LMFDB - Embedded newform 4006.2.a.f.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.50294 q^{3} +1.00000 q^{4} +1.71703 q^{5} -1.50294 q^{6} -3.21564 q^{7} +1.00000 q^{8} -0.741171 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.50294 q^{3} +1.00000 q^{4} +1.71703 q^{5} -1.50294 q^{6} -3.21564 q^{7} +1.00000 q^{8} -0.741171 q^{9} +1.71703 q^{10} +4.00332 q^{11} -1.50294 q^{12} -0.353160 q^{13} -3.21564 q^{14} -2.58059 q^{15} +1.00000 q^{16} +1.14147 q^{17} -0.741171 q^{18} -2.98537 q^{19} +1.71703 q^{20} +4.83291 q^{21} +4.00332 q^{22} -3.78980 q^{23} -1.50294 q^{24} -2.05182 q^{25} -0.353160 q^{26} +5.62276 q^{27} -3.21564 q^{28} -7.15312 q^{29} -2.58059 q^{30} +2.55794 q^{31} +1.00000 q^{32} -6.01675 q^{33} +1.14147 q^{34} -5.52133 q^{35} -0.741171 q^{36} +4.88447 q^{37} -2.98537 q^{38} +0.530778 q^{39} +1.71703 q^{40} +1.42828 q^{41} +4.83291 q^{42} -2.27480 q^{43} +4.00332 q^{44} -1.27261 q^{45} -3.78980 q^{46} -11.6311 q^{47} -1.50294 q^{48} +3.34033 q^{49} -2.05182 q^{50} -1.71556 q^{51} -0.353160 q^{52} +10.1619 q^{53} +5.62276 q^{54} +6.87381 q^{55} -3.21564 q^{56} +4.48683 q^{57} -7.15312 q^{58} -9.26219 q^{59} -2.58059 q^{60} -5.44705 q^{61} +2.55794 q^{62} +2.38334 q^{63} +1.00000 q^{64} -0.606384 q^{65} -6.01675 q^{66} -7.39396 q^{67} +1.14147 q^{68} +5.69584 q^{69} -5.52133 q^{70} +8.82095 q^{71} -0.741171 q^{72} +2.32386 q^{73} +4.88447 q^{74} +3.08377 q^{75} -2.98537 q^{76} -12.8732 q^{77} +0.530778 q^{78} -5.58319 q^{79} +1.71703 q^{80} -6.22715 q^{81} +1.42828 q^{82} +4.38777 q^{83} +4.83291 q^{84} +1.95993 q^{85} -2.27480 q^{86} +10.7507 q^{87} +4.00332 q^{88} -7.20587 q^{89} -1.27261 q^{90} +1.13563 q^{91} -3.78980 q^{92} -3.84444 q^{93} -11.6311 q^{94} -5.12596 q^{95} -1.50294 q^{96} -1.65773 q^{97} +3.34033 q^{98} -2.96715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9	\( 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9} - 23 q^{10} - 32 q^{11} - 13 q^{12} - 8 q^{13} - 18 q^{14} - 14 q^{15} + 31 q^{16} - 30 q^{17} + 20 q^{18} - 38 q^{19} - 23 q^{20} - 16 q^{21} - 32 q^{22} - 24 q^{23} - 13 q^{24} + 40 q^{25} - 8 q^{26} - 28 q^{27} - 18 q^{28} - 7 q^{29} - 14 q^{30} - 32 q^{31} + 31 q^{32} - 9 q^{33} - 30 q^{34} - 14 q^{35} + 20 q^{36} + 11 q^{37} - 38 q^{38} - 9 q^{39} - 23 q^{40} - 76 q^{41} - 16 q^{42} - 33 q^{43} - 32 q^{44} - 40 q^{45} - 24 q^{46} - 96 q^{47} - 13 q^{48} + 15 q^{49} + 40 q^{50} - 55 q^{51} - 8 q^{52} - 28 q^{53} - 28 q^{54} - 52 q^{55} - 18 q^{56} - 21 q^{57} - 7 q^{58} - 72 q^{59} - 14 q^{60} - 9 q^{61} - 32 q^{62} - 54 q^{63} + 31 q^{64} - 38 q^{65} - 9 q^{66} - 4 q^{67} - 30 q^{68} - 17 q^{69} - 14 q^{70} - 61 q^{71} + 20 q^{72} - 62 q^{73} + 11 q^{74} - 63 q^{75} - 38 q^{76} - 9 q^{77} - 9 q^{78} - 30 q^{79} - 23 q^{80} - 13 q^{81} - 76 q^{82} - 90 q^{83} - 16 q^{84} + 26 q^{85} - 33 q^{86} - 34 q^{87} - 32 q^{88} - 99 q^{89} - 40 q^{90} - 47 q^{91} - 24 q^{92} - 6 q^{93} - 96 q^{94} - 24 q^{95} - 13 q^{96} - 46 q^{97} + 15 q^{98} - 48 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9 - 23 * q^10 - 32 * q^11 - 13 * q^12 - 8 * q^13 - 18 * q^14 - 14 * q^15 + 31 * q^16 - 30 * q^17 + 20 * q^18 - 38 * q^19 - 23 * q^20 - 16 * q^21 - 32 * q^22 - 24 * q^23 - 13 * q^24 + 40 * q^25 - 8 * q^26 - 28 * q^27 - 18 * q^28 - 7 * q^29 - 14 * q^30 - 32 * q^31 + 31 * q^32 - 9 * q^33 - 30 * q^34 - 14 * q^35 + 20 * q^36 + 11 * q^37 - 38 * q^38 - 9 * q^39 - 23 * q^40 - 76 * q^41 - 16 * q^42 - 33 * q^43 - 32 * q^44 - 40 * q^45 - 24 * q^46 - 96 * q^47 - 13 * q^48 + 15 * q^49 + 40 * q^50 - 55 * q^51 - 8 * q^52 - 28 * q^53 - 28 * q^54 - 52 * q^55 - 18 * q^56 - 21 * q^57 - 7 * q^58 - 72 * q^59 - 14 * q^60 - 9 * q^61 - 32 * q^62 - 54 * q^63 + 31 * q^64 - 38 * q^65 - 9 * q^66 - 4 * q^67 - 30 * q^68 - 17 * q^69 - 14 * q^70 - 61 * q^71 + 20 * q^72 - 62 * q^73 + 11 * q^74 - 63 * q^75 - 38 * q^76 - 9 * q^77 - 9 * q^78 - 30 * q^79 - 23 * q^80 - 13 * q^81 - 76 * q^82 - 90 * q^83 - 16 * q^84 + 26 * q^85 - 33 * q^86 - 34 * q^87 - 32 * q^88 - 99 * q^89 - 40 * q^90 - 47 * q^91 - 24 * q^92 - 6 * q^93 - 96 * q^94 - 24 * q^95 - 13 * q^96 - 46 * q^97 + 15 * q^98 - 48 * 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
$3$	−1.50294	−0.867723	−0.433861	−	0.900980i	$-0.642849\pi$
$3$	−1.50294	−0.867723	−0.433861	+	0.900980i	$0.642849\pi$
$4$	1.00000	0.500000
$5$	1.71703	0.767877	0.383939	−	0.923359i	$-0.374567\pi$
$5$	1.71703	0.767877	0.383939	+	0.923359i	$0.374567\pi$
$6$	−1.50294	−0.613573
$7$	−3.21564	−1.21540	−0.607698	−	0.794168i	$-0.707907\pi$
$7$	−3.21564	−1.21540	−0.607698	+	0.794168i	$0.707907\pi$
$8$	1.00000	0.353553
$9$	−0.741171	−0.247057
$10$	1.71703	0.542971
$11$	4.00332	1.20705	0.603523	−	0.797345i	$-0.293763\pi$
$11$	4.00332	1.20705	0.603523	+	0.797345i	$0.293763\pi$
$12$	−1.50294	−0.433861
$13$	−0.353160	−0.0979489	−0.0489745	−	0.998800i	$-0.515595\pi$
$13$	−0.353160	−0.0979489	−0.0489745	+	0.998800i	$0.515595\pi$
$14$	−3.21564	−0.859415
$15$	−2.58059	−0.666305
$16$	1.00000	0.250000
$17$	1.14147	0.276847	0.138423	−	0.990373i	$-0.455797\pi$
$17$	1.14147	0.276847	0.138423	+	0.990373i	$0.455797\pi$
$18$	−0.741171	−0.174696
$19$	−2.98537	−0.684891	−0.342445	−	0.939538i	$-0.611255\pi$
$19$	−2.98537	−0.684891	−0.342445	+	0.939538i	$0.611255\pi$
$20$	1.71703	0.383939
$21$	4.83291	1.05463
$22$	4.00332	0.853511
$23$	−3.78980	−0.790228	−0.395114	−	0.918632i	$-0.629295\pi$
$23$	−3.78980	−0.790228	−0.395114	+	0.918632i	$0.629295\pi$
$24$	−1.50294	−0.306786
$25$	−2.05182	−0.410365
$26$	−0.353160	−0.0692603
$27$	5.62276	1.08210
$28$	−3.21564	−0.607698
$29$	−7.15312	−1.32830	−0.664150	−	0.747599i	$-0.731206\pi$
$29$	−7.15312	−1.32830	−0.664150	+	0.747599i	$0.731206\pi$
$30$	−2.58059	−0.471148
$31$	2.55794	0.459420	0.229710	−	0.973259i	$-0.426222\pi$
$31$	2.55794	0.459420	0.229710	+	0.973259i	$0.426222\pi$
$32$	1.00000	0.176777
$33$	−6.01675	−1.04738
$34$	1.14147	0.195760
$35$	−5.52133	−0.933276
$36$	−0.741171	−0.123529
$37$	4.88447	0.803001	0.401501	−	0.915859i	$-0.368489\pi$
$37$	4.88447	0.803001	0.401501	+	0.915859i	$0.368489\pi$
$38$	−2.98537	−0.484291
$39$	0.530778	0.0849925
$40$	1.71703	0.271486
$41$	1.42828	0.223060	0.111530	−	0.993761i	$-0.464425\pi$
$41$	1.42828	0.223060	0.111530	+	0.993761i	$0.464425\pi$
$42$	4.83291	0.745734
$43$	−2.27480	−0.346904	−0.173452	−	0.984842i	$-0.555492\pi$
$43$	−2.27480	−0.346904	−0.173452	+	0.984842i	$0.555492\pi$
$44$	4.00332	0.603523
$45$	−1.27261	−0.189710
$46$	−3.78980	−0.558775
$47$	−11.6311	−1.69657	−0.848283	−	0.529543i	$-0.822363\pi$
$47$	−11.6311	−1.69657	−0.848283	+	0.529543i	$0.822363\pi$
$48$	−1.50294	−0.216931
$49$	3.34033	0.477190
$50$	−2.05182	−0.290172
$51$	−1.71556	−0.240226
$52$	−0.353160	−0.0489745
$53$	10.1619	1.39585	0.697924	−	0.716172i	$-0.254107\pi$
$53$	10.1619	1.39585	0.697924	+	0.716172i	$0.254107\pi$
$54$	5.62276	0.765160
$55$	6.87381	0.926864
$56$	−3.21564	−0.429708
$57$	4.48683	0.594295
$58$	−7.15312	−0.939250
$59$	−9.26219	−1.20583	−0.602917	−	0.797804i	$-0.705995\pi$
$59$	−9.26219	−1.20583	−0.602917	+	0.797804i	$0.705995\pi$
$60$	−2.58059	−0.333152
$61$	−5.44705	−0.697423	−0.348711	−	0.937230i	$-0.613381\pi$
$61$	−5.44705	−0.697423	−0.348711	+	0.937230i	$0.613381\pi$
$62$	2.55794	0.324859
$63$	2.38334	0.300273
$64$	1.00000	0.125000
$65$	−0.606384	−0.0752127
$66$	−6.01675	−0.740611
$67$	−7.39396	−0.903316	−0.451658	−	0.892191i	$-0.649167\pi$
$67$	−7.39396	−0.903316	−0.451658	+	0.892191i	$0.649167\pi$
$68$	1.14147	0.138423
$69$	5.69584	0.685699
$70$	−5.52133	−0.659926
$71$	8.82095	1.04685	0.523427	−	0.852070i	$-0.324653\pi$
$71$	8.82095	1.04685	0.523427	+	0.852070i	$0.324653\pi$
$72$	−0.741171	−0.0873479
$73$	2.32386	0.271987	0.135993	−	0.990710i	$-0.456577\pi$
$73$	2.32386	0.271987	0.135993	+	0.990710i	$0.456577\pi$
$74$	4.88447	0.567808
$75$	3.08377	0.356083
$76$	−2.98537	−0.342445
$77$	−12.8732	−1.46704
$78$	0.530778	0.0600988
$79$	−5.58319	−0.628158	−0.314079	−	0.949397i	$-0.601696\pi$
$79$	−5.58319	−0.628158	−0.314079	+	0.949397i	$0.601696\pi$
$80$	1.71703	0.191969
$81$	−6.22715	−0.691906
$82$	1.42828	0.157727
$83$	4.38777	0.481620	0.240810	−	0.970572i	$-0.422587\pi$
$83$	4.38777	0.481620	0.240810	+	0.970572i	$0.422587\pi$
$84$	4.83291	0.527314
$85$	1.95993	0.212584
$86$	−2.27480	−0.245298
$87$	10.7507	1.15260
$88$	4.00332	0.426756
$89$	−7.20587	−0.763820	−0.381910	−	0.924199i	$-0.624734\pi$
$89$	−7.20587	−0.763820	−0.381910	+	0.924199i	$0.624734\pi$
$90$	−1.27261	−0.134145
$91$	1.13563	0.119047
$92$	−3.78980	−0.395114
$93$	−3.84444	−0.398649
$94$	−11.6311	−1.19965
$95$	−5.12596	−0.525912
$96$	−1.50294	−0.153393
$97$	−1.65773	−0.168317	−0.0841587	−	0.996452i	$-0.526820\pi$
$97$	−1.65773	−0.168317	−0.0841587	+	0.996452i	$0.526820\pi$
$98$	3.34033	0.337424
$99$	−2.96715	−0.298210
$100$	−2.05182	−0.205182
$101$	−9.05896	−0.901401	−0.450700	−	0.892675i	$-0.648826\pi$
$101$	−9.05896	−0.901401	−0.450700	+	0.892675i	$0.648826\pi$
$102$	−1.71556	−0.169866
$103$	−16.3093	−1.60700	−0.803499	−	0.595306i	$-0.797031\pi$
$103$	−16.3093	−1.60700	−0.803499	+	0.595306i	$0.797031\pi$
$104$	−0.353160	−0.0346302
$105$	8.29823	0.809825
$106$	10.1619	0.987014
$107$	−4.29899	−0.415599	−0.207800	−	0.978171i	$-0.566630\pi$
$107$	−4.29899	−0.415599	−0.207800	+	0.978171i	$0.566630\pi$
$108$	5.62276	0.541050
$109$	1.00038	0.0958186	0.0479093	−	0.998852i	$-0.484744\pi$
$109$	1.00038	0.0958186	0.0479093	+	0.998852i	$0.484744\pi$
$110$	6.87381	0.655392
$111$	−7.34106	−0.696783
$112$	−3.21564	−0.303849
$113$	13.3551	1.25634	0.628172	−	0.778074i	$-0.283803\pi$
$113$	13.3551	1.25634	0.628172	+	0.778074i	$0.283803\pi$
$114$	4.48683	0.420230
$115$	−6.50718	−0.606798
$116$	−7.15312	−0.664150
$117$	0.261752	0.0241990
$118$	−9.26219	−0.852653
$119$	−3.67055	−0.336479
$120$	−2.58059	−0.235574
$121$	5.02659	0.456962
$122$	−5.44705	−0.493152
$123$	−2.14662	−0.193555
$124$	2.55794	0.229710
$125$	−12.1082	−1.08299
$126$	2.38334	0.212325
$127$	−12.1515	−1.07827	−0.539134	−	0.842220i	$-0.681248\pi$
$127$	−12.1515	−1.07827	−0.539134	+	0.842220i	$0.681248\pi$
$128$	1.00000	0.0883883
$129$	3.41889	0.301016
$130$	−0.606384	−0.0531834
$131$	1.48036	0.129339	0.0646696	−	0.997907i	$-0.479401\pi$
$131$	1.48036	0.129339	0.0646696	+	0.997907i	$0.479401\pi$
$132$	−6.01675	−0.523691
$133$	9.59987	0.832414
$134$	−7.39396	−0.638741
$135$	9.65442	0.830920
$136$	1.14147	0.0978801
$137$	−3.91692	−0.334645	−0.167323	−	0.985902i	$-0.553512\pi$
$137$	−3.91692	−0.334645	−0.167323	+	0.985902i	$0.553512\pi$
$138$	5.69584	0.484862
$139$	−12.5337	−1.06309	−0.531545	−	0.847030i	$-0.678388\pi$
$139$	−12.5337	−1.06309	−0.531545	+	0.847030i	$0.678388\pi$
$140$	−5.52133	−0.466638
$141$	17.4808	1.47215
$142$	8.82095	0.740238
$143$	−1.41381	−0.118229
$144$	−0.741171	−0.0617643
$145$	−12.2821	−1.01997
$146$	2.32386	0.192324
$147$	−5.02031	−0.414068
$148$	4.88447	0.401501
$149$	−2.09653	−0.171755	−0.0858773	−	0.996306i	$-0.527369\pi$
$149$	−2.09653	−0.171755	−0.0858773	+	0.996306i	$0.527369\pi$
$150$	3.08377	0.251789
$151$	−10.7791	−0.877190	−0.438595	−	0.898685i	$-0.644524\pi$
$151$	−10.7791	−0.877190	−0.438595	+	0.898685i	$0.644524\pi$
$152$	−2.98537	−0.242145
$153$	−0.846024	−0.0683970
$154$	−12.8732	−1.03735
$155$	4.39206	0.352778
$156$	0.530778	0.0424962
$157$	−5.82168	−0.464621	−0.232310	−	0.972642i	$-0.574629\pi$
$157$	−5.82168	−0.464621	−0.232310	+	0.972642i	$0.574629\pi$
$158$	−5.58319	−0.444175
$159$	−15.2728	−1.21121
$160$	1.71703	0.135743
$161$	12.1866	0.960441
$162$	−6.22715	−0.489251
$163$	−11.8055	−0.924679	−0.462340	−	0.886703i	$-0.652990\pi$
$163$	−11.8055	−0.924679	−0.462340	+	0.886703i	$0.652990\pi$
$164$	1.42828	0.111530
$165$	−10.3309	−0.804261
$166$	4.38777	0.340557
$167$	13.5266	1.04672	0.523360	−	0.852112i	$-0.324678\pi$
$167$	13.5266	1.04672	0.523360	+	0.852112i	$0.324678\pi$
$168$	4.83291	0.372867
$169$	−12.8753	−0.990406
$170$	1.95993	0.150320
$171$	2.21267	0.169207
$172$	−2.27480	−0.173452
$173$	6.51669	0.495454	0.247727	−	0.968830i	$-0.420316\pi$
$173$	6.51669	0.495454	0.247727	+	0.968830i	$0.420316\pi$
$174$	10.7507	0.815009
$175$	6.59792	0.498756
$176$	4.00332	0.301762
$177$	13.9205	1.04633
$178$	−7.20587	−0.540102
$179$	−13.8733	−1.03694	−0.518471	−	0.855095i	$-0.673499\pi$
$179$	−13.8733	−1.03694	−0.518471	+	0.855095i	$0.673499\pi$
$180$	−1.27261	−0.0948548
$181$	9.92719	0.737882	0.368941	−	0.929453i	$-0.379720\pi$
$181$	9.92719	0.737882	0.368941	+	0.929453i	$0.379720\pi$
$182$	1.13563	0.0841788
$183$	8.18658	0.605170
$184$	−3.78980	−0.279388
$185$	8.38676	0.616607
$186$	−3.84444	−0.281888
$187$	4.56967	0.334167
$188$	−11.6311	−0.848283
$189$	−18.0807	−1.31518
$190$	−5.12596	−0.371876
$191$	2.84337	0.205739	0.102870	−	0.994695i	$-0.467198\pi$
$191$	2.84337	0.205739	0.102870	+	0.994695i	$0.467198\pi$
$192$	−1.50294	−0.108465
$193$	0.718768	0.0517381	0.0258690	−	0.999665i	$-0.491765\pi$
$193$	0.718768	0.0517381	0.0258690	+	0.999665i	$0.491765\pi$
$194$	−1.65773	−0.119018
$195$	0.911359	0.0652638
$196$	3.34033	0.238595
$197$	14.9750	1.06692	0.533462	−	0.845824i	$-0.320891\pi$
$197$	14.9750	1.06692	0.533462	+	0.845824i	$0.320891\pi$
$198$	−2.96715	−0.210866
$199$	1.74271	0.123537	0.0617686	−	0.998090i	$-0.480326\pi$
$199$	1.74271	0.123537	0.0617686	+	0.998090i	$0.480326\pi$
$200$	−2.05182	−0.145086
$201$	11.1127	0.783828
$202$	−9.05896	−0.637387
$203$	23.0018	1.61441
$204$	−1.71556	−0.120113
$205$	2.45240	0.171283
$206$	−16.3093	−1.13632
$207$	2.80889	0.195231
$208$	−0.353160	−0.0244872
$209$	−11.9514	−0.826695
$210$	8.29823	0.572632
$211$	−4.54736	−0.313054	−0.156527	−	0.987674i	$-0.550030\pi$
$211$	−4.54736	−0.313054	−0.156527	+	0.987674i	$0.550030\pi$
$212$	10.1619	0.697924
$213$	−13.2574	−0.908380
$214$	−4.29899	−0.293873
$215$	−3.90589	−0.266379
$216$	5.62276	0.382580
$217$	−8.22542	−0.558378
$218$	1.00038	0.0677540
$219$	−3.49262	−0.236009
$220$	6.87381	0.463432
$221$	−0.403121	−0.0271168
$222$	−7.34106	−0.492700
$223$	−10.9407	−0.732640	−0.366320	−	0.930489i	$-0.619383\pi$
$223$	−10.9407	−0.732640	−0.366320	+	0.930489i	$0.619383\pi$
$224$	−3.21564	−0.214854
$225$	1.52075	0.101384
$226$	13.3551	0.888370
$227$	4.78771	0.317772	0.158886	−	0.987297i	$-0.449210\pi$
$227$	4.78771	0.317772	0.158886	+	0.987297i	$0.449210\pi$
$228$	4.48683	0.297148
$229$	−9.22555	−0.609642	−0.304821	−	0.952410i	$-0.598597\pi$
$229$	−9.22555	−0.609642	−0.304821	+	0.952410i	$0.598597\pi$
$230$	−6.50718	−0.429071
$231$	19.3477	1.27299
$232$	−7.15312	−0.469625
$233$	−20.7205	−1.35744	−0.678722	−	0.734396i	$-0.737466\pi$
$233$	−20.7205	−1.35744	−0.678722	+	0.734396i	$0.737466\pi$
$234$	0.261752	0.0171113
$235$	−19.9708	−1.30275
$236$	−9.26219	−0.602917
$237$	8.39120	0.545067
$238$	−3.67055	−0.237926
$239$	15.3292	0.991561	0.495780	−	0.868448i	$-0.334882\pi$
$239$	15.3292	0.991561	0.495780	+	0.868448i	$0.334882\pi$
$240$	−2.58059	−0.166576
$241$	9.66228	0.622402	0.311201	−	0.950344i	$-0.399269\pi$
$241$	9.66228	0.622402	0.311201	+	0.950344i	$0.399269\pi$
$242$	5.02659	0.323121
$243$	−7.50924	−0.481718
$244$	−5.44705	−0.348711
$245$	5.73543	0.366423
$246$	−2.14662	−0.136864
$247$	1.05431	0.0670843
$248$	2.55794	0.162430
$249$	−6.59455	−0.417913
$250$	−12.1082	−0.765787
$251$	−8.44172	−0.532837	−0.266418	−	0.963857i	$-0.585840\pi$
$251$	−8.44172	−0.532837	−0.266418	+	0.963857i	$0.585840\pi$
$252$	2.38334	0.150136
$253$	−15.1718	−0.953842
$254$	−12.1515	−0.762450
$255$	−2.94566	−0.184464
$256$	1.00000	0.0625000
$257$	26.9045	1.67826	0.839129	−	0.543933i	$-0.183065\pi$
$257$	26.9045	1.67826	0.839129	+	0.543933i	$0.183065\pi$
$258$	3.41889	0.212851
$259$	−15.7067	−0.975966
$260$	−0.606384	−0.0376064
$261$	5.30168	0.328166
$262$	1.48036	0.0914567
$263$	−13.1648	−0.811775	−0.405888	−	0.913923i	$-0.633038\pi$
$263$	−13.1648	−0.811775	−0.405888	+	0.913923i	$0.633038\pi$
$264$	−6.01675	−0.370306
$265$	17.4483	1.07184
$266$	9.59987	0.588606
$267$	10.8300	0.662784
$268$	−7.39396	−0.451658
$269$	−5.48262	−0.334281	−0.167141	−	0.985933i	$-0.553453\pi$
$269$	−5.48262	−0.334281	−0.167141	+	0.985933i	$0.553453\pi$
$270$	9.65442	0.587549
$271$	0.0605562	0.00367852	0.00183926	−	0.999998i	$-0.499415\pi$
$271$	0.0605562	0.00367852	0.00183926	+	0.999998i	$0.499415\pi$
$272$	1.14147	0.0692117
$273$	−1.70679	−0.103300
$274$	−3.91692	−0.236630
$275$	−8.21411	−0.495329
$276$	5.69584	0.342849
$277$	−26.9875	−1.62152	−0.810762	−	0.585376i	$-0.800947\pi$
$277$	−26.9875	−1.62152	−0.810762	+	0.585376i	$0.800947\pi$
$278$	−12.5337	−0.751718
$279$	−1.89587	−0.113503
$280$	−5.52133	−0.329963
$281$	1.92934	0.115095	0.0575474	−	0.998343i	$-0.481672\pi$
$281$	1.92934	0.115095	0.0575474	+	0.998343i	$0.481672\pi$
$282$	17.4808	1.04097
$283$	−6.17109	−0.366833	−0.183417	−	0.983035i	$-0.558716\pi$
$283$	−6.17109	−0.366833	−0.183417	+	0.983035i	$0.558716\pi$
$284$	8.82095	0.523427
$285$	7.70400	0.456346
$286$	−1.41381	−0.0836005
$287$	−4.59284	−0.271107
$288$	−0.741171	−0.0436739
$289$	−15.6970	−0.923356
$290$	−12.2821	−0.721229
$291$	2.49148	0.146053
$292$	2.32386	0.135993
$293$	24.3057	1.41996	0.709978	−	0.704224i	$-0.248705\pi$
$293$	24.3057	1.41996	0.709978	+	0.704224i	$0.248705\pi$
$294$	−5.02031	−0.292791
$295$	−15.9034	−0.925932
$296$	4.88447	0.283904
$297$	22.5097	1.30615
$298$	−2.09653	−0.121449
$299$	1.33840	0.0774020
$300$	3.08377	0.178041
$301$	7.31493	0.421626
$302$	−10.7791	−0.620267
$303$	13.6151	0.782166
$304$	−2.98537	−0.171223
$305$	−9.35272	−0.535535
$306$	−0.846024	−0.0483640
$307$	−14.1889	−0.809804	−0.404902	−	0.914360i	$-0.632694\pi$
$307$	−14.1889	−0.809804	−0.404902	+	0.914360i	$0.632694\pi$
$308$	−12.8732	−0.733521
$309$	24.5118	1.39443
$310$	4.39206	0.249452
$311$	8.20570	0.465303	0.232651	−	0.972560i	$-0.425260\pi$
$311$	8.20570	0.465303	0.232651	+	0.972560i	$0.425260\pi$
$312$	0.530778	0.0300494
$313$	8.70619	0.492103	0.246052	−	0.969257i	$-0.420867\pi$
$313$	8.70619	0.492103	0.246052	+	0.969257i	$0.420867\pi$
$314$	−5.82168	−0.328537
$315$	4.09225	0.230572
$316$	−5.58319	−0.314079
$317$	8.26473	0.464194	0.232097	−	0.972693i	$-0.425441\pi$
$317$	8.26473	0.464194	0.232097	+	0.972693i	$0.425441\pi$
$318$	−15.2728	−0.856455
$319$	−28.6362	−1.60332
$320$	1.71703	0.0959846
$321$	6.46113	0.360625
$322$	12.1866	0.679134
$323$	−3.40771	−0.189610
$324$	−6.22715	−0.345953
$325$	0.724621	0.0401948
$326$	−11.8055	−0.653847
$327$	−1.50350	−0.0831440
$328$	1.42828	0.0788637
$329$	37.4013	2.06200
$330$	−10.3309	−0.568698
$331$	−11.4140	−0.627370	−0.313685	−	0.949527i	$-0.601564\pi$
$331$	−11.4140	−0.627370	−0.313685	+	0.949527i	$0.601564\pi$
$332$	4.38777	0.240810
$333$	−3.62023	−0.198387
$334$	13.5266	0.740143
$335$	−12.6956	−0.693636
$336$	4.83291	0.263657
$337$	31.6776	1.72559	0.862793	−	0.505557i	$-0.168713\pi$
$337$	31.6776	1.72559	0.862793	+	0.505557i	$0.168713\pi$
$338$	−12.8753	−0.700323
$339$	−20.0720	−1.09016
$340$	1.95993	0.106292
$341$	10.2403	0.554542
$342$	2.21267	0.119648
$343$	11.7682	0.635422
$344$	−2.27480	−0.122649
$345$	9.77991	0.526532
$346$	6.51669	0.350339
$347$	5.71152	0.306610	0.153305	−	0.988179i	$-0.451008\pi$
$347$	5.71152	0.306610	0.153305	+	0.988179i	$0.451008\pi$
$348$	10.7507	0.576298
$349$	−13.4839	−0.721775	−0.360888	−	0.932609i	$-0.617526\pi$
$349$	−13.4839	−0.721775	−0.360888	+	0.932609i	$0.617526\pi$
$350$	6.59792	0.352674
$351$	−1.98573	−0.105991
$352$	4.00332	0.213378
$353$	3.31124	0.176240	0.0881198	−	0.996110i	$-0.471914\pi$
$353$	3.31124	0.176240	0.0881198	+	0.996110i	$0.471914\pi$
$354$	13.9205	0.739867
$355$	15.1458	0.803856
$356$	−7.20587	−0.381910
$357$	5.51662	0.291970
$358$	−13.8733	−0.733229
$359$	3.20469	0.169137	0.0845686	−	0.996418i	$-0.473049\pi$
$359$	3.20469	0.169137	0.0845686	+	0.996418i	$0.473049\pi$
$360$	−1.27261	−0.0670725
$361$	−10.0876	−0.530925
$362$	9.92719	0.521762
$363$	−7.55466	−0.396517
$364$	1.13563	0.0595234
$365$	3.99012	0.208853
$366$	8.18658	0.427920
$367$	1.53401	0.0800745	0.0400372	−	0.999198i	$-0.487252\pi$
$367$	1.53401	0.0800745	0.0400372	+	0.999198i	$0.487252\pi$
$368$	−3.78980	−0.197557
$369$	−1.05860	−0.0551086
$370$	8.38676	0.436007
$371$	−32.6771	−1.69651
$372$	−3.84444	−0.199325
$373$	7.25168	0.375478	0.187739	−	0.982219i	$-0.439884\pi$
$373$	7.25168	0.375478	0.187739	+	0.982219i	$0.439884\pi$
$374$	4.56967	0.236292
$375$	18.1978	0.939732
$376$	−11.6311	−0.599827
$377$	2.52619	0.130106
$378$	−18.0807	−0.929973
$379$	14.8795	0.764309	0.382155	−	0.924098i	$-0.375182\pi$
$379$	14.8795	0.764309	0.382155	+	0.924098i	$0.375182\pi$
$380$	−5.12596	−0.262956
$381$	18.2629	0.935637
$382$	2.84337	0.145480
$383$	−1.95482	−0.0998866	−0.0499433	−	0.998752i	$-0.515904\pi$
$383$	−1.95482	−0.0998866	−0.0499433	+	0.998752i	$0.515904\pi$
$384$	−1.50294	−0.0766966
$385$	−22.1037	−1.12651
$386$	0.718768	0.0365843
$387$	1.68602	0.0857050
$388$	−1.65773	−0.0841587
$389$	19.1940	0.973176	0.486588	−	0.873632i	$-0.338241\pi$
$389$	19.1940	0.973176	0.486588	+	0.873632i	$0.338241\pi$
$390$	0.911359	0.0461485
$391$	−4.32594	−0.218772
$392$	3.34033	0.168712
$393$	−2.22489	−0.112231
$394$	14.9750	0.754429
$395$	−9.58648	−0.482348
$396$	−2.96715	−0.149105
$397$	−31.5579	−1.58385	−0.791924	−	0.610620i	$-0.790920\pi$
$397$	−31.5579	−1.58385	−0.791924	+	0.610620i	$0.790920\pi$
$398$	1.74271	0.0873541
$399$	−14.4280	−0.722305
$400$	−2.05182	−0.102591
$401$	28.6268	1.42955	0.714777	−	0.699352i	$-0.246528\pi$
$401$	28.6268	1.42955	0.714777	+	0.699352i	$0.246528\pi$
$402$	11.1127	0.554250
$403$	−0.903363	−0.0449997
$404$	−9.05896	−0.450700
$405$	−10.6922	−0.531299
$406$	23.0018	1.14156
$407$	19.5541	0.969261
$408$	−1.71556	−0.0849328
$409$	2.42224	0.119772	0.0598861	−	0.998205i	$-0.480926\pi$
$409$	2.42224	0.119772	0.0598861	+	0.998205i	$0.480926\pi$
$410$	2.45240	0.121115
$411$	5.88690	0.290379
$412$	−16.3093	−0.803499
$413$	29.7838	1.46557
$414$	2.80889	0.138049
$415$	7.53391	0.369825
$416$	−0.353160	−0.0173151
$417$	18.8373	0.922468
$418$	−11.9514	−0.584562
$419$	−12.4167	−0.606597	−0.303298	−	0.952896i	$-0.598088\pi$
$419$	−12.4167	−0.606597	−0.303298	+	0.952896i	$0.598088\pi$
$420$	8.29823	0.404912
$421$	11.6977	0.570112	0.285056	−	0.958511i	$-0.407988\pi$
$421$	11.6977	0.570112	0.285056	+	0.958511i	$0.407988\pi$
$422$	−4.54736	−0.221362
$423$	8.62062	0.419149
$424$	10.1619	0.493507
$425$	−2.34209	−0.113608
$426$	−13.2574	−0.642321
$427$	17.5157	0.847645
$428$	−4.29899	−0.207800
$429$	2.12488	0.102590
$430$	−3.90589	−0.188359
$431$	−23.4135	−1.12779	−0.563893	−	0.825848i	$-0.690697\pi$
$431$	−23.4135	−1.12779	−0.563893	+	0.825848i	$0.690697\pi$
$432$	5.62276	0.270525
$433$	30.7782	1.47910	0.739552	−	0.673099i	$-0.235037\pi$
$433$	30.7782	1.47910	0.739552	+	0.673099i	$0.235037\pi$
$434$	−8.22542	−0.394833
$435$	18.4592	0.885052
$436$	1.00038	0.0479093
$437$	11.3140	0.541220
$438$	−3.49262	−0.166884
$439$	−5.72778	−0.273372	−0.136686	−	0.990614i	$-0.543645\pi$
$439$	−5.72778	−0.273372	−0.136686	+	0.990614i	$0.543645\pi$
$440$	6.87381	0.327696
$441$	−2.47576	−0.117893
$442$	−0.403121	−0.0191745
$443$	−13.5975	−0.646038	−0.323019	−	0.946393i	$-0.604698\pi$
$443$	−13.5975	−0.646038	−0.323019	+	0.946393i	$0.604698\pi$
$444$	−7.34106	−0.348391
$445$	−12.3727	−0.586520
$446$	−10.9407	−0.518055
$447$	3.15096	0.149035
$448$	−3.21564	−0.151925
$449$	−13.0905	−0.617779	−0.308890	−	0.951098i	$-0.599957\pi$
$449$	−13.0905	−0.617779	−0.308890	+	0.951098i	$0.599957\pi$
$450$	1.52075	0.0716890
$451$	5.71788	0.269244
$452$	13.3551	0.628172
$453$	16.2003	0.761158
$454$	4.78771	0.224699
$455$	1.94991	0.0914133
$456$	4.48683	0.210115
$457$	21.1366	0.988731	0.494365	−	0.869254i	$-0.335401\pi$
$457$	21.1366	0.988731	0.494365	+	0.869254i	$0.335401\pi$
$458$	−9.22555	−0.431082
$459$	6.41820	0.299576
$460$	−6.50718	−0.303399
$461$	3.00983	0.140182	0.0700908	−	0.997541i	$-0.477671\pi$
$461$	3.00983	0.140182	0.0700908	+	0.997541i	$0.477671\pi$
$462$	19.3477	0.900136
$463$	35.9093	1.66885	0.834424	−	0.551124i	$-0.185801\pi$
$463$	35.9093	1.66885	0.834424	+	0.551124i	$0.185801\pi$
$464$	−7.15312	−0.332075
$465$	−6.60099	−0.306114
$466$	−20.7205	−0.959857
$467$	−10.8380	−0.501524	−0.250762	−	0.968049i	$-0.580681\pi$
$467$	−10.8380	−0.501524	−0.250762	+	0.968049i	$0.580681\pi$
$468$	0.261752	0.0120995
$469$	23.7763	1.09789
$470$	−19.9708	−0.921187
$471$	8.74964	0.403162
$472$	−9.26219	−0.426327
$473$	−9.10675	−0.418729
$474$	8.39120	0.385421
$475$	6.12545	0.281055
$476$	−3.67055	−0.168239
$477$	−7.53173	−0.344854
$478$	15.3292	0.701139
$479$	28.8929	1.32015	0.660074	−	0.751200i	$-0.270525\pi$
$479$	28.8929	1.32015	0.660074	+	0.751200i	$0.270525\pi$
$480$	−2.58059	−0.117787
$481$	−1.72500	−0.0786531
$482$	9.66228	0.440105
$483$	−18.3158	−0.833396
$484$	5.02659	0.228481
$485$	−2.84637	−0.129247
$486$	−7.50924	−0.340626
$487$	17.5642	0.795910	0.397955	−	0.917405i	$-0.369720\pi$
$487$	17.5642	0.795910	0.397955	+	0.917405i	$0.369720\pi$
$488$	−5.44705	−0.246576
$489$	17.7430	0.802365
$490$	5.73543	0.259100
$491$	−25.7352	−1.16141	−0.580707	−	0.814113i	$-0.697224\pi$
$491$	−25.7352	−1.16141	−0.580707	+	0.814113i	$0.697224\pi$
$492$	−2.14662	−0.0967773
$493$	−8.16506	−0.367736
$494$	1.05431	0.0474358
$495$	−5.09467	−0.228988
$496$	2.55794	0.114855
$497$	−28.3650	−1.27234
$498$	−6.59455	−0.295509
$499$	−37.8027	−1.69228	−0.846141	−	0.532959i	$-0.821080\pi$
$499$	−37.8027	−1.69228	−0.846141	+	0.532959i	$0.821080\pi$
$500$	−12.1082	−0.541493
$501$	−20.3297	−0.908263
$502$	−8.44172	−0.376773
$503$	4.66263	0.207896	0.103948	−	0.994583i	$-0.466852\pi$
$503$	4.66263	0.207896	0.103948	+	0.994583i	$0.466852\pi$
$504$	2.38334	0.106162
$505$	−15.5545	−0.692165
$506$	−15.1718	−0.674468
$507$	19.3508	0.859398
$508$	−12.1515	−0.539134
$509$	−3.96464	−0.175729	−0.0878647	−	0.996132i	$-0.528004\pi$
$509$	−3.96464	−0.175729	−0.0878647	+	0.996132i	$0.528004\pi$
$510$	−2.94566	−0.130436
$511$	−7.47268	−0.330572
$512$	1.00000	0.0441942
$513$	−16.7860	−0.741120
$514$	26.9045	1.18671
$515$	−28.0034	−1.23398
$516$	3.41889	0.150508
$517$	−46.5629	−2.04784
$518$	−15.7067	−0.690112
$519$	−9.79419	−0.429917
$520$	−0.606384	−0.0265917
$521$	−9.02045	−0.395193	−0.197597	−	0.980283i	$-0.563314\pi$
$521$	−9.02045	−0.395193	−0.197597	+	0.980283i	$0.563314\pi$
$522$	5.30168	0.232048
$523$	0.812677	0.0355359	0.0177679	−	0.999842i	$-0.494344\pi$
$523$	0.812677	0.0355359	0.0177679	+	0.999842i	$0.494344\pi$
$524$	1.48036	0.0646696
$525$	−9.91628	−0.432782
$526$	−13.1648	−0.574012
$527$	2.91981	0.127189
$528$	−6.01675	−0.261846
$529$	−8.63742	−0.375540
$530$	17.4483	0.757906
$531$	6.86487	0.297910
$532$	9.59987	0.416207
$533$	−0.504412	−0.0218485
$534$	10.8300	0.468659
$535$	−7.38148	−0.319129
$536$	−7.39396	−0.319370
$537$	20.8508	0.899779
$538$	−5.48262	−0.236372
$539$	13.3724	0.575991
$540$	9.65442	0.415460
$541$	27.0414	1.16260	0.581299	−	0.813690i	$-0.302545\pi$
$541$	27.0414	1.16260	0.581299	+	0.813690i	$0.302545\pi$
$542$	0.0605562	0.00260111
$543$	−14.9200	−0.640277
$544$	1.14147	0.0489401
$545$	1.71767	0.0735769
$546$	−1.70679	−0.0730439
$547$	−33.0032	−1.41111	−0.705557	−	0.708653i	$-0.749303\pi$
$547$	−33.0032	−1.41111	−0.705557	+	0.708653i	$0.749303\pi$
$548$	−3.91692	−0.167323
$549$	4.03719	0.172303
$550$	−8.21411	−0.350251
$551$	21.3547	0.909740
$552$	5.69584	0.242431
$553$	17.9535	0.763461
$554$	−26.9875	−1.14659
$555$	−12.6048	−0.535044
$556$	−12.5337	−0.531545
$557$	−16.6703	−0.706344	−0.353172	−	0.935558i	$-0.614897\pi$
$557$	−16.6703	−0.706344	−0.353172	+	0.935558i	$0.614897\pi$
$558$	−1.89587	−0.0802588
$559$	0.803368	0.0339788
$560$	−5.52133	−0.233319
$561$	−6.86794	−0.289964
$562$	1.92934	0.0813844
$563$	−12.0911	−0.509578	−0.254789	−	0.966997i	$-0.582006\pi$
$563$	−12.0911	−0.509578	−0.254789	+	0.966997i	$0.582006\pi$
$564$	17.4808	0.736075
$565$	22.9311	0.964719
$566$	−6.17109	−0.259390
$567$	20.0243	0.840940
$568$	8.82095	0.370119
$569$	−7.42560	−0.311297	−0.155649	−	0.987812i	$-0.549747\pi$
$569$	−7.42560	−0.311297	−0.155649	+	0.987812i	$0.549747\pi$
$570$	7.70400	0.322685
$571$	20.5096	0.858301	0.429150	−	0.903233i	$-0.358813\pi$
$571$	20.5096	0.858301	0.429150	+	0.903233i	$0.358813\pi$
$572$	−1.41381	−0.0591145
$573$	−4.27342	−0.178525
$574$	−4.59284	−0.191701
$575$	7.77600	0.324282
$576$	−0.741171	−0.0308821
$577$	10.8883	0.453285	0.226643	−	0.973978i	$-0.427225\pi$
$577$	10.8883	0.453285	0.226643	+	0.973978i	$0.427225\pi$
$578$	−15.6970	−0.652911
$579$	−1.08027	−0.0448943
$580$	−12.2821	−0.509986
$581$	−14.1095	−0.585359
$582$	2.49148	0.103275
$583$	40.6815	1.68485
$584$	2.32386	0.0961619
$585$	0.449435	0.0185818
$586$	24.3057	1.00406
$587$	−1.77390	−0.0732167	−0.0366083	−	0.999330i	$-0.511655\pi$
$587$	−1.77390	−0.0732167	−0.0366083	+	0.999330i	$0.511655\pi$
$588$	−5.02031	−0.207034
$589$	−7.63641	−0.314653
$590$	−15.9034	−0.654733
$591$	−22.5065	−0.925794
$592$	4.88447	0.200750
$593$	−5.84172	−0.239891	−0.119945	−	0.992781i	$-0.538272\pi$
$593$	−5.84172	−0.239891	−0.119945	+	0.992781i	$0.538272\pi$
$594$	22.5097	0.923584
$595$	−6.30243	−0.258374
$596$	−2.09653	−0.0858773
$597$	−2.61919	−0.107196
$598$	1.33840	0.0547314
$599$	30.7595	1.25680	0.628399	−	0.777891i	$-0.283711\pi$
$599$	30.7595	1.25680	0.628399	+	0.777891i	$0.283711\pi$
$600$	3.08377	0.125894
$601$	3.57912	0.145995	0.0729977	−	0.997332i	$-0.476743\pi$
$601$	3.57912	0.145995	0.0729977	+	0.997332i	$0.476743\pi$
$602$	7.31493	0.298134
$603$	5.48019	0.223171
$604$	−10.7791	−0.438595
$605$	8.63078	0.350891
$606$	13.6151	0.553075
$607$	−7.51379	−0.304976	−0.152488	−	0.988305i	$-0.548728\pi$
$607$	−7.51379	−0.304976	−0.152488	+	0.988305i	$0.548728\pi$
$608$	−2.98537	−0.121073
$609$	−34.5704	−1.40086
$610$	−9.35272	−0.378680
$611$	4.10763	0.166177
$612$	−0.846024	−0.0341985
$613$	23.9241	0.966286	0.483143	−	0.875542i	$-0.339495\pi$
$613$	23.9241	0.966286	0.483143	+	0.875542i	$0.339495\pi$
$614$	−14.1889	−0.572618
$615$	−3.68581	−0.148626
$616$	−12.8732	−0.518677
$617$	−3.47211	−0.139782	−0.0698910	−	0.997555i	$-0.522265\pi$
$617$	−3.47211	−0.139782	−0.0698910	+	0.997555i	$0.522265\pi$
$618$	24.5118	0.986010
$619$	−15.3162	−0.615611	−0.307805	−	0.951449i	$-0.599595\pi$
$619$	−15.3162	−0.615611	−0.307805	+	0.951449i	$0.599595\pi$
$620$	4.39206	0.176389
$621$	−21.3091	−0.855105
$622$	8.20570	0.329019
$623$	23.1715	0.928345
$624$	0.530778	0.0212481
$625$	−10.5309	−0.421236
$626$	8.70619	0.347969
$627$	17.9622	0.717342
$628$	−5.82168	−0.232310
$629$	5.57547	0.222308
$630$	4.09225	0.163039
$631$	8.09712	0.322341	0.161171	−	0.986927i	$-0.448473\pi$
$631$	8.09712	0.322341	0.161171	+	0.986927i	$0.448473\pi$
$632$	−5.58319	−0.222087
$633$	6.83442	0.271644
$634$	8.26473	0.328234
$635$	−20.8644	−0.827977
$636$	−15.2728	−0.605605
$637$	−1.17967	−0.0467402
$638$	−28.6362	−1.13372
$639$	−6.53784	−0.258633
$640$	1.71703	0.0678714
$641$	−13.2260	−0.522396	−0.261198	−	0.965285i	$-0.584118\pi$
$641$	−13.2260	−0.522396	−0.261198	+	0.965285i	$0.584118\pi$
$642$	6.46113	0.255000
$643$	16.4514	0.648781	0.324390	−	0.945923i	$-0.394841\pi$
$643$	16.4514	0.648781	0.324390	+	0.945923i	$0.394841\pi$
$644$	12.1866	0.480220
$645$	5.87032	0.231143
$646$	−3.40771	−0.134074
$647$	9.91768	0.389904	0.194952	−	0.980813i	$-0.437545\pi$
$647$	9.91768	0.389904	0.194952	+	0.980813i	$0.437545\pi$
$648$	−6.22715	−0.244626
$649$	−37.0795	−1.45550
$650$	0.724621	0.0284220
$651$	12.3623	0.484517
$652$	−11.8055	−0.462340
$653$	20.3223	0.795272	0.397636	−	0.917543i	$-0.369831\pi$
$653$	20.3223	0.795272	0.397636	+	0.917543i	$0.369831\pi$
$654$	−1.50350	−0.0587917
$655$	2.54181	0.0993167
$656$	1.42828	0.0557651
$657$	−1.72238	−0.0671963
$658$	37.4013	1.45806
$659$	−19.8550	−0.773440	−0.386720	−	0.922197i	$-0.626392\pi$
$659$	−19.8550	−0.773440	−0.386720	+	0.922197i	$0.626392\pi$
$660$	−10.3309	−0.402130
$661$	−12.9507	−0.503725	−0.251862	−	0.967763i	$-0.581043\pi$
$661$	−12.9507	−0.503725	−0.251862	+	0.967763i	$0.581043\pi$
$662$	−11.4140	−0.443618
$663$	0.605867	0.0235299
$664$	4.38777	0.170278
$665$	16.4832	0.639192
$666$	−3.62023	−0.140281
$667$	27.1089	1.04966
$668$	13.5266	0.523360
$669$	16.4431	0.635729
$670$	−12.6956	−0.490474
$671$	−21.8063	−0.841822
$672$	4.83291	0.186434
$673$	24.2472	0.934661	0.467330	−	0.884083i	$-0.345216\pi$
$673$	24.2472	0.934661	0.467330	+	0.884083i	$0.345216\pi$
$674$	31.6776	1.22017
$675$	−11.5369	−0.444056
$676$	−12.8753	−0.495203
$677$	32.0046	1.23004	0.615018	−	0.788513i	$-0.289149\pi$
$677$	32.0046	1.23004	0.615018	+	0.788513i	$0.289149\pi$
$678$	−20.0720	−0.770859
$679$	5.33068	0.204573
$680$	1.95993	0.0751599
$681$	−7.19565	−0.275738
$682$	10.2403	0.392120
$683$	34.5356	1.32147	0.660735	−	0.750620i	$-0.270245\pi$
$683$	34.5356	1.32147	0.660735	+	0.750620i	$0.270245\pi$
$684$	2.21267	0.0846036
$685$	−6.72545	−0.256966
$686$	11.7682	0.449311
$687$	13.8655	0.529000
$688$	−2.27480	−0.0867259
$689$	−3.58879	−0.136722
$690$	9.77991	0.372315
$691$	−24.0583	−0.915220	−0.457610	−	0.889153i	$-0.651294\pi$
$691$	−24.0583	−0.915220	−0.457610	+	0.889153i	$0.651294\pi$
$692$	6.51669	0.247727
$693$	9.54127	0.362443
$694$	5.71152	0.216806
$695$	−21.5206	−0.816323
$696$	10.7507	0.407504
$697$	1.63034	0.0617535
$698$	−13.4839	−0.510372
$699$	31.1416	1.17788
$700$	6.59792	0.249378
$701$	12.3830	0.467698	0.233849	−	0.972273i	$-0.424868\pi$
$701$	12.3830	0.467698	0.233849	+	0.972273i	$0.424868\pi$
$702$	−1.98573	−0.0749466
$703$	−14.5819	−0.549968
$704$	4.00332	0.150881
$705$	30.0150	1.13043
$706$	3.31124	0.124620
$707$	29.1304	1.09556
$708$	13.9205	0.523165
$709$	33.8557	1.27148	0.635738	−	0.771905i	$-0.280696\pi$
$709$	33.8557	1.27148	0.635738	+	0.771905i	$0.280696\pi$
$710$	15.1458	0.568412
$711$	4.13810	0.155191
$712$	−7.20587	−0.270051
$713$	−9.69409	−0.363047
$714$	5.51662	0.206454
$715$	−2.42755	−0.0907853
$716$	−13.8733	−0.518471
$717$	−23.0388	−0.860400
$718$	3.20469	0.119598
$719$	37.3019	1.39113	0.695563	−	0.718465i	$-0.255155\pi$
$719$	37.3019	1.39113	0.695563	+	0.718465i	$0.255155\pi$
$720$	−1.27261	−0.0474274
$721$	52.4447	1.95314
$722$	−10.0876	−0.375420
$723$	−14.5218	−0.540072
$724$	9.92719	0.368941
$725$	14.6769	0.545087
$726$	−7.55466	−0.280380
$727$	−39.6485	−1.47048	−0.735241	−	0.677806i	$-0.762931\pi$
$727$	−39.6485	−1.47048	−0.735241	+	0.677806i	$0.762931\pi$
$728$	1.13563	0.0420894
$729$	29.9674	1.10990
$730$	3.99012	0.147681
$731$	−2.59661	−0.0960392
$732$	8.18658	0.302585
$733$	−5.78148	−0.213544	−0.106772	−	0.994284i	$-0.534051\pi$
$733$	−5.78148	−0.213544	−0.106772	+	0.994284i	$0.534051\pi$
$734$	1.53401	0.0566212
$735$	−8.62001	−0.317954
$736$	−3.78980	−0.139694
$737$	−29.6004	−1.09034
$738$	−1.05860	−0.0389677
$739$	51.7619	1.90409	0.952045	−	0.305957i	$-0.0989763\pi$
$739$	51.7619	1.90409	0.952045	+	0.305957i	$0.0989763\pi$
$740$	8.38676	0.308303
$741$	−1.58457	−0.0582106
$742$	−32.6771	−1.19961
$743$	30.7153	1.12684	0.563418	−	0.826172i	$-0.309486\pi$
$743$	30.7153	1.12684	0.563418	+	0.826172i	$0.309486\pi$
$744$	−3.84444	−0.140944
$745$	−3.59980	−0.131886
$746$	7.25168	0.265503
$747$	−3.25209	−0.118988
$748$	4.56967	0.167084
$749$	13.8240	0.505118
$750$	18.1978	0.664491
$751$	39.7542	1.45065	0.725325	−	0.688406i	$-0.241689\pi$
$751$	39.7542	1.45065	0.725325	+	0.688406i	$0.241689\pi$
$752$	−11.6311	−0.424142
$753$	12.6874	0.462355
$754$	2.52619	0.0919985
$755$	−18.5080	−0.673574
$756$	−18.0807	−0.657590
$757$	14.9207	0.542303	0.271152	−	0.962537i	$-0.412596\pi$
$757$	14.9207	0.542303	0.271152	+	0.962537i	$0.412596\pi$
$758$	14.8795	0.540448
$759$	22.8023	0.827671
$760$	−5.12596	−0.185938
$761$	6.08875	0.220717	0.110359	−	0.993892i	$-0.464800\pi$
$761$	6.08875	0.220717	0.110359	+	0.993892i	$0.464800\pi$
$762$	18.2629	0.661596
$763$	−3.21684	−0.116458
$764$	2.84337	0.102870
$765$	−1.45265	−0.0525205
$766$	−1.95482	−0.0706305
$767$	3.27103	0.118110
$768$	−1.50294	−0.0542327
$769$	−4.71613	−0.170068	−0.0850341	−	0.996378i	$-0.527100\pi$
$769$	−4.71613	−0.170068	−0.0850341	+	0.996378i	$0.527100\pi$
$770$	−22.1037	−0.796561
$771$	−40.4359	−1.45626
$772$	0.718768	0.0258690
$773$	−12.2667	−0.441202	−0.220601	−	0.975364i	$-0.570802\pi$
$773$	−12.2667	−0.441202	−0.220601	+	0.975364i	$0.570802\pi$
$774$	1.68602	0.0606026
$775$	−5.24845	−0.188530
$776$	−1.65773	−0.0595092
$777$	23.6062	0.846868
$778$	19.1940	0.688140
$779$	−4.26395	−0.152772
$780$	0.911359	0.0326319
$781$	35.3131	1.26360
$782$	−4.32594	−0.154695
$783$	−40.2202	−1.43735
$784$	3.34033	0.119297
$785$	−9.99598	−0.356772
$786$	−2.22489	−0.0793590
$787$	−39.4681	−1.40688	−0.703442	−	0.710753i	$-0.748355\pi$
$787$	−39.4681	−1.40688	−0.703442	+	0.710753i	$0.748355\pi$
$788$	14.9750	0.533462
$789$	19.7859	0.704396
$790$	−9.58648	−0.341072
$791$	−42.9453	−1.52696
$792$	−2.96715	−0.105433
$793$	1.92368	0.0683118
$794$	−31.5579	−1.11995
$795$	−26.2237	−0.930060
$796$	1.74271	0.0617686
$797$	15.6916	0.555826	0.277913	−	0.960606i	$-0.410357\pi$
$797$	15.6916	0.555826	0.277913	+	0.960606i	$0.410357\pi$
$798$	−14.4280	−0.510747
$799$	−13.2765	−0.469689
$800$	−2.05182	−0.0725429
$801$	5.34078	0.188707
$802$	28.6268	1.01085
$803$	9.30315	0.328301
$804$	11.1127	0.391914
$805$	20.9247	0.737500
$806$	−0.903363	−0.0318196
$807$	8.24004	0.290063
$808$	−9.05896	−0.318693
$809$	19.6433	0.690622	0.345311	−	0.938488i	$-0.387773\pi$
$809$	19.6433	0.690622	0.345311	+	0.938488i	$0.387773\pi$
$810$	−10.6922	−0.375685
$811$	−26.3097	−0.923860	−0.461930	−	0.886916i	$-0.652843\pi$
$811$	−26.3097	−0.923860	−0.461930	+	0.886916i	$0.652843\pi$
$812$	23.0018	0.807206
$813$	−0.0910123	−0.00319194
$814$	19.5541	0.685371
$815$	−20.2704	−0.710040
$816$	−1.71556	−0.0600566
$817$	6.79112	0.237591
$818$	2.42224	0.0846918
$819$	−0.841700	−0.0294114
$820$	2.45240	0.0856415
$821$	8.54121	0.298090	0.149045	−	0.988830i	$-0.452380\pi$
$821$	8.54121	0.298090	0.149045	+	0.988830i	$0.452380\pi$
$822$	5.88690	0.205329
$823$	26.0524	0.908130	0.454065	−	0.890969i	$-0.349973\pi$
$823$	26.0524	0.908130	0.454065	+	0.890969i	$0.349973\pi$
$824$	−16.3093	−0.568160
$825$	12.3453	0.429809
$826$	29.7838	1.03631
$827$	26.0585	0.906142	0.453071	−	0.891474i	$-0.350328\pi$
$827$	26.0585	0.906142	0.453071	+	0.891474i	$0.350328\pi$
$828$	2.80889	0.0976157
$829$	10.2292	0.355274	0.177637	−	0.984096i	$-0.443155\pi$
$829$	10.2292	0.355274	0.177637	+	0.984096i	$0.443155\pi$
$830$	7.53391	0.261506
$831$	40.5607	1.40703
$832$	−0.353160	−0.0122436
$833$	3.81288	0.132109
$834$	18.8373	0.652283
$835$	23.2255	0.803753
$836$	−11.9514	−0.413348
$837$	14.3827	0.497139
$838$	−12.4167	−0.428929
$839$	−39.9349	−1.37870	−0.689352	−	0.724426i	$-0.742105\pi$
$839$	−39.9349	−1.37870	−0.689352	+	0.724426i	$0.742105\pi$
$840$	8.29823	0.286316
$841$	22.1671	0.764381
$842$	11.6977	0.403130
$843$	−2.89968	−0.0998704
$844$	−4.54736	−0.156527
$845$	−22.1072	−0.760510
$846$	8.62062	0.296383
$847$	−16.1637	−0.555391
$848$	10.1619	0.348962
$849$	9.27477	0.318309
$850$	−2.34209	−0.0803331
$851$	−18.5112	−0.634554
$852$	−13.2574	−0.454190
$853$	47.4359	1.62417	0.812087	−	0.583536i	$-0.198331\pi$
$853$	47.4359	1.62417	0.812087	+	0.583536i	$0.198331\pi$
$854$	17.5157	0.599376
$855$	3.79921	0.129930
$856$	−4.29899	−0.146936
$857$	22.7330	0.776545	0.388273	−	0.921545i	$-0.373072\pi$
$857$	22.7330	0.776545	0.388273	+	0.921545i	$0.373072\pi$
$858$	2.12488	0.0725420
$859$	34.7089	1.18425	0.592126	−	0.805846i	$-0.298289\pi$
$859$	34.7089	1.18425	0.592126	+	0.805846i	$0.298289\pi$
$860$	−3.90589	−0.133190
$861$	6.90276	0.235246
$862$	−23.4135	−0.797466
$863$	26.8833	0.915117	0.457558	−	0.889180i	$-0.348724\pi$
$863$	26.8833	0.915117	0.457558	+	0.889180i	$0.348724\pi$
$864$	5.62276	0.191290
$865$	11.1893	0.380448
$866$	30.7782	1.04589
$867$	23.5917	0.801217
$868$	−8.22542	−0.279189
$869$	−22.3513	−0.758216
$870$	18.4592	0.625827
$871$	2.61125	0.0884788
$872$	1.00038	0.0338770
$873$	1.22867	0.0415840
$874$	11.3140	0.382700
$875$	38.9355	1.31626
$876$	−3.49262	−0.118005
$877$	29.1551	0.984498	0.492249	−	0.870455i	$-0.336175\pi$
$877$	29.1551	0.984498	0.492249	+	0.870455i	$0.336175\pi$
$878$	−5.72778	−0.193303
$879$	−36.5300	−1.23213
$880$	6.87381	0.231716
$881$	−14.8442	−0.500112	−0.250056	−	0.968231i	$-0.580449\pi$
$881$	−14.8442	−0.500112	−0.250056	+	0.968231i	$0.580449\pi$
$882$	−2.47576	−0.0833631
$883$	24.6642	0.830017	0.415009	−	0.909817i	$-0.363779\pi$
$883$	24.6642	0.830017	0.415009	+	0.909817i	$0.363779\pi$
$884$	−0.403121	−0.0135584
$885$	23.9019	0.803453
$886$	−13.5975	−0.456818
$887$	11.2626	0.378162	0.189081	−	0.981961i	$-0.439449\pi$
$887$	11.2626	0.378162	0.189081	+	0.981961i	$0.439449\pi$
$888$	−7.34106	−0.246350
$889$	39.0747	1.31052
$890$	−12.3727	−0.414732
$891$	−24.9293	−0.835163
$892$	−10.9407	−0.366320
$893$	34.7230	1.16196
$894$	3.15096	0.105384
$895$	−23.8209	−0.796245
$896$	−3.21564	−0.107427
$897$	−2.01154	−0.0671634
$898$	−13.0905	−0.436836
$899$	−18.2973	−0.610248
$900$	1.52075	0.0506918
$901$	11.5995	0.386436
$902$	5.71788	0.190384
$903$	−10.9939	−0.365854
$904$	13.3551	0.444185
$905$	17.0452	0.566603
$906$	16.2003	0.538220
$907$	48.6784	1.61634	0.808169	−	0.588950i	$-0.200459\pi$
$907$	48.6784	1.61634	0.808169	+	0.588950i	$0.200459\pi$
$908$	4.78771	0.158886
$909$	6.71425	0.222697
$910$	1.94991	0.0646390
$911$	5.45084	0.180594	0.0902972	−	0.995915i	$-0.471218\pi$
$911$	5.45084	0.180594	0.0902972	+	0.995915i	$0.471218\pi$
$912$	4.48683	0.148574
$913$	17.5656	0.581338
$914$	21.1366	0.699138
$915$	14.0566	0.464696
$916$	−9.22555	−0.304821
$917$	−4.76029	−0.157199
$918$	6.41820	0.211832
$919$	−19.8558	−0.654982	−0.327491	−	0.944854i	$-0.606203\pi$
$919$	−19.8558	−0.654982	−0.327491	+	0.944854i	$0.606203\pi$
$920$	−6.50718	−0.214535
$921$	21.3251	0.702685
$922$	3.00983	0.0991234
$923$	−3.11521	−0.102538
$924$	19.3477	0.636493
$925$	−10.0221	−0.329523
$926$	35.9093	1.18005
$927$	12.0880	0.397020
$928$	−7.15312	−0.234813
$929$	5.52248	0.181187	0.0905934	−	0.995888i	$-0.471124\pi$
$929$	5.52248	0.181187	0.0905934	+	0.995888i	$0.471124\pi$
$930$	−6.60099	−0.216455
$931$	−9.97212	−0.326823
$932$	−20.7205	−0.678722
$933$	−12.3327	−0.403754
$934$	−10.8380	−0.354631
$935$	7.84624	0.256599
$936$	0.261752	0.00855563
$937$	14.2401	0.465203	0.232602	−	0.972572i	$-0.425276\pi$
$937$	14.2401	0.465203	0.232602	+	0.972572i	$0.425276\pi$
$938$	23.7763	0.776324
$939$	−13.0849	−0.427009
$940$	−19.9708	−0.651377
$941$	33.2367	1.08349	0.541743	−	0.840544i	$-0.317765\pi$
$941$	33.2367	1.08349	0.541743	+	0.840544i	$0.317765\pi$
$942$	8.74964	0.285079
$943$	−5.41291	−0.176268
$944$	−9.26219	−0.301458
$945$	−31.0451	−1.00990
$946$	−9.10675	−0.296086
$947$	2.54508	0.0827040	0.0413520	−	0.999145i	$-0.486833\pi$
$947$	2.54508	0.0827040	0.0413520	+	0.999145i	$0.486833\pi$
$948$	8.39120	0.272534
$949$	−0.820693	−0.0266408
$950$	6.12545	0.198736
$951$	−12.4214	−0.402791
$952$	−3.67055	−0.118963
$953$	23.8919	0.773933	0.386967	−	0.922094i	$-0.373523\pi$
$953$	23.8919	0.773933	0.386967	+	0.922094i	$0.373523\pi$
$954$	−7.53173	−0.243849
$955$	4.88214	0.157982
$956$	15.3292	0.495780
$957$	43.0385	1.39124
$958$	28.8929	0.933486
$959$	12.5954	0.406727
$960$	−2.58059	−0.0832881
$961$	−24.4569	−0.788933
$962$	−1.72500	−0.0556162
$963$	3.18629	0.102677
$964$	9.66228	0.311201
$965$	1.23414	0.0397285
$966$	−18.3158	−0.589300
$967$	27.0093	0.868561	0.434281	−	0.900778i	$-0.357003\pi$
$967$	27.0093	0.868561	0.434281	+	0.900778i	$0.357003\pi$
$968$	5.02659	0.161561
$969$	5.12158	0.164529
$970$	−2.84637	−0.0913915
$971$	−22.5739	−0.724432	−0.362216	−	0.932094i	$-0.617980\pi$
$971$	−22.5739	−0.724432	−0.362216	+	0.932094i	$0.617980\pi$
$972$	−7.50924	−0.240859
$973$	40.3037	1.29208
$974$	17.5642	0.562793
$975$	−1.08906	−0.0348779
$976$	−5.44705	−0.174356
$977$	−54.7935	−1.75300	−0.876500	−	0.481401i	$-0.840128\pi$
$977$	−54.7935	−1.75300	−0.876500	+	0.481401i	$0.840128\pi$
$978$	17.7430	0.567358
$979$	−28.8474	−0.921967
$980$	5.73543	0.183212
$981$	−0.741450	−0.0236727
$982$	−25.7352	−0.821243
$983$	−24.6336	−0.785691	−0.392845	−	0.919605i	$-0.628509\pi$
$983$	−24.6336	−0.785691	−0.392845	+	0.919605i	$0.628509\pi$
$984$	−2.14662	−0.0684319
$985$	25.7124	0.819266
$986$	−8.16506	−0.260028
$987$	−56.2119	−1.78925
$988$	1.05431	0.0335421
$989$	8.62103	0.274133
$990$	−5.09467	−0.161919
$991$	−21.0988	−0.670225	−0.335113	−	0.942178i	$-0.608774\pi$
$991$	−21.0988	−0.670225	−0.335113	+	0.942178i	$0.608774\pi$
$992$	2.55794	0.0812148
$993$	17.1546	0.544384
$994$	−28.3650	−0.899683
$995$	2.99227	0.0948615
$996$	−6.59455	−0.208956
$997$	−37.9512	−1.20193	−0.600963	−	0.799277i	$-0.705216\pi$
$997$	−37.9512	−1.20193	−0.600963	+	0.799277i	$0.705216\pi$
$998$	−37.8027	−1.19662
$999$	27.4642	0.868928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.f.1.12	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.f.1.12	✓	31	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.50294 q^{3} +1.00000 q^{4} +1.71703 q^{5} -1.50294 q^{6} -3.21564 q^{7} +1.00000 q^{8} -0.741171 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.50294 q^{3} +1.00000 q^{4} +1.71703 q^{5} -1.50294 q^{6} -3.21564 q^{7} +1.00000 q^{8} -0.741171 q^{9} +1.71703 q^{10} +4.00332 q^{11} -1.50294 q^{12} -0.353160 q^{13} -3.21564 q^{14} -2.58059 q^{15} +1.00000 q^{16} +1.14147 q^{17} -0.741171 q^{18} -2.98537 q^{19} +1.71703 q^{20} +4.83291 q^{21} +4.00332 q^{22} -3.78980 q^{23} -1.50294 q^{24} -2.05182 q^{25} -0.353160 q^{26} +5.62276 q^{27} -3.21564 q^{28} -7.15312 q^{29} -2.58059 q^{30} +2.55794 q^{31} +1.00000 q^{32} -6.01675 q^{33} +1.14147 q^{34} -5.52133 q^{35} -0.741171 q^{36} +4.88447 q^{37} -2.98537 q^{38} +0.530778 q^{39} +1.71703 q^{40} +1.42828 q^{41} +4.83291 q^{42} -2.27480 q^{43} +4.00332 q^{44} -1.27261 q^{45} -3.78980 q^{46} -11.6311 q^{47} -1.50294 q^{48} +3.34033 q^{49} -2.05182 q^{50} -1.71556 q^{51} -0.353160 q^{52} +10.1619 q^{53} +5.62276 q^{54} +6.87381 q^{55} -3.21564 q^{56} +4.48683 q^{57} -7.15312 q^{58} -9.26219 q^{59} -2.58059 q^{60} -5.44705 q^{61} +2.55794 q^{62} +2.38334 q^{63} +1.00000 q^{64} -0.606384 q^{65} -6.01675 q^{66} -7.39396 q^{67} +1.14147 q^{68} +5.69584 q^{69} -5.52133 q^{70} +8.82095 q^{71} -0.741171 q^{72} +2.32386 q^{73} +4.88447 q^{74} +3.08377 q^{75} -2.98537 q^{76} -12.8732 q^{77} +0.530778 q^{78} -5.58319 q^{79} +1.71703 q^{80} -6.22715 q^{81} +1.42828 q^{82} +4.38777 q^{83} +4.83291 q^{84} +1.95993 q^{85} -2.27480 q^{86} +10.7507 q^{87} +4.00332 q^{88} -7.20587 q^{89} -1.27261 q^{90} +1.13563 q^{91} -3.78980 q^{92} -3.84444 q^{93} -11.6311 q^{94} -5.12596 q^{95} -1.50294 q^{96} -1.65773 q^{97} +3.34033 q^{98} -2.96715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9	\( 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9} - 23 q^{10} - 32 q^{11} - 13 q^{12} - 8 q^{13} - 18 q^{14} - 14 q^{15} + 31 q^{16} - 30 q^{17} + 20 q^{18} - 38 q^{19} - 23 q^{20} - 16 q^{21} - 32 q^{22} - 24 q^{23} - 13 q^{24} + 40 q^{25} - 8 q^{26} - 28 q^{27} - 18 q^{28} - 7 q^{29} - 14 q^{30} - 32 q^{31} + 31 q^{32} - 9 q^{33} - 30 q^{34} - 14 q^{35} + 20 q^{36} + 11 q^{37} - 38 q^{38} - 9 q^{39} - 23 q^{40} - 76 q^{41} - 16 q^{42} - 33 q^{43} - 32 q^{44} - 40 q^{45} - 24 q^{46} - 96 q^{47} - 13 q^{48} + 15 q^{49} + 40 q^{50} - 55 q^{51} - 8 q^{52} - 28 q^{53} - 28 q^{54} - 52 q^{55} - 18 q^{56} - 21 q^{57} - 7 q^{58} - 72 q^{59} - 14 q^{60} - 9 q^{61} - 32 q^{62} - 54 q^{63} + 31 q^{64} - 38 q^{65} - 9 q^{66} - 4 q^{67} - 30 q^{68} - 17 q^{69} - 14 q^{70} - 61 q^{71} + 20 q^{72} - 62 q^{73} + 11 q^{74} - 63 q^{75} - 38 q^{76} - 9 q^{77} - 9 q^{78} - 30 q^{79} - 23 q^{80} - 13 q^{81} - 76 q^{82} - 90 q^{83} - 16 q^{84} + 26 q^{85} - 33 q^{86} - 34 q^{87} - 32 q^{88} - 99 q^{89} - 40 q^{90} - 47 q^{91} - 24 q^{92} - 6 q^{93} - 96 q^{94} - 24 q^{95} - 13 q^{96} - 46 q^{97} + 15 q^{98} - 48 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9 - 23 * q^10 - 32 * q^11 - 13 * q^12 - 8 * q^13 - 18 * q^14 - 14 * q^15 + 31 * q^16 - 30 * q^17 + 20 * q^18 - 38 * q^19 - 23 * q^20 - 16 * q^21 - 32 * q^22 - 24 * q^23 - 13 * q^24 + 40 * q^25 - 8 * q^26 - 28 * q^27 - 18 * q^28 - 7 * q^29 - 14 * q^30 - 32 * q^31 + 31 * q^32 - 9 * q^33 - 30 * q^34 - 14 * q^35 + 20 * q^36 + 11 * q^37 - 38 * q^38 - 9 * q^39 - 23 * q^40 - 76 * q^41 - 16 * q^42 - 33 * q^43 - 32 * q^44 - 40 * q^45 - 24 * q^46 - 96 * q^47 - 13 * q^48 + 15 * q^49 + 40 * q^50 - 55 * q^51 - 8 * q^52 - 28 * q^53 - 28 * q^54 - 52 * q^55 - 18 * q^56 - 21 * q^57 - 7 * q^58 - 72 * q^59 - 14 * q^60 - 9 * q^61 - 32 * q^62 - 54 * q^63 + 31 * q^64 - 38 * q^65 - 9 * q^66 - 4 * q^67 - 30 * q^68 - 17 * q^69 - 14 * q^70 - 61 * q^71 + 20 * q^72 - 62 * q^73 + 11 * q^74 - 63 * q^75 - 38 * q^76 - 9 * q^77 - 9 * q^78 - 30 * q^79 - 23 * q^80 - 13 * q^81 - 76 * q^82 - 90 * q^83 - 16 * q^84 + 26 * q^85 - 33 * q^86 - 34 * q^87 - 32 * q^88 - 99 * q^89 - 40 * q^90 - 47 * q^91 - 24 * q^92 - 6 * q^93 - 96 * q^94 - 24 * q^95 - 13 * q^96 - 46 * q^97 + 15 * q^98 - 48 * q^99

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