LMFDB - Embedded newform 731.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02811 q^{2} +1.50881 q^{3} +2.11322 q^{4} -1.59736 q^{5} +3.06003 q^{6} +3.53856 q^{7} +0.229620 q^{8} -0.723487 q^{9} +O(q^{10})$	\(q+2.02811 q^{2} +1.50881 q^{3} +2.11322 q^{4} -1.59736 q^{5} +3.06003 q^{6} +3.53856 q^{7} +0.229620 q^{8} -0.723487 q^{9} -3.23961 q^{10} +1.43007 q^{11} +3.18845 q^{12} +5.59997 q^{13} +7.17658 q^{14} -2.41011 q^{15} -3.76074 q^{16} -1.00000 q^{17} -1.46731 q^{18} +2.55708 q^{19} -3.37557 q^{20} +5.33902 q^{21} +2.90034 q^{22} -1.05900 q^{23} +0.346454 q^{24} -2.44845 q^{25} +11.3573 q^{26} -5.61804 q^{27} +7.47775 q^{28} +1.56752 q^{29} -4.88797 q^{30} +3.98716 q^{31} -8.08643 q^{32} +2.15771 q^{33} -2.02811 q^{34} -5.65235 q^{35} -1.52889 q^{36} -11.5853 q^{37} +5.18604 q^{38} +8.44930 q^{39} -0.366786 q^{40} +4.17484 q^{41} +10.8281 q^{42} +1.00000 q^{43} +3.02206 q^{44} +1.15567 q^{45} -2.14777 q^{46} -12.3512 q^{47} -5.67425 q^{48} +5.52141 q^{49} -4.96571 q^{50} -1.50881 q^{51} +11.8340 q^{52} -12.7376 q^{53} -11.3940 q^{54} -2.28434 q^{55} +0.812525 q^{56} +3.85816 q^{57} +3.17910 q^{58} +8.88790 q^{59} -5.09310 q^{60} -4.99882 q^{61} +8.08638 q^{62} -2.56010 q^{63} -8.87866 q^{64} -8.94516 q^{65} +4.37607 q^{66} +9.04283 q^{67} -2.11322 q^{68} -1.59783 q^{69} -11.4636 q^{70} +0.338375 q^{71} -0.166127 q^{72} -8.43965 q^{73} -23.4963 q^{74} -3.69424 q^{75} +5.40368 q^{76} +5.06040 q^{77} +17.1361 q^{78} +12.4185 q^{79} +6.00726 q^{80} -6.30611 q^{81} +8.46702 q^{82} -7.23340 q^{83} +11.2825 q^{84} +1.59736 q^{85} +2.02811 q^{86} +2.36509 q^{87} +0.328374 q^{88} +7.05087 q^{89} +2.34382 q^{90} +19.8158 q^{91} -2.23790 q^{92} +6.01587 q^{93} -25.0496 q^{94} -4.08458 q^{95} -12.2009 q^{96} -1.19937 q^{97} +11.1980 q^{98} -1.03464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * 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 $

$2$	2.02811	1.43409	0.717044	−	0.697028i	$-0.245495\pi$
$2$	2.02811	1.43409	0.717044	+	0.697028i	$0.245495\pi$
$3$	1.50881	0.871113	0.435556	−	0.900161i	$-0.356552\pi$
$3$	1.50881	0.871113	0.435556	+	0.900161i	$0.356552\pi$
$4$	2.11322	1.05661
$5$	−1.59736	−0.714361	−0.357180	−	0.934035i	$-0.616262\pi$
$5$	−1.59736	−0.714361	−0.357180	+	0.934035i	$0.616262\pi$
$6$	3.06003	1.24925
$7$	3.53856	1.33745	0.668725	−	0.743510i	$-0.266840\pi$
$7$	3.53856	1.33745	0.668725	+	0.743510i	$0.266840\pi$
$8$	0.229620	0.0811830
$9$	−0.723487	−0.241162
$10$	−3.23961	−1.02446
$11$	1.43007	0.431183	0.215592	−	0.976484i	$-0.430832\pi$
$11$	1.43007	0.431183	0.215592	+	0.976484i	$0.430832\pi$
$12$	3.18845	0.920426
$13$	5.59997	1.55315	0.776576	−	0.630024i	$-0.216955\pi$
$13$	5.59997	1.55315	0.776576	+	0.630024i	$0.216955\pi$
$14$	7.17658	1.91802
$15$	−2.41011	−0.622289
$16$	−3.76074	−0.940186
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.46731	−0.345848
$19$	2.55708	0.586635	0.293318	−	0.956015i	$-0.405241\pi$
$19$	2.55708	0.586635	0.293318	+	0.956015i	$0.405241\pi$
$20$	−3.37557	−0.754800
$21$	5.33902	1.16507
$22$	2.90034	0.618355
$23$	−1.05900	−0.220817	−0.110408	−	0.993886i	$-0.535216\pi$
$23$	−1.05900	−0.220817	−0.110408	+	0.993886i	$0.535216\pi$
$24$	0.346454	0.0707195
$25$	−2.44845	−0.489689
$26$	11.3573	2.22736
$27$	−5.61804	−1.08119
$28$	7.47775	1.41316
$29$	1.56752	0.291081	0.145541	−	0.989352i	$-0.453508\pi$
$29$	1.56752	0.291081	0.145541	+	0.989352i	$0.453508\pi$
$30$	−4.88797	−0.892417
$31$	3.98716	0.716115	0.358057	−	0.933700i	$-0.383439\pi$
$31$	3.98716	0.716115	0.358057	+	0.933700i	$0.383439\pi$
$32$	−8.08643	−1.42949
$33$	2.15771	0.375609
$34$	−2.02811	−0.347818
$35$	−5.65235	−0.955422
$36$	−1.52889	−0.254814
$37$	−11.5853	−1.90462	−0.952308	−	0.305138i	$-0.901297\pi$
$37$	−11.5853	−1.90462	−0.952308	+	0.305138i	$0.901297\pi$
$38$	5.18604	0.841287
$39$	8.44930	1.35297
$40$	−0.366786	−0.0579939
$41$	4.17484	0.652000	0.326000	−	0.945370i	$-0.394299\pi$
$41$	4.17484	0.652000	0.326000	+	0.945370i	$0.394299\pi$
$42$	10.8281	1.67081
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.02206	0.455592
$45$	1.15567	0.172277
$46$	−2.14777	−0.316671
$47$	−12.3512	−1.80161	−0.900804	−	0.434226i	$-0.857022\pi$
$47$	−12.3512	−1.80161	−0.900804	+	0.434226i	$0.857022\pi$
$48$	−5.67425	−0.819008
$49$	5.52141	0.788773
$50$	−4.96571	−0.702257
$51$	−1.50881	−0.211276
$52$	11.8340	1.64107
$53$	−12.7376	−1.74964	−0.874822	−	0.484444i	$-0.839022\pi$
$53$	−12.7376	−1.74964	−0.874822	+	0.484444i	$0.839022\pi$
$54$	−11.3940	−1.55053
$55$	−2.28434	−0.308020
$56$	0.812525	0.108578
$57$	3.85816	0.511026
$58$	3.17910	0.417436
$59$	8.88790	1.15711	0.578553	−	0.815645i	$-0.303617\pi$
$59$	8.88790	1.15711	0.578553	+	0.815645i	$0.303617\pi$
$60$	−5.09310	−0.657516
$61$	−4.99882	−0.640033	−0.320016	−	0.947412i	$-0.603688\pi$
$61$	−4.99882	−0.640033	−0.320016	+	0.947412i	$0.603688\pi$
$62$	8.08638	1.02697
$63$	−2.56010	−0.322543
$64$	−8.87866	−1.10983
$65$	−8.94516	−1.10951
$66$	4.37607	0.538657
$67$	9.04283	1.10476	0.552379	−	0.833593i	$-0.313720\pi$
$67$	9.04283	1.10476	0.552379	+	0.833593i	$0.313720\pi$
$68$	−2.11322	−0.256265
$69$	−1.59783	−0.192356
$70$	−11.4636	−1.37016
$71$	0.338375	0.0401577	0.0200788	−	0.999798i	$-0.493608\pi$
$71$	0.338375	0.0401577	0.0200788	+	0.999798i	$0.493608\pi$
$72$	−0.166127	−0.0195783
$73$	−8.43965	−0.987786	−0.493893	−	0.869523i	$-0.664427\pi$
$73$	−8.43965	−0.987786	−0.493893	+	0.869523i	$0.664427\pi$
$74$	−23.4963	−2.73139
$75$	−3.69424	−0.426574
$76$	5.40368	0.619844
$77$	5.06040	0.576686
$78$	17.1361	1.94028
$79$	12.4185	1.39719	0.698597	−	0.715515i	$-0.253808\pi$
$79$	12.4185	1.39719	0.698597	+	0.715515i	$0.253808\pi$
$80$	6.00726	0.671632
$81$	−6.30611	−0.700678
$82$	8.46702	0.935026
$83$	−7.23340	−0.793969	−0.396984	−	0.917825i	$-0.629943\pi$
$83$	−7.23340	−0.793969	−0.396984	+	0.917825i	$0.629943\pi$
$84$	11.2825	1.23102
$85$	1.59736	0.173258
$86$	2.02811	0.218696
$87$	2.36509	0.253564
$88$	0.328374	0.0350047
$89$	7.05087	0.747391	0.373695	−	0.927551i	$-0.378091\pi$
$89$	7.05087	0.747391	0.373695	+	0.927551i	$0.378091\pi$
$90$	2.34382	0.247060
$91$	19.8158	2.07726
$92$	−2.23790	−0.233317
$93$	6.01587	0.623817
$94$	−25.0496	−2.58366
$95$	−4.08458	−0.419069
$96$	−12.2009	−1.24525
$97$	−1.19937	−0.121778	−0.0608888	−	0.998145i	$-0.519394\pi$
$97$	−1.19937	−0.121778	−0.0608888	+	0.998145i	$0.519394\pi$
$98$	11.1980	1.13117
$99$	−1.03464	−0.103985
$100$	−5.17410	−0.517410
$101$	−3.04553	−0.303041	−0.151521	−	0.988454i	$-0.548417\pi$
$101$	−3.04553	−0.303041	−0.151521	+	0.988454i	$0.548417\pi$
$102$	−3.06003	−0.302988
$103$	6.47399	0.637902	0.318951	−	0.947771i	$-0.396670\pi$
$103$	6.47399	0.637902	0.318951	+	0.947771i	$0.396670\pi$
$104$	1.28587	0.126090
$105$	−8.52833	−0.832280
$106$	−25.8332	−2.50914
$107$	−2.28448	−0.220849	−0.110424	−	0.993885i	$-0.535221\pi$
$107$	−2.28448	−0.220849	−0.110424	+	0.993885i	$0.535221\pi$
$108$	−11.8722	−1.14240
$109$	0.547515	0.0524424	0.0262212	−	0.999656i	$-0.491653\pi$
$109$	0.547515	0.0524424	0.0262212	+	0.999656i	$0.491653\pi$
$110$	−4.63288	−0.441728
$111$	−17.4801	−1.65914
$112$	−13.3076	−1.25745
$113$	−16.9459	−1.59413	−0.797067	−	0.603890i	$-0.793616\pi$
$113$	−16.9459	−1.59413	−0.797067	+	0.603890i	$0.793616\pi$
$114$	7.82476	0.732856
$115$	1.69160	0.157743
$116$	3.31251	0.307559
$117$	−4.05150	−0.374562
$118$	18.0256	1.65939
$119$	−3.53856	−0.324379
$120$	−0.553411	−0.0505193
$121$	−8.95489	−0.814081
$122$	−10.1381	−0.917864
$123$	6.29905	0.567966
$124$	8.42574	0.756653
$125$	11.8978	1.06418
$126$	−5.19216	−0.462555
$127$	17.4500	1.54844	0.774220	−	0.632917i	$-0.218143\pi$
$127$	17.4500	1.54844	0.774220	+	0.632917i	$0.218143\pi$
$128$	−1.83402	−0.162106
$129$	1.50881	0.132843
$130$	−18.1417	−1.59114
$131$	−14.6273	−1.27799	−0.638996	−	0.769210i	$-0.720650\pi$
$131$	−14.6273	−1.27799	−0.638996	+	0.769210i	$0.720650\pi$
$132$	4.55971	0.396872
$133$	9.04840	0.784596
$134$	18.3398	1.58432
$135$	8.97403	0.772361
$136$	−0.229620	−0.0196898
$137$	10.1926	0.870816	0.435408	−	0.900233i	$-0.356604\pi$
$137$	10.1926	0.870816	0.435408	+	0.900233i	$0.356604\pi$
$138$	−3.24058	−0.275856
$139$	10.5161	0.891962	0.445981	−	0.895042i	$-0.352855\pi$
$139$	10.5161	0.891962	0.445981	+	0.895042i	$0.352855\pi$
$140$	−11.9447	−1.00951
$141$	−18.6356	−1.56940
$142$	0.686260	0.0575897
$143$	8.00836	0.669693
$144$	2.72085	0.226737
$145$	−2.50389	−0.207937
$146$	−17.1165	−1.41657
$147$	8.33077	0.687110
$148$	−24.4823	−2.01244
$149$	9.14885	0.749503	0.374751	−	0.927125i	$-0.377728\pi$
$149$	9.14885	0.749503	0.374751	+	0.927125i	$0.377728\pi$
$150$	−7.49232	−0.611745
$151$	8.18143	0.665795	0.332898	−	0.942963i	$-0.391974\pi$
$151$	8.18143	0.665795	0.332898	+	0.942963i	$0.391974\pi$
$152$	0.587158	0.0476248
$153$	0.723487	0.0584905
$154$	10.2630	0.827019
$155$	−6.36892	−0.511564
$156$	17.8552	1.42956
$157$	21.3642	1.70505	0.852525	−	0.522686i	$-0.175070\pi$
$157$	21.3642	1.70505	0.852525	+	0.522686i	$0.175070\pi$
$158$	25.1861	2.00370
$159$	−19.2186	−1.52414
$160$	12.9169	1.02117
$161$	−3.74734	−0.295332
$162$	−12.7895	−1.00483
$163$	9.75999	0.764461	0.382231	−	0.924067i	$-0.375156\pi$
$163$	9.75999	0.764461	0.382231	+	0.924067i	$0.375156\pi$
$164$	8.82235	0.688910
$165$	−3.44664	−0.268320
$166$	−14.6701	−1.13862
$167$	19.0758	1.47613	0.738065	−	0.674729i	$-0.235740\pi$
$167$	19.0758	1.47613	0.738065	+	0.674729i	$0.235740\pi$
$168$	1.22595	0.0945839
$169$	18.3596	1.41228
$170$	3.23961	0.248467
$171$	−1.85002	−0.141474
$172$	2.11322	0.161131
$173$	−19.6404	−1.49323	−0.746615	−	0.665257i	$-0.768322\pi$
$173$	−19.6404	−1.49323	−0.746615	+	0.665257i	$0.768322\pi$
$174$	4.79666	0.363634
$175$	−8.66397	−0.654935
$176$	−5.37814	−0.405392
$177$	13.4102	1.00797
$178$	14.2999	1.07182
$179$	21.2054	1.58496	0.792482	−	0.609895i	$-0.208788\pi$
$179$	21.2054	1.58496	0.792482	+	0.609895i	$0.208788\pi$
$180$	2.44218	0.182029
$181$	−14.5875	−1.08428	−0.542141	−	0.840288i	$-0.682386\pi$
$181$	−14.5875	−1.08428	−0.542141	+	0.840288i	$0.682386\pi$
$182$	40.1886	2.97898
$183$	−7.54227	−0.557541
$184$	−0.243168	−0.0179266
$185$	18.5059	1.36058
$186$	12.2008	0.894608
$187$	−1.43007	−0.104577
$188$	−26.1008	−1.90360
$189$	−19.8798	−1.44604
$190$	−8.28397	−0.600982
$191$	0.220780	0.0159751	0.00798753	−	0.999968i	$-0.497457\pi$
$191$	0.220780	0.0159751	0.00798753	+	0.999968i	$0.497457\pi$
$192$	−13.3962	−0.966790
$193$	21.2311	1.52825	0.764124	−	0.645069i	$-0.223172\pi$
$193$	21.2311	1.52825	0.764124	+	0.645069i	$0.223172\pi$
$194$	−2.43245	−0.174640
$195$	−13.4966	−0.966509
$196$	11.6679	0.833425
$197$	−17.1909	−1.22480	−0.612399	−	0.790548i	$-0.709796\pi$
$197$	−17.1909	−1.22480	−0.612399	+	0.790548i	$0.709796\pi$
$198$	−2.09836	−0.149124
$199$	−5.84736	−0.414509	−0.207254	−	0.978287i	$-0.566453\pi$
$199$	−5.84736	−0.414509	−0.207254	+	0.978287i	$0.566453\pi$
$200$	−0.562212	−0.0397544
$201$	13.6439	0.962368
$202$	−6.17666	−0.434588
$203$	5.54676	0.389306
$204$	−3.18845	−0.223236
$205$	−6.66872	−0.465763
$206$	13.1300	0.914807
$207$	0.766174	0.0532527
$208$	−21.0600	−1.46025
$209$	3.65682	0.252947
$210$	−17.2964	−1.19356
$211$	−16.6081	−1.14335	−0.571673	−	0.820482i	$-0.693705\pi$
$211$	−16.6081	−1.14335	−0.571673	+	0.820482i	$0.693705\pi$
$212$	−26.9173	−1.84869
$213$	0.510544	0.0349819
$214$	−4.63317	−0.316717
$215$	−1.59736	−0.108939
$216$	−1.29002	−0.0877744
$217$	14.1088	0.957767
$218$	1.11042	0.0752070
$219$	−12.7338	−0.860474
$220$	−4.82731	−0.325457
$221$	−5.59997	−0.376695
$222$	−35.4515	−2.37935
$223$	−17.4052	−1.16554	−0.582770	−	0.812637i	$-0.698031\pi$
$223$	−17.4052	−1.16554	−0.582770	+	0.812637i	$0.698031\pi$
$224$	−28.6143	−1.91188
$225$	1.77142	0.118095
$226$	−34.3681	−2.28613
$227$	−2.88364	−0.191394	−0.0956970	−	0.995411i	$-0.530508\pi$
$227$	−2.88364	−0.191394	−0.0956970	+	0.995411i	$0.530508\pi$
$228$	8.15313	0.539955
$229$	1.33664	0.0883277	0.0441639	−	0.999024i	$-0.485938\pi$
$229$	1.33664	0.0883277	0.0441639	+	0.999024i	$0.485938\pi$
$230$	3.43076	0.226217
$231$	7.63519	0.502359
$232$	0.359934	0.0236308
$233$	−20.5040	−1.34326	−0.671631	−	0.740885i	$-0.734406\pi$
$233$	−20.5040	−1.34326	−0.671631	+	0.740885i	$0.734406\pi$
$234$	−8.21689	−0.537155
$235$	19.7293	1.28700
$236$	18.7821	1.22261
$237$	18.7372	1.21711
$238$	−7.17658	−0.465189
$239$	27.4237	1.77389	0.886946	−	0.461872i	$-0.152822\pi$
$239$	27.4237	1.77389	0.886946	+	0.461872i	$0.152822\pi$
$240$	9.06382	0.585067
$241$	−18.8780	−1.21604	−0.608020	−	0.793921i	$-0.708036\pi$
$241$	−18.8780	−1.21604	−0.608020	+	0.793921i	$0.708036\pi$
$242$	−18.1615	−1.16746
$243$	7.33940	0.470823
$244$	−10.5636	−0.676265
$245$	−8.81967	−0.563468
$246$	12.7751	0.814513
$247$	14.3196	0.911134
$248$	0.915532	0.0581363
$249$	−10.9138	−0.691637
$250$	24.1301	1.52612
$251$	17.3194	1.09319	0.546597	−	0.837396i	$-0.315923\pi$
$251$	17.3194	1.09319	0.546597	+	0.837396i	$0.315923\pi$
$252$	−5.41006	−0.340802
$253$	−1.51445	−0.0952125
$254$	35.3905	2.22060
$255$	2.41011	0.150927
$256$	14.0377	0.877359
$257$	−8.09219	−0.504777	−0.252388	−	0.967626i	$-0.581216\pi$
$257$	−8.09219	−0.504777	−0.252388	+	0.967626i	$0.581216\pi$
$258$	3.06003	0.190509
$259$	−40.9954	−2.54733
$260$	−18.9031	−1.17232
$261$	−1.13408	−0.0701978
$262$	−29.6657	−1.83275
$263$	−13.6857	−0.843899	−0.421949	−	0.906619i	$-0.638654\pi$
$263$	−13.6857	−0.843899	−0.421949	+	0.906619i	$0.638654\pi$
$264$	0.495454	0.0304931
$265$	20.3465	1.24988
$266$	18.3511	1.12518
$267$	10.6384	0.651062
$268$	19.1095	1.16730
$269$	−4.89631	−0.298533	−0.149267	−	0.988797i	$-0.547691\pi$
$269$	−4.89631	−0.298533	−0.149267	+	0.988797i	$0.547691\pi$
$270$	18.2003	1.10763
$271$	−5.29594	−0.321706	−0.160853	−	0.986978i	$-0.551424\pi$
$271$	−5.29594	−0.321706	−0.160853	+	0.986978i	$0.551424\pi$
$272$	3.76074	0.228029
$273$	29.8984	1.80953
$274$	20.6718	1.24883
$275$	−3.50145	−0.211146
$276$	−3.37657	−0.203246
$277$	3.85458	0.231599	0.115800	−	0.993273i	$-0.463057\pi$
$277$	3.85458	0.231599	0.115800	+	0.993273i	$0.463057\pi$
$278$	21.3277	1.27915
$279$	−2.88466	−0.172700
$280$	−1.29789	−0.0775640
$281$	27.1800	1.62142	0.810712	−	0.585444i	$-0.199080\pi$
$281$	27.1800	1.62142	0.810712	+	0.585444i	$0.199080\pi$
$282$	−37.7951	−2.25066
$283$	−13.4060	−0.796902	−0.398451	−	0.917190i	$-0.630452\pi$
$283$	−13.4060	−0.796902	−0.398451	+	0.917190i	$0.630452\pi$
$284$	0.715060	0.0424310
$285$	−6.16286	−0.365057
$286$	16.2418	0.960399
$287$	14.7729	0.872018
$288$	5.85043	0.344740
$289$	1.00000	0.0588235
$290$	−5.07816	−0.298200
$291$	−1.80962	−0.106082
$292$	−17.8348	−1.04370
$293$	21.8183	1.27464	0.637319	−	0.770600i	$-0.280043\pi$
$293$	21.8183	1.27464	0.637319	+	0.770600i	$0.280043\pi$
$294$	16.8957	0.985377
$295$	−14.1972	−0.826591
$296$	−2.66023	−0.154622
$297$	−8.03421	−0.466192
$298$	18.5548	1.07485
$299$	−5.93037	−0.342962
$300$	−7.80674	−0.450723
$301$	3.53856	0.203959
$302$	16.5928	0.954809
$303$	−4.59513	−0.263983
$304$	−9.61654	−0.551546
$305$	7.98490	0.457214
$306$	1.46731	0.0838805
$307$	−23.4111	−1.33614	−0.668072	−	0.744096i	$-0.732880\pi$
$307$	−23.4111	−1.33614	−0.668072	+	0.744096i	$0.732880\pi$
$308$	10.6937	0.609332
$309$	9.76804	0.555684
$310$	−12.9169	−0.733628
$311$	0.600675	0.0340611	0.0170306	−	0.999855i	$-0.494579\pi$
$311$	0.600675	0.0340611	0.0170306	+	0.999855i	$0.494579\pi$
$312$	1.94013	0.109838
$313$	33.0127	1.86599	0.932995	−	0.359890i	$-0.117186\pi$
$313$	33.0127	1.86599	0.932995	+	0.359890i	$0.117186\pi$
$314$	43.3289	2.44519
$315$	4.08940	0.230412
$316$	26.2431	1.47629
$317$	9.16017	0.514487	0.257243	−	0.966347i	$-0.417186\pi$
$317$	9.16017	0.514487	0.257243	+	0.966347i	$0.417186\pi$
$318$	−38.9775	−2.18575
$319$	2.24167	0.125509
$320$	14.1824	0.792821
$321$	−3.44685	−0.192384
$322$	−7.60000	−0.423532
$323$	−2.55708	−0.142280
$324$	−13.3262	−0.740343
$325$	−13.7112	−0.760561
$326$	19.7943	1.09630
$327$	0.826097	0.0456833
$328$	0.958627	0.0529313
$329$	−43.7055	−2.40956
$330$	−6.99015	−0.384795
$331$	5.91557	0.325149	0.162574	−	0.986696i	$-0.448020\pi$
$331$	5.91557	0.325149	0.162574	+	0.986696i	$0.448020\pi$
$332$	−15.2858	−0.838915
$333$	8.38184	0.459322
$334$	38.6878	2.11690
$335$	−14.4446	−0.789195
$336$	−20.0787	−1.09538
$337$	−11.9737	−0.652248	−0.326124	−	0.945327i	$-0.605743\pi$
$337$	−11.9737	−0.652248	−0.326124	+	0.945327i	$0.605743\pi$
$338$	37.2353	2.02534
$339$	−25.5682	−1.38867
$340$	3.37557	0.183066
$341$	5.70192	0.308777
$342$	−3.75203	−0.202887
$343$	−5.23208	−0.282506
$344$	0.229620	0.0123803
$345$	2.55231	0.137412
$346$	−39.8328	−2.14142
$347$	9.11641	0.489394	0.244697	−	0.969600i	$-0.421311\pi$
$347$	9.11641	0.489394	0.244697	+	0.969600i	$0.421311\pi$
$348$	4.99796	0.267919
$349$	10.0185	0.536278	0.268139	−	0.963380i	$-0.413591\pi$
$349$	10.0185	0.536278	0.268139	+	0.963380i	$0.413591\pi$
$350$	−17.5715	−0.939234
$351$	−31.4609	−1.67926
$352$	−11.5642	−0.616373
$353$	−9.96957	−0.530627	−0.265313	−	0.964162i	$-0.585475\pi$
$353$	−9.96957	−0.530627	−0.265313	+	0.964162i	$0.585475\pi$
$354$	27.1973	1.44552
$355$	−0.540506	−0.0286871
$356$	14.9000	0.789700
$357$	−5.33902	−0.282571
$358$	43.0068	2.27298
$359$	3.59574	0.189776	0.0948880	−	0.995488i	$-0.469751\pi$
$359$	3.59574	0.189776	0.0948880	+	0.995488i	$0.469751\pi$
$360$	0.265365	0.0139860
$361$	−12.4613	−0.655859
$362$	−29.5850	−1.55495
$363$	−13.5112	−0.709157
$364$	41.8752	2.19486
$365$	13.4812	0.705636
$366$	−15.2965	−0.799563
$367$	1.76978	0.0923816	0.0461908	−	0.998933i	$-0.485292\pi$
$367$	1.76978	0.0923816	0.0461908	+	0.998933i	$0.485292\pi$
$368$	3.98263	0.207609
$369$	−3.02044	−0.157238
$370$	37.5320	1.95120
$371$	−45.0728	−2.34006
$372$	12.7128	0.659131
$373$	4.06315	0.210382	0.105191	−	0.994452i	$-0.466455\pi$
$373$	4.06315	0.210382	0.105191	+	0.994452i	$0.466455\pi$
$374$	−2.90034	−0.149973
$375$	17.9516	0.927017
$376$	−2.83608	−0.146260
$377$	8.77806	0.452093
$378$	−40.3183	−2.07375
$379$	−8.86943	−0.455592	−0.227796	−	0.973709i	$-0.573152\pi$
$379$	−8.86943	−0.455592	−0.227796	+	0.973709i	$0.573152\pi$
$380$	−8.63161	−0.442792
$381$	26.3288	1.34887
$382$	0.447765	0.0229096
$383$	−6.96947	−0.356123	−0.178062	−	0.984019i	$-0.556983\pi$
$383$	−6.96947	−0.356123	−0.178062	+	0.984019i	$0.556983\pi$
$384$	−2.76719	−0.141212
$385$	−8.08327	−0.411962
$386$	43.0589	2.19164
$387$	−0.723487	−0.0367769
$388$	−2.53453	−0.128671
$389$	24.8201	1.25843	0.629215	−	0.777232i	$-0.283377\pi$
$389$	24.8201	1.25843	0.629215	+	0.777232i	$0.283377\pi$
$390$	−27.3725	−1.38606
$391$	1.05900	0.0535560
$392$	1.26783	0.0640349
$393$	−22.0698	−1.11327
$394$	−34.8649	−1.75647
$395$	−19.8368	−0.998100
$396$	−2.18642	−0.109872
$397$	27.7511	1.39279	0.696393	−	0.717661i	$-0.254787\pi$
$397$	27.7511	1.39279	0.696393	+	0.717661i	$0.254787\pi$
$398$	−11.8591	−0.594442
$399$	13.6523	0.683471
$400$	9.20797	0.460399
$401$	−18.2968	−0.913699	−0.456850	−	0.889544i	$-0.651022\pi$
$401$	−18.2968	−0.913699	−0.456850	+	0.889544i	$0.651022\pi$
$402$	27.6713	1.38012
$403$	22.3280	1.11223
$404$	−6.43587	−0.320197
$405$	10.0731	0.500537
$406$	11.2494	0.558300
$407$	−16.5679	−0.821238
$408$	−0.346454	−0.0171520
$409$	11.2895	0.558231	0.279115	−	0.960258i	$-0.409959\pi$
$409$	11.2895	0.558231	0.279115	+	0.960258i	$0.409959\pi$
$410$	−13.5249	−0.667946
$411$	15.3788	0.758579
$412$	13.6810	0.674013
$413$	31.4504	1.54757
$414$	1.55388	0.0763691
$415$	11.5543	0.567180
$416$	−45.2838	−2.22022
$417$	15.8668	0.776999
$418$	7.41642	0.362749
$419$	−11.1003	−0.542288	−0.271144	−	0.962539i	$-0.587402\pi$
$419$	−11.1003	−0.542288	−0.271144	+	0.962539i	$0.587402\pi$
$420$	−18.0222	−0.879395
$421$	35.8485	1.74715	0.873574	−	0.486691i	$-0.161796\pi$
$421$	35.8485	1.74715	0.873574	+	0.486691i	$0.161796\pi$
$422$	−33.6829	−1.63966
$423$	8.93593	0.434480
$424$	−2.92481	−0.142041
$425$	2.44845	0.118767
$426$	1.03544	0.0501671
$427$	−17.6886	−0.856012
$428$	−4.82760	−0.233351
$429$	12.0831	0.583378
$430$	−3.23961	−0.156228
$431$	−3.49739	−0.168463	−0.0842316	−	0.996446i	$-0.526844\pi$
$431$	−3.49739	−0.168463	−0.0842316	+	0.996446i	$0.526844\pi$
$432$	21.1280	1.01652
$433$	21.8333	1.04924	0.524620	−	0.851337i	$-0.324207\pi$
$433$	21.8333	1.04924	0.524620	+	0.851337i	$0.324207\pi$
$434$	28.6142	1.37352
$435$	−3.77790	−0.181136
$436$	1.15702	0.0554111
$437$	−2.70795	−0.129539
$438$	−25.8256	−1.23400
$439$	−9.67012	−0.461529	−0.230765	−	0.973010i	$-0.574123\pi$
$439$	−9.67012	−0.461529	−0.230765	+	0.973010i	$0.574123\pi$
$440$	−0.524530	−0.0250060
$441$	−3.99467	−0.190222
$442$	−11.3573	−0.540213
$443$	−18.1730	−0.863427	−0.431714	−	0.902011i	$-0.642091\pi$
$443$	−18.1730	−0.863427	−0.431714	+	0.902011i	$0.642091\pi$
$444$	−36.9392	−1.75306
$445$	−11.2628	−0.533907
$446$	−35.2996	−1.67149
$447$	13.8039	0.652902
$448$	−31.4177	−1.48435
$449$	7.87798	0.371785	0.185892	−	0.982570i	$-0.440482\pi$
$449$	7.87798	0.371785	0.185892	+	0.982570i	$0.440482\pi$
$450$	3.59263	0.169358
$451$	5.97032	0.281132
$452$	−35.8104	−1.68438
$453$	12.3442	0.579983
$454$	−5.84833	−0.274476
$455$	−31.6530	−1.48391
$456$	0.885911	0.0414866
$457$	−22.2733	−1.04190	−0.520951	−	0.853587i	$-0.674422\pi$
$457$	−22.2733	−1.04190	−0.520951	+	0.853587i	$0.674422\pi$
$458$	2.71085	0.126670
$459$	5.61804	0.262228
$460$	3.57473	0.166673
$461$	31.2962	1.45761	0.728805	−	0.684722i	$-0.240076\pi$
$461$	31.2962	1.45761	0.728805	+	0.684722i	$0.240076\pi$
$462$	15.4850	0.720427
$463$	7.20301	0.334752	0.167376	−	0.985893i	$-0.446471\pi$
$463$	7.20301	0.334752	0.167376	+	0.985893i	$0.446471\pi$
$464$	−5.89504	−0.273670
$465$	−9.60950	−0.445630
$466$	−41.5843	−1.92636
$467$	19.8826	0.920059	0.460030	−	0.887904i	$-0.347839\pi$
$467$	19.8826	0.920059	0.460030	+	0.887904i	$0.347839\pi$
$468$	−8.56172	−0.395766
$469$	31.9986	1.47756
$470$	40.0131	1.84567
$471$	32.2346	1.48529
$472$	2.04084	0.0939374
$473$	1.43007	0.0657548
$474$	38.0011	1.74545
$475$	−6.26088	−0.287269
$476$	−7.47775	−0.342742
$477$	9.21549	0.421948
$478$	55.6182	2.54392
$479$	29.9063	1.36645	0.683227	−	0.730206i	$-0.260576\pi$
$479$	29.9063	1.36645	0.683227	+	0.730206i	$0.260576\pi$
$480$	19.4892	0.889557
$481$	−64.8775	−2.95816
$482$	−38.2867	−1.74391
$483$	−5.65403	−0.257267
$484$	−18.9236	−0.860166
$485$	1.91583	0.0869931
$486$	14.8851	0.675201
$487$	7.91764	0.358782	0.179391	−	0.983778i	$-0.442587\pi$
$487$	7.91764	0.358782	0.179391	+	0.983778i	$0.442587\pi$
$488$	−1.14783	−0.0519598
$489$	14.7260	0.665932
$490$	−17.8872	−0.808063
$491$	11.0492	0.498643	0.249322	−	0.968421i	$-0.419792\pi$
$491$	11.0492	0.498643	0.249322	+	0.968421i	$0.419792\pi$
$492$	13.3113	0.600118
$493$	−1.56752	−0.0705975
$494$	29.0417	1.30665
$495$	1.65269	0.0742829
$496$	−14.9947	−0.673281
$497$	1.19736	0.0537089
$498$	−22.1344	−0.991868
$499$	23.8203	1.06634	0.533171	−	0.846008i	$-0.321000\pi$
$499$	23.8203	1.06634	0.533171	+	0.846008i	$0.321000\pi$
$500$	25.1427	1.12442
$501$	28.7818	1.28588
$502$	35.1257	1.56774
$503$	6.30206	0.280995	0.140497	−	0.990081i	$-0.455130\pi$
$503$	6.30206	0.280995	0.140497	+	0.990081i	$0.455130\pi$
$504$	−0.587851	−0.0261850
$505$	4.86480	0.216481
$506$	−3.07146	−0.136543
$507$	27.7012	1.23026
$508$	36.8757	1.63610
$509$	−39.0122	−1.72919	−0.864593	−	0.502473i	$-0.832424\pi$
$509$	−39.0122	−1.72919	−0.864593	+	0.502473i	$0.832424\pi$
$510$	4.88797	0.216443
$511$	−29.8642	−1.32112
$512$	32.1381	1.42032
$513$	−14.3658	−0.634266
$514$	−16.4118	−0.723894
$515$	−10.3413	−0.455692
$516$	3.18845	0.140364
$517$	−17.6631	−0.776823
$518$	−83.1430	−3.65310
$519$	−29.6336	−1.30077
$520$	−2.05399	−0.0900734
$521$	−15.9938	−0.700702	−0.350351	−	0.936619i	$-0.613938\pi$
$521$	−15.9938	−0.700702	−0.350351	+	0.936619i	$0.613938\pi$
$522$	−2.30004	−0.100670
$523$	−44.6624	−1.95295	−0.976475	−	0.215629i	$-0.930820\pi$
$523$	−44.6624	−1.95295	−0.976475	+	0.215629i	$0.930820\pi$
$524$	−30.9106	−1.35034
$525$	−13.0723	−0.570522
$526$	−27.7561	−1.21023
$527$	−3.98716	−0.173683
$528$	−8.11460	−0.353142
$529$	−21.8785	−0.951240
$530$	41.2649	1.79243
$531$	−6.43028	−0.279051
$532$	19.1212	0.829011
$533$	23.3790	1.01266
$534$	21.5759	0.933680
$535$	3.64913	0.157766
$536$	2.07642	0.0896875
$537$	31.9949	1.38068
$538$	−9.93024	−0.428123
$539$	7.89602	0.340105
$540$	18.9641	0.816084
$541$	29.7473	1.27894	0.639468	−	0.768818i	$-0.279155\pi$
$541$	29.7473	1.27894	0.639468	+	0.768818i	$0.279155\pi$
$542$	−10.7407	−0.461354
$543$	−22.0098	−0.944531
$544$	8.08643	0.346703
$545$	−0.874577	−0.0374628
$546$	60.6371	2.59503
$547$	34.8067	1.48823	0.744113	−	0.668054i	$-0.232872\pi$
$547$	34.8067	1.48823	0.744113	+	0.668054i	$0.232872\pi$
$548$	21.5393	0.920113
$549$	3.61658	0.154352
$550$	−7.10133	−0.302802
$551$	4.00828	0.170758
$552$	−0.366895	−0.0156161
$553$	43.9437	1.86868
$554$	7.81750	0.332134
$555$	27.9220	1.18522
$556$	22.2228	0.942455
$557$	−23.1908	−0.982624	−0.491312	−	0.870984i	$-0.663483\pi$
$557$	−23.1908	−0.982624	−0.491312	+	0.870984i	$0.663483\pi$
$558$	−5.85039	−0.247667
$559$	5.59997	0.236853
$560$	21.2570	0.898274
$561$	−2.15771	−0.0910986
$562$	55.1240	2.32527
$563$	−13.9003	−0.585829	−0.292914	−	0.956139i	$-0.594625\pi$
$563$	−13.9003	−0.585829	−0.292914	+	0.956139i	$0.594625\pi$
$564$	−39.3812	−1.65825
$565$	27.0687	1.13879
$566$	−27.1887	−1.14283
$567$	−22.3145	−0.937122
$568$	0.0776977	0.00326012
$569$	1.82137	0.0763560	0.0381780	−	0.999271i	$-0.487845\pi$
$569$	1.82137	0.0763560	0.0381780	+	0.999271i	$0.487845\pi$
$570$	−12.4989	−0.523523
$571$	−11.5558	−0.483597	−0.241799	−	0.970326i	$-0.577737\pi$
$571$	−11.5558	−0.483597	−0.241799	+	0.970326i	$0.577737\pi$
$572$	16.9234	0.707604
$573$	0.333115	0.0139161
$574$	29.9611	1.25055
$575$	2.59291	0.108132
$576$	6.42360	0.267650
$577$	−26.3008	−1.09491	−0.547457	−	0.836834i	$-0.684404\pi$
$577$	−26.3008	−1.09491	−0.547457	+	0.836834i	$0.684404\pi$
$578$	2.02811	0.0843581
$579$	32.0337	1.33128
$580$	−5.29127	−0.219708
$581$	−25.5958	−1.06189
$582$	−3.67011	−0.152131
$583$	−18.2157	−0.754417
$584$	−1.93791	−0.0801915
$585$	6.47171	0.267572
$586$	44.2498	1.82794
$587$	−17.2987	−0.713992	−0.356996	−	0.934106i	$-0.616199\pi$
$587$	−17.2987	−0.713992	−0.356996	+	0.934106i	$0.616199\pi$
$588$	17.6047	0.726007
$589$	10.1955	0.420098
$590$	−28.7934	−1.18541
$591$	−25.9378	−1.06694
$592$	43.5695	1.79069
$593$	−19.0355	−0.781696	−0.390848	−	0.920455i	$-0.627818\pi$
$593$	−19.0355	−0.781696	−0.390848	+	0.920455i	$0.627818\pi$
$594$	−16.2942	−0.668560
$595$	5.65235	0.231724
$596$	19.3335	0.791932
$597$	−8.82257	−0.361084
$598$	−12.0274	−0.491838
$599$	−0.245606	−0.0100352	−0.00501759	−	0.999987i	$-0.501597\pi$
$599$	−0.245606	−0.0100352	−0.00501759	+	0.999987i	$0.501597\pi$
$600$	−0.848273	−0.0346306
$601$	27.1977	1.10942	0.554708	−	0.832045i	$-0.312830\pi$
$601$	27.1977	1.10942	0.554708	+	0.832045i	$0.312830\pi$
$602$	7.17658	0.292496
$603$	−6.54237	−0.266426
$604$	17.2892	0.703486
$605$	14.3042	0.581547
$606$	−9.31942	−0.378575
$607$	−42.4417	−1.72266	−0.861328	−	0.508050i	$-0.830367\pi$
$607$	−42.4417	−1.72266	−0.861328	+	0.508050i	$0.830367\pi$
$608$	−20.6777	−0.838591
$609$	8.36902	0.339130
$610$	16.1942	0.655685
$611$	−69.1663	−2.79817
$612$	1.52889	0.0618016
$613$	21.2573	0.858574	0.429287	−	0.903168i	$-0.358765\pi$
$613$	21.2573	0.858574	0.429287	+	0.903168i	$0.358765\pi$
$614$	−47.4803	−1.91615
$615$	−10.0618	−0.405732
$616$	1.16197	0.0468171
$617$	−15.2683	−0.614678	−0.307339	−	0.951600i	$-0.599439\pi$
$617$	−15.2683	−0.614678	−0.307339	+	0.951600i	$0.599439\pi$
$618$	19.8106	0.796900
$619$	18.2876	0.735042	0.367521	−	0.930015i	$-0.380207\pi$
$619$	18.2876	0.735042	0.367521	+	0.930015i	$0.380207\pi$
$620$	−13.4589	−0.540523
$621$	5.94951	0.238746
$622$	1.21823	0.0488467
$623$	24.9499	0.999598
$624$	−31.7756	−1.27204
$625$	−6.76289	−0.270516
$626$	66.9533	2.67599
$627$	5.51745	0.220346
$628$	45.1473	1.80157
$629$	11.5853	0.461937
$630$	8.29375	0.330431
$631$	−4.61202	−0.183602	−0.0918009	−	0.995777i	$-0.529262\pi$
$631$	−4.61202	−0.183602	−0.0918009	+	0.995777i	$0.529262\pi$
$632$	2.85155	0.113428
$633$	−25.0584	−0.995983
$634$	18.5778	0.737819
$635$	−27.8739	−1.10614
$636$	−40.6132	−1.61042
$637$	30.9197	1.22508
$638$	4.54634	0.179991
$639$	−0.244810	−0.00968452
$640$	2.92958	0.115802
$641$	−38.5868	−1.52409	−0.762044	−	0.647526i	$-0.775804\pi$
$641$	−38.5868	−1.52409	−0.762044	+	0.647526i	$0.775804\pi$
$642$	−6.99058	−0.275896
$643$	−22.7670	−0.897843	−0.448922	−	0.893571i	$-0.648192\pi$
$643$	−22.7670	−0.897843	−0.448922	+	0.893571i	$0.648192\pi$
$644$	−7.91895	−0.312050
$645$	−2.41011	−0.0948981
$646$	−5.18604	−0.204042
$647$	7.37000	0.289745	0.144872	−	0.989450i	$-0.453723\pi$
$647$	7.37000	0.289745	0.144872	+	0.989450i	$0.453723\pi$
$648$	−1.44801	−0.0568832
$649$	12.7103	0.498925
$650$	−27.8078	−1.09071
$651$	21.2875	0.834324
$652$	20.6250	0.807737
$653$	−8.32344	−0.325721	−0.162861	−	0.986649i	$-0.552072\pi$
$653$	−8.32344	−0.325721	−0.162861	+	0.986649i	$0.552072\pi$
$654$	1.67541	0.0655138
$655$	23.3650	0.912947
$656$	−15.7005	−0.613002
$657$	6.10598	0.238217
$658$	−88.6394	−3.45552
$659$	−16.9623	−0.660758	−0.330379	−	0.943848i	$-0.607177\pi$
$659$	−16.9623	−0.660758	−0.330379	+	0.943848i	$0.607177\pi$
$660$	−7.28350	−0.283510
$661$	−11.5168	−0.447951	−0.223975	−	0.974595i	$-0.571904\pi$
$661$	−11.5168	−0.447951	−0.223975	+	0.974595i	$0.571904\pi$
$662$	11.9974	0.466292
$663$	−8.44930	−0.328144
$664$	−1.66093	−0.0644568
$665$	−14.4535	−0.560484
$666$	16.9993	0.658708
$667$	−1.66000	−0.0642756
$668$	40.3114	1.55969
$669$	−26.2612	−1.01532
$670$	−29.2953	−1.13178
$671$	−7.14867	−0.275971
$672$	−43.1736	−1.66546
$673$	−32.8469	−1.26616	−0.633078	−	0.774088i	$-0.718209\pi$
$673$	−32.8469	−1.26616	−0.633078	+	0.774088i	$0.718209\pi$
$674$	−24.2839	−0.935381
$675$	13.7555	0.529448
$676$	38.7980	1.49223
$677$	21.5441	0.828006	0.414003	−	0.910276i	$-0.364130\pi$
$677$	21.5441	0.828006	0.414003	+	0.910276i	$0.364130\pi$
$678$	−51.8550	−1.99148
$679$	−4.24405	−0.162872
$680$	0.366786	0.0140656
$681$	−4.35087	−0.166726
$682$	11.5641	0.442813
$683$	37.2476	1.42524	0.712619	−	0.701551i	$-0.247509\pi$
$683$	37.2476	1.42524	0.712619	+	0.701551i	$0.247509\pi$
$684$	−3.90949	−0.149483
$685$	−16.2813	−0.622077
$686$	−10.6112	−0.405139
$687$	2.01674	0.0769434
$688$	−3.76074	−0.143377
$689$	−71.3302	−2.71746
$690$	5.17636	0.197061
$691$	33.1321	1.26040	0.630202	−	0.776431i	$-0.282972\pi$
$691$	33.1321	1.26040	0.630202	+	0.776431i	$0.282972\pi$
$692$	−41.5044	−1.57776
$693$	−3.66113	−0.139075
$694$	18.4891	0.701835
$695$	−16.7979	−0.637182
$696$	0.543073	0.0205851
$697$	−4.17484	−0.158133
$698$	20.3186	0.769070
$699$	−30.9367	−1.17013
$700$	−18.3089	−0.692010
$701$	23.1632	0.874863	0.437432	−	0.899252i	$-0.355888\pi$
$701$	23.1632	0.874863	0.437432	+	0.899252i	$0.355888\pi$
$702$	−63.8060	−2.40820
$703$	−29.6247	−1.11732
$704$	−12.6971	−0.478541
$705$	29.7678	1.12112
$706$	−20.2194	−0.760965
$707$	−10.7768	−0.405303
$708$	28.3386	1.06503
$709$	44.0339	1.65373	0.826863	−	0.562403i	$-0.190123\pi$
$709$	44.0339	1.65373	0.826863	+	0.562403i	$0.190123\pi$
$710$	−1.09620	−0.0411398
$711$	−8.98465	−0.336951
$712$	1.61902	0.0606754
$713$	−4.22240	−0.158130
$714$	−10.8281	−0.405232
$715$	−12.7922	−0.478402
$716$	44.8116	1.67469
$717$	41.3772	1.54526
$718$	7.29255	0.272155
$719$	−19.5888	−0.730541	−0.365270	−	0.930901i	$-0.619023\pi$
$719$	−19.5888	−0.730541	−0.365270	+	0.930901i	$0.619023\pi$
$720$	−4.34617	−0.161972
$721$	22.9086	0.853162
$722$	−25.2729	−0.940560
$723$	−28.4834	−1.05931
$724$	−30.8266	−1.14566
$725$	−3.83799	−0.142539
$726$	−27.4023	−1.01699
$727$	2.00621	0.0744060	0.0372030	−	0.999308i	$-0.488155\pi$
$727$	2.00621	0.0744060	0.0372030	+	0.999308i	$0.488155\pi$
$728$	4.55011	0.168638
$729$	29.9921	1.11082
$730$	27.3412	1.01194
$731$	−1.00000	−0.0369863
$732$	−15.9385	−0.589103
$733$	30.9210	1.14209	0.571047	−	0.820917i	$-0.306537\pi$
$733$	30.9210	1.14209	0.571047	+	0.820917i	$0.306537\pi$
$734$	3.58930	0.132483
$735$	−13.3072	−0.490844
$736$	8.56354	0.315656
$737$	12.9319	0.476353
$738$	−6.12578	−0.225493
$739$	−32.4971	−1.19542	−0.597712	−	0.801711i	$-0.703923\pi$
$739$	−32.4971	−1.19542	−0.597712	+	0.801711i	$0.703923\pi$
$740$	39.1071	1.43760
$741$	21.6056	0.793700
$742$	−91.4124	−3.35586
$743$	−21.2378	−0.779139	−0.389569	−	0.920997i	$-0.627376\pi$
$743$	−21.2378	−0.779139	−0.389569	+	0.920997i	$0.627376\pi$
$744$	1.38136	0.0506433
$745$	−14.6140	−0.535415
$746$	8.24050	0.301706
$747$	5.23327	0.191475
$748$	−3.02206	−0.110497
$749$	−8.08376	−0.295374
$750$	36.4078	1.32942
$751$	−25.1478	−0.917656	−0.458828	−	0.888525i	$-0.651731\pi$
$751$	−25.1478	−0.917656	−0.458828	+	0.888525i	$0.651731\pi$
$752$	46.4497	1.69385
$753$	26.1318	0.952295
$754$	17.8028	0.648341
$755$	−13.0687	−0.475618
$756$	−42.0103	−1.52790
$757$	−8.97978	−0.326376	−0.163188	−	0.986595i	$-0.552178\pi$
$757$	−8.97978	−0.326376	−0.163188	+	0.986595i	$0.552178\pi$
$758$	−17.9882	−0.653359
$759$	−2.28502	−0.0829409
$760$	−0.937902	−0.0340213
$761$	−10.2650	−0.372107	−0.186054	−	0.982540i	$-0.559570\pi$
$761$	−10.2650	−0.372107	−0.186054	+	0.982540i	$0.559570\pi$
$762$	53.3976	1.93439
$763$	1.93741	0.0701391
$764$	0.466556	0.0168794
$765$	−1.15567	−0.0417833
$766$	−14.1348	−0.510713
$767$	49.7720	1.79716
$768$	21.1803	0.764279
$769$	−39.2946	−1.41700	−0.708499	−	0.705711i	$-0.750628\pi$
$769$	−39.2946	−1.41700	−0.708499	+	0.705711i	$0.750628\pi$
$770$	−16.3937	−0.590789
$771$	−12.2096	−0.439717
$772$	44.8660	1.61476
$773$	11.7224	0.421625	0.210813	−	0.977526i	$-0.432389\pi$
$773$	11.7224	0.421625	0.210813	+	0.977526i	$0.432389\pi$
$774$	−1.46731	−0.0527413
$775$	−9.76234	−0.350673
$776$	−0.275400	−0.00988627
$777$	−61.8543	−2.21901
$778$	50.3378	1.80470
$779$	10.6754	0.382487
$780$	−28.5212	−1.02122
$781$	0.483900	0.0173153
$782$	2.14777	0.0768040
$783$	−8.80639	−0.314715
$784$	−20.7646	−0.741593
$785$	−34.1263	−1.21802
$786$	−44.7599	−1.59653
$787$	20.1559	0.718480	0.359240	−	0.933245i	$-0.383036\pi$
$787$	20.1559	0.718480	0.359240	+	0.933245i	$0.383036\pi$
$788$	−36.3281	−1.29413
$789$	−20.6492	−0.735131
$790$	−40.2313	−1.43136
$791$	−59.9640	−2.13208
$792$	−0.237574	−0.00844183
$793$	−27.9932	−0.994068
$794$	56.2821	1.99738
$795$	30.6991	1.08878
$796$	−12.3568	−0.437974
$797$	−11.2660	−0.399061	−0.199531	−	0.979892i	$-0.563942\pi$
$797$	−11.2660	−0.399061	−0.199531	+	0.979892i	$0.563942\pi$
$798$	27.6884	0.980158
$799$	12.3512	0.436954
$800$	19.7992	0.700007
$801$	−5.10122	−0.180243
$802$	−37.1079	−1.31033
$803$	−12.0693	−0.425917
$804$	28.8326	1.01685
$805$	5.98584	0.210973
$806$	45.2835	1.59504
$807$	−7.38761	−0.260056
$808$	−0.699315	−0.0246018
$809$	−17.6491	−0.620508	−0.310254	−	0.950654i	$-0.600414\pi$
$809$	−17.6491	−0.620508	−0.310254	+	0.950654i	$0.600414\pi$
$810$	20.4294	0.717814
$811$	−12.0300	−0.422429	−0.211215	−	0.977440i	$-0.567742\pi$
$811$	−12.0300	−0.422429	−0.211215	+	0.977440i	$0.567742\pi$
$812$	11.7215	0.411345
$813$	−7.99058	−0.280242
$814$	−33.6014	−1.17773
$815$	−15.5902	−0.546101
$816$	5.67425	0.198639
$817$	2.55708	0.0894611
$818$	22.8963	0.800552
$819$	−14.3365	−0.500958
$820$	−14.0925	−0.492130
$821$	−47.9218	−1.67248	−0.836242	−	0.548361i	$-0.815252\pi$
$821$	−47.9218	−1.67248	−0.836242	+	0.548361i	$0.815252\pi$
$822$	31.1898	1.08787
$823$	−21.1905	−0.738654	−0.369327	−	0.929299i	$-0.620412\pi$
$823$	−21.1905	−0.738654	−0.369327	+	0.929299i	$0.620412\pi$
$824$	1.48656	0.0517868
$825$	−5.28304	−0.183932
$826$	63.7848	2.21936
$827$	−41.4566	−1.44159	−0.720793	−	0.693150i	$-0.756222\pi$
$827$	−41.4566	−1.44159	−0.720793	+	0.693150i	$0.756222\pi$
$828$	1.61909	0.0562674
$829$	3.13397	0.108847	0.0544236	−	0.998518i	$-0.482668\pi$
$829$	3.13397	0.108847	0.0544236	+	0.998518i	$0.482668\pi$
$830$	23.4334	0.813386
$831$	5.81584	0.201749
$832$	−49.7202	−1.72374
$833$	−5.52141	−0.191305
$834$	32.1795	1.11429
$835$	−30.4709	−1.05449
$836$	7.72765	0.267266
$837$	−22.4000	−0.774258
$838$	−22.5127	−0.777688
$839$	−30.7529	−1.06171	−0.530854	−	0.847463i	$-0.678129\pi$
$839$	−30.7529	−1.06171	−0.530854	+	0.847463i	$0.678129\pi$
$840$	−1.95828	−0.0675670
$841$	−26.5429	−0.915272
$842$	72.7046	2.50556
$843$	41.0096	1.41244
$844$	−35.0965	−1.20807
$845$	−29.3269	−1.00888
$846$	18.1230	0.623083
$847$	−31.6874	−1.08879
$848$	47.9029	1.64499
$849$	−20.2271	−0.694192
$850$	4.96571	0.170322
$851$	12.2689	0.420572
$852$	1.07889	0.0369622
$853$	17.7258	0.606919	0.303460	−	0.952844i	$-0.401858\pi$
$853$	17.7258	0.606919	0.303460	+	0.952844i	$0.401858\pi$
$854$	−35.8744	−1.22760
$855$	2.95514	0.101064
$856$	−0.524562	−0.0179292
$857$	−49.4766	−1.69009	−0.845044	−	0.534697i	$-0.820426\pi$
$857$	−49.4766	−1.69009	−0.845044	+	0.534697i	$0.820426\pi$
$858$	24.5058	0.836616
$859$	−34.0466	−1.16165	−0.580827	−	0.814027i	$-0.697271\pi$
$859$	−34.0466	−1.16165	−0.580827	+	0.814027i	$0.697271\pi$
$860$	−3.37557	−0.115106
$861$	22.2896	0.759626
$862$	−7.09308	−0.241591
$863$	28.4538	0.968580	0.484290	−	0.874908i	$-0.339078\pi$
$863$	28.4538	0.968580	0.484290	+	0.874908i	$0.339078\pi$
$864$	45.4299	1.54556
$865$	31.3727	1.06670
$866$	44.2802	1.50470
$867$	1.50881	0.0512419
$868$	29.8150	1.01199
$869$	17.7594	0.602446
$870$	−7.66199	−0.259766
$871$	50.6396	1.71586
$872$	0.125720	0.00425743
$873$	0.867729	0.0293682
$874$	−5.49202	−0.185770
$875$	42.1012	1.42328
$876$	−26.9094	−0.909184
$877$	−7.69127	−0.259716	−0.129858	−	0.991533i	$-0.541452\pi$
$877$	−7.69127	−0.259716	−0.129858	+	0.991533i	$0.541452\pi$
$878$	−19.6120	−0.661874
$879$	32.9197	1.11035
$880$	8.59081	0.289596
$881$	−13.0476	−0.439585	−0.219793	−	0.975547i	$-0.570538\pi$
$881$	−13.0476	−0.439585	−0.219793	+	0.975547i	$0.570538\pi$
$882$	−8.10162	−0.272796
$883$	42.5905	1.43328	0.716642	−	0.697441i	$-0.245678\pi$
$883$	42.5905	1.43328	0.716642	+	0.697441i	$0.245678\pi$
$884$	−11.8340	−0.398019
$885$	−21.4209	−0.720054
$886$	−36.8569	−1.23823
$887$	52.7346	1.77065	0.885327	−	0.464968i	$-0.153934\pi$
$887$	52.7346	1.77065	0.885327	+	0.464968i	$0.153934\pi$
$888$	−4.01378	−0.134694
$889$	61.7480	2.07096
$890$	−22.8421	−0.765669
$891$	−9.01819	−0.302121
$892$	−36.7810	−1.23152
$893$	−31.5831	−1.05689
$894$	27.9958	0.936319
$895$	−33.8726	−1.13224
$896$	−6.48978	−0.216808
$897$	−8.94781	−0.298759
$898$	15.9774	0.533173
$899$	6.24995	0.208447
$900$	3.74340	0.124780
$901$	12.7376	0.424351
$902$	12.1085	0.403168
$903$	5.33902	0.177672
$904$	−3.89112	−0.129417
$905$	23.3015	0.774568
$906$	25.0354	0.831747
$907$	22.8362	0.758264	0.379132	−	0.925343i	$-0.376223\pi$
$907$	22.8362	0.758264	0.379132	+	0.925343i	$0.376223\pi$
$908$	−6.09376	−0.202229
$909$	2.20340	0.0730822
$910$	−64.1956	−2.12806
$911$	−21.5151	−0.712828	−0.356414	−	0.934328i	$-0.616001\pi$
$911$	−21.5151	−0.712828	−0.356414	+	0.934328i	$0.616001\pi$
$912$	−14.5095	−0.480459
$913$	−10.3443	−0.342346
$914$	−45.1726	−1.49418
$915$	12.0477	0.398285
$916$	2.82462	0.0933279
$917$	−51.7595	−1.70925
$918$	11.3940	0.376058
$919$	14.7566	0.486774	0.243387	−	0.969929i	$-0.421742\pi$
$919$	14.7566	0.486774	0.243387	+	0.969929i	$0.421742\pi$
$920$	0.388426	0.0128060
$921$	−35.3230	−1.16393
$922$	63.4721	2.09034
$923$	1.89489	0.0623710
$924$	16.1348	0.530797
$925$	28.3660	0.932670
$926$	14.6085	0.480064
$927$	−4.68385	−0.153838
$928$	−12.6756	−0.416098
$929$	−22.9137	−0.751775	−0.375888	−	0.926665i	$-0.622662\pi$
$929$	−22.9137	−0.751775	−0.375888	+	0.926665i	$0.622662\pi$
$930$	−19.4891	−0.639073
$931$	14.1187	0.462722
$932$	−43.3295	−1.41930
$933$	0.906305	0.0296711
$934$	40.3241	1.31945
$935$	2.28434	0.0747059
$936$	−0.930307	−0.0304080
$937$	32.7505	1.06991	0.534956	−	0.844880i	$-0.320328\pi$
$937$	32.7505	1.06991	0.534956	+	0.844880i	$0.320328\pi$
$938$	64.8966	2.11895
$939$	49.8100	1.62549
$940$	41.6923	1.35985
$941$	−26.1679	−0.853050	−0.426525	−	0.904476i	$-0.640262\pi$
$941$	−26.1679	−0.853050	−0.426525	+	0.904476i	$0.640262\pi$
$942$	65.3752	2.13004
$943$	−4.42116	−0.143973
$944$	−33.4251	−1.08790
$945$	31.7551	1.03299
$946$	2.90034	0.0942982
$947$	−5.06449	−0.164574	−0.0822869	−	0.996609i	$-0.526222\pi$
$947$	−5.06449	−0.164574	−0.0822869	+	0.996609i	$0.526222\pi$
$948$	39.5959	1.28601
$949$	−47.2618	−1.53418
$950$	−12.6977	−0.411969
$951$	13.8210	0.448176
$952$	−0.812525	−0.0263341
$953$	33.2465	1.07696	0.538479	−	0.842639i	$-0.318999\pi$
$953$	33.2465	1.07696	0.538479	+	0.842639i	$0.318999\pi$
$954$	18.6900	0.605111
$955$	−0.352664	−0.0114119
$956$	57.9523	1.87431
$957$	3.38225	0.109333
$958$	60.6532	1.95962
$959$	36.0673	1.16467
$960$	21.3986	0.690636
$961$	−15.1026	−0.487180
$962$	−131.578	−4.24226
$963$	1.65279	0.0532604
$964$	−39.8934	−1.28488
$965$	−33.9137	−1.09172
$966$	−11.4670	−0.368944
$967$	−42.0618	−1.35262	−0.676308	−	0.736619i	$-0.736421\pi$
$967$	−42.0618	−1.35262	−0.676308	+	0.736619i	$0.736421\pi$
$968$	−2.05622	−0.0660895
$969$	−3.85816	−0.123942
$970$	3.88550	0.124756
$971$	−41.1429	−1.32034	−0.660170	−	0.751116i	$-0.729516\pi$
$971$	−41.1429	−1.32034	−0.660170	+	0.751116i	$0.729516\pi$
$972$	15.5098	0.497476
$973$	37.2118	1.19295
$974$	16.0578	0.514526
$975$	−20.6876	−0.662535
$976$	18.7993	0.601750
$977$	30.0579	0.961638	0.480819	−	0.876820i	$-0.340339\pi$
$977$	30.0579	0.961638	0.480819	+	0.876820i	$0.340339\pi$
$978$	29.8659	0.955005
$979$	10.0833	0.322262
$980$	−18.6379	−0.595366
$981$	−0.396120	−0.0126471
$982$	22.4090	0.715098
$983$	−34.7999	−1.10995	−0.554973	−	0.831869i	$-0.687271\pi$
$983$	−34.7999	−1.10995	−0.554973	+	0.831869i	$0.687271\pi$
$984$	1.44639	0.0461092
$985$	27.4600	0.874948
$986$	−3.17910	−0.101243
$987$	−65.9433	−2.09900
$988$	30.2604	0.962713
$989$	−1.05900	−0.0336743
$990$	3.35183	0.106528
$991$	−8.95568	−0.284486	−0.142243	−	0.989832i	$-0.545432\pi$
$991$	−8.95568	−0.284486	−0.142243	+	0.989832i	$0.545432\pi$
$992$	−32.2419	−1.02368
$993$	8.92548	0.283241
$994$	2.42837	0.0770233
$995$	9.34034	0.296109
$996$	−23.0633	−0.730790
$997$	−48.3419	−1.53100	−0.765502	−	0.643433i	$-0.777509\pi$
$997$	−48.3419	−1.53100	−0.765502	+	0.643433i	$0.777509\pi$
$998$	48.3101	1.52923
$999$	65.0869	2.05926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.16	✓	21
3.2	odd	2		6579.2.a.u.1.6		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.16	✓	21	1.1	even	1	trivial
6579.2.a.u.1.6		21	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q+2.02811 q^{2} +1.50881 q^{3} +2.11322 q^{4} -1.59736 q^{5} +3.06003 q^{6} +3.53856 q^{7} +0.229620 q^{8} -0.723487 q^{9} +O(q^{10})\)	\(q+2.02811 q^{2} +1.50881 q^{3} +2.11322 q^{4} -1.59736 q^{5} +3.06003 q^{6} +3.53856 q^{7} +0.229620 q^{8} -0.723487 q^{9} -3.23961 q^{10} +1.43007 q^{11} +3.18845 q^{12} +5.59997 q^{13} +7.17658 q^{14} -2.41011 q^{15} -3.76074 q^{16} -1.00000 q^{17} -1.46731 q^{18} +2.55708 q^{19} -3.37557 q^{20} +5.33902 q^{21} +2.90034 q^{22} -1.05900 q^{23} +0.346454 q^{24} -2.44845 q^{25} +11.3573 q^{26} -5.61804 q^{27} +7.47775 q^{28} +1.56752 q^{29} -4.88797 q^{30} +3.98716 q^{31} -8.08643 q^{32} +2.15771 q^{33} -2.02811 q^{34} -5.65235 q^{35} -1.52889 q^{36} -11.5853 q^{37} +5.18604 q^{38} +8.44930 q^{39} -0.366786 q^{40} +4.17484 q^{41} +10.8281 q^{42} +1.00000 q^{43} +3.02206 q^{44} +1.15567 q^{45} -2.14777 q^{46} -12.3512 q^{47} -5.67425 q^{48} +5.52141 q^{49} -4.96571 q^{50} -1.50881 q^{51} +11.8340 q^{52} -12.7376 q^{53} -11.3940 q^{54} -2.28434 q^{55} +0.812525 q^{56} +3.85816 q^{57} +3.17910 q^{58} +8.88790 q^{59} -5.09310 q^{60} -4.99882 q^{61} +8.08638 q^{62} -2.56010 q^{63} -8.87866 q^{64} -8.94516 q^{65} +4.37607 q^{66} +9.04283 q^{67} -2.11322 q^{68} -1.59783 q^{69} -11.4636 q^{70} +0.338375 q^{71} -0.166127 q^{72} -8.43965 q^{73} -23.4963 q^{74} -3.69424 q^{75} +5.40368 q^{76} +5.06040 q^{77} +17.1361 q^{78} +12.4185 q^{79} +6.00726 q^{80} -6.30611 q^{81} +8.46702 q^{82} -7.23340 q^{83} +11.2825 q^{84} +1.59736 q^{85} +2.02811 q^{86} +2.36509 q^{87} +0.328374 q^{88} +7.05087 q^{89} +2.34382 q^{90} +19.8158 q^{91} -2.23790 q^{92} +6.01587 q^{93} -25.0496 q^{94} -4.08458 q^{95} -12.2009 q^{96} -1.19937 q^{97} +11.1980 q^{98} -1.03464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

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