LMFDB - Embedded newform 4006.2.a.g.1.2

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			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.11880 q^{3} +1.00000 q^{4} +1.57138 q^{5} +3.11880 q^{6} +2.57640 q^{7} -1.00000 q^{8} +6.72691 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.11880 q^{3} +1.00000 q^{4} +1.57138 q^{5} +3.11880 q^{6} +2.57640 q^{7} -1.00000 q^{8} +6.72691 q^{9} -1.57138 q^{10} -2.27747 q^{11} -3.11880 q^{12} +0.272260 q^{13} -2.57640 q^{14} -4.90081 q^{15} +1.00000 q^{16} +3.49514 q^{17} -6.72691 q^{18} +3.02570 q^{19} +1.57138 q^{20} -8.03526 q^{21} +2.27747 q^{22} +1.09989 q^{23} +3.11880 q^{24} -2.53078 q^{25} -0.272260 q^{26} -11.6235 q^{27} +2.57640 q^{28} -7.94298 q^{29} +4.90081 q^{30} +6.65335 q^{31} -1.00000 q^{32} +7.10296 q^{33} -3.49514 q^{34} +4.04849 q^{35} +6.72691 q^{36} -10.2457 q^{37} -3.02570 q^{38} -0.849126 q^{39} -1.57138 q^{40} -7.55369 q^{41} +8.03526 q^{42} -9.00970 q^{43} -2.27747 q^{44} +10.5705 q^{45} -1.09989 q^{46} +11.7619 q^{47} -3.11880 q^{48} -0.362182 q^{49} +2.53078 q^{50} -10.9006 q^{51} +0.272260 q^{52} -9.15701 q^{53} +11.6235 q^{54} -3.57875 q^{55} -2.57640 q^{56} -9.43656 q^{57} +7.94298 q^{58} -10.0195 q^{59} -4.90081 q^{60} -5.73379 q^{61} -6.65335 q^{62} +17.3312 q^{63} +1.00000 q^{64} +0.427824 q^{65} -7.10296 q^{66} -2.90990 q^{67} +3.49514 q^{68} -3.43035 q^{69} -4.04849 q^{70} -10.4554 q^{71} -6.72691 q^{72} +2.02729 q^{73} +10.2457 q^{74} +7.89299 q^{75} +3.02570 q^{76} -5.86765 q^{77} +0.849126 q^{78} +15.4765 q^{79} +1.57138 q^{80} +16.0706 q^{81} +7.55369 q^{82} +11.0624 q^{83} -8.03526 q^{84} +5.49217 q^{85} +9.00970 q^{86} +24.7726 q^{87} +2.27747 q^{88} -9.06665 q^{89} -10.5705 q^{90} +0.701451 q^{91} +1.09989 q^{92} -20.7505 q^{93} -11.7619 q^{94} +4.75452 q^{95} +3.11880 q^{96} -9.97049 q^{97} +0.362182 q^{98} -15.3203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.11880	−1.80064	−0.900320	−	0.435229i	$-0.856667\pi$
$3$	−3.11880	−1.80064	−0.900320	+	0.435229i	$0.856667\pi$
$4$	1.00000	0.500000
$5$	1.57138	0.702741	0.351370	−	0.936237i	$-0.385716\pi$
$5$	1.57138	0.702741	0.351370	+	0.936237i	$0.385716\pi$
$6$	3.11880	1.27324
$7$	2.57640	0.973786	0.486893	−	0.873462i	$-0.338130\pi$
$7$	2.57640	0.973786	0.486893	+	0.873462i	$0.338130\pi$
$8$	−1.00000	−0.353553
$9$	6.72691	2.24230
$10$	−1.57138	−0.496913
$11$	−2.27747	−0.686682	−0.343341	−	0.939211i	$-0.611559\pi$
$11$	−2.27747	−0.686682	−0.343341	+	0.939211i	$0.611559\pi$
$12$	−3.11880	−0.900320
$13$	0.272260	0.0755115	0.0377557	−	0.999287i	$-0.487979\pi$
$13$	0.272260	0.0755115	0.0377557	+	0.999287i	$0.487979\pi$
$14$	−2.57640	−0.688571
$15$	−4.90081	−1.26538
$16$	1.00000	0.250000
$17$	3.49514	0.847695	0.423847	−	0.905734i	$-0.360679\pi$
$17$	3.49514	0.847695	0.423847	+	0.905734i	$0.360679\pi$
$18$	−6.72691	−1.58555
$19$	3.02570	0.694144	0.347072	−	0.937839i	$-0.387176\pi$
$19$	3.02570	0.694144	0.347072	+	0.937839i	$0.387176\pi$
$20$	1.57138	0.351370
$21$	−8.03526	−1.75344
$22$	2.27747	0.485557
$23$	1.09989	0.229344	0.114672	−	0.993403i	$-0.463418\pi$
$23$	1.09989	0.229344	0.114672	+	0.993403i	$0.463418\pi$
$24$	3.11880	0.636622
$25$	−2.53078	−0.506155
$26$	−0.272260	−0.0533947
$27$	−11.6235	−2.23694
$28$	2.57640	0.486893
$29$	−7.94298	−1.47497	−0.737487	−	0.675362i	$-0.763988\pi$
$29$	−7.94298	−1.47497	−0.737487	+	0.675362i	$0.763988\pi$
$30$	4.90081	0.894761
$31$	6.65335	1.19498	0.597489	−	0.801877i	$-0.296165\pi$
$31$	6.65335	1.19498	0.597489	+	0.801877i	$0.296165\pi$
$32$	−1.00000	−0.176777
$33$	7.10296	1.23647
$34$	−3.49514	−0.599411
$35$	4.04849	0.684319
$36$	6.72691	1.12115
$37$	−10.2457	−1.68437	−0.842187	−	0.539185i	$-0.818732\pi$
$37$	−10.2457	−1.68437	−0.842187	+	0.539185i	$0.818732\pi$
$38$	−3.02570	−0.490834
$39$	−0.849126	−0.135969
$40$	−1.57138	−0.248456
$41$	−7.55369	−1.17969	−0.589844	−	0.807517i	$-0.700811\pi$
$41$	−7.55369	−1.17969	−0.589844	+	0.807517i	$0.700811\pi$
$42$	8.03526	1.23987
$43$	−9.00970	−1.37397	−0.686983	−	0.726673i	$-0.741065\pi$
$43$	−9.00970	−1.37397	−0.686983	+	0.726673i	$0.741065\pi$
$44$	−2.27747	−0.343341
$45$	10.5705	1.57576
$46$	−1.09989	−0.162171
$47$	11.7619	1.71565	0.857823	−	0.513945i	$-0.171817\pi$
$47$	11.7619	1.71565	0.857823	+	0.513945i	$0.171817\pi$
$48$	−3.11880	−0.450160
$49$	−0.362182	−0.0517403
$50$	2.53078	0.357906
$51$	−10.9006	−1.52639
$52$	0.272260	0.0377557
$53$	−9.15701	−1.25781	−0.628906	−	0.777481i	$-0.716497\pi$
$53$	−9.15701	−1.25781	−0.628906	+	0.777481i	$0.716497\pi$
$54$	11.6235	1.58176
$55$	−3.57875	−0.482559
$56$	−2.57640	−0.344285
$57$	−9.43656	−1.24990
$58$	7.94298	1.04296
$59$	−10.0195	−1.30443	−0.652213	−	0.758036i	$-0.726159\pi$
$59$	−10.0195	−1.30443	−0.652213	+	0.758036i	$0.726159\pi$
$60$	−4.90081	−0.632691
$61$	−5.73379	−0.734137	−0.367068	−	0.930194i	$-0.619638\pi$
$61$	−5.73379	−0.734137	−0.367068	+	0.930194i	$0.619638\pi$
$62$	−6.65335	−0.844976
$63$	17.3312	2.18352
$64$	1.00000	0.125000
$65$	0.427824	0.0530650
$66$	−7.10296	−0.874314
$67$	−2.90990	−0.355501	−0.177750	−	0.984076i	$-0.556882\pi$
$67$	−2.90990	−0.355501	−0.177750	+	0.984076i	$0.556882\pi$
$68$	3.49514	0.423847
$69$	−3.43035	−0.412966
$70$	−4.04849	−0.483887
$71$	−10.4554	−1.24083	−0.620413	−	0.784275i	$-0.713035\pi$
$71$	−10.4554	−1.24083	−0.620413	+	0.784275i	$0.713035\pi$
$72$	−6.72691	−0.792774
$73$	2.02729	0.237276	0.118638	−	0.992938i	$-0.462147\pi$
$73$	2.02729	0.237276	0.118638	+	0.992938i	$0.462147\pi$
$74$	10.2457	1.19103
$75$	7.89299	0.911404
$76$	3.02570	0.347072
$77$	−5.86765	−0.668681
$78$	0.849126	0.0961446
$79$	15.4765	1.74124	0.870619	−	0.491957i	$-0.163718\pi$
$79$	15.4765	1.74124	0.870619	+	0.491957i	$0.163718\pi$
$80$	1.57138	0.175685
$81$	16.0706	1.78562
$82$	7.55369	0.834165
$83$	11.0624	1.21426	0.607128	−	0.794604i	$-0.292321\pi$
$83$	11.0624	1.21426	0.607128	+	0.794604i	$0.292321\pi$
$84$	−8.03526	−0.876719
$85$	5.49217	0.595710
$86$	9.00970	0.971541
$87$	24.7726	2.65590
$88$	2.27747	0.242779
$89$	−9.06665	−0.961062	−0.480531	−	0.876978i	$-0.659556\pi$
$89$	−9.06665	−0.961062	−0.480531	+	0.876978i	$0.659556\pi$
$90$	−10.5705	−1.11423
$91$	0.701451	0.0735320
$92$	1.09989	0.114672
$93$	−20.7505	−2.15172
$94$	−11.7619	−1.21314
$95$	4.75452	0.487803
$96$	3.11880	0.318311
$97$	−9.97049	−1.01235	−0.506175	−	0.862431i	$-0.668941\pi$
$97$	−9.97049	−1.01235	−0.506175	+	0.862431i	$0.668941\pi$
$98$	0.362182	0.0365859
$99$	−15.3203	−1.53975
$100$	−2.53078	−0.253078
$101$	1.94659	0.193693	0.0968463	−	0.995299i	$-0.469124\pi$
$101$	1.94659	0.193693	0.0968463	+	0.995299i	$0.469124\pi$
$102$	10.9006	1.07932
$103$	14.7599	1.45434	0.727168	−	0.686459i	$-0.240836\pi$
$103$	14.7599	1.45434	0.727168	+	0.686459i	$0.240836\pi$
$104$	−0.272260	−0.0266973
$105$	−12.6264	−1.23221
$106$	9.15701	0.889407
$107$	−8.76868	−0.847701	−0.423850	−	0.905732i	$-0.639322\pi$
$107$	−8.76868	−0.847701	−0.423850	+	0.905732i	$0.639322\pi$
$108$	−11.6235	−1.11847
$109$	16.3775	1.56868	0.784341	−	0.620331i	$-0.213002\pi$
$109$	16.3775	1.56868	0.784341	+	0.620331i	$0.213002\pi$
$110$	3.57875	0.341221
$111$	31.9541	3.03295
$112$	2.57640	0.243447
$113$	8.31720	0.782416	0.391208	−	0.920302i	$-0.372057\pi$
$113$	8.31720	0.782416	0.391208	+	0.920302i	$0.372057\pi$
$114$	9.43656	0.883815
$115$	1.72835	0.161169
$116$	−7.94298	−0.737487
$117$	1.83147	0.169320
$118$	10.0195	0.922368
$119$	9.00485	0.825474
$120$	4.90081	0.447380
$121$	−5.81315	−0.528468
$122$	5.73379	0.519113
$123$	23.5584	2.12419
$124$	6.65335	0.597489
$125$	−11.8337	−1.05844
$126$	−17.3312	−1.54398
$127$	10.5055	0.932211	0.466106	−	0.884729i	$-0.345657\pi$
$127$	10.5055	0.932211	0.466106	+	0.884729i	$0.345657\pi$
$128$	−1.00000	−0.0883883
$129$	28.0994	2.47402
$130$	−0.427824	−0.0375226
$131$	9.40784	0.821967	0.410983	−	0.911643i	$-0.365185\pi$
$131$	9.40784	0.821967	0.410983	+	0.911643i	$0.365185\pi$
$132$	7.10296	0.618233
$133$	7.79541	0.675948
$134$	2.90990	0.251377
$135$	−18.2649	−1.57199
$136$	−3.49514	−0.299705
$137$	2.24860	0.192111	0.0960554	−	0.995376i	$-0.469377\pi$
$137$	2.24860	0.192111	0.0960554	+	0.995376i	$0.469377\pi$
$138$	3.43035	0.292011
$139$	−10.9625	−0.929828	−0.464914	−	0.885356i	$-0.653915\pi$
$139$	−10.9625	−0.929828	−0.464914	+	0.885356i	$0.653915\pi$
$140$	4.04849	0.342160
$141$	−36.6829	−3.08926
$142$	10.4554	0.877397
$143$	−0.620064	−0.0518523
$144$	6.72691	0.560576
$145$	−12.4814	−1.03652
$146$	−2.02729	−0.167780
$147$	1.12957	0.0931656
$148$	−10.2457	−0.842187
$149$	−20.6707	−1.69341	−0.846703	−	0.532065i	$-0.821416\pi$
$149$	−20.6707	−1.69341	−0.846703	+	0.532065i	$0.821416\pi$
$150$	−7.89299	−0.644460
$151$	−11.1355	−0.906196	−0.453098	−	0.891461i	$-0.649681\pi$
$151$	−11.1355	−0.906196	−0.453098	+	0.891461i	$0.649681\pi$
$152$	−3.02570	−0.245417
$153$	23.5115	1.90079
$154$	5.86765	0.472829
$155$	10.4549	0.839759
$156$	−0.849126	−0.0679845
$157$	15.4422	1.23242	0.616211	−	0.787581i	$-0.288667\pi$
$157$	15.4422	1.23242	0.616211	+	0.787581i	$0.288667\pi$
$158$	−15.4765	−1.23124
$159$	28.5589	2.26487
$160$	−1.57138	−0.124228
$161$	2.83377	0.223332
$162$	−16.0706	−1.26263
$163$	−19.4247	−1.52146	−0.760728	−	0.649071i	$-0.775158\pi$
$163$	−19.4247	−1.52146	−0.760728	+	0.649071i	$0.775158\pi$
$164$	−7.55369	−0.589844
$165$	11.1614	0.868915
$166$	−11.0624	−0.858609
$167$	−23.0061	−1.78026	−0.890132	−	0.455703i	$-0.849388\pi$
$167$	−23.0061	−1.78026	−0.890132	+	0.455703i	$0.849388\pi$
$168$	8.03526	0.619934
$169$	−12.9259	−0.994298
$170$	−5.49217	−0.421230
$171$	20.3536	1.55648
$172$	−9.00970	−0.686983
$173$	12.6019	0.958103	0.479051	−	0.877787i	$-0.340981\pi$
$173$	12.6019	0.958103	0.479051	+	0.877787i	$0.340981\pi$
$174$	−24.7726	−1.87800
$175$	−6.52029	−0.492887
$176$	−2.27747	−0.171670
$177$	31.2488	2.34880
$178$	9.06665	0.679574
$179$	−4.22919	−0.316105	−0.158052	−	0.987431i	$-0.550521\pi$
$179$	−4.22919	−0.316105	−0.158052	+	0.987431i	$0.550521\pi$
$180$	10.5705	0.787879
$181$	8.10763	0.602635	0.301318	−	0.953524i	$-0.402574\pi$
$181$	8.10763	0.602635	0.301318	+	0.953524i	$0.402574\pi$
$182$	−0.701451	−0.0519950
$183$	17.8825	1.32192
$184$	−1.09989	−0.0810853
$185$	−16.0998	−1.18368
$186$	20.7505	1.52150
$187$	−7.96005	−0.582096
$188$	11.7619	0.857823
$189$	−29.9467	−2.17830
$190$	−4.75452	−0.344929
$191$	3.58116	0.259124	0.129562	−	0.991571i	$-0.458643\pi$
$191$	3.58116	0.259124	0.129562	+	0.991571i	$0.458643\pi$
$192$	−3.11880	−0.225080
$193$	−4.77286	−0.343558	−0.171779	−	0.985135i	$-0.554952\pi$
$193$	−4.77286	−0.343558	−0.171779	+	0.985135i	$0.554952\pi$
$194$	9.97049	0.715840
$195$	−1.33430	−0.0955509
$196$	−0.362182	−0.0258701
$197$	3.42352	0.243915	0.121958	−	0.992535i	$-0.461083\pi$
$197$	3.42352	0.243915	0.121958	+	0.992535i	$0.461083\pi$
$198$	15.3203	1.08877
$199$	20.7544	1.47124	0.735619	−	0.677395i	$-0.236891\pi$
$199$	20.7544	1.47124	0.735619	+	0.677395i	$0.236891\pi$
$200$	2.53078	0.178953
$201$	9.07539	0.640129
$202$	−1.94659	−0.136961
$203$	−20.4643	−1.43631
$204$	−10.9006	−0.763196
$205$	−11.8697	−0.829015
$206$	−14.7599	−1.02837
$207$	7.39889	0.514259
$208$	0.272260	0.0188779
$209$	−6.89093	−0.476656
$210$	12.6264	0.871306
$211$	17.2684	1.18881	0.594403	−	0.804167i	$-0.297388\pi$
$211$	17.2684	1.18881	0.594403	+	0.804167i	$0.297388\pi$
$212$	−9.15701	−0.628906
$213$	32.6083	2.23428
$214$	8.76868	0.599415
$215$	−14.1576	−0.965542
$216$	11.6235	0.790878
$217$	17.1417	1.16365
$218$	−16.3775	−1.10923
$219$	−6.32270	−0.427249
$220$	−3.57875	−0.241280
$221$	0.951587	0.0640107
$222$	−31.9541	−2.14462
$223$	19.1328	1.28123	0.640613	−	0.767864i	$-0.278680\pi$
$223$	19.1328	1.28123	0.640613	+	0.767864i	$0.278680\pi$
$224$	−2.57640	−0.172143
$225$	−17.0243	−1.13495
$226$	−8.31720	−0.553252
$227$	−9.58723	−0.636327	−0.318163	−	0.948036i	$-0.603066\pi$
$227$	−9.58723	−0.636327	−0.318163	+	0.948036i	$0.603066\pi$
$228$	−9.43656	−0.624952
$229$	−15.4499	−1.02096	−0.510478	−	0.859891i	$-0.670532\pi$
$229$	−15.4499	−1.02096	−0.510478	+	0.859891i	$0.670532\pi$
$230$	−1.72835	−0.113964
$231$	18.3000	1.20405
$232$	7.94298	0.521482
$233$	12.3262	0.807513	0.403757	−	0.914866i	$-0.367704\pi$
$233$	12.3262	0.807513	0.403757	+	0.914866i	$0.367704\pi$
$234$	−1.83147	−0.119727
$235$	18.4823	1.20565
$236$	−10.0195	−0.652213
$237$	−48.2680	−3.13534
$238$	−9.00485	−0.583698
$239$	−25.2462	−1.63304	−0.816520	−	0.577317i	$-0.804100\pi$
$239$	−25.2462	−1.63304	−0.816520	+	0.577317i	$0.804100\pi$
$240$	−4.90081	−0.316346
$241$	−16.5545	−1.06637	−0.533184	−	0.845999i	$-0.679005\pi$
$241$	−16.5545	−1.06637	−0.533184	+	0.845999i	$0.679005\pi$
$242$	5.81315	0.373683
$243$	−15.2505	−0.978320
$244$	−5.73379	−0.367068
$245$	−0.569124	−0.0363600
$246$	−23.5584	−1.50203
$247$	0.823779	0.0524158
$248$	−6.65335	−0.422488
$249$	−34.5014	−2.18644
$250$	11.8337	0.748428
$251$	23.4094	1.47759	0.738793	−	0.673933i	$-0.235396\pi$
$251$	23.4094	1.47759	0.738793	+	0.673933i	$0.235396\pi$
$252$	17.3312	1.09176
$253$	−2.50497	−0.157486
$254$	−10.5055	−0.659173
$255$	−17.1290	−1.07266
$256$	1.00000	0.0625000
$257$	−9.81989	−0.612548	−0.306274	−	0.951943i	$-0.599082\pi$
$257$	−9.81989	−0.612548	−0.306274	+	0.951943i	$0.599082\pi$
$258$	−28.0994	−1.74939
$259$	−26.3969	−1.64022
$260$	0.427824	0.0265325
$261$	−53.4317	−3.30734
$262$	−9.40784	−0.581218
$263$	−28.8537	−1.77919	−0.889596	−	0.456747i	$-0.849014\pi$
$263$	−28.8537	−1.77919	−0.889596	+	0.456747i	$0.849014\pi$
$264$	−7.10296	−0.437157
$265$	−14.3891	−0.883916
$266$	−7.79541	−0.477967
$267$	28.2770	1.73053
$268$	−2.90990	−0.177750
$269$	−11.8656	−0.723461	−0.361731	−	0.932283i	$-0.617814\pi$
$269$	−11.8656	−0.723461	−0.361731	+	0.932283i	$0.617814\pi$
$270$	18.2649	1.11156
$271$	−4.36320	−0.265046	−0.132523	−	0.991180i	$-0.542308\pi$
$271$	−4.36320	−0.265046	−0.132523	+	0.991180i	$0.542308\pi$
$272$	3.49514	0.211924
$273$	−2.18768	−0.132405
$274$	−2.24860	−0.135843
$275$	5.76376	0.347568
$276$	−3.43035	−0.206483
$277$	18.1159	1.08848	0.544239	−	0.838930i	$-0.316819\pi$
$277$	18.1159	1.08848	0.544239	+	0.838930i	$0.316819\pi$
$278$	10.9625	0.657488
$279$	44.7565	2.67950
$280$	−4.04849	−0.241943
$281$	−28.0924	−1.67585	−0.837927	−	0.545782i	$-0.816233\pi$
$281$	−28.0924	−1.67585	−0.837927	+	0.545782i	$0.816233\pi$
$282$	36.6829	2.18444
$283$	13.8475	0.823148	0.411574	−	0.911376i	$-0.364979\pi$
$283$	13.8475	0.823148	0.411574	+	0.911376i	$0.364979\pi$
$284$	−10.4554	−0.620413
$285$	−14.8284	−0.878358
$286$	0.620064	0.0366651
$287$	−19.4613	−1.14876
$288$	−6.72691	−0.396387
$289$	−4.78403	−0.281414
$290$	12.4814	0.732933
$291$	31.0960	1.82288
$292$	2.02729	0.118638
$293$	−15.2879	−0.893129	−0.446564	−	0.894751i	$-0.647353\pi$
$293$	−15.2879	−0.893129	−0.446564	+	0.894751i	$0.647353\pi$
$294$	−1.12957	−0.0658780
$295$	−15.7444	−0.916673
$296$	10.2457	0.595516
$297$	26.4721	1.53607
$298$	20.6707	1.19742
$299$	0.299458	0.0173181
$300$	7.89299	0.455702
$301$	−23.2126	−1.33795
$302$	11.1355	0.640777
$303$	−6.07102	−0.348771
$304$	3.02570	0.173536
$305$	−9.00994	−0.515908
$306$	−23.5115	−1.34406
$307$	−18.5486	−1.05862	−0.529312	−	0.848427i	$-0.677550\pi$
$307$	−18.5486	−1.05862	−0.529312	+	0.848427i	$0.677550\pi$
$308$	−5.86765	−0.334341
$309$	−46.0332	−2.61874
$310$	−10.4549	−0.593799
$311$	−15.5169	−0.879880	−0.439940	−	0.898027i	$-0.645000\pi$
$311$	−15.5169	−0.879880	−0.439940	+	0.898027i	$0.645000\pi$
$312$	0.849126	0.0480723
$313$	−2.30508	−0.130291	−0.0651455	−	0.997876i	$-0.520751\pi$
$313$	−2.30508	−0.130291	−0.0651455	+	0.997876i	$0.520751\pi$
$314$	−15.4422	−0.871454
$315$	27.2338	1.53445
$316$	15.4765	0.870619
$317$	11.3746	0.638864	0.319432	−	0.947609i	$-0.396508\pi$
$317$	11.3746	0.638864	0.319432	+	0.947609i	$0.396508\pi$
$318$	−28.5589	−1.60150
$319$	18.0899	1.01284
$320$	1.57138	0.0878426
$321$	27.3478	1.52640
$322$	−2.83377	−0.157920
$323$	10.5752	0.588422
$324$	16.0706	0.892811
$325$	−0.689030	−0.0382205
$326$	19.4247	1.07583
$327$	−51.0782	−2.82463
$328$	7.55369	0.417083
$329$	30.3032	1.67067
$330$	−11.1614	−0.614416
$331$	−14.3485	−0.788663	−0.394332	−	0.918968i	$-0.629024\pi$
$331$	−14.3485	−0.788663	−0.394332	+	0.918968i	$0.629024\pi$
$332$	11.0624	0.607128
$333$	−68.9216	−3.77688
$334$	23.0061	1.25884
$335$	−4.57254	−0.249825
$336$	−8.03526	−0.438360
$337$	−33.0436	−1.80000	−0.900000	−	0.435890i	$-0.856434\pi$
$337$	−33.0436	−1.80000	−0.900000	+	0.435890i	$0.856434\pi$
$338$	12.9259	0.703075
$339$	−25.9397	−1.40885
$340$	5.49217	0.297855
$341$	−15.1528	−0.820569
$342$	−20.3536	−1.10060
$343$	−18.9679	−1.02417
$344$	9.00970	0.485770
$345$	−5.39037	−0.290208
$346$	−12.6019	−0.677481
$347$	1.25935	0.0676054	0.0338027	−	0.999429i	$-0.489238\pi$
$347$	1.25935	0.0676054	0.0338027	+	0.999429i	$0.489238\pi$
$348$	24.7726	1.32795
$349$	−5.46754	−0.292671	−0.146335	−	0.989235i	$-0.546748\pi$
$349$	−5.46754	−0.292671	−0.146335	+	0.989235i	$0.546748\pi$
$350$	6.52029	0.348524
$351$	−3.16462	−0.168915
$352$	2.27747	0.121389
$353$	28.6896	1.52699	0.763497	−	0.645811i	$-0.223481\pi$
$353$	28.6896	1.52699	0.763497	+	0.645811i	$0.223481\pi$
$354$	−31.2488	−1.66085
$355$	−16.4293	−0.871979
$356$	−9.06665	−0.480531
$357$	−28.0843	−1.48638
$358$	4.22919	0.223520
$359$	3.40290	0.179598	0.0897992	−	0.995960i	$-0.471377\pi$
$359$	3.40290	0.179598	0.0897992	+	0.995960i	$0.471377\pi$
$360$	−10.5705	−0.557115
$361$	−9.84512	−0.518164
$362$	−8.10763	−0.426127
$363$	18.1301	0.951581
$364$	0.701451	0.0367660
$365$	3.18563	0.166744
$366$	−17.8825	−0.934735
$367$	−15.4357	−0.805735	−0.402868	−	0.915258i	$-0.631987\pi$
$367$	−15.4357	−0.805735	−0.402868	+	0.915258i	$0.631987\pi$
$368$	1.09989	0.0573360
$369$	−50.8130	−2.64522
$370$	16.0998	0.836987
$371$	−23.5921	−1.22484
$372$	−20.7505	−1.07586
$373$	31.0288	1.60661	0.803304	−	0.595569i	$-0.203073\pi$
$373$	31.0288	1.60661	0.803304	+	0.595569i	$0.203073\pi$
$374$	7.96005	0.411604
$375$	36.9069	1.90586
$376$	−11.7619	−0.606572
$377$	−2.16256	−0.111377
$378$	29.9467	1.54029
$379$	0.478507	0.0245793	0.0122896	−	0.999924i	$-0.496088\pi$
$379$	0.478507	0.0245793	0.0122896	+	0.999924i	$0.496088\pi$
$380$	4.75452	0.243902
$381$	−32.7645	−1.67858
$382$	−3.58116	−0.183228
$383$	−23.3872	−1.19503	−0.597515	−	0.801858i	$-0.703845\pi$
$383$	−23.3872	−1.19503	−0.597515	+	0.801858i	$0.703845\pi$
$384$	3.11880	0.159156
$385$	−9.22029	−0.469910
$386$	4.77286	0.242932
$387$	−60.6074	−3.08085
$388$	−9.97049	−0.506175
$389$	24.8239	1.25862	0.629310	−	0.777155i	$-0.283338\pi$
$389$	24.8239	1.25862	0.629310	+	0.777155i	$0.283338\pi$
$390$	1.33430	0.0675647
$391$	3.84428	0.194414
$392$	0.362182	0.0182929
$393$	−29.3412	−1.48007
$394$	−3.42352	−0.172474
$395$	24.3193	1.22364
$396$	−15.3203	−0.769874
$397$	28.6504	1.43792	0.718960	−	0.695051i	$-0.244618\pi$
$397$	28.6504	1.43792	0.718960	+	0.695051i	$0.244618\pi$
$398$	−20.7544	−1.04032
$399$	−24.3123	−1.21714
$400$	−2.53078	−0.126539
$401$	16.2022	0.809098	0.404549	−	0.914516i	$-0.367429\pi$
$401$	16.2022	0.809098	0.404549	+	0.914516i	$0.367429\pi$
$402$	−9.07539	−0.452639
$403$	1.81144	0.0902345
$404$	1.94659	0.0968463
$405$	25.2529	1.25483
$406$	20.4643	1.01562
$407$	23.3341	1.15663
$408$	10.9006	0.539661
$409$	−1.44491	−0.0714460	−0.0357230	−	0.999362i	$-0.511373\pi$
$409$	−1.44491	−0.0714460	−0.0357230	+	0.999362i	$0.511373\pi$
$410$	11.8697	0.586202
$411$	−7.01293	−0.345923
$412$	14.7599	0.727168
$413$	−25.8142	−1.27023
$414$	−7.39889	−0.363636
$415$	17.3832	0.853308
$416$	−0.272260	−0.0133487
$417$	34.1899	1.67429
$418$	6.89093	0.337047
$419$	−32.9567	−1.61004	−0.805021	−	0.593246i	$-0.797846\pi$
$419$	−32.9567	−1.61004	−0.805021	+	0.593246i	$0.797846\pi$
$420$	−12.6264	−0.616106
$421$	35.1379	1.71252	0.856259	−	0.516546i	$-0.172783\pi$
$421$	35.1379	1.71252	0.856259	+	0.516546i	$0.172783\pi$
$422$	−17.2684	−0.840613
$423$	79.1211	3.84700
$424$	9.15701	0.444704
$425$	−8.84541	−0.429065
$426$	−32.6083	−1.57988
$427$	−14.7725	−0.714892
$428$	−8.76868	−0.423850
$429$	1.93385	0.0933674
$430$	14.1576	0.682741
$431$	3.44601	0.165989	0.0829943	−	0.996550i	$-0.473552\pi$
$431$	3.44601	0.165989	0.0829943	+	0.996550i	$0.473552\pi$
$432$	−11.6235	−0.559235
$433$	22.6597	1.08896	0.544479	−	0.838775i	$-0.316727\pi$
$433$	22.6597	1.08896	0.544479	+	0.838775i	$0.316727\pi$
$434$	−17.1417	−0.822826
$435$	38.9270	1.86641
$436$	16.3775	0.784341
$437$	3.32796	0.159198
$438$	6.32270	0.302110
$439$	−27.4365	−1.30947	−0.654736	−	0.755858i	$-0.727220\pi$
$439$	−27.4365	−1.30947	−0.654736	+	0.755858i	$0.727220\pi$
$440$	3.57875	0.170610
$441$	−2.43637	−0.116017
$442$	−0.951587	−0.0452624
$443$	10.7107	0.508879	0.254439	−	0.967089i	$-0.418109\pi$
$443$	10.7107	0.508879	0.254439	+	0.967089i	$0.418109\pi$
$444$	31.9541	1.51648
$445$	−14.2471	−0.675378
$446$	−19.1328	−0.905964
$447$	64.4677	3.04922
$448$	2.57640	0.121723
$449$	−23.3758	−1.10317	−0.551586	−	0.834118i	$-0.685977\pi$
$449$	−23.3758	−1.10317	−0.551586	+	0.834118i	$0.685977\pi$
$450$	17.0243	0.802534
$451$	17.2033	0.810070
$452$	8.31720	0.391208
$453$	34.7295	1.63173
$454$	9.58723	0.449951
$455$	1.10224	0.0516739
$456$	9.43656	0.441907
$457$	11.1400	0.521108	0.260554	−	0.965459i	$-0.416095\pi$
$457$	11.1400	0.521108	0.260554	+	0.965459i	$0.416095\pi$
$458$	15.4499	0.721925
$459$	−40.6257	−1.89624
$460$	1.72835	0.0805847
$461$	−22.5473	−1.05013	−0.525067	−	0.851061i	$-0.675960\pi$
$461$	−22.5473	−1.05013	−0.525067	+	0.851061i	$0.675960\pi$
$462$	−18.3000	−0.851395
$463$	21.6006	1.00387	0.501933	−	0.864907i	$-0.332622\pi$
$463$	21.6006	1.00387	0.501933	+	0.864907i	$0.332622\pi$
$464$	−7.94298	−0.368743
$465$	−32.6068	−1.51210
$466$	−12.3262	−0.570998
$467$	20.3649	0.942376	0.471188	−	0.882033i	$-0.343825\pi$
$467$	20.3649	0.942376	0.471188	+	0.882033i	$0.343825\pi$
$468$	1.83147	0.0846598
$469$	−7.49705	−0.346182
$470$	−18.4823	−0.852526
$471$	−48.1611	−2.21915
$472$	10.0195	0.461184
$473$	20.5193	0.943477
$474$	48.2680	2.21702
$475$	−7.65738	−0.351345
$476$	9.00485	0.412737
$477$	−61.5984	−2.82040
$478$	25.2462	1.15473
$479$	−2.02262	−0.0924158	−0.0462079	−	0.998932i	$-0.514714\pi$
$479$	−2.02262	−0.0924158	−0.0462079	+	0.998932i	$0.514714\pi$
$480$	4.90081	0.223690
$481$	−2.78949	−0.127190
$482$	16.5545	0.754037
$483$	−8.83795	−0.402140
$484$	−5.81315	−0.264234
$485$	−15.6674	−0.711420
$486$	15.2505	0.691777
$487$	−27.9143	−1.26492	−0.632458	−	0.774595i	$-0.717954\pi$
$487$	−27.9143	−1.26492	−0.632458	+	0.774595i	$0.717954\pi$
$488$	5.73379	0.259556
$489$	60.5816	2.73959
$490$	0.569124	0.0257104
$491$	13.4879	0.608700	0.304350	−	0.952560i	$-0.401561\pi$
$491$	13.4879	0.608700	0.304350	+	0.952560i	$0.401561\pi$
$492$	23.5584	1.06210
$493$	−27.7618	−1.25033
$494$	−0.823779	−0.0370636
$495$	−24.0740	−1.08204
$496$	6.65335	0.298744
$497$	−26.9372	−1.20830
$498$	34.5014	1.54605
$499$	−37.4379	−1.67595	−0.837975	−	0.545709i	$-0.816260\pi$
$499$	−37.4379	−1.67595	−0.837975	+	0.545709i	$0.816260\pi$
$500$	−11.8337	−0.529218
$501$	71.7514	3.20561
$502$	−23.4094	−1.04481
$503$	14.2126	0.633708	0.316854	−	0.948474i	$-0.397373\pi$
$503$	14.2126	0.633708	0.316854	+	0.948474i	$0.397373\pi$
$504$	−17.3312	−0.771992
$505$	3.05882	0.136116
$506$	2.50497	0.111360
$507$	40.3132	1.79037
$508$	10.5055	0.466106
$509$	−10.3235	−0.457583	−0.228791	−	0.973475i	$-0.573477\pi$
$509$	−10.3235	−0.457583	−0.228791	+	0.973475i	$0.573477\pi$
$510$	17.1290	0.758484
$511$	5.22310	0.231056
$512$	−1.00000	−0.0441942
$513$	−35.1692	−1.55276
$514$	9.81989	0.433137
$515$	23.1934	1.02202
$516$	28.0994	1.23701
$517$	−26.7873	−1.17810
$518$	26.3969	1.15981
$519$	−39.3027	−1.72520
$520$	−0.427824	−0.0187613
$521$	−7.17528	−0.314355	−0.157177	−	0.987570i	$-0.550239\pi$
$521$	−7.17528	−0.314355	−0.157177	+	0.987570i	$0.550239\pi$
$522$	53.4317	2.33864
$523$	−10.1334	−0.443104	−0.221552	−	0.975149i	$-0.571112\pi$
$523$	−10.1334	−0.443104	−0.221552	+	0.975149i	$0.571112\pi$
$524$	9.40784	0.410983
$525$	20.3355	0.887512
$526$	28.8537	1.25808
$527$	23.2544	1.01298
$528$	7.10296	0.309117
$529$	−21.7902	−0.947401
$530$	14.3891	0.625023
$531$	−67.4002	−2.92492
$532$	7.79541	0.337974
$533$	−2.05657	−0.0890800
$534$	−28.2770	−1.22367
$535$	−13.7789	−0.595714
$536$	2.90990	0.125688
$537$	13.1900	0.569191
$538$	11.8656	0.511564
$539$	0.824857	0.0355291
$540$	−18.2649	−0.785995
$541$	39.3072	1.68995	0.844974	−	0.534808i	$-0.179616\pi$
$541$	39.3072	1.68995	0.844974	+	0.534808i	$0.179616\pi$
$542$	4.36320	0.187416
$543$	−25.2861	−1.08513
$544$	−3.49514	−0.149853
$545$	25.7352	1.10238
$546$	2.18768	0.0936242
$547$	−27.9640	−1.19565	−0.597827	−	0.801625i	$-0.703969\pi$
$547$	−27.9640	−1.19565	−0.597827	+	0.801625i	$0.703969\pi$
$548$	2.24860	0.0960554
$549$	−38.5707	−1.64616
$550$	−5.76376	−0.245767
$551$	−24.0331	−1.02384
$552$	3.43035	0.146005
$553$	39.8735	1.69559
$554$	−18.1159	−0.769670
$555$	50.2120	2.13138
$556$	−10.9625	−0.464914
$557$	18.9856	0.804447	0.402224	−	0.915541i	$-0.368237\pi$
$557$	18.9856	0.804447	0.402224	+	0.915541i	$0.368237\pi$
$558$	−44.7565	−1.89469
$559$	−2.45298	−0.103750
$560$	4.04849	0.171080
$561$	24.8258	1.04815
$562$	28.0924	1.18501
$563$	39.5150	1.66536	0.832679	−	0.553756i	$-0.186806\pi$
$563$	39.5150	1.66536	0.832679	+	0.553756i	$0.186806\pi$
$564$	−36.6829	−1.54463
$565$	13.0694	0.549836
$566$	−13.8475	−0.582054
$567$	41.4042	1.73881
$568$	10.4554	0.438698
$569$	−17.9652	−0.753141	−0.376571	−	0.926388i	$-0.622897\pi$
$569$	−17.9652	−0.753141	−0.376571	+	0.926388i	$0.622897\pi$
$570$	14.8284	0.621093
$571$	3.03513	0.127016	0.0635082	−	0.997981i	$-0.479771\pi$
$571$	3.03513	0.127016	0.0635082	+	0.997981i	$0.479771\pi$
$572$	−0.620064	−0.0259262
$573$	−11.1689	−0.466588
$574$	19.4613	0.812299
$575$	−2.78359	−0.116084
$576$	6.72691	0.280288
$577$	2.82364	0.117550	0.0587749	−	0.998271i	$-0.481281\pi$
$577$	2.82364	0.117550	0.0587749	+	0.998271i	$0.481281\pi$
$578$	4.78403	0.198989
$579$	14.8856	0.618625
$580$	−12.4814	−0.518262
$581$	28.5011	1.18243
$582$	−31.0960	−1.28897
$583$	20.8548	0.863716
$584$	−2.02729	−0.0838898
$585$	2.87793	0.118988
$586$	15.2879	0.631537
$587$	−25.2865	−1.04369	−0.521843	−	0.853041i	$-0.674755\pi$
$587$	−25.2865	−1.04369	−0.521843	+	0.853041i	$0.674755\pi$
$588$	1.12957	0.0465828
$589$	20.1311	0.829486
$590$	15.7444	0.648186
$591$	−10.6773	−0.439204
$592$	−10.2457	−0.421094
$593$	0.413543	0.0169822	0.00849109	−	0.999964i	$-0.497297\pi$
$593$	0.413543	0.0169822	0.00849109	+	0.999964i	$0.497297\pi$
$594$	−26.4721	−1.08616
$595$	14.1500	0.580094
$596$	−20.6707	−0.846703
$597$	−64.7287	−2.64917
$598$	−0.299458	−0.0122457
$599$	10.4742	0.427965	0.213982	−	0.976838i	$-0.431356\pi$
$599$	10.4742	0.427965	0.213982	+	0.976838i	$0.431356\pi$
$600$	−7.89299	−0.322230
$601$	34.2647	1.39769	0.698844	−	0.715274i	$-0.253698\pi$
$601$	34.2647	1.39769	0.698844	+	0.715274i	$0.253698\pi$
$602$	23.2126	0.946073
$603$	−19.5746	−0.797140
$604$	−11.1355	−0.453098
$605$	−9.13465	−0.371376
$606$	6.07102	0.246618
$607$	4.29781	0.174443	0.0872213	−	0.996189i	$-0.472201\pi$
$607$	4.29781	0.174443	0.0872213	+	0.996189i	$0.472201\pi$
$608$	−3.02570	−0.122708
$609$	63.8239	2.58628
$610$	9.00994	0.364802
$611$	3.20229	0.129551
$612$	23.5115	0.950395
$613$	−36.4900	−1.47382	−0.736908	−	0.675993i	$-0.763715\pi$
$613$	−36.4900	−1.47382	−0.736908	+	0.675993i	$0.763715\pi$
$614$	18.5486	0.748561
$615$	37.0192	1.49276
$616$	5.86765	0.236415
$617$	−9.12631	−0.367411	−0.183706	−	0.982981i	$-0.558809\pi$
$617$	−9.12631	−0.367411	−0.183706	+	0.982981i	$0.558809\pi$
$618$	46.0332	1.85173
$619$	31.1512	1.25207	0.626035	−	0.779795i	$-0.284677\pi$
$619$	31.1512	1.25207	0.626035	+	0.779795i	$0.284677\pi$
$620$	10.4549	0.419880
$621$	−12.7846	−0.513029
$622$	15.5169	0.622169
$623$	−23.3593	−0.935869
$624$	−0.849126	−0.0339922
$625$	−5.94128	−0.237651
$626$	2.30508	0.0921297
$627$	21.4914	0.858286
$628$	15.4422	0.616211
$629$	−35.8099	−1.42784
$630$	−27.2338	−1.08502
$631$	−27.4566	−1.09303	−0.546515	−	0.837449i	$-0.684046\pi$
$631$	−27.4566	−1.09303	−0.546515	+	0.837449i	$0.684046\pi$
$632$	−15.4765	−0.615621
$633$	−53.8567	−2.14061
$634$	−11.3746	−0.451745
$635$	16.5081	0.655103
$636$	28.5589	1.13243
$637$	−0.0986078	−0.00390698
$638$	−18.0899	−0.716184
$639$	−70.3325	−2.78231
$640$	−1.57138	−0.0621141
$641$	−9.93186	−0.392285	−0.196142	−	0.980575i	$-0.562841\pi$
$641$	−9.93186	−0.392285	−0.196142	+	0.980575i	$0.562841\pi$
$642$	−27.3478	−1.07933
$643$	30.8635	1.21714	0.608569	−	0.793501i	$-0.291744\pi$
$643$	30.8635	1.21714	0.608569	+	0.793501i	$0.291744\pi$
$644$	2.83377	0.111666
$645$	44.1548	1.73859
$646$	−10.5752	−0.416077
$647$	−13.1275	−0.516096	−0.258048	−	0.966132i	$-0.583079\pi$
$647$	−13.1275	−0.516096	−0.258048	+	0.966132i	$0.583079\pi$
$648$	−16.0706	−0.631313
$649$	22.8190	0.895725
$650$	0.689030	0.0270260
$651$	−53.4614	−2.09532
$652$	−19.4247	−0.760728
$653$	−5.48671	−0.214711	−0.107356	−	0.994221i	$-0.534238\pi$
$653$	−5.48671	−0.214711	−0.107356	+	0.994221i	$0.534238\pi$
$654$	51.0782	1.99731
$655$	14.7833	0.577630
$656$	−7.55369	−0.294922
$657$	13.6374	0.532045
$658$	−30.3032	−1.18134
$659$	−30.1775	−1.17555	−0.587774	−	0.809025i	$-0.699996\pi$
$659$	−30.1775	−1.17555	−0.587774	+	0.809025i	$0.699996\pi$
$660$	11.1614	0.434458
$661$	−18.5785	−0.722620	−0.361310	−	0.932446i	$-0.617670\pi$
$661$	−18.5785	−0.722620	−0.361310	+	0.932446i	$0.617670\pi$
$662$	14.3485	0.557669
$663$	−2.96781	−0.115260
$664$	−11.0624	−0.429305
$665$	12.2495	0.475016
$666$	68.9216	2.67066
$667$	−8.73644	−0.338276
$668$	−23.0061	−0.890132
$669$	−59.6713	−2.30703
$670$	4.57254	0.176653
$671$	13.0585	0.504118
$672$	8.03526	0.309967
$673$	40.9287	1.57768	0.788842	−	0.614596i	$-0.210681\pi$
$673$	40.9287	1.57768	0.788842	+	0.614596i	$0.210681\pi$
$674$	33.0436	1.27279
$675$	29.4165	1.13224
$676$	−12.9259	−0.497149
$677$	−34.2455	−1.31616	−0.658080	−	0.752948i	$-0.728631\pi$
$677$	−34.2455	−1.31616	−0.658080	+	0.752948i	$0.728631\pi$
$678$	25.9397	0.996207
$679$	−25.6879	−0.985813
$680$	−5.49217	−0.210615
$681$	29.9007	1.14580
$682$	15.1528	0.580230
$683$	−23.3249	−0.892504	−0.446252	−	0.894907i	$-0.647241\pi$
$683$	−23.3249	−0.892504	−0.446252	+	0.894907i	$0.647241\pi$
$684$	20.3536	0.778241
$685$	3.53340	0.135004
$686$	18.9679	0.724198
$687$	48.1851	1.83837
$688$	−9.00970	−0.343492
$689$	−2.49309	−0.0949792
$690$	5.39037	0.205208
$691$	−18.0107	−0.685161	−0.342581	−	0.939488i	$-0.611301\pi$
$691$	−18.0107	−0.685161	−0.342581	+	0.939488i	$0.611301\pi$
$692$	12.6019	0.479051
$693$	−39.4712	−1.49939
$694$	−1.25935	−0.0478042
$695$	−17.2262	−0.653428
$696$	−24.7726	−0.939001
$697$	−26.4012	−1.00002
$698$	5.46754	0.206949
$699$	−38.4428	−1.45404
$700$	−6.52029	−0.246444
$701$	−10.0324	−0.378918	−0.189459	−	0.981889i	$-0.560673\pi$
$701$	−10.0324	−0.378918	−0.189459	+	0.981889i	$0.560673\pi$
$702$	3.16462	0.119441
$703$	−31.0003	−1.16920
$704$	−2.27747	−0.0858352
$705$	−57.6427	−2.17095
$706$	−28.6896	−1.07975
$707$	5.01518	0.188615
$708$	31.2488	1.17440
$709$	41.6972	1.56597	0.782986	−	0.622039i	$-0.213696\pi$
$709$	41.6972	1.56597	0.782986	+	0.622039i	$0.213696\pi$
$710$	16.4293	0.616582
$711$	104.109	3.90439
$712$	9.06665	0.339787
$713$	7.31799	0.274061
$714$	28.0843	1.05103
$715$	−0.974353	−0.0364387
$716$	−4.22919	−0.158052
$717$	78.7378	2.94052
$718$	−3.40290	−0.126995
$719$	−18.8814	−0.704159	−0.352080	−	0.935970i	$-0.614525\pi$
$719$	−18.8814	−0.704159	−0.352080	+	0.935970i	$0.614525\pi$
$720$	10.5705	0.393940
$721$	38.0274	1.41621
$722$	9.84512	0.366398
$723$	51.6302	1.92015
$724$	8.10763	0.301318
$725$	20.1019	0.746566
$726$	−18.1301	−0.672869
$727$	13.2857	0.492739	0.246369	−	0.969176i	$-0.420762\pi$
$727$	13.2857	0.492739	0.246369	+	0.969176i	$0.420762\pi$
$728$	−0.701451	−0.0259975
$729$	−0.648523	−0.0240194
$730$	−3.18563	−0.117906
$731$	−31.4901	−1.16470
$732$	17.8825	0.660958
$733$	−3.01860	−0.111495	−0.0557473	−	0.998445i	$-0.517754\pi$
$733$	−3.01860	−0.111495	−0.0557473	+	0.998445i	$0.517754\pi$
$734$	15.4357	0.569741
$735$	1.77498	0.0654713
$736$	−1.09989	−0.0405427
$737$	6.62719	0.244116
$738$	50.8130	1.87045
$739$	−35.8354	−1.31822	−0.659112	−	0.752044i	$-0.729068\pi$
$739$	−35.8354	−1.31822	−0.659112	+	0.752044i	$0.729068\pi$
$740$	−16.0998	−0.591839
$741$	−2.56920	−0.0943820
$742$	23.5921	0.866093
$743$	40.7369	1.49449	0.747245	−	0.664548i	$-0.231376\pi$
$743$	40.7369	1.49449	0.747245	+	0.664548i	$0.231376\pi$
$744$	20.7505	0.760749
$745$	−32.4814	−1.19003
$746$	−31.0288	−1.13604
$747$	74.4158	2.72273
$748$	−7.96005	−0.291048
$749$	−22.5916	−0.825479
$750$	−36.9069	−1.34765
$751$	−36.7976	−1.34276	−0.671381	−	0.741112i	$-0.734299\pi$
$751$	−36.7976	−1.34276	−0.671381	+	0.741112i	$0.734299\pi$
$752$	11.7619	0.428911
$753$	−73.0091	−2.66060
$754$	2.16256	0.0787557
$755$	−17.4981	−0.636821
$756$	−29.9467	−1.08915
$757$	14.3783	0.522587	0.261293	−	0.965259i	$-0.415851\pi$
$757$	14.3783	0.522587	0.261293	+	0.965259i	$0.415851\pi$
$758$	−0.478507	−0.0173802
$759$	7.81251	0.283576
$760$	−4.75452	−0.172464
$761$	−2.38705	−0.0865306	−0.0432653	−	0.999064i	$-0.513776\pi$
$761$	−2.38705	−0.0865306	−0.0432653	+	0.999064i	$0.513776\pi$
$762$	32.7645	1.18693
$763$	42.1950	1.52756
$764$	3.58116	0.129562
$765$	36.9453	1.33576
$766$	23.3872	0.845014
$767$	−2.72791	−0.0984991
$768$	−3.11880	−0.112540
$769$	49.9662	1.80183	0.900913	−	0.434000i	$-0.142898\pi$
$769$	49.9662	1.80183	0.900913	+	0.434000i	$0.142898\pi$
$770$	9.22029	0.332276
$771$	30.6263	1.10298
$772$	−4.77286	−0.171779
$773$	50.3248	1.81006	0.905028	−	0.425352i	$-0.139850\pi$
$773$	50.3248	1.81006	0.905028	+	0.425352i	$0.139850\pi$
$774$	60.6074	2.17849
$775$	−16.8381	−0.604844
$776$	9.97049	0.357920
$777$	82.3265	2.95345
$778$	−24.8239	−0.889978
$779$	−22.8552	−0.818873
$780$	−1.33430	−0.0477755
$781$	23.8118	0.852053
$782$	−3.84428	−0.137471
$783$	92.3251	3.29943
$784$	−0.362182	−0.0129351
$785$	24.2655	0.866073
$786$	29.3412	1.04656
$787$	−7.70296	−0.274581	−0.137290	−	0.990531i	$-0.543839\pi$
$787$	−7.70296	−0.274581	−0.137290	+	0.990531i	$0.543839\pi$
$788$	3.42352	0.121958
$789$	89.9888	3.20369
$790$	−24.3193	−0.865244
$791$	21.4284	0.761906
$792$	15.3203	0.544383
$793$	−1.56108	−0.0554357
$794$	−28.6504	−1.01676
$795$	44.8767	1.59161
$796$	20.7544	0.735619
$797$	5.59061	0.198030	0.0990148	−	0.995086i	$-0.468431\pi$
$797$	5.59061	0.198030	0.0990148	+	0.995086i	$0.468431\pi$
$798$	24.3123	0.860647
$799$	41.1093	1.45434
$800$	2.53078	0.0894765
$801$	−60.9905	−2.15499
$802$	−16.2022	−0.572118
$803$	−4.61708	−0.162933
$804$	9.07539	0.320064
$805$	4.45291	0.156944
$806$	−1.81144	−0.0638054
$807$	37.0066	1.30269
$808$	−1.94659	−0.0684807
$809$	−19.8905	−0.699311	−0.349656	−	0.936878i	$-0.613701\pi$
$809$	−19.8905	−0.699311	−0.349656	+	0.936878i	$0.613701\pi$
$810$	−25.2529	−0.887298
$811$	45.3870	1.59375	0.796877	−	0.604141i	$-0.206484\pi$
$811$	45.3870	1.59375	0.796877	+	0.604141i	$0.206484\pi$
$812$	−20.4643	−0.718155
$813$	13.6080	0.477252
$814$	−23.3341	−0.817860
$815$	−30.5234	−1.06919
$816$	−10.9006	−0.381598
$817$	−27.2607	−0.953730
$818$	1.44491	0.0505199
$819$	4.71860	0.164881
$820$	−11.8697	−0.414507
$821$	−44.4262	−1.55048	−0.775242	−	0.631664i	$-0.782372\pi$
$821$	−44.4262	−1.55048	−0.775242	+	0.631664i	$0.782372\pi$
$822$	7.01293	0.244604
$823$	−41.5587	−1.44864	−0.724322	−	0.689462i	$-0.757847\pi$
$823$	−41.5587	−1.44864	−0.724322	+	0.689462i	$0.757847\pi$
$824$	−14.7599	−0.514186
$825$	−17.9760	−0.625844
$826$	25.8142	0.898189
$827$	−34.3142	−1.19322	−0.596611	−	0.802530i	$-0.703487\pi$
$827$	−34.3142	−1.19322	−0.596611	+	0.802530i	$0.703487\pi$
$828$	7.39889	0.257129
$829$	23.7097	0.823472	0.411736	−	0.911303i	$-0.364923\pi$
$829$	23.7097	0.823472	0.411736	+	0.911303i	$0.364923\pi$
$830$	−17.3832	−0.603380
$831$	−56.4998	−1.95996
$832$	0.272260	0.00943893
$833$	−1.26587	−0.0438600
$834$	−34.1899	−1.18390
$835$	−36.1512	−1.25106
$836$	−6.89093	−0.238328
$837$	−77.3351	−2.67309
$838$	32.9567	1.13847
$839$	−14.8177	−0.511564	−0.255782	−	0.966735i	$-0.582333\pi$
$839$	−14.8177	−0.511564	−0.255782	+	0.966735i	$0.582333\pi$
$840$	12.6264	0.435653
$841$	34.0909	1.17555
$842$	−35.1379	−1.21093
$843$	87.6147	3.01761
$844$	17.2684	0.594403
$845$	−20.3114	−0.698734
$846$	−79.1211	−2.72024
$847$	−14.9770	−0.514615
$848$	−9.15701	−0.314453
$849$	−43.1876	−1.48219
$850$	8.84541	0.303395
$851$	−11.2691	−0.386301
$852$	32.6083	1.11714
$853$	−44.7255	−1.53137	−0.765686	−	0.643215i	$-0.777600\pi$
$853$	−44.7255	−1.53137	−0.765686	+	0.643215i	$0.777600\pi$
$854$	14.7725	0.505505
$855$	31.9832	1.09380
$856$	8.76868	0.299707
$857$	−45.9644	−1.57012	−0.785058	−	0.619422i	$-0.787367\pi$
$857$	−45.9644	−1.57012	−0.785058	+	0.619422i	$0.787367\pi$
$858$	−1.93385	−0.0660207
$859$	−20.9376	−0.714382	−0.357191	−	0.934031i	$-0.616265\pi$
$859$	−20.9376	−0.714382	−0.357191	+	0.934031i	$0.616265\pi$
$860$	−14.1576	−0.482771
$861$	60.6959	2.06851
$862$	−3.44601	−0.117372
$863$	27.1193	0.923152	0.461576	−	0.887101i	$-0.347284\pi$
$863$	27.1193	0.923152	0.461576	+	0.887101i	$0.347284\pi$
$864$	11.6235	0.395439
$865$	19.8023	0.673298
$866$	−22.6597	−0.770010
$867$	14.9204	0.506724
$868$	17.1417	0.581826
$869$	−35.2471	−1.19568
$870$	−38.9270	−1.31975
$871$	−0.792250	−0.0268444
$872$	−16.3775	−0.554613
$873$	−67.0706	−2.27000
$874$	−3.32796	−0.112570
$875$	−30.4883	−1.03069
$876$	−6.32270	−0.213624
$877$	41.1367	1.38909	0.694544	−	0.719451i	$-0.255606\pi$
$877$	41.1367	1.38909	0.694544	+	0.719451i	$0.255606\pi$
$878$	27.4365	0.925936
$879$	47.6799	1.60820
$880$	−3.57875	−0.120640
$881$	25.4253	0.856600	0.428300	−	0.903637i	$-0.359113\pi$
$881$	25.4253	0.856600	0.428300	+	0.903637i	$0.359113\pi$
$882$	2.43637	0.0820367
$883$	−22.5281	−0.758131	−0.379066	−	0.925370i	$-0.623755\pi$
$883$	−22.5281	−0.758131	−0.379066	+	0.925370i	$0.623755\pi$
$884$	0.951587	0.0320053
$885$	49.1036	1.65060
$886$	−10.7107	−0.359832
$887$	−10.1145	−0.339612	−0.169806	−	0.985477i	$-0.554314\pi$
$887$	−10.1145	−0.339612	−0.169806	+	0.985477i	$0.554314\pi$
$888$	−31.9541	−1.07231
$889$	27.0663	0.907774
$890$	14.2471	0.477564
$891$	−36.6002	−1.22615
$892$	19.1328	0.640613
$893$	35.5879	1.19090
$894$	−64.4677	−2.15612
$895$	−6.64565	−0.222140
$896$	−2.57640	−0.0860714
$897$	−0.933949	−0.0311836
$898$	23.3758	0.780060
$899$	−52.8474	−1.76256
$900$	−17.0243	−0.567477
$901$	−32.0050	−1.06624
$902$	−17.2033	−0.572806
$903$	72.3953	2.40916
$904$	−8.31720	−0.276626
$905$	12.7401	0.423496
$906$	−34.7295	−1.15381
$907$	−7.25000	−0.240732	−0.120366	−	0.992730i	$-0.538407\pi$
$907$	−7.25000	−0.240732	−0.120366	+	0.992730i	$0.538407\pi$
$908$	−9.58723	−0.318163
$909$	13.0945	0.434318
$910$	−1.10224	−0.0365390
$911$	23.8429	0.789950	0.394975	−	0.918692i	$-0.370753\pi$
$911$	23.8429	0.789950	0.394975	+	0.918692i	$0.370753\pi$
$912$	−9.43656	−0.312476
$913$	−25.1942	−0.833808
$914$	−11.1400	−0.368479
$915$	28.1002	0.928964
$916$	−15.4499	−0.510478
$917$	24.2383	0.800420
$918$	40.6257	1.34085
$919$	52.3672	1.72743	0.863717	−	0.503977i	$-0.168130\pi$
$919$	52.3672	1.72743	0.863717	+	0.503977i	$0.168130\pi$
$920$	−1.72835	−0.0569820
$921$	57.8494	1.90620
$922$	22.5473	0.742557
$923$	−2.84659	−0.0936966
$924$	18.3000	0.602027
$925$	25.9295	0.852555
$926$	−21.6006	−0.709840
$927$	99.2885	3.26106
$928$	7.94298	0.260741
$929$	−43.7670	−1.43595	−0.717974	−	0.696070i	$-0.754930\pi$
$929$	−43.7670	−1.43595	−0.717974	+	0.696070i	$0.754930\pi$
$930$	32.6068	1.06922
$931$	−1.09585	−0.0359152
$932$	12.3262	0.403757
$933$	48.3940	1.58435
$934$	−20.3649	−0.666360
$935$	−12.5082	−0.409063
$936$	−1.83147	−0.0598635
$937$	28.3684	0.926756	0.463378	−	0.886161i	$-0.346637\pi$
$937$	28.3684	0.926756	0.463378	+	0.886161i	$0.346637\pi$
$938$	7.49705	0.244787
$939$	7.18910	0.234607
$940$	18.4823	0.602827
$941$	−22.7228	−0.740743	−0.370371	−	0.928884i	$-0.620770\pi$
$941$	−22.7228	−0.740743	−0.370371	+	0.928884i	$0.620770\pi$
$942$	48.1611	1.56917
$943$	−8.30826	−0.270554
$944$	−10.0195	−0.326106
$945$	−47.0575	−1.53078
$946$	−20.5193	−0.667139
$947$	−35.7751	−1.16253	−0.581267	−	0.813713i	$-0.697443\pi$
$947$	−35.7751	−1.16253	−0.581267	+	0.813713i	$0.697443\pi$
$948$	−48.2680	−1.56767
$949$	0.551950	0.0179171
$950$	7.65738	0.248438
$951$	−35.4752	−1.15036
$952$	−9.00485	−0.291849
$953$	37.2108	1.20538	0.602688	−	0.797977i	$-0.294097\pi$
$953$	37.2108	1.20538	0.602688	+	0.797977i	$0.294097\pi$
$954$	61.5984	1.99432
$955$	5.62735	0.182097
$956$	−25.2462	−0.816520
$957$	−56.4186	−1.82376
$958$	2.02262	0.0653479
$959$	5.79329	0.187075
$960$	−4.90081	−0.158173
$961$	13.2671	0.427970
$962$	2.78949	0.0899366
$963$	−58.9862	−1.90080
$964$	−16.5545	−0.533184
$965$	−7.49997	−0.241432
$966$	8.83795	0.284356
$967$	39.4358	1.26817	0.634085	−	0.773263i	$-0.281377\pi$
$967$	39.4358	1.26817	0.634085	+	0.773263i	$0.281377\pi$
$968$	5.81315	0.186842
$969$	−32.9821	−1.05954
$970$	15.6674	0.503050
$971$	17.2603	0.553911	0.276955	−	0.960883i	$-0.410675\pi$
$971$	17.2603	0.553911	0.276955	+	0.960883i	$0.410675\pi$
$972$	−15.2505	−0.489160
$973$	−28.2438	−0.905454
$974$	27.9143	0.894431
$975$	2.14895	0.0688214
$976$	−5.73379	−0.183534
$977$	−5.50737	−0.176196	−0.0880982	−	0.996112i	$-0.528079\pi$
$977$	−5.50737	−0.176196	−0.0880982	+	0.996112i	$0.528079\pi$
$978$	−60.5816	−1.93719
$979$	20.6490	0.659944
$980$	−0.569124	−0.0181800
$981$	110.170	3.51746
$982$	−13.4879	−0.430416
$983$	32.8004	1.04617	0.523086	−	0.852280i	$-0.324781\pi$
$983$	32.8004	1.04617	0.523086	+	0.852280i	$0.324781\pi$
$984$	−23.5584	−0.751016
$985$	5.37963	0.171409
$986$	27.7618	0.884115
$987$	−94.5098	−3.00828
$988$	0.823779	0.0262079
$989$	−9.90972	−0.315111
$990$	24.0740	0.765121
$991$	−4.37186	−0.138877	−0.0694383	−	0.997586i	$-0.522121\pi$
$991$	−4.37186	−0.138877	−0.0694383	+	0.997586i	$0.522121\pi$
$992$	−6.65335	−0.211244
$993$	44.7500	1.42010
$994$	26.9372	0.854397
$995$	32.6129	1.03390
$996$	−34.5014	−1.09322
$997$	−34.1601	−1.08186	−0.540931	−	0.841067i	$-0.681928\pi$
$997$	−34.1601	−1.08186	−0.540931	+	0.841067i	$0.681928\pi$
$998$	37.4379	1.18508
$999$	119.090	3.76785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.11880 q^{3} +1.00000 q^{4} +1.57138 q^{5} +3.11880 q^{6} +2.57640 q^{7} -1.00000 q^{8} +6.72691 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.11880 q^{3} +1.00000 q^{4} +1.57138 q^{5} +3.11880 q^{6} +2.57640 q^{7} -1.00000 q^{8} +6.72691 q^{9} -1.57138 q^{10} -2.27747 q^{11} -3.11880 q^{12} +0.272260 q^{13} -2.57640 q^{14} -4.90081 q^{15} +1.00000 q^{16} +3.49514 q^{17} -6.72691 q^{18} +3.02570 q^{19} +1.57138 q^{20} -8.03526 q^{21} +2.27747 q^{22} +1.09989 q^{23} +3.11880 q^{24} -2.53078 q^{25} -0.272260 q^{26} -11.6235 q^{27} +2.57640 q^{28} -7.94298 q^{29} +4.90081 q^{30} +6.65335 q^{31} -1.00000 q^{32} +7.10296 q^{33} -3.49514 q^{34} +4.04849 q^{35} +6.72691 q^{36} -10.2457 q^{37} -3.02570 q^{38} -0.849126 q^{39} -1.57138 q^{40} -7.55369 q^{41} +8.03526 q^{42} -9.00970 q^{43} -2.27747 q^{44} +10.5705 q^{45} -1.09989 q^{46} +11.7619 q^{47} -3.11880 q^{48} -0.362182 q^{49} +2.53078 q^{50} -10.9006 q^{51} +0.272260 q^{52} -9.15701 q^{53} +11.6235 q^{54} -3.57875 q^{55} -2.57640 q^{56} -9.43656 q^{57} +7.94298 q^{58} -10.0195 q^{59} -4.90081 q^{60} -5.73379 q^{61} -6.65335 q^{62} +17.3312 q^{63} +1.00000 q^{64} +0.427824 q^{65} -7.10296 q^{66} -2.90990 q^{67} +3.49514 q^{68} -3.43035 q^{69} -4.04849 q^{70} -10.4554 q^{71} -6.72691 q^{72} +2.02729 q^{73} +10.2457 q^{74} +7.89299 q^{75} +3.02570 q^{76} -5.86765 q^{77} +0.849126 q^{78} +15.4765 q^{79} +1.57138 q^{80} +16.0706 q^{81} +7.55369 q^{82} +11.0624 q^{83} -8.03526 q^{84} +5.49217 q^{85} +9.00970 q^{86} +24.7726 q^{87} +2.27747 q^{88} -9.06665 q^{89} -10.5705 q^{90} +0.701451 q^{91} +1.09989 q^{92} -20.7505 q^{93} -11.7619 q^{94} +4.75452 q^{95} +3.11880 q^{96} -9.97049 q^{97} +0.362182 q^{98} -15.3203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 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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