LMFDB - Embedded newform 6041.2.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$112$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13001 q^{2} -1.53283 q^{3} +2.53693 q^{4} -2.08639 q^{5} +3.26494 q^{6} -1.00000 q^{7} -1.14367 q^{8} -0.650428 q^{9} +O(q^{10})$	\(q-2.13001 q^{2} -1.53283 q^{3} +2.53693 q^{4} -2.08639 q^{5} +3.26494 q^{6} -1.00000 q^{7} -1.14367 q^{8} -0.650428 q^{9} +4.44403 q^{10} +1.41016 q^{11} -3.88869 q^{12} -4.77576 q^{13} +2.13001 q^{14} +3.19808 q^{15} -2.63783 q^{16} -2.30889 q^{17} +1.38542 q^{18} +6.63482 q^{19} -5.29303 q^{20} +1.53283 q^{21} -3.00366 q^{22} +2.15374 q^{23} +1.75306 q^{24} -0.646976 q^{25} +10.1724 q^{26} +5.59549 q^{27} -2.53693 q^{28} +9.28318 q^{29} -6.81194 q^{30} -3.04435 q^{31} +7.90595 q^{32} -2.16154 q^{33} +4.91795 q^{34} +2.08639 q^{35} -1.65009 q^{36} -0.863051 q^{37} -14.1322 q^{38} +7.32043 q^{39} +2.38615 q^{40} +0.296486 q^{41} -3.26494 q^{42} -11.1548 q^{43} +3.57749 q^{44} +1.35705 q^{45} -4.58749 q^{46} -6.20334 q^{47} +4.04335 q^{48} +1.00000 q^{49} +1.37806 q^{50} +3.53913 q^{51} -12.1158 q^{52} -9.79840 q^{53} -11.9184 q^{54} -2.94215 q^{55} +1.14367 q^{56} -10.1701 q^{57} -19.7732 q^{58} +4.53175 q^{59} +8.11333 q^{60} -12.5828 q^{61} +6.48450 q^{62} +0.650428 q^{63} -11.5641 q^{64} +9.96409 q^{65} +4.60410 q^{66} +11.3899 q^{67} -5.85749 q^{68} -3.30132 q^{69} -4.44403 q^{70} -14.0468 q^{71} +0.743877 q^{72} +10.3995 q^{73} +1.83831 q^{74} +0.991706 q^{75} +16.8321 q^{76} -1.41016 q^{77} -15.5926 q^{78} +2.48465 q^{79} +5.50355 q^{80} -6.62566 q^{81} -0.631518 q^{82} -6.17987 q^{83} +3.88869 q^{84} +4.81724 q^{85} +23.7597 q^{86} -14.2296 q^{87} -1.61277 q^{88} +13.7180 q^{89} -2.89052 q^{90} +4.77576 q^{91} +5.46390 q^{92} +4.66648 q^{93} +13.2132 q^{94} -13.8428 q^{95} -12.1185 q^{96} +16.8442 q^{97} -2.13001 q^{98} -0.917209 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) $ 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * 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 $

$2$	−2.13001	−1.50614	−0.753072	−	0.657939i	$-0.771429\pi$
$2$	−2.13001	−1.50614	−0.753072	+	0.657939i	$0.771429\pi$
$3$	−1.53283	−0.884981	−0.442490	−	0.896773i	$-0.645905\pi$
$3$	−1.53283	−0.884981	−0.442490	+	0.896773i	$0.645905\pi$
$4$	2.53693	1.26847
$5$	−2.08639	−0.933062	−0.466531	−	0.884505i	$-0.654496\pi$
$5$	−2.08639	−0.933062	−0.466531	+	0.884505i	$0.654496\pi$
$6$	3.26494	1.33291
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.14367	−0.404350
$9$	−0.650428	−0.216809
$10$	4.44403	1.40532
$11$	1.41016	0.425180	0.212590	−	0.977141i	$-0.431810\pi$
$11$	1.41016	0.425180	0.212590	+	0.977141i	$0.431810\pi$
$12$	−3.88869	−1.12257
$13$	−4.77576	−1.32456	−0.662278	−	0.749258i	$-0.730410\pi$
$13$	−4.77576	−1.32456	−0.662278	+	0.749258i	$0.730410\pi$
$14$	2.13001	0.569269
$15$	3.19808	0.825742
$16$	−2.63783	−0.659458
$17$	−2.30889	−0.559987	−0.279994	−	0.960002i	$-0.590332\pi$
$17$	−2.30889	−0.559987	−0.279994	+	0.960002i	$0.590332\pi$
$18$	1.38542	0.326546
$19$	6.63482	1.52213	0.761066	−	0.648675i	$-0.224676\pi$
$19$	6.63482	1.52213	0.761066	+	0.648675i	$0.224676\pi$
$20$	−5.29303	−1.18356
$21$	1.53283	0.334491
$22$	−3.00366	−0.640382
$23$	2.15374	0.449086	0.224543	−	0.974464i	$-0.427911\pi$
$23$	2.15374	0.449086	0.224543	+	0.974464i	$0.427911\pi$
$24$	1.75306	0.357842
$25$	−0.646976	−0.129395
$26$	10.1724	1.99497
$27$	5.59549	1.07685
$28$	−2.53693	−0.479435
$29$	9.28318	1.72384	0.861922	−	0.507041i	$-0.169261\pi$
$29$	9.28318	1.72384	0.861922	+	0.507041i	$0.169261\pi$
$30$	−6.81194	−1.24369
$31$	−3.04435	−0.546782	−0.273391	−	0.961903i	$-0.588145\pi$
$31$	−3.04435	−0.546782	−0.273391	+	0.961903i	$0.588145\pi$
$32$	7.90595	1.39759
$33$	−2.16154	−0.376276
$34$	4.91795	0.843421
$35$	2.08639	0.352664
$36$	−1.65009	−0.275015
$37$	−0.863051	−0.141885	−0.0709424	−	0.997480i	$-0.522601\pi$
$37$	−0.863051	−0.141885	−0.0709424	+	0.997480i	$0.522601\pi$
$38$	−14.1322	−2.29255
$39$	7.32043	1.17221
$40$	2.38615	0.377283
$41$	0.296486	0.0463034	0.0231517	−	0.999732i	$-0.492630\pi$
$41$	0.296486	0.0463034	0.0231517	+	0.999732i	$0.492630\pi$
$42$	−3.26494	−0.503792
$43$	−11.1548	−1.70109	−0.850543	−	0.525905i	$-0.823727\pi$
$43$	−11.1548	−1.70109	−0.850543	+	0.525905i	$0.823727\pi$
$44$	3.57749	0.539327
$45$	1.35705	0.202297
$46$	−4.58749	−0.676388
$47$	−6.20334	−0.904851	−0.452425	−	0.891802i	$-0.649441\pi$
$47$	−6.20334	−0.904851	−0.452425	+	0.891802i	$0.649441\pi$
$48$	4.04335	0.583608
$49$	1.00000	0.142857
$50$	1.37806	0.194888
$51$	3.53913	0.495578
$52$	−12.1158	−1.68016
$53$	−9.79840	−1.34591	−0.672957	−	0.739681i	$-0.734976\pi$
$53$	−9.79840	−1.34591	−0.672957	+	0.739681i	$0.734976\pi$
$54$	−11.9184	−1.62189
$55$	−2.94215	−0.396719
$56$	1.14367	0.152830
$57$	−10.1701	−1.34706
$58$	−19.7732	−2.59635
$59$	4.53175	0.589983	0.294992	−	0.955500i	$-0.404683\pi$
$59$	4.53175	0.589983	0.294992	+	0.955500i	$0.404683\pi$
$60$	8.11333	1.04743
$61$	−12.5828	−1.61107	−0.805533	−	0.592551i	$-0.798121\pi$
$61$	−12.5828	−1.61107	−0.805533	+	0.592551i	$0.798121\pi$
$62$	6.48450	0.823532
$63$	0.650428	0.0819462
$64$	−11.5641	−1.44551
$65$	9.96409	1.23589
$66$	4.60410	0.566726
$67$	11.3899	1.39150	0.695751	−	0.718283i	$-0.255072\pi$
$67$	11.3899	1.39150	0.695751	+	0.718283i	$0.255072\pi$
$68$	−5.85749	−0.710325
$69$	−3.30132	−0.397433
$70$	−4.44403	−0.531163
$71$	−14.0468	−1.66705	−0.833526	−	0.552481i	$-0.813681\pi$
$71$	−14.0468	−1.66705	−0.833526	+	0.552481i	$0.813681\pi$
$72$	0.743877	0.0876668
$73$	10.3995	1.21717	0.608583	−	0.793490i	$-0.291738\pi$
$73$	10.3995	1.21717	0.608583	+	0.793490i	$0.291738\pi$
$74$	1.83831	0.213699
$75$	0.991706	0.114512
$76$	16.8321	1.93077
$77$	−1.41016	−0.160703
$78$	−15.5926	−1.76551
$79$	2.48465	0.279545	0.139773	−	0.990184i	$-0.455363\pi$
$79$	2.48465	0.279545	0.139773	+	0.990184i	$0.455363\pi$
$80$	5.50355	0.615316
$81$	−6.62566	−0.736184
$82$	−0.631518	−0.0697395
$83$	−6.17987	−0.678329	−0.339165	−	0.940727i	$-0.610144\pi$
$83$	−6.17987	−0.678329	−0.339165	+	0.940727i	$0.610144\pi$
$84$	3.88869	0.424291
$85$	4.81724	0.522503
$86$	23.7597	2.56208
$87$	−14.2296	−1.52557
$88$	−1.61277	−0.171921
$89$	13.7180	1.45411	0.727054	−	0.686581i	$-0.240889\pi$
$89$	13.7180	1.45411	0.727054	+	0.686581i	$0.240889\pi$
$90$	−2.89052	−0.304688
$91$	4.77576	0.500635
$92$	5.46390	0.569651
$93$	4.66648	0.483891
$94$	13.2132	1.36283
$95$	−13.8428	−1.42024
$96$	−12.1185	−1.23684
$97$	16.8442	1.71027	0.855133	−	0.518408i	$-0.173475\pi$
$97$	16.8442	1.71027	0.855133	+	0.518408i	$0.173475\pi$
$98$	−2.13001	−0.215163
$99$	−0.917209	−0.0921830
$100$	−1.64134	−0.164134
$101$	3.50952	0.349210	0.174605	−	0.984639i	$-0.444135\pi$
$101$	3.50952	0.349210	0.174605	+	0.984639i	$0.444135\pi$
$102$	−7.53838	−0.746411
$103$	−0.576305	−0.0567850	−0.0283925	−	0.999597i	$-0.509039\pi$
$103$	−0.576305	−0.0567850	−0.0283925	+	0.999597i	$0.509039\pi$
$104$	5.46191	0.535584
$105$	−3.19808	−0.312101
$106$	20.8707	2.02714
$107$	−14.2493	−1.37753	−0.688767	−	0.724983i	$-0.741847\pi$
$107$	−14.2493	−1.37753	−0.688767	+	0.724983i	$0.741847\pi$
$108$	14.1954	1.36595
$109$	14.3419	1.37370	0.686851	−	0.726798i	$-0.258993\pi$
$109$	14.3419	1.37370	0.686851	+	0.726798i	$0.258993\pi$
$110$	6.26680	0.597516
$111$	1.32291	0.125565
$112$	2.63783	0.249252
$113$	−17.9577	−1.68932	−0.844661	−	0.535301i	$-0.820198\pi$
$113$	−17.9577	−1.68932	−0.844661	+	0.535301i	$0.820198\pi$
$114$	21.6623	2.02886
$115$	−4.49355	−0.419025
$116$	23.5508	2.18664
$117$	3.10629	0.287176
$118$	−9.65266	−0.888599
$119$	2.30889	0.211655
$120$	−3.65757	−0.333889
$121$	−9.01144	−0.819222
$122$	26.8015	2.42650
$123$	−0.454464	−0.0409776
$124$	−7.72332	−0.693575
$125$	11.7818	1.05380
$126$	−1.38542	−0.123423
$127$	−18.1111	−1.60710	−0.803551	−	0.595236i	$-0.797058\pi$
$127$	−18.1111	−1.60710	−0.803551	+	0.595236i	$0.797058\pi$
$128$	8.81967	0.779556
$129$	17.0984	1.50543
$130$	−21.2236	−1.86143
$131$	−15.4970	−1.35398	−0.676988	−	0.735994i	$-0.736715\pi$
$131$	−15.4970	−1.35398	−0.676988	+	0.735994i	$0.736715\pi$
$132$	−5.48369	−0.477294
$133$	−6.63482	−0.575312
$134$	−24.2606	−2.09580
$135$	−11.6744	−1.00477
$136$	2.64061	0.226431
$137$	−21.2897	−1.81891	−0.909453	−	0.415807i	$-0.863499\pi$
$137$	−21.2897	−1.81891	−0.909453	+	0.415807i	$0.863499\pi$
$138$	7.03185	0.598591
$139$	−5.06995	−0.430027	−0.215014	−	0.976611i	$-0.568980\pi$
$139$	−5.06995	−0.430027	−0.215014	+	0.976611i	$0.568980\pi$
$140$	5.29303	0.447343
$141$	9.50868	0.800775
$142$	29.9198	2.51082
$143$	−6.73459	−0.563175
$144$	1.71572	0.142977
$145$	−19.3683	−1.60845
$146$	−22.1509	−1.83323
$147$	−1.53283	−0.126426
$148$	−2.18950	−0.179976
$149$	−4.72620	−0.387186	−0.193593	−	0.981082i	$-0.562014\pi$
$149$	−4.72620	−0.387186	−0.193593	+	0.981082i	$0.562014\pi$
$150$	−2.11234	−0.172472
$151$	10.1244	0.823912	0.411956	−	0.911204i	$-0.364846\pi$
$151$	10.1244	0.823912	0.411956	+	0.911204i	$0.364846\pi$
$152$	−7.58807	−0.615473
$153$	1.50176	0.121410
$154$	3.00366	0.242042
$155$	6.35171	0.510181
$156$	18.5714	1.48691
$157$	17.3784	1.38695	0.693474	−	0.720482i	$-0.256079\pi$
$157$	17.3784	1.38695	0.693474	+	0.720482i	$0.256079\pi$
$158$	−5.29233	−0.421036
$159$	15.0193	1.19111
$160$	−16.4949	−1.30404
$161$	−2.15374	−0.169739
$162$	14.1127	1.10880
$163$	−15.8208	−1.23918	−0.619590	−	0.784925i	$-0.712701\pi$
$163$	−15.8208	−1.23918	−0.619590	+	0.784925i	$0.712701\pi$
$164$	0.752166	0.0587343
$165$	4.50982	0.351089
$166$	13.1632	1.02166
$167$	−7.24737	−0.560818	−0.280409	−	0.959881i	$-0.590470\pi$
$167$	−7.24737	−0.560818	−0.280409	+	0.959881i	$0.590470\pi$
$168$	−1.75306	−0.135251
$169$	9.80785	0.754450
$170$	−10.2608	−0.786964
$171$	−4.31547	−0.330012
$172$	−28.2989	−2.15777
$173$	−18.2106	−1.38453	−0.692265	−	0.721644i	$-0.743387\pi$
$173$	−18.2106	−1.38453	−0.692265	+	0.721644i	$0.743387\pi$
$174$	30.3091	2.29772
$175$	0.646976	0.0489068
$176$	−3.71977	−0.280389
$177$	−6.94640	−0.522124
$178$	−29.2195	−2.19009
$179$	2.97339	0.222241	0.111121	−	0.993807i	$-0.464556\pi$
$179$	2.97339	0.222241	0.111121	+	0.993807i	$0.464556\pi$
$180$	3.44274	0.256606
$181$	9.94286	0.739047	0.369523	−	0.929221i	$-0.379521\pi$
$181$	9.94286	0.739047	0.369523	+	0.929221i	$0.379521\pi$
$182$	−10.1724	−0.754028
$183$	19.2874	1.42576
$184$	−2.46318	−0.181588
$185$	1.80066	0.132387
$186$	−9.93964	−0.728810
$187$	−3.25591	−0.238095
$188$	−15.7375	−1.14777
$189$	−5.59549	−0.407012
$190$	29.4853	2.13909
$191$	−26.8434	−1.94232	−0.971160	−	0.238428i	$-0.923368\pi$
$191$	−26.8434	−1.94232	−0.971160	+	0.238428i	$0.923368\pi$
$192$	17.7258	1.27925
$193$	6.33188	0.455778	0.227889	−	0.973687i	$-0.426818\pi$
$193$	6.33188	0.455778	0.227889	+	0.973687i	$0.426818\pi$
$194$	−35.8782	−2.57591
$195$	−15.2733	−1.09374
$196$	2.53693	0.181210
$197$	−13.0850	−0.932270	−0.466135	−	0.884714i	$-0.654354\pi$
$197$	−13.0850	−0.932270	−0.466135	+	0.884714i	$0.654354\pi$
$198$	1.95366	0.138841
$199$	−3.44492	−0.244204	−0.122102	−	0.992518i	$-0.538964\pi$
$199$	−3.44492	−0.244204	−0.122102	+	0.992518i	$0.538964\pi$
$200$	0.739930	0.0523210
$201$	−17.4588	−1.23145
$202$	−7.47530	−0.525960
$203$	−9.28318	−0.651552
$204$	8.97855	0.628624
$205$	−0.618586	−0.0432039
$206$	1.22753	0.0855263
$207$	−1.40085	−0.0973661
$208$	12.5977	0.873490
$209$	9.35617	0.647180
$210$	6.81194	0.470069
$211$	7.02459	0.483593	0.241796	−	0.970327i	$-0.422263\pi$
$211$	7.02459	0.483593	0.241796	+	0.970327i	$0.422263\pi$
$212$	−24.8579	−1.70725
$213$	21.5314	1.47531
$214$	30.3512	2.07476
$215$	23.2732	1.58722
$216$	−6.39942	−0.435425
$217$	3.04435	0.206664
$218$	−30.5483	−2.06899
$219$	−15.9406	−1.07717
$220$	−7.46404	−0.503225
$221$	11.0267	0.741735
$222$	−2.81781	−0.189119
$223$	25.2146	1.68849	0.844247	−	0.535955i	$-0.180048\pi$
$223$	25.2146	1.68849	0.844247	+	0.535955i	$0.180048\pi$
$224$	−7.90595	−0.528239
$225$	0.420812	0.0280541
$226$	38.2501	2.54436
$227$	2.78416	0.184791	0.0923955	−	0.995722i	$-0.470548\pi$
$227$	2.78416	0.184791	0.0923955	+	0.995722i	$0.470548\pi$
$228$	−25.8008	−1.70870
$229$	−2.40283	−0.158784	−0.0793919	−	0.996843i	$-0.525298\pi$
$229$	−2.40283	−0.158784	−0.0793919	+	0.996843i	$0.525298\pi$
$230$	9.57129	0.631112
$231$	2.16154	0.142219
$232$	−10.6169	−0.697036
$233$	−14.4423	−0.946149	−0.473074	−	0.881023i	$-0.656856\pi$
$233$	−14.4423	−0.946149	−0.473074	+	0.881023i	$0.656856\pi$
$234$	−6.61641	−0.432528
$235$	12.9426	0.844282
$236$	11.4967	0.748374
$237$	−3.80856	−0.247392
$238$	−4.91795	−0.318783
$239$	−8.82127	−0.570601	−0.285300	−	0.958438i	$-0.592093\pi$
$239$	−8.82127	−0.570601	−0.285300	+	0.958438i	$0.592093\pi$
$240$	−8.43601	−0.544542
$241$	−18.0698	−1.16398	−0.581988	−	0.813197i	$-0.697725\pi$
$241$	−18.0698	−1.16398	−0.581988	+	0.813197i	$0.697725\pi$
$242$	19.1944	1.23387
$243$	−6.63045	−0.425344
$244$	−31.9218	−2.04358
$245$	−2.08639	−0.133295
$246$	0.968011	0.0617181
$247$	−31.6863	−2.01615
$248$	3.48175	0.221091
$249$	9.47271	0.600308
$250$	−25.0953	−1.58717
$251$	−16.8136	−1.06126	−0.530631	−	0.847603i	$-0.678045\pi$
$251$	−16.8136	−1.06126	−0.530631	+	0.847603i	$0.678045\pi$
$252$	1.65009	0.103946
$253$	3.03713	0.190943
$254$	38.5768	2.42052
$255$	−7.38401	−0.462405
$256$	4.34219	0.271387
$257$	8.76472	0.546728	0.273364	−	0.961911i	$-0.411864\pi$
$257$	8.76472	0.546728	0.273364	+	0.961911i	$0.411864\pi$
$258$	−36.4197	−2.26739
$259$	0.863051	0.0536274
$260$	25.2782	1.56769
$261$	−6.03804	−0.373745
$262$	33.0086	2.03928
$263$	4.37312	0.269658	0.134829	−	0.990869i	$-0.456951\pi$
$263$	4.37312	0.269658	0.134829	+	0.990869i	$0.456951\pi$
$264$	2.47210	0.152147
$265$	20.4433	1.25582
$266$	14.1322	0.866502
$267$	−21.0274	−1.28686
$268$	28.8955	1.76507
$269$	−10.3424	−0.630587	−0.315293	−	0.948994i	$-0.602103\pi$
$269$	−10.3424	−0.630587	−0.315293	+	0.948994i	$0.602103\pi$
$270$	24.8665	1.51333
$271$	−6.55370	−0.398109	−0.199055	−	0.979988i	$-0.563787\pi$
$271$	−6.55370	−0.398109	−0.199055	+	0.979988i	$0.563787\pi$
$272$	6.09046	0.369288
$273$	−7.32043	−0.443053
$274$	45.3473	2.73953
$275$	−0.912342	−0.0550163
$276$	−8.37524	−0.504130
$277$	28.2185	1.69548	0.847741	−	0.530410i	$-0.177962\pi$
$277$	28.2185	1.69548	0.847741	+	0.530410i	$0.177962\pi$
$278$	10.7990	0.647683
$279$	1.98013	0.118547
$280$	−2.38615	−0.142600
$281$	−8.86322	−0.528735	−0.264368	−	0.964422i	$-0.585163\pi$
$281$	−8.86322	−0.528735	−0.264368	+	0.964422i	$0.585163\pi$
$282$	−20.2536	−1.20608
$283$	3.52529	0.209557	0.104778	−	0.994496i	$-0.466587\pi$
$283$	3.52529	0.209557	0.104778	+	0.994496i	$0.466587\pi$
$284$	−35.6359	−2.11460
$285$	21.2187	1.25689
$286$	14.3447	0.848222
$287$	−0.296486	−0.0175010
$288$	−5.14225	−0.303010
$289$	−11.6690	−0.686414
$290$	41.2547	2.42256
$291$	−25.8193	−1.51355
$292$	26.3828	1.54393
$293$	28.7717	1.68086	0.840430	−	0.541920i	$-0.182303\pi$
$293$	28.7717	1.68086	0.840430	+	0.541920i	$0.182303\pi$
$294$	3.26494	0.190415
$295$	−9.45499	−0.550491
$296$	0.987049	0.0573711
$297$	7.89055	0.457856
$298$	10.0668	0.583157
$299$	−10.2857	−0.594840
$300$	2.51589	0.145255
$301$	11.1548	0.642950
$302$	−21.5651	−1.24093
$303$	−5.37950	−0.309044
$304$	−17.5015	−1.00378
$305$	26.2527	1.50322
$306$	−3.19877	−0.182862
$307$	3.71877	0.212241	0.106121	−	0.994353i	$-0.466157\pi$
$307$	3.71877	0.212241	0.106121	+	0.994353i	$0.466157\pi$
$308$	−3.57749	−0.203846
$309$	0.883378	0.0502536
$310$	−13.5292	−0.768406
$311$	27.7620	1.57424	0.787120	−	0.616799i	$-0.211571\pi$
$311$	27.7620	1.57424	0.787120	+	0.616799i	$0.211571\pi$
$312$	−8.37218	−0.473982
$313$	−14.9231	−0.843501	−0.421751	−	0.906712i	$-0.638584\pi$
$313$	−14.9231	−0.843501	−0.421751	+	0.906712i	$0.638584\pi$
$314$	−37.0161	−2.08894
$315$	−1.35705	−0.0764609
$316$	6.30341	0.354594
$317$	−4.45666	−0.250311	−0.125155	−	0.992137i	$-0.539943\pi$
$317$	−4.45666	−0.250311	−0.125155	+	0.992137i	$0.539943\pi$
$318$	−31.9912	−1.79398
$319$	13.0908	0.732944
$320$	24.1272	1.34875
$321$	21.8418	1.21909
$322$	4.58749	0.255651
$323$	−15.3190	−0.852374
$324$	−16.8089	−0.933826
$325$	3.08980	0.171391
$326$	33.6984	1.86638
$327$	−21.9837	−1.21570
$328$	−0.339084	−0.0187228
$329$	6.20334	0.342001
$330$	−9.60595	−0.528790
$331$	−20.1976	−1.11016	−0.555079	−	0.831797i	$-0.687312\pi$
$331$	−20.1976	−1.11016	−0.555079	+	0.831797i	$0.687312\pi$
$332$	−15.6779	−0.860438
$333$	0.561353	0.0307619
$334$	15.4370	0.844672
$335$	−23.7638	−1.29836
$336$	−4.04335	−0.220583
$337$	−13.6798	−0.745186	−0.372593	−	0.927995i	$-0.621531\pi$
$337$	−13.6798	−0.745186	−0.372593	+	0.927995i	$0.621531\pi$
$338$	−20.8908	−1.13631
$339$	27.5262	1.49502
$340$	12.2210	0.662778
$341$	−4.29303	−0.232481
$342$	9.19199	0.497046
$343$	−1.00000	−0.0539949
$344$	12.7574	0.687834
$345$	6.88785	0.370829
$346$	38.7888	2.08530
$347$	−10.7453	−0.576840	−0.288420	−	0.957504i	$-0.593130\pi$
$347$	−10.7453	−0.576840	−0.288420	+	0.957504i	$0.593130\pi$
$348$	−36.0994	−1.93513
$349$	−18.5182	−0.991258	−0.495629	−	0.868534i	$-0.665062\pi$
$349$	−18.5182	−0.991258	−0.495629	+	0.868534i	$0.665062\pi$
$350$	−1.37806	−0.0736607
$351$	−26.7227	−1.42635
$352$	11.1487	0.594227
$353$	−24.6195	−1.31037	−0.655183	−	0.755470i	$-0.727408\pi$
$353$	−24.6195	−1.31037	−0.655183	+	0.755470i	$0.727408\pi$
$354$	14.7959	0.786393
$355$	29.3071	1.55546
$356$	34.8017	1.84449
$357$	−3.53913	−0.187311
$358$	−6.33334	−0.334727
$359$	31.4233	1.65846	0.829230	−	0.558908i	$-0.188779\pi$
$359$	31.4233	1.65846	0.829230	+	0.558908i	$0.188779\pi$
$360$	−1.55202	−0.0817986
$361$	25.0208	1.31688
$362$	−21.1784	−1.11311
$363$	13.8130	0.724996
$364$	12.1158	0.635039
$365$	−21.6973	−1.13569
$366$	−41.0822	−2.14740
$367$	−20.7542	−1.08336	−0.541679	−	0.840585i	$-0.682211\pi$
$367$	−20.7542	−1.08336	−0.541679	+	0.840585i	$0.682211\pi$
$368$	−5.68121	−0.296154
$369$	−0.192843	−0.0100390
$370$	−3.83542	−0.199394
$371$	9.79840	0.508708
$372$	11.8385	0.613800
$373$	26.7759	1.38640	0.693202	−	0.720744i	$-0.256199\pi$
$373$	26.7759	1.38640	0.693202	+	0.720744i	$0.256199\pi$
$374$	6.93511	0.358606
$375$	−18.0595	−0.932589
$376$	7.09460	0.365876
$377$	−44.3342	−2.28333
$378$	11.9184	0.613018
$379$	2.84692	0.146237	0.0731183	−	0.997323i	$-0.476705\pi$
$379$	2.84692	0.146237	0.0731183	+	0.997323i	$0.476705\pi$
$380$	−35.1183	−1.80153
$381$	27.7613	1.42225
$382$	57.1767	2.92541
$383$	36.2997	1.85483	0.927415	−	0.374035i	$-0.122026\pi$
$383$	36.2997	1.85483	0.927415	+	0.374035i	$0.122026\pi$
$384$	−13.5191	−0.689892
$385$	2.94215	0.149946
$386$	−13.4869	−0.686467
$387$	7.25537	0.368811
$388$	42.7326	2.16942
$389$	3.74553	0.189906	0.0949529	−	0.995482i	$-0.469730\pi$
$389$	3.74553	0.189906	0.0949529	+	0.995482i	$0.469730\pi$
$390$	32.5322	1.64733
$391$	−4.97275	−0.251483
$392$	−1.14367	−0.0577643
$393$	23.7542	1.19824
$394$	27.8712	1.40413
$395$	−5.18396	−0.260833
$396$	−2.32690	−0.116931
$397$	11.5495	0.579654	0.289827	−	0.957079i	$-0.406402\pi$
$397$	11.5495	0.579654	0.289827	+	0.957079i	$0.406402\pi$
$398$	7.33771	0.367806
$399$	10.1701	0.509140
$400$	1.70662	0.0853308
$401$	6.27118	0.313168	0.156584	−	0.987665i	$-0.449952\pi$
$401$	6.27118	0.313168	0.156584	+	0.987665i	$0.449952\pi$
$402$	37.1875	1.85474
$403$	14.5391	0.724243
$404$	8.90342	0.442962
$405$	13.8237	0.686906
$406$	19.7732	0.981330
$407$	−1.21704	−0.0603266
$408$	−4.04762	−0.200387
$409$	−5.25312	−0.259750	−0.129875	−	0.991530i	$-0.541458\pi$
$409$	−5.25312	−0.259750	−0.129875	+	0.991530i	$0.541458\pi$
$410$	1.31759	0.0650713
$411$	32.6336	1.60970
$412$	−1.46205	−0.0720299
$413$	−4.53175	−0.222993
$414$	2.98383	0.146647
$415$	12.8936	0.632923
$416$	−37.7569	−1.85118
$417$	7.77138	0.380566
$418$	−19.9287	−0.974745
$419$	10.6553	0.520545	0.260273	−	0.965535i	$-0.416188\pi$
$419$	10.6553	0.520545	0.260273	+	0.965535i	$0.416188\pi$
$420$	−8.11333	−0.395890
$421$	15.1961	0.740612	0.370306	−	0.928910i	$-0.379253\pi$
$421$	15.1961	0.740612	0.370306	+	0.928910i	$0.379253\pi$
$422$	−14.9624	−0.728360
$423$	4.03483	0.196180
$424$	11.2062	0.544220
$425$	1.49380	0.0724597
$426$	−45.8621	−2.22202
$427$	12.5828	0.608926
$428$	−36.1496	−1.74736
$429$	10.3230	0.498399
$430$	−49.5721	−2.39058
$431$	36.0627	1.73708	0.868540	−	0.495619i	$-0.165059\pi$
$431$	36.0627	1.73708	0.868540	+	0.495619i	$0.165059\pi$
$432$	−14.7600	−0.710140
$433$	−3.88275	−0.186593	−0.0932965	−	0.995638i	$-0.529740\pi$
$433$	−3.88275	−0.186593	−0.0932965	+	0.995638i	$0.529740\pi$
$434$	−6.48450	−0.311266
$435$	29.6884	1.42345
$436$	36.3844	1.74250
$437$	14.2897	0.683568
$438$	33.9537	1.62237
$439$	22.8555	1.09083	0.545416	−	0.838166i	$-0.316372\pi$
$439$	22.8555	1.09083	0.545416	+	0.838166i	$0.316372\pi$
$440$	3.36486	0.160413
$441$	−0.650428	−0.0309728
$442$	−23.4869	−1.11716
$443$	−30.3456	−1.44176	−0.720882	−	0.693058i	$-0.756263\pi$
$443$	−30.3456	−1.44176	−0.720882	+	0.693058i	$0.756263\pi$
$444$	3.35614	0.159275
$445$	−28.6211	−1.35677
$446$	−53.7073	−2.54311
$447$	7.24447	0.342652
$448$	11.5641	0.546351
$449$	−30.7950	−1.45331	−0.726653	−	0.687005i	$-0.758925\pi$
$449$	−30.7950	−1.45331	−0.726653	+	0.687005i	$0.758925\pi$
$450$	−0.896332	−0.0422535
$451$	0.418094	0.0196873
$452$	−45.5576	−2.14285
$453$	−15.5190	−0.729146
$454$	−5.93028	−0.278322
$455$	−9.96409	−0.467124
$456$	11.6312	0.544682
$457$	−16.9875	−0.794644	−0.397322	−	0.917679i	$-0.630060\pi$
$457$	−16.9875	−0.794644	−0.397322	+	0.917679i	$0.630060\pi$
$458$	5.11806	0.239151
$459$	−12.9194	−0.603024
$460$	−11.3998	−0.531520
$461$	22.2546	1.03650	0.518250	−	0.855229i	$-0.326584\pi$
$461$	22.2546	1.03650	0.518250	+	0.855229i	$0.326584\pi$
$462$	−4.60410	−0.214202
$463$	19.1573	0.890314	0.445157	−	0.895453i	$-0.353148\pi$
$463$	19.1573	0.890314	0.445157	+	0.895453i	$0.353148\pi$
$464$	−24.4875	−1.13680
$465$	−9.73610	−0.451501
$466$	30.7623	1.42504
$467$	28.0868	1.29970	0.649852	−	0.760061i	$-0.274831\pi$
$467$	28.0868	1.29970	0.649852	+	0.760061i	$0.274831\pi$
$468$	7.88044	0.364274
$469$	−11.3899	−0.525938
$470$	−27.5678	−1.27161
$471$	−26.6382	−1.22742
$472$	−5.18284	−0.238560
$473$	−15.7300	−0.723268
$474$	8.11226	0.372608
$475$	−4.29257	−0.196957
$476$	5.85749	0.268478
$477$	6.37316	0.291807
$478$	18.7894	0.859406
$479$	27.9130	1.27538	0.637688	−	0.770295i	$-0.279891\pi$
$479$	27.9130	1.27538	0.637688	+	0.770295i	$0.279891\pi$
$480$	25.2839	1.15405
$481$	4.12172	0.187934
$482$	38.4888	1.75311
$483$	3.30132	0.150215
$484$	−22.8614	−1.03916
$485$	−35.1435	−1.59579
$486$	14.1229	0.640629
$487$	14.9310	0.676588	0.338294	−	0.941040i	$-0.390150\pi$
$487$	14.9310	0.676588	0.338294	+	0.941040i	$0.390150\pi$
$488$	14.3907	0.651434
$489$	24.2506	1.09665
$490$	4.44403	0.200761
$491$	7.00170	0.315982	0.157991	−	0.987441i	$-0.449498\pi$
$491$	7.00170	0.315982	0.157991	+	0.987441i	$0.449498\pi$
$492$	−1.15294	−0.0519787
$493$	−21.4338	−0.965330
$494$	67.4920	3.03661
$495$	1.91366	0.0860125
$496$	8.03050	0.360580
$497$	14.0468	0.630086
$498$	−20.1769	−0.904150
$499$	−9.73341	−0.435727	−0.217864	−	0.975979i	$-0.569909\pi$
$499$	−9.73341	−0.435727	−0.217864	+	0.975979i	$0.569909\pi$
$500$	29.8896	1.33671
$501$	11.1090	0.496313
$502$	35.8130	1.59841
$503$	4.61873	0.205939	0.102969	−	0.994685i	$-0.467166\pi$
$503$	4.61873	0.205939	0.102969	+	0.994685i	$0.467166\pi$
$504$	−0.743877	−0.0331349
$505$	−7.32222	−0.325835
$506$	−6.46911	−0.287587
$507$	−15.0338	−0.667673
$508$	−45.9467	−2.03855
$509$	−27.4000	−1.21448	−0.607242	−	0.794517i	$-0.707724\pi$
$509$	−27.4000	−1.21448	−0.607242	+	0.794517i	$0.707724\pi$
$510$	15.7280	0.696448
$511$	−10.3995	−0.460045
$512$	−26.8882	−1.18830
$513$	37.1251	1.63911
$514$	−18.6689	−0.823450
$515$	1.20240	0.0529839
$516$	43.3775	1.90959
$517$	−8.74772	−0.384724
$518$	−1.83831	−0.0807705
$519$	27.9138	1.22528
$520$	−11.3957	−0.499733
$521$	16.3855	0.717863	0.358931	−	0.933364i	$-0.383141\pi$
$521$	16.3855	0.717863	0.358931	+	0.933364i	$0.383141\pi$
$522$	12.8611	0.562914
$523$	2.10906	0.0922226	0.0461113	−	0.998936i	$-0.485317\pi$
$523$	2.10906	0.0922226	0.0461113	+	0.998936i	$0.485317\pi$
$524$	−39.3147	−1.71747
$525$	−0.991706	−0.0432816
$526$	−9.31478	−0.406144
$527$	7.02907	0.306191
$528$	5.70179	0.248138
$529$	−18.3614	−0.798321
$530$	−43.5444	−1.89145
$531$	−2.94757	−0.127914
$532$	−16.8321	−0.729764
$533$	−1.41595	−0.0613314
$534$	44.7886	1.93819
$535$	29.7296	1.28532
$536$	−13.0264	−0.562653
$537$	−4.55770	−0.196679
$538$	22.0294	0.949754
$539$	1.41016	0.0607400
$540$	−29.6171	−1.27452
$541$	27.7104	1.19136	0.595681	−	0.803221i	$-0.296882\pi$
$541$	27.7104	1.19136	0.595681	+	0.803221i	$0.296882\pi$
$542$	13.9594	0.599609
$543$	−15.2407	−0.654042
$544$	−18.2540	−0.782632
$545$	−29.9227	−1.28175
$546$	15.5926	0.667300
$547$	13.0907	0.559716	0.279858	−	0.960041i	$-0.409713\pi$
$547$	13.0907	0.559716	0.279858	+	0.960041i	$0.409713\pi$
$548$	−54.0107	−2.30722
$549$	8.18422	0.349294
$550$	1.94330	0.0828624
$551$	61.5922	2.62392
$552$	3.77564	0.160702
$553$	−2.48465	−0.105658
$554$	−60.1055	−2.55364
$555$	−2.76011	−0.117160
$556$	−12.8621	−0.545476
$557$	22.8499	0.968182	0.484091	−	0.875018i	$-0.339150\pi$
$557$	22.8499	0.968182	0.484091	+	0.875018i	$0.339150\pi$
$558$	−4.21770	−0.178549
$559$	53.2725	2.25318
$560$	−5.50355	−0.232567
$561$	4.99075	0.210710
$562$	18.8787	0.796351
$563$	−2.74127	−0.115531	−0.0577655	−	0.998330i	$-0.518398\pi$
$563$	−2.74127	−0.115531	−0.0577655	+	0.998330i	$0.518398\pi$
$564$	24.1229	1.01576
$565$	37.4669	1.57624
$566$	−7.50890	−0.315623
$567$	6.62566	0.278252
$568$	16.0650	0.674072
$569$	33.3356	1.39750	0.698750	−	0.715366i	$-0.253740\pi$
$569$	33.3356	1.39750	0.698750	+	0.715366i	$0.253740\pi$
$570$	−45.1960	−1.89305
$571$	−14.6027	−0.611105	−0.305552	−	0.952175i	$-0.598841\pi$
$571$	−14.6027	−0.611105	−0.305552	+	0.952175i	$0.598841\pi$
$572$	−17.0852	−0.714369
$573$	41.1464	1.71892
$574$	0.631518	0.0263591
$575$	−1.39342	−0.0581097
$576$	7.52160	0.313400
$577$	−39.6207	−1.64943	−0.824716	−	0.565548i	$-0.808665\pi$
$577$	−39.6207	−1.64943	−0.824716	+	0.565548i	$0.808665\pi$
$578$	24.8552	1.03384
$579$	−9.70570	−0.403355
$580$	−49.1362	−2.04027
$581$	6.17987	0.256384
$582$	54.9953	2.27963
$583$	−13.8173	−0.572256
$584$	−11.8936	−0.492161
$585$	−6.48092	−0.267953
$586$	−61.2839	−2.53162
$587$	0.561126	0.0231602	0.0115801	−	0.999933i	$-0.496314\pi$
$587$	0.561126	0.0231602	0.0115801	+	0.999933i	$0.496314\pi$
$588$	−3.88869	−0.160367
$589$	−20.1987	−0.832274
$590$	20.1392	0.829118
$591$	20.0572	0.825041
$592$	2.27659	0.0935671
$593$	−19.7611	−0.811492	−0.405746	−	0.913986i	$-0.632988\pi$
$593$	−19.7611	−0.811492	−0.405746	+	0.913986i	$0.632988\pi$
$594$	−16.8069	−0.689597
$595$	−4.81724	−0.197488
$596$	−11.9901	−0.491132
$597$	5.28048	0.216116
$598$	21.9087	0.895914
$599$	22.0015	0.898958	0.449479	−	0.893291i	$-0.351610\pi$
$599$	22.0015	0.898958	0.449479	+	0.893291i	$0.351610\pi$
$600$	−1.13419	−0.0463030
$601$	27.9552	1.14032	0.570158	−	0.821535i	$-0.306882\pi$
$601$	27.9552	1.14032	0.570158	+	0.821535i	$0.306882\pi$
$602$	−23.7597	−0.968375
$603$	−7.40833	−0.301690
$604$	25.6849	1.04511
$605$	18.8014	0.764385
$606$	11.4584	0.465465
$607$	16.9110	0.686395	0.343197	−	0.939263i	$-0.388490\pi$
$607$	16.9110	0.686395	0.343197	+	0.939263i	$0.388490\pi$
$608$	52.4546	2.12731
$609$	14.2296	0.576611
$610$	−55.9184	−2.26407
$611$	29.6257	1.19853
$612$	3.80988	0.154005
$613$	17.7038	0.715049	0.357524	−	0.933904i	$-0.383621\pi$
$613$	17.7038	0.715049	0.357524	+	0.933904i	$0.383621\pi$
$614$	−7.92100	−0.319666
$615$	0.948188	0.0382346
$616$	1.61277	0.0649802
$617$	13.7782	0.554690	0.277345	−	0.960770i	$-0.410546\pi$
$617$	13.7782	0.554690	0.277345	+	0.960770i	$0.410546\pi$
$618$	−1.88160	−0.0756891
$619$	2.97226	0.119465	0.0597327	−	0.998214i	$-0.480975\pi$
$619$	2.97226	0.119465	0.0597327	+	0.998214i	$0.480975\pi$
$620$	16.1139	0.647148
$621$	12.0512	0.483600
$622$	−59.1334	−2.37103
$623$	−13.7180	−0.549601
$624$	−19.3101	−0.773022
$625$	−21.3465	−0.853862
$626$	31.7862	1.27043
$627$	−14.3414	−0.572742
$628$	44.0878	1.75930
$629$	1.99269	0.0794537
$630$	2.89052	0.115161
$631$	0.488973	0.0194657	0.00973285	−	0.999953i	$-0.496902\pi$
$631$	0.488973	0.0194657	0.00973285	+	0.999953i	$0.496902\pi$
$632$	−2.84163	−0.113034
$633$	−10.7675	−0.427970
$634$	9.49272	0.377004
$635$	37.7868	1.49953
$636$	38.1030	1.51088
$637$	−4.77576	−0.189222
$638$	−27.8835	−1.10392
$639$	9.13645	0.361432
$640$	−18.4013	−0.727374
$641$	13.0987	0.517369	0.258684	−	0.965962i	$-0.416711\pi$
$641$	13.0987	0.517369	0.258684	+	0.965962i	$0.416711\pi$
$642$	−46.5232	−1.83612
$643$	−23.8179	−0.939286	−0.469643	−	0.882857i	$-0.655617\pi$
$643$	−23.8179	−0.939286	−0.469643	+	0.882857i	$0.655617\pi$
$644$	−5.46390	−0.215308
$645$	−35.6739	−1.40466
$646$	32.6297	1.28380
$647$	−40.6398	−1.59772	−0.798858	−	0.601520i	$-0.794562\pi$
$647$	−40.6398	−1.59772	−0.798858	+	0.601520i	$0.794562\pi$
$648$	7.57759	0.297676
$649$	6.39050	0.250849
$650$	−6.58130	−0.258140
$651$	−4.66648	−0.182894
$652$	−40.1363	−1.57186
$653$	47.1622	1.84560	0.922799	−	0.385282i	$-0.125896\pi$
$653$	47.1622	1.84560	0.922799	+	0.385282i	$0.125896\pi$
$654$	46.8254	1.83102
$655$	32.3327	1.26334
$656$	−0.782082	−0.0305352
$657$	−6.76410	−0.263893
$658$	−13.2132	−0.515103
$659$	−18.6762	−0.727522	−0.363761	−	0.931492i	$-0.618507\pi$
$659$	−18.6762	−0.727522	−0.363761	+	0.931492i	$0.618507\pi$
$660$	11.4411	0.445345
$661$	43.6140	1.69639	0.848195	−	0.529684i	$-0.177690\pi$
$661$	43.6140	1.69639	0.848195	+	0.529684i	$0.177690\pi$
$662$	43.0210	1.67206
$663$	−16.9020	−0.656421
$664$	7.06776	0.274282
$665$	13.8428	0.536801
$666$	−1.19569	−0.0463319
$667$	19.9936	0.774155
$668$	−18.3861	−0.711379
$669$	−38.6497	−1.49428
$670$	50.6172	1.95551
$671$	−17.7438	−0.684993
$672$	12.1185	0.467481
$673$	−27.3584	−1.05459	−0.527295	−	0.849682i	$-0.676794\pi$
$673$	−27.3584	−1.05459	−0.527295	+	0.849682i	$0.676794\pi$
$674$	29.1381	1.12236
$675$	−3.62015	−0.139340
$676$	24.8819	0.956995
$677$	−26.8461	−1.03178	−0.515891	−	0.856654i	$-0.672539\pi$
$677$	−26.8461	−1.03178	−0.515891	+	0.856654i	$0.672539\pi$
$678$	−58.6310	−2.25171
$679$	−16.8442	−0.646420
$680$	−5.50935	−0.211274
$681$	−4.26765	−0.163537
$682$	9.14419	0.350149
$683$	36.1937	1.38491	0.692456	−	0.721460i	$-0.256528\pi$
$683$	36.1937	1.38491	0.692456	+	0.721460i	$0.256528\pi$
$684$	−10.9481	−0.418610
$685$	44.4187	1.69715
$686$	2.13001	0.0813241
$687$	3.68314	0.140521
$688$	29.4244	1.12180
$689$	46.7948	1.78274
$690$	−14.6712	−0.558522
$691$	5.54351	0.210885	0.105443	−	0.994425i	$-0.466374\pi$
$691$	5.54351	0.210885	0.105443	+	0.994425i	$0.466374\pi$
$692$	−46.1992	−1.75623
$693$	0.917209	0.0348419
$694$	22.8877	0.868804
$695$	10.5779	0.401242
$696$	16.2740	0.616863
$697$	−0.684553	−0.0259293
$698$	39.4440	1.49298
$699$	22.1377	0.837323
$700$	1.64134	0.0620367
$701$	−19.7469	−0.745831	−0.372916	−	0.927865i	$-0.621642\pi$
$701$	−19.7469	−0.745831	−0.372916	+	0.927865i	$0.621642\pi$
$702$	56.9196	2.14829
$703$	−5.72619	−0.215967
$704$	−16.3072	−0.614602
$705$	−19.8388	−0.747173
$706$	52.4398	1.97360
$707$	−3.50952	−0.131989
$708$	−17.6226	−0.662297
$709$	−14.9249	−0.560516	−0.280258	−	0.959925i	$-0.590420\pi$
$709$	−14.9249	−0.560516	−0.280258	+	0.959925i	$0.590420\pi$
$710$	−62.4245	−2.34275
$711$	−1.61609	−0.0606081
$712$	−15.6889	−0.587968
$713$	−6.55675	−0.245552
$714$	7.53838	0.282117
$715$	14.0510	0.525477
$716$	7.54329	0.281906
$717$	13.5215	0.504971
$718$	−66.9319	−2.49788
$719$	−27.6046	−1.02948	−0.514739	−	0.857347i	$-0.672111\pi$
$719$	−27.6046	−1.02948	−0.514739	+	0.857347i	$0.672111\pi$
$720$	−3.57966	−0.133406
$721$	0.576305	0.0214627
$722$	−53.2945	−1.98342
$723$	27.6979	1.03010
$724$	25.2244	0.937457
$725$	−6.00600	−0.223057
$726$	−29.4218	−1.09195
$727$	−37.2788	−1.38259	−0.691296	−	0.722571i	$-0.742960\pi$
$727$	−37.2788	−1.38259	−0.691296	+	0.722571i	$0.742960\pi$
$728$	−5.46191	−0.202432
$729$	30.0403	1.11261
$730$	46.2155	1.71051
$731$	25.7551	0.952587
$732$	48.9307	1.80853
$733$	31.1568	1.15080	0.575401	−	0.817871i	$-0.304846\pi$
$733$	31.1568	1.15080	0.575401	+	0.817871i	$0.304846\pi$
$734$	44.2065	1.63169
$735$	3.19808	0.117963
$736$	17.0274	0.627638
$737$	16.0617	0.591639
$738$	0.410757	0.0151202
$739$	−26.1124	−0.960559	−0.480280	−	0.877115i	$-0.659465\pi$
$739$	−26.1124	−0.960559	−0.480280	+	0.877115i	$0.659465\pi$
$740$	4.56816	0.167929
$741$	48.5697	1.78425
$742$	−20.8707	−0.766187
$743$	−0.809471	−0.0296966	−0.0148483	−	0.999890i	$-0.504727\pi$
$743$	−0.809471	−0.0296966	−0.0148483	+	0.999890i	$0.504727\pi$
$744$	−5.33693	−0.195661
$745$	9.86070	0.361268
$746$	−57.0329	−2.08812
$747$	4.01956	0.147068
$748$	−8.26002	−0.302016
$749$	14.2493	0.520659
$750$	38.4669	1.40461
$751$	42.6719	1.55712	0.778560	−	0.627571i	$-0.215951\pi$
$751$	42.6719	1.55712	0.778560	+	0.627571i	$0.215951\pi$
$752$	16.3634	0.596711
$753$	25.7723	0.939197
$754$	94.4322	3.43902
$755$	−21.1235	−0.768761
$756$	−14.1954	−0.516281
$757$	−32.2243	−1.17121	−0.585607	−	0.810595i	$-0.699144\pi$
$757$	−32.2243	−1.17121	−0.585607	+	0.810595i	$0.699144\pi$
$758$	−6.06397	−0.220253
$759$	−4.65540	−0.168980
$760$	15.8317	0.574275
$761$	39.8788	1.44560	0.722802	−	0.691055i	$-0.242854\pi$
$761$	39.8788	1.44560	0.722802	+	0.691055i	$0.242854\pi$
$762$	−59.1317	−2.14212
$763$	−14.3419	−0.519210
$764$	−68.0999	−2.46377
$765$	−3.13327	−0.113283
$766$	−77.3187	−2.79364
$767$	−21.6425	−0.781466
$768$	−6.65584	−0.240172
$769$	40.4297	1.45793	0.728966	−	0.684550i	$-0.240001\pi$
$769$	40.4297	1.45793	0.728966	+	0.684550i	$0.240001\pi$
$770$	−6.26680	−0.225840
$771$	−13.4348	−0.483844
$772$	16.0636	0.578140
$773$	22.5846	0.812312	0.406156	−	0.913804i	$-0.366869\pi$
$773$	22.5846	0.812312	0.406156	+	0.913804i	$0.366869\pi$
$774$	−15.4540	−0.555483
$775$	1.96962	0.0707510
$776$	−19.2642	−0.691546
$777$	−1.32291	−0.0474592
$778$	−7.97800	−0.286025
$779$	1.96713	0.0704798
$780$	−38.7473	−1.38738
$781$	−19.8083	−0.708797
$782$	10.5920	0.378769
$783$	51.9440	1.85633
$784$	−2.63783	−0.0942083
$785$	−36.2581	−1.29411
$786$	−50.5967	−1.80472
$787$	37.0274	1.31988	0.659941	−	0.751317i	$-0.270581\pi$
$787$	37.0274	1.31988	0.659941	+	0.751317i	$0.270581\pi$
$788$	−33.1959	−1.18255
$789$	−6.70325	−0.238642
$790$	11.0419	0.392852
$791$	17.9577	0.638504
$792$	1.04899	0.0372742
$793$	60.0925	2.13395
$794$	−24.6006	−0.873042
$795$	−31.3361	−1.11138
$796$	−8.73954	−0.309765
$797$	−4.71149	−0.166889	−0.0834447	−	0.996512i	$-0.526592\pi$
$797$	−4.71149	−0.166889	−0.0834447	+	0.996512i	$0.526592\pi$
$798$	−21.6623	−0.766837
$799$	14.3228	0.506705
$800$	−5.11497	−0.180841
$801$	−8.92258	−0.315264
$802$	−13.3577	−0.471675
$803$	14.6649	0.517515
$804$	−44.2919	−1.56206
$805$	4.49355	0.158377
$806$	−30.9684	−1.09081
$807$	15.8531	0.558057
$808$	−4.01374	−0.141203
$809$	−17.4120	−0.612174	−0.306087	−	0.952004i	$-0.599020\pi$
$809$	−17.4120	−0.612174	−0.306087	+	0.952004i	$0.599020\pi$
$810$	−29.4446	−1.03458
$811$	−34.1718	−1.19994	−0.599968	−	0.800024i	$-0.704820\pi$
$811$	−34.1718	−1.19994	−0.599968	+	0.800024i	$0.704820\pi$
$812$	−23.5508	−0.826472
$813$	10.0457	0.352319
$814$	2.59231	0.0908605
$815$	33.0084	1.15623
$816$	−9.33565	−0.326813
$817$	−74.0098	−2.58928
$818$	11.1892	0.391221
$819$	−3.10629	−0.108542
$820$	−1.56931	−0.0548028
$821$	−8.35169	−0.291476	−0.145738	−	0.989323i	$-0.546556\pi$
$821$	−8.35169	−0.291476	−0.145738	+	0.989323i	$0.546556\pi$
$822$	−69.5098	−2.42443
$823$	−15.0376	−0.524179	−0.262089	−	0.965044i	$-0.584412\pi$
$823$	−15.0376	−0.524179	−0.262089	+	0.965044i	$0.584412\pi$
$824$	0.659105	0.0229610
$825$	1.39847	0.0486884
$826$	9.65266	0.335859
$827$	43.7326	1.52073	0.760365	−	0.649496i	$-0.225020\pi$
$827$	43.7326	1.52073	0.760365	+	0.649496i	$0.225020\pi$
$828$	−3.55387	−0.123506
$829$	29.1543	1.01257	0.506286	−	0.862366i	$-0.331018\pi$
$829$	29.1543	1.01257	0.506286	+	0.862366i	$0.331018\pi$
$830$	−27.4635	−0.953273
$831$	−43.2541	−1.50047
$832$	55.2272	1.91466
$833$	−2.30889	−0.0799982
$834$	−16.5531	−0.573187
$835$	15.1208	0.523278
$836$	23.7360	0.820926
$837$	−17.0346	−0.588803
$838$	−22.6959	−0.784016
$839$	−9.41882	−0.325174	−0.162587	−	0.986694i	$-0.551984\pi$
$839$	−9.41882	−0.325174	−0.162587	+	0.986694i	$0.551984\pi$
$840$	3.65757	0.126198
$841$	57.1774	1.97164
$842$	−32.3678	−1.11547
$843$	13.5858	0.467920
$844$	17.8209	0.613422
$845$	−20.4630	−0.703948
$846$	−8.59422	−0.295475
$847$	9.01144	0.309637
$848$	25.8466	0.887575
$849$	−5.40368	−0.185454
$850$	−3.18180	−0.109135
$851$	−1.85879	−0.0637185
$852$	54.6238	1.87138
$853$	43.9387	1.50443	0.752216	−	0.658916i	$-0.228985\pi$
$853$	43.9387	1.50443	0.752216	+	0.658916i	$0.228985\pi$
$854$	−26.8015	−0.917129
$855$	9.00375	0.307922
$856$	16.2966	0.557005
$857$	−32.5100	−1.11052	−0.555260	−	0.831677i	$-0.687381\pi$
$857$	−32.5100	−1.11052	−0.555260	+	0.831677i	$0.687381\pi$
$858$	−21.9881	−0.750660
$859$	−28.4357	−0.970215	−0.485107	−	0.874455i	$-0.661219\pi$
$859$	−28.4357	−0.970215	−0.485107	+	0.874455i	$0.661219\pi$
$860$	59.0426	2.01333
$861$	0.454464	0.0154881
$862$	−76.8139	−2.61629
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	44.2377	1.50500
$865$	37.9945	1.29185
$866$	8.27028	0.281036
$867$	17.8867	0.607463
$868$	7.72332	0.262147
$869$	3.50377	0.118857
$870$	−63.2365	−2.14392
$871$	−54.3955	−1.84312
$872$	−16.4024	−0.555456
$873$	−10.9559	−0.370802
$874$	−30.4371	−1.02955
$875$	−11.7818	−0.398297
$876$	−40.4403	−1.36635
$877$	−31.4004	−1.06032	−0.530158	−	0.847899i	$-0.677867\pi$
$877$	−31.4004	−1.06032	−0.530158	+	0.847899i	$0.677867\pi$
$878$	−48.6823	−1.64295
$879$	−44.1021	−1.48753
$880$	7.76090	0.261620
$881$	−4.59566	−0.154832	−0.0774158	−	0.996999i	$-0.524667\pi$
$881$	−4.59566	−0.154832	−0.0774158	+	0.996999i	$0.524667\pi$
$882$	1.38542	0.0466494
$883$	11.7807	0.396451	0.198225	−	0.980156i	$-0.436482\pi$
$883$	11.7807	0.396451	0.198225	+	0.980156i	$0.436482\pi$
$884$	27.9740	0.940866
$885$	14.4929	0.487174
$886$	64.6364	2.17150
$887$	4.49907	0.151064	0.0755320	−	0.997143i	$-0.475935\pi$
$887$	4.49907	0.151064	0.0755320	+	0.997143i	$0.475935\pi$
$888$	−1.51298	−0.0507723
$889$	18.1111	0.607427
$890$	60.9633	2.04349
$891$	−9.34326	−0.313011
$892$	63.9677	2.14180
$893$	−41.1580	−1.37730
$894$	−15.4308	−0.516083
$895$	−6.20365	−0.207365
$896$	−8.81967	−0.294645
$897$	15.7663	0.526422
$898$	65.5936	2.18889
$899$	−28.2613	−0.942566
$900$	1.06757	0.0355857
$901$	22.6234	0.753695
$902$	−0.890543	−0.0296519
$903$	−17.0984	−0.568998
$904$	20.5378	0.683077
$905$	−20.7447	−0.689577
$906$	33.0556	1.09820
$907$	20.7325	0.688410	0.344205	−	0.938894i	$-0.388148\pi$
$907$	20.7325	0.688410	0.344205	+	0.938894i	$0.388148\pi$
$908$	7.06323	0.234401
$909$	−2.28269	−0.0757120
$910$	21.2236	0.703555
$911$	51.1603	1.69502	0.847508	−	0.530782i	$-0.178102\pi$
$911$	51.1603	1.69502	0.847508	+	0.530782i	$0.178102\pi$
$912$	26.8269	0.888328
$913$	−8.71463	−0.288412
$914$	36.1836	1.19685
$915$	−40.2409	−1.33032
$916$	−6.09583	−0.201412
$917$	15.4970	0.511754
$918$	27.5183	0.908240
$919$	26.2085	0.864540	0.432270	−	0.901744i	$-0.357713\pi$
$919$	26.2085	0.864540	0.432270	+	0.901744i	$0.357713\pi$
$920$	5.13915	0.169433
$921$	−5.70024	−0.187829
$922$	−47.4025	−1.56112
$923$	67.0842	2.20810
$924$	5.48369	0.180400
$925$	0.558374	0.0183592
$926$	−40.8051	−1.34094
$927$	0.374845	0.0123115
$928$	73.3924	2.40922
$929$	13.8306	0.453767	0.226884	−	0.973922i	$-0.427146\pi$
$929$	13.8306	0.453767	0.226884	+	0.973922i	$0.427146\pi$
$930$	20.7380	0.680025
$931$	6.63482	0.217447
$932$	−36.6392	−1.20016
$933$	−42.5545	−1.39317
$934$	−59.8252	−1.95754
$935$	6.79309	0.222158
$936$	−3.55258	−0.116120
$937$	20.8560	0.681336	0.340668	−	0.940184i	$-0.389347\pi$
$937$	20.8560	0.681336	0.340668	+	0.940184i	$0.389347\pi$
$938$	24.2606	0.792138
$939$	22.8745	0.746482
$940$	32.8345	1.07094
$941$	−35.0512	−1.14264	−0.571318	−	0.820729i	$-0.693568\pi$
$941$	−35.0512	−1.14264	−0.571318	+	0.820729i	$0.693568\pi$
$942$	56.7395	1.84867
$943$	0.638555	0.0207942
$944$	−11.9540	−0.389069
$945$	11.6744	0.379767
$946$	33.5051	1.08934
$947$	−23.6979	−0.770079	−0.385039	−	0.922900i	$-0.625812\pi$
$947$	−23.6979	−0.770079	−0.385039	+	0.922900i	$0.625812\pi$
$948$	−9.66206	−0.313809
$949$	−49.6653	−1.61220
$950$	9.14321	0.296645
$951$	6.83131	0.221520
$952$	−2.64061	−0.0855828
$953$	−31.1668	−1.00959	−0.504797	−	0.863238i	$-0.668432\pi$
$953$	−31.1668	−1.00959	−0.504797	+	0.863238i	$0.668432\pi$
$954$	−13.5749	−0.439503
$955$	56.0058	1.81231
$956$	−22.3790	−0.723788
$957$	−20.0660	−0.648641
$958$	−59.4548	−1.92090
$959$	21.2897	0.687482
$960$	−36.9829	−1.19362
$961$	−21.7319	−0.701030
$962$	−8.77930	−0.283056
$963$	9.26815	0.298662
$964$	−45.8418	−1.47647
$965$	−13.2108	−0.425270
$966$	−7.03185	−0.226246
$967$	36.6095	1.17728	0.588640	−	0.808395i	$-0.299663\pi$
$967$	36.6095	1.17728	0.588640	+	0.808395i	$0.299663\pi$
$968$	10.3062	0.331252
$969$	23.4815	0.754335
$970$	74.8560	2.40348
$971$	−30.1747	−0.968351	−0.484175	−	0.874971i	$-0.660880\pi$
$971$	−30.1747	−0.968351	−0.484175	+	0.874971i	$0.660880\pi$
$972$	−16.8210	−0.539534
$973$	5.06995	0.162535
$974$	−31.8031	−1.01904
$975$	−4.73615	−0.151678
$976$	33.1914	1.06243
$977$	35.3911	1.13226	0.566130	−	0.824316i	$-0.308440\pi$
$977$	35.3911	1.13226	0.566130	+	0.824316i	$0.308440\pi$
$978$	−51.6540	−1.65171
$979$	19.3446	0.618257
$980$	−5.29303	−0.169080
$981$	−9.32835	−0.297831
$982$	−14.9137	−0.475914
$983$	−40.7571	−1.29995	−0.649975	−	0.759956i	$-0.725220\pi$
$983$	−40.7571	−1.29995	−0.649975	+	0.759956i	$0.725220\pi$
$984$	0.519758	0.0165693
$985$	27.3005	0.869866
$986$	45.6542	1.45393
$987$	−9.50868	−0.302665
$988$	−80.3860	−2.55742
$989$	−24.0245	−0.763935
$990$	−4.07610	−0.129547
$991$	−10.5878	−0.336332	−0.168166	−	0.985759i	$-0.553784\pi$
$991$	−10.5878	−0.336332	−0.168166	+	0.985759i	$0.553784\pi$
$992$	−24.0685	−0.764176
$993$	30.9595	0.982469
$994$	−29.9198	−0.949000
$995$	7.18745	0.227858
$996$	24.0316	0.761471
$997$	−37.9800	−1.20284	−0.601419	−	0.798934i	$-0.705398\pi$
$997$	−37.9800	−1.20284	−0.601419	+	0.798934i	$0.705398\pi$
$998$	20.7322	0.656267
$999$	−4.82920	−0.152789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.e.1.18	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.e.1.18	✓	112	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.13001 q^{2} -1.53283 q^{3} +2.53693 q^{4} -2.08639 q^{5} +3.26494 q^{6} -1.00000 q^{7} -1.14367 q^{8} -0.650428 q^{9} +O(q^{10})\)	\(q-2.13001 q^{2} -1.53283 q^{3} +2.53693 q^{4} -2.08639 q^{5} +3.26494 q^{6} -1.00000 q^{7} -1.14367 q^{8} -0.650428 q^{9} +4.44403 q^{10} +1.41016 q^{11} -3.88869 q^{12} -4.77576 q^{13} +2.13001 q^{14} +3.19808 q^{15} -2.63783 q^{16} -2.30889 q^{17} +1.38542 q^{18} +6.63482 q^{19} -5.29303 q^{20} +1.53283 q^{21} -3.00366 q^{22} +2.15374 q^{23} +1.75306 q^{24} -0.646976 q^{25} +10.1724 q^{26} +5.59549 q^{27} -2.53693 q^{28} +9.28318 q^{29} -6.81194 q^{30} -3.04435 q^{31} +7.90595 q^{32} -2.16154 q^{33} +4.91795 q^{34} +2.08639 q^{35} -1.65009 q^{36} -0.863051 q^{37} -14.1322 q^{38} +7.32043 q^{39} +2.38615 q^{40} +0.296486 q^{41} -3.26494 q^{42} -11.1548 q^{43} +3.57749 q^{44} +1.35705 q^{45} -4.58749 q^{46} -6.20334 q^{47} +4.04335 q^{48} +1.00000 q^{49} +1.37806 q^{50} +3.53913 q^{51} -12.1158 q^{52} -9.79840 q^{53} -11.9184 q^{54} -2.94215 q^{55} +1.14367 q^{56} -10.1701 q^{57} -19.7732 q^{58} +4.53175 q^{59} +8.11333 q^{60} -12.5828 q^{61} +6.48450 q^{62} +0.650428 q^{63} -11.5641 q^{64} +9.96409 q^{65} +4.60410 q^{66} +11.3899 q^{67} -5.85749 q^{68} -3.30132 q^{69} -4.44403 q^{70} -14.0468 q^{71} +0.743877 q^{72} +10.3995 q^{73} +1.83831 q^{74} +0.991706 q^{75} +16.8321 q^{76} -1.41016 q^{77} -15.5926 q^{78} +2.48465 q^{79} +5.50355 q^{80} -6.62566 q^{81} -0.631518 q^{82} -6.17987 q^{83} +3.88869 q^{84} +4.81724 q^{85} +23.7597 q^{86} -14.2296 q^{87} -1.61277 q^{88} +13.7180 q^{89} -2.89052 q^{90} +4.77576 q^{91} +5.46390 q^{92} +4.66648 q^{93} +13.2132 q^{94} -13.8428 q^{95} -12.1185 q^{96} +16.8442 q^{97} -2.13001 q^{98} -0.917209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * q^99

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