LMFDB - Embedded newform 4022.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.05832 q^{3} +1.00000 q^{4} -2.35340 q^{5} -1.05832 q^{6} -2.98821 q^{7} +1.00000 q^{8} -1.87996 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.05832 q^{3} +1.00000 q^{4} -2.35340 q^{5} -1.05832 q^{6} -2.98821 q^{7} +1.00000 q^{8} -1.87996 q^{9} -2.35340 q^{10} -3.05468 q^{11} -1.05832 q^{12} -7.10305 q^{13} -2.98821 q^{14} +2.49065 q^{15} +1.00000 q^{16} -2.73571 q^{17} -1.87996 q^{18} +0.683005 q^{19} -2.35340 q^{20} +3.16249 q^{21} -3.05468 q^{22} -7.43448 q^{23} -1.05832 q^{24} +0.538484 q^{25} -7.10305 q^{26} +5.16456 q^{27} -2.98821 q^{28} -2.48733 q^{29} +2.49065 q^{30} +8.43120 q^{31} +1.00000 q^{32} +3.23283 q^{33} -2.73571 q^{34} +7.03246 q^{35} -1.87996 q^{36} +4.99697 q^{37} +0.683005 q^{38} +7.51730 q^{39} -2.35340 q^{40} +5.52863 q^{41} +3.16249 q^{42} +9.62075 q^{43} -3.05468 q^{44} +4.42429 q^{45} -7.43448 q^{46} -12.4155 q^{47} -1.05832 q^{48} +1.92942 q^{49} +0.538484 q^{50} +2.89525 q^{51} -7.10305 q^{52} +7.86181 q^{53} +5.16456 q^{54} +7.18887 q^{55} -2.98821 q^{56} -0.722838 q^{57} -2.48733 q^{58} -11.0293 q^{59} +2.49065 q^{60} +5.06842 q^{61} +8.43120 q^{62} +5.61772 q^{63} +1.00000 q^{64} +16.7163 q^{65} +3.23283 q^{66} +4.88627 q^{67} -2.73571 q^{68} +7.86807 q^{69} +7.03246 q^{70} -13.6506 q^{71} -1.87996 q^{72} +5.37173 q^{73} +4.99697 q^{74} -0.569888 q^{75} +0.683005 q^{76} +9.12802 q^{77} +7.51730 q^{78} -10.3728 q^{79} -2.35340 q^{80} +0.174115 q^{81} +5.52863 q^{82} +6.11041 q^{83} +3.16249 q^{84} +6.43821 q^{85} +9.62075 q^{86} +2.63239 q^{87} -3.05468 q^{88} +5.89710 q^{89} +4.42429 q^{90} +21.2254 q^{91} -7.43448 q^{92} -8.92291 q^{93} -12.4155 q^{94} -1.60738 q^{95} -1.05832 q^{96} -6.00360 q^{97} +1.92942 q^{98} +5.74266 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.05832	−0.611022	−0.305511	−	0.952189i	$-0.598827\pi$
$3$	−1.05832	−0.611022	−0.305511	+	0.952189i	$0.598827\pi$
$4$	1.00000	0.500000
$5$	−2.35340	−1.05247	−0.526236	−	0.850339i	$-0.676397\pi$
$5$	−2.35340	−1.05247	−0.526236	+	0.850339i	$0.676397\pi$
$6$	−1.05832	−0.432058
$7$	−2.98821	−1.12944	−0.564719	−	0.825283i	$-0.691016\pi$
$7$	−2.98821	−1.12944	−0.564719	+	0.825283i	$0.691016\pi$
$8$	1.00000	0.353553
$9$	−1.87996	−0.626653
$10$	−2.35340	−0.744210
$11$	−3.05468	−0.921019	−0.460510	−	0.887655i	$-0.652333\pi$
$11$	−3.05468	−0.921019	−0.460510	+	0.887655i	$0.652333\pi$
$12$	−1.05832	−0.305511
$13$	−7.10305	−1.97003	−0.985016	−	0.172466i	$-0.944827\pi$
$13$	−7.10305	−1.97003	−0.985016	+	0.172466i	$0.944827\pi$
$14$	−2.98821	−0.798634
$15$	2.49065	0.643083
$16$	1.00000	0.250000
$17$	−2.73571	−0.663506	−0.331753	−	0.943366i	$-0.607640\pi$
$17$	−2.73571	−0.663506	−0.331753	+	0.943366i	$0.607640\pi$
$18$	−1.87996	−0.443110
$19$	0.683005	0.156692	0.0783460	−	0.996926i	$-0.475036\pi$
$19$	0.683005	0.156692	0.0783460	+	0.996926i	$0.475036\pi$
$20$	−2.35340	−0.526236
$21$	3.16249	0.690111
$22$	−3.05468	−0.651259
$23$	−7.43448	−1.55020	−0.775098	−	0.631840i	$-0.782300\pi$
$23$	−7.43448	−1.55020	−0.775098	+	0.631840i	$0.782300\pi$
$24$	−1.05832	−0.216029
$25$	0.538484	0.107697
$26$	−7.10305	−1.39302
$27$	5.16456	0.993920
$28$	−2.98821	−0.564719
$29$	−2.48733	−0.461885	−0.230943	−	0.972967i	$-0.574181\pi$
$29$	−2.48733	−0.461885	−0.230943	+	0.972967i	$0.574181\pi$
$30$	2.49065	0.454728
$31$	8.43120	1.51429	0.757144	−	0.653248i	$-0.226594\pi$
$31$	8.43120	1.51429	0.757144	+	0.653248i	$0.226594\pi$
$32$	1.00000	0.176777
$33$	3.23283	0.562763
$34$	−2.73571	−0.469170
$35$	7.03246	1.18870
$36$	−1.87996	−0.313326
$37$	4.99697	0.821496	0.410748	−	0.911749i	$-0.365268\pi$
$37$	4.99697	0.821496	0.410748	+	0.911749i	$0.365268\pi$
$38$	0.683005	0.110798
$39$	7.51730	1.20373
$40$	−2.35340	−0.372105
$41$	5.52863	0.863428	0.431714	−	0.902011i	$-0.357909\pi$
$41$	5.52863	0.863428	0.431714	+	0.902011i	$0.357909\pi$
$42$	3.16249	0.487982
$43$	9.62075	1.46715	0.733575	−	0.679608i	$-0.237850\pi$
$43$	9.62075	1.46715	0.733575	+	0.679608i	$0.237850\pi$
$44$	−3.05468	−0.460510
$45$	4.42429	0.659534
$46$	−7.43448	−1.09615
$47$	−12.4155	−1.81098	−0.905491	−	0.424365i	$-0.860497\pi$
$47$	−12.4155	−1.81098	−0.905491	+	0.424365i	$0.860497\pi$
$48$	−1.05832	−0.152755
$49$	1.92942	0.275631
$50$	0.538484	0.0761531
$51$	2.89525	0.405417
$52$	−7.10305	−0.985016
$53$	7.86181	1.07990	0.539952	−	0.841696i	$-0.318443\pi$
$53$	7.86181	1.07990	0.539952	+	0.841696i	$0.318443\pi$
$54$	5.16456	0.702807
$55$	7.18887	0.969347
$56$	−2.98821	−0.399317
$57$	−0.722838	−0.0957422
$58$	−2.48733	−0.326602
$59$	−11.0293	−1.43590	−0.717949	−	0.696095i	$-0.754919\pi$
$59$	−11.0293	−1.43590	−0.717949	+	0.696095i	$0.754919\pi$
$60$	2.49065	0.321541
$61$	5.06842	0.648944	0.324472	−	0.945895i	$-0.394813\pi$
$61$	5.06842	0.648944	0.324472	+	0.945895i	$0.394813\pi$
$62$	8.43120	1.07076
$63$	5.61772	0.707766
$64$	1.00000	0.125000
$65$	16.7163	2.07340
$66$	3.23283	0.397933
$67$	4.88627	0.596953	0.298476	−	0.954417i	$-0.403522\pi$
$67$	4.88627	0.596953	0.298476	+	0.954417i	$0.403522\pi$
$68$	−2.73571	−0.331753
$69$	7.86807	0.947204
$70$	7.03246	0.840539
$71$	−13.6506	−1.62003	−0.810016	−	0.586408i	$-0.800542\pi$
$71$	−13.6506	−1.62003	−0.810016	+	0.586408i	$0.800542\pi$
$72$	−1.87996	−0.221555
$73$	5.37173	0.628713	0.314357	−	0.949305i	$-0.398211\pi$
$73$	5.37173	0.628713	0.314357	+	0.949305i	$0.398211\pi$
$74$	4.99697	0.580886
$75$	−0.569888	−0.0658050
$76$	0.683005	0.0783460
$77$	9.12802	1.04023
$78$	7.51730	0.851167
$79$	−10.3728	−1.16703	−0.583517	−	0.812101i	$-0.698324\pi$
$79$	−10.3728	−1.16703	−0.583517	+	0.812101i	$0.698324\pi$
$80$	−2.35340	−0.263118
$81$	0.174115	0.0193461
$82$	5.52863	0.610536
$83$	6.11041	0.670704	0.335352	−	0.942093i	$-0.391145\pi$
$83$	6.11041	0.670704	0.335352	+	0.942093i	$0.391145\pi$
$84$	3.16249	0.345056
$85$	6.43821	0.698322
$86$	9.62075	1.03743
$87$	2.63239	0.282222
$88$	−3.05468	−0.325629
$89$	5.89710	0.625092	0.312546	−	0.949903i	$-0.398818\pi$
$89$	5.89710	0.625092	0.312546	+	0.949903i	$0.398818\pi$
$90$	4.42429	0.466361
$91$	21.2254	2.22503
$92$	−7.43448	−0.775098
$93$	−8.92291	−0.925263
$94$	−12.4155	−1.28056
$95$	−1.60738	−0.164914
$96$	−1.05832	−0.108014
$97$	−6.00360	−0.609573	−0.304787	−	0.952421i	$-0.598585\pi$
$97$	−6.00360	−0.609573	−0.304787	+	0.952421i	$0.598585\pi$
$98$	1.92942	0.194901
$99$	5.74266	0.577159
$100$	0.538484	0.0538484
$101$	−10.1978	−1.01472	−0.507358	−	0.861735i	$-0.669378\pi$
$101$	−10.1978	−1.01472	−0.507358	+	0.861735i	$0.669378\pi$
$102$	2.89525	0.286673
$103$	0.171361	0.0168847	0.00844235	−	0.999964i	$-0.497313\pi$
$103$	0.171361	0.0168847	0.00844235	+	0.999964i	$0.497313\pi$
$104$	−7.10305	−0.696511
$105$	−7.44259	−0.726323
$106$	7.86181	0.763607
$107$	−11.6934	−1.13044	−0.565220	−	0.824940i	$-0.691209\pi$
$107$	−11.6934	−1.13044	−0.565220	+	0.824940i	$0.691209\pi$
$108$	5.16456	0.496960
$109$	−13.8960	−1.33100	−0.665499	−	0.746399i	$-0.731781\pi$
$109$	−13.8960	−1.33100	−0.665499	+	0.746399i	$0.731781\pi$
$110$	7.18887	0.685432
$111$	−5.28839	−0.501952
$112$	−2.98821	−0.282360
$113$	1.21093	0.113915	0.0569574	−	0.998377i	$-0.481860\pi$
$113$	1.21093	0.113915	0.0569574	+	0.998377i	$0.481860\pi$
$114$	−0.722838	−0.0677000
$115$	17.4963	1.63154
$116$	−2.48733	−0.230943
$117$	13.3534	1.23453
$118$	−11.0293	−1.01533
$119$	8.17488	0.749390
$120$	2.49065	0.227364
$121$	−1.66896	−0.151724
$122$	5.06842	0.458873
$123$	−5.85107	−0.527573
$124$	8.43120	0.757144
$125$	10.4997	0.939124
$126$	5.61772	0.500466
$127$	−11.7605	−1.04357	−0.521787	−	0.853076i	$-0.674734\pi$
$127$	−11.7605	−1.04357	−0.521787	+	0.853076i	$0.674734\pi$
$128$	1.00000	0.0883883
$129$	−10.1818	−0.896461
$130$	16.7163	1.46612
$131$	−10.4690	−0.914682	−0.457341	−	0.889292i	$-0.651198\pi$
$131$	−10.4690	−0.914682	−0.457341	+	0.889292i	$0.651198\pi$
$132$	3.23283	0.281381
$133$	−2.04096	−0.176974
$134$	4.88627	0.422109
$135$	−12.1543	−1.04607
$136$	−2.73571	−0.234585
$137$	−1.67501	−0.143106	−0.0715530	−	0.997437i	$-0.522796\pi$
$137$	−1.67501	−0.143106	−0.0715530	+	0.997437i	$0.522796\pi$
$138$	7.86807	0.669774
$139$	−1.53375	−0.130091	−0.0650454	−	0.997882i	$-0.520719\pi$
$139$	−1.53375	−0.130091	−0.0650454	+	0.997882i	$0.520719\pi$
$140$	7.03246	0.594351
$141$	13.1395	1.10655
$142$	−13.6506	−1.14554
$143$	21.6975	1.81444
$144$	−1.87996	−0.156663
$145$	5.85367	0.486121
$146$	5.37173	0.444567
$147$	−2.04194	−0.168417
$148$	4.99697	0.410748
$149$	−13.5430	−1.10948	−0.554742	−	0.832023i	$-0.687183\pi$
$149$	−13.5430	−1.10948	−0.554742	+	0.832023i	$0.687183\pi$
$150$	−0.569888	−0.0465312
$151$	−17.3555	−1.41237	−0.706186	−	0.708027i	$-0.749586\pi$
$151$	−17.3555	−1.41237	−0.706186	+	0.708027i	$0.749586\pi$
$152$	0.683005	0.0553990
$153$	5.14301	0.415788
$154$	9.12802	0.735557
$155$	−19.8420	−1.59375
$156$	7.51730	0.601866
$157$	5.37184	0.428720	0.214360	−	0.976755i	$-0.431233\pi$
$157$	5.37184	0.428720	0.214360	+	0.976755i	$0.431233\pi$
$158$	−10.3728	−0.825218
$159$	−8.32032	−0.659844
$160$	−2.35340	−0.186052
$161$	22.2158	1.75085
$162$	0.174115	0.0136798
$163$	17.3135	1.35610	0.678051	−	0.735015i	$-0.262825\pi$
$163$	17.3135	1.35610	0.678051	+	0.735015i	$0.262825\pi$
$164$	5.52863	0.431714
$165$	−7.60813	−0.592292
$166$	6.11041	0.474259
$167$	19.5081	1.50958	0.754790	−	0.655967i	$-0.227739\pi$
$167$	19.5081	1.50958	0.754790	+	0.655967i	$0.227739\pi$
$168$	3.16249	0.243991
$169$	37.4533	2.88102
$170$	6.43821	0.493788
$171$	−1.28402	−0.0981915
$172$	9.62075	0.733575
$173$	11.4044	0.867064	0.433532	−	0.901138i	$-0.357267\pi$
$173$	11.4044	0.867064	0.433532	+	0.901138i	$0.357267\pi$
$174$	2.63239	0.199561
$175$	−1.60910	−0.121637
$176$	−3.05468	−0.230255
$177$	11.6726	0.877365
$178$	5.89710	0.442007
$179$	21.6724	1.61987	0.809936	−	0.586518i	$-0.199502\pi$
$179$	21.6724	1.61987	0.809936	+	0.586518i	$0.199502\pi$
$180$	4.42429	0.329767
$181$	−21.6901	−1.61221	−0.806107	−	0.591769i	$-0.798430\pi$
$181$	−21.6901	−1.61221	−0.806107	+	0.591769i	$0.798430\pi$
$182$	21.2254	1.57333
$183$	−5.36401	−0.396519
$184$	−7.43448	−0.548077
$185$	−11.7599	−0.864602
$186$	−8.92291	−0.654260
$187$	8.35670	0.611102
$188$	−12.4155	−0.905491
$189$	−15.4328	−1.12257
$190$	−1.60738	−0.116612
$191$	−6.63848	−0.480343	−0.240172	−	0.970730i	$-0.577204\pi$
$191$	−6.63848	−0.480343	−0.240172	+	0.970730i	$0.577204\pi$
$192$	−1.05832	−0.0763777
$193$	−3.80614	−0.273972	−0.136986	−	0.990573i	$-0.543741\pi$
$193$	−3.80614	−0.273972	−0.136986	+	0.990573i	$0.543741\pi$
$194$	−6.00360	−0.431033
$195$	−17.6912	−1.26689
$196$	1.92942	0.137816
$197$	−8.42673	−0.600379	−0.300190	−	0.953880i	$-0.597050\pi$
$197$	−8.42673	−0.600379	−0.300190	+	0.953880i	$0.597050\pi$
$198$	5.74266	0.408113
$199$	25.5719	1.81274	0.906372	−	0.422480i	$-0.138840\pi$
$199$	25.5719	1.81274	0.906372	+	0.422480i	$0.138840\pi$
$200$	0.538484	0.0380766
$201$	−5.17124	−0.364751
$202$	−10.1978	−0.717513
$203$	7.43267	0.521671
$204$	2.89525	0.202708
$205$	−13.0111	−0.908733
$206$	0.171361	0.0119393
$207$	13.9765	0.971435
$208$	−7.10305	−0.492508
$209$	−2.08636	−0.144316
$210$	−7.44259	−0.513588
$211$	−22.1217	−1.52292	−0.761461	−	0.648210i	$-0.775518\pi$
$211$	−22.1217	−1.52292	−0.761461	+	0.648210i	$0.775518\pi$
$212$	7.86181	0.539952
$213$	14.4467	0.989874
$214$	−11.6934	−0.799342
$215$	−22.6415	−1.54413
$216$	5.16456	0.351404
$217$	−25.1942	−1.71030
$218$	−13.8960	−0.941158
$219$	−5.68501	−0.384157
$220$	7.18887	0.484673
$221$	19.4319	1.30713
$222$	−5.28839	−0.354934
$223$	24.1544	1.61750	0.808749	−	0.588153i	$-0.200145\pi$
$223$	24.1544	1.61750	0.808749	+	0.588153i	$0.200145\pi$
$224$	−2.98821	−0.199658
$225$	−1.01233	−0.0674885
$226$	1.21093	0.0805499
$227$	−1.78033	−0.118165	−0.0590824	−	0.998253i	$-0.518817\pi$
$227$	−1.78033	−0.118165	−0.0590824	+	0.998253i	$0.518817\pi$
$228$	−0.722838	−0.0478711
$229$	−19.9222	−1.31649	−0.658247	−	0.752802i	$-0.728702\pi$
$229$	−19.9222	−1.31649	−0.658247	+	0.752802i	$0.728702\pi$
$230$	17.4963	1.15367
$231$	−9.66037	−0.635606
$232$	−2.48733	−0.163301
$233$	−5.94904	−0.389734	−0.194867	−	0.980830i	$-0.562428\pi$
$233$	−5.94904	−0.389734	−0.194867	+	0.980830i	$0.562428\pi$
$234$	13.3534	0.872941
$235$	29.2185	1.90601
$236$	−11.0293	−0.717949
$237$	10.9778	0.713083
$238$	8.17488	0.529899
$239$	7.17955	0.464407	0.232203	−	0.972667i	$-0.425407\pi$
$239$	7.17955	0.464407	0.232203	+	0.972667i	$0.425407\pi$
$240$	2.49065	0.160771
$241$	−15.7864	−1.01689	−0.508447	−	0.861093i	$-0.669780\pi$
$241$	−15.7864	−1.01689	−0.508447	+	0.861093i	$0.669780\pi$
$242$	−1.66896	−0.107285
$243$	−15.6779	−1.00574
$244$	5.06842	0.324472
$245$	−4.54069	−0.290094
$246$	−5.85107	−0.373050
$247$	−4.85142	−0.308688
$248$	8.43120	0.535382
$249$	−6.46677	−0.409815
$250$	10.4997	0.664061
$251$	10.1354	0.639738	0.319869	−	0.947462i	$-0.396361\pi$
$251$	10.1354	0.639738	0.319869	+	0.947462i	$0.396361\pi$
$252$	5.61772	0.353883
$253$	22.7099	1.42776
$254$	−11.7605	−0.737918
$255$	−6.81369	−0.426690
$256$	1.00000	0.0625000
$257$	−14.8439	−0.925939	−0.462969	−	0.886374i	$-0.653216\pi$
$257$	−14.8439	−0.925939	−0.462969	+	0.886374i	$0.653216\pi$
$258$	−10.1818	−0.633894
$259$	−14.9320	−0.927830
$260$	16.7163	1.03670
$261$	4.67607	0.289442
$262$	−10.4690	−0.646778
$263$	24.4339	1.50666	0.753330	−	0.657643i	$-0.228446\pi$
$263$	24.4339	1.50666	0.753330	+	0.657643i	$0.228446\pi$
$264$	3.23283	0.198967
$265$	−18.5020	−1.13657
$266$	−2.04096	−0.125140
$267$	−6.24102	−0.381945
$268$	4.88627	0.298476
$269$	−9.31176	−0.567748	−0.283874	−	0.958862i	$-0.591620\pi$
$269$	−9.31176	−0.567748	−0.283874	+	0.958862i	$0.591620\pi$
$270$	−12.1543	−0.739685
$271$	−2.40798	−0.146274	−0.0731371	−	0.997322i	$-0.523301\pi$
$271$	−2.40798	−0.146274	−0.0731371	+	0.997322i	$0.523301\pi$
$272$	−2.73571	−0.165877
$273$	−22.4633	−1.35954
$274$	−1.67501	−0.101191
$275$	−1.64489	−0.0991908
$276$	7.86807	0.473602
$277$	−11.0254	−0.662451	−0.331226	−	0.943552i	$-0.607462\pi$
$277$	−11.0254	−0.662451	−0.331226	+	0.943552i	$0.607462\pi$
$278$	−1.53375	−0.0919881
$279$	−15.8503	−0.948933
$280$	7.03246	0.420270
$281$	8.11793	0.484275	0.242138	−	0.970242i	$-0.422151\pi$
$281$	8.11793	0.484275	0.242138	+	0.970242i	$0.422151\pi$
$282$	13.1395	0.782448
$283$	1.18113	0.0702112	0.0351056	−	0.999384i	$-0.488823\pi$
$283$	1.18113	0.0702112	0.0351056	+	0.999384i	$0.488823\pi$
$284$	−13.6506	−0.810016
$285$	1.70113	0.100766
$286$	21.6975	1.28300
$287$	−16.5207	−0.975188
$288$	−1.87996	−0.110778
$289$	−9.51591	−0.559759
$290$	5.85367	0.343740
$291$	6.35373	0.372462
$292$	5.37173	0.314357
$293$	−16.2735	−0.950707	−0.475353	−	0.879795i	$-0.657680\pi$
$293$	−16.2735	−0.950707	−0.475353	+	0.879795i	$0.657680\pi$
$294$	−2.04194	−0.119089
$295$	25.9564	1.51124
$296$	4.99697	0.290443
$297$	−15.7761	−0.915419
$298$	−13.5430	−0.784523
$299$	52.8075	3.05394
$300$	−0.569888	−0.0329025
$301$	−28.7489	−1.65706
$302$	−17.3555	−0.998697
$303$	10.7925	0.620014
$304$	0.683005	0.0391730
$305$	−11.9280	−0.682996
$306$	5.14301	0.294007
$307$	12.6153	0.719995	0.359998	−	0.932953i	$-0.382778\pi$
$307$	12.6153	0.719995	0.359998	+	0.932953i	$0.382778\pi$
$308$	9.12802	0.520117
$309$	−0.181355	−0.0103169
$310$	−19.8420	−1.12695
$311$	26.6410	1.51067	0.755335	−	0.655338i	$-0.227474\pi$
$311$	26.6410	1.51067	0.755335	+	0.655338i	$0.227474\pi$
$312$	7.51730	0.425583
$313$	13.4512	0.760307	0.380154	−	0.924923i	$-0.375871\pi$
$313$	13.4512	0.760307	0.380154	+	0.924923i	$0.375871\pi$
$314$	5.37184	0.303151
$315$	−13.2207	−0.744903
$316$	−10.3728	−0.583517
$317$	14.2267	0.799050	0.399525	−	0.916722i	$-0.369175\pi$
$317$	14.2267	0.799050	0.399525	+	0.916722i	$0.369175\pi$
$318$	−8.32032	−0.466580
$319$	7.59798	0.425405
$320$	−2.35340	−0.131559
$321$	12.3753	0.690723
$322$	22.2158	1.23804
$323$	−1.86850	−0.103966
$324$	0.174115	0.00967307
$325$	−3.82488	−0.212166
$326$	17.3135	0.958909
$327$	14.7064	0.813268
$328$	5.52863	0.305268
$329$	37.1001	2.04539
$330$	−7.60813	−0.418814
$331$	−8.56914	−0.471002	−0.235501	−	0.971874i	$-0.575673\pi$
$331$	−8.56914	−0.471002	−0.235501	+	0.971874i	$0.575673\pi$
$332$	6.11041	0.335352
$333$	−9.39409	−0.514793
$334$	19.5081	1.06743
$335$	−11.4993	−0.628276
$336$	3.16249	0.172528
$337$	26.9719	1.46925	0.734626	−	0.678473i	$-0.237358\pi$
$337$	26.9719	1.46925	0.734626	+	0.678473i	$0.237358\pi$
$338$	37.4533	2.03719
$339$	−1.28155	−0.0696044
$340$	6.43821	0.349161
$341$	−25.7546	−1.39469
$342$	−1.28402	−0.0694319
$343$	15.1520	0.818130
$344$	9.62075	0.518716
$345$	−18.5167	−0.996905
$346$	11.4044	0.613107
$347$	−12.4285	−0.667194	−0.333597	−	0.942716i	$-0.608263\pi$
$347$	−12.4285	−0.667194	−0.333597	+	0.942716i	$0.608263\pi$
$348$	2.63239	0.141111
$349$	−11.9528	−0.639821	−0.319911	−	0.947448i	$-0.603653\pi$
$349$	−11.9528	−0.639821	−0.319911	+	0.947448i	$0.603653\pi$
$350$	−1.60910	−0.0860102
$351$	−36.6841	−1.95805
$352$	−3.05468	−0.162815
$353$	13.7558	0.732146	0.366073	−	0.930586i	$-0.380702\pi$
$353$	13.7558	0.732146	0.366073	+	0.930586i	$0.380702\pi$
$354$	11.6726	0.620391
$355$	32.1254	1.70504
$356$	5.89710	0.312546
$357$	−8.65164	−0.457893
$358$	21.6724	1.14542
$359$	−1.33231	−0.0703167	−0.0351583	−	0.999382i	$-0.511194\pi$
$359$	−1.33231	−0.0703167	−0.0351583	+	0.999382i	$0.511194\pi$
$360$	4.42429	0.233181
$361$	−18.5335	−0.975448
$362$	−21.6901	−1.14001
$363$	1.76629	0.0927064
$364$	21.2254	1.11251
$365$	−12.6418	−0.661703
$366$	−5.36401	−0.280381
$367$	28.3352	1.47909	0.739544	−	0.673108i	$-0.235041\pi$
$367$	28.3352	1.47909	0.739544	+	0.673108i	$0.235041\pi$
$368$	−7.43448	−0.387549
$369$	−10.3936	−0.541069
$370$	−11.7599	−0.611366
$371$	−23.4928	−1.21968
$372$	−8.92291	−0.462631
$373$	−4.64620	−0.240571	−0.120286	−	0.992739i	$-0.538381\pi$
$373$	−4.64620	−0.240571	−0.120286	+	0.992739i	$0.538381\pi$
$374$	8.35670	0.432115
$375$	−11.1121	−0.573825
$376$	−12.4155	−0.640279
$377$	17.6676	0.909928
$378$	−15.4328	−0.793778
$379$	−4.45729	−0.228956	−0.114478	−	0.993426i	$-0.536519\pi$
$379$	−4.45729	−0.228956	−0.114478	+	0.993426i	$0.536519\pi$
$380$	−1.60738	−0.0824570
$381$	12.4464	0.637646
$382$	−6.63848	−0.339654
$383$	−1.50678	−0.0769927	−0.0384964	−	0.999259i	$-0.512257\pi$
$383$	−1.50678	−0.0769927	−0.0384964	+	0.999259i	$0.512257\pi$
$384$	−1.05832	−0.0540072
$385$	−21.4819	−1.09482
$386$	−3.80614	−0.193727
$387$	−18.0866	−0.919394
$388$	−6.00360	−0.304787
$389$	−19.4311	−0.985196	−0.492598	−	0.870257i	$-0.663953\pi$
$389$	−19.4311	−0.985196	−0.492598	+	0.870257i	$0.663953\pi$
$390$	−17.6912	−0.895829
$391$	20.3386	1.02857
$392$	1.92942	0.0974504
$393$	11.0796	0.558890
$394$	−8.42673	−0.424532
$395$	24.4114	1.22827
$396$	5.74266	0.288580
$397$	−0.833395	−0.0418269	−0.0209135	−	0.999781i	$-0.506657\pi$
$397$	−0.833395	−0.0418269	−0.0209135	+	0.999781i	$0.506657\pi$
$398$	25.5719	1.28180
$399$	2.15999	0.108135
$400$	0.538484	0.0269242
$401$	29.3779	1.46706	0.733531	−	0.679655i	$-0.237871\pi$
$401$	29.3779	1.46706	0.733531	+	0.679655i	$0.237871\pi$
$402$	−5.17124	−0.257918
$403$	−59.8872	−2.98320
$404$	−10.1978	−0.507358
$405$	−0.409763	−0.0203613
$406$	7.43267	0.368877
$407$	−15.2641	−0.756614
$408$	2.89525	0.143336
$409$	−21.5361	−1.06489	−0.532445	−	0.846465i	$-0.678727\pi$
$409$	−21.5361	−1.06489	−0.532445	+	0.846465i	$0.678727\pi$
$410$	−13.0111	−0.642571
$411$	1.77270	0.0874409
$412$	0.171361	0.00844235
$413$	32.9580	1.62176
$414$	13.9765	0.686908
$415$	−14.3802	−0.705897
$416$	−7.10305	−0.348256
$417$	1.62320	0.0794883
$418$	−2.08636	−0.102047
$419$	9.17337	0.448148	0.224074	−	0.974572i	$-0.428064\pi$
$419$	9.17337	0.448148	0.224074	+	0.974572i	$0.428064\pi$
$420$	−7.44259	−0.363161
$421$	−30.6533	−1.49395	−0.746976	−	0.664851i	$-0.768495\pi$
$421$	−30.6533	−1.49395	−0.746976	+	0.664851i	$0.768495\pi$
$422$	−22.1217	−1.07687
$423$	23.3406	1.13486
$424$	7.86181	0.381803
$425$	−1.47313	−0.0714575
$426$	14.4467	0.699947
$427$	−15.1455	−0.732943
$428$	−11.6934	−0.565220
$429$	−22.9629	−1.10866
$430$	−22.6415	−1.09187
$431$	−35.7689	−1.72293	−0.861463	−	0.507820i	$-0.830452\pi$
$431$	−35.7689	−1.72293	−0.861463	+	0.507820i	$0.830452\pi$
$432$	5.16456	0.248480
$433$	28.9791	1.39265	0.696324	−	0.717727i	$-0.254818\pi$
$433$	28.9791	1.39265	0.696324	+	0.717727i	$0.254818\pi$
$434$	−25.1942	−1.20936
$435$	−6.19506	−0.297031
$436$	−13.8960	−0.665499
$437$	−5.07779	−0.242903
$438$	−5.68501	−0.271640
$439$	30.3108	1.44666	0.723329	−	0.690504i	$-0.242611\pi$
$439$	30.3108	1.44666	0.723329	+	0.690504i	$0.242611\pi$
$440$	7.18887	0.342716
$441$	−3.62723	−0.172725
$442$	19.4319	0.924279
$443$	11.4210	0.542626	0.271313	−	0.962491i	$-0.412542\pi$
$443$	11.4210	0.542626	0.271313	+	0.962491i	$0.412542\pi$
$444$	−5.28839	−0.250976
$445$	−13.8782	−0.657891
$446$	24.1544	1.14374
$447$	14.3328	0.677919
$448$	−2.98821	−0.141180
$449$	−0.880404	−0.0415488	−0.0207744	−	0.999784i	$-0.506613\pi$
$449$	−0.880404	−0.0415488	−0.0207744	+	0.999784i	$0.506613\pi$
$450$	−1.01233	−0.0477215
$451$	−16.8882	−0.795233
$452$	1.21093	0.0569574
$453$	18.3677	0.862989
$454$	−1.78033	−0.0835551
$455$	−49.9519	−2.34178
$456$	−0.722838	−0.0338500
$457$	26.8850	1.25763	0.628814	−	0.777556i	$-0.283541\pi$
$457$	26.8850	1.25763	0.628814	+	0.777556i	$0.283541\pi$
$458$	−19.9222	−0.930902
$459$	−14.1287	−0.659472
$460$	17.4963	0.815769
$461$	8.28875	0.386046	0.193023	−	0.981194i	$-0.438171\pi$
$461$	8.28875	0.386046	0.193023	+	0.981194i	$0.438171\pi$
$462$	−9.66037	−0.449441
$463$	15.2202	0.707341	0.353671	−	0.935370i	$-0.384933\pi$
$463$	15.2202	0.707341	0.353671	+	0.935370i	$0.384933\pi$
$464$	−2.48733	−0.115471
$465$	20.9992	0.973813
$466$	−5.94904	−0.275584
$467$	12.6711	0.586349	0.293174	−	0.956059i	$-0.405288\pi$
$467$	12.6711	0.586349	0.293174	+	0.956059i	$0.405288\pi$
$468$	13.3534	0.617263
$469$	−14.6012	−0.674221
$470$	29.2185	1.34775
$471$	−5.68513	−0.261957
$472$	−11.0293	−0.507667
$473$	−29.3883	−1.35127
$474$	10.9778	0.504226
$475$	0.367787	0.0168752
$476$	8.17488	0.374695
$477$	−14.7799	−0.676724
$478$	7.17955	0.328385
$479$	−27.7908	−1.26979	−0.634896	−	0.772597i	$-0.718957\pi$
$479$	−27.7908	−1.26979	−0.634896	+	0.772597i	$0.718957\pi$
$480$	2.49065	0.113682
$481$	−35.4937	−1.61837
$482$	−15.7864	−0.719053
$483$	−23.5115	−1.06981
$484$	−1.66896	−0.0758618
$485$	14.1289	0.641558
$486$	−15.6779	−0.711166
$487$	20.0435	0.908258	0.454129	−	0.890936i	$-0.349951\pi$
$487$	20.0435	0.908258	0.454129	+	0.890936i	$0.349951\pi$
$488$	5.06842	0.229436
$489$	−18.3233	−0.828607
$490$	−4.54069	−0.205128
$491$	−9.17230	−0.413940	−0.206970	−	0.978347i	$-0.566360\pi$
$491$	−9.17230	−0.413940	−0.206970	+	0.978347i	$0.566360\pi$
$492$	−5.85107	−0.263786
$493$	6.80460	0.306464
$494$	−4.85142	−0.218275
$495$	−13.5148	−0.607444
$496$	8.43120	0.378572
$497$	40.7910	1.82973
$498$	−6.46677	−0.289783
$499$	−12.4641	−0.557969	−0.278985	−	0.960296i	$-0.589998\pi$
$499$	−12.4641	−0.557969	−0.278985	+	0.960296i	$0.589998\pi$
$500$	10.4997	0.469562
$501$	−20.6458	−0.922386
$502$	10.1354	0.452363
$503$	23.4222	1.04435	0.522173	−	0.852840i	$-0.325122\pi$
$503$	23.4222	1.04435	0.522173	+	0.852840i	$0.325122\pi$
$504$	5.61772	0.250233
$505$	23.9994	1.06796
$506$	22.7099	1.00958
$507$	−39.6376	−1.76037
$508$	−11.7605	−0.521787
$509$	−19.8056	−0.877866	−0.438933	−	0.898520i	$-0.644643\pi$
$509$	−19.8056	−0.877866	−0.438933	+	0.898520i	$0.644643\pi$
$510$	−6.81369	−0.301715
$511$	−16.0519	−0.710093
$512$	1.00000	0.0441942
$513$	3.52742	0.155739
$514$	−14.8439	−0.654738
$515$	−0.403281	−0.0177707
$516$	−10.1818	−0.448230
$517$	37.9252	1.66795
$518$	−14.9320	−0.656075
$519$	−12.0696	−0.529795
$520$	16.7163	0.733058
$521$	18.4487	0.808254	0.404127	−	0.914703i	$-0.367575\pi$
$521$	18.4487	0.808254	0.404127	+	0.914703i	$0.367575\pi$
$522$	4.67607	0.204666
$523$	13.5767	0.593666	0.296833	−	0.954929i	$-0.404070\pi$
$523$	13.5767	0.593666	0.296833	+	0.954929i	$0.404070\pi$
$524$	−10.4690	−0.457341
$525$	1.70295	0.0743227
$526$	24.4339	1.06537
$527$	−23.0653	−1.00474
$528$	3.23283	0.140691
$529$	32.2715	1.40311
$530$	−18.5020	−0.803675
$531$	20.7347	0.899810
$532$	−2.04096	−0.0884870
$533$	−39.2702	−1.70098
$534$	−6.24102	−0.270076
$535$	27.5191	1.18976
$536$	4.88627	0.211055
$537$	−22.9364	−0.989777
$538$	−9.31176	−0.401459
$539$	−5.89375	−0.253862
$540$	−12.1543	−0.523036
$541$	−5.12082	−0.220161	−0.110081	−	0.993923i	$-0.535111\pi$
$541$	−5.12082	−0.220161	−0.110081	+	0.993923i	$0.535111\pi$
$542$	−2.40798	−0.103432
$543$	22.9551	0.985098
$544$	−2.73571	−0.117292
$545$	32.7029	1.40084
$546$	−22.4633	−0.961340
$547$	−23.7139	−1.01393	−0.506967	−	0.861965i	$-0.669234\pi$
$547$	−23.7139	−1.01393	−0.506967	+	0.861965i	$0.669234\pi$
$548$	−1.67501	−0.0715530
$549$	−9.52841	−0.406663
$550$	−1.64489	−0.0701385
$551$	−1.69886	−0.0723737
$552$	7.86807	0.334887
$553$	30.9962	1.31809
$554$	−11.0254	−0.468424
$555$	12.4457	0.528290
$556$	−1.53375	−0.0650454
$557$	−18.0190	−0.763491	−0.381746	−	0.924267i	$-0.624677\pi$
$557$	−18.0190	−0.763491	−0.381746	+	0.924267i	$0.624677\pi$
$558$	−15.8503	−0.670997
$559$	−68.3367	−2.89033
$560$	7.03246	0.297176
$561$	−8.84406	−0.373397
$562$	8.11793	0.342434
$563$	−24.9420	−1.05118	−0.525590	−	0.850738i	$-0.676156\pi$
$563$	−24.9420	−1.05118	−0.525590	+	0.850738i	$0.676156\pi$
$564$	13.1395	0.553275
$565$	−2.84980	−0.119892
$566$	1.18113	0.0496468
$567$	−0.520294	−0.0218503
$568$	−13.6506	−0.572768
$569$	−19.8643	−0.832755	−0.416378	−	0.909192i	$-0.636701\pi$
$569$	−19.8643	−0.832755	−0.416378	+	0.909192i	$0.636701\pi$
$570$	1.70113	0.0712523
$571$	26.8644	1.12424	0.562120	−	0.827056i	$-0.309986\pi$
$571$	26.8644	1.12424	0.562120	+	0.827056i	$0.309986\pi$
$572$	21.6975	0.907218
$573$	7.02564	0.293500
$574$	−16.5207	−0.689562
$575$	−4.00335	−0.166951
$576$	−1.87996	−0.0783316
$577$	−30.0067	−1.24920	−0.624598	−	0.780947i	$-0.714737\pi$
$577$	−30.0067	−1.24920	−0.624598	+	0.780947i	$0.714737\pi$
$578$	−9.51591	−0.395810
$579$	4.02811	0.167403
$580$	5.85367	0.243061
$581$	−18.2592	−0.757519
$582$	6.35373	0.263371
$583$	−24.0153	−0.994611
$584$	5.37173	0.222284
$585$	−31.4259	−1.29930
$586$	−16.2735	−0.672251
$587$	−9.03342	−0.372849	−0.186425	−	0.982469i	$-0.559690\pi$
$587$	−9.03342	−0.372849	−0.186425	+	0.982469i	$0.559690\pi$
$588$	−2.04194	−0.0842083
$589$	5.75855	0.237277
$590$	25.9564	1.06861
$591$	8.91818	0.366845
$592$	4.99697	0.205374
$593$	4.41933	0.181480	0.0907400	−	0.995875i	$-0.471077\pi$
$593$	4.41933	0.181480	0.0907400	+	0.995875i	$0.471077\pi$
$594$	−15.7761	−0.647299
$595$	−19.2387	−0.788711
$596$	−13.5430	−0.554742
$597$	−27.0633	−1.10763
$598$	52.8075	2.15946
$599$	21.0222	0.858943	0.429472	−	0.903080i	$-0.358700\pi$
$599$	21.0222	0.858943	0.429472	+	0.903080i	$0.358700\pi$
$600$	−0.569888	−0.0232656
$601$	8.13914	0.332002	0.166001	−	0.986126i	$-0.446914\pi$
$601$	8.13914	0.332002	0.166001	+	0.986126i	$0.446914\pi$
$602$	−28.7489	−1.17172
$603$	−9.18598	−0.374082
$604$	−17.3555	−0.706186
$605$	3.92773	0.159685
$606$	10.7925	0.438416
$607$	30.5462	1.23983	0.619917	−	0.784668i	$-0.287166\pi$
$607$	30.5462	1.23983	0.619917	+	0.784668i	$0.287166\pi$
$608$	0.683005	0.0276995
$609$	−7.86614	−0.318752
$610$	−11.9280	−0.482951
$611$	88.1877	3.56769
$612$	5.14301	0.207894
$613$	31.3608	1.26665	0.633326	−	0.773885i	$-0.281689\pi$
$613$	31.3608	1.26665	0.633326	+	0.773885i	$0.281689\pi$
$614$	12.6153	0.509113
$615$	13.7699	0.555256
$616$	9.12802	0.367778
$617$	−39.3245	−1.58314	−0.791572	−	0.611076i	$-0.790737\pi$
$617$	−39.3245	−1.58314	−0.791572	+	0.611076i	$0.790737\pi$
$618$	−0.181355	−0.00729516
$619$	30.1907	1.21346	0.606732	−	0.794906i	$-0.292480\pi$
$619$	30.1907	1.21346	0.606732	+	0.794906i	$0.292480\pi$
$620$	−19.8420	−0.796873
$621$	−38.3958	−1.54077
$622$	26.6410	1.06821
$623$	−17.6218	−0.706003
$624$	7.51730	0.300933
$625$	−27.4025	−1.09610
$626$	13.4512	0.537618
$627$	2.20803	0.0881804
$628$	5.37184	0.214360
$629$	−13.6702	−0.545068
$630$	−13.2207	−0.526726
$631$	−1.77449	−0.0706412	−0.0353206	−	0.999376i	$-0.511245\pi$
$631$	−1.77449	−0.0706412	−0.0353206	+	0.999376i	$0.511245\pi$
$632$	−10.3728	−0.412609
$633$	23.4119	0.930539
$634$	14.2267	0.565014
$635$	27.6771	1.09833
$636$	−8.32032	−0.329922
$637$	−13.7048	−0.543002
$638$	7.59798	0.300807
$639$	25.6626	1.01520
$640$	−2.35340	−0.0930262
$641$	−20.9213	−0.826343	−0.413171	−	0.910653i	$-0.635579\pi$
$641$	−20.9213	−0.826343	−0.413171	+	0.910653i	$0.635579\pi$
$642$	12.3753	0.488415
$643$	5.54501	0.218674	0.109337	−	0.994005i	$-0.465127\pi$
$643$	5.54501	0.218674	0.109337	+	0.994005i	$0.465127\pi$
$644$	22.2158	0.875426
$645$	23.9619	0.943500
$646$	−1.86850	−0.0735152
$647$	11.0128	0.432956	0.216478	−	0.976287i	$-0.430543\pi$
$647$	11.0128	0.432956	0.216478	+	0.976287i	$0.430543\pi$
$648$	0.174115	0.00683990
$649$	33.6911	1.32249
$650$	−3.82488	−0.150024
$651$	26.6636	1.04503
$652$	17.3135	0.678051
$653$	0.908060	0.0355351	0.0177676	−	0.999842i	$-0.494344\pi$
$653$	0.908060	0.0355351	0.0177676	+	0.999842i	$0.494344\pi$
$654$	14.7064	0.575068
$655$	24.6378	0.962677
$656$	5.52863	0.215857
$657$	−10.0986	−0.393985
$658$	37.1001	1.44631
$659$	−11.4027	−0.444187	−0.222093	−	0.975025i	$-0.571289\pi$
$659$	−11.4027	−0.444187	−0.222093	+	0.975025i	$0.571289\pi$
$660$	−7.60813	−0.296146
$661$	−31.3517	−1.21944	−0.609720	−	0.792617i	$-0.708718\pi$
$661$	−31.3517	−1.21944	−0.609720	+	0.792617i	$0.708718\pi$
$662$	−8.56914	−0.333049
$663$	−20.5651	−0.798684
$664$	6.11041	0.237130
$665$	4.80320	0.186260
$666$	−9.39409	−0.364013
$667$	18.4920	0.716013
$668$	19.5081	0.754790
$669$	−25.5631	−0.988327
$670$	−11.4993	−0.444258
$671$	−15.4824	−0.597690
$672$	3.16249	0.121996
$673$	−16.8393	−0.649109	−0.324554	−	0.945867i	$-0.605214\pi$
$673$	−16.8393	−0.649109	−0.324554	+	0.945867i	$0.605214\pi$
$674$	26.9719	1.03892
$675$	2.78103	0.107042
$676$	37.4533	1.44051
$677$	−11.0375	−0.424206	−0.212103	−	0.977247i	$-0.568031\pi$
$677$	−11.0375	−0.424206	−0.212103	+	0.977247i	$0.568031\pi$
$678$	−1.28155	−0.0492177
$679$	17.9400	0.688475
$680$	6.43821	0.246894
$681$	1.88416	0.0722012
$682$	−25.7546	−0.986194
$683$	−15.2415	−0.583201	−0.291601	−	0.956540i	$-0.594188\pi$
$683$	−15.2415	−0.583201	−0.291601	+	0.956540i	$0.594188\pi$
$684$	−1.28402	−0.0490957
$685$	3.94197	0.150615
$686$	15.1520	0.578505
$687$	21.0840	0.804406
$688$	9.62075	0.366788
$689$	−55.8428	−2.12744
$690$	−18.5167	−0.704918
$691$	−34.1130	−1.29772	−0.648860	−	0.760908i	$-0.724754\pi$
$691$	−34.1130	−1.29772	−0.648860	+	0.760908i	$0.724754\pi$
$692$	11.4044	0.433532
$693$	−17.1603	−0.651866
$694$	−12.4285	−0.471778
$695$	3.60952	0.136917
$696$	2.63239	0.0997805
$697$	−15.1247	−0.572890
$698$	−11.9528	−0.452422
$699$	6.29599	0.238136
$700$	−1.60910	−0.0608184
$701$	−1.63466	−0.0617402	−0.0308701	−	0.999523i	$-0.509828\pi$
$701$	−1.63466	−0.0617402	−0.0308701	+	0.999523i	$0.509828\pi$
$702$	−36.6841	−1.38455
$703$	3.41295	0.128722
$704$	−3.05468	−0.115127
$705$	−30.9226	−1.16461
$706$	13.7558	0.517706
$707$	30.4731	1.14606
$708$	11.6726	0.438683
$709$	31.6027	1.18686	0.593432	−	0.804884i	$-0.297772\pi$
$709$	31.6027	1.18686	0.593432	+	0.804884i	$0.297772\pi$
$710$	32.1254	1.20564
$711$	19.5005	0.731325
$712$	5.89710	0.221003
$713$	−62.6816	−2.34745
$714$	−8.65164	−0.323779
$715$	−51.0629	−1.90964
$716$	21.6724	0.809936
$717$	−7.59827	−0.283762
$718$	−1.33231	−0.0497214
$719$	−34.5321	−1.28783	−0.643915	−	0.765097i	$-0.722691\pi$
$719$	−34.5321	−1.28783	−0.643915	+	0.765097i	$0.722691\pi$
$720$	4.42429	0.164884
$721$	−0.512063	−0.0190702
$722$	−18.5335	−0.689746
$723$	16.7071	0.621344
$724$	−21.6901	−0.806107
$725$	−1.33939	−0.0497435
$726$	1.76629	0.0655533
$727$	26.4504	0.980993	0.490496	−	0.871443i	$-0.336816\pi$
$727$	26.4504	0.980993	0.490496	+	0.871443i	$0.336816\pi$
$728$	21.2254	0.786666
$729$	16.0699	0.595183
$730$	−12.6418	−0.467895
$731$	−26.3196	−0.973464
$732$	−5.36401	−0.198259
$733$	−17.5455	−0.648059	−0.324030	−	0.946047i	$-0.605038\pi$
$733$	−17.5455	−0.648059	−0.324030	+	0.946047i	$0.605038\pi$
$734$	28.3352	1.04587
$735$	4.80551	0.177254
$736$	−7.43448	−0.274039
$737$	−14.9260	−0.549805
$738$	−10.3936	−0.382594
$739$	52.6236	1.93579	0.967896	−	0.251352i	$-0.0808753\pi$
$739$	52.6236	1.93579	0.967896	+	0.251352i	$0.0808753\pi$
$740$	−11.7599	−0.432301
$741$	5.13435	0.188615
$742$	−23.4928	−0.862447
$743$	−33.3701	−1.22423	−0.612114	−	0.790769i	$-0.709681\pi$
$743$	−33.3701	−1.22423	−0.612114	+	0.790769i	$0.709681\pi$
$744$	−8.92291	−0.327130
$745$	31.8720	1.16770
$746$	−4.64620	−0.170109
$747$	−11.4873	−0.420298
$748$	8.35670	0.305551
$749$	34.9423	1.27676
$750$	−11.1121	−0.405756
$751$	−37.0110	−1.35055	−0.675274	−	0.737567i	$-0.735975\pi$
$751$	−37.0110	−1.35055	−0.675274	+	0.737567i	$0.735975\pi$
$752$	−12.4155	−0.452746
$753$	−10.7265	−0.390894
$754$	17.6676	0.643416
$755$	40.8444	1.48648
$756$	−15.4328	−0.561286
$757$	48.7761	1.77280	0.886399	−	0.462922i	$-0.153199\pi$
$757$	48.7761	1.77280	0.886399	+	0.462922i	$0.153199\pi$
$758$	−4.45729	−0.161896
$759$	−24.0344	−0.872393
$760$	−1.60738	−0.0583059
$761$	13.7656	0.499004	0.249502	−	0.968374i	$-0.419733\pi$
$761$	13.7656	0.499004	0.249502	+	0.968374i	$0.419733\pi$
$762$	12.4464	0.450884
$763$	41.5243	1.50328
$764$	−6.63848	−0.240172
$765$	−12.1036	−0.437605
$766$	−1.50678	−0.0544421
$767$	78.3420	2.82876
$768$	−1.05832	−0.0381888
$769$	40.5707	1.46302	0.731508	−	0.681833i	$-0.238817\pi$
$769$	40.5707	1.46302	0.731508	+	0.681833i	$0.238817\pi$
$770$	−21.4819	−0.774153
$771$	15.7096	0.565769
$772$	−3.80614	−0.136986
$773$	−16.3002	−0.586276	−0.293138	−	0.956070i	$-0.594700\pi$
$773$	−16.3002	−0.586276	−0.293138	+	0.956070i	$0.594700\pi$
$774$	−18.0866	−0.650110
$775$	4.54007	0.163084
$776$	−6.00360	−0.215517
$777$	15.8028	0.566924
$778$	−19.4311	−0.696639
$779$	3.77608	0.135292
$780$	−17.6912	−0.633447
$781$	41.6982	1.49208
$782$	20.3386	0.727306
$783$	−12.8460	−0.459077
$784$	1.92942	0.0689078
$785$	−12.6421	−0.451216
$786$	11.0796	0.395195
$787$	8.83526	0.314943	0.157471	−	0.987524i	$-0.449666\pi$
$787$	8.83526	0.314943	0.157471	+	0.987524i	$0.449666\pi$
$788$	−8.42673	−0.300190
$789$	−25.8589	−0.920602
$790$	24.4114	0.868519
$791$	−3.61852	−0.128660
$792$	5.74266	0.204057
$793$	−36.0012	−1.27844
$794$	−0.833395	−0.0295761
$795$	19.5810	0.694467
$796$	25.5719	0.906372
$797$	−49.7598	−1.76258	−0.881291	−	0.472574i	$-0.843325\pi$
$797$	−49.7598	−1.76258	−0.881291	+	0.472574i	$0.843325\pi$
$798$	2.15999	0.0764629
$799$	33.9651	1.20160
$800$	0.538484	0.0190383
$801$	−11.0863	−0.391715
$802$	29.3779	1.03737
$803$	−16.4089	−0.579057
$804$	−5.17124	−0.182376
$805$	−52.2827	−1.84272
$806$	−59.8872	−2.10944
$807$	9.85483	0.346906
$808$	−10.1978	−0.358757
$809$	47.8469	1.68221	0.841103	−	0.540875i	$-0.181907\pi$
$809$	47.8469	1.68221	0.841103	+	0.540875i	$0.181907\pi$
$810$	−0.409763	−0.0143976
$811$	−31.5027	−1.10621	−0.553104	−	0.833112i	$-0.686557\pi$
$811$	−31.5027	−1.10621	−0.553104	+	0.833112i	$0.686557\pi$
$812$	7.43267	0.260835
$813$	2.54841	0.0893767
$814$	−15.2641	−0.535007
$815$	−40.7457	−1.42726
$816$	2.89525	0.101354
$817$	6.57102	0.229891
$818$	−21.5361	−0.752990
$819$	−39.9029	−1.39432
$820$	−13.0111	−0.454367
$821$	17.9848	0.627675	0.313837	−	0.949477i	$-0.398385\pi$
$821$	17.9848	0.627675	0.313837	+	0.949477i	$0.398385\pi$
$822$	1.77270	0.0618301
$823$	37.9215	1.32186	0.660931	−	0.750447i	$-0.270162\pi$
$823$	37.9215	1.32186	0.660931	+	0.750447i	$0.270162\pi$
$824$	0.171361	0.00596964
$825$	1.74082	0.0606077
$826$	32.9580	1.14676
$827$	27.3401	0.950707	0.475354	−	0.879795i	$-0.342320\pi$
$827$	27.3401	0.950707	0.475354	+	0.879795i	$0.342320\pi$
$828$	13.9765	0.485717
$829$	−0.111965	−0.00388872	−0.00194436	−	0.999998i	$-0.500619\pi$
$829$	−0.111965	−0.00388872	−0.00194436	+	0.999998i	$0.500619\pi$
$830$	−14.3802	−0.499145
$831$	11.6684	0.404772
$832$	−7.10305	−0.246254
$833$	−5.27832	−0.182883
$834$	1.62320	0.0562067
$835$	−45.9102	−1.58879
$836$	−2.08636	−0.0721582
$837$	43.5434	1.50508
$838$	9.17337	0.316889
$839$	41.1585	1.42095	0.710474	−	0.703723i	$-0.248481\pi$
$839$	41.1585	1.42095	0.710474	+	0.703723i	$0.248481\pi$
$840$	−7.44259	−0.256794
$841$	−22.8132	−0.786662
$842$	−30.6533	−1.05638
$843$	−8.59137	−0.295903
$844$	−22.1217	−0.761461
$845$	−88.1425	−3.03219
$846$	23.3406	0.802465
$847$	4.98721	0.171362
$848$	7.86181	0.269976
$849$	−1.25002	−0.0429005
$850$	−1.47313	−0.0505281
$851$	−37.1499	−1.27348
$852$	14.4467	0.494937
$853$	33.9541	1.16257	0.581283	−	0.813701i	$-0.302551\pi$
$853$	33.9541	1.16257	0.581283	+	0.813701i	$0.302551\pi$
$854$	−15.1455	−0.518269
$855$	3.02181	0.103344
$856$	−11.6934	−0.399671
$857$	−8.70006	−0.297188	−0.148594	−	0.988898i	$-0.547475\pi$
$857$	−8.70006	−0.297188	−0.148594	+	0.988898i	$0.547475\pi$
$858$	−22.9629	−0.783941
$859$	−5.34672	−0.182428	−0.0912139	−	0.995831i	$-0.529075\pi$
$859$	−5.34672	−0.182428	−0.0912139	+	0.995831i	$0.529075\pi$
$860$	−22.6415	−0.772067
$861$	17.4842	0.595861
$862$	−35.7689	−1.21829
$863$	−2.63929	−0.0898426	−0.0449213	−	0.998991i	$-0.514304\pi$
$863$	−2.63929	−0.0898426	−0.0449213	+	0.998991i	$0.514304\pi$
$864$	5.16456	0.175702
$865$	−26.8392	−0.912560
$866$	28.9791	0.984751
$867$	10.0709	0.342025
$868$	−25.1942	−0.855148
$869$	31.6856	1.07486
$870$	−6.19506	−0.210032
$871$	−34.7074	−1.17602
$872$	−13.8960	−0.470579
$873$	11.2865	0.381991
$874$	−5.07779	−0.171759
$875$	−31.3754	−1.06068
$876$	−5.68501	−0.192079
$877$	24.0591	0.812419	0.406210	−	0.913780i	$-0.366850\pi$
$877$	24.0591	0.812419	0.406210	+	0.913780i	$0.366850\pi$
$878$	30.3108	1.02294
$879$	17.2225	0.580902
$880$	7.18887	0.242337
$881$	−10.4838	−0.353210	−0.176605	−	0.984282i	$-0.556511\pi$
$881$	−10.4838	−0.353210	−0.176605	+	0.984282i	$0.556511\pi$
$882$	−3.62723	−0.122135
$883$	−54.1122	−1.82102	−0.910510	−	0.413486i	$-0.864311\pi$
$883$	−54.1122	−1.82102	−0.910510	+	0.413486i	$0.864311\pi$
$884$	19.4319	0.653564
$885$	−27.4702	−0.923402
$886$	11.4210	0.383695
$887$	−10.7280	−0.360209	−0.180105	−	0.983647i	$-0.557644\pi$
$887$	−10.7280	−0.360209	−0.180105	+	0.983647i	$0.557644\pi$
$888$	−5.28839	−0.177467
$889$	35.1428	1.17865
$890$	−13.8782	−0.465199
$891$	−0.531866	−0.0178182
$892$	24.1544	0.808749
$893$	−8.47982	−0.283766
$894$	14.3328	0.479361
$895$	−51.0038	−1.70487
$896$	−2.98821	−0.0998292
$897$	−55.8872	−1.86602
$898$	−0.880404	−0.0293795
$899$	−20.9712	−0.699428
$900$	−1.01233	−0.0337442
$901$	−21.5076	−0.716523
$902$	−16.8882	−0.562315
$903$	30.4255	1.01250
$904$	1.21093	0.0402750
$905$	51.0455	1.69681
$906$	18.3677	0.610226
$907$	42.5818	1.41391	0.706953	−	0.707260i	$-0.250069\pi$
$907$	42.5818	1.41391	0.706953	+	0.707260i	$0.250069\pi$
$908$	−1.78033	−0.0590824
$909$	19.1714	0.635875
$910$	−49.9519	−1.65589
$911$	−47.8580	−1.58560	−0.792802	−	0.609479i	$-0.791379\pi$
$911$	−47.8580	−1.58560	−0.792802	+	0.609479i	$0.791379\pi$
$912$	−0.722838	−0.0239356
$913$	−18.6653	−0.617731
$914$	26.8850	0.889277
$915$	12.6237	0.417325
$916$	−19.9222	−0.658247
$917$	31.2836	1.03308
$918$	−14.1287	−0.466317
$919$	40.2271	1.32697	0.663485	−	0.748189i	$-0.269076\pi$
$919$	40.2271	1.32697	0.663485	+	0.748189i	$0.269076\pi$
$920$	17.4963	0.576836
$921$	−13.3511	−0.439933
$922$	8.28875	0.272976
$923$	96.9611	3.19151
$924$	−9.66037	−0.317803
$925$	2.69079	0.0884725
$926$	15.2202	0.500166
$927$	−0.322151	−0.0105808
$928$	−2.48733	−0.0816505
$929$	−4.93374	−0.161871	−0.0809354	−	0.996719i	$-0.525791\pi$
$929$	−4.93374	−0.161871	−0.0809354	+	0.996719i	$0.525791\pi$
$930$	20.9992	0.688590
$931$	1.31780	0.0431892
$932$	−5.94904	−0.194867
$933$	−28.1947	−0.923053
$934$	12.6711	0.414611
$935$	−19.6666	−0.643168
$936$	13.3534	0.436471
$937$	12.0520	0.393720	0.196860	−	0.980432i	$-0.436926\pi$
$937$	12.0520	0.393720	0.196860	+	0.980432i	$0.436926\pi$
$938$	−14.6012	−0.476747
$939$	−14.2357	−0.464564
$940$	29.2185	0.953004
$941$	−3.46854	−0.113071	−0.0565355	−	0.998401i	$-0.518005\pi$
$941$	−3.46854	−0.113071	−0.0565355	+	0.998401i	$0.518005\pi$
$942$	−5.68513	−0.185232
$943$	−41.1025	−1.33848
$944$	−11.0293	−0.358975
$945$	36.3195	1.18147
$946$	−29.3883	−0.955495
$947$	−11.6655	−0.379077	−0.189539	−	0.981873i	$-0.560699\pi$
$947$	−11.6655	−0.379077	−0.189539	+	0.981873i	$0.560699\pi$
$948$	10.9778	0.356542
$949$	−38.1556	−1.23858
$950$	0.367787	0.0119326
$951$	−15.0564	−0.488237
$952$	8.17488	0.264949
$953$	−49.8326	−1.61423	−0.807117	−	0.590391i	$-0.798974\pi$
$953$	−49.8326	−1.61423	−0.807117	+	0.590391i	$0.798974\pi$
$954$	−14.7799	−0.478516
$955$	15.6230	0.505548
$956$	7.17955	0.232203
$957$	−8.04110	−0.259932
$958$	−27.7908	−0.897879
$959$	5.00530	0.161630
$960$	2.49065	0.0803854
$961$	40.0852	1.29307
$962$	−35.4937	−1.14436
$963$	21.9830	0.708393
$964$	−15.7864	−0.508447
$965$	8.95736	0.288348
$966$	−23.5115	−0.756469
$967$	−55.7475	−1.79272	−0.896359	−	0.443330i	$-0.853797\pi$
$967$	−55.7475	−1.79272	−0.896359	+	0.443330i	$0.853797\pi$
$968$	−1.66896	−0.0536424
$969$	1.97747	0.0635256
$970$	14.1289	0.453650
$971$	−33.1409	−1.06354	−0.531771	−	0.846888i	$-0.678473\pi$
$971$	−33.1409	−1.06354	−0.531771	+	0.846888i	$0.678473\pi$
$972$	−15.6779	−0.502870
$973$	4.58317	0.146930
$974$	20.0435	0.642235
$975$	4.04794	0.129638
$976$	5.06842	0.162236
$977$	−27.5505	−0.881418	−0.440709	−	0.897650i	$-0.645273\pi$
$977$	−27.5505	−0.881418	−0.440709	+	0.897650i	$0.645273\pi$
$978$	−18.3233	−0.585914
$979$	−18.0137	−0.575721
$980$	−4.54069	−0.145047
$981$	26.1239	0.834073
$982$	−9.17230	−0.292700
$983$	29.3441	0.935932	0.467966	−	0.883746i	$-0.344987\pi$
$983$	29.3441	0.935932	0.467966	+	0.883746i	$0.344987\pi$
$984$	−5.85107	−0.186525
$985$	19.8314	0.631882
$986$	6.80460	0.216703
$987$	−39.2638	−1.24978
$988$	−4.85142	−0.154344
$989$	−71.5253	−2.27437
$990$	−13.5148	−0.429528
$991$	51.2980	1.62953	0.814767	−	0.579788i	$-0.196865\pi$
$991$	51.2980	1.62953	0.814767	+	0.579788i	$0.196865\pi$
$992$	8.43120	0.267691
$993$	9.06889	0.287793
$994$	40.7910	1.29381
$995$	−60.1809	−1.90786
$996$	−6.46677	−0.204907
$997$	−21.3815	−0.677160	−0.338580	−	0.940938i	$-0.609947\pi$
$997$	−21.3815	−0.677160	−0.338580	+	0.940938i	$0.609947\pi$
$998$	−12.4641	−0.394544
$999$	25.8071	0.816501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.16	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.16	✓	50	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.05832 q^{3} +1.00000 q^{4} -2.35340 q^{5} -1.05832 q^{6} -2.98821 q^{7} +1.00000 q^{8} -1.87996 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.05832 q^{3} +1.00000 q^{4} -2.35340 q^{5} -1.05832 q^{6} -2.98821 q^{7} +1.00000 q^{8} -1.87996 q^{9} -2.35340 q^{10} -3.05468 q^{11} -1.05832 q^{12} -7.10305 q^{13} -2.98821 q^{14} +2.49065 q^{15} +1.00000 q^{16} -2.73571 q^{17} -1.87996 q^{18} +0.683005 q^{19} -2.35340 q^{20} +3.16249 q^{21} -3.05468 q^{22} -7.43448 q^{23} -1.05832 q^{24} +0.538484 q^{25} -7.10305 q^{26} +5.16456 q^{27} -2.98821 q^{28} -2.48733 q^{29} +2.49065 q^{30} +8.43120 q^{31} +1.00000 q^{32} +3.23283 q^{33} -2.73571 q^{34} +7.03246 q^{35} -1.87996 q^{36} +4.99697 q^{37} +0.683005 q^{38} +7.51730 q^{39} -2.35340 q^{40} +5.52863 q^{41} +3.16249 q^{42} +9.62075 q^{43} -3.05468 q^{44} +4.42429 q^{45} -7.43448 q^{46} -12.4155 q^{47} -1.05832 q^{48} +1.92942 q^{49} +0.538484 q^{50} +2.89525 q^{51} -7.10305 q^{52} +7.86181 q^{53} +5.16456 q^{54} +7.18887 q^{55} -2.98821 q^{56} -0.722838 q^{57} -2.48733 q^{58} -11.0293 q^{59} +2.49065 q^{60} +5.06842 q^{61} +8.43120 q^{62} +5.61772 q^{63} +1.00000 q^{64} +16.7163 q^{65} +3.23283 q^{66} +4.88627 q^{67} -2.73571 q^{68} +7.86807 q^{69} +7.03246 q^{70} -13.6506 q^{71} -1.87996 q^{72} +5.37173 q^{73} +4.99697 q^{74} -0.569888 q^{75} +0.683005 q^{76} +9.12802 q^{77} +7.51730 q^{78} -10.3728 q^{79} -2.35340 q^{80} +0.174115 q^{81} +5.52863 q^{82} +6.11041 q^{83} +3.16249 q^{84} +6.43821 q^{85} +9.62075 q^{86} +2.63239 q^{87} -3.05468 q^{88} +5.89710 q^{89} +4.42429 q^{90} +21.2254 q^{91} -7.43448 q^{92} -8.92291 q^{93} -12.4155 q^{94} -1.60738 q^{95} -1.05832 q^{96} -6.00360 q^{97} +1.92942 q^{98} +5.74266 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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