LMFDB - Embedded newform 4006.2.a.g.1.39

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:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.39
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)

$f(q)$	$=$	$q-1.00000 q^{2} +3.09899 q^{3} +1.00000 q^{4} -1.23455 q^{5} -3.09899 q^{6} -4.11422 q^{7} -1.00000 q^{8} +6.60371 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.09899 q^{3} +1.00000 q^{4} -1.23455 q^{5} -3.09899 q^{6} -4.11422 q^{7} -1.00000 q^{8} +6.60371 q^{9} +1.23455 q^{10} -2.95423 q^{11} +3.09899 q^{12} -4.28463 q^{13} +4.11422 q^{14} -3.82585 q^{15} +1.00000 q^{16} +7.58691 q^{17} -6.60371 q^{18} +6.52856 q^{19} -1.23455 q^{20} -12.7499 q^{21} +2.95423 q^{22} +3.37032 q^{23} -3.09899 q^{24} -3.47589 q^{25} +4.28463 q^{26} +11.1678 q^{27} -4.11422 q^{28} -6.69964 q^{29} +3.82585 q^{30} -3.82876 q^{31} -1.00000 q^{32} -9.15513 q^{33} -7.58691 q^{34} +5.07922 q^{35} +6.60371 q^{36} +1.89485 q^{37} -6.52856 q^{38} -13.2780 q^{39} +1.23455 q^{40} +0.398057 q^{41} +12.7499 q^{42} -2.23068 q^{43} -2.95423 q^{44} -8.15261 q^{45} -3.37032 q^{46} -5.86735 q^{47} +3.09899 q^{48} +9.92684 q^{49} +3.47589 q^{50} +23.5117 q^{51} -4.28463 q^{52} -2.92318 q^{53} -11.1678 q^{54} +3.64715 q^{55} +4.11422 q^{56} +20.2319 q^{57} +6.69964 q^{58} -11.4148 q^{59} -3.82585 q^{60} -8.90652 q^{61} +3.82876 q^{62} -27.1692 q^{63} +1.00000 q^{64} +5.28959 q^{65} +9.15513 q^{66} -13.7654 q^{67} +7.58691 q^{68} +10.4446 q^{69} -5.07922 q^{70} -4.74052 q^{71} -6.60371 q^{72} -5.73636 q^{73} -1.89485 q^{74} -10.7717 q^{75} +6.52856 q^{76} +12.1544 q^{77} +13.2780 q^{78} -10.7601 q^{79} -1.23455 q^{80} +14.7979 q^{81} -0.398057 q^{82} +17.2797 q^{83} -12.7499 q^{84} -9.36642 q^{85} +2.23068 q^{86} -20.7621 q^{87} +2.95423 q^{88} -16.5322 q^{89} +8.15261 q^{90} +17.6279 q^{91} +3.37032 q^{92} -11.8653 q^{93} +5.86735 q^{94} -8.05983 q^{95} -3.09899 q^{96} +1.59775 q^{97} -9.92684 q^{98} -19.5089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * 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
$3$	3.09899	1.78920	0.894600	−	0.446868i	$-0.147461\pi$
$3$	3.09899	1.78920	0.894600	+	0.446868i	$0.147461\pi$
$4$	1.00000	0.500000
$5$	−1.23455	−0.552107	−0.276054	−	0.961142i	$-0.589027\pi$
$5$	−1.23455	−0.552107	−0.276054	+	0.961142i	$0.589027\pi$
$6$	−3.09899	−1.26516
$7$	−4.11422	−1.55503	−0.777515	−	0.628864i	$-0.783520\pi$
$7$	−4.11422	−1.55503	−0.777515	+	0.628864i	$0.783520\pi$
$8$	−1.00000	−0.353553
$9$	6.60371	2.20124
$10$	1.23455	0.390399
$11$	−2.95423	−0.890735	−0.445367	−	0.895348i	$-0.646927\pi$
$11$	−2.95423	−0.890735	−0.445367	+	0.895348i	$0.646927\pi$
$12$	3.09899	0.894600
$13$	−4.28463	−1.18834	−0.594171	−	0.804339i	$-0.702520\pi$
$13$	−4.28463	−1.18834	−0.594171	+	0.804339i	$0.702520\pi$
$14$	4.11422	1.09957
$15$	−3.82585	−0.987831
$16$	1.00000	0.250000
$17$	7.58691	1.84010	0.920049	−	0.391804i	$-0.128149\pi$
$17$	7.58691	1.84010	0.920049	+	0.391804i	$0.128149\pi$
$18$	−6.60371	−1.55651
$19$	6.52856	1.49775	0.748877	−	0.662709i	$-0.230593\pi$
$19$	6.52856	1.49775	0.748877	+	0.662709i	$0.230593\pi$
$20$	−1.23455	−0.276054
$21$	−12.7499	−2.78226
$22$	2.95423	0.629845
$23$	3.37032	0.702761	0.351380	−	0.936233i	$-0.385712\pi$
$23$	3.37032	0.702761	0.351380	+	0.936233i	$0.385712\pi$
$24$	−3.09899	−0.632578
$25$	−3.47589	−0.695177
$26$	4.28463	0.840285
$27$	11.1678	2.14925
$28$	−4.11422	−0.777515
$29$	−6.69964	−1.24409	−0.622046	−	0.782981i	$-0.713698\pi$
$29$	−6.69964	−1.24409	−0.622046	+	0.782981i	$0.713698\pi$
$30$	3.82585	0.698502
$31$	−3.82876	−0.687665	−0.343833	−	0.939031i	$-0.611725\pi$
$31$	−3.82876	−0.687665	−0.343833	+	0.939031i	$0.611725\pi$
$32$	−1.00000	−0.176777
$33$	−9.15513	−1.59370
$34$	−7.58691	−1.30115
$35$	5.07922	0.858544
$36$	6.60371	1.10062
$37$	1.89485	0.311511	0.155756	−	0.987796i	$-0.450219\pi$
$37$	1.89485	0.311511	0.155756	+	0.987796i	$0.450219\pi$
$38$	−6.52856	−1.05907
$39$	−13.2780	−2.12618
$40$	1.23455	0.195199
$41$	0.398057	0.0621661	0.0310831	−	0.999517i	$-0.490104\pi$
$41$	0.398057	0.0621661	0.0310831	+	0.999517i	$0.490104\pi$
$42$	12.7499	1.96736
$43$	−2.23068	−0.340175	−0.170088	−	0.985429i	$-0.554405\pi$
$43$	−2.23068	−0.340175	−0.170088	+	0.985429i	$0.554405\pi$
$44$	−2.95423	−0.445367
$45$	−8.15261	−1.21532
$46$	−3.37032	−0.496927
$47$	−5.86735	−0.855841	−0.427920	−	0.903816i	$-0.640754\pi$
$47$	−5.86735	−0.855841	−0.427920	+	0.903816i	$0.640754\pi$
$48$	3.09899	0.447300
$49$	9.92684	1.41812
$50$	3.47589	0.491565
$51$	23.5117	3.29230
$52$	−4.28463	−0.594171
$53$	−2.92318	−0.401530	−0.200765	−	0.979639i	$-0.564343\pi$
$53$	−2.92318	−0.401530	−0.200765	+	0.979639i	$0.564343\pi$
$54$	−11.1678	−1.51975
$55$	3.64715	0.491781
$56$	4.11422	0.549786
$57$	20.2319	2.67978
$58$	6.69964	0.879705
$59$	−11.4148	−1.48609	−0.743043	−	0.669244i	$-0.766618\pi$
$59$	−11.4148	−1.48609	−0.743043	+	0.669244i	$0.766618\pi$
$60$	−3.82585	−0.493915
$61$	−8.90652	−1.14036	−0.570182	−	0.821519i	$-0.693127\pi$
$61$	−8.90652	−1.14036	−0.570182	+	0.821519i	$0.693127\pi$
$62$	3.82876	0.486253
$63$	−27.1692	−3.42299
$64$	1.00000	0.125000
$65$	5.28959	0.656093
$66$	9.15513	1.12692
$67$	−13.7654	−1.68171	−0.840853	−	0.541263i	$-0.817946\pi$
$67$	−13.7654	−1.68171	−0.840853	+	0.541263i	$0.817946\pi$
$68$	7.58691	0.920049
$69$	10.4446	1.25738
$70$	−5.07922	−0.607082
$71$	−4.74052	−0.562597	−0.281298	−	0.959620i	$-0.590765\pi$
$71$	−4.74052	−0.562597	−0.281298	+	0.959620i	$0.590765\pi$
$72$	−6.60371	−0.778255
$73$	−5.73636	−0.671390	−0.335695	−	0.941971i	$-0.608971\pi$
$73$	−5.73636	−0.671390	−0.335695	+	0.941971i	$0.608971\pi$
$74$	−1.89485	−0.220272
$75$	−10.7717	−1.24381
$76$	6.52856	0.748877
$77$	12.1544	1.38512
$78$	13.2780	1.50344
$79$	−10.7601	−1.21060	−0.605301	−	0.795997i	$-0.706947\pi$
$79$	−10.7601	−1.21060	−0.605301	+	0.795997i	$0.706947\pi$
$80$	−1.23455	−0.138027
$81$	14.7979	1.64421
$82$	−0.398057	−0.0439581
$83$	17.2797	1.89670	0.948348	−	0.317231i	$-0.102753\pi$
$83$	17.2797	1.89670	0.948348	+	0.317231i	$0.102753\pi$
$84$	−12.7499	−1.39113
$85$	−9.36642	−1.01593
$86$	2.23068	0.240540
$87$	−20.7621	−2.22593
$88$	2.95423	0.314922
$89$	−16.5322	−1.75241	−0.876207	−	0.481935i	$-0.839934\pi$
$89$	−16.5322	−1.75241	−0.876207	+	0.481935i	$0.839934\pi$
$90$	8.15261	0.859361
$91$	17.6279	1.84791
$92$	3.37032	0.351380
$93$	−11.8653	−1.23037
$94$	5.86735	0.605171
$95$	−8.05983	−0.826921
$96$	−3.09899	−0.316289
$97$	1.59775	0.162226	0.0811132	−	0.996705i	$-0.474152\pi$
$97$	1.59775	0.162226	0.0811132	+	0.996705i	$0.474152\pi$
$98$	−9.92684	−1.00276
$99$	−19.5089	−1.96072
$100$	−3.47589	−0.347589
$101$	17.2818	1.71961	0.859804	−	0.510624i	$-0.170586\pi$
$101$	17.2818	1.71961	0.859804	+	0.510624i	$0.170586\pi$
$102$	−23.5117	−2.32801
$103$	14.6834	1.44680	0.723399	−	0.690431i	$-0.242579\pi$
$103$	14.6834	1.44680	0.723399	+	0.690431i	$0.242579\pi$
$104$	4.28463	0.420142
$105$	15.7404	1.53611
$106$	2.92318	0.283925
$107$	−2.34171	−0.226381	−0.113191	−	0.993573i	$-0.536107\pi$
$107$	−2.34171	−0.226381	−0.113191	+	0.993573i	$0.536107\pi$
$108$	11.1678	1.07463
$109$	11.6080	1.11185	0.555924	−	0.831233i	$-0.312364\pi$
$109$	11.6080	1.11185	0.555924	+	0.831233i	$0.312364\pi$
$110$	−3.64715	−0.347742
$111$	5.87211	0.557356
$112$	−4.11422	−0.388758
$113$	−15.2434	−1.43398	−0.716988	−	0.697085i	$-0.754480\pi$
$113$	−15.2434	−1.43398	−0.716988	+	0.697085i	$0.754480\pi$
$114$	−20.2319	−1.89489
$115$	−4.16083	−0.387999
$116$	−6.69964	−0.622046
$117$	−28.2944	−2.61582
$118$	11.4148	1.05082
$119$	−31.2143	−2.86141
$120$	3.82585	0.349251
$121$	−2.27251	−0.206591
$122$	8.90652	0.806359
$123$	1.23357	0.111228
$124$	−3.82876	−0.343833
$125$	10.4639	0.935920
$126$	27.1692	2.42042
$127$	−19.0997	−1.69483	−0.847413	−	0.530935i	$-0.821841\pi$
$127$	−19.0997	−1.69483	−0.847413	+	0.530935i	$0.821841\pi$
$128$	−1.00000	−0.0883883
$129$	−6.91284	−0.608641
$130$	−5.28959	−0.463927
$131$	−11.5929	−1.01287	−0.506437	−	0.862277i	$-0.669038\pi$
$131$	−11.5929	−1.01287	−0.506437	+	0.862277i	$0.669038\pi$
$132$	−9.15513	−0.796851
$133$	−26.8600	−2.32905
$134$	13.7654	1.18915
$135$	−13.7873	−1.18662
$136$	−7.58691	−0.650573
$137$	−20.2290	−1.72828	−0.864141	−	0.503249i	$-0.832138\pi$
$137$	−20.2290	−1.72828	−0.864141	+	0.503249i	$0.832138\pi$
$138$	−10.4446	−0.889102
$139$	5.58926	0.474075	0.237037	−	0.971501i	$-0.423824\pi$
$139$	5.58926	0.474075	0.237037	+	0.971501i	$0.423824\pi$
$140$	5.07922	0.429272
$141$	−18.1828	−1.53127
$142$	4.74052	0.397816
$143$	12.6578	1.05850
$144$	6.60371	0.550309
$145$	8.27103	0.686872
$146$	5.73636	0.474745
$147$	30.7631	2.53730
$148$	1.89485	0.155756
$149$	−13.8710	−1.13636	−0.568180	−	0.822905i	$-0.692352\pi$
$149$	−13.8710	−1.13636	−0.568180	+	0.822905i	$0.692352\pi$
$150$	10.7717	0.879507
$151$	17.0671	1.38890	0.694450	−	0.719541i	$-0.255648\pi$
$151$	17.0671	1.38890	0.694450	+	0.719541i	$0.255648\pi$
$152$	−6.52856	−0.529536
$153$	50.1018	4.05049
$154$	−12.1544	−0.979428
$155$	4.72679	0.379665
$156$	−13.2780	−1.06309
$157$	−11.6007	−0.925835	−0.462917	−	0.886401i	$-0.653197\pi$
$157$	−11.6007	−0.925835	−0.462917	+	0.886401i	$0.653197\pi$
$158$	10.7601	0.856025
$159$	−9.05890	−0.718417
$160$	1.23455	0.0975997
$161$	−13.8663	−1.09281
$162$	−14.7979	−1.16263
$163$	−19.0545	−1.49246	−0.746232	−	0.665686i	$-0.768139\pi$
$163$	−19.0545	−1.49246	−0.746232	+	0.665686i	$0.768139\pi$
$164$	0.398057	0.0310831
$165$	11.3025	0.879895
$166$	−17.2797	−1.34117
$167$	−19.5306	−1.51132	−0.755661	−	0.654963i	$-0.772684\pi$
$167$	−19.5306	−1.51132	−0.755661	+	0.654963i	$0.772684\pi$
$168$	12.7499	0.983678
$169$	5.35804	0.412157
$170$	9.36642	0.718372
$171$	43.1127	3.29691
$172$	−2.23068	−0.170088
$173$	−2.22691	−0.169309	−0.0846544	−	0.996410i	$-0.526979\pi$
$173$	−2.22691	−0.169309	−0.0846544	+	0.996410i	$0.526979\pi$
$174$	20.7621	1.57397
$175$	14.3006	1.08102
$176$	−2.95423	−0.222684
$177$	−35.3744	−2.65891
$178$	16.5322	1.23914
$179$	17.7850	1.32931	0.664656	−	0.747150i	$-0.268578\pi$
$179$	17.7850	1.32931	0.664656	+	0.747150i	$0.268578\pi$
$180$	−8.15261	−0.607660
$181$	−2.13603	−0.158770	−0.0793850	−	0.996844i	$-0.525296\pi$
$181$	−2.13603	−0.158770	−0.0793850	+	0.996844i	$0.525296\pi$
$182$	−17.6279	−1.30667
$183$	−27.6012	−2.04034
$184$	−3.37032	−0.248463
$185$	−2.33929	−0.171988
$186$	11.8653	0.870004
$187$	−22.4135	−1.63904
$188$	−5.86735	−0.427920
$189$	−45.9470	−3.34216
$190$	8.05983	0.584721
$191$	8.51656	0.616236	0.308118	−	0.951348i	$-0.400301\pi$
$191$	8.51656	0.616236	0.308118	+	0.951348i	$0.400301\pi$
$192$	3.09899	0.223650
$193$	18.7290	1.34815	0.674073	−	0.738665i	$-0.264543\pi$
$193$	18.7290	1.34815	0.674073	+	0.738665i	$0.264543\pi$
$194$	−1.59775	−0.114711
$195$	16.3924	1.17388
$196$	9.92684	0.709060
$197$	9.71323	0.692039	0.346020	−	0.938227i	$-0.387533\pi$
$197$	9.71323	0.692039	0.346020	+	0.938227i	$0.387533\pi$
$198$	19.5089	1.38644
$199$	8.17379	0.579425	0.289712	−	0.957114i	$-0.406440\pi$
$199$	8.17379	0.579425	0.289712	+	0.957114i	$0.406440\pi$
$200$	3.47589	0.245782
$201$	−42.6587	−3.00891
$202$	−17.2818	−1.21595
$203$	27.5638	1.93460
$204$	23.5117	1.64615
$205$	−0.491422	−0.0343224
$206$	−14.6834	−1.02304
$207$	22.2566	1.54694
$208$	−4.28463	−0.297086
$209$	−19.2869	−1.33410
$210$	−15.7404	−1.08619
$211$	−4.13778	−0.284857	−0.142428	−	0.989805i	$-0.545491\pi$
$211$	−4.13778	−0.284857	−0.142428	+	0.989805i	$0.545491\pi$
$212$	−2.92318	−0.200765
$213$	−14.6908	−1.00660
$214$	2.34171	0.160076
$215$	2.75388	0.187813
$216$	−11.1678	−0.759876
$217$	15.7524	1.06934
$218$	−11.6080	−0.786195
$219$	−17.7769	−1.20125
$220$	3.64715	0.245891
$221$	−32.5071	−2.18666
$222$	−5.87211	−0.394110
$223$	−8.01109	−0.536462	−0.268231	−	0.963355i	$-0.586439\pi$
$223$	−8.01109	−0.536462	−0.268231	+	0.963355i	$0.586439\pi$
$224$	4.11422	0.274893
$225$	−22.9538	−1.53025
$226$	15.2434	1.01397
$227$	15.8211	1.05008	0.525041	−	0.851077i	$-0.324050\pi$
$227$	15.8211	1.05008	0.525041	+	0.851077i	$0.324050\pi$
$228$	20.2319	1.33989
$229$	2.34420	0.154909	0.0774544	−	0.996996i	$-0.475321\pi$
$229$	2.34420	0.154909	0.0774544	+	0.996996i	$0.475321\pi$
$230$	4.16083	0.274357
$231$	37.6662	2.47826
$232$	6.69964	0.439853
$233$	−5.05740	−0.331321	−0.165661	−	0.986183i	$-0.552976\pi$
$233$	−5.05740	−0.331321	−0.165661	+	0.986183i	$0.552976\pi$
$234$	28.2944	1.84967
$235$	7.24353	0.472516
$236$	−11.4148	−0.743043
$237$	−33.3453	−2.16601
$238$	31.2143	2.02332
$239$	−18.6305	−1.20511	−0.602553	−	0.798079i	$-0.705850\pi$
$239$	−18.6305	−1.20511	−0.602553	+	0.798079i	$0.705850\pi$
$240$	−3.82585	−0.246958
$241$	−1.27999	−0.0824517	−0.0412259	−	0.999150i	$-0.513126\pi$
$241$	−1.27999	−0.0824517	−0.0412259	+	0.999150i	$0.513126\pi$
$242$	2.27251	0.146082
$243$	12.3548	0.792563
$244$	−8.90652	−0.570182
$245$	−12.2552	−0.782955
$246$	−1.23357	−0.0786498
$247$	−27.9724	−1.77984
$248$	3.82876	0.243126
$249$	53.5496	3.39357
$250$	−10.4639	−0.661795
$251$	5.96631	0.376590	0.188295	−	0.982112i	$-0.439704\pi$
$251$	5.96631	0.376590	0.188295	+	0.982112i	$0.439704\pi$
$252$	−27.1692	−1.71150
$253$	−9.95672	−0.625973
$254$	19.0997	1.19842
$255$	−29.0264	−1.81770
$256$	1.00000	0.0625000
$257$	9.36483	0.584162	0.292081	−	0.956394i	$-0.405652\pi$
$257$	9.36483	0.584162	0.292081	+	0.956394i	$0.405652\pi$
$258$	6.91284	0.430374
$259$	−7.79584	−0.484410
$260$	5.28959	0.328046
$261$	−44.2425	−2.73854
$262$	11.5929	0.716210
$263$	9.03984	0.557420	0.278710	−	0.960375i	$-0.410093\pi$
$263$	9.03984	0.557420	0.278710	+	0.960375i	$0.410093\pi$
$264$	9.15513	0.563459
$265$	3.60881	0.221688
$266$	26.8600	1.64689
$267$	−51.2332	−3.13542
$268$	−13.7654	−0.840853
$269$	−16.5116	−1.00673	−0.503365	−	0.864074i	$-0.667905\pi$
$269$	−16.5116	−1.00673	−0.503365	+	0.864074i	$0.667905\pi$
$270$	13.7873	0.839066
$271$	27.2081	1.65277	0.826387	−	0.563103i	$-0.190392\pi$
$271$	27.2081	1.65277	0.826387	+	0.563103i	$0.190392\pi$
$272$	7.58691	0.460024
$273$	54.6287	3.30628
$274$	20.2290	1.22208
$275$	10.2686	0.619219
$276$	10.4446	0.628690
$277$	−11.3117	−0.679654	−0.339827	−	0.940488i	$-0.610368\pi$
$277$	−11.3117	−0.679654	−0.339827	+	0.940488i	$0.610368\pi$
$278$	−5.58926	−0.335221
$279$	−25.2840	−1.51371
$280$	−5.07922	−0.303541
$281$	15.7451	0.939272	0.469636	−	0.882860i	$-0.344385\pi$
$281$	15.7451	0.939272	0.469636	+	0.882860i	$0.344385\pi$
$282$	18.1828	1.08277
$283$	10.0326	0.596376	0.298188	−	0.954507i	$-0.403618\pi$
$283$	10.0326	0.596376	0.298188	+	0.954507i	$0.403618\pi$
$284$	−4.74052	−0.281298
$285$	−24.9773	−1.47953
$286$	−12.6578	−0.748471
$287$	−1.63770	−0.0966702
$288$	−6.60371	−0.389127
$289$	40.5613	2.38596
$290$	−8.27103	−0.485692
$291$	4.95139	0.290256
$292$	−5.73636	−0.335695
$293$	−3.87682	−0.226486	−0.113243	−	0.993567i	$-0.536124\pi$
$293$	−3.87682	−0.226486	−0.113243	+	0.993567i	$0.536124\pi$
$294$	−30.7631	−1.79414
$295$	14.0922	0.820479
$296$	−1.89485	−0.110136
$297$	−32.9924	−1.91441
$298$	13.8710	0.803527
$299$	−14.4406	−0.835120
$300$	−10.7717	−0.621906
$301$	9.17751	0.528983
$302$	−17.0671	−0.982101
$303$	53.5562	3.07672
$304$	6.52856	0.374438
$305$	10.9955	0.629603
$306$	−50.1018	−2.86413
$307$	18.4061	1.05049	0.525245	−	0.850951i	$-0.323974\pi$
$307$	18.4061	1.05049	0.525245	+	0.850951i	$0.323974\pi$
$308$	12.1544	0.692560
$309$	45.5036	2.58861
$310$	−4.72679	−0.268464
$311$	17.9035	1.01521	0.507607	−	0.861589i	$-0.330530\pi$
$311$	17.9035	1.01521	0.507607	+	0.861589i	$0.330530\pi$
$312$	13.2780	0.751719
$313$	15.4129	0.871190	0.435595	−	0.900143i	$-0.356538\pi$
$313$	15.4129	0.871190	0.435595	+	0.900143i	$0.356538\pi$
$314$	11.6007	0.654664
$315$	33.5417	1.88986
$316$	−10.7601	−0.605301
$317$	−7.92057	−0.444863	−0.222432	−	0.974948i	$-0.571399\pi$
$317$	−7.92057	−0.444863	−0.222432	+	0.974948i	$0.571399\pi$
$318$	9.05890	0.507998
$319$	19.7923	1.10816
$320$	−1.23455	−0.0690134
$321$	−7.25691	−0.405041
$322$	13.8663	0.772737
$323$	49.5316	2.75601
$324$	14.7979	0.822104
$325$	14.8929	0.826109
$326$	19.0545	1.05533
$327$	35.9731	1.98932
$328$	−0.398057	−0.0219790
$329$	24.1396	1.33086
$330$	−11.3025	−0.622180
$331$	3.15691	0.173520	0.0867598	−	0.996229i	$-0.472349\pi$
$331$	3.15691	0.173520	0.0867598	+	0.996229i	$0.472349\pi$
$332$	17.2797	0.948348
$333$	12.5130	0.685711
$334$	19.5306	1.06867
$335$	16.9940	0.928483
$336$	−12.7499	−0.695565
$337$	−10.1711	−0.554058	−0.277029	−	0.960862i	$-0.589350\pi$
$337$	−10.1711	−0.554058	−0.277029	+	0.960862i	$0.589350\pi$
$338$	−5.35804	−0.291439
$339$	−47.2390	−2.56567
$340$	−9.36642	−0.507966
$341$	11.3110	0.612527
$342$	−43.1127	−2.33127
$343$	−12.0417	−0.650190
$344$	2.23068	0.120270
$345$	−12.8944	−0.694209
$346$	2.22691	0.119719
$347$	33.0304	1.77316	0.886581	−	0.462573i	$-0.153074\pi$
$347$	33.0304	1.77316	0.886581	+	0.462573i	$0.153074\pi$
$348$	−20.7621	−1.11296
$349$	2.44509	0.130883	0.0654413	−	0.997856i	$-0.479154\pi$
$349$	2.44509	0.130883	0.0654413	+	0.997856i	$0.479154\pi$
$350$	−14.3006	−0.764398
$351$	−47.8501	−2.55405
$352$	2.95423	0.157461
$353$	−25.9007	−1.37856	−0.689279	−	0.724496i	$-0.742072\pi$
$353$	−25.9007	−1.37856	−0.689279	+	0.724496i	$0.742072\pi$
$354$	35.3744	1.88013
$355$	5.85241	0.310614
$356$	−16.5322	−0.876207
$357$	−96.7326	−5.11963
$358$	−17.7850	−0.939966
$359$	0.689932	0.0364132	0.0182066	−	0.999834i	$-0.494204\pi$
$359$	0.689932	0.0364132	0.0182066	+	0.999834i	$0.494204\pi$
$360$	8.15261	0.429680
$361$	23.6221	1.24327
$362$	2.13603	0.112267
$363$	−7.04246	−0.369633
$364$	17.6279	0.923954
$365$	7.08183	0.370680
$366$	27.6012	1.44274
$367$	11.4458	0.597467	0.298734	−	0.954337i	$-0.403436\pi$
$367$	11.4458	0.597467	0.298734	+	0.954337i	$0.403436\pi$
$368$	3.37032	0.175690
$369$	2.62866	0.136842
$370$	2.33929	0.121614
$371$	12.0266	0.624391
$372$	−11.8653	−0.615185
$373$	22.0504	1.14173	0.570863	−	0.821046i	$-0.306609\pi$
$373$	22.0504	1.14173	0.570863	+	0.821046i	$0.306609\pi$
$374$	22.4135	1.15898
$375$	32.4275	1.67455
$376$	5.86735	0.302585
$377$	28.7055	1.47841
$378$	45.9470	2.36326
$379$	19.5740	1.00545	0.502725	−	0.864446i	$-0.332331\pi$
$379$	19.5740	1.00545	0.502725	+	0.864446i	$0.332331\pi$
$380$	−8.05983	−0.413461
$381$	−59.1897	−3.03238
$382$	−8.51656	−0.435745
$383$	−7.52783	−0.384654	−0.192327	−	0.981331i	$-0.561603\pi$
$383$	−7.52783	−0.384654	−0.192327	+	0.981331i	$0.561603\pi$
$384$	−3.09899	−0.158144
$385$	−15.0052	−0.764735
$386$	−18.7290	−0.953283
$387$	−14.7307	−0.748806
$388$	1.59775	0.0811132
$389$	−10.7094	−0.542986	−0.271493	−	0.962440i	$-0.587517\pi$
$389$	−10.7094	−0.542986	−0.271493	+	0.962440i	$0.587517\pi$
$390$	−16.3924	−0.830059
$391$	25.5703	1.29315
$392$	−9.92684	−0.501381
$393$	−35.9262	−1.81223
$394$	−9.71323	−0.489346
$395$	13.2838	0.668382
$396$	−19.5089	−0.980359
$397$	16.5963	0.832943	0.416471	−	0.909149i	$-0.363267\pi$
$397$	16.5963	0.832943	0.416471	+	0.909149i	$0.363267\pi$
$398$	−8.17379	−0.409715
$399$	−83.2386	−4.16714
$400$	−3.47589	−0.173794
$401$	−7.94121	−0.396565	−0.198283	−	0.980145i	$-0.563536\pi$
$401$	−7.94121	−0.396565	−0.198283	+	0.980145i	$0.563536\pi$
$402$	42.6587	2.12762
$403$	16.4048	0.817182
$404$	17.2818	0.859804
$405$	−18.2687	−0.907779
$406$	−27.5638	−1.36797
$407$	−5.59783	−0.277474
$408$	−23.5117	−1.16400
$409$	16.5752	0.819591	0.409796	−	0.912177i	$-0.365600\pi$
$409$	16.5752	0.819591	0.409796	+	0.912177i	$0.365600\pi$
$410$	0.491422	0.0242696
$411$	−62.6895	−3.09224
$412$	14.6834	0.723399
$413$	46.9632	2.31091
$414$	−22.2566	−1.09385
$415$	−21.3327	−1.04718
$416$	4.28463	0.210071
$417$	17.3210	0.848215
$418$	19.2869	0.943352
$419$	−16.8223	−0.821824	−0.410912	−	0.911675i	$-0.634790\pi$
$419$	−16.8223	−0.821824	−0.410912	+	0.911675i	$0.634790\pi$
$420$	15.7404	0.768054
$421$	19.4606	0.948452	0.474226	−	0.880403i	$-0.342728\pi$
$421$	19.4606	0.948452	0.474226	+	0.880403i	$0.342728\pi$
$422$	4.13778	0.201424
$423$	−38.7463	−1.88391
$424$	2.92318	0.141962
$425$	−26.3713	−1.27919
$426$	14.6908	0.711772
$427$	36.6434	1.77330
$428$	−2.34171	−0.113191
$429$	39.2263	1.89386
$430$	−2.75388	−0.132804
$431$	−29.9451	−1.44240	−0.721201	−	0.692726i	$-0.756410\pi$
$431$	−29.9451	−1.44240	−0.721201	+	0.692726i	$0.756410\pi$
$432$	11.1678	0.537313
$433$	38.4684	1.84867	0.924337	−	0.381576i	$-0.124619\pi$
$433$	38.4684	1.84867	0.924337	+	0.381576i	$0.124619\pi$
$434$	−15.7524	−0.756138
$435$	25.6318	1.22895
$436$	11.6080	0.555924
$437$	22.0033	1.05256
$438$	17.7769	0.849413
$439$	−3.85709	−0.184089	−0.0920443	−	0.995755i	$-0.529340\pi$
$439$	−3.85709	−0.184089	−0.0920443	+	0.995755i	$0.529340\pi$
$440$	−3.64715	−0.173871
$441$	65.5540	3.12162
$442$	32.5071	1.54621
$443$	−23.6656	−1.12439	−0.562193	−	0.827006i	$-0.690042\pi$
$443$	−23.6656	−1.12439	−0.562193	+	0.827006i	$0.690042\pi$
$444$	5.87211	0.278678
$445$	20.4099	0.967521
$446$	8.01109	0.379336
$447$	−42.9861	−2.03317
$448$	−4.11422	−0.194379
$449$	−28.3574	−1.33827	−0.669135	−	0.743141i	$-0.733335\pi$
$449$	−28.3574	−1.33827	−0.669135	+	0.743141i	$0.733335\pi$
$450$	22.9538	1.08205
$451$	−1.17595	−0.0553735
$452$	−15.2434	−0.716988
$453$	52.8907	2.48502
$454$	−15.8211	−0.742520
$455$	−21.7626	−1.02024
$456$	−20.2319	−0.947446
$457$	−8.09974	−0.378890	−0.189445	−	0.981891i	$-0.560669\pi$
$457$	−8.09974	−0.378890	−0.189445	+	0.981891i	$0.560669\pi$
$458$	−2.34420	−0.109537
$459$	84.7295	3.95484
$460$	−4.16083	−0.194000
$461$	−0.555318	−0.0258637	−0.0129319	−	0.999916i	$-0.504116\pi$
$461$	−0.555318	−0.0258637	−0.0129319	+	0.999916i	$0.504116\pi$
$462$	−37.6662	−1.75239
$463$	−4.18261	−0.194383	−0.0971913	−	0.995266i	$-0.530986\pi$
$463$	−4.18261	−0.194383	−0.0971913	+	0.995266i	$0.530986\pi$
$464$	−6.69964	−0.311023
$465$	14.6483	0.679297
$466$	5.05740	0.234279
$467$	−40.0238	−1.85208	−0.926040	−	0.377425i	$-0.876810\pi$
$467$	−40.0238	−1.85208	−0.926040	+	0.377425i	$0.876810\pi$
$468$	−28.2944	−1.30791
$469$	56.6338	2.61511
$470$	−7.24353	−0.334119
$471$	−35.9503	−1.65650
$472$	11.4148	0.525411
$473$	6.58994	0.303006
$474$	33.3453	1.53160
$475$	−22.6925	−1.04120
$476$	−31.2143	−1.43070
$477$	−19.3038	−0.883863
$478$	18.6305	0.852138
$479$	−24.2695	−1.10890	−0.554451	−	0.832216i	$-0.687072\pi$
$479$	−24.2695	−1.10890	−0.554451	+	0.832216i	$0.687072\pi$
$480$	3.82585	0.174625
$481$	−8.11873	−0.370182
$482$	1.27999	0.0583022
$483$	−42.9713	−1.95526
$484$	−2.27251	−0.103296
$485$	−1.97250	−0.0895664
$486$	−12.3548	−0.560427
$487$	−4.39995	−0.199381	−0.0996903	−	0.995019i	$-0.531785\pi$
$487$	−4.39995	−0.199381	−0.0996903	+	0.995019i	$0.531785\pi$
$488$	8.90652	0.403179
$489$	−59.0496	−2.67032
$490$	12.2552	0.553633
$491$	−10.1458	−0.457873	−0.228937	−	0.973441i	$-0.573525\pi$
$491$	−10.1458	−0.457873	−0.228937	+	0.973441i	$0.573525\pi$
$492$	1.23357	0.0556138
$493$	−50.8296	−2.28925
$494$	27.9724	1.25854
$495$	24.0847	1.08253
$496$	−3.82876	−0.171916
$497$	19.5036	0.874855
$498$	−53.5496	−2.39962
$499$	13.8973	0.622127	0.311064	−	0.950389i	$-0.399315\pi$
$499$	13.8973	0.622127	0.311064	+	0.950389i	$0.399315\pi$
$500$	10.4639	0.467960
$501$	−60.5250	−2.70406
$502$	−5.96631	−0.266290
$503$	22.7932	1.01630	0.508149	−	0.861269i	$-0.330330\pi$
$503$	22.7932	1.01630	0.508149	+	0.861269i	$0.330330\pi$
$504$	27.1692	1.21021
$505$	−21.3353	−0.949409
$506$	9.95672	0.442630
$507$	16.6045	0.737431
$508$	−19.0997	−0.847413
$509$	4.79904	0.212714	0.106357	−	0.994328i	$-0.466081\pi$
$509$	4.79904	0.212714	0.106357	+	0.994328i	$0.466081\pi$
$510$	29.0264	1.28531
$511$	23.6007	1.04403
$512$	−1.00000	−0.0441942
$513$	72.9099	3.21905
$514$	−9.36483	−0.413065
$515$	−18.1274	−0.798787
$516$	−6.91284	−0.304321
$517$	17.3335	0.762327
$518$	7.79584	0.342530
$519$	−6.90116	−0.302927
$520$	−5.28959	−0.231964
$521$	24.5647	1.07620	0.538099	−	0.842882i	$-0.319143\pi$
$521$	24.5647	1.07620	0.538099	+	0.842882i	$0.319143\pi$
$522$	44.2425	1.93644
$523$	23.8713	1.04382	0.521911	−	0.853000i	$-0.325219\pi$
$523$	23.8713	1.04382	0.521911	+	0.853000i	$0.325219\pi$
$524$	−11.5929	−0.506437
$525$	44.3173	1.93416
$526$	−9.03984	−0.394156
$527$	−29.0485	−1.26537
$528$	−9.15513	−0.398426
$529$	−11.6409	−0.506127
$530$	−3.60881	−0.156757
$531$	−75.3803	−3.27123
$532$	−26.8600	−1.16453
$533$	−1.70553	−0.0738746
$534$	51.2332	2.21708
$535$	2.89095	0.124987
$536$	13.7654	0.594573
$537$	55.1154	2.37841
$538$	16.5116	0.711866
$539$	−29.3262	−1.26317
$540$	−13.7873	−0.593309
$541$	−41.7839	−1.79643	−0.898215	−	0.439557i	$-0.855135\pi$
$541$	−41.7839	−1.79643	−0.898215	+	0.439557i	$0.855135\pi$
$542$	−27.2081	−1.16869
$543$	−6.61953	−0.284071
$544$	−7.58691	−0.325286
$545$	−14.3307	−0.613860
$546$	−54.6287	−2.33789
$547$	−14.8338	−0.634249	−0.317124	−	0.948384i	$-0.602717\pi$
$547$	−14.8338	−0.634249	−0.317124	+	0.948384i	$0.602717\pi$
$548$	−20.2290	−0.864141
$549$	−58.8161	−2.51021
$550$	−10.2686	−0.437854
$551$	−43.7390	−1.86334
$552$	−10.4446	−0.444551
$553$	44.2693	1.88252
$554$	11.3117	0.480588
$555$	−7.24942	−0.307721
$556$	5.58926	0.237037
$557$	30.5762	1.29555	0.647777	−	0.761830i	$-0.275699\pi$
$557$	30.5762	1.29555	0.647777	+	0.761830i	$0.275699\pi$
$558$	25.2840	1.07036
$559$	9.55762	0.404244
$560$	5.07922	0.214636
$561$	−69.4592	−2.93257
$562$	−15.7451	−0.664165
$563$	−6.80329	−0.286725	−0.143362	−	0.989670i	$-0.545791\pi$
$563$	−6.80329	−0.286725	−0.143362	+	0.989670i	$0.545791\pi$
$564$	−18.1828	−0.765635
$565$	18.8187	0.791709
$566$	−10.0326	−0.421702
$567$	−60.8818	−2.55679
$568$	4.74052	0.198908
$569$	−22.6285	−0.948635	−0.474317	−	0.880354i	$-0.657305\pi$
$569$	−22.6285	−0.948635	−0.474317	+	0.880354i	$0.657305\pi$
$570$	24.9773	1.04618
$571$	−35.5229	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$571$	−35.5229	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$572$	12.6578	0.529249
$573$	26.3927	1.10257
$574$	1.63770	0.0683562
$575$	−11.7149	−0.488543
$576$	6.60371	0.275155
$577$	−31.6475	−1.31750	−0.658752	−	0.752360i	$-0.728915\pi$
$577$	−31.6475	−1.31750	−0.658752	+	0.752360i	$0.728915\pi$
$578$	−40.5613	−1.68713
$579$	58.0410	2.41210
$580$	8.27103	0.343436
$581$	−71.0927	−2.94942
$582$	−4.95139	−0.205242
$583$	8.63576	0.357657
$584$	5.73636	0.237372
$585$	34.9309	1.44422
$586$	3.87682	0.160150
$587$	2.34037	0.0965976	0.0482988	−	0.998833i	$-0.484620\pi$
$587$	2.34037	0.0965976	0.0482988	+	0.998833i	$0.484620\pi$
$588$	30.7631	1.26865
$589$	−24.9963	−1.02995
$590$	−14.0922	−0.580166
$591$	30.1012	1.23820
$592$	1.89485	0.0778779
$593$	−36.5052	−1.49909	−0.749544	−	0.661954i	$-0.769727\pi$
$593$	−36.5052	−1.49909	−0.749544	+	0.661954i	$0.769727\pi$
$594$	32.9924	1.35370
$595$	38.5356	1.57980
$596$	−13.8710	−0.568180
$597$	25.3305	1.03671
$598$	14.4406	0.590519
$599$	1.56734	0.0640399	0.0320199	−	0.999487i	$-0.489806\pi$
$599$	1.56734	0.0640399	0.0320199	+	0.999487i	$0.489806\pi$
$600$	10.7717	0.439754
$601$	32.1505	1.31144	0.655722	−	0.755002i	$-0.272364\pi$
$601$	32.1505	1.31144	0.655722	+	0.755002i	$0.272364\pi$
$602$	−9.17751	−0.374047
$603$	−90.9025	−3.70183
$604$	17.0671	0.694450
$605$	2.80552	0.114061
$606$	−53.5562	−2.17557
$607$	46.5193	1.88816	0.944081	−	0.329714i	$-0.106952\pi$
$607$	46.5193	1.88816	0.944081	+	0.329714i	$0.106952\pi$
$608$	−6.52856	−0.264768
$609$	85.4198	3.46139
$610$	−10.9955	−0.445197
$611$	25.1394	1.01703
$612$	50.1018	2.02524
$613$	−10.1354	−0.409364	−0.204682	−	0.978829i	$-0.565616\pi$
$613$	−10.1354	−0.409364	−0.204682	+	0.978829i	$0.565616\pi$
$614$	−18.4061	−0.742809
$615$	−1.52291	−0.0614096
$616$	−12.1544	−0.489714
$617$	23.8284	0.959295	0.479648	−	0.877461i	$-0.340764\pi$
$617$	23.8284	0.959295	0.479648	+	0.877461i	$0.340764\pi$
$618$	−45.5036	−1.83042
$619$	−1.06129	−0.0426567	−0.0213284	−	0.999773i	$-0.506790\pi$
$619$	−1.06129	−0.0426567	−0.0213284	+	0.999773i	$0.506790\pi$
$620$	4.72679	0.189833
$621$	37.6392	1.51041
$622$	−17.9035	−0.717865
$623$	68.0173	2.72506
$624$	−13.2780	−0.531545
$625$	4.46122	0.178449
$626$	−15.4129	−0.616024
$627$	−59.7698	−2.38697
$628$	−11.6007	−0.462917
$629$	14.3761	0.573211
$630$	−33.5417	−1.33633
$631$	35.4026	1.40936	0.704678	−	0.709527i	$-0.251091\pi$
$631$	35.4026	1.40936	0.704678	+	0.709527i	$0.251091\pi$
$632$	10.7601	0.428012
$633$	−12.8229	−0.509666
$634$	7.92057	0.314566
$635$	23.5795	0.935726
$636$	−9.05890	−0.359209
$637$	−42.5328	−1.68521
$638$	−19.7923	−0.783584
$639$	−31.3051	−1.23841
$640$	1.23455	0.0487999
$641$	−38.9431	−1.53816	−0.769079	−	0.639154i	$-0.779285\pi$
$641$	−38.9431	−1.53816	−0.769079	+	0.639154i	$0.779285\pi$
$642$	7.25691	0.286407
$643$	11.6771	0.460499	0.230249	−	0.973132i	$-0.426046\pi$
$643$	11.6771	0.460499	0.230249	+	0.973132i	$0.426046\pi$
$644$	−13.8663	−0.546407
$645$	8.53424	0.336035
$646$	−49.5316	−1.94880
$647$	43.5610	1.71256	0.856279	−	0.516513i	$-0.172770\pi$
$647$	43.5610	1.71256	0.856279	+	0.516513i	$0.172770\pi$
$648$	−14.7979	−0.581315
$649$	33.7221	1.32371
$650$	−14.8929	−0.584147
$651$	48.8164	1.91326
$652$	−19.0545	−0.746232
$653$	6.41580	0.251070	0.125535	−	0.992089i	$-0.459935\pi$
$653$	6.41580	0.251070	0.125535	+	0.992089i	$0.459935\pi$
$654$	−35.9731	−1.40666
$655$	14.3120	0.559215
$656$	0.398057	0.0155415
$657$	−37.8813	−1.47789
$658$	−24.1396	−0.941059
$659$	−50.3312	−1.96062	−0.980312	−	0.197456i	$-0.936732\pi$
$659$	−50.3312	−1.96062	−0.980312	+	0.197456i	$0.936732\pi$
$660$	11.3025	0.439948
$661$	−32.9951	−1.28336	−0.641681	−	0.766971i	$-0.721763\pi$
$661$	−32.9951	−1.28336	−0.641681	+	0.766971i	$0.721763\pi$
$662$	−3.15691	−0.122697
$663$	−100.739	−3.91238
$664$	−17.2797	−0.670584
$665$	33.1599	1.28589
$666$	−12.5130	−0.484871
$667$	−22.5799	−0.874298
$668$	−19.5306	−0.755661
$669$	−24.8262	−0.959838
$670$	−16.9940	−0.656536
$671$	26.3119	1.01576
$672$	12.7499	0.491839
$673$	21.6766	0.835571	0.417785	−	0.908546i	$-0.362806\pi$
$673$	21.6766	0.835571	0.417785	+	0.908546i	$0.362806\pi$
$674$	10.1711	0.391778
$675$	−38.8182	−1.49411
$676$	5.35804	0.206078
$677$	28.1896	1.08342	0.541708	−	0.840567i	$-0.317778\pi$
$677$	28.1896	1.08342	0.541708	+	0.840567i	$0.317778\pi$
$678$	47.2390	1.81420
$679$	−6.57348	−0.252267
$680$	9.36642	0.359186
$681$	49.0293	1.87881
$682$	−11.3110	−0.433122
$683$	−19.5598	−0.748435	−0.374217	−	0.927341i	$-0.622089\pi$
$683$	−19.5598	−0.748435	−0.374217	+	0.927341i	$0.622089\pi$
$684$	43.1127	1.64846
$685$	24.9737	0.954198
$686$	12.0417	0.459754
$687$	7.26463	0.277163
$688$	−2.23068	−0.0850438
$689$	12.5247	0.477155
$690$	12.8944	0.490880
$691$	−35.4835	−1.34985	−0.674927	−	0.737884i	$-0.735825\pi$
$691$	−35.4835	−1.34985	−0.674927	+	0.737884i	$0.735825\pi$
$692$	−2.22691	−0.0846544
$693$	80.2640	3.04898
$694$	−33.0304	−1.25382
$695$	−6.90022	−0.261740
$696$	20.7621	0.786984
$697$	3.02003	0.114392
$698$	−2.44509	−0.0925480
$699$	−15.6728	−0.592800
$700$	14.3006	0.540511
$701$	28.0522	1.05952	0.529758	−	0.848149i	$-0.322283\pi$
$701$	28.0522	1.05952	0.529758	+	0.848149i	$0.322283\pi$
$702$	47.8501	1.80599
$703$	12.3706	0.466567
$704$	−2.95423	−0.111342
$705$	22.4476	0.845426
$706$	25.9007	0.974787
$707$	−71.1014	−2.67404
$708$	−35.3744	−1.32945
$709$	−22.4197	−0.841991	−0.420995	−	0.907063i	$-0.638319\pi$
$709$	−22.4197	−0.841991	−0.420995	+	0.907063i	$0.638319\pi$
$710$	−5.85241	−0.219637
$711$	−71.0564	−2.66482
$712$	16.5322	0.619572
$713$	−12.9041	−0.483264
$714$	96.7326	3.62013
$715$	−15.6267	−0.584404
$716$	17.7850	0.664656
$717$	−57.7356	−2.15617
$718$	−0.689932	−0.0257480
$719$	−4.51246	−0.168286	−0.0841432	−	0.996454i	$-0.526815\pi$
$719$	−4.51246	−0.168286	−0.0841432	+	0.996454i	$0.526815\pi$
$720$	−8.15261	−0.303830
$721$	−60.4107	−2.24981
$722$	−23.6221	−0.879122
$723$	−3.96669	−0.147523
$724$	−2.13603	−0.0793850
$725$	23.2872	0.864864
$726$	7.04246	0.261370
$727$	6.29915	0.233622	0.116811	−	0.993154i	$-0.462733\pi$
$727$	6.29915	0.233622	0.116811	+	0.993154i	$0.462733\pi$
$728$	−17.6279	−0.653334
$729$	−6.10616	−0.226154
$730$	−7.08183	−0.262110
$731$	−16.9240	−0.625955
$732$	−27.6012	−1.02017
$733$	−22.5810	−0.834047	−0.417023	−	0.908896i	$-0.636927\pi$
$733$	−22.5810	−0.834047	−0.417023	+	0.908896i	$0.636927\pi$
$734$	−11.4458	−0.422473
$735$	−37.9786	−1.40086
$736$	−3.37032	−0.124232
$737$	40.6661	1.49795
$738$	−2.62866	−0.0967622
$739$	−37.2100	−1.36879	−0.684396	−	0.729110i	$-0.739934\pi$
$739$	−37.2100	−1.36879	−0.684396	+	0.729110i	$0.739934\pi$
$740$	−2.33929	−0.0859939
$741$	−86.6862	−3.18450
$742$	−12.0266	−0.441511
$743$	19.1031	0.700826	0.350413	−	0.936595i	$-0.386041\pi$
$743$	19.1031	0.700826	0.350413	+	0.936595i	$0.386041\pi$
$744$	11.8653	0.435002
$745$	17.1245	0.627392
$746$	−22.0504	−0.807322
$747$	114.110	4.17508
$748$	−22.4135	−0.819519
$749$	9.63430	0.352030
$750$	−32.4275	−1.18408
$751$	−21.5253	−0.785470	−0.392735	−	0.919652i	$-0.628471\pi$
$751$	−21.5253	−0.785470	−0.392735	+	0.919652i	$0.628471\pi$
$752$	−5.86735	−0.213960
$753$	18.4895	0.673795
$754$	−28.7055	−1.04539
$755$	−21.0702	−0.766822
$756$	−45.9470	−1.67108
$757$	−26.0751	−0.947714	−0.473857	−	0.880602i	$-0.657139\pi$
$757$	−26.0751	−0.947714	−0.473857	+	0.880602i	$0.657139\pi$
$758$	−19.5740	−0.710961
$759$	−30.8557	−1.11999
$760$	8.05983	0.292361
$761$	34.1832	1.23914	0.619569	−	0.784942i	$-0.287307\pi$
$761$	34.1832	1.23914	0.619569	+	0.784942i	$0.287307\pi$
$762$	59.1897	2.14422
$763$	−47.7581	−1.72896
$764$	8.51656	0.308118
$765$	−61.8532	−2.23631
$766$	7.52783	0.271992
$767$	48.9084	1.76598
$768$	3.09899	0.111825
$769$	7.28334	0.262644	0.131322	−	0.991340i	$-0.458078\pi$
$769$	7.28334	0.262644	0.131322	+	0.991340i	$0.458078\pi$
$770$	15.0052	0.540749
$771$	29.0215	1.04518
$772$	18.7290	0.674073
$773$	−5.38788	−0.193788	−0.0968942	−	0.995295i	$-0.530891\pi$
$773$	−5.38788	−0.193788	−0.0968942	+	0.995295i	$0.530891\pi$
$774$	14.7307	0.529486
$775$	13.3083	0.478049
$776$	−1.59775	−0.0573557
$777$	−24.1592	−0.866706
$778$	10.7094	0.383949
$779$	2.59874	0.0931095
$780$	16.3924	0.586940
$781$	14.0046	0.501124
$782$	−25.5703	−0.914394
$783$	−74.8205	−2.67387
$784$	9.92684	0.354530
$785$	14.3216	0.511160
$786$	35.9262	1.28144
$787$	−4.64031	−0.165409	−0.0827046	−	0.996574i	$-0.526356\pi$
$787$	−4.64031	−0.165409	−0.0827046	+	0.996574i	$0.526356\pi$
$788$	9.71323	0.346020
$789$	28.0143	0.997337
$790$	−13.2838	−0.472618
$791$	62.7147	2.22988
$792$	19.5089	0.693219
$793$	38.1611	1.35514
$794$	−16.5963	−0.588980
$795$	11.1837	0.396644
$796$	8.17379	0.289712
$797$	−6.47372	−0.229311	−0.114656	−	0.993405i	$-0.536576\pi$
$797$	−6.47372	−0.229311	−0.114656	+	0.993405i	$0.536576\pi$
$798$	83.2386	2.94661
$799$	−44.5151	−1.57483
$800$	3.47589	0.122891
$801$	−109.174	−3.85748
$802$	7.94121	0.280414
$803$	16.9466	0.598031
$804$	−42.6587	−1.50445
$805$	17.1186	0.603351
$806$	−16.4048	−0.577835
$807$	−51.1692	−1.80124
$808$	−17.2818	−0.607973
$809$	−34.1721	−1.20143	−0.600714	−	0.799464i	$-0.705117\pi$
$809$	−34.1721	−1.20143	−0.600714	+	0.799464i	$0.705117\pi$
$810$	18.2687	0.641897
$811$	1.94236	0.0682053	0.0341027	−	0.999418i	$-0.489143\pi$
$811$	1.94236	0.0682053	0.0341027	+	0.999418i	$0.489143\pi$
$812$	27.5638	0.967300
$813$	84.3175	2.95714
$814$	5.59783	0.196204
$815$	23.5237	0.824000
$816$	23.5117	0.823075
$817$	−14.5631	−0.509499
$818$	−16.5752	−0.579539
$819$	116.410	4.06768
$820$	−0.491422	−0.0171612
$821$	−22.5890	−0.788362	−0.394181	−	0.919033i	$-0.628972\pi$
$821$	−22.5890	−0.788362	−0.394181	+	0.919033i	$0.628972\pi$
$822$	62.6895	2.18655
$823$	43.8370	1.52806	0.764032	−	0.645179i	$-0.223217\pi$
$823$	43.8370	1.52806	0.764032	+	0.645179i	$0.223217\pi$
$824$	−14.6834	−0.511520
$825$	31.8222	1.10791
$826$	−46.9632	−1.63406
$827$	−20.2573	−0.704415	−0.352207	−	0.935922i	$-0.614569\pi$
$827$	−20.2573	−0.704415	−0.352207	+	0.935922i	$0.614569\pi$
$828$	22.2566	0.773471
$829$	−11.7269	−0.407292	−0.203646	−	0.979045i	$-0.565279\pi$
$829$	−11.7269	−0.407292	−0.203646	+	0.979045i	$0.565279\pi$
$830$	21.3327	0.740468
$831$	−35.0548	−1.21604
$832$	−4.28463	−0.148543
$833$	75.3141	2.60948
$834$	−17.3210	−0.599778
$835$	24.1115	0.834412
$836$	−19.2869	−0.667051
$837$	−42.7590	−1.47797
$838$	16.8223	0.581117
$839$	7.31783	0.252640	0.126320	−	0.991990i	$-0.459683\pi$
$839$	7.31783	0.252640	0.126320	+	0.991990i	$0.459683\pi$
$840$	−15.7404	−0.543096
$841$	15.8851	0.547763
$842$	−19.4606	−0.670657
$843$	48.7937	1.68054
$844$	−4.13778	−0.142428
$845$	−6.61477	−0.227555
$846$	38.7463	1.33212
$847$	9.34960	0.321256
$848$	−2.92318	−0.100382
$849$	31.0909	1.06704
$850$	26.3713	0.904527
$851$	6.38625	0.218918
$852$	−14.6908	−0.503299
$853$	47.6855	1.63272	0.816360	−	0.577543i	$-0.195988\pi$
$853$	47.6855	1.63272	0.816360	+	0.577543i	$0.195988\pi$
$854$	−36.6434	−1.25391
$855$	−53.2248	−1.82025
$856$	2.34171	0.0800378
$857$	11.0791	0.378454	0.189227	−	0.981933i	$-0.439402\pi$
$857$	11.0791	0.378454	0.189227	+	0.981933i	$0.439402\pi$
$858$	−39.2263	−1.33916
$859$	47.2189	1.61109	0.805545	−	0.592535i	$-0.201873\pi$
$859$	47.2189	1.61109	0.805545	+	0.592535i	$0.201873\pi$
$860$	2.75388	0.0939066
$861$	−5.07520	−0.172962
$862$	29.9451	1.01993
$863$	7.75409	0.263952	0.131976	−	0.991253i	$-0.457868\pi$
$863$	7.75409	0.263952	0.131976	+	0.991253i	$0.457868\pi$
$864$	−11.1678	−0.379938
$865$	2.74923	0.0934767
$866$	−38.4684	−1.30721
$867$	125.699	4.26895
$868$	15.7524	0.534670
$869$	31.7877	1.07833
$870$	−25.6318	−0.869000
$871$	58.9795	1.99844
$872$	−11.6080	−0.393098
$873$	10.5510	0.357099
$874$	−22.0033	−0.744274
$875$	−43.0509	−1.45538
$876$	−17.7769	−0.600626
$877$	5.59878	0.189058	0.0945288	−	0.995522i	$-0.469866\pi$
$877$	5.59878	0.189058	0.0945288	+	0.995522i	$0.469866\pi$
$878$	3.85709	0.130170
$879$	−12.0142	−0.405229
$880$	3.64715	0.122945
$881$	9.16664	0.308832	0.154416	−	0.988006i	$-0.450650\pi$
$881$	9.16664	0.308832	0.154416	+	0.988006i	$0.450650\pi$
$882$	−65.5540	−2.20732
$883$	−49.6948	−1.67236	−0.836181	−	0.548453i	$-0.815217\pi$
$883$	−49.6948	−1.67236	−0.836181	+	0.548453i	$0.815217\pi$
$884$	−32.5071	−1.09333
$885$	43.6715	1.46800
$886$	23.6656	0.795062
$887$	−19.5540	−0.656558	−0.328279	−	0.944581i	$-0.606469\pi$
$887$	−19.5540	−0.656558	−0.328279	+	0.944581i	$0.606469\pi$
$888$	−5.87211	−0.197055
$889$	78.5805	2.63551
$890$	−20.4099	−0.684140
$891$	−43.7164	−1.46455
$892$	−8.01109	−0.268231
$893$	−38.3053	−1.28184
$894$	42.9861	1.43767
$895$	−21.9564	−0.733923
$896$	4.11422	0.137447
$897$	−44.7511	−1.49420
$898$	28.3574	0.946299
$899$	25.6513	0.855518
$900$	−22.9538	−0.765125
$901$	−22.1779	−0.738854
$902$	1.17595	0.0391550
$903$	28.4410	0.946456
$904$	15.2434	0.506987
$905$	2.63704	0.0876581
$906$	−52.8907	−1.75717
$907$	−6.63422	−0.220286	−0.110143	−	0.993916i	$-0.535131\pi$
$907$	−6.63422	−0.220286	−0.110143	+	0.993916i	$0.535131\pi$
$908$	15.8211	0.525041
$909$	114.124	3.78527
$910$	21.7626	0.721422
$911$	−26.1347	−0.865882	−0.432941	−	0.901422i	$-0.642524\pi$
$911$	−26.1347	−0.865882	−0.432941	+	0.901422i	$0.642524\pi$
$912$	20.2319	0.669945
$913$	−51.0484	−1.68945
$914$	8.09974	0.267916
$915$	34.0750	1.12649
$916$	2.34420	0.0774544
$917$	47.6957	1.57505
$918$	−84.7295	−2.79649
$919$	22.1142	0.729479	0.364739	−	0.931110i	$-0.381158\pi$
$919$	22.1142	0.729479	0.364739	+	0.931110i	$0.381158\pi$
$920$	4.16083	0.137179
$921$	57.0402	1.87954
$922$	0.555318	0.0182884
$923$	20.3114	0.668557
$924$	37.6662	1.23913
$925$	−6.58628	−0.216556
$926$	4.18261	0.137449
$927$	96.9648	3.18474
$928$	6.69964	0.219926
$929$	−26.8485	−0.880870	−0.440435	−	0.897785i	$-0.645176\pi$
$929$	−26.8485	−0.880870	−0.440435	+	0.897785i	$0.645176\pi$
$930$	−14.6483	−0.480335
$931$	64.8080	2.12400
$932$	−5.05740	−0.165661
$933$	55.4827	1.81642
$934$	40.0238	1.30962
$935$	27.6706	0.904925
$936$	28.2944	0.924833
$937$	10.8493	0.354433	0.177216	−	0.984172i	$-0.443291\pi$
$937$	10.8493	0.354433	0.177216	+	0.984172i	$0.443291\pi$
$938$	−56.6338	−1.84916
$939$	47.7644	1.55873
$940$	7.24353	0.236258
$941$	36.9578	1.20479	0.602395	−	0.798198i	$-0.294213\pi$
$941$	36.9578	1.20479	0.602395	+	0.798198i	$0.294213\pi$
$942$	35.9503	1.17132
$943$	1.34158	0.0436879
$944$	−11.4148	−0.371522
$945$	56.7239	1.84523
$946$	−6.58994	−0.214257
$947$	−34.6849	−1.12711	−0.563553	−	0.826080i	$-0.690566\pi$
$947$	−34.6849	−1.12711	−0.563553	+	0.826080i	$0.690566\pi$
$948$	−33.3453	−1.08300
$949$	24.5782	0.797842
$950$	22.6925	0.736243
$951$	−24.5457	−0.795950
$952$	31.2143	1.01166
$953$	23.0427	0.746426	0.373213	−	0.927746i	$-0.378256\pi$
$953$	23.0427	0.746426	0.373213	+	0.927746i	$0.378256\pi$
$954$	19.3038	0.624985
$955$	−10.5141	−0.340229
$956$	−18.6305	−0.602553
$957$	61.3360	1.98271
$958$	24.2695	0.784113
$959$	83.2268	2.68753
$960$	−3.82585	−0.123479
$961$	−16.3406	−0.527116
$962$	8.11873	0.261758
$963$	−15.4639	−0.498319
$964$	−1.27999	−0.0412259
$965$	−23.1219	−0.744321
$966$	42.9713	1.38258
$967$	44.2550	1.42315	0.711573	−	0.702613i	$-0.247983\pi$
$967$	44.2550	1.42315	0.711573	+	0.702613i	$0.247983\pi$
$968$	2.27251	0.0730411
$969$	153.498	4.93106
$970$	1.97250	0.0633330
$971$	42.6141	1.36755	0.683775	−	0.729693i	$-0.260337\pi$
$971$	42.6141	1.36755	0.683775	+	0.729693i	$0.260337\pi$
$972$	12.3548	0.396281
$973$	−22.9955	−0.737201
$974$	4.39995	0.140983
$975$	46.1528	1.47807
$976$	−8.90652	−0.285091
$977$	−39.0782	−1.25022	−0.625112	−	0.780535i	$-0.714947\pi$
$977$	−39.0782	−1.25022	−0.625112	+	0.780535i	$0.714947\pi$
$978$	59.0496	1.88820
$979$	48.8401	1.56094
$980$	−12.2552	−0.391477
$981$	76.6561	2.44744
$982$	10.1458	0.323765
$983$	39.5364	1.26102	0.630508	−	0.776183i	$-0.282847\pi$
$983$	39.5364	1.26102	0.630508	+	0.776183i	$0.282847\pi$
$984$	−1.23357	−0.0393249
$985$	−11.9915	−0.382080
$986$	50.8296	1.61874
$987$	74.8082	2.38117
$988$	−27.9724	−0.889922
$989$	−7.51810	−0.239062
$990$	−24.0847	−0.765462
$991$	−6.64752	−0.211165	−0.105583	−	0.994411i	$-0.533671\pi$
$991$	−6.64752	−0.211165	−0.105583	+	0.994411i	$0.533671\pi$
$992$	3.82876	0.121563
$993$	9.78322	0.310461
$994$	−19.5036	−0.618616
$995$	−10.0910	−0.319905
$996$	53.5496	1.69679
$997$	29.1092	0.921898	0.460949	−	0.887427i	$-0.347509\pi$
$997$	29.1092	0.921898	0.460949	+	0.887427i	$0.347509\pi$
$998$	−13.8973	−0.439910
$999$	21.1614	0.669517

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.39	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.39	✓	40	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.09899 q^{3} +1.00000 q^{4} -1.23455 q^{5} -3.09899 q^{6} -4.11422 q^{7} -1.00000 q^{8} +6.60371 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.09899 q^{3} +1.00000 q^{4} -1.23455 q^{5} -3.09899 q^{6} -4.11422 q^{7} -1.00000 q^{8} +6.60371 q^{9} +1.23455 q^{10} -2.95423 q^{11} +3.09899 q^{12} -4.28463 q^{13} +4.11422 q^{14} -3.82585 q^{15} +1.00000 q^{16} +7.58691 q^{17} -6.60371 q^{18} +6.52856 q^{19} -1.23455 q^{20} -12.7499 q^{21} +2.95423 q^{22} +3.37032 q^{23} -3.09899 q^{24} -3.47589 q^{25} +4.28463 q^{26} +11.1678 q^{27} -4.11422 q^{28} -6.69964 q^{29} +3.82585 q^{30} -3.82876 q^{31} -1.00000 q^{32} -9.15513 q^{33} -7.58691 q^{34} +5.07922 q^{35} +6.60371 q^{36} +1.89485 q^{37} -6.52856 q^{38} -13.2780 q^{39} +1.23455 q^{40} +0.398057 q^{41} +12.7499 q^{42} -2.23068 q^{43} -2.95423 q^{44} -8.15261 q^{45} -3.37032 q^{46} -5.86735 q^{47} +3.09899 q^{48} +9.92684 q^{49} +3.47589 q^{50} +23.5117 q^{51} -4.28463 q^{52} -2.92318 q^{53} -11.1678 q^{54} +3.64715 q^{55} +4.11422 q^{56} +20.2319 q^{57} +6.69964 q^{58} -11.4148 q^{59} -3.82585 q^{60} -8.90652 q^{61} +3.82876 q^{62} -27.1692 q^{63} +1.00000 q^{64} +5.28959 q^{65} +9.15513 q^{66} -13.7654 q^{67} +7.58691 q^{68} +10.4446 q^{69} -5.07922 q^{70} -4.74052 q^{71} -6.60371 q^{72} -5.73636 q^{73} -1.89485 q^{74} -10.7717 q^{75} +6.52856 q^{76} +12.1544 q^{77} +13.2780 q^{78} -10.7601 q^{79} -1.23455 q^{80} +14.7979 q^{81} -0.398057 q^{82} +17.2797 q^{83} -12.7499 q^{84} -9.36642 q^{85} +2.23068 q^{86} -20.7621 q^{87} +2.95423 q^{88} -16.5322 q^{89} +8.15261 q^{90} +17.6279 q^{91} +3.37032 q^{92} -11.8653 q^{93} +5.86735 q^{94} -8.05983 q^{95} -3.09899 q^{96} +1.59775 q^{97} -9.92684 q^{98} -19.5089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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