LMFDB - Embedded newform 8041.2.a.e.1.20

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			1.20
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)

$f(q)$	$=$	$q-1.19284 q^{2} -3.20142 q^{3} -0.577127 q^{4} -3.80611 q^{5} +3.81880 q^{6} +4.55130 q^{7} +3.07411 q^{8} +7.24912 q^{9} +O(q^{10})$	\(q-1.19284 q^{2} -3.20142 q^{3} -0.577127 q^{4} -3.80611 q^{5} +3.81880 q^{6} +4.55130 q^{7} +3.07411 q^{8} +7.24912 q^{9} +4.54009 q^{10} -1.00000 q^{11} +1.84763 q^{12} -4.62859 q^{13} -5.42899 q^{14} +12.1850 q^{15} -2.51267 q^{16} -1.00000 q^{17} -8.64706 q^{18} -1.71039 q^{19} +2.19661 q^{20} -14.5707 q^{21} +1.19284 q^{22} +1.64462 q^{23} -9.84152 q^{24} +9.48648 q^{25} +5.52118 q^{26} -13.6032 q^{27} -2.62668 q^{28} +5.55266 q^{29} -14.5348 q^{30} +9.50452 q^{31} -3.15099 q^{32} +3.20142 q^{33} +1.19284 q^{34} -17.3228 q^{35} -4.18366 q^{36} +0.412317 q^{37} +2.04022 q^{38} +14.8181 q^{39} -11.7004 q^{40} +8.24530 q^{41} +17.3805 q^{42} +1.00000 q^{43} +0.577127 q^{44} -27.5910 q^{45} -1.96177 q^{46} +9.01862 q^{47} +8.04413 q^{48} +13.7144 q^{49} -11.3159 q^{50} +3.20142 q^{51} +2.67128 q^{52} +4.88189 q^{53} +16.2265 q^{54} +3.80611 q^{55} +13.9912 q^{56} +5.47567 q^{57} -6.62345 q^{58} +3.05297 q^{59} -7.03228 q^{60} +4.61620 q^{61} -11.3374 q^{62} +32.9929 q^{63} +8.78398 q^{64} +17.6169 q^{65} -3.81880 q^{66} +8.61645 q^{67} +0.577127 q^{68} -5.26513 q^{69} +20.6633 q^{70} +0.0173717 q^{71} +22.2846 q^{72} -8.17786 q^{73} -0.491829 q^{74} -30.3703 q^{75} +0.987109 q^{76} -4.55130 q^{77} -17.6756 q^{78} -0.663460 q^{79} +9.56351 q^{80} +21.8024 q^{81} -9.83535 q^{82} +12.3577 q^{83} +8.40911 q^{84} +3.80611 q^{85} -1.19284 q^{86} -17.7764 q^{87} -3.07411 q^{88} +14.1739 q^{89} +32.9117 q^{90} -21.0661 q^{91} -0.949154 q^{92} -30.4280 q^{93} -10.7578 q^{94} +6.50992 q^{95} +10.0877 q^{96} -11.6291 q^{97} -16.3591 q^{98} -7.24912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.19284	−0.843467	−0.421734	−	0.906720i	$-0.638578\pi$
$2$	−1.19284	−0.843467	−0.421734	+	0.906720i	$0.638578\pi$
$3$	−3.20142	−1.84834	−0.924172	−	0.381977i	$-0.875243\pi$
$3$	−3.20142	−1.84834	−0.924172	+	0.381977i	$0.875243\pi$
$4$	−0.577127	−0.288563
$5$	−3.80611	−1.70214	−0.851072	−	0.525048i	$-0.824047\pi$
$5$	−3.80611	−1.70214	−0.851072	+	0.525048i	$0.824047\pi$
$6$	3.81880	1.55902
$7$	4.55130	1.72023	0.860115	−	0.510099i	$-0.170391\pi$
$7$	4.55130	1.72023	0.860115	+	0.510099i	$0.170391\pi$
$8$	3.07411	1.08686
$9$	7.24912	2.41637
$10$	4.54009	1.43570
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.84763	0.533364
$13$	−4.62859	−1.28374	−0.641870	−	0.766813i	$-0.721841\pi$
$13$	−4.62859	−1.28374	−0.641870	+	0.766813i	$0.721841\pi$
$14$	−5.42899	−1.45096
$15$	12.1850	3.14615
$16$	−2.51267	−0.628168
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−8.64706	−2.03813
$19$	−1.71039	−0.392389	−0.196195	−	0.980565i	$-0.562858\pi$
$19$	−1.71039	−0.392389	−0.196195	+	0.980565i	$0.562858\pi$
$20$	2.19661	0.491177
$21$	−14.5707	−3.17958
$22$	1.19284	0.254315
$23$	1.64462	0.342927	0.171463	−	0.985190i	$-0.445150\pi$
$23$	1.64462	0.342927	0.171463	+	0.985190i	$0.445150\pi$
$24$	−9.84152	−2.00889
$25$	9.48648	1.89730
$26$	5.52118	1.08279
$27$	−13.6032	−2.61795
$28$	−2.62668	−0.496396
$29$	5.55266	1.03110	0.515551	−	0.856859i	$-0.327587\pi$
$29$	5.55266	1.03110	0.515551	+	0.856859i	$0.327587\pi$
$30$	−14.5348	−2.65367
$31$	9.50452	1.70706	0.853531	−	0.521042i	$-0.174456\pi$
$31$	9.50452	1.70706	0.853531	+	0.521042i	$0.174456\pi$
$32$	−3.15099	−0.557022
$33$	3.20142	0.557297
$34$	1.19284	0.204571
$35$	−17.3228	−2.92808
$36$	−4.18366	−0.697277
$37$	0.412317	0.0677845	0.0338922	−	0.999425i	$-0.489210\pi$
$37$	0.412317	0.0677845	0.0338922	+	0.999425i	$0.489210\pi$
$38$	2.04022	0.330967
$39$	14.8181	2.37279
$40$	−11.7004	−1.84999
$41$	8.24530	1.28770	0.643850	−	0.765152i	$-0.277336\pi$
$41$	8.24530	1.28770	0.643850	+	0.765152i	$0.277336\pi$
$42$	17.3805	2.68187
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.577127	0.0870051
$45$	−27.5910	−4.11302
$46$	−1.96177	−0.289247
$47$	9.01862	1.31550	0.657750	−	0.753236i	$-0.271508\pi$
$47$	9.01862	1.31550	0.657750	+	0.753236i	$0.271508\pi$
$48$	8.04413	1.16107
$49$	13.7144	1.95919
$50$	−11.3159	−1.60031
$51$	3.20142	0.448289
$52$	2.67128	0.370441
$53$	4.88189	0.670579	0.335290	−	0.942115i	$-0.391166\pi$
$53$	4.88189	0.670579	0.335290	+	0.942115i	$0.391166\pi$
$54$	16.2265	2.20815
$55$	3.80611	0.513216
$56$	13.9912	1.86965
$57$	5.47567	0.725270
$58$	−6.62345	−0.869701
$59$	3.05297	0.397463	0.198731	−	0.980054i	$-0.436318\pi$
$59$	3.05297	0.397463	0.198731	+	0.980054i	$0.436318\pi$
$60$	−7.03228	−0.907863
$61$	4.61620	0.591044	0.295522	−	0.955336i	$-0.404506\pi$
$61$	4.61620	0.591044	0.295522	+	0.955336i	$0.404506\pi$
$62$	−11.3374	−1.43985
$63$	32.9929	4.15672
$64$	8.78398	1.09800
$65$	17.6169	2.18511
$66$	−3.81880	−0.470061
$67$	8.61645	1.05267	0.526334	−	0.850278i	$-0.323566\pi$
$67$	8.61645	1.05267	0.526334	+	0.850278i	$0.323566\pi$
$68$	0.577127	0.0699869
$69$	−5.26513	−0.633847
$70$	20.6633	2.46974
$71$	0.0173717	0.00206165	0.00103082	−	0.999999i	$-0.499672\pi$
$71$	0.0173717	0.00206165	0.00103082	+	0.999999i	$0.499672\pi$
$72$	22.2846	2.62626
$73$	−8.17786	−0.957146	−0.478573	−	0.878048i	$-0.658846\pi$
$73$	−8.17786	−0.957146	−0.478573	+	0.878048i	$0.658846\pi$
$74$	−0.491829	−0.0571740
$75$	−30.3703	−3.50686
$76$	0.987109	0.113229
$77$	−4.55130	−0.518669
$78$	−17.6756	−2.00137
$79$	−0.663460	−0.0746451	−0.0373225	−	0.999303i	$-0.511883\pi$
$79$	−0.663460	−0.0746451	−0.0373225	+	0.999303i	$0.511883\pi$
$80$	9.56351	1.06923
$81$	21.8024	2.42249
$82$	−9.83535	−1.08613
$83$	12.3577	1.35643	0.678215	−	0.734863i	$-0.262754\pi$
$83$	12.3577	1.35643	0.678215	+	0.734863i	$0.262754\pi$
$84$	8.40911	0.917510
$85$	3.80611	0.412831
$86$	−1.19284	−0.128628
$87$	−17.7764	−1.90583
$88$	−3.07411	−0.327701
$89$	14.1739	1.50243	0.751213	−	0.660060i	$-0.229469\pi$
$89$	14.1739	1.50243	0.751213	+	0.660060i	$0.229469\pi$
$90$	32.9117	3.46919
$91$	−21.0661	−2.20833
$92$	−0.949154	−0.0989561
$93$	−30.4280	−3.15524
$94$	−10.7578	−1.10958
$95$	6.50992	0.667903
$96$	10.0877	1.02957
$97$	−11.6291	−1.18076	−0.590380	−	0.807126i	$-0.701022\pi$
$97$	−11.6291	−1.18076	−0.590380	+	0.807126i	$0.701022\pi$
$98$	−16.3591	−1.65252
$99$	−7.24912	−0.728564
$100$	−5.47490	−0.547490
$101$	5.55952	0.553193	0.276596	−	0.960986i	$-0.410793\pi$
$101$	5.55952	0.553193	0.276596	+	0.960986i	$0.410793\pi$
$102$	−3.81880	−0.378117
$103$	−16.8522	−1.66050	−0.830249	−	0.557393i	$-0.811802\pi$
$103$	−16.8522	−1.66050	−0.830249	+	0.557393i	$0.811802\pi$
$104$	−14.2288	−1.39525
$105$	55.4575	5.41210
$106$	−5.82332	−0.565611
$107$	14.6684	1.41805	0.709023	−	0.705185i	$-0.249136\pi$
$107$	14.6684	1.41805	0.709023	+	0.705185i	$0.249136\pi$
$108$	7.85080	0.755443
$109$	−5.04012	−0.482756	−0.241378	−	0.970431i	$-0.577599\pi$
$109$	−5.04012	−0.482756	−0.241378	+	0.970431i	$0.577599\pi$
$110$	−4.54009	−0.432881
$111$	−1.32000	−0.125289
$112$	−11.4359	−1.08059
$113$	2.23624	0.210368	0.105184	−	0.994453i	$-0.466457\pi$
$113$	2.23624	0.210368	0.105184	+	0.994453i	$0.466457\pi$
$114$	−6.53161	−0.611741
$115$	−6.25960	−0.583711
$116$	−3.20459	−0.297539
$117$	−33.5532	−3.10200
$118$	−3.64171	−0.335247
$119$	−4.55130	−0.417217
$120$	37.4579	3.41942
$121$	1.00000	0.0909091
$122$	−5.50640	−0.498526
$123$	−26.3967	−2.38011
$124$	−5.48531	−0.492596
$125$	−17.0761	−1.52733
$126$	−39.3554	−3.50606
$127$	−10.7767	−0.956276	−0.478138	−	0.878285i	$-0.658688\pi$
$127$	−10.7767	−0.956276	−0.478138	+	0.878285i	$0.658688\pi$
$128$	−4.17592	−0.369103
$129$	−3.20142	−0.281870
$130$	−21.0142	−1.84307
$131$	3.93396	0.343711	0.171856	−	0.985122i	$-0.445024\pi$
$131$	3.93396	0.343711	0.171856	+	0.985122i	$0.445024\pi$
$132$	−1.84763	−0.160815
$133$	−7.78448	−0.675000
$134$	−10.2781	−0.887890
$135$	51.7755	4.45612
$136$	−3.07411	−0.263602
$137$	19.0701	1.62927	0.814633	−	0.579977i	$-0.196939\pi$
$137$	19.0701	1.62927	0.814633	+	0.579977i	$0.196939\pi$
$138$	6.28047	0.534629
$139$	−12.5585	−1.06520	−0.532600	−	0.846367i	$-0.678785\pi$
$139$	−12.5585	−1.06520	−0.532600	+	0.846367i	$0.678785\pi$
$140$	9.99743	0.844937
$141$	−28.8724	−2.43150
$142$	−0.0207217	−0.00173893
$143$	4.62859	0.387062
$144$	−18.2147	−1.51789
$145$	−21.1340	−1.75509
$146$	9.75490	0.807321
$147$	−43.9055	−3.62126
$148$	−0.237959	−0.0195601
$149$	2.01402	0.164995	0.0824973	−	0.996591i	$-0.473710\pi$
$149$	2.01402	0.164995	0.0824973	+	0.996591i	$0.473710\pi$
$150$	36.2269	2.95792
$151$	11.4926	0.935252	0.467626	−	0.883926i	$-0.345109\pi$
$151$	11.4926	0.935252	0.467626	+	0.883926i	$0.345109\pi$
$152$	−5.25791	−0.426472
$153$	−7.24912	−0.586057
$154$	5.42899	0.437480
$155$	−36.1753	−2.90567
$156$	−8.55192	−0.684701
$157$	8.70914	0.695065	0.347532	−	0.937668i	$-0.387020\pi$
$157$	8.70914	0.695065	0.347532	+	0.937668i	$0.387020\pi$
$158$	0.791403	0.0629606
$159$	−15.6290	−1.23946
$160$	11.9930	0.948132
$161$	7.48516	0.589913
$162$	−26.0068	−2.04329
$163$	−0.850870	−0.0666453	−0.0333226	−	0.999445i	$-0.510609\pi$
$163$	−0.850870	−0.0666453	−0.0333226	+	0.999445i	$0.510609\pi$
$164$	−4.75859	−0.371583
$165$	−12.1850	−0.948599
$166$	−14.7408	−1.14410
$167$	−2.25749	−0.174690	−0.0873451	−	0.996178i	$-0.527838\pi$
$167$	−2.25749	−0.174690	−0.0873451	+	0.996178i	$0.527838\pi$
$168$	−44.7917	−3.45576
$169$	8.42387	0.647990
$170$	−4.54009	−0.348209
$171$	−12.3988	−0.948159
$172$	−0.577127	−0.0440055
$173$	16.9657	1.28988	0.644941	−	0.764232i	$-0.276882\pi$
$173$	16.9657	1.28988	0.644941	+	0.764232i	$0.276882\pi$
$174$	21.2045	1.60751
$175$	43.1759	3.26379
$176$	2.51267	0.189400
$177$	−9.77385	−0.734647
$178$	−16.9072	−1.26725
$179$	9.29687	0.694881	0.347440	−	0.937702i	$-0.387051\pi$
$179$	9.29687	0.694881	0.347440	+	0.937702i	$0.387051\pi$
$180$	15.9235	1.18687
$181$	−2.15359	−0.160075	−0.0800374	−	0.996792i	$-0.525504\pi$
$181$	−2.15359	−0.160075	−0.0800374	+	0.996792i	$0.525504\pi$
$182$	25.1286	1.86265
$183$	−14.7784	−1.09245
$184$	5.05573	0.372714
$185$	−1.56932	−0.115379
$186$	36.2958	2.66134
$187$	1.00000	0.0731272
$188$	−5.20488	−0.379605
$189$	−61.9125	−4.50347
$190$	−7.76530	−0.563354
$191$	−27.1664	−1.96569	−0.982846	−	0.184426i	$-0.940957\pi$
$191$	−27.1664	−1.96569	−0.982846	+	0.184426i	$0.940957\pi$
$192$	−28.1212	−2.02948
$193$	−8.41742	−0.605899	−0.302950	−	0.953007i	$-0.597971\pi$
$193$	−8.41742	−0.605899	−0.302950	+	0.953007i	$0.597971\pi$
$194$	13.8717	0.995932
$195$	−56.3993	−4.03884
$196$	−7.91492	−0.565352
$197$	19.7687	1.40846	0.704231	−	0.709971i	$-0.251292\pi$
$197$	19.7687	1.40846	0.704231	+	0.709971i	$0.251292\pi$
$198$	8.64706	0.614520
$199$	4.37509	0.310142	0.155071	−	0.987903i	$-0.450439\pi$
$199$	4.37509	0.310142	0.155071	+	0.987903i	$0.450439\pi$
$200$	29.1625	2.06210
$201$	−27.5849	−1.94569
$202$	−6.63163	−0.466600
$203$	25.2718	1.77374
$204$	−1.84763	−0.129360
$205$	−31.3825	−2.19185
$206$	20.1020	1.40057
$207$	11.9220	0.828639
$208$	11.6301	0.806404
$209$	1.71039	0.118310
$210$	−66.1521	−4.56493
$211$	26.4808	1.82302	0.911508	−	0.411282i	$-0.134919\pi$
$211$	26.4808	1.82302	0.911508	+	0.411282i	$0.134919\pi$
$212$	−2.81747	−0.193505
$213$	−0.0556143	−0.00381063
$214$	−17.4971	−1.19608
$215$	−3.80611	−0.259575
$216$	−41.8178	−2.84534
$217$	43.2580	2.93654
$218$	6.01207	0.407188
$219$	26.1808	1.76913
$220$	−2.19661	−0.148095
$221$	4.62859	0.311353
$222$	1.57455	0.105677
$223$	−20.9276	−1.40142	−0.700709	−	0.713447i	$-0.747133\pi$
$223$	−20.9276	−1.40142	−0.700709	+	0.713447i	$0.747133\pi$
$224$	−14.3411	−0.958206
$225$	68.7687	4.58458
$226$	−2.66748	−0.177438
$227$	−13.9075	−0.923075	−0.461537	−	0.887121i	$-0.652702\pi$
$227$	−13.9075	−0.923075	−0.461537	+	0.887121i	$0.652702\pi$
$228$	−3.16016	−0.209286
$229$	−6.65808	−0.439978	−0.219989	−	0.975502i	$-0.570602\pi$
$229$	−6.65808	−0.439978	−0.219989	+	0.975502i	$0.570602\pi$
$230$	7.46672	0.492341
$231$	14.5707	0.958679
$232$	17.0695	1.12067
$233$	−2.75522	−0.180500	−0.0902502	−	0.995919i	$-0.528767\pi$
$233$	−2.75522	−0.180500	−0.0902502	+	0.995919i	$0.528767\pi$
$234$	40.0237	2.61643
$235$	−34.3259	−2.23917
$236$	−1.76195	−0.114693
$237$	2.12402	0.137970
$238$	5.42899	0.351909
$239$	12.6616	0.819009	0.409505	−	0.912308i	$-0.365702\pi$
$239$	12.6616	0.819009	0.409505	+	0.912308i	$0.365702\pi$
$240$	−30.6168	−1.97631
$241$	6.14672	0.395945	0.197972	−	0.980208i	$-0.436564\pi$
$241$	6.14672	0.395945	0.197972	+	0.980208i	$0.436564\pi$
$242$	−1.19284	−0.0766788
$243$	−28.9890	−1.85965
$244$	−2.66413	−0.170554
$245$	−52.1984	−3.33483
$246$	31.4871	2.00755
$247$	7.91668	0.503726
$248$	29.2179	1.85534
$249$	−39.5622	−2.50715
$250$	20.3690	1.28825
$251$	−27.1128	−1.71135	−0.855673	−	0.517517i	$-0.826857\pi$
$251$	−27.1128	−1.71135	−0.855673	+	0.517517i	$0.826857\pi$
$252$	−19.0411	−1.19948
$253$	−1.64462	−0.103396
$254$	12.8549	0.806587
$255$	−12.1850	−0.763053
$256$	−12.5867	−0.786671
$257$	10.8139	0.674551	0.337275	−	0.941406i	$-0.390495\pi$
$257$	10.8139	0.674551	0.337275	+	0.941406i	$0.390495\pi$
$258$	3.81880	0.237748
$259$	1.87658	0.116605
$260$	−10.1672	−0.630543
$261$	40.2519	2.49153
$262$	−4.69259	−0.289909
$263$	−23.9857	−1.47902	−0.739511	−	0.673144i	$-0.764943\pi$
$263$	−23.9857	−1.47902	−0.739511	+	0.673144i	$0.764943\pi$
$264$	9.84152	0.605704
$265$	−18.5810	−1.14142
$266$	9.28566	0.569340
$267$	−45.3765	−2.77700
$268$	−4.97278	−0.303761
$269$	−23.8519	−1.45428	−0.727139	−	0.686490i	$-0.759151\pi$
$269$	−23.8519	−1.45428	−0.727139	+	0.686490i	$0.759151\pi$
$270$	−61.7600	−3.75859
$271$	7.22201	0.438706	0.219353	−	0.975646i	$-0.429605\pi$
$271$	7.22201	0.438706	0.219353	+	0.975646i	$0.429605\pi$
$272$	2.51267	0.152353
$273$	67.4416	4.08175
$274$	−22.7476	−1.37423
$275$	−9.48648	−0.572056
$276$	3.03864	0.182905
$277$	21.8948	1.31553	0.657764	−	0.753224i	$-0.271502\pi$
$277$	21.8948	1.31553	0.657764	+	0.753224i	$0.271502\pi$
$278$	14.9803	0.898461
$279$	68.8994	4.12490
$280$	−53.2520	−3.18242
$281$	−30.2742	−1.80600	−0.903002	−	0.429635i	$-0.858642\pi$
$281$	−30.2742	−1.80600	−0.903002	+	0.429635i	$0.858642\pi$
$282$	34.4403	2.05089
$283$	−21.4787	−1.27678	−0.638389	−	0.769714i	$-0.720399\pi$
$283$	−21.4787	−1.27678	−0.638389	+	0.769714i	$0.720399\pi$
$284$	−0.0100257	−0.000594915 0
$285$	−20.8410	−1.23451
$286$	−5.52118	−0.326474
$287$	37.5269	2.21514
$288$	−22.8419	−1.34597
$289$	1.00000	0.0588235
$290$	25.2096	1.48036
$291$	37.2298	2.18245
$292$	4.71966	0.276197
$293$	4.97679	0.290747	0.145374	−	0.989377i	$-0.453562\pi$
$293$	4.97679	0.290747	0.145374	+	0.989377i	$0.453562\pi$
$294$	52.3723	3.05442
$295$	−11.6199	−0.676539
$296$	1.26751	0.0736723
$297$	13.6032	0.789340
$298$	−2.40240	−0.139167
$299$	−7.61227	−0.440229
$300$	17.5275	1.01195
$301$	4.55130	0.262333
$302$	−13.7088	−0.788854
$303$	−17.7984	−1.02249
$304$	4.29764	0.246486
$305$	−17.5698	−1.00604
$306$	8.64706	0.494320
$307$	−25.6694	−1.46503	−0.732516	−	0.680750i	$-0.761654\pi$
$307$	−25.6694	−1.46503	−0.732516	+	0.680750i	$0.761654\pi$
$308$	2.62668	0.149669
$309$	53.9511	3.06917
$310$	43.1514	2.45083
$311$	29.4030	1.66729	0.833645	−	0.552301i	$-0.186250\pi$
$311$	29.4030	1.66729	0.833645	+	0.552301i	$0.186250\pi$
$312$	45.5524	2.57890
$313$	−14.8056	−0.836861	−0.418431	−	0.908249i	$-0.637420\pi$
$313$	−14.8056	−0.836861	−0.418431	+	0.908249i	$0.637420\pi$
$314$	−10.3886	−0.586264
$315$	−125.575	−7.07534
$316$	0.382900	0.0215398
$317$	0.293010	0.0164571	0.00822855	−	0.999966i	$-0.497381\pi$
$317$	0.293010	0.0164571	0.00822855	+	0.999966i	$0.497381\pi$
$318$	18.6429	1.04544
$319$	−5.55266	−0.310889
$320$	−33.4328	−1.86895
$321$	−46.9597	−2.62104
$322$	−8.92862	−0.497572
$323$	1.71039	0.0951684
$324$	−12.5827	−0.699041
$325$	−43.9091	−2.43564
$326$	1.01495	0.0562131
$327$	16.1356	0.892298
$328$	25.3469	1.39955
$329$	41.0465	2.26296
$330$	14.5348	0.800112
$331$	−3.38624	−0.186124	−0.0930622	−	0.995660i	$-0.529666\pi$
$331$	−3.38624	−0.186124	−0.0930622	+	0.995660i	$0.529666\pi$
$332$	−7.13194	−0.391416
$333$	2.98894	0.163793
$334$	2.69284	0.147345
$335$	−32.7952	−1.79179
$336$	36.6113	1.99731
$337$	6.19181	0.337289	0.168645	−	0.985677i	$-0.446061\pi$
$337$	6.19181	0.337289	0.168645	+	0.985677i	$0.446061\pi$
$338$	−10.0483	−0.546558
$339$	−7.15915	−0.388832
$340$	−2.19661	−0.119128
$341$	−9.50452	−0.514699
$342$	14.7898	0.799741
$343$	30.5591	1.65004
$344$	3.07411	0.165745
$345$	20.0397	1.07890
$346$	−20.2375	−1.08797
$347$	−24.7001	−1.32597	−0.662985	−	0.748633i	$-0.730710\pi$
$347$	−24.7001	−1.32597	−0.662985	+	0.748633i	$0.730710\pi$
$348$	10.2592	0.549953
$349$	−1.05540	−0.0564943	−0.0282472	−	0.999601i	$-0.508993\pi$
$349$	−1.05540	−0.0564943	−0.0282472	+	0.999601i	$0.508993\pi$
$350$	−51.5020	−2.75290
$351$	62.9639	3.36076
$352$	3.15099	0.167948
$353$	3.46491	0.184419	0.0922093	−	0.995740i	$-0.470607\pi$
$353$	3.46491	0.184419	0.0922093	+	0.995740i	$0.470607\pi$
$354$	11.6587	0.619651
$355$	−0.0661187	−0.00350922
$356$	−8.18011	−0.433545
$357$	14.5707	0.771161
$358$	−11.0897	−0.586109
$359$	15.3574	0.810531	0.405265	−	0.914199i	$-0.367179\pi$
$359$	15.3574	0.810531	0.405265	+	0.914199i	$0.367179\pi$
$360$	−84.8176	−4.47028
$361$	−16.0746	−0.846031
$362$	2.56889	0.135018
$363$	−3.20142	−0.168031
$364$	12.1578	0.637243
$365$	31.1258	1.62920
$366$	17.6283	0.921447
$367$	27.8931	1.45601	0.728005	−	0.685572i	$-0.240448\pi$
$367$	27.8931	1.45601	0.728005	+	0.685572i	$0.240448\pi$
$368$	−4.13239	−0.215416
$369$	59.7712	3.11157
$370$	1.87196	0.0973184
$371$	22.2190	1.15355
$372$	17.5608	0.910486
$373$	33.8116	1.75070	0.875349	−	0.483491i	$-0.160631\pi$
$373$	33.8116	1.75070	0.875349	+	0.483491i	$0.160631\pi$
$374$	−1.19284	−0.0616804
$375$	54.6677	2.82303
$376$	27.7242	1.42977
$377$	−25.7010	−1.32367
$378$	73.8518	3.79853
$379$	34.7426	1.78461	0.892304	−	0.451436i	$-0.149088\pi$
$379$	34.7426	1.78461	0.892304	+	0.451436i	$0.149088\pi$
$380$	−3.75705	−0.192732
$381$	34.5008	1.76753
$382$	32.4053	1.65800
$383$	−5.10255	−0.260728	−0.130364	−	0.991466i	$-0.541615\pi$
$383$	−5.10255	−0.260728	−0.130364	+	0.991466i	$0.541615\pi$
$384$	13.3689	0.682229
$385$	17.3228	0.882850
$386$	10.0407	0.511056
$387$	7.24912	0.368494
$388$	6.71149	0.340724
$389$	14.4820	0.734267	0.367134	−	0.930168i	$-0.380339\pi$
$389$	14.4820	0.734267	0.367134	+	0.930168i	$0.380339\pi$
$390$	67.2755	3.40663
$391$	−1.64462	−0.0831720
$392$	42.1594	2.12937
$393$	−12.5943	−0.635297
$394$	−23.5809	−1.18799
$395$	2.52520	0.127057
$396$	4.18366	0.210237
$397$	8.75313	0.439307	0.219654	−	0.975578i	$-0.429507\pi$
$397$	8.75313	0.439307	0.219654	+	0.975578i	$0.429507\pi$
$398$	−5.21880	−0.261595
$399$	24.9214	1.24763
$400$	−23.8364	−1.19182
$401$	22.5790	1.12754	0.563771	−	0.825931i	$-0.309350\pi$
$401$	22.5790	1.12754	0.563771	+	0.825931i	$0.309350\pi$
$402$	32.9045	1.64113
$403$	−43.9926	−2.19143
$404$	−3.20855	−0.159631
$405$	−82.9823	−4.12343
$406$	−30.1453	−1.49609
$407$	−0.412317	−0.0204378
$408$	9.84152	0.487228
$409$	−17.6323	−0.871859	−0.435930	−	0.899981i	$-0.643580\pi$
$409$	−17.6323	−0.871859	−0.435930	+	0.899981i	$0.643580\pi$
$410$	37.4344	1.84876
$411$	−61.0514	−3.01144
$412$	9.72586	0.479159
$413$	13.8950	0.683727
$414$	−14.2211	−0.698930
$415$	−47.0347	−2.30884
$416$	14.5847	0.715072
$417$	40.2052	1.96886
$418$	−2.04022	−0.0997904
$419$	−7.65613	−0.374026	−0.187013	−	0.982357i	$-0.559881\pi$
$419$	−7.65613	−0.374026	−0.187013	+	0.982357i	$0.559881\pi$
$420$	−32.0060	−1.56173
$421$	−39.1232	−1.90675	−0.953375	−	0.301787i	$-0.902417\pi$
$421$	−39.1232	−1.90675	−0.953375	+	0.301787i	$0.902417\pi$
$422$	−31.5875	−1.53765
$423$	65.3770	3.17874
$424$	15.0074	0.728826
$425$	−9.48648	−0.460162
$426$	0.0663391	0.00321414
$427$	21.0097	1.01673
$428$	−8.46552	−0.409196
$429$	−14.8181	−0.715424
$430$	4.54009	0.218943
$431$	2.86139	0.137828	0.0689142	−	0.997623i	$-0.478047\pi$
$431$	2.86139	0.137828	0.0689142	+	0.997623i	$0.478047\pi$
$432$	34.1805	1.64451
$433$	9.09839	0.437241	0.218620	−	0.975810i	$-0.429844\pi$
$433$	9.09839	0.437241	0.218620	+	0.975810i	$0.429844\pi$
$434$	−51.5999	−2.47688
$435$	67.6590	3.24400
$436$	2.90879	0.139306
$437$	−2.81293	−0.134561
$438$	−31.2296	−1.49221
$439$	13.1384	0.627061	0.313530	−	0.949578i	$-0.398488\pi$
$439$	13.1384	0.627061	0.313530	+	0.949578i	$0.398488\pi$
$440$	11.7004	0.557794
$441$	99.4171	4.73415
$442$	−5.52118	−0.262616
$443$	9.50184	0.451446	0.225723	−	0.974192i	$-0.427526\pi$
$443$	9.50184	0.451446	0.225723	+	0.974192i	$0.427526\pi$
$444$	0.761808	0.0361538
$445$	−53.9473	−2.55735
$446$	24.9634	1.18205
$447$	−6.44772	−0.304967
$448$	39.9786	1.88881
$449$	−18.8135	−0.887866	−0.443933	−	0.896060i	$-0.646417\pi$
$449$	−18.8135	−0.887866	−0.443933	+	0.896060i	$0.646417\pi$
$450$	−82.0302	−3.86694
$451$	−8.24530	−0.388256
$452$	−1.29059	−0.0607044
$453$	−36.7926	−1.72867
$454$	16.5895	0.778583
$455$	80.1800	3.75890
$456$	16.8328	0.788268
$457$	26.8265	1.25489	0.627445	−	0.778661i	$-0.284101\pi$
$457$	26.8265	1.25489	0.627445	+	0.778661i	$0.284101\pi$
$458$	7.94204	0.371107
$459$	13.6032	0.634945
$460$	3.61259	0.168438
$461$	−10.3500	−0.482049	−0.241025	−	0.970519i	$-0.577483\pi$
$461$	−10.3500	−0.482049	−0.241025	+	0.970519i	$0.577483\pi$
$462$	−17.3805	−0.808614
$463$	−19.7114	−0.916068	−0.458034	−	0.888935i	$-0.651446\pi$
$463$	−19.7114	−0.916068	−0.458034	+	0.888935i	$0.651446\pi$
$464$	−13.9520	−0.647706
$465$	115.812	5.37067
$466$	3.28654	0.152246
$467$	11.9899	0.554826	0.277413	−	0.960751i	$-0.410523\pi$
$467$	11.9899	0.554826	0.277413	+	0.960751i	$0.410523\pi$
$468$	19.3645	0.895123
$469$	39.2161	1.81083
$470$	40.9453	1.88867
$471$	−27.8817	−1.28472
$472$	9.38515	0.431986
$473$	−1.00000	−0.0459800
$474$	−2.53362	−0.116373
$475$	−16.2255	−0.744479
$476$	2.62668	0.120394
$477$	35.3894	1.62037
$478$	−15.1033	−0.690807
$479$	−41.1534	−1.88035	−0.940173	−	0.340697i	$-0.889337\pi$
$479$	−41.1534	−1.88035	−0.940173	+	0.340697i	$0.889337\pi$
$480$	−38.3948	−1.75247
$481$	−1.90845	−0.0870177
$482$	−7.33206	−0.333966
$483$	−23.9632	−1.09036
$484$	−0.577127	−0.0262330
$485$	44.2618	2.00982
$486$	34.5793	1.56855
$487$	−9.59413	−0.434752	−0.217376	−	0.976088i	$-0.569750\pi$
$487$	−9.59413	−0.434752	−0.217376	+	0.976088i	$0.569750\pi$
$488$	14.1907	0.642382
$489$	2.72400	0.123183
$490$	62.2644	2.81282
$491$	−29.5035	−1.33148	−0.665738	−	0.746186i	$-0.731883\pi$
$491$	−29.5035	−1.33148	−0.665738	+	0.746186i	$0.731883\pi$
$492$	15.2343	0.686813
$493$	−5.55266	−0.250079
$494$	−9.44335	−0.424876
$495$	27.5910	1.24012
$496$	−23.8817	−1.07232
$497$	0.0790640	0.00354651
$498$	47.1914	2.11470
$499$	30.7791	1.37786	0.688930	−	0.724828i	$-0.258081\pi$
$499$	30.7791	1.37786	0.688930	+	0.724828i	$0.258081\pi$
$500$	9.85505	0.440731
$501$	7.22720	0.322887
$502$	32.3413	1.44346
$503$	−34.9122	−1.55666	−0.778329	−	0.627856i	$-0.783933\pi$
$503$	−34.9122	−1.55666	−0.778329	+	0.627856i	$0.783933\pi$
$504$	101.424	4.51778
$505$	−21.1601	−0.941614
$506$	1.96177	0.0872114
$507$	−26.9684	−1.19771
$508$	6.21951	0.275946
$509$	42.0053	1.86185	0.930926	−	0.365208i	$-0.119002\pi$
$509$	42.0053	1.86185	0.930926	+	0.365208i	$0.119002\pi$
$510$	14.5348	0.643610
$511$	−37.2199	−1.64651
$512$	23.3658	1.03263
$513$	23.2668	1.02725
$514$	−12.8992	−0.568961
$515$	64.1414	2.82641
$516$	1.84763	0.0813373
$517$	−9.01862	−0.396638
$518$	−2.23846	−0.0983525
$519$	−54.3146	−2.38414
$520$	54.1563	2.37491
$521$	−22.3388	−0.978682	−0.489341	−	0.872093i	$-0.662763\pi$
$521$	−22.3388	−0.978682	−0.489341	+	0.872093i	$0.662763\pi$
$522$	−48.0142	−2.10152
$523$	14.0658	0.615056	0.307528	−	0.951539i	$-0.400498\pi$
$523$	14.0658	0.615056	0.307528	+	0.951539i	$0.400498\pi$
$524$	−2.27039	−0.0991825
$525$	−138.224	−6.03260
$526$	28.6112	1.24751
$527$	−9.50452	−0.414023
$528$	−8.04413	−0.350076
$529$	−20.2952	−0.882401
$530$	22.1642	0.962752
$531$	22.1313	0.960418
$532$	4.49263	0.194780
$533$	−38.1642	−1.65307
$534$	54.1271	2.34231
$535$	−55.8295	−2.41372
$536$	26.4879	1.14410
$537$	−29.7632	−1.28438
$538$	28.4516	1.22664
$539$	−13.7144	−0.590719
$540$	−29.8810	−1.28587
$541$	28.6357	1.23114	0.615572	−	0.788081i	$-0.288925\pi$
$541$	28.6357	1.23114	0.615572	+	0.788081i	$0.288925\pi$
$542$	−8.61472	−0.370034
$543$	6.89455	0.295873
$544$	3.15099	0.135098
$545$	19.1832	0.821720
$546$	−80.4472	−3.44282
$547$	−5.76451	−0.246473	−0.123236	−	0.992377i	$-0.539327\pi$
$547$	−5.76451	−0.246473	−0.123236	+	0.992377i	$0.539327\pi$
$548$	−11.0058	−0.470146
$549$	33.4634	1.42818
$550$	11.3159	0.482511
$551$	−9.49719	−0.404594
$552$	−16.1856	−0.688903
$553$	−3.01961	−0.128407
$554$	−26.1170	−1.10960
$555$	5.02407	0.213260
$556$	7.24786	0.307378
$557$	−33.6105	−1.42412	−0.712061	−	0.702117i	$-0.752238\pi$
$557$	−33.6105	−1.42412	−0.712061	+	0.702117i	$0.752238\pi$
$558$	−82.1862	−3.47922
$559$	−4.62859	−0.195769
$560$	43.5264	1.83933
$561$	−3.20142	−0.135164
$562$	36.1123	1.52331
$563$	27.0526	1.14013	0.570065	−	0.821599i	$-0.306918\pi$
$563$	27.0526	1.14013	0.570065	+	0.821599i	$0.306918\pi$
$564$	16.6630	0.701641
$565$	−8.51138	−0.358076
$566$	25.6207	1.07692
$567$	99.2293	4.16724
$568$	0.0534026	0.00224072
$569$	22.2340	0.932098	0.466049	−	0.884759i	$-0.345677\pi$
$569$	22.2340	0.932098	0.466049	+	0.884759i	$0.345677\pi$
$570$	24.8600	1.04127
$571$	−16.3411	−0.683854	−0.341927	−	0.939726i	$-0.611080\pi$
$571$	−16.3411	−0.683854	−0.341927	+	0.939726i	$0.611080\pi$
$572$	−2.67128	−0.111692
$573$	86.9712	3.63328
$574$	−44.7637	−1.86840
$575$	15.6017	0.650634
$576$	63.6761	2.65317
$577$	−11.6541	−0.485167	−0.242584	−	0.970131i	$-0.577995\pi$
$577$	−11.6541	−0.485167	−0.242584	+	0.970131i	$0.577995\pi$
$578$	−1.19284	−0.0496157
$579$	26.9477	1.11991
$580$	12.1970	0.506454
$581$	56.2435	2.33337
$582$	−44.4093	−1.84082
$583$	−4.88189	−0.202187
$584$	−25.1396	−1.04028
$585$	127.707	5.28005
$586$	−5.93653	−0.245236
$587$	−23.0235	−0.950281	−0.475141	−	0.879910i	$-0.657603\pi$
$587$	−23.0235	−0.950281	−0.475141	+	0.879910i	$0.657603\pi$
$588$	25.3390	1.04496
$589$	−16.2564	−0.669833
$590$	13.8608	0.570638
$591$	−63.2880	−2.60332
$592$	−1.03602	−0.0425800
$593$	−6.20681	−0.254883	−0.127442	−	0.991846i	$-0.540677\pi$
$593$	−6.20681	−0.254883	−0.127442	+	0.991846i	$0.540677\pi$
$594$	−16.2265	−0.665782
$595$	17.3228	0.710164
$596$	−1.16234	−0.0476114
$597$	−14.0065	−0.573249
$598$	9.08024	0.371319
$599$	41.2675	1.68614	0.843072	−	0.537800i	$-0.180745\pi$
$599$	41.2675	1.68614	0.843072	+	0.537800i	$0.180745\pi$
$600$	−93.3614	−3.81146
$601$	−7.54601	−0.307808	−0.153904	−	0.988086i	$-0.549185\pi$
$601$	−7.54601	−0.307808	−0.153904	+	0.988086i	$0.549185\pi$
$602$	−5.42899	−0.221269
$603$	62.4617	2.54364
$604$	−6.63267	−0.269880
$605$	−3.80611	−0.154740
$606$	21.2307	0.862437
$607$	37.0519	1.50389	0.751944	−	0.659227i	$-0.229116\pi$
$607$	37.0519	1.50389	0.751944	+	0.659227i	$0.229116\pi$
$608$	5.38941	0.218569
$609$	−80.9059	−3.27847
$610$	20.9580	0.848563
$611$	−41.7435	−1.68876
$612$	4.18366	0.169115
$613$	15.1320	0.611175	0.305587	−	0.952164i	$-0.401147\pi$
$613$	15.1320	0.611175	0.305587	+	0.952164i	$0.401147\pi$
$614$	30.6196	1.23571
$615$	100.469	4.05130
$616$	−13.9912	−0.563721
$617$	9.93142	0.399824	0.199912	−	0.979814i	$-0.435934\pi$
$617$	9.93142	0.399824	0.199912	+	0.979814i	$0.435934\pi$
$618$	−64.3551	−2.58874
$619$	17.4246	0.700353	0.350177	−	0.936684i	$-0.386122\pi$
$619$	17.4246	0.700353	0.350177	+	0.936684i	$0.386122\pi$
$620$	20.8777	0.838469
$621$	−22.3722	−0.897764
$622$	−35.0731	−1.40630
$623$	64.5095	2.58452
$624$	−37.2330	−1.49051
$625$	17.5609	0.702438
$626$	17.6607	0.705865
$627$	−5.47567	−0.218677
$628$	−5.02628	−0.200570
$629$	−0.412317	−0.0164402
$630$	149.791	5.96782
$631$	21.9417	0.873485	0.436743	−	0.899586i	$-0.356132\pi$
$631$	21.9417	0.873485	0.436743	+	0.899586i	$0.356132\pi$
$632$	−2.03955	−0.0811288
$633$	−84.7764	−3.36956
$634$	−0.349515	−0.0138810
$635$	41.0173	1.62772
$636$	9.01992	0.357663
$637$	−63.4782	−2.51510
$638$	6.62345	0.262225
$639$	0.125930	0.00498171
$640$	15.8940	0.628266
$641$	44.3073	1.75003	0.875017	−	0.484093i	$-0.160850\pi$
$641$	44.3073	1.75003	0.875017	+	0.484093i	$0.160850\pi$
$642$	56.0156	2.21076
$643$	4.29112	0.169225	0.0846127	−	0.996414i	$-0.473035\pi$
$643$	4.29112	0.169225	0.0846127	+	0.996414i	$0.473035\pi$
$644$	−4.31989	−0.170227
$645$	12.1850	0.479783
$646$	−2.04022	−0.0802714
$647$	−23.1997	−0.912075	−0.456037	−	0.889961i	$-0.650732\pi$
$647$	−23.1997	−0.912075	−0.456037	+	0.889961i	$0.650732\pi$
$648$	67.0229	2.63291
$649$	−3.05297	−0.119839
$650$	52.3766	2.05438
$651$	−138.487	−5.42774
$652$	0.491060	0.0192314
$653$	1.64657	0.0644352	0.0322176	−	0.999481i	$-0.489743\pi$
$653$	1.64657	0.0644352	0.0322176	+	0.999481i	$0.489743\pi$
$654$	−19.2472	−0.752624
$655$	−14.9731	−0.585047
$656$	−20.7177	−0.808892
$657$	−59.2823	−2.31282
$658$	−48.9620	−1.90874
$659$	18.0128	0.701680	0.350840	−	0.936435i	$-0.385896\pi$
$659$	18.0128	0.701680	0.350840	+	0.936435i	$0.385896\pi$
$660$	7.03228	0.273731
$661$	−23.5704	−0.916782	−0.458391	−	0.888751i	$-0.651574\pi$
$661$	−23.5704	−0.916782	−0.458391	+	0.888751i	$0.651574\pi$
$662$	4.03925	0.156990
$663$	−14.8181	−0.575487
$664$	37.9888	1.47425
$665$	29.6286	1.14895
$666$	−3.56533	−0.138154
$667$	9.13201	0.353593
$668$	1.30286	0.0504092
$669$	66.9983	2.59030
$670$	39.1195	1.51132
$671$	−4.61620	−0.178206
$672$	45.9120	1.77109
$673$	−38.9631	−1.50192	−0.750958	−	0.660350i	$-0.770408\pi$
$673$	−38.9631	−1.50192	−0.750958	+	0.660350i	$0.770408\pi$
$674$	−7.38585	−0.284492
$675$	−129.047	−4.96702
$676$	−4.86164	−0.186986
$677$	−30.8090	−1.18409	−0.592043	−	0.805907i	$-0.701678\pi$
$677$	−30.8090	−1.18409	−0.592043	+	0.805907i	$0.701678\pi$
$678$	8.53974	0.327967
$679$	−52.9277	−2.03118
$680$	11.7004	0.448690
$681$	44.5239	1.70616
$682$	11.3374	0.434131
$683$	30.8790	1.18155	0.590776	−	0.806836i	$-0.298822\pi$
$683$	30.8790	1.18155	0.590776	+	0.806836i	$0.298822\pi$
$684$	7.15567	0.273604
$685$	−72.5828	−2.77325
$686$	−36.4522	−1.39175
$687$	21.3153	0.813231
$688$	−2.51267	−0.0957947
$689$	−22.5963	−0.860850
$690$	−23.9041	−0.910015
$691$	−10.1751	−0.387078	−0.193539	−	0.981093i	$-0.561997\pi$
$691$	−10.1751	−0.387078	−0.193539	+	0.981093i	$0.561997\pi$
$692$	−9.79139	−0.372213
$693$	−32.9929	−1.25330
$694$	29.4633	1.11841
$695$	47.7991	1.81312
$696$	−54.6466	−2.07137
$697$	−8.24530	−0.312313
$698$	1.25893	0.0476511
$699$	8.82062	0.333627
$700$	−24.9179	−0.941810
$701$	19.6169	0.740919	0.370459	−	0.928849i	$-0.379200\pi$
$701$	19.6169	0.740919	0.370459	+	0.928849i	$0.379200\pi$
$702$	−75.1060	−2.83469
$703$	−0.705221	−0.0265979
$704$	−8.78398	−0.331059
$705$	109.892	4.13876
$706$	−4.13309	−0.155551
$707$	25.3031	0.951619
$708$	5.64075	0.211992
$709$	−14.4519	−0.542751	−0.271375	−	0.962474i	$-0.587478\pi$
$709$	−14.4519	−0.542751	−0.271375	+	0.962474i	$0.587478\pi$
$710$	0.0788692	0.00295991
$711$	−4.80950	−0.180370
$712$	43.5719	1.63293
$713$	15.6313	0.585397
$714$	−17.3805	−0.650449
$715$	−17.6169	−0.658836
$716$	−5.36547	−0.200517
$717$	−40.5351	−1.51381
$718$	−18.3189	−0.683656
$719$	30.2611	1.12855	0.564274	−	0.825588i	$-0.309156\pi$
$719$	30.2611	1.12855	0.564274	+	0.825588i	$0.309156\pi$
$720$	69.3270	2.58367
$721$	−76.6995	−2.85644
$722$	19.1744	0.713599
$723$	−19.6782	−0.731842
$724$	1.24289	0.0461918
$725$	52.6752	1.95631
$726$	3.81880	0.141729
$727$	2.27763	0.0844726	0.0422363	−	0.999108i	$-0.486552\pi$
$727$	2.27763	0.0844726	0.0422363	+	0.999108i	$0.486552\pi$
$728$	−64.7595	−2.40015
$729$	27.3989	1.01478
$730$	−37.1282	−1.37418
$731$	−1.00000	−0.0369863
$732$	8.52902	0.315242
$733$	10.3136	0.380941	0.190470	−	0.981693i	$-0.438999\pi$
$733$	10.3136	0.380941	0.190470	+	0.981693i	$0.438999\pi$
$734$	−33.2721	−1.22810
$735$	167.109	6.16392
$736$	−5.18218	−0.191018
$737$	−8.61645	−0.317391
$738$	−71.2976	−2.62450
$739$	−12.6625	−0.465796	−0.232898	−	0.972501i	$-0.574821\pi$
$739$	−12.6625	−0.465796	−0.232898	+	0.972501i	$0.574821\pi$
$740$	0.905699	0.0332942
$741$	−25.3446	−0.931059
$742$	−26.5037	−0.972982
$743$	31.5298	1.15672	0.578358	−	0.815783i	$-0.303694\pi$
$743$	31.5298	1.15672	0.578358	+	0.815783i	$0.303694\pi$
$744$	−93.5389	−3.42930
$745$	−7.66557	−0.280845
$746$	−40.3319	−1.47666
$747$	89.5823	3.27764
$748$	−0.577127	−0.0211018
$749$	66.7603	2.43937
$750$	−65.2100	−2.38113
$751$	15.1811	0.553966	0.276983	−	0.960875i	$-0.410665\pi$
$751$	15.1811	0.553966	0.276983	+	0.960875i	$0.410665\pi$
$752$	−22.6608	−0.826355
$753$	86.7997	3.16316
$754$	30.6572	1.11647
$755$	−43.7420	−1.59193
$756$	35.7313	1.29954
$757$	−46.1975	−1.67908	−0.839539	−	0.543299i	$-0.817175\pi$
$757$	−46.1975	−1.67908	−0.839539	+	0.543299i	$0.817175\pi$
$758$	−41.4424	−1.50526
$759$	5.26513	0.191112
$760$	20.0122	0.725918
$761$	16.1712	0.586204	0.293102	−	0.956081i	$-0.405312\pi$
$761$	16.1712	0.586204	0.293102	+	0.956081i	$0.405312\pi$
$762$	−41.1540	−1.49085
$763$	−22.9391	−0.830451
$764$	15.6785	0.567227
$765$	27.5910	0.997553
$766$	6.08654	0.219916
$767$	−14.1309	−0.510239
$768$	40.2955	1.45404
$769$	17.1655	0.619004	0.309502	−	0.950899i	$-0.399838\pi$
$769$	17.1655	0.619004	0.309502	+	0.950899i	$0.399838\pi$
$770$	−20.6633	−0.744655
$771$	−34.6198	−1.24680
$772$	4.85792	0.174840
$773$	−53.6522	−1.92973	−0.964867	−	0.262739i	$-0.915374\pi$
$773$	−53.6522	−1.92973	−0.964867	+	0.262739i	$0.915374\pi$
$774$	−8.64706	−0.310812
$775$	90.1645	3.23880
$776$	−35.7492	−1.28332
$777$	−6.00773	−0.215526
$778$	−17.2748	−0.619330
$779$	−14.1026	−0.505280
$780$	32.5495	1.16546
$781$	−0.0173717	−0.000621609 0
$782$	1.96177	0.0701528
$783$	−75.5342	−2.69937
$784$	−34.4597	−1.23070
$785$	−33.1480	−1.18310
$786$	15.0230	0.535852
$787$	−19.0632	−0.679528	−0.339764	−	0.940511i	$-0.610347\pi$
$787$	−19.0632	−0.679528	−0.339764	+	0.940511i	$0.610347\pi$
$788$	−11.4090	−0.406430
$789$	76.7885	2.73374
$790$	−3.01217	−0.107168
$791$	10.1778	0.361881
$792$	−22.2846	−0.791848
$793$	−21.3665	−0.758747
$794$	−10.4411	−0.370541
$795$	59.4857	2.10974
$796$	−2.52498	−0.0894957
$797$	6.10365	0.216202	0.108101	−	0.994140i	$-0.465523\pi$
$797$	6.10365	0.216202	0.108101	+	0.994140i	$0.465523\pi$
$798$	−29.7273	−1.05234
$799$	−9.01862	−0.319056
$800$	−29.8918	−1.05684
$801$	102.748	3.63042
$802$	−26.9332	−0.951045
$803$	8.17786	0.288590
$804$	15.9200	0.561455
$805$	−28.4894	−1.00412
$806$	52.4762	1.84839
$807$	76.3602	2.68801
$808$	17.0906	0.601244
$809$	2.43949	0.0857679	0.0428840	−	0.999080i	$-0.486345\pi$
$809$	2.43949	0.0857679	0.0428840	+	0.999080i	$0.486345\pi$
$810$	98.9849	3.47797
$811$	14.1342	0.496318	0.248159	−	0.968719i	$-0.420174\pi$
$811$	14.1342	0.496318	0.248159	+	0.968719i	$0.420174\pi$
$812$	−14.5851	−0.511835
$813$	−23.1207	−0.810879
$814$	0.491829	0.0172386
$815$	3.23850	0.113440
$816$	−8.04413	−0.281601
$817$	−1.71039	−0.0598388
$818$	21.0325	0.735385
$819$	−152.711	−5.33615
$820$	18.1117	0.632488
$821$	−49.4787	−1.72682	−0.863409	−	0.504505i	$-0.831675\pi$
$821$	−49.4787	−1.72682	−0.863409	+	0.504505i	$0.831675\pi$
$822$	72.8247	2.54005
$823$	45.4981	1.58597	0.792983	−	0.609244i	$-0.208527\pi$
$823$	45.4981	1.58597	0.792983	+	0.609244i	$0.208527\pi$
$824$	−51.8055	−1.80473
$825$	30.3703	1.05736
$826$	−16.5745	−0.576701
$827$	23.5178	0.817793	0.408897	−	0.912581i	$-0.365914\pi$
$827$	23.5178	0.817793	0.408897	+	0.912581i	$0.365914\pi$
$828$	−6.88053	−0.239115
$829$	−14.5413	−0.505039	−0.252520	−	0.967592i	$-0.581259\pi$
$829$	−14.5413	−0.505039	−0.252520	+	0.967592i	$0.581259\pi$
$830$	56.1050	1.94743
$831$	−70.0944	−2.43155
$832$	−40.6575	−1.40954
$833$	−13.7144	−0.475174
$834$	−47.9584	−1.66066
$835$	8.59227	0.297348
$836$	−0.987109	−0.0341399
$837$	−129.292	−4.46900
$838$	9.13255	0.315479
$839$	10.8595	0.374911	0.187456	−	0.982273i	$-0.439976\pi$
$839$	10.8595	0.374911	0.187456	+	0.982273i	$0.439976\pi$
$840$	170.482	5.88220
$841$	1.83202	0.0631732
$842$	46.6679	1.60828
$843$	96.9204	3.33812
$844$	−15.2828	−0.526056
$845$	−32.0622	−1.10297
$846$	−77.9845	−2.68116
$847$	4.55130	0.156385
$848$	−12.2666	−0.421236
$849$	68.7625	2.35992
$850$	11.3159	0.388131
$851$	0.678105	0.0232451
$852$	0.0320965	0.00109961
$853$	43.5868	1.49239	0.746193	−	0.665730i	$-0.231880\pi$
$853$	43.5868	1.49239	0.746193	+	0.665730i	$0.231880\pi$
$854$	−25.0613	−0.857580
$855$	47.1912	1.61390
$856$	45.0922	1.54122
$857$	38.8472	1.32699	0.663497	−	0.748179i	$-0.269071\pi$
$857$	38.8472	1.32699	0.663497	+	0.748179i	$0.269071\pi$
$858$	17.6756	0.603437
$859$	6.00887	0.205020	0.102510	−	0.994732i	$-0.467313\pi$
$859$	6.00887	0.205020	0.102510	+	0.994732i	$0.467313\pi$
$860$	2.19661	0.0749037
$861$	−120.139	−4.09434
$862$	−3.41319	−0.116254
$863$	−29.1987	−0.993935	−0.496967	−	0.867769i	$-0.665553\pi$
$863$	−29.1987	−0.993935	−0.496967	+	0.867769i	$0.665553\pi$
$864$	42.8637	1.45825
$865$	−64.5735	−2.19557
$866$	−10.8529	−0.368798
$867$	−3.20142	−0.108726
$868$	−24.9653	−0.847378
$869$	0.663460	0.0225063
$870$	−80.7066	−2.73621
$871$	−39.8820	−1.35135
$872$	−15.4939	−0.524688
$873$	−84.3010	−2.85316
$874$	3.35539	0.113498
$875$	−77.7183	−2.62736
$876$	−15.1096	−0.510507
$877$	−21.8620	−0.738228	−0.369114	−	0.929384i	$-0.620339\pi$
$877$	−21.8620	−0.738228	−0.369114	+	0.929384i	$0.620339\pi$
$878$	−15.6720	−0.528905
$879$	−15.9328	−0.537401
$880$	−9.56351	−0.322386
$881$	4.91945	0.165740	0.0828702	−	0.996560i	$-0.473591\pi$
$881$	4.91945	0.165740	0.0828702	+	0.996560i	$0.473591\pi$
$882$	−118.589	−3.99310
$883$	−34.5537	−1.16282	−0.581412	−	0.813609i	$-0.697500\pi$
$883$	−34.5537	−1.16282	−0.581412	+	0.813609i	$0.697500\pi$
$884$	−2.67128	−0.0898450
$885$	37.2003	1.25048
$886$	−11.3342	−0.380780
$887$	−45.5090	−1.52804	−0.764022	−	0.645191i	$-0.776778\pi$
$887$	−45.5090	−1.52804	−0.764022	+	0.645191i	$0.776778\pi$
$888$	−4.05783	−0.136172
$889$	−49.0480	−1.64502
$890$	64.3506	2.15704
$891$	−21.8024	−0.730408
$892$	12.0779	0.404398
$893$	−15.4253	−0.516188
$894$	7.69111	0.257229
$895$	−35.3849	−1.18279
$896$	−19.0059	−0.634942
$897$	24.3701	0.813695
$898$	22.4416	0.748885
$899$	52.7754	1.76016
$900$	−39.6882	−1.32294
$901$	−4.88189	−0.162639
$902$	9.83535	0.327481
$903$	−14.5707	−0.484881
$904$	6.87444	0.228640
$905$	8.19679	0.272471
$906$	43.8878	1.45807
$907$	9.79725	0.325312	0.162656	−	0.986683i	$-0.447994\pi$
$907$	9.79725	0.325312	0.162656	+	0.986683i	$0.447994\pi$
$908$	8.02640	0.266366
$909$	40.3016	1.33672
$910$	−95.6421	−3.17051
$911$	21.4413	0.710382	0.355191	−	0.934794i	$-0.384416\pi$
$911$	21.4413	0.710382	0.355191	+	0.934794i	$0.384416\pi$
$912$	−13.7586	−0.455591
$913$	−12.3577	−0.408979
$914$	−31.9998	−1.05846
$915$	56.2483	1.85951
$916$	3.84256	0.126962
$917$	17.9046	0.591263
$918$	−16.2265	−0.535555
$919$	16.6525	0.549314	0.274657	−	0.961542i	$-0.411436\pi$
$919$	16.6525	0.549314	0.274657	+	0.961542i	$0.411436\pi$
$920$	−19.2427	−0.634413
$921$	82.1787	2.70788
$922$	12.3460	0.406593
$923$	−0.0804067	−0.00264662
$924$	−8.40911	−0.276640
$925$	3.91144	0.128607
$926$	23.5126	0.772673
$927$	−122.164	−4.01238
$928$	−17.4964	−0.574347
$929$	21.3563	0.700676	0.350338	−	0.936623i	$-0.386067\pi$
$929$	21.3563	0.700676	0.350338	+	0.936623i	$0.386067\pi$
$930$	−138.146	−4.52998
$931$	−23.4568	−0.768767
$932$	1.59011	0.0520858
$933$	−94.1314	−3.08172
$934$	−14.3020	−0.467977
$935$	−3.80611	−0.124473
$936$	−103.146	−3.37144
$937$	−36.3830	−1.18858	−0.594290	−	0.804251i	$-0.702567\pi$
$937$	−36.3830	−1.18858	−0.594290	+	0.804251i	$0.702567\pi$
$938$	−46.7786	−1.52738
$939$	47.3990	1.54681
$940$	19.8104	0.646143
$941$	−19.7214	−0.642900	−0.321450	−	0.946927i	$-0.604170\pi$
$941$	−19.7214	−0.642900	−0.321450	+	0.946927i	$0.604170\pi$
$942$	33.2584	1.08362
$943$	13.5604	0.441587
$944$	−7.67110	−0.249673
$945$	235.646	7.66556
$946$	1.19284	0.0387827
$947$	−40.2197	−1.30697	−0.653483	−	0.756941i	$-0.726693\pi$
$947$	−40.2197	−1.30697	−0.653483	+	0.756941i	$0.726693\pi$
$948$	−1.22583	−0.0398130
$949$	37.8520	1.22873
$950$	19.3545	0.627943
$951$	−0.938051	−0.0304184
$952$	−13.9912	−0.453457
$953$	−0.527070	−0.0170735	−0.00853674	−	0.999964i	$-0.502717\pi$
$953$	−0.527070	−0.0170735	−0.00853674	+	0.999964i	$0.502717\pi$
$954$	−42.2140	−1.36673
$955$	103.398	3.34589
$956$	−7.30734	−0.236336
$957$	17.7764	0.574630
$958$	49.0895	1.58601
$959$	86.7936	2.80271
$960$	107.033	3.45446
$961$	59.3359	1.91406
$962$	2.27648	0.0733966
$963$	106.333	3.42653
$964$	−3.54743	−0.114255
$965$	32.0376	1.03133
$966$	28.5843	0.919685
$967$	29.6390	0.953125	0.476563	−	0.879141i	$-0.341883\pi$
$967$	29.6390	0.953125	0.476563	+	0.879141i	$0.341883\pi$
$968$	3.07411	0.0988055
$969$	−5.47567	−0.175904
$970$	−52.7973	−1.69522
$971$	6.13221	0.196792	0.0983959	−	0.995147i	$-0.468629\pi$
$971$	6.13221	0.196792	0.0983959	+	0.995147i	$0.468629\pi$
$972$	16.7303	0.536626
$973$	−57.1577	−1.83239
$974$	11.4443	0.366699
$975$	140.572	4.50189
$976$	−11.5990	−0.371275
$977$	−41.0983	−1.31485	−0.657425	−	0.753520i	$-0.728354\pi$
$977$	−41.0983	−1.31485	−0.657425	+	0.753520i	$0.728354\pi$
$978$	−3.24930	−0.103901
$979$	−14.1739	−0.452998
$980$	30.1251	0.962310
$981$	−36.5364	−1.16652
$982$	35.1931	1.12306
$983$	−49.8853	−1.59109	−0.795547	−	0.605892i	$-0.792816\pi$
$983$	−49.8853	−1.59109	−0.795547	+	0.605892i	$0.792816\pi$
$984$	−81.1463	−2.58685
$985$	−75.2419	−2.39741
$986$	6.62345	0.210934
$987$	−131.407	−4.18274
$988$	−4.56893	−0.145357
$989$	1.64462	0.0522959
$990$	−32.9117	−1.04600
$991$	20.4142	0.648480	0.324240	−	0.945975i	$-0.394892\pi$
$991$	20.4142	0.648480	0.324240	+	0.945975i	$0.394892\pi$
$992$	−29.9487	−0.950871
$993$	10.8408	0.344022
$994$	−0.0943109	−0.00299136
$995$	−16.6521	−0.527907
$996$	22.8324	0.723472
$997$	28.8659	0.914193	0.457097	−	0.889417i	$-0.348889\pi$
$997$	28.8659	0.914193	0.457097	+	0.889417i	$0.348889\pi$
$998$	−36.7146	−1.16218
$999$	−5.60885	−0.177456

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.20	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-1.19284 q^{2} -3.20142 q^{3} -0.577127 q^{4} -3.80611 q^{5} +3.81880 q^{6} +4.55130 q^{7} +3.07411 q^{8} +7.24912 q^{9} +O(q^{10})\)	\(q-1.19284 q^{2} -3.20142 q^{3} -0.577127 q^{4} -3.80611 q^{5} +3.81880 q^{6} +4.55130 q^{7} +3.07411 q^{8} +7.24912 q^{9} +4.54009 q^{10} -1.00000 q^{11} +1.84763 q^{12} -4.62859 q^{13} -5.42899 q^{14} +12.1850 q^{15} -2.51267 q^{16} -1.00000 q^{17} -8.64706 q^{18} -1.71039 q^{19} +2.19661 q^{20} -14.5707 q^{21} +1.19284 q^{22} +1.64462 q^{23} -9.84152 q^{24} +9.48648 q^{25} +5.52118 q^{26} -13.6032 q^{27} -2.62668 q^{28} +5.55266 q^{29} -14.5348 q^{30} +9.50452 q^{31} -3.15099 q^{32} +3.20142 q^{33} +1.19284 q^{34} -17.3228 q^{35} -4.18366 q^{36} +0.412317 q^{37} +2.04022 q^{38} +14.8181 q^{39} -11.7004 q^{40} +8.24530 q^{41} +17.3805 q^{42} +1.00000 q^{43} +0.577127 q^{44} -27.5910 q^{45} -1.96177 q^{46} +9.01862 q^{47} +8.04413 q^{48} +13.7144 q^{49} -11.3159 q^{50} +3.20142 q^{51} +2.67128 q^{52} +4.88189 q^{53} +16.2265 q^{54} +3.80611 q^{55} +13.9912 q^{56} +5.47567 q^{57} -6.62345 q^{58} +3.05297 q^{59} -7.03228 q^{60} +4.61620 q^{61} -11.3374 q^{62} +32.9929 q^{63} +8.78398 q^{64} +17.6169 q^{65} -3.81880 q^{66} +8.61645 q^{67} +0.577127 q^{68} -5.26513 q^{69} +20.6633 q^{70} +0.0173717 q^{71} +22.2846 q^{72} -8.17786 q^{73} -0.491829 q^{74} -30.3703 q^{75} +0.987109 q^{76} -4.55130 q^{77} -17.6756 q^{78} -0.663460 q^{79} +9.56351 q^{80} +21.8024 q^{81} -9.83535 q^{82} +12.3577 q^{83} +8.40911 q^{84} +3.80611 q^{85} -1.19284 q^{86} -17.7764 q^{87} -3.07411 q^{88} +14.1739 q^{89} +32.9117 q^{90} -21.0661 q^{91} -0.949154 q^{92} -30.4280 q^{93} -10.7578 q^{94} +6.50992 q^{95} +10.0877 q^{96} -11.6291 q^{97} -16.3591 q^{98} -7.24912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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