LMFDB - Embedded newform 8043.2.a.t.1.6

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:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.35415 q^{2} -1.00000 q^{3} +3.54201 q^{4} -1.85354 q^{5} +2.35415 q^{6} +1.00000 q^{7} -3.63012 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.35415 q^{2} -1.00000 q^{3} +3.54201 q^{4} -1.85354 q^{5} +2.35415 q^{6} +1.00000 q^{7} -3.63012 q^{8} +1.00000 q^{9} +4.36349 q^{10} -4.89366 q^{11} -3.54201 q^{12} +4.60003 q^{13} -2.35415 q^{14} +1.85354 q^{15} +1.46181 q^{16} -1.22303 q^{17} -2.35415 q^{18} -2.61498 q^{19} -6.56524 q^{20} -1.00000 q^{21} +11.5204 q^{22} -1.19009 q^{23} +3.63012 q^{24} -1.56441 q^{25} -10.8292 q^{26} -1.00000 q^{27} +3.54201 q^{28} +3.14129 q^{29} -4.36349 q^{30} +4.94813 q^{31} +3.81891 q^{32} +4.89366 q^{33} +2.87920 q^{34} -1.85354 q^{35} +3.54201 q^{36} +4.92663 q^{37} +6.15604 q^{38} -4.60003 q^{39} +6.72855 q^{40} +7.78435 q^{41} +2.35415 q^{42} -9.42641 q^{43} -17.3334 q^{44} -1.85354 q^{45} +2.80164 q^{46} -10.0129 q^{47} -1.46181 q^{48} +1.00000 q^{49} +3.68285 q^{50} +1.22303 q^{51} +16.2934 q^{52} -10.1192 q^{53} +2.35415 q^{54} +9.07056 q^{55} -3.63012 q^{56} +2.61498 q^{57} -7.39505 q^{58} -8.79243 q^{59} +6.56524 q^{60} -6.61793 q^{61} -11.6486 q^{62} +1.00000 q^{63} -11.9139 q^{64} -8.52632 q^{65} -11.5204 q^{66} +8.06470 q^{67} -4.33199 q^{68} +1.19009 q^{69} +4.36349 q^{70} -4.14638 q^{71} -3.63012 q^{72} +7.78221 q^{73} -11.5980 q^{74} +1.56441 q^{75} -9.26227 q^{76} -4.89366 q^{77} +10.8292 q^{78} +1.22109 q^{79} -2.70952 q^{80} +1.00000 q^{81} -18.3255 q^{82} +7.07122 q^{83} -3.54201 q^{84} +2.26693 q^{85} +22.1912 q^{86} -3.14129 q^{87} +17.7645 q^{88} +10.1317 q^{89} +4.36349 q^{90} +4.60003 q^{91} -4.21530 q^{92} -4.94813 q^{93} +23.5719 q^{94} +4.84695 q^{95} -3.81891 q^{96} -10.3978 q^{97} -2.35415 q^{98} -4.89366 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.35415	−1.66463	−0.832317	−	0.554300i	$-0.812986\pi$
$2$	−2.35415	−1.66463	−0.832317	+	0.554300i	$0.812986\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.54201	1.77100
$5$	−1.85354	−0.828926	−0.414463	−	0.910066i	$-0.636031\pi$
$5$	−1.85354	−0.828926	−0.414463	+	0.910066i	$0.636031\pi$
$6$	2.35415	0.961077
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.63012	−1.28344
$9$	1.00000	0.333333
$10$	4.36349	1.37986
$11$	−4.89366	−1.47549	−0.737746	−	0.675078i	$-0.764110\pi$
$11$	−4.89366	−1.47549	−0.737746	+	0.675078i	$0.764110\pi$
$12$	−3.54201	−1.02249
$13$	4.60003	1.27582	0.637910	−	0.770111i	$-0.279799\pi$
$13$	4.60003	1.27582	0.637910	+	0.770111i	$0.279799\pi$
$14$	−2.35415	−0.629172
$15$	1.85354	0.478581
$16$	1.46181	0.365453
$17$	−1.22303	−0.296629	−0.148314	−	0.988940i	$-0.547385\pi$
$17$	−1.22303	−0.296629	−0.148314	+	0.988940i	$0.547385\pi$
$18$	−2.35415	−0.554878
$19$	−2.61498	−0.599916	−0.299958	−	0.953952i	$-0.596973\pi$
$19$	−2.61498	−0.599916	−0.299958	+	0.953952i	$0.596973\pi$
$20$	−6.56524	−1.46803
$21$	−1.00000	−0.218218
$22$	11.5204	2.45615
$23$	−1.19009	−0.248150	−0.124075	−	0.992273i	$-0.539596\pi$
$23$	−1.19009	−0.248150	−0.124075	+	0.992273i	$0.539596\pi$
$24$	3.63012	0.740995
$25$	−1.56441	−0.312882
$26$	−10.8292	−2.12377
$27$	−1.00000	−0.192450
$28$	3.54201	0.669377
$29$	3.14129	0.583322	0.291661	−	0.956522i	$-0.405792\pi$
$29$	3.14129	0.583322	0.291661	+	0.956522i	$0.405792\pi$
$30$	−4.36349	−0.796661
$31$	4.94813	0.888711	0.444356	−	0.895851i	$-0.353433\pi$
$31$	4.94813	0.888711	0.444356	+	0.895851i	$0.353433\pi$
$32$	3.81891	0.675095
$33$	4.89366	0.851876
$34$	2.87920	0.493778
$35$	−1.85354	−0.313305
$36$	3.54201	0.590335
$37$	4.92663	0.809932	0.404966	−	0.914332i	$-0.367283\pi$
$37$	4.92663	0.809932	0.404966	+	0.914332i	$0.367283\pi$
$38$	6.15604	0.998641
$39$	−4.60003	−0.736595
$40$	6.72855	1.06388
$41$	7.78435	1.21571	0.607856	−	0.794047i	$-0.292030\pi$
$41$	7.78435	1.21571	0.607856	+	0.794047i	$0.292030\pi$
$42$	2.35415	0.363253
$43$	−9.42641	−1.43751	−0.718757	−	0.695261i	$-0.755289\pi$
$43$	−9.42641	−1.43751	−0.718757	+	0.695261i	$0.755289\pi$
$44$	−17.3334	−2.61310
$45$	−1.85354	−0.276309
$46$	2.80164	0.413079
$47$	−10.0129	−1.46054	−0.730269	−	0.683160i	$-0.760605\pi$
$47$	−10.0129	−1.46054	−0.730269	+	0.683160i	$0.760605\pi$
$48$	−1.46181	−0.210994
$49$	1.00000	0.142857
$50$	3.68285	0.520833
$51$	1.22303	0.171259
$52$	16.2934	2.25948
$53$	−10.1192	−1.38998	−0.694989	−	0.719021i	$-0.744591\pi$
$53$	−10.1192	−1.38998	−0.694989	+	0.719021i	$0.744591\pi$
$54$	2.35415	0.320359
$55$	9.07056	1.22307
$56$	−3.63012	−0.485095
$57$	2.61498	0.346362
$58$	−7.39505	−0.971018
$59$	−8.79243	−1.14468	−0.572339	−	0.820017i	$-0.693964\pi$
$59$	−8.79243	−1.14468	−0.572339	+	0.820017i	$0.693964\pi$
$60$	6.56524	0.847569
$61$	−6.61793	−0.847339	−0.423669	−	0.905817i	$-0.639258\pi$
$61$	−6.61793	−0.847339	−0.423669	+	0.905817i	$0.639258\pi$
$62$	−11.6486	−1.47938
$63$	1.00000	0.125988
$64$	−11.9139	−1.48924
$65$	−8.52632	−1.05756
$66$	−11.5204	−1.41806
$67$	8.06470	0.985260	0.492630	−	0.870239i	$-0.336036\pi$
$67$	8.06470	0.985260	0.492630	+	0.870239i	$0.336036\pi$
$68$	−4.33199	−0.525331
$69$	1.19009	0.143270
$70$	4.36349	0.521537
$71$	−4.14638	−0.492085	−0.246042	−	0.969259i	$-0.579130\pi$
$71$	−4.14638	−0.492085	−0.246042	+	0.969259i	$0.579130\pi$
$72$	−3.63012	−0.427813
$73$	7.78221	0.910839	0.455419	−	0.890277i	$-0.349489\pi$
$73$	7.78221	0.910839	0.455419	+	0.890277i	$0.349489\pi$
$74$	−11.5980	−1.34824
$75$	1.56441	0.180642
$76$	−9.26227	−1.06245
$77$	−4.89366	−0.557684
$78$	10.8292	1.22616
$79$	1.22109	0.137383	0.0686914	−	0.997638i	$-0.478118\pi$
$79$	1.22109	0.137383	0.0686914	+	0.997638i	$0.478118\pi$
$80$	−2.70952	−0.302933
$81$	1.00000	0.111111
$82$	−18.3255	−2.02371
$83$	7.07122	0.776167	0.388084	−	0.921624i	$-0.373137\pi$
$83$	7.07122	0.776167	0.388084	+	0.921624i	$0.373137\pi$
$84$	−3.54201	−0.386465
$85$	2.26693	0.245883
$86$	22.1912	2.39293
$87$	−3.14129	−0.336781
$88$	17.7645	1.89371
$89$	10.1317	1.07395	0.536977	−	0.843597i	$-0.319566\pi$
$89$	10.1317	1.07395	0.536977	+	0.843597i	$0.319566\pi$
$90$	4.36349	0.459953
$91$	4.60003	0.482215
$92$	−4.21530	−0.439475
$93$	−4.94813	−0.513098
$94$	23.5719	2.43126
$95$	4.84695	0.497286
$96$	−3.81891	−0.389766
$97$	−10.3978	−1.05574	−0.527871	−	0.849325i	$-0.677009\pi$
$97$	−10.3978	−1.05574	−0.527871	+	0.849325i	$0.677009\pi$
$98$	−2.35415	−0.237805
$99$	−4.89366	−0.491831
$100$	−5.54115	−0.554115
$101$	16.3808	1.62995	0.814975	−	0.579496i	$-0.196751\pi$
$101$	16.3808	1.62995	0.814975	+	0.579496i	$0.196751\pi$
$102$	−2.87920	−0.285083
$103$	3.30738	0.325885	0.162943	−	0.986636i	$-0.447901\pi$
$103$	3.30738	0.325885	0.162943	+	0.986636i	$0.447901\pi$
$104$	−16.6987	−1.63744
$105$	1.85354	0.180887
$106$	23.8221	2.31380
$107$	−7.82407	−0.756382	−0.378191	−	0.925728i	$-0.623454\pi$
$107$	−7.82407	−0.756382	−0.378191	+	0.925728i	$0.623454\pi$
$108$	−3.54201	−0.340830
$109$	17.0627	1.63431	0.817157	−	0.576416i	$-0.195549\pi$
$109$	17.0627	1.63431	0.817157	+	0.576416i	$0.195549\pi$
$110$	−21.3534	−2.03597
$111$	−4.92663	−0.467615
$112$	1.46181	0.138128
$113$	−1.97723	−0.186002	−0.0930012	−	0.995666i	$-0.529646\pi$
$113$	−1.97723	−0.186002	−0.0930012	+	0.995666i	$0.529646\pi$
$114$	−6.15604	−0.576566
$115$	2.20587	0.205698
$116$	11.1265	1.03307
$117$	4.60003	0.425273
$118$	20.6987	1.90547
$119$	−1.22303	−0.112115
$120$	−6.72855	−0.614230
$121$	12.9479	1.17708
$122$	15.5796	1.41051
$123$	−7.78435	−0.701892
$124$	17.5263	1.57391
$125$	12.1674	1.08828
$126$	−2.35415	−0.209724
$127$	−10.9174	−0.968764	−0.484382	−	0.874857i	$-0.660956\pi$
$127$	−10.9174	−0.968764	−0.484382	+	0.874857i	$0.660956\pi$
$128$	20.4093	1.80394
$129$	9.42641	0.829949
$130$	20.0722	1.76045
$131$	−18.4955	−1.61596	−0.807978	−	0.589213i	$-0.799438\pi$
$131$	−18.4955	−1.61596	−0.807978	+	0.589213i	$0.799438\pi$
$132$	17.3334	1.50868
$133$	−2.61498	−0.226747
$134$	−18.9855	−1.64010
$135$	1.85354	0.159527
$136$	4.43975	0.380705
$137$	−17.6056	−1.50415	−0.752073	−	0.659080i	$-0.770946\pi$
$137$	−17.6056	−1.50415	−0.752073	+	0.659080i	$0.770946\pi$
$138$	−2.80164	−0.238492
$139$	3.45178	0.292776	0.146388	−	0.989227i	$-0.453235\pi$
$139$	3.45178	0.292776	0.146388	+	0.989227i	$0.453235\pi$
$140$	−6.56524	−0.554864
$141$	10.0129	0.843242
$142$	9.76119	0.819141
$143$	−22.5110	−1.88246
$144$	1.46181	0.121818
$145$	−5.82249	−0.483531
$146$	−18.3205	−1.51621
$147$	−1.00000	−0.0824786
$148$	17.4502	1.43439
$149$	−8.98603	−0.736164	−0.368082	−	0.929793i	$-0.619985\pi$
$149$	−8.98603	−0.736164	−0.368082	+	0.929793i	$0.619985\pi$
$150$	−3.68285	−0.300703
$151$	−21.2363	−1.72818	−0.864091	−	0.503336i	$-0.832106\pi$
$151$	−21.2363	−1.72818	−0.864091	+	0.503336i	$0.832106\pi$
$152$	9.49267	0.769957
$153$	−1.22303	−0.0988763
$154$	11.5204	0.928339
$155$	−9.17154	−0.736676
$156$	−16.2934	−1.30451
$157$	23.5031	1.87575	0.937874	−	0.346976i	$-0.112791\pi$
$157$	23.5031	1.87575	0.937874	+	0.346976i	$0.112791\pi$
$158$	−2.87461	−0.228692
$159$	10.1192	0.802504
$160$	−7.07849	−0.559604
$161$	−1.19009	−0.0937920
$162$	−2.35415	−0.184959
$163$	−9.13294	−0.715347	−0.357673	−	0.933847i	$-0.616430\pi$
$163$	−9.13294	−0.715347	−0.357673	+	0.933847i	$0.616430\pi$
$164$	27.5723	2.15303
$165$	−9.07056	−0.706142
$166$	−16.6467	−1.29203
$167$	12.3621	0.956608	0.478304	−	0.878194i	$-0.341252\pi$
$167$	12.3621	0.956608	0.478304	+	0.878194i	$0.341252\pi$
$168$	3.63012	0.280070
$169$	8.16031	0.627716
$170$	−5.33669	−0.409306
$171$	−2.61498	−0.199972
$172$	−33.3884	−2.54584
$173$	−2.75338	−0.209336	−0.104668	−	0.994507i	$-0.533378\pi$
$173$	−2.75338	−0.209336	−0.104668	+	0.994507i	$0.533378\pi$
$174$	7.39505	0.560617
$175$	−1.56441	−0.118258
$176$	−7.15360	−0.539223
$177$	8.79243	0.660880
$178$	−23.8514	−1.78774
$179$	9.71086	0.725824	0.362912	−	0.931823i	$-0.381783\pi$
$179$	9.71086	0.725824	0.362912	+	0.931823i	$0.381783\pi$
$180$	−6.56524	−0.489344
$181$	−18.5594	−1.37951	−0.689754	−	0.724044i	$-0.742281\pi$
$181$	−18.5594	−1.37951	−0.689754	+	0.724044i	$0.742281\pi$
$182$	−10.8292	−0.802710
$183$	6.61793	0.489211
$184$	4.32016	0.318486
$185$	−9.13167	−0.671374
$186$	11.6486	0.854119
$187$	5.98510	0.437674
$188$	−35.4659	−2.58662
$189$	−1.00000	−0.0727393
$190$	−11.4104	−0.827800
$191$	2.05200	0.148477	0.0742386	−	0.997241i	$-0.476347\pi$
$191$	2.05200	0.148477	0.0742386	+	0.997241i	$0.476347\pi$
$192$	11.9139	0.859812
$193$	2.11366	0.152144	0.0760722	−	0.997102i	$-0.475762\pi$
$193$	2.11366	0.152144	0.0760722	+	0.997102i	$0.475762\pi$
$194$	24.4781	1.75742
$195$	8.52632	0.610583
$196$	3.54201	0.253001
$197$	18.0674	1.28725	0.643623	−	0.765342i	$-0.277430\pi$
$197$	18.0674	1.28725	0.643623	+	0.765342i	$0.277430\pi$
$198$	11.5204	0.818718
$199$	−20.2945	−1.43864	−0.719321	−	0.694678i	$-0.755547\pi$
$199$	−20.2945	−1.43864	−0.719321	+	0.694678i	$0.755547\pi$
$200$	5.67898	0.401565
$201$	−8.06470	−0.568840
$202$	−38.5628	−2.71327
$203$	3.14129	0.220475
$204$	4.33199	0.303300
$205$	−14.4286	−1.00774
$206$	−7.78605	−0.542480
$207$	−1.19009	−0.0827168
$208$	6.72438	0.466252
$209$	12.7968	0.885172
$210$	−4.36349	−0.301110
$211$	11.1772	0.769470	0.384735	−	0.923027i	$-0.374293\pi$
$211$	11.1772	0.769470	0.384735	+	0.923027i	$0.374293\pi$
$212$	−35.8423	−2.46166
$213$	4.14638	0.284105
$214$	18.4190	1.25910
$215$	17.4722	1.19159
$216$	3.63012	0.246998
$217$	4.94813	0.335901
$218$	−40.1682	−2.72053
$219$	−7.78221	−0.525873
$220$	32.1280	2.16607
$221$	−5.62599	−0.378445
$222$	11.5980	0.778407
$223$	3.42614	0.229431	0.114716	−	0.993398i	$-0.463404\pi$
$223$	3.42614	0.229431	0.114716	+	0.993398i	$0.463404\pi$
$224$	3.81891	0.255162
$225$	−1.56441	−0.104294
$226$	4.65470	0.309626
$227$	−6.56401	−0.435669	−0.217834	−	0.975986i	$-0.569899\pi$
$227$	−6.56401	−0.435669	−0.217834	+	0.975986i	$0.569899\pi$
$228$	9.26227	0.613409
$229$	15.2317	1.00654	0.503268	−	0.864130i	$-0.332131\pi$
$229$	15.2317	1.00654	0.503268	+	0.864130i	$0.332131\pi$
$230$	−5.19294	−0.342412
$231$	4.89366	0.321979
$232$	−11.4032	−0.748659
$233$	−16.4911	−1.08037	−0.540185	−	0.841546i	$-0.681646\pi$
$233$	−16.4911	−1.08037	−0.540185	+	0.841546i	$0.681646\pi$
$234$	−10.8292	−0.707924
$235$	18.5593	1.21068
$236$	−31.1429	−2.02723
$237$	−1.22109	−0.0793180
$238$	2.87920	0.186631
$239$	11.2169	0.725561	0.362780	−	0.931875i	$-0.381828\pi$
$239$	11.2169	0.725561	0.362780	+	0.931875i	$0.381828\pi$
$240$	2.70952	0.174899
$241$	−15.9218	−1.02561	−0.512805	−	0.858505i	$-0.671394\pi$
$241$	−15.9218	−1.02561	−0.512805	+	0.858505i	$0.671394\pi$
$242$	−30.4812	−1.95940
$243$	−1.00000	−0.0641500
$244$	−23.4408	−1.50064
$245$	−1.85354	−0.118418
$246$	18.3255	1.16839
$247$	−12.0290	−0.765385
$248$	−17.9623	−1.14061
$249$	−7.07122	−0.448120
$250$	−28.6438	−1.81159
$251$	26.2970	1.65985	0.829925	−	0.557875i	$-0.188383\pi$
$251$	26.2970	1.65985	0.829925	+	0.557875i	$0.188383\pi$
$252$	3.54201	0.223126
$253$	5.82388	0.366144
$254$	25.7012	1.61264
$255$	−2.26693	−0.141961
$256$	−24.2186	−1.51366
$257$	−20.9871	−1.30914	−0.654571	−	0.756000i	$-0.727151\pi$
$257$	−20.9871	−1.30914	−0.654571	+	0.756000i	$0.727151\pi$
$258$	−22.1912	−1.38156
$259$	4.92663	0.306126
$260$	−30.2003	−1.87294
$261$	3.14129	0.194441
$262$	43.5410	2.68997
$263$	9.81052	0.604942	0.302471	−	0.953159i	$-0.402188\pi$
$263$	9.81052	0.604942	0.302471	+	0.953159i	$0.402188\pi$
$264$	−17.7645	−1.09333
$265$	18.7563	1.15219
$266$	6.15604	0.377451
$267$	−10.1317	−0.620048
$268$	28.5652	1.74490
$269$	−18.6174	−1.13513	−0.567563	−	0.823330i	$-0.692114\pi$
$269$	−18.6174	−1.13513	−0.567563	+	0.823330i	$0.692114\pi$
$270$	−4.36349	−0.265554
$271$	−7.90843	−0.480403	−0.240202	−	0.970723i	$-0.577214\pi$
$271$	−7.90843	−0.480403	−0.240202	+	0.970723i	$0.577214\pi$
$272$	−1.78784	−0.108404
$273$	−4.60003	−0.278407
$274$	41.4461	2.50385
$275$	7.65567	0.461654
$276$	4.21530	0.253731
$277$	10.3134	0.619671	0.309836	−	0.950790i	$-0.399726\pi$
$277$	10.3134	0.619671	0.309836	+	0.950790i	$0.399726\pi$
$278$	−8.12599	−0.487365
$279$	4.94813	0.296237
$280$	6.72855	0.402108
$281$	18.2638	1.08953	0.544765	−	0.838589i	$-0.316619\pi$
$281$	18.2638	1.08953	0.544765	+	0.838589i	$0.316619\pi$
$282$	−23.5719	−1.40369
$283$	10.3572	0.615671	0.307836	−	0.951440i	$-0.400395\pi$
$283$	10.3572	0.615671	0.307836	+	0.951440i	$0.400395\pi$
$284$	−14.6865	−0.871485
$285$	−4.84695	−0.287108
$286$	52.9942	3.13361
$287$	7.78435	0.459496
$288$	3.81891	0.225032
$289$	−15.5042	−0.912011
$290$	13.7070	0.804902
$291$	10.3978	0.609532
$292$	27.5647	1.61310
$293$	−28.6888	−1.67602	−0.838008	−	0.545657i	$-0.816280\pi$
$293$	−28.6888	−1.67602	−0.838008	+	0.545657i	$0.816280\pi$
$294$	2.35415	0.137297
$295$	16.2971	0.948853
$296$	−17.8842	−1.03950
$297$	4.89366	0.283959
$298$	21.1544	1.22544
$299$	−5.47444	−0.316595
$300$	5.54115	0.319918
$301$	−9.42641	−0.543329
$302$	49.9933	2.87679
$303$	−16.3808	−0.941052
$304$	−3.82260	−0.219241
$305$	12.2666	0.702381
$306$	2.87920	0.164593
$307$	1.95046	0.111318	0.0556592	−	0.998450i	$-0.482274\pi$
$307$	1.95046	0.111318	0.0556592	+	0.998450i	$0.482274\pi$
$308$	−17.3334	−0.987661
$309$	−3.30738	−0.188150
$310$	21.5912	1.22630
$311$	−21.1800	−1.20101	−0.600505	−	0.799621i	$-0.705034\pi$
$311$	−21.1800	−1.20101	−0.600505	+	0.799621i	$0.705034\pi$
$312$	16.6987	0.945376
$313$	−12.8187	−0.724555	−0.362278	−	0.932070i	$-0.618001\pi$
$313$	−12.8187	−0.724555	−0.362278	+	0.932070i	$0.618001\pi$
$314$	−55.3297	−3.12243
$315$	−1.85354	−0.104435
$316$	4.32510	0.243306
$317$	4.36874	0.245373	0.122686	−	0.992445i	$-0.460849\pi$
$317$	4.36874	0.245373	0.122686	+	0.992445i	$0.460849\pi$
$318$	−23.8221	−1.33587
$319$	−15.3724	−0.860688
$320$	22.0829	1.23447
$321$	7.82407	0.436697
$322$	2.80164	0.156129
$323$	3.19820	0.177953
$324$	3.54201	0.196778
$325$	−7.19633	−0.399180
$326$	21.5003	1.19079
$327$	−17.0627	−0.943571
$328$	−28.2581	−1.56029
$329$	−10.0129	−0.552031
$330$	21.3534	1.17547
$331$	−21.3008	−1.17080	−0.585400	−	0.810745i	$-0.699063\pi$
$331$	−21.3008	−1.17080	−0.585400	+	0.810745i	$0.699063\pi$
$332$	25.0463	1.37460
$333$	4.92663	0.269977
$334$	−29.1022	−1.59240
$335$	−14.9482	−0.816707
$336$	−1.46181	−0.0797484
$337$	13.2733	0.723044	0.361522	−	0.932364i	$-0.382257\pi$
$337$	13.2733	0.723044	0.361522	+	0.932364i	$0.382257\pi$
$338$	−19.2106	−1.04492
$339$	1.97723	0.107389
$340$	8.02950	0.435461
$341$	−24.2145	−1.31129
$342$	6.15604	0.332880
$343$	1.00000	0.0539949
$344$	34.2190	1.84496
$345$	−2.20587	−0.118760
$346$	6.48187	0.348468
$347$	28.8843	1.55059	0.775295	−	0.631599i	$-0.217601\pi$
$347$	28.8843	1.55059	0.775295	+	0.631599i	$0.217601\pi$
$348$	−11.1265	−0.596441
$349$	−15.8185	−0.846746	−0.423373	−	0.905955i	$-0.639154\pi$
$349$	−15.8185	−0.846746	−0.423373	+	0.905955i	$0.639154\pi$
$350$	3.68285	0.196856
$351$	−4.60003	−0.245532
$352$	−18.6885	−0.996098
$353$	−4.09048	−0.217714	−0.108857	−	0.994057i	$-0.534719\pi$
$353$	−4.09048	−0.217714	−0.108857	+	0.994057i	$0.534719\pi$
$354$	−20.6987	−1.10012
$355$	7.68546	0.407902
$356$	35.8865	1.90198
$357$	1.22303	0.0647297
$358$	−22.8608	−1.20823
$359$	0.184855	0.00975628	0.00487814	−	0.999988i	$-0.498447\pi$
$359$	0.184855	0.00975628	0.00487814	+	0.999988i	$0.498447\pi$
$360$	6.72855	0.354626
$361$	−12.1619	−0.640100
$362$	43.6915	2.29637
$363$	−12.9479	−0.679587
$364$	16.2934	0.854004
$365$	−14.4246	−0.755018
$366$	−15.5796	−0.814357
$367$	−35.7770	−1.86754	−0.933772	−	0.357869i	$-0.883503\pi$
$367$	−35.7770	−1.86754	−0.933772	+	0.357869i	$0.883503\pi$
$368$	−1.73968	−0.0906873
$369$	7.78435	0.405237
$370$	21.4973	1.11759
$371$	−10.1192	−0.525362
$372$	−17.5263	−0.908698
$373$	29.1089	1.50720	0.753600	−	0.657333i	$-0.228316\pi$
$373$	29.1089	1.50720	0.753600	+	0.657333i	$0.228316\pi$
$374$	−14.0898	−0.728566
$375$	−12.1674	−0.628320
$376$	36.3482	1.87451
$377$	14.4500	0.744214
$378$	2.35415	0.121084
$379$	−16.4447	−0.844707	−0.422353	−	0.906431i	$-0.638796\pi$
$379$	−16.4447	−0.844707	−0.422353	+	0.906431i	$0.638796\pi$
$380$	17.1679	0.880697
$381$	10.9174	0.559316
$382$	−4.83070	−0.247160
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−20.4093	−1.04151
$385$	9.07056	0.462279
$386$	−4.97586	−0.253265
$387$	−9.42641	−0.479172
$388$	−36.8293	−1.86972
$389$	−1.58700	−0.0804643	−0.0402322	−	0.999190i	$-0.512810\pi$
$389$	−1.58700	−0.0804643	−0.0402322	+	0.999190i	$0.512810\pi$
$390$	−20.0722	−1.01640
$391$	1.45552	0.0736086
$392$	−3.63012	−0.183349
$393$	18.4955	0.932972
$394$	−42.5332	−2.14279
$395$	−2.26332	−0.113880
$396$	−17.3334	−0.871035
$397$	39.6043	1.98768	0.993841	−	0.110818i	$-0.0353470\pi$
$397$	39.6043	1.98768	0.993841	+	0.110818i	$0.0353470\pi$
$398$	47.7764	2.39481
$399$	2.61498	0.130913
$400$	−2.28687	−0.114343
$401$	−3.21257	−0.160428	−0.0802141	−	0.996778i	$-0.525560\pi$
$401$	−3.21257	−0.160428	−0.0802141	+	0.996778i	$0.525560\pi$
$402$	18.9855	0.946910
$403$	22.7616	1.13384
$404$	58.0209	2.88665
$405$	−1.85354	−0.0921029
$406$	−7.39505	−0.367010
$407$	−24.1092	−1.19505
$408$	−4.43975	−0.219800
$409$	−6.10980	−0.302110	−0.151055	−	0.988525i	$-0.548267\pi$
$409$	−6.10980	−0.302110	−0.151055	+	0.988525i	$0.548267\pi$
$410$	33.9670	1.67751
$411$	17.6056	0.868419
$412$	11.7148	0.577144
$413$	−8.79243	−0.432647
$414$	2.80164	0.137693
$415$	−13.1068	−0.643385
$416$	17.5671	0.861300
$417$	−3.45178	−0.169034
$418$	−30.1255	−1.47349
$419$	6.65302	0.325022	0.162511	−	0.986707i	$-0.448041\pi$
$419$	6.65302	0.325022	0.162511	+	0.986707i	$0.448041\pi$
$420$	6.56524	0.320351
$421$	−15.2817	−0.744784	−0.372392	−	0.928075i	$-0.621462\pi$
$421$	−15.2817	−0.744784	−0.372392	+	0.928075i	$0.621462\pi$
$422$	−26.3128	−1.28089
$423$	−10.0129	−0.486846
$424$	36.7338	1.78395
$425$	1.91332	0.0928097
$426$	−9.76119	−0.472931
$427$	−6.61793	−0.320264
$428$	−27.7129	−1.33956
$429$	22.5110	1.08684
$430$	−41.1321	−1.98357
$431$	−10.5743	−0.509345	−0.254673	−	0.967027i	$-0.581968\pi$
$431$	−10.5743	−0.509345	−0.254673	+	0.967027i	$0.581968\pi$
$432$	−1.46181	−0.0703314
$433$	26.5598	1.27638	0.638192	−	0.769877i	$-0.279683\pi$
$433$	26.5598	1.27638	0.638192	+	0.769877i	$0.279683\pi$
$434$	−11.6486	−0.559152
$435$	5.82249	0.279167
$436$	60.4363	2.89438
$437$	3.11205	0.148869
$438$	18.3205	0.875386
$439$	−1.21182	−0.0578369	−0.0289184	−	0.999582i	$-0.509206\pi$
$439$	−1.21182	−0.0578369	−0.0289184	+	0.999582i	$0.509206\pi$
$440$	−32.9272	−1.56974
$441$	1.00000	0.0476190
$442$	13.2444	0.629972
$443$	9.53937	0.453229	0.226615	−	0.973984i	$-0.427234\pi$
$443$	9.53937	0.453229	0.226615	+	0.973984i	$0.427234\pi$
$444$	−17.4502	−0.828148
$445$	−18.7794	−0.890229
$446$	−8.06564	−0.381919
$447$	8.98603	0.425024
$448$	−11.9139	−0.562879
$449$	16.3208	0.770224	0.385112	−	0.922870i	$-0.374163\pi$
$449$	16.3208	0.770224	0.385112	+	0.922870i	$0.374163\pi$
$450$	3.68285	0.173611
$451$	−38.0940	−1.79377
$452$	−7.00338	−0.329411
$453$	21.2363	0.997766
$454$	15.4526	0.725229
$455$	−8.52632	−0.399720
$456$	−9.49267	−0.444535
$457$	−13.3906	−0.626384	−0.313192	−	0.949690i	$-0.601398\pi$
$457$	−13.3906	−0.626384	−0.313192	+	0.949690i	$0.601398\pi$
$458$	−35.8576	−1.67551
$459$	1.22303	0.0570863
$460$	7.81321	0.364293
$461$	22.5156	1.04865	0.524327	−	0.851517i	$-0.324317\pi$
$461$	22.5156	1.04865	0.524327	+	0.851517i	$0.324317\pi$
$462$	−11.5204	−0.535977
$463$	−10.9731	−0.509963	−0.254981	−	0.966946i	$-0.582069\pi$
$463$	−10.9731	−0.509963	−0.254981	+	0.966946i	$0.582069\pi$
$464$	4.59197	0.213177
$465$	9.17154	0.425320
$466$	38.8226	1.79842
$467$	8.77488	0.406053	0.203027	−	0.979173i	$-0.434922\pi$
$467$	8.77488	0.406053	0.203027	+	0.979173i	$0.434922\pi$
$468$	16.2934	0.753161
$469$	8.06470	0.372393
$470$	−43.6914	−2.01533
$471$	−23.5031	−1.08296
$472$	31.9176	1.46913
$473$	46.1296	2.12104
$474$	2.87461	0.132035
$475$	4.09089	0.187703
$476$	−4.33199	−0.198557
$477$	−10.1192	−0.463326
$478$	−26.4062	−1.20779
$479$	−25.5503	−1.16742	−0.583711	−	0.811962i	$-0.698400\pi$
$479$	−25.5503	−1.16742	−0.583711	+	0.811962i	$0.698400\pi$
$480$	7.07849	0.323087
$481$	22.6626	1.03333
$482$	37.4822	1.70727
$483$	1.19009	0.0541509
$484$	45.8615	2.08461
$485$	19.2728	0.875131
$486$	2.35415	0.106786
$487$	−11.6535	−0.528069	−0.264035	−	0.964513i	$-0.585053\pi$
$487$	−11.6535	−0.528069	−0.264035	+	0.964513i	$0.585053\pi$
$488$	24.0238	1.08751
$489$	9.13294	0.413006
$490$	4.36349	0.197123
$491$	9.35777	0.422310	0.211155	−	0.977453i	$-0.432277\pi$
$491$	9.35777	0.422310	0.211155	+	0.977453i	$0.432277\pi$
$492$	−27.5723	−1.24305
$493$	−3.84190	−0.173030
$494$	28.3180	1.27409
$495$	9.07056	0.407691
$496$	7.23324	0.324782
$497$	−4.14638	−0.185991
$498$	16.6467	0.745956
$499$	−19.1838	−0.858783	−0.429392	−	0.903118i	$-0.641272\pi$
$499$	−19.1838	−0.858783	−0.429392	+	0.903118i	$0.641272\pi$
$500$	43.0969	1.92735
$501$	−12.3621	−0.552298
$502$	−61.9069	−2.76304
$503$	0.363491	0.0162073	0.00810363	−	0.999967i	$-0.497421\pi$
$503$	0.363491	0.0162073	0.00810363	+	0.999967i	$0.497421\pi$
$504$	−3.63012	−0.161698
$505$	−30.3624	−1.35111
$506$	−13.7103	−0.609496
$507$	−8.16031	−0.362412
$508$	−38.6696	−1.71569
$509$	−22.5669	−1.00026	−0.500130	−	0.865951i	$-0.666714\pi$
$509$	−22.5669	−1.00026	−0.500130	+	0.865951i	$0.666714\pi$
$510$	5.33669	0.236313
$511$	7.78221	0.344265
$512$	16.1956	0.715752
$513$	2.61498	0.115454
$514$	49.4068	2.17924
$515$	−6.13034	−0.270135
$516$	33.3884	1.46984
$517$	48.9999	2.15501
$518$	−11.5980	−0.509587
$519$	2.75338	0.120860
$520$	30.9516	1.35732
$521$	20.1970	0.884846	0.442423	−	0.896806i	$-0.354119\pi$
$521$	20.1970	0.884846	0.442423	+	0.896806i	$0.354119\pi$
$522$	−7.39505	−0.323673
$523$	20.7367	0.906752	0.453376	−	0.891319i	$-0.350220\pi$
$523$	20.7367	0.906752	0.453376	+	0.891319i	$0.350220\pi$
$524$	−65.5111	−2.86186
$525$	1.56441	0.0682763
$526$	−23.0954	−1.00701
$527$	−6.05173	−0.263617
$528$	7.15360	0.311321
$529$	−21.5837	−0.938421
$530$	−44.1550	−1.91797
$531$	−8.79243	−0.381559
$532$	−9.26227	−0.401570
$533$	35.8083	1.55103
$534$	23.8514	1.03215
$535$	14.5022	0.626984
$536$	−29.2758	−1.26452
$537$	−9.71086	−0.419055
$538$	43.8282	1.88957
$539$	−4.89366	−0.210785
$540$	6.56524	0.282523
$541$	28.4854	1.22468	0.612341	−	0.790594i	$-0.290228\pi$
$541$	28.4854	1.22468	0.612341	+	0.790594i	$0.290228\pi$
$542$	18.6176	0.799695
$543$	18.5594	0.796459
$544$	−4.67066	−0.200253
$545$	−31.6264	−1.35472
$546$	10.8292	0.463445
$547$	−12.0685	−0.516012	−0.258006	−	0.966143i	$-0.583065\pi$
$547$	−12.0685	−0.516012	−0.258006	+	0.966143i	$0.583065\pi$
$548$	−62.3591	−2.66385
$549$	−6.61793	−0.282446
$550$	−18.0226	−0.768485
$551$	−8.21439	−0.349945
$552$	−4.32016	−0.183878
$553$	1.22109	0.0519258
$554$	−24.2792	−1.03153
$555$	9.13167	0.387618
$556$	12.2262	0.518508
$557$	26.4991	1.12280	0.561401	−	0.827544i	$-0.310263\pi$
$557$	26.4991	1.12280	0.561401	+	0.827544i	$0.310263\pi$
$558$	−11.6486	−0.493126
$559$	−43.3618	−1.83401
$560$	−2.70952	−0.114498
$561$	−5.98510	−0.252691
$562$	−42.9958	−1.81367
$563$	10.1578	0.428100	0.214050	−	0.976823i	$-0.431334\pi$
$563$	10.1578	0.428100	0.214050	+	0.976823i	$0.431334\pi$
$564$	35.4659	1.49339
$565$	3.66487	0.154182
$566$	−24.3824	−1.02487
$567$	1.00000	0.0419961
$568$	15.0519	0.631562
$569$	−24.7666	−1.03827	−0.519134	−	0.854693i	$-0.673745\pi$
$569$	−24.7666	−1.03827	−0.519134	+	0.854693i	$0.673745\pi$
$570$	11.4104	0.477930
$571$	12.4559	0.521262	0.260631	−	0.965438i	$-0.416069\pi$
$571$	12.4559	0.521262	0.260631	+	0.965438i	$0.416069\pi$
$572$	−79.7341	−3.33385
$573$	−2.05200	−0.0857234
$574$	−18.3255	−0.764892
$575$	1.86178	0.0776417
$576$	−11.9139	−0.496413
$577$	−18.5600	−0.772661	−0.386331	−	0.922360i	$-0.626258\pi$
$577$	−18.5600	−0.772661	−0.386331	+	0.922360i	$0.626258\pi$
$578$	36.4992	1.51816
$579$	−2.11366	−0.0878406
$580$	−20.6233	−0.856336
$581$	7.07122	0.293364
$582$	−24.4781	−1.01465
$583$	49.5198	2.05090
$584$	−28.2503	−1.16901
$585$	−8.52632	−0.352520
$586$	67.5376	2.78995
$587$	10.2136	0.421561	0.210780	−	0.977533i	$-0.432399\pi$
$587$	10.2136	0.421561	0.210780	+	0.977533i	$0.432399\pi$
$588$	−3.54201	−0.146070
$589$	−12.9392	−0.533152
$590$	−38.3657	−1.57949
$591$	−18.0674	−0.743192
$592$	7.20180	0.295992
$593$	−21.0053	−0.862586	−0.431293	−	0.902212i	$-0.641942\pi$
$593$	−21.0053	−0.862586	−0.431293	+	0.902212i	$0.641942\pi$
$594$	−11.5204	−0.472687
$595$	2.26693	0.0929352
$596$	−31.8286	−1.30375
$597$	20.2945	0.830601
$598$	12.8876	0.527015
$599$	−25.1037	−1.02571	−0.512854	−	0.858476i	$-0.671412\pi$
$599$	−25.1037	−1.02571	−0.512854	+	0.858476i	$0.671412\pi$
$600$	−5.67898	−0.231844
$601$	25.3801	1.03528	0.517638	−	0.855600i	$-0.326811\pi$
$601$	25.3801	1.03528	0.517638	+	0.855600i	$0.326811\pi$
$602$	22.1912	0.904444
$603$	8.06470	0.328420
$604$	−75.2190	−3.06062
$605$	−23.9993	−0.975711
$606$	38.5628	1.56651
$607$	36.0789	1.46440	0.732199	−	0.681091i	$-0.238494\pi$
$607$	36.0789	1.46440	0.732199	+	0.681091i	$0.238494\pi$
$608$	−9.98637	−0.405001
$609$	−3.14129	−0.127291
$610$	−28.8773	−1.16921
$611$	−46.0599	−1.86338
$612$	−4.33199	−0.175110
$613$	13.6296	0.550494	0.275247	−	0.961374i	$-0.411240\pi$
$613$	13.6296	0.550494	0.275247	+	0.961374i	$0.411240\pi$
$614$	−4.59166	−0.185304
$615$	14.4286	0.581816
$616$	17.7645	0.715754
$617$	48.8545	1.96681	0.983404	−	0.181429i	$-0.0580722\pi$
$617$	48.8545	1.96681	0.983404	+	0.181429i	$0.0580722\pi$
$618$	7.78605	0.313201
$619$	−12.7279	−0.511576	−0.255788	−	0.966733i	$-0.582335\pi$
$619$	−12.7279	−0.511576	−0.255788	+	0.966733i	$0.582335\pi$
$620$	−32.4857	−1.30466
$621$	1.19009	0.0477566
$622$	49.8609	1.99924
$623$	10.1317	0.405917
$624$	−6.72438	−0.269191
$625$	−14.7306	−0.589224
$626$	30.1771	1.20612
$627$	−12.7968	−0.511055
$628$	83.2480	3.32196
$629$	−6.02542	−0.240249
$630$	4.36349	0.173846
$631$	15.6795	0.624191	0.312095	−	0.950051i	$-0.398969\pi$
$631$	15.6795	0.624191	0.312095	+	0.950051i	$0.398969\pi$
$632$	−4.43268	−0.176323
$633$	−11.1772	−0.444254
$634$	−10.2847	−0.408456
$635$	20.2358	0.803034
$636$	35.8423	1.42124
$637$	4.60003	0.182260
$638$	36.1888	1.43273
$639$	−4.14638	−0.164028
$640$	−37.8293	−1.49533
$641$	38.5578	1.52294	0.761470	−	0.648200i	$-0.224478\pi$
$641$	38.5578	1.52294	0.761470	+	0.648200i	$0.224478\pi$
$642$	−18.4190	−0.726941
$643$	−12.1674	−0.479834	−0.239917	−	0.970793i	$-0.577120\pi$
$643$	−12.1674	−0.479834	−0.239917	+	0.970793i	$0.577120\pi$
$644$	−4.21530	−0.166106
$645$	−17.4722	−0.687967
$646$	−7.52903	−0.296226
$647$	30.9802	1.21796	0.608978	−	0.793187i	$-0.291580\pi$
$647$	30.9802	1.21796	0.608978	+	0.793187i	$0.291580\pi$
$648$	−3.63012	−0.142604
$649$	43.0271	1.68896
$650$	16.9412	0.664489
$651$	−4.94813	−0.193933
$652$	−32.3489	−1.26688
$653$	29.5979	1.15825	0.579127	−	0.815237i	$-0.303393\pi$
$653$	29.5979	1.15825	0.579127	+	0.815237i	$0.303393\pi$
$654$	40.1682	1.57070
$655$	34.2820	1.33951
$656$	11.3793	0.444285
$657$	7.78221	0.303613
$658$	23.5719	0.918930
$659$	34.0802	1.32758	0.663788	−	0.747920i	$-0.268948\pi$
$659$	34.0802	1.32758	0.663788	+	0.747920i	$0.268948\pi$
$660$	−32.1280	−1.25058
$661$	21.6834	0.843388	0.421694	−	0.906738i	$-0.361436\pi$
$661$	21.6834	0.843388	0.421694	+	0.906738i	$0.361436\pi$
$662$	50.1453	1.94895
$663$	5.62599	0.218495
$664$	−25.6694	−0.996164
$665$	4.84695	0.187957
$666$	−11.5980	−0.449413
$667$	−3.73841	−0.144752
$668$	43.7867	1.69416
$669$	−3.42614	−0.132462
$670$	35.1903	1.35952
$671$	32.3859	1.25024
$672$	−3.81891	−0.147318
$673$	43.4986	1.67675	0.838373	−	0.545097i	$-0.183507\pi$
$673$	43.4986	1.67675	0.838373	+	0.545097i	$0.183507\pi$
$674$	−31.2474	−1.20360
$675$	1.56441	0.0602141
$676$	28.9039	1.11169
$677$	42.2892	1.62531	0.812654	−	0.582747i	$-0.198022\pi$
$677$	42.2892	1.62531	0.812654	+	0.582747i	$0.198022\pi$
$678$	−4.65470	−0.178763
$679$	−10.3978	−0.399033
$680$	−8.22923	−0.315577
$681$	6.56401	0.251533
$682$	57.0044	2.18281
$683$	−45.2459	−1.73128	−0.865642	−	0.500663i	$-0.833090\pi$
$683$	−45.2459	−1.73128	−0.865642	+	0.500663i	$0.833090\pi$
$684$	−9.26227	−0.354152
$685$	32.6326	1.24683
$686$	−2.35415	−0.0898818
$687$	−15.2317	−0.581124
$688$	−13.7796	−0.525344
$689$	−46.5486	−1.77336
$690$	5.19294	0.197692
$691$	49.2823	1.87479	0.937393	−	0.348273i	$-0.113232\pi$
$691$	49.2823	1.87479	0.937393	+	0.348273i	$0.113232\pi$
$692$	−9.75251	−0.370735
$693$	−4.89366	−0.185895
$694$	−67.9979	−2.58117
$695$	−6.39799	−0.242690
$696$	11.4032	0.432239
$697$	−9.52052	−0.360615
$698$	37.2391	1.40952
$699$	16.4911	0.623752
$700$	−5.54115	−0.209436
$701$	−8.56365	−0.323445	−0.161722	−	0.986836i	$-0.551705\pi$
$701$	−8.56365	−0.323445	−0.161722	+	0.986836i	$0.551705\pi$
$702$	10.8292	0.408720
$703$	−12.8830	−0.485892
$704$	58.3026	2.19736
$705$	−18.5593	−0.698985
$706$	9.62960	0.362415
$707$	16.3808	0.616063
$708$	31.1429	1.17042
$709$	−48.8916	−1.83616	−0.918081	−	0.396393i	$-0.870262\pi$
$709$	−48.8916	−1.83616	−0.918081	+	0.396393i	$0.870262\pi$
$710$	−18.0927	−0.679007
$711$	1.22109	0.0457943
$712$	−36.7792	−1.37836
$713$	−5.88871	−0.220534
$714$	−2.87920	−0.107751
$715$	41.7249	1.56042
$716$	34.3960	1.28544
$717$	−11.2169	−0.418903
$718$	−0.435176	−0.0162406
$719$	−0.993109	−0.0370367	−0.0185184	−	0.999829i	$-0.505895\pi$
$719$	−0.993109	−0.0370367	−0.0185184	+	0.999829i	$0.505895\pi$
$720$	−2.70952	−0.100978
$721$	3.30738	0.123173
$722$	28.6309	1.06553
$723$	15.9218	0.592136
$724$	−65.7375	−2.44311
$725$	−4.91425	−0.182511
$726$	30.4812	1.13126
$727$	23.9986	0.890058	0.445029	−	0.895516i	$-0.353193\pi$
$727$	23.9986	0.890058	0.445029	+	0.895516i	$0.353193\pi$
$728$	−16.6987	−0.618894
$729$	1.00000	0.0370370
$730$	33.9576	1.25683
$731$	11.5288	0.426408
$732$	23.4408	0.866395
$733$	22.4447	0.829012	0.414506	−	0.910047i	$-0.363954\pi$
$733$	22.4447	0.829012	0.414506	+	0.910047i	$0.363954\pi$
$734$	84.2243	3.10878
$735$	1.85354	0.0683687
$736$	−4.54484	−0.167525
$737$	−39.4659	−1.45374
$738$	−18.3255	−0.674572
$739$	47.7930	1.75809	0.879046	−	0.476737i	$-0.158180\pi$
$739$	47.7930	1.75809	0.879046	+	0.476737i	$0.158180\pi$
$740$	−32.3445	−1.18901
$741$	12.0290	0.441895
$742$	23.8221	0.874535
$743$	28.0421	1.02876	0.514382	−	0.857561i	$-0.328021\pi$
$743$	28.0421	1.02876	0.514382	+	0.857561i	$0.328021\pi$
$744$	17.9623	0.658530
$745$	16.6559	0.610225
$746$	−68.5266	−2.50894
$747$	7.07122	0.258722
$748$	21.1993	0.775122
$749$	−7.82407	−0.285885
$750$	28.6438	1.04592
$751$	−28.9560	−1.05662	−0.528309	−	0.849052i	$-0.677174\pi$
$751$	−28.9560	−1.05662	−0.528309	+	0.849052i	$0.677174\pi$
$752$	−14.6370	−0.533758
$753$	−26.2970	−0.958315
$754$	−34.0175	−1.23884
$755$	39.3621	1.43254
$756$	−3.54201	−0.128822
$757$	16.7150	0.607518	0.303759	−	0.952749i	$-0.401758\pi$
$757$	16.7150	0.607518	0.303759	+	0.952749i	$0.401758\pi$
$758$	38.7132	1.40613
$759$	−5.82388	−0.211393
$760$	−17.5950	−0.638237
$761$	−39.8124	−1.44320	−0.721599	−	0.692311i	$-0.756593\pi$
$761$	−39.8124	−1.44320	−0.721599	+	0.692311i	$0.756593\pi$
$762$	−25.7012	−0.931056
$763$	17.0627	0.617712
$764$	7.26819	0.262954
$765$	2.26693	0.0819611
$766$	2.35415	0.0850588
$767$	−40.4455	−1.46040
$768$	24.2186	0.873914
$769$	26.5906	0.958881	0.479441	−	0.877574i	$-0.340840\pi$
$769$	26.5906	0.958881	0.479441	+	0.877574i	$0.340840\pi$
$770$	−21.3534	−0.769525
$771$	20.9871	0.755834
$772$	7.48660	0.269449
$773$	36.2738	1.30468	0.652339	−	0.757927i	$-0.273788\pi$
$773$	36.2738	1.30468	0.652339	+	0.757927i	$0.273788\pi$
$774$	22.1912	0.797645
$775$	−7.74090	−0.278061
$776$	37.7454	1.35498
$777$	−4.92663	−0.176742
$778$	3.73604	0.133944
$779$	−20.3559	−0.729326
$780$	30.2003	1.08134
$781$	20.2910	0.726068
$782$	−3.42650	−0.122531
$783$	−3.14129	−0.112260
$784$	1.46181	0.0522076
$785$	−43.5637	−1.55486
$786$	−43.5410	−1.55306
$787$	24.8943	0.887385	0.443692	−	0.896179i	$-0.353668\pi$
$787$	24.8943	0.887385	0.443692	+	0.896179i	$0.353668\pi$
$788$	63.9948	2.27972
$789$	−9.81052	−0.349264
$790$	5.32820	0.189569
$791$	−1.97723	−0.0703023
$792$	17.7645	0.631236
$793$	−30.4427	−1.08105
$794$	−93.2343	−3.30876
$795$	−18.7563	−0.665216
$796$	−71.8835	−2.54784
$797$	−3.18869	−0.112949	−0.0564747	−	0.998404i	$-0.517986\pi$
$797$	−3.18869	−0.112949	−0.0564747	+	0.998404i	$0.517986\pi$
$798$	−6.15604	−0.217921
$799$	12.2462	0.433238
$800$	−5.97434	−0.211225
$801$	10.1317	0.357985
$802$	7.56287	0.267054
$803$	−38.0835	−1.34394
$804$	−28.5652	−1.00742
$805$	2.20587	0.0777467
$806$	−53.5841	−1.88742
$807$	18.6174	0.655365
$808$	−59.4642	−2.09194
$809$	53.2753	1.87306	0.936529	−	0.350589i	$-0.114019\pi$
$809$	53.2753	1.87306	0.936529	+	0.350589i	$0.114019\pi$
$810$	4.36349	0.153318
$811$	35.7884	1.25670	0.628351	−	0.777930i	$-0.283730\pi$
$811$	35.7884	1.25670	0.628351	+	0.777930i	$0.283730\pi$
$812$	11.1265	0.390462
$813$	7.90843	0.277361
$814$	56.7566	1.98932
$815$	16.9282	0.592970
$816$	1.78784	0.0625870
$817$	24.6498	0.862389
$818$	14.3834	0.502903
$819$	4.60003	0.160738
$820$	−51.1061	−1.78470
$821$	14.0268	0.489540	0.244770	−	0.969581i	$-0.421288\pi$
$821$	14.0268	0.489540	0.244770	+	0.969581i	$0.421288\pi$
$822$	−41.4461	−1.44560
$823$	32.5594	1.13495	0.567475	−	0.823391i	$-0.307921\pi$
$823$	32.5594	1.13495	0.567475	+	0.823391i	$0.307921\pi$
$824$	−12.0062	−0.418254
$825$	−7.65567	−0.266536
$826$	20.6987	0.720199
$827$	−32.5828	−1.13301	−0.566507	−	0.824057i	$-0.691705\pi$
$827$	−32.5828	−1.13301	−0.566507	+	0.824057i	$0.691705\pi$
$828$	−4.21530	−0.146492
$829$	−21.0641	−0.731585	−0.365793	−	0.930696i	$-0.619202\pi$
$829$	−21.0641	−0.731585	−0.365793	+	0.930696i	$0.619202\pi$
$830$	30.8552	1.07100
$831$	−10.3134	−0.357767
$832$	−54.8044	−1.90000
$833$	−1.22303	−0.0423756
$834$	8.12599	0.281380
$835$	−22.9136	−0.792957
$836$	45.3263	1.56764
$837$	−4.94813	−0.171033
$838$	−15.6622	−0.541042
$839$	31.6584	1.09297	0.546485	−	0.837469i	$-0.315966\pi$
$839$	31.6584	1.09297	0.546485	+	0.837469i	$0.315966\pi$
$840$	−6.72855	−0.232157
$841$	−19.1323	−0.659735
$842$	35.9754	1.23979
$843$	−18.2638	−0.629040
$844$	39.5897	1.36274
$845$	−15.1254	−0.520330
$846$	23.5719	0.810420
$847$	12.9479	0.444894
$848$	−14.7923	−0.507971
$849$	−10.3572	−0.355458
$850$	−4.50424	−0.154494
$851$	−5.86312	−0.200985
$852$	14.6865	0.503152
$853$	−15.9443	−0.545924	−0.272962	−	0.962025i	$-0.588003\pi$
$853$	−15.9443	−0.545924	−0.272962	+	0.962025i	$0.588003\pi$
$854$	15.5796	0.533122
$855$	4.84695	0.165762
$856$	28.4023	0.970771
$857$	−22.9826	−0.785072	−0.392536	−	0.919737i	$-0.628402\pi$
$857$	−22.9826	−0.785072	−0.392536	+	0.919737i	$0.628402\pi$
$858$	−52.9942	−1.80919
$859$	−7.19134	−0.245365	−0.122683	−	0.992446i	$-0.539150\pi$
$859$	−7.19134	−0.245365	−0.122683	+	0.992446i	$0.539150\pi$
$860$	61.8867	2.11032
$861$	−7.78435	−0.265290
$862$	24.8934	0.847873
$863$	−16.8748	−0.574424	−0.287212	−	0.957867i	$-0.592728\pi$
$863$	−16.8748	−0.574424	−0.287212	+	0.957867i	$0.592728\pi$
$864$	−3.81891	−0.129922
$865$	5.10349	0.173524
$866$	−62.5257	−2.12471
$867$	15.5042	0.526550
$868$	17.5263	0.594883
$869$	−5.97557	−0.202707
$870$	−13.7070	−0.464710
$871$	37.0979	1.25701
$872$	−61.9397	−2.09754
$873$	−10.3978	−0.351914
$874$	−7.32622	−0.247813
$875$	12.1674	0.411332
$876$	−27.5647	−0.931323
$877$	−7.00838	−0.236656	−0.118328	−	0.992975i	$-0.537753\pi$
$877$	−7.00838	−0.236656	−0.118328	+	0.992975i	$0.537753\pi$
$878$	2.85279	0.0962772
$879$	28.6888	0.967649
$880$	13.2595	0.446976
$881$	−12.9394	−0.435938	−0.217969	−	0.975956i	$-0.569943\pi$
$881$	−12.9394	−0.435938	−0.217969	+	0.975956i	$0.569943\pi$
$882$	−2.35415	−0.0792683
$883$	37.9016	1.27549	0.637744	−	0.770248i	$-0.279868\pi$
$883$	37.9016	1.27549	0.637744	+	0.770248i	$0.279868\pi$
$884$	−19.9273	−0.670228
$885$	−16.2971	−0.547821
$886$	−22.4571	−0.754461
$887$	−16.3022	−0.547375	−0.273688	−	0.961819i	$-0.588243\pi$
$887$	−16.3022	−0.547375	−0.273688	+	0.961819i	$0.588243\pi$
$888$	17.8842	0.600155
$889$	−10.9174	−0.366158
$890$	44.2095	1.48191
$891$	−4.89366	−0.163944
$892$	12.1354	0.406324
$893$	26.1836	0.876201
$894$	−21.1544	−0.707510
$895$	−17.9994	−0.601654
$896$	20.4093	0.681826
$897$	5.47444	0.182786
$898$	−38.4215	−1.28214
$899$	15.5435	0.518405
$900$	−5.54115	−0.184705
$901$	12.3761	0.412307
$902$	89.6788	2.98598
$903$	9.42641	0.313691
$904$	7.17759	0.238723
$905$	34.4004	1.14351
$906$	−49.9933	−1.66092
$907$	58.4566	1.94102	0.970510	−	0.241059i	$-0.0774949\pi$
$907$	58.4566	1.94102	0.970510	+	0.241059i	$0.0774949\pi$
$908$	−23.2498	−0.771571
$909$	16.3808	0.543317
$910$	20.0722	0.665388
$911$	40.9171	1.35565	0.677823	−	0.735225i	$-0.262924\pi$
$911$	40.9171	1.35565	0.677823	+	0.735225i	$0.262924\pi$
$912$	3.82260	0.126579
$913$	−34.6041	−1.14523
$914$	31.5233	1.04270
$915$	−12.2666	−0.405520
$916$	53.9507	1.78258
$917$	−18.4955	−0.610774
$918$	−2.87920	−0.0950277
$919$	52.0962	1.71850	0.859248	−	0.511559i	$-0.170932\pi$
$919$	52.0962	1.71850	0.859248	+	0.511559i	$0.170932\pi$
$920$	−8.00756	−0.264002
$921$	−1.95046	−0.0642697
$922$	−53.0050	−1.74563
$923$	−19.0735	−0.627812
$924$	17.3334	0.570226
$925$	−7.70725	−0.253413
$926$	25.8323	0.848901
$927$	3.30738	0.108628
$928$	11.9963	0.393798
$929$	38.2945	1.25640	0.628201	−	0.778051i	$-0.283791\pi$
$929$	38.2945	1.25640	0.628201	+	0.778051i	$0.283791\pi$
$930$	−21.5912	−0.708002
$931$	−2.61498	−0.0857024
$932$	−58.4118	−1.91334
$933$	21.1800	0.693403
$934$	−20.6574	−0.675930
$935$	−11.0936	−0.362799
$936$	−16.6987	−0.545813
$937$	−1.38476	−0.0452380	−0.0226190	−	0.999744i	$-0.507200\pi$
$937$	−1.38476	−0.0452380	−0.0226190	+	0.999744i	$0.507200\pi$
$938$	−18.9855	−0.619898
$939$	12.8187	0.418322
$940$	65.7374	2.14412
$941$	3.25997	0.106272	0.0531360	−	0.998587i	$-0.483078\pi$
$941$	3.25997	0.106272	0.0531360	+	0.998587i	$0.483078\pi$
$942$	55.3297	1.80274
$943$	−9.26406	−0.301679
$944$	−12.8529	−0.418326
$945$	1.85354	0.0602955
$946$	−108.596	−3.53076
$947$	36.0830	1.17254	0.586271	−	0.810115i	$-0.300596\pi$
$947$	36.0830	1.17254	0.586271	+	0.810115i	$0.300596\pi$
$948$	−4.32510	−0.140473
$949$	35.7984	1.16207
$950$	−9.63055	−0.312456
$951$	−4.36874	−0.141666
$952$	4.43975	0.143893
$953$	28.6766	0.928926	0.464463	−	0.885593i	$-0.346247\pi$
$953$	28.6766	0.928926	0.464463	+	0.885593i	$0.346247\pi$
$954$	23.8221	0.771267
$955$	−3.80345	−0.123077
$956$	39.7304	1.28497
$957$	15.3724	0.496918
$958$	60.1491	1.94333
$959$	−17.6056	−0.568514
$960$	−22.0829	−0.712721
$961$	−6.51597	−0.210193
$962$	−53.3512	−1.72011
$963$	−7.82407	−0.252127
$964$	−56.3950	−1.81636
$965$	−3.91774	−0.126116
$966$	−2.80164	−0.0901413
$967$	−44.5008	−1.43105	−0.715524	−	0.698588i	$-0.753812\pi$
$967$	−44.5008	−1.43105	−0.715524	+	0.698588i	$0.753812\pi$
$968$	−47.0023	−1.51071
$969$	−3.19820	−0.102741
$970$	−45.3709	−1.45677
$971$	12.7056	0.407742	0.203871	−	0.978998i	$-0.434648\pi$
$971$	12.7056	0.407742	0.203871	+	0.978998i	$0.434648\pi$
$972$	−3.54201	−0.113610
$973$	3.45178	0.110659
$974$	27.4340	0.879042
$975$	7.19633	0.230467
$976$	−9.67416	−0.309662
$977$	8.47552	0.271156	0.135578	−	0.990767i	$-0.456711\pi$
$977$	8.47552	0.271156	0.135578	+	0.990767i	$0.456711\pi$
$978$	−21.5003	−0.687503
$979$	−49.5809	−1.58461
$980$	−6.56524	−0.209719
$981$	17.0627	0.544771
$982$	−22.0296	−0.702992
$983$	−42.9901	−1.37117	−0.685586	−	0.727992i	$-0.740454\pi$
$983$	−42.9901	−1.37117	−0.685586	+	0.727992i	$0.740454\pi$
$984$	28.2581	0.900836
$985$	−33.4885	−1.06703
$986$	9.04439	0.288032
$987$	10.0129	0.318715
$988$	−42.6067	−1.35550
$989$	11.2183	0.356720
$990$	−21.3534	−0.678657
$991$	−11.4870	−0.364895	−0.182448	−	0.983216i	$-0.558402\pi$
$991$	−11.4870	−0.364895	−0.182448	+	0.983216i	$0.558402\pi$
$992$	18.8965	0.599964
$993$	21.3008	0.675962
$994$	9.76119	0.309606
$995$	37.6167	1.19253
$996$	−25.0463	−0.793623
$997$	41.3523	1.30964	0.654820	−	0.755785i	$-0.272745\pi$
$997$	41.3523	1.30964	0.654820	+	0.755785i	$0.272745\pi$
$998$	45.1614	1.42956
$999$	−4.92663	−0.155872

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.6	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.6	✓	52	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)

\(f(q)\)	\(=\)	\(q-2.35415 q^{2} -1.00000 q^{3} +3.54201 q^{4} -1.85354 q^{5} +2.35415 q^{6} +1.00000 q^{7} -3.63012 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.35415 q^{2} -1.00000 q^{3} +3.54201 q^{4} -1.85354 q^{5} +2.35415 q^{6} +1.00000 q^{7} -3.63012 q^{8} +1.00000 q^{9} +4.36349 q^{10} -4.89366 q^{11} -3.54201 q^{12} +4.60003 q^{13} -2.35415 q^{14} +1.85354 q^{15} +1.46181 q^{16} -1.22303 q^{17} -2.35415 q^{18} -2.61498 q^{19} -6.56524 q^{20} -1.00000 q^{21} +11.5204 q^{22} -1.19009 q^{23} +3.63012 q^{24} -1.56441 q^{25} -10.8292 q^{26} -1.00000 q^{27} +3.54201 q^{28} +3.14129 q^{29} -4.36349 q^{30} +4.94813 q^{31} +3.81891 q^{32} +4.89366 q^{33} +2.87920 q^{34} -1.85354 q^{35} +3.54201 q^{36} +4.92663 q^{37} +6.15604 q^{38} -4.60003 q^{39} +6.72855 q^{40} +7.78435 q^{41} +2.35415 q^{42} -9.42641 q^{43} -17.3334 q^{44} -1.85354 q^{45} +2.80164 q^{46} -10.0129 q^{47} -1.46181 q^{48} +1.00000 q^{49} +3.68285 q^{50} +1.22303 q^{51} +16.2934 q^{52} -10.1192 q^{53} +2.35415 q^{54} +9.07056 q^{55} -3.63012 q^{56} +2.61498 q^{57} -7.39505 q^{58} -8.79243 q^{59} +6.56524 q^{60} -6.61793 q^{61} -11.6486 q^{62} +1.00000 q^{63} -11.9139 q^{64} -8.52632 q^{65} -11.5204 q^{66} +8.06470 q^{67} -4.33199 q^{68} +1.19009 q^{69} +4.36349 q^{70} -4.14638 q^{71} -3.63012 q^{72} +7.78221 q^{73} -11.5980 q^{74} +1.56441 q^{75} -9.26227 q^{76} -4.89366 q^{77} +10.8292 q^{78} +1.22109 q^{79} -2.70952 q^{80} +1.00000 q^{81} -18.3255 q^{82} +7.07122 q^{83} -3.54201 q^{84} +2.26693 q^{85} +22.1912 q^{86} -3.14129 q^{87} +17.7645 q^{88} +10.1317 q^{89} +4.36349 q^{90} +4.60003 q^{91} -4.21530 q^{92} -4.94813 q^{93} +23.5719 q^{94} +4.84695 q^{95} -3.81891 q^{96} -10.3978 q^{97} -2.35415 q^{98} -4.89366 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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