LMFDB - Embedded newform 8043.2.a.t.1.43

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:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.43
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)

$f(q)$	$=$	$q+2.19545 q^{2} -1.00000 q^{3} +2.82002 q^{4} +4.21837 q^{5} -2.19545 q^{6} +1.00000 q^{7} +1.80031 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.19545 q^{2} -1.00000 q^{3} +2.82002 q^{4} +4.21837 q^{5} -2.19545 q^{6} +1.00000 q^{7} +1.80031 q^{8} +1.00000 q^{9} +9.26124 q^{10} -1.86322 q^{11} -2.82002 q^{12} +7.10449 q^{13} +2.19545 q^{14} -4.21837 q^{15} -1.68754 q^{16} +3.10077 q^{17} +2.19545 q^{18} -0.529760 q^{19} +11.8959 q^{20} -1.00000 q^{21} -4.09061 q^{22} +3.54125 q^{23} -1.80031 q^{24} +12.7947 q^{25} +15.5976 q^{26} -1.00000 q^{27} +2.82002 q^{28} -7.75844 q^{29} -9.26124 q^{30} +5.88019 q^{31} -7.30553 q^{32} +1.86322 q^{33} +6.80759 q^{34} +4.21837 q^{35} +2.82002 q^{36} -7.96976 q^{37} -1.16306 q^{38} -7.10449 q^{39} +7.59436 q^{40} +3.04195 q^{41} -2.19545 q^{42} +0.508504 q^{43} -5.25431 q^{44} +4.21837 q^{45} +7.77466 q^{46} +3.71913 q^{47} +1.68754 q^{48} +1.00000 q^{49} +28.0901 q^{50} -3.10077 q^{51} +20.0348 q^{52} -2.38571 q^{53} -2.19545 q^{54} -7.85976 q^{55} +1.80031 q^{56} +0.529760 q^{57} -17.0333 q^{58} -1.30798 q^{59} -11.8959 q^{60} +3.47580 q^{61} +12.9097 q^{62} +1.00000 q^{63} -12.6639 q^{64} +29.9694 q^{65} +4.09061 q^{66} -4.11826 q^{67} +8.74421 q^{68} -3.54125 q^{69} +9.26124 q^{70} -12.8448 q^{71} +1.80031 q^{72} -7.58629 q^{73} -17.4972 q^{74} -12.7947 q^{75} -1.49393 q^{76} -1.86322 q^{77} -15.5976 q^{78} -4.42542 q^{79} -7.11869 q^{80} +1.00000 q^{81} +6.67847 q^{82} -5.10705 q^{83} -2.82002 q^{84} +13.0802 q^{85} +1.11640 q^{86} +7.75844 q^{87} -3.35437 q^{88} +4.45620 q^{89} +9.26124 q^{90} +7.10449 q^{91} +9.98639 q^{92} -5.88019 q^{93} +8.16517 q^{94} -2.23472 q^{95} +7.30553 q^{96} +9.35481 q^{97} +2.19545 q^{98} -1.86322 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * 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 $

$2$	2.19545	1.55242	0.776210	−	0.630474i	$-0.217140\pi$
$2$	2.19545	1.55242	0.776210	+	0.630474i	$0.217140\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.82002	1.41001
$5$	4.21837	1.88651	0.943257	−	0.332063i	$-0.107745\pi$
$5$	4.21837	1.88651	0.943257	+	0.332063i	$0.107745\pi$
$6$	−2.19545	−0.896290
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.80031	0.636504
$9$	1.00000	0.333333
$10$	9.26124	2.92866
$11$	−1.86322	−0.561782	−0.280891	−	0.959740i	$-0.590630\pi$
$11$	−1.86322	−0.561782	−0.280891	+	0.959740i	$0.590630\pi$
$12$	−2.82002	−0.814068
$13$	7.10449	1.97043	0.985215	−	0.171324i	$-0.0548043\pi$
$13$	7.10449	1.97043	0.985215	+	0.171324i	$0.0548043\pi$
$14$	2.19545	0.586760
$15$	−4.21837	−1.08918
$16$	−1.68754	−0.421886
$17$	3.10077	0.752047	0.376023	−	0.926610i	$-0.377291\pi$
$17$	3.10077	0.752047	0.376023	+	0.926610i	$0.377291\pi$
$18$	2.19545	0.517473
$19$	−0.529760	−0.121535	−0.0607676	−	0.998152i	$-0.519355\pi$
$19$	−0.529760	−0.121535	−0.0607676	+	0.998152i	$0.519355\pi$
$20$	11.8959	2.66000
$21$	−1.00000	−0.218218
$22$	−4.09061	−0.872122
$23$	3.54125	0.738403	0.369201	−	0.929349i	$-0.379631\pi$
$23$	3.54125	0.738403	0.369201	+	0.929349i	$0.379631\pi$
$24$	−1.80031	−0.367486
$25$	12.7947	2.55894
$26$	15.5976	3.05893
$27$	−1.00000	−0.192450
$28$	2.82002	0.532933
$29$	−7.75844	−1.44071	−0.720353	−	0.693608i	$-0.756020\pi$
$29$	−7.75844	−1.44071	−0.720353	+	0.693608i	$0.756020\pi$
$30$	−9.26124	−1.69086
$31$	5.88019	1.05611	0.528056	−	0.849209i	$-0.322921\pi$
$31$	5.88019	1.05611	0.528056	+	0.849209i	$0.322921\pi$
$32$	−7.30553	−1.29145
$33$	1.86322	0.324345
$34$	6.80759	1.16749
$35$	4.21837	0.713035
$36$	2.82002	0.470003
$37$	−7.96976	−1.31022	−0.655110	−	0.755533i	$-0.727378\pi$
$37$	−7.96976	−1.31022	−0.655110	+	0.755533i	$0.727378\pi$
$38$	−1.16306	−0.188674
$39$	−7.10449	−1.13763
$40$	7.59436	1.20077
$41$	3.04195	0.475074	0.237537	−	0.971379i	$-0.423660\pi$
$41$	3.04195	0.475074	0.237537	+	0.971379i	$0.423660\pi$
$42$	−2.19545	−0.338766
$43$	0.508504	0.0775461	0.0387730	−	0.999248i	$-0.487655\pi$
$43$	0.508504	0.0775461	0.0387730	+	0.999248i	$0.487655\pi$
$44$	−5.25431	−0.792117
$45$	4.21837	0.628838
$46$	7.77466	1.14631
$47$	3.71913	0.542490	0.271245	−	0.962510i	$-0.412565\pi$
$47$	3.71913	0.542490	0.271245	+	0.962510i	$0.412565\pi$
$48$	1.68754	0.243576
$49$	1.00000	0.142857
$50$	28.0901	3.97254
$51$	−3.10077	−0.434194
$52$	20.0348	2.77832
$53$	−2.38571	−0.327703	−0.163851	−	0.986485i	$-0.552392\pi$
$53$	−2.38571	−0.327703	−0.163851	+	0.986485i	$0.552392\pi$
$54$	−2.19545	−0.298763
$55$	−7.85976	−1.05981
$56$	1.80031	0.240576
$57$	0.529760	0.0701684
$58$	−17.0333	−2.23658
$59$	−1.30798	−0.170285	−0.0851424	−	0.996369i	$-0.527135\pi$
$59$	−1.30798	−0.170285	−0.0851424	+	0.996369i	$0.527135\pi$
$60$	−11.8959	−1.53575
$61$	3.47580	0.445031	0.222516	−	0.974929i	$-0.428573\pi$
$61$	3.47580	0.445031	0.222516	+	0.974929i	$0.428573\pi$
$62$	12.9097	1.63953
$63$	1.00000	0.125988
$64$	−12.6639	−1.58298
$65$	29.9694	3.71724
$66$	4.09061	0.503520
$67$	−4.11826	−0.503126	−0.251563	−	0.967841i	$-0.580945\pi$
$67$	−4.11826	−0.503126	−0.251563	+	0.967841i	$0.580945\pi$
$68$	8.74421	1.06039
$69$	−3.54125	−0.426317
$70$	9.26124	1.10693
$71$	−12.8448	−1.52440	−0.762200	−	0.647342i	$-0.775881\pi$
$71$	−12.8448	−1.52440	−0.762200	+	0.647342i	$0.775881\pi$
$72$	1.80031	0.212168
$73$	−7.58629	−0.887908	−0.443954	−	0.896050i	$-0.646425\pi$
$73$	−7.58629	−0.887908	−0.443954	+	0.896050i	$0.646425\pi$
$74$	−17.4972	−2.03401
$75$	−12.7947	−1.47740
$76$	−1.49393	−0.171366
$77$	−1.86322	−0.212334
$78$	−15.5976	−1.76608
$79$	−4.42542	−0.497899	−0.248949	−	0.968516i	$-0.580085\pi$
$79$	−4.42542	−0.497899	−0.248949	+	0.968516i	$0.580085\pi$
$80$	−7.11869	−0.795894
$81$	1.00000	0.111111
$82$	6.67847	0.737514
$83$	−5.10705	−0.560571	−0.280286	−	0.959917i	$-0.590429\pi$
$83$	−5.10705	−0.560571	−0.280286	+	0.959917i	$0.590429\pi$
$84$	−2.82002	−0.307689
$85$	13.0802	1.41875
$86$	1.11640	0.120384
$87$	7.75844	0.831792
$88$	−3.35437	−0.357577
$89$	4.45620	0.472356	0.236178	−	0.971710i	$-0.424105\pi$
$89$	4.45620	0.472356	0.236178	+	0.971710i	$0.424105\pi$
$90$	9.26124	0.976221
$91$	7.10449	0.744752
$92$	9.98639	1.04115
$93$	−5.88019	−0.609747
$94$	8.16517	0.842173
$95$	−2.23472	−0.229278
$96$	7.30553	0.745618
$97$	9.35481	0.949837	0.474919	−	0.880030i	$-0.342477\pi$
$97$	9.35481	0.949837	0.474919	+	0.880030i	$0.342477\pi$
$98$	2.19545	0.221774
$99$	−1.86322	−0.187261
$100$	36.0812	3.60812
$101$	−14.5347	−1.44626	−0.723128	−	0.690714i	$-0.757296\pi$
$101$	−14.5347	−1.44626	−0.723128	+	0.690714i	$0.757296\pi$
$102$	−6.80759	−0.674052
$103$	18.0813	1.78160	0.890800	−	0.454396i	$-0.150145\pi$
$103$	18.0813	1.78160	0.890800	+	0.454396i	$0.150145\pi$
$104$	12.7902	1.25419
$105$	−4.21837	−0.411671
$106$	−5.23772	−0.508732
$107$	−3.56618	−0.344756	−0.172378	−	0.985031i	$-0.555145\pi$
$107$	−3.56618	−0.344756	−0.172378	+	0.985031i	$0.555145\pi$
$108$	−2.82002	−0.271356
$109$	18.7449	1.79544	0.897720	−	0.440567i	$-0.145223\pi$
$109$	18.7449	1.79544	0.897720	+	0.440567i	$0.145223\pi$
$110$	−17.2557	−1.64527
$111$	7.96976	0.756456
$112$	−1.68754	−0.159458
$113$	1.73057	0.162798	0.0813990	−	0.996682i	$-0.474061\pi$
$113$	1.73057	0.162798	0.0813990	+	0.996682i	$0.474061\pi$
$114$	1.16306	0.108931
$115$	14.9383	1.39301
$116$	−21.8789	−2.03141
$117$	7.10449	0.656810
$118$	−2.87161	−0.264354
$119$	3.10077	0.284247
$120$	−7.59436	−0.693267
$121$	−7.52841	−0.684401
$122$	7.63097	0.690875
$123$	−3.04195	−0.274284
$124$	16.5822	1.48913
$125$	32.8809	2.94095
$126$	2.19545	0.195587
$127$	−4.30518	−0.382023	−0.191012	−	0.981588i	$-0.561177\pi$
$127$	−4.30518	−0.382023	−0.191012	+	0.981588i	$0.561177\pi$
$128$	−13.1919	−1.16601
$129$	−0.508504	−0.0447712
$130$	65.7964	5.77072
$131$	−6.14930	−0.537267	−0.268634	−	0.963242i	$-0.586572\pi$
$131$	−6.14930	−0.537267	−0.268634	+	0.963242i	$0.586572\pi$
$132$	5.25431	0.457329
$133$	−0.529760	−0.0459360
$134$	−9.04145	−0.781063
$135$	−4.21837	−0.363060
$136$	5.58233	0.478681
$137$	9.25062	0.790334	0.395167	−	0.918609i	$-0.370687\pi$
$137$	9.25062	0.790334	0.395167	+	0.918609i	$0.370687\pi$
$138$	−7.77466	−0.661823
$139$	8.43552	0.715491	0.357746	−	0.933819i	$-0.383545\pi$
$139$	8.43552	0.715491	0.357746	+	0.933819i	$0.383545\pi$
$140$	11.8959	1.00539
$141$	−3.71913	−0.313207
$142$	−28.2002	−2.36651
$143$	−13.2372	−1.10695
$144$	−1.68754	−0.140629
$145$	−32.7280	−2.71791
$146$	−16.6553	−1.37841
$147$	−1.00000	−0.0824786
$148$	−22.4748	−1.84742
$149$	−12.2995	−1.00761	−0.503807	−	0.863816i	$-0.668068\pi$
$149$	−12.2995	−1.00761	−0.503807	+	0.863816i	$0.668068\pi$
$150$	−28.0901	−2.29355
$151$	−20.0132	−1.62865	−0.814326	−	0.580407i	$-0.802893\pi$
$151$	−20.0132	−1.62865	−0.814326	+	0.580407i	$0.802893\pi$
$152$	−0.953729	−0.0773577
$153$	3.10077	0.250682
$154$	−4.09061	−0.329631
$155$	24.8048	1.99237
$156$	−20.0348	−1.60406
$157$	−0.146577	−0.0116982	−0.00584908	−	0.999983i	$-0.501862\pi$
$157$	−0.146577	−0.0116982	−0.00584908	+	0.999983i	$0.501862\pi$
$158$	−9.71581	−0.772948
$159$	2.38571	0.189199
$160$	−30.8175	−2.43634
$161$	3.54125	0.279090
$162$	2.19545	0.172491
$163$	−8.85854	−0.693854	−0.346927	−	0.937892i	$-0.612775\pi$
$163$	−8.85854	−0.693854	−0.346927	+	0.937892i	$0.612775\pi$
$164$	8.57836	0.669857
$165$	7.85976	0.611882
$166$	−11.2123	−0.870242
$167$	21.0526	1.62910	0.814551	−	0.580092i	$-0.196983\pi$
$167$	21.0526	1.62910	0.814551	+	0.580092i	$0.196983\pi$
$168$	−1.80031	−0.138897
$169$	37.4737	2.88259
$170$	28.7170	2.20249
$171$	−0.529760	−0.0405117
$172$	1.43399	0.109341
$173$	−15.1654	−1.15301	−0.576503	−	0.817095i	$-0.695583\pi$
$173$	−15.1654	−1.15301	−0.576503	+	0.817095i	$0.695583\pi$
$174$	17.0333	1.29129
$175$	12.7947	0.967187
$176$	3.14427	0.237008
$177$	1.30798	0.0983140
$178$	9.78338	0.733295
$179$	−2.26726	−0.169463	−0.0847313	−	0.996404i	$-0.527003\pi$
$179$	−2.26726	−0.169463	−0.0847313	+	0.996404i	$0.527003\pi$
$180$	11.8959	0.886667
$181$	13.6000	1.01088	0.505441	−	0.862861i	$-0.331330\pi$
$181$	13.6000	1.01088	0.505441	+	0.862861i	$0.331330\pi$
$182$	15.5976	1.15617
$183$	−3.47580	−0.256939
$184$	6.37534	0.469996
$185$	−33.6194	−2.47175
$186$	−12.9097	−0.946583
$187$	−5.77742	−0.422486
$188$	10.4880	0.764916
$189$	−1.00000	−0.0727393
$190$	−4.90623	−0.355936
$191$	−10.5010	−0.759823	−0.379912	−	0.925023i	$-0.624046\pi$
$191$	−10.5010	−0.759823	−0.379912	+	0.925023i	$0.624046\pi$
$192$	12.6639	0.913936
$193$	7.47587	0.538125	0.269063	−	0.963123i	$-0.413286\pi$
$193$	7.47587	0.538125	0.269063	+	0.963123i	$0.413286\pi$
$194$	20.5381	1.47455
$195$	−29.9694	−2.14615
$196$	2.82002	0.201430
$197$	8.06293	0.574460	0.287230	−	0.957862i	$-0.407266\pi$
$197$	8.06293	0.574460	0.287230	+	0.957862i	$0.407266\pi$
$198$	−4.09061	−0.290707
$199$	−15.5487	−1.10222	−0.551108	−	0.834434i	$-0.685795\pi$
$199$	−15.5487	−1.10222	−0.551108	+	0.834434i	$0.685795\pi$
$200$	23.0343	1.62877
$201$	4.11826	0.290480
$202$	−31.9102	−2.24520
$203$	−7.75844	−0.544536
$204$	−8.74421	−0.612218
$205$	12.8321	0.896233
$206$	39.6966	2.76579
$207$	3.54125	0.246134
$208$	−11.9891	−0.831296
$209$	0.987059	0.0682763
$210$	−9.26124	−0.639087
$211$	24.3290	1.67488	0.837439	−	0.546531i	$-0.184052\pi$
$211$	24.3290	1.67488	0.837439	+	0.546531i	$0.184052\pi$
$212$	−6.72774	−0.462063
$213$	12.8448	0.880113
$214$	−7.82938	−0.535206
$215$	2.14506	0.146292
$216$	−1.80031	−0.122495
$217$	5.88019	0.399173
$218$	41.1536	2.78728
$219$	7.58629	0.512634
$220$	−22.1647	−1.49434
$221$	22.0294	1.48186
$222$	17.4972	1.17434
$223$	−14.6404	−0.980394	−0.490197	−	0.871612i	$-0.663075\pi$
$223$	−14.6404	−0.980394	−0.490197	+	0.871612i	$0.663075\pi$
$224$	−7.30553	−0.488122
$225$	12.7947	0.852979
$226$	3.79938	0.252731
$227$	−24.4756	−1.62450	−0.812251	−	0.583308i	$-0.801758\pi$
$227$	−24.4756	−1.62450	−0.812251	+	0.583308i	$0.801758\pi$
$228$	1.49393	0.0989380
$229$	16.7245	1.10519	0.552594	−	0.833451i	$-0.313638\pi$
$229$	16.7245	1.10519	0.552594	+	0.833451i	$0.313638\pi$
$230$	32.7964	2.16253
$231$	1.86322	0.122591
$232$	−13.9676	−0.917015
$233$	−24.1742	−1.58371	−0.791853	−	0.610712i	$-0.790884\pi$
$233$	−24.1742	−1.58371	−0.791853	+	0.610712i	$0.790884\pi$
$234$	15.5976	1.01964
$235$	15.6887	1.02342
$236$	−3.68853	−0.240103
$237$	4.42542	0.287462
$238$	6.80759	0.441271
$239$	14.0472	0.908635	0.454317	−	0.890840i	$-0.349883\pi$
$239$	14.0472	0.908635	0.454317	+	0.890840i	$0.349883\pi$
$240$	7.11869	0.459509
$241$	6.30449	0.406108	0.203054	−	0.979168i	$-0.434913\pi$
$241$	6.30449	0.406108	0.203054	+	0.979168i	$0.434913\pi$
$242$	−16.5283	−1.06248
$243$	−1.00000	−0.0641500
$244$	9.80182	0.627497
$245$	4.21837	0.269502
$246$	−6.67847	−0.425804
$247$	−3.76367	−0.239477
$248$	10.5861	0.672220
$249$	5.10705	0.323646
$250$	72.1884	4.56560
$251$	−3.95090	−0.249379	−0.124689	−	0.992196i	$-0.539793\pi$
$251$	−3.95090	−0.249379	−0.124689	+	0.992196i	$0.539793\pi$
$252$	2.82002	0.177644
$253$	−6.59814	−0.414821
$254$	−9.45183	−0.593061
$255$	−13.0802	−0.819114
$256$	−3.63440	−0.227150
$257$	8.93082	0.557089	0.278545	−	0.960423i	$-0.410148\pi$
$257$	8.93082	0.557089	0.278545	+	0.960423i	$0.410148\pi$
$258$	−1.11640	−0.0695038
$259$	−7.96976	−0.495217
$260$	84.5141	5.24134
$261$	−7.75844	−0.480235
$262$	−13.5005	−0.834064
$263$	−2.99783	−0.184854	−0.0924271	−	0.995719i	$-0.529463\pi$
$263$	−2.99783	−0.184854	−0.0924271	+	0.995719i	$0.529463\pi$
$264$	3.35437	0.206447
$265$	−10.0638	−0.618216
$266$	−1.16306	−0.0713119
$267$	−4.45620	−0.272715
$268$	−11.6136	−0.709411
$269$	10.1308	0.617684	0.308842	−	0.951113i	$-0.400059\pi$
$269$	10.1308	0.617684	0.308842	+	0.951113i	$0.400059\pi$
$270$	−9.26124	−0.563621
$271$	−22.6698	−1.37709	−0.688546	−	0.725193i	$-0.741751\pi$
$271$	−22.6698	−1.37709	−0.688546	+	0.725193i	$0.741751\pi$
$272$	−5.23268	−0.317278
$273$	−7.10449	−0.429983
$274$	20.3093	1.22693
$275$	−23.8393	−1.43756
$276$	−9.98639	−0.601110
$277$	−11.1878	−0.672209	−0.336104	−	0.941825i	$-0.609109\pi$
$277$	−11.1878	−0.672209	−0.336104	+	0.941825i	$0.609109\pi$
$278$	18.5198	1.11074
$279$	5.88019	0.352038
$280$	7.59436	0.453850
$281$	−21.3543	−1.27389	−0.636947	−	0.770908i	$-0.719803\pi$
$281$	−21.3543	−1.27389	−0.636947	+	0.770908i	$0.719803\pi$
$282$	−8.16517	−0.486229
$283$	6.26470	0.372398	0.186199	−	0.982512i	$-0.440383\pi$
$283$	6.26470	0.372398	0.186199	+	0.982512i	$0.440383\pi$
$284$	−36.2226	−2.14942
$285$	2.23472	0.132374
$286$	−29.0617	−1.71845
$287$	3.04195	0.179561
$288$	−7.30553	−0.430483
$289$	−7.38524	−0.434426
$290$	−71.8528	−4.21934
$291$	−9.35481	−0.548389
$292$	−21.3934	−1.25196
$293$	11.9972	0.700882	0.350441	−	0.936585i	$-0.386032\pi$
$293$	11.9972	0.700882	0.350441	+	0.936585i	$0.386032\pi$
$294$	−2.19545	−0.128041
$295$	−5.51756	−0.321245
$296$	−14.3480	−0.833961
$297$	1.86322	0.108115
$298$	−27.0030	−1.56424
$299$	25.1588	1.45497
$300$	−36.0812	−2.08315
$301$	0.508504	0.0293097
$302$	−43.9381	−2.52835
$303$	14.5347	0.834996
$304$	0.893992	0.0512740
$305$	14.6622	0.839558
$306$	6.80759	0.389164
$307$	−1.50840	−0.0860890	−0.0430445	−	0.999073i	$-0.513706\pi$
$307$	−1.50840	−0.0860890	−0.0430445	+	0.999073i	$0.513706\pi$
$308$	−5.25431	−0.299392
$309$	−18.0813	−1.02861
$310$	54.4578	3.09300
$311$	−13.3690	−0.758088	−0.379044	−	0.925379i	$-0.623747\pi$
$311$	−13.3690	−0.758088	−0.379044	+	0.925379i	$0.623747\pi$
$312$	−12.7902	−0.724105
$313$	2.88428	0.163029	0.0815146	−	0.996672i	$-0.474024\pi$
$313$	2.88428	0.163029	0.0815146	+	0.996672i	$0.474024\pi$
$314$	−0.321804	−0.0181604
$315$	4.21837	0.237678
$316$	−12.4798	−0.702041
$317$	18.2840	1.02693	0.513465	−	0.858111i	$-0.328362\pi$
$317$	18.2840	1.02693	0.513465	+	0.858111i	$0.328362\pi$
$318$	5.23772	0.293717
$319$	14.4557	0.809363
$320$	−53.4210	−2.98632
$321$	3.56618	0.199045
$322$	7.77466	0.433265
$323$	−1.64266	−0.0914002
$324$	2.82002	0.156668
$325$	90.8996	5.04220
$326$	−19.4485	−1.07715
$327$	−18.7449	−1.03660
$328$	5.47645	0.302386
$329$	3.71913	0.205042
$330$	17.2557	0.949897
$331$	29.7199	1.63355	0.816776	−	0.576954i	$-0.195759\pi$
$331$	29.7199	1.63355	0.816776	+	0.576954i	$0.195759\pi$
$332$	−14.4020	−0.790410
$333$	−7.96976	−0.436740
$334$	46.2201	2.52905
$335$	−17.3724	−0.949154
$336$	1.68754	0.0920630
$337$	−11.9817	−0.652683	−0.326341	−	0.945252i	$-0.605816\pi$
$337$	−11.9817	−0.652683	−0.326341	+	0.945252i	$0.605816\pi$
$338$	82.2718	4.47499
$339$	−1.73057	−0.0939914
$340$	36.8864	2.00044
$341$	−10.9561	−0.593305
$342$	−1.16306	−0.0628912
$343$	1.00000	0.0539949
$344$	0.915462	0.0493584
$345$	−14.9383	−0.804253
$346$	−33.2950	−1.78995
$347$	−24.1315	−1.29545	−0.647724	−	0.761875i	$-0.724279\pi$
$347$	−24.1315	−1.29545	−0.647724	+	0.761875i	$0.724279\pi$
$348$	21.8789	1.17283
$349$	−3.28839	−0.176024	−0.0880118	−	0.996119i	$-0.528051\pi$
$349$	−3.28839	−0.176024	−0.0880118	+	0.996119i	$0.528051\pi$
$350$	28.0901	1.50148
$351$	−7.10449	−0.379209
$352$	13.6118	0.725513
$353$	2.81282	0.149711	0.0748557	−	0.997194i	$-0.476150\pi$
$353$	2.81282	0.149711	0.0748557	+	0.997194i	$0.476150\pi$
$354$	2.87161	0.152625
$355$	−54.1843	−2.87580
$356$	12.5666	0.666026
$357$	−3.10077	−0.164110
$358$	−4.97765	−0.263077
$359$	−5.81349	−0.306824	−0.153412	−	0.988162i	$-0.549026\pi$
$359$	−5.81349	−0.306824	−0.153412	+	0.988162i	$0.549026\pi$
$360$	7.59436	0.400258
$361$	−18.7194	−0.985229
$362$	29.8583	1.56931
$363$	7.52841	0.395139
$364$	20.0348	1.05011
$365$	−32.0018	−1.67505
$366$	−7.63097	−0.398877
$367$	−1.74954	−0.0913254	−0.0456627	−	0.998957i	$-0.514540\pi$
$367$	−1.74954	−0.0913254	−0.0456627	+	0.998957i	$0.514540\pi$
$368$	−5.97602	−0.311522
$369$	3.04195	0.158358
$370$	−73.8099	−3.83719
$371$	−2.38571	−0.123860
$372$	−16.5822	−0.859748
$373$	−10.2564	−0.531055	−0.265528	−	0.964103i	$-0.585546\pi$
$373$	−10.2564	−0.531055	−0.265528	+	0.964103i	$0.585546\pi$
$374$	−12.6840	−0.655876
$375$	−32.8809	−1.69796
$376$	6.69557	0.345297
$377$	−55.1197	−2.83881
$378$	−2.19545	−0.112922
$379$	25.8315	1.32687	0.663437	−	0.748232i	$-0.269097\pi$
$379$	25.8315	1.32687	0.663437	+	0.748232i	$0.269097\pi$
$380$	−6.30196	−0.323284
$381$	4.30518	0.220561
$382$	−23.0544	−1.17956
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	13.1919	0.673195
$385$	−7.85976	−0.400571
$386$	16.4129	0.835396
$387$	0.508504	0.0258487
$388$	26.3807	1.33928
$389$	17.8373	0.904387	0.452193	−	0.891920i	$-0.350642\pi$
$389$	17.8373	0.904387	0.452193	+	0.891920i	$0.350642\pi$
$390$	−65.7964	−3.33173
$391$	10.9806	0.555313
$392$	1.80031	0.0909292
$393$	6.14930	0.310191
$394$	17.7018	0.891803
$395$	−18.6681	−0.939293
$396$	−5.25431	−0.264039
$397$	21.1747	1.06273	0.531364	−	0.847143i	$-0.321680\pi$
$397$	21.1747	1.06273	0.531364	+	0.847143i	$0.321680\pi$
$398$	−34.1364	−1.71110
$399$	0.529760	0.0265212
$400$	−21.5916	−1.07958
$401$	20.5743	1.02743	0.513716	−	0.857961i	$-0.328269\pi$
$401$	20.5743	1.02743	0.513716	+	0.857961i	$0.328269\pi$
$402$	9.04145	0.450947
$403$	41.7757	2.08100
$404$	−40.9881	−2.03923
$405$	4.21837	0.209613
$406$	−17.0333	−0.845348
$407$	14.8494	0.736059
$408$	−5.58233	−0.276367
$409$	−12.1648	−0.601510	−0.300755	−	0.953701i	$-0.597239\pi$
$409$	−12.1648	−0.601510	−0.300755	+	0.953701i	$0.597239\pi$
$410$	28.1723	1.39133
$411$	−9.25062	−0.456300
$412$	50.9894	2.51207
$413$	−1.30798	−0.0643616
$414$	7.77466	0.382104
$415$	−21.5434	−1.05753
$416$	−51.9021	−2.54471
$417$	−8.43552	−0.413089
$418$	2.16704	0.105994
$419$	−6.99551	−0.341753	−0.170876	−	0.985292i	$-0.554660\pi$
$419$	−6.99551	−0.341753	−0.170876	+	0.985292i	$0.554660\pi$
$420$	−11.8959	−0.580460
$421$	−5.99266	−0.292064	−0.146032	−	0.989280i	$-0.546650\pi$
$421$	−5.99266	−0.292064	−0.146032	+	0.989280i	$0.546650\pi$
$422$	53.4132	2.60011
$423$	3.71913	0.180830
$424$	−4.29501	−0.208584
$425$	39.6733	1.92444
$426$	28.2002	1.36630
$427$	3.47580	0.168206
$428$	−10.0567	−0.486108
$429$	13.2372	0.639099
$430$	4.70938	0.227106
$431$	−1.59618	−0.0768851	−0.0384426	−	0.999261i	$-0.512240\pi$
$431$	−1.59618	−0.0768851	−0.0384426	+	0.999261i	$0.512240\pi$
$432$	1.68754	0.0811920
$433$	9.73971	0.468061	0.234030	−	0.972229i	$-0.424808\pi$
$433$	9.73971	0.468061	0.234030	+	0.972229i	$0.424808\pi$
$434$	12.9097	0.619684
$435$	32.7280	1.56919
$436$	52.8610	2.53158
$437$	−1.87601	−0.0897419
$438$	16.6553	0.795823
$439$	−39.8533	−1.90209	−0.951047	−	0.309046i	$-0.899990\pi$
$439$	−39.8533	−1.90209	−0.951047	+	0.309046i	$0.899990\pi$
$440$	−14.1500	−0.674574
$441$	1.00000	0.0476190
$442$	48.3644	2.30046
$443$	11.5291	0.547764	0.273882	−	0.961763i	$-0.411692\pi$
$443$	11.5291	0.547764	0.273882	+	0.961763i	$0.411692\pi$
$444$	22.4748	1.06661
$445$	18.7979	0.891107
$446$	−32.1423	−1.52198
$447$	12.2995	0.581746
$448$	−12.6639	−0.598312
$449$	22.1935	1.04737	0.523687	−	0.851911i	$-0.324556\pi$
$449$	22.1935	1.04737	0.523687	+	0.851911i	$0.324556\pi$
$450$	28.0901	1.32418
$451$	−5.66783	−0.266888
$452$	4.88022	0.229546
$453$	20.0132	0.940303
$454$	−53.7350	−2.52191
$455$	29.9694	1.40499
$456$	0.953729	0.0446625
$457$	−11.4603	−0.536092	−0.268046	−	0.963406i	$-0.586378\pi$
$457$	−11.4603	−0.536092	−0.268046	+	0.963406i	$0.586378\pi$
$458$	36.7179	1.71571
$459$	−3.10077	−0.144731
$460$	42.1263	1.96415
$461$	25.6597	1.19509	0.597545	−	0.801835i	$-0.296143\pi$
$461$	25.6597	1.19509	0.597545	+	0.801835i	$0.296143\pi$
$462$	4.09061	0.190313
$463$	31.0692	1.44391	0.721953	−	0.691942i	$-0.243245\pi$
$463$	31.0692	1.44391	0.721953	+	0.691942i	$0.243245\pi$
$464$	13.0927	0.607813
$465$	−24.8048	−1.15030
$466$	−53.0734	−2.45858
$467$	−15.5283	−0.718562	−0.359281	−	0.933229i	$-0.616978\pi$
$467$	−15.5283	−0.718562	−0.359281	+	0.933229i	$0.616978\pi$
$468$	20.0348	0.926107
$469$	−4.11826	−0.190164
$470$	34.4437	1.58877
$471$	0.146577	0.00675393
$472$	−2.35477	−0.108387
$473$	−0.947454	−0.0435640
$474$	9.71581	0.446262
$475$	−6.77811	−0.311001
$476$	8.74421	0.400790
$477$	−2.38571	−0.109234
$478$	30.8399	1.41058
$479$	24.3080	1.11066	0.555331	−	0.831629i	$-0.312591\pi$
$479$	24.3080	1.11066	0.555331	+	0.831629i	$0.312591\pi$
$480$	30.8175	1.40662
$481$	−56.6210	−2.58170
$482$	13.8412	0.630450
$483$	−3.54125	−0.161133
$484$	−21.2302	−0.965010
$485$	39.4621	1.79188
$486$	−2.19545	−0.0995878
$487$	−24.0735	−1.09087	−0.545436	−	0.838152i	$-0.683636\pi$
$487$	−24.0735	−1.09087	−0.545436	+	0.838152i	$0.683636\pi$
$488$	6.25751	0.283264
$489$	8.85854	0.400597
$490$	9.26124	0.418380
$491$	11.9019	0.537125	0.268563	−	0.963262i	$-0.413451\pi$
$491$	11.9019	0.537125	0.268563	+	0.963262i	$0.413451\pi$
$492$	−8.57836	−0.386742
$493$	−24.0571	−1.08348
$494$	−8.26296	−0.371768
$495$	−7.85976	−0.353270
$496$	−9.92307	−0.445559
$497$	−12.8448	−0.576169
$498$	11.2123	0.502434
$499$	26.3987	1.18177	0.590884	−	0.806756i	$-0.298779\pi$
$499$	26.3987	1.18177	0.590884	+	0.806756i	$0.298779\pi$
$500$	92.7246	4.14677
$501$	−21.0526	−0.940563
$502$	−8.67403	−0.387141
$503$	−32.0683	−1.42985	−0.714927	−	0.699199i	$-0.753540\pi$
$503$	−32.0683	−1.42985	−0.714927	+	0.699199i	$0.753540\pi$
$504$	1.80031	0.0801920
$505$	−61.3128	−2.72838
$506$	−14.4859	−0.643977
$507$	−37.4737	−1.66427
$508$	−12.1407	−0.538656
$509$	27.4241	1.21555	0.607777	−	0.794108i	$-0.292062\pi$
$509$	27.4241	1.21555	0.607777	+	0.794108i	$0.292062\pi$
$510$	−28.7170	−1.27161
$511$	−7.58629	−0.335598
$512$	18.4046	0.813376
$513$	0.529760	0.0233895
$514$	19.6072	0.864836
$515$	76.2735	3.36101
$516$	−1.43399	−0.0631278
$517$	−6.92955	−0.304761
$518$	−17.4972	−0.768784
$519$	15.1654	0.665689
$520$	53.9540	2.36604
$521$	9.43897	0.413529	0.206764	−	0.978391i	$-0.433707\pi$
$521$	9.43897	0.413529	0.206764	+	0.978391i	$0.433707\pi$
$522$	−17.0333	−0.745527
$523$	−24.1311	−1.05518	−0.527590	−	0.849499i	$-0.676904\pi$
$523$	−24.1311	−1.05518	−0.527590	+	0.849499i	$0.676904\pi$
$524$	−17.3411	−0.757551
$525$	−12.7947	−0.558406
$526$	−6.58160	−0.286971
$527$	18.2331	0.794246
$528$	−3.14427	−0.136837
$529$	−10.4595	−0.454762
$530$	−22.0946	−0.959730
$531$	−1.30798	−0.0567616
$532$	−1.49393	−0.0647701
$533$	21.6115	0.936099
$534$	−9.78338	−0.423368
$535$	−15.0435	−0.650386
$536$	−7.41413	−0.320242
$537$	2.26726	0.0978393
$538$	22.2416	0.958906
$539$	−1.86322	−0.0802546
$540$	−11.8959	−0.511917
$541$	13.5717	0.583493	0.291747	−	0.956496i	$-0.405764\pi$
$541$	13.5717	0.583493	0.291747	+	0.956496i	$0.405764\pi$
$542$	−49.7705	−2.13782
$543$	−13.6000	−0.583634
$544$	−22.6528	−0.971230
$545$	79.0731	3.38712
$546$	−15.5976	−0.667514
$547$	−31.2410	−1.33577	−0.667885	−	0.744265i	$-0.732800\pi$
$547$	−31.2410	−1.33577	−0.667885	+	0.744265i	$0.732800\pi$
$548$	26.0869	1.11438
$549$	3.47580	0.148344
$550$	−52.3381	−2.23170
$551$	4.11011	0.175096
$552$	−6.37534	−0.271353
$553$	−4.42542	−0.188188
$554$	−24.5622	−1.04355
$555$	33.6194	1.42707
$556$	23.7883	1.00885
$557$	14.9481	0.633373	0.316687	−	0.948530i	$-0.397430\pi$
$557$	14.9481	0.633373	0.316687	+	0.948530i	$0.397430\pi$
$558$	12.9097	0.546510
$559$	3.61266	0.152799
$560$	−7.11869	−0.300820
$561$	5.77742	0.243923
$562$	−46.8825	−1.97762
$563$	−10.5860	−0.446148	−0.223074	−	0.974801i	$-0.571609\pi$
$563$	−10.5860	−0.446148	−0.223074	+	0.974801i	$0.571609\pi$
$564$	−10.4880	−0.441624
$565$	7.30017	0.307121
$566$	13.7539	0.578117
$567$	1.00000	0.0419961
$568$	−23.1246	−0.970287
$569$	−31.6259	−1.32583	−0.662913	−	0.748697i	$-0.730680\pi$
$569$	−31.6259	−1.32583	−0.662913	+	0.748697i	$0.730680\pi$
$570$	4.90623	0.205499
$571$	−23.0662	−0.965292	−0.482646	−	0.875815i	$-0.660324\pi$
$571$	−23.0662	−0.965292	−0.482646	+	0.875815i	$0.660324\pi$
$572$	−37.3292	−1.56081
$573$	10.5010	0.438684
$574$	6.67847	0.278754
$575$	45.3092	1.88953
$576$	−12.6639	−0.527661
$577$	32.3531	1.34688	0.673439	−	0.739243i	$-0.264816\pi$
$577$	32.3531	1.34688	0.673439	+	0.739243i	$0.264816\pi$
$578$	−16.2139	−0.674411
$579$	−7.47587	−0.310687
$580$	−92.2934	−3.83228
$581$	−5.10705	−0.211876
$582$	−20.5381	−0.851330
$583$	4.44511	0.184097
$584$	−13.6576	−0.565157
$585$	29.9694	1.23908
$586$	26.3392	1.08806
$587$	11.4343	0.471946	0.235973	−	0.971760i	$-0.424172\pi$
$587$	11.4343	0.471946	0.235973	+	0.971760i	$0.424172\pi$
$588$	−2.82002	−0.116295
$589$	−3.11509	−0.128355
$590$	−12.1135	−0.498707
$591$	−8.06293	−0.331665
$592$	13.4493	0.552763
$593$	−43.1524	−1.77206	−0.886029	−	0.463629i	$-0.846547\pi$
$593$	−43.1524	−1.77206	−0.886029	+	0.463629i	$0.846547\pi$
$594$	4.09061	0.167840
$595$	13.0802	0.536236
$596$	−34.6848	−1.42074
$597$	15.5487	0.636364
$598$	55.2350	2.25873
$599$	−8.46508	−0.345874	−0.172937	−	0.984933i	$-0.555326\pi$
$599$	−8.46508	−0.345874	−0.172937	+	0.984933i	$0.555326\pi$
$600$	−23.0343	−0.940373
$601$	40.0122	1.63213	0.816066	−	0.577958i	$-0.196150\pi$
$601$	40.0122	1.63213	0.816066	+	0.577958i	$0.196150\pi$
$602$	1.11640	0.0455009
$603$	−4.11826	−0.167709
$604$	−56.4376	−2.29641
$605$	−31.7576	−1.29113
$606$	31.9102	1.29627
$607$	−17.9548	−0.728762	−0.364381	−	0.931250i	$-0.618719\pi$
$607$	−17.9548	−0.728762	−0.364381	+	0.931250i	$0.618719\pi$
$608$	3.87018	0.156956
$609$	7.75844	0.314388
$610$	32.1903	1.30335
$611$	26.4225	1.06894
$612$	8.74421	0.353464
$613$	45.1445	1.82337	0.911685	−	0.410890i	$-0.134782\pi$
$613$	45.1445	1.82337	0.911685	+	0.410890i	$0.134782\pi$
$614$	−3.31163	−0.133646
$615$	−12.8321	−0.517440
$616$	−3.35437	−0.135151
$617$	−25.8436	−1.04042	−0.520212	−	0.854037i	$-0.674147\pi$
$617$	−25.8436	−1.04042	−0.520212	+	0.854037i	$0.674147\pi$
$618$	−39.6966	−1.59683
$619$	−1.13065	−0.0454447	−0.0227223	−	0.999742i	$-0.507233\pi$
$619$	−1.13065	−0.0454447	−0.0227223	+	0.999742i	$0.507233\pi$
$620$	69.9500	2.80926
$621$	−3.54125	−0.142106
$622$	−29.3511	−1.17687
$623$	4.45620	0.178534
$624$	11.9891	0.479949
$625$	74.7304	2.98922
$626$	6.33231	0.253090
$627$	−0.987059	−0.0394193
$628$	−0.413351	−0.0164945
$629$	−24.7124	−0.985347
$630$	9.26124	0.368977
$631$	−17.7609	−0.707051	−0.353526	−	0.935425i	$-0.615017\pi$
$631$	−17.7609	−0.707051	−0.353526	+	0.935425i	$0.615017\pi$
$632$	−7.96711	−0.316915
$633$	−24.3290	−0.966991
$634$	40.1416	1.59423
$635$	−18.1609	−0.720692
$636$	6.72774	0.266772
$637$	7.10449	0.281490
$638$	31.7368	1.25647
$639$	−12.8448	−0.508133
$640$	−55.6483	−2.19969
$641$	17.6206	0.695970	0.347985	−	0.937500i	$-0.386866\pi$
$641$	17.6206	0.695970	0.347985	+	0.937500i	$0.386866\pi$
$642$	7.82938	0.309001
$643$	−33.5938	−1.32481	−0.662404	−	0.749146i	$-0.730464\pi$
$643$	−33.5938	−1.32481	−0.662404	+	0.749146i	$0.730464\pi$
$644$	9.98639	0.393519
$645$	−2.14506	−0.0844616
$646$	−3.60639	−0.141891
$647$	15.4941	0.609137	0.304568	−	0.952490i	$-0.401488\pi$
$647$	15.4941	0.609137	0.304568	+	0.952490i	$0.401488\pi$
$648$	1.80031	0.0707227
$649$	2.43706	0.0956630
$650$	199.566	7.82762
$651$	−5.88019	−0.230463
$652$	−24.9812	−0.978340
$653$	43.1742	1.68954	0.844769	−	0.535131i	$-0.179738\pi$
$653$	43.1742	1.68954	0.844769	+	0.535131i	$0.179738\pi$
$654$	−41.1536	−1.60923
$655$	−25.9401	−1.01356
$656$	−5.13343	−0.200427
$657$	−7.58629	−0.295969
$658$	8.16517	0.318311
$659$	3.18102	0.123915	0.0619576	−	0.998079i	$-0.480266\pi$
$659$	3.18102	0.123915	0.0619576	+	0.998079i	$0.480266\pi$
$660$	22.1647	0.862758
$661$	−26.4654	−1.02939	−0.514693	−	0.857375i	$-0.672094\pi$
$661$	−26.4654	−1.02939	−0.514693	+	0.857375i	$0.672094\pi$
$662$	65.2486	2.53596
$663$	−22.0294	−0.855550
$664$	−9.19425	−0.356806
$665$	−2.23472	−0.0866589
$666$	−17.4972	−0.678004
$667$	−27.4746	−1.06382
$668$	59.3688	2.29705
$669$	14.6404	0.566031
$670$	−38.1402	−1.47349
$671$	−6.47619	−0.250011
$672$	7.30553	0.281817
$673$	−48.6421	−1.87501	−0.937507	−	0.347967i	$-0.886872\pi$
$673$	−48.6421	−1.87501	−0.937507	+	0.347967i	$0.886872\pi$
$674$	−26.3052	−1.01324
$675$	−12.7947	−0.492467
$676$	105.676	4.06448
$677$	28.8193	1.10762	0.553808	−	0.832644i	$-0.313174\pi$
$677$	28.8193	1.10762	0.553808	+	0.832644i	$0.313174\pi$
$678$	−3.79938	−0.145914
$679$	9.35481	0.359005
$680$	23.5484	0.903038
$681$	24.4756	0.937906
$682$	−24.0536	−0.921059
$683$	−30.9062	−1.18259	−0.591296	−	0.806455i	$-0.701383\pi$
$683$	−30.9062	−1.18259	−0.591296	+	0.806455i	$0.701383\pi$
$684$	−1.49393	−0.0571219
$685$	39.0226	1.49098
$686$	2.19545	0.0838228
$687$	−16.7245	−0.638080
$688$	−0.858122	−0.0327156
$689$	−16.9492	−0.645715
$690$	−32.7964	−1.24854
$691$	6.82756	0.259733	0.129866	−	0.991532i	$-0.458545\pi$
$691$	6.82756	0.259733	0.129866	+	0.991532i	$0.458545\pi$
$692$	−42.7668	−1.62575
$693$	−1.86322	−0.0707779
$694$	−52.9796	−2.01108
$695$	35.5842	1.34978
$696$	13.9676	0.529439
$697$	9.43240	0.357278
$698$	−7.21951	−0.273262
$699$	24.1742	0.914353
$700$	36.0812	1.36374
$701$	7.48764	0.282804	0.141402	−	0.989952i	$-0.454839\pi$
$701$	7.48764	0.282804	0.141402	+	0.989952i	$0.454839\pi$
$702$	−15.5976	−0.588692
$703$	4.22206	0.159238
$704$	23.5956	0.889292
$705$	−15.6887	−0.590869
$706$	6.17542	0.232415
$707$	−14.5347	−0.546633
$708$	3.68853	0.138623
$709$	−26.0860	−0.979680	−0.489840	−	0.871812i	$-0.662945\pi$
$709$	−26.0860	−0.979680	−0.489840	+	0.871812i	$0.662945\pi$
$710$	−118.959	−4.46445
$711$	−4.42542	−0.165966
$712$	8.02252	0.300657
$713$	20.8232	0.779836
$714$	−6.80759	−0.254768
$715$	−55.8396	−2.08828
$716$	−6.39370	−0.238944
$717$	−14.0472	−0.524601
$718$	−12.7632	−0.476320
$719$	−47.8781	−1.78555	−0.892776	−	0.450501i	$-0.851246\pi$
$719$	−47.8781	−1.78555	−0.892776	+	0.450501i	$0.851246\pi$
$720$	−7.11869	−0.265298
$721$	18.0813	0.673381
$722$	−41.0975	−1.52949
$723$	−6.30449	−0.234466
$724$	38.3523	1.42535
$725$	−99.2667	−3.68667
$726$	16.5283	0.613422
$727$	48.3818	1.79438	0.897191	−	0.441643i	$-0.145604\pi$
$727$	48.3818	1.79438	0.897191	+	0.441643i	$0.145604\pi$
$728$	12.7902	0.474038
$729$	1.00000	0.0370370
$730$	−70.2585	−2.60038
$731$	1.57675	0.0583183
$732$	−9.80182	−0.362286
$733$	10.7771	0.398062	0.199031	−	0.979993i	$-0.436221\pi$
$733$	10.7771	0.398062	0.199031	+	0.979993i	$0.436221\pi$
$734$	−3.84104	−0.141775
$735$	−4.21837	−0.155597
$736$	−25.8708	−0.953609
$737$	7.67323	0.282647
$738$	6.67847	0.245838
$739$	−53.9406	−1.98424	−0.992119	−	0.125302i	$-0.960010\pi$
$739$	−53.9406	−1.98424	−0.992119	+	0.125302i	$0.960010\pi$
$740$	−94.8073	−3.48519
$741$	3.76367	0.138262
$742$	−5.23772	−0.192283
$743$	−14.5901	−0.535260	−0.267630	−	0.963522i	$-0.586241\pi$
$743$	−14.5901	−0.535260	−0.267630	+	0.963522i	$0.586241\pi$
$744$	−10.5861	−0.388106
$745$	−51.8839	−1.90088
$746$	−22.5174	−0.824421
$747$	−5.10705	−0.186857
$748$	−16.2924	−0.595709
$749$	−3.56618	−0.130305
$750$	−72.1884	−2.63595
$751$	15.4981	0.565532	0.282766	−	0.959189i	$-0.408748\pi$
$751$	15.4981	0.565532	0.282766	+	0.959189i	$0.408748\pi$
$752$	−6.27619	−0.228869
$753$	3.95090	0.143979
$754$	−121.013	−4.40702
$755$	−84.4232	−3.07248
$756$	−2.82002	−0.102563
$757$	−25.5800	−0.929720	−0.464860	−	0.885384i	$-0.653895\pi$
$757$	−25.5800	−0.929720	−0.464860	+	0.885384i	$0.653895\pi$
$758$	56.7118	2.05987
$759$	6.59814	0.239497
$760$	−4.02319	−0.145936
$761$	1.70694	0.0618766	0.0309383	−	0.999521i	$-0.490150\pi$
$761$	1.70694	0.0618766	0.0309383	+	0.999521i	$0.490150\pi$
$762$	9.45183	0.342404
$763$	18.7449	0.678612
$764$	−29.6129	−1.07136
$765$	13.0802	0.472916
$766$	−2.19545	−0.0793250
$767$	−9.29254	−0.335534
$768$	3.63440	0.131145
$769$	−24.2282	−0.873690	−0.436845	−	0.899537i	$-0.643904\pi$
$769$	−24.2282	−0.873690	−0.436845	+	0.899537i	$0.643904\pi$
$770$	−17.2557	−0.621854
$771$	−8.93082	−0.321636
$772$	21.0821	0.758761
$773$	−20.6755	−0.743645	−0.371823	−	0.928304i	$-0.621267\pi$
$773$	−20.6755	−0.743645	−0.371823	+	0.928304i	$0.621267\pi$
$774$	1.11640	0.0401280
$775$	75.2351	2.70252
$776$	16.8415	0.604575
$777$	7.96976	0.285914
$778$	39.1610	1.40399
$779$	−1.61150	−0.0577382
$780$	−84.5141	−3.02609
$781$	23.9327	0.856381
$782$	24.1074	0.862080
$783$	7.75844	0.277264
$784$	−1.68754	−0.0602694
$785$	−0.618319	−0.0220687
$786$	13.5005	0.481547
$787$	−12.1368	−0.432629	−0.216314	−	0.976324i	$-0.569404\pi$
$787$	−12.1368	−0.432629	−0.216314	+	0.976324i	$0.569404\pi$
$788$	22.7376	0.809993
$789$	2.99783	0.106726
$790$	−40.9849	−1.45818
$791$	1.73057	0.0615318
$792$	−3.35437	−0.119192
$793$	24.6938	0.876903
$794$	46.4881	1.64980
$795$	10.0638	0.356927
$796$	−43.8475	−1.55413
$797$	21.0957	0.747247	0.373623	−	0.927580i	$-0.378115\pi$
$797$	21.0957	0.747247	0.373623	+	0.927580i	$0.378115\pi$
$798$	1.16306	0.0411720
$799$	11.5322	0.407978
$800$	−93.4720	−3.30473
$801$	4.45620	0.157452
$802$	45.1699	1.59500
$803$	14.1349	0.498811
$804$	11.6136	0.409579
$805$	14.9383	0.526507
$806$	91.7166	3.23058
$807$	−10.1308	−0.356620
$808$	−26.1669	−0.920548
$809$	−3.01677	−0.106064	−0.0530320	−	0.998593i	$-0.516889\pi$
$809$	−3.01677	−0.106064	−0.0530320	+	0.998593i	$0.516889\pi$
$810$	9.26124	0.325407
$811$	43.2339	1.51815	0.759074	−	0.651004i	$-0.225652\pi$
$811$	43.2339	1.51815	0.759074	+	0.651004i	$0.225652\pi$
$812$	−21.8789	−0.767799
$813$	22.6698	0.795064
$814$	32.6012	1.14267
$815$	−37.3686	−1.30897
$816$	5.23268	0.183180
$817$	−0.269385	−0.00942458
$818$	−26.7072	−0.933796
$819$	7.10449	0.248251
$820$	36.1867	1.26370
$821$	42.1699	1.47174	0.735870	−	0.677123i	$-0.236773\pi$
$821$	42.1699	1.47174	0.735870	+	0.677123i	$0.236773\pi$
$822$	−20.3093	−0.708369
$823$	−45.9985	−1.60341	−0.801704	−	0.597721i	$-0.796073\pi$
$823$	−45.9985	−1.60341	−0.801704	+	0.597721i	$0.796073\pi$
$824$	32.5518	1.13400
$825$	23.8393	0.829978
$826$	−2.87161	−0.0999163
$827$	−13.9160	−0.483907	−0.241954	−	0.970288i	$-0.577788\pi$
$827$	−13.9160	−0.483907	−0.241954	+	0.970288i	$0.577788\pi$
$828$	9.98639	0.347051
$829$	0.856472	0.0297465	0.0148733	−	0.999889i	$-0.495266\pi$
$829$	0.856472	0.0297465	0.0148733	+	0.999889i	$0.495266\pi$
$830$	−47.2976	−1.64172
$831$	11.1878	0.388100
$832$	−89.9703	−3.11916
$833$	3.10077	0.107435
$834$	−18.5198	−0.641288
$835$	88.8079	3.07332
$836$	2.78352	0.0962701
$837$	−5.88019	−0.203249
$838$	−15.3583	−0.530544
$839$	−44.3625	−1.53156	−0.765781	−	0.643101i	$-0.777648\pi$
$839$	−44.3625	−1.53156	−0.765781	+	0.643101i	$0.777648\pi$
$840$	−7.59436	−0.262030
$841$	31.1934	1.07563
$842$	−13.1566	−0.453406
$843$	21.3543	0.735482
$844$	68.6082	2.36159
$845$	158.078	5.43805
$846$	8.16517	0.280724
$847$	−7.52841	−0.258679
$848$	4.02599	0.138253
$849$	−6.26470	−0.215004
$850$	87.1010	2.98754
$851$	−28.2230	−0.967470
$852$	36.2226	1.24097
$853$	16.8006	0.575243	0.287621	−	0.957744i	$-0.407135\pi$
$853$	16.8006	0.575243	0.287621	+	0.957744i	$0.407135\pi$
$854$	7.63097	0.261126
$855$	−2.23472	−0.0764260
$856$	−6.42022	−0.219438
$857$	15.1126	0.516238	0.258119	−	0.966113i	$-0.416897\pi$
$857$	15.1126	0.516238	0.258119	+	0.966113i	$0.416897\pi$
$858$	29.0617	0.992150
$859$	38.3631	1.30893	0.654466	−	0.756091i	$-0.272893\pi$
$859$	38.3631	1.30893	0.654466	+	0.756091i	$0.272893\pi$
$860$	6.04910	0.206273
$861$	−3.04195	−0.103670
$862$	−3.50433	−0.119358
$863$	−45.5857	−1.55176	−0.775878	−	0.630883i	$-0.782693\pi$
$863$	−45.5857	−1.55176	−0.775878	+	0.630883i	$0.782693\pi$
$864$	7.30553	0.248539
$865$	−63.9735	−2.17516
$866$	21.3831	0.726627
$867$	7.38524	0.250816
$868$	16.5822	0.562837
$869$	8.24554	0.279711
$870$	71.8528	2.43604
$871$	−29.2581	−0.991374
$872$	33.7466	1.14280
$873$	9.35481	0.316612
$874$	−4.11870	−0.139317
$875$	32.8809	1.11158
$876$	21.3934	0.722818
$877$	6.90950	0.233317	0.116659	−	0.993172i	$-0.462782\pi$
$877$	6.90950	0.233317	0.116659	+	0.993172i	$0.462782\pi$
$878$	−87.4960	−2.95285
$879$	−11.9972	−0.404654
$880$	13.2637	0.447119
$881$	12.8338	0.432381	0.216191	−	0.976351i	$-0.430637\pi$
$881$	12.8338	0.432381	0.216191	+	0.976351i	$0.430637\pi$
$882$	2.19545	0.0739248
$883$	23.8492	0.802589	0.401295	−	0.915949i	$-0.368560\pi$
$883$	23.8492	0.802589	0.401295	+	0.915949i	$0.368560\pi$
$884$	62.1231	2.08943
$885$	5.51756	0.185471
$886$	25.3116	0.850360
$887$	−24.8918	−0.835786	−0.417893	−	0.908496i	$-0.637231\pi$
$887$	−24.8918	−0.835786	−0.417893	+	0.908496i	$0.637231\pi$
$888$	14.3480	0.481488
$889$	−4.30518	−0.144391
$890$	41.2700	1.38337
$891$	−1.86322	−0.0624202
$892$	−41.2862	−1.38236
$893$	−1.97024	−0.0659317
$894$	27.0030	0.903115
$895$	−9.56413	−0.319694
$896$	−13.1919	−0.440710
$897$	−25.1588	−0.840028
$898$	48.7247	1.62596
$899$	−45.6211	−1.52155
$900$	36.0812	1.20271
$901$	−7.39754	−0.246448
$902$	−12.4435	−0.414322
$903$	−0.508504	−0.0169219
$904$	3.11555	0.103622
$905$	57.3701	1.90705
$906$	43.9381	1.45975
$907$	−51.8181	−1.72059	−0.860295	−	0.509796i	$-0.829721\pi$
$907$	−51.8181	−1.72059	−0.860295	+	0.509796i	$0.829721\pi$
$908$	−69.0215	−2.29056
$909$	−14.5347	−0.482085
$910$	65.7964	2.18113
$911$	−7.60485	−0.251960	−0.125980	−	0.992033i	$-0.540208\pi$
$911$	−7.60485	−0.251960	−0.125980	+	0.992033i	$0.540208\pi$
$912$	−0.893992	−0.0296030
$913$	9.51556	0.314919
$914$	−25.1606	−0.832240
$915$	−14.6622	−0.484719
$916$	47.1634	1.55832
$917$	−6.14930	−0.203068
$918$	−6.80759	−0.224684
$919$	−44.2742	−1.46047	−0.730235	−	0.683196i	$-0.760590\pi$
$919$	−44.2742	−1.46047	−0.730235	+	0.683196i	$0.760590\pi$
$920$	26.8936	0.886655
$921$	1.50840	0.0497035
$922$	56.3346	1.85528
$923$	−91.2558	−3.00372
$924$	5.25431	0.172854
$925$	−101.971	−3.35277
$926$	68.2109	2.24155
$927$	18.0813	0.593867
$928$	56.6795	1.86060
$929$	−7.45234	−0.244503	−0.122252	−	0.992499i	$-0.539012\pi$
$929$	−7.45234	−0.244503	−0.122252	+	0.992499i	$0.539012\pi$
$930$	−54.4578	−1.78574
$931$	−0.529760	−0.0173622
$932$	−68.1717	−2.23304
$933$	13.3690	0.437682
$934$	−34.0916	−1.11551
$935$	−24.3713	−0.797027
$936$	12.7902	0.418062
$937$	−49.7602	−1.62559	−0.812797	−	0.582547i	$-0.802056\pi$
$937$	−49.7602	−1.62559	−0.812797	+	0.582547i	$0.802056\pi$
$938$	−9.04145	−0.295214
$939$	−2.88428	−0.0941250
$940$	44.2423	1.44302
$941$	−2.32288	−0.0757238	−0.0378619	−	0.999283i	$-0.512055\pi$
$941$	−2.32288	−0.0757238	−0.0378619	+	0.999283i	$0.512055\pi$
$942$	0.321804	0.0104849
$943$	10.7723	0.350796
$944$	2.20728	0.0718408
$945$	−4.21837	−0.137224
$946$	−2.08009	−0.0676296
$947$	44.8028	1.45590	0.727948	−	0.685632i	$-0.240474\pi$
$947$	44.8028	1.45590	0.727948	+	0.685632i	$0.240474\pi$
$948$	12.4798	0.405324
$949$	−53.8967	−1.74956
$950$	−14.8810	−0.482804
$951$	−18.2840	−0.592898
$952$	5.58233	0.180924
$953$	−55.1203	−1.78552	−0.892760	−	0.450532i	$-0.851234\pi$
$953$	−55.1203	−1.78552	−0.892760	+	0.450532i	$0.851234\pi$
$954$	−5.23772	−0.169577
$955$	−44.2970	−1.43342
$956$	39.6132	1.28118
$957$	−14.4557	−0.467286
$958$	53.3672	1.72421
$959$	9.25062	0.298718
$960$	53.4210	1.72415
$961$	3.57659	0.115374
$962$	−124.309	−4.00788
$963$	−3.56618	−0.114919
$964$	17.7787	0.572615
$965$	31.5360	1.01518
$966$	−7.77466	−0.250146
$967$	24.6199	0.791723	0.395862	−	0.918310i	$-0.370446\pi$
$967$	24.6199	0.791723	0.395862	+	0.918310i	$0.370446\pi$
$968$	−13.5534	−0.435624
$969$	1.64266	0.0527699
$970$	86.6372	2.78175
$971$	−23.3372	−0.748928	−0.374464	−	0.927242i	$-0.622173\pi$
$971$	−23.3372	−0.748928	−0.374464	+	0.927242i	$0.622173\pi$
$972$	−2.82002	−0.0904520
$973$	8.43552	0.270430
$974$	−52.8522	−1.69349
$975$	−90.8996	−2.91112
$976$	−5.86557	−0.187752
$977$	54.4539	1.74214	0.871068	−	0.491162i	$-0.163428\pi$
$977$	54.4539	1.74214	0.871068	+	0.491162i	$0.163428\pi$
$978$	19.4485	0.621895
$979$	−8.30288	−0.265361
$980$	11.8959	0.380000
$981$	18.7449	0.598480
$982$	26.1301	0.833844
$983$	−8.87317	−0.283010	−0.141505	−	0.989938i	$-0.545194\pi$
$983$	−8.87317	−0.283010	−0.141505	+	0.989938i	$0.545194\pi$
$984$	−5.47645	−0.174583
$985$	34.0125	1.08373
$986$	−52.8163	−1.68201
$987$	−3.71913	−0.118381
$988$	−10.6136	−0.337664
$989$	1.80074	0.0572602
$990$	−17.2557	−0.548423
$991$	16.5459	0.525599	0.262799	−	0.964851i	$-0.415354\pi$
$991$	16.5459	0.525599	0.262799	+	0.964851i	$0.415354\pi$
$992$	−42.9579	−1.36391
$993$	−29.7199	−0.943132
$994$	−28.2002	−0.894456
$995$	−65.5901	−2.07934
$996$	14.4020	0.456343
$997$	20.8056	0.658918	0.329459	−	0.944170i	$-0.393134\pi$
$997$	20.8056	0.658918	0.329459	+	0.944170i	$0.393134\pi$
$998$	57.9571	1.83460
$999$	7.96976	0.252152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.43	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.43	✓	52	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)

\(f(q)\)	\(=\)	\(q+2.19545 q^{2} -1.00000 q^{3} +2.82002 q^{4} +4.21837 q^{5} -2.19545 q^{6} +1.00000 q^{7} +1.80031 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.19545 q^{2} -1.00000 q^{3} +2.82002 q^{4} +4.21837 q^{5} -2.19545 q^{6} +1.00000 q^{7} +1.80031 q^{8} +1.00000 q^{9} +9.26124 q^{10} -1.86322 q^{11} -2.82002 q^{12} +7.10449 q^{13} +2.19545 q^{14} -4.21837 q^{15} -1.68754 q^{16} +3.10077 q^{17} +2.19545 q^{18} -0.529760 q^{19} +11.8959 q^{20} -1.00000 q^{21} -4.09061 q^{22} +3.54125 q^{23} -1.80031 q^{24} +12.7947 q^{25} +15.5976 q^{26} -1.00000 q^{27} +2.82002 q^{28} -7.75844 q^{29} -9.26124 q^{30} +5.88019 q^{31} -7.30553 q^{32} +1.86322 q^{33} +6.80759 q^{34} +4.21837 q^{35} +2.82002 q^{36} -7.96976 q^{37} -1.16306 q^{38} -7.10449 q^{39} +7.59436 q^{40} +3.04195 q^{41} -2.19545 q^{42} +0.508504 q^{43} -5.25431 q^{44} +4.21837 q^{45} +7.77466 q^{46} +3.71913 q^{47} +1.68754 q^{48} +1.00000 q^{49} +28.0901 q^{50} -3.10077 q^{51} +20.0348 q^{52} -2.38571 q^{53} -2.19545 q^{54} -7.85976 q^{55} +1.80031 q^{56} +0.529760 q^{57} -17.0333 q^{58} -1.30798 q^{59} -11.8959 q^{60} +3.47580 q^{61} +12.9097 q^{62} +1.00000 q^{63} -12.6639 q^{64} +29.9694 q^{65} +4.09061 q^{66} -4.11826 q^{67} +8.74421 q^{68} -3.54125 q^{69} +9.26124 q^{70} -12.8448 q^{71} +1.80031 q^{72} -7.58629 q^{73} -17.4972 q^{74} -12.7947 q^{75} -1.49393 q^{76} -1.86322 q^{77} -15.5976 q^{78} -4.42542 q^{79} -7.11869 q^{80} +1.00000 q^{81} +6.67847 q^{82} -5.10705 q^{83} -2.82002 q^{84} +13.0802 q^{85} +1.11640 q^{86} +7.75844 q^{87} -3.35437 q^{88} +4.45620 q^{89} +9.26124 q^{90} +7.10449 q^{91} +9.98639 q^{92} -5.88019 q^{93} +8.16517 q^{94} -2.23472 q^{95} +7.30553 q^{96} +9.35481 q^{97} +2.19545 q^{98} -1.86322 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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