LMFDB - Embedded newform 8043.2.a.p.1.19

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:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-0.0276074 q^{2} +1.00000 q^{3} -1.99924 q^{4} +0.000693755 q^{5} -0.0276074 q^{6} -1.00000 q^{7} +0.110409 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0276074 q^{2} +1.00000 q^{3} -1.99924 q^{4} +0.000693755 q^{5} -0.0276074 q^{6} -1.00000 q^{7} +0.110409 q^{8} +1.00000 q^{9} -1.91528e-5 q^{10} +2.09887 q^{11} -1.99924 q^{12} -3.11096 q^{13} +0.0276074 q^{14} +0.000693755 q^{15} +3.99543 q^{16} -4.87747 q^{17} -0.0276074 q^{18} -1.17048 q^{19} -0.00138698 q^{20} -1.00000 q^{21} -0.0579443 q^{22} -4.52984 q^{23} +0.110409 q^{24} -5.00000 q^{25} +0.0858856 q^{26} +1.00000 q^{27} +1.99924 q^{28} +7.48581 q^{29} -1.91528e-5 q^{30} -6.39632 q^{31} -0.331120 q^{32} +2.09887 q^{33} +0.134654 q^{34} -0.000693755 q^{35} -1.99924 q^{36} -1.26724 q^{37} +0.0323139 q^{38} -3.11096 q^{39} +7.65965e-5 q^{40} +3.80000 q^{41} +0.0276074 q^{42} +10.3287 q^{43} -4.19614 q^{44} +0.000693755 q^{45} +0.125057 q^{46} +0.0229046 q^{47} +3.99543 q^{48} +1.00000 q^{49} +0.138037 q^{50} -4.87747 q^{51} +6.21955 q^{52} +5.18235 q^{53} -0.0276074 q^{54} +0.00145610 q^{55} -0.110409 q^{56} -1.17048 q^{57} -0.206664 q^{58} -11.5946 q^{59} -0.00138698 q^{60} +6.65336 q^{61} +0.176586 q^{62} -1.00000 q^{63} -7.98171 q^{64} -0.00215825 q^{65} -0.0579443 q^{66} +1.51697 q^{67} +9.75121 q^{68} -4.52984 q^{69} +1.91528e-5 q^{70} -13.6369 q^{71} +0.110409 q^{72} +13.4068 q^{73} +0.0349852 q^{74} -5.00000 q^{75} +2.34007 q^{76} -2.09887 q^{77} +0.0858856 q^{78} +10.7651 q^{79} +0.00277185 q^{80} +1.00000 q^{81} -0.104908 q^{82} -3.55428 q^{83} +1.99924 q^{84} -0.00338377 q^{85} -0.285149 q^{86} +7.48581 q^{87} +0.231733 q^{88} +8.05865 q^{89} -1.91528e-5 q^{90} +3.11096 q^{91} +9.05624 q^{92} -6.39632 q^{93} -0.000632337 q^{94} -0.000812026 q^{95} -0.331120 q^{96} +12.3568 q^{97} -0.0276074 q^{98} +2.09887 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9}+O(q^{10}) $ 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9	\( 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9} + 18 q^{10} + 8 q^{11} + 45 q^{12} + 23 q^{13} - 7 q^{14} + 17 q^{15} + 37 q^{16} + 15 q^{17} + 7 q^{18} + 15 q^{19} + 53 q^{20} - 41 q^{21} + 13 q^{22} + 44 q^{23} + 12 q^{24} + 58 q^{25} + 9 q^{26} + 41 q^{27} - 45 q^{28} + 21 q^{29} + 18 q^{30} + 39 q^{31} + 61 q^{32} + 8 q^{33} + 9 q^{34} - 17 q^{35} + 45 q^{36} + 11 q^{37} + 44 q^{38} + 23 q^{39} + 24 q^{40} + 17 q^{41} - 7 q^{42} + 7 q^{43} + 30 q^{44} + 17 q^{45} - 12 q^{46} + 36 q^{47} + 37 q^{48} + 41 q^{49} + 28 q^{50} + 15 q^{51} + 58 q^{52} + 26 q^{53} + 7 q^{54} + 32 q^{55} - 12 q^{56} + 15 q^{57} - 4 q^{58} + 33 q^{59} + 53 q^{60} + 59 q^{61} - q^{62} - 41 q^{63} + 16 q^{64} + 72 q^{65} + 13 q^{66} + 12 q^{67} + 52 q^{68} + 44 q^{69} - 18 q^{70} + 33 q^{71} + 12 q^{72} + 18 q^{73} + 42 q^{74} + 58 q^{75} + 7 q^{76} - 8 q^{77} + 9 q^{78} + 22 q^{79} + 69 q^{80} + 41 q^{81} + 41 q^{82} + 32 q^{83} - 45 q^{84} - 44 q^{85} + 11 q^{86} + 21 q^{87} + 52 q^{88} + 63 q^{89} + 18 q^{90} - 23 q^{91} + 52 q^{92} + 39 q^{93} + 17 q^{94} + 37 q^{95} + 61 q^{96} + 8 q^{97} + 7 q^{98} + 8 q^{99}+O(q^{100}) \) 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9 + 18 * q^10 + 8 * q^11 + 45 * q^12 + 23 * q^13 - 7 * q^14 + 17 * q^15 + 37 * q^16 + 15 * q^17 + 7 * q^18 + 15 * q^19 + 53 * q^20 - 41 * q^21 + 13 * q^22 + 44 * q^23 + 12 * q^24 + 58 * q^25 + 9 * q^26 + 41 * q^27 - 45 * q^28 + 21 * q^29 + 18 * q^30 + 39 * q^31 + 61 * q^32 + 8 * q^33 + 9 * q^34 - 17 * q^35 + 45 * q^36 + 11 * q^37 + 44 * q^38 + 23 * q^39 + 24 * q^40 + 17 * q^41 - 7 * q^42 + 7 * q^43 + 30 * q^44 + 17 * q^45 - 12 * q^46 + 36 * q^47 + 37 * q^48 + 41 * q^49 + 28 * q^50 + 15 * q^51 + 58 * q^52 + 26 * q^53 + 7 * q^54 + 32 * q^55 - 12 * q^56 + 15 * q^57 - 4 * q^58 + 33 * q^59 + 53 * q^60 + 59 * q^61 - q^62 - 41 * q^63 + 16 * q^64 + 72 * q^65 + 13 * q^66 + 12 * q^67 + 52 * q^68 + 44 * q^69 - 18 * q^70 + 33 * q^71 + 12 * q^72 + 18 * q^73 + 42 * q^74 + 58 * q^75 + 7 * q^76 - 8 * q^77 + 9 * q^78 + 22 * q^79 + 69 * q^80 + 41 * q^81 + 41 * q^82 + 32 * q^83 - 45 * q^84 - 44 * q^85 + 11 * q^86 + 21 * q^87 + 52 * q^88 + 63 * q^89 + 18 * q^90 - 23 * q^91 + 52 * q^92 + 39 * q^93 + 17 * q^94 + 37 * q^95 + 61 * q^96 + 8 * q^97 + 7 * q^98 + 8 * 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 $

$2$	−0.0276074	−0.0195214	−0.00976069	−	0.999952i	$-0.503107\pi$
$2$	−0.0276074	−0.0195214	−0.00976069	+	0.999952i	$0.503107\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.99924	−0.999619
$5$	0.000693755 0	0.000310257 0	0.000155128	−	1.00000i	$-0.499951\pi$
$5$	0.000693755 0	0.000310257 0	0.000155128		1.00000i	$0.499951\pi$
$6$	−0.0276074	−0.0112707
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.110409	0.0390353
$9$	1.00000	0.333333
$10$	−1.91528e−5 0	−6.05664e−6 0
$11$	2.09887	0.632833	0.316416	−	0.948620i	$-0.397520\pi$
$11$	2.09887	0.632833	0.316416	+	0.948620i	$0.397520\pi$
$12$	−1.99924	−0.577130
$13$	−3.11096	−0.862826	−0.431413	−	0.902155i	$-0.641985\pi$
$13$	−3.11096	−0.862826	−0.431413	+	0.902155i	$0.641985\pi$
$14$	0.0276074	0.00737839
$15$	0.000693755 0	0.000179127 0
$16$	3.99543	0.998857
$17$	−4.87747	−1.18296	−0.591480	−	0.806320i	$-0.701456\pi$
$17$	−4.87747	−1.18296	−0.591480	+	0.806320i	$0.701456\pi$
$18$	−0.0276074	−0.00650713
$19$	−1.17048	−0.268526	−0.134263	−	0.990946i	$-0.542867\pi$
$19$	−1.17048	−0.268526	−0.134263	+	0.990946i	$0.542867\pi$
$20$	−0.00138698	−0.000310139 0
$21$	−1.00000	−0.218218
$22$	−0.0579443	−0.0123538
$23$	−4.52984	−0.944538	−0.472269	−	0.881455i	$-0.656565\pi$
$23$	−4.52984	−0.944538	−0.472269	+	0.881455i	$0.656565\pi$
$24$	0.110409	0.0225371
$25$	−5.00000	−1.00000
$26$	0.0858856	0.0168435
$27$	1.00000	0.192450
$28$	1.99924	0.377820
$29$	7.48581	1.39008	0.695040	−	0.718971i	$-0.255387\pi$
$29$	7.48581	1.39008	0.695040	+	0.718971i	$0.255387\pi$
$30$	−1.91528e−5 0	−3.49680e−6 0
$31$	−6.39632	−1.14881	−0.574406	−	0.818570i	$-0.694767\pi$
$31$	−6.39632	−1.14881	−0.574406	+	0.818570i	$0.694767\pi$
$32$	−0.331120	−0.0585344
$33$	2.09887	0.365366
$34$	0.134654	0.0230930
$35$	−0.000693755 0	−0.000117266 0
$36$	−1.99924	−0.333206
$37$	−1.26724	−0.208333	−0.104167	−	0.994560i	$-0.533218\pi$
$37$	−1.26724	−0.208333	−0.104167	+	0.994560i	$0.533218\pi$
$38$	0.0323139	0.00524200
$39$	−3.11096	−0.498153
$40$	7.65965e−5 0	1.21110e−5 0
$41$	3.80000	0.593460	0.296730	−	0.954961i	$-0.404104\pi$
$41$	3.80000	0.593460	0.296730	+	0.954961i	$0.404104\pi$
$42$	0.0276074	0.00425991
$43$	10.3287	1.57511	0.787557	−	0.616242i	$-0.211345\pi$
$43$	10.3287	1.57511	0.787557	+	0.616242i	$0.211345\pi$
$44$	−4.19614	−0.632592
$45$	0.000693755 0	0.000103419 0
$46$	0.125057	0.0184387
$47$	0.0229046	0.00334098	0.00167049	−	0.999999i	$-0.499468\pi$
$47$	0.0229046	0.00334098	0.00167049	+	0.999999i	$0.499468\pi$
$48$	3.99543	0.576690
$49$	1.00000	0.142857
$50$	0.138037	0.0195214
$51$	−4.87747	−0.682982
$52$	6.21955	0.862497
$53$	5.18235	0.711851	0.355925	−	0.934514i	$-0.384166\pi$
$53$	5.18235	0.711851	0.355925	+	0.934514i	$0.384166\pi$
$54$	−0.0276074	−0.00375689
$55$	0.00145610	0.000196341 0
$56$	−0.110409	−0.0147540
$57$	−1.17048	−0.155034
$58$	−0.206664	−0.0271363
$59$	−11.5946	−1.50949	−0.754743	−	0.656021i	$-0.772238\pi$
$59$	−11.5946	−1.50949	−0.754743	+	0.656021i	$0.772238\pi$
$60$	−0.00138698	−0.000179059 0
$61$	6.65336	0.851875	0.425938	−	0.904753i	$-0.359944\pi$
$61$	6.65336	0.851875	0.425938	+	0.904753i	$0.359944\pi$
$62$	0.176586	0.0224264
$63$	−1.00000	−0.125988
$64$	−7.98171	−0.997714
$65$	−0.00215825	−0.000267698 0
$66$	−0.0579443	−0.00713245
$67$	1.51697	0.185327	0.0926635	−	0.995697i	$-0.470462\pi$
$67$	1.51697	0.185327	0.0926635	+	0.995697i	$0.470462\pi$
$68$	9.75121	1.18251
$69$	−4.52984	−0.545329
$70$	1.91528e−5 0	2.28920e−6 0
$71$	−13.6369	−1.61841	−0.809203	−	0.587529i	$-0.800101\pi$
$71$	−13.6369	−1.61841	−0.809203	+	0.587529i	$0.800101\pi$
$72$	0.110409	0.0130118
$73$	13.4068	1.56915	0.784576	−	0.620032i	$-0.212881\pi$
$73$	13.4068	1.56915	0.784576	+	0.620032i	$0.212881\pi$
$74$	0.0349852	0.00406695
$75$	−5.00000	−0.577350
$76$	2.34007	0.268424
$77$	−2.09887	−0.239188
$78$	0.0858856	0.00972463
$79$	10.7651	1.21117	0.605585	−	0.795781i	$-0.292939\pi$
$79$	10.7651	1.21117	0.605585	+	0.795781i	$0.292939\pi$
$80$	0.00277185	0.000309902 0
$81$	1.00000	0.111111
$82$	−0.104908	−0.0115852
$83$	−3.55428	−0.390133	−0.195067	−	0.980790i	$-0.562492\pi$
$83$	−3.55428	−0.390133	−0.195067	+	0.980790i	$0.562492\pi$
$84$	1.99924	0.218135
$85$	−0.00338377	−0.000367021 0
$86$	−0.285149	−0.0307484
$87$	7.48581	0.802563
$88$	0.231733	0.0247028
$89$	8.05865	0.854216	0.427108	−	0.904201i	$-0.359532\pi$
$89$	8.05865	0.854216	0.427108	+	0.904201i	$0.359532\pi$
$90$	−1.91528e−5 0	−2.01888e−6 0
$91$	3.11096	0.326117
$92$	9.05624	0.944178
$93$	−6.39632	−0.663267
$94$	−0.000632337 0	−6.52206e−5 0
$95$	−0.000812026 0	−8.33121e−5 0
$96$	−0.331120	−0.0337948
$97$	12.3568	1.25464	0.627321	−	0.778761i	$-0.284151\pi$
$97$	12.3568	1.25464	0.627321	+	0.778761i	$0.284151\pi$
$98$	−0.0276074	−0.00278877
$99$	2.09887	0.210944
$100$	9.99619	0.999619
$101$	8.97232	0.892779	0.446389	−	0.894839i	$-0.352710\pi$
$101$	8.97232	0.892779	0.446389	+	0.894839i	$0.352710\pi$
$102$	0.134654	0.0133327
$103$	−17.7910	−1.75300	−0.876502	−	0.481398i	$-0.840129\pi$
$103$	−17.7910	−1.75300	−0.876502	+	0.481398i	$0.840129\pi$
$104$	−0.343477	−0.0336807
$105$	−0.000693755 0	−6.77036e−5 0
$106$	−0.143071	−0.0138963
$107$	−10.1367	−0.979954	−0.489977	−	0.871735i	$-0.662995\pi$
$107$	−10.1367	−0.979954	−0.489977	+	0.871735i	$0.662995\pi$
$108$	−1.99924	−0.192377
$109$	−3.54956	−0.339986	−0.169993	−	0.985445i	$-0.554375\pi$
$109$	−3.54956	−0.339986	−0.169993	+	0.985445i	$0.554375\pi$
$110$	−4.01992e−5 0	−3.83284e−6 0
$111$	−1.26724	−0.120281
$112$	−3.99543	−0.377532
$113$	12.0378	1.13242	0.566212	−	0.824260i	$-0.308408\pi$
$113$	12.0378	1.13242	0.566212	+	0.824260i	$0.308408\pi$
$114$	0.0323139	0.00302647
$115$	−0.00314260	−0.000293049 0
$116$	−14.9659	−1.38955
$117$	−3.11096	−0.287609
$118$	0.320096	0.0294672
$119$	4.87747	0.447117
$120$	7.65965e−5 0	6.99227e−6 0
$121$	−6.59475	−0.599523
$122$	−0.183682	−0.0166298
$123$	3.80000	0.342634
$124$	12.7878	1.14837
$125$	−0.00693755	−0.000620514 0
$126$	0.0276074	0.00245946
$127$	4.96854	0.440887	0.220443	−	0.975400i	$-0.429250\pi$
$127$	4.96854	0.440887	0.220443	+	0.975400i	$0.429250\pi$
$128$	0.882595	0.0780111
$129$	10.3287	0.909393
$130$	5.95836e−5 0	5.22583e−6 0
$131$	6.66928	0.582697	0.291349	−	0.956617i	$-0.405896\pi$
$131$	6.66928	0.582697	0.291349	+	0.956617i	$0.405896\pi$
$132$	−4.19614	−0.365227
$133$	1.17048	0.101493
$134$	−0.0418795	−0.00361784
$135$	0.000693755 0	5.97090e−5 0
$136$	−0.538514	−0.0461772
$137$	0.329540	0.0281545	0.0140773	−	0.999901i	$-0.495519\pi$
$137$	0.329540	0.0281545	0.0140773	+	0.999901i	$0.495519\pi$
$138$	0.125057	0.0106456
$139$	20.0571	1.70122	0.850611	−	0.525795i	$-0.176232\pi$
$139$	20.0571	1.70122	0.850611	+	0.525795i	$0.176232\pi$
$140$	0.00138698	0.000117221 0
$141$	0.0229046	0.00192892
$142$	0.376480	0.0315935
$143$	−6.52950	−0.546024
$144$	3.99543	0.332952
$145$	0.00519332	0.000431282 0
$146$	−0.370128	−0.0306320
$147$	1.00000	0.0824786
$148$	2.53352	0.208254
$149$	2.75156	0.225416	0.112708	−	0.993628i	$-0.464048\pi$
$149$	2.75156	0.225416	0.112708	+	0.993628i	$0.464048\pi$
$150$	0.138037	0.0112707
$151$	−7.83062	−0.637247	−0.318624	−	0.947881i	$-0.603221\pi$
$151$	−7.83062	−0.637247	−0.318624	+	0.947881i	$0.603221\pi$
$152$	−0.129231	−0.0104820
$153$	−4.87747	−0.394320
$154$	0.0579443	0.00466928
$155$	−0.00443748	−0.000356427 0
$156$	6.21955	0.497963
$157$	−8.69531	−0.693961	−0.346981	−	0.937872i	$-0.612793\pi$
$157$	−8.69531	−0.693961	−0.346981	+	0.937872i	$0.612793\pi$
$158$	−0.297197	−0.0236437
$159$	5.18235	0.410987
$160$	−0.000229717 0	−1.81607e−5 0
$161$	4.52984	0.357002
$162$	−0.0276074	−0.00216904
$163$	−23.7152	−1.85752	−0.928760	−	0.370681i	$-0.879124\pi$
$163$	−23.7152	−1.85752	−0.928760	+	0.370681i	$0.879124\pi$
$164$	−7.59710	−0.593234
$165$	0.00145610	0.000113357 0
$166$	0.0981246	0.00761594
$167$	21.1462	1.63634	0.818170	−	0.574976i	$-0.194989\pi$
$167$	21.1462	1.63634	0.818170	+	0.574976i	$0.194989\pi$
$168$	−0.110409	−0.00851820
$169$	−3.32191	−0.255532
$170$	9.34170e−5 0	7.16476e−6 0
$171$	−1.17048	−0.0895088
$172$	−20.6496	−1.57451
$173$	13.4579	1.02318	0.511592	−	0.859229i	$-0.329056\pi$
$173$	13.4579	1.02318	0.511592	+	0.859229i	$0.329056\pi$
$174$	−0.206664	−0.0156671
$175$	5.00000	0.377964
$176$	8.38588	0.632109
$177$	−11.5946	−0.871502
$178$	−0.222478	−0.0166755
$179$	−5.75942	−0.430479	−0.215239	−	0.976561i	$-0.569053\pi$
$179$	−5.75942	−0.430479	−0.215239	+	0.976561i	$0.569053\pi$
$180$	−0.00138698	−0.000103380 0
$181$	13.8410	1.02879	0.514397	−	0.857552i	$-0.328016\pi$
$181$	13.8410	1.02879	0.514397	+	0.857552i	$0.328016\pi$
$182$	−0.0858856	−0.00636626
$183$	6.65336	0.491830
$184$	−0.500134	−0.0368703
$185$	−0.000879155 0	−6.46368e−5 0
$186$	0.176586	0.0129479
$187$	−10.2372	−0.748615
$188$	−0.0457918	−0.00333971
$189$	−1.00000	−0.0727393
$190$	2.24179e−5 0	1.62637e−6 0
$191$	12.9813	0.939297	0.469649	−	0.882853i	$-0.344381\pi$
$191$	12.9813	0.939297	0.469649	+	0.882853i	$0.344381\pi$
$192$	−7.98171	−0.576031
$193$	5.53231	0.398224	0.199112	−	0.979977i	$-0.436194\pi$
$193$	5.53231	0.398224	0.199112	+	0.979977i	$0.436194\pi$
$194$	−0.341139	−0.0244923
$195$	−0.00215825	−0.000154555 0
$196$	−1.99924	−0.142803
$197$	−16.8759	−1.20236	−0.601180	−	0.799114i	$-0.705302\pi$
$197$	−16.8759	−1.20236	−0.601180	+	0.799114i	$0.705302\pi$
$198$	−0.0579443	−0.00411792
$199$	0.427056	0.0302732	0.0151366	−	0.999885i	$-0.495182\pi$
$199$	0.427056	0.0302732	0.0151366	+	0.999885i	$0.495182\pi$
$200$	−0.552043	−0.0390353
$201$	1.51697	0.106999
$202$	−0.247702	−0.0174283
$203$	−7.48581	−0.525401
$204$	9.75121	0.682722
$205$	0.00263627	0.000184125 0
$206$	0.491164	0.0342210
$207$	−4.52984	−0.314846
$208$	−12.4296	−0.861839
$209$	−2.45668	−0.169932
$210$	1.91528e−5 0	1.32167e−6 0
$211$	12.4940	0.860123	0.430062	−	0.902800i	$-0.358492\pi$
$211$	12.4940	0.860123	0.430062	+	0.902800i	$0.358492\pi$
$212$	−10.3608	−0.711579
$213$	−13.6369	−0.934387
$214$	0.279849	0.0191301
$215$	0.00716560	0.000488690 0
$216$	0.110409	0.00751235
$217$	6.39632	0.434210
$218$	0.0979940	0.00663699
$219$	13.4068	0.905950
$220$	−0.00291109	−0.000196266 0
$221$	15.1736	1.02069
$222$	0.0349852	0.00234805
$223$	28.4472	1.90496	0.952482	−	0.304595i	$-0.0985212\pi$
$223$	28.4472	1.90496	0.952482	+	0.304595i	$0.0985212\pi$
$224$	0.331120	0.0221239
$225$	−5.00000	−0.333333
$226$	−0.332333	−0.0221065
$227$	−11.1953	−0.743059	−0.371530	−	0.928421i	$-0.621167\pi$
$227$	−11.1953	−0.743059	−0.371530	+	0.928421i	$0.621167\pi$
$228$	2.34007	0.154975
$229$	9.39290	0.620700	0.310350	−	0.950622i	$-0.399554\pi$
$229$	9.39290	0.620700	0.310350	+	0.950622i	$0.399554\pi$
$230$	8.67591e−5 0	5.72073e−6 0
$231$	−2.09887	−0.138095
$232$	0.826498	0.0542622
$233$	−25.2539	−1.65443	−0.827217	−	0.561882i	$-0.810078\pi$
$233$	−25.2539	−1.65443	−0.827217	+	0.561882i	$0.810078\pi$
$234$	0.0858856	0.00561452
$235$	1.58902e−5 0	1.03656e−6 0
$236$	23.1803	1.50891
$237$	10.7651	0.699269
$238$	−0.134654	−0.00872833
$239$	−14.2606	−0.922442	−0.461221	−	0.887285i	$-0.652588\pi$
$239$	−14.2606	−0.922442	−0.461221	+	0.887285i	$0.652588\pi$
$240$	0.00277185	0.000178922 0
$241$	−18.4447	−1.18812	−0.594062	−	0.804419i	$-0.702477\pi$
$241$	−18.4447	−1.18812	−0.594062	+	0.804419i	$0.702477\pi$
$242$	0.182064	0.0117035
$243$	1.00000	0.0641500
$244$	−13.3016	−0.851550
$245$	0.000693755 0	4.43224e−5 0
$246$	−0.104908	−0.00668869
$247$	3.64132	0.231691
$248$	−0.706208	−0.0448443
$249$	−3.55428	−0.225244
$250$	0.000191528 0	1.21133e−5 0
$251$	−9.36123	−0.590876	−0.295438	−	0.955362i	$-0.595466\pi$
$251$	−9.36123	−0.590876	−0.295438	+	0.955362i	$0.595466\pi$
$252$	1.99924	0.125940
$253$	−9.50755	−0.597734
$254$	−0.137169	−0.00860672
$255$	−0.00338377	−0.000211900 0
$256$	15.9391	0.996191
$257$	24.7560	1.54424	0.772119	−	0.635478i	$-0.219197\pi$
$257$	24.7560	1.54424	0.772119	+	0.635478i	$0.219197\pi$
$258$	−0.285149	−0.0177526
$259$	1.26724	0.0787425
$260$	0.00431485	0.000267596 0
$261$	7.48581	0.463360
$262$	−0.184121	−0.0113751
$263$	18.5552	1.14416	0.572082	−	0.820197i	$-0.306136\pi$
$263$	18.5552	1.14416	0.572082	+	0.820197i	$0.306136\pi$
$264$	0.231733	0.0142622
$265$	0.00359528	0.000220857 0
$266$	−0.0323139	−0.00198129
$267$	8.05865	0.493182
$268$	−3.03278	−0.185256
$269$	27.0515	1.64936	0.824679	−	0.565601i	$-0.191356\pi$
$269$	27.0515	1.64936	0.824679	+	0.565601i	$0.191356\pi$
$270$	−1.91528e−5 0	−1.16560e−6 0
$271$	15.6544	0.950936	0.475468	−	0.879733i	$-0.342279\pi$
$271$	15.6544	0.950936	0.475468	+	0.879733i	$0.342279\pi$
$272$	−19.4876	−1.18161
$273$	3.11096	0.188284
$274$	−0.00909775	−0.000549615 0
$275$	−10.4943	−0.632833
$276$	9.05624	0.545121
$277$	23.5113	1.41266	0.706330	−	0.707883i	$-0.250350\pi$
$277$	23.5113	1.41266	0.706330	+	0.707883i	$0.250350\pi$
$278$	−0.553725	−0.0332102
$279$	−6.39632	−0.382937
$280$	−7.65965e−5 0	−4.57752e−6 0
$281$	−17.1412	−1.02256	−0.511279	−	0.859415i	$-0.670828\pi$
$281$	−17.1412	−1.02256	−0.511279	+	0.859415i	$0.670828\pi$
$282$	−0.000632337 0	−3.76551e−5 0
$283$	20.5817	1.22346	0.611729	−	0.791068i	$-0.290474\pi$
$283$	20.5817	1.22346	0.611729	+	0.791068i	$0.290474\pi$
$284$	27.2635	1.61779
$285$	−0.000812026 0	−4.81003e−5 0
$286$	0.180263	0.0106591
$287$	−3.80000	−0.224307
$288$	−0.331120	−0.0195115
$289$	6.78968	0.399393
$290$	−0.000143374 0	−8.41922e−6 0
$291$	12.3568	0.724368
$292$	−26.8035	−1.56855
$293$	20.5962	1.20324	0.601620	−	0.798782i	$-0.294522\pi$
$293$	20.5962	1.20324	0.601620	+	0.798782i	$0.294522\pi$
$294$	−0.0276074	−0.00161010
$295$	−0.00804380	−0.000468328 0
$296$	−0.139914	−0.00813235
$297$	2.09887	0.121789
$298$	−0.0759633	−0.00440043
$299$	14.0922	0.814972
$300$	9.99619	0.577130
$301$	−10.3287	−0.595337
$302$	0.216183	0.0124399
$303$	8.97232	0.515446
$304$	−4.67656	−0.268219
$305$	0.00461580	0.000264300 0
$306$	0.134654	0.00769767
$307$	10.4166	0.594504	0.297252	−	0.954799i	$-0.403930\pi$
$307$	10.4166	0.594504	0.297252	+	0.954799i	$0.403930\pi$
$308$	4.19614	0.239097
$309$	−17.7910	−1.01210
$310$	0.000122507 0	6.95795e−6 0
$311$	4.11831	0.233528	0.116764	−	0.993160i	$-0.462748\pi$
$311$	4.11831	0.233528	0.116764	+	0.993160i	$0.462748\pi$
$312$	−0.343477	−0.0194455
$313$	25.9353	1.46595	0.732975	−	0.680256i	$-0.238131\pi$
$313$	25.9353	1.46595	0.732975	+	0.680256i	$0.238131\pi$
$314$	0.240055	0.0135471
$315$	−0.000693755 0	−3.90887e−5 0
$316$	−21.5220	−1.21071
$317$	−2.62645	−0.147516	−0.0737581	−	0.997276i	$-0.523499\pi$
$317$	−2.62645	−0.147516	−0.0737581	+	0.997276i	$0.523499\pi$
$318$	−0.143071	−0.00802303
$319$	15.7117	0.879688
$320$	−0.00553736	−0.000309548 0
$321$	−10.1367	−0.565777
$322$	−0.125057	−0.00696917
$323$	5.70897	0.317656
$324$	−1.99924	−0.111069
$325$	15.5548	0.862826
$326$	0.654716	0.0362614
$327$	−3.54956	−0.196291
$328$	0.419552	0.0231659
$329$	−0.0229046	−0.00126277
$330$	−4.01992e−5 0	−2.21289e−6 0
$331$	−3.69297	−0.202984	−0.101492	−	0.994836i	$-0.532362\pi$
$331$	−3.69297	−0.202984	−0.101492	+	0.994836i	$0.532362\pi$
$332$	7.10586	0.389985
$333$	−1.26724	−0.0694444
$334$	−0.583791	−0.0319436
$335$	0.00105240	5.74990e−5 0
$336$	−3.99543	−0.217968
$337$	−12.4693	−0.679245	−0.339623	−	0.940562i	$-0.610299\pi$
$337$	−12.4693	−0.679245	−0.339623	+	0.940562i	$0.610299\pi$
$338$	0.0917094	0.00498833
$339$	12.0378	0.653805
$340$	0.00676496	0.000366881 0
$341$	−13.4250	−0.727006
$342$	0.0323139	0.00174733
$343$	−1.00000	−0.0539949
$344$	1.14038	0.0614851
$345$	−0.00314260	−0.000169192 0
$346$	−0.371537	−0.0199740
$347$	10.5034	0.563849	0.281925	−	0.959437i	$-0.409027\pi$
$347$	10.5034	0.563849	0.281925	+	0.959437i	$0.409027\pi$
$348$	−14.9659	−0.802258
$349$	1.08450	0.0580519	0.0290259	−	0.999579i	$-0.490759\pi$
$349$	1.08450	0.0580519	0.0290259	+	0.999579i	$0.490759\pi$
$350$	−0.138037	−0.00737839
$351$	−3.11096	−0.166051
$352$	−0.694978	−0.0370425
$353$	−16.2994	−0.867532	−0.433766	−	0.901026i	$-0.642815\pi$
$353$	−16.2994	−0.867532	−0.433766	+	0.901026i	$0.642815\pi$
$354$	0.320096	0.0170129
$355$	−0.00946069	−0.000502122 0
$356$	−16.1112	−0.853890
$357$	4.87747	0.258143
$358$	0.159002	0.00840354
$359$	13.5021	0.712616	0.356308	−	0.934369i	$-0.384035\pi$
$359$	13.5021	0.712616	0.356308	+	0.934369i	$0.384035\pi$
$360$	7.65965e−5 0	4.03699e−6 0
$361$	−17.6300	−0.927894
$362$	−0.382114	−0.0200835
$363$	−6.59475	−0.346135
$364$	−6.21955	−0.325993
$365$	0.00930107	0.000486840 0
$366$	−0.183682	−0.00960121
$367$	15.0952	0.787962	0.393981	−	0.919118i	$-0.371097\pi$
$367$	15.0952	0.787962	0.393981	+	0.919118i	$0.371097\pi$
$368$	−18.0987	−0.943458
$369$	3.80000	0.197820
$370$	2.42712e−5 0	1.26180e−6 0
$371$	−5.18235	−0.269054
$372$	12.7878	0.663014
$373$	21.8334	1.13049	0.565246	−	0.824923i	$-0.308781\pi$
$373$	21.8334	1.13049	0.565246	+	0.824923i	$0.308781\pi$
$374$	0.282621	0.0146140
$375$	−0.00693755	−0.000358254 0
$376$	0.00252887	0.000130416 0
$377$	−23.2881	−1.19940
$378$	0.0276074	0.00141997
$379$	21.3451	1.09643	0.548213	−	0.836339i	$-0.315308\pi$
$379$	21.3451	1.09643	0.548213	+	0.836339i	$0.315308\pi$
$380$	0.00162343	8.32804e−5 0
$381$	4.96854	0.254546
$382$	−0.358381	−0.0183364
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	0.882595	0.0450398
$385$	−0.00145610	−7.42098e−5 0
$386$	−0.152733	−0.00777389
$387$	10.3287	0.525038
$388$	−24.7042	−1.25416
$389$	32.7697	1.66149	0.830745	−	0.556652i	$-0.187915\pi$
$389$	32.7697	1.66149	0.830745	+	0.556652i	$0.187915\pi$
$390$	5.95836e−5 0	3.01713e−6 0
$391$	22.0942	1.11735
$392$	0.110409	0.00557647
$393$	6.66928	0.336420
$394$	0.465900	0.0234717
$395$	0.00746835	0.000375774 0
$396$	−4.19614	−0.210864
$397$	0.310929	0.0156051	0.00780254	−	0.999970i	$-0.497516\pi$
$397$	0.310929	0.0156051	0.00780254	+	0.999970i	$0.497516\pi$
$398$	−0.0117899	−0.000590974 0
$399$	1.17048	0.0585973
$400$	−19.9771	−0.998857
$401$	−31.5224	−1.57415	−0.787076	−	0.616857i	$-0.788406\pi$
$401$	−31.5224	−1.57415	−0.787076	+	0.616857i	$0.788406\pi$
$402$	−0.0418795	−0.00208876
$403$	19.8987	0.991225
$404$	−17.9378	−0.892439
$405$	0.000693755 0	3.44730e−5 0
$406$	0.206664	0.0102566
$407$	−2.65977	−0.131840
$408$	−0.538514	−0.0266604
$409$	6.96512	0.344403	0.172201	−	0.985062i	$-0.444912\pi$
$409$	6.96512	0.344403	0.172201	+	0.985062i	$0.444912\pi$
$410$	−7.27805e−5 0	−3.59437e−6 0
$411$	0.329540	0.0162550
$412$	35.5685	1.75234
$413$	11.5946	0.570532
$414$	0.125057	0.00614623
$415$	−0.00246580	−0.000121042 0
$416$	1.03010	0.0505050
$417$	20.0571	0.982201
$418$	0.0678226	0.00331731
$419$	−24.5320	−1.19847	−0.599234	−	0.800574i	$-0.704528\pi$
$419$	−24.5320	−1.19847	−0.599234	+	0.800574i	$0.704528\pi$
$420$	0.00138698	6.76778e−5 0
$421$	−13.6716	−0.666311	−0.333156	−	0.942872i	$-0.608113\pi$
$421$	−13.6716	−0.666311	−0.333156	+	0.942872i	$0.608113\pi$
$422$	−0.344927	−0.0167908
$423$	0.0229046	0.00111366
$424$	0.572176	0.0277873
$425$	24.3873	1.18296
$426$	0.376480	0.0182405
$427$	−6.65336	−0.321979
$428$	20.2657	0.979581
$429$	−6.52950	−0.315247
$430$	−0.000197824 0	−9.53990e−6 0
$431$	12.1703	0.586222	0.293111	−	0.956078i	$-0.405309\pi$
$431$	12.1703	0.586222	0.293111	+	0.956078i	$0.405309\pi$
$432$	3.99543	0.192230
$433$	25.6544	1.23287	0.616435	−	0.787406i	$-0.288576\pi$
$433$	25.6544	1.23287	0.616435	+	0.787406i	$0.288576\pi$
$434$	−0.176586	−0.00847638
$435$	0.00519332	0.000249001 0
$436$	7.09641	0.339856
$437$	5.30209	0.253633
$438$	−0.370128	−0.0176854
$439$	7.65558	0.365381	0.182690	−	0.983171i	$-0.441519\pi$
$439$	7.65558	0.365381	0.182690	+	0.983171i	$0.441519\pi$
$440$	0.000160766 0	7.66422e−6 0
$441$	1.00000	0.0476190
$442$	−0.418904	−0.0199252
$443$	9.68628	0.460209	0.230104	−	0.973166i	$-0.426093\pi$
$443$	9.68628	0.460209	0.230104	+	0.973166i	$0.426093\pi$
$444$	2.53352	0.120235
$445$	0.00559074	0.000265026 0
$446$	−0.785353	−0.0371875
$447$	2.75156	0.130144
$448$	7.98171	0.377101
$449$	−0.959294	−0.0452719	−0.0226360	−	0.999744i	$-0.507206\pi$
$449$	−0.959294	−0.0452719	−0.0226360	+	0.999744i	$0.507206\pi$
$450$	0.138037	0.00650713
$451$	7.97569	0.375561
$452$	−24.0665	−1.13199
$453$	−7.83062	−0.367915
$454$	0.309074	0.0145055
$455$	0.00215825	0.000101180 0
$456$	−0.129231	−0.00605179
$457$	−11.7965	−0.551819	−0.275910	−	0.961184i	$-0.588979\pi$
$457$	−11.7965	−0.551819	−0.275910	+	0.961184i	$0.588979\pi$
$458$	−0.259314	−0.0121169
$459$	−4.87747	−0.227661
$460$	0.00628281	0.000292938 0
$461$	5.30232	0.246954	0.123477	−	0.992347i	$-0.460596\pi$
$461$	5.30232	0.246954	0.123477	+	0.992347i	$0.460596\pi$
$462$	0.0579443	0.00269581
$463$	8.22699	0.382340	0.191170	−	0.981557i	$-0.438772\pi$
$463$	8.22699	0.382340	0.191170	+	0.981557i	$0.438772\pi$
$464$	29.9090	1.38849
$465$	−0.00443748	−0.000205783 0
$466$	0.697193	0.0322968
$467$	20.9703	0.970389	0.485194	−	0.874406i	$-0.338749\pi$
$467$	20.9703	0.970389	0.485194	+	0.874406i	$0.338749\pi$
$468$	6.21955	0.287499
$469$	−1.51697	−0.0700470
$470$	−4.38687e−7 0	−2.02351e−8 0
$471$	−8.69531	−0.400659
$472$	−1.28014	−0.0589233
$473$	21.6786	0.996784
$474$	−0.297197	−0.0136507
$475$	5.85240	0.268526
$476$	−9.75121	−0.446946
$477$	5.18235	0.237284
$478$	0.393698	0.0180073
$479$	22.5102	1.02852	0.514258	−	0.857636i	$-0.328067\pi$
$479$	22.5102	1.02852	0.514258	+	0.857636i	$0.328067\pi$
$480$	−0.000229717 0	−1.04851e−5 0
$481$	3.94234	0.179755
$482$	0.509209	0.0231938
$483$	4.52984	0.206115
$484$	13.1845	0.599294
$485$	0.00857259	0.000389261 0
$486$	−0.0276074	−0.00125230
$487$	24.1844	1.09590	0.547949	−	0.836511i	$-0.315409\pi$
$487$	24.1844	1.09590	0.547949	+	0.836511i	$0.315409\pi$
$488$	0.734587	0.0332532
$489$	−23.7152	−1.07244
$490$	−1.91528e−5 0	−8.65234e−7 0
$491$	1.58952	0.0717340	0.0358670	−	0.999357i	$-0.488581\pi$
$491$	1.58952	0.0717340	0.0358670	+	0.999357i	$0.488581\pi$
$492$	−7.59710	−0.342504
$493$	−36.5118	−1.64441
$494$	−0.100527	−0.00452294
$495$	0.00145610	6.54469e−5 0
$496$	−25.5560	−1.14750
$497$	13.6369	0.611700
$498$	0.0981246	0.00439707
$499$	2.99779	0.134199	0.0670996	−	0.997746i	$-0.478625\pi$
$499$	2.99779	0.134199	0.0670996	+	0.997746i	$0.478625\pi$
$500$	0.0138698	0.000620277 0
$501$	21.1462	0.944742
$502$	0.258439	0.0115347
$503$	44.5295	1.98547	0.992735	−	0.120320i	$-0.0383921\pi$
$503$	44.5295	1.98547	0.992735	+	0.120320i	$0.0383921\pi$
$504$	−0.110409	−0.00491799
$505$	0.00622459	0.000276991 0
$506$	0.262479	0.0116686
$507$	−3.32191	−0.147531
$508$	−9.93330	−0.440719
$509$	−20.6103	−0.913535	−0.456768	−	0.889586i	$-0.650993\pi$
$509$	−20.6103	−0.913535	−0.456768	+	0.889586i	$0.650993\pi$
$510$	9.34170e−5 0	4.13658e−6 0
$511$	−13.4068	−0.593084
$512$	−2.20523	−0.0974582
$513$	−1.17048	−0.0516779
$514$	−0.683450	−0.0301457
$515$	−0.0123426	−0.000543881 0
$516$	−20.6496	−0.909046
$517$	0.0480738	0.00211428
$518$	−0.0349852	−0.00153716
$519$	13.4579	0.590735
$520$	−0.000238289 0	−1.04497e−5 0
$521$	−7.39483	−0.323973	−0.161987	−	0.986793i	$-0.551790\pi$
$521$	−7.39483	−0.323973	−0.161987	+	0.986793i	$0.551790\pi$
$522$	−0.206664	−0.00904543
$523$	−7.18231	−0.314060	−0.157030	−	0.987594i	$-0.550192\pi$
$523$	−7.18231	−0.314060	−0.157030	+	0.987594i	$0.550192\pi$
$524$	−13.3335	−0.582475
$525$	5.00000	0.218218
$526$	−0.512261	−0.0223356
$527$	31.1978	1.35900
$528$	8.38588	0.364948
$529$	−2.48051	−0.107848
$530$	−9.92564e−5 0	−4.31142e−6 0
$531$	−11.5946	−0.503162
$532$	−2.34007	−0.101455
$533$	−11.8216	−0.512052
$534$	−0.222478	−0.00962759
$535$	−0.00703241	−0.000304037 0
$536$	0.167486	0.00723430
$537$	−5.75942	−0.248537
$538$	−0.746821	−0.0321977
$539$	2.09887	0.0904047
$540$	−0.00138698	−5.96862e−5 0
$541$	1.55170	0.0667126	0.0333563	−	0.999444i	$-0.489380\pi$
$541$	1.55170	0.0667126	0.0333563	+	0.999444i	$0.489380\pi$
$542$	−0.432177	−0.0185636
$543$	13.8410	0.593974
$544$	1.61503	0.0692438
$545$	−0.00246252	−0.000105483 0
$546$	−0.0858856	−0.00367556
$547$	−2.21171	−0.0945657	−0.0472829	−	0.998882i	$-0.515056\pi$
$547$	−2.21171	−0.0945657	−0.0472829	+	0.998882i	$0.515056\pi$
$548$	−0.658830	−0.0281438
$549$	6.65336	0.283958
$550$	0.289721	0.0123538
$551$	−8.76199	−0.373273
$552$	−0.500134	−0.0212871
$553$	−10.7651	−0.457779
$554$	−0.649087	−0.0275771
$555$	−0.000879155 0	−3.73181e−5 0
$556$	−40.0989	−1.70057
$557$	25.3542	1.07429	0.537145	−	0.843490i	$-0.319503\pi$
$557$	25.3542	1.07429	0.537145	+	0.843490i	$0.319503\pi$
$558$	0.176586	0.00747547
$559$	−32.1322	−1.35905
$560$	−0.00277185	−0.000117132 0
$561$	−10.2372	−0.432213
$562$	0.473224	0.0199617
$563$	11.8875	0.500999	0.250499	−	0.968117i	$-0.419405\pi$
$563$	11.8875	0.500999	0.250499	+	0.968117i	$0.419405\pi$
$564$	−0.0457918	−0.00192818
$565$	0.00835131	0.000351342 0
$566$	−0.568208	−0.0238836
$567$	−1.00000	−0.0419961
$568$	−1.50563	−0.0631750
$569$	−14.6365	−0.613595	−0.306798	−	0.951775i	$-0.599258\pi$
$569$	−14.6365	−0.613595	−0.306798	+	0.951775i	$0.599258\pi$
$570$	2.24179e−5 0	9.38984e−7 0
$571$	−27.8095	−1.16379	−0.581895	−	0.813264i	$-0.697688\pi$
$571$	−27.8095	−1.16379	−0.581895	+	0.813264i	$0.697688\pi$
$572$	13.0540	0.545816
$573$	12.9813	0.542304
$574$	0.104908	0.00437878
$575$	22.6492	0.944538
$576$	−7.98171	−0.332571
$577$	−11.9874	−0.499041	−0.249521	−	0.968369i	$-0.580273\pi$
$577$	−11.9874	−0.499041	−0.249521	+	0.968369i	$0.580273\pi$
$578$	−0.187445	−0.00779670
$579$	5.53231	0.229915
$580$	−0.0103827	−0.000431118 0
$581$	3.55428	0.147457
$582$	−0.341139	−0.0141407
$583$	10.8771	0.450482
$584$	1.48023	0.0612524
$585$	−0.00215825	−8.92325e−5 0
$586$	−0.568607	−0.0234889
$587$	−11.0713	−0.456960	−0.228480	−	0.973549i	$-0.573375\pi$
$587$	−11.0713	−0.456960	−0.228480	+	0.973549i	$0.573375\pi$
$588$	−1.99924	−0.0824472
$589$	7.48676	0.308486
$590$	0.000222068 0	9.14241e−6 0
$591$	−16.8759	−0.694182
$592$	−5.06317	−0.208095
$593$	34.8462	1.43096	0.715481	−	0.698633i	$-0.246208\pi$
$593$	34.8462	1.43096	0.715481	+	0.698633i	$0.246208\pi$
$594$	−0.0579443	−0.00237748
$595$	0.00338377	0.000138721 0
$596$	−5.50101	−0.225330
$597$	0.427056	0.0174782
$598$	−0.389048	−0.0159094
$599$	−33.0824	−1.35171	−0.675855	−	0.737034i	$-0.736226\pi$
$599$	−33.0824	−1.35171	−0.675855	+	0.737034i	$0.736226\pi$
$600$	−0.552043	−0.0225370
$601$	−28.5110	−1.16299	−0.581494	−	0.813550i	$-0.697532\pi$
$601$	−28.5110	−1.16299	−0.581494	+	0.813550i	$0.697532\pi$
$602$	0.285149	0.0116218
$603$	1.51697	0.0617757
$604$	15.6553	0.637004
$605$	−0.00457514	−0.000186006 0
$606$	−0.247702	−0.0100622
$607$	−5.24715	−0.212975	−0.106488	−	0.994314i	$-0.533960\pi$
$607$	−5.24715	−0.212975	−0.106488	+	0.994314i	$0.533960\pi$
$608$	0.387570	0.0157180
$609$	−7.48581	−0.303340
$610$	−0.000127430 0	−5.15950e−6 0
$611$	−0.0712554	−0.00288268
$612$	9.75121	0.394169
$613$	−12.6453	−0.510737	−0.255369	−	0.966844i	$-0.582197\pi$
$613$	−12.6453	−0.510737	−0.255369	+	0.966844i	$0.582197\pi$
$614$	−0.287574	−0.0116055
$615$	0.00263627	0.000106305 0
$616$	−0.231733	−0.00933679
$617$	38.3105	1.54232	0.771161	−	0.636640i	$-0.219676\pi$
$617$	38.3105	1.54232	0.771161	+	0.636640i	$0.219676\pi$
$618$	0.491164	0.0197575
$619$	17.3312	0.696601	0.348300	−	0.937383i	$-0.386759\pi$
$619$	17.3312	0.696601	0.348300	+	0.937383i	$0.386759\pi$
$620$	0.00887158	0.000356291 0
$621$	−4.52984	−0.181776
$622$	−0.113696	−0.00455879
$623$	−8.05865	−0.322863
$624$	−12.4296	−0.497583
$625$	25.0000	1.00000
$626$	−0.716006	−0.0286174
$627$	−2.45668	−0.0981104
$628$	17.3840	0.693697
$629$	6.18092	0.246450
$630$	1.91528e−5 0	7.63065e−7 0
$631$	−5.88561	−0.234302	−0.117151	−	0.993114i	$-0.537376\pi$
$631$	−5.88561	−0.234302	−0.117151	+	0.993114i	$0.537376\pi$
$632$	1.18856	0.0472784
$633$	12.4940	0.496592
$634$	0.0725095	0.00287972
$635$	0.00344695	0.000136788 0
$636$	−10.3608	−0.410830
$637$	−3.11096	−0.123261
$638$	−0.433760	−0.0171727
$639$	−13.6369	−0.539469
$640$	0.000612305 0	2.42035e−5 0
$641$	16.5059	0.651943	0.325972	−	0.945380i	$-0.394309\pi$
$641$	16.5059	0.651943	0.325972	+	0.945380i	$0.394309\pi$
$642$	0.279849	0.0110447
$643$	−45.3100	−1.78685	−0.893427	−	0.449209i	$-0.851706\pi$
$643$	−45.3100	−1.78685	−0.893427	+	0.449209i	$0.851706\pi$
$644$	−9.05624	−0.356866
$645$	0.00716560	0.000282145 0
$646$	−0.157610	−0.00620108
$647$	44.2398	1.73925	0.869623	−	0.493716i	$-0.164362\pi$
$647$	44.2398	1.73925	0.869623	+	0.493716i	$0.164362\pi$
$648$	0.110409	0.00433726
$649$	−24.3355	−0.955252
$650$	−0.429428	−0.0168435
$651$	6.39632	0.250691
$652$	47.4124	1.85681
$653$	−8.34623	−0.326613	−0.163307	−	0.986575i	$-0.552216\pi$
$653$	−8.34623	−0.326613	−0.163307	+	0.986575i	$0.552216\pi$
$654$	0.0979940	0.00383187
$655$	0.00462685	0.000180786 0
$656$	15.1826	0.592781
$657$	13.4068	0.523051
$658$	0.000632337 0	2.46511e−5 0
$659$	18.9617	0.738644	0.369322	−	0.929301i	$-0.379590\pi$
$659$	18.9617	0.738644	0.369322	+	0.929301i	$0.379590\pi$
$660$	−0.00291109	−0.000113314 0
$661$	−45.2335	−1.75938	−0.879690	−	0.475547i	$-0.842250\pi$
$661$	−45.2335	−1.75938	−0.879690	+	0.475547i	$0.842250\pi$
$662$	0.101953	0.00396253
$663$	15.1736	0.589294
$664$	−0.392423	−0.0152290
$665$	0.000812026 0	3.14890e−5 0
$666$	0.0349852	0.00135565
$667$	−33.9096	−1.31298
$668$	−42.2763	−1.63572
$669$	28.4472	1.09983
$670$	−2.90541e−5 0	−1.12246e−6 0
$671$	13.9645	0.539094
$672$	0.331120	0.0127732
$673$	31.2838	1.20590	0.602951	−	0.797778i	$-0.293991\pi$
$673$	31.2838	1.20590	0.602951	+	0.797778i	$0.293991\pi$
$674$	0.344244	0.0132598
$675$	−5.00000	−0.192450
$676$	6.64129	0.255434
$677$	14.0468	0.539863	0.269932	−	0.962879i	$-0.412999\pi$
$677$	14.0468	0.539863	0.269932	+	0.962879i	$0.412999\pi$
$678$	−0.332333	−0.0127632
$679$	−12.3568	−0.474210
$680$	−0.000373597 0	−1.43268e−5 0
$681$	−11.1953	−0.429005
$682$	0.370630	0.0141922
$683$	−17.1926	−0.657855	−0.328928	−	0.944355i	$-0.606687\pi$
$683$	−17.1926	−0.657855	−0.328928	+	0.944355i	$0.606687\pi$
$684$	2.34007	0.0894747
$685$	0.000228620 0	8.73514e−6 0
$686$	0.0276074	0.00105406
$687$	9.39290	0.358361
$688$	41.2676	1.57331
$689$	−16.1221	−0.614203
$690$	8.67591e−5 0	3.30286e−6 0
$691$	28.1144	1.06952	0.534762	−	0.845003i	$-0.320401\pi$
$691$	28.1144	1.06952	0.534762	+	0.845003i	$0.320401\pi$
$692$	−26.9055	−1.02279
$693$	−2.09887	−0.0797294
$694$	−0.289970	−0.0110071
$695$	0.0139147	0.000527816 0
$696$	0.826498	0.0313283
$697$	−18.5344	−0.702039
$698$	−0.0299402	−0.00113325
$699$	−25.2539	−0.955188
$700$	−9.99619	−0.377820
$701$	−22.1765	−0.837595	−0.418797	−	0.908080i	$-0.637548\pi$
$701$	−22.1765	−0.837595	−0.418797	+	0.908080i	$0.637548\pi$
$702$	0.0858856	0.00324154
$703$	1.48328	0.0559429
$704$	−16.7526	−0.631386
$705$	1.58902e−5 0	5.98460e−7 0
$706$	0.449985	0.0169354
$707$	−8.97232	−0.337439
$708$	23.1803	0.871170
$709$	−26.9124	−1.01072	−0.505358	−	0.862910i	$-0.668639\pi$
$709$	−26.9124	−1.01072	−0.505358	+	0.862910i	$0.668639\pi$
$710$	0.000261185 0	9.80210e−6 0
$711$	10.7651	0.403723
$712$	0.889744	0.0333446
$713$	28.9743	1.08510
$714$	−0.134654	−0.00503930
$715$	−0.00452988	−0.000169408 0
$716$	11.5144	0.430315
$717$	−14.2606	−0.532572
$718$	−0.372759	−0.0139112
$719$	14.8401	0.553442	0.276721	−	0.960950i	$-0.410752\pi$
$719$	14.8401	0.553442	0.276721	+	0.960950i	$0.410752\pi$
$720$	0.00277185	0.000103301 0
$721$	17.7910	0.662573
$722$	0.486718	0.0181138
$723$	−18.4447	−0.685964
$724$	−27.6714	−1.02840
$725$	−37.4291	−1.39008
$726$	0.182064	0.00675703
$727$	24.9238	0.924374	0.462187	−	0.886782i	$-0.347065\pi$
$727$	24.9238	0.924374	0.462187	+	0.886782i	$0.347065\pi$
$728$	0.343477	0.0127301
$729$	1.00000	0.0370370
$730$	−0.000256778 0	−9.50379e−6 0
$731$	−50.3780	−1.86330
$732$	−13.3016	−0.491643
$733$	−28.4964	−1.05254	−0.526268	−	0.850318i	$-0.676409\pi$
$733$	−28.4964	−1.05254	−0.526268	+	0.850318i	$0.676409\pi$
$734$	−0.416739	−0.0153821
$735$	0.000693755 0	2.55896e−5 0
$736$	1.49992	0.0552879
$737$	3.18391	0.117281
$738$	−0.104908	−0.00386172
$739$	−19.3144	−0.710493	−0.355246	−	0.934773i	$-0.615603\pi$
$739$	−19.3144	−0.710493	−0.355246	+	0.934773i	$0.615603\pi$
$740$	0.00175764	6.46121e−5 0
$741$	3.64132	0.133767
$742$	0.143071	0.00525231
$743$	12.4005	0.454929	0.227464	−	0.973786i	$-0.426956\pi$
$743$	12.4005	0.454929	0.227464	+	0.973786i	$0.426956\pi$
$744$	−0.706208	−0.0258908
$745$	0.00190891	6.99369e−5 0
$746$	−0.602764	−0.0220688
$747$	−3.55428	−0.130044
$748$	20.4665	0.748330
$749$	10.1367	0.370388
$750$	0.000191528 0	6.99361e−6 0
$751$	−38.7614	−1.41442	−0.707212	−	0.707002i	$-0.750047\pi$
$751$	−38.7614	−1.41442	−0.707212	+	0.707002i	$0.750047\pi$
$752$	0.0915137	0.00333716
$753$	−9.36123	−0.341142
$754$	0.642923	0.0234139
$755$	−0.00543254	−0.000197710 0
$756$	1.99924	0.0727116
$757$	−18.3732	−0.667785	−0.333892	−	0.942611i	$-0.608362\pi$
$757$	−18.3732	−0.667785	−0.333892	+	0.942611i	$0.608362\pi$
$758$	−0.589283	−0.0214037
$759$	−9.50755	−0.345102
$760$	−8.96546e−5 0	−3.25212e−6 0
$761$	23.7362	0.860435	0.430218	−	0.902725i	$-0.358437\pi$
$761$	23.7362	0.860435	0.430218	+	0.902725i	$0.358437\pi$
$762$	−0.137169	−0.00496909
$763$	3.54956	0.128503
$764$	−25.9528	−0.938939
$765$	−0.00338377	−0.000122340 0
$766$	0.0276074	0.000997496 0
$767$	36.0703	1.30242
$768$	15.9391	0.575151
$769$	−13.3791	−0.482462	−0.241231	−	0.970468i	$-0.577551\pi$
$769$	−13.3791	−0.482462	−0.241231	+	0.970468i	$0.577551\pi$
$770$	4.01992e−5 0	1.44868e−6 0
$771$	24.7560	0.891567
$772$	−11.0604	−0.398072
$773$	−17.5585	−0.631534	−0.315767	−	0.948837i	$-0.602262\pi$
$773$	−17.5585	−0.631534	−0.315767	+	0.948837i	$0.602262\pi$
$774$	−0.285149	−0.0102495
$775$	31.9816	1.14881
$776$	1.36429	0.0489753
$777$	1.26724	0.0454620
$778$	−0.904687	−0.0324346
$779$	−4.44782	−0.159360
$780$	0.00431485	0.000154496 0
$781$	−28.6221	−1.02418
$782$	−0.609962	−0.0218122
$783$	7.48581	0.267521
$784$	3.99543	0.142694
$785$	−0.00603242	−0.000215306 0
$786$	−0.184121	−0.00656739
$787$	−50.7600	−1.80940	−0.904700	−	0.426050i	$-0.859905\pi$
$787$	−50.7600	−1.80940	−0.904700	+	0.426050i	$0.859905\pi$
$788$	33.7390	1.20190
$789$	18.5552	0.660583
$790$	−0.000206182 0	−7.33562e−6 0
$791$	−12.0378	−0.428016
$792$	0.231733	0.00823427
$793$	−20.6983	−0.735020
$794$	−0.00858395	−0.000304633 0
$795$	0.00359528	0.000127512 0
$796$	−0.853786	−0.0302616
$797$	51.5558	1.82620	0.913100	−	0.407736i	$-0.133681\pi$
$797$	51.5558	1.82620	0.913100	+	0.407736i	$0.133681\pi$
$798$	−0.0323139	−0.00114390
$799$	−0.111716	−0.00395225
$800$	1.65560	0.0585344
$801$	8.05865	0.284739
$802$	0.870250	0.0307296
$803$	28.1392	0.993011
$804$	−3.03278	−0.106958
$805$	0.00314260	0.000110762 0
$806$	−0.549351	−0.0193501
$807$	27.0515	0.952258
$808$	0.990620	0.0348499
$809$	13.8641	0.487434	0.243717	−	0.969846i	$-0.421633\pi$
$809$	13.8641	0.487434	0.243717	+	0.969846i	$0.421633\pi$
$810$	−1.91528e−5 0	−6.72960e−7 0
$811$	−5.61681	−0.197233	−0.0986164	−	0.995126i	$-0.531442\pi$
$811$	−5.61681	−0.197233	−0.0986164	+	0.995126i	$0.531442\pi$
$812$	14.9659	0.525201
$813$	15.6544	0.549023
$814$	0.0734294	0.00257370
$815$	−0.0164526	−0.000576308 0
$816$	−19.4876	−0.682201
$817$	−12.0895	−0.422960
$818$	−0.192289	−0.00672322
$819$	3.11096	0.108706
$820$	−0.00527053	−0.000184055 0
$821$	22.1020	0.771364	0.385682	−	0.922632i	$-0.373966\pi$
$821$	22.1020	0.771364	0.385682	+	0.922632i	$0.373966\pi$
$822$	−0.00909775	−0.000317321 0
$823$	−26.2360	−0.914528	−0.457264	−	0.889331i	$-0.651171\pi$
$823$	−26.2360	−0.914528	−0.457264	+	0.889331i	$0.651171\pi$
$824$	−1.96428	−0.0684291
$825$	−10.4943	−0.365366
$826$	−0.320096	−0.0111376
$827$	17.6028	0.612110	0.306055	−	0.952014i	$-0.400991\pi$
$827$	17.6028	0.612110	0.306055	+	0.952014i	$0.400991\pi$
$828$	9.05624	0.314726
$829$	−14.7943	−0.513827	−0.256913	−	0.966434i	$-0.582706\pi$
$829$	−14.7943	−0.513827	−0.256913	+	0.966434i	$0.582706\pi$
$830$	6.80744e−5 0	2.36290e−6 0
$831$	23.5113	0.815599
$832$	24.8308	0.860853
$833$	−4.87747	−0.168994
$834$	−0.553725	−0.0191739
$835$	0.0146703	0.000507686 0
$836$	4.91149	0.169867
$837$	−6.39632	−0.221089
$838$	0.677266	0.0233958
$839$	−26.7147	−0.922294	−0.461147	−	0.887324i	$-0.652562\pi$
$839$	−26.7147	−0.922294	−0.461147	+	0.887324i	$0.652562\pi$
$840$	−7.65965e−5 0	−2.64283e−6 0
$841$	27.0374	0.932324
$842$	0.377436	0.0130073
$843$	−17.1412	−0.590374
$844$	−24.9785	−0.859795
$845$	−0.00230460	−7.92805e−5 0
$846$	−0.000632337 0	−2.17402e−5 0
$847$	6.59475	0.226598
$848$	20.7057	0.711037
$849$	20.5817	0.706364
$850$	−0.673271	−0.0230930
$851$	5.74040	0.196779
$852$	27.2635	0.934031
$853$	33.0455	1.13145	0.565727	−	0.824592i	$-0.308595\pi$
$853$	33.0455	1.13145	0.565727	+	0.824592i	$0.308595\pi$
$854$	0.183682	0.00628546
$855$	−0.000812026 0	−2.77707e−5 0
$856$	−1.11918	−0.0382528
$857$	−28.2141	−0.963777	−0.481888	−	0.876233i	$-0.660049\pi$
$857$	−28.2141	−0.963777	−0.481888	+	0.876233i	$0.660049\pi$
$858$	0.180263	0.00615406
$859$	−21.6510	−0.738723	−0.369362	−	0.929286i	$-0.620424\pi$
$859$	−21.6510	−0.738723	−0.369362	+	0.929286i	$0.620424\pi$
$860$	−0.0143257	−0.000488504 0
$861$	−3.80000	−0.129504
$862$	−0.335990	−0.0114439
$863$	20.1748	0.686759	0.343380	−	0.939197i	$-0.388428\pi$
$863$	20.1748	0.686759	0.343380	+	0.939197i	$0.388428\pi$
$864$	−0.331120	−0.0112649
$865$	0.00933648	0.000317450 0
$866$	−0.708250	−0.0240673
$867$	6.78968	0.230589
$868$	−12.7878	−0.434045
$869$	22.5946	0.766468
$870$	−0.000143374 0	−4.86084e−6 0
$871$	−4.71923	−0.159905
$872$	−0.391902	−0.0132715
$873$	12.3568	0.418214
$874$	−0.146377	−0.00495127
$875$	0.00693755	0.000234532 0
$876$	−26.8035	−0.905605
$877$	−14.8290	−0.500740	−0.250370	−	0.968150i	$-0.580552\pi$
$877$	−14.8290	−0.500740	−0.250370	+	0.968150i	$0.580552\pi$
$878$	−0.211351	−0.00713273
$879$	20.5962	0.694691
$880$	0.00581775	0.000196116 0
$881$	4.87267	0.164164	0.0820822	−	0.996626i	$-0.473843\pi$
$881$	4.87267	0.164164	0.0820822	+	0.996626i	$0.473843\pi$
$882$	−0.0276074	−0.000929589 0
$883$	−46.0328	−1.54913	−0.774564	−	0.632496i	$-0.782030\pi$
$883$	−46.0328	−1.54913	−0.774564	+	0.632496i	$0.782030\pi$
$884$	−30.3357	−1.02030
$885$	−0.00804380	−0.000270389 0
$886$	−0.267413	−0.00898391
$887$	34.5479	1.16000	0.580002	−	0.814615i	$-0.303052\pi$
$887$	34.5479	1.16000	0.580002	+	0.814615i	$0.303052\pi$
$888$	−0.139914	−0.00469521
$889$	−4.96854	−0.166640
$890$	−0.000154346 0	−5.17368e−6 0
$891$	2.09887	0.0703147
$892$	−56.8727	−1.90424
$893$	−0.0268094	−0.000897142 0
$894$	−0.0759633	−0.00254059
$895$	−0.00399563	−0.000133559 0
$896$	−0.882595	−0.0294854
$897$	14.0922	0.470524
$898$	0.0264836	0.000883770 0
$899$	−47.8816	−1.59694
$900$	9.99619	0.333206
$901$	−25.2767	−0.842090
$902$	−0.220188	−0.00733146
$903$	−10.3287	−0.343718
$904$	1.32908	0.0442045
$905$	0.00960227	0.000319190 0
$906$	0.216183	0.00718220
$907$	0.0822732	0.00273184	0.00136592	−	0.999999i	$-0.499565\pi$
$907$	0.0822732	0.00273184	0.00136592	+	0.999999i	$0.499565\pi$
$908$	22.3821	0.742776
$909$	8.97232	0.297593
$910$	−5.95836e−5 0	−1.97518e−6 0
$911$	1.81559	0.0601531	0.0300765	−	0.999548i	$-0.490425\pi$
$911$	1.81559	0.0601531	0.0300765	+	0.999548i	$0.490425\pi$
$912$	−4.67656	−0.154857
$913$	−7.45998	−0.246889
$914$	0.325672	0.0107723
$915$	0.00461580	0.000152594 0
$916$	−18.7786	−0.620464
$917$	−6.66928	−0.220239
$918$	0.134654	0.00444425
$919$	−36.1763	−1.19335	−0.596674	−	0.802484i	$-0.703511\pi$
$919$	−36.1763	−1.19335	−0.596674	+	0.802484i	$0.703511\pi$
$920$	−0.000346970 0	−1.14393e−5 0
$921$	10.4166	0.343237
$922$	−0.146383	−0.00482087
$923$	42.4240	1.39640
$924$	4.19614	0.138043
$925$	6.33620	0.208333
$926$	−0.227126	−0.00746381
$927$	−17.7910	−0.584335
$928$	−2.47871	−0.0813675
$929$	1.04992	0.0344467	0.0172234	−	0.999852i	$-0.494517\pi$
$929$	1.04992	0.0344467	0.0172234	+	0.999852i	$0.494517\pi$
$930$	0.000122507 0	4.01717e−6 0
$931$	−1.17048	−0.0383609
$932$	50.4885	1.65380
$933$	4.11831	0.134827
$934$	−0.578935	−0.0189433
$935$	−0.00710209	−0.000232263 0
$936$	−0.343477	−0.0112269
$937$	−23.2359	−0.759083	−0.379541	−	0.925175i	$-0.623918\pi$
$937$	−23.2359	−0.759083	−0.379541	+	0.925175i	$0.623918\pi$
$938$	0.0418795	0.00136741
$939$	25.9353	0.846366
$940$	−3.17683e−5 0	−1.03617e−6 0
$941$	−12.9797	−0.423126	−0.211563	−	0.977364i	$-0.567855\pi$
$941$	−12.9797	−0.423126	−0.211563	+	0.977364i	$0.567855\pi$
$942$	0.240055	0.00782141
$943$	−17.2134	−0.560545
$944$	−46.3253	−1.50776
$945$	−0.000693755 0	−2.25679e−5 0
$946$	−0.598490	−0.0194586
$947$	1.97147	0.0640641	0.0320321	−	0.999487i	$-0.489802\pi$
$947$	1.97147	0.0640641	0.0320321	+	0.999487i	$0.489802\pi$
$948$	−21.5220	−0.699003
$949$	−41.7082	−1.35390
$950$	−0.161569	−0.00524200
$951$	−2.62645	−0.0851686
$952$	0.538514	0.0174533
$953$	−5.79576	−0.187743	−0.0938715	−	0.995584i	$-0.529924\pi$
$953$	−5.79576	−0.187743	−0.0938715	+	0.995584i	$0.529924\pi$
$954$	−0.143071	−0.00463210
$955$	0.00900588	0.000291423 0
$956$	28.5103	0.922090
$957$	15.7117	0.507888
$958$	−0.621447	−0.0200780
$959$	−0.329540	−0.0106414
$960$	−0.00553736	−0.000178717 0
$961$	9.91287	0.319770
$962$	−0.108838	−0.00350907
$963$	−10.1367	−0.326651
$964$	36.8753	1.18767
$965$	0.00383807	0.000123552 0
$966$	−0.125057	−0.00402365
$967$	−50.6353	−1.62832	−0.814161	−	0.580639i	$-0.802803\pi$
$967$	−50.6353	−1.62832	−0.814161	+	0.580639i	$0.802803\pi$
$968$	−0.728117	−0.0234026
$969$	5.70897	0.183399
$970$	−0.000236667 0	−7.59891e−6 0
$971$	−41.8888	−1.34427	−0.672137	−	0.740427i	$-0.734623\pi$
$971$	−41.8888	−1.34427	−0.672137	+	0.740427i	$0.734623\pi$
$972$	−1.99924	−0.0641256
$973$	−20.0571	−0.643002
$974$	−0.667668	−0.0213935
$975$	15.5548	0.498153
$976$	26.5830	0.850901
$977$	39.0699	1.24996	0.624979	−	0.780642i	$-0.285108\pi$
$977$	39.0699	1.24996	0.624979	+	0.780642i	$0.285108\pi$
$978$	0.654716	0.0209355
$979$	16.9141	0.540576
$980$	−0.00138698	−4.43055e−5 0
$981$	−3.54956	−0.113329
$982$	−0.0438825	−0.00140035
$983$	−50.5236	−1.61145	−0.805726	−	0.592288i	$-0.798225\pi$
$983$	−50.5236	−1.61145	−0.805726	+	0.592288i	$0.798225\pi$
$984$	0.419552	0.0133748
$985$	−0.0117078	−0.000373040 0
$986$	1.00800	0.0321011
$987$	−0.0229046	−0.000729062 0
$988$	−7.27986	−0.231603
$989$	−46.7875	−1.48776
$990$	−4.01992e−5 0	−1.27761e−6 0
$991$	27.5622	0.875542	0.437771	−	0.899086i	$-0.355768\pi$
$991$	27.5622	0.875542	0.437771	+	0.899086i	$0.355768\pi$
$992$	2.11795	0.0672450
$993$	−3.69297	−0.117193
$994$	−0.376480	−0.0119412
$995$	0.000296272 0	9.39246e−6 0
$996$	7.10586	0.225158
$997$	0.991448	0.0313995	0.0156997	−	0.999877i	$-0.495002\pi$
$997$	0.991448	0.0313995	0.0156997	+	0.999877i	$0.495002\pi$
$998$	−0.0827611	−0.00261976
$999$	−1.26724	−0.0400937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.p.1.19	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.p.1.19	✓	41	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)

\(f(q)\)	\(=\)	\(q-0.0276074 q^{2} +1.00000 q^{3} -1.99924 q^{4} +0.000693755 q^{5} -0.0276074 q^{6} -1.00000 q^{7} +0.110409 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0276074 q^{2} +1.00000 q^{3} -1.99924 q^{4} +0.000693755 q^{5} -0.0276074 q^{6} -1.00000 q^{7} +0.110409 q^{8} +1.00000 q^{9} -1.91528e-5 q^{10} +2.09887 q^{11} -1.99924 q^{12} -3.11096 q^{13} +0.0276074 q^{14} +0.000693755 q^{15} +3.99543 q^{16} -4.87747 q^{17} -0.0276074 q^{18} -1.17048 q^{19} -0.00138698 q^{20} -1.00000 q^{21} -0.0579443 q^{22} -4.52984 q^{23} +0.110409 q^{24} -5.00000 q^{25} +0.0858856 q^{26} +1.00000 q^{27} +1.99924 q^{28} +7.48581 q^{29} -1.91528e-5 q^{30} -6.39632 q^{31} -0.331120 q^{32} +2.09887 q^{33} +0.134654 q^{34} -0.000693755 q^{35} -1.99924 q^{36} -1.26724 q^{37} +0.0323139 q^{38} -3.11096 q^{39} +7.65965e-5 q^{40} +3.80000 q^{41} +0.0276074 q^{42} +10.3287 q^{43} -4.19614 q^{44} +0.000693755 q^{45} +0.125057 q^{46} +0.0229046 q^{47} +3.99543 q^{48} +1.00000 q^{49} +0.138037 q^{50} -4.87747 q^{51} +6.21955 q^{52} +5.18235 q^{53} -0.0276074 q^{54} +0.00145610 q^{55} -0.110409 q^{56} -1.17048 q^{57} -0.206664 q^{58} -11.5946 q^{59} -0.00138698 q^{60} +6.65336 q^{61} +0.176586 q^{62} -1.00000 q^{63} -7.98171 q^{64} -0.00215825 q^{65} -0.0579443 q^{66} +1.51697 q^{67} +9.75121 q^{68} -4.52984 q^{69} +1.91528e-5 q^{70} -13.6369 q^{71} +0.110409 q^{72} +13.4068 q^{73} +0.0349852 q^{74} -5.00000 q^{75} +2.34007 q^{76} -2.09887 q^{77} +0.0858856 q^{78} +10.7651 q^{79} +0.00277185 q^{80} +1.00000 q^{81} -0.104908 q^{82} -3.55428 q^{83} +1.99924 q^{84} -0.00338377 q^{85} -0.285149 q^{86} +7.48581 q^{87} +0.231733 q^{88} +8.05865 q^{89} -1.91528e-5 q^{90} +3.11096 q^{91} +9.05624 q^{92} -6.39632 q^{93} -0.000632337 q^{94} -0.000812026 q^{95} -0.331120 q^{96} +12.3568 q^{97} -0.0276074 q^{98} +2.09887 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9}+O(q^{10}) \) 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9	\( 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9} + 18 q^{10} + 8 q^{11} + 45 q^{12} + 23 q^{13} - 7 q^{14} + 17 q^{15} + 37 q^{16} + 15 q^{17} + 7 q^{18} + 15 q^{19} + 53 q^{20} - 41 q^{21} + 13 q^{22} + 44 q^{23} + 12 q^{24} + 58 q^{25} + 9 q^{26} + 41 q^{27} - 45 q^{28} + 21 q^{29} + 18 q^{30} + 39 q^{31} + 61 q^{32} + 8 q^{33} + 9 q^{34} - 17 q^{35} + 45 q^{36} + 11 q^{37} + 44 q^{38} + 23 q^{39} + 24 q^{40} + 17 q^{41} - 7 q^{42} + 7 q^{43} + 30 q^{44} + 17 q^{45} - 12 q^{46} + 36 q^{47} + 37 q^{48} + 41 q^{49} + 28 q^{50} + 15 q^{51} + 58 q^{52} + 26 q^{53} + 7 q^{54} + 32 q^{55} - 12 q^{56} + 15 q^{57} - 4 q^{58} + 33 q^{59} + 53 q^{60} + 59 q^{61} - q^{62} - 41 q^{63} + 16 q^{64} + 72 q^{65} + 13 q^{66} + 12 q^{67} + 52 q^{68} + 44 q^{69} - 18 q^{70} + 33 q^{71} + 12 q^{72} + 18 q^{73} + 42 q^{74} + 58 q^{75} + 7 q^{76} - 8 q^{77} + 9 q^{78} + 22 q^{79} + 69 q^{80} + 41 q^{81} + 41 q^{82} + 32 q^{83} - 45 q^{84} - 44 q^{85} + 11 q^{86} + 21 q^{87} + 52 q^{88} + 63 q^{89} + 18 q^{90} - 23 q^{91} + 52 q^{92} + 39 q^{93} + 17 q^{94} + 37 q^{95} + 61 q^{96} + 8 q^{97} + 7 q^{98} + 8 q^{99}+O(q^{100}) \) 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9 + 18 * q^10 + 8 * q^11 + 45 * q^12 + 23 * q^13 - 7 * q^14 + 17 * q^15 + 37 * q^16 + 15 * q^17 + 7 * q^18 + 15 * q^19 + 53 * q^20 - 41 * q^21 + 13 * q^22 + 44 * q^23 + 12 * q^24 + 58 * q^25 + 9 * q^26 + 41 * q^27 - 45 * q^28 + 21 * q^29 + 18 * q^30 + 39 * q^31 + 61 * q^32 + 8 * q^33 + 9 * q^34 - 17 * q^35 + 45 * q^36 + 11 * q^37 + 44 * q^38 + 23 * q^39 + 24 * q^40 + 17 * q^41 - 7 * q^42 + 7 * q^43 + 30 * q^44 + 17 * q^45 - 12 * q^46 + 36 * q^47 + 37 * q^48 + 41 * q^49 + 28 * q^50 + 15 * q^51 + 58 * q^52 + 26 * q^53 + 7 * q^54 + 32 * q^55 - 12 * q^56 + 15 * q^57 - 4 * q^58 + 33 * q^59 + 53 * q^60 + 59 * q^61 - q^62 - 41 * q^63 + 16 * q^64 + 72 * q^65 + 13 * q^66 + 12 * q^67 + 52 * q^68 + 44 * q^69 - 18 * q^70 + 33 * q^71 + 12 * q^72 + 18 * q^73 + 42 * q^74 + 58 * q^75 + 7 * q^76 - 8 * q^77 + 9 * q^78 + 22 * q^79 + 69 * q^80 + 41 * q^81 + 41 * q^82 + 32 * q^83 - 45 * q^84 - 44 * q^85 + 11 * q^86 + 21 * q^87 + 52 * q^88 + 63 * q^89 + 18 * q^90 - 23 * q^91 + 52 * q^92 + 39 * q^93 + 17 * q^94 + 37 * q^95 + 61 * q^96 + 8 * q^97 + 7 * q^98 + 8 * q^99

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