LMFDB - Embedded newform 579.2.a.g.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [579,2,Mod(1,579)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(579, 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("579.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 579 = 3 \cdot 193 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	579.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:	$4.62333827703$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 20 x^{11} + 39 x^{10} + 148 x^{9} - 275 x^{8} - 508 x^{7} + 865 x^{6} + 823 x^{5} + \cdots - 48 $ x^13 - 2x^12 - 20x^11 + 39x^10 + 148x^9 - 275x^8 - 508x^7 + 865x^6 + 823x^5 - 1187x^4 - 556x^3 + 576x^2 + 64x - 48
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.294774$ of defining polynomial
Character	$\chi$	$=$	579.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.294774 q^{2} +1.00000 q^{3} -1.91311 q^{4} +0.386624 q^{5} +0.294774 q^{6} +2.95689 q^{7} -1.15348 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.294774 q^{2} +1.00000 q^{3} -1.91311 q^{4} +0.386624 q^{5} +0.294774 q^{6} +2.95689 q^{7} -1.15348 q^{8} +1.00000 q^{9} +0.113967 q^{10} -1.64913 q^{11} -1.91311 q^{12} +2.41755 q^{13} +0.871617 q^{14} +0.386624 q^{15} +3.48620 q^{16} +1.61931 q^{17} +0.294774 q^{18} +4.40371 q^{19} -0.739653 q^{20} +2.95689 q^{21} -0.486122 q^{22} +6.60080 q^{23} -1.15348 q^{24} -4.85052 q^{25} +0.712633 q^{26} +1.00000 q^{27} -5.65686 q^{28} -1.93504 q^{29} +0.113967 q^{30} -4.51636 q^{31} +3.33461 q^{32} -1.64913 q^{33} +0.477331 q^{34} +1.14321 q^{35} -1.91311 q^{36} +5.95105 q^{37} +1.29810 q^{38} +2.41755 q^{39} -0.445964 q^{40} +5.29889 q^{41} +0.871617 q^{42} +8.10944 q^{43} +3.15497 q^{44} +0.386624 q^{45} +1.94575 q^{46} +0.468667 q^{47} +3.48620 q^{48} +1.74322 q^{49} -1.42981 q^{50} +1.61931 q^{51} -4.62504 q^{52} -13.5817 q^{53} +0.294774 q^{54} -0.637594 q^{55} -3.41073 q^{56} +4.40371 q^{57} -0.570400 q^{58} -11.3947 q^{59} -0.739653 q^{60} +8.10307 q^{61} -1.33131 q^{62} +2.95689 q^{63} -5.98944 q^{64} +0.934684 q^{65} -0.486122 q^{66} -1.47560 q^{67} -3.09792 q^{68} +6.60080 q^{69} +0.336988 q^{70} -12.1544 q^{71} -1.15348 q^{72} +4.78747 q^{73} +1.75422 q^{74} -4.85052 q^{75} -8.42477 q^{76} -4.87631 q^{77} +0.712633 q^{78} -6.29813 q^{79} +1.34785 q^{80} +1.00000 q^{81} +1.56198 q^{82} -4.71520 q^{83} -5.65686 q^{84} +0.626064 q^{85} +2.39046 q^{86} -1.93504 q^{87} +1.90225 q^{88} -3.18967 q^{89} +0.113967 q^{90} +7.14845 q^{91} -12.6281 q^{92} -4.51636 q^{93} +0.138151 q^{94} +1.70258 q^{95} +3.33461 q^{96} +9.16299 q^{97} +0.513857 q^{98} -1.64913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9} - q^{10} + 3 q^{11} + 18 q^{12} + 11 q^{13} - 4 q^{14} + 6 q^{15} + 20 q^{16} - 2 q^{17} + 2 q^{18} + 9 q^{19} - 9 q^{20} + 15 q^{21} - 8 q^{22} - 8 q^{23} + 3 q^{24} + 21 q^{25} - 15 q^{26} + 13 q^{27} + 16 q^{28} + 5 q^{29} - q^{30} + 25 q^{31} - 17 q^{32} + 3 q^{33} - 10 q^{34} - 10 q^{35} + 18 q^{36} + 29 q^{37} - 40 q^{38} + 11 q^{39} - 21 q^{40} - 11 q^{41} - 4 q^{42} + 8 q^{43} - 18 q^{44} + 6 q^{45} - 6 q^{46} - 12 q^{47} + 20 q^{48} + 20 q^{49} - 4 q^{50} - 2 q^{51} + 2 q^{52} + 14 q^{53} + 2 q^{54} + 12 q^{55} - 7 q^{56} + 9 q^{57} + 9 q^{58} + 10 q^{59} - 9 q^{60} + 6 q^{61} - 14 q^{62} + 15 q^{63} + 23 q^{64} - 15 q^{65} - 8 q^{66} + 25 q^{67} - 33 q^{68} - 8 q^{69} - 21 q^{70} + 3 q^{72} + 8 q^{73} - 2 q^{74} + 21 q^{75} + 20 q^{76} - 25 q^{77} - 15 q^{78} + 7 q^{79} - 40 q^{80} + 13 q^{81} - 19 q^{82} - 28 q^{83} + 16 q^{84} - 3 q^{85} + 2 q^{86} + 5 q^{87} - 21 q^{88} + 7 q^{89} - q^{90} + 7 q^{91} + 9 q^{92} + 25 q^{93} - 35 q^{94} - 26 q^{95} - 17 q^{96} + 26 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9 - q^10 + 3 * q^11 + 18 * q^12 + 11 * q^13 - 4 * q^14 + 6 * q^15 + 20 * q^16 - 2 * q^17 + 2 * q^18 + 9 * q^19 - 9 * q^20 + 15 * q^21 - 8 * q^22 - 8 * q^23 + 3 * q^24 + 21 * q^25 - 15 * q^26 + 13 * q^27 + 16 * q^28 + 5 * q^29 - q^30 + 25 * q^31 - 17 * q^32 + 3 * q^33 - 10 * q^34 - 10 * q^35 + 18 * q^36 + 29 * q^37 - 40 * q^38 + 11 * q^39 - 21 * q^40 - 11 * q^41 - 4 * q^42 + 8 * q^43 - 18 * q^44 + 6 * q^45 - 6 * q^46 - 12 * q^47 + 20 * q^48 + 20 * q^49 - 4 * q^50 - 2 * q^51 + 2 * q^52 + 14 * q^53 + 2 * q^54 + 12 * q^55 - 7 * q^56 + 9 * q^57 + 9 * q^58 + 10 * q^59 - 9 * q^60 + 6 * q^61 - 14 * q^62 + 15 * q^63 + 23 * q^64 - 15 * q^65 - 8 * q^66 + 25 * q^67 - 33 * q^68 - 8 * q^69 - 21 * q^70 + 3 * q^72 + 8 * q^73 - 2 * q^74 + 21 * q^75 + 20 * q^76 - 25 * q^77 - 15 * q^78 + 7 * q^79 - 40 * q^80 + 13 * q^81 - 19 * q^82 - 28 * q^83 + 16 * q^84 - 3 * q^85 + 2 * q^86 + 5 * q^87 - 21 * q^88 + 7 * q^89 - q^90 + 7 * q^91 + 9 * q^92 + 25 * q^93 - 35 * q^94 - 26 * q^95 - 17 * q^96 + 26 * q^97 - 14 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.294774	0.208437	0.104218	−	0.994554i	$-0.466766\pi$
$2$	0.294774	0.208437	0.104218	+	0.994554i	$0.466766\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.91311	−0.956554
$5$	0.386624	0.172903	0.0864517	−	0.996256i	$-0.472447\pi$
$5$	0.386624	0.172903	0.0864517	+	0.996256i	$0.472447\pi$
$6$	0.294774	0.120341
$7$	2.95689	1.11760	0.558800	−	0.829302i	$-0.311262\pi$
$7$	2.95689	1.11760	0.558800	+	0.829302i	$0.311262\pi$
$8$	−1.15348	−0.407818
$9$	1.00000	0.333333
$10$	0.113967	0.0360395
$11$	−1.64913	−0.497232	−0.248616	−	0.968602i	$-0.579976\pi$
$11$	−1.64913	−0.497232	−0.248616	+	0.968602i	$0.579976\pi$
$12$	−1.91311	−0.552267
$13$	2.41755	0.670509	0.335254	−	0.942128i	$-0.391178\pi$
$13$	2.41755	0.670509	0.335254	+	0.942128i	$0.391178\pi$
$14$	0.871617	0.232949
$15$	0.386624	0.0998258
$16$	3.48620	0.871550
$17$	1.61931	0.392740	0.196370	−	0.980530i	$-0.437085\pi$
$17$	1.61931	0.392740	0.196370	+	0.980530i	$0.437085\pi$
$18$	0.294774	0.0694790
$19$	4.40371	1.01028	0.505140	−	0.863037i	$-0.331441\pi$
$19$	4.40371	1.01028	0.505140	+	0.863037i	$0.331441\pi$
$20$	−0.739653	−0.165391
$21$	2.95689	0.645247
$22$	−0.486122	−0.103642
$23$	6.60080	1.37636	0.688181	−	0.725539i	$-0.258409\pi$
$23$	6.60080	1.37636	0.688181	+	0.725539i	$0.258409\pi$
$24$	−1.15348	−0.235454
$25$	−4.85052	−0.970104
$26$	0.712633	0.139759
$27$	1.00000	0.192450
$28$	−5.65686	−1.06905
$29$	−1.93504	−0.359328	−0.179664	−	0.983728i	$-0.557501\pi$
$29$	−1.93504	−0.359328	−0.179664	+	0.983728i	$0.557501\pi$
$30$	0.113967	0.0208074
$31$	−4.51636	−0.811162	−0.405581	−	0.914059i	$-0.632931\pi$
$31$	−4.51636	−0.811162	−0.405581	+	0.914059i	$0.632931\pi$
$32$	3.33461	0.589481
$33$	−1.64913	−0.287077
$34$	0.477331	0.0818616
$35$	1.14321	0.193237
$36$	−1.91311	−0.318851
$37$	5.95105	0.978346	0.489173	−	0.872187i	$-0.337299\pi$
$37$	5.95105	0.978346	0.489173	+	0.872187i	$0.337299\pi$
$38$	1.29810	0.210580
$39$	2.41755	0.387118
$40$	−0.445964	−0.0705132
$41$	5.29889	0.827547	0.413774	−	0.910380i	$-0.364210\pi$
$41$	5.29889	0.827547	0.413774	+	0.910380i	$0.364210\pi$
$42$	0.871617	0.134493
$43$	8.10944	1.23668	0.618339	−	0.785912i	$-0.287806\pi$
$43$	8.10944	1.23668	0.618339	+	0.785912i	$0.287806\pi$
$44$	3.15497	0.475630
$45$	0.386624	0.0576345
$46$	1.94575	0.286885
$47$	0.468667	0.0683622	0.0341811	−	0.999416i	$-0.489118\pi$
$47$	0.468667	0.0683622	0.0341811	+	0.999416i	$0.489118\pi$
$48$	3.48620	0.503189
$49$	1.74322	0.249032
$50$	−1.42981	−0.202206
$51$	1.61931	0.226749
$52$	−4.62504	−0.641378
$53$	−13.5817	−1.86559	−0.932795	−	0.360408i	$-0.882638\pi$
$53$	−13.5817	−1.86559	−0.932795	+	0.360408i	$0.882638\pi$
$54$	0.294774	0.0401137
$55$	−0.637594	−0.0859732
$56$	−3.41073	−0.455778
$57$	4.40371	0.583285
$58$	−0.570400	−0.0748972
$59$	−11.3947	−1.48346	−0.741730	−	0.670699i	$-0.765994\pi$
$59$	−11.3947	−1.48346	−0.741730	+	0.670699i	$0.765994\pi$
$60$	−0.739653	−0.0954888
$61$	8.10307	1.03749	0.518746	−	0.854929i	$-0.326399\pi$
$61$	8.10307	1.03749	0.518746	+	0.854929i	$0.326399\pi$
$62$	−1.33131	−0.169076
$63$	2.95689	0.372534
$64$	−5.98944	−0.748680
$65$	0.934684	0.115933
$66$	−0.486122	−0.0598375
$67$	−1.47560	−0.180273	−0.0901366	−	0.995929i	$-0.528730\pi$
$67$	−1.47560	−0.180273	−0.0901366	+	0.995929i	$0.528730\pi$
$68$	−3.09792	−0.375677
$69$	6.60080	0.794643
$70$	0.336988	0.0402777
$71$	−12.1544	−1.44246	−0.721231	−	0.692695i	$-0.756423\pi$
$71$	−12.1544	−1.44246	−0.721231	+	0.692695i	$0.756423\pi$
$72$	−1.15348	−0.135939
$73$	4.78747	0.560331	0.280166	−	0.959952i	$-0.409611\pi$
$73$	4.78747	0.560331	0.280166	+	0.959952i	$0.409611\pi$
$74$	1.75422	0.203924
$75$	−4.85052	−0.560090
$76$	−8.42477	−0.966387
$77$	−4.87631	−0.555707
$78$	0.712633	0.0806898
$79$	−6.29813	−0.708595	−0.354298	−	0.935133i	$-0.615280\pi$
$79$	−6.29813	−0.708595	−0.354298	+	0.935133i	$0.615280\pi$
$80$	1.34785	0.150694
$81$	1.00000	0.111111
$82$	1.56198	0.172491
$83$	−4.71520	−0.517560	−0.258780	−	0.965936i	$-0.583321\pi$
$83$	−4.71520	−0.517560	−0.258780	+	0.965936i	$0.583321\pi$
$84$	−5.65686	−0.617214
$85$	0.626064	0.0679062
$86$	2.39046	0.257769
$87$	−1.93504	−0.207458
$88$	1.90225	0.202780
$89$	−3.18967	−0.338105	−0.169052	−	0.985607i	$-0.554071\pi$
$89$	−3.18967	−0.338105	−0.169052	+	0.985607i	$0.554071\pi$
$90$	0.113967	0.0120132
$91$	7.14845	0.749361
$92$	−12.6281	−1.31657
$93$	−4.51636	−0.468325
$94$	0.138151	0.0142492
$95$	1.70258	0.174681
$96$	3.33461	0.340337
$97$	9.16299	0.930360	0.465180	−	0.885216i	$-0.345990\pi$
$97$	9.16299	0.930360	0.465180	+	0.885216i	$0.345990\pi$
$98$	0.513857	0.0519074
$99$	−1.64913	−0.165744
$100$	9.27957	0.927957
$101$	−4.65337	−0.463028	−0.231514	−	0.972832i	$-0.574368\pi$
$101$	−4.65337	−0.463028	−0.231514	+	0.972832i	$0.574368\pi$
$102$	0.477331	0.0472628
$103$	−10.5042	−1.03501	−0.517505	−	0.855680i	$-0.673139\pi$
$103$	−10.5042	−1.03501	−0.517505	+	0.855680i	$0.673139\pi$
$104$	−2.78861	−0.273446
$105$	1.14321	0.111565
$106$	−4.00354	−0.388858
$107$	11.1723	1.08006	0.540031	−	0.841645i	$-0.318412\pi$
$107$	11.1723	1.08006	0.540031	+	0.841645i	$0.318412\pi$
$108$	−1.91311	−0.184089
$109$	−12.3271	−1.18072	−0.590360	−	0.807140i	$-0.701014\pi$
$109$	−12.3271	−1.18072	−0.590360	+	0.807140i	$0.701014\pi$
$110$	−0.187946	−0.0179200
$111$	5.95105	0.564848
$112$	10.3083	0.974045
$113$	−10.5371	−0.991244	−0.495622	−	0.868538i	$-0.665060\pi$
$113$	−10.5371	−0.991244	−0.495622	+	0.868538i	$0.665060\pi$
$114$	1.29810	0.121578
$115$	2.55203	0.237978
$116$	3.70194	0.343717
$117$	2.41755	0.223503
$118$	−3.35886	−0.309208
$119$	4.78813	0.438927
$120$	−0.445964	−0.0407108
$121$	−8.28036	−0.752760
$122$	2.38858	0.216252
$123$	5.29889	0.477785
$124$	8.64028	0.775920
$125$	−3.80845	−0.340638
$126$	0.871617	0.0776498
$127$	10.1860	0.903860	0.451930	−	0.892054i	$-0.350736\pi$
$127$	10.1860	0.903860	0.451930	+	0.892054i	$0.350736\pi$
$128$	−8.43475	−0.745534
$129$	8.10944	0.713996
$130$	0.275521	0.0241648
$131$	−14.0131	−1.22433	−0.612166	−	0.790729i	$-0.709702\pi$
$131$	−14.0131	−1.22433	−0.612166	+	0.790729i	$0.709702\pi$
$132$	3.15497	0.274605
$133$	13.0213	1.12909
$134$	−0.434969	−0.0375756
$135$	0.386624	0.0332753
$136$	−1.86785	−0.160167
$137$	−2.28952	−0.195607	−0.0978034	−	0.995206i	$-0.531182\pi$
$137$	−2.28952	−0.195607	−0.0978034	+	0.995206i	$0.531182\pi$
$138$	1.94575	0.165633
$139$	5.39959	0.457987	0.228994	−	0.973428i	$-0.426456\pi$
$139$	5.39959	0.457987	0.228994	+	0.973428i	$0.426456\pi$
$140$	−2.18708	−0.184842
$141$	0.468667	0.0394689
$142$	−3.58280	−0.300662
$143$	−3.98687	−0.333399
$144$	3.48620	0.290517
$145$	−0.748133	−0.0621290
$146$	1.41122	0.116794
$147$	1.74322	0.143779
$148$	−11.3850	−0.935841
$149$	−18.9607	−1.55332	−0.776660	−	0.629920i	$-0.783088\pi$
$149$	−18.9607	−1.55332	−0.776660	+	0.629920i	$0.783088\pi$
$150$	−1.42981	−0.116743
$151$	3.13560	0.255172	0.127586	−	0.991828i	$-0.459277\pi$
$151$	3.13560	0.255172	0.127586	+	0.991828i	$0.459277\pi$
$152$	−5.07961	−0.412011
$153$	1.61931	0.130913
$154$	−1.43741	−0.115830
$155$	−1.74613	−0.140253
$156$	−4.62504	−0.370300
$157$	−0.982994	−0.0784514	−0.0392257	−	0.999230i	$-0.512489\pi$
$157$	−0.982994	−0.0784514	−0.0392257	+	0.999230i	$0.512489\pi$
$158$	−1.85653	−0.147697
$159$	−13.5817	−1.07710
$160$	1.28924	0.101923
$161$	19.5179	1.53822
$162$	0.294774	0.0231597
$163$	9.07562	0.710858	0.355429	−	0.934703i	$-0.384335\pi$
$163$	9.07562	0.710858	0.355429	+	0.934703i	$0.384335\pi$
$164$	−10.1373	−0.791594
$165$	−0.637594	−0.0496366
$166$	−1.38992	−0.107879
$167$	8.80527	0.681372	0.340686	−	0.940177i	$-0.389341\pi$
$167$	8.80527	0.681372	0.340686	+	0.940177i	$0.389341\pi$
$168$	−3.41073	−0.263144
$169$	−7.15544	−0.550418
$170$	0.184548	0.0141542
$171$	4.40371	0.336760
$172$	−15.5142	−1.18295
$173$	10.4539	0.794797	0.397399	−	0.917646i	$-0.369913\pi$
$173$	10.4539	0.794797	0.397399	+	0.917646i	$0.369913\pi$
$174$	−0.570400	−0.0432419
$175$	−14.3425	−1.08419
$176$	−5.74921	−0.433363
$177$	−11.3947	−0.856476
$178$	−0.940234	−0.0704735
$179$	0.748038	0.0559110	0.0279555	−	0.999609i	$-0.491100\pi$
$179$	0.748038	0.0559110	0.0279555	+	0.999609i	$0.491100\pi$
$180$	−0.739653	−0.0551305
$181$	23.6329	1.75662	0.878312	−	0.478089i	$-0.158670\pi$
$181$	23.6329	1.75662	0.878312	+	0.478089i	$0.158670\pi$
$182$	2.10718	0.156195
$183$	8.10307	0.598996
$184$	−7.61392	−0.561306
$185$	2.30082	0.169159
$186$	−1.33131	−0.0976162
$187$	−2.67046	−0.195283
$188$	−0.896611	−0.0653921
$189$	2.95689	0.215082
$190$	0.501876	0.0364099
$191$	−2.29905	−0.166354	−0.0831768	−	0.996535i	$-0.526507\pi$
$191$	−2.29905	−0.166354	−0.0831768	+	0.996535i	$0.526507\pi$
$192$	−5.98944	−0.432251
$193$	−1.00000	−0.0719816
$193$	−1.00000	−0.0719816
$194$	2.70101	0.193921
$195$	0.934684	0.0669341
$196$	−3.33497	−0.238212
$197$	10.4443	0.744126	0.372063	−	0.928208i	$-0.378651\pi$
$197$	10.4443	0.744126	0.372063	+	0.928208i	$0.378651\pi$
$198$	−0.486122	−0.0345472
$199$	−22.2811	−1.57947	−0.789734	−	0.613450i	$-0.789781\pi$
$199$	−22.2811	−1.57947	−0.789734	+	0.613450i	$0.789781\pi$
$200$	5.59500	0.395626
$201$	−1.47560	−0.104081
$202$	−1.37170	−0.0965122
$203$	−5.72171	−0.401585
$204$	−3.09792	−0.216897
$205$	2.04868	0.143086
$206$	−3.09637	−0.215734
$207$	6.60080	0.458788
$208$	8.42807	0.584382
$209$	−7.26230	−0.502344
$210$	0.336988	0.0232544
$211$	−15.0302	−1.03473	−0.517363	−	0.855766i	$-0.673086\pi$
$211$	−15.0302	−1.03473	−0.517363	+	0.855766i	$0.673086\pi$
$212$	25.9833	1.78454
$213$	−12.1544	−0.832805
$214$	3.29329	0.225125
$215$	3.13530	0.213826
$216$	−1.15348	−0.0784847
$217$	−13.3544	−0.906556
$218$	−3.63371	−0.246106
$219$	4.78747	0.323507
$220$	1.21979	0.0822380
$221$	3.91477	0.263336
$222$	1.75422	0.117735
$223$	1.92583	0.128963	0.0644815	−	0.997919i	$-0.479461\pi$
$223$	1.92583	0.128963	0.0644815	+	0.997919i	$0.479461\pi$
$224$	9.86009	0.658805
$225$	−4.85052	−0.323368
$226$	−3.10606	−0.206612
$227$	15.3169	1.01662	0.508311	−	0.861174i	$-0.330270\pi$
$227$	15.3169	1.01662	0.508311	+	0.861174i	$0.330270\pi$
$228$	−8.42477	−0.557944
$229$	−8.99568	−0.594451	−0.297226	−	0.954807i	$-0.596061\pi$
$229$	−8.99568	−0.594451	−0.297226	+	0.954807i	$0.596061\pi$
$230$	0.752272	0.0496034
$231$	−4.87631	−0.320838
$232$	2.23204	0.146540
$233$	−9.57715	−0.627420	−0.313710	−	0.949519i	$-0.601572\pi$
$233$	−9.57715	−0.627420	−0.313710	+	0.949519i	$0.601572\pi$
$234$	0.712633	0.0465863
$235$	0.181198	0.0118200
$236$	21.7992	1.41901
$237$	−6.29813	−0.409108
$238$	1.41142	0.0914886
$239$	−9.43060	−0.610015	−0.305007	−	0.952350i	$-0.598659\pi$
$239$	−9.43060	−0.610015	−0.305007	+	0.952350i	$0.598659\pi$
$240$	1.34785	0.0870032
$241$	26.1794	1.68636	0.843181	−	0.537629i	$-0.180680\pi$
$241$	26.1794	1.68636	0.843181	+	0.537629i	$0.180680\pi$
$242$	−2.44084	−0.156903
$243$	1.00000	0.0641500
$244$	−15.5020	−0.992416
$245$	0.673971	0.0430584
$246$	1.56198	0.0995880
$247$	10.6462	0.677401
$248$	5.20955	0.330807
$249$	−4.71520	−0.298814
$250$	−1.12263	−0.0710015
$251$	−19.3074	−1.21868	−0.609338	−	0.792911i	$-0.708565\pi$
$251$	−19.3074	−1.21868	−0.609338	+	0.792911i	$0.708565\pi$
$252$	−5.65686	−0.356349
$253$	−10.8856	−0.684372
$254$	3.00257	0.188398
$255$	0.626064	0.0392056
$256$	9.49253	0.593283
$257$	26.4489	1.64984	0.824919	−	0.565251i	$-0.191221\pi$
$257$	26.4489	1.64984	0.824919	+	0.565251i	$0.191221\pi$
$258$	2.39046	0.148823
$259$	17.5966	1.09340
$260$	−1.78815	−0.110896
$261$	−1.93504	−0.119776
$262$	−4.13071	−0.255196
$263$	0.0522246	0.00322031	0.00161015	−	0.999999i	$-0.499487\pi$
$263$	0.0522246	0.00322031	0.00161015	+	0.999999i	$0.499487\pi$
$264$	1.90225	0.117075
$265$	−5.25101	−0.322567
$266$	3.83835	0.235344
$267$	−3.18967	−0.195205
$268$	2.82298	0.172441
$269$	28.9995	1.76813	0.884066	−	0.467363i	$-0.154796\pi$
$269$	28.9995	1.76813	0.884066	+	0.467363i	$0.154796\pi$
$270$	0.113967	0.00693580
$271$	9.97419	0.605889	0.302944	−	0.953008i	$-0.402030\pi$
$271$	9.97419	0.605889	0.302944	+	0.953008i	$0.402030\pi$
$272$	5.64524	0.342293
$273$	7.14845	0.432644
$274$	−0.674892	−0.0407717
$275$	7.99916	0.482367
$276$	−12.6281	−0.760119
$277$	30.8325	1.85254	0.926272	−	0.376856i	$-0.122995\pi$
$277$	30.8325	1.85254	0.926272	+	0.376856i	$0.122995\pi$
$278$	1.59166	0.0954615
$279$	−4.51636	−0.270387
$280$	−1.31867	−0.0788056
$281$	−24.7955	−1.47918	−0.739588	−	0.673060i	$-0.764980\pi$
$281$	−24.7955	−1.47918	−0.739588	+	0.673060i	$0.764980\pi$
$282$	0.138151	0.00822678
$283$	−11.5613	−0.687245	−0.343623	−	0.939108i	$-0.611654\pi$
$283$	−11.5613	−0.687245	−0.343623	+	0.939108i	$0.611654\pi$
$284$	23.2527	1.37979
$285$	1.70258	0.100852
$286$	−1.17523	−0.0694926
$287$	15.6683	0.924868
$288$	3.33461	0.196494
$289$	−14.3778	−0.845755
$290$	−0.220530	−0.0129500
$291$	9.16299	0.537144
$292$	−9.15895	−0.535987
$293$	−0.0556420	−0.00325064	−0.00162532	−	0.999999i	$-0.500517\pi$
$293$	−0.0556420	−0.00325064	−0.00162532	+	0.999999i	$0.500517\pi$
$294$	0.513857	0.0299688
$295$	−4.40545	−0.256495
$296$	−6.86444	−0.398987
$297$	−1.64913	−0.0956924
$298$	−5.58913	−0.323769
$299$	15.9578	0.922863
$300$	9.27957	0.535756
$301$	23.9788	1.38211
$302$	0.924295	0.0531872
$303$	−4.65337	−0.267329
$304$	15.3522	0.880509
$305$	3.13284	0.179386
$306$	0.477331	0.0272872
$307$	9.31741	0.531773	0.265886	−	0.964004i	$-0.414335\pi$
$307$	9.31741	0.531773	0.265886	+	0.964004i	$0.414335\pi$
$308$	9.32891	0.531564
$309$	−10.5042	−0.597563
$310$	−0.514715	−0.0292338
$311$	−10.4901	−0.594842	−0.297421	−	0.954746i	$-0.596126\pi$
$311$	−10.4901	−0.594842	−0.297421	+	0.954746i	$0.596126\pi$
$312$	−2.78861	−0.157874
$313$	5.09321	0.287885	0.143943	−	0.989586i	$-0.454022\pi$
$313$	5.09321	0.287885	0.143943	+	0.989586i	$0.454022\pi$
$314$	−0.289761	−0.0163522
$315$	1.14321	0.0644123
$316$	12.0490	0.677810
$317$	10.2012	0.572954	0.286477	−	0.958087i	$-0.407516\pi$
$317$	10.2012	0.572954	0.286477	+	0.958087i	$0.407516\pi$
$318$	−4.00354	−0.224507
$319$	3.19114	0.178669
$320$	−2.31566	−0.129449
$321$	11.1723	0.623574
$322$	5.75337	0.320623
$323$	7.13097	0.396778
$324$	−1.91311	−0.106284
$325$	−11.7264	−0.650463
$326$	2.67526	0.148169
$327$	−12.3271	−0.681689
$328$	−6.11218	−0.337489
$329$	1.38580	0.0764016
$330$	−0.187946	−0.0103461
$331$	−5.48496	−0.301481	−0.150740	−	0.988573i	$-0.548166\pi$
$331$	−5.48496	−0.301481	−0.150740	+	0.988573i	$0.548166\pi$
$332$	9.02069	0.495074
$333$	5.95105	0.326115
$334$	2.59557	0.142023
$335$	−0.570502	−0.0311698
$336$	10.3083	0.562365
$337$	19.6957	1.07289	0.536446	−	0.843935i	$-0.319767\pi$
$337$	19.6957	1.07289	0.536446	+	0.843935i	$0.319767\pi$
$338$	−2.10924	−0.114727
$339$	−10.5371	−0.572295
$340$	−1.19773	−0.0649559
$341$	7.44808	0.403336
$342$	1.29810	0.0701932
$343$	−15.5437	−0.839283
$344$	−9.35411	−0.504340
$345$	2.55203	0.137397
$346$	3.08155	0.165665
$347$	−19.5450	−1.04923	−0.524614	−	0.851340i	$-0.675790\pi$
$347$	−19.5450	−1.04923	−0.524614	+	0.851340i	$0.675790\pi$
$348$	3.70194	0.198445
$349$	16.5795	0.887481	0.443741	−	0.896155i	$-0.353651\pi$
$349$	16.5795	0.887481	0.443741	+	0.896155i	$0.353651\pi$
$350$	−4.22780	−0.225985
$351$	2.41755	0.129039
$352$	−5.49922	−0.293109
$353$	10.8463	0.577293	0.288646	−	0.957436i	$-0.406795\pi$
$353$	10.8463	0.577293	0.288646	+	0.957436i	$0.406795\pi$
$354$	−3.35886	−0.178521
$355$	−4.69918	−0.249406
$356$	6.10219	0.323415
$357$	4.78813	0.253415
$358$	0.220502	0.0116539
$359$	10.9324	0.576989	0.288495	−	0.957482i	$-0.406845\pi$
$359$	10.9324	0.576989	0.288495	+	0.957482i	$0.406845\pi$
$360$	−0.445964	−0.0235044
$361$	0.392642	0.0206654
$362$	6.96639	0.366145
$363$	−8.28036	−0.434606
$364$	−13.6758	−0.716804
$365$	1.85095	0.0968832
$366$	2.38858	0.124853
$367$	−23.1751	−1.20973	−0.604866	−	0.796327i	$-0.706773\pi$
$367$	−23.1751	−1.20973	−0.604866	+	0.796327i	$0.706773\pi$
$368$	23.0117	1.19957
$369$	5.29889	0.275849
$370$	0.678222	0.0352591
$371$	−40.1596	−2.08498
$372$	8.64028	0.447978
$373$	14.1209	0.731152	0.365576	−	0.930781i	$-0.380872\pi$
$373$	14.1209	0.731152	0.365576	+	0.930781i	$0.380872\pi$
$374$	−0.787183	−0.0407042
$375$	−3.80845	−0.196667
$376$	−0.540600	−0.0278793
$377$	−4.67806	−0.240933
$378$	0.871617	0.0448311
$379$	−4.66154	−0.239447	−0.119724	−	0.992807i	$-0.538201\pi$
$379$	−4.66154	−0.239447	−0.119724	+	0.992807i	$0.538201\pi$
$380$	−3.25722	−0.167092
$381$	10.1860	0.521844
$382$	−0.677702	−0.0346743
$383$	−31.0020	−1.58413	−0.792064	−	0.610439i	$-0.790993\pi$
$383$	−31.0020	−1.58413	−0.792064	+	0.610439i	$0.790993\pi$
$384$	−8.43475	−0.430434
$385$	−1.88530	−0.0960837
$386$	−0.294774	−0.0150036
$387$	8.10944	0.412226
$388$	−17.5298	−0.889940
$389$	36.4992	1.85058	0.925292	−	0.379256i	$-0.123820\pi$
$389$	36.4992	1.85058	0.925292	+	0.379256i	$0.123820\pi$
$390$	0.275521	0.0139515
$391$	10.6888	0.540553
$392$	−2.01078	−0.101560
$393$	−14.0131	−0.706869
$394$	3.07871	0.155103
$395$	−2.43501	−0.122519
$396$	3.15497	0.158543
$397$	−6.45524	−0.323979	−0.161990	−	0.986792i	$-0.551791\pi$
$397$	−6.45524	−0.323979	−0.161990	+	0.986792i	$0.551791\pi$
$398$	−6.56791	−0.329219
$399$	13.0213	0.651880
$400$	−16.9099	−0.845494
$401$	26.8631	1.34148	0.670739	−	0.741694i	$-0.265977\pi$
$401$	26.8631	1.34148	0.670739	+	0.741694i	$0.265977\pi$
$402$	−0.434969	−0.0216943
$403$	−10.9185	−0.543891
$404$	8.90241	0.442911
$405$	0.386624	0.0192115
$406$	−1.68661	−0.0837052
$407$	−9.81407	−0.486465
$408$	−1.86785	−0.0924723
$409$	−26.6585	−1.31818	−0.659090	−	0.752064i	$-0.729058\pi$
$409$	−26.6585	−1.31818	−0.659090	+	0.752064i	$0.729058\pi$
$410$	0.603897	0.0298244
$411$	−2.28952	−0.112934
$412$	20.0957	0.990043
$413$	−33.6928	−1.65792
$414$	1.94575	0.0956283
$415$	−1.82301	−0.0894880
$416$	8.06160	0.395252
$417$	5.39959	0.264419
$418$	−2.14074	−0.104707
$419$	−15.4930	−0.756881	−0.378440	−	0.925626i	$-0.623539\pi$
$419$	−15.4930	−0.756881	−0.378440	+	0.925626i	$0.623539\pi$
$420$	−2.18708	−0.106718
$421$	12.3456	0.601688	0.300844	−	0.953673i	$-0.402732\pi$
$421$	12.3456	0.601688	0.300844	+	0.953673i	$0.402732\pi$
$422$	−4.43053	−0.215675
$423$	0.468667	0.0227874
$424$	15.6663	0.760822
$425$	−7.85450	−0.380999
$426$	−3.58280	−0.173587
$427$	23.9599	1.15950
$428$	−21.3737	−1.03314
$429$	−3.98687	−0.192488
$430$	0.924207	0.0445692
$431$	−33.5269	−1.61494	−0.807468	−	0.589912i	$-0.799163\pi$
$431$	−33.5269	−1.61494	−0.807468	+	0.589912i	$0.799163\pi$
$432$	3.48620	0.167730
$433$	−37.4726	−1.80082	−0.900409	−	0.435045i	$-0.856732\pi$
$433$	−37.4726	−1.80082	−0.900409	+	0.435045i	$0.856732\pi$
$434$	−3.93653	−0.188960
$435$	−0.748133	−0.0358702
$436$	23.5830	1.12942
$437$	29.0680	1.39051
$438$	1.41122	0.0674309
$439$	25.1610	1.20087	0.600433	−	0.799675i	$-0.294995\pi$
$439$	25.1610	1.20087	0.600433	+	0.799675i	$0.294995\pi$
$440$	0.735455	0.0350614
$441$	1.74322	0.0830106
$442$	1.15397	0.0548889
$443$	−5.63898	−0.267916	−0.133958	−	0.990987i	$-0.542769\pi$
$443$	−5.63898	−0.267916	−0.133958	+	0.990987i	$0.542769\pi$
$444$	−11.3850	−0.540308
$445$	−1.23320	−0.0584595
$446$	0.567685	0.0268807
$447$	−18.9607	−0.896810
$448$	−17.7101	−0.836725
$449$	28.6396	1.35158	0.675792	−	0.737092i	$-0.263802\pi$
$449$	28.6396	1.35158	0.675792	+	0.737092i	$0.263802\pi$
$450$	−1.42981	−0.0674019
$451$	−8.73857	−0.411483
$452$	20.1586	0.948179
$453$	3.13560	0.147323
$454$	4.51504	0.211901
$455$	2.76376	0.129567
$456$	−5.07961	−0.237874
$457$	−2.45744	−0.114954	−0.0574771	−	0.998347i	$-0.518306\pi$
$457$	−2.45744	−0.114954	−0.0574771	+	0.998347i	$0.518306\pi$
$458$	−2.65170	−0.123906
$459$	1.61931	0.0755829
$460$	−4.88230	−0.227639
$461$	29.5424	1.37593	0.687964	−	0.725744i	$-0.258505\pi$
$461$	29.5424	1.37593	0.687964	+	0.725744i	$0.258505\pi$
$462$	−1.43741	−0.0668745
$463$	−17.9373	−0.833616	−0.416808	−	0.908995i	$-0.636851\pi$
$463$	−17.9373	−0.833616	−0.416808	+	0.908995i	$0.636851\pi$
$464$	−6.74593	−0.313172
$465$	−1.74613	−0.0809749
$466$	−2.82310	−0.130777
$467$	−1.62765	−0.0753189	−0.0376594	−	0.999291i	$-0.511990\pi$
$467$	−1.62765	−0.0753189	−0.0376594	+	0.999291i	$0.511990\pi$
$468$	−4.62504	−0.213793
$469$	−4.36319	−0.201473
$470$	0.0534125	0.00246374
$471$	−0.982994	−0.0452939
$472$	13.1436	0.604982
$473$	−13.3735	−0.614916
$474$	−1.85653	−0.0852732
$475$	−21.3603	−0.980077
$476$	−9.16021	−0.419857
$477$	−13.5817	−0.621863
$478$	−2.77990	−0.127150
$479$	1.13852	0.0520205	0.0260103	−	0.999662i	$-0.491720\pi$
$479$	1.13852	0.0520205	0.0260103	+	0.999662i	$0.491720\pi$
$480$	1.28924	0.0588455
$481$	14.3870	0.655990
$482$	7.71701	0.351500
$483$	19.5179	0.888094
$484$	15.8412	0.720056
$485$	3.54263	0.160862
$486$	0.294774	0.0133712
$487$	−22.2904	−1.01007	−0.505037	−	0.863098i	$-0.668521\pi$
$487$	−22.2904	−1.01007	−0.505037	+	0.863098i	$0.668521\pi$
$488$	−9.34676	−0.423108
$489$	9.07562	0.410414
$490$	0.198669	0.00897497
$491$	0.713701	0.0322089	0.0161044	−	0.999870i	$-0.494874\pi$
$491$	0.713701	0.0322089	0.0161044	+	0.999870i	$0.494874\pi$
$492$	−10.1373	−0.457027
$493$	−3.13343	−0.141123
$494$	3.13823	0.141195
$495$	−0.637594	−0.0286577
$496$	−15.7449	−0.706968
$497$	−35.9393	−1.61210
$498$	−1.38992	−0.0622838
$499$	−22.5329	−1.00871	−0.504355	−	0.863496i	$-0.668270\pi$
$499$	−22.5329	−1.00871	−0.504355	+	0.863496i	$0.668270\pi$
$500$	7.28597	0.325838
$501$	8.80527	0.393390
$502$	−5.69134	−0.254017
$503$	9.57917	0.427114	0.213557	−	0.976931i	$-0.431495\pi$
$503$	9.57917	0.427114	0.213557	+	0.976931i	$0.431495\pi$
$504$	−3.41073	−0.151926
$505$	−1.79910	−0.0800591
$506$	−3.20880	−0.142648
$507$	−7.15544	−0.317784
$508$	−19.4869	−0.864590
$509$	−11.3671	−0.503837	−0.251918	−	0.967748i	$-0.581061\pi$
$509$	−11.3671	−0.503837	−0.251918	+	0.967748i	$0.581061\pi$
$510$	0.184548	0.00817191
$511$	14.1560	0.626227
$512$	19.6677	0.869196
$513$	4.40371	0.194428
$514$	7.79646	0.343887
$515$	−4.06117	−0.178957
$516$	−15.5142	−0.682976
$517$	−0.772895	−0.0339919
$518$	5.18703	0.227905
$519$	10.4539	0.458877
$520$	−1.07814	−0.0472797
$521$	−32.2592	−1.41330	−0.706650	−	0.707564i	$-0.749794\pi$
$521$	−32.2592	−1.41330	−0.706650	+	0.707564i	$0.749794\pi$
$522$	−0.570400	−0.0249657
$523$	−19.6194	−0.857898	−0.428949	−	0.903329i	$-0.641116\pi$
$523$	−19.6194	−0.857898	−0.428949	+	0.903329i	$0.641116\pi$
$524$	26.8086	1.17114
$525$	−14.3425	−0.625957
$526$	0.0153945	0.000671232 0
$527$	−7.31339	−0.318576
$528$	−5.74921	−0.250202
$529$	20.5706	0.894374
$530$	−1.54786	−0.0672349
$531$	−11.3947	−0.494487
$532$	−24.9111	−1.08004
$533$	12.8103	0.554878
$534$	−0.940234	−0.0406879
$535$	4.31946	0.186747
$536$	1.70208	0.0735187
$537$	0.748038	0.0322802
$538$	8.54831	0.368544
$539$	−2.87481	−0.123827
$540$	−0.739653	−0.0318296
$541$	−35.0884	−1.50857	−0.754283	−	0.656549i	$-0.772015\pi$
$541$	−35.0884	−1.50857	−0.754283	+	0.656549i	$0.772015\pi$
$542$	2.94014	0.126290
$543$	23.6329	1.01419
$544$	5.39977	0.231513
$545$	−4.76594	−0.204150
$546$	2.10718	0.0901790
$547$	−22.1329	−0.946335	−0.473167	−	0.880972i	$-0.656889\pi$
$547$	−22.1329	−0.946335	−0.473167	+	0.880972i	$0.656889\pi$
$548$	4.38010	0.187109
$549$	8.10307	0.345830
$550$	2.35795	0.100543
$551$	−8.52135	−0.363022
$552$	−7.61392	−0.324070
$553$	−18.6229	−0.791927
$554$	9.08862	0.386139
$555$	2.30082	0.0976642
$556$	−10.3300	−0.438090
$557$	24.9672	1.05789	0.528947	−	0.848655i	$-0.322587\pi$
$557$	24.9672	1.05789	0.528947	+	0.848655i	$0.322587\pi$
$558$	−1.33131	−0.0563587
$559$	19.6050	0.829203
$560$	3.98544	0.168416
$561$	−2.67046	−0.112747
$562$	−7.30908	−0.308315
$563$	35.1548	1.48160	0.740800	−	0.671726i	$-0.234447\pi$
$563$	35.1548	1.48160	0.740800	+	0.671726i	$0.234447\pi$
$564$	−0.896611	−0.0377541
$565$	−4.07388	−0.171390
$566$	−3.40796	−0.143247
$567$	2.95689	0.124178
$568$	14.0199	0.588262
$569$	10.2789	0.430914	0.215457	−	0.976513i	$-0.430876\pi$
$569$	10.2789	0.430914	0.215457	+	0.976513i	$0.430876\pi$
$570$	0.501876	0.0210213
$571$	−3.31684	−0.138805	−0.0694027	−	0.997589i	$-0.522109\pi$
$571$	−3.31684	−0.138805	−0.0694027	+	0.997589i	$0.522109\pi$
$572$	7.62731	0.318914
$573$	−2.29905	−0.0960443
$574$	4.61860	0.192777
$575$	−32.0173	−1.33522
$576$	−5.98944	−0.249560
$577$	−40.5837	−1.68952	−0.844761	−	0.535143i	$-0.820258\pi$
$577$	−40.5837	−1.68952	−0.844761	+	0.535143i	$0.820258\pi$
$578$	−4.23822	−0.176287
$579$	−1.00000	−0.0415586
$580$	1.43126	0.0594298
$581$	−13.9423	−0.578426
$582$	2.70101	0.111961
$583$	22.3980	0.927632
$584$	−5.52227	−0.228513
$585$	0.934684	0.0386444
$586$	−0.0164018	−0.000677553 0
$587$	2.51455	0.103786	0.0518932	−	0.998653i	$-0.483474\pi$
$587$	2.51455	0.103786	0.0518932	+	0.998653i	$0.483474\pi$
$588$	−3.33497	−0.137532
$589$	−19.8887	−0.819501
$590$	−1.29861	−0.0534631
$591$	10.4443	0.429621
$592$	20.7465	0.852677
$593$	15.1643	0.622725	0.311362	−	0.950291i	$-0.399215\pi$
$593$	15.1643	0.622725	0.311362	+	0.950291i	$0.399215\pi$
$594$	−0.486122	−0.0199458
$595$	1.85120	0.0758920
$596$	36.2739	1.48584
$597$	−22.2811	−0.911906
$598$	4.70395	0.192359
$599$	25.4874	1.04139	0.520693	−	0.853744i	$-0.325674\pi$
$599$	25.4874	1.04139	0.520693	+	0.853744i	$0.325674\pi$
$600$	5.59500	0.228415
$601$	8.83051	0.360204	0.180102	−	0.983648i	$-0.442357\pi$
$601$	8.83051	0.360204	0.180102	+	0.983648i	$0.442357\pi$
$602$	7.06832	0.288083
$603$	−1.47560	−0.0600910
$604$	−5.99874	−0.244085
$605$	−3.20138	−0.130155
$606$	−1.37170	−0.0557213
$607$	34.5555	1.40256	0.701282	−	0.712884i	$-0.252611\pi$
$607$	34.5555	1.40256	0.701282	+	0.712884i	$0.252611\pi$
$608$	14.6846	0.595541
$609$	−5.72171	−0.231855
$610$	0.923480	0.0373906
$611$	1.13303	0.0458374
$612$	−3.09792	−0.125226
$613$	−10.9389	−0.441816	−0.220908	−	0.975295i	$-0.570902\pi$
$613$	−10.9389	−0.441816	−0.220908	+	0.975295i	$0.570902\pi$
$614$	2.74653	0.110841
$615$	2.04868	0.0826106
$616$	5.62475	0.226628
$617$	−10.4100	−0.419092	−0.209546	−	0.977799i	$-0.567199\pi$
$617$	−10.4100	−0.419092	−0.209546	+	0.977799i	$0.567199\pi$
$618$	−3.09637	−0.124554
$619$	−17.3083	−0.695679	−0.347840	−	0.937554i	$-0.613085\pi$
$619$	−17.3083	−0.695679	−0.347840	+	0.937554i	$0.613085\pi$
$620$	3.34054	0.134159
$621$	6.60080	0.264881
$622$	−3.09223	−0.123987
$623$	−9.43153	−0.377866
$624$	8.42807	0.337393
$625$	22.7802	0.911207
$626$	1.50135	0.0600059
$627$	−7.26230	−0.290028
$628$	1.88057	0.0750430
$629$	9.63659	0.384236
$630$	0.336988	0.0134259
$631$	18.8163	0.749065	0.374533	−	0.927214i	$-0.377803\pi$
$631$	18.8163	0.749065	0.374533	+	0.927214i	$0.377803\pi$
$632$	7.26480	0.288978
$633$	−15.0302	−0.597399
$634$	3.00704	0.119425
$635$	3.93814	0.156280
$636$	25.9833	1.03030
$637$	4.21433	0.166978
$638$	0.940666	0.0372413
$639$	−12.1544	−0.480820
$640$	−3.26108	−0.128905
$641$	−1.48842	−0.0587889	−0.0293945	−	0.999568i	$-0.509358\pi$
$641$	−1.48842	−0.0587889	−0.0293945	+	0.999568i	$0.509358\pi$
$642$	3.29329	0.129976
$643$	−12.0794	−0.476364	−0.238182	−	0.971221i	$-0.576551\pi$
$643$	−12.0794	−0.476364	−0.238182	+	0.971221i	$0.576551\pi$
$644$	−37.3398	−1.47139
$645$	3.13530	0.123452
$646$	2.10203	0.0827032
$647$	−14.9732	−0.588659	−0.294329	−	0.955704i	$-0.595096\pi$
$647$	−14.9732	−0.588659	−0.294329	+	0.955704i	$0.595096\pi$
$648$	−1.15348	−0.0453131
$649$	18.7913	0.737624
$650$	−3.45664	−0.135581
$651$	−13.3544	−0.523400
$652$	−17.3627	−0.679974
$653$	−42.5269	−1.66421	−0.832103	−	0.554621i	$-0.812863\pi$
$653$	−42.5269	−1.66421	−0.832103	+	0.554621i	$0.812863\pi$
$654$	−3.63371	−0.142089
$655$	−5.41781	−0.211691
$656$	18.4730	0.721249
$657$	4.78747	0.186777
$658$	0.408498	0.0159249
$659$	−43.1340	−1.68026	−0.840130	−	0.542384i	$-0.817522\pi$
$659$	−43.1340	−1.68026	−0.840130	+	0.542384i	$0.817522\pi$
$660$	1.21979	0.0474801
$661$	−8.21019	−0.319339	−0.159670	−	0.987170i	$-0.551043\pi$
$661$	−8.21019	−0.319339	−0.159670	+	0.987170i	$0.551043\pi$
$662$	−1.61683	−0.0628397
$663$	3.91477	0.152037
$664$	5.43891	0.211071
$665$	5.03434	0.195223
$666$	1.75422	0.0679745
$667$	−12.7728	−0.494566
$668$	−16.8454	−0.651769
$669$	1.92583	0.0744568
$670$	−0.168169	−0.00649695
$671$	−13.3630	−0.515874
$672$	9.86009	0.380361
$673$	2.96230	0.114188	0.0570941	−	0.998369i	$-0.481816\pi$
$673$	2.96230	0.114188	0.0570941	+	0.998369i	$0.481816\pi$
$674$	5.80578	0.223630
$675$	−4.85052	−0.186697
$676$	13.6891	0.526505
$677$	25.5130	0.980546	0.490273	−	0.871569i	$-0.336897\pi$
$677$	25.5130	0.980546	0.490273	+	0.871569i	$0.336897\pi$
$678$	−3.10606	−0.119287
$679$	27.0940	1.03977
$680$	−0.722155	−0.0276934
$681$	15.3169	0.586947
$682$	2.19550	0.0840702
$683$	−13.1682	−0.503868	−0.251934	−	0.967744i	$-0.581067\pi$
$683$	−13.1682	−0.503868	−0.251934	+	0.967744i	$0.581067\pi$
$684$	−8.42477	−0.322129
$685$	−0.885183	−0.0338211
$686$	−4.58190	−0.174938
$687$	−8.99568	−0.343207
$688$	28.2711	1.07783
$689$	−32.8345	−1.25089
$690$	0.752272	0.0286385
$691$	−13.9444	−0.530469	−0.265235	−	0.964184i	$-0.585449\pi$
$691$	−13.9444	−0.530469	−0.265235	+	0.964184i	$0.585449\pi$
$692$	−19.9995	−0.760267
$693$	−4.87631	−0.185236
$694$	−5.76135	−0.218698
$695$	2.08761	0.0791876
$696$	2.23204	0.0846052
$697$	8.58055	0.325011
$698$	4.88722	0.184984
$699$	−9.57715	−0.362241
$700$	27.4387	1.03709
$701$	18.4080	0.695261	0.347630	−	0.937632i	$-0.386986\pi$
$701$	18.4080	0.695261	0.347630	+	0.937632i	$0.386986\pi$
$702$	0.712633	0.0268966
$703$	26.2067	0.988404
$704$	9.87738	0.372268
$705$	0.181198	0.00682431
$706$	3.19722	0.120329
$707$	−13.7595	−0.517480
$708$	21.7992	0.819265
$709$	−19.5435	−0.733973	−0.366987	−	0.930226i	$-0.619611\pi$
$709$	−19.5435	−0.733973	−0.366987	+	0.930226i	$0.619611\pi$
$710$	−1.38520	−0.0519855
$711$	−6.29813	−0.236198
$712$	3.67924	0.137885
$713$	−29.8116	−1.11645
$714$	1.41142	0.0528210
$715$	−1.54142	−0.0576457
$716$	−1.43108	−0.0534819
$717$	−9.43060	−0.352192
$718$	3.22259	0.120266
$719$	−41.7189	−1.55585	−0.777926	−	0.628356i	$-0.783728\pi$
$719$	−41.7189	−1.55585	−0.777926	+	0.628356i	$0.783728\pi$
$720$	1.34785	0.0502313
$721$	−31.0598	−1.15673
$722$	0.115741	0.00430743
$723$	26.1794	0.973622
$724$	−45.2124	−1.68031
$725$	9.38596	0.348586
$726$	−2.44084	−0.0905880
$727$	−36.7985	−1.36478	−0.682391	−	0.730988i	$-0.739060\pi$
$727$	−36.7985	−1.36478	−0.682391	+	0.730988i	$0.739060\pi$
$728$	−8.24562	−0.305603
$729$	1.00000	0.0370370
$730$	0.545613	0.0201940
$731$	13.1317	0.485693
$732$	−15.5020	−0.572972
$733$	14.2467	0.526214	0.263107	−	0.964767i	$-0.415253\pi$
$733$	14.2467	0.526214	0.263107	+	0.964767i	$0.415253\pi$
$734$	−6.83144	−0.252153
$735$	0.673971	0.0248598
$736$	22.0111	0.811340
$737$	2.43346	0.0896376
$738$	1.56198	0.0574972
$739$	−5.54835	−0.204099	−0.102050	−	0.994779i	$-0.532540\pi$
$739$	−5.54835	−0.204099	−0.102050	+	0.994779i	$0.532540\pi$
$740$	−4.40171	−0.161810
$741$	10.6462	0.391098
$742$	−11.8380	−0.434588
$743$	−25.0698	−0.919721	−0.459860	−	0.887991i	$-0.652101\pi$
$743$	−25.0698	−0.919721	−0.459860	+	0.887991i	$0.652101\pi$
$744$	5.20955	0.190991
$745$	−7.33065	−0.268574
$746$	4.16248	0.152399
$747$	−4.71520	−0.172520
$748$	5.10888	0.186799
$749$	33.0352	1.20708
$750$	−1.12263	−0.0409927
$751$	8.14507	0.297218	0.148609	−	0.988896i	$-0.452520\pi$
$751$	8.14507	0.297218	0.148609	+	0.988896i	$0.452520\pi$
$752$	1.63387	0.0595810
$753$	−19.3074	−0.703602
$754$	−1.37897	−0.0502192
$755$	1.21230	0.0441200
$756$	−5.65686	−0.205738
$757$	−46.9170	−1.70523	−0.852614	−	0.522541i	$-0.824984\pi$
$757$	−46.9170	−1.70523	−0.852614	+	0.522541i	$0.824984\pi$
$758$	−1.37410	−0.0499096
$759$	−10.8856	−0.395122
$760$	−1.96390	−0.0712380
$761$	8.37311	0.303525	0.151763	−	0.988417i	$-0.451505\pi$
$761$	8.37311	0.303525	0.151763	+	0.988417i	$0.451505\pi$
$762$	3.00257	0.108771
$763$	−36.4499	−1.31957
$764$	4.39834	0.159126
$765$	0.626064	0.0226354
$766$	−9.13859	−0.330191
$767$	−27.5472	−0.994673
$768$	9.49253	0.342532
$769$	−2.79625	−0.100836	−0.0504178	−	0.998728i	$-0.516055\pi$
$769$	−2.79625	−0.100836	−0.0504178	+	0.998728i	$0.516055\pi$
$770$	−0.555738	−0.0200274
$771$	26.4489	0.952534
$772$	1.91311	0.0688543
$773$	−24.9660	−0.897964	−0.448982	−	0.893541i	$-0.648213\pi$
$773$	−24.9660	−0.897964	−0.448982	+	0.893541i	$0.648213\pi$
$774$	2.39046	0.0859231
$775$	21.9067	0.786912
$776$	−10.5694	−0.379418
$777$	17.5966	0.631275
$778$	10.7590	0.385730
$779$	23.3348	0.836054
$780$	−1.78815	−0.0640261
$781$	20.0442	0.717238
$782$	3.15077	0.112671
$783$	−1.93504	−0.0691527
$784$	6.07722	0.217044
$785$	−0.380049	−0.0135645
$786$	−4.13071	−0.147338
$787$	31.1004	1.10861	0.554305	−	0.832314i	$-0.312984\pi$
$787$	31.1004	1.10861	0.554305	+	0.832314i	$0.312984\pi$
$788$	−19.9811	−0.711797
$789$	0.0522246	0.00185925
$790$	−0.717778	−0.0255374
$791$	−31.1570	−1.10782
$792$	1.90225	0.0675935
$793$	19.5896	0.695647
$794$	−1.90284	−0.0675292
$795$	−5.25101	−0.186234
$796$	42.6262	1.51085
$797$	32.9709	1.16789	0.583945	−	0.811793i	$-0.301509\pi$
$797$	32.9709	1.16789	0.583945	+	0.811793i	$0.301509\pi$
$798$	3.83835	0.135876
$799$	0.758918	0.0268486
$800$	−16.1746	−0.571858
$801$	−3.18967	−0.112702
$802$	7.91854	0.279613
$803$	−7.89518	−0.278615
$804$	2.82298	0.0995589
$805$	7.54608	0.265964
$806$	−3.21851	−0.113367
$807$	28.9995	1.02083
$808$	5.36759	0.188831
$809$	11.3949	0.400624	0.200312	−	0.979732i	$-0.435804\pi$
$809$	11.3949	0.400624	0.200312	+	0.979732i	$0.435804\pi$
$810$	0.113967	0.00400438
$811$	38.4944	1.35172	0.675861	−	0.737029i	$-0.263772\pi$
$811$	38.4944	1.35172	0.675861	+	0.737029i	$0.263772\pi$
$812$	10.9462	0.384138
$813$	9.97419	0.349810
$814$	−2.89294	−0.101397
$815$	3.50885	0.122910
$816$	5.64524	0.197623
$817$	35.7116	1.24939
$818$	−7.85825	−0.274757
$819$	7.14845	0.249787
$820$	−3.91934	−0.136869
$821$	33.2875	1.16174	0.580871	−	0.813995i	$-0.302712\pi$
$821$	33.2875	1.16174	0.580871	+	0.813995i	$0.302712\pi$
$822$	−0.674892	−0.0235396
$823$	36.1651	1.26064	0.630318	−	0.776337i	$-0.282925\pi$
$823$	36.1651	1.26064	0.630318	+	0.776337i	$0.282925\pi$
$824$	12.1164	0.422096
$825$	7.99916	0.278495
$826$	−9.93178	−0.345571
$827$	−15.3233	−0.532844	−0.266422	−	0.963856i	$-0.585841\pi$
$827$	−15.3233	−0.532844	−0.266422	+	0.963856i	$0.585841\pi$
$828$	−12.6281	−0.438855
$829$	38.9987	1.35448	0.677241	−	0.735761i	$-0.263175\pi$
$829$	38.9987	1.35448	0.677241	+	0.735761i	$0.263175\pi$
$830$	−0.537376	−0.0186526
$831$	30.8325	1.06957
$832$	−14.4798	−0.501996
$833$	2.82282	0.0978049
$834$	1.59166	0.0551147
$835$	3.40433	0.117812
$836$	13.8936	0.480519
$837$	−4.51636	−0.156108
$838$	−4.56693	−0.157762
$839$	41.0475	1.41712	0.708558	−	0.705652i	$-0.249346\pi$
$839$	41.0475	1.41712	0.708558	+	0.705652i	$0.249346\pi$
$840$	−1.31867	−0.0454984
$841$	−25.2556	−0.870883
$842$	3.63917	0.125414
$843$	−24.7955	−0.854003
$844$	28.7545	0.989770
$845$	−2.76646	−0.0951692
$846$	0.138151	0.00474973
$847$	−24.4841	−0.841285
$848$	−47.3485	−1.62595
$849$	−11.5613	−0.396781
$850$	−2.31531	−0.0794143
$851$	39.2817	1.34656
$852$	23.2527	0.796623
$853$	−6.76197	−0.231525	−0.115763	−	0.993277i	$-0.536931\pi$
$853$	−6.76197	−0.231525	−0.115763	+	0.993277i	$0.536931\pi$
$854$	7.06277	0.241683
$855$	1.70258	0.0582269
$856$	−12.8870	−0.440469
$857$	−54.8218	−1.87268	−0.936338	−	0.351101i	$-0.885808\pi$
$857$	−54.8218	−1.87268	−0.936338	+	0.351101i	$0.885808\pi$
$858$	−1.17523	−0.0401216
$859$	23.1196	0.788832	0.394416	−	0.918932i	$-0.370947\pi$
$859$	23.1196	0.788832	0.394416	+	0.918932i	$0.370947\pi$
$860$	−5.99817	−0.204536
$861$	15.6683	0.533973
$862$	−9.88288	−0.336612
$863$	56.7469	1.93169	0.965843	−	0.259129i	$-0.0834353\pi$
$863$	56.7469	1.93169	0.965843	+	0.259129i	$0.0834353\pi$
$864$	3.33461	0.113446
$865$	4.04174	0.137423
$866$	−11.0460	−0.375357
$867$	−14.3778	−0.488297
$868$	25.5484	0.867169
$869$	10.3865	0.352337
$870$	−0.220530	−0.00747668
$871$	−3.56734	−0.120875
$872$	14.2191	0.481519
$873$	9.16299	0.310120
$874$	8.56851	0.289834
$875$	−11.2612	−0.380697
$876$	−9.15895	−0.309452
$877$	49.6547	1.67672	0.838361	−	0.545116i	$-0.183514\pi$
$877$	49.6547	1.67672	0.838361	+	0.545116i	$0.183514\pi$
$878$	7.41681	0.250305
$879$	−0.0556420	−0.00187676
$880$	−2.22278	−0.0749299
$881$	49.7113	1.67481	0.837407	−	0.546579i	$-0.184070\pi$
$881$	49.7113	1.67481	0.837407	+	0.546579i	$0.184070\pi$
$882$	0.513857	0.0173025
$883$	25.4170	0.855350	0.427675	−	0.903933i	$-0.359333\pi$
$883$	25.4170	0.855350	0.427675	+	0.903933i	$0.359333\pi$
$884$	−7.48938	−0.251895
$885$	−4.40545	−0.148088
$886$	−1.66223	−0.0558436
$887$	−23.7582	−0.797722	−0.398861	−	0.917011i	$-0.630594\pi$
$887$	−23.7582	−0.797722	−0.398861	+	0.917011i	$0.630594\pi$
$888$	−6.86444	−0.230355
$889$	30.1189	1.01015
$890$	−0.363517	−0.0121851
$891$	−1.64913	−0.0552480
$892$	−3.68432	−0.123360
$893$	2.06387	0.0690649
$894$	−5.58913	−0.186928
$895$	0.289209	0.00966720
$896$	−24.9407	−0.833209
$897$	15.9578	0.532815
$898$	8.44221	0.281720
$899$	8.73934	0.291473
$900$	9.27957	0.309319
$901$	−21.9930	−0.732693
$902$	−2.57591	−0.0857683
$903$	23.9788	0.797963
$904$	12.1543	0.404248
$905$	9.13706	0.303726
$906$	0.924295	0.0307076
$907$	28.6444	0.951122	0.475561	−	0.879683i	$-0.342245\pi$
$907$	28.6444	0.951122	0.475561	+	0.879683i	$0.342245\pi$
$908$	−29.3030	−0.972453
$909$	−4.65337	−0.154343
$910$	0.814686	0.0270066
$911$	10.5213	0.348587	0.174294	−	0.984694i	$-0.444236\pi$
$911$	10.5213	0.348587	0.174294	+	0.984694i	$0.444236\pi$
$912$	15.3522	0.508362
$913$	7.77599	0.257348
$914$	−0.724391	−0.0239607
$915$	3.13284	0.103568
$916$	17.2097	0.568625
$917$	−41.4353	−1.36831
$918$	0.477331	0.0157543
$919$	−25.6911	−0.847472	−0.423736	−	0.905786i	$-0.639282\pi$
$919$	−25.6911	−0.847472	−0.423736	+	0.905786i	$0.639282\pi$
$920$	−2.94372	−0.0970517
$921$	9.31741	0.307019
$922$	8.70836	0.286794
$923$	−29.3839	−0.967183
$924$	9.32891	0.306899
$925$	−28.8657	−0.949098
$926$	−5.28745	−0.173756
$927$	−10.5042	−0.345003
$928$	−6.45261	−0.211817
$929$	−0.526368	−0.0172696	−0.00863479	−	0.999963i	$-0.502749\pi$
$929$	−0.526368	−0.0172696	−0.00863479	+	0.999963i	$0.502749\pi$
$930$	−0.514715	−0.0168782
$931$	7.67664	0.251592
$932$	18.3221	0.600161
$933$	−10.4901	−0.343432
$934$	−0.479791	−0.0156992
$935$	−1.03246	−0.0337651
$936$	−2.78861	−0.0911485
$937$	13.3213	0.435189	0.217595	−	0.976039i	$-0.430179\pi$
$937$	13.3213	0.435189	0.217595	+	0.976039i	$0.430179\pi$
$938$	−1.28616	−0.0419945
$939$	5.09321	0.166211
$940$	−0.346651	−0.0113065
$941$	10.8935	0.355118	0.177559	−	0.984110i	$-0.443180\pi$
$941$	10.8935	0.355118	0.177559	+	0.984110i	$0.443180\pi$
$942$	−0.289761	−0.00944093
$943$	34.9769	1.13901
$944$	−39.7241	−1.29291
$945$	1.14321	0.0371885
$946$	−3.94218	−0.128171
$947$	−14.8853	−0.483708	−0.241854	−	0.970313i	$-0.577756\pi$
$947$	−14.8853	−0.483708	−0.241854	+	0.970313i	$0.577756\pi$
$948$	12.0490	0.391334
$949$	11.5740	0.375707
$950$	−6.29646	−0.204284
$951$	10.2012	0.330795
$952$	−5.52303	−0.179002
$953$	50.4649	1.63472	0.817359	−	0.576129i	$-0.195437\pi$
$953$	50.4649	1.63472	0.817359	+	0.576129i	$0.195437\pi$
$954$	−4.00354	−0.129619
$955$	−0.888869	−0.0287631
$956$	18.0417	0.583512
$957$	3.19114	0.103155
$958$	0.335608	0.0108430
$959$	−6.76987	−0.218610
$960$	−2.31566	−0.0747376
$961$	−10.6025	−0.342016
$962$	4.24091	0.136733
$963$	11.1723	0.360021
$964$	−50.0840	−1.61310
$965$	−0.386624	−0.0124459
$966$	5.75337	0.185112
$967$	−12.1726	−0.391444	−0.195722	−	0.980659i	$-0.562705\pi$
$967$	−12.1726	−0.391444	−0.195722	+	0.980659i	$0.562705\pi$
$968$	9.55126	0.306989
$969$	7.13097	0.229080
$970$	1.04428	0.0335297
$971$	8.88819	0.285235	0.142618	−	0.989778i	$-0.454448\pi$
$971$	8.88819	0.285235	0.142618	+	0.989778i	$0.454448\pi$
$972$	−1.91311	−0.0613630
$973$	15.9660	0.511847
$974$	−6.57063	−0.210537
$975$	−11.7264	−0.375545
$976$	28.2489	0.904225
$977$	31.0236	0.992533	0.496266	−	0.868170i	$-0.334704\pi$
$977$	31.0236	0.992533	0.496266	+	0.868170i	$0.334704\pi$
$978$	2.67526	0.0855454
$979$	5.26020	0.168117
$980$	−1.28938	−0.0411877
$981$	−12.3271	−0.393573
$982$	0.210381	0.00671352
$983$	10.8807	0.347039	0.173520	−	0.984830i	$-0.444486\pi$
$983$	10.8807	0.347039	0.173520	+	0.984830i	$0.444486\pi$
$984$	−6.11218	−0.194849
$985$	4.03802	0.128662
$986$	−0.923655	−0.0294152
$987$	1.38580	0.0441105
$988$	−20.3673	−0.647971
$989$	53.5288	1.70212
$990$	−0.187946	−0.00597333
$991$	30.8501	0.979987	0.489994	−	0.871726i	$-0.336999\pi$
$991$	30.8501	0.979987	0.489994	+	0.871726i	$0.336999\pi$
$992$	−15.0603	−0.478165
$993$	−5.48496	−0.174060
$994$	−10.5940	−0.336020
$995$	−8.61441	−0.273095
$996$	9.02069	0.285831
$997$	25.6836	0.813407	0.406704	−	0.913560i	$-0.366678\pi$
$997$	25.6836	0.813407	0.406704	+	0.913560i	$0.366678\pi$
$998$	−6.64212	−0.210253
$999$	5.95105	0.188283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	579.2.a.g.1.7	✓	13
3.2	odd	2		1737.2.a.j.1.7		13
4.3	odd	2		9264.2.a.bp.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
579.2.a.g.1.7	✓	13	1.1	even	1	trivial
1737.2.a.j.1.7		13	3.2	odd	2
9264.2.a.bp.1.7		13	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:	\( N \)	\(=\)	\( 579 = 3 \cdot 193 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	579.a (trivial)

\(f(q)\)	\(=\)	\(q+0.294774 q^{2} +1.00000 q^{3} -1.91311 q^{4} +0.386624 q^{5} +0.294774 q^{6} +2.95689 q^{7} -1.15348 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.294774 q^{2} +1.00000 q^{3} -1.91311 q^{4} +0.386624 q^{5} +0.294774 q^{6} +2.95689 q^{7} -1.15348 q^{8} +1.00000 q^{9} +0.113967 q^{10} -1.64913 q^{11} -1.91311 q^{12} +2.41755 q^{13} +0.871617 q^{14} +0.386624 q^{15} +3.48620 q^{16} +1.61931 q^{17} +0.294774 q^{18} +4.40371 q^{19} -0.739653 q^{20} +2.95689 q^{21} -0.486122 q^{22} +6.60080 q^{23} -1.15348 q^{24} -4.85052 q^{25} +0.712633 q^{26} +1.00000 q^{27} -5.65686 q^{28} -1.93504 q^{29} +0.113967 q^{30} -4.51636 q^{31} +3.33461 q^{32} -1.64913 q^{33} +0.477331 q^{34} +1.14321 q^{35} -1.91311 q^{36} +5.95105 q^{37} +1.29810 q^{38} +2.41755 q^{39} -0.445964 q^{40} +5.29889 q^{41} +0.871617 q^{42} +8.10944 q^{43} +3.15497 q^{44} +0.386624 q^{45} +1.94575 q^{46} +0.468667 q^{47} +3.48620 q^{48} +1.74322 q^{49} -1.42981 q^{50} +1.61931 q^{51} -4.62504 q^{52} -13.5817 q^{53} +0.294774 q^{54} -0.637594 q^{55} -3.41073 q^{56} +4.40371 q^{57} -0.570400 q^{58} -11.3947 q^{59} -0.739653 q^{60} +8.10307 q^{61} -1.33131 q^{62} +2.95689 q^{63} -5.98944 q^{64} +0.934684 q^{65} -0.486122 q^{66} -1.47560 q^{67} -3.09792 q^{68} +6.60080 q^{69} +0.336988 q^{70} -12.1544 q^{71} -1.15348 q^{72} +4.78747 q^{73} +1.75422 q^{74} -4.85052 q^{75} -8.42477 q^{76} -4.87631 q^{77} +0.712633 q^{78} -6.29813 q^{79} +1.34785 q^{80} +1.00000 q^{81} +1.56198 q^{82} -4.71520 q^{83} -5.65686 q^{84} +0.626064 q^{85} +2.39046 q^{86} -1.93504 q^{87} +1.90225 q^{88} -3.18967 q^{89} +0.113967 q^{90} +7.14845 q^{91} -12.6281 q^{92} -4.51636 q^{93} +0.138151 q^{94} +1.70258 q^{95} +3.33461 q^{96} +9.16299 q^{97} +0.513857 q^{98} -1.64913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} + 13 q^{3} + 18 q^{4} + 6 q^{5} + 2 q^{6} + 15 q^{7} + 3 q^{8} + 13 q^{9} - q^{10} + 3 q^{11} + 18 q^{12} + 11 q^{13} - 4 q^{14} + 6 q^{15} + 20 q^{16} - 2 q^{17} + 2 q^{18} + 9 q^{19} - 9 q^{20} + 15 q^{21} - 8 q^{22} - 8 q^{23} + 3 q^{24} + 21 q^{25} - 15 q^{26} + 13 q^{27} + 16 q^{28} + 5 q^{29} - q^{30} + 25 q^{31} - 17 q^{32} + 3 q^{33} - 10 q^{34} - 10 q^{35} + 18 q^{36} + 29 q^{37} - 40 q^{38} + 11 q^{39} - 21 q^{40} - 11 q^{41} - 4 q^{42} + 8 q^{43} - 18 q^{44} + 6 q^{45} - 6 q^{46} - 12 q^{47} + 20 q^{48} + 20 q^{49} - 4 q^{50} - 2 q^{51} + 2 q^{52} + 14 q^{53} + 2 q^{54} + 12 q^{55} - 7 q^{56} + 9 q^{57} + 9 q^{58} + 10 q^{59} - 9 q^{60} + 6 q^{61} - 14 q^{62} + 15 q^{63} + 23 q^{64} - 15 q^{65} - 8 q^{66} + 25 q^{67} - 33 q^{68} - 8 q^{69} - 21 q^{70} + 3 q^{72} + 8 q^{73} - 2 q^{74} + 21 q^{75} + 20 q^{76} - 25 q^{77} - 15 q^{78} + 7 q^{79} - 40 q^{80} + 13 q^{81} - 19 q^{82} - 28 q^{83} + 16 q^{84} - 3 q^{85} + 2 q^{86} + 5 q^{87} - 21 q^{88} + 7 q^{89} - q^{90} + 7 q^{91} + 9 q^{92} + 25 q^{93} - 35 q^{94} - 26 q^{95} - 17 q^{96} + 26 q^{97} - 14 q^{98} + 3 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 + 13 * q^3 + 18 * q^4 + 6 * q^5 + 2 * q^6 + 15 * q^7 + 3 * q^8 + 13 * q^9 - q^10 + 3 * q^11 + 18 * q^12 + 11 * q^13 - 4 * q^14 + 6 * q^15 + 20 * q^16 - 2 * q^17 + 2 * q^18 + 9 * q^19 - 9 * q^20 + 15 * q^21 - 8 * q^22 - 8 * q^23 + 3 * q^24 + 21 * q^25 - 15 * q^26 + 13 * q^27 + 16 * q^28 + 5 * q^29 - q^30 + 25 * q^31 - 17 * q^32 + 3 * q^33 - 10 * q^34 - 10 * q^35 + 18 * q^36 + 29 * q^37 - 40 * q^38 + 11 * q^39 - 21 * q^40 - 11 * q^41 - 4 * q^42 + 8 * q^43 - 18 * q^44 + 6 * q^45 - 6 * q^46 - 12 * q^47 + 20 * q^48 + 20 * q^49 - 4 * q^50 - 2 * q^51 + 2 * q^52 + 14 * q^53 + 2 * q^54 + 12 * q^55 - 7 * q^56 + 9 * q^57 + 9 * q^58 + 10 * q^59 - 9 * q^60 + 6 * q^61 - 14 * q^62 + 15 * q^63 + 23 * q^64 - 15 * q^65 - 8 * q^66 + 25 * q^67 - 33 * q^68 - 8 * q^69 - 21 * q^70 + 3 * q^72 + 8 * q^73 - 2 * q^74 + 21 * q^75 + 20 * q^76 - 25 * q^77 - 15 * q^78 + 7 * q^79 - 40 * q^80 + 13 * q^81 - 19 * q^82 - 28 * q^83 + 16 * q^84 - 3 * q^85 + 2 * q^86 + 5 * q^87 - 21 * q^88 + 7 * q^89 - q^90 + 7 * q^91 + 9 * q^92 + 25 * q^93 - 35 * q^94 - 26 * q^95 - 17 * q^96 + 26 * q^97 - 14 * q^98 + 3 * q^99

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