LMFDB - Embedded newform 151.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(1,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, 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("151.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.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:	$1.20574107052$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
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			1.3
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.801938 q^{2} -1.80194 q^{3} -1.35690 q^{4} -2.44504 q^{5} -1.44504 q^{6} -1.00000 q^{7} -2.69202 q^{8} +0.246980 q^{9} +O(q^{10})$	\(q+0.801938 q^{2} -1.80194 q^{3} -1.35690 q^{4} -2.44504 q^{5} -1.44504 q^{6} -1.00000 q^{7} -2.69202 q^{8} +0.246980 q^{9} -1.96077 q^{10} +1.49396 q^{11} +2.44504 q^{12} +2.93900 q^{13} -0.801938 q^{14} +4.40581 q^{15} +0.554958 q^{16} -5.93900 q^{17} +0.198062 q^{18} -3.02715 q^{19} +3.31767 q^{20} +1.80194 q^{21} +1.19806 q^{22} +4.74094 q^{23} +4.85086 q^{24} +0.978230 q^{25} +2.35690 q^{26} +4.96077 q^{27} +1.35690 q^{28} -9.25667 q^{29} +3.53319 q^{30} -5.18598 q^{31} +5.82908 q^{32} -2.69202 q^{33} -4.76271 q^{34} +2.44504 q^{35} -0.335126 q^{36} +1.06100 q^{37} -2.42758 q^{38} -5.29590 q^{39} +6.58211 q^{40} -0.902165 q^{41} +1.44504 q^{42} +8.82908 q^{43} -2.02715 q^{44} -0.603875 q^{45} +3.80194 q^{46} -11.1957 q^{47} -1.00000 q^{48} -6.00000 q^{49} +0.784479 q^{50} +10.7017 q^{51} -3.98792 q^{52} -5.26875 q^{53} +3.97823 q^{54} -3.65279 q^{55} +2.69202 q^{56} +5.45473 q^{57} -7.42327 q^{58} +1.91723 q^{59} -5.97823 q^{60} +7.00969 q^{61} -4.15883 q^{62} -0.246980 q^{63} +3.56465 q^{64} -7.18598 q^{65} -2.15883 q^{66} +0.241603 q^{67} +8.05861 q^{68} -8.54288 q^{69} +1.96077 q^{70} +7.64071 q^{71} -0.664874 q^{72} -2.82371 q^{73} +0.850855 q^{74} -1.76271 q^{75} +4.10752 q^{76} -1.49396 q^{77} -4.24698 q^{78} -3.37867 q^{79} -1.35690 q^{80} -9.67994 q^{81} -0.723480 q^{82} -4.38404 q^{83} -2.44504 q^{84} +14.5211 q^{85} +7.08038 q^{86} +16.6799 q^{87} -4.02177 q^{88} -12.0000 q^{89} -0.484271 q^{90} -2.93900 q^{91} -6.43296 q^{92} +9.34481 q^{93} -8.97823 q^{94} +7.40150 q^{95} -10.5036 q^{96} +5.07606 q^{97} -4.81163 q^{98} +0.368977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - q^{3} - 7 q^{5} - 4 q^{6} - 3 q^{7} - 3 q^{8} - 4 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - q^3 - 7 * q^5 - 4 * q^6 - 3 * q^7 - 3 * q^8 - 4 * q^9	$ 3 q - 2 q^{2} - q^{3} - 7 q^{5} - 4 q^{6} - 3 q^{7} - 3 q^{8} - 4 q^{9} + 7 q^{10} - 5 q^{11} + 7 q^{12} - q^{13} + 2 q^{14} + 2 q^{16} - 8 q^{17} + 5 q^{18} - 3 q^{19} - 7 q^{20} + q^{21} + 8 q^{22} + q^{24} + 6 q^{25} + 3 q^{26} + 2 q^{27} - q^{29} + 14 q^{30} - q^{31} + 7 q^{32} - 3 q^{33} + 3 q^{34} + 7 q^{35} + 13 q^{37} + 9 q^{38} - 2 q^{39} + 14 q^{40} - 21 q^{41} + 4 q^{42} + 16 q^{43} + 7 q^{45} + 7 q^{46} + 3 q^{47} - 3 q^{48} - 18 q^{49} - 18 q^{50} + 5 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{54} + 7 q^{55} + 3 q^{56} - 6 q^{57} - 25 q^{58} - q^{59} - 21 q^{60} - q^{61} - 4 q^{62} + 4 q^{63} - 11 q^{64} - 7 q^{65} + 2 q^{66} - q^{67} - 7 q^{68} - 7 q^{69} - 7 q^{70} - 14 q^{71} - 3 q^{72} - q^{73} - 11 q^{74} + 12 q^{75} - 28 q^{76} + 5 q^{77} - 8 q^{78} - 3 q^{79} - 5 q^{81} + 28 q^{82} - 3 q^{83} - 7 q^{84} + 28 q^{85} - 13 q^{86} + 26 q^{87} - 9 q^{88} - 36 q^{89} - 14 q^{90} + q^{91} + 5 q^{93} - 30 q^{94} + 28 q^{95} + 12 q^{98} + 16 q^{99}+O(q^{100}) $ 3 * q - 2 * q^2 - q^3 - 7 * q^5 - 4 * q^6 - 3 * q^7 - 3 * q^8 - 4 * q^9 + 7 * q^10 - 5 * q^11 + 7 * q^12 - q^13 + 2 * q^14 + 2 * q^16 - 8 * q^17 + 5 * q^18 - 3 * q^19 - 7 * q^20 + q^21 + 8 * q^22 + q^24 + 6 * q^25 + 3 * q^26 + 2 * q^27 - q^29 + 14 * q^30 - q^31 + 7 * q^32 - 3 * q^33 + 3 * q^34 + 7 * q^35 + 13 * q^37 + 9 * q^38 - 2 * q^39 + 14 * q^40 - 21 * q^41 + 4 * q^42 + 16 * q^43 + 7 * q^45 + 7 * q^46 + 3 * q^47 - 3 * q^48 - 18 * q^49 - 18 * q^50 + 5 * q^51 + 7 * q^52 - 8 * q^53 + 15 * q^54 + 7 * q^55 + 3 * q^56 - 6 * q^57 - 25 * q^58 - q^59 - 21 * q^60 - q^61 - 4 * q^62 + 4 * q^63 - 11 * q^64 - 7 * q^65 + 2 * q^66 - q^67 - 7 * q^68 - 7 * q^69 - 7 * q^70 - 14 * q^71 - 3 * q^72 - q^73 - 11 * q^74 + 12 * q^75 - 28 * q^76 + 5 * q^77 - 8 * q^78 - 3 * q^79 - 5 * q^81 + 28 * q^82 - 3 * q^83 - 7 * q^84 + 28 * q^85 - 13 * q^86 + 26 * q^87 - 9 * q^88 - 36 * q^89 - 14 * q^90 + q^91 + 5 * q^93 - 30 * q^94 + 28 * q^95 + 12 * q^98 + 16 * 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 $

$2$	0.801938	0.567056	0.283528	−	0.958964i	$-0.408495\pi$
$2$	0.801938	0.567056	0.283528	+	0.958964i	$0.408495\pi$
$3$	−1.80194	−1.04035	−0.520175	−	0.854060i	$-0.674133\pi$
$3$	−1.80194	−1.04035	−0.520175	+	0.854060i	$0.674133\pi$
$4$	−1.35690	−0.678448
$5$	−2.44504	−1.09346	−0.546728	−	0.837310i	$-0.684127\pi$
$5$	−2.44504	−1.09346	−0.546728	+	0.837310i	$0.684127\pi$
$6$	−1.44504	−0.589936
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−2.69202	−0.951773
$9$	0.246980	0.0823265
$10$	−1.96077	−0.620050
$11$	1.49396	0.450446	0.225223	−	0.974307i	$-0.427689\pi$
$11$	1.49396	0.450446	0.225223	+	0.974307i	$0.427689\pi$
$12$	2.44504	0.705823
$13$	2.93900	0.815132	0.407566	−	0.913176i	$-0.366378\pi$
$13$	2.93900	0.815132	0.407566	+	0.913176i	$0.366378\pi$
$14$	−0.801938	−0.214327
$15$	4.40581	1.13758
$16$	0.554958	0.138740
$17$	−5.93900	−1.44042	−0.720210	−	0.693756i	$-0.755954\pi$
$17$	−5.93900	−1.44042	−0.720210	+	0.693756i	$0.755954\pi$
$18$	0.198062	0.0466837
$19$	−3.02715	−0.694475	−0.347238	−	0.937777i	$-0.612880\pi$
$19$	−3.02715	−0.694475	−0.347238	+	0.937777i	$0.612880\pi$
$20$	3.31767	0.741853
$21$	1.80194	0.393215
$22$	1.19806	0.255428
$23$	4.74094	0.988554	0.494277	−	0.869304i	$-0.335433\pi$
$23$	4.74094	0.988554	0.494277	+	0.869304i	$0.335433\pi$
$24$	4.85086	0.990177
$25$	0.978230	0.195646
$26$	2.35690	0.462225
$27$	4.96077	0.954701
$28$	1.35690	0.256429
$29$	−9.25667	−1.71892	−0.859460	−	0.511203i	$-0.829200\pi$
$29$	−9.25667	−1.71892	−0.859460	+	0.511203i	$0.829200\pi$
$30$	3.53319	0.645069
$31$	−5.18598	−0.931430	−0.465715	−	0.884935i	$-0.654203\pi$
$31$	−5.18598	−0.931430	−0.465715	+	0.884935i	$0.654203\pi$
$32$	5.82908	1.03045
$33$	−2.69202	−0.468621
$34$	−4.76271	−0.816798
$35$	2.44504	0.413288
$36$	−0.335126	−0.0558543
$37$	1.06100	0.174427	0.0872136	−	0.996190i	$-0.472204\pi$
$37$	1.06100	0.174427	0.0872136	+	0.996190i	$0.472204\pi$
$38$	−2.42758	−0.393806
$39$	−5.29590	−0.848022
$40$	6.58211	1.04072
$41$	−0.902165	−0.140895	−0.0704473	−	0.997516i	$-0.522443\pi$
$41$	−0.902165	−0.140895	−0.0704473	+	0.997516i	$0.522443\pi$
$42$	1.44504	0.222975
$43$	8.82908	1.34642	0.673211	−	0.739450i	$-0.264914\pi$
$43$	8.82908	1.34642	0.673211	+	0.739450i	$0.264914\pi$
$44$	−2.02715	−0.305604
$45$	−0.603875	−0.0900204
$46$	3.80194	0.560565
$47$	−11.1957	−1.63306	−0.816528	−	0.577306i	$-0.804104\pi$
$47$	−11.1957	−1.63306	−0.816528	+	0.577306i	$0.804104\pi$
$48$	−1.00000	−0.144338
$49$	−6.00000	−0.857143
$50$	0.784479	0.110942
$51$	10.7017	1.49854
$52$	−3.98792	−0.553025
$53$	−5.26875	−0.723718	−0.361859	−	0.932233i	$-0.617858\pi$
$53$	−5.26875	−0.723718	−0.361859	+	0.932233i	$0.617858\pi$
$54$	3.97823	0.541368
$55$	−3.65279	−0.492542
$56$	2.69202	0.359737
$57$	5.45473	0.722497
$58$	−7.42327	−0.974723
$59$	1.91723	0.249602	0.124801	−	0.992182i	$-0.460171\pi$
$59$	1.91723	0.249602	0.124801	+	0.992182i	$0.460171\pi$
$60$	−5.97823	−0.771786
$61$	7.00969	0.897499	0.448749	−	0.893658i	$-0.351870\pi$
$61$	7.00969	0.897499	0.448749	+	0.893658i	$0.351870\pi$
$62$	−4.15883	−0.528172
$63$	−0.246980	−0.0311165
$64$	3.56465	0.445581
$65$	−7.18598	−0.891311
$66$	−2.15883	−0.265734
$67$	0.241603	0.0295165	0.0147582	−	0.999891i	$-0.495302\pi$
$67$	0.241603	0.0295165	0.0147582	+	0.999891i	$0.495302\pi$
$68$	8.05861	0.977250
$69$	−8.54288	−1.02844
$70$	1.96077	0.234357
$71$	7.64071	0.906786	0.453393	−	0.891311i	$-0.350213\pi$
$71$	7.64071	0.906786	0.453393	+	0.891311i	$0.350213\pi$
$72$	−0.664874	−0.0783562
$73$	−2.82371	−0.330490	−0.165245	−	0.986253i	$-0.552841\pi$
$73$	−2.82371	−0.330490	−0.165245	+	0.986253i	$0.552841\pi$
$74$	0.850855	0.0989099
$75$	−1.76271	−0.203540
$76$	4.10752	0.471165
$77$	−1.49396	−0.170252
$78$	−4.24698	−0.480876
$79$	−3.37867	−0.380130	−0.190065	−	0.981772i	$-0.560870\pi$
$79$	−3.37867	−0.380130	−0.190065	+	0.981772i	$0.560870\pi$
$80$	−1.35690	−0.151706
$81$	−9.67994	−1.07555
$82$	−0.723480	−0.0798950
$83$	−4.38404	−0.481211	−0.240606	−	0.970623i	$-0.577346\pi$
$83$	−4.38404	−0.481211	−0.240606	+	0.970623i	$0.577346\pi$
$84$	−2.44504	−0.266776
$85$	14.5211	1.57504
$86$	7.08038	0.763497
$87$	16.6799	1.78828
$88$	−4.02177	−0.428722
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	−0.484271	−0.0510466
$91$	−2.93900	−0.308091
$92$	−6.43296	−0.670682
$93$	9.34481	0.969012
$94$	−8.97823	−0.926034
$95$	7.40150	0.759378
$96$	−10.5036	−1.07202
$97$	5.07606	0.515396	0.257698	−	0.966225i	$-0.417036\pi$
$97$	5.07606	0.515396	0.257698	+	0.966225i	$0.417036\pi$
$98$	−4.81163	−0.486048
$99$	0.368977	0.0370836
$100$	−1.32736	−0.132736
$101$	−17.5646	−1.74775	−0.873874	−	0.486153i	$-0.838400\pi$
$101$	−17.5646	−1.74775	−0.873874	+	0.486153i	$0.838400\pi$
$102$	8.58211	0.849755
$103$	6.40044	0.630654	0.315327	−	0.948983i	$-0.397886\pi$
$103$	6.40044	0.630654	0.315327	+	0.948983i	$0.397886\pi$
$104$	−7.91185	−0.775821
$105$	−4.40581	−0.429963
$106$	−4.22521	−0.410389
$107$	1.59419	0.154116	0.0770579	−	0.997027i	$-0.475447\pi$
$107$	1.59419	0.154116	0.0770579	+	0.997027i	$0.475447\pi$
$108$	−6.73125	−0.647715
$109$	14.4644	1.38544	0.692720	−	0.721207i	$-0.256412\pi$
$109$	14.4644	1.38544	0.692720	+	0.721207i	$0.256412\pi$
$110$	−2.92931	−0.279299
$111$	−1.91185	−0.181465
$112$	−0.554958	−0.0524386
$113$	−3.20344	−0.301354	−0.150677	−	0.988583i	$-0.548145\pi$
$113$	−3.20344	−0.301354	−0.150677	+	0.988583i	$0.548145\pi$
$114$	4.37435	0.409696
$115$	−11.5918	−1.08094
$116$	12.5603	1.16620
$117$	0.725873	0.0671070
$118$	1.53750	0.141538
$119$	5.93900	0.544427
$120$	−11.8605	−1.08271
$121$	−8.76809	−0.797099
$122$	5.62133	0.508932
$123$	1.62565	0.146580
$124$	7.03684	0.631927
$125$	9.83340	0.879526
$126$	−0.198062	−0.0176448
$127$	21.8267	1.93681	0.968403	−	0.249391i	$-0.0802305\pi$
$127$	21.8267	1.93681	0.968403	+	0.249391i	$0.0802305\pi$
$128$	−8.79954	−0.777777
$129$	−15.9095	−1.40075
$130$	−5.76271	−0.505423
$131$	0.149145	0.0130309	0.00651543	−	0.999979i	$-0.497926\pi$
$131$	0.149145	0.0130309	0.00651543	+	0.999979i	$0.497926\pi$
$132$	3.65279	0.317935
$133$	3.02715	0.262487
$134$	0.193750	0.0167375
$135$	−12.1293	−1.04392
$136$	15.9879	1.37095
$137$	−3.92931	−0.335704	−0.167852	−	0.985812i	$-0.553683\pi$
$137$	−3.92931	−0.335704	−0.167852	+	0.985812i	$0.553683\pi$
$138$	−6.85086	−0.583184
$139$	5.60388	0.475315	0.237657	−	0.971349i	$-0.423620\pi$
$139$	5.60388	0.475315	0.237657	+	0.971349i	$0.423620\pi$
$140$	−3.31767	−0.280394
$141$	20.1739	1.69895
$142$	6.12737	0.514198
$143$	4.39075	0.367173
$144$	0.137063	0.0114219
$145$	22.6329	1.87956
$146$	−2.26444	−0.187406
$147$	10.8116	0.891728
$148$	−1.43967	−0.118340
$149$	−1.76271	−0.144407	−0.0722034	−	0.997390i	$-0.523003\pi$
$149$	−1.76271	−0.144407	−0.0722034	+	0.997390i	$0.523003\pi$
$150$	−1.41358	−0.115419
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	8.14914	0.660983
$153$	−1.46681	−0.118585
$154$	−1.19806	−0.0965426
$155$	12.6799	1.01848
$156$	7.18598	0.575339
$157$	10.5526	0.842186	0.421093	−	0.907017i	$-0.361647\pi$
$157$	10.5526	0.842186	0.421093	+	0.907017i	$0.361647\pi$
$158$	−2.70948	−0.215555
$159$	9.49396	0.752920
$160$	−14.2524	−1.12675
$161$	−4.74094	−0.373638
$162$	−7.76271	−0.609896
$163$	23.1957	1.81683	0.908413	−	0.418075i	$-0.137295\pi$
$163$	23.1957	1.81683	0.908413	+	0.418075i	$0.137295\pi$
$164$	1.22414	0.0955896
$165$	6.58211	0.512416
$166$	−3.51573	−0.272874
$167$	−16.0858	−1.24475	−0.622376	−	0.782718i	$-0.713833\pi$
$167$	−16.0858	−1.24475	−0.622376	+	0.782718i	$0.713833\pi$
$168$	−4.85086	−0.374252
$169$	−4.36227	−0.335559
$170$	11.6450	0.893133
$171$	−0.747644	−0.0571737
$172$	−11.9801	−0.913478
$173$	6.87800	0.522925	0.261462	−	0.965214i	$-0.415795\pi$
$173$	6.87800	0.522925	0.261462	+	0.965214i	$0.415795\pi$
$174$	13.3763	1.01405
$175$	−0.978230	−0.0739472
$176$	0.829085	0.0624946
$177$	−3.45473	−0.259673
$178$	−9.62325	−0.721293
$179$	−13.5821	−1.01517	−0.507587	−	0.861600i	$-0.669462\pi$
$179$	−13.5821	−1.01517	−0.507587	+	0.861600i	$0.669462\pi$
$180$	0.819396	0.0610742
$181$	−13.6679	−1.01592	−0.507962	−	0.861380i	$-0.669601\pi$
$181$	−13.6679	−1.01592	−0.507962	+	0.861380i	$0.669601\pi$
$182$	−2.35690	−0.174705
$183$	−12.6310	−0.933712
$184$	−12.7627	−0.940879
$185$	−2.59419	−0.190728
$186$	7.49396	0.549484
$187$	−8.87263	−0.648831
$188$	15.1914	1.10794
$189$	−4.96077	−0.360843
$190$	5.93554	0.430610
$191$	17.0097	1.23078	0.615389	−	0.788224i	$-0.288999\pi$
$191$	17.0097	1.23078	0.615389	+	0.788224i	$0.288999\pi$
$192$	−6.42327	−0.463560
$193$	−21.6571	−1.55891	−0.779456	−	0.626457i	$-0.784505\pi$
$193$	−21.6571	−1.55891	−0.779456	+	0.626457i	$0.784505\pi$
$194$	4.07069	0.292258
$195$	12.9487	0.927275
$196$	8.14138	0.581527
$197$	23.7409	1.69147	0.845736	−	0.533602i	$-0.179162\pi$
$197$	23.7409	1.69147	0.845736	+	0.533602i	$0.179162\pi$
$198$	0.295897	0.0210285
$199$	−24.4131	−1.73060	−0.865300	−	0.501255i	$-0.832872\pi$
$199$	−24.4131	−1.73060	−0.865300	+	0.501255i	$0.832872\pi$
$200$	−2.63342	−0.186211
$201$	−0.435353	−0.0307074
$202$	−14.0858	−0.991070
$203$	9.25667	0.649691
$204$	−14.5211	−1.01668
$205$	2.20583	0.154062
$206$	5.13275	0.357616
$207$	1.17092	0.0813842
$208$	1.63102	0.113091
$209$	−4.52243	−0.312823
$210$	−3.53319	−0.243813
$211$	−11.9825	−0.824912	−0.412456	−	0.910977i	$-0.635329\pi$
$211$	−11.9825	−0.824912	−0.412456	+	0.910977i	$0.635329\pi$
$212$	7.14914	0.491005
$213$	−13.7681	−0.943374
$214$	1.27844	0.0873923
$215$	−21.5875	−1.47225
$216$	−13.3545	−0.908659
$217$	5.18598	0.352047
$218$	11.5996	0.785622
$219$	5.08815	0.343825
$220$	4.95646	0.334164
$221$	−17.4547	−1.17413
$222$	−1.53319	−0.102901
$223$	−21.8334	−1.46207	−0.731036	−	0.682339i	$-0.760963\pi$
$223$	−21.8334	−1.46207	−0.731036	+	0.682339i	$0.760963\pi$
$224$	−5.82908	−0.389472
$225$	0.241603	0.0161069
$226$	−2.56896	−0.170885
$227$	−21.3763	−1.41879	−0.709397	−	0.704810i	$-0.751032\pi$
$227$	−21.3763	−1.41879	−0.709397	+	0.704810i	$0.751032\pi$
$228$	−7.40150	−0.490176
$229$	3.89977	0.257704	0.128852	−	0.991664i	$-0.458871\pi$
$229$	3.89977	0.257704	0.128852	+	0.991664i	$0.458871\pi$
$230$	−9.29590	−0.612953
$231$	2.69202	0.177122
$232$	24.9191	1.63602
$233$	10.8605	0.711498	0.355749	−	0.934582i	$-0.384226\pi$
$233$	10.8605	0.711498	0.355749	+	0.934582i	$0.384226\pi$
$234$	0.582105	0.0380534
$235$	27.3739	1.78568
$236$	−2.60148	−0.169342
$237$	6.08815	0.395468
$238$	4.76271	0.308721
$239$	−13.4577	−0.870507	−0.435254	−	0.900308i	$-0.643341\pi$
$239$	−13.4577	−0.870507	−0.435254	+	0.900308i	$0.643341\pi$
$240$	2.44504	0.157827
$241$	−26.1890	−1.68698	−0.843490	−	0.537145i	$-0.819503\pi$
$241$	−26.1890	−1.68698	−0.843490	+	0.537145i	$0.819503\pi$
$242$	−7.03146	−0.451999
$243$	2.56033	0.164246
$244$	−9.51142	−0.608906
$245$	14.6703	0.937248
$246$	1.30367	0.0831188
$247$	−8.89679	−0.566089
$248$	13.9608	0.886510
$249$	7.89977	0.500628
$250$	7.88577	0.498740
$251$	−23.5351	−1.48552	−0.742761	−	0.669556i	$-0.766484\pi$
$251$	−23.5351	−1.48552	−0.742761	+	0.669556i	$0.766484\pi$
$252$	0.335126	0.0211109
$253$	7.08277	0.445290
$254$	17.5036	1.09828
$255$	−26.1661	−1.63859
$256$	−14.1860	−0.886624
$257$	20.4185	1.27367	0.636835	−	0.771000i	$-0.280243\pi$
$257$	20.4185	1.27367	0.636835	+	0.771000i	$0.280243\pi$
$258$	−12.7584	−0.794303
$259$	−1.06100	−0.0659273
$260$	9.75063	0.604708
$261$	−2.28621	−0.141513
$262$	0.119605	0.00738922
$263$	−10.2131	−0.629768	−0.314884	−	0.949130i	$-0.601966\pi$
$263$	−10.2131	−0.629768	−0.314884	+	0.949130i	$0.601966\pi$
$264$	7.24698	0.446021
$265$	12.8823	0.791354
$266$	2.42758	0.148845
$267$	21.6233	1.32332
$268$	−0.327830	−0.0200254
$269$	25.3642	1.54648	0.773241	−	0.634112i	$-0.218634\pi$
$269$	25.3642	1.54648	0.773241	+	0.634112i	$0.218634\pi$
$270$	−9.72694	−0.591963
$271$	15.2814	0.928280	0.464140	−	0.885762i	$-0.346363\pi$
$271$	15.2814	0.928280	0.464140	+	0.885762i	$0.346363\pi$
$272$	−3.29590	−0.199843
$273$	5.29590	0.320522
$274$	−3.15106	−0.190363
$275$	1.46144	0.0881279
$276$	11.5918	0.697744
$277$	−18.6558	−1.12092	−0.560458	−	0.828183i	$-0.689375\pi$
$277$	−18.6558	−1.12092	−0.560458	+	0.828183i	$0.689375\pi$
$278$	4.49396	0.269530
$279$	−1.28083	−0.0766814
$280$	−6.58211	−0.393356
$281$	−18.6571	−1.11299	−0.556495	−	0.830851i	$-0.687854\pi$
$281$	−18.6571	−1.11299	−0.556495	+	0.830851i	$0.687854\pi$
$282$	16.1782	0.963398
$283$	−19.1957	−1.14106	−0.570532	−	0.821275i	$-0.693263\pi$
$283$	−19.1957	−1.14106	−0.570532	+	0.821275i	$0.693263\pi$
$284$	−10.3676	−0.615207
$285$	−13.3370	−0.790018
$286$	3.52111	0.208207
$287$	0.902165	0.0532531
$288$	1.43967	0.0848331
$289$	18.2717	1.07481
$290$	18.1502	1.06582
$291$	−9.14675	−0.536192
$292$	3.83148	0.224220
$293$	4.49827	0.262792	0.131396	−	0.991330i	$-0.458054\pi$
$293$	4.49827	0.262792	0.131396	+	0.991330i	$0.458054\pi$
$294$	8.67025	0.505659
$295$	−4.68771	−0.272929
$296$	−2.85623	−0.166015
$297$	7.41119	0.430041
$298$	−1.41358	−0.0818867
$299$	13.9336	0.805802
$300$	2.39181	0.138091
$301$	−8.82908	−0.508900
$302$	−0.801938	−0.0461463
$303$	31.6504	1.81827
$304$	−1.67994	−0.0963512
$305$	−17.1390	−0.981375
$306$	−1.17629	−0.0672441
$307$	0.158834	0.00906511	0.00453256	−	0.999990i	$-0.498557\pi$
$307$	0.158834	0.00906511	0.00453256	+	0.999990i	$0.498557\pi$
$308$	2.02715	0.115507
$309$	−11.5332	−0.656100
$310$	10.1685	0.577533
$311$	22.2935	1.26415	0.632074	−	0.774908i	$-0.282204\pi$
$311$	22.2935	1.26415	0.632074	+	0.774908i	$0.282204\pi$
$312$	14.2567	0.807125
$313$	−29.3467	−1.65878	−0.829388	−	0.558673i	$-0.811311\pi$
$313$	−29.3467	−1.65878	−0.829388	+	0.558673i	$0.811311\pi$
$314$	8.46250	0.477567
$315$	0.603875	0.0340245
$316$	4.58450	0.257898
$317$	−18.4849	−1.03821	−0.519107	−	0.854709i	$-0.673735\pi$
$317$	−18.4849	−1.03821	−0.519107	+	0.854709i	$0.673735\pi$
$318$	7.61356	0.426947
$319$	−13.8291	−0.774280
$320$	−8.71571	−0.487223
$321$	−2.87263	−0.160334
$322$	−3.80194	−0.211874
$323$	17.9782	1.00034
$324$	13.1347	0.729704
$325$	2.87502	0.159477
$326$	18.6015	1.03024
$327$	−26.0640	−1.44134
$328$	2.42865	0.134100
$329$	11.1957	0.617237
$330$	5.27844	0.290568
$331$	−24.4819	−1.34565	−0.672823	−	0.739804i	$-0.734918\pi$
$331$	−24.4819	−1.34565	−0.672823	+	0.739804i	$0.734918\pi$
$332$	5.94869	0.326477
$333$	0.262045	0.0143600
$334$	−12.8998	−0.705844
$335$	−0.590729	−0.0322750
$336$	1.00000	0.0545545
$337$	34.7942	1.89536	0.947680	−	0.319223i	$-0.103422\pi$
$337$	34.7942	1.89536	0.947680	+	0.319223i	$0.103422\pi$
$338$	−3.49827	−0.190281
$339$	5.77240	0.313514
$340$	−19.7036	−1.06858
$341$	−7.74764	−0.419558
$342$	−0.599564	−0.0324207
$343$	13.0000	0.701934
$344$	−23.7681	−1.28149
$345$	20.8877	1.12456
$346$	5.51573	0.296527
$347$	26.2422	1.40875	0.704377	−	0.709826i	$-0.251226\pi$
$347$	26.2422	1.40875	0.704377	+	0.709826i	$0.251226\pi$
$348$	−22.6329	−1.21325
$349$	33.1280	1.77330	0.886650	−	0.462442i	$-0.153027\pi$
$349$	33.1280	1.77330	0.886650	+	0.462442i	$0.153027\pi$
$350$	−0.784479	−0.0419322
$351$	14.5797	0.778207
$352$	8.70841	0.464160
$353$	21.6775	1.15378	0.576890	−	0.816822i	$-0.304266\pi$
$353$	21.6775	1.15378	0.576890	+	0.816822i	$0.304266\pi$
$354$	−2.77048	−0.147249
$355$	−18.6819	−0.991530
$356$	16.2828	0.862984
$357$	−10.7017	−0.566395
$358$	−10.8920	−0.575660
$359$	−14.2959	−0.754509	−0.377254	−	0.926110i	$-0.623132\pi$
$359$	−14.2959	−0.754509	−0.377254	+	0.926110i	$0.623132\pi$
$360$	1.62565	0.0856791
$361$	−9.83638	−0.517704
$362$	−10.9608	−0.576085
$363$	15.7995	0.829261
$364$	3.98792	0.209024
$365$	6.90408	0.361376
$366$	−10.1293	−0.529467
$367$	27.6819	1.44498	0.722491	−	0.691381i	$-0.242997\pi$
$367$	27.6819	1.44498	0.722491	+	0.691381i	$0.242997\pi$
$368$	2.63102	0.137152
$369$	−0.222816	−0.0115994
$370$	−2.08038	−0.108154
$371$	5.26875	0.273540
$372$	−12.6799	−0.657424
$373$	−34.1280	−1.76708	−0.883540	−	0.468357i	$-0.844846\pi$
$373$	−34.1280	−1.76708	−0.883540	+	0.468357i	$0.844846\pi$
$374$	−7.11529	−0.367923
$375$	−17.7192	−0.915014
$376$	30.1390	1.55430
$377$	−27.2054	−1.40115
$378$	−3.97823	−0.204618
$379$	−11.9584	−0.614261	−0.307130	−	0.951667i	$-0.599369\pi$
$379$	−11.9584	−0.614261	−0.307130	+	0.951667i	$0.599369\pi$
$380$	−10.0431	−0.515198
$381$	−39.3303	−2.01495
$382$	13.6407	0.697920
$383$	9.66727	0.493974	0.246987	−	0.969019i	$-0.420559\pi$
$383$	9.66727	0.493974	0.246987	+	0.969019i	$0.420559\pi$
$384$	15.8562	0.809160
$385$	3.65279	0.186164
$386$	−17.3676	−0.883990
$387$	2.18060	0.110846
$388$	−6.88769	−0.349670
$389$	19.8237	1.00510	0.502551	−	0.864548i	$-0.332395\pi$
$389$	19.8237	1.00510	0.502551	+	0.864548i	$0.332395\pi$
$390$	10.3840	0.525816
$391$	−28.1564	−1.42393
$392$	16.1521	0.815806
$393$	−0.268750	−0.0135566
$394$	19.0388	0.959159
$395$	8.26098	0.415655
$396$	−0.500664	−0.0251593
$397$	−6.28919	−0.315646	−0.157823	−	0.987467i	$-0.550447\pi$
$397$	−6.28919	−0.315646	−0.157823	+	0.987467i	$0.550447\pi$
$398$	−19.5778	−0.981346
$399$	−5.45473	−0.273078
$400$	0.542877	0.0271438
$401$	8.75600	0.437254	0.218627	−	0.975809i	$-0.429842\pi$
$401$	8.75600	0.437254	0.218627	+	0.975809i	$0.429842\pi$
$402$	−0.349126	−0.0174128
$403$	−15.2416	−0.759238
$404$	23.8334	1.18576
$405$	23.6679	1.17607
$406$	7.42327	0.368411
$407$	1.58509	0.0785700
$408$	−28.8092	−1.42627
$409$	20.3260	1.00506	0.502529	−	0.864561i	$-0.332403\pi$
$409$	20.3260	1.00506	0.502529	+	0.864561i	$0.332403\pi$
$410$	1.76894	0.0873617
$411$	7.08038	0.349249
$412$	−8.68473	−0.427866
$413$	−1.91723	−0.0943408
$414$	0.939001	0.0461494
$415$	10.7192	0.526183
$416$	17.1317	0.839950
$417$	−10.0978	−0.494493
$418$	−3.62671	−0.177388
$419$	15.2379	0.744419	0.372210	−	0.928149i	$-0.378600\pi$
$419$	15.2379	0.744419	0.372210	+	0.928149i	$0.378600\pi$
$420$	5.97823	0.291708
$421$	19.0325	0.927588	0.463794	−	0.885943i	$-0.346488\pi$
$421$	19.0325	0.927588	0.463794	+	0.885943i	$0.346488\pi$
$422$	−9.60925	−0.467771
$423$	−2.76510	−0.134444
$424$	14.1836	0.688816
$425$	−5.80971	−0.281812
$426$	−11.0411	−0.534945
$427$	−7.00969	−0.339223
$428$	−2.16315	−0.104560
$429$	−7.91185	−0.381988
$430$	−17.3118	−0.834850
$431$	6.29888	0.303406	0.151703	−	0.988426i	$-0.451524\pi$
$431$	6.29888	0.303406	0.151703	+	0.988426i	$0.451524\pi$
$432$	2.75302	0.132455
$433$	−19.8877	−0.955741	−0.477871	−	0.878430i	$-0.658591\pi$
$433$	−19.8877	−0.955741	−0.477871	+	0.878430i	$0.658591\pi$
$434$	4.15883	0.199630
$435$	−40.7832	−1.95540
$436$	−19.6267	−0.939949
$437$	−14.3515	−0.686526
$438$	4.08038	0.194968
$439$	2.30367	0.109948	0.0549740	−	0.998488i	$-0.482492\pi$
$439$	2.30367	0.109948	0.0549740	+	0.998488i	$0.482492\pi$
$440$	9.83340	0.468789
$441$	−1.48188	−0.0705656
$442$	−13.9976	−0.665798
$443$	−22.2204	−1.05572	−0.527862	−	0.849330i	$-0.677006\pi$
$443$	−22.2204	−1.05572	−0.527862	+	0.849330i	$0.677006\pi$
$444$	2.59419	0.123115
$445$	29.3405	1.39087
$446$	−17.5090	−0.829076
$447$	3.17629	0.150233
$448$	−3.56465	−0.168414
$449$	−30.0043	−1.41599	−0.707996	−	0.706217i	$-0.750400\pi$
$449$	−30.0043	−1.41599	−0.707996	+	0.706217i	$0.750400\pi$
$450$	0.193750	0.00913348
$451$	−1.34780	−0.0634653
$452$	4.34673	0.204453
$453$	1.80194	0.0846624
$454$	−17.1424	−0.804535
$455$	7.18598	0.336884
$456$	−14.6843	−0.687653
$457$	−18.1696	−0.849937	−0.424969	−	0.905208i	$-0.639715\pi$
$457$	−18.1696	−0.849937	−0.424969	+	0.905208i	$0.639715\pi$
$458$	3.12737	0.146133
$459$	−29.4620	−1.37517
$460$	15.7289	0.733362
$461$	13.2459	0.616924	0.308462	−	0.951237i	$-0.400186\pi$
$461$	13.2459	0.616924	0.308462	+	0.951237i	$0.400186\pi$
$462$	2.15883	0.100438
$463$	8.72455	0.405464	0.202732	−	0.979234i	$-0.435018\pi$
$463$	8.72455	0.405464	0.202732	+	0.979234i	$0.435018\pi$
$464$	−5.13706	−0.238482
$465$	−22.8485	−1.05957
$466$	8.70948	0.403459
$467$	−0.926328	−0.0428654	−0.0214327	−	0.999770i	$-0.506823\pi$
$467$	−0.926328	−0.0428654	−0.0214327	+	0.999770i	$0.506823\pi$
$468$	−0.984935	−0.0455286
$469$	−0.241603	−0.0111562
$470$	21.9521	1.01258
$471$	−19.0151	−0.876168
$472$	−5.16123	−0.237565
$473$	13.1903	0.606490
$474$	4.88231	0.224252
$475$	−2.96125	−0.135871
$476$	−8.05861	−0.369366
$477$	−1.30127	−0.0595812
$478$	−10.7922	−0.493626
$479$	−5.73663	−0.262113	−0.131057	−	0.991375i	$-0.541837\pi$
$479$	−5.73663	−0.262113	−0.131057	+	0.991375i	$0.541837\pi$
$480$	25.6819	1.17221
$481$	3.11828	0.142181
$482$	−21.0019	−0.956611
$483$	8.54288	0.388714
$484$	11.8974	0.540790
$485$	−12.4112	−0.563563
$486$	2.05323	0.0931364
$487$	4.32065	0.195787	0.0978937	−	0.995197i	$-0.468789\pi$
$487$	4.32065	0.195787	0.0978937	+	0.995197i	$0.468789\pi$
$488$	−18.8702	−0.854215
$489$	−41.7972	−1.89013
$490$	11.7646	0.531472
$491$	−15.1051	−0.681685	−0.340842	−	0.940120i	$-0.610712\pi$
$491$	−15.1051	−0.681685	−0.340842	+	0.940120i	$0.610712\pi$
$492$	−2.20583	−0.0994466
$493$	54.9754	2.47597
$494$	−7.13467	−0.321004
$495$	−0.902165	−0.0405493
$496$	−2.87800	−0.129226
$497$	−7.64071	−0.342733
$498$	6.33513	0.283884
$499$	25.5453	1.14356	0.571782	−	0.820406i	$-0.306252\pi$
$499$	25.5453	1.14356	0.571782	+	0.820406i	$0.306252\pi$
$500$	−13.3429	−0.596712
$501$	28.9855	1.29498
$502$	−18.8737	−0.842374
$503$	41.1148	1.83322	0.916610	−	0.399784i	$-0.130915\pi$
$503$	41.1148	1.83322	0.916610	+	0.399784i	$0.130915\pi$
$504$	0.664874	0.0296159
$505$	42.9463	1.91109
$506$	5.67994	0.252504
$507$	7.86054	0.349099
$508$	−29.6165	−1.31402
$509$	9.88231	0.438026	0.219013	−	0.975722i	$-0.429716\pi$
$509$	9.88231	0.438026	0.219013	+	0.975722i	$0.429716\pi$
$510$	−20.9836	−0.929170
$511$	2.82371	0.124913
$512$	6.22282	0.275012
$513$	−15.0170	−0.663016
$514$	16.3744	0.722242
$515$	−15.6493	−0.689592
$516$	21.5875	0.950336
$517$	−16.7259	−0.735603
$518$	−0.850855	−0.0373844
$519$	−12.3937	−0.544024
$520$	19.3448	0.848326
$521$	16.8987	0.740346	0.370173	−	0.928963i	$-0.379298\pi$
$521$	16.8987	0.740346	0.370173	+	0.928963i	$0.379298\pi$
$522$	−1.83340	−0.0802456
$523$	−23.7429	−1.03820	−0.519101	−	0.854713i	$-0.673733\pi$
$523$	−23.7429	−1.03820	−0.519101	+	0.854713i	$0.673733\pi$
$524$	−0.202374	−0.00884076
$525$	1.76271	0.0769309
$526$	−8.19029	−0.357114
$527$	30.7995	1.34165
$528$	−1.49396	−0.0650162
$529$	−0.523499	−0.0227608
$530$	10.3308	0.448742
$531$	0.473517	0.0205489
$532$	−4.10752	−0.178084
$533$	−2.65146	−0.114848
$534$	17.3405	0.750397
$535$	−3.89785	−0.168519
$536$	−0.650400	−0.0280930
$537$	24.4741	1.05614
$538$	20.3405	0.876941
$539$	−8.96376	−0.386096
$540$	16.4582	0.708248
$541$	12.0325	0.517319	0.258659	−	0.965969i	$-0.416719\pi$
$541$	12.0325	0.517319	0.258659	+	0.965969i	$0.416719\pi$
$542$	12.2547	0.526387
$543$	24.6286	1.05692
$544$	−34.6189	−1.48427
$545$	−35.3661	−1.51492
$546$	4.24698	0.181754
$547$	4.79656	0.205086	0.102543	−	0.994729i	$-0.467302\pi$
$547$	4.79656	0.205086	0.102543	+	0.994729i	$0.467302\pi$
$548$	5.33167	0.227758
$549$	1.73125	0.0738880
$550$	1.17198	0.0499734
$551$	28.0213	1.19375
$552$	22.9976	0.978843
$553$	3.37867	0.143675
$554$	−14.9608	−0.635622
$555$	4.67456	0.198424
$556$	−7.60388	−0.322476
$557$	−25.2911	−1.07162	−0.535809	−	0.844339i	$-0.679993\pi$
$557$	−25.2911	−1.07162	−0.535809	+	0.844339i	$0.679993\pi$
$558$	−1.02715	−0.0434826
$559$	25.9487	1.09751
$560$	1.35690	0.0573393
$561$	15.9879	0.675010
$562$	−14.9618	−0.631127
$563$	28.6926	1.20925	0.604625	−	0.796510i	$-0.293323\pi$
$563$	28.6926	1.20925	0.604625	+	0.796510i	$0.293323\pi$
$564$	−27.3739	−1.15265
$565$	7.83254	0.329518
$566$	−15.3937	−0.647047
$567$	9.67994	0.406519
$568$	−20.5690	−0.863054
$569$	−16.1987	−0.679083	−0.339541	−	0.940591i	$-0.610272\pi$
$569$	−16.1987	−0.679083	−0.339541	+	0.940591i	$0.610272\pi$
$570$	−10.6955	−0.447984
$571$	19.3840	0.811197	0.405598	−	0.914051i	$-0.367063\pi$
$571$	19.3840	0.811197	0.405598	+	0.914051i	$0.367063\pi$
$572$	−5.95779	−0.249108
$573$	−30.6504	−1.28044
$574$	0.723480	0.0301975
$575$	4.63773	0.193407
$576$	0.880395	0.0366831
$577$	8.94007	0.372180	0.186090	−	0.982533i	$-0.440418\pi$
$577$	8.94007	0.372180	0.186090	+	0.982533i	$0.440418\pi$
$578$	14.6528	0.609476
$579$	39.0248	1.62181
$580$	−30.7105	−1.27519
$581$	4.38404	0.181881
$582$	−7.33513	−0.304051
$583$	−7.87130	−0.325996
$584$	7.60148	0.314552
$585$	−1.77479	−0.0733786
$586$	3.60733	0.149018
$587$	−31.4862	−1.29957	−0.649787	−	0.760116i	$-0.725142\pi$
$587$	−31.4862	−1.29957	−0.649787	+	0.760116i	$0.725142\pi$
$588$	−14.6703	−0.604991
$589$	15.6987	0.646855
$590$	−3.75925	−0.154766
$591$	−42.7797	−1.75972
$592$	0.588810	0.0241999
$593$	22.6383	0.929644	0.464822	−	0.885404i	$-0.346118\pi$
$593$	22.6383	0.929644	0.464822	+	0.885404i	$0.346118\pi$
$594$	5.94331	0.243857
$595$	−14.5211	−0.595307
$596$	2.39181	0.0979725
$597$	43.9909	1.80043
$598$	11.1739	0.456935
$599$	−13.6853	−0.559167	−0.279583	−	0.960121i	$-0.590196\pi$
$599$	−13.6853	−0.559167	−0.279583	+	0.960121i	$0.590196\pi$
$600$	4.74525	0.193724
$601$	−19.5730	−0.798400	−0.399200	−	0.916864i	$-0.630712\pi$
$601$	−19.5730	−0.798400	−0.399200	+	0.916864i	$0.630712\pi$
$602$	−7.08038	−0.288575
$603$	0.0596710	0.00242999
$604$	1.35690	0.0552113
$605$	21.4383	0.871592
$606$	25.3817	1.03106
$607$	18.0446	0.732408	0.366204	−	0.930535i	$-0.380657\pi$
$607$	18.0446	0.732408	0.366204	+	0.930535i	$0.380657\pi$
$608$	−17.6455	−0.715619
$609$	−16.6799	−0.675905
$610$	−13.7444	−0.556494
$611$	−32.9041	−1.33116
$612$	1.99031	0.0804536
$613$	−4.25965	−0.172046	−0.0860229	−	0.996293i	$-0.527416\pi$
$613$	−4.25965	−0.172046	−0.0860229	+	0.996293i	$0.527416\pi$
$614$	0.127375	0.00514042
$615$	−3.97477	−0.160278
$616$	4.02177	0.162042
$617$	29.9071	1.20401	0.602007	−	0.798491i	$-0.294368\pi$
$617$	29.9071	1.20401	0.602007	+	0.798491i	$0.294368\pi$
$618$	−9.24890	−0.372045
$619$	−9.44935	−0.379802	−0.189901	−	0.981803i	$-0.560817\pi$
$619$	−9.44935	−0.379802	−0.189901	+	0.981803i	$0.560817\pi$
$620$	−17.2054	−0.690984
$621$	23.5187	0.943773
$622$	17.8780	0.716843
$623$	12.0000	0.480770
$624$	−2.93900	−0.117654
$625$	−28.9342	−1.15737
$626$	−23.5343	−0.940618
$627$	8.14914	0.325446
$628$	−14.3187	−0.571380
$629$	−6.30127	−0.251248
$630$	0.484271	0.0192938
$631$	29.3086	1.16676	0.583378	−	0.812201i	$-0.301731\pi$
$631$	29.3086	1.16676	0.583378	+	0.812201i	$0.301731\pi$
$632$	9.09544	0.361797
$633$	21.5918	0.858197
$634$	−14.8237	−0.588725
$635$	−53.3672	−2.11781
$636$	−12.8823	−0.510817
$637$	−17.6340	−0.698685
$638$	−11.0901	−0.439060
$639$	1.88710	0.0746525
$640$	21.5153	0.850465
$641$	18.1836	0.718209	0.359104	−	0.933297i	$-0.383082\pi$
$641$	18.1836	0.718209	0.359104	+	0.933297i	$0.383082\pi$
$642$	−2.30367	−0.0909185
$643$	8.31096	0.327752	0.163876	−	0.986481i	$-0.447600\pi$
$643$	8.31096	0.327752	0.163876	+	0.986481i	$0.447600\pi$
$644$	6.43296	0.253494
$645$	38.8993	1.53166
$646$	14.4174	0.567246
$647$	−17.7192	−0.696612	−0.348306	−	0.937381i	$-0.613243\pi$
$647$	−17.7192	−0.696612	−0.348306	+	0.937381i	$0.613243\pi$
$648$	26.0586	1.02368
$649$	2.86426	0.112432
$650$	2.30559	0.0904325
$651$	−9.34481	−0.366252
$652$	−31.4741	−1.23262
$653$	13.1943	0.516334	0.258167	−	0.966100i	$-0.416881\pi$
$653$	13.1943	0.516334	0.258167	+	0.966100i	$0.416881\pi$
$654$	−20.9017	−0.817321
$655$	−0.364666	−0.0142487
$656$	−0.500664	−0.0195476
$657$	−0.697398	−0.0272081
$658$	8.97823	0.350008
$659$	7.70948	0.300319	0.150159	−	0.988662i	$-0.452021\pi$
$659$	7.70948	0.300319	0.150159	+	0.988662i	$0.452021\pi$
$660$	−8.93123	−0.347648
$661$	35.6413	1.38629	0.693143	−	0.720800i	$-0.256225\pi$
$661$	35.6413	1.38629	0.693143	+	0.720800i	$0.256225\pi$
$662$	−19.6329	−0.763056
$663$	31.4523	1.22151
$664$	11.8019	0.458004
$665$	−7.40150	−0.287018
$666$	0.210144	0.00814291
$667$	−43.8853	−1.69925
$668$	21.8267	0.844500
$669$	39.3424	1.52107
$670$	−0.473728	−0.0183017
$671$	10.4722	0.404274
$672$	10.5036	0.405187
$673$	36.9995	1.42623	0.713113	−	0.701049i	$-0.247284\pi$
$673$	36.9995	1.42623	0.713113	+	0.701049i	$0.247284\pi$
$674$	27.9028	1.07477
$675$	4.85277	0.186783
$676$	5.91915	0.227660
$677$	7.98121	0.306743	0.153371	−	0.988169i	$-0.450987\pi$
$677$	7.98121	0.306743	0.153371	+	0.988169i	$0.450987\pi$
$678$	4.62910	0.177780
$679$	−5.07606	−0.194801
$680$	−39.0911	−1.49908
$681$	38.5187	1.47604
$682$	−6.21313	−0.237913
$683$	2.76569	0.105826	0.0529132	−	0.998599i	$-0.483149\pi$
$683$	2.76569	0.105826	0.0529132	+	0.998599i	$0.483149\pi$
$684$	1.01447	0.0387894
$685$	9.60733	0.367077
$686$	10.4252	0.398036
$687$	−7.02715	−0.268102
$688$	4.89977	0.186802
$689$	−15.4849	−0.589926
$690$	16.7506	0.637685
$691$	7.13169	0.271302	0.135651	−	0.990757i	$-0.456687\pi$
$691$	7.13169	0.271302	0.135651	+	0.990757i	$0.456687\pi$
$692$	−9.33273	−0.354777
$693$	−0.368977	−0.0140163
$694$	21.0446	0.798842
$695$	−13.7017	−0.519735
$696$	−44.9028	−1.70203
$697$	5.35796	0.202947
$698$	26.5666	1.00556
$699$	−19.5700	−0.740206
$700$	1.32736	0.0501693
$701$	−39.8592	−1.50546	−0.752731	−	0.658328i	$-0.771264\pi$
$701$	−39.8592	−1.50546	−0.752731	+	0.658328i	$0.771264\pi$
$702$	11.6920	0.441287
$703$	−3.21180	−0.121135
$704$	5.32544	0.200710
$705$	−49.3260	−1.85773
$706$	17.3840	0.654257
$707$	17.5646	0.660587
$708$	4.68771	0.176175
$709$	−10.7108	−0.402253	−0.201126	−	0.979565i	$-0.564460\pi$
$709$	−10.7108	−0.402253	−0.201126	+	0.979565i	$0.564460\pi$
$710$	−14.9817	−0.562253
$711$	−0.834462	−0.0312948
$712$	32.3043	1.21065
$713$	−24.5864	−0.920769
$714$	−8.58211	−0.321177
$715$	−10.7356	−0.401487
$716$	18.4295	0.688743
$717$	24.2500	0.905631
$718$	−11.4644	−0.427848
$719$	−25.6213	−0.955515	−0.477757	−	0.878492i	$-0.658550\pi$
$719$	−25.6213	−0.955515	−0.477757	+	0.878492i	$0.658550\pi$
$720$	−0.335126	−0.0124894
$721$	−6.40044	−0.238365
$722$	−7.88816	−0.293567
$723$	47.1909	1.75505
$724$	18.5459	0.689251
$725$	−9.05515	−0.336300
$726$	12.6703	0.470237
$727$	−42.3317	−1.56999	−0.784997	−	0.619499i	$-0.787336\pi$
$727$	−42.3317	−1.56999	−0.784997	+	0.619499i	$0.787336\pi$
$728$	7.91185	0.293233
$729$	24.4263	0.904676
$730$	5.53665	0.204920
$731$	−52.4359	−1.93941
$732$	17.1390	0.633475
$733$	−28.7362	−1.06139	−0.530697	−	0.847562i	$-0.678070\pi$
$733$	−28.7362	−1.06139	−0.530697	+	0.847562i	$0.678070\pi$
$734$	22.1991	0.819385
$735$	−26.4349	−0.975065
$736$	27.6353	1.01865
$737$	0.360945	0.0132956
$738$	−0.178685	−0.00657748
$739$	−36.7114	−1.35045	−0.675225	−	0.737612i	$-0.735954\pi$
$739$	−36.7114	−1.35045	−0.675225	+	0.737612i	$0.735954\pi$
$740$	3.52004	0.129399
$741$	16.0315	0.588930
$742$	4.22521	0.155112
$743$	−30.9560	−1.13566	−0.567832	−	0.823144i	$-0.692218\pi$
$743$	−30.9560	−1.13566	−0.567832	+	0.823144i	$0.692218\pi$
$744$	−25.1564	−0.922280
$745$	4.30990	0.157902
$746$	−27.3685	−1.00203
$747$	−1.08277	−0.0396165
$748$	12.0392	0.440198
$749$	−1.59419	−0.0582503
$750$	−14.2097	−0.518864
$751$	−45.7778	−1.67045	−0.835227	−	0.549905i	$-0.814664\pi$
$751$	−45.7778	−1.67045	−0.835227	+	0.549905i	$0.814664\pi$
$752$	−6.21313	−0.226569
$753$	42.4088	1.54546
$754$	−21.8170	−0.794528
$755$	2.44504	0.0889842
$756$	6.73125	0.244813
$757$	−37.4403	−1.36079	−0.680395	−	0.732846i	$-0.738192\pi$
$757$	−37.4403	−1.36079	−0.680395	+	0.732846i	$0.738192\pi$
$758$	−9.58987	−0.348320
$759$	−12.7627	−0.463257
$760$	−19.9250	−0.722756
$761$	−29.1709	−1.05744	−0.528722	−	0.848795i	$-0.677329\pi$
$761$	−29.1709	−1.05744	−0.528722	+	0.848795i	$0.677329\pi$
$762$	−31.5405	−1.14259
$763$	−14.4644	−0.523647
$764$	−23.0804	−0.835019
$765$	3.58642	0.129667
$766$	7.75255	0.280111
$767$	5.63474	0.203459
$768$	25.5623	0.922398
$769$	−31.7058	−1.14334	−0.571669	−	0.820484i	$-0.693704\pi$
$769$	−31.7058	−1.14334	−0.571669	+	0.820484i	$0.693704\pi$
$770$	2.92931	0.105565
$771$	−36.7928	−1.32506
$772$	29.3864	1.05764
$773$	19.1250	0.687878	0.343939	−	0.938992i	$-0.388239\pi$
$773$	19.1250	0.687878	0.343939	+	0.938992i	$0.388239\pi$
$774$	1.74871	0.0628560
$775$	−5.07308	−0.182230
$776$	−13.6649	−0.490540
$777$	1.91185	0.0685874
$778$	15.8974	0.569949
$779$	2.73099	0.0978478
$780$	−17.5700	−0.629108
$781$	11.4149	0.408458
$782$	−22.5797	−0.807449
$783$	−45.9202	−1.64105
$784$	−3.32975	−0.118920
$785$	−25.8015	−0.920894
$786$	−0.215521	−0.00768737
$787$	−23.0164	−0.820446	−0.410223	−	0.911985i	$-0.634549\pi$
$787$	−23.0164	−0.820446	−0.410223	+	0.911985i	$0.634549\pi$
$788$	−32.2140	−1.14758
$789$	18.4034	0.655179
$790$	6.62479	0.235700
$791$	3.20344	0.113901
$792$	−0.993295	−0.0352952
$793$	20.6015	0.731580
$794$	−5.04354	−0.178989
$795$	−23.2131	−0.823285
$796$	33.1260	1.17412
$797$	−16.6920	−0.591262	−0.295631	−	0.955302i	$-0.595530\pi$
$797$	−16.6920	−0.591262	−0.295631	+	0.955302i	$0.595530\pi$
$798$	−4.37435	−0.154850
$799$	66.4911	2.35229
$800$	5.70218	0.201603
$801$	−2.96376	−0.104719
$802$	7.02177	0.247947
$803$	−4.21850	−0.148868
$804$	0.590729	0.0208334
$805$	11.5918	0.408557
$806$	−12.2228	−0.430530
$807$	−45.7047	−1.60888
$808$	47.2844	1.66346
$809$	20.8509	0.733077	0.366539	−	0.930403i	$-0.380543\pi$
$809$	20.8509	0.733077	0.366539	+	0.930403i	$0.380543\pi$
$810$	18.9801	0.666894
$811$	38.7603	1.36106	0.680529	−	0.732721i	$-0.261750\pi$
$811$	38.7603	1.36106	0.680529	+	0.732721i	$0.261750\pi$
$812$	−12.5603	−0.440781
$813$	−27.5362	−0.965736
$814$	1.27114	0.0445535
$815$	−56.7144	−1.98662
$816$	5.93900	0.207907
$817$	−26.7269	−0.935057
$818$	16.3002	0.569923
$819$	−0.725873	−0.0253641
$820$	−2.99308	−0.104523
$821$	−30.5297	−1.06549	−0.532747	−	0.846274i	$-0.678840\pi$
$821$	−30.5297	−1.06549	−0.532747	+	0.846274i	$0.678840\pi$
$822$	5.67802	0.198044
$823$	12.9119	0.450079	0.225039	−	0.974350i	$-0.427749\pi$
$823$	12.9119	0.450079	0.225039	+	0.974350i	$0.427749\pi$
$824$	−17.2301	−0.600239
$825$	−2.63342	−0.0916838
$826$	−1.53750	−0.0534965
$827$	−23.8442	−0.829142	−0.414571	−	0.910017i	$-0.636068\pi$
$827$	−23.8442	−0.829142	−0.414571	+	0.910017i	$0.636068\pi$
$828$	−1.58881	−0.0552150
$829$	14.8039	0.514159	0.257080	−	0.966390i	$-0.417240\pi$
$829$	14.8039	0.514159	0.257080	+	0.966390i	$0.417240\pi$
$830$	8.59611	0.298375
$831$	33.6165	1.16615
$832$	10.4765	0.363207
$833$	35.6340	1.23465
$834$	−8.09783	−0.280405
$835$	39.3303	1.36108
$836$	6.13647	0.212234
$837$	−25.7265	−0.889237
$838$	12.2198	0.422127
$839$	28.8060	0.994493	0.497247	−	0.867609i	$-0.334344\pi$
$839$	28.8060	0.994493	0.497247	+	0.867609i	$0.334344\pi$
$840$	11.8605	0.409228
$841$	56.6859	1.95469
$842$	15.2629	0.525994
$843$	33.6189	1.15790
$844$	16.2591	0.559660
$845$	10.6659	0.366919
$846$	−2.21744	−0.0762371
$847$	8.76809	0.301275
$848$	−2.92394	−0.100408
$849$	34.5894	1.18711
$850$	−4.65902	−0.159803
$851$	5.03013	0.172431
$852$	18.6819	0.640030
$853$	−13.3400	−0.456754	−0.228377	−	0.973573i	$-0.573342\pi$
$853$	−13.3400	−0.456754	−0.228377	+	0.973573i	$0.573342\pi$
$854$	−5.62133	−0.192358
$855$	1.82802	0.0625170
$856$	−4.29159	−0.146683
$857$	−3.03816	−0.103782	−0.0518908	−	0.998653i	$-0.516525\pi$
$857$	−3.03816	−0.103782	−0.0518908	+	0.998653i	$0.516525\pi$
$858$	−6.34481	−0.216608
$859$	31.6872	1.08115	0.540577	−	0.841294i	$-0.318206\pi$
$859$	31.6872	1.08115	0.540577	+	0.841294i	$0.318206\pi$
$860$	29.2920	0.998848
$861$	−1.62565	−0.0554019
$862$	5.05131	0.172048
$863$	−1.22713	−0.0417719	−0.0208860	−	0.999782i	$-0.506649\pi$
$863$	−1.22713	−0.0417719	−0.0208860	+	0.999782i	$0.506649\pi$
$864$	28.9168	0.983768
$865$	−16.8170	−0.571795
$866$	−15.9487	−0.541959
$867$	−32.9245	−1.11818
$868$	−7.03684	−0.238846
$869$	−5.04759	−0.171228
$870$	−32.7055	−1.10882
$871$	0.710071	0.0240598
$872$	−38.9385	−1.31862
$873$	1.25368	0.0424308
$874$	−11.5090	−0.389299
$875$	−9.83340	−0.332429
$876$	−6.90408	−0.233267
$877$	−31.3067	−1.05715	−0.528575	−	0.848886i	$-0.677274\pi$
$877$	−31.3067	−1.05715	−0.528575	+	0.848886i	$0.677274\pi$
$878$	1.84740	0.0623466
$879$	−8.10560	−0.273395
$880$	−2.02715	−0.0683351
$881$	−34.8931	−1.17558	−0.587789	−	0.809015i	$-0.700001\pi$
$881$	−34.8931	−1.17558	−0.587789	+	0.809015i	$0.700001\pi$
$882$	−1.18837	−0.0400146
$883$	−1.68100	−0.0565703	−0.0282852	−	0.999600i	$-0.509005\pi$
$883$	−1.68100	−0.0565703	−0.0282852	+	0.999600i	$0.509005\pi$
$884$	23.6843	0.796588
$885$	8.44696	0.283941
$886$	−17.8194	−0.598654
$887$	40.1739	1.34891	0.674454	−	0.738317i	$-0.264379\pi$
$887$	40.1739	1.34891	0.674454	+	0.738317i	$0.264379\pi$
$888$	5.14675	0.172714
$889$	−21.8267	−0.732044
$890$	23.5293	0.788702
$891$	−14.4614	−0.484476
$892$	29.6256	0.991940
$893$	33.8909	1.13412
$894$	2.54719	0.0851907
$895$	33.2088	1.11005
$896$	8.79954	0.293972
$897$	−25.1075	−0.838316
$898$	−24.0616	−0.802946
$899$	48.0049	1.60105
$900$	−0.327830	−0.0109277
$901$	31.2911	1.04246
$902$	−1.08085	−0.0359884
$903$	15.9095	0.529434
$904$	8.62373	0.286821
$905$	33.4185	1.11087
$906$	1.44504	0.0480083
$907$	−16.2064	−0.538125	−0.269063	−	0.963123i	$-0.586714\pi$
$907$	−16.2064	−0.538125	−0.269063	+	0.963123i	$0.586714\pi$
$908$	29.0054	0.962577
$909$	−4.33811	−0.143886
$910$	5.76271	0.191032
$911$	23.9288	0.792798	0.396399	−	0.918078i	$-0.370260\pi$
$911$	23.9288	0.792798	0.396399	+	0.918078i	$0.370260\pi$
$912$	3.02715	0.100239
$913$	−6.54958	−0.216760
$914$	−14.5709	−0.481962
$915$	30.8834	1.02097
$916$	−5.29159	−0.174839
$917$	−0.149145	−0.00492520
$918$	−23.6267	−0.779798
$919$	7.24698	0.239056	0.119528	−	0.992831i	$-0.461862\pi$
$919$	7.24698	0.239056	0.119528	+	0.992831i	$0.461862\pi$
$920$	31.2054	1.02881
$921$	−0.286208	−0.00943088
$922$	10.6224	0.349830
$923$	22.4561	0.739150
$924$	−3.65279	−0.120168
$925$	1.03790	0.0341260
$926$	6.99654	0.229921
$927$	1.58078	0.0519195
$928$	−53.9579	−1.77125
$929$	−13.5302	−0.443912	−0.221956	−	0.975057i	$-0.571244\pi$
$929$	−13.5302	−0.443912	−0.221956	+	0.975057i	$0.571244\pi$
$930$	−18.3230	−0.600836
$931$	18.1629	0.595264
$932$	−14.7366	−0.482714
$933$	−40.1715	−1.31516
$934$	−0.742858	−0.0243070
$935$	21.6939	0.709468
$936$	−1.95407	−0.0638707
$937$	−22.8412	−0.746188	−0.373094	−	0.927793i	$-0.621703\pi$
$937$	−22.8412	−0.746188	−0.373094	+	0.927793i	$0.621703\pi$
$938$	−0.193750	−0.00632617
$939$	52.8810	1.72571
$940$	−37.1435	−1.21149
$941$	36.4566	1.18845	0.594226	−	0.804298i	$-0.297458\pi$
$941$	36.4566	1.18845	0.594226	+	0.804298i	$0.297458\pi$
$942$	−15.2489	−0.496836
$943$	−4.27711	−0.139282
$944$	1.06398	0.0346297
$945$	12.1293	0.394566
$946$	10.5778	0.343914
$947$	−27.8528	−0.905094	−0.452547	−	0.891741i	$-0.649484\pi$
$947$	−27.8528	−0.905094	−0.452547	+	0.891741i	$0.649484\pi$
$948$	−8.26098	−0.268304
$949$	−8.29888	−0.269393
$950$	−2.37473	−0.0770466
$951$	33.3086	1.08010
$952$	−15.9879	−0.518171
$953$	−45.1667	−1.46309	−0.731547	−	0.681791i	$-0.761201\pi$
$953$	−45.1667	−1.46309	−0.731547	+	0.681791i	$0.761201\pi$
$954$	−1.04354	−0.0337859
$955$	−41.5894	−1.34580
$956$	18.2607	0.590594
$957$	24.9191	0.805522
$958$	−4.60042	−0.148633
$959$	3.92931	0.126884
$960$	15.7052	0.506882
$961$	−4.10560	−0.132439
$962$	2.50066	0.0806246
$963$	0.393732	0.0126878
$964$	35.5357	1.14453
$965$	52.9525	1.70460
$966$	6.85086	0.220423
$967$	10.1860	0.327559	0.163780	−	0.986497i	$-0.447631\pi$
$967$	10.1860	0.327559	0.163780	+	0.986497i	$0.447631\pi$
$968$	23.6039	0.758657
$969$	−32.3957	−1.04070
$970$	−9.95300	−0.319572
$971$	34.1651	1.09641	0.548205	−	0.836344i	$-0.315312\pi$
$971$	34.1651	1.09641	0.548205	+	0.836344i	$0.315312\pi$
$972$	−3.47411	−0.111432
$973$	−5.60388	−0.179652
$974$	3.46489	0.111022
$975$	−5.18060	−0.165912
$976$	3.89008	0.124519
$977$	−32.8183	−1.04995	−0.524976	−	0.851117i	$-0.675926\pi$
$977$	−32.8183	−1.04995	−0.524976	+	0.851117i	$0.675926\pi$
$978$	−33.5187	−1.07181
$979$	−17.9275	−0.572966
$980$	−19.9060	−0.635874
$981$	3.57242	0.114058
$982$	−12.1134	−0.386553
$983$	27.6877	0.883101	0.441550	−	0.897236i	$-0.354429\pi$
$983$	27.6877	0.883101	0.441550	+	0.897236i	$0.354429\pi$
$984$	−4.37627	−0.139510
$985$	−58.0476	−1.84955
$986$	44.0868	1.40401
$987$	−20.1739	−0.642142
$988$	12.0720	0.384062
$989$	41.8582	1.33101
$990$	−0.723480	−0.0229937
$991$	38.5888	1.22581	0.612907	−	0.790155i	$-0.290000\pi$
$991$	38.5888	1.22581	0.612907	+	0.790155i	$0.290000\pi$
$992$	−30.2295	−0.959788
$993$	44.1148	1.39994
$994$	−6.12737	−0.194349
$995$	59.6911	1.89233
$996$	−10.7192	−0.339650
$997$	2.14244	0.0678518	0.0339259	−	0.999424i	$-0.489199\pi$
$997$	2.14244	0.0678518	0.0339259	+	0.999424i	$0.489199\pi$
$998$	20.4857	0.648464
$999$	5.26337	0.166526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.a.a.1.3	✓	3
3.2	odd	2		1359.2.a.g.1.1		3
4.3	odd	2		2416.2.a.h.1.3		3
5.4	even	2		3775.2.a.k.1.1		3
7.6	odd	2		7399.2.a.b.1.3		3
8.3	odd	2		9664.2.a.p.1.1		3
8.5	even	2		9664.2.a.t.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.a.a.1.3	✓	3	1.1	even	1	trivial
1359.2.a.g.1.1		3	3.2	odd	2
2416.2.a.h.1.3		3	4.3	odd	2
3775.2.a.k.1.1		3	5.4	even	2
7399.2.a.b.1.3		3	7.6	odd	2
9664.2.a.p.1.1		3	8.3	odd	2
9664.2.a.t.1.3		3	8.5	even	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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.a (trivial)

\(f(q)\)	\(=\)	\(q+0.801938 q^{2} -1.80194 q^{3} -1.35690 q^{4} -2.44504 q^{5} -1.44504 q^{6} -1.00000 q^{7} -2.69202 q^{8} +0.246980 q^{9} +O(q^{10})\)	\(q+0.801938 q^{2} -1.80194 q^{3} -1.35690 q^{4} -2.44504 q^{5} -1.44504 q^{6} -1.00000 q^{7} -2.69202 q^{8} +0.246980 q^{9} -1.96077 q^{10} +1.49396 q^{11} +2.44504 q^{12} +2.93900 q^{13} -0.801938 q^{14} +4.40581 q^{15} +0.554958 q^{16} -5.93900 q^{17} +0.198062 q^{18} -3.02715 q^{19} +3.31767 q^{20} +1.80194 q^{21} +1.19806 q^{22} +4.74094 q^{23} +4.85086 q^{24} +0.978230 q^{25} +2.35690 q^{26} +4.96077 q^{27} +1.35690 q^{28} -9.25667 q^{29} +3.53319 q^{30} -5.18598 q^{31} +5.82908 q^{32} -2.69202 q^{33} -4.76271 q^{34} +2.44504 q^{35} -0.335126 q^{36} +1.06100 q^{37} -2.42758 q^{38} -5.29590 q^{39} +6.58211 q^{40} -0.902165 q^{41} +1.44504 q^{42} +8.82908 q^{43} -2.02715 q^{44} -0.603875 q^{45} +3.80194 q^{46} -11.1957 q^{47} -1.00000 q^{48} -6.00000 q^{49} +0.784479 q^{50} +10.7017 q^{51} -3.98792 q^{52} -5.26875 q^{53} +3.97823 q^{54} -3.65279 q^{55} +2.69202 q^{56} +5.45473 q^{57} -7.42327 q^{58} +1.91723 q^{59} -5.97823 q^{60} +7.00969 q^{61} -4.15883 q^{62} -0.246980 q^{63} +3.56465 q^{64} -7.18598 q^{65} -2.15883 q^{66} +0.241603 q^{67} +8.05861 q^{68} -8.54288 q^{69} +1.96077 q^{70} +7.64071 q^{71} -0.664874 q^{72} -2.82371 q^{73} +0.850855 q^{74} -1.76271 q^{75} +4.10752 q^{76} -1.49396 q^{77} -4.24698 q^{78} -3.37867 q^{79} -1.35690 q^{80} -9.67994 q^{81} -0.723480 q^{82} -4.38404 q^{83} -2.44504 q^{84} +14.5211 q^{85} +7.08038 q^{86} +16.6799 q^{87} -4.02177 q^{88} -12.0000 q^{89} -0.484271 q^{90} -2.93900 q^{91} -6.43296 q^{92} +9.34481 q^{93} -8.97823 q^{94} +7.40150 q^{95} -10.5036 q^{96} +5.07606 q^{97} -4.81163 q^{98} +0.368977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - q^{3} - 7 q^{5} - 4 q^{6} - 3 q^{7} - 3 q^{8} - 4 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - q^3 - 7 * q^5 - 4 * q^6 - 3 * q^7 - 3 * q^8 - 4 * q^9	\( 3 q - 2 q^{2} - q^{3} - 7 q^{5} - 4 q^{6} - 3 q^{7} - 3 q^{8} - 4 q^{9} + 7 q^{10} - 5 q^{11} + 7 q^{12} - q^{13} + 2 q^{14} + 2 q^{16} - 8 q^{17} + 5 q^{18} - 3 q^{19} - 7 q^{20} + q^{21} + 8 q^{22} + q^{24} + 6 q^{25} + 3 q^{26} + 2 q^{27} - q^{29} + 14 q^{30} - q^{31} + 7 q^{32} - 3 q^{33} + 3 q^{34} + 7 q^{35} + 13 q^{37} + 9 q^{38} - 2 q^{39} + 14 q^{40} - 21 q^{41} + 4 q^{42} + 16 q^{43} + 7 q^{45} + 7 q^{46} + 3 q^{47} - 3 q^{48} - 18 q^{49} - 18 q^{50} + 5 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{54} + 7 q^{55} + 3 q^{56} - 6 q^{57} - 25 q^{58} - q^{59} - 21 q^{60} - q^{61} - 4 q^{62} + 4 q^{63} - 11 q^{64} - 7 q^{65} + 2 q^{66} - q^{67} - 7 q^{68} - 7 q^{69} - 7 q^{70} - 14 q^{71} - 3 q^{72} - q^{73} - 11 q^{74} + 12 q^{75} - 28 q^{76} + 5 q^{77} - 8 q^{78} - 3 q^{79} - 5 q^{81} + 28 q^{82} - 3 q^{83} - 7 q^{84} + 28 q^{85} - 13 q^{86} + 26 q^{87} - 9 q^{88} - 36 q^{89} - 14 q^{90} + q^{91} + 5 q^{93} - 30 q^{94} + 28 q^{95} + 12 q^{98} + 16 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - q^3 - 7 * q^5 - 4 * q^6 - 3 * q^7 - 3 * q^8 - 4 * q^9 + 7 * q^10 - 5 * q^11 + 7 * q^12 - q^13 + 2 * q^14 + 2 * q^16 - 8 * q^17 + 5 * q^18 - 3 * q^19 - 7 * q^20 + q^21 + 8 * q^22 + q^24 + 6 * q^25 + 3 * q^26 + 2 * q^27 - q^29 + 14 * q^30 - q^31 + 7 * q^32 - 3 * q^33 + 3 * q^34 + 7 * q^35 + 13 * q^37 + 9 * q^38 - 2 * q^39 + 14 * q^40 - 21 * q^41 + 4 * q^42 + 16 * q^43 + 7 * q^45 + 7 * q^46 + 3 * q^47 - 3 * q^48 - 18 * q^49 - 18 * q^50 + 5 * q^51 + 7 * q^52 - 8 * q^53 + 15 * q^54 + 7 * q^55 + 3 * q^56 - 6 * q^57 - 25 * q^58 - q^59 - 21 * q^60 - q^61 - 4 * q^62 + 4 * q^63 - 11 * q^64 - 7 * q^65 + 2 * q^66 - q^67 - 7 * q^68 - 7 * q^69 - 7 * q^70 - 14 * q^71 - 3 * q^72 - q^73 - 11 * q^74 + 12 * q^75 - 28 * q^76 + 5 * q^77 - 8 * q^78 - 3 * q^79 - 5 * q^81 + 28 * q^82 - 3 * q^83 - 7 * q^84 + 28 * q^85 - 13 * q^86 + 26 * q^87 - 9 * q^88 - 36 * q^89 - 14 * q^90 + q^91 + 5 * q^93 - 30 * q^94 + 28 * q^95 + 12 * q^98 + 16 * q^99

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