LMFDB - Embedded newform 547.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.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:	$4.36781699056$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41421 q^{2} +1.41421 q^{3} +3.82843 q^{4} -1.41421 q^{5} -3.41421 q^{6} +2.00000 q^{7} -4.41421 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.41421 q^{2} +1.41421 q^{3} +3.82843 q^{4} -1.41421 q^{5} -3.41421 q^{6} +2.00000 q^{7} -4.41421 q^{8} -1.00000 q^{9} +3.41421 q^{10} -6.41421 q^{11} +5.41421 q^{12} +3.00000 q^{13} -4.82843 q^{14} -2.00000 q^{15} +3.00000 q^{16} -4.58579 q^{17} +2.41421 q^{18} -5.24264 q^{19} -5.41421 q^{20} +2.82843 q^{21} +15.4853 q^{22} +5.07107 q^{23} -6.24264 q^{24} -3.00000 q^{25} -7.24264 q^{26} -5.65685 q^{27} +7.65685 q^{28} -4.17157 q^{29} +4.82843 q^{30} +4.82843 q^{31} +1.58579 q^{32} -9.07107 q^{33} +11.0711 q^{34} -2.82843 q^{35} -3.82843 q^{36} -3.41421 q^{37} +12.6569 q^{38} +4.24264 q^{39} +6.24264 q^{40} +11.0711 q^{41} -6.82843 q^{42} -8.00000 q^{43} -24.5563 q^{44} +1.41421 q^{45} -12.2426 q^{46} +12.4142 q^{47} +4.24264 q^{48} -3.00000 q^{49} +7.24264 q^{50} -6.48528 q^{51} +11.4853 q^{52} -12.6569 q^{53} +13.6569 q^{54} +9.07107 q^{55} -8.82843 q^{56} -7.41421 q^{57} +10.0711 q^{58} -10.2426 q^{59} -7.65685 q^{60} +3.41421 q^{61} -11.6569 q^{62} -2.00000 q^{63} -9.82843 q^{64} -4.24264 q^{65} +21.8995 q^{66} -14.8995 q^{67} -17.5563 q^{68} +7.17157 q^{69} +6.82843 q^{70} -1.41421 q^{71} +4.41421 q^{72} -6.65685 q^{73} +8.24264 q^{74} -4.24264 q^{75} -20.0711 q^{76} -12.8284 q^{77} -10.2426 q^{78} -11.0711 q^{79} -4.24264 q^{80} -5.00000 q^{81} -26.7279 q^{82} +0.928932 q^{83} +10.8284 q^{84} +6.48528 q^{85} +19.3137 q^{86} -5.89949 q^{87} +28.3137 q^{88} +4.24264 q^{89} -3.41421 q^{90} +6.00000 q^{91} +19.4142 q^{92} +6.82843 q^{93} -29.9706 q^{94} +7.41421 q^{95} +2.24264 q^{96} +17.4853 q^{97} +7.24264 q^{98} +6.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 - 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} - 2 q^{9} + 4 q^{10} - 10 q^{11} + 8 q^{12} + 6 q^{13} - 4 q^{14} - 4 q^{15} + 6 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{19} - 8 q^{20} + 14 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 6 q^{26} + 4 q^{28} - 14 q^{29} + 4 q^{30} + 4 q^{31} + 6 q^{32} - 4 q^{33} + 8 q^{34} - 2 q^{36} - 4 q^{37} + 14 q^{38} + 4 q^{40} + 8 q^{41} - 8 q^{42} - 16 q^{43} - 18 q^{44} - 16 q^{46} + 22 q^{47} - 6 q^{49} + 6 q^{50} + 4 q^{51} + 6 q^{52} - 14 q^{53} + 16 q^{54} + 4 q^{55} - 12 q^{56} - 12 q^{57} + 6 q^{58} - 12 q^{59} - 4 q^{60} + 4 q^{61} - 12 q^{62} - 4 q^{63} - 14 q^{64} + 24 q^{66} - 10 q^{67} - 4 q^{68} + 20 q^{69} + 8 q^{70} + 6 q^{72} - 2 q^{73} + 8 q^{74} - 26 q^{76} - 20 q^{77} - 12 q^{78} - 8 q^{79} - 10 q^{81} - 28 q^{82} + 16 q^{83} + 16 q^{84} - 4 q^{85} + 16 q^{86} + 8 q^{87} + 34 q^{88} - 4 q^{90} + 12 q^{91} + 36 q^{92} + 8 q^{93} - 26 q^{94} + 12 q^{95} - 4 q^{96} + 18 q^{97} + 6 q^{98} + 10 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 - 2 * q^9 + 4 * q^10 - 10 * q^11 + 8 * q^12 + 6 * q^13 - 4 * q^14 - 4 * q^15 + 6 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^19 - 8 * q^20 + 14 * q^22 - 4 * q^23 - 4 * q^24 - 6 * q^25 - 6 * q^26 + 4 * q^28 - 14 * q^29 + 4 * q^30 + 4 * q^31 + 6 * q^32 - 4 * q^33 + 8 * q^34 - 2 * q^36 - 4 * q^37 + 14 * q^38 + 4 * q^40 + 8 * q^41 - 8 * q^42 - 16 * q^43 - 18 * q^44 - 16 * q^46 + 22 * q^47 - 6 * q^49 + 6 * q^50 + 4 * q^51 + 6 * q^52 - 14 * q^53 + 16 * q^54 + 4 * q^55 - 12 * q^56 - 12 * q^57 + 6 * q^58 - 12 * q^59 - 4 * q^60 + 4 * q^61 - 12 * q^62 - 4 * q^63 - 14 * q^64 + 24 * q^66 - 10 * q^67 - 4 * q^68 + 20 * q^69 + 8 * q^70 + 6 * q^72 - 2 * q^73 + 8 * q^74 - 26 * q^76 - 20 * q^77 - 12 * q^78 - 8 * q^79 - 10 * q^81 - 28 * q^82 + 16 * q^83 + 16 * q^84 - 4 * q^85 + 16 * q^86 + 8 * q^87 + 34 * q^88 - 4 * q^90 + 12 * q^91 + 36 * q^92 + 8 * q^93 - 26 * q^94 + 12 * q^95 - 4 * q^96 + 18 * q^97 + 6 * q^98 + 10 * 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 $

$2$	−2.41421	−1.70711	−0.853553	−	0.521005i	$-0.825557\pi$
$2$	−2.41421	−1.70711	−0.853553	+	0.521005i	$0.825557\pi$
$3$	1.41421	0.816497	0.408248	−	0.912871i	$-0.366140\pi$
$3$	1.41421	0.816497	0.408248	+	0.912871i	$0.366140\pi$
$4$	3.82843	1.91421
$5$	−1.41421	−0.632456	−0.316228	−	0.948683i	$-0.602416\pi$
$5$	−1.41421	−0.632456	−0.316228	+	0.948683i	$0.602416\pi$
$6$	−3.41421	−1.39385
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	−4.41421	−1.56066
$9$	−1.00000	−0.333333
$10$	3.41421	1.07967
$11$	−6.41421	−1.93396	−0.966979	−	0.254856i	$-0.917972\pi$
$11$	−6.41421	−1.93396	−0.966979	+	0.254856i	$0.917972\pi$
$12$	5.41421	1.56295
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	−4.82843	−1.29045
$15$	−2.00000	−0.516398
$16$	3.00000	0.750000
$17$	−4.58579	−1.11222	−0.556108	−	0.831110i	$-0.687706\pi$
$17$	−4.58579	−1.11222	−0.556108	+	0.831110i	$0.687706\pi$
$18$	2.41421	0.569036
$19$	−5.24264	−1.20274	−0.601372	−	0.798969i	$-0.705379\pi$
$19$	−5.24264	−1.20274	−0.601372	+	0.798969i	$0.705379\pi$
$20$	−5.41421	−1.21065
$21$	2.82843	0.617213
$22$	15.4853	3.30147
$23$	5.07107	1.05739	0.528695	−	0.848812i	$-0.322681\pi$
$23$	5.07107	1.05739	0.528695	+	0.848812i	$0.322681\pi$
$24$	−6.24264	−1.27427
$25$	−3.00000	−0.600000
$26$	−7.24264	−1.42040
$27$	−5.65685	−1.08866
$28$	7.65685	1.44701
$29$	−4.17157	−0.774642	−0.387321	−	0.921945i	$-0.626599\pi$
$29$	−4.17157	−0.774642	−0.387321	+	0.921945i	$0.626599\pi$
$30$	4.82843	0.881546
$31$	4.82843	0.867211	0.433606	−	0.901103i	$-0.357241\pi$
$31$	4.82843	0.867211	0.433606	+	0.901103i	$0.357241\pi$
$32$	1.58579	0.280330
$33$	−9.07107	−1.57907
$34$	11.0711	1.89867
$35$	−2.82843	−0.478091
$36$	−3.82843	−0.638071
$37$	−3.41421	−0.561293	−0.280647	−	0.959811i	$-0.590549\pi$
$37$	−3.41421	−0.561293	−0.280647	+	0.959811i	$0.590549\pi$
$38$	12.6569	2.05321
$39$	4.24264	0.679366
$40$	6.24264	0.987048
$41$	11.0711	1.72901	0.864505	−	0.502624i	$-0.167632\pi$
$41$	11.0711	1.72901	0.864505	+	0.502624i	$0.167632\pi$
$42$	−6.82843	−1.05365
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−24.5563	−3.70201
$45$	1.41421	0.210819
$46$	−12.2426	−1.80508
$47$	12.4142	1.81080	0.905400	−	0.424560i	$-0.139571\pi$
$47$	12.4142	1.81080	0.905400	+	0.424560i	$0.139571\pi$
$48$	4.24264	0.612372
$49$	−3.00000	−0.428571
$50$	7.24264	1.02426
$51$	−6.48528	−0.908121
$52$	11.4853	1.59272
$53$	−12.6569	−1.73855	−0.869276	−	0.494326i	$-0.835415\pi$
$53$	−12.6569	−1.73855	−0.869276	+	0.494326i	$0.835415\pi$
$54$	13.6569	1.85846
$55$	9.07107	1.22314
$56$	−8.82843	−1.17975
$57$	−7.41421	−0.982037
$58$	10.0711	1.32240
$59$	−10.2426	−1.33348	−0.666739	−	0.745291i	$-0.732310\pi$
$59$	−10.2426	−1.33348	−0.666739	+	0.745291i	$0.732310\pi$
$60$	−7.65685	−0.988496
$61$	3.41421	0.437145	0.218573	−	0.975821i	$-0.429860\pi$
$61$	3.41421	0.437145	0.218573	+	0.975821i	$0.429860\pi$
$62$	−11.6569	−1.48042
$63$	−2.00000	−0.251976
$64$	−9.82843	−1.22855
$65$	−4.24264	−0.526235
$66$	21.8995	2.69564
$67$	−14.8995	−1.82026	−0.910132	−	0.414319i	$-0.864020\pi$
$67$	−14.8995	−1.82026	−0.910132	+	0.414319i	$0.864020\pi$
$68$	−17.5563	−2.12902
$69$	7.17157	0.863356
$70$	6.82843	0.816153
$71$	−1.41421	−0.167836	−0.0839181	−	0.996473i	$-0.526743\pi$
$71$	−1.41421	−0.167836	−0.0839181	+	0.996473i	$0.526743\pi$
$72$	4.41421	0.520220
$73$	−6.65685	−0.779126	−0.389563	−	0.921000i	$-0.627374\pi$
$73$	−6.65685	−0.779126	−0.389563	+	0.921000i	$0.627374\pi$
$74$	8.24264	0.958188
$75$	−4.24264	−0.489898
$76$	−20.0711	−2.30231
$77$	−12.8284	−1.46193
$78$	−10.2426	−1.15975
$79$	−11.0711	−1.24559	−0.622796	−	0.782384i	$-0.714003\pi$
$79$	−11.0711	−1.24559	−0.622796	+	0.782384i	$0.714003\pi$
$80$	−4.24264	−0.474342
$81$	−5.00000	−0.555556
$82$	−26.7279	−2.95161
$83$	0.928932	0.101964	0.0509818	−	0.998700i	$-0.483765\pi$
$83$	0.928932	0.101964	0.0509818	+	0.998700i	$0.483765\pi$
$84$	10.8284	1.18148
$85$	6.48528	0.703428
$86$	19.3137	2.08265
$87$	−5.89949	−0.632492
$88$	28.3137	3.01825
$89$	4.24264	0.449719	0.224860	−	0.974391i	$-0.427808\pi$
$89$	4.24264	0.449719	0.224860	+	0.974391i	$0.427808\pi$
$90$	−3.41421	−0.359890
$91$	6.00000	0.628971
$92$	19.4142	2.02407
$93$	6.82843	0.708075
$94$	−29.9706	−3.09123
$95$	7.41421	0.760682
$96$	2.24264	0.228889
$97$	17.4853	1.77536	0.887681	−	0.460460i	$-0.152315\pi$
$97$	17.4853	1.77536	0.887681	+	0.460460i	$0.152315\pi$
$98$	7.24264	0.731617
$99$	6.41421	0.644653
$100$	−11.4853	−1.14853
$101$	4.34315	0.432159	0.216080	−	0.976376i	$-0.430673\pi$
$101$	4.34315	0.432159	0.216080	+	0.976376i	$0.430673\pi$
$102$	15.6569	1.55026
$103$	5.75736	0.567289	0.283645	−	0.958929i	$-0.408456\pi$
$103$	5.75736	0.567289	0.283645	+	0.958929i	$0.408456\pi$
$104$	−13.2426	−1.29855
$105$	−4.00000	−0.390360
$106$	30.5563	2.96789
$107$	−1.75736	−0.169890	−0.0849452	−	0.996386i	$-0.527072\pi$
$107$	−1.75736	−0.169890	−0.0849452	+	0.996386i	$0.527072\pi$
$108$	−21.6569	−2.08393
$109$	10.2426	0.981067	0.490534	−	0.871422i	$-0.336802\pi$
$109$	10.2426	0.981067	0.490534	+	0.871422i	$0.336802\pi$
$110$	−21.8995	−2.08803
$111$	−4.82843	−0.458294
$112$	6.00000	0.566947
$113$	−9.34315	−0.878929	−0.439465	−	0.898260i	$-0.644832\pi$
$113$	−9.34315	−0.878929	−0.439465	+	0.898260i	$0.644832\pi$
$114$	17.8995	1.67644
$115$	−7.17157	−0.668753
$116$	−15.9706	−1.48283
$117$	−3.00000	−0.277350
$118$	24.7279	2.27639
$119$	−9.17157	−0.840757
$120$	8.82843	0.805921
$121$	30.1421	2.74019
$122$	−8.24264	−0.746254
$123$	15.6569	1.41173
$124$	18.4853	1.66003
$125$	11.3137	1.01193
$126$	4.82843	0.430150
$127$	−9.72792	−0.863213	−0.431607	−	0.902062i	$-0.642053\pi$
$127$	−9.72792	−0.863213	−0.431607	+	0.902062i	$0.642053\pi$
$128$	20.5563	1.81694
$129$	−11.3137	−0.996116
$130$	10.2426	0.898339
$131$	8.89949	0.777552	0.388776	−	0.921332i	$-0.372898\pi$
$131$	8.89949	0.777552	0.388776	+	0.921332i	$0.372898\pi$
$132$	−34.7279	−3.02268
$133$	−10.4853	−0.909189
$134$	35.9706	3.10738
$135$	8.00000	0.688530
$136$	20.2426	1.73579
$137$	−9.65685	−0.825041	−0.412520	−	0.910948i	$-0.635351\pi$
$137$	−9.65685	−0.825041	−0.412520	+	0.910948i	$0.635351\pi$
$138$	−17.3137	−1.47384
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	−10.8284	−0.915169
$141$	17.5563	1.47851
$142$	3.41421	0.286514
$143$	−19.2426	−1.60915
$144$	−3.00000	−0.250000
$145$	5.89949	0.489926
$146$	16.0711	1.33005
$147$	−4.24264	−0.349927
$148$	−13.0711	−1.07444
$149$	−1.31371	−0.107623	−0.0538116	−	0.998551i	$-0.517137\pi$
$149$	−1.31371	−0.107623	−0.0538116	+	0.998551i	$0.517137\pi$
$150$	10.2426	0.836308
$151$	14.9706	1.21829	0.609144	−	0.793060i	$-0.291513\pi$
$151$	14.9706	1.21829	0.609144	+	0.793060i	$0.291513\pi$
$152$	23.1421	1.87708
$153$	4.58579	0.370739
$154$	30.9706	2.49568
$155$	−6.82843	−0.548472
$156$	16.2426	1.30045
$157$	−9.65685	−0.770701	−0.385350	−	0.922770i	$-0.625919\pi$
$157$	−9.65685	−0.770701	−0.385350	+	0.922770i	$0.625919\pi$
$158$	26.7279	2.12636
$159$	−17.8995	−1.41952
$160$	−2.24264	−0.177296
$161$	10.1421	0.799312
$162$	12.0711	0.948393
$163$	10.1421	0.794393	0.397197	−	0.917734i	$-0.369983\pi$
$163$	10.1421	0.794393	0.397197	+	0.917734i	$0.369983\pi$
$164$	42.3848	3.30969
$165$	12.8284	0.998692
$166$	−2.24264	−0.174063
$167$	−1.31371	−0.101658	−0.0508289	−	0.998707i	$-0.516186\pi$
$167$	−1.31371	−0.101658	−0.0508289	+	0.998707i	$0.516186\pi$
$168$	−12.4853	−0.963260
$169$	−4.00000	−0.307692
$170$	−15.6569	−1.20083
$171$	5.24264	0.400915
$172$	−30.6274	−2.33532
$173$	2.48528	0.188952	0.0944762	−	0.995527i	$-0.469882\pi$
$173$	2.48528	0.188952	0.0944762	+	0.995527i	$0.469882\pi$
$174$	14.2426	1.07973
$175$	−6.00000	−0.453557
$176$	−19.2426	−1.45047
$177$	−14.4853	−1.08878
$178$	−10.2426	−0.767718
$179$	3.65685	0.273326	0.136663	−	0.990618i	$-0.456362\pi$
$179$	3.65685	0.273326	0.136663	+	0.990618i	$0.456362\pi$
$180$	5.41421	0.403552
$181$	−5.00000	−0.371647	−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000	−0.371647	−0.185824	+	0.982583i	$0.559495\pi$
$182$	−14.4853	−1.07372
$183$	4.82843	0.356928
$184$	−22.3848	−1.65023
$185$	4.82843	0.354993
$186$	−16.4853	−1.20876
$187$	29.4142	2.15098
$188$	47.5269	3.46626
$189$	−11.3137	−0.822951
$190$	−17.8995	−1.29857
$191$	−3.72792	−0.269743	−0.134871	−	0.990863i	$-0.543062\pi$
$191$	−3.72792	−0.269743	−0.134871	+	0.990863i	$0.543062\pi$
$192$	−13.8995	−1.00311
$193$	−3.51472	−0.252995	−0.126497	−	0.991967i	$-0.540374\pi$
$193$	−3.51472	−0.252995	−0.126497	+	0.991967i	$0.540374\pi$
$194$	−42.2132	−3.03073
$195$	−6.00000	−0.429669
$196$	−11.4853	−0.820377
$197$	22.9706	1.63658	0.818292	−	0.574802i	$-0.194921\pi$
$197$	22.9706	1.63658	0.818292	+	0.574802i	$0.194921\pi$
$198$	−15.4853	−1.10049
$199$	−2.07107	−0.146814	−0.0734071	−	0.997302i	$-0.523387\pi$
$199$	−2.07107	−0.146814	−0.0734071	+	0.997302i	$0.523387\pi$
$200$	13.2426	0.936396
$201$	−21.0711	−1.48624
$202$	−10.4853	−0.737742
$203$	−8.34315	−0.585574
$204$	−24.8284	−1.73834
$205$	−15.6569	−1.09352
$206$	−13.8995	−0.968424
$207$	−5.07107	−0.352464
$208$	9.00000	0.624038
$209$	33.6274	2.32606
$210$	9.65685	0.666386
$211$	22.9706	1.58136	0.790679	−	0.612230i	$-0.209728\pi$
$211$	22.9706	1.58136	0.790679	+	0.612230i	$0.209728\pi$
$212$	−48.4558	−3.32796
$213$	−2.00000	−0.137038
$214$	4.24264	0.290021
$215$	11.3137	0.771589
$216$	24.9706	1.69903
$217$	9.65685	0.655550
$218$	−24.7279	−1.67479
$219$	−9.41421	−0.636154
$220$	34.7279	2.34136
$221$	−13.7574	−0.925420
$222$	11.6569	0.782357
$223$	21.2132	1.42054	0.710271	−	0.703929i	$-0.248573\pi$
$223$	21.2132	1.42054	0.710271	+	0.703929i	$0.248573\pi$
$224$	3.17157	0.211910
$225$	3.00000	0.200000
$226$	22.5563	1.50043
$227$	−14.8284	−0.984197	−0.492099	−	0.870539i	$-0.663770\pi$
$227$	−14.8284	−0.984197	−0.492099	+	0.870539i	$0.663770\pi$
$228$	−28.3848	−1.87983
$229$	3.51472	0.232259	0.116130	−	0.993234i	$-0.462951\pi$
$229$	3.51472	0.232259	0.116130	+	0.993234i	$0.462951\pi$
$230$	17.3137	1.14163
$231$	−18.1421	−1.19366
$232$	18.4142	1.20895
$233$	−11.1421	−0.729946	−0.364973	−	0.931018i	$-0.618922\pi$
$233$	−11.1421	−0.729946	−0.364973	+	0.931018i	$0.618922\pi$
$234$	7.24264	0.473466
$235$	−17.5563	−1.14525
$236$	−39.2132	−2.55256
$237$	−15.6569	−1.01702
$238$	22.1421	1.43526
$239$	−15.7279	−1.01735	−0.508677	−	0.860957i	$-0.669865\pi$
$239$	−15.7279	−1.01735	−0.508677	+	0.860957i	$0.669865\pi$
$240$	−6.00000	−0.387298
$241$	−22.4853	−1.44840	−0.724202	−	0.689588i	$-0.757792\pi$
$241$	−22.4853	−1.44840	−0.724202	+	0.689588i	$0.757792\pi$
$242$	−72.7696	−4.67780
$243$	9.89949	0.635053
$244$	13.0711	0.836789
$245$	4.24264	0.271052
$246$	−37.7990	−2.40998
$247$	−15.7279	−1.00074
$248$	−21.3137	−1.35342
$249$	1.31371	0.0832529
$250$	−27.3137	−1.72747
$251$	4.82843	0.304768	0.152384	−	0.988321i	$-0.451305\pi$
$251$	4.82843	0.304768	0.152384	+	0.988321i	$0.451305\pi$
$252$	−7.65685	−0.482336
$253$	−32.5269	−2.04495
$254$	23.4853	1.47360
$255$	9.17157	0.574346
$256$	−29.9706	−1.87316
$257$	−31.4558	−1.96216	−0.981081	−	0.193599i	$-0.937984\pi$
$257$	−31.4558	−1.96216	−0.981081	+	0.193599i	$0.937984\pi$
$258$	27.3137	1.70048
$259$	−6.82843	−0.424298
$260$	−16.2426	−1.00733
$261$	4.17157	0.258214
$262$	−21.4853	−1.32737
$263$	12.0711	0.744334	0.372167	−	0.928166i	$-0.378615\pi$
$263$	12.0711	0.744334	0.372167	+	0.928166i	$0.378615\pi$
$264$	40.0416	2.46439
$265$	17.8995	1.09956
$266$	25.3137	1.55208
$267$	6.00000	0.367194
$268$	−57.0416	−3.48437
$269$	8.48528	0.517357	0.258678	−	0.965964i	$-0.416713\pi$
$269$	8.48528	0.517357	0.258678	+	0.965964i	$0.416713\pi$
$270$	−19.3137	−1.17539
$271$	15.7574	0.957191	0.478596	−	0.878035i	$-0.341146\pi$
$271$	15.7574	0.957191	0.478596	+	0.878035i	$0.341146\pi$
$272$	−13.7574	−0.834162
$273$	8.48528	0.513553
$274$	23.3137	1.40843
$275$	19.2426	1.16037
$276$	27.4558	1.65265
$277$	−8.17157	−0.490982	−0.245491	−	0.969399i	$-0.578949\pi$
$277$	−8.17157	−0.490982	−0.245491	+	0.969399i	$0.578949\pi$
$278$	9.65685	0.579180
$279$	−4.82843	−0.289070
$280$	12.4853	0.746138
$281$	−11.1716	−0.666440	−0.333220	−	0.942849i	$-0.608135\pi$
$281$	−11.1716	−0.666440	−0.333220	+	0.942849i	$0.608135\pi$
$282$	−42.3848	−2.52398
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	−5.41421	−0.321274
$285$	10.4853	0.621094
$286$	46.4558	2.74699
$287$	22.1421	1.30701
$288$	−1.58579	−0.0934434
$289$	4.02944	0.237026
$290$	−14.2426	−0.836357
$291$	24.7279	1.44958
$292$	−25.4853	−1.49141
$293$	13.6569	0.797842	0.398921	−	0.916985i	$-0.369385\pi$
$293$	13.6569	0.797842	0.398921	+	0.916985i	$0.369385\pi$
$294$	10.2426	0.597363
$295$	14.4853	0.843366
$296$	15.0711	0.875988
$297$	36.2843	2.10543
$298$	3.17157	0.183724
$299$	15.2132	0.879802
$300$	−16.2426	−0.937769
$301$	−16.0000	−0.922225
$302$	−36.1421	−2.07975
$303$	6.14214	0.352856
$304$	−15.7279	−0.902058
$305$	−4.82843	−0.276475
$306$	−11.0711	−0.632891
$307$	24.6274	1.40556	0.702780	−	0.711407i	$-0.251942\pi$
$307$	24.6274	1.40556	0.702780	+	0.711407i	$0.251942\pi$
$308$	−49.1127	−2.79846
$309$	8.14214	0.463190
$310$	16.4853	0.936301
$311$	9.58579	0.543560	0.271780	−	0.962359i	$-0.412388\pi$
$311$	9.58579	0.543560	0.271780	+	0.962359i	$0.412388\pi$
$312$	−18.7279	−1.06026
$313$	8.79899	0.497348	0.248674	−	0.968587i	$-0.420005\pi$
$313$	8.79899	0.497348	0.248674	+	0.968587i	$0.420005\pi$
$314$	23.3137	1.31567
$315$	2.82843	0.159364
$316$	−42.3848	−2.38433
$317$	−21.6274	−1.21472	−0.607358	−	0.794428i	$-0.707771\pi$
$317$	−21.6274	−1.21472	−0.607358	+	0.794428i	$0.707771\pi$
$318$	43.2132	2.42328
$319$	26.7574	1.49812
$320$	13.8995	0.777005
$321$	−2.48528	−0.138715
$322$	−24.4853	−1.36451
$323$	24.0416	1.33771
$324$	−19.1421	−1.06345
$325$	−9.00000	−0.499230
$326$	−24.4853	−1.35611
$327$	14.4853	0.801038
$328$	−48.8701	−2.69840
$329$	24.8284	1.36884
$330$	−30.9706	−1.70487
$331$	−29.6985	−1.63238	−0.816188	−	0.577786i	$-0.803917\pi$
$331$	−29.6985	−1.63238	−0.816188	+	0.577786i	$0.803917\pi$
$332$	3.55635	0.195180
$333$	3.41421	0.187098
$334$	3.17157	0.173541
$335$	21.0711	1.15124
$336$	8.48528	0.462910
$337$	21.3137	1.16103	0.580516	−	0.814249i	$-0.302851\pi$
$337$	21.3137	1.16103	0.580516	+	0.814249i	$0.302851\pi$
$338$	9.65685	0.525264
$339$	−13.2132	−0.717643
$340$	24.8284	1.34651
$341$	−30.9706	−1.67715
$342$	−12.6569	−0.684404
$343$	−20.0000	−1.07990
$344$	35.3137	1.90399
$345$	−10.1421	−0.546034
$346$	−6.00000	−0.322562
$347$	16.6274	0.892607	0.446303	−	0.894882i	$-0.352740\pi$
$347$	16.6274	0.892607	0.446303	+	0.894882i	$0.352740\pi$
$348$	−22.5858	−1.21073
$349$	3.48528	0.186563	0.0932814	−	0.995640i	$-0.470264\pi$
$349$	3.48528	0.186563	0.0932814	+	0.995640i	$0.470264\pi$
$350$	14.4853	0.774271
$351$	−16.9706	−0.905822
$352$	−10.1716	−0.542147
$353$	−23.8284	−1.26826	−0.634130	−	0.773227i	$-0.718641\pi$
$353$	−23.8284	−1.26826	−0.634130	+	0.773227i	$0.718641\pi$
$354$	34.9706	1.85866
$355$	2.00000	0.106149
$356$	16.2426	0.860858
$357$	−12.9706	−0.686475
$358$	−8.82843	−0.466597
$359$	25.0711	1.32320	0.661600	−	0.749857i	$-0.269878\pi$
$359$	25.0711	1.32320	0.661600	+	0.749857i	$0.269878\pi$
$360$	−6.24264	−0.329016
$361$	8.48528	0.446594
$362$	12.0711	0.634441
$363$	42.6274	2.23736
$364$	22.9706	1.20398
$365$	9.41421	0.492762
$366$	−11.6569	−0.609314
$367$	17.2426	0.900059	0.450029	−	0.893014i	$-0.351414\pi$
$367$	17.2426	0.900059	0.450029	+	0.893014i	$0.351414\pi$
$368$	15.2132	0.793043
$369$	−11.0711	−0.576337
$370$	−11.6569	−0.606011
$371$	−25.3137	−1.31422
$372$	26.1421	1.35541
$373$	−24.2426	−1.25524	−0.627618	−	0.778521i	$-0.715970\pi$
$373$	−24.2426	−1.25524	−0.627618	+	0.778521i	$0.715970\pi$
$374$	−71.0122	−3.67195
$375$	16.0000	0.826236
$376$	−54.7990	−2.82604
$377$	−12.5147	−0.644541
$378$	27.3137	1.40487
$379$	−24.2132	−1.24375	−0.621874	−	0.783117i	$-0.713629\pi$
$379$	−24.2132	−1.24375	−0.621874	+	0.783117i	$0.713629\pi$
$380$	28.3848	1.45611
$381$	−13.7574	−0.704811
$382$	9.00000	0.460480
$383$	−7.58579	−0.387616	−0.193808	−	0.981040i	$-0.562084\pi$
$383$	−7.58579	−0.387616	−0.193808	+	0.981040i	$0.562084\pi$
$384$	29.0711	1.48353
$385$	18.1421	0.924609
$386$	8.48528	0.431889
$387$	8.00000	0.406663
$388$	66.9411	3.39842
$389$	−0.928932	−0.0470987	−0.0235494	−	0.999723i	$-0.507497\pi$
$389$	−0.928932	−0.0470987	−0.0235494	+	0.999723i	$0.507497\pi$
$390$	14.4853	0.733491
$391$	−23.2548	−1.17605
$392$	13.2426	0.668854
$393$	12.5858	0.634869
$394$	−55.4558	−2.79383
$395$	15.6569	0.787782
$396$	24.5563	1.23400
$397$	−1.75736	−0.0881993	−0.0440997	−	0.999027i	$-0.514042\pi$
$397$	−1.75736	−0.0881993	−0.0440997	+	0.999027i	$0.514042\pi$
$398$	5.00000	0.250627
$399$	−14.8284	−0.742350
$400$	−9.00000	−0.450000
$401$	−30.3137	−1.51379	−0.756897	−	0.653534i	$-0.773286\pi$
$401$	−30.3137	−1.51379	−0.756897	+	0.653534i	$0.773286\pi$
$402$	50.8701	2.53717
$403$	14.4853	0.721563
$404$	16.6274	0.827245
$405$	7.07107	0.351364
$406$	20.1421	0.999637
$407$	21.8995	1.08552
$408$	28.6274	1.41727
$409$	3.02944	0.149796	0.0748980	−	0.997191i	$-0.476137\pi$
$409$	3.02944	0.149796	0.0748980	+	0.997191i	$0.476137\pi$
$410$	37.7990	1.86676
$411$	−13.6569	−0.673643
$412$	22.0416	1.08591
$413$	−20.4853	−1.00801
$414$	12.2426	0.601693
$415$	−1.31371	−0.0644874
$416$	4.75736	0.233249
$417$	−5.65685	−0.277017
$418$	−81.1838	−3.97083
$419$	28.0711	1.37136	0.685681	−	0.727902i	$-0.259505\pi$
$419$	28.0711	1.37136	0.685681	+	0.727902i	$0.259505\pi$
$420$	−15.3137	−0.747232
$421$	−31.8995	−1.55469	−0.777343	−	0.629077i	$-0.783433\pi$
$421$	−31.8995	−1.55469	−0.777343	+	0.629077i	$0.783433\pi$
$422$	−55.4558	−2.69955
$423$	−12.4142	−0.603600
$424$	55.8701	2.71329
$425$	13.7574	0.667330
$426$	4.82843	0.233938
$427$	6.82843	0.330451
$428$	−6.72792	−0.325206
$429$	−27.2132	−1.31387
$430$	−27.3137	−1.31718
$431$	18.9289	0.911775	0.455887	−	0.890038i	$-0.349322\pi$
$431$	18.9289	0.911775	0.455887	+	0.890038i	$0.349322\pi$
$432$	−16.9706	−0.816497
$433$	−13.5563	−0.651477	−0.325738	−	0.945460i	$-0.605613\pi$
$433$	−13.5563	−0.651477	−0.325738	+	0.945460i	$0.605613\pi$
$434$	−23.3137	−1.11909
$435$	8.34315	0.400023
$436$	39.2132	1.87797
$437$	−26.5858	−1.27177
$438$	22.7279	1.08598
$439$	4.27208	0.203895	0.101948	−	0.994790i	$-0.467493\pi$
$439$	4.27208	0.203895	0.101948	+	0.994790i	$0.467493\pi$
$440$	−40.0416	−1.90891
$441$	3.00000	0.142857
$442$	33.2132	1.57979
$443$	−8.48528	−0.403148	−0.201574	−	0.979473i	$-0.564606\pi$
$443$	−8.48528	−0.403148	−0.201574	+	0.979473i	$0.564606\pi$
$444$	−18.4853	−0.877273
$445$	−6.00000	−0.284427
$446$	−51.2132	−2.42502
$447$	−1.85786	−0.0878740
$448$	−19.6569	−0.928699
$449$	22.3137	1.05305	0.526525	−	0.850160i	$-0.323495\pi$
$449$	22.3137	1.05305	0.526525	+	0.850160i	$0.323495\pi$
$450$	−7.24264	−0.341421
$451$	−71.0122	−3.34383
$452$	−35.7696	−1.68246
$453$	21.1716	0.994727
$454$	35.7990	1.68013
$455$	−8.48528	−0.397796
$456$	32.7279	1.53263
$457$	3.21320	0.150307	0.0751537	−	0.997172i	$-0.476055\pi$
$457$	3.21320	0.150307	0.0751537	+	0.997172i	$0.476055\pi$
$458$	−8.48528	−0.396491
$459$	25.9411	1.21083
$460$	−27.4558	−1.28014
$461$	14.4853	0.674647	0.337323	−	0.941389i	$-0.390478\pi$
$461$	14.4853	0.674647	0.337323	+	0.941389i	$0.390478\pi$
$462$	43.7990	2.03771
$463$	−18.9289	−0.879702	−0.439851	−	0.898071i	$-0.644969\pi$
$463$	−18.9289	−0.879702	−0.439851	+	0.898071i	$0.644969\pi$
$464$	−12.5147	−0.580981
$465$	−9.65685	−0.447826
$466$	26.8995	1.24610
$467$	−29.5858	−1.36907	−0.684533	−	0.728981i	$-0.739994\pi$
$467$	−29.5858	−1.36907	−0.684533	+	0.728981i	$0.739994\pi$
$468$	−11.4853	−0.530907
$469$	−29.7990	−1.37599
$470$	42.3848	1.95506
$471$	−13.6569	−0.629275
$472$	45.2132	2.08111
$473$	51.3137	2.35941
$474$	37.7990	1.73617
$475$	15.7279	0.721647
$476$	−35.1127	−1.60939
$477$	12.6569	0.579518
$478$	37.9706	1.73673
$479$	7.31371	0.334172	0.167086	−	0.985942i	$-0.446564\pi$
$479$	7.31371	0.334172	0.167086	+	0.985942i	$0.446564\pi$
$480$	−3.17157	−0.144762
$481$	−10.2426	−0.467024
$482$	54.2843	2.47258
$483$	14.3431	0.652636
$484$	115.397	5.24532
$485$	−24.7279	−1.12284
$486$	−23.8995	−1.08410
$487$	−12.9706	−0.587752	−0.293876	−	0.955844i	$-0.594945\pi$
$487$	−12.9706	−0.587752	−0.293876	+	0.955844i	$0.594945\pi$
$488$	−15.0711	−0.682235
$489$	14.3431	0.648619
$490$	−10.2426	−0.462715
$491$	13.4558	0.607254	0.303627	−	0.952791i	$-0.401802\pi$
$491$	13.4558	0.607254	0.303627	+	0.952791i	$0.401802\pi$
$492$	59.9411	2.70235
$493$	19.1299	0.861569
$494$	37.9706	1.70838
$495$	−9.07107	−0.407714
$496$	14.4853	0.650408
$497$	−2.82843	−0.126872
$498$	−3.17157	−0.142122
$499$	−25.2426	−1.13002	−0.565008	−	0.825085i	$-0.691127\pi$
$499$	−25.2426	−1.13002	−0.565008	+	0.825085i	$0.691127\pi$
$500$	43.3137	1.93705
$501$	−1.85786	−0.0830033
$502$	−11.6569	−0.520271
$503$	0.928932	0.0414190	0.0207095	−	0.999786i	$-0.493407\pi$
$503$	0.928932	0.0414190	0.0207095	+	0.999786i	$0.493407\pi$
$504$	8.82843	0.393249
$505$	−6.14214	−0.273321
$506$	78.5269	3.49095
$507$	−5.65685	−0.251230
$508$	−37.2426	−1.65237
$509$	−15.8284	−0.701583	−0.350791	−	0.936454i	$-0.614087\pi$
$509$	−15.8284	−0.701583	−0.350791	+	0.936454i	$0.614087\pi$
$510$	−22.1421	−0.980470
$511$	−13.3137	−0.588964
$512$	31.2426	1.38074
$513$	29.6569	1.30938
$514$	75.9411	3.34962
$515$	−8.14214	−0.358785
$516$	−43.3137	−1.90678
$517$	−79.6274	−3.50201
$518$	16.4853	0.724322
$519$	3.51472	0.154279
$520$	18.7279	0.821274
$521$	−7.97056	−0.349197	−0.174598	−	0.984640i	$-0.555863\pi$
$521$	−7.97056	−0.349197	−0.174598	+	0.984640i	$0.555863\pi$
$522$	−10.0711	−0.440799
$523$	35.6985	1.56099	0.780493	−	0.625165i	$-0.214968\pi$
$523$	35.6985	1.56099	0.780493	+	0.625165i	$0.214968\pi$
$524$	34.0711	1.48840
$525$	−8.48528	−0.370328
$526$	−29.1421	−1.27066
$527$	−22.1421	−0.964527
$528$	−27.2132	−1.18430
$529$	2.71573	0.118075
$530$	−43.2132	−1.87706
$531$	10.2426	0.444493
$532$	−40.1421	−1.74038
$533$	33.2132	1.43862
$534$	−14.4853	−0.626839
$535$	2.48528	0.107448
$536$	65.7696	2.84081
$537$	5.17157	0.223170
$538$	−20.4853	−0.883183
$539$	19.2426	0.828839
$540$	30.6274	1.31799
$541$	12.0000	0.515920	0.257960	−	0.966156i	$-0.416950\pi$
$541$	12.0000	0.515920	0.257960	+	0.966156i	$0.416950\pi$
$542$	−38.0416	−1.63403
$543$	−7.07107	−0.303449
$544$	−7.27208	−0.311788
$545$	−14.4853	−0.620481
$546$	−20.4853	−0.876689
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−36.9706	−1.57930
$549$	−3.41421	−0.145715
$550$	−46.4558	−1.98088
$551$	21.8701	0.931696
$552$	−31.6569	−1.34741
$553$	−22.1421	−0.941579
$554$	19.7279	0.838159
$555$	6.82843	0.289851
$556$	−15.3137	−0.649446
$557$	14.3431	0.607739	0.303869	−	0.952714i	$-0.401721\pi$
$557$	14.3431	0.607739	0.303869	+	0.952714i	$0.401721\pi$
$558$	11.6569	0.493474
$559$	−24.0000	−1.01509
$560$	−8.48528	−0.358569
$561$	41.5980	1.75627
$562$	26.9706	1.13768
$563$	9.31371	0.392526	0.196263	−	0.980551i	$-0.437119\pi$
$563$	9.31371	0.392526	0.196263	+	0.980551i	$0.437119\pi$
$564$	67.2132	2.83019
$565$	13.2132	0.555884
$566$	−14.4853	−0.608862
$567$	−10.0000	−0.419961
$568$	6.24264	0.261935
$569$	0.727922	0.0305161	0.0152580	−	0.999884i	$-0.495143\pi$
$569$	0.727922	0.0305161	0.0152580	+	0.999884i	$0.495143\pi$
$570$	−25.3137	−1.06027
$571$	1.24264	0.0520029	0.0260014	−	0.999662i	$-0.491723\pi$
$571$	1.24264	0.0520029	0.0260014	+	0.999662i	$0.491723\pi$
$572$	−73.6690	−3.08026
$573$	−5.27208	−0.220244
$574$	−53.4558	−2.23120
$575$	−15.2132	−0.634434
$576$	9.82843	0.409518
$577$	−5.17157	−0.215295	−0.107648	−	0.994189i	$-0.534332\pi$
$577$	−5.17157	−0.215295	−0.107648	+	0.994189i	$0.534332\pi$
$578$	−9.72792	−0.404628
$579$	−4.97056	−0.206570
$580$	22.5858	0.937824
$581$	1.85786	0.0770772
$582$	−59.6985	−2.47458
$583$	81.1838	3.36229
$584$	29.3848	1.21595
$585$	4.24264	0.175412
$586$	−32.9706	−1.36200
$587$	−15.0416	−0.620835	−0.310417	−	0.950600i	$-0.600469\pi$
$587$	−15.0416	−0.620835	−0.310417	+	0.950600i	$0.600469\pi$
$588$	−16.2426	−0.669835
$589$	−25.3137	−1.04303
$590$	−34.9706	−1.43972
$591$	32.4853	1.33627
$592$	−10.2426	−0.420970
$593$	−27.7696	−1.14036	−0.570179	−	0.821520i	$-0.693126\pi$
$593$	−27.7696	−1.14036	−0.570179	+	0.821520i	$0.693126\pi$
$594$	−87.5980	−3.59419
$595$	12.9706	0.531741
$596$	−5.02944	−0.206014
$597$	−2.92893	−0.119873
$598$	−36.7279	−1.50192
$599$	−41.6569	−1.70205	−0.851026	−	0.525123i	$-0.824019\pi$
$599$	−41.6569	−1.70205	−0.851026	+	0.525123i	$0.824019\pi$
$600$	18.7279	0.764564
$601$	24.7990	1.01157	0.505786	−	0.862659i	$-0.331203\pi$
$601$	24.7990	1.01157	0.505786	+	0.862659i	$0.331203\pi$
$602$	38.6274	1.57434
$603$	14.8995	0.606754
$604$	57.3137	2.33206
$605$	−42.6274	−1.73305
$606$	−14.8284	−0.602364
$607$	−47.0416	−1.90936	−0.954680	−	0.297633i	$-0.903803\pi$
$607$	−47.0416	−1.90936	−0.954680	+	0.297633i	$0.903803\pi$
$608$	−8.31371	−0.337165
$609$	−11.7990	−0.478119
$610$	11.6569	0.471972
$611$	37.2426	1.50668
$612$	17.5563	0.709673
$613$	−37.9706	−1.53362	−0.766808	−	0.641876i	$-0.778156\pi$
$613$	−37.9706	−1.53362	−0.766808	+	0.641876i	$0.778156\pi$
$614$	−59.4558	−2.39944
$615$	−22.1421	−0.892857
$616$	56.6274	2.28158
$617$	−14.1421	−0.569341	−0.284670	−	0.958625i	$-0.591884\pi$
$617$	−14.1421	−0.569341	−0.284670	+	0.958625i	$0.591884\pi$
$618$	−19.6569	−0.790715
$619$	15.7990	0.635015	0.317508	−	0.948256i	$-0.397154\pi$
$619$	15.7990	0.635015	0.317508	+	0.948256i	$0.397154\pi$
$620$	−26.1421	−1.04989
$621$	−28.6863	−1.15114
$622$	−23.1421	−0.927915
$623$	8.48528	0.339956
$624$	12.7279	0.509525
$625$	−1.00000	−0.0400000
$626$	−21.2426	−0.849027
$627$	47.5563	1.89922
$628$	−36.9706	−1.47529
$629$	15.6569	0.624280
$630$	−6.82843	−0.272051
$631$	−5.58579	−0.222367	−0.111183	−	0.993800i	$-0.535464\pi$
$631$	−5.58579	−0.222367	−0.111183	+	0.993800i	$0.535464\pi$
$632$	48.8701	1.94395
$633$	32.4853	1.29117
$634$	52.2132	2.07365
$635$	13.7574	0.545944
$636$	−68.5269	−2.71727
$637$	−9.00000	−0.356593
$638$	−64.5980	−2.55746
$639$	1.41421	0.0559454
$640$	−29.0711	−1.14913
$641$	−37.7990	−1.49297	−0.746485	−	0.665402i	$-0.768260\pi$
$641$	−37.7990	−1.49297	−0.746485	+	0.665402i	$0.768260\pi$
$642$	6.00000	0.236801
$643$	−8.97056	−0.353764	−0.176882	−	0.984232i	$-0.556601\pi$
$643$	−8.97056	−0.353764	−0.176882	+	0.984232i	$0.556601\pi$
$644$	38.8284	1.53005
$645$	16.0000	0.629999
$646$	−58.0416	−2.28362
$647$	−17.1716	−0.675084	−0.337542	−	0.941310i	$-0.609596\pi$
$647$	−17.1716	−0.675084	−0.337542	+	0.941310i	$0.609596\pi$
$648$	22.0711	0.867033
$649$	65.6985	2.57889
$650$	21.7279	0.852239
$651$	13.6569	0.535254
$652$	38.8284	1.52064
$653$	12.7279	0.498082	0.249041	−	0.968493i	$-0.419885\pi$
$653$	12.7279	0.498082	0.249041	+	0.968493i	$0.419885\pi$
$654$	−34.9706	−1.36746
$655$	−12.5858	−0.491767
$656$	33.2132	1.29676
$657$	6.65685	0.259709
$658$	−59.9411	−2.33675
$659$	−31.8995	−1.24263	−0.621314	−	0.783562i	$-0.713401\pi$
$659$	−31.8995	−1.24263	−0.621314	+	0.783562i	$0.713401\pi$
$660$	49.1127	1.91171
$661$	32.1127	1.24904	0.624520	−	0.781009i	$-0.285295\pi$
$661$	32.1127	1.24904	0.624520	+	0.781009i	$0.285295\pi$
$662$	71.6985	2.78664
$663$	−19.4558	−0.755602
$664$	−4.10051	−0.159130
$665$	14.8284	0.575022
$666$	−8.24264	−0.319396
$667$	−21.1543	−0.819099
$668$	−5.02944	−0.194595
$669$	30.0000	1.15987
$670$	−50.8701	−1.96528
$671$	−21.8995	−0.845421
$672$	4.48528	0.173023
$673$	−38.4558	−1.48236	−0.741182	−	0.671304i	$-0.765734\pi$
$673$	−38.4558	−1.48236	−0.741182	+	0.671304i	$0.765734\pi$
$674$	−51.4558	−1.98201
$675$	16.9706	0.653197
$676$	−15.3137	−0.588989
$677$	28.1127	1.08046	0.540229	−	0.841518i	$-0.318337\pi$
$677$	28.1127	1.08046	0.540229	+	0.841518i	$0.318337\pi$
$678$	31.8995	1.22509
$679$	34.9706	1.34205
$680$	−28.6274	−1.09781
$681$	−20.9706	−0.803594
$682$	74.7696	2.86307
$683$	7.24264	0.277132	0.138566	−	0.990353i	$-0.455751\pi$
$683$	7.24264	0.277132	0.138566	+	0.990353i	$0.455751\pi$
$684$	20.0711	0.767436
$685$	13.6569	0.521802
$686$	48.2843	1.84350
$687$	4.97056	0.189639
$688$	−24.0000	−0.914991
$689$	−37.9706	−1.44656
$690$	24.4853	0.932139
$691$	19.6569	0.747782	0.373891	−	0.927473i	$-0.378023\pi$
$691$	19.6569	0.747782	0.373891	+	0.927473i	$0.378023\pi$
$692$	9.51472	0.361695
$693$	12.8284	0.487312
$694$	−40.1421	−1.52377
$695$	5.65685	0.214577
$696$	26.0416	0.987105
$697$	−50.7696	−1.92303
$698$	−8.41421	−0.318483
$699$	−15.7574	−0.595998
$700$	−22.9706	−0.868206
$701$	−22.4558	−0.848146	−0.424073	−	0.905628i	$-0.639400\pi$
$701$	−22.4558	−0.848146	−0.424073	+	0.905628i	$0.639400\pi$
$702$	40.9706	1.54633
$703$	17.8995	0.675092
$704$	63.0416	2.37597
$705$	−24.8284	−0.935093
$706$	57.5269	2.16505
$707$	8.68629	0.326682
$708$	−55.4558	−2.08416
$709$	26.3848	0.990901	0.495451	−	0.868636i	$-0.335003\pi$
$709$	26.3848	0.990901	0.495451	+	0.868636i	$0.335003\pi$
$710$	−4.82843	−0.181208
$711$	11.0711	0.415197
$712$	−18.7279	−0.701859
$713$	24.4853	0.916981
$714$	31.3137	1.17189
$715$	27.2132	1.01772
$716$	14.0000	0.523205
$717$	−22.2426	−0.830667
$718$	−60.5269	−2.25884
$719$	15.5147	0.578601	0.289301	−	0.957238i	$-0.406577\pi$
$719$	15.5147	0.578601	0.289301	+	0.957238i	$0.406577\pi$
$720$	4.24264	0.158114
$721$	11.5147	0.428831
$722$	−20.4853	−0.762383
$723$	−31.7990	−1.18262
$724$	−19.1421	−0.711412
$725$	12.5147	0.464785
$726$	−102.912	−3.81941
$727$	0.727922	0.0269971	0.0134986	−	0.999909i	$-0.495703\pi$
$727$	0.727922	0.0269971	0.0134986	+	0.999909i	$0.495703\pi$
$728$	−26.4853	−0.981610
$729$	29.0000	1.07407
$730$	−22.7279	−0.841198
$731$	36.6863	1.35689
$732$	18.4853	0.683236
$733$	45.9411	1.69687	0.848437	−	0.529296i	$-0.177544\pi$
$733$	45.9411	1.69687	0.848437	+	0.529296i	$0.177544\pi$
$734$	−41.6274	−1.53650
$735$	6.00000	0.221313
$736$	8.04163	0.296418
$737$	95.5685	3.52031
$738$	26.7279	0.983868
$739$	6.72792	0.247491	0.123745	−	0.992314i	$-0.460509\pi$
$739$	6.72792	0.247491	0.123745	+	0.992314i	$0.460509\pi$
$740$	18.4853	0.679532
$741$	−22.2426	−0.817104
$742$	61.1127	2.24352
$743$	−21.8579	−0.801887	−0.400944	−	0.916103i	$-0.631318\pi$
$743$	−21.8579	−0.801887	−0.400944	+	0.916103i	$0.631318\pi$
$744$	−30.1421	−1.10506
$745$	1.85786	0.0680669
$746$	58.5269	2.14282
$747$	−0.928932	−0.0339879
$748$	112.610	4.11744
$749$	−3.51472	−0.128425
$750$	−38.6274	−1.41047
$751$	40.6985	1.48511	0.742554	−	0.669786i	$-0.233614\pi$
$751$	40.6985	1.48511	0.742554	+	0.669786i	$0.233614\pi$
$752$	37.2426	1.35810
$753$	6.82843	0.248842
$754$	30.2132	1.10030
$755$	−21.1716	−0.770512
$756$	−43.3137	−1.57530
$757$	−32.4558	−1.17963	−0.589814	−	0.807539i	$-0.700799\pi$
$757$	−32.4558	−1.17963	−0.589814	+	0.807539i	$0.700799\pi$
$758$	58.4558	2.12321
$759$	−46.0000	−1.66969
$760$	−32.7279	−1.18717
$761$	−30.1716	−1.09372	−0.546859	−	0.837225i	$-0.684177\pi$
$761$	−30.1716	−1.09372	−0.546859	+	0.837225i	$0.684177\pi$
$762$	33.2132	1.20319
$763$	20.4853	0.741617
$764$	−14.2721	−0.516346
$765$	−6.48528	−0.234476
$766$	18.3137	0.661701
$767$	−30.7279	−1.10952
$768$	−42.3848	−1.52943
$769$	−16.0000	−0.576975	−0.288487	−	0.957484i	$-0.593152\pi$
$769$	−16.0000	−0.576975	−0.288487	+	0.957484i	$0.593152\pi$
$770$	−43.7990	−1.57841
$771$	−44.4853	−1.60210
$772$	−13.4558	−0.484286
$773$	0.384776	0.0138394	0.00691972	−	0.999976i	$-0.497797\pi$
$773$	0.384776	0.0138394	0.00691972	+	0.999976i	$0.497797\pi$
$774$	−19.3137	−0.694217
$775$	−14.4853	−0.520327
$776$	−77.1838	−2.77074
$777$	−9.65685	−0.346438
$778$	2.24264	0.0804026
$779$	−58.0416	−2.07956
$780$	−22.9706	−0.822478
$781$	9.07107	0.324588
$782$	56.1421	2.00764
$783$	23.5980	0.843323
$784$	−9.00000	−0.321429
$785$	13.6569	0.487434
$786$	−30.3848	−1.08379
$787$	−19.0294	−0.678326	−0.339163	−	0.940728i	$-0.610144\pi$
$787$	−19.0294	−0.678326	−0.339163	+	0.940728i	$0.610144\pi$
$788$	87.9411	3.13277
$789$	17.0711	0.607746
$790$	−37.7990	−1.34483
$791$	−18.6863	−0.664408
$792$	−28.3137	−1.00608
$793$	10.2426	0.363727
$794$	4.24264	0.150566
$795$	25.3137	0.897785
$796$	−7.92893	−0.281034
$797$	−29.1421	−1.03227	−0.516134	−	0.856508i	$-0.672629\pi$
$797$	−29.1421	−1.03227	−0.516134	+	0.856508i	$0.672629\pi$
$798$	35.7990	1.26727
$799$	−56.9289	−2.01400
$800$	−4.75736	−0.168198
$801$	−4.24264	−0.149906
$802$	73.1838	2.58421
$803$	42.6985	1.50680
$804$	−80.6690	−2.84498
$805$	−14.3431	−0.505529
$806$	−34.9706	−1.23179
$807$	12.0000	0.422420
$808$	−19.1716	−0.674454
$809$	15.7990	0.555463	0.277731	−	0.960659i	$-0.410417\pi$
$809$	15.7990	0.555463	0.277731	+	0.960659i	$0.410417\pi$
$810$	−17.0711	−0.599816
$811$	17.2426	0.605471	0.302736	−	0.953075i	$-0.402100\pi$
$811$	17.2426	0.605471	0.302736	+	0.953075i	$0.402100\pi$
$812$	−31.9411	−1.12091
$813$	22.2843	0.781544
$814$	−52.8701	−1.85309
$815$	−14.3431	−0.502418
$816$	−19.4558	−0.681091
$817$	41.9411	1.46733
$818$	−7.31371	−0.255718
$819$	−6.00000	−0.209657
$820$	−59.9411	−2.09323
$821$	−13.4142	−0.468159	−0.234080	−	0.972217i	$-0.575208\pi$
$821$	−13.4142	−0.468159	−0.234080	+	0.972217i	$0.575208\pi$
$822$	32.9706	1.14998
$823$	−27.7279	−0.966535	−0.483267	−	0.875473i	$-0.660550\pi$
$823$	−27.7279	−0.966535	−0.483267	+	0.875473i	$0.660550\pi$
$824$	−25.4142	−0.885346
$825$	27.2132	0.947442
$826$	49.4558	1.72079
$827$	−41.7990	−1.45349	−0.726747	−	0.686906i	$-0.758969\pi$
$827$	−41.7990	−1.45349	−0.726747	+	0.686906i	$0.758969\pi$
$828$	−19.4142	−0.674691
$829$	11.0000	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$830$	3.17157	0.110087
$831$	−11.5563	−0.400885
$832$	−29.4853	−1.02222
$833$	13.7574	0.476664
$834$	13.6569	0.472898
$835$	1.85786	0.0642940
$836$	128.740	4.45257
$837$	−27.3137	−0.944100
$838$	−67.7696	−2.34106
$839$	22.1421	0.764431	0.382216	−	0.924073i	$-0.375161\pi$
$839$	22.1421	0.764431	0.382216	+	0.924073i	$0.375161\pi$
$840$	17.6569	0.609219
$841$	−11.5980	−0.399930
$842$	77.0122	2.65402
$843$	−15.7990	−0.544146
$844$	87.9411	3.02706
$845$	5.65685	0.194602
$846$	29.9706	1.03041
$847$	60.2843	2.07139
$848$	−37.9706	−1.30391
$849$	8.48528	0.291214
$850$	−33.2132	−1.13920
$851$	−17.3137	−0.593506
$852$	−7.65685	−0.262320
$853$	4.45584	0.152565	0.0762826	−	0.997086i	$-0.475695\pi$
$853$	4.45584	0.152565	0.0762826	+	0.997086i	$0.475695\pi$
$854$	−16.4853	−0.564115
$855$	−7.41421	−0.253561
$856$	7.75736	0.265141
$857$	−15.8579	−0.541694	−0.270847	−	0.962622i	$-0.587304\pi$
$857$	−15.8579	−0.541694	−0.270847	+	0.962622i	$0.587304\pi$
$858$	65.6985	2.24291
$859$	−13.2426	−0.451833	−0.225917	−	0.974147i	$-0.572538\pi$
$859$	−13.2426	−0.451833	−0.225917	+	0.974147i	$0.572538\pi$
$860$	43.3137	1.47699
$861$	31.3137	1.06717
$862$	−45.6985	−1.55650
$863$	−0.100505	−0.00342123	−0.00171062	−	0.999999i	$-0.500545\pi$
$863$	−0.100505	−0.00342123	−0.00171062	+	0.999999i	$0.500545\pi$
$864$	−8.97056	−0.305185
$865$	−3.51472	−0.119504
$866$	32.7279	1.11214
$867$	5.69848	0.193531
$868$	36.9706	1.25486
$869$	71.0122	2.40892
$870$	−20.1421	−0.682882
$871$	−44.6985	−1.51455
$872$	−45.2132	−1.53111
$873$	−17.4853	−0.591787
$874$	64.1838	2.17105
$875$	22.6274	0.764946
$876$	−36.0416	−1.21773
$877$	8.20101	0.276928	0.138464	−	0.990367i	$-0.455783\pi$
$877$	8.20101	0.276928	0.138464	+	0.990367i	$0.455783\pi$
$878$	−10.3137	−0.348071
$879$	19.3137	0.651435
$880$	27.2132	0.917357
$881$	−5.07107	−0.170849	−0.0854243	−	0.996345i	$-0.527225\pi$
$881$	−5.07107	−0.170849	−0.0854243	+	0.996345i	$0.527225\pi$
$882$	−7.24264	−0.243872
$883$	−42.2132	−1.42059	−0.710294	−	0.703905i	$-0.751438\pi$
$883$	−42.2132	−1.42059	−0.710294	+	0.703905i	$0.751438\pi$
$884$	−52.6690	−1.77145
$885$	20.4853	0.688605
$886$	20.4853	0.688216
$887$	41.1838	1.38282	0.691408	−	0.722465i	$-0.256991\pi$
$887$	41.1838	1.38282	0.691408	+	0.722465i	$0.256991\pi$
$888$	21.3137	0.715241
$889$	−19.4558	−0.652528
$890$	14.4853	0.485548
$891$	32.0711	1.07442
$892$	81.2132	2.71922
$893$	−65.0833	−2.17793
$894$	4.48528	0.150010
$895$	−5.17157	−0.172867
$896$	41.1127	1.37348
$897$	21.5147	0.718356
$898$	−53.8701	−1.79767
$899$	−20.1421	−0.671778
$900$	11.4853	0.382843
$901$	58.0416	1.93365
$902$	171.439	5.70828
$903$	−22.6274	−0.752993
$904$	41.2426	1.37171
$905$	7.07107	0.235050
$906$	−51.1127	−1.69811
$907$	14.2132	0.471942	0.235971	−	0.971760i	$-0.424173\pi$
$907$	14.2132	0.471942	0.235971	+	0.971760i	$0.424173\pi$
$908$	−56.7696	−1.88396
$909$	−4.34315	−0.144053
$910$	20.4853	0.679080
$911$	14.6863	0.486579	0.243289	−	0.969954i	$-0.421774\pi$
$911$	14.6863	0.486579	0.243289	+	0.969954i	$0.421774\pi$
$912$	−22.2426	−0.736527
$913$	−5.95837	−0.197193
$914$	−7.75736	−0.256591
$915$	−6.82843	−0.225741
$916$	13.4558	0.444594
$917$	17.7990	0.587774
$918$	−62.6274	−2.06701
$919$	−14.5563	−0.480170	−0.240085	−	0.970752i	$-0.577175\pi$
$919$	−14.5563	−0.480170	−0.240085	+	0.970752i	$0.577175\pi$
$920$	31.6569	1.04370
$921$	34.8284	1.14764
$922$	−34.9706	−1.15169
$923$	−4.24264	−0.139648
$924$	−69.4558	−2.28493
$925$	10.2426	0.336776
$926$	45.6985	1.50175
$927$	−5.75736	−0.189096
$928$	−6.61522	−0.217155
$929$	−37.4142	−1.22752	−0.613760	−	0.789492i	$-0.710344\pi$
$929$	−37.4142	−1.22752	−0.613760	+	0.789492i	$0.710344\pi$
$930$	23.3137	0.764487
$931$	15.7279	0.515462
$932$	−42.6569	−1.39727
$933$	13.5563	0.443815
$934$	71.4264	2.33714
$935$	−41.5980	−1.36040
$936$	13.2426	0.432849
$937$	−6.97056	−0.227718	−0.113859	−	0.993497i	$-0.536321\pi$
$937$	−6.97056	−0.227718	−0.113859	+	0.993497i	$0.536321\pi$
$938$	71.9411	2.34896
$939$	12.4437	0.406083
$940$	−67.2132	−2.19225
$941$	−48.5980	−1.58425	−0.792124	−	0.610360i	$-0.791025\pi$
$941$	−48.5980	−1.58425	−0.792124	+	0.610360i	$0.791025\pi$
$942$	32.9706	1.07424
$943$	56.1421	1.82824
$944$	−30.7279	−1.00011
$945$	16.0000	0.520480
$946$	−123.882	−4.02776
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	−59.9411	−1.94680
$949$	−19.9706	−0.648272
$950$	−37.9706	−1.23193
$951$	−30.5858	−0.991812
$952$	40.4853	1.31214
$953$	−8.65685	−0.280423	−0.140212	−	0.990122i	$-0.544778\pi$
$953$	−8.65685	−0.280423	−0.140212	+	0.990122i	$0.544778\pi$
$954$	−30.5563	−0.989298
$955$	5.27208	0.170600
$956$	−60.2132	−1.94743
$957$	37.8406	1.22321
$958$	−17.6569	−0.570467
$959$	−19.3137	−0.623672
$960$	19.6569	0.634422
$961$	−7.68629	−0.247945
$962$	24.7279	0.797260
$963$	1.75736	0.0566301
$964$	−86.0833	−2.77256
$965$	4.97056	0.160008
$966$	−34.6274	−1.11412
$967$	−24.6274	−0.791964	−0.395982	−	0.918258i	$-0.629596\pi$
$967$	−24.6274	−0.791964	−0.395982	+	0.918258i	$0.629596\pi$
$968$	−133.054	−4.27651
$969$	34.0000	1.09224
$970$	59.6985	1.91680
$971$	−1.89949	−0.0609577	−0.0304788	−	0.999535i	$-0.509703\pi$
$971$	−1.89949	−0.0609577	−0.0304788	+	0.999535i	$0.509703\pi$
$972$	37.8995	1.21563
$973$	−8.00000	−0.256468
$974$	31.3137	1.00336
$975$	−12.7279	−0.407620
$976$	10.2426	0.327859
$977$	−20.4437	−0.654050	−0.327025	−	0.945016i	$-0.606046\pi$
$977$	−20.4437	−0.654050	−0.327025	+	0.945016i	$0.606046\pi$
$978$	−34.6274	−1.10726
$979$	−27.2132	−0.869738
$980$	16.2426	0.518852
$981$	−10.2426	−0.327022
$982$	−32.4853	−1.03665
$983$	5.61522	0.179098	0.0895489	−	0.995982i	$-0.471457\pi$
$983$	5.61522	0.179098	0.0895489	+	0.995982i	$0.471457\pi$
$984$	−69.1127	−2.20323
$985$	−32.4853	−1.03507
$986$	−46.1838	−1.47079
$987$	35.1127	1.11765
$988$	−60.2132	−1.91564
$989$	−40.5685	−1.29000
$990$	21.8995	0.696012
$991$	39.2426	1.24658	0.623292	−	0.781989i	$-0.285795\pi$
$991$	39.2426	1.24658	0.623292	+	0.781989i	$0.285795\pi$
$992$	7.65685	0.243105
$993$	−42.0000	−1.33283
$994$	6.82843	0.216585
$995$	2.92893	0.0928534
$996$	5.02944	0.159364
$997$	−29.9411	−0.948245	−0.474122	−	0.880459i	$-0.657235\pi$
$997$	−29.9411	−0.948245	−0.474122	+	0.880459i	$0.657235\pi$
$998$	60.9411	1.92906
$999$	19.3137	0.611059

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.a.1.1	✓	2
3.2	odd	2		4923.2.a.h.1.2		2
4.3	odd	2		8752.2.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.a.1.1	✓	2	1.1	even	1	trivial
4923.2.a.h.1.2		2	3.2	odd	2
8752.2.a.n.1.1		2	4.3	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41421 q^{2} +1.41421 q^{3} +3.82843 q^{4} -1.41421 q^{5} -3.41421 q^{6} +2.00000 q^{7} -4.41421 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.41421 q^{2} +1.41421 q^{3} +3.82843 q^{4} -1.41421 q^{5} -3.41421 q^{6} +2.00000 q^{7} -4.41421 q^{8} -1.00000 q^{9} +3.41421 q^{10} -6.41421 q^{11} +5.41421 q^{12} +3.00000 q^{13} -4.82843 q^{14} -2.00000 q^{15} +3.00000 q^{16} -4.58579 q^{17} +2.41421 q^{18} -5.24264 q^{19} -5.41421 q^{20} +2.82843 q^{21} +15.4853 q^{22} +5.07107 q^{23} -6.24264 q^{24} -3.00000 q^{25} -7.24264 q^{26} -5.65685 q^{27} +7.65685 q^{28} -4.17157 q^{29} +4.82843 q^{30} +4.82843 q^{31} +1.58579 q^{32} -9.07107 q^{33} +11.0711 q^{34} -2.82843 q^{35} -3.82843 q^{36} -3.41421 q^{37} +12.6569 q^{38} +4.24264 q^{39} +6.24264 q^{40} +11.0711 q^{41} -6.82843 q^{42} -8.00000 q^{43} -24.5563 q^{44} +1.41421 q^{45} -12.2426 q^{46} +12.4142 q^{47} +4.24264 q^{48} -3.00000 q^{49} +7.24264 q^{50} -6.48528 q^{51} +11.4853 q^{52} -12.6569 q^{53} +13.6569 q^{54} +9.07107 q^{55} -8.82843 q^{56} -7.41421 q^{57} +10.0711 q^{58} -10.2426 q^{59} -7.65685 q^{60} +3.41421 q^{61} -11.6569 q^{62} -2.00000 q^{63} -9.82843 q^{64} -4.24264 q^{65} +21.8995 q^{66} -14.8995 q^{67} -17.5563 q^{68} +7.17157 q^{69} +6.82843 q^{70} -1.41421 q^{71} +4.41421 q^{72} -6.65685 q^{73} +8.24264 q^{74} -4.24264 q^{75} -20.0711 q^{76} -12.8284 q^{77} -10.2426 q^{78} -11.0711 q^{79} -4.24264 q^{80} -5.00000 q^{81} -26.7279 q^{82} +0.928932 q^{83} +10.8284 q^{84} +6.48528 q^{85} +19.3137 q^{86} -5.89949 q^{87} +28.3137 q^{88} +4.24264 q^{89} -3.41421 q^{90} +6.00000 q^{91} +19.4142 q^{92} +6.82843 q^{93} -29.9706 q^{94} +7.41421 q^{95} +2.24264 q^{96} +17.4853 q^{97} +7.24264 q^{98} +6.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 - 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} - 2 q^{9} + 4 q^{10} - 10 q^{11} + 8 q^{12} + 6 q^{13} - 4 q^{14} - 4 q^{15} + 6 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{19} - 8 q^{20} + 14 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 6 q^{26} + 4 q^{28} - 14 q^{29} + 4 q^{30} + 4 q^{31} + 6 q^{32} - 4 q^{33} + 8 q^{34} - 2 q^{36} - 4 q^{37} + 14 q^{38} + 4 q^{40} + 8 q^{41} - 8 q^{42} - 16 q^{43} - 18 q^{44} - 16 q^{46} + 22 q^{47} - 6 q^{49} + 6 q^{50} + 4 q^{51} + 6 q^{52} - 14 q^{53} + 16 q^{54} + 4 q^{55} - 12 q^{56} - 12 q^{57} + 6 q^{58} - 12 q^{59} - 4 q^{60} + 4 q^{61} - 12 q^{62} - 4 q^{63} - 14 q^{64} + 24 q^{66} - 10 q^{67} - 4 q^{68} + 20 q^{69} + 8 q^{70} + 6 q^{72} - 2 q^{73} + 8 q^{74} - 26 q^{76} - 20 q^{77} - 12 q^{78} - 8 q^{79} - 10 q^{81} - 28 q^{82} + 16 q^{83} + 16 q^{84} - 4 q^{85} + 16 q^{86} + 8 q^{87} + 34 q^{88} - 4 q^{90} + 12 q^{91} + 36 q^{92} + 8 q^{93} - 26 q^{94} + 12 q^{95} - 4 q^{96} + 18 q^{97} + 6 q^{98} + 10 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 - 2 * q^9 + 4 * q^10 - 10 * q^11 + 8 * q^12 + 6 * q^13 - 4 * q^14 - 4 * q^15 + 6 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^19 - 8 * q^20 + 14 * q^22 - 4 * q^23 - 4 * q^24 - 6 * q^25 - 6 * q^26 + 4 * q^28 - 14 * q^29 + 4 * q^30 + 4 * q^31 + 6 * q^32 - 4 * q^33 + 8 * q^34 - 2 * q^36 - 4 * q^37 + 14 * q^38 + 4 * q^40 + 8 * q^41 - 8 * q^42 - 16 * q^43 - 18 * q^44 - 16 * q^46 + 22 * q^47 - 6 * q^49 + 6 * q^50 + 4 * q^51 + 6 * q^52 - 14 * q^53 + 16 * q^54 + 4 * q^55 - 12 * q^56 - 12 * q^57 + 6 * q^58 - 12 * q^59 - 4 * q^60 + 4 * q^61 - 12 * q^62 - 4 * q^63 - 14 * q^64 + 24 * q^66 - 10 * q^67 - 4 * q^68 + 20 * q^69 + 8 * q^70 + 6 * q^72 - 2 * q^73 + 8 * q^74 - 26 * q^76 - 20 * q^77 - 12 * q^78 - 8 * q^79 - 10 * q^81 - 28 * q^82 + 16 * q^83 + 16 * q^84 - 4 * q^85 + 16 * q^86 + 8 * q^87 + 34 * q^88 - 4 * q^90 + 12 * q^91 + 36 * q^92 + 8 * q^93 - 26 * q^94 + 12 * q^95 - 4 * q^96 + 18 * q^97 + 6 * q^98 + 10 * q^99

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