} +1.90236 q^{28} -6.11501 q^{29} +12.2403 q^{30} -9.72777 q^{31} -2.33251 q^{32} +2.00067 q^{33} +1.25705 q^{34} -20.1936 q^{35} -0.744881 q^{36} -7.06982 q^{37} -1.79519 q^{38} -8.35781 q^{39} +13.5557 q^{40} -2.81715 q^{41} -12.4461 q^{42} +9.73889 q^{43} +0.384403 q^{44} +7.90692 q^{45} +0.980778 q^{46} +7.06168 q^{47} +6.52030 q^{48} +13.5332 q^{49} -18.6794 q^{50} +2.18501 q^{51} -1.60585 q^{52} +1.70503 q^{53} -3.36666 q^{54} -4.08044 q^{55} -13.7837 q^{56} -3.12041 q^{57} +7.68689 q^{58} +1.00000 q^{59} +4.08795 q^{60} +14.8112 q^{61} +12.2283 q^{62} -8.03988 q^{63} +8.90029 q^{64} +17.0461 q^{65} -2.51494 q^{66} +2.99668 q^{67} +0.419822 q^{68} +1.70479 q^{69} +25.3844 q^{70} +7.46938 q^{71} +5.39707 q^{72} -1.83235 q^{73} +8.88713 q^{74} -32.4685 q^{75} -0.599548 q^{76} +4.14906 q^{77} +10.5062 q^{78} +7.75629 q^{79} -13.2984 q^{80} -11.1748 q^{81} +3.54130 q^{82} +9.33260 q^{83} -4.15669 q^{84} -4.45642 q^{85} -12.2423 q^{86} +13.3614 q^{87} -2.78521 q^{88} +3.95837 q^{89} -9.93940 q^{90} -17.3327 q^{91} +0.327554 q^{92} +21.2553 q^{93} -8.87689 q^{94} +6.36421 q^{95} +5.09656 q^{96} +1.94270 q^{97} -17.0119 q^{98} -1.62459 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.25705	−0.888869	−0.444435	−	0.895811i	$-0.646595\pi$
$2$	−1.25705	−0.888869	−0.444435	+	0.895811i	$0.646595\pi$
$3$	−2.18501	−1.26152	−0.630759	−	0.775979i	$-0.717256\pi$
$3$	−2.18501	−1.26152	−0.630759	+	0.775979i	$0.717256\pi$
$4$	−0.419822	−0.209911
$5$	4.45642	1.99297	0.996485	−	0.0837661i	$-0.0266949\pi$
$5$	4.45642	1.99297	0.996485	+	0.0837661i	$0.0266949\pi$
$6$	2.74667	1.12132
$7$	−4.53135	−1.71269	−0.856345	−	0.516403i	$-0.827271\pi$
$7$	−4.53135	−1.71269	−0.856345	+	0.516403i	$0.827271\pi$
$8$	3.04184	1.07545
$9$	1.77428	0.591426
$10$	−5.60195	−1.77149
$11$	−0.915633	−0.276074	−0.138037	−	0.990427i	$-0.544079\pi$
$11$	−0.915633	−0.276074	−0.138037	+	0.990427i	$0.544079\pi$
$12$	0.917317	0.264807
$13$	3.82507	1.06088	0.530441	−	0.847722i	$-0.322026\pi$
$13$	3.82507	1.06088	0.530441	+	0.847722i	$0.322026\pi$
$14$	5.69614	1.52236
$15$	−9.73733	−2.51417
$16$	−2.98410	−0.746026
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.23036	−0.525700
$19$	1.42810	0.327628	0.163814	−	0.986491i	$-0.447620\pi$
$19$	1.42810	0.327628	0.163814	+	0.986491i	$0.447620\pi$
$20$	−1.87090	−0.418347
$21$	9.90106	2.16059
$22$	1.15100	0.245394
$23$	−0.780221	−0.162687	−0.0813437	−	0.996686i	$-0.525921\pi$
$23$	−0.780221	−0.162687	−0.0813437	+	0.996686i	$0.525921\pi$
$24$	−6.64646	−1.35670
$25$	14.8597	2.97193
$26$	−4.80830	−0.942986
$27$	2.67822	0.515424
$28$	1.90236	0.359513
$29$	−6.11501	−1.13553	−0.567765	−	0.823191i	$-0.692192\pi$
$29$	−6.11501	−1.13553	−0.567765	+	0.823191i	$0.692192\pi$
$30$	12.2403	2.23477
$31$	−9.72777	−1.74716	−0.873579	−	0.486682i	$-0.838207\pi$
$31$	−9.72777	−1.74716	−0.873579	+	0.486682i	$0.838207\pi$
$32$	−2.33251	−0.412333
$33$	2.00067	0.348272
$34$	1.25705	0.215582
$35$	−20.1936	−3.41334
$36$	−0.744881	−0.124147
$37$	−7.06982	−1.16227	−0.581136	−	0.813807i	$-0.697392\pi$
$37$	−7.06982	−1.16227	−0.581136	+	0.813807i	$0.697392\pi$
$38$	−1.79519	−0.291219
$39$	−8.35781	−1.33832
$40$	13.5557	2.14335
$41$	−2.81715	−0.439964	−0.219982	−	0.975504i	$-0.570600\pi$
$41$	−2.81715	−0.439964	−0.219982	+	0.975504i	$0.570600\pi$
$42$	−12.4461	−1.92048
$43$	9.73889	1.48517	0.742583	−	0.669754i	$-0.233600\pi$
$43$	9.73889	1.48517	0.742583	+	0.669754i	$0.233600\pi$
$44$	0.384403	0.0579510
$45$	7.90692	1.17869
$46$	0.980778	0.144608
$47$	7.06168	1.03005	0.515026	−	0.857175i	$-0.327782\pi$
$47$	7.06168	1.03005	0.515026	+	0.857175i	$0.327782\pi$
$48$	6.52030	0.941125
$49$	13.5332	1.93331
$50$	−18.6794	−2.64166
$51$	2.18501	0.305963
$52$	−1.60585	−0.222691
$53$	1.70503	0.234204	0.117102	−	0.993120i	$-0.462640\pi$
$53$	1.70503	0.234204	0.117102	+	0.993120i	$0.462640\pi$
$54$	−3.36666	−0.458144
$55$	−4.08044	−0.550207
$56$	−13.7837	−1.84192
$57$	−3.12041	−0.413309
$58$	7.68689	1.00934
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	4.08795	0.527752
$61$	14.8112	1.89638	0.948192	−	0.317699i	$-0.102910\pi$
$61$	14.8112	1.89638	0.948192	+	0.317699i	$0.102910\pi$
$62$	12.2283	1.55300
$63$	−8.03988	−1.01293
$64$	8.90029	1.11254
$65$	17.0461	2.11431
$66$	−2.51494	−0.309568
$67$	2.99668	0.366103	0.183052	−	0.983103i	$-0.441402\pi$
$67$	2.99668	0.366103	0.183052	+	0.983103i	$0.441402\pi$
$68$	0.419822	0.0509109
$69$	1.70479	0.205233
$70$	25.3844	3.03402
$71$	7.46938	0.886453	0.443226	−	0.896410i	$-0.353834\pi$
$71$	7.46938	0.886453	0.443226	+	0.896410i	$0.353834\pi$
$72$	5.39707	0.636051
$73$	−1.83235	−0.214460	−0.107230	−	0.994234i	$-0.534198\pi$
$73$	−1.83235	−0.214460	−0.107230	+	0.994234i	$0.534198\pi$
$74$	8.88713	1.03311
$75$	−32.4685	−3.74914
$76$	−0.599548	−0.0687729
$77$	4.14906	0.472829
$78$	10.5062	1.18959
$79$	7.75629	0.872651	0.436326	−	0.899789i	$-0.356280\pi$
$79$	7.75629	0.872651	0.436326	+	0.899789i	$0.356280\pi$
$80$	−13.2984	−1.48681
$81$	−11.1748	−1.24164
$82$	3.54130	0.391071
$83$	9.33260	1.02439	0.512193	−	0.858870i	$-0.328833\pi$
$83$	9.33260	1.02439	0.512193	+	0.858870i	$0.328833\pi$
$84$	−4.15669	−0.453532
$85$	−4.45642	−0.483366
$86$	−12.2423	−1.32012
$87$	13.3614	1.43249
$88$	−2.78521	−0.296904
$89$	3.95837	0.419586	0.209793	−	0.977746i	$-0.432721\pi$
$89$	3.95837	0.419586	0.209793	+	0.977746i	$0.432721\pi$
$90$	−9.93940	−1.04771
$91$	−17.3327	−1.81696
$92$	0.327554	0.0341499
$93$	21.2553	2.20407
$94$	−8.87689	−0.915581
$95$	6.36421	0.652954
$96$	5.09656	0.520166
$97$	1.94270	0.197252	0.0986258	−	0.995125i	$-0.468555\pi$
$97$	1.94270	0.197252	0.0986258	+	0.995125i	$0.468555\pi$
$98$	−17.0119	−1.71846
$99$	−1.62459	−0.163277
$100$	−6.23842	−0.623842
$101$	5.77502	0.574636	0.287318	−	0.957835i	$-0.407236\pi$
$101$	5.77502	0.574636	0.287318	+	0.957835i	$0.407236\pi$
$102$	−2.74667	−0.271961
$103$	14.0230	1.38172	0.690862	−	0.722987i	$-0.257231\pi$
$103$	14.0230	1.38172	0.690862	+	0.722987i	$0.257231\pi$
$104$	11.6352	1.14093
$105$	44.1233	4.30599
$106$	−2.14331	−0.208177
$107$	2.35894	0.228047	0.114023	−	0.993478i	$-0.463626\pi$
$107$	2.35894	0.228047	0.114023	+	0.993478i	$0.463626\pi$
$108$	−1.12438	−0.108193
$109$	1.90193	0.182172	0.0910859	−	0.995843i	$-0.470966\pi$
$109$	1.90193	0.182172	0.0910859	+	0.995843i	$0.470966\pi$
$110$	5.12933	0.489062
$111$	15.4476	1.46623
$112$	13.5220	1.27771
$113$	5.25196	0.494063	0.247032	−	0.969007i	$-0.420545\pi$
$113$	5.25196	0.494063	0.247032	+	0.969007i	$0.420545\pi$
$114$	3.92252	0.367378
$115$	−3.47699	−0.324231
$116$	2.56722	0.238360
$117$	6.78673	0.627433
$118$	−1.25705	−0.115721
$119$	4.53135	0.415389
$120$	−29.6194	−2.70387
$121$	−10.1616	−0.923783
$122$	−18.6185	−1.68564
$123$	6.15550	0.555023
$124$	4.08393	0.366748
$125$	43.9388	3.93001
$126$	10.1065	0.900362
$127$	9.54293	0.846798	0.423399	−	0.905943i	$-0.360837\pi$
$127$	9.54293	0.846798	0.423399	+	0.905943i	$0.360837\pi$
$128$	−6.52310	−0.576566
$129$	−21.2796	−1.87356
$130$	−21.4278	−1.87934
$131$	−11.9765	−1.04639	−0.523195	−	0.852213i	$-0.675260\pi$
$131$	−11.9765	−1.04639	−0.523195	+	0.852213i	$0.675260\pi$
$132$	−0.839926	−0.0731062
$133$	−6.47122	−0.561126
$134$	−3.76699	−0.325418
$135$	11.9353	1.02722
$136$	−3.04184	−0.260836
$137$	13.5278	1.15576	0.577879	−	0.816122i	$-0.303880\pi$
$137$	13.5278	1.15576	0.577879	+	0.816122i	$0.303880\pi$
$138$	−2.14301	−0.182425
$139$	−12.4306	−1.05435	−0.527174	−	0.849757i	$-0.676748\pi$
$139$	−12.4306	−1.05435	−0.527174	+	0.849757i	$0.676748\pi$
$140$	8.47773	0.716499
$141$	−15.4298	−1.29943
$142$	−9.38940	−0.787941
$143$	−3.50236	−0.292882
$144$	−5.29463	−0.441219
$145$	−27.2511	−2.26308
$146$	2.30335	0.190627
$147$	−29.5701	−2.43890
$148$	2.96807	0.243974
$149$	−11.9509	−0.979053	−0.489526	−	0.871988i	$-0.662830\pi$
$149$	−11.9509	−0.979053	−0.489526	+	0.871988i	$0.662830\pi$
$150$	40.8146	3.33250
$151$	10.2551	0.834550	0.417275	−	0.908780i	$-0.362985\pi$
$151$	10.2551	0.834550	0.417275	+	0.908780i	$0.362985\pi$
$152$	4.34405	0.352349
$153$	−1.77428	−0.143442
$154$	−5.21558	−0.420283
$155$	−43.3510	−3.48204
$156$	3.50880	0.280929
$157$	−10.1070	−0.806627	−0.403313	−	0.915062i	$-0.632142\pi$
$157$	−10.1070	−0.806627	−0.403313	+	0.915062i	$0.632142\pi$
$158$	−9.75006	−0.775673
$159$	−3.72551	−0.295452
$160$	−10.3946	−0.821768
$161$	3.53546	0.278633
$162$	14.0473	1.10366
$163$	22.2758	1.74478	0.872388	−	0.488814i	$-0.162570\pi$
$163$	22.2758	1.74478	0.872388	+	0.488814i	$0.162570\pi$
$164$	1.18270	0.0923535
$165$	8.91582	0.694096
$166$	−11.7316	−0.910546
$167$	17.2141	1.33207	0.666034	−	0.745922i	$-0.267991\pi$
$167$	17.2141	1.33207	0.666034	+	0.745922i	$0.267991\pi$
$168$	30.1175	2.32361
$169$	1.63113	0.125472
$170$	5.60195	0.429650
$171$	2.53384	0.193768
$172$	−4.08860	−0.311753
$173$	4.36291	0.331706	0.165853	−	0.986150i	$-0.446962\pi$
$173$	4.36291	0.331706	0.165853	+	0.986150i	$0.446962\pi$
$174$	−16.7959	−1.27330
$175$	−67.3344	−5.09000
$176$	2.73234	0.205958
$177$	−2.18501	−0.164236
$178$	−4.97587	−0.372957
$179$	−16.3957	−1.22547	−0.612735	−	0.790288i	$-0.709931\pi$
$179$	−16.3957	−1.22547	−0.612735	+	0.790288i	$0.709931\pi$
$180$	−3.31950	−0.247421
$181$	−19.9117	−1.48002	−0.740011	−	0.672594i	$-0.765180\pi$
$181$	−19.9117	−1.48002	−0.740011	+	0.672594i	$0.765180\pi$
$182$	21.7881	1.61504
$183$	−32.3627	−2.39232
$184$	−2.37331	−0.174963
$185$	−31.5061	−2.31637
$186$	−26.7190	−1.95913
$187$	0.915633	0.0669577
$188$	−2.96465	−0.216219
$189$	−12.1360	−0.882761
$190$	−8.00013	−0.580391
$191$	18.2980	1.32399	0.661997	−	0.749507i	$-0.269709\pi$
$191$	18.2980	1.32399	0.661997	+	0.749507i	$0.269709\pi$
$192$	−19.4472	−1.40348
$193$	13.3411	0.960315	0.480157	−	0.877182i	$-0.340580\pi$
$193$	13.3411	0.960315	0.480157	+	0.877182i	$0.340580\pi$
$194$	−2.44208	−0.175331
$195$	−37.2459	−2.66724
$196$	−5.68153	−0.405823
$197$	−0.906200	−0.0645641	−0.0322820	−	0.999479i	$-0.510277\pi$
$197$	−0.906200	−0.0645641	−0.0322820	+	0.999479i	$0.510277\pi$
$198$	2.04219	0.145132
$199$	14.8203	1.05058	0.525292	−	0.850922i	$-0.323956\pi$
$199$	14.8203	1.05058	0.525292	+	0.850922i	$0.323956\pi$
$200$	45.2007	3.19617
$201$	−6.54779	−0.461846
$202$	−7.25950	−0.510777
$203$	27.7093	1.94481
$204$	−0.917317	−0.0642250
$205$	−12.5544	−0.876836
$206$	−17.6276	−1.22817
$207$	−1.38433	−0.0962175
$208$	−11.4144	−0.791446
$209$	−1.30761	−0.0904496
$210$	−55.4652	−3.82746
$211$	4.85635	0.334325	0.167163	−	0.985929i	$-0.446540\pi$
$211$	4.85635	0.334325	0.167163	+	0.985929i	$0.446540\pi$
$212$	−0.715810	−0.0491620
$213$	−16.3207	−1.11828
$214$	−2.96530	−0.202704
$215$	43.4006	2.95989
$216$	8.14672	0.554314
$217$	44.0800	2.99234
$218$	−2.39082	−0.161927
$219$	4.00370	0.270545
$220$	1.71306	0.115495
$221$	−3.82507	−0.257302
$222$	−19.4185	−1.30328
$223$	−16.7155	−1.11935	−0.559677	−	0.828711i	$-0.689075\pi$
$223$	−16.7155	−1.11935	−0.559677	+	0.828711i	$0.689075\pi$
$224$	10.5694	0.706199
$225$	26.3652	1.75768
$226$	−6.60199	−0.439158
$227$	−14.5578	−0.966235	−0.483118	−	0.875555i	$-0.660496\pi$
$227$	−14.5578	−0.966235	−0.483118	+	0.875555i	$0.660496\pi$
$228$	1.31002	0.0867582
$229$	20.8556	1.37817	0.689087	−	0.724679i	$-0.258012\pi$
$229$	20.8556	1.37817	0.689087	+	0.724679i	$0.258012\pi$
$230$	4.37076	0.288199
$231$	−9.06574	−0.596482
$232$	−18.6009	−1.22121
$233$	23.6058	1.54647	0.773233	−	0.634122i	$-0.218638\pi$
$233$	23.6058	1.54647	0.773233	+	0.634122i	$0.218638\pi$
$234$	−8.53126	−0.557706
$235$	31.4698	2.05286
$236$	−0.419822	−0.0273281
$237$	−16.9476	−1.10086
$238$	−5.69614	−0.369226
$239$	−11.1346	−0.720236	−0.360118	−	0.932907i	$-0.617264\pi$
$239$	−11.1346	−0.720236	−0.360118	+	0.932907i	$0.617264\pi$
$240$	29.0572	1.87563
$241$	−12.7192	−0.819318	−0.409659	−	0.912239i	$-0.634352\pi$
$241$	−12.7192	−0.819318	−0.409659	+	0.912239i	$0.634352\pi$
$242$	12.7737	0.821123
$243$	16.3824	1.05093
$244$	−6.21808	−0.398072
$245$	60.3095	3.85303
$246$	−7.73778	−0.493343
$247$	5.46257	0.347575
$248$	−29.5903	−1.87899
$249$	−20.3919	−1.29228
$250$	−55.2333	−3.49326
$251$	−10.1016	−0.637605	−0.318803	−	0.947821i	$-0.603281\pi$
$251$	−10.1016	−0.637605	−0.318803	+	0.947821i	$0.603281\pi$
$252$	3.37532	0.212625
$253$	0.714397	0.0449137
$254$	−11.9960	−0.752693
$255$	9.73733	0.609775
$256$	−9.60071	−0.600044
$257$	13.9502	0.870187	0.435094	−	0.900385i	$-0.356715\pi$
$257$	13.9502	0.870187	0.435094	+	0.900385i	$0.356715\pi$
$258$	26.7495	1.66535
$259$	32.0359	1.99061
$260$	−7.15633	−0.443817
$261$	−10.8497	−0.671581
$262$	15.0550	0.930104
$263$	3.56640	0.219913	0.109957	−	0.993936i	$-0.464929\pi$
$263$	3.56640	0.219913	0.109957	+	0.993936i	$0.464929\pi$
$264$	6.08572	0.374550
$265$	7.59833	0.466761
$266$	8.13466	0.498768
$267$	−8.64908	−0.529315
$268$	−1.25808	−0.0768492
$269$	21.6252	1.31851	0.659256	−	0.751918i	$-0.270871\pi$
$269$	21.6252	1.31851	0.659256	+	0.751918i	$0.270871\pi$
$270$	−15.0032	−0.913068
$271$	−8.57790	−0.521070	−0.260535	−	0.965464i	$-0.583899\pi$
$271$	−8.57790	−0.521070	−0.260535	+	0.965464i	$0.583899\pi$
$272$	2.98410	0.180938
$273$	37.8722	2.29213
$274$	−17.0051	−1.02732
$275$	−13.6060	−0.820473
$276$	−0.715710	−0.0430807
$277$	−26.0331	−1.56418	−0.782088	−	0.623168i	$-0.785845\pi$
$277$	−26.0331	−1.56418	−0.782088	+	0.623168i	$0.785845\pi$
$278$	15.6259	0.937178
$279$	−17.2598	−1.03331
$280$	−61.4257	−3.67089
$281$	−12.2351	−0.729885	−0.364943	−	0.931030i	$-0.618911\pi$
$281$	−12.2351	−0.729885	−0.364943	+	0.931030i	$0.618911\pi$
$282$	19.3961	1.15502
$283$	−6.45587	−0.383762	−0.191881	−	0.981418i	$-0.561459\pi$
$283$	−6.45587	−0.383762	−0.191881	+	0.981418i	$0.561459\pi$
$284$	−3.13581	−0.186076
$285$	−13.9059	−0.823713
$286$	4.40264	0.260334
$287$	12.7655	0.753523
$288$	−4.13852	−0.243864
$289$	1.00000	0.0588235
$290$	34.2560	2.01158
$291$	−4.24483	−0.248836
$292$	0.769261	0.0450176
$293$	−21.8157	−1.27449	−0.637243	−	0.770663i	$-0.719925\pi$
$293$	−21.8157	−1.27449	−0.637243	+	0.770663i	$0.719925\pi$
$294$	37.1712	2.16787
$295$	4.45642	0.259463
$296$	−21.5053	−1.24997
$297$	−2.45227	−0.142295
$298$	15.0228	0.870250
$299$	−2.98440	−0.172592
$300$	13.6310	0.786987
$301$	−44.1303	−2.54363
$302$	−12.8912	−0.741806
$303$	−12.6185	−0.724914
$304$	−4.26160	−0.244419
$305$	66.0050	3.77944
$306$	2.23036	0.127501
$307$	1.58631	0.0905356	0.0452678	−	0.998975i	$-0.485586\pi$
$307$	1.58631	0.0905356	0.0452678	+	0.998975i	$0.485586\pi$
$308$	−1.74187	−0.0992521
$309$	−30.6404	−1.74307
$310$	54.4944	3.09508
$311$	−9.02296	−0.511645	−0.255822	−	0.966724i	$-0.582346\pi$
$311$	−9.02296	−0.511645	−0.255822	+	0.966724i	$0.582346\pi$
$312$	−25.4231	−1.43930
$313$	0.616626	0.0348538	0.0174269	−	0.999848i	$-0.494453\pi$
$313$	0.616626	0.0348538	0.0174269	+	0.999848i	$0.494453\pi$
$314$	12.7050	0.716986
$315$	−35.8291	−2.01874
$316$	−3.25627	−0.183179
$317$	17.6042	0.988748	0.494374	−	0.869249i	$-0.335397\pi$
$317$	17.6042	0.988748	0.494374	+	0.869249i	$0.335397\pi$
$318$	4.68316	0.262618
$319$	5.59911	0.313490
$320$	39.6634	2.21725
$321$	−5.15430	−0.287685
$322$	−4.44425	−0.247669
$323$	−1.42810	−0.0794616
$324$	4.69142	0.260634
$325$	56.8392	3.15287
$326$	−28.0018	−1.55088
$327$	−4.15574	−0.229813
$328$	−8.56931	−0.473161
$329$	−31.9990	−1.76416
$330$	−11.2076	−0.616960
$331$	27.2825	1.49958	0.749792	−	0.661674i	$-0.230154\pi$
$331$	27.2825	1.49958	0.749792	+	0.661674i	$0.230154\pi$
$332$	−3.91804	−0.215030
$333$	−12.5438	−0.687397
$334$	−21.6390	−1.18403
$335$	13.3545	0.729633
$336$	−29.5458	−1.61186
$337$	−1.78685	−0.0973358	−0.0486679	−	0.998815i	$-0.515498\pi$
$337$	−1.78685	−0.0973358	−0.0486679	+	0.998815i	$0.515498\pi$
$338$	−2.05041	−0.111528
$339$	−11.4756	−0.623269
$340$	1.87090	0.101464
$341$	8.90707	0.482345
$342$	−3.18517	−0.172234
$343$	−29.6041	−1.59847
$344$	29.6241	1.59723
$345$	7.59727	0.409023
$346$	−5.48441	−0.294843
$347$	0.439345	0.0235853	0.0117926	−	0.999930i	$-0.496246\pi$
$347$	0.439345	0.0235853	0.0117926	+	0.999930i	$0.496246\pi$
$348$	−5.60941	−0.300696
$349$	14.5872	0.780837	0.390419	−	0.920637i	$-0.372330\pi$
$349$	14.5872	0.780837	0.390419	+	0.920637i	$0.372330\pi$
$350$	84.6428	4.52435
$351$	10.2444	0.546804
$352$	2.13572	0.113834
$353$	8.40691	0.447455	0.223727	−	0.974652i	$-0.428177\pi$
$353$	8.40691	0.447455	0.223727	+	0.974652i	$0.428177\pi$
$354$	2.74667	0.145984
$355$	33.2867	1.76667
$356$	−1.66181	−0.0880758
$357$	−9.90106	−0.524020
$358$	20.6102	1.08928
$359$	−20.9214	−1.10419	−0.552095	−	0.833781i	$-0.686171\pi$
$359$	−20.9214	−1.10419	−0.552095	+	0.833781i	$0.686171\pi$
$360$	24.0516	1.26763
$361$	−16.9605	−0.892660
$362$	25.0300	1.31555
$363$	22.2033	1.16537
$364$	7.27667	0.381401
$365$	−8.16571	−0.427413
$366$	40.6816	2.12646
$367$	7.80272	0.407299	0.203649	−	0.979044i	$-0.434720\pi$
$367$	7.80272	0.407299	0.203649	+	0.979044i	$0.434720\pi$
$368$	2.32826	0.121369
$369$	−4.99840	−0.260206
$370$	39.6048	2.05895
$371$	−7.72609	−0.401119
$372$	−8.92345	−0.462659
$373$	1.47715	0.0764838	0.0382419	−	0.999269i	$-0.487824\pi$
$373$	1.47715	0.0764838	0.0382419	+	0.999269i	$0.487824\pi$
$374$	−1.15100	−0.0595167
$375$	−96.0068	−4.95777
$376$	21.4805	1.10777
$377$	−23.3903	−1.20466
$378$	15.2555	0.784659
$379$	10.3247	0.530347	0.265173	−	0.964201i	$-0.414571\pi$
$379$	10.3247	0.530347	0.265173	+	0.964201i	$0.414571\pi$
$380$	−2.67184	−0.137062
$381$	−20.8514	−1.06825
$382$	−23.0015	−1.17686
$383$	−19.9657	−1.02020	−0.510101	−	0.860115i	$-0.670392\pi$
$383$	−19.9657	−1.02020	−0.510101	+	0.860115i	$0.670392\pi$
$384$	14.2531	0.727348
$385$	18.4899	0.942334
$386$	−16.7705	−0.853594
$387$	17.2795	0.878365
$388$	−0.815590	−0.0414053
$389$	21.6096	1.09565	0.547825	−	0.836593i	$-0.315456\pi$
$389$	21.6096	1.09565	0.547825	+	0.836593i	$0.315456\pi$
$390$	46.8200	2.37082
$391$	0.780221	0.0394575
$392$	41.1657	2.07918
$393$	26.1688	1.32004
$394$	1.13914	0.0573890
$395$	34.5653	1.73917
$396$	0.682038	0.0342737
$397$	6.15682	0.309002	0.154501	−	0.987993i	$-0.450623\pi$
$397$	6.15682	0.309002	0.154501	+	0.987993i	$0.450623\pi$
$398$	−18.6299	−0.933831
$399$	14.1397	0.707870
$400$	−44.3428	−2.21714
$401$	−15.8075	−0.789388	−0.394694	−	0.918813i	$-0.629149\pi$
$401$	−15.8075	−0.789388	−0.394694	+	0.918813i	$0.629149\pi$
$402$	8.23091	0.410520
$403$	−37.2094	−1.85353
$404$	−2.42448	−0.120623
$405$	−49.7995	−2.47456
$406$	−34.8320	−1.72868
$407$	6.47336	0.320873
$408$	6.64646	0.329049
$409$	−4.38180	−0.216666	−0.108333	−	0.994115i	$-0.534551\pi$
$409$	−4.38180	−0.216666	−0.108333	+	0.994115i	$0.534551\pi$
$410$	15.7815	0.779393
$411$	−29.5584	−1.45801
$412$	−5.88716	−0.290039
$413$	−4.53135	−0.222973
$414$	1.74017	0.0855248
$415$	41.5900	2.04157
$416$	−8.92200	−0.437437
$417$	27.1610	1.33008
$418$	1.64374	0.0803979
$419$	−3.19791	−0.156228	−0.0781140	−	0.996944i	$-0.524890\pi$
$419$	−3.19791	−0.156228	−0.0781140	+	0.996944i	$0.524890\pi$
$420$	−18.5239	−0.903876
$421$	8.85004	0.431325	0.215662	−	0.976468i	$-0.430809\pi$
$421$	8.85004	0.431325	0.215662	+	0.976468i	$0.430809\pi$
$422$	−6.10469	−0.297171
$423$	12.5294	0.609199
$424$	5.18643	0.251875
$425$	−14.8597	−0.720800
$426$	20.5159	0.994001
$427$	−67.1149	−3.24792
$428$	−0.990334	−0.0478696
$429$	7.65269	0.369475
$430$	−54.5567	−2.63096
$431$	35.3494	1.70272	0.851361	−	0.524581i	$-0.175778\pi$
$431$	35.3494	1.70272	0.851361	+	0.524581i	$0.175778\pi$
$432$	−7.99209	−0.384519
$433$	−30.7434	−1.47743	−0.738717	−	0.674016i	$-0.764568\pi$
$433$	−30.7434	−1.47743	−0.738717	+	0.674016i	$0.764568\pi$
$434$	−55.4108	−2.65980
$435$	59.5439	2.85491
$436$	−0.798472	−0.0382399
$437$	−1.11423	−0.0533010
$438$	−5.03286	−0.240479
$439$	−5.20239	−0.248297	−0.124148	−	0.992264i	$-0.539620\pi$
$439$	−5.20239	−0.248297	−0.124148	+	0.992264i	$0.539620\pi$
$440$	−12.4121	−0.591722
$441$	24.0116	1.14341
$442$	4.80830	0.228708
$443$	−17.9098	−0.850921	−0.425461	−	0.904977i	$-0.639888\pi$
$443$	−17.9098	−0.850921	−0.425461	+	0.904977i	$0.639888\pi$
$444$	−6.48527	−0.307777
$445$	17.6401	0.836223
$446$	21.0123	0.994959
$447$	26.1128	1.23509
$448$	−40.3304	−1.90543
$449$	38.5662	1.82005	0.910026	−	0.414551i	$-0.136061\pi$
$449$	38.5662	1.82005	0.910026	+	0.414551i	$0.136061\pi$
$450$	−33.1424	−1.56235
$451$	2.57947	0.121463
$452$	−2.20489	−0.103709
$453$	−22.4076	−1.05280
$454$	18.2999	0.858857
$455$	−77.2419	−3.62116
$456$	−9.49180	−0.444494
$457$	8.44499	0.395040	0.197520	−	0.980299i	$-0.436711\pi$
$457$	8.44499	0.395040	0.197520	+	0.980299i	$0.436711\pi$
$458$	−26.2165	−1.22502
$459$	−2.67822	−0.125009
$460$	1.45972	0.0680598
$461$	−13.6096	−0.633861	−0.316930	−	0.948449i	$-0.602652\pi$
$461$	−13.6096	−0.633861	−0.316930	+	0.948449i	$0.602652\pi$
$462$	11.3961	0.530195
$463$	−19.4811	−0.905362	−0.452681	−	0.891672i	$-0.649532\pi$
$463$	−19.4811	−0.905362	−0.452681	+	0.891672i	$0.649532\pi$
$464$	18.2478	0.847135
$465$	94.7225	4.39265
$466$	−29.6737	−1.37461
$467$	−36.3117	−1.68031	−0.840153	−	0.542349i	$-0.817535\pi$
$467$	−36.3117	−1.68031	−0.840153	+	0.542349i	$0.817535\pi$
$468$	−2.84922	−0.131705
$469$	−13.5790	−0.627022
$470$	−39.5591	−1.82473
$471$	22.0839	1.01757
$472$	3.04184	0.140012
$473$	−8.91725	−0.410015
$474$	21.3040	0.978525
$475$	21.2211	0.973690
$476$	−1.90236	−0.0871947
$477$	3.02520	0.138514
$478$	13.9967	0.640196
$479$	38.4537	1.75699	0.878497	−	0.477748i	$-0.158547\pi$
$479$	38.4537	1.75699	0.878497	+	0.477748i	$0.158547\pi$
$480$	22.7124	1.03667
$481$	−27.0425	−1.23303
$482$	15.9887	0.728266
$483$	−7.72502	−0.351501
$484$	4.26607	0.193912
$485$	8.65749	0.393117
$486$	−20.5935	−0.934138
$487$	17.3060	0.784209	0.392105	−	0.919921i	$-0.371747\pi$
$487$	17.3060	0.784209	0.392105	+	0.919921i	$0.371747\pi$
$488$	45.0534	2.03947
$489$	−48.6729	−2.20107
$490$	−75.8121	−3.42484
$491$	−2.36353	−0.106665	−0.0533323	−	0.998577i	$-0.516984\pi$
$491$	−2.36353	−0.106665	−0.0533323	+	0.998577i	$0.516984\pi$
$492$	−2.58422	−0.116505
$493$	6.11501	0.275406
$494$	−6.86673	−0.308949
$495$	−7.23984	−0.325407
$496$	29.0287	1.30343
$497$	−33.8464	−1.51822
$498$	25.6336	1.14867
$499$	8.29098	0.371155	0.185578	−	0.982630i	$-0.440584\pi$
$499$	8.29098	0.371155	0.185578	+	0.982630i	$0.440584\pi$
$500$	−18.4465	−0.824952
$501$	−37.6130	−1.68043
$502$	12.6982	0.566748
$503$	−22.4476	−1.00089	−0.500444	−	0.865769i	$-0.666830\pi$
$503$	−22.4476	−1.00089	−0.500444	+	0.865769i	$0.666830\pi$
$504$	−24.4560	−1.08936
$505$	25.7359	1.14523
$506$	−0.898033	−0.0399224
$507$	−3.56404	−0.158285
$508$	−4.00634	−0.177752
$509$	−12.4653	−0.552513	−0.276256	−	0.961084i	$-0.589094\pi$
$509$	−12.4653	−0.552513	−0.276256	+	0.961084i	$0.589094\pi$
$510$	−12.2403	−0.542010
$511$	8.30302	0.367304
$512$	25.1148	1.10993
$513$	3.82476	0.168867
$514$	−17.5361	−0.773483
$515$	62.4922	2.75374
$516$	8.93365	0.393282
$517$	−6.46591	−0.284370
$518$	−40.2707	−1.76939
$519$	−9.53302	−0.418453
$520$	51.8515	2.27384
$521$	−9.25287	−0.405376	−0.202688	−	0.979243i	$-0.564968\pi$
$521$	−9.25287	−0.405376	−0.202688	+	0.979243i	$0.564968\pi$
$522$	13.6387	0.596948
$523$	−19.9599	−0.872784	−0.436392	−	0.899757i	$-0.643744\pi$
$523$	−19.9599	−0.872784	−0.436392	+	0.899757i	$0.643744\pi$
$524$	5.02799	0.219649
$525$	147.126	6.42113
$526$	−4.48314	−0.195474
$527$	9.72777	0.423748
$528$	−5.97021	−0.259820
$529$	−22.3913	−0.973533
$530$	−9.55148	−0.414890
$531$	1.77428	0.0769971
$532$	2.71676	0.117787
$533$	−10.7758	−0.466751
$534$	10.8723	0.470492
$535$	10.5124	0.454491
$536$	9.11544	0.393727
$537$	35.8247	1.54595
$538$	−27.1840	−1.17199
$539$	−12.3914	−0.533736
$540$	−5.01069	−0.215626
$541$	−29.7993	−1.28117	−0.640586	−	0.767886i	$-0.721309\pi$
$541$	−29.7993	−1.28117	−0.640586	+	0.767886i	$0.721309\pi$
$542$	10.7829	0.463163
$543$	43.5072	1.86707
$544$	2.33251	0.100006
$545$	8.47579	0.363063
$546$	−47.6073	−2.03741
$547$	18.3989	0.786680	0.393340	−	0.919393i	$-0.371320\pi$
$547$	18.3989	0.786680	0.393340	+	0.919393i	$0.371320\pi$
$548$	−5.67928	−0.242607
$549$	26.2792	1.12157
$550$	17.1034	0.729293
$551$	−8.73285	−0.372032
$552$	5.18571	0.220718
$553$	−35.1465	−1.49458
$554$	32.7249	1.39035
$555$	68.8412	2.92215
$556$	5.21864	0.221319
$557$	21.2525	0.900495	0.450248	−	0.892904i	$-0.351336\pi$
$557$	21.2525	0.900495	0.450248	+	0.892904i	$0.351336\pi$
$558$	21.6964	0.918482
$559$	37.2519	1.57559
$560$	60.2598	2.54644
$561$	−2.00067	−0.0844683
$562$	15.3802	0.648773
$563$	13.0274	0.549040	0.274520	−	0.961581i	$-0.411481\pi$
$563$	13.0274	0.549040	0.274520	+	0.961581i	$0.411481\pi$
$564$	6.47780	0.272764
$565$	23.4050	0.984654
$566$	8.11536	0.341114
$567$	50.6369	2.12655
$568$	22.7207	0.953338
$569$	21.5266	0.902442	0.451221	−	0.892412i	$-0.350989\pi$
$569$	21.5266	0.902442	0.451221	+	0.892412i	$0.350989\pi$
$570$	17.4804	0.732173
$571$	4.87105	0.203847	0.101924	−	0.994792i	$-0.467500\pi$
$571$	4.87105	0.203847	0.101924	+	0.994792i	$0.467500\pi$
$572$	1.47037	0.0614792
$573$	−39.9812	−1.67024
$574$	−16.0469	−0.669784
$575$	−11.5938	−0.483496
$576$	15.7916	0.657983
$577$	2.24315	0.0933834	0.0466917	−	0.998909i	$-0.485132\pi$
$577$	2.24315	0.0933834	0.0466917	+	0.998909i	$0.485132\pi$
$578$	−1.25705	−0.0522864
$579$	−29.1505	−1.21145
$580$	11.4406	0.475045
$581$	−42.2893	−1.75446
$582$	5.33597	0.221183
$583$	−1.56118	−0.0646575
$584$	−5.57371	−0.230642
$585$	30.2445	1.25046
$586$	27.4234	1.13285
$587$	37.3695	1.54240	0.771202	−	0.636591i	$-0.219656\pi$
$587$	37.3695	1.54240	0.771202	+	0.636591i	$0.219656\pi$
$588$	12.4142	0.511953
$589$	−13.8922	−0.572419
$590$	−5.60195	−0.230628
$591$	1.98006	0.0814487
$592$	21.0971	0.867085
$593$	6.07955	0.249657	0.124829	−	0.992178i	$-0.460162\pi$
$593$	6.07955	0.249657	0.124829	+	0.992178i	$0.460162\pi$
$594$	3.08262	0.126482
$595$	20.1936	0.827857
$596$	5.01724	0.205514
$597$	−32.3825	−1.32533
$598$	3.75154	0.153412
$599$	−10.4221	−0.425834	−0.212917	−	0.977070i	$-0.568296\pi$
$599$	−10.4221	−0.425834	−0.212917	+	0.977070i	$0.568296\pi$
$600$	−98.7641	−4.03203
$601$	4.18206	0.170590	0.0852950	−	0.996356i	$-0.472817\pi$
$601$	4.18206	0.170590	0.0852950	+	0.996356i	$0.472817\pi$
$602$	55.4741	2.26096
$603$	5.31695	0.216523
$604$	−4.30533	−0.175181
$605$	−45.2844	−1.84107
$606$	15.8621	0.644353
$607$	1.59804	0.0648625	0.0324312	−	0.999474i	$-0.489675\pi$
$607$	1.59804	0.0648625	0.0324312	+	0.999474i	$0.489675\pi$
$608$	−3.33105	−0.135092
$609$	−60.5451	−2.45341
$610$	−82.9717	−3.35943
$611$	27.0114	1.09276
$612$	0.744881	0.0301100
$613$	−30.7692	−1.24276	−0.621378	−	0.783511i	$-0.713427\pi$
$613$	−30.7692	−1.24276	−0.621378	+	0.783511i	$0.713427\pi$
$614$	−1.99407	−0.0804743
$615$	27.4315	1.10614
$616$	12.6208	0.508505
$617$	26.7629	1.07743	0.538717	−	0.842487i	$-0.318909\pi$
$617$	26.7629	1.07743	0.538717	+	0.842487i	$0.318909\pi$
$618$	38.5165	1.54936
$619$	−45.7589	−1.83920	−0.919602	−	0.392852i	$-0.871489\pi$
$619$	−45.7589	−1.83920	−0.919602	+	0.392852i	$0.871489\pi$
$620$	18.1997	0.730918
$621$	−2.08960	−0.0838529
$622$	11.3423	0.454786
$623$	−17.9368	−0.718622
$624$	24.9406	0.998423
$625$	121.511	4.86045
$626$	−0.775131	−0.0309805
$627$	2.85715	0.114104
$628$	4.24315	0.169320
$629$	7.06982	0.281892
$630$	45.0390	1.79440
$631$	5.03387	0.200395	0.100198	−	0.994968i	$-0.468052\pi$
$631$	5.03387	0.200395	0.100198	+	0.994968i	$0.468052\pi$
$632$	23.5934	0.938495
$633$	−10.6112	−0.421757
$634$	−22.1293	−0.878868
$635$	42.5273	1.68764
$636$	1.56405	0.0620187
$637$	51.7653	2.05101
$638$	−7.03837	−0.278652
$639$	13.2528	0.524271
$640$	−29.0697	−1.14908
$641$	−26.4135	−1.04327	−0.521636	−	0.853168i	$-0.674678\pi$
$641$	−26.4135	−1.04327	−0.521636	+	0.853168i	$0.674678\pi$
$642$	6.47922	0.255714
$643$	−3.19059	−0.125824	−0.0629122	−	0.998019i	$-0.520039\pi$
$643$	−3.19059	−0.125824	−0.0629122	+	0.998019i	$0.520039\pi$
$644$	−1.48427	−0.0584882
$645$	−94.8307	−3.73396
$646$	1.79519	0.0706309
$647$	40.4945	1.59200	0.796001	−	0.605295i	$-0.206945\pi$
$647$	40.4945	1.59200	0.796001	+	0.605295i	$0.206945\pi$
$648$	−33.9919	−1.33533
$649$	−0.915633	−0.0359417
$650$	−71.4498	−2.80249
$651$	−96.3152	−3.77489
$652$	−9.35189	−0.366248
$653$	48.5753	1.90090	0.950450	−	0.310878i	$-0.100623\pi$
$653$	48.5753	1.90090	0.950450	+	0.310878i	$0.100623\pi$
$654$	5.22397	0.204274
$655$	−53.3722	−2.08542
$656$	8.40666	0.328225
$657$	−3.25109	−0.126837
$658$	40.2243	1.56811
$659$	−16.4749	−0.641772	−0.320886	−	0.947118i	$-0.603981\pi$
$659$	−16.4749	−0.641772	−0.320886	+	0.947118i	$0.603981\pi$
$660$	−3.74306	−0.145698
$661$	−21.2671	−0.827194	−0.413597	−	0.910460i	$-0.635728\pi$
$661$	−21.2671	−0.827194	−0.413597	+	0.910460i	$0.635728\pi$
$662$	−34.2955	−1.33293
$663$	8.35781	0.324591
$664$	28.3883	1.10168
$665$	−28.8385	−1.11831
$666$	15.7682	0.611007
$667$	4.77107	0.184736
$668$	−7.22687	−0.279616
$669$	36.5236	1.41208
$670$	−16.7873	−0.648549
$671$	−13.5616	−0.523542
$672$	−23.0943	−0.890883
$673$	−17.8915	−0.689667	−0.344834	−	0.938664i	$-0.612065\pi$
$673$	−17.8915	−0.689667	−0.344834	+	0.938664i	$0.612065\pi$
$674$	2.24616	0.0865188
$675$	39.7974	1.53180
$676$	−0.684785	−0.0263379
$677$	−24.3752	−0.936814	−0.468407	−	0.883513i	$-0.655172\pi$
$677$	−24.3752	−0.936814	−0.468407	+	0.883513i	$0.655172\pi$
$678$	14.4254	0.554005
$679$	−8.80307	−0.337831
$680$	−13.5557	−0.519838
$681$	31.8090	1.21892
$682$	−11.1966	−0.428741
$683$	−34.5389	−1.32159	−0.660797	−	0.750565i	$-0.729782\pi$
$683$	−34.5389	−1.32159	−0.660797	+	0.750565i	$0.729782\pi$
$684$	−1.06376	−0.0406740
$685$	60.2856	2.30339
$686$	37.2139	1.42083
$687$	−45.5696	−1.73859
$688$	−29.0619	−1.10797
$689$	6.52185	0.248463
$690$	−9.55016	−0.363568
$691$	41.0129	1.56020	0.780102	−	0.625653i	$-0.215167\pi$
$691$	41.0129	1.56020	0.780102	+	0.625653i	$0.215167\pi$
$692$	−1.83165	−0.0696288
$693$	7.36158	0.279643
$694$	−0.552279	−0.0209642
$695$	−55.3959	−2.10128
$696$	40.6432	1.54058
$697$	2.81715	0.106707
$698$	−18.3369	−0.694063
$699$	−51.5789	−1.95089
$700$	28.2685	1.06845
$701$	−2.15107	−0.0812447	−0.0406223	−	0.999175i	$-0.512934\pi$
$701$	−2.15107	−0.0812447	−0.0406223	+	0.999175i	$0.512934\pi$
$702$	−12.8777	−0.486037
$703$	−10.0964	−0.380793
$704$	−8.14940	−0.307142
$705$	−68.7619	−2.58972
$706$	−10.5679	−0.397729
$707$	−26.1687	−0.984174
$708$	0.917317	0.0344749
$709$	24.6682	0.926432	0.463216	−	0.886245i	$-0.346695\pi$
$709$	24.6682	0.926432	0.463216	+	0.886245i	$0.346695\pi$
$710$	−41.8431	−1.57034
$711$	13.7618	0.516108
$712$	12.0407	0.451245
$713$	7.58981	0.284241
$714$	12.4461	0.465785
$715$	−15.6080	−0.583705
$716$	6.88327	0.257240
$717$	24.3292	0.908590
$718$	26.2993	0.981481
$719$	−20.1625	−0.751934	−0.375967	−	0.926633i	$-0.622689\pi$
$719$	−20.1625	−0.751934	−0.375967	+	0.926633i	$0.622689\pi$
$720$	−23.5951	−0.879337
$721$	−63.5430	−2.36647
$722$	21.3203	0.793458
$723$	27.7917	1.03358
$724$	8.35937	0.310673
$725$	−90.8671	−3.37472
$726$	−27.9106	−1.03586
$727$	33.7430	1.25146	0.625729	−	0.780040i	$-0.284801\pi$
$727$	33.7430	1.25146	0.625729	+	0.780040i	$0.284801\pi$
$728$	−52.7234	−1.95406
$729$	−2.27132	−0.0841230
$730$	10.2647	0.379914
$731$	−9.73889	−0.360206
$732$	13.5866	0.502175
$733$	14.3378	0.529578	0.264789	−	0.964306i	$-0.414698\pi$
$733$	14.3378	0.529578	0.264789	+	0.964306i	$0.414698\pi$
$734$	−9.80842	−0.362035
$735$	−131.777	−4.86066
$736$	1.81987	0.0670814
$737$	−2.74386	−0.101072
$738$	6.28324	0.231289
$739$	4.08134	0.150135	0.0750673	−	0.997178i	$-0.476083\pi$
$739$	4.08134	0.150135	0.0750673	+	0.997178i	$0.476083\pi$
$740$	13.2270	0.486233
$741$	−11.9358	−0.438472
$742$	9.71209	0.356542
$743$	−16.7348	−0.613942	−0.306971	−	0.951719i	$-0.599315\pi$
$743$	−16.7348	−0.613942	−0.306971	+	0.951719i	$0.599315\pi$
$744$	64.6552	2.37037
$745$	−53.2581	−1.95122
$746$	−1.85685	−0.0679841
$747$	16.5586	0.605848
$748$	−0.384403	−0.0140552
$749$	−10.6892	−0.390574
$750$	120.685	4.40681
$751$	−8.97244	−0.327409	−0.163704	−	0.986509i	$-0.552344\pi$
$751$	−8.97244	−0.327409	−0.163704	+	0.986509i	$0.552344\pi$
$752$	−21.0728	−0.768445
$753$	22.0720	0.804350
$754$	29.4028	1.07079
$755$	45.7011	1.66323
$756$	5.09495	0.185301
$757$	−7.60113	−0.276268	−0.138134	−	0.990414i	$-0.544110\pi$
$757$	−7.60113	−0.276268	−0.138134	+	0.990414i	$0.544110\pi$
$758$	−12.9787	−0.471409
$759$	−1.56097	−0.0566594
$760$	19.3589	0.702221
$761$	−13.8835	−0.503278	−0.251639	−	0.967821i	$-0.580970\pi$
$761$	−13.8835	−0.503278	−0.251639	+	0.967821i	$0.580970\pi$
$762$	26.2113	0.949536
$763$	−8.61831	−0.312004
$764$	−7.68189	−0.277921
$765$	−7.90692	−0.285875
$766$	25.0979	0.906826
$767$	3.82507	0.138115
$768$	20.9777	0.756966
$769$	34.5879	1.24727	0.623635	−	0.781716i	$-0.285655\pi$
$769$	34.5879	1.24727	0.623635	+	0.781716i	$0.285655\pi$
$770$	−23.2428	−0.837612
$771$	−30.4813	−1.09776
$772$	−5.60090	−0.201581
$773$	43.8665	1.57777	0.788885	−	0.614541i	$-0.210659\pi$
$773$	43.8665	1.57777	0.788885	+	0.614541i	$0.210659\pi$
$774$	−21.7212	−0.780752
$775$	−144.551	−5.19244
$776$	5.90939	0.212135
$777$	−69.9988	−2.51119
$778$	−27.1644	−0.973889
$779$	−4.02317	−0.144145
$780$	15.6367	0.559883
$781$	−6.83921	−0.244726
$782$	−0.980778	−0.0350726
$783$	−16.3773	−0.585279
$784$	−40.3844	−1.44230
$785$	−45.0411	−1.60758
$786$	−32.8955	−1.17334
$787$	10.9701	0.391043	0.195521	−	0.980699i	$-0.437360\pi$
$787$	10.9701	0.391043	0.195521	+	0.980699i	$0.437360\pi$
$788$	0.380443	0.0135527
$789$	−7.79262	−0.277425
$790$	−43.4503	−1.54589
$791$	−23.7985	−0.846178
$792$	−4.94173	−0.175597
$793$	56.6539	2.01184
$794$	−7.73944	−0.274663
$795$	−16.6024	−0.588828
$796$	−6.22189	−0.220529
$797$	11.6171	0.411497	0.205749	−	0.978605i	$-0.434037\pi$
$797$	11.6171	0.411497	0.205749	+	0.978605i	$0.434037\pi$
$798$	−17.7743	−0.629204
$799$	−7.06168	−0.249824
$800$	−34.6603	−1.22543
$801$	7.02324	0.248154
$802$	19.8708	0.701663
$803$	1.67776	0.0592068
$804$	2.74891	0.0969466
$805$	15.7555	0.555308
$806$	46.7741	1.64755
$807$	−47.2513	−1.66333
$808$	17.5667	0.617994
$809$	−35.7901	−1.25831	−0.629157	−	0.777278i	$-0.716600\pi$
$809$	−35.7901	−1.25831	−0.629157	+	0.777278i	$0.716600\pi$
$810$	62.6005	2.19956
$811$	−21.2327	−0.745579	−0.372790	−	0.927916i	$-0.621599\pi$
$811$	−21.2327	−0.745579	−0.372790	+	0.927916i	$0.621599\pi$
$812$	−11.6330	−0.408238
$813$	18.7428	0.657339
$814$	−8.13735	−0.285214
$815$	99.2703	3.47729
$816$	−6.52030	−0.228256
$817$	13.9081	0.486583
$818$	5.50815	0.192588
$819$	−30.7531	−1.07460
$820$	5.27061	0.184058
$821$	−5.33728	−0.186272	−0.0931361	−	0.995653i	$-0.529689\pi$
$821$	−5.33728	−0.186272	−0.0931361	+	0.995653i	$0.529689\pi$
$822$	37.1565	1.29598
$823$	14.1101	0.491847	0.245923	−	0.969289i	$-0.420909\pi$
$823$	14.1101	0.491847	0.245923	+	0.969289i	$0.420909\pi$
$824$	42.6556	1.48598
$825$	29.7293	1.03504
$826$	5.69614	0.198194
$827$	5.91929	0.205834	0.102917	−	0.994690i	$-0.467182\pi$
$827$	5.91929	0.205834	0.102917	+	0.994690i	$0.467182\pi$
$828$	0.581172	0.0201971
$829$	−54.1187	−1.87962	−0.939810	−	0.341698i	$-0.888998\pi$
$829$	−54.1187	−1.87962	−0.939810	+	0.341698i	$0.888998\pi$
$830$	−52.2807	−1.81469
$831$	56.8826	1.97323
$832$	34.0442	1.18027
$833$	−13.5332	−0.468897
$834$	−34.1427	−1.18227
$835$	76.7133	2.65477
$836$	0.548966	0.0189864
$837$	−26.0531	−0.900527
$838$	4.01993	0.138866
$839$	17.1688	0.592733	0.296367	−	0.955074i	$-0.404225\pi$
$839$	17.1688	0.592733	0.296367	+	0.955074i	$0.404225\pi$
$840$	134.216	4.63089
$841$	8.39340	0.289428
$842$	−11.1250	−0.383391
$843$	26.7339	0.920763
$844$	−2.03881	−0.0701786
$845$	7.26900	0.250061
$846$	−15.7501	−0.541498
$847$	46.0459	1.58216
$848$	−5.08799	−0.174722
$849$	14.1062	0.484122
$850$	18.6794	0.640697
$851$	5.51603	0.189087
$852$	6.85179	0.234738
$853$	17.4231	0.596557	0.298278	−	0.954479i	$-0.403588\pi$
$853$	17.4231	0.596557	0.298278	+	0.954479i	$0.403588\pi$
$854$	84.3669	2.88698
$855$	11.2919	0.386174
$856$	7.17550	0.245254
$857$	−39.2747	−1.34160	−0.670799	−	0.741640i	$-0.734048\pi$
$857$	−39.2747	−1.34160	−0.670799	+	0.741640i	$0.734048\pi$
$858$	−9.61983	−0.328415
$859$	7.34581	0.250636	0.125318	−	0.992117i	$-0.460005\pi$
$859$	7.34581	0.250636	0.125318	+	0.992117i	$0.460005\pi$
$860$	−18.2205	−0.621315
$861$	−27.8928	−0.950582
$862$	−44.4360	−1.51350
$863$	−17.3522	−0.590674	−0.295337	−	0.955393i	$-0.595432\pi$
$863$	−17.3522	−0.590674	−0.295337	+	0.955393i	$0.595432\pi$
$864$	−6.24697	−0.212526
$865$	19.4430	0.661081
$866$	38.6460	1.31325
$867$	−2.18501	−0.0742069
$868$	−18.5058	−0.628126
$869$	−7.10192	−0.240916
$870$	−74.8497	−2.53764
$871$	11.4625	0.388393
$872$	5.78536	0.195917
$873$	3.44689	0.116660
$874$	1.40065	0.0473776
$875$	−199.102	−6.73088
$876$	−1.68084	−0.0567904
$877$	6.31142	0.213122	0.106561	−	0.994306i	$-0.466016\pi$
$877$	6.31142	0.213122	0.106561	+	0.994306i	$0.466016\pi$
$878$	6.53967	0.220703
$879$	47.6675	1.60779
$880$	12.1765	0.410469
$881$	27.3067	0.919984	0.459992	−	0.887923i	$-0.347852\pi$
$881$	27.3067	0.919984	0.459992	+	0.887923i	$0.347852\pi$
$882$	−30.1838	−1.01634
$883$	49.8529	1.67768	0.838841	−	0.544376i	$-0.183234\pi$
$883$	49.8529	1.67768	0.838841	+	0.544376i	$0.183234\pi$
$884$	1.60585	0.0540105
$885$	−9.73733	−0.327317
$886$	22.5136	0.756358
$887$	−46.1086	−1.54817	−0.774087	−	0.633079i	$-0.781791\pi$
$887$	−46.1086	−1.54817	−0.774087	+	0.633079i	$0.781791\pi$
$888$	46.9893	1.57686
$889$	−43.2424	−1.45030
$890$	−22.1746	−0.743293
$891$	10.2320	0.342785
$892$	7.01755	0.234965
$893$	10.0848	0.337474
$894$	−32.8251	−1.09784
$895$	−73.0660	−2.44233
$896$	29.5585	0.987480
$897$	6.52095	0.217728
$898$	−48.4797	−1.61779
$899$	59.4854	1.98395
$900$	−11.0687	−0.368956
$901$	−1.70503	−0.0568028
$902$	−3.24253	−0.107964
$903$	96.4253	3.20883
$904$	15.9756	0.531342
$905$	−88.7347	−2.94964
$906$	28.1674	0.935801
$907$	−13.1428	−0.436398	−0.218199	−	0.975904i	$-0.570018\pi$
$907$	−13.1428	−0.436398	−0.218199	+	0.975904i	$0.570018\pi$
$908$	6.11169	0.202824
$909$	10.2465	0.339855
$910$	97.0970	3.21873
$911$	38.8024	1.28558	0.642791	−	0.766042i	$-0.277776\pi$
$911$	38.8024	1.28558	0.642791	+	0.766042i	$0.277776\pi$
$912$	9.31164	0.308339
$913$	−8.54524	−0.282806
$914$	−10.6158	−0.351139
$915$	−144.222	−4.76782
$916$	−8.75563	−0.289294
$917$	54.2697	1.79214
$918$	3.36666	0.111116
$919$	−10.4101	−0.343398	−0.171699	−	0.985149i	$-0.554926\pi$
$919$	−10.4101	−0.343398	−0.171699	+	0.985149i	$0.554926\pi$
$920$	−10.5765	−0.348696
$921$	−3.46611	−0.114212
$922$	17.1079	0.563419
$923$	28.5709	0.940422
$924$	3.80600	0.125208
$925$	−105.055	−3.45419
$926$	24.4887	0.804749
$927$	24.8806	0.817187
$928$	14.2633	0.468217
$929$	19.4214	0.637196	0.318598	−	0.947890i	$-0.396788\pi$
$929$	19.4214	0.637196	0.318598	+	0.947890i	$0.396788\pi$
$930$	−119.071	−3.90449
$931$	19.3267	0.633407
$932$	−9.91024	−0.324621
$933$	19.7153	0.645449
$934$	45.6457	1.49357
$935$	4.08044	0.133445
$936$	20.6441	0.674775
$937$	−13.1185	−0.428562	−0.214281	−	0.976772i	$-0.568741\pi$
$937$	−13.1185	−0.428562	−0.214281	+	0.976772i	$0.568741\pi$
$938$	17.0695	0.557340
$939$	−1.34734	−0.0439686
$940$	−13.2117	−0.430919
$941$	−29.4917	−0.961402	−0.480701	−	0.876885i	$-0.659618\pi$
$941$	−29.4917	−0.961402	−0.480701	+	0.876885i	$0.659618\pi$
$942$	−27.7606	−0.904490
$943$	2.19800	0.0715767
$944$	−2.98410	−0.0971243
$945$	−54.0829	−1.75932
$946$	11.2094	0.364450
$947$	−38.8262	−1.26168	−0.630840	−	0.775913i	$-0.717290\pi$
$947$	−38.8262	−1.26168	−0.630840	+	0.775913i	$0.717290\pi$
$948$	7.11498	0.231084
$949$	−7.00885	−0.227517
$950$	−26.6760	−0.865483
$951$	−38.4653	−1.24732
$952$	13.7837	0.446731
$953$	−11.2221	−0.363518	−0.181759	−	0.983343i	$-0.558179\pi$
$953$	−11.2221	−0.363518	−0.181759	+	0.983343i	$0.558179\pi$
$954$	−3.80282	−0.123121
$955$	81.5433	2.63868
$956$	4.67455	0.151186
$957$	−12.2341	−0.395473
$958$	−48.3382	−1.56174
$959$	−61.2993	−1.97946
$960$	−86.6651	−2.79710
$961$	63.6295	2.05256
$962$	33.9939	1.09601
$963$	4.18540	0.134873
$964$	5.33982	0.171984
$965$	59.4536	1.91388
$966$	9.71075	0.312438
$967$	−52.2615	−1.68062	−0.840309	−	0.542108i	$-0.817626\pi$
$967$	−52.2615	−1.68062	−0.840309	+	0.542108i	$0.817626\pi$
$968$	−30.9100	−0.993486
$969$	3.12041	0.100242
$970$	−10.8829	−0.349429
$971$	4.69164	0.150562	0.0752809	−	0.997162i	$-0.476015\pi$
$971$	4.69164	0.150562	0.0752809	+	0.997162i	$0.476015\pi$
$972$	−6.87768	−0.220602
$973$	56.3274	1.80577
$974$	−21.7545	−0.697060
$975$	−124.194	−3.97740
$976$	−44.1982	−1.41475
$977$	13.7183	0.438889	0.219444	−	0.975625i	$-0.429576\pi$
$977$	13.7183	0.438889	0.219444	+	0.975625i	$0.429576\pi$
$978$	61.1843	1.95646
$979$	−3.62441	−0.115837
$980$	−25.3193	−0.808794
$981$	3.37455	0.107741
$982$	2.97108	0.0948109
$983$	21.6358	0.690073	0.345037	−	0.938589i	$-0.387866\pi$
$983$	21.6358	0.690073	0.345037	+	0.938589i	$0.387866\pi$
$984$	18.7241	0.596901
$985$	−4.03841	−0.128674
$986$	−7.68689	−0.244800
$987$	69.9181	2.22552
$988$	−2.29331	−0.0729599
$989$	−7.59849	−0.241618
$990$	9.10085	0.289244
$991$	−33.7420	−1.07185	−0.535925	−	0.844265i	$-0.680037\pi$
$991$	−33.7420	−1.07185	−0.535925	+	0.844265i	$0.680037\pi$
$992$	22.6901	0.720412
$993$	−59.6127	−1.89175
$994$	42.5467	1.34950
$995$	66.0455	2.09378
$996$	8.56096	0.271264
$997$	−2.33928	−0.0740858	−0.0370429	−	0.999314i	$-0.511794\pi$
$997$	−2.33928	−0.0740858	−0.0370429	+	0.999314i	$0.511794\pi$
$998$	−10.4222	−0.329908
$999$	−18.9345	−0.599062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.j.1.7	✓	22
3.2	odd	2		9027.2.a.s.1.16		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.j.1.7	✓	22	1.1	even	1	trivial
9027.2.a.s.1.16		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)

\(f(q)\)	\(=\)	\(q-1.25705 q^{2} -2.18501 q^{3} -0.419822 q^{4} +4.45642 q^{5} +2.74667 q^{6} -4.53135 q^{7} +3.04184 q^{8} +1.77428 q^{9} +O(q^{10})\)	\(q-1.25705 q^{2} -2.18501 q^{3} -0.419822 q^{4} +4.45642 q^{5} +2.74667 q^{6} -4.53135 q^{7} +3.04184 q^{8} +1.77428 q^{9} -5.60195 q^{10} -0.915633 q^{11} +0.917317 q^{12} +3.82507 q^{13} +5.69614 q^{14} -9.73733 q^{15} -2.98410 q^{16} -1.00000 q^{17} -2.23036 q^{18} +1.42810 q^{19} -1.87090 q^{20} +9.90106 q^{21} +1.15100 q^{22} -0.780221 q^{23} -6.64646 q^{24} +14.8597 q^{25} -4.80830 q^{26} +2.67822 q^{27} +1.90236 q^{28} -6.11501 q^{29} +12.2403 q^{30} -9.72777 q^{31} -2.33251 q^{32} +2.00067 q^{33} +1.25705 q^{34} -20.1936 q^{35} -0.744881 q^{36} -7.06982 q^{37} -1.79519 q^{38} -8.35781 q^{39} +13.5557 q^{40} -2.81715 q^{41} -12.4461 q^{42} +9.73889 q^{43} +0.384403 q^{44} +7.90692 q^{45} +0.980778 q^{46} +7.06168 q^{47} +6.52030 q^{48} +13.5332 q^{49} -18.6794 q^{50} +2.18501 q^{51} -1.60585 q^{52} +1.70503 q^{53} -3.36666 q^{54} -4.08044 q^{55} -13.7837 q^{56} -3.12041 q^{57} +7.68689 q^{58} +1.00000 q^{59} +4.08795 q^{60} +14.8112 q^{61} +12.2283 q^{62} -8.03988 q^{63} +8.90029 q^{64} +17.0461 q^{65} -2.51494 q^{66} +2.99668 q^{67} +0.419822 q^{68} +1.70479 q^{69} +25.3844 q^{70} +7.46938 q^{71} +5.39707 q^{72} -1.83235 q^{73} +8.88713 q^{74} -32.4685 q^{75} -0.599548 q^{76} +4.14906 q^{77} +10.5062 q^{78} +7.75629 q^{79} -13.2984 q^{80} -11.1748 q^{81} +3.54130 q^{82} +9.33260 q^{83} -4.15669 q^{84} -4.45642 q^{85} -12.2423 q^{86} +13.3614 q^{87} -2.78521 q^{88} +3.95837 q^{89} -9.93940 q^{90} -17.3327 q^{91} +0.327554 q^{92} +21.2553 q^{93} -8.87689 q^{94} +6.36421 q^{95} +5.09656 q^{96} +1.94270 q^{97} -17.0119 q^{98} -1.62459 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 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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