LMFDB - Embedded newform 5043.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5043,2,Mod(1,5043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5043, 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("5043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5043 = 3 \cdot 41^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5043.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:	$40.2685577393$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 123)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.81361$ of defining polynomial
Character	$\chi$	$=$	5043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} -1.10278 q^{5} -1.81361 q^{6} -2.52444 q^{7} +1.28917 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} -1.10278 q^{5} -1.81361 q^{6} -2.52444 q^{7} +1.28917 q^{8} +1.00000 q^{9} +2.00000 q^{10} -0.813607 q^{11} +1.28917 q^{12} -5.10278 q^{13} +4.57834 q^{14} -1.10278 q^{15} -4.91638 q^{16} -3.39194 q^{17} -1.81361 q^{18} -3.10278 q^{19} -1.42166 q^{20} -2.52444 q^{21} +1.47556 q^{22} -0.897225 q^{23} +1.28917 q^{24} -3.78389 q^{25} +9.25443 q^{26} +1.00000 q^{27} -3.25443 q^{28} -4.44082 q^{29} +2.00000 q^{30} -8.96526 q^{31} +6.33804 q^{32} -0.813607 q^{33} +6.15165 q^{34} +2.78389 q^{35} +1.28917 q^{36} +2.08362 q^{37} +5.62721 q^{38} -5.10278 q^{39} -1.42166 q^{40} +4.57834 q^{42} +9.07306 q^{43} -1.04888 q^{44} -1.10278 q^{45} +1.62721 q^{46} +0.235269 q^{47} -4.91638 q^{48} -0.627213 q^{49} +6.86248 q^{50} -3.39194 q^{51} -6.57834 q^{52} -13.8328 q^{53} -1.81361 q^{54} +0.897225 q^{55} -3.25443 q^{56} -3.10278 q^{57} +8.05390 q^{58} +1.04888 q^{59} -1.42166 q^{60} +1.91638 q^{61} +16.2594 q^{62} -2.52444 q^{63} -1.66196 q^{64} +5.62721 q^{65} +1.47556 q^{66} +10.0383 q^{67} -4.37279 q^{68} -0.897225 q^{69} -5.04888 q^{70} +12.8136 q^{71} +1.28917 q^{72} +4.75971 q^{73} -3.77886 q^{74} -3.78389 q^{75} -4.00000 q^{76} +2.05390 q^{77} +9.25443 q^{78} +15.8328 q^{79} +5.42166 q^{80} +1.00000 q^{81} -7.68111 q^{83} -3.25443 q^{84} +3.74055 q^{85} -16.4550 q^{86} -4.44082 q^{87} -1.04888 q^{88} -13.2544 q^{89} +2.00000 q^{90} +12.8816 q^{91} -1.15667 q^{92} -8.96526 q^{93} -0.426686 q^{94} +3.42166 q^{95} +6.33804 q^{96} -2.72999 q^{97} +1.13752 q^{98} -0.813607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 + q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9} + 6 q^{10} + 4 q^{11} + 3 q^{12} - 8 q^{13} + 12 q^{14} + 4 q^{15} - q^{16} - 2 q^{17} + q^{18} - 2 q^{19} - 6 q^{20} - 2 q^{21} + 10 q^{22} - 10 q^{23} + 3 q^{24} + 5 q^{25} + 2 q^{26} + 3 q^{27} + 16 q^{28} + 6 q^{29} + 6 q^{30} - 2 q^{31} + 7 q^{32} + 4 q^{33} - 8 q^{35} + 3 q^{36} + 20 q^{37} + 4 q^{38} - 8 q^{39} - 6 q^{40} + 12 q^{42} + 10 q^{43} + 8 q^{44} + 4 q^{45} - 8 q^{46} - 4 q^{47} - q^{48} + 11 q^{49} + 3 q^{50} - 2 q^{51} - 18 q^{52} - 14 q^{53} + q^{54} + 10 q^{55} + 16 q^{56} - 2 q^{57} + 28 q^{58} - 8 q^{59} - 6 q^{60} - 8 q^{61} + 38 q^{62} - 2 q^{63} - 17 q^{64} + 4 q^{65} + 10 q^{66} - 12 q^{67} - 26 q^{68} - 10 q^{69} - 4 q^{70} + 32 q^{71} + 3 q^{72} + 4 q^{73} + 20 q^{74} + 5 q^{75} - 12 q^{76} + 10 q^{77} + 2 q^{78} + 20 q^{79} + 18 q^{80} + 3 q^{81} - 14 q^{83} + 16 q^{84} + 22 q^{85} + 6 q^{86} + 6 q^{87} + 8 q^{88} - 14 q^{89} + 6 q^{90} - 2 q^{93} - 18 q^{94} + 12 q^{95} + 7 q^{96} + 12 q^{97} + 21 q^{98} + 4 q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 + q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9 + 6 * q^10 + 4 * q^11 + 3 * q^12 - 8 * q^13 + 12 * q^14 + 4 * q^15 - q^16 - 2 * q^17 + q^18 - 2 * q^19 - 6 * q^20 - 2 * q^21 + 10 * q^22 - 10 * q^23 + 3 * q^24 + 5 * q^25 + 2 * q^26 + 3 * q^27 + 16 * q^28 + 6 * q^29 + 6 * q^30 - 2 * q^31 + 7 * q^32 + 4 * q^33 - 8 * q^35 + 3 * q^36 + 20 * q^37 + 4 * q^38 - 8 * q^39 - 6 * q^40 + 12 * q^42 + 10 * q^43 + 8 * q^44 + 4 * q^45 - 8 * q^46 - 4 * q^47 - q^48 + 11 * q^49 + 3 * q^50 - 2 * q^51 - 18 * q^52 - 14 * q^53 + q^54 + 10 * q^55 + 16 * q^56 - 2 * q^57 + 28 * q^58 - 8 * q^59 - 6 * q^60 - 8 * q^61 + 38 * q^62 - 2 * q^63 - 17 * q^64 + 4 * q^65 + 10 * q^66 - 12 * q^67 - 26 * q^68 - 10 * q^69 - 4 * q^70 + 32 * q^71 + 3 * q^72 + 4 * q^73 + 20 * q^74 + 5 * q^75 - 12 * q^76 + 10 * q^77 + 2 * q^78 + 20 * q^79 + 18 * q^80 + 3 * q^81 - 14 * q^83 + 16 * q^84 + 22 * q^85 + 6 * q^86 + 6 * q^87 + 8 * q^88 - 14 * q^89 + 6 * q^90 - 2 * q^93 - 18 * q^94 + 12 * q^95 + 7 * q^96 + 12 * q^97 + 21 * q^98 + 4 * 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 $

$2$	−1.81361	−1.28241	−0.641207	−	0.767368i	$-0.721566\pi$
$2$	−1.81361	−1.28241	−0.641207	+	0.767368i	$0.721566\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.28917	0.644584
$5$	−1.10278	−0.493176	−0.246588	−	0.969120i	$-0.579309\pi$
$5$	−1.10278	−0.493176	−0.246588	+	0.969120i	$0.579309\pi$
$6$	−1.81361	−0.740402
$7$	−2.52444	−0.954148	−0.477074	−	0.878863i	$-0.658303\pi$
$7$	−2.52444	−0.954148	−0.477074	+	0.878863i	$0.658303\pi$
$8$	1.28917	0.455790
$9$	1.00000	0.333333
$10$	2.00000	0.632456
$11$	−0.813607	−0.245312	−0.122656	−	0.992449i	$-0.539141\pi$
$11$	−0.813607	−0.245312	−0.122656	+	0.992449i	$0.539141\pi$
$12$	1.28917	0.372151
$13$	−5.10278	−1.41526	−0.707628	−	0.706586i	$-0.750235\pi$
$13$	−5.10278	−1.41526	−0.707628	+	0.706586i	$0.750235\pi$
$14$	4.57834	1.22361
$15$	−1.10278	−0.284735
$16$	−4.91638	−1.22910
$17$	−3.39194	−0.822667	−0.411334	−	0.911485i	$-0.634937\pi$
$17$	−3.39194	−0.822667	−0.411334	+	0.911485i	$0.634937\pi$
$18$	−1.81361	−0.427471
$19$	−3.10278	−0.711825	−0.355913	−	0.934519i	$-0.615830\pi$
$19$	−3.10278	−0.711825	−0.355913	+	0.934519i	$0.615830\pi$
$20$	−1.42166	−0.317893
$21$	−2.52444	−0.550878
$22$	1.47556	0.314591
$23$	−0.897225	−0.187084	−0.0935422	−	0.995615i	$-0.529819\pi$
$23$	−0.897225	−0.187084	−0.0935422	+	0.995615i	$0.529819\pi$
$24$	1.28917	0.263150
$25$	−3.78389	−0.756777
$26$	9.25443	1.81494
$27$	1.00000	0.192450
$28$	−3.25443	−0.615029
$29$	−4.44082	−0.824639	−0.412320	−	0.911039i	$-0.635281\pi$
$29$	−4.44082	−0.824639	−0.412320	+	0.911039i	$0.635281\pi$
$30$	2.00000	0.365148
$31$	−8.96526	−1.61021	−0.805104	−	0.593134i	$-0.797890\pi$
$31$	−8.96526	−1.61021	−0.805104	+	0.593134i	$0.797890\pi$
$32$	6.33804	1.12042
$33$	−0.813607	−0.141631
$34$	6.15165	1.05500
$35$	2.78389	0.470563
$36$	1.28917	0.214861
$37$	2.08362	0.342545	0.171272	−	0.985224i	$-0.445212\pi$
$37$	2.08362	0.342545	0.171272	+	0.985224i	$0.445212\pi$
$38$	5.62721	0.912854
$39$	−5.10278	−0.817098
$40$	−1.42166	−0.224785
$41$	0	0
$41$	0	0
$42$	4.57834	0.706453
$43$	9.07306	1.38363	0.691814	−	0.722076i	$-0.256812\pi$
$43$	9.07306	1.38363	0.691814	+	0.722076i	$0.256812\pi$
$44$	−1.04888	−0.158124
$45$	−1.10278	−0.164392
$46$	1.62721	0.239919
$47$	0.235269	0.0343176	0.0171588	−	0.999853i	$-0.494538\pi$
$47$	0.235269	0.0343176	0.0171588	+	0.999853i	$0.494538\pi$
$48$	−4.91638	−0.709619
$49$	−0.627213	−0.0896019
$50$	6.86248	0.970502
$51$	−3.39194	−0.474967
$52$	−6.57834	−0.912251
$53$	−13.8328	−1.90008	−0.950038	−	0.312134i	$-0.898956\pi$
$53$	−13.8328	−1.90008	−0.950038	+	0.312134i	$0.898956\pi$
$54$	−1.81361	−0.246801
$55$	0.897225	0.120982
$56$	−3.25443	−0.434891
$57$	−3.10278	−0.410973
$58$	8.05390	1.05753
$59$	1.04888	0.136552	0.0682760	−	0.997666i	$-0.478250\pi$
$59$	1.04888	0.136552	0.0682760	+	0.997666i	$0.478250\pi$
$60$	−1.42166	−0.183536
$61$	1.91638	0.245368	0.122684	−	0.992446i	$-0.460850\pi$
$61$	1.91638	0.245368	0.122684	+	0.992446i	$0.460850\pi$
$62$	16.2594	2.06495
$63$	−2.52444	−0.318049
$64$	−1.66196	−0.207744
$65$	5.62721	0.697970
$66$	1.47556	0.181629
$67$	10.0383	1.22638	0.613188	−	0.789937i	$-0.289887\pi$
$67$	10.0383	1.22638	0.613188	+	0.789937i	$0.289887\pi$
$68$	−4.37279	−0.530278
$69$	−0.897225	−0.108013
$70$	−5.04888	−0.603456
$71$	12.8136	1.52070	0.760348	−	0.649516i	$-0.225029\pi$
$71$	12.8136	1.52070	0.760348	+	0.649516i	$0.225029\pi$
$72$	1.28917	0.151930
$73$	4.75971	0.557082	0.278541	−	0.960424i	$-0.410149\pi$
$73$	4.75971	0.557082	0.278541	+	0.960424i	$0.410149\pi$
$74$	−3.77886	−0.439284
$75$	−3.78389	−0.436926
$76$	−4.00000	−0.458831
$77$	2.05390	0.234064
$78$	9.25443	1.04786
$79$	15.8328	1.78133	0.890663	−	0.454665i	$-0.150241\pi$
$79$	15.8328	1.78133	0.890663	+	0.454665i	$0.150241\pi$
$80$	5.42166	0.606160
$81$	1.00000	0.111111
$82$	0	0
$83$	−7.68111	−0.843112	−0.421556	−	0.906802i	$-0.638516\pi$
$83$	−7.68111	−0.843112	−0.421556	+	0.906802i	$0.638516\pi$
$84$	−3.25443	−0.355087
$85$	3.74055	0.405720
$86$	−16.4550	−1.77438
$87$	−4.44082	−0.476106
$88$	−1.04888	−0.111811
$89$	−13.2544	−1.40497	−0.702483	−	0.711700i	$-0.747925\pi$
$89$	−13.2544	−1.40497	−0.702483	+	0.711700i	$0.747925\pi$
$90$	2.00000	0.210819
$91$	12.8816	1.35036
$92$	−1.15667	−0.120592
$93$	−8.96526	−0.929654
$94$	−0.426686	−0.0440093
$95$	3.42166	0.351055
$96$	6.33804	0.646874
$97$	−2.72999	−0.277188	−0.138594	−	0.990349i	$-0.544258\pi$
$97$	−2.72999	−0.277188	−0.138594	+	0.990349i	$0.544258\pi$
$98$	1.13752	0.114907
$99$	−0.813607	−0.0817705
$100$	−4.87807	−0.487807
$101$	11.8625	1.18036	0.590181	−	0.807271i	$-0.299057\pi$
$101$	11.8625	1.18036	0.590181	+	0.807271i	$0.299057\pi$
$102$	6.15165	0.609104
$103$	−0.494719	−0.0487461	−0.0243730	−	0.999703i	$-0.507759\pi$
$103$	−0.494719	−0.0487461	−0.0243730	+	0.999703i	$0.507759\pi$
$104$	−6.57834	−0.645059
$105$	2.78389	0.271680
$106$	25.0872	2.43668
$107$	−15.0872	−1.45853	−0.729267	−	0.684229i	$-0.760139\pi$
$107$	−15.0872	−1.45853	−0.729267	+	0.684229i	$0.760139\pi$
$108$	1.28917	0.124050
$109$	−5.10278	−0.488757	−0.244379	−	0.969680i	$-0.578584\pi$
$109$	−5.10278	−0.488757	−0.244379	+	0.969680i	$0.578584\pi$
$110$	−1.62721	−0.155149
$111$	2.08362	0.197768
$112$	12.4111	1.17274
$113$	−17.5139	−1.64757	−0.823783	−	0.566905i	$-0.808141\pi$
$113$	−17.5139	−1.64757	−0.823783	+	0.566905i	$0.808141\pi$
$114$	5.62721	0.527037
$115$	0.989437	0.0922655
$116$	−5.72496	−0.531550
$117$	−5.10278	−0.471752
$118$	−1.90225	−0.175116
$119$	8.56275	0.784946
$120$	−1.42166	−0.129779
$121$	−10.3380	−0.939822
$122$	−3.47556	−0.314663
$123$	0	0
$124$	−11.5577	−1.03791
$125$	9.68665	0.866400
$126$	4.57834	0.407871
$127$	12.8816	1.14306	0.571530	−	0.820581i	$-0.306350\pi$
$127$	12.8816	1.14306	0.571530	+	0.820581i	$0.306350\pi$
$128$	−9.66196	−0.854004
$129$	9.07306	0.798838
$130$	−10.2056	−0.895086
$131$	−6.35720	−0.555431	−0.277716	−	0.960663i	$-0.589577\pi$
$131$	−6.35720	−0.555431	−0.277716	+	0.960663i	$0.589577\pi$
$132$	−1.04888	−0.0912929
$133$	7.83276	0.679187
$134$	−18.2056	−1.57272
$135$	−1.10278	−0.0949118
$136$	−4.37279	−0.374963
$137$	17.4897	1.49425	0.747123	−	0.664686i	$-0.231435\pi$
$137$	17.4897	1.49425	0.747123	+	0.664686i	$0.231435\pi$
$138$	1.62721	0.138518
$139$	15.7250	1.33377	0.666887	−	0.745159i	$-0.267626\pi$
$139$	15.7250	1.33377	0.666887	+	0.745159i	$0.267626\pi$
$140$	3.58890	0.303317
$141$	0.235269	0.0198133
$142$	−23.2388	−1.95016
$143$	4.15165	0.347178
$144$	−4.91638	−0.409698
$145$	4.89722	0.406692
$146$	−8.63224	−0.714409
$147$	−0.627213	−0.0517317
$148$	2.68614	0.220799
$149$	−11.5678	−0.947669	−0.473835	−	0.880614i	$-0.657131\pi$
$149$	−11.5678	−0.947669	−0.473835	+	0.880614i	$0.657131\pi$
$150$	6.86248	0.560319
$151$	−19.2544	−1.56690	−0.783451	−	0.621453i	$-0.786543\pi$
$151$	−19.2544	−1.56690	−0.783451	+	0.621453i	$0.786543\pi$
$152$	−4.00000	−0.324443
$153$	−3.39194	−0.274222
$154$	−3.72496	−0.300166
$155$	9.88666	0.794116
$156$	−6.57834	−0.526688
$157$	20.9200	1.66959	0.834797	−	0.550558i	$-0.185585\pi$
$157$	20.9200	1.66959	0.834797	+	0.550558i	$0.185585\pi$
$158$	−28.7144	−2.28440
$159$	−13.8328	−1.09701
$160$	−6.98944	−0.552564
$161$	2.26499	0.178506
$162$	−1.81361	−0.142490
$163$	−12.7980	−1.00242	−0.501209	−	0.865326i	$-0.667111\pi$
$163$	−12.7980	−1.00242	−0.501209	+	0.865326i	$0.667111\pi$
$164$	0	0
$165$	0.897225	0.0698489
$166$	13.9305	1.08122
$167$	−9.62721	−0.744976	−0.372488	−	0.928037i	$-0.621495\pi$
$167$	−9.62721	−0.744976	−0.372488	+	0.928037i	$0.621495\pi$
$168$	−3.25443	−0.251084
$169$	13.0383	1.00295
$170$	−6.78389	−0.520300
$171$	−3.10278	−0.237275
$172$	11.6967	0.891865
$173$	11.9461	0.908245	0.454123	−	0.890939i	$-0.349953\pi$
$173$	11.9461	0.908245	0.454123	+	0.890939i	$0.349953\pi$
$174$	8.05390	0.610565
$175$	9.55219	0.722078
$176$	4.00000	0.301511
$177$	1.04888	0.0788383
$178$	24.0383	1.80175
$179$	2.13752	0.159766	0.0798828	−	0.996804i	$-0.474545\pi$
$179$	2.13752	0.159766	0.0798828	+	0.996804i	$0.474545\pi$
$180$	−1.42166	−0.105964
$181$	1.83276	0.136228	0.0681141	−	0.997678i	$-0.478302\pi$
$181$	1.83276	0.136228	0.0681141	+	0.997678i	$0.478302\pi$
$182$	−23.3622	−1.73172
$183$	1.91638	0.141663
$184$	−1.15667	−0.0852712
$185$	−2.29776	−0.168935
$186$	16.2594	1.19220
$187$	2.75971	0.201810
$188$	0.303302	0.0221206
$189$	−2.52444	−0.183626
$190$	−6.20555	−0.450198
$191$	18.6167	1.34705	0.673527	−	0.739163i	$-0.264779\pi$
$191$	18.6167	1.34705	0.673527	+	0.739163i	$0.264779\pi$
$192$	−1.66196	−0.119941
$193$	−15.6116	−1.12375	−0.561875	−	0.827222i	$-0.689920\pi$
$193$	−15.6116	−1.12375	−0.561875	+	0.827222i	$0.689920\pi$
$194$	4.95112	0.355470
$195$	5.62721	0.402973
$196$	−0.808583	−0.0577559
$197$	−5.21057	−0.371238	−0.185619	−	0.982622i	$-0.559429\pi$
$197$	−5.21057	−0.371238	−0.185619	+	0.982622i	$0.559429\pi$
$198$	1.47556	0.104864
$199$	−2.05390	−0.145597	−0.0727985	−	0.997347i	$-0.523193\pi$
$199$	−2.05390	−0.145597	−0.0727985	+	0.997347i	$0.523193\pi$
$200$	−4.87807	−0.344932
$201$	10.0383	0.708048
$202$	−21.5139	−1.51371
$203$	11.2106	0.786828
$204$	−4.37279	−0.306156
$205$	0	0
$206$	0.897225	0.0625126
$207$	−0.897225	−0.0623614
$208$	25.0872	1.73948
$209$	2.52444	0.174619
$210$	−5.04888	−0.348406
$211$	9.04888	0.622950	0.311475	−	0.950254i	$-0.399177\pi$
$211$	9.04888	0.622950	0.311475	+	0.950254i	$0.399177\pi$
$212$	−17.8328	−1.22476
$213$	12.8136	0.877974
$214$	27.3622	1.87044
$215$	−10.0055	−0.682372
$216$	1.28917	0.0877168
$217$	22.6322	1.53638
$218$	9.25443	0.626789
$219$	4.75971	0.321631
$220$	1.15667	0.0779830
$221$	17.3083	1.16428
$222$	−3.77886	−0.253621
$223$	24.8222	1.66222	0.831109	−	0.556110i	$-0.187707\pi$
$223$	24.8222	1.66222	0.831109	+	0.556110i	$0.187707\pi$
$224$	−16.0000	−1.06904
$225$	−3.78389	−0.252259
$226$	31.7633	2.11286
$227$	−16.6464	−1.10486	−0.552429	−	0.833560i	$-0.686299\pi$
$227$	−16.6464	−1.10486	−0.552429	+	0.833560i	$0.686299\pi$
$228$	−4.00000	−0.264906
$229$	15.7789	1.04270	0.521348	−	0.853344i	$-0.325429\pi$
$229$	15.7789	1.04270	0.521348	+	0.853344i	$0.325429\pi$
$230$	−1.79445	−0.118323
$231$	2.05390	0.135137
$232$	−5.72496	−0.375862
$233$	24.9200	1.63256	0.816280	−	0.577656i	$-0.196033\pi$
$233$	24.9200	1.63256	0.816280	+	0.577656i	$0.196033\pi$
$234$	9.25443	0.604981
$235$	−0.259449	−0.0169246
$236$	1.35218	0.0880193
$237$	15.8328	1.02845
$238$	−15.5295	−1.00663
$239$	2.95112	0.190892	0.0954462	−	0.995435i	$-0.469572\pi$
$239$	2.95112	0.190892	0.0954462	+	0.995435i	$0.469572\pi$
$240$	5.42166	0.349967
$241$	−16.5925	−1.06881	−0.534407	−	0.845227i	$-0.679465\pi$
$241$	−16.5925	−1.06881	−0.534407	+	0.845227i	$0.679465\pi$
$242$	18.7491	1.20524
$243$	1.00000	0.0641500
$244$	2.47054	0.158160
$245$	0.691675	0.0441895
$246$	0	0
$247$	15.8328	1.00741
$248$	−11.5577	−0.733916
$249$	−7.68111	−0.486771
$250$	−17.5678	−1.11108
$251$	−20.1361	−1.27098	−0.635489	−	0.772110i	$-0.719201\pi$
$251$	−20.1361	−1.27098	−0.635489	+	0.772110i	$0.719201\pi$
$252$	−3.25443	−0.205010
$253$	0.729988	0.0458940
$254$	−23.3622	−1.46588
$255$	3.74055	0.234242
$256$	20.8469	1.30293
$257$	−25.9008	−1.61565	−0.807824	−	0.589424i	$-0.799355\pi$
$257$	−25.9008	−1.61565	−0.807824	+	0.589424i	$0.799355\pi$
$258$	−16.4550	−1.02444
$259$	−5.25997	−0.326838
$260$	7.25443	0.449900
$261$	−4.44082	−0.274880
$262$	11.5295	0.712292
$263$	22.4408	1.38376	0.691880	−	0.722012i	$-0.256783\pi$
$263$	22.4408	1.38376	0.691880	+	0.722012i	$0.256783\pi$
$264$	−1.04888	−0.0645538
$265$	15.2544	0.937072
$266$	−14.2056	−0.870998
$267$	−13.2544	−0.811158
$268$	12.9411	0.790502
$269$	7.62721	0.465039	0.232520	−	0.972592i	$-0.425303\pi$
$269$	7.62721	0.465039	0.232520	+	0.972592i	$0.425303\pi$
$270$	2.00000	0.121716
$271$	19.9164	1.20983	0.604917	−	0.796289i	$-0.293206\pi$
$271$	19.9164	1.20983	0.604917	+	0.796289i	$0.293206\pi$
$272$	16.6761	1.01114
$273$	12.8816	0.779632
$274$	−31.7194	−1.91624
$275$	3.07860	0.185646
$276$	−1.15667	−0.0696236
$277$	−17.6413	−1.05997	−0.529983	−	0.848008i	$-0.677802\pi$
$277$	−17.6413	−1.05997	−0.529983	+	0.848008i	$0.677802\pi$
$278$	−28.5189	−1.71045
$279$	−8.96526	−0.536736
$280$	3.58890	0.214478
$281$	0.0297193	0.00177291	0.000886453	−	1.00000i	$-0.499718\pi$
$281$	0.0297193	0.00177291	0.000886453		1.00000i	$0.499718\pi$
$282$	−0.426686	−0.0254088
$283$	−10.1814	−0.605220	−0.302610	−	0.953115i	$-0.597858\pi$
$283$	−10.1814	−0.605220	−0.302610	+	0.953115i	$0.597858\pi$
$284$	16.5189	0.980216
$285$	3.42166	0.202682
$286$	−7.52946	−0.445226
$287$	0	0
$288$	6.33804	0.373473
$289$	−5.49472	−0.323219
$290$	−8.88164	−0.521548
$291$	−2.72999	−0.160035
$292$	6.13607	0.359086
$293$	−3.14808	−0.183913	−0.0919564	−	0.995763i	$-0.529312\pi$
$293$	−3.14808	−0.183913	−0.0919564	+	0.995763i	$0.529312\pi$
$294$	1.13752	0.0663414
$295$	−1.15667	−0.0673442
$296$	2.68614	0.156128
$297$	−0.813607	−0.0472102
$298$	20.9794	1.21530
$299$	4.57834	0.264772
$300$	−4.87807	−0.281635
$301$	−22.9044	−1.32019
$302$	34.9200	2.00942
$303$	11.8625	0.681482
$304$	15.2544	0.874901
$305$	−2.11334	−0.121009
$306$	6.15165	0.351666
$307$	−12.7980	−0.730422	−0.365211	−	0.930925i	$-0.619003\pi$
$307$	−12.7980	−0.730422	−0.365211	+	0.930925i	$0.619003\pi$
$308$	2.64782	0.150874
$309$	−0.494719	−0.0281436
$310$	−17.9305	−1.01838
$311$	−26.6167	−1.50929	−0.754646	−	0.656132i	$-0.772191\pi$
$311$	−26.6167	−1.50929	−0.754646	+	0.656132i	$0.772191\pi$
$312$	−6.57834	−0.372425
$313$	3.00502	0.169854	0.0849270	−	0.996387i	$-0.472934\pi$
$313$	3.00502	0.169854	0.0849270	+	0.996387i	$0.472934\pi$
$314$	−37.9406	−2.14111
$315$	2.78389	0.156854
$316$	20.4111	1.14821
$317$	4.33302	0.243367	0.121683	−	0.992569i	$-0.461171\pi$
$317$	4.33302	0.243367	0.121683	+	0.992569i	$0.461171\pi$
$318$	25.0872	1.40682
$319$	3.61308	0.202294
$320$	1.83276	0.102455
$321$	−15.0872	−0.842085
$322$	−4.10780	−0.228919
$323$	10.5244	0.585595
$324$	1.28917	0.0716205
$325$	19.3083	1.07103
$326$	23.2106	1.28551
$327$	−5.10278	−0.282184
$328$	0	0
$329$	−0.593923	−0.0327440
$330$	−1.62721	−0.0895751
$331$	−5.53500	−0.304231	−0.152116	−	0.988363i	$-0.548609\pi$
$331$	−5.53500	−0.304231	−0.152116	+	0.988363i	$0.548609\pi$
$332$	−9.90225	−0.543456
$333$	2.08362	0.114182
$334$	17.4600	0.955367
$335$	−11.0700	−0.604819
$336$	12.4111	0.677081
$337$	−3.71083	−0.202142	−0.101071	−	0.994879i	$-0.532227\pi$
$337$	−3.71083	−0.202142	−0.101071	+	0.994879i	$0.532227\pi$
$338$	−23.6464	−1.28619
$339$	−17.5139	−0.951223
$340$	4.82220	0.261521
$341$	7.29419	0.395003
$342$	5.62721	0.304285
$343$	19.2544	1.03964
$344$	11.6967	0.630644
$345$	0.989437	0.0532695
$346$	−21.6655	−1.16475
$347$	−3.07860	−0.165268	−0.0826338	−	0.996580i	$-0.526333\pi$
$347$	−3.07860	−0.165268	−0.0826338	+	0.996580i	$0.526333\pi$
$348$	−5.72496	−0.306890
$349$	14.7980	0.792120	0.396060	−	0.918225i	$-0.370377\pi$
$349$	14.7980	0.792120	0.396060	+	0.918225i	$0.370377\pi$
$350$	−17.3239	−0.926002
$351$	−5.10278	−0.272366
$352$	−5.15667	−0.274852
$353$	26.8222	1.42760	0.713801	−	0.700349i	$-0.246972\pi$
$353$	26.8222	1.42760	0.713801	+	0.700349i	$0.246972\pi$
$354$	−1.90225	−0.101103
$355$	−14.1305	−0.749970
$356$	−17.0872	−0.905619
$357$	8.56275	0.453189
$358$	−3.87662	−0.204886
$359$	2.35720	0.124408	0.0622042	−	0.998063i	$-0.480187\pi$
$359$	2.35720	0.124408	0.0622042	+	0.998063i	$0.480187\pi$
$360$	−1.42166	−0.0749282
$361$	−9.37279	−0.493305
$362$	−3.32391	−0.174701
$363$	−10.3380	−0.542607
$364$	16.6066	0.870423
$365$	−5.24889	−0.274739
$366$	−3.47556	−0.181671
$367$	23.1708	1.20951	0.604753	−	0.796413i	$-0.293272\pi$
$367$	23.1708	1.20951	0.604753	+	0.796413i	$0.293272\pi$
$368$	4.41110	0.229944
$369$	0	0
$370$	4.16724	0.216644
$371$	34.9200	1.81295
$372$	−11.5577	−0.599240
$373$	35.2091	1.82306	0.911530	−	0.411235i	$-0.134902\pi$
$373$	35.2091	1.82306	0.911530	+	0.411235i	$0.134902\pi$
$374$	−5.00502	−0.258804
$375$	9.68665	0.500217
$376$	0.303302	0.0156416
$377$	22.6605	1.16708
$378$	4.57834	0.235484
$379$	−26.0383	−1.33750	−0.668749	−	0.743488i	$-0.733170\pi$
$379$	−26.0383	−1.33750	−0.668749	+	0.743488i	$0.733170\pi$
$380$	4.41110	0.226285
$381$	12.8816	0.659946
$382$	−33.7633	−1.72748
$383$	−15.3819	−0.785978	−0.392989	−	0.919543i	$-0.628559\pi$
$383$	−15.3819	−0.785978	−0.392989	+	0.919543i	$0.628559\pi$
$384$	−9.66196	−0.493060
$385$	−2.26499	−0.115435
$386$	28.3133	1.44111
$387$	9.07306	0.461209
$388$	−3.51941	−0.178671
$389$	4.46500	0.226384	0.113192	−	0.993573i	$-0.463892\pi$
$389$	4.46500	0.226384	0.113192	+	0.993573i	$0.463892\pi$
$390$	−10.2056	−0.516778
$391$	3.04334	0.153908
$392$	−0.808583	−0.0408396
$393$	−6.35720	−0.320678
$394$	9.44993	0.476081
$395$	−17.4600	−0.878507
$396$	−1.04888	−0.0527080
$397$	10.5628	0.530129	0.265065	−	0.964231i	$-0.414607\pi$
$397$	10.5628	0.530129	0.265065	+	0.964231i	$0.414607\pi$
$398$	3.72496	0.186716
$399$	7.83276	0.392129
$400$	18.6030	0.930152
$401$	13.0872	0.653543	0.326772	−	0.945103i	$-0.394039\pi$
$401$	13.0872	0.653543	0.326772	+	0.945103i	$0.394039\pi$
$402$	−18.2056	−0.908010
$403$	45.7477	2.27885
$404$	15.2927	0.760842
$405$	−1.10278	−0.0547973
$406$	−20.3316	−1.00904
$407$	−1.69525	−0.0840302
$408$	−4.37279	−0.216485
$409$	−18.5542	−0.917444	−0.458722	−	0.888580i	$-0.651693\pi$
$409$	−18.5542	−0.917444	−0.458722	+	0.888580i	$0.651693\pi$
$410$	0	0
$411$	17.4897	0.862703
$412$	−0.637776	−0.0314210
$413$	−2.64782	−0.130291
$414$	1.62721	0.0799732
$415$	8.47054	0.415802
$416$	−32.3416	−1.58568
$417$	15.7250	0.770055
$418$	−4.57834	−0.223934
$419$	−25.6116	−1.25121	−0.625605	−	0.780140i	$-0.715148\pi$
$419$	−25.6116	−1.25121	−0.625605	+	0.780140i	$0.715148\pi$
$420$	3.58890	0.175120
$421$	8.67609	0.422847	0.211423	−	0.977395i	$-0.432190\pi$
$421$	8.67609	0.422847	0.211423	+	0.977395i	$0.432190\pi$
$422$	−16.4111	−0.798880
$423$	0.235269	0.0114392
$424$	−17.8328	−0.866036
$425$	12.8347	0.622576
$426$	−23.2388	−1.12593
$427$	−4.83779	−0.234117
$428$	−19.4499	−0.940148
$429$	4.15165	0.200444
$430$	18.1461	0.875083
$431$	7.10278	0.342129	0.171064	−	0.985260i	$-0.445279\pi$
$431$	7.10278	0.342129	0.171064	+	0.985260i	$0.445279\pi$
$432$	−4.91638	−0.236540
$433$	−11.0247	−0.529813	−0.264907	−	0.964274i	$-0.585341\pi$
$433$	−11.0247	−0.529813	−0.264907	+	0.964274i	$0.585341\pi$
$434$	−41.0460	−1.97027
$435$	4.89722	0.234804
$436$	−6.57834	−0.315045
$437$	2.78389	0.133171
$438$	−8.63224	−0.412464
$439$	1.32391	0.0631868	0.0315934	−	0.999501i	$-0.489942\pi$
$439$	1.32391	0.0631868	0.0315934	+	0.999501i	$0.489942\pi$
$440$	1.15667	0.0551423
$441$	−0.627213	−0.0298673
$442$	−31.3905	−1.49309
$443$	15.5889	0.740651	0.370325	−	0.928902i	$-0.379246\pi$
$443$	15.5889	0.740651	0.370325	+	0.928902i	$0.379246\pi$
$444$	2.68614	0.127478
$445$	14.6167	0.692896
$446$	−45.0177	−2.13165
$447$	−11.5678	−0.547137
$448$	4.19550	0.198219
$449$	−32.7839	−1.54717	−0.773584	−	0.633694i	$-0.781538\pi$
$449$	−32.7839	−1.54717	−0.773584	+	0.633694i	$0.781538\pi$
$450$	6.86248	0.323501
$451$	0	0
$452$	−22.5783	−1.06200
$453$	−19.2544	−0.904652
$454$	30.1900	1.41689
$455$	−14.2056	−0.665966
$456$	−4.00000	−0.187317
$457$	14.1672	0.662715	0.331358	−	0.943505i	$-0.392493\pi$
$457$	14.1672	0.662715	0.331358	+	0.943505i	$0.392493\pi$
$458$	−28.6167	−1.33717
$459$	−3.39194	−0.158322
$460$	1.27555	0.0594729
$461$	−30.0766	−1.40081	−0.700404	−	0.713747i	$-0.746997\pi$
$461$	−30.0766	−1.40081	−0.700404	+	0.713747i	$0.746997\pi$
$462$	−3.72496	−0.173301
$463$	23.8766	1.10964	0.554820	−	0.831970i	$-0.312787\pi$
$463$	23.8766	1.10964	0.554820	+	0.831970i	$0.312787\pi$
$464$	21.8328	1.01356
$465$	9.88666	0.458483
$466$	−45.1950	−2.09362
$467$	−9.73501	−0.450483	−0.225241	−	0.974303i	$-0.572317\pi$
$467$	−9.73501	−0.450483	−0.225241	+	0.974303i	$0.572317\pi$
$468$	−6.57834	−0.304084
$469$	−25.3411	−1.17014
$470$	0.470539	0.0217043
$471$	20.9200	0.963941
$472$	1.35218	0.0622390
$473$	−7.38190	−0.339420
$474$	−28.7144	−1.31890
$475$	11.7406	0.538693
$476$	11.0388	0.505964
$477$	−13.8328	−0.633359
$478$	−5.35218	−0.244803
$479$	1.17635	0.0537487	0.0268743	−	0.999639i	$-0.491445\pi$
$479$	1.17635	0.0537487	0.0268743	+	0.999639i	$0.491445\pi$
$480$	−6.98944	−0.319023
$481$	−10.6322	−0.484788
$482$	30.0922	1.37066
$483$	2.26499	0.103061
$484$	−13.3275	−0.605795
$485$	3.01056	0.136703
$486$	−1.81361	−0.0822669
$487$	20.6025	0.933589	0.466795	−	0.884366i	$-0.345409\pi$
$487$	20.6025	0.933589	0.466795	+	0.884366i	$0.345409\pi$
$488$	2.47054	0.111836
$489$	−12.7980	−0.578746
$490$	−1.25443	−0.0566692
$491$	14.1900	0.640384	0.320192	−	0.947353i	$-0.396253\pi$
$491$	14.1900	0.640384	0.320192	+	0.947353i	$0.396253\pi$
$492$	0	0
$493$	15.0630	0.678404
$494$	−28.7144	−1.29192
$495$	0.897225	0.0403273
$496$	44.0766	1.97910
$497$	−32.3472	−1.45097
$498$	13.9305	0.624241
$499$	21.4600	0.960680	0.480340	−	0.877082i	$-0.340513\pi$
$499$	21.4600	0.960680	0.480340	+	0.877082i	$0.340513\pi$
$500$	12.4877	0.558468
$501$	−9.62721	−0.430112
$502$	36.5189	1.62992
$503$	15.5491	0.693302	0.346651	−	0.937994i	$-0.387319\pi$
$503$	15.5491	0.693302	0.346651	+	0.937994i	$0.387319\pi$
$504$	−3.25443	−0.144964
$505$	−13.0816	−0.582126
$506$	−1.32391	−0.0588550
$507$	13.0383	0.579052
$508$	16.6066	0.736799
$509$	−22.7542	−1.00856	−0.504280	−	0.863540i	$-0.668242\pi$
$509$	−22.7542	−1.00856	−0.504280	+	0.863540i	$0.668242\pi$
$510$	−6.78389	−0.300396
$511$	−12.0156	−0.531538
$512$	−18.4842	−0.816892
$513$	−3.10278	−0.136991
$514$	46.9739	2.07193
$515$	0.545563	0.0240404
$516$	11.6967	0.514918
$517$	−0.191417	−0.00841850
$518$	9.53951	0.419142
$519$	11.9461	0.524376
$520$	7.25443	0.318128
$521$	38.7230	1.69649	0.848243	−	0.529608i	$-0.177661\pi$
$521$	38.7230	1.69649	0.848243	+	0.529608i	$0.177661\pi$
$522$	8.05390	0.352510
$523$	6.56829	0.287211	0.143606	−	0.989635i	$-0.454130\pi$
$523$	6.56829	0.287211	0.143606	+	0.989635i	$0.454130\pi$
$524$	−8.19550	−0.358022
$525$	9.55219	0.416892
$526$	−40.6988	−1.77455
$527$	30.4096	1.32467
$528$	4.00000	0.174078
$529$	−22.1950	−0.964999
$530$	−27.6655	−1.20171
$531$	1.04888	0.0455173
$532$	10.0978	0.437793
$533$	0	0
$534$	24.0383	1.04024
$535$	16.6378	0.719314
$536$	12.9411	0.558969
$537$	2.13752	0.0922407
$538$	−13.8328	−0.596373
$539$	0.510305	0.0219804
$540$	−1.42166	−0.0611786
$541$	42.0766	1.80902	0.904508	−	0.426457i	$-0.140239\pi$
$541$	42.0766	1.80902	0.904508	+	0.426457i	$0.140239\pi$
$542$	−36.1205	−1.55151
$543$	1.83276	0.0786514
$544$	−21.4983	−0.921732
$545$	5.62721	0.241043
$546$	−23.3622	−0.999811
$547$	−19.9688	−0.853805	−0.426903	−	0.904298i	$-0.640395\pi$
$547$	−19.9688	−0.853805	−0.426903	+	0.904298i	$0.640395\pi$
$548$	22.5472	0.963167
$549$	1.91638	0.0817892
$550$	−5.58336	−0.238075
$551$	13.7789	0.586999
$552$	−1.15667	−0.0492313
$553$	−39.9688	−1.69965
$554$	31.9945	1.35931
$555$	−2.29776	−0.0975346
$556$	20.2721	0.859730
$557$	−13.5491	−0.574095	−0.287048	−	0.957916i	$-0.592674\pi$
$557$	−13.5491	−0.574095	−0.287048	+	0.957916i	$0.592674\pi$
$558$	16.2594	0.688317
$559$	−46.2978	−1.95819
$560$	−13.6867	−0.578367
$561$	2.75971	0.116515
$562$	−0.0538991	−0.00227360
$563$	−9.75468	−0.411111	−0.205555	−	0.978645i	$-0.565900\pi$
$563$	−9.75468	−0.411111	−0.205555	+	0.978645i	$0.565900\pi$
$564$	0.303302	0.0127713
$565$	19.3139	0.812540
$566$	18.4650	0.776142
$567$	−2.52444	−0.106016
$568$	16.5189	0.693118
$569$	−21.4544	−0.899417	−0.449708	−	0.893175i	$-0.648472\pi$
$569$	−21.4544	−0.899417	−0.449708	+	0.893175i	$0.648472\pi$
$570$	−6.20555	−0.259922
$571$	−20.9411	−0.876357	−0.438178	−	0.898888i	$-0.644376\pi$
$571$	−20.9411	−0.876357	−0.438178	+	0.898888i	$0.644376\pi$
$572$	5.35218	0.223786
$573$	18.6167	0.777722
$574$	0	0
$575$	3.39500	0.141581
$576$	−1.66196	−0.0692481
$577$	−18.4705	−0.768939	−0.384469	−	0.923138i	$-0.625616\pi$
$577$	−18.4705	−0.768939	−0.384469	+	0.923138i	$0.625616\pi$
$578$	9.96526	0.414500
$579$	−15.6116	−0.648797
$580$	6.31335	0.262148
$581$	19.3905	0.804453
$582$	4.95112	0.205231
$583$	11.2544	0.466111
$584$	6.13607	0.253912
$585$	5.62721	0.232657
$586$	5.70938	0.235852
$587$	0.127471	0.00526130	0.00263065	−	0.999997i	$-0.499163\pi$
$587$	0.127471	0.00526130	0.00263065	+	0.999997i	$0.499163\pi$
$588$	−0.808583	−0.0333454
$589$	27.8172	1.14619
$590$	2.09775	0.0863631
$591$	−5.21057	−0.214334
$592$	−10.2439	−0.421020
$593$	27.2841	1.12043	0.560213	−	0.828349i	$-0.310719\pi$
$593$	27.2841	1.12043	0.560213	+	0.828349i	$0.310719\pi$
$594$	1.47556	0.0605430
$595$	−9.44279	−0.387117
$596$	−14.9128	−0.610853
$597$	−2.05390	−0.0840605
$598$	−8.30330	−0.339547
$599$	−42.3260	−1.72939	−0.864697	−	0.502293i	$-0.832490\pi$
$599$	−42.3260	−1.72939	−0.864697	+	0.502293i	$0.832490\pi$
$600$	−4.87807	−0.199146
$601$	15.6756	0.639420	0.319710	−	0.947515i	$-0.396415\pi$
$601$	15.6756	0.639420	0.319710	+	0.947515i	$0.396415\pi$
$602$	41.5395	1.69302
$603$	10.0383	0.408792
$604$	−24.8222	−1.01000
$605$	11.4005	0.463498
$606$	−21.5139	−0.873941
$607$	−1.93051	−0.0783572	−0.0391786	−	0.999232i	$-0.512474\pi$
$607$	−1.93051	−0.0783572	−0.0391786	+	0.999232i	$0.512474\pi$
$608$	−19.6655	−0.797542
$609$	11.2106	0.454275
$610$	3.83276	0.155184
$611$	−1.20053	−0.0485681
$612$	−4.37279	−0.176759
$613$	−0.372787	−0.0150567	−0.00752836	−	0.999972i	$-0.502396\pi$
$613$	−0.372787	−0.0150567	−0.00752836	+	0.999972i	$0.502396\pi$
$614$	23.2106	0.936703
$615$	0	0
$616$	2.64782	0.106684
$617$	31.3083	1.26043	0.630213	−	0.776422i	$-0.282968\pi$
$617$	31.3083	1.26043	0.630213	+	0.776422i	$0.282968\pi$
$618$	0.897225	0.0360917
$619$	34.3658	1.38128	0.690639	−	0.723200i	$-0.257329\pi$
$619$	34.3658	1.38128	0.690639	+	0.723200i	$0.257329\pi$
$620$	12.7456	0.511875
$621$	−0.897225	−0.0360044
$622$	48.2721	1.93554
$623$	33.4600	1.34055
$624$	25.0872	1.00429
$625$	8.23724	0.329490
$626$	−5.44993	−0.217823
$627$	2.52444	0.100816
$628$	26.9693	1.07619
$629$	−7.06752	−0.281800
$630$	−5.04888	−0.201152
$631$	7.33804	0.292123	0.146061	−	0.989276i	$-0.453340\pi$
$631$	7.33804	0.292123	0.146061	+	0.989276i	$0.453340\pi$
$632$	20.4111	0.811910
$633$	9.04888	0.359661
$634$	−7.85840	−0.312097
$635$	−14.2056	−0.563730
$636$	−17.8328	−0.707115
$637$	3.20053	0.126809
$638$	−6.55270	−0.259424
$639$	12.8136	0.506898
$640$	10.6550	0.421174
$641$	31.5764	1.24719	0.623596	−	0.781747i	$-0.285671\pi$
$641$	31.5764	1.24719	0.623596	+	0.781747i	$0.285671\pi$
$642$	27.3622	1.07990
$643$	4.51890	0.178208	0.0891040	−	0.996022i	$-0.471600\pi$
$643$	4.51890	0.178208	0.0891040	+	0.996022i	$0.471600\pi$
$644$	2.91995	0.115062
$645$	−10.0055	−0.393968
$646$	−19.0872	−0.750975
$647$	−20.6705	−0.812643	−0.406322	−	0.913730i	$-0.633189\pi$
$647$	−20.6705	−0.812643	−0.406322	+	0.913730i	$0.633189\pi$
$648$	1.28917	0.0506433
$649$	−0.853372	−0.0334978
$650$	−35.0177	−1.37351
$651$	22.6322	0.887027
$652$	−16.4988	−0.646143
$653$	−0.381381	−0.0149246	−0.00746229	−	0.999972i	$-0.502375\pi$
$653$	−0.381381	−0.0149246	−0.00746229	+	0.999972i	$0.502375\pi$
$654$	9.25443	0.361877
$655$	7.01056	0.273925
$656$	0	0
$657$	4.75971	0.185694
$658$	1.07714	0.0419914
$659$	−13.4600	−0.524326	−0.262163	−	0.965024i	$-0.584436\pi$
$659$	−13.4600	−0.524326	−0.262163	+	0.965024i	$0.584436\pi$
$660$	1.15667	0.0450235
$661$	30.7738	1.19696	0.598482	−	0.801136i	$-0.295771\pi$
$661$	30.7738	1.19696	0.598482	+	0.801136i	$0.295771\pi$
$662$	10.0383	0.390150
$663$	17.3083	0.672200
$664$	−9.90225	−0.384282
$665$	−8.63778	−0.334959
$666$	−3.77886	−0.146428
$667$	3.98441	0.154277
$668$	−12.4111	−0.480200
$669$	24.8222	0.959682
$670$	20.0766	0.775628
$671$	−1.55918	−0.0601915
$672$	−16.0000	−0.617213
$673$	−1.48110	−0.0570923	−0.0285461	−	0.999592i	$-0.509088\pi$
$673$	−1.48110	−0.0570923	−0.0285461	+	0.999592i	$0.509088\pi$
$674$	6.72999	0.259229
$675$	−3.78389	−0.145642
$676$	16.8086	0.646484
$677$	45.3749	1.74390	0.871950	−	0.489596i	$-0.162856\pi$
$677$	45.3749	1.74390	0.871950	+	0.489596i	$0.162856\pi$
$678$	31.7633	1.21986
$679$	6.89169	0.264479
$680$	4.82220	0.184923
$681$	−16.6464	−0.637890
$682$	−13.2288	−0.506557
$683$	0.0594386	0.00227436	0.00113718	−	0.999999i	$-0.499638\pi$
$683$	0.0594386	0.00227436	0.00113718	+	0.999999i	$0.499638\pi$
$684$	−4.00000	−0.152944
$685$	−19.2872	−0.736926
$686$	−34.9200	−1.33325
$687$	15.7789	0.602001
$688$	−44.6066	−1.70061
$689$	70.5855	2.68909
$690$	−1.79445	−0.0683135
$691$	18.9355	0.720342	0.360171	−	0.932886i	$-0.382718\pi$
$691$	18.9355	0.720342	0.360171	+	0.932886i	$0.382718\pi$
$692$	15.4005	0.585441
$693$	2.05390	0.0780212
$694$	5.58336	0.211941
$695$	−17.3411	−0.657785
$696$	−5.72496	−0.217004
$697$	0	0
$698$	−26.8378	−1.01583
$699$	24.9200	0.942559
$700$	12.3144	0.465440
$701$	−0.540024	−0.0203964	−0.0101982	−	0.999948i	$-0.503246\pi$
$701$	−0.540024	−0.0203964	−0.0101982	+	0.999948i	$0.503246\pi$
$702$	9.25443	0.349286
$703$	−6.46500	−0.243832
$704$	1.35218	0.0509621
$705$	−0.259449	−0.00977142
$706$	−48.6449	−1.83078
$707$	−29.9461	−1.12624
$708$	1.35218	0.0508180
$709$	−28.0867	−1.05482	−0.527409	−	0.849612i	$-0.676836\pi$
$709$	−28.0867	−1.05482	−0.527409	+	0.849612i	$0.676836\pi$
$710$	25.6272	0.961772
$711$	15.8328	0.593775
$712$	−17.0872	−0.640369
$713$	8.04385	0.301245
$714$	−15.5295	−0.581175
$715$	−4.57834	−0.171220
$716$	2.75562	0.102982
$717$	2.95112	0.110212
$718$	−4.27504	−0.159543
$719$	−9.86248	−0.367809	−0.183904	−	0.982944i	$-0.558874\pi$
$719$	−9.86248	−0.367809	−0.183904	+	0.982944i	$0.558874\pi$
$720$	5.42166	0.202053
$721$	1.24889	0.0465110
$722$	16.9985	0.632620
$723$	−16.5925	−0.617081
$724$	2.36274	0.0878106
$725$	16.8036	0.624069
$726$	18.7491	0.695846
$727$	30.4650	1.12988	0.564942	−	0.825131i	$-0.308898\pi$
$727$	30.4650	1.12988	0.564942	+	0.825131i	$0.308898\pi$
$728$	16.6066	0.615482
$729$	1.00000	0.0370370
$730$	9.51941	0.352329
$731$	−30.7753	−1.13827
$732$	2.47054	0.0913137
$733$	27.5436	1.01735	0.508673	−	0.860960i	$-0.330136\pi$
$733$	27.5436	1.01735	0.508673	+	0.860960i	$0.330136\pi$
$734$	−42.0227	−1.55109
$735$	0.691675	0.0255128
$736$	−5.68665	−0.209613
$737$	−8.16724	−0.300844
$738$	0	0
$739$	13.1013	0.481940	0.240970	−	0.970533i	$-0.422534\pi$
$739$	13.1013	0.481940	0.240970	+	0.970533i	$0.422534\pi$
$740$	−2.96220	−0.108893
$741$	15.8328	0.581631
$742$	−63.3311	−2.32496
$743$	34.7527	1.27495	0.637477	−	0.770470i	$-0.279978\pi$
$743$	34.7527	1.27495	0.637477	+	0.770470i	$0.279978\pi$
$744$	−11.5577	−0.423727
$745$	12.7567	0.467368
$746$	−63.8555	−2.33792
$747$	−7.68111	−0.281037
$748$	3.55773	0.130083
$749$	38.0867	1.39166
$750$	−17.5678	−0.641484
$751$	−32.7738	−1.19593	−0.597967	−	0.801521i	$-0.704025\pi$
$751$	−32.7738	−1.19593	−0.597967	+	0.801521i	$0.704025\pi$
$752$	−1.15667	−0.0421796
$753$	−20.1361	−0.733799
$754$	−41.0972	−1.49667
$755$	21.2333	0.772759
$756$	−3.25443	−0.118362
$757$	32.2978	1.17388	0.586941	−	0.809630i	$-0.300332\pi$
$757$	32.2978	1.17388	0.586941	+	0.809630i	$0.300332\pi$
$758$	47.2233	1.71523
$759$	0.729988	0.0264969
$760$	4.41110	0.160007
$761$	44.4494	1.61129	0.805645	−	0.592399i	$-0.201819\pi$
$761$	44.4494	1.61129	0.805645	+	0.592399i	$0.201819\pi$
$762$	−23.3622	−0.846324
$763$	12.8816	0.466347
$764$	24.0000	0.868290
$765$	3.74055	0.135240
$766$	27.8967	1.00795
$767$	−5.35218	−0.193256
$768$	20.8469	0.752248
$769$	−19.7108	−0.710791	−0.355395	−	0.934716i	$-0.615654\pi$
$769$	−19.7108	−0.710791	−0.355395	+	0.934716i	$0.615654\pi$
$770$	4.10780	0.148035
$771$	−25.9008	−0.932794
$772$	−20.1260	−0.724351
$773$	−43.2530	−1.55570	−0.777851	−	0.628449i	$-0.783690\pi$
$773$	−43.2530	−1.55570	−0.777851	+	0.628449i	$0.783690\pi$
$774$	−16.4550	−0.591461
$775$	33.9235	1.21857
$776$	−3.51941	−0.126340
$777$	−5.25997	−0.188700
$778$	−8.09775	−0.290318
$779$	0	0
$780$	7.25443	0.259750
$781$	−10.4252	−0.373044
$782$	−5.51941	−0.197374
$783$	−4.44082	−0.158702
$784$	3.08362	0.110129
$785$	−23.0700	−0.823404
$786$	11.5295	0.411242
$787$	−21.4358	−0.764104	−0.382052	−	0.924141i	$-0.624782\pi$
$787$	−21.4358	−0.764104	−0.382052	+	0.924141i	$0.624782\pi$
$788$	−6.71731	−0.239294
$789$	22.4408	0.798914
$790$	31.6655	1.12661
$791$	44.2127	1.57202
$792$	−1.04888	−0.0372702
$793$	−9.77886	−0.347258
$794$	−19.1567	−0.679845
$795$	15.2544	0.541019
$796$	−2.64782	−0.0938496
$797$	−4.40105	−0.155893	−0.0779467	−	0.996958i	$-0.524836\pi$
$797$	−4.40105	−0.155893	−0.0779467	+	0.996958i	$0.524836\pi$
$798$	−14.2056	−0.502871
$799$	−0.798021	−0.0282319
$800$	−23.9824	−0.847907
$801$	−13.2544	−0.468322
$802$	−23.7350	−0.838112
$803$	−3.87253	−0.136659
$804$	12.9411	0.456397
$805$	−2.49777	−0.0880349
$806$	−82.9683	−2.92243
$807$	7.62721	0.268491
$808$	15.2927	0.537997
$809$	26.3799	0.927469	0.463734	−	0.885974i	$-0.346509\pi$
$809$	26.3799	0.927469	0.463734	+	0.885974i	$0.346509\pi$
$810$	2.00000	0.0702728
$811$	4.96526	0.174354	0.0871769	−	0.996193i	$-0.472215\pi$
$811$	4.96526	0.174354	0.0871769	+	0.996193i	$0.472215\pi$
$812$	14.4523	0.507177
$813$	19.9164	0.698498
$814$	3.07451	0.107761
$815$	14.1133	0.494369
$816$	16.6761	0.583780
$817$	−28.1517	−0.984902
$818$	33.6499	1.17654
$819$	12.8816	0.450121
$820$	0	0
$821$	−15.7789	−0.550686	−0.275343	−	0.961346i	$-0.588791\pi$
$821$	−15.7789	−0.550686	−0.275343	+	0.961346i	$0.588791\pi$
$822$	−31.7194	−1.10634
$823$	8.35166	0.291121	0.145560	−	0.989349i	$-0.453502\pi$
$823$	8.35166	0.291121	0.145560	+	0.989349i	$0.453502\pi$
$824$	−0.637776	−0.0222180
$825$	3.07860	0.107183
$826$	4.80211	0.167087
$827$	18.3925	0.639568	0.319784	−	0.947490i	$-0.396390\pi$
$827$	18.3925	0.639568	0.319784	+	0.947490i	$0.396390\pi$
$828$	−1.15667	−0.0401972
$829$	−29.4147	−1.02161	−0.510807	−	0.859695i	$-0.670653\pi$
$829$	−29.4147	−1.02161	−0.510807	+	0.859695i	$0.670653\pi$
$830$	−15.3622	−0.533231
$831$	−17.6413	−0.611972
$832$	8.48059	0.294011
$833$	2.12747	0.0737125
$834$	−28.5189	−0.987529
$835$	10.6167	0.367404
$836$	3.25443	0.112557
$837$	−8.96526	−0.309885
$838$	46.4494	1.60457
$839$	33.4600	1.15517	0.577583	−	0.816332i	$-0.303996\pi$
$839$	33.4600	1.15517	0.577583	+	0.816332i	$0.303996\pi$
$840$	3.58890	0.123829
$841$	−9.27912	−0.319970
$842$	−15.7350	−0.542264
$843$	0.0297193	0.00102359
$844$	11.6655	0.401544
$845$	−14.3783	−0.494629
$846$	−0.426686	−0.0146698
$847$	26.0978	0.896729
$848$	68.0071	2.33537
$849$	−10.1814	−0.349424
$850$	−23.2772	−0.798400
$851$	−1.86947	−0.0640848
$852$	16.5189	0.565928
$853$	40.4494	1.38496	0.692481	−	0.721436i	$-0.256518\pi$
$853$	40.4494	1.38496	0.692481	+	0.721436i	$0.256518\pi$
$854$	8.77384	0.300235
$855$	3.42166	0.117018
$856$	−19.4499	−0.664785
$857$	12.4494	0.425264	0.212632	−	0.977132i	$-0.431796\pi$
$857$	12.4494	0.425264	0.212632	+	0.977132i	$0.431796\pi$
$858$	−7.52946	−0.257052
$859$	−21.6514	−0.738736	−0.369368	−	0.929283i	$-0.620426\pi$
$859$	−21.6514	−0.738736	−0.369368	+	0.929283i	$0.620426\pi$
$860$	−12.8988	−0.439846
$861$	0	0
$862$	−12.8816	−0.438750
$863$	19.3778	0.659628	0.329814	−	0.944046i	$-0.393014\pi$
$863$	19.3778	0.659628	0.329814	+	0.944046i	$0.393014\pi$
$864$	6.33804	0.215625
$865$	−13.1739	−0.447925
$866$	19.9945	0.679439
$867$	−5.49472	−0.186610
$868$	29.1768	0.990324
$869$	−12.8816	−0.436980
$870$	−8.88164	−0.301116
$871$	−51.2233	−1.73563
$872$	−6.57834	−0.222771
$873$	−2.72999	−0.0923961
$874$	−5.04888	−0.170781
$875$	−24.4534	−0.826674
$876$	6.13607	0.207318
$877$	−3.08413	−0.104144	−0.0520719	−	0.998643i	$-0.516583\pi$
$877$	−3.08413	−0.104144	−0.0520719	+	0.998643i	$0.516583\pi$
$878$	−2.40105	−0.0810316
$879$	−3.14808	−0.106182
$880$	−4.41110	−0.148698
$881$	−34.5783	−1.16497	−0.582487	−	0.812840i	$-0.697920\pi$
$881$	−34.5783	−1.16497	−0.582487	+	0.812840i	$0.697920\pi$
$882$	1.13752	0.0383022
$883$	9.64280	0.324506	0.162253	−	0.986749i	$-0.448124\pi$
$883$	9.64280	0.324506	0.162253	+	0.986749i	$0.448124\pi$
$884$	22.3133	0.750479
$885$	−1.15667	−0.0388812
$886$	−28.2721	−0.949821
$887$	−32.2041	−1.08131	−0.540654	−	0.841245i	$-0.681823\pi$
$887$	−32.2041	−1.08131	−0.540654	+	0.841245i	$0.681823\pi$
$888$	2.68614	0.0901408
$889$	−32.5189	−1.09065
$890$	−26.5089	−0.888579
$891$	−0.813607	−0.0272568
$892$	32.0000	1.07144
$893$	−0.729988	−0.0244281
$894$	20.9794	0.701656
$895$	−2.35720	−0.0787925
$896$	24.3910	0.814846
$897$	4.57834	0.152866
$898$	59.4571	1.98411
$899$	39.8131	1.32784
$900$	−4.87807	−0.162602
$901$	46.9200	1.56313
$902$	0	0
$903$	−22.9044	−0.762210
$904$	−22.5783	−0.750944
$905$	−2.02113	−0.0671845
$906$	34.9200	1.16014
$907$	−17.8227	−0.591794	−0.295897	−	0.955220i	$-0.595618\pi$
$907$	−17.8227	−0.591794	−0.295897	+	0.955220i	$0.595618\pi$
$908$	−21.4600	−0.712174
$909$	11.8625	0.393454
$910$	25.7633	0.854044
$911$	−20.7894	−0.688784	−0.344392	−	0.938826i	$-0.611915\pi$
$911$	−20.7894	−0.688784	−0.344392	+	0.938826i	$0.611915\pi$
$912$	15.2544	0.505125
$913$	6.24940	0.206825
$914$	−25.6938	−0.849875
$915$	−2.11334	−0.0698648
$916$	20.3416	0.672106
$917$	16.0484	0.529964
$918$	6.15165	0.203035
$919$	−33.8555	−1.11679	−0.558395	−	0.829575i	$-0.688583\pi$
$919$	−33.8555	−1.11679	−0.558395	+	0.829575i	$0.688583\pi$
$920$	1.27555	0.0420537
$921$	−12.7980	−0.421709
$922$	54.5472	1.79642
$923$	−65.3850	−2.15217
$924$	2.64782	0.0871070
$925$	−7.88418	−0.259230
$926$	−43.3028	−1.42302
$927$	−0.494719	−0.0162487
$928$	−28.1461	−0.923941
$929$	4.10635	0.134725	0.0673624	−	0.997729i	$-0.478542\pi$
$929$	4.10635	0.134725	0.0673624	+	0.997729i	$0.478542\pi$
$930$	−17.9305	−0.587965
$931$	1.94610	0.0637809
$932$	32.1260	1.05232
$933$	−26.6167	−0.871390
$934$	17.6555	0.577705
$935$	−3.04334	−0.0995277
$936$	−6.57834	−0.215020
$937$	−13.3028	−0.434583	−0.217292	−	0.976107i	$-0.569722\pi$
$937$	−13.3028	−0.434583	−0.217292	+	0.976107i	$0.569722\pi$
$938$	45.9588	1.50061
$939$	3.00502	0.0980652
$940$	−0.334474	−0.0109093
$941$	−11.7633	−0.383472	−0.191736	−	0.981447i	$-0.561412\pi$
$941$	−11.7633	−0.383472	−0.191736	+	0.981447i	$0.561412\pi$
$942$	−37.9406	−1.23617
$943$	0	0
$944$	−5.15667	−0.167835
$945$	2.78389	0.0905599
$946$	13.3879	0.435277
$947$	1.40054	0.0455114	0.0227557	−	0.999741i	$-0.492756\pi$
$947$	1.40054	0.0455114	0.0227557	+	0.999741i	$0.492756\pi$
$948$	20.4111	0.662922
$949$	−24.2877	−0.788413
$950$	−21.2927	−0.690828
$951$	4.33302	0.140508
$952$	11.0388	0.357771
$953$	33.7577	1.09352	0.546760	−	0.837289i	$-0.315861\pi$
$953$	33.7577	1.09352	0.546760	+	0.837289i	$0.315861\pi$
$954$	25.0872	0.812228
$955$	−20.5300	−0.664334
$956$	3.80450	0.123046
$957$	3.61308	0.116794
$958$	−2.13343	−0.0689280
$959$	−44.1517	−1.42573
$960$	1.83276	0.0591522
$961$	49.3758	1.59277
$962$	19.2827	0.621699
$963$	−15.0872	−0.486178
$964$	−21.3905	−0.688941
$965$	17.2161	0.554206
$966$	−4.10780	−0.132166
$967$	10.4806	0.337033	0.168516	−	0.985699i	$-0.446102\pi$
$967$	10.4806	0.337033	0.168516	+	0.985699i	$0.446102\pi$
$968$	−13.3275	−0.428361
$969$	10.5244	0.338094
$970$	−5.45998	−0.175309
$971$	−57.6358	−1.84962	−0.924811	−	0.380428i	$-0.875777\pi$
$971$	−57.6358	−1.84962	−0.924811	+	0.380428i	$0.875777\pi$
$972$	1.28917	0.0413501
$973$	−39.6967	−1.27262
$974$	−37.3649	−1.19725
$975$	19.3083	0.618361
$976$	−9.42166	−0.301580
$977$	−41.9008	−1.34053	−0.670263	−	0.742124i	$-0.733819\pi$
$977$	−41.9008	−1.34053	−0.670263	+	0.742124i	$0.733819\pi$
$978$	23.2106	0.742192
$979$	10.7839	0.344655
$980$	0.891685	0.0284838
$981$	−5.10278	−0.162919
$982$	−25.7350	−0.821237
$983$	−18.4056	−0.587046	−0.293523	−	0.955952i	$-0.594828\pi$
$983$	−18.4056	−0.587046	−0.293523	+	0.955952i	$0.594828\pi$
$984$	0	0
$985$	5.74609	0.183086
$986$	−27.3184	−0.869994
$987$	−0.593923	−0.0189048
$988$	20.4111	0.649364
$989$	−8.14057	−0.258855
$990$	−1.62721	−0.0517162
$991$	−26.0666	−0.828032	−0.414016	−	0.910270i	$-0.635874\pi$
$991$	−26.0666	−0.828032	−0.414016	+	0.910270i	$0.635874\pi$
$992$	−56.8222	−1.80411
$993$	−5.53500	−0.175648
$994$	58.6650	1.86074
$995$	2.26499	0.0718050
$996$	−9.90225	−0.313765
$997$	29.8483	0.945307	0.472653	−	0.881248i	$-0.343296\pi$
$997$	29.8483	0.945307	0.472653	+	0.881248i	$0.343296\pi$
$998$	−38.9200	−1.23199
$999$	2.08362	0.0659228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5043.2.a.n.1.1		3
41.40	even	2		123.2.a.d.1.1	✓	3
123.122	odd	2		369.2.a.e.1.3		3
164.163	odd	2		1968.2.a.w.1.1		3
205.204	even	2		3075.2.a.t.1.3		3
287.286	odd	2		6027.2.a.s.1.1		3
328.163	odd	2		7872.2.a.bs.1.3		3
328.245	even	2		7872.2.a.bx.1.3		3
492.491	even	2		5904.2.a.bd.1.3		3
615.614	odd	2		9225.2.a.bx.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
123.2.a.d.1.1	✓	3	41.40	even	2
369.2.a.e.1.3		3	123.122	odd	2
1968.2.a.w.1.1		3	164.163	odd	2
3075.2.a.t.1.3		3	205.204	even	2
5043.2.a.n.1.1		3	1.1	even	1	trivial
5904.2.a.bd.1.3		3	492.491	even	2
6027.2.a.s.1.1		3	287.286	odd	2
7872.2.a.bs.1.3		3	328.163	odd	2
7872.2.a.bx.1.3		3	328.245	even	2
9225.2.a.bx.1.1		3	615.614	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5043 = 3 \cdot 41^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5043.a (trivial)

\(f(q)\)	\(=\)	\(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} -1.10278 q^{5} -1.81361 q^{6} -2.52444 q^{7} +1.28917 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} -1.10278 q^{5} -1.81361 q^{6} -2.52444 q^{7} +1.28917 q^{8} +1.00000 q^{9} +2.00000 q^{10} -0.813607 q^{11} +1.28917 q^{12} -5.10278 q^{13} +4.57834 q^{14} -1.10278 q^{15} -4.91638 q^{16} -3.39194 q^{17} -1.81361 q^{18} -3.10278 q^{19} -1.42166 q^{20} -2.52444 q^{21} +1.47556 q^{22} -0.897225 q^{23} +1.28917 q^{24} -3.78389 q^{25} +9.25443 q^{26} +1.00000 q^{27} -3.25443 q^{28} -4.44082 q^{29} +2.00000 q^{30} -8.96526 q^{31} +6.33804 q^{32} -0.813607 q^{33} +6.15165 q^{34} +2.78389 q^{35} +1.28917 q^{36} +2.08362 q^{37} +5.62721 q^{38} -5.10278 q^{39} -1.42166 q^{40} +4.57834 q^{42} +9.07306 q^{43} -1.04888 q^{44} -1.10278 q^{45} +1.62721 q^{46} +0.235269 q^{47} -4.91638 q^{48} -0.627213 q^{49} +6.86248 q^{50} -3.39194 q^{51} -6.57834 q^{52} -13.8328 q^{53} -1.81361 q^{54} +0.897225 q^{55} -3.25443 q^{56} -3.10278 q^{57} +8.05390 q^{58} +1.04888 q^{59} -1.42166 q^{60} +1.91638 q^{61} +16.2594 q^{62} -2.52444 q^{63} -1.66196 q^{64} +5.62721 q^{65} +1.47556 q^{66} +10.0383 q^{67} -4.37279 q^{68} -0.897225 q^{69} -5.04888 q^{70} +12.8136 q^{71} +1.28917 q^{72} +4.75971 q^{73} -3.77886 q^{74} -3.78389 q^{75} -4.00000 q^{76} +2.05390 q^{77} +9.25443 q^{78} +15.8328 q^{79} +5.42166 q^{80} +1.00000 q^{81} -7.68111 q^{83} -3.25443 q^{84} +3.74055 q^{85} -16.4550 q^{86} -4.44082 q^{87} -1.04888 q^{88} -13.2544 q^{89} +2.00000 q^{90} +12.8816 q^{91} -1.15667 q^{92} -8.96526 q^{93} -0.426686 q^{94} +3.42166 q^{95} +6.33804 q^{96} -2.72999 q^{97} +1.13752 q^{98} -0.813607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 + q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9} + 6 q^{10} + 4 q^{11} + 3 q^{12} - 8 q^{13} + 12 q^{14} + 4 q^{15} - q^{16} - 2 q^{17} + q^{18} - 2 q^{19} - 6 q^{20} - 2 q^{21} + 10 q^{22} - 10 q^{23} + 3 q^{24} + 5 q^{25} + 2 q^{26} + 3 q^{27} + 16 q^{28} + 6 q^{29} + 6 q^{30} - 2 q^{31} + 7 q^{32} + 4 q^{33} - 8 q^{35} + 3 q^{36} + 20 q^{37} + 4 q^{38} - 8 q^{39} - 6 q^{40} + 12 q^{42} + 10 q^{43} + 8 q^{44} + 4 q^{45} - 8 q^{46} - 4 q^{47} - q^{48} + 11 q^{49} + 3 q^{50} - 2 q^{51} - 18 q^{52} - 14 q^{53} + q^{54} + 10 q^{55} + 16 q^{56} - 2 q^{57} + 28 q^{58} - 8 q^{59} - 6 q^{60} - 8 q^{61} + 38 q^{62} - 2 q^{63} - 17 q^{64} + 4 q^{65} + 10 q^{66} - 12 q^{67} - 26 q^{68} - 10 q^{69} - 4 q^{70} + 32 q^{71} + 3 q^{72} + 4 q^{73} + 20 q^{74} + 5 q^{75} - 12 q^{76} + 10 q^{77} + 2 q^{78} + 20 q^{79} + 18 q^{80} + 3 q^{81} - 14 q^{83} + 16 q^{84} + 22 q^{85} + 6 q^{86} + 6 q^{87} + 8 q^{88} - 14 q^{89} + 6 q^{90} - 2 q^{93} - 18 q^{94} + 12 q^{95} + 7 q^{96} + 12 q^{97} + 21 q^{98} + 4 q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 + q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9 + 6 * q^10 + 4 * q^11 + 3 * q^12 - 8 * q^13 + 12 * q^14 + 4 * q^15 - q^16 - 2 * q^17 + q^18 - 2 * q^19 - 6 * q^20 - 2 * q^21 + 10 * q^22 - 10 * q^23 + 3 * q^24 + 5 * q^25 + 2 * q^26 + 3 * q^27 + 16 * q^28 + 6 * q^29 + 6 * q^30 - 2 * q^31 + 7 * q^32 + 4 * q^33 - 8 * q^35 + 3 * q^36 + 20 * q^37 + 4 * q^38 - 8 * q^39 - 6 * q^40 + 12 * q^42 + 10 * q^43 + 8 * q^44 + 4 * q^45 - 8 * q^46 - 4 * q^47 - q^48 + 11 * q^49 + 3 * q^50 - 2 * q^51 - 18 * q^52 - 14 * q^53 + q^54 + 10 * q^55 + 16 * q^56 - 2 * q^57 + 28 * q^58 - 8 * q^59 - 6 * q^60 - 8 * q^61 + 38 * q^62 - 2 * q^63 - 17 * q^64 + 4 * q^65 + 10 * q^66 - 12 * q^67 - 26 * q^68 - 10 * q^69 - 4 * q^70 + 32 * q^71 + 3 * q^72 + 4 * q^73 + 20 * q^74 + 5 * q^75 - 12 * q^76 + 10 * q^77 + 2 * q^78 + 20 * q^79 + 18 * q^80 + 3 * q^81 - 14 * q^83 + 16 * q^84 + 22 * q^85 + 6 * q^86 + 6 * q^87 + 8 * q^88 - 14 * q^89 + 6 * q^90 - 2 * q^93 - 18 * q^94 + 12 * q^95 + 7 * q^96 + 12 * q^97 + 21 * q^98 + 4 * q^99

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