LMFDB - Embedded newform 6026.2.a.g.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.13204 q^{3} +1.00000 q^{4} -3.67213 q^{5} +1.13204 q^{6} -0.943976 q^{7} +1.00000 q^{8} -1.71848 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.13204 q^{3} +1.00000 q^{4} -3.67213 q^{5} +1.13204 q^{6} -0.943976 q^{7} +1.00000 q^{8} -1.71848 q^{9} -3.67213 q^{10} -2.42142 q^{11} +1.13204 q^{12} +5.67225 q^{13} -0.943976 q^{14} -4.15700 q^{15} +1.00000 q^{16} +3.06869 q^{17} -1.71848 q^{18} +0.847727 q^{19} -3.67213 q^{20} -1.06862 q^{21} -2.42142 q^{22} -1.00000 q^{23} +1.13204 q^{24} +8.48454 q^{25} +5.67225 q^{26} -5.34152 q^{27} -0.943976 q^{28} +7.36578 q^{29} -4.15700 q^{30} +2.78601 q^{31} +1.00000 q^{32} -2.74115 q^{33} +3.06869 q^{34} +3.46640 q^{35} -1.71848 q^{36} -7.52797 q^{37} +0.847727 q^{38} +6.42123 q^{39} -3.67213 q^{40} +2.56617 q^{41} -1.06862 q^{42} -8.93634 q^{43} -2.42142 q^{44} +6.31049 q^{45} -1.00000 q^{46} -2.98447 q^{47} +1.13204 q^{48} -6.10891 q^{49} +8.48454 q^{50} +3.47388 q^{51} +5.67225 q^{52} -1.01093 q^{53} -5.34152 q^{54} +8.89176 q^{55} -0.943976 q^{56} +0.959662 q^{57} +7.36578 q^{58} -9.86491 q^{59} -4.15700 q^{60} -5.95873 q^{61} +2.78601 q^{62} +1.62221 q^{63} +1.00000 q^{64} -20.8293 q^{65} -2.74115 q^{66} -3.67185 q^{67} +3.06869 q^{68} -1.13204 q^{69} +3.46640 q^{70} +8.79793 q^{71} -1.71848 q^{72} -9.83651 q^{73} -7.52797 q^{74} +9.60485 q^{75} +0.847727 q^{76} +2.28576 q^{77} +6.42123 q^{78} -13.1749 q^{79} -3.67213 q^{80} -0.891377 q^{81} +2.56617 q^{82} +7.24417 q^{83} -1.06862 q^{84} -11.2686 q^{85} -8.93634 q^{86} +8.33837 q^{87} -2.42142 q^{88} -13.6351 q^{89} +6.31049 q^{90} -5.35447 q^{91} -1.00000 q^{92} +3.15388 q^{93} -2.98447 q^{94} -3.11296 q^{95} +1.13204 q^{96} -0.0496363 q^{97} -6.10891 q^{98} +4.16116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.13204	0.653585	0.326792	−	0.945096i	$-0.394032\pi$
$3$	1.13204	0.653585	0.326792	+	0.945096i	$0.394032\pi$
$4$	1.00000	0.500000
$5$	−3.67213	−1.64223	−0.821113	−	0.570765i	$-0.806647\pi$
$5$	−3.67213	−1.64223	−0.821113	+	0.570765i	$0.806647\pi$
$6$	1.13204	0.462154
$7$	−0.943976	−0.356789	−0.178395	−	0.983959i	$-0.557090\pi$
$7$	−0.943976	−0.356789	−0.178395	+	0.983959i	$0.557090\pi$
$8$	1.00000	0.353553
$9$	−1.71848	−0.572827
$10$	−3.67213	−1.16123
$11$	−2.42142	−0.730085	−0.365042	−	0.930991i	$-0.618946\pi$
$11$	−2.42142	−0.730085	−0.365042	+	0.930991i	$0.618946\pi$
$12$	1.13204	0.326792
$13$	5.67225	1.57320	0.786600	−	0.617463i	$-0.211839\pi$
$13$	5.67225	1.57320	0.786600	+	0.617463i	$0.211839\pi$
$14$	−0.943976	−0.252288
$15$	−4.15700	−1.07333
$16$	1.00000	0.250000
$17$	3.06869	0.744265	0.372133	−	0.928180i	$-0.378627\pi$
$17$	3.06869	0.744265	0.372133	+	0.928180i	$0.378627\pi$
$18$	−1.71848	−0.405050
$19$	0.847727	0.194482	0.0972410	−	0.995261i	$-0.468998\pi$
$19$	0.847727	0.194482	0.0972410	+	0.995261i	$0.468998\pi$
$20$	−3.67213	−0.821113
$21$	−1.06862	−0.233192
$22$	−2.42142	−0.516248
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.13204	0.231077
$25$	8.48454	1.69691
$26$	5.67225	1.11242
$27$	−5.34152	−1.02798
$28$	−0.943976	−0.178395
$29$	7.36578	1.36779	0.683896	−	0.729580i	$-0.260284\pi$
$29$	7.36578	1.36779	0.683896	+	0.729580i	$0.260284\pi$
$30$	−4.15700	−0.758962
$31$	2.78601	0.500383	0.250191	−	0.968196i	$-0.419506\pi$
$31$	2.78601	0.500383	0.250191	+	0.968196i	$0.419506\pi$
$32$	1.00000	0.176777
$33$	−2.74115	−0.477172
$34$	3.06869	0.526275
$35$	3.46640	0.585929
$36$	−1.71848	−0.286414
$37$	−7.52797	−1.23759	−0.618795	−	0.785552i	$-0.712379\pi$
$37$	−7.52797	−1.23759	−0.618795	+	0.785552i	$0.712379\pi$
$38$	0.847727	0.137519
$39$	6.42123	1.02822
$40$	−3.67213	−0.580615
$41$	2.56617	0.400768	0.200384	−	0.979717i	$-0.435781\pi$
$41$	2.56617	0.400768	0.200384	+	0.979717i	$0.435781\pi$
$42$	−1.06862	−0.164892
$43$	−8.93634	−1.36278	−0.681389	−	0.731921i	$-0.738624\pi$
$43$	−8.93634	−1.36278	−0.681389	+	0.731921i	$0.738624\pi$
$44$	−2.42142	−0.365042
$45$	6.31049	0.940712
$46$	−1.00000	−0.147442
$47$	−2.98447	−0.435329	−0.217665	−	0.976024i	$-0.569844\pi$
$47$	−2.98447	−0.435329	−0.217665	+	0.976024i	$0.569844\pi$
$48$	1.13204	0.163396
$49$	−6.10891	−0.872701
$50$	8.48454	1.19989
$51$	3.47388	0.486440
$52$	5.67225	0.786600
$53$	−1.01093	−0.138861	−0.0694307	−	0.997587i	$-0.522118\pi$
$53$	−1.01093	−0.138861	−0.0694307	+	0.997587i	$0.522118\pi$
$54$	−5.34152	−0.726889
$55$	8.89176	1.19896
$56$	−0.943976	−0.126144
$57$	0.959662	0.127110
$58$	7.36578	0.967175
$59$	−9.86491	−1.28430	−0.642151	−	0.766578i	$-0.721958\pi$
$59$	−9.86491	−1.28430	−0.642151	+	0.766578i	$0.721958\pi$
$60$	−4.15700	−0.536667
$61$	−5.95873	−0.762938	−0.381469	−	0.924382i	$-0.624582\pi$
$61$	−5.95873	−0.762938	−0.381469	+	0.924382i	$0.624582\pi$
$62$	2.78601	0.353824
$63$	1.62221	0.204379
$64$	1.00000	0.125000
$65$	−20.8293	−2.58355
$66$	−2.74115	−0.337412
$67$	−3.67185	−0.448588	−0.224294	−	0.974522i	$-0.572008\pi$
$67$	−3.67185	−0.448588	−0.224294	+	0.974522i	$0.572008\pi$
$68$	3.06869	0.372133
$69$	−1.13204	−0.136282
$70$	3.46640	0.414314
$71$	8.79793	1.04412	0.522061	−	0.852908i	$-0.325163\pi$
$71$	8.79793	1.04412	0.522061	+	0.852908i	$0.325163\pi$
$72$	−1.71848	−0.202525
$73$	−9.83651	−1.15128	−0.575638	−	0.817704i	$-0.695246\pi$
$73$	−9.83651	−1.15128	−0.575638	+	0.817704i	$0.695246\pi$
$74$	−7.52797	−0.875109
$75$	9.60485	1.10907
$76$	0.847727	0.0972410
$77$	2.28576	0.260486
$78$	6.42123	0.727061
$79$	−13.1749	−1.48230	−0.741148	−	0.671342i	$-0.765718\pi$
$79$	−13.1749	−1.48230	−0.741148	+	0.671342i	$0.765718\pi$
$80$	−3.67213	−0.410557
$81$	−0.891377	−0.0990418
$82$	2.56617	0.283386
$83$	7.24417	0.795151	0.397575	−	0.917570i	$-0.369852\pi$
$83$	7.24417	0.795151	0.397575	+	0.917570i	$0.369852\pi$
$84$	−1.06862	−0.116596
$85$	−11.2686	−1.22225
$86$	−8.93634	−0.963630
$87$	8.33837	0.893968
$88$	−2.42142	−0.258124
$89$	−13.6351	−1.44531	−0.722657	−	0.691207i	$-0.757079\pi$
$89$	−13.6351	−1.44531	−0.722657	+	0.691207i	$0.757079\pi$
$90$	6.31049	0.665184
$91$	−5.35447	−0.561301
$92$	−1.00000	−0.104257
$93$	3.15388	0.327042
$94$	−2.98447	−0.307824
$95$	−3.11296	−0.319383
$96$	1.13204	0.115539
$97$	−0.0496363	−0.00503980	−0.00251990	−	0.999997i	$-0.500802\pi$
$97$	−0.0496363	−0.00503980	−0.00251990	+	0.999997i	$0.500802\pi$
$98$	−6.10891	−0.617093
$99$	4.16116	0.418212
$100$	8.48454	0.848454
$101$	−11.1557	−1.11003	−0.555017	−	0.831839i	$-0.687288\pi$
$101$	−11.1557	−1.11003	−0.555017	+	0.831839i	$0.687288\pi$
$102$	3.47388	0.343965
$103$	−8.78722	−0.865831	−0.432915	−	0.901435i	$-0.642515\pi$
$103$	−8.78722	−0.865831	−0.432915	+	0.901435i	$0.642515\pi$
$104$	5.67225	0.556210
$105$	3.92411	0.382954
$106$	−1.01093	−0.0981898
$107$	2.37374	0.229479	0.114739	−	0.993396i	$-0.463397\pi$
$107$	2.37374	0.229479	0.114739	+	0.993396i	$0.463397\pi$
$108$	−5.34152	−0.513988
$109$	−12.5236	−1.19954	−0.599770	−	0.800172i	$-0.704741\pi$
$109$	−12.5236	−1.19954	−0.599770	+	0.800172i	$0.704741\pi$
$110$	8.89176	0.847796
$111$	−8.52198	−0.808870
$112$	−0.943976	−0.0891973
$113$	−8.34863	−0.785373	−0.392686	−	0.919672i	$-0.628454\pi$
$113$	−8.34863	−0.785373	−0.392686	+	0.919672i	$0.628454\pi$
$114$	0.959662	0.0898806
$115$	3.67213	0.342428
$116$	7.36578	0.683896
$117$	−9.74766	−0.901172
$118$	−9.86491	−0.908139
$119$	−2.89676	−0.265546
$120$	−4.15700	−0.379481
$121$	−5.13674	−0.466976
$122$	−5.95873	−0.539478
$123$	2.90501	0.261936
$124$	2.78601	0.250191
$125$	−12.7957	−1.14448
$126$	1.62221	0.144518
$127$	−0.930622	−0.0825793	−0.0412897	−	0.999147i	$-0.513147\pi$
$127$	−0.930622	−0.0825793	−0.0412897	+	0.999147i	$0.513147\pi$
$128$	1.00000	0.0883883
$129$	−10.1163	−0.890691
$130$	−20.8293	−1.82685
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−2.74115	−0.238586
$133$	−0.800234	−0.0693891
$134$	−3.67185	−0.317200
$135$	19.6147	1.68817
$136$	3.06869	0.263138
$137$	16.6328	1.42103	0.710517	−	0.703680i	$-0.248461\pi$
$137$	16.6328	1.42103	0.710517	+	0.703680i	$0.248461\pi$
$138$	−1.13204	−0.0963658
$139$	16.8651	1.43048	0.715239	−	0.698879i	$-0.246318\pi$
$139$	16.8651	1.43048	0.715239	+	0.698879i	$0.246318\pi$
$140$	3.46640	0.292964
$141$	−3.37854	−0.284525
$142$	8.79793	0.738306
$143$	−13.7349	−1.14857
$144$	−1.71848	−0.143207
$145$	−27.0481	−2.24622
$146$	−9.83651	−0.814075
$147$	−6.91554	−0.570384
$148$	−7.52797	−0.618795
$149$	−6.36603	−0.521526	−0.260763	−	0.965403i	$-0.583974\pi$
$149$	−6.36603	−0.521526	−0.260763	+	0.965403i	$0.583974\pi$
$150$	9.60485	0.784233
$151$	−1.74784	−0.142237	−0.0711185	−	0.997468i	$-0.522657\pi$
$151$	−1.74784	−0.142237	−0.0711185	+	0.997468i	$0.522657\pi$
$152$	0.847727	0.0687597
$153$	−5.27348	−0.426335
$154$	2.28576	0.184192
$155$	−10.2306	−0.821742
$156$	6.42123	0.514110
$157$	16.4195	1.31042	0.655208	−	0.755449i	$-0.272581\pi$
$157$	16.4195	1.31042	0.655208	+	0.755449i	$0.272581\pi$
$158$	−13.1749	−1.04814
$159$	−1.14441	−0.0907577
$160$	−3.67213	−0.290307
$161$	0.943976	0.0743957
$162$	−0.891377	−0.0700332
$163$	13.5017	1.05753	0.528766	−	0.848768i	$-0.322655\pi$
$163$	13.5017	1.05753	0.528766	+	0.848768i	$0.322655\pi$
$164$	2.56617	0.200384
$165$	10.0658	0.783625
$166$	7.24417	0.562256
$167$	−6.45817	−0.499748	−0.249874	−	0.968278i	$-0.580389\pi$
$167$	−6.45817	−0.499748	−0.249874	+	0.968278i	$0.580389\pi$
$168$	−1.06862	−0.0824458
$169$	19.1745	1.47496
$170$	−11.2686	−0.864263
$171$	−1.45680	−0.111405
$172$	−8.93634	−0.681389
$173$	−16.8261	−1.27926	−0.639631	−	0.768683i	$-0.720913\pi$
$173$	−16.8261	−1.27926	−0.639631	+	0.768683i	$0.720913\pi$
$174$	8.33837	0.632130
$175$	−8.00920	−0.605438
$176$	−2.42142	−0.182521
$177$	−11.1675	−0.839400
$178$	−13.6351	−1.02199
$179$	−0.581998	−0.0435006	−0.0217503	−	0.999763i	$-0.506924\pi$
$179$	−0.581998	−0.0435006	−0.0217503	+	0.999763i	$0.506924\pi$
$180$	6.31049	0.470356
$181$	−21.0758	−1.56655	−0.783277	−	0.621672i	$-0.786454\pi$
$181$	−21.0758	−1.56655	−0.783277	+	0.621672i	$0.786454\pi$
$182$	−5.35447	−0.396900
$183$	−6.74553	−0.498644
$184$	−1.00000	−0.0737210
$185$	27.6437	2.03240
$186$	3.15388	0.231254
$187$	−7.43057	−0.543377
$188$	−2.98447	−0.217665
$189$	5.04226	0.366771
$190$	−3.11296	−0.225838
$191$	26.3485	1.90651	0.953256	−	0.302165i	$-0.0977093\pi$
$191$	26.3485	1.90651	0.953256	+	0.302165i	$0.0977093\pi$
$192$	1.13204	0.0816981
$193$	−21.0776	−1.51720	−0.758598	−	0.651559i	$-0.774115\pi$
$193$	−21.0776	−1.51720	−0.758598	+	0.651559i	$0.774115\pi$
$194$	−0.0496363	−0.00356368
$195$	−23.5796	−1.68857
$196$	−6.10891	−0.436351
$197$	−3.53346	−0.251748	−0.125874	−	0.992046i	$-0.540174\pi$
$197$	−3.53346	−0.251748	−0.125874	+	0.992046i	$0.540174\pi$
$198$	4.16116	0.295721
$199$	−11.7501	−0.832943	−0.416472	−	0.909149i	$-0.636733\pi$
$199$	−11.7501	−0.832943	−0.416472	+	0.909149i	$0.636733\pi$
$200$	8.48454	0.599947
$201$	−4.15669	−0.293190
$202$	−11.1557	−0.784912
$203$	−6.95312	−0.488013
$204$	3.47388	0.243220
$205$	−9.42330	−0.658152
$206$	−8.78722	−0.612235
$207$	1.71848	0.119443
$208$	5.67225	0.393300
$209$	−2.05270	−0.141988
$210$	3.92411	0.270789
$211$	−4.60248	−0.316848	−0.158424	−	0.987371i	$-0.550641\pi$
$211$	−4.60248	−0.316848	−0.158424	+	0.987371i	$0.550641\pi$
$212$	−1.01093	−0.0694307
$213$	9.95963	0.682422
$214$	2.37374	0.162266
$215$	32.8154	2.23799
$216$	−5.34152	−0.363444
$217$	−2.62993	−0.178531
$218$	−12.5236	−0.848203
$219$	−11.1353	−0.752457
$220$	8.89176	0.599482
$221$	17.4064	1.17088
$222$	−8.52198	−0.571958
$223$	−22.9582	−1.53739	−0.768696	−	0.639615i	$-0.779094\pi$
$223$	−22.9582	−1.53739	−0.768696	+	0.639615i	$0.779094\pi$
$224$	−0.943976	−0.0630720
$225$	−14.5805	−0.972035
$226$	−8.34863	−0.555342
$227$	16.8427	1.11789	0.558944	−	0.829205i	$-0.311207\pi$
$227$	16.8427	1.11789	0.558944	+	0.829205i	$0.311207\pi$
$228$	0.959662	0.0635552
$229$	12.1358	0.801959	0.400980	−	0.916087i	$-0.368670\pi$
$229$	12.1358	0.801959	0.400980	+	0.916087i	$0.368670\pi$
$230$	3.67213	0.242133
$231$	2.58758	0.170250
$232$	7.36578	0.483587
$233$	27.9168	1.82889	0.914444	−	0.404712i	$-0.132628\pi$
$233$	27.9168	1.82889	0.914444	+	0.404712i	$0.132628\pi$
$234$	−9.74766	−0.637225
$235$	10.9594	0.714909
$236$	−9.86491	−0.642151
$237$	−14.9146	−0.968806
$238$	−2.89676	−0.187769
$239$	10.2120	0.660557	0.330278	−	0.943884i	$-0.392857\pi$
$239$	10.2120	0.660557	0.330278	+	0.943884i	$0.392857\pi$
$240$	−4.15700	−0.268333
$241$	5.75645	0.370805	0.185403	−	0.982663i	$-0.440641\pi$
$241$	5.75645	0.370805	0.185403	+	0.982663i	$0.440641\pi$
$242$	−5.13674	−0.330202
$243$	15.0155	0.963243
$244$	−5.95873	−0.381469
$245$	22.4327	1.43317
$246$	2.90501	0.185217
$247$	4.80852	0.305959
$248$	2.78601	0.176912
$249$	8.20070	0.519698
$250$	−12.7957	−0.809269
$251$	−3.07206	−0.193907	−0.0969533	−	0.995289i	$-0.530910\pi$
$251$	−3.07206	−0.193907	−0.0969533	+	0.995289i	$0.530910\pi$
$252$	1.62221	0.102189
$253$	2.42142	0.152233
$254$	−0.930622	−0.0583924
$255$	−12.7565	−0.798845
$256$	1.00000	0.0625000
$257$	−26.1794	−1.63302	−0.816512	−	0.577329i	$-0.804095\pi$
$257$	−26.1794	−1.63302	−0.816512	+	0.577329i	$0.804095\pi$
$258$	−10.1163	−0.629814
$259$	7.10622	0.441559
$260$	−20.8293	−1.29178
$261$	−12.6580	−0.783508
$262$	1.00000	0.0617802
$263$	9.84148	0.606852	0.303426	−	0.952855i	$-0.401870\pi$
$263$	9.84148	0.606852	0.303426	+	0.952855i	$0.401870\pi$
$264$	−2.74115	−0.168706
$265$	3.71225	0.228042
$266$	−0.800234	−0.0490655
$267$	−15.4355	−0.944635
$268$	−3.67185	−0.224294
$269$	17.1462	1.04542	0.522712	−	0.852510i	$-0.324920\pi$
$269$	17.1462	1.04542	0.522712	+	0.852510i	$0.324920\pi$
$270$	19.6147	1.19372
$271$	−16.3187	−0.991289	−0.495645	−	0.868525i	$-0.665068\pi$
$271$	−16.3187	−0.991289	−0.495645	+	0.868525i	$0.665068\pi$
$272$	3.06869	0.186066
$273$	−6.06148	−0.366858
$274$	16.6328	1.00482
$275$	−20.5446	−1.23889
$276$	−1.13204	−0.0681409
$277$	6.69992	0.402559	0.201280	−	0.979534i	$-0.435490\pi$
$277$	6.69992	0.402559	0.201280	+	0.979534i	$0.435490\pi$
$278$	16.8651	1.01150
$279$	−4.78771	−0.286633
$280$	3.46640	0.207157
$281$	−11.6425	−0.694535	−0.347268	−	0.937766i	$-0.612890\pi$
$281$	−11.6425	−0.694535	−0.347268	+	0.937766i	$0.612890\pi$
$282$	−3.37854	−0.201189
$283$	−1.66574	−0.0990178	−0.0495089	−	0.998774i	$-0.515766\pi$
$283$	−1.66574	−0.0990178	−0.0495089	+	0.998774i	$0.515766\pi$
$284$	8.79793	0.522061
$285$	−3.52400	−0.208744
$286$	−13.7349	−0.812161
$287$	−2.42240	−0.142990
$288$	−1.71848	−0.101262
$289$	−7.58317	−0.446069
$290$	−27.0481	−1.58832
$291$	−0.0561903	−0.00329393
$292$	−9.83651	−0.575638
$293$	23.9728	1.40051	0.700253	−	0.713895i	$-0.253071\pi$
$293$	23.9728	1.40051	0.700253	+	0.713895i	$0.253071\pi$
$294$	−6.91554	−0.403323
$295$	36.2252	2.10911
$296$	−7.52797	−0.437554
$297$	12.9340	0.750509
$298$	−6.36603	−0.368774
$299$	−5.67225	−0.328035
$300$	9.60485	0.554536
$301$	8.43569	0.486225
$302$	−1.74784	−0.100577
$303$	−12.6287	−0.725500
$304$	0.847727	0.0486205
$305$	21.8812	1.25292
$306$	−5.27348	−0.301465
$307$	−0.0342658	−0.00195565	−0.000977825	−	1.00000i	$-0.500311\pi$
$307$	−0.0342658	−0.00195565	−0.000977825		1.00000i	$0.500311\pi$
$308$	2.28576	0.130243
$309$	−9.94750	−0.565894
$310$	−10.2306	−0.581059
$311$	−18.2641	−1.03566	−0.517832	−	0.855482i	$-0.673261\pi$
$311$	−18.2641	−1.03566	−0.517832	+	0.855482i	$0.673261\pi$
$312$	6.42123	0.363530
$313$	−30.2701	−1.71097	−0.855484	−	0.517829i	$-0.826740\pi$
$313$	−30.2701	−1.71097	−0.855484	+	0.517829i	$0.826740\pi$
$314$	16.4195	0.926604
$315$	−5.95695	−0.335636
$316$	−13.1749	−0.741148
$317$	−19.9262	−1.11917	−0.559583	−	0.828774i	$-0.689039\pi$
$317$	−19.9262	−1.11917	−0.559583	+	0.828774i	$0.689039\pi$
$318$	−1.14441	−0.0641754
$319$	−17.8356	−0.998604
$320$	−3.67213	−0.205278
$321$	2.68718	0.149984
$322$	0.943976	0.0526057
$323$	2.60141	0.144746
$324$	−0.891377	−0.0495209
$325$	48.1264	2.66957
$326$	13.5017	0.747787
$327$	−14.1772	−0.784001
$328$	2.56617	0.141693
$329$	2.81726	0.155321
$330$	10.0658	0.554106
$331$	−17.4927	−0.961488	−0.480744	−	0.876861i	$-0.659633\pi$
$331$	−17.4927	−0.961488	−0.480744	+	0.876861i	$0.659633\pi$
$332$	7.24417	0.397575
$333$	12.9367	0.708926
$334$	−6.45817	−0.353375
$335$	13.4835	0.736683
$336$	−1.06862	−0.0582980
$337$	30.2351	1.64701	0.823505	−	0.567310i	$-0.192016\pi$
$337$	30.2351	1.64701	0.823505	+	0.567310i	$0.192016\pi$
$338$	19.1745	1.04295
$339$	−9.45099	−0.513308
$340$	−11.2686	−0.611126
$341$	−6.74610	−0.365322
$342$	−1.45680	−0.0787749
$343$	12.3745	0.668160
$344$	−8.93634	−0.481815
$345$	4.15700	0.223806
$346$	−16.8261	−0.904574
$347$	9.62914	0.516919	0.258460	−	0.966022i	$-0.416785\pi$
$347$	9.62914	0.516919	0.258460	+	0.966022i	$0.416785\pi$
$348$	8.33837	0.446984
$349$	−24.6773	−1.32094	−0.660472	−	0.750851i	$-0.729644\pi$
$349$	−24.6773	−1.32094	−0.660472	+	0.750851i	$0.729644\pi$
$350$	−8.00920	−0.428110
$351$	−30.2984	−1.61721
$352$	−2.42142	−0.129062
$353$	−6.76825	−0.360238	−0.180119	−	0.983645i	$-0.557648\pi$
$353$	−6.76825	−0.360238	−0.180119	+	0.983645i	$0.557648\pi$
$354$	−11.1675	−0.593545
$355$	−32.3072	−1.71469
$356$	−13.6351	−0.722657
$357$	−3.27926	−0.173557
$358$	−0.581998	−0.0307596
$359$	23.2705	1.22817	0.614084	−	0.789240i	$-0.289525\pi$
$359$	23.2705	1.22817	0.614084	+	0.789240i	$0.289525\pi$
$360$	6.31049	0.332592
$361$	−18.2814	−0.962177
$362$	−21.0758	−1.10772
$363$	−5.81500	−0.305208
$364$	−5.35447	−0.280651
$365$	36.1209	1.89066
$366$	−6.74553	−0.352595
$367$	22.6160	1.18054	0.590272	−	0.807205i	$-0.299021\pi$
$367$	22.6160	1.18054	0.590272	+	0.807205i	$0.299021\pi$
$368$	−1.00000	−0.0521286
$369$	−4.40991	−0.229571
$370$	27.6437	1.43713
$371$	0.954290	0.0495443
$372$	3.15388	0.163521
$373$	11.1792	0.578835	0.289417	−	0.957203i	$-0.406538\pi$
$373$	11.1792	0.578835	0.289417	+	0.957203i	$0.406538\pi$
$374$	−7.43057	−0.384226
$375$	−14.4852	−0.748014
$376$	−2.98447	−0.153912
$377$	41.7806	2.15181
$378$	5.04226	0.259346
$379$	1.85678	0.0953763	0.0476881	−	0.998862i	$-0.484815\pi$
$379$	1.85678	0.0953763	0.0476881	+	0.998862i	$0.484815\pi$
$380$	−3.11296	−0.159692
$381$	−1.05350	−0.0539726
$382$	26.3485	1.34811
$383$	−13.2862	−0.678893	−0.339447	−	0.940625i	$-0.610240\pi$
$383$	−13.2862	−0.678893	−0.339447	+	0.940625i	$0.610240\pi$
$384$	1.13204	0.0577693
$385$	−8.39361	−0.427778
$386$	−21.0776	−1.07282
$387$	15.3569	0.780637
$388$	−0.0496363	−0.00251990
$389$	−7.52997	−0.381785	−0.190892	−	0.981611i	$-0.561138\pi$
$389$	−7.52997	−0.381785	−0.190892	+	0.981611i	$0.561138\pi$
$390$	−23.5796	−1.19400
$391$	−3.06869	−0.155190
$392$	−6.10891	−0.308547
$393$	1.13204	0.0571040
$394$	−3.53346	−0.178013
$395$	48.3801	2.43427
$396$	4.16116	0.209106
$397$	32.9367	1.65305	0.826523	−	0.562902i	$-0.190315\pi$
$397$	32.9367	1.65305	0.826523	+	0.562902i	$0.190315\pi$
$398$	−11.7501	−0.588980
$399$	−0.905898	−0.0453516
$400$	8.48454	0.424227
$401$	−9.90203	−0.494484	−0.247242	−	0.968954i	$-0.579524\pi$
$401$	−9.90203	−0.494484	−0.247242	+	0.968954i	$0.579524\pi$
$402$	−4.15669	−0.207317
$403$	15.8030	0.787202
$404$	−11.1557	−0.555017
$405$	3.27325	0.162649
$406$	−6.95312	−0.345078
$407$	18.2284	0.903546
$408$	3.47388	0.171983
$409$	−15.0201	−0.742698	−0.371349	−	0.928493i	$-0.621105\pi$
$409$	−15.0201	−0.742698	−0.371349	+	0.928493i	$0.621105\pi$
$410$	−9.42330	−0.465383
$411$	18.8290	0.928766
$412$	−8.78722	−0.432915
$413$	9.31224	0.458225
$414$	1.71848	0.0844588
$415$	−26.6015	−1.30582
$416$	5.67225	0.278105
$417$	19.0920	0.934939
$418$	−2.05270	−0.100401
$419$	−9.08217	−0.443693	−0.221846	−	0.975082i	$-0.571208\pi$
$419$	−9.08217	−0.443693	−0.221846	+	0.975082i	$0.571208\pi$
$420$	3.92411	0.191477
$421$	−6.17945	−0.301168	−0.150584	−	0.988597i	$-0.548115\pi$
$421$	−6.17945	−0.301168	−0.150584	+	0.988597i	$0.548115\pi$
$422$	−4.60248	−0.224045
$423$	5.12875	0.249368
$424$	−1.01093	−0.0490949
$425$	26.0364	1.26295
$426$	9.95963	0.482546
$427$	5.62490	0.272208
$428$	2.37374	0.114739
$429$	−15.5485	−0.750687
$430$	32.8154	1.58250
$431$	4.20913	0.202747	0.101373	−	0.994848i	$-0.467676\pi$
$431$	4.20913	0.202747	0.101373	+	0.994848i	$0.467676\pi$
$432$	−5.34152	−0.256994
$433$	1.51210	0.0726670	0.0363335	−	0.999340i	$-0.488432\pi$
$433$	1.51210	0.0726670	0.0363335	+	0.999340i	$0.488432\pi$
$434$	−2.62993	−0.126241
$435$	−30.6196	−1.46810
$436$	−12.5236	−0.599770
$437$	−0.847727	−0.0405523
$438$	−11.1353	−0.532067
$439$	25.7316	1.22810	0.614051	−	0.789267i	$-0.289539\pi$
$439$	25.7316	1.22810	0.614051	+	0.789267i	$0.289539\pi$
$440$	8.89176	0.423898
$441$	10.4980	0.499907
$442$	17.4064	0.827936
$443$	30.0084	1.42574	0.712872	−	0.701295i	$-0.247394\pi$
$443$	30.0084	1.42574	0.712872	+	0.701295i	$0.247394\pi$
$444$	−8.52198	−0.404435
$445$	50.0697	2.37353
$446$	−22.9582	−1.08710
$447$	−7.20662	−0.340861
$448$	−0.943976	−0.0445987
$449$	35.4722	1.67404	0.837019	−	0.547173i	$-0.184296\pi$
$449$	35.4722	1.67404	0.837019	+	0.547173i	$0.184296\pi$
$450$	−14.5805	−0.687332
$451$	−6.21376	−0.292595
$452$	−8.34863	−0.392686
$453$	−1.97863	−0.0929639
$454$	16.8427	0.790467
$455$	19.6623	0.921783
$456$	0.959662	0.0449403
$457$	−16.0503	−0.750799	−0.375400	−	0.926863i	$-0.622495\pi$
$457$	−16.0503	−0.750799	−0.375400	+	0.926863i	$0.622495\pi$
$458$	12.1358	0.567071
$459$	−16.3914	−0.765087
$460$	3.67213	0.171214
$461$	−6.59848	−0.307322	−0.153661	−	0.988124i	$-0.549106\pi$
$461$	−6.59848	−0.307322	−0.153661	+	0.988124i	$0.549106\pi$
$462$	2.58758	0.120385
$463$	−23.0660	−1.07197	−0.535984	−	0.844228i	$-0.680059\pi$
$463$	−23.0660	−1.07197	−0.535984	+	0.844228i	$0.680059\pi$
$464$	7.36578	0.341948
$465$	−11.5815	−0.537078
$466$	27.9168	1.29322
$467$	−20.9710	−0.970422	−0.485211	−	0.874397i	$-0.661257\pi$
$467$	−20.9710	−0.970422	−0.485211	+	0.874397i	$0.661257\pi$
$468$	−9.74766	−0.450586
$469$	3.46614	0.160051
$470$	10.9594	0.505517
$471$	18.5875	0.856468
$472$	−9.86491	−0.454069
$473$	21.6386	0.994944
$474$	−14.9146	−0.685049
$475$	7.19257	0.330018
$476$	−2.89676	−0.132773
$477$	1.73726	0.0795436
$478$	10.2120	0.467084
$479$	22.5970	1.03248	0.516242	−	0.856443i	$-0.327331\pi$
$479$	22.5970	1.03248	0.516242	+	0.856443i	$0.327331\pi$
$480$	−4.15700	−0.189740
$481$	−42.7006	−1.94698
$482$	5.75645	0.262199
$483$	1.06862	0.0486239
$484$	−5.13674	−0.233488
$485$	0.182271	0.00827649
$486$	15.0155	0.681116
$487$	−22.9224	−1.03871	−0.519357	−	0.854557i	$-0.673829\pi$
$487$	−22.9224	−1.03871	−0.519357	+	0.854557i	$0.673829\pi$
$488$	−5.95873	−0.269739
$489$	15.2844	0.691186
$490$	22.4327	1.01341
$491$	18.4216	0.831354	0.415677	−	0.909512i	$-0.363545\pi$
$491$	18.4216	0.831354	0.415677	+	0.909512i	$0.363545\pi$
$492$	2.90501	0.130968
$493$	22.6033	1.01800
$494$	4.80852	0.216346
$495$	−15.2803	−0.686800
$496$	2.78601	0.125096
$497$	−8.30504	−0.372532
$498$	8.20070	0.367482
$499$	11.7070	0.524078	0.262039	−	0.965057i	$-0.415605\pi$
$499$	11.7070	0.524078	0.262039	+	0.965057i	$0.415605\pi$
$500$	−12.7957	−0.572240
$501$	−7.31091	−0.326627
$502$	−3.07206	−0.137113
$503$	−11.5819	−0.516411	−0.258205	−	0.966090i	$-0.583131\pi$
$503$	−11.5819	−0.516411	−0.258205	+	0.966090i	$0.583131\pi$
$504$	1.62221	0.0722588
$505$	40.9652	1.82293
$506$	2.42142	0.107645
$507$	21.7063	0.964010
$508$	−0.930622	−0.0412897
$509$	14.5125	0.643254	0.321627	−	0.946867i	$-0.395770\pi$
$509$	14.5125	0.643254	0.321627	+	0.946867i	$0.395770\pi$
$510$	−12.7565	−0.564869
$511$	9.28543	0.410763
$512$	1.00000	0.0441942
$513$	−4.52815	−0.199923
$514$	−26.1794	−1.15472
$515$	32.2678	1.42189
$516$	−10.1163	−0.445346
$517$	7.22664	0.317827
$518$	7.10622	0.312229
$519$	−19.0478	−0.836105
$520$	−20.8293	−0.913423
$521$	22.1243	0.969284	0.484642	−	0.874713i	$-0.338950\pi$
$521$	22.1243	0.969284	0.484642	+	0.874713i	$0.338950\pi$
$522$	−12.6580	−0.554024
$523$	−35.8168	−1.56616	−0.783080	−	0.621920i	$-0.786353\pi$
$523$	−35.8168	−1.56616	−0.783080	+	0.621920i	$0.786353\pi$
$524$	1.00000	0.0436852
$525$	−9.06675	−0.395705
$526$	9.84148	0.429109
$527$	8.54940	0.372418
$528$	−2.74115	−0.119293
$529$	1.00000	0.0434783
$530$	3.71225	0.161250
$531$	16.9527	0.735683
$532$	−0.800234	−0.0346945
$533$	14.5559	0.630488
$534$	−15.4355	−0.667958
$535$	−8.71670	−0.376856
$536$	−3.67185	−0.158600
$537$	−0.658846	−0.0284313
$538$	17.1462	0.739226
$539$	14.7922	0.637146
$540$	19.6147	0.844084
$541$	−8.73795	−0.375674	−0.187837	−	0.982200i	$-0.560148\pi$
$541$	−8.73795	−0.375674	−0.187837	+	0.982200i	$0.560148\pi$
$542$	−16.3187	−0.700947
$543$	−23.8587	−1.02388
$544$	3.06869	0.131569
$545$	45.9882	1.96992
$546$	−6.06148	−0.259408
$547$	−17.8152	−0.761721	−0.380861	−	0.924632i	$-0.624372\pi$
$547$	−17.8152	−0.761721	−0.380861	+	0.924632i	$0.624372\pi$
$548$	16.6328	0.710517
$549$	10.2400	0.437031
$550$	−20.5446	−0.876025
$551$	6.24417	0.266011
$552$	−1.13204	−0.0481829
$553$	12.4368	0.528867
$554$	6.69992	0.284652
$555$	31.2938	1.32835
$556$	16.8651	0.715239
$557$	−27.6673	−1.17230	−0.586151	−	0.810202i	$-0.699358\pi$
$557$	−27.6673	−1.17230	−0.586151	+	0.810202i	$0.699358\pi$
$558$	−4.78771	−0.202680
$559$	−50.6892	−2.14392
$560$	3.46640	0.146482
$561$	−8.41171	−0.355143
$562$	−11.6425	−0.491111
$563$	−3.10075	−0.130681	−0.0653406	−	0.997863i	$-0.520813\pi$
$563$	−3.10075	−0.130681	−0.0653406	+	0.997863i	$0.520813\pi$
$564$	−3.37854	−0.142262
$565$	30.6572	1.28976
$566$	−1.66574	−0.0700162
$567$	0.841438	0.0353371
$568$	8.79793	0.369153
$569$	−26.6027	−1.11524	−0.557621	−	0.830096i	$-0.688286\pi$
$569$	−26.6027	−1.11524	−0.557621	+	0.830096i	$0.688286\pi$
$570$	−3.52400	−0.147604
$571$	−16.0983	−0.673693	−0.336846	−	0.941560i	$-0.609360\pi$
$571$	−16.0983	−0.673693	−0.336846	+	0.941560i	$0.609360\pi$
$572$	−13.7349	−0.574285
$573$	29.8276	1.24607
$574$	−2.42240	−0.101109
$575$	−8.48454	−0.353830
$576$	−1.71848	−0.0716034
$577$	−26.6774	−1.11060	−0.555298	−	0.831651i	$-0.687396\pi$
$577$	−26.6774	−1.11060	−0.555298	+	0.831651i	$0.687396\pi$
$578$	−7.58317	−0.315418
$579$	−23.8607	−0.991616
$580$	−27.0481	−1.12311
$581$	−6.83832	−0.283701
$582$	−0.0561903	−0.00232916
$583$	2.44787	0.101381
$584$	−9.83651	−0.407038
$585$	35.7947	1.47993
$586$	23.9728	0.990307
$587$	−15.1640	−0.625885	−0.312942	−	0.949772i	$-0.601315\pi$
$587$	−15.1640	−0.625885	−0.312942	+	0.949772i	$0.601315\pi$
$588$	−6.91554	−0.285192
$589$	2.36178	0.0973154
$590$	36.2252	1.49137
$591$	−4.00002	−0.164539
$592$	−7.52797	−0.309398
$593$	−28.6302	−1.17570	−0.587850	−	0.808970i	$-0.700025\pi$
$593$	−28.6302	−1.17570	−0.587850	+	0.808970i	$0.700025\pi$
$594$	12.9340	0.530690
$595$	10.6373	0.436087
$596$	−6.36603	−0.260763
$597$	−13.3016	−0.544399
$598$	−5.67225	−0.231956
$599$	−33.9694	−1.38795	−0.693976	−	0.719999i	$-0.744142\pi$
$599$	−33.9694	−1.38795	−0.693976	+	0.719999i	$0.744142\pi$
$600$	9.60485	0.392116
$601$	21.1849	0.864150	0.432075	−	0.901838i	$-0.357782\pi$
$601$	21.1849	0.864150	0.432075	+	0.901838i	$0.357782\pi$
$602$	8.43569	0.343813
$603$	6.31001	0.256963
$604$	−1.74784	−0.0711185
$605$	18.8628	0.766880
$606$	−12.6287	−0.513006
$607$	−19.9755	−0.810779	−0.405390	−	0.914144i	$-0.632864\pi$
$607$	−19.9755	−0.810779	−0.405390	+	0.914144i	$0.632864\pi$
$608$	0.847727	0.0343799
$609$	−7.87122	−0.318958
$610$	21.8812	0.885946
$611$	−16.9287	−0.684860
$612$	−5.27348	−0.213168
$613$	−39.9645	−1.61415	−0.807075	−	0.590448i	$-0.798951\pi$
$613$	−39.9645	−1.61415	−0.807075	+	0.590448i	$0.798951\pi$
$614$	−0.0342658	−0.00138285
$615$	−10.6676	−0.430158
$616$	2.28576	0.0920959
$617$	3.03681	0.122257	0.0611287	−	0.998130i	$-0.480530\pi$
$617$	3.03681	0.122257	0.0611287	+	0.998130i	$0.480530\pi$
$618$	−9.94750	−0.400147
$619$	6.48714	0.260740	0.130370	−	0.991465i	$-0.458383\pi$
$619$	6.48714	0.260740	0.130370	+	0.991465i	$0.458383\pi$
$620$	−10.2306	−0.410871
$621$	5.34152	0.214348
$622$	−18.2641	−0.732325
$623$	12.8712	0.515672
$624$	6.42123	0.257055
$625$	4.56468	0.182587
$626$	−30.2701	−1.20984
$627$	−2.32374	−0.0928014
$628$	16.4195	0.655208
$629$	−23.1010	−0.921096
$630$	−5.95695	−0.237330
$631$	−4.75438	−0.189269	−0.0946344	−	0.995512i	$-0.530168\pi$
$631$	−4.75438	−0.189269	−0.0946344	+	0.995512i	$0.530168\pi$
$632$	−13.1749	−0.524071
$633$	−5.21020	−0.207087
$634$	−19.9262	−0.791370
$635$	3.41736	0.135614
$636$	−1.14441	−0.0453788
$637$	−34.6513	−1.37293
$638$	−17.8356	−0.706120
$639$	−15.1191	−0.598102
$640$	−3.67213	−0.145154
$641$	20.9513	0.827526	0.413763	−	0.910385i	$-0.364214\pi$
$641$	20.9513	0.827526	0.413763	+	0.910385i	$0.364214\pi$
$642$	2.68718	0.106054
$643$	−8.29715	−0.327208	−0.163604	−	0.986526i	$-0.552312\pi$
$643$	−8.29715	−0.327208	−0.163604	+	0.986526i	$0.552312\pi$
$644$	0.943976	0.0371979
$645$	37.1484	1.46272
$646$	2.60141	0.102351
$647$	38.2656	1.50438	0.752188	−	0.658948i	$-0.228998\pi$
$647$	38.2656	1.50438	0.752188	+	0.658948i	$0.228998\pi$
$648$	−0.891377	−0.0350166
$649$	23.8871	0.937649
$650$	48.1264	1.88767
$651$	−2.97719	−0.116685
$652$	13.5017	0.528766
$653$	−13.8926	−0.543661	−0.271831	−	0.962345i	$-0.587629\pi$
$653$	−13.8926	−0.543661	−0.271831	+	0.962345i	$0.587629\pi$
$654$	−14.1772	−0.554373
$655$	−3.67213	−0.143482
$656$	2.56617	0.100192
$657$	16.9039	0.659483
$658$	2.81726	0.109828
$659$	30.7515	1.19791	0.598954	−	0.800784i	$-0.295583\pi$
$659$	30.7515	1.19791	0.598954	+	0.800784i	$0.295583\pi$
$660$	10.0658	0.391812
$661$	13.9590	0.542943	0.271471	−	0.962446i	$-0.412490\pi$
$661$	13.9590	0.542943	0.271471	+	0.962446i	$0.412490\pi$
$662$	−17.4927	−0.679875
$663$	19.7047	0.765268
$664$	7.24417	0.281128
$665$	2.93856	0.113953
$666$	12.9367	0.501286
$667$	−7.36578	−0.285204
$668$	−6.45817	−0.249874
$669$	−25.9896	−1.00482
$670$	13.4835	0.520913
$671$	14.4286	0.557009
$672$	−1.06862	−0.0412229
$673$	33.4694	1.29015	0.645075	−	0.764119i	$-0.276826\pi$
$673$	33.4694	1.29015	0.645075	+	0.764119i	$0.276826\pi$
$674$	30.2351	1.16461
$675$	−45.3203	−1.74438
$676$	19.1745	0.737479
$677$	22.3672	0.859640	0.429820	−	0.902915i	$-0.358577\pi$
$677$	22.3672	0.859640	0.429820	+	0.902915i	$0.358577\pi$
$678$	−9.45099	−0.362963
$679$	0.0468554	0.00179815
$680$	−11.2686	−0.432131
$681$	19.0666	0.730635
$682$	−6.74610	−0.258322
$683$	−3.06011	−0.117092	−0.0585459	−	0.998285i	$-0.518646\pi$
$683$	−3.06011	−0.117092	−0.0585459	+	0.998285i	$0.518646\pi$
$684$	−1.45680	−0.0557023
$685$	−61.0777	−2.33366
$686$	12.3745	0.472460
$687$	13.7383	0.524148
$688$	−8.93634	−0.340695
$689$	−5.73423	−0.218457
$690$	4.15700	0.158254
$691$	44.2356	1.68280	0.841401	−	0.540411i	$-0.181731\pi$
$691$	44.2356	1.68280	0.841401	+	0.540411i	$0.181731\pi$
$692$	−16.8261	−0.639631
$693$	−3.92804	−0.149214
$694$	9.62914	0.365517
$695$	−61.9308	−2.34917
$696$	8.33837	0.316065
$697$	7.87476	0.298278
$698$	−24.6773	−0.934048
$699$	31.6029	1.19533
$700$	−8.00920	−0.302719
$701$	−35.5515	−1.34276	−0.671380	−	0.741113i	$-0.734298\pi$
$701$	−35.5515	−1.34276	−0.671380	+	0.741113i	$0.734298\pi$
$702$	−30.2984	−1.14354
$703$	−6.38166	−0.240689
$704$	−2.42142	−0.0912606
$705$	12.4064	0.467254
$706$	−6.76825	−0.254726
$707$	10.5307	0.396048
$708$	−11.1675	−0.419700
$709$	10.7463	0.403584	0.201792	−	0.979428i	$-0.435323\pi$
$709$	10.7463	0.403584	0.201792	+	0.979428i	$0.435323\pi$
$710$	−32.3072	−1.21247
$711$	22.6409	0.849099
$712$	−13.6351	−0.510995
$713$	−2.78601	−0.104337
$714$	−3.27926	−0.122723
$715$	50.4363	1.88621
$716$	−0.581998	−0.0217503
$717$	11.5604	0.431730
$718$	23.2705	0.868447
$719$	37.2046	1.38750	0.693748	−	0.720218i	$-0.255958\pi$
$719$	37.2046	1.38750	0.693748	+	0.720218i	$0.255958\pi$
$720$	6.31049	0.235178
$721$	8.29493	0.308919
$722$	−18.2814	−0.680362
$723$	6.51654	0.242353
$724$	−21.0758	−0.783277
$725$	62.4953	2.32102
$726$	−5.81500	−0.215815
$727$	14.6346	0.542766	0.271383	−	0.962471i	$-0.412519\pi$
$727$	14.6346	0.542766	0.271383	+	0.962471i	$0.412519\pi$
$728$	−5.35447	−0.198450
$729$	19.6723	0.728603
$730$	36.1209	1.33690
$731$	−27.4228	−1.01427
$732$	−6.74553	−0.249322
$733$	−24.5804	−0.907896	−0.453948	−	0.891028i	$-0.649985\pi$
$733$	−24.5804	−0.907896	−0.453948	+	0.891028i	$0.649985\pi$
$734$	22.6160	0.834770
$735$	25.3948	0.936700
$736$	−1.00000	−0.0368605
$737$	8.89108	0.327507
$738$	−4.40991	−0.162331
$739$	7.73218	0.284433	0.142216	−	0.989836i	$-0.454577\pi$
$739$	7.73218	0.284433	0.142216	+	0.989836i	$0.454577\pi$
$740$	27.6437	1.01620
$741$	5.44345	0.199970
$742$	0.954290	0.0350331
$743$	−52.6265	−1.93068	−0.965340	−	0.260994i	$-0.915950\pi$
$743$	−52.6265	−1.93068	−0.965340	+	0.260994i	$0.915950\pi$
$744$	3.15388	0.115627
$745$	23.3769	0.856464
$746$	11.1792	0.409298
$747$	−12.4490	−0.455484
$748$	−7.43057	−0.271688
$749$	−2.24076	−0.0818755
$750$	−14.4852	−0.528926
$751$	29.7041	1.08392	0.541960	−	0.840405i	$-0.317683\pi$
$751$	29.7041	1.08392	0.541960	+	0.840405i	$0.317683\pi$
$752$	−2.98447	−0.108832
$753$	−3.47770	−0.126734
$754$	41.7806	1.52156
$755$	6.41829	0.233585
$756$	5.04226	0.183385
$757$	13.5386	0.492071	0.246035	−	0.969261i	$-0.420872\pi$
$757$	13.5386	0.492071	0.246035	+	0.969261i	$0.420872\pi$
$758$	1.85678	0.0674412
$759$	2.74115	0.0994973
$760$	−3.11296	−0.112919
$761$	10.3738	0.376051	0.188026	−	0.982164i	$-0.439791\pi$
$761$	10.3738	0.376051	0.188026	+	0.982164i	$0.439791\pi$
$762$	−1.05350	−0.0381644
$763$	11.8220	0.427983
$764$	26.3485	0.953256
$765$	19.3649	0.700139
$766$	−13.2862	−0.480050
$767$	−55.9563	−2.02046
$768$	1.13204	0.0408490
$769$	47.8601	1.72588	0.862939	−	0.505308i	$-0.168621\pi$
$769$	47.8601	1.72588	0.862939	+	0.505308i	$0.168621\pi$
$770$	−8.39361	−0.302485
$771$	−29.6361	−1.06732
$772$	−21.0776	−0.758598
$773$	−30.0187	−1.07970	−0.539849	−	0.841762i	$-0.681519\pi$
$773$	−30.0187	−1.07970	−0.539849	+	0.841762i	$0.681519\pi$
$774$	15.3569	0.551994
$775$	23.6380	0.849103
$776$	−0.0496363	−0.00178184
$777$	8.04454	0.288596
$778$	−7.52997	−0.269962
$779$	2.17541	0.0779421
$780$	−23.5796	−0.844284
$781$	−21.3035	−0.762298
$782$	−3.06869	−0.109736
$783$	−39.3445	−1.40606
$784$	−6.10891	−0.218175
$785$	−60.2944	−2.15200
$786$	1.13204	0.0403786
$787$	52.7107	1.87893	0.939467	−	0.342639i	$-0.111321\pi$
$787$	52.7107	1.87893	0.939467	+	0.342639i	$0.111321\pi$
$788$	−3.53346	−0.125874
$789$	11.1410	0.396629
$790$	48.3801	1.72129
$791$	7.88090	0.280213
$792$	4.16116	0.147860
$793$	−33.7994	−1.20025
$794$	32.9367	1.16888
$795$	4.20242	0.149045
$796$	−11.7501	−0.416472
$797$	−9.05064	−0.320590	−0.160295	−	0.987069i	$-0.551245\pi$
$797$	−9.05064	−0.320590	−0.160295	+	0.987069i	$0.551245\pi$
$798$	−0.905898	−0.0320684
$799$	−9.15839	−0.324001
$800$	8.48454	0.299974
$801$	23.4316	0.827915
$802$	−9.90203	−0.349653
$803$	23.8183	0.840530
$804$	−4.15669	−0.146595
$805$	−3.46640	−0.122175
$806$	15.8030	0.556636
$807$	19.4102	0.683272
$808$	−11.1557	−0.392456
$809$	−41.6116	−1.46299	−0.731493	−	0.681849i	$-0.761176\pi$
$809$	−41.6116	−1.46299	−0.731493	+	0.681849i	$0.761176\pi$
$810$	3.27325	0.115010
$811$	−14.1406	−0.496542	−0.248271	−	0.968691i	$-0.579862\pi$
$811$	−14.1406	−0.496542	−0.248271	+	0.968691i	$0.579862\pi$
$812$	−6.95312	−0.244007
$813$	−18.4734	−0.647891
$814$	18.2284	0.638904
$815$	−49.5798	−1.73671
$816$	3.47388	0.121610
$817$	−7.57557	−0.265036
$818$	−15.0201	−0.525167
$819$	9.20156	0.321528
$820$	−9.42330	−0.329076
$821$	−2.19624	−0.0766493	−0.0383247	−	0.999265i	$-0.512202\pi$
$821$	−2.19624	−0.0766493	−0.0383247	+	0.999265i	$0.512202\pi$
$822$	18.8290	0.656737
$823$	−14.1008	−0.491523	−0.245761	−	0.969330i	$-0.579038\pi$
$823$	−14.1008	−0.491523	−0.245761	+	0.969330i	$0.579038\pi$
$824$	−8.78722	−0.306117
$825$	−23.2574	−0.809717
$826$	9.31224	0.324014
$827$	−20.5055	−0.713047	−0.356524	−	0.934286i	$-0.616038\pi$
$827$	−20.5055	−0.713047	−0.356524	+	0.934286i	$0.616038\pi$
$828$	1.71848	0.0597214
$829$	−16.8546	−0.585384	−0.292692	−	0.956207i	$-0.594551\pi$
$829$	−16.8546	−0.585384	−0.292692	+	0.956207i	$0.594551\pi$
$830$	−26.6015	−0.923352
$831$	7.58459	0.263106
$832$	5.67225	0.196650
$833$	−18.7463	−0.649521
$834$	19.0920	0.661102
$835$	23.7152	0.820699
$836$	−2.05270	−0.0709941
$837$	−14.8815	−0.514381
$838$	−9.08217	−0.313738
$839$	−8.11258	−0.280078	−0.140039	−	0.990146i	$-0.544723\pi$
$839$	−8.11258	−0.280078	−0.140039	+	0.990146i	$0.544723\pi$
$840$	3.92411	0.135395
$841$	25.2548	0.870854
$842$	−6.17945	−0.212958
$843$	−13.1798	−0.453938
$844$	−4.60248	−0.158424
$845$	−70.4111	−2.42222
$846$	5.12875	0.176330
$847$	4.84896	0.166612
$848$	−1.01093	−0.0347154
$849$	−1.88568	−0.0647165
$850$	26.0364	0.893040
$851$	7.52797	0.258056
$852$	9.95963	0.341211
$853$	39.4402	1.35041	0.675203	−	0.737632i	$-0.264056\pi$
$853$	39.4402	1.35041	0.675203	+	0.737632i	$0.264056\pi$
$854$	5.62490	0.192480
$855$	5.34957	0.182951
$856$	2.37374	0.0811329
$857$	10.6275	0.363030	0.181515	−	0.983388i	$-0.441900\pi$
$857$	10.6275	0.363030	0.181515	+	0.983388i	$0.441900\pi$
$858$	−15.5485	−0.530816
$859$	−10.3204	−0.352128	−0.176064	−	0.984379i	$-0.556337\pi$
$859$	−10.3204	−0.352128	−0.176064	+	0.984379i	$0.556337\pi$
$860$	32.8154	1.11900
$861$	−2.74226	−0.0934559
$862$	4.20913	0.143364
$863$	−52.5280	−1.78807	−0.894036	−	0.447995i	$-0.852138\pi$
$863$	−52.5280	−1.78807	−0.894036	+	0.447995i	$0.852138\pi$
$864$	−5.34152	−0.181722
$865$	61.7874	2.10084
$866$	1.51210	0.0513833
$867$	−8.58447	−0.291544
$868$	−2.62993	−0.0892656
$869$	31.9020	1.08220
$870$	−30.6196	−1.03810
$871$	−20.8277	−0.705719
$872$	−12.5236	−0.424102
$873$	0.0852990	0.00288693
$874$	−0.847727	−0.0286748
$875$	12.0788	0.408338
$876$	−11.1353	−0.376228
$877$	−21.0627	−0.711238	−0.355619	−	0.934631i	$-0.615730\pi$
$877$	−21.0627	−0.711238	−0.355619	+	0.934631i	$0.615730\pi$
$878$	25.7316	0.868399
$879$	27.1382	0.915349
$880$	8.89176	0.299741
$881$	−17.3518	−0.584597	−0.292298	−	0.956327i	$-0.594420\pi$
$881$	−17.3518	−0.584597	−0.292298	+	0.956327i	$0.594420\pi$
$882$	10.4980	0.353488
$883$	−3.76169	−0.126591	−0.0632955	−	0.997995i	$-0.520161\pi$
$883$	−3.76169	−0.126591	−0.0632955	+	0.997995i	$0.520161\pi$
$884$	17.4064	0.585439
$885$	41.0085	1.37848
$886$	30.0084	1.00815
$887$	52.8503	1.77454	0.887270	−	0.461251i	$-0.152599\pi$
$887$	52.8503	1.77454	0.887270	+	0.461251i	$0.152599\pi$
$888$	−8.52198	−0.285979
$889$	0.878484	0.0294634
$890$	50.0697	1.67834
$891$	2.15839	0.0723089
$892$	−22.9582	−0.768696
$893$	−2.53001	−0.0846637
$894$	−7.20662	−0.241025
$895$	2.13717	0.0714378
$896$	−0.943976	−0.0315360
$897$	−6.42123	−0.214399
$898$	35.4722	1.18372
$899$	20.5212	0.684419
$900$	−14.5805	−0.486017
$901$	−3.10221	−0.103350
$902$	−6.21376	−0.206896
$903$	9.54955	0.317789
$904$	−8.34863	−0.277671
$905$	77.3932	2.57264
$906$	−1.97863	−0.0657354
$907$	35.8689	1.19101	0.595504	−	0.803352i	$-0.296952\pi$
$907$	35.8689	1.19101	0.595504	+	0.803352i	$0.296952\pi$
$908$	16.8427	0.558944
$909$	19.1709	0.635857
$910$	19.6623	0.651799
$911$	−24.6678	−0.817282	−0.408641	−	0.912695i	$-0.633997\pi$
$911$	−24.6678	−0.817282	−0.408641	+	0.912695i	$0.633997\pi$
$912$	0.959662	0.0317776
$913$	−17.5412	−0.580527
$914$	−16.0503	−0.530895
$915$	24.7705	0.818887
$916$	12.1358	0.400980
$917$	−0.943976	−0.0311728
$918$	−16.3914	−0.540998
$919$	13.5898	0.448287	0.224144	−	0.974556i	$-0.428041\pi$
$919$	13.5898	0.448287	0.224144	+	0.974556i	$0.428041\pi$
$920$	3.67213	0.121067
$921$	−0.0387903	−0.00127818
$922$	−6.59848	−0.217309
$923$	49.9041	1.64261
$924$	2.58758	0.0851250
$925$	−63.8713	−2.10008
$926$	−23.0660	−0.757996
$927$	15.1007	0.495971
$928$	7.36578	0.241794
$929$	31.4509	1.03187	0.515935	−	0.856628i	$-0.327445\pi$
$929$	31.4509	1.03187	0.515935	+	0.856628i	$0.327445\pi$
$930$	−11.5815	−0.379771
$931$	−5.17869	−0.169725
$932$	27.9168	0.914444
$933$	−20.6758	−0.676894
$934$	−20.9710	−0.686192
$935$	27.2860	0.892348
$936$	−9.74766	−0.318612
$937$	42.6450	1.39315	0.696576	−	0.717483i	$-0.254706\pi$
$937$	42.6450	1.39315	0.696576	+	0.717483i	$0.254706\pi$
$938$	3.46614	0.113173
$939$	−34.2670	−1.11826
$940$	10.9594	0.357455
$941$	16.1548	0.526632	0.263316	−	0.964710i	$-0.415184\pi$
$941$	16.1548	0.526632	0.263316	+	0.964710i	$0.415184\pi$
$942$	18.5875	0.605614
$943$	−2.56617	−0.0835659
$944$	−9.86491	−0.321075
$945$	−18.5158	−0.602321
$946$	21.6386	0.703532
$947$	−21.5767	−0.701149	−0.350574	−	0.936535i	$-0.614014\pi$
$947$	−21.5767	−0.701149	−0.350574	+	0.936535i	$0.614014\pi$
$948$	−14.9146	−0.484403
$949$	−55.7952	−1.81119
$950$	7.19257	0.233358
$951$	−22.5573	−0.731470
$952$	−2.89676	−0.0938847
$953$	39.5609	1.28150	0.640751	−	0.767749i	$-0.278623\pi$
$953$	39.5609	1.28150	0.640751	+	0.767749i	$0.278623\pi$
$954$	1.73726	0.0562458
$955$	−96.7552	−3.13092
$956$	10.2120	0.330278
$957$	−20.1907	−0.652672
$958$	22.5970	0.730076
$959$	−15.7009	−0.507010
$960$	−4.15700	−0.134167
$961$	−23.2381	−0.749617
$962$	−42.7006	−1.37672
$963$	−4.07924	−0.131452
$964$	5.75645	0.185403
$965$	77.3995	2.49158
$966$	1.06862	0.0343823
$967$	−15.5286	−0.499367	−0.249683	−	0.968328i	$-0.580327\pi$
$967$	−15.5286	−0.499367	−0.249683	+	0.968328i	$0.580327\pi$
$968$	−5.13674	−0.165101
$969$	2.94490	0.0946039
$970$	0.182271	0.00585236
$971$	20.0999	0.645036	0.322518	−	0.946563i	$-0.395471\pi$
$971$	20.0999	0.645036	0.322518	+	0.946563i	$0.395471\pi$
$972$	15.0155	0.481622
$973$	−15.9202	−0.510380
$974$	−22.9224	−0.734482
$975$	54.4811	1.74479
$976$	−5.95873	−0.190734
$977$	−5.32743	−0.170440	−0.0852199	−	0.996362i	$-0.527159\pi$
$977$	−5.32743	−0.170440	−0.0852199	+	0.996362i	$0.527159\pi$
$978$	15.2844	0.488742
$979$	33.0162	1.05520
$980$	22.4327	0.716587
$981$	21.5215	0.687130
$982$	18.4216	0.587856
$983$	−47.6060	−1.51840	−0.759198	−	0.650860i	$-0.774408\pi$
$983$	−47.6060	−1.51840	−0.759198	+	0.650860i	$0.774408\pi$
$984$	2.90501	0.0926083
$985$	12.9753	0.413428
$986$	22.6033	0.719835
$987$	3.18926	0.101515
$988$	4.80852	0.152979
$989$	8.93634	0.284159
$990$	−15.2803	−0.485641
$991$	−8.00642	−0.254332	−0.127166	−	0.991881i	$-0.540588\pi$
$991$	−8.00642	−0.254332	−0.127166	+	0.991881i	$0.540588\pi$
$992$	2.78601	0.0884560
$993$	−19.8025	−0.628414
$994$	−8.30504	−0.263420
$995$	43.1479	1.36788
$996$	8.20070	0.259849
$997$	7.21442	0.228483	0.114241	−	0.993453i	$-0.463556\pi$
$997$	7.21442	0.228483	0.114241	+	0.993453i	$0.463556\pi$
$998$	11.7070	0.370579
$999$	40.2108	1.27221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.g.1.16	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.g.1.16	✓	21	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.13204 q^{3} +1.00000 q^{4} -3.67213 q^{5} +1.13204 q^{6} -0.943976 q^{7} +1.00000 q^{8} -1.71848 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.13204 q^{3} +1.00000 q^{4} -3.67213 q^{5} +1.13204 q^{6} -0.943976 q^{7} +1.00000 q^{8} -1.71848 q^{9} -3.67213 q^{10} -2.42142 q^{11} +1.13204 q^{12} +5.67225 q^{13} -0.943976 q^{14} -4.15700 q^{15} +1.00000 q^{16} +3.06869 q^{17} -1.71848 q^{18} +0.847727 q^{19} -3.67213 q^{20} -1.06862 q^{21} -2.42142 q^{22} -1.00000 q^{23} +1.13204 q^{24} +8.48454 q^{25} +5.67225 q^{26} -5.34152 q^{27} -0.943976 q^{28} +7.36578 q^{29} -4.15700 q^{30} +2.78601 q^{31} +1.00000 q^{32} -2.74115 q^{33} +3.06869 q^{34} +3.46640 q^{35} -1.71848 q^{36} -7.52797 q^{37} +0.847727 q^{38} +6.42123 q^{39} -3.67213 q^{40} +2.56617 q^{41} -1.06862 q^{42} -8.93634 q^{43} -2.42142 q^{44} +6.31049 q^{45} -1.00000 q^{46} -2.98447 q^{47} +1.13204 q^{48} -6.10891 q^{49} +8.48454 q^{50} +3.47388 q^{51} +5.67225 q^{52} -1.01093 q^{53} -5.34152 q^{54} +8.89176 q^{55} -0.943976 q^{56} +0.959662 q^{57} +7.36578 q^{58} -9.86491 q^{59} -4.15700 q^{60} -5.95873 q^{61} +2.78601 q^{62} +1.62221 q^{63} +1.00000 q^{64} -20.8293 q^{65} -2.74115 q^{66} -3.67185 q^{67} +3.06869 q^{68} -1.13204 q^{69} +3.46640 q^{70} +8.79793 q^{71} -1.71848 q^{72} -9.83651 q^{73} -7.52797 q^{74} +9.60485 q^{75} +0.847727 q^{76} +2.28576 q^{77} +6.42123 q^{78} -13.1749 q^{79} -3.67213 q^{80} -0.891377 q^{81} +2.56617 q^{82} +7.24417 q^{83} -1.06862 q^{84} -11.2686 q^{85} -8.93634 q^{86} +8.33837 q^{87} -2.42142 q^{88} -13.6351 q^{89} +6.31049 q^{90} -5.35447 q^{91} -1.00000 q^{92} +3.15388 q^{93} -2.98447 q^{94} -3.11296 q^{95} +1.13204 q^{96} -0.0496363 q^{97} -6.10891 q^{98} +4.16116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more