LMFDB - Embedded newform 8041.2.a.j.1.7

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:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.40536 q^{2} -1.47389 q^{3} +3.78577 q^{4} -0.987275 q^{5} +3.54525 q^{6} +2.06145 q^{7} -4.29541 q^{8} -0.827635 q^{9} +O(q^{10})$	\(q-2.40536 q^{2} -1.47389 q^{3} +3.78577 q^{4} -0.987275 q^{5} +3.54525 q^{6} +2.06145 q^{7} -4.29541 q^{8} -0.827635 q^{9} +2.37475 q^{10} +1.00000 q^{11} -5.57982 q^{12} -2.64454 q^{13} -4.95853 q^{14} +1.45514 q^{15} +2.76049 q^{16} +1.00000 q^{17} +1.99076 q^{18} +3.84969 q^{19} -3.73759 q^{20} -3.03836 q^{21} -2.40536 q^{22} -3.24980 q^{23} +6.33098 q^{24} -4.02529 q^{25} +6.36107 q^{26} +5.64153 q^{27} +7.80416 q^{28} +8.79752 q^{29} -3.50014 q^{30} -6.44883 q^{31} +1.95085 q^{32} -1.47389 q^{33} -2.40536 q^{34} -2.03522 q^{35} -3.13323 q^{36} +5.60389 q^{37} -9.25991 q^{38} +3.89777 q^{39} +4.24075 q^{40} -6.40638 q^{41} +7.30835 q^{42} +1.00000 q^{43} +3.78577 q^{44} +0.817103 q^{45} +7.81695 q^{46} +4.14107 q^{47} -4.06867 q^{48} -2.75043 q^{49} +9.68227 q^{50} -1.47389 q^{51} -10.0116 q^{52} -5.18596 q^{53} -13.5699 q^{54} -0.987275 q^{55} -8.85477 q^{56} -5.67404 q^{57} -21.1612 q^{58} +11.0935 q^{59} +5.50882 q^{60} -12.4336 q^{61} +15.5118 q^{62} -1.70613 q^{63} -10.2135 q^{64} +2.61089 q^{65} +3.54525 q^{66} -7.38800 q^{67} +3.78577 q^{68} +4.78986 q^{69} +4.89543 q^{70} -14.7253 q^{71} +3.55503 q^{72} +9.93884 q^{73} -13.4794 q^{74} +5.93285 q^{75} +14.5740 q^{76} +2.06145 q^{77} -9.37555 q^{78} +4.82250 q^{79} -2.72536 q^{80} -5.83212 q^{81} +15.4097 q^{82} +8.60895 q^{83} -11.5025 q^{84} -0.987275 q^{85} -2.40536 q^{86} -12.9666 q^{87} -4.29541 q^{88} +11.7923 q^{89} -1.96543 q^{90} -5.45158 q^{91} -12.3030 q^{92} +9.50490 q^{93} -9.96077 q^{94} -3.80071 q^{95} -2.87535 q^{96} +6.59082 q^{97} +6.61578 q^{98} -0.827635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.40536	−1.70085	−0.850424	−	0.526098i	$-0.823654\pi$
$2$	−2.40536	−1.70085	−0.850424	+	0.526098i	$0.823654\pi$
$3$	−1.47389	−0.850953	−0.425477	−	0.904969i	$-0.639894\pi$
$3$	−1.47389	−0.850953	−0.425477	+	0.904969i	$0.639894\pi$
$4$	3.78577	1.89288
$5$	−0.987275	−0.441523	−0.220761	−	0.975328i	$-0.570854\pi$
$5$	−0.987275	−0.441523	−0.220761	+	0.975328i	$0.570854\pi$
$6$	3.54525	1.44734
$7$	2.06145	0.779154	0.389577	−	0.920994i	$-0.372621\pi$
$7$	2.06145	0.779154	0.389577	+	0.920994i	$0.372621\pi$
$8$	−4.29541	−1.51866
$9$	−0.827635	−0.275878
$10$	2.37475	0.750963
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−5.57982	−1.61075
$13$	−2.64454	−0.733463	−0.366731	−	0.930327i	$-0.619523\pi$
$13$	−2.64454	−0.733463	−0.366731	+	0.930327i	$0.619523\pi$
$14$	−4.95853	−1.32522
$15$	1.45514	0.375715
$16$	2.76049	0.690122
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.99076	0.469227
$19$	3.84969	0.883180	0.441590	−	0.897217i	$-0.354415\pi$
$19$	3.84969	0.883180	0.441590	+	0.897217i	$0.354415\pi$
$20$	−3.73759	−0.835751
$21$	−3.03836	−0.663024
$22$	−2.40536	−0.512825
$23$	−3.24980	−0.677630	−0.338815	−	0.940853i	$-0.610026\pi$
$23$	−3.24980	−0.677630	−0.338815	+	0.940853i	$0.610026\pi$
$24$	6.33098	1.29231
$25$	−4.02529	−0.805058
$26$	6.36107	1.24751
$27$	5.64153	1.08571
$28$	7.80416	1.47485
$29$	8.79752	1.63366	0.816829	−	0.576879i	$-0.195730\pi$
$29$	8.79752	1.63366	0.816829	+	0.576879i	$0.195730\pi$
$30$	−3.50014	−0.639035
$31$	−6.44883	−1.15824	−0.579122	−	0.815241i	$-0.696605\pi$
$31$	−6.44883	−1.15824	−0.579122	+	0.815241i	$0.696605\pi$
$32$	1.95085	0.344865
$33$	−1.47389	−0.256572
$34$	−2.40536	−0.412516
$35$	−2.03522	−0.344015
$36$	−3.13323	−0.522205
$37$	5.60389	0.921274	0.460637	−	0.887589i	$-0.347621\pi$
$37$	5.60389	0.921274	0.460637	+	0.887589i	$0.347621\pi$
$38$	−9.25991	−1.50216
$39$	3.89777	0.624143
$40$	4.24075	0.670522
$41$	−6.40638	−1.00051	−0.500254	−	0.865879i	$-0.666760\pi$
$41$	−6.40638	−1.00051	−0.500254	+	0.865879i	$0.666760\pi$
$42$	7.30835	1.12770
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.78577	0.570726
$45$	0.817103	0.121807
$46$	7.81695	1.15255
$47$	4.14107	0.604037	0.302019	−	0.953302i	$-0.402340\pi$
$47$	4.14107	0.604037	0.302019	+	0.953302i	$0.402340\pi$
$48$	−4.06867	−0.587261
$49$	−2.75043	−0.392918
$50$	9.68227	1.36928
$51$	−1.47389	−0.206387
$52$	−10.0116	−1.38836
$53$	−5.18596	−0.712346	−0.356173	−	0.934420i	$-0.615919\pi$
$53$	−5.18596	−0.712346	−0.356173	+	0.934420i	$0.615919\pi$
$54$	−13.5699	−1.84663
$55$	−0.987275	−0.133124
$56$	−8.85477	−1.18327
$57$	−5.67404	−0.751545
$58$	−21.1612	−2.77860
$59$	11.0935	1.44425	0.722127	−	0.691760i	$-0.243164\pi$
$59$	11.0935	1.44425	0.722127	+	0.691760i	$0.243164\pi$
$60$	5.50882	0.711185
$61$	−12.4336	−1.59196	−0.795980	−	0.605322i	$-0.793044\pi$
$61$	−12.4336	−1.59196	−0.795980	+	0.605322i	$0.793044\pi$
$62$	15.5118	1.97000
$63$	−1.70613	−0.214952
$64$	−10.2135	−1.27668
$65$	2.61089	0.323841
$66$	3.54525	0.436390
$67$	−7.38800	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$67$	−7.38800	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$68$	3.78577	0.459091
$69$	4.78986	0.576632
$70$	4.89543	0.585116
$71$	−14.7253	−1.74758	−0.873788	−	0.486307i	$-0.838344\pi$
$71$	−14.7253	−1.74758	−0.873788	+	0.486307i	$0.838344\pi$
$72$	3.55503	0.418965
$73$	9.93884	1.16325	0.581627	−	0.813456i	$-0.302417\pi$
$73$	9.93884	1.16325	0.581627	+	0.813456i	$0.302417\pi$
$74$	−13.4794	−1.56695
$75$	5.93285	0.685066
$76$	14.5740	1.67176
$77$	2.06145	0.234924
$78$	−9.37555	−1.06157
$79$	4.82250	0.542574	0.271287	−	0.962499i	$-0.412551\pi$
$79$	4.82250	0.542574	0.271287	+	0.962499i	$0.412551\pi$
$80$	−2.72536	−0.304705
$81$	−5.83212	−0.648013
$82$	15.4097	1.70171
$83$	8.60895	0.944955	0.472477	−	0.881343i	$-0.343360\pi$
$83$	8.60895	0.944955	0.472477	+	0.881343i	$0.343360\pi$
$84$	−11.5025	−1.25503
$85$	−0.987275	−0.107085
$86$	−2.40536	−0.259377
$87$	−12.9666	−1.39017
$88$	−4.29541	−0.457892
$89$	11.7923	1.24999	0.624993	−	0.780631i	$-0.285102\pi$
$89$	11.7923	1.24999	0.624993	+	0.780631i	$0.285102\pi$
$90$	−1.96543	−0.207174
$91$	−5.45158	−0.571481
$92$	−12.3030	−1.28267
$93$	9.50490	0.985612
$94$	−9.96077	−1.02738
$95$	−3.80071	−0.389944
$96$	−2.87535	−0.293464
$97$	6.59082	0.669197	0.334598	−	0.942361i	$-0.391399\pi$
$97$	6.59082	0.669197	0.334598	+	0.942361i	$0.391399\pi$
$98$	6.61578	0.668294
$99$	−0.827635	−0.0831804
$100$	−15.2388	−1.52388
$101$	7.51432	0.747703	0.373851	−	0.927489i	$-0.378037\pi$
$101$	7.51432	0.747703	0.373851	+	0.927489i	$0.378037\pi$
$102$	3.54525	0.351032
$103$	−11.6014	−1.14312	−0.571559	−	0.820561i	$-0.693661\pi$
$103$	−11.6014	−1.14312	−0.571559	+	0.820561i	$0.693661\pi$
$104$	11.3594	1.11388
$105$	2.99970	0.292740
$106$	12.4741	1.21159
$107$	3.76762	0.364229	0.182115	−	0.983277i	$-0.441706\pi$
$107$	3.76762	0.364229	0.182115	+	0.983277i	$0.441706\pi$
$108$	21.3575	2.05513
$109$	15.0296	1.43957	0.719787	−	0.694195i	$-0.244239\pi$
$109$	15.0296	1.43957	0.719787	+	0.694195i	$0.244239\pi$
$110$	2.37475	0.226424
$111$	−8.25955	−0.783962
$112$	5.69060	0.537711
$113$	−12.7104	−1.19570	−0.597848	−	0.801609i	$-0.703977\pi$
$113$	−12.7104	−1.19570	−0.597848	+	0.801609i	$0.703977\pi$
$114$	13.6481	1.27826
$115$	3.20845	0.299189
$116$	33.3054	3.09232
$117$	2.18871	0.202347
$118$	−26.6840	−2.45646
$119$	2.06145	0.188973
$120$	−6.25042	−0.570583
$121$	1.00000	0.0909091
$122$	29.9073	2.70768
$123$	9.44232	0.851386
$124$	−24.4138	−2.19242
$125$	8.91044	0.796974
$126$	4.10385	0.365600
$127$	−7.43855	−0.660065	−0.330032	−	0.943970i	$-0.607060\pi$
$127$	−7.43855	−0.660065	−0.330032	+	0.943970i	$0.607060\pi$
$128$	20.6654	1.82658
$129$	−1.47389	−0.129769
$130$	−6.28013	−0.550804
$131$	8.64044	0.754919	0.377459	−	0.926026i	$-0.376798\pi$
$131$	8.64044	0.754919	0.377459	+	0.926026i	$0.376798\pi$
$132$	−5.57982	−0.485661
$133$	7.93595	0.688134
$134$	17.7708	1.53516
$135$	−5.56974	−0.479367
$136$	−4.29541	−0.368328
$137$	−15.3858	−1.31450	−0.657248	−	0.753674i	$-0.728280\pi$
$137$	−15.3858	−1.31450	−0.657248	+	0.753674i	$0.728280\pi$
$138$	−11.5214	−0.980763
$139$	14.4728	1.22757	0.613785	−	0.789473i	$-0.289646\pi$
$139$	14.4728	1.22757	0.613785	+	0.789473i	$0.289646\pi$
$140$	−7.70485	−0.651179
$141$	−6.10350	−0.514008
$142$	35.4198	2.97236
$143$	−2.64454	−0.221147
$144$	−2.28468	−0.190390
$145$	−8.68558	−0.721298
$146$	−23.9065	−1.97852
$147$	4.05384	0.334355
$148$	21.2150	1.74386
$149$	9.15871	0.750311	0.375155	−	0.926962i	$-0.377589\pi$
$149$	9.15871	0.750311	0.375155	+	0.926962i	$0.377589\pi$
$150$	−14.2706	−1.16519
$151$	−17.5699	−1.42982	−0.714910	−	0.699217i	$-0.753532\pi$
$151$	−17.5699	−1.42982	−0.714910	+	0.699217i	$0.753532\pi$
$152$	−16.5360	−1.34125
$153$	−0.827635	−0.0669103
$154$	−4.95853	−0.399570
$155$	6.36677	0.511392
$156$	14.7560	1.18143
$157$	4.74343	0.378567	0.189283	−	0.981922i	$-0.439384\pi$
$157$	4.74343	0.378567	0.189283	+	0.981922i	$0.439384\pi$
$158$	−11.5999	−0.922835
$159$	7.64355	0.606173
$160$	−1.92603	−0.152266
$161$	−6.69930	−0.527979
$162$	14.0283	1.10217
$163$	−17.2930	−1.35449	−0.677244	−	0.735758i	$-0.736826\pi$
$163$	−17.2930	−1.35449	−0.677244	+	0.735758i	$0.736826\pi$
$164$	−24.2530	−1.89384
$165$	1.45514	0.113282
$166$	−20.7076	−1.60722
$167$	−8.95644	−0.693070	−0.346535	−	0.938037i	$-0.612642\pi$
$167$	−8.95644	−0.693070	−0.346535	+	0.938037i	$0.612642\pi$
$168$	13.0510	1.00691
$169$	−6.00642	−0.462032
$170$	2.37475	0.182135
$171$	−3.18614	−0.243650
$172$	3.78577	0.288662
$173$	−0.349949	−0.0266061	−0.0133031	−	0.999912i	$-0.504235\pi$
$173$	−0.349949	−0.0266061	−0.0133031	+	0.999912i	$0.504235\pi$
$174$	31.1894	2.36446
$175$	−8.29792	−0.627264
$176$	2.76049	0.208080
$177$	−16.3507	−1.22899
$178$	−28.3648	−2.12603
$179$	21.3273	1.59408	0.797038	−	0.603929i	$-0.206399\pi$
$179$	21.3273	1.59408	0.797038	+	0.603929i	$0.206399\pi$
$180$	3.09336	0.230566
$181$	13.5630	1.00813	0.504066	−	0.863665i	$-0.331837\pi$
$181$	13.5630	1.00813	0.504066	+	0.863665i	$0.331837\pi$
$182$	13.1130	0.972002
$183$	18.3258	1.35468
$184$	13.9592	1.02909
$185$	−5.53259	−0.406764
$186$	−22.8627	−1.67638
$187$	1.00000	0.0731272
$188$	15.6771	1.14337
$189$	11.6297	0.845938
$190$	9.14208	0.663236
$191$	−1.98654	−0.143741	−0.0718704	−	0.997414i	$-0.522897\pi$
$191$	−1.98654	−0.143741	−0.0718704	+	0.997414i	$0.522897\pi$
$192$	15.0536	1.08640
$193$	−23.0371	−1.65825	−0.829125	−	0.559064i	$-0.811161\pi$
$193$	−23.0371	−1.65825	−0.829125	+	0.559064i	$0.811161\pi$
$194$	−15.8533	−1.13820
$195$	−3.84817	−0.275573
$196$	−10.4125	−0.743748
$197$	16.3494	1.16485	0.582423	−	0.812886i	$-0.302105\pi$
$197$	16.3494	1.16485	0.582423	+	0.812886i	$0.302105\pi$
$198$	1.99076	0.141477
$199$	5.41930	0.384164	0.192082	−	0.981379i	$-0.438476\pi$
$199$	5.41930	0.384164	0.192082	+	0.981379i	$0.438476\pi$
$200$	17.2903	1.22261
$201$	10.8891	0.768060
$202$	−18.0747	−1.27173
$203$	18.1356	1.27287
$204$	−5.57982	−0.390665
$205$	6.32486	0.441747
$206$	27.9055	1.94427
$207$	2.68965	0.186943
$208$	−7.30021	−0.506179
$209$	3.84969	0.266289
$210$	−7.21535	−0.497907
$211$	6.29905	0.433645	0.216822	−	0.976211i	$-0.430431\pi$
$211$	6.29905	0.433645	0.216822	+	0.976211i	$0.430431\pi$
$212$	−19.6328	−1.34839
$213$	21.7036	1.48711
$214$	−9.06249	−0.619499
$215$	−0.987275	−0.0673316
$216$	−24.2327	−1.64883
$217$	−13.2939	−0.902451
$218$	−36.1516	−2.44850
$219$	−14.6488	−0.989874
$220$	−3.73759	−0.251988
$221$	−2.64454	−0.177891
$222$	19.8672	1.33340
$223$	−1.31950	−0.0883602	−0.0441801	−	0.999024i	$-0.514068\pi$
$223$	−1.31950	−0.0883602	−0.0441801	+	0.999024i	$0.514068\pi$
$224$	4.02158	0.268703
$225$	3.33147	0.222098
$226$	30.5732	2.03370
$227$	−29.2913	−1.94413	−0.972066	−	0.234709i	$-0.924586\pi$
$227$	−29.2913	−1.94413	−0.972066	+	0.234709i	$0.924586\pi$
$228$	−21.4806	−1.42259
$229$	−7.64512	−0.505203	−0.252602	−	0.967570i	$-0.581286\pi$
$229$	−7.64512	−0.505203	−0.252602	+	0.967570i	$0.581286\pi$
$230$	−7.71748	−0.508875
$231$	−3.03836	−0.199909
$232$	−37.7890	−2.48097
$233$	12.7491	0.835220	0.417610	−	0.908626i	$-0.362868\pi$
$233$	12.7491	0.835220	0.417610	+	0.908626i	$0.362868\pi$
$234$	−5.26464	−0.344161
$235$	−4.08838	−0.266696
$236$	41.9975	2.73380
$237$	−7.10786	−0.461705
$238$	−4.95853	−0.321414
$239$	15.1406	0.979364	0.489682	−	0.871901i	$-0.337113\pi$
$239$	15.1406	0.979364	0.489682	+	0.871901i	$0.337113\pi$
$240$	4.01689	0.259289
$241$	22.0554	1.42072	0.710358	−	0.703841i	$-0.248533\pi$
$241$	22.0554	1.42072	0.710358	+	0.703841i	$0.248533\pi$
$242$	−2.40536	−0.154623
$243$	−8.32867	−0.534284
$244$	−47.0707	−3.01339
$245$	2.71543	0.173483
$246$	−22.7122	−1.44808
$247$	−10.1807	−0.647780
$248$	27.7004	1.75898
$249$	−12.6887	−0.804113
$250$	−21.4328	−1.35553
$251$	13.7086	0.865282	0.432641	−	0.901566i	$-0.357582\pi$
$251$	13.7086	0.865282	0.432641	+	0.901566i	$0.357582\pi$
$252$	−6.45900	−0.406878
$253$	−3.24980	−0.204313
$254$	17.8924	1.12267
$255$	1.45514	0.0911244
$256$	−29.2808	−1.83005
$257$	6.09794	0.380379	0.190189	−	0.981747i	$-0.439090\pi$
$257$	6.09794	0.380379	0.190189	+	0.981747i	$0.439090\pi$
$258$	3.54525	0.220718
$259$	11.5521	0.717815
$260$	9.88421	0.612992
$261$	−7.28114	−0.450691
$262$	−20.7834	−1.28400
$263$	15.0991	0.931049	0.465524	−	0.885035i	$-0.345866\pi$
$263$	15.0991	0.931049	0.465524	+	0.885035i	$0.345866\pi$
$264$	6.33098	0.389645
$265$	5.11997	0.314517
$266$	−19.0888	−1.17041
$267$	−17.3807	−1.06368
$268$	−27.9692	−1.70849
$269$	−13.6639	−0.833102	−0.416551	−	0.909112i	$-0.636761\pi$
$269$	−13.6639	−0.833102	−0.416551	+	0.909112i	$0.636761\pi$
$270$	13.3972	0.815330
$271$	−17.4052	−1.05729	−0.528645	−	0.848843i	$-0.677300\pi$
$271$	−17.4052	−1.05729	−0.528645	+	0.848843i	$0.677300\pi$
$272$	2.76049	0.167379
$273$	8.03505	0.486304
$274$	37.0084	2.23576
$275$	−4.02529	−0.242734
$276$	18.1333	1.09150
$277$	3.05875	0.183783	0.0918913	−	0.995769i	$-0.470709\pi$
$277$	3.05875	0.183783	0.0918913	+	0.995769i	$0.470709\pi$
$278$	−34.8124	−2.08791
$279$	5.33728	0.319535
$280$	8.74209	0.522440
$281$	−31.1221	−1.85659	−0.928293	−	0.371849i	$-0.878724\pi$
$281$	−31.1221	−1.85659	−0.928293	+	0.371849i	$0.878724\pi$
$282$	14.6811	0.874249
$283$	−23.3710	−1.38926	−0.694629	−	0.719368i	$-0.744432\pi$
$283$	−23.3710	−1.38926	−0.694629	+	0.719368i	$0.744432\pi$
$284$	−55.7467	−3.30796
$285$	5.60184	0.331824
$286$	6.36107	0.376138
$287$	−13.2064	−0.779550
$288$	−1.61459	−0.0951408
$289$	1.00000	0.0588235
$290$	20.8920	1.22682
$291$	−9.71418	−0.569455
$292$	37.6261	2.20190
$293$	−10.1359	−0.592144	−0.296072	−	0.955166i	$-0.595677\pi$
$293$	−10.1359	−0.592144	−0.296072	+	0.955166i	$0.595677\pi$
$294$	−9.75096	−0.568687
$295$	−10.9524	−0.637672
$296$	−24.0710	−1.39910
$297$	5.64153	0.327355
$298$	−22.0300	−1.27616
$299$	8.59422	0.497017
$300$	22.4604	1.29675
$301$	2.06145	0.118820
$302$	42.2620	2.43190
$303$	−11.0753	−0.636260
$304$	10.6270	0.609502
$305$	12.2754	0.702887
$306$	1.99076	0.113804
$307$	−22.4745	−1.28269	−0.641345	−	0.767253i	$-0.721623\pi$
$307$	−22.4745	−1.28269	−0.641345	+	0.767253i	$0.721623\pi$
$308$	7.80416	0.444683
$309$	17.0992	0.972739
$310$	−15.3144	−0.869799
$311$	10.3116	0.584717	0.292358	−	0.956309i	$-0.405560\pi$
$311$	10.3116	0.584717	0.292358	+	0.956309i	$0.405560\pi$
$312$	−16.7425	−0.947859
$313$	−25.5763	−1.44566	−0.722828	−	0.691028i	$-0.757158\pi$
$313$	−25.5763	−1.44566	−0.722828	+	0.691028i	$0.757158\pi$
$314$	−11.4097	−0.643884
$315$	1.68442	0.0949061
$316$	18.2569	1.02703
$317$	19.6776	1.10520	0.552602	−	0.833445i	$-0.313635\pi$
$317$	19.6776	1.10520	0.552602	+	0.833445i	$0.313635\pi$
$318$	−18.3855	−1.03101
$319$	8.79752	0.492567
$320$	10.0835	0.563686
$321$	−5.55307	−0.309942
$322$	16.1142	0.898011
$323$	3.84969	0.214203
$324$	−22.0790	−1.22661
$325$	10.6450	0.590480
$326$	41.5958	2.30378
$327$	−22.1520	−1.22501
$328$	27.5180	1.51943
$329$	8.53660	0.470638
$330$	−3.50014	−0.192676
$331$	−28.2756	−1.55417	−0.777083	−	0.629398i	$-0.783302\pi$
$331$	−28.2756	−1.55417	−0.777083	+	0.629398i	$0.783302\pi$
$332$	32.5915	1.78869
$333$	−4.63798	−0.254160
$334$	21.5435	1.17881
$335$	7.29399	0.398513
$336$	−8.38735	−0.457567
$337$	18.7095	1.01917	0.509585	−	0.860420i	$-0.329799\pi$
$337$	18.7095	1.01917	0.509585	+	0.860420i	$0.329799\pi$
$338$	14.4476	0.785846
$339$	18.7338	1.01748
$340$	−3.73759	−0.202699
$341$	−6.44883	−0.349224
$342$	7.66382	0.414412
$343$	−20.1000	−1.08530
$344$	−4.29541	−0.231593
$345$	−4.72891	−0.254596
$346$	0.841753	0.0452529
$347$	2.92477	0.157010	0.0785049	−	0.996914i	$-0.474985\pi$
$347$	2.92477	0.157010	0.0785049	+	0.996914i	$0.474985\pi$
$348$	−49.0886	−2.63142
$349$	10.0716	0.539119	0.269559	−	0.962984i	$-0.413122\pi$
$349$	10.0716	0.539119	0.269559	+	0.962984i	$0.413122\pi$
$350$	19.9595	1.06688
$351$	−14.9192	−0.796330
$352$	1.95085	0.103981
$353$	7.49767	0.399061	0.199530	−	0.979892i	$-0.436058\pi$
$353$	7.49767	0.399061	0.199530	+	0.979892i	$0.436058\pi$
$354$	39.3293	2.09033
$355$	14.5380	0.771595
$356$	44.6430	2.36607
$357$	−3.03836	−0.160807
$358$	−51.2998	−2.71128
$359$	7.16623	0.378219	0.189110	−	0.981956i	$-0.439440\pi$
$359$	7.16623	0.378219	0.189110	+	0.981956i	$0.439440\pi$
$360$	−3.50980	−0.184982
$361$	−4.17986	−0.219992
$362$	−32.6240	−1.71468
$363$	−1.47389	−0.0773594
$364$	−20.6384	−1.08175
$365$	−9.81237	−0.513603
$366$	−44.0803	−2.30411
$367$	−24.1812	−1.26225	−0.631123	−	0.775682i	$-0.717406\pi$
$367$	−24.1812	−1.26225	−0.631123	+	0.775682i	$0.717406\pi$
$368$	−8.97103	−0.467647
$369$	5.30214	0.276018
$370$	13.3079	0.691843
$371$	−10.6906	−0.555027
$372$	35.9833	1.86565
$373$	−4.72110	−0.244449	−0.122225	−	0.992502i	$-0.539003\pi$
$373$	−4.72110	−0.244449	−0.122225	+	0.992502i	$0.539003\pi$
$374$	−2.40536	−0.124378
$375$	−13.1331	−0.678188
$376$	−17.7876	−0.917325
$377$	−23.2654	−1.19823
$378$	−27.9737	−1.43881
$379$	2.33631	0.120008	0.0600040	−	0.998198i	$-0.480889\pi$
$379$	2.33631	0.120008	0.0600040	+	0.998198i	$0.480889\pi$
$380$	−14.3886	−0.738119
$381$	10.9636	0.561685
$382$	4.77834	0.244481
$383$	−15.3444	−0.784064	−0.392032	−	0.919951i	$-0.628228\pi$
$383$	−15.3444	−0.784064	−0.392032	+	0.919951i	$0.628228\pi$
$384$	−30.4586	−1.55434
$385$	−2.03522	−0.103724
$386$	55.4126	2.82043
$387$	−0.827635	−0.0420710
$388$	24.9513	1.26671
$389$	3.50565	0.177743	0.0888717	−	0.996043i	$-0.471674\pi$
$389$	3.50565	0.177743	0.0888717	+	0.996043i	$0.471674\pi$
$390$	9.25625	0.468708
$391$	−3.24980	−0.164349
$392$	11.8142	0.596708
$393$	−12.7351	−0.642401
$394$	−39.3262	−1.98122
$395$	−4.76114	−0.239559
$396$	−3.13323	−0.157451
$397$	−8.66248	−0.434758	−0.217379	−	0.976087i	$-0.569751\pi$
$397$	−8.66248	−0.434758	−0.217379	+	0.976087i	$0.569751\pi$
$398$	−13.0354	−0.653405
$399$	−11.6967	−0.585570
$400$	−11.1118	−0.555588
$401$	11.0482	0.551720	0.275860	−	0.961198i	$-0.411037\pi$
$401$	11.0482	0.551720	0.275860	+	0.961198i	$0.411037\pi$
$402$	−26.1923	−1.30635
$403$	17.0542	0.849529
$404$	28.4474	1.41531
$405$	5.75790	0.286113
$406$	−43.6228	−2.16496
$407$	5.60389	0.277775
$408$	6.33098	0.313430
$409$	30.4248	1.50441	0.752204	−	0.658930i	$-0.228991\pi$
$409$	30.4248	1.50441	0.752204	+	0.658930i	$0.228991\pi$
$410$	−15.2136	−0.751345
$411$	22.6770	1.11858
$412$	−43.9201	−2.16379
$413$	22.8687	1.12530
$414$	−6.46958	−0.317962
$415$	−8.49940	−0.417219
$416$	−5.15910	−0.252946
$417$	−21.3315	−1.04461
$418$	−9.25991	−0.452917
$419$	−25.4592	−1.24377	−0.621883	−	0.783110i	$-0.713632\pi$
$419$	−25.4592	−1.24377	−0.621883	+	0.783110i	$0.713632\pi$
$420$	11.3561	0.554123
$421$	3.53805	0.172434	0.0862170	−	0.996276i	$-0.472522\pi$
$421$	3.53805	0.172434	0.0862170	+	0.996276i	$0.472522\pi$
$422$	−15.1515	−0.737563
$423$	−3.42729	−0.166641
$424$	22.2758	1.08181
$425$	−4.02529	−0.195255
$426$	−52.2050	−2.52934
$427$	−25.6312	−1.24038
$428$	14.2633	0.689444
$429$	3.89777	0.188186
$430$	2.37475	0.114521
$431$	34.3999	1.65699	0.828493	−	0.560000i	$-0.189199\pi$
$431$	34.3999	1.65699	0.828493	+	0.560000i	$0.189199\pi$
$432$	15.5734	0.749274
$433$	27.1683	1.30563	0.652814	−	0.757519i	$-0.273589\pi$
$433$	27.1683	1.30563	0.652814	+	0.757519i	$0.273589\pi$
$434$	31.9767	1.53493
$435$	12.8016	0.613791
$436$	56.8985	2.72494
$437$	−12.5107	−0.598470
$438$	35.2357	1.68363
$439$	12.5764	0.600237	0.300119	−	0.953902i	$-0.402974\pi$
$439$	12.5764	0.600237	0.300119	+	0.953902i	$0.402974\pi$
$440$	4.24075	0.202170
$441$	2.27635	0.108398
$442$	6.36107	0.302565
$443$	−38.5505	−1.83159	−0.915795	−	0.401645i	$-0.868439\pi$
$443$	−38.5505	−1.83159	−0.915795	+	0.401645i	$0.868439\pi$
$444$	−31.2687	−1.48395
$445$	−11.6423	−0.551897
$446$	3.17387	0.150287
$447$	−13.4990	−0.638479
$448$	−21.0546	−0.994735
$449$	−9.43354	−0.445196	−0.222598	−	0.974910i	$-0.571454\pi$
$449$	−9.43354	−0.445196	−0.222598	+	0.974910i	$0.571454\pi$
$450$	−8.01339	−0.377755
$451$	−6.40638	−0.301665
$452$	−48.1187	−2.26331
$453$	25.8962	1.21671
$454$	70.4561	3.30667
$455$	5.38221	0.252322
$456$	24.3723	1.14134
$457$	−19.3286	−0.904155	−0.452077	−	0.891979i	$-0.649317\pi$
$457$	−19.3286	−0.904155	−0.452077	+	0.891979i	$0.649317\pi$
$458$	18.3893	0.859274
$459$	5.64153	0.263324
$460$	12.1464	0.566330
$461$	−17.0327	−0.793292	−0.396646	−	0.917972i	$-0.629826\pi$
$461$	−17.0327	−0.793292	−0.396646	+	0.917972i	$0.629826\pi$
$462$	7.30835	0.340015
$463$	1.05646	0.0490977	0.0245488	−	0.999699i	$-0.492185\pi$
$463$	1.05646	0.0490977	0.0245488	+	0.999699i	$0.492185\pi$
$464$	24.2854	1.12742
$465$	−9.38395	−0.435170
$466$	−30.6662	−1.42058
$467$	16.5290	0.764871	0.382435	−	0.923982i	$-0.375085\pi$
$467$	16.5290	0.764871	0.382435	+	0.923982i	$0.375085\pi$
$468$	8.28595	0.383018
$469$	−15.2300	−0.703255
$470$	9.83402	0.453610
$471$	−6.99131	−0.322143
$472$	−47.6513	−2.19333
$473$	1.00000	0.0459800
$474$	17.0970	0.785290
$475$	−15.4961	−0.711011
$476$	7.80416	0.357703
$477$	4.29208	0.196521
$478$	−36.4186	−1.66575
$479$	13.0759	0.597452	0.298726	−	0.954339i	$-0.403438\pi$
$479$	13.0759	0.597452	0.298726	+	0.954339i	$0.403438\pi$
$480$	2.83876	0.129571
$481$	−14.8197	−0.675721
$482$	−53.0513	−2.41642
$483$	9.87406	0.449285
$484$	3.78577	0.172080
$485$	−6.50696	−0.295466
$486$	20.0335	0.908736
$487$	25.7698	1.16774	0.583870	−	0.811847i	$-0.301538\pi$
$487$	25.7698	1.16774	0.583870	+	0.811847i	$0.301538\pi$
$488$	53.4075	2.41764
$489$	25.4880	1.15261
$490$	−6.53159	−0.295067
$491$	−37.0485	−1.67197	−0.835987	−	0.548749i	$-0.815104\pi$
$491$	−37.0485	−1.67197	−0.835987	+	0.548749i	$0.815104\pi$
$492$	35.7464	1.61157
$493$	8.79752	0.396220
$494$	24.4882	1.10178
$495$	0.817103	0.0367261
$496$	−17.8019	−0.799330
$497$	−30.3555	−1.36163
$498$	30.5209	1.36767
$499$	−7.09788	−0.317745	−0.158872	−	0.987299i	$-0.550786\pi$
$499$	−7.09788	−0.317745	−0.158872	+	0.987299i	$0.550786\pi$
$500$	33.7328	1.50858
$501$	13.2008	0.589770
$502$	−32.9743	−1.47171
$503$	23.2120	1.03497	0.517486	−	0.855691i	$-0.326868\pi$
$503$	23.2120	1.03497	0.517486	+	0.855691i	$0.326868\pi$
$504$	7.32852	0.326438
$505$	−7.41870	−0.330128
$506$	7.81695	0.347506
$507$	8.85283	0.393168
$508$	−28.1606	−1.24943
$509$	5.44423	0.241311	0.120656	−	0.992694i	$-0.461500\pi$
$509$	5.44423	0.241311	0.120656	+	0.992694i	$0.461500\pi$
$510$	−3.50014	−0.154989
$511$	20.4884	0.906354
$512$	29.1002	1.28606
$513$	21.7182	0.958880
$514$	−14.6677	−0.646966
$515$	11.4537	0.504712
$516$	−5.57982	−0.245638
$517$	4.14107	0.182124
$518$	−27.7871	−1.22089
$519$	0.515787	0.0226406
$520$	−11.2148	−0.491803
$521$	23.2761	1.01975	0.509873	−	0.860250i	$-0.329692\pi$
$521$	23.2761	1.01975	0.509873	+	0.860250i	$0.329692\pi$
$522$	17.5138	0.766557
$523$	45.5096	1.99000	0.994999	−	0.0998876i	$-0.0318483\pi$
$523$	45.5096	1.99000	0.994999	+	0.0998876i	$0.0318483\pi$
$524$	32.7107	1.42897
$525$	12.2303	0.533773
$526$	−36.3187	−1.58357
$527$	−6.44883	−0.280916
$528$	−4.06867	−0.177066
$529$	−12.4388	−0.540817
$530$	−12.3154	−0.534946
$531$	−9.18139	−0.398439
$532$	30.0436	1.30256
$533$	16.9419	0.733836
$534$	41.8068	1.80916
$535$	−3.71968	−0.160816
$536$	31.7345	1.37072
$537$	−31.4342	−1.35648
$538$	32.8666	1.41698
$539$	−2.75043	−0.118469
$540$	−21.0857	−0.907386
$541$	−0.628675	−0.0270288	−0.0135144	−	0.999909i	$-0.504302\pi$
$541$	−0.628675	−0.0270288	−0.0135144	+	0.999909i	$0.504302\pi$
$542$	41.8657	1.79829
$543$	−19.9905	−0.857873
$544$	1.95085	0.0836421
$545$	−14.8383	−0.635605
$546$	−19.3272	−0.827128
$547$	7.36356	0.314843	0.157422	−	0.987531i	$-0.449682\pi$
$547$	7.36356	0.314843	0.157422	+	0.987531i	$0.449682\pi$
$548$	−58.2470	−2.48819
$549$	10.2905	0.439187
$550$	9.68227	0.412853
$551$	33.8678	1.44282
$552$	−20.5744	−0.875706
$553$	9.94134	0.422749
$554$	−7.35741	−0.312586
$555$	8.15445	0.346137
$556$	54.7908	2.32365
$557$	20.2286	0.857112	0.428556	−	0.903515i	$-0.359022\pi$
$557$	20.2286	0.857112	0.428556	+	0.903515i	$0.359022\pi$
$558$	−12.8381	−0.543480
$559$	−2.64454	−0.111852
$560$	−5.61819	−0.237412
$561$	−1.47389	−0.0622279
$562$	74.8598	3.15777
$563$	9.48037	0.399550	0.199775	−	0.979842i	$-0.435979\pi$
$563$	9.48037	0.399550	0.199775	+	0.979842i	$0.435979\pi$
$564$	−23.1064	−0.972956
$565$	12.5487	0.527927
$566$	56.2156	2.36292
$567$	−12.0226	−0.504902
$568$	63.2514	2.65397
$569$	21.9908	0.921902	0.460951	−	0.887426i	$-0.347508\pi$
$569$	21.9908	0.921902	0.460951	+	0.887426i	$0.347508\pi$
$570$	−13.4745	−0.564383
$571$	15.3929	0.644171	0.322085	−	0.946711i	$-0.395616\pi$
$571$	15.3929	0.644171	0.322085	+	0.946711i	$0.395616\pi$
$572$	−10.0116	−0.418606
$573$	2.92795	0.122317
$574$	31.7662	1.32590
$575$	13.0814	0.545531
$576$	8.45303	0.352210
$577$	13.0014	0.541256	0.270628	−	0.962684i	$-0.412769\pi$
$577$	13.0014	0.541256	0.270628	+	0.962684i	$0.412769\pi$
$578$	−2.40536	−0.100050
$579$	33.9543	1.41109
$580$	−32.8815	−1.36533
$581$	17.7469	0.736266
$582$	23.3661	0.968557
$583$	−5.18596	−0.214780
$584$	−42.6914	−1.76658
$585$	−2.16086	−0.0893406
$586$	24.3805	1.00715
$587$	26.3874	1.08912	0.544562	−	0.838720i	$-0.316696\pi$
$587$	26.3874	1.08912	0.544562	+	0.838720i	$0.316696\pi$
$588$	15.3469	0.632895
$589$	−24.8260	−1.02294
$590$	26.3444	1.08458
$591$	−24.0973	−0.991229
$592$	15.4695	0.635791
$593$	−15.4234	−0.633361	−0.316681	−	0.948532i	$-0.602568\pi$
$593$	−15.4234	−0.633361	−0.316681	+	0.948532i	$0.602568\pi$
$594$	−13.5699	−0.556781
$595$	−2.03522	−0.0834358
$596$	34.6727	1.42025
$597$	−7.98748	−0.326906
$598$	−20.6722	−0.845350
$599$	−10.7494	−0.439207	−0.219604	−	0.975589i	$-0.570476\pi$
$599$	−10.7494	−0.439207	−0.219604	+	0.975589i	$0.570476\pi$
$600$	−25.4840	−1.04038
$601$	−40.4766	−1.65107	−0.825537	−	0.564347i	$-0.809128\pi$
$601$	−40.4766	−1.65107	−0.825537	+	0.564347i	$0.809128\pi$
$602$	−4.95853	−0.202095
$603$	6.11456	0.249004
$604$	−66.5156	−2.70648
$605$	−0.987275	−0.0401384
$606$	26.6401	1.08218
$607$	28.2905	1.14827	0.574137	−	0.818759i	$-0.305338\pi$
$607$	28.2905	1.14827	0.574137	+	0.818759i	$0.305338\pi$
$608$	7.51019	0.304578
$609$	−26.7300	−1.08316
$610$	−29.5268	−1.19550
$611$	−10.9512	−0.443039
$612$	−3.13323	−0.126653
$613$	−32.1870	−1.30002	−0.650010	−	0.759925i	$-0.725235\pi$
$613$	−32.1870	−1.30002	−0.650010	+	0.759925i	$0.725235\pi$
$614$	54.0594	2.18166
$615$	−9.32217	−0.375906
$616$	−8.85477	−0.356769
$617$	11.3483	0.456865	0.228433	−	0.973560i	$-0.426640\pi$
$617$	11.3483	0.456865	0.228433	+	0.973560i	$0.426640\pi$
$618$	−41.1298	−1.65448
$619$	19.7454	0.793634	0.396817	−	0.917898i	$-0.370115\pi$
$619$	19.7454	0.793634	0.396817	+	0.917898i	$0.370115\pi$
$620$	24.1031	0.968004
$621$	−18.3338	−0.735712
$622$	−24.8031	−0.994514
$623$	24.3093	0.973931
$624$	10.7597	0.430734
$625$	11.3294	0.453175
$626$	61.5202	2.45884
$627$	−5.67404	−0.226599
$628$	17.9575	0.716582
$629$	5.60389	0.223442
$630$	−4.05163	−0.161421
$631$	16.9738	0.675716	0.337858	−	0.941197i	$-0.390298\pi$
$631$	16.9738	0.675716	0.337858	+	0.941197i	$0.390298\pi$
$632$	−20.7146	−0.823984
$633$	−9.28414	−0.369011
$634$	−47.3317	−1.87978
$635$	7.34390	0.291434
$636$	28.9367	1.14741
$637$	7.27362	0.288191
$638$	−21.1612	−0.837781
$639$	12.1872	0.482118
$640$	−20.4024	−0.806477
$641$	35.5955	1.40594	0.702970	−	0.711220i	$-0.251857\pi$
$641$	35.5955	1.40594	0.702970	+	0.711220i	$0.251857\pi$
$642$	13.3571	0.527165
$643$	32.6214	1.28646	0.643232	−	0.765672i	$-0.277593\pi$
$643$	32.6214	1.28646	0.643232	+	0.765672i	$0.277593\pi$
$644$	−25.3620	−0.999401
$645$	1.45514	0.0572961
$646$	−9.25991	−0.364326
$647$	19.9820	0.785575	0.392787	−	0.919629i	$-0.371511\pi$
$647$	19.9820	0.785575	0.392787	+	0.919629i	$0.371511\pi$
$648$	25.0513	0.984109
$649$	11.0935	0.435459
$650$	−25.6051	−1.00432
$651$	19.5939	0.767944
$652$	−65.4671	−2.56389
$653$	−46.1641	−1.80654	−0.903270	−	0.429073i	$-0.858840\pi$
$653$	−46.1641	−1.80654	−0.903270	+	0.429073i	$0.858840\pi$
$654$	53.2837	2.08356
$655$	−8.53049	−0.333314
$656$	−17.6847	−0.690472
$657$	−8.22573	−0.320916
$658$	−20.5336	−0.800484
$659$	−29.4285	−1.14637	−0.573187	−	0.819425i	$-0.694293\pi$
$659$	−29.4285	−1.14637	−0.573187	+	0.819425i	$0.694293\pi$
$660$	5.50882	0.214430
$661$	37.7954	1.47007	0.735036	−	0.678029i	$-0.237165\pi$
$661$	37.7954	1.47007	0.735036	+	0.678029i	$0.237165\pi$
$662$	68.0130	2.64340
$663$	3.89777	0.151377
$664$	−36.9790	−1.43506
$665$	−7.83496	−0.303827
$666$	11.1560	0.432287
$667$	−28.5902	−1.10702
$668$	−33.9070	−1.31190
$669$	1.94480	0.0751904
$670$	−17.5447	−0.677810
$671$	−12.4336	−0.479994
$672$	−5.92739	−0.228654
$673$	−11.5302	−0.444458	−0.222229	−	0.974994i	$-0.571333\pi$
$673$	−11.5302	−0.444458	−0.222229	+	0.974994i	$0.571333\pi$
$674$	−45.0031	−1.73345
$675$	−22.7088	−0.874061
$676$	−22.7389	−0.874573
$677$	−22.4057	−0.861120	−0.430560	−	0.902562i	$-0.641684\pi$
$677$	−22.4057	−0.861120	−0.430560	+	0.902562i	$0.641684\pi$
$678$	−45.0616	−1.73058
$679$	13.5866	0.521408
$680$	4.24075	0.162625
$681$	43.1723	1.65437
$682$	15.5118	0.593977
$683$	19.5024	0.746238	0.373119	−	0.927784i	$-0.378288\pi$
$683$	19.5024	0.746238	0.373119	+	0.927784i	$0.378288\pi$
$684$	−12.0620	−0.461201
$685$	15.1900	0.580380
$686$	48.3478	1.84593
$687$	11.2681	0.429905
$688$	2.76049	0.105243
$689$	13.7145	0.522479
$690$	11.3747	0.433029
$691$	−29.4952	−1.12205	−0.561025	−	0.827799i	$-0.689593\pi$
$691$	−29.4952	−1.12205	−0.561025	+	0.827799i	$0.689593\pi$
$692$	−1.32482	−0.0503622
$693$	−1.70613	−0.0648104
$694$	−7.03513	−0.267050
$695$	−14.2887	−0.542001
$696$	55.6970	2.11119
$697$	−6.40638	−0.242659
$698$	−24.2258	−0.916959
$699$	−18.7908	−0.710734
$700$	−31.4140	−1.18734
$701$	33.2824	1.25706	0.628530	−	0.777785i	$-0.283657\pi$
$701$	33.2824	1.25706	0.628530	+	0.777785i	$0.283657\pi$
$702$	35.8862	1.35444
$703$	21.5733	0.813652
$704$	−10.2135	−0.384935
$705$	6.02584	0.226946
$706$	−18.0346	−0.678741
$707$	15.4904	0.582576
$708$	−61.8999	−2.32634
$709$	−0.673003	−0.0252751	−0.0126376	−	0.999920i	$-0.504023\pi$
$709$	−0.673003	−0.0252751	−0.0126376	+	0.999920i	$0.504023\pi$
$710$	−34.9691	−1.31237
$711$	−3.99127	−0.149684
$712$	−50.6529	−1.89830
$713$	20.9574	0.784862
$714$	7.30835	0.273508
$715$	2.61089	0.0976416
$716$	80.7401	3.01740
$717$	−22.3156	−0.833393
$718$	−17.2374	−0.643294
$719$	17.9741	0.670320	0.335160	−	0.942161i	$-0.391210\pi$
$719$	17.9741	0.670320	0.335160	+	0.942161i	$0.391210\pi$
$720$	2.25560	0.0840614
$721$	−23.9156	−0.890665
$722$	10.0541	0.374174
$723$	−32.5074	−1.20896
$724$	51.3464	1.90827
$725$	−35.4126	−1.31519
$726$	3.54525	0.131577
$727$	−7.94965	−0.294836	−0.147418	−	0.989074i	$-0.547096\pi$
$727$	−7.94965	−0.294836	−0.147418	+	0.989074i	$0.547096\pi$
$728$	23.4168	0.867883
$729$	29.7719	1.10266
$730$	23.6023	0.873560
$731$	1.00000	0.0369863
$732$	69.3773	2.56426
$733$	−2.62809	−0.0970706	−0.0485353	−	0.998821i	$-0.515455\pi$
$733$	−2.62809	−0.0970706	−0.0485353	+	0.998821i	$0.515455\pi$
$734$	58.1645	2.14689
$735$	−4.00226	−0.147626
$736$	−6.33988	−0.233691
$737$	−7.38800	−0.272140
$738$	−12.7536	−0.469465
$739$	−19.4104	−0.714024	−0.357012	−	0.934100i	$-0.616204\pi$
$739$	−19.4104	−0.714024	−0.357012	+	0.934100i	$0.616204\pi$
$740$	−20.9451	−0.769956
$741$	15.0052	0.551231
$742$	25.7147	0.944017
$743$	2.48204	0.0910574	0.0455287	−	0.998963i	$-0.485503\pi$
$743$	2.48204	0.0910574	0.0455287	+	0.998963i	$0.485503\pi$
$744$	−40.8274	−1.49681
$745$	−9.04217	−0.331279
$746$	11.3560	0.415771
$747$	−7.12507	−0.260693
$748$	3.78577	0.138421
$749$	7.76675	0.283791
$750$	31.5897	1.15349
$751$	43.4560	1.58573	0.792867	−	0.609395i	$-0.208588\pi$
$751$	43.4560	1.58573	0.792867	+	0.609395i	$0.208588\pi$
$752$	11.4314	0.416859
$753$	−20.2051	−0.736315
$754$	55.9617	2.03800
$755$	17.3463	0.631298
$756$	44.0274	1.60126
$757$	4.22737	0.153647	0.0768233	−	0.997045i	$-0.475522\pi$
$757$	4.22737	0.153647	0.0768233	+	0.997045i	$0.475522\pi$
$758$	−5.61966	−0.204115
$759$	4.78986	0.173861
$760$	16.3256	0.592192
$761$	18.1964	0.659618	0.329809	−	0.944048i	$-0.393016\pi$
$761$	18.1964	0.659618	0.329809	+	0.944048i	$0.393016\pi$
$762$	−26.3715	−0.955340
$763$	30.9827	1.12165
$764$	−7.52057	−0.272085
$765$	0.817103	0.0295424
$766$	36.9089	1.33357
$767$	−29.3373	−1.05931
$768$	43.1568	1.55729
$769$	−10.8017	−0.389520	−0.194760	−	0.980851i	$-0.562393\pi$
$769$	−10.8017	−0.389520	−0.194760	+	0.980851i	$0.562393\pi$
$770$	4.89543	0.176419
$771$	−8.98771	−0.323685
$772$	−87.2132	−3.13887
$773$	9.23912	0.332308	0.166154	−	0.986100i	$-0.446865\pi$
$773$	9.23912	0.332308	0.166154	+	0.986100i	$0.446865\pi$
$774$	1.99076	0.0715564
$775$	25.9584	0.932454
$776$	−28.3103	−1.01628
$777$	−17.0266	−0.610827
$778$	−8.43235	−0.302314
$779$	−24.6626	−0.883629
$780$	−14.5683	−0.521628
$781$	−14.7253	−0.526914
$782$	7.81695	0.279533
$783$	49.6315	1.77368
$784$	−7.59252	−0.271162
$785$	−4.68307	−0.167146
$786$	30.6325	1.09263
$787$	−17.2385	−0.614485	−0.307242	−	0.951631i	$-0.599406\pi$
$787$	−17.2385	−0.614485	−0.307242	+	0.951631i	$0.599406\pi$
$788$	61.8949	2.20492
$789$	−22.2544	−0.792279
$790$	11.4523	0.407453
$791$	−26.2019	−0.931632
$792$	3.55503	0.126323
$793$	32.8812	1.16764
$794$	20.8364	0.739456
$795$	−7.54629	−0.267639
$796$	20.5162	0.727178
$797$	2.00217	0.0709206	0.0354603	−	0.999371i	$-0.488710\pi$
$797$	2.00217	0.0709206	0.0354603	+	0.999371i	$0.488710\pi$
$798$	28.1349	0.995965
$799$	4.14107	0.146501
$800$	−7.85274	−0.277636
$801$	−9.75975	−0.344844
$802$	−26.5749	−0.938391
$803$	9.93884	0.350734
$804$	41.2237	1.45385
$805$	6.61405	0.233115
$806$	−41.0215	−1.44492
$807$	20.1391	0.708931
$808$	−32.2771	−1.13550
$809$	31.3323	1.10159	0.550793	−	0.834642i	$-0.314325\pi$
$809$	31.3323	1.10159	0.550793	+	0.834642i	$0.314325\pi$
$810$	−13.8498	−0.486634
$811$	8.42017	0.295672	0.147836	−	0.989012i	$-0.452769\pi$
$811$	8.42017	0.295672	0.147836	+	0.989012i	$0.452769\pi$
$812$	68.6573	2.40940
$813$	25.6534	0.899704
$814$	−13.4794	−0.472452
$815$	17.0729	0.598038
$816$	−4.06867	−0.142432
$817$	3.84969	0.134684
$818$	−73.1826	−2.55877
$819$	4.51192	0.157659
$820$	23.9444	0.836176
$821$	5.50003	0.191952	0.0959761	−	0.995384i	$-0.469403\pi$
$821$	5.50003	0.191952	0.0959761	+	0.995384i	$0.469403\pi$
$822$	−54.5464	−1.90253
$823$	31.6995	1.10498	0.552488	−	0.833521i	$-0.313678\pi$
$823$	31.6995	1.10498	0.552488	+	0.833521i	$0.313678\pi$
$824$	49.8327	1.73600
$825$	5.93285	0.206555
$826$	−55.0076	−1.91396
$827$	29.8951	1.03955	0.519777	−	0.854302i	$-0.326015\pi$
$827$	29.8951	1.03955	0.519777	+	0.854302i	$0.326015\pi$
$828$	10.1824	0.353862
$829$	15.0707	0.523427	0.261714	−	0.965146i	$-0.415712\pi$
$829$	15.0707	0.523427	0.261714	+	0.965146i	$0.415712\pi$
$830$	20.4441	0.709626
$831$	−4.50828	−0.156391
$832$	27.0099	0.936401
$833$	−2.75043	−0.0952967
$834$	51.3099	1.77672
$835$	8.84247	0.306006
$836$	14.5740	0.504054
$837$	−36.3813	−1.25752
$838$	61.2387	2.11546
$839$	21.8486	0.754296	0.377148	−	0.926153i	$-0.376905\pi$
$839$	21.8486	0.754296	0.377148	+	0.926153i	$0.376905\pi$
$840$	−12.8849	−0.444572
$841$	48.3964	1.66884
$842$	−8.51029	−0.293284
$843$	45.8706	1.57987
$844$	23.8467	0.820838
$845$	5.92999	0.203998
$846$	8.24388	0.283431
$847$	2.06145	0.0708322
$848$	−14.3158	−0.491605
$849$	34.4463	1.18219
$850$	9.68227	0.332099
$851$	−18.2115	−0.624283
$852$	82.1647	2.81492
$853$	−17.4996	−0.599174	−0.299587	−	0.954069i	$-0.596849\pi$
$853$	−17.4996	−0.599174	−0.299587	+	0.954069i	$0.596849\pi$
$854$	61.6524	2.10970
$855$	3.14560	0.107577
$856$	−16.1835	−0.553140
$857$	−12.5450	−0.428528	−0.214264	−	0.976776i	$-0.568735\pi$
$857$	−12.5450	−0.428528	−0.214264	+	0.976776i	$0.568735\pi$
$858$	−9.37555	−0.320076
$859$	−27.7860	−0.948045	−0.474023	−	0.880513i	$-0.657199\pi$
$859$	−27.7860	−0.948045	−0.474023	+	0.880513i	$0.657199\pi$
$860$	−3.73759	−0.127451
$861$	19.4649	0.663361
$862$	−82.7442	−2.81828
$863$	57.2248	1.94796	0.973978	−	0.226643i	$-0.0727752\pi$
$863$	57.2248	1.94796	0.973978	+	0.226643i	$0.0727752\pi$
$864$	11.0058	0.374425
$865$	0.345496	0.0117472
$866$	−65.3497	−2.22067
$867$	−1.47389	−0.0500561
$868$	−50.3277	−1.70823
$869$	4.82250	0.163592
$870$	−30.7925	−1.04396
$871$	19.5378	0.662014
$872$	−64.5583	−2.18622
$873$	−5.45480	−0.184617
$874$	30.0929	1.01791
$875$	18.3684	0.620966
$876$	−55.4569	−1.87372
$877$	−33.2111	−1.12146	−0.560729	−	0.828000i	$-0.689479\pi$
$877$	−33.2111	−1.12146	−0.560729	+	0.828000i	$0.689479\pi$
$878$	−30.2507	−1.02091
$879$	14.9392	0.503887
$880$	−2.72536	−0.0918719
$881$	21.6329	0.728830	0.364415	−	0.931237i	$-0.381269\pi$
$881$	21.6329	0.728830	0.364415	+	0.931237i	$0.381269\pi$
$882$	−5.47545	−0.184368
$883$	28.7331	0.966945	0.483472	−	0.875360i	$-0.339375\pi$
$883$	28.7331	0.966945	0.483472	+	0.875360i	$0.339375\pi$
$884$	−10.0116	−0.336727
$885$	16.1426	0.542629
$886$	92.7280	3.11526
$887$	−24.3445	−0.817408	−0.408704	−	0.912667i	$-0.634019\pi$
$887$	−24.3445	−0.817408	−0.408704	+	0.912667i	$0.634019\pi$
$888$	35.4782	1.19057
$889$	−15.3342	−0.514292
$890$	28.0039	0.938693
$891$	−5.83212	−0.195383
$892$	−4.99531	−0.167256
$893$	15.9419	0.533474
$894$	32.4699	1.08596
$895$	−21.0559	−0.703821
$896$	42.6007	1.42319
$897$	−12.6670	−0.422938
$898$	22.6911	0.757211
$899$	−56.7338	−1.89218
$900$	12.6122	0.420405
$901$	−5.18596	−0.172769
$902$	15.4097	0.513085
$903$	−3.03836	−0.101110
$904$	54.5965	1.81585
$905$	−13.3904	−0.445113
$906$	−62.2897	−2.06944
$907$	45.0911	1.49722	0.748612	−	0.663008i	$-0.230721\pi$
$907$	45.0911	1.49722	0.748612	+	0.663008i	$0.230721\pi$
$908$	−110.890	−3.68001
$909$	−6.21911	−0.206275
$910$	−12.9462	−0.429161
$911$	29.6073	0.980933	0.490467	−	0.871460i	$-0.336826\pi$
$911$	29.6073	0.980933	0.490467	+	0.871460i	$0.336826\pi$
$912$	−15.6631	−0.518658
$913$	8.60895	0.284915
$914$	46.4923	1.53783
$915$	−18.0926	−0.598124
$916$	−28.9426	−0.956291
$917$	17.8118	0.588198
$918$	−13.5699	−0.447874
$919$	59.7985	1.97257	0.986285	−	0.165054i	$-0.0527799\pi$
$919$	59.7985	1.97257	0.986285	+	0.165054i	$0.0527799\pi$
$920$	−13.7816	−0.454366
$921$	33.1251	1.09151
$922$	40.9698	1.34927
$923$	38.9417	1.28178
$924$	−11.5025	−0.378405
$925$	−22.5573	−0.741679
$926$	−2.54116	−0.0835077
$927$	9.60170	0.315361
$928$	17.1627	0.563392
$929$	19.0077	0.623623	0.311812	−	0.950144i	$-0.399064\pi$
$929$	19.0077	0.623623	0.311812	+	0.950144i	$0.399064\pi$
$930$	22.5718	0.740158
$931$	−10.5883	−0.347018
$932$	48.2650	1.58097
$933$	−15.1982	−0.497567
$934$	−39.7582	−1.30093
$935$	−0.987275	−0.0322874
$936$	−9.40142	−0.307295
$937$	41.3137	1.34966	0.674830	−	0.737973i	$-0.264217\pi$
$937$	41.3137	1.34966	0.674830	+	0.737973i	$0.264217\pi$
$938$	36.6336	1.19613
$939$	37.6967	1.23019
$940$	−15.4776	−0.504825
$941$	−20.5984	−0.671489	−0.335745	−	0.941953i	$-0.608988\pi$
$941$	−20.5984	−0.671489	−0.335745	+	0.941953i	$0.608988\pi$
$942$	16.8166	0.547916
$943$	20.8194	0.677975
$944$	30.6235	0.996712
$945$	−11.4817	−0.373501
$946$	−2.40536	−0.0782051
$947$	−42.5498	−1.38268	−0.691341	−	0.722529i	$-0.742980\pi$
$947$	−42.5498	−1.38268	−0.691341	+	0.722529i	$0.742980\pi$
$948$	−26.9087	−0.873953
$949$	−26.2836	−0.853203
$950$	37.2738	1.20932
$951$	−29.0027	−0.940477
$952$	−8.85477	−0.286985
$953$	9.20992	0.298338	0.149169	−	0.988812i	$-0.452340\pi$
$953$	9.20992	0.298338	0.149169	+	0.988812i	$0.452340\pi$
$954$	−10.3240	−0.334252
$955$	1.96126	0.0634649
$956$	57.3187	1.85382
$957$	−12.9666	−0.419151
$958$	−31.4522	−1.01617
$959$	−31.7170	−1.02420
$960$	−14.8620	−0.479670
$961$	10.5874	0.341531
$962$	35.6468	1.14930
$963$	−3.11821	−0.100483
$964$	83.4967	2.68925
$965$	22.7440	0.732155
$966$	−23.7507	−0.764166
$967$	3.71476	0.119459	0.0597293	−	0.998215i	$-0.480976\pi$
$967$	3.71476	0.119459	0.0597293	+	0.998215i	$0.480976\pi$
$968$	−4.29541	−0.138060
$969$	−5.67404	−0.182277
$970$	15.6516	0.502542
$971$	34.6745	1.11276	0.556379	−	0.830928i	$-0.312190\pi$
$971$	34.6745	1.11276	0.556379	+	0.830928i	$0.312190\pi$
$972$	−31.5304	−1.01134
$973$	29.8350	0.956467
$974$	−61.9857	−1.98615
$975$	−15.6896	−0.502471
$976$	−34.3228	−1.09865
$977$	11.2460	0.359792	0.179896	−	0.983686i	$-0.442424\pi$
$977$	11.2460	0.359792	0.179896	+	0.983686i	$0.442424\pi$
$978$	−61.3078	−1.96041
$979$	11.7923	0.376885
$980$	10.2800	0.328382
$981$	−12.4390	−0.397147
$982$	89.1150	2.84377
$983$	−31.6420	−1.00922	−0.504611	−	0.863347i	$-0.668364\pi$
$983$	−31.6420	−1.00922	−0.504611	+	0.863347i	$0.668364\pi$
$984$	−40.5587	−1.29296
$985$	−16.1413	−0.514306
$986$	−21.1612	−0.673911
$987$	−12.5821	−0.400491
$988$	−38.5416	−1.22617
$989$	−3.24980	−0.103338
$990$	−1.96543	−0.0624654
$991$	−16.0853	−0.510967	−0.255483	−	0.966813i	$-0.582235\pi$
$991$	−16.0853	−0.510967	−0.255483	+	0.966813i	$0.582235\pi$
$992$	−12.5807	−0.399438
$993$	41.6752	1.32252
$994$	73.0160	2.31593
$995$	−5.35034	−0.169617
$996$	−48.0364	−1.52209
$997$	48.8873	1.54827	0.774137	−	0.633018i	$-0.218184\pi$
$997$	48.8873	1.54827	0.774137	+	0.633018i	$0.218184\pi$
$998$	17.0730	0.540436
$999$	31.6145	1.00024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.7	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.7	✓	82	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)

\(f(q)\)	\(=\)	\(q-2.40536 q^{2} -1.47389 q^{3} +3.78577 q^{4} -0.987275 q^{5} +3.54525 q^{6} +2.06145 q^{7} -4.29541 q^{8} -0.827635 q^{9} +O(q^{10})\)	\(q-2.40536 q^{2} -1.47389 q^{3} +3.78577 q^{4} -0.987275 q^{5} +3.54525 q^{6} +2.06145 q^{7} -4.29541 q^{8} -0.827635 q^{9} +2.37475 q^{10} +1.00000 q^{11} -5.57982 q^{12} -2.64454 q^{13} -4.95853 q^{14} +1.45514 q^{15} +2.76049 q^{16} +1.00000 q^{17} +1.99076 q^{18} +3.84969 q^{19} -3.73759 q^{20} -3.03836 q^{21} -2.40536 q^{22} -3.24980 q^{23} +6.33098 q^{24} -4.02529 q^{25} +6.36107 q^{26} +5.64153 q^{27} +7.80416 q^{28} +8.79752 q^{29} -3.50014 q^{30} -6.44883 q^{31} +1.95085 q^{32} -1.47389 q^{33} -2.40536 q^{34} -2.03522 q^{35} -3.13323 q^{36} +5.60389 q^{37} -9.25991 q^{38} +3.89777 q^{39} +4.24075 q^{40} -6.40638 q^{41} +7.30835 q^{42} +1.00000 q^{43} +3.78577 q^{44} +0.817103 q^{45} +7.81695 q^{46} +4.14107 q^{47} -4.06867 q^{48} -2.75043 q^{49} +9.68227 q^{50} -1.47389 q^{51} -10.0116 q^{52} -5.18596 q^{53} -13.5699 q^{54} -0.987275 q^{55} -8.85477 q^{56} -5.67404 q^{57} -21.1612 q^{58} +11.0935 q^{59} +5.50882 q^{60} -12.4336 q^{61} +15.5118 q^{62} -1.70613 q^{63} -10.2135 q^{64} +2.61089 q^{65} +3.54525 q^{66} -7.38800 q^{67} +3.78577 q^{68} +4.78986 q^{69} +4.89543 q^{70} -14.7253 q^{71} +3.55503 q^{72} +9.93884 q^{73} -13.4794 q^{74} +5.93285 q^{75} +14.5740 q^{76} +2.06145 q^{77} -9.37555 q^{78} +4.82250 q^{79} -2.72536 q^{80} -5.83212 q^{81} +15.4097 q^{82} +8.60895 q^{83} -11.5025 q^{84} -0.987275 q^{85} -2.40536 q^{86} -12.9666 q^{87} -4.29541 q^{88} +11.7923 q^{89} -1.96543 q^{90} -5.45158 q^{91} -12.3030 q^{92} +9.50490 q^{93} -9.96077 q^{94} -3.80071 q^{95} -2.87535 q^{96} +6.59082 q^{97} +6.61578 q^{98} -0.827635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

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