LMFDB - Embedded newform 731.2.a.f.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.48059 q^{2} +2.78565 q^{3} +4.15334 q^{4} -4.06907 q^{5} -6.91006 q^{6} +4.55433 q^{7} -5.34155 q^{8} +4.75983 q^{9} +O(q^{10})$	\(q-2.48059 q^{2} +2.78565 q^{3} +4.15334 q^{4} -4.06907 q^{5} -6.91006 q^{6} +4.55433 q^{7} -5.34155 q^{8} +4.75983 q^{9} +10.0937 q^{10} +3.82923 q^{11} +11.5697 q^{12} +2.15503 q^{13} -11.2974 q^{14} -11.3350 q^{15} +4.94354 q^{16} -1.00000 q^{17} -11.8072 q^{18} -6.06029 q^{19} -16.9002 q^{20} +12.6867 q^{21} -9.49876 q^{22} +1.03722 q^{23} -14.8797 q^{24} +11.5573 q^{25} -5.34575 q^{26} +4.90228 q^{27} +18.9157 q^{28} +5.63738 q^{29} +28.1175 q^{30} -2.23106 q^{31} -1.57980 q^{32} +10.6669 q^{33} +2.48059 q^{34} -18.5319 q^{35} +19.7692 q^{36} -1.94232 q^{37} +15.0331 q^{38} +6.00315 q^{39} +21.7352 q^{40} -8.20092 q^{41} -31.4706 q^{42} +1.00000 q^{43} +15.9041 q^{44} -19.3681 q^{45} -2.57293 q^{46} +12.2637 q^{47} +13.7710 q^{48} +13.7419 q^{49} -28.6690 q^{50} -2.78565 q^{51} +8.95056 q^{52} -1.37284 q^{53} -12.1606 q^{54} -15.5814 q^{55} -24.3272 q^{56} -16.8818 q^{57} -13.9840 q^{58} +8.39796 q^{59} -47.0781 q^{60} +9.32134 q^{61} +5.53434 q^{62} +21.6778 q^{63} -5.96824 q^{64} -8.76896 q^{65} -26.4602 q^{66} +6.91822 q^{67} -4.15334 q^{68} +2.88934 q^{69} +45.9700 q^{70} +2.82790 q^{71} -25.4249 q^{72} -7.13217 q^{73} +4.81811 q^{74} +32.1947 q^{75} -25.1704 q^{76} +17.4396 q^{77} -14.8914 q^{78} +3.27782 q^{79} -20.1156 q^{80} -0.623478 q^{81} +20.3431 q^{82} -2.88422 q^{83} +52.6924 q^{84} +4.06907 q^{85} -2.48059 q^{86} +15.7038 q^{87} -20.4540 q^{88} -13.9853 q^{89} +48.0444 q^{90} +9.81470 q^{91} +4.30794 q^{92} -6.21494 q^{93} -30.4212 q^{94} +24.6597 q^{95} -4.40077 q^{96} -11.0449 q^{97} -34.0880 q^{98} +18.2265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.48059	−1.75404	−0.877022	−	0.480451i	$-0.840473\pi$
$2$	−2.48059	−1.75404	−0.877022	+	0.480451i	$0.840473\pi$
$3$	2.78565	1.60829	0.804147	−	0.594430i	$-0.202622\pi$
$3$	2.78565	1.60829	0.804147	+	0.594430i	$0.202622\pi$
$4$	4.15334	2.07667
$5$	−4.06907	−1.81974	−0.909872	−	0.414890i	$-0.863820\pi$
$5$	−4.06907	−1.81974	−0.909872	+	0.414890i	$0.863820\pi$
$6$	−6.91006	−2.82102
$7$	4.55433	1.72137	0.860687	−	0.509135i	$-0.170035\pi$
$7$	4.55433	1.72137	0.860687	+	0.509135i	$0.170035\pi$
$8$	−5.34155	−1.88852
$9$	4.75983	1.58661
$10$	10.0937	3.19191
$11$	3.82923	1.15456	0.577278	−	0.816547i	$-0.304115\pi$
$11$	3.82923	1.15456	0.577278	+	0.816547i	$0.304115\pi$
$12$	11.5697	3.33990
$13$	2.15503	0.597697	0.298849	−	0.954300i	$-0.403397\pi$
$13$	2.15503	0.597697	0.298849	+	0.954300i	$0.403397\pi$
$14$	−11.2974	−3.01936
$15$	−11.3350	−2.92668
$16$	4.94354	1.23588
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−11.8072	−2.78299
$19$	−6.06029	−1.39033	−0.695163	−	0.718852i	$-0.744668\pi$
$19$	−6.06029	−1.39033	−0.695163	+	0.718852i	$0.744668\pi$
$20$	−16.9002	−3.77900
$21$	12.6867	2.76848
$22$	−9.49876	−2.02514
$23$	1.03722	0.216276	0.108138	−	0.994136i	$-0.465511\pi$
$23$	1.03722	0.216276	0.108138	+	0.994136i	$0.465511\pi$
$24$	−14.8797	−3.03730
$25$	11.5573	2.31147
$26$	−5.34575	−1.04839
$27$	4.90228	0.943444
$28$	18.9157	3.57472
$29$	5.63738	1.04684	0.523418	−	0.852076i	$-0.324657\pi$
$29$	5.63738	1.04684	0.523418	+	0.852076i	$0.324657\pi$
$30$	28.1175	5.13353
$31$	−2.23106	−0.400710	−0.200355	−	0.979723i	$-0.564209\pi$
$31$	−2.23106	−0.400710	−0.200355	+	0.979723i	$0.564209\pi$
$32$	−1.57980	−0.279272
$33$	10.6669	1.85687
$34$	2.48059	0.425418
$35$	−18.5319	−3.13246
$36$	19.7692	3.29487
$37$	−1.94232	−0.319316	−0.159658	−	0.987172i	$-0.551039\pi$
$37$	−1.94232	−0.319316	−0.159658	+	0.987172i	$0.551039\pi$
$38$	15.0331	2.43869
$39$	6.00315	0.961274
$40$	21.7352	3.43663
$41$	−8.20092	−1.28077	−0.640384	−	0.768055i	$-0.721225\pi$
$41$	−8.20092	−1.28077	−0.640384	+	0.768055i	$0.721225\pi$
$42$	−31.4706	−4.85603
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	15.9041	2.39763
$45$	−19.3681	−2.88723
$46$	−2.57293	−0.379358
$47$	12.2637	1.78884	0.894421	−	0.447227i	$-0.147588\pi$
$47$	12.2637	1.78884	0.894421	+	0.447227i	$0.147588\pi$
$48$	13.7710	1.98767
$49$	13.7419	1.96313
$50$	−28.6690	−4.05441
$51$	−2.78565	−0.390069
$52$	8.95056	1.24122
$53$	−1.37284	−0.188574	−0.0942872	−	0.995545i	$-0.530057\pi$
$53$	−1.37284	−0.188574	−0.0942872	+	0.995545i	$0.530057\pi$
$54$	−12.1606	−1.65484
$55$	−15.5814	−2.10100
$56$	−24.3272	−3.25086
$57$	−16.8818	−2.23605
$58$	−13.9840	−1.83620
$59$	8.39796	1.09332	0.546661	−	0.837354i	$-0.315899\pi$
$59$	8.39796	1.09332	0.546661	+	0.837354i	$0.315899\pi$
$60$	−47.0781	−6.07775
$61$	9.32134	1.19347	0.596737	−	0.802437i	$-0.296463\pi$
$61$	9.32134	1.19347	0.596737	+	0.802437i	$0.296463\pi$
$62$	5.53434	0.702862
$63$	21.6778	2.73115
$64$	−5.96824	−0.746030
$65$	−8.76896	−1.08766
$66$	−26.4602	−3.25703
$67$	6.91822	0.845195	0.422597	−	0.906317i	$-0.361118\pi$
$67$	6.91822	0.845195	0.422597	+	0.906317i	$0.361118\pi$
$68$	−4.15334	−0.503666
$69$	2.88934	0.347836
$70$	45.9700	5.49447
$71$	2.82790	0.335610	0.167805	−	0.985820i	$-0.446332\pi$
$71$	2.82790	0.335610	0.167805	+	0.985820i	$0.446332\pi$
$72$	−25.4249	−2.99635
$73$	−7.13217	−0.834758	−0.417379	−	0.908733i	$-0.637051\pi$
$73$	−7.13217	−0.834758	−0.417379	+	0.908733i	$0.637051\pi$
$74$	4.81811	0.560094
$75$	32.1947	3.71752
$76$	−25.1704	−2.88725
$77$	17.4396	1.98742
$78$	−14.8914	−1.68612
$79$	3.27782	0.368784	0.184392	−	0.982853i	$-0.440968\pi$
$79$	3.27782	0.368784	0.184392	+	0.982853i	$0.440968\pi$
$80$	−20.1156	−2.24899
$81$	−0.623478	−0.0692753
$82$	20.3431	2.24652
$83$	−2.88422	−0.316584	−0.158292	−	0.987392i	$-0.550599\pi$
$83$	−2.88422	−0.316584	−0.158292	+	0.987392i	$0.550599\pi$
$84$	52.6924	5.74921
$85$	4.06907	0.441353
$86$	−2.48059	−0.267489
$87$	15.7038	1.68362
$88$	−20.4540	−2.18041
$89$	−13.9853	−1.48244	−0.741221	−	0.671261i	$-0.765753\pi$
$89$	−13.9853	−1.48244	−0.741221	+	0.671261i	$0.765753\pi$
$90$	48.0444	5.06432
$91$	9.81470	1.02886
$92$	4.30794	0.449134
$93$	−6.21494	−0.644459
$94$	−30.4212	−3.13771
$95$	24.6597	2.53004
$96$	−4.40077	−0.449151
$97$	−11.0449	−1.12144	−0.560718	−	0.828007i	$-0.689475\pi$
$97$	−11.0449	−1.12144	−0.560718	+	0.828007i	$0.689475\pi$
$98$	−34.0880	−3.44341
$99$	18.2265	1.83183
$100$	48.0015	4.80015
$101$	−0.434601	−0.0432444	−0.0216222	−	0.999766i	$-0.506883\pi$
$101$	−0.434601	−0.0432444	−0.0216222	+	0.999766i	$0.506883\pi$
$102$	6.91006	0.684198
$103$	1.48041	0.145869	0.0729346	−	0.997337i	$-0.476764\pi$
$103$	1.48041	0.145869	0.0729346	+	0.997337i	$0.476764\pi$
$104$	−11.5112	−1.12877
$105$	−51.6233	−5.03791
$106$	3.40546	0.330768
$107$	14.4862	1.40043	0.700215	−	0.713932i	$-0.253087\pi$
$107$	14.4862	1.40043	0.700215	+	0.713932i	$0.253087\pi$
$108$	20.3608	1.95922
$109$	15.9845	1.53103	0.765517	−	0.643416i	$-0.222483\pi$
$109$	15.9845	1.53103	0.765517	+	0.643416i	$0.222483\pi$
$110$	38.6511	3.68524
$111$	−5.41063	−0.513554
$112$	22.5145	2.12742
$113$	10.2808	0.967138	0.483569	−	0.875306i	$-0.339340\pi$
$113$	10.2808	0.967138	0.483569	+	0.875306i	$0.339340\pi$
$114$	41.8769	3.92213
$115$	−4.22054	−0.393567
$116$	23.4140	2.17393
$117$	10.2576	0.948314
$118$	−20.8319	−1.91773
$119$	−4.55433	−0.417494
$120$	60.5465	5.52711
$121$	3.66302	0.333002
$122$	−23.1224	−2.09341
$123$	−22.8449	−2.05985
$124$	−9.26633	−0.832141
$125$	−26.6822	−2.38653
$126$	−53.7739	−4.79056
$127$	−5.73017	−0.508471	−0.254235	−	0.967142i	$-0.581824\pi$
$127$	−5.73017	−0.508471	−0.254235	+	0.967142i	$0.581824\pi$
$128$	17.9644	1.58784
$129$	2.78565	0.245263
$130$	21.7522	1.90780
$131$	−2.86564	−0.250372	−0.125186	−	0.992133i	$-0.539953\pi$
$131$	−2.86564	−0.250372	−0.125186	+	0.992133i	$0.539953\pi$
$132$	44.3032	3.85610
$133$	−27.6005	−2.39327
$134$	−17.1613	−1.48251
$135$	−19.9477	−1.71683
$136$	5.34155	0.458034
$137$	−13.5267	−1.15567	−0.577833	−	0.816155i	$-0.696102\pi$
$137$	−13.5267	−1.15567	−0.577833	+	0.816155i	$0.696102\pi$
$138$	−7.16728	−0.610119
$139$	4.17926	0.354480	0.177240	−	0.984168i	$-0.443283\pi$
$139$	4.17926	0.354480	0.177240	+	0.984168i	$0.443283\pi$
$140$	−76.9691	−6.50508
$141$	34.1623	2.87698
$142$	−7.01486	−0.588674
$143$	8.25211	0.690076
$144$	23.5304	1.96087
$145$	−22.9389	−1.90497
$146$	17.6920	1.46420
$147$	38.2801	3.15729
$148$	−8.06713	−0.663114
$149$	−3.07897	−0.252239	−0.126120	−	0.992015i	$-0.540252\pi$
$149$	−3.07897	−0.252239	−0.126120	+	0.992015i	$0.540252\pi$
$150$	−79.8618	−6.52069
$151$	−5.15576	−0.419570	−0.209785	−	0.977748i	$-0.567276\pi$
$151$	−5.15576	−0.419570	−0.209785	+	0.977748i	$0.567276\pi$
$152$	32.3714	2.62566
$153$	−4.75983	−0.384810
$154$	−43.2605	−3.48603
$155$	9.07833	0.729189
$156$	24.9331	1.99625
$157$	−0.0643619	−0.00513664	−0.00256832	−	0.999997i	$-0.500818\pi$
$157$	−0.0643619	−0.00513664	−0.00256832	+	0.999997i	$0.500818\pi$
$158$	−8.13094	−0.646863
$159$	−3.82425	−0.303283
$160$	6.42832	0.508203
$161$	4.72386	0.372292
$162$	1.54659	0.121512
$163$	−20.1635	−1.57932	−0.789662	−	0.613542i	$-0.789744\pi$
$163$	−20.1635	−1.57932	−0.789662	+	0.613542i	$0.789744\pi$
$164$	−34.0612	−2.65973
$165$	−43.4043	−3.37902
$166$	7.15457	0.555302
$167$	−6.05211	−0.468326	−0.234163	−	0.972197i	$-0.575235\pi$
$167$	−6.05211	−0.468326	−0.234163	+	0.972197i	$0.575235\pi$
$168$	−67.7669	−5.22833
$169$	−8.35585	−0.642758
$170$	−10.0937	−0.774152
$171$	−28.8460	−2.20591
$172$	4.15334	0.316689
$173$	6.53813	0.497085	0.248543	−	0.968621i	$-0.420048\pi$
$173$	6.53813	0.497085	0.248543	+	0.968621i	$0.420048\pi$
$174$	−38.9546	−2.95314
$175$	52.6358	3.97890
$176$	18.9300	1.42690
$177$	23.3938	1.75838
$178$	34.6919	2.60027
$179$	−6.28139	−0.469493	−0.234747	−	0.972057i	$-0.575426\pi$
$179$	−6.28139	−0.469493	−0.234747	+	0.972057i	$0.575426\pi$
$180$	−80.4423	−5.99581
$181$	5.55161	0.412648	0.206324	−	0.978484i	$-0.433850\pi$
$181$	5.55161	0.412648	0.206324	+	0.978484i	$0.433850\pi$
$182$	−24.3463	−1.80467
$183$	25.9660	1.91946
$184$	−5.54039	−0.408443
$185$	7.90345	0.581073
$186$	15.4167	1.13041
$187$	−3.82923	−0.280021
$188$	50.9352	3.71483
$189$	22.3266	1.62402
$190$	−61.1708	−4.43779
$191$	17.0417	1.23310	0.616548	−	0.787318i	$-0.288531\pi$
$191$	17.0417	1.23310	0.616548	+	0.787318i	$0.288531\pi$
$192$	−16.6254	−1.19984
$193$	−23.8156	−1.71429	−0.857144	−	0.515077i	$-0.827763\pi$
$193$	−23.8156	−1.71429	−0.857144	+	0.515077i	$0.827763\pi$
$194$	27.3978	1.96705
$195$	−24.4272	−1.74927
$196$	57.0747	4.07676
$197$	2.91359	0.207585	0.103792	−	0.994599i	$-0.466902\pi$
$197$	2.91359	0.207585	0.103792	+	0.994599i	$0.466902\pi$
$198$	−45.2125	−3.21312
$199$	0.406409	0.0288096	0.0144048	−	0.999896i	$-0.495415\pi$
$199$	0.406409	0.0288096	0.0144048	+	0.999896i	$0.495415\pi$
$200$	−61.7341	−4.36526
$201$	19.2717	1.35932
$202$	1.07807	0.0758526
$203$	25.6745	1.80199
$204$	−11.5697	−0.810044
$205$	33.3701	2.33067
$206$	−3.67229	−0.255861
$207$	4.93701	0.343146
$208$	10.6535	0.738685
$209$	−23.2063	−1.60521
$210$	128.056	8.83672
$211$	−4.17306	−0.287285	−0.143643	−	0.989630i	$-0.545882\pi$
$211$	−4.17306	−0.287285	−0.143643	+	0.989630i	$0.545882\pi$
$212$	−5.70188	−0.391607
$213$	7.87753	0.539759
$214$	−35.9343	−2.45642
$215$	−4.06907	−0.277508
$216$	−26.1858	−1.78172
$217$	−10.1610	−0.689771
$218$	−39.6509	−2.68550
$219$	−19.8677	−1.34254
$220$	−64.7149	−4.36308
$221$	−2.15503	−0.144963
$222$	13.4216	0.900796
$223$	−13.0102	−0.871225	−0.435613	−	0.900134i	$-0.643468\pi$
$223$	−13.0102	−0.871225	−0.435613	+	0.900134i	$0.643468\pi$
$224$	−7.19493	−0.480731
$225$	55.0110	3.66740
$226$	−25.5025	−1.69640
$227$	13.4861	0.895102	0.447551	−	0.894258i	$-0.352296\pi$
$227$	13.4861	0.895102	0.447551	+	0.894258i	$0.352296\pi$
$228$	−70.1160	−4.64354
$229$	−25.6883	−1.69753	−0.848764	−	0.528772i	$-0.822653\pi$
$229$	−25.6883	−1.69753	−0.848764	+	0.528772i	$0.822653\pi$
$230$	10.4694	0.690334
$231$	48.5805	3.19636
$232$	−30.1124	−1.97697
$233$	−10.6834	−0.699895	−0.349947	−	0.936769i	$-0.613801\pi$
$233$	−10.6834	−0.699895	−0.349947	+	0.936769i	$0.613801\pi$
$234$	−25.4449	−1.66338
$235$	−49.9018	−3.25523
$236$	34.8796	2.27047
$237$	9.13086	0.593113
$238$	11.2974	0.732303
$239$	−13.3220	−0.861732	−0.430866	−	0.902416i	$-0.641792\pi$
$239$	−13.3220	−0.861732	−0.430866	+	0.902416i	$0.641792\pi$
$240$	−56.0350	−3.61704
$241$	14.0599	0.905679	0.452840	−	0.891592i	$-0.350411\pi$
$241$	14.0599	0.905679	0.452840	+	0.891592i	$0.350411\pi$
$242$	−9.08646	−0.584100
$243$	−16.4436	−1.05486
$244$	38.7147	2.47845
$245$	−55.9167	−3.57239
$246$	56.6688	3.61307
$247$	−13.0601	−0.830994
$248$	11.9173	0.756750
$249$	−8.03442	−0.509161
$250$	66.1877	4.18608
$251$	−6.04680	−0.381671	−0.190835	−	0.981622i	$-0.561120\pi$
$251$	−6.04680	−0.381671	−0.190835	+	0.981622i	$0.561120\pi$
$252$	90.0354	5.67170
$253$	3.97177	0.249703
$254$	14.2142	0.891880
$255$	11.3350	0.709825
$256$	−32.6258	−2.03911
$257$	−12.6087	−0.786508	−0.393254	−	0.919430i	$-0.628651\pi$
$257$	−12.6087	−0.786508	−0.393254	+	0.919430i	$0.628651\pi$
$258$	−6.91006	−0.430201
$259$	−8.84597	−0.549662
$260$	−36.4205	−2.25870
$261$	26.8330	1.66092
$262$	7.10848	0.439163
$263$	−19.8828	−1.22603	−0.613013	−	0.790073i	$-0.710043\pi$
$263$	−19.8828	−1.22603	−0.613013	+	0.790073i	$0.710043\pi$
$264$	−56.9778	−3.50674
$265$	5.58619	0.343157
$266$	68.4657	4.19790
$267$	−38.9582	−2.38420
$268$	28.7337	1.75519
$269$	−17.8123	−1.08603	−0.543016	−	0.839722i	$-0.682718\pi$
$269$	−17.8123	−1.08603	−0.543016	+	0.839722i	$0.682718\pi$
$270$	49.4822	3.01139
$271$	5.54966	0.337118	0.168559	−	0.985692i	$-0.446089\pi$
$271$	5.54966	0.337118	0.168559	+	0.985692i	$0.446089\pi$
$272$	−4.94354	−0.299746
$273$	27.3403	1.65471
$274$	33.5543	2.02709
$275$	44.2557	2.66872
$276$	12.0004	0.722340
$277$	−2.63355	−0.158235	−0.0791174	−	0.996865i	$-0.525210\pi$
$277$	−2.63355	−0.158235	−0.0791174	+	0.996865i	$0.525210\pi$
$278$	−10.3670	−0.621774
$279$	−10.6195	−0.635771
$280$	98.9890	5.91572
$281$	15.2271	0.908370	0.454185	−	0.890907i	$-0.349931\pi$
$281$	15.2271	0.908370	0.454185	+	0.890907i	$0.349931\pi$
$282$	−84.7427	−5.04635
$283$	−10.3635	−0.616046	−0.308023	−	0.951379i	$-0.599667\pi$
$283$	−10.3635	−0.616046	−0.308023	+	0.951379i	$0.599667\pi$
$284$	11.7452	0.696950
$285$	68.6934	4.06904
$286$	−20.4701	−1.21042
$287$	−37.3496	−2.20468
$288$	−7.51959	−0.443096
$289$	1.00000	0.0588235
$290$	56.9021	3.34140
$291$	−30.7671	−1.80360
$292$	−29.6223	−1.73352
$293$	−7.54789	−0.440952	−0.220476	−	0.975392i	$-0.570761\pi$
$293$	−7.54789	−0.440952	−0.220476	+	0.975392i	$0.570761\pi$
$294$	−94.9572	−5.53802
$295$	−34.1719	−1.98957
$296$	10.3750	0.603036
$297$	18.7720	1.08926
$298$	7.63768	0.442439
$299$	2.23525	0.129268
$300$	133.715	7.72005
$301$	4.55433	0.262507
$302$	12.7893	0.735943
$303$	−1.21065	−0.0695498
$304$	−29.9593	−1.71828
$305$	−37.9292	−2.17182
$306$	11.8072	0.674973
$307$	21.3074	1.21608	0.608039	−	0.793907i	$-0.291956\pi$
$307$	21.3074	1.21608	0.608039	+	0.793907i	$0.291956\pi$
$308$	72.4324	4.12722
$309$	4.12390	0.234601
$310$	−22.5196	−1.27903
$311$	−6.31119	−0.357874	−0.178937	−	0.983860i	$-0.557266\pi$
$311$	−6.31119	−0.357874	−0.178937	+	0.983860i	$0.557266\pi$
$312$	−32.0662	−1.81539
$313$	−20.7131	−1.17077	−0.585387	−	0.810754i	$-0.699057\pi$
$313$	−20.7131	−1.17077	−0.585387	+	0.810754i	$0.699057\pi$
$314$	0.159656	0.00900989
$315$	−88.2086	−4.96999
$316$	13.6139	0.765842
$317$	−25.0169	−1.40509	−0.702546	−	0.711639i	$-0.747953\pi$
$317$	−25.0169	−1.40509	−0.702546	+	0.711639i	$0.747953\pi$
$318$	9.48642	0.531972
$319$	21.5868	1.20863
$320$	24.2852	1.35758
$321$	40.3534	2.25230
$322$	−11.7180	−0.653016
$323$	6.06029	0.337204
$324$	−2.58952	−0.143862
$325$	24.9064	1.38156
$326$	50.0173	2.77020
$327$	44.5271	2.46235
$328$	43.8056	2.41876
$329$	55.8528	3.07926
$330$	107.668	5.92695
$331$	32.0224	1.76011	0.880056	−	0.474870i	$-0.157505\pi$
$331$	32.0224	1.76011	0.880056	+	0.474870i	$0.157505\pi$
$332$	−11.9791	−0.657441
$333$	−9.24514	−0.506630
$334$	15.0128	0.821464
$335$	−28.1507	−1.53804
$336$	62.7174	3.42152
$337$	−14.8315	−0.807924	−0.403962	−	0.914776i	$-0.632367\pi$
$337$	−14.8315	−0.807924	−0.403962	+	0.914776i	$0.632367\pi$
$338$	20.7275	1.12743
$339$	28.6387	1.55544
$340$	16.9002	0.916543
$341$	−8.54323	−0.462642
$342$	71.5551	3.86926
$343$	30.7047	1.65790
$344$	−5.34155	−0.287997
$345$	−11.7569	−0.632972
$346$	−16.2184	−0.871909
$347$	10.3717	0.556783	0.278391	−	0.960468i	$-0.410199\pi$
$347$	10.3717	0.556783	0.278391	+	0.960468i	$0.410199\pi$
$348$	65.2230	3.49632
$349$	15.9351	0.852988	0.426494	−	0.904490i	$-0.359749\pi$
$349$	15.9351	0.852988	0.426494	+	0.904490i	$0.359749\pi$
$350$	−130.568	−6.97916
$351$	10.5646	0.563894
$352$	−6.04942	−0.322435
$353$	−36.7603	−1.95655	−0.978277	−	0.207302i	$-0.933532\pi$
$353$	−36.7603	−1.95655	−0.978277	+	0.207302i	$0.933532\pi$
$354$	−58.0304	−3.08428
$355$	−11.5069	−0.610724
$356$	−58.0858	−3.07854
$357$	−12.6867	−0.671454
$358$	15.5816	0.823511
$359$	10.5105	0.554722	0.277361	−	0.960766i	$-0.410540\pi$
$359$	10.5105	0.554722	0.277361	+	0.960766i	$0.410540\pi$
$360$	103.456	5.45260
$361$	17.7271	0.933005
$362$	−13.7713	−0.723803
$363$	10.2039	0.535565
$364$	40.7638	2.13660
$365$	29.0213	1.51904
$366$	−64.4110	−3.36682
$367$	14.2694	0.744855	0.372428	−	0.928061i	$-0.378525\pi$
$367$	14.2694	0.744855	0.372428	+	0.928061i	$0.378525\pi$
$368$	5.12756	0.267292
$369$	−39.0350	−2.03208
$370$	−19.6052	−1.01923
$371$	−6.25237	−0.324607
$372$	−25.8127	−1.33833
$373$	−3.94669	−0.204352	−0.102176	−	0.994766i	$-0.532580\pi$
$373$	−3.94669	−0.204352	−0.102176	+	0.994766i	$0.532580\pi$
$374$	9.49876	0.491169
$375$	−74.3273	−3.83825
$376$	−65.5071	−3.37827
$377$	12.1487	0.625691
$378$	−55.3831	−2.84860
$379$	26.0381	1.33749	0.668744	−	0.743493i	$-0.266832\pi$
$379$	26.0381	1.33749	0.668744	+	0.743493i	$0.266832\pi$
$380$	102.420	5.25405
$381$	−15.9622	−0.817771
$382$	−42.2735	−2.16290
$383$	−37.0869	−1.89505	−0.947525	−	0.319680i	$-0.896424\pi$
$383$	−37.0869	−1.89505	−0.947525	+	0.319680i	$0.896424\pi$
$384$	50.0424	2.55372
$385$	−70.9628	−3.61660
$386$	59.0769	3.00694
$387$	4.75983	0.241956
$388$	−45.8731	−2.32885
$389$	−1.44492	−0.0732605	−0.0366303	−	0.999329i	$-0.511662\pi$
$389$	−1.44492	−0.0732605	−0.0366303	+	0.999329i	$0.511662\pi$
$390$	60.5940	3.06830
$391$	−1.03722	−0.0524547
$392$	−73.4030	−3.70741
$393$	−7.98266	−0.402672
$394$	−7.22743	−0.364113
$395$	−13.3377	−0.671092
$396$	75.7009	3.80411
$397$	−12.3915	−0.621914	−0.310957	−	0.950424i	$-0.600649\pi$
$397$	−12.3915	−0.621914	−0.310957	+	0.950424i	$0.600649\pi$
$398$	−1.00813	−0.0505332
$399$	−76.8854	−3.84908
$400$	57.1341	2.85671
$401$	19.5576	0.976662	0.488331	−	0.872658i	$-0.337606\pi$
$401$	19.5576	0.976662	0.488331	+	0.872658i	$0.337606\pi$
$402$	−47.8053	−2.38431
$403$	−4.80799	−0.239503
$404$	−1.80505	−0.0898044
$405$	2.53698	0.126063
$406$	−63.6879	−3.16078
$407$	−7.43761	−0.368668
$408$	14.8797	0.736654
$409$	−14.0040	−0.692453	−0.346226	−	0.938151i	$-0.612537\pi$
$409$	−14.0040	−0.692453	−0.346226	+	0.938151i	$0.612537\pi$
$410$	−82.7776	−4.08810
$411$	−37.6807	−1.85865
$412$	6.14864	0.302922
$413$	38.2471	1.88202
$414$	−12.2467	−0.601893
$415$	11.7361	0.576102
$416$	−3.40452	−0.166920
$417$	11.6419	0.570108
$418$	57.5653	2.81561
$419$	−27.1958	−1.32860	−0.664300	−	0.747466i	$-0.731270\pi$
$419$	−27.1958	−1.32860	−0.664300	+	0.747466i	$0.731270\pi$
$420$	−214.409	−10.4621
$421$	13.6726	0.666364	0.333182	−	0.942863i	$-0.391878\pi$
$421$	13.6726	0.666364	0.333182	+	0.942863i	$0.391878\pi$
$422$	10.3517	0.503911
$423$	58.3731	2.83820
$424$	7.33311	0.356127
$425$	−11.5573	−0.560613
$426$	−19.5409	−0.946761
$427$	42.4524	2.05442
$428$	60.1659	2.90823
$429$	22.9875	1.10985
$430$	10.0937	0.486762
$431$	−4.71726	−0.227223	−0.113611	−	0.993525i	$-0.536242\pi$
$431$	−4.71726	−0.227223	−0.113611	+	0.993525i	$0.536242\pi$
$432$	24.2346	1.16599
$433$	−16.2643	−0.781612	−0.390806	−	0.920473i	$-0.627804\pi$
$433$	−16.2643	−0.781612	−0.390806	+	0.920473i	$0.627804\pi$
$434$	25.2052	1.20989
$435$	−63.8997	−3.06376
$436$	66.3889	3.17945
$437$	−6.28588	−0.300694
$438$	49.2837	2.35487
$439$	34.0998	1.62749	0.813747	−	0.581220i	$-0.197424\pi$
$439$	34.0998	1.62749	0.813747	+	0.581220i	$0.197424\pi$
$440$	83.2289	3.96778
$441$	65.4091	3.11472
$442$	5.34575	0.254271
$443$	−19.5153	−0.927200	−0.463600	−	0.886044i	$-0.653443\pi$
$443$	−19.5153	−0.927200	−0.463600	+	0.886044i	$0.653443\pi$
$444$	−22.4722	−1.06648
$445$	56.9073	2.69767
$446$	32.2729	1.52817
$447$	−8.57694	−0.405675
$448$	−27.1813	−1.28420
$449$	−32.8151	−1.54864	−0.774321	−	0.632794i	$-0.781908\pi$
$449$	−32.8151	−1.54864	−0.774321	+	0.632794i	$0.781908\pi$
$450$	−136.460	−6.43278
$451$	−31.4032	−1.47872
$452$	42.6997	2.00843
$453$	−14.3621	−0.674791
$454$	−33.4534	−1.57005
$455$	−39.9367	−1.87226
$456$	90.1752	4.22284
$457$	−12.4002	−0.580058	−0.290029	−	0.957018i	$-0.593665\pi$
$457$	−12.4002	−0.580058	−0.290029	+	0.957018i	$0.593665\pi$
$458$	63.7221	2.97754
$459$	−4.90228	−0.228819
$460$	−17.5293	−0.817308
$461$	−40.5330	−1.88781	−0.943905	−	0.330216i	$-0.892878\pi$
$461$	−40.5330	−1.88781	−0.943905	+	0.330216i	$0.892878\pi$
$462$	−120.508	−5.60656
$463$	−7.04611	−0.327460	−0.163730	−	0.986505i	$-0.552353\pi$
$463$	−7.04611	−0.327460	−0.163730	+	0.986505i	$0.552353\pi$
$464$	27.8686	1.29377
$465$	25.2890	1.17275
$466$	26.5012	1.22765
$467$	22.5741	1.04460	0.522301	−	0.852761i	$-0.325074\pi$
$467$	22.5741	1.04460	0.522301	+	0.852761i	$0.325074\pi$
$468$	42.6032	1.96933
$469$	31.5078	1.45490
$470$	123.786	5.70982
$471$	−0.179290	−0.00826123
$472$	−44.8582	−2.06476
$473$	3.82923	0.176068
$474$	−22.6499	−1.04035
$475$	−70.0408	−3.21369
$476$	−18.9157	−0.866998
$477$	−6.53450	−0.299194
$478$	33.0466	1.51151
$479$	32.7935	1.49837	0.749186	−	0.662359i	$-0.230445\pi$
$479$	32.7935	1.49837	0.749186	+	0.662359i	$0.230445\pi$
$480$	17.9070	0.817340
$481$	−4.18576	−0.190854
$482$	−34.8769	−1.58860
$483$	13.1590	0.598755
$484$	15.2138	0.691534
$485$	44.9423	2.04073
$486$	40.7899	1.85027
$487$	20.4082	0.924782	0.462391	−	0.886676i	$-0.346992\pi$
$487$	20.4082	0.924782	0.462391	+	0.886676i	$0.346992\pi$
$488$	−49.7904	−2.25391
$489$	−56.1683	−2.54002
$490$	138.706	6.26612
$491$	8.56788	0.386663	0.193332	−	0.981133i	$-0.438071\pi$
$491$	8.56788	0.386663	0.193332	+	0.981133i	$0.438071\pi$
$492$	−94.8825	−4.27763
$493$	−5.63738	−0.253895
$494$	32.3968	1.45760
$495$	−74.1649	−3.33347
$496$	−11.0293	−0.495231
$497$	12.8792	0.577710
$498$	19.9301	0.893090
$499$	0.172232	0.00771016	0.00385508	−	0.999993i	$-0.498773\pi$
$499$	0.172232	0.00771016	0.00385508	+	0.999993i	$0.498773\pi$
$500$	−110.820	−4.95604
$501$	−16.8590	−0.753206
$502$	14.9996	0.669467
$503$	7.07367	0.315399	0.157700	−	0.987487i	$-0.449592\pi$
$503$	7.07367	0.315399	0.157700	+	0.987487i	$0.449592\pi$
$504$	−115.793	−5.15784
$505$	1.76842	0.0786938
$506$	−9.85234	−0.437990
$507$	−23.2765	−1.03374
$508$	−23.7993	−1.05593
$509$	21.8084	0.966641	0.483321	−	0.875443i	$-0.339430\pi$
$509$	21.8084	0.966641	0.483321	+	0.875443i	$0.339430\pi$
$510$	−28.1175	−1.24506
$511$	−32.4822	−1.43693
$512$	45.0026	1.98885
$513$	−29.7092	−1.31169
$514$	31.2770	1.37957
$515$	−6.02389	−0.265444
$516$	11.5697	0.509329
$517$	46.9605	2.06532
$518$	21.9433	0.964131
$519$	18.2129	0.799459
$520$	46.8399	2.05406
$521$	17.4873	0.766132	0.383066	−	0.923721i	$-0.374868\pi$
$521$	17.4873	0.766132	0.383066	+	0.923721i	$0.374868\pi$
$522$	−66.5617	−2.91333
$523$	16.6200	0.726742	0.363371	−	0.931645i	$-0.381626\pi$
$523$	16.6200	0.726742	0.363371	+	0.931645i	$0.381626\pi$
$524$	−11.9020	−0.519940
$525$	146.625	6.39924
$526$	49.3211	2.15050
$527$	2.23106	0.0971864
$528$	52.7322	2.29487
$529$	−21.9242	−0.953225
$530$	−13.8571	−0.601912
$531$	39.9729	1.73468
$532$	−114.634	−4.97003
$533$	−17.6732	−0.765512
$534$	96.6395	4.18200
$535$	−58.9452	−2.54842
$536$	−36.9540	−1.59617
$537$	−17.4977	−0.755083
$538$	44.1850	1.90495
$539$	52.6209	2.26654
$540$	−82.8496	−3.56528
$541$	2.77365	0.119248	0.0596242	−	0.998221i	$-0.481010\pi$
$541$	2.77365	0.119248	0.0596242	+	0.998221i	$0.481010\pi$
$542$	−13.7664	−0.591319
$543$	15.4648	0.663660
$544$	1.57980	0.0677334
$545$	−65.0419	−2.78609
$546$	−67.8202	−2.90243
$547$	−2.02513	−0.0865884	−0.0432942	−	0.999062i	$-0.513785\pi$
$547$	−2.02513	−0.0865884	−0.0432942	+	0.999062i	$0.513785\pi$
$548$	−56.1811	−2.39994
$549$	44.3680	1.89358
$550$	−109.780	−4.68105
$551$	−34.1642	−1.45544
$552$	−15.4336	−0.656896
$553$	14.9283	0.634815
$554$	6.53277	0.277551
$555$	22.0162	0.934537
$556$	17.3579	0.736138
$557$	38.8516	1.64619	0.823097	−	0.567901i	$-0.192245\pi$
$557$	38.8516	1.64619	0.823097	+	0.567901i	$0.192245\pi$
$558$	26.3426	1.11517
$559$	2.15503	0.0911480
$560$	−91.6130	−3.87136
$561$	−10.6669	−0.450357
$562$	−37.7721	−1.59332
$563$	13.8825	0.585078	0.292539	−	0.956254i	$-0.405500\pi$
$563$	13.8825	0.585078	0.292539	+	0.956254i	$0.405500\pi$
$564$	141.888	5.97454
$565$	−41.8334	−1.75994
$566$	25.7076	1.08057
$567$	−2.83952	−0.119249
$568$	−15.1054	−0.633807
$569$	−2.78978	−0.116954	−0.0584768	−	0.998289i	$-0.518624\pi$
$569$	−2.78978	−0.116954	−0.0584768	+	0.998289i	$0.518624\pi$
$570$	−170.400	−7.13728
$571$	−12.6884	−0.530992	−0.265496	−	0.964112i	$-0.585536\pi$
$571$	−12.6884	−0.530992	−0.265496	+	0.964112i	$0.585536\pi$
$572$	34.2738	1.43306
$573$	47.4722	1.98318
$574$	92.6492	3.86710
$575$	11.9875	0.499915
$576$	−28.4078	−1.18366
$577$	−5.12588	−0.213393	−0.106697	−	0.994292i	$-0.534027\pi$
$577$	−5.12588	−0.213393	−0.106697	+	0.994292i	$0.534027\pi$
$578$	−2.48059	−0.103179
$579$	−66.3420	−2.75708
$580$	−95.2730	−3.95600
$581$	−13.1357	−0.544960
$582$	76.3207	3.16359
$583$	−5.25693	−0.217720
$584$	38.0969	1.57646
$585$	−41.7388	−1.72569
$586$	18.7232	0.773450
$587$	−8.50449	−0.351018	−0.175509	−	0.984478i	$-0.556157\pi$
$587$	−8.50449	−0.351018	−0.175509	+	0.984478i	$0.556157\pi$
$588$	158.990	6.55664
$589$	13.5208	0.557117
$590$	84.7666	3.48978
$591$	8.11624	0.333857
$592$	−9.60195	−0.394638
$593$	−30.8266	−1.26590	−0.632948	−	0.774195i	$-0.718155\pi$
$593$	−30.8266	−1.26590	−0.632948	+	0.774195i	$0.718155\pi$
$594$	−46.5656	−1.91061
$595$	18.5319	0.759733
$596$	−12.7880	−0.523818
$597$	1.13211	0.0463343
$598$	−5.54474	−0.226741
$599$	40.5809	1.65809	0.829045	−	0.559182i	$-0.188885\pi$
$599$	40.5809	1.65809	0.829045	+	0.559182i	$0.188885\pi$
$600$	−171.969	−7.02062
$601$	4.01238	0.163668	0.0818342	−	0.996646i	$-0.473922\pi$
$601$	4.01238	0.163668	0.0818342	+	0.996646i	$0.473922\pi$
$602$	−11.2974	−0.460449
$603$	32.9296	1.34100
$604$	−21.4136	−0.871307
$605$	−14.9051	−0.605978
$606$	3.00312	0.121993
$607$	−32.7130	−1.32778	−0.663891	−	0.747830i	$-0.731096\pi$
$607$	−32.7130	−1.32778	−0.663891	+	0.747830i	$0.731096\pi$
$608$	9.57405	0.388279
$609$	71.5200	2.89814
$610$	94.0868	3.80946
$611$	26.4286	1.06919
$612$	−19.7692	−0.799123
$613$	31.7393	1.28194	0.640968	−	0.767567i	$-0.278533\pi$
$613$	31.7393	1.28194	0.640968	+	0.767567i	$0.278533\pi$
$614$	−52.8550	−2.13305
$615$	92.9574	3.74840
$616$	−93.1544	−3.75330
$617$	−15.4404	−0.621608	−0.310804	−	0.950474i	$-0.600598\pi$
$617$	−15.4404	−0.621608	−0.310804	+	0.950474i	$0.600598\pi$
$618$	−10.2297	−0.411500
$619$	9.29863	0.373744	0.186872	−	0.982384i	$-0.440165\pi$
$619$	9.29863	0.373744	0.186872	+	0.982384i	$0.440165\pi$
$620$	37.7054	1.51428
$621$	5.08476	0.204044
$622$	15.6555	0.627727
$623$	−63.6938	−2.55184
$624$	29.6768	1.18802
$625$	50.7852	2.03141
$626$	51.3807	2.05359
$627$	−64.6445	−2.58165
$628$	−0.267317	−0.0106671
$629$	1.94232	0.0774455
$630$	218.810	8.71759
$631$	3.59068	0.142943	0.0714713	−	0.997443i	$-0.477231\pi$
$631$	3.59068	0.142943	0.0714713	+	0.997443i	$0.477231\pi$
$632$	−17.5087	−0.696457
$633$	−11.6247	−0.462039
$634$	62.0568	2.46459
$635$	23.3165	0.925286
$636$	−15.8834	−0.629819
$637$	29.6142	1.17336
$638$	−53.5482	−2.11999
$639$	13.4603	0.532482
$640$	−73.0983	−2.88946
$641$	15.4744	0.611203	0.305602	−	0.952159i	$-0.401142\pi$
$641$	15.4744	0.611203	0.305602	+	0.952159i	$0.401142\pi$
$642$	−100.100	−3.95064
$643$	9.65295	0.380675	0.190338	−	0.981719i	$-0.439042\pi$
$643$	9.65295	0.380675	0.190338	+	0.981719i	$0.439042\pi$
$644$	19.6198	0.773127
$645$	−11.3350	−0.446315
$646$	−15.0331	−0.591470
$647$	43.9613	1.72830	0.864149	−	0.503236i	$-0.167857\pi$
$647$	43.9613	1.72830	0.864149	+	0.503236i	$0.167857\pi$
$648$	3.33034	0.130828
$649$	32.1578	1.26230
$650$	−61.7826	−2.42331
$651$	−28.3049	−1.10935
$652$	−83.7457	−3.27973
$653$	−33.0446	−1.29314	−0.646568	−	0.762856i	$-0.723796\pi$
$653$	−33.0446	−1.29314	−0.646568	+	0.762856i	$0.723796\pi$
$654$	−110.454	−4.31908
$655$	11.6605	0.455613
$656$	−40.5416	−1.58288
$657$	−33.9480	−1.32444
$658$	−138.548	−5.40116
$659$	38.9809	1.51848	0.759240	−	0.650811i	$-0.225571\pi$
$659$	38.9809	1.51848	0.759240	+	0.650811i	$0.225571\pi$
$660$	−180.273	−7.01711
$661$	20.6053	0.801453	0.400726	−	0.916198i	$-0.368758\pi$
$661$	20.6053	0.801453	0.400726	+	0.916198i	$0.368758\pi$
$662$	−79.4346	−3.08731
$663$	−6.00315	−0.233143
$664$	15.4062	0.597877
$665$	112.308	4.35514
$666$	22.9334	0.888652
$667$	5.84723	0.226406
$668$	−25.1364	−0.972558
$669$	−36.2418	−1.40119
$670$	69.8304	2.69779
$671$	35.6936	1.37793
$672$	−20.0425	−0.773157
$673$	8.96507	0.345578	0.172789	−	0.984959i	$-0.444722\pi$
$673$	8.96507	0.345578	0.172789	+	0.984959i	$0.444722\pi$
$674$	36.7909	1.41713
$675$	56.6573	2.18074
$676$	−34.7047	−1.33480
$677$	−38.6197	−1.48428	−0.742138	−	0.670247i	$-0.766188\pi$
$677$	−38.6197	−1.48428	−0.742138	+	0.670247i	$0.766188\pi$
$678$	−71.0410	−2.72831
$679$	−50.3019	−1.93041
$680$	−21.7352	−0.833505
$681$	37.5674	1.43959
$682$	21.1923	0.811494
$683$	−46.5785	−1.78228	−0.891138	−	0.453732i	$-0.850092\pi$
$683$	−46.5785	−1.78228	−0.891138	+	0.453732i	$0.850092\pi$
$684$	−119.807	−4.58094
$685$	55.0412	2.10302
$686$	−76.1659	−2.90803
$687$	−71.5584	−2.73012
$688$	4.94354	0.188471
$689$	−2.95851	−0.112710
$690$	29.1641	1.11026
$691$	33.2050	1.26318	0.631590	−	0.775303i	$-0.282403\pi$
$691$	33.2050	1.26318	0.631590	+	0.775303i	$0.282403\pi$
$692$	27.1551	1.03228
$693$	83.0095	3.15327
$694$	−25.7280	−0.976621
$695$	−17.0057	−0.645063
$696$	−83.8825	−3.17956
$697$	8.20092	0.310632
$698$	−39.5285	−1.49618
$699$	−29.7603	−1.12564
$700$	218.614	8.26285
$701$	25.9610	0.980534	0.490267	−	0.871572i	$-0.336899\pi$
$701$	25.9610	0.980534	0.490267	+	0.871572i	$0.336899\pi$
$702$	−26.2064	−0.989095
$703$	11.7710	0.443953
$704$	−22.8538	−0.861334
$705$	−139.009	−5.23537
$706$	91.1873	3.43188
$707$	−1.97932	−0.0744398
$708$	97.1622	3.65158
$709$	−9.64056	−0.362059	−0.181029	−	0.983478i	$-0.557943\pi$
$709$	−9.64056	−0.362059	−0.181029	+	0.983478i	$0.557943\pi$
$710$	28.5440	1.07124
$711$	15.6019	0.585117
$712$	74.7034	2.79963
$713$	−2.31411	−0.0866639
$714$	31.4706	1.17776
$715$	−33.5784	−1.25576
$716$	−26.0887	−0.974982
$717$	−37.1105	−1.38592
$718$	−26.0722	−0.973006
$719$	−42.4671	−1.58376	−0.791878	−	0.610680i	$-0.790896\pi$
$719$	−42.4671	−1.58376	−0.791878	+	0.610680i	$0.790896\pi$
$720$	−95.7470	−3.56828
$721$	6.74227	0.251095
$722$	−43.9737	−1.63653
$723$	39.1660	1.45660
$724$	23.0577	0.856933
$725$	65.1531	2.41972
$726$	−25.3117	−0.939404
$727$	−38.8535	−1.44100	−0.720498	−	0.693457i	$-0.756087\pi$
$727$	−38.8535	−1.44100	−0.720498	+	0.693457i	$0.756087\pi$
$728$	−52.4258	−1.94303
$729$	−43.9357	−1.62725
$730$	−71.9900	−2.66447
$731$	−1.00000	−0.0369863
$732$	107.845	3.98608
$733$	−12.0362	−0.444569	−0.222284	−	0.974982i	$-0.571351\pi$
$733$	−12.0362	−0.444569	−0.222284	+	0.974982i	$0.571351\pi$
$734$	−35.3965	−1.30651
$735$	−155.764	−5.74545
$736$	−1.63861	−0.0603998
$737$	26.4915	0.975826
$738$	96.8299	3.56436
$739$	3.98023	0.146415	0.0732075	−	0.997317i	$-0.476676\pi$
$739$	3.98023	0.146415	0.0732075	+	0.997317i	$0.476676\pi$
$740$	32.8257	1.20670
$741$	−36.3808	−1.33648
$742$	15.5096	0.569375
$743$	26.7666	0.981970	0.490985	−	0.871168i	$-0.336637\pi$
$743$	26.7666	0.981970	0.490985	+	0.871168i	$0.336637\pi$
$744$	33.1974	1.21708
$745$	12.5286	0.459011
$746$	9.79012	0.358442
$747$	−13.7284	−0.502296
$748$	−15.9041	−0.581511
$749$	65.9747	2.41066
$750$	184.376	6.73245
$751$	−35.3719	−1.29074	−0.645369	−	0.763871i	$-0.723296\pi$
$751$	−35.3719	−1.29074	−0.645369	+	0.763871i	$0.723296\pi$
$752$	60.6260	2.21080
$753$	−16.8443	−0.613839
$754$	−30.1360	−1.09749
$755$	20.9791	0.763509
$756$	92.7298	3.37255
$757$	−20.9522	−0.761521	−0.380761	−	0.924674i	$-0.624338\pi$
$757$	−20.9522	−0.761521	−0.380761	+	0.924674i	$0.624338\pi$
$758$	−64.5899	−2.34601
$759$	11.0640	0.401596
$760$	−131.721	−4.77803
$761$	48.4420	1.75602	0.878010	−	0.478642i	$-0.158871\pi$
$761$	48.4420	1.75602	0.878010	+	0.478642i	$0.158871\pi$
$762$	39.5958	1.43441
$763$	72.7984	2.63548
$764$	70.7800	2.56073
$765$	19.3681	0.700255
$766$	91.9974	3.32400
$767$	18.0979	0.653476
$768$	−90.8840	−3.27949
$769$	−15.3698	−0.554249	−0.277125	−	0.960834i	$-0.589382\pi$
$769$	−15.3698	−0.554249	−0.277125	+	0.960834i	$0.589382\pi$
$770$	176.030	6.34368
$771$	−35.1234	−1.26494
$772$	−98.9144	−3.56001
$773$	10.4326	0.375233	0.187616	−	0.982242i	$-0.439924\pi$
$773$	10.4326	0.375233	0.187616	+	0.982242i	$0.439924\pi$
$774$	−11.8072	−0.424401
$775$	−25.7851	−0.926227
$776$	58.9967	2.11786
$777$	−24.6418	−0.884018
$778$	3.58427	0.128502
$779$	49.6999	1.78068
$780$	−101.455	−3.63266
$781$	10.8287	0.387481
$782$	2.57293	0.0920078
$783$	27.6360	0.987631
$784$	67.9336	2.42620
$785$	0.261893	0.00934737
$786$	19.8017	0.706304
$787$	51.1549	1.82347	0.911737	−	0.410774i	$-0.134742\pi$
$787$	51.1549	1.82347	0.911737	+	0.410774i	$0.134742\pi$
$788$	12.1011	0.431085
$789$	−55.3865	−1.97181
$790$	33.0854	1.17712
$791$	46.8222	1.66481
$792$	−97.3579	−3.45946
$793$	20.0878	0.713337
$794$	30.7384	1.09086
$795$	15.5612	0.551897
$796$	1.68795	0.0598279
$797$	0.907720	0.0321531	0.0160765	−	0.999871i	$-0.494882\pi$
$797$	0.907720	0.0321531	0.0160765	+	0.999871i	$0.494882\pi$
$798$	190.721	6.75146
$799$	−12.2637	−0.433858
$800$	−18.2583	−0.645527
$801$	−66.5679	−2.35206
$802$	−48.5145	−1.71311
$803$	−27.3107	−0.963775
$804$	80.0420	2.82286
$805$	−19.2217	−0.677476
$806$	11.9267	0.420099
$807$	−49.6187	−1.74666
$808$	2.32145	0.0816682
$809$	−27.2179	−0.956931	−0.478466	−	0.878106i	$-0.658807\pi$
$809$	−27.2179	−0.956931	−0.478466	+	0.878106i	$0.658807\pi$
$810$	−6.29320	−0.221121
$811$	−16.0905	−0.565016	−0.282508	−	0.959265i	$-0.591166\pi$
$811$	−16.0905	−0.565016	−0.282508	+	0.959265i	$0.591166\pi$
$812$	106.635	3.74215
$813$	15.4594	0.542185
$814$	18.4497	0.646661
$815$	82.0465	2.87396
$816$	−13.7710	−0.482080
$817$	−6.06029	−0.212023
$818$	34.7382	1.21459
$819$	46.7164	1.63240
$820$	138.597	4.84003
$821$	4.01072	0.139975	0.0699876	−	0.997548i	$-0.477704\pi$
$821$	4.01072	0.139975	0.0699876	+	0.997548i	$0.477704\pi$
$822$	93.4705	3.26016
$823$	9.80537	0.341794	0.170897	−	0.985289i	$-0.445334\pi$
$823$	9.80537	0.341794	0.170897	+	0.985289i	$0.445334\pi$
$824$	−7.90769	−0.275477
$825$	123.281	4.29209
$826$	−94.8754	−3.30114
$827$	3.15985	0.109879	0.0549394	−	0.998490i	$-0.482503\pi$
$827$	3.15985	0.109879	0.0549394	+	0.998490i	$0.482503\pi$
$828$	20.5051	0.712601
$829$	−6.91550	−0.240185	−0.120093	−	0.992763i	$-0.538319\pi$
$829$	−6.91550	−0.240185	−0.120093	+	0.992763i	$0.538319\pi$
$830$	−29.1125	−1.01051
$831$	−7.33615	−0.254488
$832$	−12.8617	−0.445900
$833$	−13.7419	−0.476128
$834$	−28.8789	−0.999995
$835$	24.6264	0.852233
$836$	−96.3834	−3.33349
$837$	−10.9373	−0.378047
$838$	67.4616	2.33042
$839$	−41.5894	−1.43582	−0.717912	−	0.696134i	$-0.754902\pi$
$839$	−41.5894	−1.43582	−0.717912	+	0.696134i	$0.754902\pi$
$840$	275.748	9.51422
$841$	2.78007	0.0958646
$842$	−33.9162	−1.16883
$843$	42.4172	1.46093
$844$	−17.3321	−0.596596
$845$	34.0005	1.16965
$846$	−144.800	−4.97832
$847$	16.6826	0.573220
$848$	−6.78670	−0.233056
$849$	−28.8690	−0.990783
$850$	28.6690	0.983339
$851$	−2.01462	−0.0690604
$852$	32.7180	1.12090
$853$	−7.92137	−0.271222	−0.135611	−	0.990762i	$-0.543300\pi$
$853$	−7.92137	−0.271222	−0.135611	+	0.990762i	$0.543300\pi$
$854$	−105.307	−3.60354
$855$	117.376	4.01418
$856$	−77.3786	−2.64475
$857$	20.7771	0.709733	0.354866	−	0.934917i	$-0.384526\pi$
$857$	20.7771	0.709733	0.354866	+	0.934917i	$0.384526\pi$
$858$	−57.0225	−1.94672
$859$	−6.88708	−0.234984	−0.117492	−	0.993074i	$-0.537485\pi$
$859$	−6.88708	−0.234984	−0.117492	+	0.993074i	$0.537485\pi$
$860$	−16.9002	−0.576293
$861$	−104.043	−3.54577
$862$	11.7016	0.398558
$863$	−8.66992	−0.295128	−0.147564	−	0.989053i	$-0.547143\pi$
$863$	−8.66992	−0.295128	−0.147564	+	0.989053i	$0.547143\pi$
$864$	−7.74462	−0.263477
$865$	−26.6041	−0.904567
$866$	40.3451	1.37098
$867$	2.78565	0.0946056
$868$	−42.2019	−1.43243
$869$	12.5515	0.425782
$870$	158.509	5.37396
$871$	14.9090	0.505171
$872$	−85.3819	−2.89139
$873$	−52.5717	−1.77928
$874$	15.5927	0.527431
$875$	−121.520	−4.10811
$876$	−82.5174	−2.78800
$877$	31.8137	1.07427	0.537136	−	0.843495i	$-0.319506\pi$
$877$	31.8137	1.07427	0.537136	+	0.843495i	$0.319506\pi$
$878$	−84.5876	−2.85469
$879$	−21.0258	−0.709182
$880$	−77.0273	−2.59659
$881$	52.4675	1.76767	0.883837	−	0.467796i	$-0.154952\pi$
$881$	52.4675	1.76767	0.883837	+	0.467796i	$0.154952\pi$
$882$	−162.253	−5.46335
$883$	−20.1417	−0.677823	−0.338912	−	0.940818i	$-0.610059\pi$
$883$	−20.1417	−0.677823	−0.338912	+	0.940818i	$0.610059\pi$
$884$	−8.95056	−0.301040
$885$	−95.1909	−3.19981
$886$	48.4095	1.62635
$887$	19.9311	0.669222	0.334611	−	0.942356i	$-0.391395\pi$
$887$	19.9311	0.669222	0.334611	+	0.942356i	$0.391395\pi$
$888$	28.9012	0.969860
$889$	−26.0971	−0.875268
$890$	−141.164	−4.73182
$891$	−2.38744	−0.0799823
$892$	−54.0356	−1.80925
$893$	−74.3214	−2.48707
$894$	21.2759	0.711572
$895$	25.5594	0.854357
$896$	81.8156	2.73327
$897$	6.22661	0.207901
$898$	81.4009	2.71638
$899$	−12.5773	−0.419477
$900$	228.479	7.61597
$901$	1.37284	0.0457360
$902$	77.8986	2.59374
$903$	12.6867	0.422189
$904$	−54.9155	−1.82646
$905$	−22.5899	−0.750913
$906$	35.6266	1.18361
$907$	−24.7102	−0.820488	−0.410244	−	0.911976i	$-0.634556\pi$
$907$	−24.7102	−0.820488	−0.410244	+	0.911976i	$0.634556\pi$
$908$	56.0122	1.85883
$909$	−2.06863	−0.0686121
$910$	99.0667	3.28403
$911$	15.4518	0.511942	0.255971	−	0.966684i	$-0.417605\pi$
$911$	15.4518	0.511942	0.255971	+	0.966684i	$0.417605\pi$
$912$	−83.4560	−2.76350
$913$	−11.0443	−0.365514
$914$	30.7599	1.01745
$915$	−105.657	−3.49292
$916$	−106.692	−3.52520
$917$	−13.0511	−0.430984
$918$	12.1606	0.401358
$919$	14.5815	0.480998	0.240499	−	0.970649i	$-0.422689\pi$
$919$	14.5815	0.480998	0.240499	+	0.970649i	$0.422689\pi$
$920$	22.5442	0.743261
$921$	59.3549	1.95581
$922$	100.546	3.31130
$923$	6.09420	0.200593
$924$	201.771	6.63779
$925$	−22.4481	−0.738088
$926$	17.4785	0.574380
$927$	7.04651	0.231438
$928$	−8.90594	−0.292352
$929$	−48.4089	−1.58824	−0.794122	−	0.607758i	$-0.792069\pi$
$929$	−48.4089	−1.58824	−0.794122	+	0.607758i	$0.792069\pi$
$930$	−62.7318	−2.05706
$931$	−83.2798	−2.72938
$932$	−44.3719	−1.45345
$933$	−17.5807	−0.575568
$934$	−55.9970	−1.83228
$935$	15.5814	0.509567
$936$	−54.7914	−1.79091
$937$	−59.9747	−1.95929	−0.979644	−	0.200745i	$-0.935664\pi$
$937$	−59.9747	−1.95929	−0.979644	+	0.200745i	$0.935664\pi$
$938$	−78.1581	−2.55195
$939$	−57.6994	−1.88295
$940$	−207.259	−6.76004
$941$	−57.5004	−1.87446	−0.937230	−	0.348713i	$-0.886619\pi$
$941$	−57.5004	−1.87446	−0.937230	+	0.348713i	$0.886619\pi$
$942$	0.444745	0.0144906
$943$	−8.50619	−0.277000
$944$	41.5157	1.35122
$945$	−90.8484	−2.95530
$946$	−9.49876	−0.308831
$947$	−5.42181	−0.176185	−0.0880925	−	0.996112i	$-0.528077\pi$
$947$	−5.42181	−0.176185	−0.0880925	+	0.996112i	$0.528077\pi$
$948$	37.9236	1.23170
$949$	−15.3700	−0.498933
$950$	173.743	5.63695
$951$	−69.6884	−2.25980
$952$	24.3272	0.788448
$953$	47.2136	1.52940	0.764699	−	0.644388i	$-0.222888\pi$
$953$	47.2136	1.52940	0.764699	+	0.644388i	$0.222888\pi$
$954$	16.2094	0.524800
$955$	−69.3439	−2.24392
$956$	−55.3310	−1.78953
$957$	60.1333	1.94384
$958$	−81.3473	−2.62821
$959$	−61.6051	−1.98933
$960$	67.6500	2.18339
$961$	−26.0224	−0.839432
$962$	10.3832	0.334767
$963$	68.9517	2.22194
$964$	58.3956	1.88080
$965$	96.9075	3.11956
$966$	−32.6421	−1.05024
$967$	−0.895778	−0.0288063	−0.0144031	−	0.999896i	$-0.504585\pi$
$967$	−0.895778	−0.0288063	−0.0144031	+	0.999896i	$0.504585\pi$
$968$	−19.5662	−0.628882
$969$	16.8818	0.542323
$970$	−111.484	−3.57952
$971$	−45.7637	−1.46863	−0.734313	−	0.678811i	$-0.762496\pi$
$971$	−45.7637	−1.46863	−0.734313	+	0.678811i	$0.762496\pi$
$972$	−68.2960	−2.19059
$973$	19.0337	0.610193
$974$	−50.6243	−1.62211
$975$	69.3804	2.22195
$976$	46.0804	1.47500
$977$	49.1942	1.57386	0.786931	−	0.617041i	$-0.211669\pi$
$977$	49.1942	1.57386	0.786931	+	0.617041i	$0.211669\pi$
$978$	139.331	4.45530
$979$	−53.5531	−1.71156
$980$	−232.241	−7.41866
$981$	76.0834	2.42916
$982$	−21.2534	−0.678224
$983$	−4.74944	−0.151484	−0.0757419	−	0.997127i	$-0.524133\pi$
$983$	−4.74944	−0.151484	−0.0757419	+	0.997127i	$0.524133\pi$
$984$	122.027	3.89008
$985$	−11.8556	−0.377751
$986$	13.9840	0.445343
$987$	155.586	4.95236
$988$	−54.2430	−1.72570
$989$	1.03722	0.0329818
$990$	183.973	5.84705
$991$	3.00013	0.0953024	0.0476512	−	0.998864i	$-0.484826\pi$
$991$	3.00013	0.0953024	0.0476512	+	0.998864i	$0.484826\pi$
$992$	3.52462	0.111907
$993$	89.2032	2.83078
$994$	−31.9480	−1.01333
$995$	−1.65371	−0.0524260
$996$	−33.3697	−1.05736
$997$	−52.5162	−1.66321	−0.831603	−	0.555371i	$-0.812576\pi$
$997$	−52.5162	−1.66321	−0.831603	+	0.555371i	$0.812576\pi$
$998$	−0.427237	−0.0135240
$999$	−9.52181	−0.301257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.3	✓	21
3.2	odd	2		6579.2.a.u.1.19		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.3	✓	21	1.1	even	1	trivial
6579.2.a.u.1.19		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)

\(f(q)\)	\(=\)	\(q-2.48059 q^{2} +2.78565 q^{3} +4.15334 q^{4} -4.06907 q^{5} -6.91006 q^{6} +4.55433 q^{7} -5.34155 q^{8} +4.75983 q^{9} +O(q^{10})\)	\(q-2.48059 q^{2} +2.78565 q^{3} +4.15334 q^{4} -4.06907 q^{5} -6.91006 q^{6} +4.55433 q^{7} -5.34155 q^{8} +4.75983 q^{9} +10.0937 q^{10} +3.82923 q^{11} +11.5697 q^{12} +2.15503 q^{13} -11.2974 q^{14} -11.3350 q^{15} +4.94354 q^{16} -1.00000 q^{17} -11.8072 q^{18} -6.06029 q^{19} -16.9002 q^{20} +12.6867 q^{21} -9.49876 q^{22} +1.03722 q^{23} -14.8797 q^{24} +11.5573 q^{25} -5.34575 q^{26} +4.90228 q^{27} +18.9157 q^{28} +5.63738 q^{29} +28.1175 q^{30} -2.23106 q^{31} -1.57980 q^{32} +10.6669 q^{33} +2.48059 q^{34} -18.5319 q^{35} +19.7692 q^{36} -1.94232 q^{37} +15.0331 q^{38} +6.00315 q^{39} +21.7352 q^{40} -8.20092 q^{41} -31.4706 q^{42} +1.00000 q^{43} +15.9041 q^{44} -19.3681 q^{45} -2.57293 q^{46} +12.2637 q^{47} +13.7710 q^{48} +13.7419 q^{49} -28.6690 q^{50} -2.78565 q^{51} +8.95056 q^{52} -1.37284 q^{53} -12.1606 q^{54} -15.5814 q^{55} -24.3272 q^{56} -16.8818 q^{57} -13.9840 q^{58} +8.39796 q^{59} -47.0781 q^{60} +9.32134 q^{61} +5.53434 q^{62} +21.6778 q^{63} -5.96824 q^{64} -8.76896 q^{65} -26.4602 q^{66} +6.91822 q^{67} -4.15334 q^{68} +2.88934 q^{69} +45.9700 q^{70} +2.82790 q^{71} -25.4249 q^{72} -7.13217 q^{73} +4.81811 q^{74} +32.1947 q^{75} -25.1704 q^{76} +17.4396 q^{77} -14.8914 q^{78} +3.27782 q^{79} -20.1156 q^{80} -0.623478 q^{81} +20.3431 q^{82} -2.88422 q^{83} +52.6924 q^{84} +4.06907 q^{85} -2.48059 q^{86} +15.7038 q^{87} -20.4540 q^{88} -13.9853 q^{89} +48.0444 q^{90} +9.81470 q^{91} +4.30794 q^{92} -6.21494 q^{93} -30.4212 q^{94} +24.6597 q^{95} -4.40077 q^{96} -11.0449 q^{97} -34.0880 q^{98} +18.2265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 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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