LMFDB - Embedded newform 8049.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62888 q^{2} -1.00000 q^{3} +4.91100 q^{4} +3.06865 q^{5} +2.62888 q^{6} -2.79906 q^{7} -7.65266 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.62888 q^{2} -1.00000 q^{3} +4.91100 q^{4} +3.06865 q^{5} +2.62888 q^{6} -2.79906 q^{7} -7.65266 q^{8} +1.00000 q^{9} -8.06710 q^{10} -1.33946 q^{11} -4.91100 q^{12} -5.90109 q^{13} +7.35840 q^{14} -3.06865 q^{15} +10.2959 q^{16} -6.89629 q^{17} -2.62888 q^{18} -4.20871 q^{19} +15.0701 q^{20} +2.79906 q^{21} +3.52128 q^{22} -4.32059 q^{23} +7.65266 q^{24} +4.41659 q^{25} +15.5132 q^{26} -1.00000 q^{27} -13.7462 q^{28} +0.148574 q^{29} +8.06710 q^{30} +9.63587 q^{31} -11.7614 q^{32} +1.33946 q^{33} +18.1295 q^{34} -8.58934 q^{35} +4.91100 q^{36} -2.30626 q^{37} +11.0642 q^{38} +5.90109 q^{39} -23.4833 q^{40} -8.72336 q^{41} -7.35840 q^{42} -1.09926 q^{43} -6.57809 q^{44} +3.06865 q^{45} +11.3583 q^{46} -7.04117 q^{47} -10.2959 q^{48} +0.834765 q^{49} -11.6107 q^{50} +6.89629 q^{51} -28.9803 q^{52} +11.0033 q^{53} +2.62888 q^{54} -4.11033 q^{55} +21.4203 q^{56} +4.20871 q^{57} -0.390583 q^{58} +2.42230 q^{59} -15.0701 q^{60} -15.2971 q^{61} -25.3315 q^{62} -2.79906 q^{63} +10.3274 q^{64} -18.1084 q^{65} -3.52128 q^{66} +3.63709 q^{67} -33.8677 q^{68} +4.32059 q^{69} +22.5803 q^{70} +1.09166 q^{71} -7.65266 q^{72} +3.06759 q^{73} +6.06287 q^{74} -4.41659 q^{75} -20.6690 q^{76} +3.74924 q^{77} -15.5132 q^{78} -5.99662 q^{79} +31.5945 q^{80} +1.00000 q^{81} +22.9326 q^{82} -6.00459 q^{83} +13.7462 q^{84} -21.1623 q^{85} +2.88981 q^{86} -0.148574 q^{87} +10.2504 q^{88} -2.96909 q^{89} -8.06710 q^{90} +16.5175 q^{91} -21.2184 q^{92} -9.63587 q^{93} +18.5104 q^{94} -12.9150 q^{95} +11.7614 q^{96} -11.0022 q^{97} -2.19449 q^{98} -1.33946 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * 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 $

$2$	−2.62888	−1.85890	−0.929449	−	0.368951i	$-0.879717\pi$
$2$	−2.62888	−1.85890	−0.929449	+	0.368951i	$0.879717\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.91100	2.45550
$5$	3.06865	1.37234	0.686170	−	0.727441i	$-0.259291\pi$
$5$	3.06865	1.37234	0.686170	+	0.727441i	$0.259291\pi$
$6$	2.62888	1.07323
$7$	−2.79906	−1.05795	−0.528974	−	0.848638i	$-0.677423\pi$
$7$	−2.79906	−1.05795	−0.528974	+	0.848638i	$0.677423\pi$
$8$	−7.65266	−2.70562
$9$	1.00000	0.333333
$10$	−8.06710	−2.55104
$11$	−1.33946	−0.403863	−0.201931	−	0.979400i	$-0.564722\pi$
$11$	−1.33946	−0.403863	−0.201931	+	0.979400i	$0.564722\pi$
$12$	−4.91100	−1.41768
$13$	−5.90109	−1.63667	−0.818334	−	0.574743i	$-0.805102\pi$
$13$	−5.90109	−1.63667	−0.818334	+	0.574743i	$0.805102\pi$
$14$	7.35840	1.96662
$15$	−3.06865	−0.792321
$16$	10.2959	2.57398
$17$	−6.89629	−1.67260	−0.836298	−	0.548276i	$-0.815284\pi$
$17$	−6.89629	−1.67260	−0.836298	+	0.548276i	$0.815284\pi$
$18$	−2.62888	−0.619632
$19$	−4.20871	−0.965544	−0.482772	−	0.875746i	$-0.660370\pi$
$19$	−4.20871	−0.965544	−0.482772	+	0.875746i	$0.660370\pi$
$20$	15.0701	3.36978
$21$	2.79906	0.610806
$22$	3.52128	0.750739
$23$	−4.32059	−0.900905	−0.450453	−	0.892800i	$-0.648737\pi$
$23$	−4.32059	−0.900905	−0.450453	+	0.892800i	$0.648737\pi$
$24$	7.65266	1.56209
$25$	4.41659	0.883318
$26$	15.5132	3.04240
$27$	−1.00000	−0.192450
$28$	−13.7462	−2.59779
$29$	0.148574	0.0275895	0.0137948	−	0.999905i	$-0.495609\pi$
$29$	0.148574	0.0275895	0.0137948	+	0.999905i	$0.495609\pi$
$30$	8.06710	1.47284
$31$	9.63587	1.73065	0.865327	−	0.501208i	$-0.167111\pi$
$31$	9.63587	1.73065	0.865327	+	0.501208i	$0.167111\pi$
$32$	−11.7614	−2.07914
$33$	1.33946	0.233170
$34$	18.1295	3.10918
$35$	−8.58934	−1.45186
$36$	4.91100	0.818500
$37$	−2.30626	−0.379146	−0.189573	−	0.981867i	$-0.560710\pi$
$37$	−2.30626	−0.379146	−0.189573	+	0.981867i	$0.560710\pi$
$38$	11.0642	1.79485
$39$	5.90109	0.944931
$40$	−23.4833	−3.71304
$41$	−8.72336	−1.36236	−0.681180	−	0.732116i	$-0.738533\pi$
$41$	−8.72336	−1.36236	−0.681180	+	0.732116i	$0.738533\pi$
$42$	−7.35840	−1.13543
$43$	−1.09926	−0.167635	−0.0838175	−	0.996481i	$-0.526711\pi$
$43$	−1.09926	−0.167635	−0.0838175	+	0.996481i	$0.526711\pi$
$44$	−6.57809	−0.991685
$45$	3.06865	0.457447
$46$	11.3583	1.67469
$47$	−7.04117	−1.02706	−0.513530	−	0.858072i	$-0.671663\pi$
$47$	−7.04117	−1.02706	−0.513530	+	0.858072i	$0.671663\pi$
$48$	−10.2959	−1.48609
$49$	0.834765	0.119252
$50$	−11.6107	−1.64200
$51$	6.89629	0.965673
$52$	−28.9803	−4.01884
$53$	11.0033	1.51142	0.755711	−	0.654905i	$-0.227291\pi$
$53$	11.0033	1.51142	0.755711	+	0.654905i	$0.227291\pi$
$54$	2.62888	0.357745
$55$	−4.11033	−0.554237
$56$	21.4203	2.86241
$57$	4.20871	0.557457
$58$	−0.390583	−0.0512861
$59$	2.42230	0.315357	0.157678	−	0.987491i	$-0.449599\pi$
$59$	2.42230	0.315357	0.157678	+	0.987491i	$0.449599\pi$
$60$	−15.0701	−1.94554
$61$	−15.2971	−1.95859	−0.979294	−	0.202443i	$-0.935112\pi$
$61$	−15.2971	−1.95859	−0.979294	+	0.202443i	$0.935112\pi$
$62$	−25.3315	−3.21711
$63$	−2.79906	−0.352649
$64$	10.3274	1.29092
$65$	−18.1084	−2.24607
$66$	−3.52128	−0.433440
$67$	3.63709	0.444341	0.222170	−	0.975008i	$-0.428686\pi$
$67$	3.63709	0.444341	0.222170	+	0.975008i	$0.428686\pi$
$68$	−33.8677	−4.10706
$69$	4.32059	0.520138
$70$	22.5803	2.69887
$71$	1.09166	0.129557	0.0647783	−	0.997900i	$-0.479366\pi$
$71$	1.09166	0.129557	0.0647783	+	0.997900i	$0.479366\pi$
$72$	−7.65266	−0.901875
$73$	3.06759	0.359035	0.179517	−	0.983755i	$-0.442546\pi$
$73$	3.06759	0.359035	0.179517	+	0.983755i	$0.442546\pi$
$74$	6.06287	0.704794
$75$	−4.41659	−0.509984
$76$	−20.6690	−2.37089
$77$	3.74924	0.427265
$78$	−15.5132	−1.75653
$79$	−5.99662	−0.674672	−0.337336	−	0.941384i	$-0.609526\pi$
$79$	−5.99662	−0.674672	−0.337336	+	0.941384i	$0.609526\pi$
$80$	31.5945	3.53237
$81$	1.00000	0.111111
$82$	22.9326	2.53249
$83$	−6.00459	−0.659089	−0.329545	−	0.944140i	$-0.606895\pi$
$83$	−6.00459	−0.659089	−0.329545	+	0.944140i	$0.606895\pi$
$84$	13.7462	1.49983
$85$	−21.1623	−2.29537
$86$	2.88981	0.311616
$87$	−0.148574	−0.0159288
$88$	10.2504	1.09270
$89$	−2.96909	−0.314723	−0.157362	−	0.987541i	$-0.550299\pi$
$89$	−2.96909	−0.314723	−0.157362	+	0.987541i	$0.550299\pi$
$90$	−8.06710	−0.850347
$91$	16.5175	1.73151
$92$	−21.2184	−2.21217
$93$	−9.63587	−0.999193
$94$	18.5104	1.90920
$95$	−12.9150	−1.32505
$96$	11.7614	1.20039
$97$	−11.0022	−1.11710	−0.558551	−	0.829470i	$-0.688643\pi$
$97$	−11.0022	−1.11710	−0.558551	+	0.829470i	$0.688643\pi$
$98$	−2.19449	−0.221677
$99$	−1.33946	−0.134621
$100$	21.6899	2.16899
$101$	14.2679	1.41971	0.709854	−	0.704349i	$-0.248761\pi$
$101$	14.2679	1.41971	0.709854	+	0.704349i	$0.248761\pi$
$102$	−18.1295	−1.79509
$103$	−19.9253	−1.96330	−0.981649	−	0.190699i	$-0.938925\pi$
$103$	−19.9253	−1.96330	−0.981649	+	0.190699i	$0.938925\pi$
$104$	45.1590	4.42821
$105$	8.58934	0.838234
$106$	−28.9264	−2.80958
$107$	2.76248	0.267059	0.133530	−	0.991045i	$-0.457369\pi$
$107$	2.76248	0.267059	0.133530	+	0.991045i	$0.457369\pi$
$108$	−4.91100	−0.472561
$109$	2.50520	0.239955	0.119977	−	0.992777i	$-0.461718\pi$
$109$	2.50520	0.239955	0.119977	+	0.992777i	$0.461718\pi$
$110$	10.8056	1.03027
$111$	2.30626	0.218900
$112$	−28.8189	−2.72313
$113$	−6.21684	−0.584831	−0.292416	−	0.956291i	$-0.594459\pi$
$113$	−6.21684	−0.584831	−0.292416	+	0.956291i	$0.594459\pi$
$114$	−11.0642	−1.03626
$115$	−13.2584	−1.23635
$116$	0.729648	0.0677461
$117$	−5.90109	−0.545556
$118$	−6.36793	−0.586215
$119$	19.3032	1.76952
$120$	23.4833	2.14372
$121$	−9.20584	−0.836895
$122$	40.2141	3.64081
$123$	8.72336	0.786559
$124$	47.3218	4.24962
$125$	−1.79028	−0.160128
$126$	7.35840	0.655538
$127$	−0.283373	−0.0251453	−0.0125727	−	0.999921i	$-0.504002\pi$
$127$	−0.283373	−0.0251453	−0.0125727	+	0.999921i	$0.504002\pi$
$128$	−3.62670	−0.320558
$129$	1.09926	0.0967842
$130$	47.6047	4.17521
$131$	10.9340	0.955311	0.477656	−	0.878547i	$-0.341487\pi$
$131$	10.9340	0.955311	0.477656	+	0.878547i	$0.341487\pi$
$132$	6.57809	0.572549
$133$	11.7804	1.02149
$134$	−9.56146	−0.825984
$135$	−3.06865	−0.264107
$136$	52.7749	4.52541
$137$	−13.2587	−1.13277	−0.566386	−	0.824140i	$-0.691659\pi$
$137$	−13.2587	−1.13277	−0.566386	+	0.824140i	$0.691659\pi$
$138$	−11.3583	−0.966883
$139$	−14.3482	−1.21700	−0.608499	−	0.793555i	$-0.708228\pi$
$139$	−14.3482	−1.21700	−0.608499	+	0.793555i	$0.708228\pi$
$140$	−42.1822	−3.56505
$141$	7.04117	0.592974
$142$	−2.86985	−0.240833
$143$	7.90428	0.660989
$144$	10.2959	0.857993
$145$	0.455922	0.0378622
$146$	−8.06433	−0.667409
$147$	−0.834765	−0.0688502
$148$	−11.3260	−0.930993
$149$	8.03855	0.658544	0.329272	−	0.944235i	$-0.393197\pi$
$149$	8.03855	0.658544	0.329272	+	0.944235i	$0.393197\pi$
$150$	11.6107	0.948008
$151$	1.14045	0.0928087	0.0464043	−	0.998923i	$-0.485224\pi$
$151$	1.14045	0.0928087	0.0464043	+	0.998923i	$0.485224\pi$
$152$	32.2078	2.61240
$153$	−6.89629	−0.557532
$154$	−9.85629	−0.794243
$155$	29.5691	2.37505
$156$	28.9803	2.32028
$157$	−12.9757	−1.03558	−0.517788	−	0.855509i	$-0.673244\pi$
$157$	−12.9757	−1.03558	−0.517788	+	0.855509i	$0.673244\pi$
$158$	15.7644	1.25415
$159$	−11.0033	−0.872620
$160$	−36.0915	−2.85328
$161$	12.0936	0.953110
$162$	−2.62888	−0.206544
$163$	14.8412	1.16245	0.581226	−	0.813742i	$-0.302573\pi$
$163$	14.8412	1.16245	0.581226	+	0.813742i	$0.302573\pi$
$164$	−42.8404	−3.34527
$165$	4.11033	0.319989
$166$	15.7853	1.22518
$167$	15.9795	1.23653	0.618265	−	0.785970i	$-0.287836\pi$
$167$	15.9795	1.23653	0.618265	+	0.785970i	$0.287836\pi$
$168$	−21.4203	−1.65261
$169$	21.8229	1.67868
$170$	55.6330	4.26686
$171$	−4.20871	−0.321848
$172$	−5.39845	−0.411628
$173$	4.25814	0.323741	0.161870	−	0.986812i	$-0.448247\pi$
$173$	4.25814	0.323741	0.161870	+	0.986812i	$0.448247\pi$
$174$	0.390583	0.0296101
$175$	−12.3623	−0.934504
$176$	−13.7910	−1.03953
$177$	−2.42230	−0.182071
$178$	7.80538	0.585038
$179$	19.9021	1.48755	0.743777	−	0.668428i	$-0.233032\pi$
$179$	19.9021	1.48755	0.743777	+	0.668428i	$0.233032\pi$
$180$	15.0701	1.12326
$181$	11.6344	0.864781	0.432390	−	0.901686i	$-0.357670\pi$
$181$	11.6344	0.864781	0.432390	+	0.901686i	$0.357670\pi$
$182$	−43.4226	−3.21870
$183$	15.2971	1.13079
$184$	33.0640	2.43751
$185$	−7.07708	−0.520318
$186$	25.3315	1.85740
$187$	9.23731	0.675499
$188$	−34.5792	−2.52195
$189$	2.79906	0.203602
$190$	33.9521	2.46314
$191$	−25.0035	−1.80919	−0.904595	−	0.426272i	$-0.859827\pi$
$191$	−25.0035	−1.80919	−0.904595	+	0.426272i	$0.859827\pi$
$192$	−10.3274	−0.745315
$193$	13.7833	0.992147	0.496073	−	0.868281i	$-0.334775\pi$
$193$	13.7833	0.992147	0.496073	+	0.868281i	$0.334775\pi$
$194$	28.9234	2.07658
$195$	18.1084	1.29677
$196$	4.09953	0.292823
$197$	12.6014	0.897810	0.448905	−	0.893579i	$-0.351814\pi$
$197$	12.6014	0.897810	0.448905	+	0.893579i	$0.351814\pi$
$198$	3.52128	0.250246
$199$	4.47268	0.317060	0.158530	−	0.987354i	$-0.449325\pi$
$199$	4.47268	0.317060	0.158530	+	0.987354i	$0.449325\pi$
$200$	−33.7987	−2.38993
$201$	−3.63709	−0.256540
$202$	−37.5085	−2.63909
$203$	−0.415869	−0.0291883
$204$	33.8677	2.37121
$205$	−26.7689	−1.86962
$206$	52.3812	3.64957
$207$	−4.32059	−0.300302
$208$	−60.7571	−4.21275
$209$	5.63740	0.389947
$210$	−22.5803	−1.55819
$211$	6.65525	0.458167	0.229083	−	0.973407i	$-0.426427\pi$
$211$	6.65525	0.458167	0.229083	+	0.973407i	$0.426427\pi$
$212$	54.0373	3.71130
$213$	−1.09166	−0.0747996
$214$	−7.26223	−0.496436
$215$	−3.37323	−0.230052
$216$	7.65266	0.520698
$217$	−26.9714	−1.83094
$218$	−6.58587	−0.446051
$219$	−3.06759	−0.207289
$220$	−20.1858	−1.36093
$221$	40.6956	2.73748
$222$	−6.06287	−0.406913
$223$	−26.7522	−1.79146	−0.895729	−	0.444600i	$-0.853346\pi$
$223$	−26.7522	−1.79146	−0.895729	+	0.444600i	$0.853346\pi$
$224$	32.9208	2.19962
$225$	4.41659	0.294439
$226$	16.3433	1.08714
$227$	17.1925	1.14111	0.570553	−	0.821261i	$-0.306729\pi$
$227$	17.1925	1.14111	0.570553	+	0.821261i	$0.306729\pi$
$228$	20.6690	1.36884
$229$	−15.8431	−1.04694	−0.523472	−	0.852043i	$-0.675364\pi$
$229$	−15.8431	−1.04694	−0.523472	+	0.852043i	$0.675364\pi$
$230$	34.8546	2.29824
$231$	−3.74924	−0.246682
$232$	−1.13699	−0.0746469
$233$	9.61120	0.629651	0.314825	−	0.949150i	$-0.398054\pi$
$233$	9.61120	0.629651	0.314825	+	0.949150i	$0.398054\pi$
$234$	15.5132	1.01413
$235$	−21.6069	−1.40948
$236$	11.8959	0.774358
$237$	5.99662	0.389522
$238$	−50.7456	−3.28935
$239$	−0.806168	−0.0521467	−0.0260733	−	0.999660i	$-0.508300\pi$
$239$	−0.806168	−0.0521467	−0.0260733	+	0.999660i	$0.508300\pi$
$240$	−31.5945	−2.03942
$241$	−20.9343	−1.34850	−0.674249	−	0.738504i	$-0.735533\pi$
$241$	−20.9343	−1.34850	−0.674249	+	0.738504i	$0.735533\pi$
$242$	24.2010	1.55570
$243$	−1.00000	−0.0641500
$244$	−75.1239	−4.80931
$245$	2.56160	0.163654
$246$	−22.9326	−1.46213
$247$	24.8360	1.58028
$248$	−73.7400	−4.68250
$249$	6.00459	0.380525
$250$	4.70643	0.297661
$251$	−7.61918	−0.480918	−0.240459	−	0.970659i	$-0.577298\pi$
$251$	−7.61918	−0.480918	−0.240459	+	0.970659i	$0.577298\pi$
$252$	−13.7462	−0.865930
$253$	5.78726	0.363842
$254$	0.744954	0.0467426
$255$	21.1623	1.32523
$256$	−11.1206	−0.695039
$257$	0.519415	0.0324002	0.0162001	−	0.999869i	$-0.494843\pi$
$257$	0.519415	0.0324002	0.0162001	+	0.999869i	$0.494843\pi$
$258$	−2.88981	−0.179912
$259$	6.45536	0.401117
$260$	−88.9301	−5.51521
$261$	0.148574	0.00919651
$262$	−28.7442	−1.77583
$263$	22.5254	1.38898	0.694488	−	0.719504i	$-0.255631\pi$
$263$	22.5254	1.38898	0.694488	+	0.719504i	$0.255631\pi$
$264$	−10.2504	−0.630871
$265$	33.7653	2.07419
$266$	−30.9694	−1.89885
$267$	2.96909	0.181706
$268$	17.8617	1.09108
$269$	19.4180	1.18394	0.591969	−	0.805961i	$-0.298351\pi$
$269$	19.4180	1.18394	0.591969	+	0.805961i	$0.298351\pi$
$270$	8.06710	0.490948
$271$	−9.15195	−0.555941	−0.277971	−	0.960590i	$-0.589662\pi$
$271$	−9.15195	−0.555941	−0.277971	+	0.960590i	$0.589662\pi$
$272$	−71.0036	−4.30522
$273$	−16.5175	−0.999687
$274$	34.8556	2.10571
$275$	−5.91585	−0.356739
$276$	21.2184	1.27720
$277$	26.0506	1.56523	0.782615	−	0.622506i	$-0.213886\pi$
$277$	26.0506	1.56523	0.782615	+	0.622506i	$0.213886\pi$
$278$	37.7196	2.26227
$279$	9.63587	0.576885
$280$	65.7313	3.92820
$281$	−13.2776	−0.792077	−0.396038	−	0.918234i	$-0.629615\pi$
$281$	−13.2776	−0.792077	−0.396038	+	0.918234i	$0.629615\pi$
$282$	−18.5104	−1.10228
$283$	16.8825	1.00356	0.501781	−	0.864995i	$-0.332678\pi$
$283$	16.8825	1.00356	0.501781	+	0.864995i	$0.332678\pi$
$284$	5.36116	0.318126
$285$	12.9150	0.765021
$286$	−20.7794	−1.22871
$287$	24.4172	1.44130
$288$	−11.7614	−0.693046
$289$	30.5588	1.79757
$290$	−1.19856	−0.0703820
$291$	11.0022	0.644960
$292$	15.0649	0.881609
$293$	−28.1084	−1.64211	−0.821056	−	0.570848i	$-0.806615\pi$
$293$	−28.1084	−1.64211	−0.821056	+	0.570848i	$0.806615\pi$
$294$	2.19449	0.127986
$295$	7.43318	0.432776
$296$	17.6490	1.02583
$297$	1.33946	0.0777234
$298$	−21.1324	−1.22417
$299$	25.4962	1.47448
$300$	−21.6899	−1.25226
$301$	3.07689	0.177349
$302$	−2.99811	−0.172522
$303$	−14.2679	−0.819668
$304$	−43.3325	−2.48529
$305$	−46.9413	−2.68785
$306$	18.1295	1.03639
$307$	−32.7721	−1.87040	−0.935202	−	0.354114i	$-0.884782\pi$
$307$	−32.7721	−1.87040	−0.935202	+	0.354114i	$0.884782\pi$
$308$	18.4125	1.04915
$309$	19.9253	1.13351
$310$	−77.7335	−4.41497
$311$	23.9215	1.35647	0.678233	−	0.734847i	$-0.262746\pi$
$311$	23.9215	1.35647	0.678233	+	0.734847i	$0.262746\pi$
$312$	−45.1590	−2.55663
$313$	−1.91506	−0.108246	−0.0541228	−	0.998534i	$-0.517236\pi$
$313$	−1.91506	−0.108246	−0.0541228	+	0.998534i	$0.517236\pi$
$314$	34.1116	1.92503
$315$	−8.58934	−0.483954
$316$	−29.4494	−1.65666
$317$	−2.22720	−0.125092	−0.0625460	−	0.998042i	$-0.519922\pi$
$317$	−2.22720	−0.125092	−0.0625460	+	0.998042i	$0.519922\pi$
$318$	28.9264	1.62211
$319$	−0.199009	−0.0111424
$320$	31.6911	1.77159
$321$	−2.76248	−0.154187
$322$	−31.7926	−1.77173
$323$	29.0245	1.61496
$324$	4.91100	0.272833
$325$	−26.0627	−1.44570
$326$	−39.0157	−2.16088
$327$	−2.50520	−0.138538
$328$	66.7569	3.68603
$329$	19.7087	1.08658
$330$	−10.8056	−0.594827
$331$	−13.3695	−0.734853	−0.367427	−	0.930052i	$-0.619761\pi$
$331$	−13.3695	−0.734853	−0.367427	+	0.930052i	$0.619761\pi$
$332$	−29.4885	−1.61839
$333$	−2.30626	−0.126382
$334$	−42.0081	−2.29858
$335$	11.1609	0.609787
$336$	28.8189	1.57220
$337$	−6.92137	−0.377031	−0.188516	−	0.982070i	$-0.560368\pi$
$337$	−6.92137	−0.377031	−0.188516	+	0.982070i	$0.560368\pi$
$338$	−57.3697	−3.12050
$339$	6.21684	0.337653
$340$	−103.928	−5.63628
$341$	−12.9069	−0.698946
$342$	11.0642	0.598282
$343$	17.2569	0.931785
$344$	8.41224	0.453557
$345$	13.2584	0.713806
$346$	−11.1941	−0.601801
$347$	25.7572	1.38272	0.691358	−	0.722512i	$-0.257013\pi$
$347$	25.7572	1.38272	0.691358	+	0.722512i	$0.257013\pi$
$348$	−0.729648	−0.0391132
$349$	−25.7163	−1.37656	−0.688280	−	0.725445i	$-0.741634\pi$
$349$	−25.7163	−1.37656	−0.688280	+	0.725445i	$0.741634\pi$
$350$	32.4990	1.73715
$351$	5.90109	0.314977
$352$	15.7539	0.839686
$353$	−31.5583	−1.67968	−0.839840	−	0.542834i	$-0.817351\pi$
$353$	−31.5583	−1.67968	−0.839840	+	0.542834i	$0.817351\pi$
$354$	6.36793	0.338452
$355$	3.34993	0.177796
$356$	−14.5812	−0.772803
$357$	−19.3032	−1.02163
$358$	−52.3202	−2.76521
$359$	24.1520	1.27469	0.637347	−	0.770577i	$-0.280032\pi$
$359$	24.1520	1.27469	0.637347	+	0.770577i	$0.280032\pi$
$360$	−23.4833	−1.23768
$361$	−1.28677	−0.0677248
$362$	−30.5855	−1.60754
$363$	9.20584	0.483181
$364$	81.1176	4.25172
$365$	9.41336	0.492718
$366$	−40.2141	−2.10203
$367$	9.01121	0.470381	0.235191	−	0.971949i	$-0.424429\pi$
$367$	9.01121	0.470381	0.235191	+	0.971949i	$0.424429\pi$
$368$	−44.4844	−2.31891
$369$	−8.72336	−0.454120
$370$	18.6048	0.967217
$371$	−30.7990	−1.59900
$372$	−47.3218	−2.45352
$373$	−5.51983	−0.285806	−0.142903	−	0.989737i	$-0.545644\pi$
$373$	−5.51983	−0.285806	−0.142903	+	0.989737i	$0.545644\pi$
$374$	−24.2838	−1.25568
$375$	1.79028	0.0924497
$376$	53.8837	2.77884
$377$	−0.876750	−0.0451549
$378$	−7.35840	−0.378475
$379$	24.2819	1.24728	0.623639	−	0.781712i	$-0.285653\pi$
$379$	24.2819	1.24728	0.623639	+	0.781712i	$0.285653\pi$
$380$	−63.4257	−3.25367
$381$	0.283373	0.0145177
$382$	65.7312	3.36310
$383$	4.07523	0.208234	0.104117	−	0.994565i	$-0.466798\pi$
$383$	4.07523	0.208234	0.104117	+	0.994565i	$0.466798\pi$
$384$	3.62670	0.185074
$385$	11.5051	0.586354
$386$	−36.2347	−1.84430
$387$	−1.09926	−0.0558784
$388$	−54.0317	−2.74305
$389$	−24.8095	−1.25789	−0.628946	−	0.777449i	$-0.716513\pi$
$389$	−24.8095	−1.25789	−0.628946	+	0.777449i	$0.716513\pi$
$390$	−47.6047	−2.41056
$391$	29.7960	1.50685
$392$	−6.38817	−0.322651
$393$	−10.9340	−0.551549
$394$	−33.1275	−1.66894
$395$	−18.4015	−0.925880
$396$	−6.57809	−0.330562
$397$	3.01533	0.151335	0.0756676	−	0.997133i	$-0.475891\pi$
$397$	3.01533	0.151335	0.0756676	+	0.997133i	$0.475891\pi$
$398$	−11.7581	−0.589381
$399$	−11.7804	−0.589760
$400$	45.4728	2.27364
$401$	−0.972015	−0.0485401	−0.0242701	−	0.999705i	$-0.507726\pi$
$401$	−0.972015	−0.0485401	−0.0242701	+	0.999705i	$0.507726\pi$
$402$	9.56146	0.476882
$403$	−56.8622	−2.83251
$404$	70.0695	3.48609
$405$	3.06865	0.152482
$406$	1.09327	0.0542580
$407$	3.08914	0.153123
$408$	−52.7749	−2.61275
$409$	11.6425	0.575683	0.287842	−	0.957678i	$-0.407062\pi$
$409$	11.6425	0.575683	0.287842	+	0.957678i	$0.407062\pi$
$410$	70.3722	3.47543
$411$	13.2587	0.654006
$412$	−97.8531	−4.82087
$413$	−6.78017	−0.333631
$414$	11.3583	0.558230
$415$	−18.4260	−0.904494
$416$	69.4049	3.40286
$417$	14.3482	0.702634
$418$	−14.8200	−0.724872
$419$	−0.597139	−0.0291722	−0.0145861	−	0.999894i	$-0.504643\pi$
$419$	−0.597139	−0.0291722	−0.0145861	+	0.999894i	$0.504643\pi$
$420$	42.1822	2.05828
$421$	20.8789	1.01758	0.508788	−	0.860892i	$-0.330094\pi$
$421$	20.8789	1.01758	0.508788	+	0.860892i	$0.330094\pi$
$422$	−17.4958	−0.851685
$423$	−7.04117	−0.342353
$424$	−84.2047	−4.08934
$425$	−30.4581	−1.47743
$426$	2.86985	0.139045
$427$	42.8175	2.07208
$428$	13.5665	0.655764
$429$	−7.90428	−0.381622
$430$	8.86781	0.427644
$431$	−23.3845	−1.12639	−0.563197	−	0.826323i	$-0.690429\pi$
$431$	−23.3845	−1.12639	−0.563197	+	0.826323i	$0.690429\pi$
$432$	−10.2959	−0.495362
$433$	−23.3762	−1.12339	−0.561695	−	0.827345i	$-0.689850\pi$
$433$	−23.3762	−1.12339	−0.561695	+	0.827345i	$0.689850\pi$
$434$	70.9046	3.40353
$435$	−0.455922	−0.0218598
$436$	12.3030	0.589209
$437$	18.1841	0.869864
$438$	8.06433	0.385329
$439$	−18.4267	−0.879457	−0.439729	−	0.898131i	$-0.644925\pi$
$439$	−18.4267	−0.879457	−0.439729	+	0.898131i	$0.644925\pi$
$440$	31.4550	1.49956
$441$	0.834765	0.0397507
$442$	−106.984	−5.08870
$443$	27.7395	1.31794	0.658971	−	0.752168i	$-0.270992\pi$
$443$	27.7395	1.31794	0.658971	+	0.752168i	$0.270992\pi$
$444$	11.3260	0.537509
$445$	−9.11110	−0.431907
$446$	70.3282	3.33014
$447$	−8.03855	−0.380211
$448$	−28.9070	−1.36573
$449$	−0.724559	−0.0341941	−0.0170970	−	0.999854i	$-0.505442\pi$
$449$	−0.724559	−0.0341941	−0.0170970	+	0.999854i	$0.505442\pi$
$450$	−11.6107	−0.547332
$451$	11.6846	0.550206
$452$	−30.5309	−1.43605
$453$	−1.14045	−0.0535831
$454$	−45.1970	−2.12120
$455$	50.6865	2.37622
$456$	−32.2078	−1.50827
$457$	−13.6583	−0.638907	−0.319453	−	0.947602i	$-0.603499\pi$
$457$	−13.6583	−0.638907	−0.319453	+	0.947602i	$0.603499\pi$
$458$	41.6497	1.94616
$459$	6.89629	0.321891
$460$	−65.1118	−3.03585
$461$	15.0968	0.703128	0.351564	−	0.936164i	$-0.385650\pi$
$461$	15.0968	0.703128	0.351564	+	0.936164i	$0.385650\pi$
$462$	9.85629	0.458556
$463$	11.7577	0.546425	0.273213	−	0.961954i	$-0.411914\pi$
$463$	11.7577	0.546425	0.273213	+	0.961954i	$0.411914\pi$
$464$	1.52971	0.0710149
$465$	−29.5691	−1.37123
$466$	−25.2667	−1.17046
$467$	−5.78976	−0.267918	−0.133959	−	0.990987i	$-0.542769\pi$
$467$	−5.78976	−0.267918	−0.133959	+	0.990987i	$0.542769\pi$
$468$	−28.9803	−1.33961
$469$	−10.1804	−0.470089
$470$	56.8018	2.62007
$471$	12.9757	0.597890
$472$	−18.5370	−0.853236
$473$	1.47241	0.0677016
$474$	−15.7644	−0.724082
$475$	−18.5881	−0.852882
$476$	94.7978	4.34505
$477$	11.0033	0.503807
$478$	2.11932	0.0969353
$479$	−3.57379	−0.163291	−0.0816454	−	0.996661i	$-0.526017\pi$
$479$	−3.57379	−0.163291	−0.0816454	+	0.996661i	$0.526017\pi$
$480$	36.0915	1.64734
$481$	13.6094	0.620537
$482$	55.0338	2.50672
$483$	−12.0936	−0.550278
$484$	−45.2099	−2.05499
$485$	−33.7618	−1.53305
$486$	2.62888	0.119248
$487$	−10.0461	−0.455232	−0.227616	−	0.973751i	$-0.573093\pi$
$487$	−10.0461	−0.455232	−0.227616	+	0.973751i	$0.573093\pi$
$488$	117.063	5.29920
$489$	−14.8412	−0.671142
$490$	−6.73413	−0.304217
$491$	3.17891	0.143462	0.0717311	−	0.997424i	$-0.477148\pi$
$491$	3.17891	0.143462	0.0717311	+	0.997424i	$0.477148\pi$
$492$	42.8404	1.93139
$493$	−1.02461	−0.0461461
$494$	−65.2907	−2.93757
$495$	−4.11033	−0.184746
$496$	99.2101	4.45466
$497$	−3.05564	−0.137064
$498$	−15.7853	−0.707357
$499$	−8.44591	−0.378091	−0.189045	−	0.981968i	$-0.560539\pi$
$499$	−8.44591	−0.378091	−0.189045	+	0.981968i	$0.560539\pi$
$500$	−8.79207	−0.393193
$501$	−15.9795	−0.713911
$502$	20.0299	0.893978
$503$	11.2048	0.499596	0.249798	−	0.968298i	$-0.419636\pi$
$503$	11.2048	0.499596	0.249798	+	0.968298i	$0.419636\pi$
$504$	21.4203	0.954136
$505$	43.7831	1.94832
$506$	−15.2140	−0.676345
$507$	−21.8229	−0.969188
$508$	−1.39165	−0.0617443
$509$	−14.6637	−0.649955	−0.324978	−	0.945722i	$-0.605357\pi$
$509$	−14.6637	−0.649955	−0.324978	+	0.945722i	$0.605357\pi$
$510$	−55.6330	−2.46347
$511$	−8.58639	−0.379840
$512$	36.4882	1.61256
$513$	4.20871	0.185819
$514$	−1.36548	−0.0602287
$515$	−61.1437	−2.69431
$516$	5.39845	0.237653
$517$	9.43137	0.414791
$518$	−16.9704	−0.745635
$519$	−4.25814	−0.186912
$520$	138.577	6.07701
$521$	38.0447	1.66677	0.833384	−	0.552694i	$-0.186400\pi$
$521$	38.0447	1.66677	0.833384	+	0.552694i	$0.186400\pi$
$522$	−0.390583	−0.0170954
$523$	33.8172	1.47872	0.739362	−	0.673308i	$-0.235127\pi$
$523$	33.8172	1.47872	0.739362	+	0.673308i	$0.235127\pi$
$524$	53.6970	2.34577
$525$	12.3623	0.539536
$526$	−59.2165	−2.58196
$527$	−66.4517	−2.89468
$528$	13.7910	0.600175
$529$	−4.33251	−0.188370
$530$	−88.7648	−3.85570
$531$	2.42230	0.105119
$532$	57.8538	2.50828
$533$	51.4773	2.22973
$534$	−7.80538	−0.337772
$535$	8.47708	0.366496
$536$	−27.8334	−1.20222
$537$	−19.9021	−0.858840
$538$	−51.0476	−2.20082
$539$	−1.11814	−0.0481615
$540$	−15.0701	−0.648515
$541$	5.35346	0.230163	0.115082	−	0.993356i	$-0.463287\pi$
$541$	5.35346	0.230163	0.115082	+	0.993356i	$0.463287\pi$
$542$	24.0594	1.03344
$543$	−11.6344	−0.499282
$544$	81.1098	3.47755
$545$	7.68757	0.329299
$546$	43.4226	1.85832
$547$	−9.21262	−0.393903	−0.196952	−	0.980413i	$-0.563104\pi$
$547$	−9.21262	−0.393903	−0.196952	+	0.980413i	$0.563104\pi$
$548$	−65.1137	−2.78152
$549$	−15.2971	−0.652863
$550$	15.5520	0.663142
$551$	−0.625306	−0.0266389
$552$	−33.0640	−1.40730
$553$	16.7849	0.713767
$554$	−68.4839	−2.90960
$555$	7.07708	0.300406
$556$	−70.4639	−2.98834
$557$	−10.8955	−0.461655	−0.230828	−	0.972995i	$-0.574143\pi$
$557$	−10.8955	−0.461655	−0.230828	+	0.972995i	$0.574143\pi$
$558$	−25.3315	−1.07237
$559$	6.48681	0.274363
$560$	−88.4351	−3.73706
$561$	−9.23731	−0.389999
$562$	34.9053	1.47239
$563$	−40.9363	−1.72526	−0.862630	−	0.505835i	$-0.831185\pi$
$563$	−40.9363	−1.72526	−0.862630	+	0.505835i	$0.831185\pi$
$564$	34.5792	1.45605
$565$	−19.0773	−0.802588
$566$	−44.3821	−1.86552
$567$	−2.79906	−0.117550
$568$	−8.35413	−0.350532
$569$	−19.6964	−0.825716	−0.412858	−	0.910795i	$-0.635469\pi$
$569$	−19.6964	−0.825716	−0.412858	+	0.910795i	$0.635469\pi$
$570$	−33.9521	−1.42210
$571$	−3.67389	−0.153748	−0.0768738	−	0.997041i	$-0.524494\pi$
$571$	−3.67389	−0.153748	−0.0768738	+	0.997041i	$0.524494\pi$
$572$	38.8179	1.62306
$573$	25.0035	1.04454
$574$	−64.1900	−2.67924
$575$	−19.0823	−0.795786
$576$	10.3274	0.430308
$577$	20.6878	0.861244	0.430622	−	0.902532i	$-0.358294\pi$
$577$	20.6878	0.861244	0.430622	+	0.902532i	$0.358294\pi$
$578$	−80.3353	−3.34151
$579$	−13.7833	−0.572816
$580$	2.23903	0.0929707
$581$	16.8072	0.697281
$582$	−28.9234	−1.19891
$583$	−14.7385	−0.610407
$584$	−23.4752	−0.971413
$585$	−18.1084	−0.748689
$586$	73.8936	3.05252
$587$	29.9767	1.23727	0.618635	−	0.785678i	$-0.287686\pi$
$587$	29.9767	1.23727	0.618635	+	0.785678i	$0.287686\pi$
$588$	−4.09953	−0.169062
$589$	−40.5546	−1.67102
$590$	−19.5409	−0.804487
$591$	−12.6014	−0.518351
$592$	−23.7450	−0.975914
$593$	34.9508	1.43526	0.717630	−	0.696425i	$-0.245227\pi$
$593$	34.9508	1.43526	0.717630	+	0.696425i	$0.245227\pi$
$594$	−3.52128	−0.144480
$595$	59.2345	2.42838
$596$	39.4773	1.61705
$597$	−4.47268	−0.183054
$598$	−67.0264	−2.74091
$599$	9.56973	0.391009	0.195504	−	0.980703i	$-0.437366\pi$
$599$	9.56973	0.391009	0.195504	+	0.980703i	$0.437366\pi$
$600$	33.7987	1.37982
$601$	27.4395	1.11928	0.559639	−	0.828736i	$-0.310940\pi$
$601$	27.4395	1.11928	0.559639	+	0.828736i	$0.310940\pi$
$602$	−8.08877	−0.329674
$603$	3.63709	0.148114
$604$	5.60076	0.227892
$605$	−28.2495	−1.14850
$606$	37.5085	1.52368
$607$	−34.5863	−1.40381	−0.701907	−	0.712268i	$-0.747668\pi$
$607$	−34.5863	−1.40381	−0.701907	+	0.712268i	$0.747668\pi$
$608$	49.5002	2.00750
$609$	0.415869	0.0168519
$610$	123.403	4.99644
$611$	41.5506	1.68096
$612$	−33.8677	−1.36902
$613$	−14.6490	−0.591667	−0.295834	−	0.955240i	$-0.595597\pi$
$613$	−14.6490	−0.591667	−0.295834	+	0.955240i	$0.595597\pi$
$614$	86.1539	3.47689
$615$	26.7689	1.07943
$616$	−28.6917	−1.15602
$617$	11.5367	0.464448	0.232224	−	0.972662i	$-0.425400\pi$
$617$	11.5367	0.464448	0.232224	+	0.972662i	$0.425400\pi$
$618$	−52.3812	−2.10708
$619$	8.14194	0.327252	0.163626	−	0.986522i	$-0.447681\pi$
$619$	8.14194	0.327252	0.163626	+	0.986522i	$0.447681\pi$
$620$	145.214	5.83192
$621$	4.32059	0.173379
$622$	−62.8868	−2.52153
$623$	8.31069	0.332961
$624$	60.7571	2.43223
$625$	−27.5767	−1.10307
$626$	5.03446	0.201218
$627$	−5.63740	−0.225136
$628$	−63.7238	−2.54286
$629$	15.9046	0.634158
$630$	22.5803	0.899622
$631$	44.7508	1.78150	0.890751	−	0.454492i	$-0.150179\pi$
$631$	44.7508	1.78150	0.890751	+	0.454492i	$0.150179\pi$
$632$	45.8901	1.82541
$633$	−6.65525	−0.264523
$634$	5.85504	0.232533
$635$	−0.869572	−0.0345079
$636$	−54.0373	−2.14272
$637$	−4.92602	−0.195176
$638$	0.523171	0.0207126
$639$	1.09166	0.0431856
$640$	−11.1291	−0.439915
$641$	−31.7892	−1.25560	−0.627800	−	0.778375i	$-0.716044\pi$
$641$	−31.7892	−1.25560	−0.627800	+	0.778375i	$0.716044\pi$
$642$	7.26223	0.286617
$643$	31.9940	1.26172	0.630860	−	0.775897i	$-0.282702\pi$
$643$	31.9940	1.26172	0.630860	+	0.775897i	$0.282702\pi$
$644$	59.3917	2.34036
$645$	3.37323	0.132821
$646$	−76.3018	−3.00205
$647$	23.3491	0.917948	0.458974	−	0.888450i	$-0.348217\pi$
$647$	23.3491	0.917948	0.458974	+	0.888450i	$0.348217\pi$
$648$	−7.65266	−0.300625
$649$	−3.24458	−0.127361
$650$	68.5156	2.68740
$651$	26.9714	1.05709
$652$	72.8851	2.85440
$653$	7.77362	0.304205	0.152103	−	0.988365i	$-0.451396\pi$
$653$	7.77362	0.304205	0.152103	+	0.988365i	$0.451396\pi$
$654$	6.58587	0.257528
$655$	33.5527	1.31101
$656$	−89.8149	−3.50668
$657$	3.06759	0.119678
$658$	−51.8117	−2.01983
$659$	17.4067	0.678070	0.339035	−	0.940774i	$-0.389899\pi$
$659$	17.4067	0.678070	0.339035	+	0.940774i	$0.389899\pi$
$660$	20.1858	0.785733
$661$	21.8821	0.851117	0.425558	−	0.904931i	$-0.360078\pi$
$661$	21.8821	0.851117	0.425558	+	0.904931i	$0.360078\pi$
$662$	35.1467	1.36602
$663$	−40.6956	−1.58049
$664$	45.9511	1.78325
$665$	36.1500	1.40184
$666$	6.06287	0.234931
$667$	−0.641928	−0.0248556
$668$	78.4753	3.03630
$669$	26.7522	1.03430
$670$	−29.3407	−1.13353
$671$	20.4898	0.791001
$672$	−32.9208	−1.26995
$673$	22.5844	0.870565	0.435283	−	0.900294i	$-0.356648\pi$
$673$	22.5844	0.870565	0.435283	+	0.900294i	$0.356648\pi$
$674$	18.1954	0.700862
$675$	−4.41659	−0.169995
$676$	107.172	4.12200
$677$	−5.17181	−0.198769	−0.0993843	−	0.995049i	$-0.531687\pi$
$677$	−5.17181	−0.198769	−0.0993843	+	0.995049i	$0.531687\pi$
$678$	−16.3433	−0.627661
$679$	30.7958	1.18184
$680$	161.948	6.21041
$681$	−17.1925	−0.658818
$682$	33.9306	1.29927
$683$	10.5384	0.403239	0.201619	−	0.979464i	$-0.435380\pi$
$683$	10.5384	0.403239	0.201619	+	0.979464i	$0.435380\pi$
$684$	−20.6690	−0.790298
$685$	−40.6864	−1.55455
$686$	−45.3663	−1.73209
$687$	15.8431	0.604454
$688$	−11.3178	−0.431489
$689$	−64.9316	−2.47370
$690$	−34.8546	−1.32689
$691$	−18.6845	−0.710792	−0.355396	−	0.934716i	$-0.615654\pi$
$691$	−18.6845	−0.710792	−0.355396	+	0.934716i	$0.615654\pi$
$692$	20.9117	0.794945
$693$	3.74924	0.142422
$694$	−67.7124	−2.57033
$695$	−44.0295	−1.67013
$696$	1.13699	0.0430974
$697$	60.1588	2.27868
$698$	67.6049	2.55888
$699$	−9.61120	−0.363529
$700$	−60.7113	−2.29467
$701$	−40.3328	−1.52335	−0.761674	−	0.647961i	$-0.775622\pi$
$701$	−40.3328	−1.52335	−0.761674	+	0.647961i	$0.775622\pi$
$702$	−15.5132	−0.585510
$703$	9.70636	0.366082
$704$	−13.8331	−0.521356
$705$	21.6069	0.813761
$706$	82.9630	3.12235
$707$	−39.9367	−1.50198
$708$	−11.8959	−0.447076
$709$	−36.9210	−1.38660	−0.693299	−	0.720650i	$-0.743843\pi$
$709$	−36.9210	−1.38660	−0.693299	+	0.720650i	$0.743843\pi$
$710$	−8.80656	−0.330504
$711$	−5.99662	−0.224891
$712$	22.7215	0.851523
$713$	−41.6326	−1.55915
$714$	50.7456	1.89911
$715$	24.2554	0.907102
$716$	97.7393	3.65269
$717$	0.806168	0.0301069
$718$	−63.4927	−2.36953
$719$	45.7947	1.70786	0.853928	−	0.520392i	$-0.174214\pi$
$719$	45.7947	1.70786	0.853928	+	0.520392i	$0.174214\pi$
$720$	31.5945	1.17746
$721$	55.7722	2.07706
$722$	3.38277	0.125894
$723$	20.9343	0.778556
$724$	57.1367	2.12347
$725$	0.656191	0.0243703
$726$	−24.2010	−0.898185
$727$	−52.5361	−1.94846	−0.974228	−	0.225568i	$-0.927576\pi$
$727$	−52.5361	−1.94846	−0.974228	+	0.225568i	$0.927576\pi$
$728$	−126.403	−4.68481
$729$	1.00000	0.0370370
$730$	−24.7466	−0.915912
$731$	7.58079	0.280386
$732$	75.1239	2.77666
$733$	−13.9783	−0.516299	−0.258150	−	0.966105i	$-0.583113\pi$
$733$	−13.9783	−0.516299	−0.258150	+	0.966105i	$0.583113\pi$
$734$	−23.6894	−0.874390
$735$	−2.56160	−0.0944860
$736$	50.8161	1.87310
$737$	−4.87174	−0.179453
$738$	22.9326	0.844162
$739$	−12.5457	−0.461502	−0.230751	−	0.973013i	$-0.574118\pi$
$739$	−12.5457	−0.461502	−0.230751	+	0.973013i	$0.574118\pi$
$740$	−34.7556	−1.27764
$741$	−24.8360	−0.912372
$742$	80.9668	2.97239
$743$	5.44535	0.199770	0.0998852	−	0.994999i	$-0.468152\pi$
$743$	5.44535	0.199770	0.0998852	+	0.994999i	$0.468152\pi$
$744$	73.7400	2.70344
$745$	24.6675	0.903746
$746$	14.5110	0.531284
$747$	−6.00459	−0.219696
$748$	45.3644	1.65869
$749$	−7.73237	−0.282535
$750$	−4.70643	−0.171855
$751$	51.3821	1.87496	0.937480	−	0.348039i	$-0.113152\pi$
$751$	51.3821	1.87496	0.937480	+	0.348039i	$0.113152\pi$
$752$	−72.4953	−2.64363
$753$	7.61918	0.277658
$754$	2.30487	0.0839384
$755$	3.49964	0.127365
$756$	13.7462	0.499945
$757$	4.90854	0.178404	0.0892019	−	0.996014i	$-0.471568\pi$
$757$	4.90854	0.178404	0.0892019	+	0.996014i	$0.471568\pi$
$758$	−63.8342	−2.31856
$759$	−5.78726	−0.210064
$760$	98.8344	3.58510
$761$	4.18004	0.151526	0.0757632	−	0.997126i	$-0.475861\pi$
$761$	4.18004	0.151526	0.0757632	+	0.997126i	$0.475861\pi$
$762$	−0.744954	−0.0269868
$763$	−7.01222	−0.253859
$764$	−122.792	−4.44247
$765$	−21.1623	−0.765123
$766$	−10.7133	−0.387086
$767$	−14.2942	−0.516134
$768$	11.1206	0.401281
$769$	22.7725	0.821197	0.410599	−	0.911816i	$-0.365320\pi$
$769$	22.7725	0.821197	0.410599	+	0.911816i	$0.365320\pi$
$770$	−30.2455	−1.08997
$771$	−0.519415	−0.0187063
$772$	67.6900	2.43622
$773$	−15.0922	−0.542828	−0.271414	−	0.962463i	$-0.587491\pi$
$773$	−15.0922	−0.542828	−0.271414	+	0.962463i	$0.587491\pi$
$774$	2.88981	0.103872
$775$	42.5577	1.52872
$776$	84.1960	3.02246
$777$	−6.45536	−0.231585
$778$	65.2211	2.33829
$779$	36.7141	1.31542
$780$	88.9301	3.18421
$781$	−1.46224	−0.0523231
$782$	−78.3301	−2.80108
$783$	−0.148574	−0.00530961
$784$	8.59466	0.306952
$785$	−39.8179	−1.42116
$786$	28.7442	1.02527
$787$	20.6408	0.735765	0.367883	−	0.929872i	$-0.380083\pi$
$787$	20.6408	0.735765	0.367883	+	0.929872i	$0.380083\pi$
$788$	61.8853	2.20457
$789$	−22.5254	−0.801926
$790$	48.3753	1.72112
$791$	17.4013	0.618721
$792$	10.2504	0.364234
$793$	90.2694	3.20556
$794$	−7.92694	−0.281317
$795$	−33.7653	−1.19753
$796$	21.9653	0.778539
$797$	−47.9358	−1.69797	−0.848987	−	0.528415i	$-0.822787\pi$
$797$	−47.9358	−1.69797	−0.848987	+	0.528415i	$0.822787\pi$
$798$	30.9694	1.09630
$799$	48.5579	1.71786
$800$	−51.9452	−1.83654
$801$	−2.96909	−0.104908
$802$	2.55531	0.0902311
$803$	−4.10892	−0.145001
$804$	−17.8617	−0.629934
$805$	37.1110	1.30799
$806$	149.484	5.26534
$807$	−19.4180	−0.683546
$808$	−109.187	−3.84119
$809$	17.0828	0.600599	0.300299	−	0.953845i	$-0.402913\pi$
$809$	17.0828	0.600599	0.300299	+	0.953845i	$0.402913\pi$
$810$	−8.06710	−0.283449
$811$	3.21572	0.112919	0.0564596	−	0.998405i	$-0.482019\pi$
$811$	3.21572	0.112919	0.0564596	+	0.998405i	$0.482019\pi$
$812$	−2.04233	−0.0716718
$813$	9.15195	0.320973
$814$	−8.12097	−0.284640
$815$	45.5424	1.59528
$816$	71.0036	2.48562
$817$	4.62645	0.161859
$818$	−30.6066	−1.07014
$819$	16.5175	0.577169
$820$	−131.462	−4.59085
$821$	−20.2180	−0.705612	−0.352806	−	0.935696i	$-0.614772\pi$
$821$	−20.2180	−0.705612	−0.352806	+	0.935696i	$0.614772\pi$
$822$	−34.8556	−1.21573
$823$	8.00907	0.279179	0.139589	−	0.990209i	$-0.455422\pi$
$823$	8.00907	0.279179	0.139589	+	0.990209i	$0.455422\pi$
$824$	152.481	5.31194
$825$	5.91585	0.205963
$826$	17.8242	0.620185
$827$	23.7895	0.827243	0.413622	−	0.910449i	$-0.364264\pi$
$827$	23.7895	0.827243	0.413622	+	0.910449i	$0.364264\pi$
$828$	−21.2184	−0.737391
$829$	−52.0347	−1.80724	−0.903620	−	0.428335i	$-0.859100\pi$
$829$	−52.0347	−1.80724	−0.903620	+	0.428335i	$0.859100\pi$
$830$	48.4396	1.68136
$831$	−26.0506	−0.903686
$832$	−60.9429	−2.11281
$833$	−5.75678	−0.199461
$834$	−37.7196	−1.30612
$835$	49.0354	1.69694
$836$	27.6853	0.957515
$837$	−9.63587	−0.333064
$838$	1.56981	0.0542280
$839$	−55.1350	−1.90347	−0.951735	−	0.306920i	$-0.900702\pi$
$839$	−55.1350	−1.90347	−0.951735	+	0.306920i	$0.900702\pi$
$840$	−65.7313	−2.26795
$841$	−28.9779	−0.999239
$842$	−54.8881	−1.89157
$843$	13.2776	0.457306
$844$	32.6839	1.12503
$845$	66.9667	2.30372
$846$	18.5104	0.636400
$847$	25.7678	0.885391
$848$	113.289	3.89037
$849$	−16.8825	−0.579407
$850$	80.0705	2.74640
$851$	9.96439	0.341575
$852$	−5.36116	−0.183670
$853$	36.1783	1.23872	0.619361	−	0.785106i	$-0.287392\pi$
$853$	36.1783	1.23872	0.619361	+	0.785106i	$0.287392\pi$
$854$	−112.562	−3.85179
$855$	−12.9150	−0.441685
$856$	−21.1403	−0.722562
$857$	−35.2246	−1.20325	−0.601624	−	0.798779i	$-0.705479\pi$
$857$	−35.2246	−1.20325	−0.601624	+	0.798779i	$0.705479\pi$
$858$	20.7794	0.709397
$859$	28.0626	0.957483	0.478742	−	0.877956i	$-0.341093\pi$
$859$	28.0626	0.957483	0.478742	+	0.877956i	$0.341093\pi$
$860$	−16.5659	−0.564893
$861$	−24.4172	−0.832138
$862$	61.4751	2.09385
$863$	−37.6219	−1.28067	−0.640333	−	0.768098i	$-0.721204\pi$
$863$	−37.6219	−1.28067	−0.640333	+	0.768098i	$0.721204\pi$
$864$	11.7614	0.400130
$865$	13.0667	0.444282
$866$	61.4532	2.08826
$867$	−30.5588	−1.03783
$868$	−132.457	−4.49587
$869$	8.03223	0.272475
$870$	1.19856	0.0406351
$871$	−21.4628	−0.727238
$872$	−19.1714	−0.649227
$873$	−11.0022	−0.372368
$874$	−47.8038	−1.61699
$875$	5.01111	0.169407
$876$	−15.0649	−0.508997
$877$	16.4710	0.556186	0.278093	−	0.960554i	$-0.410298\pi$
$877$	16.4710	0.556186	0.278093	+	0.960554i	$0.410298\pi$
$878$	48.4415	1.63482
$879$	28.1084	0.948073
$880$	−42.3196	−1.42659
$881$	40.6458	1.36939	0.684696	−	0.728829i	$-0.259935\pi$
$881$	40.6458	1.36939	0.684696	+	0.728829i	$0.259935\pi$
$882$	−2.19449	−0.0738925
$883$	44.4007	1.49420	0.747101	−	0.664711i	$-0.231445\pi$
$883$	44.4007	1.49420	0.747101	+	0.664711i	$0.231445\pi$
$884$	199.856	6.72189
$885$	−7.43318	−0.249864
$886$	−72.9237	−2.44992
$887$	−39.5498	−1.32795	−0.663976	−	0.747754i	$-0.731132\pi$
$887$	−39.5498	−1.32795	−0.663976	+	0.747754i	$0.731132\pi$
$888$	−17.6490	−0.592262
$889$	0.793180	0.0266024
$890$	23.9520	0.802872
$891$	−1.33946	−0.0448736
$892$	−131.380	−4.39893
$893$	29.6342	0.991672
$894$	21.1324	0.706772
$895$	61.0726	2.04143
$896$	10.1514	0.339134
$897$	−25.4962	−0.851293
$898$	1.90478	0.0635633
$899$	1.43164	0.0477479
$900$	21.6899	0.722995
$901$	−75.8820	−2.52800
$902$	−30.7174	−1.02278
$903$	−3.07689	−0.102393
$904$	47.5754	1.58233
$905$	35.7020	1.18677
$906$	2.99811	0.0996055
$907$	18.7158	0.621448	0.310724	−	0.950500i	$-0.399429\pi$
$907$	18.7158	0.621448	0.310724	+	0.950500i	$0.399429\pi$
$908$	84.4324	2.80199
$909$	14.2679	0.473236
$910$	−133.249	−4.41715
$911$	34.6163	1.14689	0.573445	−	0.819244i	$-0.305606\pi$
$911$	34.6163	1.14689	0.573445	+	0.819244i	$0.305606\pi$
$912$	43.3325	1.43488
$913$	8.04291	0.266182
$914$	35.9059	1.18766
$915$	46.9413	1.55183
$916$	−77.8057	−2.57077
$917$	−30.6051	−1.01067
$918$	−18.1295	−0.598362
$919$	26.8918	0.887080	0.443540	−	0.896255i	$-0.353722\pi$
$919$	26.8918	0.887080	0.443540	+	0.896255i	$0.353722\pi$
$920$	101.462	3.34509
$921$	32.7721	1.07988
$922$	−39.6876	−1.30704
$923$	−6.44201	−0.212041
$924$	−18.4125	−0.605727
$925$	−10.1858	−0.334907
$926$	−30.9095	−1.01575
$927$	−19.9253	−0.654432
$928$	−1.74744	−0.0573624
$929$	51.4099	1.68671	0.843353	−	0.537360i	$-0.180578\pi$
$929$	51.4099	1.68671	0.843353	+	0.537360i	$0.180578\pi$
$930$	77.7335	2.54898
$931$	−3.51328	−0.115143
$932$	47.2006	1.54611
$933$	−23.9215	−0.783156
$934$	15.2206	0.498032
$935$	28.3460	0.927014
$936$	45.1590	1.47607
$937$	32.0728	1.04777	0.523886	−	0.851788i	$-0.324482\pi$
$937$	32.0728	1.04777	0.523886	+	0.851788i	$0.324482\pi$
$938$	26.7631	0.873847
$939$	1.91506	0.0624956
$940$	−106.111	−3.46097
$941$	−9.66015	−0.314912	−0.157456	−	0.987526i	$-0.550329\pi$
$941$	−9.66015	−0.314912	−0.157456	+	0.987526i	$0.550329\pi$
$942$	−34.1116	−1.11142
$943$	37.6901	1.22736
$944$	24.9398	0.811721
$945$	8.58934	0.279411
$946$	−3.87079	−0.125850
$947$	34.2296	1.11231	0.556157	−	0.831077i	$-0.312275\pi$
$947$	34.2296	1.11231	0.556157	+	0.831077i	$0.312275\pi$
$948$	29.4494	0.956471
$949$	−18.1021	−0.587621
$950$	48.8659	1.58542
$951$	2.22720	0.0722219
$952$	−147.720	−4.78765
$953$	−33.3740	−1.08109	−0.540545	−	0.841315i	$-0.681782\pi$
$953$	−33.3740	−1.08109	−0.540545	+	0.841315i	$0.681782\pi$
$954$	−28.9264	−0.936526
$955$	−76.7269	−2.48282
$956$	−3.95909	−0.128046
$957$	0.199009	0.00643306
$958$	9.39506	0.303541
$959$	37.1121	1.19841
$960$	−31.6911	−1.02283
$961$	61.8500	1.99516
$962$	−35.7775	−1.15351
$963$	2.76248	0.0890198
$964$	−102.808	−3.31124
$965$	42.2962	1.36156
$966$	31.7926	1.02291
$967$	22.5173	0.724109	0.362054	−	0.932157i	$-0.382075\pi$
$967$	22.5173	0.724109	0.362054	+	0.932157i	$0.382075\pi$
$968$	70.4492	2.26432
$969$	−29.0245	−0.932400
$970$	88.7557	2.84977
$971$	−39.5306	−1.26860	−0.634298	−	0.773089i	$-0.718711\pi$
$971$	−39.5306	−1.26860	−0.634298	+	0.773089i	$0.718711\pi$
$972$	−4.91100	−0.157520
$973$	40.1615	1.28752
$974$	26.4100	0.846229
$975$	26.0627	0.834674
$976$	−157.497	−5.04136
$977$	25.3754	0.811830	0.405915	−	0.913911i	$-0.366953\pi$
$977$	25.3754	0.811830	0.405915	+	0.913911i	$0.366953\pi$
$978$	39.0157	1.24758
$979$	3.97699	0.127105
$980$	12.5800	0.401853
$981$	2.50520	0.0799849
$982$	−8.35697	−0.266681
$983$	14.5956	0.465529	0.232764	−	0.972533i	$-0.425223\pi$
$983$	14.5956	0.465529	0.232764	+	0.972533i	$0.425223\pi$
$984$	−66.7569	−2.12813
$985$	38.6691	1.23210
$986$	2.69358	0.0857809
$987$	−19.7087	−0.627335
$988$	121.969	3.88036
$989$	4.74944	0.151023
$990$	10.8056	0.343423
$991$	−1.51900	−0.0482526	−0.0241263	−	0.999709i	$-0.507680\pi$
$991$	−1.51900	−0.0482526	−0.0241263	+	0.999709i	$0.507680\pi$
$992$	−113.331	−3.59827
$993$	13.3695	0.424268
$994$	8.03290	0.254788
$995$	13.7251	0.435114
$996$	29.4885	0.934379
$997$	35.7551	1.13237	0.566187	−	0.824277i	$-0.308418\pi$
$997$	35.7551	1.13237	0.566187	+	0.824277i	$0.308418\pi$
$998$	22.2033	0.702832
$999$	2.30626	0.0729667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.6	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.6	✓	119	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62888 q^{2} -1.00000 q^{3} +4.91100 q^{4} +3.06865 q^{5} +2.62888 q^{6} -2.79906 q^{7} -7.65266 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.62888 q^{2} -1.00000 q^{3} +4.91100 q^{4} +3.06865 q^{5} +2.62888 q^{6} -2.79906 q^{7} -7.65266 q^{8} +1.00000 q^{9} -8.06710 q^{10} -1.33946 q^{11} -4.91100 q^{12} -5.90109 q^{13} +7.35840 q^{14} -3.06865 q^{15} +10.2959 q^{16} -6.89629 q^{17} -2.62888 q^{18} -4.20871 q^{19} +15.0701 q^{20} +2.79906 q^{21} +3.52128 q^{22} -4.32059 q^{23} +7.65266 q^{24} +4.41659 q^{25} +15.5132 q^{26} -1.00000 q^{27} -13.7462 q^{28} +0.148574 q^{29} +8.06710 q^{30} +9.63587 q^{31} -11.7614 q^{32} +1.33946 q^{33} +18.1295 q^{34} -8.58934 q^{35} +4.91100 q^{36} -2.30626 q^{37} +11.0642 q^{38} +5.90109 q^{39} -23.4833 q^{40} -8.72336 q^{41} -7.35840 q^{42} -1.09926 q^{43} -6.57809 q^{44} +3.06865 q^{45} +11.3583 q^{46} -7.04117 q^{47} -10.2959 q^{48} +0.834765 q^{49} -11.6107 q^{50} +6.89629 q^{51} -28.9803 q^{52} +11.0033 q^{53} +2.62888 q^{54} -4.11033 q^{55} +21.4203 q^{56} +4.20871 q^{57} -0.390583 q^{58} +2.42230 q^{59} -15.0701 q^{60} -15.2971 q^{61} -25.3315 q^{62} -2.79906 q^{63} +10.3274 q^{64} -18.1084 q^{65} -3.52128 q^{66} +3.63709 q^{67} -33.8677 q^{68} +4.32059 q^{69} +22.5803 q^{70} +1.09166 q^{71} -7.65266 q^{72} +3.06759 q^{73} +6.06287 q^{74} -4.41659 q^{75} -20.6690 q^{76} +3.74924 q^{77} -15.5132 q^{78} -5.99662 q^{79} +31.5945 q^{80} +1.00000 q^{81} +22.9326 q^{82} -6.00459 q^{83} +13.7462 q^{84} -21.1623 q^{85} +2.88981 q^{86} -0.148574 q^{87} +10.2504 q^{88} -2.96909 q^{89} -8.06710 q^{90} +16.5175 q^{91} -21.2184 q^{92} -9.63587 q^{93} +18.5104 q^{94} -12.9150 q^{95} +11.7614 q^{96} -11.0022 q^{97} -2.19449 q^{98} -1.33946 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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