LMFDB - Embedded newform 4006.2.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.788172 q^{3} +1.00000 q^{4} +4.07685 q^{5} -0.788172 q^{6} -1.81597 q^{7} +1.00000 q^{8} -2.37879 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.788172 q^{3} +1.00000 q^{4} +4.07685 q^{5} -0.788172 q^{6} -1.81597 q^{7} +1.00000 q^{8} -2.37879 q^{9} +4.07685 q^{10} -6.23077 q^{11} -0.788172 q^{12} +1.33843 q^{13} -1.81597 q^{14} -3.21326 q^{15} +1.00000 q^{16} -5.71463 q^{17} -2.37879 q^{18} -5.18174 q^{19} +4.07685 q^{20} +1.43130 q^{21} -6.23077 q^{22} +6.95946 q^{23} -0.788172 q^{24} +11.6207 q^{25} +1.33843 q^{26} +4.23941 q^{27} -1.81597 q^{28} -1.49533 q^{29} -3.21326 q^{30} +4.58595 q^{31} +1.00000 q^{32} +4.91092 q^{33} -5.71463 q^{34} -7.40344 q^{35} -2.37879 q^{36} +5.10869 q^{37} -5.18174 q^{38} -1.05492 q^{39} +4.07685 q^{40} -5.79450 q^{41} +1.43130 q^{42} -6.81909 q^{43} -6.23077 q^{44} -9.69795 q^{45} +6.95946 q^{46} -7.99073 q^{47} -0.788172 q^{48} -3.70225 q^{49} +11.6207 q^{50} +4.50411 q^{51} +1.33843 q^{52} -9.02427 q^{53} +4.23941 q^{54} -25.4019 q^{55} -1.81597 q^{56} +4.08410 q^{57} -1.49533 q^{58} -14.0706 q^{59} -3.21326 q^{60} +9.97061 q^{61} +4.58595 q^{62} +4.31980 q^{63} +1.00000 q^{64} +5.45659 q^{65} +4.91092 q^{66} -11.6267 q^{67} -5.71463 q^{68} -5.48525 q^{69} -7.40344 q^{70} -6.38308 q^{71} -2.37879 q^{72} -0.321882 q^{73} +5.10869 q^{74} -9.15910 q^{75} -5.18174 q^{76} +11.3149 q^{77} -1.05492 q^{78} +6.21675 q^{79} +4.07685 q^{80} +3.79497 q^{81} -5.79450 q^{82} +1.21704 q^{83} +1.43130 q^{84} -23.2977 q^{85} -6.81909 q^{86} +1.17858 q^{87} -6.23077 q^{88} -9.16366 q^{89} -9.69795 q^{90} -2.43056 q^{91} +6.95946 q^{92} -3.61452 q^{93} -7.99073 q^{94} -21.1252 q^{95} -0.788172 q^{96} -9.75058 q^{97} -3.70225 q^{98} +14.8217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9	\( 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9} - 23 q^{10} - 32 q^{11} - 13 q^{12} - 8 q^{13} - 18 q^{14} - 14 q^{15} + 31 q^{16} - 30 q^{17} + 20 q^{18} - 38 q^{19} - 23 q^{20} - 16 q^{21} - 32 q^{22} - 24 q^{23} - 13 q^{24} + 40 q^{25} - 8 q^{26} - 28 q^{27} - 18 q^{28} - 7 q^{29} - 14 q^{30} - 32 q^{31} + 31 q^{32} - 9 q^{33} - 30 q^{34} - 14 q^{35} + 20 q^{36} + 11 q^{37} - 38 q^{38} - 9 q^{39} - 23 q^{40} - 76 q^{41} - 16 q^{42} - 33 q^{43} - 32 q^{44} - 40 q^{45} - 24 q^{46} - 96 q^{47} - 13 q^{48} + 15 q^{49} + 40 q^{50} - 55 q^{51} - 8 q^{52} - 28 q^{53} - 28 q^{54} - 52 q^{55} - 18 q^{56} - 21 q^{57} - 7 q^{58} - 72 q^{59} - 14 q^{60} - 9 q^{61} - 32 q^{62} - 54 q^{63} + 31 q^{64} - 38 q^{65} - 9 q^{66} - 4 q^{67} - 30 q^{68} - 17 q^{69} - 14 q^{70} - 61 q^{71} + 20 q^{72} - 62 q^{73} + 11 q^{74} - 63 q^{75} - 38 q^{76} - 9 q^{77} - 9 q^{78} - 30 q^{79} - 23 q^{80} - 13 q^{81} - 76 q^{82} - 90 q^{83} - 16 q^{84} + 26 q^{85} - 33 q^{86} - 34 q^{87} - 32 q^{88} - 99 q^{89} - 40 q^{90} - 47 q^{91} - 24 q^{92} - 6 q^{93} - 96 q^{94} - 24 q^{95} - 13 q^{96} - 46 q^{97} + 15 q^{98} - 48 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9 - 23 * q^10 - 32 * q^11 - 13 * q^12 - 8 * q^13 - 18 * q^14 - 14 * q^15 + 31 * q^16 - 30 * q^17 + 20 * q^18 - 38 * q^19 - 23 * q^20 - 16 * q^21 - 32 * q^22 - 24 * q^23 - 13 * q^24 + 40 * q^25 - 8 * q^26 - 28 * q^27 - 18 * q^28 - 7 * q^29 - 14 * q^30 - 32 * q^31 + 31 * q^32 - 9 * q^33 - 30 * q^34 - 14 * q^35 + 20 * q^36 + 11 * q^37 - 38 * q^38 - 9 * q^39 - 23 * q^40 - 76 * q^41 - 16 * q^42 - 33 * q^43 - 32 * q^44 - 40 * q^45 - 24 * q^46 - 96 * q^47 - 13 * q^48 + 15 * q^49 + 40 * q^50 - 55 * q^51 - 8 * q^52 - 28 * q^53 - 28 * q^54 - 52 * q^55 - 18 * q^56 - 21 * q^57 - 7 * q^58 - 72 * q^59 - 14 * q^60 - 9 * q^61 - 32 * q^62 - 54 * q^63 + 31 * q^64 - 38 * q^65 - 9 * q^66 - 4 * q^67 - 30 * q^68 - 17 * q^69 - 14 * q^70 - 61 * q^71 + 20 * q^72 - 62 * q^73 + 11 * q^74 - 63 * q^75 - 38 * q^76 - 9 * q^77 - 9 * q^78 - 30 * q^79 - 23 * q^80 - 13 * q^81 - 76 * q^82 - 90 * q^83 - 16 * q^84 + 26 * q^85 - 33 * q^86 - 34 * q^87 - 32 * q^88 - 99 * q^89 - 40 * q^90 - 47 * q^91 - 24 * q^92 - 6 * q^93 - 96 * q^94 - 24 * q^95 - 13 * q^96 - 46 * q^97 + 15 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.788172	−0.455051	−0.227526	−	0.973772i	$-0.573064\pi$
$3$	−0.788172	−0.455051	−0.227526	+	0.973772i	$0.573064\pi$
$4$	1.00000	0.500000
$5$	4.07685	1.82322	0.911611	−	0.411054i	$-0.134839\pi$
$5$	4.07685	1.82322	0.911611	+	0.411054i	$0.134839\pi$
$6$	−0.788172	−0.321770
$7$	−1.81597	−0.686372	−0.343186	−	0.939267i	$-0.611506\pi$
$7$	−1.81597	−0.686372	−0.343186	+	0.939267i	$0.611506\pi$
$8$	1.00000	0.353553
$9$	−2.37879	−0.792928
$10$	4.07685	1.28921
$11$	−6.23077	−1.87865	−0.939324	−	0.343032i	$-0.888546\pi$
$11$	−6.23077	−1.87865	−0.939324	+	0.343032i	$0.888546\pi$
$12$	−0.788172	−0.227526
$13$	1.33843	0.371215	0.185607	−	0.982624i	$-0.440575\pi$
$13$	1.33843	0.371215	0.185607	+	0.982624i	$0.440575\pi$
$14$	−1.81597	−0.485339
$15$	−3.21326	−0.829659
$16$	1.00000	0.250000
$17$	−5.71463	−1.38600	−0.693001	−	0.720937i	$-0.743712\pi$
$17$	−5.71463	−1.38600	−0.693001	+	0.720937i	$0.743712\pi$
$18$	−2.37879	−0.560685
$19$	−5.18174	−1.18877	−0.594387	−	0.804179i	$-0.702605\pi$
$19$	−5.18174	−1.18877	−0.594387	+	0.804179i	$0.702605\pi$
$20$	4.07685	0.911611
$21$	1.43130	0.312335
$22$	−6.23077	−1.32840
$23$	6.95946	1.45115	0.725574	−	0.688145i	$-0.241575\pi$
$23$	6.95946	1.45115	0.725574	+	0.688145i	$0.241575\pi$
$24$	−0.788172	−0.160885
$25$	11.6207	2.32414
$26$	1.33843	0.262489
$27$	4.23941	0.815874
$28$	−1.81597	−0.343186
$29$	−1.49533	−0.277676	−0.138838	−	0.990315i	$-0.544337\pi$
$29$	−1.49533	−0.277676	−0.138838	+	0.990315i	$0.544337\pi$
$30$	−3.21326	−0.586658
$31$	4.58595	0.823661	0.411831	−	0.911260i	$-0.364890\pi$
$31$	4.58595	0.823661	0.411831	+	0.911260i	$0.364890\pi$
$32$	1.00000	0.176777
$33$	4.91092	0.854881
$34$	−5.71463	−0.980051
$35$	−7.40344	−1.25141
$36$	−2.37879	−0.396464
$37$	5.10869	0.839864	0.419932	−	0.907556i	$-0.362054\pi$
$37$	5.10869	0.839864	0.419932	+	0.907556i	$0.362054\pi$
$38$	−5.18174	−0.840590
$39$	−1.05492	−0.168922
$40$	4.07685	0.644606
$41$	−5.79450	−0.904949	−0.452475	−	0.891777i	$-0.649459\pi$
$41$	−5.79450	−0.904949	−0.452475	+	0.891777i	$0.649459\pi$
$42$	1.43130	0.220854
$43$	−6.81909	−1.03990	−0.519951	−	0.854196i	$-0.674050\pi$
$43$	−6.81909	−1.03990	−0.519951	+	0.854196i	$0.674050\pi$
$44$	−6.23077	−0.939324
$45$	−9.69795	−1.44568
$46$	6.95946	1.02612
$47$	−7.99073	−1.16557	−0.582784	−	0.812627i	$-0.698037\pi$
$47$	−7.99073	−1.16557	−0.582784	+	0.812627i	$0.698037\pi$
$48$	−0.788172	−0.113763
$49$	−3.70225	−0.528893
$50$	11.6207	1.64341
$51$	4.50411	0.630702
$52$	1.33843	0.185607
$53$	−9.02427	−1.23958	−0.619790	−	0.784768i	$-0.712782\pi$
$53$	−9.02427	−1.23958	−0.619790	+	0.784768i	$0.712782\pi$
$54$	4.23941	0.576910
$55$	−25.4019	−3.42519
$56$	−1.81597	−0.242669
$57$	4.08410	0.540953
$58$	−1.49533	−0.196347
$59$	−14.0706	−1.83184	−0.915919	−	0.401363i	$-0.868536\pi$
$59$	−14.0706	−1.83184	−0.915919	+	0.401363i	$0.868536\pi$
$60$	−3.21326	−0.414830
$61$	9.97061	1.27661	0.638303	−	0.769785i	$-0.279637\pi$
$61$	9.97061	1.27661	0.638303	+	0.769785i	$0.279637\pi$
$62$	4.58595	0.582416
$63$	4.31980	0.544244
$64$	1.00000	0.125000
$65$	5.45659	0.676807
$66$	4.91092	0.604492
$67$	−11.6267	−1.42043	−0.710214	−	0.703986i	$-0.751402\pi$
$67$	−11.6267	−1.42043	−0.710214	+	0.703986i	$0.751402\pi$
$68$	−5.71463	−0.693001
$69$	−5.48525	−0.660346
$70$	−7.40344	−0.884880
$71$	−6.38308	−0.757532	−0.378766	−	0.925492i	$-0.623652\pi$
$71$	−6.38308	−0.757532	−0.378766	+	0.925492i	$0.623652\pi$
$72$	−2.37879	−0.280343
$73$	−0.321882	−0.0376734	−0.0188367	−	0.999823i	$-0.505996\pi$
$73$	−0.321882	−0.0376734	−0.0188367	+	0.999823i	$0.505996\pi$
$74$	5.10869	0.593873
$75$	−9.15910	−1.05760
$76$	−5.18174	−0.594387
$77$	11.3149	1.28945
$78$	−1.05492	−0.119446
$79$	6.21675	0.699439	0.349720	−	0.936854i	$-0.386277\pi$
$79$	6.21675	0.699439	0.349720	+	0.936854i	$0.386277\pi$
$80$	4.07685	0.455805
$81$	3.79497	0.421664
$82$	−5.79450	−0.639896
$83$	1.21704	0.133588	0.0667940	−	0.997767i	$-0.478723\pi$
$83$	1.21704	0.133588	0.0667940	+	0.997767i	$0.478723\pi$
$84$	1.43130	0.156167
$85$	−23.2977	−2.52699
$86$	−6.81909	−0.735321
$87$	1.17858	0.126357
$88$	−6.23077	−0.664202
$89$	−9.16366	−0.971346	−0.485673	−	0.874141i	$-0.661425\pi$
$89$	−9.16366	−0.971346	−0.485673	+	0.874141i	$0.661425\pi$
$90$	−9.69795	−1.02225
$91$	−2.43056	−0.254792
$92$	6.95946	0.725574
$93$	−3.61452	−0.374808
$94$	−7.99073	−0.824181
$95$	−21.1252	−2.16740
$96$	−0.788172	−0.0804425
$97$	−9.75058	−0.990022	−0.495011	−	0.868887i	$-0.664836\pi$
$97$	−9.75058	−0.990022	−0.495011	+	0.868887i	$0.664836\pi$
$98$	−3.70225	−0.373984
$99$	14.8217	1.48963
$100$	11.6207	1.16207
$101$	−1.76522	−0.175646	−0.0878230	−	0.996136i	$-0.527991\pi$
$101$	−1.76522	−0.175646	−0.0878230	+	0.996136i	$0.527991\pi$
$102$	4.50411	0.445973
$103$	−10.0638	−0.991618	−0.495809	−	0.868432i	$-0.665128\pi$
$103$	−10.0638	−0.991618	−0.495809	+	0.868432i	$0.665128\pi$
$104$	1.33843	0.131244
$105$	5.83518	0.569455
$106$	−9.02427	−0.876515
$107$	2.99754	0.289783	0.144892	−	0.989448i	$-0.453717\pi$
$107$	2.99754	0.289783	0.144892	+	0.989448i	$0.453717\pi$
$108$	4.23941	0.407937
$109$	19.3093	1.84949	0.924747	−	0.380583i	$-0.124277\pi$
$109$	19.3093	1.84949	0.924747	+	0.380583i	$0.124277\pi$
$110$	−25.4019	−2.42198
$111$	−4.02653	−0.382181
$112$	−1.81597	−0.171593
$113$	−19.0951	−1.79631	−0.898156	−	0.439676i	$-0.855093\pi$
$113$	−19.0951	−1.79631	−0.898156	+	0.439676i	$0.855093\pi$
$114$	4.08410	0.382511
$115$	28.3727	2.64576
$116$	−1.49533	−0.138838
$117$	−3.18385	−0.294347
$118$	−14.0706	−1.29530
$119$	10.3776	0.951313
$120$	−3.21326	−0.293329
$121$	27.8225	2.52932
$122$	9.97061	0.902697
$123$	4.56706	0.411798
$124$	4.58595	0.411831
$125$	26.9916	2.41420
$126$	4.31980	0.384839
$127$	16.3051	1.44684	0.723422	−	0.690406i	$-0.242568\pi$
$127$	16.3051	1.44684	0.723422	+	0.690406i	$0.242568\pi$
$128$	1.00000	0.0883883
$129$	5.37461	0.473208
$130$	5.45659	0.478575
$131$	−8.44363	−0.737723	−0.368862	−	0.929484i	$-0.620252\pi$
$131$	−8.44363	−0.737723	−0.368862	+	0.929484i	$0.620252\pi$
$132$	4.91092	0.427440
$133$	9.40989	0.815941
$134$	−11.6267	−1.00439
$135$	17.2834	1.48752
$136$	−5.71463	−0.490025
$137$	7.41048	0.633120	0.316560	−	0.948573i	$-0.397472\pi$
$137$	7.41048	0.633120	0.316560	+	0.948573i	$0.397472\pi$
$138$	−5.48525	−0.466935
$139$	0.993897	0.0843012	0.0421506	−	0.999111i	$-0.486579\pi$
$139$	0.993897	0.0843012	0.0421506	+	0.999111i	$0.486579\pi$
$140$	−7.40344	−0.625705
$141$	6.29807	0.530393
$142$	−6.38308	−0.535656
$143$	−8.33948	−0.697382
$144$	−2.37879	−0.198232
$145$	−6.09624	−0.506265
$146$	−0.321882	−0.0266391
$147$	2.91801	0.240673
$148$	5.10869	0.419932
$149$	−13.7049	−1.12275	−0.561373	−	0.827563i	$-0.689727\pi$
$149$	−13.7049	−1.12275	−0.561373	+	0.827563i	$0.689727\pi$
$150$	−9.15910	−0.747838
$151$	−5.75158	−0.468057	−0.234028	−	0.972230i	$-0.575191\pi$
$151$	−5.75158	−0.468057	−0.234028	+	0.972230i	$0.575191\pi$
$152$	−5.18174	−0.420295
$153$	13.5939	1.09900
$154$	11.3149	0.911780
$155$	18.6962	1.50172
$156$	−1.05492	−0.0844609
$157$	13.0946	1.04506	0.522532	−	0.852620i	$-0.324988\pi$
$157$	13.0946	1.04506	0.522532	+	0.852620i	$0.324988\pi$
$158$	6.21675	0.494578
$159$	7.11268	0.564072
$160$	4.07685	0.322303
$161$	−12.6382	−0.996027
$162$	3.79497	0.298161
$163$	−16.1558	−1.26542	−0.632708	−	0.774390i	$-0.718057\pi$
$163$	−16.1558	−1.26542	−0.632708	+	0.774390i	$0.718057\pi$
$164$	−5.79450	−0.452475
$165$	20.0211	1.55864
$166$	1.21704	0.0944609
$167$	−12.9132	−0.999251	−0.499626	−	0.866241i	$-0.666529\pi$
$167$	−12.9132	−0.999251	−0.499626	+	0.866241i	$0.666529\pi$
$168$	1.43130	0.110427
$169$	−11.2086	−0.862199
$170$	−23.2977	−1.78685
$171$	12.3263	0.942612
$172$	−6.81909	−0.519951
$173$	−5.31599	−0.404167	−0.202084	−	0.979368i	$-0.564771\pi$
$173$	−5.31599	−0.404167	−0.202084	+	0.979368i	$0.564771\pi$
$174$	1.17858	0.0893478
$175$	−21.1028	−1.59522
$176$	−6.23077	−0.469662
$177$	11.0901	0.833580
$178$	−9.16366	−0.686845
$179$	10.7974	0.807035	0.403518	−	0.914972i	$-0.367787\pi$
$179$	10.7974	0.807035	0.403518	+	0.914972i	$0.367787\pi$
$180$	−9.69795	−0.722842
$181$	−0.670973	−0.0498730	−0.0249365	−	0.999689i	$-0.507938\pi$
$181$	−0.670973	−0.0498730	−0.0249365	+	0.999689i	$0.507938\pi$
$182$	−2.43056	−0.180165
$183$	−7.85856	−0.580921
$184$	6.95946	0.513058
$185$	20.8274	1.53126
$186$	−3.61452	−0.265029
$187$	35.6065	2.60381
$188$	−7.99073	−0.582784
$189$	−7.69864	−0.559994
$190$	−21.1252	−1.53258
$191$	24.5383	1.77553	0.887765	−	0.460298i	$-0.152257\pi$
$191$	24.5383	1.77553	0.887765	+	0.460298i	$0.152257\pi$
$192$	−0.788172	−0.0568814
$193$	18.9782	1.36608	0.683040	−	0.730381i	$-0.260658\pi$
$193$	18.9782	1.36608	0.683040	+	0.730381i	$0.260658\pi$
$194$	−9.75058	−0.700051
$195$	−4.30073	−0.307982
$196$	−3.70225	−0.264447
$197$	10.5662	0.752811	0.376406	−	0.926455i	$-0.377160\pi$
$197$	10.5662	0.752811	0.376406	+	0.926455i	$0.377160\pi$
$198$	14.8217	1.05333
$199$	−22.2583	−1.57785	−0.788926	−	0.614489i	$-0.789362\pi$
$199$	−22.2583	−1.57785	−0.788926	+	0.614489i	$0.789362\pi$
$200$	11.6207	0.821707
$201$	9.16384	0.646367
$202$	−1.76522	−0.124200
$203$	2.71548	0.190589
$204$	4.50411	0.315351
$205$	−23.6233	−1.64992
$206$	−10.0638	−0.701180
$207$	−16.5551	−1.15066
$208$	1.33843	0.0928037
$209$	32.2862	2.23329
$210$	5.83518	0.402666
$211$	4.71735	0.324756	0.162378	−	0.986729i	$-0.448084\pi$
$211$	4.71735	0.324756	0.162378	+	0.986729i	$0.448084\pi$
$212$	−9.02427	−0.619790
$213$	5.03097	0.344716
$214$	2.99754	0.204908
$215$	−27.8004	−1.89597
$216$	4.23941	0.288455
$217$	−8.32795	−0.565338
$218$	19.3093	1.30779
$219$	0.253698	0.0171433
$220$	−25.4019	−1.71260
$221$	−7.64866	−0.514504
$222$	−4.02653	−0.270243
$223$	−26.3754	−1.76623	−0.883115	−	0.469157i	$-0.844558\pi$
$223$	−26.3754	−1.76623	−0.883115	+	0.469157i	$0.844558\pi$
$224$	−1.81597	−0.121335
$225$	−27.6431	−1.84288
$226$	−19.0951	−1.27018
$227$	5.34544	0.354789	0.177395	−	0.984140i	$-0.443233\pi$
$227$	5.34544	0.354789	0.177395	+	0.984140i	$0.443233\pi$
$228$	4.08410	0.270476
$229$	25.6939	1.69790	0.848949	−	0.528475i	$-0.177236\pi$
$229$	25.6939	1.69790	0.848949	+	0.528475i	$0.177236\pi$
$230$	28.3727	1.87084
$231$	−8.91808	−0.586767
$232$	−1.49533	−0.0981733
$233$	−1.94956	−0.127720	−0.0638599	−	0.997959i	$-0.520341\pi$
$233$	−1.94956	−0.127720	−0.0638599	+	0.997959i	$0.520341\pi$
$234$	−3.18385	−0.208135
$235$	−32.5770	−2.12509
$236$	−14.0706	−0.915919
$237$	−4.89987	−0.318281
$238$	10.3776	0.672680
$239$	−10.9553	−0.708641	−0.354321	−	0.935124i	$-0.615288\pi$
$239$	−10.9553	−0.708641	−0.354321	+	0.935124i	$0.615288\pi$
$240$	−3.21326	−0.207415
$241$	−1.54121	−0.0992784	−0.0496392	−	0.998767i	$-0.515807\pi$
$241$	−1.54121	−0.0992784	−0.0496392	+	0.998767i	$0.515807\pi$
$242$	27.8225	1.78850
$243$	−15.7093	−1.00775
$244$	9.97061	0.638303
$245$	−15.0935	−0.964289
$246$	4.56706	0.291185
$247$	−6.93542	−0.441290
$248$	4.58595	0.291208
$249$	−0.959240	−0.0607894
$250$	26.9916	1.70710
$251$	3.12749	0.197406	0.0987028	−	0.995117i	$-0.468531\pi$
$251$	3.12749	0.197406	0.0987028	+	0.995117i	$0.468531\pi$
$252$	4.31980	0.272122
$253$	−43.3628	−2.72619
$254$	16.3051	1.02307
$255$	18.3626	1.14991
$256$	1.00000	0.0625000
$257$	−9.22651	−0.575534	−0.287767	−	0.957700i	$-0.592913\pi$
$257$	−9.22651	−0.575534	−0.287767	+	0.957700i	$0.592913\pi$
$258$	5.37461	0.334609
$259$	−9.27723	−0.576459
$260$	5.45659	0.338404
$261$	3.55707	0.220177
$262$	−8.44363	−0.521649
$263$	−16.2807	−1.00391	−0.501957	−	0.864893i	$-0.667386\pi$
$263$	−16.2807	−1.00391	−0.501957	+	0.864893i	$0.667386\pi$
$264$	4.91092	0.302246
$265$	−36.7906	−2.26003
$266$	9.40989	0.576958
$267$	7.22254	0.442012
$268$	−11.6267	−0.710214
$269$	24.7813	1.51094	0.755472	−	0.655181i	$-0.227408\pi$
$269$	24.7813	1.51094	0.755472	+	0.655181i	$0.227408\pi$
$270$	17.2834	1.05184
$271$	28.1830	1.71200	0.855998	−	0.516979i	$-0.172944\pi$
$271$	28.1830	1.71200	0.855998	+	0.516979i	$0.172944\pi$
$272$	−5.71463	−0.346500
$273$	1.91570	0.115943
$274$	7.41048	0.447683
$275$	−72.4058	−4.36624
$276$	−5.48525	−0.330173
$277$	32.0978	1.92857	0.964285	−	0.264868i	$-0.0853283\pi$
$277$	32.0978	1.92857	0.964285	+	0.264868i	$0.0853283\pi$
$278$	0.993897	0.0596100
$279$	−10.9090	−0.653104
$280$	−7.40344	−0.442440
$281$	7.24178	0.432008	0.216004	−	0.976392i	$-0.430698\pi$
$281$	7.24178	0.432008	0.216004	+	0.976392i	$0.430698\pi$
$282$	6.29807	0.375044
$283$	−17.8642	−1.06191	−0.530957	−	0.847399i	$-0.678167\pi$
$283$	−17.8642	−1.06191	−0.530957	+	0.847399i	$0.678167\pi$
$284$	−6.38308	−0.378766
$285$	16.6503	0.986277
$286$	−8.33948	−0.493124
$287$	10.5226	0.621132
$288$	−2.37879	−0.140171
$289$	15.6570	0.920999
$290$	−6.09624	−0.357983
$291$	7.68513	0.450511
$292$	−0.321882	−0.0188367
$293$	−11.0885	−0.647797	−0.323899	−	0.946092i	$-0.604994\pi$
$293$	−11.0885	−0.647797	−0.323899	+	0.946092i	$0.604994\pi$
$294$	2.91801	0.170182
$295$	−57.3638	−3.33985
$296$	5.10869	0.296937
$297$	−26.4148	−1.53274
$298$	−13.7049	−0.793902
$299$	9.31478	0.538688
$300$	−9.15910	−0.528801
$301$	12.3833	0.713759
$302$	−5.75158	−0.330966
$303$	1.39130	0.0799279
$304$	−5.18174	−0.297193
$305$	40.6487	2.32754
$306$	13.5939	0.777110
$307$	2.81666	0.160755	0.0803777	−	0.996764i	$-0.474387\pi$
$307$	2.81666	0.160755	0.0803777	+	0.996764i	$0.474387\pi$
$308$	11.3149	0.644726
$309$	7.93202	0.451237
$310$	18.6962	1.06187
$311$	33.1801	1.88147	0.940736	−	0.339140i	$-0.110136\pi$
$311$	33.1801	1.88147	0.940736	+	0.339140i	$0.110136\pi$
$312$	−1.05492	−0.0597229
$313$	30.9266	1.74808	0.874038	−	0.485858i	$-0.161493\pi$
$313$	30.9266	1.74808	0.874038	+	0.485858i	$0.161493\pi$
$314$	13.0946	0.738971
$315$	17.6112	0.992278
$316$	6.21675	0.349720
$317$	1.78697	0.100366	0.0501831	−	0.998740i	$-0.484020\pi$
$317$	1.78697	0.100366	0.0501831	+	0.998740i	$0.484020\pi$
$318$	7.11268	0.398859
$319$	9.31706	0.521655
$320$	4.07685	0.227903
$321$	−2.36258	−0.131866
$322$	−12.6382	−0.704298
$323$	29.6117	1.64764
$324$	3.79497	0.210832
$325$	15.5535	0.862755
$326$	−16.1558	−0.894784
$327$	−15.2190	−0.841614
$328$	−5.79450	−0.319948
$329$	14.5109	0.800013
$330$	20.0211	1.10212
$331$	−29.3984	−1.61588	−0.807941	−	0.589263i	$-0.799418\pi$
$331$	−29.3984	−1.61588	−0.807941	+	0.589263i	$0.799418\pi$
$332$	1.21704	0.0667940
$333$	−12.1525	−0.665952
$334$	−12.9132	−0.706577
$335$	−47.4003	−2.58976
$336$	1.43130	0.0780836
$337$	30.9502	1.68596	0.842981	−	0.537943i	$-0.180798\pi$
$337$	30.9502	1.68596	0.842981	+	0.537943i	$0.180798\pi$
$338$	−11.2086	−0.609667
$339$	15.0502	0.817414
$340$	−23.2977	−1.26349
$341$	−28.5740	−1.54737
$342$	12.3263	0.666527
$343$	19.4350	1.04939
$344$	−6.81909	−0.367661
$345$	−22.3625	−1.20396
$346$	−5.31599	−0.285789
$347$	6.54590	0.351403	0.175701	−	0.984444i	$-0.443781\pi$
$347$	6.54590	0.351403	0.175701	+	0.984444i	$0.443781\pi$
$348$	1.17858	0.0631784
$349$	11.9959	0.642128	0.321064	−	0.947058i	$-0.395960\pi$
$349$	11.9959	0.642128	0.321064	+	0.947058i	$0.395960\pi$
$350$	−21.1028	−1.12799
$351$	5.67417	0.302865
$352$	−6.23077	−0.332101
$353$	2.38482	0.126931	0.0634655	−	0.997984i	$-0.479785\pi$
$353$	2.38482	0.126931	0.0634655	+	0.997984i	$0.479785\pi$
$354$	11.0901	0.589430
$355$	−26.0229	−1.38115
$356$	−9.16366	−0.485673
$357$	−8.17933	−0.432896
$358$	10.7974	0.570660
$359$	1.88328	0.0993956	0.0496978	−	0.998764i	$-0.484174\pi$
$359$	1.88328	0.0993956	0.0496978	+	0.998764i	$0.484174\pi$
$360$	−9.69795	−0.511127
$361$	7.85047	0.413182
$362$	−0.670973	−0.0352656
$363$	−21.9289	−1.15097
$364$	−2.43056	−0.127396
$365$	−1.31226	−0.0686870
$366$	−7.85856	−0.410773
$367$	20.8924	1.09057	0.545287	−	0.838249i	$-0.316421\pi$
$367$	20.8924	1.09057	0.545287	+	0.838249i	$0.316421\pi$
$368$	6.95946	0.362787
$369$	13.7839	0.717560
$370$	20.8274	1.08276
$371$	16.3878	0.850813
$372$	−3.61452	−0.187404
$373$	0.401095	0.0207679	0.0103840	−	0.999946i	$-0.496695\pi$
$373$	0.401095	0.0207679	0.0103840	+	0.999946i	$0.496695\pi$
$374$	35.6065	1.84117
$375$	−21.2740	−1.09858
$376$	−7.99073	−0.412090
$377$	−2.00140	−0.103077
$378$	−7.69864	−0.395975
$379$	6.59853	0.338944	0.169472	−	0.985535i	$-0.445794\pi$
$379$	6.59853	0.338944	0.169472	+	0.985535i	$0.445794\pi$
$380$	−21.1252	−1.08370
$381$	−12.8512	−0.658389
$382$	24.5383	1.25549
$383$	20.3378	1.03921	0.519607	−	0.854405i	$-0.326078\pi$
$383$	20.3378	1.03921	0.519607	+	0.854405i	$0.326078\pi$
$384$	−0.788172	−0.0402212
$385$	46.1291	2.35096
$386$	18.9782	0.965964
$387$	16.2211	0.824567
$388$	−9.75058	−0.495011
$389$	−34.1005	−1.72896	−0.864481	−	0.502665i	$-0.832353\pi$
$389$	−34.1005	−1.72896	−0.864481	+	0.502665i	$0.832353\pi$
$390$	−4.30073	−0.217776
$391$	−39.7707	−2.01129
$392$	−3.70225	−0.186992
$393$	6.65503	0.335702
$394$	10.5662	0.532318
$395$	25.3448	1.27523
$396$	14.8217	0.744816
$397$	−17.4242	−0.874496	−0.437248	−	0.899341i	$-0.644047\pi$
$397$	−17.4242	−0.874496	−0.437248	+	0.899341i	$0.644047\pi$
$398$	−22.2583	−1.11571
$399$	−7.41661	−0.371295
$400$	11.6207	0.581035
$401$	−14.9273	−0.745434	−0.372717	−	0.927945i	$-0.621574\pi$
$401$	−14.9273	−0.745434	−0.372717	+	0.927945i	$0.621574\pi$
$402$	9.16384	0.457051
$403$	6.13799	0.305755
$404$	−1.76522	−0.0878230
$405$	15.4715	0.768787
$406$	2.71548	0.134767
$407$	−31.8311	−1.57781
$408$	4.50411	0.222987
$409$	18.3666	0.908168	0.454084	−	0.890959i	$-0.349967\pi$
$409$	18.3666	0.908168	0.454084	+	0.890959i	$0.349967\pi$
$410$	−23.6233	−1.16667
$411$	−5.84073	−0.288102
$412$	−10.0638	−0.495809
$413$	25.5518	1.25732
$414$	−16.5551	−0.813636
$415$	4.96170	0.243560
$416$	1.33843	0.0656222
$417$	−0.783362	−0.0383614
$418$	32.2862	1.57917
$419$	−10.2547	−0.500975	−0.250488	−	0.968120i	$-0.580591\pi$
$419$	−10.2547	−0.500975	−0.250488	+	0.968120i	$0.580591\pi$
$420$	5.83518	0.284728
$421$	1.56690	0.0763661	0.0381831	−	0.999271i	$-0.487843\pi$
$421$	1.56690	0.0763661	0.0381831	+	0.999271i	$0.487843\pi$
$422$	4.71735	0.229637
$423$	19.0082	0.924212
$424$	−9.02427	−0.438258
$425$	−66.4079	−3.22126
$426$	5.03097	0.243751
$427$	−18.1063	−0.876227
$428$	2.99754	0.144892
$429$	6.57294	0.317345
$430$	−27.8004	−1.34065
$431$	2.59148	0.124827	0.0624137	−	0.998050i	$-0.480120\pi$
$431$	2.59148	0.124827	0.0624137	+	0.998050i	$0.480120\pi$
$432$	4.23941	0.203969
$433$	−33.1373	−1.59248	−0.796238	−	0.604983i	$-0.793180\pi$
$433$	−33.1373	−1.59248	−0.796238	+	0.604983i	$0.793180\pi$
$434$	−8.32795	−0.399754
$435$	4.80488	0.230377
$436$	19.3093	0.924747
$437$	−36.0621	−1.72509
$438$	0.253698	0.0121222
$439$	28.4868	1.35960	0.679800	−	0.733398i	$-0.262067\pi$
$439$	28.4868	1.35960	0.679800	+	0.733398i	$0.262067\pi$
$440$	−25.4019	−1.21099
$441$	8.80686	0.419374
$442$	−7.64866	−0.363810
$443$	24.3962	1.15910	0.579549	−	0.814937i	$-0.303229\pi$
$443$	24.3962	1.15910	0.579549	+	0.814937i	$0.303229\pi$
$444$	−4.02653	−0.191091
$445$	−37.3589	−1.77098
$446$	−26.3754	−1.24891
$447$	10.8018	0.510907
$448$	−1.81597	−0.0857965
$449$	22.4502	1.05949	0.529745	−	0.848157i	$-0.322288\pi$
$449$	22.4502	1.05949	0.529745	+	0.848157i	$0.322288\pi$
$450$	−27.6431	−1.30311
$451$	36.1042	1.70008
$452$	−19.0951	−0.898156
$453$	4.53323	0.212990
$454$	5.34544	0.250874
$455$	−9.90901	−0.464542
$456$	4.08410	0.191256
$457$	−15.1440	−0.708408	−0.354204	−	0.935168i	$-0.615248\pi$
$457$	−15.1440	−0.708408	−0.354204	+	0.935168i	$0.615248\pi$
$458$	25.6939	1.20060
$459$	−24.2266	−1.13080
$460$	28.3727	1.32288
$461$	12.8340	0.597739	0.298869	−	0.954294i	$-0.403390\pi$
$461$	12.8340	0.597739	0.298869	+	0.954294i	$0.403390\pi$
$462$	−8.91808	−0.414907
$463$	−18.0112	−0.837051	−0.418525	−	0.908205i	$-0.637453\pi$
$463$	−18.0112	−0.837051	−0.418525	+	0.908205i	$0.637453\pi$
$464$	−1.49533	−0.0694190
$465$	−14.7358	−0.683358
$466$	−1.94956	−0.0903115
$467$	30.4290	1.40808	0.704042	−	0.710158i	$-0.251377\pi$
$467$	30.4290	1.40808	0.704042	+	0.710158i	$0.251377\pi$
$468$	−3.18385	−0.147173
$469$	21.1137	0.974942
$470$	−32.5770	−1.50266
$471$	−10.3208	−0.475557
$472$	−14.0706	−0.647652
$473$	42.4882	1.95361
$474$	−4.89987	−0.225058
$475$	−60.2154	−2.76287
$476$	10.3776	0.475656
$477$	21.4668	0.982898
$478$	−10.9553	−0.501085
$479$	−1.92352	−0.0878877	−0.0439439	−	0.999034i	$-0.513992\pi$
$479$	−1.92352	−0.0878877	−0.0439439	+	0.999034i	$0.513992\pi$
$480$	−3.21326	−0.146664
$481$	6.83765	0.311770
$482$	−1.54121	−0.0702004
$483$	9.96105	0.453243
$484$	27.8225	1.26466
$485$	−39.7516	−1.80503
$486$	−15.7093	−0.712589
$487$	−30.4571	−1.38014	−0.690071	−	0.723741i	$-0.742421\pi$
$487$	−30.4571	−1.38014	−0.690071	+	0.723741i	$0.742421\pi$
$488$	9.97061	0.451348
$489$	12.7335	0.575829
$490$	−15.0935	−0.681856
$491$	−22.8613	−1.03172	−0.515859	−	0.856674i	$-0.672527\pi$
$491$	−22.8613	−1.03172	−0.515859	+	0.856674i	$0.672527\pi$
$492$	4.56706	0.205899
$493$	8.54526	0.384859
$494$	−6.93542	−0.312039
$495$	60.4257	2.71593
$496$	4.58595	0.205915
$497$	11.5915	0.519949
$498$	−0.959240	−0.0429846
$499$	−11.3889	−0.509835	−0.254918	−	0.966963i	$-0.582048\pi$
$499$	−11.3889	−0.509835	−0.254918	+	0.966963i	$0.582048\pi$
$500$	26.9916	1.20710
$501$	10.1778	0.454711
$502$	3.12749	0.139587
$503$	16.7443	0.746590	0.373295	−	0.927713i	$-0.378228\pi$
$503$	16.7443	0.746590	0.373295	+	0.927713i	$0.378228\pi$
$504$	4.31980	0.192419
$505$	−7.19653	−0.320242
$506$	−43.3628	−1.92771
$507$	8.83430	0.392345
$508$	16.3051	0.723422
$509$	−32.9647	−1.46113	−0.730566	−	0.682842i	$-0.760744\pi$
$509$	−32.9647	−1.46113	−0.730566	+	0.682842i	$0.760744\pi$
$510$	18.3626	0.813108
$511$	0.584528	0.0258580
$512$	1.00000	0.0441942
$513$	−21.9675	−0.969890
$514$	−9.22651	−0.406964
$515$	−41.0287	−1.80794
$516$	5.37461	0.236604
$517$	49.7884	2.18969
$518$	−9.27723	−0.407618
$519$	4.18991	0.183917
$520$	5.45659	0.239287
$521$	33.1029	1.45026	0.725132	−	0.688610i	$-0.241779\pi$
$521$	33.1029	1.45026	0.725132	+	0.688610i	$0.241779\pi$
$522$	3.55707	0.155689
$523$	0.898388	0.0392838	0.0196419	−	0.999807i	$-0.493747\pi$
$523$	0.898388	0.0392838	0.0196419	+	0.999807i	$0.493747\pi$
$524$	−8.44363	−0.368862
$525$	16.6327	0.725909
$526$	−16.2807	−0.709874
$527$	−26.2070	−1.14160
$528$	4.91092	0.213720
$529$	25.4340	1.10583
$530$	−36.7906	−1.59808
$531$	33.4710	1.45252
$532$	9.40989	0.407971
$533$	−7.75556	−0.335931
$534$	7.22254	0.312550
$535$	12.2205	0.528339
$536$	−11.6267	−0.502197
$537$	−8.51020	−0.367242
$538$	24.7813	1.06840
$539$	23.0679	0.993604
$540$	17.2834	0.743760
$541$	−22.8848	−0.983896	−0.491948	−	0.870624i	$-0.663715\pi$
$541$	−22.8848	−0.983896	−0.491948	+	0.870624i	$0.663715\pi$
$542$	28.1830	1.21056
$543$	0.528842	0.0226948
$544$	−5.71463	−0.245013
$545$	78.7210	3.37204
$546$	1.91570	0.0819843
$547$	−37.3475	−1.59687	−0.798433	−	0.602084i	$-0.794337\pi$
$547$	−37.3475	−1.59687	−0.798433	+	0.602084i	$0.794337\pi$
$548$	7.41048	0.316560
$549$	−23.7179	−1.01226
$550$	−72.4058	−3.08740
$551$	7.74842	0.330094
$552$	−5.48525	−0.233468
$553$	−11.2894	−0.480076
$554$	32.0978	1.36370
$555$	−16.4155	−0.696801
$556$	0.993897	0.0421506
$557$	−37.2569	−1.57862	−0.789312	−	0.613992i	$-0.789563\pi$
$557$	−37.2569	−1.57862	−0.789312	+	0.613992i	$0.789563\pi$
$558$	−10.9090	−0.461814
$559$	−9.12690	−0.386027
$560$	−7.40344	−0.312852
$561$	−28.0641	−1.18487
$562$	7.24178	0.305476
$563$	−1.62586	−0.0685219	−0.0342609	−	0.999413i	$-0.510908\pi$
$563$	−1.62586	−0.0685219	−0.0342609	+	0.999413i	$0.510908\pi$
$564$	6.29807	0.265197
$565$	−77.8477	−3.27508
$566$	−17.8642	−0.750887
$567$	−6.89156	−0.289418
$568$	−6.38308	−0.267828
$569$	−16.5906	−0.695514	−0.347757	−	0.937585i	$-0.613057\pi$
$569$	−16.5906	−0.695514	−0.347757	+	0.937585i	$0.613057\pi$
$570$	16.6503	0.697403
$571$	24.5876	1.02896	0.514480	−	0.857503i	$-0.327985\pi$
$571$	24.5876	1.02896	0.514480	+	0.857503i	$0.327985\pi$
$572$	−8.33948	−0.348691
$573$	−19.3404	−0.807957
$574$	10.5226	0.439207
$575$	80.8737	3.37267
$576$	−2.37879	−0.0991160
$577$	−16.8592	−0.701859	−0.350930	−	0.936402i	$-0.614134\pi$
$577$	−16.8592	−0.701859	−0.350930	+	0.936402i	$0.614134\pi$
$578$	15.6570	0.651245
$579$	−14.9581	−0.621636
$580$	−6.09624	−0.253133
$581$	−2.21012	−0.0916911
$582$	7.68513	0.318559
$583$	56.2282	2.32873
$584$	−0.321882	−0.0133196
$585$	−12.9801	−0.536660
$586$	−11.0885	−0.458062
$587$	38.4435	1.58673	0.793366	−	0.608746i	$-0.208327\pi$
$587$	38.4435	1.58673	0.793366	+	0.608746i	$0.208327\pi$
$588$	2.91801	0.120337
$589$	−23.7632	−0.979146
$590$	−57.3638	−2.36163
$591$	−8.32799	−0.342568
$592$	5.10869	0.209966
$593$	3.38696	0.139086	0.0695428	−	0.997579i	$-0.477846\pi$
$593$	3.38696	0.139086	0.0695428	+	0.997579i	$0.477846\pi$
$594$	−26.4148	−1.08381
$595$	42.3079	1.73445
$596$	−13.7049	−0.561373
$597$	17.5434	0.718003
$598$	9.31478	0.380910
$599$	−22.2986	−0.911098	−0.455549	−	0.890211i	$-0.650557\pi$
$599$	−22.2986	−0.911098	−0.455549	+	0.890211i	$0.650557\pi$
$600$	−9.15910	−0.373919
$601$	14.0028	0.571186	0.285593	−	0.958351i	$-0.407809\pi$
$601$	14.0028	0.571186	0.285593	+	0.958351i	$0.407809\pi$
$602$	12.3833	0.504704
$603$	27.6574	1.12630
$604$	−5.75158	−0.234028
$605$	113.428	4.61150
$606$	1.39130	0.0565176
$607$	−25.3231	−1.02783	−0.513916	−	0.857841i	$-0.671806\pi$
$607$	−25.3231	−1.02783	−0.513916	+	0.857841i	$0.671806\pi$
$608$	−5.18174	−0.210147
$609$	−2.14026	−0.0867278
$610$	40.6487	1.64582
$611$	−10.6951	−0.432676
$612$	13.5939	0.549500
$613$	−6.57459	−0.265545	−0.132773	−	0.991147i	$-0.542388\pi$
$613$	−6.57459	−0.265545	−0.132773	+	0.991147i	$0.542388\pi$
$614$	2.81666	0.113671
$615$	18.6192	0.750800
$616$	11.3149	0.455890
$617$	36.8517	1.48359	0.741797	−	0.670625i	$-0.233974\pi$
$617$	36.8517	1.48359	0.741797	+	0.670625i	$0.233974\pi$
$618$	7.93202	0.319073
$619$	−38.7966	−1.55937	−0.779684	−	0.626173i	$-0.784620\pi$
$619$	−38.7966	−1.55937	−0.779684	+	0.626173i	$0.784620\pi$
$620$	18.6962	0.750858
$621$	29.5040	1.18395
$622$	33.1801	1.33040
$623$	16.6409	0.666705
$624$	−1.05492	−0.0422305
$625$	51.9370	2.07748
$626$	30.9266	1.23608
$627$	−25.4471	−1.01626
$628$	13.0946	0.522532
$629$	−29.1943	−1.16405
$630$	17.6112	0.701646
$631$	−24.4120	−0.971826	−0.485913	−	0.874007i	$-0.661513\pi$
$631$	−24.4120	−0.971826	−0.485913	+	0.874007i	$0.661513\pi$
$632$	6.21675	0.247289
$633$	−3.71808	−0.147780
$634$	1.78697	0.0709696
$635$	66.4735	2.63792
$636$	7.11268	0.282036
$637$	−4.95522	−0.196333
$638$	9.31706	0.368866
$639$	15.1840	0.600669
$640$	4.07685	0.161152
$641$	−22.1379	−0.874396	−0.437198	−	0.899365i	$-0.644029\pi$
$641$	−22.1379	−0.874396	−0.437198	+	0.899365i	$0.644029\pi$
$642$	−2.36258	−0.0932434
$643$	6.15755	0.242830	0.121415	−	0.992602i	$-0.461257\pi$
$643$	6.15755	0.242830	0.121415	+	0.992602i	$0.461257\pi$
$644$	−12.6382	−0.498014
$645$	21.9115	0.862764
$646$	29.6117	1.16506
$647$	−27.5044	−1.08131	−0.540656	−	0.841244i	$-0.681824\pi$
$647$	−27.5044	−1.08131	−0.540656	+	0.841244i	$0.681824\pi$
$648$	3.79497	0.149081
$649$	87.6707	3.44138
$650$	15.5535	0.610060
$651$	6.56386	0.257258
$652$	−16.1558	−0.632708
$653$	−29.5382	−1.15592	−0.577960	−	0.816065i	$-0.696151\pi$
$653$	−29.5382	−1.15592	−0.577960	+	0.816065i	$0.696151\pi$
$654$	−15.2190	−0.595111
$655$	−34.4234	−1.34503
$656$	−5.79450	−0.226237
$657$	0.765688	0.0298723
$658$	14.5109	0.565695
$659$	−10.8411	−0.422310	−0.211155	−	0.977453i	$-0.567722\pi$
$659$	−10.8411	−0.422310	−0.211155	+	0.977453i	$0.567722\pi$
$660$	20.0211	0.779319
$661$	−46.3517	−1.80287	−0.901436	−	0.432912i	$-0.857486\pi$
$661$	−46.3517	−1.80287	−0.901436	+	0.432912i	$0.857486\pi$
$662$	−29.3984	−1.14260
$663$	6.02846	0.234126
$664$	1.21704	0.0472305
$665$	38.3627	1.48764
$666$	−12.1525	−0.470899
$667$	−10.4067	−0.402949
$668$	−12.9132	−0.499626
$669$	20.7884	0.803725
$670$	−47.4003	−1.83123
$671$	−62.1246	−2.39829
$672$	1.43130	0.0552135
$673$	−43.6051	−1.68085	−0.840426	−	0.541927i	$-0.817695\pi$
$673$	−43.6051	−1.68085	−0.840426	+	0.541927i	$0.817695\pi$
$674$	30.9502	1.19216
$675$	49.2648	1.89620
$676$	−11.2086	−0.431100
$677$	39.0977	1.50265	0.751323	−	0.659934i	$-0.229416\pi$
$677$	39.0977	1.50265	0.751323	+	0.659934i	$0.229416\pi$
$678$	15.0502	0.577999
$679$	17.7068	0.679523
$680$	−23.2977	−0.893425
$681$	−4.21313	−0.161447
$682$	−28.5740	−1.09415
$683$	47.1680	1.80483	0.902416	−	0.430866i	$-0.141792\pi$
$683$	47.1680	1.80483	0.902416	+	0.430866i	$0.141792\pi$
$684$	12.3263	0.471306
$685$	30.2114	1.15432
$686$	19.4350	0.742031
$687$	−20.2512	−0.772631
$688$	−6.81909	−0.259975
$689$	−12.0784	−0.460150
$690$	−22.3625	−0.851327
$691$	−17.8797	−0.680176	−0.340088	−	0.940394i	$-0.610457\pi$
$691$	−17.8797	−0.680176	−0.340088	+	0.940394i	$0.610457\pi$
$692$	−5.31599	−0.202084
$693$	−26.9157	−1.02244
$694$	6.54590	0.248479
$695$	4.05197	0.153700
$696$	1.17858	0.0446739
$697$	33.1134	1.25426
$698$	11.9959	0.454053
$699$	1.53659	0.0581190
$700$	−21.1028	−0.797612
$701$	6.22104	0.234965	0.117483	−	0.993075i	$-0.462518\pi$
$701$	6.22104	0.234965	0.117483	+	0.993075i	$0.462518\pi$
$702$	5.67417	0.214158
$703$	−26.4719	−0.998408
$704$	−6.23077	−0.234831
$705$	25.6763	0.967024
$706$	2.38482	0.0897538
$707$	3.20559	0.120559
$708$	11.0901	0.416790
$709$	10.8033	0.405727	0.202863	−	0.979207i	$-0.434975\pi$
$709$	10.8033	0.405727	0.202863	+	0.979207i	$0.434975\pi$
$710$	−26.0229	−0.976620
$711$	−14.7883	−0.554605
$712$	−9.16366	−0.343423
$713$	31.9157	1.19525
$714$	−8.17933	−0.306104
$715$	−33.9988	−1.27148
$716$	10.7974	0.403518
$717$	8.63468	0.322468
$718$	1.88328	0.0702833
$719$	−30.8080	−1.14894	−0.574472	−	0.818524i	$-0.694793\pi$
$719$	−30.8080	−1.14894	−0.574472	+	0.818524i	$0.694793\pi$
$720$	−9.69795	−0.361421
$721$	18.2756	0.680619
$722$	7.85047	0.292164
$723$	1.21474	0.0451768
$724$	−0.670973	−0.0249365
$725$	−17.3768	−0.645357
$726$	−21.9289	−0.813858
$727$	−22.8793	−0.848546	−0.424273	−	0.905534i	$-0.639470\pi$
$727$	−22.8793	−0.848546	−0.424273	+	0.905534i	$0.639470\pi$
$728$	−2.43056	−0.0900825
$729$	0.996718	0.0369155
$730$	−1.31226	−0.0485690
$731$	38.9686	1.44130
$732$	−7.85856	−0.290461
$733$	−26.6669	−0.984966	−0.492483	−	0.870322i	$-0.663911\pi$
$733$	−26.6669	−0.984966	−0.492483	+	0.870322i	$0.663911\pi$
$734$	20.8924	0.771153
$735$	11.8963	0.438801
$736$	6.95946	0.256529
$737$	72.4433	2.66848
$738$	13.7839	0.507391
$739$	30.1750	1.11000	0.555002	−	0.831849i	$-0.312717\pi$
$739$	30.1750	1.11000	0.555002	+	0.831849i	$0.312717\pi$
$740$	20.8274	0.765629
$741$	5.46631	0.200810
$742$	16.3878	0.601616
$743$	28.3064	1.03846	0.519231	−	0.854634i	$-0.326219\pi$
$743$	28.3064	1.03846	0.519231	+	0.854634i	$0.326219\pi$
$744$	−3.61452	−0.132515
$745$	−55.8727	−2.04702
$746$	0.401095	0.0146851
$747$	−2.89509	−0.105926
$748$	35.6065	1.30190
$749$	−5.44344	−0.198899
$750$	−21.2740	−0.776816
$751$	22.0996	0.806425	0.403212	−	0.915106i	$-0.367894\pi$
$751$	22.0996	0.806425	0.403212	+	0.915106i	$0.367894\pi$
$752$	−7.99073	−0.291392
$753$	−2.46500	−0.0898297
$754$	−2.00140	−0.0728868
$755$	−23.4483	−0.853371
$756$	−7.69864	−0.279997
$757$	2.81183	0.102198	0.0510988	−	0.998694i	$-0.483728\pi$
$757$	2.81183	0.102198	0.0510988	+	0.998694i	$0.483728\pi$
$758$	6.59853	0.239669
$759$	34.1773	1.24056
$760$	−21.1252	−0.766291
$761$	−44.3960	−1.60935	−0.804677	−	0.593712i	$-0.797662\pi$
$761$	−44.3960	−1.60935	−0.804677	+	0.593712i	$0.797662\pi$
$762$	−12.8512	−0.465551
$763$	−35.0651	−1.26944
$764$	24.5383	0.887765
$765$	55.4202	2.00372
$766$	20.3378	0.734835
$767$	−18.8326	−0.680006
$768$	−0.788172	−0.0284407
$769$	−4.73252	−0.170659	−0.0853296	−	0.996353i	$-0.527194\pi$
$769$	−4.73252	−0.170659	−0.0853296	+	0.996353i	$0.527194\pi$
$770$	46.1291	1.66238
$771$	7.27208	0.261898
$772$	18.9782	0.683040
$773$	−2.92371	−0.105159	−0.0525793	−	0.998617i	$-0.516744\pi$
$773$	−2.92371	−0.105159	−0.0525793	+	0.998617i	$0.516744\pi$
$774$	16.2211	0.583057
$775$	53.2919	1.91430
$776$	−9.75058	−0.350026
$777$	7.31206	0.262319
$778$	−34.1005	−1.22256
$779$	30.0256	1.07578
$780$	−4.30073	−0.153991
$781$	39.7715	1.42314
$782$	−39.7707	−1.42220
$783$	−6.33932	−0.226549
$784$	−3.70225	−0.132223
$785$	53.3847	1.90538
$786$	6.65503	0.237377
$787$	26.5263	0.945562	0.472781	−	0.881180i	$-0.343250\pi$
$787$	26.5263	0.945562	0.472781	+	0.881180i	$0.343250\pi$
$788$	10.5662	0.376406
$789$	12.8320	0.456832
$790$	25.3448	0.901726
$791$	34.6761	1.23294
$792$	14.8217	0.526665
$793$	13.3450	0.473895
$794$	−17.4242	−0.618362
$795$	28.9973	1.02843
$796$	−22.2583	−0.788926
$797$	−11.6562	−0.412884	−0.206442	−	0.978459i	$-0.566188\pi$
$797$	−11.6562	−0.412884	−0.206442	+	0.978459i	$0.566188\pi$
$798$	−7.41661	−0.262545
$799$	45.6641	1.61548
$800$	11.6207	0.410853
$801$	21.7984	0.770208
$802$	−14.9273	−0.527101
$803$	2.00557	0.0707751
$804$	9.16384	0.323184
$805$	−51.5239	−1.81598
$806$	6.13799	0.216202
$807$	−19.5319	−0.687557
$808$	−1.76522	−0.0621002
$809$	20.1954	0.710031	0.355016	−	0.934860i	$-0.384476\pi$
$809$	20.1954	0.710031	0.355016	+	0.934860i	$0.384476\pi$
$810$	15.4715	0.543614
$811$	17.3030	0.607590	0.303795	−	0.952737i	$-0.401746\pi$
$811$	17.3030	0.607590	0.303795	+	0.952737i	$0.401746\pi$
$812$	2.71548	0.0952946
$813$	−22.2131	−0.779046
$814$	−31.8311	−1.11568
$815$	−65.8646	−2.30713
$816$	4.50411	0.157675
$817$	35.3348	1.23621
$818$	18.3666	0.642171
$819$	5.78177	0.202032
$820$	−23.6233	−0.824962
$821$	19.6170	0.684638	0.342319	−	0.939584i	$-0.388788\pi$
$821$	19.6170	0.684638	0.342319	+	0.939584i	$0.388788\pi$
$822$	−5.84073	−0.203719
$823$	−13.2062	−0.460340	−0.230170	−	0.973150i	$-0.573928\pi$
$823$	−13.2062	−0.460340	−0.230170	+	0.973150i	$0.573928\pi$
$824$	−10.0638	−0.350590
$825$	57.0682	1.98686
$826$	25.5518	0.889061
$827$	−31.3910	−1.09157	−0.545786	−	0.837924i	$-0.683769\pi$
$827$	−31.3910	−1.09157	−0.545786	+	0.837924i	$0.683769\pi$
$828$	−16.5551	−0.575328
$829$	−12.7409	−0.442510	−0.221255	−	0.975216i	$-0.571015\pi$
$829$	−12.7409	−0.442510	−0.221255	+	0.975216i	$0.571015\pi$
$830$	4.96170	0.172223
$831$	−25.2986	−0.877598
$832$	1.33843	0.0464019
$833$	21.1570	0.733046
$834$	−0.783362	−0.0271256
$835$	−52.6450	−1.82186
$836$	32.2862	1.11664
$837$	19.4417	0.672004
$838$	−10.2547	−0.354243
$839$	11.4013	0.393617	0.196808	−	0.980442i	$-0.436942\pi$
$839$	11.4013	0.393617	0.196808	+	0.980442i	$0.436942\pi$
$840$	5.83518	0.201333
$841$	−26.7640	−0.922896
$842$	1.56690	0.0539990
$843$	−5.70777	−0.196586
$844$	4.71735	0.162378
$845$	−45.6957	−1.57198
$846$	19.0082	0.653516
$847$	−50.5248	−1.73605
$848$	−9.02427	−0.309895
$849$	14.0800	0.483225
$850$	−66.4079	−2.27777
$851$	35.5537	1.21877
$852$	5.03097	0.172358
$853$	−16.2253	−0.555543	−0.277772	−	0.960647i	$-0.589596\pi$
$853$	−16.2253	−0.555543	−0.277772	+	0.960647i	$0.589596\pi$
$854$	−18.1063	−0.619586
$855$	50.2523	1.71859
$856$	2.99754	0.102454
$857$	−34.2451	−1.16979	−0.584895	−	0.811109i	$-0.698864\pi$
$857$	−34.2451	−1.16979	−0.584895	+	0.811109i	$0.698864\pi$
$858$	6.57294	0.224396
$859$	−29.4010	−1.00315	−0.501574	−	0.865115i	$-0.667246\pi$
$859$	−29.4010	−1.00315	−0.501574	+	0.865115i	$0.667246\pi$
$860$	−27.8004	−0.947985
$861$	−8.29365	−0.282647
$862$	2.59148	0.0882663
$863$	−39.7245	−1.35224	−0.676120	−	0.736792i	$-0.736340\pi$
$863$	−39.7245	−1.35224	−0.676120	+	0.736792i	$0.736340\pi$
$864$	4.23941	0.144228
$865$	−21.6725	−0.736887
$866$	−33.1373	−1.12605
$867$	−12.3404	−0.419102
$868$	−8.32795	−0.282669
$869$	−38.7351	−1.31400
$870$	4.80488	0.162901
$871$	−15.5616	−0.527284
$872$	19.3093	0.653895
$873$	23.1945	0.785016
$874$	−36.0621	−1.21982
$875$	−49.0159	−1.65704
$876$	0.253698	0.00857167
$877$	3.77609	0.127509	0.0637547	−	0.997966i	$-0.479692\pi$
$877$	3.77609	0.127509	0.0637547	+	0.997966i	$0.479692\pi$
$878$	28.4868	0.961382
$879$	8.73965	0.294781
$880$	−25.4019	−0.856298
$881$	10.9162	0.367776	0.183888	−	0.982947i	$-0.441132\pi$
$881$	10.9162	0.367776	0.183888	+	0.982947i	$0.441132\pi$
$882$	8.80686	0.296542
$883$	−31.7147	−1.06728	−0.533642	−	0.845711i	$-0.679177\pi$
$883$	−31.7147	−1.06728	−0.533642	+	0.845711i	$0.679177\pi$
$884$	−7.64866	−0.257252
$885$	45.2125	1.51980
$886$	24.3962	0.819607
$887$	46.8524	1.57315	0.786576	−	0.617494i	$-0.211852\pi$
$887$	46.8524	1.57315	0.786576	+	0.617494i	$0.211852\pi$
$888$	−4.02653	−0.135121
$889$	−29.6096	−0.993074
$890$	−37.3589	−1.25227
$891$	−23.6456	−0.792157
$892$	−26.3754	−0.883115
$893$	41.4059	1.38560
$894$	10.8018	0.361266
$895$	44.0193	1.47140
$896$	−1.81597	−0.0606673
$897$	−7.34165	−0.245130
$898$	22.4502	0.749173
$899$	−6.85752	−0.228711
$900$	−27.6431	−0.921438
$901$	51.5704	1.71806
$902$	36.1042	1.20214
$903$	−9.76014	−0.324797
$904$	−19.0951	−0.635092
$905$	−2.73546	−0.0909296
$906$	4.53323	0.150607
$907$	3.65512	0.121366	0.0606831	−	0.998157i	$-0.480672\pi$
$907$	3.65512	0.121366	0.0606831	+	0.998157i	$0.480672\pi$
$908$	5.34544	0.177395
$909$	4.19908	0.139275
$910$	−9.90901	−0.328481
$911$	16.4954	0.546517	0.273258	−	0.961941i	$-0.411899\pi$
$911$	16.4954	0.546517	0.273258	+	0.961941i	$0.411899\pi$
$912$	4.08410	0.135238
$913$	−7.58312	−0.250965
$914$	−15.1440	−0.500920
$915$	−32.0381	−1.05915
$916$	25.6939	0.848949
$917$	15.3334	0.506353
$918$	−24.2266	−0.799598
$919$	42.2716	1.39441	0.697206	−	0.716871i	$-0.254426\pi$
$919$	42.2716	1.39441	0.697206	+	0.716871i	$0.254426\pi$
$920$	28.3727	0.935419
$921$	−2.22001	−0.0731519
$922$	12.8340	0.422665
$923$	−8.54334	−0.281207
$924$	−8.91808	−0.293383
$925$	59.3665	1.95196
$926$	−18.0112	−0.591884
$927$	23.9397	0.786282
$928$	−1.49533	−0.0490867
$929$	−0.445280	−0.0146091	−0.00730457	−	0.999973i	$-0.502325\pi$
$929$	−0.445280	−0.0146091	−0.00730457	+	0.999973i	$0.502325\pi$
$930$	−14.7358	−0.483207
$931$	19.1841	0.628734
$932$	−1.94956	−0.0638599
$933$	−26.1516	−0.856166
$934$	30.4290	0.995666
$935$	145.162	4.74732
$936$	−3.18385	−0.104067
$937$	1.05475	0.0344573	0.0172287	−	0.999852i	$-0.494516\pi$
$937$	1.05475	0.0344573	0.0172287	+	0.999852i	$0.494516\pi$
$938$	21.1137	0.689388
$939$	−24.3755	−0.795464
$940$	−32.5770	−1.06254
$941$	−50.0583	−1.63185	−0.815927	−	0.578156i	$-0.803773\pi$
$941$	−50.0583	−1.63185	−0.815927	+	0.578156i	$0.803773\pi$
$942$	−10.3208	−0.336270
$943$	−40.3266	−1.31321
$944$	−14.0706	−0.457959
$945$	−31.3862	−1.02099
$946$	42.4882	1.38141
$947$	18.1864	0.590979	0.295489	−	0.955346i	$-0.404517\pi$
$947$	18.1864	0.590979	0.295489	+	0.955346i	$0.404517\pi$
$948$	−4.89987	−0.159140
$949$	−0.430818	−0.0139849
$950$	−60.2154	−1.95365
$951$	−1.40844	−0.0456717
$952$	10.3776	0.336340
$953$	20.9352	0.678157	0.339079	−	0.940758i	$-0.389885\pi$
$953$	20.9352	0.678157	0.339079	+	0.940758i	$0.389885\pi$
$954$	21.4668	0.695014
$955$	100.039	3.23718
$956$	−10.9553	−0.354321
$957$	−7.34345	−0.237380
$958$	−1.92352	−0.0621460
$959$	−13.4572	−0.434556
$960$	−3.21326	−0.103707
$961$	−9.96906	−0.321582
$962$	6.83765	0.220455
$963$	−7.13050	−0.229777
$964$	−1.54121	−0.0496392
$965$	77.3712	2.49067
$966$	9.96105	0.320492
$967$	47.0521	1.51309	0.756547	−	0.653939i	$-0.226885\pi$
$967$	47.0521	1.51309	0.756547	+	0.653939i	$0.226885\pi$
$968$	27.8225	0.894248
$969$	−23.3391	−0.749761
$970$	−39.7516	−1.27635
$971$	51.9881	1.66838	0.834188	−	0.551480i	$-0.185937\pi$
$971$	51.9881	1.66838	0.834188	+	0.551480i	$0.185937\pi$
$972$	−15.7093	−0.503876
$973$	−1.80489	−0.0578620
$974$	−30.4571	−0.975908
$975$	−12.2589	−0.392598
$976$	9.97061	0.319151
$977$	−49.1871	−1.57364	−0.786818	−	0.617185i	$-0.788273\pi$
$977$	−49.1871	−1.57364	−0.786818	+	0.617185i	$0.788273\pi$
$978$	12.7335	0.407173
$979$	57.0967	1.82482
$980$	−15.0935	−0.482145
$981$	−45.9326	−1.46652
$982$	−22.8613	−0.729534
$983$	32.1518	1.02548	0.512741	−	0.858543i	$-0.328630\pi$
$983$	32.1518	1.02548	0.512741	+	0.858543i	$0.328630\pi$
$984$	4.56706	0.145593
$985$	43.0768	1.37254
$986$	8.54526	0.272137
$987$	−11.4371	−0.364047
$988$	−6.93542	−0.220645
$989$	−47.4572	−1.50905
$990$	60.4257	1.92045
$991$	8.91246	0.283114	0.141557	−	0.989930i	$-0.454789\pi$
$991$	8.91246	0.283114	0.141557	+	0.989930i	$0.454789\pi$
$992$	4.58595	0.145604
$993$	23.1710	0.735309
$994$	11.5915	0.367660
$995$	−90.7439	−2.87677
$996$	−0.959240	−0.0303947
$997$	57.5947	1.82404	0.912022	−	0.410141i	$-0.134521\pi$
$997$	57.5947	1.82404	0.912022	+	0.410141i	$0.134521\pi$
$998$	−11.3889	−0.360508
$999$	21.6578	0.685223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.f.1.14	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.f.1.14	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.788172 q^{3} +1.00000 q^{4} +4.07685 q^{5} -0.788172 q^{6} -1.81597 q^{7} +1.00000 q^{8} -2.37879 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.788172 q^{3} +1.00000 q^{4} +4.07685 q^{5} -0.788172 q^{6} -1.81597 q^{7} +1.00000 q^{8} -2.37879 q^{9} +4.07685 q^{10} -6.23077 q^{11} -0.788172 q^{12} +1.33843 q^{13} -1.81597 q^{14} -3.21326 q^{15} +1.00000 q^{16} -5.71463 q^{17} -2.37879 q^{18} -5.18174 q^{19} +4.07685 q^{20} +1.43130 q^{21} -6.23077 q^{22} +6.95946 q^{23} -0.788172 q^{24} +11.6207 q^{25} +1.33843 q^{26} +4.23941 q^{27} -1.81597 q^{28} -1.49533 q^{29} -3.21326 q^{30} +4.58595 q^{31} +1.00000 q^{32} +4.91092 q^{33} -5.71463 q^{34} -7.40344 q^{35} -2.37879 q^{36} +5.10869 q^{37} -5.18174 q^{38} -1.05492 q^{39} +4.07685 q^{40} -5.79450 q^{41} +1.43130 q^{42} -6.81909 q^{43} -6.23077 q^{44} -9.69795 q^{45} +6.95946 q^{46} -7.99073 q^{47} -0.788172 q^{48} -3.70225 q^{49} +11.6207 q^{50} +4.50411 q^{51} +1.33843 q^{52} -9.02427 q^{53} +4.23941 q^{54} -25.4019 q^{55} -1.81597 q^{56} +4.08410 q^{57} -1.49533 q^{58} -14.0706 q^{59} -3.21326 q^{60} +9.97061 q^{61} +4.58595 q^{62} +4.31980 q^{63} +1.00000 q^{64} +5.45659 q^{65} +4.91092 q^{66} -11.6267 q^{67} -5.71463 q^{68} -5.48525 q^{69} -7.40344 q^{70} -6.38308 q^{71} -2.37879 q^{72} -0.321882 q^{73} +5.10869 q^{74} -9.15910 q^{75} -5.18174 q^{76} +11.3149 q^{77} -1.05492 q^{78} +6.21675 q^{79} +4.07685 q^{80} +3.79497 q^{81} -5.79450 q^{82} +1.21704 q^{83} +1.43130 q^{84} -23.2977 q^{85} -6.81909 q^{86} +1.17858 q^{87} -6.23077 q^{88} -9.16366 q^{89} -9.69795 q^{90} -2.43056 q^{91} +6.95946 q^{92} -3.61452 q^{93} -7.99073 q^{94} -21.1252 q^{95} -0.788172 q^{96} -9.75058 q^{97} -3.70225 q^{98} +14.8217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9	\( 31 q + 31 q^{2} - 13 q^{3} + 31 q^{4} - 23 q^{5} - 13 q^{6} - 18 q^{7} + 31 q^{8} + 20 q^{9} - 23 q^{10} - 32 q^{11} - 13 q^{12} - 8 q^{13} - 18 q^{14} - 14 q^{15} + 31 q^{16} - 30 q^{17} + 20 q^{18} - 38 q^{19} - 23 q^{20} - 16 q^{21} - 32 q^{22} - 24 q^{23} - 13 q^{24} + 40 q^{25} - 8 q^{26} - 28 q^{27} - 18 q^{28} - 7 q^{29} - 14 q^{30} - 32 q^{31} + 31 q^{32} - 9 q^{33} - 30 q^{34} - 14 q^{35} + 20 q^{36} + 11 q^{37} - 38 q^{38} - 9 q^{39} - 23 q^{40} - 76 q^{41} - 16 q^{42} - 33 q^{43} - 32 q^{44} - 40 q^{45} - 24 q^{46} - 96 q^{47} - 13 q^{48} + 15 q^{49} + 40 q^{50} - 55 q^{51} - 8 q^{52} - 28 q^{53} - 28 q^{54} - 52 q^{55} - 18 q^{56} - 21 q^{57} - 7 q^{58} - 72 q^{59} - 14 q^{60} - 9 q^{61} - 32 q^{62} - 54 q^{63} + 31 q^{64} - 38 q^{65} - 9 q^{66} - 4 q^{67} - 30 q^{68} - 17 q^{69} - 14 q^{70} - 61 q^{71} + 20 q^{72} - 62 q^{73} + 11 q^{74} - 63 q^{75} - 38 q^{76} - 9 q^{77} - 9 q^{78} - 30 q^{79} - 23 q^{80} - 13 q^{81} - 76 q^{82} - 90 q^{83} - 16 q^{84} + 26 q^{85} - 33 q^{86} - 34 q^{87} - 32 q^{88} - 99 q^{89} - 40 q^{90} - 47 q^{91} - 24 q^{92} - 6 q^{93} - 96 q^{94} - 24 q^{95} - 13 q^{96} - 46 q^{97} + 15 q^{98} - 48 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 13 * q^3 + 31 * q^4 - 23 * q^5 - 13 * q^6 - 18 * q^7 + 31 * q^8 + 20 * q^9 - 23 * q^10 - 32 * q^11 - 13 * q^12 - 8 * q^13 - 18 * q^14 - 14 * q^15 + 31 * q^16 - 30 * q^17 + 20 * q^18 - 38 * q^19 - 23 * q^20 - 16 * q^21 - 32 * q^22 - 24 * q^23 - 13 * q^24 + 40 * q^25 - 8 * q^26 - 28 * q^27 - 18 * q^28 - 7 * q^29 - 14 * q^30 - 32 * q^31 + 31 * q^32 - 9 * q^33 - 30 * q^34 - 14 * q^35 + 20 * q^36 + 11 * q^37 - 38 * q^38 - 9 * q^39 - 23 * q^40 - 76 * q^41 - 16 * q^42 - 33 * q^43 - 32 * q^44 - 40 * q^45 - 24 * q^46 - 96 * q^47 - 13 * q^48 + 15 * q^49 + 40 * q^50 - 55 * q^51 - 8 * q^52 - 28 * q^53 - 28 * q^54 - 52 * q^55 - 18 * q^56 - 21 * q^57 - 7 * q^58 - 72 * q^59 - 14 * q^60 - 9 * q^61 - 32 * q^62 - 54 * q^63 + 31 * q^64 - 38 * q^65 - 9 * q^66 - 4 * q^67 - 30 * q^68 - 17 * q^69 - 14 * q^70 - 61 * q^71 + 20 * q^72 - 62 * q^73 + 11 * q^74 - 63 * q^75 - 38 * q^76 - 9 * q^77 - 9 * q^78 - 30 * q^79 - 23 * q^80 - 13 * q^81 - 76 * q^82 - 90 * q^83 - 16 * q^84 + 26 * q^85 - 33 * q^86 - 34 * q^87 - 32 * q^88 - 99 * q^89 - 40 * q^90 - 47 * q^91 - 24 * q^92 - 6 * q^93 - 96 * q^94 - 24 * q^95 - 13 * q^96 - 46 * q^97 + 15 * q^98 - 48 * q^99

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