LMFDB - Embedded newform 667.2.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
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} - 3x^{9} - 10x^{8} + 32x^{7} + 32x^{6} - 118x^{5} - 29x^{4} + 182x^{3} - 28x^{2} - 101x + 43 $ x^10 - 3x^9 - 10x^8 + 32x^7 + 32x^6 - 118x^5 - 29x^4 + 182x^3 - 28x^2 - 101*x + 43
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.788514$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.788514 q^{2} -2.59585 q^{3} -1.37825 q^{4} -4.42591 q^{5} +2.04687 q^{6} +4.56405 q^{7} +2.66379 q^{8} +3.73846 q^{9} +O(q^{10})$	\(q-0.788514 q^{2} -2.59585 q^{3} -1.37825 q^{4} -4.42591 q^{5} +2.04687 q^{6} +4.56405 q^{7} +2.66379 q^{8} +3.73846 q^{9} +3.48989 q^{10} +0.971788 q^{11} +3.57772 q^{12} +1.44606 q^{13} -3.59882 q^{14} +11.4890 q^{15} +0.656051 q^{16} -0.0568213 q^{17} -2.94783 q^{18} -6.61190 q^{19} +6.09999 q^{20} -11.8476 q^{21} -0.766268 q^{22} +1.00000 q^{23} -6.91482 q^{24} +14.5887 q^{25} -1.14024 q^{26} -1.91692 q^{27} -6.29038 q^{28} +1.00000 q^{29} -9.05925 q^{30} -5.35524 q^{31} -5.84489 q^{32} -2.52262 q^{33} +0.0448044 q^{34} -20.2001 q^{35} -5.15251 q^{36} +2.47461 q^{37} +5.21357 q^{38} -3.75377 q^{39} -11.7897 q^{40} +0.833377 q^{41} +9.34200 q^{42} +5.45093 q^{43} -1.33936 q^{44} -16.5461 q^{45} -0.788514 q^{46} -7.60521 q^{47} -1.70301 q^{48} +13.8305 q^{49} -11.5034 q^{50} +0.147500 q^{51} -1.99303 q^{52} -13.0511 q^{53} +1.51152 q^{54} -4.30104 q^{55} +12.1577 q^{56} +17.1635 q^{57} -0.788514 q^{58} +0.684766 q^{59} -15.8347 q^{60} +4.29402 q^{61} +4.22268 q^{62} +17.0625 q^{63} +3.29668 q^{64} -6.40015 q^{65} +1.98912 q^{66} +7.51469 q^{67} +0.0783137 q^{68} -2.59585 q^{69} +15.9280 q^{70} -6.31375 q^{71} +9.95848 q^{72} -7.03766 q^{73} -1.95126 q^{74} -37.8701 q^{75} +9.11282 q^{76} +4.43529 q^{77} +2.95990 q^{78} +3.77644 q^{79} -2.90362 q^{80} -6.23932 q^{81} -0.657130 q^{82} -0.317021 q^{83} +16.3289 q^{84} +0.251486 q^{85} -4.29814 q^{86} -2.59585 q^{87} +2.58864 q^{88} +10.6212 q^{89} +13.0468 q^{90} +6.59991 q^{91} -1.37825 q^{92} +13.9014 q^{93} +5.99682 q^{94} +29.2637 q^{95} +15.1725 q^{96} +2.19178 q^{97} -10.9056 q^{98} +3.63299 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9} - 6 q^{10} - 17 q^{12} - 13 q^{13} - 12 q^{14} + 2 q^{15} - 5 q^{16} - 22 q^{17} + 12 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 3 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 25 q^{26} - 24 q^{27} + 19 q^{28} + 10 q^{29} - 3 q^{30} - 22 q^{31} - 31 q^{32} - 9 q^{33} + 13 q^{34} - 15 q^{35} + 19 q^{36} - 9 q^{37} - 10 q^{38} + 4 q^{39} - 6 q^{40} - 25 q^{41} - 34 q^{42} + 3 q^{43} - 27 q^{44} - 28 q^{45} - 3 q^{46} - 17 q^{47} - 3 q^{48} + 17 q^{49} + 2 q^{50} + 38 q^{51} - 18 q^{52} - 43 q^{53} - 47 q^{54} - 11 q^{55} - 7 q^{56} + 18 q^{57} - 3 q^{58} - 7 q^{59} - 21 q^{60} - 6 q^{61} + 3 q^{62} + 11 q^{63} + 33 q^{64} + 11 q^{65} + 55 q^{66} + 11 q^{67} - 51 q^{68} - 9 q^{69} + 34 q^{70} - 17 q^{71} + 34 q^{72} - 44 q^{73} + 9 q^{74} + q^{75} + 24 q^{76} - 71 q^{77} + 38 q^{78} + 5 q^{79} + 38 q^{80} + 18 q^{81} + 33 q^{82} - 32 q^{83} + 14 q^{84} + 16 q^{85} - 9 q^{86} - 9 q^{87} + 18 q^{88} - 10 q^{89} - 9 q^{90} - 3 q^{91} + 9 q^{92} - 8 q^{93} + 47 q^{94} - 8 q^{95} + 60 q^{96} + 6 q^{97} - 73 q^{98} + 26 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9 - 6 * q^10 - 17 * q^12 - 13 * q^13 - 12 * q^14 + 2 * q^15 - 5 * q^16 - 22 * q^17 + 12 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 3 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 25 * q^26 - 24 * q^27 + 19 * q^28 + 10 * q^29 - 3 * q^30 - 22 * q^31 - 31 * q^32 - 9 * q^33 + 13 * q^34 - 15 * q^35 + 19 * q^36 - 9 * q^37 - 10 * q^38 + 4 * q^39 - 6 * q^40 - 25 * q^41 - 34 * q^42 + 3 * q^43 - 27 * q^44 - 28 * q^45 - 3 * q^46 - 17 * q^47 - 3 * q^48 + 17 * q^49 + 2 * q^50 + 38 * q^51 - 18 * q^52 - 43 * q^53 - 47 * q^54 - 11 * q^55 - 7 * q^56 + 18 * q^57 - 3 * q^58 - 7 * q^59 - 21 * q^60 - 6 * q^61 + 3 * q^62 + 11 * q^63 + 33 * q^64 + 11 * q^65 + 55 * q^66 + 11 * q^67 - 51 * q^68 - 9 * q^69 + 34 * q^70 - 17 * q^71 + 34 * q^72 - 44 * q^73 + 9 * q^74 + q^75 + 24 * q^76 - 71 * q^77 + 38 * q^78 + 5 * q^79 + 38 * q^80 + 18 * q^81 + 33 * q^82 - 32 * q^83 + 14 * q^84 + 16 * q^85 - 9 * q^86 - 9 * q^87 + 18 * q^88 - 10 * q^89 - 9 * q^90 - 3 * q^91 + 9 * q^92 - 8 * q^93 + 47 * q^94 - 8 * q^95 + 60 * q^96 + 6 * q^97 - 73 * q^98 + 26 * 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 $

$2$	−0.788514	−0.557564	−0.278782	−	0.960354i	$-0.589931\pi$
$2$	−0.788514	−0.557564	−0.278782	+	0.960354i	$0.589931\pi$
$3$	−2.59585	−1.49872	−0.749358	−	0.662165i	$-0.769638\pi$
$3$	−2.59585	−1.49872	−0.749358	+	0.662165i	$0.769638\pi$
$4$	−1.37825	−0.689123
$5$	−4.42591	−1.97933	−0.989663	−	0.143410i	$-0.954193\pi$
$5$	−4.42591	−1.97933	−0.989663	+	0.143410i	$0.954193\pi$
$6$	2.04687	0.835630
$7$	4.56405	1.72505	0.862524	−	0.506016i	$-0.168882\pi$
$7$	4.56405	1.72505	0.862524	+	0.506016i	$0.168882\pi$
$8$	2.66379	0.941794
$9$	3.73846	1.24615
$10$	3.48989	1.10360
$11$	0.971788	0.293005	0.146503	−	0.989210i	$-0.453198\pi$
$11$	0.971788	0.293005	0.146503	+	0.989210i	$0.453198\pi$
$12$	3.57772	1.03280
$13$	1.44606	0.401066	0.200533	−	0.979687i	$-0.435733\pi$
$13$	1.44606	0.401066	0.200533	+	0.979687i	$0.435733\pi$
$14$	−3.59882	−0.961825
$15$	11.4890	2.96645
$16$	0.656051	0.164013
$17$	−0.0568213	−0.0137812	−0.00689059	−	0.999976i	$-0.502193\pi$
$17$	−0.0568213	−0.0137812	−0.00689059	+	0.999976i	$0.502193\pi$
$18$	−2.94783	−0.694809
$19$	−6.61190	−1.51687	−0.758437	−	0.651747i	$-0.774037\pi$
$19$	−6.61190	−1.51687	−0.758437	+	0.651747i	$0.774037\pi$
$20$	6.09999	1.36400
$21$	−11.8476	−2.58536
$22$	−0.766268	−0.163369
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−6.91482	−1.41148
$25$	14.5887	2.91773
$26$	−1.14024	−0.223620
$27$	−1.91692	−0.368912
$28$	−6.29038	−1.18877
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−9.05925	−1.65399
$31$	−5.35524	−0.961829	−0.480915	−	0.876767i	$-0.659695\pi$
$31$	−5.35524	−0.961829	−0.480915	+	0.876767i	$0.659695\pi$
$32$	−5.84489	−1.03324
$33$	−2.52262	−0.439132
$34$	0.0448044	0.00768389
$35$	−20.2001	−3.41443
$36$	−5.15251	−0.858752
$37$	2.47461	0.406823	0.203411	−	0.979093i	$-0.434797\pi$
$37$	2.47461	0.406823	0.203411	+	0.979093i	$0.434797\pi$
$38$	5.21357	0.845754
$39$	−3.75377	−0.601085
$40$	−11.7897	−1.86412
$41$	0.833377	0.130152	0.0650758	−	0.997880i	$-0.479271\pi$
$41$	0.833377	0.130152	0.0650758	+	0.997880i	$0.479271\pi$
$42$	9.34200	1.44150
$43$	5.45093	0.831260	0.415630	−	0.909534i	$-0.363561\pi$
$43$	5.45093	0.831260	0.415630	+	0.909534i	$0.363561\pi$
$44$	−1.33936	−0.201916
$45$	−16.5461	−2.46654
$46$	−0.788514	−0.116260
$47$	−7.60521	−1.10933	−0.554667	−	0.832072i	$-0.687154\pi$
$47$	−7.60521	−1.10933	−0.554667	+	0.832072i	$0.687154\pi$
$48$	−1.70301	−0.245809
$49$	13.8305	1.97579
$50$	−11.5034	−1.62682
$51$	0.147500	0.0206541
$52$	−1.99303	−0.276384
$53$	−13.0511	−1.79271	−0.896355	−	0.443337i	$-0.853794\pi$
$53$	−13.0511	−1.79271	−0.896355	+	0.443337i	$0.853794\pi$
$54$	1.51152	0.205692
$55$	−4.30104	−0.579953
$56$	12.1577	1.62464
$57$	17.1635	2.27336
$58$	−0.788514	−0.103537
$59$	0.684766	0.0891490	0.0445745	−	0.999006i	$-0.485807\pi$
$59$	0.684766	0.0891490	0.0445745	+	0.999006i	$0.485807\pi$
$60$	−15.8347	−2.04425
$61$	4.29402	0.549793	0.274897	−	0.961474i	$-0.411356\pi$
$61$	4.29402	0.549793	0.274897	+	0.961474i	$0.411356\pi$
$62$	4.22268	0.536281
$63$	17.0625	2.14967
$64$	3.29668	0.412085
$65$	−6.40015	−0.793841
$66$	1.98912	0.244844
$67$	7.51469	0.918066	0.459033	−	0.888419i	$-0.348196\pi$
$67$	7.51469	0.918066	0.459033	+	0.888419i	$0.348196\pi$
$68$	0.0783137	0.00949693
$69$	−2.59585	−0.312504
$70$	15.9280	1.90377
$71$	−6.31375	−0.749305	−0.374652	−	0.927165i	$-0.622238\pi$
$71$	−6.31375	−0.749305	−0.374652	+	0.927165i	$0.622238\pi$
$72$	9.95848	1.17362
$73$	−7.03766	−0.823696	−0.411848	−	0.911253i	$-0.635116\pi$
$73$	−7.03766	−0.823696	−0.411848	+	0.911253i	$0.635116\pi$
$74$	−1.95126	−0.226830
$75$	−37.8701	−4.37286
$76$	9.11282	1.04531
$77$	4.43529	0.505448
$78$	2.95990	0.335143
$79$	3.77644	0.424882	0.212441	−	0.977174i	$-0.431859\pi$
$79$	3.77644	0.424882	0.212441	+	0.977174i	$0.431859\pi$
$80$	−2.90362	−0.324635
$81$	−6.23932	−0.693257
$82$	−0.657130	−0.0725679
$83$	−0.317021	−0.0347976	−0.0173988	−	0.999849i	$-0.505538\pi$
$83$	−0.317021	−0.0347976	−0.0173988	+	0.999849i	$0.505538\pi$
$84$	16.3289	1.78163
$85$	0.251486	0.0272775
$86$	−4.29814	−0.463480
$87$	−2.59585	−0.278305
$88$	2.58864	0.275950
$89$	10.6212	1.12585	0.562923	−	0.826509i	$-0.309677\pi$
$89$	10.6212	1.12585	0.562923	+	0.826509i	$0.309677\pi$
$90$	13.0468	1.37525
$91$	6.59991	0.691859
$92$	−1.37825	−0.143692
$93$	13.9014	1.44151
$94$	5.99682	0.618524
$95$	29.2637	3.00239
$96$	15.1725	1.54854
$97$	2.19178	0.222542	0.111271	−	0.993790i	$-0.464508\pi$
$97$	2.19178	0.222542	0.111271	+	0.993790i	$0.464508\pi$
$98$	−10.9056	−1.10163
$99$	3.63299	0.365129
$100$	−20.1068	−2.01068
$101$	−10.6242	−1.05715	−0.528575	−	0.848886i	$-0.677274\pi$
$101$	−10.6242	−1.05715	−0.528575	+	0.848886i	$0.677274\pi$
$102$	−0.116306	−0.0115160
$103$	−14.3802	−1.41692	−0.708461	−	0.705750i	$-0.750610\pi$
$103$	−14.3802	−1.41692	−0.708461	+	0.705750i	$0.750610\pi$
$104$	3.85202	0.377722
$105$	52.4364	5.11727
$106$	10.2910	0.999550
$107$	3.32297	0.321244	0.160622	−	0.987016i	$-0.448650\pi$
$107$	3.32297	0.321244	0.160622	+	0.987016i	$0.448650\pi$
$108$	2.64199	0.254226
$109$	−11.9413	−1.14377	−0.571883	−	0.820335i	$-0.693787\pi$
$109$	−11.9413	−1.14377	−0.571883	+	0.820335i	$0.693787\pi$
$110$	3.39143	0.323361
$111$	−6.42372	−0.609712
$112$	2.99425	0.282930
$113$	−20.2976	−1.90944	−0.954719	−	0.297510i	$-0.903844\pi$
$113$	−20.2976	−1.90944	−0.954719	+	0.297510i	$0.903844\pi$
$114$	−13.5337	−1.26755
$115$	−4.42591	−0.412718
$116$	−1.37825	−0.127967
$117$	5.40605	0.499789
$118$	−0.539948	−0.0497062
$119$	−0.259335	−0.0237732
$120$	30.6044	2.79378
$121$	−10.0556	−0.914148
$122$	−3.38590	−0.306545
$123$	−2.16333	−0.195060
$124$	7.38083	0.662818
$125$	−42.4386	−3.79582
$126$	−13.4540	−1.19858
$127$	7.57249	0.671950	0.335975	−	0.941871i	$-0.390934\pi$
$127$	7.57249	0.671950	0.335975	+	0.941871i	$0.390934\pi$
$128$	9.09031	0.803477
$129$	−14.1498	−1.24582
$130$	5.04661	0.442617
$131$	−12.0704	−1.05460	−0.527298	−	0.849681i	$-0.676795\pi$
$131$	−12.0704	−1.05460	−0.527298	+	0.849681i	$0.676795\pi$
$132$	3.47679	0.302616
$133$	−30.1770	−2.61668
$134$	−5.92544	−0.511880
$135$	8.48413	0.730198
$136$	−0.151360	−0.0129790
$137$	−5.96681	−0.509779	−0.254890	−	0.966970i	$-0.582039\pi$
$137$	−5.96681	−0.509779	−0.254890	+	0.966970i	$0.582039\pi$
$138$	2.04687	0.174241
$139$	−5.58706	−0.473888	−0.236944	−	0.971523i	$-0.576146\pi$
$139$	−5.58706	−0.473888	−0.236944	+	0.971523i	$0.576146\pi$
$140$	27.8407	2.35296
$141$	19.7420	1.66258
$142$	4.97849	0.417785
$143$	1.40527	0.117514
$144$	2.45262	0.204385
$145$	−4.42591	−0.367552
$146$	5.54929	0.459263
$147$	−35.9021	−2.96115
$148$	−3.41062	−0.280351
$149$	7.26437	0.595120	0.297560	−	0.954703i	$-0.403827\pi$
$149$	7.26437	0.595120	0.297560	+	0.954703i	$0.403827\pi$
$150$	29.8611	2.43815
$151$	7.50901	0.611075	0.305537	−	0.952180i	$-0.401164\pi$
$151$	7.50901	0.611075	0.305537	+	0.952180i	$0.401164\pi$
$152$	−17.6127	−1.42858
$153$	−0.212424	−0.0171735
$154$	−3.49729	−0.281819
$155$	23.7018	1.90377
$156$	5.17362	0.414221
$157$	−14.7483	−1.17704	−0.588520	−	0.808483i	$-0.700289\pi$
$157$	−14.7483	−1.17704	−0.588520	+	0.808483i	$0.700289\pi$
$158$	−2.97778	−0.236899
$159$	33.8788	2.68676
$160$	25.8690	2.04512
$161$	4.56405	0.359697
$162$	4.91979	0.386535
$163$	−19.5997	−1.53517	−0.767585	−	0.640947i	$-0.778542\pi$
$163$	−19.5997	−1.53517	−0.767585	+	0.640947i	$0.778542\pi$
$164$	−1.14860	−0.0896905
$165$	11.1649	0.869185
$166$	0.249976	0.0194019
$167$	21.8892	1.69384	0.846919	−	0.531722i	$-0.178455\pi$
$167$	21.8892	1.69384	0.846919	+	0.531722i	$0.178455\pi$
$168$	−31.5596	−2.43487
$169$	−10.9089	−0.839146
$170$	−0.198300	−0.0152089
$171$	−24.7183	−1.89025
$172$	−7.51273	−0.572840
$173$	−20.2451	−1.53920	−0.769602	−	0.638524i	$-0.779545\pi$
$173$	−20.2451	−1.53920	−0.769602	+	0.638524i	$0.779545\pi$
$174$	2.04687	0.155173
$175$	66.5834	5.03323
$176$	0.637542	0.0480566
$177$	−1.77755	−0.133609
$178$	−8.37498	−0.627731
$179$	17.4449	1.30389	0.651945	−	0.758266i	$-0.273953\pi$
$179$	17.4449	1.30389	0.651945	+	0.758266i	$0.273953\pi$
$180$	22.8045	1.69975
$181$	23.8598	1.77348	0.886742	−	0.462264i	$-0.152963\pi$
$181$	23.8598	1.77348	0.886742	+	0.462264i	$0.152963\pi$
$182$	−5.20412	−0.385755
$183$	−11.1467	−0.823985
$184$	2.66379	0.196378
$185$	−10.9524	−0.805235
$186$	−10.9615	−0.803734
$187$	−0.0552182	−0.00403796
$188$	10.4818	0.764467
$189$	−8.74893	−0.636391
$190$	−23.0748	−1.67402
$191$	5.36063	0.387881	0.193941	−	0.981013i	$-0.437873\pi$
$191$	5.36063	0.387881	0.193941	+	0.981013i	$0.437873\pi$
$192$	−8.55770	−0.617599
$193$	−2.28387	−0.164396	−0.0821981	−	0.996616i	$-0.526194\pi$
$193$	−2.28387	−0.164396	−0.0821981	+	0.996616i	$0.526194\pi$
$194$	−1.72825	−0.124081
$195$	16.6139	1.18974
$196$	−19.0619	−1.36156
$197$	−1.45927	−0.103969	−0.0519845	−	0.998648i	$-0.516555\pi$
$197$	−1.45927	−0.103969	−0.0519845	+	0.998648i	$0.516555\pi$
$198$	−2.86466	−0.203583
$199$	18.1387	1.28581	0.642907	−	0.765944i	$-0.277728\pi$
$199$	18.1387	1.28581	0.642907	+	0.765944i	$0.277728\pi$
$200$	38.8612	2.74790
$201$	−19.5070	−1.37592
$202$	8.37736	0.589429
$203$	4.56405	0.320333
$204$	−0.203291	−0.0142332
$205$	−3.68845	−0.257613
$206$	11.3390	0.790024
$207$	3.73846	0.259841
$208$	0.948692	0.0657800
$209$	−6.42536	−0.444451
$210$	−41.3469	−2.85320
$211$	−18.1784	−1.25146	−0.625728	−	0.780041i	$-0.715198\pi$
$211$	−18.1784	−1.25146	−0.625728	+	0.780041i	$0.715198\pi$
$212$	17.9877	1.23540
$213$	16.3896	1.12300
$214$	−2.62021	−0.179114
$215$	−24.1253	−1.64533
$216$	−5.10629	−0.347439
$217$	−24.4416	−1.65920
$218$	9.41587	0.637723
$219$	18.2687	1.23449
$220$	5.92789	0.399659
$221$	−0.0821673	−0.00552717
$222$	5.06519	0.339953
$223$	−5.56544	−0.372689	−0.186345	−	0.982484i	$-0.559664\pi$
$223$	−5.56544	−0.372689	−0.186345	+	0.982484i	$0.559664\pi$
$224$	−26.6764	−1.78239
$225$	54.5391	3.63594
$226$	16.0049	1.06463
$227$	−3.23939	−0.215006	−0.107503	−	0.994205i	$-0.534286\pi$
$227$	−3.23939	−0.215006	−0.107503	+	0.994205i	$0.534286\pi$
$228$	−23.6555	−1.56663
$229$	−19.9421	−1.31781	−0.658906	−	0.752225i	$-0.728980\pi$
$229$	−19.9421	−1.31781	−0.658906	+	0.752225i	$0.728980\pi$
$230$	3.48989	0.230117
$231$	−11.5134	−0.757523
$232$	2.66379	0.174887
$233$	−2.47616	−0.162219	−0.0811093	−	0.996705i	$-0.525846\pi$
$233$	−2.47616	−0.162219	−0.0811093	+	0.996705i	$0.525846\pi$
$234$	−4.26275	−0.278664
$235$	33.6600	2.19573
$236$	−0.943776	−0.0614346
$237$	−9.80308	−0.636779
$238$	0.204489	0.0132551
$239$	15.8645	1.02619	0.513094	−	0.858332i	$-0.328499\pi$
$239$	15.8645	1.02619	0.513094	+	0.858332i	$0.328499\pi$
$240$	7.53738	0.486536
$241$	30.9141	1.99135	0.995675	−	0.0929091i	$-0.0296166\pi$
$241$	30.9141	1.99135	0.995675	+	0.0929091i	$0.0296166\pi$
$242$	7.92901	0.509696
$243$	21.9471	1.40791
$244$	−5.91822	−0.378875
$245$	−61.2128	−3.91074
$246$	1.70581	0.108759
$247$	−9.56123	−0.608367
$248$	−14.2653	−0.905845
$249$	0.822940	0.0521517
$250$	33.4634	2.11641
$251$	−13.7741	−0.869414	−0.434707	−	0.900572i	$-0.643148\pi$
$251$	−13.7741	−0.869414	−0.434707	+	0.900572i	$0.643148\pi$
$252$	−23.5163	−1.48139
$253$	0.971788	0.0610958
$254$	−5.97102	−0.374655
$255$	−0.652820	−0.0408812
$256$	−13.7612	−0.860075
$257$	−15.1706	−0.946314	−0.473157	−	0.880978i	$-0.656886\pi$
$257$	−15.1706	−0.946314	−0.473157	+	0.880978i	$0.656886\pi$
$258$	11.1573	0.694626
$259$	11.2942	0.701789
$260$	8.82098	0.547054
$261$	3.73846	0.231405
$262$	9.51768	0.588004
$263$	−22.0942	−1.36239	−0.681193	−	0.732104i	$-0.738538\pi$
$263$	−22.0942	−1.36239	−0.681193	+	0.732104i	$0.738538\pi$
$264$	−6.71974	−0.413571
$265$	57.7631	3.54836
$266$	23.7950	1.45897
$267$	−27.5711	−1.68733
$268$	−10.3571	−0.632660
$269$	9.47294	0.577575	0.288788	−	0.957393i	$-0.406748\pi$
$269$	9.47294	0.577575	0.288788	+	0.957393i	$0.406748\pi$
$270$	−6.68986	−0.407132
$271$	−4.85162	−0.294715	−0.147358	−	0.989083i	$-0.547077\pi$
$271$	−4.85162	−0.294715	−0.147358	+	0.989083i	$0.547077\pi$
$272$	−0.0372777	−0.00226029
$273$	−17.1324	−1.03690
$274$	4.70492	0.284234
$275$	14.1771	0.854911
$276$	3.57772	0.215354
$277$	2.45191	0.147321	0.0736604	−	0.997283i	$-0.476532\pi$
$277$	2.45191	0.147321	0.0736604	+	0.997283i	$0.476532\pi$
$278$	4.40548	0.264223
$279$	−20.0203	−1.19859
$280$	−53.8088	−3.21569
$281$	−3.85270	−0.229833	−0.114917	−	0.993375i	$-0.536660\pi$
$281$	−3.85270	−0.229833	−0.114917	+	0.993375i	$0.536660\pi$
$282$	−15.5669	−0.926993
$283$	−27.0373	−1.60720	−0.803599	−	0.595171i	$-0.797084\pi$
$283$	−27.0373	−1.60720	−0.803599	+	0.595171i	$0.797084\pi$
$284$	8.70190	0.516363
$285$	−75.9642	−4.49973
$286$	−1.10807	−0.0655218
$287$	3.80358	0.224518
$288$	−21.8509	−1.28758
$289$	−16.9968	−0.999810
$290$	3.48989	0.204934
$291$	−5.68954	−0.333527
$292$	9.69962	0.567627
$293$	23.4393	1.36934	0.684668	−	0.728855i	$-0.259947\pi$
$293$	23.4393	1.36934	0.684668	+	0.728855i	$0.259947\pi$
$294$	28.3093	1.65103
$295$	−3.03071	−0.176455
$296$	6.59184	0.383143
$297$	−1.86284	−0.108093
$298$	−5.72806	−0.331817
$299$	1.44606	0.0836281
$300$	52.1942	3.01344
$301$	24.8783	1.43396
$302$	−5.92096	−0.340713
$303$	27.5790	1.58437
$304$	−4.33774	−0.248787
$305$	−19.0050	−1.08822
$306$	0.167499	0.00957529
$307$	−4.94078	−0.281985	−0.140993	−	0.990011i	$-0.545029\pi$
$307$	−4.94078	−0.281985	−0.140993	+	0.990011i	$0.545029\pi$
$308$	−6.11291	−0.348316
$309$	37.3288	2.12356
$310$	−18.6892	−1.06148
$311$	−0.00645604	−0.000366088 0	−0.000183044	−	1.00000i	$-0.500058\pi$
$311$	−0.00645604	−0.000366088 0	−0.000183044		1.00000i	$0.500058\pi$
$312$	−9.99928	−0.566098
$313$	−16.9277	−0.956811	−0.478406	−	0.878139i	$-0.658785\pi$
$313$	−16.9277	−0.956811	−0.478406	+	0.878139i	$0.658785\pi$
$314$	11.6292	0.656275
$315$	−75.5171	−4.25490
$316$	−5.20486	−0.292796
$317$	−29.7059	−1.66845	−0.834225	−	0.551424i	$-0.814084\pi$
$317$	−29.7059	−1.66845	−0.834225	+	0.551424i	$0.814084\pi$
$318$	−26.7139	−1.49804
$319$	0.971788	0.0544097
$320$	−14.5908	−0.815651
$321$	−8.62595	−0.481454
$322$	−3.59882	−0.200554
$323$	0.375697	0.0209043
$324$	8.59931	0.477739
$325$	21.0962	1.17020
$326$	15.4547	0.855955
$327$	30.9978	1.71418
$328$	2.21995	0.122576
$329$	−34.7106	−1.91366
$330$	−8.80367	−0.484626
$331$	−1.81835	−0.0999455	−0.0499728	−	0.998751i	$-0.515913\pi$
$331$	−1.81835	−0.0999455	−0.0499728	+	0.998751i	$0.515913\pi$
$332$	0.436933	0.0239798
$333$	9.25121	0.506963
$334$	−17.2599	−0.944422
$335$	−33.2593	−1.81715
$336$	−7.77263	−0.424032
$337$	−6.95659	−0.378950	−0.189475	−	0.981886i	$-0.560679\pi$
$337$	−6.95659	−0.378950	−0.189475	+	0.981886i	$0.560679\pi$
$338$	8.60182	0.467877
$339$	52.6896	2.86171
$340$	−0.346609	−0.0187975
$341$	−5.20416	−0.281821
$342$	19.4907	1.05394
$343$	31.1750	1.68329
$344$	14.5202	0.782875
$345$	11.4890	0.618548
$346$	15.9635	0.858204
$347$	22.6284	1.21475	0.607377	−	0.794414i	$-0.292222\pi$
$347$	22.6284	1.21475	0.607377	+	0.794414i	$0.292222\pi$
$348$	3.57772	0.191786
$349$	19.8304	1.06150	0.530749	−	0.847529i	$-0.321911\pi$
$349$	19.8304	1.06150	0.530749	+	0.847529i	$0.321911\pi$
$350$	−52.5020	−2.80635
$351$	−2.77200	−0.147958
$352$	−5.68000	−0.302745
$353$	0.979999	0.0521601	0.0260801	−	0.999660i	$-0.491698\pi$
$353$	0.979999	0.0521601	0.0260801	+	0.999660i	$0.491698\pi$
$354$	1.40163	0.0744956
$355$	27.9441	1.48312
$356$	−14.6386	−0.775847
$357$	0.673196	0.0356293
$358$	−13.7555	−0.727002
$359$	−17.3119	−0.913688	−0.456844	−	0.889547i	$-0.651020\pi$
$359$	−17.3119	−0.913688	−0.456844	+	0.889547i	$0.651020\pi$
$360$	−44.0753	−2.32297
$361$	24.7172	1.30090
$362$	−18.8138	−0.988831
$363$	26.1029	1.37005
$364$	−9.09630	−0.476776
$365$	31.1480	1.63036
$366$	8.78930	0.459424
$367$	−11.0013	−0.574263	−0.287131	−	0.957891i	$-0.592702\pi$
$367$	−11.0013	−0.574263	−0.287131	+	0.957891i	$0.592702\pi$
$368$	0.656051	0.0341990
$369$	3.11554	0.162189
$370$	8.63611	0.448970
$371$	−59.5660	−3.09251
$372$	−19.1596	−0.993377
$373$	−29.7538	−1.54059	−0.770297	−	0.637685i	$-0.779892\pi$
$373$	−29.7538	−1.54059	−0.770297	+	0.637685i	$0.779892\pi$
$374$	0.0435404	0.00225142
$375$	110.164	5.68886
$376$	−20.2587	−1.04476
$377$	1.44606	0.0744761
$378$	6.89866	0.354829
$379$	−12.4190	−0.637919	−0.318959	−	0.947768i	$-0.603333\pi$
$379$	−12.4190	−0.637919	−0.318959	+	0.947768i	$0.603333\pi$
$380$	−40.3325	−2.06901
$381$	−19.6571	−1.00706
$382$	−4.22693	−0.216269
$383$	10.6566	0.544525	0.272263	−	0.962223i	$-0.412228\pi$
$383$	10.6566	0.544525	0.272263	+	0.962223i	$0.412228\pi$
$384$	−23.5971	−1.20419
$385$	−19.6302	−1.00045
$386$	1.80086	0.0916614
$387$	20.3781	1.03588
$388$	−3.02081	−0.153359
$389$	13.9256	0.706055	0.353028	−	0.935613i	$-0.385152\pi$
$389$	13.9256	0.706055	0.353028	+	0.935613i	$0.385152\pi$
$390$	−13.1003	−0.663358
$391$	−0.0568213	−0.00287358
$392$	36.8417	1.86079
$393$	31.3330	1.58054
$394$	1.15066	0.0579693
$395$	−16.7142	−0.840981
$396$	−5.00715	−0.251619
$397$	30.0646	1.50890	0.754449	−	0.656359i	$-0.227904\pi$
$397$	30.0646	1.50890	0.754449	+	0.656359i	$0.227904\pi$
$398$	−14.3026	−0.716924
$399$	78.3351	3.92166
$400$	9.57092	0.478546
$401$	20.6876	1.03309	0.516544	−	0.856260i	$-0.327218\pi$
$401$	20.6876	1.03309	0.516544	+	0.856260i	$0.327218\pi$
$402$	15.3816	0.767163
$403$	−7.74402	−0.385757
$404$	14.6428	0.728507
$405$	27.6146	1.37218
$406$	−3.59882	−0.178606
$407$	2.40479	0.119201
$408$	0.392909	0.0194519
$409$	−5.74910	−0.284275	−0.142137	−	0.989847i	$-0.545397\pi$
$409$	−5.74910	−0.284275	−0.142137	+	0.989847i	$0.545397\pi$
$410$	2.90840	0.143635
$411$	15.4890	0.764015
$412$	19.8194	0.976433
$413$	3.12531	0.153786
$414$	−2.94783	−0.144878
$415$	1.40311	0.0688758
$416$	−8.45210	−0.414398
$417$	14.5032	0.710225
$418$	5.06649	0.247810
$419$	−2.93195	−0.143235	−0.0716176	−	0.997432i	$-0.522816\pi$
$419$	−2.93195	−0.143235	−0.0716176	+	0.997432i	$0.522816\pi$
$420$	−72.2703	−3.52643
$421$	−16.2930	−0.794072	−0.397036	−	0.917803i	$-0.629961\pi$
$421$	−16.2930	−0.794072	−0.397036	+	0.917803i	$0.629961\pi$
$422$	14.3340	0.697766
$423$	−28.4317	−1.38240
$424$	−34.7655	−1.68836
$425$	−0.828947	−0.0402098
$426$	−12.9234	−0.626142
$427$	19.5981	0.948420
$428$	−4.57987	−0.221376
$429$	−3.64787	−0.176121
$430$	19.0232	0.917379
$431$	−12.6223	−0.607997	−0.303998	−	0.952673i	$-0.598322\pi$
$431$	−12.6223	−0.607997	−0.303998	+	0.952673i	$0.598322\pi$
$432$	−1.25760	−0.0605063
$433$	−25.7176	−1.23591	−0.617954	−	0.786214i	$-0.712038\pi$
$433$	−25.7176	−1.23591	−0.617954	+	0.786214i	$0.712038\pi$
$434$	19.2725	0.925111
$435$	11.4890	0.550856
$436$	16.4580	0.788196
$437$	−6.61190	−0.316290
$438$	−14.4052	−0.688305
$439$	−24.1748	−1.15380	−0.576901	−	0.816814i	$-0.695738\pi$
$439$	−24.1748	−1.15380	−0.576901	+	0.816814i	$0.695738\pi$
$440$	−11.4571	−0.546196
$441$	51.7049	2.46214
$442$	0.0647900	0.00308175
$443$	12.5815	0.597765	0.298882	−	0.954290i	$-0.403386\pi$
$443$	12.5815	0.597765	0.298882	+	0.954290i	$0.403386\pi$
$444$	8.85346	0.420167
$445$	−47.0085	−2.22842
$446$	4.38842	0.207798
$447$	−18.8572	−0.891916
$448$	15.0462	0.710867
$449$	−19.8996	−0.939120	−0.469560	−	0.882901i	$-0.655587\pi$
$449$	−19.8996	−0.939120	−0.469560	+	0.882901i	$0.655587\pi$
$450$	−43.0049	−2.02727
$451$	0.809866	0.0381351
$452$	27.9751	1.31584
$453$	−19.4923	−0.915828
$454$	2.55431	0.119880
$455$	−29.2106	−1.36941
$456$	45.7201	2.14104
$457$	−6.35371	−0.297214	−0.148607	−	0.988896i	$-0.547479\pi$
$457$	−6.35371	−0.297214	−0.148607	+	0.988896i	$0.547479\pi$
$458$	15.7246	0.734764
$459$	0.108922	0.00508405
$460$	6.09999	0.284413
$461$	−17.0533	−0.794253	−0.397126	−	0.917764i	$-0.629993\pi$
$461$	−17.0533	−0.794253	−0.397126	+	0.917764i	$0.629993\pi$
$462$	9.07844	0.422367
$463$	6.39589	0.297242	0.148621	−	0.988894i	$-0.452517\pi$
$463$	6.39589	0.297242	0.148621	+	0.988894i	$0.452517\pi$
$464$	0.656051	0.0304564
$465$	−61.5264	−2.85322
$466$	1.95249	0.0904472
$467$	31.1497	1.44144	0.720718	−	0.693229i	$-0.243812\pi$
$467$	31.1497	1.44144	0.720718	+	0.693229i	$0.243812\pi$
$468$	−7.45086	−0.344416
$469$	34.2974	1.58371
$470$	−26.5414	−1.22426
$471$	38.2844	1.76405
$472$	1.82408	0.0839600
$473$	5.29715	0.243563
$474$	7.72987	0.355045
$475$	−96.4588	−4.42583
$476$	0.357427	0.0163827
$477$	−48.7911	−2.23399
$478$	−12.5094	−0.572166
$479$	12.4698	0.569760	0.284880	−	0.958563i	$-0.408046\pi$
$479$	12.4698	0.569760	0.284880	+	0.958563i	$0.408046\pi$
$480$	−67.1521	−3.06506
$481$	3.57844	0.163163
$482$	−24.3762	−1.11030
$483$	−11.8476	−0.539085
$484$	13.8591	0.629960
$485$	−9.70063	−0.440483
$486$	−17.3056	−0.784999
$487$	−16.5055	−0.747935	−0.373967	−	0.927442i	$-0.622003\pi$
$487$	−16.5055	−0.747935	−0.373967	+	0.927442i	$0.622003\pi$
$488$	11.4384	0.517792
$489$	50.8781	2.30079
$490$	48.2671	2.18049
$491$	35.0380	1.58124	0.790621	−	0.612306i	$-0.209758\pi$
$491$	35.0380	1.58124	0.790621	+	0.612306i	$0.209758\pi$
$492$	2.98159	0.134421
$493$	−0.0568213	−0.00255910
$494$	7.53917	0.339203
$495$	−16.0793	−0.722709
$496$	−3.51331	−0.157752
$497$	−28.8163	−1.29259
$498$	−0.648900	−0.0290779
$499$	11.4451	0.512353	0.256177	−	0.966630i	$-0.417537\pi$
$499$	11.4451	0.512353	0.256177	+	0.966630i	$0.417537\pi$
$500$	58.4908	2.61579
$501$	−56.8212	−2.53858
$502$	10.8611	0.484754
$503$	−3.49570	−0.155866	−0.0779328	−	0.996959i	$-0.524832\pi$
$503$	−3.49570	−0.155866	−0.0779328	+	0.996959i	$0.524832\pi$
$504$	45.4510	2.02455
$505$	47.0219	2.09245
$506$	−0.766268	−0.0340648
$507$	28.3179	1.25764
$508$	−10.4367	−0.463056
$509$	−40.6943	−1.80374	−0.901872	−	0.432004i	$-0.857807\pi$
$509$	−40.6943	−1.80374	−0.901872	+	0.432004i	$0.857807\pi$
$510$	0.514758	0.0227939
$511$	−32.1202	−1.42091
$512$	−7.32972	−0.323931
$513$	12.6745	0.559593
$514$	11.9622	0.527631
$515$	63.6454	2.80455
$516$	19.5019	0.858525
$517$	−7.39065	−0.325040
$518$	−8.90566	−0.391292
$519$	52.5532	2.30683
$520$	−17.0487	−0.747634
$521$	10.4305	0.456968	0.228484	−	0.973548i	$-0.426623\pi$
$521$	10.4305	0.456968	0.228484	+	0.973548i	$0.426623\pi$
$522$	−2.94783	−0.129023
$523$	31.5770	1.38076	0.690382	−	0.723445i	$-0.257443\pi$
$523$	31.5770	1.38076	0.690382	+	0.723445i	$0.257443\pi$
$524$	16.6360	0.726746
$525$	−172.841	−7.54339
$526$	17.4216	0.759617
$527$	0.304292	0.0132551
$528$	−1.65497	−0.0720232
$529$	1.00000	0.0434783
$530$	−45.5470	−1.97844
$531$	2.55997	0.111093
$532$	41.5914	1.80321
$533$	1.20512	0.0521994
$534$	21.7402	0.940791
$535$	−14.7072	−0.635847
$536$	20.0176	0.864628
$537$	−45.2843	−1.95416
$538$	−7.46955	−0.322035
$539$	13.4404	0.578917
$540$	−11.6932	−0.503196
$541$	6.43644	0.276724	0.138362	−	0.990382i	$-0.455816\pi$
$541$	6.43644	0.276724	0.138362	+	0.990382i	$0.455816\pi$
$542$	3.82557	0.164322
$543$	−61.9365	−2.65795
$544$	0.332114	0.0142393
$545$	52.8510	2.26389
$546$	13.5091	0.578138
$547$	25.8162	1.10382	0.551910	−	0.833904i	$-0.313899\pi$
$547$	25.8162	1.10382	0.551910	+	0.833904i	$0.313899\pi$
$548$	8.22373	0.351300
$549$	16.0530	0.685126
$550$	−11.1788	−0.476667
$551$	−6.61190	−0.281676
$552$	−6.91482	−0.294314
$553$	17.2359	0.732943
$554$	−1.93336	−0.0821408
$555$	28.4308	1.20682
$556$	7.70034	0.326567
$557$	−27.2165	−1.15320	−0.576599	−	0.817027i	$-0.695621\pi$
$557$	−27.2165	−1.15320	−0.576599	+	0.817027i	$0.695621\pi$
$558$	15.7863	0.668288
$559$	7.88240	0.333390
$560$	−13.2523	−0.560011
$561$	0.143338	0.00605175
$562$	3.03791	0.128147
$563$	6.69521	0.282170	0.141085	−	0.989998i	$-0.454941\pi$
$563$	6.69521	0.282170	0.141085	+	0.989998i	$0.454941\pi$
$564$	−27.2093	−1.14572
$565$	89.8353	3.77940
$566$	21.3193	0.896116
$567$	−28.4765	−1.19590
$568$	−16.8185	−0.705690
$569$	−25.6138	−1.07379	−0.536894	−	0.843650i	$-0.680402\pi$
$569$	−25.6138	−1.07379	−0.536894	+	0.843650i	$0.680402\pi$
$570$	59.8988	2.50889
$571$	−11.0344	−0.461775	−0.230887	−	0.972980i	$-0.574163\pi$
$571$	−11.0344	−0.461775	−0.230887	+	0.972980i	$0.574163\pi$
$572$	−1.93680	−0.0809818
$573$	−13.9154	−0.581324
$574$	−2.99917	−0.125183
$575$	14.5887	0.608390
$576$	12.3245	0.513521
$577$	−7.32211	−0.304824	−0.152412	−	0.988317i	$-0.548704\pi$
$577$	−7.32211	−0.304824	−0.152412	+	0.988317i	$0.548704\pi$
$578$	13.4022	0.557458
$579$	5.92858	0.246383
$580$	6.09999	0.253288
$581$	−1.44690	−0.0600275
$582$	4.48629	0.185963
$583$	−12.6829	−0.525273
$584$	−18.7469	−0.775751
$585$	−23.9267	−0.989247
$586$	−18.4822	−0.763492
$587$	−19.5531	−0.807042	−0.403521	−	0.914970i	$-0.632214\pi$
$587$	−19.5531	−0.807042	−0.403521	+	0.914970i	$0.632214\pi$
$588$	49.4819	2.04060
$589$	35.4083	1.45897
$590$	2.38976	0.0983849
$591$	3.78806	0.155820
$592$	1.62347	0.0667241
$593$	8.98149	0.368826	0.184413	−	0.982849i	$-0.440962\pi$
$593$	8.98149	0.368826	0.184413	+	0.982849i	$0.440962\pi$
$594$	1.46888	0.0602688
$595$	1.14779	0.0470550
$596$	−10.0121	−0.410111
$597$	−47.0853	−1.92707
$598$	−1.14024	−0.0466280
$599$	−29.2178	−1.19381	−0.596904	−	0.802313i	$-0.703603\pi$
$599$	−29.2178	−1.19381	−0.596904	+	0.802313i	$0.703603\pi$
$600$	−100.878	−4.11833
$601$	−38.1135	−1.55468	−0.777342	−	0.629079i	$-0.783432\pi$
$601$	−38.1135	−1.55468	−0.777342	+	0.629079i	$0.783432\pi$
$602$	−19.6169	−0.799526
$603$	28.0933	1.14405
$604$	−10.3493	−0.421105
$605$	44.5053	1.80940
$606$	−21.7464	−0.883387
$607$	15.5962	0.633031	0.316516	−	0.948587i	$-0.397487\pi$
$607$	15.5962	0.633031	0.316516	+	0.948587i	$0.397487\pi$
$608$	38.6458	1.56730
$609$	−11.8476	−0.480089
$610$	14.9857	0.606752
$611$	−10.9976	−0.444916
$612$	0.292772	0.0118346
$613$	−24.0287	−0.970511	−0.485255	−	0.874373i	$-0.661273\pi$
$613$	−24.0287	−0.970511	−0.485255	+	0.874373i	$0.661273\pi$
$614$	3.89588	0.157225
$615$	9.57468	0.386088
$616$	11.8147	0.476028
$617$	−3.99551	−0.160853	−0.0804266	−	0.996761i	$-0.525628\pi$
$617$	−3.99551	−0.160853	−0.0804266	+	0.996761i	$0.525628\pi$
$618$	−29.4343	−1.18402
$619$	24.8970	1.00070	0.500348	−	0.865824i	$-0.333205\pi$
$619$	24.8970	1.00070	0.500348	+	0.865824i	$0.333205\pi$
$620$	−32.6669	−1.31193
$621$	−1.91692	−0.0769235
$622$	0.00509068	0.000204118 0
$623$	48.4758	1.94214
$624$	−2.46267	−0.0985856
$625$	114.886	4.59544
$626$	13.3477	0.533483
$627$	16.6793	0.666107
$628$	20.3267	0.811125
$629$	−0.140610	−0.00560650
$630$	59.5463	2.37238
$631$	16.4605	0.655282	0.327641	−	0.944802i	$-0.393746\pi$
$631$	16.4605	0.655282	0.327641	+	0.944802i	$0.393746\pi$
$632$	10.0597	0.400152
$633$	47.1886	1.87558
$634$	23.4235	0.930267
$635$	−33.5152	−1.33001
$636$	−46.6933	−1.85151
$637$	19.9999	0.792424
$638$	−0.766268	−0.0303369
$639$	−23.6037	−0.933748
$640$	−40.2329	−1.59034
$641$	−9.75924	−0.385467	−0.192733	−	0.981251i	$-0.561735\pi$
$641$	−9.75924	−0.385467	−0.192733	+	0.981251i	$0.561735\pi$
$642$	6.80169	0.268441
$643$	4.93677	0.194687	0.0973436	−	0.995251i	$-0.468965\pi$
$643$	4.93677	0.194687	0.0973436	+	0.995251i	$0.468965\pi$
$644$	−6.29038	−0.247876
$645$	62.6259	2.46589
$646$	−0.296242	−0.0116555
$647$	−48.0277	−1.88817	−0.944083	−	0.329709i	$-0.893049\pi$
$647$	−48.0277	−1.88817	−0.944083	+	0.329709i	$0.893049\pi$
$648$	−16.6203	−0.652905
$649$	0.665448	0.0261211
$650$	−16.6346	−0.652464
$651$	63.4468	2.48667
$652$	27.0133	1.05792
$653$	2.66096	0.104132	0.0520658	−	0.998644i	$-0.483419\pi$
$653$	2.66096	0.104132	0.0520658	+	0.998644i	$0.483419\pi$
$654$	−24.4422	−0.955766
$655$	53.4225	2.08739
$656$	0.546738	0.0213465
$657$	−26.3100	−1.02645
$658$	27.3698	1.06698
$659$	23.7591	0.925522	0.462761	−	0.886483i	$-0.346859\pi$
$659$	23.7591	0.925522	0.462761	+	0.886483i	$0.346859\pi$
$660$	−15.3879	−0.598975
$661$	−20.3618	−0.791982	−0.395991	−	0.918254i	$-0.629599\pi$
$661$	−20.3618	−0.791982	−0.395991	+	0.918254i	$0.629599\pi$
$662$	1.43379	0.0557260
$663$	0.213294	0.00828366
$664$	−0.844479	−0.0327721
$665$	133.561	5.17927
$666$	−7.29471	−0.282664
$667$	1.00000	0.0387202
$668$	−30.1687	−1.16726
$669$	14.4471	0.558555
$670$	26.2255	1.01318
$671$	4.17288	0.161092
$672$	69.2480	2.67130
$673$	−12.7272	−0.490597	−0.245298	−	0.969448i	$-0.578886\pi$
$673$	−12.7272	−0.490597	−0.245298	+	0.969448i	$0.578886\pi$
$674$	5.48537	0.211289
$675$	−27.9654	−1.07639
$676$	15.0351	0.578274
$677$	35.3656	1.35921	0.679605	−	0.733578i	$-0.262151\pi$
$677$	35.3656	1.35921	0.679605	+	0.733578i	$0.262151\pi$
$678$	−41.5465	−1.59558
$679$	10.0034	0.383895
$680$	0.669907	0.0256897
$681$	8.40899	0.322233
$682$	4.10355	0.157133
$683$	41.7902	1.59906	0.799528	−	0.600629i	$-0.205083\pi$
$683$	41.7902	1.59906	0.799528	+	0.600629i	$0.205083\pi$
$684$	34.0679	1.30262
$685$	26.4086	1.00902
$686$	−24.5819	−0.938541
$687$	51.7668	1.97503
$688$	3.57609	0.136337
$689$	−18.8728	−0.718995
$690$	−9.05925	−0.344880
$691$	15.8890	0.604445	0.302223	−	0.953237i	$-0.402271\pi$
$691$	15.8890	0.604445	0.302223	+	0.953237i	$0.402271\pi$
$692$	27.9027	1.06070
$693$	16.5811	0.629865
$694$	−17.8428	−0.677303
$695$	24.7278	0.937980
$696$	−6.91482	−0.262106
$697$	−0.0473536	−0.00179364
$698$	−15.6366	−0.591853
$699$	6.42775	0.243120
$700$	−91.7683	−3.46852
$701$	21.3507	0.806405	0.403202	−	0.915111i	$-0.367897\pi$
$701$	21.3507	0.806405	0.403202	+	0.915111i	$0.367897\pi$
$702$	2.18576	0.0824961
$703$	−16.3618	−0.617099
$704$	3.20367	0.120743
$705$	−87.3764	−3.29078
$706$	−0.772743	−0.0290826
$707$	−48.4895	−1.82364
$708$	2.44990	0.0920731
$709$	18.8418	0.707621	0.353810	−	0.935317i	$-0.384886\pi$
$709$	18.8418	0.707621	0.353810	+	0.935317i	$0.384886\pi$
$710$	−22.0343	−0.826933
$711$	14.1180	0.529468
$712$	28.2927	1.06032
$713$	−5.35524	−0.200555
$714$	−0.530825	−0.0198656
$715$	−6.21959	−0.232599
$716$	−24.0433	−0.898540
$717$	−41.1819	−1.53797
$718$	13.6507	0.509439
$719$	−23.9009	−0.891353	−0.445676	−	0.895194i	$-0.647037\pi$
$719$	−23.9009	−0.891353	−0.445676	+	0.895194i	$0.647037\pi$
$720$	−10.8551	−0.404544
$721$	−65.6319	−2.44426
$722$	−19.4899	−0.725337
$723$	−80.2484	−2.98447
$724$	−32.8846	−1.22215
$725$	14.5887	0.541810
$726$	−20.5825	−0.763890
$727$	−10.1899	−0.377921	−0.188961	−	0.981985i	$-0.560512\pi$
$727$	−10.1899	−0.377921	−0.188961	+	0.981985i	$0.560512\pi$
$728$	17.5808	0.651588
$729$	−38.2536	−1.41680
$730$	−24.5607	−0.909031
$731$	−0.309729	−0.0114557
$732$	15.3628	0.567826
$733$	20.2364	0.747449	0.373725	−	0.927540i	$-0.378081\pi$
$733$	20.2364	0.747449	0.373725	+	0.927540i	$0.378081\pi$
$734$	8.67467	0.320188
$735$	158.899	5.86109
$736$	−5.84489	−0.215446
$737$	7.30269	0.268998
$738$	−2.45665	−0.0904306
$739$	−8.48223	−0.312024	−0.156012	−	0.987755i	$-0.549864\pi$
$739$	−8.48223	−0.312024	−0.156012	+	0.987755i	$0.549864\pi$
$740$	15.0951	0.554906
$741$	24.8196	0.911769
$742$	46.9686	1.72427
$743$	−14.3027	−0.524714	−0.262357	−	0.964971i	$-0.584500\pi$
$743$	−14.3027	−0.524714	−0.262357	+	0.964971i	$0.584500\pi$
$744$	37.0305	1.35760
$745$	−32.1514	−1.17794
$746$	23.4613	0.858980
$747$	−1.18517	−0.0433631
$748$	0.0761043	0.00278265
$749$	15.1662	0.554161
$750$	−86.8662	−3.17190
$751$	34.5002	1.25893	0.629465	−	0.777029i	$-0.283274\pi$
$751$	34.5002	1.25893	0.629465	+	0.777029i	$0.283274\pi$
$752$	−4.98941	−0.181945
$753$	35.7556	1.30300
$754$	−1.14024	−0.0415252
$755$	−33.2342	−1.20952
$756$	12.0582	0.438552
$757$	−50.8560	−1.84839	−0.924197	−	0.381916i	$-0.875264\pi$
$757$	−50.8560	−1.84839	−0.924197	+	0.381916i	$0.875264\pi$
$758$	9.79252	0.355680
$759$	−2.52262	−0.0915653
$760$	77.9524	2.82763
$761$	8.04562	0.291654	0.145827	−	0.989310i	$-0.453416\pi$
$761$	8.04562	0.291654	0.145827	+	0.989310i	$0.453416\pi$
$762$	15.4999	0.561501
$763$	−54.5006	−1.97305
$764$	−7.38826	−0.267298
$765$	0.940169	0.0339919
$766$	−8.40286	−0.303608
$767$	0.990217	0.0357547
$768$	35.7221	1.28901
$769$	−26.9814	−0.972972	−0.486486	−	0.873688i	$-0.661722\pi$
$769$	−26.9814	−0.972972	−0.486486	+	0.873688i	$0.661722\pi$
$770$	15.4787	0.557813
$771$	39.3806	1.41826
$772$	3.14773	0.113289
$773$	2.39973	0.0863124	0.0431562	−	0.999068i	$-0.486259\pi$
$773$	2.39973	0.0863124	0.0431562	+	0.999068i	$0.486259\pi$
$774$	−16.0684	−0.577567
$775$	−78.1258	−2.80636
$776$	5.83846	0.209588
$777$	−29.3182	−1.05178
$778$	−10.9805	−0.393671
$779$	−5.51021	−0.197424
$780$	−22.8980	−0.819879
$781$	−6.13563	−0.219550
$782$	0.0448044	0.00160220
$783$	−1.91692	−0.0685053
$784$	9.07355	0.324055
$785$	65.2745	2.32975
$786$	−24.7065	−0.881252
$787$	−8.26011	−0.294441	−0.147221	−	0.989104i	$-0.547033\pi$
$787$	−8.26011	−0.294441	−0.147221	+	0.989104i	$0.547033\pi$
$788$	2.01124	0.0716474
$789$	57.3533	2.04183
$790$	13.1794	0.468901
$791$	−92.6392	−3.29387
$792$	9.67753	0.343876
$793$	6.20944	0.220504
$794$	−23.7063	−0.841307
$795$	−149.945	−5.31798
$796$	−24.9995	−0.886084
$797$	−27.0627	−0.958609	−0.479304	−	0.877649i	$-0.659111\pi$
$797$	−27.0627	−0.958609	−0.479304	+	0.877649i	$0.659111\pi$
$798$	−61.7684	−2.18658
$799$	0.432138	0.0152879
$800$	−85.2693	−3.01472
$801$	39.7070	1.40298
$802$	−16.3125	−0.576013
$803$	−6.83911	−0.241347
$804$	26.8855	0.948178
$805$	−20.2001	−0.711959
$806$	6.10627	0.215084
$807$	−24.5904	−0.865622
$808$	−28.3008	−0.995618
$809$	51.5850	1.81363	0.906816	−	0.421527i	$-0.138506\pi$
$809$	51.5850	1.81363	0.906816	+	0.421527i	$0.138506\pi$
$810$	−21.7745	−0.765079
$811$	−7.79381	−0.273678	−0.136839	−	0.990593i	$-0.543694\pi$
$811$	−7.79381	−0.273678	−0.136839	+	0.990593i	$0.543694\pi$
$812$	−6.29038	−0.220749
$813$	12.5941	0.441695
$814$	−1.89621	−0.0664622
$815$	86.7467	3.03860
$816$	0.0967674	0.00338754
$817$	−36.0410	−1.26092
$818$	4.53325	0.158501
$819$	24.6735	0.862161
$820$	5.08359	0.177527
$821$	−16.1824	−0.564768	−0.282384	−	0.959301i	$-0.591125\pi$
$821$	−16.1824	−0.564768	−0.282384	+	0.959301i	$0.591125\pi$
$822$	−12.2133	−0.425987
$823$	−30.4948	−1.06298	−0.531491	−	0.847064i	$-0.678368\pi$
$823$	−30.4948	−1.06298	−0.531491	+	0.847064i	$0.678368\pi$
$824$	−38.3058	−1.33445
$825$	−36.8017	−1.28127
$826$	−2.46435	−0.0857457
$827$	25.4166	0.883821	0.441910	−	0.897059i	$-0.354301\pi$
$827$	25.4166	0.883821	0.441910	+	0.897059i	$0.354301\pi$
$828$	−5.15251	−0.179062
$829$	−12.0734	−0.419325	−0.209662	−	0.977774i	$-0.567236\pi$
$829$	−12.0734	−0.419325	−0.209662	+	0.977774i	$0.567236\pi$
$830$	−1.10637	−0.0384026
$831$	−6.36479	−0.220792
$832$	4.76721	0.165273
$833$	−0.785870	−0.0272288
$834$	−11.4360	−0.395995
$835$	−96.8796	−3.35266
$836$	8.85572	0.306282
$837$	10.2656	0.354830
$838$	2.31189	0.0798628
$839$	13.2682	0.458070	0.229035	−	0.973418i	$-0.426443\pi$
$839$	13.2682	0.458070	0.229035	+	0.973418i	$0.426443\pi$
$840$	139.680	4.81941
$841$	1.00000	0.0344828
$842$	12.8473	0.442746
$843$	10.0011	0.344455
$844$	25.0544	0.862406
$845$	48.2818	1.66094
$846$	22.4188	0.770775
$847$	−45.8944	−1.57695
$848$	−8.56220	−0.294027
$849$	70.1848	2.40874
$850$	0.653637	0.0224196
$851$	2.47461	0.0848284
$852$	−22.5889	−0.773882
$853$	−23.3140	−0.798257	−0.399128	−	0.916895i	$-0.630687\pi$
$853$	−23.3140	−0.798257	−0.399128	+	0.916895i	$0.630687\pi$
$854$	−15.4534	−0.528805
$855$	109.401	3.74143
$856$	8.85172	0.302545
$857$	8.93197	0.305110	0.152555	−	0.988295i	$-0.451250\pi$
$857$	8.93197	0.305110	0.152555	+	0.988295i	$0.451250\pi$
$858$	2.87640	0.0981986
$859$	32.2563	1.10057	0.550285	−	0.834977i	$-0.314519\pi$
$859$	32.2563	1.10057	0.550285	+	0.834977i	$0.314519\pi$
$860$	33.2506	1.13384
$861$	−9.87353	−0.336489
$862$	9.95290	0.338997
$863$	25.9820	0.884438	0.442219	−	0.896907i	$-0.354191\pi$
$863$	25.9820	0.884438	0.442219	+	0.896907i	$0.354191\pi$
$864$	11.2042	0.381175
$865$	89.6028	3.04659
$866$	20.2787	0.689098
$867$	44.1211	1.49843
$868$	33.6865	1.14339
$869$	3.66990	0.124493
$870$	−9.05925	−0.307137
$871$	10.8667	0.368205
$872$	−31.8091	−1.07719
$873$	8.19388	0.277321
$874$	5.21357	0.176352
$875$	−193.692	−6.54798
$876$	−25.1788	−0.850713
$877$	−38.5168	−1.30062	−0.650310	−	0.759669i	$-0.725361\pi$
$877$	−38.5168	−1.30062	−0.650310	+	0.759669i	$0.725361\pi$
$878$	19.0622	0.643318
$879$	−60.8449	−2.05225
$880$	−2.82170	−0.0951197
$881$	−9.03179	−0.304289	−0.152144	−	0.988358i	$-0.548618\pi$
$881$	−9.03179	−0.304289	−0.152144	+	0.988358i	$0.548618\pi$
$882$	−40.7700	−1.37280
$883$	14.7822	0.497461	0.248731	−	0.968573i	$-0.419987\pi$
$883$	14.7822	0.497461	0.248731	+	0.968573i	$0.419987\pi$
$884$	0.113247	0.00380890
$885$	7.86729	0.264456
$886$	−9.92069	−0.333292
$887$	−22.3455	−0.750288	−0.375144	−	0.926967i	$-0.622407\pi$
$887$	−22.3455	−0.750288	−0.375144	+	0.926967i	$0.622407\pi$
$888$	−17.1115	−0.574223
$889$	34.5612	1.15915
$890$	37.0669	1.24249
$891$	−6.06329	−0.203128
$892$	7.67054	0.256829
$893$	50.2849	1.68272
$894$	14.8692	0.497300
$895$	−77.2093	−2.58082
$896$	41.4886	1.38604
$897$	−3.75377	−0.125335
$898$	15.6911	0.523619
$899$	−5.35524	−0.178607
$900$	−75.1683	−2.50561
$901$	0.741582	0.0247057
$902$	−0.638591	−0.0212627
$903$	−64.5805	−2.14910
$904$	−54.0686	−1.79830
$905$	−105.601	−3.51031
$906$	15.3699	0.510632
$907$	28.3340	0.940815	0.470408	−	0.882449i	$-0.344107\pi$
$907$	28.3340	0.940815	0.470408	+	0.882449i	$0.344107\pi$
$908$	4.46468	0.148165
$909$	−39.7182	−1.31737
$910$	23.0330	0.763536
$911$	48.1142	1.59409	0.797047	−	0.603918i	$-0.206395\pi$
$911$	48.1142	1.59409	0.797047	+	0.603918i	$0.206395\pi$
$912$	11.2601	0.372861
$913$	−0.308077	−0.0101959
$914$	5.00999	0.165716
$915$	49.3341	1.63093
$916$	27.4851	0.908134
$917$	−55.0899	−1.81923
$918$	−0.0858866	−0.00283468
$919$	−40.0565	−1.32134	−0.660670	−	0.750676i	$-0.729728\pi$
$919$	−40.0565	−1.32134	−0.660670	+	0.750676i	$0.729728\pi$
$920$	−11.7897	−0.388695
$921$	12.8256	0.422616
$922$	13.4468	0.442847
$923$	−9.13010	−0.300521
$924$	15.8682	0.522026
$925$	36.1012	1.18700
$926$	−5.04325	−0.165731
$927$	−53.7597	−1.76570
$928$	−5.84489	−0.191868
$929$	−1.53798	−0.0504594	−0.0252297	−	0.999682i	$-0.508032\pi$
$929$	−1.53798	−0.0504594	−0.0252297	+	0.999682i	$0.508032\pi$
$930$	48.5144	1.59085
$931$	−91.4462	−2.99703
$932$	3.41276	0.111789
$933$	0.0167589	0.000548663 0
$934$	−24.5620	−0.803692
$935$	0.244391	0.00799244
$936$	14.4006	0.470698
$937$	−26.3637	−0.861265	−0.430633	−	0.902527i	$-0.641709\pi$
$937$	−26.3637	−0.861265	−0.430633	+	0.902527i	$0.641709\pi$
$938$	−27.0440	−0.883018
$939$	43.9419	1.43399
$940$	−46.3917	−1.51313
$941$	25.2287	0.822431	0.411215	−	0.911538i	$-0.365104\pi$
$941$	25.2287	0.822431	0.411215	+	0.911538i	$0.365104\pi$
$942$	−30.1878	−0.983570
$943$	0.833377	0.0271385
$944$	0.449242	0.0146216
$945$	38.7220	1.25963
$946$	−4.17688	−0.135802
$947$	−29.2642	−0.950960	−0.475480	−	0.879727i	$-0.657726\pi$
$947$	−29.2642	−0.950960	−0.475480	+	0.879727i	$0.657726\pi$
$948$	13.5111	0.438819
$949$	−10.1769	−0.330356
$950$	76.0591	2.46768
$951$	77.1122	2.50053
$952$	−0.690816	−0.0223895
$953$	8.99660	0.291429	0.145714	−	0.989327i	$-0.453452\pi$
$953$	8.99660	0.291429	0.145714	+	0.989327i	$0.453452\pi$
$954$	38.4724	1.24559
$955$	−23.7257	−0.767744
$956$	−21.8652	−0.707170
$957$	−2.52262	−0.0815447
$958$	−9.83261	−0.317677
$959$	−27.2328	−0.879394
$960$	37.8756	1.22243
$961$	−2.32141	−0.0748842
$962$	−2.82165	−0.0909737
$963$	12.4228	0.400319
$964$	−42.6072	−1.37228
$965$	10.1082	0.325394
$966$	9.34200	0.300574
$967$	−33.0807	−1.06380	−0.531902	−	0.846806i	$-0.678523\pi$
$967$	−33.0807	−1.06380	−0.531902	+	0.846806i	$0.678523\pi$
$968$	−26.7861	−0.860939
$969$	−0.975253	−0.0313296
$970$	7.64908	0.245597
$971$	24.4046	0.783181	0.391590	−	0.920140i	$-0.371925\pi$
$971$	24.4046	0.783181	0.391590	+	0.920140i	$0.371925\pi$
$972$	−30.2485	−0.970222
$973$	−25.4996	−0.817481
$974$	13.0148	0.417021
$975$	−54.7626	−1.75381
$976$	2.81710	0.0901731
$977$	24.2885	0.777057	0.388529	−	0.921437i	$-0.372983\pi$
$977$	24.2885	0.777057	0.388529	+	0.921437i	$0.372983\pi$
$978$	−40.1181	−1.28283
$979$	10.3216	0.329879
$980$	84.3662	2.69498
$981$	−44.6419	−1.42531
$982$	−27.6279	−0.881643
$983$	39.1212	1.24777	0.623886	−	0.781515i	$-0.285553\pi$
$983$	39.1212	1.24777	0.623886	+	0.781515i	$0.285553\pi$
$984$	−5.76265	−0.183707
$985$	6.45861	0.205789
$986$	0.0448044	0.00142686
$987$	90.1035	2.86803
$988$	13.1777	0.419239
$989$	5.45093	0.173330
$990$	12.6787	0.402956
$991$	−1.20143	−0.0381648	−0.0190824	−	0.999818i	$-0.506074\pi$
$991$	−1.20143	−0.0381648	−0.0190824	+	0.999818i	$0.506074\pi$
$992$	31.3008	0.993802
$993$	4.72017	0.149790
$994$	22.7221	0.720700
$995$	−80.2800	−2.54505
$996$	−1.13421	−0.0359389
$997$	−13.8251	−0.437845	−0.218923	−	0.975742i	$-0.570254\pi$
$997$	−13.8251	−0.437845	−0.218923	+	0.975742i	$0.570254\pi$
$998$	−9.02463	−0.285670
$999$	−4.74363	−0.150082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.a.1.5	✓	10
3.2	odd	2		6003.2.a.l.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.a.1.5	✓	10	1.1	even	1	trivial
6003.2.a.l.1.6		10	3.2	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-0.788514 q^{2} -2.59585 q^{3} -1.37825 q^{4} -4.42591 q^{5} +2.04687 q^{6} +4.56405 q^{7} +2.66379 q^{8} +3.73846 q^{9} +O(q^{10})\)	\(q-0.788514 q^{2} -2.59585 q^{3} -1.37825 q^{4} -4.42591 q^{5} +2.04687 q^{6} +4.56405 q^{7} +2.66379 q^{8} +3.73846 q^{9} +3.48989 q^{10} +0.971788 q^{11} +3.57772 q^{12} +1.44606 q^{13} -3.59882 q^{14} +11.4890 q^{15} +0.656051 q^{16} -0.0568213 q^{17} -2.94783 q^{18} -6.61190 q^{19} +6.09999 q^{20} -11.8476 q^{21} -0.766268 q^{22} +1.00000 q^{23} -6.91482 q^{24} +14.5887 q^{25} -1.14024 q^{26} -1.91692 q^{27} -6.29038 q^{28} +1.00000 q^{29} -9.05925 q^{30} -5.35524 q^{31} -5.84489 q^{32} -2.52262 q^{33} +0.0448044 q^{34} -20.2001 q^{35} -5.15251 q^{36} +2.47461 q^{37} +5.21357 q^{38} -3.75377 q^{39} -11.7897 q^{40} +0.833377 q^{41} +9.34200 q^{42} +5.45093 q^{43} -1.33936 q^{44} -16.5461 q^{45} -0.788514 q^{46} -7.60521 q^{47} -1.70301 q^{48} +13.8305 q^{49} -11.5034 q^{50} +0.147500 q^{51} -1.99303 q^{52} -13.0511 q^{53} +1.51152 q^{54} -4.30104 q^{55} +12.1577 q^{56} +17.1635 q^{57} -0.788514 q^{58} +0.684766 q^{59} -15.8347 q^{60} +4.29402 q^{61} +4.22268 q^{62} +17.0625 q^{63} +3.29668 q^{64} -6.40015 q^{65} +1.98912 q^{66} +7.51469 q^{67} +0.0783137 q^{68} -2.59585 q^{69} +15.9280 q^{70} -6.31375 q^{71} +9.95848 q^{72} -7.03766 q^{73} -1.95126 q^{74} -37.8701 q^{75} +9.11282 q^{76} +4.43529 q^{77} +2.95990 q^{78} +3.77644 q^{79} -2.90362 q^{80} -6.23932 q^{81} -0.657130 q^{82} -0.317021 q^{83} +16.3289 q^{84} +0.251486 q^{85} -4.29814 q^{86} -2.59585 q^{87} +2.58864 q^{88} +10.6212 q^{89} +13.0468 q^{90} +6.59991 q^{91} -1.37825 q^{92} +13.9014 q^{93} +5.99682 q^{94} +29.2637 q^{95} +15.1725 q^{96} +2.19178 q^{97} -10.9056 q^{98} +3.63299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9} - 6 q^{10} - 17 q^{12} - 13 q^{13} - 12 q^{14} + 2 q^{15} - 5 q^{16} - 22 q^{17} + 12 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 3 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 25 q^{26} - 24 q^{27} + 19 q^{28} + 10 q^{29} - 3 q^{30} - 22 q^{31} - 31 q^{32} - 9 q^{33} + 13 q^{34} - 15 q^{35} + 19 q^{36} - 9 q^{37} - 10 q^{38} + 4 q^{39} - 6 q^{40} - 25 q^{41} - 34 q^{42} + 3 q^{43} - 27 q^{44} - 28 q^{45} - 3 q^{46} - 17 q^{47} - 3 q^{48} + 17 q^{49} + 2 q^{50} + 38 q^{51} - 18 q^{52} - 43 q^{53} - 47 q^{54} - 11 q^{55} - 7 q^{56} + 18 q^{57} - 3 q^{58} - 7 q^{59} - 21 q^{60} - 6 q^{61} + 3 q^{62} + 11 q^{63} + 33 q^{64} + 11 q^{65} + 55 q^{66} + 11 q^{67} - 51 q^{68} - 9 q^{69} + 34 q^{70} - 17 q^{71} + 34 q^{72} - 44 q^{73} + 9 q^{74} + q^{75} + 24 q^{76} - 71 q^{77} + 38 q^{78} + 5 q^{79} + 38 q^{80} + 18 q^{81} + 33 q^{82} - 32 q^{83} + 14 q^{84} + 16 q^{85} - 9 q^{86} - 9 q^{87} + 18 q^{88} - 10 q^{89} - 9 q^{90} - 3 q^{91} + 9 q^{92} - 8 q^{93} + 47 q^{94} - 8 q^{95} + 60 q^{96} + 6 q^{97} - 73 q^{98} + 26 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9 - 6 * q^10 - 17 * q^12 - 13 * q^13 - 12 * q^14 + 2 * q^15 - 5 * q^16 - 22 * q^17 + 12 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 3 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 25 * q^26 - 24 * q^27 + 19 * q^28 + 10 * q^29 - 3 * q^30 - 22 * q^31 - 31 * q^32 - 9 * q^33 + 13 * q^34 - 15 * q^35 + 19 * q^36 - 9 * q^37 - 10 * q^38 + 4 * q^39 - 6 * q^40 - 25 * q^41 - 34 * q^42 + 3 * q^43 - 27 * q^44 - 28 * q^45 - 3 * q^46 - 17 * q^47 - 3 * q^48 + 17 * q^49 + 2 * q^50 + 38 * q^51 - 18 * q^52 - 43 * q^53 - 47 * q^54 - 11 * q^55 - 7 * q^56 + 18 * q^57 - 3 * q^58 - 7 * q^59 - 21 * q^60 - 6 * q^61 + 3 * q^62 + 11 * q^63 + 33 * q^64 + 11 * q^65 + 55 * q^66 + 11 * q^67 - 51 * q^68 - 9 * q^69 + 34 * q^70 - 17 * q^71 + 34 * q^72 - 44 * q^73 + 9 * q^74 + q^75 + 24 * q^76 - 71 * q^77 + 38 * q^78 + 5 * q^79 + 38 * q^80 + 18 * q^81 + 33 * q^82 - 32 * q^83 + 14 * q^84 + 16 * q^85 - 9 * q^86 - 9 * q^87 + 18 * q^88 - 10 * q^89 - 9 * q^90 - 3 * q^91 + 9 * q^92 - 8 * q^93 + 47 * q^94 - 8 * q^95 + 60 * q^96 + 6 * q^97 - 73 * q^98 + 26 * q^99

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