LMFDB - Embedded newform 6023.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57032 q^{2} -2.26358 q^{3} +4.60652 q^{4} -0.389233 q^{5} +5.81812 q^{6} +0.261062 q^{7} -6.69959 q^{8} +2.12381 q^{9} +O(q^{10})$	\(q-2.57032 q^{2} -2.26358 q^{3} +4.60652 q^{4} -0.389233 q^{5} +5.81812 q^{6} +0.261062 q^{7} -6.69959 q^{8} +2.12381 q^{9} +1.00045 q^{10} +2.83648 q^{11} -10.4272 q^{12} +6.21071 q^{13} -0.671011 q^{14} +0.881061 q^{15} +8.00701 q^{16} +1.82721 q^{17} -5.45885 q^{18} +1.00000 q^{19} -1.79301 q^{20} -0.590935 q^{21} -7.29065 q^{22} -0.403002 q^{23} +15.1651 q^{24} -4.84850 q^{25} -15.9635 q^{26} +1.98334 q^{27} +1.20259 q^{28} +0.228883 q^{29} -2.26461 q^{30} +3.66452 q^{31} -7.18137 q^{32} -6.42060 q^{33} -4.69650 q^{34} -0.101614 q^{35} +9.78337 q^{36} +8.81137 q^{37} -2.57032 q^{38} -14.0585 q^{39} +2.60770 q^{40} +9.09414 q^{41} +1.51889 q^{42} +10.5100 q^{43} +13.0663 q^{44} -0.826656 q^{45} +1.03584 q^{46} +10.3283 q^{47} -18.1245 q^{48} -6.93185 q^{49} +12.4622 q^{50} -4.13603 q^{51} +28.6098 q^{52} -6.23235 q^{53} -5.09780 q^{54} -1.10405 q^{55} -1.74901 q^{56} -2.26358 q^{57} -0.588301 q^{58} +8.88436 q^{59} +4.05863 q^{60} +1.67277 q^{61} -9.41898 q^{62} +0.554445 q^{63} +2.44436 q^{64} -2.41741 q^{65} +16.5030 q^{66} +8.44237 q^{67} +8.41707 q^{68} +0.912228 q^{69} +0.261180 q^{70} -13.2711 q^{71} -14.2286 q^{72} +4.34841 q^{73} -22.6480 q^{74} +10.9750 q^{75} +4.60652 q^{76} +0.740496 q^{77} +36.1347 q^{78} +12.5066 q^{79} -3.11659 q^{80} -10.8609 q^{81} -23.3748 q^{82} +1.26870 q^{83} -2.72216 q^{84} -0.711210 q^{85} -27.0140 q^{86} -0.518095 q^{87} -19.0032 q^{88} +8.59720 q^{89} +2.12477 q^{90} +1.62138 q^{91} -1.85644 q^{92} -8.29495 q^{93} -26.5471 q^{94} -0.389233 q^{95} +16.2556 q^{96} +14.7253 q^{97} +17.8170 q^{98} +6.02413 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.57032	−1.81749	−0.908744	−	0.417354i	$-0.862957\pi$
$2$	−2.57032	−1.81749	−0.908744	+	0.417354i	$0.862957\pi$
$3$	−2.26358	−1.30688	−0.653440	−	0.756978i	$-0.726675\pi$
$3$	−2.26358	−1.30688	−0.653440	+	0.756978i	$0.726675\pi$
$4$	4.60652	2.30326
$5$	−0.389233	−0.174070	−0.0870352	−	0.996205i	$-0.527739\pi$
$5$	−0.389233	−0.174070	−0.0870352	+	0.996205i	$0.527739\pi$
$6$	5.81812	2.37524
$7$	0.261062	0.0986721	0.0493361	−	0.998782i	$-0.484289\pi$
$7$	0.261062	0.0986721	0.0493361	+	0.998782i	$0.484289\pi$
$8$	−6.69959	−2.36866
$9$	2.12381	0.707936
$10$	1.00045	0.316371
$11$	2.83648	0.855230	0.427615	−	0.903961i	$-0.359354\pi$
$11$	2.83648	0.855230	0.427615	+	0.903961i	$0.359354\pi$
$12$	−10.4272	−3.01009
$13$	6.21071	1.72254	0.861270	−	0.508147i	$-0.169669\pi$
$13$	6.21071	1.72254	0.861270	+	0.508147i	$0.169669\pi$
$14$	−0.671011	−0.179335
$15$	0.881061	0.227489
$16$	8.00701	2.00175
$17$	1.82721	0.443163	0.221581	−	0.975142i	$-0.428878\pi$
$17$	1.82721	0.443163	0.221581	+	0.975142i	$0.428878\pi$
$18$	−5.45885	−1.28666
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.79301	−0.400930
$21$	−0.590935	−0.128953
$22$	−7.29065	−1.55437
$23$	−0.403002	−0.0840317	−0.0420158	−	0.999117i	$-0.513378\pi$
$23$	−0.403002	−0.0840317	−0.0420158	+	0.999117i	$0.513378\pi$
$24$	15.1651	3.09556
$25$	−4.84850	−0.969700
$26$	−15.9635	−3.13070
$27$	1.98334	0.381693
$28$	1.20259	0.227268
$29$	0.228883	0.0425025	0.0212512	−	0.999774i	$-0.493235\pi$
$29$	0.228883	0.0425025	0.0212512	+	0.999774i	$0.493235\pi$
$30$	−2.26461	−0.413459
$31$	3.66452	0.658167	0.329084	−	0.944301i	$-0.393260\pi$
$31$	3.66452	0.658167	0.329084	+	0.944301i	$0.393260\pi$
$32$	−7.18137	−1.26950
$33$	−6.42060	−1.11768
$34$	−4.69650	−0.805443
$35$	−0.101614	−0.0171759
$36$	9.78337	1.63056
$37$	8.81137	1.44858	0.724290	−	0.689495i	$-0.242168\pi$
$37$	8.81137	1.44858	0.724290	+	0.689495i	$0.242168\pi$
$38$	−2.57032	−0.416960
$39$	−14.0585	−2.25115
$40$	2.60770	0.412314
$41$	9.09414	1.42027	0.710133	−	0.704067i	$-0.248635\pi$
$41$	9.09414	1.42027	0.710133	+	0.704067i	$0.248635\pi$
$42$	1.51889	0.234370
$43$	10.5100	1.60276	0.801378	−	0.598158i	$-0.204101\pi$
$43$	10.5100	1.60276	0.801378	+	0.598158i	$0.204101\pi$
$44$	13.0663	1.96982
$45$	−0.826656	−0.123231
$46$	1.03584	0.152727
$47$	10.3283	1.50654	0.753271	−	0.657710i	$-0.228475\pi$
$47$	10.3283	1.50654	0.753271	+	0.657710i	$0.228475\pi$
$48$	−18.1245	−2.61605
$49$	−6.93185	−0.990264
$50$	12.4622	1.76242
$51$	−4.13603	−0.579161
$52$	28.6098	3.96746
$53$	−6.23235	−0.856079	−0.428039	−	0.903760i	$-0.640796\pi$
$53$	−6.23235	−0.856079	−0.428039	+	0.903760i	$0.640796\pi$
$54$	−5.09780	−0.693722
$55$	−1.10405	−0.148870
$56$	−1.74901	−0.233721
$57$	−2.26358	−0.299819
$58$	−0.588301	−0.0772477
$59$	8.88436	1.15665	0.578323	−	0.815808i	$-0.303707\pi$
$59$	8.88436	1.15665	0.578323	+	0.815808i	$0.303707\pi$
$60$	4.05863	0.523967
$61$	1.67277	0.214176	0.107088	−	0.994250i	$-0.465847\pi$
$61$	1.67277	0.214176	0.107088	+	0.994250i	$0.465847\pi$
$62$	−9.41898	−1.19621
$63$	0.554445	0.0698535
$64$	2.44436	0.305545
$65$	−2.41741	−0.299843
$66$	16.5030	2.03138
$67$	8.44237	1.03140	0.515700	−	0.856769i	$-0.327532\pi$
$67$	8.44237	1.03140	0.515700	+	0.856769i	$0.327532\pi$
$68$	8.41707	1.02072
$69$	0.912228	0.109819
$70$	0.261180	0.0312170
$71$	−13.2711	−1.57499	−0.787494	−	0.616322i	$-0.788622\pi$
$71$	−13.2711	−1.57499	−0.787494	+	0.616322i	$0.788622\pi$
$72$	−14.2286	−1.67686
$73$	4.34841	0.508942	0.254471	−	0.967080i	$-0.418099\pi$
$73$	4.34841	0.508942	0.254471	+	0.967080i	$0.418099\pi$
$74$	−22.6480	−2.63278
$75$	10.9750	1.26728
$76$	4.60652	0.528404
$77$	0.740496	0.0843874
$78$	36.1347	4.09144
$79$	12.5066	1.40710	0.703549	−	0.710647i	$-0.251597\pi$
$79$	12.5066	1.40710	0.703549	+	0.710647i	$0.251597\pi$
$80$	−3.11659	−0.348446
$81$	−10.8609	−1.20676
$82$	−23.3748	−2.58132
$83$	1.26870	0.139258	0.0696291	−	0.997573i	$-0.477818\pi$
$83$	1.26870	0.139258	0.0696291	+	0.997573i	$0.477818\pi$
$84$	−2.72216	−0.297012
$85$	−0.711210	−0.0771415
$86$	−27.0140	−2.91299
$87$	−0.518095	−0.0555456
$88$	−19.0032	−2.02575
$89$	8.59720	0.911302	0.455651	−	0.890159i	$-0.349407\pi$
$89$	8.59720	0.911302	0.455651	+	0.890159i	$0.349407\pi$
$90$	2.12477	0.223970
$91$	1.62138	0.169967
$92$	−1.85644	−0.193547
$93$	−8.29495	−0.860146
$94$	−26.5471	−2.73812
$95$	−0.389233	−0.0399345
$96$	16.2556	1.65908
$97$	14.7253	1.49512	0.747562	−	0.664192i	$-0.231224\pi$
$97$	14.7253	1.49512	0.747562	+	0.664192i	$0.231224\pi$
$98$	17.8170	1.79979
$99$	6.02413	0.605448
$100$	−22.3347	−2.23347
$101$	7.75298	0.771450	0.385725	−	0.922614i	$-0.373951\pi$
$101$	7.75298	0.771450	0.385725	+	0.922614i	$0.373951\pi$
$102$	10.6309	1.05262
$103$	5.04758	0.497353	0.248677	−	0.968587i	$-0.420004\pi$
$103$	5.04758	0.497353	0.248677	+	0.968587i	$0.420004\pi$
$104$	−41.6092	−4.08012
$105$	0.230012	0.0224468
$106$	16.0191	1.55591
$107$	−7.05328	−0.681866	−0.340933	−	0.940088i	$-0.610743\pi$
$107$	−7.05328	−0.681866	−0.340933	+	0.940088i	$0.610743\pi$
$108$	9.13628	0.879139
$109$	12.3951	1.18723	0.593615	−	0.804749i	$-0.297700\pi$
$109$	12.3951	1.18723	0.593615	+	0.804749i	$0.297700\pi$
$110$	2.83776	0.270570
$111$	−19.9453	−1.89312
$112$	2.09032	0.197517
$113$	−8.81915	−0.829636	−0.414818	−	0.909904i	$-0.636155\pi$
$113$	−8.81915	−0.829636	−0.414818	+	0.909904i	$0.636155\pi$
$114$	5.81812	0.544917
$115$	0.156862	0.0146274
$116$	1.05435	0.0978943
$117$	13.1903	1.21945
$118$	−22.8356	−2.10219
$119$	0.477014	0.0437278
$120$	−5.90275	−0.538845
$121$	−2.95439	−0.268581
$122$	−4.29954	−0.389262
$123$	−20.5853	−1.85612
$124$	16.8807	1.51593
$125$	3.83336	0.342866
$126$	−1.42510	−0.126958
$127$	19.8536	1.76172	0.880861	−	0.473375i	$-0.156964\pi$
$127$	19.8536	1.76172	0.880861	+	0.473375i	$0.156964\pi$
$128$	8.07995	0.714173
$129$	−23.7902	−2.09461
$130$	6.21352	0.544961
$131$	−3.72048	−0.325060	−0.162530	−	0.986704i	$-0.551965\pi$
$131$	−3.72048	−0.325060	−0.162530	+	0.986704i	$0.551965\pi$
$132$	−29.5767	−2.57432
$133$	0.261062	0.0226369
$134$	−21.6995	−1.87456
$135$	−0.771980	−0.0664414
$136$	−12.2415	−1.04970
$137$	−13.6918	−1.16977	−0.584885	−	0.811116i	$-0.698860\pi$
$137$	−13.6918	−1.16977	−0.584885	+	0.811116i	$0.698860\pi$
$138$	−2.34471	−0.199595
$139$	−3.04790	−0.258519	−0.129260	−	0.991611i	$-0.541260\pi$
$139$	−3.04790	−0.258519	−0.129260	+	0.991611i	$0.541260\pi$
$140$	−0.468087	−0.0395606
$141$	−23.3790	−1.96887
$142$	34.1109	2.86252
$143$	17.6165	1.47317
$144$	17.0053	1.41711
$145$	−0.0890888	−0.00739842
$146$	−11.1768	−0.924997
$147$	15.6908	1.29416
$148$	40.5898	3.33646
$149$	6.24501	0.511611	0.255805	−	0.966728i	$-0.417659\pi$
$149$	6.24501	0.511611	0.255805	+	0.966728i	$0.417659\pi$
$150$	−28.2092	−2.30327
$151$	4.43448	0.360873	0.180437	−	0.983587i	$-0.442249\pi$
$151$	4.43448	0.360873	0.180437	+	0.983587i	$0.442249\pi$
$152$	−6.69959	−0.543408
$153$	3.88064	0.313731
$154$	−1.90331	−0.153373
$155$	−1.42635	−0.114567
$156$	−64.7606	−5.18500
$157$	1.97698	0.157780	0.0788901	−	0.996883i	$-0.474862\pi$
$157$	1.97698	0.157780	0.0788901	+	0.996883i	$0.474862\pi$
$158$	−32.1458	−2.55738
$159$	14.1074	1.11879
$160$	2.79523	0.220982
$161$	−0.105208	−0.00829158
$162$	27.9159	2.19328
$163$	−11.1343	−0.872105	−0.436053	−	0.899921i	$-0.643624\pi$
$163$	−11.1343	−0.872105	−0.436053	+	0.899921i	$0.643624\pi$
$164$	41.8924	3.27124
$165$	2.49911	0.194556
$166$	−3.26097	−0.253100
$167$	−9.87228	−0.763940	−0.381970	−	0.924175i	$-0.624754\pi$
$167$	−9.87228	−0.763940	−0.381970	+	0.924175i	$0.624754\pi$
$168$	3.95902	0.305445
$169$	25.5729	1.96715
$170$	1.82803	0.140204
$171$	2.12381	0.162412
$172$	48.4144	3.69157
$173$	17.0667	1.29756	0.648779	−	0.760977i	$-0.275280\pi$
$173$	17.0667	1.29756	0.648779	+	0.760977i	$0.275280\pi$
$174$	1.33167	0.100954
$175$	−1.26576	−0.0956823
$176$	22.7117	1.71196
$177$	−20.1105	−1.51160
$178$	−22.0975	−1.65628
$179$	−26.6526	−1.99211	−0.996055	−	0.0887352i	$-0.971718\pi$
$179$	−26.6526	−1.99211	−0.996055	+	0.0887352i	$0.971718\pi$
$180$	−3.80801	−0.283832
$181$	−1.86303	−0.138478	−0.0692390	−	0.997600i	$-0.522057\pi$
$181$	−1.86303	−0.138478	−0.0692390	+	0.997600i	$0.522057\pi$
$182$	−4.16746	−0.308912
$183$	−3.78645	−0.279902
$184$	2.69995	0.199043
$185$	−3.42968	−0.252155
$186$	21.3206	1.56330
$187$	5.18283	0.379006
$188$	47.5777	3.46996
$189$	0.517773	0.0376625
$190$	1.00045	0.0725804
$191$	−8.03702	−0.581538	−0.290769	−	0.956793i	$-0.593911\pi$
$191$	−8.03702	−0.581538	−0.290769	+	0.956793i	$0.593911\pi$
$192$	−5.53302	−0.399311
$193$	6.32329	0.455160	0.227580	−	0.973759i	$-0.426919\pi$
$193$	6.32329	0.455160	0.227580	+	0.973759i	$0.426919\pi$
$194$	−37.8486	−2.71737
$195$	5.47202	0.391859
$196$	−31.9317	−2.28084
$197$	26.9129	1.91747	0.958734	−	0.284306i	$-0.0917632\pi$
$197$	26.9129	1.91747	0.958734	+	0.284306i	$0.0917632\pi$
$198$	−15.4839	−1.10039
$199$	−20.8689	−1.47936	−0.739678	−	0.672961i	$-0.765022\pi$
$199$	−20.8689	−1.47936	−0.739678	+	0.672961i	$0.765022\pi$
$200$	32.4829	2.29689
$201$	−19.1100	−1.34792
$202$	−19.9276	−1.40210
$203$	0.0597526	0.00419381
$204$	−19.0527	−1.33396
$205$	−3.53974	−0.247226
$206$	−12.9739	−0.903933
$207$	−0.855898	−0.0594890
$208$	49.7292	3.44810
$209$	2.83648	0.196203
$210$	−0.591202	−0.0407968
$211$	−4.38654	−0.301982	−0.150991	−	0.988535i	$-0.548246\pi$
$211$	−4.38654	−0.301982	−0.150991	+	0.988535i	$0.548246\pi$
$212$	−28.7095	−1.97177
$213$	30.0402	2.05832
$214$	18.1291	1.23928
$215$	−4.09083	−0.278992
$216$	−13.2875	−0.904102
$217$	0.956666	0.0649428
$218$	−31.8592	−2.15778
$219$	−9.84298	−0.665127
$220$	−5.08584	−0.342887
$221$	11.3483	0.763366
$222$	51.2656	3.44072
$223$	−8.04127	−0.538483	−0.269241	−	0.963073i	$-0.586773\pi$
$223$	−8.04127	−0.538483	−0.269241	+	0.963073i	$0.586773\pi$
$224$	−1.87478	−0.125264
$225$	−10.2973	−0.686485
$226$	22.6680	1.50785
$227$	−14.4362	−0.958165	−0.479082	−	0.877770i	$-0.659031\pi$
$227$	−14.4362	−0.958165	−0.479082	+	0.877770i	$0.659031\pi$
$228$	−10.4272	−0.690561
$229$	0.219641	0.0145143	0.00725715	−	0.999974i	$-0.497690\pi$
$229$	0.219641	0.0145143	0.00725715	+	0.999974i	$0.497690\pi$
$230$	−0.403184	−0.0265852
$231$	−1.67617	−0.110284
$232$	−1.53342	−0.100674
$233$	−10.2445	−0.671140	−0.335570	−	0.942015i	$-0.608929\pi$
$233$	−10.2445	−0.671140	−0.335570	+	0.942015i	$0.608929\pi$
$234$	−33.9034	−2.21633
$235$	−4.02013	−0.262244
$236$	40.9260	2.66406
$237$	−28.3096	−1.83891
$238$	−1.22608	−0.0794748
$239$	−10.1930	−0.659331	−0.329666	−	0.944098i	$-0.606936\pi$
$239$	−10.1930	−0.659331	−0.329666	+	0.944098i	$0.606936\pi$
$240$	7.05467	0.455377
$241$	−20.9999	−1.35272	−0.676361	−	0.736570i	$-0.736444\pi$
$241$	−20.9999	−1.35272	−0.676361	+	0.736570i	$0.736444\pi$
$242$	7.59371	0.488142
$243$	18.6345	1.19540
$244$	7.70565	0.493304
$245$	2.69810	0.172376
$246$	52.9108	3.37347
$247$	6.21071	0.395178
$248$	−24.5508	−1.55898
$249$	−2.87181	−0.181994
$250$	−9.85295	−0.623155
$251$	−13.2291	−0.835013	−0.417507	−	0.908674i	$-0.637096\pi$
$251$	−13.2291	−0.835013	−0.417507	+	0.908674i	$0.637096\pi$
$252$	2.55406	0.160891
$253$	−1.14311	−0.0718665
$254$	−51.0300	−3.20191
$255$	1.60988	0.100815
$256$	−25.6567	−1.60355
$257$	−20.1449	−1.25660	−0.628301	−	0.777971i	$-0.716249\pi$
$257$	−20.1449	−1.25660	−0.628301	+	0.777971i	$0.716249\pi$
$258$	61.1483	3.80693
$259$	2.30031	0.142934
$260$	−11.1359	−0.690617
$261$	0.486103	0.0300890
$262$	9.56282	0.590793
$263$	−21.1638	−1.30502	−0.652508	−	0.757782i	$-0.726283\pi$
$263$	−21.1638	−1.30502	−0.652508	+	0.757782i	$0.726283\pi$
$264$	43.0154	2.64741
$265$	2.42584	0.149018
$266$	−0.671011	−0.0411423
$267$	−19.4605	−1.19096
$268$	38.8900	2.37558
$269$	3.82036	0.232932	0.116466	−	0.993195i	$-0.462843\pi$
$269$	3.82036	0.232932	0.116466	+	0.993195i	$0.462843\pi$
$270$	1.98423	0.120756
$271$	−25.7355	−1.56332	−0.781660	−	0.623705i	$-0.785627\pi$
$271$	−25.7355	−1.56332	−0.781660	+	0.623705i	$0.785627\pi$
$272$	14.6305	0.887102
$273$	−3.67013	−0.222126
$274$	35.1923	2.12604
$275$	−13.7527	−0.829317
$276$	4.20220	0.252943
$277$	20.7462	1.24652	0.623258	−	0.782016i	$-0.285809\pi$
$277$	20.7462	1.24652	0.623258	+	0.782016i	$0.285809\pi$
$278$	7.83406	0.469856
$279$	7.78273	0.465940
$280$	0.680771	0.0406839
$281$	−7.73977	−0.461716	−0.230858	−	0.972987i	$-0.574153\pi$
$281$	−7.73977	−0.461716	−0.230858	+	0.972987i	$0.574153\pi$
$282$	60.0915	3.57840
$283$	26.8246	1.59456	0.797279	−	0.603610i	$-0.206272\pi$
$283$	26.8246	1.59456	0.797279	+	0.603610i	$0.206272\pi$
$284$	−61.1336	−3.62761
$285$	0.881061	0.0521896
$286$	−45.2801	−2.67747
$287$	2.37413	0.140141
$288$	−15.2518	−0.898723
$289$	−13.6613	−0.803607
$290$	0.228986	0.0134465
$291$	−33.3318	−1.95395
$292$	20.0310	1.17223
$293$	−16.1767	−0.945053	−0.472527	−	0.881316i	$-0.656658\pi$
$293$	−16.1767	−0.945053	−0.472527	+	0.881316i	$0.656658\pi$
$294$	−40.3303	−2.35211
$295$	−3.45809	−0.201338
$296$	−59.0325	−3.43120
$297$	5.62569	0.326436
$298$	−16.0516	−0.929846
$299$	−2.50293	−0.144748
$300$	50.5565	2.91888
$301$	2.74375	0.158147
$302$	−11.3980	−0.655882
$303$	−17.5495	−1.00819
$304$	8.00701	0.459233
$305$	−0.651097	−0.0372817
$306$	−9.97446	−0.570202
$307$	−1.11707	−0.0637548	−0.0318774	−	0.999492i	$-0.510149\pi$
$307$	−1.11707	−0.0637548	−0.0318774	+	0.999492i	$0.510149\pi$
$308$	3.41111	0.194366
$309$	−11.4256	−0.649981
$310$	3.66618	0.208225
$311$	−31.5539	−1.78926	−0.894628	−	0.446812i	$-0.852559\pi$
$311$	−31.5539	−1.78926	−0.894628	+	0.446812i	$0.852559\pi$
$312$	94.1858	5.33222
$313$	10.2668	0.580311	0.290156	−	0.956979i	$-0.406293\pi$
$313$	10.2668	0.580311	0.290156	+	0.956979i	$0.406293\pi$
$314$	−5.08147	−0.286764
$315$	−0.215808	−0.0121594
$316$	57.6118	3.24092
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−36.2606	−2.03339
$319$	0.649221	0.0363494
$320$	−0.951427	−0.0531864
$321$	15.9657	0.891117
$322$	0.270419	0.0150698
$323$	1.82721	0.101669
$324$	−50.0308	−2.77949
$325$	−30.1126	−1.67035
$326$	28.6186	1.58504
$327$	−28.0572	−1.55157
$328$	−60.9270	−3.36413
$329$	2.69633	0.148654
$330$	−6.42351	−0.353602
$331$	−5.48845	−0.301672	−0.150836	−	0.988559i	$-0.548197\pi$
$331$	−5.48845	−0.301672	−0.150836	+	0.988559i	$0.548197\pi$
$332$	5.84431	0.320748
$333$	18.7136	1.02550
$334$	25.3749	1.38845
$335$	−3.28605	−0.179536
$336$	−4.73162	−0.258131
$337$	−9.99695	−0.544569	−0.272284	−	0.962217i	$-0.587779\pi$
$337$	−9.99695	−0.544569	−0.272284	+	0.962217i	$0.587779\pi$
$338$	−65.7304	−3.57526
$339$	19.9629	1.08424
$340$	−3.27620	−0.177677
$341$	10.3943	0.562885
$342$	−5.45885	−0.295181
$343$	−3.63707	−0.196384
$344$	−70.4125	−3.79639
$345$	−0.355069	−0.0191163
$346$	−43.8668	−2.35830
$347$	−8.89686	−0.477608	−0.238804	−	0.971068i	$-0.576755\pi$
$347$	−8.89686	−0.477608	−0.238804	+	0.971068i	$0.576755\pi$
$348$	−2.38662	−0.127936
$349$	22.4803	1.20334	0.601672	−	0.798743i	$-0.294502\pi$
$349$	22.4803	1.20334	0.601672	+	0.798743i	$0.294502\pi$
$350$	3.25340	0.173901
$351$	12.3179	0.657482
$352$	−20.3698	−1.08571
$353$	25.1311	1.33759	0.668796	−	0.743446i	$-0.266810\pi$
$353$	25.1311	1.33759	0.668796	+	0.743446i	$0.266810\pi$
$354$	51.6903	2.74731
$355$	5.16555	0.274159
$356$	39.6032	2.09897
$357$	−1.07976	−0.0571470
$358$	68.5057	3.62064
$359$	5.42795	0.286476	0.143238	−	0.989688i	$-0.454249\pi$
$359$	5.42795	0.286476	0.143238	+	0.989688i	$0.454249\pi$
$360$	5.53825	0.291892
$361$	1.00000	0.0526316
$362$	4.78858	0.251682
$363$	6.68750	0.351003
$364$	7.46892	0.391478
$365$	−1.69254	−0.0885918
$366$	9.73237	0.508719
$367$	−34.1429	−1.78225	−0.891123	−	0.453762i	$-0.850082\pi$
$367$	−34.1429	−1.78225	−0.891123	+	0.453762i	$0.850082\pi$
$368$	−3.22684	−0.168211
$369$	19.3142	1.00546
$370$	8.81535	0.458288
$371$	−1.62703	−0.0844711
$372$	−38.2109	−1.98114
$373$	−22.0575	−1.14210	−0.571048	−	0.820917i	$-0.693463\pi$
$373$	−22.0575	−1.14210	−0.571048	+	0.820917i	$0.693463\pi$
$374$	−13.3215	−0.688839
$375$	−8.67713	−0.448085
$376$	−69.1956	−3.56849
$377$	1.42152	0.0732122
$378$	−1.33084	−0.0684510
$379$	2.05827	0.105726	0.0528632	−	0.998602i	$-0.483165\pi$
$379$	2.05827	0.105726	0.0528632	+	0.998602i	$0.483165\pi$
$380$	−1.79301	−0.0919795
$381$	−44.9403	−2.30236
$382$	20.6577	1.05694
$383$	21.8098	1.11443	0.557215	−	0.830369i	$-0.311870\pi$
$383$	21.8098	1.11443	0.557215	+	0.830369i	$0.311870\pi$
$384$	−18.2896	−0.933339
$385$	−0.288226	−0.0146893
$386$	−16.2528	−0.827248
$387$	22.3212	1.13465
$388$	67.8323	3.44366
$389$	−28.5151	−1.44577	−0.722886	−	0.690967i	$-0.757185\pi$
$389$	−28.5151	−1.44577	−0.722886	+	0.690967i	$0.757185\pi$
$390$	−14.0648	−0.712199
$391$	−0.736368	−0.0372397
$392$	46.4405	2.34560
$393$	8.42162	0.424815
$394$	−69.1747	−3.48497
$395$	−4.86797	−0.244934
$396$	27.7503	1.39451
$397$	−0.946267	−0.0474918	−0.0237459	−	0.999718i	$-0.507559\pi$
$397$	−0.946267	−0.0474918	−0.0237459	+	0.999718i	$0.507559\pi$
$398$	53.6396	2.68871
$399$	−0.590935	−0.0295838
$400$	−38.8220	−1.94110
$401$	31.2975	1.56292	0.781462	−	0.623953i	$-0.214474\pi$
$401$	31.2975	1.56292	0.781462	+	0.623953i	$0.214474\pi$
$402$	49.1187	2.44982
$403$	22.7593	1.13372
$404$	35.7143	1.77685
$405$	4.22741	0.210062
$406$	−0.153583	−0.00762219
$407$	24.9933	1.23887
$408$	27.7097	1.37184
$409$	23.9694	1.18521	0.592606	−	0.805493i	$-0.298099\pi$
$409$	23.9694	1.18521	0.592606	+	0.805493i	$0.298099\pi$
$410$	9.09825	0.449331
$411$	30.9925	1.52875
$412$	23.2518	1.14553
$413$	2.31937	0.114129
$414$	2.19993	0.108121
$415$	−0.493821	−0.0242407
$416$	−44.6014	−2.18676
$417$	6.89917	0.337854
$418$	−7.29065	−0.356597
$419$	23.7334	1.15945	0.579727	−	0.814811i	$-0.303159\pi$
$419$	23.7334	1.15945	0.579727	+	0.814811i	$0.303159\pi$
$420$	1.05955	0.0517009
$421$	7.43771	0.362492	0.181246	−	0.983438i	$-0.441987\pi$
$421$	7.43771	0.362492	0.181246	+	0.983438i	$0.441987\pi$
$422$	11.2748	0.548849
$423$	21.9354	1.06654
$424$	41.7542	2.02776
$425$	−8.85921	−0.429735
$426$	−77.2128	−3.74097
$427$	0.436696	0.0211332
$428$	−32.4911	−1.57052
$429$	−39.8765	−1.92526
$430$	10.5147	0.507065
$431$	−9.73853	−0.469089	−0.234544	−	0.972105i	$-0.575360\pi$
$431$	−9.73853	−0.469089	−0.234544	+	0.972105i	$0.575360\pi$
$432$	15.8806	0.764055
$433$	17.4701	0.839559	0.419780	−	0.907626i	$-0.362107\pi$
$433$	17.4701	0.839559	0.419780	+	0.907626i	$0.362107\pi$
$434$	−2.45893	−0.118033
$435$	0.201660	0.00966885
$436$	57.0981	2.73450
$437$	−0.403002	−0.0192782
$438$	25.2996	1.20886
$439$	−12.1478	−0.579785	−0.289892	−	0.957059i	$-0.593620\pi$
$439$	−12.1478	−0.579785	−0.289892	+	0.957059i	$0.593620\pi$
$440$	7.39669	0.352623
$441$	−14.7219	−0.701043
$442$	−29.1686	−1.38741
$443$	−24.0304	−1.14172	−0.570859	−	0.821048i	$-0.693390\pi$
$443$	−24.0304	−1.14172	−0.570859	+	0.821048i	$0.693390\pi$
$444$	−91.8783	−4.36035
$445$	−3.34632	−0.158631
$446$	20.6686	0.978686
$447$	−14.1361	−0.668614
$448$	0.638130	0.0301488
$449$	21.7301	1.02551	0.512753	−	0.858536i	$-0.328626\pi$
$449$	21.7301	1.02551	0.512753	+	0.858536i	$0.328626\pi$
$450$	26.4672	1.24768
$451$	25.7953	1.21466
$452$	−40.6256	−1.91087
$453$	−10.0378	−0.471618
$454$	37.1056	1.74145
$455$	−0.631094	−0.0295862
$456$	15.1651	0.710170
$457$	16.3713	0.765817	0.382909	−	0.923786i	$-0.374922\pi$
$457$	16.3713	0.765817	0.382909	+	0.923786i	$0.374922\pi$
$458$	−0.564547	−0.0263796
$459$	3.62396	0.169152
$460$	0.722587	0.0336908
$461$	30.1192	1.40279	0.701395	−	0.712773i	$-0.252561\pi$
$461$	30.1192	1.40279	0.701395	+	0.712773i	$0.252561\pi$
$462$	4.30830	0.200440
$463$	8.41881	0.391255	0.195628	−	0.980678i	$-0.437326\pi$
$463$	8.41881	0.391255	0.195628	+	0.980678i	$0.437326\pi$
$464$	1.83267	0.0850794
$465$	3.22867	0.149726
$466$	26.3316	1.21979
$467$	8.68359	0.401829	0.200914	−	0.979609i	$-0.435609\pi$
$467$	8.68359	0.401829	0.200914	+	0.979609i	$0.435609\pi$
$468$	60.7616	2.80871
$469$	2.20398	0.101770
$470$	10.3330	0.476626
$471$	−4.47506	−0.206200
$472$	−59.5216	−2.73970
$473$	29.8113	1.37073
$474$	72.7647	3.34219
$475$	−4.84850	−0.222464
$476$	2.19738	0.100717
$477$	−13.2363	−0.606049
$478$	26.1993	1.19833
$479$	12.0446	0.550330	0.275165	−	0.961397i	$-0.411267\pi$
$479$	12.0446	0.550330	0.275165	+	0.961397i	$0.411267\pi$
$480$	−6.32723	−0.288797
$481$	54.7248	2.49524
$482$	53.9764	2.45856
$483$	0.238148	0.0108361
$484$	−13.6095	−0.618612
$485$	−5.73156	−0.260257
$486$	−47.8964	−2.17263
$487$	−26.5900	−1.20491	−0.602454	−	0.798154i	$-0.705810\pi$
$487$	−26.5900	−1.20491	−0.602454	+	0.798154i	$0.705810\pi$
$488$	−11.2069	−0.507311
$489$	25.2034	1.13974
$490$	−6.93498	−0.313290
$491$	−8.74221	−0.394531	−0.197265	−	0.980350i	$-0.563206\pi$
$491$	−8.74221	−0.394531	−0.197265	+	0.980350i	$0.563206\pi$
$492$	−94.8269	−4.27513
$493$	0.418216	0.0188355
$494$	−15.9635	−0.718231
$495$	−2.34479	−0.105391
$496$	29.3419	1.31749
$497$	−3.46457	−0.155407
$498$	7.38146	0.330771
$499$	−36.4866	−1.63336	−0.816682	−	0.577088i	$-0.804189\pi$
$499$	−36.4866	−1.63336	−0.816682	+	0.577088i	$0.804189\pi$
$500$	17.6585	0.789711
$501$	22.3467	0.998378
$502$	34.0030	1.51763
$503$	2.53535	0.113046	0.0565229	−	0.998401i	$-0.481999\pi$
$503$	2.53535	0.113046	0.0565229	+	0.998401i	$0.481999\pi$
$504$	−3.71455	−0.165459
$505$	−3.01772	−0.134287
$506$	2.93814	0.130616
$507$	−57.8864	−2.57082
$508$	91.4561	4.05771
$509$	3.46789	0.153712	0.0768558	−	0.997042i	$-0.475512\pi$
$509$	3.46789	0.153712	0.0768558	+	0.997042i	$0.475512\pi$
$510$	−4.13790	−0.183229
$511$	1.13520	0.0502184
$512$	49.7860	2.20025
$513$	1.98334	0.0875664
$514$	51.7786	2.28386
$515$	−1.96469	−0.0865744
$516$	−109.590	−4.82443
$517$	29.2961	1.28844
$518$	−5.91253	−0.259782
$519$	−38.6319	−1.69575
$520$	16.1957	0.710227
$521$	−32.0007	−1.40198	−0.700989	−	0.713172i	$-0.747258\pi$
$521$	−32.0007	−1.40198	−0.700989	+	0.713172i	$0.747258\pi$
$522$	−1.24944	−0.0546864
$523$	44.2759	1.93605	0.968026	−	0.250851i	$-0.0807105\pi$
$523$	44.2759	1.93605	0.968026	+	0.250851i	$0.0807105\pi$
$524$	−17.1385	−0.748699
$525$	2.86515	0.125045
$526$	54.3977	2.37185
$527$	6.69584	0.291675
$528$	−51.4098	−2.23733
$529$	−22.8376	−0.992939
$530$	−6.23516	−0.270838
$531$	18.8687	0.818831
$532$	1.20259	0.0521388
$533$	56.4811	2.44647
$534$	50.0196	2.16456
$535$	2.74537	0.118693
$536$	−56.5604	−2.44304
$537$	60.3304	2.60345
$538$	−9.81954	−0.423350
$539$	−19.6620	−0.846904
$540$	−3.55614	−0.153032
$541$	−11.8885	−0.511128	−0.255564	−	0.966792i	$-0.582261\pi$
$541$	−11.8885	−0.511128	−0.255564	+	0.966792i	$0.582261\pi$
$542$	66.1483	2.84131
$543$	4.21713	0.180974
$544$	−13.1218	−0.562595
$545$	−4.82457	−0.206662
$546$	9.43338	0.403711
$547$	−30.1491	−1.28908	−0.644540	−	0.764570i	$-0.722951\pi$
$547$	−30.1491	−1.28908	−0.644540	+	0.764570i	$0.722951\pi$
$548$	−63.0716	−2.69429
$549$	3.55264	0.151623
$550$	35.3487	1.50727
$551$	0.228883	0.00975073
$552$	−6.11155	−0.260125
$553$	3.26499	0.138841
$554$	−53.3242	−2.26553
$555$	7.76336	0.329536
$556$	−14.0402	−0.595438
$557$	−21.2197	−0.899109	−0.449555	−	0.893253i	$-0.648417\pi$
$557$	−21.2197	−0.899109	−0.449555	+	0.893253i	$0.648417\pi$
$558$	−20.0041	−0.846841
$559$	65.2744	2.76081
$560$	−0.813624	−0.0343819
$561$	−11.7318	−0.495316
$562$	19.8937	0.839163
$563$	43.2392	1.82232	0.911158	−	0.412056i	$-0.135189\pi$
$563$	43.2392	1.82232	0.911158	+	0.412056i	$0.135189\pi$
$564$	−107.696	−4.53482
$565$	3.43271	0.144415
$566$	−68.9478	−2.89809
$567$	−2.83536	−0.119074
$568$	88.9108	3.73061
$569$	−41.0411	−1.72053	−0.860265	−	0.509847i	$-0.829702\pi$
$569$	−41.0411	−1.72053	−0.860265	+	0.509847i	$0.829702\pi$
$570$	−2.26461	−0.0948539
$571$	38.0669	1.59305	0.796525	−	0.604606i	$-0.206669\pi$
$571$	38.0669	1.59305	0.796525	+	0.604606i	$0.206669\pi$
$572$	81.1510	3.39309
$573$	18.1925	0.760001
$574$	−6.10227	−0.254704
$575$	1.95395	0.0814855
$576$	5.19136	0.216306
$577$	−32.6493	−1.35921	−0.679604	−	0.733579i	$-0.737848\pi$
$577$	−32.6493	−1.35921	−0.679604	+	0.733579i	$0.737848\pi$
$578$	35.1139	1.46055
$579$	−14.3133	−0.594840
$580$	−0.410389	−0.0170405
$581$	0.331210	0.0137409
$582$	85.6734	3.55128
$583$	−17.6779	−0.732145
$584$	−29.1325	−1.20551
$585$	−5.13412	−0.212270
$586$	41.5792	1.71762
$587$	−11.5269	−0.475764	−0.237882	−	0.971294i	$-0.576453\pi$
$587$	−11.5269	−0.475764	−0.237882	+	0.971294i	$0.576453\pi$
$588$	72.2801	2.98078
$589$	3.66452	0.150994
$590$	8.88838	0.365929
$591$	−60.9197	−2.50590
$592$	70.5527	2.89970
$593$	44.8019	1.83980	0.919898	−	0.392158i	$-0.128271\pi$
$593$	44.8019	1.83980	0.919898	+	0.392158i	$0.128271\pi$
$594$	−14.4598	−0.593293
$595$	−0.185670	−0.00761171
$596$	28.7678	1.17837
$597$	47.2384	1.93334
$598$	6.43331	0.263078
$599$	23.4373	0.957622	0.478811	−	0.877918i	$-0.341068\pi$
$599$	23.4373	0.957622	0.478811	+	0.877918i	$0.341068\pi$
$600$	−73.5278	−3.00176
$601$	−13.3710	−0.545416	−0.272708	−	0.962097i	$-0.587919\pi$
$601$	−13.3710	−0.545416	−0.272708	+	0.962097i	$0.587919\pi$
$602$	−7.05231	−0.287431
$603$	17.9300	0.730164
$604$	20.4275	0.831185
$605$	1.14995	0.0467520
$606$	45.1078	1.83238
$607$	−20.8131	−0.844779	−0.422389	−	0.906415i	$-0.638808\pi$
$607$	−20.8131	−0.844779	−0.422389	+	0.906415i	$0.638808\pi$
$608$	−7.18137	−0.291243
$609$	−0.135255	−0.00548080
$610$	1.67352	0.0677590
$611$	64.1463	2.59508
$612$	17.8762	0.722604
$613$	23.0730	0.931909	0.465954	−	0.884809i	$-0.345711\pi$
$613$	23.0730	0.931909	0.465954	+	0.884809i	$0.345711\pi$
$614$	2.87123	0.115874
$615$	8.01250	0.323095
$616$	−4.96102	−0.199885
$617$	32.3922	1.30406	0.652030	−	0.758194i	$-0.273918\pi$
$617$	32.3922	1.30406	0.652030	+	0.758194i	$0.273918\pi$
$618$	29.3675	1.18133
$619$	8.21280	0.330100	0.165050	−	0.986285i	$-0.447221\pi$
$619$	8.21280	0.330100	0.165050	+	0.986285i	$0.447221\pi$
$620$	−6.57053	−0.263879
$621$	−0.799288	−0.0320743
$622$	81.1034	3.25195
$623$	2.24440	0.0899201
$624$	−112.566	−4.50625
$625$	22.7504	0.910017
$626$	−26.3888	−1.05471
$627$	−6.42060	−0.256414
$628$	9.10701	0.363409
$629$	16.1002	0.641957
$630$	0.554696	0.0220996
$631$	−8.87342	−0.353245	−0.176623	−	0.984279i	$-0.556517\pi$
$631$	−8.87342	−0.353245	−0.176623	+	0.984279i	$0.556517\pi$
$632$	−83.7888	−3.33294
$633$	9.92930	0.394654
$634$	2.57032	0.102080
$635$	−7.72768	−0.306664
$636$	64.9862	2.57687
$637$	−43.0517	−1.70577
$638$	−1.66870	−0.0660646
$639$	−28.1852	−1.11499
$640$	−3.14498	−0.124316
$641$	8.30188	0.327904	0.163952	−	0.986468i	$-0.447576\pi$
$641$	8.30188	0.327904	0.163952	+	0.986468i	$0.447576\pi$
$642$	−41.0368	−1.61959
$643$	25.3821	1.00097	0.500486	−	0.865745i	$-0.333155\pi$
$643$	25.3821	1.00097	0.500486	+	0.865745i	$0.333155\pi$
$644$	−0.484645	−0.0190977
$645$	9.25993	0.364609
$646$	−4.69650	−0.184781
$647$	8.28222	0.325608	0.162804	−	0.986658i	$-0.447946\pi$
$647$	8.28222	0.325608	0.162804	+	0.986658i	$0.447946\pi$
$648$	72.7633	2.85841
$649$	25.2003	0.989198
$650$	77.3989	3.03583
$651$	−2.16549	−0.0848724
$652$	−51.2904	−2.00869
$653$	−43.7494	−1.71205	−0.856023	−	0.516938i	$-0.827072\pi$
$653$	−43.7494	−1.71205	−0.856023	+	0.516938i	$0.827072\pi$
$654$	72.1160	2.81996
$655$	1.44814	0.0565833
$656$	72.8169	2.84302
$657$	9.23518	0.360299
$658$	−6.93043	−0.270176
$659$	6.14363	0.239322	0.119661	−	0.992815i	$-0.461819\pi$
$659$	6.14363	0.239322	0.119661	+	0.992815i	$0.461819\pi$
$660$	11.5122	0.448112
$661$	−24.6511	−0.958817	−0.479408	−	0.877592i	$-0.659149\pi$
$661$	−24.6511	−0.958817	−0.479408	+	0.877592i	$0.659149\pi$
$662$	14.1070	0.548286
$663$	−25.6877	−0.997628
$664$	−8.49978	−0.329855
$665$	−0.101614	−0.00394042
$666$	−48.1000	−1.86384
$667$	−0.0922402	−0.00357155
$668$	−45.4769	−1.75955
$669$	18.2021	0.703733
$670$	8.44618	0.326304
$671$	4.74477	0.183170
$672$	4.24372	0.163705
$673$	−48.7271	−1.87829	−0.939146	−	0.343519i	$-0.888381\pi$
$673$	−48.7271	−1.87829	−0.939146	+	0.343519i	$0.888381\pi$
$674$	25.6953	0.989747
$675$	−9.61620	−0.370128
$676$	117.802	4.53085
$677$	49.9803	1.92090	0.960450	−	0.278453i	$-0.0898217\pi$
$677$	49.9803	1.92090	0.960450	+	0.278453i	$0.0898217\pi$
$678$	−51.3109	−1.97058
$679$	3.84420	0.147527
$680$	4.76481	0.182722
$681$	32.6776	1.25221
$682$	−26.7167	−1.02304
$683$	−43.0006	−1.64537	−0.822687	−	0.568495i	$-0.807526\pi$
$683$	−43.0006	−1.64537	−0.822687	+	0.568495i	$0.807526\pi$
$684$	9.78337	0.374076
$685$	5.32931	0.203622
$686$	9.34843	0.356925
$687$	−0.497176	−0.0189685
$688$	84.1535	3.20832
$689$	−38.7073	−1.47463
$690$	0.912640	0.0347436
$691$	−9.90413	−0.376771	−0.188385	−	0.982095i	$-0.560325\pi$
$691$	−9.90413	−0.376771	−0.188385	+	0.982095i	$0.560325\pi$
$692$	78.6182	2.98862
$693$	1.57267	0.0597408
$694$	22.8677	0.868047
$695$	1.18634	0.0450006
$696$	3.47102	0.131569
$697$	16.6169	0.629409
$698$	−57.7815	−2.18706
$699$	23.1893	0.877100
$700$	−5.83074	−0.220381
$701$	−36.1342	−1.36477	−0.682384	−	0.730994i	$-0.739057\pi$
$701$	−36.1342	−1.36477	−0.682384	+	0.730994i	$0.739057\pi$
$702$	−31.6609	−1.19496
$703$	8.81137	0.332327
$704$	6.93338	0.261312
$705$	9.09990	0.342722
$706$	−64.5948	−2.43106
$707$	2.02401	0.0761206
$708$	−92.6394	−3.48160
$709$	30.0400	1.12818	0.564089	−	0.825714i	$-0.309228\pi$
$709$	30.0400	1.12818	0.564089	+	0.825714i	$0.309228\pi$
$710$	−13.2771	−0.498280
$711$	26.5615	0.996135
$712$	−57.5977	−2.15857
$713$	−1.47681	−0.0553069
$714$	2.77533	0.103864
$715$	−6.85694	−0.256435
$716$	−122.776	−4.58835
$717$	23.0727	0.861667
$718$	−13.9515	−0.520667
$719$	11.1463	0.415687	0.207844	−	0.978162i	$-0.433355\pi$
$719$	11.1463	0.415687	0.207844	+	0.978162i	$0.433355\pi$
$720$	−6.61904	−0.246677
$721$	1.31773	0.0490749
$722$	−2.57032	−0.0956572
$723$	47.5350	1.76785
$724$	−8.58210	−0.318951
$725$	−1.10974	−0.0412146
$726$	−17.1890	−0.637944
$727$	2.27191	0.0842603	0.0421301	−	0.999112i	$-0.486586\pi$
$727$	2.27191	0.0842603	0.0421301	+	0.999112i	$0.486586\pi$
$728$	−10.8626	−0.402594
$729$	−9.59805	−0.355483
$730$	4.35037	0.161014
$731$	19.2039	0.710282
$732$	−17.4424	−0.644689
$733$	14.5363	0.536912	0.268456	−	0.963292i	$-0.413487\pi$
$733$	14.5363	0.536912	0.268456	+	0.963292i	$0.413487\pi$
$734$	87.7581	3.23921
$735$	−6.10738	−0.225274
$736$	2.89410	0.106678
$737$	23.9466	0.882084
$738$	−49.6436	−1.82741
$739$	−31.1036	−1.14416	−0.572082	−	0.820196i	$-0.693864\pi$
$739$	−31.1036	−1.14416	−0.572082	+	0.820196i	$0.693864\pi$
$740$	−15.7989	−0.580779
$741$	−14.0585	−0.516450
$742$	4.18198	0.153525
$743$	−13.0070	−0.477179	−0.238590	−	0.971121i	$-0.576685\pi$
$743$	−13.0070	−0.477179	−0.238590	+	0.971121i	$0.576685\pi$
$744$	55.5727	2.03739
$745$	−2.43076	−0.0890563
$746$	56.6948	2.07575
$747$	2.69448	0.0985858
$748$	23.8748	0.872951
$749$	−1.84134	−0.0672812
$750$	22.3030	0.814389
$751$	14.0902	0.514159	0.257079	−	0.966390i	$-0.417240\pi$
$751$	14.0902	0.514159	0.257079	+	0.966390i	$0.417240\pi$
$752$	82.6991	3.01573
$753$	29.9452	1.09126
$754$	−3.65377	−0.133062
$755$	−1.72605	−0.0628173
$756$	2.38513	0.0867465
$757$	52.0521	1.89187	0.945934	−	0.324360i	$-0.105149\pi$
$757$	52.0521	1.89187	0.945934	+	0.324360i	$0.105149\pi$
$758$	−5.29041	−0.192156
$759$	2.58751	0.0939208
$760$	2.60770	0.0945913
$761$	9.92267	0.359697	0.179848	−	0.983694i	$-0.442439\pi$
$761$	9.92267	0.359697	0.179848	+	0.983694i	$0.442439\pi$
$762$	115.511	4.18451
$763$	3.23588	0.117147
$764$	−37.0227	−1.33943
$765$	−1.51047	−0.0546112
$766$	−56.0581	−2.02546
$767$	55.1782	1.99237
$768$	58.0762	2.09564
$769$	5.01560	0.180867	0.0904336	−	0.995902i	$-0.471175\pi$
$769$	5.01560	0.180867	0.0904336	+	0.995902i	$0.471175\pi$
$770$	0.740831	0.0266977
$771$	45.5995	1.64223
$772$	29.1284	1.04835
$773$	1.72554	0.0620633	0.0310316	−	0.999518i	$-0.490121\pi$
$773$	1.72554	0.0620633	0.0310316	+	0.999518i	$0.490121\pi$
$774$	−57.3724	−2.06221
$775$	−17.7674	−0.638225
$776$	−98.6532	−3.54144
$777$	−5.20695	−0.186798
$778$	73.2928	2.62767
$779$	9.09414	0.325831
$780$	25.2070	0.902554
$781$	−37.6431	−1.34698
$782$	1.89270	0.0676827
$783$	0.453951	0.0162229
$784$	−55.5034	−1.98226
$785$	−0.769507	−0.0274649
$786$	−21.6462	−0.772095
$787$	−31.1711	−1.11113	−0.555564	−	0.831474i	$-0.687498\pi$
$787$	−31.1711	−1.11113	−0.555564	+	0.831474i	$0.687498\pi$
$788$	123.975	4.41643
$789$	47.9060	1.70550
$790$	12.5122	0.445165
$791$	−2.30234	−0.0818620
$792$	−40.3592	−1.43410
$793$	10.3891	0.368927
$794$	2.43221	0.0863158
$795$	−5.49108	−0.194749
$796$	−96.1330	−3.40734
$797$	−24.6786	−0.874160	−0.437080	−	0.899423i	$-0.643987\pi$
$797$	−24.6786	−0.874160	−0.437080	+	0.899423i	$0.643987\pi$
$798$	1.51889	0.0537681
$799$	18.8720	0.667644
$800$	34.8188	1.23103
$801$	18.2588	0.645143
$802$	−80.4446	−2.84060
$803$	12.3342	0.435263
$804$	−88.0306	−3.10460
$805$	0.0409506	0.00144332
$806$	−58.4985	−2.06052
$807$	−8.64771	−0.304414
$808$	−51.9417	−1.82730
$809$	−30.8835	−1.08581	−0.542903	−	0.839796i	$-0.682675\pi$
$809$	−30.8835	−1.08581	−0.542903	+	0.839796i	$0.682675\pi$
$810$	−10.8658	−0.381784
$811$	47.2251	1.65830	0.829149	−	0.559028i	$-0.188825\pi$
$811$	47.2251	1.65830	0.829149	+	0.559028i	$0.188825\pi$
$812$	0.275252	0.00965944
$813$	58.2544	2.04307
$814$	−64.2406	−2.25163
$815$	4.33384	0.151808
$816$	−33.1173	−1.15934
$817$	10.5100	0.367697
$818$	−61.6090	−2.15411
$819$	3.44350	0.120325
$820$	−16.3059	−0.569427
$821$	−1.73350	−0.0604996	−0.0302498	−	0.999542i	$-0.509630\pi$
$821$	−1.73350	−0.0604996	−0.0302498	+	0.999542i	$0.509630\pi$
$822$	−79.6606	−2.77848
$823$	−4.90121	−0.170845	−0.0854226	−	0.996345i	$-0.527224\pi$
$823$	−4.90121	−0.170845	−0.0854226	+	0.996345i	$0.527224\pi$
$824$	−33.8167	−1.17806
$825$	31.1303	1.08382
$826$	−5.96151	−0.207427
$827$	44.5839	1.55033	0.775166	−	0.631757i	$-0.217666\pi$
$827$	44.5839	1.55033	0.775166	+	0.631757i	$0.217666\pi$
$828$	−3.94271	−0.137019
$829$	55.2477	1.91883	0.959416	−	0.281994i	$-0.0909960\pi$
$829$	55.2477	1.91883	0.959416	+	0.281994i	$0.0909960\pi$
$830$	1.26928	0.0440572
$831$	−46.9606	−1.62905
$832$	15.1812	0.526314
$833$	−12.6659	−0.438848
$834$	−17.7331	−0.614045
$835$	3.84262	0.132979
$836$	13.0663	0.451908
$837$	7.26797	0.251218
$838$	−61.0024	−2.10729
$839$	24.4296	0.843403	0.421701	−	0.906735i	$-0.361433\pi$
$839$	24.4296	0.843403	0.421701	+	0.906735i	$0.361433\pi$
$840$	−1.54098	−0.0531689
$841$	−28.9476	−0.998194
$842$	−19.1173	−0.658824
$843$	17.5196	0.603407
$844$	−20.2067	−0.695544
$845$	−9.95382	−0.342422
$846$	−56.3809	−1.93842
$847$	−0.771278	−0.0265014
$848$	−49.9025	−1.71366
$849$	−60.7198	−2.08390
$850$	22.7710	0.781038
$851$	−3.55100	−0.121727
$852$	138.381	4.74085
$853$	49.9712	1.71098	0.855491	−	0.517818i	$-0.173255\pi$
$853$	49.9712	1.71098	0.855491	+	0.517818i	$0.173255\pi$
$854$	−1.12245	−0.0384093
$855$	−0.826656	−0.0282710
$856$	47.2540	1.61511
$857$	−20.4368	−0.698108	−0.349054	−	0.937103i	$-0.613497\pi$
$857$	−20.4368	−0.698108	−0.349054	+	0.937103i	$0.613497\pi$
$858$	102.495	3.49913
$859$	−45.7877	−1.56226	−0.781129	−	0.624370i	$-0.785356\pi$
$859$	−45.7877	−1.56226	−0.781129	+	0.624370i	$0.785356\pi$
$860$	−18.8445	−0.642592
$861$	−5.37405	−0.183147
$862$	25.0311	0.852563
$863$	32.7482	1.11476	0.557381	−	0.830257i	$-0.311806\pi$
$863$	32.7482	1.11476	0.557381	+	0.830257i	$0.311806\pi$
$864$	−14.2431	−0.484559
$865$	−6.64293	−0.225866
$866$	−44.9037	−1.52589
$867$	30.9235	1.05022
$868$	4.40691	0.149580
$869$	35.4746	1.20339
$870$	−0.518329	−0.0175730
$871$	52.4331	1.77663
$872$	−83.0418	−2.81215
$873$	31.2736	1.05845
$874$	1.03584	0.0350379
$875$	1.00074	0.0338313
$876$	−45.3419	−1.53196
$877$	−35.5233	−1.19954	−0.599768	−	0.800174i	$-0.704740\pi$
$877$	−35.5233	−1.19954	−0.599768	+	0.800174i	$0.704740\pi$
$878$	31.2238	1.05375
$879$	36.6173	1.23507
$880$	−8.84015	−0.298001
$881$	−53.0188	−1.78625	−0.893124	−	0.449810i	$-0.851492\pi$
$881$	−53.0188	−1.78625	−0.893124	+	0.449810i	$0.851492\pi$
$882$	37.8399	1.27414
$883$	−13.7047	−0.461199	−0.230600	−	0.973049i	$-0.574069\pi$
$883$	−13.7047	−0.461199	−0.230600	+	0.973049i	$0.574069\pi$
$884$	52.2760	1.75823
$885$	7.82767	0.263124
$886$	61.7657	2.07506
$887$	−47.1599	−1.58348	−0.791738	−	0.610861i	$-0.790823\pi$
$887$	−47.1599	−1.58348	−0.791738	+	0.610861i	$0.790823\pi$
$888$	133.625	4.48416
$889$	5.18302	0.173833
$890$	8.60109	0.288309
$891$	−30.8066	−1.03206
$892$	−37.0423	−1.24027
$893$	10.3283	0.345625
$894$	36.3342	1.21520
$895$	10.3741	0.346767
$896$	2.10937	0.0704690
$897$	5.66558	0.189168
$898$	−55.8532	−1.86384
$899$	0.838746	0.0279737
$900$	−47.4346	−1.58115
$901$	−11.3878	−0.379382
$902$	−66.3022	−2.20762
$903$	−6.21071	−0.206680
$904$	59.0847	1.96513
$905$	0.725154	0.0241049
$906$	25.8004	0.857160
$907$	−16.0112	−0.531644	−0.265822	−	0.964022i	$-0.585643\pi$
$907$	−16.0112	−0.531644	−0.265822	+	0.964022i	$0.585643\pi$
$908$	−66.5007	−2.20690
$909$	16.4658	0.546137
$910$	1.62211	0.0537725
$911$	−20.1277	−0.666861	−0.333431	−	0.942775i	$-0.608206\pi$
$911$	−20.1277	−0.666861	−0.333431	+	0.942775i	$0.608206\pi$
$912$	−18.1245	−0.600163
$913$	3.59865	0.119098
$914$	−42.0794	−1.39186
$915$	1.47381	0.0487227
$916$	1.01178	0.0334302
$917$	−0.971276	−0.0320744
$918$	−9.31473	−0.307432
$919$	15.5624	0.513358	0.256679	−	0.966497i	$-0.417372\pi$
$919$	15.5624	0.513358	0.256679	+	0.966497i	$0.417372\pi$
$920$	−1.05091	−0.0346474
$921$	2.52859	0.0833199
$922$	−77.4158	−2.54955
$923$	−82.4228	−2.71298
$924$	−7.72134	−0.254013
$925$	−42.7219	−1.40469
$926$	−21.6390	−0.711102
$927$	10.7201	0.352094
$928$	−1.64369	−0.0539568
$929$	−0.460968	−0.0151239	−0.00756194	−	0.999971i	$-0.502407\pi$
$929$	−0.460968	−0.0151239	−0.00756194	+	0.999971i	$0.502407\pi$
$930$	−8.29869	−0.272125
$931$	−6.93185	−0.227182
$932$	−47.1916	−1.54581
$933$	71.4248	2.33834
$934$	−22.3196	−0.730319
$935$	−2.01733	−0.0659738
$936$	−88.3699	−2.88846
$937$	1.33035	0.0434606	0.0217303	−	0.999764i	$-0.493082\pi$
$937$	1.33035	0.0434606	0.0217303	+	0.999764i	$0.493082\pi$
$938$	−5.66492	−0.184966
$939$	−23.2396	−0.758397
$940$	−18.5188	−0.604017
$941$	56.4087	1.83887	0.919435	−	0.393242i	$-0.128647\pi$
$941$	56.4087	1.83887	0.919435	+	0.393242i	$0.128647\pi$
$942$	11.5023	0.374766
$943$	−3.66496	−0.119347
$944$	71.1372	2.31532
$945$	−0.201534	−0.00655592
$946$	−76.6245	−2.49128
$947$	−2.87326	−0.0933683	−0.0466842	−	0.998910i	$-0.514865\pi$
$947$	−2.87326	−0.0933683	−0.0466842	+	0.998910i	$0.514865\pi$
$948$	−130.409	−4.23549
$949$	27.0067	0.876674
$950$	12.4622	0.404326
$951$	2.26358	0.0734017
$952$	−3.19580	−0.103576
$953$	61.4032	1.98904	0.994522	−	0.104528i	$-0.0333331\pi$
$953$	61.4032	1.98904	0.994522	+	0.104528i	$0.0333331\pi$
$954$	34.0215	1.10149
$955$	3.12827	0.101229
$956$	−46.9544	−1.51861
$957$	−1.46957	−0.0475043
$958$	−30.9583	−1.00022
$959$	−3.57441	−0.115424
$960$	2.15363	0.0695082
$961$	−17.5713	−0.566816
$962$	−140.660	−4.53506
$963$	−14.9798	−0.482717
$964$	−96.7365	−3.11567
$965$	−2.46123	−0.0792299
$966$	−0.612115	−0.0196945
$967$	−17.7315	−0.570207	−0.285104	−	0.958497i	$-0.592028\pi$
$967$	−17.7315	−0.570207	−0.285104	+	0.958497i	$0.592028\pi$
$968$	19.7932	0.636177
$969$	−4.13603	−0.132869
$970$	14.7319	0.473013
$971$	−14.9571	−0.479995	−0.239997	−	0.970774i	$-0.577147\pi$
$971$	−14.9571	−0.479995	−0.239997	+	0.970774i	$0.577147\pi$
$972$	85.8401	2.75332
$973$	−0.795690	−0.0255087
$974$	68.3447	2.18991
$975$	68.1624	2.18294
$976$	13.3939	0.428728
$977$	−18.9957	−0.607728	−0.303864	−	0.952715i	$-0.598277\pi$
$977$	−18.9957	−0.607728	−0.303864	+	0.952715i	$0.598277\pi$
$978$	−64.7807	−2.07146
$979$	24.3858	0.779373
$980$	12.4289	0.397026
$981$	26.3247	0.840483
$982$	22.4702	0.717054
$983$	−9.34839	−0.298167	−0.149084	−	0.988825i	$-0.547632\pi$
$983$	−9.34839	−0.298167	−0.149084	+	0.988825i	$0.547632\pi$
$984$	137.913	4.39652
$985$	−10.4754	−0.333774
$986$	−1.07495	−0.0342333
$987$	−6.10338	−0.194273
$988$	28.6098	0.910198
$989$	−4.23554	−0.134682
$990$	6.02686	0.191546
$991$	21.0788	0.669589	0.334794	−	0.942291i	$-0.391333\pi$
$991$	21.0788	0.669589	0.334794	+	0.942291i	$0.391333\pi$
$992$	−26.3163	−0.835542
$993$	12.4236	0.394250
$994$	8.90505	0.282451
$995$	8.12286	0.257512
$996$	−13.2291	−0.419179
$997$	−49.3293	−1.56227	−0.781137	−	0.624359i	$-0.785360\pi$
$997$	−49.3293	−1.56227	−0.781137	+	0.624359i	$0.785360\pi$
$998$	93.7820	2.96862
$999$	17.4759	0.552913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.8	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.8	✓	138	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57032 q^{2} -2.26358 q^{3} +4.60652 q^{4} -0.389233 q^{5} +5.81812 q^{6} +0.261062 q^{7} -6.69959 q^{8} +2.12381 q^{9} +O(q^{10})\)	\(q-2.57032 q^{2} -2.26358 q^{3} +4.60652 q^{4} -0.389233 q^{5} +5.81812 q^{6} +0.261062 q^{7} -6.69959 q^{8} +2.12381 q^{9} +1.00045 q^{10} +2.83648 q^{11} -10.4272 q^{12} +6.21071 q^{13} -0.671011 q^{14} +0.881061 q^{15} +8.00701 q^{16} +1.82721 q^{17} -5.45885 q^{18} +1.00000 q^{19} -1.79301 q^{20} -0.590935 q^{21} -7.29065 q^{22} -0.403002 q^{23} +15.1651 q^{24} -4.84850 q^{25} -15.9635 q^{26} +1.98334 q^{27} +1.20259 q^{28} +0.228883 q^{29} -2.26461 q^{30} +3.66452 q^{31} -7.18137 q^{32} -6.42060 q^{33} -4.69650 q^{34} -0.101614 q^{35} +9.78337 q^{36} +8.81137 q^{37} -2.57032 q^{38} -14.0585 q^{39} +2.60770 q^{40} +9.09414 q^{41} +1.51889 q^{42} +10.5100 q^{43} +13.0663 q^{44} -0.826656 q^{45} +1.03584 q^{46} +10.3283 q^{47} -18.1245 q^{48} -6.93185 q^{49} +12.4622 q^{50} -4.13603 q^{51} +28.6098 q^{52} -6.23235 q^{53} -5.09780 q^{54} -1.10405 q^{55} -1.74901 q^{56} -2.26358 q^{57} -0.588301 q^{58} +8.88436 q^{59} +4.05863 q^{60} +1.67277 q^{61} -9.41898 q^{62} +0.554445 q^{63} +2.44436 q^{64} -2.41741 q^{65} +16.5030 q^{66} +8.44237 q^{67} +8.41707 q^{68} +0.912228 q^{69} +0.261180 q^{70} -13.2711 q^{71} -14.2286 q^{72} +4.34841 q^{73} -22.6480 q^{74} +10.9750 q^{75} +4.60652 q^{76} +0.740496 q^{77} +36.1347 q^{78} +12.5066 q^{79} -3.11659 q^{80} -10.8609 q^{81} -23.3748 q^{82} +1.26870 q^{83} -2.72216 q^{84} -0.711210 q^{85} -27.0140 q^{86} -0.518095 q^{87} -19.0032 q^{88} +8.59720 q^{89} +2.12477 q^{90} +1.62138 q^{91} -1.85644 q^{92} -8.29495 q^{93} -26.5471 q^{94} -0.389233 q^{95} +16.2556 q^{96} +14.7253 q^{97} +17.8170 q^{98} +6.02413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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