LMFDB - Embedded newform 8030.2.a.be.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 3 x^{14} - 24 x^{13} + 64 x^{12} + 237 x^{11} - 524 x^{10} - 1225 x^{9} + 2074 x^{8} + \cdots - 52 $ x^15 - 3x^14 - 24x^13 + 64x^12 + 237x^11 - 524x^10 - 1225x^9 + 2074x^8 + 3463x^7 - 4142x^6 - 5157x^5 + 3892x^4 + 3622x^3 - 1239x^2 - 907x - 52
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.37460$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.37460 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.37460 q^{6} -1.30659 q^{7} -1.00000 q^{8} +2.63872 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.37460 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.37460 q^{6} -1.30659 q^{7} -1.00000 q^{8} +2.63872 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.37460 q^{12} -0.938943 q^{13} +1.30659 q^{14} -2.37460 q^{15} +1.00000 q^{16} +2.96742 q^{17} -2.63872 q^{18} -4.61666 q^{19} +1.00000 q^{20} +3.10262 q^{21} +1.00000 q^{22} -7.47513 q^{23} +2.37460 q^{24} +1.00000 q^{25} +0.938943 q^{26} +0.857899 q^{27} -1.30659 q^{28} -7.77522 q^{29} +2.37460 q^{30} -10.4500 q^{31} -1.00000 q^{32} +2.37460 q^{33} -2.96742 q^{34} -1.30659 q^{35} +2.63872 q^{36} +3.94005 q^{37} +4.61666 q^{38} +2.22961 q^{39} -1.00000 q^{40} -0.261267 q^{41} -3.10262 q^{42} +12.8184 q^{43} -1.00000 q^{44} +2.63872 q^{45} +7.47513 q^{46} -9.23125 q^{47} -2.37460 q^{48} -5.29283 q^{49} -1.00000 q^{50} -7.04643 q^{51} -0.938943 q^{52} -2.88070 q^{53} -0.857899 q^{54} -1.00000 q^{55} +1.30659 q^{56} +10.9627 q^{57} +7.77522 q^{58} -1.14900 q^{59} -2.37460 q^{60} +6.27310 q^{61} +10.4500 q^{62} -3.44771 q^{63} +1.00000 q^{64} -0.938943 q^{65} -2.37460 q^{66} -0.178097 q^{67} +2.96742 q^{68} +17.7504 q^{69} +1.30659 q^{70} +14.8326 q^{71} -2.63872 q^{72} -1.00000 q^{73} -3.94005 q^{74} -2.37460 q^{75} -4.61666 q^{76} +1.30659 q^{77} -2.22961 q^{78} -13.7485 q^{79} +1.00000 q^{80} -9.95332 q^{81} +0.261267 q^{82} -14.1434 q^{83} +3.10262 q^{84} +2.96742 q^{85} -12.8184 q^{86} +18.4630 q^{87} +1.00000 q^{88} -5.15145 q^{89} -2.63872 q^{90} +1.22681 q^{91} -7.47513 q^{92} +24.8146 q^{93} +9.23125 q^{94} -4.61666 q^{95} +2.37460 q^{96} +4.39877 q^{97} +5.29283 q^{98} -2.63872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9	\( 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9} - 15 q^{10} - 15 q^{11} + 3 q^{12} + 13 q^{13} - 7 q^{14} + 3 q^{15} + 15 q^{16} + 20 q^{17} - 12 q^{18} + 3 q^{19} + 15 q^{20} + 22 q^{21} + 15 q^{22} + 2 q^{23} - 3 q^{24} + 15 q^{25} - 13 q^{26} + 33 q^{27} + 7 q^{28} + 11 q^{29} - 3 q^{30} - 3 q^{31} - 15 q^{32} - 3 q^{33} - 20 q^{34} + 7 q^{35} + 12 q^{36} + 9 q^{37} - 3 q^{38} + 11 q^{39} - 15 q^{40} + 17 q^{41} - 22 q^{42} + 29 q^{43} - 15 q^{44} + 12 q^{45} - 2 q^{46} - 2 q^{47} + 3 q^{48} + 20 q^{49} - 15 q^{50} + 7 q^{51} + 13 q^{52} + 3 q^{53} - 33 q^{54} - 15 q^{55} - 7 q^{56} + 13 q^{57} - 11 q^{58} - 32 q^{59} + 3 q^{60} + 61 q^{61} + 3 q^{62} + 20 q^{63} + 15 q^{64} + 13 q^{65} + 3 q^{66} + 7 q^{67} + 20 q^{68} - 23 q^{69} - 7 q^{70} - 6 q^{71} - 12 q^{72} - 15 q^{73} - 9 q^{74} + 3 q^{75} + 3 q^{76} - 7 q^{77} - 11 q^{78} + 12 q^{79} + 15 q^{80} + 3 q^{81} - 17 q^{82} + 17 q^{83} + 22 q^{84} + 20 q^{85} - 29 q^{86} + 23 q^{87} + 15 q^{88} - 18 q^{89} - 12 q^{90} - 15 q^{91} + 2 q^{92} + 32 q^{93} + 2 q^{94} + 3 q^{95} - 3 q^{96} + 36 q^{97} - 20 q^{98} - 12 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9 - 15 * q^10 - 15 * q^11 + 3 * q^12 + 13 * q^13 - 7 * q^14 + 3 * q^15 + 15 * q^16 + 20 * q^17 - 12 * q^18 + 3 * q^19 + 15 * q^20 + 22 * q^21 + 15 * q^22 + 2 * q^23 - 3 * q^24 + 15 * q^25 - 13 * q^26 + 33 * q^27 + 7 * q^28 + 11 * q^29 - 3 * q^30 - 3 * q^31 - 15 * q^32 - 3 * q^33 - 20 * q^34 + 7 * q^35 + 12 * q^36 + 9 * q^37 - 3 * q^38 + 11 * q^39 - 15 * q^40 + 17 * q^41 - 22 * q^42 + 29 * q^43 - 15 * q^44 + 12 * q^45 - 2 * q^46 - 2 * q^47 + 3 * q^48 + 20 * q^49 - 15 * q^50 + 7 * q^51 + 13 * q^52 + 3 * q^53 - 33 * q^54 - 15 * q^55 - 7 * q^56 + 13 * q^57 - 11 * q^58 - 32 * q^59 + 3 * q^60 + 61 * q^61 + 3 * q^62 + 20 * q^63 + 15 * q^64 + 13 * q^65 + 3 * q^66 + 7 * q^67 + 20 * q^68 - 23 * q^69 - 7 * q^70 - 6 * q^71 - 12 * q^72 - 15 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 - 7 * q^77 - 11 * q^78 + 12 * q^79 + 15 * q^80 + 3 * q^81 - 17 * q^82 + 17 * q^83 + 22 * q^84 + 20 * q^85 - 29 * q^86 + 23 * q^87 + 15 * q^88 - 18 * q^89 - 12 * q^90 - 15 * q^91 + 2 * q^92 + 32 * q^93 + 2 * q^94 + 3 * q^95 - 3 * q^96 + 36 * q^97 - 20 * q^98 - 12 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.37460	−1.37098	−0.685488	−	0.728084i	$-0.740411\pi$
$3$	−2.37460	−1.37098	−0.685488	+	0.728084i	$0.740411\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.37460	0.969426
$7$	−1.30659	−0.493843	−0.246922	−	0.969035i	$-0.579419\pi$
$7$	−1.30659	−0.493843	−0.246922	+	0.969035i	$0.579419\pi$
$8$	−1.00000	−0.353553
$9$	2.63872	0.879573
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.37460	−0.685488
$13$	−0.938943	−0.260416	−0.130208	−	0.991487i	$-0.541564\pi$
$13$	−0.938943	−0.260416	−0.130208	+	0.991487i	$0.541564\pi$
$14$	1.30659	0.349200
$15$	−2.37460	−0.613119
$16$	1.00000	0.250000
$17$	2.96742	0.719705	0.359853	−	0.933009i	$-0.382827\pi$
$17$	2.96742	0.719705	0.359853	+	0.933009i	$0.382827\pi$
$18$	−2.63872	−0.621952
$19$	−4.61666	−1.05914	−0.529568	−	0.848268i	$-0.677646\pi$
$19$	−4.61666	−1.05914	−0.529568	+	0.848268i	$0.677646\pi$
$20$	1.00000	0.223607
$21$	3.10262	0.677047
$22$	1.00000	0.213201
$23$	−7.47513	−1.55867	−0.779336	−	0.626606i	$-0.784443\pi$
$23$	−7.47513	−1.55867	−0.779336	+	0.626606i	$0.784443\pi$
$24$	2.37460	0.484713
$25$	1.00000	0.200000
$26$	0.938943	0.184142
$27$	0.857899	0.165103
$28$	−1.30659	−0.246922
$29$	−7.77522	−1.44382	−0.721911	−	0.691986i	$-0.756736\pi$
$29$	−7.77522	−1.44382	−0.721911	+	0.691986i	$0.756736\pi$
$30$	2.37460	0.433540
$31$	−10.4500	−1.87688	−0.938439	−	0.345444i	$-0.887728\pi$
$31$	−10.4500	−1.87688	−0.938439	+	0.345444i	$0.887728\pi$
$32$	−1.00000	−0.176777
$33$	2.37460	0.413365
$34$	−2.96742	−0.508908
$35$	−1.30659	−0.220853
$36$	2.63872	0.439786
$37$	3.94005	0.647740	0.323870	−	0.946102i	$-0.395016\pi$
$37$	3.94005	0.647740	0.323870	+	0.946102i	$0.395016\pi$
$38$	4.61666	0.748922
$39$	2.22961	0.357024
$40$	−1.00000	−0.158114
$41$	−0.261267	−0.0408030	−0.0204015	−	0.999792i	$-0.506494\pi$
$41$	−0.261267	−0.0408030	−0.0204015	+	0.999792i	$0.506494\pi$
$42$	−3.10262	−0.478744
$43$	12.8184	1.95479	0.977397	−	0.211411i	$-0.0678058\pi$
$43$	12.8184	1.95479	0.977397	+	0.211411i	$0.0678058\pi$
$44$	−1.00000	−0.150756
$45$	2.63872	0.393357
$46$	7.47513	1.10215
$47$	−9.23125	−1.34652	−0.673258	−	0.739408i	$-0.735106\pi$
$47$	−9.23125	−1.34652	−0.673258	+	0.739408i	$0.735106\pi$
$48$	−2.37460	−0.342744
$49$	−5.29283	−0.756119
$50$	−1.00000	−0.141421
$51$	−7.04643	−0.986698
$52$	−0.938943	−0.130208
$53$	−2.88070	−0.395694	−0.197847	−	0.980233i	$-0.563395\pi$
$53$	−2.88070	−0.395694	−0.197847	+	0.980233i	$0.563395\pi$
$54$	−0.857899	−0.116745
$55$	−1.00000	−0.134840
$56$	1.30659	0.174600
$57$	10.9627	1.45205
$58$	7.77522	1.02094
$59$	−1.14900	−0.149587	−0.0747934	−	0.997199i	$-0.523830\pi$
$59$	−1.14900	−0.149587	−0.0747934	+	0.997199i	$0.523830\pi$
$60$	−2.37460	−0.306559
$61$	6.27310	0.803189	0.401594	−	0.915818i	$-0.368456\pi$
$61$	6.27310	0.803189	0.401594	+	0.915818i	$0.368456\pi$
$62$	10.4500	1.32715
$63$	−3.44771	−0.434371
$64$	1.00000	0.125000
$65$	−0.938943	−0.116462
$66$	−2.37460	−0.292293
$67$	−0.178097	−0.0217580	−0.0108790	−	0.999941i	$-0.503463\pi$
$67$	−0.178097	−0.0217580	−0.0108790	+	0.999941i	$0.503463\pi$
$68$	2.96742	0.359853
$69$	17.7504	2.13690
$70$	1.30659	0.156167
$71$	14.8326	1.76031	0.880153	−	0.474690i	$-0.157440\pi$
$71$	14.8326	1.76031	0.880153	+	0.474690i	$0.157440\pi$
$72$	−2.63872	−0.310976
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−3.94005	−0.458021
$75$	−2.37460	−0.274195
$76$	−4.61666	−0.529568
$77$	1.30659	0.148899
$78$	−2.22961	−0.252454
$79$	−13.7485	−1.54683	−0.773416	−	0.633899i	$-0.781454\pi$
$79$	−13.7485	−1.54683	−0.773416	+	0.633899i	$0.781454\pi$
$80$	1.00000	0.111803
$81$	−9.95332	−1.10592
$82$	0.261267	0.0288521
$83$	−14.1434	−1.55244	−0.776220	−	0.630463i	$-0.782865\pi$
$83$	−14.1434	−1.55244	−0.776220	+	0.630463i	$0.782865\pi$
$84$	3.10262	0.338523
$85$	2.96742	0.321862
$86$	−12.8184	−1.38225
$87$	18.4630	1.97944
$88$	1.00000	0.106600
$89$	−5.15145	−0.546053	−0.273026	−	0.962007i	$-0.588025\pi$
$89$	−5.15145	−0.546053	−0.273026	+	0.962007i	$0.588025\pi$
$90$	−2.63872	−0.278145
$91$	1.22681	0.128605
$92$	−7.47513	−0.779336
$93$	24.8146	2.57315
$94$	9.23125	0.952130
$95$	−4.61666	−0.473660
$96$	2.37460	0.242356
$97$	4.39877	0.446627	0.223314	−	0.974747i	$-0.428313\pi$
$97$	4.39877	0.446627	0.223314	+	0.974747i	$0.428313\pi$
$98$	5.29283	0.534657
$99$	−2.63872	−0.265201
$100$	1.00000	0.100000
$101$	−0.140352	−0.0139656	−0.00698278	−	0.999976i	$-0.502223\pi$
$101$	−0.140352	−0.0139656	−0.00698278	+	0.999976i	$0.502223\pi$
$102$	7.04643	0.697701
$103$	16.3371	1.60974	0.804872	−	0.593449i	$-0.202234\pi$
$103$	16.3371	1.60974	0.804872	+	0.593449i	$0.202234\pi$
$104$	0.938943	0.0920709
$105$	3.10262	0.302785
$106$	2.88070	0.279798
$107$	−2.04128	−0.197338	−0.0986688	−	0.995120i	$-0.531458\pi$
$107$	−2.04128	−0.197338	−0.0986688	+	0.995120i	$0.531458\pi$
$108$	0.857899	0.0825514
$109$	−17.5308	−1.67914	−0.839572	−	0.543248i	$-0.817194\pi$
$109$	−17.5308	−1.67914	−0.839572	+	0.543248i	$0.817194\pi$
$110$	1.00000	0.0953463
$111$	−9.35603	−0.888035
$112$	−1.30659	−0.123461
$113$	5.91460	0.556399	0.278199	−	0.960523i	$-0.410262\pi$
$113$	5.91460	0.556399	0.278199	+	0.960523i	$0.410262\pi$
$114$	−10.9627	−1.02675
$115$	−7.47513	−0.697059
$116$	−7.77522	−0.721911
$117$	−2.47761	−0.229055
$118$	1.14900	0.105774
$119$	−3.87719	−0.355422
$120$	2.37460	0.216770
$121$	1.00000	0.0909091
$122$	−6.27310	−0.567940
$123$	0.620404	0.0559399
$124$	−10.4500	−0.938439
$125$	1.00000	0.0894427
$126$	3.44771	0.307147
$127$	5.58915	0.495957	0.247979	−	0.968766i	$-0.420234\pi$
$127$	5.58915	0.495957	0.247979	+	0.968766i	$0.420234\pi$
$128$	−1.00000	−0.0883883
$129$	−30.4387	−2.67997
$130$	0.938943	0.0823507
$131$	−4.55293	−0.397791	−0.198896	−	0.980021i	$-0.563736\pi$
$131$	−4.55293	−0.397791	−0.198896	+	0.980021i	$0.563736\pi$
$132$	2.37460	0.206682
$133$	6.03207	0.523047
$134$	0.178097	0.0153852
$135$	0.857899	0.0738362
$136$	−2.96742	−0.254454
$137$	5.69987	0.486973	0.243487	−	0.969904i	$-0.421709\pi$
$137$	5.69987	0.486973	0.243487	+	0.969904i	$0.421709\pi$
$138$	−17.7504	−1.51102
$139$	5.45493	0.462681	0.231341	−	0.972873i	$-0.425689\pi$
$139$	5.45493	0.462681	0.231341	+	0.972873i	$0.425689\pi$
$140$	−1.30659	−0.110427
$141$	21.9205	1.84604
$142$	−14.8326	−1.24472
$143$	0.938943	0.0785183
$144$	2.63872	0.219893
$145$	−7.77522	−0.645697
$146$	1.00000	0.0827606
$147$	12.5683	1.03662
$148$	3.94005	0.323870
$149$	18.8881	1.54737	0.773685	−	0.633570i	$-0.218411\pi$
$149$	18.8881	1.54737	0.773685	+	0.633570i	$0.218411\pi$
$150$	2.37460	0.193885
$151$	−12.6369	−1.02838	−0.514188	−	0.857678i	$-0.671906\pi$
$151$	−12.6369	−1.02838	−0.514188	+	0.857678i	$0.671906\pi$
$152$	4.61666	0.374461
$153$	7.83019	0.633033
$154$	−1.30659	−0.105288
$155$	−10.4500	−0.839366
$156$	2.22961	0.178512
$157$	13.0232	1.03936	0.519682	−	0.854359i	$-0.326050\pi$
$157$	13.0232	1.03936	0.519682	+	0.854359i	$0.326050\pi$
$158$	13.7485	1.09378
$159$	6.84050	0.542487
$160$	−1.00000	−0.0790569
$161$	9.76690	0.769740
$162$	9.95332	0.782007
$163$	−20.9282	−1.63923	−0.819613	−	0.572917i	$-0.805812\pi$
$163$	−20.9282	−1.63923	−0.819613	+	0.572917i	$0.805812\pi$
$164$	−0.261267	−0.0204015
$165$	2.37460	0.184862
$166$	14.1434	1.09774
$167$	−10.8865	−0.842423	−0.421211	−	0.906963i	$-0.638395\pi$
$167$	−10.8865	−0.842423	−0.421211	+	0.906963i	$0.638395\pi$
$168$	−3.10262	−0.239372
$169$	−12.1184	−0.932184
$170$	−2.96742	−0.227591
$171$	−12.1821	−0.931587
$172$	12.8184	0.977397
$173$	20.9575	1.59337	0.796684	−	0.604396i	$-0.206585\pi$
$173$	20.9575	1.59337	0.796684	+	0.604396i	$0.206585\pi$
$174$	−18.4630	−1.39968
$175$	−1.30659	−0.0987687
$176$	−1.00000	−0.0753778
$177$	2.72841	0.205080
$178$	5.15145	0.386118
$179$	−6.45512	−0.482478	−0.241239	−	0.970466i	$-0.577554\pi$
$179$	−6.45512	−0.482478	−0.241239	+	0.970466i	$0.577554\pi$
$180$	2.63872	0.196678
$181$	10.3972	0.772821	0.386411	−	0.922327i	$-0.373715\pi$
$181$	10.3972	0.772821	0.386411	+	0.922327i	$0.373715\pi$
$182$	−1.22681	−0.0909372
$183$	−14.8961	−1.10115
$184$	7.47513	0.551074
$185$	3.94005	0.289678
$186$	−24.8146	−1.81949
$187$	−2.96742	−0.216999
$188$	−9.23125	−0.673258
$189$	−1.12092	−0.0815349
$190$	4.61666	0.334928
$191$	15.7785	1.14170	0.570848	−	0.821056i	$-0.306615\pi$
$191$	15.7785	1.14170	0.570848	+	0.821056i	$0.306615\pi$
$192$	−2.37460	−0.171372
$193$	−10.5379	−0.758534	−0.379267	−	0.925287i	$-0.623824\pi$
$193$	−10.5379	−0.758534	−0.379267	+	0.925287i	$0.623824\pi$
$194$	−4.39877	−0.315813
$195$	2.22961	0.159666
$196$	−5.29283	−0.378059
$197$	−11.1741	−0.796121	−0.398060	−	0.917359i	$-0.630317\pi$
$197$	−11.1741	−0.796121	−0.398060	+	0.917359i	$0.630317\pi$
$198$	2.63872	0.187526
$199$	−13.8712	−0.983304	−0.491652	−	0.870792i	$-0.663607\pi$
$199$	−13.8712	−0.983304	−0.491652	+	0.870792i	$0.663607\pi$
$200$	−1.00000	−0.0707107
$201$	0.422908	0.0298296
$202$	0.140352	0.00987514
$203$	10.1590	0.713022
$204$	−7.04643	−0.493349
$205$	−0.261267	−0.0182477
$206$	−16.3371	−1.13826
$207$	−19.7248	−1.37097
$208$	−0.938943	−0.0651040
$209$	4.61666	0.319341
$210$	−3.10262	−0.214101
$211$	−20.7687	−1.42978	−0.714890	−	0.699237i	$-0.753523\pi$
$211$	−20.7687	−1.42978	−0.714890	+	0.699237i	$0.753523\pi$
$212$	−2.88070	−0.197847
$213$	−35.2215	−2.41334
$214$	2.04128	0.139539
$215$	12.8184	0.874211
$216$	−0.857899	−0.0583726
$217$	13.6539	0.926884
$218$	17.5308	1.18733
$219$	2.37460	0.160460
$220$	−1.00000	−0.0674200
$221$	−2.78624	−0.187423
$222$	9.35603	0.627935
$223$	−13.7903	−0.923464	−0.461732	−	0.887020i	$-0.652772\pi$
$223$	−13.7903	−0.923464	−0.461732	+	0.887020i	$0.652772\pi$
$224$	1.30659	0.0873000
$225$	2.63872	0.175915
$226$	−5.91460	−0.393433
$227$	−2.08515	−0.138396	−0.0691982	−	0.997603i	$-0.522044\pi$
$227$	−2.08515	−0.138396	−0.0691982	+	0.997603i	$0.522044\pi$
$228$	10.9627	0.726024
$229$	6.82537	0.451033	0.225516	−	0.974239i	$-0.427593\pi$
$229$	6.82537	0.451033	0.225516	+	0.974239i	$0.427593\pi$
$230$	7.47513	0.492895
$231$	−3.10262	−0.204137
$232$	7.77522	0.510468
$233$	29.3529	1.92297	0.961486	−	0.274854i	$-0.0886294\pi$
$233$	29.3529	1.92297	0.961486	+	0.274854i	$0.0886294\pi$
$234$	2.47761	0.161966
$235$	−9.23125	−0.602180
$236$	−1.14900	−0.0747934
$237$	32.6473	2.12067
$238$	3.87719	0.251321
$239$	−3.13344	−0.202685	−0.101343	−	0.994852i	$-0.532314\pi$
$239$	−3.13344	−0.202685	−0.101343	+	0.994852i	$0.532314\pi$
$240$	−2.37460	−0.153280
$241$	5.21734	0.336078	0.168039	−	0.985780i	$-0.446257\pi$
$241$	5.21734	0.336078	0.168039	+	0.985780i	$0.446257\pi$
$242$	−1.00000	−0.0642824
$243$	21.0614	1.35109
$244$	6.27310	0.401594
$245$	−5.29283	−0.338147
$246$	−0.620404	−0.0395555
$247$	4.33478	0.275816
$248$	10.4500	0.663577
$249$	33.5849	2.12836
$250$	−1.00000	−0.0632456
$251$	28.2521	1.78326	0.891628	−	0.452769i	$-0.149564\pi$
$251$	28.2521	1.78326	0.891628	+	0.452769i	$0.149564\pi$
$252$	−3.44771	−0.217186
$253$	7.47513	0.469957
$254$	−5.58915	−0.350695
$255$	−7.04643	−0.441265
$256$	1.00000	0.0625000
$257$	−27.9694	−1.74468	−0.872340	−	0.488899i	$-0.837399\pi$
$257$	−27.9694	−1.74468	−0.872340	+	0.488899i	$0.837399\pi$
$258$	30.4387	1.89503
$259$	−5.14801	−0.319882
$260$	−0.938943	−0.0582308
$261$	−20.5166	−1.26995
$262$	4.55293	0.281281
$263$	−8.03836	−0.495667	−0.247833	−	0.968803i	$-0.579719\pi$
$263$	−8.03836	−0.495667	−0.247833	+	0.968803i	$0.579719\pi$
$264$	−2.37460	−0.146146
$265$	−2.88070	−0.176960
$266$	−6.03207	−0.369850
$267$	12.2326	0.748625
$268$	−0.178097	−0.0108790
$269$	−18.8937	−1.15197	−0.575984	−	0.817461i	$-0.695381\pi$
$269$	−18.8937	−1.15197	−0.575984	+	0.817461i	$0.695381\pi$
$270$	−0.857899	−0.0522101
$271$	−9.83595	−0.597492	−0.298746	−	0.954333i	$-0.596568\pi$
$271$	−9.83595	−0.597492	−0.298746	+	0.954333i	$0.596568\pi$
$272$	2.96742	0.179926
$273$	−2.91318	−0.176314
$274$	−5.69987	−0.344342
$275$	−1.00000	−0.0603023
$276$	17.7504	1.06845
$277$	1.04854	0.0630009	0.0315005	−	0.999504i	$-0.489971\pi$
$277$	1.04854	0.0630009	0.0315005	+	0.999504i	$0.489971\pi$
$278$	−5.45493	−0.327165
$279$	−27.5747	−1.65085
$280$	1.30659	0.0780835
$281$	−13.7676	−0.821307	−0.410653	−	0.911792i	$-0.634699\pi$
$281$	−13.7676	−0.821307	−0.410653	+	0.911792i	$0.634699\pi$
$282$	−21.9205	−1.30535
$283$	21.9231	1.30319	0.651596	−	0.758566i	$-0.274100\pi$
$283$	21.9231	1.30319	0.651596	+	0.758566i	$0.274100\pi$
$284$	14.8326	0.880153
$285$	10.9627	0.649376
$286$	−0.938943	−0.0555209
$287$	0.341368	0.0201503
$288$	−2.63872	−0.155488
$289$	−8.19441	−0.482024
$290$	7.77522	0.456577
$291$	−10.4453	−0.612315
$292$	−1.00000	−0.0585206
$293$	11.1827	0.653302	0.326651	−	0.945145i	$-0.394080\pi$
$293$	11.1827	0.653302	0.326651	+	0.945145i	$0.394080\pi$
$294$	−12.5683	−0.733001
$295$	−1.14900	−0.0668973
$296$	−3.94005	−0.229011
$297$	−0.857899	−0.0497804
$298$	−18.8881	−1.09416
$299$	7.01872	0.405903
$300$	−2.37460	−0.137098
$301$	−16.7484	−0.965362
$302$	12.6369	0.727171
$303$	0.333280	0.0191464
$304$	−4.61666	−0.264784
$305$	6.27310	0.359197
$306$	−7.83019	−0.447622
$307$	−30.4341	−1.73697	−0.868483	−	0.495718i	$-0.834905\pi$
$307$	−30.4341	−1.73697	−0.868483	+	0.495718i	$0.834905\pi$
$308$	1.30659	0.0744497
$309$	−38.7941	−2.20692
$310$	10.4500	0.593521
$311$	−29.0197	−1.64556	−0.822779	−	0.568361i	$-0.807578\pi$
$311$	−29.0197	−1.64556	−0.822779	+	0.568361i	$0.807578\pi$
$312$	−2.22961	−0.126227
$313$	24.3063	1.37387	0.686936	−	0.726718i	$-0.258955\pi$
$313$	24.3063	1.37387	0.686936	+	0.726718i	$0.258955\pi$
$314$	−13.0232	−0.734942
$315$	−3.44771	−0.194257
$316$	−13.7485	−0.773416
$317$	−12.0481	−0.676687	−0.338344	−	0.941023i	$-0.609867\pi$
$317$	−12.0481	−0.676687	−0.338344	+	0.941023i	$0.609867\pi$
$318$	−6.84050	−0.383596
$319$	7.77522	0.435329
$320$	1.00000	0.0559017
$321$	4.84721	0.270545
$322$	−9.76690	−0.544288
$323$	−13.6996	−0.762265
$324$	−9.95332	−0.552962
$325$	−0.938943	−0.0520832
$326$	20.9282	1.15911
$327$	41.6286	2.30206
$328$	0.261267	0.0144260
$329$	12.0614	0.664968
$330$	−2.37460	−0.130717
$331$	14.0183	0.770514	0.385257	−	0.922809i	$-0.374113\pi$
$331$	14.0183	0.770514	0.385257	+	0.922809i	$0.374113\pi$
$332$	−14.1434	−0.776220
$333$	10.3967	0.569734
$334$	10.8865	0.595683
$335$	−0.178097	−0.00973046
$336$	3.10262	0.169262
$337$	21.2660	1.15843	0.579215	−	0.815174i	$-0.303359\pi$
$337$	21.2660	1.15843	0.579215	+	0.815174i	$0.303359\pi$
$338$	12.1184	0.659153
$339$	−14.0448	−0.762809
$340$	2.96742	0.160931
$341$	10.4500	0.565900
$342$	12.1821	0.658731
$343$	16.0616	0.867248
$344$	−12.8184	−0.691124
$345$	17.7504	0.955651
$346$	−20.9575	−1.12668
$347$	13.0702	0.701647	0.350824	−	0.936442i	$-0.385902\pi$
$347$	13.0702	0.701647	0.350824	+	0.936442i	$0.385902\pi$
$348$	18.4630	0.989722
$349$	−10.0773	−0.539425	−0.269712	−	0.962941i	$-0.586929\pi$
$349$	−10.0773	−0.539425	−0.269712	+	0.962941i	$0.586929\pi$
$350$	1.30659	0.0698400
$351$	−0.805518	−0.0429954
$352$	1.00000	0.0533002
$353$	−24.8330	−1.32173	−0.660864	−	0.750505i	$-0.729810\pi$
$353$	−24.8330	−1.32173	−0.660864	+	0.750505i	$0.729810\pi$
$354$	−2.72841	−0.145013
$355$	14.8326	0.787233
$356$	−5.15145	−0.273026
$357$	9.20678	0.487274
$358$	6.45512	0.341164
$359$	−13.3369	−0.703897	−0.351949	−	0.936019i	$-0.614481\pi$
$359$	−13.3369	−0.703897	−0.351949	+	0.936019i	$0.614481\pi$
$360$	−2.63872	−0.139073
$361$	2.31359	0.121768
$362$	−10.3972	−0.546467
$363$	−2.37460	−0.124634
$364$	1.22681	0.0643023
$365$	−1.00000	−0.0523424
$366$	14.8961	0.778632
$367$	30.3265	1.58303	0.791516	−	0.611148i	$-0.209292\pi$
$367$	30.3265	1.58303	0.791516	+	0.611148i	$0.209292\pi$
$368$	−7.47513	−0.389668
$369$	−0.689409	−0.0358892
$370$	−3.94005	−0.204833
$371$	3.76388	0.195411
$372$	24.8146	1.28658
$373$	4.33322	0.224366	0.112183	−	0.993688i	$-0.464216\pi$
$373$	4.33322	0.224366	0.112183	+	0.993688i	$0.464216\pi$
$374$	2.96742	0.153442
$375$	−2.37460	−0.122624
$376$	9.23125	0.476065
$377$	7.30049	0.375994
$378$	1.12092	0.0576539
$379$	−6.23145	−0.320088	−0.160044	−	0.987110i	$-0.551164\pi$
$379$	−6.23145	−0.320088	−0.160044	+	0.987110i	$0.551164\pi$
$380$	−4.61666	−0.236830
$381$	−13.2720	−0.679945
$382$	−15.7785	−0.807300
$383$	−2.69439	−0.137677	−0.0688385	−	0.997628i	$-0.521929\pi$
$383$	−2.69439	−0.137677	−0.0688385	+	0.997628i	$0.521929\pi$
$384$	2.37460	0.121178
$385$	1.30659	0.0665898
$386$	10.5379	0.536364
$387$	33.8243	1.71938
$388$	4.39877	0.223314
$389$	−16.9504	−0.859419	−0.429710	−	0.902967i	$-0.641384\pi$
$389$	−16.9504	−0.859419	−0.429710	+	0.902967i	$0.641384\pi$
$390$	−2.22961	−0.112901
$391$	−22.1819	−1.12178
$392$	5.29283	0.267328
$393$	10.8114	0.545362
$394$	11.1741	0.562943
$395$	−13.7485	−0.691764
$396$	−2.63872	−0.132601
$397$	2.07688	0.104236	0.0521179	−	0.998641i	$-0.483403\pi$
$397$	2.07688	0.104236	0.0521179	+	0.998641i	$0.483403\pi$
$398$	13.8712	0.695301
$399$	−14.3237	−0.717084
$400$	1.00000	0.0500000
$401$	22.3615	1.11668	0.558341	−	0.829612i	$-0.311438\pi$
$401$	22.3615	1.11668	0.558341	+	0.829612i	$0.311438\pi$
$402$	−0.422908	−0.0210927
$403$	9.81197	0.488769
$404$	−0.140352	−0.00698278
$405$	−9.95332	−0.494584
$406$	−10.1590	−0.504183
$407$	−3.94005	−0.195301
$408$	7.04643	0.348850
$409$	39.1742	1.93704	0.968519	−	0.248941i	$-0.0800824\pi$
$409$	39.1742	1.93704	0.968519	+	0.248941i	$0.0800824\pi$
$410$	0.261267	0.0129030
$411$	−13.5349	−0.667628
$412$	16.3371	0.804872
$413$	1.50127	0.0738725
$414$	19.7248	0.969419
$415$	−14.1434	−0.694272
$416$	0.938943	0.0460355
$417$	−12.9533	−0.634324
$418$	−4.61666	−0.225808
$419$	4.72149	0.230660	0.115330	−	0.993327i	$-0.463207\pi$
$419$	4.72149	0.230660	0.115330	+	0.993327i	$0.463207\pi$
$420$	3.10262	0.151392
$421$	−25.9140	−1.26297	−0.631485	−	0.775388i	$-0.717554\pi$
$421$	−25.9140	−1.26297	−0.631485	+	0.775388i	$0.717554\pi$
$422$	20.7687	1.01101
$423$	−24.3587	−1.18436
$424$	2.88070	0.139899
$425$	2.96742	0.143941
$426$	35.2215	1.70649
$427$	−8.19635	−0.396649
$428$	−2.04128	−0.0986688
$429$	−2.22961	−0.107647
$430$	−12.8184	−0.618160
$431$	−1.53993	−0.0741759	−0.0370879	−	0.999312i	$-0.511808\pi$
$431$	−1.53993	−0.0741759	−0.0370879	+	0.999312i	$0.511808\pi$
$432$	0.857899	0.0412757
$433$	−6.19343	−0.297637	−0.148819	−	0.988864i	$-0.547547\pi$
$433$	−6.19343	−0.297637	−0.148819	+	0.988864i	$0.547547\pi$
$434$	−13.6539	−0.655406
$435$	18.4630	0.885234
$436$	−17.5308	−0.839572
$437$	34.5102	1.65084
$438$	−2.37460	−0.113463
$439$	22.1778	1.05849	0.529244	−	0.848470i	$-0.322476\pi$
$439$	22.1778	1.05849	0.529244	+	0.848470i	$0.322476\pi$
$440$	1.00000	0.0476731
$441$	−13.9663	−0.665061
$442$	2.78624	0.132528
$443$	−39.5043	−1.87690	−0.938452	−	0.345409i	$-0.887740\pi$
$443$	−39.5043	−1.87690	−0.938452	+	0.345409i	$0.887740\pi$
$444$	−9.35603	−0.444017
$445$	−5.15145	−0.244202
$446$	13.7903	0.652988
$447$	−44.8516	−2.12141
$448$	−1.30659	−0.0617304
$449$	5.16712	0.243852	0.121926	−	0.992539i	$-0.461093\pi$
$449$	5.16712	0.243852	0.121926	+	0.992539i	$0.461093\pi$
$450$	−2.63872	−0.124390
$451$	0.261267	0.0123026
$452$	5.91460	0.278199
$453$	30.0075	1.40988
$454$	2.08515	0.0978610
$455$	1.22681	0.0575137
$456$	−10.9627	−0.513377
$457$	24.0382	1.12446	0.562230	−	0.826981i	$-0.309944\pi$
$457$	24.0382	1.12446	0.562230	+	0.826981i	$0.309944\pi$
$458$	−6.82537	−0.318928
$459$	2.54575	0.118825
$460$	−7.47513	−0.348530
$461$	−22.2905	−1.03817	−0.519085	−	0.854723i	$-0.673727\pi$
$461$	−22.2905	−1.03817	−0.519085	+	0.854723i	$0.673727\pi$
$462$	3.10262	0.144347
$463$	21.8957	1.01758	0.508790	−	0.860891i	$-0.330093\pi$
$463$	21.8957	1.01758	0.508790	+	0.860891i	$0.330093\pi$
$464$	−7.77522	−0.360956
$465$	24.8146	1.15075
$466$	−29.3529	−1.35975
$467$	11.4980	0.532065	0.266032	−	0.963964i	$-0.414287\pi$
$467$	11.4980	0.532065	0.266032	+	0.963964i	$0.414287\pi$
$468$	−2.47761	−0.114527
$469$	0.232699	0.0107450
$470$	9.23125	0.425806
$471$	−30.9249	−1.42494
$472$	1.14900	0.0528869
$473$	−12.8184	−0.589393
$474$	−32.6473	−1.49954
$475$	−4.61666	−0.211827
$476$	−3.87719	−0.177711
$477$	−7.60135	−0.348042
$478$	3.13344	0.143320
$479$	14.6002	0.667098	0.333549	−	0.942733i	$-0.391754\pi$
$479$	14.6002	0.667098	0.333549	+	0.942733i	$0.391754\pi$
$480$	2.37460	0.108385
$481$	−3.69948	−0.168682
$482$	−5.21734	−0.237643
$483$	−23.1925	−1.05529
$484$	1.00000	0.0454545
$485$	4.39877	0.199738
$486$	−21.0614	−0.955366
$487$	−6.74394	−0.305597	−0.152799	−	0.988257i	$-0.548829\pi$
$487$	−6.74394	−0.305597	−0.152799	+	0.988257i	$0.548829\pi$
$488$	−6.27310	−0.283970
$489$	49.6962	2.24734
$490$	5.29283	0.239106
$491$	18.2001	0.821360	0.410680	−	0.911780i	$-0.365291\pi$
$491$	18.2001	0.821360	0.410680	+	0.911780i	$0.365291\pi$
$492$	0.620404	0.0279700
$493$	−23.0724	−1.03913
$494$	−4.33478	−0.195031
$495$	−2.63872	−0.118602
$496$	−10.4500	−0.469220
$497$	−19.3801	−0.869315
$498$	−33.5849	−1.50497
$499$	11.0901	0.496462	0.248231	−	0.968701i	$-0.420151\pi$
$499$	11.0901	0.496462	0.248231	+	0.968701i	$0.420151\pi$
$500$	1.00000	0.0447214
$501$	25.8511	1.15494
$502$	−28.2521	−1.26095
$503$	6.23887	0.278178	0.139089	−	0.990280i	$-0.455583\pi$
$503$	6.23887	0.278178	0.139089	+	0.990280i	$0.455583\pi$
$504$	3.44771	0.153573
$505$	−0.140352	−0.00624558
$506$	−7.47513	−0.332310
$507$	28.7763	1.27800
$508$	5.58915	0.247979
$509$	−28.1805	−1.24908	−0.624539	−	0.780994i	$-0.714713\pi$
$509$	−28.1805	−1.24908	−0.624539	+	0.780994i	$0.714713\pi$
$510$	7.04643	0.312021
$511$	1.30659	0.0578000
$512$	−1.00000	−0.0441942
$513$	−3.96063	−0.174866
$514$	27.9694	1.23368
$515$	16.3371	0.719899
$516$	−30.4387	−1.33999
$517$	9.23125	0.405990
$518$	5.14801	0.226191
$519$	−49.7656	−2.18447
$520$	0.938943	0.0411754
$521$	35.9059	1.57307	0.786533	−	0.617549i	$-0.211874\pi$
$521$	35.9059	1.57307	0.786533	+	0.617549i	$0.211874\pi$
$522$	20.5166	0.897988
$523$	2.13584	0.0933939	0.0466970	−	0.998909i	$-0.485130\pi$
$523$	2.13584	0.0933939	0.0466970	+	0.998909i	$0.485130\pi$
$524$	−4.55293	−0.198896
$525$	3.10262	0.135409
$526$	8.03836	0.350489
$527$	−31.0096	−1.35080
$528$	2.37460	0.103341
$529$	32.8776	1.42946
$530$	2.88070	0.125130
$531$	−3.03188	−0.131573
$532$	6.03207	0.261523
$533$	0.245315	0.0106258
$534$	−12.2326	−0.529358
$535$	−2.04128	−0.0882521
$536$	0.178097	0.00769260
$537$	15.3283	0.661466
$538$	18.8937	0.814565
$539$	5.29283	0.227978
$540$	0.857899	0.0369181
$541$	6.05356	0.260263	0.130132	−	0.991497i	$-0.458460\pi$
$541$	6.05356	0.260263	0.130132	+	0.991497i	$0.458460\pi$
$542$	9.83595	0.422490
$543$	−24.6893	−1.05952
$544$	−2.96742	−0.127227
$545$	−17.5308	−0.750936
$546$	2.91318	0.124673
$547$	25.1867	1.07690	0.538452	−	0.842656i	$-0.319009\pi$
$547$	25.1867	1.07690	0.538452	+	0.842656i	$0.319009\pi$
$548$	5.69987	0.243487
$549$	16.5530	0.706463
$550$	1.00000	0.0426401
$551$	35.8956	1.52920
$552$	−17.7504	−0.755508
$553$	17.9637	0.763893
$554$	−1.04854	−0.0445484
$555$	−9.35603	−0.397141
$556$	5.45493	0.231341
$557$	8.01498	0.339606	0.169803	−	0.985478i	$-0.445687\pi$
$557$	8.01498	0.339606	0.169803	+	0.985478i	$0.445687\pi$
$558$	27.5747	1.16733
$559$	−12.0358	−0.509060
$560$	−1.30659	−0.0552134
$561$	7.04643	0.297501
$562$	13.7676	0.580752
$563$	5.49702	0.231672	0.115836	−	0.993268i	$-0.463045\pi$
$563$	5.49702	0.231672	0.115836	+	0.993268i	$0.463045\pi$
$564$	21.9205	0.923020
$565$	5.91460	0.248829
$566$	−21.9231	−0.921496
$567$	13.0049	0.546153
$568$	−14.8326	−0.622362
$569$	27.1941	1.14004	0.570018	−	0.821633i	$-0.306936\pi$
$569$	27.1941	1.14004	0.570018	+	0.821633i	$0.306936\pi$
$570$	−10.9627	−0.459178
$571$	18.0248	0.754313	0.377157	−	0.926150i	$-0.376902\pi$
$571$	18.0248	0.754313	0.377157	+	0.926150i	$0.376902\pi$
$572$	0.938943	0.0392592
$573$	−37.4677	−1.56524
$574$	−0.341368	−0.0142484
$575$	−7.47513	−0.311734
$576$	2.63872	0.109947
$577$	25.9519	1.08039	0.540195	−	0.841540i	$-0.318350\pi$
$577$	25.9519	1.08039	0.540195	+	0.841540i	$0.318350\pi$
$578$	8.19441	0.340843
$579$	25.0233	1.03993
$580$	−7.77522	−0.322848
$581$	18.4796	0.766662
$582$	10.4453	0.432972
$583$	2.88070	0.119306
$584$	1.00000	0.0413803
$585$	−2.47761	−0.102436
$586$	−11.1827	−0.461954
$587$	43.2735	1.78609	0.893043	−	0.449970i	$-0.148565\pi$
$587$	43.2735	1.78609	0.893043	+	0.449970i	$0.148565\pi$
$588$	12.5683	0.518310
$589$	48.2442	1.98787
$590$	1.14900	0.0473035
$591$	26.5340	1.09146
$592$	3.94005	0.161935
$593$	17.8848	0.734440	0.367220	−	0.930134i	$-0.380310\pi$
$593$	17.8848	0.734440	0.367220	+	0.930134i	$0.380310\pi$
$594$	0.857899	0.0352000
$595$	−3.87719	−0.158949
$596$	18.8881	0.773685
$597$	32.9386	1.34809
$598$	−7.01872	−0.287017
$599$	44.7112	1.82685	0.913425	−	0.407008i	$-0.133428\pi$
$599$	44.7112	1.82685	0.913425	+	0.407008i	$0.133428\pi$
$600$	2.37460	0.0969426
$601$	43.0903	1.75769	0.878845	−	0.477107i	$-0.158315\pi$
$601$	43.0903	1.75769	0.878845	+	0.477107i	$0.158315\pi$
$602$	16.7484	0.682614
$603$	−0.469947	−0.0191377
$604$	−12.6369	−0.514188
$605$	1.00000	0.0406558
$606$	−0.333280	−0.0135386
$607$	1.66608	0.0676242	0.0338121	−	0.999428i	$-0.489235\pi$
$607$	1.66608	0.0676242	0.0338121	+	0.999428i	$0.489235\pi$
$608$	4.61666	0.187230
$609$	−24.1235	−0.977535
$610$	−6.27310	−0.253991
$611$	8.66761	0.350654
$612$	7.83019	0.316517
$613$	−15.3568	−0.620254	−0.310127	−	0.950695i	$-0.600372\pi$
$613$	−15.3568	−0.620254	−0.310127	+	0.950695i	$0.600372\pi$
$614$	30.4341	1.22822
$615$	0.620404	0.0250171
$616$	−1.30659	−0.0526439
$617$	−40.8877	−1.64608	−0.823039	−	0.567985i	$-0.807723\pi$
$617$	−40.8877	−1.64608	−0.823039	+	0.567985i	$0.807723\pi$
$618$	38.7941	1.56053
$619$	29.2733	1.17659	0.588297	−	0.808645i	$-0.299799\pi$
$619$	29.2733	1.17659	0.588297	+	0.808645i	$0.299799\pi$
$620$	−10.4500	−0.419683
$621$	−6.41291	−0.257341
$622$	29.0197	1.16359
$623$	6.73082	0.269665
$624$	2.22961	0.0892559
$625$	1.00000	0.0400000
$626$	−24.3063	−0.971475
$627$	−10.9627	−0.437809
$628$	13.0232	0.519682
$629$	11.6918	0.466182
$630$	3.44771	0.137360
$631$	40.3277	1.60542	0.802710	−	0.596369i	$-0.203390\pi$
$631$	40.3277	1.60542	0.802710	+	0.596369i	$0.203390\pi$
$632$	13.7485	0.546888
$633$	49.3174	1.96019
$634$	12.0481	0.478490
$635$	5.58915	0.221799
$636$	6.84050	0.271244
$637$	4.96967	0.196905
$638$	−7.77522	−0.307824
$639$	39.1391	1.54832
$640$	−1.00000	−0.0395285
$641$	34.9503	1.38045	0.690226	−	0.723594i	$-0.257511\pi$
$641$	34.9503	1.38045	0.690226	+	0.723594i	$0.257511\pi$
$642$	−4.84721	−0.191304
$643$	−6.66085	−0.262678	−0.131339	−	0.991337i	$-0.541928\pi$
$643$	−6.66085	−0.262678	−0.131339	+	0.991337i	$0.541928\pi$
$644$	9.76690	0.384870
$645$	−30.4387	−1.19852
$646$	13.6996	0.539003
$647$	−8.42205	−0.331105	−0.165553	−	0.986201i	$-0.552941\pi$
$647$	−8.42205	−0.331105	−0.165553	+	0.986201i	$0.552941\pi$
$648$	9.95332	0.391003
$649$	1.14900	0.0451021
$650$	0.938943	0.0368284
$651$	−32.4224	−1.27073
$652$	−20.9282	−0.819613
$653$	−0.140061	−0.00548100	−0.00274050	−	0.999996i	$-0.500872\pi$
$653$	−0.140061	−0.00548100	−0.00274050	+	0.999996i	$0.500872\pi$
$654$	−41.6286	−1.62781
$655$	−4.55293	−0.177898
$656$	−0.261267	−0.0102008
$657$	−2.63872	−0.102946
$658$	−12.0614	−0.470203
$659$	15.0519	0.586340	0.293170	−	0.956060i	$-0.405290\pi$
$659$	15.0519	0.586340	0.293170	+	0.956060i	$0.405290\pi$
$660$	2.37460	0.0924311
$661$	25.5278	0.992916	0.496458	−	0.868061i	$-0.334634\pi$
$661$	25.5278	0.992916	0.496458	+	0.868061i	$0.334634\pi$
$662$	−14.0183	−0.544835
$663$	6.61620	0.256952
$664$	14.1434	0.548870
$665$	6.03207	0.233914
$666$	−10.3967	−0.402863
$667$	58.1208	2.25045
$668$	−10.8865	−0.421211
$669$	32.7463	1.26605
$670$	0.178097	0.00688047
$671$	−6.27310	−0.242170
$672$	−3.10262	−0.119686
$673$	5.28413	0.203688	0.101844	−	0.994800i	$-0.467526\pi$
$673$	5.28413	0.203688	0.101844	+	0.994800i	$0.467526\pi$
$674$	−21.2660	−0.819134
$675$	0.857899	0.0330206
$676$	−12.1184	−0.466092
$677$	−8.09263	−0.311025	−0.155512	−	0.987834i	$-0.549703\pi$
$677$	−8.09263	−0.311025	−0.155512	+	0.987834i	$0.549703\pi$
$678$	14.0448	0.539387
$679$	−5.74737	−0.220564
$680$	−2.96742	−0.113795
$681$	4.95140	0.189738
$682$	−10.4500	−0.400152
$683$	−19.2441	−0.736356	−0.368178	−	0.929755i	$-0.620018\pi$
$683$	−19.2441	−0.736356	−0.368178	+	0.929755i	$0.620018\pi$
$684$	−12.1821	−0.465793
$685$	5.69987	0.217781
$686$	−16.0616	−0.613237
$687$	−16.2075	−0.618355
$688$	12.8184	0.488699
$689$	2.70481	0.103045
$690$	−17.7504	−0.675747
$691$	−24.8432	−0.945079	−0.472540	−	0.881309i	$-0.656663\pi$
$691$	−24.8432	−0.945079	−0.472540	+	0.881309i	$0.656663\pi$
$692$	20.9575	0.796684
$693$	3.44771	0.130968
$694$	−13.0702	−0.496140
$695$	5.45493	0.206917
$696$	−18.4630	−0.699839
$697$	−0.775289	−0.0293661
$698$	10.0773	0.381431
$699$	−69.7013	−2.63635
$700$	−1.30659	−0.0493843
$701$	13.7470	0.519215	0.259608	−	0.965714i	$-0.416407\pi$
$701$	13.7470	0.519215	0.259608	+	0.965714i	$0.416407\pi$
$702$	0.805518	0.0304023
$703$	−18.1899	−0.686044
$704$	−1.00000	−0.0376889
$705$	21.9205	0.825574
$706$	24.8330	0.934603
$707$	0.183382	0.00689679
$708$	2.72841	0.102540
$709$	−41.7924	−1.56954	−0.784772	−	0.619784i	$-0.787220\pi$
$709$	−41.7924	−1.56954	−0.784772	+	0.619784i	$0.787220\pi$
$710$	−14.8326	−0.556658
$711$	−36.2785	−1.36055
$712$	5.15145	0.193059
$713$	78.1152	2.92544
$714$	−9.20678	−0.344555
$715$	0.938943	0.0351145
$716$	−6.45512	−0.241239
$717$	7.44065	0.277876
$718$	13.3369	0.497730
$719$	−29.6313	−1.10506	−0.552530	−	0.833493i	$-0.686338\pi$
$719$	−29.6313	−1.10506	−0.552530	+	0.833493i	$0.686338\pi$
$720$	2.63872	0.0983392
$721$	−21.3459	−0.794961
$722$	−2.31359	−0.0861029
$723$	−12.3891	−0.460755
$724$	10.3972	0.386411
$725$	−7.77522	−0.288764
$726$	2.37460	0.0881296
$727$	2.92775	0.108584	0.0542922	−	0.998525i	$-0.482710\pi$
$727$	2.92775	0.108584	0.0542922	+	0.998525i	$0.482710\pi$
$728$	−1.22681	−0.0454686
$729$	−20.1525	−0.746389
$730$	1.00000	0.0370117
$731$	38.0377	1.40688
$732$	−14.8961	−0.550576
$733$	−17.5073	−0.646647	−0.323324	−	0.946288i	$-0.604800\pi$
$733$	−17.5073	−0.646647	−0.323324	+	0.946288i	$0.604800\pi$
$734$	−30.3265	−1.11937
$735$	12.5683	0.463591
$736$	7.47513	0.275537
$737$	0.178097	0.00656027
$738$	0.689409	0.0253775
$739$	13.9372	0.512687	0.256344	−	0.966586i	$-0.417482\pi$
$739$	13.9372	0.512687	0.256344	+	0.966586i	$0.417482\pi$
$740$	3.94005	0.144839
$741$	−10.2934	−0.378136
$742$	−3.76388	−0.138176
$743$	8.57282	0.314506	0.157253	−	0.987558i	$-0.449736\pi$
$743$	8.57282	0.314506	0.157253	+	0.987558i	$0.449736\pi$
$744$	−24.8146	−0.909747
$745$	18.8881	0.692005
$746$	−4.33322	−0.158650
$747$	−37.3204	−1.36548
$748$	−2.96742	−0.108500
$749$	2.66710	0.0974539
$750$	2.37460	0.0867081
$751$	49.3914	1.80232	0.901159	−	0.433488i	$-0.142717\pi$
$751$	49.3914	1.80232	0.901159	+	0.433488i	$0.142717\pi$
$752$	−9.23125	−0.336629
$753$	−67.0874	−2.44480
$754$	−7.30049	−0.265868
$755$	−12.6369	−0.459903
$756$	−1.12092	−0.0407675
$757$	−1.66658	−0.0605727	−0.0302864	−	0.999541i	$-0.509642\pi$
$757$	−1.66658	−0.0605727	−0.0302864	+	0.999541i	$0.509642\pi$
$758$	6.23145	0.226336
$759$	−17.7504	−0.644300
$760$	4.61666	0.167464
$761$	−23.5489	−0.853646	−0.426823	−	0.904335i	$-0.640367\pi$
$761$	−23.5489	−0.853646	−0.426823	+	0.904335i	$0.640367\pi$
$762$	13.2720	0.480794
$763$	22.9055	0.829234
$764$	15.7785	0.570848
$765$	7.83019	0.283101
$766$	2.69439	0.0973524
$767$	1.07884	0.0389548
$768$	−2.37460	−0.0856859
$769$	46.9862	1.69436	0.847182	−	0.531302i	$-0.178297\pi$
$769$	46.9862	1.69436	0.847182	+	0.531302i	$0.178297\pi$
$770$	−1.30659	−0.0470861
$771$	66.4160	2.39191
$772$	−10.5379	−0.379267
$773$	−28.6479	−1.03039	−0.515197	−	0.857072i	$-0.672281\pi$
$773$	−28.6479	−1.03039	−0.515197	+	0.857072i	$0.672281\pi$
$774$	−33.8243	−1.21579
$775$	−10.4500	−0.375376
$776$	−4.39877	−0.157907
$777$	12.2245	0.438550
$778$	16.9504	0.607701
$779$	1.20618	0.0432159
$780$	2.22961	0.0798329
$781$	−14.8326	−0.530752
$782$	22.1819	0.793221
$783$	−6.67036	−0.238379
$784$	−5.29283	−0.189030
$785$	13.0232	0.464818
$786$	−10.8114	−0.385629
$787$	19.3733	0.690583	0.345291	−	0.938496i	$-0.387780\pi$
$787$	19.3733	0.690583	0.345291	+	0.938496i	$0.387780\pi$
$788$	−11.1741	−0.398060
$789$	19.0879	0.679547
$790$	13.7485	0.489151
$791$	−7.72794	−0.274774
$792$	2.63872	0.0937628
$793$	−5.89009	−0.209163
$794$	−2.07688	−0.0737059
$795$	6.84050	0.242608
$796$	−13.8712	−0.491652
$797$	−3.34919	−0.118634	−0.0593172	−	0.998239i	$-0.518892\pi$
$797$	−3.34919	−0.118634	−0.0593172	+	0.998239i	$0.518892\pi$
$798$	14.3237	0.507055
$799$	−27.3930	−0.969094
$800$	−1.00000	−0.0353553
$801$	−13.5932	−0.480293
$802$	−22.3615	−0.789613
$803$	1.00000	0.0352892
$804$	0.422908	0.0149148
$805$	9.76690	0.344238
$806$	−9.81197	−0.345612
$807$	44.8649	1.57932
$808$	0.140352	0.00493757
$809$	−49.8186	−1.75153	−0.875764	−	0.482740i	$-0.839642\pi$
$809$	−49.8186	−1.75153	−0.875764	+	0.482740i	$0.839642\pi$
$810$	9.95332	0.349724
$811$	53.3168	1.87221	0.936103	−	0.351727i	$-0.114405\pi$
$811$	53.3168	1.87221	0.936103	+	0.351727i	$0.114405\pi$
$812$	10.1590	0.356511
$813$	23.3564	0.819146
$814$	3.94005	0.138099
$815$	−20.9282	−0.733084
$816$	−7.04643	−0.246675
$817$	−59.1785	−2.07039
$818$	−39.1742	−1.36969
$819$	3.23721	0.113117
$820$	−0.261267	−0.00912383
$821$	22.1155	0.771837	0.385918	−	0.922533i	$-0.373885\pi$
$821$	22.1155	0.771837	0.385918	+	0.922533i	$0.373885\pi$
$822$	13.5349	0.472084
$823$	51.2392	1.78609	0.893043	−	0.449971i	$-0.148566\pi$
$823$	51.2392	1.78609	0.893043	+	0.449971i	$0.148566\pi$
$824$	−16.3371	−0.569130
$825$	2.37460	0.0826729
$826$	−1.50127	−0.0522357
$827$	−24.9453	−0.867432	−0.433716	−	0.901050i	$-0.642798\pi$
$827$	−24.9453	−0.867432	−0.433716	+	0.901050i	$0.642798\pi$
$828$	−19.7248	−0.685483
$829$	−57.1795	−1.98592	−0.992962	−	0.118430i	$-0.962214\pi$
$829$	−57.1795	−1.98592	−0.992962	+	0.118430i	$0.962214\pi$
$830$	14.1434	0.490924
$831$	−2.48987	−0.0863727
$832$	−0.938943	−0.0325520
$833$	−15.7061	−0.544183
$834$	12.9533	0.448535
$835$	−10.8865	−0.376743
$836$	4.61666	0.159671
$837$	−8.96506	−0.309878
$838$	−4.72149	−0.163101
$839$	35.5452	1.22716	0.613578	−	0.789634i	$-0.289730\pi$
$839$	35.5452	1.22716	0.613578	+	0.789634i	$0.289730\pi$
$840$	−3.10262	−0.107051
$841$	31.4541	1.08462
$842$	25.9140	0.893054
$843$	32.6925	1.12599
$844$	−20.7687	−0.714890
$845$	−12.1184	−0.416885
$846$	24.3587	0.837468
$847$	−1.30659	−0.0448948
$848$	−2.88070	−0.0989236
$849$	−52.0585	−1.78664
$850$	−2.96742	−0.101782
$851$	−29.4524	−1.00961
$852$	−35.2215	−1.20667
$853$	16.0888	0.550872	0.275436	−	0.961319i	$-0.411178\pi$
$853$	16.0888	0.550872	0.275436	+	0.961319i	$0.411178\pi$
$854$	8.19635	0.280473
$855$	−12.1821	−0.416618
$856$	2.04128	0.0697694
$857$	−1.23440	−0.0421663	−0.0210831	−	0.999778i	$-0.506711\pi$
$857$	−1.23440	−0.0421663	−0.0210831	+	0.999778i	$0.506711\pi$
$858$	2.22961	0.0761177
$859$	−44.9107	−1.53233	−0.766167	−	0.642642i	$-0.777838\pi$
$859$	−44.9107	−1.53233	−0.766167	+	0.642642i	$0.777838\pi$
$860$	12.8184	0.437105
$861$	−0.810611	−0.0276256
$862$	1.53993	0.0524503
$863$	6.65765	0.226629	0.113314	−	0.993559i	$-0.463853\pi$
$863$	6.65765	0.226629	0.113314	+	0.993559i	$0.463853\pi$
$864$	−0.857899	−0.0291863
$865$	20.9575	0.712576
$866$	6.19343	0.210461
$867$	19.4584	0.660843
$868$	13.6539	0.463442
$869$	13.7485	0.466387
$870$	−18.4630	−0.625955
$871$	0.167223	0.00566612
$872$	17.5308	0.593667
$873$	11.6071	0.392841
$874$	−34.5102	−1.16732
$875$	−1.30659	−0.0441707
$876$	2.37460	0.0802302
$877$	27.7803	0.938075	0.469038	−	0.883178i	$-0.344601\pi$
$877$	27.7803	0.938075	0.469038	+	0.883178i	$0.344601\pi$
$878$	−22.1778	−0.748464
$879$	−26.5545	−0.895661
$880$	−1.00000	−0.0337100
$881$	8.25116	0.277989	0.138994	−	0.990293i	$-0.455613\pi$
$881$	8.25116	0.277989	0.138994	+	0.990293i	$0.455613\pi$
$882$	13.9663	0.470269
$883$	35.9019	1.20819	0.604097	−	0.796911i	$-0.293534\pi$
$883$	35.9019	1.20819	0.604097	+	0.796911i	$0.293534\pi$
$884$	−2.78624	−0.0937113
$885$	2.72841	0.0917145
$886$	39.5043	1.32717
$887$	35.3358	1.18646	0.593231	−	0.805033i	$-0.297852\pi$
$887$	35.3358	1.18646	0.593231	+	0.805033i	$0.297852\pi$
$888$	9.35603	0.313968
$889$	−7.30271	−0.244925
$890$	5.15145	0.172677
$891$	9.95332	0.333449
$892$	−13.7903	−0.461732
$893$	42.6176	1.42614
$894$	44.8516	1.50006
$895$	−6.45512	−0.215771
$896$	1.30659	0.0436500
$897$	−16.6666	−0.556483
$898$	−5.16712	−0.172429
$899$	81.2512	2.70988
$900$	2.63872	0.0879573
$901$	−8.54825	−0.284783
$902$	−0.261267	−0.00869923
$903$	39.7707	1.32349
$904$	−5.91460	−0.196717
$905$	10.3972	0.345616
$906$	−30.0075	−0.996933
$907$	−13.4023	−0.445015	−0.222508	−	0.974931i	$-0.571424\pi$
$907$	−13.4023	−0.445015	−0.222508	+	0.974931i	$0.571424\pi$
$908$	−2.08515	−0.0691982
$909$	−0.370350	−0.0122837
$910$	−1.22681	−0.0406684
$911$	−39.6825	−1.31474	−0.657371	−	0.753567i	$-0.728331\pi$
$911$	−39.6825	−1.31474	−0.657371	+	0.753567i	$0.728331\pi$
$912$	10.9627	0.363012
$913$	14.1434	0.468078
$914$	−24.0382	−0.795113
$915$	−14.8961	−0.492450
$916$	6.82537	0.225516
$917$	5.94880	0.196447
$918$	−2.54575	−0.0840222
$919$	−1.20172	−0.0396411	−0.0198206	−	0.999804i	$-0.506309\pi$
$919$	−1.20172	−0.0396411	−0.0198206	+	0.999804i	$0.506309\pi$
$920$	7.47513	0.246448
$921$	72.2688	2.38134
$922$	22.2905	0.734097
$923$	−13.9270	−0.458412
$924$	−3.10262	−0.102069
$925$	3.94005	0.129548
$926$	−21.8957	−0.719537
$927$	43.1090	1.41589
$928$	7.77522	0.255234
$929$	−35.1790	−1.15418	−0.577092	−	0.816679i	$-0.695813\pi$
$929$	−35.1790	−1.15418	−0.577092	+	0.816679i	$0.695813\pi$
$930$	−24.8146	−0.813703
$931$	24.4352	0.800832
$932$	29.3529	0.961486
$933$	68.9102	2.25602
$934$	−11.4980	−0.376226
$935$	−2.96742	−0.0970450
$936$	2.47761	0.0809831
$937$	28.7313	0.938609	0.469305	−	0.883036i	$-0.344505\pi$
$937$	28.7313	0.938609	0.469305	+	0.883036i	$0.344505\pi$
$938$	−0.232699	−0.00759788
$939$	−57.7177	−1.88354
$940$	−9.23125	−0.301090
$941$	−0.912738	−0.0297544	−0.0148772	−	0.999889i	$-0.504736\pi$
$941$	−0.912738	−0.0297544	−0.0148772	+	0.999889i	$0.504736\pi$
$942$	30.9249	1.00759
$943$	1.95300	0.0635985
$944$	−1.14900	−0.0373967
$945$	−1.12092	−0.0364635
$946$	12.8184	0.416764
$947$	−30.8578	−1.00274	−0.501372	−	0.865232i	$-0.667171\pi$
$947$	−30.8578	−1.00274	−0.501372	+	0.865232i	$0.667171\pi$
$948$	32.6473	1.06033
$949$	0.938943	0.0304794
$950$	4.61666	0.149784
$951$	28.6093	0.927721
$952$	3.87719	0.125661
$953$	23.4044	0.758144	0.379072	−	0.925367i	$-0.376243\pi$
$953$	23.4044	0.758144	0.379072	+	0.925367i	$0.376243\pi$
$954$	7.60135	0.246103
$955$	15.7785	0.510582
$956$	−3.13344	−0.101343
$957$	−18.4630	−0.596825
$958$	−14.6002	−0.471710
$959$	−7.44738	−0.240488
$960$	−2.37460	−0.0766398
$961$	78.2029	2.52267
$962$	3.69948	0.119276
$963$	−5.38635	−0.173573
$964$	5.21734	0.168039
$965$	−10.5379	−0.339227
$966$	23.1925	0.746206
$967$	16.7059	0.537224	0.268612	−	0.963248i	$-0.413435\pi$
$967$	16.7059	0.537224	0.268612	+	0.963248i	$0.413435\pi$
$968$	−1.00000	−0.0321412
$969$	32.5310	1.04505
$970$	−4.39877	−0.141236
$971$	−37.6675	−1.20881	−0.604404	−	0.796678i	$-0.706589\pi$
$971$	−37.6675	−1.20881	−0.604404	+	0.796678i	$0.706589\pi$
$972$	21.0614	0.675546
$973$	−7.12734	−0.228492
$974$	6.74394	0.216090
$975$	2.22961	0.0714047
$976$	6.27310	0.200797
$977$	−44.6623	−1.42887	−0.714437	−	0.699699i	$-0.753317\pi$
$977$	−44.6623	−1.42887	−0.714437	+	0.699699i	$0.753317\pi$
$978$	−49.6962	−1.58911
$979$	5.15145	0.164641
$980$	−5.29283	−0.169073
$981$	−46.2588	−1.47693
$982$	−18.2001	−0.580789
$983$	−57.8128	−1.84394	−0.921971	−	0.387259i	$-0.873422\pi$
$983$	−57.8128	−1.84394	−0.921971	+	0.387259i	$0.873422\pi$
$984$	−0.620404	−0.0197777
$985$	−11.1741	−0.356036
$986$	23.0724	0.734773
$987$	−28.6410	−0.911654
$988$	4.33478	0.137908
$989$	−95.8195	−3.04688
$990$	2.63872	0.0838640
$991$	24.7878	0.787410	0.393705	−	0.919237i	$-0.371193\pi$
$991$	24.7878	0.787410	0.393705	+	0.919237i	$0.371193\pi$
$992$	10.4500	0.331788
$993$	−33.2878	−1.05635
$994$	19.3801	0.614699
$995$	−13.8712	−0.439747
$996$	33.5849	1.06418
$997$	32.0417	1.01477	0.507386	−	0.861719i	$-0.330612\pi$
$997$	32.0417	1.01477	0.507386	+	0.861719i	$0.330612\pi$
$998$	−11.0901	−0.351052
$999$	3.38016	0.106944

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.be.1.2	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.be.1.2	✓	15	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.37460 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.37460 q^{6} -1.30659 q^{7} -1.00000 q^{8} +2.63872 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.37460 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.37460 q^{6} -1.30659 q^{7} -1.00000 q^{8} +2.63872 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.37460 q^{12} -0.938943 q^{13} +1.30659 q^{14} -2.37460 q^{15} +1.00000 q^{16} +2.96742 q^{17} -2.63872 q^{18} -4.61666 q^{19} +1.00000 q^{20} +3.10262 q^{21} +1.00000 q^{22} -7.47513 q^{23} +2.37460 q^{24} +1.00000 q^{25} +0.938943 q^{26} +0.857899 q^{27} -1.30659 q^{28} -7.77522 q^{29} +2.37460 q^{30} -10.4500 q^{31} -1.00000 q^{32} +2.37460 q^{33} -2.96742 q^{34} -1.30659 q^{35} +2.63872 q^{36} +3.94005 q^{37} +4.61666 q^{38} +2.22961 q^{39} -1.00000 q^{40} -0.261267 q^{41} -3.10262 q^{42} +12.8184 q^{43} -1.00000 q^{44} +2.63872 q^{45} +7.47513 q^{46} -9.23125 q^{47} -2.37460 q^{48} -5.29283 q^{49} -1.00000 q^{50} -7.04643 q^{51} -0.938943 q^{52} -2.88070 q^{53} -0.857899 q^{54} -1.00000 q^{55} +1.30659 q^{56} +10.9627 q^{57} +7.77522 q^{58} -1.14900 q^{59} -2.37460 q^{60} +6.27310 q^{61} +10.4500 q^{62} -3.44771 q^{63} +1.00000 q^{64} -0.938943 q^{65} -2.37460 q^{66} -0.178097 q^{67} +2.96742 q^{68} +17.7504 q^{69} +1.30659 q^{70} +14.8326 q^{71} -2.63872 q^{72} -1.00000 q^{73} -3.94005 q^{74} -2.37460 q^{75} -4.61666 q^{76} +1.30659 q^{77} -2.22961 q^{78} -13.7485 q^{79} +1.00000 q^{80} -9.95332 q^{81} +0.261267 q^{82} -14.1434 q^{83} +3.10262 q^{84} +2.96742 q^{85} -12.8184 q^{86} +18.4630 q^{87} +1.00000 q^{88} -5.15145 q^{89} -2.63872 q^{90} +1.22681 q^{91} -7.47513 q^{92} +24.8146 q^{93} +9.23125 q^{94} -4.61666 q^{95} +2.37460 q^{96} +4.39877 q^{97} +5.29283 q^{98} -2.63872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9	\( 15 q - 15 q^{2} + 3 q^{3} + 15 q^{4} + 15 q^{5} - 3 q^{6} + 7 q^{7} - 15 q^{8} + 12 q^{9} - 15 q^{10} - 15 q^{11} + 3 q^{12} + 13 q^{13} - 7 q^{14} + 3 q^{15} + 15 q^{16} + 20 q^{17} - 12 q^{18} + 3 q^{19} + 15 q^{20} + 22 q^{21} + 15 q^{22} + 2 q^{23} - 3 q^{24} + 15 q^{25} - 13 q^{26} + 33 q^{27} + 7 q^{28} + 11 q^{29} - 3 q^{30} - 3 q^{31} - 15 q^{32} - 3 q^{33} - 20 q^{34} + 7 q^{35} + 12 q^{36} + 9 q^{37} - 3 q^{38} + 11 q^{39} - 15 q^{40} + 17 q^{41} - 22 q^{42} + 29 q^{43} - 15 q^{44} + 12 q^{45} - 2 q^{46} - 2 q^{47} + 3 q^{48} + 20 q^{49} - 15 q^{50} + 7 q^{51} + 13 q^{52} + 3 q^{53} - 33 q^{54} - 15 q^{55} - 7 q^{56} + 13 q^{57} - 11 q^{58} - 32 q^{59} + 3 q^{60} + 61 q^{61} + 3 q^{62} + 20 q^{63} + 15 q^{64} + 13 q^{65} + 3 q^{66} + 7 q^{67} + 20 q^{68} - 23 q^{69} - 7 q^{70} - 6 q^{71} - 12 q^{72} - 15 q^{73} - 9 q^{74} + 3 q^{75} + 3 q^{76} - 7 q^{77} - 11 q^{78} + 12 q^{79} + 15 q^{80} + 3 q^{81} - 17 q^{82} + 17 q^{83} + 22 q^{84} + 20 q^{85} - 29 q^{86} + 23 q^{87} + 15 q^{88} - 18 q^{89} - 12 q^{90} - 15 q^{91} + 2 q^{92} + 32 q^{93} + 2 q^{94} + 3 q^{95} - 3 q^{96} + 36 q^{97} - 20 q^{98} - 12 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 + 3 * q^3 + 15 * q^4 + 15 * q^5 - 3 * q^6 + 7 * q^7 - 15 * q^8 + 12 * q^9 - 15 * q^10 - 15 * q^11 + 3 * q^12 + 13 * q^13 - 7 * q^14 + 3 * q^15 + 15 * q^16 + 20 * q^17 - 12 * q^18 + 3 * q^19 + 15 * q^20 + 22 * q^21 + 15 * q^22 + 2 * q^23 - 3 * q^24 + 15 * q^25 - 13 * q^26 + 33 * q^27 + 7 * q^28 + 11 * q^29 - 3 * q^30 - 3 * q^31 - 15 * q^32 - 3 * q^33 - 20 * q^34 + 7 * q^35 + 12 * q^36 + 9 * q^37 - 3 * q^38 + 11 * q^39 - 15 * q^40 + 17 * q^41 - 22 * q^42 + 29 * q^43 - 15 * q^44 + 12 * q^45 - 2 * q^46 - 2 * q^47 + 3 * q^48 + 20 * q^49 - 15 * q^50 + 7 * q^51 + 13 * q^52 + 3 * q^53 - 33 * q^54 - 15 * q^55 - 7 * q^56 + 13 * q^57 - 11 * q^58 - 32 * q^59 + 3 * q^60 + 61 * q^61 + 3 * q^62 + 20 * q^63 + 15 * q^64 + 13 * q^65 + 3 * q^66 + 7 * q^67 + 20 * q^68 - 23 * q^69 - 7 * q^70 - 6 * q^71 - 12 * q^72 - 15 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 - 7 * q^77 - 11 * q^78 + 12 * q^79 + 15 * q^80 + 3 * q^81 - 17 * q^82 + 17 * q^83 + 22 * q^84 + 20 * q^85 - 29 * q^86 + 23 * q^87 + 15 * q^88 - 18 * q^89 - 12 * q^90 - 15 * q^91 + 2 * q^92 + 32 * q^93 + 2 * q^94 + 3 * q^95 - 3 * q^96 + 36 * q^97 - 20 * q^98 - 12 * q^99

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