LMFDB - Embedded newform 8043.2.a.s.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84012 q^{2} -1.00000 q^{3} +1.38605 q^{4} -2.07033 q^{5} +1.84012 q^{6} -1.00000 q^{7} +1.12975 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.84012 q^{2} -1.00000 q^{3} +1.38605 q^{4} -2.07033 q^{5} +1.84012 q^{6} -1.00000 q^{7} +1.12975 q^{8} +1.00000 q^{9} +3.80966 q^{10} +3.35847 q^{11} -1.38605 q^{12} -2.38156 q^{13} +1.84012 q^{14} +2.07033 q^{15} -4.85097 q^{16} +5.66000 q^{17} -1.84012 q^{18} -1.77188 q^{19} -2.86958 q^{20} +1.00000 q^{21} -6.18000 q^{22} -4.68383 q^{23} -1.12975 q^{24} -0.713733 q^{25} +4.38235 q^{26} -1.00000 q^{27} -1.38605 q^{28} +4.29220 q^{29} -3.80966 q^{30} -4.55374 q^{31} +6.66688 q^{32} -3.35847 q^{33} -10.4151 q^{34} +2.07033 q^{35} +1.38605 q^{36} +11.3297 q^{37} +3.26047 q^{38} +2.38156 q^{39} -2.33895 q^{40} -6.98593 q^{41} -1.84012 q^{42} +2.71086 q^{43} +4.65500 q^{44} -2.07033 q^{45} +8.61882 q^{46} +10.5602 q^{47} +4.85097 q^{48} +1.00000 q^{49} +1.31336 q^{50} -5.66000 q^{51} -3.30095 q^{52} -12.4339 q^{53} +1.84012 q^{54} -6.95314 q^{55} -1.12975 q^{56} +1.77188 q^{57} -7.89818 q^{58} +10.3828 q^{59} +2.86958 q^{60} +2.00358 q^{61} +8.37943 q^{62} -1.00000 q^{63} -2.56593 q^{64} +4.93061 q^{65} +6.18000 q^{66} +7.31952 q^{67} +7.84503 q^{68} +4.68383 q^{69} -3.80966 q^{70} -11.5842 q^{71} +1.12975 q^{72} +3.14006 q^{73} -20.8481 q^{74} +0.713733 q^{75} -2.45591 q^{76} -3.35847 q^{77} -4.38235 q^{78} +17.0850 q^{79} +10.0431 q^{80} +1.00000 q^{81} +12.8550 q^{82} -14.5597 q^{83} +1.38605 q^{84} -11.7181 q^{85} -4.98832 q^{86} -4.29220 q^{87} +3.79422 q^{88} +18.3821 q^{89} +3.80966 q^{90} +2.38156 q^{91} -6.49202 q^{92} +4.55374 q^{93} -19.4321 q^{94} +3.66837 q^{95} -6.66688 q^{96} +7.95126 q^{97} -1.84012 q^{98} +3.35847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) $ 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * 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 $

$2$	−1.84012	−1.30116	−0.650581	−	0.759437i	$-0.725475\pi$
$2$	−1.84012	−1.30116	−0.650581	+	0.759437i	$0.725475\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.38605	0.693024
$5$	−2.07033	−0.925880	−0.462940	−	0.886390i	$-0.653205\pi$
$5$	−2.07033	−0.925880	−0.462940	+	0.886390i	$0.653205\pi$
$6$	1.84012	0.751227
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.12975	0.399426
$9$	1.00000	0.333333
$10$	3.80966	1.20472
$11$	3.35847	1.01262	0.506309	−	0.862352i	$-0.331010\pi$
$11$	3.35847	1.01262	0.506309	+	0.862352i	$0.331010\pi$
$12$	−1.38605	−0.400118
$13$	−2.38156	−0.660525	−0.330262	−	0.943889i	$-0.607137\pi$
$13$	−2.38156	−0.660525	−0.330262	+	0.943889i	$0.607137\pi$
$14$	1.84012	0.491793
$15$	2.07033	0.534557
$16$	−4.85097	−1.21274
$17$	5.66000	1.37275	0.686376	−	0.727247i	$-0.259200\pi$
$17$	5.66000	1.37275	0.686376	+	0.727247i	$0.259200\pi$
$18$	−1.84012	−0.433721
$19$	−1.77188	−0.406496	−0.203248	−	0.979127i	$-0.565150\pi$
$19$	−1.77188	−0.406496	−0.203248	+	0.979127i	$0.565150\pi$
$20$	−2.86958	−0.641657
$21$	1.00000	0.218218
$22$	−6.18000	−1.31758
$23$	−4.68383	−0.976647	−0.488323	−	0.872663i	$-0.662391\pi$
$23$	−4.68383	−0.976647	−0.488323	+	0.872663i	$0.662391\pi$
$24$	−1.12975	−0.230608
$25$	−0.713733	−0.142747
$26$	4.38235	0.859450
$27$	−1.00000	−0.192450
$28$	−1.38605	−0.261939
$29$	4.29220	0.797042	0.398521	−	0.917159i	$-0.369524\pi$
$29$	4.29220	0.797042	0.398521	+	0.917159i	$0.369524\pi$
$30$	−3.80966	−0.695545
$31$	−4.55374	−0.817875	−0.408938	−	0.912562i	$-0.634101\pi$
$31$	−4.55374	−0.817875	−0.408938	+	0.912562i	$0.634101\pi$
$32$	6.66688	1.17855
$33$	−3.35847	−0.584635
$34$	−10.4151	−1.78617
$35$	2.07033	0.349950
$36$	1.38605	0.231008
$37$	11.3297	1.86260	0.931299	−	0.364255i	$-0.118676\pi$
$37$	11.3297	1.86260	0.931299	+	0.364255i	$0.118676\pi$
$38$	3.26047	0.528918
$39$	2.38156	0.381354
$40$	−2.33895	−0.369820
$41$	−6.98593	−1.09102	−0.545509	−	0.838105i	$-0.683664\pi$
$41$	−6.98593	−1.09102	−0.545509	+	0.838105i	$0.683664\pi$
$42$	−1.84012	−0.283937
$43$	2.71086	0.413403	0.206701	−	0.978404i	$-0.433727\pi$
$43$	2.71086	0.413403	0.206701	+	0.978404i	$0.433727\pi$
$44$	4.65500	0.701768
$45$	−2.07033	−0.308627
$46$	8.61882	1.27078
$47$	10.5602	1.54037	0.770183	−	0.637823i	$-0.220165\pi$
$47$	10.5602	1.54037	0.770183	+	0.637823i	$0.220165\pi$
$48$	4.85097	0.700177
$49$	1.00000	0.142857
$50$	1.31336	0.185737
$51$	−5.66000	−0.792559
$52$	−3.30095	−0.457760
$53$	−12.4339	−1.70792	−0.853962	−	0.520336i	$-0.825807\pi$
$53$	−12.4339	−1.70792	−0.853962	+	0.520336i	$0.825807\pi$
$54$	1.84012	0.250409
$55$	−6.95314	−0.937562
$56$	−1.12975	−0.150969
$57$	1.77188	0.234691
$58$	−7.89818	−1.03708
$59$	10.3828	1.35173	0.675863	−	0.737027i	$-0.263771\pi$
$59$	10.3828	1.35173	0.675863	+	0.737027i	$0.263771\pi$
$60$	2.86958	0.370461
$61$	2.00358	0.256533	0.128266	−	0.991740i	$-0.459059\pi$
$61$	2.00358	0.256533	0.128266	+	0.991740i	$0.459059\pi$
$62$	8.37943	1.06419
$63$	−1.00000	−0.125988
$64$	−2.56593	−0.320742
$65$	4.93061	0.611567
$66$	6.18000	0.760705
$67$	7.31952	0.894221	0.447111	−	0.894479i	$-0.352453\pi$
$67$	7.31952	0.894221	0.447111	+	0.894479i	$0.352453\pi$
$68$	7.84503	0.951350
$69$	4.68383	0.563867
$70$	−3.80966	−0.455341
$71$	−11.5842	−1.37479	−0.687394	−	0.726285i	$-0.741245\pi$
$71$	−11.5842	−1.37479	−0.687394	+	0.726285i	$0.741245\pi$
$72$	1.12975	0.133142
$73$	3.14006	0.367516	0.183758	−	0.982972i	$-0.441174\pi$
$73$	3.14006	0.367516	0.183758	+	0.982972i	$0.441174\pi$
$74$	−20.8481	−2.42354
$75$	0.713733	0.0824148
$76$	−2.45591	−0.281712
$77$	−3.35847	−0.382733
$78$	−4.38235	−0.496204
$79$	17.0850	1.92221	0.961107	−	0.276178i	$-0.0890678\pi$
$79$	17.0850	1.92221	0.961107	+	0.276178i	$0.0890678\pi$
$80$	10.0431	1.12285
$81$	1.00000	0.111111
$82$	12.8550	1.41959
$83$	−14.5597	−1.59813	−0.799067	−	0.601241i	$-0.794673\pi$
$83$	−14.5597	−1.59813	−0.799067	+	0.601241i	$0.794673\pi$
$84$	1.38605	0.151230
$85$	−11.7181	−1.27100
$86$	−4.98832	−0.537904
$87$	−4.29220	−0.460172
$88$	3.79422	0.404465
$89$	18.3821	1.94850	0.974248	−	0.225478i	$-0.0723943\pi$
$89$	18.3821	1.94850	0.974248	+	0.225478i	$0.0723943\pi$
$90$	3.80966	0.401573
$91$	2.38156	0.249655
$92$	−6.49202	−0.676840
$93$	4.55374	0.472201
$94$	−19.4321	−2.00427
$95$	3.66837	0.376367
$96$	−6.66688	−0.680435
$97$	7.95126	0.807328	0.403664	−	0.914907i	$-0.367736\pi$
$97$	7.95126	0.807328	0.403664	+	0.914907i	$0.367736\pi$
$98$	−1.84012	−0.185880
$99$	3.35847	0.337539
$100$	−0.989269	−0.0989269
$101$	3.40457	0.338767	0.169384	−	0.985550i	$-0.445822\pi$
$101$	3.40457	0.338767	0.169384	+	0.985550i	$0.445822\pi$
$102$	10.4151	1.03125
$103$	1.57223	0.154916	0.0774580	−	0.996996i	$-0.475320\pi$
$103$	1.57223	0.154916	0.0774580	+	0.996996i	$0.475320\pi$
$104$	−2.69055	−0.263831
$105$	−2.07033	−0.202044
$106$	22.8798	2.22229
$107$	−9.44862	−0.913432	−0.456716	−	0.889612i	$-0.650975\pi$
$107$	−9.44862	−0.913432	−0.456716	+	0.889612i	$0.650975\pi$
$108$	−1.38605	−0.133373
$109$	−14.8581	−1.42315	−0.711574	−	0.702611i	$-0.752018\pi$
$109$	−14.8581	−1.42315	−0.711574	+	0.702611i	$0.752018\pi$
$110$	12.7946	1.21992
$111$	−11.3297	−1.07537
$112$	4.85097	0.458373
$113$	−8.49065	−0.798733	−0.399367	−	0.916791i	$-0.630770\pi$
$113$	−8.49065	−0.798733	−0.399367	+	0.916791i	$0.630770\pi$
$114$	−3.26047	−0.305371
$115$	9.69708	0.904257
$116$	5.94920	0.552369
$117$	−2.38156	−0.220175
$118$	−19.1056	−1.75882
$119$	−5.66000	−0.518851
$120$	2.33895	0.213516
$121$	0.279326	0.0253933
$122$	−3.68684	−0.333791
$123$	6.98593	0.629900
$124$	−6.31170	−0.566807
$125$	11.8293	1.05805
$126$	1.84012	0.163931
$127$	−8.23379	−0.730631	−0.365315	−	0.930884i	$-0.619039\pi$
$127$	−8.23379	−0.730631	−0.365315	+	0.930884i	$0.619039\pi$
$128$	−8.61213	−0.761212
$129$	−2.71086	−0.238678
$130$	−9.07292	−0.795748
$131$	−0.0593319	−0.00518385	−0.00259193	−	0.999997i	$-0.500825\pi$
$131$	−0.0593319	−0.00518385	−0.00259193	+	0.999997i	$0.500825\pi$
$132$	−4.65500	−0.405166
$133$	1.77188	0.153641
$134$	−13.4688	−1.16353
$135$	2.07033	0.178186
$136$	6.39436	0.548312
$137$	−4.01950	−0.343409	−0.171705	−	0.985148i	$-0.554927\pi$
$137$	−4.01950	−0.343409	−0.171705	+	0.985148i	$0.554927\pi$
$138$	−8.61882	−0.733683
$139$	−8.72068	−0.739678	−0.369839	−	0.929096i	$-0.620587\pi$
$139$	−8.72068	−0.739678	−0.369839	+	0.929096i	$0.620587\pi$
$140$	2.86958	0.242524
$141$	−10.5602	−0.889331
$142$	21.3163	1.78882
$143$	−7.99839	−0.668859
$144$	−4.85097	−0.404247
$145$	−8.88628	−0.737965
$146$	−5.77808	−0.478198
$147$	−1.00000	−0.0824786
$148$	15.7036	1.29083
$149$	−12.6904	−1.03964	−0.519821	−	0.854275i	$-0.674001\pi$
$149$	−12.6904	−1.03964	−0.519821	+	0.854275i	$0.674001\pi$
$150$	−1.31336	−0.107235
$151$	0.711315	0.0578860	0.0289430	−	0.999581i	$-0.490786\pi$
$151$	0.711315	0.0578860	0.0289430	+	0.999581i	$0.490786\pi$
$152$	−2.00177	−0.162365
$153$	5.66000	0.457584
$154$	6.18000	0.497998
$155$	9.42774	0.757254
$156$	3.30095	0.264288
$157$	18.2772	1.45868	0.729339	−	0.684153i	$-0.239828\pi$
$157$	18.2772	1.45868	0.729339	+	0.684153i	$0.239828\pi$
$158$	−31.4385	−2.50111
$159$	12.4339	0.986070
$160$	−13.8026	−1.09119
$161$	4.68383	0.369138
$162$	−1.84012	−0.144574
$163$	3.07744	0.241043	0.120522	−	0.992711i	$-0.461543\pi$
$163$	3.07744	0.241043	0.120522	+	0.992711i	$0.461543\pi$
$164$	−9.68284	−0.756102
$165$	6.95314	0.541301
$166$	26.7916	2.07943
$167$	−7.68294	−0.594524	−0.297262	−	0.954796i	$-0.596073\pi$
$167$	−7.68294	−0.594524	−0.297262	+	0.954796i	$0.596073\pi$
$168$	1.12975	0.0871618
$169$	−7.32819	−0.563707
$170$	21.5627	1.65378
$171$	−1.77188	−0.135499
$172$	3.75739	0.286498
$173$	−10.7957	−0.820781	−0.410391	−	0.911910i	$-0.634608\pi$
$173$	−10.7957	−0.820781	−0.410391	+	0.911910i	$0.634608\pi$
$174$	7.89818	0.598759
$175$	0.713733	0.0539532
$176$	−16.2918	−1.22804
$177$	−10.3828	−0.780419
$178$	−33.8253	−2.53531
$179$	−20.6029	−1.53993	−0.769965	−	0.638086i	$-0.779726\pi$
$179$	−20.6029	−1.53993	−0.769965	+	0.638086i	$0.779726\pi$
$180$	−2.86958	−0.213886
$181$	15.1738	1.12786	0.563931	−	0.825822i	$-0.309288\pi$
$181$	15.1738	1.12786	0.563931	+	0.825822i	$0.309288\pi$
$182$	−4.38235	−0.324842
$183$	−2.00358	−0.148109
$184$	−5.29154	−0.390098
$185$	−23.4563	−1.72454
$186$	−8.37943	−0.614410
$187$	19.0089	1.39007
$188$	14.6370	1.06751
$189$	1.00000	0.0727393
$190$	−6.75024	−0.489714
$191$	−0.993855	−0.0719128	−0.0359564	−	0.999353i	$-0.511448\pi$
$191$	−0.993855	−0.0719128	−0.0359564	+	0.999353i	$0.511448\pi$
$192$	2.56593	0.185180
$193$	−24.6528	−1.77455	−0.887273	−	0.461245i	$-0.847403\pi$
$193$	−24.6528	−1.77455	−0.887273	+	0.461245i	$0.847403\pi$
$194$	−14.6313	−1.05047
$195$	−4.93061	−0.353088
$196$	1.38605	0.0990034
$197$	−6.23146	−0.443973	−0.221987	−	0.975050i	$-0.571254\pi$
$197$	−6.23146	−0.443973	−0.221987	+	0.975050i	$0.571254\pi$
$198$	−6.18000	−0.439193
$199$	−17.4510	−1.23707	−0.618533	−	0.785759i	$-0.712273\pi$
$199$	−17.4510	−1.23707	−0.618533	+	0.785759i	$0.712273\pi$
$200$	−0.806337	−0.0570167
$201$	−7.31952	−0.516279
$202$	−6.26482	−0.440791
$203$	−4.29220	−0.301254
$204$	−7.84503	−0.549262
$205$	14.4632	1.01015
$206$	−2.89309	−0.201571
$207$	−4.68383	−0.325549
$208$	11.5529	0.801046
$209$	−5.95079	−0.411625
$210$	3.80966	0.262891
$211$	−1.95659	−0.134697	−0.0673486	−	0.997730i	$-0.521454\pi$
$211$	−1.95659	−0.134697	−0.0673486	+	0.997730i	$0.521454\pi$
$212$	−17.2339	−1.18363
$213$	11.5842	0.793734
$214$	17.3866	1.18852
$215$	−5.61238	−0.382761
$216$	−1.12975	−0.0768695
$217$	4.55374	0.309128
$218$	27.3407	1.85175
$219$	−3.14006	−0.212185
$220$	−9.63739	−0.649753
$221$	−13.4796	−0.906737
$222$	20.8481	1.39923
$223$	25.1975	1.68735	0.843673	−	0.536857i	$-0.180389\pi$
$223$	25.1975	1.68735	0.843673	+	0.536857i	$0.180389\pi$
$224$	−6.66688	−0.445450
$225$	−0.713733	−0.0475822
$226$	15.6238	1.03928
$227$	−1.30886	−0.0868723	−0.0434362	−	0.999056i	$-0.513831\pi$
$227$	−1.30886	−0.0868723	−0.0434362	+	0.999056i	$0.513831\pi$
$228$	2.45591	0.162646
$229$	25.8601	1.70889	0.854443	−	0.519545i	$-0.173899\pi$
$229$	25.8601	1.70889	0.854443	+	0.519545i	$0.173899\pi$
$230$	−17.8438	−1.17659
$231$	3.35847	0.220971
$232$	4.84910	0.318359
$233$	−12.0419	−0.788889	−0.394445	−	0.918920i	$-0.629063\pi$
$233$	−12.0419	−0.788889	−0.394445	+	0.918920i	$0.629063\pi$
$234$	4.38235	0.286483
$235$	−21.8631	−1.42619
$236$	14.3911	0.936779
$237$	−17.0850	−1.10979
$238$	10.4151	0.675110
$239$	−9.20293	−0.595288	−0.297644	−	0.954677i	$-0.596201\pi$
$239$	−9.20293	−0.595288	−0.297644	+	0.954677i	$0.596201\pi$
$240$	−10.0431	−0.648279
$241$	10.9467	0.705140	0.352570	−	0.935785i	$-0.385308\pi$
$241$	10.9467	0.705140	0.352570	+	0.935785i	$0.385308\pi$
$242$	−0.513994	−0.0330408
$243$	−1.00000	−0.0641500
$244$	2.77707	0.177783
$245$	−2.07033	−0.132269
$246$	−12.8550	−0.819602
$247$	4.21982	0.268501
$248$	−5.14457	−0.326680
$249$	14.5597	0.922684
$250$	−21.7674	−1.37669
$251$	−22.7505	−1.43600	−0.717999	−	0.696044i	$-0.754942\pi$
$251$	−22.7505	−1.43600	−0.717999	+	0.696044i	$0.754942\pi$
$252$	−1.38605	−0.0873128
$253$	−15.7305	−0.988969
$254$	15.1512	0.950669
$255$	11.7181	0.733814
$256$	20.9792	1.31120
$257$	15.2743	0.952782	0.476391	−	0.879234i	$-0.341945\pi$
$257$	15.2743	0.952782	0.476391	+	0.879234i	$0.341945\pi$
$258$	4.98832	0.310559
$259$	−11.3297	−0.703996
$260$	6.83406	0.423830
$261$	4.29220	0.265681
$262$	0.109178	0.00674504
$263$	19.9020	1.22721	0.613605	−	0.789613i	$-0.289719\pi$
$263$	19.9020	1.22721	0.613605	+	0.789613i	$0.289719\pi$
$264$	−3.79422	−0.233518
$265$	25.7422	1.58133
$266$	−3.26047	−0.199912
$267$	−18.3821	−1.12497
$268$	10.1452	0.619717
$269$	3.74242	0.228179	0.114090	−	0.993470i	$-0.463605\pi$
$269$	3.74242	0.228179	0.114090	+	0.993470i	$0.463605\pi$
$270$	−3.80966	−0.231848
$271$	1.49694	0.0909326	0.0454663	−	0.998966i	$-0.485523\pi$
$271$	1.49694	0.0909326	0.0454663	+	0.998966i	$0.485523\pi$
$272$	−27.4565	−1.66479
$273$	−2.38156	−0.144138
$274$	7.39637	0.446831
$275$	−2.39705	−0.144548
$276$	6.49202	0.390774
$277$	5.53426	0.332522	0.166261	−	0.986082i	$-0.446831\pi$
$277$	5.53426	0.332522	0.166261	+	0.986082i	$0.446831\pi$
$278$	16.0471	0.962442
$279$	−4.55374	−0.272625
$280$	2.33895	0.139779
$281$	2.06357	0.123102	0.0615511	−	0.998104i	$-0.480395\pi$
$281$	2.06357	0.123102	0.0615511	+	0.998104i	$0.480395\pi$
$282$	19.4321	1.15716
$283$	−12.9283	−0.768510	−0.384255	−	0.923227i	$-0.625542\pi$
$283$	−12.9283	−0.768510	−0.384255	+	0.923227i	$0.625542\pi$
$284$	−16.0562	−0.952761
$285$	−3.66837	−0.217295
$286$	14.7180	0.870294
$287$	6.98593	0.412366
$288$	6.66688	0.392850
$289$	15.0356	0.884448
$290$	16.3518	0.960213
$291$	−7.95126	−0.466111
$292$	4.35227	0.254697
$293$	6.23925	0.364501	0.182251	−	0.983252i	$-0.441662\pi$
$293$	6.23925	0.364501	0.182251	+	0.983252i	$0.441662\pi$
$294$	1.84012	0.107318
$295$	−21.4958	−1.25154
$296$	12.7997	0.743969
$297$	−3.35847	−0.194878
$298$	23.3520	1.35274
$299$	11.1548	0.645099
$300$	0.989269	0.0571155
$301$	−2.71086	−0.156251
$302$	−1.30891	−0.0753191
$303$	−3.40457	−0.195587
$304$	8.59531	0.492975
$305$	−4.14808	−0.237518
$306$	−10.4151	−0.595391
$307$	−3.67020	−0.209469	−0.104735	−	0.994500i	$-0.533399\pi$
$307$	−3.67020	−0.209469	−0.104735	+	0.994500i	$0.533399\pi$
$308$	−4.65500	−0.265243
$309$	−1.57223	−0.0894408
$310$	−17.3482	−0.985311
$311$	10.6503	0.603923	0.301962	−	0.953320i	$-0.402359\pi$
$311$	10.6503	0.603923	0.301962	+	0.953320i	$0.402359\pi$
$312$	2.69055	0.152323
$313$	−20.5436	−1.16119	−0.580597	−	0.814191i	$-0.697181\pi$
$313$	−20.5436	−1.16119	−0.580597	+	0.814191i	$0.697181\pi$
$314$	−33.6322	−1.89798
$315$	2.07033	0.116650
$316$	23.6806	1.33214
$317$	19.8684	1.11592	0.557961	−	0.829867i	$-0.311584\pi$
$317$	19.8684	1.11592	0.557961	+	0.829867i	$0.311584\pi$
$318$	−22.8798	−1.28304
$319$	14.4152	0.807098
$320$	5.31233	0.296968
$321$	9.44862	0.527370
$322$	−8.61882	−0.480308
$323$	−10.0288	−0.558018
$324$	1.38605	0.0770027
$325$	1.69980	0.0942877
$326$	−5.66286	−0.313637
$327$	14.8581	0.821655
$328$	−7.89233	−0.435781
$329$	−10.5602	−0.582204
$330$	−12.7946	−0.704321
$331$	7.73682	0.425254	0.212627	−	0.977133i	$-0.431798\pi$
$331$	7.73682	0.425254	0.212627	+	0.977133i	$0.431798\pi$
$332$	−20.1804	−1.10755
$333$	11.3297	0.620866
$334$	14.1376	0.773573
$335$	−15.1538	−0.827941
$336$	−4.85097	−0.264642
$337$	12.1854	0.663783	0.331892	−	0.943318i	$-0.392313\pi$
$337$	12.1854	0.663783	0.331892	+	0.943318i	$0.392313\pi$
$338$	13.4848	0.733474
$339$	8.49065	0.461149
$340$	−16.2418	−0.880836
$341$	−15.2936	−0.828195
$342$	3.26047	0.176306
$343$	−1.00000	−0.0539949
$344$	3.06259	0.165124
$345$	−9.69708	−0.522073
$346$	19.8654	1.06797
$347$	−21.7515	−1.16768	−0.583842	−	0.811867i	$-0.698451\pi$
$347$	−21.7515	−1.16768	−0.583842	+	0.811867i	$0.698451\pi$
$348$	−5.94920	−0.318911
$349$	−5.95553	−0.318792	−0.159396	−	0.987215i	$-0.550955\pi$
$349$	−5.95553	−0.318792	−0.159396	+	0.987215i	$0.550955\pi$
$350$	−1.31336	−0.0702019
$351$	2.38156	0.127118
$352$	22.3905	1.19342
$353$	25.4315	1.35358	0.676791	−	0.736176i	$-0.263370\pi$
$353$	25.4315	1.35358	0.676791	+	0.736176i	$0.263370\pi$
$354$	19.1056	1.01545
$355$	23.9831	1.27289
$356$	25.4785	1.35036
$357$	5.66000	0.299559
$358$	37.9118	2.00370
$359$	23.4100	1.23553	0.617766	−	0.786362i	$-0.288038\pi$
$359$	23.4100	1.23553	0.617766	+	0.786362i	$0.288038\pi$
$360$	−2.33895	−0.123273
$361$	−15.8605	−0.834761
$362$	−27.9217	−1.46753
$363$	−0.279326	−0.0146608
$364$	3.30095	0.173017
$365$	−6.50095	−0.340275
$366$	3.68684	0.192714
$367$	11.0295	0.575736	0.287868	−	0.957670i	$-0.407054\pi$
$367$	11.0295	0.575736	0.287868	+	0.957670i	$0.407054\pi$
$368$	22.7211	1.18442
$369$	−6.98593	−0.363673
$370$	43.1625	2.24391
$371$	12.4339	0.645534
$372$	6.31170	0.327246
$373$	12.0217	0.622461	0.311230	−	0.950334i	$-0.399259\pi$
$373$	12.0217	0.622461	0.311230	+	0.950334i	$0.399259\pi$
$374$	−34.9788	−1.80871
$375$	−11.8293	−0.610863
$376$	11.9304	0.615262
$377$	−10.2221	−0.526466
$378$	−1.84012	−0.0946457
$379$	−17.7513	−0.911825	−0.455913	−	0.890025i	$-0.650687\pi$
$379$	−17.7513	−0.911825	−0.455913	+	0.890025i	$0.650687\pi$
$380$	5.08453	0.260831
$381$	8.23379	0.421830
$382$	1.82881	0.0935703
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	8.61213	0.439486
$385$	6.95314	0.354365
$386$	45.3641	2.30897
$387$	2.71086	0.137801
$388$	11.0208	0.559498
$389$	15.0306	0.762083	0.381042	−	0.924558i	$-0.375565\pi$
$389$	15.0306	0.762083	0.381042	+	0.924558i	$0.375565\pi$
$390$	9.07292	0.459425
$391$	−26.5105	−1.34069
$392$	1.12975	0.0570608
$393$	0.0593319	0.00299290
$394$	11.4666	0.577681
$395$	−35.3716	−1.77974
$396$	4.65500	0.233923
$397$	1.35083	0.0677963	0.0338981	−	0.999425i	$-0.489208\pi$
$397$	1.35083	0.0677963	0.0338981	+	0.999425i	$0.489208\pi$
$398$	32.1119	1.60963
$399$	−1.77188	−0.0887047
$400$	3.46230	0.173115
$401$	−13.7249	−0.685390	−0.342695	−	0.939447i	$-0.611340\pi$
$401$	−13.7249	−0.685390	−0.342695	+	0.939447i	$0.611340\pi$
$402$	13.4688	0.671763
$403$	10.8450	0.540227
$404$	4.71889	0.234774
$405$	−2.07033	−0.102876
$406$	7.89818	0.391980
$407$	38.0506	1.88610
$408$	−6.39436	−0.316568
$409$	−3.03187	−0.149916	−0.0749581	−	0.997187i	$-0.523882\pi$
$409$	−3.03187	−0.149916	−0.0749581	+	0.997187i	$0.523882\pi$
$410$	−26.6140	−1.31437
$411$	4.01950	0.198267
$412$	2.17918	0.107360
$413$	−10.3828	−0.510904
$414$	8.61882	0.423592
$415$	30.1434	1.47968
$416$	−15.8775	−0.778461
$417$	8.72068	0.427053
$418$	10.9502	0.535591
$419$	4.21293	0.205815	0.102907	−	0.994691i	$-0.467185\pi$
$419$	4.21293	0.205815	0.102907	+	0.994691i	$0.467185\pi$
$420$	−2.86958	−0.140021
$421$	−38.2780	−1.86556	−0.932779	−	0.360450i	$-0.882623\pi$
$421$	−38.2780	−1.86556	−0.932779	+	0.360450i	$0.882623\pi$
$422$	3.60037	0.175263
$423$	10.5602	0.513455
$424$	−14.0471	−0.682188
$425$	−4.03973	−0.195956
$426$	−21.3163	−1.03278
$427$	−2.00358	−0.0969603
$428$	−13.0962	−0.633031
$429$	7.99839	0.386166
$430$	10.3275	0.498034
$431$	−11.0511	−0.532311	−0.266156	−	0.963930i	$-0.585754\pi$
$431$	−11.0511	−0.532311	−0.266156	+	0.963930i	$0.585754\pi$
$432$	4.85097	0.233392
$433$	7.08996	0.340722	0.170361	−	0.985382i	$-0.445507\pi$
$433$	7.08996	0.340722	0.170361	+	0.985382i	$0.445507\pi$
$434$	−8.37943	−0.402226
$435$	8.88628	0.426064
$436$	−20.5941	−0.986277
$437$	8.29917	0.397003
$438$	5.77808	0.276088
$439$	−18.4839	−0.882188	−0.441094	−	0.897461i	$-0.645410\pi$
$439$	−18.4839	−0.882188	−0.441094	+	0.897461i	$0.645410\pi$
$440$	−7.85529	−0.374486
$441$	1.00000	0.0476190
$442$	24.8041	1.17981
$443$	8.43096	0.400567	0.200283	−	0.979738i	$-0.435814\pi$
$443$	8.43096	0.400567	0.200283	+	0.979738i	$0.435814\pi$
$444$	−15.7036	−0.745259
$445$	−38.0570	−1.80407
$446$	−46.3664	−2.19551
$447$	12.6904	0.600238
$448$	2.56593	0.121229
$449$	2.70156	0.127495	0.0637474	−	0.997966i	$-0.479695\pi$
$449$	2.70156	0.127495	0.0637474	+	0.997966i	$0.479695\pi$
$450$	1.31336	0.0619122
$451$	−23.4620	−1.10478
$452$	−11.7684	−0.553541
$453$	−0.711315	−0.0334205
$454$	2.40847	0.113035
$455$	−4.93061	−0.231150
$456$	2.00177	0.0937414
$457$	2.15597	0.100852	0.0504261	−	0.998728i	$-0.483942\pi$
$457$	2.15597	0.100852	0.0504261	+	0.998728i	$0.483942\pi$
$458$	−47.5858	−2.22354
$459$	−5.66000	−0.264186
$460$	13.4406	0.626672
$461$	34.1712	1.59151	0.795756	−	0.605618i	$-0.207074\pi$
$461$	34.1712	1.59151	0.795756	+	0.605618i	$0.207074\pi$
$462$	−6.18000	−0.287519
$463$	28.1047	1.30614	0.653069	−	0.757298i	$-0.273481\pi$
$463$	28.1047	1.30614	0.653069	+	0.757298i	$0.273481\pi$
$464$	−20.8213	−0.966606
$465$	−9.42774	−0.437201
$466$	22.1585	1.02647
$467$	−29.1090	−1.34700	−0.673502	−	0.739185i	$-0.735211\pi$
$467$	−29.1090	−1.34700	−0.673502	+	0.739185i	$0.735211\pi$
$468$	−3.30095	−0.152587
$469$	−7.31952	−0.337984
$470$	40.2308	1.85571
$471$	−18.2772	−0.842168
$472$	11.7299	0.539914
$473$	9.10435	0.418618
$474$	31.4385	1.44402
$475$	1.26465	0.0580260
$476$	−7.84503	−0.359577
$477$	−12.4339	−0.569308
$478$	16.9345	0.774567
$479$	−3.57235	−0.163225	−0.0816123	−	0.996664i	$-0.526007\pi$
$479$	−3.57235	−0.163225	−0.0816123	+	0.996664i	$0.526007\pi$
$480$	13.8026	0.630001
$481$	−26.9824	−1.23029
$482$	−20.1433	−0.917502
$483$	−4.68383	−0.213122
$484$	0.387159	0.0175981
$485$	−16.4617	−0.747489
$486$	1.84012	0.0834696
$487$	38.5171	1.74537	0.872687	−	0.488279i	$-0.162375\pi$
$487$	38.5171	1.74537	0.872687	+	0.488279i	$0.162375\pi$
$488$	2.26354	0.102466
$489$	−3.07744	−0.139167
$490$	3.80966	0.172103
$491$	6.88055	0.310515	0.155258	−	0.987874i	$-0.450379\pi$
$491$	6.88055	0.310515	0.155258	+	0.987874i	$0.450379\pi$
$492$	9.68284	0.436536
$493$	24.2939	1.09414
$494$	−7.76499	−0.349363
$495$	−6.95314	−0.312521
$496$	22.0900	0.991872
$497$	11.5842	0.519621
$498$	−26.7916	−1.20056
$499$	9.43827	0.422515	0.211257	−	0.977430i	$-0.432244\pi$
$499$	9.43827	0.422515	0.211257	+	0.977430i	$0.432244\pi$
$500$	16.3960	0.733251
$501$	7.68294	0.343249
$502$	41.8637	1.86847
$503$	44.0872	1.96575	0.982875	−	0.184276i	$-0.0589939\pi$
$503$	44.0872	1.96575	0.982875	+	0.184276i	$0.0589939\pi$
$504$	−1.12975	−0.0503229
$505$	−7.04858	−0.313658
$506$	28.9461	1.28681
$507$	7.32819	0.325456
$508$	−11.4124	−0.506345
$509$	−9.51422	−0.421711	−0.210855	−	0.977517i	$-0.567625\pi$
$509$	−9.51422	−0.421711	−0.210855	+	0.977517i	$0.567625\pi$
$510$	−21.5627	−0.954811
$511$	−3.14006	−0.138908
$512$	−21.3801	−0.944875
$513$	1.77188	0.0782302
$514$	−28.1065	−1.23972
$515$	−3.25502	−0.143434
$516$	−3.75739	−0.165410
$517$	35.4662	1.55980
$518$	20.8481	0.916013
$519$	10.7957	0.473878
$520$	5.57033	0.244275
$521$	−30.1592	−1.32130	−0.660649	−	0.750695i	$-0.729719\pi$
$521$	−30.1592	−1.32130	−0.660649	+	0.750695i	$0.729719\pi$
$522$	−7.89818	−0.345694
$523$	28.5115	1.24672	0.623360	−	0.781935i	$-0.285767\pi$
$523$	28.5115	1.24672	0.623360	+	0.781935i	$0.285767\pi$
$524$	−0.0822369	−0.00359254
$525$	−0.713733	−0.0311499
$526$	−36.6221	−1.59680
$527$	−25.7742	−1.12274
$528$	16.2918	0.709011
$529$	−1.06171	−0.0461615
$530$	−47.3688	−2.05757
$531$	10.3828	0.450575
$532$	2.45591	0.106477
$533$	16.6374	0.720645
$534$	33.8253	1.46376
$535$	19.5618	0.845729
$536$	8.26920	0.357175
$537$	20.6029	0.889079
$538$	−6.88651	−0.296898
$539$	3.35847	0.144660
$540$	2.86958	0.123487
$541$	9.71125	0.417519	0.208760	−	0.977967i	$-0.433057\pi$
$541$	9.71125	0.417519	0.208760	+	0.977967i	$0.433057\pi$
$542$	−2.75455	−0.118318
$543$	−15.1738	−0.651172
$544$	37.7345	1.61785
$545$	30.7612	1.31766
$546$	4.38235	0.187547
$547$	11.3160	0.483837	0.241918	−	0.970297i	$-0.422223\pi$
$547$	11.3160	0.483837	0.241918	+	0.970297i	$0.422223\pi$
$548$	−5.57122	−0.237991
$549$	2.00358	0.0855109
$550$	4.41087	0.188080
$551$	−7.60525	−0.323995
$552$	5.29154	0.225223
$553$	−17.0850	−0.726528
$554$	−10.1837	−0.432665
$555$	23.4563	0.995665
$556$	−12.0873	−0.512615
$557$	22.4874	0.952823	0.476411	−	0.879223i	$-0.341937\pi$
$557$	22.4874	0.952823	0.476411	+	0.879223i	$0.341937\pi$
$558$	8.37943	0.354730
$559$	−6.45607	−0.273063
$560$	−10.0431	−0.424399
$561$	−19.0089	−0.802558
$562$	−3.79722	−0.160176
$563$	12.5056	0.527050	0.263525	−	0.964653i	$-0.415115\pi$
$563$	12.5056	0.527050	0.263525	+	0.964653i	$0.415115\pi$
$564$	−14.6370	−0.616328
$565$	17.5784	0.739531
$566$	23.7897	0.999956
$567$	−1.00000	−0.0419961
$568$	−13.0872	−0.549125
$569$	1.64643	0.0690221	0.0345110	−	0.999404i	$-0.489013\pi$
$569$	1.64643	0.0690221	0.0345110	+	0.999404i	$0.489013\pi$
$570$	6.75024	0.282737
$571$	−17.4457	−0.730080	−0.365040	−	0.930992i	$-0.618945\pi$
$571$	−17.4457	−0.730080	−0.365040	+	0.930992i	$0.618945\pi$
$572$	−11.0862	−0.463535
$573$	0.993855	0.0415189
$574$	−12.8550	−0.536556
$575$	3.34301	0.139413
$576$	−2.56593	−0.106914
$577$	3.48750	0.145187	0.0725933	−	0.997362i	$-0.476872\pi$
$577$	3.48750	0.145187	0.0725933	+	0.997362i	$0.476872\pi$
$578$	−27.6674	−1.15081
$579$	24.6528	1.02453
$580$	−12.3168	−0.511428
$581$	14.5597	0.604038
$582$	14.6313	0.606487
$583$	−41.7588	−1.72947
$584$	3.54746	0.146795
$585$	4.93061	0.203856
$586$	−11.4810	−0.474275
$587$	−20.6844	−0.853737	−0.426869	−	0.904314i	$-0.640383\pi$
$587$	−20.6844	−0.853737	−0.426869	+	0.904314i	$0.640383\pi$
$588$	−1.38605	−0.0571597
$589$	8.06866	0.332463
$590$	39.5550	1.62845
$591$	6.23146	0.256328
$592$	−54.9602	−2.25885
$593$	−3.21011	−0.131823	−0.0659117	−	0.997825i	$-0.520996\pi$
$593$	−3.21011	−0.131823	−0.0659117	+	0.997825i	$0.520996\pi$
$594$	6.18000	0.253568
$595$	11.7181	0.480394
$596$	−17.5896	−0.720497
$597$	17.4510	0.714221
$598$	−20.5262	−0.839379
$599$	5.71474	0.233498	0.116749	−	0.993161i	$-0.462753\pi$
$599$	5.71474	0.233498	0.116749	+	0.993161i	$0.462753\pi$
$600$	0.806337	0.0329186
$601$	−11.4534	−0.467193	−0.233596	−	0.972334i	$-0.575049\pi$
$601$	−11.4534	−0.467193	−0.233596	+	0.972334i	$0.575049\pi$
$602$	4.98832	0.203309
$603$	7.31952	0.298074
$604$	0.985917	0.0401164
$605$	−0.578297	−0.0235111
$606$	6.26482	0.254491
$607$	10.7828	0.437660	0.218830	−	0.975763i	$-0.429776\pi$
$607$	10.7828	0.437660	0.218830	+	0.975763i	$0.429776\pi$
$608$	−11.8129	−0.479075
$609$	4.29220	0.173929
$610$	7.63298	0.309050
$611$	−25.1498	−1.01745
$612$	7.84503	0.317117
$613$	33.4992	1.35302	0.676511	−	0.736433i	$-0.263491\pi$
$613$	33.4992	1.35302	0.676511	+	0.736433i	$0.263491\pi$
$614$	6.75361	0.272554
$615$	−14.4632	−0.583212
$616$	−3.79422	−0.152873
$617$	−0.929054	−0.0374023	−0.0187012	−	0.999825i	$-0.505953\pi$
$617$	−0.929054	−0.0374023	−0.0187012	+	0.999825i	$0.505953\pi$
$618$	2.89309	0.116377
$619$	1.12137	0.0450715	0.0225357	−	0.999746i	$-0.492826\pi$
$619$	1.12137	0.0450715	0.0225357	+	0.999746i	$0.492826\pi$
$620$	13.0673	0.524796
$621$	4.68383	0.187956
$622$	−19.5979	−0.785803
$623$	−18.3821	−0.736462
$624$	−11.5529	−0.462484
$625$	−20.9219	−0.836877
$626$	37.8028	1.51090
$627$	5.95079	0.237652
$628$	25.3330	1.01090
$629$	64.1264	2.55689
$630$	−3.80966	−0.151780
$631$	−13.0594	−0.519887	−0.259944	−	0.965624i	$-0.583704\pi$
$631$	−13.0594	−0.519887	−0.259944	+	0.965624i	$0.583704\pi$
$632$	19.3017	0.767781
$633$	1.95659	0.0777675
$634$	−36.5603	−1.45200
$635$	17.0467	0.676476
$636$	17.2339	0.683370
$637$	−2.38156	−0.0943607
$638$	−26.5258	−1.05017
$639$	−11.5842	−0.458263
$640$	17.8299	0.704790
$641$	15.8658	0.626660	0.313330	−	0.949644i	$-0.398555\pi$
$641$	15.8658	0.626660	0.313330	+	0.949644i	$0.398555\pi$
$642$	−17.3866	−0.686195
$643$	−13.2859	−0.523944	−0.261972	−	0.965075i	$-0.584373\pi$
$643$	−13.2859	−0.523944	−0.261972	+	0.965075i	$0.584373\pi$
$644$	6.49202	0.255821
$645$	5.61238	0.220987
$646$	18.4542	0.726073
$647$	10.6071	0.417010	0.208505	−	0.978021i	$-0.433140\pi$
$647$	10.6071	0.417010	0.208505	+	0.978021i	$0.433140\pi$
$648$	1.12975	0.0443806
$649$	34.8703	1.36878
$650$	−3.12783	−0.122684
$651$	−4.55374	−0.178475
$652$	4.26548	0.167049
$653$	6.32325	0.247448	0.123724	−	0.992317i	$-0.460516\pi$
$653$	6.32325	0.247448	0.123724	+	0.992317i	$0.460516\pi$
$654$	−27.3407	−1.06911
$655$	0.122837	0.00479962
$656$	33.8885	1.32312
$657$	3.14006	0.122505
$658$	19.4321	0.757542
$659$	31.9620	1.24506	0.622532	−	0.782595i	$-0.286104\pi$
$659$	31.9620	1.24506	0.622532	+	0.782595i	$0.286104\pi$
$660$	9.63739	0.375135
$661$	7.92854	0.308384	0.154192	−	0.988041i	$-0.450722\pi$
$661$	7.92854	0.308384	0.154192	+	0.988041i	$0.450722\pi$
$662$	−14.2367	−0.553325
$663$	13.4796	0.523505
$664$	−16.4488	−0.638336
$665$	−3.66837	−0.142253
$666$	−20.8481	−0.807848
$667$	−20.1040	−0.778428
$668$	−10.6489	−0.412020
$669$	−25.1975	−0.974190
$670$	27.8849	1.07729
$671$	6.72898	0.259769
$672$	6.66688	0.257180
$673$	49.3786	1.90341	0.951703	−	0.307019i	$-0.0993317\pi$
$673$	49.3786	1.90341	0.951703	+	0.307019i	$0.0993317\pi$
$674$	−22.4227	−0.863690
$675$	0.713733	0.0274716
$676$	−10.1572	−0.390662
$677$	−12.4392	−0.478079	−0.239039	−	0.971010i	$-0.576833\pi$
$677$	−12.4392	−0.478079	−0.239039	+	0.971010i	$0.576833\pi$
$678$	−15.6238	−0.600030
$679$	−7.95126	−0.305141
$680$	−13.2384	−0.507671
$681$	1.30886	0.0501558
$682$	28.1421	1.07762
$683$	−40.6111	−1.55394	−0.776970	−	0.629538i	$-0.783244\pi$
$683$	−40.6111	−1.55394	−0.776970	+	0.629538i	$0.783244\pi$
$684$	−2.45591	−0.0939039
$685$	8.32170	0.317956
$686$	1.84012	0.0702562
$687$	−25.8601	−0.986626
$688$	−13.1503	−0.501351
$689$	29.6120	1.12813
$690$	17.8438	0.679302
$691$	10.8503	0.412764	0.206382	−	0.978471i	$-0.433831\pi$
$691$	10.8503	0.412764	0.206382	+	0.978471i	$0.433831\pi$
$692$	−14.9634	−0.568821
$693$	−3.35847	−0.127578
$694$	40.0255	1.51935
$695$	18.0547	0.684853
$696$	−4.84910	−0.183805
$697$	−39.5404	−1.49770
$698$	10.9589	0.414800
$699$	12.0419	0.455465
$700$	0.989269	0.0373909
$701$	−19.6737	−0.743067	−0.371534	−	0.928420i	$-0.621168\pi$
$701$	−19.6737	−0.743067	−0.371534	+	0.928420i	$0.621168\pi$
$702$	−4.38235	−0.165401
$703$	−20.0749	−0.757139
$704$	−8.61761	−0.324789
$705$	21.8631	0.823413
$706$	−46.7970	−1.76123
$707$	−3.40457	−0.128042
$708$	−14.3911	−0.540849
$709$	−42.5450	−1.59781	−0.798906	−	0.601456i	$-0.794588\pi$
$709$	−42.5450	−1.59781	−0.798906	+	0.601456i	$0.794588\pi$
$710$	−44.1317	−1.65623
$711$	17.0850	0.640738
$712$	20.7671	0.778279
$713$	21.3289	0.798775
$714$	−10.4151	−0.389775
$715$	16.5593	0.619283
$716$	−28.5566	−1.06721
$717$	9.20293	0.343690
$718$	−43.0773	−1.60763
$719$	25.0299	0.933458	0.466729	−	0.884400i	$-0.345432\pi$
$719$	25.0299	0.933458	0.466729	+	0.884400i	$0.345432\pi$
$720$	10.0431	0.374284
$721$	−1.57223	−0.0585527
$722$	29.1852	1.08616
$723$	−10.9467	−0.407113
$724$	21.0317	0.781636
$725$	−3.06349	−0.113775
$726$	0.513994	0.0190761
$727$	11.2454	0.417069	0.208535	−	0.978015i	$-0.433131\pi$
$727$	11.2454	0.417069	0.208535	+	0.978015i	$0.433131\pi$
$728$	2.69055	0.0997186
$729$	1.00000	0.0370370
$730$	11.9625	0.442754
$731$	15.3435	0.567499
$732$	−2.77707	−0.102643
$733$	5.35361	0.197740	0.0988701	−	0.995100i	$-0.468477\pi$
$733$	5.35361	0.197740	0.0988701	+	0.995100i	$0.468477\pi$
$734$	−20.2956	−0.749126
$735$	2.07033	0.0763653
$736$	−31.2265	−1.15103
$737$	24.5824	0.905504
$738$	12.8550	0.473198
$739$	−11.0117	−0.405072	−0.202536	−	0.979275i	$-0.564918\pi$
$739$	−11.0117	−0.405072	−0.202536	+	0.979275i	$0.564918\pi$
$740$	−32.5116	−1.19515
$741$	−4.21982	−0.155019
$742$	−22.8798	−0.839945
$743$	−37.4219	−1.37288	−0.686438	−	0.727189i	$-0.740827\pi$
$743$	−37.4219	−1.37288	−0.686438	+	0.727189i	$0.740827\pi$
$744$	5.14457	0.188609
$745$	26.2734	0.962584
$746$	−22.1214	−0.809923
$747$	−14.5597	−0.532712
$748$	26.3473	0.963353
$749$	9.44862	0.345245
$750$	21.7674	0.794832
$751$	22.8958	0.835479	0.417740	−	0.908567i	$-0.362822\pi$
$751$	22.8958	0.835479	0.417740	+	0.908567i	$0.362822\pi$
$752$	−51.2273	−1.86807
$753$	22.7505	0.829074
$754$	18.8100	0.685018
$755$	−1.47266	−0.0535955
$756$	1.38605	0.0504101
$757$	42.3785	1.54027	0.770137	−	0.637878i	$-0.220188\pi$
$757$	42.3785	1.54027	0.770137	+	0.637878i	$0.220188\pi$
$758$	32.6646	1.18643
$759$	15.7305	0.570981
$760$	4.14432	0.150330
$761$	−34.2375	−1.24111	−0.620554	−	0.784164i	$-0.713092\pi$
$761$	−34.2375	−1.24111	−0.620554	+	0.784164i	$0.713092\pi$
$762$	−15.1512	−0.548869
$763$	14.8581	0.537900
$764$	−1.37753	−0.0498373
$765$	−11.7181	−0.423668
$766$	−1.84012	−0.0664863
$767$	−24.7272	−0.892849
$768$	−20.9792	−0.757023
$769$	−13.5171	−0.487437	−0.243719	−	0.969846i	$-0.578367\pi$
$769$	−13.5171	−0.487437	−0.243719	+	0.969846i	$0.578367\pi$
$770$	−12.7946	−0.461086
$771$	−15.2743	−0.550089
$772$	−34.1699	−1.22980
$773$	10.7759	0.387584	0.193792	−	0.981043i	$-0.437921\pi$
$773$	10.7759	0.387584	0.193792	+	0.981043i	$0.437921\pi$
$774$	−4.98832	−0.179301
$775$	3.25015	0.116749
$776$	8.98291	0.322468
$777$	11.3297	0.406452
$778$	−27.6582	−0.991594
$779$	12.3782	0.443495
$780$	−6.83406	−0.244699
$781$	−38.9051	−1.39213
$782$	48.7825	1.74446
$783$	−4.29220	−0.153391
$784$	−4.85097	−0.173249
$785$	−37.8398	−1.35056
$786$	−0.109178	−0.00389425
$787$	47.5834	1.69617	0.848083	−	0.529863i	$-0.177757\pi$
$787$	47.5834	1.69617	0.848083	+	0.529863i	$0.177757\pi$
$788$	−8.63711	−0.307684
$789$	−19.9020	−0.708530
$790$	65.0881	2.31573
$791$	8.49065	0.301893
$792$	3.79422	0.134822
$793$	−4.77165	−0.169446
$794$	−2.48569	−0.0882140
$795$	−25.7422	−0.912982
$796$	−24.1879	−0.857317
$797$	13.5294	0.479236	0.239618	−	0.970867i	$-0.422978\pi$
$797$	13.5294	0.479236	0.239618	+	0.970867i	$0.422978\pi$
$798$	3.26047	0.115419
$799$	59.7708	2.11454
$800$	−4.75837	−0.168234
$801$	18.3821	0.649499
$802$	25.2555	0.891804
$803$	10.5458	0.372153
$804$	−10.1452	−0.357794
$805$	−9.69708	−0.341777
$806$	−19.9561	−0.702923
$807$	−3.74242	−0.131739
$808$	3.84630	0.135312
$809$	−51.3894	−1.80676	−0.903378	−	0.428845i	$-0.858921\pi$
$809$	−51.3894	−1.80676	−0.903378	+	0.428845i	$0.858921\pi$
$810$	3.80966	0.133858
$811$	15.3407	0.538686	0.269343	−	0.963044i	$-0.413193\pi$
$811$	15.3407	0.538686	0.269343	+	0.963044i	$0.413193\pi$
$812$	−5.94920	−0.208776
$813$	−1.49694	−0.0525000
$814$	−70.0178	−2.45412
$815$	−6.37131	−0.223177
$816$	27.4565	0.961169
$817$	−4.80331	−0.168047
$818$	5.57900	0.195065
$819$	2.38156	0.0832183
$820$	20.0467	0.700060
$821$	−1.70944	−0.0596599	−0.0298299	−	0.999555i	$-0.509497\pi$
$821$	−1.70944	−0.0596599	−0.0298299	+	0.999555i	$0.509497\pi$
$822$	−7.39637	−0.257978
$823$	13.4954	0.470421	0.235211	−	0.971944i	$-0.424422\pi$
$823$	13.4954	0.470421	0.235211	+	0.971944i	$0.424422\pi$
$824$	1.77621	0.0618774
$825$	2.39705	0.0834547
$826$	19.1056	0.664770
$827$	−0.0494304	−0.00171886	−0.000859431	−	1.00000i	$-0.500274\pi$
$827$	−0.0494304	−0.00171886	−0.000859431		1.00000i	$0.500274\pi$
$828$	−6.49202	−0.225613
$829$	21.8305	0.758206	0.379103	−	0.925355i	$-0.376233\pi$
$829$	21.8305	0.758206	0.379103	+	0.925355i	$0.376233\pi$
$830$	−55.4675	−1.92531
$831$	−5.53426	−0.191981
$832$	6.11092	0.211858
$833$	5.66000	0.196107
$834$	−16.0471	−0.555666
$835$	15.9062	0.550458
$836$	−8.24809	−0.285266
$837$	4.55374	0.157400
$838$	−7.75230	−0.267799
$839$	−10.6998	−0.369398	−0.184699	−	0.982795i	$-0.559131\pi$
$839$	−10.6998	−0.369398	−0.184699	+	0.982795i	$0.559131\pi$
$840$	−2.33895	−0.0807013
$841$	−10.5770	−0.364724
$842$	70.4362	2.42739
$843$	−2.06357	−0.0710730
$844$	−2.71193	−0.0933485
$845$	15.1718	0.521925
$846$	−19.4321	−0.668089
$847$	−0.279326	−0.00959775
$848$	60.3163	2.07127
$849$	12.9283	0.443699
$850$	7.43360	0.254970
$851$	−53.0666	−1.81910
$852$	16.0562	0.550077
$853$	−10.0960	−0.345681	−0.172841	−	0.984950i	$-0.555295\pi$
$853$	−10.0960	−0.345681	−0.172841	+	0.984950i	$0.555295\pi$
$854$	3.68684	0.126161
$855$	3.66837	0.125456
$856$	−10.6745	−0.364848
$857$	35.5830	1.21549	0.607746	−	0.794132i	$-0.292074\pi$
$857$	35.5830	1.21549	0.607746	+	0.794132i	$0.292074\pi$
$858$	−14.7180	−0.502465
$859$	50.8457	1.73483	0.867417	−	0.497582i	$-0.165779\pi$
$859$	50.8457	1.73483	0.867417	+	0.497582i	$0.165779\pi$
$860$	−7.77903	−0.265263
$861$	−6.98593	−0.238080
$862$	20.3353	0.692623
$863$	4.91709	0.167380	0.0836899	−	0.996492i	$-0.473329\pi$
$863$	4.91709	0.167380	0.0836899	+	0.996492i	$0.473329\pi$
$864$	−6.66688	−0.226812
$865$	22.3507	0.759945
$866$	−13.0464	−0.443335
$867$	−15.0356	−0.510636
$868$	6.31170	0.214233
$869$	57.3795	1.94647
$870$	−16.3518	−0.554379
$871$	−17.4318	−0.590656
$872$	−16.7859	−0.568442
$873$	7.95126	0.269109
$874$	−15.2715	−0.516566
$875$	−11.8293	−0.399904
$876$	−4.35227	−0.147050
$877$	56.1640	1.89652	0.948262	−	0.317490i	$-0.102840\pi$
$877$	56.1640	1.89652	0.948262	+	0.317490i	$0.102840\pi$
$878$	34.0126	1.14787
$879$	−6.23925	−0.210445
$880$	33.7295	1.13702
$881$	25.8173	0.869806	0.434903	−	0.900477i	$-0.356783\pi$
$881$	25.8173	0.869806	0.434903	+	0.900477i	$0.356783\pi$
$882$	−1.84012	−0.0619601
$883$	33.5804	1.13007	0.565035	−	0.825067i	$-0.308863\pi$
$883$	33.5804	1.13007	0.565035	+	0.825067i	$0.308863\pi$
$884$	−18.6834	−0.628391
$885$	21.4958	0.722575
$886$	−15.5140	−0.521203
$887$	26.0466	0.874559	0.437280	−	0.899326i	$-0.355942\pi$
$887$	26.0466	0.874559	0.437280	+	0.899326i	$0.355942\pi$
$888$	−12.7997	−0.429531
$889$	8.23379	0.276152
$890$	70.0295	2.34739
$891$	3.35847	0.112513
$892$	34.9249	1.16937
$893$	−18.7114	−0.626153
$894$	−23.3520	−0.781007
$895$	42.6547	1.42579
$896$	8.61213	0.287711
$897$	−11.1548	−0.372448
$898$	−4.97121	−0.165891
$899$	−19.5456	−0.651881
$900$	−0.989269	−0.0329756
$901$	−70.3757	−2.34456
$902$	43.1730	1.43750
$903$	2.71086	0.0902118
$904$	−9.59228	−0.319034
$905$	−31.4149	−1.04427
$906$	1.30891	0.0434855
$907$	−23.3157	−0.774184	−0.387092	−	0.922041i	$-0.626520\pi$
$907$	−23.3157	−0.774184	−0.387092	+	0.922041i	$0.626520\pi$
$908$	−1.81415	−0.0602046
$909$	3.40457	0.112922
$910$	9.07292	0.300764
$911$	−44.1166	−1.46165	−0.730824	−	0.682566i	$-0.760864\pi$
$911$	−44.1166	−1.46165	−0.730824	+	0.682566i	$0.760864\pi$
$912$	−8.59531	−0.284619
$913$	−48.8983	−1.61830
$914$	−3.96725	−0.131225
$915$	4.14808	0.137131
$916$	35.8434	1.18430
$917$	0.0593319	0.00195931
$918$	10.4151	0.343749
$919$	42.5758	1.40445	0.702223	−	0.711957i	$-0.252191\pi$
$919$	42.5758	1.40445	0.702223	+	0.711957i	$0.252191\pi$
$920$	10.9552	0.361183
$921$	3.67020	0.120937
$922$	−62.8792	−2.07081
$923$	27.5884	0.908082
$924$	4.65500	0.153138
$925$	−8.08642	−0.265880
$926$	−51.7162	−1.69950
$927$	1.57223	0.0516386
$928$	28.6156	0.939353
$929$	20.9959	0.688852	0.344426	−	0.938813i	$-0.388074\pi$
$929$	20.9959	0.688852	0.344426	+	0.938813i	$0.388074\pi$
$930$	17.3482	0.568870
$931$	−1.77188	−0.0580709
$932$	−16.6906	−0.546719
$933$	−10.6503	−0.348675
$934$	53.5641	1.75267
$935$	−39.3548	−1.28704
$936$	−2.69055	−0.0879435
$937$	−48.9867	−1.60033	−0.800163	−	0.599782i	$-0.795254\pi$
$937$	−48.9867	−1.60033	−0.800163	+	0.599782i	$0.795254\pi$
$938$	13.4688	0.439772
$939$	20.5436	0.670416
$940$	−30.3034	−0.988387
$941$	31.5234	1.02763	0.513817	−	0.857900i	$-0.328231\pi$
$941$	31.5234	1.02763	0.513817	+	0.857900i	$0.328231\pi$
$942$	33.6322	1.09580
$943$	32.7209	1.06554
$944$	−50.3666	−1.63929
$945$	−2.07033	−0.0673478
$946$	−16.7531	−0.544691
$947$	−32.7121	−1.06300	−0.531500	−	0.847058i	$-0.678371\pi$
$947$	−32.7121	−1.06300	−0.531500	+	0.847058i	$0.678371\pi$
$948$	−23.6806	−0.769111
$949$	−7.47822	−0.242753
$950$	−2.32710	−0.0755012
$951$	−19.8684	−0.644278
$952$	−6.39436	−0.207243
$953$	60.5516	1.96146	0.980729	−	0.195371i	$-0.0625910\pi$
$953$	60.5516	1.96146	0.980729	+	0.195371i	$0.0625910\pi$
$954$	22.8798	0.740762
$955$	2.05761	0.0665826
$956$	−12.7557	−0.412549
$957$	−14.4152	−0.465978
$958$	6.57355	0.212382
$959$	4.01950	0.129796
$960$	−5.31233	−0.171455
$961$	−10.2635	−0.331080
$962$	49.6510	1.60081
$963$	−9.44862	−0.304477
$964$	15.1727	0.488679
$965$	51.0394	1.64302
$966$	8.61882	0.277306
$967$	27.8408	0.895299	0.447649	−	0.894209i	$-0.352261\pi$
$967$	27.8408	0.895299	0.447649	+	0.894209i	$0.352261\pi$
$968$	0.315567	0.0101427
$969$	10.0288	0.322172
$970$	30.2916	0.972605
$971$	43.7800	1.40497	0.702483	−	0.711700i	$-0.252075\pi$
$971$	43.7800	1.40497	0.702483	+	0.711700i	$0.252075\pi$
$972$	−1.38605	−0.0444575
$973$	8.72068	0.279572
$974$	−70.8761	−2.27102
$975$	−1.69980	−0.0544371
$976$	−9.71932	−0.311108
$977$	29.0667	0.929926	0.464963	−	0.885330i	$-0.346068\pi$
$977$	29.0667	0.929926	0.464963	+	0.885330i	$0.346068\pi$
$978$	5.66286	0.181078
$979$	61.7357	1.97308
$980$	−2.86958	−0.0916653
$981$	−14.8581	−0.474383
$982$	−12.6611	−0.404031
$983$	24.3633	0.777070	0.388535	−	0.921434i	$-0.372981\pi$
$983$	24.3633	0.777070	0.388535	+	0.921434i	$0.372981\pi$
$984$	7.89233	0.251598
$985$	12.9012	0.411066
$986$	−44.7037	−1.42366
$987$	10.5602	0.336135
$988$	5.84888	0.186078
$989$	−12.6972	−0.403748
$990$	12.7946	0.406640
$991$	−60.7223	−1.92891	−0.964454	−	0.264252i	$-0.914875\pi$
$991$	−60.7223	−1.92891	−0.964454	+	0.264252i	$0.914875\pi$
$992$	−30.3592	−0.963906
$993$	−7.73682	−0.245520
$994$	−21.3163	−0.676111
$995$	36.1293	1.14538
$996$	20.1804	0.639442
$997$	−13.9352	−0.441333	−0.220667	−	0.975349i	$-0.570823\pi$
$997$	−13.9352	−0.441333	−0.220667	+	0.975349i	$0.570823\pi$
$998$	−17.3676	−0.549761
$999$	−11.3297	−0.358457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.s.1.11	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.s.1.11	✓	50	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-1.84012 q^{2} -1.00000 q^{3} +1.38605 q^{4} -2.07033 q^{5} +1.84012 q^{6} -1.00000 q^{7} +1.12975 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.84012 q^{2} -1.00000 q^{3} +1.38605 q^{4} -2.07033 q^{5} +1.84012 q^{6} -1.00000 q^{7} +1.12975 q^{8} +1.00000 q^{9} +3.80966 q^{10} +3.35847 q^{11} -1.38605 q^{12} -2.38156 q^{13} +1.84012 q^{14} +2.07033 q^{15} -4.85097 q^{16} +5.66000 q^{17} -1.84012 q^{18} -1.77188 q^{19} -2.86958 q^{20} +1.00000 q^{21} -6.18000 q^{22} -4.68383 q^{23} -1.12975 q^{24} -0.713733 q^{25} +4.38235 q^{26} -1.00000 q^{27} -1.38605 q^{28} +4.29220 q^{29} -3.80966 q^{30} -4.55374 q^{31} +6.66688 q^{32} -3.35847 q^{33} -10.4151 q^{34} +2.07033 q^{35} +1.38605 q^{36} +11.3297 q^{37} +3.26047 q^{38} +2.38156 q^{39} -2.33895 q^{40} -6.98593 q^{41} -1.84012 q^{42} +2.71086 q^{43} +4.65500 q^{44} -2.07033 q^{45} +8.61882 q^{46} +10.5602 q^{47} +4.85097 q^{48} +1.00000 q^{49} +1.31336 q^{50} -5.66000 q^{51} -3.30095 q^{52} -12.4339 q^{53} +1.84012 q^{54} -6.95314 q^{55} -1.12975 q^{56} +1.77188 q^{57} -7.89818 q^{58} +10.3828 q^{59} +2.86958 q^{60} +2.00358 q^{61} +8.37943 q^{62} -1.00000 q^{63} -2.56593 q^{64} +4.93061 q^{65} +6.18000 q^{66} +7.31952 q^{67} +7.84503 q^{68} +4.68383 q^{69} -3.80966 q^{70} -11.5842 q^{71} +1.12975 q^{72} +3.14006 q^{73} -20.8481 q^{74} +0.713733 q^{75} -2.45591 q^{76} -3.35847 q^{77} -4.38235 q^{78} +17.0850 q^{79} +10.0431 q^{80} +1.00000 q^{81} +12.8550 q^{82} -14.5597 q^{83} +1.38605 q^{84} -11.7181 q^{85} -4.98832 q^{86} -4.29220 q^{87} +3.79422 q^{88} +18.3821 q^{89} +3.80966 q^{90} +2.38156 q^{91} -6.49202 q^{92} +4.55374 q^{93} -19.4321 q^{94} +3.66837 q^{95} -6.66688 q^{96} +7.95126 q^{97} -1.84012 q^{98} +3.35847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * q^99

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