LMFDB - Embedded newform 547.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$4.36781699056$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 $ x^18 - 4x^17 - 18x^16 + 84x^15 + 116x^14 - 708x^13 - 282x^12 + 3104x^11 - 137x^10 - 7703x^9 + 2068x^8 + 11068x^7 - 4274x^6 - 9021x^5 + 4048x^4 + 3834x^3 - 1851x^2 - 654*x + 328
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-1.52216$ of defining polynomial
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.52216 q^{2} -2.58636 q^{3} +0.316965 q^{4} +1.24712 q^{5} -3.93684 q^{6} -0.899316 q^{7} -2.56184 q^{8} +3.68924 q^{9} +O(q^{10})$	\(q+1.52216 q^{2} -2.58636 q^{3} +0.316965 q^{4} +1.24712 q^{5} -3.93684 q^{6} -0.899316 q^{7} -2.56184 q^{8} +3.68924 q^{9} +1.89831 q^{10} +3.77827 q^{11} -0.819785 q^{12} -4.29029 q^{13} -1.36890 q^{14} -3.22549 q^{15} -4.53346 q^{16} -7.86362 q^{17} +5.61560 q^{18} -6.61960 q^{19} +0.395293 q^{20} +2.32595 q^{21} +5.75113 q^{22} +3.37854 q^{23} +6.62584 q^{24} -3.44470 q^{25} -6.53050 q^{26} -1.78261 q^{27} -0.285052 q^{28} -2.81309 q^{29} -4.90970 q^{30} -1.72157 q^{31} -1.77696 q^{32} -9.77196 q^{33} -11.9697 q^{34} -1.12155 q^{35} +1.16936 q^{36} -4.86769 q^{37} -10.0761 q^{38} +11.0962 q^{39} -3.19492 q^{40} +5.86463 q^{41} +3.54046 q^{42} +7.30517 q^{43} +1.19758 q^{44} +4.60091 q^{45} +5.14268 q^{46} +2.08319 q^{47} +11.7252 q^{48} -6.19123 q^{49} -5.24338 q^{50} +20.3381 q^{51} -1.35987 q^{52} +3.26386 q^{53} -2.71342 q^{54} +4.71195 q^{55} +2.30391 q^{56} +17.1206 q^{57} -4.28196 q^{58} -6.21926 q^{59} -1.02237 q^{60} +12.5220 q^{61} -2.62050 q^{62} -3.31779 q^{63} +6.36212 q^{64} -5.35050 q^{65} -14.8745 q^{66} -10.3052 q^{67} -2.49250 q^{68} -8.73812 q^{69} -1.70718 q^{70} +16.3692 q^{71} -9.45125 q^{72} -15.5143 q^{73} -7.40939 q^{74} +8.90922 q^{75} -2.09818 q^{76} -3.39786 q^{77} +16.8902 q^{78} +5.15466 q^{79} -5.65376 q^{80} -6.45724 q^{81} +8.92689 q^{82} +6.55843 q^{83} +0.737245 q^{84} -9.80686 q^{85} +11.1196 q^{86} +7.27565 q^{87} -9.67935 q^{88} -4.60031 q^{89} +7.00331 q^{90} +3.85833 q^{91} +1.07088 q^{92} +4.45258 q^{93} +3.17095 q^{94} -8.25541 q^{95} +4.59585 q^{96} +9.16155 q^{97} -9.42403 q^{98} +13.9389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9} - 5 q^{10} + 2 q^{11} - 32 q^{12} - 25 q^{13} - 7 q^{14} + 9 q^{15} + 8 q^{16} - 30 q^{17} - 10 q^{18} + 4 q^{19} - 41 q^{20} - 16 q^{21} - 24 q^{22} - 26 q^{23} - 12 q^{24} + 31 q^{25} - 18 q^{26} - 37 q^{27} - 16 q^{28} - 18 q^{29} + 8 q^{30} - 5 q^{31} - 28 q^{32} - 10 q^{33} + 5 q^{34} - 9 q^{35} + 31 q^{36} - 18 q^{37} - 45 q^{38} + 7 q^{39} + 7 q^{40} - 17 q^{41} + 4 q^{42} + 8 q^{43} + 12 q^{44} - 44 q^{45} + 30 q^{46} - 52 q^{47} - 7 q^{48} + 29 q^{49} + 13 q^{50} + 19 q^{51} - 14 q^{52} - 60 q^{53} + 11 q^{54} + 11 q^{55} + 7 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 86 q^{60} - 26 q^{61} + 4 q^{62} - q^{63} + 44 q^{64} - 6 q^{65} + 18 q^{66} + 12 q^{67} - 61 q^{68} - 38 q^{69} + 35 q^{70} - q^{71} + 28 q^{72} - 2 q^{73} + 16 q^{74} - 17 q^{75} + 66 q^{76} - 73 q^{77} + 115 q^{78} + 18 q^{79} - 32 q^{80} + 18 q^{81} + 44 q^{82} - 43 q^{83} + 41 q^{84} + 51 q^{85} + 4 q^{86} + 3 q^{87} - 17 q^{88} - 28 q^{89} + 58 q^{90} - q^{91} - 68 q^{92} - 60 q^{93} + 78 q^{94} - 18 q^{95} + 29 q^{96} - 34 q^{97} + 34 q^{98} + 15 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9 - 5 * q^10 + 2 * q^11 - 32 * q^12 - 25 * q^13 - 7 * q^14 + 9 * q^15 + 8 * q^16 - 30 * q^17 - 10 * q^18 + 4 * q^19 - 41 * q^20 - 16 * q^21 - 24 * q^22 - 26 * q^23 - 12 * q^24 + 31 * q^25 - 18 * q^26 - 37 * q^27 - 16 * q^28 - 18 * q^29 + 8 * q^30 - 5 * q^31 - 28 * q^32 - 10 * q^33 + 5 * q^34 - 9 * q^35 + 31 * q^36 - 18 * q^37 - 45 * q^38 + 7 * q^39 + 7 * q^40 - 17 * q^41 + 4 * q^42 + 8 * q^43 + 12 * q^44 - 44 * q^45 + 30 * q^46 - 52 * q^47 - 7 * q^48 + 29 * q^49 + 13 * q^50 + 19 * q^51 - 14 * q^52 - 60 * q^53 + 11 * q^54 + 11 * q^55 + 7 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 86 * q^60 - 26 * q^61 + 4 * q^62 - q^63 + 44 * q^64 - 6 * q^65 + 18 * q^66 + 12 * q^67 - 61 * q^68 - 38 * q^69 + 35 * q^70 - q^71 + 28 * q^72 - 2 * q^73 + 16 * q^74 - 17 * q^75 + 66 * q^76 - 73 * q^77 + 115 * q^78 + 18 * q^79 - 32 * q^80 + 18 * q^81 + 44 * q^82 - 43 * q^83 + 41 * q^84 + 51 * q^85 + 4 * q^86 + 3 * q^87 - 17 * q^88 - 28 * q^89 + 58 * q^90 - q^91 - 68 * q^92 - 60 * q^93 + 78 * q^94 - 18 * q^95 + 29 * q^96 - 34 * q^97 + 34 * q^98 + 15 * 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 $

$2$	1.52216	1.07633	0.538164	−	0.842840i	$-0.319118\pi$
$2$	1.52216	1.07633	0.538164	+	0.842840i	$0.319118\pi$
$3$	−2.58636	−1.49323	−0.746617	−	0.665254i	$-0.768323\pi$
$3$	−2.58636	−1.49323	−0.746617	+	0.665254i	$0.768323\pi$
$4$	0.316965	0.158483
$5$	1.24712	0.557728	0.278864	−	0.960331i	$-0.410042\pi$
$5$	1.24712	0.557728	0.278864	+	0.960331i	$0.410042\pi$
$6$	−3.93684	−1.60721
$7$	−0.899316	−0.339909	−0.169955	−	0.985452i	$-0.554362\pi$
$7$	−0.899316	−0.339909	−0.169955	+	0.985452i	$0.554362\pi$
$8$	−2.56184	−0.905749
$9$	3.68924	1.22975
$10$	1.89831	0.600298
$11$	3.77827	1.13919	0.569596	−	0.821925i	$-0.307100\pi$
$11$	3.77827	1.13919	0.569596	+	0.821925i	$0.307100\pi$
$12$	−0.819785	−0.236652
$13$	−4.29029	−1.18991	−0.594957	−	0.803758i	$-0.702831\pi$
$13$	−4.29029	−1.18991	−0.594957	+	0.803758i	$0.702831\pi$
$14$	−1.36890	−0.365854
$15$	−3.22549	−0.832818
$16$	−4.53346	−1.13337
$17$	−7.86362	−1.90721	−0.953604	−	0.301063i	$-0.902658\pi$
$17$	−7.86362	−1.90721	−0.953604	+	0.301063i	$0.902658\pi$
$18$	5.61560	1.32361
$19$	−6.61960	−1.51864	−0.759320	−	0.650718i	$-0.774468\pi$
$19$	−6.61960	−1.51864	−0.759320	+	0.650718i	$0.774468\pi$
$20$	0.395293	0.0883902
$21$	2.32595	0.507564
$22$	5.75113	1.22614
$23$	3.37854	0.704475	0.352238	−	0.935911i	$-0.385421\pi$
$23$	3.37854	0.704475	0.352238	+	0.935911i	$0.385421\pi$
$24$	6.62584	1.35249
$25$	−3.44470	−0.688940
$26$	−6.53050	−1.28074
$27$	−1.78261	−0.343064
$28$	−0.285052	−0.0538697
$29$	−2.81309	−0.522377	−0.261189	−	0.965288i	$-0.584114\pi$
$29$	−2.81309	−0.522377	−0.261189	+	0.965288i	$0.584114\pi$
$30$	−4.90970	−0.896385
$31$	−1.72157	−0.309202	−0.154601	−	0.987977i	$-0.549409\pi$
$31$	−1.72157	−0.309202	−0.154601	+	0.987977i	$0.549409\pi$
$32$	−1.77696	−0.314125
$33$	−9.77196	−1.70108
$34$	−11.9697	−2.05278
$35$	−1.12155	−0.189577
$36$	1.16936	0.194893
$37$	−4.86769	−0.800243	−0.400122	−	0.916462i	$-0.631032\pi$
$37$	−4.86769	−0.800243	−0.400122	+	0.916462i	$0.631032\pi$
$38$	−10.0761	−1.63456
$39$	11.0962	1.77682
$40$	−3.19492	−0.505161
$41$	5.86463	0.915901	0.457951	−	0.888978i	$-0.348584\pi$
$41$	5.86463	0.915901	0.457951	+	0.888978i	$0.348584\pi$
$42$	3.54046	0.546305
$43$	7.30517	1.11403	0.557014	−	0.830503i	$-0.311947\pi$
$43$	7.30517	1.11403	0.557014	+	0.830503i	$0.311947\pi$
$44$	1.19758	0.180542
$45$	4.60091	0.685863
$46$	5.14268	0.758247
$47$	2.08319	0.303865	0.151932	−	0.988391i	$-0.451450\pi$
$47$	2.08319	0.303865	0.151932	+	0.988391i	$0.451450\pi$
$48$	11.7252	1.69238
$49$	−6.19123	−0.884462
$50$	−5.24338	−0.741525
$51$	20.3381	2.84791
$52$	−1.35987	−0.188581
$53$	3.26386	0.448325	0.224163	−	0.974552i	$-0.428035\pi$
$53$	3.26386	0.448325	0.224163	+	0.974552i	$0.428035\pi$
$54$	−2.71342	−0.369250
$55$	4.71195	0.635359
$56$	2.30391	0.307873
$57$	17.1206	2.26768
$58$	−4.28196	−0.562250
$59$	−6.21926	−0.809679	−0.404840	−	0.914388i	$-0.632673\pi$
$59$	−6.21926	−0.809679	−0.404840	+	0.914388i	$0.632673\pi$
$60$	−1.02237	−0.131987
$61$	12.5220	1.60327	0.801636	−	0.597812i	$-0.203963\pi$
$61$	12.5220	1.60327	0.801636	+	0.597812i	$0.203963\pi$
$62$	−2.62050	−0.332803
$63$	−3.31779	−0.418002
$64$	6.36212	0.795264
$65$	−5.35050	−0.663648
$66$	−14.8745	−1.83092
$67$	−10.3052	−1.25898	−0.629491	−	0.777008i	$-0.716737\pi$
$67$	−10.3052	−1.25898	−0.629491	+	0.777008i	$0.716737\pi$
$68$	−2.49250	−0.302259
$69$	−8.73812	−1.05195
$70$	−1.70718	−0.204047
$71$	16.3692	1.94267	0.971334	−	0.237718i	$-0.0763994\pi$
$71$	16.3692	1.94267	0.971334	+	0.237718i	$0.0763994\pi$
$72$	−9.45125	−1.11384
$73$	−15.5143	−1.81581	−0.907907	−	0.419172i	$-0.862320\pi$
$73$	−15.5143	−1.81581	−0.907907	+	0.419172i	$0.862320\pi$
$74$	−7.40939	−0.861324
$75$	8.90922	1.02875
$76$	−2.09818	−0.240678
$77$	−3.39786	−0.387222
$78$	16.8902	1.91244
$79$	5.15466	0.579945	0.289973	−	0.957035i	$-0.406354\pi$
$79$	5.15466	0.579945	0.289973	+	0.957035i	$0.406354\pi$
$80$	−5.65376	−0.632109
$81$	−6.45724	−0.717471
$82$	8.92689	0.985811
$83$	6.55843	0.719881	0.359941	−	0.932975i	$-0.382797\pi$
$83$	6.55843	0.719881	0.359941	+	0.932975i	$0.382797\pi$
$84$	0.737245	0.0804401
$85$	−9.80686	−1.06370
$86$	11.1196	1.19906
$87$	7.27565	0.780031
$88$	−9.67935	−1.03182
$89$	−4.60031	−0.487632	−0.243816	−	0.969822i	$-0.578399\pi$
$89$	−4.60031	−0.487632	−0.243816	+	0.969822i	$0.578399\pi$
$90$	7.00331	0.738214
$91$	3.85833	0.404463
$92$	1.07088	0.111647
$93$	4.45258	0.461711
$94$	3.17095	0.327058
$95$	−8.25541	−0.846987
$96$	4.59585	0.469062
$97$	9.16155	0.930215	0.465107	−	0.885254i	$-0.346016\pi$
$97$	9.16155	0.930215	0.465107	+	0.885254i	$0.346016\pi$
$98$	−9.42403	−0.951971
$99$	13.9389	1.40092
$100$	−1.09185	−0.109185
$101$	−11.0854	−1.10304	−0.551521	−	0.834161i	$-0.685952\pi$
$101$	−11.0854	−1.10304	−0.551521	+	0.834161i	$0.685952\pi$
$102$	30.9578	3.06528
$103$	−4.38943	−0.432503	−0.216252	−	0.976338i	$-0.569383\pi$
$103$	−4.38943	−0.432503	−0.216252	+	0.976338i	$0.569383\pi$
$104$	10.9911	1.07776
$105$	2.90073	0.283082
$106$	4.96811	0.482545
$107$	−19.0618	−1.84277	−0.921385	−	0.388650i	$-0.872941\pi$
$107$	−19.0618	−1.84277	−0.921385	+	0.388650i	$0.872941\pi$
$108$	−0.565027	−0.0543697
$109$	4.54306	0.435147	0.217573	−	0.976044i	$-0.430186\pi$
$109$	4.54306	0.435147	0.217573	+	0.976044i	$0.430186\pi$
$110$	7.17233	0.683855
$111$	12.5896	1.19495
$112$	4.07701	0.385242
$113$	11.6865	1.09937	0.549685	−	0.835372i	$-0.314748\pi$
$113$	11.6865	1.09937	0.549685	+	0.835372i	$0.314748\pi$
$114$	26.0603	2.44077
$115$	4.21344	0.392905
$116$	−0.891651	−0.0827877
$117$	−15.8279	−1.46329
$118$	−9.46670	−0.871481
$119$	7.07188	0.648278
$120$	8.26320	0.754324
$121$	3.27535	0.297759
$122$	19.0604	1.72565
$123$	−15.1680	−1.36765
$124$	−0.545677	−0.0490032
$125$	−10.5315	−0.941968
$126$	−5.05020	−0.449907
$127$	−13.7079	−1.21638	−0.608189	−	0.793792i	$-0.708104\pi$
$127$	−13.7079	−1.21638	−0.608189	+	0.793792i	$0.708104\pi$
$128$	13.2381	1.17009
$129$	−18.8938	−1.66350
$130$	−8.14430	−0.714303
$131$	15.4415	1.34913	0.674563	−	0.738217i	$-0.264332\pi$
$131$	15.4415	1.34913	0.674563	+	0.738217i	$0.264332\pi$
$132$	−3.09737	−0.269592
$133$	5.95311	0.516200
$134$	−15.6862	−1.35508
$135$	−2.22313	−0.191336
$136$	20.1454	1.72745
$137$	0.634397	0.0542002	0.0271001	−	0.999633i	$-0.491373\pi$
$137$	0.634397	0.0542002	0.0271001	+	0.999633i	$0.491373\pi$
$138$	−13.3008	−1.13224
$139$	8.90062	0.754941	0.377470	−	0.926022i	$-0.376794\pi$
$139$	8.90062	0.754941	0.377470	+	0.926022i	$0.376794\pi$
$140$	−0.355493	−0.0300446
$141$	−5.38787	−0.453741
$142$	24.9165	2.09095
$143$	−16.2099	−1.35554
$144$	−16.7250	−1.39375
$145$	−3.50825	−0.291344
$146$	−23.6152	−1.95441
$147$	16.0127	1.32071
$148$	−1.54289	−0.126825
$149$	0.864000	0.0707816	0.0353908	−	0.999374i	$-0.488732\pi$
$149$	0.864000	0.0707816	0.0353908	+	0.999374i	$0.488732\pi$
$150$	13.5612	1.10727
$151$	9.82722	0.799728	0.399864	−	0.916575i	$-0.369057\pi$
$151$	9.82722	0.799728	0.399864	+	0.916575i	$0.369057\pi$
$152$	16.9584	1.37551
$153$	−29.0108	−2.34538
$154$	−5.17208	−0.416778
$155$	−2.14699	−0.172451
$156$	3.51712	0.281595
$157$	−11.4355	−0.912656	−0.456328	−	0.889812i	$-0.650836\pi$
$157$	−11.4355	−0.912656	−0.456328	+	0.889812i	$0.650836\pi$
$158$	7.84621	0.624211
$159$	−8.44150	−0.669454
$160$	−2.21608	−0.175196
$161$	−3.03838	−0.239458
$162$	−9.82894	−0.772234
$163$	−19.1215	−1.49771	−0.748854	−	0.662735i	$-0.769396\pi$
$163$	−19.1215	−1.49771	−0.748854	+	0.662735i	$0.769396\pi$
$164$	1.85888	0.145154
$165$	−12.1868	−0.948739
$166$	9.98297	0.774828
$167$	13.2573	1.02588	0.512942	−	0.858423i	$-0.328556\pi$
$167$	13.2573	1.02588	0.512942	+	0.858423i	$0.328556\pi$
$168$	−5.95872	−0.459725
$169$	5.40662	0.415893
$170$	−14.9276	−1.14489
$171$	−24.4213	−1.86754
$172$	2.31549	0.176554
$173$	−1.24666	−0.0947815	−0.0473907	−	0.998876i	$-0.515091\pi$
$173$	−1.24666	−0.0947815	−0.0473907	+	0.998876i	$0.515091\pi$
$174$	11.0747	0.839570
$175$	3.09787	0.234177
$176$	−17.1287	−1.29112
$177$	16.0852	1.20904
$178$	−7.00240	−0.524852
$179$	0.595954	0.0445437	0.0222718	−	0.999752i	$-0.492910\pi$
$179$	0.595954	0.0445437	0.0222718	+	0.999752i	$0.492910\pi$
$180$	1.45833	0.108697
$181$	−9.48635	−0.705115	−0.352557	−	0.935790i	$-0.614688\pi$
$181$	−9.48635	−0.705115	−0.352557	+	0.935790i	$0.614688\pi$
$182$	5.87298	0.435335
$183$	−32.3862	−2.39406
$184$	−8.65531	−0.638078
$185$	−6.07058	−0.446318
$186$	6.77753	0.496953
$187$	−29.7109	−2.17268
$188$	0.660299	0.0481573
$189$	1.60313	0.116611
$190$	−12.5660	−0.911637
$191$	7.23592	0.523573	0.261786	−	0.965126i	$-0.415688\pi$
$191$	7.23592	0.523573	0.261786	+	0.965126i	$0.415688\pi$
$192$	−16.4547	−1.18752
$193$	4.36945	0.314520	0.157260	−	0.987557i	$-0.449734\pi$
$193$	4.36945	0.314520	0.157260	+	0.987557i	$0.449734\pi$
$194$	13.9453	1.00122
$195$	13.8383	0.990981
$196$	−1.96241	−0.140172
$197$	−19.5262	−1.39118	−0.695592	−	0.718437i	$-0.744858\pi$
$197$	−19.5262	−1.39118	−0.695592	+	0.718437i	$0.744858\pi$
$198$	21.2173	1.50785
$199$	0.0647319	0.00458872	0.00229436	−	0.999997i	$-0.499270\pi$
$199$	0.0647319	0.00458872	0.00229436	+	0.999997i	$0.499270\pi$
$200$	8.82479	0.624007
$201$	26.6529	1.87995
$202$	−16.8738	−1.18723
$203$	2.52985	0.177561
$204$	6.44648	0.451344
$205$	7.31388	0.510824
$206$	−6.68141	−0.465516
$207$	12.4643	0.866325
$208$	19.4499	1.34861
$209$	−25.0106	−1.73002
$210$	4.41537	0.304690
$211$	9.65449	0.664642	0.332321	−	0.943166i	$-0.392168\pi$
$211$	9.65449	0.664642	0.332321	+	0.943166i	$0.392168\pi$
$212$	1.03453	0.0710518
$213$	−42.3366	−2.90086
$214$	−29.0150	−1.98343
$215$	9.11040	0.621324
$216$	4.56678	0.310730
$217$	1.54823	0.105101
$218$	6.91526	0.468361
$219$	40.1256	2.71143
$220$	1.49352	0.100693
$221$	33.7372	2.26941
$222$	19.1633	1.28616
$223$	12.7892	0.856429	0.428215	−	0.903677i	$-0.359143\pi$
$223$	12.7892	0.856429	0.428215	+	0.903677i	$0.359143\pi$
$224$	1.59805	0.106774
$225$	−12.7083	−0.847221
$226$	17.7887	1.18328
$227$	4.94823	0.328426	0.164213	−	0.986425i	$-0.447492\pi$
$227$	4.94823	0.328426	0.164213	+	0.986425i	$0.447492\pi$
$228$	5.42665	0.359389
$229$	−26.7697	−1.76899	−0.884496	−	0.466548i	$-0.845497\pi$
$229$	−26.7697	−1.76899	−0.884496	+	0.466548i	$0.845497\pi$
$230$	6.41352	0.422895
$231$	8.78808	0.578213
$232$	7.20670	0.473143
$233$	−22.2664	−1.45872	−0.729361	−	0.684129i	$-0.760182\pi$
$233$	−22.2664	−1.45872	−0.729361	+	0.684129i	$0.760182\pi$
$234$	−24.0926	−1.57498
$235$	2.59798	0.169474
$236$	−1.97129	−0.128320
$237$	−13.3318	−0.865993
$238$	10.7645	0.697760
$239$	−18.3982	−1.19008	−0.595041	−	0.803695i	$-0.702864\pi$
$239$	−18.3982	−1.19008	−0.595041	+	0.803695i	$0.702864\pi$
$240$	14.6226	0.943887
$241$	21.7977	1.40411	0.702056	−	0.712122i	$-0.252266\pi$
$241$	21.7977	1.40411	0.702056	+	0.712122i	$0.252266\pi$
$242$	4.98560	0.320486
$243$	22.0486	1.41442
$244$	3.96903	0.254091
$245$	−7.72119	−0.493289
$246$	−23.0881	−1.47205
$247$	28.4000	1.80705
$248$	4.41038	0.280060
$249$	−16.9624	−1.07495
$250$	−16.0307	−1.01387
$251$	−22.0114	−1.38935	−0.694674	−	0.719325i	$-0.744451\pi$
$251$	−22.0114	−1.38935	−0.694674	+	0.719325i	$0.744451\pi$
$252$	−1.05162	−0.0662461
$253$	12.7651	0.802533
$254$	−20.8656	−1.30922
$255$	25.3640	1.58836
$256$	7.42619	0.464137
$257$	9.18964	0.573234	0.286617	−	0.958045i	$-0.407469\pi$
$257$	9.18964	0.573234	0.286617	+	0.958045i	$0.407469\pi$
$258$	−28.7593	−1.79048
$259$	4.37759	0.272010
$260$	−1.69592	−0.105177
$261$	−10.3781	−0.642391
$262$	23.5043	1.45210
$263$	−15.6117	−0.962656	−0.481328	−	0.876540i	$-0.659845\pi$
$263$	−15.6117	−0.962656	−0.481328	+	0.876540i	$0.659845\pi$
$264$	25.0342	1.54075
$265$	4.07041	0.250043
$266$	9.06157	0.555600
$267$	11.8980	0.728148
$268$	−3.26639	−0.199527
$269$	−17.8631	−1.08913	−0.544566	−	0.838718i	$-0.683306\pi$
$269$	−17.8631	−1.08913	−0.544566	+	0.838718i	$0.683306\pi$
$270$	−3.38395	−0.205941
$271$	−16.5337	−1.00435	−0.502174	−	0.864767i	$-0.667466\pi$
$271$	−16.5337	−1.00435	−0.502174	+	0.864767i	$0.667466\pi$
$272$	35.6494	2.16156
$273$	−9.97901	−0.603957
$274$	0.965653	0.0583372
$275$	−13.0150	−0.784835
$276$	−2.76968	−0.166715
$277$	28.3672	1.70442	0.852210	−	0.523199i	$-0.175262\pi$
$277$	28.3672	1.70442	0.852210	+	0.523199i	$0.175262\pi$
$278$	13.5482	0.812564
$279$	−6.35126	−0.380240
$280$	2.87324	0.171709
$281$	1.04933	0.0625977	0.0312988	−	0.999510i	$-0.490036\pi$
$281$	1.04933	0.0625977	0.0312988	+	0.999510i	$0.490036\pi$
$282$	−8.20120	−0.488374
$283$	−13.8367	−0.822505	−0.411253	−	0.911521i	$-0.634909\pi$
$283$	−13.8367	−0.822505	−0.411253	+	0.911521i	$0.634909\pi$
$284$	5.18847	0.307879
$285$	21.3514	1.26475
$286$	−24.6740	−1.45901
$287$	−5.27415	−0.311323
$288$	−6.55562	−0.386294
$289$	44.8365	2.63744
$290$	−5.34011	−0.313582
$291$	−23.6950	−1.38903
$292$	−4.91750	−0.287775
$293$	8.25156	0.482061	0.241031	−	0.970517i	$-0.422515\pi$
$293$	8.25156	0.482061	0.241031	+	0.970517i	$0.422515\pi$
$294$	24.3739	1.42152
$295$	−7.75615	−0.451581
$296$	12.4703	0.724819
$297$	−6.73520	−0.390816
$298$	1.31514	0.0761842
$299$	−14.4949	−0.838264
$300$	2.82391	0.163039
$301$	−6.56965	−0.378669
$302$	14.9586	0.860770
$303$	28.6709	1.64710
$304$	30.0097	1.72117
$305$	15.6163	0.894189
$306$	−44.1590	−2.52440
$307$	−5.46378	−0.311835	−0.155917	−	0.987770i	$-0.549833\pi$
$307$	−5.46378	−0.311835	−0.155917	+	0.987770i	$0.549833\pi$
$308$	−1.07700	−0.0613680
$309$	11.3526	0.645829
$310$	−3.26806	−0.185614
$311$	−18.4424	−1.04577	−0.522887	−	0.852402i	$-0.675145\pi$
$311$	−18.4424	−1.04577	−0.522887	+	0.852402i	$0.675145\pi$
$312$	−28.4268	−1.60935
$313$	−21.9260	−1.23933	−0.619664	−	0.784867i	$-0.712731\pi$
$313$	−21.9260	−1.23933	−0.619664	+	0.784867i	$0.712731\pi$
$314$	−17.4067	−0.982317
$315$	−4.13767	−0.233131
$316$	1.63385	0.0919112
$317$	−7.73837	−0.434630	−0.217315	−	0.976102i	$-0.569730\pi$
$317$	−7.73837	−0.434630	−0.217315	+	0.976102i	$0.569730\pi$
$318$	−12.8493	−0.720553
$319$	−10.6286	−0.595088
$320$	7.93430	0.443541
$321$	49.3005	2.75169
$322$	−4.62489	−0.257735
$323$	52.0540	2.89636
$324$	−2.04672	−0.113707
$325$	14.7788	0.819779
$326$	−29.1059	−1.61203
$327$	−11.7500	−0.649775
$328$	−15.0243	−0.829577
$329$	−1.87345	−0.103286
$330$	−18.5502	−1.02115
$331$	−21.2914	−1.17028	−0.585140	−	0.810932i	$-0.698960\pi$
$331$	−21.2914	−1.17028	−0.585140	+	0.810932i	$0.698960\pi$
$332$	2.07879	0.114089
$333$	−17.9581	−0.984096
$334$	20.1798	1.10419
$335$	−12.8518	−0.702169
$336$	−10.5446	−0.575256
$337$	21.3815	1.16472	0.582362	−	0.812930i	$-0.302129\pi$
$337$	21.3815	1.16472	0.582362	+	0.812930i	$0.302129\pi$
$338$	8.22972	0.447638
$339$	−30.2254	−1.64162
$340$	−3.10843	−0.168578
$341$	−6.50455	−0.352241
$342$	−37.1730	−2.01009
$343$	11.8631	0.640546
$344$	−18.7147	−1.00903
$345$	−10.8975	−0.586699
$346$	−1.89761	−0.102016
$347$	−7.25286	−0.389354	−0.194677	−	0.980867i	$-0.562366\pi$
$347$	−7.25286	−0.389354	−0.194677	+	0.980867i	$0.562366\pi$
$348$	2.30613	0.123621
$349$	24.7806	1.32647	0.663236	−	0.748410i	$-0.269182\pi$
$349$	24.7806	1.32647	0.663236	+	0.748410i	$0.269182\pi$
$350$	4.71545	0.252051
$351$	7.64793	0.408217
$352$	−6.71384	−0.357849
$353$	−24.3581	−1.29645	−0.648227	−	0.761447i	$-0.724489\pi$
$353$	−24.3581	−1.29645	−0.648227	+	0.761447i	$0.724489\pi$
$354$	24.4843	1.30132
$355$	20.4143	1.08348
$356$	−1.45814	−0.0772811
$357$	−18.2904	−0.968030
$358$	0.907136	0.0479436
$359$	24.9267	1.31558	0.657790	−	0.753201i	$-0.271491\pi$
$359$	24.9267	1.31558	0.657790	+	0.753201i	$0.271491\pi$
$360$	−11.7868	−0.621220
$361$	24.8191	1.30627
$362$	−14.4397	−0.758935
$363$	−8.47122	−0.444624
$364$	1.22296	0.0641003
$365$	−19.3482	−1.01273
$366$	−49.2970	−2.57679
$367$	−2.52376	−0.131739	−0.0658695	−	0.997828i	$-0.520982\pi$
$367$	−2.52376	−0.131739	−0.0658695	+	0.997828i	$0.520982\pi$
$368$	−15.3165	−0.798428
$369$	21.6360	1.12633
$370$	−9.24038	−0.480384
$371$	−2.93524	−0.152390
$372$	1.41131	0.0731732
$373$	27.2959	1.41333	0.706664	−	0.707549i	$-0.250199\pi$
$373$	27.2959	1.41333	0.706664	+	0.707549i	$0.250199\pi$
$374$	−45.2247	−2.33851
$375$	27.2383	1.40658
$376$	−5.33681	−0.275225
$377$	12.0690	0.621584
$378$	2.44022	0.125511
$379$	−8.84527	−0.454351	−0.227175	−	0.973854i	$-0.572949\pi$
$379$	−8.84527	−0.454351	−0.227175	+	0.973854i	$0.572949\pi$
$380$	−2.61668	−0.134233
$381$	35.4535	1.81634
$382$	11.0142	0.563536
$383$	−9.56433	−0.488715	−0.244357	−	0.969685i	$-0.578577\pi$
$383$	−9.56433	−0.488715	−0.244357	+	0.969685i	$0.578577\pi$
$384$	−34.2383	−1.74722
$385$	−4.23753	−0.215964
$386$	6.65099	0.338527
$387$	26.9505	1.36997
$388$	2.90389	0.147423
$389$	−0.0942924	−0.00478081	−0.00239041	−	0.999997i	$-0.500761\pi$
$389$	−0.0942924	−0.00478081	−0.00239041	+	0.999997i	$0.500761\pi$
$390$	21.0641	1.06662
$391$	−26.5676	−1.34358
$392$	15.8610	0.801100
$393$	−39.9371	−2.01456
$394$	−29.7220	−1.49737
$395$	6.42847	0.323451
$396$	4.41816	0.222021
$397$	−29.4428	−1.47769	−0.738847	−	0.673873i	$-0.764629\pi$
$397$	−29.4428	−1.47769	−0.738847	+	0.673873i	$0.764629\pi$
$398$	0.0985322	0.00493897
$399$	−15.3969	−0.770807
$400$	15.6164	0.780821
$401$	−28.1453	−1.40551	−0.702756	−	0.711431i	$-0.748047\pi$
$401$	−28.1453	−1.40551	−0.702756	+	0.711431i	$0.748047\pi$
$402$	40.5700	2.02345
$403$	7.38602	0.367924
$404$	−3.51370	−0.174813
$405$	−8.05293	−0.400153
$406$	3.85084	0.191114
$407$	−18.3915	−0.911631
$408$	−52.1031	−2.57949
$409$	10.4165	0.515062	0.257531	−	0.966270i	$-0.417091\pi$
$409$	10.4165	0.515062	0.257531	+	0.966270i	$0.417091\pi$
$410$	11.1329	0.549814
$411$	−1.64078	−0.0809336
$412$	−1.39130	−0.0685443
$413$	5.59308	0.275218
$414$	18.9726	0.932450
$415$	8.17913	0.401498
$416$	7.62367	0.373781
$417$	−23.0202	−1.12730
$418$	−38.0702	−1.86207
$419$	−10.1329	−0.495026	−0.247513	−	0.968885i	$-0.579613\pi$
$419$	−10.1329	−0.495026	−0.247513	+	0.968885i	$0.579613\pi$
$420$	0.919431	0.0448637
$421$	−34.9879	−1.70521	−0.852603	−	0.522559i	$-0.824977\pi$
$421$	−34.9879	−1.70521	−0.852603	+	0.522559i	$0.824977\pi$
$422$	14.6957	0.715373
$423$	7.68539	0.373676
$424$	−8.36150	−0.406070
$425$	27.0878	1.31395
$426$	−64.4430	−3.12227
$427$	−11.2612	−0.544967
$428$	−6.04192	−0.292047
$429$	41.9246	2.02414
$430$	13.8675	0.668749
$431$	5.20902	0.250910	0.125455	−	0.992099i	$-0.459961\pi$
$431$	5.20902	0.250910	0.125455	+	0.992099i	$0.459961\pi$
$432$	8.08141	0.388817
$433$	15.2360	0.732196	0.366098	−	0.930576i	$-0.380693\pi$
$433$	15.2360	0.732196	0.366098	+	0.930576i	$0.380693\pi$
$434$	2.35665	0.113123
$435$	9.07358	0.435045
$436$	1.43999	0.0689632
$437$	−22.3646	−1.06984
$438$	61.0774	2.91839
$439$	1.92960	0.0920947	0.0460473	−	0.998939i	$-0.485337\pi$
$439$	1.92960	0.0920947	0.0460473	+	0.998939i	$0.485337\pi$
$440$	−12.0713	−0.575476
$441$	−22.8409	−1.08766
$442$	51.3534	2.44263
$443$	12.2961	0.584204	0.292102	−	0.956387i	$-0.405645\pi$
$443$	12.2961	0.584204	0.292102	+	0.956387i	$0.405645\pi$
$444$	3.99046	0.189379
$445$	−5.73712	−0.271966
$446$	19.4672	0.921799
$447$	−2.23461	−0.105693
$448$	−5.72155	−0.270318
$449$	26.8719	1.26816	0.634082	−	0.773266i	$-0.281378\pi$
$449$	26.8719	1.26816	0.634082	+	0.773266i	$0.281378\pi$
$450$	−19.3441	−0.911888
$451$	22.1582	1.04339
$452$	3.70421	0.174231
$453$	−25.4167	−1.19418
$454$	7.53199	0.353494
$455$	4.81179	0.225580
$456$	−43.8604	−2.05395
$457$	−0.906919	−0.0424239	−0.0212119	−	0.999775i	$-0.506752\pi$
$457$	−0.906919	−0.0424239	−0.0212119	+	0.999775i	$0.506752\pi$
$458$	−40.7477	−1.90402
$459$	14.0178	0.654295
$460$	1.33551	0.0622687
$461$	4.46280	0.207853	0.103927	−	0.994585i	$-0.466859\pi$
$461$	4.46280	0.207853	0.103927	+	0.994585i	$0.466859\pi$
$462$	13.3768	0.622347
$463$	23.4974	1.09202	0.546009	−	0.837779i	$-0.316146\pi$
$463$	23.4974	1.09202	0.546009	+	0.837779i	$0.316146\pi$
$464$	12.7530	0.592045
$465$	5.55289	0.257509
$466$	−33.8930	−1.57006
$467$	8.31369	0.384712	0.192356	−	0.981325i	$-0.438387\pi$
$467$	8.31369	0.384712	0.192356	+	0.981325i	$0.438387\pi$
$468$	−5.01690	−0.231906
$469$	9.26764	0.427940
$470$	3.95454	0.182409
$471$	29.5764	1.36281
$472$	15.9328	0.733366
$473$	27.6009	1.26909
$474$	−20.2931	−0.932093
$475$	22.8025	1.04625
$476$	2.24154	0.102741
$477$	12.0411	0.551326
$478$	−28.0050	−1.28092
$479$	21.3313	0.974651	0.487325	−	0.873220i	$-0.337973\pi$
$479$	21.3313	0.974651	0.487325	+	0.873220i	$0.337973\pi$
$480$	5.73156	0.261609
$481$	20.8838	0.952220
$482$	33.1795	1.51129
$483$	7.85832	0.357566
$484$	1.03817	0.0471896
$485$	11.4255	0.518806
$486$	33.5614	1.52238
$487$	15.0513	0.682038	0.341019	−	0.940056i	$-0.389228\pi$
$487$	15.0513	0.682038	0.341019	+	0.940056i	$0.389228\pi$
$488$	−32.0793	−1.45216
$489$	49.4549	2.23643
$490$	−11.7529	−0.530941
$491$	−43.1675	−1.94812	−0.974060	−	0.226289i	$-0.927341\pi$
$491$	−43.1675	−1.94812	−0.974060	+	0.226289i	$0.927341\pi$
$492$	−4.80774	−0.216750
$493$	22.1211	0.996282
$494$	43.2293	1.94498
$495$	17.3835	0.781330
$496$	7.80465	0.350439
$497$	−14.7211	−0.660331
$498$	−25.8195	−1.15700
$499$	16.8824	0.755759	0.377880	−	0.925855i	$-0.376653\pi$
$499$	16.8824	0.755759	0.377880	+	0.925855i	$0.376653\pi$
$500$	−3.33813	−0.149286
$501$	−34.2882	−1.53188
$502$	−33.5048	−1.49539
$503$	−13.4026	−0.597592	−0.298796	−	0.954317i	$-0.596585\pi$
$503$	−13.4026	−0.597592	−0.298796	+	0.954317i	$0.596585\pi$
$504$	8.49966	0.378605
$505$	−13.8248	−0.615197
$506$	19.4304	0.863789
$507$	−13.9834	−0.621026
$508$	−4.34492	−0.192775
$509$	−17.5986	−0.780045	−0.390022	−	0.920805i	$-0.627533\pi$
$509$	−17.5986	−0.780045	−0.390022	+	0.920805i	$0.627533\pi$
$510$	38.6080	1.70959
$511$	13.9523	0.617212
$512$	−15.1723	−0.670527
$513$	11.8002	0.520991
$514$	13.9881	0.616988
$515$	−5.47413	−0.241219
$516$	−5.98867	−0.263637
$517$	7.87086	0.346160
$518$	6.66338	0.292772
$519$	3.22430	0.141531
$520$	13.7071	0.601098
$521$	−9.08215	−0.397896	−0.198948	−	0.980010i	$-0.563753\pi$
$521$	−9.08215	−0.397896	−0.198948	+	0.980010i	$0.563753\pi$
$522$	−15.7972	−0.691424
$523$	12.7052	0.555561	0.277780	−	0.960645i	$-0.410401\pi$
$523$	12.7052	0.555561	0.277780	+	0.960645i	$0.410401\pi$
$524$	4.89440	0.213813
$525$	−8.01220	−0.349681
$526$	−23.7634	−1.03613
$527$	13.5377	0.589713
$528$	44.3008	1.92795
$529$	−11.5854	−0.503715
$530$	6.19581	0.269129
$531$	−22.9443	−0.995700
$532$	1.88693	0.0818087
$533$	−25.1610	−1.08984
$534$	18.1107	0.783726
$535$	−23.7723	−1.02776
$536$	26.4004	1.14032
$537$	−1.54135	−0.0665141
$538$	−27.1905	−1.17226
$539$	−23.3922	−1.00757
$540$	−0.704654	−0.0303235
$541$	37.0432	1.59261	0.796306	−	0.604894i	$-0.206785\pi$
$541$	37.0432	1.59261	0.796306	+	0.604894i	$0.206785\pi$
$542$	−25.1668	−1.08101
$543$	24.5351	1.05290
$544$	13.9733	0.599102
$545$	5.66573	0.242693
$546$	−15.1896	−0.650056
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	0.201082	0.00858980
$549$	46.1965	1.97162
$550$	−19.8109	−0.844740
$551$	18.6215	0.793303
$552$	22.3857	0.952799
$553$	−4.63567	−0.197129
$554$	43.1794	1.83452
$555$	15.7007	0.666456
$556$	2.82119	0.119645
$557$	−46.3948	−1.96581	−0.982905	−	0.184111i	$-0.941059\pi$
$557$	−46.3948	−1.96581	−0.982905	+	0.184111i	$0.941059\pi$
$558$	−9.66763	−0.409263
$559$	−31.3413	−1.32560
$560$	5.08451	0.214860
$561$	76.8430	3.24431
$562$	1.59724	0.0673757
$563$	−25.5383	−1.07631	−0.538155	−	0.842846i	$-0.680878\pi$
$563$	−25.5383	−1.07631	−0.538155	+	0.842846i	$0.680878\pi$
$564$	−1.70777	−0.0719100
$565$	14.5744	0.613149
$566$	−21.0616	−0.885286
$567$	5.80710	0.243875
$568$	−41.9354	−1.75957
$569$	34.7766	1.45791	0.728956	−	0.684560i	$-0.240006\pi$
$569$	34.7766	1.45791	0.728956	+	0.684560i	$0.240006\pi$
$570$	32.5003	1.36129
$571$	−18.0804	−0.756643	−0.378322	−	0.925674i	$-0.623499\pi$
$571$	−18.0804	−0.756643	−0.378322	+	0.925674i	$0.623499\pi$
$572$	−5.13798	−0.214830
$573$	−18.7147	−0.781816
$574$	−8.02809	−0.335086
$575$	−11.6381	−0.485341
$576$	23.4714	0.977973
$577$	17.7760	0.740025	0.370012	−	0.929027i	$-0.379353\pi$
$577$	17.7760	0.740025	0.370012	+	0.929027i	$0.379353\pi$
$578$	68.2483	2.83876
$579$	−11.3010	−0.469652
$580$	−1.11199	−0.0461730
$581$	−5.89810	−0.244694
$582$	−36.0676	−1.49505
$583$	12.3317	0.510729
$584$	39.7453	1.64467
$585$	−19.7393	−0.816118
$586$	12.5602	0.518856
$587$	−12.4600	−0.514279	−0.257139	−	0.966374i	$-0.582780\pi$
$587$	−12.4600	−0.514279	−0.257139	+	0.966374i	$0.582780\pi$
$588$	5.07548	0.209309
$589$	11.3961	0.469567
$590$	−11.8061	−0.486049
$591$	50.5017	2.07736
$592$	22.0675	0.906968
$593$	−5.62287	−0.230904	−0.115452	−	0.993313i	$-0.536832\pi$
$593$	−5.62287	−0.230904	−0.115452	+	0.993313i	$0.536832\pi$
$594$	−10.2520	−0.420646
$595$	8.81946	0.361563
$596$	0.273858	0.0112177
$597$	−0.167420	−0.00685203
$598$	−22.0636	−0.902248
$599$	19.3513	0.790673	0.395337	−	0.918536i	$-0.370628\pi$
$599$	19.3513	0.790673	0.395337	+	0.918536i	$0.370628\pi$
$600$	−22.8240	−0.931787
$601$	−25.3645	−1.03464	−0.517321	−	0.855792i	$-0.673071\pi$
$601$	−25.3645	−1.03464	−0.517321	+	0.855792i	$0.673071\pi$
$602$	−10.0001	−0.407572
$603$	−38.0184	−1.54823
$604$	3.11489	0.126743
$605$	4.08474	0.166068
$606$	43.6416	1.77282
$607$	13.9505	0.566235	0.283117	−	0.959085i	$-0.408631\pi$
$607$	13.9505	0.566235	0.283117	+	0.959085i	$0.408631\pi$
$608$	11.7628	0.477043
$609$	−6.54310	−0.265140
$610$	23.7705	0.962441
$611$	−8.93750	−0.361573
$612$	−9.19541	−0.371702
$613$	25.5058	1.03017	0.515084	−	0.857139i	$-0.327761\pi$
$613$	25.5058	1.03017	0.515084	+	0.857139i	$0.327761\pi$
$614$	−8.31674	−0.335636
$615$	−18.9163	−0.762779
$616$	8.70479	0.350726
$617$	7.43879	0.299474	0.149737	−	0.988726i	$-0.452157\pi$
$617$	7.43879	0.299474	0.149737	+	0.988726i	$0.452157\pi$
$618$	17.2805	0.695124
$619$	10.5397	0.423626	0.211813	−	0.977310i	$-0.432063\pi$
$619$	10.5397	0.423626	0.211813	+	0.977310i	$0.432063\pi$
$620$	−0.680522	−0.0273304
$621$	−6.02264	−0.241680
$622$	−28.0723	−1.12560
$623$	4.13713	0.165751
$624$	−50.3043	−2.01379
$625$	4.08945	0.163578
$626$	−33.3748	−1.33392
$627$	64.6864	2.58333
$628$	−3.62467	−0.144640
$629$	38.2777	1.52623
$630$	−6.29819	−0.250926
$631$	23.4904	0.935139	0.467570	−	0.883956i	$-0.345130\pi$
$631$	23.4904	0.935139	0.467570	+	0.883956i	$0.345130\pi$
$632$	−13.2055	−0.525285
$633$	−24.9699	−0.992466
$634$	−11.7790	−0.467805
$635$	−17.0953	−0.678408
$636$	−2.67566	−0.106097
$637$	26.5622	1.05243
$638$	−16.1784	−0.640510
$639$	60.3899	2.38899
$640$	16.5094	0.652592
$641$	−12.1894	−0.481454	−0.240727	−	0.970593i	$-0.577386\pi$
$641$	−12.1894	−0.481454	−0.240727	+	0.970593i	$0.577386\pi$
$642$	75.0432	2.96172
$643$	−45.5594	−1.79669	−0.898343	−	0.439295i	$-0.855228\pi$
$643$	−45.5594	−1.79669	−0.898343	+	0.439295i	$0.855228\pi$
$644$	−0.963060	−0.0379499
$645$	−23.5627	−0.927782
$646$	79.2344	3.11744
$647$	−13.8400	−0.544107	−0.272054	−	0.962282i	$-0.587703\pi$
$647$	−13.8400	−0.544107	−0.272054	+	0.962282i	$0.587703\pi$
$648$	16.5424	0.649849
$649$	−23.4981	−0.922380
$650$	22.4956	0.882351
$651$	−4.00428	−0.156940
$652$	−6.06084	−0.237361
$653$	−37.0134	−1.44845	−0.724224	−	0.689565i	$-0.757802\pi$
$653$	−37.0134	−1.44845	−0.724224	+	0.689565i	$0.757802\pi$
$654$	−17.8853	−0.699372
$655$	19.2573	0.752445
$656$	−26.5871	−1.03805
$657$	−57.2360	−2.23299
$658$	−2.85168	−0.111170
$659$	4.58672	0.178673	0.0893366	−	0.996001i	$-0.471525\pi$
$659$	4.58672	0.178673	0.0893366	+	0.996001i	$0.471525\pi$
$660$	−3.86279	−0.150359
$661$	33.9504	1.32052	0.660259	−	0.751038i	$-0.270446\pi$
$661$	33.9504	1.32052	0.660259	+	0.751038i	$0.270446\pi$
$662$	−32.4088	−1.25961
$663$	−87.2565	−3.38876
$664$	−16.8017	−0.652032
$665$	7.42422	0.287899
$666$	−27.3350	−1.05921
$667$	−9.50414	−0.368002
$668$	4.20212	0.162585
$669$	−33.0775	−1.27885
$670$	−19.5625	−0.755764
$671$	47.3114	1.82644
$672$	−4.13312	−0.159438
$673$	−19.4772	−0.750792	−0.375396	−	0.926865i	$-0.622493\pi$
$673$	−19.4772	−0.750792	−0.375396	+	0.926865i	$0.622493\pi$
$674$	32.5460	1.25363
$675$	6.14057	0.236351
$676$	1.71371	0.0659119
$677$	4.07259	0.156523	0.0782613	−	0.996933i	$-0.475063\pi$
$677$	4.07259	0.156523	0.0782613	+	0.996933i	$0.475063\pi$
$678$	−46.0078	−1.76692
$679$	−8.23913	−0.316189
$680$	25.1236	0.963448
$681$	−12.7979	−0.490416
$682$	−9.90095	−0.379127
$683$	−0.965668	−0.0369503	−0.0184751	−	0.999829i	$-0.505881\pi$
$683$	−0.965668	−0.0369503	−0.0184751	+	0.999829i	$0.505881\pi$
$684$	−7.74069	−0.295973
$685$	0.791168	0.0302290
$686$	18.0575	0.689438
$687$	69.2360	2.64152
$688$	−33.1177	−1.26260
$689$	−14.0029	−0.533468
$690$	−16.5876	−0.631481
$691$	−9.03055	−0.343538	−0.171769	−	0.985137i	$-0.554948\pi$
$691$	−9.03055	−0.343538	−0.171769	+	0.985137i	$0.554948\pi$
$692$	−0.395147	−0.0150212
$693$	−12.5355	−0.476185
$694$	−11.0400	−0.419073
$695$	11.1001	0.421051
$696$	−18.6391	−0.706512
$697$	−46.1172	−1.74681
$698$	37.7199	1.42772
$699$	57.5889	2.17821
$700$	0.981918	0.0371130
$701$	9.28360	0.350637	0.175318	−	0.984512i	$-0.443905\pi$
$701$	9.28360	0.350637	0.175318	+	0.984512i	$0.443905\pi$
$702$	11.6414	0.439375
$703$	32.2221	1.21528
$704$	24.0378	0.905959
$705$	−6.71931	−0.253064
$706$	−37.0770	−1.39541
$707$	9.96930	0.374934
$708$	5.09846	0.191612
$709$	−42.7085	−1.60395	−0.801976	−	0.597357i	$-0.796218\pi$
$709$	−42.7085	−1.60395	−0.801976	+	0.597357i	$0.796218\pi$
$710$	31.0738	1.16618
$711$	19.0168	0.713185
$712$	11.7853	0.441672
$713$	−5.81639	−0.217825
$714$	−27.8409	−1.04192
$715$	−20.2156	−0.756022
$716$	0.188897	0.00705940
$717$	47.5844	1.77707
$718$	37.9424	1.41600
$719$	3.48301	0.129895	0.0649473	−	0.997889i	$-0.479312\pi$
$719$	3.48301	0.129895	0.0649473	+	0.997889i	$0.479312\pi$
$720$	−20.8581	−0.777334
$721$	3.94748	0.147012
$722$	37.7786	1.40597
$723$	−56.3766	−2.09667
$724$	−3.00684	−0.111748
$725$	9.69024	0.359887
$726$	−12.8945	−0.478561
$727$	−43.5536	−1.61531	−0.807657	−	0.589652i	$-0.799265\pi$
$727$	−43.5536	−1.61531	−0.807657	+	0.589652i	$0.799265\pi$
$728$	−9.88444	−0.366342
$729$	−37.6537	−1.39458
$730$	−29.4510	−1.09003
$731$	−57.4451	−2.12468
$732$	−10.2653	−0.379417
$733$	35.9769	1.32884	0.664418	−	0.747361i	$-0.268679\pi$
$733$	35.9769	1.32884	0.664418	+	0.747361i	$0.268679\pi$
$734$	−3.84155	−0.141794
$735$	19.9697	0.736595
$736$	−6.00353	−0.221293
$737$	−38.9359	−1.43422
$738$	32.9334	1.21230
$739$	−9.01253	−0.331531	−0.165766	−	0.986165i	$-0.553010\pi$
$739$	−9.01253	−0.331531	−0.165766	+	0.986165i	$0.553010\pi$
$740$	−1.92416	−0.0707336
$741$	−73.4525	−2.69835
$742$	−4.46790	−0.164022
$743$	−27.7846	−1.01932	−0.509658	−	0.860377i	$-0.670228\pi$
$743$	−27.7846	−1.01932	−0.509658	+	0.860377i	$0.670228\pi$
$744$	−11.4068	−0.418194
$745$	1.07751	0.0394769
$746$	41.5487	1.52120
$747$	24.1956	0.885271
$748$	−9.41733	−0.344332
$749$	17.1425	0.626375
$750$	41.4610	1.51394
$751$	−35.3238	−1.28898	−0.644492	−	0.764611i	$-0.722931\pi$
$751$	−35.3238	−1.28898	−0.644492	+	0.764611i	$0.722931\pi$
$752$	−9.44407	−0.344390
$753$	56.9293	2.07462
$754$	18.3709	0.669028
$755$	12.2557	0.446030
$756$	0.508137	0.0184808
$757$	−7.21058	−0.262073	−0.131036	−	0.991378i	$-0.541830\pi$
$757$	−7.21058	−0.262073	−0.131036	+	0.991378i	$0.541830\pi$
$758$	−13.4639	−0.489031
$759$	−33.0150	−1.19837
$760$	21.1491	0.767158
$761$	15.5783	0.564712	0.282356	−	0.959310i	$-0.408884\pi$
$761$	15.5783	0.564712	0.282356	+	0.959310i	$0.408884\pi$
$762$	53.9658	1.95497
$763$	−4.08565	−0.147910
$764$	2.29353	0.0829772
$765$	−36.1798	−1.30808
$766$	−14.5584	−0.526017
$767$	26.6825	0.963448
$768$	−19.2068	−0.693065
$769$	24.1433	0.870629	0.435314	−	0.900279i	$-0.356637\pi$
$769$	24.1433	0.870629	0.435314	+	0.900279i	$0.356637\pi$
$770$	−6.45019	−0.232449
$771$	−23.7677	−0.855972
$772$	1.38496	0.0498460
$773$	−23.9888	−0.862818	−0.431409	−	0.902156i	$-0.641983\pi$
$773$	−23.9888	−0.862818	−0.431409	+	0.902156i	$0.641983\pi$
$774$	41.0229	1.47454
$775$	5.93028	0.213022
$776$	−23.4705	−0.842541
$777$	−11.3220	−0.406175
$778$	−0.143528	−0.00514572
$779$	−38.8215	−1.39092
$780$	4.38626	0.157053
$781$	61.8474	2.21307
$782$	−40.4401	−1.44613
$783$	5.01465	0.179209
$784$	28.0677	1.00242
$785$	−14.2615	−0.509013
$786$	−60.7906	−2.16833
$787$	−5.35961	−0.191050	−0.0955248	−	0.995427i	$-0.530453\pi$
$787$	−5.35961	−0.191050	−0.0955248	+	0.995427i	$0.530453\pi$
$788$	−6.18913	−0.220479
$789$	40.3773	1.43747
$790$	9.78515	0.348140
$791$	−10.5098	−0.373686
$792$	−35.7094	−1.26888
$793$	−53.7229	−1.90776
$794$	−44.8167	−1.59048
$795$	−10.5275	−0.373373
$796$	0.0205178	0.000727233 0
$797$	−19.3882	−0.686766	−0.343383	−	0.939195i	$-0.611573\pi$
$797$	−19.3882	−0.686766	−0.343383	+	0.939195i	$0.611573\pi$
$798$	−23.4364	−0.829641
$799$	−16.3814	−0.579533
$800$	6.12109	0.216413
$801$	−16.9716	−0.599663
$802$	−42.8417	−1.51279
$803$	−58.6173	−2.06856
$804$	8.44806	0.297940
$805$	−3.78921	−0.133552
$806$	11.2427	0.396007
$807$	46.2003	1.62633
$808$	28.3992	0.999079
$809$	−35.6076	−1.25190	−0.625948	−	0.779865i	$-0.715288\pi$
$809$	−35.6076	−1.25190	−0.625948	+	0.779865i	$0.715288\pi$
$810$	−12.2578	−0.430696
$811$	7.02922	0.246829	0.123415	−	0.992355i	$-0.460615\pi$
$811$	7.02922	0.246829	0.123415	+	0.992355i	$0.460615\pi$
$812$	0.801876	0.0281403
$813$	42.7619	1.49973
$814$	−27.9947	−0.981214
$815$	−23.8467	−0.835314
$816$	−92.2021	−3.22772
$817$	−48.3573	−1.69181
$818$	15.8555	0.554376
$819$	14.2343	0.497386
$820$	2.31825	0.0809567
$821$	−11.9108	−0.415691	−0.207845	−	0.978162i	$-0.566645\pi$
$821$	−11.9108	−0.415691	−0.207845	+	0.978162i	$0.566645\pi$
$822$	−2.49752	−0.0871111
$823$	38.1506	1.32985	0.664924	−	0.746911i	$-0.268464\pi$
$823$	38.1506	1.32985	0.664924	+	0.746911i	$0.268464\pi$
$824$	11.2450	0.391740
$825$	33.6615	1.17194
$826$	8.51355	0.296224
$827$	22.1837	0.771404	0.385702	−	0.922623i	$-0.373959\pi$
$827$	22.1837	0.771404	0.385702	+	0.922623i	$0.373959\pi$
$828$	3.95074	0.137298
$829$	−26.7091	−0.927646	−0.463823	−	0.885928i	$-0.653523\pi$
$829$	−26.7091	−0.927646	−0.463823	+	0.885928i	$0.653523\pi$
$830$	12.4499	0.432143
$831$	−73.3677	−2.54510
$832$	−27.2953	−0.946296
$833$	48.6855	1.68685
$834$	−35.0403	−1.21335
$835$	16.5335	0.572164
$836$	−7.92751	−0.274179
$837$	3.06889	0.106076
$838$	−15.4239	−0.532810
$839$	−24.3713	−0.841392	−0.420696	−	0.907202i	$-0.638214\pi$
$839$	−24.3713	−0.841392	−0.420696	+	0.907202i	$0.638214\pi$
$840$	−7.43122	−0.256402
$841$	−21.0865	−0.727122
$842$	−53.2571	−1.83536
$843$	−2.71394	−0.0934730
$844$	3.06014	0.105334
$845$	6.74268	0.231955
$846$	11.6984	0.402198
$847$	−2.94557	−0.101211
$848$	−14.7966	−0.508117
$849$	35.7866	1.22819
$850$	41.2319	1.41424
$851$	−16.4457	−0.563751
$852$	−13.4192	−0.459736
$853$	−21.5357	−0.737369	−0.368685	−	0.929555i	$-0.620192\pi$
$853$	−21.5357	−0.737369	−0.368685	+	0.929555i	$0.620192\pi$
$854$	−17.1413	−0.586564
$855$	−30.4562	−1.04158
$856$	48.8333	1.66909
$857$	10.1092	0.345325	0.172663	−	0.984981i	$-0.444763\pi$
$857$	10.1092	0.345325	0.172663	+	0.984981i	$0.444763\pi$
$858$	63.8158	2.17864
$859$	29.3539	1.00154	0.500771	−	0.865580i	$-0.333050\pi$
$859$	29.3539	1.00154	0.500771	+	0.865580i	$0.333050\pi$
$860$	2.88768	0.0984691
$861$	13.6408	0.464878
$862$	7.92895	0.270061
$863$	9.84744	0.335211	0.167605	−	0.985854i	$-0.446397\pi$
$863$	9.84744	0.335211	0.167605	+	0.985854i	$0.446397\pi$
$864$	3.16763	0.107765
$865$	−1.55473	−0.0528622
$866$	23.1916	0.788083
$867$	−115.963	−3.93832
$868$	0.490735	0.0166566
$869$	19.4757	0.660669
$870$	13.8114	0.468251
$871$	44.2124	1.49808
$872$	−11.6386	−0.394134
$873$	33.7991	1.14393
$874$	−34.0425	−1.15150
$875$	9.47117	0.320184
$876$	12.7184	0.429715
$877$	−32.9822	−1.11373	−0.556864	−	0.830603i	$-0.687996\pi$
$877$	−32.9822	−1.11373	−0.556864	+	0.830603i	$0.687996\pi$
$878$	2.93715	0.0991241
$879$	−21.3415	−0.719830
$880$	−21.3614	−0.720094
$881$	34.3375	1.15686	0.578429	−	0.815733i	$-0.303666\pi$
$881$	34.3375	1.15686	0.578429	+	0.815733i	$0.303666\pi$
$882$	−34.7675	−1.17068
$883$	12.5688	0.422974	0.211487	−	0.977381i	$-0.432169\pi$
$883$	12.5688	0.422974	0.211487	+	0.977381i	$0.432169\pi$
$884$	10.6935	0.359662
$885$	20.0602	0.674315
$886$	18.7166	0.628795
$887$	34.7329	1.16622	0.583109	−	0.812394i	$-0.301836\pi$
$887$	34.7329	1.16622	0.583109	+	0.812394i	$0.301836\pi$
$888$	−32.2525	−1.08232
$889$	12.3277	0.413458
$890$	−8.73281	−0.292724
$891$	−24.3972	−0.817337
$892$	4.05374	0.135729
$893$	−13.7899	−0.461461
$894$	−3.40143	−0.113761
$895$	0.743224	0.0248432
$896$	−11.9052	−0.397725
$897$	37.4891	1.25172
$898$	40.9033	1.36496
$899$	4.84292	0.161520
$900$	−4.02809	−0.134270
$901$	−25.6657	−0.855050
$902$	33.7282	1.12303
$903$	16.9915	0.565441
$904$	−29.9389	−0.995754
$905$	−11.8306	−0.393262
$906$	−38.6882	−1.28533
$907$	18.5744	0.616753	0.308376	−	0.951264i	$-0.400214\pi$
$907$	18.5744	0.616753	0.308376	+	0.951264i	$0.400214\pi$
$908$	1.56842	0.0520498
$909$	−40.8968	−1.35646
$910$	7.32430	0.242798
$911$	−4.83712	−0.160261	−0.0801304	−	0.996784i	$-0.525534\pi$
$911$	−4.83712	−0.160261	−0.0801304	+	0.996784i	$0.525534\pi$
$912$	−77.6158	−2.57012
$913$	24.7795	0.820083
$914$	−1.38047	−0.0456620
$915$	−40.3894	−1.33523
$916$	−8.48506	−0.280354
$917$	−13.8867	−0.458580
$918$	21.3373	0.704236
$919$	57.3488	1.89176	0.945881	−	0.324513i	$-0.105200\pi$
$919$	57.3488	1.89176	0.945881	+	0.324513i	$0.105200\pi$
$920$	−10.7942	−0.355874
$921$	14.1313	0.465642
$922$	6.79309	0.223718
$923$	−70.2287	−2.31161
$924$	2.78551	0.0916367
$925$	16.7677	0.551319
$926$	35.7668	1.17537
$927$	−16.1937	−0.531869
$928$	4.99874	0.164092
$929$	46.6546	1.53069	0.765344	−	0.643622i	$-0.222569\pi$
$929$	46.6546	1.53069	0.765344	+	0.643622i	$0.222569\pi$
$930$	8.45238	0.277164
$931$	40.9835	1.34318
$932$	−7.05768	−0.231182
$933$	47.6987	1.56159
$934$	12.6547	0.414076
$935$	−37.0530	−1.21176
$936$	40.5487	1.32537
$937$	20.5835	0.672433	0.336217	−	0.941785i	$-0.390853\pi$
$937$	20.5835	0.672433	0.336217	+	0.941785i	$0.390853\pi$
$938$	14.1068	0.460604
$939$	56.7083	1.85061
$940$	0.823470	0.0268586
$941$	26.4195	0.861251	0.430625	−	0.902531i	$-0.358293\pi$
$941$	26.4195	0.861251	0.430625	+	0.902531i	$0.358293\pi$
$942$	45.0199	1.46683
$943$	19.8139	0.645230
$944$	28.1948	0.917663
$945$	1.99929	0.0650370
$946$	42.0130	1.36596
$947$	30.9279	1.00502	0.502510	−	0.864571i	$-0.332410\pi$
$947$	30.9279	1.00502	0.502510	+	0.864571i	$0.332410\pi$
$948$	−4.22572	−0.137245
$949$	66.5610	2.16066
$950$	34.7090	1.12611
$951$	20.0142	0.649004
$952$	−18.1171	−0.587177
$953$	31.9144	1.03381	0.516905	−	0.856043i	$-0.327084\pi$
$953$	31.9144	1.03381	0.516905	+	0.856043i	$0.327084\pi$
$954$	18.3285	0.593408
$955$	9.02404	0.292011
$956$	−5.83160	−0.188607
$957$	27.4894	0.888606
$958$	32.4696	1.04904
$959$	−0.570523	−0.0184232
$960$	−20.5209	−0.662310
$961$	−28.0362	−0.904394
$962$	31.7885	1.02490
$963$	−70.3234	−2.26614
$964$	6.90911	0.222527
$965$	5.44922	0.175416
$966$	11.9616	0.384859
$967$	25.3550	0.815363	0.407682	−	0.913124i	$-0.366337\pi$
$967$	25.3550	0.815363	0.407682	+	0.913124i	$0.366337\pi$
$968$	−8.39094	−0.269695
$969$	−134.630	−4.32495
$970$	17.3915	0.558406
$971$	4.38779	0.140811	0.0704054	−	0.997518i	$-0.477571\pi$
$971$	4.38779	0.140811	0.0704054	+	0.997518i	$0.477571\pi$
$972$	6.98863	0.224160
$973$	−8.00447	−0.256611
$974$	22.9104	0.734097
$975$	−38.2232	−1.22412
$976$	−56.7678	−1.81709
$977$	3.45588	0.110563	0.0552817	−	0.998471i	$-0.482394\pi$
$977$	3.45588	0.110563	0.0552817	+	0.998471i	$0.482394\pi$
$978$	75.2782	2.40713
$979$	−17.3812	−0.555506
$980$	−2.44735	−0.0781777
$981$	16.7604	0.535120
$982$	−65.7077	−2.09682
$983$	56.4424	1.80023	0.900117	−	0.435648i	$-0.143481\pi$
$983$	56.4424	1.80023	0.900117	+	0.435648i	$0.143481\pi$
$984$	38.8581	1.23875
$985$	−24.3515	−0.775902
$986$	33.6717	1.07233
$987$	4.84540	0.154231
$988$	9.00182	0.286386
$989$	24.6808	0.784805
$990$	26.4604	0.840968
$991$	−55.5706	−1.76526	−0.882629	−	0.470069i	$-0.844229\pi$
$991$	−55.5706	−1.76526	−0.882629	+	0.470069i	$0.844229\pi$
$992$	3.05915	0.0971281
$993$	55.0671	1.74750
$994$	−22.4078	−0.710733
$995$	0.0807282	0.00255926
$996$	−5.37650	−0.170361
$997$	−20.1408	−0.637866	−0.318933	−	0.947777i	$-0.603324\pi$
$997$	−20.1408	−0.637866	−0.318933	+	0.947777i	$0.603324\pi$
$998$	25.6977	0.813445
$999$	8.67721	0.274535

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.15	✓	18
3.2	odd	2		4923.2.a.l.1.4		18
4.3	odd	2		8752.2.a.s.1.14		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.15	✓	18	1.1	even	1	trivial
4923.2.a.l.1.4		18	3.2	odd	2
8752.2.a.s.1.14		18	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q+1.52216 q^{2} -2.58636 q^{3} +0.316965 q^{4} +1.24712 q^{5} -3.93684 q^{6} -0.899316 q^{7} -2.56184 q^{8} +3.68924 q^{9} +O(q^{10})\)	\(q+1.52216 q^{2} -2.58636 q^{3} +0.316965 q^{4} +1.24712 q^{5} -3.93684 q^{6} -0.899316 q^{7} -2.56184 q^{8} +3.68924 q^{9} +1.89831 q^{10} +3.77827 q^{11} -0.819785 q^{12} -4.29029 q^{13} -1.36890 q^{14} -3.22549 q^{15} -4.53346 q^{16} -7.86362 q^{17} +5.61560 q^{18} -6.61960 q^{19} +0.395293 q^{20} +2.32595 q^{21} +5.75113 q^{22} +3.37854 q^{23} +6.62584 q^{24} -3.44470 q^{25} -6.53050 q^{26} -1.78261 q^{27} -0.285052 q^{28} -2.81309 q^{29} -4.90970 q^{30} -1.72157 q^{31} -1.77696 q^{32} -9.77196 q^{33} -11.9697 q^{34} -1.12155 q^{35} +1.16936 q^{36} -4.86769 q^{37} -10.0761 q^{38} +11.0962 q^{39} -3.19492 q^{40} +5.86463 q^{41} +3.54046 q^{42} +7.30517 q^{43} +1.19758 q^{44} +4.60091 q^{45} +5.14268 q^{46} +2.08319 q^{47} +11.7252 q^{48} -6.19123 q^{49} -5.24338 q^{50} +20.3381 q^{51} -1.35987 q^{52} +3.26386 q^{53} -2.71342 q^{54} +4.71195 q^{55} +2.30391 q^{56} +17.1206 q^{57} -4.28196 q^{58} -6.21926 q^{59} -1.02237 q^{60} +12.5220 q^{61} -2.62050 q^{62} -3.31779 q^{63} +6.36212 q^{64} -5.35050 q^{65} -14.8745 q^{66} -10.3052 q^{67} -2.49250 q^{68} -8.73812 q^{69} -1.70718 q^{70} +16.3692 q^{71} -9.45125 q^{72} -15.5143 q^{73} -7.40939 q^{74} +8.90922 q^{75} -2.09818 q^{76} -3.39786 q^{77} +16.8902 q^{78} +5.15466 q^{79} -5.65376 q^{80} -6.45724 q^{81} +8.92689 q^{82} +6.55843 q^{83} +0.737245 q^{84} -9.80686 q^{85} +11.1196 q^{86} +7.27565 q^{87} -9.67935 q^{88} -4.60031 q^{89} +7.00331 q^{90} +3.85833 q^{91} +1.07088 q^{92} +4.45258 q^{93} +3.17095 q^{94} -8.25541 q^{95} +4.59585 q^{96} +9.16155 q^{97} -9.42403 q^{98} +13.9389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9} - 5 q^{10} + 2 q^{11} - 32 q^{12} - 25 q^{13} - 7 q^{14} + 9 q^{15} + 8 q^{16} - 30 q^{17} - 10 q^{18} + 4 q^{19} - 41 q^{20} - 16 q^{21} - 24 q^{22} - 26 q^{23} - 12 q^{24} + 31 q^{25} - 18 q^{26} - 37 q^{27} - 16 q^{28} - 18 q^{29} + 8 q^{30} - 5 q^{31} - 28 q^{32} - 10 q^{33} + 5 q^{34} - 9 q^{35} + 31 q^{36} - 18 q^{37} - 45 q^{38} + 7 q^{39} + 7 q^{40} - 17 q^{41} + 4 q^{42} + 8 q^{43} + 12 q^{44} - 44 q^{45} + 30 q^{46} - 52 q^{47} - 7 q^{48} + 29 q^{49} + 13 q^{50} + 19 q^{51} - 14 q^{52} - 60 q^{53} + 11 q^{54} + 11 q^{55} + 7 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 86 q^{60} - 26 q^{61} + 4 q^{62} - q^{63} + 44 q^{64} - 6 q^{65} + 18 q^{66} + 12 q^{67} - 61 q^{68} - 38 q^{69} + 35 q^{70} - q^{71} + 28 q^{72} - 2 q^{73} + 16 q^{74} - 17 q^{75} + 66 q^{76} - 73 q^{77} + 115 q^{78} + 18 q^{79} - 32 q^{80} + 18 q^{81} + 44 q^{82} - 43 q^{83} + 41 q^{84} + 51 q^{85} + 4 q^{86} + 3 q^{87} - 17 q^{88} - 28 q^{89} + 58 q^{90} - q^{91} - 68 q^{92} - 60 q^{93} + 78 q^{94} - 18 q^{95} + 29 q^{96} - 34 q^{97} + 34 q^{98} + 15 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9 - 5 * q^10 + 2 * q^11 - 32 * q^12 - 25 * q^13 - 7 * q^14 + 9 * q^15 + 8 * q^16 - 30 * q^17 - 10 * q^18 + 4 * q^19 - 41 * q^20 - 16 * q^21 - 24 * q^22 - 26 * q^23 - 12 * q^24 + 31 * q^25 - 18 * q^26 - 37 * q^27 - 16 * q^28 - 18 * q^29 + 8 * q^30 - 5 * q^31 - 28 * q^32 - 10 * q^33 + 5 * q^34 - 9 * q^35 + 31 * q^36 - 18 * q^37 - 45 * q^38 + 7 * q^39 + 7 * q^40 - 17 * q^41 + 4 * q^42 + 8 * q^43 + 12 * q^44 - 44 * q^45 + 30 * q^46 - 52 * q^47 - 7 * q^48 + 29 * q^49 + 13 * q^50 + 19 * q^51 - 14 * q^52 - 60 * q^53 + 11 * q^54 + 11 * q^55 + 7 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 86 * q^60 - 26 * q^61 + 4 * q^62 - q^63 + 44 * q^64 - 6 * q^65 + 18 * q^66 + 12 * q^67 - 61 * q^68 - 38 * q^69 + 35 * q^70 - q^71 + 28 * q^72 - 2 * q^73 + 16 * q^74 - 17 * q^75 + 66 * q^76 - 73 * q^77 + 115 * q^78 + 18 * q^79 - 32 * q^80 + 18 * q^81 + 44 * q^82 - 43 * q^83 + 41 * q^84 + 51 * q^85 + 4 * q^86 + 3 * q^87 - 17 * q^88 - 28 * q^89 + 58 * q^90 - q^91 - 68 * q^92 - 60 * q^93 + 78 * q^94 - 18 * q^95 + 29 * q^96 - 34 * q^97 + 34 * q^98 + 15 * q^99

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