LMFDB - Embedded newform 4006.2.a.i.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:	$0$
Dimension:	$46$
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.38097 q^{3} +1.00000 q^{4} -1.46012 q^{5} -1.38097 q^{6} +0.773639 q^{7} +1.00000 q^{8} -1.09292 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.38097 q^{3} +1.00000 q^{4} -1.46012 q^{5} -1.38097 q^{6} +0.773639 q^{7} +1.00000 q^{8} -1.09292 q^{9} -1.46012 q^{10} +2.99112 q^{11} -1.38097 q^{12} +3.76507 q^{13} +0.773639 q^{14} +2.01638 q^{15} +1.00000 q^{16} -2.55144 q^{17} -1.09292 q^{18} +2.03294 q^{19} -1.46012 q^{20} -1.06837 q^{21} +2.99112 q^{22} -6.63772 q^{23} -1.38097 q^{24} -2.86805 q^{25} +3.76507 q^{26} +5.65220 q^{27} +0.773639 q^{28} +3.84595 q^{29} +2.01638 q^{30} -0.975143 q^{31} +1.00000 q^{32} -4.13066 q^{33} -2.55144 q^{34} -1.12961 q^{35} -1.09292 q^{36} +10.7569 q^{37} +2.03294 q^{38} -5.19946 q^{39} -1.46012 q^{40} +1.33302 q^{41} -1.06837 q^{42} -7.94638 q^{43} +2.99112 q^{44} +1.59579 q^{45} -6.63772 q^{46} +5.68312 q^{47} -1.38097 q^{48} -6.40148 q^{49} -2.86805 q^{50} +3.52347 q^{51} +3.76507 q^{52} +4.50574 q^{53} +5.65220 q^{54} -4.36740 q^{55} +0.773639 q^{56} -2.80743 q^{57} +3.84595 q^{58} -4.26994 q^{59} +2.01638 q^{60} -4.68170 q^{61} -0.975143 q^{62} -0.845524 q^{63} +1.00000 q^{64} -5.49746 q^{65} -4.13066 q^{66} +11.2065 q^{67} -2.55144 q^{68} +9.16650 q^{69} -1.12961 q^{70} +7.35280 q^{71} -1.09292 q^{72} -2.27439 q^{73} +10.7569 q^{74} +3.96069 q^{75} +2.03294 q^{76} +2.31405 q^{77} -5.19946 q^{78} -7.15183 q^{79} -1.46012 q^{80} -4.52678 q^{81} +1.33302 q^{82} +12.6854 q^{83} -1.06837 q^{84} +3.72541 q^{85} -7.94638 q^{86} -5.31115 q^{87} +2.99112 q^{88} +10.4057 q^{89} +1.59579 q^{90} +2.91281 q^{91} -6.63772 q^{92} +1.34665 q^{93} +5.68312 q^{94} -2.96834 q^{95} -1.38097 q^{96} +4.58327 q^{97} -6.40148 q^{98} -3.26905 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) $ 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * 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
$3$	−1.38097	−0.797304	−0.398652	−	0.917102i	$-0.630522\pi$
$3$	−1.38097	−0.797304	−0.398652	+	0.917102i	$0.630522\pi$
$4$	1.00000	0.500000
$5$	−1.46012	−0.652986	−0.326493	−	0.945200i	$-0.605867\pi$
$5$	−1.46012	−0.652986	−0.326493	+	0.945200i	$0.605867\pi$
$6$	−1.38097	−0.563779
$7$	0.773639	0.292408	0.146204	−	0.989254i	$-0.453294\pi$
$7$	0.773639	0.292408	0.146204	+	0.989254i	$0.453294\pi$
$8$	1.00000	0.353553
$9$	−1.09292	−0.364306
$10$	−1.46012	−0.461731
$11$	2.99112	0.901857	0.450929	−	0.892560i	$-0.351093\pi$
$11$	2.99112	0.901857	0.450929	+	0.892560i	$0.351093\pi$
$12$	−1.38097	−0.398652
$13$	3.76507	1.04424	0.522121	−	0.852871i	$-0.325141\pi$
$13$	3.76507	1.04424	0.522121	+	0.852871i	$0.325141\pi$
$14$	0.773639	0.206764
$15$	2.01638	0.520628
$16$	1.00000	0.250000
$17$	−2.55144	−0.618815	−0.309407	−	0.950930i	$-0.600131\pi$
$17$	−2.55144	−0.618815	−0.309407	+	0.950930i	$0.600131\pi$
$18$	−1.09292	−0.257603
$19$	2.03294	0.466388	0.233194	−	0.972430i	$-0.425082\pi$
$19$	2.03294	0.466388	0.233194	+	0.972430i	$0.425082\pi$
$20$	−1.46012	−0.326493
$21$	−1.06837	−0.233138
$22$	2.99112	0.637709
$23$	−6.63772	−1.38406	−0.692030	−	0.721869i	$-0.743283\pi$
$23$	−6.63772	−1.38406	−0.692030	+	0.721869i	$0.743283\pi$
$24$	−1.38097	−0.281890
$25$	−2.86805	−0.573610
$26$	3.76507	0.738391
$27$	5.65220	1.08777
$28$	0.773639	0.146204
$29$	3.84595	0.714175	0.357088	−	0.934071i	$-0.383770\pi$
$29$	3.84595	0.714175	0.357088	+	0.934071i	$0.383770\pi$
$30$	2.01638	0.368140
$31$	−0.975143	−0.175141	−0.0875705	−	0.996158i	$-0.527910\pi$
$31$	−0.975143	−0.175141	−0.0875705	+	0.996158i	$0.527910\pi$
$32$	1.00000	0.176777
$33$	−4.13066	−0.719055
$34$	−2.55144	−0.437568
$35$	−1.12961	−0.190938
$36$	−1.09292	−0.182153
$37$	10.7569	1.76842	0.884210	−	0.467089i	$-0.154697\pi$
$37$	10.7569	1.76842	0.884210	+	0.467089i	$0.154697\pi$
$38$	2.03294	0.329786
$39$	−5.19946	−0.832579
$40$	−1.46012	−0.230865
$41$	1.33302	0.208183	0.104091	−	0.994568i	$-0.466807\pi$
$41$	1.33302	0.208183	0.104091	+	0.994568i	$0.466807\pi$
$42$	−1.06837	−0.164854
$43$	−7.94638	−1.21181	−0.605906	−	0.795537i	$-0.707189\pi$
$43$	−7.94638	−1.21181	−0.605906	+	0.795537i	$0.707189\pi$
$44$	2.99112	0.450929
$45$	1.59579	0.237886
$46$	−6.63772	−0.978678
$47$	5.68312	0.828968	0.414484	−	0.910057i	$-0.363962\pi$
$47$	5.68312	0.828968	0.414484	+	0.910057i	$0.363962\pi$
$48$	−1.38097	−0.199326
$49$	−6.40148	−0.914497
$50$	−2.86805	−0.405603
$51$	3.52347	0.493384
$52$	3.76507	0.522121
$53$	4.50574	0.618912	0.309456	−	0.950914i	$-0.399853\pi$
$53$	4.50574	0.618912	0.309456	+	0.950914i	$0.399853\pi$
$54$	5.65220	0.769167
$55$	−4.36740	−0.588900
$56$	0.773639	0.103382
$57$	−2.80743	−0.371853
$58$	3.84595	0.504998
$59$	−4.26994	−0.555899	−0.277949	−	0.960596i	$-0.589655\pi$
$59$	−4.26994	−0.555899	−0.277949	+	0.960596i	$0.589655\pi$
$60$	2.01638	0.260314
$61$	−4.68170	−0.599430	−0.299715	−	0.954029i	$-0.596892\pi$
$61$	−4.68170	−0.599430	−0.299715	+	0.954029i	$0.596892\pi$
$62$	−0.975143	−0.123843
$63$	−0.845524	−0.106526
$64$	1.00000	0.125000
$65$	−5.49746	−0.681876
$66$	−4.13066	−0.508449
$67$	11.2065	1.36910	0.684548	−	0.728967i	$-0.259999\pi$
$67$	11.2065	1.36910	0.684548	+	0.728967i	$0.259999\pi$
$68$	−2.55144	−0.309407
$69$	9.16650	1.10352
$70$	−1.12961	−0.135014
$71$	7.35280	0.872616	0.436308	−	0.899797i	$-0.356286\pi$
$71$	7.35280	0.872616	0.436308	+	0.899797i	$0.356286\pi$
$72$	−1.09292	−0.128802
$73$	−2.27439	−0.266197	−0.133098	−	0.991103i	$-0.542493\pi$
$73$	−2.27439	−0.266197	−0.133098	+	0.991103i	$0.542493\pi$
$74$	10.7569	1.25046
$75$	3.96069	0.457341
$76$	2.03294	0.233194
$77$	2.31405	0.263711
$78$	−5.19946	−0.588723
$79$	−7.15183	−0.804643	−0.402322	−	0.915498i	$-0.631797\pi$
$79$	−7.15183	−0.804643	−0.402322	+	0.915498i	$0.631797\pi$
$80$	−1.46012	−0.163246
$81$	−4.52678	−0.502976
$82$	1.33302	0.147207
$83$	12.6854	1.39240	0.696202	−	0.717846i	$-0.254872\pi$
$83$	12.6854	1.39240	0.696202	+	0.717846i	$0.254872\pi$
$84$	−1.06837	−0.116569
$85$	3.72541	0.404077
$86$	−7.94638	−0.856880
$87$	−5.31115	−0.569415
$88$	2.99112	0.318855
$89$	10.4057	1.10300	0.551501	−	0.834175i	$-0.314055\pi$
$89$	10.4057	1.10300	0.551501	+	0.834175i	$0.314055\pi$
$90$	1.59579	0.168211
$91$	2.91281	0.305345
$92$	−6.63772	−0.692030
$93$	1.34665	0.139641
$94$	5.68312	0.586169
$95$	−2.96834	−0.304545
$96$	−1.38097	−0.140945
$97$	4.58327	0.465360	0.232680	−	0.972553i	$-0.425250\pi$
$97$	4.58327	0.465360	0.232680	+	0.972553i	$0.425250\pi$
$98$	−6.40148	−0.646647
$99$	−3.26905	−0.328552
$100$	−2.86805	−0.286805
$101$	−1.55857	−0.155083	−0.0775416	−	0.996989i	$-0.524707\pi$
$101$	−1.55857	−0.155083	−0.0775416	+	0.996989i	$0.524707\pi$
$102$	3.52347	0.348875
$103$	6.81422	0.671425	0.335712	−	0.941965i	$-0.391023\pi$
$103$	6.81422	0.671425	0.335712	+	0.941965i	$0.391023\pi$
$104$	3.76507	0.369196
$105$	1.55995	0.152236
$106$	4.50574	0.437637
$107$	9.72878	0.940517	0.470259	−	0.882529i	$-0.344161\pi$
$107$	9.72878	0.940517	0.470259	+	0.882529i	$0.344161\pi$
$108$	5.65220	0.543883
$109$	8.54918	0.818863	0.409431	−	0.912341i	$-0.365727\pi$
$109$	8.54918	0.818863	0.409431	+	0.912341i	$0.365727\pi$
$110$	−4.36740	−0.416415
$111$	−14.8549	−1.40997
$112$	0.773639	0.0731021
$113$	−7.76698	−0.730656	−0.365328	−	0.930879i	$-0.619043\pi$
$113$	−7.76698	−0.730656	−0.365328	+	0.930879i	$0.619043\pi$
$114$	−2.80743	−0.262940
$115$	9.69186	0.903771
$116$	3.84595	0.357088
$117$	−4.11491	−0.380424
$118$	−4.26994	−0.393080
$119$	−1.97389	−0.180947
$120$	2.01638	0.184070
$121$	−2.05319	−0.186653
$122$	−4.68170	−0.423861
$123$	−1.84086	−0.165985
$124$	−0.975143	−0.0875705
$125$	11.4883	1.02754
$126$	−0.845524	−0.0753253
$127$	−9.54442	−0.846931	−0.423465	−	0.905912i	$-0.639186\pi$
$127$	−9.54442	−0.846931	−0.423465	+	0.905912i	$0.639186\pi$
$128$	1.00000	0.0883883
$129$	10.9737	0.966182
$130$	−5.49746	−0.482159
$131$	3.28056	0.286624	0.143312	−	0.989678i	$-0.454225\pi$
$131$	3.28056	0.286624	0.143312	+	0.989678i	$0.454225\pi$
$132$	−4.13066	−0.359527
$133$	1.57276	0.136376
$134$	11.2065	0.968098
$135$	−8.25290	−0.710296
$136$	−2.55144	−0.218784
$137$	11.2286	0.959321	0.479661	−	0.877454i	$-0.340760\pi$
$137$	11.2286	0.959321	0.479661	+	0.877454i	$0.340760\pi$
$138$	9.16650	0.780304
$139$	6.76677	0.573950	0.286975	−	0.957938i	$-0.407350\pi$
$139$	6.76677	0.573950	0.286975	+	0.957938i	$0.407350\pi$
$140$	−1.12961	−0.0954692
$141$	−7.84823	−0.660940
$142$	7.35280	0.617033
$143$	11.2618	0.941758
$144$	−1.09292	−0.0910764
$145$	−5.61555	−0.466346
$146$	−2.27439	−0.188230
$147$	8.84027	0.729133
$148$	10.7569	0.884210
$149$	23.8967	1.95770	0.978849	−	0.204584i	$-0.0655842\pi$
$149$	23.8967	1.95770	0.978849	+	0.204584i	$0.0655842\pi$
$150$	3.96069	0.323389
$151$	4.27945	0.348257	0.174128	−	0.984723i	$-0.444289\pi$
$151$	4.27945	0.348257	0.174128	+	0.984723i	$0.444289\pi$
$152$	2.03294	0.164893
$153$	2.78851	0.225438
$154$	2.31405	0.186471
$155$	1.42383	0.114365
$156$	−5.19946	−0.416290
$157$	−6.20376	−0.495114	−0.247557	−	0.968873i	$-0.579628\pi$
$157$	−6.20376	−0.495114	−0.247557	+	0.968873i	$0.579628\pi$
$158$	−7.15183	−0.568969
$159$	−6.22231	−0.493461
$160$	−1.46012	−0.115433
$161$	−5.13520	−0.404710
$162$	−4.52678	−0.355657
$163$	−4.32920	−0.339089	−0.169545	−	0.985523i	$-0.554230\pi$
$163$	−4.32920	−0.339089	−0.169545	+	0.985523i	$0.554230\pi$
$164$	1.33302	0.104091
$165$	6.03125	0.469533
$166$	12.6854	0.984579
$167$	−2.39340	−0.185207	−0.0926034	−	0.995703i	$-0.529519\pi$
$167$	−2.39340	−0.185207	−0.0926034	+	0.995703i	$0.529519\pi$
$168$	−1.06837	−0.0824269
$169$	1.17576	0.0904433
$170$	3.72541	0.285726
$171$	−2.22183	−0.169908
$172$	−7.94638	−0.605906
$173$	12.9717	0.986220	0.493110	−	0.869967i	$-0.335860\pi$
$173$	12.9717	0.986220	0.493110	+	0.869967i	$0.335860\pi$
$174$	−5.31115	−0.402637
$175$	−2.21884	−0.167728
$176$	2.99112	0.225464
$177$	5.89666	0.443220
$178$	10.4057	0.779940
$179$	25.4275	1.90054	0.950270	−	0.311427i	$-0.100807\pi$
$179$	25.4275	1.90054	0.950270	+	0.311427i	$0.100807\pi$
$180$	1.59579	0.118943
$181$	3.03578	0.225647	0.112824	−	0.993615i	$-0.464010\pi$
$181$	3.03578	0.225647	0.112824	+	0.993615i	$0.464010\pi$
$182$	2.91281	0.215912
$183$	6.46530	0.477929
$184$	−6.63772	−0.489339
$185$	−15.7063	−1.15475
$186$	1.34665	0.0987408
$187$	−7.63167	−0.558083
$188$	5.68312	0.414484
$189$	4.37277	0.318072
$190$	−2.96834	−0.215346
$191$	27.2057	1.96853	0.984267	−	0.176690i	$-0.0565390\pi$
$191$	27.2057	1.96853	0.984267	+	0.176690i	$0.0565390\pi$
$192$	−1.38097	−0.0996630
$193$	−5.95014	−0.428300	−0.214150	−	0.976801i	$-0.568698\pi$
$193$	−5.95014	−0.428300	−0.214150	+	0.976801i	$0.568698\pi$
$194$	4.58327	0.329059
$195$	7.59183	0.543662
$196$	−6.40148	−0.457249
$197$	24.1009	1.71711	0.858557	−	0.512718i	$-0.171361\pi$
$197$	24.1009	1.71711	0.858557	+	0.512718i	$0.171361\pi$
$198$	−3.26905	−0.232321
$199$	6.74955	0.478463	0.239231	−	0.970963i	$-0.423105\pi$
$199$	6.74955	0.478463	0.239231	+	0.970963i	$0.423105\pi$
$200$	−2.86805	−0.202802
$201$	−15.4759	−1.09159
$202$	−1.55857	−0.109660
$203$	2.97538	0.208831
$204$	3.52347	0.246692
$205$	−1.94637	−0.135940
$206$	6.81422	0.474769
$207$	7.25447	0.504221
$208$	3.76507	0.261061
$209$	6.08077	0.420616
$210$	1.55995	0.107647
$211$	−15.3508	−1.05679	−0.528396	−	0.848998i	$-0.677206\pi$
$211$	−15.3508	−1.05679	−0.528396	+	0.848998i	$0.677206\pi$
$212$	4.50574	0.309456
$213$	−10.1540	−0.695741
$214$	9.72878	0.665046
$215$	11.6027	0.791295
$216$	5.65220	0.384584
$217$	−0.754409	−0.0512126
$218$	8.54918	0.579023
$219$	3.14086	0.212240
$220$	−4.36740	−0.294450
$221$	−9.60635	−0.646193
$222$	−14.8549	−0.996999
$223$	9.78797	0.655451	0.327726	−	0.944773i	$-0.393718\pi$
$223$	9.78797	0.655451	0.327726	+	0.944773i	$0.393718\pi$
$224$	0.773639	0.0516910
$225$	3.13454	0.208969
$226$	−7.76698	−0.516652
$227$	−17.0136	−1.12923	−0.564615	−	0.825354i	$-0.690975\pi$
$227$	−17.0136	−1.12923	−0.564615	+	0.825354i	$0.690975\pi$
$228$	−2.80743	−0.185927
$229$	18.2387	1.20525	0.602624	−	0.798025i	$-0.294122\pi$
$229$	18.2387	1.20525	0.602624	+	0.798025i	$0.294122\pi$
$230$	9.69186	0.639063
$231$	−3.19564	−0.210258
$232$	3.84595	0.252499
$233$	26.3814	1.72831	0.864153	−	0.503229i	$-0.167855\pi$
$233$	26.3814	1.72831	0.864153	+	0.503229i	$0.167855\pi$
$234$	−4.11491	−0.269000
$235$	−8.29804	−0.541304
$236$	−4.26994	−0.277949
$237$	9.87647	0.641546
$238$	−1.97389	−0.127949
$239$	−26.7753	−1.73195	−0.865974	−	0.500089i	$-0.833301\pi$
$239$	−26.7753	−1.73195	−0.865974	+	0.500089i	$0.833301\pi$
$240$	2.01638	0.130157
$241$	9.57584	0.616834	0.308417	−	0.951251i	$-0.400201\pi$
$241$	9.57584	0.616834	0.308417	+	0.951251i	$0.400201\pi$
$242$	−2.05319	−0.131984
$243$	−10.7053	−0.686742
$244$	−4.68170	−0.299715
$245$	9.34693	0.597154
$246$	−1.84086	−0.117369
$247$	7.65416	0.487023
$248$	−0.975143	−0.0619217
$249$	−17.5182	−1.11017
$250$	11.4883	0.726584
$251$	−22.3131	−1.40839	−0.704196	−	0.710005i	$-0.748692\pi$
$251$	−22.3131	−1.40839	−0.704196	+	0.710005i	$0.748692\pi$
$252$	−0.845524	−0.0532630
$253$	−19.8542	−1.24822
$254$	−9.54442	−0.598870
$255$	−5.14468	−0.322173
$256$	1.00000	0.0625000
$257$	19.3223	1.20529	0.602647	−	0.798008i	$-0.294113\pi$
$257$	19.3223	1.20529	0.602647	+	0.798008i	$0.294113\pi$
$258$	10.9737	0.683194
$259$	8.32195	0.517101
$260$	−5.49746	−0.340938
$261$	−4.20331	−0.260178
$262$	3.28056	0.202674
$263$	−16.2204	−1.00019	−0.500097	−	0.865969i	$-0.666702\pi$
$263$	−16.2204	−1.00019	−0.500097	+	0.865969i	$0.666702\pi$
$264$	−4.13066	−0.254224
$265$	−6.57893	−0.404140
$266$	1.57276	0.0964322
$267$	−14.3700	−0.879428
$268$	11.2065	0.684548
$269$	10.2240	0.623367	0.311683	−	0.950186i	$-0.399107\pi$
$269$	10.2240	0.623367	0.311683	+	0.950186i	$0.399107\pi$
$270$	−8.25290	−0.502255
$271$	24.3000	1.47612	0.738059	−	0.674736i	$-0.235742\pi$
$271$	24.3000	1.47612	0.738059	+	0.674736i	$0.235742\pi$
$272$	−2.55144	−0.154704
$273$	−4.02250	−0.243453
$274$	11.2286	0.678343
$275$	−8.57868	−0.517314
$276$	9.16650	0.551758
$277$	−2.28884	−0.137523	−0.0687615	−	0.997633i	$-0.521905\pi$
$277$	−2.28884	−0.137523	−0.0687615	+	0.997633i	$0.521905\pi$
$278$	6.76677	0.405844
$279$	1.06575	0.0638048
$280$	−1.12961	−0.0675069
$281$	−19.4986	−1.16319	−0.581596	−	0.813478i	$-0.697572\pi$
$281$	−19.4986	−1.16319	−0.581596	+	0.813478i	$0.697572\pi$
$282$	−7.84823	−0.467355
$283$	−14.0614	−0.835866	−0.417933	−	0.908478i	$-0.637245\pi$
$283$	−14.0614	−0.835866	−0.417933	+	0.908478i	$0.637245\pi$
$284$	7.35280	0.436308
$285$	4.09919	0.242815
$286$	11.2618	0.665924
$287$	1.03128	0.0608744
$288$	−1.09292	−0.0644008
$289$	−10.4902	−0.617068
$290$	−5.61555	−0.329757
$291$	−6.32936	−0.371034
$292$	−2.27439	−0.133098
$293$	−17.3792	−1.01530	−0.507652	−	0.861562i	$-0.669486\pi$
$293$	−17.3792	−1.01530	−0.507652	+	0.861562i	$0.669486\pi$
$294$	8.84027	0.515575
$295$	6.23463	0.362994
$296$	10.7569	0.625231
$297$	16.9064	0.981011
$298$	23.8967	1.38430
$299$	−24.9915	−1.44529
$300$	3.96069	0.228671
$301$	−6.14763	−0.354344
$302$	4.27945	0.246255
$303$	2.15234	0.123649
$304$	2.03294	0.116597
$305$	6.83585	0.391420
$306$	2.78851	0.159409
$307$	−12.8072	−0.730948	−0.365474	−	0.930822i	$-0.619093\pi$
$307$	−12.8072	−0.730948	−0.365474	+	0.930822i	$0.619093\pi$
$308$	2.31405	0.131855
$309$	−9.41024	−0.535330
$310$	1.42383	0.0808679
$311$	25.1891	1.42834	0.714170	−	0.699972i	$-0.246804\pi$
$311$	25.1891	1.42834	0.714170	+	0.699972i	$0.246804\pi$
$312$	−5.19946	−0.294361
$313$	−8.61146	−0.486749	−0.243374	−	0.969932i	$-0.578254\pi$
$313$	−8.61146	−0.486749	−0.243374	+	0.969932i	$0.578254\pi$
$314$	−6.20376	−0.350099
$315$	1.23457	0.0695600
$316$	−7.15183	−0.402322
$317$	−20.8395	−1.17046	−0.585232	−	0.810866i	$-0.698996\pi$
$317$	−20.8395	−1.17046	−0.585232	+	0.810866i	$0.698996\pi$
$318$	−6.22231	−0.348930
$319$	11.5037	0.644084
$320$	−1.46012	−0.0816232
$321$	−13.4352	−0.749878
$322$	−5.13520	−0.286173
$323$	−5.18692	−0.288608
$324$	−4.52678	−0.251488
$325$	−10.7984	−0.598988
$326$	−4.32920	−0.239772
$327$	−11.8062	−0.652883
$328$	1.33302	0.0736037
$329$	4.39668	0.242397
$330$	6.03125	0.332010
$331$	29.0664	1.59764	0.798818	−	0.601573i	$-0.205459\pi$
$331$	29.0664	1.59764	0.798818	+	0.601573i	$0.205459\pi$
$332$	12.6854	0.696202
$333$	−11.7564	−0.644246
$334$	−2.39340	−0.130961
$335$	−16.3629	−0.894001
$336$	−1.06837	−0.0582846
$337$	−26.4290	−1.43968	−0.719838	−	0.694142i	$-0.755784\pi$
$337$	−26.4290	−1.43968	−0.719838	+	0.694142i	$0.755784\pi$
$338$	1.17576	0.0639531
$339$	10.7260	0.582555
$340$	3.72541	0.202039
$341$	−2.91677	−0.157952
$342$	−2.22183	−0.120143
$343$	−10.3679	−0.559815
$344$	−7.94638	−0.428440
$345$	−13.3842	−0.720581
$346$	12.9717	0.697363
$347$	4.80578	0.257988	0.128994	−	0.991645i	$-0.458825\pi$
$347$	4.80578	0.257988	0.128994	+	0.991645i	$0.458825\pi$
$348$	−5.31115	−0.284707
$349$	1.08083	0.0578556	0.0289278	−	0.999582i	$-0.490791\pi$
$349$	1.08083	0.0578556	0.0289278	+	0.999582i	$0.490791\pi$
$350$	−2.21884	−0.118602
$351$	21.2809	1.13589
$352$	2.99112	0.159427
$353$	−21.0364	−1.11966	−0.559828	−	0.828609i	$-0.689133\pi$
$353$	−21.0364	−1.11966	−0.559828	+	0.828609i	$0.689133\pi$
$354$	5.89666	0.313404
$355$	−10.7360	−0.569806
$356$	10.4057	0.551501
$357$	2.72589	0.144269
$358$	25.4275	1.34388
$359$	−23.2553	−1.22737	−0.613684	−	0.789552i	$-0.710313\pi$
$359$	−23.2553	−1.22737	−0.613684	+	0.789552i	$0.710313\pi$
$360$	1.59579	0.0841056
$361$	−14.8672	−0.782482
$362$	3.03578	0.159557
$363$	2.83539	0.148819
$364$	2.91281	0.152673
$365$	3.32088	0.173823
$366$	6.46530	0.337946
$367$	−19.1475	−0.999491	−0.499745	−	0.866172i	$-0.666573\pi$
$367$	−19.1475	−0.999491	−0.499745	+	0.866172i	$0.666573\pi$
$368$	−6.63772	−0.346015
$369$	−1.45688	−0.0758422
$370$	−15.7063	−0.816534
$371$	3.48582	0.180975
$372$	1.34665	0.0698203
$373$	0.0977257	0.00506004	0.00253002	−	0.999997i	$-0.499195\pi$
$373$	0.0977257	0.00506004	0.00253002	+	0.999997i	$0.499195\pi$
$374$	−7.63167	−0.394624
$375$	−15.8650	−0.819266
$376$	5.68312	0.293084
$377$	14.4803	0.745772
$378$	4.37277	0.224911
$379$	30.8185	1.58304	0.791520	−	0.611144i	$-0.209290\pi$
$379$	30.8185	1.58304	0.791520	+	0.611144i	$0.209290\pi$
$380$	−2.96834	−0.152272
$381$	13.1806	0.675261
$382$	27.2057	1.39196
$383$	27.4362	1.40193	0.700963	−	0.713197i	$-0.252754\pi$
$383$	27.4362	1.40193	0.700963	+	0.713197i	$0.252754\pi$
$384$	−1.38097	−0.0704724
$385$	−3.37879	−0.172199
$386$	−5.95014	−0.302854
$387$	8.68473	0.441470
$388$	4.58327	0.232680
$389$	−18.9413	−0.960361	−0.480181	−	0.877170i	$-0.659429\pi$
$389$	−18.9413	−0.960361	−0.480181	+	0.877170i	$0.659429\pi$
$390$	7.59183	0.384427
$391$	16.9357	0.856477
$392$	−6.40148	−0.323324
$393$	−4.53036	−0.228526
$394$	24.1009	1.21418
$395$	10.4425	0.525421
$396$	−3.26905	−0.164276
$397$	13.7160	0.688387	0.344194	−	0.938899i	$-0.388152\pi$
$397$	13.7160	0.688387	0.344194	+	0.938899i	$0.388152\pi$
$398$	6.74955	0.338324
$399$	−2.17194	−0.108733
$400$	−2.86805	−0.143402
$401$	0.415854	0.0207668	0.0103834	−	0.999946i	$-0.496695\pi$
$401$	0.415854	0.0207668	0.0103834	+	0.999946i	$0.496695\pi$
$402$	−15.4759	−0.771868
$403$	−3.67148	−0.182890
$404$	−1.55857	−0.0775416
$405$	6.60964	0.328436
$406$	2.97538	0.147666
$407$	32.1751	1.59486
$408$	3.52347	0.174438
$409$	5.44526	0.269251	0.134625	−	0.990897i	$-0.457017\pi$
$409$	5.44526	0.269251	0.134625	+	0.990897i	$0.457017\pi$
$410$	−1.94637	−0.0961244
$411$	−15.5063	−0.764871
$412$	6.81422	0.335712
$413$	−3.30339	−0.162549
$414$	7.25447	0.356538
$415$	−18.5222	−0.909220
$416$	3.76507	0.184598
$417$	−9.34472	−0.457613
$418$	6.08077	0.297420
$419$	24.5266	1.19820	0.599102	−	0.800673i	$-0.295524\pi$
$419$	24.5266	1.19820	0.599102	+	0.800673i	$0.295524\pi$
$420$	1.55995	0.0761180
$421$	−32.3408	−1.57619	−0.788096	−	0.615552i	$-0.788933\pi$
$421$	−32.3408	−1.57619	−0.788096	+	0.615552i	$0.788933\pi$
$422$	−15.3508	−0.747264
$423$	−6.21118	−0.301998
$424$	4.50574	0.218818
$425$	7.31765	0.354958
$426$	−10.1540	−0.491963
$427$	−3.62195	−0.175278
$428$	9.72878	0.470259
$429$	−15.5522	−0.750868
$430$	11.6027	0.559530
$431$	8.05725	0.388104	0.194052	−	0.980991i	$-0.437837\pi$
$431$	8.05725	0.388104	0.194052	+	0.980991i	$0.437837\pi$
$432$	5.65220	0.271942
$433$	−28.5878	−1.37384	−0.686922	−	0.726731i	$-0.741039\pi$
$433$	−28.5878	−1.37384	−0.686922	+	0.726731i	$0.741039\pi$
$434$	−0.754409	−0.0362128
$435$	7.75492	0.371820
$436$	8.54918	0.409431
$437$	−13.4941	−0.645509
$438$	3.14086	0.150076
$439$	23.9386	1.14253	0.571264	−	0.820766i	$-0.306453\pi$
$439$	23.9386	1.14253	0.571264	+	0.820766i	$0.306453\pi$
$440$	−4.36740	−0.208208
$441$	6.99629	0.333157
$442$	−9.60635	−0.456928
$443$	30.7135	1.45924	0.729622	−	0.683850i	$-0.239696\pi$
$443$	30.7135	1.45924	0.729622	+	0.683850i	$0.239696\pi$
$444$	−14.8549	−0.704985
$445$	−15.1936	−0.720244
$446$	9.78797	0.463474
$447$	−33.0007	−1.56088
$448$	0.773639	0.0365510
$449$	−32.7518	−1.54565	−0.772827	−	0.634617i	$-0.781158\pi$
$449$	−32.7518	−1.54565	−0.772827	+	0.634617i	$0.781158\pi$
$450$	3.13454	0.147764
$451$	3.98723	0.187751
$452$	−7.76698	−0.365328
$453$	−5.90980	−0.277667
$454$	−17.0136	−0.798486
$455$	−4.25305	−0.199386
$456$	−2.80743	−0.131470
$457$	−21.9030	−1.02458	−0.512290	−	0.858812i	$-0.671203\pi$
$457$	−21.9030	−1.02458	−0.512290	+	0.858812i	$0.671203\pi$
$458$	18.2387	0.852239
$459$	−14.4213	−0.673126
$460$	9.69186	0.451885
$461$	5.41558	0.252229	0.126114	−	0.992016i	$-0.459749\pi$
$461$	5.41558	0.252229	0.126114	+	0.992016i	$0.459749\pi$
$462$	−3.19564	−0.148675
$463$	−3.28004	−0.152436	−0.0762181	−	0.997091i	$-0.524285\pi$
$463$	−3.28004	−0.152436	−0.0762181	+	0.997091i	$0.524285\pi$
$464$	3.84595	0.178544
$465$	−1.96626	−0.0911833
$466$	26.3814	1.22210
$467$	36.6391	1.69546	0.847728	−	0.530431i	$-0.177970\pi$
$467$	36.6391	1.69546	0.847728	+	0.530431i	$0.177970\pi$
$468$	−4.11491	−0.190212
$469$	8.66982	0.400335
$470$	−8.29804	−0.382760
$471$	8.56722	0.394757
$472$	−4.26994	−0.196540
$473$	−23.7686	−1.09288
$474$	9.87647	0.453641
$475$	−5.83057	−0.267525
$476$	−1.97389	−0.0904733
$477$	−4.92441	−0.225473
$478$	−26.7753	−1.22467
$479$	−22.5037	−1.02822	−0.514110	−	0.857724i	$-0.671878\pi$
$479$	−22.5037	−1.02822	−0.514110	+	0.857724i	$0.671878\pi$
$480$	2.01638	0.0920350
$481$	40.5004	1.84666
$482$	9.57584	0.436167
$483$	7.09156	0.322677
$484$	−2.05319	−0.0933266
$485$	−6.69212	−0.303874
$486$	−10.7053	−0.485600
$487$	−14.0746	−0.637782	−0.318891	−	0.947791i	$-0.603310\pi$
$487$	−14.0746	−0.637782	−0.318891	+	0.947791i	$0.603310\pi$
$488$	−4.68170	−0.211931
$489$	5.97850	0.270357
$490$	9.34693	0.422251
$491$	−32.8055	−1.48049	−0.740245	−	0.672337i	$-0.765290\pi$
$491$	−32.8055	−1.48049	−0.740245	+	0.672337i	$0.765290\pi$
$492$	−1.84086	−0.0829925
$493$	−9.81271	−0.441942
$494$	7.65416	0.344377
$495$	4.77321	0.214540
$496$	−0.975143	−0.0437852
$497$	5.68841	0.255160
$498$	−17.5182	−0.785009
$499$	24.0271	1.07560	0.537801	−	0.843072i	$-0.319255\pi$
$499$	24.0271	1.07560	0.537801	+	0.843072i	$0.319255\pi$
$500$	11.4883	0.513772
$501$	3.30522	0.147666
$502$	−22.3131	−0.995884
$503$	−7.87878	−0.351297	−0.175649	−	0.984453i	$-0.556202\pi$
$503$	−7.87878	−0.351297	−0.175649	+	0.984453i	$0.556202\pi$
$504$	−0.845524	−0.0376626
$505$	2.27570	0.101267
$506$	−19.8542	−0.882628
$507$	−1.62370	−0.0721108
$508$	−9.54442	−0.423465
$509$	−12.5889	−0.557995	−0.278997	−	0.960292i	$-0.590002\pi$
$509$	−12.5889	−0.557995	−0.278997	+	0.960292i	$0.590002\pi$
$510$	−5.14468	−0.227810
$511$	−1.75955	−0.0778381
$512$	1.00000	0.0441942
$513$	11.4906	0.507322
$514$	19.3223	0.852272
$515$	−9.94958	−0.438431
$516$	10.9737	0.483091
$517$	16.9989	0.747611
$518$	8.32195	0.365645
$519$	−17.9135	−0.786317
$520$	−5.49746	−0.241079
$521$	9.51964	0.417063	0.208531	−	0.978016i	$-0.433132\pi$
$521$	9.51964	0.417063	0.208531	+	0.978016i	$0.433132\pi$
$522$	−4.20331	−0.183974
$523$	28.5770	1.24958	0.624792	−	0.780791i	$-0.285184\pi$
$523$	28.5770	1.24958	0.624792	+	0.780791i	$0.285184\pi$
$524$	3.28056	0.143312
$525$	3.06415	0.133730
$526$	−16.2204	−0.707244
$527$	2.48802	0.108380
$528$	−4.13066	−0.179764
$529$	21.0593	0.915620
$530$	−6.57893	−0.285770
$531$	4.66669	0.202517
$532$	1.57276	0.0681879
$533$	5.01892	0.217393
$534$	−14.3700	−0.621849
$535$	−14.2052	−0.614144
$536$	11.2065	0.484049
$537$	−35.1147	−1.51531
$538$	10.2240	0.440787
$539$	−19.1476	−0.824746
$540$	−8.25290	−0.355148
$541$	−12.4250	−0.534192	−0.267096	−	0.963670i	$-0.586064\pi$
$541$	−12.4250	−0.534192	−0.267096	+	0.963670i	$0.586064\pi$
$542$	24.3000	1.04377
$543$	−4.19232	−0.179910
$544$	−2.55144	−0.109392
$545$	−12.4828	−0.534706
$546$	−4.02250	−0.172147
$547$	−34.0644	−1.45649	−0.728245	−	0.685317i	$-0.759664\pi$
$547$	−34.0644	−1.45649	−0.728245	+	0.685317i	$0.759664\pi$
$548$	11.2286	0.479661
$549$	5.11671	0.218376
$550$	−8.57868	−0.365796
$551$	7.81858	0.333083
$552$	9.16650	0.390152
$553$	−5.53294	−0.235284
$554$	−2.28884	−0.0972435
$555$	21.6900	0.920690
$556$	6.76677	0.286975
$557$	−34.3380	−1.45495	−0.727474	−	0.686136i	$-0.759306\pi$
$557$	−34.3380	−1.45495	−0.727474	+	0.686136i	$0.759306\pi$
$558$	1.06575	0.0451168
$559$	−29.9187	−1.26543
$560$	−1.12961	−0.0477346
$561$	10.5391	0.444962
$562$	−19.4986	−0.822501
$563$	−9.00681	−0.379592	−0.189796	−	0.981824i	$-0.560783\pi$
$563$	−9.00681	−0.379592	−0.189796	+	0.981824i	$0.560783\pi$
$564$	−7.84823	−0.330470
$565$	11.3407	0.477108
$566$	−14.0614	−0.591046
$567$	−3.50210	−0.147074
$568$	7.35280	0.308516
$569$	15.0912	0.632655	0.316327	−	0.948650i	$-0.397550\pi$
$569$	15.0912	0.632655	0.316327	+	0.948650i	$0.397550\pi$
$570$	4.09919	0.171696
$571$	−21.3105	−0.891818	−0.445909	−	0.895078i	$-0.647120\pi$
$571$	−21.3105	−0.891818	−0.445909	+	0.895078i	$0.647120\pi$
$572$	11.2618	0.470879
$573$	−37.5703	−1.56952
$574$	1.03128	0.0430447
$575$	19.0373	0.793910
$576$	−1.09292	−0.0455382
$577$	14.8922	0.619971	0.309985	−	0.950741i	$-0.399676\pi$
$577$	14.8922	0.619971	0.309985	+	0.950741i	$0.399676\pi$
$578$	−10.4902	−0.436333
$579$	8.21697	0.341486
$580$	−5.61555	−0.233173
$581$	9.81393	0.407151
$582$	−6.32936	−0.262361
$583$	13.4772	0.558170
$584$	−2.27439	−0.0941148
$585$	6.00827	0.248411
$586$	−17.3792	−0.717928
$587$	33.0842	1.36553	0.682765	−	0.730638i	$-0.260777\pi$
$587$	33.0842	1.36553	0.682765	+	0.730638i	$0.260777\pi$
$588$	8.84027	0.364566
$589$	−1.98241	−0.0816837
$590$	6.23463	0.256675
$591$	−33.2826	−1.36906
$592$	10.7569	0.442105
$593$	−33.2107	−1.36380	−0.681900	−	0.731445i	$-0.738846\pi$
$593$	−33.2107	−1.36380	−0.681900	+	0.731445i	$0.738846\pi$
$594$	16.9064	0.693679
$595$	2.88212	0.118156
$596$	23.8967	0.978849
$597$	−9.32093	−0.381480
$598$	−24.9915	−1.02198
$599$	1.21908	0.0498104	0.0249052	−	0.999690i	$-0.492072\pi$
$599$	1.21908	0.0498104	0.0249052	+	0.999690i	$0.492072\pi$
$600$	3.96069	0.161695
$601$	11.5176	0.469811	0.234906	−	0.972018i	$-0.424522\pi$
$601$	11.5176	0.469811	0.234906	+	0.972018i	$0.424522\pi$
$602$	−6.14763	−0.250559
$603$	−12.2478	−0.498770
$604$	4.27945	0.174128
$605$	2.99790	0.121882
$606$	2.15234	0.0874327
$607$	22.0915	0.896666	0.448333	−	0.893867i	$-0.352018\pi$
$607$	22.0915	0.896666	0.448333	+	0.893867i	$0.352018\pi$
$608$	2.03294	0.0824466
$609$	−4.10891	−0.166502
$610$	6.83585	0.276775
$611$	21.3973	0.865644
$612$	2.78851	0.112719
$613$	−25.4770	−1.02901	−0.514503	−	0.857488i	$-0.672024\pi$
$613$	−25.4770	−1.02901	−0.514503	+	0.857488i	$0.672024\pi$
$614$	−12.8072	−0.516858
$615$	2.68788	0.108386
$616$	2.31405	0.0932357
$617$	−42.3851	−1.70636	−0.853179	−	0.521618i	$-0.825329\pi$
$617$	−42.3851	−1.70636	−0.853179	+	0.521618i	$0.825329\pi$
$618$	−9.41024	−0.378535
$619$	3.55087	0.142722	0.0713608	−	0.997451i	$-0.477266\pi$
$619$	3.55087	0.142722	0.0713608	+	0.997451i	$0.477266\pi$
$620$	1.42383	0.0571823
$621$	−37.5177	−1.50553
$622$	25.1891	1.00999
$623$	8.05025	0.322527
$624$	−5.19946	−0.208145
$625$	−2.43406	−0.0973623
$626$	−8.61146	−0.344183
$627$	−8.39737	−0.335359
$628$	−6.20376	−0.247557
$629$	−27.4455	−1.09432
$630$	1.23457	0.0491863
$631$	19.9557	0.794424	0.397212	−	0.917727i	$-0.369978\pi$
$631$	19.9557	0.794424	0.397212	+	0.917727i	$0.369978\pi$
$632$	−7.15183	−0.284484
$633$	21.1990	0.842584
$634$	−20.8395	−0.827643
$635$	13.9360	0.553034
$636$	−6.22231	−0.246730
$637$	−24.1020	−0.954957
$638$	11.5037	0.455436
$639$	−8.03600	−0.317899
$640$	−1.46012	−0.0577163
$641$	27.3797	1.08143	0.540717	−	0.841205i	$-0.318153\pi$
$641$	27.3797	1.08143	0.540717	+	0.841205i	$0.318153\pi$
$642$	−13.4352	−0.530244
$643$	31.8909	1.25765	0.628826	−	0.777546i	$-0.283536\pi$
$643$	31.8909	1.25765	0.628826	+	0.777546i	$0.283536\pi$
$644$	−5.13520	−0.202355
$645$	−16.0230	−0.630903
$646$	−5.18692	−0.204077
$647$	32.9141	1.29399	0.646994	−	0.762495i	$-0.276026\pi$
$647$	32.9141	1.29399	0.646994	+	0.762495i	$0.276026\pi$
$648$	−4.52678	−0.177829
$649$	−12.7719	−0.501341
$650$	−10.7984	−0.423548
$651$	1.04182	0.0408321
$652$	−4.32920	−0.169545
$653$	3.96990	0.155354	0.0776770	−	0.996979i	$-0.475250\pi$
$653$	3.96990	0.155354	0.0776770	+	0.996979i	$0.475250\pi$
$654$	−11.8062	−0.461658
$655$	−4.79001	−0.187161
$656$	1.33302	0.0520457
$657$	2.48572	0.0969770
$658$	4.39668	0.171401
$659$	−14.9999	−0.584314	−0.292157	−	0.956370i	$-0.594373\pi$
$659$	−14.9999	−0.584314	−0.292157	+	0.956370i	$0.594373\pi$
$660$	6.03125	0.234766
$661$	−10.8001	−0.420077	−0.210038	−	0.977693i	$-0.567359\pi$
$661$	−10.8001	−0.420077	−0.210038	+	0.977693i	$0.567359\pi$
$662$	29.0664	1.12970
$663$	13.2661	0.515213
$664$	12.6854	0.492289
$665$	−2.29642	−0.0890514
$666$	−11.7564	−0.455551
$667$	−25.5283	−0.988461
$668$	−2.39340	−0.0926034
$669$	−13.5169	−0.522594
$670$	−16.3629	−0.632154
$671$	−14.0035	−0.540601
$672$	−1.06837	−0.0412134
$673$	−5.45764	−0.210377	−0.105188	−	0.994452i	$-0.533545\pi$
$673$	−5.45764	−0.210377	−0.105188	+	0.994452i	$0.533545\pi$
$674$	−26.4290	−1.01801
$675$	−16.2108	−0.623954
$676$	1.17576	0.0452217
$677$	−23.2072	−0.891926	−0.445963	−	0.895052i	$-0.647139\pi$
$677$	−23.2072	−0.891926	−0.445963	+	0.895052i	$0.647139\pi$
$678$	10.7260	0.411929
$679$	3.54580	0.136075
$680$	3.72541	0.142863
$681$	23.4953	0.900340
$682$	−2.91677	−0.111689
$683$	7.07614	0.270761	0.135380	−	0.990794i	$-0.456774\pi$
$683$	7.07614	0.270761	0.135380	+	0.990794i	$0.456774\pi$
$684$	−2.22183	−0.0849540
$685$	−16.3951	−0.626423
$686$	−10.3679	−0.395849
$687$	−25.1871	−0.960949
$688$	−7.94638	−0.302953
$689$	16.9644	0.646294
$690$	−13.3842	−0.509527
$691$	15.7188	0.597970	0.298985	−	0.954258i	$-0.403352\pi$
$691$	15.7188	0.597970	0.298985	+	0.954258i	$0.403352\pi$
$692$	12.9717	0.493110
$693$	−2.52907	−0.0960713
$694$	4.80578	0.182425
$695$	−9.88030	−0.374781
$696$	−5.31115	−0.201319
$697$	−3.40112	−0.128827
$698$	1.08083	0.0409101
$699$	−36.4320	−1.37799
$700$	−2.21884	−0.0838641
$701$	21.4195	0.809004	0.404502	−	0.914537i	$-0.367445\pi$
$701$	21.4195	0.809004	0.404502	+	0.914537i	$0.367445\pi$
$702$	21.2809	0.803198
$703$	21.8681	0.824770
$704$	2.99112	0.112732
$705$	11.4594	0.431584
$706$	−21.0364	−0.791717
$707$	−1.20577	−0.0453476
$708$	5.89666	0.221610
$709$	−11.1230	−0.417735	−0.208867	−	0.977944i	$-0.566978\pi$
$709$	−11.1230	−0.417735	−0.208867	+	0.977944i	$0.566978\pi$
$710$	−10.7360	−0.402914
$711$	7.81636	0.293136
$712$	10.4057	0.389970
$713$	6.47272	0.242405
$714$	2.72589	0.102014
$715$	−16.4436	−0.614955
$716$	25.4275	0.950270
$717$	36.9759	1.38089
$718$	−23.2553	−0.867880
$719$	35.3620	1.31878	0.659390	−	0.751801i	$-0.270814\pi$
$719$	35.3620	1.31878	0.659390	+	0.751801i	$0.270814\pi$
$720$	1.59579	0.0594716
$721$	5.27175	0.196330
$722$	−14.8672	−0.553298
$723$	−13.2240	−0.491804
$724$	3.03578	0.112824
$725$	−11.0304	−0.409658
$726$	2.83539	0.105231
$727$	6.25009	0.231803	0.115902	−	0.993261i	$-0.463024\pi$
$727$	6.25009	0.231803	0.115902	+	0.993261i	$0.463024\pi$
$728$	2.91281	0.107956
$729$	28.3640	1.05052
$730$	3.32088	0.122911
$731$	20.2747	0.749887
$732$	6.46530	0.238964
$733$	−50.5338	−1.86651	−0.933253	−	0.359219i	$-0.883043\pi$
$733$	−50.5338	−1.86651	−0.933253	+	0.359219i	$0.883043\pi$
$734$	−19.1475	−0.706747
$735$	−12.9079	−0.476113
$736$	−6.63772	−0.244669
$737$	33.5201	1.23473
$738$	−1.45688	−0.0536285
$739$	−3.78821	−0.139352	−0.0696758	−	0.997570i	$-0.522196\pi$
$739$	−3.78821	−0.139352	−0.0696758	+	0.997570i	$0.522196\pi$
$740$	−15.7063	−0.577377
$741$	−10.5702	−0.388305
$742$	3.48582	0.127969
$743$	−24.5777	−0.901667	−0.450833	−	0.892608i	$-0.648873\pi$
$743$	−24.5777	−0.901667	−0.450833	+	0.892608i	$0.648873\pi$
$744$	1.34665	0.0493704
$745$	−34.8921	−1.27835
$746$	0.0977257	0.00357799
$747$	−13.8641	−0.507261
$748$	−7.63167	−0.279041
$749$	7.52657	0.275015
$750$	−15.8650	−0.579308
$751$	−38.8454	−1.41749	−0.708745	−	0.705464i	$-0.750738\pi$
$751$	−38.8454	−1.41749	−0.708745	+	0.705464i	$0.750738\pi$
$752$	5.68312	0.207242
$753$	30.8138	1.12292
$754$	14.4803	0.527341
$755$	−6.24851	−0.227407
$756$	4.37277	0.159036
$757$	32.2380	1.17171	0.585855	−	0.810416i	$-0.300759\pi$
$757$	32.2380	1.17171	0.585855	+	0.810416i	$0.300759\pi$
$758$	30.8185	1.11938
$759$	27.4181	0.995214
$760$	−2.96834	−0.107673
$761$	5.85613	0.212284	0.106142	−	0.994351i	$-0.466150\pi$
$761$	5.85613	0.212284	0.106142	+	0.994351i	$0.466150\pi$
$762$	13.1806	0.477482
$763$	6.61398	0.239442
$764$	27.2057	0.984267
$765$	−4.07156	−0.147208
$766$	27.4362	0.991312
$767$	−16.0766	−0.580493
$768$	−1.38097	−0.0498315
$769$	−5.98914	−0.215974	−0.107987	−	0.994152i	$-0.534440\pi$
$769$	−5.98914	−0.215974	−0.107987	+	0.994152i	$0.534440\pi$
$770$	−3.37879	−0.121763
$771$	−26.6836	−0.960987
$772$	−5.95014	−0.214150
$773$	21.6702	0.779421	0.389711	−	0.920937i	$-0.372575\pi$
$773$	21.6702	0.779421	0.389711	+	0.920937i	$0.372575\pi$
$774$	8.68473	0.312166
$775$	2.79676	0.100463
$776$	4.58327	0.164530
$777$	−11.4924	−0.412287
$778$	−18.9413	−0.679078
$779$	2.70995	0.0970940
$780$	7.59183	0.271831
$781$	21.9931	0.786976
$782$	16.9357	0.605620
$783$	21.7381	0.776856
$784$	−6.40148	−0.228624
$785$	9.05824	0.323302
$786$	−4.53036	−0.161593
$787$	4.11607	0.146722	0.0733610	−	0.997305i	$-0.476627\pi$
$787$	4.11607	0.146722	0.0733610	+	0.997305i	$0.476627\pi$
$788$	24.1009	0.858557
$789$	22.4000	0.797459
$790$	10.4425	0.371528
$791$	−6.00884	−0.213650
$792$	−3.26905	−0.116161
$793$	−17.6269	−0.625951
$794$	13.7160	0.486763
$795$	9.08532	0.322223
$796$	6.74955	0.239231
$797$	12.5055	0.442968	0.221484	−	0.975164i	$-0.428910\pi$
$797$	12.5055	0.442968	0.221484	+	0.975164i	$0.428910\pi$
$798$	−2.17194	−0.0768858
$799$	−14.5001	−0.512978
$800$	−2.86805	−0.101401
$801$	−11.3726	−0.401830
$802$	0.415854	0.0146843
$803$	−6.80297	−0.240072
$804$	−15.4759	−0.545793
$805$	7.49801	0.264270
$806$	−3.67148	−0.129323
$807$	−14.1190	−0.497013
$808$	−1.55857	−0.0548302
$809$	−19.7960	−0.695989	−0.347995	−	0.937497i	$-0.613137\pi$
$809$	−19.7960	−0.695989	−0.347995	+	0.937497i	$0.613137\pi$
$810$	6.60964	0.232239
$811$	13.8291	0.485604	0.242802	−	0.970076i	$-0.421933\pi$
$811$	13.8291	0.485604	0.242802	+	0.970076i	$0.421933\pi$
$812$	2.97538	0.104415
$813$	−33.5576	−1.17692
$814$	32.1751	1.12774
$815$	6.32115	0.221420
$816$	3.52347	0.123346
$817$	−16.1545	−0.565174
$818$	5.44526	0.190389
$819$	−3.18346	−0.111239
$820$	−1.94637	−0.0679702
$821$	−11.4967	−0.401239	−0.200619	−	0.979669i	$-0.564295\pi$
$821$	−11.4967	−0.401239	−0.200619	+	0.979669i	$0.564295\pi$
$822$	−15.5063	−0.540846
$823$	5.76947	0.201111	0.100556	−	0.994931i	$-0.467938\pi$
$823$	5.76947	0.201111	0.100556	+	0.994931i	$0.467938\pi$
$824$	6.81422	0.237384
$825$	11.8469	0.412457
$826$	−3.30339	−0.114940
$827$	−36.6104	−1.27307	−0.636534	−	0.771249i	$-0.719633\pi$
$827$	−36.6104	−1.27307	−0.636534	+	0.771249i	$0.719633\pi$
$828$	7.25447	0.252110
$829$	−9.26132	−0.321659	−0.160830	−	0.986982i	$-0.551417\pi$
$829$	−9.26132	−0.321659	−0.160830	+	0.986982i	$0.551417\pi$
$830$	−18.5222	−0.642916
$831$	3.16082	0.109648
$832$	3.76507	0.130530
$833$	16.3330	0.565905
$834$	−9.34472	−0.323581
$835$	3.49465	0.120937
$836$	6.08077	0.210308
$837$	−5.51171	−0.190513
$838$	24.5266	0.847258
$839$	−23.6522	−0.816564	−0.408282	−	0.912856i	$-0.633872\pi$
$839$	−23.6522	−0.816564	−0.408282	+	0.912856i	$0.633872\pi$
$840$	1.55995	0.0538236
$841$	−14.2087	−0.489954
$842$	−32.3408	−1.11454
$843$	26.9271	0.927418
$844$	−15.3508	−0.528396
$845$	−1.71676	−0.0590582
$846$	−6.21118	−0.213545
$847$	−1.58843	−0.0545790
$848$	4.50574	0.154728
$849$	19.4184	0.666439
$850$	7.31765	0.250993
$851$	−71.4011	−2.44760
$852$	−10.1540	−0.347870
$853$	−33.5882	−1.15004	−0.575019	−	0.818140i	$-0.695006\pi$
$853$	−33.5882	−1.15004	−0.575019	+	0.818140i	$0.695006\pi$
$854$	−3.62195	−0.123941
$855$	3.24415	0.110947
$856$	9.72878	0.332523
$857$	−36.4966	−1.24670	−0.623350	−	0.781943i	$-0.714229\pi$
$857$	−36.4966	−1.24670	−0.623350	+	0.781943i	$0.714229\pi$
$858$	−15.5522	−0.530944
$859$	32.2056	1.09884	0.549421	−	0.835546i	$-0.314848\pi$
$859$	32.2056	1.09884	0.549421	+	0.835546i	$0.314848\pi$
$860$	11.6027	0.395648
$861$	−1.42416	−0.0485354
$862$	8.05725	0.274431
$863$	40.0892	1.36465	0.682326	−	0.731048i	$-0.260968\pi$
$863$	40.0892	1.36465	0.682326	+	0.731048i	$0.260968\pi$
$864$	5.65220	0.192292
$865$	−18.9402	−0.643987
$866$	−28.5878	−0.971454
$867$	14.4866	0.491991
$868$	−0.754409	−0.0256063
$869$	−21.3920	−0.725674
$870$	7.75492	0.262916
$871$	42.1934	1.42967
$872$	8.54918	0.289512
$873$	−5.00913	−0.169533
$874$	−13.4941	−0.456444
$875$	8.88780	0.300462
$876$	3.14086	0.106120
$877$	−5.22253	−0.176352	−0.0881762	−	0.996105i	$-0.528104\pi$
$877$	−5.22253	−0.176352	−0.0881762	+	0.996105i	$0.528104\pi$
$878$	23.9386	0.807889
$879$	24.0002	0.809506
$880$	−4.36740	−0.147225
$881$	52.2718	1.76108	0.880540	−	0.473971i	$-0.157180\pi$
$881$	52.2718	1.76108	0.880540	+	0.473971i	$0.157180\pi$
$882$	6.99629	0.235577
$883$	−29.2763	−0.985226	−0.492613	−	0.870249i	$-0.663958\pi$
$883$	−29.2763	−0.985226	−0.492613	+	0.870249i	$0.663958\pi$
$884$	−9.60635	−0.323097
$885$	−8.60984	−0.289417
$886$	30.7135	1.03184
$887$	−8.23277	−0.276429	−0.138215	−	0.990402i	$-0.544136\pi$
$887$	−8.23277	−0.276429	−0.138215	+	0.990402i	$0.544136\pi$
$888$	−14.8549	−0.498499
$889$	−7.38394	−0.247649
$890$	−15.1936	−0.509289
$891$	−13.5402	−0.453612
$892$	9.78797	0.327726
$893$	11.5534	0.386621
$894$	−33.0007	−1.10371
$895$	−37.1272	−1.24103
$896$	0.773639	0.0258455
$897$	34.5125	1.15234
$898$	−32.7518	−1.09294
$899$	−3.75035	−0.125081
$900$	3.13454	0.104485
$901$	−11.4961	−0.382992
$902$	3.98723	0.132760
$903$	8.48970	0.282520
$904$	−7.76698	−0.258326
$905$	−4.43260	−0.147345
$906$	−5.90980	−0.196340
$907$	−11.4465	−0.380076	−0.190038	−	0.981777i	$-0.560861\pi$
$907$	−11.4465	−0.380076	−0.190038	+	0.981777i	$0.560861\pi$
$908$	−17.0136	−0.564615
$909$	1.70339	0.0564977
$910$	−4.25305	−0.140987
$911$	−10.3633	−0.343350	−0.171675	−	0.985154i	$-0.554918\pi$
$911$	−10.3633	−0.343350	−0.171675	+	0.985154i	$0.554918\pi$
$912$	−2.80743	−0.0929633
$913$	37.9436	1.25575
$914$	−21.9030	−0.724488
$915$	−9.44011	−0.312080
$916$	18.2387	0.602624
$917$	2.53797	0.0838112
$918$	−14.4213	−0.475972
$919$	−24.7400	−0.816097	−0.408049	−	0.912960i	$-0.633791\pi$
$919$	−24.7400	−0.816097	−0.408049	+	0.912960i	$0.633791\pi$
$920$	9.69186	0.319531
$921$	17.6864	0.582788
$922$	5.41558	0.178353
$923$	27.6838	0.911224
$924$	−3.19564	−0.105129
$925$	−30.8513	−1.01438
$926$	−3.28004	−0.107789
$927$	−7.44737	−0.244604
$928$	3.84595	0.126250
$929$	−46.6787	−1.53148	−0.765739	−	0.643151i	$-0.777627\pi$
$929$	−46.6787	−1.53148	−0.765739	+	0.643151i	$0.777627\pi$
$930$	−1.96626	−0.0644764
$931$	−13.0138	−0.426511
$932$	26.3814	0.864153
$933$	−34.7854	−1.13882
$934$	36.6391	1.19887
$935$	11.1432	0.364420
$936$	−4.11491	−0.134500
$937$	−39.3858	−1.28668	−0.643339	−	0.765581i	$-0.722451\pi$
$937$	−39.3858	−1.28668	−0.643339	+	0.765581i	$0.722451\pi$
$938$	8.66982	0.283080
$939$	11.8922	0.388087
$940$	−8.29804	−0.270652
$941$	−30.4127	−0.991424	−0.495712	−	0.868487i	$-0.665093\pi$
$941$	−30.4127	−0.991424	−0.495712	+	0.868487i	$0.665093\pi$
$942$	8.56722	0.279135
$943$	−8.84821	−0.288137
$944$	−4.26994	−0.138975
$945$	−6.38477	−0.207696
$946$	−23.7686	−0.772783
$947$	−29.1742	−0.948035	−0.474017	−	0.880515i	$-0.657197\pi$
$947$	−29.1742	−0.948035	−0.474017	+	0.880515i	$0.657197\pi$
$948$	9.87647	0.320773
$949$	−8.56323	−0.277974
$950$	−5.83057	−0.189169
$951$	28.7788	0.933215
$952$	−1.97389	−0.0639743
$953$	−36.6049	−1.18575	−0.592874	−	0.805295i	$-0.702007\pi$
$953$	−36.6049	−1.18575	−0.592874	+	0.805295i	$0.702007\pi$
$954$	−4.92441	−0.159434
$955$	−39.7236	−1.28542
$956$	−26.7753	−0.865974
$957$	−15.8863	−0.513531
$958$	−22.5037	−0.727061
$959$	8.68686	0.280513
$960$	2.01638	0.0650785
$961$	−30.0491	−0.969326
$962$	40.5004	1.30579
$963$	−10.6328	−0.342636
$964$	9.57584	0.308417
$965$	8.68792	0.279674
$966$	7.09156	0.228167
$967$	8.72422	0.280552	0.140276	−	0.990112i	$-0.455201\pi$
$967$	8.72422	0.280552	0.140276	+	0.990112i	$0.455201\pi$
$968$	−2.05319	−0.0659919
$969$	7.16299	0.230108
$970$	−6.69212	−0.214871
$971$	27.8063	0.892348	0.446174	−	0.894946i	$-0.352786\pi$
$971$	27.8063	0.892348	0.446174	+	0.894946i	$0.352786\pi$
$972$	−10.7053	−0.343371
$973$	5.23504	0.167828
$974$	−14.0746	−0.450980
$975$	14.9123	0.477576
$976$	−4.68170	−0.149858
$977$	60.2622	1.92796	0.963980	−	0.265976i	$-0.0856941\pi$
$977$	60.2622	1.92796	0.963980	+	0.265976i	$0.0856941\pi$
$978$	5.97850	0.191171
$979$	31.1247	0.994750
$980$	9.34693	0.298577
$981$	−9.34355	−0.298316
$982$	−32.8055	−1.04686
$983$	16.1652	0.515591	0.257796	−	0.966199i	$-0.417004\pi$
$983$	16.1652	0.515591	0.257796	+	0.966199i	$0.417004\pi$
$984$	−1.84086	−0.0586846
$985$	−35.1901	−1.12125
$986$	−9.81271	−0.312500
$987$	−6.07170	−0.193264
$988$	7.65416	0.243511
$989$	52.7458	1.67722
$990$	4.77321	0.151702
$991$	53.3759	1.69554	0.847771	−	0.530363i	$-0.177944\pi$
$991$	53.3759	1.69554	0.847771	+	0.530363i	$0.177944\pi$
$992$	−0.975143	−0.0309608
$993$	−40.1399	−1.27380
$994$	5.68841	0.180426
$995$	−9.85515	−0.312429
$996$	−17.5182	−0.555085
$997$	14.7883	0.468350	0.234175	−	0.972194i	$-0.424761\pi$
$997$	14.7883	0.468350	0.234175	+	0.972194i	$0.424761\pi$
$998$	24.0271	0.760566
$999$	60.8001	1.92363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.i.1.12	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.i.1.12	✓	46	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.38097 q^{3} +1.00000 q^{4} -1.46012 q^{5} -1.38097 q^{6} +0.773639 q^{7} +1.00000 q^{8} -1.09292 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.38097 q^{3} +1.00000 q^{4} -1.46012 q^{5} -1.38097 q^{6} +0.773639 q^{7} +1.00000 q^{8} -1.09292 q^{9} -1.46012 q^{10} +2.99112 q^{11} -1.38097 q^{12} +3.76507 q^{13} +0.773639 q^{14} +2.01638 q^{15} +1.00000 q^{16} -2.55144 q^{17} -1.09292 q^{18} +2.03294 q^{19} -1.46012 q^{20} -1.06837 q^{21} +2.99112 q^{22} -6.63772 q^{23} -1.38097 q^{24} -2.86805 q^{25} +3.76507 q^{26} +5.65220 q^{27} +0.773639 q^{28} +3.84595 q^{29} +2.01638 q^{30} -0.975143 q^{31} +1.00000 q^{32} -4.13066 q^{33} -2.55144 q^{34} -1.12961 q^{35} -1.09292 q^{36} +10.7569 q^{37} +2.03294 q^{38} -5.19946 q^{39} -1.46012 q^{40} +1.33302 q^{41} -1.06837 q^{42} -7.94638 q^{43} +2.99112 q^{44} +1.59579 q^{45} -6.63772 q^{46} +5.68312 q^{47} -1.38097 q^{48} -6.40148 q^{49} -2.86805 q^{50} +3.52347 q^{51} +3.76507 q^{52} +4.50574 q^{53} +5.65220 q^{54} -4.36740 q^{55} +0.773639 q^{56} -2.80743 q^{57} +3.84595 q^{58} -4.26994 q^{59} +2.01638 q^{60} -4.68170 q^{61} -0.975143 q^{62} -0.845524 q^{63} +1.00000 q^{64} -5.49746 q^{65} -4.13066 q^{66} +11.2065 q^{67} -2.55144 q^{68} +9.16650 q^{69} -1.12961 q^{70} +7.35280 q^{71} -1.09292 q^{72} -2.27439 q^{73} +10.7569 q^{74} +3.96069 q^{75} +2.03294 q^{76} +2.31405 q^{77} -5.19946 q^{78} -7.15183 q^{79} -1.46012 q^{80} -4.52678 q^{81} +1.33302 q^{82} +12.6854 q^{83} -1.06837 q^{84} +3.72541 q^{85} -7.94638 q^{86} -5.31115 q^{87} +2.99112 q^{88} +10.4057 q^{89} +1.59579 q^{90} +2.91281 q^{91} -6.63772 q^{92} +1.34665 q^{93} +5.68312 q^{94} -2.96834 q^{95} -1.38097 q^{96} +4.58327 q^{97} -6.40148 q^{98} -3.26905 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

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