LMFDB - Embedded newform 8041.2.a.f.1.44

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			1.44
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)

$f(q)$	$=$	$q+1.17752 q^{2} -0.937959 q^{3} -0.613454 q^{4} +2.42244 q^{5} -1.10446 q^{6} -0.490967 q^{7} -3.07739 q^{8} -2.12023 q^{9} +O(q^{10})$	\(q+1.17752 q^{2} -0.937959 q^{3} -0.613454 q^{4} +2.42244 q^{5} -1.10446 q^{6} -0.490967 q^{7} -3.07739 q^{8} -2.12023 q^{9} +2.85247 q^{10} -1.00000 q^{11} +0.575395 q^{12} -2.96677 q^{13} -0.578122 q^{14} -2.27215 q^{15} -2.39676 q^{16} +1.00000 q^{17} -2.49661 q^{18} -0.937135 q^{19} -1.48606 q^{20} +0.460507 q^{21} -1.17752 q^{22} -3.83186 q^{23} +2.88646 q^{24} +0.868225 q^{25} -3.49342 q^{26} +4.80257 q^{27} +0.301186 q^{28} -1.30660 q^{29} -2.67550 q^{30} +2.86735 q^{31} +3.33254 q^{32} +0.937959 q^{33} +1.17752 q^{34} -1.18934 q^{35} +1.30067 q^{36} +2.32846 q^{37} -1.10349 q^{38} +2.78271 q^{39} -7.45479 q^{40} -2.18657 q^{41} +0.542254 q^{42} -1.00000 q^{43} +0.613454 q^{44} -5.13614 q^{45} -4.51208 q^{46} -8.29189 q^{47} +2.24807 q^{48} -6.75895 q^{49} +1.02235 q^{50} -0.937959 q^{51} +1.81998 q^{52} +11.6749 q^{53} +5.65510 q^{54} -2.42244 q^{55} +1.51089 q^{56} +0.878994 q^{57} -1.53854 q^{58} -2.07184 q^{59} +1.39386 q^{60} +3.29863 q^{61} +3.37635 q^{62} +1.04096 q^{63} +8.71765 q^{64} -7.18682 q^{65} +1.10446 q^{66} +13.9095 q^{67} -0.613454 q^{68} +3.59412 q^{69} -1.40047 q^{70} +9.75810 q^{71} +6.52478 q^{72} -1.85064 q^{73} +2.74181 q^{74} -0.814359 q^{75} +0.574889 q^{76} +0.490967 q^{77} +3.27668 q^{78} +13.8138 q^{79} -5.80602 q^{80} +1.85609 q^{81} -2.57472 q^{82} -2.99238 q^{83} -0.282500 q^{84} +2.42244 q^{85} -1.17752 q^{86} +1.22554 q^{87} +3.07739 q^{88} +1.39655 q^{89} -6.04789 q^{90} +1.45658 q^{91} +2.35067 q^{92} -2.68945 q^{93} -9.76383 q^{94} -2.27015 q^{95} -3.12579 q^{96} -7.16533 q^{97} -7.95878 q^{98} +2.12023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * 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 $

$2$	1.17752	0.832630	0.416315	−	0.909220i	$-0.363321\pi$
$2$	1.17752	0.832630	0.416315	+	0.909220i	$0.363321\pi$
$3$	−0.937959	−0.541531	−0.270765	−	0.962645i	$-0.587277\pi$
$3$	−0.937959	−0.541531	−0.270765	+	0.962645i	$0.587277\pi$
$4$	−0.613454	−0.306727
$5$	2.42244	1.08335	0.541674	−	0.840588i	$-0.317791\pi$
$5$	2.42244	1.08335	0.541674	+	0.840588i	$0.317791\pi$
$6$	−1.10446	−0.450895
$7$	−0.490967	−0.185568	−0.0927840	−	0.995686i	$-0.529577\pi$
$7$	−0.490967	−0.185568	−0.0927840	+	0.995686i	$0.529577\pi$
$8$	−3.07739	−1.08802
$9$	−2.12023	−0.706744
$10$	2.85247	0.902029
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.575395	0.166102
$13$	−2.96677	−0.822833	−0.411417	−	0.911447i	$-0.634966\pi$
$13$	−2.96677	−0.822833	−0.411417	+	0.911447i	$0.634966\pi$
$14$	−0.578122	−0.154510
$15$	−2.27215	−0.586667
$16$	−2.39676	−0.599191
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.49661	−0.588457
$19$	−0.937135	−0.214993	−0.107497	−	0.994205i	$-0.534284\pi$
$19$	−0.937135	−0.214993	−0.107497	+	0.994205i	$0.534284\pi$
$20$	−1.48606	−0.332293
$21$	0.460507	0.100491
$22$	−1.17752	−0.251047
$23$	−3.83186	−0.798997	−0.399499	−	0.916734i	$-0.630816\pi$
$23$	−3.83186	−0.798997	−0.399499	+	0.916734i	$0.630816\pi$
$24$	2.88646	0.589196
$25$	0.868225	0.173645
$26$	−3.49342	−0.685116
$27$	4.80257	0.924255
$28$	0.301186	0.0569188
$29$	−1.30660	−0.242629	−0.121315	−	0.992614i	$-0.538711\pi$
$29$	−1.30660	−0.242629	−0.121315	+	0.992614i	$0.538711\pi$
$30$	−2.67550	−0.488476
$31$	2.86735	0.514991	0.257496	−	0.966279i	$-0.417103\pi$
$31$	2.86735	0.514991	0.257496	+	0.966279i	$0.417103\pi$
$32$	3.33254	0.589116
$33$	0.937959	0.163278
$34$	1.17752	0.201942
$35$	−1.18934	−0.201035
$36$	1.30067	0.216778
$37$	2.32846	0.382797	0.191399	−	0.981512i	$-0.438698\pi$
$37$	2.32846	0.382797	0.191399	+	0.981512i	$0.438698\pi$
$38$	−1.10349	−0.179010
$39$	2.78271	0.445590
$40$	−7.45479	−1.17871
$41$	−2.18657	−0.341485	−0.170742	−	0.985316i	$-0.554617\pi$
$41$	−2.18657	−0.341485	−0.170742	+	0.985316i	$0.554617\pi$
$42$	0.542254	0.0836717
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.613454	0.0924817
$45$	−5.13614	−0.765651
$46$	−4.51208	−0.665269
$47$	−8.29189	−1.20950	−0.604748	−	0.796417i	$-0.706726\pi$
$47$	−8.29189	−1.20950	−0.604748	+	0.796417i	$0.706726\pi$
$48$	2.24807	0.324480
$49$	−6.75895	−0.965565
$50$	1.02235	0.144582
$51$	−0.937959	−0.131340
$52$	1.81998	0.252385
$53$	11.6749	1.60367	0.801834	−	0.597547i	$-0.203858\pi$
$53$	11.6749	1.60367	0.801834	+	0.597547i	$0.203858\pi$
$54$	5.65510	0.769562
$55$	−2.42244	−0.326642
$56$	1.51089	0.201902
$57$	0.878994	0.116426
$58$	−1.53854	−0.202021
$59$	−2.07184	−0.269731	−0.134865	−	0.990864i	$-0.543060\pi$
$59$	−2.07184	−0.269731	−0.134865	+	0.990864i	$0.543060\pi$
$60$	1.39386	0.179947
$61$	3.29863	0.422346	0.211173	−	0.977449i	$-0.432272\pi$
$61$	3.29863	0.422346	0.211173	+	0.977449i	$0.432272\pi$
$62$	3.37635	0.428797
$63$	1.04096	0.131149
$64$	8.71765	1.08971
$65$	−7.18682	−0.891416
$66$	1.10446	0.135950
$67$	13.9095	1.69931	0.849655	−	0.527338i	$-0.176810\pi$
$67$	13.9095	1.69931	0.849655	+	0.527338i	$0.176810\pi$
$68$	−0.613454	−0.0743923
$69$	3.59412	0.432682
$70$	−1.40047	−0.167388
$71$	9.75810	1.15807	0.579037	−	0.815301i	$-0.303429\pi$
$71$	9.75810	1.15807	0.579037	+	0.815301i	$0.303429\pi$
$72$	6.52478	0.768952
$73$	−1.85064	−0.216601	−0.108300	−	0.994118i	$-0.534541\pi$
$73$	−1.85064	−0.216601	−0.108300	+	0.994118i	$0.534541\pi$
$74$	2.74181	0.318728
$75$	−0.814359	−0.0940341
$76$	0.574889	0.0659443
$77$	0.490967	0.0559509
$78$	3.27668	0.371011
$79$	13.8138	1.55418	0.777089	−	0.629390i	$-0.216695\pi$
$79$	13.8138	1.55418	0.777089	+	0.629390i	$0.216695\pi$
$80$	−5.80602	−0.649133
$81$	1.85609	0.206232
$82$	−2.57472	−0.284331
$83$	−2.99238	−0.328456	−0.164228	−	0.986422i	$-0.552513\pi$
$83$	−2.99238	−0.328456	−0.164228	+	0.986422i	$0.552513\pi$
$84$	−0.282500	−0.0308233
$85$	2.42244	0.262751
$86$	−1.17752	−0.126975
$87$	1.22554	0.131391
$88$	3.07739	0.328050
$89$	1.39655	0.148033	0.0740167	−	0.997257i	$-0.476418\pi$
$89$	1.39655	0.148033	0.0740167	+	0.997257i	$0.476418\pi$
$90$	−6.04789	−0.637504
$91$	1.45658	0.152692
$92$	2.35067	0.245074
$93$	−2.68945	−0.278883
$94$	−9.76383	−1.00706
$95$	−2.27015	−0.232913
$96$	−3.12579	−0.319024
$97$	−7.16533	−0.727529	−0.363765	−	0.931491i	$-0.618509\pi$
$97$	−7.16533	−0.727529	−0.363765	+	0.931491i	$0.618509\pi$
$98$	−7.95878	−0.803958
$99$	2.12023	0.213091
$100$	−0.532617	−0.0532617
$101$	2.73662	0.272304	0.136152	−	0.990688i	$-0.456526\pi$
$101$	2.73662	0.272304	0.136152	+	0.990688i	$0.456526\pi$
$102$	−1.10446	−0.109358
$103$	−11.4700	−1.13018	−0.565088	−	0.825031i	$-0.691158\pi$
$103$	−11.4700	−1.13018	−0.565088	+	0.825031i	$0.691158\pi$
$104$	9.12989	0.895259
$105$	1.11555	0.108867
$106$	13.7474	1.33526
$107$	10.4493	1.01017	0.505084	−	0.863070i	$-0.331461\pi$
$107$	10.4493	1.01017	0.505084	+	0.863070i	$0.331461\pi$
$108$	−2.94616	−0.283494
$109$	9.85207	0.943657	0.471829	−	0.881690i	$-0.343594\pi$
$109$	9.85207	0.943657	0.471829	+	0.881690i	$0.343594\pi$
$110$	−2.85247	−0.271972
$111$	−2.18400	−0.207296
$112$	1.17673	0.111191
$113$	−5.59507	−0.526340	−0.263170	−	0.964749i	$-0.584768\pi$
$113$	−5.59507	−0.526340	−0.263170	+	0.964749i	$0.584768\pi$
$114$	1.03503	0.0969394
$115$	−9.28245	−0.865593
$116$	0.801539	0.0744210
$117$	6.29024	0.581533
$118$	−2.43963	−0.224586
$119$	−0.490967	−0.0450069
$120$	6.99229	0.638305
$121$	1.00000	0.0909091
$122$	3.88419	0.351658
$123$	2.05091	0.184925
$124$	−1.75899	−0.157962
$125$	−10.0090	−0.895231
$126$	1.22575	0.109199
$127$	−16.0375	−1.42310	−0.711550	−	0.702635i	$-0.752007\pi$
$127$	−16.0375	−1.42310	−0.711550	+	0.702635i	$0.752007\pi$
$128$	3.60010	0.318207
$129$	0.937959	0.0825827
$130$	−8.46260	−0.742219
$131$	9.82555	0.858462	0.429231	−	0.903195i	$-0.358785\pi$
$131$	9.82555	0.858462	0.429231	+	0.903195i	$0.358785\pi$
$132$	−0.575395	−0.0500817
$133$	0.460102	0.0398959
$134$	16.3786	1.41490
$135$	11.6339	1.00129
$136$	−3.07739	−0.263884
$137$	12.9217	1.10398	0.551988	−	0.833852i	$-0.313869\pi$
$137$	12.9217	1.10398	0.551988	+	0.833852i	$0.313869\pi$
$138$	4.23214	0.360264
$139$	−5.20687	−0.441641	−0.220820	−	0.975315i	$-0.570873\pi$
$139$	−5.20687	−0.441641	−0.220820	+	0.975315i	$0.570873\pi$
$140$	0.729605	0.0616629
$141$	7.77745	0.654979
$142$	11.4903	0.964247
$143$	2.96677	0.248094
$144$	5.08170	0.423475
$145$	−3.16516	−0.262852
$146$	−2.17916	−0.180348
$147$	6.33962	0.522883
$148$	−1.42841	−0.117414
$149$	12.0269	0.985283	0.492642	−	0.870232i	$-0.336031\pi$
$149$	12.0269	0.985283	0.492642	+	0.870232i	$0.336031\pi$
$150$	−0.958922	−0.0782956
$151$	−13.1058	−1.06654	−0.533268	−	0.845946i	$-0.679036\pi$
$151$	−13.1058	−1.06654	−0.533268	+	0.845946i	$0.679036\pi$
$152$	2.88392	0.233917
$153$	−2.12023	−0.171411
$154$	0.578122	0.0465864
$155$	6.94599	0.557915
$156$	−1.70706	−0.136674
$157$	−1.04890	−0.0837111	−0.0418555	−	0.999124i	$-0.513327\pi$
$157$	−1.04890	−0.0837111	−0.0418555	+	0.999124i	$0.513327\pi$
$158$	16.2660	1.29406
$159$	−10.9506	−0.868435
$160$	8.07289	0.638218
$161$	1.88131	0.148268
$162$	2.18558	0.171715
$163$	24.0716	1.88543	0.942716	−	0.333597i	$-0.108263\pi$
$163$	24.0716	1.88543	0.942716	+	0.333597i	$0.108263\pi$
$164$	1.34136	0.104743
$165$	2.27215	0.176887
$166$	−3.52358	−0.273483
$167$	1.46128	0.113077	0.0565384	−	0.998400i	$-0.481994\pi$
$167$	1.46128	0.113077	0.0565384	+	0.998400i	$0.481994\pi$
$168$	−1.41716	−0.109336
$169$	−4.19829	−0.322945
$170$	2.85247	0.218774
$171$	1.98694	0.151945
$172$	0.613454	0.0467755
$173$	14.4392	1.09779	0.548897	−	0.835890i	$-0.315048\pi$
$173$	14.4392	1.09779	0.548897	+	0.835890i	$0.315048\pi$
$174$	1.44309	0.109400
$175$	−0.426270	−0.0322230
$176$	2.39676	0.180663
$177$	1.94330	0.146067
$178$	1.64446	0.123257
$179$	5.56318	0.415811	0.207906	−	0.978149i	$-0.433335\pi$
$179$	5.56318	0.415811	0.207906	+	0.978149i	$0.433335\pi$
$180$	3.15079	0.234846
$181$	3.64881	0.271214	0.135607	−	0.990763i	$-0.456702\pi$
$181$	3.64881	0.271214	0.135607	+	0.990763i	$0.456702\pi$
$182$	1.71515	0.127136
$183$	−3.09398	−0.228713
$184$	11.7921	0.869325
$185$	5.64057	0.414703
$186$	−3.16688	−0.232207
$187$	−1.00000	−0.0731272
$188$	5.08669	0.370985
$189$	−2.35790	−0.171512
$190$	−2.67314	−0.193930
$191$	3.17133	0.229470	0.114735	−	0.993396i	$-0.463398\pi$
$191$	3.17133	0.229470	0.114735	+	0.993396i	$0.463398\pi$
$192$	−8.17680	−0.590110
$193$	13.1868	0.949210	0.474605	−	0.880199i	$-0.342591\pi$
$193$	13.1868	0.949210	0.474605	+	0.880199i	$0.342591\pi$
$194$	−8.43730	−0.605763
$195$	6.74094	0.482729
$196$	4.14631	0.296165
$197$	−1.45767	−0.103855	−0.0519273	−	0.998651i	$-0.516536\pi$
$197$	−1.45767	−0.103855	−0.0519273	+	0.998651i	$0.516536\pi$
$198$	2.49661	0.177426
$199$	13.5802	0.962678	0.481339	−	0.876535i	$-0.340151\pi$
$199$	13.5802	0.962678	0.481339	+	0.876535i	$0.340151\pi$
$200$	−2.67186	−0.188929
$201$	−13.0465	−0.920229
$202$	3.22242	0.226729
$203$	0.641497	0.0450243
$204$	0.575395	0.0402857
$205$	−5.29684	−0.369947
$206$	−13.5061	−0.941018
$207$	8.12443	0.564687
$208$	7.11064	0.493034
$209$	0.937135	0.0648230
$210$	1.31358	0.0906456
$211$	20.8350	1.43434	0.717169	−	0.696899i	$-0.245437\pi$
$211$	20.8350	1.43434	0.717169	+	0.696899i	$0.245437\pi$
$212$	−7.16200	−0.491889
$213$	−9.15270	−0.627133
$214$	12.3042	0.841097
$215$	−2.42244	−0.165209
$216$	−14.7794	−1.00561
$217$	−1.40777	−0.0955659
$218$	11.6010	0.785717
$219$	1.73582	0.117296
$220$	1.48606	0.100190
$221$	−2.96677	−0.199566
$222$	−2.57170	−0.172601
$223$	−4.86385	−0.325708	−0.162854	−	0.986650i	$-0.552070\pi$
$223$	−4.86385	−0.325708	−0.162854	+	0.986650i	$0.552070\pi$
$224$	−1.63617	−0.109321
$225$	−1.84084	−0.122723
$226$	−6.58829	−0.438247
$227$	15.6370	1.03786	0.518932	−	0.854815i	$-0.326330\pi$
$227$	15.6370	1.03786	0.518932	+	0.854815i	$0.326330\pi$
$228$	−0.539222	−0.0357109
$229$	18.0079	1.19000	0.594998	−	0.803727i	$-0.297153\pi$
$229$	18.0079	1.19000	0.594998	+	0.803727i	$0.297153\pi$
$230$	−10.9302	−0.720719
$231$	−0.460507	−0.0302991
$232$	4.02091	0.263986
$233$	−12.4232	−0.813871	−0.406936	−	0.913457i	$-0.633403\pi$
$233$	−12.4232	−0.813871	−0.406936	+	0.913457i	$0.633403\pi$
$234$	7.40686	0.484202
$235$	−20.0866	−1.31031
$236$	1.27098	0.0827337
$237$	−12.9568	−0.841636
$238$	−0.578122	−0.0374741
$239$	8.72444	0.564337	0.282168	−	0.959365i	$-0.408946\pi$
$239$	8.72444	0.564337	0.282168	+	0.959365i	$0.408946\pi$
$240$	5.44581	0.351526
$241$	0.529461	0.0341056	0.0170528	−	0.999855i	$-0.494572\pi$
$241$	0.529461	0.0341056	0.0170528	+	0.999855i	$0.494572\pi$
$242$	1.17752	0.0756936
$243$	−16.1486	−1.03594
$244$	−2.02356	−0.129545
$245$	−16.3732	−1.04604
$246$	2.41498	0.153974
$247$	2.78026	0.176904
$248$	−8.82394	−0.560321
$249$	2.80673	0.177869
$250$	−11.7857	−0.745396
$251$	−28.9569	−1.82774	−0.913871	−	0.406005i	$-0.866922\pi$
$251$	−28.9569	−1.82774	−0.913871	+	0.406005i	$0.866922\pi$
$252$	−0.638584	−0.0402270
$253$	3.83186	0.240907
$254$	−18.8845	−1.18492
$255$	−2.27215	−0.142288
$256$	−13.1961	−0.824758
$257$	−1.31302	−0.0819040	−0.0409520	−	0.999161i	$-0.513039\pi$
$257$	−1.31302	−0.0819040	−0.0409520	+	0.999161i	$0.513039\pi$
$258$	1.10446	0.0687608
$259$	−1.14320	−0.0710349
$260$	4.40879	0.273421
$261$	2.77030	0.171477
$262$	11.5697	0.714781
$263$	4.84120	0.298521	0.149261	−	0.988798i	$-0.452311\pi$
$263$	4.84120	0.298521	0.149261	+	0.988798i	$0.452311\pi$
$264$	−2.88646	−0.177649
$265$	28.2817	1.73733
$266$	0.541778	0.0332185
$267$	−1.30990	−0.0801647
$268$	−8.53282	−0.521225
$269$	2.31954	0.141425	0.0707126	−	0.997497i	$-0.477473\pi$
$269$	2.31954	0.141425	0.0707126	+	0.997497i	$0.477473\pi$
$270$	13.6992	0.833704
$271$	1.31424	0.0798346	0.0399173	−	0.999203i	$-0.487291\pi$
$271$	1.31424	0.0798346	0.0399173	+	0.999203i	$0.487291\pi$
$272$	−2.39676	−0.145325
$273$	−1.36622	−0.0826872
$274$	15.2155	0.919204
$275$	−0.868225	−0.0523560
$276$	−2.20483	−0.132715
$277$	−3.74768	−0.225176	−0.112588	−	0.993642i	$-0.535914\pi$
$277$	−3.74768	−0.225176	−0.112588	+	0.993642i	$0.535914\pi$
$278$	−6.13117	−0.367723
$279$	−6.07945	−0.363967
$280$	3.66005	0.218730
$281$	−16.3214	−0.973656	−0.486828	−	0.873498i	$-0.661846\pi$
$281$	−16.3214	−0.973656	−0.486828	+	0.873498i	$0.661846\pi$
$282$	9.15807	0.545355
$283$	9.19701	0.546706	0.273353	−	0.961914i	$-0.411867\pi$
$283$	9.19701	0.546706	0.273353	+	0.961914i	$0.411867\pi$
$284$	−5.98615	−0.355213
$285$	2.12931	0.126129
$286$	3.49342	0.206570
$287$	1.07353	0.0633687
$288$	−7.06577	−0.416354
$289$	1.00000	0.0588235
$290$	−3.72703	−0.218859
$291$	6.72078	0.393979
$292$	1.13528	0.0664374
$293$	−18.1460	−1.06010	−0.530049	−	0.847967i	$-0.677827\pi$
$293$	−18.1460	−1.06010	−0.530049	+	0.847967i	$0.677827\pi$
$294$	7.46501	0.435368
$295$	−5.01891	−0.292212
$296$	−7.16558	−0.416491
$297$	−4.80257	−0.278673
$298$	14.1619	0.820377
$299$	11.3682	0.657442
$300$	0.499572	0.0288428
$301$	0.490967	0.0282989
$302$	−15.4323	−0.888030
$303$	−2.56684	−0.147461
$304$	2.24609	0.128822
$305$	7.99074	0.457548
$306$	−2.49661	−0.142722
$307$	13.3688	0.763000	0.381500	−	0.924369i	$-0.375408\pi$
$307$	13.3688	0.763000	0.381500	+	0.924369i	$0.375408\pi$
$308$	−0.301186	−0.0171617
$309$	10.7584	0.612025
$310$	8.17901	0.464537
$311$	16.2672	0.922429	0.461214	−	0.887289i	$-0.347414\pi$
$311$	16.2672	0.922429	0.461214	+	0.887289i	$0.347414\pi$
$312$	−8.56346	−0.484810
$313$	−16.5182	−0.933661	−0.466831	−	0.884347i	$-0.654604\pi$
$313$	−16.5182	−0.933661	−0.466831	+	0.884347i	$0.654604\pi$
$314$	−1.23509	−0.0697003
$315$	2.52168	0.142080
$316$	−8.47416	−0.476709
$317$	−2.70947	−0.152179	−0.0760895	−	0.997101i	$-0.524243\pi$
$317$	−2.70947	−0.152179	−0.0760895	+	0.997101i	$0.524243\pi$
$318$	−12.8945	−0.723085
$319$	1.30660	0.0731555
$320$	21.1180	1.18053
$321$	−9.80098	−0.547037
$322$	2.21528	0.123453
$323$	−0.937135	−0.0521436
$324$	−1.13863	−0.0632570
$325$	−2.57582	−0.142881
$326$	28.3447	1.56987
$327$	−9.24084	−0.511019
$328$	6.72892	0.371542
$329$	4.07104	0.224444
$330$	2.67550	0.147281
$331$	−3.27256	−0.179876	−0.0899381	−	0.995947i	$-0.528667\pi$
$331$	−3.27256	−0.179876	−0.0899381	+	0.995947i	$0.528667\pi$
$332$	1.83569	0.100746
$333$	−4.93689	−0.270540
$334$	1.72068	0.0941512
$335$	33.6949	1.84095
$336$	−1.10373	−0.0602132
$337$	26.0783	1.42057	0.710287	−	0.703913i	$-0.248565\pi$
$337$	26.0783	1.42057	0.710287	+	0.703913i	$0.248565\pi$
$338$	−4.94356	−0.268894
$339$	5.24795	0.285029
$340$	−1.48606	−0.0805928
$341$	−2.86735	−0.155276
$342$	2.33966	0.126514
$343$	6.75519	0.364746
$344$	3.07739	0.165922
$345$	8.70656	0.468745
$346$	17.0024	0.914057
$347$	−12.6576	−0.679497	−0.339748	−	0.940516i	$-0.610342\pi$
$347$	−12.6576	−0.679497	−0.339748	+	0.940516i	$0.610342\pi$
$348$	−0.751811	−0.0403013
$349$	−8.42216	−0.450828	−0.225414	−	0.974263i	$-0.572373\pi$
$349$	−8.42216	−0.450828	−0.225414	+	0.974263i	$0.572373\pi$
$350$	−0.501940	−0.0268298
$351$	−14.2481	−0.760507
$352$	−3.33254	−0.177625
$353$	9.36291	0.498337	0.249169	−	0.968460i	$-0.419843\pi$
$353$	9.36291	0.498337	0.249169	+	0.968460i	$0.419843\pi$
$354$	2.28827	0.121620
$355$	23.6384	1.25460
$356$	−0.856717	−0.0454059
$357$	0.460507	0.0243726
$358$	6.55073	0.346217
$359$	−7.18187	−0.379045	−0.189522	−	0.981876i	$-0.560694\pi$
$359$	−7.18187	−0.379045	−0.189522	+	0.981876i	$0.560694\pi$
$360$	15.8059	0.833044
$361$	−18.1218	−0.953778
$362$	4.29653	0.225821
$363$	−0.937959	−0.0492301
$364$	−0.893548	−0.0468347
$365$	−4.48306	−0.234654
$366$	−3.64321	−0.190434
$367$	−1.00083	−0.0522427	−0.0261214	−	0.999659i	$-0.508316\pi$
$367$	−1.00083	−0.0522427	−0.0261214	+	0.999659i	$0.508316\pi$
$368$	9.18406	0.478752
$369$	4.63604	0.241343
$370$	6.64186	0.345294
$371$	−5.73198	−0.297589
$372$	1.64986	0.0855412
$373$	−8.84176	−0.457809	−0.228904	−	0.973449i	$-0.573514\pi$
$373$	−8.84176	−0.457809	−0.228904	+	0.973449i	$0.573514\pi$
$374$	−1.17752	−0.0608879
$375$	9.38801	0.484795
$376$	25.5173	1.31596
$377$	3.87638	0.199644
$378$	−2.77647	−0.142806
$379$	−21.9816	−1.12912	−0.564560	−	0.825392i	$-0.690954\pi$
$379$	−21.9816	−1.12912	−0.564560	+	0.825392i	$0.690954\pi$
$380$	1.39264	0.0714407
$381$	15.0425	0.770653
$382$	3.73430	0.191063
$383$	−32.6035	−1.66596	−0.832980	−	0.553303i	$-0.813367\pi$
$383$	−32.6035	−1.66596	−0.832980	+	0.553303i	$0.813367\pi$
$384$	−3.37674	−0.172319
$385$	1.18934	0.0606143
$386$	15.5277	0.790341
$387$	2.12023	0.107778
$388$	4.39560	0.223153
$389$	27.6239	1.40059	0.700294	−	0.713855i	$-0.253052\pi$
$389$	27.6239	1.40059	0.700294	+	0.713855i	$0.253052\pi$
$390$	7.93757	0.401935
$391$	−3.83186	−0.193785
$392$	20.7999	1.05055
$393$	−9.21596	−0.464884
$394$	−1.71643	−0.0864724
$395$	33.4632	1.68372
$396$	−1.30067	−0.0653610
$397$	32.3239	1.62229	0.811145	−	0.584844i	$-0.198844\pi$
$397$	32.3239	1.62229	0.811145	+	0.584844i	$0.198844\pi$
$398$	15.9910	0.801555
$399$	−0.431557	−0.0216049
$400$	−2.08093	−0.104047
$401$	−3.47635	−0.173601	−0.0868004	−	0.996226i	$-0.527664\pi$
$401$	−3.47635	−0.173601	−0.0868004	+	0.996226i	$0.527664\pi$
$402$	−15.3625	−0.766210
$403$	−8.50676	−0.423752
$404$	−1.67879	−0.0835231
$405$	4.49627	0.223421
$406$	0.755373	0.0374886
$407$	−2.32846	−0.115418
$408$	2.88646	0.142901
$409$	0.763628	0.0377590	0.0188795	−	0.999822i	$-0.493990\pi$
$409$	0.763628	0.0377590	0.0188795	+	0.999822i	$0.493990\pi$
$410$	−6.23712	−0.308029
$411$	−12.1200	−0.597837
$412$	7.03634	0.346655
$413$	1.01720	0.0500534
$414$	9.56665	0.470175
$415$	−7.24886	−0.355833
$416$	−9.88688	−0.484744
$417$	4.88383	0.239162
$418$	1.10349	0.0539735
$419$	30.2812	1.47933	0.739666	−	0.672974i	$-0.234983\pi$
$419$	30.2812	1.47933	0.739666	+	0.672974i	$0.234983\pi$
$420$	−0.684340	−0.0333923
$421$	−1.54920	−0.0755033	−0.0377516	−	0.999287i	$-0.512020\pi$
$421$	−1.54920	−0.0755033	−0.0377516	+	0.999287i	$0.512020\pi$
$422$	24.5335	1.19427
$423$	17.5807	0.854804
$424$	−35.9281	−1.74482
$425$	0.868225	0.0421151
$426$	−10.7775	−0.522169
$427$	−1.61952	−0.0783740
$428$	−6.41015	−0.309846
$429$	−2.78271	−0.134350
$430$	−2.85247	−0.137558
$431$	−5.02867	−0.242222	−0.121111	−	0.992639i	$-0.538646\pi$
$431$	−5.02867	−0.242222	−0.121111	+	0.992639i	$0.538646\pi$
$432$	−11.5106	−0.553805
$433$	−29.3895	−1.41237	−0.706184	−	0.708028i	$-0.749585\pi$
$433$	−29.3895	−1.41237	−0.706184	+	0.708028i	$0.749585\pi$
$434$	−1.65768	−0.0795710
$435$	2.96879	0.142343
$436$	−6.04380	−0.289445
$437$	3.59097	0.171779
$438$	2.04396	0.0976642
$439$	−7.90658	−0.377360	−0.188680	−	0.982039i	$-0.560421\pi$
$439$	−7.90658	−0.377360	−0.188680	+	0.982039i	$0.560421\pi$
$440$	7.45479	0.355393
$441$	14.3306	0.682407
$442$	−3.49342	−0.166165
$443$	−0.911964	−0.0433287	−0.0216643	−	0.999765i	$-0.506897\pi$
$443$	−0.911964	−0.0433287	−0.0216643	+	0.999765i	$0.506897\pi$
$444$	1.33979	0.0635834
$445$	3.38305	0.160372
$446$	−5.72727	−0.271194
$447$	−11.2808	−0.533561
$448$	−4.28008	−0.202215
$449$	5.22658	0.246657	0.123329	−	0.992366i	$-0.460643\pi$
$449$	5.22658	0.246657	0.123329	+	0.992366i	$0.460643\pi$
$450$	−2.16762	−0.102183
$451$	2.18657	0.102962
$452$	3.43232	0.161443
$453$	12.2927	0.577562
$454$	18.4128	0.864157
$455$	3.52849	0.165418
$456$	−2.70500	−0.126673
$457$	−25.7898	−1.20640	−0.603199	−	0.797591i	$-0.706108\pi$
$457$	−25.7898	−1.20640	−0.603199	+	0.797591i	$0.706108\pi$
$458$	21.2046	0.990826
$459$	4.80257	0.224165
$460$	5.69436	0.265501
$461$	2.83373	0.131980	0.0659900	−	0.997820i	$-0.478979\pi$
$461$	2.83373	0.131980	0.0659900	+	0.997820i	$0.478979\pi$
$462$	−0.542254	−0.0252280
$463$	6.69289	0.311045	0.155523	−	0.987832i	$-0.450294\pi$
$463$	6.69289	0.311045	0.155523	+	0.987832i	$0.450294\pi$
$464$	3.13161	0.145381
$465$	−6.51505	−0.302128
$466$	−14.6285	−0.677654
$467$	33.7385	1.56123	0.780615	−	0.625012i	$-0.214906\pi$
$467$	33.7385	1.56123	0.780615	+	0.625012i	$0.214906\pi$
$468$	−3.85878	−0.178372
$469$	−6.82908	−0.315338
$470$	−23.6523	−1.09100
$471$	0.983822	0.0453321
$472$	6.37585	0.293472
$473$	1.00000	0.0459800
$474$	−15.2569	−0.700771
$475$	−0.813644	−0.0373325
$476$	0.301186	0.0138048
$477$	−24.7535	−1.13338
$478$	10.2732	0.469884
$479$	−20.3225	−0.928557	−0.464278	−	0.885689i	$-0.653686\pi$
$479$	−20.3225	−0.928557	−0.464278	+	0.885689i	$0.653686\pi$
$480$	−7.57204	−0.345615
$481$	−6.90801	−0.314978
$482$	0.623449	0.0283973
$483$	−1.76460	−0.0802919
$484$	−0.613454	−0.0278843
$485$	−17.3576	−0.788168
$486$	−19.0153	−0.862551
$487$	40.9339	1.85489	0.927447	−	0.373954i	$-0.121998\pi$
$487$	40.9339	1.85489	0.927447	+	0.373954i	$0.121998\pi$
$488$	−10.1512	−0.459521
$489$	−22.5781	−1.02102
$490$	−19.2797	−0.870967
$491$	37.0109	1.67028	0.835139	−	0.550039i	$-0.185387\pi$
$491$	37.0109	1.67028	0.835139	+	0.550039i	$0.185387\pi$
$492$	−1.25814	−0.0567214
$493$	−1.30660	−0.0588463
$494$	3.27380	0.147295
$495$	5.13614	0.230852
$496$	−6.87236	−0.308578
$497$	−4.79091	−0.214902
$498$	3.30497	0.148099
$499$	26.4844	1.18561	0.592803	−	0.805348i	$-0.298021\pi$
$499$	26.4844	1.18561	0.592803	+	0.805348i	$0.298021\pi$
$500$	6.14006	0.274592
$501$	−1.37062	−0.0612346
$502$	−34.0972	−1.52183
$503$	13.5179	0.602734	0.301367	−	0.953508i	$-0.402557\pi$
$503$	13.5179	0.602734	0.301367	+	0.953508i	$0.402557\pi$
$504$	−3.20345	−0.142693
$505$	6.62931	0.295001
$506$	4.51208	0.200586
$507$	3.93782	0.174885
$508$	9.83829	0.436504
$509$	−5.35699	−0.237444	−0.118722	−	0.992928i	$-0.537880\pi$
$509$	−5.35699	−0.237444	−0.118722	+	0.992928i	$0.537880\pi$
$510$	−2.67550	−0.118473
$511$	0.908602	0.0401942
$512$	−22.7389	−1.00493
$513$	−4.50065	−0.198709
$514$	−1.54610	−0.0681957
$515$	−27.7855	−1.22437
$516$	−0.575395	−0.0253303
$517$	8.29189	0.364677
$518$	−1.34614	−0.0591458
$519$	−13.5434	−0.594490
$520$	22.1166	0.969878
$521$	1.68559	0.0738470	0.0369235	−	0.999318i	$-0.488244\pi$
$521$	1.68559	0.0738470	0.0369235	+	0.999318i	$0.488244\pi$
$522$	3.26207	0.142777
$523$	26.7876	1.17134	0.585670	−	0.810550i	$-0.300831\pi$
$523$	26.7876	1.17134	0.585670	+	0.810550i	$0.300831\pi$
$524$	−6.02753	−0.263314
$525$	0.399824	0.0174497
$526$	5.70059	0.248558
$527$	2.86735	0.124904
$528$	−2.24807	−0.0978345
$529$	−8.31687	−0.361603
$530$	33.3022	1.44655
$531$	4.39278	0.190631
$532$	−0.282252	−0.0122372
$533$	6.48704	0.280985
$534$	−1.54243	−0.0667475
$535$	25.3127	1.09436
$536$	−42.8048	−1.84888
$537$	−5.21803	−0.225175
$538$	2.73130	0.117755
$539$	6.75895	0.291129
$540$	−7.13689	−0.307123
$541$	−17.1931	−0.739189	−0.369595	−	0.929193i	$-0.620503\pi$
$541$	−17.1931	−0.739189	−0.369595	+	0.929193i	$0.620503\pi$
$542$	1.54754	0.0664727
$543$	−3.42243	−0.146870
$544$	3.33254	0.142882
$545$	23.8661	1.02231
$546$	−1.60874	−0.0688478
$547$	31.4170	1.34330	0.671648	−	0.740871i	$-0.265587\pi$
$547$	31.4170	1.34330	0.671648	+	0.740871i	$0.265587\pi$
$548$	−7.92688	−0.338620
$549$	−6.99386	−0.298491
$550$	−1.02235	−0.0435931
$551$	1.22446	0.0521637
$552$	−11.0605	−0.470766
$553$	−6.78214	−0.288406
$554$	−4.41295	−0.187488
$555$	−5.29062	−0.224574
$556$	3.19417	0.135463
$557$	41.9771	1.77863	0.889313	−	0.457298i	$-0.151183\pi$
$557$	41.9771	1.77863	0.889313	+	0.457298i	$0.151183\pi$
$558$	−7.15865	−0.303050
$559$	2.96677	0.125481
$560$	2.85057	0.120458
$561$	0.937959	0.0396006
$562$	−19.2188	−0.810695
$563$	26.8635	1.13216	0.566081	−	0.824350i	$-0.308459\pi$
$563$	26.8635	1.13216	0.566081	+	0.824350i	$0.308459\pi$
$564$	−4.77111	−0.200900
$565$	−13.5537	−0.570210
$566$	10.8296	0.455204
$567$	−0.911279	−0.0382701
$568$	−30.0295	−1.26001
$569$	−31.2488	−1.31002	−0.655008	−	0.755622i	$-0.727335\pi$
$569$	−31.2488	−1.31002	−0.655008	+	0.755622i	$0.727335\pi$
$570$	2.50730	0.105019
$571$	9.75484	0.408227	0.204114	−	0.978947i	$-0.434569\pi$
$571$	9.75484	0.408227	0.204114	+	0.978947i	$0.434569\pi$
$572$	−1.81998	−0.0760970
$573$	−2.97458	−0.124265
$574$	1.26410	0.0527627
$575$	−3.32691	−0.138742
$576$	−18.4835	−0.770144
$577$	3.85339	0.160419	0.0802095	−	0.996778i	$-0.474441\pi$
$577$	3.85339	0.160419	0.0802095	+	0.996778i	$0.474441\pi$
$578$	1.17752	0.0489782
$579$	−12.3687	−0.514026
$580$	1.94168	0.0806240
$581$	1.46916	0.0609510
$582$	7.91384	0.328039
$583$	−11.6749	−0.483524
$584$	5.69513	0.235666
$585$	15.2377	0.630003
$586$	−21.3672	−0.882670
$587$	−25.2326	−1.04146	−0.520729	−	0.853722i	$-0.674340\pi$
$587$	−25.2326	−1.04146	−0.520729	+	0.853722i	$0.674340\pi$
$588$	−3.88907	−0.160382
$589$	−2.68709	−0.110720
$590$	−5.90985	−0.243305
$591$	1.36723	0.0562404
$592$	−5.58078	−0.229369
$593$	31.4229	1.29038	0.645192	−	0.764021i	$-0.276777\pi$
$593$	31.4229	1.29038	0.645192	+	0.764021i	$0.276777\pi$
$594$	−5.65510	−0.232032
$595$	−1.18934	−0.0487581
$596$	−7.37796	−0.302213
$597$	−12.7377	−0.521320
$598$	13.3863	0.547406
$599$	9.86362	0.403016	0.201508	−	0.979487i	$-0.435416\pi$
$599$	9.86362	0.403016	0.201508	+	0.979487i	$0.435416\pi$
$600$	2.50610	0.102311
$601$	6.93153	0.282743	0.141371	−	0.989957i	$-0.454849\pi$
$601$	6.93153	0.282743	0.141371	+	0.989957i	$0.454849\pi$
$602$	0.578122	0.0235625
$603$	−29.4913	−1.20098
$604$	8.03982	0.327136
$605$	2.42244	0.0984863
$606$	−3.02250	−0.122781
$607$	4.33606	0.175995	0.0879976	−	0.996121i	$-0.471953\pi$
$607$	4.33606	0.175995	0.0879976	+	0.996121i	$0.471953\pi$
$608$	−3.12304	−0.126656
$609$	−0.601698	−0.0243820
$610$	9.40923	0.380969
$611$	24.6001	0.995213
$612$	1.30067	0.0525763
$613$	−10.7529	−0.434305	−0.217153	−	0.976138i	$-0.569677\pi$
$613$	−10.7529	−0.434305	−0.217153	+	0.976138i	$0.569677\pi$
$614$	15.7420	0.635297
$615$	4.96822	0.200338
$616$	−1.51089	−0.0608757
$617$	20.3821	0.820553	0.410277	−	0.911961i	$-0.365432\pi$
$617$	20.3821	0.820553	0.410277	+	0.911961i	$0.365432\pi$
$618$	12.6682	0.509590
$619$	35.3181	1.41955	0.709776	−	0.704427i	$-0.248796\pi$
$619$	35.3181	1.41955	0.709776	+	0.704427i	$0.248796\pi$
$620$	−4.26105	−0.171128
$621$	−18.4028	−0.738477
$622$	19.1549	0.768042
$623$	−0.685657	−0.0274703
$624$	−6.66949	−0.266993
$625$	−28.5873	−1.14349
$626$	−19.4504	−0.777394
$627$	−0.878994	−0.0351036
$628$	0.643450	0.0256765
$629$	2.32846	0.0928419
$630$	2.96932	0.118300
$631$	5.71953	0.227691	0.113845	−	0.993498i	$-0.463683\pi$
$631$	5.71953	0.227691	0.113845	+	0.993498i	$0.463683\pi$
$632$	−42.5105	−1.69098
$633$	−19.5423	−0.776739
$634$	−3.19045	−0.126709
$635$	−38.8500	−1.54171
$636$	6.71767	0.266373
$637$	20.0522	0.794499
$638$	1.53854	0.0609115
$639$	−20.6895	−0.818462
$640$	8.72103	0.344729
$641$	−7.78516	−0.307495	−0.153748	−	0.988110i	$-0.549134\pi$
$641$	−7.78516	−0.307495	−0.153748	+	0.988110i	$0.549134\pi$
$642$	−11.5408	−0.455480
$643$	−5.19937	−0.205043	−0.102521	−	0.994731i	$-0.532691\pi$
$643$	−5.19937	−0.205043	−0.102521	+	0.994731i	$0.532691\pi$
$644$	−1.15410	−0.0454779
$645$	2.27215	0.0894658
$646$	−1.10349	−0.0434163
$647$	32.2940	1.26961	0.634804	−	0.772673i	$-0.281081\pi$
$647$	32.2940	1.26961	0.634804	+	0.772673i	$0.281081\pi$
$648$	−5.71191	−0.224385
$649$	2.07184	0.0813268
$650$	−3.03307	−0.118967
$651$	1.32043	0.0517519
$652$	−14.7668	−0.578313
$653$	−30.9400	−1.21078	−0.605388	−	0.795931i	$-0.706982\pi$
$653$	−30.9400	−1.21078	−0.605388	+	0.795931i	$0.706982\pi$
$654$	−10.8812	−0.425490
$655$	23.8018	0.930014
$656$	5.24069	0.204615
$657$	3.92378	0.153081
$658$	4.79372	0.186879
$659$	12.2367	0.476673	0.238337	−	0.971183i	$-0.423398\pi$
$659$	12.2367	0.476673	0.238337	+	0.971183i	$0.423398\pi$
$660$	−1.39386	−0.0542560
$661$	3.53661	0.137558	0.0687790	−	0.997632i	$-0.478090\pi$
$661$	3.53661	0.137558	0.0687790	+	0.997632i	$0.478090\pi$
$662$	−3.85350	−0.149770
$663$	2.78271	0.108071
$664$	9.20870	0.357367
$665$	1.11457	0.0432212
$666$	−5.81327	−0.225260
$667$	5.00670	0.193860
$668$	−0.896426	−0.0346838
$669$	4.56209	0.176381
$670$	39.6763	1.53283
$671$	−3.29863	−0.127342
$672$	1.53466	0.0592007
$673$	38.6219	1.48876	0.744382	−	0.667754i	$-0.232744\pi$
$673$	38.6219	1.48876	0.744382	+	0.667754i	$0.232744\pi$
$674$	30.7076	1.18281
$675$	4.16971	0.160492
$676$	2.57546	0.0990561
$677$	21.8584	0.840086	0.420043	−	0.907504i	$-0.362015\pi$
$677$	21.8584	0.840086	0.420043	+	0.907504i	$0.362015\pi$
$678$	6.17955	0.237324
$679$	3.51794	0.135006
$680$	−7.45479	−0.285878
$681$	−14.6669	−0.562035
$682$	−3.37635	−0.129287
$683$	24.3564	0.931973	0.465987	−	0.884792i	$-0.345700\pi$
$683$	24.3564	0.931973	0.465987	+	0.884792i	$0.345700\pi$
$684$	−1.21890	−0.0466058
$685$	31.3021	1.19599
$686$	7.95435	0.303698
$687$	−16.8907	−0.644419
$688$	2.39676	0.0913758
$689$	−34.6366	−1.31955
$690$	10.2521	0.390291
$691$	−38.8433	−1.47767	−0.738835	−	0.673886i	$-0.764624\pi$
$691$	−38.8433	−1.47767	−0.738835	+	0.673886i	$0.764624\pi$
$692$	−8.85781	−0.336724
$693$	−1.04096	−0.0395430
$694$	−14.9046	−0.565769
$695$	−12.6133	−0.478451
$696$	−3.77145	−0.142956
$697$	−2.18657	−0.0828222
$698$	−9.91724	−0.375373
$699$	11.6525	0.440736
$700$	0.261497	0.00988366
$701$	−6.43451	−0.243028	−0.121514	−	0.992590i	$-0.538775\pi$
$701$	−6.43451	−0.243028	−0.121514	+	0.992590i	$0.538775\pi$
$702$	−16.7774	−0.633221
$703$	−2.18208	−0.0822989
$704$	−8.71765	−0.328559
$705$	18.8404	0.709571
$706$	11.0250	0.414931
$707$	−1.34359	−0.0505310
$708$	−1.19213	−0.0448028
$709$	−4.62613	−0.173738	−0.0868689	−	0.996220i	$-0.527686\pi$
$709$	−4.62613	−0.173738	−0.0868689	+	0.996220i	$0.527686\pi$
$710$	27.8347	1.04462
$711$	−29.2886	−1.09841
$712$	−4.29771	−0.161063
$713$	−10.9873	−0.411476
$714$	0.542254	0.0202934
$715$	7.18682	0.268772
$716$	−3.41276	−0.127541
$717$	−8.18316	−0.305606
$718$	−8.45677	−0.315604
$719$	−9.37472	−0.349618	−0.174809	−	0.984602i	$-0.555931\pi$
$719$	−9.37472	−0.349618	−0.174809	+	0.984602i	$0.555931\pi$
$720$	12.3101	0.458771
$721$	5.63140	0.209724
$722$	−21.3387	−0.794144
$723$	−0.496612	−0.0184692
$724$	−2.23838	−0.0831886
$725$	−1.13442	−0.0421314
$726$	−1.10446	−0.0409904
$727$	−14.3313	−0.531520	−0.265760	−	0.964039i	$-0.585623\pi$
$727$	−14.3313	−0.531520	−0.265760	+	0.964039i	$0.585623\pi$
$728$	−4.48247	−0.166132
$729$	9.57849	0.354759
$730$	−5.27888	−0.195380
$731$	−1.00000	−0.0369863
$732$	1.89801	0.0701526
$733$	13.8861	0.512895	0.256447	−	0.966558i	$-0.417448\pi$
$733$	13.8861	0.512895	0.256447	+	0.966558i	$0.417448\pi$
$734$	−1.17849	−0.0434989
$735$	15.3574	0.566465
$736$	−12.7698	−0.470702
$737$	−13.9095	−0.512361
$738$	5.45901	0.200949
$739$	−24.2392	−0.891654	−0.445827	−	0.895119i	$-0.647090\pi$
$739$	−24.2392	−0.891654	−0.445827	+	0.895119i	$0.647090\pi$
$740$	−3.46023	−0.127201
$741$	−2.60777	−0.0957988
$742$	−6.74950	−0.247782
$743$	−22.7414	−0.834303	−0.417151	−	0.908837i	$-0.636972\pi$
$743$	−22.7414	−0.834303	−0.417151	+	0.908837i	$0.636972\pi$
$744$	8.27649	0.303431
$745$	29.1345	1.06741
$746$	−10.4113	−0.381185
$747$	6.34454	0.232135
$748$	0.613454	0.0224301
$749$	−5.13024	−0.187455
$750$	11.0545	0.403655
$751$	30.6146	1.11714	0.558571	−	0.829457i	$-0.311350\pi$
$751$	30.6146	1.11714	0.558571	+	0.829457i	$0.311350\pi$
$752$	19.8737	0.724719
$753$	27.1604	0.989778
$754$	4.56450	0.166229
$755$	−31.7481	−1.15543
$756$	1.44647	0.0526074
$757$	5.47452	0.198975	0.0994874	−	0.995039i	$-0.468280\pi$
$757$	5.47452	0.198975	0.0994874	+	0.995039i	$0.468280\pi$
$758$	−25.8837	−0.940140
$759$	−3.59412	−0.130458
$760$	6.98614	0.253414
$761$	14.8871	0.539658	0.269829	−	0.962908i	$-0.413033\pi$
$761$	14.8871	0.539658	0.269829	+	0.962908i	$0.413033\pi$
$762$	17.7128	0.641668
$763$	−4.83704	−0.175113
$764$	−1.94547	−0.0703846
$765$	−5.13614	−0.185698
$766$	−38.3911	−1.38713
$767$	6.14667	0.221943
$768$	12.3774	0.446632
$769$	44.0166	1.58728	0.793640	−	0.608388i	$-0.208184\pi$
$769$	44.0166	1.58728	0.793640	+	0.608388i	$0.208184\pi$
$770$	1.40047	0.0504693
$771$	1.23156	0.0443535
$772$	−8.08953	−0.291149
$773$	−11.0834	−0.398643	−0.199322	−	0.979934i	$-0.563874\pi$
$773$	−11.0834	−0.398643	−0.199322	+	0.979934i	$0.563874\pi$
$774$	2.49661	0.0897388
$775$	2.48950	0.0894256
$776$	22.0505	0.791566
$777$	1.07227	0.0384676
$778$	32.5276	1.16617
$779$	2.04911	0.0734170
$780$	−4.13526	−0.148066
$781$	−9.75810	−0.349172
$782$	−4.51208	−0.161351
$783$	−6.27503	−0.224251
$784$	16.1996	0.578558
$785$	−2.54089	−0.0906883
$786$	−10.8519	−0.387076
$787$	41.7902	1.48966	0.744830	−	0.667255i	$-0.232531\pi$
$787$	41.7902	1.48966	0.744830	+	0.667255i	$0.232531\pi$
$788$	0.894213	0.0318550
$789$	−4.54085	−0.161658
$790$	39.4035	1.40191
$791$	2.74700	0.0976719
$792$	−6.52478	−0.231848
$793$	−9.78627	−0.347521
$794$	38.0620	1.35077
$795$	−26.5271	−0.940819
$796$	−8.33086	−0.295280
$797$	1.36233	0.0482561	0.0241281	−	0.999709i	$-0.492319\pi$
$797$	1.36233	0.0482561	0.0241281	+	0.999709i	$0.492319\pi$
$798$	−0.508165	−0.0179889
$799$	−8.29189	−0.293346
$800$	2.89340	0.102297
$801$	−2.96100	−0.104622
$802$	−4.09347	−0.144545
$803$	1.85064	0.0653076
$804$	8.00343	0.282259
$805$	4.55738	0.160626
$806$	−10.0168	−0.352828
$807$	−2.17564	−0.0765860
$808$	−8.42165	−0.296273
$809$	18.0433	0.634369	0.317185	−	0.948364i	$-0.397263\pi$
$809$	18.0433	0.634369	0.317185	+	0.948364i	$0.397263\pi$
$810$	5.29443	0.186027
$811$	36.7971	1.29212	0.646061	−	0.763286i	$-0.276415\pi$
$811$	36.7971	1.29212	0.646061	+	0.763286i	$0.276415\pi$
$812$	−0.393529	−0.0138102
$813$	−1.23271	−0.0432329
$814$	−2.74181	−0.0961002
$815$	58.3120	2.04258
$816$	2.24807	0.0786981
$817$	0.937135	0.0327862
$818$	0.899185	0.0314393
$819$	−3.08830	−0.107914
$820$	3.24937	0.113473
$821$	22.6320	0.789863	0.394931	−	0.918711i	$-0.370768\pi$
$821$	22.6320	0.789863	0.394931	+	0.918711i	$0.370768\pi$
$822$	−14.2715	−0.497777
$823$	11.1888	0.390016	0.195008	−	0.980802i	$-0.437527\pi$
$823$	11.1888	0.390016	0.195008	+	0.980802i	$0.437527\pi$
$824$	35.2977	1.22965
$825$	0.814359	0.0283524
$826$	1.19778	0.0416759
$827$	−23.9680	−0.833448	−0.416724	−	0.909033i	$-0.636822\pi$
$827$	−23.9680	−0.833448	−0.416724	+	0.909033i	$0.636822\pi$
$828$	−4.98397	−0.173205
$829$	−24.0085	−0.833850	−0.416925	−	0.908941i	$-0.636892\pi$
$829$	−24.0085	−0.833850	−0.416925	+	0.908941i	$0.636892\pi$
$830$	−8.53566	−0.296277
$831$	3.51517	0.121940
$832$	−25.8633	−0.896647
$833$	−6.75895	−0.234184
$834$	5.75079	0.199133
$835$	3.53985	0.122502
$836$	−0.574889	−0.0198830
$837$	13.7706	0.475983
$838$	35.6566	1.23174
$839$	0.951893	0.0328630	0.0164315	−	0.999865i	$-0.494769\pi$
$839$	0.951893	0.0328630	0.0164315	+	0.999865i	$0.494769\pi$
$840$	−3.43298	−0.118449
$841$	−27.2928	−0.941131
$842$	−1.82421	−0.0628663
$843$	15.3088	0.527265
$844$	−12.7813	−0.439951
$845$	−10.1701	−0.349863
$846$	20.7016	0.711736
$847$	−0.490967	−0.0168698
$848$	−27.9819	−0.960904
$849$	−8.62642	−0.296058
$850$	1.02235	0.0350663
$851$	−8.92234	−0.305854
$852$	5.61476	0.192359
$853$	−32.6530	−1.11802	−0.559009	−	0.829162i	$-0.688818\pi$
$853$	−32.6530	−1.11802	−0.559009	+	0.829162i	$0.688818\pi$
$854$	−1.90701	−0.0652565
$855$	4.81326	0.164610
$856$	−32.1564	−1.09908
$857$	−41.5152	−1.41813	−0.709066	−	0.705142i	$-0.750883\pi$
$857$	−41.5152	−1.41813	−0.709066	+	0.705142i	$0.750883\pi$
$858$	−3.27668	−0.111864
$859$	−13.9536	−0.476092	−0.238046	−	0.971254i	$-0.576507\pi$
$859$	−13.9536	−0.476092	−0.238046	+	0.971254i	$0.576507\pi$
$860$	1.48606	0.0506741
$861$	−1.00693	−0.0343161
$862$	−5.92134	−0.201682
$863$	−52.9568	−1.80267	−0.901335	−	0.433122i	$-0.857412\pi$
$863$	−52.9568	−1.80267	−0.901335	+	0.433122i	$0.857412\pi$
$864$	16.0048	0.544493
$865$	34.9782	1.18929
$866$	−34.6066	−1.17598
$867$	−0.937959	−0.0318547
$868$	0.863605	0.0293127
$869$	−13.8138	−0.468603
$870$	3.49580	0.118519
$871$	−41.2661	−1.39825
$872$	−30.3186	−1.02672
$873$	15.1922	0.514177
$874$	4.22842	0.143028
$875$	4.91408	0.166126
$876$	−1.06485	−0.0359779
$877$	−45.4689	−1.53537	−0.767687	−	0.640825i	$-0.778593\pi$
$877$	−45.4689	−1.53537	−0.767687	+	0.640825i	$0.778593\pi$
$878$	−9.31012	−0.314201
$879$	17.0202	0.574076
$880$	5.80602	0.195721
$881$	−24.6726	−0.831241	−0.415621	−	0.909538i	$-0.636436\pi$
$881$	−24.6726	−0.831241	−0.415621	+	0.909538i	$0.636436\pi$
$882$	16.8745	0.568193
$883$	−23.0329	−0.775117	−0.387559	−	0.921845i	$-0.626682\pi$
$883$	−23.0329	−0.775117	−0.387559	+	0.921845i	$0.626682\pi$
$884$	1.81998	0.0612124
$885$	4.70753	0.158242
$886$	−1.07385	−0.0360768
$887$	−31.0308	−1.04191	−0.520956	−	0.853584i	$-0.674424\pi$
$887$	−31.0308	−1.04191	−0.520956	+	0.853584i	$0.674424\pi$
$888$	6.72102	0.225543
$889$	7.87389	0.264082
$890$	3.98360	0.133530
$891$	−1.85609	−0.0621813
$892$	2.98375	0.0999034
$893$	7.77061	0.260034
$894$	−13.2833	−0.444259
$895$	13.4765	0.450469
$896$	−1.76753	−0.0590490
$897$	−10.6629	−0.356025
$898$	6.15438	0.205374
$899$	−3.74648	−0.124952
$900$	1.12927	0.0376424
$901$	11.6749	0.388947
$902$	2.57472	0.0857289
$903$	−0.460507	−0.0153247
$904$	17.2182	0.572669
$905$	8.83902	0.293819
$906$	14.4749	0.480896
$907$	−1.32952	−0.0441460	−0.0220730	−	0.999756i	$-0.507027\pi$
$907$	−1.32952	−0.0441460	−0.0220730	+	0.999756i	$0.507027\pi$
$908$	−9.59259	−0.318341
$909$	−5.80228	−0.192450
$910$	4.15486	0.137732
$911$	−24.7084	−0.818625	−0.409312	−	0.912394i	$-0.634231\pi$
$911$	−24.7084	−0.818625	−0.409312	+	0.912394i	$0.634231\pi$
$912$	−2.10674	−0.0697612
$913$	2.99238	0.0990333
$914$	−30.3680	−1.00448
$915$	−7.49498	−0.247777
$916$	−11.0470	−0.365004
$917$	−4.82402	−0.159303
$918$	5.65510	0.186646
$919$	50.5793	1.66846	0.834229	−	0.551418i	$-0.185913\pi$
$919$	50.5793	1.66846	0.834229	+	0.551418i	$0.185913\pi$
$920$	28.5657	0.941783
$921$	−12.5394	−0.413188
$922$	3.33677	0.109891
$923$	−28.9500	−0.952902
$924$	0.282500	0.00929356
$925$	2.02163	0.0664708
$926$	7.88099	0.258985
$927$	24.3191	0.798745
$928$	−4.35430	−0.142937
$929$	37.0212	1.21463	0.607313	−	0.794462i	$-0.292247\pi$
$929$	37.0212	1.21463	0.607313	+	0.794462i	$0.292247\pi$
$930$	−7.67158	−0.251561
$931$	6.33405	0.207590
$932$	7.62107	0.249636
$933$	−15.2580	−0.499523
$934$	39.7276	1.29993
$935$	−2.42244	−0.0792223
$936$	−19.3575	−0.632720
$937$	−35.3407	−1.15453	−0.577266	−	0.816556i	$-0.695880\pi$
$937$	−35.3407	−1.15453	−0.577266	+	0.816556i	$0.695880\pi$
$938$	−8.04136	−0.262560
$939$	15.4933	0.505606
$940$	12.3222	0.401907
$941$	−45.4989	−1.48322	−0.741610	−	0.670831i	$-0.765938\pi$
$941$	−45.4989	−1.48322	−0.741610	+	0.670831i	$0.765938\pi$
$942$	1.15847	0.0377449
$943$	8.37862	0.272845
$944$	4.96571	0.161620
$945$	−5.71188	−0.185807
$946$	1.17752	0.0382844
$947$	−21.2406	−0.690226	−0.345113	−	0.938561i	$-0.612159\pi$
$947$	−21.2406	−0.690226	−0.345113	+	0.938561i	$0.612159\pi$
$948$	7.94842	0.258153
$949$	5.49041	0.178226
$950$	−0.958079	−0.0310842
$951$	2.54137	0.0824096
$952$	1.51089	0.0489684
$953$	−36.4126	−1.17952	−0.589760	−	0.807578i	$-0.700778\pi$
$953$	−36.4126	−1.17952	−0.589760	+	0.807578i	$0.700778\pi$
$954$	−29.1476	−0.943689
$955$	7.68237	0.248596
$956$	−5.35204	−0.173097
$957$	−1.22554	−0.0396160
$958$	−23.9300	−0.773144
$959$	−6.34413	−0.204863
$960$	−19.8078	−0.639295
$961$	−22.7783	−0.734784
$962$	−8.13430	−0.262260
$963$	−22.1549	−0.713931
$964$	−0.324800	−0.0104611
$965$	31.9444	1.02833
$966$	−2.07784	−0.0668534
$967$	19.7339	0.634598	0.317299	−	0.948326i	$-0.397224\pi$
$967$	19.7339	0.634598	0.317299	+	0.948326i	$0.397224\pi$
$968$	−3.07739	−0.0989109
$969$	0.878994	0.0282373
$970$	−20.4389	−0.656252
$971$	−33.8969	−1.08780	−0.543902	−	0.839148i	$-0.683054\pi$
$971$	−33.8969	−1.08780	−0.543902	+	0.839148i	$0.683054\pi$
$972$	9.90645	0.317750
$973$	2.55640	0.0819544
$974$	48.2004	1.54444
$975$	2.41602	0.0773744
$976$	−7.90604	−0.253066
$977$	27.4727	0.878930	0.439465	−	0.898260i	$-0.355168\pi$
$977$	27.4727	0.878930	0.439465	+	0.898260i	$0.355168\pi$
$978$	−26.5861	−0.850131
$979$	−1.39655	−0.0446338
$980$	10.0442	0.320850
$981$	−20.8887	−0.666925
$982$	43.5809	1.39072
$983$	−47.3615	−1.51060	−0.755299	−	0.655381i	$-0.772508\pi$
$983$	−47.3615	−1.51060	−0.755299	+	0.655381i	$0.772508\pi$
$984$	−6.31145	−0.201202
$985$	−3.53112	−0.112511
$986$	−1.53854	−0.0489972
$987$	−3.81847	−0.121543
$988$	−1.70556	−0.0542612
$989$	3.83186	0.121846
$990$	6.04789	0.192215
$991$	38.8154	1.23301	0.616506	−	0.787350i	$-0.288548\pi$
$991$	38.8154	1.23301	0.616506	+	0.787350i	$0.288548\pi$
$992$	9.55556	0.303389
$993$	3.06953	0.0974085
$994$	−5.64137	−0.178933
$995$	32.8974	1.04292
$996$	−1.72180	−0.0545573
$997$	−7.68188	−0.243287	−0.121644	−	0.992574i	$-0.538817\pi$
$997$	−7.68188	−0.243287	−0.121644	+	0.992574i	$0.538817\pi$
$998$	31.1859	0.987171
$999$	11.1826	0.353802

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.44	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.44	✓	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)

\(f(q)\)	\(=\)	\(q+1.17752 q^{2} -0.937959 q^{3} -0.613454 q^{4} +2.42244 q^{5} -1.10446 q^{6} -0.490967 q^{7} -3.07739 q^{8} -2.12023 q^{9} +O(q^{10})\)	\(q+1.17752 q^{2} -0.937959 q^{3} -0.613454 q^{4} +2.42244 q^{5} -1.10446 q^{6} -0.490967 q^{7} -3.07739 q^{8} -2.12023 q^{9} +2.85247 q^{10} -1.00000 q^{11} +0.575395 q^{12} -2.96677 q^{13} -0.578122 q^{14} -2.27215 q^{15} -2.39676 q^{16} +1.00000 q^{17} -2.49661 q^{18} -0.937135 q^{19} -1.48606 q^{20} +0.460507 q^{21} -1.17752 q^{22} -3.83186 q^{23} +2.88646 q^{24} +0.868225 q^{25} -3.49342 q^{26} +4.80257 q^{27} +0.301186 q^{28} -1.30660 q^{29} -2.67550 q^{30} +2.86735 q^{31} +3.33254 q^{32} +0.937959 q^{33} +1.17752 q^{34} -1.18934 q^{35} +1.30067 q^{36} +2.32846 q^{37} -1.10349 q^{38} +2.78271 q^{39} -7.45479 q^{40} -2.18657 q^{41} +0.542254 q^{42} -1.00000 q^{43} +0.613454 q^{44} -5.13614 q^{45} -4.51208 q^{46} -8.29189 q^{47} +2.24807 q^{48} -6.75895 q^{49} +1.02235 q^{50} -0.937959 q^{51} +1.81998 q^{52} +11.6749 q^{53} +5.65510 q^{54} -2.42244 q^{55} +1.51089 q^{56} +0.878994 q^{57} -1.53854 q^{58} -2.07184 q^{59} +1.39386 q^{60} +3.29863 q^{61} +3.37635 q^{62} +1.04096 q^{63} +8.71765 q^{64} -7.18682 q^{65} +1.10446 q^{66} +13.9095 q^{67} -0.613454 q^{68} +3.59412 q^{69} -1.40047 q^{70} +9.75810 q^{71} +6.52478 q^{72} -1.85064 q^{73} +2.74181 q^{74} -0.814359 q^{75} +0.574889 q^{76} +0.490967 q^{77} +3.27668 q^{78} +13.8138 q^{79} -5.80602 q^{80} +1.85609 q^{81} -2.57472 q^{82} -2.99238 q^{83} -0.282500 q^{84} +2.42244 q^{85} -1.17752 q^{86} +1.22554 q^{87} +3.07739 q^{88} +1.39655 q^{89} -6.04789 q^{90} +1.45658 q^{91} +2.35067 q^{92} -2.68945 q^{93} -9.76383 q^{94} -2.27015 q^{95} -3.12579 q^{96} -7.16533 q^{97} -7.95878 q^{98} +2.12023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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