LMFDB - Embedded newform 4002.2.a.y.1.3

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:	$3$
Coefficient field:	3.3.1772.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 12x + 8 $ x^3 - x^2 - 12*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.32803$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.32803 q^{5} +1.00000 q^{6} +5.20191 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.32803 q^{5} +1.00000 q^{6} +5.20191 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.32803 q^{10} +3.32803 q^{11} -1.00000 q^{12} -1.32803 q^{13} -5.20191 q^{14} -3.32803 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} -1.20191 q^{19} +3.32803 q^{20} -5.20191 q^{21} -3.32803 q^{22} +1.00000 q^{23} +1.00000 q^{24} +6.07579 q^{25} +1.32803 q^{26} -1.00000 q^{27} +5.20191 q^{28} -1.00000 q^{29} +3.32803 q^{30} -1.32803 q^{31} -1.00000 q^{32} -3.32803 q^{33} -4.00000 q^{34} +17.3121 q^{35} +1.00000 q^{36} -5.07579 q^{37} +1.20191 q^{38} +1.32803 q^{39} -3.32803 q^{40} -0.924208 q^{41} +5.20191 q^{42} +11.8580 q^{43} +3.32803 q^{44} +3.32803 q^{45} -1.00000 q^{46} -10.6561 q^{47} -1.00000 q^{48} +20.0599 q^{49} -6.07579 q^{50} -4.00000 q^{51} -1.32803 q^{52} +6.65606 q^{53} +1.00000 q^{54} +11.0758 q^{55} -5.20191 q^{56} +1.20191 q^{57} +1.00000 q^{58} +11.3280 q^{59} -3.32803 q^{60} +1.32803 q^{61} +1.32803 q^{62} +5.20191 q^{63} +1.00000 q^{64} -4.41973 q^{65} +3.32803 q^{66} +1.32803 q^{67} +4.00000 q^{68} -1.00000 q^{69} -17.3121 q^{70} -9.58027 q^{71} -1.00000 q^{72} -2.25224 q^{73} +5.07579 q^{74} -6.07579 q^{75} -1.20191 q^{76} +17.3121 q^{77} -1.32803 q^{78} -8.40382 q^{79} +3.32803 q^{80} +1.00000 q^{81} +0.924208 q^{82} -9.60574 q^{83} -5.20191 q^{84} +13.3121 q^{85} -11.8580 q^{86} +1.00000 q^{87} -3.32803 q^{88} -10.6561 q^{89} -3.32803 q^{90} -6.90830 q^{91} +1.00000 q^{92} +1.32803 q^{93} +10.6561 q^{94} -4.00000 q^{95} +1.00000 q^{96} +13.4542 q^{97} -20.0599 q^{98} +3.32803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} + 3 q^{6} + 6 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 + 3 * q^6 + 6 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} + 3 q^{6} + 6 q^{7} - 3 q^{8} + 3 q^{9} + q^{10} - q^{11} - 3 q^{12} + 7 q^{13} - 6 q^{14} + q^{15} + 3 q^{16} + 12 q^{17} - 3 q^{18} + 6 q^{19} - q^{20} - 6 q^{21} + q^{22} + 3 q^{23} + 3 q^{24} + 10 q^{25} - 7 q^{26} - 3 q^{27} + 6 q^{28} - 3 q^{29} - q^{30} + 7 q^{31} - 3 q^{32} + q^{33} - 12 q^{34} + 8 q^{35} + 3 q^{36} - 7 q^{37} - 6 q^{38} - 7 q^{39} + q^{40} - 11 q^{41} + 6 q^{42} + 4 q^{43} - q^{44} - q^{45} - 3 q^{46} - 10 q^{47} - 3 q^{48} + 19 q^{49} - 10 q^{50} - 12 q^{51} + 7 q^{52} - 2 q^{53} + 3 q^{54} + 25 q^{55} - 6 q^{56} - 6 q^{57} + 3 q^{58} + 23 q^{59} + q^{60} - 7 q^{61} - 7 q^{62} + 6 q^{63} + 3 q^{64} - 27 q^{65} - q^{66} - 7 q^{67} + 12 q^{68} - 3 q^{69} - 8 q^{70} - 15 q^{71} - 3 q^{72} - 4 q^{73} + 7 q^{74} - 10 q^{75} + 6 q^{76} + 8 q^{77} + 7 q^{78} - 6 q^{79} - q^{80} + 3 q^{81} + 11 q^{82} - 6 q^{84} - 4 q^{85} - 4 q^{86} + 3 q^{87} + q^{88} - 10 q^{89} + q^{90} + 4 q^{91} + 3 q^{92} - 7 q^{93} + 10 q^{94} - 12 q^{95} + 3 q^{96} + 28 q^{97} - 19 q^{98} - q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 + 3 * q^6 + 6 * q^7 - 3 * q^8 + 3 * q^9 + q^10 - q^11 - 3 * q^12 + 7 * q^13 - 6 * q^14 + q^15 + 3 * q^16 + 12 * q^17 - 3 * q^18 + 6 * q^19 - q^20 - 6 * q^21 + q^22 + 3 * q^23 + 3 * q^24 + 10 * q^25 - 7 * q^26 - 3 * q^27 + 6 * q^28 - 3 * q^29 - q^30 + 7 * q^31 - 3 * q^32 + q^33 - 12 * q^34 + 8 * q^35 + 3 * q^36 - 7 * q^37 - 6 * q^38 - 7 * q^39 + q^40 - 11 * q^41 + 6 * q^42 + 4 * q^43 - q^44 - q^45 - 3 * q^46 - 10 * q^47 - 3 * q^48 + 19 * q^49 - 10 * q^50 - 12 * q^51 + 7 * q^52 - 2 * q^53 + 3 * q^54 + 25 * q^55 - 6 * q^56 - 6 * q^57 + 3 * q^58 + 23 * q^59 + q^60 - 7 * q^61 - 7 * q^62 + 6 * q^63 + 3 * q^64 - 27 * q^65 - q^66 - 7 * q^67 + 12 * q^68 - 3 * q^69 - 8 * q^70 - 15 * q^71 - 3 * q^72 - 4 * q^73 + 7 * q^74 - 10 * q^75 + 6 * q^76 + 8 * q^77 + 7 * q^78 - 6 * q^79 - q^80 + 3 * q^81 + 11 * q^82 - 6 * q^84 - 4 * q^85 - 4 * q^86 + 3 * q^87 + q^88 - 10 * q^89 + q^90 + 4 * q^91 + 3 * q^92 - 7 * q^93 + 10 * q^94 - 12 * q^95 + 3 * q^96 + 28 * q^97 - 19 * q^98 - 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
$5$	3.32803	1.48834	0.744170	−	0.667990i	$-0.232845\pi$
$5$	3.32803	1.48834	0.744170	+	0.667990i	$0.232845\pi$
$6$	1.00000	0.408248
$7$	5.20191	1.96614	0.983069	−	0.183236i	$-0.0586573\pi$
$7$	5.20191	1.96614	0.983069	+	0.183236i	$0.0586573\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.32803	−1.05242
$11$	3.32803	1.00344	0.501720	−	0.865030i	$-0.332701\pi$
$11$	3.32803	1.00344	0.501720	+	0.865030i	$0.332701\pi$
$12$	−1.00000	−0.288675
$13$	−1.32803	−0.368330	−0.184165	−	0.982895i	$-0.558958\pi$
$13$	−1.32803	−0.368330	−0.184165	+	0.982895i	$0.558958\pi$
$14$	−5.20191	−1.39027
$15$	−3.32803	−0.859294
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	−1.00000	−0.235702
$19$	−1.20191	−0.275737	−0.137869	−	0.990451i	$-0.544025\pi$
$19$	−1.20191	−0.275737	−0.137869	+	0.990451i	$0.544025\pi$
$20$	3.32803	0.744170
$21$	−5.20191	−1.13515
$22$	−3.32803	−0.709539
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	6.07579	1.21516
$26$	1.32803	0.260448
$27$	−1.00000	−0.192450
$28$	5.20191	0.983069
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.32803	0.607613
$31$	−1.32803	−0.238521	−0.119261	−	0.992863i	$-0.538052\pi$
$31$	−1.32803	−0.238521	−0.119261	+	0.992863i	$0.538052\pi$
$32$	−1.00000	−0.176777
$33$	−3.32803	−0.579336
$34$	−4.00000	−0.685994
$35$	17.3121	2.92628
$36$	1.00000	0.166667
$37$	−5.07579	−0.834455	−0.417228	−	0.908802i	$-0.636998\pi$
$37$	−5.07579	−0.834455	−0.417228	+	0.908802i	$0.636998\pi$
$38$	1.20191	0.194976
$39$	1.32803	0.212655
$40$	−3.32803	−0.526208
$41$	−0.924208	−0.144337	−0.0721685	−	0.997392i	$-0.522992\pi$
$41$	−0.924208	−0.144337	−0.0721685	+	0.997392i	$0.522992\pi$
$42$	5.20191	0.802672
$43$	11.8580	1.80832	0.904162	−	0.427190i	$-0.140496\pi$
$43$	11.8580	1.80832	0.904162	+	0.427190i	$0.140496\pi$
$44$	3.32803	0.501720
$45$	3.32803	0.496114
$46$	−1.00000	−0.147442
$47$	−10.6561	−1.55435	−0.777173	−	0.629287i	$-0.783347\pi$
$47$	−10.6561	−1.55435	−0.777173	+	0.629287i	$0.783347\pi$
$48$	−1.00000	−0.144338
$49$	20.0599	2.86570
$50$	−6.07579	−0.859247
$51$	−4.00000	−0.560112
$52$	−1.32803	−0.184165
$53$	6.65606	0.914281	0.457140	−	0.889395i	$-0.348874\pi$
$53$	6.65606	0.914281	0.457140	+	0.889395i	$0.348874\pi$
$54$	1.00000	0.136083
$55$	11.0758	1.49346
$56$	−5.20191	−0.695135
$57$	1.20191	0.159197
$58$	1.00000	0.131306
$59$	11.3280	1.47478	0.737392	−	0.675465i	$-0.236057\pi$
$59$	11.3280	1.47478	0.737392	+	0.675465i	$0.236057\pi$
$60$	−3.32803	−0.429647
$61$	1.32803	0.170037	0.0850185	−	0.996379i	$-0.472905\pi$
$61$	1.32803	0.170037	0.0850185	+	0.996379i	$0.472905\pi$
$62$	1.32803	0.168660
$63$	5.20191	0.655379
$64$	1.00000	0.125000
$65$	−4.41973	−0.548200
$66$	3.32803	0.409652
$67$	1.32803	0.162245	0.0811224	−	0.996704i	$-0.474150\pi$
$67$	1.32803	0.162245	0.0811224	+	0.996704i	$0.474150\pi$
$68$	4.00000	0.485071
$69$	−1.00000	−0.120386
$70$	−17.3121	−2.06919
$71$	−9.58027	−1.13697	−0.568484	−	0.822694i	$-0.692470\pi$
$71$	−9.58027	−1.13697	−0.568484	+	0.822694i	$0.692470\pi$
$72$	−1.00000	−0.117851
$73$	−2.25224	−0.263605	−0.131802	−	0.991276i	$-0.542076\pi$
$73$	−2.25224	−0.263605	−0.131802	+	0.991276i	$0.542076\pi$
$74$	5.07579	0.590049
$75$	−6.07579	−0.701572
$76$	−1.20191	−0.137869
$77$	17.3121	1.97290
$78$	−1.32803	−0.150370
$79$	−8.40382	−0.945504	−0.472752	−	0.881196i	$-0.656739\pi$
$79$	−8.40382	−0.945504	−0.472752	+	0.881196i	$0.656739\pi$
$80$	3.32803	0.372085
$81$	1.00000	0.111111
$82$	0.924208	0.102062
$83$	−9.60574	−1.05437	−0.527183	−	0.849752i	$-0.676752\pi$
$83$	−9.60574	−1.05437	−0.527183	+	0.849752i	$0.676752\pi$
$84$	−5.20191	−0.567575
$85$	13.3121	1.44390
$86$	−11.8580	−1.27868
$87$	1.00000	0.107211
$88$	−3.32803	−0.354769
$89$	−10.6561	−1.12954	−0.564770	−	0.825248i	$-0.691035\pi$
$89$	−10.6561	−1.12954	−0.564770	+	0.825248i	$0.691035\pi$
$90$	−3.32803	−0.350805
$91$	−6.90830	−0.724187
$92$	1.00000	0.104257
$93$	1.32803	0.137710
$94$	10.6561	1.09909
$95$	−4.00000	−0.410391
$96$	1.00000	0.102062
$97$	13.4542	1.36606	0.683031	−	0.730389i	$-0.260661\pi$
$97$	13.4542	1.36606	0.683031	+	0.730389i	$0.260661\pi$
$98$	−20.0599	−2.02635
$99$	3.32803	0.334480
$100$	6.07579	0.607579
$101$	19.4796	1.93829	0.969147	−	0.246483i	$-0.0792750\pi$
$101$	19.4796	1.93829	0.969147	+	0.246483i	$0.0792750\pi$
$102$	4.00000	0.396059
$103$	6.12612	0.603624	0.301812	−	0.953367i	$-0.402408\pi$
$103$	6.12612	0.603624	0.301812	+	0.953367i	$0.402408\pi$
$104$	1.32803	0.130224
$105$	−17.3121	−1.68949
$106$	−6.65606	−0.646494
$107$	−7.45415	−0.720620	−0.360310	−	0.932833i	$-0.617329\pi$
$107$	−7.45415	−0.720620	−0.360310	+	0.932833i	$0.617329\pi$
$108$	−1.00000	−0.0962250
$109$	3.05033	0.292168	0.146084	−	0.989272i	$-0.453333\pi$
$109$	3.05033	0.292168	0.146084	+	0.989272i	$0.453333\pi$
$110$	−11.0758	−1.05604
$111$	5.07579	0.481773
$112$	5.20191	0.491534
$113$	−16.5554	−1.55740	−0.778701	−	0.627395i	$-0.784121\pi$
$113$	−16.5554	−1.55740	−0.778701	+	0.627395i	$0.784121\pi$
$114$	−1.20191	−0.112569
$115$	3.32803	0.310341
$116$	−1.00000	−0.0928477
$117$	−1.32803	−0.122777
$118$	−11.3280	−1.04283
$119$	20.8076	1.90743
$120$	3.32803	0.303806
$121$	0.0757923	0.00689021
$122$	−1.32803	−0.120234
$123$	0.924208	0.0833330
$124$	−1.32803	−0.119261
$125$	3.58027	0.320229
$126$	−5.20191	−0.463423
$127$	0.924208	0.0820102	0.0410051	−	0.999159i	$-0.486944\pi$
$127$	0.924208	0.0820102	0.0410051	+	0.999159i	$0.486944\pi$
$128$	−1.00000	−0.0883883
$129$	−11.8580	−1.04404
$130$	4.41973	0.387636
$131$	−21.4637	−1.87529	−0.937647	−	0.347590i	$-0.887000\pi$
$131$	−21.4637	−1.87529	−0.937647	+	0.347590i	$0.887000\pi$
$132$	−3.32803	−0.289668
$133$	−6.25224	−0.542138
$134$	−1.32803	−0.114724
$135$	−3.32803	−0.286431
$136$	−4.00000	−0.342997
$137$	−14.9083	−1.27370	−0.636851	−	0.770987i	$-0.719763\pi$
$137$	−14.9083	−1.27370	−0.636851	+	0.770987i	$0.719763\pi$
$138$	1.00000	0.0851257
$139$	−0.403824	−0.0342519	−0.0171259	−	0.999853i	$-0.505452\pi$
$139$	−0.403824	−0.0342519	−0.0171259	+	0.999853i	$0.505452\pi$
$140$	17.3121	1.46314
$141$	10.6561	0.897402
$142$	9.58027	0.803958
$143$	−4.41973	−0.369596
$144$	1.00000	0.0833333
$145$	−3.32803	−0.276378
$146$	2.25224	0.186397
$147$	−20.0599	−1.65451
$148$	−5.07579	−0.417228
$149$	−18.2363	−1.49398	−0.746989	−	0.664836i	$-0.768501\pi$
$149$	−18.2363	−1.49398	−0.746989	+	0.664836i	$0.768501\pi$
$150$	6.07579	0.496086
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	1.20191	0.0974879
$153$	4.00000	0.323381
$154$	−17.3121	−1.39505
$155$	−4.41973	−0.355001
$156$	1.32803	0.106328
$157$	−5.49552	−0.438590	−0.219295	−	0.975659i	$-0.570376\pi$
$157$	−5.49552	−0.438590	−0.219295	+	0.975659i	$0.570376\pi$
$158$	8.40382	0.668572
$159$	−6.65606	−0.527860
$160$	−3.32803	−0.263104
$161$	5.20191	0.409968
$162$	−1.00000	−0.0785674
$163$	−9.47962	−0.742501	−0.371250	−	0.928533i	$-0.621071\pi$
$163$	−9.47962	−0.742501	−0.371250	+	0.928533i	$0.621071\pi$
$164$	−0.924208	−0.0721685
$165$	−11.0758	−0.862249
$166$	9.60574	0.745550
$167$	−16.3879	−1.26814	−0.634068	−	0.773278i	$-0.718616\pi$
$167$	−16.3879	−1.26814	−0.634068	+	0.773278i	$0.718616\pi$
$168$	5.20191	0.401336
$169$	−11.2363	−0.864333
$170$	−13.3121	−1.02099
$171$	−1.20191	−0.0919125
$172$	11.8580	0.904162
$173$	−14.6561	−1.11428	−0.557140	−	0.830419i	$-0.688101\pi$
$173$	−14.6561	−1.11428	−0.557140	+	0.830419i	$0.688101\pi$
$174$	−1.00000	−0.0758098
$175$	31.6057	2.38917
$176$	3.32803	0.250860
$177$	−11.3280	−0.851467
$178$	10.6561	0.798706
$179$	22.4038	1.67454	0.837270	−	0.546789i	$-0.184150\pi$
$179$	22.4038	1.67454	0.837270	+	0.546789i	$0.184150\pi$
$180$	3.32803	0.248057
$181$	1.45415	0.108086	0.0540431	−	0.998539i	$-0.482789\pi$
$181$	1.45415	0.108086	0.0540431	+	0.998539i	$0.482789\pi$
$182$	6.90830	0.512077
$183$	−1.32803	−0.0981709
$184$	−1.00000	−0.0737210
$185$	−16.8924	−1.24195
$186$	−1.32803	−0.0973760
$187$	13.3121	0.973479
$188$	−10.6561	−0.777173
$189$	−5.20191	−0.378383
$190$	4.00000	0.290191
$191$	13.1860	0.954106	0.477053	−	0.878875i	$-0.341705\pi$
$191$	13.1860	0.954106	0.477053	+	0.878875i	$0.341705\pi$
$192$	−1.00000	−0.0721688
$193$	−8.65606	−0.623077	−0.311539	−	0.950234i	$-0.600844\pi$
$193$	−8.65606	−0.623077	−0.311539	+	0.950234i	$0.600844\pi$
$194$	−13.4542	−0.965952
$195$	4.41973	0.316503
$196$	20.0599	1.43285
$197$	−2.50448	−0.178437	−0.0892183	−	0.996012i	$-0.528437\pi$
$197$	−2.50448	−0.178437	−0.0892183	+	0.996012i	$0.528437\pi$
$198$	−3.32803	−0.236513
$199$	12.5299	0.888224	0.444112	−	0.895971i	$-0.353519\pi$
$199$	12.5299	0.888224	0.444112	+	0.895971i	$0.353519\pi$
$200$	−6.07579	−0.429623
$201$	−1.32803	−0.0936721
$202$	−19.4796	−1.37058
$203$	−5.20191	−0.365103
$204$	−4.00000	−0.280056
$205$	−3.07579	−0.214823
$206$	−6.12612	−0.426827
$207$	1.00000	0.0695048
$208$	−1.32803	−0.0920824
$209$	−4.00000	−0.276686
$210$	17.3121	1.19465
$211$	0.671969	0.0462602	0.0231301	−	0.999732i	$-0.492637\pi$
$211$	0.671969	0.0462602	0.0231301	+	0.999732i	$0.492637\pi$
$212$	6.65606	0.457140
$213$	9.58027	0.656429
$214$	7.45415	0.509555
$215$	39.4637	2.69140
$216$	1.00000	0.0680414
$217$	−6.90830	−0.468966
$218$	−3.05033	−0.206594
$219$	2.25224	0.152192
$220$	11.0758	0.746730
$221$	−5.31213	−0.357332
$222$	−5.07579	−0.340665
$223$	29.3121	1.96289	0.981443	−	0.191756i	$-0.0614184\pi$
$223$	29.3121	1.96289	0.981443	+	0.191756i	$0.0614184\pi$
$224$	−5.20191	−0.347567
$225$	6.07579	0.405053
$226$	16.5554	1.10125
$227$	9.60574	0.637555	0.318778	−	0.947830i	$-0.396728\pi$
$227$	9.60574	0.637555	0.318778	+	0.947830i	$0.396728\pi$
$228$	1.20191	0.0795986
$229$	−21.2962	−1.40729	−0.703647	−	0.710550i	$-0.748446\pi$
$229$	−21.2962	−1.40729	−0.703647	+	0.710550i	$0.748446\pi$
$230$	−3.32803	−0.219444
$231$	−17.3121	−1.13905
$232$	1.00000	0.0656532
$233$	13.7478	0.900646	0.450323	−	0.892866i	$-0.351309\pi$
$233$	13.7478	0.900646	0.450323	+	0.892866i	$0.351309\pi$
$234$	1.32803	0.0868161
$235$	−35.4637	−2.31340
$236$	11.3280	0.737392
$237$	8.40382	0.545887
$238$	−20.8076	−1.34876
$239$	12.2363	0.791503	0.395751	−	0.918358i	$-0.370484\pi$
$239$	12.2363	0.791503	0.395751	+	0.918358i	$0.370484\pi$
$240$	−3.32803	−0.214823
$241$	−7.05989	−0.454767	−0.227384	−	0.973805i	$-0.573017\pi$
$241$	−7.05989	−0.454767	−0.227384	+	0.973805i	$0.573017\pi$
$242$	−0.0757923	−0.00487211
$243$	−1.00000	−0.0641500
$244$	1.32803	0.0850185
$245$	66.7599	4.26514
$246$	−0.924208	−0.0589253
$247$	1.59618	0.101562
$248$	1.32803	0.0843301
$249$	9.60574	0.608739
$250$	−3.58027	−0.226436
$251$	−9.98409	−0.630190	−0.315095	−	0.949060i	$-0.602036\pi$
$251$	−9.98409	−0.630190	−0.315095	+	0.949060i	$0.602036\pi$
$252$	5.20191	0.327690
$253$	3.32803	0.209232
$254$	−0.924208	−0.0579900
$255$	−13.3121	−0.833638
$256$	1.00000	0.0625000
$257$	−13.2115	−0.824109	−0.412054	−	0.911159i	$-0.635189\pi$
$257$	−13.2115	−0.824109	−0.412054	+	0.911159i	$0.635189\pi$
$258$	11.8580	0.738245
$259$	−26.4038	−1.64065
$260$	−4.41973	−0.274100
$261$	−1.00000	−0.0618984
$262$	21.4637	1.32603
$263$	17.3535	1.07006	0.535031	−	0.844832i	$-0.320300\pi$
$263$	17.3535	1.07006	0.535031	+	0.844832i	$0.320300\pi$
$264$	3.32803	0.204826
$265$	22.1516	1.36076
$266$	6.25224	0.383349
$267$	10.6561	0.652140
$268$	1.32803	0.0811224
$269$	−28.4886	−1.73698	−0.868489	−	0.495708i	$-0.834909\pi$
$269$	−28.4886	−1.73698	−0.868489	+	0.495708i	$0.834909\pi$
$270$	3.32803	0.202538
$271$	−8.41973	−0.511462	−0.255731	−	0.966748i	$-0.582316\pi$
$271$	−8.41973	−0.511462	−0.255731	+	0.966748i	$0.582316\pi$
$272$	4.00000	0.242536
$273$	6.90830	0.418109
$274$	14.9083	0.900643
$275$	20.2204	1.21934
$276$	−1.00000	−0.0601929
$277$	−1.83251	−0.110105	−0.0550524	−	0.998483i	$-0.517533\pi$
$277$	−1.83251	−0.110105	−0.0550524	+	0.998483i	$0.517533\pi$
$278$	0.403824	0.0242197
$279$	−1.32803	−0.0795072
$280$	−17.3121	−1.03460
$281$	2.11021	0.125885	0.0629424	−	0.998017i	$-0.479952\pi$
$281$	2.11021	0.125885	0.0629424	+	0.998017i	$0.479952\pi$
$282$	−10.6561	−0.634559
$283$	20.8236	1.23783	0.618916	−	0.785457i	$-0.287572\pi$
$283$	20.8236	1.23783	0.618916	+	0.785457i	$0.287572\pi$
$284$	−9.58027	−0.568484
$285$	4.00000	0.236940
$286$	4.41973	0.261344
$287$	−4.80765	−0.283786
$288$	−1.00000	−0.0589256
$289$	−1.00000	−0.0588235
$290$	3.32803	0.195429
$291$	−13.4542	−0.788696
$292$	−2.25224	−0.131802
$293$	−16.2618	−0.950024	−0.475012	−	0.879979i	$-0.657556\pi$
$293$	−16.2618	−0.950024	−0.475012	+	0.879979i	$0.657556\pi$
$294$	20.0599	1.16992
$295$	37.7000	2.19498
$296$	5.07579	0.295024
$297$	−3.32803	−0.193112
$298$	18.2363	1.05640
$299$	−1.32803	−0.0768020
$300$	−6.07579	−0.350786
$301$	61.6841	3.55541
$302$	−4.00000	−0.230174
$303$	−19.4796	−1.11907
$304$	−1.20191	−0.0689344
$305$	4.41973	0.253073
$306$	−4.00000	−0.228665
$307$	−20.1357	−1.14920	−0.574602	−	0.818433i	$-0.694843\pi$
$307$	−20.1357	−1.14920	−0.574602	+	0.818433i	$0.694843\pi$
$308$	17.3121	0.986450
$309$	−6.12612	−0.348503
$310$	4.41973	0.251024
$311$	−4.25224	−0.241122	−0.120561	−	0.992706i	$-0.538469\pi$
$311$	−4.25224	−0.241122	−0.120561	+	0.992706i	$0.538469\pi$
$312$	−1.32803	−0.0751850
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	5.49552	0.310130
$315$	17.3121	0.975428
$316$	−8.40382	−0.472752
$317$	24.4886	1.37542	0.687708	−	0.725988i	$-0.258617\pi$
$317$	24.4886	1.37542	0.687708	+	0.725988i	$0.258617\pi$
$318$	6.65606	0.373253
$319$	−3.32803	−0.186334
$320$	3.32803	0.186043
$321$	7.45415	0.416050
$322$	−5.20191	−0.289891
$323$	−4.80765	−0.267505
$324$	1.00000	0.0555556
$325$	−8.06884	−0.447579
$326$	9.47962	0.525027
$327$	−3.05033	−0.168683
$328$	0.924208	0.0510308
$329$	−55.4319	−3.05606
$330$	11.0758	0.609702
$331$	23.7159	1.30355	0.651773	−	0.758414i	$-0.274025\pi$
$331$	23.7159	1.30355	0.651773	+	0.758414i	$0.274025\pi$
$332$	−9.60574	−0.527183
$333$	−5.07579	−0.278152
$334$	16.3879	0.896707
$335$	4.41973	0.241476
$336$	−5.20191	−0.283788
$337$	31.1860	1.69881	0.849405	−	0.527742i	$-0.176961\pi$
$337$	31.1860	1.69881	0.849405	+	0.527742i	$0.176961\pi$
$338$	11.2363	0.611176
$339$	16.5554	0.899166
$340$	13.3121	0.721951
$341$	−4.41973	−0.239342
$342$	1.20191	0.0649919
$343$	67.9364	3.66822
$344$	−11.8580	−0.639339
$345$	−3.32803	−0.179175
$346$	14.6561	0.787915
$347$	−10.1198	−0.543258	−0.271629	−	0.962402i	$-0.587562\pi$
$347$	−10.1198	−0.543258	−0.271629	+	0.962402i	$0.587562\pi$
$348$	1.00000	0.0536056
$349$	7.42869	0.397648	0.198824	−	0.980035i	$-0.436288\pi$
$349$	7.42869	0.397648	0.198824	+	0.980035i	$0.436288\pi$
$350$	−31.6057	−1.68940
$351$	1.32803	0.0708851
$352$	−3.32803	−0.177385
$353$	2.00000	0.106449	0.0532246	−	0.998583i	$-0.483050\pi$
$353$	2.00000	0.106449	0.0532246	+	0.998583i	$0.483050\pi$
$354$	11.3280	0.602078
$355$	−31.8834	−1.69220
$356$	−10.6561	−0.564770
$357$	−20.8076	−1.10126
$358$	−22.4038	−1.18408
$359$	28.7663	1.51823	0.759113	−	0.650959i	$-0.225633\pi$
$359$	28.7663	1.51823	0.759113	+	0.650959i	$0.225633\pi$
$360$	−3.32803	−0.175403
$361$	−17.5554	−0.923969
$362$	−1.45415	−0.0764285
$363$	−0.0757923	−0.00397806
$364$	−6.90830	−0.362093
$365$	−7.49552	−0.392334
$366$	1.32803	0.0694173
$367$	15.5962	0.814114	0.407057	−	0.913403i	$-0.366555\pi$
$367$	15.5962	0.814114	0.407057	+	0.913403i	$0.366555\pi$
$368$	1.00000	0.0521286
$369$	−0.924208	−0.0481123
$370$	16.8924	0.878194
$371$	34.6243	1.79760
$372$	1.32803	0.0688552
$373$	−29.1701	−1.51037	−0.755185	−	0.655511i	$-0.772453\pi$
$373$	−29.1701	−1.51037	−0.755185	+	0.655511i	$0.772453\pi$
$374$	−13.3121	−0.688354
$375$	−3.58027	−0.184884
$376$	10.6561	0.549544
$377$	1.32803	0.0683971
$378$	5.20191	0.267557
$379$	−6.26180	−0.321647	−0.160823	−	0.986983i	$-0.551415\pi$
$379$	−6.26180	−0.321647	−0.160823	+	0.986983i	$0.551415\pi$
$380$	−4.00000	−0.205196
$381$	−0.924208	−0.0473486
$382$	−13.1860	−0.674655
$383$	30.1516	1.54067	0.770337	−	0.637637i	$-0.220088\pi$
$383$	30.1516	1.54067	0.770337	+	0.637637i	$0.220088\pi$
$384$	1.00000	0.0510310
$385$	57.6153	2.93635
$386$	8.65606	0.440582
$387$	11.8580	0.602775
$388$	13.4542	0.683031
$389$	−18.3625	−0.931013	−0.465507	−	0.885044i	$-0.654128\pi$
$389$	−18.3625	−0.931013	−0.465507	+	0.885044i	$0.654128\pi$
$390$	−4.41973	−0.223802
$391$	4.00000	0.202289
$392$	−20.0599	−1.01318
$393$	21.4637	1.08270
$394$	2.50448	0.126174
$395$	−27.9682	−1.40723
$396$	3.32803	0.167240
$397$	−10.0000	−0.501886	−0.250943	−	0.968002i	$-0.580741\pi$
$397$	−10.0000	−0.501886	−0.250943	+	0.968002i	$0.580741\pi$
$398$	−12.5299	−0.628069
$399$	6.25224	0.313003
$400$	6.07579	0.303790
$401$	−5.18601	−0.258977	−0.129488	−	0.991581i	$-0.541333\pi$
$401$	−5.18601	−0.258977	−0.129488	+	0.991581i	$0.541333\pi$
$402$	1.32803	0.0662362
$403$	1.76367	0.0878545
$404$	19.4796	0.969147
$405$	3.32803	0.165371
$406$	5.20191	0.258167
$407$	−16.8924	−0.837325
$408$	4.00000	0.198030
$409$	11.8166	0.584293	0.292147	−	0.956374i	$-0.405630\pi$
$409$	11.8166	0.584293	0.292147	+	0.956374i	$0.405630\pi$
$410$	3.07579	0.151903
$411$	14.9083	0.735372
$412$	6.12612	0.301812
$413$	58.9274	2.89963
$414$	−1.00000	−0.0491473
$415$	−31.9682	−1.56926
$416$	1.32803	0.0651121
$417$	0.403824	0.0197753
$418$	4.00000	0.195646
$419$	−26.1102	−1.27557	−0.637784	−	0.770216i	$-0.720149\pi$
$419$	−26.1102	−1.27557	−0.637784	+	0.770216i	$0.720149\pi$
$420$	−17.3121	−0.844745
$421$	4.48857	0.218760	0.109380	−	0.994000i	$-0.465114\pi$
$421$	4.48857	0.218760	0.109380	+	0.994000i	$0.465114\pi$
$422$	−0.671969	−0.0327109
$423$	−10.6561	−0.518115
$424$	−6.65606	−0.323247
$425$	24.3032	1.17888
$426$	−9.58027	−0.464166
$427$	6.90830	0.334316
$428$	−7.45415	−0.360310
$429$	4.41973	0.213387
$430$	−39.4637	−1.90311
$431$	−9.56436	−0.460699	−0.230350	−	0.973108i	$-0.573987\pi$
$431$	−9.56436	−0.460699	−0.230350	+	0.973108i	$0.573987\pi$
$432$	−1.00000	−0.0481125
$433$	23.3535	1.12230	0.561149	−	0.827715i	$-0.310360\pi$
$433$	23.3535	1.12230	0.561149	+	0.827715i	$0.310360\pi$
$434$	6.90830	0.331609
$435$	3.32803	0.159567
$436$	3.05033	0.146084
$437$	−1.20191	−0.0574952
$438$	−2.25224	−0.107616
$439$	4.83946	0.230975	0.115487	−	0.993309i	$-0.463157\pi$
$439$	4.83946	0.230975	0.115487	+	0.993309i	$0.463157\pi$
$440$	−11.0758	−0.528018
$441$	20.0599	0.955233
$442$	5.31213	0.252672
$443$	37.4319	1.77844	0.889222	−	0.457477i	$-0.151247\pi$
$443$	37.4319	1.77844	0.889222	+	0.457477i	$0.151247\pi$
$444$	5.07579	0.240886
$445$	−35.4637	−1.68114
$446$	−29.3121	−1.38797
$447$	18.2363	0.862549
$448$	5.20191	0.245767
$449$	−1.42869	−0.0674239	−0.0337119	−	0.999432i	$-0.510733\pi$
$449$	−1.42869	−0.0674239	−0.0337119	+	0.999432i	$0.510733\pi$
$450$	−6.07579	−0.286416
$451$	−3.07579	−0.144833
$452$	−16.5554	−0.778701
$453$	−4.00000	−0.187936
$454$	−9.60574	−0.450819
$455$	−22.9910	−1.07784
$456$	−1.20191	−0.0562847
$457$	−7.84842	−0.367133	−0.183567	−	0.983007i	$-0.558764\pi$
$457$	−7.84842	−0.367133	−0.183567	+	0.983007i	$0.558764\pi$
$458$	21.2962	0.995107
$459$	−4.00000	−0.186704
$460$	3.32803	0.155170
$461$	−35.9523	−1.67446	−0.837232	−	0.546847i	$-0.815828\pi$
$461$	−35.9523	−1.67446	−0.837232	+	0.546847i	$0.815828\pi$
$462$	17.3121	0.805433
$463$	28.3032	1.31536	0.657680	−	0.753298i	$-0.271538\pi$
$463$	28.3032	1.31536	0.657680	+	0.753298i	$0.271538\pi$
$464$	−1.00000	−0.0464238
$465$	4.41973	0.204960
$466$	−13.7478	−0.636853
$467$	−37.7000	−1.74455	−0.872275	−	0.489016i	$-0.837356\pi$
$467$	−37.7000	−1.74455	−0.872275	+	0.489016i	$0.837356\pi$
$468$	−1.32803	−0.0613883
$469$	6.90830	0.318996
$470$	35.4637	1.63582
$471$	5.49552	0.253220
$472$	−11.3280	−0.521415
$473$	39.4637	1.81454
$474$	−8.40382	−0.386000
$475$	−7.30257	−0.335065
$476$	20.8076	0.953717
$477$	6.65606	0.304760
$478$	−12.2363	−0.559677
$479$	−13.7732	−0.629315	−0.314657	−	0.949205i	$-0.601890\pi$
$479$	−13.7732	−0.629315	−0.314657	+	0.949205i	$0.601890\pi$
$480$	3.32803	0.151903
$481$	6.74081	0.307355
$482$	7.05989	0.321569
$483$	−5.20191	−0.236695
$484$	0.0757923	0.00344510
$485$	44.7758	2.03317
$486$	1.00000	0.0453609
$487$	−16.3032	−0.738767	−0.369384	−	0.929277i	$-0.620431\pi$
$487$	−16.3032	−0.738767	−0.369384	+	0.929277i	$0.620431\pi$
$488$	−1.32803	−0.0601172
$489$	9.47962	0.428683
$490$	−66.7599	−3.01591
$491$	3.31213	0.149474	0.0747371	−	0.997203i	$-0.476188\pi$
$491$	3.31213	0.149474	0.0747371	+	0.997203i	$0.476188\pi$
$492$	0.924208	0.0416665
$493$	−4.00000	−0.180151
$494$	−1.59618	−0.0718154
$495$	11.0758	0.497820
$496$	−1.32803	−0.0596304
$497$	−49.8357	−2.23544
$498$	−9.60574	−0.430443
$499$	−31.0281	−1.38901	−0.694504	−	0.719489i	$-0.744376\pi$
$499$	−31.0281	−1.38901	−0.694504	+	0.719489i	$0.744376\pi$
$500$	3.58027	0.160115
$501$	16.3879	0.732158
$502$	9.98409	0.445612
$503$	29.8580	1.33130	0.665651	−	0.746264i	$-0.268154\pi$
$503$	29.8580	1.33130	0.665651	+	0.746264i	$0.268154\pi$
$504$	−5.20191	−0.231712
$505$	64.8288	2.88484
$506$	−3.32803	−0.147949
$507$	11.2363	0.499023
$508$	0.924208	0.0410051
$509$	23.1605	1.02657	0.513286	−	0.858217i	$-0.328428\pi$
$509$	23.1605	1.02657	0.513286	+	0.858217i	$0.328428\pi$
$510$	13.3121	0.589471
$511$	−11.7159	−0.518283
$512$	−1.00000	−0.0441942
$513$	1.20191	0.0530657
$514$	13.2115	0.582733
$515$	20.3879	0.898399
$516$	−11.8580	−0.522018
$517$	−35.4637	−1.55969
$518$	26.4038	1.16012
$519$	14.6561	0.643330
$520$	4.41973	0.193818
$521$	−25.6057	−1.12181	−0.560904	−	0.827881i	$-0.689546\pi$
$521$	−25.6057	−1.12181	−0.560904	+	0.827881i	$0.689546\pi$
$522$	1.00000	0.0437688
$523$	1.83251	0.0801300	0.0400650	−	0.999197i	$-0.487243\pi$
$523$	1.83251	0.0801300	0.0400650	+	0.999197i	$0.487243\pi$
$524$	−21.4637	−0.937647
$525$	−31.6057	−1.37939
$526$	−17.3535	−0.756648
$527$	−5.31213	−0.231400
$528$	−3.32803	−0.144834
$529$	1.00000	0.0434783
$530$	−22.1516	−0.962203
$531$	11.3280	0.491595
$532$	−6.25224	−0.271069
$533$	1.22738	0.0531636
$534$	−10.6561	−0.461133
$535$	−24.8076	−1.07253
$536$	−1.32803	−0.0573622
$537$	−22.4038	−0.966796
$538$	28.4886	1.22823
$539$	66.7599	2.87555
$540$	−3.32803	−0.143216
$541$	2.94011	0.126405	0.0632027	−	0.998001i	$-0.479869\pi$
$541$	2.94011	0.126405	0.0632027	+	0.998001i	$0.479869\pi$
$542$	8.41973	0.361658
$543$	−1.45415	−0.0624036
$544$	−4.00000	−0.171499
$545$	10.1516	0.434846
$546$	−6.90830	−0.295648
$547$	−24.8765	−1.06364	−0.531821	−	0.846857i	$-0.678492\pi$
$547$	−24.8765	−1.06364	−0.531821	+	0.846857i	$0.678492\pi$
$548$	−14.9083	−0.636851
$549$	1.32803	0.0566790
$550$	−20.2204	−0.862202
$551$	1.20191	0.0512032
$552$	1.00000	0.0425628
$553$	−43.7159	−1.85899
$554$	1.83251	0.0778559
$555$	16.8924	0.717042
$556$	−0.403824	−0.0171259
$557$	−19.6312	−0.831801	−0.415900	−	0.909410i	$-0.636533\pi$
$557$	−19.6312	−0.831801	−0.415900	+	0.909410i	$0.636533\pi$
$558$	1.32803	0.0562200
$559$	−15.7478	−0.666059
$560$	17.3121	0.731571
$561$	−13.3121	−0.562038
$562$	−2.11021	−0.0890140
$563$	−3.02486	−0.127483	−0.0637414	−	0.997966i	$-0.520303\pi$
$563$	−3.02486	−0.127483	−0.0637414	+	0.997966i	$0.520303\pi$
$564$	10.6561	0.448701
$565$	−55.0969	−2.31794
$566$	−20.8236	−0.875279
$567$	5.20191	0.218460
$568$	9.58027	0.401979
$569$	−17.8993	−0.750380	−0.375190	−	0.926948i	$-0.622422\pi$
$569$	−17.8993	−0.750380	−0.375190	+	0.926948i	$0.622422\pi$
$570$	−4.00000	−0.167542
$571$	−4.74081	−0.198397	−0.0991984	−	0.995068i	$-0.531628\pi$
$571$	−4.74081	−0.198397	−0.0991984	+	0.995068i	$0.531628\pi$
$572$	−4.41973	−0.184798
$573$	−13.1860	−0.550853
$574$	4.80765	0.200667
$575$	6.07579	0.253378
$576$	1.00000	0.0416667
$577$	20.6561	0.859923	0.429962	−	0.902847i	$-0.358527\pi$
$577$	20.6561	0.859923	0.429962	+	0.902847i	$0.358527\pi$
$578$	1.00000	0.0415945
$579$	8.65606	0.359734
$580$	−3.32803	−0.138189
$581$	−49.9682	−2.07303
$582$	13.4542	0.557692
$583$	22.1516	0.917425
$584$	2.25224	0.0931983
$585$	−4.41973	−0.182733
$586$	16.2618	0.671769
$587$	−14.6879	−0.606233	−0.303117	−	0.952953i	$-0.598027\pi$
$587$	−14.6879	−0.606233	−0.303117	+	0.952953i	$0.598027\pi$
$588$	−20.0599	−0.827256
$589$	1.59618	0.0657693
$590$	−37.7000	−1.55209
$591$	2.50448	0.103020
$592$	−5.07579	−0.208614
$593$	1.16054	0.0476577	0.0238288	−	0.999716i	$-0.492414\pi$
$593$	1.16054	0.0476577	0.0238288	+	0.999716i	$0.492414\pi$
$594$	3.32803	0.136551
$595$	69.2485	2.83891
$596$	−18.2363	−0.746989
$597$	−12.5299	−0.512816
$598$	1.32803	0.0543072
$599$	3.41278	0.139442	0.0697212	−	0.997567i	$-0.477789\pi$
$599$	3.41278	0.139442	0.0697212	+	0.997567i	$0.477789\pi$
$600$	6.07579	0.248043
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	−61.6841	−2.51406
$603$	1.32803	0.0540816
$604$	4.00000	0.162758
$605$	0.252239	0.0102550
$606$	19.4796	0.791305
$607$	−4.94011	−0.200513	−0.100257	−	0.994962i	$-0.531966\pi$
$607$	−4.94011	−0.200513	−0.100257	+	0.994962i	$0.531966\pi$
$608$	1.20191	0.0487440
$609$	5.20191	0.210792
$610$	−4.41973	−0.178950
$611$	14.1516	0.572512
$612$	4.00000	0.161690
$613$	44.3625	1.79178	0.895891	−	0.444273i	$-0.146538\pi$
$613$	44.3625	1.79178	0.895891	+	0.444273i	$0.146538\pi$
$614$	20.1357	0.812610
$615$	3.07579	0.124028
$616$	−17.3121	−0.697525
$617$	25.5644	1.02918	0.514591	−	0.857436i	$-0.327944\pi$
$617$	25.5644	1.02918	0.514591	+	0.857436i	$0.327944\pi$
$618$	6.12612	0.246429
$619$	7.35350	0.295562	0.147781	−	0.989020i	$-0.452787\pi$
$619$	7.35350	0.295562	0.147781	+	0.989020i	$0.452787\pi$
$620$	−4.41973	−0.177501
$621$	−1.00000	−0.0401286
$622$	4.25224	0.170499
$623$	−55.4319	−2.22083
$624$	1.32803	0.0531638
$625$	−18.4637	−0.738548
$626$	−14.0000	−0.559553
$627$	4.00000	0.159745
$628$	−5.49552	−0.219295
$629$	−20.3032	−0.809540
$630$	−17.3121	−0.689732
$631$	34.0943	1.35727	0.678636	−	0.734474i	$-0.262571\pi$
$631$	34.0943	1.35727	0.678636	+	0.734474i	$0.262571\pi$
$632$	8.40382	0.334286
$633$	−0.671969	−0.0267084
$634$	−24.4886	−0.972565
$635$	3.07579	0.122059
$636$	−6.65606	−0.263930
$637$	−26.6402	−1.05552
$638$	3.32803	0.131758
$639$	−9.58027	−0.378990
$640$	−3.32803	−0.131552
$641$	−14.9083	−0.588843	−0.294421	−	0.955676i	$-0.595127\pi$
$641$	−14.9083	−0.588843	−0.294421	+	0.955676i	$0.595127\pi$
$642$	−7.45415	−0.294192
$643$	−24.0688	−0.949182	−0.474591	−	0.880206i	$-0.657404\pi$
$643$	−24.0688	−0.949182	−0.474591	+	0.880206i	$0.657404\pi$
$644$	5.20191	0.204984
$645$	−39.4637	−1.55388
$646$	4.80765	0.189154
$647$	−17.3790	−0.683237	−0.341619	−	0.939839i	$-0.610975\pi$
$647$	−17.3790	−0.683237	−0.341619	+	0.939839i	$0.610975\pi$
$648$	−1.00000	−0.0392837
$649$	37.7000	1.47986
$650$	8.06884	0.316486
$651$	6.90830	0.270758
$652$	−9.47962	−0.371250
$653$	−35.1956	−1.37731	−0.688654	−	0.725090i	$-0.741798\pi$
$653$	−35.1956	−1.37731	−0.688654	+	0.725090i	$0.741798\pi$
$654$	3.05033	0.119277
$655$	−71.4319	−2.79108
$656$	−0.924208	−0.0360842
$657$	−2.25224	−0.0878682
$658$	55.4319	2.16096
$659$	12.3032	0.479263	0.239632	−	0.970864i	$-0.422973\pi$
$659$	12.3032	0.479263	0.239632	+	0.970864i	$0.422973\pi$
$660$	−11.0758	−0.431125
$661$	34.0096	1.32282	0.661409	−	0.750025i	$-0.269959\pi$
$661$	34.0096	1.32282	0.661409	+	0.750025i	$0.269959\pi$
$662$	−23.7159	−0.921747
$663$	5.31213	0.206306
$664$	9.60574	0.372775
$665$	−20.8076	−0.806886
$666$	5.07579	0.196683
$667$	−1.00000	−0.0387202
$668$	−16.3879	−0.634068
$669$	−29.3121	−1.13327
$670$	−4.41973	−0.170749
$671$	4.41973	0.170622
$672$	5.20191	0.200668
$673$	26.0000	1.00223	0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	−31.1860	−1.20124
$675$	−6.07579	−0.233857
$676$	−11.2363	−0.432167
$677$	−44.7854	−1.72124	−0.860621	−	0.509246i	$-0.829924\pi$
$677$	−44.7854	−1.72124	−0.860621	+	0.509246i	$0.829924\pi$
$678$	−16.5554	−0.635807
$679$	69.9873	2.68587
$680$	−13.3121	−0.510497
$681$	−9.60574	−0.368093
$682$	4.41973	0.169240
$683$	24.9242	0.953698	0.476849	−	0.878985i	$-0.341779\pi$
$683$	24.9242	0.953698	0.476849	+	0.878985i	$0.341779\pi$
$684$	−1.20191	−0.0459562
$685$	−49.6153	−1.89570
$686$	−67.9364	−2.59382
$687$	21.2962	0.812501
$688$	11.8580	0.452081
$689$	−8.83946	−0.336757
$690$	3.32803	0.126696
$691$	42.9592	1.63425	0.817123	−	0.576463i	$-0.195568\pi$
$691$	42.9592	1.63425	0.817123	+	0.576463i	$0.195568\pi$
$692$	−14.6561	−0.557140
$693$	17.3121	0.657633
$694$	10.1198	0.384141
$695$	−1.34394	−0.0509785
$696$	−1.00000	−0.0379049
$697$	−3.69683	−0.140027
$698$	−7.42869	−0.281180
$699$	−13.7478	−0.519988
$700$	31.6057	1.19458
$701$	−14.8236	−0.559878	−0.279939	−	0.960018i	$-0.590314\pi$
$701$	−14.8236	−0.559878	−0.279939	+	0.960018i	$0.590314\pi$
$702$	−1.32803	−0.0501233
$703$	6.10065	0.230091
$704$	3.32803	0.125430
$705$	35.4637	1.33564
$706$	−2.00000	−0.0752710
$707$	101.331	3.81095
$708$	−11.3280	−0.425733
$709$	27.4044	1.02919	0.514597	−	0.857432i	$-0.327941\pi$
$709$	27.4044	1.02919	0.514597	+	0.857432i	$0.327941\pi$
$710$	31.8834	1.19656
$711$	−8.40382	−0.315168
$712$	10.6561	0.399353
$713$	−1.32803	−0.0497352
$714$	20.8076	0.778707
$715$	−14.7090	−0.550085
$716$	22.4038	0.837270
$717$	−12.2363	−0.456974
$718$	−28.7663	−1.07355
$719$	−2.06684	−0.0770800	−0.0385400	−	0.999257i	$-0.512271\pi$
$719$	−2.06684	−0.0770800	−0.0385400	+	0.999257i	$0.512271\pi$
$720$	3.32803	0.124028
$721$	31.8675	1.18681
$722$	17.5554	0.653345
$723$	7.05989	0.262560
$724$	1.45415	0.0540431
$725$	−6.07579	−0.225649
$726$	0.0757923	0.00281291
$727$	−5.71595	−0.211993	−0.105996	−	0.994367i	$-0.533803\pi$
$727$	−5.71595	−0.211993	−0.105996	+	0.994367i	$0.533803\pi$
$728$	6.90830	0.256039
$729$	1.00000	0.0370370
$730$	7.49552	0.277422
$731$	47.4319	1.75433
$732$	−1.32803	−0.0490854
$733$	46.6593	1.72340	0.861700	−	0.507418i	$-0.169400\pi$
$733$	46.6593	1.72340	0.861700	+	0.507418i	$0.169400\pi$
$734$	−15.5962	−0.575665
$735$	−66.7599	−2.46248
$736$	−1.00000	−0.0368605
$737$	4.41973	0.162803
$738$	0.924208	0.0340206
$739$	−26.5395	−0.976271	−0.488136	−	0.872768i	$-0.662323\pi$
$739$	−26.5395	−0.976271	−0.488136	+	0.872768i	$0.662323\pi$
$740$	−16.8924	−0.620977
$741$	−1.59618	−0.0586370
$742$	−34.6243	−1.27110
$743$	−12.6306	−0.463372	−0.231686	−	0.972791i	$-0.574424\pi$
$743$	−12.6306	−0.463372	−0.231686	+	0.972791i	$0.574424\pi$
$744$	−1.32803	−0.0486880
$745$	−60.6911	−2.22355
$746$	29.1701	1.06799
$747$	−9.60574	−0.351455
$748$	13.3121	0.486740
$749$	−38.7758	−1.41684
$750$	3.58027	0.130733
$751$	18.2522	0.666034	0.333017	−	0.942921i	$-0.391933\pi$
$751$	18.2522	0.666034	0.333017	+	0.942921i	$0.391933\pi$
$752$	−10.6561	−0.388587
$753$	9.98409	0.363841
$754$	−1.32803	−0.0483640
$755$	13.3121	0.484478
$756$	−5.20191	−0.189192
$757$	19.4478	0.706842	0.353421	−	0.935464i	$-0.385018\pi$
$757$	19.4478	0.706842	0.353421	+	0.935464i	$0.385018\pi$
$758$	6.26180	0.227439
$759$	−3.32803	−0.120800
$760$	4.00000	0.145095
$761$	−20.9274	−0.758618	−0.379309	−	0.925270i	$-0.623838\pi$
$761$	−20.9274	−0.758618	−0.379309	+	0.925270i	$0.623838\pi$
$762$	0.924208	0.0334805
$763$	15.8675	0.574443
$764$	13.1860	0.477053
$765$	13.3121	0.481301
$766$	−30.1516	−1.08942
$767$	−15.0440	−0.543207
$768$	−1.00000	−0.0360844
$769$	16.5809	0.597922	0.298961	−	0.954265i	$-0.403360\pi$
$769$	16.5809	0.597922	0.298961	+	0.954265i	$0.403360\pi$
$770$	−57.6153	−2.07631
$771$	13.2115	0.475799
$772$	−8.65606	−0.311539
$773$	21.6567	0.778936	0.389468	−	0.921040i	$-0.372659\pi$
$773$	21.6567	0.778936	0.389468	+	0.921040i	$0.372659\pi$
$774$	−11.8580	−0.426226
$775$	−8.06884	−0.289841
$776$	−13.4542	−0.482976
$777$	26.4038	0.947232
$778$	18.3625	0.658326
$779$	1.11082	0.0397991
$780$	4.41973	0.158252
$781$	−31.8834	−1.14088
$782$	−4.00000	−0.143040
$783$	1.00000	0.0357371
$784$	20.0599	0.716425
$785$	−18.2893	−0.652772
$786$	−21.4637	−0.765585
$787$	18.1675	0.647601	0.323801	−	0.946125i	$-0.395039\pi$
$787$	18.1675	0.647601	0.323801	+	0.946125i	$0.395039\pi$
$788$	−2.50448	−0.0892183
$789$	−17.3535	−0.617801
$790$	27.9682	0.995063
$791$	−86.1198	−3.06207
$792$	−3.32803	−0.118256
$793$	−1.76367	−0.0626297
$794$	10.0000	0.354887
$795$	−22.1516	−0.785636
$796$	12.5299	0.444112
$797$	−45.0185	−1.59464	−0.797319	−	0.603558i	$-0.793749\pi$
$797$	−45.0185	−1.59464	−0.797319	+	0.603558i	$0.793749\pi$
$798$	−6.25224	−0.221327
$799$	−42.6243	−1.50794
$800$	−6.07579	−0.214812
$801$	−10.6561	−0.376513
$802$	5.18601	0.183124
$803$	−7.49552	−0.264511
$804$	−1.32803	−0.0468361
$805$	17.3121	0.610172
$806$	−1.76367	−0.0621225
$807$	28.4886	1.00285
$808$	−19.4796	−0.685290
$809$	−28.3879	−0.998066	−0.499033	−	0.866583i	$-0.666311\pi$
$809$	−28.3879	−0.998066	−0.499033	+	0.866583i	$0.666311\pi$
$810$	−3.32803	−0.116935
$811$	−19.2612	−0.676352	−0.338176	−	0.941083i	$-0.609810\pi$
$811$	−19.2612	−0.676352	−0.338176	+	0.941083i	$0.609810\pi$
$812$	−5.20191	−0.182551
$813$	8.41973	0.295293
$814$	16.8924	0.592078
$815$	−31.5485	−1.10509
$816$	−4.00000	−0.140028
$817$	−14.2522	−0.498623
$818$	−11.8166	−0.413158
$819$	−6.90830	−0.241396
$820$	−3.07579	−0.107411
$821$	3.49552	0.121995	0.0609973	−	0.998138i	$-0.480572\pi$
$821$	3.49552	0.121995	0.0609973	+	0.998138i	$0.480572\pi$
$822$	−14.9083	−0.519987
$823$	−18.2045	−0.634570	−0.317285	−	0.948330i	$-0.602771\pi$
$823$	−18.2045	−0.634570	−0.317285	+	0.948330i	$0.602771\pi$
$824$	−6.12612	−0.213413
$825$	−20.2204	−0.703985
$826$	−58.9274	−2.05035
$827$	25.7000	0.893678	0.446839	−	0.894614i	$-0.352550\pi$
$827$	25.7000	0.893678	0.446839	+	0.894614i	$0.352550\pi$
$828$	1.00000	0.0347524
$829$	−34.7758	−1.20781	−0.603907	−	0.797055i	$-0.706390\pi$
$829$	−34.7758	−1.20781	−0.603907	+	0.797055i	$0.706390\pi$
$830$	31.9682	1.10963
$831$	1.83251	0.0635690
$832$	−1.32803	−0.0460412
$833$	80.2395	2.78014
$834$	−0.403824	−0.0139833
$835$	−54.5395	−1.88742
$836$	−4.00000	−0.138343
$837$	1.32803	0.0459035
$838$	26.1102	0.901962
$839$	38.2459	1.32039	0.660197	−	0.751092i	$-0.270473\pi$
$839$	38.2459	1.32039	0.660197	+	0.751092i	$0.270473\pi$
$840$	17.3121	0.597325
$841$	1.00000	0.0344828
$842$	−4.48857	−0.154686
$843$	−2.11021	−0.0726796
$844$	0.671969	0.0231301
$845$	−37.3949	−1.28642
$846$	10.6561	0.366363
$847$	0.394265	0.0135471
$848$	6.65606	0.228570
$849$	−20.8236	−0.714662
$850$	−24.3032	−0.833592
$851$	−5.07579	−0.173996
$852$	9.58027	0.328215
$853$	−53.4637	−1.83056	−0.915281	−	0.402815i	$-0.868032\pi$
$853$	−53.4637	−1.83056	−0.915281	+	0.402815i	$0.868032\pi$
$854$	−6.90830	−0.236397
$855$	−4.00000	−0.136797
$856$	7.45415	0.254778
$857$	4.10065	0.140076	0.0700378	−	0.997544i	$-0.477688\pi$
$857$	4.10065	0.140076	0.0700378	+	0.997544i	$0.477688\pi$
$858$	−4.41973	−0.150887
$859$	−49.1108	−1.67564	−0.837820	−	0.545947i	$-0.816170\pi$
$859$	−49.1108	−1.67564	−0.837820	+	0.545947i	$0.816170\pi$
$860$	39.4637	1.34570
$861$	4.80765	0.163844
$862$	9.56436	0.325764
$863$	−45.1956	−1.53847	−0.769237	−	0.638963i	$-0.779364\pi$
$863$	−45.1956	−1.53847	−0.769237	+	0.638963i	$0.779364\pi$
$864$	1.00000	0.0340207
$865$	−48.7758	−1.65843
$866$	−23.3535	−0.793584
$867$	1.00000	0.0339618
$868$	−6.90830	−0.234483
$869$	−27.9682	−0.948756
$870$	−3.32803	−0.112831
$871$	−1.76367	−0.0597596
$872$	−3.05033	−0.103297
$873$	13.4542	0.455354
$874$	1.20191	0.0406553
$875$	18.6243	0.629615
$876$	2.25224	0.0760961
$877$	27.8993	0.942094	0.471047	−	0.882108i	$-0.343876\pi$
$877$	27.8993	0.942094	0.471047	+	0.882108i	$0.343876\pi$
$878$	−4.83946	−0.163324
$879$	16.2618	0.548497
$880$	11.0758	0.373365
$881$	58.0880	1.95703	0.978517	−	0.206168i	$-0.0660994\pi$
$881$	58.0880	1.95703	0.978517	+	0.206168i	$0.0660994\pi$
$882$	−20.0599	−0.675452
$883$	1.51343	0.0509311	0.0254656	−	0.999676i	$-0.491893\pi$
$883$	1.51343	0.0509311	0.0254656	+	0.999676i	$0.491893\pi$
$884$	−5.31213	−0.178666
$885$	−37.7000	−1.26727
$886$	−37.4319	−1.25755
$887$	43.7159	1.46784	0.733919	−	0.679237i	$-0.237689\pi$
$887$	43.7159	1.46784	0.733919	+	0.679237i	$0.237689\pi$
$888$	−5.07579	−0.170332
$889$	4.80765	0.161243
$890$	35.4637	1.18875
$891$	3.32803	0.111493
$892$	29.3121	0.981443
$893$	12.8076	0.428592
$894$	−18.2363	−0.609914
$895$	74.5606	2.49229
$896$	−5.20191	−0.173784
$897$	1.32803	0.0443417
$898$	1.42869	0.0476759
$899$	1.32803	0.0442923
$900$	6.07579	0.202526
$901$	26.6243	0.886982
$902$	3.07579	0.102413
$903$	−61.6841	−2.05272
$904$	16.5554	0.550625
$905$	4.83946	0.160869
$906$	4.00000	0.132891
$907$	32.8669	1.09133	0.545664	−	0.838004i	$-0.316277\pi$
$907$	32.8669	1.09133	0.545664	+	0.838004i	$0.316277\pi$
$908$	9.60574	0.318778
$909$	19.4796	0.646098
$910$	22.9910	0.762146
$911$	41.7096	1.38190	0.690950	−	0.722902i	$-0.257192\pi$
$911$	41.7096	1.38190	0.690950	+	0.722902i	$0.257192\pi$
$912$	1.20191	0.0397993
$913$	−31.9682	−1.05799
$914$	7.84842	0.259603
$915$	−4.41973	−0.146112
$916$	−21.2962	−0.703647
$917$	−111.652	−3.68708
$918$	4.00000	0.132020
$919$	−17.8739	−0.589605	−0.294802	−	0.955558i	$-0.595254\pi$
$919$	−17.8739	−0.589605	−0.294802	+	0.955558i	$0.595254\pi$
$920$	−3.32803	−0.109722
$921$	20.1357	0.663493
$922$	35.9523	1.18403
$923$	12.7229	0.418779
$924$	−17.3121	−0.569527
$925$	−30.8395	−1.01400
$926$	−28.3032	−0.930100
$927$	6.12612	0.201208
$928$	1.00000	0.0328266
$929$	−22.0000	−0.721797	−0.360898	−	0.932605i	$-0.617530\pi$
$929$	−22.0000	−0.721797	−0.360898	+	0.932605i	$0.617530\pi$
$930$	−4.41973	−0.144929
$931$	−24.1102	−0.790180
$932$	13.7478	0.450323
$933$	4.25224	0.139212
$934$	37.7000	1.23358
$935$	44.3032	1.44887
$936$	1.32803	0.0434081
$937$	29.4319	0.961498	0.480749	−	0.876858i	$-0.340365\pi$
$937$	29.4319	0.961498	0.480749	+	0.876858i	$0.340365\pi$
$938$	−6.90830	−0.225564
$939$	−14.0000	−0.456873
$940$	−35.4637	−1.15670
$941$	46.9612	1.53089	0.765446	−	0.643500i	$-0.222518\pi$
$941$	46.9612	1.53089	0.765446	+	0.643500i	$0.222518\pi$
$942$	−5.49552	−0.179054
$943$	−0.924208	−0.0300963
$944$	11.3280	0.368696
$945$	−17.3121	−0.563163
$946$	−39.4637	−1.28308
$947$	−19.2803	−0.626526	−0.313263	−	0.949666i	$-0.601422\pi$
$947$	−19.2803	−0.626526	−0.313263	+	0.949666i	$0.601422\pi$
$948$	8.40382	0.272944
$949$	2.99104	0.0970934
$950$	7.30257	0.236927
$951$	−24.4886	−0.794096
$952$	−20.8076	−0.674380
$953$	−41.1013	−1.33140	−0.665700	−	0.746219i	$-0.731867\pi$
$953$	−41.1013	−1.33140	−0.665700	+	0.746219i	$0.731867\pi$
$954$	−6.65606	−0.215498
$955$	43.8834	1.42003
$956$	12.2363	0.395751
$957$	3.32803	0.107580
$958$	13.7732	0.444993
$959$	−77.5517	−2.50427
$960$	−3.32803	−0.107412
$961$	−29.2363	−0.943108
$962$	−6.74081	−0.217332
$963$	−7.45415	−0.240207
$964$	−7.05989	−0.227384
$965$	−28.8076	−0.927351
$966$	5.20191	0.167369
$967$	29.1108	0.936141	0.468070	−	0.883691i	$-0.344949\pi$
$967$	29.1108	0.936141	0.468070	+	0.883691i	$0.344949\pi$
$968$	−0.0757923	−0.00243606
$969$	4.80765	0.154444
$970$	−44.7758	−1.43767
$971$	32.1039	1.03026	0.515131	−	0.857111i	$-0.327743\pi$
$971$	32.1039	1.03026	0.515131	+	0.857111i	$0.327743\pi$
$972$	−1.00000	−0.0320750
$973$	−2.10065	−0.0673439
$974$	16.3032	0.522387
$975$	8.06884	0.258410
$976$	1.32803	0.0425092
$977$	−26.1950	−0.838051	−0.419026	−	0.907974i	$-0.637628\pi$
$977$	−26.1950	−0.838051	−0.419026	+	0.907974i	$0.637628\pi$
$978$	−9.47962	−0.303125
$979$	−35.4637	−1.13343
$980$	66.7599	2.13257
$981$	3.05033	0.0973895
$982$	−3.31213	−0.105694
$983$	36.3784	1.16029	0.580145	−	0.814513i	$-0.302996\pi$
$983$	36.3784	1.16029	0.580145	+	0.814513i	$0.302996\pi$
$984$	−0.924208	−0.0294627
$985$	−8.33498	−0.265575
$986$	4.00000	0.127386
$987$	55.4319	1.76442
$988$	1.59618	0.0507811
$989$	11.8580	0.377062
$990$	−11.0758	−0.352012
$991$	−16.2204	−0.515259	−0.257629	−	0.966244i	$-0.582941\pi$
$991$	−16.2204	−0.515259	−0.257629	+	0.966244i	$0.582941\pi$
$992$	1.32803	0.0421650
$993$	−23.7159	−0.752603
$994$	49.8357	1.58069
$995$	41.7000	1.32198
$996$	9.60574	0.304369
$997$	12.6243	0.399814	0.199907	−	0.979815i	$-0.435936\pi$
$997$	12.6243	0.399814	0.199907	+	0.979815i	$0.435936\pi$
$998$	31.0281	0.982177
$999$	5.07579	0.160591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.y.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.y.1.3	✓	3	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.32803 q^{5} +1.00000 q^{6} +5.20191 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.32803 q^{5} +1.00000 q^{6} +5.20191 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.32803 q^{10} +3.32803 q^{11} -1.00000 q^{12} -1.32803 q^{13} -5.20191 q^{14} -3.32803 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} -1.20191 q^{19} +3.32803 q^{20} -5.20191 q^{21} -3.32803 q^{22} +1.00000 q^{23} +1.00000 q^{24} +6.07579 q^{25} +1.32803 q^{26} -1.00000 q^{27} +5.20191 q^{28} -1.00000 q^{29} +3.32803 q^{30} -1.32803 q^{31} -1.00000 q^{32} -3.32803 q^{33} -4.00000 q^{34} +17.3121 q^{35} +1.00000 q^{36} -5.07579 q^{37} +1.20191 q^{38} +1.32803 q^{39} -3.32803 q^{40} -0.924208 q^{41} +5.20191 q^{42} +11.8580 q^{43} +3.32803 q^{44} +3.32803 q^{45} -1.00000 q^{46} -10.6561 q^{47} -1.00000 q^{48} +20.0599 q^{49} -6.07579 q^{50} -4.00000 q^{51} -1.32803 q^{52} +6.65606 q^{53} +1.00000 q^{54} +11.0758 q^{55} -5.20191 q^{56} +1.20191 q^{57} +1.00000 q^{58} +11.3280 q^{59} -3.32803 q^{60} +1.32803 q^{61} +1.32803 q^{62} +5.20191 q^{63} +1.00000 q^{64} -4.41973 q^{65} +3.32803 q^{66} +1.32803 q^{67} +4.00000 q^{68} -1.00000 q^{69} -17.3121 q^{70} -9.58027 q^{71} -1.00000 q^{72} -2.25224 q^{73} +5.07579 q^{74} -6.07579 q^{75} -1.20191 q^{76} +17.3121 q^{77} -1.32803 q^{78} -8.40382 q^{79} +3.32803 q^{80} +1.00000 q^{81} +0.924208 q^{82} -9.60574 q^{83} -5.20191 q^{84} +13.3121 q^{85} -11.8580 q^{86} +1.00000 q^{87} -3.32803 q^{88} -10.6561 q^{89} -3.32803 q^{90} -6.90830 q^{91} +1.00000 q^{92} +1.32803 q^{93} +10.6561 q^{94} -4.00000 q^{95} +1.00000 q^{96} +13.4542 q^{97} -20.0599 q^{98} +3.32803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} + 3 q^{6} + 6 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 + 3 * q^6 + 6 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} + 3 q^{6} + 6 q^{7} - 3 q^{8} + 3 q^{9} + q^{10} - q^{11} - 3 q^{12} + 7 q^{13} - 6 q^{14} + q^{15} + 3 q^{16} + 12 q^{17} - 3 q^{18} + 6 q^{19} - q^{20} - 6 q^{21} + q^{22} + 3 q^{23} + 3 q^{24} + 10 q^{25} - 7 q^{26} - 3 q^{27} + 6 q^{28} - 3 q^{29} - q^{30} + 7 q^{31} - 3 q^{32} + q^{33} - 12 q^{34} + 8 q^{35} + 3 q^{36} - 7 q^{37} - 6 q^{38} - 7 q^{39} + q^{40} - 11 q^{41} + 6 q^{42} + 4 q^{43} - q^{44} - q^{45} - 3 q^{46} - 10 q^{47} - 3 q^{48} + 19 q^{49} - 10 q^{50} - 12 q^{51} + 7 q^{52} - 2 q^{53} + 3 q^{54} + 25 q^{55} - 6 q^{56} - 6 q^{57} + 3 q^{58} + 23 q^{59} + q^{60} - 7 q^{61} - 7 q^{62} + 6 q^{63} + 3 q^{64} - 27 q^{65} - q^{66} - 7 q^{67} + 12 q^{68} - 3 q^{69} - 8 q^{70} - 15 q^{71} - 3 q^{72} - 4 q^{73} + 7 q^{74} - 10 q^{75} + 6 q^{76} + 8 q^{77} + 7 q^{78} - 6 q^{79} - q^{80} + 3 q^{81} + 11 q^{82} - 6 q^{84} - 4 q^{85} - 4 q^{86} + 3 q^{87} + q^{88} - 10 q^{89} + q^{90} + 4 q^{91} + 3 q^{92} - 7 q^{93} + 10 q^{94} - 12 q^{95} + 3 q^{96} + 28 q^{97} - 19 q^{98} - q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 + 3 * q^6 + 6 * q^7 - 3 * q^8 + 3 * q^9 + q^10 - q^11 - 3 * q^12 + 7 * q^13 - 6 * q^14 + q^15 + 3 * q^16 + 12 * q^17 - 3 * q^18 + 6 * q^19 - q^20 - 6 * q^21 + q^22 + 3 * q^23 + 3 * q^24 + 10 * q^25 - 7 * q^26 - 3 * q^27 + 6 * q^28 - 3 * q^29 - q^30 + 7 * q^31 - 3 * q^32 + q^33 - 12 * q^34 + 8 * q^35 + 3 * q^36 - 7 * q^37 - 6 * q^38 - 7 * q^39 + q^40 - 11 * q^41 + 6 * q^42 + 4 * q^43 - q^44 - q^45 - 3 * q^46 - 10 * q^47 - 3 * q^48 + 19 * q^49 - 10 * q^50 - 12 * q^51 + 7 * q^52 - 2 * q^53 + 3 * q^54 + 25 * q^55 - 6 * q^56 - 6 * q^57 + 3 * q^58 + 23 * q^59 + q^60 - 7 * q^61 - 7 * q^62 + 6 * q^63 + 3 * q^64 - 27 * q^65 - q^66 - 7 * q^67 + 12 * q^68 - 3 * q^69 - 8 * q^70 - 15 * q^71 - 3 * q^72 - 4 * q^73 + 7 * q^74 - 10 * q^75 + 6 * q^76 + 8 * q^77 + 7 * q^78 - 6 * q^79 - q^80 + 3 * q^81 + 11 * q^82 - 6 * q^84 - 4 * q^85 - 4 * q^86 + 3 * q^87 + q^88 - 10 * q^89 + q^90 + 4 * q^91 + 3 * q^92 - 7 * q^93 + 10 * q^94 - 12 * q^95 + 3 * q^96 + 28 * q^97 - 19 * q^98 - q^99

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