LMFDB - Embedded newform 8043.2.a.o.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:	$1$
Dimension:	$41$
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)

$f(q)$	$=$	$q-2.34884 q^{2} -1.00000 q^{3} +3.51704 q^{4} +1.78966 q^{5} +2.34884 q^{6} +1.00000 q^{7} -3.56329 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.34884 q^{2} -1.00000 q^{3} +3.51704 q^{4} +1.78966 q^{5} +2.34884 q^{6} +1.00000 q^{7} -3.56329 q^{8} +1.00000 q^{9} -4.20363 q^{10} +4.79343 q^{11} -3.51704 q^{12} -1.06639 q^{13} -2.34884 q^{14} -1.78966 q^{15} +1.33550 q^{16} -6.56571 q^{17} -2.34884 q^{18} +1.65753 q^{19} +6.29432 q^{20} -1.00000 q^{21} -11.2590 q^{22} -4.89639 q^{23} +3.56329 q^{24} -1.79710 q^{25} +2.50477 q^{26} -1.00000 q^{27} +3.51704 q^{28} +2.03624 q^{29} +4.20363 q^{30} -3.51787 q^{31} +3.98970 q^{32} -4.79343 q^{33} +15.4218 q^{34} +1.78966 q^{35} +3.51704 q^{36} +11.2996 q^{37} -3.89326 q^{38} +1.06639 q^{39} -6.37709 q^{40} +5.38793 q^{41} +2.34884 q^{42} -6.67556 q^{43} +16.8587 q^{44} +1.78966 q^{45} +11.5008 q^{46} +2.16056 q^{47} -1.33550 q^{48} +1.00000 q^{49} +4.22110 q^{50} +6.56571 q^{51} -3.75053 q^{52} -8.82480 q^{53} +2.34884 q^{54} +8.57863 q^{55} -3.56329 q^{56} -1.65753 q^{57} -4.78279 q^{58} -1.10786 q^{59} -6.29432 q^{60} -9.20813 q^{61} +8.26290 q^{62} +1.00000 q^{63} -12.0422 q^{64} -1.90847 q^{65} +11.2590 q^{66} -4.37307 q^{67} -23.0919 q^{68} +4.89639 q^{69} -4.20363 q^{70} +14.2556 q^{71} -3.56329 q^{72} +8.79953 q^{73} -26.5408 q^{74} +1.79710 q^{75} +5.82959 q^{76} +4.79343 q^{77} -2.50477 q^{78} -1.77043 q^{79} +2.39010 q^{80} +1.00000 q^{81} -12.6554 q^{82} -5.39456 q^{83} -3.51704 q^{84} -11.7504 q^{85} +15.6798 q^{86} -2.03624 q^{87} -17.0804 q^{88} -7.92565 q^{89} -4.20363 q^{90} -1.06639 q^{91} -17.2208 q^{92} +3.51787 q^{93} -5.07481 q^{94} +2.96642 q^{95} -3.98970 q^{96} -6.39555 q^{97} -2.34884 q^{98} +4.79343 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) $ 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * 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 $

$2$	−2.34884	−1.66088	−0.830440	−	0.557108i	$-0.811911\pi$
$2$	−2.34884	−1.66088	−0.830440	+	0.557108i	$0.811911\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.51704	1.75852
$5$	1.78966	0.800362	0.400181	−	0.916436i	$-0.368947\pi$
$5$	1.78966	0.800362	0.400181	+	0.916436i	$0.368947\pi$
$6$	2.34884	0.958909
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.56329	−1.25981
$9$	1.00000	0.333333
$10$	−4.20363	−1.32930
$11$	4.79343	1.44527	0.722637	−	0.691228i	$-0.242930\pi$
$11$	4.79343	1.44527	0.722637	+	0.691228i	$0.242930\pi$
$12$	−3.51704	−1.01528
$13$	−1.06639	−0.295762	−0.147881	−	0.989005i	$-0.547245\pi$
$13$	−1.06639	−0.295762	−0.147881	+	0.989005i	$0.547245\pi$
$14$	−2.34884	−0.627753
$15$	−1.78966	−0.462089
$16$	1.33550	0.333875
$17$	−6.56571	−1.59242	−0.796210	−	0.605021i	$-0.793165\pi$
$17$	−6.56571	−1.59242	−0.796210	+	0.605021i	$0.793165\pi$
$18$	−2.34884	−0.553627
$19$	1.65753	0.380263	0.190131	−	0.981759i	$-0.439109\pi$
$19$	1.65753	0.380263	0.190131	+	0.981759i	$0.439109\pi$
$20$	6.29432	1.40745
$21$	−1.00000	−0.218218
$22$	−11.2590	−2.40042
$23$	−4.89639	−1.02097	−0.510484	−	0.859887i	$-0.670534\pi$
$23$	−4.89639	−1.02097	−0.510484	+	0.859887i	$0.670534\pi$
$24$	3.56329	0.727353
$25$	−1.79710	−0.359421
$26$	2.50477	0.491226
$27$	−1.00000	−0.192450
$28$	3.51704	0.664658
$29$	2.03624	0.378120	0.189060	−	0.981966i	$-0.439456\pi$
$29$	2.03624	0.378120	0.189060	+	0.981966i	$0.439456\pi$
$30$	4.20363	0.767475
$31$	−3.51787	−0.631828	−0.315914	−	0.948788i	$-0.602311\pi$
$31$	−3.51787	−0.631828	−0.315914	+	0.948788i	$0.602311\pi$
$32$	3.98970	0.705286
$33$	−4.79343	−0.834429
$34$	15.4218	2.64482
$35$	1.78966	0.302508
$36$	3.51704	0.586174
$37$	11.2996	1.85764	0.928818	−	0.370537i	$-0.120826\pi$
$37$	11.2996	1.85764	0.928818	+	0.370537i	$0.120826\pi$
$38$	−3.89326	−0.631571
$39$	1.06639	0.170759
$40$	−6.37709	−1.00831
$41$	5.38793	0.841453	0.420727	−	0.907187i	$-0.361775\pi$
$41$	5.38793	0.841453	0.420727	+	0.907187i	$0.361775\pi$
$42$	2.34884	0.362434
$43$	−6.67556	−1.01801	−0.509007	−	0.860763i	$-0.669987\pi$
$43$	−6.67556	−1.01801	−0.509007	+	0.860763i	$0.669987\pi$
$44$	16.8587	2.54154
$45$	1.78966	0.266787
$46$	11.5008	1.69570
$47$	2.16056	0.315150	0.157575	−	0.987507i	$-0.449632\pi$
$47$	2.16056	0.315150	0.157575	+	0.987507i	$0.449632\pi$
$48$	−1.33550	−0.192763
$49$	1.00000	0.142857
$50$	4.22110	0.596954
$51$	6.56571	0.919384
$52$	−3.75053	−0.520104
$53$	−8.82480	−1.21218	−0.606089	−	0.795396i	$-0.707263\pi$
$53$	−8.82480	−1.21218	−0.606089	+	0.795396i	$0.707263\pi$
$54$	2.34884	0.319636
$55$	8.57863	1.15674
$56$	−3.56329	−0.476164
$57$	−1.65753	−0.219545
$58$	−4.78279	−0.628012
$59$	−1.10786	−0.144231	−0.0721155	−	0.997396i	$-0.522975\pi$
$59$	−1.10786	−0.144231	−0.0721155	+	0.997396i	$0.522975\pi$
$60$	−6.29432	−0.812594
$61$	−9.20813	−1.17898	−0.589490	−	0.807775i	$-0.700671\pi$
$61$	−9.20813	−1.17898	−0.589490	+	0.807775i	$0.700671\pi$
$62$	8.26290	1.04939
$63$	1.00000	0.125988
$64$	−12.0422	−1.50527
$65$	−1.90847	−0.236717
$66$	11.2590	1.38589
$67$	−4.37307	−0.534256	−0.267128	−	0.963661i	$-0.586075\pi$
$67$	−4.37307	−0.534256	−0.267128	+	0.963661i	$0.586075\pi$
$68$	−23.0919	−2.80030
$69$	4.89639	0.589456
$70$	−4.20363	−0.502430
$71$	14.2556	1.69183	0.845914	−	0.533320i	$-0.179056\pi$
$71$	14.2556	1.69183	0.845914	+	0.533320i	$0.179056\pi$
$72$	−3.56329	−0.419937
$73$	8.79953	1.02991	0.514954	−	0.857218i	$-0.327809\pi$
$73$	8.79953	1.02991	0.514954	+	0.857218i	$0.327809\pi$
$74$	−26.5408	−3.08531
$75$	1.79710	0.207512
$76$	5.82959	0.668700
$77$	4.79343	0.546262
$78$	−2.50477	−0.283609
$79$	−1.77043	−0.199189	−0.0995946	−	0.995028i	$-0.531755\pi$
$79$	−1.77043	−0.199189	−0.0995946	+	0.995028i	$0.531755\pi$
$80$	2.39010	0.267221
$81$	1.00000	0.111111
$82$	−12.6554	−1.39755
$83$	−5.39456	−0.592130	−0.296065	−	0.955168i	$-0.595674\pi$
$83$	−5.39456	−0.592130	−0.296065	+	0.955168i	$0.595674\pi$
$84$	−3.51704	−0.383741
$85$	−11.7504	−1.27451
$86$	15.6798	1.69080
$87$	−2.03624	−0.218308
$88$	−17.0804	−1.82077
$89$	−7.92565	−0.840118	−0.420059	−	0.907497i	$-0.637991\pi$
$89$	−7.92565	−0.840118	−0.420059	+	0.907497i	$0.637991\pi$
$90$	−4.20363	−0.443102
$91$	−1.06639	−0.111788
$92$	−17.2208	−1.79539
$93$	3.51787	0.364786
$94$	−5.07481	−0.523427
$95$	2.96642	0.304348
$96$	−3.98970	−0.407197
$97$	−6.39555	−0.649370	−0.324685	−	0.945822i	$-0.605258\pi$
$97$	−6.39555	−0.649370	−0.324685	+	0.945822i	$0.605258\pi$
$98$	−2.34884	−0.237269
$99$	4.79343	0.481758
$100$	−6.32049	−0.632049
$101$	13.1191	1.30540	0.652702	−	0.757615i	$-0.273635\pi$
$101$	13.1191	1.30540	0.652702	+	0.757615i	$0.273635\pi$
$102$	−15.4218	−1.52699
$103$	−7.77671	−0.766262	−0.383131	−	0.923694i	$-0.625154\pi$
$103$	−7.77671	−0.766262	−0.383131	+	0.923694i	$0.625154\pi$
$104$	3.79984	0.372605
$105$	−1.78966	−0.174653
$106$	20.7280	2.01328
$107$	−5.43275	−0.525204	−0.262602	−	0.964904i	$-0.584581\pi$
$107$	−5.43275	−0.525204	−0.262602	+	0.964904i	$0.584581\pi$
$108$	−3.51704	−0.338428
$109$	−17.5165	−1.67777	−0.838886	−	0.544307i	$-0.816793\pi$
$109$	−17.5165	−1.67777	−0.838886	+	0.544307i	$0.816793\pi$
$110$	−20.1498	−1.92121
$111$	−11.2996	−1.07251
$112$	1.33550	0.126193
$113$	−13.8401	−1.30197	−0.650983	−	0.759092i	$-0.725643\pi$
$113$	−13.8401	−1.30197	−0.650983	+	0.759092i	$0.725643\pi$
$114$	3.89326	0.364638
$115$	−8.76289	−0.817143
$116$	7.16154	0.664932
$117$	−1.06639	−0.0985875
$118$	2.60218	0.239550
$119$	−6.56571	−0.601878
$120$	6.37709	0.582146
$121$	11.9770	1.08881
$122$	21.6284	1.95814
$123$	−5.38793	−0.485813
$124$	−12.3725	−1.11108
$125$	−12.1645	−1.08803
$126$	−2.34884	−0.209251
$127$	−21.3395	−1.89358	−0.946788	−	0.321857i	$-0.895693\pi$
$127$	−21.3395	−1.89358	−0.946788	+	0.321857i	$0.895693\pi$
$128$	20.3057	1.79479
$129$	6.67556	0.587750
$130$	4.48270	0.393158
$131$	10.4521	0.913201	0.456600	−	0.889672i	$-0.349067\pi$
$131$	10.4521	0.913201	0.456600	+	0.889672i	$0.349067\pi$
$132$	−16.8587	−1.46736
$133$	1.65753	0.143726
$134$	10.2716	0.887335
$135$	−1.78966	−0.154030
$136$	23.3955	2.00615
$137$	13.6240	1.16398	0.581989	−	0.813197i	$-0.302275\pi$
$137$	13.6240	1.16398	0.581989	+	0.813197i	$0.302275\pi$
$138$	−11.5008	−0.979015
$139$	12.4625	1.05706	0.528529	−	0.848915i	$-0.322744\pi$
$139$	12.4625	1.05706	0.528529	+	0.848915i	$0.322744\pi$
$140$	6.29432	0.531967
$141$	−2.16056	−0.181952
$142$	−33.4841	−2.80992
$143$	−5.11165	−0.427458
$144$	1.33550	0.111292
$145$	3.64418	0.302633
$146$	−20.6687	−1.71055
$147$	−1.00000	−0.0824786
$148$	39.7410	3.26669
$149$	−5.50950	−0.451355	−0.225678	−	0.974202i	$-0.572460\pi$
$149$	−5.50950	−0.451355	−0.225678	+	0.974202i	$0.572460\pi$
$150$	−4.22110	−0.344652
$151$	−15.5894	−1.26865	−0.634324	−	0.773067i	$-0.718722\pi$
$151$	−15.5894	−1.26865	−0.634324	+	0.773067i	$0.718722\pi$
$152$	−5.90624	−0.479060
$153$	−6.56571	−0.530806
$154$	−11.2590	−0.907275
$155$	−6.29580	−0.505691
$156$	3.75053	0.300282
$157$	−4.16901	−0.332723	−0.166362	−	0.986065i	$-0.553202\pi$
$157$	−4.16901	−0.332723	−0.166362	+	0.986065i	$0.553202\pi$
$158$	4.15846	0.330829
$159$	8.82480	0.699852
$160$	7.14022	0.564484
$161$	−4.89639	−0.385889
$162$	−2.34884	−0.184542
$163$	16.1175	1.26242	0.631211	−	0.775611i	$-0.282558\pi$
$163$	16.1175	1.26242	0.631211	+	0.775611i	$0.282558\pi$
$164$	18.9496	1.47971
$165$	−8.57863	−0.667845
$166$	12.6710	0.983457
$167$	−13.9633	−1.08051	−0.540257	−	0.841500i	$-0.681673\pi$
$167$	−13.9633	−1.08051	−0.540257	+	0.841500i	$0.681673\pi$
$168$	3.56329	0.274914
$169$	−11.8628	−0.912525
$170$	27.5998	2.11681
$171$	1.65753	0.126754
$172$	−23.4782	−1.79020
$173$	14.9147	1.13394	0.566970	−	0.823738i	$-0.308116\pi$
$173$	14.9147	1.13394	0.566970	+	0.823738i	$0.308116\pi$
$174$	4.78279	0.362583
$175$	−1.79710	−0.135848
$176$	6.40163	0.482541
$177$	1.10786	0.0832718
$178$	18.6161	1.39533
$179$	0.329446	0.0246240	0.0123120	−	0.999924i	$-0.496081\pi$
$179$	0.329446	0.0246240	0.0123120	+	0.999924i	$0.496081\pi$
$180$	6.29432	0.469151
$181$	13.8325	1.02816	0.514080	−	0.857742i	$-0.328133\pi$
$181$	13.8325	1.02816	0.514080	+	0.857742i	$0.328133\pi$
$182$	2.50477	0.185666
$183$	9.20813	0.680685
$184$	17.4472	1.28623
$185$	20.2224	1.48678
$186$	−8.26290	−0.605865
$187$	−31.4723	−2.30148
$188$	7.59879	0.554199
$189$	−1.00000	−0.0727393
$190$	−6.96763	−0.505485
$191$	−8.27446	−0.598719	−0.299359	−	0.954140i	$-0.596773\pi$
$191$	−8.27446	−0.598719	−0.299359	+	0.954140i	$0.596773\pi$
$192$	12.0422	0.869068
$193$	12.9062	0.929010	0.464505	−	0.885570i	$-0.346232\pi$
$193$	12.9062	0.929010	0.464505	+	0.885570i	$0.346232\pi$
$194$	15.0221	1.07852
$195$	1.90847	0.136669
$196$	3.51704	0.251217
$197$	−20.8658	−1.48663	−0.743315	−	0.668942i	$-0.766748\pi$
$197$	−20.8658	−1.48663	−0.743315	+	0.668942i	$0.766748\pi$
$198$	−11.2590	−0.800142
$199$	−24.2695	−1.72042	−0.860208	−	0.509943i	$-0.829667\pi$
$199$	−24.2695	−1.72042	−0.860208	+	0.509943i	$0.829667\pi$
$200$	6.40359	0.452802
$201$	4.37307	0.308453
$202$	−30.8147	−2.16812
$203$	2.03624	0.142916
$204$	23.0919	1.61676
$205$	9.64258	0.673467
$206$	18.2662	1.27267
$207$	−4.89639	−0.340322
$208$	−1.42416	−0.0987477
$209$	7.94524	0.549584
$210$	4.20363	0.290078
$211$	−10.2932	−0.708613	−0.354306	−	0.935129i	$-0.615283\pi$
$211$	−10.2932	−0.708613	−0.354306	+	0.935129i	$0.615283\pi$
$212$	−31.0372	−2.13164
$213$	−14.2556	−0.976777
$214$	12.7607	0.872301
$215$	−11.9470	−0.814779
$216$	3.56329	0.242451
$217$	−3.51787	−0.238808
$218$	41.1433	2.78658
$219$	−8.79953	−0.594617
$220$	30.1714	2.03415
$221$	7.00159	0.470978
$222$	26.5408	1.78130
$223$	−3.48466	−0.233350	−0.116675	−	0.993170i	$-0.537224\pi$
$223$	−3.48466	−0.233350	−0.116675	+	0.993170i	$0.537224\pi$
$224$	3.98970	0.266573
$225$	−1.79710	−0.119807
$226$	32.5081	2.16241
$227$	21.9471	1.45668	0.728339	−	0.685217i	$-0.240293\pi$
$227$	21.9471	1.45668	0.728339	+	0.685217i	$0.240293\pi$
$228$	−5.82959	−0.386074
$229$	−20.2393	−1.33745	−0.668724	−	0.743511i	$-0.733159\pi$
$229$	−20.2393	−1.33745	−0.668724	+	0.743511i	$0.733159\pi$
$230$	20.5826	1.35718
$231$	−4.79343	−0.315384
$232$	−7.25570	−0.476360
$233$	−12.1501	−0.795978	−0.397989	−	0.917390i	$-0.630292\pi$
$233$	−12.1501	−0.795978	−0.397989	+	0.917390i	$0.630292\pi$
$234$	2.50477	0.163742
$235$	3.86668	0.252234
$236$	−3.89639	−0.253633
$237$	1.77043	0.115002
$238$	15.4218	0.999647
$239$	24.5217	1.58618	0.793090	−	0.609105i	$-0.208471\pi$
$239$	24.5217	1.58618	0.793090	+	0.609105i	$0.208471\pi$
$240$	−2.39010	−0.154280
$241$	10.9657	0.706361	0.353180	−	0.935555i	$-0.385100\pi$
$241$	10.9657	0.706361	0.353180	+	0.935555i	$0.385100\pi$
$242$	−28.1319	−1.80839
$243$	−1.00000	−0.0641500
$244$	−32.3854	−2.07326
$245$	1.78966	0.114337
$246$	12.6554	0.806877
$247$	−1.76756	−0.112467
$248$	12.5352	0.795984
$249$	5.39456	0.341866
$250$	28.5725	1.80708
$251$	0.805691	0.0508547	0.0254274	−	0.999677i	$-0.491905\pi$
$251$	0.805691	0.0508547	0.0254274	+	0.999677i	$0.491905\pi$
$252$	3.51704	0.221553
$253$	−23.4705	−1.47558
$254$	50.1231	3.14500
$255$	11.7504	0.735840
$256$	−23.6105	−1.47565
$257$	15.8990	0.991751	0.495876	−	0.868394i	$-0.334847\pi$
$257$	15.8990	0.991751	0.495876	+	0.868394i	$0.334847\pi$
$258$	−15.6798	−0.976182
$259$	11.2996	0.702120
$260$	−6.71218	−0.416272
$261$	2.03624	0.126040
$262$	−24.5502	−1.51672
$263$	−22.4361	−1.38347	−0.691733	−	0.722153i	$-0.743153\pi$
$263$	−22.4361	−1.38347	−0.691733	+	0.722153i	$0.743153\pi$
$264$	17.0804	1.05122
$265$	−15.7934	−0.970182
$266$	−3.89326	−0.238711
$267$	7.92565	0.485042
$268$	−15.3803	−0.939501
$269$	13.7305	0.837166	0.418583	−	0.908178i	$-0.362527\pi$
$269$	13.7305	0.837166	0.418583	+	0.908178i	$0.362527\pi$
$270$	4.20363	0.255825
$271$	−7.74110	−0.470238	−0.235119	−	0.971967i	$-0.575548\pi$
$271$	−7.74110	−0.470238	−0.235119	+	0.971967i	$0.575548\pi$
$272$	−8.76852	−0.531669
$273$	1.06639	0.0645407
$274$	−32.0006	−1.93323
$275$	−8.61429	−0.519461
$276$	17.2208	1.03657
$277$	−10.2475	−0.615713	−0.307856	−	0.951433i	$-0.599612\pi$
$277$	−10.2475	−0.615713	−0.307856	+	0.951433i	$0.599612\pi$
$278$	−29.2725	−1.75565
$279$	−3.51787	−0.210609
$280$	−6.37709	−0.381104
$281$	−29.6769	−1.77038	−0.885188	−	0.465233i	$-0.845971\pi$
$281$	−29.6769	−1.77038	−0.885188	+	0.465233i	$0.845971\pi$
$282$	5.07481	0.302201
$283$	−16.4144	−0.975732	−0.487866	−	0.872918i	$-0.662225\pi$
$283$	−16.4144	−0.975732	−0.487866	+	0.872918i	$0.662225\pi$
$284$	50.1375	2.97511
$285$	−2.96642	−0.175715
$286$	12.0064	0.709955
$287$	5.38793	0.318039
$288$	3.98970	0.235095
$289$	26.1086	1.53580
$290$	−8.55959	−0.502637
$291$	6.39555	0.374914
$292$	30.9483	1.81111
$293$	22.8566	1.33530	0.667649	−	0.744476i	$-0.267301\pi$
$293$	22.8566	1.33530	0.667649	+	0.744476i	$0.267301\pi$
$294$	2.34884	0.136987
$295$	−1.98270	−0.115437
$296$	−40.2636	−2.34027
$297$	−4.79343	−0.278143
$298$	12.9409	0.749647
$299$	5.22144	0.301964
$300$	6.32049	0.364914
$301$	−6.67556	−0.384773
$302$	36.6170	2.10707
$303$	−13.1191	−0.753675
$304$	2.21363	0.126960
$305$	−16.4795	−0.943611
$306$	15.4218	0.881606
$307$	−13.3346	−0.761046	−0.380523	−	0.924771i	$-0.624256\pi$
$307$	−13.3346	−0.761046	−0.380523	+	0.924771i	$0.624256\pi$
$308$	16.8587	0.960613
$309$	7.77671	0.442402
$310$	14.7878	0.839892
$311$	24.7498	1.40344	0.701718	−	0.712455i	$-0.252417\pi$
$311$	24.7498	1.40344	0.701718	+	0.712455i	$0.252417\pi$
$312$	−3.79984	−0.215124
$313$	−28.0995	−1.58828	−0.794138	−	0.607738i	$-0.792077\pi$
$313$	−28.0995	−1.58828	−0.794138	+	0.607738i	$0.792077\pi$
$314$	9.79233	0.552613
$315$	1.78966	0.100836
$316$	−6.22668	−0.350278
$317$	−14.1378	−0.794056	−0.397028	−	0.917806i	$-0.629958\pi$
$317$	−14.1378	−0.794056	−0.397028	+	0.917806i	$0.629958\pi$
$318$	−20.7280	−1.16237
$319$	9.76056	0.546487
$320$	−21.5514	−1.20476
$321$	5.43275	0.303227
$322$	11.5008	0.640916
$323$	−10.8828	−0.605538
$324$	3.51704	0.195391
$325$	1.91641	0.106303
$326$	−37.8575	−2.09673
$327$	17.5165	0.968662
$328$	−19.1987	−1.06007
$329$	2.16056	0.119116
$330$	20.1498	1.10921
$331$	−5.41182	−0.297461	−0.148730	−	0.988878i	$-0.547519\pi$
$331$	−5.41182	−0.297461	−0.148730	+	0.988878i	$0.547519\pi$
$332$	−18.9729	−1.04127
$333$	11.2996	0.619212
$334$	32.7976	1.79460
$335$	−7.82633	−0.427598
$336$	−1.33550	−0.0728575
$337$	−29.1072	−1.58557	−0.792784	−	0.609503i	$-0.791369\pi$
$337$	−29.1072	−1.58557	−0.792784	+	0.609503i	$0.791369\pi$
$338$	27.8638	1.51559
$339$	13.8401	0.751690
$340$	−41.3267	−2.24126
$341$	−16.8626	−0.913163
$342$	−3.89326	−0.210524
$343$	1.00000	0.0539949
$344$	23.7869	1.28251
$345$	8.76289	0.471778
$346$	−35.0321	−1.88334
$347$	32.7869	1.76010	0.880048	−	0.474885i	$-0.157510\pi$
$347$	32.7869	1.76010	0.880048	+	0.474885i	$0.157510\pi$
$348$	−7.16154	−0.383899
$349$	2.18155	0.116776	0.0583878	−	0.998294i	$-0.481404\pi$
$349$	2.18155	0.116776	0.0583878	+	0.998294i	$0.481404\pi$
$350$	4.22110	0.225628
$351$	1.06639	0.0569195
$352$	19.1243	1.01933
$353$	−6.05344	−0.322192	−0.161096	−	0.986939i	$-0.551503\pi$
$353$	−6.05344	−0.322192	−0.161096	+	0.986939i	$0.551503\pi$
$354$	−2.60218	−0.138304
$355$	25.5127	1.35407
$356$	−27.8749	−1.47736
$357$	6.56571	0.347494
$358$	−0.773816	−0.0408975
$359$	19.1226	1.00925	0.504627	−	0.863337i	$-0.331630\pi$
$359$	19.1226	1.00925	0.504627	+	0.863337i	$0.331630\pi$
$360$	−6.37709	−0.336102
$361$	−16.2526	−0.855400
$362$	−32.4903	−1.70765
$363$	−11.9770	−0.628627
$364$	−3.75053	−0.196581
$365$	15.7482	0.824299
$366$	−21.6284	−1.13054
$367$	−30.8234	−1.60897	−0.804484	−	0.593974i	$-0.797558\pi$
$367$	−30.8234	−1.60897	−0.804484	+	0.593974i	$0.797558\pi$
$368$	−6.53913	−0.340876
$369$	5.38793	0.280484
$370$	−47.4992	−2.46936
$371$	−8.82480	−0.458161
$372$	12.3725	0.641484
$373$	8.23483	0.426383	0.213192	−	0.977010i	$-0.431614\pi$
$373$	8.23483	0.426383	0.213192	+	0.977010i	$0.431614\pi$
$374$	73.9233	3.82248
$375$	12.1645	0.628174
$376$	−7.69870	−0.397030
$377$	−2.17142	−0.111834
$378$	2.34884	0.120811
$379$	23.5064	1.20744	0.603722	−	0.797195i	$-0.293684\pi$
$379$	23.5064	1.20744	0.603722	+	0.797195i	$0.293684\pi$
$380$	10.4330	0.535202
$381$	21.3395	1.09326
$382$	19.4354	0.994400
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−20.3057	−1.03622
$385$	8.57863	0.437207
$386$	−30.3146	−1.54297
$387$	−6.67556	−0.339338
$388$	−22.4934	−1.14193
$389$	−9.24537	−0.468759	−0.234379	−	0.972145i	$-0.575306\pi$
$389$	−9.24537	−0.468759	−0.234379	+	0.972145i	$0.575306\pi$
$390$	−4.48270	−0.226990
$391$	32.1483	1.62581
$392$	−3.56329	−0.179973
$393$	−10.4521	−0.527237
$394$	49.0105	2.46911
$395$	−3.16848	−0.159423
$396$	16.8587	0.847181
$397$	13.1714	0.661053	0.330526	−	0.943797i	$-0.392774\pi$
$397$	13.1714	0.661053	0.330526	+	0.943797i	$0.392774\pi$
$398$	57.0051	2.85741
$399$	−1.65753	−0.0829801
$400$	−2.40003	−0.120002
$401$	23.0178	1.14945	0.574726	−	0.818346i	$-0.305108\pi$
$401$	23.0178	1.14945	0.574726	+	0.818346i	$0.305108\pi$
$402$	−10.2716	−0.512303
$403$	3.75141	0.186871
$404$	46.1406	2.29558
$405$	1.78966	0.0889291
$406$	−4.78279	−0.237366
$407$	54.1636	2.68479
$408$	−23.3955	−1.15825
$409$	−38.6338	−1.91032	−0.955158	−	0.296096i	$-0.904315\pi$
$409$	−38.6338	−1.91032	−0.955158	+	0.296096i	$0.904315\pi$
$410$	−22.6489	−1.11855
$411$	−13.6240	−0.672023
$412$	−27.3510	−1.34749
$413$	−1.10786	−0.0545142
$414$	11.5008	0.565235
$415$	−9.65445	−0.473918
$416$	−4.25456	−0.208597
$417$	−12.4625	−0.610293
$418$	−18.6621	−0.912792
$419$	5.54998	0.271134	0.135567	−	0.990768i	$-0.456714\pi$
$419$	5.54998	0.271134	0.135567	+	0.990768i	$0.456714\pi$
$420$	−6.29432	−0.307132
$421$	22.4746	1.09535	0.547673	−	0.836692i	$-0.315514\pi$
$421$	22.4746	1.09535	0.547673	+	0.836692i	$0.315514\pi$
$422$	24.1770	1.17692
$423$	2.16056	0.105050
$424$	31.4453	1.52712
$425$	11.7993	0.572348
$426$	33.4841	1.62231
$427$	−9.20813	−0.445613
$428$	−19.1072	−0.923583
$429$	5.11165	0.246793
$430$	28.0616	1.35325
$431$	−5.26736	−0.253720	−0.126860	−	0.991921i	$-0.540490\pi$
$431$	−5.26736	−0.253720	−0.126860	+	0.991921i	$0.540490\pi$
$432$	−1.33550	−0.0642543
$433$	38.3991	1.84534	0.922671	−	0.385589i	$-0.126002\pi$
$433$	38.3991	1.84534	0.922671	+	0.385589i	$0.126002\pi$
$434$	8.26290	0.396632
$435$	−3.64418	−0.174725
$436$	−61.6061	−2.95040
$437$	−8.11589	−0.388236
$438$	20.6687	0.987588
$439$	32.0642	1.53034	0.765170	−	0.643829i	$-0.222655\pi$
$439$	32.0642	1.53034	0.765170	+	0.643829i	$0.222655\pi$
$440$	−30.5681	−1.45728
$441$	1.00000	0.0476190
$442$	−16.4456	−0.782237
$443$	15.5519	0.738894	0.369447	−	0.929252i	$-0.379547\pi$
$443$	15.5519	0.738894	0.369447	+	0.929252i	$0.379547\pi$
$444$	−39.7410	−1.88602
$445$	−14.1843	−0.672398
$446$	8.18491	0.387567
$447$	5.50950	0.260590
$448$	−12.0422	−0.568938
$449$	−24.4450	−1.15363	−0.576816	−	0.816874i	$-0.695705\pi$
$449$	−24.4450	−1.15363	−0.576816	+	0.816874i	$0.695705\pi$
$450$	4.22110	0.198985
$451$	25.8267	1.21613
$452$	−48.6762	−2.28953
$453$	15.5894	0.732455
$454$	−51.5501	−2.41937
$455$	−1.90847	−0.0894706
$456$	5.90624	0.276585
$457$	37.3114	1.74535	0.872677	−	0.488297i	$-0.162382\pi$
$457$	37.3114	1.74535	0.872677	+	0.488297i	$0.162382\pi$
$458$	47.5387	2.22134
$459$	6.56571	0.306461
$460$	−30.8194	−1.43696
$461$	32.5353	1.51532	0.757661	−	0.652649i	$-0.226342\pi$
$461$	32.5353	1.51532	0.757661	+	0.652649i	$0.226342\pi$
$462$	11.2590	0.523816
$463$	−35.9575	−1.67109	−0.835544	−	0.549423i	$-0.814848\pi$
$463$	−35.9575	−1.67109	−0.835544	+	0.549423i	$0.814848\pi$
$464$	2.71940	0.126245
$465$	6.29580	0.291961
$466$	28.5386	1.32202
$467$	−25.9891	−1.20263	−0.601316	−	0.799011i	$-0.705357\pi$
$467$	−25.9891	−1.20263	−0.601316	+	0.799011i	$0.705357\pi$
$468$	−3.75053	−0.173368
$469$	−4.37307	−0.201930
$470$	−9.08221	−0.418931
$471$	4.16901	0.192098
$472$	3.94762	0.181704
$473$	−31.9988	−1.47131
$474$	−4.15846	−0.191004
$475$	−2.97875	−0.136674
$476$	−23.0919	−1.05841
$477$	−8.82480	−0.404060
$478$	−57.5976	−2.63445
$479$	20.7434	0.947790	0.473895	−	0.880581i	$-0.342848\pi$
$479$	20.7434	0.947790	0.473895	+	0.880581i	$0.342848\pi$
$480$	−7.14022	−0.325905
$481$	−12.0497	−0.549419
$482$	−25.7566	−1.17318
$483$	4.89639	0.222793
$484$	42.1235	1.91470
$485$	−11.4459	−0.519731
$486$	2.34884	0.106545
$487$	−23.8709	−1.08169	−0.540847	−	0.841121i	$-0.681896\pi$
$487$	−23.8709	−1.08169	−0.540847	+	0.841121i	$0.681896\pi$
$488$	32.8112	1.48529
$489$	−16.1175	−0.728860
$490$	−4.20363	−0.189901
$491$	−30.9317	−1.39593	−0.697963	−	0.716133i	$-0.745910\pi$
$491$	−30.9317	−1.39593	−0.697963	+	0.716133i	$0.745910\pi$
$492$	−18.9496	−0.854313
$493$	−13.3694	−0.602125
$494$	4.15172	0.186795
$495$	8.57863	0.385581
$496$	−4.69811	−0.210952
$497$	14.2556	0.639451
$498$	−12.6710	−0.567799
$499$	−18.0399	−0.807575	−0.403787	−	0.914853i	$-0.632306\pi$
$499$	−18.0399	−0.807575	−0.403787	+	0.914853i	$0.632306\pi$
$500$	−42.7832	−1.91332
$501$	13.9633	0.623835
$502$	−1.89244	−0.0844636
$503$	22.0758	0.984309	0.492155	−	0.870508i	$-0.336209\pi$
$503$	22.0758	0.984309	0.492155	+	0.870508i	$0.336209\pi$
$504$	−3.56329	−0.158721
$505$	23.4789	1.04480
$506$	55.1284	2.45076
$507$	11.8628	0.526846
$508$	−75.0520	−3.32989
$509$	−5.57461	−0.247090	−0.123545	−	0.992339i	$-0.539426\pi$
$509$	−5.57461	−0.247090	−0.123545	+	0.992339i	$0.539426\pi$
$510$	−27.5998	−1.22214
$511$	8.79953	0.389268
$512$	14.8458	0.656097
$513$	−1.65753	−0.0731816
$514$	−37.3441	−1.64718
$515$	−13.9177	−0.613287
$516$	23.4782	1.03357
$517$	10.3565	0.455478
$518$	−26.5408	−1.16614
$519$	−14.9147	−0.654681
$520$	6.80044	0.298219
$521$	17.0832	0.748430	0.374215	−	0.927342i	$-0.377912\pi$
$521$	17.0832	0.748430	0.374215	+	0.927342i	$0.377912\pi$
$522$	−4.78279	−0.209337
$523$	23.8942	1.04482	0.522409	−	0.852695i	$-0.325033\pi$
$523$	23.8942	1.04482	0.522409	+	0.852695i	$0.325033\pi$
$524$	36.7603	1.60588
$525$	1.79710	0.0784320
$526$	52.6987	2.29777
$527$	23.0973	1.00613
$528$	−6.40163	−0.278595
$529$	0.974606	0.0423742
$530$	37.0962	1.61136
$531$	−1.10786	−0.0480770
$532$	5.82959	0.252745
$533$	−5.74562	−0.248870
$534$	−18.6161	−0.805597
$535$	−9.72280	−0.420353
$536$	15.5825	0.673062
$537$	−0.329446	−0.0142167
$538$	−32.2508	−1.39043
$539$	4.79343	0.206468
$540$	−6.29432	−0.270865
$541$	−5.86602	−0.252200	−0.126100	−	0.992018i	$-0.540246\pi$
$541$	−5.86602	−0.252200	−0.126100	+	0.992018i	$0.540246\pi$
$542$	18.1826	0.781009
$543$	−13.8325	−0.593609
$544$	−26.1952	−1.12311
$545$	−31.3486	−1.34282
$546$	−2.50477	−0.107194
$547$	38.4598	1.64442	0.822212	−	0.569182i	$-0.192740\pi$
$547$	38.4598	1.64442	0.822212	+	0.569182i	$0.192740\pi$
$548$	47.9162	2.04688
$549$	−9.20813	−0.392994
$550$	20.2336	0.862762
$551$	3.37512	0.143785
$552$	−17.4472	−0.742603
$553$	−1.77043	−0.0752864
$554$	24.0697	1.02262
$555$	−20.2224	−0.858393
$556$	43.8313	1.85886
$557$	−8.53715	−0.361731	−0.180865	−	0.983508i	$-0.557890\pi$
$557$	−8.53715	−0.361731	−0.180865	+	0.983508i	$0.557890\pi$
$558$	8.26290	0.349797
$559$	7.11873	0.301090
$560$	2.39010	0.101000
$561$	31.4723	1.32876
$562$	69.7063	2.94038
$563$	−7.48979	−0.315657	−0.157829	−	0.987467i	$-0.550449\pi$
$563$	−7.48979	−0.315657	−0.157829	+	0.987467i	$0.550449\pi$
$564$	−7.59879	−0.319967
$565$	−24.7691	−1.04204
$566$	38.5547	1.62057
$567$	1.00000	0.0419961
$568$	−50.7968	−2.13138
$569$	−33.4406	−1.40190	−0.700952	−	0.713209i	$-0.747241\pi$
$569$	−33.4406	−1.40190	−0.700952	+	0.713209i	$0.747241\pi$
$570$	6.96763	0.291842
$571$	−14.7179	−0.615923	−0.307962	−	0.951399i	$-0.599647\pi$
$571$	−14.7179	−0.615923	−0.307962	+	0.951399i	$0.599647\pi$
$572$	−17.9779	−0.751693
$573$	8.27446	0.345670
$574$	−12.6554	−0.528225
$575$	8.79931	0.366957
$576$	−12.0422	−0.501757
$577$	8.44789	0.351690	0.175845	−	0.984418i	$-0.443734\pi$
$577$	8.44789	0.351690	0.175845	+	0.984418i	$0.443734\pi$
$578$	−61.3248	−2.55078
$579$	−12.9062	−0.536364
$580$	12.8167	0.532186
$581$	−5.39456	−0.223804
$582$	−15.0221	−0.622686
$583$	−42.3010	−1.75193
$584$	−31.3553	−1.29749
$585$	−1.90847	−0.0789057
$586$	−53.6865	−2.21777
$587$	9.16600	0.378321	0.189161	−	0.981946i	$-0.439423\pi$
$587$	9.16600	0.378321	0.189161	+	0.981946i	$0.439423\pi$
$588$	−3.51704	−0.145040
$589$	−5.83096	−0.240261
$590$	4.65703	0.191727
$591$	20.8658	0.858306
$592$	15.0906	0.620218
$593$	42.3979	1.74107	0.870537	−	0.492103i	$-0.163772\pi$
$593$	42.3979	1.74107	0.870537	+	0.492103i	$0.163772\pi$
$594$	11.2590	0.461962
$595$	−11.7504	−0.481720
$596$	−19.3771	−0.793718
$597$	24.2695	0.993283
$598$	−12.2643	−0.501525
$599$	1.16440	0.0475761	0.0237881	−	0.999717i	$-0.492427\pi$
$599$	1.16440	0.0475761	0.0237881	+	0.999717i	$0.492427\pi$
$600$	−6.40359	−0.261426
$601$	−36.3409	−1.48238	−0.741188	−	0.671297i	$-0.765737\pi$
$601$	−36.3409	−1.48238	−0.741188	+	0.671297i	$0.765737\pi$
$602$	15.6798	0.639061
$603$	−4.37307	−0.178085
$604$	−54.8286	−2.23095
$605$	21.4347	0.871446
$606$	30.8147	1.25176
$607$	−9.10341	−0.369496	−0.184748	−	0.982786i	$-0.559147\pi$
$607$	−9.10341	−0.369496	−0.184748	+	0.982786i	$0.559147\pi$
$608$	6.61303	0.268194
$609$	−2.03624	−0.0825125
$610$	38.7076	1.56722
$611$	−2.30399	−0.0932096
$612$	−23.0919	−0.933434
$613$	7.12252	0.287676	0.143838	−	0.989601i	$-0.454056\pi$
$613$	7.12252	0.287676	0.143838	+	0.989601i	$0.454056\pi$
$614$	31.3208	1.26401
$615$	−9.64258	−0.388826
$616$	−17.0804	−0.688187
$617$	−17.3220	−0.697356	−0.348678	−	0.937243i	$-0.613369\pi$
$617$	−17.3220	−0.697356	−0.348678	+	0.937243i	$0.613369\pi$
$618$	−18.2662	−0.734776
$619$	45.3336	1.82211	0.911056	−	0.412282i	$-0.135268\pi$
$619$	45.3336	1.82211	0.911056	+	0.412282i	$0.135268\pi$
$620$	−22.1426	−0.889268
$621$	4.89639	0.196485
$622$	−58.1334	−2.33094
$623$	−7.92565	−0.317535
$624$	1.42416	0.0570120
$625$	−12.7849	−0.511396
$626$	66.0011	2.63793
$627$	−7.94524	−0.317302
$628$	−14.6626	−0.585101
$629$	−74.1896	−2.95813
$630$	−4.20363	−0.167477
$631$	−40.8279	−1.62533	−0.812667	−	0.582729i	$-0.801985\pi$
$631$	−40.8279	−1.62533	−0.812667	+	0.582729i	$0.801985\pi$
$632$	6.30856	0.250941
$633$	10.2932	0.409118
$634$	33.2073	1.31883
$635$	−38.1906	−1.51555
$636$	31.0372	1.23070
$637$	−1.06639	−0.0422518
$638$	−22.9260	−0.907648
$639$	14.2556	0.563942
$640$	36.3404	1.43648
$641$	−2.13175	−0.0841993	−0.0420996	−	0.999113i	$-0.513405\pi$
$641$	−2.13175	−0.0841993	−0.0420996	+	0.999113i	$0.513405\pi$
$642$	−12.7607	−0.503623
$643$	−25.2224	−0.994673	−0.497336	−	0.867558i	$-0.665689\pi$
$643$	−25.2224	−0.994673	−0.497336	+	0.867558i	$0.665689\pi$
$644$	−17.2208	−0.678595
$645$	11.9470	0.470413
$646$	25.5620	1.00573
$647$	−43.1092	−1.69480	−0.847399	−	0.530956i	$-0.821833\pi$
$647$	−43.1092	−1.69480	−0.847399	+	0.530956i	$0.821833\pi$
$648$	−3.56329	−0.139979
$649$	−5.31044	−0.208453
$650$	−4.50133	−0.176557
$651$	3.51787	0.137876
$652$	56.6860	2.22000
$653$	3.33193	0.130389	0.0651943	−	0.997873i	$-0.479233\pi$
$653$	3.33193	0.130389	0.0651943	+	0.997873i	$0.479233\pi$
$654$	−41.1433	−1.60883
$655$	18.7057	0.730891
$656$	7.19558	0.280940
$657$	8.79953	0.343302
$658$	−5.07481	−0.197837
$659$	−47.8423	−1.86367	−0.931836	−	0.362880i	$-0.881793\pi$
$659$	−47.8423	−1.86367	−0.931836	+	0.362880i	$0.881793\pi$
$660$	−30.1714	−1.17442
$661$	20.5945	0.801033	0.400517	−	0.916289i	$-0.368831\pi$
$661$	20.5945	0.801033	0.400517	+	0.916289i	$0.368831\pi$
$662$	12.7115	0.494046
$663$	−7.00159	−0.271919
$664$	19.2224	0.745972
$665$	2.96642	0.115033
$666$	−26.5408	−1.02844
$667$	−9.97021	−0.386048
$668$	−49.1096	−1.90011
$669$	3.48466	0.134725
$670$	18.3828	0.710189
$671$	−44.1385	−1.70395
$672$	−3.98970	−0.153906
$673$	−44.0393	−1.69759	−0.848795	−	0.528722i	$-0.822671\pi$
$673$	−44.0393	−1.69759	−0.848795	+	0.528722i	$0.822671\pi$
$674$	68.3680	2.63344
$675$	1.79710	0.0691705
$676$	−41.7220	−1.60469
$677$	32.6300	1.25407	0.627037	−	0.778990i	$-0.284268\pi$
$677$	32.6300	1.25407	0.627037	+	0.778990i	$0.284268\pi$
$678$	−32.5081	−1.24847
$679$	−6.39555	−0.245439
$680$	41.8701	1.60565
$681$	−21.9471	−0.841013
$682$	39.6076	1.51665
$683$	−33.5339	−1.28314	−0.641569	−	0.767065i	$-0.721716\pi$
$683$	−33.5339	−1.28314	−0.641569	+	0.767065i	$0.721716\pi$
$684$	5.82959	0.222900
$685$	24.3824	0.931604
$686$	−2.34884	−0.0896791
$687$	20.2393	0.772176
$688$	−8.91521	−0.339889
$689$	9.41064	0.358517
$690$	−20.5826	−0.783566
$691$	42.2117	1.60581	0.802905	−	0.596107i	$-0.203286\pi$
$691$	42.2117	1.60581	0.802905	+	0.596107i	$0.203286\pi$
$692$	52.4555	1.99406
$693$	4.79343	0.182087
$694$	−77.0112	−2.92331
$695$	22.3038	0.846030
$696$	7.25570	0.275027
$697$	−35.3756	−1.33995
$698$	−5.12410	−0.193950
$699$	12.1501	0.459558
$700$	−6.32049	−0.238892
$701$	11.4826	0.433692	0.216846	−	0.976206i	$-0.430423\pi$
$701$	11.4826	0.433692	0.216846	+	0.976206i	$0.430423\pi$
$702$	−2.50477	−0.0945365
$703$	18.7293	0.706390
$704$	−57.7232	−2.17553
$705$	−3.86668	−0.145628
$706$	14.2185	0.535122
$707$	13.1191	0.493396
$708$	3.89639	0.146435
$709$	0.849749	0.0319130	0.0159565	−	0.999873i	$-0.494921\pi$
$709$	0.849749	0.0319130	0.0159565	+	0.999873i	$0.494921\pi$
$710$	−59.9252	−2.24895
$711$	−1.77043	−0.0663964
$712$	28.2414	1.05839
$713$	17.2248	0.645075
$714$	−15.4218	−0.577146
$715$	−9.14813	−0.342121
$716$	1.15868	0.0433018
$717$	−24.5217	−0.915781
$718$	−44.9160	−1.67625
$719$	0.500513	0.0186660	0.00933300	−	0.999956i	$-0.497029\pi$
$719$	0.500513	0.0186660	0.00933300	+	0.999956i	$0.497029\pi$
$720$	2.39010	0.0890737
$721$	−7.77671	−0.289620
$722$	38.1747	1.42072
$723$	−10.9657	−0.407817
$724$	48.6494	1.80804
$725$	−3.65933	−0.135904
$726$	28.1319	1.04407
$727$	−4.25544	−0.157826	−0.0789128	−	0.996882i	$-0.525145\pi$
$727$	−4.25544	−0.157826	−0.0789128	+	0.996882i	$0.525145\pi$
$728$	3.79984	0.140831
$729$	1.00000	0.0370370
$730$	−36.9900	−1.36906
$731$	43.8298	1.62110
$732$	32.3854	1.19700
$733$	22.9381	0.847239	0.423619	−	0.905840i	$-0.360759\pi$
$733$	22.9381	0.847239	0.423619	+	0.905840i	$0.360759\pi$
$734$	72.3992	2.67230
$735$	−1.78966	−0.0660127
$736$	−19.5351	−0.720074
$737$	−20.9620	−0.772146
$738$	−12.6554	−0.465851
$739$	−31.1375	−1.14541	−0.572707	−	0.819760i	$-0.694107\pi$
$739$	−31.1375	−1.14541	−0.572707	+	0.819760i	$0.694107\pi$
$740$	71.1230	2.61454
$741$	1.76756	0.0649331
$742$	20.7280	0.760950
$743$	−15.9923	−0.586699	−0.293349	−	0.956005i	$-0.594770\pi$
$743$	−15.9923	−0.586699	−0.293349	+	0.956005i	$0.594770\pi$
$744$	−12.5352	−0.459562
$745$	−9.86015	−0.361248
$746$	−19.3423	−0.708171
$747$	−5.39456	−0.197377
$748$	−110.689	−4.04720
$749$	−5.43275	−0.198509
$750$	−28.5725	−1.04332
$751$	30.6892	1.11987	0.559933	−	0.828538i	$-0.310827\pi$
$751$	30.6892	1.11987	0.559933	+	0.828538i	$0.310827\pi$
$752$	2.88543	0.105221
$753$	−0.805691	−0.0293610
$754$	5.10031	0.185742
$755$	−27.8998	−1.01538
$756$	−3.51704	−0.127914
$757$	34.5448	1.25555	0.627776	−	0.778394i	$-0.283965\pi$
$757$	34.5448	1.25555	0.627776	+	0.778394i	$0.283965\pi$
$758$	−55.2128	−2.00542
$759$	23.4705	0.851925
$760$	−10.5702	−0.383421
$761$	−43.8905	−1.59103	−0.795514	−	0.605935i	$-0.792799\pi$
$761$	−43.8905	−1.59103	−0.795514	+	0.605935i	$0.792799\pi$
$762$	−50.1231	−1.81577
$763$	−17.5165	−0.634138
$764$	−29.1016	−1.05286
$765$	−11.7504	−0.424837
$766$	−2.34884	−0.0848670
$767$	1.18141	0.0426581
$768$	23.6105	0.851969
$769$	−26.9503	−0.971852	−0.485926	−	0.874000i	$-0.661518\pi$
$769$	−26.9503	−0.971852	−0.485926	+	0.874000i	$0.661518\pi$
$770$	−20.1498	−0.726149
$771$	−15.8990	−0.572588
$772$	45.3917	1.63368
$773$	−39.8555	−1.43350	−0.716752	−	0.697329i	$-0.754372\pi$
$773$	−39.8555	−1.43350	−0.716752	+	0.697329i	$0.754372\pi$
$774$	15.6798	0.563599
$775$	6.32197	0.227092
$776$	22.7892	0.818084
$777$	−11.2996	−0.405369
$778$	21.7159	0.778552
$779$	8.93064	0.319973
$780$	6.71218	0.240335
$781$	68.3332	2.44515
$782$	−75.5111	−2.70027
$783$	−2.03624	−0.0727692
$784$	1.33550	0.0476965
$785$	−7.46113	−0.266299
$786$	24.5502	0.875677
$787$	−34.4777	−1.22900	−0.614499	−	0.788917i	$-0.710642\pi$
$787$	−34.4777	−1.22900	−0.614499	+	0.788917i	$0.710642\pi$
$788$	−73.3861	−2.61427
$789$	22.4361	0.798745
$790$	7.44224	0.264783
$791$	−13.8401	−0.492097
$792$	−17.0804	−0.606924
$793$	9.81943	0.348698
$794$	−30.9374	−1.09793
$795$	15.7934	0.560135
$796$	−85.3567	−3.02539
$797$	−1.62918	−0.0577084	−0.0288542	−	0.999584i	$-0.509186\pi$
$797$	−1.62918	−0.0577084	−0.0288542	+	0.999584i	$0.509186\pi$
$798$	3.89326	0.137820
$799$	−14.1856	−0.501851
$800$	−7.16990	−0.253494
$801$	−7.92565	−0.280039
$802$	−54.0650	−1.90910
$803$	42.1799	1.48850
$804$	15.3803	0.542421
$805$	−8.76289	−0.308851
$806$	−8.81145	−0.310370
$807$	−13.7305	−0.483338
$808$	−46.7473	−1.64456
$809$	27.6076	0.970633	0.485317	−	0.874338i	$-0.338704\pi$
$809$	27.6076	0.970633	0.485317	+	0.874338i	$0.338704\pi$
$810$	−4.20363	−0.147701
$811$	−35.6874	−1.25316	−0.626578	−	0.779359i	$-0.715545\pi$
$811$	−35.6874	−1.25316	−0.626578	+	0.779359i	$0.715545\pi$
$812$	7.16154	0.251321
$813$	7.74110	0.271492
$814$	−127.222	−4.45911
$815$	28.8450	1.01039
$816$	8.76852	0.306959
$817$	−11.0649	−0.387113
$818$	90.7444	3.17281
$819$	−1.06639	−0.0372626
$820$	33.9134	1.18431
$821$	−34.1809	−1.19292	−0.596460	−	0.802643i	$-0.703427\pi$
$821$	−34.1809	−1.19292	−0.596460	+	0.802643i	$0.703427\pi$
$822$	32.0006	1.11615
$823$	−51.0491	−1.77946	−0.889730	−	0.456488i	$-0.849107\pi$
$823$	−51.0491	−1.77946	−0.889730	+	0.456488i	$0.849107\pi$
$824$	27.7107	0.965346
$825$	8.61429	0.299911
$826$	2.60218	0.0905415
$827$	22.6449	0.787442	0.393721	−	0.919230i	$-0.371188\pi$
$827$	22.6449	0.787442	0.393721	+	0.919230i	$0.371188\pi$
$828$	−17.2208	−0.598464
$829$	−2.82704	−0.0981871	−0.0490936	−	0.998794i	$-0.515633\pi$
$829$	−2.82704	−0.0981871	−0.0490936	+	0.998794i	$0.515633\pi$
$830$	22.6767	0.787121
$831$	10.2475	0.355482
$832$	12.8416	0.445202
$833$	−6.56571	−0.227488
$834$	29.2725	1.01362
$835$	−24.9896	−0.864802
$836$	27.9437	0.966454
$837$	3.51787	0.121595
$838$	−13.0360	−0.450321
$839$	−37.8966	−1.30834	−0.654168	−	0.756349i	$-0.726981\pi$
$839$	−37.8966	−1.30834	−0.654168	+	0.756349i	$0.726981\pi$
$840$	6.37709	0.220030
$841$	−24.8537	−0.857025
$842$	−52.7893	−1.81924
$843$	29.6769	1.02213
$844$	−36.2016	−1.24611
$845$	−21.2305	−0.730350
$846$	−5.07481	−0.174476
$847$	11.9770	0.411533
$848$	−11.7855	−0.404717
$849$	16.4144	0.563339
$850$	−27.7146	−0.950602
$851$	−55.3270	−1.89658
$852$	−50.1375	−1.71768
$853$	11.8296	0.405039	0.202519	−	0.979278i	$-0.435087\pi$
$853$	11.8296	0.405039	0.202519	+	0.979278i	$0.435087\pi$
$854$	21.6284	0.740109
$855$	2.96642	0.101449
$856$	19.3585	0.661659
$857$	−14.0985	−0.481595	−0.240798	−	0.970575i	$-0.577409\pi$
$857$	−14.0985	−0.481595	−0.240798	+	0.970575i	$0.577409\pi$
$858$	−12.0064	−0.409893
$859$	11.6354	0.396994	0.198497	−	0.980102i	$-0.436394\pi$
$859$	11.6354	0.396994	0.198497	+	0.980102i	$0.436394\pi$
$860$	−42.0181	−1.43281
$861$	−5.38793	−0.183620
$862$	12.3722	0.421398
$863$	27.9306	0.950769	0.475385	−	0.879778i	$-0.342309\pi$
$863$	27.9306	0.950769	0.475385	+	0.879778i	$0.342309\pi$
$864$	−3.98970	−0.135732
$865$	26.6922	0.907563
$866$	−90.1932	−3.06489
$867$	−26.1086	−0.886694
$868$	−12.3725	−0.419950
$869$	−8.48644	−0.287883
$870$	8.55959	0.290197
$871$	4.66339	0.158013
$872$	62.4161	2.11368
$873$	−6.39555	−0.216457
$874$	19.0629	0.644813
$875$	−12.1645	−0.411236
$876$	−30.9483	−1.04565
$877$	−29.7413	−1.00429	−0.502146	−	0.864783i	$-0.667456\pi$
$877$	−29.7413	−1.00429	−0.502146	+	0.864783i	$0.667456\pi$
$878$	−75.3136	−2.54171
$879$	−22.8566	−0.770935
$880$	11.4568	0.386207
$881$	7.24231	0.244000	0.122000	−	0.992530i	$-0.461069\pi$
$881$	7.24231	0.244000	0.122000	+	0.992530i	$0.461069\pi$
$882$	−2.34884	−0.0790895
$883$	−16.7364	−0.563226	−0.281613	−	0.959528i	$-0.590869\pi$
$883$	−16.7364	−0.563226	−0.281613	+	0.959528i	$0.590869\pi$
$884$	24.6249	0.828224
$885$	1.98270	0.0666476
$886$	−36.5290	−1.22721
$887$	37.2702	1.25141	0.625705	−	0.780060i	$-0.284812\pi$
$887$	37.2702	1.25141	0.625705	+	0.780060i	$0.284812\pi$
$888$	40.2636	1.35116
$889$	−21.3395	−0.715705
$890$	33.3165	1.11677
$891$	4.79343	0.160586
$892$	−12.2557	−0.410352
$893$	3.58119	0.119840
$894$	−12.9409	−0.432809
$895$	0.589598	0.0197081
$896$	20.3057	0.678365
$897$	−5.22144	−0.174339
$898$	57.4174	1.91604
$899$	−7.16322	−0.238907
$900$	−6.32049	−0.210683
$901$	57.9411	1.93030
$902$	−60.6626	−2.01985
$903$	6.67556	0.222149
$904$	49.3162	1.64023
$905$	24.7555	0.822900
$906$	−36.6170	−1.21652
$907$	46.1276	1.53164	0.765821	−	0.643054i	$-0.222333\pi$
$907$	46.1276	1.53164	0.765821	+	0.643054i	$0.222333\pi$
$908$	77.1887	2.56160
$909$	13.1191	0.435134
$910$	4.48270	0.148600
$911$	−38.4728	−1.27466	−0.637331	−	0.770590i	$-0.719962\pi$
$911$	−38.4728	−1.27466	−0.637331	+	0.770590i	$0.719962\pi$
$912$	−2.21363	−0.0733006
$913$	−25.8584	−0.855789
$914$	−87.6385	−2.89882
$915$	16.4795	0.544794
$916$	−71.1823	−2.35193
$917$	10.4521	0.345157
$918$	−15.4218	−0.508995
$919$	32.8799	1.08461	0.542304	−	0.840182i	$-0.317552\pi$
$919$	32.8799	1.08461	0.542304	+	0.840182i	$0.317552\pi$
$920$	31.2247	1.02945
$921$	13.3346	0.439390
$922$	−76.4202	−2.51677
$923$	−15.2020	−0.500379
$924$	−16.8587	−0.554610
$925$	−20.3065	−0.667672
$926$	84.4585	2.77548
$927$	−7.77671	−0.255421
$928$	8.12398	0.266683
$929$	−18.7021	−0.613594	−0.306797	−	0.951775i	$-0.599257\pi$
$929$	−18.7021	−0.613594	−0.306797	+	0.951775i	$0.599257\pi$
$930$	−14.7878	−0.484912
$931$	1.65753	0.0543233
$932$	−42.7323	−1.39974
$933$	−24.7498	−0.810274
$934$	61.0442	1.99743
$935$	−56.3248	−1.84202
$936$	3.79984	0.124202
$937$	7.45801	0.243643	0.121821	−	0.992552i	$-0.461127\pi$
$937$	7.45801	0.243643	0.121821	+	0.992552i	$0.461127\pi$
$938$	10.2716	0.335381
$939$	28.0995	0.916991
$940$	13.5993	0.443559
$941$	−33.1156	−1.07954	−0.539769	−	0.841813i	$-0.681488\pi$
$941$	−33.1156	−1.07954	−0.539769	+	0.841813i	$0.681488\pi$
$942$	−9.79233	−0.319051
$943$	−26.3814	−0.859096
$944$	−1.47955	−0.0481551
$945$	−1.78966	−0.0582178
$946$	75.1600	2.44366
$947$	7.23487	0.235102	0.117551	−	0.993067i	$-0.462496\pi$
$947$	7.23487	0.235102	0.117551	+	0.993067i	$0.462496\pi$
$948$	6.22668	0.202233
$949$	−9.38370	−0.304608
$950$	6.99660	0.227000
$951$	14.1378	0.458448
$952$	23.3955	0.758253
$953$	−35.9718	−1.16524	−0.582621	−	0.812744i	$-0.697973\pi$
$953$	−35.9718	−1.16524	−0.582621	+	0.812744i	$0.697973\pi$
$954$	20.7280	0.671094
$955$	−14.8085	−0.479192
$956$	86.2440	2.78933
$957$	−9.76056	−0.315514
$958$	−48.7229	−1.57416
$959$	13.6240	0.439942
$960$	21.5514	0.695569
$961$	−18.6246	−0.600794
$962$	28.3028	0.912518
$963$	−5.43275	−0.175068
$964$	38.5667	1.24215
$965$	23.0978	0.743545
$966$	−11.5008	−0.370033
$967$	28.8841	0.928851	0.464426	−	0.885612i	$-0.346261\pi$
$967$	28.8841	0.928851	0.464426	+	0.885612i	$0.346261\pi$
$968$	−42.6773	−1.37170
$969$	10.8828	0.349607
$970$	26.8845	0.863210
$971$	56.6701	1.81863	0.909316	−	0.416107i	$-0.136606\pi$
$971$	56.6701	1.81863	0.909316	+	0.416107i	$0.136606\pi$
$972$	−3.51704	−0.112809
$973$	12.4625	0.399531
$974$	56.0689	1.79656
$975$	−1.91641	−0.0613741
$976$	−12.2975	−0.393632
$977$	−31.8647	−1.01944	−0.509721	−	0.860340i	$-0.670251\pi$
$977$	−31.8647	−1.01944	−0.509721	+	0.860340i	$0.670251\pi$
$978$	37.8575	1.21055
$979$	−37.9911	−1.21420
$980$	6.29432	0.201065
$981$	−17.5165	−0.559257
$982$	72.6535	2.31847
$983$	−20.5528	−0.655531	−0.327765	−	0.944759i	$-0.606296\pi$
$983$	−20.5528	−0.655531	−0.327765	+	0.944759i	$0.606296\pi$
$984$	19.1987	0.612033
$985$	−37.3429	−1.18984
$986$	31.4025	1.00006
$987$	−2.16056	−0.0687714
$988$	−6.21660	−0.197776
$989$	32.6861	1.03936
$990$	−20.1498	−0.640403
$991$	30.5478	0.970383	0.485191	−	0.874408i	$-0.338750\pi$
$991$	30.5478	0.970383	0.485191	+	0.874408i	$0.338750\pi$
$992$	−14.0352	−0.445619
$993$	5.41182	0.171739
$994$	−33.4841	−1.06205
$995$	−43.4342	−1.37696
$996$	18.9729	0.601179
$997$	20.0503	0.634999	0.317500	−	0.948258i	$-0.397157\pi$
$997$	20.0503	0.634999	0.317500	+	0.948258i	$0.397157\pi$
$998$	42.3727	1.34128
$999$	−11.2996	−0.357502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.o.1.6	✓	41

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

\(f(q)\)	\(=\)	\(q-2.34884 q^{2} -1.00000 q^{3} +3.51704 q^{4} +1.78966 q^{5} +2.34884 q^{6} +1.00000 q^{7} -3.56329 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.34884 q^{2} -1.00000 q^{3} +3.51704 q^{4} +1.78966 q^{5} +2.34884 q^{6} +1.00000 q^{7} -3.56329 q^{8} +1.00000 q^{9} -4.20363 q^{10} +4.79343 q^{11} -3.51704 q^{12} -1.06639 q^{13} -2.34884 q^{14} -1.78966 q^{15} +1.33550 q^{16} -6.56571 q^{17} -2.34884 q^{18} +1.65753 q^{19} +6.29432 q^{20} -1.00000 q^{21} -11.2590 q^{22} -4.89639 q^{23} +3.56329 q^{24} -1.79710 q^{25} +2.50477 q^{26} -1.00000 q^{27} +3.51704 q^{28} +2.03624 q^{29} +4.20363 q^{30} -3.51787 q^{31} +3.98970 q^{32} -4.79343 q^{33} +15.4218 q^{34} +1.78966 q^{35} +3.51704 q^{36} +11.2996 q^{37} -3.89326 q^{38} +1.06639 q^{39} -6.37709 q^{40} +5.38793 q^{41} +2.34884 q^{42} -6.67556 q^{43} +16.8587 q^{44} +1.78966 q^{45} +11.5008 q^{46} +2.16056 q^{47} -1.33550 q^{48} +1.00000 q^{49} +4.22110 q^{50} +6.56571 q^{51} -3.75053 q^{52} -8.82480 q^{53} +2.34884 q^{54} +8.57863 q^{55} -3.56329 q^{56} -1.65753 q^{57} -4.78279 q^{58} -1.10786 q^{59} -6.29432 q^{60} -9.20813 q^{61} +8.26290 q^{62} +1.00000 q^{63} -12.0422 q^{64} -1.90847 q^{65} +11.2590 q^{66} -4.37307 q^{67} -23.0919 q^{68} +4.89639 q^{69} -4.20363 q^{70} +14.2556 q^{71} -3.56329 q^{72} +8.79953 q^{73} -26.5408 q^{74} +1.79710 q^{75} +5.82959 q^{76} +4.79343 q^{77} -2.50477 q^{78} -1.77043 q^{79} +2.39010 q^{80} +1.00000 q^{81} -12.6554 q^{82} -5.39456 q^{83} -3.51704 q^{84} -11.7504 q^{85} +15.6798 q^{86} -2.03624 q^{87} -17.0804 q^{88} -7.92565 q^{89} -4.20363 q^{90} -1.06639 q^{91} -17.2208 q^{92} +3.51787 q^{93} -5.07481 q^{94} +2.96642 q^{95} -3.98970 q^{96} -6.39555 q^{97} -2.34884 q^{98} +4.79343 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * q^99

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