LMFDB - Embedded newform 4006.2.a.i.1.16

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			1.16
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.506267 q^{3} +1.00000 q^{4} +2.89870 q^{5} -0.506267 q^{6} +0.00816549 q^{7} +1.00000 q^{8} -2.74369 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.506267 q^{3} +1.00000 q^{4} +2.89870 q^{5} -0.506267 q^{6} +0.00816549 q^{7} +1.00000 q^{8} -2.74369 q^{9} +2.89870 q^{10} -2.74928 q^{11} -0.506267 q^{12} +3.54892 q^{13} +0.00816549 q^{14} -1.46752 q^{15} +1.00000 q^{16} +3.16852 q^{17} -2.74369 q^{18} +4.10565 q^{19} +2.89870 q^{20} -0.00413392 q^{21} -2.74928 q^{22} -1.79364 q^{23} -0.506267 q^{24} +3.40246 q^{25} +3.54892 q^{26} +2.90784 q^{27} +0.00816549 q^{28} -3.56194 q^{29} -1.46752 q^{30} +2.27524 q^{31} +1.00000 q^{32} +1.39187 q^{33} +3.16852 q^{34} +0.0236693 q^{35} -2.74369 q^{36} +5.71526 q^{37} +4.10565 q^{38} -1.79670 q^{39} +2.89870 q^{40} +1.09724 q^{41} -0.00413392 q^{42} +4.86475 q^{43} -2.74928 q^{44} -7.95314 q^{45} -1.79364 q^{46} +2.41687 q^{47} -0.506267 q^{48} -6.99993 q^{49} +3.40246 q^{50} -1.60412 q^{51} +3.54892 q^{52} +1.19141 q^{53} +2.90784 q^{54} -7.96934 q^{55} +0.00816549 q^{56} -2.07855 q^{57} -3.56194 q^{58} +13.4936 q^{59} -1.46752 q^{60} -1.70242 q^{61} +2.27524 q^{62} -0.0224036 q^{63} +1.00000 q^{64} +10.2872 q^{65} +1.39187 q^{66} +15.4707 q^{67} +3.16852 q^{68} +0.908061 q^{69} +0.0236693 q^{70} -3.09586 q^{71} -2.74369 q^{72} -13.9202 q^{73} +5.71526 q^{74} -1.72255 q^{75} +4.10565 q^{76} -0.0224492 q^{77} -1.79670 q^{78} +9.77318 q^{79} +2.89870 q^{80} +6.75894 q^{81} +1.09724 q^{82} +17.4480 q^{83} -0.00413392 q^{84} +9.18458 q^{85} +4.86475 q^{86} +1.80329 q^{87} -2.74928 q^{88} -3.58563 q^{89} -7.95314 q^{90} +0.0289787 q^{91} -1.79364 q^{92} -1.15188 q^{93} +2.41687 q^{94} +11.9010 q^{95} -0.506267 q^{96} -6.68727 q^{97} -6.99993 q^{98} +7.54318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.506267	−0.292293	−0.146147	−	0.989263i	$-0.546687\pi$
$3$	−0.506267	−0.292293	−0.146147	+	0.989263i	$0.546687\pi$
$4$	1.00000	0.500000
$5$	2.89870	1.29634	0.648169	−	0.761497i	$-0.275535\pi$
$5$	2.89870	1.29634	0.648169	+	0.761497i	$0.275535\pi$
$6$	−0.506267	−0.206683
$7$	0.00816549	0.00308627	0.00154313	−	0.999999i	$-0.499509\pi$
$7$	0.00816549	0.00308627	0.00154313	+	0.999999i	$0.499509\pi$
$8$	1.00000	0.353553
$9$	−2.74369	−0.914565
$10$	2.89870	0.916649
$11$	−2.74928	−0.828939	−0.414470	−	0.910063i	$-0.636033\pi$
$11$	−2.74928	−0.828939	−0.414470	+	0.910063i	$0.636033\pi$
$12$	−0.506267	−0.146147
$13$	3.54892	0.984293	0.492146	−	0.870513i	$-0.336213\pi$
$13$	3.54892	0.984293	0.492146	+	0.870513i	$0.336213\pi$
$14$	0.00816549	0.00218232
$15$	−1.46752	−0.378911
$16$	1.00000	0.250000
$17$	3.16852	0.768479	0.384239	−	0.923234i	$-0.374464\pi$
$17$	3.16852	0.768479	0.384239	+	0.923234i	$0.374464\pi$
$18$	−2.74369	−0.646695
$19$	4.10565	0.941900	0.470950	−	0.882160i	$-0.343911\pi$
$19$	4.10565	0.941900	0.470950	+	0.882160i	$0.343911\pi$
$20$	2.89870	0.648169
$21$	−0.00413392	−0.000902095 0
$22$	−2.74928	−0.586149
$23$	−1.79364	−0.374000	−0.187000	−	0.982360i	$-0.559876\pi$
$23$	−1.79364	−0.374000	−0.187000	+	0.982360i	$0.559876\pi$
$24$	−0.506267	−0.103341
$25$	3.40246	0.680492
$26$	3.54892	0.696000
$27$	2.90784	0.559615
$28$	0.00816549	0.00154313
$29$	−3.56194	−0.661435	−0.330718	−	0.943730i	$-0.607291\pi$
$29$	−3.56194	−0.661435	−0.330718	+	0.943730i	$0.607291\pi$
$30$	−1.46752	−0.267931
$31$	2.27524	0.408645	0.204322	−	0.978904i	$-0.434501\pi$
$31$	2.27524	0.408645	0.204322	+	0.978904i	$0.434501\pi$
$32$	1.00000	0.176777
$33$	1.39187	0.242294
$34$	3.16852	0.543396
$35$	0.0236693	0.00400084
$36$	−2.74369	−0.457282
$37$	5.71526	0.939583	0.469792	−	0.882777i	$-0.344329\pi$
$37$	5.71526	0.939583	0.469792	+	0.882777i	$0.344329\pi$
$38$	4.10565	0.666024
$39$	−1.79670	−0.287702
$40$	2.89870	0.458325
$41$	1.09724	0.171360	0.0856798	−	0.996323i	$-0.472694\pi$
$41$	1.09724	0.171360	0.0856798	+	0.996323i	$0.472694\pi$
$42$	−0.00413392	−0.000637878 0
$43$	4.86475	0.741868	0.370934	−	0.928659i	$-0.379038\pi$
$43$	4.86475	0.741868	0.370934	+	0.928659i	$0.379038\pi$
$44$	−2.74928	−0.414470
$45$	−7.95314	−1.18558
$46$	−1.79364	−0.264458
$47$	2.41687	0.352537	0.176269	−	0.984342i	$-0.443597\pi$
$47$	2.41687	0.352537	0.176269	+	0.984342i	$0.443597\pi$
$48$	−0.506267	−0.0730734
$49$	−6.99993	−0.999990
$50$	3.40246	0.481180
$51$	−1.60412	−0.224621
$52$	3.54892	0.492146
$53$	1.19141	0.163653	0.0818265	−	0.996647i	$-0.473925\pi$
$53$	1.19141	0.163653	0.0818265	+	0.996647i	$0.473925\pi$
$54$	2.90784	0.395707
$55$	−7.96934	−1.07459
$56$	0.00816549	0.00109116
$57$	−2.07855	−0.275311
$58$	−3.56194	−0.467705
$59$	13.4936	1.75671	0.878356	−	0.478007i	$-0.158641\pi$
$59$	13.4936	1.75671	0.878356	+	0.478007i	$0.158641\pi$
$60$	−1.46752	−0.189455
$61$	−1.70242	−0.217972	−0.108986	−	0.994043i	$-0.534760\pi$
$61$	−1.70242	−0.217972	−0.108986	+	0.994043i	$0.534760\pi$
$62$	2.27524	0.288956
$63$	−0.0224036	−0.00282259
$64$	1.00000	0.125000
$65$	10.2872	1.27598
$66$	1.39187	0.171327
$67$	15.4707	1.89004	0.945021	−	0.327009i	$-0.106041\pi$
$67$	15.4707	1.89004	0.945021	+	0.327009i	$0.106041\pi$
$68$	3.16852	0.384239
$69$	0.908061	0.109318
$70$	0.0236693	0.00282902
$71$	−3.09586	−0.367411	−0.183706	−	0.982981i	$-0.558809\pi$
$71$	−3.09586	−0.367411	−0.183706	+	0.982981i	$0.558809\pi$
$72$	−2.74369	−0.323347
$73$	−13.9202	−1.62923	−0.814617	−	0.579999i	$-0.803053\pi$
$73$	−13.9202	−1.62923	−0.814617	+	0.579999i	$0.803053\pi$
$74$	5.71526	0.664386
$75$	−1.72255	−0.198903
$76$	4.10565	0.470950
$77$	−0.0224492	−0.00255833
$78$	−1.79670	−0.203436
$79$	9.77318	1.09957	0.549784	−	0.835307i	$-0.314710\pi$
$79$	9.77318	1.09957	0.549784	+	0.835307i	$0.314710\pi$
$80$	2.89870	0.324084
$81$	6.75894	0.750993
$82$	1.09724	0.121170
$83$	17.4480	1.91516	0.957582	−	0.288162i	$-0.0930442\pi$
$83$	17.4480	1.91516	0.957582	+	0.288162i	$0.0930442\pi$
$84$	−0.00413392	−0.000451048 0
$85$	9.18458	0.996208
$86$	4.86475	0.524580
$87$	1.80329	0.193333
$88$	−2.74928	−0.293074
$89$	−3.58563	−0.380077	−0.190038	−	0.981777i	$-0.560861\pi$
$89$	−3.58563	−0.380077	−0.190038	+	0.981777i	$0.560861\pi$
$90$	−7.95314	−0.838335
$91$	0.0289787	0.00303779
$92$	−1.79364	−0.187000
$93$	−1.15188	−0.119444
$94$	2.41687	0.249281
$95$	11.9010	1.22102
$96$	−0.506267	−0.0516707
$97$	−6.68727	−0.678989	−0.339495	−	0.940608i	$-0.610256\pi$
$97$	−6.68727	−0.678989	−0.339495	+	0.940608i	$0.610256\pi$
$98$	−6.99993	−0.707100
$99$	7.54318	0.758119
$100$	3.40246	0.340246
$101$	0.764937	0.0761140	0.0380570	−	0.999276i	$-0.487883\pi$
$101$	0.764937	0.0761140	0.0380570	+	0.999276i	$0.487883\pi$
$102$	−1.60412	−0.158831
$103$	−8.24853	−0.812751	−0.406376	−	0.913706i	$-0.633208\pi$
$103$	−8.24853	−0.812751	−0.406376	+	0.913706i	$0.633208\pi$
$104$	3.54892	0.348000
$105$	−0.0119830	−0.00116942
$106$	1.19141	0.115720
$107$	2.61157	0.252470	0.126235	−	0.992000i	$-0.459711\pi$
$107$	2.61157	0.252470	0.126235	+	0.992000i	$0.459711\pi$
$108$	2.90784	0.279807
$109$	−12.5299	−1.20014	−0.600072	−	0.799946i	$-0.704861\pi$
$109$	−12.5299	−1.20014	−0.600072	+	0.799946i	$0.704861\pi$
$110$	−7.96934	−0.759847
$111$	−2.89345	−0.274634
$112$	0.00816549	0.000771566 0
$113$	6.45257	0.607007	0.303504	−	0.952830i	$-0.401844\pi$
$113$	6.45257	0.607007	0.303504	+	0.952830i	$0.401844\pi$
$114$	−2.07855	−0.194674
$115$	−5.19922	−0.484830
$116$	−3.56194	−0.330718
$117$	−9.73714	−0.900199
$118$	13.4936	1.24218
$119$	0.0258725	0.00237173
$120$	−1.46752	−0.133965
$121$	−3.44146	−0.312860
$122$	−1.70242	−0.154130
$123$	−0.555495	−0.0500873
$124$	2.27524	0.204322
$125$	−4.63079	−0.414191
$126$	−0.0224036	−0.00199587
$127$	−5.04219	−0.447422	−0.223711	−	0.974656i	$-0.571817\pi$
$127$	−5.04219	−0.447422	−0.223711	+	0.974656i	$0.571817\pi$
$128$	1.00000	0.0883883
$129$	−2.46286	−0.216843
$130$	10.2872	0.902251
$131$	14.6016	1.27575	0.637874	−	0.770141i	$-0.279814\pi$
$131$	14.6016	1.27575	0.637874	+	0.770141i	$0.279814\pi$
$132$	1.39187	0.121147
$133$	0.0335246	0.00290695
$134$	15.4707	1.33646
$135$	8.42896	0.725450
$136$	3.16852	0.271698
$137$	8.23913	0.703916	0.351958	−	0.936016i	$-0.385516\pi$
$137$	8.23913	0.703916	0.351958	+	0.936016i	$0.385516\pi$
$138$	0.908061	0.0772993
$139$	7.09209	0.601543	0.300771	−	0.953696i	$-0.402756\pi$
$139$	7.09209	0.601543	0.300771	+	0.953696i	$0.402756\pi$
$140$	0.0236693	0.00200042
$141$	−1.22358	−0.103044
$142$	−3.09586	−0.259799
$143$	−9.75697	−0.815919
$144$	−2.74369	−0.228641
$145$	−10.3250	−0.857444
$146$	−13.9202	−1.15204
$147$	3.54384	0.292291
$148$	5.71526	0.469792
$149$	−9.17904	−0.751977	−0.375988	−	0.926624i	$-0.622697\pi$
$149$	−9.17904	−0.751977	−0.375988	+	0.926624i	$0.622697\pi$
$150$	−1.72255	−0.140646
$151$	−10.7967	−0.878621	−0.439311	−	0.898335i	$-0.644777\pi$
$151$	−10.7967	−0.878621	−0.439311	+	0.898335i	$0.644777\pi$
$152$	4.10565	0.333012
$153$	−8.69345	−0.702823
$154$	−0.0224492	−0.00180901
$155$	6.59523	0.529742
$156$	−1.79670	−0.143851
$157$	7.19267	0.574037	0.287019	−	0.957925i	$-0.407336\pi$
$157$	7.19267	0.574037	0.287019	+	0.957925i	$0.407336\pi$
$158$	9.77318	0.777512
$159$	−0.603172	−0.0478347
$160$	2.89870	0.229162
$161$	−0.0146460	−0.00115426
$162$	6.75894	0.531032
$163$	7.13921	0.559186	0.279593	−	0.960119i	$-0.409800\pi$
$163$	7.13921	0.559186	0.279593	+	0.960119i	$0.409800\pi$
$164$	1.09724	0.0856798
$165$	4.03461	0.314094
$166$	17.4480	1.35422
$167$	5.33473	0.412813	0.206407	−	0.978466i	$-0.433823\pi$
$167$	5.33473	0.412813	0.206407	+	0.978466i	$0.433823\pi$
$168$	−0.00413392	−0.000318939 0
$169$	−0.405186	−0.0311681
$170$	9.18458	0.704425
$171$	−11.2646	−0.861428
$172$	4.86475	0.370934
$173$	−1.50661	−0.114545	−0.0572726	−	0.998359i	$-0.518240\pi$
$173$	−1.50661	−0.114545	−0.0572726	+	0.998359i	$0.518240\pi$
$174$	1.80329	0.136707
$175$	0.0277827	0.00210018
$176$	−2.74928	−0.207235
$177$	−6.83135	−0.513475
$178$	−3.58563	−0.268755
$179$	−4.14959	−0.310155	−0.155078	−	0.987902i	$-0.549563\pi$
$179$	−4.14959	−0.310155	−0.155078	+	0.987902i	$0.549563\pi$
$180$	−7.95314	−0.592792
$181$	−3.39583	−0.252410	−0.126205	−	0.992004i	$-0.540280\pi$
$181$	−3.39583	−0.252410	−0.126205	+	0.992004i	$0.540280\pi$
$182$	0.0289787	0.00214804
$183$	0.861879	0.0637119
$184$	−1.79364	−0.132229
$185$	16.5668	1.21802
$186$	−1.15188	−0.0844598
$187$	−8.71115	−0.637022
$188$	2.41687	0.176269
$189$	0.0237440	0.00172712
$190$	11.9010	0.863392
$191$	−6.39023	−0.462381	−0.231190	−	0.972909i	$-0.574262\pi$
$191$	−6.39023	−0.462381	−0.231190	+	0.972909i	$0.574262\pi$
$192$	−0.506267	−0.0365367
$193$	5.47887	0.394378	0.197189	−	0.980365i	$-0.436819\pi$
$193$	5.47887	0.394378	0.197189	+	0.980365i	$0.436819\pi$
$194$	−6.68727	−0.480118
$195$	−5.20809	−0.372959
$196$	−6.99993	−0.499995
$197$	−5.27529	−0.375849	−0.187924	−	0.982184i	$-0.560176\pi$
$197$	−5.27529	−0.375849	−0.187924	+	0.982184i	$0.560176\pi$
$198$	7.54318	0.536071
$199$	−12.0299	−0.852777	−0.426389	−	0.904540i	$-0.640214\pi$
$199$	−12.0299	−0.852777	−0.426389	+	0.904540i	$0.640214\pi$
$200$	3.40246	0.240590
$201$	−7.83229	−0.552447
$202$	0.764937	0.0538208
$203$	−0.0290850	−0.00204137
$204$	−1.60412	−0.112311
$205$	3.18056	0.222140
$206$	−8.24853	−0.574702
$207$	4.92120	0.342047
$208$	3.54892	0.246073
$209$	−11.2876	−0.780778
$210$	−0.0119830	−0.000826905 0
$211$	−15.4494	−1.06358	−0.531789	−	0.846877i	$-0.678480\pi$
$211$	−15.4494	−1.06358	−0.531789	+	0.846877i	$0.678480\pi$
$212$	1.19141	0.0818265
$213$	1.56733	0.107392
$214$	2.61157	0.178523
$215$	14.1015	0.961711
$216$	2.90784	0.197854
$217$	0.0185784	0.00126119
$218$	−12.5299	−0.848629
$219$	7.04733	0.476214
$220$	−7.96934	−0.537293
$221$	11.2448	0.756408
$222$	−2.89345	−0.194196
$223$	8.70679	0.583050	0.291525	−	0.956563i	$-0.405837\pi$
$223$	8.70679	0.583050	0.291525	+	0.956563i	$0.405837\pi$
$224$	0.00816549	0.000545580 0
$225$	−9.33530	−0.622353
$226$	6.45257	0.429219
$227$	10.5593	0.700848	0.350424	−	0.936591i	$-0.386038\pi$
$227$	10.5593	0.700848	0.350424	+	0.936591i	$0.386038\pi$
$228$	−2.07855	−0.137656
$229$	1.00038	0.0661072	0.0330536	−	0.999454i	$-0.489477\pi$
$229$	1.00038	0.0661072	0.0330536	+	0.999454i	$0.489477\pi$
$230$	−5.19922	−0.342827
$231$	0.0113653	0.000747782 0
$232$	−3.56194	−0.233853
$233$	9.33598	0.611621	0.305810	−	0.952092i	$-0.401073\pi$
$233$	9.33598	0.611621	0.305810	+	0.952092i	$0.401073\pi$
$234$	−9.73714	−0.636537
$235$	7.00579	0.457007
$236$	13.4936	0.878356
$237$	−4.94784	−0.321397
$238$	0.0258725	0.00167707
$239$	22.7559	1.47196	0.735980	−	0.677003i	$-0.236722\pi$
$239$	22.7559	1.47196	0.735980	+	0.677003i	$0.236722\pi$
$240$	−1.46752	−0.0947277
$241$	−8.71394	−0.561314	−0.280657	−	0.959808i	$-0.590552\pi$
$241$	−8.71394	−0.561314	−0.280657	+	0.959808i	$0.590552\pi$
$242$	−3.44146	−0.221225
$243$	−12.1454	−0.779125
$244$	−1.70242	−0.108986
$245$	−20.2907	−1.29633
$246$	−0.555495	−0.0354171
$247$	14.5706	0.927105
$248$	2.27524	0.144478
$249$	−8.83333	−0.559790
$250$	−4.63079	−0.292877
$251$	−14.0940	−0.889603	−0.444801	−	0.895629i	$-0.646726\pi$
$251$	−14.0940	−0.889603	−0.444801	+	0.895629i	$0.646726\pi$
$252$	−0.0224036	−0.00141129
$253$	4.93122	0.310023
$254$	−5.04219	−0.316375
$255$	−4.64985	−0.291185
$256$	1.00000	0.0625000
$257$	−23.5755	−1.47060	−0.735300	−	0.677742i	$-0.762959\pi$
$257$	−23.5755	−1.47060	−0.735300	+	0.677742i	$0.762959\pi$
$258$	−2.46286	−0.153331
$259$	0.0466679	0.00289980
$260$	10.2872	0.637988
$261$	9.77287	0.604925
$262$	14.6016	0.902090
$263$	−14.6322	−0.902262	−0.451131	−	0.892458i	$-0.648979\pi$
$263$	−14.6322	−0.902262	−0.451131	+	0.892458i	$0.648979\pi$
$264$	1.39187	0.0856637
$265$	3.45354	0.212149
$266$	0.0335246	0.00205553
$267$	1.81529	0.111094
$268$	15.4707	0.945021
$269$	−21.7720	−1.32746	−0.663732	−	0.747970i	$-0.731029\pi$
$269$	−21.7720	−1.32746	−0.663732	+	0.747970i	$0.731029\pi$
$270$	8.42896	0.512970
$271$	−2.29490	−0.139405	−0.0697025	−	0.997568i	$-0.522205\pi$
$271$	−2.29490	−0.139405	−0.0697025	+	0.997568i	$0.522205\pi$
$272$	3.16852	0.192120
$273$	−0.0146709	−0.000887926 0
$274$	8.23913	0.497744
$275$	−9.35431	−0.564086
$276$	0.908061	0.0546589
$277$	24.8625	1.49384	0.746920	−	0.664914i	$-0.231532\pi$
$277$	24.8625	1.49384	0.746920	+	0.664914i	$0.231532\pi$
$278$	7.09209	0.425355
$279$	−6.24256	−0.373732
$280$	0.0236693	0.00141451
$281$	−19.5155	−1.16420	−0.582098	−	0.813119i	$-0.697768\pi$
$281$	−19.5155	−1.16420	−0.582098	+	0.813119i	$0.697768\pi$
$282$	−1.22358	−0.0728633
$283$	−3.21686	−0.191223	−0.0956113	−	0.995419i	$-0.530481\pi$
$283$	−3.21686	−0.191223	−0.0956113	+	0.995419i	$0.530481\pi$
$284$	−3.09586	−0.183706
$285$	−6.02510	−0.356896
$286$	−9.75697	−0.576942
$287$	0.00895948	0.000528861 0
$288$	−2.74369	−0.161674
$289$	−6.96049	−0.409440
$290$	−10.3250	−0.606304
$291$	3.38554	0.198464
$292$	−13.9202	−0.814617
$293$	12.8325	0.749683	0.374841	−	0.927089i	$-0.377697\pi$
$293$	12.8325	0.749683	0.374841	+	0.927089i	$0.377697\pi$
$294$	3.54384	0.206681
$295$	39.1138	2.27729
$296$	5.71526	0.332193
$297$	−7.99448	−0.463887
$298$	−9.17904	−0.531728
$299$	−6.36548	−0.368125
$300$	−1.72255	−0.0994516
$301$	0.0397231	0.00228960
$302$	−10.7967	−0.621279
$303$	−0.387262	−0.0222476
$304$	4.10565	0.235475
$305$	−4.93480	−0.282566
$306$	−8.69345	−0.496971
$307$	−12.2571	−0.699549	−0.349775	−	0.936834i	$-0.613742\pi$
$307$	−12.2571	−0.699549	−0.349775	+	0.936834i	$0.613742\pi$
$308$	−0.0224492	−0.00127916
$309$	4.17596	0.237562
$310$	6.59523	0.374584
$311$	5.72980	0.324907	0.162454	−	0.986716i	$-0.448059\pi$
$311$	5.72980	0.324907	0.162454	+	0.986716i	$0.448059\pi$
$312$	−1.79670	−0.101718
$313$	18.2371	1.03082	0.515412	−	0.856943i	$-0.327639\pi$
$313$	18.2371	1.03082	0.515412	+	0.856943i	$0.327639\pi$
$314$	7.19267	0.405906
$315$	−0.0649413	−0.00365903
$316$	9.77318	0.549784
$317$	29.8458	1.67631	0.838154	−	0.545434i	$-0.183635\pi$
$317$	29.8458	1.67631	0.838154	+	0.545434i	$0.183635\pi$
$318$	−0.603172	−0.0338242
$319$	9.79277	0.548290
$320$	2.89870	0.162042
$321$	−1.32215	−0.0737954
$322$	−0.0146460	−0.000816187 0
$323$	13.0088	0.723830
$324$	6.75894	0.375496
$325$	12.0750	0.669803
$326$	7.13921	0.395404
$327$	6.34346	0.350794
$328$	1.09724	0.0605848
$329$	0.0197350	0.00108802
$330$	4.03461	0.222098
$331$	−9.32901	−0.512769	−0.256384	−	0.966575i	$-0.582531\pi$
$331$	−9.32901	−0.512769	−0.256384	+	0.966575i	$0.582531\pi$
$332$	17.4480	0.957582
$333$	−15.6809	−0.859310
$334$	5.33473	0.291903
$335$	44.8448	2.45013
$336$	−0.00413392	−0.000225524 0
$337$	20.3419	1.10809	0.554046	−	0.832486i	$-0.313083\pi$
$337$	20.3419	1.10809	0.554046	+	0.832486i	$0.313083\pi$
$338$	−0.405186	−0.0220392
$339$	−3.26673	−0.177424
$340$	9.18458	0.498104
$341$	−6.25527	−0.338742
$342$	−11.2646	−0.609122
$343$	−0.114316	−0.00617250
$344$	4.86475	0.262290
$345$	2.63220	0.141713
$346$	−1.50661	−0.0809957
$347$	10.2304	0.549199	0.274600	−	0.961559i	$-0.411455\pi$
$347$	10.2304	0.549199	0.274600	+	0.961559i	$0.411455\pi$
$348$	1.80329	0.0966666
$349$	−7.03462	−0.376554	−0.188277	−	0.982116i	$-0.560290\pi$
$349$	−7.03462	−0.376554	−0.188277	+	0.982116i	$0.560290\pi$
$350$	0.0277827	0.00148505
$351$	10.3197	0.550825
$352$	−2.74928	−0.146537
$353$	7.75420	0.412714	0.206357	−	0.978477i	$-0.433839\pi$
$353$	7.75420	0.412714	0.206357	+	0.978477i	$0.433839\pi$
$354$	−6.83135	−0.363082
$355$	−8.97398	−0.476289
$356$	−3.58563	−0.190038
$357$	−0.0130984	−0.000693241 0
$358$	−4.14959	−0.219313
$359$	−35.0226	−1.84842	−0.924211	−	0.381883i	$-0.875276\pi$
$359$	−35.0226	−1.84842	−0.924211	+	0.381883i	$0.875276\pi$
$360$	−7.95314	−0.419167
$361$	−2.14366	−0.112824
$362$	−3.39583	−0.178481
$363$	1.74230	0.0914468
$364$	0.0289787	0.00151889
$365$	−40.3504	−2.11204
$366$	0.861879	0.0450511
$367$	−33.1460	−1.73021	−0.865103	−	0.501594i	$-0.832747\pi$
$367$	−33.1460	−1.73021	−0.865103	+	0.501594i	$0.832747\pi$
$368$	−1.79364	−0.0935000
$369$	−3.01048	−0.156719
$370$	16.5668	0.861268
$371$	0.00972846	0.000505076 0
$372$	−1.15188	−0.0597221
$373$	17.7784	0.920532	0.460266	−	0.887781i	$-0.347754\pi$
$373$	17.7784	0.920532	0.460266	+	0.887781i	$0.347754\pi$
$374$	−8.71115	−0.450443
$375$	2.34442	0.121065
$376$	2.41687	0.124641
$377$	−12.6410	−0.651046
$378$	0.0237440	0.00122126
$379$	22.2603	1.14344	0.571718	−	0.820450i	$-0.306277\pi$
$379$	22.2603	1.14344	0.571718	+	0.820450i	$0.306277\pi$
$380$	11.9010	0.610510
$381$	2.55269	0.130778
$382$	−6.39023	−0.326953
$383$	0.908171	0.0464054	0.0232027	−	0.999731i	$-0.492614\pi$
$383$	0.908171	0.0464054	0.0232027	+	0.999731i	$0.492614\pi$
$384$	−0.506267	−0.0258353
$385$	−0.0650736	−0.00331646
$386$	5.47887	0.278867
$387$	−13.3474	−0.678486
$388$	−6.68727	−0.339495
$389$	17.4792	0.886231	0.443115	−	0.896465i	$-0.353873\pi$
$389$	17.4792	0.886231	0.443115	+	0.896465i	$0.353873\pi$
$390$	−5.20809	−0.263722
$391$	−5.68318	−0.287411
$392$	−6.99993	−0.353550
$393$	−7.39231	−0.372893
$394$	−5.27529	−0.265765
$395$	28.3295	1.42541
$396$	7.54318	0.379059
$397$	−6.25742	−0.314051	−0.157025	−	0.987595i	$-0.550190\pi$
$397$	−6.25742	−0.314051	−0.157025	+	0.987595i	$0.550190\pi$
$398$	−12.0299	−0.603005
$399$	−0.0169724	−0.000849683 0
$400$	3.40246	0.170123
$401$	24.6645	1.23169	0.615844	−	0.787868i	$-0.288815\pi$
$401$	24.6645	1.23169	0.615844	+	0.787868i	$0.288815\pi$
$402$	−7.83229	−0.390639
$403$	8.07464	0.402226
$404$	0.764937	0.0380570
$405$	19.5921	0.973540
$406$	−0.0290850	−0.00144346
$407$	−15.7129	−0.778858
$408$	−1.60412	−0.0794156
$409$	−28.4224	−1.40540	−0.702699	−	0.711488i	$-0.748022\pi$
$409$	−28.4224	−1.40540	−0.702699	+	0.711488i	$0.748022\pi$
$410$	3.18056	0.157077
$411$	−4.17120	−0.205750
$412$	−8.24853	−0.406376
$413$	0.110182	0.00542168
$414$	4.92120	0.241864
$415$	50.5764	2.48270
$416$	3.54892	0.174000
$417$	−3.59049	−0.175827
$418$	−11.2876	−0.552093
$419$	7.57299	0.369965	0.184982	−	0.982742i	$-0.440777\pi$
$419$	7.57299	0.369965	0.184982	+	0.982742i	$0.440777\pi$
$420$	−0.0119830	−0.000584710 0
$421$	−8.25370	−0.402261	−0.201130	−	0.979564i	$-0.564461\pi$
$421$	−8.25370	−0.402261	−0.201130	+	0.979564i	$0.564461\pi$
$422$	−15.4494	−0.752063
$423$	−6.63116	−0.322418
$424$	1.19141	0.0578600
$425$	10.7808	0.522943
$426$	1.56733	0.0759376
$427$	−0.0139011	−0.000672721 0
$428$	2.61157	0.126235
$429$	4.93963	0.238488
$430$	14.1015	0.680033
$431$	−2.03301	−0.0979266	−0.0489633	−	0.998801i	$-0.515592\pi$
$431$	−2.03301	−0.0979266	−0.0489633	+	0.998801i	$0.515592\pi$
$432$	2.90784	0.139904
$433$	−14.3677	−0.690469	−0.345235	−	0.938516i	$-0.612201\pi$
$433$	−14.3677	−0.690469	−0.345235	+	0.938516i	$0.612201\pi$
$434$	0.0185784	0.000891794 0
$435$	5.22720	0.250625
$436$	−12.5299	−0.600072
$437$	−7.36405	−0.352270
$438$	7.04733	0.336734
$439$	−32.9373	−1.57201	−0.786006	−	0.618219i	$-0.787854\pi$
$439$	−32.9373	−1.57201	−0.786006	+	0.618219i	$0.787854\pi$
$440$	−7.96934	−0.379923
$441$	19.2057	0.914556
$442$	11.2448	0.534861
$443$	−30.8743	−1.46688	−0.733441	−	0.679753i	$-0.762087\pi$
$443$	−30.8743	−1.46688	−0.733441	+	0.679753i	$0.762087\pi$
$444$	−2.89345	−0.137317
$445$	−10.3937	−0.492708
$446$	8.70679	0.412278
$447$	4.64705	0.219798
$448$	0.00816549	0.000385783 0
$449$	25.4801	1.20248	0.601239	−	0.799069i	$-0.294674\pi$
$449$	25.4801	1.20248	0.601239	+	0.799069i	$0.294674\pi$
$450$	−9.33530	−0.440070
$451$	−3.01661	−0.142047
$452$	6.45257	0.303504
$453$	5.46600	0.256815
$454$	10.5593	0.495574
$455$	0.0840004	0.00393800
$456$	−2.07855	−0.0973372
$457$	7.64423	0.357582	0.178791	−	0.983887i	$-0.442781\pi$
$457$	7.64423	0.357582	0.178791	+	0.983887i	$0.442781\pi$
$458$	1.00038	0.0467448
$459$	9.21356	0.430052
$460$	−5.19922	−0.242415
$461$	−13.3677	−0.622598	−0.311299	−	0.950312i	$-0.600764\pi$
$461$	−13.3677	−0.622598	−0.311299	+	0.950312i	$0.600764\pi$
$462$	0.0113653	0.000528762 0
$463$	−4.15725	−0.193204	−0.0966020	−	0.995323i	$-0.530797\pi$
$463$	−4.15725	−0.193204	−0.0966020	+	0.995323i	$0.530797\pi$
$464$	−3.56194	−0.165359
$465$	−3.33895	−0.154840
$466$	9.33598	0.432481
$467$	6.62025	0.306349	0.153174	−	0.988199i	$-0.451050\pi$
$467$	6.62025	0.306349	0.153174	+	0.988199i	$0.451050\pi$
$468$	−9.73714	−0.450100
$469$	0.126326	0.00583317
$470$	7.00579	0.323153
$471$	−3.64141	−0.167787
$472$	13.4936	0.621092
$473$	−13.3746	−0.614963
$474$	−4.94784	−0.227262
$475$	13.9693	0.640955
$476$	0.0258725	0.00118586
$477$	−3.26887	−0.149671
$478$	22.7559	1.04083
$479$	−0.0727538	−0.00332420	−0.00166210	−	0.999999i	$-0.500529\pi$
$479$	−0.0727538	−0.00332420	−0.00166210	+	0.999999i	$0.500529\pi$
$480$	−1.46752	−0.0669826
$481$	20.2830	0.924825
$482$	−8.71394	−0.396909
$483$	0.00741476	0.000337383 0
$484$	−3.44146	−0.156430
$485$	−19.3844	−0.880199
$486$	−12.1454	−0.550925
$487$	−0.841272	−0.0381217	−0.0190608	−	0.999818i	$-0.506068\pi$
$487$	−0.841272	−0.0381217	−0.0190608	+	0.999818i	$0.506068\pi$
$488$	−1.70242	−0.0770649
$489$	−3.61435	−0.163446
$490$	−20.2907	−0.916640
$491$	9.27025	0.418361	0.209180	−	0.977877i	$-0.432920\pi$
$491$	9.27025	0.418361	0.209180	+	0.977877i	$0.432920\pi$
$492$	−0.555495	−0.0250436
$493$	−11.2861	−0.508299
$494$	14.5706	0.655562
$495$	21.8654	0.982778
$496$	2.27524	0.102161
$497$	−0.0252793	−0.00113393
$498$	−8.83333	−0.395831
$499$	14.8063	0.662820	0.331410	−	0.943487i	$-0.392476\pi$
$499$	14.8063	0.662820	0.331410	+	0.943487i	$0.392476\pi$
$500$	−4.63079	−0.207095
$501$	−2.70080	−0.120663
$502$	−14.0940	−0.629044
$503$	31.4382	1.40176	0.700880	−	0.713279i	$-0.252791\pi$
$503$	31.4382	1.40176	0.700880	+	0.713279i	$0.252791\pi$
$504$	−0.0224036	−0.000997936 0
$505$	2.21732	0.0986695
$506$	4.93122	0.219219
$507$	0.205132	0.00911024
$508$	−5.04219	−0.223711
$509$	−27.8235	−1.23325	−0.616627	−	0.787255i	$-0.711501\pi$
$509$	−27.8235	−1.23325	−0.616627	+	0.787255i	$0.711501\pi$
$510$	−4.64985	−0.205899
$511$	−0.113665	−0.00502825
$512$	1.00000	0.0441942
$513$	11.9386	0.527101
$514$	−23.5755	−1.03987
$515$	−23.9100	−1.05360
$516$	−2.46286	−0.108422
$517$	−6.64466	−0.292232
$518$	0.0466679	0.00205047
$519$	0.762745	0.0334808
$520$	10.2872	0.451126
$521$	4.80209	0.210383	0.105192	−	0.994452i	$-0.466454\pi$
$521$	4.80209	0.210383	0.105192	+	0.994452i	$0.466454\pi$
$522$	9.77287	0.427747
$523$	21.1949	0.926790	0.463395	−	0.886152i	$-0.346631\pi$
$523$	21.1949	0.926790	0.463395	+	0.886152i	$0.346631\pi$
$524$	14.6016	0.637874
$525$	−0.0140655	−0.000613868 0
$526$	−14.6322	−0.637996
$527$	7.20914	0.314035
$528$	1.39187	0.0605734
$529$	−19.7829	−0.860124
$530$	3.45354	0.150012
$531$	−37.0222	−1.60663
$532$	0.0335246	0.00145348
$533$	3.89400	0.168668
$534$	1.81529	0.0785552
$535$	7.57016	0.327287
$536$	15.4707	0.668231
$537$	2.10080	0.0906563
$538$	−21.7720	−0.938659
$539$	19.2448	0.828931
$540$	8.42896	0.362725
$541$	34.7507	1.49405	0.747024	−	0.664797i	$-0.231482\pi$
$541$	34.7507	1.49405	0.747024	+	0.664797i	$0.231482\pi$
$542$	−2.29490	−0.0985742
$543$	1.71920	0.0737779
$544$	3.16852	0.135849
$545$	−36.3203	−1.55579
$546$	−0.0146709	−0.000627858 0
$547$	42.0133	1.79636	0.898178	−	0.439631i	$-0.144891\pi$
$547$	42.0133	1.79636	0.898178	+	0.439631i	$0.144891\pi$
$548$	8.23913	0.351958
$549$	4.67092	0.199350
$550$	−9.35431	−0.398869
$551$	−14.6241	−0.623006
$552$	0.908061	0.0386496
$553$	0.0798028	0.00339356
$554$	24.8625	1.05630
$555$	−8.38724	−0.356018
$556$	7.09209	0.300771
$557$	−10.1070	−0.428248	−0.214124	−	0.976806i	$-0.568690\pi$
$557$	−10.1070	−0.428248	−0.214124	+	0.976806i	$0.568690\pi$
$558$	−6.24256	−0.264269
$559$	17.2646	0.730215
$560$	0.0236693	0.00100021
$561$	4.41017	0.186197
$562$	−19.5155	−0.823210
$563$	−22.9056	−0.965357	−0.482679	−	0.875798i	$-0.660336\pi$
$563$	−22.9056	−0.965357	−0.482679	+	0.875798i	$0.660336\pi$
$564$	−1.22358	−0.0515221
$565$	18.7041	0.786886
$566$	−3.21686	−0.135215
$567$	0.0551900	0.00231776
$568$	−3.09586	−0.129900
$569$	−22.1901	−0.930259	−0.465130	−	0.885243i	$-0.653992\pi$
$569$	−22.1901	−0.930259	−0.465130	+	0.885243i	$0.653992\pi$
$570$	−6.02510	−0.252364
$571$	−20.4581	−0.856145	−0.428073	−	0.903744i	$-0.640807\pi$
$571$	−20.4581	−0.856145	−0.428073	+	0.903744i	$0.640807\pi$
$572$	−9.75697	−0.407959
$573$	3.23516	0.135151
$574$	0.00895948	0.000373961 0
$575$	−6.10279	−0.254504
$576$	−2.74369	−0.114321
$577$	−11.7402	−0.488753	−0.244376	−	0.969680i	$-0.578583\pi$
$577$	−11.7402	−0.488753	−0.244376	+	0.969680i	$0.578583\pi$
$578$	−6.96049	−0.289518
$579$	−2.77377	−0.115274
$580$	−10.3250	−0.428722
$581$	0.142471	0.00591070
$582$	3.38554	0.140335
$583$	−3.27552	−0.135658
$584$	−13.9202	−0.576021
$585$	−28.2250	−1.16696
$586$	12.8325	0.530106
$587$	4.34043	0.179149	0.0895743	−	0.995980i	$-0.471449\pi$
$587$	4.34043	0.179149	0.0895743	+	0.995980i	$0.471449\pi$
$588$	3.54384	0.146145
$589$	9.34133	0.384903
$590$	39.1138	1.61029
$591$	2.67070	0.109858
$592$	5.71526	0.234896
$593$	−11.1496	−0.457860	−0.228930	−	0.973443i	$-0.573523\pi$
$593$	−11.1496	−0.457860	−0.228930	+	0.973443i	$0.573523\pi$
$594$	−7.99448	−0.328017
$595$	0.0749966	0.00307456
$596$	−9.17904	−0.375988
$597$	6.09034	0.249261
$598$	−6.36548	−0.260304
$599$	−27.4647	−1.12218	−0.561089	−	0.827756i	$-0.689617\pi$
$599$	−27.4647	−1.12218	−0.561089	+	0.827756i	$0.689617\pi$
$600$	−1.72255	−0.0703229
$601$	−37.4514	−1.52767	−0.763837	−	0.645409i	$-0.776687\pi$
$601$	−37.4514	−1.52767	−0.763837	+	0.645409i	$0.776687\pi$
$602$	0.0397231	0.00161899
$603$	−42.4468	−1.72857
$604$	−10.7967	−0.439311
$605$	−9.97575	−0.405572
$606$	−0.387262	−0.0157315
$607$	−33.3032	−1.35173	−0.675867	−	0.737024i	$-0.736230\pi$
$607$	−33.3032	−1.35173	−0.675867	+	0.737024i	$0.736230\pi$
$608$	4.10565	0.166506
$609$	0.0147248	0.000596678 0
$610$	−4.93480	−0.199804
$611$	8.57728	0.347000
$612$	−8.69345	−0.351412
$613$	−13.0658	−0.527723	−0.263862	−	0.964561i	$-0.584996\pi$
$613$	−13.0658	−0.527723	−0.263862	+	0.964561i	$0.584996\pi$
$614$	−12.2571	−0.494656
$615$	−1.61021	−0.0649300
$616$	−0.0224492	−0.000904505 0
$617$	−10.5401	−0.424330	−0.212165	−	0.977234i	$-0.568051\pi$
$617$	−10.5401	−0.424330	−0.212165	+	0.977234i	$0.568051\pi$
$618$	4.17596	0.167982
$619$	−13.0642	−0.525096	−0.262548	−	0.964919i	$-0.584563\pi$
$619$	−13.0642	−0.525096	−0.262548	+	0.964919i	$0.584563\pi$
$620$	6.59523	0.264871
$621$	−5.21562	−0.209296
$622$	5.72980	0.229744
$623$	−0.0292785	−0.00117302
$624$	−1.79670	−0.0719256
$625$	−30.4356	−1.21742
$626$	18.2371	0.728903
$627$	5.71453	0.228216
$628$	7.19267	0.287019
$629$	18.1089	0.722050
$630$	−0.0649413	−0.00258732
$631$	−41.2728	−1.64305	−0.821523	−	0.570175i	$-0.806875\pi$
$631$	−41.2728	−1.64305	−0.821523	+	0.570175i	$0.806875\pi$
$632$	9.77318	0.388756
$633$	7.82151	0.310877
$634$	29.8458	1.18533
$635$	−14.6158	−0.580010
$636$	−0.603172	−0.0239173
$637$	−24.8422	−0.984283
$638$	9.79277	0.387699
$639$	8.49410	0.336022
$640$	2.89870	0.114581
$641$	14.7551	0.582791	0.291395	−	0.956603i	$-0.405880\pi$
$641$	14.7551	0.582791	0.291395	+	0.956603i	$0.405880\pi$
$642$	−1.32215	−0.0521812
$643$	−34.6092	−1.36485	−0.682427	−	0.730954i	$-0.739075\pi$
$643$	−34.6092	−1.36485	−0.682427	+	0.730954i	$0.739075\pi$
$644$	−0.0146460	−0.000577131 0
$645$	−7.13910	−0.281102
$646$	13.0088	0.511825
$647$	−7.64017	−0.300366	−0.150183	−	0.988658i	$-0.547986\pi$
$647$	−7.64017	−0.300366	−0.150183	+	0.988658i	$0.547986\pi$
$648$	6.75894	0.265516
$649$	−37.0976	−1.45621
$650$	12.0750	0.473622
$651$	−0.00940565	−0.000368637 0
$652$	7.13921	0.279593
$653$	28.0815	1.09891	0.549456	−	0.835523i	$-0.314835\pi$
$653$	28.0815	1.09891	0.549456	+	0.835523i	$0.314835\pi$
$654$	6.34346	0.248049
$655$	42.3256	1.65380
$656$	1.09724	0.0428399
$657$	38.1927	1.49004
$658$	0.0197350	0.000769349 0
$659$	2.34529	0.0913594	0.0456797	−	0.998956i	$-0.485455\pi$
$659$	2.34529	0.0913594	0.0456797	+	0.998956i	$0.485455\pi$
$660$	4.03461	0.157047
$661$	−6.76368	−0.263077	−0.131538	−	0.991311i	$-0.541992\pi$
$661$	−6.76368	−0.263077	−0.131538	+	0.991311i	$0.541992\pi$
$662$	−9.32901	−0.362582
$663$	−5.69288	−0.221093
$664$	17.4480	0.677112
$665$	0.0971778	0.00376839
$666$	−15.6809	−0.607624
$667$	6.38884	0.247377
$668$	5.33473	0.206407
$669$	−4.40796	−0.170422
$670$	44.8448	1.73251
$671$	4.68043	0.180686
$672$	−0.00413392	−0.000159469 0
$673$	−15.9612	−0.615259	−0.307630	−	0.951506i	$-0.599536\pi$
$673$	−15.9612	−0.615259	−0.307630	+	0.951506i	$0.599536\pi$
$674$	20.3419	0.783540
$675$	9.89381	0.380813
$676$	−0.405186	−0.0155841
$677$	−38.6420	−1.48513	−0.742566	−	0.669773i	$-0.766391\pi$
$677$	−38.6420	−1.48513	−0.742566	+	0.669773i	$0.766391\pi$
$678$	−3.26673	−0.125458
$679$	−0.0546048	−0.00209554
$680$	9.18458	0.352213
$681$	−5.34585	−0.204853
$682$	−6.25527	−0.239527
$683$	−43.5329	−1.66574	−0.832870	−	0.553469i	$-0.813304\pi$
$683$	−43.5329	−1.66574	−0.832870	+	0.553469i	$0.813304\pi$
$684$	−11.2646	−0.430714
$685$	23.8828	0.912513
$686$	−0.114316	−0.00436462
$687$	−0.506461	−0.0193227
$688$	4.86475	0.185467
$689$	4.22822	0.161082
$690$	2.63220	0.100206
$691$	−15.8402	−0.602590	−0.301295	−	0.953531i	$-0.597419\pi$
$691$	−15.8402	−0.602590	−0.301295	+	0.953531i	$0.597419\pi$
$692$	−1.50661	−0.0572726
$693$	0.0615938	0.00233976
$694$	10.2304	0.388342
$695$	20.5578	0.779803
$696$	1.80329	0.0683536
$697$	3.47662	0.131686
$698$	−7.03462	−0.266264
$699$	−4.72650	−0.178773
$700$	0.0277827	0.00105009
$701$	36.6619	1.38470	0.692351	−	0.721561i	$-0.256575\pi$
$701$	36.6619	1.38470	0.692351	+	0.721561i	$0.256575\pi$
$702$	10.3197	0.389492
$703$	23.4648	0.884994
$704$	−2.74928	−0.103617
$705$	−3.54680	−0.133580
$706$	7.75420	0.291833
$707$	0.00624608	0.000234908 0
$708$	−6.83135	−0.256738
$709$	30.4866	1.14495	0.572474	−	0.819923i	$-0.305984\pi$
$709$	30.4866	1.14495	0.572474	+	0.819923i	$0.305984\pi$
$710$	−8.97398	−0.336787
$711$	−26.8146	−1.00563
$712$	−3.58563	−0.134377
$713$	−4.08096	−0.152833
$714$	−0.0130984	−0.000490195 0
$715$	−28.2825	−1.05771
$716$	−4.14959	−0.155078
$717$	−11.5206	−0.430244
$718$	−35.0226	−1.30703
$719$	15.8701	0.591854	0.295927	−	0.955210i	$-0.404371\pi$
$719$	15.8701	0.591854	0.295927	+	0.955210i	$0.404371\pi$
$720$	−7.95314	−0.296396
$721$	−0.0673533	−0.00250837
$722$	−2.14366	−0.0797789
$723$	4.41158	0.164068
$724$	−3.39583	−0.126205
$725$	−12.1193	−0.450101
$726$	1.74230	0.0646627
$727$	−32.5569	−1.20747	−0.603735	−	0.797185i	$-0.706321\pi$
$727$	−32.5569	−1.20747	−0.603735	+	0.797185i	$0.706321\pi$
$728$	0.0289787	0.00107402
$729$	−14.1280	−0.523260
$730$	−40.3504	−1.49344
$731$	15.4141	0.570110
$732$	0.861879	0.0318560
$733$	−14.7274	−0.543967	−0.271984	−	0.962302i	$-0.587680\pi$
$733$	−14.7274	−0.543967	−0.271984	+	0.962302i	$0.587680\pi$
$734$	−33.1460	−1.22344
$735$	10.2725	0.378907
$736$	−1.79364	−0.0661145
$737$	−42.5332	−1.56673
$738$	−3.01048	−0.110817
$739$	21.1635	0.778511	0.389255	−	0.921130i	$-0.372732\pi$
$739$	21.1635	0.778511	0.389255	+	0.921130i	$0.372732\pi$
$740$	16.5668	0.609009
$741$	−7.37662	−0.270987
$742$	0.00972846	0.000357143 0
$743$	−34.2636	−1.25701	−0.628505	−	0.777805i	$-0.716333\pi$
$743$	−34.2636	−1.25701	−0.628505	+	0.777805i	$0.716333\pi$
$744$	−1.15188	−0.0422299
$745$	−26.6073	−0.974816
$746$	17.7784	0.650914
$747$	−47.8719	−1.75154
$748$	−8.71115	−0.318511
$749$	0.0213248	0.000779190 0
$750$	2.34442	0.0856061
$751$	−9.23291	−0.336914	−0.168457	−	0.985709i	$-0.553878\pi$
$751$	−9.23291	−0.336914	−0.168457	+	0.985709i	$0.553878\pi$
$752$	2.41687	0.0881343
$753$	7.13531	0.260025
$754$	−12.6410	−0.460359
$755$	−31.2963	−1.13899
$756$	0.0237440	0.000863560 0
$757$	4.84108	0.175952	0.0879759	−	0.996123i	$-0.471960\pi$
$757$	4.84108	0.175952	0.0879759	+	0.996123i	$0.471960\pi$
$758$	22.2603	0.808532
$759$	−2.49651	−0.0906177
$760$	11.9010	0.431696
$761$	−33.0638	−1.19856	−0.599281	−	0.800539i	$-0.704547\pi$
$761$	−33.0638	−1.19856	−0.599281	+	0.800539i	$0.704547\pi$
$762$	2.55269	0.0924743
$763$	−0.102313	−0.00370396
$764$	−6.39023	−0.231190
$765$	−25.1997	−0.911096
$766$	0.908171	0.0328136
$767$	47.8875	1.72912
$768$	−0.506267	−0.0182683
$769$	−21.0184	−0.757943	−0.378972	−	0.925408i	$-0.623722\pi$
$769$	−21.0184	−0.757943	−0.378972	+	0.925408i	$0.623722\pi$
$770$	−0.0650736	−0.00234509
$771$	11.9355	0.429847
$772$	5.47887	0.197189
$773$	−28.6883	−1.03185	−0.515923	−	0.856635i	$-0.672551\pi$
$773$	−28.6883	−1.03185	−0.515923	+	0.856635i	$0.672551\pi$
$774$	−13.3474	−0.479762
$775$	7.74140	0.278079
$776$	−6.68727	−0.240059
$777$	−0.0236264	−0.000847594 0
$778$	17.4792	0.626660
$779$	4.50487	0.161404
$780$	−5.20809	−0.186480
$781$	8.51140	0.304562
$782$	−5.68318	−0.203230
$783$	−10.3576	−0.370149
$784$	−6.99993	−0.249998
$785$	20.8494	0.744146
$786$	−7.39231	−0.263675
$787$	3.62160	0.129096	0.0645480	−	0.997915i	$-0.479439\pi$
$787$	3.62160	0.129096	0.0645480	+	0.997915i	$0.479439\pi$
$788$	−5.27529	−0.187924
$789$	7.40782	0.263725
$790$	28.3295	1.00792
$791$	0.0526884	0.00187339
$792$	7.54318	0.268035
$793$	−6.04174	−0.214549
$794$	−6.25742	−0.222068
$795$	−1.74842	−0.0620099
$796$	−12.0299	−0.426389
$797$	−9.32411	−0.330277	−0.165138	−	0.986270i	$-0.552807\pi$
$797$	−9.32411	−0.330277	−0.165138	+	0.986270i	$0.552807\pi$
$798$	−0.0169724	−0.000600817 0
$799$	7.65791	0.270917
$800$	3.40246	0.120295
$801$	9.83788	0.347604
$802$	24.6645	0.870935
$803$	38.2705	1.35054
$804$	−7.83229	−0.276224
$805$	−0.0424542	−0.00149631
$806$	8.07464	0.284417
$807$	11.0225	0.388009
$808$	0.764937	0.0269104
$809$	−35.5716	−1.25063	−0.625316	−	0.780372i	$-0.715030\pi$
$809$	−35.5716	−1.25063	−0.625316	+	0.780372i	$0.715030\pi$
$810$	19.5921	0.688397
$811$	5.76063	0.202283	0.101142	−	0.994872i	$-0.467751\pi$
$811$	5.76063	0.202283	0.101142	+	0.994872i	$0.467751\pi$
$812$	−0.0290850	−0.00102068
$813$	1.16183	0.0407472
$814$	−15.7129	−0.550735
$815$	20.6944	0.724894
$816$	−1.60412	−0.0561553
$817$	19.9730	0.698765
$818$	−28.4224	−0.993766
$819$	−0.0795086	−0.00277825
$820$	3.18056	0.111070
$821$	−24.9731	−0.871566	−0.435783	−	0.900052i	$-0.643528\pi$
$821$	−24.9731	−0.871566	−0.435783	+	0.900052i	$0.643528\pi$
$822$	−4.17120	−0.145487
$823$	28.3519	0.988285	0.494143	−	0.869381i	$-0.335482\pi$
$823$	28.3519	0.988285	0.494143	+	0.869381i	$0.335482\pi$
$824$	−8.24853	−0.287351
$825$	4.73578	0.164879
$826$	0.110182	0.00383371
$827$	−24.8748	−0.864982	−0.432491	−	0.901638i	$-0.642365\pi$
$827$	−24.8748	−0.864982	−0.432491	+	0.901638i	$0.642365\pi$
$828$	4.92120	0.171024
$829$	28.3558	0.984837	0.492418	−	0.870359i	$-0.336113\pi$
$829$	28.3558	0.984837	0.492418	+	0.870359i	$0.336113\pi$
$830$	50.5764	1.75553
$831$	−12.5870	−0.436640
$832$	3.54892	0.123037
$833$	−22.1794	−0.768471
$834$	−3.59049	−0.124328
$835$	15.4638	0.535146
$836$	−11.2876	−0.390389
$837$	6.61604	0.228684
$838$	7.57299	0.261605
$839$	−2.81322	−0.0971232	−0.0485616	−	0.998820i	$-0.515464\pi$
$839$	−2.81322	−0.0971232	−0.0485616	+	0.998820i	$0.515464\pi$
$840$	−0.0119830	−0.000413452 0
$841$	−16.3126	−0.562503
$842$	−8.25370	−0.284441
$843$	9.88004	0.340287
$844$	−15.4494	−0.531789
$845$	−1.17451	−0.0404044
$846$	−6.63116	−0.227984
$847$	−0.0281012	−0.000965568 0
$848$	1.19141	0.0409132
$849$	1.62859	0.0558931
$850$	10.7808	0.369777
$851$	−10.2511	−0.351404
$852$	1.56733	0.0536960
$853$	10.4926	0.359259	0.179629	−	0.983734i	$-0.442510\pi$
$853$	10.4926	0.359259	0.179629	+	0.983734i	$0.442510\pi$
$854$	−0.0139011	−0.000475685 0
$855$	−32.6528	−1.11670
$856$	2.61157	0.0892617
$857$	23.9775	0.819055	0.409528	−	0.912298i	$-0.365694\pi$
$857$	23.9775	0.819055	0.409528	+	0.912298i	$0.365694\pi$
$858$	4.93963	0.168636
$859$	25.8863	0.883230	0.441615	−	0.897205i	$-0.354406\pi$
$859$	25.8863	0.883230	0.441615	+	0.897205i	$0.354406\pi$
$860$	14.1015	0.480856
$861$	−0.00453589	−0.000154583 0
$862$	−2.03301	−0.0692446
$863$	−31.0877	−1.05824	−0.529119	−	0.848548i	$-0.677477\pi$
$863$	−31.0877	−1.05824	−0.529119	+	0.848548i	$0.677477\pi$
$864$	2.90784	0.0989268
$865$	−4.36720	−0.148489
$866$	−14.3677	−0.488235
$867$	3.52387	0.119677
$868$	0.0185784	0.000630594 0
$869$	−26.8692	−0.911476
$870$	5.22720	0.177219
$871$	54.9041	1.86036
$872$	−12.5299	−0.424315
$873$	18.3478	0.620979
$874$	−7.36405	−0.249093
$875$	−0.0378127	−0.00127830
$876$	7.04733	0.238107
$877$	8.23543	0.278091	0.139045	−	0.990286i	$-0.455597\pi$
$877$	8.23543	0.278091	0.139045	+	0.990286i	$0.455597\pi$
$878$	−32.9373	−1.11158
$879$	−6.49667	−0.219127
$880$	−7.96934	−0.268646
$881$	−58.5361	−1.97213	−0.986065	−	0.166361i	$-0.946798\pi$
$881$	−58.5361	−1.97213	−0.986065	+	0.166361i	$0.946798\pi$
$882$	19.2057	0.646689
$883$	−37.7037	−1.26883	−0.634415	−	0.772992i	$-0.718759\pi$
$883$	−37.7037	−1.26883	−0.634415	+	0.772992i	$0.718759\pi$
$884$	11.2448	0.378204
$885$	−19.8020	−0.665638
$886$	−30.8743	−1.03724
$887$	17.4879	0.587186	0.293593	−	0.955930i	$-0.405149\pi$
$887$	17.4879	0.587186	0.293593	+	0.955930i	$0.405149\pi$
$888$	−2.89345	−0.0970978
$889$	−0.0411719	−0.00138086
$890$	−10.3937	−0.348397
$891$	−18.5822	−0.622528
$892$	8.70679	0.291525
$893$	9.92283	0.332055
$894$	4.64705	0.155421
$895$	−12.0284	−0.402066
$896$	0.00816549	0.000272790 0
$897$	3.22263	0.107601
$898$	25.4801	0.850280
$899$	−8.10426	−0.270292
$900$	−9.33530	−0.311177
$901$	3.77501	0.125764
$902$	−3.01661	−0.100442
$903$	−0.0201105	−0.000669235 0
$904$	6.45257	0.214609
$905$	−9.84350	−0.327209
$906$	5.46600	0.181596
$907$	13.1080	0.435245	0.217622	−	0.976033i	$-0.430170\pi$
$907$	13.1080	0.435245	0.217622	+	0.976033i	$0.430170\pi$
$908$	10.5593	0.350424
$909$	−2.09875	−0.0696112
$910$	0.0840004	0.00278459
$911$	−6.03470	−0.199938	−0.0999692	−	0.994991i	$-0.531874\pi$
$911$	−6.03470	−0.199938	−0.0999692	+	0.994991i	$0.531874\pi$
$912$	−2.07855	−0.0688278
$913$	−47.9694	−1.58755
$914$	7.64423	0.252849
$915$	2.49833	0.0825921
$916$	1.00038	0.0330536
$917$	0.119229	0.00393730
$918$	9.21356	0.304093
$919$	6.47987	0.213751	0.106876	−	0.994272i	$-0.465915\pi$
$919$	6.47987	0.213751	0.106876	+	0.994272i	$0.465915\pi$
$920$	−5.19922	−0.171413
$921$	6.20536	0.204474
$922$	−13.3677	−0.440243
$923$	−10.9870	−0.361640
$924$	0.0113653	0.000373891 0
$925$	19.4459	0.639378
$926$	−4.15725	−0.136616
$927$	22.6314	0.743314
$928$	−3.56194	−0.116926
$929$	16.5711	0.543681	0.271841	−	0.962342i	$-0.412368\pi$
$929$	16.5711	0.543681	0.271841	+	0.962342i	$0.412368\pi$
$930$	−3.33895	−0.109488
$931$	−28.7393	−0.941891
$932$	9.33598	0.305810
$933$	−2.90081	−0.0949682
$934$	6.62025	0.216621
$935$	−25.2510	−0.825796
$936$	−9.73714	−0.318268
$937$	−18.2400	−0.595874	−0.297937	−	0.954586i	$-0.596298\pi$
$937$	−18.2400	−0.595874	−0.297937	+	0.954586i	$0.596298\pi$
$938$	0.126326	0.00412468
$939$	−9.23286	−0.301303
$940$	7.00579	0.228504
$941$	−42.4894	−1.38511	−0.692557	−	0.721363i	$-0.743516\pi$
$941$	−42.4894	−1.38511	−0.692557	+	0.721363i	$0.743516\pi$
$942$	−3.64141	−0.118644
$943$	−1.96805	−0.0640885
$944$	13.4936	0.439178
$945$	0.0688266	0.00223893
$946$	−13.3746	−0.434845
$947$	48.8198	1.58643	0.793215	−	0.608941i	$-0.208405\pi$
$947$	48.8198	1.58643	0.793215	+	0.608941i	$0.208405\pi$
$948$	−4.94784	−0.160698
$949$	−49.4016	−1.60364
$950$	13.9693	0.453224
$951$	−15.1099	−0.489974
$952$	0.0258725	0.000838533 0
$953$	26.0942	0.845273	0.422637	−	0.906299i	$-0.361105\pi$
$953$	26.0942	0.845273	0.422637	+	0.906299i	$0.361105\pi$
$954$	−3.26887	−0.105833
$955$	−18.5234	−0.599402
$956$	22.7559	0.735980
$957$	−4.95776	−0.160262
$958$	−0.0727538	−0.00235057
$959$	0.0672765	0.00217247
$960$	−1.46752	−0.0473639
$961$	−25.8233	−0.833009
$962$	20.2830	0.653950
$963$	−7.16535	−0.230900
$964$	−8.71394	−0.280657
$965$	15.8816	0.511247
$966$	0.00741476	0.000238566 0
$967$	−49.8717	−1.60377	−0.801883	−	0.597481i	$-0.796168\pi$
$967$	−49.8717	−1.60377	−0.801883	+	0.597481i	$0.796168\pi$
$968$	−3.44146	−0.110613
$969$	−6.58594	−0.211571
$970$	−19.3844	−0.622395
$971$	34.8393	1.11805	0.559023	−	0.829152i	$-0.311176\pi$
$971$	34.8393	1.11805	0.559023	+	0.829152i	$0.311176\pi$
$972$	−12.1454	−0.389562
$973$	0.0579104	0.00185652
$974$	−0.841272	−0.0269561
$975$	−6.11320	−0.195779
$976$	−1.70242	−0.0544931
$977$	−33.8710	−1.08363	−0.541815	−	0.840498i	$-0.682263\pi$
$977$	−33.8710	−1.08363	−0.541815	+	0.840498i	$0.682263\pi$
$978$	−3.61435	−0.115574
$979$	9.85792	0.315060
$980$	−20.2907	−0.648163
$981$	34.3781	1.09761
$982$	9.27025	0.295826
$983$	25.3231	0.807683	0.403841	−	0.914829i	$-0.367675\pi$
$983$	25.3231	0.807683	0.403841	+	0.914829i	$0.367675\pi$
$984$	−0.555495	−0.0177085
$985$	−15.2915	−0.487227
$986$	−11.2861	−0.359422
$987$	−0.00999116	−0.000318022 0
$988$	14.5706	0.463553
$989$	−8.72562	−0.277458
$990$	21.8654	0.694929
$991$	−35.5542	−1.12942	−0.564709	−	0.825290i	$-0.691011\pi$
$991$	−35.5542	−1.12942	−0.564709	+	0.825290i	$0.691011\pi$
$992$	2.27524	0.0722389
$993$	4.72297	0.149879
$994$	−0.0252793	−0.000801809 0
$995$	−34.8711	−1.10549
$996$	−8.83333	−0.279895
$997$	51.9958	1.64672	0.823362	−	0.567516i	$-0.192096\pi$
$997$	51.9958	1.64672	0.823362	+	0.567516i	$0.192096\pi$
$998$	14.8063	0.468684
$999$	16.6191	0.525805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.i.1.16	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.i.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.506267 q^{3} +1.00000 q^{4} +2.89870 q^{5} -0.506267 q^{6} +0.00816549 q^{7} +1.00000 q^{8} -2.74369 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.506267 q^{3} +1.00000 q^{4} +2.89870 q^{5} -0.506267 q^{6} +0.00816549 q^{7} +1.00000 q^{8} -2.74369 q^{9} +2.89870 q^{10} -2.74928 q^{11} -0.506267 q^{12} +3.54892 q^{13} +0.00816549 q^{14} -1.46752 q^{15} +1.00000 q^{16} +3.16852 q^{17} -2.74369 q^{18} +4.10565 q^{19} +2.89870 q^{20} -0.00413392 q^{21} -2.74928 q^{22} -1.79364 q^{23} -0.506267 q^{24} +3.40246 q^{25} +3.54892 q^{26} +2.90784 q^{27} +0.00816549 q^{28} -3.56194 q^{29} -1.46752 q^{30} +2.27524 q^{31} +1.00000 q^{32} +1.39187 q^{33} +3.16852 q^{34} +0.0236693 q^{35} -2.74369 q^{36} +5.71526 q^{37} +4.10565 q^{38} -1.79670 q^{39} +2.89870 q^{40} +1.09724 q^{41} -0.00413392 q^{42} +4.86475 q^{43} -2.74928 q^{44} -7.95314 q^{45} -1.79364 q^{46} +2.41687 q^{47} -0.506267 q^{48} -6.99993 q^{49} +3.40246 q^{50} -1.60412 q^{51} +3.54892 q^{52} +1.19141 q^{53} +2.90784 q^{54} -7.96934 q^{55} +0.00816549 q^{56} -2.07855 q^{57} -3.56194 q^{58} +13.4936 q^{59} -1.46752 q^{60} -1.70242 q^{61} +2.27524 q^{62} -0.0224036 q^{63} +1.00000 q^{64} +10.2872 q^{65} +1.39187 q^{66} +15.4707 q^{67} +3.16852 q^{68} +0.908061 q^{69} +0.0236693 q^{70} -3.09586 q^{71} -2.74369 q^{72} -13.9202 q^{73} +5.71526 q^{74} -1.72255 q^{75} +4.10565 q^{76} -0.0224492 q^{77} -1.79670 q^{78} +9.77318 q^{79} +2.89870 q^{80} +6.75894 q^{81} +1.09724 q^{82} +17.4480 q^{83} -0.00413392 q^{84} +9.18458 q^{85} +4.86475 q^{86} +1.80329 q^{87} -2.74928 q^{88} -3.58563 q^{89} -7.95314 q^{90} +0.0289787 q^{91} -1.79364 q^{92} -1.15188 q^{93} +2.41687 q^{94} +11.9010 q^{95} -0.506267 q^{96} -6.68727 q^{97} -6.99993 q^{98} +7.54318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) 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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