LMFDB - Embedded newform 8041.2.a.f.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.30842 q^{2} -0.505193 q^{3} -0.288029 q^{4} +1.89375 q^{5} +0.661007 q^{6} -3.03323 q^{7} +2.99371 q^{8} -2.74478 q^{9} +O(q^{10})$	\(q-1.30842 q^{2} -0.505193 q^{3} -0.288029 q^{4} +1.89375 q^{5} +0.661007 q^{6} -3.03323 q^{7} +2.99371 q^{8} -2.74478 q^{9} -2.47782 q^{10} -1.00000 q^{11} +0.145510 q^{12} -6.24301 q^{13} +3.96874 q^{14} -0.956708 q^{15} -3.34098 q^{16} +1.00000 q^{17} +3.59133 q^{18} +2.28848 q^{19} -0.545453 q^{20} +1.53237 q^{21} +1.30842 q^{22} -3.46769 q^{23} -1.51240 q^{24} -1.41373 q^{25} +8.16850 q^{26} +2.90222 q^{27} +0.873656 q^{28} +4.34709 q^{29} +1.25178 q^{30} -4.24723 q^{31} -1.61600 q^{32} +0.505193 q^{33} -1.30842 q^{34} -5.74416 q^{35} +0.790575 q^{36} +0.285368 q^{37} -2.99430 q^{38} +3.15393 q^{39} +5.66933 q^{40} -6.95498 q^{41} -2.00498 q^{42} -1.00000 q^{43} +0.288029 q^{44} -5.19791 q^{45} +4.53720 q^{46} +6.26374 q^{47} +1.68784 q^{48} +2.20045 q^{49} +1.84975 q^{50} -0.505193 q^{51} +1.79817 q^{52} -3.13348 q^{53} -3.79734 q^{54} -1.89375 q^{55} -9.08060 q^{56} -1.15612 q^{57} -5.68783 q^{58} -5.10433 q^{59} +0.275559 q^{60} -11.0171 q^{61} +5.55717 q^{62} +8.32553 q^{63} +8.79638 q^{64} -11.8227 q^{65} -0.661007 q^{66} -15.8511 q^{67} -0.288029 q^{68} +1.75185 q^{69} +7.51579 q^{70} -7.25254 q^{71} -8.21707 q^{72} -3.89643 q^{73} -0.373382 q^{74} +0.714206 q^{75} -0.659147 q^{76} +3.03323 q^{77} -4.12667 q^{78} +2.67903 q^{79} -6.32697 q^{80} +6.76815 q^{81} +9.10006 q^{82} -11.7900 q^{83} -0.441365 q^{84} +1.89375 q^{85} +1.30842 q^{86} -2.19612 q^{87} -2.99371 q^{88} +8.12427 q^{89} +6.80107 q^{90} +18.9364 q^{91} +0.998794 q^{92} +2.14567 q^{93} -8.19563 q^{94} +4.33379 q^{95} +0.816393 q^{96} -5.99783 q^{97} -2.87913 q^{98} +2.74478 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.30842	−0.925195	−0.462597	−	0.886568i	$-0.653082\pi$
$2$	−1.30842	−0.925195	−0.462597	+	0.886568i	$0.653082\pi$
$3$	−0.505193	−0.291674	−0.145837	−	0.989309i	$-0.546587\pi$
$3$	−0.505193	−0.291674	−0.145837	+	0.989309i	$0.546587\pi$
$4$	−0.288029	−0.144014
$5$	1.89375	0.846909	0.423454	−	0.905917i	$-0.360817\pi$
$5$	1.89375	0.846909	0.423454	+	0.905917i	$0.360817\pi$
$6$	0.661007	0.269855
$7$	−3.03323	−1.14645	−0.573226	−	0.819398i	$-0.694308\pi$
$7$	−3.03323	−1.14645	−0.573226	+	0.819398i	$0.694308\pi$
$8$	2.99371	1.05844
$9$	−2.74478	−0.914927
$10$	−2.47782	−0.783556
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.145510	0.0420052
$13$	−6.24301	−1.73150	−0.865749	−	0.500478i	$-0.833158\pi$
$13$	−6.24301	−1.73150	−0.865749	+	0.500478i	$0.833158\pi$
$14$	3.96874	1.06069
$15$	−0.956708	−0.247021
$16$	−3.34098	−0.835246
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	3.59133	0.846485
$19$	2.28848	0.525012	0.262506	−	0.964930i	$-0.415451\pi$
$19$	2.28848	0.525012	0.262506	+	0.964930i	$0.415451\pi$
$20$	−0.545453	−0.121967
$21$	1.53237	0.334389
$22$	1.30842	0.278957
$23$	−3.46769	−0.723063	−0.361532	−	0.932360i	$-0.617746\pi$
$23$	−3.46769	−0.723063	−0.361532	+	0.932360i	$0.617746\pi$
$24$	−1.51240	−0.308718
$25$	−1.41373	−0.282745
$26$	8.16850	1.60197
$27$	2.90222	0.558533
$28$	0.873656	0.165105
$29$	4.34709	0.807234	0.403617	−	0.914928i	$-0.367753\pi$
$29$	4.34709	0.807234	0.403617	+	0.914928i	$0.367753\pi$
$30$	1.25178	0.228542
$31$	−4.24723	−0.762825	−0.381412	−	0.924405i	$-0.624562\pi$
$31$	−4.24723	−0.762825	−0.381412	+	0.924405i	$0.624562\pi$
$32$	−1.61600	−0.285671
$33$	0.505193	0.0879429
$34$	−1.30842	−0.224393
$35$	−5.74416	−0.970940
$36$	0.790575	0.131763
$37$	0.285368	0.0469142	0.0234571	−	0.999725i	$-0.492533\pi$
$37$	0.285368	0.0469142	0.0234571	+	0.999725i	$0.492533\pi$
$38$	−2.99430	−0.485739
$39$	3.15393	0.505032
$40$	5.66933	0.896399
$41$	−6.95498	−1.08619	−0.543093	−	0.839673i	$-0.682747\pi$
$41$	−6.95498	−1.08619	−0.543093	+	0.839673i	$0.682747\pi$
$42$	−2.00498	−0.309375
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.288029	0.0434220
$45$	−5.19791	−0.774859
$46$	4.53720	0.668974
$47$	6.26374	0.913661	0.456830	−	0.889554i	$-0.348985\pi$
$47$	6.26374	0.913661	0.456830	+	0.889554i	$0.348985\pi$
$48$	1.68784	0.243619
$49$	2.20045	0.314351
$50$	1.84975	0.261595
$51$	−0.505193	−0.0707412
$52$	1.79817	0.249361
$53$	−3.13348	−0.430417	−0.215208	−	0.976568i	$-0.569043\pi$
$53$	−3.13348	−0.430417	−0.215208	+	0.976568i	$0.569043\pi$
$54$	−3.79734	−0.516752
$55$	−1.89375	−0.255353
$56$	−9.08060	−1.21345
$57$	−1.15612	−0.153132
$58$	−5.68783	−0.746849
$59$	−5.10433	−0.664527	−0.332263	−	0.943187i	$-0.607812\pi$
$59$	−5.10433	−0.664527	−0.332263	+	0.943187i	$0.607812\pi$
$60$	0.275559	0.0355745
$61$	−11.0171	−1.41060	−0.705298	−	0.708911i	$-0.749187\pi$
$61$	−11.0171	−1.41060	−0.705298	+	0.708911i	$0.749187\pi$
$62$	5.55717	0.705762
$63$	8.32553	1.04892
$64$	8.79638	1.09955
$65$	−11.8227	−1.46642
$66$	−0.661007	−0.0813643
$67$	−15.8511	−1.93652	−0.968258	−	0.249951i	$-0.919585\pi$
$67$	−15.8511	−1.93652	−0.968258	+	0.249951i	$0.919585\pi$
$68$	−0.288029	−0.0349286
$69$	1.75185	0.210898
$70$	7.51579	0.898309
$71$	−7.25254	−0.860718	−0.430359	−	0.902658i	$-0.641613\pi$
$71$	−7.25254	−0.860718	−0.430359	+	0.902658i	$0.641613\pi$
$72$	−8.21707	−0.968391
$73$	−3.89643	−0.456042	−0.228021	−	0.973656i	$-0.573225\pi$
$73$	−3.89643	−0.456042	−0.228021	+	0.973656i	$0.573225\pi$
$74$	−0.373382	−0.0434048
$75$	0.714206	0.0824694
$76$	−0.659147	−0.0756093
$77$	3.03323	0.345668
$78$	−4.12667	−0.467253
$79$	2.67903	0.301415	0.150707	−	0.988578i	$-0.451845\pi$
$79$	2.67903	0.301415	0.150707	+	0.988578i	$0.451845\pi$
$80$	−6.32697	−0.707377
$81$	6.76815	0.752017
$82$	9.10006	1.00493
$83$	−11.7900	−1.29412	−0.647058	−	0.762440i	$-0.724001\pi$
$83$	−11.7900	−1.29412	−0.647058	+	0.762440i	$0.724001\pi$
$84$	−0.441365	−0.0481569
$85$	1.89375	0.205406
$86$	1.30842	0.141091
$87$	−2.19612	−0.235449
$88$	−2.99371	−0.319131
$89$	8.12427	0.861171	0.430586	−	0.902550i	$-0.358307\pi$
$89$	8.12427	0.861171	0.430586	+	0.902550i	$0.358307\pi$
$90$	6.80107	0.716896
$91$	18.9364	1.98508
$92$	0.998794	0.104131
$93$	2.14567	0.222496
$94$	−8.19563	−0.845314
$95$	4.33379	0.444638
$96$	0.816393	0.0833228
$97$	−5.99783	−0.608988	−0.304494	−	0.952514i	$-0.598487\pi$
$97$	−5.99783	−0.608988	−0.304494	+	0.952514i	$0.598487\pi$
$98$	−2.87913	−0.290836
$99$	2.74478	0.275861
$100$	0.407194	0.0407194
$101$	−12.7530	−1.26897	−0.634483	−	0.772937i	$-0.718787\pi$
$101$	−12.7530	−1.26897	−0.634483	+	0.772937i	$0.718787\pi$
$102$	0.661007	0.0654494
$103$	2.79556	0.275454	0.137727	−	0.990470i	$-0.456020\pi$
$103$	2.79556	0.275454	0.137727	+	0.990470i	$0.456020\pi$
$104$	−18.6898	−1.83268
$105$	2.90191	0.283197
$106$	4.09992	0.398220
$107$	13.1480	1.27106	0.635531	−	0.772076i	$-0.280781\pi$
$107$	13.1480	1.27106	0.635531	+	0.772076i	$0.280781\pi$
$108$	−0.835924	−0.0804368
$109$	10.4136	0.997438	0.498719	−	0.866764i	$-0.333804\pi$
$109$	10.4136	0.997438	0.498719	+	0.866764i	$0.333804\pi$
$110$	2.47782	0.236251
$111$	−0.144166	−0.0136836
$112$	10.1340	0.957568
$113$	2.96980	0.279375	0.139687	−	0.990196i	$-0.455390\pi$
$113$	2.96980	0.279375	0.139687	+	0.990196i	$0.455390\pi$
$114$	1.51270	0.141677
$115$	−6.56692	−0.612369
$116$	−1.25209	−0.116253
$117$	17.1357	1.58419
$118$	6.67862	0.614817
$119$	−3.03323	−0.278055
$120$	−2.86411	−0.261456
$121$	1.00000	0.0909091
$122$	14.4150	1.30508
$123$	3.51361	0.316811
$124$	1.22332	0.109858
$125$	−12.1460	−1.08637
$126$	−10.8933	−0.970454
$127$	8.16112	0.724182	0.362091	−	0.932143i	$-0.382063\pi$
$127$	8.16112	0.724182	0.362091	+	0.932143i	$0.382063\pi$
$128$	−8.27738	−0.731624
$129$	0.505193	0.0444798
$130$	15.4691	1.35673
$131$	−12.3921	−1.08270	−0.541349	−	0.840798i	$-0.682086\pi$
$131$	−12.3921	−1.08270	−0.541349	+	0.840798i	$0.682086\pi$
$132$	−0.145510	−0.0126650
$133$	−6.94146	−0.601901
$134$	20.7399	1.79166
$135$	5.49608	0.473027
$136$	2.99371	0.256709
$137$	−8.80586	−0.752335	−0.376168	−	0.926552i	$-0.622758\pi$
$137$	−8.80586	−0.752335	−0.376168	+	0.926552i	$0.622758\pi$
$138$	−2.29217	−0.195122
$139$	−13.5526	−1.14952	−0.574758	−	0.818324i	$-0.694904\pi$
$139$	−13.5526	−1.14952	−0.574758	+	0.818324i	$0.694904\pi$
$140$	1.65448	0.139829
$141$	−3.16440	−0.266491
$142$	9.48939	0.796332
$143$	6.24301	0.522067
$144$	9.17026	0.764188
$145$	8.23228	0.683654
$146$	5.09817	0.421928
$147$	−1.11166	−0.0916878
$148$	−0.0821942	−0.00675632
$149$	−4.42329	−0.362370	−0.181185	−	0.983449i	$-0.557993\pi$
$149$	−4.42329	−0.362370	−0.181185	+	0.983449i	$0.557993\pi$
$150$	−0.934483	−0.0763002
$151$	5.41767	0.440884	0.220442	−	0.975400i	$-0.429250\pi$
$151$	5.41767	0.440884	0.220442	+	0.975400i	$0.429250\pi$
$152$	6.85103	0.555692
$153$	−2.74478	−0.221902
$154$	−3.96874	−0.319810
$155$	−8.04317	−0.646043
$156$	−0.908421	−0.0727319
$157$	2.11661	0.168924	0.0844618	−	0.996427i	$-0.473083\pi$
$157$	2.11661	0.168924	0.0844618	+	0.996427i	$0.473083\pi$
$158$	−3.50531	−0.278867
$159$	1.58301	0.125541
$160$	−3.06030	−0.241938
$161$	10.5183	0.828957
$162$	−8.85561	−0.695762
$163$	10.9819	0.860165	0.430083	−	0.902790i	$-0.358484\pi$
$163$	10.9819	0.860165	0.430083	+	0.902790i	$0.358484\pi$
$164$	2.00323	0.156426
$165$	0.956708	0.0744796
$166$	15.4263	1.19731
$167$	−19.2135	−1.48678	−0.743391	−	0.668857i	$-0.766784\pi$
$167$	−19.2135	−1.48678	−0.743391	+	0.668857i	$0.766784\pi$
$168$	4.58746	0.353930
$169$	25.9751	1.99809
$170$	−2.47782	−0.190040
$171$	−6.28136	−0.480348
$172$	0.288029	0.0219620
$173$	−11.8393	−0.900127	−0.450063	−	0.892997i	$-0.648599\pi$
$173$	−11.8393	−0.900127	−0.450063	+	0.892997i	$0.648599\pi$
$174$	2.87345	0.217836
$175$	4.28815	0.324154
$176$	3.34098	0.251836
$177$	2.57867	0.193825
$178$	−10.6300	−0.796751
$179$	−7.43719	−0.555882	−0.277941	−	0.960598i	$-0.589652\pi$
$179$	−7.43719	−0.555882	−0.277941	+	0.960598i	$0.589652\pi$
$180$	1.49715	0.111591
$181$	9.80951	0.729135	0.364567	−	0.931177i	$-0.381217\pi$
$181$	9.80951	0.729135	0.364567	+	0.931177i	$0.381217\pi$
$182$	−24.7769	−1.83659
$183$	5.56577	0.411433
$184$	−10.3813	−0.765316
$185$	0.540415	0.0397321
$186$	−2.80745	−0.205852
$187$	−1.00000	−0.0731272
$188$	−1.80414	−0.131580
$189$	−8.80310	−0.640331
$190$	−5.67043	−0.411377
$191$	8.66585	0.627039	0.313519	−	0.949582i	$-0.398492\pi$
$191$	8.66585	0.627039	0.313519	+	0.949582i	$0.398492\pi$
$192$	−4.44387	−0.320709
$193$	21.7659	1.56675	0.783373	−	0.621552i	$-0.213497\pi$
$193$	21.7659	1.56675	0.783373	+	0.621552i	$0.213497\pi$
$194$	7.84771	0.563432
$195$	5.97273	0.427716
$196$	−0.633794	−0.0452710
$197$	22.8990	1.63148	0.815742	−	0.578416i	$-0.196329\pi$
$197$	22.8990	1.63148	0.815742	+	0.578416i	$0.196329\pi$
$198$	−3.59133	−0.255225
$199$	−8.03632	−0.569679	−0.284840	−	0.958575i	$-0.591940\pi$
$199$	−8.03632	−0.569679	−0.284840	+	0.958575i	$0.591940\pi$
$200$	−4.23229	−0.299268
$201$	8.00786	0.564831
$202$	16.6863	1.17404
$203$	−13.1857	−0.925455
$204$	0.145510	0.0101877
$205$	−13.1710	−0.919900
$206$	−3.65777	−0.254849
$207$	9.51804	0.661550
$208$	20.8578	1.44623
$209$	−2.28848	−0.158297
$210$	−3.79693	−0.262013
$211$	4.84539	0.333570	0.166785	−	0.985993i	$-0.446661\pi$
$211$	4.84539	0.333570	0.166785	+	0.985993i	$0.446661\pi$
$212$	0.902533	0.0619862
$213$	3.66393	0.251049
$214$	−17.2031	−1.17598
$215$	−1.89375	−0.129152
$216$	8.68842	0.591172
$217$	12.8828	0.874542
$218$	−13.6253	−0.922824
$219$	1.96845	0.133015
$220$	0.545453	0.0367744
$221$	−6.24301	−0.419950
$222$	0.188630	0.0126600
$223$	−22.8608	−1.53087	−0.765435	−	0.643513i	$-0.777476\pi$
$223$	−22.8608	−1.53087	−0.765435	+	0.643513i	$0.777476\pi$
$224$	4.90170	0.327508
$225$	3.88037	0.258691
$226$	−3.88575	−0.258476
$227$	−7.09686	−0.471035	−0.235518	−	0.971870i	$-0.575679\pi$
$227$	−7.09686	−0.471035	−0.235518	+	0.971870i	$0.575679\pi$
$228$	0.332997	0.0220532
$229$	12.4847	0.825009	0.412505	−	0.910956i	$-0.364654\pi$
$229$	12.4847	0.825009	0.412505	+	0.910956i	$0.364654\pi$
$230$	8.59231	0.566560
$231$	−1.53237	−0.100822
$232$	13.0139	0.854406
$233$	0.185205	0.0121332	0.00606659	−	0.999982i	$-0.498069\pi$
$233$	0.185205	0.0121332	0.00606659	+	0.999982i	$0.498069\pi$
$234$	−22.4207	−1.46569
$235$	11.8619	0.773787
$236$	1.47019	0.0957014
$237$	−1.35343	−0.0879146
$238$	3.96874	0.257255
$239$	14.3400	0.927580	0.463790	−	0.885945i	$-0.346489\pi$
$239$	14.3400	0.927580	0.463790	+	0.885945i	$0.346489\pi$
$240$	3.19634	0.206323
$241$	11.1221	0.716441	0.358220	−	0.933637i	$-0.383384\pi$
$241$	11.1221	0.716441	0.358220	+	0.933637i	$0.383384\pi$
$242$	−1.30842	−0.0841086
$243$	−12.1259	−0.777877
$244$	3.17324	0.203146
$245$	4.16710	0.266226
$246$	−4.59729	−0.293112
$247$	−14.2870	−0.909058
$248$	−12.7150	−0.807401
$249$	5.95621	0.377460
$250$	15.8921	1.00510
$251$	15.4021	0.972174	0.486087	−	0.873910i	$-0.338424\pi$
$251$	15.4021	0.972174	0.486087	+	0.873910i	$0.338424\pi$
$252$	−2.39799	−0.151059
$253$	3.46769	0.218012
$254$	−10.6782	−0.670010
$255$	−0.956708	−0.0599114
$256$	−6.76244	−0.422652
$257$	−20.0519	−1.25080	−0.625400	−	0.780304i	$-0.715064\pi$
$257$	−20.0519	−1.25080	−0.625400	+	0.780304i	$0.715064\pi$
$258$	−0.661007	−0.0411525
$259$	−0.865586	−0.0537849
$260$	3.40527	0.211186
$261$	−11.9318	−0.738560
$262$	16.2141	1.00171
$263$	14.6856	0.905550	0.452775	−	0.891625i	$-0.350434\pi$
$263$	14.6856	0.905550	0.452775	+	0.891625i	$0.350434\pi$
$264$	1.51240	0.0930819
$265$	−5.93402	−0.364524
$266$	9.08237	0.556876
$267$	−4.10433	−0.251181
$268$	4.56556	0.278886
$269$	−4.68872	−0.285876	−0.142938	−	0.989732i	$-0.545655\pi$
$269$	−4.68872	−0.285876	−0.142938	+	0.989732i	$0.545655\pi$
$270$	−7.19119	−0.437642
$271$	3.74350	0.227401	0.113701	−	0.993515i	$-0.463730\pi$
$271$	3.74350	0.227401	0.113701	+	0.993515i	$0.463730\pi$
$272$	−3.34098	−0.202577
$273$	−9.56657	−0.578995
$274$	11.5218	0.696057
$275$	1.41373	0.0852510
$276$	−0.504584	−0.0303724
$277$	−15.3178	−0.920357	−0.460179	−	0.887826i	$-0.652215\pi$
$277$	−15.3178	−0.920357	−0.460179	+	0.887826i	$0.652215\pi$
$278$	17.7325	1.06353
$279$	11.6577	0.697929
$280$	−17.1963	−1.02768
$281$	8.50265	0.507225	0.253613	−	0.967306i	$-0.418381\pi$
$281$	8.50265	0.507225	0.253613	+	0.967306i	$0.418381\pi$
$282$	4.14038	0.246556
$283$	6.86632	0.408161	0.204080	−	0.978954i	$-0.434580\pi$
$283$	6.86632	0.408161	0.204080	+	0.978954i	$0.434580\pi$
$284$	2.08894	0.123956
$285$	−2.18940	−0.129689
$286$	−8.16850	−0.483013
$287$	21.0960	1.24526
$288$	4.43557	0.261368
$289$	1.00000	0.0588235
$290$	−10.7713	−0.632513
$291$	3.03007	0.177626
$292$	1.12228	0.0656766
$293$	−22.8049	−1.33228	−0.666138	−	0.745829i	$-0.732054\pi$
$293$	−22.8049	−1.33228	−0.666138	+	0.745829i	$0.732054\pi$
$294$	1.45452	0.0848291
$295$	−9.66630	−0.562794
$296$	0.854309	0.0496557
$297$	−2.90222	−0.168404
$298$	5.78754	0.335263
$299$	21.6488	1.25198
$300$	−0.205712	−0.0118768
$301$	3.03323	0.174832
$302$	−7.08861	−0.407904
$303$	6.44271	0.370124
$304$	−7.64576	−0.438514
$305$	−20.8636	−1.19465
$306$	3.59133	0.205303
$307$	−13.0536	−0.745009	−0.372505	−	0.928030i	$-0.621501\pi$
$307$	−13.0536	−0.745009	−0.372505	+	0.928030i	$0.621501\pi$
$308$	−0.873656	−0.0497812
$309$	−1.41230	−0.0803427
$310$	10.5239	0.597716
$311$	2.60473	0.147700	0.0738502	−	0.997269i	$-0.476471\pi$
$311$	2.60473	0.147700	0.0738502	+	0.997269i	$0.476471\pi$
$312$	9.44194	0.534545
$313$	−20.2549	−1.14487	−0.572437	−	0.819949i	$-0.694002\pi$
$313$	−20.2549	−1.14487	−0.572437	+	0.819949i	$0.694002\pi$
$314$	−2.76942	−0.156287
$315$	15.7664	0.888339
$316$	−0.771638	−0.0434080
$317$	−12.1281	−0.681183	−0.340591	−	0.940211i	$-0.610627\pi$
$317$	−12.1281	−0.681183	−0.340591	+	0.940211i	$0.610627\pi$
$318$	−2.07125	−0.116150
$319$	−4.34709	−0.243390
$320$	16.6581	0.931216
$321$	−6.64226	−0.370735
$322$	−13.7624	−0.766946
$323$	2.28848	0.127334
$324$	−1.94942	−0.108301
$325$	8.82591	0.489573
$326$	−14.3689	−0.795820
$327$	−5.26086	−0.290926
$328$	−20.8212	−1.14966
$329$	−18.9993	−1.04747
$330$	−1.25178	−0.0689081
$331$	21.8491	1.20094	0.600468	−	0.799648i	$-0.294981\pi$
$331$	21.8491	1.20094	0.600468	+	0.799648i	$0.294981\pi$
$332$	3.39585	0.186371
$333$	−0.783273	−0.0429231
$334$	25.1393	1.37556
$335$	−30.0179	−1.64005
$336$	−5.11960	−0.279297
$337$	11.2527	0.612972	0.306486	−	0.951875i	$-0.400847\pi$
$337$	11.2527	0.612972	0.306486	+	0.951875i	$0.400847\pi$
$338$	−33.9865	−1.84862
$339$	−1.50032	−0.0814862
$340$	−0.545453	−0.0295813
$341$	4.24723	0.230000
$342$	8.21868	0.444415
$343$	14.5581	0.786064
$344$	−2.99371	−0.161410
$345$	3.31756	0.178612
$346$	15.4908	0.832793
$347$	−8.15172	−0.437607	−0.218804	−	0.975769i	$-0.570215\pi$
$347$	−8.15172	−0.437607	−0.218804	+	0.975769i	$0.570215\pi$
$348$	0.632546	0.0339080
$349$	−21.4552	−1.14847	−0.574236	−	0.818690i	$-0.694701\pi$
$349$	−21.4552	−1.14847	−0.574236	+	0.818690i	$0.694701\pi$
$350$	−5.61072	−0.299906
$351$	−18.1186	−0.967100
$352$	1.61600	0.0861331
$353$	−0.684827	−0.0364496	−0.0182248	−	0.999834i	$-0.505801\pi$
$353$	−0.684827	−0.0364496	−0.0182248	+	0.999834i	$0.505801\pi$
$354$	−3.37400	−0.179326
$355$	−13.7345	−0.728950
$356$	−2.34002	−0.124021
$357$	1.53237	0.0811014
$358$	9.73099	0.514299
$359$	10.0813	0.532071	0.266036	−	0.963963i	$-0.414286\pi$
$359$	10.0813	0.532071	0.266036	+	0.963963i	$0.414286\pi$
$360$	−15.5610	−0.820139
$361$	−13.7629	−0.724362
$362$	−12.8350	−0.674592
$363$	−0.505193	−0.0265158
$364$	−5.45424	−0.285880
$365$	−7.37884	−0.386226
$366$	−7.28238	−0.380656
$367$	16.3572	0.853837	0.426919	−	0.904290i	$-0.359599\pi$
$367$	16.3572	0.853837	0.426919	+	0.904290i	$0.359599\pi$
$368$	11.5855	0.603935
$369$	19.0899	0.993780
$370$	−0.707091	−0.0367599
$371$	9.50456	0.493452
$372$	−0.618015	−0.0320426
$373$	19.0370	0.985698	0.492849	−	0.870115i	$-0.335955\pi$
$373$	19.0370	0.985698	0.492849	+	0.870115i	$0.335955\pi$
$374$	1.30842	0.0676570
$375$	6.13606	0.316865
$376$	18.7518	0.967052
$377$	−27.1389	−1.39772
$378$	11.5182	0.592431
$379$	−12.9929	−0.667400	−0.333700	−	0.942679i	$-0.608297\pi$
$379$	−12.9929	−0.667400	−0.333700	+	0.942679i	$0.608297\pi$
$380$	−1.24826	−0.0640342
$381$	−4.12294	−0.211225
$382$	−11.3386	−0.580133
$383$	−9.16112	−0.468112	−0.234056	−	0.972223i	$-0.575200\pi$
$383$	−9.16112	−0.468112	−0.234056	+	0.972223i	$0.575200\pi$
$384$	4.18168	0.213395
$385$	5.74416	0.292749
$386$	−28.4791	−1.44955
$387$	2.74478	0.139525
$388$	1.72755	0.0877030
$389$	−34.8985	−1.76943	−0.884713	−	0.466136i	$-0.845646\pi$
$389$	−34.8985	−1.76943	−0.884713	+	0.466136i	$0.845646\pi$
$390$	−7.81486	−0.395721
$391$	−3.46769	−0.175369
$392$	6.58752	0.332720
$393$	6.26038	0.315795
$394$	−29.9615	−1.50944
$395$	5.07340	0.255271
$396$	−0.790575	−0.0397279
$397$	−17.0353	−0.854978	−0.427489	−	0.904020i	$-0.640602\pi$
$397$	−17.0353	−0.854978	−0.427489	+	0.904020i	$0.640602\pi$
$398$	10.5149	0.527064
$399$	3.50678	0.175559
$400$	4.72324	0.236162
$401$	15.8681	0.792413	0.396207	−	0.918161i	$-0.370326\pi$
$401$	15.8681	0.792413	0.396207	+	0.918161i	$0.370326\pi$
$402$	−10.4777	−0.522578
$403$	26.5155	1.32083
$404$	3.67322	0.182749
$405$	12.8172	0.636890
$406$	17.2525	0.856226
$407$	−0.285368	−0.0141452
$408$	−1.51240	−0.0748751
$409$	16.9766	0.839438	0.419719	−	0.907654i	$-0.362129\pi$
$409$	16.9766	0.839438	0.419719	+	0.907654i	$0.362129\pi$
$410$	17.2332	0.851087
$411$	4.44866	0.219436
$412$	−0.805200	−0.0396694
$413$	15.4826	0.761848
$414$	−12.4536	−0.612062
$415$	−22.3272	−1.09600
$416$	10.0887	0.494640
$417$	6.84668	0.335283
$418$	2.99430	0.146456
$419$	−14.5419	−0.710420	−0.355210	−	0.934786i	$-0.615591\pi$
$419$	−14.5419	−0.710420	−0.355210	+	0.934786i	$0.615591\pi$
$420$	−0.835833	−0.0407845
$421$	−5.91057	−0.288064	−0.144032	−	0.989573i	$-0.546007\pi$
$421$	−5.91057	−0.288064	−0.144032	+	0.989573i	$0.546007\pi$
$422$	−6.33981	−0.308617
$423$	−17.1926	−0.835933
$424$	−9.38074	−0.455569
$425$	−1.41373	−0.0685758
$426$	−4.79398	−0.232269
$427$	33.4174	1.61718
$428$	−3.78699	−0.183051
$429$	−3.15393	−0.152273
$430$	2.47782	0.119491
$431$	−6.14515	−0.296001	−0.148001	−	0.988987i	$-0.547284\pi$
$431$	−6.14515	−0.296001	−0.148001	+	0.988987i	$0.547284\pi$
$432$	−9.69628	−0.466512
$433$	21.4325	1.02998	0.514990	−	0.857196i	$-0.327795\pi$
$433$	21.4325	1.02998	0.514990	+	0.857196i	$0.327795\pi$
$434$	−16.8562	−0.809121
$435$	−4.15889	−0.199404
$436$	−2.99940	−0.143645
$437$	−7.93572	−0.379617
$438$	−2.57556	−0.123065
$439$	10.0657	0.480409	0.240205	−	0.970722i	$-0.422785\pi$
$439$	10.0657	0.480409	0.240205	+	0.970722i	$0.422785\pi$
$440$	−5.66933	−0.270274
$441$	−6.03976	−0.287608
$442$	8.16850	0.388536
$443$	10.3265	0.490628	0.245314	−	0.969444i	$-0.421109\pi$
$443$	10.3265	0.490628	0.245314	+	0.969444i	$0.421109\pi$
$444$	0.0415240	0.00197064
$445$	15.3853	0.729334
$446$	29.9116	1.41635
$447$	2.23462	0.105694
$448$	−26.6814	−1.26058
$449$	−13.8060	−0.651544	−0.325772	−	0.945448i	$-0.605624\pi$
$449$	−13.8060	−0.651544	−0.325772	+	0.945448i	$0.605624\pi$
$450$	−5.07717	−0.239340
$451$	6.95498	0.327497
$452$	−0.855386	−0.0402340
$453$	−2.73697	−0.128594
$454$	9.28570	0.435799
$455$	35.8608	1.68118
$456$	−3.46110	−0.162081
$457$	−10.8357	−0.506874	−0.253437	−	0.967352i	$-0.581561\pi$
$457$	−10.8357	−0.506874	−0.253437	+	0.967352i	$0.581561\pi$
$458$	−16.3352	−0.763294
$459$	2.90222	0.135464
$460$	1.89146	0.0881898
$461$	14.9943	0.698352	0.349176	−	0.937057i	$-0.386461\pi$
$461$	14.9943	0.698352	0.349176	+	0.937057i	$0.386461\pi$
$462$	2.00498	0.0932802
$463$	25.3845	1.17972	0.589859	−	0.807506i	$-0.299183\pi$
$463$	25.3845	1.17972	0.589859	+	0.807506i	$0.299183\pi$
$464$	−14.5235	−0.674239
$465$	4.06336	0.188434
$466$	−0.242326	−0.0112256
$467$	9.50526	0.439851	0.219925	−	0.975517i	$-0.429419\pi$
$467$	9.50526	0.439851	0.219925	+	0.975517i	$0.429419\pi$
$468$	−4.93557	−0.228147
$469$	48.0799	2.22012
$470$	−15.5204	−0.715904
$471$	−1.06930	−0.0492705
$472$	−15.2809	−0.703359
$473$	1.00000	0.0459800
$474$	1.77086	0.0813382
$475$	−3.23528	−0.148445
$476$	0.873656	0.0400439
$477$	8.60072	0.393800
$478$	−18.7628	−0.858192
$479$	28.6902	1.31089	0.655444	−	0.755243i	$-0.272481\pi$
$479$	28.6902	1.31089	0.655444	+	0.755243i	$0.272481\pi$
$480$	1.54604	0.0705668
$481$	−1.78156	−0.0812319
$482$	−14.5525	−0.662847
$483$	−5.31377	−0.241785
$484$	−0.288029	−0.0130922
$485$	−11.3584	−0.515757
$486$	15.8658	0.719688
$487$	21.7078	0.983676	0.491838	−	0.870687i	$-0.336325\pi$
$487$	21.7078	0.983676	0.491838	+	0.870687i	$0.336325\pi$
$488$	−32.9820	−1.49303
$489$	−5.54796	−0.250887
$490$	−5.45233	−0.246311
$491$	25.7364	1.16147	0.580734	−	0.814094i	$-0.302766\pi$
$491$	25.7364	1.16147	0.580734	+	0.814094i	$0.302766\pi$
$492$	−1.01202	−0.0456254
$493$	4.34709	0.195783
$494$	18.6934	0.841056
$495$	5.19791	0.233629
$496$	14.1899	0.637146
$497$	21.9986	0.986771
$498$	−7.79325	−0.349224
$499$	27.3266	1.22331	0.611654	−	0.791125i	$-0.290504\pi$
$499$	27.3266	1.22331	0.611654	+	0.791125i	$0.290504\pi$
$500$	3.49839	0.156453
$501$	9.70651	0.433655
$502$	−20.1525	−0.899451
$503$	6.25973	0.279108	0.139554	−	0.990214i	$-0.455433\pi$
$503$	6.25973	0.279108	0.139554	+	0.990214i	$0.455433\pi$
$504$	24.9242	1.11021
$505$	−24.1509	−1.07470
$506$	−4.53720	−0.201703
$507$	−13.1225	−0.582789
$508$	−2.35064	−0.104293
$509$	−10.1346	−0.449209	−0.224604	−	0.974450i	$-0.572109\pi$
$509$	−10.1346	−0.449209	−0.224604	+	0.974450i	$0.572109\pi$
$510$	1.25178	0.0554297
$511$	11.8187	0.522830
$512$	25.4029	1.12266
$513$	6.64167	0.293237
$514$	26.2363	1.15723
$515$	5.29407	0.233285
$516$	−0.145510	−0.00640573
$517$	−6.26374	−0.275479
$518$	1.13255	0.0497615
$519$	5.98115	0.262543
$520$	−35.3936	−1.55211
$521$	5.02801	0.220281	0.110141	−	0.993916i	$-0.464870\pi$
$521$	5.02801	0.220281	0.110141	+	0.993916i	$0.464870\pi$
$522$	15.6118	0.683312
$523$	13.9419	0.609637	0.304819	−	0.952410i	$-0.401404\pi$
$523$	13.9419	0.609637	0.304819	+	0.952410i	$0.401404\pi$
$524$	3.56927	0.155924
$525$	−2.16635	−0.0945471
$526$	−19.2149	−0.837810
$527$	−4.24723	−0.185012
$528$	−1.68784	−0.0734539
$529$	−10.9751	−0.477180
$530$	7.76421	0.337256
$531$	14.0103	0.607993
$532$	1.99934	0.0866824
$533$	43.4200	1.88073
$534$	5.37020	0.232391
$535$	24.8989	1.07647
$536$	−47.4535	−2.04968
$537$	3.75722	0.162136
$538$	6.13483	0.264491
$539$	−2.20045	−0.0947803
$540$	−1.58303	−0.0681226
$541$	0.737970	0.0317278	0.0158639	−	0.999874i	$-0.494950\pi$
$541$	0.737970	0.0317278	0.0158639	+	0.999874i	$0.494950\pi$
$542$	−4.89808	−0.210391
$543$	−4.95570	−0.212669
$544$	−1.61600	−0.0692855
$545$	19.7206	0.844739
$546$	12.5171	0.535683
$547$	−5.61357	−0.240019	−0.120010	−	0.992773i	$-0.538293\pi$
$547$	−5.61357	−0.240019	−0.120010	+	0.992773i	$0.538293\pi$
$548$	2.53634	0.108347
$549$	30.2395	1.29059
$550$	−1.84975	−0.0788738
$551$	9.94821	0.423808
$552$	5.24454	0.223222
$553$	−8.12610	−0.345557
$554$	20.0422	0.851510
$555$	−0.273014	−0.0115888
$556$	3.90353	0.165547
$557$	16.2260	0.687516	0.343758	−	0.939058i	$-0.388300\pi$
$557$	16.2260	0.687516	0.343758	+	0.939058i	$0.388300\pi$
$558$	−15.2532	−0.645720
$559$	6.24301	0.264051
$560$	19.1911	0.810973
$561$	0.505193	0.0213293
$562$	−11.1251	−0.469282
$563$	−15.4828	−0.652523	−0.326262	−	0.945279i	$-0.605789\pi$
$563$	−15.4828	−0.652523	−0.326262	+	0.945279i	$0.605789\pi$
$564$	0.911438	0.0383785
$565$	5.62404	0.236605
$566$	−8.98406	−0.377628
$567$	−20.5293	−0.862151
$568$	−21.7120	−0.911015
$569$	7.49197	0.314080	0.157040	−	0.987592i	$-0.449805\pi$
$569$	7.49197	0.314080	0.157040	+	0.987592i	$0.449805\pi$
$570$	2.86467	0.119988
$571$	24.7171	1.03438	0.517188	−	0.855872i	$-0.326979\pi$
$571$	24.7171	1.03438	0.517188	+	0.855872i	$0.326979\pi$
$572$	−1.79817	−0.0751851
$573$	−4.37793	−0.182891
$574$	−27.6025	−1.15211
$575$	4.90237	0.204443
$576$	−24.1441	−1.00600
$577$	−27.5768	−1.14804	−0.574019	−	0.818842i	$-0.694617\pi$
$577$	−27.5768	−1.14804	−0.574019	+	0.818842i	$0.694617\pi$
$578$	−1.30842	−0.0544232
$579$	−10.9960	−0.456978
$580$	−2.37113	−0.0984559
$581$	35.7616	1.48364
$582$	−3.96461	−0.164338
$583$	3.13348	0.129776
$584$	−11.6648	−0.482691
$585$	32.4506	1.34167
$586$	29.8384	1.23261
$587$	20.0904	0.829220	0.414610	−	0.909999i	$-0.363918\pi$
$587$	20.0904	0.829220	0.414610	+	0.909999i	$0.363918\pi$
$588$	0.320189	0.0132044
$589$	−9.71968	−0.400493
$590$	12.6476	0.520694
$591$	−11.5684	−0.475861
$592$	−0.953410	−0.0391849
$593$	−12.8581	−0.528021	−0.264010	−	0.964520i	$-0.585045\pi$
$593$	−12.8581	−0.528021	−0.264010	+	0.964520i	$0.585045\pi$
$594$	3.79734	0.155807
$595$	−5.74416	−0.235487
$596$	1.27404	0.0521865
$597$	4.05989	0.166160
$598$	−28.3258	−1.15833
$599$	−22.2600	−0.909520	−0.454760	−	0.890614i	$-0.650275\pi$
$599$	−22.2600	−0.909520	−0.454760	+	0.890614i	$0.650275\pi$
$600$	2.13812	0.0872886
$601$	31.3975	1.28073	0.640366	−	0.768070i	$-0.278783\pi$
$601$	31.3975	1.28073	0.640366	+	0.768070i	$0.278783\pi$
$602$	−3.96874	−0.161754
$603$	43.5077	1.77177
$604$	−1.56044	−0.0634936
$605$	1.89375	0.0769917
$606$	−8.42979	−0.342437
$607$	−24.7536	−1.00472	−0.502359	−	0.864659i	$-0.667534\pi$
$607$	−24.7536	−1.00472	−0.502359	+	0.864659i	$0.667534\pi$
$608$	−3.69818	−0.149981
$609$	6.66133	0.269931
$610$	27.2984	1.10528
$611$	−39.1046	−1.58200
$612$	0.790575	0.0319571
$613$	13.5349	0.546670	0.273335	−	0.961919i	$-0.411873\pi$
$613$	13.5349	0.546670	0.273335	+	0.961919i	$0.411873\pi$
$614$	17.0797	0.689279
$615$	6.65388	0.268310
$616$	9.08060	0.365868
$617$	−42.0962	−1.69473	−0.847365	−	0.531011i	$-0.821812\pi$
$617$	−42.0962	−1.69473	−0.847365	+	0.531011i	$0.821812\pi$
$618$	1.84788	0.0743327
$619$	31.4678	1.26480	0.632399	−	0.774643i	$-0.282070\pi$
$619$	31.4678	1.26480	0.632399	+	0.774643i	$0.282070\pi$
$620$	2.31666	0.0930395
$621$	−10.0640	−0.403855
$622$	−3.40808	−0.136652
$623$	−24.6427	−0.987291
$624$	−10.5372	−0.421826
$625$	−15.9327	−0.637310
$626$	26.5020	1.05923
$627$	1.15612	0.0461711
$628$	−0.609643	−0.0243274
$629$	0.285368	0.0113784
$630$	−20.6292	−0.821886
$631$	−18.9219	−0.753268	−0.376634	−	0.926362i	$-0.622919\pi$
$631$	−18.9219	−0.753268	−0.376634	+	0.926362i	$0.622919\pi$
$632$	8.02024	0.319028
$633$	−2.44786	−0.0972936
$634$	15.8687	0.630227
$635$	15.4551	0.613316
$636$	−0.455954	−0.0180797
$637$	−13.7375	−0.544298
$638$	5.68783	0.225183
$639$	19.9066	0.787494
$640$	−15.6753	−0.619619
$641$	19.5237	0.771139	0.385570	−	0.922679i	$-0.374005\pi$
$641$	19.5237	0.771139	0.385570	+	0.922679i	$0.374005\pi$
$642$	8.69089	0.343002
$643$	−0.123708	−0.00487856	−0.00243928	−	0.999997i	$-0.500776\pi$
$643$	−0.123708	−0.00487856	−0.00243928	+	0.999997i	$0.500776\pi$
$644$	−3.02957	−0.119382
$645$	0.956708	0.0376703
$646$	−2.99430	−0.117809
$647$	−27.0903	−1.06503	−0.532515	−	0.846420i	$-0.678753\pi$
$647$	−27.0903	−1.06503	−0.532515	+	0.846420i	$0.678753\pi$
$648$	20.2619	0.795962
$649$	5.10433	0.200362
$650$	−11.5480	−0.452951
$651$	−6.50831	−0.255081
$652$	−3.16309	−0.123876
$653$	25.3316	0.991301	0.495651	−	0.868522i	$-0.334930\pi$
$653$	25.3316	0.991301	0.495651	+	0.868522i	$0.334930\pi$
$654$	6.88343	0.269163
$655$	−23.4674	−0.916947
$656$	23.2365	0.907231
$657$	10.6948	0.417245
$658$	24.8592	0.969112
$659$	1.18730	0.0462507	0.0231253	−	0.999733i	$-0.492638\pi$
$659$	1.18730	0.0462507	0.0231253	+	0.999733i	$0.492638\pi$
$660$	−0.275559	−0.0107261
$661$	−30.6663	−1.19278	−0.596390	−	0.802695i	$-0.703399\pi$
$661$	−30.6663	−1.19278	−0.596390	+	0.802695i	$0.703399\pi$
$662$	−28.5879	−1.11110
$663$	3.15393	0.122488
$664$	−35.2957	−1.36974
$665$	−13.1454	−0.509755
$666$	1.02485	0.0397122
$667$	−15.0743	−0.583681
$668$	5.53403	0.214118
$669$	11.5491	0.446514
$670$	39.2761	1.51737
$671$	11.0171	0.425311
$672$	−2.47630	−0.0955255
$673$	17.5104	0.674978	0.337489	−	0.941329i	$-0.390422\pi$
$673$	17.5104	0.674978	0.337489	+	0.941329i	$0.390422\pi$
$674$	−14.7233	−0.567119
$675$	−4.10295	−0.157923
$676$	−7.48159	−0.287753
$677$	39.5668	1.52068	0.760338	−	0.649528i	$-0.225033\pi$
$677$	39.5668	1.52068	0.760338	+	0.649528i	$0.225033\pi$
$678$	1.96305	0.0753907
$679$	18.1928	0.698175
$680$	5.66933	0.217409
$681$	3.58529	0.137389
$682$	−5.55717	−0.212795
$683$	4.74707	0.181642	0.0908208	−	0.995867i	$-0.471051\pi$
$683$	4.74707	0.181642	0.0908208	+	0.995867i	$0.471051\pi$
$684$	1.80921	0.0691770
$685$	−16.6761	−0.637159
$686$	−19.0482	−0.727262
$687$	−6.30716	−0.240633
$688$	3.34098	0.127374
$689$	19.5624	0.745266
$690$	−4.34078	−0.165251
$691$	25.9885	0.988651	0.494325	−	0.869277i	$-0.335415\pi$
$691$	25.9885	0.988651	0.494325	+	0.869277i	$0.335415\pi$
$692$	3.41006	0.129631
$693$	−8.32553	−0.316261
$694$	10.6659	0.404872
$695$	−25.6652	−0.973535
$696$	−6.57455	−0.249208
$697$	−6.95498	−0.263439
$698$	28.0725	1.06256
$699$	−0.0935643	−0.00353893
$700$	−1.23511	−0.0466828
$701$	16.1510	0.610016	0.305008	−	0.952350i	$-0.401341\pi$
$701$	16.1510	0.610016	0.305008	+	0.952350i	$0.401341\pi$
$702$	23.7068	0.894756
$703$	0.653058	0.0246306
$704$	−8.79638	−0.331526
$705$	−5.99257	−0.225693
$706$	0.896043	0.0337230
$707$	38.6826	1.45481
$708$	−0.742732	−0.0279136
$709$	−3.55979	−0.133691	−0.0668454	−	0.997763i	$-0.521293\pi$
$709$	−3.55979	−0.133691	−0.0668454	+	0.997763i	$0.521293\pi$
$710$	17.9705	0.674420
$711$	−7.35335	−0.275772
$712$	24.3217	0.911495
$713$	14.7281	0.551570
$714$	−2.00498	−0.0750346
$715$	11.8227	0.442143
$716$	2.14212	0.0800549
$717$	−7.24449	−0.270550
$718$	−13.1906	−0.492270
$719$	−19.7342	−0.735963	−0.367981	−	0.929833i	$-0.619951\pi$
$719$	−19.7342	−0.735963	−0.367981	+	0.929833i	$0.619951\pi$
$720$	17.3661	0.647198
$721$	−8.47955	−0.315795
$722$	18.0077	0.670176
$723$	−5.61883	−0.208967
$724$	−2.82542	−0.105006
$725$	−6.14560	−0.228242
$726$	0.661007	0.0245323
$727$	2.86893	0.106403	0.0532013	−	0.998584i	$-0.483058\pi$
$727$	2.86893	0.106403	0.0532013	+	0.998584i	$0.483058\pi$
$728$	56.6902	2.10108
$729$	−14.1785	−0.525131
$730$	9.65464	0.357334
$731$	−1.00000	−0.0369863
$732$	−1.60310	−0.0592523
$733$	31.5501	1.16533	0.582664	−	0.812713i	$-0.302010\pi$
$733$	31.5501	1.16533	0.582664	+	0.812713i	$0.302010\pi$
$734$	−21.4021	−0.789966
$735$	−2.10519	−0.0776512
$736$	5.60379	0.206558
$737$	15.8511	0.583882
$738$	−24.9776	−0.919440
$739$	36.6465	1.34806	0.674032	−	0.738702i	$-0.264561\pi$
$739$	36.6465	1.34806	0.674032	+	0.738702i	$0.264561\pi$
$740$	−0.155655	−0.00572199
$741$	7.21768	0.265148
$742$	−12.4360	−0.456539
$743$	−13.6639	−0.501279	−0.250640	−	0.968080i	$-0.580641\pi$
$743$	−13.6639	−0.501279	−0.250640	+	0.968080i	$0.580641\pi$
$744$	6.42352	0.235498
$745$	−8.37659	−0.306895
$746$	−24.9085	−0.911963
$747$	32.3609	1.18402
$748$	0.288029	0.0105314
$749$	−39.8807	−1.45721
$750$	−8.02857	−0.293162
$751$	−14.2887	−0.521402	−0.260701	−	0.965420i	$-0.583954\pi$
$751$	−14.2887	−0.521402	−0.260701	+	0.965420i	$0.583954\pi$
$752$	−20.9271	−0.763131
$753$	−7.78106	−0.283557
$754$	35.5092	1.29317
$755$	10.2597	0.373388
$756$	2.53555	0.0922169
$757$	−20.7994	−0.755966	−0.377983	−	0.925813i	$-0.623382\pi$
$757$	−20.7994	−0.755966	−0.377983	+	0.925813i	$0.623382\pi$
$758$	17.0002	0.617475
$759$	−1.75185	−0.0635882
$760$	12.9741	0.470621
$761$	25.7210	0.932387	0.466194	−	0.884683i	$-0.345625\pi$
$761$	25.7210	0.932387	0.466194	+	0.884683i	$0.345625\pi$
$762$	5.39455	0.195424
$763$	−31.5867	−1.14351
$764$	−2.49601	−0.0903026
$765$	−5.19791	−0.187931
$766$	11.9866	0.433094
$767$	31.8664	1.15063
$768$	3.41634	0.123276
$769$	25.4701	0.918476	0.459238	−	0.888313i	$-0.348122\pi$
$769$	25.4701	0.918476	0.459238	+	0.888313i	$0.348122\pi$
$770$	−7.51579	−0.270850
$771$	10.1301	0.364825
$772$	−6.26921	−0.225634
$773$	14.1231	0.507973	0.253986	−	0.967208i	$-0.418258\pi$
$773$	14.1231	0.507973	0.253986	+	0.967208i	$0.418258\pi$
$774$	−3.59133	−0.129088
$775$	6.00442	0.215685
$776$	−17.9558	−0.644575
$777$	0.437288	0.0156876
$778$	45.6621	1.63706
$779$	−15.9163	−0.570261
$780$	−1.72032	−0.0615973
$781$	7.25254	0.259516
$782$	4.53720	0.162250
$783$	12.6162	0.450867
$784$	−7.35168	−0.262560
$785$	4.00831	0.143063
$786$	−8.19123	−0.292172
$787$	29.4285	1.04901	0.524506	−	0.851407i	$-0.324250\pi$
$787$	29.4285	1.04901	0.524506	+	0.851407i	$0.324250\pi$
$788$	−6.59556	−0.234957
$789$	−7.41904	−0.264125
$790$	−6.63816	−0.236175
$791$	−9.00806	−0.320290
$792$	8.21707	0.291981
$793$	68.7799	2.44244
$794$	22.2894	0.791022
$795$	2.99783	0.106322
$796$	2.31469	0.0820420
$797$	−16.6947	−0.591356	−0.295678	−	0.955288i	$-0.595545\pi$
$797$	−16.6947	−0.591356	−0.295678	+	0.955288i	$0.595545\pi$
$798$	−4.58835	−0.162426
$799$	6.26374	0.221595
$800$	2.28458	0.0807723
$801$	−22.2993	−0.787908
$802$	−20.7621	−0.733137
$803$	3.89643	0.137502
$804$	−2.30649	−0.0813437
$805$	19.9189	0.702051
$806$	−34.6935	−1.22203
$807$	2.36871	0.0833826
$808$	−38.1786	−1.34312
$809$	37.2332	1.30905	0.654524	−	0.756041i	$-0.272869\pi$
$809$	37.2332	1.30905	0.654524	+	0.756041i	$0.272869\pi$
$810$	−16.7703	−0.589247
$811$	−33.6520	−1.18168	−0.590841	−	0.806788i	$-0.701204\pi$
$811$	−33.6520	−1.18168	−0.590841	+	0.806788i	$0.701204\pi$
$812$	3.79786	0.133279
$813$	−1.89119	−0.0663269
$814$	0.373382	0.0130870
$815$	20.7968	0.728481
$816$	1.68784	0.0590863
$817$	−2.28848	−0.0800637
$818$	−22.2126	−0.776644
$819$	−51.9764	−1.81620
$820$	3.79361	0.132479
$821$	31.3633	1.09459	0.547293	−	0.836941i	$-0.315658\pi$
$821$	31.3633	1.09459	0.547293	+	0.836941i	$0.315658\pi$
$822$	−5.82073	−0.203021
$823$	−20.5813	−0.717419	−0.358709	−	0.933449i	$-0.616783\pi$
$823$	−20.5813	−0.717419	−0.358709	+	0.933449i	$0.616783\pi$
$824$	8.36908	0.291551
$825$	−0.714206	−0.0248654
$826$	−20.2578	−0.704858
$827$	33.3663	1.16026	0.580131	−	0.814523i	$-0.303001\pi$
$827$	33.3663	1.16026	0.580131	+	0.814523i	$0.303001\pi$
$828$	−2.74147	−0.0952726
$829$	−35.1682	−1.22144	−0.610721	−	0.791846i	$-0.709120\pi$
$829$	−35.1682	−1.22144	−0.610721	+	0.791846i	$0.709120\pi$
$830$	29.2134	1.01401
$831$	7.73845	0.268444
$832$	−54.9159	−1.90386
$833$	2.20045	0.0762412
$834$	−8.95835	−0.310202
$835$	−36.3854	−1.25917
$836$	0.659147	0.0227971
$837$	−12.3264	−0.426063
$838$	19.0270	0.657277
$839$	44.7676	1.54555	0.772774	−	0.634681i	$-0.218869\pi$
$839$	44.7676	1.54555	0.772774	+	0.634681i	$0.218869\pi$
$840$	8.68748	0.299746
$841$	−10.1028	−0.348373
$842$	7.73353	0.266515
$843$	−4.29548	−0.147944
$844$	−1.39561	−0.0480389
$845$	49.1903	1.69220
$846$	22.4952	0.773401
$847$	−3.03323	−0.104223
$848$	10.4689	0.359504
$849$	−3.46882	−0.119050
$850$	1.84975	0.0634460
$851$	−0.989568	−0.0339220
$852$	−1.05532	−0.0361546
$853$	−28.3828	−0.971810	−0.485905	−	0.874012i	$-0.661510\pi$
$853$	−28.3828	−0.971810	−0.485905	+	0.874012i	$0.661510\pi$
$854$	−43.7240	−1.49621
$855$	−11.8953	−0.406811
$856$	39.3612	1.34534
$857$	−16.2635	−0.555551	−0.277775	−	0.960646i	$-0.589597\pi$
$857$	−16.2635	−0.555551	−0.277775	+	0.960646i	$0.589597\pi$
$858$	4.12667	0.140882
$859$	18.0445	0.615669	0.307834	−	0.951440i	$-0.400396\pi$
$859$	18.0445	0.615669	0.307834	+	0.951440i	$0.400396\pi$
$860$	0.545453	0.0185998
$861$	−10.6576	−0.363209
$862$	8.04045	0.273859
$863$	24.5155	0.834517	0.417258	−	0.908788i	$-0.362991\pi$
$863$	24.5155	0.834517	0.417258	+	0.908788i	$0.362991\pi$
$864$	−4.69000	−0.159557
$865$	−22.4207	−0.762325
$866$	−28.0428	−0.952933
$867$	−0.505193	−0.0171573
$868$	−3.71062	−0.125947
$869$	−2.67903	−0.0908799
$870$	5.44159	0.184487
$871$	98.9584	3.35308
$872$	31.1752	1.05572
$873$	16.4627	0.557179
$874$	10.3833	0.351220
$875$	36.8415	1.24547
$876$	−0.566969	−0.0191561
$877$	−13.0174	−0.439566	−0.219783	−	0.975549i	$-0.570535\pi$
$877$	−13.0174	−0.439566	−0.219783	+	0.975549i	$0.570535\pi$
$878$	−13.1702	−0.444472
$879$	11.5209	0.388589
$880$	6.32697	0.213282
$881$	−25.2122	−0.849421	−0.424711	−	0.905329i	$-0.639624\pi$
$881$	−25.2122	−0.849421	−0.424711	+	0.905329i	$0.639624\pi$
$882$	7.90257	0.266093
$883$	36.2990	1.22156	0.610779	−	0.791801i	$-0.290856\pi$
$883$	36.2990	1.22156	0.610779	+	0.791801i	$0.290856\pi$
$884$	1.79817	0.0604788
$885$	4.88335	0.164152
$886$	−13.5115	−0.453926
$887$	2.65294	0.0890769	0.0445385	−	0.999008i	$-0.485818\pi$
$887$	2.65294	0.0890769	0.0445385	+	0.999008i	$0.485818\pi$
$888$	−0.431591	−0.0144833
$889$	−24.7545	−0.830240
$890$	−20.1305	−0.674776
$891$	−6.76815	−0.226742
$892$	6.58456	0.220467
$893$	14.3344	0.479683
$894$	−2.92383	−0.0977874
$895$	−14.0841	−0.470781
$896$	25.1072	0.838772
$897$	−10.9368	−0.365170
$898$	18.0640	0.602805
$899$	−18.4631	−0.615778
$900$	−1.11766	−0.0372553
$901$	−3.13348	−0.104391
$902$	−9.10006	−0.302999
$903$	−1.53237	−0.0509939
$904$	8.89071	0.295700
$905$	18.5767	0.617511
$906$	3.58112	0.118975
$907$	15.6031	0.518092	0.259046	−	0.965865i	$-0.416592\pi$
$907$	15.6031	0.518092	0.259046	+	0.965865i	$0.416592\pi$
$908$	2.04410	0.0678358
$909$	35.0040	1.16101
$910$	−46.9211	−1.55542
$911$	34.0575	1.12838	0.564188	−	0.825646i	$-0.309189\pi$
$911$	34.0575	1.12838	0.564188	+	0.825646i	$0.309189\pi$
$912$	3.86259	0.127903
$913$	11.7900	0.390191
$914$	14.1777	0.468957
$915$	10.5401	0.348447
$916$	−3.59594	−0.118813
$917$	37.5879	1.24126
$918$	−3.79734	−0.125331
$919$	11.4980	0.379284	0.189642	−	0.981853i	$-0.439267\pi$
$919$	11.4980	0.379284	0.189642	+	0.981853i	$0.439267\pi$
$920$	−19.6595	−0.648153
$921$	6.59460	0.217299
$922$	−19.6188	−0.646112
$923$	45.2776	1.49033
$924$	0.441365	0.0145198
$925$	−0.403433	−0.0132648
$926$	−33.2137	−1.09147
$927$	−7.67318	−0.252020
$928$	−7.02490	−0.230604
$929$	−34.2786	−1.12465	−0.562323	−	0.826918i	$-0.690092\pi$
$929$	−34.2786	−1.12465	−0.562323	+	0.826918i	$0.690092\pi$
$930$	−5.31659	−0.174338
$931$	5.03569	0.165038
$932$	−0.0533443	−0.00174735
$933$	−1.31589	−0.0430803
$934$	−12.4369	−0.406948
$935$	−1.89375	−0.0619321
$936$	51.2993	1.67677
$937$	−41.7597	−1.36423	−0.682115	−	0.731245i	$-0.738940\pi$
$937$	−41.7597	−1.36423	−0.682115	+	0.731245i	$0.738940\pi$
$938$	−62.9088	−2.05405
$939$	10.2326	0.333929
$940$	−3.41658	−0.111436
$941$	46.5964	1.51900	0.759500	−	0.650507i	$-0.225444\pi$
$941$	46.5964	1.51900	0.759500	+	0.650507i	$0.225444\pi$
$942$	1.39909	0.0455848
$943$	24.1177	0.785380
$944$	17.0535	0.555043
$945$	−16.6708	−0.542302
$946$	−1.30842	−0.0425405
$947$	−27.2468	−0.885403	−0.442702	−	0.896669i	$-0.645980\pi$
$947$	−27.2468	−0.885403	−0.442702	+	0.896669i	$0.645980\pi$
$948$	0.389826	0.0126610
$949$	24.3254	0.789636
$950$	4.23312	0.137340
$951$	6.12704	0.198683
$952$	−9.08060	−0.294304
$953$	−25.5543	−0.827786	−0.413893	−	0.910325i	$-0.635831\pi$
$953$	−25.5543	−0.827786	−0.413893	+	0.910325i	$0.635831\pi$
$954$	−11.2534	−0.364342
$955$	16.4109	0.531045
$956$	−4.13034	−0.133585
$957$	2.19612	0.0709905
$958$	−37.5389	−1.21283
$959$	26.7101	0.862516
$960$	−8.41556	−0.271611
$961$	−12.9610	−0.418098
$962$	2.33103	0.0751554
$963$	−36.0883	−1.16293
$964$	−3.20350	−0.103178
$965$	41.2192	1.32689
$966$	6.95265	0.223698
$967$	56.9087	1.83006	0.915031	−	0.403384i	$-0.132166\pi$
$967$	56.9087	1.83006	0.915031	+	0.403384i	$0.132166\pi$
$968$	2.99371	0.0962215
$969$	−1.15612	−0.0371400
$970$	14.8616	0.477176
$971$	21.6997	0.696378	0.348189	−	0.937424i	$-0.386797\pi$
$971$	21.6997	0.696378	0.348189	+	0.937424i	$0.386797\pi$
$972$	3.49261	0.112025
$973$	41.1080	1.31786
$974$	−28.4030	−0.910092
$975$	−4.45879	−0.142796
$976$	36.8079	1.17819
$977$	0.125334	0.00400979	0.00200489	−	0.999998i	$-0.499362\pi$
$977$	0.125334	0.00400979	0.00200489	+	0.999998i	$0.499362\pi$
$978$	7.25908	0.232120
$979$	−8.12427	−0.259653
$980$	−1.20024	−0.0383404
$981$	−28.5829	−0.912582
$982$	−33.6741	−1.07458
$983$	6.51992	0.207953	0.103977	−	0.994580i	$-0.466843\pi$
$983$	6.51992	0.207953	0.103977	+	0.994580i	$0.466843\pi$
$984$	10.5187	0.335325
$985$	43.3648	1.38172
$986$	−5.68783	−0.181137
$987$	9.59834	0.305519
$988$	4.11506	0.130917
$989$	3.46769	0.110266
$990$	−6.80107	−0.216152
$991$	−7.49209	−0.237994	−0.118997	−	0.992895i	$-0.537968\pi$
$991$	−7.49209	−0.237994	−0.118997	+	0.992895i	$0.537968\pi$
$992$	6.86353	0.217917
$993$	−11.0380	−0.350282
$994$	−28.7835	−0.912956
$995$	−15.2187	−0.482466
$996$	−1.71556	−0.0543596
$997$	−5.62193	−0.178048	−0.0890241	−	0.996029i	$-0.528375\pi$
$997$	−5.62193	−0.178048	−0.0890241	+	0.996029i	$0.528375\pi$
$998$	−35.7548	−1.13180
$999$	0.828202	0.0262032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.17	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-1.30842 q^{2} -0.505193 q^{3} -0.288029 q^{4} +1.89375 q^{5} +0.661007 q^{6} -3.03323 q^{7} +2.99371 q^{8} -2.74478 q^{9} +O(q^{10})\)	\(q-1.30842 q^{2} -0.505193 q^{3} -0.288029 q^{4} +1.89375 q^{5} +0.661007 q^{6} -3.03323 q^{7} +2.99371 q^{8} -2.74478 q^{9} -2.47782 q^{10} -1.00000 q^{11} +0.145510 q^{12} -6.24301 q^{13} +3.96874 q^{14} -0.956708 q^{15} -3.34098 q^{16} +1.00000 q^{17} +3.59133 q^{18} +2.28848 q^{19} -0.545453 q^{20} +1.53237 q^{21} +1.30842 q^{22} -3.46769 q^{23} -1.51240 q^{24} -1.41373 q^{25} +8.16850 q^{26} +2.90222 q^{27} +0.873656 q^{28} +4.34709 q^{29} +1.25178 q^{30} -4.24723 q^{31} -1.61600 q^{32} +0.505193 q^{33} -1.30842 q^{34} -5.74416 q^{35} +0.790575 q^{36} +0.285368 q^{37} -2.99430 q^{38} +3.15393 q^{39} +5.66933 q^{40} -6.95498 q^{41} -2.00498 q^{42} -1.00000 q^{43} +0.288029 q^{44} -5.19791 q^{45} +4.53720 q^{46} +6.26374 q^{47} +1.68784 q^{48} +2.20045 q^{49} +1.84975 q^{50} -0.505193 q^{51} +1.79817 q^{52} -3.13348 q^{53} -3.79734 q^{54} -1.89375 q^{55} -9.08060 q^{56} -1.15612 q^{57} -5.68783 q^{58} -5.10433 q^{59} +0.275559 q^{60} -11.0171 q^{61} +5.55717 q^{62} +8.32553 q^{63} +8.79638 q^{64} -11.8227 q^{65} -0.661007 q^{66} -15.8511 q^{67} -0.288029 q^{68} +1.75185 q^{69} +7.51579 q^{70} -7.25254 q^{71} -8.21707 q^{72} -3.89643 q^{73} -0.373382 q^{74} +0.714206 q^{75} -0.659147 q^{76} +3.03323 q^{77} -4.12667 q^{78} +2.67903 q^{79} -6.32697 q^{80} +6.76815 q^{81} +9.10006 q^{82} -11.7900 q^{83} -0.441365 q^{84} +1.89375 q^{85} +1.30842 q^{86} -2.19612 q^{87} -2.99371 q^{88} +8.12427 q^{89} +6.80107 q^{90} +18.9364 q^{91} +0.998794 q^{92} +2.14567 q^{93} -8.19563 q^{94} +4.33379 q^{95} +0.816393 q^{96} -5.99783 q^{97} -2.87913 q^{98} +2.74478 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 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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