LMFDB - Embedded newform 6019.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34535 q^{2} -1.65067 q^{3} +3.50065 q^{4} -1.17678 q^{5} +3.87140 q^{6} +2.05341 q^{7} -3.51955 q^{8} -0.275278 q^{9} +O(q^{10})$	\(q-2.34535 q^{2} -1.65067 q^{3} +3.50065 q^{4} -1.17678 q^{5} +3.87140 q^{6} +2.05341 q^{7} -3.51955 q^{8} -0.275278 q^{9} +2.75996 q^{10} +3.35882 q^{11} -5.77843 q^{12} -1.00000 q^{13} -4.81595 q^{14} +1.94248 q^{15} +1.25326 q^{16} +4.47018 q^{17} +0.645622 q^{18} +7.77434 q^{19} -4.11949 q^{20} -3.38950 q^{21} -7.87759 q^{22} -7.71657 q^{23} +5.80962 q^{24} -3.61519 q^{25} +2.34535 q^{26} +5.40641 q^{27} +7.18826 q^{28} +1.46185 q^{29} -4.55578 q^{30} -3.68184 q^{31} +4.09977 q^{32} -5.54431 q^{33} -10.4841 q^{34} -2.41640 q^{35} -0.963653 q^{36} +6.86030 q^{37} -18.2335 q^{38} +1.65067 q^{39} +4.14173 q^{40} -4.73919 q^{41} +7.94956 q^{42} +4.69953 q^{43} +11.7581 q^{44} +0.323941 q^{45} +18.0980 q^{46} -9.86429 q^{47} -2.06872 q^{48} -2.78353 q^{49} +8.47888 q^{50} -7.37880 q^{51} -3.50065 q^{52} -4.33860 q^{53} -12.6799 q^{54} -3.95259 q^{55} -7.22706 q^{56} -12.8329 q^{57} -3.42855 q^{58} +0.235407 q^{59} +6.79994 q^{60} -0.187165 q^{61} +8.63518 q^{62} -0.565257 q^{63} -12.1219 q^{64} +1.17678 q^{65} +13.0033 q^{66} +1.31340 q^{67} +15.6485 q^{68} +12.7375 q^{69} +5.66731 q^{70} -7.95224 q^{71} +0.968855 q^{72} -1.12431 q^{73} -16.0898 q^{74} +5.96750 q^{75} +27.2153 q^{76} +6.89702 q^{77} -3.87140 q^{78} -8.42207 q^{79} -1.47481 q^{80} -8.09839 q^{81} +11.1150 q^{82} +16.3277 q^{83} -11.8655 q^{84} -5.26041 q^{85} -11.0220 q^{86} -2.41304 q^{87} -11.8215 q^{88} -13.9408 q^{89} -0.759755 q^{90} -2.05341 q^{91} -27.0130 q^{92} +6.07751 q^{93} +23.1352 q^{94} -9.14868 q^{95} -6.76738 q^{96} +14.7783 q^{97} +6.52833 q^{98} -0.924609 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * 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 $

$2$	−2.34535	−1.65841	−0.829205	−	0.558944i	$-0.811207\pi$
$2$	−2.34535	−1.65841	−0.829205	+	0.558944i	$0.811207\pi$
$3$	−1.65067	−0.953017	−0.476508	−	0.879170i	$-0.658098\pi$
$3$	−1.65067	−0.953017	−0.476508	+	0.879170i	$0.658098\pi$
$4$	3.50065	1.75033
$5$	−1.17678	−0.526272	−0.263136	−	0.964759i	$-0.584757\pi$
$5$	−1.17678	−0.526272	−0.263136	+	0.964759i	$0.584757\pi$
$6$	3.87140	1.58049
$7$	2.05341	0.776114	0.388057	−	0.921635i	$-0.373146\pi$
$7$	2.05341	0.776114	0.388057	+	0.921635i	$0.373146\pi$
$8$	−3.51955	−1.24435
$9$	−0.275278	−0.0917593
$10$	2.75996	0.872774
$11$	3.35882	1.01272	0.506361	−	0.862322i	$-0.330990\pi$
$11$	3.35882	1.01272	0.506361	+	0.862322i	$0.330990\pi$
$12$	−5.77843	−1.66809
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.81595	−1.28712
$15$	1.94248	0.501546
$16$	1.25326	0.313315
$17$	4.47018	1.08418	0.542089	−	0.840321i	$-0.317634\pi$
$17$	4.47018	1.08418	0.542089	+	0.840321i	$0.317634\pi$
$18$	0.645622	0.152175
$19$	7.77434	1.78356	0.891778	−	0.452474i	$-0.149458\pi$
$19$	7.77434	1.78356	0.891778	+	0.452474i	$0.149458\pi$
$20$	−4.11949	−0.921147
$21$	−3.38950	−0.739650
$22$	−7.87759	−1.67951
$23$	−7.71657	−1.60902	−0.804508	−	0.593942i	$-0.797571\pi$
$23$	−7.71657	−1.60902	−0.804508	+	0.593942i	$0.797571\pi$
$24$	5.80962	1.18588
$25$	−3.61519	−0.723038
$26$	2.34535	0.459960
$27$	5.40641	1.04046
$28$	7.18826	1.35845
$29$	1.46185	0.271459	0.135730	−	0.990746i	$-0.456662\pi$
$29$	1.46185	0.271459	0.135730	+	0.990746i	$0.456662\pi$
$30$	−4.55578	−0.831769
$31$	−3.68184	−0.661277	−0.330639	−	0.943757i	$-0.607264\pi$
$31$	−3.68184	−0.661277	−0.330639	+	0.943757i	$0.607264\pi$
$32$	4.09977	0.724744
$33$	−5.54431	−0.965141
$34$	−10.4841	−1.79801
$35$	−2.41640	−0.408447
$36$	−0.963653	−0.160609
$37$	6.86030	1.12783	0.563913	−	0.825834i	$-0.309295\pi$
$37$	6.86030	1.12783	0.563913	+	0.825834i	$0.309295\pi$
$38$	−18.2335	−2.95787
$39$	1.65067	0.264319
$40$	4.14173	0.654865
$41$	−4.73919	−0.740136	−0.370068	−	0.929005i	$-0.620666\pi$
$41$	−4.73919	−0.740136	−0.370068	+	0.929005i	$0.620666\pi$
$42$	7.94956	1.22664
$43$	4.69953	0.716671	0.358335	−	0.933593i	$-0.383344\pi$
$43$	4.69953	0.716671	0.358335	+	0.933593i	$0.383344\pi$
$44$	11.7581	1.77259
$45$	0.323941	0.0482903
$46$	18.0980	2.66841
$47$	−9.86429	−1.43885	−0.719427	−	0.694568i	$-0.755596\pi$
$47$	−9.86429	−1.43885	−0.719427	+	0.694568i	$0.755596\pi$
$48$	−2.06872	−0.298594
$49$	−2.78353	−0.397646
$50$	8.47888	1.19909
$51$	−7.37880	−1.03324
$52$	−3.50065	−0.485453
$53$	−4.33860	−0.595952	−0.297976	−	0.954573i	$-0.596312\pi$
$53$	−4.33860	−0.595952	−0.297976	+	0.954573i	$0.596312\pi$
$54$	−12.6799	−1.72552
$55$	−3.95259	−0.532967
$56$	−7.22706	−0.965757
$57$	−12.8329	−1.69976
$58$	−3.42855	−0.450191
$59$	0.235407	0.0306474	0.0153237	−	0.999883i	$-0.495122\pi$
$59$	0.235407	0.0306474	0.0153237	+	0.999883i	$0.495122\pi$
$60$	6.79994	0.877868
$61$	−0.187165	−0.0239640	−0.0119820	−	0.999928i	$-0.503814\pi$
$61$	−0.187165	−0.0239640	−0.0119820	+	0.999928i	$0.503814\pi$
$62$	8.63518	1.09667
$63$	−0.565257	−0.0712157
$64$	−12.1219	−1.51524
$65$	1.17678	0.145961
$66$	13.0033	1.60060
$67$	1.31340	0.160458	0.0802289	−	0.996776i	$-0.474435\pi$
$67$	1.31340	0.160458	0.0802289	+	0.996776i	$0.474435\pi$
$68$	15.6485	1.89766
$69$	12.7375	1.53342
$70$	5.66731	0.677373
$71$	−7.95224	−0.943758	−0.471879	−	0.881663i	$-0.656424\pi$
$71$	−7.95224	−0.943758	−0.471879	+	0.881663i	$0.656424\pi$
$72$	0.968855	0.114181
$73$	−1.12431	−0.131590	−0.0657950	−	0.997833i	$-0.520958\pi$
$73$	−1.12431	−0.131590	−0.0657950	+	0.997833i	$0.520958\pi$
$74$	−16.0898	−1.87040
$75$	5.96750	0.689067
$76$	27.2153	3.12180
$77$	6.89702	0.785988
$78$	−3.87140	−0.438350
$79$	−8.42207	−0.947556	−0.473778	−	0.880644i	$-0.657110\pi$
$79$	−8.42207	−0.947556	−0.473778	+	0.880644i	$0.657110\pi$
$80$	−1.47481	−0.164889
$81$	−8.09839	−0.899821
$82$	11.1150	1.22745
$83$	16.3277	1.79220	0.896100	−	0.443853i	$-0.146389\pi$
$83$	16.3277	1.79220	0.896100	+	0.443853i	$0.146389\pi$
$84$	−11.8655	−1.29463
$85$	−5.26041	−0.570572
$86$	−11.0220	−1.18853
$87$	−2.41304	−0.258705
$88$	−11.8215	−1.26018
$89$	−13.9408	−1.47772	−0.738860	−	0.673859i	$-0.764636\pi$
$89$	−13.9408	−1.47772	−0.738860	+	0.673859i	$0.764636\pi$
$90$	−0.759755	−0.0800852
$91$	−2.05341	−0.215255
$92$	−27.0130	−2.81630
$93$	6.07751	0.630208
$94$	23.1352	2.38621
$95$	−9.14868	−0.938635
$96$	−6.76738	−0.690693
$97$	14.7783	1.50051	0.750257	−	0.661147i	$-0.229930\pi$
$97$	14.7783	1.50051	0.750257	+	0.661147i	$0.229930\pi$
$98$	6.52833	0.659461
$99$	−0.924609	−0.0929267
$100$	−12.6555	−1.26555
$101$	−18.8061	−1.87128	−0.935640	−	0.352957i	$-0.885176\pi$
$101$	−18.8061	−1.87128	−0.935640	+	0.352957i	$0.885176\pi$
$102$	17.3059	1.71353
$103$	−16.7076	−1.64625	−0.823124	−	0.567862i	$-0.807771\pi$
$103$	−16.7076	−1.64625	−0.823124	+	0.567862i	$0.807771\pi$
$104$	3.51955	0.345120
$105$	3.98869	0.389257
$106$	10.1755	0.988334
$107$	−8.30921	−0.803282	−0.401641	−	0.915797i	$-0.631560\pi$
$107$	−8.30921	−0.803282	−0.401641	+	0.915797i	$0.631560\pi$
$108$	18.9260	1.82115
$109$	9.20099	0.881295	0.440648	−	0.897680i	$-0.354749\pi$
$109$	9.20099	0.881295	0.440648	+	0.897680i	$0.354749\pi$
$110$	9.27019	0.883878
$111$	−11.3241	−1.07484
$112$	2.57345	0.243168
$113$	11.6455	1.09551	0.547757	−	0.836638i	$-0.315482\pi$
$113$	11.6455	1.09551	0.547757	+	0.836638i	$0.315482\pi$
$114$	30.0976	2.81890
$115$	9.08069	0.846779
$116$	5.11744	0.475142
$117$	0.275278	0.0254495
$118$	−0.552111	−0.0508259
$119$	9.17909	0.841446
$120$	−6.83664	−0.624097
$121$	0.281657	0.0256052
$122$	0.438967	0.0397422
$123$	7.82285	0.705362
$124$	−12.8888	−1.15745
$125$	10.1382	0.906786
$126$	1.32572	0.118105
$127$	−4.31315	−0.382730	−0.191365	−	0.981519i	$-0.561291\pi$
$127$	−4.31315	−0.382730	−0.191365	+	0.981519i	$0.561291\pi$
$128$	20.2305	1.78814
$129$	−7.75738	−0.682999
$130$	−2.75996	−0.242064
$131$	−8.61452	−0.752654	−0.376327	−	0.926487i	$-0.622813\pi$
$131$	−8.61452	−0.752654	−0.376327	+	0.926487i	$0.622813\pi$
$132$	−19.4087	−1.68931
$133$	15.9639	1.38424
$134$	−3.08039	−0.266105
$135$	−6.36215	−0.547567
$136$	−15.7330	−1.34909
$137$	−7.75851	−0.662854	−0.331427	−	0.943481i	$-0.607530\pi$
$137$	−7.75851	−0.662854	−0.331427	+	0.943481i	$0.607530\pi$
$138$	−29.8739	−2.54304
$139$	15.5249	1.31681	0.658404	−	0.752665i	$-0.271232\pi$
$139$	15.5249	1.31681	0.658404	+	0.752665i	$0.271232\pi$
$140$	−8.45899	−0.714915
$141$	16.2827	1.37125
$142$	18.6508	1.56514
$143$	−3.35882	−0.280878
$144$	−0.344995	−0.0287496
$145$	−1.72028	−0.142861
$146$	2.63689	0.218230
$147$	4.59469	0.378964
$148$	24.0155	1.97406
$149$	4.85569	0.397794	0.198897	−	0.980020i	$-0.436264\pi$
$149$	4.85569	0.397794	0.198897	+	0.980020i	$0.436264\pi$
$150$	−13.9959	−1.14276
$151$	−16.5480	−1.34666	−0.673330	−	0.739342i	$-0.735136\pi$
$151$	−16.5480	−1.34666	−0.673330	+	0.739342i	$0.735136\pi$
$152$	−27.3622	−2.21936
$153$	−1.23054	−0.0994834
$154$	−16.1759	−1.30349
$155$	4.33271	0.348012
$156$	5.77843	0.462645
$157$	−20.7001	−1.65205	−0.826023	−	0.563636i	$-0.809402\pi$
$157$	−20.7001	−1.65205	−0.826023	+	0.563636i	$0.809402\pi$
$158$	19.7527	1.57144
$159$	7.16161	0.567953
$160$	−4.82452	−0.381412
$161$	−15.8452	−1.24878
$162$	18.9935	1.49227
$163$	6.13774	0.480745	0.240372	−	0.970681i	$-0.422730\pi$
$163$	6.13774	0.480745	0.240372	+	0.970681i	$0.422730\pi$
$164$	−16.5902	−1.29548
$165$	6.52443	0.507926
$166$	−38.2942	−2.97220
$167$	−16.8358	−1.30279	−0.651396	−	0.758738i	$-0.725816\pi$
$167$	−16.8358	−1.30279	−0.651396	+	0.758738i	$0.725816\pi$
$168$	11.9295	0.920382
$169$	1.00000	0.0769231
$170$	12.3375	0.946242
$171$	−2.14010	−0.163658
$172$	16.4514	1.25441
$173$	19.0864	1.45111	0.725556	−	0.688164i	$-0.241583\pi$
$173$	19.0864	1.45111	0.725556	+	0.688164i	$0.241583\pi$
$174$	5.65942	0.429039
$175$	−7.42345	−0.561160
$176$	4.20947	0.317301
$177$	−0.388580	−0.0292074
$178$	32.6960	2.45067
$179$	−10.3164	−0.771082	−0.385541	−	0.922691i	$-0.625985\pi$
$179$	−10.3164	−0.771082	−0.385541	+	0.922691i	$0.625985\pi$
$180$	1.13401	0.0845238
$181$	10.3258	0.767509	0.383755	−	0.923435i	$-0.374631\pi$
$181$	10.3258	0.767509	0.383755	+	0.923435i	$0.374631\pi$
$182$	4.81595	0.356982
$183$	0.308949	0.0228381
$184$	27.1588	2.00218
$185$	−8.07306	−0.593543
$186$	−14.2539	−1.04514
$187$	15.0145	1.09797
$188$	−34.5314	−2.51846
$189$	11.1016	0.807520
$190$	21.4568	1.55664
$191$	22.4150	1.62190	0.810948	−	0.585118i	$-0.198952\pi$
$191$	22.4150	1.62190	0.810948	+	0.585118i	$0.198952\pi$
$192$	20.0093	1.44405
$193$	18.3953	1.32412	0.662061	−	0.749450i	$-0.269682\pi$
$193$	18.3953	1.32412	0.662061	+	0.749450i	$0.269682\pi$
$194$	−34.6603	−2.48847
$195$	−1.94248	−0.139104
$196$	−9.74415	−0.696011
$197$	−0.515714	−0.0367431	−0.0183715	−	0.999831i	$-0.505848\pi$
$197$	−0.515714	−0.0367431	−0.0183715	+	0.999831i	$0.505848\pi$
$198$	2.16853	0.154111
$199$	0.637140	0.0451656	0.0225828	−	0.999745i	$-0.492811\pi$
$199$	0.637140	0.0451656	0.0225828	+	0.999745i	$0.492811\pi$
$200$	12.7238	0.899711
$201$	−2.16800	−0.152919
$202$	44.1069	3.10335
$203$	3.00178	0.210683
$204$	−25.8306	−1.80851
$205$	5.57697	0.389513
$206$	39.1851	2.73016
$207$	2.12420	0.147642
$208$	−1.25326	−0.0868979
$209$	26.1126	1.80625
$210$	−9.35487	−0.645547
$211$	−5.19925	−0.357931	−0.178965	−	0.983855i	$-0.557275\pi$
$211$	−5.19925	−0.357931	−0.178965	+	0.983855i	$0.557275\pi$
$212$	−15.1879	−1.04311
$213$	13.1266	0.899417
$214$	19.4880	1.33217
$215$	−5.53030	−0.377164
$216$	−19.0281	−1.29470
$217$	−7.56030	−0.513227
$218$	−21.5795	−1.46155
$219$	1.85586	0.125407
$220$	−13.8366	−0.932865
$221$	−4.47018	−0.300697
$222$	26.5590	1.78252
$223$	10.0622	0.673811	0.336906	−	0.941538i	$-0.390620\pi$
$223$	10.0622	0.673811	0.336906	+	0.941538i	$0.390620\pi$
$224$	8.41849	0.562484
$225$	0.995183	0.0663455
$226$	−27.3127	−1.81681
$227$	−4.70794	−0.312477	−0.156239	−	0.987719i	$-0.549937\pi$
$227$	−4.70794	−0.312477	−0.156239	+	0.987719i	$0.549937\pi$
$228$	−44.9235	−2.97513
$229$	20.1233	1.32978	0.664891	−	0.746940i	$-0.268478\pi$
$229$	20.1233	1.32978	0.664891	+	0.746940i	$0.268478\pi$
$230$	−21.2974	−1.40431
$231$	−11.3847	−0.749059
$232$	−5.14506	−0.337790
$233$	2.30660	0.151110	0.0755551	−	0.997142i	$-0.475927\pi$
$233$	2.30660	0.151110	0.0755551	+	0.997142i	$0.475927\pi$
$234$	−0.645622	−0.0422057
$235$	11.6081	0.757228
$236$	0.824078	0.0536429
$237$	13.9021	0.903037
$238$	−21.5281	−1.39546
$239$	1.72415	0.111526	0.0557630	−	0.998444i	$-0.482241\pi$
$239$	1.72415	0.111526	0.0557630	+	0.998444i	$0.482241\pi$
$240$	2.43443	0.157142
$241$	−11.0609	−0.712495	−0.356247	−	0.934392i	$-0.615944\pi$
$241$	−11.0609	−0.712495	−0.356247	+	0.934392i	$0.615944\pi$
$242$	−0.660584	−0.0424640
$243$	−2.85145	−0.182921
$244$	−0.655200	−0.0419449
$245$	3.27559	0.209270
$246$	−18.3473	−1.16978
$247$	−7.77434	−0.494669
$248$	12.9584	0.822860
$249$	−26.9517	−1.70800
$250$	−23.7775	−1.50382
$251$	−7.59593	−0.479451	−0.239725	−	0.970841i	$-0.577057\pi$
$251$	−7.59593	−0.479451	−0.239725	+	0.970841i	$0.577057\pi$
$252$	−1.97877	−0.124651
$253$	−25.9185	−1.62948
$254$	10.1158	0.634724
$255$	8.68322	0.543764
$256$	−23.2038	−1.45024
$257$	5.40333	0.337050	0.168525	−	0.985697i	$-0.446100\pi$
$257$	5.40333	0.337050	0.168525	+	0.985697i	$0.446100\pi$
$258$	18.1937	1.13269
$259$	14.0870	0.875322
$260$	4.11949	0.255480
$261$	−0.402416	−0.0249089
$262$	20.2040	1.24821
$263$	−8.13411	−0.501570	−0.250785	−	0.968043i	$-0.580689\pi$
$263$	−8.13411	−0.501570	−0.250785	+	0.968043i	$0.580689\pi$
$264$	19.5135	1.20097
$265$	5.10557	0.313633
$266$	−37.4408	−2.29564
$267$	23.0117	1.40829
$268$	4.59777	0.280854
$269$	−15.9763	−0.974095	−0.487048	−	0.873375i	$-0.661926\pi$
$269$	−15.9763	−0.974095	−0.487048	+	0.873375i	$0.661926\pi$
$270$	14.9215	0.908091
$271$	21.1591	1.28532	0.642662	−	0.766150i	$-0.277830\pi$
$271$	21.1591	1.28532	0.642662	+	0.766150i	$0.277830\pi$
$272$	5.60229	0.339689
$273$	3.38950	0.205142
$274$	18.1964	1.09928
$275$	−12.1428	−0.732236
$276$	44.5896	2.68398
$277$	1.47859	0.0888399	0.0444199	−	0.999013i	$-0.485856\pi$
$277$	1.47859	0.0888399	0.0444199	+	0.999013i	$0.485856\pi$
$278$	−36.4114	−2.18381
$279$	1.01353	0.0606784
$280$	8.50465	0.508250
$281$	18.4673	1.10167	0.550834	−	0.834615i	$-0.314310\pi$
$281$	18.4673	1.10167	0.550834	+	0.834615i	$0.314310\pi$
$282$	−38.1886	−2.27410
$283$	−5.32122	−0.316314	−0.158157	−	0.987414i	$-0.550555\pi$
$283$	−5.32122	−0.316314	−0.158157	+	0.987414i	$0.550555\pi$
$284$	−27.8380	−1.65188
$285$	15.1015	0.894534
$286$	7.87759	0.465812
$287$	−9.73147	−0.574430
$288$	−1.12858	−0.0665020
$289$	2.98249	0.175441
$290$	4.03465	0.236923
$291$	−24.3942	−1.43001
$292$	−3.93580	−0.230325
$293$	−7.40227	−0.432445	−0.216223	−	0.976344i	$-0.569374\pi$
$293$	−7.40227	−0.432445	−0.216223	+	0.976344i	$0.569374\pi$
$294$	−10.7761	−0.628477
$295$	−0.277022	−0.0161288
$296$	−24.1452	−1.40341
$297$	18.1592	1.05370
$298$	−11.3883	−0.659705
$299$	7.71657	0.446260
$300$	20.8901	1.20609
$301$	9.65003	0.556219
$302$	38.8109	2.23331
$303$	31.0428	1.78336
$304$	9.74326	0.558814
$305$	0.220252	0.0126116
$306$	2.88605	0.164984
$307$	12.9999	0.741943	0.370971	−	0.928644i	$-0.379025\pi$
$307$	12.9999	0.741943	0.370971	+	0.928644i	$0.379025\pi$
$308$	24.1440	1.37573
$309$	27.5788	1.56890
$310$	−10.1617	−0.577146
$311$	−20.4378	−1.15892	−0.579460	−	0.815001i	$-0.696736\pi$
$311$	−20.4378	−1.15892	−0.579460	+	0.815001i	$0.696736\pi$
$312$	−5.80962	−0.328905
$313$	−3.72032	−0.210285	−0.105142	−	0.994457i	$-0.533530\pi$
$313$	−3.72032	−0.210285	−0.105142	+	0.994457i	$0.533530\pi$
$314$	48.5489	2.73977
$315$	0.665183	0.0374788
$316$	−29.4827	−1.65853
$317$	−0.799939	−0.0449291	−0.0224645	−	0.999748i	$-0.507151\pi$
$317$	−0.799939	−0.0449291	−0.0224645	+	0.999748i	$0.507151\pi$
$318$	−16.7965	−0.941898
$319$	4.91010	0.274913
$320$	14.2648	0.797427
$321$	13.7158	0.765541
$322$	37.1626	2.07099
$323$	34.7527	1.93369
$324$	−28.3496	−1.57498
$325$	3.61519	0.200535
$326$	−14.3951	−0.797273
$327$	−15.1878	−0.839889
$328$	16.6798	0.920988
$329$	−20.2554	−1.11672
$330$	−15.3020	−0.842350
$331$	8.15231	0.448092	0.224046	−	0.974579i	$-0.428073\pi$
$331$	8.15231	0.448092	0.224046	+	0.974579i	$0.428073\pi$
$332$	57.1576	3.13693
$333$	−1.88849	−0.103489
$334$	39.4857	2.16056
$335$	−1.54559	−0.0844444
$336$	−4.24792	−0.231743
$337$	27.5642	1.50152	0.750758	−	0.660577i	$-0.229688\pi$
$337$	27.5642	1.50152	0.750758	+	0.660577i	$0.229688\pi$
$338$	−2.34535	−0.127570
$339$	−19.2229	−1.04404
$340$	−18.4149	−0.998687
$341$	−12.3666	−0.669690
$342$	5.01929	0.271412
$343$	−20.0895	−1.08473
$344$	−16.5402	−0.891788
$345$	−14.9893	−0.806994
$346$	−44.7642	−2.40654
$347$	−7.70956	−0.413871	−0.206935	−	0.978355i	$-0.566349\pi$
$347$	−7.70956	−0.413871	−0.206935	+	0.978355i	$0.566349\pi$
$348$	−8.44722	−0.452818
$349$	−10.2107	−0.546565	−0.273283	−	0.961934i	$-0.588109\pi$
$349$	−10.2107	−0.546565	−0.273283	+	0.961934i	$0.588109\pi$
$350$	17.4106	0.930634
$351$	−5.40641	−0.288573
$352$	13.7704	0.733964
$353$	30.0421	1.59898	0.799491	−	0.600678i	$-0.205103\pi$
$353$	30.0421	1.59898	0.799491	+	0.600678i	$0.205103\pi$
$354$	0.911354	0.0484379
$355$	9.35803	0.496673
$356$	−48.8018	−2.58649
$357$	−15.1517	−0.801912
$358$	24.1955	1.27877
$359$	20.9090	1.10353	0.551767	−	0.833999i	$-0.313954\pi$
$359$	20.9090	1.10353	0.551767	+	0.833999i	$0.313954\pi$
$360$	−1.14013	−0.0600900
$361$	41.4403	2.18107
$362$	−24.2175	−1.27285
$363$	−0.464924	−0.0244022
$364$	−7.18826	−0.376767
$365$	1.32306	0.0692521
$366$	−0.724592	−0.0378750
$367$	22.4231	1.17048	0.585238	−	0.810862i	$-0.301001\pi$
$367$	22.4231	1.17048	0.585238	+	0.810862i	$0.301001\pi$
$368$	−9.67086	−0.504128
$369$	1.30459	0.0679144
$370$	18.9341	0.984338
$371$	−8.90890	−0.462527
$372$	21.2752	1.10307
$373$	17.8447	0.923963	0.461981	−	0.886890i	$-0.347139\pi$
$373$	17.8447	0.923963	0.461981	+	0.886890i	$0.347139\pi$
$374$	−35.2142	−1.82089
$375$	−16.7348	−0.864182
$376$	34.7179	1.79044
$377$	−1.46185	−0.0752892
$378$	−26.0370	−1.33920
$379$	20.2510	1.04023	0.520113	−	0.854098i	$-0.325890\pi$
$379$	20.2510	1.04023	0.520113	+	0.854098i	$0.325890\pi$
$380$	−32.0263	−1.64292
$381$	7.11960	0.364748
$382$	−52.5711	−2.68977
$383$	−30.1757	−1.54191	−0.770954	−	0.636891i	$-0.780220\pi$
$383$	−30.1757	−1.54191	−0.770954	+	0.636891i	$0.780220\pi$
$384$	−33.3940	−1.70413
$385$	−8.11626	−0.413643
$386$	−43.1433	−2.19594
$387$	−1.29368	−0.0657613
$388$	51.7338	2.62639
$389$	−12.7978	−0.648875	−0.324438	−	0.945907i	$-0.605175\pi$
$389$	−12.7978	−0.648875	−0.324438	+	0.945907i	$0.605175\pi$
$390$	4.55578	0.230691
$391$	−34.4944	−1.74446
$392$	9.79675	0.494811
$393$	14.2198	0.717292
$394$	1.20953	0.0609351
$395$	9.91091	0.498672
$396$	−3.23673	−0.162652
$397$	−6.97484	−0.350057	−0.175029	−	0.984563i	$-0.556002\pi$
$397$	−6.97484	−0.350057	−0.175029	+	0.984563i	$0.556002\pi$
$398$	−1.49431	−0.0749032
$399$	−26.3511	−1.31921
$400$	−4.53077	−0.226539
$401$	−32.7327	−1.63459	−0.817296	−	0.576218i	$-0.804528\pi$
$401$	−32.7327	−1.63459	−0.817296	+	0.576218i	$0.804528\pi$
$402$	5.08471	0.253602
$403$	3.68184	0.183405
$404$	−65.8337	−3.27535
$405$	9.53001	0.473550
$406$	−7.04021	−0.349400
$407$	23.0425	1.14217
$408$	25.9701	1.28571
$409$	−34.1250	−1.68737	−0.843686	−	0.536837i	$-0.819619\pi$
$409$	−34.1250	−1.68737	−0.843686	+	0.536837i	$0.819619\pi$
$410$	−13.0799	−0.645972
$411$	12.8068	0.631711
$412$	−58.4875	−2.88147
$413$	0.483386	0.0237859
$414$	−4.98199	−0.244851
$415$	−19.2141	−0.943184
$416$	−4.09977	−0.201008
$417$	−25.6266	−1.25494
$418$	−61.2431	−2.99550
$419$	−7.87824	−0.384877	−0.192439	−	0.981309i	$-0.561640\pi$
$419$	−7.87824	−0.384877	−0.192439	+	0.981309i	$0.561640\pi$
$420$	13.9630	0.681326
$421$	−10.3585	−0.504841	−0.252421	−	0.967618i	$-0.581227\pi$
$421$	−10.3585	−0.504841	−0.252421	+	0.967618i	$0.581227\pi$
$422$	12.1940	0.593597
$423$	2.71542	0.132028
$424$	15.2699	0.741572
$425$	−16.1605	−0.783902
$426$	−30.7863	−1.49160
$427$	−0.384326	−0.0185988
$428$	−29.0877	−1.40600
$429$	5.54431	0.267682
$430$	12.9705	0.625492
$431$	−40.9375	−1.97189	−0.985946	−	0.167066i	$-0.946571\pi$
$431$	−40.9375	−1.97189	−0.985946	+	0.167066i	$0.946571\pi$
$432$	6.77564	0.325993
$433$	−2.56626	−0.123326	−0.0616632	−	0.998097i	$-0.519640\pi$
$433$	−2.56626	−0.123326	−0.0616632	+	0.998097i	$0.519640\pi$
$434$	17.7315	0.851141
$435$	2.83962	0.136149
$436$	32.2095	1.54255
$437$	−59.9912	−2.86977
$438$	−4.35264	−0.207977
$439$	11.4464	0.546307	0.273154	−	0.961970i	$-0.411933\pi$
$439$	11.4464	0.546307	0.273154	+	0.961970i	$0.411933\pi$
$440$	13.9113	0.663196
$441$	0.766243	0.0364878
$442$	10.4841	0.498679
$443$	38.6806	1.83777	0.918885	−	0.394525i	$-0.129091\pi$
$443$	38.6806	1.83777	0.918885	+	0.394525i	$0.129091\pi$
$444$	−39.6418	−1.88131
$445$	16.4052	0.777682
$446$	−23.5992	−1.11746
$447$	−8.01516	−0.379104
$448$	−24.8912	−1.17600
$449$	−32.4700	−1.53236	−0.766178	−	0.642629i	$-0.777844\pi$
$449$	−32.4700	−1.53236	−0.766178	+	0.642629i	$0.777844\pi$
$450$	−2.33405	−0.110028
$451$	−15.9181	−0.749552
$452$	40.7667	1.91751
$453$	27.3154	1.28339
$454$	11.0418	0.518215
$455$	2.41640	0.113283
$456$	45.1660	2.11509
$457$	−27.5969	−1.29093	−0.645465	−	0.763790i	$-0.723336\pi$
$457$	−27.5969	−1.29093	−0.645465	+	0.763790i	$0.723336\pi$
$458$	−47.1960	−2.20533
$459$	24.1676	1.12805
$460$	31.7883	1.48214
$461$	−7.76824	−0.361803	−0.180902	−	0.983501i	$-0.557902\pi$
$461$	−7.76824	−0.361803	−0.180902	+	0.983501i	$0.557902\pi$
$462$	26.7011	1.24225
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	1.83208	0.0850522
$465$	−7.15189	−0.331661
$466$	−5.40977	−0.250603
$467$	3.51723	0.162758	0.0813789	−	0.996683i	$-0.474068\pi$
$467$	3.51723	0.162758	0.0813789	+	0.996683i	$0.474068\pi$
$468$	0.963653	0.0445449
$469$	2.69695	0.124534
$470$	−27.2250	−1.25580
$471$	34.1691	1.57443
$472$	−0.828526	−0.0381360
$473$	15.7848	0.725788
$474$	−32.6052	−1.49761
$475$	−28.1057	−1.28958
$476$	32.1328	1.47280
$477$	1.19432	0.0546842
$478$	−4.04373	−0.184956
$479$	−20.8676	−0.953463	−0.476731	−	0.879049i	$-0.658179\pi$
$479$	−20.8676	−0.953463	−0.476731	+	0.879049i	$0.658179\pi$
$480$	7.96371	0.363492
$481$	−6.86030	−0.312803
$482$	25.9416	1.18161
$483$	26.1553	1.19011
$484$	0.985985	0.0448175
$485$	−17.3908	−0.789678
$486$	6.68764	0.303357
$487$	−10.6513	−0.482656	−0.241328	−	0.970444i	$-0.577583\pi$
$487$	−10.6513	−0.482656	−0.241328	+	0.970444i	$0.577583\pi$
$488$	0.658737	0.0298196
$489$	−10.1314	−0.458158
$490$	−7.68240	−0.347056
$491$	−21.4034	−0.965921	−0.482960	−	0.875642i	$-0.660438\pi$
$491$	−21.4034	−0.965921	−0.482960	+	0.875642i	$0.660438\pi$
$492$	27.3851	1.23461
$493$	6.53474	0.294310
$494$	18.2335	0.820365
$495$	1.08806	0.0489047
$496$	−4.61430	−0.207188
$497$	−16.3292	−0.732464
$498$	63.2111	2.83256
$499$	−16.1760	−0.724139	−0.362070	−	0.932151i	$-0.617930\pi$
$499$	−16.1760	−0.724139	−0.362070	+	0.932151i	$0.617930\pi$
$500$	35.4902	1.58717
$501$	27.7904	1.24158
$502$	17.8151	0.795126
$503$	−36.7061	−1.63664	−0.818321	−	0.574761i	$-0.805095\pi$
$503$	−36.7061	−1.63664	−0.818321	+	0.574761i	$0.805095\pi$
$504$	1.98945	0.0886172
$505$	22.1307	0.984801
$506$	60.7880	2.70235
$507$	−1.65067	−0.0733090
$508$	−15.0988	−0.669902
$509$	10.0322	0.444670	0.222335	−	0.974970i	$-0.428632\pi$
$509$	10.0322	0.444670	0.222335	+	0.974970i	$0.428632\pi$
$510$	−20.3652	−0.901785
$511$	−2.30866	−0.102129
$512$	13.9599	0.616946
$513$	42.0313	1.85573
$514$	−12.6727	−0.558968
$515$	19.6611	0.866374
$516$	−27.1559	−1.19547
$517$	−33.1324	−1.45716
$518$	−33.0388	−1.45164
$519$	−31.5054	−1.38293
$520$	−4.14173	−0.181627
$521$	−39.8464	−1.74570	−0.872851	−	0.487988i	$-0.837731\pi$
$521$	−39.8464	−1.74570	−0.872851	+	0.487988i	$0.837731\pi$
$522$	0.943805	0.0413092
$523$	4.33379	0.189503	0.0947516	−	0.995501i	$-0.469794\pi$
$523$	4.33379	0.189503	0.0947516	+	0.995501i	$0.469794\pi$
$524$	−30.1564	−1.31739
$525$	12.2537	0.534795
$526$	19.0773	0.831810
$527$	−16.4585	−0.716942
$528$	−6.94846	−0.302393
$529$	36.5454	1.58893
$530$	−11.9743	−0.520132
$531$	−0.0648023	−0.00281218
$532$	55.8840	2.42288
$533$	4.73919	0.205277
$534$	−53.9704	−2.33553
$535$	9.77811	0.422744
$536$	−4.62259	−0.199665
$537$	17.0290	0.734854
$538$	37.4701	1.61545
$539$	−9.34935	−0.402705
$540$	−22.2717	−0.958421
$541$	−34.5042	−1.48345	−0.741726	−	0.670703i	$-0.765993\pi$
$541$	−34.5042	−1.48345	−0.741726	+	0.670703i	$0.765993\pi$
$542$	−49.6254	−2.13159
$543$	−17.0445	−0.731449
$544$	18.3267	0.785751
$545$	−10.8275	−0.463801
$546$	−7.94956	−0.340210
$547$	15.2149	0.650542	0.325271	−	0.945621i	$-0.394545\pi$
$547$	15.2149	0.650542	0.325271	+	0.945621i	$0.394545\pi$
$548$	−27.1598	−1.16021
$549$	0.0515225	0.00219893
$550$	28.4790	1.21435
$551$	11.3649	0.484163
$552$	−44.8304	−1.90811
$553$	−17.2939	−0.735412
$554$	−3.46781	−0.147333
$555$	13.3260	0.565656
$556$	54.3474	2.30484
$557$	−11.6392	−0.493170	−0.246585	−	0.969121i	$-0.579308\pi$
$557$	−11.6392	−0.493170	−0.246585	+	0.969121i	$0.579308\pi$
$558$	−2.37708	−0.100630
$559$	−4.69953	−0.198769
$560$	−3.02838	−0.127972
$561$	−24.7841	−1.04638
$562$	−43.3123	−1.82702
$563$	−5.24610	−0.221097	−0.110548	−	0.993871i	$-0.535261\pi$
$563$	−5.24610	−0.221097	−0.110548	+	0.993871i	$0.535261\pi$
$564$	57.0001	2.40014
$565$	−13.7041	−0.576538
$566$	12.4801	0.524578
$567$	−16.6293	−0.698364
$568$	27.9883	1.17436
$569$	30.3721	1.27326	0.636632	−	0.771168i	$-0.280327\pi$
$569$	30.3721	1.27326	0.636632	+	0.771168i	$0.280327\pi$
$570$	−35.4182	−1.48351
$571$	8.55417	0.357981	0.178990	−	0.983851i	$-0.442717\pi$
$571$	8.55417	0.357981	0.178990	+	0.983851i	$0.442717\pi$
$572$	−11.7581	−0.491629
$573$	−36.9999	−1.54569
$574$	22.8237	0.952642
$575$	27.8969	1.16338
$576$	3.33689	0.139037
$577$	−16.3414	−0.680301	−0.340150	−	0.940371i	$-0.610478\pi$
$577$	−16.3414	−0.680301	−0.340150	+	0.940371i	$0.610478\pi$
$578$	−6.99498	−0.290953
$579$	−30.3646	−1.26191
$580$	−6.02209	−0.250054
$581$	33.5274	1.39095
$582$	57.2129	2.37155
$583$	−14.5726	−0.603534
$584$	3.95705	0.163744
$585$	−0.323941	−0.0133933
$586$	17.3609	0.717172
$587$	6.71206	0.277036	0.138518	−	0.990360i	$-0.455766\pi$
$587$	6.71206	0.277036	0.138518	+	0.990360i	$0.455766\pi$
$588$	16.0844	0.663310
$589$	−28.6238	−1.17943
$590$	0.649712	0.0267482
$591$	0.851275	0.0350168
$592$	8.59773	0.353365
$593$	34.6077	1.42117	0.710584	−	0.703612i	$-0.248431\pi$
$593$	34.6077	1.42117	0.710584	+	0.703612i	$0.248431\pi$
$594$	−42.5895	−1.74747
$595$	−10.8018	−0.442829
$596$	16.9981	0.696268
$597$	−1.05171	−0.0430436
$598$	−18.0980	−0.740083
$599$	−23.5561	−0.962476	−0.481238	−	0.876590i	$-0.659813\pi$
$599$	−23.5561	−0.962476	−0.481238	+	0.876590i	$0.659813\pi$
$600$	−21.0029	−0.857440
$601$	−3.39434	−0.138458	−0.0692289	−	0.997601i	$-0.522054\pi$
$601$	−3.39434	−0.138458	−0.0692289	+	0.997601i	$0.522054\pi$
$602$	−22.6327	−0.922439
$603$	−0.361551	−0.0147235
$604$	−57.9289	−2.35709
$605$	−0.331449	−0.0134753
$606$	−72.8060	−2.95754
$607$	−13.2356	−0.537217	−0.268608	−	0.963249i	$-0.586564\pi$
$607$	−13.2356	−0.537217	−0.268608	+	0.963249i	$0.586564\pi$
$608$	31.8730	1.29262
$609$	−4.95495	−0.200785
$610$	−0.516568	−0.0209152
$611$	9.86429	0.399066
$612$	−4.30770	−0.174128
$613$	−40.9304	−1.65316	−0.826581	−	0.562818i	$-0.809717\pi$
$613$	−40.9304	−1.65316	−0.826581	+	0.562818i	$0.809717\pi$
$614$	−30.4892	−1.23045
$615$	−9.20576	−0.371212
$616$	−24.2744	−0.978043
$617$	−36.9601	−1.48796	−0.743978	−	0.668204i	$-0.767063\pi$
$617$	−36.9601	−1.48796	−0.743978	+	0.668204i	$0.767063\pi$
$618$	−64.6818	−2.60188
$619$	−43.7376	−1.75796	−0.878982	−	0.476855i	$-0.841777\pi$
$619$	−43.7376	−1.75796	−0.878982	+	0.476855i	$0.841777\pi$
$620$	15.1673	0.609134
$621$	−41.7189	−1.67412
$622$	47.9337	1.92196
$623$	−28.6261	−1.14688
$624$	2.06872	0.0828151
$625$	6.14556	0.245822
$626$	8.72544	0.348739
$627$	−43.1033	−1.72138
$628$	−72.4638	−2.89162
$629$	30.6668	1.22276
$630$	−1.56009	−0.0621553
$631$	38.5065	1.53292	0.766460	−	0.642292i	$-0.222016\pi$
$631$	38.5065	1.53292	0.766460	+	0.642292i	$0.222016\pi$
$632$	29.6419	1.17909
$633$	8.58226	0.341114
$634$	1.87614	0.0745108
$635$	5.07562	0.201420
$636$	25.0703	0.994102
$637$	2.78353	0.110287
$638$	−11.5159	−0.455918
$639$	2.18908	0.0865986
$640$	−23.8069	−0.941049
$641$	33.1894	1.31090	0.655451	−	0.755238i	$-0.272479\pi$
$641$	33.1894	1.31090	0.655451	+	0.755238i	$0.272479\pi$
$642$	−32.1683	−1.26958
$643$	7.86750	0.310264	0.155132	−	0.987894i	$-0.450420\pi$
$643$	7.86750	0.310264	0.155132	+	0.987894i	$0.450420\pi$
$644$	−55.4687	−2.18577
$645$	9.12872	0.359443
$646$	−81.5071	−3.20685
$647$	14.9166	0.586430	0.293215	−	0.956046i	$-0.405275\pi$
$647$	14.9166	0.586430	0.293215	+	0.956046i	$0.405275\pi$
$648$	28.5027	1.11969
$649$	0.790689	0.0310373
$650$	−8.47888	−0.332569
$651$	12.4796	0.489114
$652$	21.4861	0.841460
$653$	1.58211	0.0619126	0.0309563	−	0.999521i	$-0.490145\pi$
$653$	1.58211	0.0619126	0.0309563	+	0.999521i	$0.490145\pi$
$654$	35.6207	1.39288
$655$	10.1374	0.396100
$656$	−5.93943	−0.231896
$657$	0.309497	0.0120746
$658$	47.5059	1.85197
$659$	−29.6557	−1.15522	−0.577612	−	0.816312i	$-0.696015\pi$
$659$	−29.6557	−1.15522	−0.577612	+	0.816312i	$0.696015\pi$
$660$	22.8398	0.889036
$661$	3.01285	0.117186	0.0585932	−	0.998282i	$-0.481339\pi$
$661$	3.01285	0.117186	0.0585932	+	0.998282i	$0.481339\pi$
$662$	−19.1200	−0.743120
$663$	7.37880	0.286569
$664$	−57.4662	−2.23012
$665$	−18.7859	−0.728488
$666$	4.42916	0.171627
$667$	−11.2805	−0.436782
$668$	−58.9362	−2.28031
$669$	−16.6093	−0.642153
$670$	3.62494	0.140043
$671$	−0.628654	−0.0242689
$672$	−13.8962	−0.536057
$673$	30.3291	1.16910	0.584551	−	0.811357i	$-0.301271\pi$
$673$	30.3291	1.16910	0.584551	+	0.811357i	$0.301271\pi$
$674$	−64.6476	−2.49013
$675$	−19.5452	−0.752296
$676$	3.50065	0.134640
$677$	−23.5122	−0.903649	−0.451825	−	0.892107i	$-0.649227\pi$
$677$	−23.5122	−0.903649	−0.451825	+	0.892107i	$0.649227\pi$
$678$	45.0843	1.73145
$679$	30.3459	1.16457
$680$	18.5143	0.709990
$681$	7.77127	0.297796
$682$	29.0040	1.11062
$683$	−26.7500	−1.02356	−0.511781	−	0.859116i	$-0.671014\pi$
$683$	−26.7500	−1.02356	−0.511781	+	0.859116i	$0.671014\pi$
$684$	−7.49176	−0.286455
$685$	9.13005	0.348841
$686$	47.1170	1.79893
$687$	−33.2169	−1.26731
$688$	5.88972	0.224544
$689$	4.33860	0.165287
$690$	35.1550	1.33833
$691$	−4.32225	−0.164426	−0.0822131	−	0.996615i	$-0.526199\pi$
$691$	−4.32225	−0.164426	−0.0822131	+	0.996615i	$0.526199\pi$
$692$	66.8148	2.53992
$693$	−1.89860	−0.0721217
$694$	18.0816	0.686368
$695$	−18.2694	−0.692999
$696$	8.49282	0.321919
$697$	−21.1850	−0.802439
$698$	23.9476	0.906430
$699$	−3.80744	−0.144011
$700$	−25.9869	−0.982213
$701$	6.69840	0.252995	0.126498	−	0.991967i	$-0.459626\pi$
$701$	6.69840	0.252995	0.126498	+	0.991967i	$0.459626\pi$
$702$	12.6799	0.478573
$703$	53.3343	2.01154
$704$	−40.7153	−1.53451
$705$	−19.1612	−0.721651
$706$	−70.4592	−2.65177
$707$	−38.6166	−1.45233
$708$	−1.36028	−0.0511226
$709$	4.31526	0.162063	0.0810315	−	0.996712i	$-0.474179\pi$
$709$	4.31526	0.162063	0.0810315	+	0.996712i	$0.474179\pi$
$710$	−21.9478	−0.823688
$711$	2.31841	0.0869472
$712$	49.0653	1.83880
$713$	28.4111	1.06401
$714$	35.5359	1.32990
$715$	3.95259	0.147818
$716$	−36.1140	−1.34964
$717$	−2.84601	−0.106286
$718$	−49.0388	−1.83011
$719$	2.76799	0.103229	0.0516144	−	0.998667i	$-0.483563\pi$
$719$	2.76799	0.103229	0.0516144	+	0.998667i	$0.483563\pi$
$720$	0.405983	0.0151301
$721$	−34.3075	−1.27768
$722$	−97.1920	−3.61711
$723$	18.2579	0.679019
$724$	36.1470	1.34339
$725$	−5.28488	−0.196275
$726$	1.09041	0.0404689
$727$	7.45861	0.276624	0.138312	−	0.990389i	$-0.455832\pi$
$727$	7.45861	0.276624	0.138312	+	0.990389i	$0.455832\pi$
$728$	7.22706	0.267853
$729$	29.0020	1.07415
$730$	−3.10303	−0.114848
$731$	21.0077	0.776998
$732$	1.08152	0.0399742
$733$	−16.9100	−0.624585	−0.312292	−	0.949986i	$-0.601097\pi$
$733$	−16.9100	−0.624585	−0.312292	+	0.949986i	$0.601097\pi$
$734$	−52.5899	−1.94113
$735$	−5.40694	−0.199438
$736$	−31.6361	−1.16612
$737$	4.41148	0.162499
$738$	−3.05972	−0.112630
$739$	−23.8035	−0.875627	−0.437814	−	0.899066i	$-0.644247\pi$
$739$	−23.8035	−0.875627	−0.437814	+	0.899066i	$0.644247\pi$
$740$	−28.2610	−1.03889
$741$	12.8329	0.471428
$742$	20.8945	0.767060
$743$	−37.3549	−1.37042	−0.685209	−	0.728347i	$-0.740289\pi$
$743$	−37.3549	−1.37042	−0.685209	+	0.728347i	$0.740289\pi$
$744$	−21.3901	−0.784199
$745$	−5.71407	−0.209347
$746$	−41.8520	−1.53231
$747$	−4.49466	−0.164451
$748$	52.5606	1.92181
$749$	−17.0622	−0.623439
$750$	39.2489	1.43317
$751$	35.7899	1.30599	0.652995	−	0.757362i	$-0.273512\pi$
$751$	35.7899	1.30599	0.652995	+	0.757362i	$0.273512\pi$
$752$	−12.3625	−0.450814
$753$	12.5384	0.456924
$754$	3.42855	0.124860
$755$	19.4734	0.708708
$756$	38.8627	1.41342
$757$	5.64469	0.205160	0.102580	−	0.994725i	$-0.467290\pi$
$757$	5.64469	0.205160	0.102580	+	0.994725i	$0.467290\pi$
$758$	−47.4957	−1.72512
$759$	42.7830	1.55293
$760$	32.1992	1.16799
$761$	−22.2716	−0.807343	−0.403672	−	0.914904i	$-0.632266\pi$
$761$	−22.2716	−0.807343	−0.403672	+	0.914904i	$0.632266\pi$
$762$	−16.6979	−0.604902
$763$	18.8934	0.683986
$764$	78.4673	2.83885
$765$	1.44808	0.0523553
$766$	70.7726	2.55712
$767$	−0.235407	−0.00850005
$768$	38.3019	1.38210
$769$	−32.3340	−1.16600	−0.582998	−	0.812474i	$-0.698120\pi$
$769$	−32.3340	−1.16600	−0.582998	+	0.812474i	$0.698120\pi$
$770$	19.0355	0.685990
$771$	−8.91913	−0.321215
$772$	64.3955	2.31765
$773$	−24.4466	−0.879283	−0.439642	−	0.898173i	$-0.644895\pi$
$773$	−24.4466	−0.879283	−0.439642	+	0.898173i	$0.644895\pi$
$774$	3.03412	0.109059
$775$	13.3105	0.478129
$776$	−52.0131	−1.86716
$777$	−23.2530	−0.834196
$778$	30.0153	1.07610
$779$	−36.8440	−1.32007
$780$	−6.79994	−0.243477
$781$	−26.7101	−0.955764
$782$	80.9014	2.89303
$783$	7.90338	0.282444
$784$	−3.48848	−0.124589
$785$	24.3594	0.869425
$786$	−33.3503	−1.18956
$787$	−13.4491	−0.479410	−0.239705	−	0.970846i	$-0.577051\pi$
$787$	−13.4491	−0.479410	−0.239705	+	0.970846i	$0.577051\pi$
$788$	−1.80533	−0.0643123
$789$	13.4268	0.478005
$790$	−23.2445	−0.827003
$791$	23.9129	0.850244
$792$	3.25421	0.115633
$793$	0.187165	0.00664643
$794$	16.3584	0.580538
$795$	−8.42763	−0.298897
$796$	2.23040	0.0790546
$797$	35.6487	1.26274	0.631370	−	0.775481i	$-0.282493\pi$
$797$	35.6487	1.26274	0.631370	+	0.775481i	$0.282493\pi$
$798$	61.8025	2.18779
$799$	−44.0951	−1.55997
$800$	−14.8215	−0.524017
$801$	3.83759	0.135595
$802$	76.7695	2.71083
$803$	−3.77634	−0.133264
$804$	−7.58942	−0.267658
$805$	18.6463	0.657197
$806$	−8.63518	−0.304161
$807$	26.3717	0.928329
$808$	66.1891	2.32852
$809$	−25.3556	−0.891455	−0.445728	−	0.895169i	$-0.647055\pi$
$809$	−25.3556	−0.891455	−0.445728	+	0.895169i	$0.647055\pi$
$810$	−22.3512	−0.785341
$811$	42.3734	1.48793	0.743966	−	0.668217i	$-0.232942\pi$
$811$	42.3734	1.48793	0.743966	+	0.668217i	$0.232942\pi$
$812$	10.5082	0.368765
$813$	−34.9268	−1.22494
$814$	−54.0426	−1.89419
$815$	−7.22276	−0.253002
$816$	−9.24755	−0.323729
$817$	36.5357	1.27822
$818$	80.0349	2.79836
$819$	0.565257	0.0197517
$820$	19.5230	0.681774
$821$	−34.9901	−1.22116	−0.610582	−	0.791953i	$-0.709065\pi$
$821$	−34.9901	−1.22116	−0.610582	+	0.791953i	$0.709065\pi$
$822$	−30.0363	−1.04764
$823$	26.2436	0.914794	0.457397	−	0.889263i	$-0.348782\pi$
$823$	26.2436	0.914794	0.457397	+	0.889263i	$0.348782\pi$
$824$	58.8032	2.04851
$825$	20.0437	0.697834
$826$	−1.13371	−0.0394467
$827$	35.8718	1.24739	0.623693	−	0.781670i	$-0.285632\pi$
$827$	35.8718	1.24739	0.623693	+	0.781670i	$0.285632\pi$
$828$	7.43609	0.258422
$829$	22.3899	0.777634	0.388817	−	0.921315i	$-0.372884\pi$
$829$	22.3899	0.777634	0.388817	+	0.921315i	$0.372884\pi$
$830$	45.0638	1.56419
$831$	−2.44067	−0.0846659
$832$	12.1219	0.420251
$833$	−12.4429	−0.431119
$834$	60.1033	2.08121
$835$	19.8120	0.685622
$836$	91.4111	3.16152
$837$	−19.9055	−0.688036
$838$	18.4772	0.638285
$839$	−9.31199	−0.321485	−0.160743	−	0.986996i	$-0.551389\pi$
$839$	−9.31199	−0.321485	−0.160743	+	0.986996i	$0.551389\pi$
$840$	−14.0384	−0.484371
$841$	−26.8630	−0.926310
$842$	24.2942	0.837234
$843$	−30.4835	−1.04991
$844$	−18.2008	−0.626496
$845$	−1.17678	−0.0404824
$846$	−6.36861	−0.218957
$847$	0.578357	0.0198726
$848$	−5.43739	−0.186721
$849$	8.78360	0.301452
$850$	37.9021	1.30003
$851$	−52.9379	−1.81469
$852$	45.9515	1.57427
$853$	−25.6209	−0.877243	−0.438621	−	0.898672i	$-0.644533\pi$
$853$	−25.6209	−0.877243	−0.438621	+	0.898672i	$0.644533\pi$
$854$	0.901378	0.0308445
$855$	2.51843	0.0861285
$856$	29.2447	0.999562
$857$	7.85009	0.268154	0.134077	−	0.990971i	$-0.457193\pi$
$857$	7.85009	0.268154	0.134077	+	0.990971i	$0.457193\pi$
$858$	−13.0033	−0.443926
$859$	−18.5076	−0.631470	−0.315735	−	0.948847i	$-0.602251\pi$
$859$	−18.5076	−0.631470	−0.315735	+	0.948847i	$0.602251\pi$
$860$	−19.3597	−0.660159
$861$	16.0635	0.547442
$862$	96.0127	3.27021
$863$	5.32755	0.181352	0.0906759	−	0.995880i	$-0.471097\pi$
$863$	5.32755	0.181352	0.0906759	+	0.995880i	$0.471097\pi$
$864$	22.1651	0.754070
$865$	−22.4605	−0.763679
$866$	6.01876	0.204526
$867$	−4.92312	−0.167198
$868$	−26.4660	−0.898314
$869$	−28.2882	−0.959611
$870$	−6.65988	−0.225791
$871$	−1.31340	−0.0445030
$872$	−32.3833	−1.09664
$873$	−4.06815	−0.137686
$874$	140.700	4.75925
$875$	20.8178	0.703770
$876$	6.49672	0.219504
$877$	−2.07870	−0.0701926	−0.0350963	−	0.999384i	$-0.511174\pi$
$877$	−2.07870	−0.0701926	−0.0350963	+	0.999384i	$0.511174\pi$
$878$	−26.8458	−0.906002
$879$	12.2187	0.412128
$880$	−4.95362	−0.166986
$881$	11.5668	0.389695	0.194847	−	0.980834i	$-0.437579\pi$
$881$	11.5668	0.389695	0.194847	+	0.980834i	$0.437579\pi$
$882$	−1.79711	−0.0605117
$883$	−11.2769	−0.379498	−0.189749	−	0.981833i	$-0.560767\pi$
$883$	−11.2769	−0.379498	−0.189749	+	0.981833i	$0.560767\pi$
$884$	−15.6485	−0.526317
$885$	0.457273	0.0153711
$886$	−90.7194	−3.04778
$887$	−55.4726	−1.86259	−0.931294	−	0.364269i	$-0.881319\pi$
$887$	−55.4726	−1.86259	−0.931294	+	0.364269i	$0.881319\pi$
$888$	39.8558	1.33747
$889$	−8.85664	−0.297042
$890$	−38.4759	−1.28972
$891$	−27.2010	−0.911268
$892$	35.2241	1.17939
$893$	−76.6883	−2.56628
$894$	18.7983	0.628710
$895$	12.1401	0.405798
$896$	41.5415	1.38780
$897$	−12.7375	−0.425294
$898$	76.1535	2.54127
$899$	−5.38230	−0.179510
$900$	3.48379	0.116126
$901$	−19.3943	−0.646118
$902$	37.3334	1.24307
$903$	−15.9290	−0.530086
$904$	−40.9868	−1.36320
$905$	−12.1512	−0.403918
$906$	−64.0640	−2.12839
$907$	−31.6157	−1.04978	−0.524892	−	0.851169i	$-0.675894\pi$
$907$	−31.6157	−1.04978	−0.524892	+	0.851169i	$0.675894\pi$
$908$	−16.4809	−0.546937
$909$	5.17691	0.171707
$910$	−5.66731	−0.187869
$911$	7.69749	0.255029	0.127515	−	0.991837i	$-0.459300\pi$
$911$	7.69749	0.255029	0.127515	+	0.991837i	$0.459300\pi$
$912$	−16.0829	−0.532559
$913$	54.8418	1.81500
$914$	64.7244	2.14089
$915$	−0.363564	−0.0120191
$916$	70.4445	2.32755
$917$	−17.6891	−0.584146
$918$	−56.6815	−1.87077
$919$	−15.7089	−0.518190	−0.259095	−	0.965852i	$-0.583424\pi$
$919$	−15.7089	−0.518190	−0.259095	+	0.965852i	$0.583424\pi$
$920$	−31.9599	−1.05369
$921$	−21.4586	−0.707084
$922$	18.2192	0.600018
$923$	7.95224	0.261751
$924$	−39.8539	−1.31110
$925$	−24.8013	−0.815461
$926$	2.34535	0.0770729
$927$	4.59923	0.151059
$928$	5.99326	0.196738
$929$	−26.0229	−0.853784	−0.426892	−	0.904303i	$-0.640392\pi$
$929$	−26.0229	−0.853784	−0.426892	+	0.904303i	$0.640392\pi$
$930$	16.7737	0.550030
$931$	−21.6401	−0.709225
$932$	8.07459	0.264492
$933$	33.7361	1.10447
$934$	−8.24912	−0.269919
$935$	−17.6688	−0.577830
$936$	−0.968855	−0.0316680
$937$	−10.9730	−0.358472	−0.179236	−	0.983806i	$-0.557363\pi$
$937$	−10.9730	−0.358472	−0.179236	+	0.983806i	$0.557363\pi$
$938$	−6.32529	−0.206528
$939$	6.14103	0.200405
$940$	40.6359	1.32540
$941$	9.68440	0.315702	0.157851	−	0.987463i	$-0.449543\pi$
$941$	9.68440	0.315702	0.157851	+	0.987463i	$0.449543\pi$
$942$	−80.1383	−2.61105
$943$	36.5702	1.19089
$944$	0.295026	0.00960227
$945$	−13.0641	−0.424975
$946$	−37.0209	−1.20365
$947$	29.3611	0.954106	0.477053	−	0.878874i	$-0.341705\pi$
$947$	29.3611	0.954106	0.477053	+	0.878874i	$0.341705\pi$
$948$	48.6663	1.58061
$949$	1.12431	0.0364965
$950$	65.9177	2.13865
$951$	1.32044	0.0428181
$952$	−32.3063	−1.04705
$953$	32.0233	1.03734	0.518668	−	0.854976i	$-0.326428\pi$
$953$	32.0233	1.03734	0.518668	+	0.854976i	$0.326428\pi$
$954$	−2.80110	−0.0906889
$955$	−26.3776	−0.853558
$956$	6.03565	0.195207
$957$	−8.10496	−0.261996
$958$	48.9416	1.58123
$959$	−15.9314	−0.514450
$960$	−23.5465	−0.759961
$961$	−17.4441	−0.562712
$962$	16.0898	0.518755
$963$	2.28734	0.0737086
$964$	−38.7203	−1.24710
$965$	−21.6472	−0.696848
$966$	−61.3433	−1.97369
$967$	−17.7899	−0.572084	−0.286042	−	0.958217i	$-0.592340\pi$
$967$	−17.7899	−0.572084	−0.286042	+	0.958217i	$0.592340\pi$
$968$	−0.991307	−0.0318618
$969$	−57.3653	−1.84284
$970$	40.7876	1.30961
$971$	−4.79097	−0.153749	−0.0768747	−	0.997041i	$-0.524494\pi$
$971$	−4.79097	−0.153749	−0.0768747	+	0.997041i	$0.524494\pi$
$972$	−9.98193	−0.320171
$973$	31.8790	1.02199
$974$	24.9809	0.800441
$975$	−5.96750	−0.191113
$976$	−0.234567	−0.00750829
$977$	−60.0639	−1.92161	−0.960807	−	0.277218i	$-0.910588\pi$
$977$	−60.0639	−1.92161	−0.960807	+	0.277218i	$0.910588\pi$
$978$	23.7617	0.759814
$979$	−46.8246	−1.49652
$980$	11.4667	0.366291
$981$	−2.53283	−0.0808671
$982$	50.1983	1.60189
$983$	−17.7583	−0.566403	−0.283202	−	0.959060i	$-0.591397\pi$
$983$	−17.7583	−0.566403	−0.283202	+	0.959060i	$0.591397\pi$
$984$	−27.5329	−0.877716
$985$	0.606881	0.0193368
$986$	−15.3262	−0.488087
$987$	33.4350	1.06425
$988$	−27.2153	−0.865833
$989$	−36.2642	−1.15313
$990$	−2.55188	−0.0811040
$991$	−24.5801	−0.780813	−0.390407	−	0.920643i	$-0.627666\pi$
$991$	−24.5801	−0.780813	−0.390407	+	0.920643i	$0.627666\pi$
$992$	−15.0947	−0.479257
$993$	−13.4568	−0.427039
$994$	38.2976	1.21473
$995$	−0.749773	−0.0237694
$996$	−94.3486	−2.98955
$997$	−29.0419	−0.919767	−0.459884	−	0.887979i	$-0.652109\pi$
$997$	−29.0419	−0.919767	−0.459884	+	0.887979i	$0.652109\pi$
$998$	37.9384	1.20092
$999$	37.0896	1.17346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.12	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.12	✓	108	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34535 q^{2} -1.65067 q^{3} +3.50065 q^{4} -1.17678 q^{5} +3.87140 q^{6} +2.05341 q^{7} -3.51955 q^{8} -0.275278 q^{9} +O(q^{10})\)	\(q-2.34535 q^{2} -1.65067 q^{3} +3.50065 q^{4} -1.17678 q^{5} +3.87140 q^{6} +2.05341 q^{7} -3.51955 q^{8} -0.275278 q^{9} +2.75996 q^{10} +3.35882 q^{11} -5.77843 q^{12} -1.00000 q^{13} -4.81595 q^{14} +1.94248 q^{15} +1.25326 q^{16} +4.47018 q^{17} +0.645622 q^{18} +7.77434 q^{19} -4.11949 q^{20} -3.38950 q^{21} -7.87759 q^{22} -7.71657 q^{23} +5.80962 q^{24} -3.61519 q^{25} +2.34535 q^{26} +5.40641 q^{27} +7.18826 q^{28} +1.46185 q^{29} -4.55578 q^{30} -3.68184 q^{31} +4.09977 q^{32} -5.54431 q^{33} -10.4841 q^{34} -2.41640 q^{35} -0.963653 q^{36} +6.86030 q^{37} -18.2335 q^{38} +1.65067 q^{39} +4.14173 q^{40} -4.73919 q^{41} +7.94956 q^{42} +4.69953 q^{43} +11.7581 q^{44} +0.323941 q^{45} +18.0980 q^{46} -9.86429 q^{47} -2.06872 q^{48} -2.78353 q^{49} +8.47888 q^{50} -7.37880 q^{51} -3.50065 q^{52} -4.33860 q^{53} -12.6799 q^{54} -3.95259 q^{55} -7.22706 q^{56} -12.8329 q^{57} -3.42855 q^{58} +0.235407 q^{59} +6.79994 q^{60} -0.187165 q^{61} +8.63518 q^{62} -0.565257 q^{63} -12.1219 q^{64} +1.17678 q^{65} +13.0033 q^{66} +1.31340 q^{67} +15.6485 q^{68} +12.7375 q^{69} +5.66731 q^{70} -7.95224 q^{71} +0.968855 q^{72} -1.12431 q^{73} -16.0898 q^{74} +5.96750 q^{75} +27.2153 q^{76} +6.89702 q^{77} -3.87140 q^{78} -8.42207 q^{79} -1.47481 q^{80} -8.09839 q^{81} +11.1150 q^{82} +16.3277 q^{83} -11.8655 q^{84} -5.26041 q^{85} -11.0220 q^{86} -2.41304 q^{87} -11.8215 q^{88} -13.9408 q^{89} -0.759755 q^{90} -2.05341 q^{91} -27.0130 q^{92} +6.07751 q^{93} +23.1352 q^{94} -9.14868 q^{95} -6.76738 q^{96} +14.7783 q^{97} +6.52833 q^{98} -0.924609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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