LMFDB - Embedded newform 4006.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.77148 q^{3} +1.00000 q^{4} -2.30505 q^{5} -1.77148 q^{6} +0.622882 q^{7} +1.00000 q^{8} +0.138156 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.77148 q^{3} +1.00000 q^{4} -2.30505 q^{5} -1.77148 q^{6} +0.622882 q^{7} +1.00000 q^{8} +0.138156 q^{9} -2.30505 q^{10} +3.36260 q^{11} -1.77148 q^{12} +1.06080 q^{13} +0.622882 q^{14} +4.08336 q^{15} +1.00000 q^{16} -5.10012 q^{17} +0.138156 q^{18} -4.45963 q^{19} -2.30505 q^{20} -1.10343 q^{21} +3.36260 q^{22} +4.96248 q^{23} -1.77148 q^{24} +0.313245 q^{25} +1.06080 q^{26} +5.06971 q^{27} +0.622882 q^{28} +1.99470 q^{29} +4.08336 q^{30} +5.21853 q^{31} +1.00000 q^{32} -5.95679 q^{33} -5.10012 q^{34} -1.43577 q^{35} +0.138156 q^{36} -3.14244 q^{37} -4.45963 q^{38} -1.87919 q^{39} -2.30505 q^{40} +3.72343 q^{41} -1.10343 q^{42} +3.30448 q^{43} +3.36260 q^{44} -0.318456 q^{45} +4.96248 q^{46} -7.37894 q^{47} -1.77148 q^{48} -6.61202 q^{49} +0.313245 q^{50} +9.03479 q^{51} +1.06080 q^{52} -2.35587 q^{53} +5.06971 q^{54} -7.75095 q^{55} +0.622882 q^{56} +7.90016 q^{57} +1.99470 q^{58} +0.261997 q^{59} +4.08336 q^{60} -6.12890 q^{61} +5.21853 q^{62} +0.0860550 q^{63} +1.00000 q^{64} -2.44519 q^{65} -5.95679 q^{66} -3.18890 q^{67} -5.10012 q^{68} -8.79096 q^{69} -1.43577 q^{70} +9.01056 q^{71} +0.138156 q^{72} +11.9508 q^{73} -3.14244 q^{74} -0.554908 q^{75} -4.45963 q^{76} +2.09450 q^{77} -1.87919 q^{78} -4.23178 q^{79} -2.30505 q^{80} -9.39538 q^{81} +3.72343 q^{82} -10.9019 q^{83} -1.10343 q^{84} +11.7560 q^{85} +3.30448 q^{86} -3.53358 q^{87} +3.36260 q^{88} -16.4403 q^{89} -0.318456 q^{90} +0.660753 q^{91} +4.96248 q^{92} -9.24454 q^{93} -7.37894 q^{94} +10.2797 q^{95} -1.77148 q^{96} +4.21648 q^{97} -6.61202 q^{98} +0.464563 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9	\( 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9} - 23 q^{10} - 32 q^{11} - 13 q^{12} - 8 q^{13} - 18 q^{14} - 14 q^{15} + 31 q^{16} - 30 q^{17} + 20 q^{18} - 38 q^{19} - 23 q^{20} - 16 q^{21} - 32 q^{22} - 24 q^{23} - 13 q^{24} + 40 q^{25} - 8 q^{26} - 28 q^{27} - 18 q^{28} - 7 q^{29} - 14 q^{30} - 32 q^{31} + 31 q^{32} - 9 q^{33} - 30 q^{34} - 14 q^{35} + 20 q^{36} + 11 q^{37} - 38 q^{38} - 9 q^{39} - 23 q^{40} - 76 q^{41} - 16 q^{42} - 33 q^{43} - 32 q^{44} - 40 q^{45} - 24 q^{46} - 96 q^{47} - 13 q^{48} + 15 q^{49} + 40 q^{50} - 55 q^{51} - 8 q^{52} - 28 q^{53} - 28 q^{54} - 52 q^{55} - 18 q^{56} - 21 q^{57} - 7 q^{58} - 72 q^{59} - 14 q^{60} - 9 q^{61} - 32 q^{62} - 54 q^{63} + 31 q^{64} - 38 q^{65} - 9 q^{66} - 4 q^{67} - 30 q^{68} - 17 q^{69} - 14 q^{70} - 61 q^{71} + 20 q^{72} - 62 q^{73} + 11 q^{74} - 63 q^{75} - 38 q^{76} - 9 q^{77} - 9 q^{78} - 30 q^{79} - 23 q^{80} - 13 q^{81} - 76 q^{82} - 90 q^{83} - 16 q^{84} + 26 q^{85} - 33 q^{86} - 34 q^{87} - 32 q^{88} - 99 q^{89} - 40 q^{90} - 47 q^{91} - 24 q^{92} - 6 q^{93} - 96 q^{94} - 24 q^{95} - 13 q^{96} - 46 q^{97} + 15 q^{98} - 48 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9 - 23 * q^10 - 32 * q^11 - 13 * q^12 - 8 * q^13 - 18 * q^14 - 14 * q^15 + 31 * q^16 - 30 * q^17 + 20 * q^18 - 38 * q^19 - 23 * q^20 - 16 * q^21 - 32 * q^22 - 24 * q^23 - 13 * q^24 + 40 * q^25 - 8 * q^26 - 28 * q^27 - 18 * q^28 - 7 * q^29 - 14 * q^30 - 32 * q^31 + 31 * q^32 - 9 * q^33 - 30 * q^34 - 14 * q^35 + 20 * q^36 + 11 * q^37 - 38 * q^38 - 9 * q^39 - 23 * q^40 - 76 * q^41 - 16 * q^42 - 33 * q^43 - 32 * q^44 - 40 * q^45 - 24 * q^46 - 96 * q^47 - 13 * q^48 + 15 * q^49 + 40 * q^50 - 55 * q^51 - 8 * q^52 - 28 * q^53 - 28 * q^54 - 52 * q^55 - 18 * q^56 - 21 * q^57 - 7 * q^58 - 72 * q^59 - 14 * q^60 - 9 * q^61 - 32 * q^62 - 54 * q^63 + 31 * q^64 - 38 * q^65 - 9 * q^66 - 4 * q^67 - 30 * q^68 - 17 * q^69 - 14 * q^70 - 61 * q^71 + 20 * q^72 - 62 * q^73 + 11 * q^74 - 63 * q^75 - 38 * q^76 - 9 * q^77 - 9 * q^78 - 30 * q^79 - 23 * q^80 - 13 * q^81 - 76 * q^82 - 90 * q^83 - 16 * q^84 + 26 * q^85 - 33 * q^86 - 34 * q^87 - 32 * q^88 - 99 * q^89 - 40 * q^90 - 47 * q^91 - 24 * q^92 - 6 * q^93 - 96 * q^94 - 24 * q^95 - 13 * q^96 - 46 * q^97 + 15 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.77148	−1.02277	−0.511383	−	0.859353i	$-0.670867\pi$
$3$	−1.77148	−1.02277	−0.511383	+	0.859353i	$0.670867\pi$
$4$	1.00000	0.500000
$5$	−2.30505	−1.03085	−0.515424	−	0.856935i	$-0.672366\pi$
$5$	−2.30505	−1.03085	−0.515424	+	0.856935i	$0.672366\pi$
$6$	−1.77148	−0.723205
$7$	0.622882	0.235427	0.117714	−	0.993048i	$-0.462443\pi$
$7$	0.622882	0.235427	0.117714	+	0.993048i	$0.462443\pi$
$8$	1.00000	0.353553
$9$	0.138156	0.0460520
$10$	−2.30505	−0.728920
$11$	3.36260	1.01386	0.506931	−	0.861987i	$-0.330780\pi$
$11$	3.36260	1.01386	0.506931	+	0.861987i	$0.330780\pi$
$12$	−1.77148	−0.511383
$13$	1.06080	0.294213	0.147106	−	0.989121i	$-0.453004\pi$
$13$	1.06080	0.294213	0.147106	+	0.989121i	$0.453004\pi$
$14$	0.622882	0.166472
$15$	4.08336	1.05432
$16$	1.00000	0.250000
$17$	−5.10012	−1.23696	−0.618481	−	0.785800i	$-0.712252\pi$
$17$	−5.10012	−1.23696	−0.618481	+	0.785800i	$0.712252\pi$
$18$	0.138156	0.0325637
$19$	−4.45963	−1.02311	−0.511554	−	0.859251i	$-0.670930\pi$
$19$	−4.45963	−1.02311	−0.511554	+	0.859251i	$0.670930\pi$
$20$	−2.30505	−0.515424
$21$	−1.10343	−0.240787
$22$	3.36260	0.716908
$23$	4.96248	1.03475	0.517375	−	0.855759i	$-0.326909\pi$
$23$	4.96248	1.03475	0.517375	+	0.855759i	$0.326909\pi$
$24$	−1.77148	−0.361603
$25$	0.313245	0.0626490
$26$	1.06080	0.208040
$27$	5.06971	0.975666
$28$	0.622882	0.117714
$29$	1.99470	0.370406	0.185203	−	0.982700i	$-0.440706\pi$
$29$	1.99470	0.370406	0.185203	+	0.982700i	$0.440706\pi$
$30$	4.08336	0.745515
$31$	5.21853	0.937276	0.468638	−	0.883390i	$-0.344745\pi$
$31$	5.21853	0.937276	0.468638	+	0.883390i	$0.344745\pi$
$32$	1.00000	0.176777
$33$	−5.95679	−1.03694
$34$	−5.10012	−0.874664
$35$	−1.43577	−0.242690
$36$	0.138156	0.0230260
$37$	−3.14244	−0.516614	−0.258307	−	0.966063i	$-0.583165\pi$
$37$	−3.14244	−0.516614	−0.258307	+	0.966063i	$0.583165\pi$
$38$	−4.45963	−0.723447
$39$	−1.87919	−0.300911
$40$	−2.30505	−0.364460
$41$	3.72343	0.581502	0.290751	−	0.956799i	$-0.406095\pi$
$41$	3.72343	0.581502	0.290751	+	0.956799i	$0.406095\pi$
$42$	−1.10343	−0.170262
$43$	3.30448	0.503928	0.251964	−	0.967737i	$-0.418923\pi$
$43$	3.30448	0.503928	0.251964	+	0.967737i	$0.418923\pi$
$44$	3.36260	0.506931
$45$	−0.318456	−0.0474727
$46$	4.96248	0.731678
$47$	−7.37894	−1.07633	−0.538165	−	0.842840i	$-0.680882\pi$
$47$	−7.37894	−1.07633	−0.538165	+	0.842840i	$0.680882\pi$
$48$	−1.77148	−0.255692
$49$	−6.61202	−0.944574
$50$	0.313245	0.0442995
$51$	9.03479	1.26512
$52$	1.06080	0.147106
$53$	−2.35587	−0.323603	−0.161802	−	0.986823i	$-0.551730\pi$
$53$	−2.35587	−0.323603	−0.161802	+	0.986823i	$0.551730\pi$
$54$	5.06971	0.689900
$55$	−7.75095	−1.04514
$56$	0.622882	0.0832362
$57$	7.90016	1.04640
$58$	1.99470	0.261917
$59$	0.261997	0.0341091	0.0170545	−	0.999855i	$-0.494571\pi$
$59$	0.261997	0.0341091	0.0170545	+	0.999855i	$0.494571\pi$
$60$	4.08336	0.527159
$61$	−6.12890	−0.784725	−0.392362	−	0.919811i	$-0.628342\pi$
$61$	−6.12890	−0.784725	−0.392362	+	0.919811i	$0.628342\pi$
$62$	5.21853	0.662754
$63$	0.0860550	0.0108419
$64$	1.00000	0.125000
$65$	−2.44519	−0.303289
$66$	−5.95679	−0.733230
$67$	−3.18890	−0.389586	−0.194793	−	0.980844i	$-0.562404\pi$
$67$	−3.18890	−0.389586	−0.194793	+	0.980844i	$0.562404\pi$
$68$	−5.10012	−0.618481
$69$	−8.79096	−1.05831
$70$	−1.43577	−0.171608
$71$	9.01056	1.06936	0.534678	−	0.845056i	$-0.320433\pi$
$71$	9.01056	1.06936	0.534678	+	0.845056i	$0.320433\pi$
$72$	0.138156	0.0162819
$73$	11.9508	1.39874	0.699368	−	0.714762i	$-0.253465\pi$
$73$	11.9508	1.39874	0.699368	+	0.714762i	$0.253465\pi$
$74$	−3.14244	−0.365301
$75$	−0.554908	−0.0640753
$76$	−4.45963	−0.511554
$77$	2.09450	0.238691
$78$	−1.87919	−0.212776
$79$	−4.23178	−0.476113	−0.238056	−	0.971251i	$-0.576510\pi$
$79$	−4.23178	−0.476113	−0.238056	+	0.971251i	$0.576510\pi$
$80$	−2.30505	−0.257712
$81$	−9.39538	−1.04393
$82$	3.72343	0.411184
$83$	−10.9019	−1.19664	−0.598320	−	0.801257i	$-0.704165\pi$
$83$	−10.9019	−1.19664	−0.598320	+	0.801257i	$0.704165\pi$
$84$	−1.10343	−0.120394
$85$	11.7560	1.27512
$86$	3.30448	0.356331
$87$	−3.53358	−0.378839
$88$	3.36260	0.358454
$89$	−16.4403	−1.74267	−0.871334	−	0.490690i	$-0.836745\pi$
$89$	−16.4403	−1.74267	−0.871334	+	0.490690i	$0.836745\pi$
$90$	−0.318456	−0.0335682
$91$	0.660753	0.0692658
$92$	4.96248	0.517375
$93$	−9.24454	−0.958614
$94$	−7.37894	−0.761080
$95$	10.2797	1.05467
$96$	−1.77148	−0.180801
$97$	4.21648	0.428119	0.214060	−	0.976821i	$-0.431331\pi$
$97$	4.21648	0.428119	0.214060	+	0.976821i	$0.431331\pi$
$98$	−6.61202	−0.667915
$99$	0.464563	0.0466904
$100$	0.313245	0.0313245
$101$	−6.30019	−0.626893	−0.313446	−	0.949606i	$-0.601484\pi$
$101$	−6.30019	−0.626893	−0.313446	+	0.949606i	$0.601484\pi$
$102$	9.03479	0.894577
$103$	−12.4368	−1.22544	−0.612719	−	0.790301i	$-0.709924\pi$
$103$	−12.4368	−1.22544	−0.612719	+	0.790301i	$0.709924\pi$
$104$	1.06080	0.104020
$105$	2.54345	0.248215
$106$	−2.35587	−0.228822
$107$	13.9031	1.34407	0.672034	−	0.740520i	$-0.265421\pi$
$107$	13.9031	1.34407	0.672034	+	0.740520i	$0.265421\pi$
$108$	5.06971	0.487833
$109$	−14.2353	−1.36350	−0.681748	−	0.731587i	$-0.738780\pi$
$109$	−14.2353	−1.36350	−0.681748	+	0.731587i	$0.738780\pi$
$110$	−7.75095	−0.739024
$111$	5.56678	0.528375
$112$	0.622882	0.0588569
$113$	−15.8448	−1.49055	−0.745276	−	0.666756i	$-0.767682\pi$
$113$	−15.8448	−1.49055	−0.745276	+	0.666756i	$0.767682\pi$
$114$	7.90016	0.739918
$115$	−11.4388	−1.06667
$116$	1.99470	0.185203
$117$	0.146556	0.0135491
$118$	0.261997	0.0241187
$119$	−3.17678	−0.291215
$120$	4.08336	0.372758
$121$	0.307066	0.0279151
$122$	−6.12890	−0.554884
$123$	−6.59600	−0.594741
$124$	5.21853	0.468638
$125$	10.8032	0.966267
$126$	0.0860550	0.00766639
$127$	0.532748	0.0472738	0.0236369	−	0.999721i	$-0.492475\pi$
$127$	0.532748	0.0472738	0.0236369	+	0.999721i	$0.492475\pi$
$128$	1.00000	0.0883883
$129$	−5.85383	−0.515401
$130$	−2.44519	−0.214458
$131$	−8.81545	−0.770210	−0.385105	−	0.922873i	$-0.625835\pi$
$131$	−8.81545	−0.770210	−0.385105	+	0.922873i	$0.625835\pi$
$132$	−5.95679	−0.518472
$133$	−2.77782	−0.240868
$134$	−3.18890	−0.275479
$135$	−11.6859	−1.00576
$136$	−5.10012	−0.437332
$137$	−2.07317	−0.177123	−0.0885616	−	0.996071i	$-0.528227\pi$
$137$	−2.07317	−0.177123	−0.0885616	+	0.996071i	$0.528227\pi$
$138$	−8.79096	−0.748336
$139$	18.1367	1.53833	0.769167	−	0.639048i	$-0.220671\pi$
$139$	18.1367	1.53833	0.769167	+	0.639048i	$0.220671\pi$
$140$	−1.43577	−0.121345
$141$	13.0717	1.10083
$142$	9.01056	0.756149
$143$	3.56704	0.298291
$144$	0.138156	0.0115130
$145$	−4.59788	−0.381833
$146$	11.9508	0.989055
$147$	11.7131	0.966079
$148$	−3.14244	−0.258307
$149$	3.40767	0.279168	0.139584	−	0.990210i	$-0.455424\pi$
$149$	3.40767	0.279168	0.139584	+	0.990210i	$0.455424\pi$
$150$	−0.554908	−0.0453081
$151$	−1.69757	−0.138147	−0.0690733	−	0.997612i	$-0.522004\pi$
$151$	−1.69757	−0.138147	−0.0690733	+	0.997612i	$0.522004\pi$
$152$	−4.45963	−0.361724
$153$	−0.704613	−0.0569646
$154$	2.09450	0.168780
$155$	−12.0290	−0.966189
$156$	−1.87919	−0.150456
$157$	−13.7420	−1.09673	−0.548367	−	0.836238i	$-0.684750\pi$
$157$	−13.7420	−1.09673	−0.548367	+	0.836238i	$0.684750\pi$
$158$	−4.23178	−0.336662
$159$	4.17338	0.330970
$160$	−2.30505	−0.182230
$161$	3.09104	0.243608
$162$	−9.39538	−0.738171
$163$	8.20445	0.642622	0.321311	−	0.946974i	$-0.395876\pi$
$163$	8.20445	0.642622	0.321311	+	0.946974i	$0.395876\pi$
$164$	3.72343	0.290751
$165$	13.7307	1.06893
$166$	−10.9019	−0.846153
$167$	−9.75794	−0.755092	−0.377546	−	0.925991i	$-0.623232\pi$
$167$	−9.75794	−0.755092	−0.377546	+	0.925991i	$0.623232\pi$
$168$	−1.10343	−0.0851312
$169$	−11.8747	−0.913439
$170$	11.7560	0.901646
$171$	−0.616125	−0.0471162
$172$	3.30448	0.251964
$173$	−19.6157	−1.49135	−0.745677	−	0.666308i	$-0.767874\pi$
$173$	−19.6157	−1.49135	−0.745677	+	0.666308i	$0.767874\pi$
$174$	−3.53358	−0.267880
$175$	0.195115	0.0147493
$176$	3.36260	0.253465
$177$	−0.464123	−0.0348856
$178$	−16.4403	−1.23225
$179$	−6.48249	−0.484524	−0.242262	−	0.970211i	$-0.577889\pi$
$179$	−6.48249	−0.484524	−0.242262	+	0.970211i	$0.577889\pi$
$180$	−0.318456	−0.0237363
$181$	3.35239	0.249181	0.124591	−	0.992208i	$-0.460238\pi$
$181$	3.35239	0.249181	0.124591	+	0.992208i	$0.460238\pi$
$182$	0.660753	0.0489783
$183$	10.8572	0.802590
$184$	4.96248	0.365839
$185$	7.24347	0.532551
$186$	−9.24454	−0.677843
$187$	−17.1497	−1.25411
$188$	−7.37894	−0.538165
$189$	3.15783	0.229699
$190$	10.2797	0.745765
$191$	−12.1757	−0.881004	−0.440502	−	0.897752i	$-0.645200\pi$
$191$	−12.1757	−0.881004	−0.440502	+	0.897752i	$0.645200\pi$
$192$	−1.77148	−0.127846
$193$	10.4291	0.750706	0.375353	−	0.926882i	$-0.377522\pi$
$193$	10.4291	0.750706	0.375353	+	0.926882i	$0.377522\pi$
$194$	4.21648	0.302726
$195$	4.33162	0.310194
$196$	−6.61202	−0.472287
$197$	−18.6075	−1.32573	−0.662866	−	0.748738i	$-0.730660\pi$
$197$	−18.6075	−1.32573	−0.662866	+	0.748738i	$0.730660\pi$
$198$	0.464563	0.0330151
$199$	−18.5075	−1.31197	−0.655983	−	0.754776i	$-0.727746\pi$
$199$	−18.5075	−1.31197	−0.655983	+	0.754776i	$0.727746\pi$
$200$	0.313245	0.0221498
$201$	5.64909	0.398456
$202$	−6.30019	−0.443280
$203$	1.24246	0.0872038
$204$	9.03479	0.632562
$205$	−8.58269	−0.599441
$206$	−12.4368	−0.866515
$207$	0.685597	0.0476523
$208$	1.06080	0.0735532
$209$	−14.9959	−1.03729
$210$	2.54345	0.175515
$211$	−23.2754	−1.60234	−0.801171	−	0.598436i	$-0.795789\pi$
$211$	−23.2754	−1.60234	−0.801171	+	0.598436i	$0.795789\pi$
$212$	−2.35587	−0.161802
$213$	−15.9621	−1.09370
$214$	13.9031	0.950399
$215$	−7.61698	−0.519474
$216$	5.06971	0.344950
$217$	3.25053	0.220660
$218$	−14.2353	−0.964138
$219$	−21.1707	−1.43058
$220$	−7.75095	−0.522569
$221$	−5.41021	−0.363930
$222$	5.56678	0.373618
$223$	15.2495	1.02118	0.510590	−	0.859824i	$-0.329427\pi$
$223$	15.2495	1.02118	0.510590	+	0.859824i	$0.329427\pi$
$224$	0.622882	0.0416181
$225$	0.0432767	0.00288511
$226$	−15.8448	−1.05398
$227$	−20.7568	−1.37768	−0.688840	−	0.724914i	$-0.741880\pi$
$227$	−20.7568	−1.37768	−0.688840	+	0.724914i	$0.741880\pi$
$228$	7.90016	0.523201
$229$	4.16386	0.275156	0.137578	−	0.990491i	$-0.456068\pi$
$229$	4.16386	0.275156	0.137578	+	0.990491i	$0.456068\pi$
$230$	−11.4388	−0.754249
$231$	−3.71038	−0.244125
$232$	1.99470	0.130958
$233$	6.12585	0.401318	0.200659	−	0.979661i	$-0.435692\pi$
$233$	6.12585	0.401318	0.200659	+	0.979661i	$0.435692\pi$
$234$	0.146556	0.00958066
$235$	17.0088	1.10953
$236$	0.261997	0.0170545
$237$	7.49653	0.486952
$238$	−3.17678	−0.205920
$239$	−10.3640	−0.670392	−0.335196	−	0.942148i	$-0.608803\pi$
$239$	−10.3640	−0.670392	−0.335196	+	0.942148i	$0.608803\pi$
$240$	4.08336	0.263579
$241$	−15.2730	−0.983817	−0.491909	−	0.870647i	$-0.663701\pi$
$241$	−15.2730	−0.983817	−0.491909	+	0.870647i	$0.663701\pi$
$242$	0.307066	0.0197389
$243$	1.43464	0.0920319
$244$	−6.12890	−0.392362
$245$	15.2410	0.973713
$246$	−6.59600	−0.420546
$247$	−4.73077	−0.301012
$248$	5.21853	0.331377
$249$	19.3126	1.22388
$250$	10.8032	0.683254
$251$	7.53042	0.475316	0.237658	−	0.971349i	$-0.423620\pi$
$251$	7.53042	0.475316	0.237658	+	0.971349i	$0.423620\pi$
$252$	0.0860550	0.00542096
$253$	16.6868	1.04909
$254$	0.532748	0.0334276
$255$	−20.8256	−1.30415
$256$	1.00000	0.0625000
$257$	−21.3949	−1.33458	−0.667289	−	0.744799i	$-0.732545\pi$
$257$	−21.3949	−1.33458	−0.667289	+	0.744799i	$0.732545\pi$
$258$	−5.85383	−0.364444
$259$	−1.95737	−0.121625
$260$	−2.44519	−0.151644
$261$	0.275580	0.0170580
$262$	−8.81545	−0.544620
$263$	−10.1599	−0.626487	−0.313243	−	0.949673i	$-0.601416\pi$
$263$	−10.1599	−0.626487	−0.313243	+	0.949673i	$0.601416\pi$
$264$	−5.95679	−0.366615
$265$	5.43038	0.333586
$266$	−2.77782	−0.170319
$267$	29.1237	1.78234
$268$	−3.18890	−0.194793
$269$	4.84086	0.295152	0.147576	−	0.989051i	$-0.452853\pi$
$269$	4.84086	0.295152	0.147576	+	0.989051i	$0.452853\pi$
$270$	−11.6859	−0.711183
$271$	−10.1646	−0.617455	−0.308727	−	0.951151i	$-0.599903\pi$
$271$	−10.1646	−0.617455	−0.308727	+	0.951151i	$0.599903\pi$
$272$	−5.10012	−0.309240
$273$	−1.17051	−0.0708427
$274$	−2.07317	−0.125245
$275$	1.05332	0.0635174
$276$	−8.79096	−0.529154
$277$	28.6604	1.72204	0.861018	−	0.508574i	$-0.169827\pi$
$277$	28.6604	1.72204	0.861018	+	0.508574i	$0.169827\pi$
$278$	18.1367	1.08777
$279$	0.720972	0.0431634
$280$	−1.43577	−0.0858039
$281$	8.41729	0.502134	0.251067	−	0.967970i	$-0.419219\pi$
$281$	8.41729	0.502134	0.251067	+	0.967970i	$0.419219\pi$
$282$	13.0717	0.778407
$283$	−3.33782	−0.198413	−0.0992065	−	0.995067i	$-0.531630\pi$
$283$	−3.33782	−0.198413	−0.0992065	+	0.995067i	$0.531630\pi$
$284$	9.01056	0.534678
$285$	−18.2102	−1.07868
$286$	3.56704	0.210924
$287$	2.31926	0.136902
$288$	0.138156	0.00814093
$289$	9.01126	0.530074
$290$	−4.59788	−0.269997
$291$	−7.46944	−0.437866
$292$	11.9508	0.699368
$293$	−19.0607	−1.11354	−0.556768	−	0.830668i	$-0.687959\pi$
$293$	−19.0607	−1.11354	−0.556768	+	0.830668i	$0.687959\pi$
$294$	11.7131	0.683121
$295$	−0.603915	−0.0351613
$296$	−3.14244	−0.182651
$297$	17.0474	0.989191
$298$	3.40767	0.197401
$299$	5.26420	0.304436
$300$	−0.554908	−0.0320376
$301$	2.05830	0.118639
$302$	−1.69757	−0.0976844
$303$	11.1607	0.641165
$304$	−4.45963	−0.255777
$305$	14.1274	0.808932
$306$	−0.704613	−0.0402800
$307$	−7.05121	−0.402434	−0.201217	−	0.979547i	$-0.564490\pi$
$307$	−7.05121	−0.402434	−0.201217	+	0.979547i	$0.564490\pi$
$308$	2.09450	0.119345
$309$	22.0317	1.25334
$310$	−12.0290	−0.683199
$311$	−9.04391	−0.512833	−0.256417	−	0.966566i	$-0.582542\pi$
$311$	−9.04391	−0.512833	−0.256417	+	0.966566i	$0.582542\pi$
$312$	−1.87919	−0.106388
$313$	−13.9257	−0.787126	−0.393563	−	0.919298i	$-0.628758\pi$
$313$	−13.9257	−0.787126	−0.393563	+	0.919298i	$0.628758\pi$
$314$	−13.7420	−0.775508
$315$	−0.198361	−0.0111764
$316$	−4.23178	−0.238056
$317$	29.0300	1.63049	0.815243	−	0.579119i	$-0.196603\pi$
$317$	29.0300	1.63049	0.815243	+	0.579119i	$0.196603\pi$
$318$	4.17338	0.234031
$319$	6.70737	0.375541
$320$	−2.30505	−0.128856
$321$	−24.6292	−1.37467
$322$	3.09104	0.172257
$323$	22.7447	1.26555
$324$	−9.39538	−0.521966
$325$	0.332290	0.0184321
$326$	8.20445	0.454403
$327$	25.2176	1.39454
$328$	3.72343	0.205592
$329$	−4.59622	−0.253398
$330$	13.7307	0.755849
$331$	9.70840	0.533622	0.266811	−	0.963749i	$-0.414030\pi$
$331$	9.70840	0.533622	0.266811	+	0.963749i	$0.414030\pi$
$332$	−10.9019	−0.598320
$333$	−0.434147	−0.0237911
$334$	−9.75794	−0.533931
$335$	7.35057	0.401605
$336$	−1.10343	−0.0601968
$337$	29.6304	1.61407	0.807034	−	0.590504i	$-0.201071\pi$
$337$	29.6304	1.61407	0.807034	+	0.590504i	$0.201071\pi$
$338$	−11.8747	−0.645899
$339$	28.0688	1.52449
$340$	11.7560	0.637560
$341$	17.5478	0.950268
$342$	−0.616125	−0.0333162
$343$	−8.47869	−0.457806
$344$	3.30448	0.178166
$345$	20.2636	1.09095
$346$	−19.6157	−1.05455
$347$	26.5626	1.42595	0.712976	−	0.701188i	$-0.247347\pi$
$347$	26.5626	1.42595	0.712976	+	0.701188i	$0.247347\pi$
$348$	−3.53358	−0.189420
$349$	17.5713	0.940572	0.470286	−	0.882514i	$-0.344151\pi$
$349$	17.5713	0.940572	0.470286	+	0.882514i	$0.344151\pi$
$350$	0.195115	0.0104293
$351$	5.37795	0.287054
$352$	3.36260	0.179227
$353$	21.7784	1.15915	0.579574	−	0.814920i	$-0.303219\pi$
$353$	21.7784	1.15915	0.579574	+	0.814920i	$0.303219\pi$
$354$	−0.464123	−0.0246679
$355$	−20.7698	−1.10234
$356$	−16.4403	−0.871334
$357$	5.62761	0.297845
$358$	−6.48249	−0.342610
$359$	−11.5842	−0.611393	−0.305697	−	0.952129i	$-0.598889\pi$
$359$	−11.5842	−0.611393	−0.305697	+	0.952129i	$0.598889\pi$
$360$	−0.318456	−0.0167841
$361$	0.888282	0.0467517
$362$	3.35239	0.176198
$363$	−0.543962	−0.0285506
$364$	0.660753	0.0346329
$365$	−27.5472	−1.44188
$366$	10.8572	0.567517
$367$	9.79912	0.511510	0.255755	−	0.966742i	$-0.417676\pi$
$367$	9.79912	0.511510	0.255755	+	0.966742i	$0.417676\pi$
$368$	4.96248	0.258687
$369$	0.514415	0.0267794
$370$	7.24347	0.376570
$371$	−1.46743	−0.0761850
$372$	−9.24454	−0.479307
$373$	2.35560	0.121968	0.0609842	−	0.998139i	$-0.480576\pi$
$373$	2.35560	0.121968	0.0609842	+	0.998139i	$0.480576\pi$
$374$	−17.1497	−0.886788
$375$	−19.1377	−0.988266
$376$	−7.37894	−0.380540
$377$	2.11598	0.108978
$378$	3.15783	0.162421
$379$	−22.8214	−1.17225	−0.586127	−	0.810219i	$-0.699348\pi$
$379$	−22.8214	−1.17225	−0.586127	+	0.810219i	$0.699348\pi$
$380$	10.2797	0.527335
$381$	−0.943755	−0.0483501
$382$	−12.1757	−0.622964
$383$	−14.5936	−0.745697	−0.372848	−	0.927892i	$-0.621619\pi$
$383$	−14.5936	−0.745697	−0.372848	+	0.927892i	$0.621619\pi$
$384$	−1.77148	−0.0904007
$385$	−4.82793	−0.246054
$386$	10.4291	0.530829
$387$	0.456534	0.0232069
$388$	4.21648	0.214060
$389$	−25.0487	−1.27002	−0.635009	−	0.772505i	$-0.719004\pi$
$389$	−25.0487	−1.27002	−0.635009	+	0.772505i	$0.719004\pi$
$390$	4.33162	0.219340
$391$	−25.3093	−1.27994
$392$	−6.61202	−0.333957
$393$	15.6164	0.787745
$394$	−18.6075	−0.937434
$395$	9.75446	0.490800
$396$	0.464563	0.0233452
$397$	13.7573	0.690460	0.345230	−	0.938518i	$-0.387801\pi$
$397$	13.7573	0.690460	0.345230	+	0.938518i	$0.387801\pi$
$398$	−18.5075	−0.927699
$399$	4.92087	0.246352
$400$	0.313245	0.0156622
$401$	30.2787	1.51205	0.756024	−	0.654544i	$-0.227139\pi$
$401$	30.2787	1.51205	0.756024	+	0.654544i	$0.227139\pi$
$402$	5.64909	0.281751
$403$	5.53581	0.275758
$404$	−6.30019	−0.313446
$405$	21.6568	1.07614
$406$	1.24246	0.0616624
$407$	−10.5668	−0.523775
$408$	9.03479	0.447289
$409$	20.5843	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$409$	20.5843	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$410$	−8.58269	−0.423869
$411$	3.67260	0.181156
$412$	−12.4368	−0.612719
$413$	0.163193	0.00803021
$414$	0.685597	0.0336953
$415$	25.1294	1.23356
$416$	1.06080	0.0520100
$417$	−32.1289	−1.57336
$418$	−14.9959	−0.733475
$419$	14.0100	0.684435	0.342217	−	0.939621i	$-0.388822\pi$
$419$	14.0100	0.684435	0.342217	+	0.939621i	$0.388822\pi$
$420$	2.54345	0.124108
$421$	38.3830	1.87067	0.935337	−	0.353758i	$-0.115096\pi$
$421$	38.3830	1.87067	0.935337	+	0.353758i	$0.115096\pi$
$422$	−23.2754	−1.13303
$423$	−1.01945	−0.0495672
$424$	−2.35587	−0.114411
$425$	−1.59759	−0.0774944
$426$	−15.9621	−0.773364
$427$	−3.81758	−0.184746
$428$	13.9031	0.672034
$429$	−6.31896	−0.305082
$430$	−7.61698	−0.367324
$431$	2.21916	0.106893	0.0534465	−	0.998571i	$-0.482979\pi$
$431$	2.21916	0.106893	0.0534465	+	0.998571i	$0.482979\pi$
$432$	5.06971	0.243917
$433$	33.7492	1.62188	0.810942	−	0.585127i	$-0.198955\pi$
$433$	33.7492	1.62188	0.810942	+	0.585127i	$0.198955\pi$
$434$	3.25053	0.156030
$435$	8.14507	0.390526
$436$	−14.2353	−0.681748
$437$	−22.1308	−1.05866
$438$	−21.1707	−1.01157
$439$	−14.6749	−0.700396	−0.350198	−	0.936676i	$-0.613886\pi$
$439$	−14.6749	−0.700396	−0.350198	+	0.936676i	$0.613886\pi$
$440$	−7.75095	−0.369512
$441$	−0.913490	−0.0434995
$442$	−5.41021	−0.257337
$443$	11.1085	0.527779	0.263890	−	0.964553i	$-0.414995\pi$
$443$	11.1085	0.527779	0.263890	+	0.964553i	$0.414995\pi$
$444$	5.56678	0.264188
$445$	37.8957	1.79643
$446$	15.2495	0.722083
$447$	−6.03664	−0.285523
$448$	0.622882	0.0294284
$449$	−14.8139	−0.699113	−0.349556	−	0.936915i	$-0.613668\pi$
$449$	−14.8139	−0.699113	−0.349556	+	0.936915i	$0.613668\pi$
$450$	0.0432767	0.00204008
$451$	12.5204	0.589563
$452$	−15.8448	−0.745276
$453$	3.00723	0.141292
$454$	−20.7568	−0.974167
$455$	−1.52307	−0.0714025
$456$	7.90016	0.369959
$457$	−33.9864	−1.58982	−0.794909	−	0.606728i	$-0.792482\pi$
$457$	−33.9864	−1.58982	−0.794909	+	0.606728i	$0.792482\pi$
$458$	4.16386	0.194564
$459$	−25.8562	−1.20686
$460$	−11.4388	−0.533335
$461$	−9.26245	−0.431395	−0.215698	−	0.976460i	$-0.569203\pi$
$461$	−9.26245	−0.431395	−0.215698	+	0.976460i	$0.569203\pi$
$462$	−3.71038	−0.172622
$463$	10.0028	0.464871	0.232435	−	0.972612i	$-0.425331\pi$
$463$	10.0028	0.464871	0.232435	+	0.972612i	$0.425331\pi$
$464$	1.99470	0.0926016
$465$	21.3091	0.988186
$466$	6.12585	0.283774
$467$	−31.5251	−1.45881	−0.729404	−	0.684083i	$-0.760202\pi$
$467$	−31.5251	−1.45881	−0.729404	+	0.684083i	$0.760202\pi$
$468$	0.146556	0.00677455
$469$	−1.98631	−0.0917194
$470$	17.0088	0.784558
$471$	24.3438	1.12170
$472$	0.261997	0.0120594
$473$	11.1116	0.510914
$474$	7.49653	0.344327
$475$	−1.39696	−0.0640967
$476$	−3.17678	−0.145607
$477$	−0.325477	−0.0149026
$478$	−10.3640	−0.474039
$479$	−4.45903	−0.203738	−0.101869	−	0.994798i	$-0.532482\pi$
$479$	−4.45903	−0.203738	−0.101869	+	0.994798i	$0.532482\pi$
$480$	4.08336	0.186379
$481$	−3.33350	−0.151994
$482$	−15.2730	−0.695664
$483$	−5.47573	−0.249155
$484$	0.307066	0.0139575
$485$	−9.71920	−0.441326
$486$	1.43464	0.0650764
$487$	−10.8506	−0.491688	−0.245844	−	0.969309i	$-0.579065\pi$
$487$	−10.8506	−0.491688	−0.245844	+	0.969309i	$0.579065\pi$
$488$	−6.12890	−0.277442
$489$	−14.5341	−0.657253
$490$	15.2410	0.688519
$491$	19.1192	0.862837	0.431418	−	0.902152i	$-0.358013\pi$
$491$	19.1192	0.862837	0.431418	+	0.902152i	$0.358013\pi$
$492$	−6.59600	−0.297371
$493$	−10.1732	−0.458178
$494$	−4.73077	−0.212847
$495$	−1.07084	−0.0481307
$496$	5.21853	0.234319
$497$	5.61252	0.251756
$498$	19.3126	0.865417
$499$	17.9160	0.802030	0.401015	−	0.916071i	$-0.368657\pi$
$499$	17.9160	0.802030	0.401015	+	0.916071i	$0.368657\pi$
$500$	10.8032	0.483134
$501$	17.2860	0.772283
$502$	7.53042	0.336099
$503$	3.76010	0.167654	0.0838272	−	0.996480i	$-0.473286\pi$
$503$	3.76010	0.167654	0.0838272	+	0.996480i	$0.473286\pi$
$504$	0.0860550	0.00383319
$505$	14.5222	0.646231
$506$	16.6868	0.741820
$507$	21.0359	0.934235
$508$	0.532748	0.0236369
$509$	−6.81369	−0.302011	−0.151006	−	0.988533i	$-0.548251\pi$
$509$	−6.81369	−0.302011	−0.151006	+	0.988533i	$0.548251\pi$
$510$	−20.8256	−0.922174
$511$	7.44394	0.329301
$512$	1.00000	0.0441942
$513$	−22.6090	−0.998213
$514$	−21.3949	−0.943689
$515$	28.6675	1.26324
$516$	−5.85383	−0.257701
$517$	−24.8124	−1.09125
$518$	−1.95737	−0.0860019
$519$	34.7489	1.52531
$520$	−2.44519	−0.107229
$521$	7.03856	0.308365	0.154182	−	0.988042i	$-0.450726\pi$
$521$	7.03856	0.308365	0.154182	+	0.988042i	$0.450726\pi$
$522$	0.275580	0.0120618
$523$	36.9091	1.61392	0.806961	−	0.590605i	$-0.201111\pi$
$523$	36.9091	1.61392	0.806961	+	0.590605i	$0.201111\pi$
$524$	−8.81545	−0.385105
$525$	−0.345643	−0.0150851
$526$	−10.1599	−0.442993
$527$	−26.6151	−1.15937
$528$	−5.95679	−0.259236
$529$	1.62623	0.0707057
$530$	5.43038	0.235881
$531$	0.0361964	0.00157079
$532$	−2.77782	−0.120434
$533$	3.94981	0.171085
$534$	29.1237	1.26031
$535$	−32.0474	−1.38553
$536$	−3.18890	−0.137740
$537$	11.4836	0.495555
$538$	4.84086	0.208704
$539$	−22.2336	−0.957667
$540$	−11.6859	−0.502882
$541$	29.0850	1.25046	0.625231	−	0.780439i	$-0.285005\pi$
$541$	29.0850	1.25046	0.625231	+	0.780439i	$0.285005\pi$
$542$	−10.1646	−0.436606
$543$	−5.93871	−0.254854
$544$	−5.10012	−0.218666
$545$	32.8131	1.40556
$546$	−1.17051	−0.0500934
$547$	27.7115	1.18486	0.592429	−	0.805622i	$-0.298169\pi$
$547$	27.7115	1.18486	0.592429	+	0.805622i	$0.298169\pi$
$548$	−2.07317	−0.0885616
$549$	−0.846744	−0.0361382
$550$	1.05332	0.0449136
$551$	−8.89562	−0.378966
$552$	−8.79096	−0.374168
$553$	−2.63590	−0.112090
$554$	28.6604	1.21766
$555$	−12.8317	−0.544675
$556$	18.1367	0.769167
$557$	−9.70812	−0.411346	−0.205673	−	0.978621i	$-0.565938\pi$
$557$	−9.70812	−0.411346	−0.205673	+	0.978621i	$0.565938\pi$
$558$	0.720972	0.0305212
$559$	3.50539	0.148262
$560$	−1.43577	−0.0606725
$561$	30.3804	1.28266
$562$	8.41729	0.355062
$563$	−16.2619	−0.685357	−0.342678	−	0.939453i	$-0.611334\pi$
$563$	−16.2619	−0.685357	−0.342678	+	0.939453i	$0.611334\pi$
$564$	13.0717	0.550417
$565$	36.5230	1.53653
$566$	−3.33782	−0.140299
$567$	−5.85222	−0.245770
$568$	9.01056	0.378075
$569$	30.7118	1.28750	0.643752	−	0.765234i	$-0.277377\pi$
$569$	30.7118	1.28750	0.643752	+	0.765234i	$0.277377\pi$
$570$	−18.2102	−0.762743
$571$	11.7415	0.491367	0.245683	−	0.969350i	$-0.420988\pi$
$571$	11.7415	0.491367	0.245683	+	0.969350i	$0.420988\pi$
$572$	3.56704	0.149145
$573$	21.5691	0.901062
$574$	2.31926	0.0968040
$575$	1.55447	0.0648260
$576$	0.138156	0.00575650
$577$	23.7738	0.989716	0.494858	−	0.868974i	$-0.335220\pi$
$577$	23.7738	0.989716	0.494858	+	0.868974i	$0.335220\pi$
$578$	9.01126	0.374819
$579$	−18.4751	−0.767797
$580$	−4.59788	−0.190916
$581$	−6.79061	−0.281722
$582$	−7.46944	−0.309618
$583$	−7.92183	−0.328089
$584$	11.9508	0.494528
$585$	−0.337818	−0.0139671
$586$	−19.0607	−0.787389
$587$	21.2043	0.875197	0.437598	−	0.899170i	$-0.355829\pi$
$587$	21.2043	0.875197	0.437598	+	0.899170i	$0.355829\pi$
$588$	11.7131	0.483039
$589$	−23.2727	−0.958935
$590$	−0.603915	−0.0248628
$591$	32.9629	1.35591
$592$	−3.14244	−0.129153
$593$	−29.4501	−1.20937	−0.604685	−	0.796465i	$-0.706701\pi$
$593$	−29.4501	−1.20937	−0.604685	+	0.796465i	$0.706701\pi$
$594$	17.0474	0.699463
$595$	7.32262	0.300198
$596$	3.40767	0.139584
$597$	32.7858	1.34183
$598$	5.26420	0.215269
$599$	−23.1498	−0.945876	−0.472938	−	0.881096i	$-0.656807\pi$
$599$	−23.1498	−0.945876	−0.472938	+	0.881096i	$0.656807\pi$
$600$	−0.554908	−0.0226540
$601$	−21.7720	−0.888098	−0.444049	−	0.896002i	$-0.646458\pi$
$601$	−21.7720	−0.888098	−0.444049	+	0.896002i	$0.646458\pi$
$602$	2.05830	0.0838902
$603$	−0.440566	−0.0179412
$604$	−1.69757	−0.0690733
$605$	−0.707801	−0.0287762
$606$	11.1607	0.453372
$607$	−0.570471	−0.0231547	−0.0115774	−	0.999933i	$-0.503685\pi$
$607$	−0.570471	−0.0231547	−0.0115774	+	0.999933i	$0.503685\pi$
$608$	−4.45963	−0.180862
$609$	−2.20100	−0.0891892
$610$	14.1274	0.572002
$611$	−7.82758	−0.316670
$612$	−0.704613	−0.0284823
$613$	29.3860	1.18689	0.593444	−	0.804875i	$-0.297768\pi$
$613$	29.3860	1.18689	0.593444	+	0.804875i	$0.297768\pi$
$614$	−7.05121	−0.284564
$615$	15.2041	0.613088
$616$	2.09450	0.0843899
$617$	19.4783	0.784166	0.392083	−	0.919930i	$-0.371755\pi$
$617$	19.4783	0.784166	0.392083	+	0.919930i	$0.371755\pi$
$618$	22.0317	0.886243
$619$	10.2279	0.411093	0.205546	−	0.978647i	$-0.434103\pi$
$619$	10.2279	0.411093	0.205546	+	0.978647i	$0.434103\pi$
$620$	−12.0290	−0.483095
$621$	25.1584	1.00957
$622$	−9.04391	−0.362628
$623$	−10.2404	−0.410272
$624$	−1.87919	−0.0752278
$625$	−26.4681	−1.05872
$626$	−13.9257	−0.556582
$627$	26.5651	1.06091
$628$	−13.7420	−0.548367
$629$	16.0268	0.639031
$630$	−0.198361	−0.00790289
$631$	−40.3211	−1.60516	−0.802579	−	0.596545i	$-0.796540\pi$
$631$	−40.3211	−1.60516	−0.802579	+	0.596545i	$0.796540\pi$
$632$	−4.23178	−0.168331
$633$	41.2319	1.63882
$634$	29.0300	1.15293
$635$	−1.22801	−0.0487321
$636$	4.17338	0.165485
$637$	−7.01402	−0.277906
$638$	6.70737	0.265547
$639$	1.24486	0.0492460
$640$	−2.30505	−0.0911150
$641$	−19.5124	−0.770695	−0.385347	−	0.922772i	$-0.625918\pi$
$641$	−19.5124	−0.770695	−0.385347	+	0.922772i	$0.625918\pi$
$642$	−24.6292	−0.972037
$643$	−32.1379	−1.26740	−0.633698	−	0.773580i	$-0.718464\pi$
$643$	−32.1379	−1.26740	−0.633698	+	0.773580i	$0.718464\pi$
$644$	3.09104	0.121804
$645$	13.4934	0.531301
$646$	22.7447	0.894876
$647$	18.6841	0.734546	0.367273	−	0.930113i	$-0.380291\pi$
$647$	18.6841	0.734546	0.367273	+	0.930113i	$0.380291\pi$
$648$	−9.39538	−0.369085
$649$	0.880989	0.0345819
$650$	0.332290	0.0130335
$651$	−5.75826	−0.225684
$652$	8.20445	0.321311
$653$	−16.2014	−0.634010	−0.317005	−	0.948424i	$-0.602677\pi$
$653$	−16.2014	−0.634010	−0.317005	+	0.948424i	$0.602677\pi$
$654$	25.2176	0.986088
$655$	20.3200	0.793970
$656$	3.72343	0.145376
$657$	1.65108	0.0644146
$658$	−4.59622	−0.179179
$659$	1.65610	0.0645124	0.0322562	−	0.999480i	$-0.489731\pi$
$659$	1.65610	0.0645124	0.0322562	+	0.999480i	$0.489731\pi$
$660$	13.7307	0.534466
$661$	10.2241	0.397671	0.198835	−	0.980033i	$-0.436284\pi$
$661$	10.2241	0.397671	0.198835	+	0.980033i	$0.436284\pi$
$662$	9.70840	0.377328
$663$	9.58410	0.372215
$664$	−10.9019	−0.423076
$665$	6.40302	0.248298
$666$	−0.434147	−0.0168229
$667$	9.89866	0.383278
$668$	−9.75794	−0.377546
$669$	−27.0142	−1.04443
$670$	7.35057	0.283977
$671$	−20.6090	−0.795602
$672$	−1.10343	−0.0425656
$673$	−0.696375	−0.0268433	−0.0134216	−	0.999910i	$-0.504272\pi$
$673$	−0.696375	−0.0268433	−0.0134216	+	0.999910i	$0.504272\pi$
$674$	29.6304	1.14132
$675$	1.58806	0.0611245
$676$	−11.8747	−0.456719
$677$	−47.6850	−1.83268	−0.916341	−	0.400399i	$-0.868872\pi$
$677$	−47.6850	−1.83268	−0.916341	+	0.400399i	$0.868872\pi$
$678$	28.0688	1.07797
$679$	2.62637	0.100791
$680$	11.7560	0.450823
$681$	36.7704	1.40905
$682$	17.5478	0.671941
$683$	−36.5822	−1.39978	−0.699889	−	0.714251i	$-0.746767\pi$
$683$	−36.5822	−1.39978	−0.699889	+	0.714251i	$0.746767\pi$
$684$	−0.616125	−0.0235581
$685$	4.77877	0.182587
$686$	−8.47869	−0.323718
$687$	−7.37621	−0.281420
$688$	3.30448	0.125982
$689$	−2.49910	−0.0952082
$690$	20.2636	0.771421
$691$	−9.26350	−0.352400	−0.176200	−	0.984354i	$-0.556381\pi$
$691$	−9.26350	−0.352400	−0.176200	+	0.984354i	$0.556381\pi$
$692$	−19.6157	−0.745677
$693$	0.289368	0.0109922
$694$	26.5626	1.00830
$695$	−41.8060	−1.58579
$696$	−3.53358	−0.133940
$697$	−18.9900	−0.719296
$698$	17.5713	0.665085
$699$	−10.8518	−0.410454
$700$	0.195115	0.00737464
$701$	−36.8967	−1.39357	−0.696785	−	0.717280i	$-0.745387\pi$
$701$	−36.8967	−1.39357	−0.696785	+	0.717280i	$0.745387\pi$
$702$	5.37795	0.202977
$703$	14.0141	0.528552
$704$	3.36260	0.126733
$705$	−30.1309	−1.13479
$706$	21.7784	0.819641
$707$	−3.92428	−0.147588
$708$	−0.464123	−0.0174428
$709$	14.0542	0.527816	0.263908	−	0.964548i	$-0.414988\pi$
$709$	14.0542	0.527816	0.263908	+	0.964548i	$0.414988\pi$
$710$	−20.7698	−0.779475
$711$	−0.584646	−0.0219260
$712$	−16.4403	−0.616126
$713$	25.8969	0.969845
$714$	5.62761	0.210608
$715$	−8.22220	−0.307493
$716$	−6.48249	−0.242262
$717$	18.3597	0.685655
$718$	−11.5842	−0.432320
$719$	9.54353	0.355914	0.177957	−	0.984038i	$-0.443051\pi$
$719$	9.54353	0.355914	0.177957	+	0.984038i	$0.443051\pi$
$720$	−0.318456	−0.0118682
$721$	−7.74669	−0.288502
$722$	0.888282	0.0330584
$723$	27.0558	1.00622
$724$	3.35239	0.124591
$725$	0.624829	0.0232056
$726$	−0.543962	−0.0201883
$727$	40.0581	1.48567	0.742836	−	0.669473i	$-0.233480\pi$
$727$	40.0581	1.48567	0.742836	+	0.669473i	$0.233480\pi$
$728$	0.660753	0.0244891
$729$	25.6447	0.949804
$730$	−27.5472	−1.01957
$731$	−16.8533	−0.623340
$732$	10.8572	0.401295
$733$	−32.7988	−1.21145	−0.605725	−	0.795674i	$-0.707117\pi$
$733$	−32.7988	−1.21145	−0.605725	+	0.795674i	$0.707117\pi$
$734$	9.79912	0.361692
$735$	−26.9992	−0.995881
$736$	4.96248	0.182920
$737$	−10.7230	−0.394987
$738$	0.514415	0.0189359
$739$	−49.9396	−1.83706	−0.918529	−	0.395353i	$-0.870622\pi$
$739$	−49.9396	−1.83706	−0.918529	+	0.395353i	$0.870622\pi$
$740$	7.24347	0.266275
$741$	8.38048	0.307865
$742$	−1.46743	−0.0538710
$743$	−28.8497	−1.05839	−0.529197	−	0.848499i	$-0.677507\pi$
$743$	−28.8497	−1.05839	−0.529197	+	0.848499i	$0.677507\pi$
$744$	−9.24454	−0.338921
$745$	−7.85485	−0.287779
$746$	2.35560	0.0862446
$747$	−1.50617	−0.0551077
$748$	−17.1497	−0.627054
$749$	8.66003	0.316430
$750$	−19.1377	−0.698810
$751$	−15.9585	−0.582334	−0.291167	−	0.956672i	$-0.594043\pi$
$751$	−15.9585	−0.582334	−0.291167	+	0.956672i	$0.594043\pi$
$752$	−7.37894	−0.269082
$753$	−13.3400	−0.486138
$754$	2.11598	0.0770593
$755$	3.91299	0.142408
$756$	3.15783	0.114849
$757$	4.79577	0.174305	0.0871527	−	0.996195i	$-0.472223\pi$
$757$	4.79577	0.174305	0.0871527	+	0.996195i	$0.472223\pi$
$758$	−22.8214	−0.828909
$759$	−29.5605	−1.07298
$760$	10.2797	0.372882
$761$	−0.804919	−0.0291783	−0.0145891	−	0.999894i	$-0.504644\pi$
$761$	−0.804919	−0.0291783	−0.0145891	+	0.999894i	$0.504644\pi$
$762$	−0.943755	−0.0341887
$763$	−8.86693	−0.321005
$764$	−12.1757	−0.440502
$765$	1.62417	0.0587219
$766$	−14.5936	−0.527287
$767$	0.277926	0.0100353
$768$	−1.77148	−0.0639229
$769$	26.3923	0.951730	0.475865	−	0.879518i	$-0.342135\pi$
$769$	26.3923	0.951730	0.475865	+	0.879518i	$0.342135\pi$
$770$	−4.82793	−0.173987
$771$	37.9008	1.36496
$772$	10.4291	0.375353
$773$	33.8848	1.21875	0.609376	−	0.792882i	$-0.291420\pi$
$773$	33.8848	1.21875	0.609376	+	0.792882i	$0.291420\pi$
$774$	0.456534	0.0164098
$775$	1.63468	0.0587194
$776$	4.21648	0.151363
$777$	3.46745	0.124394
$778$	−25.0487	−0.898038
$779$	−16.6051	−0.594940
$780$	4.33162	0.155097
$781$	30.2989	1.08418
$782$	−25.3093	−0.905058
$783$	10.1125	0.361393
$784$	−6.61202	−0.236143
$785$	31.6761	1.13057
$786$	15.6164	0.557020
$787$	9.46180	0.337277	0.168638	−	0.985678i	$-0.446063\pi$
$787$	9.46180	0.337277	0.168638	+	0.985678i	$0.446063\pi$
$788$	−18.6075	−0.662866
$789$	17.9981	0.640750
$790$	9.75446	0.347048
$791$	−9.86944	−0.350917
$792$	0.464563	0.0165075
$793$	−6.50153	−0.230876
$794$	13.7573	0.488229
$795$	−9.61984	−0.341180
$796$	−18.5075	−0.655983
$797$	−37.6640	−1.33413	−0.667064	−	0.745000i	$-0.732449\pi$
$797$	−37.6640	−1.33413	−0.667064	+	0.745000i	$0.732449\pi$
$798$	4.92087	0.174197
$799$	37.6335	1.33138
$800$	0.313245	0.0110749
$801$	−2.27133	−0.0802534
$802$	30.2787	1.06918
$803$	40.1857	1.41812
$804$	5.64909	0.199228
$805$	−7.12500	−0.251123
$806$	5.53581	0.194991
$807$	−8.57551	−0.301872
$808$	−6.30019	−0.221640
$809$	−41.6702	−1.46505	−0.732523	−	0.680742i	$-0.761658\pi$
$809$	−41.6702	−1.46505	−0.732523	+	0.680742i	$0.761658\pi$
$810$	21.6568	0.760942
$811$	19.8293	0.696300	0.348150	−	0.937439i	$-0.386810\pi$
$811$	19.8293	0.696300	0.348150	+	0.937439i	$0.386810\pi$
$812$	1.24246	0.0436019
$813$	18.0064	0.631512
$814$	−10.5668	−0.370365
$815$	−18.9117	−0.662446
$816$	9.03479	0.316281
$817$	−14.7368	−0.515574
$818$	20.5843	0.719712
$819$	0.0912871	0.00318983
$820$	−8.58269	−0.299720
$821$	20.3319	0.709587	0.354793	−	0.934945i	$-0.384551\pi$
$821$	20.3319	0.709587	0.354793	+	0.934945i	$0.384551\pi$
$822$	3.67260	0.128097
$823$	−18.7887	−0.654933	−0.327467	−	0.944863i	$-0.606195\pi$
$823$	−18.7887	−0.654933	−0.327467	+	0.944863i	$0.606195\pi$
$824$	−12.4368	−0.433258
$825$	−1.86593	−0.0649635
$826$	0.163193	0.00567821
$827$	13.8412	0.481305	0.240652	−	0.970611i	$-0.422639\pi$
$827$	13.8412	0.481305	0.240652	+	0.970611i	$0.422639\pi$
$828$	0.685597	0.0238261
$829$	48.2420	1.67551	0.837757	−	0.546043i	$-0.183867\pi$
$829$	48.2420	1.67551	0.837757	+	0.546043i	$0.183867\pi$
$830$	25.1294	0.872255
$831$	−50.7715	−1.76124
$832$	1.06080	0.0367766
$833$	33.7221	1.16840
$834$	−32.1289	−1.11253
$835$	22.4925	0.778386
$836$	−14.9959	−0.518645
$837$	26.4564	0.914468
$838$	14.0100	0.483968
$839$	12.9867	0.448349	0.224174	−	0.974549i	$-0.428031\pi$
$839$	12.9867	0.448349	0.224174	+	0.974549i	$0.428031\pi$
$840$	2.54345	0.0877574
$841$	−25.0212	−0.862799
$842$	38.3830	1.32277
$843$	−14.9111	−0.513566
$844$	−23.2754	−0.801171
$845$	27.3718	0.941617
$846$	−1.01945	−0.0350493
$847$	0.191266	0.00657197
$848$	−2.35587	−0.0809008
$849$	5.91290	0.202930
$850$	−1.59759	−0.0547968
$851$	−15.5943	−0.534566
$852$	−15.9621	−0.546851
$853$	13.5312	0.463301	0.231650	−	0.972799i	$-0.425587\pi$
$853$	13.5312	0.463301	0.231650	+	0.972799i	$0.425587\pi$
$854$	−3.81758	−0.130635
$855$	1.42020	0.0485697
$856$	13.9031	0.475200
$857$	−28.0477	−0.958091	−0.479046	−	0.877790i	$-0.659017\pi$
$857$	−28.0477	−0.958091	−0.479046	+	0.877790i	$0.659017\pi$
$858$	−6.31896	−0.215726
$859$	1.27676	0.0435626	0.0217813	−	0.999763i	$-0.493066\pi$
$859$	1.27676	0.0435626	0.0217813	+	0.999763i	$0.493066\pi$
$860$	−7.61698	−0.259737
$861$	−4.10853	−0.140018
$862$	2.21916	0.0755848
$863$	40.6154	1.38256	0.691282	−	0.722585i	$-0.257046\pi$
$863$	40.6154	1.38256	0.691282	+	0.722585i	$0.257046\pi$
$864$	5.06971	0.172475
$865$	45.2151	1.53736
$866$	33.7492	1.14684
$867$	−15.9633	−0.542142
$868$	3.25053	0.110330
$869$	−14.2298	−0.482712
$870$	8.14507	0.276144
$871$	−3.38279	−0.114621
$872$	−14.2353	−0.482069
$873$	0.582533	0.0197158
$874$	−22.1308	−0.748586
$875$	6.72912	0.227486
$876$	−21.1707	−0.715290
$877$	−0.0655217	−0.00221251	−0.00110625	−	0.999999i	$-0.500352\pi$
$877$	−0.0655217	−0.00221251	−0.00110625	+	0.999999i	$0.500352\pi$
$878$	−14.6749	−0.495255
$879$	33.7657	1.13889
$880$	−7.75095	−0.261284
$881$	−31.4470	−1.05947	−0.529737	−	0.848162i	$-0.677710\pi$
$881$	−31.4470	−1.05947	−0.529737	+	0.848162i	$0.677710\pi$
$882$	−0.913490	−0.0307588
$883$	55.7457	1.87599	0.937997	−	0.346645i	$-0.112679\pi$
$883$	55.7457	1.87599	0.937997	+	0.346645i	$0.112679\pi$
$884$	−5.41021	−0.181965
$885$	1.06983	0.0359618
$886$	11.1085	0.373196
$887$	−43.6691	−1.46627	−0.733133	−	0.680086i	$-0.761943\pi$
$887$	−43.6691	−1.46627	−0.733133	+	0.680086i	$0.761943\pi$
$888$	5.56678	0.186809
$889$	0.331840	0.0111295
$890$	37.8957	1.27027
$891$	−31.5929	−1.05840
$892$	15.2495	0.510590
$893$	32.9073	1.10120
$894$	−6.03664	−0.201895
$895$	14.9424	0.499471
$896$	0.622882	0.0208090
$897$	−9.32544	−0.311367
$898$	−14.8139	−0.494347
$899$	10.4094	0.347173
$900$	0.0432767	0.00144256
$901$	12.0152	0.400285
$902$	12.5204	0.416884
$903$	−3.64625	−0.121340
$904$	−15.8448	−0.526990
$905$	−7.72742	−0.256868
$906$	3.00723	0.0999084
$907$	−23.7491	−0.788575	−0.394287	−	0.918987i	$-0.629009\pi$
$907$	−23.7491	−0.788575	−0.394287	+	0.918987i	$0.629009\pi$
$908$	−20.7568	−0.688840
$909$	−0.870410	−0.0288697
$910$	−1.52307	−0.0504892
$911$	−16.9602	−0.561916	−0.280958	−	0.959720i	$-0.590652\pi$
$911$	−16.9602	−0.561916	−0.280958	+	0.959720i	$0.590652\pi$
$912$	7.90016	0.261600
$913$	−36.6588	−1.21323
$914$	−33.9864	−1.12417
$915$	−25.0265	−0.827349
$916$	4.16386	0.137578
$917$	−5.49099	−0.181328
$918$	−25.8562	−0.853380
$919$	−36.6827	−1.21005	−0.605025	−	0.796207i	$-0.706837\pi$
$919$	−36.6827	−1.21005	−0.605025	+	0.796207i	$0.706837\pi$
$920$	−11.4388	−0.377125
$921$	12.4911	0.411596
$922$	−9.26245	−0.305043
$923$	9.55839	0.314618
$924$	−3.71038	−0.122063
$925$	−0.984353	−0.0323653
$926$	10.0028	0.328713
$927$	−1.71822	−0.0564339
$928$	1.99470	0.0654792
$929$	−27.5267	−0.903121	−0.451561	−	0.892240i	$-0.649132\pi$
$929$	−27.5267	−0.903121	−0.451561	+	0.892240i	$0.649132\pi$
$930$	21.3091	0.698753
$931$	29.4871	0.966402
$932$	6.12585	0.200659
$933$	16.0211	0.524509
$934$	−31.5251	−1.03153
$935$	39.5308	1.29280
$936$	0.146556	0.00479033
$937$	−10.9997	−0.359344	−0.179672	−	0.983727i	$-0.557504\pi$
$937$	−10.9997	−0.359344	−0.179672	+	0.983727i	$0.557504\pi$
$938$	−1.98631	−0.0648554
$939$	24.6691	0.805046
$940$	17.0088	0.554766
$941$	44.4224	1.44813	0.724064	−	0.689733i	$-0.242272\pi$
$941$	44.4224	1.44813	0.724064	+	0.689733i	$0.242272\pi$
$942$	24.3438	0.793164
$943$	18.4775	0.601709
$944$	0.261997	0.00852726
$945$	−7.27896	−0.236785
$946$	11.1116	0.361270
$947$	−21.3091	−0.692452	−0.346226	−	0.938151i	$-0.612537\pi$
$947$	−21.3091	−0.692452	−0.346226	+	0.938151i	$0.612537\pi$
$948$	7.49653	0.243476
$949$	12.6774	0.411526
$950$	−1.39696	−0.0453232
$951$	−51.4261	−1.66761
$952$	−3.17678	−0.102960
$953$	19.5484	0.633236	0.316618	−	0.948553i	$-0.397453\pi$
$953$	19.5484	0.633236	0.316618	+	0.948553i	$0.397453\pi$
$954$	−0.325477	−0.0105377
$955$	28.0656	0.908182
$956$	−10.3640	−0.335196
$957$	−11.8820	−0.384091
$958$	−4.45903	−0.144065
$959$	−1.29134	−0.0416997
$960$	4.08336	0.131790
$961$	−3.76695	−0.121514
$962$	−3.33350	−0.107476
$963$	1.92080	0.0618970
$964$	−15.2730	−0.491909
$965$	−24.0397	−0.773864
$966$	−5.47573	−0.176179
$967$	3.40974	0.109650	0.0548250	−	0.998496i	$-0.482540\pi$
$967$	3.40974	0.109650	0.0548250	+	0.998496i	$0.482540\pi$
$968$	0.307066	0.00986946
$969$	−40.2918	−1.29436
$970$	−9.71920	−0.312065
$971$	18.3100	0.587595	0.293797	−	0.955868i	$-0.405081\pi$
$971$	18.3100	0.587595	0.293797	+	0.955868i	$0.405081\pi$
$972$	1.43464	0.0460160
$973$	11.2970	0.362166
$974$	−10.8506	−0.347676
$975$	−0.588646	−0.0188518
$976$	−6.12890	−0.196181
$977$	−37.0855	−1.18647	−0.593235	−	0.805029i	$-0.702150\pi$
$977$	−37.0855	−1.18647	−0.593235	+	0.805029i	$0.702150\pi$
$978$	−14.5341	−0.464748
$979$	−55.2821	−1.76682
$980$	15.2410	0.486856
$981$	−1.96670	−0.0627918
$982$	19.1192	0.610118
$983$	14.1970	0.452814	0.226407	−	0.974033i	$-0.427302\pi$
$983$	14.1970	0.452814	0.226407	+	0.974033i	$0.427302\pi$
$984$	−6.59600	−0.210273
$985$	42.8912	1.36663
$986$	−10.1732	−0.323981
$987$	8.14212	0.259167
$988$	−4.73077	−0.150506
$989$	16.3984	0.521440
$990$	−1.07084	−0.0340336
$991$	−12.8545	−0.408337	−0.204169	−	0.978936i	$-0.565449\pi$
$991$	−12.8545	−0.408337	−0.204169	+	0.978936i	$0.565449\pi$
$992$	5.21853	0.165688
$993$	−17.1983	−0.545771
$994$	5.61252	0.178018
$995$	42.6608	1.35244
$996$	19.3126	0.611942
$997$	−10.6351	−0.336815	−0.168408	−	0.985717i	$-0.553863\pi$
$997$	−10.6351	−0.336815	−0.168408	+	0.985717i	$0.553863\pi$
$998$	17.9160	0.567121
$999$	−15.9313	−0.504043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.f.1.9	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.f.1.9	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.77148 q^{3} +1.00000 q^{4} -2.30505 q^{5} -1.77148 q^{6} +0.622882 q^{7} +1.00000 q^{8} +0.138156 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.77148 q^{3} +1.00000 q^{4} -2.30505 q^{5} -1.77148 q^{6} +0.622882 q^{7} +1.00000 q^{8} +0.138156 q^{9} -2.30505 q^{10} +3.36260 q^{11} -1.77148 q^{12} +1.06080 q^{13} +0.622882 q^{14} +4.08336 q^{15} +1.00000 q^{16} -5.10012 q^{17} +0.138156 q^{18} -4.45963 q^{19} -2.30505 q^{20} -1.10343 q^{21} +3.36260 q^{22} +4.96248 q^{23} -1.77148 q^{24} +0.313245 q^{25} +1.06080 q^{26} +5.06971 q^{27} +0.622882 q^{28} +1.99470 q^{29} +4.08336 q^{30} +5.21853 q^{31} +1.00000 q^{32} -5.95679 q^{33} -5.10012 q^{34} -1.43577 q^{35} +0.138156 q^{36} -3.14244 q^{37} -4.45963 q^{38} -1.87919 q^{39} -2.30505 q^{40} +3.72343 q^{41} -1.10343 q^{42} +3.30448 q^{43} +3.36260 q^{44} -0.318456 q^{45} +4.96248 q^{46} -7.37894 q^{47} -1.77148 q^{48} -6.61202 q^{49} +0.313245 q^{50} +9.03479 q^{51} +1.06080 q^{52} -2.35587 q^{53} +5.06971 q^{54} -7.75095 q^{55} +0.622882 q^{56} +7.90016 q^{57} +1.99470 q^{58} +0.261997 q^{59} +4.08336 q^{60} -6.12890 q^{61} +5.21853 q^{62} +0.0860550 q^{63} +1.00000 q^{64} -2.44519 q^{65} -5.95679 q^{66} -3.18890 q^{67} -5.10012 q^{68} -8.79096 q^{69} -1.43577 q^{70} +9.01056 q^{71} +0.138156 q^{72} +11.9508 q^{73} -3.14244 q^{74} -0.554908 q^{75} -4.45963 q^{76} +2.09450 q^{77} -1.87919 q^{78} -4.23178 q^{79} -2.30505 q^{80} -9.39538 q^{81} +3.72343 q^{82} -10.9019 q^{83} -1.10343 q^{84} +11.7560 q^{85} +3.30448 q^{86} -3.53358 q^{87} +3.36260 q^{88} -16.4403 q^{89} -0.318456 q^{90} +0.660753 q^{91} +4.96248 q^{92} -9.24454 q^{93} -7.37894 q^{94} +10.2797 q^{95} -1.77148 q^{96} +4.21648 q^{97} -6.61202 q^{98} +0.464563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9	\( 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9} - 23 q^{10} - 32 q^{11} - 13 q^{12} - 8 q^{13} - 18 q^{14} - 14 q^{15} + 31 q^{16} - 30 q^{17} + 20 q^{18} - 38 q^{19} - 23 q^{20} - 16 q^{21} - 32 q^{22} - 24 q^{23} - 13 q^{24} + 40 q^{25} - 8 q^{26} - 28 q^{27} - 18 q^{28} - 7 q^{29} - 14 q^{30} - 32 q^{31} + 31 q^{32} - 9 q^{33} - 30 q^{34} - 14 q^{35} + 20 q^{36} + 11 q^{37} - 38 q^{38} - 9 q^{39} - 23 q^{40} - 76 q^{41} - 16 q^{42} - 33 q^{43} - 32 q^{44} - 40 q^{45} - 24 q^{46} - 96 q^{47} - 13 q^{48} + 15 q^{49} + 40 q^{50} - 55 q^{51} - 8 q^{52} - 28 q^{53} - 28 q^{54} - 52 q^{55} - 18 q^{56} - 21 q^{57} - 7 q^{58} - 72 q^{59} - 14 q^{60} - 9 q^{61} - 32 q^{62} - 54 q^{63} + 31 q^{64} - 38 q^{65} - 9 q^{66} - 4 q^{67} - 30 q^{68} - 17 q^{69} - 14 q^{70} - 61 q^{71} + 20 q^{72} - 62 q^{73} + 11 q^{74} - 63 q^{75} - 38 q^{76} - 9 q^{77} - 9 q^{78} - 30 q^{79} - 23 q^{80} - 13 q^{81} - 76 q^{82} - 90 q^{83} - 16 q^{84} + 26 q^{85} - 33 q^{86} - 34 q^{87} - 32 q^{88} - 99 q^{89} - 40 q^{90} - 47 q^{91} - 24 q^{92} - 6 q^{93} - 96 q^{94} - 24 q^{95} - 13 q^{96} - 46 q^{97} + 15 q^{98} - 48 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9 - 23 * q^10 - 32 * q^11 - 13 * q^12 - 8 * q^13 - 18 * q^14 - 14 * q^15 + 31 * q^16 - 30 * q^17 + 20 * q^18 - 38 * q^19 - 23 * q^20 - 16 * q^21 - 32 * q^22 - 24 * q^23 - 13 * q^24 + 40 * q^25 - 8 * q^26 - 28 * q^27 - 18 * q^28 - 7 * q^29 - 14 * q^30 - 32 * q^31 + 31 * q^32 - 9 * q^33 - 30 * q^34 - 14 * q^35 + 20 * q^36 + 11 * q^37 - 38 * q^38 - 9 * q^39 - 23 * q^40 - 76 * q^41 - 16 * q^42 - 33 * q^43 - 32 * q^44 - 40 * q^45 - 24 * q^46 - 96 * q^47 - 13 * q^48 + 15 * q^49 + 40 * q^50 - 55 * q^51 - 8 * q^52 - 28 * q^53 - 28 * q^54 - 52 * q^55 - 18 * q^56 - 21 * q^57 - 7 * q^58 - 72 * q^59 - 14 * q^60 - 9 * q^61 - 32 * q^62 - 54 * q^63 + 31 * q^64 - 38 * q^65 - 9 * q^66 - 4 * q^67 - 30 * q^68 - 17 * q^69 - 14 * q^70 - 61 * q^71 + 20 * q^72 - 62 * q^73 + 11 * q^74 - 63 * q^75 - 38 * q^76 - 9 * q^77 - 9 * q^78 - 30 * q^79 - 23 * q^80 - 13 * q^81 - 76 * q^82 - 90 * q^83 - 16 * q^84 + 26 * q^85 - 33 * q^86 - 34 * q^87 - 32 * q^88 - 99 * q^89 - 40 * q^90 - 47 * q^91 - 24 * q^92 - 6 * q^93 - 96 * q^94 - 24 * q^95 - 13 * q^96 - 46 * q^97 + 15 * q^98 - 48 * q^99

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