LMFDB - Embedded newform 731.2.a.f.1.13

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			1.13
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)

$f(q)$	$=$	$q+0.715531 q^{2} -2.68508 q^{3} -1.48801 q^{4} +1.60306 q^{5} -1.92126 q^{6} -4.82676 q^{7} -2.49578 q^{8} +4.20967 q^{9} +O(q^{10})$	\(q+0.715531 q^{2} -2.68508 q^{3} -1.48801 q^{4} +1.60306 q^{5} -1.92126 q^{6} -4.82676 q^{7} -2.49578 q^{8} +4.20967 q^{9} +1.14704 q^{10} -4.41244 q^{11} +3.99544 q^{12} +5.87360 q^{13} -3.45370 q^{14} -4.30436 q^{15} +1.19022 q^{16} -1.00000 q^{17} +3.01215 q^{18} +8.08130 q^{19} -2.38538 q^{20} +12.9603 q^{21} -3.15724 q^{22} +0.285665 q^{23} +6.70139 q^{24} -2.43018 q^{25} +4.20274 q^{26} -3.24807 q^{27} +7.18229 q^{28} -8.29481 q^{29} -3.07991 q^{30} +3.66886 q^{31} +5.84321 q^{32} +11.8478 q^{33} -0.715531 q^{34} -7.73761 q^{35} -6.26406 q^{36} -0.830724 q^{37} +5.78242 q^{38} -15.7711 q^{39} -4.00090 q^{40} +10.2847 q^{41} +9.27347 q^{42} +1.00000 q^{43} +6.56577 q^{44} +6.74838 q^{45} +0.204402 q^{46} +9.56174 q^{47} -3.19583 q^{48} +16.2976 q^{49} -1.73887 q^{50} +2.68508 q^{51} -8.74000 q^{52} -1.12810 q^{53} -2.32410 q^{54} -7.07342 q^{55} +12.0466 q^{56} -21.6990 q^{57} -5.93520 q^{58} -1.65528 q^{59} +6.40495 q^{60} +6.27176 q^{61} +2.62518 q^{62} -20.3191 q^{63} +1.80056 q^{64} +9.41575 q^{65} +8.47745 q^{66} -8.41447 q^{67} +1.48801 q^{68} -0.767035 q^{69} -5.53650 q^{70} -1.05520 q^{71} -10.5064 q^{72} -3.71114 q^{73} -0.594409 q^{74} +6.52525 q^{75} -12.0251 q^{76} +21.2978 q^{77} -11.2847 q^{78} +11.9680 q^{79} +1.90800 q^{80} -3.90768 q^{81} +7.35901 q^{82} -3.72452 q^{83} -19.2851 q^{84} -1.60306 q^{85} +0.715531 q^{86} +22.2723 q^{87} +11.0125 q^{88} +1.57564 q^{89} +4.82868 q^{90} -28.3505 q^{91} -0.425074 q^{92} -9.85119 q^{93} +6.84173 q^{94} +12.9548 q^{95} -15.6895 q^{96} +3.35405 q^{97} +11.6615 q^{98} -18.5749 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.715531	0.505957	0.252979	−	0.967472i	$-0.418590\pi$
$2$	0.715531	0.505957	0.252979	+	0.967472i	$0.418590\pi$
$3$	−2.68508	−1.55023	−0.775117	−	0.631818i	$-0.782309\pi$
$3$	−2.68508	−1.55023	−0.775117	+	0.631818i	$0.782309\pi$
$4$	−1.48801	−0.744007
$5$	1.60306	0.716912	0.358456	−	0.933547i	$-0.383303\pi$
$5$	1.60306	0.716912	0.358456	+	0.933547i	$0.383303\pi$
$6$	−1.92126	−0.784352
$7$	−4.82676	−1.82434	−0.912172	−	0.409807i	$-0.865596\pi$
$7$	−4.82676	−1.82434	−0.912172	+	0.409807i	$0.865596\pi$
$8$	−2.49578	−0.882393
$9$	4.20967	1.40322
$10$	1.14704	0.362727
$11$	−4.41244	−1.33040	−0.665200	−	0.746665i	$-0.731654\pi$
$11$	−4.41244	−1.33040	−0.665200	+	0.746665i	$0.731654\pi$
$12$	3.99544	1.15339
$13$	5.87360	1.62904	0.814521	−	0.580134i	$-0.197000\pi$
$13$	5.87360	1.62904	0.814521	+	0.580134i	$0.197000\pi$
$14$	−3.45370	−0.923040
$15$	−4.30436	−1.11138
$16$	1.19022	0.297554
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.01215	0.709971
$19$	8.08130	1.85398	0.926988	−	0.375090i	$-0.122388\pi$
$19$	8.08130	1.85398	0.926988	+	0.375090i	$0.122388\pi$
$20$	−2.38538	−0.533388
$21$	12.9603	2.82816
$22$	−3.15724	−0.673125
$23$	0.285665	0.0595653	0.0297827	−	0.999556i	$-0.490518\pi$
$23$	0.285665	0.0595653	0.0297827	+	0.999556i	$0.490518\pi$
$24$	6.70139	1.36792
$25$	−2.43018	−0.486037
$26$	4.20274	0.824226
$27$	−3.24807	−0.625092
$28$	7.18229	1.35733
$29$	−8.29481	−1.54031	−0.770154	−	0.637858i	$-0.779821\pi$
$29$	−8.29481	−1.54031	−0.770154	+	0.637858i	$0.779821\pi$
$30$	−3.07991	−0.562311
$31$	3.66886	0.658947	0.329473	−	0.944165i	$-0.393129\pi$
$31$	3.66886	0.658947	0.329473	+	0.944165i	$0.393129\pi$
$32$	5.84321	1.03294
$33$	11.8478	2.06243
$34$	−0.715531	−0.122713
$35$	−7.73761	−1.30789
$36$	−6.26406	−1.04401
$37$	−0.830724	−0.136570	−0.0682851	−	0.997666i	$-0.521753\pi$
$37$	−0.830724	−0.136570	−0.0682851	+	0.997666i	$0.521753\pi$
$38$	5.78242	0.938033
$39$	−15.7711	−2.52540
$40$	−4.00090	−0.632598
$41$	10.2847	1.60620	0.803098	−	0.595846i	$-0.203183\pi$
$41$	10.2847	1.60620	0.803098	+	0.595846i	$0.203183\pi$
$42$	9.27347	1.43093
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	6.56577	0.989827
$45$	6.74838	1.00599
$46$	0.204402	0.0301375
$47$	9.56174	1.39472	0.697362	−	0.716719i	$-0.254357\pi$
$47$	9.56174	1.39472	0.697362	+	0.716719i	$0.254357\pi$
$48$	−3.19583	−0.461279
$49$	16.2976	2.32823
$50$	−1.73887	−0.245914
$51$	2.68508	0.375987
$52$	−8.74000	−1.21202
$53$	−1.12810	−0.154956	−0.0774781	−	0.996994i	$-0.524687\pi$
$53$	−1.12810	−0.154956	−0.0774781	+	0.996994i	$0.524687\pi$
$54$	−2.32410	−0.316270
$55$	−7.07342	−0.953780
$56$	12.0466	1.60979
$57$	−21.6990	−2.87410
$58$	−5.93520	−0.779330
$59$	−1.65528	−0.215498	−0.107749	−	0.994178i	$-0.534364\pi$
$59$	−1.65528	−0.215498	−0.107749	+	0.994178i	$0.534364\pi$
$60$	6.40495	0.826876
$61$	6.27176	0.803017	0.401508	−	0.915855i	$-0.368486\pi$
$61$	6.27176	0.803017	0.401508	+	0.915855i	$0.368486\pi$
$62$	2.62518	0.333399
$63$	−20.3191	−2.55996
$64$	1.80056	0.225070
$65$	9.41575	1.16788
$66$	8.47745	1.04350
$67$	−8.41447	−1.02799	−0.513996	−	0.857793i	$-0.671835\pi$
$67$	−8.41447	−1.02799	−0.513996	+	0.857793i	$0.671835\pi$
$68$	1.48801	0.180448
$69$	−0.767035	−0.0923402
$70$	−5.53650	−0.661739
$71$	−1.05520	−0.125229	−0.0626146	−	0.998038i	$-0.519944\pi$
$71$	−1.05520	−0.125229	−0.0626146	+	0.998038i	$0.519944\pi$
$72$	−10.5064	−1.23820
$73$	−3.71114	−0.434356	−0.217178	−	0.976132i	$-0.569685\pi$
$73$	−3.71114	−0.434356	−0.217178	+	0.976132i	$0.569685\pi$
$74$	−0.594409	−0.0690987
$75$	6.52525	0.753471
$76$	−12.0251	−1.37937
$77$	21.2978	2.42711
$78$	−11.2847	−1.27774
$79$	11.9680	1.34650	0.673250	−	0.739415i	$-0.264898\pi$
$79$	11.9680	1.34650	0.673250	+	0.739415i	$0.264898\pi$
$80$	1.90800	0.213320
$81$	−3.90768	−0.434186
$82$	7.35901	0.812667
$83$	−3.72452	−0.408819	−0.204410	−	0.978885i	$-0.565527\pi$
$83$	−3.72452	−0.408819	−0.204410	+	0.978885i	$0.565527\pi$
$84$	−19.2851	−2.10417
$85$	−1.60306	−0.173877
$86$	0.715531	0.0771577
$87$	22.2723	2.38784
$88$	11.0125	1.17394
$89$	1.57564	0.167017	0.0835085	−	0.996507i	$-0.473387\pi$
$89$	1.57564	0.167017	0.0835085	+	0.996507i	$0.473387\pi$
$90$	4.82868	0.508987
$91$	−28.3505	−2.97193
$92$	−0.425074	−0.0443170
$93$	−9.85119	−1.02152
$94$	6.84173	0.705670
$95$	12.9548	1.32914
$96$	−15.6895	−1.60130
$97$	3.35405	0.340552	0.170276	−	0.985396i	$-0.445534\pi$
$97$	3.35405	0.340552	0.170276	+	0.985396i	$0.445534\pi$
$98$	11.6615	1.17799
$99$	−18.5749	−1.86685
$100$	3.61615	0.361615
$101$	−8.88837	−0.884426	−0.442213	−	0.896910i	$-0.645806\pi$
$101$	−8.88837	−0.884426	−0.442213	+	0.896910i	$0.645806\pi$
$102$	1.92126	0.190233
$103$	−5.82179	−0.573638	−0.286819	−	0.957985i	$-0.592598\pi$
$103$	−5.82179	−0.573638	−0.286819	+	0.957985i	$0.592598\pi$
$104$	−14.6592	−1.43746
$105$	20.7761	2.02754
$106$	−0.807190	−0.0784012
$107$	−5.72634	−0.553586	−0.276793	−	0.960930i	$-0.589272\pi$
$107$	−5.72634	−0.553586	−0.276793	+	0.960930i	$0.589272\pi$
$108$	4.83318	0.465073
$109$	12.1112	1.16004	0.580019	−	0.814603i	$-0.303045\pi$
$109$	12.1112	1.16004	0.580019	+	0.814603i	$0.303045\pi$
$110$	−5.06126	−0.482572
$111$	2.23056	0.211716
$112$	−5.74490	−0.542842
$113$	14.4119	1.35575	0.677877	−	0.735175i	$-0.262900\pi$
$113$	14.4119	1.35575	0.677877	+	0.735175i	$0.262900\pi$
$114$	−15.5263	−1.45417
$115$	0.457940	0.0427031
$116$	12.3428	1.14600
$117$	24.7259	2.28591
$118$	−1.18440	−0.109033
$119$	4.82676	0.442469
$120$	10.7428	0.980675
$121$	8.46960	0.769964
$122$	4.48764	0.406292
$123$	−27.6152	−2.48998
$124$	−5.45932	−0.490261
$125$	−11.9111	−1.06536
$126$	−14.5389	−1.29523
$127$	−2.09099	−0.185545	−0.0927726	−	0.995687i	$-0.529573\pi$
$127$	−2.09099	−0.185545	−0.0927726	+	0.995687i	$0.529573\pi$
$128$	−10.3981	−0.919067
$129$	−2.68508	−0.236408
$130$	6.73727	0.590897
$131$	−5.22744	−0.456724	−0.228362	−	0.973576i	$-0.573337\pi$
$131$	−5.22744	−0.456724	−0.228362	+	0.973576i	$0.573337\pi$
$132$	−17.6296	−1.53446
$133$	−39.0065	−3.38229
$134$	−6.02082	−0.520120
$135$	−5.20687	−0.448136
$136$	2.49578	0.214012
$137$	1.88217	0.160804	0.0804022	−	0.996762i	$-0.474380\pi$
$137$	1.88217	0.160804	0.0804022	+	0.996762i	$0.474380\pi$
$138$	−0.548838	−0.0467202
$139$	15.0111	1.27322	0.636612	−	0.771184i	$-0.280335\pi$
$139$	15.0111	1.27322	0.636612	+	0.771184i	$0.280335\pi$
$140$	11.5137	0.973084
$141$	−25.6741	−2.16215
$142$	−0.755029	−0.0633606
$143$	−25.9169	−2.16728
$144$	5.01043	0.417536
$145$	−13.2971	−1.10427
$146$	−2.65544	−0.219765
$147$	−43.7605	−3.60931
$148$	1.23613	0.101609
$149$	19.9180	1.63175	0.815873	−	0.578232i	$-0.196257\pi$
$149$	19.9180	1.63175	0.815873	+	0.578232i	$0.196257\pi$
$150$	4.66902	0.381224
$151$	−20.8795	−1.69915	−0.849576	−	0.527467i	$-0.823142\pi$
$151$	−20.8795	−1.69915	−0.849576	+	0.527467i	$0.823142\pi$
$152$	−20.1692	−1.63594
$153$	−4.20967	−0.340332
$154$	15.2392	1.22801
$155$	5.88142	0.472407
$156$	23.4676	1.87891
$157$	−9.42096	−0.751875	−0.375937	−	0.926645i	$-0.622679\pi$
$157$	−9.42096	−0.751875	−0.375937	+	0.926645i	$0.622679\pi$
$158$	8.56345	0.681272
$159$	3.02904	0.240218
$160$	9.36704	0.740529
$161$	−1.37884	−0.108668
$162$	−2.79606	−0.219680
$163$	0.920843	0.0721260	0.0360630	−	0.999350i	$-0.488518\pi$
$163$	0.920843	0.0721260	0.0360630	+	0.999350i	$0.488518\pi$
$164$	−15.3038	−1.19502
$165$	18.9927	1.47858
$166$	−2.66501	−0.206845
$167$	10.2288	0.791529	0.395764	−	0.918352i	$-0.370480\pi$
$167$	10.2288	0.791529	0.395764	+	0.918352i	$0.370480\pi$
$168$	−32.3460	−2.49555
$169$	21.4991	1.65378
$170$	−1.14704	−0.0879742
$171$	34.0196	2.60154
$172$	−1.48801	−0.113460
$173$	−10.4922	−0.797710	−0.398855	−	0.917014i	$-0.630592\pi$
$173$	−10.4922	−0.797710	−0.398855	+	0.917014i	$0.630592\pi$
$174$	15.9365	1.20814
$175$	11.7299	0.886699
$176$	−5.25176	−0.395866
$177$	4.44455	0.334073
$178$	1.12742	0.0845034
$179$	13.4852	1.00793	0.503966	−	0.863723i	$-0.331874\pi$
$179$	13.4852	1.00793	0.503966	+	0.863723i	$0.331874\pi$
$180$	−10.0417	−0.748463
$181$	23.8503	1.77278	0.886390	−	0.462938i	$-0.153205\pi$
$181$	23.8503	1.77278	0.886390	+	0.462938i	$0.153205\pi$
$182$	−20.2856	−1.50367
$183$	−16.8402	−1.24486
$184$	−0.712959	−0.0525600
$185$	−1.33170	−0.0979088
$186$	−7.04884	−0.516846
$187$	4.41244	0.322669
$188$	−14.2280	−1.03768
$189$	15.6777	1.14038
$190$	9.26960	0.672487
$191$	−5.20850	−0.376874	−0.188437	−	0.982085i	$-0.560342\pi$
$191$	−5.20850	−0.376874	−0.188437	+	0.982085i	$0.560342\pi$
$192$	−4.83466	−0.348911
$193$	6.53969	0.470737	0.235368	−	0.971906i	$-0.424370\pi$
$193$	6.53969	0.470737	0.235368	+	0.971906i	$0.424370\pi$
$194$	2.39993	0.172305
$195$	−25.2821	−1.81049
$196$	−24.2511	−1.73222
$197$	13.1044	0.933648	0.466824	−	0.884350i	$-0.345398\pi$
$197$	13.1044	0.933648	0.466824	+	0.884350i	$0.345398\pi$
$198$	−13.2909	−0.944546
$199$	16.5276	1.17161	0.585806	−	0.810451i	$-0.300778\pi$
$199$	16.5276	1.17161	0.585806	+	0.810451i	$0.300778\pi$
$200$	6.06521	0.428875
$201$	22.5936	1.59363
$202$	−6.35991	−0.447481
$203$	40.0371	2.81005
$204$	−3.99544	−0.279737
$205$	16.4870	1.15150
$206$	−4.16567	−0.290236
$207$	1.20256	0.0835835
$208$	6.99086	0.484729
$209$	−35.6582	−2.46653
$210$	14.8660	1.02585
$211$	12.9921	0.894415	0.447207	−	0.894430i	$-0.352419\pi$
$211$	12.9921	0.894415	0.447207	+	0.894430i	$0.352419\pi$
$212$	1.67863	0.115289
$213$	2.83330	0.194134
$214$	−4.09737	−0.280091
$215$	1.60306	0.109328
$216$	8.10648	0.551576
$217$	−17.7087	−1.20215
$218$	8.66591	0.586930
$219$	9.96472	0.673353
$220$	10.5254	0.709619
$221$	−5.87360	−0.395101
$222$	1.59604	0.107119
$223$	12.0298	0.805573	0.402786	−	0.915294i	$-0.368042\pi$
$223$	12.0298	0.805573	0.402786	+	0.915294i	$0.368042\pi$
$224$	−28.2038	−1.88444
$225$	−10.2303	−0.682019
$226$	10.3121	0.685953
$227$	18.8118	1.24858	0.624292	−	0.781191i	$-0.285388\pi$
$227$	18.8118	1.24858	0.624292	+	0.781191i	$0.285388\pi$
$228$	32.2884	2.13835
$229$	23.7029	1.56633	0.783167	−	0.621811i	$-0.213603\pi$
$229$	23.7029	1.56633	0.783167	+	0.621811i	$0.213603\pi$
$230$	0.327670	0.0216059
$231$	−57.1863	−3.76258
$232$	20.7021	1.35916
$233$	−13.3207	−0.872669	−0.436335	−	0.899785i	$-0.643724\pi$
$233$	−13.3207	−0.872669	−0.436335	+	0.899785i	$0.643724\pi$
$234$	17.6922	1.15657
$235$	15.3281	0.999894
$236$	2.46307	0.160332
$237$	−32.1350	−2.08739
$238$	3.45370	0.223870
$239$	10.9011	0.705133	0.352566	−	0.935787i	$-0.385309\pi$
$239$	10.9011	0.705133	0.352566	+	0.935787i	$0.385309\pi$
$240$	−5.12313	−0.330697
$241$	−12.4403	−0.801350	−0.400675	−	0.916220i	$-0.631224\pi$
$241$	−12.4403	−0.801350	−0.400675	+	0.916220i	$0.631224\pi$
$242$	6.06027	0.389569
$243$	20.2366	1.29818
$244$	−9.33248	−0.597451
$245$	26.1262	1.66914
$246$	−19.7596	−1.25982
$247$	47.4663	3.02021
$248$	−9.15668	−0.581450
$249$	10.0007	0.633766
$250$	−8.52274	−0.539025
$251$	18.6944	1.17998	0.589990	−	0.807410i	$-0.299132\pi$
$251$	18.6944	1.17998	0.589990	+	0.807410i	$0.299132\pi$
$252$	30.2351	1.90463
$253$	−1.26048	−0.0792457
$254$	−1.49617	−0.0938779
$255$	4.30436	0.269550
$256$	−11.0413	−0.690079
$257$	−7.98471	−0.498073	−0.249036	−	0.968494i	$-0.580114\pi$
$257$	−7.98471	−0.498073	−0.249036	+	0.968494i	$0.580114\pi$
$258$	−1.92126	−0.119613
$259$	4.00971	0.249151
$260$	−14.0108	−0.868912
$261$	−34.9184	−2.16140
$262$	−3.74040	−0.231083
$263$	−17.3787	−1.07162	−0.535808	−	0.844340i	$-0.679993\pi$
$263$	−17.3787	−1.07162	−0.535808	+	0.844340i	$0.679993\pi$
$264$	−29.5695	−1.81987
$265$	−1.80841	−0.111090
$266$	−27.9104	−1.71129
$267$	−4.23071	−0.258915
$268$	12.5209	0.764833
$269$	4.88314	0.297730	0.148865	−	0.988858i	$-0.452438\pi$
$269$	4.88314	0.297730	0.148865	+	0.988858i	$0.452438\pi$
$270$	−3.72568	−0.226738
$271$	7.52760	0.457269	0.228635	−	0.973512i	$-0.426574\pi$
$271$	7.52760	0.457269	0.228635	+	0.973512i	$0.426574\pi$
$272$	−1.19022	−0.0721676
$273$	76.1233	4.60719
$274$	1.34675	0.0813602
$275$	10.7230	0.646623
$276$	1.14136	0.0687018
$277$	5.32426	0.319904	0.159952	−	0.987125i	$-0.448866\pi$
$277$	5.32426	0.319904	0.159952	+	0.987125i	$0.448866\pi$
$278$	10.7409	0.644197
$279$	15.4447	0.924650
$280$	19.3114	1.15408
$281$	2.22125	0.132509	0.0662543	−	0.997803i	$-0.478895\pi$
$281$	2.22125	0.132509	0.0662543	+	0.997803i	$0.478895\pi$
$282$	−18.3706	−1.09395
$283$	−1.82012	−0.108195	−0.0540973	−	0.998536i	$-0.517228\pi$
$283$	−1.82012	−0.108195	−0.0540973	+	0.998536i	$0.517228\pi$
$284$	1.57015	0.0931714
$285$	−34.7848	−2.06048
$286$	−18.5443	−1.09655
$287$	−49.6417	−2.93026
$288$	24.5980	1.44945
$289$	1.00000	0.0588235
$290$	−9.51451	−0.558711
$291$	−9.00590	−0.527935
$292$	5.52223	0.323164
$293$	−2.63633	−0.154016	−0.0770079	−	0.997030i	$-0.524537\pi$
$293$	−2.63633	−0.154016	−0.0770079	+	0.997030i	$0.524537\pi$
$294$	−31.3120	−1.82615
$295$	−2.65351	−0.154493
$296$	2.07331	0.120509
$297$	14.3319	0.831622
$298$	14.2519	0.825593
$299$	1.67788	0.0970344
$300$	−9.70966	−0.560588
$301$	−4.82676	−0.278210
$302$	−14.9400	−0.859698
$303$	23.8660	1.37107
$304$	9.61850	0.551659
$305$	10.0540	0.575693
$306$	−3.01215	−0.172193
$307$	18.7513	1.07019	0.535095	−	0.844792i	$-0.320276\pi$
$307$	18.7513	1.07019	0.535095	+	0.844792i	$0.320276\pi$
$308$	−31.6914	−1.80579
$309$	15.6320	0.889273
$310$	4.20834	0.239018
$311$	4.99561	0.283275	0.141637	−	0.989919i	$-0.454763\pi$
$311$	4.99561	0.283275	0.141637	+	0.989919i	$0.454763\pi$
$312$	39.3612	2.22839
$313$	3.76756	0.212955	0.106478	−	0.994315i	$-0.466043\pi$
$313$	3.76756	0.212955	0.106478	+	0.994315i	$0.466043\pi$
$314$	−6.74100	−0.380416
$315$	−32.5728	−1.83527
$316$	−17.8085	−1.00181
$317$	−25.6077	−1.43827	−0.719135	−	0.694871i	$-0.755462\pi$
$317$	−25.6077	−1.43827	−0.719135	+	0.694871i	$0.755462\pi$
$318$	2.16737	0.121540
$319$	36.6003	2.04923
$320$	2.88642	0.161356
$321$	15.3757	0.858188
$322$	−0.986602	−0.0549812
$323$	−8.08130	−0.449655
$324$	5.81468	0.323038
$325$	−14.2739	−0.791775
$326$	0.658892	0.0364927
$327$	−32.5195	−1.79833
$328$	−25.6683	−1.41730
$329$	−46.1522	−2.54446
$330$	13.5899	0.748099
$331$	2.77629	0.152599	0.0762993	−	0.997085i	$-0.475690\pi$
$331$	2.77629	0.152599	0.0762993	+	0.997085i	$0.475690\pi$
$332$	5.54214	0.304165
$333$	−3.49708	−0.191639
$334$	7.31903	0.400480
$335$	−13.4889	−0.736980
$336$	15.4255	0.841532
$337$	−31.2018	−1.69967	−0.849835	−	0.527048i	$-0.823299\pi$
$337$	−31.2018	−1.69967	−0.849835	+	0.527048i	$0.823299\pi$
$338$	15.3833	0.836741
$339$	−38.6970	−2.10173
$340$	2.38538	0.129366
$341$	−16.1886	−0.876663
$342$	24.3421	1.31627
$343$	−44.8775	−2.42316
$344$	−2.49578	−0.134564
$345$	−1.22961	−0.0661998
$346$	−7.50752	−0.403607
$347$	11.3608	0.609882	0.304941	−	0.952371i	$-0.401363\pi$
$347$	11.3608	0.609882	0.304941	+	0.952371i	$0.401363\pi$
$348$	−33.1415	−1.77657
$349$	−21.1007	−1.12949	−0.564746	−	0.825265i	$-0.691026\pi$
$349$	−21.1007	−1.12949	−0.564746	+	0.825265i	$0.691026\pi$
$350$	8.39313	0.448631
$351$	−19.0779	−1.01830
$352$	−25.7828	−1.37423
$353$	9.86750	0.525194	0.262597	−	0.964906i	$-0.415421\pi$
$353$	9.86750	0.525194	0.262597	+	0.964906i	$0.415421\pi$
$354$	3.18022	0.169027
$355$	−1.69155	−0.0897783
$356$	−2.34457	−0.124262
$357$	−12.9603	−0.685930
$358$	9.64910	0.509971
$359$	−14.3034	−0.754906	−0.377453	−	0.926029i	$-0.623200\pi$
$359$	−14.3034	−0.754906	−0.377453	+	0.926029i	$0.623200\pi$
$360$	−16.8425	−0.887677
$361$	46.3074	2.43723
$362$	17.0657	0.896951
$363$	−22.7416	−1.19362
$364$	42.1859	2.21114
$365$	−5.94919	−0.311395
$366$	−12.0497	−0.629848
$367$	27.3893	1.42971	0.714856	−	0.699272i	$-0.246492\pi$
$367$	27.3893	1.42971	0.714856	+	0.699272i	$0.246492\pi$
$368$	0.340004	0.0177239
$369$	43.2951	2.25385
$370$	−0.952876	−0.0495377
$371$	5.44506	0.282694
$372$	14.6587	0.760019
$373$	−6.22609	−0.322375	−0.161187	−	0.986924i	$-0.551532\pi$
$373$	−6.22609	−0.322375	−0.161187	+	0.986924i	$0.551532\pi$
$374$	3.15724	0.163257
$375$	31.9822	1.65155
$376$	−23.8640	−1.23069
$377$	−48.7204	−2.50923
$378$	11.2179	0.576985
$379$	−10.0588	−0.516685	−0.258342	−	0.966053i	$-0.583176\pi$
$379$	−10.0588	−0.516685	−0.258342	+	0.966053i	$0.583176\pi$
$380$	−19.2770	−0.988889
$381$	5.61447	0.287638
$382$	−3.72684	−0.190682
$383$	2.39604	0.122432	0.0612160	−	0.998125i	$-0.480502\pi$
$383$	2.39604	0.122432	0.0612160	+	0.998125i	$0.480502\pi$
$384$	27.9196	1.42477
$385$	34.1417	1.74002
$386$	4.67935	0.238173
$387$	4.20967	0.213990
$388$	−4.99088	−0.253373
$389$	18.6837	0.947302	0.473651	−	0.880713i	$-0.342936\pi$
$389$	18.6837	0.947302	0.473651	+	0.880713i	$0.342936\pi$
$390$	−18.0901	−0.916029
$391$	−0.285665	−0.0144467
$392$	−40.6754	−2.05442
$393$	14.0361	0.708028
$394$	9.37659	0.472386
$395$	19.1854	0.965323
$396$	27.6398	1.38895
$397$	−3.25647	−0.163437	−0.0817187	−	0.996655i	$-0.526041\pi$
$397$	−3.25647	−0.163437	−0.0817187	+	0.996655i	$0.526041\pi$
$398$	11.8260	0.592785
$399$	104.736	5.24334
$400$	−2.89245	−0.144622
$401$	−12.8023	−0.639319	−0.319659	−	0.947533i	$-0.603568\pi$
$401$	−12.8023	−0.639319	−0.319659	+	0.947533i	$0.603568\pi$
$402$	16.1664	0.806307
$403$	21.5494	1.07345
$404$	13.2260	0.658019
$405$	−6.26426	−0.311273
$406$	28.6478	1.42177
$407$	3.66552	0.181693
$408$	−6.70139	−0.331768
$409$	−1.89893	−0.0938960	−0.0469480	−	0.998897i	$-0.514950\pi$
$409$	−1.89893	−0.0938960	−0.0469480	+	0.998897i	$0.514950\pi$
$410$	11.7970	0.582611
$411$	−5.05378	−0.249285
$412$	8.66291	0.426791
$413$	7.98962	0.393143
$414$	0.860467	0.0422897
$415$	−5.97065	−0.293088
$416$	34.3206	1.68271
$417$	−40.3060	−1.97380
$418$	−25.5146	−1.24796
$419$	19.6617	0.960535	0.480267	−	0.877122i	$-0.340540\pi$
$419$	19.6617	0.960535	0.480267	+	0.877122i	$0.340540\pi$
$420$	−30.9152	−1.50851
$421$	5.64381	0.275063	0.137531	−	0.990497i	$-0.456083\pi$
$421$	5.64381	0.275063	0.137531	+	0.990497i	$0.456083\pi$
$422$	9.29627	0.452535
$423$	40.2518	1.95711
$424$	2.81549	0.136732
$425$	2.43018	0.117881
$426$	2.02731	0.0982237
$427$	−30.2723	−1.46498
$428$	8.52088	0.411872
$429$	69.5890	3.35979
$430$	1.14704	0.0553153
$431$	−17.5167	−0.843751	−0.421876	−	0.906654i	$-0.638628\pi$
$431$	−17.5167	−0.843751	−0.421876	+	0.906654i	$0.638628\pi$
$432$	−3.86591	−0.185999
$433$	−9.32560	−0.448160	−0.224080	−	0.974571i	$-0.571938\pi$
$433$	−9.32560	−0.448160	−0.224080	+	0.974571i	$0.571938\pi$
$434$	−12.6711	−0.608234
$435$	35.7039	1.71187
$436$	−18.0216	−0.863077
$437$	2.30855	0.110433
$438$	7.13007	0.340688
$439$	−19.3087	−0.921552	−0.460776	−	0.887517i	$-0.652429\pi$
$439$	−19.3087	−0.921552	−0.460776	+	0.887517i	$0.652429\pi$
$440$	17.6537	0.841609
$441$	68.6077	3.26703
$442$	−4.20274	−0.199904
$443$	−8.29615	−0.394162	−0.197081	−	0.980387i	$-0.563146\pi$
$443$	−8.29615	−0.394162	−0.197081	+	0.980387i	$0.563146\pi$
$444$	−3.31911	−0.157518
$445$	2.52585	0.119737
$446$	8.60768	0.407585
$447$	−53.4815	−2.52959
$448$	−8.69088	−0.410606
$449$	−8.54698	−0.403357	−0.201678	−	0.979452i	$-0.564640\pi$
$449$	−8.54698	−0.403357	−0.201678	+	0.979452i	$0.564640\pi$
$450$	−7.32009	−0.345072
$451$	−45.3805	−2.13688
$452$	−21.4451	−1.00869
$453$	56.0633	2.63408
$454$	13.4604	0.631730
$455$	−45.4476	−2.13062
$456$	54.1559	2.53608
$457$	−26.3305	−1.23169	−0.615845	−	0.787867i	$-0.711185\pi$
$457$	−26.3305	−1.23169	−0.615845	+	0.787867i	$0.711185\pi$
$458$	16.9602	0.792498
$459$	3.24807	0.151607
$460$	−0.681421	−0.0317714
$461$	27.9981	1.30400	0.652002	−	0.758217i	$-0.273929\pi$
$461$	27.9981	1.30400	0.652002	+	0.758217i	$0.273929\pi$
$462$	−40.9186	−1.90371
$463$	−15.8436	−0.736314	−0.368157	−	0.929764i	$-0.620011\pi$
$463$	−15.8436	−0.736314	−0.368157	+	0.929764i	$0.620011\pi$
$464$	−9.87264	−0.458326
$465$	−15.7921	−0.732341
$466$	−9.53139	−0.441533
$467$	17.4779	0.808781	0.404390	−	0.914586i	$-0.367484\pi$
$467$	17.4779	0.808781	0.404390	+	0.914586i	$0.367484\pi$
$468$	−36.7925	−1.70074
$469$	40.6147	1.87541
$470$	10.9677	0.505904
$471$	25.2961	1.16558
$472$	4.13121	0.190154
$473$	−4.41244	−0.202884
$474$	−22.9936	−1.05613
$475$	−19.6390	−0.901101
$476$	−7.18229	−0.329200
$477$	−4.74893	−0.217438
$478$	7.80007	0.356767
$479$	35.3720	1.61619	0.808093	−	0.589054i	$-0.200500\pi$
$479$	35.3720	1.61619	0.808093	+	0.589054i	$0.200500\pi$
$480$	−25.1513	−1.14799
$481$	−4.87934	−0.222479
$482$	−8.90142	−0.405449
$483$	3.70230	0.168460
$484$	−12.6029	−0.572859
$485$	5.37676	0.244146
$486$	14.4800	0.656824
$487$	−10.6344	−0.481891	−0.240945	−	0.970539i	$-0.577457\pi$
$487$	−10.6344	−0.481891	−0.240945	+	0.970539i	$0.577457\pi$
$488$	−15.6530	−0.708576
$489$	−2.47254	−0.111812
$490$	18.6941	0.844513
$491$	−12.1886	−0.550065	−0.275033	−	0.961435i	$-0.588689\pi$
$491$	−12.1886	−0.550065	−0.275033	+	0.961435i	$0.588689\pi$
$492$	41.0919	1.85256
$493$	8.29481	0.373580
$494$	33.9636	1.52809
$495$	−29.7768	−1.33837
$496$	4.36674	0.196073
$497$	5.09320	0.228461
$498$	7.15578	0.320658
$499$	1.89471	0.0848190	0.0424095	−	0.999100i	$-0.486497\pi$
$499$	1.89471	0.0848190	0.0424095	+	0.999100i	$0.486497\pi$
$500$	17.7238	0.792634
$501$	−27.4652	−1.22705
$502$	13.3764	0.597019
$503$	−14.8287	−0.661179	−0.330590	−	0.943775i	$-0.607248\pi$
$503$	−14.8287	−0.661179	−0.330590	+	0.943775i	$0.607248\pi$
$504$	50.7121	2.25889
$505$	−14.2486	−0.634056
$506$	−0.901913	−0.0400949
$507$	−57.7270	−2.56374
$508$	3.11142	0.138047
$509$	2.86619	0.127042	0.0635209	−	0.997981i	$-0.479767\pi$
$509$	2.86619	0.127042	0.0635209	+	0.997981i	$0.479767\pi$
$510$	3.07991	0.136381
$511$	17.9128	0.792415
$512$	12.8957	0.569917
$513$	−26.2486	−1.15891
$514$	−5.71331	−0.252003
$515$	−9.33271	−0.411248
$516$	3.99544	0.175890
$517$	−42.1906	−1.85554
$518$	2.86907	0.126060
$519$	28.1725	1.23664
$520$	−23.4997	−1.03053
$521$	−40.5575	−1.77686	−0.888428	−	0.459016i	$-0.848202\pi$
$521$	−40.5575	−1.77686	−0.888428	+	0.459016i	$0.848202\pi$
$522$	−24.9852	−1.09357
$523$	−13.5484	−0.592431	−0.296215	−	0.955121i	$-0.595725\pi$
$523$	−13.5484	−0.592431	−0.296215	+	0.955121i	$0.595725\pi$
$524$	7.77851	0.339806
$525$	−31.4958	−1.37459
$526$	−12.4350	−0.542192
$527$	−3.66886	−0.159818
$528$	14.1014	0.613685
$529$	−22.9184	−0.996452
$530$	−1.29398	−0.0562068
$531$	−6.96817	−0.302393
$532$	58.0423	2.51645
$533$	60.4080	2.61656
$534$	−3.02721	−0.131000
$535$	−9.17969	−0.396873
$536$	21.0007	0.907092
$537$	−36.2089	−1.56253
$538$	3.49404	0.150639
$539$	−71.9123	−3.09748
$540$	7.74790	0.333416
$541$	19.3693	0.832752	0.416376	−	0.909193i	$-0.363300\pi$
$541$	19.3693	0.832752	0.416376	+	0.909193i	$0.363300\pi$
$542$	5.38623	0.231359
$543$	−64.0401	−2.74822
$544$	−5.84321	−0.250525
$545$	19.4150	0.831646
$546$	54.4686	2.33104
$547$	26.6926	1.14129	0.570647	−	0.821195i	$-0.306692\pi$
$547$	26.6926	1.14129	0.570647	+	0.821195i	$0.306692\pi$
$548$	−2.80069	−0.119640
$549$	26.4021	1.12681
$550$	7.67267	0.327164
$551$	−67.0329	−2.85570
$552$	1.91435	0.0814803
$553$	−57.7665	−2.45648
$554$	3.80967	0.161858
$555$	3.57574	0.151782
$556$	−22.3367	−0.947288
$557$	−0.00272568	−0.000115491 0	−5.77453e−5	−	1.00000i	$-0.500018\pi$
$557$	−0.00272568	−0.000115491 0	−5.77453e−5		1.00000i	$0.500018\pi$
$558$	11.0512	0.467833
$559$	5.87360	0.248427
$560$	−9.20944	−0.389170
$561$	−11.8478	−0.500213
$562$	1.58937	0.0670436
$563$	24.7249	1.04203	0.521015	−	0.853548i	$-0.325554\pi$
$563$	24.7249	1.04203	0.521015	+	0.853548i	$0.325554\pi$
$564$	38.2034	1.60865
$565$	23.1031	0.971956
$566$	−1.30235	−0.0547418
$567$	18.8614	0.792105
$568$	2.63355	0.110501
$569$	−2.83737	−0.118949	−0.0594744	−	0.998230i	$-0.518942\pi$
$569$	−2.83737	−0.118949	−0.0594744	+	0.998230i	$0.518942\pi$
$570$	−24.8896	−1.04251
$571$	−13.8859	−0.581108	−0.290554	−	0.956859i	$-0.593840\pi$
$571$	−13.8859	−0.581108	−0.290554	+	0.956859i	$0.593840\pi$
$572$	38.5647	1.61247
$573$	13.9853	0.584242
$574$	−35.5202	−1.48258
$575$	−0.694219	−0.0289509
$576$	7.57978	0.315824
$577$	42.1024	1.75275	0.876373	−	0.481632i	$-0.159956\pi$
$577$	42.1024	1.75275	0.876373	+	0.481632i	$0.159956\pi$
$578$	0.715531	0.0297622
$579$	−17.5596	−0.729752
$580$	19.7863	0.821582
$581$	17.9774	0.745827
$582$	−6.44401	−0.267113
$583$	4.97766	0.206154
$584$	9.26220	0.383273
$585$	39.6372	1.63880
$586$	−1.88638	−0.0779254
$587$	−18.0375	−0.744487	−0.372244	−	0.928135i	$-0.621411\pi$
$587$	−18.0375	−0.744487	−0.372244	+	0.928135i	$0.621411\pi$
$588$	65.1163	2.68535
$589$	29.6491	1.22167
$590$	−1.89867	−0.0781671
$591$	−35.1863	−1.44737
$592$	−0.988743	−0.0406371
$593$	19.3163	0.793226	0.396613	−	0.917986i	$-0.370185\pi$
$593$	19.3163	0.793226	0.396613	+	0.917986i	$0.370185\pi$
$594$	10.2549	0.420765
$595$	7.73761	0.317211
$596$	−29.6383	−1.21403
$597$	−44.3780	−1.81627
$598$	1.20058	0.0490953
$599$	−9.38337	−0.383394	−0.191697	−	0.981454i	$-0.561399\pi$
$599$	−9.38337	−0.383394	−0.191697	+	0.981454i	$0.561399\pi$
$600$	−16.2856	−0.664857
$601$	2.19075	0.0893625	0.0446812	−	0.999001i	$-0.485773\pi$
$601$	2.19075	0.0893625	0.0446812	+	0.999001i	$0.485773\pi$
$602$	−3.45370	−0.140762
$603$	−35.4222	−1.44250
$604$	31.0690	1.26418
$605$	13.5773	0.551997
$606$	17.0769	0.693701
$607$	20.3853	0.827415	0.413708	−	0.910410i	$-0.364234\pi$
$607$	20.3853	0.827415	0.413708	+	0.910410i	$0.364234\pi$
$608$	47.2207	1.91505
$609$	−107.503	−4.35624
$610$	7.19398	0.291276
$611$	56.1618	2.27206
$612$	6.26406	0.253209
$613$	−23.2357	−0.938483	−0.469242	−	0.883070i	$-0.655473\pi$
$613$	−23.2357	−0.938483	−0.469242	+	0.883070i	$0.655473\pi$
$614$	13.4171	0.541471
$615$	−44.2690	−1.78510
$616$	−53.1547	−2.14166
$617$	20.2667	0.815908	0.407954	−	0.913003i	$-0.366242\pi$
$617$	20.2667	0.815908	0.407954	+	0.913003i	$0.366242\pi$
$618$	11.1852	0.449934
$619$	40.7881	1.63941	0.819706	−	0.572784i	$-0.194137\pi$
$619$	40.7881	1.63941	0.819706	+	0.572784i	$0.194137\pi$
$620$	−8.75164	−0.351474
$621$	−0.927861	−0.0372338
$622$	3.57451	0.143325
$623$	−7.60522	−0.304697
$624$	−18.7710	−0.751443
$625$	−6.94328	−0.277731
$626$	2.69581	0.107746
$627$	95.7453	3.82370
$628$	14.0185	0.559400
$629$	0.830724	0.0331231
$630$	−23.3069	−0.928568
$631$	37.7365	1.50226	0.751132	−	0.660152i	$-0.229508\pi$
$631$	37.7365	1.50226	0.751132	+	0.660152i	$0.229508\pi$
$632$	−29.8694	−1.18814
$633$	−34.8849	−1.38655
$634$	−18.3231	−0.727702
$635$	−3.35199	−0.133020
$636$	−4.50725	−0.178724
$637$	95.7257	3.79279
$638$	26.1887	1.03682
$639$	−4.44205	−0.175725
$640$	−16.6688	−0.658890
$641$	−35.3354	−1.39567	−0.697833	−	0.716261i	$-0.745852\pi$
$641$	−35.3354	−1.39567	−0.697833	+	0.716261i	$0.745852\pi$
$642$	11.0018	0.434206
$643$	17.6062	0.694321	0.347160	−	0.937806i	$-0.387146\pi$
$643$	17.6062	0.694321	0.347160	+	0.937806i	$0.387146\pi$
$644$	2.05173	0.0808496
$645$	−4.30436	−0.169484
$646$	−5.78242	−0.227506
$647$	16.8295	0.661634	0.330817	−	0.943695i	$-0.392676\pi$
$647$	16.8295	0.661634	0.330817	+	0.943695i	$0.392676\pi$
$648$	9.75271	0.383123
$649$	7.30380	0.286699
$650$	−10.2134	−0.400604
$651$	47.5494	1.86361
$652$	−1.37023	−0.0536623
$653$	−48.9543	−1.91573	−0.957865	−	0.287218i	$-0.907270\pi$
$653$	−48.9543	−1.91573	−0.957865	+	0.287218i	$0.907270\pi$
$654$	−23.2687	−0.909878
$655$	−8.37992	−0.327431
$656$	12.2410	0.477931
$657$	−15.6227	−0.609499
$658$	−33.0234	−1.28739
$659$	10.2348	0.398690	0.199345	−	0.979929i	$-0.436119\pi$
$659$	10.2348	0.398690	0.199345	+	0.979929i	$0.436119\pi$
$660$	−28.2615	−1.10008
$661$	−17.5405	−0.682247	−0.341123	−	0.940019i	$-0.610807\pi$
$661$	−17.5405	−0.682247	−0.341123	+	0.940019i	$0.610807\pi$
$662$	1.98652	0.0772083
$663$	15.7711	0.612499
$664$	9.29560	0.360739
$665$	−62.5299	−2.42481
$666$	−2.50227	−0.0969609
$667$	−2.36954	−0.0917490
$668$	−15.2206	−0.588903
$669$	−32.3009	−1.24883
$670$	−9.65176	−0.372880
$671$	−27.6738	−1.06833
$672$	75.7295	2.92133
$673$	38.4467	1.48201	0.741005	−	0.671499i	$-0.234349\pi$
$673$	38.4467	1.48201	0.741005	+	0.671499i	$0.234349\pi$
$674$	−22.3259	−0.859960
$675$	7.89341	0.303818
$676$	−31.9910	−1.23042
$677$	−36.5850	−1.40608	−0.703039	−	0.711152i	$-0.748174\pi$
$677$	−36.5850	−1.40608	−0.703039	+	0.711152i	$0.748174\pi$
$678$	−27.6889	−1.06339
$679$	−16.1892	−0.621284
$680$	4.00090	0.153428
$681$	−50.5113	−1.93560
$682$	−11.5835	−0.443554
$683$	−12.9004	−0.493620	−0.246810	−	0.969064i	$-0.579382\pi$
$683$	−12.9004	−0.493620	−0.246810	+	0.969064i	$0.579382\pi$
$684$	−50.6217	−1.93557
$685$	3.01724	0.115283
$686$	−32.1112	−1.22601
$687$	−63.6444	−2.42818
$688$	1.19022	0.0453766
$689$	−6.62600	−0.252430
$690$	−0.879822	−0.0334943
$691$	−40.0989	−1.52543	−0.762716	−	0.646733i	$-0.776135\pi$
$691$	−40.0989	−1.52543	−0.762716	+	0.646733i	$0.776135\pi$
$692$	15.6126	0.593502
$693$	89.6567	3.40578
$694$	8.12904	0.308574
$695$	24.0638	0.912790
$696$	−55.5868	−2.10701
$697$	−10.2847	−0.389560
$698$	−15.0982	−0.571475
$699$	35.7672	1.35284
$700$	−17.4543	−0.659710
$701$	−44.9281	−1.69691	−0.848456	−	0.529266i	$-0.822467\pi$
$701$	−44.9281	−1.69691	−0.848456	+	0.529266i	$0.822467\pi$
$702$	−13.6508	−0.515216
$703$	−6.71333	−0.253198
$704$	−7.94487	−0.299433
$705$	−41.1572	−1.55007
$706$	7.06050	0.265726
$707$	42.9020	1.61350
$708$	−6.61356	−0.248553
$709$	52.7913	1.98262	0.991310	−	0.131544i	$-0.0419935\pi$
$709$	52.7913	1.98262	0.991310	+	0.131544i	$0.0419935\pi$
$710$	−1.21036	−0.0454240
$711$	50.3812	1.88944
$712$	−3.93245	−0.147375
$713$	1.04807	0.0392504
$714$	−9.27347	−0.347051
$715$	−41.5464	−1.55375
$716$	−20.0662	−0.749909
$717$	−29.2703	−1.09312
$718$	−10.2345	−0.381950
$719$	−2.10913	−0.0786572	−0.0393286	−	0.999226i	$-0.512522\pi$
$719$	−2.10913	−0.0786572	−0.0393286	+	0.999226i	$0.512522\pi$
$720$	8.03204	0.299336
$721$	28.1004	1.04651
$722$	33.1344	1.23313
$723$	33.4032	1.24228
$724$	−35.4896	−1.31896
$725$	20.1579	0.748647
$726$	−16.2723	−0.603923
$727$	−45.5656	−1.68993	−0.844967	−	0.534818i	$-0.820380\pi$
$727$	−45.5656	−1.68993	−0.844967	+	0.534818i	$0.820380\pi$
$728$	70.7566	2.62241
$729$	−42.6141	−1.57830
$730$	−4.25684	−0.157553
$731$	−1.00000	−0.0369863
$732$	25.0585	0.926188
$733$	5.48523	0.202601	0.101301	−	0.994856i	$-0.467700\pi$
$733$	5.48523	0.202601	0.101301	+	0.994856i	$0.467700\pi$
$734$	19.5979	0.723373
$735$	−70.1509	−2.58756
$736$	1.66920	0.0615276
$737$	37.1283	1.36764
$738$	30.9790	1.14035
$739$	9.87625	0.363304	0.181652	−	0.983363i	$-0.441856\pi$
$739$	9.87625	0.363304	0.181652	+	0.983363i	$0.441856\pi$
$740$	1.98160	0.0728449
$741$	−127.451	−4.68203
$742$	3.89611	0.143031
$743$	−43.7158	−1.60378	−0.801888	−	0.597474i	$-0.796171\pi$
$743$	−43.7158	−1.60378	−0.801888	+	0.597474i	$0.796171\pi$
$744$	24.5865	0.901383
$745$	31.9298	1.16982
$746$	−4.45497	−0.163108
$747$	−15.6790	−0.573665
$748$	−6.56577	−0.240068
$749$	27.6397	1.00993
$750$	22.8843	0.835615
$751$	−7.62153	−0.278114	−0.139057	−	0.990284i	$-0.544407\pi$
$751$	−7.62153	−0.278114	−0.139057	+	0.990284i	$0.544407\pi$
$752$	11.3806	0.415006
$753$	−50.1960	−1.82925
$754$	−34.8610	−1.26956
$755$	−33.4712	−1.21814
$756$	−23.3286	−0.848453
$757$	21.1390	0.768310	0.384155	−	0.923269i	$-0.374493\pi$
$757$	21.1390	0.768310	0.384155	+	0.923269i	$0.374493\pi$
$758$	−7.19737	−0.261420
$759$	3.38449	0.122849
$760$	−32.3325	−1.17282
$761$	15.4700	0.560789	0.280394	−	0.959885i	$-0.409535\pi$
$761$	15.4700	0.560789	0.280394	+	0.959885i	$0.409535\pi$
$762$	4.01733	0.145533
$763$	−58.4577	−2.11631
$764$	7.75032	0.280397
$765$	−6.74838	−0.243988
$766$	1.71444	0.0619454
$767$	−9.72242	−0.351056
$768$	29.6467	1.06978
$769$	8.54704	0.308214	0.154107	−	0.988054i	$-0.450750\pi$
$769$	8.54704	0.308214	0.154107	+	0.988054i	$0.450750\pi$
$770$	24.4295	0.880377
$771$	21.4396	0.772129
$772$	−9.73115	−0.350232
$773$	21.1957	0.762357	0.381179	−	0.924501i	$-0.375518\pi$
$773$	21.1957	0.762357	0.381179	+	0.924501i	$0.375518\pi$
$774$	3.01215	0.108270
$775$	−8.91601	−0.320272
$776$	−8.37098	−0.300501
$777$	−10.7664	−0.386242
$778$	13.3688	0.479294
$779$	83.1135	2.97785
$780$	37.6201	1.34702
$781$	4.65600	0.166605
$782$	−0.204402	−0.00730942
$783$	26.9421	0.962834
$784$	19.3977	0.692776
$785$	−15.1024	−0.539028
$786$	10.0433	0.358232
$787$	32.6240	1.16292	0.581461	−	0.813574i	$-0.302481\pi$
$787$	32.6240	1.16292	0.581461	+	0.813574i	$0.302481\pi$
$788$	−19.4995	−0.694641
$789$	46.6633	1.66126
$790$	13.7278	0.488412
$791$	−69.5626	−2.47336
$792$	46.3590	1.64729
$793$	36.8378	1.30815
$794$	−2.33010	−0.0826923
$795$	4.85574	0.172216
$796$	−24.5933	−0.871688
$797$	−41.9646	−1.48646	−0.743231	−	0.669034i	$-0.766708\pi$
$797$	−41.9646	−1.48646	−0.743231	+	0.669034i	$0.766708\pi$
$798$	74.9417	2.65291
$799$	−9.56174	−0.338270
$800$	−14.2001	−0.502048
$801$	6.63291	0.234362
$802$	−9.16048	−0.323468
$803$	16.3752	0.577867
$804$	−33.6196	−1.18567
$805$	−2.21037	−0.0779052
$806$	15.4193	0.543121
$807$	−13.1116	−0.461551
$808$	22.1834	0.780411
$809$	−3.98728	−0.140185	−0.0700927	−	0.997540i	$-0.522330\pi$
$809$	−3.98728	−0.140185	−0.0700927	+	0.997540i	$0.522330\pi$
$810$	−4.48227	−0.157491
$811$	−5.78075	−0.202989	−0.101495	−	0.994836i	$-0.532363\pi$
$811$	−5.78075	−0.202989	−0.101495	+	0.994836i	$0.532363\pi$
$812$	−59.5758	−2.09070
$813$	−20.2122	−0.708874
$814$	2.62279	0.0919288
$815$	1.47617	0.0517080
$816$	3.19583	0.111877
$817$	8.08130	0.282729
$818$	−1.35874	−0.0475073
$819$	−119.346	−4.17029
$820$	−24.5329	−0.856726
$821$	27.0116	0.942711	0.471356	−	0.881943i	$-0.343765\pi$
$821$	27.0116	0.942711	0.471356	+	0.881943i	$0.343765\pi$
$822$	−3.61614	−0.126127
$823$	−14.0570	−0.489995	−0.244997	−	0.969524i	$-0.578787\pi$
$823$	−14.0570	−0.489995	−0.244997	+	0.969524i	$0.578787\pi$
$824$	14.5299	0.506174
$825$	−28.7922	−1.00242
$826$	5.71682	0.198914
$827$	39.7538	1.38238	0.691188	−	0.722675i	$-0.257088\pi$
$827$	39.7538	1.38238	0.691188	+	0.722675i	$0.257088\pi$
$828$	−1.78942	−0.0621867
$829$	30.4414	1.05727	0.528636	−	0.848849i	$-0.322704\pi$
$829$	30.4414	1.05727	0.528636	+	0.848849i	$0.322704\pi$
$830$	−4.27219	−0.148290
$831$	−14.2961	−0.495926
$832$	10.5758	0.366649
$833$	−16.2976	−0.564680
$834$	−28.8402	−0.998656
$835$	16.3974	0.567457
$836$	53.0600	1.83512
$837$	−11.9167	−0.411902
$838$	14.0685	0.485989
$839$	7.53085	0.259994	0.129997	−	0.991514i	$-0.458503\pi$
$839$	7.53085	0.259994	0.129997	+	0.991514i	$0.458503\pi$
$840$	−51.8527	−1.78909
$841$	39.8039	1.37255
$842$	4.03832	0.139170
$843$	−5.96424	−0.205419
$844$	−19.3325	−0.665451
$845$	34.4645	1.18561
$846$	28.8014	0.990213
$847$	−40.8808	−1.40468
$848$	−1.34268	−0.0461079
$849$	4.88716	0.167727
$850$	1.73887	0.0596429
$851$	−0.237309	−0.00813485
$852$	−4.21599	−0.144437
$853$	−3.34450	−0.114514	−0.0572568	−	0.998359i	$-0.518235\pi$
$853$	−3.34450	−0.114514	−0.0572568	+	0.998359i	$0.518235\pi$
$854$	−21.6608	−0.741217
$855$	54.5356	1.86508
$856$	14.2917	0.488480
$857$	5.50739	0.188129	0.0940644	−	0.995566i	$-0.470014\pi$
$857$	5.50739	0.188129	0.0940644	+	0.995566i	$0.470014\pi$
$858$	49.7931	1.69991
$859$	−54.8043	−1.86990	−0.934950	−	0.354781i	$-0.884556\pi$
$859$	−54.8043	−1.86990	−0.934950	+	0.354781i	$0.884556\pi$
$860$	−2.38538	−0.0813409
$861$	133.292	4.54258
$862$	−12.5338	−0.426902
$863$	−20.2431	−0.689084	−0.344542	−	0.938771i	$-0.611966\pi$
$863$	−20.2431	−0.689084	−0.344542	+	0.938771i	$0.611966\pi$
$864$	−18.9792	−0.645684
$865$	−16.8197	−0.571888
$866$	−6.67276	−0.226750
$867$	−2.68508	−0.0911902
$868$	26.3508	0.894405
$869$	−52.8079	−1.79138
$870$	25.5472	0.866133
$871$	−49.4232	−1.67464
$872$	−30.2268	−1.02361
$873$	14.1194	0.477871
$874$	1.65184	0.0558742
$875$	57.4919	1.94358
$876$	−14.8276	−0.500980
$877$	−15.2436	−0.514741	−0.257371	−	0.966313i	$-0.582856\pi$
$877$	−15.2436	−0.514741	−0.257371	+	0.966313i	$0.582856\pi$
$878$	−13.8159	−0.466266
$879$	7.07876	0.238761
$880$	−8.41891	−0.283802
$881$	−46.6154	−1.57051	−0.785256	−	0.619172i	$-0.787468\pi$
$881$	−46.6154	−1.57051	−0.785256	+	0.619172i	$0.787468\pi$
$882$	49.0910	1.65298
$883$	46.3548	1.55996	0.779981	−	0.625803i	$-0.215229\pi$
$883$	46.3548	1.55996	0.779981	+	0.625803i	$0.215229\pi$
$884$	8.74000	0.293958
$885$	7.12490	0.239501
$886$	−5.93616	−0.199429
$887$	−49.6009	−1.66544	−0.832718	−	0.553697i	$-0.813217\pi$
$887$	−49.6009	−1.66544	−0.832718	+	0.553697i	$0.813217\pi$
$888$	−5.56700	−0.186816
$889$	10.0927	0.338498
$890$	1.80732	0.0605816
$891$	17.2424	0.577641
$892$	−17.9005	−0.599352
$893$	77.2713	2.58578
$894$	−38.2677	−1.27986
$895$	21.6177	0.722599
$896$	50.1889	1.67669
$897$	−4.50525	−0.150426
$898$	−6.11563	−0.204081
$899$	−30.4325	−1.01498
$900$	15.2228	0.507427
$901$	1.12810	0.0375824
$902$	−32.4712	−1.08117
$903$	12.9603	0.431290
$904$	−35.9689	−1.19631
$905$	38.2336	1.27093
$906$	40.1150	1.33273
$907$	−20.7240	−0.688128	−0.344064	−	0.938946i	$-0.611804\pi$
$907$	−20.7240	−0.688128	−0.344064	+	0.938946i	$0.611804\pi$
$908$	−27.9922	−0.928955
$909$	−37.4171	−1.24105
$910$	−32.5192	−1.07800
$911$	47.0080	1.55744	0.778722	−	0.627370i	$-0.215868\pi$
$911$	47.0080	1.55744	0.778722	+	0.627370i	$0.215868\pi$
$912$	−25.8265	−0.855200
$913$	16.4342	0.543893
$914$	−18.8403	−0.623182
$915$	−26.9959	−0.892458
$916$	−35.2703	−1.16536
$917$	25.2316	0.833221
$918$	2.32410	0.0767066
$919$	−43.3686	−1.43060	−0.715299	−	0.698819i	$-0.753709\pi$
$919$	−43.3686	−1.43060	−0.715299	+	0.698819i	$0.753709\pi$
$920$	−1.14292	−0.0376809
$921$	−50.3487	−1.65905
$922$	20.0336	0.659770
$923$	−6.19782	−0.204004
$924$	85.0941	2.79939
$925$	2.01881	0.0663781
$926$	−11.3366	−0.372543
$927$	−24.5078	−0.804943
$928$	−48.4683	−1.59105
$929$	−27.1627	−0.891178	−0.445589	−	0.895238i	$-0.647006\pi$
$929$	−27.1627	−0.891178	−0.445589	+	0.895238i	$0.647006\pi$
$930$	−11.2997	−0.370533
$931$	131.706	4.31649
$932$	19.8214	0.649272
$933$	−13.4136	−0.439142
$934$	12.5060	0.409208
$935$	7.07342	0.231326
$936$	−61.7105	−2.01707
$937$	51.9982	1.69871	0.849354	−	0.527824i	$-0.176992\pi$
$937$	51.9982	1.69871	0.849354	+	0.527824i	$0.176992\pi$
$938$	29.0611	0.948877
$939$	−10.1162	−0.330130
$940$	−22.8084	−0.743929
$941$	−49.6341	−1.61803	−0.809013	−	0.587791i	$-0.799998\pi$
$941$	−49.6341	−1.61803	−0.809013	+	0.587791i	$0.799998\pi$
$942$	18.1001	0.589734
$943$	2.93798	0.0956736
$944$	−1.97014	−0.0641225
$945$	25.1323	0.817554
$946$	−3.15724	−0.102651
$947$	−51.9160	−1.68704	−0.843522	−	0.537094i	$-0.819522\pi$
$947$	−51.9160	−1.68704	−0.843522	+	0.537094i	$0.819522\pi$
$948$	47.8173	1.55303
$949$	−21.7977	−0.707584
$950$	−14.0523	−0.455918
$951$	68.7587	2.22965
$952$	−12.0466	−0.390431
$953$	−12.9705	−0.420154	−0.210077	−	0.977685i	$-0.567371\pi$
$953$	−12.9705	−0.420154	−0.210077	+	0.977685i	$0.567371\pi$
$954$	−3.39801	−0.110014
$955$	−8.34956	−0.270185
$956$	−16.2210	−0.524624
$957$	−98.2750	−3.17678
$958$	25.3098	0.817721
$959$	−9.08478	−0.293363
$960$	−7.75027	−0.250139
$961$	−17.5395	−0.565789
$962$	−3.49132	−0.112565
$963$	−24.1060	−0.776805
$964$	18.5113	0.596210
$965$	10.4835	0.337477
$966$	2.64911	0.0852337
$967$	44.8511	1.44231	0.721157	−	0.692771i	$-0.243610\pi$
$967$	44.8511	1.44231	0.721157	+	0.692771i	$0.243610\pi$
$968$	−21.1383	−0.679411
$969$	21.6990	0.697071
$970$	3.84724	0.123527
$971$	−11.0164	−0.353534	−0.176767	−	0.984253i	$-0.556564\pi$
$971$	−11.0164	−0.353534	−0.176767	+	0.984253i	$0.556564\pi$
$972$	−30.1124	−0.965857
$973$	−72.4550	−2.32280
$974$	−7.60925	−0.243816
$975$	38.3267	1.22744
$976$	7.46476	0.238941
$977$	−4.59410	−0.146978	−0.0734891	−	0.997296i	$-0.523413\pi$
$977$	−4.59410	−0.146978	−0.0734891	+	0.997296i	$0.523413\pi$
$978$	−1.76918	−0.0565722
$979$	−6.95239	−0.222199
$980$	−38.8761	−1.24185
$981$	50.9840	1.62779
$982$	−8.72135	−0.278309
$983$	18.8216	0.600315	0.300157	−	0.953890i	$-0.402961\pi$
$983$	18.8216	0.600315	0.300157	+	0.953890i	$0.402961\pi$
$984$	68.9216	2.19714
$985$	21.0072	0.669344
$986$	5.93520	0.189015
$987$	123.923	3.94450
$988$	−70.6305	−2.24706
$989$	0.285665	0.00908363
$990$	−21.3062	−0.677156
$991$	−41.9360	−1.33214	−0.666070	−	0.745889i	$-0.732025\pi$
$991$	−41.9360	−1.33214	−0.666070	+	0.745889i	$0.732025\pi$
$992$	21.4379	0.680654
$993$	−7.45456	−0.236563
$994$	3.64434	0.115592
$995$	26.4948	0.839943
$996$	−14.8811	−0.471526
$997$	9.12570	0.289014	0.144507	−	0.989504i	$-0.453840\pi$
$997$	9.12570	0.289014	0.144507	+	0.989504i	$0.453840\pi$
$998$	1.35573	0.0429148
$999$	2.69825	0.0853689

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.13	✓	21
3.2	odd	2		6579.2.a.u.1.9		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.13	✓	21	1.1	even	1	trivial
6579.2.a.u.1.9		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)

\(f(q)\)	\(=\)	\(q+0.715531 q^{2} -2.68508 q^{3} -1.48801 q^{4} +1.60306 q^{5} -1.92126 q^{6} -4.82676 q^{7} -2.49578 q^{8} +4.20967 q^{9} +O(q^{10})\)	\(q+0.715531 q^{2} -2.68508 q^{3} -1.48801 q^{4} +1.60306 q^{5} -1.92126 q^{6} -4.82676 q^{7} -2.49578 q^{8} +4.20967 q^{9} +1.14704 q^{10} -4.41244 q^{11} +3.99544 q^{12} +5.87360 q^{13} -3.45370 q^{14} -4.30436 q^{15} +1.19022 q^{16} -1.00000 q^{17} +3.01215 q^{18} +8.08130 q^{19} -2.38538 q^{20} +12.9603 q^{21} -3.15724 q^{22} +0.285665 q^{23} +6.70139 q^{24} -2.43018 q^{25} +4.20274 q^{26} -3.24807 q^{27} +7.18229 q^{28} -8.29481 q^{29} -3.07991 q^{30} +3.66886 q^{31} +5.84321 q^{32} +11.8478 q^{33} -0.715531 q^{34} -7.73761 q^{35} -6.26406 q^{36} -0.830724 q^{37} +5.78242 q^{38} -15.7711 q^{39} -4.00090 q^{40} +10.2847 q^{41} +9.27347 q^{42} +1.00000 q^{43} +6.56577 q^{44} +6.74838 q^{45} +0.204402 q^{46} +9.56174 q^{47} -3.19583 q^{48} +16.2976 q^{49} -1.73887 q^{50} +2.68508 q^{51} -8.74000 q^{52} -1.12810 q^{53} -2.32410 q^{54} -7.07342 q^{55} +12.0466 q^{56} -21.6990 q^{57} -5.93520 q^{58} -1.65528 q^{59} +6.40495 q^{60} +6.27176 q^{61} +2.62518 q^{62} -20.3191 q^{63} +1.80056 q^{64} +9.41575 q^{65} +8.47745 q^{66} -8.41447 q^{67} +1.48801 q^{68} -0.767035 q^{69} -5.53650 q^{70} -1.05520 q^{71} -10.5064 q^{72} -3.71114 q^{73} -0.594409 q^{74} +6.52525 q^{75} -12.0251 q^{76} +21.2978 q^{77} -11.2847 q^{78} +11.9680 q^{79} +1.90800 q^{80} -3.90768 q^{81} +7.35901 q^{82} -3.72452 q^{83} -19.2851 q^{84} -1.60306 q^{85} +0.715531 q^{86} +22.2723 q^{87} +11.0125 q^{88} +1.57564 q^{89} +4.82868 q^{90} -28.3505 q^{91} -0.425074 q^{92} -9.85119 q^{93} +6.84173 q^{94} +12.9548 q^{95} -15.6895 q^{96} +3.35405 q^{97} +11.6615 q^{98} -18.5749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 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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