LMFDB - Embedded newform 4010.2.a.m.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, 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("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 35 x^{18} + 154 x^{17} + 460 x^{16} - 2392 x^{15} - 2591 x^{14} + 19157 x^{13} + \cdots + 104 $ x^20 - 4x^19 - 35x^18 + 154x^17 + 460x^16 - 2392x^15 - 2591x^14 + 19157x^13 + 2776x^12 - 83577x^11 + 34362x^10 + 190617x^9 - 150697x^8 - 189098x^7 + 211360x^6 + 37365x^5 - 68876x^4 - 8984x^3 + 7920x^2 + 1972*x + 104
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$2.32194$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.32194 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.32194 q^{6} +1.00226 q^{7} -1.00000 q^{8} +2.39142 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.32194 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.32194 q^{6} +1.00226 q^{7} -1.00000 q^{8} +2.39142 q^{9} -1.00000 q^{10} -0.100439 q^{11} +2.32194 q^{12} +4.75377 q^{13} -1.00226 q^{14} +2.32194 q^{15} +1.00000 q^{16} +7.59968 q^{17} -2.39142 q^{18} +6.05061 q^{19} +1.00000 q^{20} +2.32720 q^{21} +0.100439 q^{22} -5.89368 q^{23} -2.32194 q^{24} +1.00000 q^{25} -4.75377 q^{26} -1.41309 q^{27} +1.00226 q^{28} -3.17341 q^{29} -2.32194 q^{30} +3.07263 q^{31} -1.00000 q^{32} -0.233213 q^{33} -7.59968 q^{34} +1.00226 q^{35} +2.39142 q^{36} +12.0629 q^{37} -6.05061 q^{38} +11.0380 q^{39} -1.00000 q^{40} -2.81396 q^{41} -2.32720 q^{42} +11.9210 q^{43} -0.100439 q^{44} +2.39142 q^{45} +5.89368 q^{46} -11.1479 q^{47} +2.32194 q^{48} -5.99547 q^{49} -1.00000 q^{50} +17.6460 q^{51} +4.75377 q^{52} -12.5149 q^{53} +1.41309 q^{54} -0.100439 q^{55} -1.00226 q^{56} +14.0492 q^{57} +3.17341 q^{58} -8.79853 q^{59} +2.32194 q^{60} -9.57495 q^{61} -3.07263 q^{62} +2.39683 q^{63} +1.00000 q^{64} +4.75377 q^{65} +0.233213 q^{66} -16.1207 q^{67} +7.59968 q^{68} -13.6848 q^{69} -1.00226 q^{70} +3.80916 q^{71} -2.39142 q^{72} -1.60086 q^{73} -12.0629 q^{74} +2.32194 q^{75} +6.05061 q^{76} -0.100666 q^{77} -11.0380 q^{78} +0.972634 q^{79} +1.00000 q^{80} -10.4554 q^{81} +2.81396 q^{82} +6.67734 q^{83} +2.32720 q^{84} +7.59968 q^{85} -11.9210 q^{86} -7.36848 q^{87} +0.100439 q^{88} -6.50261 q^{89} -2.39142 q^{90} +4.76453 q^{91} -5.89368 q^{92} +7.13448 q^{93} +11.1479 q^{94} +6.05061 q^{95} -2.32194 q^{96} -1.29416 q^{97} +5.99547 q^{98} -0.240191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * 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
$3$	2.32194	1.34057	0.670287	−	0.742102i	$-0.266171\pi$
$3$	2.32194	1.34057	0.670287	+	0.742102i	$0.266171\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.32194	−0.947929
$7$	1.00226	0.378820	0.189410	−	0.981898i	$-0.439343\pi$
$7$	1.00226	0.378820	0.189410	+	0.981898i	$0.439343\pi$
$8$	−1.00000	−0.353553
$9$	2.39142	0.797139
$10$	−1.00000	−0.316228
$11$	−0.100439	−0.0302834	−0.0151417	−	0.999885i	$-0.504820\pi$
$11$	−0.100439	−0.0302834	−0.0151417	+	0.999885i	$0.504820\pi$
$12$	2.32194	0.670287
$13$	4.75377	1.31846	0.659230	−	0.751942i	$-0.270882\pi$
$13$	4.75377	1.31846	0.659230	+	0.751942i	$0.270882\pi$
$14$	−1.00226	−0.267866
$15$	2.32194	0.599523
$16$	1.00000	0.250000
$17$	7.59968	1.84319	0.921597	−	0.388149i	$-0.126885\pi$
$17$	7.59968	1.84319	0.921597	+	0.388149i	$0.126885\pi$
$18$	−2.39142	−0.563663
$19$	6.05061	1.38811	0.694053	−	0.719924i	$-0.255823\pi$
$19$	6.05061	1.38811	0.694053	+	0.719924i	$0.255823\pi$
$20$	1.00000	0.223607
$21$	2.32720	0.507836
$22$	0.100439	0.0214136
$23$	−5.89368	−1.22892	−0.614459	−	0.788949i	$-0.710626\pi$
$23$	−5.89368	−1.22892	−0.614459	+	0.788949i	$0.710626\pi$
$24$	−2.32194	−0.473965
$25$	1.00000	0.200000
$26$	−4.75377	−0.932292
$27$	−1.41309	−0.271950
$28$	1.00226	0.189410
$29$	−3.17341	−0.589288	−0.294644	−	0.955607i	$-0.595201\pi$
$29$	−3.17341	−0.589288	−0.294644	+	0.955607i	$0.595201\pi$
$30$	−2.32194	−0.423927
$31$	3.07263	0.551862	0.275931	−	0.961178i	$-0.411014\pi$
$31$	3.07263	0.551862	0.275931	+	0.961178i	$0.411014\pi$
$32$	−1.00000	−0.176777
$33$	−0.233213	−0.0405971
$34$	−7.59968	−1.30333
$35$	1.00226	0.169413
$36$	2.39142	0.398570
$37$	12.0629	1.98313	0.991564	−	0.129618i	$-0.0413752\pi$
$37$	12.0629	1.98313	0.991564	+	0.129618i	$0.0413752\pi$
$38$	−6.05061	−0.981539
$39$	11.0380	1.76749
$40$	−1.00000	−0.158114
$41$	−2.81396	−0.439466	−0.219733	−	0.975560i	$-0.570519\pi$
$41$	−2.81396	−0.439466	−0.219733	+	0.975560i	$0.570519\pi$
$42$	−2.32720	−0.359094
$43$	11.9210	1.81793	0.908967	−	0.416869i	$-0.136873\pi$
$43$	11.9210	1.81793	0.908967	+	0.416869i	$0.136873\pi$
$44$	−0.100439	−0.0151417
$45$	2.39142	0.356492
$46$	5.89368	0.868976
$47$	−11.1479	−1.62609	−0.813047	−	0.582198i	$-0.802193\pi$
$47$	−11.1479	−1.62609	−0.813047	+	0.582198i	$0.802193\pi$
$48$	2.32194	0.335144
$49$	−5.99547	−0.856496
$50$	−1.00000	−0.141421
$51$	17.6460	2.47094
$52$	4.75377	0.659230
$53$	−12.5149	−1.71906	−0.859528	−	0.511088i	$-0.829242\pi$
$53$	−12.5149	−1.71906	−0.859528	+	0.511088i	$0.829242\pi$
$54$	1.41309	0.192298
$55$	−0.100439	−0.0135431
$56$	−1.00226	−0.133933
$57$	14.0492	1.86086
$58$	3.17341	0.416689
$59$	−8.79853	−1.14547	−0.572735	−	0.819740i	$-0.694118\pi$
$59$	−8.79853	−1.14547	−0.572735	+	0.819740i	$0.694118\pi$
$60$	2.32194	0.299762
$61$	−9.57495	−1.22595	−0.612974	−	0.790103i	$-0.710027\pi$
$61$	−9.57495	−1.22595	−0.612974	+	0.790103i	$0.710027\pi$
$62$	−3.07263	−0.390225
$63$	2.39683	0.301972
$64$	1.00000	0.125000
$65$	4.75377	0.589633
$66$	0.233213	0.0287065
$67$	−16.1207	−1.96946	−0.984729	−	0.174092i	$-0.944301\pi$
$67$	−16.1207	−1.96946	−0.984729	+	0.174092i	$0.944301\pi$
$68$	7.59968	0.921597
$69$	−13.6848	−1.64746
$70$	−1.00226	−0.119793
$71$	3.80916	0.452064	0.226032	−	0.974120i	$-0.427425\pi$
$71$	3.80916	0.452064	0.226032	+	0.974120i	$0.427425\pi$
$72$	−2.39142	−0.281831
$73$	−1.60086	−0.187367	−0.0936835	−	0.995602i	$-0.529864\pi$
$73$	−1.60086	−0.187367	−0.0936835	+	0.995602i	$0.529864\pi$
$74$	−12.0629	−1.40228
$75$	2.32194	0.268115
$76$	6.05061	0.694053
$77$	−0.100666	−0.0114719
$78$	−11.0380	−1.24981
$79$	0.972634	0.109430	0.0547149	−	0.998502i	$-0.482575\pi$
$79$	0.972634	0.109430	0.0547149	+	0.998502i	$0.482575\pi$
$80$	1.00000	0.111803
$81$	−10.4554	−1.16171
$82$	2.81396	0.310749
$83$	6.67734	0.732934	0.366467	−	0.930431i	$-0.380567\pi$
$83$	6.67734	0.732934	0.366467	+	0.930431i	$0.380567\pi$
$84$	2.32720	0.253918
$85$	7.59968	0.824301
$86$	−11.9210	−1.28547
$87$	−7.36848	−0.789984
$88$	0.100439	0.0107068
$89$	−6.50261	−0.689275	−0.344638	−	0.938736i	$-0.611998\pi$
$89$	−6.50261	−0.689275	−0.344638	+	0.938736i	$0.611998\pi$
$90$	−2.39142	−0.252078
$91$	4.76453	0.499458
$92$	−5.89368	−0.614459
$93$	7.13448	0.739811
$94$	11.1479	1.14982
$95$	6.05061	0.620780
$96$	−2.32194	−0.236982
$97$	−1.29416	−0.131402	−0.0657010	−	0.997839i	$-0.520928\pi$
$97$	−1.29416	−0.131402	−0.0657010	+	0.997839i	$0.520928\pi$
$98$	5.99547	0.605634
$99$	−0.240191	−0.0241401
$100$	1.00000	0.100000
$101$	3.73268	0.371416	0.185708	−	0.982605i	$-0.440542\pi$
$101$	3.73268	0.371416	0.185708	+	0.982605i	$0.440542\pi$
$102$	−17.6460	−1.74722
$103$	4.88703	0.481534	0.240767	−	0.970583i	$-0.422601\pi$
$103$	4.88703	0.481534	0.240767	+	0.970583i	$0.422601\pi$
$104$	−4.75377	−0.466146
$105$	2.32720	0.227111
$106$	12.5149	1.21556
$107$	18.5605	1.79431	0.897157	−	0.441713i	$-0.145629\pi$
$107$	18.5605	1.79431	0.897157	+	0.441713i	$0.145629\pi$
$108$	−1.41309	−0.135975
$109$	1.07320	0.102794	0.0513971	−	0.998678i	$-0.483633\pi$
$109$	1.07320	0.102794	0.0513971	+	0.998678i	$0.483633\pi$
$110$	0.100439	0.00957645
$111$	28.0094	2.65853
$112$	1.00226	0.0947049
$113$	12.8704	1.21075	0.605375	−	0.795940i	$-0.293023\pi$
$113$	12.8704	1.21075	0.605375	+	0.795940i	$0.293023\pi$
$114$	−14.0492	−1.31583
$115$	−5.89368	−0.549589
$116$	−3.17341	−0.294644
$117$	11.3683	1.05100
$118$	8.79853	0.809970
$119$	7.61687	0.698238
$120$	−2.32194	−0.211963
$121$	−10.9899	−0.999083
$122$	9.57495	0.866876
$123$	−6.53384	−0.589137
$124$	3.07263	0.275931
$125$	1.00000	0.0894427
$126$	−2.39683	−0.213526
$127$	−4.80638	−0.426497	−0.213249	−	0.976998i	$-0.568404\pi$
$127$	−4.80638	−0.426497	−0.213249	+	0.976998i	$0.568404\pi$
$128$	−1.00000	−0.0883883
$129$	27.6798	2.43707
$130$	−4.75377	−0.416933
$131$	9.97336	0.871377	0.435688	−	0.900098i	$-0.356505\pi$
$131$	9.97336	0.871377	0.435688	+	0.900098i	$0.356505\pi$
$132$	−0.233213	−0.0202986
$133$	6.06430	0.525841
$134$	16.1207	1.39262
$135$	−1.41309	−0.121620
$136$	−7.59968	−0.651667
$137$	13.8007	1.17907	0.589535	−	0.807743i	$-0.299311\pi$
$137$	13.8007	1.17907	0.589535	+	0.807743i	$0.299311\pi$
$138$	13.6848	1.16493
$139$	16.5925	1.40735	0.703677	−	0.710520i	$-0.251540\pi$
$139$	16.5925	1.40735	0.703677	+	0.710520i	$0.251540\pi$
$140$	1.00226	0.0847066
$141$	−25.8849	−2.17990
$142$	−3.80916	−0.319658
$143$	−0.477463	−0.0399274
$144$	2.39142	0.199285
$145$	−3.17341	−0.263538
$146$	1.60086	0.132489
$147$	−13.9211	−1.14820
$148$	12.0629	0.991564
$149$	−5.94886	−0.487350	−0.243675	−	0.969857i	$-0.578353\pi$
$149$	−5.94886	−0.487350	−0.243675	+	0.969857i	$0.578353\pi$
$150$	−2.32194	−0.189586
$151$	10.8154	0.880146	0.440073	−	0.897962i	$-0.354953\pi$
$151$	10.8154	0.880146	0.440073	+	0.897962i	$0.354953\pi$
$152$	−6.05061	−0.490769
$153$	18.1740	1.46928
$154$	0.100666	0.00811189
$155$	3.07263	0.246800
$156$	11.0380	0.883746
$157$	−14.2912	−1.14056	−0.570281	−	0.821450i	$-0.693166\pi$
$157$	−14.2912	−1.14056	−0.570281	+	0.821450i	$0.693166\pi$
$158$	−0.972634	−0.0773786
$159$	−29.0589	−2.30452
$160$	−1.00000	−0.0790569
$161$	−5.90701	−0.465538
$162$	10.4554	0.821452
$163$	16.1635	1.26602	0.633012	−	0.774142i	$-0.281818\pi$
$163$	16.1635	1.26602	0.633012	+	0.774142i	$0.281818\pi$
$164$	−2.81396	−0.219733
$165$	−0.233213	−0.0181556
$166$	−6.67734	−0.518262
$167$	12.5864	0.973969	0.486984	−	0.873411i	$-0.338097\pi$
$167$	12.5864	0.973969	0.486984	+	0.873411i	$0.338097\pi$
$168$	−2.32720	−0.179547
$169$	9.59836	0.738335
$170$	−7.59968	−0.582869
$171$	14.4695	1.10651
$172$	11.9210	0.908967
$173$	−3.63810	−0.276599	−0.138300	−	0.990390i	$-0.544164\pi$
$173$	−3.63810	−0.276599	−0.138300	+	0.990390i	$0.544164\pi$
$174$	7.36848	0.558603
$175$	1.00226	0.0757639
$176$	−0.100439	−0.00757085
$177$	−20.4297	−1.53559
$178$	6.50261	0.487391
$179$	8.57072	0.640606	0.320303	−	0.947315i	$-0.396215\pi$
$179$	8.57072	0.640606	0.320303	+	0.947315i	$0.396215\pi$
$180$	2.39142	0.178246
$181$	−10.8974	−0.809995	−0.404997	−	0.914318i	$-0.632728\pi$
$181$	−10.8974	−0.809995	−0.404997	+	0.914318i	$0.632728\pi$
$182$	−4.76453	−0.353170
$183$	−22.2325	−1.64347
$184$	5.89368	0.434488
$185$	12.0629	0.886882
$186$	−7.13448	−0.523126
$187$	−0.763302	−0.0558181
$188$	−11.1479	−0.813047
$189$	−1.41629	−0.103020
$190$	−6.05061	−0.438957
$191$	13.3672	0.967213	0.483607	−	0.875286i	$-0.339327\pi$
$191$	13.3672	0.967213	0.483607	+	0.875286i	$0.339327\pi$
$192$	2.32194	0.167572
$193$	−5.68441	−0.409173	−0.204586	−	0.978849i	$-0.565585\pi$
$193$	−5.68441	−0.409173	−0.204586	+	0.978849i	$0.565585\pi$
$194$	1.29416	0.0929152
$195$	11.0380	0.790447
$196$	−5.99547	−0.428248
$197$	−8.45322	−0.602267	−0.301133	−	0.953582i	$-0.597365\pi$
$197$	−8.45322	−0.602267	−0.301133	+	0.953582i	$0.597365\pi$
$198$	0.240191	0.0170696
$199$	−2.85955	−0.202708	−0.101354	−	0.994850i	$-0.532317\pi$
$199$	−2.85955	−0.202708	−0.101354	+	0.994850i	$0.532317\pi$
$200$	−1.00000	−0.0707107
$201$	−37.4314	−2.64021
$202$	−3.73268	−0.262631
$203$	−3.18059	−0.223234
$204$	17.6460	1.23547
$205$	−2.81396	−0.196535
$206$	−4.88703	−0.340496
$207$	−14.0943	−0.979618
$208$	4.75377	0.329615
$209$	−0.607715	−0.0420365
$210$	−2.32720	−0.160592
$211$	−0.857110	−0.0590059	−0.0295029	−	0.999565i	$-0.509392\pi$
$211$	−0.857110	−0.0590059	−0.0295029	+	0.999565i	$0.509392\pi$
$212$	−12.5149	−0.859528
$213$	8.84465	0.606026
$214$	−18.5605	−1.26877
$215$	11.9210	0.813004
$216$	1.41309	0.0961488
$217$	3.07959	0.209056
$218$	−1.07320	−0.0726864
$219$	−3.71712	−0.251179
$220$	−0.100439	−0.00677157
$221$	36.1272	2.43018
$222$	−28.0094	−1.87986
$223$	−0.534205	−0.0357730	−0.0178865	−	0.999840i	$-0.505694\pi$
$223$	−0.534205	−0.0357730	−0.0178865	+	0.999840i	$0.505694\pi$
$224$	−1.00226	−0.0669665
$225$	2.39142	0.159428
$226$	−12.8704	−0.856130
$227$	−27.1656	−1.80304	−0.901522	−	0.432732i	$-0.857549\pi$
$227$	−27.1656	−1.80304	−0.901522	+	0.432732i	$0.857549\pi$
$228$	14.0492	0.930429
$229$	−2.31059	−0.152688	−0.0763442	−	0.997082i	$-0.524325\pi$
$229$	−2.31059	−0.152688	−0.0763442	+	0.997082i	$0.524325\pi$
$230$	5.89368	0.388618
$231$	−0.233740	−0.0153790
$232$	3.17341	0.208345
$233$	24.6839	1.61709	0.808547	−	0.588431i	$-0.200254\pi$
$233$	24.6839	1.61709	0.808547	+	0.588431i	$0.200254\pi$
$234$	−11.3683	−0.743166
$235$	−11.1479	−0.727212
$236$	−8.79853	−0.572735
$237$	2.25840	0.146699
$238$	−7.61687	−0.493729
$239$	−26.2464	−1.69774	−0.848870	−	0.528602i	$-0.822717\pi$
$239$	−26.2464	−1.69774	−0.848870	+	0.528602i	$0.822717\pi$
$240$	2.32194	0.149881
$241$	−6.72237	−0.433026	−0.216513	−	0.976280i	$-0.569468\pi$
$241$	−6.72237	−0.433026	−0.216513	+	0.976280i	$0.569468\pi$
$242$	10.9899	0.706458
$243$	−20.0375	−1.28541
$244$	−9.57495	−0.612974
$245$	−5.99547	−0.383037
$246$	6.53384	0.416583
$247$	28.7632	1.83016
$248$	−3.07263	−0.195113
$249$	15.5044	0.982552
$250$	−1.00000	−0.0632456
$251$	−20.8752	−1.31763	−0.658815	−	0.752305i	$-0.728942\pi$
$251$	−20.8752	−1.31763	−0.658815	+	0.752305i	$0.728942\pi$
$252$	2.39683	0.150986
$253$	0.591953	0.0372158
$254$	4.80638	0.301579
$255$	17.6460	1.10504
$256$	1.00000	0.0625000
$257$	−15.9835	−0.997023	−0.498512	−	0.866883i	$-0.666120\pi$
$257$	−15.9835	−0.997023	−0.498512	+	0.866883i	$0.666120\pi$
$258$	−27.6798	−1.72327
$259$	12.0902	0.751248
$260$	4.75377	0.294816
$261$	−7.58896	−0.469745
$262$	−9.97336	−0.616157
$263$	13.6444	0.841348	0.420674	−	0.907212i	$-0.361794\pi$
$263$	13.6444	0.841348	0.420674	+	0.907212i	$0.361794\pi$
$264$	0.233213	0.0143533
$265$	−12.5149	−0.768785
$266$	−6.06430	−0.371826
$267$	−15.0987	−0.924025
$268$	−16.1207	−0.984729
$269$	30.5624	1.86342	0.931712	−	0.363197i	$-0.118315\pi$
$269$	30.5624	1.86342	0.931712	+	0.363197i	$0.118315\pi$
$270$	1.41309	0.0859981
$271$	19.2016	1.16641	0.583207	−	0.812323i	$-0.301798\pi$
$271$	19.2016	1.16641	0.583207	+	0.812323i	$0.301798\pi$
$272$	7.59968	0.460798
$273$	11.0630	0.669561
$274$	−13.8007	−0.833728
$275$	−0.100439	−0.00605668
$276$	−13.6848	−0.823728
$277$	−26.1073	−1.56864	−0.784318	−	0.620359i	$-0.786987\pi$
$277$	−26.1073	−1.56864	−0.784318	+	0.620359i	$0.786987\pi$
$278$	−16.5925	−0.995150
$279$	7.34795	0.439911
$280$	−1.00226	−0.0598966
$281$	−6.76306	−0.403450	−0.201725	−	0.979442i	$-0.564655\pi$
$281$	−6.76306	−0.403450	−0.201725	+	0.979442i	$0.564655\pi$
$282$	25.8849	1.54142
$283$	3.11151	0.184960	0.0924799	−	0.995715i	$-0.470521\pi$
$283$	3.11151	0.184960	0.0924799	+	0.995715i	$0.470521\pi$
$284$	3.80916	0.226032
$285$	14.0492	0.832201
$286$	0.477463	0.0282330
$287$	−2.82032	−0.166478
$288$	−2.39142	−0.140916
$289$	40.7551	2.39736
$290$	3.17341	0.186349
$291$	−3.00496	−0.176154
$292$	−1.60086	−0.0936835
$293$	−21.8787	−1.27817	−0.639084	−	0.769137i	$-0.720686\pi$
$293$	−21.8787	−1.27817	−0.639084	+	0.769137i	$0.720686\pi$
$294$	13.9211	0.811897
$295$	−8.79853	−0.512270
$296$	−12.0629	−0.701142
$297$	0.141929	0.00823556
$298$	5.94886	0.344608
$299$	−28.0172	−1.62028
$300$	2.32194	0.134057
$301$	11.9480	0.688669
$302$	−10.8154	−0.622357
$303$	8.66708	0.497911
$304$	6.05061	0.347026
$305$	−9.57495	−0.548260
$306$	−18.1740	−1.03894
$307$	−13.1852	−0.752520	−0.376260	−	0.926514i	$-0.622790\pi$
$307$	−13.1852	−0.752520	−0.376260	+	0.926514i	$0.622790\pi$
$308$	−0.100666	−0.00573597
$309$	11.3474	0.645532
$310$	−3.07263	−0.174514
$311$	8.53085	0.483740	0.241870	−	0.970309i	$-0.422239\pi$
$311$	8.53085	0.483740	0.241870	+	0.970309i	$0.422239\pi$
$312$	−11.0380	−0.624903
$313$	3.83262	0.216633	0.108316	−	0.994116i	$-0.465454\pi$
$313$	3.83262	0.216633	0.108316	+	0.994116i	$0.465454\pi$
$314$	14.2912	0.806499
$315$	2.39683	0.135046
$316$	0.972634	0.0547149
$317$	−13.0704	−0.734104	−0.367052	−	0.930200i	$-0.619633\pi$
$317$	−13.0704	−0.734104	−0.367052	+	0.930200i	$0.619633\pi$
$318$	29.0589	1.62954
$319$	0.318733	0.0178456
$320$	1.00000	0.0559017
$321$	43.0965	2.40541
$322$	5.90701	0.329185
$323$	45.9827	2.55855
$324$	−10.4554	−0.580854
$325$	4.75377	0.263692
$326$	−16.1635	−0.895215
$327$	2.49191	0.137803
$328$	2.81396	0.155375
$329$	−11.1732	−0.615996
$330$	0.233213	0.0128379
$331$	−0.415964	−0.0228635	−0.0114317	−	0.999935i	$-0.503639\pi$
$331$	−0.415964	−0.0228635	−0.0114317	+	0.999935i	$0.503639\pi$
$332$	6.67734	0.366467
$333$	28.8474	1.58083
$334$	−12.5864	−0.688700
$335$	−16.1207	−0.880769
$336$	2.32720	0.126959
$337$	5.96765	0.325079	0.162539	−	0.986702i	$-0.448032\pi$
$337$	5.96765	0.325079	0.162539	+	0.986702i	$0.448032\pi$
$338$	−9.59836	−0.522082
$339$	29.8844	1.62310
$340$	7.59968	0.412151
$341$	−0.308611	−0.0167122
$342$	−14.4695	−0.782423
$343$	−13.0249	−0.703277
$344$	−11.9210	−0.642736
$345$	−13.6848	−0.736764
$346$	3.63810	0.195585
$347$	0.723471	0.0388379	0.0194190	−	0.999811i	$-0.493818\pi$
$347$	0.723471	0.0388379	0.0194190	+	0.999811i	$0.493818\pi$
$348$	−7.36848	−0.394992
$349$	25.6014	1.37041	0.685205	−	0.728350i	$-0.259713\pi$
$349$	25.6014	1.37041	0.685205	+	0.728350i	$0.259713\pi$
$350$	−1.00226	−0.0535732
$351$	−6.71752	−0.358555
$352$	0.100439	0.00535340
$353$	−16.8800	−0.898434	−0.449217	−	0.893423i	$-0.648297\pi$
$353$	−16.8800	−0.898434	−0.449217	+	0.893423i	$0.648297\pi$
$354$	20.4297	1.08583
$355$	3.80916	0.202169
$356$	−6.50261	−0.344638
$357$	17.6859	0.936039
$358$	−8.57072	−0.452977
$359$	−11.0961	−0.585627	−0.292814	−	0.956170i	$-0.594592\pi$
$359$	−11.0961	−0.585627	−0.292814	+	0.956170i	$0.594592\pi$
$360$	−2.39142	−0.126039
$361$	17.6099	0.926836
$362$	10.8974	0.572753
$363$	−25.5179	−1.33934
$364$	4.76453	0.249729
$365$	−1.60086	−0.0837931
$366$	22.2325	1.16211
$367$	−28.0345	−1.46339	−0.731694	−	0.681634i	$-0.761270\pi$
$367$	−28.0345	−1.46339	−0.731694	+	0.681634i	$0.761270\pi$
$368$	−5.89368	−0.307229
$369$	−6.72935	−0.350316
$370$	−12.0629	−0.627120
$371$	−12.5432	−0.651212
$372$	7.13448	0.369906
$373$	18.7554	0.971116	0.485558	−	0.874204i	$-0.338616\pi$
$373$	18.7554	0.971116	0.485558	+	0.874204i	$0.338616\pi$
$374$	0.763302	0.0394694
$375$	2.32194	0.119905
$376$	11.1479	0.574911
$377$	−15.0857	−0.776952
$378$	1.41629	0.0728461
$379$	29.1260	1.49610	0.748052	−	0.663640i	$-0.230989\pi$
$379$	29.1260	1.49610	0.748052	+	0.663640i	$0.230989\pi$
$380$	6.05061	0.310390
$381$	−11.1601	−0.571751
$382$	−13.3672	−0.683923
$383$	14.1299	0.722005	0.361003	−	0.932565i	$-0.382435\pi$
$383$	14.1299	0.722005	0.361003	+	0.932565i	$0.382435\pi$
$384$	−2.32194	−0.118491
$385$	−0.100666	−0.00513041
$386$	5.68441	0.289329
$387$	28.5081	1.44915
$388$	−1.29416	−0.0657010
$389$	−21.3146	−1.08070	−0.540348	−	0.841442i	$-0.681707\pi$
$389$	−21.3146	−1.08070	−0.540348	+	0.841442i	$0.681707\pi$
$390$	−11.0380	−0.558930
$391$	−44.7901	−2.26513
$392$	5.99547	0.302817
$393$	23.1576	1.16815
$394$	8.45322	0.425867
$395$	0.972634	0.0489385
$396$	−0.240191	−0.0120700
$397$	−20.1305	−1.01032	−0.505162	−	0.863025i	$-0.668567\pi$
$397$	−20.1305	−1.01032	−0.505162	+	0.863025i	$0.668567\pi$
$398$	2.85955	0.143336
$399$	14.0810	0.704930
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	37.4314	1.86691
$403$	14.6066	0.727607
$404$	3.73268	0.185708
$405$	−10.4554	−0.519532
$406$	3.18059	0.157850
$407$	−1.21158	−0.0600558
$408$	−17.6460	−0.873608
$409$	−21.2779	−1.05213	−0.526063	−	0.850446i	$-0.676332\pi$
$409$	−21.2779	−1.05213	−0.526063	+	0.850446i	$0.676332\pi$
$410$	2.81396	0.138971
$411$	32.0443	1.58063
$412$	4.88703	0.240767
$413$	−8.81843	−0.433927
$414$	14.0943	0.692695
$415$	6.67734	0.327778
$416$	−4.75377	−0.233073
$417$	38.5268	1.88666
$418$	0.607715	0.0297243
$419$	−30.0402	−1.46756	−0.733779	−	0.679388i	$-0.762245\pi$
$419$	−30.0402	−1.46756	−0.733779	+	0.679388i	$0.762245\pi$
$420$	2.32720	0.113556
$421$	−15.3414	−0.747694	−0.373847	−	0.927490i	$-0.621962\pi$
$421$	−15.3414	−0.747694	−0.373847	+	0.927490i	$0.621962\pi$
$422$	0.857110	0.0417235
$423$	−26.6594	−1.29622
$424$	12.5149	0.607778
$425$	7.59968	0.368639
$426$	−8.84465	−0.428525
$427$	−9.59662	−0.464413
$428$	18.5605	0.897157
$429$	−1.10864	−0.0535257
$430$	−11.9210	−0.574881
$431$	4.94001	0.237952	0.118976	−	0.992897i	$-0.462039\pi$
$431$	4.94001	0.237952	0.118976	+	0.992897i	$0.462039\pi$
$432$	−1.41309	−0.0679874
$433$	12.5278	0.602048	0.301024	−	0.953617i	$-0.402672\pi$
$433$	12.5278	0.602048	0.301024	+	0.953617i	$0.402672\pi$
$434$	−3.07959	−0.147825
$435$	−7.36848	−0.353292
$436$	1.07320	0.0513971
$437$	−35.6604	−1.70587
$438$	3.71712	0.177611
$439$	6.65174	0.317470	0.158735	−	0.987321i	$-0.449258\pi$
$439$	6.65174	0.317470	0.158735	+	0.987321i	$0.449258\pi$
$440$	0.100439	0.00478822
$441$	−14.3377	−0.682746
$442$	−36.1272	−1.71839
$443$	−0.682149	−0.0324099	−0.0162049	−	0.999869i	$-0.505158\pi$
$443$	−0.682149	−0.0324099	−0.0162049	+	0.999869i	$0.505158\pi$
$444$	28.0094	1.32927
$445$	−6.50261	−0.308253
$446$	0.534205	0.0252954
$447$	−13.8129	−0.653328
$448$	1.00226	0.0473524
$449$	0.981671	0.0463279	0.0231640	−	0.999732i	$-0.492626\pi$
$449$	0.981671	0.0463279	0.0231640	+	0.999732i	$0.492626\pi$
$450$	−2.39142	−0.112733
$451$	0.282630	0.0133085
$452$	12.8704	0.605375
$453$	25.1128	1.17990
$454$	27.1656	1.27495
$455$	4.76453	0.223365
$456$	−14.0492	−0.657913
$457$	5.68196	0.265791	0.132895	−	0.991130i	$-0.457573\pi$
$457$	5.68196	0.265791	0.132895	+	0.991130i	$0.457573\pi$
$458$	2.31059	0.107967
$459$	−10.7390	−0.501256
$460$	−5.89368	−0.274794
$461$	−11.8077	−0.549938	−0.274969	−	0.961453i	$-0.588668\pi$
$461$	−11.8077	−0.549938	−0.274969	+	0.961453i	$0.588668\pi$
$462$	0.233740	0.0108746
$463$	−25.4495	−1.18274	−0.591369	−	0.806401i	$-0.701412\pi$
$463$	−25.4495	−1.18274	−0.591369	+	0.806401i	$0.701412\pi$
$464$	−3.17341	−0.147322
$465$	7.13448	0.330854
$466$	−24.6839	−1.14346
$467$	−27.5015	−1.27262	−0.636309	−	0.771434i	$-0.719540\pi$
$467$	−27.5015	−1.27262	−0.636309	+	0.771434i	$0.719540\pi$
$468$	11.3683	0.525498
$469$	−16.1572	−0.746069
$470$	11.1479	0.514216
$471$	−33.1834	−1.52901
$472$	8.79853	0.404985
$473$	−1.19733	−0.0550532
$474$	−2.25840	−0.103732
$475$	6.05061	0.277621
$476$	7.61687	0.349119
$477$	−29.9284	−1.37033
$478$	26.2464	1.20048
$479$	34.2537	1.56509	0.782545	−	0.622594i	$-0.213921\pi$
$479$	34.2537	1.56509	0.782545	+	0.622594i	$0.213921\pi$
$480$	−2.32194	−0.105982
$481$	57.3443	2.61467
$482$	6.72237	0.306196
$483$	−13.7157	−0.624088
$484$	−10.9899	−0.499541
$485$	−1.29416	−0.0587647
$486$	20.0375	0.908920
$487$	8.39120	0.380242	0.190121	−	0.981761i	$-0.439112\pi$
$487$	8.39120	0.380242	0.190121	+	0.981761i	$0.439112\pi$
$488$	9.57495	0.433438
$489$	37.5308	1.69720
$490$	5.99547	0.270848
$491$	−29.7272	−1.34157	−0.670785	−	0.741652i	$-0.734043\pi$
$491$	−29.7272	−1.34157	−0.670785	+	0.741652i	$0.734043\pi$
$492$	−6.53384	−0.294568
$493$	−24.1169	−1.08617
$494$	−28.7632	−1.29412
$495$	−0.240191	−0.0107958
$496$	3.07263	0.137965
$497$	3.81778	0.171251
$498$	−15.5044	−0.694769
$499$	14.3645	0.643043	0.321522	−	0.946902i	$-0.395806\pi$
$499$	14.3645	0.643043	0.321522	+	0.946902i	$0.395806\pi$
$500$	1.00000	0.0447214
$501$	29.2250	1.30568
$502$	20.8752	0.931705
$503$	−29.1101	−1.29795	−0.648977	−	0.760808i	$-0.724803\pi$
$503$	−29.1101	−1.29795	−0.648977	+	0.760808i	$0.724803\pi$
$504$	−2.39683	−0.106763
$505$	3.73268	0.166102
$506$	−0.591953	−0.0263155
$507$	22.2868	0.989793
$508$	−4.80638	−0.213249
$509$	15.7303	0.697235	0.348617	−	0.937265i	$-0.386651\pi$
$509$	15.7303	0.697235	0.348617	+	0.937265i	$0.386651\pi$
$510$	−17.6460	−0.781379
$511$	−1.60449	−0.0709783
$512$	−1.00000	−0.0441942
$513$	−8.55007	−0.377495
$514$	15.9835	0.705002
$515$	4.88703	0.215348
$516$	27.6798	1.21854
$517$	1.11968	0.0492437
$518$	−12.0902	−0.531212
$519$	−8.44746	−0.370802
$520$	−4.75377	−0.208467
$521$	−2.02577	−0.0887505	−0.0443752	−	0.999015i	$-0.514130\pi$
$521$	−2.02577	−0.0887505	−0.0443752	+	0.999015i	$0.514130\pi$
$522$	7.58896	0.332160
$523$	26.3225	1.15100	0.575501	−	0.817801i	$-0.304807\pi$
$523$	26.3225	1.15100	0.575501	+	0.817801i	$0.304807\pi$
$524$	9.97336	0.435688
$525$	2.32720	0.101567
$526$	−13.6444	−0.594923
$527$	23.3510	1.01719
$528$	−0.233213	−0.0101493
$529$	11.7355	0.510238
$530$	12.5149	0.543613
$531$	−21.0410	−0.913100
$532$	6.06430	0.262921
$533$	−13.3769	−0.579418
$534$	15.0987	0.653384
$535$	18.5605	0.802441
$536$	16.1207	0.696309
$537$	19.9007	0.858779
$538$	−30.5624	−1.31764
$539$	0.602177	0.0259376
$540$	−1.41309	−0.0608098
$541$	14.0303	0.603211	0.301606	−	0.953433i	$-0.402477\pi$
$541$	14.0303	0.603211	0.301606	+	0.953433i	$0.402477\pi$
$542$	−19.2016	−0.824779
$543$	−25.3031	−1.08586
$544$	−7.59968	−0.325834
$545$	1.07320	0.0459709
$546$	−11.0630	−0.473451
$547$	7.93761	0.339388	0.169694	−	0.985497i	$-0.445722\pi$
$547$	7.93761	0.339388	0.169694	+	0.985497i	$0.445722\pi$
$548$	13.8007	0.589535
$549$	−22.8977	−0.977251
$550$	0.100439	0.00428272
$551$	−19.2011	−0.817994
$552$	13.6848	0.582463
$553$	0.974834	0.0414542
$554$	26.1073	1.10919
$555$	28.0094	1.18893
$556$	16.5925	0.703677
$557$	21.4580	0.909206	0.454603	−	0.890694i	$-0.349781\pi$
$557$	21.4580	0.909206	0.454603	+	0.890694i	$0.349781\pi$
$558$	−7.34795	−0.311064
$559$	56.6697	2.39687
$560$	1.00226	0.0423533
$561$	−1.77234	−0.0748284
$562$	6.76306	0.285283
$563$	−21.5501	−0.908228	−0.454114	−	0.890944i	$-0.650044\pi$
$563$	−21.5501	−0.908228	−0.454114	+	0.890944i	$0.650044\pi$
$564$	−25.8849	−1.08995
$565$	12.8704	0.541464
$566$	−3.11151	−0.130786
$567$	−10.4790	−0.440078
$568$	−3.80916	−0.159829
$569$	−33.7226	−1.41372	−0.706862	−	0.707351i	$-0.749890\pi$
$569$	−33.7226	−1.41372	−0.706862	+	0.707351i	$0.749890\pi$
$570$	−14.0492	−0.588455
$571$	34.6770	1.45119	0.725593	−	0.688124i	$-0.241565\pi$
$571$	34.6770	1.45119	0.725593	+	0.688124i	$0.241565\pi$
$572$	−0.477463	−0.0199637
$573$	31.0378	1.29662
$574$	2.82032	0.117718
$575$	−5.89368	−0.245783
$576$	2.39142	0.0996424
$577$	−40.1546	−1.67166	−0.835828	−	0.548991i	$-0.815012\pi$
$577$	−40.1546	−1.67166	−0.835828	+	0.548991i	$0.815012\pi$
$578$	−40.7551	−1.69519
$579$	−13.1989	−0.548526
$580$	−3.17341	−0.131769
$581$	6.69245	0.277650
$582$	3.00496	0.124560
$583$	1.25698	0.0520589
$584$	1.60086	0.0662443
$585$	11.3683	0.470020
$586$	21.8787	0.903802
$587$	−20.4847	−0.845496	−0.422748	−	0.906247i	$-0.638934\pi$
$587$	−20.4847	−0.845496	−0.422748	+	0.906247i	$0.638934\pi$
$588$	−13.9211	−0.574098
$589$	18.5913	0.766042
$590$	8.79853	0.362230
$591$	−19.6279	−0.807383
$592$	12.0629	0.495782
$593$	1.05997	0.0435278	0.0217639	−	0.999763i	$-0.493072\pi$
$593$	1.05997	0.0435278	0.0217639	+	0.999763i	$0.493072\pi$
$594$	−0.141929	−0.00582342
$595$	7.61687	0.312261
$596$	−5.94886	−0.243675
$597$	−6.63971	−0.271745
$598$	28.0172	1.14571
$599$	27.5563	1.12592	0.562961	−	0.826484i	$-0.309662\pi$
$599$	27.5563	1.12592	0.562961	+	0.826484i	$0.309662\pi$
$600$	−2.32194	−0.0947929
$601$	−31.0102	−1.26493	−0.632466	−	0.774588i	$-0.717957\pi$
$601$	−31.0102	−1.26493	−0.632466	+	0.774588i	$0.717957\pi$
$602$	−11.9480	−0.486962
$603$	−38.5514	−1.56993
$604$	10.8154	0.440073
$605$	−10.9899	−0.446803
$606$	−8.66708	−0.352076
$607$	−15.3837	−0.624404	−0.312202	−	0.950016i	$-0.601066\pi$
$607$	−15.3837	−0.624404	−0.312202	+	0.950016i	$0.601066\pi$
$608$	−6.05061	−0.245385
$609$	−7.38515	−0.299261
$610$	9.57495	0.387679
$611$	−52.9948	−2.14394
$612$	18.1740	0.734641
$613$	10.3396	0.417613	0.208806	−	0.977957i	$-0.433042\pi$
$613$	10.3396	0.417613	0.208806	+	0.977957i	$0.433042\pi$
$614$	13.1852	0.532112
$615$	−6.53384	−0.263470
$616$	0.100666	0.00405594
$617$	27.0342	1.08835	0.544177	−	0.838970i	$-0.316842\pi$
$617$	27.0342	1.08835	0.544177	+	0.838970i	$0.316842\pi$
$618$	−11.3474	−0.456460
$619$	33.7618	1.35700	0.678500	−	0.734601i	$-0.262630\pi$
$619$	33.7618	1.35700	0.678500	+	0.734601i	$0.262630\pi$
$620$	3.07263	0.123400
$621$	8.32832	0.334204
$622$	−8.53085	−0.342056
$623$	−6.51732	−0.261111
$624$	11.0380	0.441873
$625$	1.00000	0.0400000
$626$	−3.83262	−0.153182
$627$	−1.41108	−0.0563531
$628$	−14.2912	−0.570281
$629$	91.6742	3.65529
$630$	−2.39683	−0.0954919
$631$	−6.33945	−0.252369	−0.126185	−	0.992007i	$-0.540273\pi$
$631$	−6.33945	−0.252369	−0.126185	+	0.992007i	$0.540273\pi$
$632$	−0.972634	−0.0386893
$633$	−1.99016	−0.0791018
$634$	13.0704	0.519090
$635$	−4.80638	−0.190735
$636$	−29.0589	−1.15226
$637$	−28.5011	−1.12925
$638$	−0.318733	−0.0126188
$639$	9.10930	0.360358
$640$	−1.00000	−0.0395285
$641$	26.4011	1.04278	0.521390	−	0.853318i	$-0.325414\pi$
$641$	26.4011	1.04278	0.521390	+	0.853318i	$0.325414\pi$
$642$	−43.0965	−1.70088
$643$	27.7479	1.09427	0.547135	−	0.837044i	$-0.315718\pi$
$643$	27.7479	1.09427	0.547135	+	0.837044i	$0.315718\pi$
$644$	−5.90701	−0.232769
$645$	27.6798	1.08989
$646$	−45.9827	−1.80917
$647$	26.1088	1.02644	0.513221	−	0.858257i	$-0.328452\pi$
$647$	26.1088	1.02644	0.513221	+	0.858257i	$0.328452\pi$
$648$	10.4554	0.410726
$649$	0.883712	0.0346887
$650$	−4.75377	−0.186458
$651$	7.15062	0.280255
$652$	16.1635	0.633012
$653$	−9.52959	−0.372922	−0.186461	−	0.982462i	$-0.559702\pi$
$653$	−9.52959	−0.372922	−0.186461	+	0.982462i	$0.559702\pi$
$654$	−2.49191	−0.0974415
$655$	9.97336	0.389692
$656$	−2.81396	−0.109867
$657$	−3.82834	−0.149358
$658$	11.1732	0.435575
$659$	−28.6371	−1.11554	−0.557771	−	0.829995i	$-0.688343\pi$
$659$	−28.6371	−1.11554	−0.557771	+	0.829995i	$0.688343\pi$
$660$	−0.233213	−0.00907780
$661$	−9.75905	−0.379583	−0.189792	−	0.981824i	$-0.560781\pi$
$661$	−9.75905	−0.379583	−0.189792	+	0.981824i	$0.560781\pi$
$662$	0.415964	0.0161669
$663$	83.8852	3.25783
$664$	−6.67734	−0.259131
$665$	6.06430	0.235163
$666$	−28.8474	−1.11782
$667$	18.7031	0.724186
$668$	12.5864	0.486984
$669$	−1.24039	−0.0479564
$670$	16.1207	0.622798
$671$	0.961695	0.0371258
$672$	−2.32720	−0.0897735
$673$	28.3981	1.09467	0.547333	−	0.836915i	$-0.315643\pi$
$673$	28.3981	1.09467	0.547333	+	0.836915i	$0.315643\pi$
$674$	−5.96765	−0.229865
$675$	−1.41309	−0.0543899
$676$	9.59836	0.369168
$677$	−7.26635	−0.279269	−0.139634	−	0.990203i	$-0.544593\pi$
$677$	−7.26635	−0.279269	−0.139634	+	0.990203i	$0.544593\pi$
$678$	−29.8844	−1.14771
$679$	−1.29709	−0.0497776
$680$	−7.59968	−0.291434
$681$	−63.0770	−2.41712
$682$	0.308611	0.0118173
$683$	2.05562	0.0786561	0.0393281	−	0.999226i	$-0.487478\pi$
$683$	2.05562	0.0786561	0.0393281	+	0.999226i	$0.487478\pi$
$684$	14.4695	0.553257
$685$	13.8007	0.527296
$686$	13.0249	0.497292
$687$	−5.36507	−0.204690
$688$	11.9210	0.454483
$689$	−59.4931	−2.26651
$690$	13.6848	0.520971
$691$	−7.03333	−0.267561	−0.133780	−	0.991011i	$-0.542712\pi$
$691$	−7.03333	−0.267561	−0.133780	+	0.991011i	$0.542712\pi$
$692$	−3.63810	−0.138300
$693$	−0.240734	−0.00914474
$694$	−0.723471	−0.0274626
$695$	16.5925	0.629388
$696$	7.36848	0.279302
$697$	−21.3852	−0.810021
$698$	−25.6014	−0.969026
$699$	57.3146	2.16784
$700$	1.00226	0.0378820
$701$	−2.50129	−0.0944726	−0.0472363	−	0.998884i	$-0.515041\pi$
$701$	−2.50129	−0.0944726	−0.0472363	+	0.998884i	$0.515041\pi$
$702$	6.71752	0.253536
$703$	72.9879	2.75279
$704$	−0.100439	−0.00378542
$705$	−25.8849	−0.974881
$706$	16.8800	0.635289
$707$	3.74113	0.140700
$708$	−20.4297	−0.767794
$709$	−29.9271	−1.12394	−0.561968	−	0.827159i	$-0.689956\pi$
$709$	−29.9271	−1.12394	−0.561968	+	0.827159i	$0.689956\pi$
$710$	−3.80916	−0.142955
$711$	2.32597	0.0872308
$712$	6.50261	0.243696
$713$	−18.1091	−0.678192
$714$	−17.6859	−0.661880
$715$	−0.477463	−0.0178561
$716$	8.57072	0.320303
$717$	−60.9427	−2.27595
$718$	11.0961	0.414101
$719$	−0.794209	−0.0296190	−0.0148095	−	0.999890i	$-0.504714\pi$
$719$	−0.794209	−0.0296190	−0.0148095	+	0.999890i	$0.504714\pi$
$720$	2.39142	0.0891229
$721$	4.89809	0.182414
$722$	−17.6099	−0.655372
$723$	−15.6090	−0.580504
$724$	−10.8974	−0.404997
$725$	−3.17341	−0.117858
$726$	25.5179	0.947060
$727$	−7.62985	−0.282976	−0.141488	−	0.989940i	$-0.545189\pi$
$727$	−7.62985	−0.282976	−0.141488	+	0.989940i	$0.545189\pi$
$728$	−4.76453	−0.176585
$729$	−15.1598	−0.561474
$730$	1.60086	0.0592507
$731$	90.5957	3.35080
$732$	−22.2325	−0.821737
$733$	−27.4248	−1.01296	−0.506480	−	0.862252i	$-0.669053\pi$
$733$	−27.4248	−1.01296	−0.506480	+	0.862252i	$0.669053\pi$
$734$	28.0345	1.03477
$735$	−13.9211	−0.513489
$736$	5.89368	0.217244
$737$	1.61914	0.0596419
$738$	6.72935	0.247711
$739$	15.7748	0.580287	0.290143	−	0.956983i	$-0.406297\pi$
$739$	15.7748	0.580287	0.290143	+	0.956983i	$0.406297\pi$
$740$	12.0629	0.443441
$741$	66.7866	2.45347
$742$	12.5432	0.460477
$743$	−42.3587	−1.55399	−0.776995	−	0.629507i	$-0.783257\pi$
$743$	−42.3587	−1.55399	−0.776995	+	0.629507i	$0.783257\pi$
$744$	−7.13448	−0.261563
$745$	−5.94886	−0.217949
$746$	−18.7554	−0.686683
$747$	15.9683	0.584250
$748$	−0.763302	−0.0279091
$749$	18.6025	0.679721
$750$	−2.32194	−0.0847854
$751$	13.4053	0.489166	0.244583	−	0.969628i	$-0.421349\pi$
$751$	13.4053	0.489166	0.244583	+	0.969628i	$0.421349\pi$
$752$	−11.1479	−0.406524
$753$	−48.4710	−1.76638
$754$	15.0857	0.549388
$755$	10.8154	0.393613
$756$	−1.41629	−0.0515099
$757$	−52.0482	−1.89172	−0.945861	−	0.324571i	$-0.894780\pi$
$757$	−52.0482	−1.89172	−0.945861	+	0.324571i	$0.894780\pi$
$758$	−29.1260	−1.05791
$759$	1.37448	0.0498905
$760$	−6.05061	−0.219479
$761$	23.8009	0.862783	0.431391	−	0.902165i	$-0.358023\pi$
$761$	23.8009	0.862783	0.431391	+	0.902165i	$0.358023\pi$
$762$	11.1601	0.404289
$763$	1.07563	0.0389404
$764$	13.3672	0.483607
$765$	18.1740	0.657083
$766$	−14.1299	−0.510535
$767$	−41.8262	−1.51026
$768$	2.32194	0.0837859
$769$	−26.3676	−0.950840	−0.475420	−	0.879759i	$-0.657704\pi$
$769$	−26.3676	−0.950840	−0.475420	+	0.879759i	$0.657704\pi$
$770$	0.100666	0.00362775
$771$	−37.1128	−1.33658
$772$	−5.68441	−0.204586
$773$	47.6275	1.71304	0.856522	−	0.516111i	$-0.172621\pi$
$773$	47.6275	1.71304	0.856522	+	0.516111i	$0.172621\pi$
$774$	−28.5081	−1.02470
$775$	3.07263	0.110372
$776$	1.29416	0.0464576
$777$	28.0727	1.00710
$778$	21.3146	0.764167
$779$	−17.0262	−0.610025
$780$	11.0380	0.395223
$781$	−0.382587	−0.0136900
$782$	44.7901	1.60169
$783$	4.48432	0.160257
$784$	−5.99547	−0.214124
$785$	−14.2912	−0.510075
$786$	−23.1576	−0.826004
$787$	−18.8524	−0.672016	−0.336008	−	0.941859i	$-0.609077\pi$
$787$	−18.8524	−0.672016	−0.336008	+	0.941859i	$0.609077\pi$
$788$	−8.45322	−0.301133
$789$	31.6814	1.12789
$790$	−0.972634	−0.0346048
$791$	12.8996	0.458656
$792$	0.240191	0.00853481
$793$	−45.5172	−1.61636
$794$	20.1305	0.714406
$795$	−29.0589	−1.03061
$796$	−2.85955	−0.101354
$797$	−18.0476	−0.639280	−0.319640	−	0.947539i	$-0.603562\pi$
$797$	−18.0476	−0.639280	−0.319640	+	0.947539i	$0.603562\pi$
$798$	−14.0810	−0.498460
$799$	−84.7208	−2.99721
$800$	−1.00000	−0.0353553
$801$	−15.5505	−0.549449
$802$	1.00000	0.0353112
$803$	0.160789	0.00567411
$804$	−37.4314	−1.32010
$805$	−5.90701	−0.208195
$806$	−14.6066	−0.514496
$807$	70.9642	2.49806
$808$	−3.73268	−0.131315
$809$	22.7074	0.798350	0.399175	−	0.916875i	$-0.369297\pi$
$809$	22.7074	0.798350	0.399175	+	0.916875i	$0.369297\pi$
$810$	10.4554	0.367364
$811$	−11.3067	−0.397031	−0.198515	−	0.980098i	$-0.563612\pi$
$811$	−11.3067	−0.397031	−0.198515	+	0.980098i	$0.563612\pi$
$812$	−3.18059	−0.111617
$813$	44.5850	1.56367
$814$	1.21158	0.0424659
$815$	16.1635	0.566183
$816$	17.6460	0.617734
$817$	72.1292	2.52348
$818$	21.2779	0.743965
$819$	11.3940	0.398138
$820$	−2.81396	−0.0982676
$821$	41.5267	1.44929	0.724646	−	0.689122i	$-0.242003\pi$
$821$	41.5267	1.44929	0.724646	+	0.689122i	$0.242003\pi$
$822$	−32.0443	−1.11767
$823$	−18.0149	−0.627961	−0.313980	−	0.949429i	$-0.601663\pi$
$823$	−18.0149	−0.627961	−0.313980	+	0.949429i	$0.601663\pi$
$824$	−4.88703	−0.170248
$825$	−0.233213	−0.00811943
$826$	8.81843	0.306832
$827$	−34.0812	−1.18512	−0.592560	−	0.805526i	$-0.701883\pi$
$827$	−34.0812	−1.18512	−0.592560	+	0.805526i	$0.701883\pi$
$828$	−14.0943	−0.489809
$829$	2.27683	0.0790777	0.0395389	−	0.999218i	$-0.487411\pi$
$829$	2.27683	0.0790777	0.0395389	+	0.999218i	$0.487411\pi$
$830$	−6.67734	−0.231774
$831$	−60.6197	−2.10287
$832$	4.75377	0.164807
$833$	−45.5637	−1.57869
$834$	−38.5268	−1.33407
$835$	12.5864	0.435572
$836$	−0.607715	−0.0210183
$837$	−4.34192	−0.150079
$838$	30.0402	1.03772
$839$	51.5922	1.78116	0.890580	−	0.454828i	$-0.150299\pi$
$839$	51.5922	1.78116	0.890580	+	0.454828i	$0.150299\pi$
$840$	−2.32720	−0.0802959
$841$	−18.9295	−0.652740
$842$	15.3414	0.528700
$843$	−15.7034	−0.540855
$844$	−0.857110	−0.0295029
$845$	9.59836	0.330194
$846$	26.6594	0.916569
$847$	−11.0148	−0.378472
$848$	−12.5149	−0.429764
$849$	7.22474	0.247952
$850$	−7.59968	−0.260667
$851$	−71.0949	−2.43710
$852$	8.84465	0.303013
$853$	−7.16454	−0.245309	−0.122655	−	0.992449i	$-0.539141\pi$
$853$	−7.16454	−0.245309	−0.122655	+	0.992449i	$0.539141\pi$
$854$	9.59662	0.328389
$855$	14.4695	0.494848
$856$	−18.5605	−0.634386
$857$	7.41856	0.253413	0.126707	−	0.991940i	$-0.459559\pi$
$857$	7.41856	0.253413	0.126707	+	0.991940i	$0.459559\pi$
$858$	1.10864	0.0378484
$859$	−39.6370	−1.35240	−0.676198	−	0.736720i	$-0.736374\pi$
$859$	−39.6370	−1.35240	−0.676198	+	0.736720i	$0.736374\pi$
$860$	11.9210	0.406502
$861$	−6.54863	−0.223177
$862$	−4.94001	−0.168257
$863$	−46.1052	−1.56944	−0.784719	−	0.619851i	$-0.787193\pi$
$863$	−46.1052	−1.56944	−0.784719	+	0.619851i	$0.787193\pi$
$864$	1.41309	0.0480744
$865$	−3.63810	−0.123699
$866$	−12.5278	−0.425712
$867$	94.6311	3.21384
$868$	3.07959	0.104528
$869$	−0.0976900	−0.00331391
$870$	7.36848	0.249815
$871$	−76.6342	−2.59665
$872$	−1.07320	−0.0363432
$873$	−3.09488	−0.104746
$874$	35.6604	1.20623
$875$	1.00226	0.0338827
$876$	−3.71712	−0.125590
$877$	−42.2024	−1.42507	−0.712537	−	0.701634i	$-0.752454\pi$
$877$	−42.2024	−1.42507	−0.712537	+	0.701634i	$0.752454\pi$
$878$	−6.65174	−0.224485
$879$	−50.8011	−1.71348
$880$	−0.100439	−0.00338579
$881$	−4.27447	−0.144010	−0.0720052	−	0.997404i	$-0.522940\pi$
$881$	−4.27447	−0.144010	−0.0720052	+	0.997404i	$0.522940\pi$
$882$	14.3377	0.482775
$883$	−12.2112	−0.410939	−0.205470	−	0.978663i	$-0.565872\pi$
$883$	−12.2112	−0.410939	−0.205470	+	0.978663i	$0.565872\pi$
$884$	36.1272	1.21509
$885$	−20.4297	−0.686736
$886$	0.682149	0.0229172
$887$	−16.8673	−0.566349	−0.283175	−	0.959068i	$-0.591388\pi$
$887$	−16.8673	−0.566349	−0.283175	+	0.959068i	$0.591388\pi$
$888$	−28.0094	−0.939932
$889$	−4.81725	−0.161566
$890$	6.50261	0.217968
$891$	1.05012	0.0351805
$892$	−0.534205	−0.0178865
$893$	−67.4519	−2.25719
$894$	13.8129	0.461973
$895$	8.57072	0.286488
$896$	−1.00226	−0.0334832
$897$	−65.0544	−2.17210
$898$	−0.981671	−0.0327588
$899$	−9.75074	−0.325205
$900$	2.39142	0.0797139
$901$	−95.1094	−3.16855
$902$	−0.282630	−0.00941055
$903$	27.7425	0.923211
$904$	−12.8704	−0.428065
$905$	−10.8974	−0.362241
$906$	−25.1128	−0.834316
$907$	26.1590	0.868594	0.434297	−	0.900770i	$-0.356997\pi$
$907$	26.1590	0.868594	0.434297	+	0.900770i	$0.356997\pi$
$908$	−27.1656	−0.901522
$909$	8.92641	0.296070
$910$	−4.76453	−0.157943
$911$	−43.3376	−1.43584	−0.717920	−	0.696126i	$-0.754905\pi$
$911$	−43.3376	−1.43584	−0.717920	+	0.696126i	$0.754905\pi$
$912$	14.0492	0.465215
$913$	−0.670663	−0.0221957
$914$	−5.68196	−0.187943
$915$	−22.2325	−0.734984
$916$	−2.31059	−0.0763442
$917$	9.99593	0.330095
$918$	10.7390	0.354441
$919$	33.9230	1.11902	0.559509	−	0.828824i	$-0.310990\pi$
$919$	33.9230	1.11902	0.559509	+	0.828824i	$0.310990\pi$
$920$	5.89368	0.194309
$921$	−30.6153	−1.00881
$922$	11.8077	0.388865
$923$	18.1079	0.596028
$924$	−0.233740	−0.00768949
$925$	12.0629	0.396626
$926$	25.4495	0.836323
$927$	11.6869	0.383850
$928$	3.17341	0.104172
$929$	50.7657	1.66557	0.832785	−	0.553597i	$-0.186745\pi$
$929$	50.7657	1.66557	0.832785	+	0.553597i	$0.186745\pi$
$930$	−7.13448	−0.233949
$931$	−36.2763	−1.18891
$932$	24.6839	0.808547
$933$	19.8081	0.648489
$934$	27.5015	0.899877
$935$	−0.763302	−0.0249626
$936$	−11.3683	−0.371583
$937$	−39.6993	−1.29692	−0.648459	−	0.761250i	$-0.724586\pi$
$937$	−39.6993	−1.29692	−0.648459	+	0.761250i	$0.724586\pi$
$938$	16.1572	0.527551
$939$	8.89913	0.290412
$940$	−11.1479	−0.363606
$941$	−3.68999	−0.120290	−0.0601451	−	0.998190i	$-0.519156\pi$
$941$	−3.68999	−0.120290	−0.0601451	+	0.998190i	$0.519156\pi$
$942$	33.1834	1.08117
$943$	16.5846	0.540068
$944$	−8.79853	−0.286368
$945$	−1.41629	−0.0460719
$946$	1.19733	0.0389285
$947$	−35.9431	−1.16799	−0.583997	−	0.811756i	$-0.698512\pi$
$947$	−35.9431	−1.16799	−0.583997	+	0.811756i	$0.698512\pi$
$948$	2.25840	0.0733494
$949$	−7.61015	−0.247036
$950$	−6.05061	−0.196308
$951$	−30.3486	−0.984121
$952$	−7.61687	−0.246864
$953$	−5.14347	−0.166613	−0.0833067	−	0.996524i	$-0.526548\pi$
$953$	−5.14347	−0.166613	−0.0833067	+	0.996524i	$0.526548\pi$
$954$	29.9284	0.968968
$955$	13.3672	0.432551
$956$	−26.2464	−0.848870
$957$	0.740080	0.0239234
$958$	−34.2537	−1.10669
$959$	13.8319	0.446655
$960$	2.32194	0.0749404
$961$	−21.5589	−0.695449
$962$	−57.3443	−1.84885
$963$	44.3860	1.43032
$964$	−6.72237	−0.216513
$965$	−5.68441	−0.182988
$966$	13.7157	0.441297
$967$	44.2132	1.42180	0.710900	−	0.703293i	$-0.248288\pi$
$967$	44.2132	1.42180	0.710900	+	0.703293i	$0.248288\pi$
$968$	10.9899	0.353229
$969$	106.769	3.42992
$970$	1.29416	0.0415529
$971$	−12.5271	−0.402012	−0.201006	−	0.979590i	$-0.564421\pi$
$971$	−12.5271	−0.402012	−0.201006	+	0.979590i	$0.564421\pi$
$972$	−20.0375	−0.642703
$973$	16.6300	0.533134
$974$	−8.39120	−0.268871
$975$	11.0380	0.353499
$976$	−9.57495	−0.306487
$977$	11.3444	0.362941	0.181470	−	0.983396i	$-0.441914\pi$
$977$	11.3444	0.362941	0.181470	+	0.983396i	$0.441914\pi$
$978$	−37.5308	−1.20010
$979$	0.653114	0.0208736
$980$	−5.99547	−0.191518
$981$	2.56648	0.0819412
$982$	29.7272	0.948634
$983$	36.1645	1.15347	0.576734	−	0.816932i	$-0.304327\pi$
$983$	36.1645	1.15347	0.576734	+	0.816932i	$0.304327\pi$
$984$	6.53384	0.208291
$985$	−8.45322	−0.269342
$986$	24.1169	0.768039
$987$	−25.9434	−0.825789
$988$	28.7632	0.915080
$989$	−70.2585	−2.23409
$990$	0.240191	0.00763376
$991$	−47.3693	−1.50474	−0.752368	−	0.658743i	$-0.771088\pi$
$991$	−47.3693	−1.50474	−0.752368	+	0.658743i	$0.771088\pi$
$992$	−3.07263	−0.0975563
$993$	−0.965846	−0.0306502
$994$	−3.81778	−0.121093
$995$	−2.85955	−0.0906538
$996$	15.5044	0.491276
$997$	37.6526	1.19247	0.596235	−	0.802810i	$-0.296663\pi$
$997$	37.6526	1.19247	0.596235	+	0.802810i	$0.296663\pi$
$998$	−14.3645	−0.454700
$999$	−17.0460	−0.539311

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.m.1.16	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.m.1.16	✓	20	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.32194 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.32194 q^{6} +1.00226 q^{7} -1.00000 q^{8} +2.39142 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.32194 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.32194 q^{6} +1.00226 q^{7} -1.00000 q^{8} +2.39142 q^{9} -1.00000 q^{10} -0.100439 q^{11} +2.32194 q^{12} +4.75377 q^{13} -1.00226 q^{14} +2.32194 q^{15} +1.00000 q^{16} +7.59968 q^{17} -2.39142 q^{18} +6.05061 q^{19} +1.00000 q^{20} +2.32720 q^{21} +0.100439 q^{22} -5.89368 q^{23} -2.32194 q^{24} +1.00000 q^{25} -4.75377 q^{26} -1.41309 q^{27} +1.00226 q^{28} -3.17341 q^{29} -2.32194 q^{30} +3.07263 q^{31} -1.00000 q^{32} -0.233213 q^{33} -7.59968 q^{34} +1.00226 q^{35} +2.39142 q^{36} +12.0629 q^{37} -6.05061 q^{38} +11.0380 q^{39} -1.00000 q^{40} -2.81396 q^{41} -2.32720 q^{42} +11.9210 q^{43} -0.100439 q^{44} +2.39142 q^{45} +5.89368 q^{46} -11.1479 q^{47} +2.32194 q^{48} -5.99547 q^{49} -1.00000 q^{50} +17.6460 q^{51} +4.75377 q^{52} -12.5149 q^{53} +1.41309 q^{54} -0.100439 q^{55} -1.00226 q^{56} +14.0492 q^{57} +3.17341 q^{58} -8.79853 q^{59} +2.32194 q^{60} -9.57495 q^{61} -3.07263 q^{62} +2.39683 q^{63} +1.00000 q^{64} +4.75377 q^{65} +0.233213 q^{66} -16.1207 q^{67} +7.59968 q^{68} -13.6848 q^{69} -1.00226 q^{70} +3.80916 q^{71} -2.39142 q^{72} -1.60086 q^{73} -12.0629 q^{74} +2.32194 q^{75} +6.05061 q^{76} -0.100666 q^{77} -11.0380 q^{78} +0.972634 q^{79} +1.00000 q^{80} -10.4554 q^{81} +2.81396 q^{82} +6.67734 q^{83} +2.32720 q^{84} +7.59968 q^{85} -11.9210 q^{86} -7.36848 q^{87} +0.100439 q^{88} -6.50261 q^{89} -2.39142 q^{90} +4.76453 q^{91} -5.89368 q^{92} +7.13448 q^{93} +11.1479 q^{94} +6.05061 q^{95} -2.32194 q^{96} -1.29416 q^{97} +5.99547 q^{98} -0.240191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * q^99

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