LMFDB - Embedded newform 5290.2.a.bj.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 15x^{8} + 35x^{7} + 78x^{6} - 123x^{5} - 185x^{4} + 140x^{3} + 177x^{2} - 15x - 23 $ x^10 - 3x^9 - 15x^8 + 35x^7 + 78x^6 - 123x^5 - 185x^4 + 140x^3 + 177x^2 - 15*x - 23
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.414299$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.26320 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.26320 q^{6} -0.287092 q^{7} -1.00000 q^{8} +2.12206 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.26320 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.26320 q^{6} -0.287092 q^{7} -1.00000 q^{8} +2.12206 q^{9} -1.00000 q^{10} +1.47643 q^{11} -2.26320 q^{12} +1.73974 q^{13} +0.287092 q^{14} -2.26320 q^{15} +1.00000 q^{16} -4.99392 q^{17} -2.12206 q^{18} -5.09401 q^{19} +1.00000 q^{20} +0.649745 q^{21} -1.47643 q^{22} +2.26320 q^{24} +1.00000 q^{25} -1.73974 q^{26} +1.98694 q^{27} -0.287092 q^{28} -5.01931 q^{29} +2.26320 q^{30} +0.0426355 q^{31} -1.00000 q^{32} -3.34145 q^{33} +4.99392 q^{34} -0.287092 q^{35} +2.12206 q^{36} -4.38155 q^{37} +5.09401 q^{38} -3.93737 q^{39} -1.00000 q^{40} +8.06043 q^{41} -0.649745 q^{42} +3.92017 q^{43} +1.47643 q^{44} +2.12206 q^{45} +4.95602 q^{47} -2.26320 q^{48} -6.91758 q^{49} -1.00000 q^{50} +11.3022 q^{51} +1.73974 q^{52} -1.93961 q^{53} -1.98694 q^{54} +1.47643 q^{55} +0.287092 q^{56} +11.5287 q^{57} +5.01931 q^{58} +5.45392 q^{59} -2.26320 q^{60} +9.80969 q^{61} -0.0426355 q^{62} -0.609227 q^{63} +1.00000 q^{64} +1.73974 q^{65} +3.34145 q^{66} -6.75326 q^{67} -4.99392 q^{68} +0.287092 q^{70} +3.56589 q^{71} -2.12206 q^{72} -11.6872 q^{73} +4.38155 q^{74} -2.26320 q^{75} -5.09401 q^{76} -0.423871 q^{77} +3.93737 q^{78} +13.5746 q^{79} +1.00000 q^{80} -10.8630 q^{81} -8.06043 q^{82} -9.75885 q^{83} +0.649745 q^{84} -4.99392 q^{85} -3.92017 q^{86} +11.3597 q^{87} -1.47643 q^{88} -3.29769 q^{89} -2.12206 q^{90} -0.499464 q^{91} -0.0964927 q^{93} -4.95602 q^{94} -5.09401 q^{95} +2.26320 q^{96} +4.84385 q^{97} +6.91758 q^{98} +3.13308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 9 q^{11} + 4 q^{12} - 7 q^{13} + 7 q^{14} + 4 q^{15} + 10 q^{16} - 18 q^{17} - 14 q^{18} + 16 q^{19} + 10 q^{20} + 12 q^{21} - 9 q^{22} - 4 q^{24} + 10 q^{25} + 7 q^{26} + 13 q^{27} - 7 q^{28} + 10 q^{29} - 4 q^{30} - 3 q^{31} - 10 q^{32} + 25 q^{33} + 18 q^{34} - 7 q^{35} + 14 q^{36} - 8 q^{37} - 16 q^{38} + 12 q^{39} - 10 q^{40} + 10 q^{41} - 12 q^{42} - 9 q^{43} + 9 q^{44} + 14 q^{45} + 21 q^{47} + 4 q^{48} + 7 q^{49} - 10 q^{50} - 9 q^{51} - 7 q^{52} - 40 q^{53} - 13 q^{54} + 9 q^{55} + 7 q^{56} + 9 q^{57} - 10 q^{58} + 29 q^{59} + 4 q^{60} + 25 q^{61} + 3 q^{62} + 6 q^{63} + 10 q^{64} - 7 q^{65} - 25 q^{66} - 7 q^{67} - 18 q^{68} + 7 q^{70} + 64 q^{71} - 14 q^{72} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 16 q^{76} + 57 q^{77} - 12 q^{78} + 44 q^{79} + 10 q^{80} + 14 q^{81} - 10 q^{82} - 26 q^{83} + 12 q^{84} - 18 q^{85} + 9 q^{86} + 25 q^{87} - 9 q^{88} + 11 q^{89} - 14 q^{90} + 5 q^{93} - 21 q^{94} + 16 q^{95} - 4 q^{96} - 10 q^{97} - 7 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 9 * q^11 + 4 * q^12 - 7 * q^13 + 7 * q^14 + 4 * q^15 + 10 * q^16 - 18 * q^17 - 14 * q^18 + 16 * q^19 + 10 * q^20 + 12 * q^21 - 9 * q^22 - 4 * q^24 + 10 * q^25 + 7 * q^26 + 13 * q^27 - 7 * q^28 + 10 * q^29 - 4 * q^30 - 3 * q^31 - 10 * q^32 + 25 * q^33 + 18 * q^34 - 7 * q^35 + 14 * q^36 - 8 * q^37 - 16 * q^38 + 12 * q^39 - 10 * q^40 + 10 * q^41 - 12 * q^42 - 9 * q^43 + 9 * q^44 + 14 * q^45 + 21 * q^47 + 4 * q^48 + 7 * q^49 - 10 * q^50 - 9 * q^51 - 7 * q^52 - 40 * q^53 - 13 * q^54 + 9 * q^55 + 7 * q^56 + 9 * q^57 - 10 * q^58 + 29 * q^59 + 4 * q^60 + 25 * q^61 + 3 * q^62 + 6 * q^63 + 10 * q^64 - 7 * q^65 - 25 * q^66 - 7 * q^67 - 18 * q^68 + 7 * q^70 + 64 * q^71 - 14 * q^72 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 16 * q^76 + 57 * q^77 - 12 * q^78 + 44 * q^79 + 10 * q^80 + 14 * q^81 - 10 * q^82 - 26 * q^83 + 12 * q^84 - 18 * q^85 + 9 * q^86 + 25 * q^87 - 9 * q^88 + 11 * q^89 - 14 * q^90 + 5 * q^93 - 21 * q^94 + 16 * q^95 - 4 * q^96 - 10 * q^97 - 7 * q^98 + 13 * 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
$3$	−2.26320	−1.30666	−0.653329	−	0.757074i	$-0.726628\pi$
$3$	−2.26320	−1.30666	−0.653329	+	0.757074i	$0.726628\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.26320	0.923947
$7$	−0.287092	−0.108510	−0.0542552	−	0.998527i	$-0.517278\pi$
$7$	−0.287092	−0.108510	−0.0542552	+	0.998527i	$0.517278\pi$
$8$	−1.00000	−0.353553
$9$	2.12206	0.707355
$10$	−1.00000	−0.316228
$11$	1.47643	0.445160	0.222580	−	0.974914i	$-0.428552\pi$
$11$	1.47643	0.445160	0.222580	+	0.974914i	$0.428552\pi$
$12$	−2.26320	−0.653329
$13$	1.73974	0.482516	0.241258	−	0.970461i	$-0.422440\pi$
$13$	1.73974	0.482516	0.241258	+	0.970461i	$0.422440\pi$
$14$	0.287092	0.0767285
$15$	−2.26320	−0.584355
$16$	1.00000	0.250000
$17$	−4.99392	−1.21120	−0.605602	−	0.795767i	$-0.707068\pi$
$17$	−4.99392	−1.21120	−0.605602	+	0.795767i	$0.707068\pi$
$18$	−2.12206	−0.500175
$19$	−5.09401	−1.16864	−0.584322	−	0.811522i	$-0.698640\pi$
$19$	−5.09401	−1.16864	−0.584322	+	0.811522i	$0.698640\pi$
$20$	1.00000	0.223607
$21$	0.649745	0.141786
$22$	−1.47643	−0.314776
$23$	0	0
$23$	0	0
$24$	2.26320	0.461973
$25$	1.00000	0.200000
$26$	−1.73974	−0.341190
$27$	1.98694	0.382387
$28$	−0.287092	−0.0542552
$29$	−5.01931	−0.932062	−0.466031	−	0.884768i	$-0.654317\pi$
$29$	−5.01931	−0.932062	−0.466031	+	0.884768i	$0.654317\pi$
$30$	2.26320	0.413201
$31$	0.0426355	0.00765757	0.00382879	−	0.999993i	$-0.498781\pi$
$31$	0.0426355	0.00765757	0.00382879	+	0.999993i	$0.498781\pi$
$32$	−1.00000	−0.176777
$33$	−3.34145	−0.581672
$34$	4.99392	0.856451
$35$	−0.287092	−0.0485274
$36$	2.12206	0.353677
$37$	−4.38155	−0.720322	−0.360161	−	0.932890i	$-0.617278\pi$
$37$	−4.38155	−0.720322	−0.360161	+	0.932890i	$0.617278\pi$
$38$	5.09401	0.826357
$39$	−3.93737	−0.630483
$40$	−1.00000	−0.158114
$41$	8.06043	1.25883	0.629414	−	0.777070i	$-0.283295\pi$
$41$	8.06043	1.25883	0.629414	+	0.777070i	$0.283295\pi$
$42$	−0.649745	−0.100258
$43$	3.92017	0.597820	0.298910	−	0.954281i	$-0.403377\pi$
$43$	3.92017	0.597820	0.298910	+	0.954281i	$0.403377\pi$
$44$	1.47643	0.222580
$45$	2.12206	0.316339
$46$	0	0
$47$	4.95602	0.722909	0.361455	−	0.932390i	$-0.382280\pi$
$47$	4.95602	0.722909	0.361455	+	0.932390i	$0.382280\pi$
$48$	−2.26320	−0.326664
$49$	−6.91758	−0.988225
$50$	−1.00000	−0.141421
$51$	11.3022	1.58263
$52$	1.73974	0.241258
$53$	−1.93961	−0.266427	−0.133213	−	0.991087i	$-0.542530\pi$
$53$	−1.93961	−0.266427	−0.133213	+	0.991087i	$0.542530\pi$
$54$	−1.98694	−0.270389
$55$	1.47643	0.199082
$56$	0.287092	0.0383642
$57$	11.5287	1.52702
$58$	5.01931	0.659068
$59$	5.45392	0.710040	0.355020	−	0.934859i	$-0.384474\pi$
$59$	5.45392	0.710040	0.355020	+	0.934859i	$0.384474\pi$
$60$	−2.26320	−0.292178
$61$	9.80969	1.25600	0.628001	−	0.778212i	$-0.283873\pi$
$61$	9.80969	1.25600	0.628001	+	0.778212i	$0.283873\pi$
$62$	−0.0426355	−0.00541472
$63$	−0.609227	−0.0767554
$64$	1.00000	0.125000
$65$	1.73974	0.215788
$66$	3.34145	0.411304
$67$	−6.75326	−0.825043	−0.412521	−	0.910948i	$-0.635352\pi$
$67$	−6.75326	−0.825043	−0.412521	+	0.910948i	$0.635352\pi$
$68$	−4.99392	−0.605602
$69$	0	0
$70$	0.287092	0.0343140
$71$	3.56589	0.423193	0.211596	−	0.977357i	$-0.432134\pi$
$71$	3.56589	0.423193	0.211596	+	0.977357i	$0.432134\pi$
$72$	−2.12206	−0.250088
$73$	−11.6872	−1.36788	−0.683941	−	0.729538i	$-0.739735\pi$
$73$	−11.6872	−1.36788	−0.683941	+	0.729538i	$0.739735\pi$
$74$	4.38155	0.509344
$75$	−2.26320	−0.261332
$76$	−5.09401	−0.584322
$77$	−0.423871	−0.0483045
$78$	3.93737	0.445819
$79$	13.5746	1.52726	0.763629	−	0.645656i	$-0.223416\pi$
$79$	13.5746	1.52726	0.763629	+	0.645656i	$0.223416\pi$
$80$	1.00000	0.111803
$81$	−10.8630	−1.20700
$82$	−8.06043	−0.890126
$83$	−9.75885	−1.07117	−0.535586	−	0.844480i	$-0.679909\pi$
$83$	−9.75885	−1.07117	−0.535586	+	0.844480i	$0.679909\pi$
$84$	0.649745	0.0708930
$85$	−4.99392	−0.541667
$86$	−3.92017	−0.422723
$87$	11.3597	1.21789
$88$	−1.47643	−0.157388
$89$	−3.29769	−0.349555	−0.174777	−	0.984608i	$-0.555921\pi$
$89$	−3.29769	−0.349555	−0.174777	+	0.984608i	$0.555921\pi$
$90$	−2.12206	−0.223685
$91$	−0.499464	−0.0523580
$92$	0	0
$93$	−0.0964927	−0.0100058
$94$	−4.95602	−0.511174
$95$	−5.09401	−0.522634
$96$	2.26320	0.230987
$97$	4.84385	0.491818	0.245909	−	0.969293i	$-0.420914\pi$
$97$	4.84385	0.491818	0.245909	+	0.969293i	$0.420914\pi$
$98$	6.91758	0.698781
$99$	3.13308	0.314886
$100$	1.00000	0.100000
$101$	12.9575	1.28932	0.644658	−	0.764471i	$-0.277000\pi$
$101$	12.9575	1.28932	0.644658	+	0.764471i	$0.277000\pi$
$102$	−11.3022	−1.11909
$103$	6.09164	0.600227	0.300113	−	0.953904i	$-0.402975\pi$
$103$	6.09164	0.600227	0.300113	+	0.953904i	$0.402975\pi$
$104$	−1.73974	−0.170595
$105$	0.649745	0.0634086
$106$	1.93961	0.188392
$107$	−15.3428	−1.48325	−0.741625	−	0.670815i	$-0.765944\pi$
$107$	−15.3428	−1.48325	−0.741625	+	0.670815i	$0.765944\pi$
$108$	1.98694	0.191194
$109$	18.4053	1.76291	0.881453	−	0.472271i	$-0.156566\pi$
$109$	18.4053	1.76291	0.881453	+	0.472271i	$0.156566\pi$
$110$	−1.47643	−0.140772
$111$	9.91630	0.941214
$112$	−0.287092	−0.0271276
$113$	−11.9384	−1.12307	−0.561534	−	0.827454i	$-0.689789\pi$
$113$	−11.9384	−1.12307	−0.561534	+	0.827454i	$0.689789\pi$
$114$	−11.5287	−1.07977
$115$	0	0
$116$	−5.01931	−0.466031
$117$	3.69183	0.341310
$118$	−5.45392	−0.502074
$119$	1.43371	0.131428
$120$	2.26320	0.206601
$121$	−8.82016	−0.801832
$122$	−9.80969	−0.888128
$123$	−18.2424	−1.64486
$124$	0.0426355	0.00382879
$125$	1.00000	0.0894427
$126$	0.609227	0.0542742
$127$	−17.9846	−1.59588	−0.797938	−	0.602739i	$-0.794076\pi$
$127$	−17.9846	−1.59588	−0.797938	+	0.602739i	$0.794076\pi$
$128$	−1.00000	−0.0883883
$129$	−8.87212	−0.781146
$130$	−1.73974	−0.152585
$131$	3.63829	0.317879	0.158939	−	0.987288i	$-0.449193\pi$
$131$	3.63829	0.317879	0.158939	+	0.987288i	$0.449193\pi$
$132$	−3.34145	−0.290836
$133$	1.46245	0.126810
$134$	6.75326	0.583393
$135$	1.98694	0.171009
$136$	4.99392	0.428225
$137$	0.659606	0.0563539	0.0281770	−	0.999603i	$-0.491030\pi$
$137$	0.659606	0.0563539	0.0281770	+	0.999603i	$0.491030\pi$
$138$	0	0
$139$	0.478719	0.0406044	0.0203022	−	0.999794i	$-0.493537\pi$
$139$	0.478719	0.0406044	0.0203022	+	0.999794i	$0.493537\pi$
$140$	−0.287092	−0.0242637
$141$	−11.2164	−0.944595
$142$	−3.56589	−0.299242
$143$	2.56860	0.214797
$144$	2.12206	0.176839
$145$	−5.01931	−0.416831
$146$	11.6872	0.967238
$147$	15.6558	1.29127
$148$	−4.38155	−0.360161
$149$	19.6763	1.61195	0.805974	−	0.591951i	$-0.201642\pi$
$149$	19.6763	1.61195	0.805974	+	0.591951i	$0.201642\pi$
$150$	2.26320	0.184789
$151$	12.4321	1.01171	0.505855	−	0.862618i	$-0.331177\pi$
$151$	12.4321	1.01171	0.505855	+	0.862618i	$0.331177\pi$
$152$	5.09401	0.413178
$153$	−10.5974	−0.856751
$154$	0.423871	0.0341565
$155$	0.0426355	0.00342457
$156$	−3.93737	−0.315242
$157$	−15.6353	−1.24784	−0.623918	−	0.781490i	$-0.714460\pi$
$157$	−15.6353	−1.24784	−0.623918	+	0.781490i	$0.714460\pi$
$158$	−13.5746	−1.07993
$159$	4.38973	0.348128
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	10.8630	0.853481
$163$	14.5893	1.14272	0.571360	−	0.820700i	$-0.306416\pi$
$163$	14.5893	1.14272	0.571360	+	0.820700i	$0.306416\pi$
$164$	8.06043	0.629414
$165$	−3.34145	−0.260132
$166$	9.75885	0.757433
$167$	16.7923	1.29943	0.649713	−	0.760179i	$-0.274889\pi$
$167$	16.7923	1.29943	0.649713	+	0.760179i	$0.274889\pi$
$168$	−0.649745	−0.0501289
$169$	−9.97332	−0.767178
$170$	4.99392	0.383017
$171$	−10.8098	−0.826646
$172$	3.92017	0.298910
$173$	−7.23851	−0.550334	−0.275167	−	0.961396i	$-0.588733\pi$
$173$	−7.23851	−0.550334	−0.275167	+	0.961396i	$0.588733\pi$
$174$	−11.3597	−0.861176
$175$	−0.287092	−0.0217021
$176$	1.47643	0.111290
$177$	−12.3433	−0.927780
$178$	3.29769	0.247173
$179$	14.3176	1.07015	0.535074	−	0.844805i	$-0.320284\pi$
$179$	14.3176	1.07015	0.535074	+	0.844805i	$0.320284\pi$
$180$	2.12206	0.158169
$181$	−11.0338	−0.820137	−0.410068	−	0.912055i	$-0.634495\pi$
$181$	−11.0338	−0.820137	−0.410068	+	0.912055i	$0.634495\pi$
$182$	0.499464	0.0370227
$183$	−22.2013	−1.64117
$184$	0	0
$185$	−4.38155	−0.322138
$186$	0.0964927	0.00707519
$187$	−7.37318	−0.539180
$188$	4.95602	0.361455
$189$	−0.570435	−0.0414930
$190$	5.09401	0.369558
$191$	13.0842	0.946738	0.473369	−	0.880864i	$-0.343038\pi$
$191$	13.0842	0.946738	0.473369	+	0.880864i	$0.343038\pi$
$192$	−2.26320	−0.163332
$193$	3.12659	0.225057	0.112528	−	0.993649i	$-0.464105\pi$
$193$	3.12659	0.225057	0.112528	+	0.993649i	$0.464105\pi$
$194$	−4.84385	−0.347768
$195$	−3.93737	−0.281961
$196$	−6.91758	−0.494113
$197$	−26.2306	−1.86885	−0.934425	−	0.356159i	$-0.884086\pi$
$197$	−26.2306	−1.86885	−0.934425	+	0.356159i	$0.884086\pi$
$198$	−3.13308	−0.222658
$199$	−3.18688	−0.225912	−0.112956	−	0.993600i	$-0.536032\pi$
$199$	−3.18688	−0.225912	−0.112956	+	0.993600i	$0.536032\pi$
$200$	−1.00000	−0.0707107
$201$	15.2840	1.07805
$202$	−12.9575	−0.911685
$203$	1.44100	0.101138
$204$	11.3022	0.791315
$205$	8.06043	0.562965
$206$	−6.09164	−0.424424
$207$	0	0
$208$	1.73974	0.120629
$209$	−7.52094	−0.520234
$210$	−0.649745	−0.0448367
$211$	−25.8850	−1.78200	−0.890998	−	0.454006i	$-0.849994\pi$
$211$	−25.8850	−1.78200	−0.890998	+	0.454006i	$0.849994\pi$
$212$	−1.93961	−0.133213
$213$	−8.07030	−0.552968
$214$	15.3428	1.04882
$215$	3.92017	0.267353
$216$	−1.98694	−0.135194
$217$	−0.0122403	−0.000830926 0
$218$	−18.4053	−1.24656
$219$	26.4504	1.78735
$220$	1.47643	0.0995409
$221$	−8.68811	−0.584426
$222$	−9.91630	−0.665539
$223$	5.42870	0.363533	0.181766	−	0.983342i	$-0.441819\pi$
$223$	5.42870	0.363533	0.181766	+	0.983342i	$0.441819\pi$
$224$	0.287092	0.0191821
$225$	2.12206	0.141471
$226$	11.9384	0.794129
$227$	−8.00402	−0.531245	−0.265623	−	0.964077i	$-0.585578\pi$
$227$	−8.00402	−0.531245	−0.265623	+	0.964077i	$0.585578\pi$
$228$	11.5287	0.763510
$229$	−26.0106	−1.71883	−0.859413	−	0.511281i	$-0.829171\pi$
$229$	−26.0106	−1.71883	−0.859413	+	0.511281i	$0.829171\pi$
$230$	0	0
$231$	0.959303	0.0631175
$232$	5.01931	0.329534
$233$	26.1749	1.71478	0.857389	−	0.514669i	$-0.172085\pi$
$233$	26.1749	1.71478	0.857389	+	0.514669i	$0.172085\pi$
$234$	−3.69183	−0.241343
$235$	4.95602	0.323295
$236$	5.45392	0.355020
$237$	−30.7219	−1.99560
$238$	−1.43371	−0.0929339
$239$	−13.2099	−0.854476	−0.427238	−	0.904139i	$-0.640513\pi$
$239$	−13.2099	−0.854476	−0.427238	+	0.904139i	$0.640513\pi$
$240$	−2.26320	−0.146089
$241$	8.64367	0.556788	0.278394	−	0.960467i	$-0.410198\pi$
$241$	8.64367	0.556788	0.278394	+	0.960467i	$0.410198\pi$
$242$	8.82016	0.566981
$243$	18.6244	1.19475
$244$	9.80969	0.628001
$245$	−6.91758	−0.441948
$246$	18.2424	1.16309
$247$	−8.86223	−0.563890
$248$	−0.0426355	−0.00270736
$249$	22.0862	1.39966
$250$	−1.00000	−0.0632456
$251$	24.1286	1.52298	0.761491	−	0.648175i	$-0.224468\pi$
$251$	24.1286	1.52298	0.761491	+	0.648175i	$0.224468\pi$
$252$	−0.609227	−0.0383777
$253$	0	0
$254$	17.9846	1.12845
$255$	11.3022	0.707774
$256$	1.00000	0.0625000
$257$	−5.74820	−0.358563	−0.179281	−	0.983798i	$-0.557377\pi$
$257$	−5.74820	−0.358563	−0.179281	+	0.983798i	$0.557377\pi$
$258$	8.87212	0.552354
$259$	1.25791	0.0781624
$260$	1.73974	0.107894
$261$	−10.6513	−0.659299
$262$	−3.63829	−0.224774
$263$	28.0121	1.72730	0.863649	−	0.504094i	$-0.168173\pi$
$263$	28.0121	1.72730	0.863649	+	0.504094i	$0.168173\pi$
$264$	3.34145	0.205652
$265$	−1.93961	−0.119150
$266$	−1.46245	−0.0896684
$267$	7.46333	0.456748
$268$	−6.75326	−0.412521
$269$	3.06357	0.186789	0.0933946	−	0.995629i	$-0.470228\pi$
$269$	3.06357	0.186789	0.0933946	+	0.995629i	$0.470228\pi$
$270$	−1.98694	−0.120921
$271$	23.4264	1.42305	0.711526	−	0.702660i	$-0.248004\pi$
$271$	23.4264	1.42305	0.711526	+	0.702660i	$0.248004\pi$
$272$	−4.99392	−0.302801
$273$	1.13039	0.0684140
$274$	−0.659606	−0.0398482
$275$	1.47643	0.0890320
$276$	0	0
$277$	7.10279	0.426765	0.213383	−	0.976969i	$-0.431552\pi$
$277$	7.10279	0.426765	0.213383	+	0.976969i	$0.431552\pi$
$278$	−0.478719	−0.0287117
$279$	0.0904754	0.00541662
$280$	0.287092	0.0171570
$281$	8.12262	0.484555	0.242277	−	0.970207i	$-0.422106\pi$
$281$	8.12262	0.484555	0.242277	+	0.970207i	$0.422106\pi$
$282$	11.2164	0.667930
$283$	14.0350	0.834292	0.417146	−	0.908839i	$-0.363030\pi$
$283$	14.0350	0.834292	0.417146	+	0.908839i	$0.363030\pi$
$284$	3.56589	0.211596
$285$	11.5287	0.682904
$286$	−2.56860	−0.151884
$287$	−2.31408	−0.136596
$288$	−2.12206	−0.125044
$289$	7.93928	0.467017
$290$	5.01931	0.294744
$291$	−10.9626	−0.642638
$292$	−11.6872	−0.683941
$293$	15.9441	0.931461	0.465731	−	0.884927i	$-0.345792\pi$
$293$	15.9441	0.931461	0.465731	+	0.884927i	$0.345792\pi$
$294$	−15.6558	−0.913068
$295$	5.45392	0.317540
$296$	4.38155	0.254672
$297$	2.93358	0.170224
$298$	−19.6763	−1.13982
$299$	0	0
$300$	−2.26320	−0.130666
$301$	−1.12545	−0.0648697
$302$	−12.4321	−0.715388
$303$	−29.3253	−1.68470
$304$	−5.09401	−0.292161
$305$	9.80969	0.561701
$306$	10.5974	0.605815
$307$	20.5547	1.17312	0.586561	−	0.809905i	$-0.300482\pi$
$307$	20.5547	1.17312	0.586561	+	0.809905i	$0.300482\pi$
$308$	−0.423871	−0.0241523
$309$	−13.7866	−0.784291
$310$	−0.0426355	−0.00242154
$311$	8.60372	0.487872	0.243936	−	0.969791i	$-0.421561\pi$
$311$	8.60372	0.487872	0.243936	+	0.969791i	$0.421561\pi$
$312$	3.93737	0.222910
$313$	−10.6201	−0.600285	−0.300142	−	0.953894i	$-0.597034\pi$
$313$	−10.6201	−0.600285	−0.300142	+	0.953894i	$0.597034\pi$
$314$	15.6353	0.882353
$315$	−0.609227	−0.0343260
$316$	13.5746	0.763629
$317$	18.8686	1.05977	0.529884	−	0.848070i	$-0.322235\pi$
$317$	18.8686	1.05977	0.529884	+	0.848070i	$0.322235\pi$
$318$	−4.38973	−0.246164
$319$	−7.41066	−0.414917
$320$	1.00000	0.0559017
$321$	34.7239	1.93810
$322$	0	0
$323$	25.4391	1.41547
$324$	−10.8630	−0.603502
$325$	1.73974	0.0965032
$326$	−14.5893	−0.808025
$327$	−41.6548	−2.30352
$328$	−8.06043	−0.445063
$329$	−1.42283	−0.0784432
$330$	3.34145	0.183941
$331$	0.488401	0.0268450	0.0134225	−	0.999910i	$-0.495727\pi$
$331$	0.488401	0.0268450	0.0134225	+	0.999910i	$0.495727\pi$
$332$	−9.75885	−0.535586
$333$	−9.29792	−0.509523
$334$	−16.7923	−0.918833
$335$	−6.75326	−0.368970
$336$	0.649745	0.0354465
$337$	−35.5337	−1.93565	−0.967823	−	0.251633i	$-0.919033\pi$
$337$	−35.5337	−1.93565	−0.967823	+	0.251633i	$0.919033\pi$
$338$	9.97332	0.542477
$339$	27.0189	1.46747
$340$	−4.99392	−0.270834
$341$	0.0629484	0.00340885
$342$	10.8098	0.584527
$343$	3.99562	0.215743
$344$	−3.92017	−0.211361
$345$	0	0
$346$	7.23851	0.389145
$347$	34.4773	1.85084	0.925419	−	0.378947i	$-0.123714\pi$
$347$	34.4773	1.85084	0.925419	+	0.378947i	$0.123714\pi$
$348$	11.3597	0.608943
$349$	10.0373	0.537285	0.268643	−	0.963240i	$-0.413425\pi$
$349$	10.0373	0.537285	0.268643	+	0.963240i	$0.413425\pi$
$350$	0.287092	0.0153457
$351$	3.45676	0.184508
$352$	−1.47643	−0.0786940
$353$	−5.55257	−0.295534	−0.147767	−	0.989022i	$-0.547209\pi$
$353$	−5.55257	−0.295534	−0.147767	+	0.989022i	$0.547209\pi$
$354$	12.3433	0.656039
$355$	3.56589	0.189258
$356$	−3.29769	−0.174777
$357$	−3.24478	−0.171732
$358$	−14.3176	−0.756710
$359$	−9.59994	−0.506665	−0.253333	−	0.967379i	$-0.581527\pi$
$359$	−9.59994	−0.506665	−0.253333	+	0.967379i	$0.581527\pi$
$360$	−2.12206	−0.111843
$361$	6.94889	0.365731
$362$	11.0338	0.579924
$363$	19.9618	1.04772
$364$	−0.499464	−0.0261790
$365$	−11.6872	−0.611735
$366$	22.2013	1.16048
$367$	17.0936	0.892280	0.446140	−	0.894963i	$-0.352798\pi$
$367$	17.0936	0.892280	0.446140	+	0.894963i	$0.352798\pi$
$368$	0	0
$369$	17.1048	0.890438
$370$	4.38155	0.227786
$371$	0.556847	0.0289101
$372$	−0.0964927	−0.00500291
$373$	−2.92633	−0.151520	−0.0757599	−	0.997126i	$-0.524138\pi$
$373$	−2.92633	−0.151520	−0.0757599	+	0.997126i	$0.524138\pi$
$374$	7.37318	0.381258
$375$	−2.26320	−0.116871
$376$	−4.95602	−0.255587
$377$	−8.73227	−0.449735
$378$	0.570435	0.0293400
$379$	−5.01053	−0.257374	−0.128687	−	0.991685i	$-0.541076\pi$
$379$	−5.01053	−0.257374	−0.128687	+	0.991685i	$0.541076\pi$
$380$	−5.09401	−0.261317
$381$	40.7027	2.08526
$382$	−13.0842	−0.669445
$383$	9.63174	0.492159	0.246080	−	0.969250i	$-0.420858\pi$
$383$	9.63174	0.492159	0.246080	+	0.969250i	$0.420858\pi$
$384$	2.26320	0.115493
$385$	−0.423871	−0.0216024
$386$	−3.12659	−0.159139
$387$	8.31885	0.422871
$388$	4.84385	0.245909
$389$	−4.14519	−0.210169	−0.105085	−	0.994463i	$-0.533511\pi$
$389$	−4.14519	−0.210169	−0.105085	+	0.994463i	$0.533511\pi$
$390$	3.93737	0.199376
$391$	0	0
$392$	6.91758	0.349390
$393$	−8.23417	−0.415359
$394$	26.2306	1.32148
$395$	13.5746	0.683010
$396$	3.13308	0.157443
$397$	34.6537	1.73922	0.869609	−	0.493741i	$-0.164371\pi$
$397$	34.6537	1.73922	0.869609	+	0.493741i	$0.164371\pi$
$398$	3.18688	0.159744
$399$	−3.30981	−0.165698
$400$	1.00000	0.0500000
$401$	−17.8386	−0.890817	−0.445409	−	0.895327i	$-0.646942\pi$
$401$	−17.8386	−0.890817	−0.445409	+	0.895327i	$0.646942\pi$
$402$	−15.2840	−0.762295
$403$	0.0741746	0.00369490
$404$	12.9575	0.644658
$405$	−10.8630	−0.539789
$406$	−1.44100	−0.0715157
$407$	−6.46904	−0.320659
$408$	−11.3022	−0.559544
$409$	20.6034	1.01877	0.509386	−	0.860538i	$-0.329873\pi$
$409$	20.6034	1.01877	0.509386	+	0.860538i	$0.329873\pi$
$410$	−8.06043	−0.398076
$411$	−1.49282	−0.0736353
$412$	6.09164	0.300113
$413$	−1.56578	−0.0770468
$414$	0	0
$415$	−9.75885	−0.479043
$416$	−1.73974	−0.0852976
$417$	−1.08344	−0.0530561
$418$	7.52094	0.367861
$419$	−37.4974	−1.83187	−0.915933	−	0.401332i	$-0.868547\pi$
$419$	−37.4974	−1.83187	−0.915933	+	0.401332i	$0.868547\pi$
$420$	0.649745	0.0317043
$421$	2.21098	0.107756	0.0538782	−	0.998548i	$-0.482842\pi$
$421$	2.21098	0.107756	0.0538782	+	0.998548i	$0.482842\pi$
$422$	25.8850	1.26006
$423$	10.5170	0.511353
$424$	1.93961	0.0941960
$425$	−4.99392	−0.242241
$426$	8.07030	0.391008
$427$	−2.81628	−0.136289
$428$	−15.3428	−0.741625
$429$	−5.81325	−0.280666
$430$	−3.92017	−0.189047
$431$	−4.20202	−0.202404	−0.101202	−	0.994866i	$-0.532269\pi$
$431$	−4.20202	−0.202404	−0.101202	+	0.994866i	$0.532269\pi$
$432$	1.98694	0.0955968
$433$	4.09492	0.196789	0.0983947	−	0.995147i	$-0.468629\pi$
$433$	4.09492	0.196789	0.0983947	+	0.995147i	$0.468629\pi$
$434$	0.0122403	0.000587554 0
$435$	11.3597	0.544655
$436$	18.4053	0.881453
$437$	0	0
$438$	−26.4504	−1.26385
$439$	−0.667729	−0.0318690	−0.0159345	−	0.999873i	$-0.505072\pi$
$439$	−0.667729	−0.0318690	−0.0159345	+	0.999873i	$0.505072\pi$
$440$	−1.47643	−0.0703860
$441$	−14.6795	−0.699026
$442$	8.68811	0.413251
$443$	41.0447	1.95009	0.975045	−	0.222005i	$-0.0712602\pi$
$443$	41.0447	1.95009	0.975045	+	0.222005i	$0.0712602\pi$
$444$	9.91630	0.470607
$445$	−3.29769	−0.156326
$446$	−5.42870	−0.257056
$447$	−44.5314	−2.10626
$448$	−0.287092	−0.0135638
$449$	33.8722	1.59853	0.799265	−	0.600979i	$-0.205222\pi$
$449$	33.8722	1.59853	0.799265	+	0.600979i	$0.205222\pi$
$450$	−2.12206	−0.100035
$451$	11.9007	0.560380
$452$	−11.9384	−0.561534
$453$	−28.1363	−1.32196
$454$	8.00402	0.375647
$455$	−0.499464	−0.0234152
$456$	−11.5287	−0.539883
$457$	25.1770	1.17773	0.588866	−	0.808231i	$-0.299575\pi$
$457$	25.1770	1.17773	0.588866	+	0.808231i	$0.299575\pi$
$458$	26.0106	1.21539
$459$	−9.92264	−0.463149
$460$	0	0
$461$	−14.7495	−0.686955	−0.343477	−	0.939161i	$-0.611605\pi$
$461$	−14.7495	−0.686955	−0.343477	+	0.939161i	$0.611605\pi$
$462$	−0.959303	−0.0446308
$463$	38.1622	1.77355	0.886774	−	0.462204i	$-0.152941\pi$
$463$	38.1622	1.77355	0.886774	+	0.462204i	$0.152941\pi$
$464$	−5.01931	−0.233016
$465$	−0.0964927	−0.00447474
$466$	−26.1749	−1.21253
$467$	−29.9686	−1.38678	−0.693391	−	0.720562i	$-0.743884\pi$
$467$	−29.9686	−1.38678	−0.693391	+	0.720562i	$0.743884\pi$
$468$	3.69183	0.170655
$469$	1.93881	0.0895257
$470$	−4.95602	−0.228604
$471$	35.3858	1.63049
$472$	−5.45392	−0.251037
$473$	5.78785	0.266126
$474$	30.7219	1.41110
$475$	−5.09401	−0.233729
$476$	1.43371	0.0657142
$477$	−4.11599	−0.188458
$478$	13.2099	0.604205
$479$	−8.60714	−0.393270	−0.196635	−	0.980477i	$-0.563001\pi$
$479$	−8.60714	−0.393270	−0.196635	+	0.980477i	$0.563001\pi$
$480$	2.26320	0.103300
$481$	−7.62273	−0.347567
$482$	−8.64367	−0.393708
$483$	0	0
$484$	−8.82016	−0.400916
$485$	4.84385	0.219948
$486$	−18.6244	−0.844819
$487$	32.7761	1.48523	0.742613	−	0.669721i	$-0.233586\pi$
$487$	32.7761	1.48523	0.742613	+	0.669721i	$0.233586\pi$
$488$	−9.80969	−0.444064
$489$	−33.0184	−1.49314
$490$	6.91758	0.312504
$491$	34.5730	1.56026	0.780129	−	0.625619i	$-0.215154\pi$
$491$	34.5730	1.56026	0.780129	+	0.625619i	$0.215154\pi$
$492$	−18.2424	−0.822429
$493$	25.0660	1.12892
$494$	8.86223	0.398730
$495$	3.13308	0.140821
$496$	0.0426355	0.00191439
$497$	−1.02374	−0.0459208
$498$	−22.0862	−0.989706
$499$	29.2733	1.31045	0.655227	−	0.755432i	$-0.272573\pi$
$499$	29.2733	1.31045	0.655227	+	0.755432i	$0.272573\pi$
$500$	1.00000	0.0447214
$501$	−38.0043	−1.69791
$502$	−24.1286	−1.07691
$503$	−3.80569	−0.169687	−0.0848437	−	0.996394i	$-0.527039\pi$
$503$	−3.80569	−0.169687	−0.0848437	+	0.996394i	$0.527039\pi$
$504$	0.609227	0.0271371
$505$	12.9575	0.576600
$506$	0	0
$507$	22.5716	1.00244
$508$	−17.9846	−0.797938
$509$	30.8219	1.36616	0.683078	−	0.730345i	$-0.260641\pi$
$509$	30.8219	1.36616	0.683078	+	0.730345i	$0.260641\pi$
$510$	−11.3022	−0.500472
$511$	3.35529	0.148429
$512$	−1.00000	−0.0441942
$513$	−10.1215	−0.446875
$514$	5.74820	0.253542
$515$	6.09164	0.268430
$516$	−8.87212	−0.390573
$517$	7.31721	0.321810
$518$	−1.25791	−0.0552692
$519$	16.3822	0.719098
$520$	−1.73974	−0.0762925
$521$	18.3515	0.803993	0.401997	−	0.915641i	$-0.368316\pi$
$521$	18.3515	0.803993	0.401997	+	0.915641i	$0.368316\pi$
$522$	10.6513	0.466194
$523$	11.7841	0.515281	0.257641	−	0.966241i	$-0.417055\pi$
$523$	11.7841	0.515281	0.257641	+	0.966241i	$0.417055\pi$
$524$	3.63829	0.158939
$525$	0.649745	0.0283572
$526$	−28.0121	−1.22138
$527$	−0.212919	−0.00927488
$528$	−3.34145	−0.145418
$529$	0	0
$530$	1.93961	0.0842515
$531$	11.5736	0.502250
$532$	1.46245	0.0634051
$533$	14.0230	0.607405
$534$	−7.46333	−0.322970
$535$	−15.3428	−0.663329
$536$	6.75326	0.291697
$537$	−32.4036	−1.39832
$538$	−3.06357	−0.132080
$539$	−10.2133	−0.439919
$540$	1.98694	0.0855044
$541$	−21.5387	−0.926021	−0.463010	−	0.886353i	$-0.653231\pi$
$541$	−21.5387	−0.926021	−0.463010	+	0.886353i	$0.653231\pi$
$542$	−23.4264	−1.00625
$543$	24.9717	1.07164
$544$	4.99392	0.214113
$545$	18.4053	0.788396
$546$	−1.13039	−0.0483760
$547$	36.3781	1.55542	0.777709	−	0.628625i	$-0.216382\pi$
$547$	36.3781	1.55542	0.777709	+	0.628625i	$0.216382\pi$
$548$	0.659606	0.0281770
$549$	20.8168	0.888439
$550$	−1.47643	−0.0629552
$551$	25.5684	1.08925
$552$	0	0
$553$	−3.89714	−0.165723
$554$	−7.10279	−0.301769
$555$	9.91630	0.420924
$556$	0.478719	0.0203022
$557$	29.5873	1.25365	0.626827	−	0.779159i	$-0.284353\pi$
$557$	29.5873	1.25365	0.626827	+	0.779159i	$0.284353\pi$
$558$	−0.0904754	−0.00383013
$559$	6.82006	0.288458
$560$	−0.287092	−0.0121318
$561$	16.6870	0.704524
$562$	−8.12262	−0.342632
$563$	−9.35697	−0.394349	−0.197175	−	0.980368i	$-0.563177\pi$
$563$	−9.35697	−0.394349	−0.197175	+	0.980368i	$0.563177\pi$
$564$	−11.2164	−0.472298
$565$	−11.9384	−0.502251
$566$	−14.0350	−0.589934
$567$	3.11869	0.130973
$568$	−3.56589	−0.149621
$569$	33.9807	1.42455	0.712273	−	0.701903i	$-0.247666\pi$
$569$	33.9807	1.42455	0.712273	+	0.701903i	$0.247666\pi$
$570$	−11.5287	−0.482886
$571$	−8.68333	−0.363386	−0.181693	−	0.983355i	$-0.558158\pi$
$571$	−8.68333	−0.363386	−0.181693	+	0.983355i	$0.558158\pi$
$572$	2.56860	0.107398
$573$	−29.6121	−1.23706
$574$	2.31408	0.0965880
$575$	0	0
$576$	2.12206	0.0884193
$577$	−29.5153	−1.22874	−0.614370	−	0.789018i	$-0.710590\pi$
$577$	−29.5153	−1.22874	−0.614370	+	0.789018i	$0.710590\pi$
$578$	−7.93928	−0.330231
$579$	−7.07609	−0.294072
$580$	−5.01931	−0.208415
$581$	2.80168	0.116233
$582$	10.9626	0.454414
$583$	−2.86370	−0.118603
$584$	11.6872	0.483619
$585$	3.69183	0.152638
$586$	−15.9441	−0.658643
$587$	8.37477	0.345664	0.172832	−	0.984951i	$-0.444708\pi$
$587$	8.37477	0.345664	0.172832	+	0.984951i	$0.444708\pi$
$588$	15.6558	0.645636
$589$	−0.217186	−0.00894898
$590$	−5.45392	−0.224534
$591$	59.3650	2.44195
$592$	−4.38155	−0.180080
$593$	−38.7287	−1.59040	−0.795198	−	0.606350i	$-0.792633\pi$
$593$	−38.7287	−1.59040	−0.795198	+	0.606350i	$0.792633\pi$
$594$	−2.93358	−0.120366
$595$	1.43371	0.0587766
$596$	19.6763	0.805974
$597$	7.21255	0.295190
$598$	0	0
$599$	−13.0692	−0.533994	−0.266997	−	0.963697i	$-0.586031\pi$
$599$	−13.0692	−0.533994	−0.266997	+	0.963697i	$0.586031\pi$
$600$	2.26320	0.0923947
$601$	10.0729	0.410884	0.205442	−	0.978669i	$-0.434137\pi$
$601$	10.0729	0.410884	0.205442	+	0.978669i	$0.434137\pi$
$602$	1.12545	0.0458698
$603$	−14.3309	−0.583598
$604$	12.4321	0.505855
$605$	−8.82016	−0.358590
$606$	29.3253	1.19126
$607$	1.45402	0.0590167	0.0295083	−	0.999565i	$-0.490606\pi$
$607$	1.45402	0.0590167	0.0295083	+	0.999565i	$0.490606\pi$
$608$	5.09401	0.206589
$609$	−3.26127	−0.132153
$610$	−9.80969	−0.397183
$611$	8.62216	0.348815
$612$	−10.5974	−0.428376
$613$	15.4071	0.622287	0.311144	−	0.950363i	$-0.399288\pi$
$613$	15.4071	0.622287	0.311144	+	0.950363i	$0.399288\pi$
$614$	−20.5547	−0.829522
$615$	−18.2424	−0.735603
$616$	0.423871	0.0170782
$617$	19.2541	0.775142	0.387571	−	0.921840i	$-0.373314\pi$
$617$	19.2541	0.775142	0.387571	+	0.921840i	$0.373314\pi$
$618$	13.7866	0.554578
$619$	−19.9216	−0.800715	−0.400358	−	0.916359i	$-0.631114\pi$
$619$	−19.9216	−0.800715	−0.400358	+	0.916359i	$0.631114\pi$
$620$	0.0426355	0.00171228
$621$	0	0
$622$	−8.60372	−0.344978
$623$	0.946740	0.0379303
$624$	−3.93737	−0.157621
$625$	1.00000	0.0400000
$626$	10.6201	0.424466
$627$	17.0214	0.679768
$628$	−15.6353	−0.623918
$629$	21.8811	0.872457
$630$	0.609227	0.0242722
$631$	33.3152	1.32626	0.663129	−	0.748505i	$-0.269228\pi$
$631$	33.3152	1.32626	0.663129	+	0.748505i	$0.269228\pi$
$632$	−13.5746	−0.539967
$633$	58.5829	2.32846
$634$	−18.8686	−0.749369
$635$	−17.9846	−0.713698
$636$	4.38973	0.174064
$637$	−12.0348	−0.476835
$638$	7.41066	0.293391
$639$	7.56704	0.299347
$640$	−1.00000	−0.0395285
$641$	−34.4383	−1.36023	−0.680115	−	0.733105i	$-0.738070\pi$
$641$	−34.4383	−1.36023	−0.680115	+	0.733105i	$0.738070\pi$
$642$	−34.7239	−1.37044
$643$	−19.8518	−0.782880	−0.391440	−	0.920204i	$-0.628023\pi$
$643$	−19.8518	−0.782880	−0.391440	+	0.920204i	$0.628023\pi$
$644$	0	0
$645$	−8.87212	−0.349339
$646$	−25.4391	−1.00089
$647$	−13.1046	−0.515197	−0.257598	−	0.966252i	$-0.582931\pi$
$647$	−13.1046	−0.515197	−0.257598	+	0.966252i	$0.582931\pi$
$648$	10.8630	0.426740
$649$	8.05233	0.316082
$650$	−1.73974	−0.0682381
$651$	0.0277022	0.00108574
$652$	14.5893	0.571360
$653$	34.2592	1.34066	0.670332	−	0.742061i	$-0.266152\pi$
$653$	34.2592	1.34066	0.670332	+	0.742061i	$0.266152\pi$
$654$	41.6548	1.62883
$655$	3.63829	0.142160
$656$	8.06043	0.314707
$657$	−24.8010	−0.967577
$658$	1.42283	0.0554677
$659$	47.4860	1.84979	0.924896	−	0.380221i	$-0.124152\pi$
$659$	47.4860	1.84979	0.924896	+	0.380221i	$0.124152\pi$
$660$	−3.34145	−0.130066
$661$	7.96253	0.309707	0.154853	−	0.987937i	$-0.450509\pi$
$661$	7.96253	0.309707	0.154853	+	0.987937i	$0.450509\pi$
$662$	−0.488401	−0.0189823
$663$	19.6629	0.763644
$664$	9.75885	0.378717
$665$	1.46245	0.0567112
$666$	9.29792	0.360287
$667$	0	0
$668$	16.7923	0.649713
$669$	−12.2862	−0.475013
$670$	6.75326	0.260901
$671$	14.4833	0.559122
$672$	−0.649745	−0.0250645
$673$	−2.97419	−0.114647	−0.0573233	−	0.998356i	$-0.518257\pi$
$673$	−2.97419	−0.114647	−0.0573233	+	0.998356i	$0.518257\pi$
$674$	35.5337	1.36871
$675$	1.98694	0.0764775
$676$	−9.97332	−0.383589
$677$	11.1810	0.429721	0.214861	−	0.976645i	$-0.431070\pi$
$677$	11.1810	0.429721	0.214861	+	0.976645i	$0.431070\pi$
$678$	−27.0189	−1.03766
$679$	−1.39063	−0.0533674
$680$	4.99392	0.191508
$681$	18.1147	0.694156
$682$	−0.0629484	−0.00241042
$683$	−0.273541	−0.0104667	−0.00523337	−	0.999986i	$-0.501666\pi$
$683$	−0.273541	−0.0104667	−0.00523337	+	0.999986i	$0.501666\pi$
$684$	−10.8098	−0.413323
$685$	0.659606	0.0252022
$686$	−3.99562	−0.152554
$687$	58.8671	2.24592
$688$	3.92017	0.149455
$689$	−3.37442	−0.128555
$690$	0	0
$691$	22.5420	0.857537	0.428768	−	0.903414i	$-0.358948\pi$
$691$	22.5420	0.857537	0.428768	+	0.903414i	$0.358948\pi$
$692$	−7.23851	−0.275167
$693$	−0.899481	−0.0341684
$694$	−34.4773	−1.30874
$695$	0.478719	0.0181588
$696$	−11.3597	−0.430588
$697$	−40.2532	−1.52470
$698$	−10.0373	−0.379918
$699$	−59.2391	−2.24063
$700$	−0.287092	−0.0108510
$701$	37.7324	1.42513	0.712566	−	0.701605i	$-0.247533\pi$
$701$	37.7324	1.42513	0.712566	+	0.701605i	$0.247533\pi$
$702$	−3.45676	−0.130467
$703$	22.3196	0.841800
$704$	1.47643	0.0556450
$705$	−11.2164	−0.422436
$706$	5.55257	0.208974
$707$	−3.71998	−0.139904
$708$	−12.3433	−0.463890
$709$	−24.1454	−0.906801	−0.453401	−	0.891307i	$-0.649789\pi$
$709$	−24.1454	−0.906801	−0.453401	+	0.891307i	$0.649789\pi$
$710$	−3.56589	−0.133825
$711$	28.8061	1.08031
$712$	3.29769	0.123586
$713$	0	0
$714$	3.24478	0.121433
$715$	2.56860	0.0960601
$716$	14.3176	0.535074
$717$	29.8966	1.11651
$718$	9.59994	0.358266
$719$	6.67129	0.248797	0.124399	−	0.992232i	$-0.460300\pi$
$719$	6.67129	0.248797	0.124399	+	0.992232i	$0.460300\pi$
$720$	2.12206	0.0790847
$721$	−1.74886	−0.0651309
$722$	−6.94889	−0.258611
$723$	−19.5623	−0.727531
$724$	−11.0338	−0.410068
$725$	−5.01931	−0.186412
$726$	−19.9618	−0.740850
$727$	37.0655	1.37468	0.687342	−	0.726334i	$-0.258778\pi$
$727$	37.0655	1.37468	0.687342	+	0.726334i	$0.258778\pi$
$728$	0.499464	0.0185114
$729$	−9.56153	−0.354131
$730$	11.6872	0.432562
$731$	−19.5770	−0.724082
$732$	−22.2013	−0.820583
$733$	27.8901	1.03014	0.515072	−	0.857147i	$-0.327765\pi$
$733$	27.8901	1.03014	0.515072	+	0.857147i	$0.327765\pi$
$734$	−17.0936	−0.630938
$735$	15.6558	0.577475
$736$	0	0
$737$	−9.97072	−0.367276
$738$	−17.1048	−0.629635
$739$	−39.1651	−1.44071	−0.720356	−	0.693605i	$-0.756021\pi$
$739$	−39.1651	−1.44071	−0.720356	+	0.693605i	$0.756021\pi$
$740$	−4.38155	−0.161069
$741$	20.0570	0.736811
$742$	−0.556847	−0.0204425
$743$	17.4161	0.638937	0.319468	−	0.947597i	$-0.396496\pi$
$743$	17.4161	0.638937	0.319468	+	0.947597i	$0.396496\pi$
$744$	0.0964927	0.00353759
$745$	19.6763	0.720885
$746$	2.92633	0.107141
$747$	−20.7089	−0.757699
$748$	−7.37318	−0.269590
$749$	4.40480	0.160948
$750$	2.26320	0.0826403
$751$	−22.3683	−0.816232	−0.408116	−	0.912930i	$-0.633814\pi$
$751$	−22.3683	−0.816232	−0.408116	+	0.912930i	$0.633814\pi$
$752$	4.95602	0.180727
$753$	−54.6077	−1.99002
$754$	8.73227	0.318011
$755$	12.4321	0.452451
$756$	−0.570435	−0.0207465
$757$	−28.8047	−1.04692	−0.523462	−	0.852049i	$-0.675360\pi$
$757$	−28.8047	−1.04692	−0.523462	+	0.852049i	$0.675360\pi$
$758$	5.01053	0.181991
$759$	0	0
$760$	5.09401	0.184779
$761$	−3.50032	−0.126887	−0.0634433	−	0.997985i	$-0.520208\pi$
$761$	−3.50032	−0.126887	−0.0634433	+	0.997985i	$0.520208\pi$
$762$	−40.7027	−1.47450
$763$	−5.28401	−0.191294
$764$	13.0842	0.473369
$765$	−10.5974	−0.383151
$766$	−9.63174	−0.348009
$767$	9.48839	0.342606
$768$	−2.26320	−0.0816661
$769$	5.05532	0.182299	0.0911497	−	0.995837i	$-0.470946\pi$
$769$	5.05532	0.182299	0.0911497	+	0.995837i	$0.470946\pi$
$770$	0.423871	0.0152752
$771$	13.0093	0.468519
$772$	3.12659	0.112528
$773$	12.6617	0.455409	0.227705	−	0.973730i	$-0.426878\pi$
$773$	12.6617	0.455409	0.227705	+	0.973730i	$0.426878\pi$
$774$	−8.31885	−0.299015
$775$	0.0426355	0.00153151
$776$	−4.84385	−0.173884
$777$	−2.84689	−0.102132
$778$	4.14519	0.148612
$779$	−41.0599	−1.47112
$780$	−3.93737	−0.140980
$781$	5.26478	0.188389
$782$	0	0
$783$	−9.97308	−0.356409
$784$	−6.91758	−0.247056
$785$	−15.6353	−0.558049
$786$	8.23417	0.293703
$787$	−37.4072	−1.33342	−0.666711	−	0.745316i	$-0.732299\pi$
$787$	−37.4072	−1.33342	−0.666711	+	0.745316i	$0.732299\pi$
$788$	−26.2306	−0.934425
$789$	−63.3968	−2.25699
$790$	−13.5746	−0.482961
$791$	3.42741	0.121865
$792$	−3.13308	−0.111329
$793$	17.0663	0.606041
$794$	−34.6537	−1.22981
$795$	4.38973	0.155688
$796$	−3.18688	−0.112956
$797$	47.3867	1.67852	0.839261	−	0.543729i	$-0.182988\pi$
$797$	47.3867	1.67852	0.839261	+	0.543729i	$0.182988\pi$
$798$	3.30981	0.117166
$799$	−24.7500	−0.875591
$800$	−1.00000	−0.0353553
$801$	−6.99792	−0.247259
$802$	17.8386	0.629903
$803$	−17.2553	−0.608926
$804$	15.2840	0.539024
$805$	0	0
$806$	−0.0741746	−0.00261269
$807$	−6.93347	−0.244070
$808$	−12.9575	−0.455842
$809$	21.2838	0.748299	0.374150	−	0.927368i	$-0.377935\pi$
$809$	21.2838	0.748299	0.374150	+	0.927368i	$0.377935\pi$
$810$	10.8630	0.381688
$811$	−43.1924	−1.51669	−0.758346	−	0.651853i	$-0.773992\pi$
$811$	−43.1924	−1.51669	−0.758346	+	0.651853i	$0.773992\pi$
$812$	1.44100	0.0505692
$813$	−53.0186	−1.85944
$814$	6.46904	0.226740
$815$	14.5893	0.511040
$816$	11.3022	0.395657
$817$	−19.9694	−0.698639
$818$	−20.6034	−0.720380
$819$	−1.05989	−0.0370357
$820$	8.06043	0.281483
$821$	50.4149	1.75949	0.879746	−	0.475443i	$-0.157712\pi$
$821$	50.4149	1.75949	0.879746	+	0.475443i	$0.157712\pi$
$822$	1.49282	0.0520680
$823$	−17.0884	−0.595665	−0.297832	−	0.954618i	$-0.596264\pi$
$823$	−17.0884	−0.595665	−0.297832	+	0.954618i	$0.596264\pi$
$824$	−6.09164	−0.212212
$825$	−3.34145	−0.116334
$826$	1.56578	0.0544803
$827$	−36.5200	−1.26993	−0.634963	−	0.772543i	$-0.718985\pi$
$827$	−36.5200	−1.26993	−0.634963	+	0.772543i	$0.718985\pi$
$828$	0	0
$829$	−46.9819	−1.63175	−0.815874	−	0.578229i	$-0.803744\pi$
$829$	−46.9819	−1.63175	−0.815874	+	0.578229i	$0.803744\pi$
$830$	9.75885	0.338735
$831$	−16.0750	−0.557636
$832$	1.73974	0.0603145
$833$	34.5459	1.19694
$834$	1.08344	0.0375163
$835$	16.7923	0.581121
$836$	−7.52094	−0.260117
$837$	0.0847144	0.00292816
$838$	37.4974	1.29532
$839$	−55.2125	−1.90615	−0.953074	−	0.302737i	$-0.902100\pi$
$839$	−55.2125	−1.90615	−0.953074	+	0.302737i	$0.902100\pi$
$840$	−0.649745	−0.0224183
$841$	−3.80654	−0.131260
$842$	−2.21098	−0.0761953
$843$	−18.3831	−0.633147
$844$	−25.8850	−0.890998
$845$	−9.97332	−0.343093
$846$	−10.5170	−0.361581
$847$	2.53219	0.0870072
$848$	−1.93961	−0.0666066
$849$	−31.7639	−1.09013
$850$	4.99392	0.171290
$851$	0	0
$852$	−8.07030	−0.276484
$853$	6.03095	0.206496	0.103248	−	0.994656i	$-0.467077\pi$
$853$	6.03095	0.206496	0.103248	+	0.994656i	$0.467077\pi$
$854$	2.81628	0.0963712
$855$	−10.8098	−0.369688
$856$	15.3428	0.524408
$857$	2.56814	0.0877259	0.0438629	−	0.999038i	$-0.486034\pi$
$857$	2.56814	0.0877259	0.0438629	+	0.999038i	$0.486034\pi$
$858$	5.81325	0.198461
$859$	−11.6777	−0.398438	−0.199219	−	0.979955i	$-0.563840\pi$
$859$	−11.6777	−0.398438	−0.199219	+	0.979955i	$0.563840\pi$
$860$	3.92017	0.133677
$861$	5.23723	0.178484
$862$	4.20202	0.143122
$863$	29.6420	1.00902	0.504512	−	0.863405i	$-0.331672\pi$
$863$	29.6420	1.00902	0.504512	+	0.863405i	$0.331672\pi$
$864$	−1.98694	−0.0675972
$865$	−7.23851	−0.246117
$866$	−4.09492	−0.139151
$867$	−17.9682	−0.610231
$868$	−0.0122403	−0.000415463 0
$869$	20.0419	0.679874
$870$	−11.3597	−0.385129
$871$	−11.7489	−0.398096
$872$	−18.4053	−0.623282
$873$	10.2790	0.347890
$874$	0	0
$875$	−0.287092	−0.00970547
$876$	26.4504	0.893676
$877$	−7.15134	−0.241484	−0.120742	−	0.992684i	$-0.538527\pi$
$877$	−7.15134	−0.241484	−0.120742	+	0.992684i	$0.538527\pi$
$878$	0.667729	0.0225348
$879$	−36.0845	−1.21710
$880$	1.47643	0.0497704
$881$	13.8985	0.468252	0.234126	−	0.972206i	$-0.424777\pi$
$881$	13.8985	0.468252	0.234126	+	0.972206i	$0.424777\pi$
$882$	14.6795	0.494286
$883$	−12.8363	−0.431975	−0.215987	−	0.976396i	$-0.569297\pi$
$883$	−12.8363	−0.431975	−0.215987	+	0.976396i	$0.569297\pi$
$884$	−8.68811	−0.292213
$885$	−12.3433	−0.414916
$886$	−41.0447	−1.37892
$887$	−29.2906	−0.983483	−0.491741	−	0.870741i	$-0.663639\pi$
$887$	−29.2906	−0.983483	−0.491741	+	0.870741i	$0.663639\pi$
$888$	−9.91630	−0.332769
$889$	5.16323	0.173169
$890$	3.29769	0.110539
$891$	−16.0385	−0.537310
$892$	5.42870	0.181766
$893$	−25.2460	−0.844824
$894$	44.5314	1.48935
$895$	14.3176	0.478585
$896$	0.287092	0.00959106
$897$	0	0
$898$	−33.8722	−1.13033
$899$	−0.214001	−0.00713733
$900$	2.12206	0.0707355
$901$	9.68629	0.322697
$902$	−11.9007	−0.396249
$903$	2.54711	0.0847625
$904$	11.9384	0.397065
$905$	−11.0338	−0.366776
$906$	28.1363	0.934767
$907$	28.1166	0.933598	0.466799	−	0.884364i	$-0.345407\pi$
$907$	28.1166	0.933598	0.466799	+	0.884364i	$0.345407\pi$
$908$	−8.00402	−0.265623
$909$	27.4966	0.912004
$910$	0.499464	0.0165571
$911$	34.9626	1.15836	0.579182	−	0.815199i	$-0.303372\pi$
$911$	34.9626	1.15836	0.579182	+	0.815199i	$0.303372\pi$
$912$	11.5287	0.381755
$913$	−14.4083	−0.476843
$914$	−25.1770	−0.832782
$915$	−22.2013	−0.733951
$916$	−26.0106	−0.859413
$917$	−1.04452	−0.0344932
$918$	9.92264	0.327496
$919$	−15.5315	−0.512337	−0.256168	−	0.966632i	$-0.582460\pi$
$919$	−15.5315	−0.512337	−0.256168	+	0.966632i	$0.582460\pi$
$920$	0	0
$921$	−46.5194	−1.53287
$922$	14.7495	0.485750
$923$	6.20370	0.204197
$924$	0.959303	0.0315588
$925$	−4.38155	−0.144064
$926$	−38.1622	−1.25409
$927$	12.9268	0.424573
$928$	5.01931	0.164767
$929$	22.8252	0.748871	0.374436	−	0.927253i	$-0.377836\pi$
$929$	22.8252	0.748871	0.374436	+	0.927253i	$0.377836\pi$
$930$	0.0964927	0.00316412
$931$	35.2382	1.15488
$932$	26.1749	0.857389
$933$	−19.4719	−0.637482
$934$	29.9686	0.980602
$935$	−7.37318	−0.241129
$936$	−3.69183	−0.120671
$937$	−48.7945	−1.59405	−0.797024	−	0.603948i	$-0.793593\pi$
$937$	−48.7945	−1.59405	−0.797024	+	0.603948i	$0.793593\pi$
$938$	−1.93881	−0.0633043
$939$	24.0354	0.784367
$940$	4.95602	0.161647
$941$	−59.5102	−1.93998	−0.969988	−	0.243153i	$-0.921818\pi$
$941$	−59.5102	−1.93998	−0.969988	+	0.243153i	$0.921818\pi$
$942$	−35.3858	−1.15293
$943$	0	0
$944$	5.45392	0.177510
$945$	−0.570435	−0.0185562
$946$	−5.78785	−0.188179
$947$	11.5389	0.374965	0.187483	−	0.982268i	$-0.439967\pi$
$947$	11.5389	0.374965	0.187483	+	0.982268i	$0.439967\pi$
$948$	−30.7219	−0.997801
$949$	−20.3326	−0.660025
$950$	5.09401	0.165271
$951$	−42.7034	−1.38475
$952$	−1.43371	−0.0464669
$953$	−11.5985	−0.375711	−0.187856	−	0.982197i	$-0.560154\pi$
$953$	−11.5985	−0.375711	−0.187856	+	0.982197i	$0.560154\pi$
$954$	4.11599	0.133260
$955$	13.0842	0.423394
$956$	−13.2099	−0.427238
$957$	16.7718	0.542155
$958$	8.60714	0.278084
$959$	−0.189367	−0.00611499
$960$	−2.26320	−0.0730444
$961$	−30.9982	−0.999941
$962$	7.62273	0.245767
$963$	−32.5585	−1.04918
$964$	8.64367	0.278394
$965$	3.12659	0.100648
$966$	0	0
$967$	−13.6713	−0.439641	−0.219820	−	0.975540i	$-0.570547\pi$
$967$	−13.6713	−0.439641	−0.219820	+	0.975540i	$0.570547\pi$
$968$	8.82016	0.283491
$969$	−57.5737	−1.84953
$970$	−4.84385	−0.155527
$971$	48.3218	1.55072	0.775361	−	0.631519i	$-0.217568\pi$
$971$	48.3218	1.55072	0.775361	+	0.631519i	$0.217568\pi$
$972$	18.6244	0.597377
$973$	−0.137436	−0.00440600
$974$	−32.7761	−1.05021
$975$	−3.93737	−0.126097
$976$	9.80969	0.314001
$977$	−5.30083	−0.169589	−0.0847943	−	0.996398i	$-0.527023\pi$
$977$	−5.30083	−0.169589	−0.0847943	+	0.996398i	$0.527023\pi$
$978$	33.0184	1.05581
$979$	−4.86881	−0.155608
$980$	−6.91758	−0.220974
$981$	39.0572	1.24700
$982$	−34.5730	−1.10327
$983$	−4.56967	−0.145750	−0.0728749	−	0.997341i	$-0.523217\pi$
$983$	−4.56967	−0.145750	−0.0728749	+	0.997341i	$0.523217\pi$
$984$	18.2424	0.581545
$985$	−26.2306	−0.835775
$986$	−25.0660	−0.798266
$987$	3.22015	0.102498
$988$	−8.86223	−0.281945
$989$	0	0
$990$	−3.13308	−0.0995757
$991$	22.7834	0.723740	0.361870	−	0.932229i	$-0.382138\pi$
$991$	22.7834	0.723740	0.361870	+	0.932229i	$0.382138\pi$
$992$	−0.0426355	−0.00135368
$993$	−1.10535	−0.0350772
$994$	1.02374	0.0324709
$995$	−3.18688	−0.101031
$996$	22.0862	0.699828
$997$	−0.717177	−0.0227132	−0.0113566	−	0.999936i	$-0.503615\pi$
$997$	−0.717177	−0.0227132	−0.0113566	+	0.999936i	$0.503615\pi$
$998$	−29.2733	−0.926631
$999$	−8.70588	−0.275442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bj.1.2		10
23.3	even	11		230.2.g.b.101.2	yes	20
23.8	even	11		230.2.g.b.41.2	✓	20
23.22	odd	2		5290.2.a.bi.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.41.2	✓	20	23.8	even	11
230.2.g.b.101.2	yes	20	23.3	even	11
5290.2.a.bi.1.2		10	23.22	odd	2
5290.2.a.bj.1.2		10	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.26320 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.26320 q^{6} -0.287092 q^{7} -1.00000 q^{8} +2.12206 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.26320 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.26320 q^{6} -0.287092 q^{7} -1.00000 q^{8} +2.12206 q^{9} -1.00000 q^{10} +1.47643 q^{11} -2.26320 q^{12} +1.73974 q^{13} +0.287092 q^{14} -2.26320 q^{15} +1.00000 q^{16} -4.99392 q^{17} -2.12206 q^{18} -5.09401 q^{19} +1.00000 q^{20} +0.649745 q^{21} -1.47643 q^{22} +2.26320 q^{24} +1.00000 q^{25} -1.73974 q^{26} +1.98694 q^{27} -0.287092 q^{28} -5.01931 q^{29} +2.26320 q^{30} +0.0426355 q^{31} -1.00000 q^{32} -3.34145 q^{33} +4.99392 q^{34} -0.287092 q^{35} +2.12206 q^{36} -4.38155 q^{37} +5.09401 q^{38} -3.93737 q^{39} -1.00000 q^{40} +8.06043 q^{41} -0.649745 q^{42} +3.92017 q^{43} +1.47643 q^{44} +2.12206 q^{45} +4.95602 q^{47} -2.26320 q^{48} -6.91758 q^{49} -1.00000 q^{50} +11.3022 q^{51} +1.73974 q^{52} -1.93961 q^{53} -1.98694 q^{54} +1.47643 q^{55} +0.287092 q^{56} +11.5287 q^{57} +5.01931 q^{58} +5.45392 q^{59} -2.26320 q^{60} +9.80969 q^{61} -0.0426355 q^{62} -0.609227 q^{63} +1.00000 q^{64} +1.73974 q^{65} +3.34145 q^{66} -6.75326 q^{67} -4.99392 q^{68} +0.287092 q^{70} +3.56589 q^{71} -2.12206 q^{72} -11.6872 q^{73} +4.38155 q^{74} -2.26320 q^{75} -5.09401 q^{76} -0.423871 q^{77} +3.93737 q^{78} +13.5746 q^{79} +1.00000 q^{80} -10.8630 q^{81} -8.06043 q^{82} -9.75885 q^{83} +0.649745 q^{84} -4.99392 q^{85} -3.92017 q^{86} +11.3597 q^{87} -1.47643 q^{88} -3.29769 q^{89} -2.12206 q^{90} -0.499464 q^{91} -0.0964927 q^{93} -4.95602 q^{94} -5.09401 q^{95} +2.26320 q^{96} +4.84385 q^{97} +6.91758 q^{98} +3.13308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 9 q^{11} + 4 q^{12} - 7 q^{13} + 7 q^{14} + 4 q^{15} + 10 q^{16} - 18 q^{17} - 14 q^{18} + 16 q^{19} + 10 q^{20} + 12 q^{21} - 9 q^{22} - 4 q^{24} + 10 q^{25} + 7 q^{26} + 13 q^{27} - 7 q^{28} + 10 q^{29} - 4 q^{30} - 3 q^{31} - 10 q^{32} + 25 q^{33} + 18 q^{34} - 7 q^{35} + 14 q^{36} - 8 q^{37} - 16 q^{38} + 12 q^{39} - 10 q^{40} + 10 q^{41} - 12 q^{42} - 9 q^{43} + 9 q^{44} + 14 q^{45} + 21 q^{47} + 4 q^{48} + 7 q^{49} - 10 q^{50} - 9 q^{51} - 7 q^{52} - 40 q^{53} - 13 q^{54} + 9 q^{55} + 7 q^{56} + 9 q^{57} - 10 q^{58} + 29 q^{59} + 4 q^{60} + 25 q^{61} + 3 q^{62} + 6 q^{63} + 10 q^{64} - 7 q^{65} - 25 q^{66} - 7 q^{67} - 18 q^{68} + 7 q^{70} + 64 q^{71} - 14 q^{72} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 16 q^{76} + 57 q^{77} - 12 q^{78} + 44 q^{79} + 10 q^{80} + 14 q^{81} - 10 q^{82} - 26 q^{83} + 12 q^{84} - 18 q^{85} + 9 q^{86} + 25 q^{87} - 9 q^{88} + 11 q^{89} - 14 q^{90} + 5 q^{93} - 21 q^{94} + 16 q^{95} - 4 q^{96} - 10 q^{97} - 7 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 9 * q^11 + 4 * q^12 - 7 * q^13 + 7 * q^14 + 4 * q^15 + 10 * q^16 - 18 * q^17 - 14 * q^18 + 16 * q^19 + 10 * q^20 + 12 * q^21 - 9 * q^22 - 4 * q^24 + 10 * q^25 + 7 * q^26 + 13 * q^27 - 7 * q^28 + 10 * q^29 - 4 * q^30 - 3 * q^31 - 10 * q^32 + 25 * q^33 + 18 * q^34 - 7 * q^35 + 14 * q^36 - 8 * q^37 - 16 * q^38 + 12 * q^39 - 10 * q^40 + 10 * q^41 - 12 * q^42 - 9 * q^43 + 9 * q^44 + 14 * q^45 + 21 * q^47 + 4 * q^48 + 7 * q^49 - 10 * q^50 - 9 * q^51 - 7 * q^52 - 40 * q^53 - 13 * q^54 + 9 * q^55 + 7 * q^56 + 9 * q^57 - 10 * q^58 + 29 * q^59 + 4 * q^60 + 25 * q^61 + 3 * q^62 + 6 * q^63 + 10 * q^64 - 7 * q^65 - 25 * q^66 - 7 * q^67 - 18 * q^68 + 7 * q^70 + 64 * q^71 - 14 * q^72 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 16 * q^76 + 57 * q^77 - 12 * q^78 + 44 * q^79 + 10 * q^80 + 14 * q^81 - 10 * q^82 - 26 * q^83 + 12 * q^84 - 18 * q^85 + 9 * q^86 + 25 * q^87 - 9 * q^88 + 11 * q^89 - 14 * q^90 + 5 * q^93 - 21 * q^94 + 16 * q^95 - 4 * q^96 - 10 * q^97 - 7 * q^98 + 13 * q^99

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