LMFDB - Embedded newform 2001.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + \cdots - 192 $ x^16 - x^15 - 28x^14 + 27x^13 + 316x^12 - 295x^11 - 1835x^10 + 1665x^9 + 5778x^8 - 5124x^7 - 9405x^6 + 8288x^5 + 6405x^4 - 6032x^3 - 400x^2 + 1088x - 192
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.63319$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63319 q^{2} +1.00000 q^{3} +4.93371 q^{4} +0.107081 q^{5} -2.63319 q^{6} +4.37350 q^{7} -7.72501 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.63319 q^{2} +1.00000 q^{3} +4.93371 q^{4} +0.107081 q^{5} -2.63319 q^{6} +4.37350 q^{7} -7.72501 q^{8} +1.00000 q^{9} -0.281966 q^{10} +0.577904 q^{11} +4.93371 q^{12} -4.16712 q^{13} -11.5163 q^{14} +0.107081 q^{15} +10.4740 q^{16} -3.07903 q^{17} -2.63319 q^{18} +3.22665 q^{19} +0.528308 q^{20} +4.37350 q^{21} -1.52173 q^{22} -1.00000 q^{23} -7.72501 q^{24} -4.98853 q^{25} +10.9728 q^{26} +1.00000 q^{27} +21.5775 q^{28} -1.00000 q^{29} -0.281966 q^{30} +6.08061 q^{31} -12.1301 q^{32} +0.577904 q^{33} +8.10767 q^{34} +0.468320 q^{35} +4.93371 q^{36} +4.83016 q^{37} -8.49640 q^{38} -4.16712 q^{39} -0.827205 q^{40} +10.9057 q^{41} -11.5163 q^{42} +0.619192 q^{43} +2.85121 q^{44} +0.107081 q^{45} +2.63319 q^{46} +0.421227 q^{47} +10.4740 q^{48} +12.1275 q^{49} +13.1358 q^{50} -3.07903 q^{51} -20.5593 q^{52} +2.63809 q^{53} -2.63319 q^{54} +0.0618828 q^{55} -33.7853 q^{56} +3.22665 q^{57} +2.63319 q^{58} -0.709195 q^{59} +0.528308 q^{60} +8.89266 q^{61} -16.0114 q^{62} +4.37350 q^{63} +10.9929 q^{64} -0.446221 q^{65} -1.52173 q^{66} +2.95956 q^{67} -15.1910 q^{68} -1.00000 q^{69} -1.23318 q^{70} +2.68706 q^{71} -7.72501 q^{72} +9.79583 q^{73} -12.7187 q^{74} -4.98853 q^{75} +15.9194 q^{76} +2.52746 q^{77} +10.9728 q^{78} +0.714717 q^{79} +1.12157 q^{80} +1.00000 q^{81} -28.7167 q^{82} +4.88987 q^{83} +21.5775 q^{84} -0.329706 q^{85} -1.63045 q^{86} -1.00000 q^{87} -4.46432 q^{88} +9.26100 q^{89} -0.281966 q^{90} -18.2249 q^{91} -4.93371 q^{92} +6.08061 q^{93} -1.10917 q^{94} +0.345514 q^{95} -12.1301 q^{96} -5.58813 q^{97} -31.9340 q^{98} +0.577904 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * 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 $

$2$	−2.63319	−1.86195	−0.930974	−	0.365085i	$-0.881040\pi$
$2$	−2.63319	−1.86195	−0.930974	+	0.365085i	$0.881040\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.93371	2.46685
$5$	0.107081	0.0478883	0.0239441	−	0.999713i	$-0.492378\pi$
$5$	0.107081	0.0478883	0.0239441	+	0.999713i	$0.492378\pi$
$6$	−2.63319	−1.07500
$7$	4.37350	1.65303	0.826513	−	0.562917i	$-0.190321\pi$
$7$	4.37350	1.65303	0.826513	+	0.562917i	$0.190321\pi$
$8$	−7.72501	−2.73120
$9$	1.00000	0.333333
$10$	−0.281966	−0.0891655
$11$	0.577904	0.174245	0.0871224	−	0.996198i	$-0.472233\pi$
$11$	0.577904	0.174245	0.0871224	+	0.996198i	$0.472233\pi$
$12$	4.93371	1.42424
$13$	−4.16712	−1.15575	−0.577876	−	0.816125i	$-0.696118\pi$
$13$	−4.16712	−1.15575	−0.577876	+	0.816125i	$0.696118\pi$
$14$	−11.5163	−3.07785
$15$	0.107081	0.0276483
$16$	10.4740	2.61851
$17$	−3.07903	−0.746773	−0.373387	−	0.927676i	$-0.621804\pi$
$17$	−3.07903	−0.746773	−0.373387	+	0.927676i	$0.621804\pi$
$18$	−2.63319	−0.620650
$19$	3.22665	0.740245	0.370122	−	0.928983i	$-0.379316\pi$
$19$	3.22665	0.740245	0.370122	+	0.928983i	$0.379316\pi$
$20$	0.528308	0.118133
$21$	4.37350	0.954375
$22$	−1.52173	−0.324435
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−7.72501	−1.57686
$25$	−4.98853	−0.997707
$26$	10.9728	2.15195
$27$	1.00000	0.192450
$28$	21.5775	4.07777
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.281966	−0.0514797
$31$	6.08061	1.09211	0.546055	−	0.837750i	$-0.316129\pi$
$31$	6.08061	1.09211	0.546055	+	0.837750i	$0.316129\pi$
$32$	−12.1301	−2.14433
$33$	0.577904	0.100600
$34$	8.10767	1.39045
$35$	0.468320	0.0791606
$36$	4.93371	0.822284
$37$	4.83016	0.794074	0.397037	−	0.917803i	$-0.370039\pi$
$37$	4.83016	0.794074	0.397037	+	0.917803i	$0.370039\pi$
$38$	−8.49640	−1.37830
$39$	−4.16712	−0.667273
$40$	−0.827205	−0.130793
$41$	10.9057	1.70318	0.851590	−	0.524208i	$-0.175639\pi$
$41$	10.9057	1.70318	0.851590	+	0.524208i	$0.175639\pi$
$42$	−11.5163	−1.77700
$43$	0.619192	0.0944259	0.0472129	−	0.998885i	$-0.484966\pi$
$43$	0.619192	0.0944259	0.0472129	+	0.998885i	$0.484966\pi$
$44$	2.85121	0.429836
$45$	0.107081	0.0159628
$46$	2.63319	0.388243
$47$	0.421227	0.0614422	0.0307211	−	0.999528i	$-0.490220\pi$
$47$	0.421227	0.0614422	0.0307211	+	0.999528i	$0.490220\pi$
$48$	10.4740	1.51180
$49$	12.1275	1.73250
$50$	13.1358	1.85768
$51$	−3.07903	−0.431150
$52$	−20.5593	−2.85107
$53$	2.63809	0.362369	0.181185	−	0.983449i	$-0.442007\pi$
$53$	2.63809	0.362369	0.181185	+	0.983449i	$0.442007\pi$
$54$	−2.63319	−0.358332
$55$	0.0618828	0.00834428
$56$	−33.7853	−4.51475
$57$	3.22665	0.427381
$58$	2.63319	0.345755
$59$	−0.709195	−0.0923293	−0.0461646	−	0.998934i	$-0.514700\pi$
$59$	−0.709195	−0.0923293	−0.0461646	+	0.998934i	$0.514700\pi$
$60$	0.528308	0.0682043
$61$	8.89266	1.13859	0.569294	−	0.822134i	$-0.307216\pi$
$61$	8.89266	1.13859	0.569294	+	0.822134i	$0.307216\pi$
$62$	−16.0114	−2.03345
$63$	4.37350	0.551009
$64$	10.9929	1.37411
$65$	−0.446221	−0.0553469
$66$	−1.52173	−0.187312
$67$	2.95956	0.361568	0.180784	−	0.983523i	$-0.442137\pi$
$67$	2.95956	0.361568	0.180784	+	0.983523i	$0.442137\pi$
$68$	−15.1910	−1.84218
$69$	−1.00000	−0.120386
$70$	−1.23318	−0.147393
$71$	2.68706	0.318896	0.159448	−	0.987206i	$-0.449029\pi$
$71$	2.68706	0.318896	0.159448	+	0.987206i	$0.449029\pi$
$72$	−7.72501	−0.910401
$73$	9.79583	1.14652	0.573258	−	0.819375i	$-0.305679\pi$
$73$	9.79583	1.14652	0.573258	+	0.819375i	$0.305679\pi$
$74$	−12.7187	−1.47852
$75$	−4.98853	−0.576026
$76$	15.9194	1.82607
$77$	2.52746	0.288031
$78$	10.9728	1.24243
$79$	0.714717	0.0804119	0.0402060	−	0.999191i	$-0.487199\pi$
$79$	0.714717	0.0804119	0.0402060	+	0.999191i	$0.487199\pi$
$80$	1.12157	0.125396
$81$	1.00000	0.111111
$82$	−28.7167	−3.17123
$83$	4.88987	0.536733	0.268366	−	0.963317i	$-0.413516\pi$
$83$	4.88987	0.536733	0.268366	+	0.963317i	$0.413516\pi$
$84$	21.5775	2.35430
$85$	−0.329706	−0.0357617
$86$	−1.63045	−0.175816
$87$	−1.00000	−0.107211
$88$	−4.46432	−0.475898
$89$	9.26100	0.981664	0.490832	−	0.871254i	$-0.336693\pi$
$89$	9.26100	0.981664	0.490832	+	0.871254i	$0.336693\pi$
$90$	−0.281966	−0.0297218
$91$	−18.2249	−1.91049
$92$	−4.93371	−0.514374
$93$	6.08061	0.630530
$94$	−1.10917	−0.114402
$95$	0.345514	0.0354490
$96$	−12.1301	−1.23803
$97$	−5.58813	−0.567388	−0.283694	−	0.958915i	$-0.591560\pi$
$97$	−5.58813	−0.567388	−0.283694	+	0.958915i	$0.591560\pi$
$98$	−31.9340	−3.22582
$99$	0.577904	0.0580816
$100$	−24.6120	−2.46120
$101$	10.7237	1.06705	0.533524	−	0.845785i	$-0.320867\pi$
$101$	10.7237	1.06705	0.533524	+	0.845785i	$0.320867\pi$
$102$	8.10767	0.802779
$103$	2.43378	0.239807	0.119904	−	0.992786i	$-0.461741\pi$
$103$	2.43378	0.239807	0.119904	+	0.992786i	$0.461741\pi$
$104$	32.1911	3.15659
$105$	0.468320	0.0457034
$106$	−6.94660	−0.674713
$107$	−14.2949	−1.38194	−0.690970	−	0.722883i	$-0.742816\pi$
$107$	−14.2949	−1.38194	−0.690970	+	0.722883i	$0.742816\pi$
$108$	4.93371	0.474746
$109$	−10.2761	−0.984276	−0.492138	−	0.870517i	$-0.663784\pi$
$109$	−10.2761	−0.984276	−0.492138	+	0.870517i	$0.663784\pi$
$110$	−0.162949	−0.0155366
$111$	4.83016	0.458459
$112$	45.8082	4.32846
$113$	9.56977	0.900248	0.450124	−	0.892966i	$-0.351380\pi$
$113$	9.56977	0.900248	0.450124	+	0.892966i	$0.351380\pi$
$114$	−8.49640	−0.795761
$115$	−0.107081	−0.00998539
$116$	−4.93371	−0.458083
$117$	−4.16712	−0.385250
$118$	1.86745	0.171912
$119$	−13.4661	−1.23444
$120$	−0.827205	−0.0755132
$121$	−10.6660	−0.969639
$122$	−23.4161	−2.11999
$123$	10.9057	0.983332
$124$	29.9999	2.69407
$125$	−1.06959	−0.0956667
$126$	−11.5163	−1.02595
$127$	−5.57239	−0.494470	−0.247235	−	0.968956i	$-0.579522\pi$
$127$	−5.57239	−0.494470	−0.247235	+	0.968956i	$0.579522\pi$
$128$	−4.68619	−0.414205
$129$	0.619192	0.0545168
$130$	1.17499	0.103053
$131$	−19.6201	−1.71421	−0.857106	−	0.515140i	$-0.827740\pi$
$131$	−19.6201	−1.71421	−0.857106	+	0.515140i	$0.827740\pi$
$132$	2.85121	0.248166
$133$	14.1118	1.22364
$134$	−7.79309	−0.673220
$135$	0.107081	0.00921610
$136$	23.7855	2.03959
$137$	18.7665	1.60333	0.801664	−	0.597775i	$-0.203948\pi$
$137$	18.7665	1.60333	0.801664	+	0.597775i	$0.203948\pi$
$138$	2.63319	0.224152
$139$	8.89370	0.754354	0.377177	−	0.926141i	$-0.376895\pi$
$139$	8.89370	0.754354	0.377177	+	0.926141i	$0.376895\pi$
$140$	2.31055	0.195277
$141$	0.421227	0.0354737
$142$	−7.07556	−0.593768
$143$	−2.40820	−0.201384
$144$	10.4740	0.872836
$145$	−0.107081	−0.00889263
$146$	−25.7943	−2.13475
$147$	12.1275	1.00026
$148$	23.8306	1.95886
$149$	−7.43517	−0.609112	−0.304556	−	0.952494i	$-0.598508\pi$
$149$	−7.43517	−0.609112	−0.304556	+	0.952494i	$0.598508\pi$
$150$	13.1358	1.07253
$151$	−7.48246	−0.608914	−0.304457	−	0.952526i	$-0.598475\pi$
$151$	−7.48246	−0.608914	−0.304457	+	0.952526i	$0.598475\pi$
$152$	−24.9259	−2.02176
$153$	−3.07903	−0.248924
$154$	−6.65530	−0.536299
$155$	0.651120	0.0522992
$156$	−20.5593	−1.64607
$157$	−12.0415	−0.961012	−0.480506	−	0.876991i	$-0.659547\pi$
$157$	−12.0415	−0.961012	−0.480506	+	0.876991i	$0.659547\pi$
$158$	−1.88199	−0.149723
$159$	2.63809	0.209214
$160$	−1.29891	−0.102688
$161$	−4.37350	−0.344680
$162$	−2.63319	−0.206883
$163$	−20.6933	−1.62082	−0.810411	−	0.585862i	$-0.800756\pi$
$163$	−20.6933	−1.62082	−0.810411	+	0.585862i	$0.800756\pi$
$164$	53.8054	4.20149
$165$	0.0618828	0.00481757
$166$	−12.8760	−0.999369
$167$	3.86308	0.298934	0.149467	−	0.988767i	$-0.452244\pi$
$167$	3.86308	0.298934	0.149467	+	0.988767i	$0.452244\pi$
$168$	−33.7853	−2.60659
$169$	4.36490	0.335761
$170$	0.868181	0.0665864
$171$	3.22665	0.246748
$172$	3.05491	0.232935
$173$	1.49958	0.114011	0.0570054	−	0.998374i	$-0.481845\pi$
$173$	1.49958	0.114011	0.0570054	+	0.998374i	$0.481845\pi$
$174$	2.63319	0.199622
$175$	−21.8173	−1.64924
$176$	6.05299	0.456261
$177$	−0.709195	−0.0533063
$178$	−24.3860	−1.82781
$179$	16.2604	1.21536	0.607678	−	0.794183i	$-0.292101\pi$
$179$	16.2604	1.21536	0.607678	+	0.794183i	$0.292101\pi$
$180$	0.528308	0.0393778
$181$	18.0441	1.34121	0.670604	−	0.741816i	$-0.266035\pi$
$181$	18.0441	1.34121	0.670604	+	0.741816i	$0.266035\pi$
$182$	47.9897	3.55723
$183$	8.89266	0.657365
$184$	7.72501	0.569495
$185$	0.517221	0.0380268
$186$	−16.0114	−1.17401
$187$	−1.77938	−0.130121
$188$	2.07821	0.151569
$189$	4.37350	0.318125
$190$	−0.909806	−0.0660043
$191$	−3.04075	−0.220021	−0.110011	−	0.993930i	$-0.535088\pi$
$191$	−3.04075	−0.220021	−0.110011	+	0.993930i	$0.535088\pi$
$192$	10.9929	0.793345
$193$	11.7675	0.847046	0.423523	−	0.905885i	$-0.360793\pi$
$193$	11.7675	0.847046	0.423523	+	0.905885i	$0.360793\pi$
$194$	14.7146	1.05645
$195$	−0.446221	−0.0319546
$196$	59.8334	4.27381
$197$	5.69970	0.406087	0.203043	−	0.979170i	$-0.434917\pi$
$197$	5.69970	0.406087	0.203043	+	0.979170i	$0.434917\pi$
$198$	−1.52173	−0.108145
$199$	3.75650	0.266291	0.133146	−	0.991096i	$-0.457492\pi$
$199$	3.75650	0.266291	0.133146	+	0.991096i	$0.457492\pi$
$200$	38.5365	2.72494
$201$	2.95956	0.208751
$202$	−28.2376	−1.98679
$203$	−4.37350	−0.306959
$204$	−15.1910	−1.06358
$205$	1.16780	0.0815623
$206$	−6.40860	−0.446509
$207$	−1.00000	−0.0695048
$208$	−43.6466	−3.02635
$209$	1.86470	0.128984
$210$	−1.23318	−0.0850973
$211$	22.5764	1.55422	0.777110	−	0.629365i	$-0.216685\pi$
$211$	22.5764	1.55422	0.777110	+	0.629365i	$0.216685\pi$
$212$	13.0156	0.893912
$213$	2.68706	0.184115
$214$	37.6412	2.57310
$215$	0.0663039	0.00452189
$216$	−7.72501	−0.525620
$217$	26.5935	1.80529
$218$	27.0591	1.83267
$219$	9.79583	0.661941
$220$	0.305312	0.0205841
$221$	12.8307	0.863084
$222$	−12.7187	−0.853626
$223$	25.5794	1.71292	0.856461	−	0.516211i	$-0.172658\pi$
$223$	25.5794	1.71292	0.856461	+	0.516211i	$0.172658\pi$
$224$	−53.0511	−3.54463
$225$	−4.98853	−0.332569
$226$	−25.1990	−1.67622
$227$	−21.7903	−1.44627	−0.723137	−	0.690704i	$-0.757301\pi$
$227$	−21.7903	−1.44627	−0.723137	+	0.690704i	$0.757301\pi$
$228$	15.9194	1.05428
$229$	−18.9652	−1.25326	−0.626628	−	0.779319i	$-0.715565\pi$
$229$	−18.9652	−1.25326	−0.626628	+	0.779319i	$0.715565\pi$
$230$	0.281966	0.0185923
$231$	2.52746	0.166295
$232$	7.72501	0.507172
$233$	−3.91205	−0.256287	−0.128143	−	0.991756i	$-0.540902\pi$
$233$	−3.91205	−0.256287	−0.128143	+	0.991756i	$0.540902\pi$
$234$	10.9728	0.717317
$235$	0.0451056	0.00294236
$236$	−3.49896	−0.227763
$237$	0.714717	0.0464258
$238$	35.4589	2.29846
$239$	−2.75223	−0.178027	−0.0890136	−	0.996030i	$-0.528371\pi$
$239$	−2.75223	−0.178027	−0.0890136	+	0.996030i	$0.528371\pi$
$240$	1.12157	0.0723973
$241$	−7.53708	−0.485506	−0.242753	−	0.970088i	$-0.578050\pi$
$241$	−7.53708	−0.485506	−0.242753	+	0.970088i	$0.578050\pi$
$242$	28.0857	1.80542
$243$	1.00000	0.0641500
$244$	43.8738	2.80873
$245$	1.29863	0.0829662
$246$	−28.7167	−1.83091
$247$	−13.4459	−0.855539
$248$	−46.9728	−2.98277
$249$	4.88987	0.309883
$250$	2.81643	0.178126
$251$	17.6229	1.11235	0.556174	−	0.831066i	$-0.312269\pi$
$251$	17.6229	1.11235	0.556174	+	0.831066i	$0.312269\pi$
$252$	21.5775	1.35926
$253$	−0.577904	−0.0363325
$254$	14.6732	0.920678
$255$	−0.329706	−0.0206470
$256$	−9.64618	−0.602886
$257$	14.9898	0.935036	0.467518	−	0.883984i	$-0.345148\pi$
$257$	14.9898	0.935036	0.467518	+	0.883984i	$0.345148\pi$
$258$	−1.63045	−0.101507
$259$	21.1247	1.31262
$260$	−2.20152	−0.136533
$261$	−1.00000	−0.0618984
$262$	51.6634	3.19178
$263$	−6.66231	−0.410816	−0.205408	−	0.978676i	$-0.565852\pi$
$263$	−6.66231	−0.410816	−0.205408	+	0.978676i	$0.565852\pi$
$264$	−4.46432	−0.274760
$265$	0.282490	0.0173532
$266$	−37.1590	−2.27836
$267$	9.26100	0.566764
$268$	14.6016	0.891934
$269$	29.1775	1.77899	0.889493	−	0.456948i	$-0.151058\pi$
$269$	29.1775	1.77899	0.889493	+	0.456948i	$0.151058\pi$
$270$	−0.281966	−0.0171599
$271$	9.29717	0.564763	0.282381	−	0.959302i	$-0.408876\pi$
$271$	9.29717	0.564763	0.282381	+	0.959302i	$0.408876\pi$
$272$	−32.2498	−1.95543
$273$	−18.2249	−1.10302
$274$	−49.4158	−2.98532
$275$	−2.88290	−0.173845
$276$	−4.93371	−0.296974
$277$	−25.6693	−1.54232	−0.771161	−	0.636641i	$-0.780323\pi$
$277$	−25.6693	−1.54232	−0.771161	+	0.636641i	$0.780323\pi$
$278$	−23.4188	−1.40457
$279$	6.08061	0.364036
$280$	−3.61778	−0.216204
$281$	−13.3439	−0.796033	−0.398017	−	0.917378i	$-0.630301\pi$
$281$	−13.3439	−0.796033	−0.398017	+	0.917378i	$0.630301\pi$
$282$	−1.10917	−0.0660502
$283$	13.4857	0.801642	0.400821	−	0.916156i	$-0.368725\pi$
$283$	13.4857	0.801642	0.400821	+	0.916156i	$0.368725\pi$
$284$	13.2572	0.786669
$285$	0.345514	0.0204665
$286$	6.34125	0.374966
$287$	47.6959	2.81540
$288$	−12.1301	−0.714775
$289$	−7.51960	−0.442330
$290$	0.281966	0.0165576
$291$	−5.58813	−0.327582
$292$	48.3298	2.82829
$293$	−9.50842	−0.555488	−0.277744	−	0.960655i	$-0.589587\pi$
$293$	−9.50842	−0.555488	−0.277744	+	0.960655i	$0.589587\pi$
$294$	−31.9340	−1.86243
$295$	−0.0759416	−0.00442149
$296$	−37.3131	−2.16878
$297$	0.577904	0.0335334
$298$	19.5782	1.13414
$299$	4.16712	0.240991
$300$	−24.6120	−1.42097
$301$	2.70803	0.156088
$302$	19.7028	1.13377
$303$	10.7237	0.616061
$304$	33.7961	1.93834
$305$	0.952239	0.0545250
$306$	8.10767	0.463485
$307$	−18.8072	−1.07338	−0.536692	−	0.843778i	$-0.680326\pi$
$307$	−18.8072	−1.07338	−0.536692	+	0.843778i	$0.680326\pi$
$308$	12.4698	0.710530
$309$	2.43378	0.138453
$310$	−1.71452	−0.0973785
$311$	−1.76269	−0.0999532	−0.0499766	−	0.998750i	$-0.515915\pi$
$311$	−1.76269	−0.0999532	−0.0499766	+	0.998750i	$0.515915\pi$
$312$	32.1911	1.82246
$313$	28.4718	1.60932	0.804662	−	0.593734i	$-0.202347\pi$
$313$	28.4718	1.60932	0.804662	+	0.593734i	$0.202347\pi$
$314$	31.7075	1.78936
$315$	0.468320	0.0263869
$316$	3.52620	0.198364
$317$	26.9860	1.51568	0.757842	−	0.652439i	$-0.226254\pi$
$317$	26.9860	1.51568	0.757842	+	0.652439i	$0.226254\pi$
$318$	−6.94660	−0.389546
$319$	−0.577904	−0.0323564
$320$	1.17714	0.0658039
$321$	−14.2949	−0.797863
$322$	11.5163	0.641776
$323$	−9.93494	−0.552795
$324$	4.93371	0.274095
$325$	20.7878	1.15310
$326$	54.4893	3.01789
$327$	−10.2761	−0.568272
$328$	−84.2465	−4.65173
$329$	1.84223	0.101566
$330$	−0.162949	−0.00897007
$331$	30.0877	1.65377	0.826885	−	0.562371i	$-0.190111\pi$
$331$	30.0877	1.65377	0.826885	+	0.562371i	$0.190111\pi$
$332$	24.1252	1.32404
$333$	4.83016	0.264691
$334$	−10.1722	−0.556600
$335$	0.316914	0.0173148
$336$	45.8082	2.49904
$337$	−5.78811	−0.315298	−0.157649	−	0.987495i	$-0.550392\pi$
$337$	−5.78811	−0.315298	−0.157649	+	0.987495i	$0.550392\pi$
$338$	−11.4936	−0.625170
$339$	9.56977	0.519758
$340$	−1.62667	−0.0882188
$341$	3.51401	0.190294
$342$	−8.49640	−0.459433
$343$	22.4250	1.21084
$344$	−4.78326	−0.257896
$345$	−0.107081	−0.00576507
$346$	−3.94868	−0.212282
$347$	−25.8666	−1.38859	−0.694296	−	0.719689i	$-0.744284\pi$
$347$	−25.8666	−1.38859	−0.694296	+	0.719689i	$0.744284\pi$
$348$	−4.93371	−0.264474
$349$	2.73976	0.146656	0.0733280	−	0.997308i	$-0.476638\pi$
$349$	2.73976	0.146656	0.0733280	+	0.997308i	$0.476638\pi$
$350$	57.4493	3.07079
$351$	−4.16712	−0.222424
$352$	−7.01006	−0.373637
$353$	−23.9618	−1.27536	−0.637678	−	0.770303i	$-0.720105\pi$
$353$	−23.9618	−1.27536	−0.637678	+	0.770303i	$0.720105\pi$
$354$	1.86745	0.0992537
$355$	0.287735	0.0152714
$356$	45.6910	2.42162
$357$	−13.4661	−0.712702
$358$	−42.8167	−2.26293
$359$	−11.4574	−0.604698	−0.302349	−	0.953197i	$-0.597771\pi$
$359$	−11.4574	−0.604698	−0.302349	+	0.953197i	$0.597771\pi$
$360$	−0.827205	−0.0435975
$361$	−8.58872	−0.452038
$362$	−47.5136	−2.49726
$363$	−10.6660	−0.559821
$364$	−89.9162	−4.71289
$365$	1.04895	0.0549047
$366$	−23.4161	−1.22398
$367$	−26.2254	−1.36895	−0.684476	−	0.729035i	$-0.739969\pi$
$367$	−26.2254	−1.36895	−0.684476	+	0.729035i	$0.739969\pi$
$368$	−10.4740	−0.545997
$369$	10.9057	0.567727
$370$	−1.36194	−0.0708040
$371$	11.5377	0.599006
$372$	29.9999	1.55542
$373$	−22.7836	−1.17969	−0.589845	−	0.807517i	$-0.700811\pi$
$373$	−22.7836	−1.17969	−0.589845	+	0.807517i	$0.700811\pi$
$374$	4.68546	0.242279
$375$	−1.06959	−0.0552332
$376$	−3.25398	−0.167811
$377$	4.16712	0.214618
$378$	−11.5163	−0.592333
$379$	−13.4876	−0.692811	−0.346405	−	0.938085i	$-0.612598\pi$
$379$	−13.4876	−0.692811	−0.346405	+	0.938085i	$0.612598\pi$
$380$	1.70467	0.0874476
$381$	−5.57239	−0.285482
$382$	8.00689	0.409668
$383$	10.9777	0.560933	0.280466	−	0.959864i	$-0.409511\pi$
$383$	10.9777	0.560933	0.280466	+	0.959864i	$0.409511\pi$
$384$	−4.68619	−0.239141
$385$	0.270644	0.0137933
$386$	−30.9862	−1.57716
$387$	0.619192	0.0314753
$388$	−27.5702	−1.39966
$389$	9.84362	0.499091	0.249546	−	0.968363i	$-0.419719\pi$
$389$	9.84362	0.499091	0.249546	+	0.968363i	$0.419719\pi$
$390$	1.17499	0.0594978
$391$	3.07903	0.155713
$392$	−93.6849	−4.73180
$393$	−19.6201	−0.989701
$394$	−15.0084	−0.756112
$395$	0.0765329	0.00385079
$396$	2.85121	0.143279
$397$	−7.50407	−0.376618	−0.188309	−	0.982110i	$-0.560301\pi$
$397$	−7.50407	−0.376618	−0.188309	+	0.982110i	$0.560301\pi$
$398$	−9.89159	−0.495820
$399$	14.1118	0.706471
$400$	−52.2501	−2.61250
$401$	11.2182	0.560210	0.280105	−	0.959969i	$-0.409631\pi$
$401$	11.2182	0.560210	0.280105	+	0.959969i	$0.409631\pi$
$402$	−7.79309	−0.388684
$403$	−25.3386	−1.26221
$404$	52.9076	2.63225
$405$	0.107081	0.00532092
$406$	11.5163	0.571542
$407$	2.79137	0.138363
$408$	23.7855	1.17756
$409$	−13.1258	−0.649030	−0.324515	−	0.945881i	$-0.605201\pi$
$409$	−13.1258	−0.649030	−0.324515	+	0.945881i	$0.605201\pi$
$410$	−3.07503	−0.151865
$411$	18.7665	0.925682
$412$	12.0075	0.591569
$413$	−3.10166	−0.152623
$414$	2.63319	0.129414
$415$	0.523614	0.0257032
$416$	50.5477	2.47831
$417$	8.89370	0.435527
$418$	−4.91011	−0.240161
$419$	8.07675	0.394575	0.197288	−	0.980346i	$-0.436787\pi$
$419$	8.07675	0.394575	0.197288	+	0.980346i	$0.436787\pi$
$420$	2.31055	0.112743
$421$	−27.3782	−1.33433	−0.667167	−	0.744908i	$-0.732493\pi$
$421$	−27.3782	−1.33433	−0.667167	+	0.744908i	$0.732493\pi$
$422$	−59.4479	−2.89388
$423$	0.421227	0.0204807
$424$	−20.3793	−0.989705
$425$	15.3598	0.745061
$426$	−7.07556	−0.342812
$427$	38.8920	1.88212
$428$	−70.5268	−3.40904
$429$	−2.40820	−0.116269
$430$	−0.174591	−0.00841953
$431$	16.0046	0.770915	0.385458	−	0.922726i	$-0.374044\pi$
$431$	16.0046	0.770915	0.385458	+	0.922726i	$0.374044\pi$
$432$	10.4740	0.503932
$433$	−37.1413	−1.78489	−0.892447	−	0.451151i	$-0.851013\pi$
$433$	−37.1413	−1.78489	−0.892447	+	0.451151i	$0.851013\pi$
$434$	−70.0259	−3.36135
$435$	−0.107081	−0.00513416
$436$	−50.6995	−2.42806
$437$	−3.22665	−0.154352
$438$	−25.7943	−1.23250
$439$	8.31978	0.397081	0.198541	−	0.980093i	$-0.436380\pi$
$439$	8.31978	0.397081	0.198541	+	0.980093i	$0.436380\pi$
$440$	−0.478045	−0.0227899
$441$	12.1275	0.577499
$442$	−33.7856	−1.60702
$443$	−35.4483	−1.68420	−0.842099	−	0.539323i	$-0.818680\pi$
$443$	−35.4483	−1.68420	−0.842099	+	0.539323i	$0.818680\pi$
$444$	23.8306	1.13095
$445$	0.991681	0.0470102
$446$	−67.3555	−3.18937
$447$	−7.43517	−0.351671
$448$	48.0775	2.27145
$449$	−37.5825	−1.77363	−0.886814	−	0.462126i	$-0.847087\pi$
$449$	−37.5825	−1.77363	−0.886814	+	0.462126i	$0.847087\pi$
$450$	13.1358	0.619226
$451$	6.30244	0.296770
$452$	47.2144	2.22078
$453$	−7.48246	−0.351556
$454$	57.3781	2.69289
$455$	−1.95155	−0.0914899
$456$	−24.9259	−1.16726
$457$	−37.1511	−1.73785	−0.868927	−	0.494941i	$-0.835190\pi$
$457$	−37.1511	−1.73785	−0.868927	+	0.494941i	$0.835190\pi$
$458$	49.9390	2.33350
$459$	−3.07903	−0.143717
$460$	−0.528308	−0.0246325
$461$	−11.8338	−0.551156	−0.275578	−	0.961279i	$-0.588869\pi$
$461$	−11.8338	−0.551156	−0.275578	+	0.961279i	$0.588869\pi$
$462$	−6.65530	−0.309632
$463$	−28.3129	−1.31581	−0.657906	−	0.753100i	$-0.728558\pi$
$463$	−28.3129	−1.31581	−0.657906	+	0.753100i	$0.728558\pi$
$464$	−10.4740	−0.486245
$465$	0.651120	0.0301950
$466$	10.3012	0.477193
$467$	−0.148109	−0.00685369	−0.00342684	−	0.999994i	$-0.501091\pi$
$467$	−0.148109	−0.00685369	−0.00342684	+	0.999994i	$0.501091\pi$
$468$	−20.5593	−0.950356
$469$	12.9436	0.597681
$470$	−0.118772	−0.00547853
$471$	−12.0415	−0.554841
$472$	5.47854	0.252170
$473$	0.357834	0.0164532
$474$	−1.88199	−0.0864425
$475$	−16.0963	−0.738547
$476$	−66.4378	−3.04517
$477$	2.63809	0.120790
$478$	7.24716	0.331477
$479$	−22.0467	−1.00734	−0.503671	−	0.863896i	$-0.668017\pi$
$479$	−22.0467	−1.00734	−0.503671	+	0.863896i	$0.668017\pi$
$480$	−1.29891	−0.0592869
$481$	−20.1279	−0.917752
$482$	19.8466	0.903987
$483$	−4.37350	−0.199001
$484$	−52.6230	−2.39196
$485$	−0.598384	−0.0271712
$486$	−2.63319	−0.119444
$487$	2.36630	0.107227	0.0536137	−	0.998562i	$-0.482926\pi$
$487$	2.36630	0.107227	0.0536137	+	0.998562i	$0.482926\pi$
$488$	−68.6959	−3.10972
$489$	−20.6933	−0.935781
$490$	−3.41953	−0.154479
$491$	26.2588	1.18504	0.592521	−	0.805555i	$-0.298133\pi$
$491$	26.2588	1.18504	0.592521	+	0.805555i	$0.298133\pi$
$492$	53.8054	2.42573
$493$	3.07903	0.138672
$494$	35.4055	1.59297
$495$	0.0618828	0.00278143
$496$	63.6885	2.85970
$497$	11.7519	0.527143
$498$	−12.8760	−0.576986
$499$	16.0780	0.719750	0.359875	−	0.933001i	$-0.382819\pi$
$499$	16.0780	0.719750	0.359875	+	0.933001i	$0.382819\pi$
$500$	−5.27702	−0.235996
$501$	3.86308	0.172590
$502$	−46.4045	−2.07113
$503$	−27.4048	−1.22192	−0.610959	−	0.791662i	$-0.709216\pi$
$503$	−27.4048	−1.22192	−0.610959	+	0.791662i	$0.709216\pi$
$504$	−33.7853	−1.50492
$505$	1.14831	0.0510991
$506$	1.52173	0.0676493
$507$	4.36490	0.193852
$508$	−27.4925	−1.21978
$509$	−17.2014	−0.762438	−0.381219	−	0.924485i	$-0.624496\pi$
$509$	−17.2014	−0.762438	−0.381219	+	0.924485i	$0.624496\pi$
$510$	0.868181	0.0384437
$511$	42.8421	1.89522
$512$	34.7726	1.53675
$513$	3.22665	0.142460
$514$	−39.4709	−1.74099
$515$	0.260612	0.0114839
$516$	3.05491	0.134485
$517$	0.243429	0.0107060
$518$	−55.6254	−2.44404
$519$	1.49958	0.0658242
$520$	3.44706	0.151164
$521$	32.7452	1.43459	0.717296	−	0.696769i	$-0.245380\pi$
$521$	32.7452	1.43459	0.717296	+	0.696769i	$0.245380\pi$
$522$	2.63319	0.115252
$523$	28.2858	1.23685	0.618426	−	0.785843i	$-0.287771\pi$
$523$	28.2858	1.23685	0.618426	+	0.785843i	$0.287771\pi$
$524$	−96.7996	−4.22871
$525$	−21.8173	−0.952187
$526$	17.5432	0.764918
$527$	−18.7223	−0.815558
$528$	6.05299	0.263423
$529$	1.00000	0.0434783
$530$	−0.743852	−0.0323108
$531$	−0.709195	−0.0307764
$532$	69.6232	3.01855
$533$	−45.4453	−1.96845
$534$	−24.3860	−1.05529
$535$	−1.53072	−0.0661787
$536$	−22.8626	−0.987515
$537$	16.2604	0.701686
$538$	−76.8301	−3.31238
$539$	7.00852	0.301878
$540$	0.528308	0.0227348
$541$	40.7657	1.75265	0.876327	−	0.481717i	$-0.159987\pi$
$541$	40.7657	1.75265	0.876327	+	0.481717i	$0.159987\pi$
$542$	−24.4812	−1.05156
$543$	18.0441	0.774346
$544$	37.3490	1.60132
$545$	−1.10038	−0.0471353
$546$	47.9897	2.05377
$547$	12.3719	0.528985	0.264492	−	0.964388i	$-0.414796\pi$
$547$	12.3719	0.528985	0.264492	+	0.964388i	$0.414796\pi$
$548$	92.5883	3.95518
$549$	8.89266	0.379530
$550$	7.59122	0.323691
$551$	−3.22665	−0.137460
$552$	7.72501	0.328798
$553$	3.12581	0.132923
$554$	67.5923	2.87172
$555$	0.517221	0.0219548
$556$	43.8789	1.86088
$557$	42.2950	1.79210	0.896049	−	0.443955i	$-0.146425\pi$
$557$	42.2950	1.79210	0.896049	+	0.443955i	$0.146425\pi$
$558$	−16.0114	−0.677817
$559$	−2.58025	−0.109133
$560$	4.90520	0.207283
$561$	−1.77938	−0.0751256
$562$	35.1372	1.48217
$563$	−5.35941	−0.225872	−0.112936	−	0.993602i	$-0.536026\pi$
$563$	−5.35941	−0.225872	−0.112936	+	0.993602i	$0.536026\pi$
$564$	2.07821	0.0875084
$565$	1.02474	0.0431113
$566$	−35.5105	−1.49262
$567$	4.37350	0.183670
$568$	−20.7576	−0.870969
$569$	−34.7018	−1.45477	−0.727387	−	0.686228i	$-0.759265\pi$
$569$	−34.7018	−1.45477	−0.727387	+	0.686228i	$0.759265\pi$
$570$	−0.909806	−0.0381076
$571$	−3.30704	−0.138395	−0.0691976	−	0.997603i	$-0.522044\pi$
$571$	−3.30704	−0.138395	−0.0691976	+	0.997603i	$0.522044\pi$
$572$	−11.8813	−0.496784
$573$	−3.04075	−0.127029
$574$	−125.593	−5.24213
$575$	4.98853	0.208036
$576$	10.9929	0.458038
$577$	34.2912	1.42756	0.713780	−	0.700370i	$-0.246982\pi$
$577$	34.2912	1.42756	0.713780	+	0.700370i	$0.246982\pi$
$578$	19.8006	0.823595
$579$	11.7675	0.489042
$580$	−0.528308	−0.0219368
$581$	21.3858	0.887234
$582$	14.7146	0.609940
$583$	1.52456	0.0631410
$584$	−75.6729	−3.13137
$585$	−0.446221	−0.0184490
$586$	25.0375	1.03429
$587$	−44.6285	−1.84202	−0.921008	−	0.389544i	$-0.872632\pi$
$587$	−44.6285	−1.84202	−0.921008	+	0.389544i	$0.872632\pi$
$588$	59.8334	2.46749
$589$	19.6200	0.808428
$590$	0.199969	0.00823259
$591$	5.69970	0.234454
$592$	50.5913	2.07929
$593$	14.5083	0.595783	0.297891	−	0.954600i	$-0.403717\pi$
$593$	14.5083	0.595783	0.297891	+	0.954600i	$0.403717\pi$
$594$	−1.52173	−0.0624375
$595$	−1.44197	−0.0591150
$596$	−36.6829	−1.50259
$597$	3.75650	0.153743
$598$	−10.9728	−0.448713
$599$	45.8647	1.87398	0.936990	−	0.349355i	$-0.113599\pi$
$599$	45.8647	1.87398	0.936990	+	0.349355i	$0.113599\pi$
$600$	38.5365	1.57325
$601$	33.1860	1.35369	0.676844	−	0.736127i	$-0.263347\pi$
$601$	33.1860	1.35369	0.676844	+	0.736127i	$0.263347\pi$
$602$	−7.13077	−0.290629
$603$	2.95956	0.120523
$604$	−36.9162	−1.50210
$605$	−1.14213	−0.0464343
$606$	−28.2376	−1.14707
$607$	6.32836	0.256860	0.128430	−	0.991719i	$-0.459006\pi$
$607$	6.32836	0.256860	0.128430	+	0.991719i	$0.459006\pi$
$608$	−39.1397	−1.58733
$609$	−4.37350	−0.177223
$610$	−2.50743	−0.101523
$611$	−1.75530	−0.0710119
$612$	−15.1910	−0.614060
$613$	−32.5648	−1.31528	−0.657639	−	0.753333i	$-0.728445\pi$
$613$	−32.5648	−1.31528	−0.657639	+	0.753333i	$0.728445\pi$
$614$	49.5230	1.99858
$615$	1.16780	0.0470900
$616$	−19.5247	−0.786672
$617$	40.3377	1.62393	0.811967	−	0.583704i	$-0.198397\pi$
$617$	40.3377	1.62393	0.811967	+	0.583704i	$0.198397\pi$
$618$	−6.40860	−0.257792
$619$	−24.7758	−0.995823	−0.497912	−	0.867228i	$-0.665900\pi$
$619$	−24.7758	−0.995823	−0.497912	+	0.867228i	$0.665900\pi$
$620$	3.21243	0.129014
$621$	−1.00000	−0.0401286
$622$	4.64151	0.186108
$623$	40.5029	1.62272
$624$	−43.6466	−1.74726
$625$	24.8281	0.993125
$626$	−74.9718	−2.99648
$627$	1.86470	0.0744688
$628$	−59.4090	−2.37068
$629$	−14.8722	−0.592993
$630$	−1.23318	−0.0491310
$631$	9.96000	0.396501	0.198251	−	0.980151i	$-0.436474\pi$
$631$	9.96000	0.396501	0.198251	+	0.980151i	$0.436474\pi$
$632$	−5.52119	−0.219621
$633$	22.5764	0.897329
$634$	−71.0593	−2.82212
$635$	−0.596700	−0.0236793
$636$	13.0156	0.516100
$637$	−50.5366	−2.00233
$638$	1.52173	0.0602460
$639$	2.68706	0.106299
$640$	−0.501804	−0.0198355
$641$	31.3492	1.23822	0.619109	−	0.785305i	$-0.287494\pi$
$641$	31.3492	1.23822	0.619109	+	0.785305i	$0.287494\pi$
$642$	37.6412	1.48558
$643$	−37.0409	−1.46075	−0.730375	−	0.683046i	$-0.760655\pi$
$643$	−37.0409	−1.46075	−0.730375	+	0.683046i	$0.760655\pi$
$644$	−21.5775	−0.850274
$645$	0.0663039	0.00261071
$646$	26.1606	1.02928
$647$	−40.5752	−1.59518	−0.797588	−	0.603203i	$-0.793891\pi$
$647$	−40.5752	−1.59518	−0.797588	+	0.603203i	$0.793891\pi$
$648$	−7.72501	−0.303467
$649$	−0.409847	−0.0160879
$650$	−54.7384	−2.14701
$651$	26.5935	1.04228
$652$	−102.094	−3.99833
$653$	−26.9924	−1.05629	−0.528147	−	0.849153i	$-0.677113\pi$
$653$	−26.9924	−1.05629	−0.528147	+	0.849153i	$0.677113\pi$
$654$	27.0591	1.05809
$655$	−2.10094	−0.0820907
$656$	114.226	4.45979
$657$	9.79583	0.382172
$658$	−4.85096	−0.189110
$659$	−40.0468	−1.56000	−0.780002	−	0.625778i	$-0.784782\pi$
$659$	−40.0468	−1.56000	−0.780002	+	0.625778i	$0.784782\pi$
$660$	0.305312	0.0118842
$661$	−25.1271	−0.977332	−0.488666	−	0.872471i	$-0.662516\pi$
$661$	−25.1271	−0.977332	−0.488666	+	0.872471i	$0.662516\pi$
$662$	−79.2267	−3.07923
$663$	12.8307	0.498302
$664$	−37.7743	−1.46593
$665$	1.51111	0.0585982
$666$	−12.7187	−0.492841
$667$	1.00000	0.0387202
$668$	19.0593	0.737427
$669$	25.5794	0.988957
$670$	−0.834495	−0.0322394
$671$	5.13911	0.198393
$672$	−53.0511	−2.04649
$673$	1.31694	0.0507644	0.0253822	−	0.999678i	$-0.491920\pi$
$673$	1.31694	0.0507644	0.0253822	+	0.999678i	$0.491920\pi$
$674$	15.2412	0.587069
$675$	−4.98853	−0.192009
$676$	21.5351	0.828274
$677$	0.456948	0.0175619	0.00878096	−	0.999961i	$-0.497205\pi$
$677$	0.456948	0.0175619	0.00878096	+	0.999961i	$0.497205\pi$
$678$	−25.1990	−0.967763
$679$	−24.4396	−0.937908
$680$	2.54699	0.0976724
$681$	−21.7903	−0.835007
$682$	−9.25306	−0.354318
$683$	31.8138	1.21732	0.608660	−	0.793431i	$-0.291707\pi$
$683$	31.8138	1.21732	0.608660	+	0.793431i	$0.291707\pi$
$684$	15.9194	0.608692
$685$	2.00954	0.0767806
$686$	−59.0493	−2.25451
$687$	−18.9652	−0.723567
$688$	6.48544	0.247255
$689$	−10.9932	−0.418809
$690$	0.281966	0.0107343
$691$	25.2734	0.961444	0.480722	−	0.876873i	$-0.340375\pi$
$691$	25.2734	0.961444	0.480722	+	0.876873i	$0.340375\pi$
$692$	7.39848	0.281248
$693$	2.52746	0.0960104
$694$	68.1118	2.58549
$695$	0.952350	0.0361247
$696$	7.72501	0.292816
$697$	−33.5788	−1.27189
$698$	−7.21432	−0.273066
$699$	−3.91205	−0.147967
$700$	−107.640	−4.06842
$701$	−32.6813	−1.23436	−0.617178	−	0.786823i	$-0.711724\pi$
$701$	−32.6813	−1.23436	−0.617178	+	0.786823i	$0.711724\pi$
$702$	10.9728	0.414143
$703$	15.5853	0.587809
$704$	6.35285	0.239432
$705$	0.0451056	0.00169877
$706$	63.0959	2.37465
$707$	46.9001	1.76386
$708$	−3.49896	−0.131499
$709$	31.8573	1.19643	0.598213	−	0.801337i	$-0.295878\pi$
$709$	31.8573	1.19643	0.598213	+	0.801337i	$0.295878\pi$
$710$	−0.757661	−0.0284345
$711$	0.714717	0.0268040
$712$	−71.5413	−2.68112
$713$	−6.08061	−0.227721
$714$	35.4589	1.32701
$715$	−0.257873	−0.00964391
$716$	80.2238	2.99810
$717$	−2.75223	−0.102784
$718$	30.1695	1.12592
$719$	46.3293	1.72779	0.863896	−	0.503670i	$-0.168017\pi$
$719$	46.3293	1.72779	0.863896	+	0.503670i	$0.168017\pi$
$720$	1.12157	0.0417986
$721$	10.6441	0.396407
$722$	22.6157	0.841671
$723$	−7.53708	−0.280307
$724$	89.0242	3.30856
$725$	4.98853	0.185269
$726$	28.0857	1.04236
$727$	−10.5627	−0.391750	−0.195875	−	0.980629i	$-0.562755\pi$
$727$	−10.5627	−0.391750	−0.195875	+	0.980629i	$0.562755\pi$
$728$	140.787	5.21793
$729$	1.00000	0.0370370
$730$	−2.76209	−0.102230
$731$	−1.90651	−0.0705147
$732$	43.8738	1.62162
$733$	18.2360	0.673561	0.336781	−	0.941583i	$-0.390662\pi$
$733$	18.2360	0.673561	0.336781	+	0.941583i	$0.390662\pi$
$734$	69.0564	2.54892
$735$	1.29863	0.0479006
$736$	12.1301	0.447123
$737$	1.71034	0.0630012
$738$	−28.7167	−1.05708
$739$	−1.17079	−0.0430681	−0.0215340	−	0.999768i	$-0.506855\pi$
$739$	−1.17079	−0.0430681	−0.0215340	+	0.999768i	$0.506855\pi$
$740$	2.55181	0.0938065
$741$	−13.4459	−0.493946
$742$	−30.3809	−1.11532
$743$	−40.2036	−1.47493	−0.737464	−	0.675386i	$-0.763977\pi$
$743$	−40.2036	−1.47493	−0.737464	+	0.675386i	$0.763977\pi$
$744$	−46.9728	−1.72210
$745$	−0.796168	−0.0291693
$746$	59.9936	2.19652
$747$	4.88987	0.178911
$748$	−8.77895	−0.320990
$749$	−62.5187	−2.28438
$750$	2.81643	0.102841
$751$	−46.3017	−1.68957	−0.844786	−	0.535104i	$-0.820273\pi$
$751$	−46.3017	−1.68957	−0.844786	+	0.535104i	$0.820273\pi$
$752$	4.41194	0.160887
$753$	17.6229	0.642214
$754$	−10.9728	−0.399607
$755$	−0.801232	−0.0291598
$756$	21.5775	0.784768
$757$	39.0970	1.42101	0.710503	−	0.703695i	$-0.248468\pi$
$757$	39.0970	1.42101	0.710503	+	0.703695i	$0.248468\pi$
$758$	35.5154	1.28998
$759$	−0.577904	−0.0209766
$760$	−2.66910	−0.0968186
$761$	−7.43870	−0.269653	−0.134826	−	0.990869i	$-0.543048\pi$
$761$	−7.43870	−0.269653	−0.134826	+	0.990869i	$0.543048\pi$
$762$	14.6732	0.531554
$763$	−44.9427	−1.62703
$764$	−15.0022	−0.542760
$765$	−0.329706	−0.0119206
$766$	−28.9063	−1.04443
$767$	2.95530	0.106710
$768$	−9.64618	−0.348077
$769$	−52.6687	−1.89928	−0.949642	−	0.313338i	$-0.898553\pi$
$769$	−52.6687	−1.89928	−0.949642	+	0.313338i	$0.898553\pi$
$770$	−0.712659	−0.0256824
$771$	14.9898	0.539843
$772$	58.0576	2.08954
$773$	51.5976	1.85584	0.927918	−	0.372785i	$-0.121597\pi$
$773$	51.5976	1.85584	0.927918	+	0.372785i	$0.121597\pi$
$774$	−1.63045	−0.0586054
$775$	−30.3333	−1.08960
$776$	43.1683	1.54965
$777$	21.1247	0.757844
$778$	−25.9202	−0.929282
$779$	35.1888	1.26077
$780$	−2.20152	−0.0788272
$781$	1.55287	0.0555659
$782$	−8.10767	−0.289930
$783$	−1.00000	−0.0357371
$784$	127.024	4.53656
$785$	−1.28942	−0.0460212
$786$	51.6634	1.84277
$787$	−15.7472	−0.561325	−0.280663	−	0.959806i	$-0.590554\pi$
$787$	−15.7472	−0.561325	−0.280663	+	0.959806i	$0.590554\pi$
$788$	28.1206	1.00176
$789$	−6.66231	−0.237185
$790$	−0.201526	−0.00716997
$791$	41.8533	1.48813
$792$	−4.46432	−0.158633
$793$	−37.0568	−1.31593
$794$	19.7597	0.701244
$795$	0.282490	0.0100189
$796$	18.5335	0.656901
$797$	−55.0468	−1.94986	−0.974929	−	0.222518i	$-0.928572\pi$
$797$	−55.0468	−1.94986	−0.974929	+	0.222518i	$0.928572\pi$
$798$	−37.1590	−1.31541
$799$	−1.29697	−0.0458834
$800$	60.5116	2.13941
$801$	9.26100	0.327221
$802$	−29.5397	−1.04308
$803$	5.66106	0.199774
$804$	14.6016	0.514958
$805$	−0.468320	−0.0165061
$806$	66.7215	2.35016
$807$	29.1775	1.02710
$808$	−82.8407	−2.91433
$809$	21.8081	0.766733	0.383367	−	0.923596i	$-0.374765\pi$
$809$	21.8081	0.766733	0.383367	+	0.923596i	$0.374765\pi$
$810$	−0.281966	−0.00990728
$811$	−6.52958	−0.229285	−0.114642	−	0.993407i	$-0.536572\pi$
$811$	−6.52958	−0.229285	−0.114642	+	0.993407i	$0.536572\pi$
$812$	−21.5775	−0.757223
$813$	9.29717	0.326066
$814$	−7.35022	−0.257625
$815$	−2.21586	−0.0776183
$816$	−32.2498	−1.12897
$817$	1.99792	0.0698983
$818$	34.5628	1.20846
$819$	−18.2249	−0.636829
$820$	5.76156	0.201202
$821$	−23.8189	−0.831286	−0.415643	−	0.909528i	$-0.636444\pi$
$821$	−23.8189	−0.831286	−0.415643	+	0.909528i	$0.636444\pi$
$822$	−49.4158	−1.72357
$823$	30.3654	1.05847	0.529236	−	0.848475i	$-0.322479\pi$
$823$	30.3654	1.05847	0.529236	+	0.848475i	$0.322479\pi$
$824$	−18.8010	−0.654962
$825$	−2.88290	−0.100370
$826$	8.16727	0.284176
$827$	22.5568	0.784378	0.392189	−	0.919885i	$-0.371718\pi$
$827$	22.5568	0.784378	0.392189	+	0.919885i	$0.371718\pi$
$828$	−4.93371	−0.171458
$829$	−30.1324	−1.04654	−0.523271	−	0.852166i	$-0.675289\pi$
$829$	−30.1324	−1.04654	−0.523271	+	0.852166i	$0.675289\pi$
$830$	−1.37878	−0.0478581
$831$	−25.6693	−0.890460
$832$	−45.8088	−1.58813
$833$	−37.3408	−1.29378
$834$	−23.4188	−0.810928
$835$	0.413664	0.0143154
$836$	9.19986	0.318184
$837$	6.08061	0.210177
$838$	−21.2676	−0.734679
$839$	40.1048	1.38457	0.692285	−	0.721624i	$-0.256604\pi$
$839$	40.1048	1.38457	0.692285	+	0.721624i	$0.256604\pi$
$840$	−3.61778	−0.124825
$841$	1.00000	0.0344828
$842$	72.0922	2.48446
$843$	−13.3439	−0.459590
$844$	111.385	3.83403
$845$	0.467399	0.0160790
$846$	−1.10917	−0.0381341
$847$	−46.6478	−1.60284
$848$	27.6314	0.948868
$849$	13.4857	0.462828
$850$	−40.4454	−1.38726
$851$	−4.83016	−0.165576
$852$	13.2572	0.454183
$853$	34.8952	1.19479	0.597395	−	0.801947i	$-0.296203\pi$
$853$	34.8952	1.19479	0.597395	+	0.801947i	$0.296203\pi$
$854$	−102.410	−3.50441
$855$	0.345514	0.0118163
$856$	110.428	3.77436
$857$	9.53102	0.325573	0.162787	−	0.986661i	$-0.447952\pi$
$857$	9.53102	0.325573	0.162787	+	0.986661i	$0.447952\pi$
$858$	6.34125	0.216487
$859$	−50.0386	−1.70730	−0.853648	−	0.520851i	$-0.825615\pi$
$859$	−50.0386	−1.70730	−0.853648	+	0.520851i	$0.825615\pi$
$860$	0.327124	0.0111548
$861$	47.6959	1.62547
$862$	−42.1432	−1.43540
$863$	10.4764	0.356619	0.178310	−	0.983974i	$-0.442937\pi$
$863$	10.4764	0.356619	0.178310	+	0.983974i	$0.442937\pi$
$864$	−12.1301	−0.412676
$865$	0.160577	0.00545978
$866$	97.8001	3.32338
$867$	−7.51960	−0.255379
$868$	131.205	4.45337
$869$	0.413038	0.0140114
$870$	0.281966	0.00955954
$871$	−12.3328	−0.417882
$872$	79.3833	2.68826
$873$	−5.58813	−0.189129
$874$	8.49640	0.287395
$875$	−4.67783	−0.158140
$876$	48.3298	1.63291
$877$	−15.4914	−0.523107	−0.261553	−	0.965189i	$-0.584235\pi$
$877$	−15.4914	−0.523107	−0.261553	+	0.965189i	$0.584235\pi$
$878$	−21.9076	−0.739345
$879$	−9.50842	−0.320711
$880$	0.648163	0.0218496
$881$	−30.5666	−1.02982	−0.514908	−	0.857245i	$-0.672174\pi$
$881$	−30.5666	−1.02982	−0.514908	+	0.857245i	$0.672174\pi$
$882$	−31.9340	−1.07527
$883$	9.53520	0.320885	0.160443	−	0.987045i	$-0.448708\pi$
$883$	9.53520	0.320885	0.160443	+	0.987045i	$0.448708\pi$
$884$	63.3028	2.12910
$885$	−0.0759416	−0.00255275
$886$	93.3421	3.13589
$887$	14.1423	0.474853	0.237427	−	0.971405i	$-0.423696\pi$
$887$	14.1423	0.474853	0.237427	+	0.971405i	$0.423696\pi$
$888$	−37.3131	−1.25214
$889$	−24.3708	−0.817372
$890$	−2.61129	−0.0875305
$891$	0.577904	0.0193605
$892$	126.201	4.22553
$893$	1.35915	0.0454823
$894$	19.5782	0.654794
$895$	1.74118	0.0582013
$896$	−20.4950	−0.684691
$897$	4.16712	0.139136
$898$	98.9620	3.30241
$899$	−6.08061	−0.202800
$900$	−24.6120	−0.820398
$901$	−8.12274	−0.270608
$902$	−16.5955	−0.552571
$903$	2.70803	0.0901177
$904$	−73.9266	−2.45876
$905$	1.93219	0.0642281
$906$	19.7028	0.654580
$907$	−44.0524	−1.46273	−0.731367	−	0.681984i	$-0.761118\pi$
$907$	−44.0524	−1.46273	−0.731367	+	0.681984i	$0.761118\pi$
$908$	−107.507	−3.56775
$909$	10.7237	0.355683
$910$	5.13880	0.170350
$911$	0.877709	0.0290798	0.0145399	−	0.999894i	$-0.495372\pi$
$911$	0.877709	0.0290798	0.0145399	+	0.999894i	$0.495372\pi$
$912$	33.7961	1.11910
$913$	2.82588	0.0935229
$914$	97.8259	3.23579
$915$	0.952239	0.0314801
$916$	−93.5687	−3.09160
$917$	−85.8083	−2.83364
$918$	8.10767	0.267593
$919$	31.2834	1.03194	0.515972	−	0.856605i	$-0.327431\pi$
$919$	31.2834	1.03194	0.515972	+	0.856605i	$0.327431\pi$
$920$	0.827205	0.0272721
$921$	−18.8072	−0.619718
$922$	31.1607	1.02622
$923$	−11.1973	−0.368564
$924$	12.4698	0.410225
$925$	−24.0954	−0.792253
$926$	74.5534	2.44998
$927$	2.43378	0.0799357
$928$	12.1301	0.398191
$929$	−8.67693	−0.284681	−0.142340	−	0.989818i	$-0.545463\pi$
$929$	−8.67693	−0.284681	−0.142340	+	0.989818i	$0.545463\pi$
$930$	−1.71452	−0.0562215
$931$	39.1311	1.28247
$932$	−19.3009	−0.632222
$933$	−1.76269	−0.0577080
$934$	0.390001	0.0127612
$935$	−0.190539	−0.00623128
$936$	32.1911	1.05220
$937$	30.6375	1.00088	0.500441	−	0.865771i	$-0.333171\pi$
$937$	30.6375	1.00088	0.500441	+	0.865771i	$0.333171\pi$
$938$	−34.0830	−1.11285
$939$	28.4718	0.929143
$940$	0.222537	0.00725837
$941$	−19.6781	−0.641488	−0.320744	−	0.947166i	$-0.603933\pi$
$941$	−19.6781	−0.641488	−0.320744	+	0.947166i	$0.603933\pi$
$942$	31.7075	1.03308
$943$	−10.9057	−0.355138
$944$	−7.42813	−0.241765
$945$	0.468320	0.0152345
$946$	−0.942245	−0.0306350
$947$	−3.05092	−0.0991417	−0.0495709	−	0.998771i	$-0.515785\pi$
$947$	−3.05092	−0.0991417	−0.0495709	+	0.998771i	$0.515785\pi$
$948$	3.52620	0.114526
$949$	−40.8204	−1.32509
$950$	42.3846	1.37514
$951$	26.9860	0.875080
$952$	104.026	3.37150
$953$	20.9930	0.680031	0.340015	−	0.940420i	$-0.389568\pi$
$953$	20.9930	0.680031	0.340015	+	0.940420i	$0.389568\pi$
$954$	−6.94660	−0.224904
$955$	−0.325608	−0.0105364
$956$	−13.5787	−0.439167
$957$	−0.577904	−0.0186810
$958$	58.0533	1.87562
$959$	82.0751	2.65034
$960$	1.17714	0.0379919
$961$	5.97378	0.192703
$962$	53.0006	1.70881
$963$	−14.2949	−0.460647
$964$	−37.1857	−1.19767
$965$	1.26009	0.0405636
$966$	11.5163	0.370530
$967$	−40.0152	−1.28680	−0.643401	−	0.765529i	$-0.722477\pi$
$967$	−40.0152	−1.28680	−0.643401	+	0.765529i	$0.722477\pi$
$968$	82.3952	2.64828
$969$	−9.93494	−0.319156
$970$	1.57566	0.0505914
$971$	25.2212	0.809388	0.404694	−	0.914452i	$-0.367378\pi$
$971$	25.2212	0.809388	0.404694	+	0.914452i	$0.367378\pi$
$972$	4.93371	0.158249
$973$	38.8966	1.24697
$974$	−6.23093	−0.199652
$975$	20.7878	0.665743
$976$	93.1421	2.98141
$977$	20.5366	0.657025	0.328512	−	0.944500i	$-0.393453\pi$
$977$	20.5366	0.657025	0.328512	+	0.944500i	$0.393453\pi$
$978$	54.4893	1.74238
$979$	5.35197	0.171050
$980$	6.40704	0.204665
$981$	−10.2761	−0.328092
$982$	−69.1444	−2.20649
$983$	−35.1590	−1.12140	−0.560699	−	0.828020i	$-0.689468\pi$
$983$	−35.1590	−1.12140	−0.560699	+	0.828020i	$0.689468\pi$
$984$	−84.2465	−2.68568
$985$	0.610332	0.0194468
$986$	−8.10767	−0.258201
$987$	1.84223	0.0586389
$988$	−66.3379	−2.11049
$989$	−0.619192	−0.0196892
$990$	−0.162949	−0.00517887
$991$	53.3955	1.69616	0.848081	−	0.529866i	$-0.177758\pi$
$991$	53.3955	1.69616	0.848081	+	0.529866i	$0.177758\pi$
$992$	−73.7586	−2.34184
$993$	30.0877	0.954804
$994$	−30.9449	−0.981513
$995$	0.402251	0.0127522
$996$	24.1252	0.764435
$997$	−47.0987	−1.49163	−0.745816	−	0.666153i	$-0.767940\pi$
$997$	−47.0987	−1.49163	−0.745816	+	0.666153i	$0.767940\pi$
$998$	−42.3365	−1.34014
$999$	4.83016	0.152820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.n.1.2	✓	16
3.2	odd	2		6003.2.a.r.1.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.n.1.2	✓	16	1.1	even	1	trivial
6003.2.a.r.1.15		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63319 q^{2} +1.00000 q^{3} +4.93371 q^{4} +0.107081 q^{5} -2.63319 q^{6} +4.37350 q^{7} -7.72501 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.63319 q^{2} +1.00000 q^{3} +4.93371 q^{4} +0.107081 q^{5} -2.63319 q^{6} +4.37350 q^{7} -7.72501 q^{8} +1.00000 q^{9} -0.281966 q^{10} +0.577904 q^{11} +4.93371 q^{12} -4.16712 q^{13} -11.5163 q^{14} +0.107081 q^{15} +10.4740 q^{16} -3.07903 q^{17} -2.63319 q^{18} +3.22665 q^{19} +0.528308 q^{20} +4.37350 q^{21} -1.52173 q^{22} -1.00000 q^{23} -7.72501 q^{24} -4.98853 q^{25} +10.9728 q^{26} +1.00000 q^{27} +21.5775 q^{28} -1.00000 q^{29} -0.281966 q^{30} +6.08061 q^{31} -12.1301 q^{32} +0.577904 q^{33} +8.10767 q^{34} +0.468320 q^{35} +4.93371 q^{36} +4.83016 q^{37} -8.49640 q^{38} -4.16712 q^{39} -0.827205 q^{40} +10.9057 q^{41} -11.5163 q^{42} +0.619192 q^{43} +2.85121 q^{44} +0.107081 q^{45} +2.63319 q^{46} +0.421227 q^{47} +10.4740 q^{48} +12.1275 q^{49} +13.1358 q^{50} -3.07903 q^{51} -20.5593 q^{52} +2.63809 q^{53} -2.63319 q^{54} +0.0618828 q^{55} -33.7853 q^{56} +3.22665 q^{57} +2.63319 q^{58} -0.709195 q^{59} +0.528308 q^{60} +8.89266 q^{61} -16.0114 q^{62} +4.37350 q^{63} +10.9929 q^{64} -0.446221 q^{65} -1.52173 q^{66} +2.95956 q^{67} -15.1910 q^{68} -1.00000 q^{69} -1.23318 q^{70} +2.68706 q^{71} -7.72501 q^{72} +9.79583 q^{73} -12.7187 q^{74} -4.98853 q^{75} +15.9194 q^{76} +2.52746 q^{77} +10.9728 q^{78} +0.714717 q^{79} +1.12157 q^{80} +1.00000 q^{81} -28.7167 q^{82} +4.88987 q^{83} +21.5775 q^{84} -0.329706 q^{85} -1.63045 q^{86} -1.00000 q^{87} -4.46432 q^{88} +9.26100 q^{89} -0.281966 q^{90} -18.2249 q^{91} -4.93371 q^{92} +6.08061 q^{93} -1.10917 q^{94} +0.345514 q^{95} -12.1301 q^{96} -5.58813 q^{97} -31.9340 q^{98} +0.577904 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * q^99

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