LMFDB - Embedded newform 1003.2.a.j.1.6

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			1.6
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)

$f(q)$	$=$	$q-1.37758 q^{2} -3.34566 q^{3} -0.102265 q^{4} +1.06817 q^{5} +4.60892 q^{6} +2.01707 q^{7} +2.89604 q^{8} +8.19343 q^{9} +O(q^{10})$	\(q-1.37758 q^{2} -3.34566 q^{3} -0.102265 q^{4} +1.06817 q^{5} +4.60892 q^{6} +2.01707 q^{7} +2.89604 q^{8} +8.19343 q^{9} -1.47150 q^{10} +1.21416 q^{11} +0.342144 q^{12} +4.08405 q^{13} -2.77868 q^{14} -3.57374 q^{15} -3.78501 q^{16} -1.00000 q^{17} -11.2871 q^{18} -1.74121 q^{19} -0.109237 q^{20} -6.74843 q^{21} -1.67261 q^{22} +2.71871 q^{23} -9.68918 q^{24} -3.85901 q^{25} -5.62612 q^{26} -17.3755 q^{27} -0.206276 q^{28} +4.57485 q^{29} +4.92313 q^{30} +3.58107 q^{31} -0.577922 q^{32} -4.06217 q^{33} +1.37758 q^{34} +2.15458 q^{35} -0.837902 q^{36} +10.6872 q^{37} +2.39865 q^{38} -13.6639 q^{39} +3.09348 q^{40} -4.15825 q^{41} +9.29652 q^{42} -3.22538 q^{43} -0.124166 q^{44} +8.75200 q^{45} -3.74525 q^{46} +5.45506 q^{47} +12.6634 q^{48} -2.93143 q^{49} +5.31610 q^{50} +3.34566 q^{51} -0.417656 q^{52} +5.09517 q^{53} +23.9361 q^{54} +1.29693 q^{55} +5.84152 q^{56} +5.82548 q^{57} -6.30223 q^{58} +1.00000 q^{59} +0.365469 q^{60} +2.93848 q^{61} -4.93322 q^{62} +16.5267 q^{63} +8.36616 q^{64} +4.36248 q^{65} +5.59598 q^{66} -5.05776 q^{67} +0.102265 q^{68} -9.09587 q^{69} -2.96811 q^{70} -14.9395 q^{71} +23.7286 q^{72} -5.10704 q^{73} -14.7225 q^{74} +12.9109 q^{75} +0.178065 q^{76} +2.44905 q^{77} +18.8231 q^{78} -14.0541 q^{79} -4.04305 q^{80} +33.5521 q^{81} +5.72834 q^{82} +6.28800 q^{83} +0.690129 q^{84} -1.06817 q^{85} +4.44323 q^{86} -15.3059 q^{87} +3.51627 q^{88} +16.3407 q^{89} -12.0566 q^{90} +8.23782 q^{91} -0.278029 q^{92} -11.9810 q^{93} -7.51480 q^{94} -1.85991 q^{95} +1.93353 q^{96} +17.5889 q^{97} +4.03829 q^{98} +9.94815 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.37758	−0.974098	−0.487049	−	0.873375i	$-0.661927\pi$
$2$	−1.37758	−0.974098	−0.487049	+	0.873375i	$0.661927\pi$
$3$	−3.34566	−1.93162	−0.965809	−	0.259256i	$-0.916523\pi$
$3$	−3.34566	−1.93162	−0.965809	+	0.259256i	$0.916523\pi$
$4$	−0.102265	−0.0511326
$5$	1.06817	0.477701	0.238851	−	0.971056i	$-0.423229\pi$
$5$	1.06817	0.477701	0.238851	+	0.971056i	$0.423229\pi$
$6$	4.60892	1.88158
$7$	2.01707	0.762381	0.381190	−	0.924497i	$-0.375514\pi$
$7$	2.01707	0.762381	0.381190	+	0.924497i	$0.375514\pi$
$8$	2.89604	1.02391
$9$	8.19343	2.73114
$10$	−1.47150	−0.465328
$11$	1.21416	0.366084	0.183042	−	0.983105i	$-0.441406\pi$
$11$	1.21416	0.366084	0.183042	+	0.983105i	$0.441406\pi$
$12$	0.342144	0.0987685
$13$	4.08405	1.13271	0.566357	−	0.824160i	$-0.308353\pi$
$13$	4.08405	1.13271	0.566357	+	0.824160i	$0.308353\pi$
$14$	−2.77868	−0.742634
$15$	−3.57374	−0.922736
$16$	−3.78501	−0.946253
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−11.2871	−2.66040
$19$	−1.74121	−0.399460	−0.199730	−	0.979851i	$-0.564006\pi$
$19$	−1.74121	−0.399460	−0.199730	+	0.979851i	$0.564006\pi$
$20$	−0.109237	−0.0244261
$21$	−6.74843	−1.47263
$22$	−1.67261	−0.356601
$23$	2.71871	0.566890	0.283445	−	0.958989i	$-0.408523\pi$
$23$	2.71871	0.566890	0.283445	+	0.958989i	$0.408523\pi$
$24$	−9.68918	−1.97780
$25$	−3.85901	−0.771801
$26$	−5.62612	−1.10337
$27$	−17.3755	−3.34391
$28$	−0.206276	−0.0389825
$29$	4.57485	0.849527	0.424764	−	0.905304i	$-0.360357\pi$
$29$	4.57485	0.849527	0.424764	+	0.905304i	$0.360357\pi$
$30$	4.92313	0.898836
$31$	3.58107	0.643179	0.321590	−	0.946879i	$-0.395783\pi$
$31$	3.58107	0.643179	0.321590	+	0.946879i	$0.395783\pi$
$32$	−0.577922	−0.102163
$33$	−4.06217	−0.707133
$34$	1.37758	0.236254
$35$	2.15458	0.364190
$36$	−0.837902	−0.139650
$37$	10.6872	1.75697	0.878483	−	0.477773i	$-0.158556\pi$
$37$	10.6872	1.75697	0.878483	+	0.477773i	$0.158556\pi$
$38$	2.39865	0.389113
$39$	−13.6639	−2.18797
$40$	3.09348	0.489121
$41$	−4.15825	−0.649410	−0.324705	−	0.945815i	$-0.605265\pi$
$41$	−4.15825	−0.649410	−0.324705	+	0.945815i	$0.605265\pi$
$42$	9.29652	1.43448
$43$	−3.22538	−0.491866	−0.245933	−	0.969287i	$-0.579094\pi$
$43$	−3.22538	−0.491866	−0.245933	+	0.969287i	$0.579094\pi$
$44$	−0.124166	−0.0187188
$45$	8.75200	1.30467
$46$	−3.74525	−0.552206
$47$	5.45506	0.795702	0.397851	−	0.917450i	$-0.369756\pi$
$47$	5.45506	0.795702	0.397851	+	0.917450i	$0.369756\pi$
$48$	12.6634	1.82780
$49$	−2.93143	−0.418776
$50$	5.31610	0.751810
$51$	3.34566	0.468486
$52$	−0.417656	−0.0579185
$53$	5.09517	0.699876	0.349938	−	0.936773i	$-0.386203\pi$
$53$	5.09517	0.699876	0.349938	+	0.936773i	$0.386203\pi$
$54$	23.9361	3.25730
$55$	1.29693	0.174879
$56$	5.84152	0.780606
$57$	5.82548	0.771603
$58$	−6.30223	−0.827523
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0.365469	0.0471818
$61$	2.93848	0.376234	0.188117	−	0.982147i	$-0.439762\pi$
$61$	2.93848	0.376234	0.188117	+	0.982147i	$0.439762\pi$
$62$	−4.93322	−0.626520
$63$	16.5267	2.08217
$64$	8.36616	1.04577
$65$	4.36248	0.541098
$66$	5.59598	0.688817
$67$	−5.05776	−0.617903	−0.308952	−	0.951078i	$-0.599978\pi$
$67$	−5.05776	−0.617903	−0.308952	+	0.951078i	$0.599978\pi$
$68$	0.102265	0.0124015
$69$	−9.09587	−1.09501
$70$	−2.96811	−0.354757
$71$	−14.9395	−1.77300	−0.886498	−	0.462733i	$-0.846869\pi$
$71$	−14.9395	−1.77300	−0.886498	+	0.462733i	$0.846869\pi$
$72$	23.7286	2.79644
$73$	−5.10704	−0.597734	−0.298867	−	0.954295i	$-0.596609\pi$
$73$	−5.10704	−0.597734	−0.298867	+	0.954295i	$0.596609\pi$
$74$	−14.7225	−1.71146
$75$	12.9109	1.49082
$76$	0.178065	0.0204254
$77$	2.44905	0.279095
$78$	18.8231	2.13130
$79$	−14.0541	−1.58121	−0.790604	−	0.612328i	$-0.790233\pi$
$79$	−14.0541	−1.58121	−0.790604	+	0.612328i	$0.790233\pi$
$80$	−4.04305	−0.452026
$81$	33.5521	3.72801
$82$	5.72834	0.632589
$83$	6.28800	0.690197	0.345099	−	0.938566i	$-0.387845\pi$
$83$	6.28800	0.690197	0.345099	+	0.938566i	$0.387845\pi$
$84$	0.690129	0.0752992
$85$	−1.06817	−0.115860
$86$	4.44323	0.479126
$87$	−15.3059	−1.64096
$88$	3.51627	0.374835
$89$	16.3407	1.73211	0.866057	−	0.499945i	$-0.166646\pi$
$89$	16.3407	1.73211	0.866057	+	0.499945i	$0.166646\pi$
$90$	−12.0566	−1.27088
$91$	8.23782	0.863559
$92$	−0.278029	−0.0289865
$93$	−11.9810	−1.24238
$94$	−7.51480	−0.775092
$95$	−1.85991	−0.190822
$96$	1.93353	0.197340
$97$	17.5889	1.78588	0.892940	−	0.450176i	$-0.148639\pi$
$97$	17.5889	1.78588	0.892940	+	0.450176i	$0.148639\pi$
$98$	4.03829	0.407929
$99$	9.94815	0.999827
$100$	0.394642	0.0394642
$101$	10.1313	1.00810	0.504052	−	0.863673i	$-0.331842\pi$
$101$	10.1313	1.00810	0.504052	+	0.863673i	$0.331842\pi$
$102$	−4.60892	−0.456351
$103$	6.72326	0.662463	0.331231	−	0.943550i	$-0.392536\pi$
$103$	6.72326	0.662463	0.331231	+	0.943550i	$0.392536\pi$
$104$	11.8276	1.15979
$105$	−7.20849	−0.703476
$106$	−7.01903	−0.681748
$107$	−7.41066	−0.716416	−0.358208	−	0.933642i	$-0.616612\pi$
$107$	−7.41066	−0.716416	−0.358208	+	0.933642i	$0.616612\pi$
$108$	1.77690	0.170983
$109$	−15.9489	−1.52763	−0.763816	−	0.645434i	$-0.776676\pi$
$109$	−15.9489	−1.52763	−0.763816	+	0.645434i	$0.776676\pi$
$110$	−1.78663	−0.170349
$111$	−35.7558	−3.39379
$112$	−7.63463	−0.721405
$113$	−2.70519	−0.254482	−0.127241	−	0.991872i	$-0.540612\pi$
$113$	−2.70519	−0.254482	−0.127241	+	0.991872i	$0.540612\pi$
$114$	−8.02508	−0.751618
$115$	2.90405	0.270804
$116$	−0.467847	−0.0434385
$117$	33.4624	3.09360
$118$	−1.37758	−0.126817
$119$	−2.01707	−0.184904
$120$	−10.3497	−0.944795
$121$	−9.52581	−0.865983
$122$	−4.04800	−0.366489
$123$	13.9121	1.25441
$124$	−0.366219	−0.0328874
$125$	−9.46295	−0.846392
$126$	−22.7669	−2.02824
$127$	7.52680	0.667896	0.333948	−	0.942592i	$-0.391619\pi$
$127$	7.52680	0.667896	0.333948	+	0.942592i	$0.391619\pi$
$128$	−10.3692	−0.916519
$129$	10.7910	0.950096
$130$	−6.00967	−0.527083
$131$	15.4796	1.35246	0.676229	−	0.736691i	$-0.263613\pi$
$131$	15.4796	1.35246	0.676229	+	0.736691i	$0.263613\pi$
$132$	0.415418	0.0361575
$133$	−3.51213	−0.304540
$134$	6.96748	0.601898
$135$	−18.5600	−1.59739
$136$	−2.89604	−0.248334
$137$	14.3460	1.22566	0.612831	−	0.790214i	$-0.290031\pi$
$137$	14.3460	1.22566	0.612831	+	0.790214i	$0.290031\pi$
$138$	12.5303	1.06665
$139$	−1.42286	−0.120686	−0.0603429	−	0.998178i	$-0.519219\pi$
$139$	−1.42286	−0.120686	−0.0603429	+	0.998178i	$0.519219\pi$
$140$	−0.220338	−0.0186220
$141$	−18.2508	−1.53699
$142$	20.5804	1.72707
$143$	4.95870	0.414668
$144$	−31.0122	−2.58435
$145$	4.88672	0.405820
$146$	7.03537	0.582252
$147$	9.80756	0.808914
$148$	−1.09293	−0.0898382
$149$	8.12050	0.665258	0.332629	−	0.943058i	$-0.392064\pi$
$149$	8.12050	0.665258	0.332629	+	0.943058i	$0.392064\pi$
$150$	−17.7859	−1.45221
$151$	−12.7553	−1.03802	−0.519008	−	0.854770i	$-0.673698\pi$
$151$	−12.7553	−1.03802	−0.519008	+	0.854770i	$0.673698\pi$
$152$	−5.04261	−0.409009
$153$	−8.19343	−0.662400
$154$	−3.37377	−0.271866
$155$	3.82520	0.307248
$156$	1.39734	0.111876
$157$	16.8827	1.34738	0.673691	−	0.739013i	$-0.264708\pi$
$157$	16.8827	1.34738	0.673691	+	0.739013i	$0.264708\pi$
$158$	19.3607	1.54025
$159$	−17.0467	−1.35189
$160$	−0.617320	−0.0488034
$161$	5.48382	0.432186
$162$	−46.2207	−3.63145
$163$	3.60113	0.282063	0.141031	−	0.990005i	$-0.454958\pi$
$163$	3.60113	0.282063	0.141031	+	0.990005i	$0.454958\pi$
$164$	0.425244	0.0332060
$165$	−4.33910	−0.337798
$166$	−8.66224	−0.672320
$167$	5.30895	0.410819	0.205410	−	0.978676i	$-0.434147\pi$
$167$	5.30895	0.410819	0.205410	+	0.978676i	$0.434147\pi$
$168$	−19.5437	−1.50783
$169$	3.67950	0.283039
$170$	1.47150	0.112859
$171$	−14.2664	−1.09098
$172$	0.329844	0.0251504
$173$	−2.95797	−0.224890	−0.112445	−	0.993658i	$-0.535868\pi$
$173$	−2.95797	−0.224890	−0.112445	+	0.993658i	$0.535868\pi$
$174$	21.0851	1.59846
$175$	−7.78389	−0.588407
$176$	−4.59562	−0.346408
$177$	−3.34566	−0.251475
$178$	−22.5107	−1.68725
$179$	20.7969	1.55444	0.777218	−	0.629231i	$-0.216630\pi$
$179$	20.7969	1.55444	0.777218	+	0.629231i	$0.216630\pi$
$180$	−0.895024	−0.0667112
$181$	−1.77833	−0.132182	−0.0660912	−	0.997814i	$-0.521053\pi$
$181$	−1.77833	−0.132182	−0.0660912	+	0.997814i	$0.521053\pi$
$182$	−11.3483	−0.841191
$183$	−9.83116	−0.726740
$184$	7.87350	0.580442
$185$	11.4158	0.839305
$186$	16.5049	1.21020
$187$	−1.21416	−0.0887883
$188$	−0.557862	−0.0406863
$189$	−35.0475	−2.54933
$190$	2.56218	0.185880
$191$	−10.8760	−0.786958	−0.393479	−	0.919334i	$-0.628729\pi$
$191$	−10.8760	−0.786958	−0.393479	+	0.919334i	$0.628729\pi$
$192$	−27.9903	−2.02003
$193$	−4.87702	−0.351056	−0.175528	−	0.984474i	$-0.556163\pi$
$193$	−4.87702	−0.351056	−0.175528	+	0.984474i	$0.556163\pi$
$194$	−24.2301	−1.73962
$195$	−14.5954	−1.04520
$196$	0.299783	0.0214131
$197$	11.5208	0.820821	0.410411	−	0.911901i	$-0.365385\pi$
$197$	11.5208	0.820821	0.410411	+	0.911901i	$0.365385\pi$
$198$	−13.7044	−0.973930
$199$	−10.3407	−0.733036	−0.366518	−	0.930411i	$-0.619450\pi$
$199$	−10.3407	−0.733036	−0.366518	+	0.930411i	$0.619450\pi$
$200$	−11.1759	−0.790252
$201$	16.9215	1.19355
$202$	−13.9567	−0.981993
$203$	9.22778	0.647663
$204$	−0.342144	−0.0239549
$205$	−4.44173	−0.310224
$206$	−9.26185	−0.645304
$207$	22.2756	1.54826
$208$	−15.4582	−1.07183
$209$	−2.11410	−0.146236
$210$	9.93029	0.685255
$211$	−25.6627	−1.76669	−0.883346	−	0.468721i	$-0.844715\pi$
$211$	−25.6627	−1.76669	−0.883346	+	0.468721i	$0.844715\pi$
$212$	−0.521059	−0.0357865
$213$	49.9826	3.42475
$214$	10.2088	0.697859
$215$	−3.44526	−0.234965
$216$	−50.3201	−3.42385
$217$	7.22327	0.490347
$218$	21.9710	1.48806
$219$	17.0864	1.15459
$220$	−0.132631	−0.00894199
$221$	−4.08405	−0.274723
$222$	49.2565	3.30588
$223$	15.5438	1.04089	0.520444	−	0.853896i	$-0.325766\pi$
$223$	15.5438	1.04089	0.520444	+	0.853896i	$0.325766\pi$
$224$	−1.16571	−0.0778872
$225$	−31.6185	−2.10790
$226$	3.72662	0.247891
$227$	7.51069	0.498502	0.249251	−	0.968439i	$-0.419816\pi$
$227$	7.51069	0.498502	0.249251	+	0.968439i	$0.419816\pi$
$228$	−0.595743	−0.0394541
$229$	16.3995	1.08371	0.541854	−	0.840473i	$-0.317723\pi$
$229$	16.3995	1.08371	0.541854	+	0.840473i	$0.317723\pi$
$230$	−4.00057	−0.263790
$231$	−8.19368	−0.539105
$232$	13.2490	0.869837
$233$	22.9361	1.50259	0.751296	−	0.659966i	$-0.229429\pi$
$233$	22.9361	1.50259	0.751296	+	0.659966i	$0.229429\pi$
$234$	−46.0973	−3.01347
$235$	5.82695	0.380108
$236$	−0.102265	−0.00665689
$237$	47.0202	3.05429
$238$	2.77868	0.180115
$239$	−5.08098	−0.328661	−0.164331	−	0.986405i	$-0.552546\pi$
$239$	−5.08098	−0.328661	−0.164331	+	0.986405i	$0.552546\pi$
$240$	13.5267	0.873142
$241$	−21.6882	−1.39706	−0.698528	−	0.715582i	$-0.746161\pi$
$241$	−21.6882	−1.39706	−0.698528	+	0.715582i	$0.746161\pi$
$242$	13.1226	0.843552
$243$	−60.1274	−3.85717
$244$	−0.300504	−0.0192378
$245$	−3.13127	−0.200050
$246$	−19.1651	−1.22192
$247$	−7.11118	−0.452473
$248$	10.3709	0.658555
$249$	−21.0375	−1.33320
$250$	13.0360	0.824469
$251$	9.63258	0.608003	0.304001	−	0.952672i	$-0.401677\pi$
$251$	9.63258	0.608003	0.304001	+	0.952672i	$0.401677\pi$
$252$	−1.69011	−0.106467
$253$	3.30095	0.207529
$254$	−10.3688	−0.650596
$255$	3.57374	0.223796
$256$	−2.44784	−0.152990
$257$	−6.35258	−0.396263	−0.198131	−	0.980175i	$-0.563487\pi$
$257$	−6.35258	−0.396263	−0.198131	+	0.980175i	$0.563487\pi$
$258$	−14.8655	−0.925487
$259$	21.5568	1.33948
$260$	−0.446129	−0.0276677
$261$	37.4837	2.32018
$262$	−21.3244	−1.31743
$263$	−4.99979	−0.308300	−0.154150	−	0.988047i	$-0.549264\pi$
$263$	−4.99979	−0.308300	−0.154150	+	0.988047i	$0.549264\pi$
$264$	−11.7642	−0.724038
$265$	5.44253	0.334332
$266$	4.83825	0.296652
$267$	−54.6705	−3.34578
$268$	0.517232	0.0315950
$269$	4.36253	0.265988	0.132994	−	0.991117i	$-0.457541\pi$
$269$	4.36253	0.265988	0.132994	+	0.991117i	$0.457541\pi$
$270$	25.5679	1.55601
$271$	26.1724	1.58986	0.794929	−	0.606703i	$-0.207508\pi$
$271$	26.1724	1.58986	0.794929	+	0.606703i	$0.207508\pi$
$272$	3.78501	0.229500
$273$	−27.5609	−1.66806
$274$	−19.7628	−1.19391
$275$	−4.68546	−0.282544
$276$	0.930190	0.0559909
$277$	3.77444	0.226784	0.113392	−	0.993550i	$-0.463828\pi$
$277$	3.77444	0.226784	0.113392	+	0.993550i	$0.463828\pi$
$278$	1.96011	0.117560
$279$	29.3413	1.75662
$280$	6.23976	0.372897
$281$	9.34919	0.557726	0.278863	−	0.960331i	$-0.410042\pi$
$281$	9.34919	0.557726	0.278863	+	0.960331i	$0.410042\pi$
$282$	25.1420	1.49718
$283$	13.2770	0.789238	0.394619	−	0.918845i	$-0.370877\pi$
$283$	13.2770	0.789238	0.394619	+	0.918845i	$0.370877\pi$
$284$	1.52779	0.0906578
$285$	6.22262	0.368596
$286$	−6.83103	−0.403927
$287$	−8.38749	−0.495098
$288$	−4.73516	−0.279022
$289$	1.00000	0.0588235
$290$	−6.73187	−0.395309
$291$	−58.8464	−3.44964
$292$	0.522272	0.0305637
$293$	−15.7537	−0.920339	−0.460169	−	0.887831i	$-0.652211\pi$
$293$	−15.7537	−0.920339	−0.460169	+	0.887831i	$0.652211\pi$
$294$	−13.5107	−0.787962
$295$	1.06817	0.0621914
$296$	30.9506	1.79897
$297$	−21.0966	−1.22415
$298$	−11.1867	−0.648026
$299$	11.1034	0.642124
$300$	−1.32034	−0.0762297
$301$	−6.50582	−0.374989
$302$	17.5716	1.01113
$303$	−33.8960	−1.94727
$304$	6.59048	0.377990
$305$	3.13881	0.179728
$306$	11.2871	0.645243
$307$	2.62426	0.149775	0.0748873	−	0.997192i	$-0.476140\pi$
$307$	2.62426	0.149775	0.0748873	+	0.997192i	$0.476140\pi$
$308$	−0.250452	−0.0142708
$309$	−22.4937	−1.27962
$310$	−5.26953	−0.299289
$311$	0.917648	0.0520350	0.0260175	−	0.999661i	$-0.491717\pi$
$311$	0.917648	0.0520350	0.0260175	+	0.999661i	$0.491717\pi$
$312$	−39.5711	−2.24027
$313$	−19.7158	−1.11440	−0.557202	−	0.830377i	$-0.688125\pi$
$313$	−19.7158	−1.11440	−0.557202	+	0.830377i	$0.688125\pi$
$314$	−23.2573	−1.31248
$315$	17.6534	0.994656
$316$	1.43724	0.0808512
$317$	25.5726	1.43630	0.718150	−	0.695888i	$-0.244989\pi$
$317$	25.5726	1.43630	0.718150	+	0.695888i	$0.244989\pi$
$318$	23.4833	1.31688
$319$	5.55460	0.310998
$320$	8.93650	0.499566
$321$	24.7936	1.38384
$322$	−7.55442	−0.420992
$323$	1.74121	0.0968832
$324$	−3.43121	−0.190623
$325$	−15.7604	−0.874230
$326$	−4.96086	−0.274757
$327$	53.3597	2.95080
$328$	−12.0425	−0.664935
$329$	11.0032	0.606628
$330$	5.97747	0.329049
$331$	34.2513	1.88262	0.941311	−	0.337540i	$-0.109595\pi$
$331$	34.2513	1.88262	0.941311	+	0.337540i	$0.109595\pi$
$332$	−0.643043	−0.0352915
$333$	87.5649	4.79853
$334$	−7.31352	−0.400178
$335$	−5.40256	−0.295173
$336$	25.5429	1.39348
$337$	4.77827	0.260289	0.130144	−	0.991495i	$-0.458456\pi$
$337$	4.77827	0.260289	0.130144	+	0.991495i	$0.458456\pi$
$338$	−5.06882	−0.275708
$339$	9.05063	0.491563
$340$	0.109237	0.00592420
$341$	4.34800	0.235457
$342$	19.6532	1.06272
$343$	−20.0324	−1.08165
$344$	−9.34084	−0.503625
$345$	−9.71596	−0.523090
$346$	4.07484	0.219065
$347$	31.3430	1.68258	0.841290	−	0.540585i	$-0.181797\pi$
$347$	31.3430	1.68258	0.841290	+	0.540585i	$0.181797\pi$
$348$	1.56526	0.0839066
$349$	9.84113	0.526784	0.263392	−	0.964689i	$-0.415159\pi$
$349$	9.84113	0.526784	0.263392	+	0.964689i	$0.415159\pi$
$350$	10.7230	0.573166
$351$	−70.9623	−3.78769
$352$	−0.701690	−0.0374002
$353$	10.3036	0.548405	0.274203	−	0.961672i	$-0.411586\pi$
$353$	10.3036	0.548405	0.274203	+	0.961672i	$0.411586\pi$
$354$	4.60892	0.244961
$355$	−15.9580	−0.846962
$356$	−1.67109	−0.0885674
$357$	6.74843	0.357165
$358$	−28.6495	−1.51417
$359$	29.1419	1.53805	0.769026	−	0.639217i	$-0.220742\pi$
$359$	29.1419	1.53805	0.769026	+	0.639217i	$0.220742\pi$
$360$	25.3462	1.33586
$361$	−15.9682	−0.840432
$362$	2.44980	0.128759
$363$	31.8701	1.67275
$364$	−0.842442	−0.0441560
$365$	−5.45520	−0.285538
$366$	13.5432	0.707916
$367$	−22.6011	−1.17977	−0.589883	−	0.807489i	$-0.700826\pi$
$367$	−22.6011	−1.17977	−0.589883	+	0.807489i	$0.700826\pi$
$368$	−10.2903	−0.536421
$369$	−34.0704	−1.77363
$370$	−15.7262	−0.817566
$371$	10.2773	0.533572
$372$	1.22524	0.0635259
$373$	−29.7679	−1.54133	−0.770663	−	0.637244i	$-0.780075\pi$
$373$	−29.7679	−1.54133	−0.770663	+	0.637244i	$0.780075\pi$
$374$	1.67261	0.0864885
$375$	31.6598	1.63491
$376$	15.7981	0.814725
$377$	18.6839	0.962271
$378$	48.2809	2.48330
$379$	0.607443	0.0312023	0.0156011	−	0.999878i	$-0.495034\pi$
$379$	0.607443	0.0312023	0.0156011	+	0.999878i	$0.495034\pi$
$380$	0.190204	0.00975724
$381$	−25.1821	−1.29012
$382$	14.9826	0.766574
$383$	−16.0233	−0.818754	−0.409377	−	0.912365i	$-0.634254\pi$
$383$	−16.0233	−0.818754	−0.409377	+	0.912365i	$0.634254\pi$
$384$	34.6919	1.77036
$385$	2.61601	0.133324
$386$	6.71851	0.341963
$387$	−26.4269	−1.34336
$388$	−1.79873	−0.0913166
$389$	14.9169	0.756318	0.378159	−	0.925741i	$-0.376557\pi$
$389$	14.9169	0.756318	0.378159	+	0.925741i	$0.376557\pi$
$390$	20.1063	1.01812
$391$	−2.71871	−0.137491
$392$	−8.48955	−0.428787
$393$	−51.7894	−2.61243
$394$	−15.8708	−0.799561
$395$	−15.0122	−0.755345
$396$	−1.01735	−0.0511237
$397$	−9.85862	−0.494790	−0.247395	−	0.968915i	$-0.579575\pi$
$397$	−9.85862	−0.494790	−0.247395	+	0.968915i	$0.579575\pi$
$398$	14.2452	0.714049
$399$	11.7504	0.588256
$400$	14.6064	0.730319
$401$	−27.8542	−1.39097	−0.695487	−	0.718539i	$-0.744811\pi$
$401$	−27.8542	−1.39097	−0.695487	+	0.718539i	$0.744811\pi$
$402$	−23.3108	−1.16264
$403$	14.6253	0.728537
$404$	−1.03608	−0.0515470
$405$	35.8394	1.78087
$406$	−12.7120	−0.630888
$407$	12.9760	0.643197
$408$	9.68918	0.479686
$409$	−19.5864	−0.968487	−0.484243	−	0.874933i	$-0.660905\pi$
$409$	−19.5864	−0.968487	−0.484243	+	0.874933i	$0.660905\pi$
$410$	6.11886	0.302189
$411$	−47.9968	−2.36751
$412$	−0.687555	−0.0338734
$413$	2.01707	0.0992535
$414$	−30.6864	−1.50816
$415$	6.71666	0.329708
$416$	−2.36026	−0.115721
$417$	4.76042	0.233119
$418$	2.91235	0.142448
$419$	27.2507	1.33129	0.665643	−	0.746270i	$-0.268157\pi$
$419$	27.2507	1.33129	0.665643	+	0.746270i	$0.268157\pi$
$420$	0.737177	0.0359705
$421$	−33.9623	−1.65522	−0.827610	−	0.561303i	$-0.810300\pi$
$421$	−33.9623	−1.65522	−0.827610	+	0.561303i	$0.810300\pi$
$422$	35.3525	1.72093
$423$	44.6957	2.17318
$424$	14.7559	0.716608
$425$	3.85901	0.187189
$426$	−68.8551	−3.33604
$427$	5.92712	0.286834
$428$	0.757852	0.0366322
$429$	−16.5901	−0.800979
$430$	4.74613	0.228879
$431$	−18.6961	−0.900559	−0.450279	−	0.892888i	$-0.648676\pi$
$431$	−18.6961	−0.900559	−0.450279	+	0.892888i	$0.648676\pi$
$432$	65.7663	3.16418
$433$	−26.8346	−1.28959	−0.644795	−	0.764355i	$-0.723057\pi$
$433$	−26.8346	−1.28959	−0.644795	+	0.764355i	$0.723057\pi$
$434$	−9.95065	−0.477647
$435$	−16.3493	−0.783890
$436$	1.63102	0.0781117
$437$	−4.73383	−0.226450
$438$	−23.5380	−1.12469
$439$	11.0497	0.527375	0.263687	−	0.964608i	$-0.415061\pi$
$439$	11.0497	0.527375	0.263687	+	0.964608i	$0.415061\pi$
$440$	3.75598	0.179059
$441$	−24.0185	−1.14374
$442$	5.62612	0.267607
$443$	20.3320	0.966002	0.483001	−	0.875620i	$-0.339547\pi$
$443$	20.3320	0.966002	0.483001	+	0.875620i	$0.339547\pi$
$444$	3.65657	0.173533
$445$	17.4547	0.827433
$446$	−21.4129	−1.01393
$447$	−27.1684	−1.28502
$448$	16.8751	0.797275
$449$	24.7520	1.16812	0.584058	−	0.811712i	$-0.301464\pi$
$449$	24.7520	1.16812	0.584058	+	0.811712i	$0.301464\pi$
$450$	43.5571	2.05330
$451$	−5.04879	−0.237738
$452$	0.276646	0.0130123
$453$	42.6750	2.00505
$454$	−10.3466	−0.485590
$455$	8.79942	0.412523
$456$	16.8708	0.790050
$457$	12.8697	0.602017	0.301009	−	0.953621i	$-0.402677\pi$
$457$	12.8697	0.602017	0.301009	+	0.953621i	$0.402677\pi$
$458$	−22.5916	−1.05564
$459$	17.3755	0.811017
$460$	−0.296983	−0.0138469
$461$	−18.4913	−0.861228	−0.430614	−	0.902536i	$-0.641703\pi$
$461$	−18.4913	−0.861228	−0.430614	+	0.902536i	$0.641703\pi$
$462$	11.2875	0.525141
$463$	1.34371	0.0624476	0.0312238	−	0.999512i	$-0.490060\pi$
$463$	1.34371	0.0624476	0.0312238	+	0.999512i	$0.490060\pi$
$464$	−17.3158	−0.803868
$465$	−12.7978	−0.593485
$466$	−31.5963	−1.46367
$467$	25.2825	1.16994	0.584968	−	0.811056i	$-0.301107\pi$
$467$	25.2825	1.16994	0.584968	+	0.811056i	$0.301107\pi$
$468$	−3.42204	−0.158184
$469$	−10.2018	−0.471078
$470$	−8.02710	−0.370263
$471$	−56.4836	−2.60263
$472$	2.89604	0.133301
$473$	−3.91613	−0.180064
$474$	−64.7742	−2.97518
$475$	6.71932	0.308304
$476$	0.206276	0.00945464
$477$	41.7470	1.91146
$478$	6.99947	0.320148
$479$	−31.5317	−1.44072	−0.720360	−	0.693600i	$-0.756023\pi$
$479$	−31.5317	−1.44072	−0.720360	+	0.693600i	$0.756023\pi$
$480$	2.06534	0.0942696
$481$	43.6472	1.99014
$482$	29.8772	1.36087
$483$	−18.3470	−0.834818
$484$	0.974158	0.0442799
$485$	18.7880	0.853117
$486$	82.8305	3.75727
$487$	9.98508	0.452467	0.226233	−	0.974073i	$-0.427359\pi$
$487$	9.98508	0.452467	0.226233	+	0.974073i	$0.427359\pi$
$488$	8.50998	0.385228
$489$	−12.0482	−0.544837
$490$	4.31359	0.194868
$491$	−37.1972	−1.67869	−0.839343	−	0.543602i	$-0.817060\pi$
$491$	−37.1972	−1.67869	−0.839343	+	0.543602i	$0.817060\pi$
$492$	−1.42272	−0.0641413
$493$	−4.57485	−0.206041
$494$	9.79624	0.440754
$495$	10.6263	0.477619
$496$	−13.5544	−0.608610
$497$	−30.1341	−1.35170
$498$	28.9809	1.29866
$499$	11.4129	0.510914	0.255457	−	0.966820i	$-0.417774\pi$
$499$	11.4129	0.510914	0.255457	+	0.966820i	$0.417774\pi$
$500$	0.967729	0.0432782
$501$	−17.7619	−0.793545
$502$	−13.2697	−0.592255
$503$	−2.49538	−0.111263	−0.0556316	−	0.998451i	$-0.517717\pi$
$503$	−2.49538	−0.111263	−0.0556316	+	0.998451i	$0.517717\pi$
$504$	47.8621	2.13195
$505$	10.8220	0.481573
$506$	−4.54734	−0.202154
$507$	−12.3104	−0.546723
$508$	−0.769729	−0.0341512
$509$	43.1925	1.91447	0.957236	−	0.289308i	$-0.0934253\pi$
$509$	43.1925	1.91447	0.957236	+	0.289308i	$0.0934253\pi$
$510$	−4.92313	−0.218000
$511$	−10.3013	−0.455701
$512$	24.1106	1.06555
$513$	30.2542	1.33576
$514$	8.75120	0.385999
$515$	7.18161	0.316459
$516$	−1.10354	−0.0485809
$517$	6.62333	0.291294
$518$	−29.6963	−1.30478
$519$	9.89634	0.434401
$520$	12.6339	0.554034
$521$	−15.5783	−0.682496	−0.341248	−	0.939973i	$-0.610850\pi$
$521$	−15.5783	−0.682496	−0.341248	+	0.939973i	$0.610850\pi$
$522$	−51.6369	−2.26009
$523$	−2.30241	−0.100677	−0.0503386	−	0.998732i	$-0.516030\pi$
$523$	−2.30241	−0.100677	−0.0503386	+	0.998732i	$0.516030\pi$
$524$	−1.58302	−0.0691546
$525$	26.0422	1.13658
$526$	6.88762	0.300315
$527$	−3.58107	−0.155994
$528$	15.3754	0.669127
$529$	−15.6086	−0.678636
$530$	−7.49753	−0.325672
$531$	8.19343	0.355565
$532$	0.359169	0.0155719
$533$	−16.9825	−0.735595
$534$	75.3132	3.25912
$535$	−7.91587	−0.342233
$536$	−14.6475	−0.632675
$537$	−69.5795	−3.00258
$538$	−6.00975	−0.259099
$539$	−3.55923	−0.153307
$540$	1.89804	0.0816786
$541$	9.94068	0.427383	0.213692	−	0.976901i	$-0.431451\pi$
$541$	9.94068	0.427383	0.213692	+	0.976901i	$0.431451\pi$
$542$	−36.0546	−1.54868
$543$	5.94969	0.255326
$544$	0.577922	0.0247782
$545$	−17.0362	−0.729752
$546$	37.9675	1.62486
$547$	12.3841	0.529506	0.264753	−	0.964316i	$-0.414710\pi$
$547$	12.3841	0.529506	0.264753	+	0.964316i	$0.414710\pi$
$548$	−1.46709	−0.0626712
$549$	24.0763	1.02755
$550$	6.45461	0.275225
$551$	−7.96574	−0.339352
$552$	−26.3421	−1.12119
$553$	−28.3481	−1.20548
$554$	−5.19960	−0.220910
$555$	−38.1933	−1.62122
$556$	0.145509	0.00617097
$557$	4.68508	0.198513	0.0992567	−	0.995062i	$-0.468354\pi$
$557$	4.68508	0.198513	0.0992567	+	0.995062i	$0.468354\pi$
$558$	−40.4200	−1.71112
$559$	−13.1726	−0.557143
$560$	−8.15510	−0.344616
$561$	4.06217	0.171505
$562$	−12.8793	−0.543280
$563$	−19.3049	−0.813604	−0.406802	−	0.913516i	$-0.633356\pi$
$563$	−19.3049	−0.813604	−0.406802	+	0.913516i	$0.633356\pi$
$564$	1.86642	0.0785903
$565$	−2.88961	−0.121567
$566$	−18.2902	−0.768796
$567$	67.6768	2.84216
$568$	−43.2655	−1.81538
$569$	20.0460	0.840373	0.420186	−	0.907438i	$-0.361965\pi$
$569$	20.0460	0.840373	0.420186	+	0.907438i	$0.361965\pi$
$570$	−8.57217	−0.359049
$571$	32.5827	1.36354	0.681772	−	0.731565i	$-0.261210\pi$
$571$	32.5827	1.36354	0.681772	+	0.731565i	$0.261210\pi$
$572$	−0.507102	−0.0212030
$573$	36.3873	1.52010
$574$	11.5545	0.482274
$575$	−10.4915	−0.437526
$576$	68.5476	2.85615
$577$	39.9019	1.66114	0.830570	−	0.556915i	$-0.188015\pi$
$577$	39.9019	1.66114	0.830570	+	0.556915i	$0.188015\pi$
$578$	−1.37758	−0.0572999
$579$	16.3169	0.678106
$580$	−0.499741	−0.0207506
$581$	12.6833	0.526193
$582$	81.0658	3.36028
$583$	6.18637	0.256213
$584$	−14.7902	−0.612024
$585$	35.7437	1.47782
$586$	21.7020	0.896500
$587$	−24.3141	−1.00355	−0.501775	−	0.864998i	$-0.667319\pi$
$587$	−24.3141	−1.00355	−0.501775	+	0.864998i	$0.667319\pi$
$588$	−1.00297	−0.0413619
$589$	−6.23538	−0.256924
$590$	−1.47150	−0.0605805
$591$	−38.5446	−1.58551
$592$	−40.4512	−1.66253
$593$	5.10161	0.209498	0.104749	−	0.994499i	$-0.466596\pi$
$593$	5.10161	0.209498	0.104749	+	0.994499i	$0.466596\pi$
$594$	29.0623	1.19244
$595$	−2.15458	−0.0883291
$596$	−0.830444	−0.0340163
$597$	34.5966	1.41594
$598$	−15.2958	−0.625491
$599$	1.05304	0.0430259	0.0215129	−	0.999769i	$-0.493152\pi$
$599$	1.05304	0.0430259	0.0215129	+	0.999769i	$0.493152\pi$
$600$	37.3906	1.52647
$601$	37.9967	1.54992	0.774959	−	0.632012i	$-0.217771\pi$
$601$	37.9967	1.54992	0.774959	+	0.632012i	$0.217771\pi$
$602$	8.96230	0.365276
$603$	−41.4404	−1.68758
$604$	1.30443	0.0530764
$605$	−10.1752	−0.413681
$606$	46.6945	1.89683
$607$	−7.20627	−0.292493	−0.146247	−	0.989248i	$-0.546719\pi$
$607$	−7.20627	−0.292493	−0.146247	+	0.989248i	$0.546719\pi$
$608$	1.00628	0.0408100
$609$	−30.8730	−1.25104
$610$	−4.32397	−0.175072
$611$	22.2788	0.901302
$612$	0.837902	0.0338702
$613$	19.0958	0.771270	0.385635	−	0.922651i	$-0.373982\pi$
$613$	19.0958	0.771270	0.385635	+	0.922651i	$0.373982\pi$
$614$	−3.61514	−0.145895
$615$	14.8605	0.599234
$616$	7.09256	0.285767
$617$	10.1955	0.410456	0.205228	−	0.978714i	$-0.434206\pi$
$617$	10.1955	0.410456	0.205228	+	0.978714i	$0.434206\pi$
$618$	30.9870	1.24648
$619$	4.56919	0.183651	0.0918257	−	0.995775i	$-0.470730\pi$
$619$	4.56919	0.183651	0.0918257	+	0.995775i	$0.470730\pi$
$620$	−0.391185	−0.0157104
$621$	−47.2388	−1.89563
$622$	−1.26414	−0.0506873
$623$	32.9604	1.32053
$624$	51.7178	2.07037
$625$	9.18697	0.367479
$626$	27.1602	1.08554
$627$	7.07307	0.282471
$628$	−1.72651	−0.0688951
$629$	−10.6872	−0.426127
$630$	−24.3190	−0.968893
$631$	−42.5309	−1.69313	−0.846564	−	0.532286i	$-0.821333\pi$
$631$	−42.5309	−1.69313	−0.846564	+	0.532286i	$0.821333\pi$
$632$	−40.7012	−1.61901
$633$	85.8586	3.41257
$634$	−35.2284	−1.39910
$635$	8.03992	0.319055
$636$	1.74328	0.0691257
$637$	−11.9721	−0.474353
$638$	−7.65193	−0.302943
$639$	−122.406	−4.84231
$640$	−11.0761	−0.437823
$641$	7.17913	0.283558	0.141779	−	0.989898i	$-0.454718\pi$
$641$	7.17913	0.283558	0.141779	+	0.989898i	$0.454718\pi$
$642$	−34.1552	−1.34800
$643$	−0.607753	−0.0239674	−0.0119837	−	0.999928i	$-0.503815\pi$
$643$	−0.607753	−0.0239674	−0.0119837	+	0.999928i	$0.503815\pi$
$644$	−0.560804	−0.0220988
$645$	11.5267	0.453862
$646$	−2.39865	−0.0943738
$647$	31.7590	1.24858	0.624288	−	0.781194i	$-0.285389\pi$
$647$	31.7590	1.24858	0.624288	+	0.781194i	$0.285389\pi$
$648$	97.1683	3.81713
$649$	1.21416	0.0476600
$650$	21.7113	0.851586
$651$	−24.1666	−0.947163
$652$	−0.368270	−0.0144226
$653$	−39.8301	−1.55867	−0.779336	−	0.626606i	$-0.784443\pi$
$653$	−39.8301	−1.55867	−0.779336	+	0.626606i	$0.784443\pi$
$654$	−73.5075	−2.87437
$655$	16.5349	0.646071
$656$	15.7390	0.614506
$657$	−41.8442	−1.63250
$658$	−15.1579	−0.590915
$659$	0.168219	0.00655288	0.00327644	−	0.999995i	$-0.498957\pi$
$659$	0.168219	0.00655288	0.00327644	+	0.999995i	$0.498957\pi$
$660$	0.443739	0.0172725
$661$	24.2589	0.943561	0.471781	−	0.881716i	$-0.343611\pi$
$661$	24.2589	0.943561	0.471781	+	0.881716i	$0.343611\pi$
$662$	−47.1840	−1.83386
$663$	13.6639	0.530660
$664$	18.2103	0.706697
$665$	−3.75156	−0.145479
$666$	−120.628	−4.67424
$667$	12.4377	0.481589
$668$	−0.542921	−0.0210062
$669$	−52.0042	−2.01060
$670$	7.44247	0.287528
$671$	3.56779	0.137733
$672$	3.90006	0.150448
$673$	0.786133	0.0303032	0.0151516	−	0.999885i	$-0.495177\pi$
$673$	0.786133	0.0303032	0.0151516	+	0.999885i	$0.495177\pi$
$674$	−6.58246	−0.253547
$675$	67.0520	2.58083
$676$	−0.376285	−0.0144725
$677$	−38.5644	−1.48215	−0.741075	−	0.671423i	$-0.765684\pi$
$677$	−38.5644	−1.48215	−0.741075	+	0.671423i	$0.765684\pi$
$678$	−12.4680	−0.478830
$679$	35.4780	1.36152
$680$	−3.09348	−0.118629
$681$	−25.1282	−0.962915
$682$	−5.98973	−0.229359
$683$	−19.6784	−0.752973	−0.376486	−	0.926422i	$-0.622868\pi$
$683$	−19.6784	−0.752973	−0.376486	+	0.926422i	$0.622868\pi$
$684$	1.45896	0.0557847
$685$	15.3240	0.585500
$686$	27.5963	1.05363
$687$	−54.8670	−2.09331
$688$	12.2081	0.465429
$689$	20.8090	0.792759
$690$	13.3845	0.509541
$691$	−36.6625	−1.39471	−0.697353	−	0.716727i	$-0.745639\pi$
$691$	−36.6625	−1.39471	−0.697353	+	0.716727i	$0.745639\pi$
$692$	0.302497	0.0114992
$693$	20.0661	0.762249
$694$	−43.1776	−1.63900
$695$	−1.51986	−0.0576518
$696$	−44.3265	−1.68019
$697$	4.15825	0.157505
$698$	−13.5570	−0.513139
$699$	−76.7363	−2.90243
$700$	0.796020	0.0300867
$701$	28.9697	1.09417	0.547084	−	0.837077i	$-0.315738\pi$
$701$	28.9697	1.09417	0.547084	+	0.837077i	$0.315738\pi$
$702$	97.7565	3.68958
$703$	−18.6086	−0.701838
$704$	10.1579	0.382839
$705$	−19.4950	−0.734223
$706$	−14.1941	−0.534201
$707$	20.4356	0.768560
$708$	0.342144	0.0128586
$709$	−50.0223	−1.87863	−0.939314	−	0.343058i	$-0.888537\pi$
$709$	−50.0223	−1.87863	−0.939314	+	0.343058i	$0.888537\pi$
$710$	21.9835	0.825024
$711$	−115.151	−4.31851
$712$	47.3235	1.77352
$713$	9.73589	0.364612
$714$	−9.29652	−0.347913
$715$	5.29675	0.198087
$716$	−2.12680	−0.0794823
$717$	16.9992	0.634847
$718$	−40.1454	−1.49821
$719$	−6.14557	−0.229191	−0.114596	−	0.993412i	$-0.536557\pi$
$719$	−6.14557	−0.229191	−0.114596	+	0.993412i	$0.536557\pi$
$720$	−33.1264	−1.23455
$721$	13.5613	0.505049
$722$	21.9975	0.818663
$723$	72.5612	2.69858
$724$	0.181861	0.00675882
$725$	−17.6544	−0.655667
$726$	−43.9037	−1.62942
$727$	35.4162	1.31351	0.656757	−	0.754103i	$-0.271928\pi$
$727$	35.4162	1.31351	0.656757	+	0.754103i	$0.271928\pi$
$728$	23.8571	0.884203
$729$	100.510	3.72257
$730$	7.51499	0.278142
$731$	3.22538	0.119295
$732$	1.00538	0.0371601
$733$	37.3564	1.37979	0.689894	−	0.723910i	$-0.257657\pi$
$733$	37.3564	1.37979	0.689894	+	0.723910i	$0.257657\pi$
$734$	31.1348	1.14921
$735$	10.4762	0.386419
$736$	−1.57120	−0.0579152
$737$	−6.14093	−0.226204
$738$	46.9348	1.72769
$739$	4.08243	0.150174	0.0750872	−	0.997177i	$-0.476076\pi$
$739$	4.08243	0.150174	0.0750872	+	0.997177i	$0.476076\pi$
$740$	−1.16744	−0.0429158
$741$	23.7916	0.874005
$742$	−14.1579	−0.519752
$743$	−31.8121	−1.16707	−0.583536	−	0.812088i	$-0.698331\pi$
$743$	−31.8121	−1.16707	−0.583536	+	0.812088i	$0.698331\pi$
$744$	−34.6976	−1.27208
$745$	8.67410	0.317794
$746$	41.0078	1.50140
$747$	51.5203	1.88503
$748$	0.124166	0.00453997
$749$	−14.9478	−0.546182
$750$	−43.6140	−1.59256
$751$	24.7008	0.901344	0.450672	−	0.892690i	$-0.351184\pi$
$751$	24.7008	0.901344	0.450672	+	0.892690i	$0.351184\pi$
$752$	−20.6475	−0.752936
$753$	−32.2273	−1.17443
$754$	−25.7386	−0.937346
$755$	−13.6249	−0.495861
$756$	3.58414	0.130354
$757$	−33.5921	−1.22093	−0.610463	−	0.792045i	$-0.709016\pi$
$757$	−33.5921	−1.22093	−0.610463	+	0.792045i	$0.709016\pi$
$758$	−0.836804	−0.0303941
$759$	−11.0439	−0.400867
$760$	−5.38638	−0.195384
$761$	−44.3899	−1.60913	−0.804567	−	0.593863i	$-0.797602\pi$
$761$	−44.3899	−1.60913	−0.804567	+	0.593863i	$0.797602\pi$
$762$	34.6904	1.25670
$763$	−32.1701	−1.16464
$764$	1.11223	0.0402392
$765$	−8.75200	−0.316429
$766$	22.0735	0.797547
$767$	4.08405	0.147467
$768$	8.18963	0.295518
$769$	23.6158	0.851608	0.425804	−	0.904816i	$-0.359991\pi$
$769$	23.6158	0.851608	0.425804	+	0.904816i	$0.359991\pi$
$770$	−3.60377	−0.129871
$771$	21.2536	0.765428
$772$	0.498749	0.0179504
$773$	−28.6651	−1.03101	−0.515506	−	0.856886i	$-0.672396\pi$
$773$	−28.6651	−1.03101	−0.515506	+	0.856886i	$0.672396\pi$
$774$	36.4053	1.30856
$775$	−13.8194	−0.496407
$776$	50.9382	1.82857
$777$	−72.1219	−2.58736
$778$	−20.5493	−0.736728
$779$	7.24037	0.259413
$780$	1.49260	0.0534435
$781$	−18.1390	−0.649064
$782$	3.74525	0.133930
$783$	−79.4900	−2.84074
$784$	11.0955	0.396268
$785$	18.0336	0.643646
$786$	71.3442	2.54476
$787$	−46.2174	−1.64747	−0.823735	−	0.566974i	$-0.808114\pi$
$787$	−46.2174	−1.64747	−0.823735	+	0.566974i	$0.808114\pi$
$788$	−1.17817	−0.0419707
$789$	16.7276	0.595518
$790$	20.6805	0.735780
$791$	−5.45655	−0.194013
$792$	28.8103	1.02373
$793$	12.0009	0.426165
$794$	13.5811	0.481974
$795$	−18.2088	−0.645801
$796$	1.05750	0.0374820
$797$	−31.3533	−1.11059	−0.555296	−	0.831653i	$-0.687395\pi$
$797$	−31.3533	−1.11059	−0.555296	+	0.831653i	$0.687395\pi$
$798$	−16.1871	−0.573019
$799$	−5.45506	−0.192986
$800$	2.23020	0.0788496
$801$	133.887	4.73066
$802$	38.3715	1.35495
$803$	−6.20078	−0.218821
$804$	−1.73048	−0.0610294
$805$	5.85767	0.206456
$806$	−20.1475	−0.709667
$807$	−14.5955	−0.513787
$808$	29.3408	1.03220
$809$	−2.57506	−0.0905342	−0.0452671	−	0.998975i	$-0.514414\pi$
$809$	−2.57506	−0.0905342	−0.0452671	+	0.998975i	$0.514414\pi$
$810$	−49.3717	−1.73475
$811$	40.9352	1.43743	0.718714	−	0.695306i	$-0.244731\pi$
$811$	40.9352	1.43743	0.718714	+	0.695306i	$0.244731\pi$
$812$	−0.943680	−0.0331167
$813$	−87.5638	−3.07100
$814$	−17.8755	−0.626537
$815$	3.84663	0.134742
$816$	−12.6634	−0.443306
$817$	5.61605	0.196481
$818$	26.9819	0.943401
$819$	67.4961	2.35850
$820$	0.454234	0.0158625
$821$	−56.2702	−1.96384	−0.981922	−	0.189284i	$-0.939383\pi$
$821$	−56.2702	−1.96384	−0.981922	+	0.189284i	$0.939383\pi$
$822$	66.1196	2.30619
$823$	23.2321	0.809821	0.404910	−	0.914356i	$-0.367303\pi$
$823$	23.2321	0.809821	0.404910	+	0.914356i	$0.367303\pi$
$824$	19.4709	0.678300
$825$	15.6759	0.545766
$826$	−2.77868	−0.0966827
$827$	11.3784	0.395666	0.197833	−	0.980236i	$-0.436610\pi$
$827$	11.3784	0.395666	0.197833	+	0.980236i	$0.436610\pi$
$828$	−2.27801	−0.0791664
$829$	34.4583	1.19679	0.598394	−	0.801202i	$-0.295806\pi$
$829$	34.4583	1.19679	0.598394	+	0.801202i	$0.295806\pi$
$830$	−9.25276	−0.321168
$831$	−12.6280	−0.438060
$832$	34.1678	1.18456
$833$	2.93143	0.101568
$834$	−6.55787	−0.227081
$835$	5.67088	0.196249
$836$	0.216199	0.00747740
$837$	−62.2227	−2.15073
$838$	−37.5402	−1.29680
$839$	−17.0270	−0.587839	−0.293919	−	0.955830i	$-0.594960\pi$
$839$	−17.0270	−0.587839	−0.293919	+	0.955830i	$0.594960\pi$
$840$	−20.8761	−0.720294
$841$	−8.07079	−0.278303
$842$	46.7859	1.61235
$843$	−31.2792	−1.07731
$844$	2.62440	0.0903355
$845$	3.93035	0.135208
$846$	−61.5720	−2.11689
$847$	−19.2142	−0.660209
$848$	−19.2853	−0.662260
$849$	−44.4205	−1.52451
$850$	−5.31610	−0.182341
$851$	29.0554	0.996007
$852$	−5.11147	−0.175116
$853$	45.4970	1.55779	0.778894	−	0.627156i	$-0.215781\pi$
$853$	45.4970	1.55779	0.778894	+	0.627156i	$0.215781\pi$
$854$	−8.16510	−0.279404
$855$	−15.2390	−0.521164
$856$	−21.4616	−0.733543
$857$	−53.3026	−1.82078	−0.910390	−	0.413750i	$-0.864219\pi$
$857$	−53.3026	−1.82078	−0.910390	+	0.413750i	$0.864219\pi$
$858$	22.8543	0.780232
$859$	−17.6238	−0.601317	−0.300659	−	0.953732i	$-0.597207\pi$
$859$	−17.6238	−0.601317	−0.300659	+	0.953732i	$0.597207\pi$
$860$	0.352330	0.0120144
$861$	28.0617	0.956339
$862$	25.7554	0.877233
$863$	−17.8041	−0.606060	−0.303030	−	0.952981i	$-0.597998\pi$
$863$	−17.8041	−0.606060	−0.303030	+	0.952981i	$0.597998\pi$
$864$	10.0417	0.341624
$865$	−3.15962	−0.107430
$866$	36.9669	1.25619
$867$	−3.34566	−0.113625
$868$	−0.738688	−0.0250727
$869$	−17.0639	−0.578854
$870$	22.5225	0.763585
$871$	−20.6562	−0.699907
$872$	−46.1889	−1.56415
$873$	144.113	4.87749
$874$	6.52124	0.220584
$875$	−19.0874	−0.645273
$876$	−1.74734	−0.0590373
$877$	−56.8544	−1.91984	−0.959919	−	0.280278i	$-0.909573\pi$
$877$	−56.8544	−1.91984	−0.959919	+	0.280278i	$0.909573\pi$
$878$	−15.2219	−0.513715
$879$	52.7064	1.77774
$880$	−4.90891	−0.165479
$881$	13.3642	0.450251	0.225126	−	0.974330i	$-0.427721\pi$
$881$	13.3642	0.450251	0.225126	+	0.974330i	$0.427721\pi$
$882$	33.0874	1.11411
$883$	−21.5093	−0.723844	−0.361922	−	0.932208i	$-0.617879\pi$
$883$	−21.5093	−0.723844	−0.361922	+	0.932208i	$0.617879\pi$
$884$	0.417656	0.0140473
$885$	−3.57374	−0.120130
$886$	−28.0090	−0.940981
$887$	26.2190	0.880347	0.440173	−	0.897913i	$-0.354917\pi$
$887$	26.2190	0.880347	0.440173	+	0.897913i	$0.354917\pi$
$888$	−103.550	−3.47492
$889$	15.1821	0.509191
$890$	−24.0453	−0.806001
$891$	40.7376	1.36476
$892$	−1.58959	−0.0532233
$893$	−9.49838	−0.317851
$894$	37.4268	1.25174
$895$	22.2147	0.742556
$896$	−20.9155	−0.698737
$897$	−37.1480	−1.24034
$898$	−34.0979	−1.13786
$899$	16.3828	0.546398
$900$	3.23347	0.107782
$901$	−5.09517	−0.169745
$902$	6.95513	0.231581
$903$	21.7662	0.724335
$904$	−7.83434	−0.260566
$905$	−1.89956	−0.0631437
$906$	−58.7884	−1.95311
$907$	−18.6301	−0.618604	−0.309302	−	0.950964i	$-0.600095\pi$
$907$	−18.6301	−0.618604	−0.309302	+	0.950964i	$0.600095\pi$
$908$	−0.768082	−0.0254897
$909$	83.0104	2.75328
$910$	−12.1219	−0.401838
$911$	−19.0949	−0.632643	−0.316322	−	0.948652i	$-0.602448\pi$
$911$	−19.0949	−0.632643	−0.316322	+	0.948652i	$0.602448\pi$
$912$	−22.0495	−0.730132
$913$	7.63464	0.252670
$914$	−17.7290	−0.586424
$915$	−10.5014	−0.347165
$916$	−1.67709	−0.0554127
$917$	31.2234	1.03109
$918$	−23.9361	−0.790010
$919$	−5.73946	−0.189327	−0.0946637	−	0.995509i	$-0.530178\pi$
$919$	−5.73946	−0.189327	−0.0946637	+	0.995509i	$0.530178\pi$
$920$	8.41026	0.277278
$921$	−8.77989	−0.289307
$922$	25.4734	0.838920
$923$	−61.0138	−2.00829
$924$	0.837928	0.0275658
$925$	−41.2420	−1.35603
$926$	−1.85107	−0.0608301
$927$	55.0866	1.80928
$928$	−2.64390	−0.0867903
$929$	24.5844	0.806589	0.403295	−	0.915070i	$-0.367865\pi$
$929$	24.5844	0.806589	0.403295	+	0.915070i	$0.367865\pi$
$930$	17.6301	0.578112
$931$	5.10422	0.167284
$932$	−2.34556	−0.0768313
$933$	−3.07014	−0.100512
$934$	−34.8288	−1.13963
$935$	−1.29693	−0.0424143
$936$	96.9087	3.16756
$937$	22.7449	0.743042	0.371521	−	0.928425i	$-0.378836\pi$
$937$	22.7449	0.743042	0.371521	+	0.928425i	$0.378836\pi$
$938$	14.0539	0.458876
$939$	65.9624	2.15260
$940$	−0.595893	−0.0194359
$941$	9.57223	0.312046	0.156023	−	0.987753i	$-0.450133\pi$
$941$	9.57223	0.312046	0.156023	+	0.987753i	$0.450133\pi$
$942$	77.8108	2.53521
$943$	−11.3051	−0.368144
$944$	−3.78501	−0.123192
$945$	−37.4368	−1.21782
$946$	5.39480	0.175400
$947$	−43.4054	−1.41049	−0.705243	−	0.708966i	$-0.749162\pi$
$947$	−43.4054	−1.41049	−0.705243	+	0.708966i	$0.749162\pi$
$948$	−4.80852	−0.156174
$949$	−20.8574	−0.677061
$950$	−9.25642	−0.300318
$951$	−85.5572	−2.77438
$952$	−5.84152	−0.189325
$953$	−18.1574	−0.588177	−0.294088	−	0.955778i	$-0.595016\pi$
$953$	−18.1574	−0.588177	−0.294088	+	0.955778i	$0.595016\pi$
$954$	−57.5099	−1.86195
$955$	−11.6174	−0.375931
$956$	0.519607	0.0168053
$957$	−18.5838	−0.600729
$958$	43.4375	1.40340
$959$	28.9369	0.934420
$960$	−29.8985	−0.964969
$961$	−18.1759	−0.586321
$962$	−60.1276	−1.93859
$963$	−60.7188	−1.95664
$964$	2.21794	0.0714351
$965$	−5.20950	−0.167700
$966$	25.2745	0.813195
$967$	35.6484	1.14638	0.573188	−	0.819424i	$-0.305706\pi$
$967$	35.6484	1.14638	0.573188	+	0.819424i	$0.305706\pi$
$968$	−27.5872	−0.886685
$969$	−5.82548	−0.187141
$970$	−25.8820	−0.831020
$971$	25.4251	0.815929	0.407964	−	0.912998i	$-0.366239\pi$
$971$	25.4251	0.815929	0.407964	+	0.912998i	$0.366239\pi$
$972$	6.14893	0.197227
$973$	−2.87002	−0.0920085
$974$	−13.7553	−0.440747
$975$	52.7289	1.68868
$976$	−11.1222	−0.356013
$977$	−33.3542	−1.06709	−0.533547	−	0.845770i	$-0.679141\pi$
$977$	−33.3542	−1.06709	−0.533547	+	0.845770i	$0.679141\pi$
$978$	16.5974	0.530725
$979$	19.8403	0.634099
$980$	0.320220	0.0102291
$981$	−130.677	−4.17218
$982$	51.2422	1.63520
$983$	0.391921	0.0125003	0.00625016	−	0.999980i	$-0.498010\pi$
$983$	0.391921	0.0125003	0.00625016	+	0.999980i	$0.498010\pi$
$984$	40.2901	1.28440
$985$	12.3062	0.392107
$986$	6.30223	0.200704
$987$	−36.8131	−1.17177
$988$	0.727225	0.0231361
$989$	−8.76887	−0.278834
$990$	−14.6387	−0.465248
$991$	−29.5411	−0.938406	−0.469203	−	0.883090i	$-0.655459\pi$
$991$	−29.5411	−0.938406	−0.469203	+	0.883090i	$0.655459\pi$
$992$	−2.06958	−0.0657092
$993$	−114.593	−3.63651
$994$	41.5122	1.31669
$995$	−11.0457	−0.350172
$996$	2.15140	0.0681697
$997$	−16.7202	−0.529532	−0.264766	−	0.964313i	$-0.585295\pi$
$997$	−16.7202	−0.529532	−0.264766	+	0.964313i	$0.585295\pi$
$998$	−15.7223	−0.497680
$999$	−185.695	−5.87514

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.37758 q^{2} -3.34566 q^{3} -0.102265 q^{4} +1.06817 q^{5} +4.60892 q^{6} +2.01707 q^{7} +2.89604 q^{8} +8.19343 q^{9} +O(q^{10})\)	\(q-1.37758 q^{2} -3.34566 q^{3} -0.102265 q^{4} +1.06817 q^{5} +4.60892 q^{6} +2.01707 q^{7} +2.89604 q^{8} +8.19343 q^{9} -1.47150 q^{10} +1.21416 q^{11} +0.342144 q^{12} +4.08405 q^{13} -2.77868 q^{14} -3.57374 q^{15} -3.78501 q^{16} -1.00000 q^{17} -11.2871 q^{18} -1.74121 q^{19} -0.109237 q^{20} -6.74843 q^{21} -1.67261 q^{22} +2.71871 q^{23} -9.68918 q^{24} -3.85901 q^{25} -5.62612 q^{26} -17.3755 q^{27} -0.206276 q^{28} +4.57485 q^{29} +4.92313 q^{30} +3.58107 q^{31} -0.577922 q^{32} -4.06217 q^{33} +1.37758 q^{34} +2.15458 q^{35} -0.837902 q^{36} +10.6872 q^{37} +2.39865 q^{38} -13.6639 q^{39} +3.09348 q^{40} -4.15825 q^{41} +9.29652 q^{42} -3.22538 q^{43} -0.124166 q^{44} +8.75200 q^{45} -3.74525 q^{46} +5.45506 q^{47} +12.6634 q^{48} -2.93143 q^{49} +5.31610 q^{50} +3.34566 q^{51} -0.417656 q^{52} +5.09517 q^{53} +23.9361 q^{54} +1.29693 q^{55} +5.84152 q^{56} +5.82548 q^{57} -6.30223 q^{58} +1.00000 q^{59} +0.365469 q^{60} +2.93848 q^{61} -4.93322 q^{62} +16.5267 q^{63} +8.36616 q^{64} +4.36248 q^{65} +5.59598 q^{66} -5.05776 q^{67} +0.102265 q^{68} -9.09587 q^{69} -2.96811 q^{70} -14.9395 q^{71} +23.7286 q^{72} -5.10704 q^{73} -14.7225 q^{74} +12.9109 q^{75} +0.178065 q^{76} +2.44905 q^{77} +18.8231 q^{78} -14.0541 q^{79} -4.04305 q^{80} +33.5521 q^{81} +5.72834 q^{82} +6.28800 q^{83} +0.690129 q^{84} -1.06817 q^{85} +4.44323 q^{86} -15.3059 q^{87} +3.51627 q^{88} +16.3407 q^{89} -12.0566 q^{90} +8.23782 q^{91} -0.278029 q^{92} -11.9810 q^{93} -7.51480 q^{94} -1.85991 q^{95} +1.93353 q^{96} +17.5889 q^{97} +4.03829 q^{98} +9.94815 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 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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