LMFDB - Embedded newform 4006.2.a.g.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.69686 q^{3} +1.00000 q^{4} +3.10338 q^{5} +1.69686 q^{6} +1.10094 q^{7} -1.00000 q^{8} -0.120661 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.69686 q^{3} +1.00000 q^{4} +3.10338 q^{5} +1.69686 q^{6} +1.10094 q^{7} -1.00000 q^{8} -0.120661 q^{9} -3.10338 q^{10} -4.72621 q^{11} -1.69686 q^{12} -3.35011 q^{13} -1.10094 q^{14} -5.26601 q^{15} +1.00000 q^{16} -0.0655032 q^{17} +0.120661 q^{18} -0.989928 q^{19} +3.10338 q^{20} -1.86814 q^{21} +4.72621 q^{22} +5.99797 q^{23} +1.69686 q^{24} +4.63099 q^{25} +3.35011 q^{26} +5.29533 q^{27} +1.10094 q^{28} +8.91879 q^{29} +5.26601 q^{30} +2.81936 q^{31} -1.00000 q^{32} +8.01972 q^{33} +0.0655032 q^{34} +3.41664 q^{35} -0.120661 q^{36} -10.8162 q^{37} +0.989928 q^{38} +5.68468 q^{39} -3.10338 q^{40} -8.08940 q^{41} +1.86814 q^{42} +2.83603 q^{43} -4.72621 q^{44} -0.374456 q^{45} -5.99797 q^{46} +4.73833 q^{47} -1.69686 q^{48} -5.78793 q^{49} -4.63099 q^{50} +0.111150 q^{51} -3.35011 q^{52} -9.29937 q^{53} -5.29533 q^{54} -14.6672 q^{55} -1.10094 q^{56} +1.67977 q^{57} -8.91879 q^{58} +14.3626 q^{59} -5.26601 q^{60} +12.4972 q^{61} -2.81936 q^{62} -0.132840 q^{63} +1.00000 q^{64} -10.3967 q^{65} -8.01972 q^{66} +0.610984 q^{67} -0.0655032 q^{68} -10.1777 q^{69} -3.41664 q^{70} -15.0768 q^{71} +0.120661 q^{72} +1.56280 q^{73} +10.8162 q^{74} -7.85816 q^{75} -0.989928 q^{76} -5.20327 q^{77} -5.68468 q^{78} -15.1504 q^{79} +3.10338 q^{80} -8.62346 q^{81} +8.08940 q^{82} -5.26349 q^{83} -1.86814 q^{84} -0.203281 q^{85} -2.83603 q^{86} -15.1340 q^{87} +4.72621 q^{88} -4.59042 q^{89} +0.374456 q^{90} -3.68827 q^{91} +5.99797 q^{92} -4.78406 q^{93} -4.73833 q^{94} -3.07213 q^{95} +1.69686 q^{96} -2.77239 q^{97} +5.78793 q^{98} +0.570267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.69686	−0.979684	−0.489842	−	0.871811i	$-0.662945\pi$
$3$	−1.69686	−0.979684	−0.489842	+	0.871811i	$0.662945\pi$
$4$	1.00000	0.500000
$5$	3.10338	1.38788	0.693938	−	0.720035i	$-0.255874\pi$
$5$	3.10338	1.38788	0.693938	+	0.720035i	$0.255874\pi$
$6$	1.69686	0.692741
$7$	1.10094	0.416116	0.208058	−	0.978116i	$-0.433286\pi$
$7$	1.10094	0.416116	0.208058	+	0.978116i	$0.433286\pi$
$8$	−1.00000	−0.353553
$9$	−0.120661	−0.0402202
$10$	−3.10338	−0.981376
$11$	−4.72621	−1.42500	−0.712502	−	0.701670i	$-0.752438\pi$
$11$	−4.72621	−1.42500	−0.712502	+	0.701670i	$0.752438\pi$
$12$	−1.69686	−0.489842
$13$	−3.35011	−0.929154	−0.464577	−	0.885533i	$-0.653794\pi$
$13$	−3.35011	−0.929154	−0.464577	+	0.885533i	$0.653794\pi$
$14$	−1.10094	−0.294239
$15$	−5.26601	−1.35968
$16$	1.00000	0.250000
$17$	−0.0655032	−0.0158868	−0.00794342	−	0.999968i	$-0.502528\pi$
$17$	−0.0655032	−0.0158868	−0.00794342	+	0.999968i	$0.502528\pi$
$18$	0.120661	0.0284400
$19$	−0.989928	−0.227105	−0.113553	−	0.993532i	$-0.536223\pi$
$19$	−0.989928	−0.227105	−0.113553	+	0.993532i	$0.536223\pi$
$20$	3.10338	0.693938
$21$	−1.86814	−0.407662
$22$	4.72621	1.00763
$23$	5.99797	1.25066	0.625332	−	0.780359i	$-0.284964\pi$
$23$	5.99797	1.25066	0.625332	+	0.780359i	$0.284964\pi$
$24$	1.69686	0.346370
$25$	4.63099	0.926199
$26$	3.35011	0.657011
$27$	5.29533	1.01909
$28$	1.10094	0.208058
$29$	8.91879	1.65618	0.828089	−	0.560597i	$-0.189428\pi$
$29$	8.91879	1.65618	0.828089	+	0.560597i	$0.189428\pi$
$30$	5.26601	0.961438
$31$	2.81936	0.506371	0.253186	−	0.967418i	$-0.418522\pi$
$31$	2.81936	0.506371	0.253186	+	0.967418i	$0.418522\pi$
$32$	−1.00000	−0.176777
$33$	8.01972	1.39605
$34$	0.0655032	0.0112337
$35$	3.41664	0.577517
$36$	−0.120661	−0.0201101
$37$	−10.8162	−1.77818	−0.889089	−	0.457734i	$-0.848661\pi$
$37$	−10.8162	−1.77818	−0.889089	+	0.457734i	$0.848661\pi$
$38$	0.989928	0.160587
$39$	5.68468	0.910277
$40$	−3.10338	−0.490688
$41$	−8.08940	−1.26335	−0.631676	−	0.775233i	$-0.717633\pi$
$41$	−8.08940	−1.26335	−0.631676	+	0.775233i	$0.717633\pi$
$42$	1.86814	0.288261
$43$	2.83603	0.432491	0.216246	−	0.976339i	$-0.430619\pi$
$43$	2.83603	0.432491	0.216246	+	0.976339i	$0.430619\pi$
$44$	−4.72621	−0.712502
$45$	−0.374456	−0.0558206
$46$	−5.99797	−0.884353
$47$	4.73833	0.691157	0.345578	−	0.938390i	$-0.387683\pi$
$47$	4.73833	0.691157	0.345578	+	0.938390i	$0.387683\pi$
$48$	−1.69686	−0.244921
$49$	−5.78793	−0.826847
$50$	−4.63099	−0.654921
$51$	0.111150	0.0155641
$52$	−3.35011	−0.464577
$53$	−9.29937	−1.27737	−0.638683	−	0.769470i	$-0.720521\pi$
$53$	−9.29937	−1.27737	−0.638683	+	0.769470i	$0.720521\pi$
$54$	−5.29533	−0.720603
$55$	−14.6672	−1.97773
$56$	−1.10094	−0.147119
$57$	1.67977	0.222491
$58$	−8.91879	−1.17109
$59$	14.3626	1.86985	0.934926	−	0.354843i	$-0.115466\pi$
$59$	14.3626	1.86985	0.934926	+	0.354843i	$0.115466\pi$
$60$	−5.26601	−0.679839
$61$	12.4972	1.60010	0.800049	−	0.599934i	$-0.204807\pi$
$61$	12.4972	1.60010	0.800049	+	0.599934i	$0.204807\pi$
$62$	−2.81936	−0.358059
$63$	−0.132840	−0.0167363
$64$	1.00000	0.125000
$65$	−10.3967	−1.28955
$66$	−8.01972	−0.987159
$67$	0.610984	0.0746436	0.0373218	−	0.999303i	$-0.488117\pi$
$67$	0.610984	0.0746436	0.0373218	+	0.999303i	$0.488117\pi$
$68$	−0.0655032	−0.00794342
$69$	−10.1777	−1.22525
$70$	−3.41664	−0.408367
$71$	−15.0768	−1.78929	−0.894646	−	0.446776i	$-0.852572\pi$
$71$	−15.0768	−1.78929	−0.894646	+	0.446776i	$0.852572\pi$
$72$	0.120661	0.0142200
$73$	1.56280	0.182912	0.0914558	−	0.995809i	$-0.470848\pi$
$73$	1.56280	0.182912	0.0914558	+	0.995809i	$0.470848\pi$
$74$	10.8162	1.25736
$75$	−7.85816	−0.907382
$76$	−0.989928	−0.113553
$77$	−5.20327	−0.592968
$78$	−5.68468	−0.643663
$79$	−15.1504	−1.70455	−0.852274	−	0.523095i	$-0.824777\pi$
$79$	−15.1504	−1.70455	−0.852274	+	0.523095i	$0.824777\pi$
$80$	3.10338	0.346969
$81$	−8.62346	−0.958162
$82$	8.08940	0.893325
$83$	−5.26349	−0.577743	−0.288872	−	0.957368i	$-0.593280\pi$
$83$	−5.26349	−0.577743	−0.288872	+	0.957368i	$0.593280\pi$
$84$	−1.86814	−0.203831
$85$	−0.203281	−0.0220490
$86$	−2.83603	−0.305817
$87$	−15.1340	−1.62253
$88$	4.72621	0.503815
$89$	−4.59042	−0.486584	−0.243292	−	0.969953i	$-0.578227\pi$
$89$	−4.59042	−0.486584	−0.243292	+	0.969953i	$0.578227\pi$
$90$	0.374456	0.0394711
$91$	−3.68827	−0.386636
$92$	5.99797	0.625332
$93$	−4.78406	−0.496084
$94$	−4.73833	−0.488722
$95$	−3.07213	−0.315193
$96$	1.69686	0.173185
$97$	−2.77239	−0.281493	−0.140747	−	0.990046i	$-0.544950\pi$
$97$	−2.77239	−0.281493	−0.140747	+	0.990046i	$0.544950\pi$
$98$	5.78793	0.584669
$99$	0.570267	0.0573139
$100$	4.63099	0.463099
$101$	12.4047	1.23431	0.617157	−	0.786840i	$-0.288284\pi$
$101$	12.4047	1.23431	0.617157	+	0.786840i	$0.288284\pi$
$102$	−0.111150	−0.0110055
$103$	4.25770	0.419524	0.209762	−	0.977753i	$-0.432731\pi$
$103$	4.25770	0.419524	0.209762	+	0.977753i	$0.432731\pi$
$104$	3.35011	0.328506
$105$	−5.79756	−0.565784
$106$	9.29937	0.903235
$107$	−10.4483	−1.01007	−0.505037	−	0.863098i	$-0.668521\pi$
$107$	−10.4483	−1.01007	−0.505037	+	0.863098i	$0.668521\pi$
$108$	5.29533	0.509543
$109$	−13.4323	−1.28658	−0.643290	−	0.765623i	$-0.722431\pi$
$109$	−13.4323	−1.28658	−0.643290	+	0.765623i	$0.722431\pi$
$110$	14.6672	1.39847
$111$	18.3537	1.74205
$112$	1.10094	0.104029
$113$	−0.270586	−0.0254546	−0.0127273	−	0.999919i	$-0.504051\pi$
$113$	−0.270586	−0.0254546	−0.0127273	+	0.999919i	$0.504051\pi$
$114$	−1.67977	−0.157325
$115$	18.6140	1.73577
$116$	8.91879	0.828089
$117$	0.404226	0.0373707
$118$	−14.3626	−1.32218
$119$	−0.0721150	−0.00661077
$120$	5.26601	0.480719
$121$	11.3370	1.03064
$122$	−12.4972	−1.13144
$123$	13.7266	1.23769
$124$	2.81936	0.253186
$125$	−1.14517	−0.102427
$126$	0.132840	0.0118343
$127$	−2.70772	−0.240272	−0.120136	−	0.992757i	$-0.538333\pi$
$127$	−2.70772	−0.240272	−0.120136	+	0.992757i	$0.538333\pi$
$128$	−1.00000	−0.0883883
$129$	−4.81236	−0.423704
$130$	10.3967	0.911850
$131$	−14.5970	−1.27535	−0.637674	−	0.770306i	$-0.720103\pi$
$131$	−14.5970	−1.27535	−0.637674	+	0.770306i	$0.720103\pi$
$132$	8.01972	0.698027
$133$	−1.08985	−0.0945021
$134$	−0.610984	−0.0527810
$135$	16.4334	1.41437
$136$	0.0655032	0.00561685
$137$	−1.80758	−0.154432	−0.0772161	−	0.997014i	$-0.524603\pi$
$137$	−1.80758	−0.154432	−0.0772161	+	0.997014i	$0.524603\pi$
$138$	10.1777	0.866386
$139$	14.5191	1.23149	0.615745	−	0.787945i	$-0.288855\pi$
$139$	14.5191	1.23149	0.615745	+	0.787945i	$0.288855\pi$
$140$	3.41664	0.288759
$141$	−8.04029	−0.677115
$142$	15.0768	1.26522
$143$	15.8333	1.32405
$144$	−0.120661	−0.0100550
$145$	27.6784	2.29857
$146$	−1.56280	−0.129338
$147$	9.82132	0.810049
$148$	−10.8162	−0.889089
$149$	−6.16805	−0.505306	−0.252653	−	0.967557i	$-0.581303\pi$
$149$	−6.16805	−0.505306	−0.252653	+	0.967557i	$0.581303\pi$
$150$	7.85816	0.641616
$151$	8.22272	0.669156	0.334578	−	0.942368i	$-0.391406\pi$
$151$	8.22272	0.669156	0.334578	+	0.942368i	$0.391406\pi$
$152$	0.989928	0.0802937
$153$	0.00790365	0.000638972 0
$154$	5.20327	0.419291
$155$	8.74955	0.702780
$156$	5.68468	0.455138
$157$	−19.5862	−1.56315	−0.781575	−	0.623812i	$-0.785583\pi$
$157$	−19.5862	−1.56315	−0.781575	+	0.623812i	$0.785583\pi$
$158$	15.1504	1.20530
$159$	15.7797	1.25141
$160$	−3.10338	−0.245344
$161$	6.60341	0.520421
$162$	8.62346	0.677523
$163$	20.0890	1.57349	0.786747	−	0.617275i	$-0.211764\pi$
$163$	20.0890	1.57349	0.786747	+	0.617275i	$0.211764\pi$
$164$	−8.08940	−0.631676
$165$	24.8883	1.93755
$166$	5.26349	0.408526
$167$	2.21258	0.171215	0.0856075	−	0.996329i	$-0.472717\pi$
$167$	2.21258	0.171215	0.0856075	+	0.996329i	$0.472717\pi$
$168$	1.86814	0.144130
$169$	−1.77675	−0.136673
$170$	0.203281	0.0155910
$171$	0.119445	0.00913420
$172$	2.83603	0.216246
$173$	−17.6460	−1.34160	−0.670800	−	0.741638i	$-0.734049\pi$
$173$	−17.6460	−1.34160	−0.670800	+	0.741638i	$0.734049\pi$
$174$	15.1340	1.14730
$175$	5.09845	0.385406
$176$	−4.72621	−0.356251
$177$	−24.3714	−1.83186
$178$	4.59042	0.344067
$179$	−19.2376	−1.43789	−0.718943	−	0.695069i	$-0.755374\pi$
$179$	−19.2376	−1.43789	−0.718943	+	0.695069i	$0.755374\pi$
$180$	−0.374456	−0.0279103
$181$	−14.9357	−1.11016	−0.555081	−	0.831796i	$-0.687313\pi$
$181$	−14.9357	−1.11016	−0.555081	+	0.831796i	$0.687313\pi$
$182$	3.68827	0.273393
$183$	−21.2060	−1.56759
$184$	−5.99797	−0.442176
$185$	−33.5669	−2.46789
$186$	4.78406	0.350784
$187$	0.309581	0.0226388
$188$	4.73833	0.345578
$189$	5.82984	0.424058
$190$	3.07213	0.222875
$191$	−1.63198	−0.118086	−0.0590428	−	0.998255i	$-0.518805\pi$
$191$	−1.63198	−0.118086	−0.0590428	+	0.998255i	$0.518805\pi$
$192$	−1.69686	−0.122460
$193$	−4.81891	−0.346872	−0.173436	−	0.984845i	$-0.555487\pi$
$193$	−4.81891	−0.346872	−0.173436	+	0.984845i	$0.555487\pi$
$194$	2.77239	0.199046
$195$	17.6417	1.26335
$196$	−5.78793	−0.413424
$197$	−8.63017	−0.614874	−0.307437	−	0.951568i	$-0.599471\pi$
$197$	−8.63017	−0.614874	−0.307437	+	0.951568i	$0.599471\pi$
$198$	−0.570267	−0.0405271
$199$	1.38982	0.0985218	0.0492609	−	0.998786i	$-0.484313\pi$
$199$	1.38982	0.0985218	0.0492609	+	0.998786i	$0.484313\pi$
$200$	−4.63099	−0.327461
$201$	−1.03675	−0.0731271
$202$	−12.4047	−0.872791
$203$	9.81905	0.689162
$204$	0.111150	0.00778204
$205$	−25.1045	−1.75338
$206$	−4.25770	−0.296648
$207$	−0.723719	−0.0503019
$208$	−3.35011	−0.232288
$209$	4.67860	0.323626
$210$	5.79756	0.400070
$211$	−13.4931	−0.928900	−0.464450	−	0.885599i	$-0.653748\pi$
$211$	−13.4931	−0.928900	−0.464450	+	0.885599i	$0.653748\pi$
$212$	−9.29937	−0.638683
$213$	25.5833	1.75294
$214$	10.4483	0.714230
$215$	8.80130	0.600244
$216$	−5.29533	−0.360302
$217$	3.10394	0.210709
$218$	13.4323	0.909749
$219$	−2.65185	−0.179195
$220$	−14.6672	−0.988865
$221$	0.219443	0.0147613
$222$	−18.3537	−1.23182
$223$	11.3543	0.760341	0.380171	−	0.924916i	$-0.375865\pi$
$223$	11.3543	0.760341	0.380171	+	0.924916i	$0.375865\pi$
$224$	−1.10094	−0.0735596
$225$	−0.558778	−0.0372519
$226$	0.270586	0.0179991
$227$	−5.06546	−0.336206	−0.168103	−	0.985769i	$-0.553764\pi$
$227$	−5.06546	−0.336206	−0.168103	+	0.985769i	$0.553764\pi$
$228$	1.67977	0.111246
$229$	−10.9776	−0.725419	−0.362709	−	0.931902i	$-0.618148\pi$
$229$	−10.9776	−0.725419	−0.362709	+	0.931902i	$0.618148\pi$
$230$	−18.6140	−1.22737
$231$	8.82923	0.580921
$232$	−8.91879	−0.585547
$233$	−17.4661	−1.14424	−0.572121	−	0.820169i	$-0.693879\pi$
$233$	−17.4661	−1.14424	−0.572121	+	0.820169i	$0.693879\pi$
$234$	−0.404226	−0.0264251
$235$	14.7049	0.959240
$236$	14.3626	0.934926
$237$	25.7081	1.66992
$238$	0.0721150	0.00467452
$239$	25.3558	1.64013	0.820067	−	0.572268i	$-0.193936\pi$
$239$	25.3558	1.64013	0.820067	+	0.572268i	$0.193936\pi$
$240$	−5.26601	−0.339920
$241$	−2.09101	−0.134694	−0.0673469	−	0.997730i	$-0.521453\pi$
$241$	−2.09101	−0.134694	−0.0673469	+	0.997730i	$0.521453\pi$
$242$	−11.3370	−0.728772
$243$	−1.25317	−0.0803909
$244$	12.4972	0.800049
$245$	−17.9622	−1.14756
$246$	−13.7266	−0.875175
$247$	3.31637	0.211016
$248$	−2.81936	−0.179029
$249$	8.93142	0.566006
$250$	1.14517	0.0724269
$251$	−28.2124	−1.78075	−0.890376	−	0.455225i	$-0.849559\pi$
$251$	−28.2124	−1.78075	−0.890376	+	0.455225i	$0.849559\pi$
$252$	−0.132840	−0.00836813
$253$	−28.3477	−1.78220
$254$	2.70772	0.169898
$255$	0.344941	0.0216010
$256$	1.00000	0.0625000
$257$	−6.61315	−0.412517	−0.206259	−	0.978498i	$-0.566129\pi$
$257$	−6.61315	−0.412517	−0.206259	+	0.978498i	$0.566129\pi$
$258$	4.81236	0.299604
$259$	−11.9080	−0.739929
$260$	−10.3967	−0.644775
$261$	−1.07615	−0.0666117
$262$	14.5970	0.901808
$263$	17.7963	1.09737	0.548685	−	0.836029i	$-0.315129\pi$
$263$	17.7963	1.09737	0.548685	+	0.836029i	$0.315129\pi$
$264$	−8.01972	−0.493580
$265$	−28.8595	−1.77283
$266$	1.08985	0.0668230
$267$	7.78931	0.476698
$268$	0.610984	0.0373218
$269$	11.9618	0.729322	0.364661	−	0.931140i	$-0.381185\pi$
$269$	11.9618	0.729322	0.364661	+	0.931140i	$0.381185\pi$
$270$	−16.4334	−1.00011
$271$	−9.81810	−0.596407	−0.298204	−	0.954502i	$-0.596387\pi$
$271$	−9.81810	−0.596407	−0.298204	+	0.954502i	$0.596387\pi$
$272$	−0.0655032	−0.00397171
$273$	6.25849	0.378781
$274$	1.80758	0.109200
$275$	−21.8870	−1.31984
$276$	−10.1777	−0.612627
$277$	0.176183	0.0105858	0.00529290	−	0.999986i	$-0.498315\pi$
$277$	0.176183	0.0105858	0.00529290	+	0.999986i	$0.498315\pi$
$278$	−14.5191	−0.870796
$279$	−0.340185	−0.0203663
$280$	−3.41664	−0.204183
$281$	−5.12252	−0.305584	−0.152792	−	0.988258i	$-0.548826\pi$
$281$	−5.12252	−0.305584	−0.152792	+	0.988258i	$0.548826\pi$
$282$	8.04029	0.478793
$283$	−1.16754	−0.0694029	−0.0347015	−	0.999398i	$-0.511048\pi$
$283$	−1.16754	−0.0694029	−0.0347015	+	0.999398i	$0.511048\pi$
$284$	−15.0768	−0.894646
$285$	5.21297	0.308790
$286$	−15.8333	−0.936244
$287$	−8.90594	−0.525701
$288$	0.120661	0.00710999
$289$	−16.9957	−0.999748
$290$	−27.6784	−1.62533
$291$	4.70436	0.275774
$292$	1.56280	0.0914558
$293$	−4.67725	−0.273248	−0.136624	−	0.990623i	$-0.543625\pi$
$293$	−4.67725	−0.273248	−0.136624	+	0.990623i	$0.543625\pi$
$294$	−9.82132	−0.572791
$295$	44.5727	2.59512
$296$	10.8162	0.628681
$297$	−25.0268	−1.45220
$298$	6.16805	0.357306
$299$	−20.0939	−1.16206
$300$	−7.85816	−0.453691
$301$	3.12230	0.179967
$302$	−8.22272	−0.473165
$303$	−21.0491	−1.20924
$304$	−0.989928	−0.0567763
$305$	38.7835	2.22074
$306$	−0.00790365	−0.000451821 0
$307$	19.6394	1.12088	0.560440	−	0.828195i	$-0.310632\pi$
$307$	19.6394	1.12088	0.560440	+	0.828195i	$0.310632\pi$
$308$	−5.20327	−0.296484
$309$	−7.22473	−0.411000
$310$	−8.74955	−0.496941
$311$	5.40469	0.306472	0.153236	−	0.988190i	$-0.451031\pi$
$311$	5.40469	0.306472	0.153236	+	0.988190i	$0.451031\pi$
$312$	−5.68468	−0.321831
$313$	19.2759	1.08954	0.544771	−	0.838585i	$-0.316617\pi$
$313$	19.2759	1.08954	0.544771	+	0.838585i	$0.316617\pi$
$314$	19.5862	1.10531
$315$	−0.412253	−0.0232279
$316$	−15.1504	−0.852274
$317$	2.18365	0.122646	0.0613229	−	0.998118i	$-0.480468\pi$
$317$	2.18365	0.122646	0.0613229	+	0.998118i	$0.480468\pi$
$318$	−15.7797	−0.884884
$319$	−42.1520	−2.36006
$320$	3.10338	0.173484
$321$	17.7293	0.989552
$322$	−6.60341	−0.367994
$323$	0.0648434	0.00360798
$324$	−8.62346	−0.479081
$325$	−15.5143	−0.860581
$326$	−20.0890	−1.11263
$327$	22.7927	1.26044
$328$	8.08940	0.446662
$329$	5.21662	0.287602
$330$	−24.8883	−1.37005
$331$	25.2610	1.38847	0.694234	−	0.719750i	$-0.255743\pi$
$331$	25.2610	1.38847	0.694234	+	0.719750i	$0.255743\pi$
$332$	−5.26349	−0.288872
$333$	1.30509	0.0715187
$334$	−2.21258	−0.121067
$335$	1.89612	0.103596
$336$	−1.86814	−0.101916
$337$	24.5823	1.33908	0.669541	−	0.742775i	$-0.266491\pi$
$337$	24.5823	1.33908	0.669541	+	0.742775i	$0.266491\pi$
$338$	1.77675	0.0966424
$339$	0.459147	0.0249374
$340$	−0.203281	−0.0110245
$341$	−13.3249	−0.721582
$342$	−0.119445	−0.00645886
$343$	−14.0787	−0.760181
$344$	−2.83603	−0.152909
$345$	−31.5854	−1.70050
$346$	17.6460	0.948654
$347$	−31.8185	−1.70810	−0.854052	−	0.520187i	$-0.825862\pi$
$347$	−31.8185	−1.70810	−0.854052	+	0.520187i	$0.825862\pi$
$348$	−15.1340	−0.811265
$349$	−12.7475	−0.682360	−0.341180	−	0.939998i	$-0.610827\pi$
$349$	−12.7475	−0.682360	−0.341180	+	0.939998i	$0.610827\pi$
$350$	−5.09845	−0.272523
$351$	−17.7399	−0.946888
$352$	4.72621	0.251908
$353$	−1.51393	−0.0805784	−0.0402892	−	0.999188i	$-0.512828\pi$
$353$	−1.51393	−0.0805784	−0.0402892	+	0.999188i	$0.512828\pi$
$354$	24.3714	1.29532
$355$	−46.7892	−2.48331
$356$	−4.59042	−0.243292
$357$	0.122369	0.00647647
$358$	19.2376	1.01674
$359$	−28.3026	−1.49376	−0.746878	−	0.664962i	$-0.768448\pi$
$359$	−28.3026	−1.49376	−0.746878	+	0.664962i	$0.768448\pi$
$360$	0.374456	0.0197356
$361$	−18.0200	−0.948423
$362$	14.9357	0.785003
$363$	−19.2374	−1.00970
$364$	−3.68827	−0.193318
$365$	4.84996	0.253859
$366$	21.2060	1.10845
$367$	32.9712	1.72108	0.860541	−	0.509381i	$-0.170126\pi$
$367$	32.9712	1.72108	0.860541	+	0.509381i	$0.170126\pi$
$368$	5.99797	0.312666
$369$	0.976071	0.0508122
$370$	33.5669	1.74506
$371$	−10.2380	−0.531533
$372$	−4.78406	−0.248042
$373$	23.5082	1.21721	0.608605	−	0.793474i	$-0.291730\pi$
$373$	23.5082	1.21721	0.608605	+	0.793474i	$0.291730\pi$
$374$	−0.309581	−0.0160081
$375$	1.94319	0.100346
$376$	−4.73833	−0.244361
$377$	−29.8789	−1.53884
$378$	−5.82984	−0.299855
$379$	−13.4273	−0.689716	−0.344858	−	0.938655i	$-0.612073\pi$
$379$	−13.4273	−0.689716	−0.344858	+	0.938655i	$0.612073\pi$
$380$	−3.07213	−0.157597
$381$	4.59463	0.235390
$382$	1.63198	0.0834991
$383$	−8.49327	−0.433986	−0.216993	−	0.976173i	$-0.569625\pi$
$383$	−8.49327	−0.433986	−0.216993	+	0.976173i	$0.569625\pi$
$384$	1.69686	0.0865926
$385$	−16.1477	−0.822965
$386$	4.81891	0.245276
$387$	−0.342197	−0.0173949
$388$	−2.77239	−0.140747
$389$	−12.3274	−0.625023	−0.312512	−	0.949914i	$-0.601170\pi$
$389$	−12.3274	−0.625023	−0.312512	+	0.949914i	$0.601170\pi$
$390$	−17.6417	−0.893324
$391$	−0.392886	−0.0198691
$392$	5.78793	0.292335
$393$	24.7691	1.24944
$394$	8.63017	0.434782
$395$	−47.0174	−2.36570
$396$	0.570267	0.0286570
$397$	−28.8419	−1.44753	−0.723767	−	0.690045i	$-0.757591\pi$
$397$	−28.8419	−1.44753	−0.723767	+	0.690045i	$0.757591\pi$
$398$	−1.38982	−0.0696655
$399$	1.84933	0.0925821
$400$	4.63099	0.231550
$401$	−0.547787	−0.0273552	−0.0136776	−	0.999906i	$-0.504354\pi$
$401$	−0.547787	−0.0273552	−0.0136776	+	0.999906i	$0.504354\pi$
$402$	1.03675	0.0517086
$403$	−9.44516	−0.470497
$404$	12.4047	0.617157
$405$	−26.7619	−1.32981
$406$	−9.81905	−0.487311
$407$	51.1198	2.53391
$408$	−0.111150	−0.00550274
$409$	17.5247	0.866540	0.433270	−	0.901264i	$-0.357360\pi$
$409$	17.5247	0.866540	0.433270	+	0.901264i	$0.357360\pi$
$410$	25.1045	1.23982
$411$	3.06722	0.151295
$412$	4.25770	0.209762
$413$	15.8124	0.778075
$414$	0.723719	0.0355688
$415$	−16.3346	−0.801836
$416$	3.35011	0.164253
$417$	−24.6368	−1.20647
$418$	−4.67860	−0.228838
$419$	11.7030	0.571728	0.285864	−	0.958270i	$-0.407719\pi$
$419$	11.7030	0.571728	0.285864	+	0.958270i	$0.407719\pi$
$420$	−5.79756	−0.282892
$421$	6.40915	0.312363	0.156181	−	0.987728i	$-0.450082\pi$
$421$	6.40915	0.312363	0.156181	+	0.987728i	$0.450082\pi$
$422$	13.4931	0.656832
$423$	−0.571730	−0.0277984
$424$	9.29937	0.451617
$425$	−0.303345	−0.0147144
$426$	−25.5833	−1.23952
$427$	13.7586	0.665827
$428$	−10.4483	−0.505037
$429$	−26.8670	−1.29715
$430$	−8.80130	−0.424436
$431$	−11.8112	−0.568925	−0.284463	−	0.958687i	$-0.591815\pi$
$431$	−11.8112	−0.568925	−0.284463	+	0.958687i	$0.591815\pi$
$432$	5.29533	0.254772
$433$	−2.78930	−0.134045	−0.0670227	−	0.997751i	$-0.521350\pi$
$433$	−2.78930	−0.134045	−0.0670227	+	0.997751i	$0.521350\pi$
$434$	−3.10394	−0.148994
$435$	−46.9665	−2.25187
$436$	−13.4323	−0.643290
$437$	−5.93756	−0.284032
$438$	2.65185	0.126710
$439$	−14.4678	−0.690510	−0.345255	−	0.938509i	$-0.612208\pi$
$439$	−14.4678	−0.690510	−0.345255	+	0.938509i	$0.612208\pi$
$440$	14.6672	0.699233
$441$	0.698375	0.0332559
$442$	−0.219443	−0.0104378
$443$	−14.4703	−0.687507	−0.343753	−	0.939060i	$-0.611698\pi$
$443$	−14.4703	−0.687507	−0.343753	+	0.939060i	$0.611698\pi$
$444$	18.3537	0.871026
$445$	−14.2458	−0.675317
$446$	−11.3543	−0.537642
$447$	10.4663	0.495040
$448$	1.10094	0.0520145
$449$	−6.56567	−0.309853	−0.154926	−	0.987926i	$-0.549514\pi$
$449$	−6.56567	−0.309853	−0.154926	+	0.987926i	$0.549514\pi$
$450$	0.558778	0.0263411
$451$	38.2322	1.80028
$452$	−0.270586	−0.0127273
$453$	−13.9528	−0.655561
$454$	5.06546	0.237734
$455$	−11.4461	−0.536603
$456$	−1.67977	−0.0786625
$457$	26.1503	1.22326	0.611630	−	0.791144i	$-0.290514\pi$
$457$	26.1503	1.22326	0.611630	+	0.791144i	$0.290514\pi$
$458$	10.9776	0.512949
$459$	−0.346861	−0.0161901
$460$	18.6140	0.867883
$461$	14.0435	0.654072	0.327036	−	0.945012i	$-0.393950\pi$
$461$	14.0435	0.654072	0.327036	+	0.945012i	$0.393950\pi$
$462$	−8.82923	−0.410773
$463$	−22.8998	−1.06424	−0.532122	−	0.846668i	$-0.678605\pi$
$463$	−22.8998	−1.06424	−0.532122	+	0.846668i	$0.678605\pi$
$464$	8.91879	0.414044
$465$	−14.8468	−0.688502
$466$	17.4661	0.809101
$467$	24.2008	1.11988	0.559940	−	0.828533i	$-0.310824\pi$
$467$	24.2008	1.11988	0.559940	+	0.828533i	$0.310824\pi$
$468$	0.404226	0.0186854
$469$	0.672656	0.0310604
$470$	−14.7049	−0.678285
$471$	33.2351	1.53139
$472$	−14.3626	−0.661092
$473$	−13.4037	−0.616302
$474$	−25.7081	−1.18081
$475$	−4.58435	−0.210344
$476$	−0.0721150	−0.00330539
$477$	1.12207	0.0513759
$478$	−25.3558	−1.15975
$479$	2.46499	0.112628	0.0563141	−	0.998413i	$-0.482065\pi$
$479$	2.46499	0.112628	0.0563141	+	0.998413i	$0.482065\pi$
$480$	5.26601	0.240360
$481$	36.2356	1.65220
$482$	2.09101	0.0952430
$483$	−11.2051	−0.509848
$484$	11.3370	0.515319
$485$	−8.60379	−0.390678
$486$	1.25317	0.0568449
$487$	−11.8352	−0.536303	−0.268152	−	0.963377i	$-0.586413\pi$
$487$	−11.8352	−0.536303	−0.268152	+	0.963377i	$0.586413\pi$
$488$	−12.4972	−0.565720
$489$	−34.0883	−1.54153
$490$	17.9622	0.811448
$491$	15.4683	0.698075	0.349038	−	0.937109i	$-0.386509\pi$
$491$	15.4683	0.698075	0.349038	+	0.937109i	$0.386509\pi$
$492$	13.7266	0.618843
$493$	−0.584209	−0.0263114
$494$	−3.31637	−0.149210
$495$	1.76976	0.0795446
$496$	2.81936	0.126593
$497$	−16.5987	−0.744553
$498$	−8.93142	−0.400226
$499$	−32.7714	−1.46705	−0.733526	−	0.679662i	$-0.762127\pi$
$499$	−32.7714	−1.46705	−0.733526	+	0.679662i	$0.762127\pi$
$500$	−1.14517	−0.0512135
$501$	−3.75445	−0.167736
$502$	28.2124	1.25918
$503$	34.5762	1.54168	0.770838	−	0.637032i	$-0.219838\pi$
$503$	34.5762	1.54168	0.770838	+	0.637032i	$0.219838\pi$
$504$	0.132840	0.00591716
$505$	38.4965	1.71307
$506$	28.3477	1.26021
$507$	3.01490	0.133896
$508$	−2.70772	−0.120136
$509$	−44.7255	−1.98242	−0.991212	−	0.132286i	$-0.957768\pi$
$509$	−44.7255	−1.98242	−0.991212	+	0.132286i	$0.957768\pi$
$510$	−0.344941	−0.0152742
$511$	1.72055	0.0761125
$512$	−1.00000	−0.0441942
$513$	−5.24199	−0.231440
$514$	6.61315	0.291694
$515$	13.2133	0.582247
$516$	−4.81236	−0.211852
$517$	−22.3943	−0.984902
$518$	11.9080	0.523209
$519$	29.9428	1.31434
$520$	10.3967	0.455925
$521$	26.5235	1.16201	0.581007	−	0.813898i	$-0.302659\pi$
$521$	26.5235	1.16201	0.581007	+	0.813898i	$0.302659\pi$
$522$	1.07615	0.0471016
$523$	−32.1592	−1.40622	−0.703111	−	0.711080i	$-0.748206\pi$
$523$	−32.1592	−1.40622	−0.703111	+	0.711080i	$0.748206\pi$
$524$	−14.5970	−0.637674
$525$	−8.65136	−0.377576
$526$	−17.7963	−0.775958
$527$	−0.184677	−0.00804465
$528$	8.01972	0.349013
$529$	12.9757	0.564160
$530$	28.8595	1.25358
$531$	−1.73300	−0.0752058
$532$	−1.08985	−0.0472510
$533$	27.1004	1.17385
$534$	−7.78931	−0.337076
$535$	−32.4250	−1.40186
$536$	−0.610984	−0.0263905
$537$	32.6436	1.40867
$538$	−11.9618	−0.515709
$539$	27.3550	1.17826
$540$	16.4334	0.707183
$541$	−24.9187	−1.07134	−0.535670	−	0.844427i	$-0.679941\pi$
$541$	−24.9187	−1.07134	−0.535670	+	0.844427i	$0.679941\pi$
$542$	9.81810	0.421724
$543$	25.3438	1.08761
$544$	0.0655032	0.00280842
$545$	−41.6855	−1.78561
$546$	−6.25849	−0.267839
$547$	−5.55760	−0.237626	−0.118813	−	0.992917i	$-0.537909\pi$
$547$	−5.55760	−0.237626	−0.118813	+	0.992917i	$0.537909\pi$
$548$	−1.80758	−0.0772161
$549$	−1.50792	−0.0643563
$550$	21.8870	0.933266
$551$	−8.82896	−0.376126
$552$	10.1777	0.433193
$553$	−16.6796	−0.709290
$554$	−0.176183	−0.00748529
$555$	56.9585	2.41775
$556$	14.5191	0.615745
$557$	17.9958	0.762505	0.381252	−	0.924471i	$-0.375493\pi$
$557$	17.9958	0.762505	0.381252	+	0.924471i	$0.375493\pi$
$558$	0.340185	0.0144012
$559$	−9.50103	−0.401851
$560$	3.41664	0.144379
$561$	−0.525317	−0.0221789
$562$	5.12252	0.216080
$563$	29.6820	1.25095	0.625474	−	0.780245i	$-0.284906\pi$
$563$	29.6820	1.25095	0.625474	+	0.780245i	$0.284906\pi$
$564$	−8.04029	−0.338557
$565$	−0.839732	−0.0353278
$566$	1.16754	0.0490753
$567$	−9.49391	−0.398707
$568$	15.0768	0.632610
$569$	−19.5871	−0.821133	−0.410566	−	0.911831i	$-0.634669\pi$
$569$	−19.5871	−0.821133	−0.410566	+	0.911831i	$0.634669\pi$
$570$	−5.21297	−0.218347
$571$	−31.4220	−1.31497	−0.657484	−	0.753468i	$-0.728379\pi$
$571$	−31.4220	−1.31497	−0.657484	+	0.753468i	$0.728379\pi$
$572$	15.8333	0.662024
$573$	2.76924	0.115687
$574$	8.90594	0.371727
$575$	27.7766	1.15836
$576$	−0.120661	−0.00502752
$577$	26.3178	1.09562	0.547812	−	0.836602i	$-0.315461\pi$
$577$	26.3178	1.09562	0.547812	+	0.836602i	$0.315461\pi$
$578$	16.9957	0.706928
$579$	8.17702	0.339825
$580$	27.6784	1.14928
$581$	−5.79479	−0.240408
$582$	−4.70436	−0.195002
$583$	43.9507	1.82025
$584$	−1.56280	−0.0646690
$585$	1.25447	0.0518659
$586$	4.67725	0.193215
$587$	−34.5807	−1.42730	−0.713649	−	0.700504i	$-0.752959\pi$
$587$	−34.5807	−1.42730	−0.713649	+	0.700504i	$0.752959\pi$
$588$	9.82132	0.405024
$589$	−2.79096	−0.114999
$590$	−44.5727	−1.83503
$591$	14.6442	0.602382
$592$	−10.8162	−0.444545
$593$	−31.4655	−1.29213	−0.646066	−	0.763281i	$-0.723587\pi$
$593$	−31.4655	−1.29213	−0.646066	+	0.763281i	$0.723587\pi$
$594$	25.0268	1.02686
$595$	−0.223801	−0.00917493
$596$	−6.16805	−0.252653
$597$	−2.35833	−0.0965202
$598$	20.0939	0.821700
$599$	12.7811	0.522223	0.261111	−	0.965309i	$-0.415911\pi$
$599$	12.7811	0.522223	0.261111	+	0.965309i	$0.415911\pi$
$600$	7.85816	0.320808
$601$	31.5946	1.28877	0.644386	−	0.764701i	$-0.277113\pi$
$601$	31.5946	1.28877	0.644386	+	0.764701i	$0.277113\pi$
$602$	−3.12230	−0.127256
$603$	−0.0737216	−0.00300218
$604$	8.22272	0.334578
$605$	35.1832	1.43040
$606$	21.0491	0.855059
$607$	34.2402	1.38977	0.694884	−	0.719122i	$-0.255456\pi$
$607$	34.2402	1.38977	0.694884	+	0.719122i	$0.255456\pi$
$608$	0.989928	0.0401469
$609$	−16.6616	−0.675161
$610$	−38.7835	−1.57030
$611$	−15.8739	−0.642191
$612$	0.00790365	0.000319486 0
$613$	24.4987	0.989491	0.494746	−	0.869038i	$-0.335261\pi$
$613$	24.4987	0.989491	0.494746	+	0.869038i	$0.335261\pi$
$614$	−19.6394	−0.792582
$615$	42.5989	1.71775
$616$	5.20327	0.209646
$617$	11.3368	0.456404	0.228202	−	0.973614i	$-0.426715\pi$
$617$	11.3368	0.456404	0.228202	+	0.973614i	$0.426715\pi$
$618$	7.22473	0.290621
$619$	10.2001	0.409977	0.204988	−	0.978764i	$-0.434284\pi$
$619$	10.2001	0.409977	0.204988	+	0.978764i	$0.434284\pi$
$620$	8.74955	0.351390
$621$	31.7612	1.27453
$622$	−5.40469	−0.216708
$623$	−5.05378	−0.202475
$624$	5.68468	0.227569
$625$	−26.7089	−1.06835
$626$	−19.2759	−0.770422
$627$	−7.93894	−0.317051
$628$	−19.5862	−0.781575
$629$	0.708498	0.0282497
$630$	0.412253	0.0164246
$631$	33.4482	1.33155	0.665776	−	0.746151i	$-0.268100\pi$
$631$	33.4482	1.33155	0.665776	+	0.746151i	$0.268100\pi$
$632$	15.1504	0.602649
$633$	22.8958	0.910028
$634$	−2.18365	−0.0867237
$635$	−8.40311	−0.333467
$636$	15.7797	0.625707
$637$	19.3902	0.768268
$638$	42.1520	1.66882
$639$	1.81918	0.0719656
$640$	−3.10338	−0.122672
$641$	−37.7966	−1.49288	−0.746438	−	0.665455i	$-0.768237\pi$
$641$	−37.7966	−1.49288	−0.746438	+	0.665455i	$0.768237\pi$
$642$	−17.7293	−0.699719
$643$	−40.1016	−1.58145	−0.790725	−	0.612171i	$-0.790296\pi$
$643$	−40.1016	−1.58145	−0.790725	+	0.612171i	$0.790296\pi$
$644$	6.60341	0.260211
$645$	−14.9346	−0.588049
$646$	−0.0648434	−0.00255123
$647$	15.5390	0.610901	0.305450	−	0.952208i	$-0.401193\pi$
$647$	15.5390	0.610901	0.305450	+	0.952208i	$0.401193\pi$
$648$	8.62346	0.338761
$649$	−67.8806	−2.66455
$650$	15.5143	0.608523
$651$	−5.26696	−0.206428
$652$	20.0890	0.786747
$653$	8.28750	0.324315	0.162157	−	0.986765i	$-0.448155\pi$
$653$	8.28750	0.324315	0.162157	+	0.986765i	$0.448155\pi$
$654$	−22.7927	−0.891266
$655$	−45.3002	−1.77003
$656$	−8.08940	−0.315838
$657$	−0.188568	−0.00735674
$658$	−5.21662	−0.203365
$659$	−23.9302	−0.932187	−0.466094	−	0.884735i	$-0.654339\pi$
$659$	−23.9302	−0.932187	−0.466094	+	0.884735i	$0.654339\pi$
$660$	24.8883	0.968775
$661$	15.6173	0.607444	0.303722	−	0.952761i	$-0.401771\pi$
$661$	15.6173	0.607444	0.303722	+	0.952761i	$0.401771\pi$
$662$	−25.2610	−0.981795
$663$	−0.372364	−0.0144614
$664$	5.26349	0.204263
$665$	−3.38223	−0.131157
$666$	−1.30509	−0.0505713
$667$	53.4947	2.07132
$668$	2.21258	0.0856075
$669$	−19.2667	−0.744894
$670$	−1.89612	−0.0732534
$671$	−59.0642	−2.28015
$672$	1.86814	0.0720652
$673$	−33.9584	−1.30900	−0.654501	−	0.756061i	$-0.727121\pi$
$673$	−33.9584	−1.30900	−0.654501	+	0.756061i	$0.727121\pi$
$674$	−24.5823	−0.946874
$675$	24.5226	0.943877
$676$	−1.77675	−0.0683365
$677$	−47.5964	−1.82928	−0.914639	−	0.404273i	$-0.867525\pi$
$677$	−47.5964	−1.82928	−0.914639	+	0.404273i	$0.867525\pi$
$678$	−0.459147	−0.0176334
$679$	−3.05223	−0.117134
$680$	0.203281	0.00779549
$681$	8.59538	0.329376
$682$	13.3249	0.510235
$683$	18.4911	0.707544	0.353772	−	0.935332i	$-0.384899\pi$
$683$	18.4911	0.707544	0.353772	+	0.935332i	$0.384899\pi$
$684$	0.119445	0.00456710
$685$	−5.60962	−0.214333
$686$	14.0787	0.537529
$687$	18.6274	0.710681
$688$	2.83603	0.108123
$689$	31.1539	1.18687
$690$	31.5854	1.20244
$691$	−11.0169	−0.419101	−0.209551	−	0.977798i	$-0.567200\pi$
$691$	−11.0169	−0.419101	−0.209551	+	0.977798i	$0.567200\pi$
$692$	−17.6460	−0.670800
$693$	0.627829	0.0238493
$694$	31.8185	1.20781
$695$	45.0582	1.70916
$696$	15.1340	0.573651
$697$	0.529881	0.0200707
$698$	12.7475	0.482502
$699$	29.6375	1.12099
$700$	5.09845	0.192703
$701$	−17.5274	−0.662001	−0.331000	−	0.943631i	$-0.607386\pi$
$701$	−17.5274	−0.662001	−0.331000	+	0.943631i	$0.607386\pi$
$702$	17.7399	0.669551
$703$	10.7073	0.403833
$704$	−4.72621	−0.178126
$705$	−24.9521	−0.939751
$706$	1.51393	0.0569775
$707$	13.6568	0.513618
$708$	−24.3714	−0.915931
$709$	−20.8363	−0.782525	−0.391262	−	0.920279i	$-0.627962\pi$
$709$	−20.8363	−0.782525	−0.391262	+	0.920279i	$0.627962\pi$
$710$	46.7892	1.75597
$711$	1.82805	0.0685572
$712$	4.59042	0.172033
$713$	16.9104	0.633300
$714$	−0.122369	−0.00457955
$715$	49.1369	1.83762
$716$	−19.2376	−0.718943
$717$	−43.0254	−1.60681
$718$	28.3026	1.05624
$719$	−28.6963	−1.07019	−0.535097	−	0.844791i	$-0.679725\pi$
$719$	−28.6963	−1.07019	−0.535097	+	0.844791i	$0.679725\pi$
$720$	−0.374456	−0.0139551
$721$	4.68747	0.174571
$722$	18.0200	0.670637
$723$	3.54816	0.131957
$724$	−14.9357	−0.555081
$725$	41.3029	1.53395
$726$	19.2374	0.713966
$727$	−21.7490	−0.806626	−0.403313	−	0.915062i	$-0.632141\pi$
$727$	−21.7490	−0.806626	−0.403313	+	0.915062i	$0.632141\pi$
$728$	3.68827	0.136696
$729$	27.9968	1.03692
$730$	−4.84996	−0.179505
$731$	−0.185769	−0.00687092
$732$	−21.2060	−0.783795
$733$	44.2991	1.63622	0.818112	−	0.575059i	$-0.195021\pi$
$733$	44.2991	1.63622	0.818112	+	0.575059i	$0.195021\pi$
$734$	−32.9712	−1.21699
$735$	30.4793	1.12425
$736$	−5.99797	−0.221088
$737$	−2.88764	−0.106367
$738$	−0.976071	−0.0359297
$739$	−29.7433	−1.09412	−0.547062	−	0.837092i	$-0.684254\pi$
$739$	−29.7433	−1.09412	−0.547062	+	0.837092i	$0.684254\pi$
$740$	−33.5669	−1.23395
$741$	−5.62742	−0.206728
$742$	10.2380	0.375850
$743$	−4.80753	−0.176371	−0.0881855	−	0.996104i	$-0.528107\pi$
$743$	−4.80753	−0.176371	−0.0881855	+	0.996104i	$0.528107\pi$
$744$	4.78406	0.175392
$745$	−19.1418	−0.701302
$746$	−23.5082	−0.860697
$747$	0.635096	0.0232369
$748$	0.309581	0.0113194
$749$	−11.5029	−0.420308
$750$	−1.94319	−0.0709554
$751$	9.14523	0.333714	0.166857	−	0.985981i	$-0.446638\pi$
$751$	9.14523	0.333714	0.166857	+	0.985981i	$0.446638\pi$
$752$	4.73833	0.172789
$753$	47.8726	1.74457
$754$	29.8789	1.08813
$755$	25.5183	0.928705
$756$	5.82984	0.212029
$757$	6.83634	0.248471	0.124235	−	0.992253i	$-0.460352\pi$
$757$	6.83634	0.248471	0.124235	+	0.992253i	$0.460352\pi$
$758$	13.4273	0.487703
$759$	48.1021	1.74599
$760$	3.07213	0.111438
$761$	−17.8132	−0.645727	−0.322863	−	0.946446i	$-0.604645\pi$
$761$	−17.8132	−0.645727	−0.322863	+	0.946446i	$0.604645\pi$
$762$	−4.59463	−0.166446
$763$	−14.7881	−0.535366
$764$	−1.63198	−0.0590428
$765$	0.0245280	0.000886813 0
$766$	8.49327	0.306874
$767$	−48.1163	−1.73738
$768$	−1.69686	−0.0612302
$769$	42.8978	1.54694	0.773468	−	0.633835i	$-0.218520\pi$
$769$	42.8978	1.54694	0.773468	+	0.633835i	$0.218520\pi$
$770$	16.1477	0.581924
$771$	11.2216	0.404136
$772$	−4.81891	−0.173436
$773$	−28.2458	−1.01593	−0.507965	−	0.861378i	$-0.669602\pi$
$773$	−28.2458	−1.01593	−0.507965	+	0.861378i	$0.669602\pi$
$774$	0.342197	0.0123000
$775$	13.0564	0.469000
$776$	2.77239	0.0995229
$777$	20.2063	0.724896
$778$	12.3274	0.441958
$779$	8.00792	0.286914
$780$	17.6417	0.631675
$781$	71.2562	2.54975
$782$	0.392886	0.0140496
$783$	47.2279	1.68779
$784$	−5.78793	−0.206712
$785$	−60.7835	−2.16946
$786$	−24.7691	−0.883486
$787$	−34.2621	−1.22131	−0.610655	−	0.791897i	$-0.709094\pi$
$787$	−34.2621	−1.22131	−0.610655	+	0.791897i	$0.709094\pi$
$788$	−8.63017	−0.307437
$789$	−30.1979	−1.07508
$790$	47.0174	1.67280
$791$	−0.297899	−0.0105921
$792$	−0.570267	−0.0202635
$793$	−41.8669	−1.48674
$794$	28.8419	1.02356
$795$	48.9706	1.73681
$796$	1.38982	0.0492609
$797$	26.9633	0.955088	0.477544	−	0.878608i	$-0.341527\pi$
$797$	26.9633	0.955088	0.477544	+	0.878608i	$0.341527\pi$
$798$	−1.84933	−0.0654654
$799$	−0.310376	−0.0109803
$800$	−4.63099	−0.163730
$801$	0.553882	0.0195705
$802$	0.547787	0.0193430
$803$	−7.38610	−0.260650
$804$	−1.03675	−0.0365635
$805$	20.4929	0.722280
$806$	9.44516	0.332692
$807$	−20.2975	−0.714505
$808$	−12.4047	−0.436396
$809$	−10.2619	−0.360790	−0.180395	−	0.983594i	$-0.557738\pi$
$809$	−10.2619	−0.360790	−0.180395	+	0.983594i	$0.557738\pi$
$810$	26.7619	0.940318
$811$	−20.1632	−0.708027	−0.354014	−	0.935240i	$-0.615183\pi$
$811$	−20.1632	−0.708027	−0.354014	+	0.935240i	$0.615183\pi$
$812$	9.81905	0.344581
$813$	16.6600	0.584290
$814$	−51.1198	−1.79175
$815$	62.3440	2.18381
$816$	0.111150	0.00389102
$817$	−2.80747	−0.0982209
$818$	−17.5247	−0.612736
$819$	0.445029	0.0155506
$820$	−25.1045	−0.876688
$821$	−3.40593	−0.118868	−0.0594340	−	0.998232i	$-0.518930\pi$
$821$	−3.40593	−0.118868	−0.0594340	+	0.998232i	$0.518930\pi$
$822$	−3.06722	−0.106982
$823$	35.4925	1.23719	0.618595	−	0.785710i	$-0.287702\pi$
$823$	35.4925	1.23719	0.618595	+	0.785710i	$0.287702\pi$
$824$	−4.25770	−0.148324
$825$	37.1393	1.29302
$826$	−15.8124	−0.550182
$827$	−12.6139	−0.438629	−0.219315	−	0.975654i	$-0.570382\pi$
$827$	−12.6139	−0.438629	−0.219315	+	0.975654i	$0.570382\pi$
$828$	−0.723719	−0.0251510
$829$	23.6983	0.823076	0.411538	−	0.911392i	$-0.364992\pi$
$829$	23.6983	0.823076	0.411538	+	0.911392i	$0.364992\pi$
$830$	16.3346	0.566984
$831$	−0.298958	−0.0103707
$832$	−3.35011	−0.116144
$833$	0.379128	0.0131360
$834$	24.6368	0.853104
$835$	6.86650	0.237625
$836$	4.67860	0.161813
$837$	14.9294	0.516036
$838$	−11.7030	−0.404273
$839$	−46.3536	−1.60030	−0.800152	−	0.599797i	$-0.795248\pi$
$839$	−46.3536	−1.60030	−0.800152	+	0.599797i	$0.795248\pi$
$840$	5.79756	0.200035
$841$	50.5448	1.74292
$842$	−6.40915	−0.220874
$843$	8.69220	0.299375
$844$	−13.4931	−0.464450
$845$	−5.51393	−0.189685
$846$	0.571730	0.0196565
$847$	12.4814	0.428865
$848$	−9.29937	−0.319342
$849$	1.98115	0.0679929
$850$	0.303345	0.0104046
$851$	−64.8755	−2.22390
$852$	25.5833	0.876470
$853$	18.2913	0.626281	0.313140	−	0.949707i	$-0.398619\pi$
$853$	18.2913	0.626281	0.313140	+	0.949707i	$0.398619\pi$
$854$	−13.7586	−0.470811
$855$	0.370684	0.0126771
$856$	10.4483	0.357115
$857$	20.0439	0.684686	0.342343	−	0.939575i	$-0.388779\pi$
$857$	20.0439	0.684686	0.342343	+	0.939575i	$0.388779\pi$
$858$	26.8670	0.917223
$859$	50.0262	1.70687	0.853436	−	0.521197i	$-0.174514\pi$
$859$	50.0262	1.70687	0.853436	+	0.521197i	$0.174514\pi$
$860$	8.80130	0.300122
$861$	15.1122	0.515021
$862$	11.8112	0.402291
$863$	43.5480	1.48239	0.741195	−	0.671290i	$-0.234259\pi$
$863$	43.5480	1.48239	0.741195	+	0.671290i	$0.234259\pi$
$864$	−5.29533	−0.180151
$865$	−54.7623	−1.86197
$866$	2.78930	0.0947844
$867$	28.8394	0.979436
$868$	3.10394	0.105355
$869$	71.6037	2.42899
$870$	46.9665	1.59231
$871$	−2.04686	−0.0693554
$872$	13.4323	0.454875
$873$	0.334518	0.0113217
$874$	5.93756	0.200841
$875$	−1.26076	−0.0426216
$876$	−2.65185	−0.0895977
$877$	18.3635	0.620092	0.310046	−	0.950721i	$-0.399655\pi$
$877$	18.3635	0.620092	0.310046	+	0.950721i	$0.399655\pi$
$878$	14.4678	0.488265
$879$	7.93665	0.267696
$880$	−14.6672	−0.494432
$881$	−29.4314	−0.991569	−0.495785	−	0.868446i	$-0.665119\pi$
$881$	−29.4314	−0.991569	−0.495785	+	0.868446i	$0.665119\pi$
$882$	−0.698375	−0.0235155
$883$	−41.5248	−1.39742	−0.698711	−	0.715404i	$-0.746243\pi$
$883$	−41.5248	−1.39742	−0.698711	+	0.715404i	$0.746243\pi$
$884$	0.219443	0.00738066
$885$	−75.6337	−2.54240
$886$	14.4703	0.486141
$887$	−52.2679	−1.75498	−0.877492	−	0.479592i	$-0.840785\pi$
$887$	−52.2679	−1.75498	−0.877492	+	0.479592i	$0.840785\pi$
$888$	−18.3537	−0.615909
$889$	−2.98104	−0.0999809
$890$	14.2458	0.477522
$891$	40.7562	1.36539
$892$	11.3543	0.380171
$893$	−4.69061	−0.156965
$894$	−10.4663	−0.350046
$895$	−59.7017	−1.99561
$896$	−1.10094	−0.0367798
$897$	34.0965	1.13845
$898$	6.56567	0.219099
$899$	25.1452	0.838641
$900$	−0.558778	−0.0186259
$901$	0.609138	0.0202933
$902$	−38.2322	−1.27299
$903$	−5.29811	−0.176310
$904$	0.270586	0.00899955
$905$	−46.3512	−1.54077
$906$	13.9528	0.463552
$907$	28.6674	0.951884	0.475942	−	0.879477i	$-0.342107\pi$
$907$	28.6674	0.951884	0.475942	+	0.879477i	$0.342107\pi$
$908$	−5.06546	−0.168103
$909$	−1.49676	−0.0496443
$910$	11.4461	0.379435
$911$	−3.09718	−0.102614	−0.0513071	−	0.998683i	$-0.516339\pi$
$911$	−3.09718	−0.102614	−0.0513071	+	0.998683i	$0.516339\pi$
$912$	1.67977	0.0556228
$913$	24.8763	0.823287
$914$	−26.1503	−0.864975
$915$	−65.8103	−2.17562
$916$	−10.9776	−0.362709
$917$	−16.0705	−0.530693
$918$	0.346861	0.0114481
$919$	−35.6913	−1.17735	−0.588674	−	0.808371i	$-0.700350\pi$
$919$	−35.6913	−1.17735	−0.588674	+	0.808371i	$0.700350\pi$
$920$	−18.6140	−0.613686
$921$	−33.3254	−1.09811
$922$	−14.0435	−0.462499
$923$	50.5091	1.66253
$924$	8.82923	0.290460
$925$	−50.0899	−1.64695
$926$	22.8998	0.752534
$927$	−0.513736	−0.0168733
$928$	−8.91879	−0.292774
$929$	−54.8722	−1.80030	−0.900149	−	0.435583i	$-0.856542\pi$
$929$	−54.8722	−1.80030	−0.900149	+	0.435583i	$0.856542\pi$
$930$	14.8468	0.486845
$931$	5.72963	0.187781
$932$	−17.4661	−0.572121
$933$	−9.17101	−0.300245
$934$	−24.2008	−0.791874
$935$	0.960750	0.0314199
$936$	−0.404226	−0.0132125
$937$	4.16071	0.135924	0.0679622	−	0.997688i	$-0.478350\pi$
$937$	4.16071	0.135924	0.0679622	+	0.997688i	$0.478350\pi$
$938$	−0.672656	−0.0219630
$939$	−32.7086	−1.06741
$940$	14.7049	0.479620
$941$	11.8000	0.384670	0.192335	−	0.981329i	$-0.438394\pi$
$941$	11.8000	0.384670	0.192335	+	0.981329i	$0.438394\pi$
$942$	−33.2351	−1.08286
$943$	−48.5200	−1.58003
$944$	14.3626	0.467463
$945$	18.0922	0.588540
$946$	13.4037	0.435791
$947$	34.6398	1.12564	0.562821	−	0.826579i	$-0.309716\pi$
$947$	34.6398	1.12564	0.562821	+	0.826579i	$0.309716\pi$
$948$	25.7081	0.834959
$949$	−5.23555	−0.169953
$950$	4.58435	0.148736
$951$	−3.70535	−0.120154
$952$	0.0721150	0.00233726
$953$	6.07255	0.196709	0.0983545	−	0.995151i	$-0.468642\pi$
$953$	6.07255	0.196709	0.0983545	+	0.995151i	$0.468642\pi$
$954$	−1.12207	−0.0363282
$955$	−5.06465	−0.163888
$956$	25.3558	0.820067
$957$	71.5262	2.31211
$958$	−2.46499	−0.0796402
$959$	−1.99004	−0.0642618
$960$	−5.26601	−0.169960
$961$	−23.0512	−0.743588
$962$	−36.2356	−1.16828
$963$	1.26069	0.0406253
$964$	−2.09101	−0.0673469
$965$	−14.9549	−0.481416
$966$	11.2051	0.360517
$967$	22.3102	0.717449	0.358724	−	0.933444i	$-0.383212\pi$
$967$	22.3102	0.717449	0.358724	+	0.933444i	$0.383212\pi$
$968$	−11.3370	−0.364386
$969$	−0.110030	−0.00353468
$970$	8.60379	0.276251
$971$	−3.01548	−0.0967715	−0.0483857	−	0.998829i	$-0.515408\pi$
$971$	−3.01548	−0.0967715	−0.0483857	+	0.998829i	$0.515408\pi$
$972$	−1.25317	−0.0401954
$973$	15.9846	0.512443
$974$	11.8352	0.379224
$975$	26.3257	0.843097
$976$	12.4972	0.400025
$977$	57.7911	1.84890	0.924451	−	0.381301i	$-0.124524\pi$
$977$	57.7911	1.84890	0.924451	+	0.381301i	$0.124524\pi$
$978$	34.0883	1.09002
$979$	21.6953	0.693384
$980$	−17.9622	−0.573781
$981$	1.62075	0.0517464
$982$	−15.4683	−0.493614
$983$	17.6435	0.562739	0.281370	−	0.959599i	$-0.409211\pi$
$983$	17.6435	0.562739	0.281370	+	0.959599i	$0.409211\pi$
$984$	−13.7266	−0.437588
$985$	−26.7827	−0.853369
$986$	0.584209	0.0186050
$987$	−8.85188	−0.281758
$988$	3.31637	0.105508
$989$	17.0105	0.540901
$990$	−1.76976	−0.0562465
$991$	26.3910	0.838336	0.419168	−	0.907909i	$-0.362322\pi$
$991$	26.3910	0.838336	0.419168	+	0.907909i	$0.362322\pi$
$992$	−2.81936	−0.0895147
$993$	−42.8643	−1.36026
$994$	16.5987	0.526479
$995$	4.31315	0.136736
$996$	8.93142	0.283003
$997$	26.2794	0.832277	0.416139	−	0.909301i	$-0.363383\pi$
$997$	26.2794	0.832277	0.416139	+	0.909301i	$0.363383\pi$
$998$	32.7714	1.03736
$999$	−57.2755	−1.81212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.12	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.69686 q^{3} +1.00000 q^{4} +3.10338 q^{5} +1.69686 q^{6} +1.10094 q^{7} -1.00000 q^{8} -0.120661 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.69686 q^{3} +1.00000 q^{4} +3.10338 q^{5} +1.69686 q^{6} +1.10094 q^{7} -1.00000 q^{8} -0.120661 q^{9} -3.10338 q^{10} -4.72621 q^{11} -1.69686 q^{12} -3.35011 q^{13} -1.10094 q^{14} -5.26601 q^{15} +1.00000 q^{16} -0.0655032 q^{17} +0.120661 q^{18} -0.989928 q^{19} +3.10338 q^{20} -1.86814 q^{21} +4.72621 q^{22} +5.99797 q^{23} +1.69686 q^{24} +4.63099 q^{25} +3.35011 q^{26} +5.29533 q^{27} +1.10094 q^{28} +8.91879 q^{29} +5.26601 q^{30} +2.81936 q^{31} -1.00000 q^{32} +8.01972 q^{33} +0.0655032 q^{34} +3.41664 q^{35} -0.120661 q^{36} -10.8162 q^{37} +0.989928 q^{38} +5.68468 q^{39} -3.10338 q^{40} -8.08940 q^{41} +1.86814 q^{42} +2.83603 q^{43} -4.72621 q^{44} -0.374456 q^{45} -5.99797 q^{46} +4.73833 q^{47} -1.69686 q^{48} -5.78793 q^{49} -4.63099 q^{50} +0.111150 q^{51} -3.35011 q^{52} -9.29937 q^{53} -5.29533 q^{54} -14.6672 q^{55} -1.10094 q^{56} +1.67977 q^{57} -8.91879 q^{58} +14.3626 q^{59} -5.26601 q^{60} +12.4972 q^{61} -2.81936 q^{62} -0.132840 q^{63} +1.00000 q^{64} -10.3967 q^{65} -8.01972 q^{66} +0.610984 q^{67} -0.0655032 q^{68} -10.1777 q^{69} -3.41664 q^{70} -15.0768 q^{71} +0.120661 q^{72} +1.56280 q^{73} +10.8162 q^{74} -7.85816 q^{75} -0.989928 q^{76} -5.20327 q^{77} -5.68468 q^{78} -15.1504 q^{79} +3.10338 q^{80} -8.62346 q^{81} +8.08940 q^{82} -5.26349 q^{83} -1.86814 q^{84} -0.203281 q^{85} -2.83603 q^{86} -15.1340 q^{87} +4.72621 q^{88} -4.59042 q^{89} +0.374456 q^{90} -3.68827 q^{91} +5.99797 q^{92} -4.78406 q^{93} -4.73833 q^{94} -3.07213 q^{95} +1.69686 q^{96} -2.77239 q^{97} +5.78793 q^{98} +0.570267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 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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