LMFDB - Embedded newform 507.2.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(1,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("507.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.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:	$4.04841538248$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.24698 q^{2} +1.00000 q^{3} -0.445042 q^{4} -2.80194 q^{5} +1.24698 q^{6} -4.80194 q^{7} -3.04892 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.24698 q^{2} +1.00000 q^{3} -0.445042 q^{4} -2.80194 q^{5} +1.24698 q^{6} -4.80194 q^{7} -3.04892 q^{8} +1.00000 q^{9} -3.49396 q^{10} +1.46681 q^{11} -0.445042 q^{12} -5.98792 q^{14} -2.80194 q^{15} -2.91185 q^{16} -2.44504 q^{17} +1.24698 q^{18} +2.54288 q^{19} +1.24698 q^{20} -4.80194 q^{21} +1.82908 q^{22} -3.51573 q^{23} -3.04892 q^{24} +2.85086 q^{25} +1.00000 q^{27} +2.13706 q^{28} +1.85086 q^{29} -3.49396 q^{30} -7.63102 q^{31} +2.46681 q^{32} +1.46681 q^{33} -3.04892 q^{34} +13.4547 q^{35} -0.445042 q^{36} -4.55496 q^{37} +3.17092 q^{38} +8.54288 q^{40} +1.24698 q^{41} -5.98792 q^{42} +2.38404 q^{43} -0.652793 q^{44} -2.80194 q^{45} -4.38404 q^{46} +12.8170 q^{47} -2.91185 q^{48} +16.0586 q^{49} +3.55496 q^{50} -2.44504 q^{51} -8.85086 q^{53} +1.24698 q^{54} -4.10992 q^{55} +14.6407 q^{56} +2.54288 q^{57} +2.30798 q^{58} +2.17629 q^{59} +1.24698 q^{60} -7.82908 q^{61} -9.51573 q^{62} -4.80194 q^{63} +8.89977 q^{64} +1.82908 q^{66} -3.58211 q^{67} +1.08815 q^{68} -3.51573 q^{69} +16.7778 q^{70} -8.83877 q^{71} -3.04892 q^{72} -7.69202 q^{73} -5.67994 q^{74} +2.85086 q^{75} -1.13169 q^{76} -7.04354 q^{77} -4.02177 q^{79} +8.15883 q^{80} +1.00000 q^{81} +1.55496 q^{82} -0.652793 q^{83} +2.13706 q^{84} +6.85086 q^{85} +2.97285 q^{86} +1.85086 q^{87} -4.47219 q^{88} +6.29590 q^{89} -3.49396 q^{90} +1.56465 q^{92} -7.63102 q^{93} +15.9825 q^{94} -7.12498 q^{95} +2.46681 q^{96} -10.0315 q^{97} +20.0248 q^{98} +1.46681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{5} - q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) $ 3 * q - q^2 + 3 * q^3 - q^4 - 4 * q^5 - q^6 - 10 * q^7 + 3 * q^9	$ 3 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{5} - q^{6} - 10 q^{7} + 3 q^{9} - q^{10} + q^{11} - q^{12} + q^{14} - 4 q^{15} - 5 q^{16} - 7 q^{17} - q^{18} - 11 q^{19} - q^{20} - 10 q^{21} - 5 q^{22} + 2 q^{23} - 5 q^{25} + 3 q^{27} + q^{28} - 8 q^{29} - q^{30} - 8 q^{31} + 4 q^{32} + q^{33} + 18 q^{35} - q^{36} - 14 q^{37} + 20 q^{38} + 7 q^{40} - q^{41} + q^{42} - 3 q^{43} + 16 q^{44} - 4 q^{45} - 3 q^{46} + 9 q^{47} - 5 q^{48} + 17 q^{49} + 11 q^{50} - 7 q^{51} - 13 q^{53} - q^{54} - 13 q^{55} + 7 q^{56} - 11 q^{57} + 12 q^{58} + 14 q^{59} - q^{60} - 13 q^{61} - 16 q^{62} - 10 q^{63} + 4 q^{64} - 5 q^{66} - 5 q^{67} + 7 q^{68} + 2 q^{69} + 8 q^{70} + 6 q^{71} - 18 q^{73} + 7 q^{74} - 5 q^{75} - q^{76} - 15 q^{77} - 9 q^{79} + 16 q^{80} + 3 q^{81} + 5 q^{82} + 16 q^{83} + q^{84} + 7 q^{85} + 15 q^{86} - 8 q^{87} - 7 q^{88} + 5 q^{89} - q^{90} - 17 q^{92} - 8 q^{93} + 32 q^{94} + 3 q^{95} + 4 q^{96} - 5 q^{97} + 13 q^{98} + q^{99}+O(q^{100}) $ 3 * q - q^2 + 3 * q^3 - q^4 - 4 * q^5 - q^6 - 10 * q^7 + 3 * q^9 - q^10 + q^11 - q^12 + q^14 - 4 * q^15 - 5 * q^16 - 7 * q^17 - q^18 - 11 * q^19 - q^20 - 10 * q^21 - 5 * q^22 + 2 * q^23 - 5 * q^25 + 3 * q^27 + q^28 - 8 * q^29 - q^30 - 8 * q^31 + 4 * q^32 + q^33 + 18 * q^35 - q^36 - 14 * q^37 + 20 * q^38 + 7 * q^40 - q^41 + q^42 - 3 * q^43 + 16 * q^44 - 4 * q^45 - 3 * q^46 + 9 * q^47 - 5 * q^48 + 17 * q^49 + 11 * q^50 - 7 * q^51 - 13 * q^53 - q^54 - 13 * q^55 + 7 * q^56 - 11 * q^57 + 12 * q^58 + 14 * q^59 - q^60 - 13 * q^61 - 16 * q^62 - 10 * q^63 + 4 * q^64 - 5 * q^66 - 5 * q^67 + 7 * q^68 + 2 * q^69 + 8 * q^70 + 6 * q^71 - 18 * q^73 + 7 * q^74 - 5 * q^75 - q^76 - 15 * q^77 - 9 * q^79 + 16 * q^80 + 3 * q^81 + 5 * q^82 + 16 * q^83 + q^84 + 7 * q^85 + 15 * q^86 - 8 * q^87 - 7 * q^88 + 5 * q^89 - q^90 - 17 * q^92 - 8 * q^93 + 32 * q^94 + 3 * q^95 + 4 * q^96 - 5 * q^97 + 13 * q^98 + 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 $

$2$	1.24698	0.881748	0.440874	−	0.897569i	$-0.354669\pi$
$2$	1.24698	0.881748	0.440874	+	0.897569i	$0.354669\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.445042	−0.222521
$5$	−2.80194	−1.25306	−0.626532	−	0.779395i	$-0.715526\pi$
$5$	−2.80194	−1.25306	−0.626532	+	0.779395i	$0.715526\pi$
$6$	1.24698	0.509077
$7$	−4.80194	−1.81496	−0.907481	−	0.420093i	$-0.861997\pi$
$7$	−4.80194	−1.81496	−0.907481	+	0.420093i	$0.861997\pi$
$8$	−3.04892	−1.07796
$9$	1.00000	0.333333
$10$	−3.49396	−1.10489
$11$	1.46681	0.442260	0.221130	−	0.975244i	$-0.429025\pi$
$11$	1.46681	0.442260	0.221130	+	0.975244i	$0.429025\pi$
$12$	−0.445042	−0.128473
$13$	0	0
$13$	0	0
$14$	−5.98792	−1.60034
$15$	−2.80194	−0.723457
$16$	−2.91185	−0.727963
$17$	−2.44504	−0.593010	−0.296505	−	0.955031i	$-0.595821\pi$
$17$	−2.44504	−0.593010	−0.296505	+	0.955031i	$0.595821\pi$
$18$	1.24698	0.293916
$19$	2.54288	0.583376	0.291688	−	0.956514i	$-0.405783\pi$
$19$	2.54288	0.583376	0.291688	+	0.956514i	$0.405783\pi$
$20$	1.24698	0.278833
$21$	−4.80194	−1.04787
$22$	1.82908	0.389962
$23$	−3.51573	−0.733080	−0.366540	−	0.930402i	$-0.619458\pi$
$23$	−3.51573	−0.733080	−0.366540	+	0.930402i	$0.619458\pi$
$24$	−3.04892	−0.622358
$25$	2.85086	0.570171
$26$	0	0
$27$	1.00000	0.192450
$28$	2.13706	0.403867
$29$	1.85086	0.343695	0.171848	−	0.985124i	$-0.445026\pi$
$29$	1.85086	0.343695	0.171848	+	0.985124i	$0.445026\pi$
$30$	−3.49396	−0.637907
$31$	−7.63102	−1.37057	−0.685286	−	0.728274i	$-0.740323\pi$
$31$	−7.63102	−1.37057	−0.685286	+	0.728274i	$0.740323\pi$
$32$	2.46681	0.436075
$33$	1.46681	0.255339
$34$	−3.04892	−0.522885
$35$	13.4547	2.27426
$36$	−0.445042	−0.0741736
$37$	−4.55496	−0.748831	−0.374415	−	0.927261i	$-0.622157\pi$
$37$	−4.55496	−0.748831	−0.374415	+	0.927261i	$0.622157\pi$
$38$	3.17092	0.514390
$39$	0	0
$40$	8.54288	1.35075
$41$	1.24698	0.194745	0.0973727	−	0.995248i	$-0.468956\pi$
$41$	1.24698	0.194745	0.0973727	+	0.995248i	$0.468956\pi$
$42$	−5.98792	−0.923956
$43$	2.38404	0.363563	0.181782	−	0.983339i	$-0.441814\pi$
$43$	2.38404	0.363563	0.181782	+	0.983339i	$0.441814\pi$
$44$	−0.652793	−0.0984122
$45$	−2.80194	−0.417688
$46$	−4.38404	−0.646392
$47$	12.8170	1.86955	0.934776	−	0.355238i	$-0.115600\pi$
$47$	12.8170	1.86955	0.934776	+	0.355238i	$0.115600\pi$
$48$	−2.91185	−0.420290
$49$	16.0586	2.29409
$50$	3.55496	0.502747
$51$	−2.44504	−0.342374
$52$	0	0
$53$	−8.85086	−1.21576	−0.607879	−	0.794030i	$-0.707980\pi$
$53$	−8.85086	−1.21576	−0.607879	+	0.794030i	$0.707980\pi$
$54$	1.24698	0.169692
$55$	−4.10992	−0.554181
$56$	14.6407	1.95645
$57$	2.54288	0.336812
$58$	2.30798	0.303052
$59$	2.17629	0.283329	0.141665	−	0.989915i	$-0.454755\pi$
$59$	2.17629	0.283329	0.141665	+	0.989915i	$0.454755\pi$
$60$	1.24698	0.160984
$61$	−7.82908	−1.00241	−0.501206	−	0.865328i	$-0.667110\pi$
$61$	−7.82908	−1.00241	−0.501206	+	0.865328i	$0.667110\pi$
$62$	−9.51573	−1.20850
$63$	−4.80194	−0.604987
$64$	8.89977	1.11247
$65$	0	0
$66$	1.82908	0.225145
$67$	−3.58211	−0.437624	−0.218812	−	0.975767i	$-0.570218\pi$
$67$	−3.58211	−0.437624	−0.218812	+	0.975767i	$0.570218\pi$
$68$	1.08815	0.131957
$69$	−3.51573	−0.423244
$70$	16.7778	2.00533
$71$	−8.83877	−1.04897	−0.524485	−	0.851420i	$-0.675742\pi$
$71$	−8.83877	−1.04897	−0.524485	+	0.851420i	$0.675742\pi$
$72$	−3.04892	−0.359318
$73$	−7.69202	−0.900283	−0.450142	−	0.892957i	$-0.648626\pi$
$73$	−7.69202	−0.900283	−0.450142	+	0.892957i	$0.648626\pi$
$74$	−5.67994	−0.660280
$75$	2.85086	0.329188
$76$	−1.13169	−0.129813
$77$	−7.04354	−0.802686
$78$	0	0
$79$	−4.02177	−0.452485	−0.226242	−	0.974071i	$-0.572644\pi$
$79$	−4.02177	−0.452485	−0.226242	+	0.974071i	$0.572644\pi$
$80$	8.15883	0.912185
$81$	1.00000	0.111111
$82$	1.55496	0.171716
$83$	−0.652793	−0.0716533	−0.0358267	−	0.999358i	$-0.511406\pi$
$83$	−0.652793	−0.0716533	−0.0358267	+	0.999358i	$0.511406\pi$
$84$	2.13706	0.233173
$85$	6.85086	0.743080
$86$	2.97285	0.320571
$87$	1.85086	0.198432
$88$	−4.47219	−0.476737
$89$	6.29590	0.667364	0.333682	−	0.942686i	$-0.391709\pi$
$89$	6.29590	0.667364	0.333682	+	0.942686i	$0.391709\pi$
$90$	−3.49396	−0.368296
$91$	0	0
$92$	1.56465	0.163126
$93$	−7.63102	−0.791300
$94$	15.9825	1.64847
$95$	−7.12498	−0.731008
$96$	2.46681	0.251768
$97$	−10.0315	−1.01854	−0.509270	−	0.860607i	$-0.670085\pi$
$97$	−10.0315	−1.01854	−0.509270	+	0.860607i	$0.670085\pi$
$98$	20.0248	2.02281
$99$	1.46681	0.147420
$100$	−1.26875	−0.126875
$101$	13.8877	1.38188	0.690938	−	0.722914i	$-0.257198\pi$
$101$	13.8877	1.38188	0.690938	+	0.722914i	$0.257198\pi$
$102$	−3.04892	−0.301888
$103$	−17.4034	−1.71481	−0.857405	−	0.514642i	$-0.827925\pi$
$103$	−17.4034	−1.71481	−0.857405	+	0.514642i	$0.827925\pi$
$104$	0	0
$105$	13.4547	1.31305
$106$	−11.0368	−1.07199
$107$	10.5526	1.02015	0.510077	−	0.860128i	$-0.329617\pi$
$107$	10.5526	1.02015	0.510077	+	0.860128i	$0.329617\pi$
$108$	−0.445042	−0.0428242
$109$	1.07069	0.102553	0.0512766	−	0.998684i	$-0.483671\pi$
$109$	1.07069	0.102553	0.0512766	+	0.998684i	$0.483671\pi$
$110$	−5.12498	−0.488648
$111$	−4.55496	−0.432337
$112$	13.9825	1.32123
$113$	−16.5308	−1.55509	−0.777543	−	0.628830i	$-0.783534\pi$
$113$	−16.5308	−1.55509	−0.777543	+	0.628830i	$0.783534\pi$
$114$	3.17092	0.296983
$115$	9.85086	0.918597
$116$	−0.823708	−0.0764794
$117$	0	0
$118$	2.71379	0.249825
$119$	11.7409	1.07629
$120$	8.54288	0.779854
$121$	−8.84846	−0.804406
$122$	−9.76271	−0.883874
$123$	1.24698	0.112436
$124$	3.39612	0.304981
$125$	6.02177	0.538604
$126$	−5.98792	−0.533446
$127$	−9.53750	−0.846316	−0.423158	−	0.906056i	$-0.639079\pi$
$127$	−9.53750	−0.846316	−0.423158	+	0.906056i	$0.639079\pi$
$128$	6.16421	0.544844
$129$	2.38404	0.209903
$130$	0	0
$131$	−5.50902	−0.481326	−0.240663	−	0.970609i	$-0.577365\pi$
$131$	−5.50902	−0.481326	−0.240663	+	0.970609i	$0.577365\pi$
$132$	−0.652793	−0.0568183
$133$	−12.2107	−1.05880
$134$	−4.46681	−0.385874
$135$	−2.80194	−0.241152
$136$	7.45473	0.639238
$137$	−16.1836	−1.38266	−0.691329	−	0.722540i	$-0.742974\pi$
$137$	−16.1836	−1.38266	−0.691329	+	0.722540i	$0.742974\pi$
$138$	−4.38404	−0.373195
$139$	−10.5090	−0.891364	−0.445682	−	0.895191i	$-0.647039\pi$
$139$	−10.5090	−0.891364	−0.445682	+	0.895191i	$0.647039\pi$
$140$	−5.98792	−0.506071
$141$	12.8170	1.07939
$142$	−11.0218	−0.924926
$143$	0	0
$144$	−2.91185	−0.242654
$145$	−5.18598	−0.430672
$146$	−9.59179	−0.793823
$147$	16.0586	1.32449
$148$	2.02715	0.166630
$149$	14.3502	1.17561	0.587807	−	0.809001i	$-0.299992\pi$
$149$	14.3502	1.17561	0.587807	+	0.809001i	$0.299992\pi$
$150$	3.55496	0.290261
$151$	1.96615	0.160003	0.0800014	−	0.996795i	$-0.474508\pi$
$151$	1.96615	0.160003	0.0800014	+	0.996795i	$0.474508\pi$
$152$	−7.75302	−0.628853
$153$	−2.44504	−0.197670
$154$	−8.78315	−0.707767
$155$	21.3817	1.71742
$156$	0	0
$157$	10.7017	0.854089	0.427045	−	0.904231i	$-0.359555\pi$
$157$	10.7017	0.854089	0.427045	+	0.904231i	$0.359555\pi$
$158$	−5.01507	−0.398977
$159$	−8.85086	−0.701918
$160$	−6.91185	−0.546430
$161$	16.8823	1.33051
$162$	1.24698	0.0979720
$163$	3.89977	0.305454	0.152727	−	0.988268i	$-0.451195\pi$
$163$	3.89977	0.305454	0.152727	+	0.988268i	$0.451195\pi$
$164$	−0.554958	−0.0433349
$165$	−4.10992	−0.319957
$166$	−0.814019	−0.0631802
$167$	21.0194	1.62653	0.813264	−	0.581895i	$-0.197688\pi$
$167$	21.0194	1.62653	0.813264	+	0.581895i	$0.197688\pi$
$168$	14.6407	1.12956
$169$	0	0
$170$	8.54288	0.655209
$171$	2.54288	0.194459
$172$	−1.06100	−0.0809004
$173$	13.2349	1.00623	0.503115	−	0.864219i	$-0.332187\pi$
$173$	13.2349	1.00623	0.503115	+	0.864219i	$0.332187\pi$
$174$	2.30798	0.174967
$175$	−13.6896	−1.03484
$176$	−4.27114	−0.321950
$177$	2.17629	0.163580
$178$	7.85086	0.588446
$179$	8.52781	0.637399	0.318699	−	0.947856i	$-0.396754\pi$
$179$	8.52781	0.637399	0.318699	+	0.947856i	$0.396754\pi$
$180$	1.24698	0.0929444
$181$	−3.63640	−0.270291	−0.135146	−	0.990826i	$-0.543150\pi$
$181$	−3.63640	−0.270291	−0.135146	+	0.990826i	$0.543150\pi$
$182$	0	0
$183$	−7.82908	−0.578743
$184$	10.7192	0.790228
$185$	12.7627	0.938333
$186$	−9.51573	−0.697727
$187$	−3.58642	−0.262265
$188$	−5.70410	−0.416014
$189$	−4.80194	−0.349290
$190$	−8.88471	−0.644564
$191$	21.3817	1.54712	0.773561	−	0.633722i	$-0.218474\pi$
$191$	21.3817	1.54712	0.773561	+	0.633722i	$0.218474\pi$
$192$	8.89977	0.642286
$193$	−8.42758	−0.606631	−0.303315	−	0.952890i	$-0.598094\pi$
$193$	−8.42758	−0.606631	−0.303315	+	0.952890i	$0.598094\pi$
$194$	−12.5090	−0.898096
$195$	0	0
$196$	−7.14675	−0.510482
$197$	−26.4765	−1.88637	−0.943186	−	0.332264i	$-0.892187\pi$
$197$	−26.4765	−1.88637	−0.943186	+	0.332264i	$0.892187\pi$
$198$	1.82908	0.129987
$199$	−14.2524	−1.01032	−0.505161	−	0.863025i	$-0.668567\pi$
$199$	−14.2524	−1.01032	−0.505161	+	0.863025i	$0.668567\pi$
$200$	−8.69202	−0.614619
$201$	−3.58211	−0.252662
$202$	17.3177	1.21847
$203$	−8.88769	−0.623794
$204$	1.08815	0.0761855
$205$	−3.49396	−0.244029
$206$	−21.7017	−1.51203
$207$	−3.51573	−0.244360
$208$	0	0
$209$	3.72992	0.258004
$210$	16.7778	1.15778
$211$	1.85086	0.127418	0.0637091	−	0.997969i	$-0.479707\pi$
$211$	1.85086	0.127418	0.0637091	+	0.997969i	$0.479707\pi$
$212$	3.93900	0.270532
$213$	−8.83877	−0.605623
$214$	13.1588	0.899519
$215$	−6.67994	−0.455568
$216$	−3.04892	−0.207453
$217$	36.6437	2.48754
$218$	1.33513	0.0904261
$219$	−7.69202	−0.519779
$220$	1.82908	0.123317
$221$	0	0
$222$	−5.67994	−0.381213
$223$	18.6504	1.24892	0.624462	−	0.781056i	$-0.285318\pi$
$223$	18.6504	1.24892	0.624462	+	0.781056i	$0.285318\pi$
$224$	−11.8455	−0.791459
$225$	2.85086	0.190057
$226$	−20.6136	−1.37119
$227$	9.75733	0.647617	0.323808	−	0.946123i	$-0.395037\pi$
$227$	9.75733	0.647617	0.323808	+	0.946123i	$0.395037\pi$
$228$	−1.13169	−0.0749478
$229$	−2.86294	−0.189188	−0.0945941	−	0.995516i	$-0.530155\pi$
$229$	−2.86294	−0.189188	−0.0945941	+	0.995516i	$0.530155\pi$
$230$	12.2838	0.809971
$231$	−7.04354	−0.463431
$232$	−5.64310	−0.370488
$233$	−5.78554	−0.379024	−0.189512	−	0.981878i	$-0.560691\pi$
$233$	−5.78554	−0.379024	−0.189512	+	0.981878i	$0.560691\pi$
$234$	0	0
$235$	−35.9124	−2.34267
$236$	−0.968541	−0.0630467
$237$	−4.02177	−0.261242
$238$	14.6407	0.949016
$239$	7.09246	0.458773	0.229386	−	0.973335i	$-0.426328\pi$
$239$	7.09246	0.458773	0.229386	+	0.973335i	$0.426328\pi$
$240$	8.15883	0.526650
$241$	3.89977	0.251206	0.125603	−	0.992081i	$-0.459913\pi$
$241$	3.89977	0.251206	0.125603	+	0.992081i	$0.459913\pi$
$242$	−11.0339	−0.709283
$243$	1.00000	0.0641500
$244$	3.48427	0.223058
$245$	−44.9952	−2.87464
$246$	1.55496	0.0991405
$247$	0	0
$248$	23.2664	1.47742
$249$	−0.652793	−0.0413691
$250$	7.50902	0.474912
$251$	−2.44504	−0.154330	−0.0771648	−	0.997018i	$-0.524587\pi$
$251$	−2.44504	−0.154330	−0.0771648	+	0.997018i	$0.524587\pi$
$252$	2.13706	0.134622
$253$	−5.15691	−0.324212
$254$	−11.8931	−0.746237
$255$	6.85086	0.429017
$256$	−10.1129	−0.632056
$257$	−14.1304	−0.881428	−0.440714	−	0.897648i	$-0.645275\pi$
$257$	−14.1304	−0.881428	−0.440714	+	0.897648i	$0.645275\pi$
$258$	2.97285	0.185082
$259$	21.8726	1.35910
$260$	0	0
$261$	1.85086	0.114565
$262$	−6.86964	−0.424408
$263$	−23.7235	−1.46285	−0.731426	−	0.681921i	$-0.761145\pi$
$263$	−23.7235	−1.46285	−0.731426	+	0.681921i	$0.761145\pi$
$264$	−4.47219	−0.275244
$265$	24.7995	1.52342
$266$	−15.2265	−0.933599
$267$	6.29590	0.385303
$268$	1.59419	0.0973805
$269$	−5.91617	−0.360715	−0.180357	−	0.983601i	$-0.557725\pi$
$269$	−5.91617	−0.360715	−0.180357	+	0.983601i	$0.557725\pi$
$270$	−3.49396	−0.212636
$271$	3.19029	0.193796	0.0968982	−	0.995294i	$-0.469108\pi$
$271$	3.19029	0.193796	0.0968982	+	0.995294i	$0.469108\pi$
$272$	7.11960	0.431689
$273$	0	0
$274$	−20.1806	−1.21915
$275$	4.18167	0.252164
$276$	1.56465	0.0941807
$277$	21.9366	1.31804	0.659022	−	0.752124i	$-0.270971\pi$
$277$	21.9366	1.31804	0.659022	+	0.752124i	$0.270971\pi$
$278$	−13.1045	−0.785958
$279$	−7.63102	−0.456857
$280$	−41.0224	−2.45155
$281$	−11.9903	−0.715282	−0.357641	−	0.933859i	$-0.616419\pi$
$281$	−11.9903	−0.715282	−0.357641	+	0.933859i	$0.616419\pi$
$282$	15.9825	0.951747
$283$	−14.3666	−0.854005	−0.427002	−	0.904250i	$-0.640430\pi$
$283$	−14.3666	−0.854005	−0.427002	+	0.904250i	$0.640430\pi$
$284$	3.93362	0.233418
$285$	−7.12498	−0.422047
$286$	0	0
$287$	−5.98792	−0.353456
$288$	2.46681	0.145358
$289$	−11.0218	−0.648339
$290$	−6.46681	−0.379744
$291$	−10.0315	−0.588055
$292$	3.42327	0.200332
$293$	−18.7584	−1.09588	−0.547939	−	0.836519i	$-0.684587\pi$
$293$	−18.7584	−1.09588	−0.547939	+	0.836519i	$0.684587\pi$
$294$	20.0248	1.16787
$295$	−6.09783	−0.355030
$296$	13.8877	0.807206
$297$	1.46681	0.0851131
$298$	17.8944	1.03659
$299$	0	0
$300$	−1.26875	−0.0732513
$301$	−11.4480	−0.659853
$302$	2.45175	0.141082
$303$	13.8877	0.797827
$304$	−7.40449	−0.424676
$305$	21.9366	1.25609
$306$	−3.04892	−0.174295
$307$	−25.6262	−1.46257	−0.731283	−	0.682074i	$-0.761078\pi$
$307$	−25.6262	−1.46257	−0.731283	+	0.682074i	$0.761078\pi$
$308$	3.13467	0.178614
$309$	−17.4034	−0.990046
$310$	26.6625	1.51433
$311$	11.3817	0.645394	0.322697	−	0.946502i	$-0.395410\pi$
$311$	11.3817	0.645394	0.322697	+	0.946502i	$0.395410\pi$
$312$	0	0
$313$	27.5743	1.55859	0.779297	−	0.626655i	$-0.215576\pi$
$313$	27.5743	1.55859	0.779297	+	0.626655i	$0.215576\pi$
$314$	13.3448	0.753091
$315$	13.4547	0.758088
$316$	1.78986	0.100687
$317$	11.2597	0.632405	0.316203	−	0.948692i	$-0.397592\pi$
$317$	11.2597	0.632405	0.316203	+	0.948692i	$0.397592\pi$
$318$	−11.0368	−0.618915
$319$	2.71486	0.152003
$320$	−24.9366	−1.39400
$321$	10.5526	0.588987
$322$	21.0519	1.17318
$323$	−6.21744	−0.345948
$324$	−0.445042	−0.0247245
$325$	0	0
$326$	4.86294	0.269333
$327$	1.07069	0.0592092
$328$	−3.80194	−0.209927
$329$	−61.5465	−3.39317
$330$	−5.12498	−0.282121
$331$	11.9065	0.654439	0.327220	−	0.944948i	$-0.393888\pi$
$331$	11.9065	0.654439	0.327220	+	0.944948i	$0.393888\pi$
$332$	0.290520	0.0159444
$333$	−4.55496	−0.249610
$334$	26.2107	1.43419
$335$	10.0368	0.548371
$336$	13.9825	0.762810
$337$	17.1672	0.935157	0.467578	−	0.883952i	$-0.345127\pi$
$337$	17.1672	0.935157	0.467578	+	0.883952i	$0.345127\pi$
$338$	0	0
$339$	−16.5308	−0.897830
$340$	−3.04892	−0.165351
$341$	−11.1933	−0.606150
$342$	3.17092	0.171463
$343$	−43.4989	−2.34872
$344$	−7.26875	−0.391905
$345$	9.85086	0.530352
$346$	16.5036	0.887242
$347$	−24.2760	−1.30321	−0.651603	−	0.758560i	$-0.725903\pi$
$347$	−24.2760	−1.30321	−0.651603	+	0.758560i	$0.725903\pi$
$348$	−0.823708	−0.0441554
$349$	4.57242	0.244756	0.122378	−	0.992484i	$-0.460948\pi$
$349$	4.57242	0.244756	0.122378	+	0.992484i	$0.460948\pi$
$350$	−17.0707	−0.912467
$351$	0	0
$352$	3.61835	0.192859
$353$	6.07606	0.323396	0.161698	−	0.986840i	$-0.448303\pi$
$353$	6.07606	0.323396	0.161698	+	0.986840i	$0.448303\pi$
$354$	2.71379	0.144236
$355$	24.7657	1.31443
$356$	−2.80194	−0.148502
$357$	11.7409	0.621396
$358$	10.6340	0.562025
$359$	14.9661	0.789883	0.394942	−	0.918706i	$-0.370765\pi$
$359$	14.9661	0.789883	0.394942	+	0.918706i	$0.370765\pi$
$360$	8.54288	0.450249
$361$	−12.5338	−0.659673
$362$	−4.53452	−0.238329
$363$	−8.84846	−0.464424
$364$	0	0
$365$	21.5526	1.12811
$366$	−9.76271	−0.510305
$367$	37.0834	1.93574	0.967868	−	0.251459i	$-0.0809105\pi$
$367$	37.0834	1.93574	0.967868	+	0.251459i	$0.0809105\pi$
$368$	10.2373	0.533656
$369$	1.24698	0.0649152
$370$	15.9148	0.827373
$371$	42.5013	2.20656
$372$	3.39612	0.176081
$373$	−36.5090	−1.89037	−0.945183	−	0.326542i	$-0.894117\pi$
$373$	−36.5090	−1.89037	−0.945183	+	0.326542i	$0.894117\pi$
$374$	−4.47219	−0.231251
$375$	6.02177	0.310963
$376$	−39.0780	−2.01529
$377$	0	0
$378$	−5.98792	−0.307985
$379$	26.5851	1.36558	0.682792	−	0.730613i	$-0.260765\pi$
$379$	26.5851	1.36558	0.682792	+	0.730613i	$0.260765\pi$
$380$	3.17092	0.162665
$381$	−9.53750	−0.488621
$382$	26.6625	1.36417
$383$	14.3502	0.733261	0.366630	−	0.930367i	$-0.380511\pi$
$383$	14.3502	0.733261	0.366630	+	0.930367i	$0.380511\pi$
$384$	6.16421	0.314566
$385$	19.7356	1.00582
$386$	−10.5090	−0.534895
$387$	2.38404	0.121188
$388$	4.46442	0.226647
$389$	−22.6582	−1.14881	−0.574407	−	0.818570i	$-0.694767\pi$
$389$	−22.6582	−1.14881	−0.574407	+	0.818570i	$0.694767\pi$
$390$	0	0
$391$	8.59611	0.434724
$392$	−48.9614	−2.47292
$393$	−5.50902	−0.277894
$394$	−33.0157	−1.66330
$395$	11.2687	0.566992
$396$	−0.652793	−0.0328041
$397$	−7.90754	−0.396868	−0.198434	−	0.980114i	$-0.563586\pi$
$397$	−7.90754	−0.396868	−0.198434	+	0.980114i	$0.563586\pi$
$398$	−17.7724	−0.890850
$399$	−12.2107	−0.611301
$400$	−8.30127	−0.415064
$401$	−2.93661	−0.146647	−0.0733236	−	0.997308i	$-0.523361\pi$
$401$	−2.93661	−0.146647	−0.0733236	+	0.997308i	$0.523361\pi$
$402$	−4.46681	−0.222784
$403$	0	0
$404$	−6.18060	−0.307497
$405$	−2.80194	−0.139229
$406$	−11.0828	−0.550029
$407$	−6.68127	−0.331178
$408$	7.45473	0.369064
$409$	−11.7549	−0.581244	−0.290622	−	0.956838i	$-0.593862\pi$
$409$	−11.7549	−0.581244	−0.290622	+	0.956838i	$0.593862\pi$
$410$	−4.35690	−0.215172
$411$	−16.1836	−0.798278
$412$	7.74525	0.381581
$413$	−10.4504	−0.514231
$414$	−4.38404	−0.215464
$415$	1.82908	0.0897862
$416$	0	0
$417$	−10.5090	−0.514629
$418$	4.65114	0.227495
$419$	7.34183	0.358672	0.179336	−	0.983788i	$-0.442605\pi$
$419$	7.34183	0.358672	0.179336	+	0.983788i	$0.442605\pi$
$420$	−5.98792	−0.292181
$421$	−25.6963	−1.25236	−0.626181	−	0.779677i	$-0.715383\pi$
$421$	−25.6963	−1.25236	−0.626181	+	0.779677i	$0.715383\pi$
$422$	2.30798	0.112351
$423$	12.8170	0.623184
$424$	26.9855	1.31053
$425$	−6.97046	−0.338117
$426$	−11.0218	−0.534007
$427$	37.5948	1.81934
$428$	−4.69633	−0.227006
$429$	0	0
$430$	−8.32975	−0.401696
$431$	−8.94198	−0.430720	−0.215360	−	0.976535i	$-0.569093\pi$
$431$	−8.94198	−0.430720	−0.215360	+	0.976535i	$0.569093\pi$
$432$	−2.91185	−0.140097
$433$	2.91484	0.140078	0.0700391	−	0.997544i	$-0.477688\pi$
$433$	2.91484	0.140078	0.0700391	+	0.997544i	$0.477688\pi$
$434$	45.6939	2.19338
$435$	−5.18598	−0.248649
$436$	−0.476501	−0.0228203
$437$	−8.94007	−0.427661
$438$	−9.59179	−0.458314
$439$	9.05861	0.432344	0.216172	−	0.976355i	$-0.430643\pi$
$439$	9.05861	0.432344	0.216172	+	0.976355i	$0.430643\pi$
$440$	12.5308	0.597382
$441$	16.0586	0.764696
$442$	0	0
$443$	11.2325	0.533672	0.266836	−	0.963742i	$-0.414022\pi$
$443$	11.2325	0.533672	0.266836	+	0.963742i	$0.414022\pi$
$444$	2.02715	0.0962041
$445$	−17.6407	−0.836250
$446$	23.2567	1.10124
$447$	14.3502	0.678741
$448$	−42.7362	−2.01909
$449$	−28.7579	−1.35717	−0.678585	−	0.734522i	$-0.737407\pi$
$449$	−28.7579	−1.35717	−0.678585	+	0.734522i	$0.737407\pi$
$450$	3.55496	0.167582
$451$	1.82908	0.0861282
$452$	7.35690	0.346039
$453$	1.96615	0.0923777
$454$	12.1672	0.571035
$455$	0	0
$456$	−7.75302	−0.363068
$457$	19.0761	0.892341	0.446170	−	0.894948i	$-0.352788\pi$
$457$	19.0761	0.892341	0.446170	+	0.894948i	$0.352788\pi$
$458$	−3.57002	−0.166816
$459$	−2.44504	−0.114125
$460$	−4.38404	−0.204407
$461$	−31.7332	−1.47796	−0.738981	−	0.673727i	$-0.764692\pi$
$461$	−31.7332	−1.47796	−0.738981	+	0.673727i	$0.764692\pi$
$462$	−8.78315	−0.408629
$463$	36.4784	1.69530	0.847648	−	0.530559i	$-0.178018\pi$
$463$	36.4784	1.69530	0.847648	+	0.530559i	$0.178018\pi$
$464$	−5.38942	−0.250198
$465$	21.3817	0.991550
$466$	−7.21446	−0.334203
$467$	13.0000	0.601568	0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000	0.601568	0.300784	+	0.953692i	$0.402752\pi$
$468$	0	0
$469$	17.2010	0.794271
$470$	−44.7821	−2.06564
$471$	10.7017	0.493109
$472$	−6.63533	−0.305416
$473$	3.49694	0.160790
$474$	−5.01507	−0.230350
$475$	7.24937	0.332624
$476$	−5.22521	−0.239497
$477$	−8.85086	−0.405253
$478$	8.84415	0.404522
$479$	−5.61655	−0.256627	−0.128313	−	0.991734i	$-0.540956\pi$
$479$	−5.61655	−0.256627	−0.128313	+	0.991734i	$0.540956\pi$
$480$	−6.91185	−0.315482
$481$	0	0
$482$	4.86294	0.221501
$483$	16.8823	0.768172
$484$	3.93794	0.178997
$485$	28.1075	1.27630
$486$	1.24698	0.0565641
$487$	9.75733	0.442147	0.221073	−	0.975257i	$-0.429044\pi$
$487$	9.75733	0.442147	0.221073	+	0.975257i	$0.429044\pi$
$488$	23.8702	1.08055
$489$	3.89977	0.176354
$490$	−56.1081	−2.53471
$491$	−7.38835	−0.333432	−0.166716	−	0.986005i	$-0.553316\pi$
$491$	−7.38835	−0.333432	−0.166716	+	0.986005i	$0.553316\pi$
$492$	−0.554958	−0.0250194
$493$	−4.52542	−0.203815
$494$	0	0
$495$	−4.10992	−0.184727
$496$	22.2204	0.997726
$497$	42.4432	1.90384
$498$	−0.814019	−0.0364771
$499$	43.2814	1.93754	0.968771	−	0.247956i	$-0.0797589\pi$
$499$	43.2814	1.93754	0.968771	+	0.247956i	$0.0797589\pi$
$500$	−2.67994	−0.119851
$501$	21.0194	0.939077
$502$	−3.04892	−0.136080
$503$	10.7670	0.480078	0.240039	−	0.970763i	$-0.422840\pi$
$503$	10.7670	0.480078	0.240039	+	0.970763i	$0.422840\pi$
$504$	14.6407	0.652149
$505$	−38.9124	−1.73158
$506$	−6.43057	−0.285874
$507$	0	0
$508$	4.24459	0.188323
$509$	41.5448	1.84144	0.920720	−	0.390223i	$-0.127602\pi$
$509$	41.5448	1.84144	0.920720	+	0.390223i	$0.127602\pi$
$510$	8.54288	0.378285
$511$	36.9366	1.63398
$512$	−24.9390	−1.10216
$513$	2.54288	0.112271
$514$	−17.6203	−0.777197
$515$	48.7633	2.14877
$516$	−1.06100	−0.0467079
$517$	18.8001	0.826829
$518$	27.2747	1.19838
$519$	13.2349	0.580948
$520$	0	0
$521$	25.7198	1.12680	0.563402	−	0.826183i	$-0.309492\pi$
$521$	25.7198	1.12680	0.563402	+	0.826183i	$0.309492\pi$
$522$	2.30798	0.101017
$523$	8.59286	0.375739	0.187870	−	0.982194i	$-0.439842\pi$
$523$	8.59286	0.375739	0.187870	+	0.982194i	$0.439842\pi$
$524$	2.45175	0.107105
$525$	−13.6896	−0.597464
$526$	−29.5827	−1.28987
$527$	18.6582	0.812763
$528$	−4.27114	−0.185878
$529$	−10.6396	−0.462593
$530$	30.9245	1.34328
$531$	2.17629	0.0944430
$532$	5.43429	0.235606
$533$	0	0
$534$	7.85086	0.339740
$535$	−29.5676	−1.27832
$536$	10.9215	0.471739
$537$	8.52781	0.368002
$538$	−7.37734	−0.318060
$539$	23.5550	1.01458
$540$	1.24698	0.0536615
$541$	−31.3534	−1.34799	−0.673995	−	0.738736i	$-0.735423\pi$
$541$	−31.3534	−1.34799	−0.673995	+	0.738736i	$0.735423\pi$
$542$	3.97823	0.170880
$543$	−3.63640	−0.156053
$544$	−6.03146	−0.258597
$545$	−3.00000	−0.128506
$546$	0	0
$547$	19.9342	0.852325	0.426163	−	0.904647i	$-0.359865\pi$
$547$	19.9342	0.852325	0.426163	+	0.904647i	$0.359865\pi$
$548$	7.20237	0.307670
$549$	−7.82908	−0.334137
$550$	5.21446	0.222345
$551$	4.70650	0.200503
$552$	10.7192	0.456238
$553$	19.3123	0.821242
$554$	27.3545	1.16218
$555$	12.7627	0.541747
$556$	4.67696	0.198347
$557$	−33.2349	−1.40821	−0.704104	−	0.710097i	$-0.748651\pi$
$557$	−33.2349	−1.40821	−0.704104	+	0.710097i	$0.748651\pi$
$558$	−9.51573	−0.402833
$559$	0	0
$560$	−39.1782	−1.65558
$561$	−3.58642	−0.151419
$562$	−14.9517	−0.630698
$563$	3.87130	0.163156	0.0815779	−	0.996667i	$-0.474004\pi$
$563$	3.87130	0.163156	0.0815779	+	0.996667i	$0.474004\pi$
$564$	−5.70410	−0.240186
$565$	46.3183	1.94862
$566$	−17.9148	−0.753017
$567$	−4.80194	−0.201662
$568$	26.9487	1.13074
$569$	20.1457	0.844551	0.422276	−	0.906468i	$-0.361231\pi$
$569$	20.1457	0.844551	0.422276	+	0.906468i	$0.361231\pi$
$570$	−8.88471	−0.372139
$571$	−32.1269	−1.34447	−0.672234	−	0.740338i	$-0.734665\pi$
$571$	−32.1269	−1.34447	−0.672234	+	0.740338i	$0.734665\pi$
$572$	0	0
$573$	21.3817	0.893231
$574$	−7.46681	−0.311659
$575$	−10.0228	−0.417981
$576$	8.89977	0.370824
$577$	16.7506	0.697338	0.348669	−	0.937246i	$-0.386634\pi$
$577$	16.7506	0.697338	0.348669	+	0.937246i	$0.386634\pi$
$578$	−13.7439	−0.571672
$579$	−8.42758	−0.350238
$580$	2.30798	0.0958336
$581$	3.13467	0.130048
$582$	−12.5090	−0.518516
$583$	−12.9825	−0.537682
$584$	23.4523	0.970465
$585$	0	0
$586$	−23.3913	−0.966287
$587$	6.73795	0.278105	0.139053	−	0.990285i	$-0.455594\pi$
$587$	6.73795	0.278105	0.139053	+	0.990285i	$0.455594\pi$
$588$	−7.14675	−0.294727
$589$	−19.4047	−0.799559
$590$	−7.60388	−0.313047
$591$	−26.4765	−1.08910
$592$	13.2634	0.545121
$593$	−18.1172	−0.743985	−0.371992	−	0.928236i	$-0.621325\pi$
$593$	−18.1172	−0.743985	−0.371992	+	0.928236i	$0.621325\pi$
$594$	1.82908	0.0750483
$595$	−32.8974	−1.34866
$596$	−6.38644	−0.261599
$597$	−14.2524	−0.583310
$598$	0	0
$599$	−26.7851	−1.09441	−0.547204	−	0.836999i	$-0.684308\pi$
$599$	−26.7851	−1.09441	−0.547204	+	0.836999i	$0.684308\pi$
$600$	−8.69202	−0.354850
$601$	−4.70171	−0.191787	−0.0958934	−	0.995392i	$-0.530571\pi$
$601$	−4.70171	−0.191787	−0.0958934	+	0.995392i	$0.530571\pi$
$602$	−14.2755	−0.581824
$603$	−3.58211	−0.145875
$604$	−0.875018	−0.0356040
$605$	24.7928	1.00797
$606$	17.3177	0.703482
$607$	27.6396	1.12186	0.560929	−	0.827864i	$-0.310444\pi$
$607$	27.6396	1.12186	0.560929	+	0.827864i	$0.310444\pi$
$608$	6.27280	0.254396
$609$	−8.88769	−0.360147
$610$	27.3545	1.10755
$611$	0	0
$612$	1.08815	0.0439857
$613$	−48.1782	−1.94590	−0.972950	−	0.231017i	$-0.925795\pi$
$613$	−48.1782	−1.94590	−0.972950	+	0.231017i	$0.925795\pi$
$614$	−31.9554	−1.28961
$615$	−3.49396	−0.140890
$616$	21.4752	0.865259
$617$	−30.3043	−1.22000	−0.610002	−	0.792400i	$-0.708831\pi$
$617$	−30.3043	−1.22000	−0.610002	+	0.792400i	$0.708831\pi$
$618$	−21.7017	−0.872971
$619$	10.9041	0.438272	0.219136	−	0.975694i	$-0.429676\pi$
$619$	10.9041	0.438272	0.219136	+	0.975694i	$0.429676\pi$
$620$	−9.51573	−0.382161
$621$	−3.51573	−0.141081
$622$	14.1927	0.569075
$623$	−30.2325	−1.21124
$624$	0	0
$625$	−31.1269	−1.24508
$626$	34.3846	1.37429
$627$	3.72992	0.148959
$628$	−4.76271	−0.190053
$629$	11.1371	0.444064
$630$	16.7778	0.668443
$631$	10.4523	0.416101	0.208050	−	0.978118i	$-0.433288\pi$
$631$	10.4523	0.416101	0.208050	+	0.978118i	$0.433288\pi$
$632$	12.2620	0.487758
$633$	1.85086	0.0735649
$634$	14.0406	0.557622
$635$	26.7235	1.06049
$636$	3.93900	0.156192
$637$	0	0
$638$	3.38537	0.134028
$639$	−8.83877	−0.349656
$640$	−17.2717	−0.682725
$641$	−17.5942	−0.694929	−0.347464	−	0.937693i	$-0.612957\pi$
$641$	−17.5942	−0.694929	−0.347464	+	0.937693i	$0.612957\pi$
$642$	13.1588	0.519338
$643$	−22.6058	−0.891486	−0.445743	−	0.895161i	$-0.647060\pi$
$643$	−22.6058	−0.891486	−0.445743	+	0.895161i	$0.647060\pi$
$644$	−7.51334	−0.296067
$645$	−6.67994	−0.263022
$646$	−7.75302	−0.305039
$647$	−24.7918	−0.974665	−0.487333	−	0.873216i	$-0.662030\pi$
$647$	−24.7918	−0.974665	−0.487333	+	0.873216i	$0.662030\pi$
$648$	−3.04892	−0.119773
$649$	3.19221	0.125305
$650$	0	0
$651$	36.6437	1.43618
$652$	−1.73556	−0.0679699
$653$	−21.8106	−0.853513	−0.426757	−	0.904367i	$-0.640344\pi$
$653$	−21.8106	−0.853513	−0.426757	+	0.904367i	$0.640344\pi$
$654$	1.33513	0.0522075
$655$	15.4359	0.603132
$656$	−3.63102	−0.141768
$657$	−7.69202	−0.300094
$658$	−76.7472	−2.99192
$659$	16.5526	0.644796	0.322398	−	0.946604i	$-0.395511\pi$
$659$	16.5526	0.644796	0.322398	+	0.946604i	$0.395511\pi$
$660$	1.82908	0.0711970
$661$	15.9541	0.620541	0.310271	−	0.950648i	$-0.399580\pi$
$661$	15.9541	0.620541	0.310271	+	0.950648i	$0.399580\pi$
$662$	14.8471	0.577050
$663$	0	0
$664$	1.99031	0.0772391
$665$	34.2137	1.32675
$666$	−5.67994	−0.220093
$667$	−6.50711	−0.251956
$668$	−9.35450	−0.361937
$669$	18.6504	0.721066
$670$	12.5157	0.483525
$671$	−11.4838	−0.443327
$672$	−11.8455	−0.456949
$673$	−7.38835	−0.284800	−0.142400	−	0.989809i	$-0.545482\pi$
$673$	−7.38835	−0.284800	−0.142400	+	0.989809i	$0.545482\pi$
$674$	21.4071	0.824572
$675$	2.85086	0.109729
$676$	0	0
$677$	−22.1454	−0.851118	−0.425559	−	0.904931i	$-0.639922\pi$
$677$	−22.1454	−0.851118	−0.425559	+	0.904931i	$0.639922\pi$
$678$	−20.6136	−0.791659
$679$	48.1704	1.84861
$680$	−20.8877	−0.801006
$681$	9.75733	0.373902
$682$	−13.9578	−0.534471
$683$	−9.10023	−0.348211	−0.174105	−	0.984727i	$-0.555703\pi$
$683$	−9.10023	−0.348211	−0.174105	+	0.984727i	$0.555703\pi$
$684$	−1.13169	−0.0432711
$685$	45.3454	1.73256
$686$	−54.2422	−2.07098
$687$	−2.86294	−0.109228
$688$	−6.94198	−0.264661
$689$	0	0
$690$	12.2838	0.467637
$691$	−13.7711	−0.523876	−0.261938	−	0.965085i	$-0.584362\pi$
$691$	−13.7711	−0.523876	−0.261938	+	0.965085i	$0.584362\pi$
$692$	−5.89008	−0.223907
$693$	−7.04354	−0.267562
$694$	−30.2717	−1.14910
$695$	29.4456	1.11694
$696$	−5.64310	−0.213901
$697$	−3.04892	−0.115486
$698$	5.70171	0.215813
$699$	−5.78554	−0.218829
$700$	6.09246	0.230273
$701$	46.5090	1.75662	0.878311	−	0.478090i	$-0.158671\pi$
$701$	46.5090	1.75662	0.878311	+	0.478090i	$0.158671\pi$
$702$	0	0
$703$	−11.5827	−0.436850
$704$	13.0543	0.492002
$705$	−35.9124	−1.35254
$706$	7.57673	0.285154
$707$	−66.6878	−2.50805
$708$	−0.968541	−0.0364000
$709$	−7.24565	−0.272116	−0.136058	−	0.990701i	$-0.543443\pi$
$709$	−7.24565	−0.272116	−0.136058	+	0.990701i	$0.543443\pi$
$710$	30.8823	1.15899
$711$	−4.02177	−0.150828
$712$	−19.1957	−0.719388
$713$	26.8286	1.00474
$714$	14.6407	0.547915
$715$	0	0
$716$	−3.79523	−0.141835
$717$	7.09246	0.264873
$718$	18.6625	0.696478
$719$	25.5147	0.951536	0.475768	−	0.879571i	$-0.342170\pi$
$719$	25.5147	0.951536	0.475768	+	0.879571i	$0.342170\pi$
$720$	8.15883	0.304062
$721$	83.5701	3.11231
$722$	−15.6294	−0.581665
$723$	3.89977	0.145034
$724$	1.61835	0.0601455
$725$	5.27652	0.195965
$726$	−11.0339	−0.409505
$727$	−14.4873	−0.537303	−0.268651	−	0.963238i	$-0.586578\pi$
$727$	−14.4873	−0.537303	−0.268651	+	0.963238i	$0.586578\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	26.8756	0.994711
$731$	−5.82908	−0.215596
$732$	3.48427	0.128782
$733$	−37.5036	−1.38523	−0.692614	−	0.721308i	$-0.743541\pi$
$733$	−37.5036	−1.38523	−0.692614	+	0.721308i	$0.743541\pi$
$734$	46.2422	1.70683
$735$	−44.9952	−1.65967
$736$	−8.67264	−0.319678
$737$	−5.25428	−0.193544
$738$	1.55496	0.0572388
$739$	−43.1876	−1.58868	−0.794341	−	0.607472i	$-0.792184\pi$
$739$	−43.1876	−1.58868	−0.794341	+	0.607472i	$0.792184\pi$
$740$	−5.67994	−0.208799
$741$	0	0
$742$	52.9982	1.94563
$743$	−13.4765	−0.494405	−0.247202	−	0.968964i	$-0.579511\pi$
$743$	−13.4765	−0.494405	−0.247202	+	0.968964i	$0.579511\pi$
$744$	23.2664	0.852986
$745$	−40.2083	−1.47312
$746$	−45.5260	−1.66683
$747$	−0.652793	−0.0238844
$748$	1.59611	0.0583594
$749$	−50.6728	−1.85154
$750$	7.50902	0.274191
$751$	35.5894	1.29868	0.649338	−	0.760500i	$-0.275046\pi$
$751$	35.5894	1.29868	0.649338	+	0.760500i	$0.275046\pi$
$752$	−37.3212	−1.36097
$753$	−2.44504	−0.0891023
$754$	0	0
$755$	−5.50902	−0.200494
$756$	2.13706	0.0777242
$757$	−12.2107	−0.443807	−0.221903	−	0.975069i	$-0.571227\pi$
$757$	−12.2107	−0.443807	−0.221903	+	0.975069i	$0.571227\pi$
$758$	33.1511	1.20410
$759$	−5.15691	−0.187184
$760$	21.7235	0.787993
$761$	−30.9071	−1.12038	−0.560190	−	0.828364i	$-0.689272\pi$
$761$	−30.9071	−1.12038	−0.560190	+	0.828364i	$0.689272\pi$
$762$	−11.8931	−0.430840
$763$	−5.14138	−0.186130
$764$	−9.51573	−0.344267
$765$	6.85086	0.247693
$766$	17.8944	0.646551
$767$	0	0
$768$	−10.1129	−0.364918
$769$	−11.9892	−0.432343	−0.216172	−	0.976355i	$-0.569357\pi$
$769$	−11.9892	−0.432343	−0.216172	+	0.976355i	$0.569357\pi$
$770$	24.6098	0.886877
$771$	−14.1304	−0.508892
$772$	3.75063	0.134988
$773$	−43.9661	−1.58135	−0.790676	−	0.612235i	$-0.790271\pi$
$773$	−43.9661	−1.58135	−0.790676	+	0.612235i	$0.790271\pi$
$774$	2.97285	0.106857
$775$	−21.7549	−0.781460
$776$	30.5851	1.09794
$777$	21.8726	0.784676
$778$	−28.2543	−1.01296
$779$	3.17092	0.113610
$780$	0	0
$781$	−12.9648	−0.463918
$782$	10.7192	0.383317
$783$	1.85086	0.0661442
$784$	−46.7603	−1.67001
$785$	−29.9855	−1.07023
$786$	−6.86964	−0.245032
$787$	−30.3763	−1.08280	−0.541399	−	0.840766i	$-0.682105\pi$
$787$	−30.3763	−1.08280	−0.541399	+	0.840766i	$0.682105\pi$
$788$	11.7832	0.419757
$789$	−23.7235	−0.844578
$790$	14.0519	0.499944
$791$	79.3798	2.82242
$792$	−4.47219	−0.158912
$793$	0	0
$794$	−9.86054	−0.349938
$795$	24.7995	0.879549
$796$	6.34290	0.224818
$797$	52.5763	1.86235	0.931173	−	0.364577i	$-0.118786\pi$
$797$	52.5763	1.86235	0.931173	+	0.364577i	$0.118786\pi$
$798$	−15.2265	−0.539014
$799$	−31.3381	−1.10866
$800$	7.03252	0.248637
$801$	6.29590	0.222455
$802$	−3.66189	−0.129306
$803$	−11.2828	−0.398160
$804$	1.59419	0.0562226
$805$	−47.3032	−1.66722
$806$	0	0
$807$	−5.91617	−0.208259
$808$	−42.3424	−1.48960
$809$	49.4215	1.73757	0.868783	−	0.495193i	$-0.164903\pi$
$809$	49.4215	1.73757	0.868783	+	0.495193i	$0.164903\pi$
$810$	−3.49396	−0.122765
$811$	1.36526	0.0479406	0.0239703	−	0.999713i	$-0.492369\pi$
$811$	1.36526	0.0479406	0.0239703	+	0.999713i	$0.492369\pi$
$812$	3.95539	0.138807
$813$	3.19029	0.111888
$814$	−8.33140	−0.292016
$815$	−10.9269	−0.382753
$816$	7.11960	0.249236
$817$	6.06233	0.212094
$818$	−14.6582	−0.512511
$819$	0	0
$820$	1.55496	0.0543015
$821$	−0.665939	−0.0232414	−0.0116207	−	0.999932i	$-0.503699\pi$
$821$	−0.665939	−0.0232414	−0.0116207	+	0.999932i	$0.503699\pi$
$822$	−20.1806	−0.703879
$823$	−10.0592	−0.350642	−0.175321	−	0.984511i	$-0.556096\pi$
$823$	−10.0592	−0.350642	−0.175321	+	0.984511i	$0.556096\pi$
$824$	53.0616	1.84849
$825$	4.18167	0.145587
$826$	−13.0315	−0.453422
$827$	37.3038	1.29718	0.648590	−	0.761138i	$-0.275359\pi$
$827$	37.3038	1.29718	0.648590	+	0.761138i	$0.275359\pi$
$828$	1.56465	0.0543752
$829$	−42.6209	−1.48028	−0.740142	−	0.672451i	$-0.765242\pi$
$829$	−42.6209	−1.48028	−0.740142	+	0.672451i	$0.765242\pi$
$830$	2.28083	0.0791688
$831$	21.9366	0.760973
$832$	0	0
$833$	−39.2640	−1.36042
$834$	−13.1045	−0.453773
$835$	−58.8950	−2.03815
$836$	−1.65997	−0.0574113
$837$	−7.63102	−0.263767
$838$	9.15511	0.316258
$839$	−4.14005	−0.142930	−0.0714652	−	0.997443i	$-0.522767\pi$
$839$	−4.14005	−0.142930	−0.0714652	+	0.997443i	$0.522767\pi$
$840$	−41.0224	−1.41541
$841$	−25.5743	−0.881874
$842$	−32.0428	−1.10427
$843$	−11.9903	−0.412968
$844$	−0.823708	−0.0283532
$845$	0	0
$846$	15.9825	0.549491
$847$	42.4898	1.45997
$848$	25.7724	0.885028
$849$	−14.3666	−0.493060
$850$	−8.69202	−0.298134
$851$	16.0140	0.548953
$852$	3.93362	0.134764
$853$	−17.3502	−0.594059	−0.297030	−	0.954868i	$-0.595996\pi$
$853$	−17.3502	−0.594059	−0.297030	+	0.954868i	$0.595996\pi$
$854$	46.8799	1.60420
$855$	−7.12498	−0.243669
$856$	−32.1739	−1.09968
$857$	41.0180	1.40115	0.700575	−	0.713579i	$-0.252927\pi$
$857$	41.0180	1.40115	0.700575	+	0.713579i	$0.252927\pi$
$858$	0	0
$859$	6.59286	0.224945	0.112473	−	0.993655i	$-0.464123\pi$
$859$	6.59286	0.224945	0.112473	+	0.993655i	$0.464123\pi$
$860$	2.97285	0.101373
$861$	−5.98792	−0.204068
$862$	−11.1505	−0.379787
$863$	16.6455	0.566619	0.283310	−	0.959028i	$-0.408568\pi$
$863$	16.6455	0.566619	0.283310	+	0.959028i	$0.408568\pi$
$864$	2.46681	0.0839227
$865$	−37.0834	−1.26087
$866$	3.63474	0.123514
$867$	−11.0218	−0.374319
$868$	−16.3080	−0.553529
$869$	−5.89918	−0.200116
$870$	−6.46681	−0.219245
$871$	0	0
$872$	−3.26444	−0.110548
$873$	−10.0315	−0.339513
$874$	−11.1481	−0.377089
$875$	−28.9162	−0.977545
$876$	3.42327	0.115662
$877$	−54.4965	−1.84022	−0.920108	−	0.391666i	$-0.871899\pi$
$877$	−54.4965	−1.84022	−0.920108	+	0.391666i	$0.871899\pi$
$878$	11.2959	0.381218
$879$	−18.7584	−0.632705
$880$	11.9675	0.403424
$881$	−9.00670	−0.303444	−0.151722	−	0.988423i	$-0.548482\pi$
$881$	−9.00670	−0.303444	−0.151722	+	0.988423i	$0.548482\pi$
$882$	20.0248	0.674269
$883$	18.8907	0.635722	0.317861	−	0.948137i	$-0.397035\pi$
$883$	18.8907	0.635722	0.317861	+	0.948137i	$0.397035\pi$
$884$	0	0
$885$	−6.09783	−0.204976
$886$	14.0067	0.470564
$887$	−46.9124	−1.57517	−0.787583	−	0.616209i	$-0.788668\pi$
$887$	−46.9124	−1.57517	−0.787583	+	0.616209i	$0.788668\pi$
$888$	13.8877	0.466040
$889$	45.7985	1.53603
$890$	−21.9976	−0.737361
$891$	1.46681	0.0491401
$892$	−8.30021	−0.277912
$893$	32.5921	1.09065
$894$	17.8944	0.598478
$895$	−23.8944	−0.798702
$896$	−29.6002	−0.988872
$897$	0	0
$898$	−35.8605	−1.19668
$899$	−14.1239	−0.471059
$900$	−1.26875	−0.0422917
$901$	21.6407	0.720957
$902$	2.28083	0.0759434
$903$	−11.4480	−0.380966
$904$	50.4010	1.67631
$905$	10.1890	0.338693
$906$	2.45175	0.0814538
$907$	−35.3013	−1.17216	−0.586080	−	0.810253i	$-0.699329\pi$
$907$	−35.3013	−1.17216	−0.586080	+	0.810253i	$0.699329\pi$
$908$	−4.34242	−0.144108
$909$	13.8877	0.460626
$910$	0	0
$911$	−9.80731	−0.324931	−0.162465	−	0.986714i	$-0.551945\pi$
$911$	−9.80731	−0.324931	−0.162465	+	0.986714i	$0.551945\pi$
$912$	−7.40449	−0.245187
$913$	−0.957524	−0.0316894
$914$	23.7875	0.786819
$915$	21.9366	0.725202
$916$	1.27413	0.0420983
$917$	26.4540	0.873588
$918$	−3.04892	−0.100629
$919$	18.4655	0.609120	0.304560	−	0.952493i	$-0.401491\pi$
$919$	18.4655	0.609120	0.304560	+	0.952493i	$0.401491\pi$
$920$	−30.0344	−0.990206
$921$	−25.6262	−0.844413
$922$	−39.5706	−1.30319
$923$	0	0
$924$	3.13467	0.103123
$925$	−12.9855	−0.426961
$926$	45.4878	1.49482
$927$	−17.4034	−0.571603
$928$	4.56571	0.149877
$929$	25.6267	0.840785	0.420393	−	0.907342i	$-0.361892\pi$
$929$	25.6267	0.840785	0.420393	+	0.907342i	$0.361892\pi$
$930$	26.6625	0.874297
$931$	40.8351	1.33831
$932$	2.57481	0.0843407
$933$	11.3817	0.372618
$934$	16.2107	0.530431
$935$	10.0489	0.328635
$936$	0	0
$937$	7.54932	0.246625	0.123313	−	0.992368i	$-0.460648\pi$
$937$	7.54932	0.246625	0.123313	+	0.992368i	$0.460648\pi$
$938$	21.4494	0.700346
$939$	27.5743	0.899854
$940$	15.9825	0.521293
$941$	12.6418	0.412110	0.206055	−	0.978540i	$-0.433937\pi$
$941$	12.6418	0.412110	0.206055	+	0.978540i	$0.433937\pi$
$942$	13.3448	0.434798
$943$	−4.38404	−0.142764
$944$	−6.33704	−0.206253
$945$	13.4547	0.437682
$946$	4.36062	0.141776
$947$	−27.9801	−0.909233	−0.454616	−	0.890687i	$-0.650224\pi$
$947$	−27.9801	−0.909233	−0.454616	+	0.890687i	$0.650224\pi$
$948$	1.78986	0.0581318
$949$	0	0
$950$	9.03982	0.293290
$951$	11.2597	0.365119
$952$	−35.7972	−1.16019
$953$	4.00239	0.129650	0.0648251	−	0.997897i	$-0.479351\pi$
$953$	4.00239	0.129650	0.0648251	+	0.997897i	$0.479351\pi$
$954$	−11.0368	−0.357331
$955$	−59.9101	−1.93864
$956$	−3.15644	−0.102087
$957$	2.71486	0.0877589
$958$	−7.00372	−0.226280
$959$	77.7126	2.50947
$960$	−24.9366	−0.804826
$961$	27.2325	0.878468
$962$	0	0
$963$	10.5526	0.340052
$964$	−1.73556	−0.0558987
$965$	23.6136	0.760148
$966$	21.0519	0.677334
$967$	−12.2239	−0.393094	−0.196547	−	0.980494i	$-0.562973\pi$
$967$	−12.2239	−0.393094	−0.196547	+	0.980494i	$0.562973\pi$
$968$	26.9782	0.867113
$969$	−6.21744	−0.199733
$970$	35.0495	1.12537
$971$	−23.6401	−0.758648	−0.379324	−	0.925264i	$-0.623843\pi$
$971$	−23.6401	−0.758648	−0.379324	+	0.925264i	$0.623843\pi$
$972$	−0.445042	−0.0142747
$973$	50.4637	1.61779
$974$	12.1672	0.389862
$975$	0	0
$976$	22.7972	0.729719
$977$	−18.7313	−0.599266	−0.299633	−	0.954055i	$-0.596864\pi$
$977$	−18.7313	−0.599266	−0.299633	+	0.954055i	$0.596864\pi$
$978$	4.86294	0.155500
$979$	9.23490	0.295149
$980$	20.0248	0.639667
$981$	1.07069	0.0341844
$982$	−9.21313	−0.294003
$983$	−12.0954	−0.385785	−0.192892	−	0.981220i	$-0.561787\pi$
$983$	−12.0954	−0.385785	−0.192892	+	0.981220i	$0.561787\pi$
$984$	−3.80194	−0.121201
$985$	74.1855	2.36375
$986$	−5.64310	−0.179713
$987$	−61.5465	−1.95905
$988$	0	0
$989$	−8.38165	−0.266521
$990$	−5.12498	−0.162883
$991$	−28.5526	−0.907002	−0.453501	−	0.891256i	$-0.649825\pi$
$991$	−28.5526	−0.907002	−0.453501	+	0.891256i	$0.649825\pi$
$992$	−18.8243	−0.597672
$993$	11.9065	0.377841
$994$	52.9259	1.67871
$995$	39.9342	1.26600
$996$	0.290520	0.00920548
$997$	−23.9347	−0.758019	−0.379010	−	0.925393i	$-0.623735\pi$
$997$	−23.9347	−0.758019	−0.379010	+	0.925393i	$0.623735\pi$
$998$	53.9711	1.70842
$999$	−4.55496	−0.144112

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.a.j.1.3	✓	3
3.2	odd	2		1521.2.a.q.1.1		3
4.3	odd	2		8112.2.a.by.1.1		3
13.2	odd	12		507.2.j.h.316.5		12
13.3	even	3		507.2.e.k.22.1		6
13.4	even	6		507.2.e.j.484.3		6
13.5	odd	4		507.2.b.g.337.2		6
13.6	odd	12		507.2.j.h.361.2		12
13.7	odd	12		507.2.j.h.361.5		12
13.8	odd	4		507.2.b.g.337.5		6
13.9	even	3		507.2.e.k.484.1		6
13.10	even	6		507.2.e.j.22.3		6
13.11	odd	12		507.2.j.h.316.2		12
13.12	even	2		507.2.a.k.1.1	yes	3
39.5	even	4		1521.2.b.m.1351.5		6
39.8	even	4		1521.2.b.m.1351.2		6
39.38	odd	2		1521.2.a.p.1.3		3
52.51	odd	2		8112.2.a.cf.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.j.1.3	✓	3	1.1	even	1	trivial
507.2.a.k.1.1	yes	3	13.12	even	2
507.2.b.g.337.2		6	13.5	odd	4
507.2.b.g.337.5		6	13.8	odd	4
507.2.e.j.22.3		6	13.10	even	6
507.2.e.j.484.3		6	13.4	even	6
507.2.e.k.22.1		6	13.3	even	3
507.2.e.k.484.1		6	13.9	even	3
507.2.j.h.316.2		12	13.11	odd	12
507.2.j.h.316.5		12	13.2	odd	12
507.2.j.h.361.2		12	13.6	odd	12
507.2.j.h.361.5		12	13.7	odd	12
1521.2.a.p.1.3		3	39.38	odd	2
1521.2.a.q.1.1		3	3.2	odd	2
1521.2.b.m.1351.2		6	39.8	even	4
1521.2.b.m.1351.5		6	39.5	even	4
8112.2.a.by.1.1		3	4.3	odd	2
8112.2.a.cf.1.3		3	52.51	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.a (trivial)

\(f(q)\)	\(=\)	\(q+1.24698 q^{2} +1.00000 q^{3} -0.445042 q^{4} -2.80194 q^{5} +1.24698 q^{6} -4.80194 q^{7} -3.04892 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.24698 q^{2} +1.00000 q^{3} -0.445042 q^{4} -2.80194 q^{5} +1.24698 q^{6} -4.80194 q^{7} -3.04892 q^{8} +1.00000 q^{9} -3.49396 q^{10} +1.46681 q^{11} -0.445042 q^{12} -5.98792 q^{14} -2.80194 q^{15} -2.91185 q^{16} -2.44504 q^{17} +1.24698 q^{18} +2.54288 q^{19} +1.24698 q^{20} -4.80194 q^{21} +1.82908 q^{22} -3.51573 q^{23} -3.04892 q^{24} +2.85086 q^{25} +1.00000 q^{27} +2.13706 q^{28} +1.85086 q^{29} -3.49396 q^{30} -7.63102 q^{31} +2.46681 q^{32} +1.46681 q^{33} -3.04892 q^{34} +13.4547 q^{35} -0.445042 q^{36} -4.55496 q^{37} +3.17092 q^{38} +8.54288 q^{40} +1.24698 q^{41} -5.98792 q^{42} +2.38404 q^{43} -0.652793 q^{44} -2.80194 q^{45} -4.38404 q^{46} +12.8170 q^{47} -2.91185 q^{48} +16.0586 q^{49} +3.55496 q^{50} -2.44504 q^{51} -8.85086 q^{53} +1.24698 q^{54} -4.10992 q^{55} +14.6407 q^{56} +2.54288 q^{57} +2.30798 q^{58} +2.17629 q^{59} +1.24698 q^{60} -7.82908 q^{61} -9.51573 q^{62} -4.80194 q^{63} +8.89977 q^{64} +1.82908 q^{66} -3.58211 q^{67} +1.08815 q^{68} -3.51573 q^{69} +16.7778 q^{70} -8.83877 q^{71} -3.04892 q^{72} -7.69202 q^{73} -5.67994 q^{74} +2.85086 q^{75} -1.13169 q^{76} -7.04354 q^{77} -4.02177 q^{79} +8.15883 q^{80} +1.00000 q^{81} +1.55496 q^{82} -0.652793 q^{83} +2.13706 q^{84} +6.85086 q^{85} +2.97285 q^{86} +1.85086 q^{87} -4.47219 q^{88} +6.29590 q^{89} -3.49396 q^{90} +1.56465 q^{92} -7.63102 q^{93} +15.9825 q^{94} -7.12498 q^{95} +2.46681 q^{96} -10.0315 q^{97} +20.0248 q^{98} +1.46681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{5} - q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) \) 3 * q - q^2 + 3 * q^3 - q^4 - 4 * q^5 - q^6 - 10 * q^7 + 3 * q^9	\( 3 q - q^{2} + 3 q^{3} - q^{4} - 4 q^{5} - q^{6} - 10 q^{7} + 3 q^{9} - q^{10} + q^{11} - q^{12} + q^{14} - 4 q^{15} - 5 q^{16} - 7 q^{17} - q^{18} - 11 q^{19} - q^{20} - 10 q^{21} - 5 q^{22} + 2 q^{23} - 5 q^{25} + 3 q^{27} + q^{28} - 8 q^{29} - q^{30} - 8 q^{31} + 4 q^{32} + q^{33} + 18 q^{35} - q^{36} - 14 q^{37} + 20 q^{38} + 7 q^{40} - q^{41} + q^{42} - 3 q^{43} + 16 q^{44} - 4 q^{45} - 3 q^{46} + 9 q^{47} - 5 q^{48} + 17 q^{49} + 11 q^{50} - 7 q^{51} - 13 q^{53} - q^{54} - 13 q^{55} + 7 q^{56} - 11 q^{57} + 12 q^{58} + 14 q^{59} - q^{60} - 13 q^{61} - 16 q^{62} - 10 q^{63} + 4 q^{64} - 5 q^{66} - 5 q^{67} + 7 q^{68} + 2 q^{69} + 8 q^{70} + 6 q^{71} - 18 q^{73} + 7 q^{74} - 5 q^{75} - q^{76} - 15 q^{77} - 9 q^{79} + 16 q^{80} + 3 q^{81} + 5 q^{82} + 16 q^{83} + q^{84} + 7 q^{85} + 15 q^{86} - 8 q^{87} - 7 q^{88} + 5 q^{89} - q^{90} - 17 q^{92} - 8 q^{93} + 32 q^{94} + 3 q^{95} + 4 q^{96} - 5 q^{97} + 13 q^{98} + q^{99}+O(q^{100}) \) 3 * q - q^2 + 3 * q^3 - q^4 - 4 * q^5 - q^6 - 10 * q^7 + 3 * q^9 - q^10 + q^11 - q^12 + q^14 - 4 * q^15 - 5 * q^16 - 7 * q^17 - q^18 - 11 * q^19 - q^20 - 10 * q^21 - 5 * q^22 + 2 * q^23 - 5 * q^25 + 3 * q^27 + q^28 - 8 * q^29 - q^30 - 8 * q^31 + 4 * q^32 + q^33 + 18 * q^35 - q^36 - 14 * q^37 + 20 * q^38 + 7 * q^40 - q^41 + q^42 - 3 * q^43 + 16 * q^44 - 4 * q^45 - 3 * q^46 + 9 * q^47 - 5 * q^48 + 17 * q^49 + 11 * q^50 - 7 * q^51 - 13 * q^53 - q^54 - 13 * q^55 + 7 * q^56 - 11 * q^57 + 12 * q^58 + 14 * q^59 - q^60 - 13 * q^61 - 16 * q^62 - 10 * q^63 + 4 * q^64 - 5 * q^66 - 5 * q^67 + 7 * q^68 + 2 * q^69 + 8 * q^70 + 6 * q^71 - 18 * q^73 + 7 * q^74 - 5 * q^75 - q^76 - 15 * q^77 - 9 * q^79 + 16 * q^80 + 3 * q^81 + 5 * q^82 + 16 * q^83 + q^84 + 7 * q^85 + 15 * q^86 - 8 * q^87 - 7 * q^88 + 5 * q^89 - q^90 - 17 * q^92 - 8 * q^93 + 32 * q^94 + 3 * q^95 + 4 * q^96 - 5 * q^97 + 13 * q^98 + q^99

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