LMFDB - Embedded newform 4002.2.a.bf.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.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:	$31.9561308889$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.61157024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 8x^{4} + 8x^{3} + 17x^{2} - 4x - 4 $ x^6 - 2x^5 - 8x^4 + 8x^3 + 17x^2 - 4*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.582305$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} +3.82553 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} +3.82553 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56155 q^{10} +2.87307 q^{11} +1.00000 q^{12} +1.70846 q^{13} -3.82553 q^{14} +2.56155 q^{15} +1.00000 q^{16} +4.43329 q^{17} -1.00000 q^{18} +0.462185 q^{19} +2.56155 q^{20} +3.82553 q^{21} -2.87307 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.56155 q^{25} -1.70846 q^{26} +1.00000 q^{27} +3.82553 q^{28} +1.00000 q^{29} -2.56155 q^{30} +5.21170 q^{31} -1.00000 q^{32} +2.87307 q^{33} -4.43329 q^{34} +9.79930 q^{35} +1.00000 q^{36} -7.26486 q^{37} -0.462185 q^{38} +1.70846 q^{39} -2.56155 q^{40} -3.68916 q^{41} -3.82553 q^{42} -6.40706 q^{43} +2.87307 q^{44} +2.56155 q^{45} -1.00000 q^{46} +2.93005 q^{47} +1.00000 q^{48} +7.63469 q^{49} -1.56155 q^{50} +4.43329 q^{51} +1.70846 q^{52} -0.198735 q^{53} -1.00000 q^{54} +7.35952 q^{55} -3.82553 q^{56} +0.462185 q^{57} -1.00000 q^{58} -13.5156 q^{59} +2.56155 q^{60} +2.20096 q^{61} -5.21170 q^{62} +3.82553 q^{63} +1.00000 q^{64} +4.37631 q^{65} -2.87307 q^{66} -1.82083 q^{67} +4.43329 q^{68} +1.00000 q^{69} -9.79930 q^{70} -2.28999 q^{71} -1.00000 q^{72} +0.784477 q^{73} +7.26486 q^{74} +1.56155 q^{75} +0.462185 q^{76} +10.9910 q^{77} -1.70846 q^{78} -12.5221 q^{79} +2.56155 q^{80} +1.00000 q^{81} +3.68916 q^{82} +5.18929 q^{83} +3.82553 q^{84} +11.3561 q^{85} +6.40706 q^{86} +1.00000 q^{87} -2.87307 q^{88} +15.9787 q^{89} -2.56155 q^{90} +6.53577 q^{91} +1.00000 q^{92} +5.21170 q^{93} -2.93005 q^{94} +1.18391 q^{95} -1.00000 q^{96} -12.6401 q^{97} -7.63469 q^{98} +2.87307 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 7 q^{11} + 6 q^{12} + 3 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 7 q^{22} + 6 q^{23} - 6 q^{24} - 3 q^{25} - 3 q^{26} + 6 q^{27} + 2 q^{28} + 6 q^{29} - 3 q^{30} + q^{31} - 6 q^{32} + 7 q^{33} - 8 q^{34} + 18 q^{35} + 6 q^{36} + 7 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} + 13 q^{41} - 2 q^{42} + 7 q^{44} + 3 q^{45} - 6 q^{46} + 22 q^{47} + 6 q^{48} + 8 q^{49} + 3 q^{50} + 8 q^{51} + 3 q^{52} + 10 q^{53} - 6 q^{54} - 5 q^{55} - 2 q^{56} - 4 q^{57} - 6 q^{58} + 17 q^{59} + 3 q^{60} + q^{61} - q^{62} + 2 q^{63} + 6 q^{64} - 7 q^{65} - 7 q^{66} + 3 q^{67} + 8 q^{68} + 6 q^{69} - 18 q^{70} + 11 q^{71} - 6 q^{72} - 7 q^{74} - 3 q^{75} - 4 q^{76} - 3 q^{78} + 2 q^{79} + 3 q^{80} + 6 q^{81} - 13 q^{82} + 16 q^{83} + 2 q^{84} + 4 q^{85} + 6 q^{87} - 7 q^{88} + 16 q^{89} - 3 q^{90} - 28 q^{91} + 6 q^{92} + q^{93} - 22 q^{94} + 32 q^{95} - 6 q^{96} + 2 q^{97} - 8 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 7 * q^11 + 6 * q^12 + 3 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 7 * q^22 + 6 * q^23 - 6 * q^24 - 3 * q^25 - 3 * q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - 3 * q^30 + q^31 - 6 * q^32 + 7 * q^33 - 8 * q^34 + 18 * q^35 + 6 * q^36 + 7 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 + 13 * q^41 - 2 * q^42 + 7 * q^44 + 3 * q^45 - 6 * q^46 + 22 * q^47 + 6 * q^48 + 8 * q^49 + 3 * q^50 + 8 * q^51 + 3 * q^52 + 10 * q^53 - 6 * q^54 - 5 * q^55 - 2 * q^56 - 4 * q^57 - 6 * q^58 + 17 * q^59 + 3 * q^60 + q^61 - q^62 + 2 * q^63 + 6 * q^64 - 7 * q^65 - 7 * q^66 + 3 * q^67 + 8 * q^68 + 6 * q^69 - 18 * q^70 + 11 * q^71 - 6 * q^72 - 7 * q^74 - 3 * q^75 - 4 * q^76 - 3 * q^78 + 2 * q^79 + 3 * q^80 + 6 * q^81 - 13 * q^82 + 16 * q^83 + 2 * q^84 + 4 * q^85 + 6 * q^87 - 7 * q^88 + 16 * q^89 - 3 * q^90 - 28 * q^91 + 6 * q^92 + q^93 - 22 * q^94 + 32 * q^95 - 6 * q^96 + 2 * q^97 - 8 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.56155	1.14556	0.572781	−	0.819709i	$-0.305865\pi$
$5$	2.56155	1.14556	0.572781	+	0.819709i	$0.305865\pi$
$6$	−1.00000	−0.408248
$7$	3.82553	1.44591	0.722957	−	0.690893i	$-0.242782\pi$
$7$	3.82553	1.44591	0.722957	+	0.690893i	$0.242782\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.56155	−0.810034
$11$	2.87307	0.866263	0.433132	−	0.901331i	$-0.357408\pi$
$11$	2.87307	0.866263	0.433132	+	0.901331i	$0.357408\pi$
$12$	1.00000	0.288675
$13$	1.70846	0.473841	0.236921	−	0.971529i	$-0.423862\pi$
$13$	1.70846	0.473841	0.236921	+	0.971529i	$0.423862\pi$
$14$	−3.82553	−1.02242
$15$	2.56155	0.661390
$16$	1.00000	0.250000
$17$	4.43329	1.07523	0.537616	−	0.843190i	$-0.319325\pi$
$17$	4.43329	1.07523	0.537616	+	0.843190i	$0.319325\pi$
$18$	−1.00000	−0.235702
$19$	0.462185	0.106033	0.0530163	−	0.998594i	$-0.483116\pi$
$19$	0.462185	0.106033	0.0530163	+	0.998594i	$0.483116\pi$
$20$	2.56155	0.572781
$21$	3.82553	0.834799
$22$	−2.87307	−0.612541
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	1.56155	0.312311
$26$	−1.70846	−0.335057
$27$	1.00000	0.192450
$28$	3.82553	0.722957
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−2.56155	−0.467673
$31$	5.21170	0.936049	0.468024	−	0.883716i	$-0.344966\pi$
$31$	5.21170	0.936049	0.468024	+	0.883716i	$0.344966\pi$
$32$	−1.00000	−0.176777
$33$	2.87307	0.500137
$34$	−4.43329	−0.760303
$35$	9.79930	1.65638
$36$	1.00000	0.166667
$37$	−7.26486	−1.19434	−0.597168	−	0.802116i	$-0.703707\pi$
$37$	−7.26486	−1.19434	−0.597168	+	0.802116i	$0.703707\pi$
$38$	−0.462185	−0.0749764
$39$	1.70846	0.273573
$40$	−2.56155	−0.405017
$41$	−3.68916	−0.576150	−0.288075	−	0.957608i	$-0.593015\pi$
$41$	−3.68916	−0.576150	−0.288075	+	0.957608i	$0.593015\pi$
$42$	−3.82553	−0.590292
$43$	−6.40706	−0.977068	−0.488534	−	0.872545i	$-0.662468\pi$
$43$	−6.40706	−0.977068	−0.488534	+	0.872545i	$0.662468\pi$
$44$	2.87307	0.433132
$45$	2.56155	0.381854
$46$	−1.00000	−0.147442
$47$	2.93005	0.427392	0.213696	−	0.976900i	$-0.431450\pi$
$47$	2.93005	0.427392	0.213696	+	0.976900i	$0.431450\pi$
$48$	1.00000	0.144338
$49$	7.63469	1.09067
$50$	−1.56155	−0.220837
$51$	4.43329	0.620785
$52$	1.70846	0.236921
$53$	−0.198735	−0.0272984	−0.0136492	−	0.999907i	$-0.504345\pi$
$53$	−0.198735	−0.0272984	−0.0136492	+	0.999907i	$0.504345\pi$
$54$	−1.00000	−0.136083
$55$	7.35952	0.992358
$56$	−3.82553	−0.511208
$57$	0.462185	0.0612179
$58$	−1.00000	−0.131306
$59$	−13.5156	−1.75958	−0.879789	−	0.475365i	$-0.842316\pi$
$59$	−13.5156	−1.75958	−0.879789	+	0.475365i	$0.842316\pi$
$60$	2.56155	0.330695
$61$	2.20096	0.281804	0.140902	−	0.990024i	$-0.455000\pi$
$61$	2.20096	0.281804	0.140902	+	0.990024i	$0.455000\pi$
$62$	−5.21170	−0.661886
$63$	3.82553	0.481972
$64$	1.00000	0.125000
$65$	4.37631	0.542814
$66$	−2.87307	−0.353651
$67$	−1.82083	−0.222450	−0.111225	−	0.993795i	$-0.535477\pi$
$67$	−1.82083	−0.222450	−0.111225	+	0.993795i	$0.535477\pi$
$68$	4.43329	0.537616
$69$	1.00000	0.120386
$70$	−9.79930	−1.17124
$71$	−2.28999	−0.271772	−0.135886	−	0.990724i	$-0.543388\pi$
$71$	−2.28999	−0.271772	−0.135886	+	0.990724i	$0.543388\pi$
$72$	−1.00000	−0.117851
$73$	0.784477	0.0918161	0.0459081	−	0.998946i	$-0.485382\pi$
$73$	0.784477	0.0918161	0.0459081	+	0.998946i	$0.485382\pi$
$74$	7.26486	0.844523
$75$	1.56155	0.180313
$76$	0.462185	0.0530163
$77$	10.9910	1.25254
$78$	−1.70846	−0.193445
$79$	−12.5221	−1.40885	−0.704426	−	0.709778i	$-0.748795\pi$
$79$	−12.5221	−1.40885	−0.704426	+	0.709778i	$0.748795\pi$
$80$	2.56155	0.286390
$81$	1.00000	0.111111
$82$	3.68916	0.407399
$83$	5.18929	0.569599	0.284799	−	0.958587i	$-0.408073\pi$
$83$	5.18929	0.569599	0.284799	+	0.958587i	$0.408073\pi$
$84$	3.82553	0.417400
$85$	11.3561	1.23174
$86$	6.40706	0.690891
$87$	1.00000	0.107211
$88$	−2.87307	−0.306270
$89$	15.9787	1.69374	0.846871	−	0.531798i	$-0.178483\pi$
$89$	15.9787	1.69374	0.846871	+	0.531798i	$0.178483\pi$
$90$	−2.56155	−0.270011
$91$	6.53577	0.685134
$92$	1.00000	0.104257
$93$	5.21170	0.540428
$94$	−2.93005	−0.302212
$95$	1.18391	0.121467
$96$	−1.00000	−0.102062
$97$	−12.6401	−1.28340	−0.641702	−	0.766954i	$-0.721772\pi$
$97$	−12.6401	−1.28340	−0.641702	+	0.766954i	$0.721772\pi$
$98$	−7.63469	−0.771220
$99$	2.87307	0.288754
$100$	1.56155	0.156155
$101$	−5.90560	−0.587629	−0.293814	−	0.955862i	$-0.594925\pi$
$101$	−5.90560	−0.587629	−0.293814	+	0.955862i	$0.594925\pi$
$102$	−4.43329	−0.438961
$103$	−18.3662	−1.80968	−0.904839	−	0.425753i	$-0.860009\pi$
$103$	−18.3662	−1.80968	−0.904839	+	0.425753i	$0.860009\pi$
$104$	−1.70846	−0.167528
$105$	9.79930	0.956314
$106$	0.198735	0.0193029
$107$	−7.11037	−0.687385	−0.343693	−	0.939082i	$-0.611678\pi$
$107$	−7.11037	−0.687385	−0.343693	+	0.939082i	$0.611678\pi$
$108$	1.00000	0.0962250
$109$	−17.1265	−1.64042	−0.820212	−	0.572060i	$-0.806144\pi$
$109$	−17.1265	−1.64042	−0.820212	+	0.572060i	$0.806144\pi$
$110$	−7.35952	−0.701703
$111$	−7.26486	−0.689550
$112$	3.82553	0.361479
$113$	2.48842	0.234091	0.117045	−	0.993127i	$-0.462658\pi$
$113$	2.48842	0.234091	0.117045	+	0.993127i	$0.462658\pi$
$114$	−0.462185	−0.0432876
$115$	2.56155	0.238866
$116$	1.00000	0.0928477
$117$	1.70846	0.157947
$118$	13.5156	1.24421
$119$	16.9597	1.55469
$120$	−2.56155	−0.233837
$121$	−2.74546	−0.249588
$122$	−2.20096	−0.199266
$123$	−3.68916	−0.332640
$124$	5.21170	0.468024
$125$	−8.80776	−0.787790
$126$	−3.82553	−0.340805
$127$	10.9345	0.970276	0.485138	−	0.874438i	$-0.338769\pi$
$127$	10.9345	0.970276	0.485138	+	0.874438i	$0.338769\pi$
$128$	−1.00000	−0.0883883
$129$	−6.40706	−0.564110
$130$	−4.37631	−0.383828
$131$	3.24157	0.283217	0.141609	−	0.989923i	$-0.454773\pi$
$131$	3.24157	0.283217	0.141609	+	0.989923i	$0.454773\pi$
$132$	2.87307	0.250069
$133$	1.76810	0.153314
$134$	1.82083	0.157296
$135$	2.56155	0.220463
$136$	−4.43329	−0.380152
$137$	13.2614	1.13300	0.566501	−	0.824061i	$-0.308297\pi$
$137$	13.2614	1.13300	0.566501	+	0.824061i	$0.308297\pi$
$138$	−1.00000	−0.0851257
$139$	−11.7400	−0.995778	−0.497889	−	0.867241i	$-0.665891\pi$
$139$	−11.7400	−0.995778	−0.497889	+	0.867241i	$0.665891\pi$
$140$	9.79930	0.828192
$141$	2.93005	0.246755
$142$	2.28999	0.192172
$143$	4.90853	0.410472
$144$	1.00000	0.0833333
$145$	2.56155	0.212725
$146$	−0.784477	−0.0649238
$147$	7.63469	0.629699
$148$	−7.26486	−0.597168
$149$	−5.74350	−0.470526	−0.235263	−	0.971932i	$-0.575595\pi$
$149$	−5.74350	−0.470526	−0.235263	+	0.971932i	$0.575595\pi$
$150$	−1.56155	−0.127500
$151$	0.616288	0.0501528	0.0250764	−	0.999686i	$-0.492017\pi$
$151$	0.616288	0.0501528	0.0250764	+	0.999686i	$0.492017\pi$
$152$	−0.462185	−0.0374882
$153$	4.43329	0.358410
$154$	−10.9910	−0.885682
$155$	13.3500	1.07230
$156$	1.70846	0.136786
$157$	1.13595	0.0906587	0.0453294	−	0.998972i	$-0.485566\pi$
$157$	1.13595	0.0906587	0.0453294	+	0.998972i	$0.485566\pi$
$158$	12.5221	0.996209
$159$	−0.198735	−0.0157607
$160$	−2.56155	−0.202509
$161$	3.82553	0.301494
$162$	−1.00000	−0.0785674
$163$	−2.85111	−0.223316	−0.111658	−	0.993747i	$-0.535616\pi$
$163$	−2.85111	−0.223316	−0.111658	+	0.993747i	$0.535616\pi$
$164$	−3.68916	−0.288075
$165$	7.35952	0.572938
$166$	−5.18929	−0.402767
$167$	−7.04759	−0.545359	−0.272679	−	0.962105i	$-0.587910\pi$
$167$	−7.04759	−0.545359	−0.272679	+	0.962105i	$0.587910\pi$
$168$	−3.82553	−0.295146
$169$	−10.0812	−0.775474
$170$	−11.3561	−0.870974
$171$	0.462185	0.0353442
$172$	−6.40706	−0.488534
$173$	−7.39157	−0.561971	−0.280985	−	0.959712i	$-0.590661\pi$
$173$	−7.39157	−0.561971	−0.280985	+	0.959712i	$0.590661\pi$
$174$	−1.00000	−0.0758098
$175$	5.97377	0.451574
$176$	2.87307	0.216566
$177$	−13.5156	−1.01589
$178$	−15.9787	−1.19766
$179$	−22.7805	−1.70270	−0.851349	−	0.524600i	$-0.824215\pi$
$179$	−22.7805	−1.70270	−0.851349	+	0.524600i	$0.824215\pi$
$180$	2.56155	0.190927
$181$	−0.407188	−0.0302660	−0.0151330	−	0.999885i	$-0.504817\pi$
$181$	−0.407188	−0.0302660	−0.0151330	+	0.999885i	$0.504817\pi$
$182$	−6.53577	−0.484463
$183$	2.20096	0.162700
$184$	−1.00000	−0.0737210
$185$	−18.6093	−1.36818
$186$	−5.21170	−0.382140
$187$	12.7372	0.931434
$188$	2.93005	0.213696
$189$	3.82553	0.278266
$190$	−1.18391	−0.0858900
$191$	10.9924	0.795383	0.397692	−	0.917519i	$-0.369811\pi$
$191$	10.9924	0.795383	0.397692	+	0.917519i	$0.369811\pi$
$192$	1.00000	0.0721688
$193$	−8.10898	−0.583697	−0.291849	−	0.956465i	$-0.594270\pi$
$193$	−8.10898	−0.583697	−0.291849	+	0.956465i	$0.594270\pi$
$194$	12.6401	0.907504
$195$	4.37631	0.313394
$196$	7.63469	0.545335
$197$	−13.9780	−0.995888	−0.497944	−	0.867209i	$-0.665912\pi$
$197$	−13.9780	−0.995888	−0.497944	+	0.867209i	$0.665912\pi$
$198$	−2.87307	−0.204180
$199$	6.97388	0.494365	0.247183	−	0.968969i	$-0.420495\pi$
$199$	6.97388	0.494365	0.247183	+	0.968969i	$0.420495\pi$
$200$	−1.56155	−0.110418
$201$	−1.82083	−0.128431
$202$	5.90560	0.415516
$203$	3.82553	0.268500
$204$	4.43329	0.310393
$205$	−9.44997	−0.660015
$206$	18.3662	1.27964
$207$	1.00000	0.0695048
$208$	1.70846	0.118460
$209$	1.32789	0.0918521
$210$	−9.79930	−0.676216
$211$	3.84463	0.264675	0.132338	−	0.991205i	$-0.457752\pi$
$211$	3.84463	0.264675	0.132338	+	0.991205i	$0.457752\pi$
$212$	−0.198735	−0.0136492
$213$	−2.28999	−0.156908
$214$	7.11037	0.486055
$215$	−16.4120	−1.11929
$216$	−1.00000	−0.0680414
$217$	19.9375	1.35345
$218$	17.1265	1.15995
$219$	0.784477	0.0530101
$220$	7.35952	0.496179
$221$	7.57410	0.509489
$222$	7.26486	0.487585
$223$	2.83297	0.189710	0.0948548	−	0.995491i	$-0.469761\pi$
$223$	2.83297	0.189710	0.0948548	+	0.995491i	$0.469761\pi$
$224$	−3.82553	−0.255604
$225$	1.56155	0.104104
$226$	−2.48842	−0.165527
$227$	−19.0880	−1.26691	−0.633457	−	0.773778i	$-0.718365\pi$
$227$	−19.0880	−1.26691	−0.633457	+	0.773778i	$0.718365\pi$
$228$	0.462185	0.0306090
$229$	−8.37406	−0.553374	−0.276687	−	0.960960i	$-0.589236\pi$
$229$	−8.37406	−0.553374	−0.276687	+	0.960960i	$0.589236\pi$
$230$	−2.56155	−0.168904
$231$	10.9910	0.723156
$232$	−1.00000	−0.0656532
$233$	0.898443	0.0588589	0.0294295	−	0.999567i	$-0.490631\pi$
$233$	0.898443	0.0588589	0.0294295	+	0.999567i	$0.490631\pi$
$234$	−1.70846	−0.111686
$235$	7.50549	0.489604
$236$	−13.5156	−0.879789
$237$	−12.5221	−0.813401
$238$	−16.9597	−1.09933
$239$	24.0009	1.55249	0.776244	−	0.630432i	$-0.217122\pi$
$239$	24.0009	1.55249	0.776244	+	0.630432i	$0.217122\pi$
$240$	2.56155	0.165348
$241$	8.48633	0.546652	0.273326	−	0.961921i	$-0.411876\pi$
$241$	8.48633	0.546652	0.273326	+	0.961921i	$0.411876\pi$
$242$	2.74546	0.176485
$243$	1.00000	0.0641500
$244$	2.20096	0.140902
$245$	19.5567	1.24943
$246$	3.68916	0.235212
$247$	0.789625	0.0502426
$248$	−5.21170	−0.330943
$249$	5.18929	0.328858
$250$	8.80776	0.557052
$251$	24.2642	1.53154	0.765772	−	0.643112i	$-0.222357\pi$
$251$	24.2642	1.53154	0.765772	+	0.643112i	$0.222357\pi$
$252$	3.82553	0.240986
$253$	2.87307	0.180628
$254$	−10.9345	−0.686089
$255$	11.3561	0.711147
$256$	1.00000	0.0625000
$257$	−16.8360	−1.05020	−0.525099	−	0.851041i	$-0.675972\pi$
$257$	−16.8360	−1.05020	−0.525099	+	0.851041i	$0.675972\pi$
$258$	6.40706	0.398886
$259$	−27.7919	−1.72691
$260$	4.37631	0.271407
$261$	1.00000	0.0618984
$262$	−3.24157	−0.200265
$263$	−19.4829	−1.20136	−0.600682	−	0.799488i	$-0.705104\pi$
$263$	−19.4829	−1.20136	−0.600682	+	0.799488i	$0.705104\pi$
$264$	−2.87307	−0.176825
$265$	−0.509070	−0.0312719
$266$	−1.76810	−0.108409
$267$	15.9787	0.977883
$268$	−1.82083	−0.111225
$269$	12.3220	0.751287	0.375643	−	0.926764i	$-0.377422\pi$
$269$	12.3220	0.751287	0.375643	+	0.926764i	$0.377422\pi$
$270$	−2.56155	−0.155891
$271$	−3.55749	−0.216102	−0.108051	−	0.994145i	$-0.534461\pi$
$271$	−3.55749	−0.216102	−0.108051	+	0.994145i	$0.534461\pi$
$272$	4.43329	0.268808
$273$	6.53577	0.395563
$274$	−13.2614	−0.801153
$275$	4.48645	0.270543
$276$	1.00000	0.0601929
$277$	−22.2167	−1.33487	−0.667436	−	0.744667i	$-0.732608\pi$
$277$	−22.2167	−1.33487	−0.667436	+	0.744667i	$0.732608\pi$
$278$	11.7400	0.704121
$279$	5.21170	0.312016
$280$	−9.79930	−0.585620
$281$	−14.6265	−0.872541	−0.436270	−	0.899816i	$-0.643701\pi$
$281$	−14.6265	−0.872541	−0.436270	+	0.899816i	$0.643701\pi$
$282$	−2.93005	−0.174482
$283$	29.5344	1.75564	0.877818	−	0.478993i	$-0.158998\pi$
$283$	29.5344	1.75564	0.877818	+	0.478993i	$0.158998\pi$
$284$	−2.28999	−0.135886
$285$	1.18391	0.0701289
$286$	−4.90853	−0.290247
$287$	−14.1130	−0.833064
$288$	−1.00000	−0.0589256
$289$	2.65408	0.156123
$290$	−2.56155	−0.150420
$291$	−12.6401	−0.740974
$292$	0.784477	0.0459081
$293$	27.8409	1.62648	0.813241	−	0.581926i	$-0.197701\pi$
$293$	27.8409	1.62648	0.813241	+	0.581926i	$0.197701\pi$
$294$	−7.63469	−0.445264
$295$	−34.6208	−2.01570
$296$	7.26486	0.422261
$297$	2.87307	0.166712
$298$	5.74350	0.332712
$299$	1.70846	0.0988028
$300$	1.56155	0.0901563
$301$	−24.5104	−1.41276
$302$	−0.616288	−0.0354634
$303$	−5.90560	−0.339268
$304$	0.462185	0.0265081
$305$	5.63788	0.322824
$306$	−4.43329	−0.253434
$307$	−6.74341	−0.384867	−0.192433	−	0.981310i	$-0.561638\pi$
$307$	−6.74341	−0.384867	−0.192433	+	0.981310i	$0.561638\pi$
$308$	10.9910	0.626272
$309$	−18.3662	−1.04482
$310$	−13.3500	−0.758231
$311$	34.2339	1.94123	0.970614	−	0.240641i	$-0.0773576\pi$
$311$	34.2339	1.94123	0.970614	+	0.240641i	$0.0773576\pi$
$312$	−1.70846	−0.0967225
$313$	0.323828	0.0183038	0.00915191	−	0.999958i	$-0.497087\pi$
$313$	0.323828	0.0183038	0.00915191	+	0.999958i	$0.497087\pi$
$314$	−1.13595	−0.0641054
$315$	9.79930	0.552128
$316$	−12.5221	−0.704426
$317$	11.4115	0.640936	0.320468	−	0.947259i	$-0.396160\pi$
$317$	11.4115	0.640936	0.320468	+	0.947259i	$0.396160\pi$
$318$	0.198735	0.0111445
$319$	2.87307	0.160861
$320$	2.56155	0.143195
$321$	−7.11037	−0.396862
$322$	−3.82553	−0.213189
$323$	2.04900	0.114010
$324$	1.00000	0.0555556
$325$	2.66785	0.147986
$326$	2.85111	0.157908
$327$	−17.1265	−0.947099
$328$	3.68916	0.203700
$329$	11.2090	0.617973
$330$	−7.35952	−0.405128
$331$	−7.35316	−0.404166	−0.202083	−	0.979368i	$-0.564771\pi$
$331$	−7.35316	−0.404166	−0.202083	+	0.979368i	$0.564771\pi$
$332$	5.18929	0.284799
$333$	−7.26486	−0.398112
$334$	7.04759	0.385627
$335$	−4.66415	−0.254830
$336$	3.82553	0.208700
$337$	14.3120	0.779622	0.389811	−	0.920895i	$-0.372540\pi$
$337$	14.3120	0.779622	0.389811	+	0.920895i	$0.372540\pi$
$338$	10.0812	0.548343
$339$	2.48842	0.135152
$340$	11.3561	0.615872
$341$	14.9736	0.810865
$342$	−0.462185	−0.0249921
$343$	2.42802	0.131101
$344$	6.40706	0.345446
$345$	2.56155	0.137909
$346$	7.39157	0.397373
$347$	32.7009	1.75547	0.877737	−	0.479143i	$-0.159052\pi$
$347$	32.7009	1.75547	0.877737	+	0.479143i	$0.159052\pi$
$348$	1.00000	0.0536056
$349$	19.5602	1.04703	0.523515	−	0.852016i	$-0.324620\pi$
$349$	19.5602	1.04703	0.523515	+	0.852016i	$0.324620\pi$
$350$	−5.97377	−0.319311
$351$	1.70846	0.0911908
$352$	−2.87307	−0.153135
$353$	28.6088	1.52269	0.761346	−	0.648345i	$-0.224539\pi$
$353$	28.6088	1.52269	0.761346	+	0.648345i	$0.224539\pi$
$354$	13.5156	0.718344
$355$	−5.86593	−0.311331
$356$	15.9787	0.846871
$357$	16.9597	0.897602
$358$	22.7805	1.20399
$359$	−7.60447	−0.401348	−0.200674	−	0.979658i	$-0.564313\pi$
$359$	−7.60447	−0.401348	−0.200674	+	0.979658i	$0.564313\pi$
$360$	−2.56155	−0.135006
$361$	−18.7864	−0.988757
$362$	0.407188	0.0214013
$363$	−2.74546	−0.144100
$364$	6.53577	0.342567
$365$	2.00948	0.105181
$366$	−2.20096	−0.115046
$367$	10.1229	0.528410	0.264205	−	0.964466i	$-0.414890\pi$
$367$	10.1229	0.528410	0.264205	+	0.964466i	$0.414890\pi$
$368$	1.00000	0.0521286
$369$	−3.68916	−0.192050
$370$	18.6093	0.967452
$371$	−0.760267	−0.0394711
$372$	5.21170	0.270214
$373$	12.4725	0.645803	0.322902	−	0.946433i	$-0.395342\pi$
$373$	12.4725	0.645803	0.322902	+	0.946433i	$0.395342\pi$
$374$	−12.7372	−0.658623
$375$	−8.80776	−0.454831
$376$	−2.93005	−0.151106
$377$	1.70846	0.0879902
$378$	−3.82553	−0.196764
$379$	2.94556	0.151303	0.0756516	−	0.997134i	$-0.475896\pi$
$379$	2.94556	0.151303	0.0756516	+	0.997134i	$0.475896\pi$
$380$	1.18391	0.0607334
$381$	10.9345	0.560189
$382$	−10.9924	−0.562421
$383$	22.6645	1.15810	0.579050	−	0.815292i	$-0.303424\pi$
$383$	22.6645	1.15810	0.579050	+	0.815292i	$0.303424\pi$
$384$	−1.00000	−0.0510310
$385$	28.1541	1.43486
$386$	8.10898	0.412736
$387$	−6.40706	−0.325689
$388$	−12.6401	−0.641702
$389$	−4.64955	−0.235742	−0.117871	−	0.993029i	$-0.537607\pi$
$389$	−4.64955	−0.235742	−0.117871	+	0.993029i	$0.537607\pi$
$390$	−4.37631	−0.221603
$391$	4.43329	0.224201
$392$	−7.63469	−0.385610
$393$	3.24157	0.163516
$394$	13.9780	0.704199
$395$	−32.0761	−1.61393
$396$	2.87307	0.144377
$397$	−28.3731	−1.42400	−0.712001	−	0.702178i	$-0.752211\pi$
$397$	−28.3731	−1.42400	−0.712001	+	0.702178i	$0.752211\pi$
$398$	−6.97388	−0.349569
$399$	1.76810	0.0885159
$400$	1.56155	0.0780776
$401$	29.8660	1.49143	0.745717	−	0.666262i	$-0.232107\pi$
$401$	29.8660	1.49143	0.745717	+	0.666262i	$0.232107\pi$
$402$	1.82083	0.0908146
$403$	8.90398	0.443539
$404$	−5.90560	−0.293814
$405$	2.56155	0.127285
$406$	−3.82553	−0.189858
$407$	−20.8725	−1.03461
$408$	−4.43329	−0.219481
$409$	17.7445	0.877408	0.438704	−	0.898632i	$-0.355438\pi$
$409$	17.7445	0.877408	0.438704	+	0.898632i	$0.355438\pi$
$410$	9.44997	0.466701
$411$	13.2614	0.654139
$412$	−18.3662	−0.904839
$413$	−51.7042	−2.54420
$414$	−1.00000	−0.0491473
$415$	13.2926	0.652510
$416$	−1.70846	−0.0837641
$417$	−11.7400	−0.574912
$418$	−1.32789	−0.0649493
$419$	9.04448	0.441852	0.220926	−	0.975291i	$-0.429092\pi$
$419$	9.04448	0.441852	0.220926	+	0.975291i	$0.429092\pi$
$420$	9.79930	0.478157
$421$	3.65832	0.178295	0.0891477	−	0.996018i	$-0.471586\pi$
$421$	3.65832	0.178295	0.0891477	+	0.996018i	$0.471586\pi$
$422$	−3.84463	−0.187154
$423$	2.93005	0.142464
$424$	0.198735	0.00965143
$425$	6.92282	0.335806
$426$	2.28999	0.110950
$427$	8.41985	0.407465
$428$	−7.11037	−0.343693
$429$	4.90853	0.236986
$430$	16.4120	0.791458
$431$	7.77367	0.374444	0.187222	−	0.982318i	$-0.440052\pi$
$431$	7.77367	0.374444	0.187222	+	0.982318i	$0.440052\pi$
$432$	1.00000	0.0481125
$433$	−10.5159	−0.505361	−0.252681	−	0.967550i	$-0.581312\pi$
$433$	−10.5159	−0.505361	−0.252681	+	0.967550i	$0.581312\pi$
$434$	−19.9375	−0.957031
$435$	2.56155	0.122817
$436$	−17.1265	−0.820212
$437$	0.462185	0.0221093
$438$	−0.784477	−0.0374838
$439$	3.77214	0.180034	0.0900172	−	0.995940i	$-0.471308\pi$
$439$	3.77214	0.180034	0.0900172	+	0.995940i	$0.471308\pi$
$440$	−7.35952	−0.350851
$441$	7.63469	0.363557
$442$	−7.57410	−0.360263
$443$	−30.8713	−1.46674	−0.733370	−	0.679830i	$-0.762053\pi$
$443$	−30.8713	−1.46674	−0.733370	+	0.679830i	$0.762053\pi$
$444$	−7.26486	−0.344775
$445$	40.9304	1.94029
$446$	−2.83297	−0.134145
$447$	−5.74350	−0.271658
$448$	3.82553	0.180739
$449$	36.1308	1.70512	0.852560	−	0.522630i	$-0.175049\pi$
$449$	36.1308	1.70512	0.852560	+	0.522630i	$0.175049\pi$
$450$	−1.56155	−0.0736123
$451$	−10.5992	−0.499097
$452$	2.48842	0.117045
$453$	0.616288	0.0289558
$454$	19.0880	0.895844
$455$	16.7417	0.784864
$456$	−0.462185	−0.0216438
$457$	7.25147	0.339209	0.169605	−	0.985512i	$-0.445751\pi$
$457$	7.25147	0.339209	0.169605	+	0.985512i	$0.445751\pi$
$458$	8.37406	0.391294
$459$	4.43329	0.206928
$460$	2.56155	0.119433
$461$	24.7200	1.15133	0.575663	−	0.817687i	$-0.304744\pi$
$461$	24.7200	1.15133	0.575663	+	0.817687i	$0.304744\pi$
$462$	−10.9910	−0.511349
$463$	1.89180	0.0879192	0.0439596	−	0.999033i	$-0.486003\pi$
$463$	1.89180	0.0879192	0.0439596	+	0.999033i	$0.486003\pi$
$464$	1.00000	0.0464238
$465$	13.3500	0.619093
$466$	−0.898443	−0.0416195
$467$	18.1455	0.839672	0.419836	−	0.907600i	$-0.362088\pi$
$467$	18.1455	0.839672	0.419836	+	0.907600i	$0.362088\pi$
$468$	1.70846	0.0789736
$469$	−6.96563	−0.321643
$470$	−7.50549	−0.346202
$471$	1.13595	0.0523418
$472$	13.5156	0.622105
$473$	−18.4079	−0.846398
$474$	12.5221	0.575161
$475$	0.721727	0.0331151
$476$	16.9597	0.777347
$477$	−0.198735	−0.00909945
$478$	−24.0009	−1.09777
$479$	−15.7127	−0.717930	−0.358965	−	0.933351i	$-0.616870\pi$
$479$	−15.7127	−0.717930	−0.358965	+	0.933351i	$0.616870\pi$
$480$	−2.56155	−0.116918
$481$	−12.4117	−0.565926
$482$	−8.48633	−0.386542
$483$	3.82553	0.174068
$484$	−2.74546	−0.124794
$485$	−32.3782	−1.47022
$486$	−1.00000	−0.0453609
$487$	−5.04994	−0.228835	−0.114417	−	0.993433i	$-0.536500\pi$
$487$	−5.04994	−0.228835	−0.114417	+	0.993433i	$0.536500\pi$
$488$	−2.20096	−0.0996329
$489$	−2.85111	−0.128932
$490$	−19.5567	−0.883480
$491$	−13.1959	−0.595521	−0.297760	−	0.954641i	$-0.596240\pi$
$491$	−13.1959	−0.595521	−0.297760	+	0.954641i	$0.596240\pi$
$492$	−3.68916	−0.166320
$493$	4.43329	0.199665
$494$	−0.789625	−0.0355269
$495$	7.35952	0.330786
$496$	5.21170	0.234012
$497$	−8.76043	−0.392959
$498$	−5.18929	−0.232538
$499$	−15.9560	−0.714288	−0.357144	−	0.934049i	$-0.616250\pi$
$499$	−15.9560	−0.714288	−0.357144	+	0.934049i	$0.616250\pi$
$500$	−8.80776	−0.393895
$501$	−7.04759	−0.314863
$502$	−24.2642	−1.08297
$503$	25.4475	1.13465	0.567324	−	0.823494i	$-0.307979\pi$
$503$	25.4475	1.13465	0.567324	+	0.823494i	$0.307979\pi$
$504$	−3.82553	−0.170403
$505$	−15.1275	−0.673165
$506$	−2.87307	−0.127724
$507$	−10.0812	−0.447720
$508$	10.9345	0.485138
$509$	20.2106	0.895817	0.447908	−	0.894079i	$-0.352169\pi$
$509$	20.2106	0.895817	0.447908	+	0.894079i	$0.352169\pi$
$510$	−11.3561	−0.502857
$511$	3.00104	0.132758
$512$	−1.00000	−0.0441942
$513$	0.462185	0.0204060
$514$	16.8360	0.742602
$515$	−47.0461	−2.07310
$516$	−6.40706	−0.282055
$517$	8.41825	0.370234
$518$	27.7919	1.22111
$519$	−7.39157	−0.324454
$520$	−4.37631	−0.191914
$521$	12.7894	0.560314	0.280157	−	0.959954i	$-0.409614\pi$
$521$	12.7894	0.560314	0.280157	+	0.959954i	$0.409614\pi$
$522$	−1.00000	−0.0437688
$523$	34.1411	1.49289	0.746444	−	0.665448i	$-0.231760\pi$
$523$	34.1411	1.49289	0.746444	+	0.665448i	$0.231760\pi$
$524$	3.24157	0.141609
$525$	5.97377	0.260717
$526$	19.4829	0.849493
$527$	23.1050	1.00647
$528$	2.87307	0.125034
$529$	1.00000	0.0434783
$530$	0.509070	0.0221126
$531$	−13.5156	−0.586526
$532$	1.76810	0.0766570
$533$	−6.30278	−0.273004
$534$	−15.9787	−0.691467
$535$	−18.2136	−0.787442
$536$	1.82083	0.0786478
$537$	−22.7805	−0.983053
$538$	−12.3220	−0.531240
$539$	21.9350	0.944807
$540$	2.56155	0.110232
$541$	−38.6519	−1.66177	−0.830887	−	0.556441i	$-0.812167\pi$
$541$	−38.6519	−1.66177	−0.830887	+	0.556441i	$0.812167\pi$
$542$	3.55749	0.152807
$543$	−0.407188	−0.0174741
$544$	−4.43329	−0.190076
$545$	−43.8705	−1.87921
$546$	−6.53577	−0.279705
$547$	16.0011	0.684158	0.342079	−	0.939671i	$-0.388869\pi$
$547$	16.0011	0.684158	0.342079	+	0.939671i	$0.388869\pi$
$548$	13.2614	0.566501
$549$	2.20096	0.0939348
$550$	−4.48645	−0.191303
$551$	0.462185	0.0196898
$552$	−1.00000	−0.0425628
$553$	−47.9039	−2.03708
$554$	22.2167	0.943897
$555$	−18.6093	−0.789922
$556$	−11.7400	−0.497889
$557$	16.7142	0.708202	0.354101	−	0.935207i	$-0.384787\pi$
$557$	16.7142	0.708202	0.354101	+	0.935207i	$0.384787\pi$
$558$	−5.21170	−0.220629
$559$	−10.9462	−0.462975
$560$	9.79930	0.414096
$561$	12.7372	0.537763
$562$	14.6265	0.616980
$563$	−41.7946	−1.76143	−0.880716	−	0.473645i	$-0.842938\pi$
$563$	−41.7946	−1.76143	−0.880716	+	0.473645i	$0.842938\pi$
$564$	2.93005	0.123378
$565$	6.37421	0.268165
$566$	−29.5344	−1.24142
$567$	3.82553	0.160657
$568$	2.28999	0.0960859
$569$	39.7063	1.66457	0.832287	−	0.554346i	$-0.187031\pi$
$569$	39.7063	1.66457	0.832287	+	0.554346i	$0.187031\pi$
$570$	−1.18391	−0.0495886
$571$	37.2048	1.55697	0.778486	−	0.627662i	$-0.215988\pi$
$571$	37.2048	1.55697	0.778486	+	0.627662i	$0.215988\pi$
$572$	4.90853	0.205236
$573$	10.9924	0.459215
$574$	14.1130	0.589065
$575$	1.56155	0.0651213
$576$	1.00000	0.0416667
$577$	−5.20759	−0.216795	−0.108397	−	0.994108i	$-0.534572\pi$
$577$	−5.20759	−0.216795	−0.108397	+	0.994108i	$0.534572\pi$
$578$	−2.65408	−0.110395
$579$	−8.10898	−0.336998
$580$	2.56155	0.106363
$581$	19.8518	0.823591
$582$	12.6401	0.523948
$583$	−0.570980	−0.0236476
$584$	−0.784477	−0.0324619
$585$	4.37631	0.180938
$586$	−27.8409	−1.15010
$587$	26.1959	1.08122	0.540611	−	0.841273i	$-0.318193\pi$
$587$	26.1959	1.08122	0.540611	+	0.841273i	$0.318193\pi$
$588$	7.63469	0.314849
$589$	2.40877	0.0992517
$590$	34.6208	1.42532
$591$	−13.9780	−0.574976
$592$	−7.26486	−0.298584
$593$	17.2900	0.710015	0.355007	−	0.934864i	$-0.384478\pi$
$593$	17.2900	0.710015	0.355007	+	0.934864i	$0.384478\pi$
$594$	−2.87307	−0.117884
$595$	43.4432	1.78100
$596$	−5.74350	−0.235263
$597$	6.97388	0.285422
$598$	−1.70846	−0.0698641
$599$	−16.7991	−0.686394	−0.343197	−	0.939263i	$-0.611510\pi$
$599$	−16.7991	−0.686394	−0.343197	+	0.939263i	$0.611510\pi$
$600$	−1.56155	−0.0637501
$601$	−10.8161	−0.441197	−0.220599	−	0.975365i	$-0.570801\pi$
$601$	−10.8161	−0.441197	−0.220599	+	0.975365i	$0.570801\pi$
$602$	24.5104	0.998970
$603$	−1.82083	−0.0741498
$604$	0.616288	0.0250764
$605$	−7.03265	−0.285918
$606$	5.90560	0.239899
$607$	−27.6332	−1.12160	−0.560798	−	0.827953i	$-0.689505\pi$
$607$	−27.6332	−1.12160	−0.560798	+	0.827953i	$0.689505\pi$
$608$	−0.462185	−0.0187441
$609$	3.82553	0.155018
$610$	−5.63788	−0.228271
$611$	5.00588	0.202516
$612$	4.43329	0.179205
$613$	21.7164	0.877118	0.438559	−	0.898702i	$-0.355489\pi$
$613$	21.7164	0.877118	0.438559	+	0.898702i	$0.355489\pi$
$614$	6.74341	0.272142
$615$	−9.44997	−0.381060
$616$	−10.9910	−0.442841
$617$	−44.5441	−1.79328	−0.896638	−	0.442763i	$-0.853998\pi$
$617$	−44.5441	−1.79328	−0.896638	+	0.442763i	$0.853998\pi$
$618$	18.3662	0.738798
$619$	28.3871	1.14098	0.570488	−	0.821306i	$-0.306754\pi$
$619$	28.3871	1.14098	0.570488	+	0.821306i	$0.306754\pi$
$620$	13.3500	0.536151
$621$	1.00000	0.0401286
$622$	−34.2339	−1.37266
$623$	61.1271	2.44901
$624$	1.70846	0.0683931
$625$	−30.3693	−1.21477
$626$	−0.323828	−0.0129428
$627$	1.32789	0.0530309
$628$	1.13595	0.0453294
$629$	−32.2072	−1.28419
$630$	−9.79930	−0.390413
$631$	31.1916	1.24172	0.620860	−	0.783922i	$-0.286784\pi$
$631$	31.1916	1.24172	0.620860	+	0.783922i	$0.286784\pi$
$632$	12.5221	0.498104
$633$	3.84463	0.152810
$634$	−11.4115	−0.453210
$635$	28.0092	1.11151
$636$	−0.198735	−0.00788036
$637$	13.0436	0.516805
$638$	−2.87307	−0.113746
$639$	−2.28999	−0.0905906
$640$	−2.56155	−0.101254
$641$	16.3951	0.647567	0.323784	−	0.946131i	$-0.395045\pi$
$641$	16.3951	0.647567	0.323784	+	0.946131i	$0.395045\pi$
$642$	7.11037	0.280624
$643$	−23.6347	−0.932060	−0.466030	−	0.884769i	$-0.654316\pi$
$643$	−23.6347	−0.932060	−0.466030	+	0.884769i	$0.654316\pi$
$644$	3.82553	0.150747
$645$	−16.4120	−0.646223
$646$	−2.04900	−0.0806169
$647$	17.7066	0.696117	0.348058	−	0.937473i	$-0.386841\pi$
$647$	17.7066	0.696117	0.348058	+	0.937473i	$0.386841\pi$
$648$	−1.00000	−0.0392837
$649$	−38.8312	−1.52426
$650$	−2.66785	−0.104642
$651$	19.9375	0.781413
$652$	−2.85111	−0.111658
$653$	−8.54700	−0.334470	−0.167235	−	0.985917i	$-0.553484\pi$
$653$	−8.54700	−0.334470	−0.167235	+	0.985917i	$0.553484\pi$
$654$	17.1265	0.669700
$655$	8.30346	0.324443
$656$	−3.68916	−0.144037
$657$	0.784477	0.0306054
$658$	−11.2090	−0.436973
$659$	15.7355	0.612970	0.306485	−	0.951875i	$-0.400847\pi$
$659$	15.7355	0.612970	0.306485	+	0.951875i	$0.400847\pi$
$660$	7.35952	0.286469
$661$	−37.1623	−1.44545	−0.722724	−	0.691137i	$-0.757110\pi$
$661$	−37.1623	−1.44545	−0.722724	+	0.691137i	$0.757110\pi$
$662$	7.35316	0.285789
$663$	7.57410	0.294154
$664$	−5.18929	−0.201384
$665$	4.52909	0.175631
$666$	7.26486	0.281508
$667$	1.00000	0.0387202
$668$	−7.04759	−0.272679
$669$	2.83297	0.109529
$670$	4.66415	0.180192
$671$	6.32352	0.244117
$672$	−3.82553	−0.147573
$673$	3.76022	0.144946	0.0724728	−	0.997370i	$-0.476911\pi$
$673$	3.76022	0.144946	0.0724728	+	0.997370i	$0.476911\pi$
$674$	−14.3120	−0.551276
$675$	1.56155	0.0601042
$676$	−10.0812	−0.387737
$677$	6.06665	0.233160	0.116580	−	0.993181i	$-0.462807\pi$
$677$	6.06665	0.233160	0.116580	+	0.993181i	$0.462807\pi$
$678$	−2.48842	−0.0955670
$679$	−48.3550	−1.85569
$680$	−11.3561	−0.435487
$681$	−19.0880	−0.731453
$682$	−14.9736	−0.573368
$683$	6.41667	0.245527	0.122764	−	0.992436i	$-0.460824\pi$
$683$	6.41667	0.245527	0.122764	+	0.992436i	$0.460824\pi$
$684$	0.462185	0.0176721
$685$	33.9699	1.29792
$686$	−2.42802	−0.0927024
$687$	−8.37406	−0.319490
$688$	−6.40706	−0.244267
$689$	−0.339531	−0.0129351
$690$	−2.56155	−0.0975166
$691$	33.4935	1.27415	0.637076	−	0.770801i	$-0.280144\pi$
$691$	33.4935	1.27415	0.637076	+	0.770801i	$0.280144\pi$
$692$	−7.39157	−0.280985
$693$	10.9910	0.417514
$694$	−32.7009	−1.24131
$695$	−30.0727	−1.14072
$696$	−1.00000	−0.0379049
$697$	−16.3551	−0.619494
$698$	−19.5602	−0.740363
$699$	0.898443	0.0339822
$700$	5.97377	0.225787
$701$	−8.84400	−0.334033	−0.167017	−	0.985954i	$-0.553413\pi$
$701$	−8.84400	−0.334033	−0.167017	+	0.985954i	$0.553413\pi$
$702$	−1.70846	−0.0644817
$703$	−3.35771	−0.126638
$704$	2.87307	0.108283
$705$	7.50549	0.282673
$706$	−28.6088	−1.07671
$707$	−22.5920	−0.849661
$708$	−13.5156	−0.507946
$709$	−22.6070	−0.849023	−0.424511	−	0.905423i	$-0.639554\pi$
$709$	−22.6070	−0.849023	−0.424511	+	0.905423i	$0.639554\pi$
$710$	5.86593	0.220144
$711$	−12.5221	−0.469617
$712$	−15.9787	−0.598828
$713$	5.21170	0.195180
$714$	−16.9597	−0.634701
$715$	12.5734	0.470220
$716$	−22.7805	−0.851349
$717$	24.0009	0.896330
$718$	7.60447	0.283796
$719$	17.2390	0.642905	0.321452	−	0.946926i	$-0.395829\pi$
$719$	17.2390	0.642905	0.321452	+	0.946926i	$0.395829\pi$
$720$	2.56155	0.0954634
$721$	−70.2606	−2.61664
$722$	18.7864	0.699157
$723$	8.48633	0.315610
$724$	−0.407188	−0.0151330
$725$	1.56155	0.0579946
$726$	2.74546	0.101894
$727$	0.738351	0.0273839	0.0136920	−	0.999906i	$-0.495642\pi$
$727$	0.738351	0.0273839	0.0136920	+	0.999906i	$0.495642\pi$
$728$	−6.53577	−0.242232
$729$	1.00000	0.0370370
$730$	−2.00948	−0.0743742
$731$	−28.4044	−1.05057
$732$	2.20096	0.0813499
$733$	21.1352	0.780646	0.390323	−	0.920678i	$-0.372363\pi$
$733$	21.1352	0.780646	0.390323	+	0.920678i	$0.372363\pi$
$734$	−10.1229	−0.373643
$735$	19.5567	0.721358
$736$	−1.00000	−0.0368605
$737$	−5.23137	−0.192700
$738$	3.68916	0.135800
$739$	−14.0692	−0.517545	−0.258772	−	0.965938i	$-0.583318\pi$
$739$	−14.0692	−0.517545	−0.258772	+	0.965938i	$0.583318\pi$
$740$	−18.6093	−0.684092
$741$	0.789625	0.0290076
$742$	0.760267	0.0279103
$743$	34.8122	1.27714	0.638568	−	0.769566i	$-0.279527\pi$
$743$	34.8122	1.27714	0.638568	+	0.769566i	$0.279527\pi$
$744$	−5.21170	−0.191070
$745$	−14.7123	−0.539016
$746$	−12.4725	−0.456652
$747$	5.18929	0.189866
$748$	12.7372	0.465717
$749$	−27.2009	−0.993900
$750$	8.80776	0.321614
$751$	15.5885	0.568834	0.284417	−	0.958701i	$-0.408200\pi$
$751$	15.5885	0.568834	0.284417	+	0.958701i	$0.408200\pi$
$752$	2.93005	0.106848
$753$	24.2642	0.884237
$754$	−1.70846	−0.0622184
$755$	1.57866	0.0574531
$756$	3.82553	0.139133
$757$	−11.6376	−0.422975	−0.211488	−	0.977381i	$-0.567831\pi$
$757$	−11.6376	−0.422975	−0.211488	+	0.977381i	$0.567831\pi$
$758$	−2.94556	−0.106988
$759$	2.87307	0.104286
$760$	−1.18391	−0.0429450
$761$	13.1327	0.476062	0.238031	−	0.971258i	$-0.423498\pi$
$761$	13.1327	0.476062	0.238031	+	0.971258i	$0.423498\pi$
$762$	−10.9345	−0.396113
$763$	−65.5180	−2.37191
$764$	10.9924	0.397692
$765$	11.3561	0.410581
$766$	−22.6645	−0.818900
$767$	−23.0908	−0.833761
$768$	1.00000	0.0360844
$769$	−24.4840	−0.882917	−0.441459	−	0.897282i	$-0.645539\pi$
$769$	−24.4840	−0.882917	−0.441459	+	0.897282i	$0.645539\pi$
$770$	−28.1541	−1.01460
$771$	−16.8360	−0.606332
$772$	−8.10898	−0.291849
$773$	−29.3150	−1.05439	−0.527193	−	0.849745i	$-0.676756\pi$
$773$	−29.3150	−1.05439	−0.527193	+	0.849745i	$0.676756\pi$
$774$	6.40706	0.230297
$775$	8.13834	0.292338
$776$	12.6401	0.453752
$777$	−27.7919	−0.997030
$778$	4.64955	0.166694
$779$	−1.70507	−0.0610906
$780$	4.37631	0.156697
$781$	−6.57930	−0.235426
$782$	−4.43329	−0.158534
$783$	1.00000	0.0357371
$784$	7.63469	0.272667
$785$	2.90980	0.103855
$786$	−3.24157	−0.115623
$787$	45.3290	1.61580	0.807902	−	0.589317i	$-0.200603\pi$
$787$	45.3290	1.61580	0.807902	+	0.589317i	$0.200603\pi$
$788$	−13.9780	−0.497944
$789$	−19.4829	−0.693608
$790$	32.0761	1.14122
$791$	9.51951	0.338475
$792$	−2.87307	−0.102090
$793$	3.76025	0.133531
$794$	28.3731	1.00692
$795$	−0.509070	−0.0180549
$796$	6.97388	0.247183
$797$	31.9680	1.13236	0.566182	−	0.824280i	$-0.308420\pi$
$797$	31.9680	1.13236	0.566182	+	0.824280i	$0.308420\pi$
$798$	−1.76810	−0.0625902
$799$	12.9898	0.459546
$800$	−1.56155	−0.0552092
$801$	15.9787	0.564581
$802$	−29.8660	−1.05460
$803$	2.25386	0.0795369
$804$	−1.82083	−0.0642157
$805$	9.79930	0.345380
$806$	−8.90398	−0.313629
$807$	12.3220	0.433755
$808$	5.90560	0.207758
$809$	−27.2334	−0.957474	−0.478737	−	0.877958i	$-0.658905\pi$
$809$	−27.2334	−0.957474	−0.478737	+	0.877958i	$0.658905\pi$
$810$	−2.56155	−0.0900038
$811$	50.5507	1.77507	0.887537	−	0.460736i	$-0.152414\pi$
$811$	50.5507	1.77507	0.887537	+	0.460736i	$0.152414\pi$
$812$	3.82553	0.134250
$813$	−3.55749	−0.124767
$814$	20.8725	0.731579
$815$	−7.30326	−0.255822
$816$	4.43329	0.155196
$817$	−2.96125	−0.103601
$818$	−17.7445	−0.620421
$819$	6.53577	0.228378
$820$	−9.44997	−0.330007
$821$	−52.8713	−1.84522	−0.922610	−	0.385733i	$-0.873949\pi$
$821$	−52.8713	−1.84522	−0.922610	+	0.385733i	$0.873949\pi$
$822$	−13.2614	−0.462546
$823$	1.69862	0.0592100	0.0296050	−	0.999562i	$-0.490575\pi$
$823$	1.69862	0.0592100	0.0296050	+	0.999562i	$0.490575\pi$
$824$	18.3662	0.639818
$825$	4.48645	0.156198
$826$	51.7042	1.79902
$827$	0.582207	0.0202453	0.0101227	−	0.999949i	$-0.496778\pi$
$827$	0.582207	0.0202453	0.0101227	+	0.999949i	$0.496778\pi$
$828$	1.00000	0.0347524
$829$	−25.9926	−0.902760	−0.451380	−	0.892332i	$-0.649068\pi$
$829$	−25.9926	−0.902760	−0.451380	+	0.892332i	$0.649068\pi$
$830$	−13.2926	−0.461394
$831$	−22.2167	−0.770689
$832$	1.70846	0.0592302
$833$	33.8468	1.17272
$834$	11.7400	0.406524
$835$	−18.0528	−0.624742
$836$	1.32789	0.0459261
$837$	5.21170	0.180143
$838$	−9.04448	−0.312437
$839$	−22.4806	−0.776115	−0.388058	−	0.921635i	$-0.626854\pi$
$839$	−22.4806	−0.776115	−0.388058	+	0.921635i	$0.626854\pi$
$840$	−9.79930	−0.338108
$841$	1.00000	0.0344828
$842$	−3.65832	−0.126074
$843$	−14.6265	−0.503762
$844$	3.84463	0.132338
$845$	−25.8234	−0.888353
$846$	−2.93005	−0.100737
$847$	−10.5029	−0.360883
$848$	−0.198735	−0.00682459
$849$	29.5344	1.01362
$850$	−6.92282	−0.237451
$851$	−7.26486	−0.249036
$852$	−2.28999	−0.0784538
$853$	38.5861	1.32116	0.660582	−	0.750754i	$-0.270310\pi$
$853$	38.5861	1.32116	0.660582	+	0.750754i	$0.270310\pi$
$854$	−8.41985	−0.288121
$855$	1.18391	0.0404889
$856$	7.11037	0.243027
$857$	−4.61428	−0.157621	−0.0788104	−	0.996890i	$-0.525112\pi$
$857$	−4.61428	−0.157621	−0.0788104	+	0.996890i	$0.525112\pi$
$858$	−4.90853	−0.167574
$859$	39.8730	1.36045	0.680225	−	0.733003i	$-0.261882\pi$
$859$	39.8730	1.36045	0.680225	+	0.733003i	$0.261882\pi$
$860$	−16.4120	−0.559645
$861$	−14.1130	−0.480969
$862$	−7.77367	−0.264772
$863$	−27.3805	−0.932042	−0.466021	−	0.884774i	$-0.654313\pi$
$863$	−27.3805	−0.932042	−0.466021	+	0.884774i	$0.654313\pi$
$864$	−1.00000	−0.0340207
$865$	−18.9339	−0.643772
$866$	10.5159	0.357344
$867$	2.65408	0.0901374
$868$	19.9375	0.676723
$869$	−35.9770	−1.22044
$870$	−2.56155	−0.0868448
$871$	−3.11081	−0.105406
$872$	17.1265	0.579977
$873$	−12.6401	−0.427802
$874$	−0.462185	−0.0156336
$875$	−33.6944	−1.13908
$876$	0.784477	0.0265050
$877$	17.6076	0.594568	0.297284	−	0.954789i	$-0.403919\pi$
$877$	17.6076	0.594568	0.297284	+	0.954789i	$0.403919\pi$
$878$	−3.77214	−0.127304
$879$	27.8409	0.939050
$880$	7.35952	0.248089
$881$	8.84295	0.297927	0.148963	−	0.988843i	$-0.452406\pi$
$881$	8.84295	0.297927	0.148963	+	0.988843i	$0.452406\pi$
$882$	−7.63469	−0.257073
$883$	−0.618326	−0.0208083	−0.0104042	−	0.999946i	$-0.503312\pi$
$883$	−0.618326	−0.0208083	−0.0104042	+	0.999946i	$0.503312\pi$
$884$	7.57410	0.254745
$885$	−34.6208	−1.16377
$886$	30.8713	1.03714
$887$	1.57749	0.0529670	0.0264835	−	0.999649i	$-0.491569\pi$
$887$	1.57749	0.0529670	0.0264835	+	0.999649i	$0.491569\pi$
$888$	7.26486	0.243793
$889$	41.8301	1.40294
$890$	−40.9304	−1.37199
$891$	2.87307	0.0962515
$892$	2.83297	0.0948548
$893$	1.35423	0.0453175
$894$	5.74350	0.192091
$895$	−58.3536	−1.95054
$896$	−3.82553	−0.127802
$897$	1.70846	0.0570438
$898$	−36.1308	−1.20570
$899$	5.21170	0.173820
$900$	1.56155	0.0520518
$901$	−0.881051	−0.0293521
$902$	10.5992	0.352915
$903$	−24.5104	−0.815656
$904$	−2.48842	−0.0827635
$905$	−1.04303	−0.0346716
$906$	−0.616288	−0.0204748
$907$	4.27530	0.141959	0.0709795	−	0.997478i	$-0.477388\pi$
$907$	4.27530	0.141959	0.0709795	+	0.997478i	$0.477388\pi$
$908$	−19.0880	−0.633457
$909$	−5.90560	−0.195876
$910$	−16.7417	−0.554982
$911$	2.79965	0.0927566	0.0463783	−	0.998924i	$-0.485232\pi$
$911$	2.79965	0.0927566	0.0463783	+	0.998924i	$0.485232\pi$
$912$	0.462185	0.0153045
$913$	14.9092	0.493423
$914$	−7.25147	−0.239857
$915$	5.63788	0.186383
$916$	−8.37406	−0.276687
$917$	12.4007	0.409508
$918$	−4.43329	−0.146320
$919$	−23.7238	−0.782577	−0.391289	−	0.920268i	$-0.627971\pi$
$919$	−23.7238	−0.782577	−0.391289	+	0.920268i	$0.627971\pi$
$920$	−2.56155	−0.0844519
$921$	−6.74341	−0.222203
$922$	−24.7200	−0.814110
$923$	−3.91236	−0.128777
$924$	10.9910	0.361578
$925$	−11.3445	−0.373004
$926$	−1.89180	−0.0621683
$927$	−18.3662	−0.603226
$928$	−1.00000	−0.0328266
$929$	−21.1339	−0.693382	−0.346691	−	0.937979i	$-0.612695\pi$
$929$	−21.1339	−0.693382	−0.346691	+	0.937979i	$0.612695\pi$
$930$	−13.3500	−0.437765
$931$	3.52864	0.115647
$932$	0.898443	0.0294295
$933$	34.2339	1.12077
$934$	−18.1455	−0.593738
$935$	32.6269	1.06701
$936$	−1.70846	−0.0558428
$937$	−48.5643	−1.58653	−0.793263	−	0.608879i	$-0.791619\pi$
$937$	−48.5643	−1.58653	−0.793263	+	0.608879i	$0.791619\pi$
$938$	6.96563	0.227436
$939$	0.323828	0.0105677
$940$	7.50549	0.244802
$941$	−6.68030	−0.217772	−0.108886	−	0.994054i	$-0.534728\pi$
$941$	−6.68030	−0.217772	−0.108886	+	0.994054i	$0.534728\pi$
$942$	−1.13595	−0.0370113
$943$	−3.68916	−0.120136
$944$	−13.5156	−0.439894
$945$	9.79930	0.318771
$946$	18.4079	0.598494
$947$	19.0142	0.617879	0.308939	−	0.951082i	$-0.400026\pi$
$947$	19.0142	0.617879	0.308939	+	0.951082i	$0.400026\pi$
$948$	−12.5221	−0.406700
$949$	1.34025	0.0435063
$950$	−0.721727	−0.0234159
$951$	11.4115	0.370045
$952$	−16.9597	−0.549667
$953$	−16.4897	−0.534152	−0.267076	−	0.963675i	$-0.586058\pi$
$953$	−16.4897	−0.534152	−0.267076	+	0.963675i	$0.586058\pi$
$954$	0.198735	0.00643429
$955$	28.1577	0.911160
$956$	24.0009	0.776244
$957$	2.87307	0.0928732
$958$	15.7127	0.507653
$959$	50.7321	1.63822
$960$	2.56155	0.0826738
$961$	−3.83819	−0.123813
$962$	12.4117	0.400170
$963$	−7.11037	−0.229128
$964$	8.48633	0.273326
$965$	−20.7716	−0.668661
$966$	−3.82553	−0.123084
$967$	27.4948	0.884173	0.442087	−	0.896972i	$-0.354238\pi$
$967$	27.4948	0.884173	0.442087	+	0.896972i	$0.354238\pi$
$968$	2.74546	0.0882426
$969$	2.04900	0.0658234
$970$	32.3782	1.03960
$971$	−10.7041	−0.343511	−0.171756	−	0.985140i	$-0.554944\pi$
$971$	−10.7041	−0.343511	−0.171756	+	0.985140i	$0.554944\pi$
$972$	1.00000	0.0320750
$973$	−44.9119	−1.43981
$974$	5.04994	0.161811
$975$	2.66785	0.0854396
$976$	2.20096	0.0704511
$977$	−48.4268	−1.54931	−0.774655	−	0.632384i	$-0.782076\pi$
$977$	−48.4268	−1.54931	−0.774655	+	0.632384i	$0.782076\pi$
$978$	2.85111	0.0911684
$979$	45.9080	1.46723
$980$	19.5567	0.624715
$981$	−17.1265	−0.546808
$982$	13.1959	0.421097
$983$	−16.1280	−0.514402	−0.257201	−	0.966358i	$-0.582800\pi$
$983$	−16.1280	−0.514402	−0.257201	+	0.966358i	$0.582800\pi$
$984$	3.68916	0.117606
$985$	−35.8053	−1.14085
$986$	−4.43329	−0.141185
$987$	11.2090	0.356787
$988$	0.789625	0.0251213
$989$	−6.40706	−0.203733
$990$	−7.35952	−0.233901
$991$	−1.80448	−0.0573212	−0.0286606	−	0.999589i	$-0.509124\pi$
$991$	−1.80448	−0.0573212	−0.0286606	+	0.999589i	$0.509124\pi$
$992$	−5.21170	−0.165472
$993$	−7.35316	−0.233346
$994$	8.76043	0.277864
$995$	17.8640	0.566326
$996$	5.18929	0.164429
$997$	−50.8973	−1.61193	−0.805967	−	0.591960i	$-0.798354\pi$
$997$	−50.8973	−1.61193	−0.805967	+	0.591960i	$0.798354\pi$
$998$	15.9560	0.505078
$999$	−7.26486	−0.229850

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bf.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bf.1.6	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} +3.82553 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} +3.82553 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56155 q^{10} +2.87307 q^{11} +1.00000 q^{12} +1.70846 q^{13} -3.82553 q^{14} +2.56155 q^{15} +1.00000 q^{16} +4.43329 q^{17} -1.00000 q^{18} +0.462185 q^{19} +2.56155 q^{20} +3.82553 q^{21} -2.87307 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.56155 q^{25} -1.70846 q^{26} +1.00000 q^{27} +3.82553 q^{28} +1.00000 q^{29} -2.56155 q^{30} +5.21170 q^{31} -1.00000 q^{32} +2.87307 q^{33} -4.43329 q^{34} +9.79930 q^{35} +1.00000 q^{36} -7.26486 q^{37} -0.462185 q^{38} +1.70846 q^{39} -2.56155 q^{40} -3.68916 q^{41} -3.82553 q^{42} -6.40706 q^{43} +2.87307 q^{44} +2.56155 q^{45} -1.00000 q^{46} +2.93005 q^{47} +1.00000 q^{48} +7.63469 q^{49} -1.56155 q^{50} +4.43329 q^{51} +1.70846 q^{52} -0.198735 q^{53} -1.00000 q^{54} +7.35952 q^{55} -3.82553 q^{56} +0.462185 q^{57} -1.00000 q^{58} -13.5156 q^{59} +2.56155 q^{60} +2.20096 q^{61} -5.21170 q^{62} +3.82553 q^{63} +1.00000 q^{64} +4.37631 q^{65} -2.87307 q^{66} -1.82083 q^{67} +4.43329 q^{68} +1.00000 q^{69} -9.79930 q^{70} -2.28999 q^{71} -1.00000 q^{72} +0.784477 q^{73} +7.26486 q^{74} +1.56155 q^{75} +0.462185 q^{76} +10.9910 q^{77} -1.70846 q^{78} -12.5221 q^{79} +2.56155 q^{80} +1.00000 q^{81} +3.68916 q^{82} +5.18929 q^{83} +3.82553 q^{84} +11.3561 q^{85} +6.40706 q^{86} +1.00000 q^{87} -2.87307 q^{88} +15.9787 q^{89} -2.56155 q^{90} +6.53577 q^{91} +1.00000 q^{92} +5.21170 q^{93} -2.93005 q^{94} +1.18391 q^{95} -1.00000 q^{96} -12.6401 q^{97} -7.63469 q^{98} +2.87307 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 7 q^{11} + 6 q^{12} + 3 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 7 q^{22} + 6 q^{23} - 6 q^{24} - 3 q^{25} - 3 q^{26} + 6 q^{27} + 2 q^{28} + 6 q^{29} - 3 q^{30} + q^{31} - 6 q^{32} + 7 q^{33} - 8 q^{34} + 18 q^{35} + 6 q^{36} + 7 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} + 13 q^{41} - 2 q^{42} + 7 q^{44} + 3 q^{45} - 6 q^{46} + 22 q^{47} + 6 q^{48} + 8 q^{49} + 3 q^{50} + 8 q^{51} + 3 q^{52} + 10 q^{53} - 6 q^{54} - 5 q^{55} - 2 q^{56} - 4 q^{57} - 6 q^{58} + 17 q^{59} + 3 q^{60} + q^{61} - q^{62} + 2 q^{63} + 6 q^{64} - 7 q^{65} - 7 q^{66} + 3 q^{67} + 8 q^{68} + 6 q^{69} - 18 q^{70} + 11 q^{71} - 6 q^{72} - 7 q^{74} - 3 q^{75} - 4 q^{76} - 3 q^{78} + 2 q^{79} + 3 q^{80} + 6 q^{81} - 13 q^{82} + 16 q^{83} + 2 q^{84} + 4 q^{85} + 6 q^{87} - 7 q^{88} + 16 q^{89} - 3 q^{90} - 28 q^{91} + 6 q^{92} + q^{93} - 22 q^{94} + 32 q^{95} - 6 q^{96} + 2 q^{97} - 8 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 7 * q^11 + 6 * q^12 + 3 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 7 * q^22 + 6 * q^23 - 6 * q^24 - 3 * q^25 - 3 * q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - 3 * q^30 + q^31 - 6 * q^32 + 7 * q^33 - 8 * q^34 + 18 * q^35 + 6 * q^36 + 7 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 + 13 * q^41 - 2 * q^42 + 7 * q^44 + 3 * q^45 - 6 * q^46 + 22 * q^47 + 6 * q^48 + 8 * q^49 + 3 * q^50 + 8 * q^51 + 3 * q^52 + 10 * q^53 - 6 * q^54 - 5 * q^55 - 2 * q^56 - 4 * q^57 - 6 * q^58 + 17 * q^59 + 3 * q^60 + q^61 - q^62 + 2 * q^63 + 6 * q^64 - 7 * q^65 - 7 * q^66 + 3 * q^67 + 8 * q^68 + 6 * q^69 - 18 * q^70 + 11 * q^71 - 6 * q^72 - 7 * q^74 - 3 * q^75 - 4 * q^76 - 3 * q^78 + 2 * q^79 + 3 * q^80 + 6 * q^81 - 13 * q^82 + 16 * q^83 + 2 * q^84 + 4 * q^85 + 6 * q^87 - 7 * q^88 + 16 * q^89 - 3 * q^90 - 28 * q^91 + 6 * q^92 + q^93 - 22 * q^94 + 32 * q^95 - 6 * q^96 + 2 * q^97 - 8 * q^98 + 7 * q^99

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