LMFDB - Embedded newform 8043.2.a.n.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64192 q^{2} +1.00000 q^{3} +4.97976 q^{4} -3.51496 q^{5} -2.64192 q^{6} +1.00000 q^{7} -7.87228 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.64192 q^{2} +1.00000 q^{3} +4.97976 q^{4} -3.51496 q^{5} -2.64192 q^{6} +1.00000 q^{7} -7.87228 q^{8} +1.00000 q^{9} +9.28626 q^{10} +1.28949 q^{11} +4.97976 q^{12} +5.89163 q^{13} -2.64192 q^{14} -3.51496 q^{15} +10.8385 q^{16} -2.10418 q^{17} -2.64192 q^{18} +1.10923 q^{19} -17.5036 q^{20} +1.00000 q^{21} -3.40674 q^{22} -4.43232 q^{23} -7.87228 q^{24} +7.35495 q^{25} -15.5652 q^{26} +1.00000 q^{27} +4.97976 q^{28} -1.70007 q^{29} +9.28626 q^{30} -3.10452 q^{31} -12.8898 q^{32} +1.28949 q^{33} +5.55909 q^{34} -3.51496 q^{35} +4.97976 q^{36} -1.13873 q^{37} -2.93051 q^{38} +5.89163 q^{39} +27.6708 q^{40} +9.67284 q^{41} -2.64192 q^{42} -5.44221 q^{43} +6.42135 q^{44} -3.51496 q^{45} +11.7098 q^{46} -10.1248 q^{47} +10.8385 q^{48} +1.00000 q^{49} -19.4312 q^{50} -2.10418 q^{51} +29.3389 q^{52} +5.53437 q^{53} -2.64192 q^{54} -4.53251 q^{55} -7.87228 q^{56} +1.10923 q^{57} +4.49147 q^{58} +7.92039 q^{59} -17.5036 q^{60} -7.02905 q^{61} +8.20191 q^{62} +1.00000 q^{63} +12.3769 q^{64} -20.7089 q^{65} -3.40674 q^{66} +2.56978 q^{67} -10.4783 q^{68} -4.43232 q^{69} +9.28626 q^{70} -5.52983 q^{71} -7.87228 q^{72} -5.53507 q^{73} +3.00845 q^{74} +7.35495 q^{75} +5.52372 q^{76} +1.28949 q^{77} -15.5652 q^{78} -7.22866 q^{79} -38.0968 q^{80} +1.00000 q^{81} -25.5549 q^{82} +4.97404 q^{83} +4.97976 q^{84} +7.39612 q^{85} +14.3779 q^{86} -1.70007 q^{87} -10.1512 q^{88} -4.39739 q^{89} +9.28626 q^{90} +5.89163 q^{91} -22.0719 q^{92} -3.10452 q^{93} +26.7489 q^{94} -3.89892 q^{95} -12.8898 q^{96} -14.7726 q^{97} -2.64192 q^{98} +1.28949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9} - 14 q^{10} - 29 q^{11} + 33 q^{12} - 40 q^{13} - 9 q^{14} - 27 q^{15} + 23 q^{16} - 46 q^{17} - 9 q^{18} + 17 q^{19} - 53 q^{20} + 40 q^{21} - 15 q^{22} - 62 q^{23} - 18 q^{24} + 35 q^{25} - 29 q^{26} + 40 q^{27} + 33 q^{28} - 47 q^{29} - 14 q^{30} + q^{31} - 45 q^{32} - 29 q^{33} + 9 q^{34} - 27 q^{35} + 33 q^{36} - 49 q^{37} - 52 q^{38} - 40 q^{39} - 12 q^{40} - 49 q^{41} - 9 q^{42} - 45 q^{43} - 68 q^{44} - 27 q^{45} - 36 q^{46} - 88 q^{47} + 23 q^{48} + 40 q^{49} - 32 q^{50} - 46 q^{51} - 34 q^{52} - 96 q^{53} - 9 q^{54} + 26 q^{55} - 18 q^{56} + 17 q^{57} + 12 q^{58} - 45 q^{59} - 53 q^{60} - 23 q^{61} - 15 q^{62} + 40 q^{63} + 50 q^{64} - 32 q^{65} - 15 q^{66} - 31 q^{67} - 76 q^{68} - 62 q^{69} - 14 q^{70} - 89 q^{71} - 18 q^{72} + 4 q^{73} + 10 q^{74} + 35 q^{75} + 51 q^{76} - 29 q^{77} - 29 q^{78} - 44 q^{79} - 53 q^{80} + 40 q^{81} - 15 q^{82} - 60 q^{83} + 33 q^{84} - 24 q^{85} - 9 q^{86} - 47 q^{87} - 64 q^{88} - 39 q^{89} - 14 q^{90} - 40 q^{91} - 80 q^{92} + q^{93} + 51 q^{94} - 71 q^{95} - 45 q^{96} - 21 q^{97} - 9 q^{98} - 29 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9 - 14 * q^10 - 29 * q^11 + 33 * q^12 - 40 * q^13 - 9 * q^14 - 27 * q^15 + 23 * q^16 - 46 * q^17 - 9 * q^18 + 17 * q^19 - 53 * q^20 + 40 * q^21 - 15 * q^22 - 62 * q^23 - 18 * q^24 + 35 * q^25 - 29 * q^26 + 40 * q^27 + 33 * q^28 - 47 * q^29 - 14 * q^30 + q^31 - 45 * q^32 - 29 * q^33 + 9 * q^34 - 27 * q^35 + 33 * q^36 - 49 * q^37 - 52 * q^38 - 40 * q^39 - 12 * q^40 - 49 * q^41 - 9 * q^42 - 45 * q^43 - 68 * q^44 - 27 * q^45 - 36 * q^46 - 88 * q^47 + 23 * q^48 + 40 * q^49 - 32 * q^50 - 46 * q^51 - 34 * q^52 - 96 * q^53 - 9 * q^54 + 26 * q^55 - 18 * q^56 + 17 * q^57 + 12 * q^58 - 45 * q^59 - 53 * q^60 - 23 * q^61 - 15 * q^62 + 40 * q^63 + 50 * q^64 - 32 * q^65 - 15 * q^66 - 31 * q^67 - 76 * q^68 - 62 * q^69 - 14 * q^70 - 89 * q^71 - 18 * q^72 + 4 * q^73 + 10 * q^74 + 35 * q^75 + 51 * q^76 - 29 * q^77 - 29 * q^78 - 44 * q^79 - 53 * q^80 + 40 * q^81 - 15 * q^82 - 60 * q^83 + 33 * q^84 - 24 * q^85 - 9 * q^86 - 47 * q^87 - 64 * q^88 - 39 * q^89 - 14 * q^90 - 40 * q^91 - 80 * q^92 + q^93 + 51 * q^94 - 71 * q^95 - 45 * q^96 - 21 * q^97 - 9 * q^98 - 29 * 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 $

$2$	−2.64192	−1.86812	−0.934061	−	0.357114i	$-0.883761\pi$
$2$	−2.64192	−1.86812	−0.934061	+	0.357114i	$0.883761\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.97976	2.48988
$5$	−3.51496	−1.57194	−0.785969	−	0.618266i	$-0.787836\pi$
$5$	−3.51496	−1.57194	−0.785969	+	0.618266i	$0.787836\pi$
$6$	−2.64192	−1.07856
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−7.87228	−2.78327
$9$	1.00000	0.333333
$10$	9.28626	2.93657
$11$	1.28949	0.388796	0.194398	−	0.980923i	$-0.437725\pi$
$11$	1.28949	0.388796	0.194398	+	0.980923i	$0.437725\pi$
$12$	4.97976	1.43753
$13$	5.89163	1.63404	0.817022	−	0.576606i	$-0.195623\pi$
$13$	5.89163	1.63404	0.817022	+	0.576606i	$0.195623\pi$
$14$	−2.64192	−0.706084
$15$	−3.51496	−0.907559
$16$	10.8385	2.70961
$17$	−2.10418	−0.510339	−0.255170	−	0.966896i	$-0.582131\pi$
$17$	−2.10418	−0.510339	−0.255170	+	0.966896i	$0.582131\pi$
$18$	−2.64192	−0.622707
$19$	1.10923	0.254476	0.127238	−	0.991872i	$-0.459389\pi$
$19$	1.10923	0.254476	0.127238	+	0.991872i	$0.459389\pi$
$20$	−17.5036	−3.91393
$21$	1.00000	0.218218
$22$	−3.40674	−0.726319
$23$	−4.43232	−0.924202	−0.462101	−	0.886827i	$-0.652904\pi$
$23$	−4.43232	−0.924202	−0.462101	+	0.886827i	$0.652904\pi$
$24$	−7.87228	−1.60692
$25$	7.35495	1.47099
$26$	−15.5652	−3.05259
$27$	1.00000	0.192450
$28$	4.97976	0.941085
$29$	−1.70007	−0.315696	−0.157848	−	0.987463i	$-0.550456\pi$
$29$	−1.70007	−0.315696	−0.157848	+	0.987463i	$0.550456\pi$
$30$	9.28626	1.69543
$31$	−3.10452	−0.557588	−0.278794	−	0.960351i	$-0.589935\pi$
$31$	−3.10452	−0.557588	−0.278794	+	0.960351i	$0.589935\pi$
$32$	−12.8898	−2.27861
$33$	1.28949	0.224472
$34$	5.55909	0.953376
$35$	−3.51496	−0.594137
$36$	4.97976	0.829959
$37$	−1.13873	−0.187207	−0.0936033	−	0.995610i	$-0.529839\pi$
$37$	−1.13873	−0.187207	−0.0936033	+	0.995610i	$0.529839\pi$
$38$	−2.93051	−0.475392
$39$	5.89163	0.943416
$40$	27.6708	4.37513
$41$	9.67284	1.51064	0.755322	−	0.655354i	$-0.227480\pi$
$41$	9.67284	1.51064	0.755322	+	0.655354i	$0.227480\pi$
$42$	−2.64192	−0.407658
$43$	−5.44221	−0.829929	−0.414964	−	0.909838i	$-0.636206\pi$
$43$	−5.44221	−0.829929	−0.414964	+	0.909838i	$0.636206\pi$
$44$	6.42135	0.968055
$45$	−3.51496	−0.523980
$46$	11.7098	1.72652
$47$	−10.1248	−1.47685	−0.738427	−	0.674334i	$-0.764431\pi$
$47$	−10.1248	−1.47685	−0.738427	+	0.674334i	$0.764431\pi$
$48$	10.8385	1.56440
$49$	1.00000	0.142857
$50$	−19.4312	−2.74799
$51$	−2.10418	−0.294645
$52$	29.3389	4.06857
$53$	5.53437	0.760204	0.380102	−	0.924944i	$-0.375889\pi$
$53$	5.53437	0.760204	0.380102	+	0.924944i	$0.375889\pi$
$54$	−2.64192	−0.359520
$55$	−4.53251	−0.611164
$56$	−7.87228	−1.05198
$57$	1.10923	0.146922
$58$	4.49147	0.589758
$59$	7.92039	1.03115	0.515574	−	0.856845i	$-0.327579\pi$
$59$	7.92039	1.03115	0.515574	+	0.856845i	$0.327579\pi$
$60$	−17.5036	−2.25971
$61$	−7.02905	−0.899977	−0.449989	−	0.893034i	$-0.648572\pi$
$61$	−7.02905	−0.899977	−0.449989	+	0.893034i	$0.648572\pi$
$62$	8.20191	1.04164
$63$	1.00000	0.125988
$64$	12.3769	1.54712
$65$	−20.7089	−2.56862
$66$	−3.40674	−0.419340
$67$	2.56978	0.313949	0.156974	−	0.987603i	$-0.449826\pi$
$67$	2.56978	0.313949	0.156974	+	0.987603i	$0.449826\pi$
$68$	−10.4783	−1.27068
$69$	−4.43232	−0.533588
$70$	9.28626	1.10992
$71$	−5.52983	−0.656270	−0.328135	−	0.944631i	$-0.606420\pi$
$71$	−5.52983	−0.656270	−0.328135	+	0.944631i	$0.606420\pi$
$72$	−7.87228	−0.927758
$73$	−5.53507	−0.647831	−0.323915	−	0.946086i	$-0.604999\pi$
$73$	−5.53507	−0.647831	−0.323915	+	0.946086i	$0.604999\pi$
$74$	3.00845	0.349725
$75$	7.35495	0.849277
$76$	5.52372	0.633614
$77$	1.28949	0.146951
$78$	−15.5652	−1.76242
$79$	−7.22866	−0.813288	−0.406644	−	0.913587i	$-0.633301\pi$
$79$	−7.22866	−0.813288	−0.406644	+	0.913587i	$0.633301\pi$
$80$	−38.0968	−4.25935
$81$	1.00000	0.111111
$82$	−25.5549	−2.82207
$83$	4.97404	0.545972	0.272986	−	0.962018i	$-0.411989\pi$
$83$	4.97404	0.545972	0.272986	+	0.962018i	$0.411989\pi$
$84$	4.97976	0.543336
$85$	7.39612	0.802222
$86$	14.3779	1.55041
$87$	−1.70007	−0.182267
$88$	−10.1512	−1.08213
$89$	−4.39739	−0.466122	−0.233061	−	0.972462i	$-0.574874\pi$
$89$	−4.39739	−0.466122	−0.233061	+	0.972462i	$0.574874\pi$
$90$	9.28626	0.978857
$91$	5.89163	0.617611
$92$	−22.0719	−2.30115
$93$	−3.10452	−0.321924
$94$	26.7489	2.75894
$95$	−3.89892	−0.400021
$96$	−12.8898	−1.31556
$97$	−14.7726	−1.49993	−0.749966	−	0.661477i	$-0.769930\pi$
$97$	−14.7726	−1.49993	−0.749966	+	0.661477i	$0.769930\pi$
$98$	−2.64192	−0.266874
$99$	1.28949	0.129599
$100$	36.6259	3.66259
$101$	−7.46115	−0.742412	−0.371206	−	0.928551i	$-0.621056\pi$
$101$	−7.46115	−0.742412	−0.371206	+	0.928551i	$0.621056\pi$
$102$	5.55909	0.550432
$103$	−16.0861	−1.58501	−0.792503	−	0.609868i	$-0.791223\pi$
$103$	−16.0861	−1.58501	−0.792503	+	0.609868i	$0.791223\pi$
$104$	−46.3806	−4.54799
$105$	−3.51496	−0.343025
$106$	−14.6214	−1.42015
$107$	−3.42915	−0.331509	−0.165754	−	0.986167i	$-0.553006\pi$
$107$	−3.42915	−0.331509	−0.165754	+	0.986167i	$0.553006\pi$
$108$	4.97976	0.479177
$109$	4.70956	0.451094	0.225547	−	0.974232i	$-0.427583\pi$
$109$	4.70956	0.451094	0.225547	+	0.974232i	$0.427583\pi$
$110$	11.9745	1.14173
$111$	−1.13873	−0.108084
$112$	10.8385	1.02414
$113$	17.7823	1.67281	0.836407	−	0.548109i	$-0.184652\pi$
$113$	17.7823	1.67281	0.836407	+	0.548109i	$0.184652\pi$
$114$	−2.93051	−0.274468
$115$	15.5794	1.45279
$116$	−8.46596	−0.786044
$117$	5.89163	0.544681
$118$	−20.9251	−1.92631
$119$	−2.10418	−0.192890
$120$	27.6708	2.52598
$121$	−9.33721	−0.848837
$122$	18.5702	1.68127
$123$	9.67284	0.872171
$124$	−15.4598	−1.38833
$125$	−8.27757	−0.740369
$126$	−2.64192	−0.235361
$127$	−12.4905	−1.10836	−0.554178	−	0.832398i	$-0.686967\pi$
$127$	−12.4905	−1.10836	−0.554178	+	0.832398i	$0.686967\pi$
$128$	−6.91929	−0.611585
$129$	−5.44221	−0.479160
$130$	54.7112	4.79849
$131$	6.63288	0.579517	0.289759	−	0.957100i	$-0.406425\pi$
$131$	6.63288	0.579517	0.289759	+	0.957100i	$0.406425\pi$
$132$	6.42135	0.558907
$133$	1.10923	0.0961829
$134$	−6.78917	−0.586495
$135$	−3.51496	−0.302520
$136$	16.5647	1.42041
$137$	17.7306	1.51483	0.757414	−	0.652935i	$-0.226463\pi$
$137$	17.7306	1.51483	0.757414	+	0.652935i	$0.226463\pi$
$138$	11.7098	0.996808
$139$	12.8625	1.09098	0.545491	−	0.838117i	$-0.316343\pi$
$139$	12.8625	1.09098	0.545491	+	0.838117i	$0.316343\pi$
$140$	−17.5036	−1.47933
$141$	−10.1248	−0.852662
$142$	14.6094	1.22599
$143$	7.59721	0.635310
$144$	10.8385	0.903205
$145$	5.97570	0.496255
$146$	14.6232	1.21023
$147$	1.00000	0.0824786
$148$	−5.67061	−0.466122
$149$	−23.7443	−1.94521	−0.972603	−	0.232474i	$-0.925318\pi$
$149$	−23.7443	−1.94521	−0.972603	+	0.232474i	$0.925318\pi$
$150$	−19.4312	−1.58655
$151$	14.1859	1.15443	0.577216	−	0.816591i	$-0.304139\pi$
$151$	14.1859	1.15443	0.577216	+	0.816591i	$0.304139\pi$
$152$	−8.73221	−0.708276
$153$	−2.10418	−0.170113
$154$	−3.40674	−0.274523
$155$	10.9123	0.876495
$156$	29.3389	2.34899
$157$	−17.8360	−1.42347	−0.711735	−	0.702448i	$-0.752090\pi$
$157$	−17.8360	−1.42347	−0.711735	+	0.702448i	$0.752090\pi$
$158$	19.0976	1.51932
$159$	5.53437	0.438904
$160$	45.3071	3.58184
$161$	−4.43232	−0.349316
$162$	−2.64192	−0.207569
$163$	−2.81194	−0.220248	−0.110124	−	0.993918i	$-0.535125\pi$
$163$	−2.81194	−0.220248	−0.110124	+	0.993918i	$0.535125\pi$
$164$	48.1684	3.76132
$165$	−4.53251	−0.352856
$166$	−13.1410	−1.01994
$167$	17.9317	1.38760	0.693798	−	0.720170i	$-0.255936\pi$
$167$	17.9317	1.38760	0.693798	+	0.720170i	$0.255936\pi$
$168$	−7.87228	−0.607360
$169$	21.7113	1.67010
$170$	−19.5400	−1.49865
$171$	1.10923	0.0848253
$172$	−27.1009	−2.06642
$173$	−6.71365	−0.510430	−0.255215	−	0.966884i	$-0.582146\pi$
$173$	−6.71365	−0.510430	−0.255215	+	0.966884i	$0.582146\pi$
$174$	4.49147	0.340497
$175$	7.35495	0.555982
$176$	13.9761	1.05349
$177$	7.92039	0.595333
$178$	11.6176	0.870773
$179$	2.17740	0.162746	0.0813732	−	0.996684i	$-0.474069\pi$
$179$	2.17740	0.162746	0.0813732	+	0.996684i	$0.474069\pi$
$180$	−17.5036	−1.30464
$181$	14.9680	1.11256	0.556280	−	0.830995i	$-0.312228\pi$
$181$	14.9680	1.11256	0.556280	+	0.830995i	$0.312228\pi$
$182$	−15.5652	−1.15377
$183$	−7.02905	−0.519602
$184$	34.8925	2.57231
$185$	4.00260	0.294277
$186$	8.20191	0.601393
$187$	−2.71333	−0.198418
$188$	−50.4190	−3.67718
$189$	1.00000	0.0727393
$190$	10.3006	0.747287
$191$	10.2947	0.744901	0.372451	−	0.928052i	$-0.378518\pi$
$191$	10.2947	0.744901	0.372451	+	0.928052i	$0.378518\pi$
$192$	12.3769	0.893228
$193$	−11.0691	−0.796771	−0.398385	−	0.917218i	$-0.630429\pi$
$193$	−11.0691	−0.796771	−0.398385	+	0.917218i	$0.630429\pi$
$194$	39.0281	2.80205
$195$	−20.7089	−1.48299
$196$	4.97976	0.355697
$197$	1.76784	0.125953	0.0629767	−	0.998015i	$-0.479941\pi$
$197$	1.76784	0.125953	0.0629767	+	0.998015i	$0.479941\pi$
$198$	−3.40674	−0.242106
$199$	13.0127	0.922442	0.461221	−	0.887285i	$-0.347411\pi$
$199$	13.0127	0.922442	0.461221	+	0.887285i	$0.347411\pi$
$200$	−57.9003	−4.09417
$201$	2.56978	0.181258
$202$	19.7118	1.38692
$203$	−1.70007	−0.119322
$204$	−10.4783	−0.733629
$205$	−33.9997	−2.37464
$206$	42.4981	2.96098
$207$	−4.43232	−0.308067
$208$	63.8562	4.42763
$209$	1.43035	0.0989393
$210$	9.28626	0.640813
$211$	−0.0324951	−0.00223705	−0.00111853	−	0.999999i	$-0.500356\pi$
$211$	−0.0324951	−0.00223705	−0.00111853	+	0.999999i	$0.500356\pi$
$212$	27.5598	1.89282
$213$	−5.52983	−0.378898
$214$	9.05955	0.619298
$215$	19.1291	1.30460
$216$	−7.87228	−0.535641
$217$	−3.10452	−0.210749
$218$	−12.4423	−0.842699
$219$	−5.53507	−0.374025
$220$	−22.5708	−1.52172
$221$	−12.3971	−0.833917
$222$	3.00845	0.201914
$223$	13.4506	0.900718	0.450359	−	0.892848i	$-0.351296\pi$
$223$	13.4506	0.900718	0.450359	+	0.892848i	$0.351296\pi$
$224$	−12.8898	−0.861235
$225$	7.35495	0.490330
$226$	−46.9793	−3.12502
$227$	−20.4222	−1.35547	−0.677733	−	0.735308i	$-0.737038\pi$
$227$	−20.4222	−1.35547	−0.677733	+	0.735308i	$0.737038\pi$
$228$	5.52372	0.365817
$229$	−10.3366	−0.683063	−0.341532	−	0.939870i	$-0.610946\pi$
$229$	−10.3366	−0.683063	−0.341532	+	0.939870i	$0.610946\pi$
$230$	−41.1596	−2.71399
$231$	1.28949	0.0848423
$232$	13.3835	0.878668
$233$	6.13917	0.402190	0.201095	−	0.979572i	$-0.435550\pi$
$233$	6.13917	0.402190	0.201095	+	0.979572i	$0.435550\pi$
$234$	−15.5652	−1.01753
$235$	35.5883	2.32152
$236$	39.4416	2.56743
$237$	−7.22866	−0.469552
$238$	5.55909	0.360342
$239$	−16.5983	−1.07365	−0.536827	−	0.843692i	$-0.680377\pi$
$239$	−16.5983	−1.07365	−0.536827	+	0.843692i	$0.680377\pi$
$240$	−38.0968	−2.45913
$241$	−13.0171	−0.838503	−0.419251	−	0.907870i	$-0.637707\pi$
$241$	−13.0171	−0.838503	−0.419251	+	0.907870i	$0.637707\pi$
$242$	24.6682	1.58573
$243$	1.00000	0.0641500
$244$	−35.0029	−2.24083
$245$	−3.51496	−0.224563
$246$	−25.5549	−1.62932
$247$	6.53520	0.415825
$248$	24.4397	1.55192
$249$	4.97404	0.315217
$250$	21.8687	1.38310
$251$	−4.81832	−0.304130	−0.152065	−	0.988371i	$-0.548592\pi$
$251$	−4.81832	−0.304130	−0.152065	+	0.988371i	$0.548592\pi$
$252$	4.97976	0.313695
$253$	−5.71543	−0.359326
$254$	32.9990	2.07054
$255$	7.39612	0.463163
$256$	−6.47361	−0.404601
$257$	25.7406	1.60566	0.802828	−	0.596211i	$-0.203328\pi$
$257$	25.7406	1.60566	0.802828	+	0.596211i	$0.203328\pi$
$258$	14.3779	0.895128
$259$	−1.13873	−0.0707574
$260$	−103.125	−6.39554
$261$	−1.70007	−0.105232
$262$	−17.5236	−1.08261
$263$	−13.7283	−0.846524	−0.423262	−	0.906007i	$-0.639115\pi$
$263$	−13.7283	−0.846524	−0.423262	+	0.906007i	$0.639115\pi$
$264$	−10.1512	−0.624766
$265$	−19.4531	−1.19499
$266$	−2.93051	−0.179681
$267$	−4.39739	−0.269116
$268$	12.7969	0.781694
$269$	13.3467	0.813764	0.406882	−	0.913481i	$-0.366616\pi$
$269$	13.3467	0.813764	0.406882	+	0.913481i	$0.366616\pi$
$270$	9.28626	0.565144
$271$	−5.60590	−0.340534	−0.170267	−	0.985398i	$-0.554463\pi$
$271$	−5.60590	−0.340534	−0.170267	+	0.985398i	$0.554463\pi$
$272$	−22.8061	−1.38282
$273$	5.89163	0.356578
$274$	−46.8429	−2.82988
$275$	9.48415	0.571916
$276$	−22.0719	−1.32857
$277$	22.6286	1.35962	0.679810	−	0.733388i	$-0.262062\pi$
$277$	22.6286	1.35962	0.679810	+	0.733388i	$0.262062\pi$
$278$	−33.9817	−2.03809
$279$	−3.10452	−0.185863
$280$	27.6708	1.65365
$281$	−19.3365	−1.15352	−0.576760	−	0.816914i	$-0.695683\pi$
$281$	−19.3365	−1.15352	−0.576760	+	0.816914i	$0.695683\pi$
$282$	26.7489	1.59288
$283$	12.1382	0.721542	0.360771	−	0.932654i	$-0.382514\pi$
$283$	12.1382	0.721542	0.360771	+	0.932654i	$0.382514\pi$
$284$	−27.5372	−1.63403
$285$	−3.89892	−0.230952
$286$	−20.0712	−1.18684
$287$	9.67284	0.570970
$288$	−12.8898	−0.759538
$289$	−12.5724	−0.739554
$290$	−15.7873	−0.927064
$291$	−14.7726	−0.865986
$292$	−27.5633	−1.61302
$293$	−11.2348	−0.656343	−0.328171	−	0.944618i	$-0.606432\pi$
$293$	−11.2348	−0.656343	−0.328171	+	0.944618i	$0.606432\pi$
$294$	−2.64192	−0.154080
$295$	−27.8399	−1.62090
$296$	8.96443	0.521047
$297$	1.28949	0.0748239
$298$	62.7305	3.63388
$299$	−26.1136	−1.51019
$300$	36.6259	2.11460
$301$	−5.44221	−0.313684
$302$	−37.4781	−2.15662
$303$	−7.46115	−0.428632
$304$	12.0224	0.689531
$305$	24.7068	1.41471
$306$	5.55909	0.317792
$307$	3.98518	0.227446	0.113723	−	0.993512i	$-0.463722\pi$
$307$	3.98518	0.227446	0.113723	+	0.993512i	$0.463722\pi$
$308$	6.42135	0.365890
$309$	−16.0861	−0.915104
$310$	−28.8294	−1.63740
$311$	−2.20731	−0.125165	−0.0625826	−	0.998040i	$-0.519934\pi$
$311$	−2.20731	−0.125165	−0.0625826	+	0.998040i	$0.519934\pi$
$312$	−46.3806	−2.62578
$313$	−9.11179	−0.515029	−0.257515	−	0.966274i	$-0.582904\pi$
$313$	−9.11179	−0.515029	−0.257515	+	0.966274i	$0.582904\pi$
$314$	47.1214	2.65922
$315$	−3.51496	−0.198046
$316$	−35.9970	−2.02499
$317$	−8.49619	−0.477194	−0.238597	−	0.971119i	$-0.576687\pi$
$317$	−8.49619	−0.477194	−0.238597	+	0.971119i	$0.576687\pi$
$318$	−14.6214	−0.819926
$319$	−2.19223	−0.122741
$320$	−43.5044	−2.43197
$321$	−3.42915	−0.191397
$322$	11.7098	0.652564
$323$	−2.33403	−0.129869
$324$	4.97976	0.276653
$325$	43.3327	2.40366
$326$	7.42893	0.411450
$327$	4.70956	0.260439
$328$	−76.1474	−4.20454
$329$	−10.1248	−0.558198
$330$	11.9745	0.659177
$331$	23.1008	1.26974	0.634868	−	0.772621i	$-0.281054\pi$
$331$	23.1008	1.26974	0.634868	+	0.772621i	$0.281054\pi$
$332$	24.7695	1.35940
$333$	−1.13873	−0.0624022
$334$	−47.3741	−2.59220
$335$	−9.03269	−0.493508
$336$	10.8385	0.591286
$337$	−26.8489	−1.46255	−0.731275	−	0.682082i	$-0.761075\pi$
$337$	−26.8489	−1.46255	−0.731275	+	0.682082i	$0.761075\pi$
$338$	−57.3596	−3.11995
$339$	17.7823	0.965800
$340$	36.8309	1.99744
$341$	−4.00325	−0.216788
$342$	−2.93051	−0.158464
$343$	1.00000	0.0539949
$344$	42.8426	2.30992
$345$	15.5794	0.838768
$346$	17.7370	0.953545
$347$	−21.9279	−1.17715	−0.588576	−	0.808442i	$-0.700311\pi$
$347$	−21.9279	−1.17715	−0.588576	+	0.808442i	$0.700311\pi$
$348$	−8.46596	−0.453823
$349$	−7.72011	−0.413248	−0.206624	−	0.978420i	$-0.566248\pi$
$349$	−7.72011	−0.413248	−0.206624	+	0.978420i	$0.566248\pi$
$350$	−19.4312	−1.03864
$351$	5.89163	0.314472
$352$	−16.6213	−0.885917
$353$	−3.95887	−0.210709	−0.105355	−	0.994435i	$-0.533598\pi$
$353$	−3.95887	−0.210709	−0.105355	+	0.994435i	$0.533598\pi$
$354$	−20.9251	−1.11215
$355$	19.4371	1.03162
$356$	−21.8979	−1.16059
$357$	−2.10418	−0.111365
$358$	−5.75252	−0.304030
$359$	30.5497	1.61235	0.806176	−	0.591676i	$-0.201533\pi$
$359$	30.5497	1.61235	0.806176	+	0.591676i	$0.201533\pi$
$360$	27.6708	1.45838
$361$	−17.7696	−0.935242
$362$	−39.5442	−2.07840
$363$	−9.33721	−0.490077
$364$	29.3389	1.53778
$365$	19.4556	1.01835
$366$	18.5702	0.970680
$367$	−23.3061	−1.21657	−0.608284	−	0.793719i	$-0.708142\pi$
$367$	−23.3061	−1.21657	−0.608284	+	0.793719i	$0.708142\pi$
$368$	−48.0395	−2.50423
$369$	9.67284	0.503548
$370$	−10.5746	−0.549746
$371$	5.53437	0.287330
$372$	−15.4598	−0.801551
$373$	−12.4592	−0.645114	−0.322557	−	0.946550i	$-0.604542\pi$
$373$	−12.4592	−0.645114	−0.322557	+	0.946550i	$0.604542\pi$
$374$	7.16840	0.370669
$375$	−8.27757	−0.427452
$376$	79.7053	4.11048
$377$	−10.0162	−0.515861
$378$	−2.64192	−0.135886
$379$	26.9769	1.38571	0.692854	−	0.721078i	$-0.256353\pi$
$379$	26.9769	1.38571	0.692854	+	0.721078i	$0.256353\pi$
$380$	−19.4157	−0.996002
$381$	−12.4905	−0.639910
$382$	−27.1979	−1.39157
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−6.91929	−0.353099
$385$	−4.53251	−0.230998
$386$	29.2437	1.48846
$387$	−5.44221	−0.276643
$388$	−73.5640	−3.73464
$389$	−28.2206	−1.43084	−0.715420	−	0.698694i	$-0.753765\pi$
$389$	−28.2206	−1.43084	−0.715420	+	0.698694i	$0.753765\pi$
$390$	54.7112	2.77041
$391$	9.32641	0.471657
$392$	−7.87228	−0.397610
$393$	6.63288	0.334584
$394$	−4.67050	−0.235296
$395$	25.4085	1.27844
$396$	6.42135	0.322685
$397$	19.0506	0.956123	0.478061	−	0.878326i	$-0.341340\pi$
$397$	19.0506	0.956123	0.478061	+	0.878326i	$0.341340\pi$
$398$	−34.3784	−1.72323
$399$	1.10923	0.0555312
$400$	79.7163	3.98582
$401$	2.73850	0.136754	0.0683771	−	0.997660i	$-0.478218\pi$
$401$	2.73850	0.136754	0.0683771	+	0.997660i	$0.478218\pi$
$402$	−6.78917	−0.338613
$403$	−18.2907	−0.911124
$404$	−37.1547	−1.84852
$405$	−3.51496	−0.174660
$406$	4.49147	0.222908
$407$	−1.46839	−0.0727852
$408$	16.5647	0.820076
$409$	23.6747	1.17064	0.585319	−	0.810803i	$-0.300969\pi$
$409$	23.6747	1.17064	0.585319	+	0.810803i	$0.300969\pi$
$410$	89.8245	4.43612
$411$	17.7306	0.874586
$412$	−80.1046	−3.94647
$413$	7.92039	0.389737
$414$	11.7098	0.575507
$415$	−17.4836	−0.858234
$416$	−75.9419	−3.72336
$417$	12.8625	0.629879
$418$	−3.77887	−0.184831
$419$	−6.17616	−0.301725	−0.150862	−	0.988555i	$-0.548205\pi$
$419$	−6.17616	−0.301725	−0.150862	+	0.988555i	$0.548205\pi$
$420$	−17.5036	−0.854091
$421$	24.1019	1.17465	0.587326	−	0.809350i	$-0.300180\pi$
$421$	24.1019	1.17465	0.587326	+	0.809350i	$0.300180\pi$
$422$	0.0858494	0.00417908
$423$	−10.1248	−0.492284
$424$	−43.5681	−2.11586
$425$	−15.4762	−0.750704
$426$	14.6094	0.707827
$427$	−7.02905	−0.340159
$428$	−17.0763	−0.825416
$429$	7.59721	0.366797
$430$	−50.5377	−2.43715
$431$	−7.77398	−0.374459	−0.187230	−	0.982316i	$-0.559951\pi$
$431$	−7.77398	−0.374459	−0.187230	+	0.982316i	$0.559951\pi$
$432$	10.8385	0.521465
$433$	−18.9574	−0.911033	−0.455517	−	0.890227i	$-0.650545\pi$
$433$	−18.9574	−0.911033	−0.455517	+	0.890227i	$0.650545\pi$
$434$	8.20191	0.393704
$435$	5.97570	0.286513
$436$	23.4525	1.12317
$437$	−4.91648	−0.235187
$438$	14.6232	0.698725
$439$	10.0206	0.478258	0.239129	−	0.970988i	$-0.423138\pi$
$439$	10.0206	0.478258	0.239129	+	0.970988i	$0.423138\pi$
$440$	35.6812	1.70104
$441$	1.00000	0.0476190
$442$	32.7521	1.55786
$443$	39.3574	1.86993	0.934963	−	0.354744i	$-0.115432\pi$
$443$	39.3574	1.86993	0.934963	+	0.354744i	$0.115432\pi$
$444$	−5.67061	−0.269115
$445$	15.4566	0.732715
$446$	−35.5354	−1.68265
$447$	−23.7443	−1.12306
$448$	12.3769	0.584755
$449$	18.6877	0.881926	0.440963	−	0.897525i	$-0.354637\pi$
$449$	18.6877	0.881926	0.440963	+	0.897525i	$0.354637\pi$
$450$	−19.4312	−0.915996
$451$	12.4730	0.587333
$452$	88.5513	4.16510
$453$	14.1859	0.666512
$454$	53.9538	2.53218
$455$	−20.7089	−0.970846
$456$	−8.73221	−0.408923
$457$	4.58337	0.214401	0.107200	−	0.994237i	$-0.465811\pi$
$457$	4.58337	0.214401	0.107200	+	0.994237i	$0.465811\pi$
$458$	27.3085	1.27604
$459$	−2.10418	−0.0982149
$460$	77.5817	3.61727
$461$	−12.6795	−0.590544	−0.295272	−	0.955413i	$-0.595410\pi$
$461$	−12.6795	−0.590544	−0.295272	+	0.955413i	$0.595410\pi$
$462$	−3.40674	−0.158496
$463$	−14.5703	−0.677141	−0.338570	−	0.940941i	$-0.609943\pi$
$463$	−14.5703	−0.677141	−0.338570	+	0.940941i	$0.609943\pi$
$464$	−18.4262	−0.855414
$465$	10.9123	0.506045
$466$	−16.2192	−0.751340
$467$	−16.6725	−0.771513	−0.385757	−	0.922601i	$-0.626060\pi$
$467$	−16.6725	−0.771513	−0.385757	+	0.922601i	$0.626060\pi$
$468$	29.3389	1.35619
$469$	2.56978	0.118662
$470$	−94.0214	−4.33689
$471$	−17.8360	−0.821841
$472$	−62.3516	−2.86996
$473$	−7.01768	−0.322673
$474$	19.0976	0.877180
$475$	8.15837	0.374332
$476$	−10.4783	−0.480273
$477$	5.53437	0.253401
$478$	43.8514	2.00572
$479$	−20.4223	−0.933119	−0.466560	−	0.884490i	$-0.654507\pi$
$479$	−20.4223	−0.933119	−0.466560	+	0.884490i	$0.654507\pi$
$480$	45.3071	2.06798
$481$	−6.70900	−0.305904
$482$	34.3901	1.56642
$483$	−4.43232	−0.201677
$484$	−46.4970	−2.11350
$485$	51.9251	2.35780
$486$	−2.64192	−0.119840
$487$	−24.1334	−1.09359	−0.546794	−	0.837267i	$-0.684152\pi$
$487$	−24.1334	−1.09359	−0.546794	+	0.837267i	$0.684152\pi$
$488$	55.3347	2.50488
$489$	−2.81194	−0.127160
$490$	9.28626	0.419510
$491$	−12.5986	−0.568565	−0.284283	−	0.958741i	$-0.591755\pi$
$491$	−12.5986	−0.568565	−0.284283	+	0.958741i	$0.591755\pi$
$492$	48.1684	2.17160
$493$	3.57727	0.161112
$494$	−17.2655	−0.776811
$495$	−4.53251	−0.203721
$496$	−33.6482	−1.51085
$497$	−5.52983	−0.248047
$498$	−13.1410	−0.588864
$499$	18.3300	0.820563	0.410282	−	0.911959i	$-0.365430\pi$
$499$	18.3300	0.820563	0.410282	+	0.911959i	$0.365430\pi$
$500$	−41.2203	−1.84343
$501$	17.9317	0.801129
$502$	12.7296	0.568151
$503$	−27.4566	−1.22423	−0.612114	−	0.790769i	$-0.709681\pi$
$503$	−27.4566	−1.22423	−0.612114	+	0.790769i	$0.709681\pi$
$504$	−7.87228	−0.350659
$505$	26.2257	1.16703
$506$	15.0997	0.671265
$507$	21.7113	0.964233
$508$	−62.1998	−2.75967
$509$	3.42720	0.151908	0.0759539	−	0.997111i	$-0.475800\pi$
$509$	3.42720	0.151908	0.0759539	+	0.997111i	$0.475800\pi$
$510$	−19.5400	−0.865245
$511$	−5.53507	−0.244857
$512$	30.9414	1.36743
$513$	1.10923	0.0489739
$514$	−68.0047	−2.99956
$515$	56.5419	2.49153
$516$	−27.1009	−1.19305
$517$	−13.0558	−0.574195
$518$	3.00845	0.132184
$519$	−6.71365	−0.294697
$520$	163.026	7.14916
$521$	−41.5738	−1.82138	−0.910691	−	0.413088i	$-0.864450\pi$
$521$	−41.5738	−1.82138	−0.910691	+	0.413088i	$0.864450\pi$
$522$	4.49147	0.196586
$523$	10.0548	0.439665	0.219832	−	0.975538i	$-0.429449\pi$
$523$	10.0548	0.439665	0.219832	+	0.975538i	$0.429449\pi$
$524$	33.0301	1.44293
$525$	7.35495	0.320997
$526$	36.2691	1.58141
$527$	6.53248	0.284559
$528$	13.9761	0.608231
$529$	−3.35456	−0.145851
$530$	51.3936	2.23240
$531$	7.92039	0.343716
$532$	5.52372	0.239484
$533$	56.9888	2.46846
$534$	11.6176	0.502741
$535$	12.0533	0.521111
$536$	−20.2301	−0.873805
$537$	2.17740	0.0939617
$538$	−35.2610	−1.52021
$539$	1.28949	0.0555423
$540$	−17.5036	−0.753237
$541$	−29.9868	−1.28924	−0.644618	−	0.764505i	$-0.722983\pi$
$541$	−29.9868	−1.28924	−0.644618	+	0.764505i	$0.722983\pi$
$542$	14.8104	0.636160
$543$	14.9680	0.642337
$544$	27.1225	1.16287
$545$	−16.5539	−0.709092
$546$	−15.5652	−0.666130
$547$	31.9739	1.36711	0.683554	−	0.729900i	$-0.260434\pi$
$547$	31.9739	1.36711	0.683554	+	0.729900i	$0.260434\pi$
$548$	88.2940	3.77173
$549$	−7.02905	−0.299992
$550$	−25.0564	−1.06841
$551$	−1.88578	−0.0803370
$552$	34.8925	1.48512
$553$	−7.22866	−0.307394
$554$	−59.7830	−2.53994
$555$	4.00260	0.169901
$556$	64.0520	2.71641
$557$	−13.2097	−0.559711	−0.279856	−	0.960042i	$-0.590287\pi$
$557$	−13.2097	−0.559711	−0.279856	+	0.960042i	$0.590287\pi$
$558$	8.20191	0.347214
$559$	−32.0635	−1.35614
$560$	−38.0968	−1.60988
$561$	−2.71333	−0.114557
$562$	51.0856	2.15492
$563$	2.89898	0.122177	0.0610887	−	0.998132i	$-0.480543\pi$
$563$	2.89898	0.122177	0.0610887	+	0.998132i	$0.480543\pi$
$564$	−50.4190	−2.12302
$565$	−62.5039	−2.62956
$566$	−32.0682	−1.34793
$567$	1.00000	0.0419961
$568$	43.5324	1.82658
$569$	−30.5811	−1.28203	−0.641013	−	0.767530i	$-0.721486\pi$
$569$	−30.5811	−1.28203	−0.641013	+	0.767530i	$0.721486\pi$
$570$	10.3006	0.431446
$571$	−15.4333	−0.645864	−0.322932	−	0.946422i	$-0.604668\pi$
$571$	−15.4333	−0.645864	−0.322932	+	0.946422i	$0.604668\pi$
$572$	37.8322	1.58185
$573$	10.2947	0.430069
$574$	−25.5549	−1.06664
$575$	−32.5995	−1.35949
$576$	12.3769	0.515705
$577$	−31.3190	−1.30383	−0.651913	−	0.758294i	$-0.726033\pi$
$577$	−31.3190	−1.30383	−0.651913	+	0.758294i	$0.726033\pi$
$578$	33.2153	1.38158
$579$	−11.0691	−0.460016
$580$	29.7575	1.23561
$581$	4.97404	0.206358
$582$	39.0281	1.61777
$583$	7.13652	0.295565
$584$	43.5736	1.80309
$585$	−20.7089	−0.856206
$586$	29.6814	1.22613
$587$	−5.97530	−0.246627	−0.123313	−	0.992368i	$-0.539352\pi$
$587$	−5.97530	−0.246627	−0.123313	+	0.992368i	$0.539352\pi$
$588$	4.97976	0.205362
$589$	−3.44364	−0.141893
$590$	73.5508	3.02804
$591$	1.76784	0.0727192
$592$	−12.3421	−0.507258
$593$	−22.3406	−0.917420	−0.458710	−	0.888586i	$-0.651688\pi$
$593$	−22.3406	−0.917420	−0.458710	+	0.888586i	$0.651688\pi$
$594$	−3.40674	−0.139780
$595$	7.39612	0.303211
$596$	−118.241	−4.84332
$597$	13.0127	0.532572
$598$	68.9901	2.82121
$599$	−6.51003	−0.265992	−0.132996	−	0.991117i	$-0.542460\pi$
$599$	−6.51003	−0.265992	−0.132996	+	0.991117i	$0.542460\pi$
$600$	−57.9003	−2.36377
$601$	42.1163	1.71796	0.858980	−	0.512009i	$-0.171099\pi$
$601$	42.1163	1.71796	0.858980	+	0.512009i	$0.171099\pi$
$602$	14.3779	0.585999
$603$	2.56978	0.104650
$604$	70.6423	2.87440
$605$	32.8199	1.33432
$606$	19.7118	0.800736
$607$	25.0114	1.01518	0.507590	−	0.861599i	$-0.330537\pi$
$607$	25.0114	1.01518	0.507590	+	0.861599i	$0.330537\pi$
$608$	−14.2978	−0.579853
$609$	−1.70007	−0.0688905
$610$	−65.2735	−2.64285
$611$	−59.6516	−2.41324
$612$	−10.4783	−0.423561
$613$	−2.81429	−0.113668	−0.0568340	−	0.998384i	$-0.518101\pi$
$613$	−2.81429	−0.113668	−0.0568340	+	0.998384i	$0.518101\pi$
$614$	−10.5285	−0.424897
$615$	−33.9997	−1.37100
$616$	−10.1512	−0.409005
$617$	1.71690	0.0691200	0.0345600	−	0.999403i	$-0.488997\pi$
$617$	1.71690	0.0691200	0.0345600	+	0.999403i	$0.488997\pi$
$618$	42.4981	1.70953
$619$	43.8814	1.76374	0.881872	−	0.471489i	$-0.156283\pi$
$619$	43.8814	1.76374	0.881872	+	0.471489i	$0.156283\pi$
$620$	54.3405	2.18237
$621$	−4.43232	−0.177863
$622$	5.83155	0.233824
$623$	−4.39739	−0.176178
$624$	63.8562	2.55629
$625$	−7.67942	−0.307177
$626$	24.0727	0.962137
$627$	1.43035	0.0571226
$628$	−88.8191	−3.54427
$629$	2.39610	0.0955389
$630$	9.28626	0.369973
$631$	−4.46131	−0.177602	−0.0888009	−	0.996049i	$-0.528303\pi$
$631$	−4.46131	−0.177602	−0.0888009	+	0.996049i	$0.528303\pi$
$632$	56.9061	2.26360
$633$	−0.0324951	−0.00129156
$634$	22.4463	0.891456
$635$	43.9038	1.74227
$636$	27.5598	1.09282
$637$	5.89163	0.233435
$638$	5.79171	0.229296
$639$	−5.52983	−0.218757
$640$	24.3210	0.961374
$641$	−8.37348	−0.330733	−0.165366	−	0.986232i	$-0.552881\pi$
$641$	−8.37348	−0.330733	−0.165366	+	0.986232i	$0.552881\pi$
$642$	9.05955	0.357552
$643$	−10.4315	−0.411377	−0.205688	−	0.978618i	$-0.565943\pi$
$643$	−10.4315	−0.411377	−0.205688	+	0.978618i	$0.565943\pi$
$644$	−22.0719	−0.869753
$645$	19.1291	0.753209
$646$	6.16634	0.242611
$647$	−28.8030	−1.13236	−0.566181	−	0.824281i	$-0.691580\pi$
$647$	−28.8030	−1.13236	−0.566181	+	0.824281i	$0.691580\pi$
$648$	−7.87228	−0.309253
$649$	10.2133	0.400906
$650$	−114.482	−4.49034
$651$	−3.10452	−0.121676
$652$	−14.0028	−0.548391
$653$	8.71419	0.341013	0.170506	−	0.985357i	$-0.445460\pi$
$653$	8.71419	0.341013	0.170506	+	0.985357i	$0.445460\pi$
$654$	−12.4423	−0.486532
$655$	−23.3143	−0.910966
$656$	104.839	4.09326
$657$	−5.53507	−0.215944
$658$	26.7489	1.04278
$659$	−29.3077	−1.14167	−0.570833	−	0.821066i	$-0.693380\pi$
$659$	−29.3077	−1.14167	−0.570833	+	0.821066i	$0.693380\pi$
$660$	−22.5708	−0.878567
$661$	31.2205	1.21434	0.607168	−	0.794573i	$-0.292305\pi$
$661$	31.2205	1.21434	0.607168	+	0.794573i	$0.292305\pi$
$662$	−61.0306	−2.37202
$663$	−12.3971	−0.481462
$664$	−39.1571	−1.51959
$665$	−3.89892	−0.151194
$666$	3.00845	0.116575
$667$	7.53527	0.291767
$668$	89.2954	3.45494
$669$	13.4506	0.520030
$670$	23.8637	0.921934
$671$	−9.06390	−0.349908
$672$	−12.8898	−0.497235
$673$	−2.56016	−0.0986871	−0.0493435	−	0.998782i	$-0.515713\pi$
$673$	−2.56016	−0.0986871	−0.0493435	+	0.998782i	$0.515713\pi$
$674$	70.9326	2.73222
$675$	7.35495	0.283092
$676$	108.117	4.15835
$677$	−49.4263	−1.89961	−0.949804	−	0.312845i	$-0.898718\pi$
$677$	−49.4263	−1.89961	−0.949804	+	0.312845i	$0.898718\pi$
$678$	−46.9793	−1.80423
$679$	−14.7726	−0.566921
$680$	−58.2244	−2.23280
$681$	−20.4222	−0.782579
$682$	10.5763	0.404987
$683$	−47.5397	−1.81905	−0.909527	−	0.415644i	$-0.863556\pi$
$683$	−47.5397	−1.81905	−0.909527	+	0.415644i	$0.863556\pi$
$684$	5.52372	0.211205
$685$	−62.3224	−2.38122
$686$	−2.64192	−0.100869
$687$	−10.3366	−0.394367
$688$	−58.9851	−2.24879
$689$	32.6065	1.24221
$690$	−41.1596	−1.56692
$691$	−16.1605	−0.614773	−0.307386	−	0.951585i	$-0.599454\pi$
$691$	−16.1605	−0.614773	−0.307386	+	0.951585i	$0.599454\pi$
$692$	−33.4324	−1.27091
$693$	1.28949	0.0489837
$694$	57.9319	2.19906
$695$	−45.2112	−1.71496
$696$	13.3835	0.507299
$697$	−20.3534	−0.770941
$698$	20.3959	0.771998
$699$	6.13917	0.232205
$700$	36.6259	1.38433
$701$	−2.04472	−0.0772279	−0.0386139	−	0.999254i	$-0.512294\pi$
$701$	−2.04472	−0.0772279	−0.0386139	+	0.999254i	$0.512294\pi$
$702$	−15.5652	−0.587472
$703$	−1.26312	−0.0476396
$704$	15.9599	0.601513
$705$	35.5883	1.34033
$706$	10.4590	0.393631
$707$	−7.46115	−0.280605
$708$	39.4416	1.48231
$709$	−0.311043	−0.0116814	−0.00584072	−	0.999983i	$-0.501859\pi$
$709$	−0.311043	−0.0116814	−0.00584072	+	0.999983i	$0.501859\pi$
$710$	−51.3514	−1.92719
$711$	−7.22866	−0.271096
$712$	34.6175	1.29734
$713$	13.7602	0.515324
$714$	5.55909	0.208044
$715$	−26.7039	−0.998669
$716$	10.8429	0.405219
$717$	−16.5983	−0.619875
$718$	−80.7100	−3.01207
$719$	19.0394	0.710048	0.355024	−	0.934857i	$-0.384473\pi$
$719$	19.0394	0.710048	0.355024	+	0.934857i	$0.384473\pi$
$720$	−38.0968	−1.41978
$721$	−16.0861	−0.599076
$722$	46.9459	1.74715
$723$	−13.0171	−0.484110
$724$	74.5368	2.77014
$725$	−12.5040	−0.464386
$726$	24.6682	0.915523
$727$	−42.5362	−1.57758	−0.788790	−	0.614663i	$-0.789292\pi$
$727$	−42.5362	−1.57758	−0.788790	+	0.614663i	$0.789292\pi$
$728$	−46.3806	−1.71898
$729$	1.00000	0.0370370
$730$	−51.4001	−1.90240
$731$	11.4514	0.423545
$732$	−35.0029	−1.29375
$733$	20.6489	0.762685	0.381343	−	0.924434i	$-0.375462\pi$
$733$	20.6489	0.762685	0.381343	+	0.924434i	$0.375462\pi$
$734$	61.5729	2.27270
$735$	−3.51496	−0.129651
$736$	57.1316	2.10590
$737$	3.31371	0.122062
$738$	−25.5549	−0.940689
$739$	−1.08028	−0.0397387	−0.0198694	−	0.999803i	$-0.506325\pi$
$739$	−1.08028	−0.0397387	−0.0198694	+	0.999803i	$0.506325\pi$
$740$	19.9320	0.732714
$741$	6.53520	0.240077
$742$	−14.6214	−0.536768
$743$	38.3662	1.40752	0.703759	−	0.710438i	$-0.251503\pi$
$743$	38.3662	1.40752	0.703759	+	0.710438i	$0.251503\pi$
$744$	24.4397	0.896002
$745$	83.4601	3.05774
$746$	32.9163	1.20515
$747$	4.97404	0.181991
$748$	−13.5117	−0.494037
$749$	−3.42915	−0.125298
$750$	21.8687	0.798532
$751$	20.3533	0.742702	0.371351	−	0.928493i	$-0.378895\pi$
$751$	20.3533	0.742702	0.371351	+	0.928493i	$0.378895\pi$
$752$	−109.737	−4.00170
$753$	−4.81832	−0.175589
$754$	26.4621	0.963691
$755$	−49.8629	−1.81470
$756$	4.97976	0.181112
$757$	−8.06546	−0.293144	−0.146572	−	0.989200i	$-0.546824\pi$
$757$	−8.06546	−0.293144	−0.146572	+	0.989200i	$0.546824\pi$
$758$	−71.2708	−2.58867
$759$	−5.71543	−0.207457
$760$	30.6934	1.11337
$761$	16.5743	0.600816	0.300408	−	0.953811i	$-0.402877\pi$
$761$	16.5743	0.600816	0.300408	+	0.953811i	$0.402877\pi$
$762$	32.9990	1.19543
$763$	4.70956	0.170498
$764$	51.2653	1.85471
$765$	7.39612	0.267407
$766$	2.64192	0.0954565
$767$	46.6640	1.68494
$768$	−6.47361	−0.233596
$769$	−39.0975	−1.40989	−0.704946	−	0.709261i	$-0.749029\pi$
$769$	−39.0975	−1.40989	−0.704946	+	0.709261i	$0.749029\pi$
$770$	11.9745	0.431533
$771$	25.7406	0.927026
$772$	−55.1214	−1.98386
$773$	25.9528	0.933459	0.466729	−	0.884400i	$-0.345432\pi$
$773$	25.9528	0.933459	0.466729	+	0.884400i	$0.345432\pi$
$774$	14.3779	0.516803
$775$	−22.8336	−0.820208
$776$	116.294	4.17472
$777$	−1.13873	−0.0408518
$778$	74.5566	2.67298
$779$	10.7295	0.384423
$780$	−103.125	−3.69247
$781$	−7.13067	−0.255155
$782$	−24.6396	−0.881112
$783$	−1.70007	−0.0607557
$784$	10.8385	0.387088
$785$	62.6930	2.23761
$786$	−17.5236	−0.625044
$787$	−3.63958	−0.129737	−0.0648685	−	0.997894i	$-0.520663\pi$
$787$	−3.63958	−0.129737	−0.0648685	+	0.997894i	$0.520663\pi$
$788$	8.80341	0.313609
$789$	−13.7283	−0.488741
$790$	−67.1272	−2.38828
$791$	17.7823	0.632264
$792$	−10.1512	−0.360709
$793$	−41.4125	−1.47060
$794$	−50.3302	−1.78615
$795$	−19.4531	−0.689930
$796$	64.7998	2.29677
$797$	−19.8878	−0.704462	−0.352231	−	0.935913i	$-0.614577\pi$
$797$	−19.8878	−0.704462	−0.352231	+	0.935913i	$0.614577\pi$
$798$	−2.93051	−0.103739
$799$	21.3044	0.753696
$800$	−94.8038	−3.35182
$801$	−4.39739	−0.155374
$802$	−7.23491	−0.255473
$803$	−7.13742	−0.251874
$804$	12.7969	0.451311
$805$	15.5794	0.549103
$806$	48.3226	1.70209
$807$	13.3467	0.469827
$808$	58.7363	2.06634
$809$	−27.6811	−0.973216	−0.486608	−	0.873620i	$-0.661766\pi$
$809$	−27.6811	−0.973216	−0.486608	+	0.873620i	$0.661766\pi$
$810$	9.28626	0.326286
$811$	12.6457	0.444050	0.222025	−	0.975041i	$-0.428733\pi$
$811$	12.6457	0.444050	0.222025	+	0.975041i	$0.428733\pi$
$812$	−8.46596	−0.297097
$813$	−5.60590	−0.196608
$814$	3.87936	0.135972
$815$	9.88386	0.346217
$816$	−22.8061	−0.798373
$817$	−6.03669	−0.211197
$818$	−62.5467	−2.18689
$819$	5.89163	0.205870
$820$	−169.310	−5.91256
$821$	24.1769	0.843779	0.421889	−	0.906647i	$-0.361367\pi$
$821$	24.1769	0.843779	0.421889	+	0.906647i	$0.361367\pi$
$822$	−46.8429	−1.63383
$823$	−2.49240	−0.0868796	−0.0434398	−	0.999056i	$-0.513832\pi$
$823$	−2.49240	−0.0868796	−0.0434398	+	0.999056i	$0.513832\pi$
$824$	126.634	4.41151
$825$	9.48415	0.330196
$826$	−20.9251	−0.728076
$827$	−30.2439	−1.05168	−0.525842	−	0.850582i	$-0.676250\pi$
$827$	−30.2439	−1.05168	−0.525842	+	0.850582i	$0.676250\pi$
$828$	−22.0719	−0.767050
$829$	−7.21525	−0.250596	−0.125298	−	0.992119i	$-0.539989\pi$
$829$	−7.21525	−0.250596	−0.125298	+	0.992119i	$0.539989\pi$
$830$	46.1902	1.60329
$831$	22.6286	0.784977
$832$	72.9203	2.52806
$833$	−2.10418	−0.0729056
$834$	−33.9817	−1.17669
$835$	−63.0292	−2.18122
$836$	7.12279	0.246347
$837$	−3.10452	−0.107308
$838$	16.3169	0.563659
$839$	−38.9318	−1.34407	−0.672037	−	0.740518i	$-0.734580\pi$
$839$	−38.9318	−1.34407	−0.672037	+	0.740518i	$0.734580\pi$
$840$	27.6708	0.954732
$841$	−26.1097	−0.900336
$842$	−63.6753	−2.19439
$843$	−19.3365	−0.665985
$844$	−0.161817	−0.00556998
$845$	−76.3144	−2.62530
$846$	26.7489	0.919647
$847$	−9.33721	−0.320830
$848$	59.9840	2.05986
$849$	12.1382	0.416583
$850$	40.8868	1.40241
$851$	5.04723	0.173017
$852$	−27.5372	−0.943409
$853$	10.8008	0.369813	0.184906	−	0.982756i	$-0.440802\pi$
$853$	10.8008	0.369813	0.184906	+	0.982756i	$0.440802\pi$
$854$	18.5702	0.635459
$855$	−3.89892	−0.133340
$856$	26.9953	0.922679
$857$	−51.6125	−1.76305	−0.881524	−	0.472138i	$-0.843482\pi$
$857$	−51.6125	−1.76305	−0.881524	+	0.472138i	$0.843482\pi$
$858$	−20.0712	−0.685221
$859$	−26.7990	−0.914370	−0.457185	−	0.889372i	$-0.651142\pi$
$859$	−26.7990	−0.914370	−0.457185	+	0.889372i	$0.651142\pi$
$860$	95.2585	3.24829
$861$	9.67284	0.329650
$862$	20.5382	0.699535
$863$	7.13169	0.242765	0.121383	−	0.992606i	$-0.461267\pi$
$863$	7.13169	0.242765	0.121383	+	0.992606i	$0.461267\pi$
$864$	−12.8898	−0.438520
$865$	23.5982	0.802364
$866$	50.0839	1.70192
$867$	−12.5724	−0.426982
$868$	−15.4598	−0.524738
$869$	−9.32130	−0.316203
$870$	−15.7873	−0.535241
$871$	15.1402	0.513006
$872$	−37.0750	−1.25552
$873$	−14.7726	−0.499977
$874$	12.9890	0.439358
$875$	−8.27757	−0.279833
$876$	−27.5633	−0.931277
$877$	43.4421	1.46694	0.733468	−	0.679724i	$-0.237900\pi$
$877$	43.4421	1.46694	0.733468	+	0.679724i	$0.237900\pi$
$878$	−26.4737	−0.893445
$879$	−11.2348	−0.378940
$880$	−49.1254	−1.65602
$881$	−51.4156	−1.73224	−0.866118	−	0.499839i	$-0.833393\pi$
$881$	−51.4156	−1.73224	−0.866118	+	0.499839i	$0.833393\pi$
$882$	−2.64192	−0.0889582
$883$	−48.2607	−1.62410	−0.812051	−	0.583587i	$-0.801649\pi$
$883$	−48.2607	−1.62410	−0.812051	+	0.583587i	$0.801649\pi$
$884$	−61.7344	−2.07635
$885$	−27.8399	−0.935827
$886$	−103.979	−3.49325
$887$	2.13813	0.0717913	0.0358957	−	0.999356i	$-0.488572\pi$
$887$	2.13813	0.0717913	0.0358957	+	0.999356i	$0.488572\pi$
$888$	8.96443	0.300827
$889$	−12.4905	−0.418919
$890$	−40.8353	−1.36880
$891$	1.28949	0.0431996
$892$	66.9806	2.24268
$893$	−11.2308	−0.375824
$894$	62.7305	2.09802
$895$	−7.65347	−0.255827
$896$	−6.91929	−0.231157
$897$	−26.1136	−0.871907
$898$	−49.3714	−1.64754
$899$	5.27792	0.176028
$900$	36.6259	1.22086
$901$	−11.6453	−0.387962
$902$	−32.9528	−1.09721
$903$	−5.44221	−0.181105
$904$	−139.987	−4.65590
$905$	−52.6118	−1.74888
$906$	−37.4781	−1.24512
$907$	−40.3559	−1.34000	−0.669998	−	0.742363i	$-0.733705\pi$
$907$	−40.3559	−1.34000	−0.669998	+	0.742363i	$0.733705\pi$
$908$	−101.697	−3.37495
$909$	−7.46115	−0.247471
$910$	54.7112	1.81366
$911$	−34.3285	−1.13735	−0.568677	−	0.822561i	$-0.692545\pi$
$911$	−34.3285	−1.13735	−0.568677	+	0.822561i	$0.692545\pi$
$912$	12.0224	0.398101
$913$	6.41398	0.212272
$914$	−12.1089	−0.400527
$915$	24.7068	0.816783
$916$	−51.4738	−1.70074
$917$	6.63288	0.219037
$918$	5.55909	0.183477
$919$	16.5796	0.546911	0.273455	−	0.961885i	$-0.411833\pi$
$919$	16.5796	0.546911	0.273455	+	0.961885i	$0.411833\pi$
$920$	−122.646	−4.04351
$921$	3.98518	0.131316
$922$	33.4983	1.10321
$923$	−32.5797	−1.07237
$924$	6.42135	0.211247
$925$	−8.37533	−0.275379
$926$	38.4937	1.26498
$927$	−16.0861	−0.528335
$928$	21.9136	0.719349
$929$	23.1296	0.758859	0.379429	−	0.925221i	$-0.376120\pi$
$929$	23.1296	0.758859	0.379429	+	0.925221i	$0.376120\pi$
$930$	−28.8294	−0.945353
$931$	1.10923	0.0363537
$932$	30.5715	1.00140
$933$	−2.20731	−0.0722642
$934$	44.0476	1.44128
$935$	9.53724	0.311901
$936$	−46.3806	−1.51600
$937$	0.109188	0.00356701	0.00178351	−	0.999998i	$-0.499432\pi$
$937$	0.109188	0.00356701	0.00178351	+	0.999998i	$0.499432\pi$
$938$	−6.78917	−0.221674
$939$	−9.11179	−0.297352
$940$	177.221	5.78031
$941$	4.48259	0.146128	0.0730641	−	0.997327i	$-0.476722\pi$
$941$	4.48259	0.146128	0.0730641	+	0.997327i	$0.476722\pi$
$942$	47.1214	1.53530
$943$	−42.8731	−1.39614
$944$	85.8448	2.79401
$945$	−3.51496	−0.114342
$946$	18.5402	0.602793
$947$	−39.9168	−1.29712	−0.648560	−	0.761163i	$-0.724629\pi$
$947$	−39.9168	−1.29712	−0.648560	+	0.761163i	$0.724629\pi$
$948$	−35.9970	−1.16913
$949$	−32.6106	−1.05858
$950$	−21.5538	−0.699297
$951$	−8.49619	−0.275508
$952$	16.5647	0.536866
$953$	44.9002	1.45446	0.727231	−	0.686393i	$-0.240807\pi$
$953$	44.9002	1.45446	0.727231	+	0.686393i	$0.240807\pi$
$954$	−14.6214	−0.473385
$955$	−36.1856	−1.17094
$956$	−82.6554	−2.67327
$957$	−2.19223	−0.0708648
$958$	53.9542	1.74318
$959$	17.7306	0.572551
$960$	−43.5044	−1.40410
$961$	−21.3619	−0.689095
$962$	17.7246	0.571466
$963$	−3.42915	−0.110503
$964$	−64.8218	−2.08777
$965$	38.9074	1.25247
$966$	11.7098	0.376758
$967$	−39.1925	−1.26035	−0.630173	−	0.776455i	$-0.717016\pi$
$967$	−39.1925	−1.26035	−0.630173	+	0.776455i	$0.717016\pi$
$968$	73.5052	2.36255
$969$	−2.33403	−0.0749799
$970$	−137.182	−4.40466
$971$	36.9040	1.18431	0.592153	−	0.805826i	$-0.298278\pi$
$971$	36.9040	1.18431	0.592153	+	0.805826i	$0.298278\pi$
$972$	4.97976	0.159726
$973$	12.8625	0.412352
$974$	63.7585	2.04295
$975$	43.3327	1.38776
$976$	−76.1840	−2.43859
$977$	−14.3412	−0.458815	−0.229408	−	0.973330i	$-0.573679\pi$
$977$	−14.3412	−0.458815	−0.229408	+	0.973330i	$0.573679\pi$
$978$	7.42893	0.237551
$979$	−5.67039	−0.181226
$980$	−17.5036	−0.559134
$981$	4.70956	0.150365
$982$	33.2844	1.06215
$983$	46.0561	1.46896	0.734480	−	0.678630i	$-0.237426\pi$
$983$	46.0561	1.46896	0.734480	+	0.678630i	$0.237426\pi$
$984$	−76.1474	−2.42749
$985$	−6.21389	−0.197991
$986$	−9.45087	−0.300977
$987$	−10.1248	−0.322276
$988$	32.5437	1.03535
$989$	24.1216	0.767022
$990$	11.9745	0.380576
$991$	−39.1482	−1.24358	−0.621791	−	0.783183i	$-0.713595\pi$
$991$	−39.1482	−1.24358	−0.621791	+	0.783183i	$0.713595\pi$
$992$	40.0166	1.27053
$993$	23.1008	0.733082
$994$	14.6094	0.463382
$995$	−45.7390	−1.45002
$996$	24.7695	0.784852
$997$	−47.5117	−1.50471	−0.752355	−	0.658758i	$-0.771082\pi$
$997$	−47.5117	−1.50471	−0.752355	+	0.658758i	$0.771082\pi$
$998$	−48.4264	−1.53291
$999$	−1.13873	−0.0360279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.n.1.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.n.1.3	✓	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64192 q^{2} +1.00000 q^{3} +4.97976 q^{4} -3.51496 q^{5} -2.64192 q^{6} +1.00000 q^{7} -7.87228 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.64192 q^{2} +1.00000 q^{3} +4.97976 q^{4} -3.51496 q^{5} -2.64192 q^{6} +1.00000 q^{7} -7.87228 q^{8} +1.00000 q^{9} +9.28626 q^{10} +1.28949 q^{11} +4.97976 q^{12} +5.89163 q^{13} -2.64192 q^{14} -3.51496 q^{15} +10.8385 q^{16} -2.10418 q^{17} -2.64192 q^{18} +1.10923 q^{19} -17.5036 q^{20} +1.00000 q^{21} -3.40674 q^{22} -4.43232 q^{23} -7.87228 q^{24} +7.35495 q^{25} -15.5652 q^{26} +1.00000 q^{27} +4.97976 q^{28} -1.70007 q^{29} +9.28626 q^{30} -3.10452 q^{31} -12.8898 q^{32} +1.28949 q^{33} +5.55909 q^{34} -3.51496 q^{35} +4.97976 q^{36} -1.13873 q^{37} -2.93051 q^{38} +5.89163 q^{39} +27.6708 q^{40} +9.67284 q^{41} -2.64192 q^{42} -5.44221 q^{43} +6.42135 q^{44} -3.51496 q^{45} +11.7098 q^{46} -10.1248 q^{47} +10.8385 q^{48} +1.00000 q^{49} -19.4312 q^{50} -2.10418 q^{51} +29.3389 q^{52} +5.53437 q^{53} -2.64192 q^{54} -4.53251 q^{55} -7.87228 q^{56} +1.10923 q^{57} +4.49147 q^{58} +7.92039 q^{59} -17.5036 q^{60} -7.02905 q^{61} +8.20191 q^{62} +1.00000 q^{63} +12.3769 q^{64} -20.7089 q^{65} -3.40674 q^{66} +2.56978 q^{67} -10.4783 q^{68} -4.43232 q^{69} +9.28626 q^{70} -5.52983 q^{71} -7.87228 q^{72} -5.53507 q^{73} +3.00845 q^{74} +7.35495 q^{75} +5.52372 q^{76} +1.28949 q^{77} -15.5652 q^{78} -7.22866 q^{79} -38.0968 q^{80} +1.00000 q^{81} -25.5549 q^{82} +4.97404 q^{83} +4.97976 q^{84} +7.39612 q^{85} +14.3779 q^{86} -1.70007 q^{87} -10.1512 q^{88} -4.39739 q^{89} +9.28626 q^{90} +5.89163 q^{91} -22.0719 q^{92} -3.10452 q^{93} +26.7489 q^{94} -3.89892 q^{95} -12.8898 q^{96} -14.7726 q^{97} -2.64192 q^{98} +1.28949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9} - 14 q^{10} - 29 q^{11} + 33 q^{12} - 40 q^{13} - 9 q^{14} - 27 q^{15} + 23 q^{16} - 46 q^{17} - 9 q^{18} + 17 q^{19} - 53 q^{20} + 40 q^{21} - 15 q^{22} - 62 q^{23} - 18 q^{24} + 35 q^{25} - 29 q^{26} + 40 q^{27} + 33 q^{28} - 47 q^{29} - 14 q^{30} + q^{31} - 45 q^{32} - 29 q^{33} + 9 q^{34} - 27 q^{35} + 33 q^{36} - 49 q^{37} - 52 q^{38} - 40 q^{39} - 12 q^{40} - 49 q^{41} - 9 q^{42} - 45 q^{43} - 68 q^{44} - 27 q^{45} - 36 q^{46} - 88 q^{47} + 23 q^{48} + 40 q^{49} - 32 q^{50} - 46 q^{51} - 34 q^{52} - 96 q^{53} - 9 q^{54} + 26 q^{55} - 18 q^{56} + 17 q^{57} + 12 q^{58} - 45 q^{59} - 53 q^{60} - 23 q^{61} - 15 q^{62} + 40 q^{63} + 50 q^{64} - 32 q^{65} - 15 q^{66} - 31 q^{67} - 76 q^{68} - 62 q^{69} - 14 q^{70} - 89 q^{71} - 18 q^{72} + 4 q^{73} + 10 q^{74} + 35 q^{75} + 51 q^{76} - 29 q^{77} - 29 q^{78} - 44 q^{79} - 53 q^{80} + 40 q^{81} - 15 q^{82} - 60 q^{83} + 33 q^{84} - 24 q^{85} - 9 q^{86} - 47 q^{87} - 64 q^{88} - 39 q^{89} - 14 q^{90} - 40 q^{91} - 80 q^{92} + q^{93} + 51 q^{94} - 71 q^{95} - 45 q^{96} - 21 q^{97} - 9 q^{98} - 29 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9 - 14 * q^10 - 29 * q^11 + 33 * q^12 - 40 * q^13 - 9 * q^14 - 27 * q^15 + 23 * q^16 - 46 * q^17 - 9 * q^18 + 17 * q^19 - 53 * q^20 + 40 * q^21 - 15 * q^22 - 62 * q^23 - 18 * q^24 + 35 * q^25 - 29 * q^26 + 40 * q^27 + 33 * q^28 - 47 * q^29 - 14 * q^30 + q^31 - 45 * q^32 - 29 * q^33 + 9 * q^34 - 27 * q^35 + 33 * q^36 - 49 * q^37 - 52 * q^38 - 40 * q^39 - 12 * q^40 - 49 * q^41 - 9 * q^42 - 45 * q^43 - 68 * q^44 - 27 * q^45 - 36 * q^46 - 88 * q^47 + 23 * q^48 + 40 * q^49 - 32 * q^50 - 46 * q^51 - 34 * q^52 - 96 * q^53 - 9 * q^54 + 26 * q^55 - 18 * q^56 + 17 * q^57 + 12 * q^58 - 45 * q^59 - 53 * q^60 - 23 * q^61 - 15 * q^62 + 40 * q^63 + 50 * q^64 - 32 * q^65 - 15 * q^66 - 31 * q^67 - 76 * q^68 - 62 * q^69 - 14 * q^70 - 89 * q^71 - 18 * q^72 + 4 * q^73 + 10 * q^74 + 35 * q^75 + 51 * q^76 - 29 * q^77 - 29 * q^78 - 44 * q^79 - 53 * q^80 + 40 * q^81 - 15 * q^82 - 60 * q^83 + 33 * q^84 - 24 * q^85 - 9 * q^86 - 47 * q^87 - 64 * q^88 - 39 * q^89 - 14 * q^90 - 40 * q^91 - 80 * q^92 + q^93 + 51 * q^94 - 71 * q^95 - 45 * q^96 - 21 * q^97 - 9 * q^98 - 29 * q^99

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