LMFDB - Embedded newform 8041.2.a.e.1.54

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.54
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.96888 q^{2} +1.61944 q^{3} +1.87650 q^{4} -3.83812 q^{5} +3.18848 q^{6} -3.91179 q^{7} -0.243166 q^{8} -0.377424 q^{9} +O(q^{10})$	\(q+1.96888 q^{2} +1.61944 q^{3} +1.87650 q^{4} -3.83812 q^{5} +3.18848 q^{6} -3.91179 q^{7} -0.243166 q^{8} -0.377424 q^{9} -7.55680 q^{10} -1.00000 q^{11} +3.03887 q^{12} +2.57797 q^{13} -7.70186 q^{14} -6.21559 q^{15} -4.23176 q^{16} -1.00000 q^{17} -0.743104 q^{18} -1.27289 q^{19} -7.20221 q^{20} -6.33490 q^{21} -1.96888 q^{22} +7.53997 q^{23} -0.393792 q^{24} +9.73115 q^{25} +5.07572 q^{26} -5.46953 q^{27} -7.34046 q^{28} -5.97062 q^{29} -12.2378 q^{30} +6.22817 q^{31} -7.84550 q^{32} -1.61944 q^{33} -1.96888 q^{34} +15.0139 q^{35} -0.708235 q^{36} +4.52604 q^{37} -2.50617 q^{38} +4.17486 q^{39} +0.933299 q^{40} +2.61836 q^{41} -12.4727 q^{42} +1.00000 q^{43} -1.87650 q^{44} +1.44860 q^{45} +14.8453 q^{46} +8.63444 q^{47} -6.85306 q^{48} +8.30214 q^{49} +19.1595 q^{50} -1.61944 q^{51} +4.83755 q^{52} -6.24126 q^{53} -10.7688 q^{54} +3.83812 q^{55} +0.951214 q^{56} -2.06136 q^{57} -11.7554 q^{58} -3.36557 q^{59} -11.6635 q^{60} +3.10686 q^{61} +12.2625 q^{62} +1.47641 q^{63} -6.98334 q^{64} -9.89456 q^{65} -3.18848 q^{66} -7.73232 q^{67} -1.87650 q^{68} +12.2105 q^{69} +29.5606 q^{70} +3.13446 q^{71} +0.0917767 q^{72} +5.24564 q^{73} +8.91124 q^{74} +15.7590 q^{75} -2.38857 q^{76} +3.91179 q^{77} +8.21981 q^{78} -3.29700 q^{79} +16.2420 q^{80} -7.72528 q^{81} +5.15523 q^{82} +4.51577 q^{83} -11.8874 q^{84} +3.83812 q^{85} +1.96888 q^{86} -9.66904 q^{87} +0.243166 q^{88} +2.26289 q^{89} +2.85212 q^{90} -10.0845 q^{91} +14.1487 q^{92} +10.0861 q^{93} +17.0002 q^{94} +4.88550 q^{95} -12.7053 q^{96} +10.4697 q^{97} +16.3459 q^{98} +0.377424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * 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 $

$2$	1.96888	1.39221	0.696105	−	0.717940i	$-0.254915\pi$
$2$	1.96888	1.39221	0.696105	+	0.717940i	$0.254915\pi$
$3$	1.61944	0.934982	0.467491	−	0.883998i	$-0.345158\pi$
$3$	1.61944	0.934982	0.467491	+	0.883998i	$0.345158\pi$
$4$	1.87650	0.938248
$5$	−3.83812	−1.71646	−0.858229	−	0.513267i	$-0.828435\pi$
$5$	−3.83812	−1.71646	−0.858229	+	0.513267i	$0.828435\pi$
$6$	3.18848	1.30169
$7$	−3.91179	−1.47852	−0.739260	−	0.673420i	$-0.764824\pi$
$7$	−3.91179	−1.47852	−0.739260	+	0.673420i	$0.764824\pi$
$8$	−0.243166	−0.0859721
$9$	−0.377424	−0.125808
$10$	−7.55680	−2.38967
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.03887	0.877245
$13$	2.57797	0.715001	0.357500	−	0.933913i	$-0.383629\pi$
$13$	2.57797	0.715001	0.357500	+	0.933913i	$0.383629\pi$
$14$	−7.70186	−2.05841
$15$	−6.21559	−1.60486
$16$	−4.23176	−1.05794
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.743104	−0.175151
$19$	−1.27289	−0.292021	−0.146010	−	0.989283i	$-0.546643\pi$
$19$	−1.27289	−0.292021	−0.146010	+	0.989283i	$0.546643\pi$
$20$	−7.20221	−1.61046
$21$	−6.33490	−1.38239
$22$	−1.96888	−0.419767
$23$	7.53997	1.57219	0.786096	−	0.618105i	$-0.212099\pi$
$23$	7.53997	1.57219	0.786096	+	0.618105i	$0.212099\pi$
$24$	−0.393792	−0.0803824
$25$	9.73115	1.94623
$26$	5.07572	0.995431
$27$	−5.46953	−1.05261
$28$	−7.34046	−1.38722
$29$	−5.97062	−1.10872	−0.554358	−	0.832278i	$-0.687036\pi$
$29$	−5.97062	−1.10872	−0.554358	+	0.832278i	$0.687036\pi$
$30$	−12.2378	−2.23430
$31$	6.22817	1.11861	0.559306	−	0.828961i	$-0.311068\pi$
$31$	6.22817	1.11861	0.559306	+	0.828961i	$0.311068\pi$
$32$	−7.84550	−1.38690
$33$	−1.61944	−0.281908
$34$	−1.96888	−0.337660
$35$	15.0139	2.53782
$36$	−0.708235	−0.118039
$37$	4.52604	0.744077	0.372038	−	0.928217i	$-0.378659\pi$
$37$	4.52604	0.744077	0.372038	+	0.928217i	$0.378659\pi$
$38$	−2.50617	−0.406554
$39$	4.17486	0.668513
$40$	0.933299	0.147567
$41$	2.61836	0.408918	0.204459	−	0.978875i	$-0.434456\pi$
$41$	2.61836	0.408918	0.204459	+	0.978875i	$0.434456\pi$
$42$	−12.4727	−1.92458
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.87650	−0.282892
$45$	1.44860	0.215944
$46$	14.8453	2.18882
$47$	8.63444	1.25946	0.629732	−	0.776813i	$-0.283165\pi$
$47$	8.63444	1.25946	0.629732	+	0.776813i	$0.283165\pi$
$48$	−6.85306	−0.989154
$49$	8.30214	1.18602
$50$	19.1595	2.70956
$51$	−1.61944	−0.226767
$52$	4.83755	0.670848
$53$	−6.24126	−0.857302	−0.428651	−	0.903470i	$-0.641011\pi$
$53$	−6.24126	−0.857302	−0.428651	+	0.903470i	$0.641011\pi$
$54$	−10.7688	−1.46545
$55$	3.83812	0.517532
$56$	0.951214	0.127111
$57$	−2.06136	−0.273034
$58$	−11.7554	−1.54357
$59$	−3.36557	−0.438161	−0.219080	−	0.975707i	$-0.570306\pi$
$59$	−3.36557	−0.438161	−0.219080	+	0.975707i	$0.570306\pi$
$60$	−11.6635	−1.50575
$61$	3.10686	0.397792	0.198896	−	0.980021i	$-0.436264\pi$
$61$	3.10686	0.397792	0.198896	+	0.980021i	$0.436264\pi$
$62$	12.2625	1.55734
$63$	1.47641	0.186010
$64$	−6.98334	−0.872918
$65$	−9.89456	−1.22727
$66$	−3.18848	−0.392475
$67$	−7.73232	−0.944653	−0.472326	−	0.881424i	$-0.656586\pi$
$67$	−7.73232	−0.944653	−0.472326	+	0.881424i	$0.656586\pi$
$68$	−1.87650	−0.227559
$69$	12.2105	1.46997
$70$	29.5606	3.53317
$71$	3.13446	0.371992	0.185996	−	0.982551i	$-0.440449\pi$
$71$	3.13446	0.371992	0.185996	+	0.982551i	$0.440449\pi$
$72$	0.0917767	0.0108160
$73$	5.24564	0.613955	0.306978	−	0.951717i	$-0.400682\pi$
$73$	5.24564	0.613955	0.306978	+	0.951717i	$0.400682\pi$
$74$	8.91124	1.03591
$75$	15.7590	1.81969
$76$	−2.38857	−0.273988
$77$	3.91179	0.445790
$78$	8.21981	0.930710
$79$	−3.29700	−0.370942	−0.185471	−	0.982650i	$-0.559381\pi$
$79$	−3.29700	−0.370942	−0.185471	+	0.982650i	$0.559381\pi$
$80$	16.2420	1.81591
$81$	−7.72528	−0.858364
$82$	5.15523	0.569300
$83$	4.51577	0.495671	0.247835	−	0.968802i	$-0.420281\pi$
$83$	4.51577	0.495671	0.247835	+	0.968802i	$0.420281\pi$
$84$	−11.8874	−1.29702
$85$	3.83812	0.416302
$86$	1.96888	0.212310
$87$	−9.66904	−1.03663
$88$	0.243166	0.0259216
$89$	2.26289	0.239866	0.119933	−	0.992782i	$-0.461732\pi$
$89$	2.26289	0.239866	0.119933	+	0.992782i	$0.461732\pi$
$90$	2.85212	0.300640
$91$	−10.0845	−1.05714
$92$	14.1487	1.47511
$93$	10.0861	1.04588
$94$	17.0002	1.75344
$95$	4.88550	0.501242
$96$	−12.7053	−1.29673
$97$	10.4697	1.06303	0.531517	−	0.847048i	$-0.321622\pi$
$97$	10.4697	1.06303	0.531517	+	0.847048i	$0.321622\pi$
$98$	16.3459	1.65119
$99$	0.377424	0.0379326
$100$	18.2605	1.82605
$101$	−6.22545	−0.619455	−0.309727	−	0.950825i	$-0.600238\pi$
$101$	−6.22545	−0.619455	−0.309727	+	0.950825i	$0.600238\pi$
$102$	−3.18848	−0.315707
$103$	−2.39453	−0.235940	−0.117970	−	0.993017i	$-0.537639\pi$
$103$	−2.39453	−0.235940	−0.117970	+	0.993017i	$0.537639\pi$
$104$	−0.626874	−0.0614701
$105$	24.3141	2.37281
$106$	−12.2883	−1.19354
$107$	14.6190	1.41327	0.706635	−	0.707578i	$-0.250212\pi$
$107$	14.6190	1.41327	0.706635	+	0.707578i	$0.250212\pi$
$108$	−10.2635	−0.987610
$109$	−5.85099	−0.560424	−0.280212	−	0.959938i	$-0.590405\pi$
$109$	−5.85099	−0.560424	−0.280212	+	0.959938i	$0.590405\pi$
$110$	7.55680	0.720513
$111$	7.32964	0.695698
$112$	16.5538	1.56418
$113$	8.77547	0.825527	0.412763	−	0.910838i	$-0.364564\pi$
$113$	8.77547	0.825527	0.412763	+	0.910838i	$0.364564\pi$
$114$	−4.05858	−0.380121
$115$	−28.9393	−2.69860
$116$	−11.2038	−1.04025
$117$	−0.972989	−0.0899529
$118$	−6.62642	−0.610011
$119$	3.91179	0.358594
$120$	1.51142	0.137973
$121$	1.00000	0.0909091
$122$	6.11703	0.553810
$123$	4.24026	0.382332
$124$	11.6871	1.04954
$125$	−18.1587	−1.62416
$126$	2.90687	0.258965
$127$	17.3861	1.54277	0.771385	−	0.636368i	$-0.219564\pi$
$127$	17.3861	1.54277	0.771385	+	0.636368i	$0.219564\pi$
$128$	1.94162	0.171616
$129$	1.61944	0.142583
$130$	−19.4812	−1.70862
$131$	0.833988	0.0728659	0.0364330	−	0.999336i	$-0.488400\pi$
$131$	0.833988	0.0728659	0.0364330	+	0.999336i	$0.488400\pi$
$132$	−3.03887	−0.264499
$133$	4.97928	0.431759
$134$	−15.2240	−1.31515
$135$	20.9927	1.80676
$136$	0.243166	0.0208513
$137$	9.97582	0.852291	0.426146	−	0.904655i	$-0.359871\pi$
$137$	9.97582	0.852291	0.426146	+	0.904655i	$0.359871\pi$
$138$	24.0410	2.04651
$139$	16.8498	1.42919	0.714593	−	0.699541i	$-0.246612\pi$
$139$	16.8498	1.42919	0.714593	+	0.699541i	$0.246612\pi$
$140$	28.1736	2.38110
$141$	13.9829	1.17758
$142$	6.17138	0.517891
$143$	−2.57797	−0.215581
$144$	1.59717	0.133097
$145$	22.9159	1.90306
$146$	10.3280	0.854754
$147$	13.4448	1.10891
$148$	8.49310	0.698128
$149$	−7.22105	−0.591571	−0.295786	−	0.955254i	$-0.595581\pi$
$149$	−7.22105	−0.591571	−0.295786	+	0.955254i	$0.595581\pi$
$150$	31.0276	2.53339
$151$	−19.3773	−1.57690	−0.788452	−	0.615096i	$-0.789117\pi$
$151$	−19.3773	−1.57690	−0.788452	+	0.615096i	$0.789117\pi$
$152$	0.309523	0.0251056
$153$	0.377424	0.0305129
$154$	7.70186	0.620634
$155$	−23.9044	−1.92005
$156$	7.83411	0.627231
$157$	−1.65581	−0.132148	−0.0660740	−	0.997815i	$-0.521047\pi$
$157$	−1.65581	−0.132148	−0.0660740	+	0.997815i	$0.521047\pi$
$158$	−6.49141	−0.516429
$159$	−10.1073	−0.801563
$160$	30.1119	2.38056
$161$	−29.4948	−2.32452
$162$	−15.2102	−1.19502
$163$	−13.9451	−1.09227	−0.546133	−	0.837698i	$-0.683901\pi$
$163$	−13.9451	−1.09227	−0.546133	+	0.837698i	$0.683901\pi$
$164$	4.91333	0.383667
$165$	6.21559	0.483883
$166$	8.89103	0.690077
$167$	17.5635	1.35910	0.679551	−	0.733628i	$-0.262175\pi$
$167$	17.5635	1.35910	0.679551	+	0.733628i	$0.262175\pi$
$168$	1.54043	0.118847
$169$	−6.35406	−0.488774
$170$	7.55680	0.579580
$171$	0.480419	0.0367386
$172$	1.87650	0.143081
$173$	17.1313	1.30247	0.651234	−	0.758877i	$-0.274252\pi$
$173$	17.1313	1.30247	0.651234	+	0.758877i	$0.274252\pi$
$174$	−19.0372	−1.44321
$175$	−38.0662	−2.87754
$176$	4.23176	0.318981
$177$	−5.45034	−0.409672
$178$	4.45536	0.333943
$179$	10.6516	0.796140	0.398070	−	0.917355i	$-0.369680\pi$
$179$	10.6516	0.796140	0.398070	+	0.917355i	$0.369680\pi$
$180$	2.71829	0.202609
$181$	−11.7352	−0.872271	−0.436136	−	0.899881i	$-0.643653\pi$
$181$	−11.7352	−0.872271	−0.436136	+	0.899881i	$0.643653\pi$
$182$	−19.8552	−1.47176
$183$	5.03136	0.371929
$184$	−1.83346	−0.135165
$185$	−17.3715	−1.27718
$186$	19.8584	1.45609
$187$	1.00000	0.0731272
$188$	16.2025	1.18169
$189$	21.3957	1.55631
$190$	9.61897	0.697833
$191$	−10.1154	−0.731927	−0.365964	−	0.930629i	$-0.619261\pi$
$191$	−10.1154	−0.731927	−0.365964	+	0.930629i	$0.619261\pi$
$192$	−11.3091	−0.816163
$193$	24.1013	1.73485	0.867426	−	0.497565i	$-0.165773\pi$
$193$	24.1013	1.73485	0.867426	+	0.497565i	$0.165773\pi$
$194$	20.6135	1.47997
$195$	−16.0236	−1.14747
$196$	15.5789	1.11278
$197$	17.2994	1.23253	0.616265	−	0.787539i	$-0.288645\pi$
$197$	17.2994	1.23253	0.616265	+	0.787539i	$0.288645\pi$
$198$	0.743104	0.0528101
$199$	−19.7536	−1.40030	−0.700148	−	0.713998i	$-0.746883\pi$
$199$	−19.7536	−1.40030	−0.700148	+	0.713998i	$0.746883\pi$
$200$	−2.36628	−0.167321
$201$	−12.5220	−0.883234
$202$	−12.2572	−0.862411
$203$	23.3558	1.63926
$204$	−3.03887	−0.212763
$205$	−10.0496	−0.701891
$206$	−4.71455	−0.328478
$207$	−2.84577	−0.197794
$208$	−10.9093	−0.756427
$209$	1.27289	0.0880476
$210$	47.8716	3.30345
$211$	−15.0316	−1.03482	−0.517410	−	0.855738i	$-0.673104\pi$
$211$	−15.0316	−1.03482	−0.517410	+	0.855738i	$0.673104\pi$
$212$	−11.7117	−0.804362
$213$	5.07606	0.347806
$214$	28.7831	1.96757
$215$	−3.83812	−0.261757
$216$	1.33000	0.0904951
$217$	−24.3633	−1.65389
$218$	−11.5199	−0.780227
$219$	8.49498	0.574037
$220$	7.20221	0.485573
$221$	−2.57797	−0.173413
$222$	14.4312	0.968558
$223$	3.36888	0.225597	0.112798	−	0.993618i	$-0.464019\pi$
$223$	3.36888	0.225597	0.112798	+	0.993618i	$0.464019\pi$
$224$	30.6900	2.05056
$225$	−3.67277	−0.244851
$226$	17.2779	1.14931
$227$	−28.3451	−1.88133	−0.940666	−	0.339333i	$-0.889799\pi$
$227$	−28.3451	−1.88133	−0.940666	+	0.339333i	$0.889799\pi$
$228$	−3.86814	−0.256174
$229$	−18.3716	−1.21403	−0.607016	−	0.794690i	$-0.707634\pi$
$229$	−18.3716	−1.21403	−0.607016	+	0.794690i	$0.707634\pi$
$230$	−56.9780	−3.75702
$231$	6.33490	0.416806
$232$	1.45185	0.0953186
$233$	20.5184	1.34420	0.672101	−	0.740459i	$-0.265392\pi$
$233$	20.5184	1.34420	0.672101	+	0.740459i	$0.265392\pi$
$234$	−1.91570	−0.125233
$235$	−33.1400	−2.16182
$236$	−6.31549	−0.411103
$237$	−5.33929	−0.346824
$238$	7.70186	0.499237
$239$	19.0151	1.22998	0.614991	−	0.788534i	$-0.289160\pi$
$239$	19.0151	1.22998	0.614991	+	0.788534i	$0.289160\pi$
$240$	26.3029	1.69784
$241$	2.89324	0.186370	0.0931851	−	0.995649i	$-0.470295\pi$
$241$	2.89324	0.186370	0.0931851	+	0.995649i	$0.470295\pi$
$242$	1.96888	0.126565
$243$	3.89798	0.250055
$244$	5.83000	0.373228
$245$	−31.8646	−2.03575
$246$	8.34857	0.532286
$247$	−3.28147	−0.208795
$248$	−1.51448	−0.0961694
$249$	7.31301	0.463443
$250$	−35.7523	−2.26118
$251$	−23.3903	−1.47638	−0.738192	−	0.674591i	$-0.764320\pi$
$251$	−23.3903	−1.47638	−0.738192	+	0.674591i	$0.764320\pi$
$252$	2.77047	0.174523
$253$	−7.53997	−0.474034
$254$	34.2313	2.14786
$255$	6.21559	0.389235
$256$	17.7895	1.11184
$257$	−6.42673	−0.400888	−0.200444	−	0.979705i	$-0.564239\pi$
$257$	−6.42673	−0.400888	−0.200444	+	0.979705i	$0.564239\pi$
$258$	3.18848	0.198506
$259$	−17.7049	−1.10013
$260$	−18.5671	−1.15148
$261$	2.25346	0.139485
$262$	1.64202	0.101445
$263$	5.35393	0.330138	0.165069	−	0.986282i	$-0.447215\pi$
$263$	5.35393	0.330138	0.165069	+	0.986282i	$0.447215\pi$
$264$	0.393792	0.0242362
$265$	23.9547	1.47152
$266$	9.80362	0.601098
$267$	3.66460	0.224270
$268$	−14.5097	−0.886319
$269$	22.6753	1.38254	0.691269	−	0.722598i	$-0.257052\pi$
$269$	22.6753	1.38254	0.691269	+	0.722598i	$0.257052\pi$
$270$	41.3321	2.51539
$271$	5.94793	0.361311	0.180655	−	0.983546i	$-0.442178\pi$
$271$	5.94793	0.361311	0.180655	+	0.983546i	$0.442178\pi$
$272$	4.23176	0.256588
$273$	−16.3312	−0.988409
$274$	19.6412	1.18657
$275$	−9.73115	−0.586810
$276$	22.9129	1.37920
$277$	−30.9846	−1.86168	−0.930841	−	0.365424i	$-0.880924\pi$
$277$	−30.9846	−1.86168	−0.930841	+	0.365424i	$0.880924\pi$
$278$	33.1754	1.98973
$279$	−2.35066	−0.140730
$280$	−3.65087	−0.218181
$281$	23.4059	1.39628	0.698140	−	0.715961i	$-0.254011\pi$
$281$	23.4059	1.39628	0.698140	+	0.715961i	$0.254011\pi$
$282$	27.5307	1.63943
$283$	24.0864	1.43179	0.715893	−	0.698210i	$-0.246020\pi$
$283$	24.0864	1.43179	0.715893	+	0.698210i	$0.246020\pi$
$284$	5.88180	0.349021
$285$	7.91176	0.468652
$286$	−5.07572	−0.300134
$287$	−10.2425	−0.604594
$288$	2.96108	0.174483
$289$	1.00000	0.0588235
$290$	45.1188	2.64947
$291$	16.9550	0.993917
$292$	9.84341	0.576042
$293$	−12.5064	−0.730633	−0.365317	−	0.930883i	$-0.619039\pi$
$293$	−12.5064	−0.730633	−0.365317	+	0.930883i	$0.619039\pi$
$294$	26.4712	1.54383
$295$	12.9175	0.752084
$296$	−1.10058	−0.0639698
$297$	5.46953	0.317374
$298$	−14.2174	−0.823591
$299$	19.4378	1.12412
$300$	29.5716	1.70732
$301$	−3.91179	−0.225472
$302$	−38.1517	−2.19538
$303$	−10.0817	−0.579179
$304$	5.38656	0.308940
$305$	−11.9245	−0.682794
$306$	0.743104	0.0424804
$307$	−9.29243	−0.530347	−0.265174	−	0.964201i	$-0.585429\pi$
$307$	−9.29243	−0.530347	−0.265174	+	0.964201i	$0.585429\pi$
$308$	7.34046	0.418262
$309$	−3.87779	−0.220600
$310$	−47.0650	−2.67311
$311$	−8.28977	−0.470069	−0.235035	−	0.971987i	$-0.575520\pi$
$311$	−8.28977	−0.470069	−0.235035	+	0.971987i	$0.575520\pi$
$312$	−1.01518	−0.0574734
$313$	22.2436	1.25728	0.628641	−	0.777695i	$-0.283611\pi$
$313$	22.2436	1.25728	0.628641	+	0.777695i	$0.283611\pi$
$314$	−3.26009	−0.183978
$315$	−5.66662	−0.319278
$316$	−6.18681	−0.348036
$317$	14.3331	0.805028	0.402514	−	0.915414i	$-0.368137\pi$
$317$	14.3331	0.805028	0.402514	+	0.915414i	$0.368137\pi$
$318$	−19.9001	−1.11594
$319$	5.97062	0.334290
$320$	26.8029	1.49833
$321$	23.6745	1.32138
$322$	−58.0718	−3.23621
$323$	1.27289	0.0708255
$324$	−14.4964	−0.805358
$325$	25.0866	1.39155
$326$	−27.4563	−1.52066
$327$	−9.47531	−0.523986
$328$	−0.636694	−0.0351556
$329$	−33.7762	−1.86214
$330$	12.2378	0.673666
$331$	−9.41722	−0.517617	−0.258809	−	0.965929i	$-0.583330\pi$
$331$	−9.41722	−0.517617	−0.258809	+	0.965929i	$0.583330\pi$
$332$	8.47383	0.465062
$333$	−1.70824	−0.0936109
$334$	34.5804	1.89215
$335$	29.6775	1.62146
$336$	26.8078	1.46248
$337$	−14.4697	−0.788217	−0.394108	−	0.919064i	$-0.628947\pi$
$337$	−14.4697	−0.788217	−0.394108	+	0.919064i	$0.628947\pi$
$338$	−12.5104	−0.680476
$339$	14.2113	0.771853
$340$	7.20221	0.390595
$341$	−6.22817	−0.337274
$342$	0.945889	0.0511478
$343$	−5.09369	−0.275033
$344$	−0.243166	−0.0131106
$345$	−46.8653	−2.52314
$346$	33.7295	1.81331
$347$	−28.2338	−1.51567	−0.757836	−	0.652445i	$-0.773743\pi$
$347$	−28.2338	−1.51567	−0.757836	+	0.652445i	$0.773743\pi$
$348$	−18.1439	−0.972616
$349$	−13.8162	−0.739562	−0.369781	−	0.929119i	$-0.620567\pi$
$349$	−13.8162	−0.739562	−0.369781	+	0.929119i	$0.620567\pi$
$350$	−74.9479	−4.00614
$351$	−14.1003	−0.752617
$352$	7.84550	0.418166
$353$	−31.1332	−1.65705	−0.828525	−	0.559951i	$-0.810820\pi$
$353$	−31.1332	−1.65705	−0.828525	+	0.559951i	$0.810820\pi$
$354$	−10.7311	−0.570350
$355$	−12.0304	−0.638509
$356$	4.24630	0.225053
$357$	6.33490	0.335279
$358$	20.9718	1.10839
$359$	17.1193	0.903522	0.451761	−	0.892139i	$-0.350796\pi$
$359$	17.1193	0.903522	0.451761	+	0.892139i	$0.350796\pi$
$360$	−0.352250	−0.0185652
$361$	−17.3798	−0.914724
$362$	−23.1052	−1.21438
$363$	1.61944	0.0849984
$364$	−18.9235	−0.991861
$365$	−20.1334	−1.05383
$366$	9.90615	0.517803
$367$	29.6567	1.54807	0.774034	−	0.633144i	$-0.218236\pi$
$367$	29.6567	1.54807	0.774034	+	0.633144i	$0.218236\pi$
$368$	−31.9073	−1.66328
$369$	−0.988231	−0.0514453
$370$	−34.2024	−1.77810
$371$	24.4145	1.26754
$372$	18.9266	0.981297
$373$	7.49719	0.388190	0.194095	−	0.980983i	$-0.437823\pi$
$373$	7.49719	0.388190	0.194095	+	0.980983i	$0.437823\pi$
$374$	1.96888	0.101808
$375$	−29.4069	−1.51856
$376$	−2.09960	−0.108279
$377$	−15.3921	−0.792733
$378$	42.1255	2.16670
$379$	−28.1846	−1.44774	−0.723872	−	0.689934i	$-0.757639\pi$
$379$	−28.1846	−1.44774	−0.723872	+	0.689934i	$0.757639\pi$
$380$	9.16762	0.470289
$381$	28.1558	1.44246
$382$	−19.9161	−1.01900
$383$	23.4301	1.19722	0.598611	−	0.801040i	$-0.295720\pi$
$383$	23.4301	1.19722	0.598611	+	0.801040i	$0.295720\pi$
$384$	3.14433	0.160458
$385$	−15.0139	−0.765181
$386$	47.4527	2.41528
$387$	−0.377424	−0.0191856
$388$	19.6463	0.997388
$389$	1.20544	0.0611185	0.0305592	−	0.999533i	$-0.490271\pi$
$389$	1.20544	0.0611185	0.0305592	+	0.999533i	$0.490271\pi$
$390$	−31.5486	−1.59753
$391$	−7.53997	−0.381312
$392$	−2.01879	−0.101965
$393$	1.35059	0.0681283
$394$	34.0604	1.71594
$395$	12.6543	0.636707
$396$	0.708235	0.0355902
$397$	14.8395	0.744772	0.372386	−	0.928078i	$-0.378540\pi$
$397$	14.8395	0.744772	0.372386	+	0.928078i	$0.378540\pi$
$398$	−38.8925	−1.94951
$399$	8.06363	0.403687
$400$	−41.1798	−2.05899
$401$	−1.90508	−0.0951350	−0.0475675	−	0.998868i	$-0.515147\pi$
$401$	−1.90508	−0.0951350	−0.0475675	+	0.998868i	$0.515147\pi$
$402$	−24.6543	−1.22965
$403$	16.0560	0.799808
$404$	−11.6820	−0.581202
$405$	29.6505	1.47335
$406$	45.9849	2.28219
$407$	−4.52604	−0.224348
$408$	0.393792	0.0194956
$409$	18.7856	0.928888	0.464444	−	0.885602i	$-0.346254\pi$
$409$	18.7856	0.928888	0.464444	+	0.885602i	$0.346254\pi$
$410$	−19.7864	−0.977180
$411$	16.1552	0.796877
$412$	−4.49332	−0.221370
$413$	13.1654	0.647829
$414$	−5.60298	−0.275371
$415$	−17.3321	−0.850798
$416$	−20.2255	−0.991635
$417$	27.2873	1.33626
$418$	2.50617	0.122581
$419$	−16.4826	−0.805230	−0.402615	−	0.915369i	$-0.631899\pi$
$419$	−16.4826	−0.805230	−0.402615	+	0.915369i	$0.631899\pi$
$420$	45.6253	2.22629
$421$	−15.4948	−0.755169	−0.377584	−	0.925975i	$-0.623245\pi$
$421$	−15.4948	−0.755169	−0.377584	+	0.925975i	$0.623245\pi$
$422$	−29.5955	−1.44069
$423$	−3.25885	−0.158451
$424$	1.51766	0.0737041
$425$	−9.73115	−0.472030
$426$	9.99416	0.484219
$427$	−12.1534	−0.588144
$428$	27.4325	1.32600
$429$	−4.17486	−0.201564
$430$	−7.55680	−0.364421
$431$	18.5383	0.892957	0.446478	−	0.894794i	$-0.352678\pi$
$431$	18.5383	0.892957	0.446478	+	0.894794i	$0.352678\pi$
$432$	23.1457	1.11360
$433$	16.3979	0.788033	0.394016	−	0.919103i	$-0.371085\pi$
$433$	16.3979	0.788033	0.394016	+	0.919103i	$0.371085\pi$
$434$	−47.9685	−2.30256
$435$	37.1109	1.77933
$436$	−10.9794	−0.525816
$437$	−9.59754	−0.459113
$438$	16.7256	0.799180
$439$	−2.46037	−0.117427	−0.0587134	−	0.998275i	$-0.518700\pi$
$439$	−2.46037	−0.117427	−0.0587134	+	0.998275i	$0.518700\pi$
$440$	−0.933299	−0.0444933
$441$	−3.13343	−0.149211
$442$	−5.07572	−0.241427
$443$	−18.9879	−0.902142	−0.451071	−	0.892488i	$-0.648958\pi$
$443$	−18.9879	−0.902142	−0.451071	+	0.892488i	$0.648958\pi$
$444$	13.7540	0.652737
$445$	−8.68523	−0.411719
$446$	6.63293	0.314078
$447$	−11.6940	−0.553109
$448$	27.3174	1.29063
$449$	−7.77178	−0.366773	−0.183386	−	0.983041i	$-0.558706\pi$
$449$	−7.77178	−0.366773	−0.183386	+	0.983041i	$0.558706\pi$
$450$	−7.23125	−0.340884
$451$	−2.61836	−0.123294
$452$	16.4671	0.774548
$453$	−31.3804	−1.47438
$454$	−55.8082	−2.61921
$455$	38.7055	1.81454
$456$	0.501253	0.0234733
$457$	18.1504	0.849040	0.424520	−	0.905418i	$-0.360443\pi$
$457$	18.1504	0.849040	0.424520	+	0.905418i	$0.360443\pi$
$458$	−36.1716	−1.69019
$459$	5.46953	0.255296
$460$	−54.3044	−2.53196
$461$	23.9727	1.11652	0.558259	−	0.829666i	$-0.311469\pi$
$461$	23.9727	1.11652	0.558259	+	0.829666i	$0.311469\pi$
$462$	12.4727	0.580281
$463$	9.98057	0.463837	0.231918	−	0.972735i	$-0.425500\pi$
$463$	9.98057	0.463837	0.231918	+	0.972735i	$0.425500\pi$
$464$	25.2662	1.17295
$465$	−38.7117	−1.79521
$466$	40.3982	1.87141
$467$	−13.6909	−0.633541	−0.316771	−	0.948502i	$-0.602599\pi$
$467$	−13.6909	−0.633541	−0.316771	+	0.948502i	$0.602599\pi$
$468$	−1.82581	−0.0843981
$469$	30.2472	1.39669
$470$	−65.2488	−3.00970
$471$	−2.68148	−0.123556
$472$	0.818392	0.0376696
$473$	−1.00000	−0.0459800
$474$	−10.5124	−0.482852
$475$	−12.3867	−0.568340
$476$	7.34046	0.336450
$477$	2.35560	0.107856
$478$	37.4384	1.71239
$479$	20.3767	0.931036	0.465518	−	0.885038i	$-0.345868\pi$
$479$	20.3767	0.931036	0.465518	+	0.885038i	$0.345868\pi$
$480$	48.7644	2.22578
$481$	11.6680	0.532015
$482$	5.69645	0.259466
$483$	−47.7650	−2.17338
$484$	1.87650	0.0852953
$485$	−40.1838	−1.82465
$486$	7.67465	0.348129
$487$	17.1960	0.779223	0.389612	−	0.920979i	$-0.372609\pi$
$487$	17.1960	0.779223	0.389612	+	0.920979i	$0.372609\pi$
$488$	−0.755481	−0.0341990
$489$	−22.5832	−1.02125
$490$	−62.7376	−2.83419
$491$	17.8010	0.803346	0.401673	−	0.915783i	$-0.368429\pi$
$491$	17.8010	0.803346	0.401673	+	0.915783i	$0.368429\pi$
$492$	7.95683	0.358722
$493$	5.97062	0.268903
$494$	−6.46083	−0.290687
$495$	−1.44860	−0.0651097
$496$	−26.3561	−1.18342
$497$	−12.2614	−0.549997
$498$	14.3985	0.645210
$499$	−17.8259	−0.797997	−0.398999	−	0.916952i	$-0.630642\pi$
$499$	−17.8259	−0.797997	−0.398999	+	0.916952i	$0.630642\pi$
$500$	−34.0747	−1.52387
$501$	28.4429	1.27074
$502$	−46.0528	−2.05544
$503$	21.5327	0.960095	0.480048	−	0.877242i	$-0.340619\pi$
$503$	21.5327	0.960095	0.480048	+	0.877242i	$0.340619\pi$
$504$	−0.359011	−0.0159916
$505$	23.8940	1.06327
$506$	−14.8453	−0.659954
$507$	−10.2900	−0.456995
$508$	32.6250	1.44750
$509$	26.4943	1.17434	0.587170	−	0.809464i	$-0.300242\pi$
$509$	26.4943	1.17434	0.587170	+	0.809464i	$0.300242\pi$
$510$	12.2378	0.541897
$511$	−20.5199	−0.907745
$512$	31.1422	1.37630
$513$	6.96210	0.307384
$514$	−12.6535	−0.558121
$515$	9.19049	0.404981
$516$	3.03887	0.133779
$517$	−8.63444	−0.379742
$518$	−34.8589	−1.53161
$519$	27.7430	1.21778
$520$	2.40602	0.105511
$521$	34.9539	1.53136	0.765678	−	0.643224i	$-0.222404\pi$
$521$	34.9539	1.53136	0.765678	+	0.643224i	$0.222404\pi$
$522$	4.43679	0.194193
$523$	34.1255	1.49220	0.746101	−	0.665833i	$-0.231924\pi$
$523$	34.1255	1.49220	0.746101	+	0.665833i	$0.231924\pi$
$524$	1.56498	0.0683663
$525$	−61.6459	−2.69045
$526$	10.5413	0.459621
$527$	−6.22817	−0.271303
$528$	6.85306	0.298241
$529$	33.8511	1.47179
$530$	47.1639	2.04867
$531$	1.27025	0.0551241
$532$	9.34360	0.405096
$533$	6.75005	0.292377
$534$	7.21517	0.312231
$535$	−56.1094	−2.42582
$536$	1.88023	0.0812138
$537$	17.2496	0.744376
$538$	44.6450	1.92478
$539$	−8.30214	−0.357598
$540$	39.3927	1.69519
$541$	−18.8038	−0.808440	−0.404220	−	0.914662i	$-0.632457\pi$
$541$	−18.8038	−0.808440	−0.404220	+	0.914662i	$0.632457\pi$
$542$	11.7108	0.503020
$543$	−19.0044	−0.815558
$544$	7.84550	0.336373
$545$	22.4568	0.961944
$546$	−32.1542	−1.37607
$547$	27.8295	1.18990	0.594952	−	0.803761i	$-0.297171\pi$
$547$	27.8295	1.18990	0.594952	+	0.803761i	$0.297171\pi$
$548$	18.7196	0.799661
$549$	−1.17260	−0.0500455
$550$	−19.1595	−0.816963
$551$	7.59994	0.323768
$552$	−2.96917	−0.126376
$553$	12.8972	0.548445
$554$	−61.0049	−2.59185
$555$	−28.1320	−1.19414
$556$	31.6187	1.34093
$557$	1.28348	0.0543830	0.0271915	−	0.999630i	$-0.491344\pi$
$557$	1.28348	0.0543830	0.0271915	+	0.999630i	$0.491344\pi$
$558$	−4.62818	−0.195926
$559$	2.57797	0.109037
$560$	−63.5353	−2.68486
$561$	1.61944	0.0683727
$562$	46.0835	1.94391
$563$	−24.8828	−1.04868	−0.524342	−	0.851508i	$-0.675689\pi$
$563$	−24.8828	−1.04868	−0.524342	+	0.851508i	$0.675689\pi$
$564$	26.2389	1.10486
$565$	−33.6813	−1.41698
$566$	47.4232	1.99335
$567$	30.2197	1.26911
$568$	−0.762193	−0.0319809
$569$	−0.816044	−0.0342104	−0.0171052	−	0.999854i	$-0.505445\pi$
$569$	−0.816044	−0.0342104	−0.0171052	+	0.999854i	$0.505445\pi$
$570$	15.5773	0.652462
$571$	8.94549	0.374357	0.187179	−	0.982326i	$-0.440066\pi$
$571$	8.94549	0.374357	0.187179	+	0.982326i	$0.440066\pi$
$572$	−4.83755	−0.202268
$573$	−16.3813	−0.684339
$574$	−20.1662	−0.841721
$575$	73.3725	3.05984
$576$	2.63568	0.109820
$577$	−26.0599	−1.08489	−0.542444	−	0.840092i	$-0.682501\pi$
$577$	−26.0599	−1.08489	−0.542444	+	0.840092i	$0.682501\pi$
$578$	1.96888	0.0818947
$579$	39.0306	1.62206
$580$	43.0016	1.78555
$581$	−17.6648	−0.732859
$582$	33.3823	1.38374
$583$	6.24126	0.258486
$584$	−1.27556	−0.0527830
$585$	3.73445	0.154400
$586$	−24.6237	−1.01719
$587$	−13.5946	−0.561111	−0.280556	−	0.959838i	$-0.590519\pi$
$587$	−13.5946	−0.561111	−0.280556	+	0.959838i	$0.590519\pi$
$588$	25.2291	1.04043
$589$	−7.92777	−0.326658
$590$	25.4330	1.04706
$591$	28.0152	1.15239
$592$	−19.1531	−0.787188
$593$	−7.69017	−0.315797	−0.157899	−	0.987455i	$-0.550472\pi$
$593$	−7.69017	−0.315797	−0.157899	+	0.987455i	$0.550472\pi$
$594$	10.7688	0.441851
$595$	−15.0139	−0.615511
$596$	−13.5503	−0.555041
$597$	−31.9897	−1.30925
$598$	38.2708	1.56501
$599$	22.3723	0.914106	0.457053	−	0.889439i	$-0.348905\pi$
$599$	22.3723	0.914106	0.457053	+	0.889439i	$0.348905\pi$
$600$	−3.83204	−0.156442
$601$	−35.6434	−1.45392	−0.726962	−	0.686677i	$-0.759069\pi$
$601$	−35.6434	−1.45392	−0.726962	+	0.686677i	$0.759069\pi$
$602$	−7.70186	−0.313904
$603$	2.91836	0.118845
$604$	−36.3615	−1.47953
$605$	−3.83812	−0.156042
$606$	−19.8497	−0.806339
$607$	−3.49755	−0.141961	−0.0709805	−	0.997478i	$-0.522613\pi$
$607$	−3.49755	−0.141961	−0.0709805	+	0.997478i	$0.522613\pi$
$608$	9.98645	0.405004
$609$	37.8233	1.53268
$610$	−23.4779	−0.950592
$611$	22.2593	0.900517
$612$	0.708235	0.0286287
$613$	36.6173	1.47896	0.739480	−	0.673179i	$-0.235072\pi$
$613$	36.6173	1.47896	0.739480	+	0.673179i	$0.235072\pi$
$614$	−18.2957	−0.738354
$615$	−16.2746	−0.656256
$616$	−0.951214	−0.0383255
$617$	−23.5505	−0.948109	−0.474055	−	0.880495i	$-0.657210\pi$
$617$	−23.5505	−0.948109	−0.474055	+	0.880495i	$0.657210\pi$
$618$	−7.63491	−0.307121
$619$	−12.0743	−0.485308	−0.242654	−	0.970113i	$-0.578018\pi$
$619$	−12.0743	−0.485308	−0.242654	+	0.970113i	$0.578018\pi$
$620$	−44.8566	−1.80148
$621$	−41.2400	−1.65491
$622$	−16.3216	−0.654435
$623$	−8.85195	−0.354646
$624$	−17.6670	−0.707246
$625$	21.0395	0.841579
$626$	43.7950	1.75040
$627$	2.06136	0.0823230
$628$	−3.10712	−0.123987
$629$	−4.52604	−0.180465
$630$	−11.1569	−0.444502
$631$	−13.3953	−0.533259	−0.266629	−	0.963799i	$-0.585910\pi$
$631$	−13.3953	−0.533259	−0.266629	+	0.963799i	$0.585910\pi$
$632$	0.801719	0.0318907
$633$	−24.3428	−0.967539
$634$	28.2202	1.12077
$635$	−66.7300	−2.64810
$636$	−18.9663	−0.752064
$637$	21.4027	0.848005
$638$	11.7554	0.465402
$639$	−1.18302	−0.0467996
$640$	−7.45215	−0.294572
$641$	6.88123	0.271792	0.135896	−	0.990723i	$-0.456609\pi$
$641$	6.88123	0.271792	0.135896	+	0.990723i	$0.456609\pi$
$642$	46.6123	1.83964
$643$	−9.63642	−0.380023	−0.190012	−	0.981782i	$-0.560853\pi$
$643$	−9.63642	−0.380023	−0.190012	+	0.981782i	$0.560853\pi$
$644$	−55.3469	−2.18097
$645$	−6.21559	−0.244739
$646$	2.50617	0.0986039
$647$	34.2496	1.34649	0.673246	−	0.739419i	$-0.264900\pi$
$647$	34.2496	1.34649	0.673246	+	0.739419i	$0.264900\pi$
$648$	1.87852	0.0737953
$649$	3.36557	0.132110
$650$	49.3926	1.93734
$651$	−39.4549	−1.54636
$652$	−26.1680	−1.02482
$653$	14.7791	0.578350	0.289175	−	0.957276i	$-0.406619\pi$
$653$	14.7791	0.578350	0.289175	+	0.957276i	$0.406619\pi$
$654$	−18.6558	−0.729499
$655$	−3.20095	−0.125071
$656$	−11.0802	−0.432611
$657$	−1.97983	−0.0772405
$658$	−66.5013	−2.59249
$659$	−24.8829	−0.969300	−0.484650	−	0.874708i	$-0.661053\pi$
$659$	−24.8829	−0.969300	−0.484650	+	0.874708i	$0.661053\pi$
$660$	11.6635	0.454002
$661$	−3.45503	−0.134385	−0.0671925	−	0.997740i	$-0.521404\pi$
$661$	−3.45503	−0.134385	−0.0671925	+	0.997740i	$0.521404\pi$
$662$	−18.5414	−0.720632
$663$	−4.17486	−0.162138
$664$	−1.09808	−0.0426138
$665$	−19.1111	−0.741096
$666$	−3.36332	−0.130326
$667$	−45.0183	−1.74311
$668$	32.9578	1.27517
$669$	5.45569	0.210929
$670$	58.4316	2.25741
$671$	−3.10686	−0.119939
$672$	49.7005	1.91724
$673$	24.2043	0.933007	0.466503	−	0.884519i	$-0.345514\pi$
$673$	24.2043	0.933007	0.466503	+	0.884519i	$0.345514\pi$
$674$	−28.4892	−1.09736
$675$	−53.2247	−2.04862
$676$	−11.9234	−0.458591
$677$	−40.1908	−1.54466	−0.772329	−	0.635223i	$-0.780908\pi$
$677$	−40.1908	−1.54466	−0.772329	+	0.635223i	$0.780908\pi$
$678$	27.9804	1.07458
$679$	−40.9552	−1.57172
$680$	−0.933299	−0.0357904
$681$	−45.9032	−1.75901
$682$	−12.2625	−0.469556
$683$	22.8881	0.875787	0.437893	−	0.899027i	$-0.355725\pi$
$683$	22.8881	0.875787	0.437893	+	0.899027i	$0.355725\pi$
$684$	0.901505	0.0344699
$685$	−38.2884	−1.46292
$686$	−10.0289	−0.382904
$687$	−29.7517	−1.13510
$688$	−4.23176	−0.161334
$689$	−16.0898	−0.612972
$690$	−92.2723	−3.51275
$691$	14.1787	0.539383	0.269692	−	0.962947i	$-0.413078\pi$
$691$	14.1787	0.539383	0.269692	+	0.962947i	$0.413078\pi$
$692$	32.1468	1.22204
$693$	−1.47641	−0.0560840
$694$	−55.5891	−2.11013
$695$	−64.6717	−2.45314
$696$	2.35118	0.0891212
$697$	−2.61836	−0.0991773
$698$	−27.2024	−1.02963
$699$	33.2282	1.25681
$700$	−71.4311	−2.69984
$701$	5.74159	0.216857	0.108428	−	0.994104i	$-0.465418\pi$
$701$	5.74159	0.216857	0.108428	+	0.994104i	$0.465418\pi$
$702$	−27.7618	−1.04780
$703$	−5.76115	−0.217286
$704$	6.98334	0.263195
$705$	−53.6682	−2.02126
$706$	−61.2975	−2.30696
$707$	24.3527	0.915876
$708$	−10.2275	−0.384374
$709$	7.08222	0.265978	0.132989	−	0.991117i	$-0.457542\pi$
$709$	7.08222	0.265978	0.132989	+	0.991117i	$0.457542\pi$
$710$	−23.6865	−0.888938
$711$	1.24437	0.0466675
$712$	−0.550257	−0.0206217
$713$	46.9602	1.75867
$714$	12.4727	0.466778
$715$	9.89456	0.370035
$716$	19.9877	0.746976
$717$	30.7937	1.15001
$718$	33.7059	1.25789
$719$	48.1272	1.79484	0.897421	−	0.441176i	$-0.145439\pi$
$719$	48.1272	1.79484	0.897421	+	0.441176i	$0.145439\pi$
$720$	−6.13012	−0.228456
$721$	9.36691	0.348842
$722$	−34.2187	−1.27349
$723$	4.68542	0.174253
$724$	−22.0211	−0.818407
$725$	−58.1010	−2.15782
$726$	3.18848	0.118336
$727$	−40.6618	−1.50806	−0.754032	−	0.656837i	$-0.771894\pi$
$727$	−40.6618	−1.50806	−0.754032	+	0.656837i	$0.771894\pi$
$728$	2.45220	0.0908847
$729$	29.4884	1.09216
$730$	−39.6402	−1.46715
$731$	−1.00000	−0.0369863
$732$	9.44132	0.348961
$733$	−6.68407	−0.246882	−0.123441	−	0.992352i	$-0.539393\pi$
$733$	−6.68407	−0.246882	−0.123441	+	0.992352i	$0.539393\pi$
$734$	58.3906	2.15523
$735$	−51.6027	−1.90339
$736$	−59.1548	−2.18047
$737$	7.73232	0.284824
$738$	−1.94571	−0.0716226
$739$	−5.10387	−0.187749	−0.0938744	−	0.995584i	$-0.529925\pi$
$739$	−5.10387	−0.187749	−0.0938744	+	0.995584i	$0.529925\pi$
$740$	−32.5975	−1.19831
$741$	−5.31414	−0.195220
$742$	48.0693	1.76468
$743$	46.3050	1.69877	0.849384	−	0.527776i	$-0.176974\pi$
$743$	46.3050	1.69877	0.849384	+	0.527776i	$0.176974\pi$
$744$	−2.45260	−0.0899167
$745$	27.7152	1.01541
$746$	14.7611	0.540441
$747$	−1.70436	−0.0623594
$748$	1.87650	0.0686115
$749$	−57.1865	−2.08955
$750$	−57.8986	−2.11416
$751$	20.4253	0.745331	0.372666	−	0.927966i	$-0.378444\pi$
$751$	20.4253	0.745331	0.372666	+	0.927966i	$0.378444\pi$
$752$	−36.5389	−1.33243
$753$	−37.8792	−1.38039
$754$	−30.3052	−1.10365
$755$	74.3725	2.70669
$756$	40.1489	1.46020
$757$	13.9210	0.505966	0.252983	−	0.967471i	$-0.418588\pi$
$757$	13.9210	0.505966	0.252983	+	0.967471i	$0.418588\pi$
$758$	−55.4921	−2.01556
$759$	−12.2105	−0.443213
$760$	−1.18799	−0.0430928
$761$	7.35932	0.266775	0.133388	−	0.991064i	$-0.457414\pi$
$761$	7.35932	0.266775	0.133388	+	0.991064i	$0.457414\pi$
$762$	55.4354	2.00821
$763$	22.8879	0.828597
$764$	−18.9816	−0.686729
$765$	−1.44860	−0.0523742
$766$	46.1311	1.66678
$767$	−8.67635	−0.313285
$768$	28.8090	1.03955
$769$	−4.77893	−0.172333	−0.0861663	−	0.996281i	$-0.527462\pi$
$769$	−4.77893	−0.172333	−0.0861663	+	0.996281i	$0.527462\pi$
$770$	−29.5606	−1.06529
$771$	−10.4077	−0.374824
$772$	45.2261	1.62772
$773$	28.4298	1.02255	0.511274	−	0.859418i	$-0.329174\pi$
$773$	28.4298	1.02255	0.511274	+	0.859418i	$0.329174\pi$
$774$	−0.743104	−0.0267103
$775$	60.6072	2.17708
$776$	−2.54586	−0.0913912
$777$	−28.6720	−1.02860
$778$	2.37338	0.0850897
$779$	−3.33288	−0.119413
$780$	−30.0682	−1.07662
$781$	−3.13446	−0.112160
$782$	−14.8453	−0.530867
$783$	32.6564	1.16705
$784$	−35.1326	−1.25474
$785$	6.35519	0.226826
$786$	2.65915	0.0948489
$787$	19.3095	0.688310	0.344155	−	0.938913i	$-0.388165\pi$
$787$	19.3095	0.688310	0.344155	+	0.938913i	$0.388165\pi$
$788$	32.4622	1.15642
$789$	8.67036	0.308673
$790$	24.9148	0.886429
$791$	−34.3278	−1.22056
$792$	−0.0917767	−0.00326114
$793$	8.00939	0.284422
$794$	29.2172	1.03688
$795$	38.7931	1.37585
$796$	−37.0676	−1.31382
$797$	−6.57347	−0.232844	−0.116422	−	0.993200i	$-0.537143\pi$
$797$	−6.57347	−0.232844	−0.116422	+	0.993200i	$0.537143\pi$
$798$	15.8763	0.562016
$799$	−8.63444	−0.305465
$800$	−76.3457	−2.69923
$801$	−0.854069	−0.0301770
$802$	−3.75087	−0.132448
$803$	−5.24564	−0.185114
$804$	−23.4975	−0.828692
$805$	113.204	3.98993
$806$	31.6124	1.11350
$807$	36.7212	1.29265
$808$	1.51381	0.0532558
$809$	−3.40674	−0.119774	−0.0598872	−	0.998205i	$-0.519074\pi$
$809$	−3.40674	−0.119774	−0.0598872	+	0.998205i	$0.519074\pi$
$810$	58.3784	2.05121
$811$	40.0865	1.40763	0.703814	−	0.710385i	$-0.251479\pi$
$811$	40.0865	1.40763	0.703814	+	0.710385i	$0.251479\pi$
$812$	43.8271	1.53803
$813$	9.63229	0.337819
$814$	−8.91124	−0.312339
$815$	53.5230	1.87483
$816$	6.85306	0.239905
$817$	−1.27289	−0.0445328
$818$	36.9866	1.29321
$819$	3.80613	0.132997
$820$	−18.8579	−0.658548
$821$	−36.6431	−1.27885	−0.639427	−	0.768852i	$-0.720828\pi$
$821$	−36.6431	−1.27885	−0.639427	+	0.768852i	$0.720828\pi$
$822$	31.8077	1.10942
$823$	20.9872	0.731569	0.365785	−	0.930699i	$-0.380801\pi$
$823$	20.9872	0.731569	0.365785	+	0.930699i	$0.380801\pi$
$824$	0.582268	0.0202843
$825$	−15.7590	−0.548657
$826$	25.9212	0.901913
$827$	−2.51059	−0.0873019	−0.0436510	−	0.999047i	$-0.513899\pi$
$827$	−2.51059	−0.0873019	−0.0436510	+	0.999047i	$0.513899\pi$
$828$	−5.34007	−0.185580
$829$	49.1189	1.70597	0.852984	−	0.521937i	$-0.174790\pi$
$829$	49.1189	1.70597	0.852984	+	0.521937i	$0.174790\pi$
$830$	−34.1248	−1.18449
$831$	−50.1775	−1.74064
$832$	−18.0029	−0.624137
$833$	−8.30214	−0.287652
$834$	53.7254	1.86036
$835$	−67.4107	−2.33284
$836$	2.38857	0.0826105
$837$	−34.0651	−1.17746
$838$	−32.4524	−1.12105
$839$	−21.2050	−0.732078	−0.366039	−	0.930599i	$-0.619286\pi$
$839$	−21.2050	−0.732078	−0.366039	+	0.930599i	$0.619286\pi$
$840$	−5.91236	−0.203996
$841$	6.64828	0.229251
$842$	−30.5074	−1.05135
$843$	37.9044	1.30550
$844$	−28.2068	−0.970918
$845$	24.3876	0.838960
$846$	−6.41629	−0.220597
$847$	−3.91179	−0.134411
$848$	26.4115	0.906974
$849$	39.0063	1.33869
$850$	−19.1595	−0.657165
$851$	34.1262	1.16983
$852$	9.52520	0.326328
$853$	−8.86845	−0.303650	−0.151825	−	0.988407i	$-0.548515\pi$
$853$	−8.86845	−0.303650	−0.151825	+	0.988407i	$0.548515\pi$
$854$	−23.9286	−0.818819
$855$	−1.84391	−0.0630603
$856$	−3.55484	−0.121502
$857$	−55.3000	−1.88901	−0.944505	−	0.328496i	$-0.893458\pi$
$857$	−55.3000	−1.88901	−0.944505	+	0.328496i	$0.893458\pi$
$858$	−8.21981	−0.280620
$859$	−10.4356	−0.356058	−0.178029	−	0.984025i	$-0.556972\pi$
$859$	−10.4356	−0.356058	−0.178029	+	0.984025i	$0.556972\pi$
$860$	−7.20221	−0.245593
$861$	−16.5870	−0.565285
$862$	36.4997	1.24318
$863$	−4.38883	−0.149397	−0.0746987	−	0.997206i	$-0.523799\pi$
$863$	−4.38883	−0.149397	−0.0746987	+	0.997206i	$0.523799\pi$
$864$	42.9111	1.45987
$865$	−65.7519	−2.23563
$866$	32.2855	1.09711
$867$	1.61944	0.0549990
$868$	−45.7177	−1.55176
$869$	3.29700	0.111843
$870$	73.0670	2.47720
$871$	−19.9337	−0.675427
$872$	1.42276	0.0481808
$873$	−3.95151	−0.133738
$874$	−18.8964	−0.639181
$875$	71.0331	2.40136
$876$	15.9408	0.538589
$877$	12.4654	0.420926	0.210463	−	0.977602i	$-0.432503\pi$
$877$	12.4654	0.420926	0.210463	+	0.977602i	$0.432503\pi$
$878$	−4.84417	−0.163483
$879$	−20.2534	−0.683129
$880$	−16.2420	−0.547517
$881$	−37.5039	−1.26354	−0.631770	−	0.775156i	$-0.717671\pi$
$881$	−37.5039	−1.26354	−0.631770	+	0.775156i	$0.717671\pi$
$882$	−6.16935	−0.207733
$883$	−11.7125	−0.394157	−0.197079	−	0.980388i	$-0.563145\pi$
$883$	−11.7125	−0.394157	−0.197079	+	0.980388i	$0.563145\pi$
$884$	−4.83755	−0.162704
$885$	20.9190	0.703185
$886$	−37.3849	−1.25597
$887$	−18.1481	−0.609354	−0.304677	−	0.952456i	$-0.598549\pi$
$887$	−18.1481	−0.609354	−0.304677	+	0.952456i	$0.598549\pi$
$888$	−1.78232	−0.0598106
$889$	−68.0110	−2.28102
$890$	−17.1002	−0.573200
$891$	7.72528	0.258807
$892$	6.32169	0.211666
$893$	−10.9907	−0.367790
$894$	−23.0242	−0.770043
$895$	−40.8822	−1.36654
$896$	−7.59521	−0.253738
$897$	31.4783	1.05103
$898$	−15.3017	−0.510625
$899$	−37.1860	−1.24022
$900$	−6.89194	−0.229731
$901$	6.24126	0.207926
$902$	−5.15523	−0.171650
$903$	−6.33490	−0.210812
$904$	−2.13389	−0.0709722
$905$	45.0411	1.49722
$906$	−61.7842	−2.05264
$907$	24.4159	0.810716	0.405358	−	0.914158i	$-0.367147\pi$
$907$	24.4159	0.810716	0.405358	+	0.914158i	$0.367147\pi$
$908$	−53.1895	−1.76516
$909$	2.34963	0.0779325
$910$	76.2065	2.52622
$911$	15.9584	0.528725	0.264363	−	0.964423i	$-0.414838\pi$
$911$	15.9584	0.528725	0.264363	+	0.964423i	$0.414838\pi$
$912$	8.72319	0.288854
$913$	−4.51577	−0.149450
$914$	35.7360	1.18204
$915$	−19.3109	−0.638400
$916$	−34.4743	−1.13906
$917$	−3.26239	−0.107734
$918$	10.7688	0.355425
$919$	6.54413	0.215871	0.107935	−	0.994158i	$-0.465576\pi$
$919$	6.54413	0.215871	0.107935	+	0.994158i	$0.465576\pi$
$920$	7.03704	0.232004
$921$	−15.0485	−0.495865
$922$	47.1994	1.55443
$923$	8.08055	0.265974
$924$	11.8874	0.391067
$925$	44.0436	1.44814
$926$	19.6506	0.645758
$927$	0.903754	0.0296832
$928$	46.8425	1.53768
$929$	22.0557	0.723623	0.361812	−	0.932251i	$-0.382158\pi$
$929$	22.0557	0.723623	0.361812	+	0.932251i	$0.382158\pi$
$930$	−76.2188	−2.49931
$931$	−10.5677	−0.346342
$932$	38.5026	1.26120
$933$	−13.4248	−0.439507
$934$	−26.9558	−0.882022
$935$	−3.83812	−0.125520
$936$	0.236598	0.00773343
$937$	−0.625215	−0.0204249	−0.0102124	−	0.999948i	$-0.503251\pi$
$937$	−0.625215	−0.0204249	−0.0102124	+	0.999948i	$0.503251\pi$
$938$	59.5532	1.94448
$939$	36.0221	1.17554
$940$	−62.1871	−2.02832
$941$	30.2191	0.985114	0.492557	−	0.870280i	$-0.336062\pi$
$941$	30.2191	0.985114	0.492557	+	0.870280i	$0.336062\pi$
$942$	−5.27951	−0.172016
$943$	19.7423	0.642898
$944$	14.2423	0.463547
$945$	−82.1191	−2.67133
$946$	−1.96888	−0.0640139
$947$	4.41028	0.143315	0.0716575	−	0.997429i	$-0.477171\pi$
$947$	4.41028	0.143315	0.0716575	+	0.997429i	$0.477171\pi$
$948$	−10.0192	−0.325407
$949$	13.5231	0.438978
$950$	−24.3879	−0.791248
$951$	23.2116	0.752686
$952$	−0.951214	−0.0308290
$953$	10.6196	0.344002	0.172001	−	0.985097i	$-0.444977\pi$
$953$	10.6196	0.344002	0.172001	+	0.985097i	$0.444977\pi$
$954$	4.63790	0.150158
$955$	38.8242	1.25632
$956$	35.6817	1.15403
$957$	9.66904	0.312556
$958$	40.1193	1.29620
$959$	−39.0233	−1.26013
$960$	43.4056	1.40091
$961$	7.79008	0.251293
$962$	22.9729	0.740677
$963$	−5.51756	−0.177801
$964$	5.42916	0.174861
$965$	−92.5038	−2.97780
$966$	−94.0436	−3.02580
$967$	43.1227	1.38673	0.693367	−	0.720585i	$-0.256127\pi$
$967$	43.1227	1.38673	0.693367	+	0.720585i	$0.256127\pi$
$968$	−0.243166	−0.00781564
$969$	2.06136	0.0662206
$970$	−79.1171	−2.54030
$971$	−2.36364	−0.0758527	−0.0379263	−	0.999281i	$-0.512075\pi$
$971$	−2.36364	−0.0758527	−0.0379263	+	0.999281i	$0.512075\pi$
$972$	7.31454	0.234614
$973$	−65.9131	−2.11308
$974$	33.8568	1.08484
$975$	40.6262	1.30108
$976$	−13.1475	−0.420840
$977$	18.2891	0.585121	0.292560	−	0.956247i	$-0.405493\pi$
$977$	18.2891	0.585121	0.292560	+	0.956247i	$0.405493\pi$
$978$	−44.4637	−1.42179
$979$	−2.26289	−0.0723222
$980$	−59.7937	−1.91004
$981$	2.20831	0.0705058
$982$	35.0480	1.11843
$983$	57.5891	1.83681	0.918404	−	0.395645i	$-0.129479\pi$
$983$	57.5891	1.83681	0.918404	+	0.395645i	$0.129479\pi$
$984$	−1.03109	−0.0328698
$985$	−66.3970	−2.11559
$986$	11.7554	0.374370
$987$	−54.6984	−1.74107
$988$	−6.15767	−0.195902
$989$	7.53997	0.239757
$990$	−2.85212	−0.0906463
$991$	−14.1192	−0.448512	−0.224256	−	0.974530i	$-0.571995\pi$
$991$	−14.1192	−0.448512	−0.224256	+	0.974530i	$0.571995\pi$
$992$	−48.8631	−1.55140
$993$	−15.2506	−0.483963
$994$	−24.1412	−0.765712
$995$	75.8167	2.40355
$996$	13.7228	0.434825
$997$	38.8112	1.22916	0.614582	−	0.788853i	$-0.289325\pi$
$997$	38.8112	1.22916	0.614582	+	0.788853i	$0.289325\pi$
$998$	−35.0971	−1.11098
$999$	−24.7553	−0.783223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.54	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.54	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q+1.96888 q^{2} +1.61944 q^{3} +1.87650 q^{4} -3.83812 q^{5} +3.18848 q^{6} -3.91179 q^{7} -0.243166 q^{8} -0.377424 q^{9} +O(q^{10})\)	\(q+1.96888 q^{2} +1.61944 q^{3} +1.87650 q^{4} -3.83812 q^{5} +3.18848 q^{6} -3.91179 q^{7} -0.243166 q^{8} -0.377424 q^{9} -7.55680 q^{10} -1.00000 q^{11} +3.03887 q^{12} +2.57797 q^{13} -7.70186 q^{14} -6.21559 q^{15} -4.23176 q^{16} -1.00000 q^{17} -0.743104 q^{18} -1.27289 q^{19} -7.20221 q^{20} -6.33490 q^{21} -1.96888 q^{22} +7.53997 q^{23} -0.393792 q^{24} +9.73115 q^{25} +5.07572 q^{26} -5.46953 q^{27} -7.34046 q^{28} -5.97062 q^{29} -12.2378 q^{30} +6.22817 q^{31} -7.84550 q^{32} -1.61944 q^{33} -1.96888 q^{34} +15.0139 q^{35} -0.708235 q^{36} +4.52604 q^{37} -2.50617 q^{38} +4.17486 q^{39} +0.933299 q^{40} +2.61836 q^{41} -12.4727 q^{42} +1.00000 q^{43} -1.87650 q^{44} +1.44860 q^{45} +14.8453 q^{46} +8.63444 q^{47} -6.85306 q^{48} +8.30214 q^{49} +19.1595 q^{50} -1.61944 q^{51} +4.83755 q^{52} -6.24126 q^{53} -10.7688 q^{54} +3.83812 q^{55} +0.951214 q^{56} -2.06136 q^{57} -11.7554 q^{58} -3.36557 q^{59} -11.6635 q^{60} +3.10686 q^{61} +12.2625 q^{62} +1.47641 q^{63} -6.98334 q^{64} -9.89456 q^{65} -3.18848 q^{66} -7.73232 q^{67} -1.87650 q^{68} +12.2105 q^{69} +29.5606 q^{70} +3.13446 q^{71} +0.0917767 q^{72} +5.24564 q^{73} +8.91124 q^{74} +15.7590 q^{75} -2.38857 q^{76} +3.91179 q^{77} +8.21981 q^{78} -3.29700 q^{79} +16.2420 q^{80} -7.72528 q^{81} +5.15523 q^{82} +4.51577 q^{83} -11.8874 q^{84} +3.83812 q^{85} +1.96888 q^{86} -9.66904 q^{87} +0.243166 q^{88} +2.26289 q^{89} +2.85212 q^{90} -10.0845 q^{91} +14.1487 q^{92} +10.0861 q^{93} +17.0002 q^{94} +4.88550 q^{95} -12.7053 q^{96} +10.4697 q^{97} +16.3459 q^{98} +0.377424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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