LMFDB - Embedded newform 8043.2.a.o.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.48498 q^{2} -1.00000 q^{3} +4.17514 q^{4} -2.72732 q^{5} +2.48498 q^{6} +1.00000 q^{7} -5.40520 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.48498 q^{2} -1.00000 q^{3} +4.17514 q^{4} -2.72732 q^{5} +2.48498 q^{6} +1.00000 q^{7} -5.40520 q^{8} +1.00000 q^{9} +6.77735 q^{10} +1.40162 q^{11} -4.17514 q^{12} -3.18971 q^{13} -2.48498 q^{14} +2.72732 q^{15} +5.08154 q^{16} +6.94685 q^{17} -2.48498 q^{18} -5.84326 q^{19} -11.3870 q^{20} -1.00000 q^{21} -3.48300 q^{22} +2.50132 q^{23} +5.40520 q^{24} +2.43829 q^{25} +7.92638 q^{26} -1.00000 q^{27} +4.17514 q^{28} +4.45675 q^{29} -6.77735 q^{30} +1.94262 q^{31} -1.81714 q^{32} -1.40162 q^{33} -17.2628 q^{34} -2.72732 q^{35} +4.17514 q^{36} -8.67782 q^{37} +14.5204 q^{38} +3.18971 q^{39} +14.7417 q^{40} +1.44740 q^{41} +2.48498 q^{42} -6.61007 q^{43} +5.85196 q^{44} -2.72732 q^{45} -6.21575 q^{46} +3.78823 q^{47} -5.08154 q^{48} +1.00000 q^{49} -6.05911 q^{50} -6.94685 q^{51} -13.3175 q^{52} -11.8202 q^{53} +2.48498 q^{54} -3.82267 q^{55} -5.40520 q^{56} +5.84326 q^{57} -11.0750 q^{58} +3.46609 q^{59} +11.3870 q^{60} +6.46777 q^{61} -4.82739 q^{62} +1.00000 q^{63} -5.64750 q^{64} +8.69937 q^{65} +3.48300 q^{66} +12.5293 q^{67} +29.0041 q^{68} -2.50132 q^{69} +6.77735 q^{70} -1.58669 q^{71} -5.40520 q^{72} +14.7777 q^{73} +21.5642 q^{74} -2.43829 q^{75} -24.3965 q^{76} +1.40162 q^{77} -7.92638 q^{78} -15.0724 q^{79} -13.8590 q^{80} +1.00000 q^{81} -3.59676 q^{82} +1.14155 q^{83} -4.17514 q^{84} -18.9463 q^{85} +16.4259 q^{86} -4.45675 q^{87} -7.57603 q^{88} -12.1163 q^{89} +6.77735 q^{90} -3.18971 q^{91} +10.4434 q^{92} -1.94262 q^{93} -9.41370 q^{94} +15.9365 q^{95} +1.81714 q^{96} +0.826984 q^{97} -2.48498 q^{98} +1.40162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.48498	−1.75715	−0.878574	−	0.477606i	$-0.841505\pi$
$2$	−2.48498	−1.75715	−0.878574	+	0.477606i	$0.841505\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.17514	2.08757
$5$	−2.72732	−1.21970	−0.609848	−	0.792518i	$-0.708769\pi$
$5$	−2.72732	−1.21970	−0.609848	+	0.792518i	$0.708769\pi$
$6$	2.48498	1.01449
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.40520	−1.91103
$9$	1.00000	0.333333
$10$	6.77735	2.14319
$11$	1.40162	0.422604	0.211302	−	0.977421i	$-0.432230\pi$
$11$	1.40162	0.422604	0.211302	+	0.977421i	$0.432230\pi$
$12$	−4.17514	−1.20526
$13$	−3.18971	−0.884666	−0.442333	−	0.896851i	$-0.645849\pi$
$13$	−3.18971	−0.884666	−0.442333	+	0.896851i	$0.645849\pi$
$14$	−2.48498	−0.664140
$15$	2.72732	0.704192
$16$	5.08154	1.27038
$17$	6.94685	1.68486	0.842429	−	0.538807i	$-0.181125\pi$
$17$	6.94685	1.68486	0.842429	+	0.538807i	$0.181125\pi$
$18$	−2.48498	−0.585716
$19$	−5.84326	−1.34054	−0.670268	−	0.742119i	$-0.733821\pi$
$19$	−5.84326	−1.34054	−0.670268	+	0.742119i	$0.733821\pi$
$20$	−11.3870	−2.54620
$21$	−1.00000	−0.218218
$22$	−3.48300	−0.742578
$23$	2.50132	0.521562	0.260781	−	0.965398i	$-0.416020\pi$
$23$	2.50132	0.521562	0.260781	+	0.965398i	$0.416020\pi$
$24$	5.40520	1.10333
$25$	2.43829	0.487658
$26$	7.92638	1.55449
$27$	−1.00000	−0.192450
$28$	4.17514	0.789028
$29$	4.45675	0.827599	0.413799	−	0.910368i	$-0.364202\pi$
$29$	4.45675	0.827599	0.413799	+	0.910368i	$0.364202\pi$
$30$	−6.77735	−1.23737
$31$	1.94262	0.348905	0.174453	−	0.984666i	$-0.444184\pi$
$31$	1.94262	0.348905	0.174453	+	0.984666i	$0.444184\pi$
$32$	−1.81714	−0.321229
$33$	−1.40162	−0.243991
$34$	−17.2628	−2.96055
$35$	−2.72732	−0.461002
$36$	4.17514	0.695857
$37$	−8.67782	−1.42663	−0.713313	−	0.700846i	$-0.752806\pi$
$37$	−8.67782	−1.42663	−0.713313	+	0.700846i	$0.752806\pi$
$38$	14.5204	2.35552
$39$	3.18971	0.510762
$40$	14.7417	2.33087
$41$	1.44740	0.226046	0.113023	−	0.993592i	$-0.463947\pi$
$41$	1.44740	0.226046	0.113023	+	0.993592i	$0.463947\pi$
$42$	2.48498	0.383441
$43$	−6.61007	−1.00803	−0.504013	−	0.863696i	$-0.668144\pi$
$43$	−6.61007	−1.00803	−0.504013	+	0.863696i	$0.668144\pi$
$44$	5.85196	0.882216
$45$	−2.72732	−0.406565
$46$	−6.21575	−0.916463
$47$	3.78823	0.552571	0.276285	−	0.961076i	$-0.410897\pi$
$47$	3.78823	0.552571	0.276285	+	0.961076i	$0.410897\pi$
$48$	−5.08154	−0.733457
$49$	1.00000	0.142857
$50$	−6.05911	−0.856887
$51$	−6.94685	−0.972754
$52$	−13.3175	−1.84680
$53$	−11.8202	−1.62363	−0.811816	−	0.583913i	$-0.801521\pi$
$53$	−11.8202	−1.62363	−0.811816	+	0.583913i	$0.801521\pi$
$54$	2.48498	0.338163
$55$	−3.82267	−0.515448
$56$	−5.40520	−0.722300
$57$	5.84326	0.773959
$58$	−11.0750	−1.45421
$59$	3.46609	0.451246	0.225623	−	0.974215i	$-0.427558\pi$
$59$	3.46609	0.451246	0.225623	+	0.974215i	$0.427558\pi$
$60$	11.3870	1.47005
$61$	6.46777	0.828113	0.414057	−	0.910251i	$-0.364112\pi$
$61$	6.46777	0.828113	0.414057	+	0.910251i	$0.364112\pi$
$62$	−4.82739	−0.613079
$63$	1.00000	0.125988
$64$	−5.64750	−0.705938
$65$	8.69937	1.07902
$66$	3.48300	0.428728
$67$	12.5293	1.53069	0.765347	−	0.643617i	$-0.222567\pi$
$67$	12.5293	1.53069	0.765347	+	0.643617i	$0.222567\pi$
$68$	29.0041	3.51726
$69$	−2.50132	−0.301124
$70$	6.77735	0.810049
$71$	−1.58669	−0.188306	−0.0941530	−	0.995558i	$-0.530014\pi$
$71$	−1.58669	−0.188306	−0.0941530	+	0.995558i	$0.530014\pi$
$72$	−5.40520	−0.637009
$73$	14.7777	1.72960	0.864801	−	0.502115i	$-0.167445\pi$
$73$	14.7777	1.72960	0.864801	+	0.502115i	$0.167445\pi$
$74$	21.5642	2.50679
$75$	−2.43829	−0.281549
$76$	−24.3965	−2.79847
$77$	1.40162	0.159729
$78$	−7.92638	−0.897485
$79$	−15.0724	−1.69578	−0.847891	−	0.530171i	$-0.822128\pi$
$79$	−15.0724	−1.69578	−0.847891	+	0.530171i	$0.822128\pi$
$80$	−13.8590	−1.54948
$81$	1.00000	0.111111
$82$	−3.59676	−0.397196
$83$	1.14155	0.125301	0.0626506	−	0.998036i	$-0.480045\pi$
$83$	1.14155	0.125301	0.0626506	+	0.998036i	$0.480045\pi$
$84$	−4.17514	−0.455546
$85$	−18.9463	−2.05501
$86$	16.4259	1.77125
$87$	−4.45675	−0.477814
$88$	−7.57603	−0.807607
$89$	−12.1163	−1.28432	−0.642162	−	0.766569i	$-0.721962\pi$
$89$	−12.1163	−1.28432	−0.642162	+	0.766569i	$0.721962\pi$
$90$	6.77735	0.714396
$91$	−3.18971	−0.334372
$92$	10.4434	1.08880
$93$	−1.94262	−0.201441
$94$	−9.41370	−0.970949
$95$	15.9365	1.63505
$96$	1.81714	0.185462
$97$	0.826984	0.0839675	0.0419837	−	0.999118i	$-0.486632\pi$
$97$	0.826984	0.0839675	0.0419837	+	0.999118i	$0.486632\pi$
$98$	−2.48498	−0.251021
$99$	1.40162	0.140868
$100$	10.1802	1.01802
$101$	0.166024	0.0165200	0.00826002	−	0.999966i	$-0.497371\pi$
$101$	0.166024	0.0165200	0.00826002	+	0.999966i	$0.497371\pi$
$102$	17.2628	1.70927
$103$	−16.7829	−1.65367	−0.826835	−	0.562445i	$-0.809861\pi$
$103$	−16.7829	−1.65367	−0.826835	+	0.562445i	$0.809861\pi$
$104$	17.2410	1.69062
$105$	2.72732	0.266159
$106$	29.3731	2.85296
$107$	−16.8127	−1.62534	−0.812672	−	0.582721i	$-0.801988\pi$
$107$	−16.8127	−1.62534	−0.812672	+	0.582721i	$0.801988\pi$
$108$	−4.17514	−0.401753
$109$	6.28896	0.602373	0.301187	−	0.953565i	$-0.402617\pi$
$109$	6.28896	0.602373	0.301187	+	0.953565i	$0.402617\pi$
$110$	9.49926	0.905719
$111$	8.67782	0.823662
$112$	5.08154	0.480160
$113$	−2.25890	−0.212499	−0.106250	−	0.994339i	$-0.533884\pi$
$113$	−2.25890	−0.212499	−0.106250	+	0.994339i	$0.533884\pi$
$114$	−14.5204	−1.35996
$115$	−6.82192	−0.636147
$116$	18.6076	1.72767
$117$	−3.18971	−0.294889
$118$	−8.61317	−0.792906
$119$	6.94685	0.636817
$120$	−14.7417	−1.34573
$121$	−9.03546	−0.821406
$122$	−16.0723	−1.45512
$123$	−1.44740	−0.130508
$124$	8.11073	0.728365
$125$	6.98661	0.624902
$126$	−2.48498	−0.221380
$127$	17.4284	1.54652	0.773262	−	0.634086i	$-0.218624\pi$
$127$	17.4284	1.54652	0.773262	+	0.634086i	$0.218624\pi$
$128$	17.6682	1.56167
$129$	6.61007	0.581984
$130$	−21.6178	−1.89601
$131$	22.6140	1.97580	0.987899	−	0.155098i	$-0.0495694\pi$
$131$	22.6140	1.97580	0.987899	+	0.155098i	$0.0495694\pi$
$132$	−5.85196	−0.509348
$133$	−5.84326	−0.506675
$134$	−31.1350	−2.68966
$135$	2.72732	0.234731
$136$	−37.5491	−3.21981
$137$	16.1815	1.38247	0.691237	−	0.722628i	$-0.257066\pi$
$137$	16.1815	1.38247	0.691237	+	0.722628i	$0.257066\pi$
$138$	6.21575	0.529120
$139$	−9.58865	−0.813299	−0.406649	−	0.913584i	$-0.633303\pi$
$139$	−9.58865	−0.813299	−0.406649	+	0.913584i	$0.633303\pi$
$140$	−11.3870	−0.962374
$141$	−3.78823	−0.319027
$142$	3.94291	0.330882
$143$	−4.47076	−0.373863
$144$	5.08154	0.423461
$145$	−12.1550	−1.00942
$146$	−36.7224	−3.03917
$147$	−1.00000	−0.0824786
$148$	−36.2312	−2.97818
$149$	−1.70340	−0.139548	−0.0697741	−	0.997563i	$-0.522228\pi$
$149$	−1.70340	−0.139548	−0.0697741	+	0.997563i	$0.522228\pi$
$150$	6.05911	0.494724
$151$	−7.92361	−0.644815	−0.322407	−	0.946601i	$-0.604492\pi$
$151$	−7.92361	−0.644815	−0.322407	+	0.946601i	$0.604492\pi$
$152$	31.5840	2.56180
$153$	6.94685	0.561620
$154$	−3.48300	−0.280668
$155$	−5.29816	−0.425558
$156$	13.3175	1.06625
$157$	−25.0074	−1.99581	−0.997903	−	0.0647254i	$-0.979383\pi$
$157$	−25.0074	−1.99581	−0.997903	+	0.0647254i	$0.979383\pi$
$158$	37.4548	2.97974
$159$	11.8202	0.937405
$160$	4.95594	0.391801
$161$	2.50132	0.197132
$162$	−2.48498	−0.195239
$163$	25.0870	1.96497	0.982483	−	0.186354i	$-0.0596673\pi$
$163$	25.0870	1.96497	0.982483	+	0.186354i	$0.0596673\pi$
$164$	6.04310	0.471887
$165$	3.82267	0.297594
$166$	−2.83673	−0.220173
$167$	−3.91251	−0.302759	−0.151380	−	0.988476i	$-0.548372\pi$
$167$	−3.91251	−0.302759	−0.151380	+	0.988476i	$0.548372\pi$
$168$	5.40520	0.417020
$169$	−2.82575	−0.217366
$170$	47.0812	3.61097
$171$	−5.84326	−0.446845
$172$	−27.5980	−2.10433
$173$	1.82708	0.138910	0.0694552	−	0.997585i	$-0.477874\pi$
$173$	1.82708	0.138910	0.0694552	+	0.997585i	$0.477874\pi$
$174$	11.0750	0.839591
$175$	2.43829	0.184317
$176$	7.12238	0.536870
$177$	−3.46609	−0.260527
$178$	30.1088	2.25675
$179$	8.97261	0.670644	0.335322	−	0.942104i	$-0.391155\pi$
$179$	8.97261	0.670644	0.335322	+	0.942104i	$0.391155\pi$
$180$	−11.3870	−0.848734
$181$	6.98935	0.519515	0.259757	−	0.965674i	$-0.416357\pi$
$181$	6.98935	0.519515	0.259757	+	0.965674i	$0.416357\pi$
$182$	7.92638	0.587542
$183$	−6.46777	−0.478111
$184$	−13.5202	−0.996719
$185$	23.6672	1.74005
$186$	4.82739	0.353961
$187$	9.73684	0.712028
$188$	15.8164	1.15353
$189$	−1.00000	−0.0727393
$190$	−39.6018	−2.87302
$191$	13.2132	0.956073	0.478037	−	0.878340i	$-0.341349\pi$
$191$	13.2132	0.956073	0.478037	+	0.878340i	$0.341349\pi$
$192$	5.64750	0.407573
$193$	−17.6744	−1.27223	−0.636117	−	0.771592i	$-0.719461\pi$
$193$	−17.6744	−1.27223	−0.636117	+	0.771592i	$0.719461\pi$
$194$	−2.05504	−0.147543
$195$	−8.69937	−0.622975
$196$	4.17514	0.298225
$197$	−21.1885	−1.50961	−0.754807	−	0.655946i	$-0.772270\pi$
$197$	−21.1885	−1.50961	−0.754807	+	0.655946i	$0.772270\pi$
$198$	−3.48300	−0.247526
$199$	18.4926	1.31091	0.655453	−	0.755236i	$-0.272478\pi$
$199$	18.4926	1.31091	0.655453	+	0.755236i	$0.272478\pi$
$200$	−13.1794	−0.931926
$201$	−12.5293	−0.883747
$202$	−0.412568	−0.0290282
$203$	4.45675	0.312803
$204$	−29.0041	−2.03069
$205$	−3.94752	−0.275707
$206$	41.7053	2.90574
$207$	2.50132	0.173854
$208$	−16.2086	−1.12387
$209$	−8.19003	−0.566516
$210$	−6.77735	−0.467682
$211$	27.1795	1.87112	0.935558	−	0.353172i	$-0.114897\pi$
$211$	27.1795	1.87112	0.935558	+	0.353172i	$0.114897\pi$
$212$	−49.3511	−3.38945
$213$	1.58669	0.108718
$214$	41.7793	2.85597
$215$	18.0278	1.22948
$216$	5.40520	0.367777
$217$	1.94262	0.131874
$218$	−15.6280	−1.05846
$219$	−14.7777	−0.998586
$220$	−15.9602	−1.07604
$221$	−22.1584	−1.49054
$222$	−21.5642	−1.44730
$223$	−23.3816	−1.56575	−0.782876	−	0.622178i	$-0.786248\pi$
$223$	−23.3816	−1.56575	−0.782876	+	0.622178i	$0.786248\pi$
$224$	−1.81714	−0.121413
$225$	2.43829	0.162553
$226$	5.61332	0.373392
$227$	−22.2478	−1.47664	−0.738318	−	0.674452i	$-0.764380\pi$
$227$	−22.2478	−1.47664	−0.738318	+	0.674452i	$0.764380\pi$
$228$	24.3965	1.61569
$229$	10.9636	0.724497	0.362248	−	0.932082i	$-0.382009\pi$
$229$	10.9636	0.724497	0.362248	+	0.932082i	$0.382009\pi$
$230$	16.9524	1.11781
$231$	−1.40162	−0.0922197
$232$	−24.0896	−1.58156
$233$	−0.191555	−0.0125492	−0.00627461	−	0.999980i	$-0.501997\pi$
$233$	−0.191555	−0.0125492	−0.00627461	+	0.999980i	$0.501997\pi$
$234$	7.92638	0.518163
$235$	−10.3317	−0.673968
$236$	14.4714	0.942008
$237$	15.0724	0.979060
$238$	−17.2628	−1.11898
$239$	10.1041	0.653578	0.326789	−	0.945097i	$-0.394033\pi$
$239$	10.1041	0.653578	0.326789	+	0.945097i	$0.394033\pi$
$240$	13.8590	0.894594
$241$	20.5421	1.32323	0.661617	−	0.749842i	$-0.269871\pi$
$241$	20.5421	1.32323	0.661617	+	0.749842i	$0.269871\pi$
$242$	22.4530	1.44333
$243$	−1.00000	−0.0641500
$244$	27.0039	1.72875
$245$	−2.72732	−0.174242
$246$	3.59676	0.229321
$247$	18.6383	1.18593
$248$	−10.5003	−0.666767
$249$	−1.14155	−0.0723427
$250$	−17.3616	−1.09805
$251$	24.5821	1.55161	0.775803	−	0.630975i	$-0.217345\pi$
$251$	24.5821	1.55161	0.775803	+	0.630975i	$0.217345\pi$
$252$	4.17514	0.263009
$253$	3.50590	0.220414
$254$	−43.3094	−2.71747
$255$	18.9463	1.18646
$256$	−32.6103	−2.03814
$257$	11.8453	0.738889	0.369444	−	0.929253i	$-0.379548\pi$
$257$	11.8453	0.738889	0.369444	+	0.929253i	$0.379548\pi$
$258$	−16.4259	−1.02263
$259$	−8.67782	−0.539214
$260$	36.3211	2.25254
$261$	4.45675	0.275866
$262$	−56.1955	−3.47177
$263$	−14.0522	−0.866494	−0.433247	−	0.901275i	$-0.642632\pi$
$263$	−14.0522	−0.866494	−0.433247	+	0.901275i	$0.642632\pi$
$264$	7.57603	0.466272
$265$	32.2376	1.98034
$266$	14.5204	0.890303
$267$	12.1163	0.741505
$268$	52.3115	3.19544
$269$	9.84801	0.600444	0.300222	−	0.953869i	$-0.402939\pi$
$269$	9.84801	0.600444	0.300222	+	0.953869i	$0.402939\pi$
$270$	−6.77735	−0.412457
$271$	0.569749	0.0346098	0.0173049	−	0.999850i	$-0.494491\pi$
$271$	0.569749	0.0346098	0.0173049	+	0.999850i	$0.494491\pi$
$272$	35.3007	2.14042
$273$	3.18971	0.193050
$274$	−40.2106	−2.42921
$275$	3.41755	0.206086
$276$	−10.4434	−0.628618
$277$	−21.6072	−1.29825	−0.649125	−	0.760682i	$-0.724865\pi$
$277$	−21.6072	−1.29825	−0.649125	+	0.760682i	$0.724865\pi$
$278$	23.8276	1.42909
$279$	1.94262	0.116302
$280$	14.7417	0.880986
$281$	8.42860	0.502808	0.251404	−	0.967882i	$-0.419108\pi$
$281$	8.42860	0.502808	0.251404	+	0.967882i	$0.419108\pi$
$282$	9.41370	0.560577
$283$	1.44574	0.0859403	0.0429701	−	0.999076i	$-0.486318\pi$
$283$	1.44574	0.0859403	0.0429701	+	0.999076i	$0.486318\pi$
$284$	−6.62468	−0.393102
$285$	−15.9365	−0.943994
$286$	11.1098	0.656934
$287$	1.44740	0.0854373
$288$	−1.81714	−0.107076
$289$	31.2587	1.83875
$290$	30.2050	1.77370
$291$	−0.826984	−0.0484786
$292$	61.6991	3.61067
$293$	5.87479	0.343209	0.171604	−	0.985166i	$-0.445105\pi$
$293$	5.87479	0.343209	0.171604	+	0.985166i	$0.445105\pi$
$294$	2.48498	0.144927
$295$	−9.45313	−0.550383
$296$	46.9053	2.72632
$297$	−1.40162	−0.0813302
$298$	4.23293	0.245207
$299$	−7.97850	−0.461409
$300$	−10.1802	−0.587754
$301$	−6.61007	−0.380998
$302$	19.6900	1.13304
$303$	−0.166024	−0.00953785
$304$	−29.6928	−1.70300
$305$	−17.6397	−1.01005
$306$	−17.2628	−0.986849
$307$	−27.3075	−1.55852	−0.779259	−	0.626702i	$-0.784405\pi$
$307$	−27.3075	−1.55852	−0.779259	+	0.626702i	$0.784405\pi$
$308$	5.85196	0.333446
$309$	16.7829	0.954746
$310$	13.1658	0.747769
$311$	10.2165	0.579323	0.289661	−	0.957129i	$-0.406457\pi$
$311$	10.2165	0.579323	0.289661	+	0.957129i	$0.406457\pi$
$312$	−17.2410	−0.976080
$313$	−14.2600	−0.806021	−0.403010	−	0.915195i	$-0.632036\pi$
$313$	−14.2600	−0.806021	−0.403010	+	0.915195i	$0.632036\pi$
$314$	62.1429	3.50693
$315$	−2.72732	−0.153667
$316$	−62.9296	−3.54007
$317$	13.2348	0.743343	0.371671	−	0.928364i	$-0.378785\pi$
$317$	13.2348	0.743343	0.371671	+	0.928364i	$0.378785\pi$
$318$	−29.3731	−1.64716
$319$	6.24667	0.349746
$320$	15.4026	0.861029
$321$	16.8127	0.938393
$322$	−6.21575	−0.346390
$323$	−40.5923	−2.25861
$324$	4.17514	0.231952
$325$	−7.77743	−0.431414
$326$	−62.3408	−3.45274
$327$	−6.28896	−0.347780
$328$	−7.82348	−0.431979
$329$	3.78823	0.208852
$330$	−9.49926	−0.522917
$331$	17.2488	0.948078	0.474039	−	0.880504i	$-0.342796\pi$
$331$	17.2488	0.948078	0.474039	+	0.880504i	$0.342796\pi$
$332$	4.76613	0.261575
$333$	−8.67782	−0.475542
$334$	9.72252	0.531993
$335$	−34.1714	−1.86698
$336$	−5.08154	−0.277221
$337$	8.90639	0.485162	0.242581	−	0.970131i	$-0.422006\pi$
$337$	8.90639	0.485162	0.242581	+	0.970131i	$0.422006\pi$
$338$	7.02195	0.381944
$339$	2.25890	0.122686
$340$	−79.1035	−4.28999
$341$	2.72282	0.147449
$342$	14.5204	0.785174
$343$	1.00000	0.0539949
$344$	35.7287	1.92636
$345$	6.82192	0.367280
$346$	−4.54027	−0.244086
$347$	−19.6555	−1.05516	−0.527580	−	0.849505i	$-0.676901\pi$
$347$	−19.6555	−1.05516	−0.527580	+	0.849505i	$0.676901\pi$
$348$	−18.6076	−0.997472
$349$	8.73680	0.467670	0.233835	−	0.972276i	$-0.424872\pi$
$349$	8.73680	0.467670	0.233835	+	0.972276i	$0.424872\pi$
$350$	−6.05911	−0.323873
$351$	3.18971	0.170254
$352$	−2.54694	−0.135753
$353$	−2.35768	−0.125486	−0.0627432	−	0.998030i	$-0.519985\pi$
$353$	−2.35768	−0.125486	−0.0627432	+	0.998030i	$0.519985\pi$
$354$	8.61317	0.457785
$355$	4.32743	0.229676
$356$	−50.5873	−2.68112
$357$	−6.94685	−0.367666
$358$	−22.2968	−1.17842
$359$	−31.6147	−1.66856	−0.834280	−	0.551340i	$-0.814117\pi$
$359$	−31.6147	−1.66856	−0.834280	+	0.551340i	$0.814117\pi$
$360$	14.7417	0.776957
$361$	15.1437	0.797037
$362$	−17.3684	−0.912864
$363$	9.03546	0.474239
$364$	−13.3175	−0.698026
$365$	−40.3036	−2.10959
$366$	16.0723	0.840113
$367$	15.4199	0.804910	0.402455	−	0.915440i	$-0.368157\pi$
$367$	15.4199	0.804910	0.402455	+	0.915440i	$0.368157\pi$
$368$	12.7106	0.662585
$369$	1.44740	0.0753486
$370$	−58.8127	−3.05752
$371$	−11.8202	−0.613675
$372$	−8.11073	−0.420522
$373$	−23.5703	−1.22042	−0.610212	−	0.792238i	$-0.708916\pi$
$373$	−23.5703	−1.22042	−0.610212	+	0.792238i	$0.708916\pi$
$374$	−24.1959	−1.25114
$375$	−6.98661	−0.360787
$376$	−20.4761	−1.05598
$377$	−14.2158	−0.732149
$378$	2.48498	0.127814
$379$	−32.4959	−1.66920	−0.834600	−	0.550856i	$-0.814301\pi$
$379$	−32.4959	−1.66920	−0.834600	+	0.550856i	$0.814301\pi$
$380$	66.5370	3.41328
$381$	−17.4284	−0.892886
$382$	−32.8346	−1.67996
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−17.6682	−0.901628
$385$	−3.82267	−0.194821
$386$	43.9207	2.23551
$387$	−6.61007	−0.336009
$388$	3.45278	0.175288
$389$	−21.5807	−1.09419	−0.547093	−	0.837072i	$-0.684266\pi$
$389$	−21.5807	−1.09419	−0.547093	+	0.837072i	$0.684266\pi$
$390$	21.6178	1.09466
$391$	17.3763	0.878759
$392$	−5.40520	−0.273004
$393$	−22.6140	−1.14073
$394$	52.6530	2.65262
$395$	41.1074	2.06834
$396$	5.85196	0.294072
$397$	17.6393	0.885289	0.442645	−	0.896697i	$-0.354040\pi$
$397$	17.6393	0.885289	0.442645	+	0.896697i	$0.354040\pi$
$398$	−45.9538	−2.30346
$399$	5.84326	0.292529
$400$	12.3903	0.619513
$401$	24.4281	1.21988	0.609940	−	0.792448i	$-0.291194\pi$
$401$	24.4281	1.21988	0.609940	+	0.792448i	$0.291194\pi$
$402$	31.1350	1.55288
$403$	−6.19640	−0.308665
$404$	0.693175	0.0344868
$405$	−2.72732	−0.135522
$406$	−11.0750	−0.549641
$407$	−12.1630	−0.602897
$408$	37.5491	1.85896
$409$	35.8337	1.77186	0.885932	−	0.463815i	$-0.153520\pi$
$409$	35.8337	1.77186	0.885932	+	0.463815i	$0.153520\pi$
$410$	9.80953	0.484458
$411$	−16.1815	−0.798172
$412$	−70.0711	−3.45215
$413$	3.46609	0.170555
$414$	−6.21575	−0.305488
$415$	−3.11337	−0.152829
$416$	5.79616	0.284180
$417$	9.58865	0.469558
$418$	20.3521	0.995453
$419$	−5.45016	−0.266258	−0.133129	−	0.991099i	$-0.542502\pi$
$419$	−5.45016	−0.266258	−0.133129	+	0.991099i	$0.542502\pi$
$420$	11.3870	0.555627
$421$	0.479779	0.0233830	0.0116915	−	0.999932i	$-0.496278\pi$
$421$	0.479779	0.0233830	0.0116915	+	0.999932i	$0.496278\pi$
$422$	−67.5407	−3.28783
$423$	3.78823	0.184190
$424$	63.8906	3.10280
$425$	16.9384	0.821634
$426$	−3.94291	−0.191035
$427$	6.46777	0.312997
$428$	−70.1954	−3.39302
$429$	4.47076	0.215850
$430$	−44.7987	−2.16039
$431$	18.5284	0.892484	0.446242	−	0.894912i	$-0.352762\pi$
$431$	18.5284	0.892484	0.446242	+	0.894912i	$0.352762\pi$
$432$	−5.08154	−0.244486
$433$	40.9651	1.96866	0.984329	−	0.176341i	$-0.0564261\pi$
$433$	40.9651	1.96866	0.984329	+	0.176341i	$0.0564261\pi$
$434$	−4.82739	−0.231722
$435$	12.1550	0.582788
$436$	26.2573	1.25750
$437$	−14.6159	−0.699173
$438$	36.7224	1.75466
$439$	−24.3893	−1.16404	−0.582020	−	0.813175i	$-0.697737\pi$
$439$	−24.3893	−1.16404	−0.582020	+	0.813175i	$0.697737\pi$
$440$	20.6623	0.985035
$441$	1.00000	0.0476190
$442$	55.0633	2.61910
$443$	10.1223	0.480923	0.240462	−	0.970659i	$-0.422701\pi$
$443$	10.1223	0.480923	0.240462	+	0.970659i	$0.422701\pi$
$444$	36.2312	1.71945
$445$	33.0450	1.56648
$446$	58.1030	2.75126
$447$	1.70340	0.0805682
$448$	−5.64750	−0.266819
$449$	−40.4297	−1.90799	−0.953997	−	0.299816i	$-0.903075\pi$
$449$	−40.4297	−1.90799	−0.953997	+	0.299816i	$0.903075\pi$
$450$	−6.05911	−0.285629
$451$	2.02870	0.0955278
$452$	−9.43121	−0.443607
$453$	7.92361	0.372284
$454$	55.2854	2.59467
$455$	8.69937	0.407833
$456$	−31.5840	−1.47906
$457$	28.4781	1.33215	0.666074	−	0.745886i	$-0.267974\pi$
$457$	28.4781	1.33215	0.666074	+	0.745886i	$0.267974\pi$
$458$	−27.2444	−1.27305
$459$	−6.94685	−0.324251
$460$	−28.4825	−1.32800
$461$	35.7020	1.66281	0.831404	−	0.555669i	$-0.187538\pi$
$461$	35.7020	1.66281	0.831404	+	0.555669i	$0.187538\pi$
$462$	3.48300	0.162044
$463$	39.6842	1.84428	0.922140	−	0.386857i	$-0.126439\pi$
$463$	39.6842	1.84428	0.922140	+	0.386857i	$0.126439\pi$
$464$	22.6472	1.05137
$465$	5.29816	0.245696
$466$	0.476012	0.0220508
$467$	31.7200	1.46783	0.733914	−	0.679242i	$-0.237691\pi$
$467$	31.7200	1.46783	0.733914	+	0.679242i	$0.237691\pi$
$468$	−13.3175	−0.615601
$469$	12.5293	0.578548
$470$	25.6742	1.18426
$471$	25.0074	1.15228
$472$	−18.7349	−0.862342
$473$	−9.26479	−0.425996
$474$	−37.4548	−1.72035
$475$	−14.2476	−0.653723
$476$	29.0041	1.32940
$477$	−11.8202	−0.541211
$478$	−25.1085	−1.14843
$479$	−11.2555	−0.514279	−0.257139	−	0.966374i	$-0.582780\pi$
$479$	−11.2555	−0.514279	−0.257139	+	0.966374i	$0.582780\pi$
$480$	−4.95594	−0.226207
$481$	27.6797	1.26209
$482$	−51.0468	−2.32512
$483$	−2.50132	−0.113814
$484$	−37.7244	−1.71474
$485$	−2.25545	−0.102415
$486$	2.48498	0.112721
$487$	−22.1403	−1.00327	−0.501636	−	0.865079i	$-0.667268\pi$
$487$	−22.1403	−1.00327	−0.501636	+	0.865079i	$0.667268\pi$
$488$	−34.9596	−1.58255
$489$	−25.0870	−1.13447
$490$	6.77735	0.306170
$491$	1.25484	0.0566303	0.0283151	−	0.999599i	$-0.490986\pi$
$491$	1.25484	0.0566303	0.0283151	+	0.999599i	$0.490986\pi$
$492$	−6.04310	−0.272444
$493$	30.9604	1.39439
$494$	−46.3159	−2.08385
$495$	−3.82267	−0.171816
$496$	9.87151	0.443244
$497$	−1.58669	−0.0711730
$498$	2.83673	0.127117
$499$	−24.1390	−1.08061	−0.540305	−	0.841469i	$-0.681691\pi$
$499$	−24.1390	−1.08061	−0.540305	+	0.841469i	$0.681691\pi$
$500$	29.1701	1.30453
$501$	3.91251	0.174798
$502$	−61.0860	−2.72640
$503$	−2.27384	−0.101385	−0.0506927	−	0.998714i	$-0.516143\pi$
$503$	−2.27384	−0.101385	−0.0506927	+	0.998714i	$0.516143\pi$
$504$	−5.40520	−0.240767
$505$	−0.452802	−0.0201494
$506$	−8.71211	−0.387301
$507$	2.82575	0.125496
$508$	72.7663	3.22848
$509$	−12.6877	−0.562373	−0.281187	−	0.959653i	$-0.590728\pi$
$509$	−12.6877	−0.562373	−0.281187	+	0.959653i	$0.590728\pi$
$510$	−47.0812	−2.08479
$511$	14.7777	0.653728
$512$	45.6995	2.01965
$513$	5.84326	0.257986
$514$	−29.4354	−1.29834
$515$	45.7724	2.01697
$516$	27.5980	1.21493
$517$	5.30966	0.233519
$518$	21.5642	0.947479
$519$	−1.82708	−0.0802000
$520$	−47.0218	−2.06204
$521$	12.4981	0.547553	0.273777	−	0.961793i	$-0.411727\pi$
$521$	12.4981	0.547553	0.273777	+	0.961793i	$0.411727\pi$
$522$	−11.0750	−0.484738
$523$	−19.2841	−0.843234	−0.421617	−	0.906774i	$-0.638537\pi$
$523$	−19.2841	−0.843234	−0.421617	+	0.906774i	$0.638537\pi$
$524$	94.4169	4.12462
$525$	−2.43829	−0.106416
$526$	34.9194	1.52256
$527$	13.4951	0.587856
$528$	−7.12238	−0.309962
$529$	−16.7434	−0.727973
$530$	−80.1098	−3.47975
$531$	3.46609	0.150415
$532$	−24.3965	−1.05772
$533$	−4.61678	−0.199975
$534$	−30.1088	−1.30293
$535$	45.8537	1.98243
$536$	−67.7232	−2.92520
$537$	−8.97261	−0.387197
$538$	−24.4721	−1.05507
$539$	1.40162	0.0603720
$540$	11.3870	0.490017
$541$	12.5291	0.538666	0.269333	−	0.963047i	$-0.413197\pi$
$541$	12.5291	0.538666	0.269333	+	0.963047i	$0.413197\pi$
$542$	−1.41582	−0.0608145
$543$	−6.98935	−0.299942
$544$	−12.6234	−0.541225
$545$	−17.1520	−0.734712
$546$	−7.92638	−0.339218
$547$	−11.5194	−0.492535	−0.246268	−	0.969202i	$-0.579204\pi$
$547$	−11.5194	−0.492535	−0.246268	+	0.969202i	$0.579204\pi$
$548$	67.5599	2.88602
$549$	6.46777	0.276038
$550$	−8.49256	−0.362124
$551$	−26.0420	−1.10943
$552$	13.5202	0.575456
$553$	−15.0724	−0.640945
$554$	53.6935	2.28122
$555$	−23.6672	−1.00462
$556$	−40.0340	−1.69782
$557$	33.4939	1.41918	0.709590	−	0.704614i	$-0.248880\pi$
$557$	33.4939	1.41918	0.709590	+	0.704614i	$0.248880\pi$
$558$	−4.82739	−0.204360
$559$	21.0842	0.891766
$560$	−13.8590	−0.585649
$561$	−9.73684	−0.411090
$562$	−20.9449	−0.883509
$563$	−0.346927	−0.0146212	−0.00731061	−	0.999973i	$-0.502327\pi$
$563$	−0.346927	−0.0146212	−0.00731061	+	0.999973i	$0.502327\pi$
$564$	−15.8164	−0.665991
$565$	6.16074	0.259184
$566$	−3.59264	−0.151010
$567$	1.00000	0.0419961
$568$	8.57639	0.359857
$569$	8.23565	0.345256	0.172628	−	0.984987i	$-0.444774\pi$
$569$	8.23565	0.345256	0.172628	+	0.984987i	$0.444774\pi$
$570$	39.6018	1.65874
$571$	6.61633	0.276885	0.138442	−	0.990370i	$-0.455790\pi$
$571$	6.61633	0.276885	0.138442	+	0.990370i	$0.455790\pi$
$572$	−18.6661	−0.780467
$573$	−13.2132	−0.551989
$574$	−3.59676	−0.150126
$575$	6.09895	0.254344
$576$	−5.64750	−0.235313
$577$	−28.6456	−1.19253	−0.596267	−	0.802786i	$-0.703350\pi$
$577$	−28.6456	−1.19253	−0.596267	+	0.802786i	$0.703350\pi$
$578$	−77.6774	−3.23095
$579$	17.6744	0.734525
$580$	−50.7489	−2.10723
$581$	1.14155	0.0473594
$582$	2.05504	0.0851842
$583$	−16.5674	−0.686154
$584$	−79.8765	−3.30531
$585$	8.69937	0.359675
$586$	−14.5987	−0.603069
$587$	−8.60965	−0.355358	−0.177679	−	0.984088i	$-0.556859\pi$
$587$	−8.60965	−0.355358	−0.177679	+	0.984088i	$0.556859\pi$
$588$	−4.17514	−0.172180
$589$	−11.3513	−0.467720
$590$	23.4909	0.967104
$591$	21.1885	0.871577
$592$	−44.0967	−1.81236
$593$	4.68792	0.192510	0.0962550	−	0.995357i	$-0.469314\pi$
$593$	4.68792	0.192510	0.0962550	+	0.995357i	$0.469314\pi$
$594$	3.48300	0.142909
$595$	−18.9463	−0.776723
$596$	−7.11196	−0.291317
$597$	−18.4926	−0.756852
$598$	19.8264	0.810764
$599$	−35.0163	−1.43073	−0.715364	−	0.698752i	$-0.753739\pi$
$599$	−35.0163	−1.43073	−0.715364	+	0.698752i	$0.753739\pi$
$600$	13.1794	0.538048
$601$	19.0134	0.775573	0.387786	−	0.921749i	$-0.373240\pi$
$601$	19.0134	0.775573	0.387786	+	0.921749i	$0.373240\pi$
$602$	16.4259	0.669470
$603$	12.5293	0.510232
$604$	−33.0822	−1.34610
$605$	24.6426	1.00187
$606$	0.412568	0.0167594
$607$	−38.1699	−1.54927	−0.774633	−	0.632411i	$-0.782066\pi$
$607$	−38.1699	−1.54927	−0.774633	+	0.632411i	$0.782066\pi$
$608$	10.6181	0.430619
$609$	−4.45675	−0.180597
$610$	43.8344	1.77480
$611$	−12.0834	−0.488841
$612$	29.0041	1.17242
$613$	−19.2922	−0.779203	−0.389602	−	0.920983i	$-0.627387\pi$
$613$	−19.2922	−0.779203	−0.389602	+	0.920983i	$0.627387\pi$
$614$	67.8586	2.73855
$615$	3.94752	0.159180
$616$	−7.57603	−0.305247
$617$	−9.34099	−0.376054	−0.188027	−	0.982164i	$-0.560209\pi$
$617$	−9.34099	−0.376054	−0.188027	+	0.982164i	$0.560209\pi$
$618$	−41.7053	−1.67763
$619$	25.4708	1.02376	0.511879	−	0.859057i	$-0.328949\pi$
$619$	25.4708	1.02376	0.511879	+	0.859057i	$0.328949\pi$
$620$	−22.1206	−0.888384
$621$	−2.50132	−0.100375
$622$	−25.3877	−1.01796
$623$	−12.1163	−0.485429
$624$	16.2086	0.648864
$625$	−31.2462	−1.24985
$626$	35.4358	1.41630
$627$	8.19003	0.327078
$628$	−104.409	−4.16639
$629$	−60.2835	−2.40366
$630$	6.77735	0.270016
$631$	1.98960	0.0792049	0.0396025	−	0.999216i	$-0.487391\pi$
$631$	1.98960	0.0792049	0.0396025	+	0.999216i	$0.487391\pi$
$632$	81.4695	3.24068
$633$	−27.1795	−1.08029
$634$	−32.8884	−1.30616
$635$	−47.5330	−1.88629
$636$	49.3511	1.95690
$637$	−3.18971	−0.126381
$638$	−15.5229	−0.614557
$639$	−1.58669	−0.0627686
$640$	−48.1870	−1.90476
$641$	−39.6140	−1.56466	−0.782329	−	0.622865i	$-0.785968\pi$
$641$	−39.6140	−1.56466	−0.782329	+	0.622865i	$0.785968\pi$
$642$	−41.7793	−1.64890
$643$	−12.9592	−0.511060	−0.255530	−	0.966801i	$-0.582250\pi$
$643$	−12.9592	−0.511060	−0.255530	+	0.966801i	$0.582250\pi$
$644$	10.4434	0.411527
$645$	−18.0278	−0.709843
$646$	100.871	3.96872
$647$	18.4413	0.725001	0.362501	−	0.931984i	$-0.381923\pi$
$647$	18.4413	0.725001	0.362501	+	0.931984i	$0.381923\pi$
$648$	−5.40520	−0.212336
$649$	4.85813	0.190698
$650$	19.3268	0.758059
$651$	−1.94262	−0.0761374
$652$	104.742	4.10201
$653$	−12.9282	−0.505920	−0.252960	−	0.967477i	$-0.581404\pi$
$653$	−12.9282	−0.505920	−0.252960	+	0.967477i	$0.581404\pi$
$654$	15.6280	0.611102
$655$	−61.6758	−2.40987
$656$	7.35501	0.287165
$657$	14.7777	0.576534
$658$	−9.41370	−0.366984
$659$	−41.0669	−1.59974	−0.799870	−	0.600173i	$-0.795098\pi$
$659$	−41.0669	−1.59974	−0.799870	+	0.600173i	$0.795098\pi$
$660$	15.9602	0.621249
$661$	−24.7869	−0.964098	−0.482049	−	0.876144i	$-0.660107\pi$
$661$	−24.7869	−0.964098	−0.482049	+	0.876144i	$0.660107\pi$
$662$	−42.8629	−1.66591
$663$	22.1584	0.860562
$664$	−6.17029	−0.239454
$665$	15.9365	0.617989
$666$	21.5642	0.835598
$667$	11.1478	0.431644
$668$	−16.3353	−0.632031
$669$	23.3816	0.903987
$670$	84.9153	3.28056
$671$	9.06535	0.349964
$672$	1.81714	0.0700979
$673$	−6.27755	−0.241982	−0.120991	−	0.992654i	$-0.538607\pi$
$673$	−6.27755	−0.241982	−0.120991	+	0.992654i	$0.538607\pi$
$674$	−22.1322	−0.852502
$675$	−2.43829	−0.0938498
$676$	−11.7979	−0.453766
$677$	−13.1066	−0.503727	−0.251864	−	0.967763i	$-0.581043\pi$
$677$	−13.1066	−0.503727	−0.251864	+	0.967763i	$0.581043\pi$
$678$	−5.61332	−0.215578
$679$	0.826984	0.0317367
$680$	102.408	3.92719
$681$	22.2478	0.852537
$682$	−6.76615	−0.259089
$683$	−20.2371	−0.774351	−0.387176	−	0.922006i	$-0.626549\pi$
$683$	−20.2371	−0.774351	−0.387176	+	0.922006i	$0.626549\pi$
$684$	−24.3965	−0.932822
$685$	−44.1320	−1.68620
$686$	−2.48498	−0.0948771
$687$	−10.9636	−0.418288
$688$	−33.5893	−1.28058
$689$	37.7031	1.43637
$690$	−16.9524	−0.645365
$691$	27.6761	1.05285	0.526425	−	0.850222i	$-0.323532\pi$
$691$	27.6761	1.05285	0.526425	+	0.850222i	$0.323532\pi$
$692$	7.62833	0.289986
$693$	1.40162	0.0532431
$694$	48.8435	1.85407
$695$	26.1513	0.991977
$696$	24.0896	0.913115
$697$	10.0549	0.380855
$698$	−21.7108	−0.821767
$699$	0.191555	0.00724529
$700$	10.1802	0.384776
$701$	−25.8757	−0.977310	−0.488655	−	0.872477i	$-0.662512\pi$
$701$	−25.8757	−0.977310	−0.488655	+	0.872477i	$0.662512\pi$
$702$	−7.92638	−0.299162
$703$	50.7068	1.91244
$704$	−7.91564	−0.298332
$705$	10.3317	0.389116
$706$	5.85878	0.220498
$707$	0.166024	0.00624399
$708$	−14.4714	−0.543869
$709$	−44.9903	−1.68965	−0.844823	−	0.535046i	$-0.820294\pi$
$709$	−44.9903	−1.68965	−0.844823	+	0.535046i	$0.820294\pi$
$710$	−10.7536	−0.403575
$711$	−15.0724	−0.565261
$712$	65.4909	2.45438
$713$	4.85913	0.181976
$714$	17.2628	0.646044
$715$	12.1932	0.456000
$716$	37.4619	1.40002
$717$	−10.1041	−0.377344
$718$	78.5621	2.93191
$719$	34.1677	1.27424	0.637120	−	0.770765i	$-0.280126\pi$
$719$	34.1677	1.27424	0.637120	+	0.770765i	$0.280126\pi$
$720$	−13.8590	−0.516494
$721$	−16.7829	−0.625028
$722$	−37.6319	−1.40051
$723$	−20.5421	−0.763969
$724$	29.1816	1.08452
$725$	10.8669	0.403585
$726$	−22.4530	−0.833308
$727$	−50.0255	−1.85534	−0.927672	−	0.373396i	$-0.878193\pi$
$727$	−50.0255	−1.85534	−0.927672	+	0.373396i	$0.878193\pi$
$728$	17.2410	0.638994
$729$	1.00000	0.0370370
$730$	100.154	3.70686
$731$	−45.9191	−1.69838
$732$	−27.0039	−0.998092
$733$	−19.6984	−0.727579	−0.363789	−	0.931481i	$-0.618517\pi$
$733$	−19.6984	−0.727579	−0.363789	+	0.931481i	$0.618517\pi$
$734$	−38.3181	−1.41435
$735$	2.72732	0.100599
$736$	−4.54527	−0.167541
$737$	17.5613	0.646878
$738$	−3.59676	−0.132399
$739$	−3.90938	−0.143809	−0.0719044	−	0.997412i	$-0.522908\pi$
$739$	−3.90938	−0.143809	−0.0719044	+	0.997412i	$0.522908\pi$
$740$	98.8140	3.63248
$741$	−18.6383	−0.684695
$742$	29.3731	1.07832
$743$	54.4052	1.99593	0.997967	−	0.0637323i	$-0.0203004\pi$
$743$	54.4052	1.99593	0.997967	+	0.0637323i	$0.0203004\pi$
$744$	10.5003	0.384958
$745$	4.64573	0.170206
$746$	58.5718	2.14447
$747$	1.14155	0.0417671
$748$	40.6527	1.48641
$749$	−16.8127	−0.614323
$750$	17.3616	0.633957
$751$	−15.8567	−0.578620	−0.289310	−	0.957235i	$-0.593426\pi$
$751$	−15.8567	−0.578620	−0.289310	+	0.957235i	$0.593426\pi$
$752$	19.2500	0.701977
$753$	−24.5821	−0.895820
$754$	35.3259	1.28649
$755$	21.6103	0.786478
$756$	−4.17514	−0.151849
$757$	−30.0685	−1.09286	−0.546430	−	0.837505i	$-0.684014\pi$
$757$	−30.0685	−1.09286	−0.546430	+	0.837505i	$0.684014\pi$
$758$	80.7517	2.93303
$759$	−3.50590	−0.127256
$760$	−86.1397	−3.12462
$761$	−31.8541	−1.15471	−0.577355	−	0.816493i	$-0.695915\pi$
$761$	−31.8541	−1.15471	−0.577355	+	0.816493i	$0.695915\pi$
$762$	43.3094	1.56893
$763$	6.28896	0.227676
$764$	55.1670	1.99587
$765$	−18.9463	−0.685005
$766$	−2.48498	−0.0897861
$767$	−11.0558	−0.399202
$768$	32.6103	1.17672
$769$	8.53826	0.307898	0.153949	−	0.988079i	$-0.450801\pi$
$769$	8.53826	0.307898	0.153949	+	0.988079i	$0.450801\pi$
$770$	9.49926	0.342330
$771$	−11.8453	−0.426598
$772$	−73.7934	−2.65588
$773$	−9.95002	−0.357877	−0.178939	−	0.983860i	$-0.557266\pi$
$773$	−9.95002	−0.357877	−0.178939	+	0.983860i	$0.557266\pi$
$774$	16.4259	0.590417
$775$	4.73667	0.170146
$776$	−4.47001	−0.160464
$777$	8.67782	0.311315
$778$	53.6278	1.92265
$779$	−8.45753	−0.303023
$780$	−36.3211	−1.30050
$781$	−2.22394	−0.0795788
$782$	−43.1799	−1.54411
$783$	−4.45675	−0.159271
$784$	5.08154	0.181483
$785$	68.2032	2.43428
$786$	56.1955	2.00443
$787$	−2.67272	−0.0952723	−0.0476362	−	0.998865i	$-0.515169\pi$
$787$	−2.67272	−0.0952723	−0.0476362	+	0.998865i	$0.515169\pi$
$788$	−88.4648	−3.15143
$789$	14.0522	0.500270
$790$	−102.151	−3.63438
$791$	−2.25890	−0.0803171
$792$	−7.57603	−0.269202
$793$	−20.6303	−0.732604
$794$	−43.8333	−1.55559
$795$	−32.2376	−1.14335
$796$	77.2093	2.73661
$797$	−1.91060	−0.0676770	−0.0338385	−	0.999427i	$-0.510773\pi$
$797$	−1.91060	−0.0676770	−0.0338385	+	0.999427i	$0.510773\pi$
$798$	−14.5204	−0.514017
$799$	26.3163	0.931003
$800$	−4.43072	−0.156650
$801$	−12.1163	−0.428108
$802$	−60.7034	−2.14351
$803$	20.7127	0.730936
$804$	−52.3115	−1.84489
$805$	−6.82192	−0.240441
$806$	15.3980	0.542370
$807$	−9.84801	−0.346666
$808$	−0.897394	−0.0315702
$809$	−16.7063	−0.587361	−0.293680	−	0.955904i	$-0.594880\pi$
$809$	−16.7063	−0.587361	−0.293680	+	0.955904i	$0.594880\pi$
$810$	6.77735	0.238132
$811$	−11.6081	−0.407616	−0.203808	−	0.979011i	$-0.565332\pi$
$811$	−11.6081	−0.407616	−0.203808	+	0.979011i	$0.565332\pi$
$812$	18.6076	0.652998
$813$	−0.569749	−0.0199820
$814$	30.2249	1.05938
$815$	−68.4203	−2.39666
$816$	−35.3007	−1.23577
$817$	38.6243	1.35129
$818$	−89.0462	−3.11343
$819$	−3.18971	−0.111457
$820$	−16.4815	−0.575558
$821$	6.65213	0.232161	0.116081	−	0.993240i	$-0.462967\pi$
$821$	6.65213	0.232161	0.116081	+	0.993240i	$0.462967\pi$
$822$	40.2106	1.40251
$823$	−21.1202	−0.736203	−0.368102	−	0.929786i	$-0.619992\pi$
$823$	−21.1202	−0.736203	−0.368102	+	0.929786i	$0.619992\pi$
$824$	90.7149	3.16020
$825$	−3.41755	−0.118984
$826$	−8.61317	−0.299690
$827$	−55.8807	−1.94316	−0.971581	−	0.236708i	$-0.923931\pi$
$827$	−55.8807	−1.94316	−0.971581	+	0.236708i	$0.923931\pi$
$828$	10.4434	0.362933
$829$	−7.68326	−0.266851	−0.133425	−	0.991059i	$-0.542598\pi$
$829$	−7.68326	−0.266851	−0.133425	+	0.991059i	$0.542598\pi$
$830$	7.73667	0.268544
$831$	21.6072	0.749545
$832$	18.0139	0.624519
$833$	6.94685	0.240694
$834$	−23.8276	−0.825084
$835$	10.6707	0.369274
$836$	−34.1945	−1.18264
$837$	−1.94262	−0.0671469
$838$	13.5436	0.467855
$839$	8.91843	0.307898	0.153949	−	0.988079i	$-0.450801\pi$
$839$	8.91843	0.307898	0.153949	+	0.988079i	$0.450801\pi$
$840$	−14.7417	−0.508637
$841$	−9.13734	−0.315081
$842$	−1.19224	−0.0410874
$843$	−8.42860	−0.290296
$844$	113.478	3.90609
$845$	7.70674	0.265120
$846$	−9.41370	−0.323650
$847$	−9.03546	−0.310462
$848$	−60.0649	−2.06264
$849$	−1.44574	−0.0496176
$850$	−42.0917	−1.44373
$851$	−21.7061	−0.744074
$852$	6.62468	0.226958
$853$	−41.5861	−1.42388	−0.711941	−	0.702240i	$-0.752183\pi$
$853$	−41.5861	−1.42388	−0.711941	+	0.702240i	$0.752183\pi$
$854$	−16.0723	−0.549983
$855$	15.9365	0.545015
$856$	90.8759	3.10608
$857$	−51.4881	−1.75880	−0.879400	−	0.476084i	$-0.842056\pi$
$857$	−51.4881	−1.75880	−0.879400	+	0.476084i	$0.842056\pi$
$858$	−11.1098	−0.379281
$859$	−6.49512	−0.221610	−0.110805	−	0.993842i	$-0.535343\pi$
$859$	−6.49512	−0.221610	−0.110805	+	0.993842i	$0.535343\pi$
$860$	75.2686	2.56664
$861$	−1.44740	−0.0493272
$862$	−46.0429	−1.56823
$863$	28.7017	0.977019	0.488509	−	0.872559i	$-0.337541\pi$
$863$	28.7017	0.977019	0.488509	+	0.872559i	$0.337541\pi$
$864$	1.81714	0.0618205
$865$	−4.98304	−0.169429
$866$	−101.798	−3.45923
$867$	−31.2587	−1.06160
$868$	8.11073	0.275296
$869$	−21.1258	−0.716644
$870$	−30.2050	−1.02405
$871$	−39.9648	−1.35415
$872$	−33.9931	−1.15115
$873$	0.826984	0.0279892
$874$	36.3203	1.22855
$875$	6.98661	0.236191
$876$	−61.6991	−2.08462
$877$	−12.1004	−0.408602	−0.204301	−	0.978908i	$-0.565492\pi$
$877$	−12.1004	−0.408602	−0.204301	+	0.978908i	$0.565492\pi$
$878$	60.6071	2.04539
$879$	−5.87479	−0.198152
$880$	−19.4250	−0.654817
$881$	12.5166	0.421696	0.210848	−	0.977519i	$-0.432377\pi$
$881$	12.5166	0.421696	0.210848	+	0.977519i	$0.432377\pi$
$882$	−2.48498	−0.0836738
$883$	−20.2675	−0.682057	−0.341028	−	0.940053i	$-0.610775\pi$
$883$	−20.2675	−0.682057	−0.341028	+	0.940053i	$0.610775\pi$
$884$	−92.5146	−3.11160
$885$	9.45313	0.317764
$886$	−25.1537	−0.845053
$887$	−46.5819	−1.56407	−0.782034	−	0.623236i	$-0.785818\pi$
$887$	−46.5819	−1.56407	−0.782034	+	0.623236i	$0.785818\pi$
$888$	−46.9053	−1.57404
$889$	17.4284	0.584531
$890$	−82.1164	−2.75255
$891$	1.40162	0.0469560
$892$	−97.6217	−3.26862
$893$	−22.1356	−0.740741
$894$	−4.23293	−0.141570
$895$	−24.4712	−0.817982
$896$	17.6682	0.590254
$897$	7.97850	0.266394
$898$	100.467	3.35263
$899$	8.65779	0.288754
$900$	10.1802	0.339340
$901$	−82.1133	−2.73559
$902$	−5.04129	−0.167857
$903$	6.61007	0.219969
$904$	12.2098	0.406091
$905$	−19.0622	−0.633650
$906$	−19.6900	−0.654158
$907$	−34.2330	−1.13669	−0.568344	−	0.822791i	$-0.692416\pi$
$907$	−34.2330	−1.13669	−0.568344	+	0.822791i	$0.692416\pi$
$908$	−92.8877	−3.08259
$909$	0.166024	0.00550668
$910$	−21.6178	−0.716623
$911$	−9.39980	−0.311429	−0.155715	−	0.987802i	$-0.549768\pi$
$911$	−9.39980	−0.311429	−0.155715	+	0.987802i	$0.549768\pi$
$912$	29.6928	0.983225
$913$	1.60002	0.0529528
$914$	−70.7675	−2.34078
$915$	17.6397	0.583151
$916$	45.7747	1.51244
$917$	22.6140	0.746781
$918$	17.2628	0.569758
$919$	−8.88847	−0.293204	−0.146602	−	0.989196i	$-0.546834\pi$
$919$	−8.88847	−0.293204	−0.146602	+	0.989196i	$0.546834\pi$
$920$	36.8738	1.21569
$921$	27.3075	0.899811
$922$	−88.7188	−2.92180
$923$	5.06109	0.166588
$924$	−5.85196	−0.192515
$925$	−21.1590	−0.695705
$926$	−98.6145	−3.24067
$927$	−16.7829	−0.551223
$928$	−8.09857	−0.265849
$929$	−43.7292	−1.43471	−0.717354	−	0.696709i	$-0.754647\pi$
$929$	−43.7292	−1.43471	−0.717354	+	0.696709i	$0.754647\pi$
$930$	−13.1658	−0.431725
$931$	−5.84326	−0.191505
$932$	−0.799772	−0.0261974
$933$	−10.2165	−0.334472
$934$	−78.8238	−2.57919
$935$	−26.5555	−0.868457
$936$	17.2410	0.563540
$937$	−29.9092	−0.977090	−0.488545	−	0.872539i	$-0.662472\pi$
$937$	−29.9092	−0.977090	−0.488545	+	0.872539i	$0.662472\pi$
$938$	−31.1350	−1.01660
$939$	14.2600	0.465356
$940$	−43.1365	−1.40696
$941$	1.51328	0.0493315	0.0246658	−	0.999696i	$-0.492148\pi$
$941$	1.51328	0.0493315	0.0246658	+	0.999696i	$0.492148\pi$
$942$	−62.1429	−2.02473
$943$	3.62042	0.117897
$944$	17.6130	0.573256
$945$	2.72732	0.0887198
$946$	23.0229	0.748538
$947$	−47.7643	−1.55213	−0.776066	−	0.630652i	$-0.782788\pi$
$947$	−47.7643	−1.55213	−0.776066	+	0.630652i	$0.782788\pi$
$948$	62.9296	2.04386
$949$	−47.1366	−1.53012
$950$	35.4050	1.14869
$951$	−13.2348	−0.429169
$952$	−37.5491	−1.21697
$953$	18.9255	0.613058	0.306529	−	0.951861i	$-0.400832\pi$
$953$	18.9255	0.613058	0.306529	+	0.951861i	$0.400832\pi$
$954$	29.3731	0.950988
$955$	−36.0366	−1.16612
$956$	42.1860	1.36439
$957$	−6.24667	−0.201926
$958$	27.9698	0.903664
$959$	16.1815	0.522526
$960$	−15.4026	−0.497115
$961$	−27.2262	−0.878265
$962$	−68.7837	−2.21767
$963$	−16.8127	−0.541782
$964$	85.7662	2.76234
$965$	48.2039	1.55174
$966$	6.21575	0.199989
$967$	51.8225	1.66650	0.833249	−	0.552898i	$-0.186478\pi$
$967$	51.8225	1.66650	0.833249	+	0.552898i	$0.186478\pi$
$968$	48.8385	1.56973
$969$	40.5923	1.30401
$970$	5.60476	0.179958
$971$	0.748009	0.0240048	0.0120024	−	0.999928i	$-0.496179\pi$
$971$	0.748009	0.0240048	0.0120024	+	0.999928i	$0.496179\pi$
$972$	−4.17514	−0.133918
$973$	−9.58865	−0.307398
$974$	55.0183	1.76290
$975$	7.77743	0.249077
$976$	32.8662	1.05202
$977$	7.16249	0.229148	0.114574	−	0.993415i	$-0.463450\pi$
$977$	7.16249	0.229148	0.114574	+	0.993415i	$0.463450\pi$
$978$	62.3408	1.99344
$979$	−16.9824	−0.542761
$980$	−11.3870	−0.363743
$981$	6.28896	0.200791
$982$	−3.11826	−0.0995078
$983$	29.6992	0.947258	0.473629	−	0.880724i	$-0.342944\pi$
$983$	29.6992	0.947258	0.473629	+	0.880724i	$0.342944\pi$
$984$	7.82348	0.249403
$985$	57.7878	1.84127
$986$	−76.9361	−2.45014
$987$	−3.78823	−0.120581
$988$	77.8176	2.47571
$989$	−16.5339	−0.525748
$990$	9.49926	0.301906
$991$	19.6966	0.625685	0.312842	−	0.949805i	$-0.398719\pi$
$991$	19.6966	0.625685	0.312842	+	0.949805i	$0.398719\pi$
$992$	−3.53003	−0.112078
$993$	−17.2488	−0.547373
$994$	3.94291	0.125061
$995$	−50.4353	−1.59891
$996$	−4.76613	−0.151021
$997$	3.12934	0.0991071	0.0495536	−	0.998771i	$-0.484220\pi$
$997$	3.12934	0.0991071	0.0495536	+	0.998771i	$0.484220\pi$
$998$	59.9850	1.89879
$999$	8.67782	0.274554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.o.1.3	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.o.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.48498 q^{2} -1.00000 q^{3} +4.17514 q^{4} -2.72732 q^{5} +2.48498 q^{6} +1.00000 q^{7} -5.40520 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.48498 q^{2} -1.00000 q^{3} +4.17514 q^{4} -2.72732 q^{5} +2.48498 q^{6} +1.00000 q^{7} -5.40520 q^{8} +1.00000 q^{9} +6.77735 q^{10} +1.40162 q^{11} -4.17514 q^{12} -3.18971 q^{13} -2.48498 q^{14} +2.72732 q^{15} +5.08154 q^{16} +6.94685 q^{17} -2.48498 q^{18} -5.84326 q^{19} -11.3870 q^{20} -1.00000 q^{21} -3.48300 q^{22} +2.50132 q^{23} +5.40520 q^{24} +2.43829 q^{25} +7.92638 q^{26} -1.00000 q^{27} +4.17514 q^{28} +4.45675 q^{29} -6.77735 q^{30} +1.94262 q^{31} -1.81714 q^{32} -1.40162 q^{33} -17.2628 q^{34} -2.72732 q^{35} +4.17514 q^{36} -8.67782 q^{37} +14.5204 q^{38} +3.18971 q^{39} +14.7417 q^{40} +1.44740 q^{41} +2.48498 q^{42} -6.61007 q^{43} +5.85196 q^{44} -2.72732 q^{45} -6.21575 q^{46} +3.78823 q^{47} -5.08154 q^{48} +1.00000 q^{49} -6.05911 q^{50} -6.94685 q^{51} -13.3175 q^{52} -11.8202 q^{53} +2.48498 q^{54} -3.82267 q^{55} -5.40520 q^{56} +5.84326 q^{57} -11.0750 q^{58} +3.46609 q^{59} +11.3870 q^{60} +6.46777 q^{61} -4.82739 q^{62} +1.00000 q^{63} -5.64750 q^{64} +8.69937 q^{65} +3.48300 q^{66} +12.5293 q^{67} +29.0041 q^{68} -2.50132 q^{69} +6.77735 q^{70} -1.58669 q^{71} -5.40520 q^{72} +14.7777 q^{73} +21.5642 q^{74} -2.43829 q^{75} -24.3965 q^{76} +1.40162 q^{77} -7.92638 q^{78} -15.0724 q^{79} -13.8590 q^{80} +1.00000 q^{81} -3.59676 q^{82} +1.14155 q^{83} -4.17514 q^{84} -18.9463 q^{85} +16.4259 q^{86} -4.45675 q^{87} -7.57603 q^{88} -12.1163 q^{89} +6.77735 q^{90} -3.18971 q^{91} +10.4434 q^{92} -1.94262 q^{93} -9.41370 q^{94} +15.9365 q^{95} +1.81714 q^{96} +0.826984 q^{97} -2.48498 q^{98} +1.40162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) \) 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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