LMFDB - Embedded newform 547.2.a.b.1.18

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			1.18
Root			$-2.50138$ 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)

$f(q)$	$=$	$q+2.50138 q^{2} -3.08733 q^{3} +4.25691 q^{4} -3.57921 q^{5} -7.72259 q^{6} +1.44216 q^{7} +5.64540 q^{8} +6.53160 q^{9} +O(q^{10})$	\(q+2.50138 q^{2} -3.08733 q^{3} +4.25691 q^{4} -3.57921 q^{5} -7.72259 q^{6} +1.44216 q^{7} +5.64540 q^{8} +6.53160 q^{9} -8.95298 q^{10} -5.34528 q^{11} -13.1425 q^{12} -5.39279 q^{13} +3.60739 q^{14} +11.0502 q^{15} +5.60749 q^{16} -5.31413 q^{17} +16.3380 q^{18} +2.56610 q^{19} -15.2364 q^{20} -4.45242 q^{21} -13.3706 q^{22} -6.63074 q^{23} -17.4292 q^{24} +7.81075 q^{25} -13.4894 q^{26} -10.9032 q^{27} +6.13915 q^{28} +5.19544 q^{29} +27.6408 q^{30} +4.77081 q^{31} +2.73566 q^{32} +16.5026 q^{33} -13.2927 q^{34} -5.16179 q^{35} +27.8045 q^{36} -3.44033 q^{37} +6.41880 q^{38} +16.6493 q^{39} -20.2061 q^{40} +8.38934 q^{41} -11.1372 q^{42} +5.49566 q^{43} -22.7544 q^{44} -23.3780 q^{45} -16.5860 q^{46} -0.427891 q^{47} -17.3122 q^{48} -4.92018 q^{49} +19.5377 q^{50} +16.4065 q^{51} -22.9566 q^{52} -3.73075 q^{53} -27.2731 q^{54} +19.1319 q^{55} +8.14157 q^{56} -7.92240 q^{57} +12.9958 q^{58} +2.87686 q^{59} +47.0398 q^{60} -3.71286 q^{61} +11.9336 q^{62} +9.41961 q^{63} -4.37204 q^{64} +19.3019 q^{65} +41.2794 q^{66} +6.57367 q^{67} -22.6218 q^{68} +20.4713 q^{69} -12.9116 q^{70} -11.1354 q^{71} +36.8735 q^{72} -0.468824 q^{73} -8.60558 q^{74} -24.1144 q^{75} +10.9237 q^{76} -7.70874 q^{77} +41.6463 q^{78} +5.80618 q^{79} -20.0704 q^{80} +14.0670 q^{81} +20.9849 q^{82} +0.338379 q^{83} -18.9536 q^{84} +19.0204 q^{85} +13.7467 q^{86} -16.0400 q^{87} -30.1763 q^{88} +1.79829 q^{89} -58.4773 q^{90} -7.77726 q^{91} -28.2265 q^{92} -14.7291 q^{93} -1.07032 q^{94} -9.18462 q^{95} -8.44588 q^{96} -11.5278 q^{97} -12.3072 q^{98} -34.9132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.50138	1.76874	0.884372	−	0.466782i	$-0.154587\pi$
$2$	2.50138	1.76874	0.884372	+	0.466782i	$0.154587\pi$
$3$	−3.08733	−1.78247	−0.891235	−	0.453541i	$-0.850160\pi$
$3$	−3.08733	−1.78247	−0.891235	+	0.453541i	$0.850160\pi$
$4$	4.25691	2.12846
$5$	−3.57921	−1.60067	−0.800336	−	0.599552i	$-0.795346\pi$
$5$	−3.57921	−1.60067	−0.800336	+	0.599552i	$0.795346\pi$
$6$	−7.72259	−3.15273
$7$	1.44216	0.545085	0.272542	−	0.962144i	$-0.412135\pi$
$7$	1.44216	0.545085	0.272542	+	0.962144i	$0.412135\pi$
$8$	5.64540	1.99595
$9$	6.53160	2.17720
$10$	−8.95298	−2.83118
$11$	−5.34528	−1.61166	−0.805831	−	0.592145i	$-0.798281\pi$
$11$	−5.34528	−1.61166	−0.805831	+	0.592145i	$0.798281\pi$
$12$	−13.1425	−3.79391
$13$	−5.39279	−1.49569	−0.747845	−	0.663873i	$-0.768911\pi$
$13$	−5.39279	−1.49569	−0.747845	+	0.663873i	$0.768911\pi$
$14$	3.60739	0.964116
$15$	11.0502	2.85315
$16$	5.60749	1.40187
$17$	−5.31413	−1.28887	−0.644433	−	0.764661i	$-0.722907\pi$
$17$	−5.31413	−1.28887	−0.644433	+	0.764661i	$0.722907\pi$
$18$	16.3380	3.85091
$19$	2.56610	0.588704	0.294352	−	0.955697i	$-0.404896\pi$
$19$	2.56610	0.588704	0.294352	+	0.955697i	$0.404896\pi$
$20$	−15.2364	−3.40696
$21$	−4.45242	−0.971598
$22$	−13.3706	−2.85062
$23$	−6.63074	−1.38260	−0.691302	−	0.722566i	$-0.742963\pi$
$23$	−6.63074	−1.38260	−0.691302	+	0.722566i	$0.742963\pi$
$24$	−17.4292	−3.55772
$25$	7.81075	1.56215
$26$	−13.4894	−2.64549
$27$	−10.9032	−2.09832
$28$	6.13915	1.16019
$29$	5.19544	0.964768	0.482384	−	0.875960i	$-0.339771\pi$
$29$	5.19544	0.964768	0.482384	+	0.875960i	$0.339771\pi$
$30$	27.6408	5.04649
$31$	4.77081	0.856864	0.428432	−	0.903574i	$-0.359066\pi$
$31$	4.77081	0.856864	0.428432	+	0.903574i	$0.359066\pi$
$32$	2.73566	0.483601
$33$	16.5026	2.87274
$34$	−13.2927	−2.27967
$35$	−5.16179	−0.872502
$36$	27.8045	4.63408
$37$	−3.44033	−0.565586	−0.282793	−	0.959181i	$-0.591261\pi$
$37$	−3.44033	−0.565586	−0.282793	+	0.959181i	$0.591261\pi$
$38$	6.41880	1.04127
$39$	16.6493	2.66602
$40$	−20.2061	−3.19486
$41$	8.38934	1.31019	0.655097	−	0.755545i	$-0.272628\pi$
$41$	8.38934	1.31019	0.655097	+	0.755545i	$0.272628\pi$
$42$	−11.1372	−1.71851
$43$	5.49566	0.838080	0.419040	−	0.907968i	$-0.362367\pi$
$43$	5.49566	0.838080	0.419040	+	0.907968i	$0.362367\pi$
$44$	−22.7544	−3.43035
$45$	−23.3780	−3.48498
$46$	−16.5860	−2.44547
$47$	−0.427891	−0.0624143	−0.0312072	−	0.999513i	$-0.509935\pi$
$47$	−0.427891	−0.0624143	−0.0312072	+	0.999513i	$0.509935\pi$
$48$	−17.3122	−2.49879
$49$	−4.92018	−0.702882
$50$	19.5377	2.76304
$51$	16.4065	2.29737
$52$	−22.9566	−3.18351
$53$	−3.73075	−0.512458	−0.256229	−	0.966616i	$-0.582480\pi$
$53$	−3.73075	−0.512458	−0.256229	+	0.966616i	$0.582480\pi$
$54$	−27.2731	−3.71140
$55$	19.1319	2.57974
$56$	8.14157	1.08796
$57$	−7.92240	−1.04935
$58$	12.9958	1.70643
$59$	2.87686	0.374535	0.187268	−	0.982309i	$-0.440037\pi$
$59$	2.87686	0.374535	0.187268	+	0.982309i	$0.440037\pi$
$60$	47.0398	6.07281
$61$	−3.71286	−0.475383	−0.237691	−	0.971341i	$-0.576391\pi$
$61$	−3.71286	−0.475383	−0.237691	+	0.971341i	$0.576391\pi$
$62$	11.9336	1.51557
$63$	9.41961	1.18676
$64$	−4.37204	−0.546505
$65$	19.3019	2.39411
$66$	41.2794	5.08114
$67$	6.57367	0.803101	0.401551	−	0.915837i	$-0.368471\pi$
$67$	6.57367	0.803101	0.401551	+	0.915837i	$0.368471\pi$
$68$	−22.6218	−2.74330
$69$	20.4713	2.46445
$70$	−12.9116	−1.54323
$71$	−11.1354	−1.32153	−0.660764	−	0.750594i	$-0.729768\pi$
$71$	−11.1354	−1.32153	−0.660764	+	0.750594i	$0.729768\pi$
$72$	36.8735	4.34559
$73$	−0.468824	−0.0548717	−0.0274359	−	0.999624i	$-0.508734\pi$
$73$	−0.468824	−0.0548717	−0.0274359	+	0.999624i	$0.508734\pi$
$74$	−8.60558	−1.00038
$75$	−24.1144	−2.78449
$76$	10.9237	1.25303
$77$	−7.70874	−0.878493
$78$	41.6463	4.71551
$79$	5.80618	0.653246	0.326623	−	0.945155i	$-0.394089\pi$
$79$	5.80618	0.653246	0.326623	+	0.945155i	$0.394089\pi$
$80$	−20.0704	−2.24394
$81$	14.0670	1.56300
$82$	20.9849	2.31740
$83$	0.338379	0.0371420	0.0185710	−	0.999828i	$-0.494088\pi$
$83$	0.338379	0.0371420	0.0185710	+	0.999828i	$0.494088\pi$
$84$	−18.9536	−2.06800
$85$	19.0204	2.06305
$86$	13.7467	1.48235
$87$	−16.0400	−1.71967
$88$	−30.1763	−3.21680
$89$	1.79829	0.190618	0.0953091	−	0.995448i	$-0.469616\pi$
$89$	1.79829	0.190618	0.0953091	+	0.995448i	$0.469616\pi$
$90$	−58.4773	−6.16405
$91$	−7.77726	−0.815278
$92$	−28.2265	−2.94281
$93$	−14.7291	−1.52733
$94$	−1.07032	−0.110395
$95$	−9.18462	−0.942322
$96$	−8.44588	−0.862004
$97$	−11.5278	−1.17047	−0.585234	−	0.810864i	$-0.698997\pi$
$97$	−11.5278	−1.17047	−0.585234	+	0.810864i	$0.698997\pi$
$98$	−12.3072	−1.24322
$99$	−34.9132	−3.50891
$100$	33.2497	3.32497
$101$	−6.15589	−0.612534	−0.306267	−	0.951946i	$-0.599080\pi$
$101$	−6.15589	−0.612534	−0.306267	+	0.951946i	$0.599080\pi$
$102$	41.0389	4.06345
$103$	16.0271	1.57920	0.789601	−	0.613621i	$-0.210288\pi$
$103$	16.0271	1.57920	0.789601	+	0.613621i	$0.210288\pi$
$104$	−30.4445	−2.98533
$105$	15.9362	1.55521
$106$	−9.33203	−0.906407
$107$	0.286864	0.0277322	0.0138661	−	0.999904i	$-0.495586\pi$
$107$	0.286864	0.0277322	0.0138661	+	0.999904i	$0.495586\pi$
$108$	−46.4140	−4.46619
$109$	−15.7934	−1.51273	−0.756366	−	0.654149i	$-0.773027\pi$
$109$	−15.7934	−1.51273	−0.756366	+	0.654149i	$0.773027\pi$
$110$	47.8562	4.56291
$111$	10.6214	1.00814
$112$	8.08689	0.764139
$113$	−12.9488	−1.21812	−0.609058	−	0.793126i	$-0.708452\pi$
$113$	−12.9488	−1.21812	−0.609058	+	0.793126i	$0.708452\pi$
$114$	−19.8169	−1.85603
$115$	23.7328	2.21310
$116$	22.1165	2.05347
$117$	−35.2235	−3.25642
$118$	7.19613	0.662458
$119$	−7.66382	−0.702541
$120$	62.3829	5.69475
$121$	17.5720	1.59746
$122$	−9.28727	−0.840830
$123$	−25.9006	−2.33538
$124$	20.3089	1.82380
$125$	−10.0603	−0.899818
$126$	23.5620	2.09907
$127$	−2.62312	−0.232764	−0.116382	−	0.993205i	$-0.537130\pi$
$127$	−2.62312	−0.232764	−0.116382	+	0.993205i	$0.537130\pi$
$128$	−16.4075	−1.45023
$129$	−16.9669	−1.49385
$130$	48.2815	4.23457
$131$	1.96563	0.171738	0.0858691	−	0.996306i	$-0.472633\pi$
$131$	1.96563	0.171738	0.0858691	+	0.996306i	$0.472633\pi$
$132$	70.2503	6.11450
$133$	3.70073	0.320894
$134$	16.4433	1.42048
$135$	39.0249	3.35873
$136$	−30.0004	−2.57251
$137$	−13.8493	−1.18323	−0.591614	−	0.806221i	$-0.701509\pi$
$137$	−13.8493	−1.18323	−0.591614	+	0.806221i	$0.701509\pi$
$138$	51.2065	4.35899
$139$	3.30984	0.280737	0.140368	−	0.990099i	$-0.455171\pi$
$139$	3.30984	0.280737	0.140368	+	0.990099i	$0.455171\pi$
$140$	−21.9733	−1.85708
$141$	1.32104	0.111252
$142$	−27.8539	−2.33744
$143$	28.8260	2.41055
$144$	36.6259	3.05216
$145$	−18.5956	−1.54428
$146$	−1.17271	−0.0970541
$147$	15.1902	1.25287
$148$	−14.6452	−1.20383
$149$	1.24371	0.101889	0.0509443	−	0.998701i	$-0.483777\pi$
$149$	1.24371	0.101889	0.0509443	+	0.998701i	$0.483777\pi$
$150$	−60.3192	−4.92505
$151$	−19.7224	−1.60499	−0.802494	−	0.596660i	$-0.796494\pi$
$151$	−19.7224	−1.60499	−0.802494	+	0.596660i	$0.796494\pi$
$152$	14.4867	1.17502
$153$	−34.7098	−2.80612
$154$	−19.2825	−1.55383
$155$	−17.0758	−1.37156
$156$	70.8747	5.67452
$157$	−11.3800	−0.908221	−0.454110	−	0.890945i	$-0.650043\pi$
$157$	−11.3800	−0.908221	−0.454110	+	0.890945i	$0.650043\pi$
$158$	14.5235	1.15543
$159$	11.5181	0.913441
$160$	−9.79150	−0.774086
$161$	−9.56258	−0.753637
$162$	35.1870	2.76455
$163$	2.36146	0.184964	0.0924819	−	0.995714i	$-0.470520\pi$
$163$	2.36146	0.184964	0.0924819	+	0.995714i	$0.470520\pi$
$164$	35.7127	2.78869
$165$	−59.0664	−4.59832
$166$	0.846416	0.0656946
$167$	3.39282	0.262544	0.131272	−	0.991346i	$-0.458094\pi$
$167$	3.39282	0.262544	0.131272	+	0.991346i	$0.458094\pi$
$168$	−25.1357	−1.93926
$169$	16.0822	1.23709
$170$	47.5773	3.64901
$171$	16.7607	1.28173
$172$	23.3945	1.78382
$173$	−24.1775	−1.83819	−0.919093	−	0.394042i	$-0.871077\pi$
$173$	−24.1775	−1.83819	−0.919093	+	0.394042i	$0.871077\pi$
$174$	−40.1222	−3.04166
$175$	11.2643	0.851505
$176$	−29.9736	−2.25934
$177$	−8.88182	−0.667598
$178$	4.49821	0.337155
$179$	−9.73639	−0.727732	−0.363866	−	0.931451i	$-0.618543\pi$
$179$	−9.73639	−0.727732	−0.363866	+	0.931451i	$0.618543\pi$
$180$	−99.5180	−7.41764
$181$	−8.08741	−0.601133	−0.300566	−	0.953761i	$-0.597176\pi$
$181$	−8.08741	−0.601133	−0.300566	+	0.953761i	$0.597176\pi$
$182$	−19.4539	−1.44202
$183$	11.4628	0.847355
$184$	−37.4332	−2.75961
$185$	12.3137	0.905318
$186$	−36.8430	−2.70146
$187$	28.4055	2.07722
$188$	−1.82150	−0.132846
$189$	−15.7242	−1.14377
$190$	−22.9742	−1.66673
$191$	23.4764	1.69869	0.849347	−	0.527835i	$-0.176996\pi$
$191$	23.4764	1.69869	0.849347	+	0.527835i	$0.176996\pi$
$192$	13.4979	0.974129
$193$	0.846561	0.0609368	0.0304684	−	0.999536i	$-0.490300\pi$
$193$	0.846561	0.0609368	0.0304684	+	0.999536i	$0.490300\pi$
$194$	−28.8354	−2.07026
$195$	−59.5914	−4.26743
$196$	−20.9448	−1.49605
$197$	24.5035	1.74580	0.872900	−	0.487900i	$-0.162237\pi$
$197$	24.5035	1.74580	0.872900	+	0.487900i	$0.162237\pi$
$198$	−87.3314	−6.20637
$199$	−6.60963	−0.468544	−0.234272	−	0.972171i	$-0.575271\pi$
$199$	−6.60963	−0.468544	−0.234272	+	0.972171i	$0.575271\pi$
$200$	44.0949	3.11798
$201$	−20.2951	−1.43150
$202$	−15.3982	−1.08342
$203$	7.49265	0.525881
$204$	69.8409	4.88984
$205$	−30.0272	−2.09719
$206$	40.0900	2.79320
$207$	−43.3093	−3.01021
$208$	−30.2400	−2.09677
$209$	−13.7165	−0.948792
$210$	39.8624	2.75077
$211$	1.49983	0.103253	0.0516264	−	0.998666i	$-0.483559\pi$
$211$	1.49983	0.103253	0.0516264	+	0.998666i	$0.483559\pi$
$212$	−15.8815	−1.09074
$213$	34.3786	2.35558
$214$	0.717556	0.0490511
$215$	−19.6701	−1.34149
$216$	−61.5531	−4.18816
$217$	6.88027	0.467063
$218$	−39.5053	−2.67564
$219$	1.44741	0.0978072
$220$	81.4428	5.49087
$221$	28.6580	1.92774
$222$	26.5682	1.78314
$223$	22.0562	1.47699	0.738497	−	0.674257i	$-0.235536\pi$
$223$	22.0562	1.47699	0.738497	+	0.674257i	$0.235536\pi$
$224$	3.94526	0.263604
$225$	51.0167	3.40111
$226$	−32.3898	−2.15454
$227$	9.69637	0.643571	0.321785	−	0.946813i	$-0.395717\pi$
$227$	9.69637	0.643571	0.321785	+	0.946813i	$0.395717\pi$
$228$	−33.7250	−2.23349
$229$	12.6579	0.836460	0.418230	−	0.908341i	$-0.362651\pi$
$229$	12.6579	0.836460	0.418230	+	0.908341i	$0.362651\pi$
$230$	59.3648	3.91440
$231$	23.7994	1.56589
$232$	29.3303	1.92563
$233$	12.4477	0.815473	0.407736	−	0.913100i	$-0.366318\pi$
$233$	12.4477	0.815473	0.407736	+	0.913100i	$0.366318\pi$
$234$	−88.1075	−5.75977
$235$	1.53151	0.0999049
$236$	12.2466	0.797183
$237$	−17.9256	−1.16439
$238$	−19.1701	−1.24262
$239$	1.95816	0.126663	0.0633314	−	0.997993i	$-0.479827\pi$
$239$	1.95816	0.126663	0.0633314	+	0.997993i	$0.479827\pi$
$240$	61.9639	3.99975
$241$	−17.4587	−1.12462	−0.562308	−	0.826928i	$-0.690086\pi$
$241$	−17.4587	−1.12462	−0.562308	+	0.826928i	$0.690086\pi$
$242$	43.9543	2.82549
$243$	−10.7199	−0.687679
$244$	−15.8053	−1.01183
$245$	17.6104	1.12508
$246$	−64.7874	−4.13069
$247$	−13.8384	−0.880519
$248$	26.9332	1.71026
$249$	−1.04469	−0.0662044
$250$	−25.1646	−1.59155
$251$	3.61597	0.228238	0.114119	−	0.993467i	$-0.463595\pi$
$251$	3.61597	0.228238	0.114119	+	0.993467i	$0.463595\pi$
$252$	40.0985	2.52597
$253$	35.4432	2.22829
$254$	−6.56142	−0.411700
$255$	−58.7222	−3.67733
$256$	−32.2973	−2.01858
$257$	−10.0934	−0.629606	−0.314803	−	0.949157i	$-0.601939\pi$
$257$	−10.0934	−0.629606	−0.314803	+	0.949157i	$0.601939\pi$
$258$	−42.4407	−2.64224
$259$	−4.96150	−0.308293
$260$	82.1666	5.09576
$261$	33.9345	2.10049
$262$	4.91680	0.303761
$263$	−5.71252	−0.352249	−0.176124	−	0.984368i	$-0.556356\pi$
$263$	−5.71252	−0.352249	−0.176124	+	0.984368i	$0.556356\pi$
$264$	93.1641	5.73385
$265$	13.3531	0.820277
$266$	9.25693	0.567579
$267$	−5.55191	−0.339771
$268$	27.9835	1.70937
$269$	−11.2319	−0.684820	−0.342410	−	0.939551i	$-0.611243\pi$
$269$	−11.2319	−0.684820	−0.342410	+	0.939551i	$0.611243\pi$
$270$	97.6162	5.94073
$271$	−25.7123	−1.56191	−0.780954	−	0.624588i	$-0.785267\pi$
$271$	−25.7123	−1.56191	−0.780954	+	0.624588i	$0.785267\pi$
$272$	−29.7989	−1.80682
$273$	24.0110	1.45321
$274$	−34.6425	−2.09283
$275$	−41.7507	−2.51766
$276$	87.1444	5.24548
$277$	10.7925	0.648461	0.324231	−	0.945978i	$-0.394895\pi$
$277$	10.7925	0.648461	0.324231	+	0.945978i	$0.394895\pi$
$278$	8.27916	0.496551
$279$	31.1611	1.86556
$280$	−29.1404	−1.74147
$281$	0.316572	0.0188851	0.00944256	−	0.999955i	$-0.496994\pi$
$281$	0.316572	0.0188851	0.00944256	+	0.999955i	$0.496994\pi$
$282$	3.30443	0.196776
$283$	−30.9827	−1.84173	−0.920864	−	0.389883i	$-0.872515\pi$
$283$	−30.9827	−1.84173	−0.920864	+	0.389883i	$0.872515\pi$
$284$	−47.4024	−2.81281
$285$	28.3559	1.67966
$286$	72.1047	4.26364
$287$	12.0988	0.714167
$288$	17.8682	1.05290
$289$	11.2400	0.661175
$290$	−46.5146	−2.73143
$291$	35.5900	2.08632
$292$	−1.99574	−0.116792
$293$	−21.7659	−1.27158	−0.635789	−	0.771863i	$-0.719325\pi$
$293$	−21.7659	−1.27158	−0.635789	+	0.771863i	$0.719325\pi$
$294$	37.9965	2.21600
$295$	−10.2969	−0.599508
$296$	−19.4220	−1.12888
$297$	58.2807	3.38179
$298$	3.11099	0.180215
$299$	35.7582	2.06795
$300$	−102.653	−5.92666
$301$	7.92561	0.456825
$302$	−49.3333	−2.83881
$303$	19.0053	1.09182
$304$	14.3894	0.825287
$305$	13.2891	0.760932
$306$	−86.8224	−4.96331
$307$	3.11297	0.177667	0.0888334	−	0.996046i	$-0.471686\pi$
$307$	3.11297	0.177667	0.0888334	+	0.996046i	$0.471686\pi$
$308$	−32.8155	−1.86983
$309$	−49.4811	−2.81488
$310$	−42.7130	−2.42593
$311$	27.3164	1.54897	0.774485	−	0.632592i	$-0.218009\pi$
$311$	27.3164	1.54897	0.774485	+	0.632592i	$0.218009\pi$
$312$	93.9921	5.32125
$313$	13.8638	0.783630	0.391815	−	0.920044i	$-0.371847\pi$
$313$	13.8638	0.783630	0.391815	+	0.920044i	$0.371847\pi$
$314$	−28.4657	−1.60641
$315$	−33.7148	−1.89961
$316$	24.7164	1.39041
$317$	−14.2600	−0.800923	−0.400461	−	0.916314i	$-0.631150\pi$
$317$	−14.2600	−0.800923	−0.400461	+	0.916314i	$0.631150\pi$
$318$	28.8111	1.61564
$319$	−27.7711	−1.55488
$320$	15.6485	0.874776
$321$	−0.885643	−0.0494318
$322$	−23.9197	−1.33299
$323$	−13.6366	−0.758761
$324$	59.8821	3.32678
$325$	−42.1217	−2.33649
$326$	5.90692	0.327154
$327$	48.7594	2.69640
$328$	47.3612	2.61508
$329$	−0.617087	−0.0340211
$330$	−147.748	−8.13324
$331$	−14.0211	−0.770667	−0.385334	−	0.922777i	$-0.625914\pi$
$331$	−14.0211	−0.770667	−0.385334	+	0.922777i	$0.625914\pi$
$332$	1.44045	0.0790550
$333$	−22.4709	−1.23140
$334$	8.48675	0.464374
$335$	−23.5285	−1.28550
$336$	−24.9669	−1.36206
$337$	−2.77663	−0.151253	−0.0756263	−	0.997136i	$-0.524096\pi$
$337$	−2.77663	−0.151253	−0.0756263	+	0.997136i	$0.524096\pi$
$338$	40.2276	2.18809
$339$	39.9771	2.17126
$340$	80.9682	4.39112
$341$	−25.5013	−1.38098
$342$	41.9250	2.26705
$343$	−17.1908	−0.928216
$344$	31.0252	1.67277
$345$	−73.2710	−3.94478
$346$	−60.4773	−3.25128
$347$	34.2051	1.83623	0.918114	−	0.396317i	$-0.129712\pi$
$347$	34.2051	1.83623	0.918114	+	0.396317i	$0.129712\pi$
$348$	−68.2810	−3.66025
$349$	31.8576	1.70530	0.852649	−	0.522485i	$-0.174995\pi$
$349$	31.8576	1.70530	0.852649	+	0.522485i	$0.174995\pi$
$350$	28.1764	1.50609
$351$	58.7987	3.13844
$352$	−14.6229	−0.779402
$353$	19.7596	1.05170	0.525849	−	0.850578i	$-0.323748\pi$
$353$	19.7596	1.05170	0.525849	+	0.850578i	$0.323748\pi$
$354$	−22.2168	−1.18081
$355$	39.8559	2.11533
$356$	7.65516	0.405723
$357$	23.6607	1.25226
$358$	−24.3544	−1.28717
$359$	6.12948	0.323501	0.161751	−	0.986832i	$-0.448286\pi$
$359$	6.12948	0.323501	0.161751	+	0.986832i	$0.448286\pi$
$360$	−131.978	−6.95586
$361$	−12.4151	−0.653428
$362$	−20.2297	−1.06325
$363$	−54.2506	−2.84742
$364$	−33.1071	−1.73528
$365$	1.67802	0.0878316
$366$	28.6729	1.49876
$367$	−13.4451	−0.701828	−0.350914	−	0.936408i	$-0.614129\pi$
$367$	−13.4451	−0.701828	−0.350914	+	0.936408i	$0.614129\pi$
$368$	−37.1818	−1.93823
$369$	54.7958	2.85256
$370$	30.8012	1.60128
$371$	−5.38034	−0.279333
$372$	−62.7004	−3.25086
$373$	12.5335	0.648963	0.324481	−	0.945892i	$-0.394810\pi$
$373$	12.5335	0.648963	0.324481	+	0.945892i	$0.394810\pi$
$374$	71.0531	3.67407
$375$	31.0594	1.60390
$376$	−2.41562	−0.124576
$377$	−28.0179	−1.44299
$378$	−39.3322	−2.02303
$379$	−8.91515	−0.457940	−0.228970	−	0.973433i	$-0.573536\pi$
$379$	−8.91515	−0.457940	−0.228970	+	0.973433i	$0.573536\pi$
$380$	−39.0981	−2.00569
$381$	8.09843	0.414895
$382$	58.7235	3.00455
$383$	−8.41053	−0.429758	−0.214879	−	0.976641i	$-0.568936\pi$
$383$	−8.41053	−0.429758	−0.214879	+	0.976641i	$0.568936\pi$
$384$	50.6553	2.58499
$385$	27.5912	1.40618
$386$	2.11757	0.107782
$387$	35.8954	1.82467
$388$	−49.0727	−2.49129
$389$	−6.85721	−0.347674	−0.173837	−	0.984774i	$-0.555617\pi$
$389$	−6.85721	−0.347674	−0.173837	+	0.984774i	$0.555617\pi$
$390$	−149.061	−7.54799
$391$	35.2366	1.78199
$392$	−27.7764	−1.40292
$393$	−6.06855	−0.306118
$394$	61.2925	3.08787
$395$	−20.7815	−1.04563
$396$	−148.623	−7.46857
$397$	−7.82424	−0.392688	−0.196344	−	0.980535i	$-0.562907\pi$
$397$	−7.82424	−0.392688	−0.196344	+	0.980535i	$0.562907\pi$
$398$	−16.5332	−0.828735
$399$	−11.4254	−0.571983
$400$	43.7987	2.18993
$401$	−16.2178	−0.809879	−0.404939	−	0.914344i	$-0.632707\pi$
$401$	−16.2178	−0.809879	−0.404939	+	0.914344i	$0.632707\pi$
$402$	−50.7657	−2.53197
$403$	−25.7280	−1.28160
$404$	−26.2051	−1.30375
$405$	−50.3488	−2.50185
$406$	18.7420	0.930148
$407$	18.3895	0.911535
$408$	92.6212	4.58543
$409$	10.0577	0.497322	0.248661	−	0.968591i	$-0.420009\pi$
$409$	10.0577	0.497322	0.248661	+	0.968591i	$0.420009\pi$
$410$	−75.1095	−3.70939
$411$	42.7574	2.10907
$412$	68.2262	3.36126
$413$	4.14889	0.204154
$414$	−108.333	−5.32429
$415$	−1.21113	−0.0594521
$416$	−14.7528	−0.723317
$417$	−10.2186	−0.500405
$418$	−34.3103	−1.67817
$419$	29.3701	1.43482	0.717412	−	0.696649i	$-0.245327\pi$
$419$	29.3701	1.43482	0.717412	+	0.696649i	$0.245327\pi$
$420$	67.8388	3.31020
$421$	−28.4591	−1.38701	−0.693507	−	0.720450i	$-0.743935\pi$
$421$	−28.4591	−1.38701	−0.693507	+	0.720450i	$0.743935\pi$
$422$	3.75166	0.182628
$423$	−2.79481	−0.135889
$424$	−21.0616	−1.02284
$425$	−41.5074	−2.01340
$426$	85.9941	4.16643
$427$	−5.35453	−0.259124
$428$	1.22115	0.0590267
$429$	−88.9952	−4.29673
$430$	−49.2025	−2.37275
$431$	−16.8736	−0.812772	−0.406386	−	0.913701i	$-0.633211\pi$
$431$	−16.8736	−0.812772	−0.406386	+	0.913701i	$0.633211\pi$
$432$	−61.1396	−2.94158
$433$	−17.5129	−0.841615	−0.420807	−	0.907150i	$-0.638253\pi$
$433$	−17.5129	−0.841615	−0.420807	+	0.907150i	$0.638253\pi$
$434$	17.2102	0.826116
$435$	57.4106	2.75263
$436$	−67.2310	−3.21978
$437$	−17.0151	−0.813945
$438$	3.62054	0.172996
$439$	−1.19663	−0.0571120	−0.0285560	−	0.999592i	$-0.509091\pi$
$439$	−1.19663	−0.0571120	−0.0285560	+	0.999592i	$0.509091\pi$
$440$	108.007	5.14904
$441$	−32.1366	−1.53032
$442$	71.6846	3.40969
$443$	−1.77986	−0.0845637	−0.0422819	−	0.999106i	$-0.513463\pi$
$443$	−1.77986	−0.0845637	−0.0422819	+	0.999106i	$0.513463\pi$
$444$	45.2145	2.14578
$445$	−6.43646	−0.305117
$446$	55.1710	2.61242
$447$	−3.83974	−0.181614
$448$	−6.30518	−0.297892
$449$	35.7981	1.68942	0.844708	−	0.535227i	$-0.179774\pi$
$449$	35.7981	1.68942	0.844708	+	0.535227i	$0.179774\pi$
$450$	127.612	6.01570
$451$	−44.8433	−2.11159
$452$	−55.1217	−2.59271
$453$	60.8896	2.86084
$454$	24.2543	1.13831
$455$	27.8364	1.30499
$456$	−44.7251	−2.09445
$457$	−9.01813	−0.421850	−0.210925	−	0.977502i	$-0.567648\pi$
$457$	−9.01813	−0.421850	−0.210925	+	0.977502i	$0.567648\pi$
$458$	31.6623	1.47948
$459$	57.9411	2.70446
$460$	101.029	4.71048
$461$	−30.8599	−1.43729	−0.718646	−	0.695377i	$-0.755238\pi$
$461$	−30.8599	−1.43729	−0.718646	+	0.695377i	$0.755238\pi$
$462$	59.5315	2.76965
$463$	−1.05816	−0.0491767	−0.0245884	−	0.999698i	$-0.507828\pi$
$463$	−1.05816	−0.0491767	−0.0245884	+	0.999698i	$0.507828\pi$
$464$	29.1333	1.35248
$465$	52.7185	2.44476
$466$	31.1363	1.44236
$467$	−34.1893	−1.58209	−0.791047	−	0.611755i	$-0.790464\pi$
$467$	−34.1893	−1.58209	−0.791047	+	0.611755i	$0.790464\pi$
$468$	−149.944	−6.93114
$469$	9.48027	0.437758
$470$	3.83090	0.176706
$471$	35.1337	1.61888
$472$	16.2410	0.747555
$473$	−29.3758	−1.35070
$474$	−44.8388	−2.05951
$475$	20.0432	0.919644
$476$	−32.6242	−1.49533
$477$	−24.3678	−1.11572
$478$	4.89811	0.224034
$479$	−30.8709	−1.41053	−0.705265	−	0.708944i	$-0.749172\pi$
$479$	−30.8709	−1.41053	−0.705265	+	0.708944i	$0.749172\pi$
$480$	30.2296	1.37979
$481$	18.5530	0.845942
$482$	−43.6710	−1.98916
$483$	29.5228	1.34334
$484$	74.8026	3.40012
$485$	41.2603	1.87354
$486$	−26.8144	−1.21633
$487$	−23.2537	−1.05373	−0.526863	−	0.849950i	$-0.676632\pi$
$487$	−23.2537	−1.05373	−0.526863	+	0.849950i	$0.676632\pi$
$488$	−20.9606	−0.948841
$489$	−7.29061	−0.329693
$490$	44.0502	1.98999
$491$	−9.10242	−0.410786	−0.205393	−	0.978680i	$-0.565847\pi$
$491$	−9.10242	−0.410786	−0.205393	+	0.978680i	$0.565847\pi$
$492$	−110.257	−4.97076
$493$	−27.6092	−1.24346
$494$	−34.6152	−1.55741
$495$	124.962	5.61662
$496$	26.7523	1.20121
$497$	−16.0590	−0.720345
$498$	−2.61316	−0.117099
$499$	25.0594	1.12181	0.560907	−	0.827879i	$-0.310452\pi$
$499$	25.0594	1.12181	0.560907	+	0.827879i	$0.310452\pi$
$500$	−42.8257	−1.91522
$501$	−10.4748	−0.467978
$502$	9.04493	0.403695
$503$	−7.25454	−0.323464	−0.161732	−	0.986835i	$-0.551708\pi$
$503$	−7.25454	−0.323464	−0.161732	+	0.986835i	$0.551708\pi$
$504$	53.1775	2.36871
$505$	22.0332	0.980467
$506$	88.6569	3.94128
$507$	−49.6509	−2.20507
$508$	−11.1664	−0.495428
$509$	1.63509	0.0724740	0.0362370	−	0.999343i	$-0.488463\pi$
$509$	1.63509	0.0724740	0.0362370	+	0.999343i	$0.488463\pi$
$510$	−146.887	−6.50425
$511$	−0.676119	−0.0299098
$512$	−47.9729	−2.12012
$513$	−27.9788	−1.23529
$514$	−25.2473	−1.11361
$515$	−57.3645	−2.52778
$516$	−72.2266	−3.17960
$517$	2.28720	0.100591
$518$	−12.4106	−0.545291
$519$	74.6441	3.27651
$520$	108.967	4.77853
$521$	32.4953	1.42365	0.711823	−	0.702359i	$-0.247870\pi$
$521$	32.4953	1.42365	0.711823	+	0.702359i	$0.247870\pi$
$522$	84.8832	3.71524
$523$	42.1414	1.84272	0.921358	−	0.388714i	$-0.127081\pi$
$523$	42.1414	1.84272	0.921358	+	0.388714i	$0.127081\pi$
$524$	8.36753	0.365537
$525$	−34.7767	−1.51778
$526$	−14.2892	−0.623038
$527$	−25.3527	−1.10438
$528$	92.5383	4.02721
$529$	20.9667	0.911595
$530$	33.4013	1.45086
$531$	18.7905	0.815439
$532$	15.7537	0.683008
$533$	−45.2419	−1.95964
$534$	−13.8874	−0.600969
$535$	−1.02675	−0.0443901
$536$	37.1110	1.60295
$537$	30.0595	1.29716
$538$	−28.0952	−1.21127
$539$	26.2997	1.13281
$540$	166.126	7.14891
$541$	43.3831	1.86519	0.932593	−	0.360930i	$-0.117541\pi$
$541$	43.3831	1.86519	0.932593	+	0.360930i	$0.117541\pi$
$542$	−64.3162	−2.76262
$543$	24.9685	1.07150
$544$	−14.5377	−0.623297
$545$	56.5278	2.42139
$546$	60.0606	2.57036
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−58.9554	−2.51845
$549$	−24.2509	−1.03500
$550$	−104.434	−4.45310
$551$	13.3320	0.567963
$552$	115.569	4.91893
$553$	8.37344	0.356075
$554$	26.9963	1.14696
$555$	−38.0163	−1.61370
$556$	14.0897	0.597536
$557$	−26.5599	−1.12538	−0.562689	−	0.826669i	$-0.690233\pi$
$557$	−26.5599	−1.12538	−0.562689	+	0.826669i	$0.690233\pi$
$558$	77.9457	3.29971
$559$	−29.6369	−1.25351
$560$	−28.9447	−1.22314
$561$	−87.6972	−3.70258
$562$	0.791868	0.0334029
$563$	−41.6328	−1.75461	−0.877306	−	0.479931i	$-0.840662\pi$
$563$	−41.6328	−1.75461	−0.877306	+	0.479931i	$0.840662\pi$
$564$	5.62356	0.236794
$565$	46.3463	1.94980
$566$	−77.4995	−3.25755
$567$	20.2869	0.851969
$568$	−62.8638	−2.63771
$569$	15.6265	0.655097	0.327549	−	0.944834i	$-0.393777\pi$
$569$	15.6265	0.655097	0.327549	+	0.944834i	$0.393777\pi$
$570$	70.9290	2.97089
$571$	37.2288	1.55798	0.778988	−	0.627038i	$-0.215733\pi$
$571$	37.2288	1.55798	0.778988	+	0.627038i	$0.215733\pi$
$572$	122.710	5.13075
$573$	−72.4794	−3.02787
$574$	30.2636	1.26318
$575$	−51.7911	−2.15984
$576$	−28.5564	−1.18985
$577$	−9.81210	−0.408483	−0.204242	−	0.978921i	$-0.565473\pi$
$577$	−9.81210	−0.408483	−0.204242	+	0.978921i	$0.565473\pi$
$578$	28.1155	1.16945
$579$	−2.61361	−0.108618
$580$	−79.1597	−3.28693
$581$	0.487997	0.0202455
$582$	89.0243	3.69017
$583$	19.9419	0.825909
$584$	−2.64670	−0.109521
$585$	126.072	5.21246
$586$	−54.4449	−2.24910
$587$	9.72834	0.401532	0.200766	−	0.979639i	$-0.435657\pi$
$587$	9.72834	0.401532	0.200766	+	0.979639i	$0.435657\pi$
$588$	64.6634	2.66667
$589$	12.2424	0.504439
$590$	−25.7565	−1.06038
$591$	−75.6503	−3.11184
$592$	−19.2916	−0.792880
$593$	28.2791	1.16128	0.580642	−	0.814159i	$-0.302802\pi$
$593$	28.2791	1.16128	0.580642	+	0.814159i	$0.302802\pi$
$594$	145.782	5.98153
$595$	27.4304	1.12454
$596$	5.29436	0.216866
$597$	20.4061	0.835166
$598$	89.4448	3.65767
$599$	32.5093	1.32830	0.664148	−	0.747601i	$-0.268795\pi$
$599$	32.5093	1.32830	0.664148	+	0.747601i	$0.268795\pi$
$600$	−136.135	−5.55770
$601$	5.09124	0.207676	0.103838	−	0.994594i	$-0.466888\pi$
$601$	5.09124	0.207676	0.103838	+	0.994594i	$0.466888\pi$
$602$	19.8250	0.808006
$603$	42.9366	1.74851
$604$	−83.9567	−3.41615
$605$	−62.8940	−2.55700
$606$	47.5395	1.93116
$607$	26.8978	1.09175	0.545875	−	0.837867i	$-0.316197\pi$
$607$	26.8978	1.09175	0.545875	+	0.837867i	$0.316197\pi$
$608$	7.01998	0.284698
$609$	−23.1323	−0.937367
$610$	33.2411	1.34589
$611$	2.30753	0.0933525
$612$	−147.757	−5.97270
$613$	−6.32992	−0.255663	−0.127832	−	0.991796i	$-0.540802\pi$
$613$	−6.32992	−0.255663	−0.127832	+	0.991796i	$0.540802\pi$
$614$	7.78674	0.314247
$615$	92.7039	3.73818
$616$	−43.5190	−1.75343
$617$	−12.5277	−0.504344	−0.252172	−	0.967682i	$-0.581145\pi$
$617$	−12.5277	−0.504344	−0.252172	+	0.967682i	$0.581145\pi$
$618$	−123.771	−4.97880
$619$	30.6964	1.23379	0.616897	−	0.787044i	$-0.288389\pi$
$619$	30.6964	1.23379	0.616897	+	0.787044i	$0.288389\pi$
$620$	−72.6900	−2.91930
$621$	72.2964	2.90115
$622$	68.3287	2.73973
$623$	2.59342	0.103903
$624$	93.3608	3.73742
$625$	−3.04591	−0.121837
$626$	34.6788	1.38604
$627$	42.3474	1.69119
$628$	−48.4436	−1.93311
$629$	18.2824	0.728965
$630$	−84.3335	−3.35993
$631$	23.2190	0.924334	0.462167	−	0.886793i	$-0.347072\pi$
$631$	23.2190	0.924334	0.462167	+	0.886793i	$0.347072\pi$
$632$	32.7782	1.30385
$633$	−4.63048	−0.184045
$634$	−35.6698	−1.41663
$635$	9.38870	0.372579
$636$	49.0314	1.94422
$637$	26.5335	1.05129
$638$	−69.4660	−2.75019
$639$	−72.7319	−2.87723
$640$	58.7258	2.32134
$641$	10.2964	0.406681	0.203341	−	0.979108i	$-0.434820\pi$
$641$	10.2964	0.406681	0.203341	+	0.979108i	$0.434820\pi$
$642$	−2.21533	−0.0874322
$643$	−49.1690	−1.93903	−0.969517	−	0.245022i	$-0.921205\pi$
$643$	−49.1690	−1.93903	−0.969517	+	0.245022i	$0.921205\pi$
$644$	−40.7071	−1.60408
$645$	60.7281	2.39117
$646$	−34.1103	−1.34205
$647$	−12.1501	−0.477668	−0.238834	−	0.971060i	$-0.576765\pi$
$647$	−12.1501	−0.477668	−0.238834	+	0.971060i	$0.576765\pi$
$648$	79.4140	3.11968
$649$	−15.3776	−0.603625
$650$	−105.363	−4.13266
$651$	−21.2417	−0.832527
$652$	10.0525	0.393688
$653$	31.9760	1.25132	0.625658	−	0.780097i	$-0.284830\pi$
$653$	31.9760	1.25132	0.625658	+	0.780097i	$0.284830\pi$
$654$	121.966	4.76924
$655$	−7.03541	−0.274896
$656$	47.0431	1.83672
$657$	−3.06217	−0.119467
$658$	−1.54357	−0.0601747
$659$	−16.5352	−0.644120	−0.322060	−	0.946719i	$-0.604375\pi$
$659$	−16.5352	−0.644120	−0.322060	+	0.946719i	$0.604375\pi$
$660$	−251.441	−9.78732
$661$	4.40089	0.171175	0.0855873	−	0.996331i	$-0.472723\pi$
$661$	4.40089	0.171175	0.0855873	+	0.996331i	$0.472723\pi$
$662$	−35.0720	−1.36311
$663$	−88.4766	−3.43615
$664$	1.91029	0.0741335
$665$	−13.2457	−0.513645
$666$	−56.2082	−2.17802
$667$	−34.4496	−1.33389
$668$	14.4430	0.558815
$669$	−68.0948	−2.63270
$670$	−58.8539	−2.27372
$671$	19.8463	0.766156
$672$	−12.1803	−0.469866
$673$	−28.2504	−1.08897	−0.544487	−	0.838769i	$-0.683276\pi$
$673$	−28.2504	−1.08897	−0.544487	+	0.838769i	$0.683276\pi$
$674$	−6.94541	−0.267527
$675$	−85.1623	−3.27790
$676$	68.4604	2.63309
$677$	15.1494	0.582240	0.291120	−	0.956687i	$-0.405972\pi$
$677$	15.1494	0.582240	0.291120	+	0.956687i	$0.405972\pi$
$678$	99.9979	3.84040
$679$	−16.6249	−0.638004
$680$	107.378	4.11775
$681$	−29.9359	−1.14715
$682$	−63.7886	−2.44259
$683$	−0.816285	−0.0312343	−0.0156171	−	0.999878i	$-0.504971\pi$
$683$	−0.816285	−0.0312343	−0.0156171	+	0.999878i	$0.504971\pi$
$684$	71.3491	2.72810
$685$	49.5697	1.89396
$686$	−43.0007	−1.64178
$687$	−39.0792	−1.49097
$688$	30.8168	1.17488
$689$	20.1191	0.766478
$690$	−183.279	−6.97730
$691$	18.8709	0.717882	0.358941	−	0.933360i	$-0.383138\pi$
$691$	18.8709	0.717882	0.358941	+	0.933360i	$0.383138\pi$
$692$	−102.922	−3.91250
$693$	−50.3504	−1.91266
$694$	85.5601	3.24782
$695$	−11.8466	−0.449367
$696$	−90.5524	−3.43238
$697$	−44.5820	−1.68866
$698$	79.6880	3.01623
$699$	−38.4300	−1.45356
$700$	47.9514	1.81239
$701$	29.2476	1.10467	0.552334	−	0.833623i	$-0.313737\pi$
$701$	29.2476	1.10467	0.552334	+	0.833623i	$0.313737\pi$
$702$	147.078	5.55111
$703$	−8.82823	−0.332963
$704$	23.3698	0.880782
$705$	−4.72828	−0.178077
$706$	49.4263	1.86018
$707$	−8.87778	−0.333883
$708$	−37.8091	−1.42095
$709$	−5.19560	−0.195125	−0.0975625	−	0.995229i	$-0.531105\pi$
$709$	−5.19560	−0.195125	−0.0975625	+	0.995229i	$0.531105\pi$
$710$	99.6949	3.74148
$711$	37.9237	1.42225
$712$	10.1521	0.380465
$713$	−31.6340	−1.18470
$714$	59.1846	2.21493
$715$	−103.174	−3.85850
$716$	−41.4470	−1.54895
$717$	−6.04548	−0.225773
$718$	15.3322	0.572191
$719$	−25.5079	−0.951286	−0.475643	−	0.879638i	$-0.657785\pi$
$719$	−25.5079	−0.951286	−0.475643	+	0.879638i	$0.657785\pi$
$720$	−131.092	−4.88550
$721$	23.1137	0.860799
$722$	−31.0550	−1.15575
$723$	53.9009	2.00459
$724$	−34.4274	−1.27948
$725$	40.5803	1.50711
$726$	−135.702	−5.03636
$727$	18.2744	0.677761	0.338881	−	0.940829i	$-0.389952\pi$
$727$	18.2744	0.677761	0.338881	+	0.940829i	$0.389952\pi$
$728$	−43.9058	−1.62726
$729$	−9.10533	−0.337234
$730$	4.19737	0.155352
$731$	−29.2046	−1.08017
$732$	48.7962	1.80356
$733$	11.4034	0.421195	0.210597	−	0.977573i	$-0.432459\pi$
$733$	11.4034	0.421195	0.210597	+	0.977573i	$0.432459\pi$
$734$	−33.6313	−1.24135
$735$	−54.3690	−2.00543
$736$	−18.1394	−0.668629
$737$	−35.1381	−1.29433
$738$	137.065	5.04544
$739$	−22.2708	−0.819246	−0.409623	−	0.912255i	$-0.634340\pi$
$739$	−22.2708	−0.819246	−0.409623	+	0.912255i	$0.634340\pi$
$740$	52.4182	1.92693
$741$	42.7238	1.56950
$742$	−13.4583	−0.494069
$743$	37.4127	1.37254	0.686270	−	0.727347i	$-0.259247\pi$
$743$	37.4127	1.37254	0.686270	+	0.727347i	$0.259247\pi$
$744$	−83.1516	−3.04848
$745$	−4.45150	−0.163090
$746$	31.3512	1.14785
$747$	2.21016	0.0808655
$748$	120.920	4.42127
$749$	0.413703	0.0151164
$750$	77.6914	2.83689
$751$	20.9303	0.763758	0.381879	−	0.924212i	$-0.375277\pi$
$751$	20.9303	0.763758	0.381879	+	0.924212i	$0.375277\pi$
$752$	−2.39939	−0.0874969
$753$	−11.1637	−0.406828
$754$	−70.0834	−2.55229
$755$	70.5907	2.56906
$756$	−66.9364	−2.43445
$757$	1.08103	0.0392907	0.0196454	−	0.999807i	$-0.493746\pi$
$757$	1.08103	0.0392907	0.0196454	+	0.999807i	$0.493746\pi$
$758$	−22.3002	−0.809980
$759$	−109.425	−3.97186
$760$	−51.8509	−1.88083
$761$	−38.7659	−1.40526	−0.702631	−	0.711554i	$-0.747992\pi$
$761$	−38.7659	−1.40526	−0.702631	+	0.711554i	$0.747992\pi$
$762$	20.2573	0.733844
$763$	−22.7766	−0.824567
$764$	99.9370	3.61560
$765$	124.234	4.49168
$766$	−21.0380	−0.760132
$767$	−15.5143	−0.560189
$768$	99.7123	3.59806
$769$	−48.8853	−1.76285	−0.881424	−	0.472326i	$-0.843415\pi$
$769$	−48.8853	−1.76285	−0.881424	+	0.472326i	$0.843415\pi$
$770$	69.0162	2.48717
$771$	31.1615	1.12225
$772$	3.60374	0.129701
$773$	7.06901	0.254255	0.127127	−	0.991886i	$-0.459424\pi$
$773$	7.06901	0.254255	0.127127	+	0.991886i	$0.459424\pi$
$774$	89.7882	3.22737
$775$	37.2637	1.33855
$776$	−65.0789	−2.33620
$777$	15.3178	0.549523
$778$	−17.1525	−0.614947
$779$	21.5279	0.771316
$780$	−253.675	−9.08304
$781$	59.5218	2.12986
$782$	88.1402	3.15189
$783$	−56.6470	−2.02440
$784$	−27.5898	−0.985351
$785$	40.7313	1.45376
$786$	−15.1798	−0.541445
$787$	30.3453	1.08169	0.540847	−	0.841121i	$-0.318104\pi$
$787$	30.3453	1.08169	0.540847	+	0.841121i	$0.318104\pi$
$788$	104.309	3.71586
$789$	17.6364	0.627873
$790$	−51.9826	−1.84946
$791$	−18.6742	−0.663977
$792$	−197.099	−7.00362
$793$	20.0226	0.711025
$794$	−19.5714	−0.694564
$795$	−41.2256	−1.46212
$796$	−28.1366	−0.997276
$797$	−36.9392	−1.30845	−0.654227	−	0.756299i	$-0.727006\pi$
$797$	−36.9392	−1.30845	−0.654227	+	0.756299i	$0.727006\pi$
$798$	−28.5792	−1.01169
$799$	2.27387	0.0804437
$800$	21.3676	0.755457
$801$	11.7457	0.415014
$802$	−40.5669	−1.43247
$803$	2.50600	0.0884347
$804$	−86.3944	−3.04689
$805$	34.2265	1.20633
$806$	−64.3555	−2.26683
$807$	34.6765	1.22067
$808$	−34.7525	−1.22259
$809$	−35.3975	−1.24451	−0.622255	−	0.782815i	$-0.713783\pi$
$809$	−35.3975	−1.24451	−0.622255	+	0.782815i	$0.713783\pi$
$810$	−125.942	−4.42514
$811$	−26.8628	−0.943281	−0.471641	−	0.881791i	$-0.656338\pi$
$811$	−26.8628	−0.943281	−0.471641	+	0.881791i	$0.656338\pi$
$812$	31.8955	1.11931
$813$	79.3822	2.78406
$814$	45.9992	1.61227
$815$	−8.45217	−0.296066
$816$	91.9991	3.22061
$817$	14.1024	0.493381
$818$	25.1582	0.879636
$819$	−50.7979	−1.77502
$820$	−127.823	−4.46378
$821$	33.5285	1.17015	0.585077	−	0.810978i	$-0.301064\pi$
$821$	33.5285	1.17015	0.585077	+	0.810978i	$0.301064\pi$
$822$	106.953	3.73040
$823$	−17.8795	−0.623240	−0.311620	−	0.950207i	$-0.600872\pi$
$823$	−17.8795	−0.623240	−0.311620	+	0.950207i	$0.600872\pi$
$824$	90.4797	3.15201
$825$	128.898	4.48765
$826$	10.3780	0.361096
$827$	23.8898	0.830729	0.415364	−	0.909655i	$-0.363654\pi$
$827$	23.8898	0.830729	0.415364	+	0.909655i	$0.363654\pi$
$828$	−184.364	−6.40710
$829$	29.2441	1.01569	0.507844	−	0.861449i	$-0.330443\pi$
$829$	29.2441	1.01569	0.507844	+	0.861449i	$0.330443\pi$
$830$	−3.02950	−0.105156
$831$	−33.3201	−1.15586
$832$	23.5775	0.817402
$833$	26.1465	0.905921
$834$	−25.5605	−0.885088
$835$	−12.1436	−0.420248
$836$	−58.3901	−2.01946
$837$	−52.0172	−1.79798
$838$	73.4659	2.53784
$839$	−50.1966	−1.73298	−0.866489	−	0.499196i	$-0.833629\pi$
$839$	−50.1966	−1.73298	−0.866489	+	0.499196i	$0.833629\pi$
$840$	89.9660	3.10412
$841$	−2.00744	−0.0692221
$842$	−71.1872	−2.45327
$843$	−0.977363	−0.0336622
$844$	6.38467	0.219769
$845$	−57.5614	−1.98017
$846$	−6.99090	−0.240352
$847$	25.3416	0.870749
$848$	−20.9201	−0.718400
$849$	95.6537	3.28283
$850$	−103.826	−3.56119
$851$	22.8119	0.781982
$852$	146.347	5.01376
$853$	48.6698	1.66642	0.833212	−	0.552954i	$-0.186499\pi$
$853$	48.6698	1.66642	0.833212	+	0.552954i	$0.186499\pi$
$854$	−13.3937	−0.458324
$855$	−59.9903	−2.05162
$856$	1.61946	0.0553521
$857$	21.2395	0.725528	0.362764	−	0.931881i	$-0.381833\pi$
$857$	21.2395	0.725528	0.362764	+	0.931881i	$0.381833\pi$
$858$	−222.611	−7.59982
$859$	16.2261	0.553626	0.276813	−	0.960924i	$-0.410722\pi$
$859$	16.2261	0.553626	0.276813	+	0.960924i	$0.410722\pi$
$860$	−83.7340	−2.85531
$861$	−37.3528	−1.27298
$862$	−42.2073	−1.43759
$863$	−12.9330	−0.440243	−0.220122	−	0.975472i	$-0.570645\pi$
$863$	−12.9330	−0.440243	−0.220122	+	0.975472i	$0.570645\pi$
$864$	−29.8275	−1.01475
$865$	86.5366	2.94233
$866$	−43.8064	−1.48860
$867$	−34.7015	−1.17853
$868$	29.2887	0.994124
$869$	−31.0357	−1.05281
$870$	143.606	4.86870
$871$	−35.4504	−1.20119
$872$	−89.1600	−3.01934
$873$	−75.2948	−2.54834
$874$	−42.5614	−1.43966
$875$	−14.5085	−0.490477
$876$	6.16152	0.208178
$877$	−4.82463	−0.162916	−0.0814581	−	0.996677i	$-0.525958\pi$
$877$	−4.82463	−0.162916	−0.0814581	+	0.996677i	$0.525958\pi$
$878$	−2.99323	−0.101016
$879$	67.1985	2.26655
$880$	107.282	3.61647
$881$	31.5509	1.06298	0.531489	−	0.847065i	$-0.321633\pi$
$881$	31.5509	1.06298	0.531489	+	0.847065i	$0.321633\pi$
$882$	−80.3860	−2.70674
$883$	40.4305	1.36059	0.680297	−	0.732937i	$-0.261851\pi$
$883$	40.4305	1.36059	0.680297	+	0.732937i	$0.261851\pi$
$884$	121.995	4.10312
$885$	31.7899	1.06861
$886$	−4.45211	−0.149572
$887$	30.6420	1.02886	0.514428	−	0.857534i	$-0.328004\pi$
$887$	30.6420	1.02886	0.514428	+	0.857534i	$0.328004\pi$
$888$	59.9622	2.01220
$889$	−3.78295	−0.126876
$890$	−16.1000	−0.539674
$891$	−75.1921	−2.51903
$892$	93.8914	3.14372
$893$	−1.09801	−0.0367436
$894$	−9.60466	−0.321228
$895$	34.8486	1.16486
$896$	−23.6622	−0.790498
$897$	−110.397	−3.68606
$898$	89.5447	2.98815
$899$	24.7865	0.826675
$900$	217.174	7.23913
$901$	19.8257	0.660490
$902$	−112.170	−3.73486
$903$	−24.4690	−0.814277
$904$	−73.1009	−2.43130
$905$	28.9466	0.962216
$906$	152.308	5.06010
$907$	31.9314	1.06026	0.530132	−	0.847915i	$-0.322142\pi$
$907$	31.9314	1.06026	0.530132	+	0.847915i	$0.322142\pi$
$908$	41.2766	1.36981
$909$	−40.2079	−1.33361
$910$	69.6296	2.30820
$911$	−0.929435	−0.0307936	−0.0153968	−	0.999881i	$-0.504901\pi$
$911$	−0.929435	−0.0307936	−0.0153968	+	0.999881i	$0.504901\pi$
$912$	−44.4247	−1.47105
$913$	−1.80873	−0.0598603
$914$	−22.5578	−0.746145
$915$	−41.0278	−1.35634
$916$	53.8838	1.78037
$917$	2.83475	0.0936119
$918$	144.933	4.78350
$919$	−58.0653	−1.91540	−0.957698	−	0.287775i	$-0.907084\pi$
$919$	−58.0653	−1.91540	−0.957698	+	0.287775i	$0.907084\pi$
$920$	133.981	4.41723
$921$	−9.61078	−0.316686
$922$	−77.1925	−2.54220
$923$	60.0508	1.97660
$924$	101.312	3.33292
$925$	−26.8716	−0.883531
$926$	−2.64685	−0.0869810
$927$	104.683	3.43824
$928$	14.2129	0.466563
$929$	−43.9547	−1.44211	−0.721054	−	0.692879i	$-0.756342\pi$
$929$	−43.9547	−1.44211	−0.721054	+	0.692879i	$0.756342\pi$
$930$	131.869	4.32416
$931$	−12.6257	−0.413790
$932$	52.9886	1.73570
$933$	−84.3347	−2.76099
$934$	−85.5206	−2.79832
$935$	−101.669	−3.32494
$936$	−198.851	−6.49965
$937$	−40.6735	−1.32875	−0.664373	−	0.747401i	$-0.731301\pi$
$937$	−40.6735	−1.32875	−0.664373	+	0.747401i	$0.731301\pi$
$938$	23.7138	0.774283
$939$	−42.8022	−1.39680
$940$	6.51952	0.212643
$941$	32.6479	1.06429	0.532146	−	0.846653i	$-0.321386\pi$
$941$	32.6479	1.06429	0.532146	+	0.846653i	$0.321386\pi$
$942$	87.8829	2.86338
$943$	−55.6275	−1.81148
$944$	16.1320	0.525051
$945$	56.2801	1.83079
$946$	−73.4802	−2.38905
$947$	23.2833	0.756605	0.378303	−	0.925682i	$-0.376508\pi$
$947$	23.2833	0.756605	0.378303	+	0.925682i	$0.376508\pi$
$948$	−76.3077	−2.47836
$949$	2.52827	0.0820711
$950$	50.1357	1.62662
$951$	44.0254	1.42762
$952$	−43.2654	−1.40224
$953$	9.41717	0.305052	0.152526	−	0.988299i	$-0.451259\pi$
$953$	9.41717	0.305052	0.152526	+	0.988299i	$0.451259\pi$
$954$	−60.9531	−1.97343
$955$	−84.0270	−2.71905
$956$	8.33571	0.269596
$957$	85.7384	2.77153
$958$	−77.2200	−2.49487
$959$	−19.9729	−0.644960
$960$	−48.3119	−1.55926
$961$	−8.23933	−0.265785
$962$	46.4080	1.49626
$963$	1.87368	0.0603785
$964$	−74.3203	−2.39370
$965$	−3.03002	−0.0975398
$966$	73.8479	2.37602
$967$	−14.0391	−0.451467	−0.225734	−	0.974189i	$-0.572478\pi$
$967$	−14.0391	−0.451467	−0.225734	+	0.974189i	$0.572478\pi$
$968$	99.2011	3.18845
$969$	42.1007	1.35247
$970$	103.208	3.31380
$971$	16.1363	0.517838	0.258919	−	0.965899i	$-0.416634\pi$
$971$	16.1363	0.517838	0.258919	+	0.965899i	$0.416634\pi$
$972$	−45.6335	−1.46369
$973$	4.77331	0.153025
$974$	−58.1664	−1.86377
$975$	130.044	4.16473
$976$	−20.8198	−0.666425
$977$	9.00176	0.287992	0.143996	−	0.989578i	$-0.454005\pi$
$977$	9.00176	0.287992	0.143996	+	0.989578i	$0.454005\pi$
$978$	−18.2366	−0.583142
$979$	−9.61236	−0.307212
$980$	74.9658	2.39469
$981$	−103.156	−3.29352
$982$	−22.7686	−0.726576
$983$	−50.8826	−1.62290	−0.811451	−	0.584421i	$-0.801322\pi$
$983$	−50.8826	−1.62290	−0.811451	+	0.584421i	$0.801322\pi$
$984$	−146.220	−4.66131
$985$	−87.7031	−2.79445
$986$	−69.0612	−2.19936
$987$	1.90515	0.0606416
$988$	−58.9090	−1.87415
$989$	−36.4403	−1.15873
$990$	312.577	9.93436
$991$	−20.2975	−0.644772	−0.322386	−	0.946608i	$-0.604485\pi$
$991$	−20.2975	−0.644772	−0.322386	+	0.946608i	$0.604485\pi$
$992$	13.0513	0.414380
$993$	43.2876	1.37369
$994$	−40.1697	−1.27411
$995$	23.6573	0.749985
$996$	−4.44715	−0.140913
$997$	−45.1716	−1.43060	−0.715300	−	0.698817i	$-0.753710\pi$
$997$	−45.1716	−1.43060	−0.715300	+	0.698817i	$0.753710\pi$
$998$	62.6832	1.98420
$999$	37.5106	1.18678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.18	✓	18
3.2	odd	2		4923.2.a.l.1.1		18
4.3	odd	2		8752.2.a.s.1.16		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.18	✓	18	1.1	even	1	trivial
4923.2.a.l.1.1		18	3.2	odd	2
8752.2.a.s.1.16		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)

\(f(q)\)	\(=\)	\(q+2.50138 q^{2} -3.08733 q^{3} +4.25691 q^{4} -3.57921 q^{5} -7.72259 q^{6} +1.44216 q^{7} +5.64540 q^{8} +6.53160 q^{9} +O(q^{10})\)	\(q+2.50138 q^{2} -3.08733 q^{3} +4.25691 q^{4} -3.57921 q^{5} -7.72259 q^{6} +1.44216 q^{7} +5.64540 q^{8} +6.53160 q^{9} -8.95298 q^{10} -5.34528 q^{11} -13.1425 q^{12} -5.39279 q^{13} +3.60739 q^{14} +11.0502 q^{15} +5.60749 q^{16} -5.31413 q^{17} +16.3380 q^{18} +2.56610 q^{19} -15.2364 q^{20} -4.45242 q^{21} -13.3706 q^{22} -6.63074 q^{23} -17.4292 q^{24} +7.81075 q^{25} -13.4894 q^{26} -10.9032 q^{27} +6.13915 q^{28} +5.19544 q^{29} +27.6408 q^{30} +4.77081 q^{31} +2.73566 q^{32} +16.5026 q^{33} -13.2927 q^{34} -5.16179 q^{35} +27.8045 q^{36} -3.44033 q^{37} +6.41880 q^{38} +16.6493 q^{39} -20.2061 q^{40} +8.38934 q^{41} -11.1372 q^{42} +5.49566 q^{43} -22.7544 q^{44} -23.3780 q^{45} -16.5860 q^{46} -0.427891 q^{47} -17.3122 q^{48} -4.92018 q^{49} +19.5377 q^{50} +16.4065 q^{51} -22.9566 q^{52} -3.73075 q^{53} -27.2731 q^{54} +19.1319 q^{55} +8.14157 q^{56} -7.92240 q^{57} +12.9958 q^{58} +2.87686 q^{59} +47.0398 q^{60} -3.71286 q^{61} +11.9336 q^{62} +9.41961 q^{63} -4.37204 q^{64} +19.3019 q^{65} +41.2794 q^{66} +6.57367 q^{67} -22.6218 q^{68} +20.4713 q^{69} -12.9116 q^{70} -11.1354 q^{71} +36.8735 q^{72} -0.468824 q^{73} -8.60558 q^{74} -24.1144 q^{75} +10.9237 q^{76} -7.70874 q^{77} +41.6463 q^{78} +5.80618 q^{79} -20.0704 q^{80} +14.0670 q^{81} +20.9849 q^{82} +0.338379 q^{83} -18.9536 q^{84} +19.0204 q^{85} +13.7467 q^{86} -16.0400 q^{87} -30.1763 q^{88} +1.79829 q^{89} -58.4773 q^{90} -7.77726 q^{91} -28.2265 q^{92} -14.7291 q^{93} -1.07032 q^{94} -9.18462 q^{95} -8.44588 q^{96} -11.5278 q^{97} -12.3072 q^{98} -34.9132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 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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