LMFDB - Embedded newform 503.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$4.01647522167$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 $ x^10 - 2x^9 - 9x^8 + 14x^7 + 27x^6 - 27x^5 - 34x^4 + 14x^3 + 17x^2 + x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.78533$ of defining polynomial
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.03947 q^{2} +1.78533 q^{3} +2.15945 q^{4} -0.701114 q^{5} -3.64112 q^{6} -2.02991 q^{7} -0.325186 q^{8} +0.187388 q^{9} +O(q^{10})$	\(q-2.03947 q^{2} +1.78533 q^{3} +2.15945 q^{4} -0.701114 q^{5} -3.64112 q^{6} -2.02991 q^{7} -0.325186 q^{8} +0.187388 q^{9} +1.42990 q^{10} -0.626970 q^{11} +3.85531 q^{12} -2.93743 q^{13} +4.13995 q^{14} -1.25172 q^{15} -3.65568 q^{16} -2.71003 q^{17} -0.382172 q^{18} -1.11114 q^{19} -1.51402 q^{20} -3.62406 q^{21} +1.27869 q^{22} -0.412395 q^{23} -0.580563 q^{24} -4.50844 q^{25} +5.99081 q^{26} -5.02143 q^{27} -4.38349 q^{28} +6.46349 q^{29} +2.55284 q^{30} -4.14074 q^{31} +8.10604 q^{32} -1.11935 q^{33} +5.52704 q^{34} +1.42320 q^{35} +0.404653 q^{36} +2.98634 q^{37} +2.26613 q^{38} -5.24427 q^{39} +0.227992 q^{40} -0.135430 q^{41} +7.39116 q^{42} -0.861393 q^{43} -1.35391 q^{44} -0.131380 q^{45} +0.841067 q^{46} +1.67307 q^{47} -6.52659 q^{48} -2.87945 q^{49} +9.19483 q^{50} -4.83829 q^{51} -6.34323 q^{52} -8.51721 q^{53} +10.2411 q^{54} +0.439578 q^{55} +0.660099 q^{56} -1.98374 q^{57} -13.1821 q^{58} -0.406685 q^{59} -2.70302 q^{60} -8.53132 q^{61} +8.44492 q^{62} -0.380381 q^{63} -9.22067 q^{64} +2.05948 q^{65} +2.28288 q^{66} -13.0293 q^{67} -5.85217 q^{68} -0.736259 q^{69} -2.90258 q^{70} +2.78095 q^{71} -0.0609358 q^{72} -2.11734 q^{73} -6.09055 q^{74} -8.04903 q^{75} -2.39944 q^{76} +1.27270 q^{77} +10.6955 q^{78} -0.317368 q^{79} +2.56305 q^{80} -9.52705 q^{81} +0.276205 q^{82} -5.05120 q^{83} -7.82595 q^{84} +1.90004 q^{85} +1.75679 q^{86} +11.5394 q^{87} +0.203882 q^{88} +16.4699 q^{89} +0.267946 q^{90} +5.96273 q^{91} -0.890544 q^{92} -7.39256 q^{93} -3.41218 q^{94} +0.779033 q^{95} +14.4719 q^{96} +7.68873 q^{97} +5.87256 q^{98} -0.117486 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - 7 q^{12} - 18 q^{13} + q^{14} - 2 q^{15} - 4 q^{16} - 11 q^{17} - q^{18} - 3 q^{20} + q^{21} - 18 q^{22} - 2 q^{23} + 10 q^{24} - 27 q^{25} + 11 q^{26} - 2 q^{27} - 22 q^{28} - 9 q^{29} + 12 q^{30} - 22 q^{31} - 10 q^{32} - 10 q^{33} - 10 q^{34} - 6 q^{35} + 2 q^{36} - 35 q^{37} + 2 q^{38} + 8 q^{39} - 19 q^{40} - 4 q^{41} + 4 q^{42} - 20 q^{43} + 9 q^{44} + 2 q^{45} - q^{46} + 7 q^{47} - 27 q^{49} + 16 q^{50} + 9 q^{51} - 7 q^{52} - 24 q^{53} + 17 q^{54} - 11 q^{55} + 12 q^{56} - 23 q^{57} + 2 q^{58} + 17 q^{59} - 4 q^{61} + 8 q^{62} + 10 q^{63} + 3 q^{64} - 16 q^{65} + 46 q^{66} - 6 q^{67} + 28 q^{68} - 2 q^{69} + 26 q^{70} - q^{71} - q^{72} - 31 q^{73} + 11 q^{74} + 30 q^{75} + 20 q^{76} + 3 q^{77} + 11 q^{78} - 10 q^{79} + 24 q^{80} - 6 q^{81} - 9 q^{82} + 22 q^{83} + 22 q^{84} - 6 q^{85} + 38 q^{86} + 25 q^{87} - 3 q^{88} + q^{89} + 2 q^{90} + 10 q^{91} + 27 q^{92} - 6 q^{93} + 33 q^{94} + 39 q^{95} + 46 q^{96} - 57 q^{97} + 40 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9 - 4 * q^10 - 3 * q^11 - 7 * q^12 - 18 * q^13 + q^14 - 2 * q^15 - 4 * q^16 - 11 * q^17 - q^18 - 3 * q^20 + q^21 - 18 * q^22 - 2 * q^23 + 10 * q^24 - 27 * q^25 + 11 * q^26 - 2 * q^27 - 22 * q^28 - 9 * q^29 + 12 * q^30 - 22 * q^31 - 10 * q^32 - 10 * q^33 - 10 * q^34 - 6 * q^35 + 2 * q^36 - 35 * q^37 + 2 * q^38 + 8 * q^39 - 19 * q^40 - 4 * q^41 + 4 * q^42 - 20 * q^43 + 9 * q^44 + 2 * q^45 - q^46 + 7 * q^47 - 27 * q^49 + 16 * q^50 + 9 * q^51 - 7 * q^52 - 24 * q^53 + 17 * q^54 - 11 * q^55 + 12 * q^56 - 23 * q^57 + 2 * q^58 + 17 * q^59 - 4 * q^61 + 8 * q^62 + 10 * q^63 + 3 * q^64 - 16 * q^65 + 46 * q^66 - 6 * q^67 + 28 * q^68 - 2 * q^69 + 26 * q^70 - q^71 - q^72 - 31 * q^73 + 11 * q^74 + 30 * q^75 + 20 * q^76 + 3 * q^77 + 11 * q^78 - 10 * q^79 + 24 * q^80 - 6 * q^81 - 9 * q^82 + 22 * q^83 + 22 * q^84 - 6 * q^85 + 38 * q^86 + 25 * q^87 - 3 * q^88 + q^89 + 2 * q^90 + 10 * q^91 + 27 * q^92 - 6 * q^93 + 33 * q^94 + 39 * q^95 + 46 * q^96 - 57 * q^97 + 40 * q^98 + 35 * 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 $

$2$	−2.03947	−1.44212	−0.721062	−	0.692870i	$-0.756346\pi$
$2$	−2.03947	−1.44212	−0.721062	+	0.692870i	$0.756346\pi$
$3$	1.78533	1.03076	0.515379	−	0.856962i	$-0.327651\pi$
$3$	1.78533	1.03076	0.515379	+	0.856962i	$0.327651\pi$
$4$	2.15945	1.07972
$5$	−0.701114	−0.313548	−0.156774	−	0.987635i	$-0.550109\pi$
$5$	−0.701114	−0.313548	−0.156774	+	0.987635i	$0.550109\pi$
$6$	−3.64112	−1.48648
$7$	−2.02991	−0.767235	−0.383618	−	0.923492i	$-0.625322\pi$
$7$	−2.02991	−0.767235	−0.383618	+	0.923492i	$0.625322\pi$
$8$	−0.325186	−0.114971
$9$	0.187388	0.0624625
$10$	1.42990	0.452175
$11$	−0.626970	−0.189039	−0.0945194	−	0.995523i	$-0.530131\pi$
$11$	−0.626970	−0.189039	−0.0945194	+	0.995523i	$0.530131\pi$
$12$	3.85531	1.11293
$13$	−2.93743	−0.814697	−0.407349	−	0.913273i	$-0.633547\pi$
$13$	−2.93743	−0.814697	−0.407349	+	0.913273i	$0.633547\pi$
$14$	4.13995	1.10645
$15$	−1.25172	−0.323192
$16$	−3.65568	−0.913921
$17$	−2.71003	−0.657280	−0.328640	−	0.944455i	$-0.606590\pi$
$17$	−2.71003	−0.657280	−0.328640	+	0.944455i	$0.606590\pi$
$18$	−0.382172	−0.0900787
$19$	−1.11114	−0.254912	−0.127456	−	0.991844i	$-0.540681\pi$
$19$	−1.11114	−0.254912	−0.127456	+	0.991844i	$0.540681\pi$
$20$	−1.51402	−0.338545
$21$	−3.62406	−0.790834
$22$	1.27869	0.272617
$23$	−0.412395	−0.0859902	−0.0429951	−	0.999075i	$-0.513690\pi$
$23$	−0.412395	−0.0859902	−0.0429951	+	0.999075i	$0.513690\pi$
$24$	−0.580563	−0.118507
$25$	−4.50844	−0.901688
$26$	5.99081	1.17489
$27$	−5.02143	−0.966374
$28$	−4.38349	−0.828402
$29$	6.46349	1.20024	0.600120	−	0.799910i	$-0.295120\pi$
$29$	6.46349	1.20024	0.600120	+	0.799910i	$0.295120\pi$
$30$	2.55284	0.466083
$31$	−4.14074	−0.743698	−0.371849	−	0.928293i	$-0.621276\pi$
$31$	−4.14074	−0.743698	−0.371849	+	0.928293i	$0.621276\pi$
$32$	8.10604	1.43296
$33$	−1.11935	−0.194853
$34$	5.52704	0.947879
$35$	1.42320	0.240565
$36$	0.404653	0.0674422
$37$	2.98634	0.490951	0.245475	−	0.969403i	$-0.421056\pi$
$37$	2.98634	0.490951	0.245475	+	0.969403i	$0.421056\pi$
$38$	2.26613	0.367615
$39$	−5.24427	−0.839756
$40$	0.227992	0.0360488
$41$	−0.135430	−0.0211505	−0.0105753	−	0.999944i	$-0.503366\pi$
$41$	−0.135430	−0.0211505	−0.0105753	+	0.999944i	$0.503366\pi$
$42$	7.39116	1.14048
$43$	−0.861393	−0.131361	−0.0656806	−	0.997841i	$-0.520922\pi$
$43$	−0.861393	−0.131361	−0.0656806	+	0.997841i	$0.520922\pi$
$44$	−1.35391	−0.204109
$45$	−0.131380	−0.0195850
$46$	0.841067	0.124009
$47$	1.67307	0.244043	0.122021	−	0.992527i	$-0.461062\pi$
$47$	1.67307	0.244043	0.122021	+	0.992527i	$0.461062\pi$
$48$	−6.52659	−0.942032
$49$	−2.87945	−0.411350
$50$	9.19483	1.30035
$51$	−4.83829	−0.677497
$52$	−6.34323	−0.879647
$53$	−8.51721	−1.16993	−0.584964	−	0.811059i	$-0.698892\pi$
$53$	−8.51721	−1.16993	−0.584964	+	0.811059i	$0.698892\pi$
$54$	10.2411	1.39363
$55$	0.439578	0.0592727
$56$	0.660099	0.0882095
$57$	−1.98374	−0.262753
$58$	−13.1821	−1.73089
$59$	−0.406685	−0.0529459	−0.0264729	−	0.999650i	$-0.508428\pi$
$59$	−0.406685	−0.0529459	−0.0264729	+	0.999650i	$0.508428\pi$
$60$	−2.70302	−0.348958
$61$	−8.53132	−1.09232	−0.546162	−	0.837680i	$-0.683912\pi$
$61$	−8.53132	−1.09232	−0.546162	+	0.837680i	$0.683912\pi$
$62$	8.44492	1.07251
$63$	−0.380381	−0.0479234
$64$	−9.22067	−1.15258
$65$	2.05948	0.255446
$66$	2.28288	0.281003
$67$	−13.0293	−1.59178	−0.795889	−	0.605443i	$-0.792996\pi$
$67$	−13.0293	−1.59178	−0.795889	+	0.605443i	$0.792996\pi$
$68$	−5.85217	−0.709680
$69$	−0.736259	−0.0886352
$70$	−2.90258	−0.346925
$71$	2.78095	0.330039	0.165019	−	0.986290i	$-0.447231\pi$
$71$	2.78095	0.330039	0.165019	+	0.986290i	$0.447231\pi$
$72$	−0.0609358	−0.00718135
$73$	−2.11734	−0.247816	−0.123908	−	0.992294i	$-0.539543\pi$
$73$	−2.11734	−0.247816	−0.123908	+	0.992294i	$0.539543\pi$
$74$	−6.09055	−0.708012
$75$	−8.04903	−0.929422
$76$	−2.39944	−0.275234
$77$	1.27270	0.145037
$78$	10.6955	1.21103
$79$	−0.317368	−0.0357067	−0.0178534	−	0.999841i	$-0.505683\pi$
$79$	−0.317368	−0.0357067	−0.0178534	+	0.999841i	$0.505683\pi$
$80$	2.56305	0.286558
$81$	−9.52705	−1.05856
$82$	0.276205	0.0305017
$83$	−5.05120	−0.554442	−0.277221	−	0.960806i	$-0.589413\pi$
$83$	−5.05120	−0.554442	−0.277221	+	0.960806i	$0.589413\pi$
$84$	−7.82595	−0.853882
$85$	1.90004	0.206089
$86$	1.75679	0.189439
$87$	11.5394	1.23716
$88$	0.203882	0.0217339
$89$	16.4699	1.74580	0.872901	−	0.487897i	$-0.162236\pi$
$89$	16.4699	1.74580	0.872901	+	0.487897i	$0.162236\pi$
$90$	0.267946	0.0282440
$91$	5.96273	0.625064
$92$	−0.890544	−0.0928456
$93$	−7.39256	−0.766573
$94$	−3.41218	−0.351940
$95$	0.779033	0.0799271
$96$	14.4719	1.47703
$97$	7.68873	0.780673	0.390336	−	0.920672i	$-0.372359\pi$
$97$	7.68873	0.780673	0.390336	+	0.920672i	$0.372359\pi$
$98$	5.87256	0.593218
$99$	−0.117486	−0.0118078
$100$	−9.73573	−0.973573
$101$	−0.549020	−0.0546296	−0.0273148	−	0.999627i	$-0.508696\pi$
$101$	−0.549020	−0.0546296	−0.0273148	+	0.999627i	$0.508696\pi$
$102$	9.86757	0.977035
$103$	1.32758	0.130810	0.0654051	−	0.997859i	$-0.479166\pi$
$103$	1.32758	0.130810	0.0654051	+	0.997859i	$0.479166\pi$
$104$	0.955211	0.0936662
$105$	2.54088	0.247964
$106$	17.3706	1.68718
$107$	2.57528	0.248961	0.124481	−	0.992222i	$-0.460274\pi$
$107$	2.57528	0.248961	0.124481	+	0.992222i	$0.460274\pi$
$108$	−10.8435	−1.04342
$109$	8.89011	0.851518	0.425759	−	0.904837i	$-0.360007\pi$
$109$	8.89011	0.851518	0.425759	+	0.904837i	$0.360007\pi$
$110$	−0.896507	−0.0854786
$111$	5.33159	0.506052
$112$	7.42072	0.701192
$113$	−1.91987	−0.180606	−0.0903032	−	0.995914i	$-0.528784\pi$
$113$	−1.91987	−0.180606	−0.0903032	+	0.995914i	$0.528784\pi$
$114$	4.04578	0.378922
$115$	0.289136	0.0269621
$116$	13.9576	1.29593
$117$	−0.550438	−0.0508880
$118$	0.829423	0.0763546
$119$	5.50114	0.504288
$120$	0.407041	0.0371576
$121$	−10.6069	−0.964264
$122$	17.3994	1.57527
$123$	−0.241786	−0.0218011
$124$	−8.94170	−0.802988
$125$	6.66650	0.596270
$126$	0.775776	0.0691116
$127$	21.8010	1.93452	0.967261	−	0.253782i	$-0.0816746\pi$
$127$	21.8010	1.93452	0.967261	+	0.253782i	$0.0816746\pi$
$128$	2.59322	0.229210
$129$	−1.53787	−0.135402
$130$	−4.20024	−0.368386
$131$	8.78145	0.767239	0.383620	−	0.923491i	$-0.374677\pi$
$131$	8.78145	0.767239	0.383620	+	0.923491i	$0.374677\pi$
$132$	−2.41717	−0.210387
$133$	2.25551	0.195577
$134$	26.5728	2.29554
$135$	3.52060	0.303005
$136$	0.881265	0.0755678
$137$	−4.26127	−0.364065	−0.182032	−	0.983293i	$-0.558268\pi$
$137$	−4.26127	−0.364065	−0.182032	+	0.983293i	$0.558268\pi$
$138$	1.50158	0.127823
$139$	13.4951	1.14464	0.572321	−	0.820030i	$-0.306043\pi$
$139$	13.4951	1.14464	0.572321	+	0.820030i	$0.306043\pi$
$140$	3.07333	0.259743
$141$	2.98698	0.251549
$142$	−5.67168	−0.475957
$143$	1.84168	0.154009
$144$	−0.685030	−0.0570858
$145$	−4.53164	−0.376332
$146$	4.31826	0.357382
$147$	−5.14076	−0.424003
$148$	6.44884	0.530091
$149$	11.2453	0.921253	0.460626	−	0.887594i	$-0.347625\pi$
$149$	11.2453	0.921253	0.460626	+	0.887594i	$0.347625\pi$
$150$	16.4158	1.34034
$151$	−2.36107	−0.192141	−0.0960705	−	0.995375i	$-0.530627\pi$
$151$	−2.36107	−0.192141	−0.0960705	+	0.995375i	$0.530627\pi$
$152$	0.361325	0.0293074
$153$	−0.507827	−0.0410554
$154$	−2.59563	−0.209162
$155$	2.90313	0.233185
$156$	−11.3247	−0.906704
$157$	−17.5242	−1.39859	−0.699293	−	0.714835i	$-0.746502\pi$
$157$	−17.5242	−1.39859	−0.699293	+	0.714835i	$0.746502\pi$
$158$	0.647264	0.0514936
$159$	−15.2060	−1.20591
$160$	−5.68326	−0.449301
$161$	0.837126	0.0659747
$162$	19.4301	1.52658
$163$	−7.12153	−0.557801	−0.278901	−	0.960320i	$-0.589970\pi$
$163$	−7.12153	−0.557801	−0.278901	+	0.960320i	$0.589970\pi$
$164$	−0.292453	−0.0228367
$165$	0.784790	0.0610958
$166$	10.3018	0.799574
$167$	4.56080	0.352925	0.176463	−	0.984307i	$-0.443535\pi$
$167$	4.56080	0.352925	0.176463	+	0.984307i	$0.443535\pi$
$168$	1.17849	0.0909226
$169$	−4.37149	−0.336269
$170$	−3.87509	−0.297206
$171$	−0.208213	−0.0159224
$172$	−1.86013	−0.141834
$173$	2.91357	0.221514	0.110757	−	0.993847i	$-0.464672\pi$
$173$	2.91357	0.221514	0.110757	+	0.993847i	$0.464672\pi$
$174$	−23.5343	−1.78413
$175$	9.15174	0.691807
$176$	2.29201	0.172766
$177$	−0.726065	−0.0545744
$178$	−33.5898	−2.51766
$179$	−9.01141	−0.673544	−0.336772	−	0.941586i	$-0.609335\pi$
$179$	−9.01141	−0.673544	−0.336772	+	0.941586i	$0.609335\pi$
$180$	−0.283708	−0.0211464
$181$	14.4065	1.07082	0.535412	−	0.844591i	$-0.320156\pi$
$181$	14.4065	1.07082	0.535412	+	0.844591i	$0.320156\pi$
$182$	−12.1608	−0.901420
$183$	−15.2312	−1.12592
$184$	0.134105	0.00988635
$185$	−2.09376	−0.153937
$186$	15.0769	1.10549
$187$	1.69911	0.124251
$188$	3.61291	0.263499
$189$	10.1931	0.741437
$190$	−1.58882	−0.115265
$191$	4.40730	0.318901	0.159450	−	0.987206i	$-0.449028\pi$
$191$	4.40730	0.318901	0.159450	+	0.987206i	$0.449028\pi$
$192$	−16.4619	−1.18804
$193$	−2.90027	−0.208766	−0.104383	−	0.994537i	$-0.533287\pi$
$193$	−2.90027	−0.208766	−0.104383	+	0.994537i	$0.533287\pi$
$194$	−15.6810	−1.12583
$195$	3.67683	0.263304
$196$	−6.21802	−0.444144
$197$	5.91510	0.421433	0.210717	−	0.977547i	$-0.432420\pi$
$197$	5.91510	0.421433	0.210717	+	0.977547i	$0.432420\pi$
$198$	0.239610	0.0170284
$199$	−4.73473	−0.335636	−0.167818	−	0.985818i	$-0.553672\pi$
$199$	−4.73473	−0.335636	−0.167818	+	0.985818i	$0.553672\pi$
$200$	1.46608	0.103668
$201$	−23.2615	−1.64074
$202$	1.11971	0.0787827
$203$	−13.1203	−0.920866
$204$	−10.4480	−0.731509
$205$	0.0949516	0.00663171
$206$	−2.70756	−0.188644
$207$	−0.0772776	−0.00537117
$208$	10.7383	0.744569
$209$	0.696649	0.0481882
$210$	−5.18205	−0.357595
$211$	−1.50671	−0.103726	−0.0518631	−	0.998654i	$-0.516516\pi$
$211$	−1.50671	−0.103726	−0.0518631	+	0.998654i	$0.516516\pi$
$212$	−18.3925	−1.26320
$213$	4.96491	0.340190
$214$	−5.25220	−0.359033
$215$	0.603935	0.0411880
$216$	1.63290	0.111105
$217$	8.40534	0.570591
$218$	−18.1311	−1.22799
$219$	−3.78014	−0.255438
$220$	0.949245	0.0639981
$221$	7.96054	0.535484
$222$	−10.8736	−0.729790
$223$	−9.79220	−0.655734	−0.327867	−	0.944724i	$-0.606330\pi$
$223$	−9.79220	−0.655734	−0.327867	+	0.944724i	$0.606330\pi$
$224$	−16.4546	−1.09942
$225$	−0.844825	−0.0563217
$226$	3.91552	0.260457
$227$	6.88512	0.456981	0.228491	−	0.973546i	$-0.426621\pi$
$227$	6.88512	0.456981	0.228491	+	0.973546i	$0.426621\pi$
$228$	−4.28378	−0.283700
$229$	12.1880	0.805405	0.402703	−	0.915331i	$-0.368071\pi$
$229$	12.1880	0.805405	0.402703	+	0.915331i	$0.368071\pi$
$230$	−0.589684	−0.0388826
$231$	2.27218	0.149498
$232$	−2.10183	−0.137992
$233$	−21.0547	−1.37934	−0.689669	−	0.724125i	$-0.742244\pi$
$233$	−21.0547	−1.37934	−0.689669	+	0.724125i	$0.742244\pi$
$234$	1.12260	0.0733869
$235$	−1.17301	−0.0765190
$236$	−0.878215	−0.0571669
$237$	−0.566606	−0.0368050
$238$	−11.2194	−0.727247
$239$	9.11944	0.589888	0.294944	−	0.955515i	$-0.404699\pi$
$239$	9.11944	0.589888	0.294944	+	0.955515i	$0.404699\pi$
$240$	4.57588	0.295372
$241$	22.7352	1.46450	0.732252	−	0.681034i	$-0.238469\pi$
$241$	22.7352	1.46450	0.732252	+	0.681034i	$0.238469\pi$
$242$	21.6325	1.39059
$243$	−1.94460	−0.124746
$244$	−18.4229	−1.17941
$245$	2.01882	0.128978
$246$	0.493116	0.0314399
$247$	3.26388	0.207676
$248$	1.34651	0.0855034
$249$	−9.01804	−0.571495
$250$	−13.5961	−0.859896
$251$	−11.6824	−0.737385	−0.368692	−	0.929551i	$-0.620194\pi$
$251$	−11.6824	−0.737385	−0.368692	+	0.929551i	$0.620194\pi$
$252$	−0.821411	−0.0517441
$253$	0.258559	0.0162555
$254$	−44.4625	−2.78982
$255$	3.39220	0.212428
$256$	13.1525	0.822034
$257$	−16.3010	−1.01683	−0.508415	−	0.861112i	$-0.669768\pi$
$257$	−16.3010	−1.01683	−0.508415	+	0.861112i	$0.669768\pi$
$258$	3.13644	0.195266
$259$	−6.06201	−0.376675
$260$	4.44733	0.275811
$261$	1.21118	0.0749700
$262$	−17.9095	−1.10645
$263$	−15.7955	−0.973993	−0.486996	−	0.873404i	$-0.661907\pi$
$263$	−15.7955	−0.973993	−0.486996	+	0.873404i	$0.661907\pi$
$264$	0.363996	0.0224024
$265$	5.97154	0.366829
$266$	−4.60005	−0.282047
$267$	29.4041	1.79950
$268$	−28.1360	−1.71868
$269$	11.2401	0.685323	0.342662	−	0.939459i	$-0.388672\pi$
$269$	11.2401	0.685323	0.342662	+	0.939459i	$0.388672\pi$
$270$	−7.18016	−0.436970
$271$	22.7114	1.37962	0.689809	−	0.723991i	$-0.257694\pi$
$271$	22.7114	1.37962	0.689809	+	0.723991i	$0.257694\pi$
$272$	9.90703	0.600702
$273$	10.6454	0.644290
$274$	8.69074	0.525027
$275$	2.82666	0.170454
$276$	−1.58991	−0.0957014
$277$	−3.42609	−0.205854	−0.102927	−	0.994689i	$-0.532821\pi$
$277$	−3.42609	−0.205854	−0.102927	+	0.994689i	$0.532821\pi$
$278$	−27.5229	−1.65072
$279$	−0.775923	−0.0464533
$280$	−0.462805	−0.0276579
$281$	−6.41168	−0.382488	−0.191244	−	0.981542i	$-0.561252\pi$
$281$	−6.41168	−0.382488	−0.191244	+	0.981542i	$0.561252\pi$
$282$	−6.09186	−0.362765
$283$	−22.3462	−1.32834	−0.664172	−	0.747580i	$-0.731216\pi$
$283$	−22.3462	−1.32834	−0.664172	+	0.747580i	$0.731216\pi$
$284$	6.00532	0.356350
$285$	1.39083	0.0823855
$286$	−3.75606	−0.222101
$287$	0.274910	0.0162274
$288$	1.51897	0.0895062
$289$	−9.65571	−0.567983
$290$	9.24216	0.542718
$291$	13.7269	0.804685
$292$	−4.57228	−0.267573
$293$	4.95366	0.289396	0.144698	−	0.989476i	$-0.453779\pi$
$293$	4.95366	0.289396	0.144698	+	0.989476i	$0.453779\pi$
$294$	10.4844	0.611464
$295$	0.285133	0.0166011
$296$	−0.971115	−0.0564449
$297$	3.14829	0.182682
$298$	−22.9345	−1.32856
$299$	1.21138	0.0700560
$300$	−17.3814	−1.00352
$301$	1.74855	0.100785
$302$	4.81533	0.277091
$303$	−0.980180	−0.0563099
$304$	4.06196	0.232969
$305$	5.98143	0.342496
$306$	1.03570	0.0592069
$307$	−1.86937	−0.106690	−0.0533452	−	0.998576i	$-0.516988\pi$
$307$	−1.86937	−0.106690	−0.0533452	+	0.998576i	$0.516988\pi$
$308$	2.74832	0.156600
$309$	2.37016	0.134834
$310$	−5.92085	−0.336282
$311$	−4.29662	−0.243639	−0.121819	−	0.992552i	$-0.538873\pi$
$311$	−4.29662	−0.243639	−0.121819	+	0.992552i	$0.538873\pi$
$312$	1.70536	0.0965472
$313$	−24.2378	−1.37000	−0.684999	−	0.728544i	$-0.740198\pi$
$313$	−24.2378	−1.37000	−0.684999	+	0.728544i	$0.740198\pi$
$314$	35.7402	2.01693
$315$	0.266690	0.0150263
$316$	−0.685340	−0.0385534
$317$	−28.1902	−1.58332	−0.791661	−	0.610961i	$-0.790783\pi$
$317$	−28.1902	−1.58332	−0.791661	+	0.610961i	$0.790783\pi$
$318$	31.0122	1.73908
$319$	−4.05242	−0.226892
$320$	6.46474	0.361390
$321$	4.59771	0.256619
$322$	−1.70729	−0.0951438
$323$	3.01121	0.167548
$324$	−20.5731	−1.14295
$325$	13.2432	0.734602
$326$	14.5242	0.804419
$327$	15.8717	0.877709
$328$	0.0440398	0.00243169
$329$	−3.39619	−0.187238
$330$	−1.60056	−0.0881077
$331$	13.5185	0.743046	0.371523	−	0.928424i	$-0.378836\pi$
$331$	13.5185	0.743046	0.371523	+	0.928424i	$0.378836\pi$
$332$	−10.9078	−0.598644
$333$	0.559603	0.0306660
$334$	−9.30162	−0.508962
$335$	9.13500	0.499098
$336$	13.2484	0.722760
$337$	−1.73199	−0.0943475	−0.0471738	−	0.998887i	$-0.515021\pi$
$337$	−1.73199	−0.0943475	−0.0471738	+	0.998887i	$0.515021\pi$
$338$	8.91554	0.484941
$339$	−3.42760	−0.186161
$340$	4.10304	0.222519
$341$	2.59612	0.140588
$342$	0.424644	0.0229621
$343$	20.0544	1.08284
$344$	0.280113	0.0151027
$345$	0.516202	0.0277914
$346$	−5.94214	−0.319451
$347$	−27.7262	−1.48842	−0.744210	−	0.667946i	$-0.767174\pi$
$347$	−27.7262	−1.48842	−0.744210	+	0.667946i	$0.767174\pi$
$348$	24.9188	1.33579
$349$	−16.0612	−0.859737	−0.429869	−	0.902891i	$-0.641440\pi$
$349$	−16.0612	−0.859737	−0.429869	+	0.902891i	$0.641440\pi$
$350$	−18.6647	−0.997671
$351$	14.7501	0.787302
$352$	−5.08225	−0.270885
$353$	−16.0011	−0.851652	−0.425826	−	0.904805i	$-0.640016\pi$
$353$	−16.0011	−0.851652	−0.425826	+	0.904805i	$0.640016\pi$
$354$	1.48079	0.0787031
$355$	−1.94977	−0.103483
$356$	35.5658	1.88498
$357$	9.82132	0.519799
$358$	18.3785	0.971335
$359$	29.2698	1.54480	0.772400	−	0.635136i	$-0.219056\pi$
$359$	29.2698	1.54480	0.772400	+	0.635136i	$0.219056\pi$
$360$	0.0427229	0.00225170
$361$	−17.7654	−0.935020
$362$	−29.3816	−1.54426
$363$	−18.9368	−0.993923
$364$	12.8762	0.674896
$365$	1.48450	0.0777022
$366$	31.0636	1.62372
$367$	19.5331	1.01962	0.509810	−	0.860287i	$-0.329716\pi$
$367$	19.5331	1.01962	0.509810	+	0.860287i	$0.329716\pi$
$368$	1.50759	0.0785883
$369$	−0.0253778	−0.00132112
$370$	4.27017	0.221996
$371$	17.2892	0.897611
$372$	−15.9638	−0.827687
$373$	−22.0592	−1.14218	−0.571091	−	0.820887i	$-0.693480\pi$
$373$	−22.0592	−1.14218	−0.571091	+	0.820887i	$0.693480\pi$
$374$	−3.46529	−0.179186
$375$	11.9019	0.614610
$376$	−0.544059	−0.0280577
$377$	−18.9861	−0.977832
$378$	−20.7885	−1.06924
$379$	10.7429	0.551828	0.275914	−	0.961182i	$-0.411020\pi$
$379$	10.7429	0.551828	0.275914	+	0.961182i	$0.411020\pi$
$380$	1.68228	0.0862991
$381$	38.9218	1.99403
$382$	−8.98856	−0.459895
$383$	7.81876	0.399520	0.199760	−	0.979845i	$-0.435984\pi$
$383$	7.81876	0.399520	0.199760	+	0.979845i	$0.435984\pi$
$384$	4.62974	0.236261
$385$	−0.892305	−0.0454761
$386$	5.91502	0.301067
$387$	−0.161414	−0.00820515
$388$	16.6034	0.842910
$389$	−35.0312	−1.77615	−0.888075	−	0.459698i	$-0.847957\pi$
$389$	−35.0312	−1.77615	−0.888075	+	0.459698i	$0.847957\pi$
$390$	−7.49880	−0.379717
$391$	1.11760	0.0565197
$392$	0.936357	0.0472932
$393$	15.6778	0.790838
$394$	−12.0637	−0.607759
$395$	0.222512	0.0111958
$396$	−0.253706	−0.0127492
$397$	−0.245438	−0.0123182	−0.00615909	−	0.999981i	$-0.501961\pi$
$397$	−0.245438	−0.0123182	−0.00615909	+	0.999981i	$0.501961\pi$
$398$	9.65635	0.484029
$399$	4.02682	0.201593
$400$	16.4814	0.824072
$401$	−16.3434	−0.816151	−0.408075	−	0.912948i	$-0.633800\pi$
$401$	−16.3434	−0.816151	−0.408075	+	0.912948i	$0.633800\pi$
$402$	47.4411	2.36615
$403$	12.1631	0.605889
$404$	−1.18558	−0.0589848
$405$	6.67955	0.331909
$406$	26.7585	1.32800
$407$	−1.87235	−0.0928087
$408$	1.57334	0.0778922
$409$	4.60893	0.227897	0.113948	−	0.993487i	$-0.463650\pi$
$409$	4.60893	0.227897	0.113948	+	0.993487i	$0.463650\pi$
$410$	−0.193651	−0.00956375
$411$	−7.60775	−0.375263
$412$	2.86683	0.141239
$413$	0.825536	0.0406220
$414$	0.157606	0.00774589
$415$	3.54147	0.173844
$416$	−23.8109	−1.16743
$417$	24.0932	1.17985
$418$	−1.42080	−0.0694934
$419$	11.4509	0.559414	0.279707	−	0.960085i	$-0.409763\pi$
$419$	11.4509	0.559414	0.279707	+	0.960085i	$0.409763\pi$
$420$	5.48689	0.267733
$421$	−22.2626	−1.08501	−0.542505	−	0.840052i	$-0.682524\pi$
$421$	−22.2626	−1.08501	−0.542505	+	0.840052i	$0.682524\pi$
$422$	3.07289	0.149586
$423$	0.313513	0.0152435
$424$	2.76968	0.134507
$425$	12.2180	0.592661
$426$	−10.1258	−0.490596
$427$	17.3178	0.838069
$428$	5.56117	0.268809
$429$	3.28800	0.158746
$430$	−1.23171	−0.0593982
$431$	−1.13299	−0.0545741	−0.0272871	−	0.999628i	$-0.508687\pi$
$431$	−1.13299	−0.0545741	−0.0272871	+	0.999628i	$0.508687\pi$
$432$	18.3568	0.883190
$433$	−2.65692	−0.127683	−0.0638417	−	0.997960i	$-0.520335\pi$
$433$	−2.65692	−0.127683	−0.0638417	+	0.997960i	$0.520335\pi$
$434$	−17.1425	−0.822864
$435$	−8.09046	−0.387908
$436$	19.1977	0.919403
$437$	0.458226	0.0219199
$438$	7.70950	0.368374
$439$	6.57228	0.313678	0.156839	−	0.987624i	$-0.449870\pi$
$439$	6.57228	0.313678	0.156839	+	0.987624i	$0.449870\pi$
$440$	−0.142945	−0.00681461
$441$	−0.539573	−0.0256940
$442$	−16.2353	−0.772235
$443$	1.34406	0.0638583	0.0319291	−	0.999490i	$-0.489835\pi$
$443$	1.34406	0.0638583	0.0319291	+	0.999490i	$0.489835\pi$
$444$	11.5133	0.546396
$445$	−11.5473	−0.547393
$446$	19.9709	0.945650
$447$	20.0766	0.949589
$448$	18.7172	0.884303
$449$	26.3410	1.24311	0.621555	−	0.783371i	$-0.286501\pi$
$449$	26.3410	1.24311	0.621555	+	0.783371i	$0.286501\pi$
$450$	1.72300	0.0812229
$451$	0.0849103	0.00399827
$452$	−4.14586	−0.195005
$453$	−4.21528	−0.198051
$454$	−14.0420	−0.659024
$455$	−4.18056	−0.195988
$456$	0.645084	0.0302088
$457$	−30.0693	−1.40658	−0.703290	−	0.710903i	$-0.748287\pi$
$457$	−30.0693	−1.40658	−0.703290	+	0.710903i	$0.748287\pi$
$458$	−24.8571	−1.16149
$459$	13.6082	0.635179
$460$	0.624373	0.0291115
$461$	−7.72477	−0.359778	−0.179889	−	0.983687i	$-0.557574\pi$
$461$	−7.72477	−0.359778	−0.179889	+	0.983687i	$0.557574\pi$
$462$	−4.63404	−0.215595
$463$	7.82961	0.363873	0.181936	−	0.983310i	$-0.441764\pi$
$463$	7.82961	0.363873	0.181936	+	0.983310i	$0.441764\pi$
$464$	−23.6285	−1.09692
$465$	5.18303	0.240357
$466$	42.9404	1.98918
$467$	−7.19623	−0.333002	−0.166501	−	0.986041i	$-0.553247\pi$
$467$	−7.19623	−0.333002	−0.166501	+	0.986041i	$0.553247\pi$
$468$	−1.18864	−0.0549450
$469$	26.4483	1.22127
$470$	2.39233	0.110350
$471$	−31.2865	−1.44160
$472$	0.132248	0.00608722
$473$	0.540068	0.0248323
$474$	1.15558	0.0530774
$475$	5.00948	0.229851
$476$	11.8794	0.544492
$477$	−1.59602	−0.0730767
$478$	−18.5988	−0.850691
$479$	−12.1955	−0.557229	−0.278614	−	0.960403i	$-0.589875\pi$
$479$	−12.1955	−0.557229	−0.278614	+	0.960403i	$0.589875\pi$
$480$	−10.1465	−0.463121
$481$	−8.77217	−0.399976
$482$	−46.3678	−2.11200
$483$	1.49454	0.0680040
$484$	−22.9050	−1.04114
$485$	−5.39068	−0.244778
$486$	3.96595	0.179899
$487$	35.9684	1.62988	0.814942	−	0.579543i	$-0.196769\pi$
$487$	35.9684	1.62988	0.814942	+	0.579543i	$0.196769\pi$
$488$	2.77426	0.125585
$489$	−12.7142	−0.574958
$490$	−4.11734	−0.186002
$491$	−17.3618	−0.783527	−0.391763	−	0.920066i	$-0.628135\pi$
$491$	−17.3618	−0.783527	−0.391763	+	0.920066i	$0.628135\pi$
$492$	−0.522124	−0.0235392
$493$	−17.5163	−0.788893
$494$	−6.65660	−0.299495
$495$	0.0823714	0.00370232
$496$	15.1372	0.679682
$497$	−5.64510	−0.253217
$498$	18.3921	0.824167
$499$	−30.0817	−1.34664	−0.673320	−	0.739351i	$-0.735133\pi$
$499$	−30.0817	−1.34664	−0.673320	+	0.739351i	$0.735133\pi$
$500$	14.3960	0.643806
$501$	8.14251	0.363781
$502$	23.8259	1.06340
$503$	−1.00000	−0.0445878
$503$	−1.00000	−0.0445878
$504$	0.123694	0.00550979
$505$	0.384926	0.0171290
$506$	−0.527324	−0.0234424
$507$	−7.80454	−0.346612
$508$	47.0780	2.08875
$509$	−32.5495	−1.44273	−0.721366	−	0.692554i	$-0.756485\pi$
$509$	−32.5495	−1.44273	−0.721366	+	0.692554i	$0.756485\pi$
$510$	−6.91829	−0.306347
$511$	4.29802	0.190133
$512$	−32.0107	−1.41469
$513$	5.57949	0.246340
$514$	33.2455	1.46639
$515$	−0.930784	−0.0410152
$516$	−3.32094	−0.146196
$517$	−1.04897	−0.0461335
$518$	12.3633	0.543212
$519$	5.20166	0.228328
$520$	−0.669712	−0.0293688
$521$	−12.6474	−0.554094	−0.277047	−	0.960856i	$-0.589356\pi$
$521$	−12.6474	−0.554094	−0.277047	+	0.960856i	$0.589356\pi$
$522$	−2.47016	−0.108116
$523$	14.7294	0.644073	0.322036	−	0.946727i	$-0.395633\pi$
$523$	14.7294	0.644073	0.322036	+	0.946727i	$0.395633\pi$
$524$	18.9631	0.828406
$525$	16.3388	0.713085
$526$	32.2145	1.40462
$527$	11.2215	0.488818
$528$	4.09198	0.178080
$529$	−22.8299	−0.992606
$530$	−12.1788	−0.529013
$531$	−0.0762077	−0.00330713
$532$	4.87065	0.211169
$533$	0.397815	0.0172313
$534$	−59.9688	−2.59510
$535$	−1.80556	−0.0780613
$536$	4.23693	0.183008
$537$	−16.0883	−0.694261
$538$	−22.9239	−0.988321
$539$	1.80533	0.0777611
$540$	7.60254	0.327161
$541$	−27.4172	−1.17876	−0.589379	−	0.807857i	$-0.700627\pi$
$541$	−27.4172	−1.17876	−0.589379	+	0.807857i	$0.700627\pi$
$542$	−46.3192	−1.98958
$543$	25.7202	1.10376
$544$	−21.9676	−0.941855
$545$	−6.23298	−0.266992
$546$	−21.7110	−0.929147
$547$	−16.1884	−0.692164	−0.346082	−	0.938204i	$-0.612488\pi$
$547$	−16.1884	−0.692164	−0.346082	+	0.938204i	$0.612488\pi$
$548$	−9.20198	−0.393089
$549$	−1.59866	−0.0682293
$550$	−5.76489	−0.245816
$551$	−7.18181	−0.305955
$552$	0.239421	0.0101904
$553$	0.644231	0.0273955
$554$	6.98742	0.296867
$555$	−3.73805	−0.158671
$556$	29.1420	1.23590
$557$	−13.3858	−0.567176	−0.283588	−	0.958946i	$-0.591525\pi$
$557$	−13.3858	−0.567176	−0.283588	+	0.958946i	$0.591525\pi$
$558$	1.58247	0.0669914
$559$	2.53028	0.107020
$560$	−5.20277	−0.219857
$561$	3.03347	0.128073
$562$	13.0764	0.551596
$563$	23.3845	0.985538	0.492769	−	0.870160i	$-0.335985\pi$
$563$	23.3845	0.985538	0.492769	+	0.870160i	$0.335985\pi$
$564$	6.45022	0.271603
$565$	1.34605	0.0566287
$566$	45.5745	1.91564
$567$	19.3391	0.812165
$568$	−0.904327	−0.0379447
$569$	43.0171	1.80337	0.901685	−	0.432393i	$-0.142331\pi$
$569$	43.0171	1.80337	0.901685	+	0.432393i	$0.142331\pi$
$570$	−2.83655	−0.118810
$571$	−1.24920	−0.0522772	−0.0261386	−	0.999658i	$-0.508321\pi$
$571$	−1.24920	−0.0522772	−0.0261386	+	0.999658i	$0.508321\pi$
$572$	3.97702	0.166287
$573$	7.86846	0.328710
$574$	−0.560672	−0.0234020
$575$	1.85926	0.0775364
$576$	−1.72784	−0.0719933
$577$	−38.6392	−1.60857	−0.804284	−	0.594244i	$-0.797451\pi$
$577$	−38.6392	−1.60857	−0.804284	+	0.594244i	$0.797451\pi$
$578$	19.6926	0.819102
$579$	−5.17793	−0.215187
$580$	−9.78584	−0.406335
$581$	10.2535	0.425387
$582$	−27.9956	−1.16046
$583$	5.34004	0.221162
$584$	0.688529	0.0284915
$585$	0.385920	0.0159558
$586$	−10.1029	−0.417345
$587$	−13.5179	−0.557943	−0.278972	−	0.960299i	$-0.589994\pi$
$587$	−13.5179	−0.557943	−0.278972	+	0.960299i	$0.589994\pi$
$588$	−11.1012	−0.457805
$589$	4.60092	0.189578
$590$	−0.581520	−0.0239408
$591$	10.5604	0.434396
$592$	−10.9171	−0.448690
$593$	−6.72274	−0.276070	−0.138035	−	0.990427i	$-0.544079\pi$
$593$	−6.72274	−0.276070	−0.138035	+	0.990427i	$0.544079\pi$
$594$	−6.42084	−0.263450
$595$	−3.85692	−0.158118
$596$	24.2837	0.994698
$597$	−8.45303	−0.345960
$598$	−2.47058	−0.101029
$599$	4.15139	0.169621	0.0848106	−	0.996397i	$-0.472971\pi$
$599$	4.15139	0.169621	0.0848106	+	0.996397i	$0.472971\pi$
$600$	2.61743	0.106856
$601$	−39.8754	−1.62655	−0.813276	−	0.581878i	$-0.802318\pi$
$601$	−39.8754	−1.62655	−0.813276	+	0.581878i	$0.802318\pi$
$602$	−3.56612	−0.145344
$603$	−2.44152	−0.0994264
$604$	−5.09860	−0.207459
$605$	7.43665	0.302343
$606$	1.99905	0.0812059
$607$	−27.9713	−1.13532	−0.567660	−	0.823263i	$-0.692151\pi$
$607$	−27.9713	−1.13532	−0.567660	+	0.823263i	$0.692151\pi$
$608$	−9.00690	−0.365278
$609$	−23.4240	−0.949190
$610$	−12.1990	−0.493921
$611$	−4.91454	−0.198821
$612$	−1.09662	−0.0443284
$613$	−30.7521	−1.24207	−0.621033	−	0.783785i	$-0.713287\pi$
$613$	−30.7521	−1.24207	−0.621033	+	0.783785i	$0.713287\pi$
$614$	3.81252	0.153861
$615$	0.169520	0.00683569
$616$	−0.413863	−0.0166750
$617$	−24.4669	−0.984999	−0.492500	−	0.870313i	$-0.663917\pi$
$617$	−24.4669	−0.984999	−0.492500	+	0.870313i	$0.663917\pi$
$618$	−4.83387	−0.194447
$619$	37.1492	1.49315	0.746575	−	0.665301i	$-0.231697\pi$
$619$	37.1492	1.49315	0.746575	+	0.665301i	$0.231697\pi$
$620$	6.26915	0.251775
$621$	2.07081	0.0830988
$622$	8.76284	0.351358
$623$	−33.4324	−1.33944
$624$	19.1714	0.767471
$625$	17.8682	0.714729
$626$	49.4322	1.97571
$627$	1.24375	0.0496704
$628$	−37.8426	−1.51009
$629$	−8.09308	−0.322692
$630$	−0.543907	−0.0216698
$631$	−15.7642	−0.627563	−0.313781	−	0.949495i	$-0.601596\pi$
$631$	−15.7642	−0.627563	−0.313781	+	0.949495i	$0.601596\pi$
$632$	0.103204	0.00410522
$633$	−2.68997	−0.106917
$634$	57.4932	2.28335
$635$	−15.2850	−0.606565
$636$	−32.8365	−1.30205
$637$	8.45819	0.335126
$638$	8.26479	0.327206
$639$	0.521116	0.0206150
$640$	−1.81814	−0.0718684
$641$	48.3528	1.90982	0.954911	−	0.296892i	$-0.0959503\pi$
$641$	48.3528	1.90982	0.954911	+	0.296892i	$0.0959503\pi$
$642$	−9.37689	−0.370076
$643$	3.30378	0.130288	0.0651441	−	0.997876i	$-0.479249\pi$
$643$	3.30378	0.130288	0.0651441	+	0.997876i	$0.479249\pi$
$644$	1.80773	0.0712344
$645$	1.07822	0.0424549
$646$	−6.14129	−0.241626
$647$	34.3017	1.34854	0.674269	−	0.738486i	$-0.264459\pi$
$647$	34.3017	1.34854	0.674269	+	0.738486i	$0.264459\pi$
$648$	3.09806	0.121703
$649$	0.254980	0.0100088
$650$	−27.0092	−1.05939
$651$	15.0063	0.588142
$652$	−15.3786	−0.602271
$653$	−13.5211	−0.529120	−0.264560	−	0.964369i	$-0.585227\pi$
$653$	−13.5211	−0.529120	−0.264560	+	0.964369i	$0.585227\pi$
$654$	−32.3700	−1.26577
$655$	−6.15680	−0.240566
$656$	0.495088	0.0193299
$657$	−0.396763	−0.0154792
$658$	6.92644	0.270021
$659$	29.2605	1.13983	0.569914	−	0.821704i	$-0.306977\pi$
$659$	29.2605	1.13983	0.569914	+	0.821704i	$0.306977\pi$
$660$	1.69471	0.0659665
$661$	36.0006	1.40026	0.700131	−	0.714015i	$-0.253125\pi$
$661$	36.0006	1.40026	0.700131	+	0.714015i	$0.253125\pi$
$662$	−27.5707	−1.07157
$663$	14.2122	0.551955
$664$	1.64258	0.0637445
$665$	−1.58137	−0.0613229
$666$	−1.14129	−0.0442242
$667$	−2.66551	−0.103209
$668$	9.84880	0.381061
$669$	−17.4823	−0.675903
$670$	−18.6306	−0.719762
$671$	5.34889	0.206491
$672$	−29.3767	−1.13323
$673$	14.3874	0.554595	0.277298	−	0.960784i	$-0.410561\pi$
$673$	14.3874	0.554595	0.277298	+	0.960784i	$0.410561\pi$
$674$	3.53235	0.136061
$675$	22.6388	0.871368
$676$	−9.44000	−0.363077
$677$	25.3712	0.975094	0.487547	−	0.873097i	$-0.337892\pi$
$677$	25.3712	0.975094	0.487547	+	0.873097i	$0.337892\pi$
$678$	6.99049	0.268468
$679$	−15.6075	−0.598960
$680$	−0.617867	−0.0236941
$681$	12.2922	0.471037
$682$	−5.29471	−0.202745
$683$	31.2549	1.19594	0.597968	−	0.801520i	$-0.295975\pi$
$683$	31.2549	1.19594	0.597968	+	0.801520i	$0.295975\pi$
$684$	−0.449625	−0.0171918
$685$	2.98764	0.114152
$686$	−40.9005	−1.56159
$687$	21.7595	0.830178
$688$	3.14898	0.120054
$689$	25.0187	0.953138
$690$	−1.05278	−0.0400786
$691$	−1.92143	−0.0730946	−0.0365473	−	0.999332i	$-0.511636\pi$
$691$	−1.92143	−0.0730946	−0.0365473	+	0.999332i	$0.511636\pi$
$692$	6.29169	0.239174
$693$	0.238487	0.00905939
$694$	56.5468	2.14649
$695$	−9.46162	−0.358900
$696$	−3.75246	−0.142237
$697$	0.367019	0.0139018
$698$	32.7564	1.23985
$699$	−37.5894	−1.42176
$700$	19.7627	0.746960
$701$	5.22129	0.197205	0.0986027	−	0.995127i	$-0.468563\pi$
$701$	5.22129	0.197205	0.0986027	+	0.995127i	$0.468563\pi$
$702$	−30.0824	−1.13539
$703$	−3.31823	−0.125149
$704$	5.78109	0.217883
$705$	−2.09421	−0.0788726
$706$	32.6338	1.22819
$707$	1.11446	0.0419137
$708$	−1.56790	−0.0589253
$709$	1.68414	0.0632493	0.0316247	−	0.999500i	$-0.489932\pi$
$709$	1.68414	0.0632493	0.0316247	+	0.999500i	$0.489932\pi$
$710$	3.97649	0.149235
$711$	−0.0594709	−0.00223033
$712$	−5.35577	−0.200716
$713$	1.70762	0.0639508
$714$	−20.0303	−0.749615
$715$	−1.29123	−0.0482893
$716$	−19.4596	−0.727241
$717$	16.2812	0.608032
$718$	−59.6949	−2.22779
$719$	−38.7868	−1.44651	−0.723253	−	0.690583i	$-0.757354\pi$
$719$	−38.7868	−1.44651	−0.723253	+	0.690583i	$0.757354\pi$
$720$	0.480284	0.0178991
$721$	−2.69487	−0.100362
$722$	36.2320	1.34842
$723$	40.5898	1.50955
$724$	31.1100	1.15619
$725$	−29.1402	−1.08224
$726$	38.6210	1.43336
$727$	−18.0472	−0.669333	−0.334666	−	0.942337i	$-0.608624\pi$
$727$	−18.0472	−0.669333	−0.334666	+	0.942337i	$0.608624\pi$
$728$	−1.93900	−0.0718640
$729$	25.1094	0.929978
$730$	−3.02759	−0.112056
$731$	2.33440	0.0863410
$732$	−32.8909	−1.21568
$733$	2.36945	0.0875175	0.0437587	−	0.999042i	$-0.486067\pi$
$733$	2.36945	0.0875175	0.0437587	+	0.999042i	$0.486067\pi$
$734$	−39.8373	−1.47042
$735$	3.60426	0.132945
$736$	−3.34289	−0.123220
$737$	8.16896	0.300907
$738$	0.0517574	0.00190521
$739$	23.0868	0.849260	0.424630	−	0.905367i	$-0.360404\pi$
$739$	23.0868	0.849260	0.424630	+	0.905367i	$0.360404\pi$
$740$	−4.52137	−0.166209
$741$	5.82710	0.214064
$742$	−35.2608	−1.29447
$743$	2.24456	0.0823449	0.0411725	−	0.999152i	$-0.486891\pi$
$743$	2.24456	0.0823449	0.0411725	+	0.999152i	$0.486891\pi$
$744$	2.40396	0.0881333
$745$	−7.88426	−0.288857
$746$	44.9891	1.64717
$747$	−0.946533	−0.0346318
$748$	3.66914	0.134157
$749$	−5.22759	−0.191012
$750$	−24.2735	−0.886344
$751$	54.7798	1.99894	0.999472	−	0.0324826i	$-0.0103413\pi$
$751$	54.7798	1.99894	0.999472	+	0.0324826i	$0.0103413\pi$
$752$	−6.11622	−0.223036
$753$	−20.8568	−0.760065
$754$	38.7215	1.41015
$755$	1.65538	0.0602454
$756$	22.0114	0.800546
$757$	−5.96003	−0.216621	−0.108311	−	0.994117i	$-0.534544\pi$
$757$	−5.96003	−0.216621	−0.108311	+	0.994117i	$0.534544\pi$
$758$	−21.9099	−0.795804
$759$	0.461613	0.0167555
$760$	−0.253330	−0.00918926
$761$	−33.5210	−1.21513	−0.607567	−	0.794268i	$-0.707854\pi$
$761$	−33.5210	−1.21513	−0.607567	+	0.794268i	$0.707854\pi$
$762$	−79.3800	−2.87563
$763$	−18.0461	−0.653314
$764$	9.51732	0.344325
$765$	0.356045	0.0128728
$766$	−15.9461	−0.576158
$767$	1.19461	0.0431349
$768$	23.4816	0.847318
$769$	−41.9889	−1.51416	−0.757080	−	0.653322i	$-0.773375\pi$
$769$	−41.9889	−1.51416	−0.757080	+	0.653322i	$0.773375\pi$
$770$	1.81983	0.0655822
$771$	−29.1026	−1.04810
$772$	−6.26298	−0.225409
$773$	11.9695	0.430512	0.215256	−	0.976558i	$-0.430941\pi$
$773$	11.9695	0.430512	0.215256	+	0.976558i	$0.430941\pi$
$774$	0.329200	0.0118328
$775$	18.6683	0.670584
$776$	−2.50027	−0.0897544
$777$	−10.8227	−0.388261
$778$	71.4451	2.56143
$779$	0.150481	0.00539153
$780$	7.93993	0.284295
$781$	−1.74358	−0.0623901
$782$	−2.27932	−0.0815084
$783$	−32.4559	−1.15988
$784$	10.5264	0.375942
$785$	12.2865	0.438523
$786$	−31.9743	−1.14049
$787$	−14.5883	−0.520017	−0.260008	−	0.965606i	$-0.583725\pi$
$787$	−14.5883	−0.520017	−0.260008	+	0.965606i	$0.583725\pi$
$788$	12.7733	0.455031
$789$	−28.2001	−1.00395
$790$	−0.453806	−0.0161457
$791$	3.89717	0.138568
$792$	0.0382049	0.00135755
$793$	25.0602	0.889913
$794$	0.500564	0.0177643
$795$	10.6611	0.378112
$796$	−10.2244	−0.362394
$797$	13.0225	0.461281	0.230641	−	0.973039i	$-0.425918\pi$
$797$	13.0225	0.461281	0.230641	+	0.973039i	$0.425918\pi$
$798$	−8.21258	−0.290722
$799$	−4.53408	−0.160404
$800$	−36.5456	−1.29208
$801$	3.08625	0.109047
$802$	33.3319	1.17699
$803$	1.32751	0.0468468
$804$	−50.2319	−1.77154
$805$	−0.586921	−0.0206862
$806$	−24.8064	−0.873767
$807$	20.0673	0.706403
$808$	0.178534	0.00628079
$809$	23.5857	0.829230	0.414615	−	0.909997i	$-0.363916\pi$
$809$	23.5857	0.829230	0.414615	+	0.909997i	$0.363916\pi$
$810$	−13.6228	−0.478655
$811$	44.3230	1.55639	0.778195	−	0.628023i	$-0.216136\pi$
$811$	44.3230	1.55639	0.778195	+	0.628023i	$0.216136\pi$
$812$	−28.3326	−0.994280
$813$	40.5472	1.42205
$814$	3.81860	0.133842
$815$	4.99300	0.174897
$816$	17.6873	0.619179
$817$	0.957124	0.0334855
$818$	−9.39977	−0.328655
$819$	1.11734	0.0390431
$820$	0.205043	0.00716041
$821$	−11.0481	−0.385581	−0.192791	−	0.981240i	$-0.561754\pi$
$821$	−11.0481	−0.385581	−0.192791	+	0.981240i	$0.561754\pi$
$822$	15.5158	0.541176
$823$	8.97374	0.312805	0.156403	−	0.987693i	$-0.450010\pi$
$823$	8.97374	0.312805	0.156403	+	0.987693i	$0.450010\pi$
$824$	−0.431710	−0.0150393
$825$	5.04650	0.175697
$826$	−1.68366	−0.0585819
$827$	36.0996	1.25531	0.627654	−	0.778493i	$-0.284015\pi$
$827$	36.0996	1.25531	0.627654	+	0.778493i	$0.284015\pi$
$828$	−0.166877	−0.00579937
$829$	−5.63971	−0.195875	−0.0979375	−	0.995193i	$-0.531225\pi$
$829$	−5.63971	−0.195875	−0.0979375	+	0.995193i	$0.531225\pi$
$830$	−7.22273	−0.250705
$831$	−6.11669	−0.212186
$832$	27.0851	0.939007
$833$	7.80341	0.270372
$834$	−49.1374	−1.70149
$835$	−3.19764	−0.110659
$836$	1.50438	0.0520299
$837$	20.7924	0.718691
$838$	−23.3538	−0.806745
$839$	−19.2580	−0.664859	−0.332429	−	0.943128i	$-0.607868\pi$
$839$	−19.2580	−0.664859	−0.332429	+	0.943128i	$0.607868\pi$
$840$	−0.826257	−0.0285086
$841$	12.7767	0.440575
$842$	45.4039	1.56472
$843$	−11.4469	−0.394253
$844$	−3.25366	−0.111996
$845$	3.06492	0.105436
$846$	−0.639401	−0.0219831
$847$	21.5311	0.739818
$848$	31.1362	1.06922
$849$	−39.8953	−1.36920
$850$	−24.9183	−0.854691
$851$	−1.23155	−0.0422170
$852$	10.7215	0.367311
$853$	29.1126	0.996796	0.498398	−	0.866948i	$-0.333922\pi$
$853$	29.1126	0.996796	0.498398	+	0.866948i	$0.333922\pi$
$854$	−35.3193	−1.20860
$855$	0.145981	0.00499245
$856$	−0.837443	−0.0286232
$857$	−18.6286	−0.636342	−0.318171	−	0.948033i	$-0.603069\pi$
$857$	−18.6286	−0.636342	−0.318171	+	0.948033i	$0.603069\pi$
$858$	−6.70579	−0.228932
$859$	18.5140	0.631690	0.315845	−	0.948811i	$-0.397712\pi$
$859$	18.5140	0.631690	0.315845	+	0.948811i	$0.397712\pi$
$860$	1.30416	0.0444716
$861$	0.490804	0.0167266
$862$	2.31070	0.0787027
$863$	−43.5150	−1.48127	−0.740635	−	0.671908i	$-0.765475\pi$
$863$	−43.5150	−1.48127	−0.740635	+	0.671908i	$0.765475\pi$
$864$	−40.7039	−1.38477
$865$	−2.04274	−0.0694553
$866$	5.41872	0.184135
$867$	−17.2386	−0.585453
$868$	18.1509	0.616081
$869$	0.198981	0.00674996
$870$	16.5003	0.559411
$871$	38.2726	1.29682
$872$	−2.89094	−0.0978995
$873$	1.44077	0.0487628
$874$	−0.934540	−0.0316113
$875$	−13.5324	−0.457479
$876$	−8.16302	−0.275803
$877$	11.9837	0.404662	0.202331	−	0.979317i	$-0.435148\pi$
$877$	11.9837	0.404662	0.202331	+	0.979317i	$0.435148\pi$
$878$	−13.4040	−0.452363
$879$	8.84390	0.298297
$880$	−1.60696	−0.0541705
$881$	−8.33770	−0.280904	−0.140452	−	0.990087i	$-0.544856\pi$
$881$	−8.33770	−0.280904	−0.140452	+	0.990087i	$0.544856\pi$
$882$	1.10044	0.0370539
$883$	14.7773	0.497296	0.248648	−	0.968594i	$-0.420014\pi$
$883$	14.7773	0.497296	0.248648	+	0.968594i	$0.420014\pi$
$884$	17.1904	0.578174
$885$	0.509055	0.0171117
$886$	−2.74118	−0.0920916
$887$	−26.6636	−0.895278	−0.447639	−	0.894214i	$-0.647735\pi$
$887$	−26.6636	−0.895278	−0.447639	+	0.894214i	$0.647735\pi$
$888$	−1.73376	−0.0581811
$889$	−44.2541	−1.48423
$890$	23.5503	0.789408
$891$	5.97318	0.200109
$892$	−21.1457	−0.708011
$893$	−1.85901	−0.0622094
$894$	−40.9456	−1.36943
$895$	6.31803	0.211188
$896$	−5.26401	−0.175858
$897$	2.16271	0.0722108
$898$	−53.7218	−1.79272
$899$	−26.7636	−0.892616
$900$	−1.82435	−0.0608118
$901$	23.0819	0.768971
$902$	−0.173172	−0.00576601
$903$	3.12174	0.103885
$904$	0.624315	0.0207644
$905$	−10.1006	−0.335754
$906$	8.59694	0.285614
$907$	−41.3358	−1.37253	−0.686266	−	0.727351i	$-0.740751\pi$
$907$	−41.3358	−1.37253	−0.686266	+	0.727351i	$0.740751\pi$
$908$	14.8680	0.493413
$909$	−0.102880	−0.00341230
$910$	8.52613	0.282638
$911$	−32.2613	−1.06887	−0.534433	−	0.845211i	$-0.679475\pi$
$911$	−32.2613	−1.06887	−0.534433	+	0.845211i	$0.679475\pi$
$912$	7.25192	0.240135
$913$	3.16696	0.104811
$914$	61.3254	2.02846
$915$	10.6788	0.353030
$916$	26.3193	0.869615
$917$	−17.8256	−0.588653
$918$	−27.7536	−0.916007
$919$	−48.5538	−1.60164	−0.800821	−	0.598903i	$-0.795603\pi$
$919$	−48.5538	−1.60164	−0.800821	+	0.598903i	$0.795603\pi$
$920$	−0.0940229	−0.00309984
$921$	−3.33743	−0.109972
$922$	15.7545	0.518845
$923$	−8.16886	−0.268881
$924$	4.90664	0.161417
$925$	−13.4637	−0.442684
$926$	−15.9683	−0.524750
$927$	0.248772	0.00817073
$928$	52.3933	1.71989
$929$	28.1849	0.924717	0.462358	−	0.886693i	$-0.347003\pi$
$929$	28.1849	0.924717	0.462358	+	0.886693i	$0.347003\pi$
$930$	−10.5706	−0.346625
$931$	3.19946	0.104858
$932$	−45.4664	−1.48930
$933$	−7.67087	−0.251133
$934$	14.6765	0.480230
$935$	−1.19127	−0.0389587
$936$	0.178995	0.00585063
$937$	−59.4487	−1.94211	−0.971053	−	0.238865i	$-0.923225\pi$
$937$	−59.4487	−1.94211	−0.971053	+	0.238865i	$0.923225\pi$
$938$	−53.9405	−1.76122
$939$	−43.2723	−1.41214
$940$	−2.53306	−0.0826194
$941$	24.0890	0.785277	0.392639	−	0.919693i	$-0.371562\pi$
$941$	24.0890	0.785277	0.392639	+	0.919693i	$0.371562\pi$
$942$	63.8078	2.07897
$943$	0.0558504	0.00181874
$944$	1.48671	0.0483884
$945$	−7.14650	−0.232476
$946$	−1.10145	−0.0358113
$947$	40.0415	1.30117	0.650586	−	0.759432i	$-0.274523\pi$
$947$	40.0415	1.30117	0.650586	+	0.759432i	$0.274523\pi$
$948$	−1.22356	−0.0397392
$949$	6.21955	0.201895
$950$	−10.2167	−0.331474
$951$	−50.3288	−1.63202
$952$	−1.78889	−0.0579783
$953$	−24.4039	−0.790521	−0.395261	−	0.918569i	$-0.629346\pi$
$953$	−24.4039	−0.790521	−0.395261	+	0.918569i	$0.629346\pi$
$954$	3.25504	0.105386
$955$	−3.09002	−0.0999907
$956$	19.6929	0.636915
$957$	−7.23488	−0.233870
$958$	24.8725	0.803593
$959$	8.65001	0.279323
$960$	11.5417	0.372506
$961$	−13.8543	−0.446913
$962$	17.8906	0.576816
$963$	0.482575	0.0155508
$964$	49.0955	1.58126
$965$	2.03342	0.0654581
$966$	−3.04808	−0.0980702
$967$	−16.2701	−0.523212	−0.261606	−	0.965175i	$-0.584252\pi$
$967$	−16.2701	−0.523212	−0.261606	+	0.965175i	$0.584252\pi$
$968$	3.44922	0.110862
$969$	5.37600	0.172702
$970$	10.9941	0.353001
$971$	−53.0256	−1.70167	−0.850837	−	0.525430i	$-0.823904\pi$
$971$	−53.0256	−1.70167	−0.850837	+	0.525430i	$0.823904\pi$
$972$	−4.19925	−0.134691
$973$	−27.3939	−0.878209
$974$	−73.3565	−2.35050
$975$	23.6435	0.757197
$976$	31.1878	0.998298
$977$	−47.0435	−1.50505	−0.752527	−	0.658561i	$-0.771165\pi$
$977$	−47.0435	−1.50505	−0.752527	+	0.658561i	$0.771165\pi$
$978$	25.9303	0.829161
$979$	−10.3261	−0.330024
$980$	4.35954	0.139260
$981$	1.66590	0.0531879
$982$	35.4089	1.12994
$983$	−10.9007	−0.347678	−0.173839	−	0.984774i	$-0.555617\pi$
$983$	−10.9007	−0.347678	−0.173839	+	0.984774i	$0.555617\pi$
$984$	0.0786254	0.00250648
$985$	−4.14716	−0.132139
$986$	35.7239	1.13768
$987$	−6.06331	−0.192997
$988$	7.04818	0.224233
$989$	0.355234	0.0112958
$990$	−0.167994	−0.00533921
$991$	−48.5839	−1.54332	−0.771659	−	0.636036i	$-0.780573\pi$
$991$	−48.5839	−1.54332	−0.771659	+	0.636036i	$0.780573\pi$
$992$	−33.5650	−1.06569
$993$	24.1350	0.765901
$994$	11.5130	0.365171
$995$	3.31959	0.105238
$996$	−19.4740	−0.617057
$997$	20.3630	0.644902	0.322451	−	0.946586i	$-0.395493\pi$
$997$	20.3630	0.644902	0.322451	+	0.946586i	$0.395493\pi$
$998$	61.3507	1.94202
$999$	−14.9957	−0.474442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.e.1.2	✓	10
3.2	odd	2		4527.2.a.k.1.9		10
4.3	odd	2		8048.2.a.p.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.e.1.2	✓	10	1.1	even	1	trivial
4527.2.a.k.1.9		10	3.2	odd	2
8048.2.a.p.1.1		10	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q-2.03947 q^{2} +1.78533 q^{3} +2.15945 q^{4} -0.701114 q^{5} -3.64112 q^{6} -2.02991 q^{7} -0.325186 q^{8} +0.187388 q^{9} +O(q^{10})\)	\(q-2.03947 q^{2} +1.78533 q^{3} +2.15945 q^{4} -0.701114 q^{5} -3.64112 q^{6} -2.02991 q^{7} -0.325186 q^{8} +0.187388 q^{9} +1.42990 q^{10} -0.626970 q^{11} +3.85531 q^{12} -2.93743 q^{13} +4.13995 q^{14} -1.25172 q^{15} -3.65568 q^{16} -2.71003 q^{17} -0.382172 q^{18} -1.11114 q^{19} -1.51402 q^{20} -3.62406 q^{21} +1.27869 q^{22} -0.412395 q^{23} -0.580563 q^{24} -4.50844 q^{25} +5.99081 q^{26} -5.02143 q^{27} -4.38349 q^{28} +6.46349 q^{29} +2.55284 q^{30} -4.14074 q^{31} +8.10604 q^{32} -1.11935 q^{33} +5.52704 q^{34} +1.42320 q^{35} +0.404653 q^{36} +2.98634 q^{37} +2.26613 q^{38} -5.24427 q^{39} +0.227992 q^{40} -0.135430 q^{41} +7.39116 q^{42} -0.861393 q^{43} -1.35391 q^{44} -0.131380 q^{45} +0.841067 q^{46} +1.67307 q^{47} -6.52659 q^{48} -2.87945 q^{49} +9.19483 q^{50} -4.83829 q^{51} -6.34323 q^{52} -8.51721 q^{53} +10.2411 q^{54} +0.439578 q^{55} +0.660099 q^{56} -1.98374 q^{57} -13.1821 q^{58} -0.406685 q^{59} -2.70302 q^{60} -8.53132 q^{61} +8.44492 q^{62} -0.380381 q^{63} -9.22067 q^{64} +2.05948 q^{65} +2.28288 q^{66} -13.0293 q^{67} -5.85217 q^{68} -0.736259 q^{69} -2.90258 q^{70} +2.78095 q^{71} -0.0609358 q^{72} -2.11734 q^{73} -6.09055 q^{74} -8.04903 q^{75} -2.39944 q^{76} +1.27270 q^{77} +10.6955 q^{78} -0.317368 q^{79} +2.56305 q^{80} -9.52705 q^{81} +0.276205 q^{82} -5.05120 q^{83} -7.82595 q^{84} +1.90004 q^{85} +1.75679 q^{86} +11.5394 q^{87} +0.203882 q^{88} +16.4699 q^{89} +0.267946 q^{90} +5.96273 q^{91} -0.890544 q^{92} -7.39256 q^{93} -3.41218 q^{94} +0.779033 q^{95} +14.4719 q^{96} +7.68873 q^{97} +5.87256 q^{98} -0.117486 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - 7 q^{12} - 18 q^{13} + q^{14} - 2 q^{15} - 4 q^{16} - 11 q^{17} - q^{18} - 3 q^{20} + q^{21} - 18 q^{22} - 2 q^{23} + 10 q^{24} - 27 q^{25} + 11 q^{26} - 2 q^{27} - 22 q^{28} - 9 q^{29} + 12 q^{30} - 22 q^{31} - 10 q^{32} - 10 q^{33} - 10 q^{34} - 6 q^{35} + 2 q^{36} - 35 q^{37} + 2 q^{38} + 8 q^{39} - 19 q^{40} - 4 q^{41} + 4 q^{42} - 20 q^{43} + 9 q^{44} + 2 q^{45} - q^{46} + 7 q^{47} - 27 q^{49} + 16 q^{50} + 9 q^{51} - 7 q^{52} - 24 q^{53} + 17 q^{54} - 11 q^{55} + 12 q^{56} - 23 q^{57} + 2 q^{58} + 17 q^{59} - 4 q^{61} + 8 q^{62} + 10 q^{63} + 3 q^{64} - 16 q^{65} + 46 q^{66} - 6 q^{67} + 28 q^{68} - 2 q^{69} + 26 q^{70} - q^{71} - q^{72} - 31 q^{73} + 11 q^{74} + 30 q^{75} + 20 q^{76} + 3 q^{77} + 11 q^{78} - 10 q^{79} + 24 q^{80} - 6 q^{81} - 9 q^{82} + 22 q^{83} + 22 q^{84} - 6 q^{85} + 38 q^{86} + 25 q^{87} - 3 q^{88} + q^{89} + 2 q^{90} + 10 q^{91} + 27 q^{92} - 6 q^{93} + 33 q^{94} + 39 q^{95} + 46 q^{96} - 57 q^{97} + 40 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9 - 4 * q^10 - 3 * q^11 - 7 * q^12 - 18 * q^13 + q^14 - 2 * q^15 - 4 * q^16 - 11 * q^17 - q^18 - 3 * q^20 + q^21 - 18 * q^22 - 2 * q^23 + 10 * q^24 - 27 * q^25 + 11 * q^26 - 2 * q^27 - 22 * q^28 - 9 * q^29 + 12 * q^30 - 22 * q^31 - 10 * q^32 - 10 * q^33 - 10 * q^34 - 6 * q^35 + 2 * q^36 - 35 * q^37 + 2 * q^38 + 8 * q^39 - 19 * q^40 - 4 * q^41 + 4 * q^42 - 20 * q^43 + 9 * q^44 + 2 * q^45 - q^46 + 7 * q^47 - 27 * q^49 + 16 * q^50 + 9 * q^51 - 7 * q^52 - 24 * q^53 + 17 * q^54 - 11 * q^55 + 12 * q^56 - 23 * q^57 + 2 * q^58 + 17 * q^59 - 4 * q^61 + 8 * q^62 + 10 * q^63 + 3 * q^64 - 16 * q^65 + 46 * q^66 - 6 * q^67 + 28 * q^68 - 2 * q^69 + 26 * q^70 - q^71 - q^72 - 31 * q^73 + 11 * q^74 + 30 * q^75 + 20 * q^76 + 3 * q^77 + 11 * q^78 - 10 * q^79 + 24 * q^80 - 6 * q^81 - 9 * q^82 + 22 * q^83 + 22 * q^84 - 6 * q^85 + 38 * q^86 + 25 * q^87 - 3 * q^88 + q^89 + 2 * q^90 + 10 * q^91 + 27 * q^92 - 6 * q^93 + 33 * q^94 + 39 * q^95 + 46 * q^96 - 57 * q^97 + 40 * q^98 + 35 * q^99

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