LMFDB - Embedded newform 6019.2.a.c.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.39631 q^{2} -0.467815 q^{3} +3.74231 q^{4} +2.01057 q^{5} +1.12103 q^{6} -2.84779 q^{7} -4.17511 q^{8} -2.78115 q^{9} +O(q^{10})$	\(q-2.39631 q^{2} -0.467815 q^{3} +3.74231 q^{4} +2.01057 q^{5} +1.12103 q^{6} -2.84779 q^{7} -4.17511 q^{8} -2.78115 q^{9} -4.81795 q^{10} +3.93458 q^{11} -1.75071 q^{12} -1.00000 q^{13} +6.82420 q^{14} -0.940573 q^{15} +2.52025 q^{16} +6.24553 q^{17} +6.66450 q^{18} +4.17763 q^{19} +7.52416 q^{20} +1.33224 q^{21} -9.42848 q^{22} +2.17631 q^{23} +1.95318 q^{24} -0.957616 q^{25} +2.39631 q^{26} +2.70451 q^{27} -10.6573 q^{28} -10.0386 q^{29} +2.25391 q^{30} -5.13693 q^{31} +2.31092 q^{32} -1.84065 q^{33} -14.9662 q^{34} -5.72568 q^{35} -10.4079 q^{36} -5.97286 q^{37} -10.0109 q^{38} +0.467815 q^{39} -8.39434 q^{40} +9.83118 q^{41} -3.19246 q^{42} -9.39726 q^{43} +14.7244 q^{44} -5.59169 q^{45} -5.21512 q^{46} +4.75131 q^{47} -1.17901 q^{48} +1.10992 q^{49} +2.29475 q^{50} -2.92175 q^{51} -3.74231 q^{52} +4.79505 q^{53} -6.48084 q^{54} +7.91074 q^{55} +11.8898 q^{56} -1.95436 q^{57} +24.0555 q^{58} -10.1207 q^{59} -3.51991 q^{60} -2.61639 q^{61} +12.3097 q^{62} +7.92014 q^{63} -10.5782 q^{64} -2.01057 q^{65} +4.41078 q^{66} +7.15184 q^{67} +23.3727 q^{68} -1.01811 q^{69} +13.7205 q^{70} -11.5021 q^{71} +11.6116 q^{72} -13.4207 q^{73} +14.3128 q^{74} +0.447987 q^{75} +15.6340 q^{76} -11.2049 q^{77} -1.12103 q^{78} +2.13610 q^{79} +5.06713 q^{80} +7.07824 q^{81} -23.5586 q^{82} +4.34501 q^{83} +4.98565 q^{84} +12.5571 q^{85} +22.5188 q^{86} +4.69619 q^{87} -16.4273 q^{88} +16.8366 q^{89} +13.3994 q^{90} +2.84779 q^{91} +8.14443 q^{92} +2.40313 q^{93} -11.3856 q^{94} +8.39942 q^{95} -1.08108 q^{96} -0.381896 q^{97} -2.65971 q^{98} -10.9427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.39631	−1.69445	−0.847224	−	0.531236i	$-0.821728\pi$
$2$	−2.39631	−1.69445	−0.847224	+	0.531236i	$0.821728\pi$
$3$	−0.467815	−0.270093	−0.135046	−	0.990839i	$-0.543118\pi$
$3$	−0.467815	−0.270093	−0.135046	+	0.990839i	$0.543118\pi$
$4$	3.74231	1.87115
$5$	2.01057	0.899153	0.449577	−	0.893242i	$-0.351575\pi$
$5$	2.01057	0.899153	0.449577	+	0.893242i	$0.351575\pi$
$6$	1.12103	0.457658
$7$	−2.84779	−1.07636	−0.538182	−	0.842829i	$-0.680889\pi$
$7$	−2.84779	−1.07636	−0.538182	+	0.842829i	$0.680889\pi$
$8$	−4.17511	−1.47612
$9$	−2.78115	−0.927050
$10$	−4.81795	−1.52357
$11$	3.93458	1.18632	0.593160	−	0.805085i	$-0.297880\pi$
$11$	3.93458	1.18632	0.593160	+	0.805085i	$0.297880\pi$
$12$	−1.75071	−0.505385
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	6.82420	1.82384
$15$	−0.940573	−0.242855
$16$	2.52025	0.630062
$17$	6.24553	1.51476	0.757381	−	0.652973i	$-0.226478\pi$
$17$	6.24553	1.51476	0.757381	+	0.652973i	$0.226478\pi$
$18$	6.66450	1.57084
$19$	4.17763	0.958415	0.479208	−	0.877702i	$-0.340924\pi$
$19$	4.17763	0.958415	0.479208	+	0.877702i	$0.340924\pi$
$20$	7.52416	1.68245
$21$	1.33224	0.290718
$22$	−9.42848	−2.01016
$23$	2.17631	0.453793	0.226896	−	0.973919i	$-0.427142\pi$
$23$	2.17631	0.453793	0.226896	+	0.973919i	$0.427142\pi$
$24$	1.95318	0.398691
$25$	−0.957616	−0.191523
$26$	2.39631	0.469955
$27$	2.70451	0.520483
$28$	−10.6573	−2.01404
$29$	−10.0386	−1.86411	−0.932057	−	0.362312i	$-0.881987\pi$
$29$	−10.0386	−1.86411	−0.932057	+	0.362312i	$0.881987\pi$
$30$	2.25391	0.411505
$31$	−5.13693	−0.922620	−0.461310	−	0.887239i	$-0.652620\pi$
$31$	−5.13693	−0.922620	−0.461310	+	0.887239i	$0.652620\pi$
$32$	2.31092	0.408517
$33$	−1.84065	−0.320417
$34$	−14.9662	−2.56669
$35$	−5.72568	−0.967816
$36$	−10.4079	−1.73465
$37$	−5.97286	−0.981932	−0.490966	−	0.871179i	$-0.663356\pi$
$37$	−5.97286	−0.981932	−0.490966	+	0.871179i	$0.663356\pi$
$38$	−10.0109	−1.62398
$39$	0.467815	0.0749103
$40$	−8.39434	−1.32726
$41$	9.83118	1.53537	0.767686	−	0.640826i	$-0.221408\pi$
$41$	9.83118	1.53537	0.767686	+	0.640826i	$0.221408\pi$
$42$	−3.19246	−0.492607
$43$	−9.39726	−1.43307	−0.716535	−	0.697552i	$-0.754273\pi$
$43$	−9.39726	−1.43307	−0.716535	+	0.697552i	$0.754273\pi$
$44$	14.7244	2.21979
$45$	−5.59169	−0.833560
$46$	−5.21512	−0.768928
$47$	4.75131	0.693049	0.346525	−	0.938041i	$-0.387362\pi$
$47$	4.75131	0.693049	0.346525	+	0.938041i	$0.387362\pi$
$48$	−1.17901	−0.170175
$49$	1.10992	0.158560
$50$	2.29475	0.324526
$51$	−2.92175	−0.409127
$52$	−3.74231	−0.518965
$53$	4.79505	0.658651	0.329325	−	0.944217i	$-0.393179\pi$
$53$	4.79505	0.658651	0.329325	+	0.944217i	$0.393179\pi$
$54$	−6.48084	−0.881930
$55$	7.91074	1.06668
$56$	11.8898	1.58885
$57$	−1.95436	−0.258861
$58$	24.0555	3.15864
$59$	−10.1207	−1.31761	−0.658804	−	0.752315i	$-0.728937\pi$
$59$	−10.1207	−1.31761	−0.658804	+	0.752315i	$0.728937\pi$
$60$	−3.51991	−0.454419
$61$	−2.61639	−0.334994	−0.167497	−	0.985873i	$-0.553569\pi$
$61$	−2.61639	−0.334994	−0.167497	+	0.985873i	$0.553569\pi$
$62$	12.3097	1.56333
$63$	7.92014	0.997843
$64$	−10.5782	−1.32227
$65$	−2.01057	−0.249380
$66$	4.41078	0.542929
$67$	7.15184	0.873736	0.436868	−	0.899526i	$-0.356088\pi$
$67$	7.15184	0.873736	0.436868	+	0.899526i	$0.356088\pi$
$68$	23.3727	2.83435
$69$	−1.01811	−0.122566
$70$	13.7205	1.63991
$71$	−11.5021	−1.36504	−0.682522	−	0.730865i	$-0.739117\pi$
$71$	−11.5021	−1.36504	−0.682522	+	0.730865i	$0.739117\pi$
$72$	11.6116	1.36844
$73$	−13.4207	−1.57078	−0.785389	−	0.619002i	$-0.787537\pi$
$73$	−13.4207	−1.57078	−0.785389	+	0.619002i	$0.787537\pi$
$74$	14.3128	1.66383
$75$	0.447987	0.0517291
$76$	15.6340	1.79334
$77$	−11.2049	−1.27691
$78$	−1.12103	−0.126932
$79$	2.13610	0.240329	0.120165	−	0.992754i	$-0.461658\pi$
$79$	2.13610	0.240329	0.120165	+	0.992754i	$0.461658\pi$
$80$	5.06713	0.566522
$81$	7.07824	0.786471
$82$	−23.5586	−2.60161
$83$	4.34501	0.476927	0.238463	−	0.971152i	$-0.423356\pi$
$83$	4.34501	0.476927	0.238463	+	0.971152i	$0.423356\pi$
$84$	4.98565	0.543979
$85$	12.5571	1.36200
$86$	22.5188	2.42826
$87$	4.69619	0.503484
$88$	−16.4273	−1.75116
$89$	16.8366	1.78468	0.892340	−	0.451364i	$-0.149062\pi$
$89$	16.8366	1.78468	0.892340	+	0.451364i	$0.149062\pi$
$90$	13.3994	1.41242
$91$	2.84779	0.298530
$92$	8.14443	0.849116
$93$	2.40313	0.249193
$94$	−11.3856	−1.17434
$95$	8.39942	0.861762
$96$	−1.08108	−0.110338
$97$	−0.381896	−0.0387756	−0.0193878	−	0.999812i	$-0.506172\pi$
$97$	−0.381896	−0.0387756	−0.0193878	+	0.999812i	$0.506172\pi$
$98$	−2.65971	−0.268671
$99$	−10.9427	−1.09978
$100$	−3.58369	−0.358369
$101$	6.25916	0.622809	0.311405	−	0.950277i	$-0.399201\pi$
$101$	6.25916	0.622809	0.311405	+	0.950277i	$0.399201\pi$
$102$	7.00142	0.693244
$103$	5.22663	0.514996	0.257498	−	0.966279i	$-0.417102\pi$
$103$	5.22663	0.514996	0.257498	+	0.966279i	$0.417102\pi$
$104$	4.17511	0.409403
$105$	2.67856	0.261400
$106$	−11.4904	−1.11605
$107$	−6.75189	−0.652730	−0.326365	−	0.945244i	$-0.605824\pi$
$107$	−6.75189	−0.652730	−0.326365	+	0.945244i	$0.605824\pi$
$108$	10.1211	0.973903
$109$	−1.76444	−0.169002	−0.0845012	−	0.996423i	$-0.526930\pi$
$109$	−1.76444	−0.169002	−0.0845012	+	0.996423i	$0.526930\pi$
$110$	−18.9566	−1.80744
$111$	2.79419	0.265213
$112$	−7.17714	−0.678176
$113$	15.1277	1.42309	0.711545	−	0.702640i	$-0.247996\pi$
$113$	15.1277	1.42309	0.711545	+	0.702640i	$0.247996\pi$
$114$	4.68325	0.438627
$115$	4.37563	0.408029
$116$	−37.5674	−3.48804
$117$	2.78115	0.257117
$118$	24.2524	2.23262
$119$	−17.7860	−1.63044
$120$	3.92700	0.358484
$121$	4.48091	0.407356
$122$	6.26969	0.567631
$123$	−4.59917	−0.414693
$124$	−19.2240	−1.72636
$125$	−11.9782	−1.07136
$126$	−18.9791	−1.69079
$127$	−6.17853	−0.548256	−0.274128	−	0.961693i	$-0.588389\pi$
$127$	−6.17853	−0.548256	−0.274128	+	0.961693i	$0.588389\pi$
$128$	20.7268	1.83201
$129$	4.39618	0.387062
$130$	4.81795	0.422562
$131$	−17.3072	−1.51214	−0.756070	−	0.654491i	$-0.772883\pi$
$131$	−17.3072	−1.51214	−0.756070	+	0.654491i	$0.772883\pi$
$132$	−6.88829	−0.599549
$133$	−11.8970	−1.03160
$134$	−17.1380	−1.48050
$135$	5.43759	0.467994
$136$	−26.0758	−2.23598
$137$	−14.0679	−1.20190	−0.600950	−	0.799287i	$-0.705211\pi$
$137$	−14.0679	−1.20190	−0.600950	+	0.799287i	$0.705211\pi$
$138$	2.43971	0.207682
$139$	−5.44710	−0.462017	−0.231009	−	0.972952i	$-0.574203\pi$
$139$	−5.44710	−0.462017	−0.231009	+	0.972952i	$0.574203\pi$
$140$	−21.4272	−1.81093
$141$	−2.22273	−0.187188
$142$	27.5625	2.31300
$143$	−3.93458	−0.329026
$144$	−7.00918	−0.584099
$145$	−20.1832	−1.67612
$146$	32.1603	2.66160
$147$	−0.519236	−0.0428259
$148$	−22.3523	−1.83735
$149$	−0.757208	−0.0620329	−0.0310165	−	0.999519i	$-0.509874\pi$
$149$	−0.757208	−0.0620329	−0.0310165	+	0.999519i	$0.509874\pi$
$150$	−1.07352	−0.0876522
$151$	12.1697	0.990355	0.495177	−	0.868792i	$-0.335103\pi$
$151$	12.1697	0.990355	0.495177	+	0.868792i	$0.335103\pi$
$152$	−17.4421	−1.41474
$153$	−17.3697	−1.40426
$154$	26.8503	2.16366
$155$	−10.3281	−0.829577
$156$	1.75071	0.140169
$157$	21.0201	1.67759	0.838794	−	0.544449i	$-0.183261\pi$
$157$	21.0201	1.67759	0.838794	+	0.544449i	$0.183261\pi$
$158$	−5.11875	−0.407226
$159$	−2.24319	−0.177897
$160$	4.64627	0.367320
$161$	−6.19769	−0.488446
$162$	−16.9617	−1.33263
$163$	−8.82872	−0.691518	−0.345759	−	0.938323i	$-0.612379\pi$
$163$	−8.82872	−0.691518	−0.345759	+	0.938323i	$0.612379\pi$
$164$	36.7913	2.87292
$165$	−3.70076	−0.288104
$166$	−10.4120	−0.808127
$167$	12.5955	0.974667	0.487333	−	0.873216i	$-0.337970\pi$
$167$	12.5955	0.974667	0.487333	+	0.873216i	$0.337970\pi$
$168$	−5.56224	−0.429136
$169$	1.00000	0.0769231
$170$	−30.0906	−2.30784
$171$	−11.6186	−0.888499
$172$	−35.1674	−2.68149
$173$	−1.84505	−0.140276	−0.0701382	−	0.997537i	$-0.522344\pi$
$173$	−1.84505	−0.140276	−0.0701382	+	0.997537i	$0.522344\pi$
$174$	−11.2535	−0.853127
$175$	2.72709	0.206149
$176$	9.91611	0.747455
$177$	4.73463	0.355877
$178$	−40.3458	−3.02405
$179$	−18.2217	−1.36195	−0.680976	−	0.732305i	$-0.738444\pi$
$179$	−18.2217	−1.36195	−0.680976	+	0.732305i	$0.738444\pi$
$180$	−20.9258	−1.55972
$181$	−26.3820	−1.96096	−0.980479	−	0.196625i	$-0.937002\pi$
$181$	−26.3820	−1.96096	−0.980479	+	0.196625i	$0.937002\pi$
$182$	−6.82420	−0.505843
$183$	1.22399	0.0904796
$184$	−9.08635	−0.669854
$185$	−12.0088	−0.882908
$186$	−5.75865	−0.422245
$187$	24.5735	1.79699
$188$	17.7808	1.29680
$189$	−7.70187	−0.560229
$190$	−20.1276	−1.46021
$191$	4.49622	0.325335	0.162668	−	0.986681i	$-0.447990\pi$
$191$	4.49622	0.325335	0.162668	+	0.986681i	$0.447990\pi$
$192$	4.94863	0.357137
$193$	−2.19085	−0.157701	−0.0788505	−	0.996886i	$-0.525125\pi$
$193$	−2.19085	−0.157701	−0.0788505	+	0.996886i	$0.525125\pi$
$194$	0.915140	0.0657033
$195$	0.940573	0.0673558
$196$	4.15366	0.296690
$197$	−18.2275	−1.29865	−0.649327	−	0.760510i	$-0.724949\pi$
$197$	−18.2275	−1.29865	−0.649327	+	0.760510i	$0.724949\pi$
$198$	26.2220	1.86352
$199$	12.3473	0.875278	0.437639	−	0.899151i	$-0.355815\pi$
$199$	12.3473	0.875278	0.437639	+	0.899151i	$0.355815\pi$
$200$	3.99815	0.282712
$201$	−3.34574	−0.235990
$202$	−14.9989	−1.05532
$203$	28.5877	2.00647
$204$	−10.9341	−0.765539
$205$	19.7663	1.38053
$206$	−12.5246	−0.872633
$207$	−6.05265	−0.420688
$208$	−2.52025	−0.174748
$209$	16.4372	1.13699
$210$	−6.41866	−0.442929
$211$	2.01021	0.138389	0.0691943	−	0.997603i	$-0.477957\pi$
$211$	2.01021	0.138389	0.0691943	+	0.997603i	$0.477957\pi$
$212$	17.9445	1.23244
$213$	5.38083	0.368689
$214$	16.1796	1.10602
$215$	−18.8938	−1.28855
$216$	−11.2916	−0.768297
$217$	14.6289	0.993075
$218$	4.22814	0.286366
$219$	6.27842	0.424256
$220$	29.6044	1.99593
$221$	−6.24553	−0.420120
$222$	−6.69575	−0.449389
$223$	19.9498	1.33593	0.667967	−	0.744191i	$-0.267165\pi$
$223$	19.9498	1.33593	0.667967	+	0.744191i	$0.267165\pi$
$224$	−6.58103	−0.439713
$225$	2.66327	0.177552
$226$	−36.2506	−2.41135
$227$	−25.1071	−1.66641	−0.833207	−	0.552961i	$-0.813498\pi$
$227$	−25.1071	−1.66641	−0.833207	+	0.552961i	$0.813498\pi$
$228$	−7.31381	−0.484369
$229$	−11.8858	−0.785434	−0.392717	−	0.919659i	$-0.628465\pi$
$229$	−11.8858	−0.785434	−0.392717	+	0.919659i	$0.628465\pi$
$230$	−10.4854	−0.691384
$231$	5.24180	0.344885
$232$	41.9121	2.75166
$233$	27.7935	1.82081	0.910407	−	0.413713i	$-0.135768\pi$
$233$	27.7935	1.82081	0.910407	+	0.413713i	$0.135768\pi$
$234$	−6.66450	−0.435672
$235$	9.55282	0.623157
$236$	−37.8749	−2.46545
$237$	−0.999297	−0.0649113
$238$	42.6207	2.76269
$239$	15.6532	1.01252	0.506260	−	0.862381i	$-0.331028\pi$
$239$	15.6532	1.01252	0.506260	+	0.862381i	$0.331028\pi$
$240$	−2.37048	−0.153014
$241$	−12.6601	−0.815509	−0.407754	−	0.913092i	$-0.633688\pi$
$241$	−12.6601	−0.815509	−0.407754	+	0.913092i	$0.633688\pi$
$242$	−10.7377	−0.690243
$243$	−11.4248	−0.732903
$244$	−9.79134	−0.626826
$245$	2.23157	0.142570
$246$	11.0210	0.702676
$247$	−4.17763	−0.265817
$248$	21.4472	1.36190
$249$	−2.03266	−0.128814
$250$	28.7035	1.81537
$251$	−9.54280	−0.602336	−0.301168	−	0.953571i	$-0.597377\pi$
$251$	−9.54280	−0.602336	−0.301168	+	0.953571i	$0.597377\pi$
$252$	29.6396	1.86712
$253$	8.56288	0.538343
$254$	14.8057	0.928991
$255$	−5.87437	−0.367868
$256$	−28.5114	−1.78196
$257$	18.9925	1.18472	0.592361	−	0.805673i	$-0.298196\pi$
$257$	18.9925	1.18472	0.592361	+	0.805673i	$0.298196\pi$
$258$	−10.5346	−0.655856
$259$	17.0095	1.05692
$260$	−7.52416	−0.466629
$261$	27.9187	1.72813
$262$	41.4735	2.56224
$263$	23.2697	1.43487	0.717436	−	0.696624i	$-0.245315\pi$
$263$	23.2697	1.43487	0.717436	+	0.696624i	$0.245315\pi$
$264$	7.68493	0.472975
$265$	9.64077	0.592228
$266$	28.5090	1.74800
$267$	−7.87643	−0.482029
$268$	26.7644	1.63489
$269$	22.7962	1.38991	0.694954	−	0.719054i	$-0.255425\pi$
$269$	22.7962	1.38991	0.694954	+	0.719054i	$0.255425\pi$
$270$	−13.0302	−0.792991
$271$	11.7381	0.713042	0.356521	−	0.934287i	$-0.383963\pi$
$271$	11.7381	0.713042	0.356521	+	0.934287i	$0.383963\pi$
$272$	15.7403	0.954394
$273$	−1.33224	−0.0806308
$274$	33.7110	2.03656
$275$	−3.76782	−0.227208
$276$	−3.81008	−0.229340
$277$	−19.2798	−1.15841	−0.579206	−	0.815181i	$-0.696637\pi$
$277$	−19.2798	−1.15841	−0.579206	+	0.815181i	$0.696637\pi$
$278$	13.0529	0.782864
$279$	14.2866	0.855314
$280$	23.9053	1.42862
$281$	−12.3166	−0.734746	−0.367373	−	0.930074i	$-0.619743\pi$
$281$	−12.3166	−0.734746	−0.367373	+	0.930074i	$0.619743\pi$
$282$	5.32635	0.317180
$283$	−32.0267	−1.90379	−0.951896	−	0.306422i	$-0.900868\pi$
$283$	−32.0267	−1.90379	−0.951896	+	0.306422i	$0.900868\pi$
$284$	−43.0442	−2.55421
$285$	−3.92937	−0.232756
$286$	9.42848	0.557517
$287$	−27.9971	−1.65262
$288$	−6.42702	−0.378716
$289$	22.0066	1.29451
$290$	48.3652	2.84010
$291$	0.178656	0.0104730
$292$	−50.2245	−2.93917
$293$	−5.26310	−0.307474	−0.153737	−	0.988112i	$-0.549131\pi$
$293$	−5.26310	−0.307474	−0.153737	+	0.988112i	$0.549131\pi$
$294$	1.24425	0.0725662
$295$	−20.3484	−1.18473
$296$	24.9373	1.44945
$297$	10.6411	0.617459
$298$	1.81451	0.105112
$299$	−2.17631	−0.125859
$300$	1.67650	0.0967930
$301$	26.7615	1.54250
$302$	−29.1623	−1.67810
$303$	−2.92812	−0.168216
$304$	10.5287	0.603861
$305$	−5.26043	−0.301211
$306$	41.6233	2.37945
$307$	3.53681	0.201856	0.100928	−	0.994894i	$-0.467819\pi$
$307$	3.53681	0.201856	0.100928	+	0.994894i	$0.467819\pi$
$308$	−41.9320	−2.38930
$309$	−2.44510	−0.139097
$310$	24.7494	1.40567
$311$	−4.37339	−0.247992	−0.123996	−	0.992283i	$-0.539571\pi$
$311$	−4.37339	−0.247992	−0.123996	+	0.992283i	$0.539571\pi$
$312$	−1.95318	−0.110577
$313$	15.5436	0.878574	0.439287	−	0.898347i	$-0.355231\pi$
$313$	15.5436	0.878574	0.439287	+	0.898347i	$0.355231\pi$
$314$	−50.3708	−2.84259
$315$	15.9240	0.897214
$316$	7.99392	0.449693
$317$	−9.49770	−0.533444	−0.266722	−	0.963773i	$-0.585941\pi$
$317$	−9.49770	−0.533444	−0.266722	+	0.963773i	$0.585941\pi$
$318$	5.37539	0.301437
$319$	−39.4975	−2.21144
$320$	−21.2682	−1.18893
$321$	3.15863	0.176298
$322$	14.8516	0.827647
$323$	26.0915	1.45177
$324$	26.4889	1.47161
$325$	0.957616	0.0531190
$326$	21.1564	1.17174
$327$	0.825430	0.0456464
$328$	−41.0462	−2.26640
$329$	−13.5307	−0.745973
$330$	8.86817	0.488177
$331$	14.3158	0.786865	0.393432	−	0.919354i	$-0.371288\pi$
$331$	14.3158	0.786865	0.393432	+	0.919354i	$0.371288\pi$
$332$	16.2604	0.892403
$333$	16.6114	0.910300
$334$	−30.1827	−1.65152
$335$	14.3793	0.785623
$336$	3.35757	0.183171
$337$	32.7525	1.78415	0.892073	−	0.451892i	$-0.149251\pi$
$337$	32.7525	1.78415	0.892073	+	0.451892i	$0.149251\pi$
$338$	−2.39631	−0.130342
$339$	−7.07694	−0.384367
$340$	46.9924	2.54852
$341$	−20.2117	−1.09452
$342$	27.8418	1.50551
$343$	16.7737	0.905696
$344$	39.2346	2.11539
$345$	−2.04698	−0.110206
$346$	4.42131	0.237691
$347$	1.81334	0.0973454	0.0486727	−	0.998815i	$-0.484501\pi$
$347$	1.81334	0.0973454	0.0486727	+	0.998815i	$0.484501\pi$
$348$	17.5746	0.942096
$349$	−18.0235	−0.964774	−0.482387	−	0.875958i	$-0.660230\pi$
$349$	−18.0235	−0.964774	−0.482387	+	0.875958i	$0.660230\pi$
$350$	−6.53496	−0.349308
$351$	−2.70451	−0.144356
$352$	9.09251	0.484632
$353$	−12.4036	−0.660177	−0.330089	−	0.943950i	$-0.607079\pi$
$353$	−12.4036	−0.660177	−0.330089	+	0.943950i	$0.607079\pi$
$354$	−11.3456	−0.603014
$355$	−23.1257	−1.22738
$356$	63.0079	3.33941
$357$	8.32053	0.440369
$358$	43.6648	2.30776
$359$	−35.6576	−1.88194	−0.940968	−	0.338496i	$-0.890082\pi$
$359$	−35.6576	−1.88194	−0.940968	+	0.338496i	$0.890082\pi$
$360$	23.3459	1.23044
$361$	−1.54737	−0.0814406
$362$	63.2195	3.32274
$363$	−2.09624	−0.110024
$364$	10.6573	0.558595
$365$	−26.9833	−1.41237
$366$	−2.93305	−0.153313
$367$	−0.292180	−0.0152517	−0.00762583	−	0.999971i	$-0.502427\pi$
$367$	−0.292180	−0.0152517	−0.00762583	+	0.999971i	$0.502427\pi$
$368$	5.48485	0.285917
$369$	−27.3420	−1.42337
$370$	28.7769	1.49604
$371$	−13.6553	−0.708948
$372$	8.99325	0.466278
$373$	−23.1064	−1.19640	−0.598202	−	0.801346i	$-0.704118\pi$
$373$	−23.1064	−1.19640	−0.598202	+	0.801346i	$0.704118\pi$
$374$	−58.8858	−3.04491
$375$	5.60357	0.289367
$376$	−19.8372	−1.02303
$377$	10.0386	0.517012
$378$	18.4561	0.949278
$379$	−21.7120	−1.11527	−0.557635	−	0.830086i	$-0.688291\pi$
$379$	−21.7120	−1.11527	−0.557635	+	0.830086i	$0.688291\pi$
$380$	31.4332	1.61249
$381$	2.89041	0.148080
$382$	−10.7744	−0.551264
$383$	−3.86968	−0.197732	−0.0988658	−	0.995101i	$-0.531521\pi$
$383$	−3.86968	−0.197732	−0.0988658	+	0.995101i	$0.531521\pi$
$384$	−9.69629	−0.494812
$385$	−22.5281	−1.14814
$386$	5.24996	0.267216
$387$	26.1352	1.32853
$388$	−1.42917	−0.0725551
$389$	−37.7862	−1.91584	−0.957919	−	0.287037i	$-0.907330\pi$
$389$	−37.7862	−1.91584	−0.957919	+	0.287037i	$0.907330\pi$
$390$	−2.25391	−0.114131
$391$	13.5922	0.687388
$392$	−4.63403	−0.234054
$393$	8.09658	0.408418
$394$	43.6787	2.20050
$395$	4.29476	0.216093
$396$	−40.9508	−2.05785
$397$	−24.9587	−1.25264	−0.626320	−	0.779566i	$-0.715440\pi$
$397$	−24.9587	−1.25264	−0.626320	+	0.779566i	$0.715440\pi$
$398$	−29.5880	−1.48311
$399$	5.56561	0.278629
$400$	−2.41343	−0.120671
$401$	−4.09085	−0.204287	−0.102144	−	0.994770i	$-0.532570\pi$
$401$	−4.09085	−0.204287	−0.102144	+	0.994770i	$0.532570\pi$
$402$	8.01742	0.399873
$403$	5.13693	0.255889
$404$	23.4237	1.16537
$405$	14.2313	0.707158
$406$	−68.5051	−3.39985
$407$	−23.5007	−1.16489
$408$	12.1986	0.603922
$409$	−14.7898	−0.731309	−0.365654	−	0.930751i	$-0.619155\pi$
$409$	−14.7898	−0.731309	−0.365654	+	0.930751i	$0.619155\pi$
$410$	−47.3661	−2.33924
$411$	6.58116	0.324625
$412$	19.5597	0.963636
$413$	28.8218	1.41823
$414$	14.5040	0.712835
$415$	8.73593	0.428830
$416$	−2.31092	−0.113302
$417$	2.54823	0.124788
$418$	−39.3887	−1.92657
$419$	−32.0938	−1.56788	−0.783942	−	0.620834i	$-0.786794\pi$
$419$	−32.0938	−1.56788	−0.783942	+	0.620834i	$0.786794\pi$
$420$	10.0240	0.489120
$421$	−34.6060	−1.68659	−0.843295	−	0.537450i	$-0.819388\pi$
$421$	−34.6060	−1.68659	−0.843295	+	0.537450i	$0.819388\pi$
$422$	−4.81709	−0.234492
$423$	−13.2141	−0.642491
$424$	−20.0199	−0.972250
$425$	−5.98082	−0.290112
$426$	−12.8942	−0.624724
$427$	7.45094	0.360576
$428$	−25.2676	−1.22136
$429$	1.84065	0.0888676
$430$	45.2755	2.18338
$431$	19.9857	0.962676	0.481338	−	0.876535i	$-0.340151\pi$
$431$	19.9857	0.962676	0.481338	+	0.876535i	$0.340151\pi$
$432$	6.81602	0.327936
$433$	−17.5098	−0.841469	−0.420734	−	0.907184i	$-0.638228\pi$
$433$	−17.5098	−0.841469	−0.420734	+	0.907184i	$0.638228\pi$
$434$	−35.0554	−1.68271
$435$	9.44200	0.452709
$436$	−6.60307	−0.316229
$437$	9.09184	0.434922
$438$	−15.0450	−0.718880
$439$	−7.38986	−0.352699	−0.176349	−	0.984328i	$-0.556429\pi$
$439$	−7.38986	−0.352699	−0.176349	+	0.984328i	$0.556429\pi$
$440$	−33.0282	−1.57456
$441$	−3.08685	−0.146993
$442$	14.9662	0.711871
$443$	28.9317	1.37459	0.687293	−	0.726380i	$-0.258799\pi$
$443$	28.9317	1.37459	0.687293	+	0.726380i	$0.258799\pi$
$444$	10.4567	0.496254
$445$	33.8512	1.60470
$446$	−47.8058	−2.26367
$447$	0.354233	0.0167547
$448$	30.1245	1.42325
$449$	10.7850	0.508976	0.254488	−	0.967076i	$-0.418093\pi$
$449$	10.7850	0.508976	0.254488	+	0.967076i	$0.418093\pi$
$450$	−6.38203	−0.300852
$451$	38.6815	1.82144
$452$	56.6123	2.66282
$453$	−5.69316	−0.267488
$454$	60.1643	2.82365
$455$	5.72568	0.268424
$456$	8.15966	0.382111
$457$	7.80116	0.364923	0.182461	−	0.983213i	$-0.441594\pi$
$457$	7.80116	0.364923	0.182461	+	0.983213i	$0.441594\pi$
$458$	28.4820	1.33088
$459$	16.8911	0.788408
$460$	16.3749	0.763485
$461$	−3.48670	−0.162392	−0.0811960	−	0.996698i	$-0.525874\pi$
$461$	−3.48670	−0.162392	−0.0811960	+	0.996698i	$0.525874\pi$
$462$	−12.5610	−0.584390
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−25.2996	−1.17451
$465$	4.83166	0.224063
$466$	−66.6019	−3.08527
$467$	18.0970	0.837428	0.418714	−	0.908118i	$-0.362481\pi$
$467$	18.0970	0.837428	0.418714	+	0.908118i	$0.362481\pi$
$468$	10.4079	0.481106
$469$	−20.3670	−0.940458
$470$	−22.8915	−1.05591
$471$	−9.83352	−0.453105
$472$	42.2552	1.94495
$473$	−36.9743	−1.70008
$474$	2.39463	0.109989
$475$	−4.00057	−0.183559
$476$	−66.5605	−3.05080
$477$	−13.3357	−0.610602
$478$	−37.5099	−1.71566
$479$	−10.2940	−0.470346	−0.235173	−	0.971953i	$-0.575566\pi$
$479$	−10.2940	−0.470346	−0.235173	+	0.971953i	$0.575566\pi$
$480$	−2.17359	−0.0992104
$481$	5.97286	0.272339
$482$	30.3375	1.38184
$483$	2.89937	0.131926
$484$	16.7690	0.762225
$485$	−0.767827	−0.0348652
$486$	27.3774	1.24187
$487$	−9.82419	−0.445176	−0.222588	−	0.974913i	$-0.571451\pi$
$487$	−9.82419	−0.445176	−0.222588	+	0.974913i	$0.571451\pi$
$488$	10.9237	0.494493
$489$	4.13020	0.186774
$490$	−5.34753	−0.241577
$491$	4.04593	0.182590	0.0912951	−	0.995824i	$-0.470899\pi$
$491$	4.04593	0.182590	0.0912951	+	0.995824i	$0.470899\pi$
$492$	−17.2115	−0.775954
$493$	−62.6961	−2.82369
$494$	10.0109	0.450412
$495$	−22.0009	−0.988869
$496$	−12.9463	−0.581307
$497$	32.7555	1.46928
$498$	4.87088	0.218269
$499$	8.22113	0.368028	0.184014	−	0.982924i	$-0.441091\pi$
$499$	8.22113	0.368028	0.184014	+	0.982924i	$0.441091\pi$
$500$	−44.8261	−2.00468
$501$	−5.89235	−0.263251
$502$	22.8675	1.02063
$503$	18.2359	0.813098	0.406549	−	0.913629i	$-0.366732\pi$
$503$	18.2359	0.813098	0.406549	+	0.913629i	$0.366732\pi$
$504$	−33.0674	−1.47294
$505$	12.5845	0.560001
$506$	−20.5193	−0.912195
$507$	−0.467815	−0.0207764
$508$	−23.1219	−1.02587
$509$	7.95577	0.352634	0.176317	−	0.984333i	$-0.443582\pi$
$509$	7.95577	0.352634	0.176317	+	0.984333i	$0.443582\pi$
$510$	14.0768	0.623333
$511$	38.2195	1.69073
$512$	26.8687	1.18744
$513$	11.2984	0.498838
$514$	−45.5120	−2.00745
$515$	10.5085	0.463060
$516$	16.4518	0.724252
$517$	18.6944	0.822178
$518$	−40.7600	−1.79089
$519$	0.863140	0.0378877
$520$	8.39434	0.368116
$521$	−12.2503	−0.536696	−0.268348	−	0.963322i	$-0.586478\pi$
$521$	−12.2503	−0.536696	−0.268348	+	0.963322i	$0.586478\pi$
$522$	−66.9020	−2.92822
$523$	29.8998	1.30743	0.653713	−	0.756742i	$-0.273210\pi$
$523$	29.8998	1.30743	0.653713	+	0.756742i	$0.273210\pi$
$524$	−64.7690	−2.82945
$525$	−1.27577	−0.0556793
$526$	−55.7615	−2.43132
$527$	−32.0828	−1.39755
$528$	−4.63890	−0.201882
$529$	−18.2637	−0.794072
$530$	−23.1023	−1.00350
$531$	28.1473	1.22149
$532$	−44.5224	−1.93029
$533$	−9.83118	−0.425836
$534$	18.8744	0.816774
$535$	−13.5751	−0.586904
$536$	−29.8597	−1.28974
$537$	8.52437	0.367854
$538$	−54.6268	−2.35513
$539$	4.36706	0.188103
$540$	20.3491	0.875688
$541$	−37.3343	−1.60513	−0.802564	−	0.596566i	$-0.796532\pi$
$541$	−37.3343	−1.60513	−0.802564	+	0.596566i	$0.796532\pi$
$542$	−28.1282	−1.20821
$543$	12.3419	0.529641
$544$	14.4329	0.618807
$545$	−3.54752	−0.151959
$546$	3.19246	0.136625
$547$	22.5833	0.965592	0.482796	−	0.875733i	$-0.339621\pi$
$547$	22.5833	0.965592	0.482796	+	0.875733i	$0.339621\pi$
$548$	−52.6463	−2.24894
$549$	7.27657	0.310557
$550$	9.02886	0.384992
$551$	−41.9374	−1.78659
$552$	4.25073	0.180923
$553$	−6.08315	−0.258682
$554$	46.2004	1.96287
$555$	5.61791	0.238467
$556$	−20.3847	−0.864505
$557$	−7.57210	−0.320840	−0.160420	−	0.987049i	$-0.551285\pi$
$557$	−7.57210	−0.320840	−0.160420	+	0.987049i	$0.551285\pi$
$558$	−34.2351	−1.44929
$559$	9.39726	0.397462
$560$	−14.4301	−0.609784
$561$	−11.4959	−0.485355
$562$	29.5144	1.24499
$563$	−31.4051	−1.32357	−0.661784	−	0.749695i	$-0.730200\pi$
$563$	−31.4051	−1.32357	−0.661784	+	0.749695i	$0.730200\pi$
$564$	−8.31814	−0.350257
$565$	30.4152	1.27958
$566$	76.7460	3.22588
$567$	−20.1574	−0.846529
$568$	48.0224	2.01497
$569$	−33.4899	−1.40397	−0.701985	−	0.712192i	$-0.747703\pi$
$569$	−33.4899	−1.40397	−0.701985	+	0.712192i	$0.747703\pi$
$570$	9.41599	0.394393
$571$	26.8201	1.12239	0.561194	−	0.827684i	$-0.310342\pi$
$571$	26.8201	1.12239	0.561194	+	0.827684i	$0.310342\pi$
$572$	−14.7244	−0.615658
$573$	−2.10340	−0.0878708
$574$	67.0899	2.80028
$575$	−2.08407	−0.0869119
$576$	29.4195	1.22581
$577$	−7.95789	−0.331291	−0.165646	−	0.986185i	$-0.552971\pi$
$577$	−7.95789	−0.331291	−0.165646	+	0.986185i	$0.552971\pi$
$578$	−52.7347	−2.19347
$579$	1.02491	0.0425939
$580$	−75.5318	−3.13629
$581$	−12.3737	−0.513347
$582$	−0.428116	−0.0177460
$583$	18.8665	0.781371
$584$	56.0331	2.31866
$585$	5.59169	0.231188
$586$	12.6120	0.520998
$587$	13.5868	0.560786	0.280393	−	0.959885i	$-0.409535\pi$
$587$	13.5868	0.560786	0.280393	+	0.959885i	$0.409535\pi$
$588$	−1.94314	−0.0801338
$589$	−21.4602	−0.884253
$590$	48.7612	2.00747
$591$	8.52708	0.350757
$592$	−15.0531	−0.618678
$593$	−23.3075	−0.957124	−0.478562	−	0.878054i	$-0.658842\pi$
$593$	−23.3075	−0.957124	−0.478562	+	0.878054i	$0.658842\pi$
$594$	−25.4994	−1.04625
$595$	−35.7599	−1.46601
$596$	−2.83371	−0.116073
$597$	−5.77626	−0.236407
$598$	5.21512	0.213262
$599$	−12.4832	−0.510048	−0.255024	−	0.966935i	$-0.582083\pi$
$599$	−12.4832	−0.510048	−0.255024	+	0.966935i	$0.582083\pi$
$600$	−1.87039	−0.0763585
$601$	5.84598	0.238462	0.119231	−	0.992867i	$-0.461957\pi$
$601$	5.84598	0.238462	0.119231	+	0.992867i	$0.461957\pi$
$602$	−64.1288	−2.61369
$603$	−19.8903	−0.809997
$604$	45.5427	1.85311
$605$	9.00918	0.366275
$606$	7.01670	0.285034
$607$	3.92658	0.159375	0.0796874	−	0.996820i	$-0.474608\pi$
$607$	3.92658	0.159375	0.0796874	+	0.996820i	$0.474608\pi$
$608$	9.65419	0.391529
$609$	−13.3738	−0.541932
$610$	12.6056	0.510387
$611$	−4.75131	−0.192217
$612$	−65.0029	−2.62759
$613$	27.6069	1.11503	0.557516	−	0.830167i	$-0.311755\pi$
$613$	27.6069	1.11503	0.557516	+	0.830167i	$0.311755\pi$
$614$	−8.47530	−0.342035
$615$	−9.24694	−0.372873
$616$	46.7815	1.88488
$617$	−39.8336	−1.60364	−0.801821	−	0.597565i	$-0.796135\pi$
$617$	−39.8336	−1.60364	−0.801821	+	0.597565i	$0.796135\pi$
$618$	5.85921	0.235692
$619$	−12.4259	−0.499438	−0.249719	−	0.968318i	$-0.580338\pi$
$619$	−12.4259	−0.499438	−0.249719	+	0.968318i	$0.580338\pi$
$620$	−38.6511	−1.55227
$621$	5.88585	0.236191
$622$	10.4800	0.420210
$623$	−47.9472	−1.92097
$624$	1.17901	0.0471981
$625$	−19.2949	−0.771796
$626$	−37.2472	−1.48870
$627$	−7.68958	−0.307092
$628$	78.6637	3.13903
$629$	−37.3037	−1.48739
$630$	−38.1588	−1.52028
$631$	20.2478	0.806054	0.403027	−	0.915188i	$-0.367958\pi$
$631$	20.2478	0.806054	0.403027	+	0.915188i	$0.367958\pi$
$632$	−8.91843	−0.354756
$633$	−0.940406	−0.0373778
$634$	22.7595	0.903893
$635$	−12.4224	−0.492966
$636$	−8.39472	−0.332872
$637$	−1.10992	−0.0439766
$638$	94.6483	3.74716
$639$	31.9890	1.26546
$640$	41.6726	1.64725
$641$	−29.4215	−1.16208	−0.581040	−	0.813875i	$-0.697354\pi$
$641$	−29.4215	−1.16208	−0.581040	+	0.813875i	$0.697354\pi$
$642$	−7.56907	−0.298727
$643$	−13.2214	−0.521402	−0.260701	−	0.965420i	$-0.583954\pi$
$643$	−13.2214	−0.521402	−0.260701	+	0.965420i	$0.583954\pi$
$644$	−23.1936	−0.913958
$645$	8.83881	0.348028
$646$	−62.5234	−2.45995
$647$	−6.70718	−0.263687	−0.131843	−	0.991271i	$-0.542090\pi$
$647$	−6.70718	−0.263687	−0.131843	+	0.991271i	$0.542090\pi$
$648$	−29.5524	−1.16093
$649$	−39.8209	−1.56311
$650$	−2.29475	−0.0900074
$651$	−6.84362	−0.268222
$652$	−33.0398	−1.29394
$653$	12.6801	0.496210	0.248105	−	0.968733i	$-0.420192\pi$
$653$	12.6801	0.496210	0.248105	+	0.968733i	$0.420192\pi$
$654$	−1.97799	−0.0773454
$655$	−34.7974	−1.35965
$656$	24.7770	0.967379
$657$	37.3251	1.45619
$658$	32.4238	1.26401
$659$	−8.87171	−0.345593	−0.172796	−	0.984958i	$-0.555280\pi$
$659$	−8.87171	−0.345593	−0.172796	+	0.984958i	$0.555280\pi$
$660$	−13.8494	−0.539086
$661$	−12.1598	−0.472960	−0.236480	−	0.971636i	$-0.575994\pi$
$661$	−12.1598	−0.472960	−0.236480	+	0.971636i	$0.575994\pi$
$662$	−34.3050	−1.33330
$663$	2.92175	0.113471
$664$	−18.1409	−0.704003
$665$	−23.9198	−0.927570
$666$	−39.8061	−1.54246
$667$	−21.8471	−0.845921
$668$	47.1361	1.82375
$669$	−9.33279	−0.360826
$670$	−34.4572	−1.33120
$671$	−10.2944	−0.397411
$672$	3.07870	0.118763
$673$	32.9877	1.27158	0.635792	−	0.771861i	$-0.280674\pi$
$673$	32.9877	1.27158	0.635792	+	0.771861i	$0.280674\pi$
$674$	−78.4853	−3.02314
$675$	−2.58988	−0.0996845
$676$	3.74231	0.143935
$677$	−2.49942	−0.0960606	−0.0480303	−	0.998846i	$-0.515294\pi$
$677$	−2.49942	−0.0960606	−0.0480303	+	0.998846i	$0.515294\pi$
$678$	16.9585	0.651289
$679$	1.08756	0.0417367
$680$	−52.4271	−2.01049
$681$	11.7455	0.450087
$682$	48.4334	1.85461
$683$	−20.1647	−0.771581	−0.385790	−	0.922586i	$-0.626071\pi$
$683$	−20.1647	−0.771581	−0.385790	+	0.922586i	$0.626071\pi$
$684$	−43.4805	−1.66252
$685$	−28.2844	−1.08069
$686$	−40.1951	−1.53465
$687$	5.56034	0.212140
$688$	−23.6834	−0.902922
$689$	−4.79505	−0.182677
$690$	4.90521	0.186738
$691$	3.89707	0.148251	0.0741257	−	0.997249i	$-0.476383\pi$
$691$	3.89707	0.148251	0.0741257	+	0.997249i	$0.476383\pi$
$692$	−6.90473	−0.262479
$693$	31.1624	1.18376
$694$	−4.34533	−0.164947
$695$	−10.9518	−0.415424
$696$	−19.6071	−0.743205
$697$	61.4009	2.32572
$698$	43.1898	1.63476
$699$	−13.0022	−0.491789
$700$	10.2056	0.385736
$701$	−11.3525	−0.428778	−0.214389	−	0.976748i	$-0.568776\pi$
$701$	−11.3525	−0.428778	−0.214389	+	0.976748i	$0.568776\pi$
$702$	6.48084	0.244603
$703$	−24.9524	−0.941098
$704$	−41.6207	−1.56864
$705$	−4.46895	−0.168310
$706$	29.7229	1.11864
$707$	−17.8248	−0.670370
$708$	17.7184	0.665900
$709$	−38.2924	−1.43810	−0.719051	−	0.694958i	$-0.755423\pi$
$709$	−38.2924	−1.43810	−0.719051	+	0.694958i	$0.755423\pi$
$710$	55.4163	2.07974
$711$	−5.94080	−0.222797
$712$	−70.2948	−2.63441
$713$	−11.1796	−0.418678
$714$	−19.9386	−0.746183
$715$	−7.91074	−0.295845
$716$	−68.1911	−2.54842
$717$	−7.32278	−0.273474
$718$	85.4467	3.18884
$719$	−4.37499	−0.163160	−0.0815798	−	0.996667i	$-0.525997\pi$
$719$	−4.37499	−0.163160	−0.0815798	+	0.996667i	$0.525997\pi$
$720$	−14.0924	−0.525194
$721$	−14.8844	−0.554323
$722$	3.70798	0.137997
$723$	5.92258	0.220263
$724$	−98.7295	−3.66925
$725$	9.61309	0.357021
$726$	5.02324	0.186430
$727$	−16.7606	−0.621616	−0.310808	−	0.950473i	$-0.600600\pi$
$727$	−16.7606	−0.621616	−0.310808	+	0.950473i	$0.600600\pi$
$728$	−11.8898	−0.440667
$729$	−15.8900	−0.588519
$730$	64.6604	2.39319
$731$	−58.6909	−2.17076
$732$	4.58053	0.169301
$733$	−45.3073	−1.67346	−0.836732	−	0.547613i	$-0.815537\pi$
$733$	−45.3073	−1.67346	−0.836732	+	0.547613i	$0.815537\pi$
$734$	0.700154	0.0258431
$735$	−1.04396	−0.0385070
$736$	5.02929	0.185382
$737$	28.1395	1.03653
$738$	65.5199	2.41182
$739$	16.1646	0.594626	0.297313	−	0.954780i	$-0.403909\pi$
$739$	16.1646	0.594626	0.297313	+	0.954780i	$0.403909\pi$
$740$	−44.9408	−1.65206
$741$	1.95436	0.0717952
$742$	32.7224	1.20128
$743$	−13.9951	−0.513429	−0.256715	−	0.966487i	$-0.582640\pi$
$743$	−13.9951	−0.513429	−0.256715	+	0.966487i	$0.582640\pi$
$744$	−10.0333	−0.367840
$745$	−1.52242	−0.0557771
$746$	55.3701	2.02724
$747$	−12.0841	−0.442135
$748$	91.9617	3.36245
$749$	19.2280	0.702575
$750$	−13.4279	−0.490318
$751$	35.9601	1.31220	0.656101	−	0.754673i	$-0.272205\pi$
$751$	35.9601	1.31220	0.656101	+	0.754673i	$0.272205\pi$
$752$	11.9745	0.436664
$753$	4.46426	0.162687
$754$	−24.0555	−0.876050
$755$	24.4680	0.890481
$756$	−28.8228	−1.04827
$757$	−33.8182	−1.22915	−0.614573	−	0.788860i	$-0.710671\pi$
$757$	−33.8182	−1.22915	−0.614573	+	0.788860i	$0.710671\pi$
$758$	52.0287	1.88977
$759$	−4.00584	−0.145403
$760$	−35.0685	−1.27207
$761$	52.7614	1.91260	0.956300	−	0.292386i	$-0.0944492\pi$
$761$	52.7614	1.91260	0.956300	+	0.292386i	$0.0944492\pi$
$762$	−6.92631	−0.250914
$763$	5.02475	0.181908
$764$	16.8262	0.608752
$765$	−34.9231	−1.26265
$766$	9.27296	0.335046
$767$	10.1207	0.365439
$768$	13.3381	0.481296
$769$	15.4646	0.557666	0.278833	−	0.960340i	$-0.410052\pi$
$769$	15.4646	0.557666	0.278833	+	0.960340i	$0.410052\pi$
$770$	53.9844	1.94546
$771$	−8.88499	−0.319985
$772$	−8.19884	−0.295083
$773$	−27.7960	−0.999753	−0.499877	−	0.866097i	$-0.666621\pi$
$773$	−27.7960	−0.999753	−0.499877	+	0.866097i	$0.666621\pi$
$774$	−62.6281	−2.25112
$775$	4.91921	0.176703
$776$	1.59446	0.0572376
$777$	−7.95728	−0.285466
$778$	90.5476	3.24629
$779$	41.0711	1.47152
$780$	3.51991	0.126033
$781$	−45.2558	−1.61938
$782$	−32.5712	−1.16474
$783$	−27.1493	−0.970239
$784$	2.79727	0.0999025
$785$	42.2624	1.50841
$786$	−19.4019	−0.692044
$787$	13.5449	0.482825	0.241412	−	0.970423i	$-0.422389\pi$
$787$	13.5449	0.482825	0.241412	+	0.970423i	$0.422389\pi$
$788$	−68.2128	−2.42998
$789$	−10.8859	−0.387549
$790$	−10.2916	−0.366158
$791$	−43.0804	−1.53176
$792$	45.6868	1.62341
$793$	2.61639	0.0929107
$794$	59.8087	2.12253
$795$	−4.51009	−0.159957
$796$	46.2075	1.63778
$797$	1.77673	0.0629352	0.0314676	−	0.999505i	$-0.489982\pi$
$797$	1.77673	0.0629352	0.0314676	+	0.999505i	$0.489982\pi$
$798$	−13.3369	−0.472122
$799$	29.6744	1.04980
$800$	−2.21298	−0.0782406
$801$	−46.8252	−1.65449
$802$	9.80295	0.346154
$803$	−52.8050	−1.86345
$804$	−12.5208	−0.441573
$805$	−12.4609	−0.439188
$806$	−12.3097	−0.433590
$807$	−10.6644	−0.375404
$808$	−26.1327	−0.919344
$809$	28.0992	0.987916	0.493958	−	0.869486i	$-0.335550\pi$
$809$	28.0992	0.987916	0.493958	+	0.869486i	$0.335550\pi$
$810$	−34.1026	−1.19824
$811$	−17.8135	−0.625518	−0.312759	−	0.949833i	$-0.601253\pi$
$811$	−17.8135	−0.625518	−0.312759	+	0.949833i	$0.601253\pi$
$812$	106.984	3.75440
$813$	−5.49128	−0.192587
$814$	56.3150	1.97384
$815$	−17.7507	−0.621781
$816$	−7.36353	−0.257775
$817$	−39.2583	−1.37348
$818$	35.4410	1.23916
$819$	−7.92014	−0.276752
$820$	73.9714	2.58319
$821$	−2.41218	−0.0841857	−0.0420929	−	0.999114i	$-0.513403\pi$
$821$	−2.41218	−0.0841857	−0.0420929	+	0.999114i	$0.513403\pi$
$822$	−15.7705	−0.550059
$823$	−29.8032	−1.03887	−0.519437	−	0.854509i	$-0.673858\pi$
$823$	−29.8032	−1.03887	−0.519437	+	0.854509i	$0.673858\pi$
$824$	−21.8218	−0.760197
$825$	1.76264	0.0613672
$826$	−69.0659	−2.40311
$827$	22.4131	0.779381	0.389691	−	0.920946i	$-0.372582\pi$
$827$	22.4131	0.779381	0.389691	+	0.920946i	$0.372582\pi$
$828$	−22.6509	−0.787173
$829$	−41.7553	−1.45022	−0.725111	−	0.688632i	$-0.758211\pi$
$829$	−41.7553	−1.45022	−0.725111	+	0.688632i	$0.758211\pi$
$830$	−20.9340	−0.726630
$831$	9.01938	0.312879
$832$	10.5782	0.366733
$833$	6.93203	0.240181
$834$	−6.10636	−0.211446
$835$	25.3241	0.876375
$836$	61.5132	2.12748
$837$	−13.8929	−0.480207
$838$	76.9067	2.65670
$839$	−24.4753	−0.844980	−0.422490	−	0.906368i	$-0.638844\pi$
$839$	−24.4753	−0.844980	−0.422490	+	0.906368i	$0.638844\pi$
$840$	−11.1833	−0.385859
$841$	71.7727	2.47492
$842$	82.9266	2.85784
$843$	5.76188	0.198450
$844$	7.52282	0.258946
$845$	2.01057	0.0691656
$846$	31.6651	1.08867
$847$	−12.7607	−0.438463
$848$	12.0847	0.414991
$849$	14.9826	0.514201
$850$	14.3319	0.491580
$851$	−12.9988	−0.445594
$852$	20.1367	0.689873
$853$	5.20965	0.178375	0.0891875	−	0.996015i	$-0.471573\pi$
$853$	5.20965	0.178375	0.0891875	+	0.996015i	$0.471573\pi$
$854$	−17.8548	−0.610977
$855$	−23.3600	−0.798896
$856$	28.1899	0.963510
$857$	33.4396	1.14228	0.571138	−	0.820854i	$-0.306502\pi$
$857$	33.4396	1.14228	0.571138	+	0.820854i	$0.306502\pi$
$858$	−4.41078	−0.150582
$859$	−49.7923	−1.69889	−0.849446	−	0.527676i	$-0.823064\pi$
$859$	−49.7923	−1.69889	−0.849446	+	0.527676i	$0.823064\pi$
$860$	−70.7065	−2.41107
$861$	13.0975	0.446361
$862$	−47.8919	−1.63120
$863$	−7.94831	−0.270564	−0.135282	−	0.990807i	$-0.543194\pi$
$863$	−7.94831	−0.270564	−0.135282	+	0.990807i	$0.543194\pi$
$864$	6.24991	0.212626
$865$	−3.70959	−0.126130
$866$	41.9590	1.42582
$867$	−10.2950	−0.349637
$868$	54.7459	1.85820
$869$	8.40464	0.285108
$870$	−22.6260	−0.767092
$871$	−7.15184	−0.242331
$872$	7.36672	0.249469
$873$	1.06211	0.0359469
$874$	−21.7869	−0.736952
$875$	34.1114	1.15318
$876$	23.4958	0.793849
$877$	−24.7177	−0.834658	−0.417329	−	0.908756i	$-0.637034\pi$
$877$	−24.7177	−0.834658	−0.417329	+	0.908756i	$0.637034\pi$
$878$	17.7084	0.597630
$879$	2.46215	0.0830464
$880$	19.9370	0.672077
$881$	−49.4786	−1.66698	−0.833488	−	0.552537i	$-0.813660\pi$
$881$	−49.4786	−1.66698	−0.833488	+	0.552537i	$0.813660\pi$
$882$	7.39705	0.249072
$883$	22.8327	0.768380	0.384190	−	0.923254i	$-0.374481\pi$
$883$	22.8327	0.768380	0.384190	+	0.923254i	$0.374481\pi$
$884$	−23.3727	−0.786108
$885$	9.51930	0.319988
$886$	−69.3294	−2.32917
$887$	32.7464	1.09952	0.549758	−	0.835324i	$-0.314720\pi$
$887$	32.7464	1.09952	0.549758	+	0.835324i	$0.314720\pi$
$888$	−11.6661	−0.391487
$889$	17.5952	0.590123
$890$	−81.1180	−2.71908
$891$	27.8499	0.933007
$892$	74.6581	2.49974
$893$	19.8492	0.664229
$894$	−0.848853	−0.0283899
$895$	−36.6359	−1.22460
$896$	−59.0255	−1.97190
$897$	1.01811	0.0339937
$898$	−25.8442	−0.862433
$899$	51.5674	1.71987
$900$	9.96679	0.332226
$901$	29.9476	0.997700
$902$	−92.6930	−3.08634
$903$	−12.5194	−0.416619
$904$	−63.1596	−2.10066
$905$	−53.0428	−1.76320
$906$	13.6426	0.453244
$907$	16.6782	0.553790	0.276895	−	0.960900i	$-0.410695\pi$
$907$	16.6782	0.553790	0.276895	+	0.960900i	$0.410695\pi$
$908$	−93.9583	−3.11812
$909$	−17.4076	−0.577375
$910$	−13.7205	−0.454830
$911$	50.3435	1.66796	0.833978	−	0.551798i	$-0.186058\pi$
$911$	50.3435	1.66796	0.833978	+	0.551798i	$0.186058\pi$
$912$	−4.92547	−0.163098
$913$	17.0958	0.565788
$914$	−18.6940	−0.618343
$915$	2.46091	0.0813551
$916$	−44.4802	−1.46967
$917$	49.2874	1.62761
$918$	−40.4763	−1.33592
$919$	−24.6359	−0.812665	−0.406332	−	0.913725i	$-0.633193\pi$
$919$	−24.6359	−0.812665	−0.406332	+	0.913725i	$0.633193\pi$
$920$	−18.2687	−0.602302
$921$	−1.65457	−0.0545200
$922$	8.35523	0.275165
$923$	11.5021	0.378595
$924$	19.6164	0.645333
$925$	5.71971	0.188063
$926$	2.39631	0.0787477
$927$	−14.5361	−0.477427
$928$	−23.1983	−0.761523
$929$	−7.41679	−0.243337	−0.121668	−	0.992571i	$-0.538824\pi$
$929$	−7.41679	−0.243337	−0.121668	+	0.992571i	$0.538824\pi$
$930$	−11.5782	−0.379663
$931$	4.63684	0.151966
$932$	104.012	3.40702
$933$	2.04594	0.0669809
$934$	−43.3660	−1.41898
$935$	49.4067	1.61577
$936$	−11.6116	−0.379537
$937$	41.4803	1.35510	0.677551	−	0.735476i	$-0.263041\pi$
$937$	41.4803	1.35510	0.677551	+	0.735476i	$0.263041\pi$
$938$	48.8056	1.59356
$939$	−7.27151	−0.237297
$940$	35.7496	1.16602
$941$	27.0010	0.880206	0.440103	−	0.897947i	$-0.354942\pi$
$941$	27.0010	0.880206	0.440103	+	0.897947i	$0.354942\pi$
$942$	23.5642	0.767762
$943$	21.3957	0.696741
$944$	−25.5068	−0.830175
$945$	−15.4851	−0.503732
$946$	88.6019	2.88070
$947$	−3.25673	−0.105829	−0.0529147	−	0.998599i	$-0.516851\pi$
$947$	−3.25673	−0.105829	−0.0529147	+	0.998599i	$0.516851\pi$
$948$	−3.73967	−0.121459
$949$	13.4207	0.435656
$950$	9.58661	0.311031
$951$	4.44316	0.144079
$952$	74.2583	2.40673
$953$	−33.9932	−1.10115	−0.550574	−	0.834786i	$-0.685591\pi$
$953$	−33.9932	−1.10115	−0.550574	+	0.834786i	$0.685591\pi$
$954$	31.9566	1.03463
$955$	9.03996	0.292526
$956$	58.5790	1.89458
$957$	18.4775	0.597293
$958$	24.6677	0.796978
$959$	40.0624	1.29368
$960$	9.94956	0.321121
$961$	−4.61196	−0.148773
$962$	−14.3128	−0.461464
$963$	18.7780	0.605113
$964$	−47.3780	−1.52594
$965$	−4.40486	−0.141797
$966$	−6.94779	−0.223541
$967$	−47.6609	−1.53267	−0.766335	−	0.642441i	$-0.777922\pi$
$967$	−47.6609	−1.53267	−0.766335	+	0.642441i	$0.777922\pi$
$968$	−18.7083	−0.601308
$969$	−12.2060	−0.392113
$970$	1.83995	0.0590773
$971$	−53.3486	−1.71204	−0.856018	−	0.516946i	$-0.827069\pi$
$971$	−53.3486	−1.71204	−0.856018	+	0.516946i	$0.827069\pi$
$972$	−42.7552	−1.37137
$973$	15.5122	0.497299
$974$	23.5418	0.754328
$975$	−0.447987	−0.0143471
$976$	−6.59395	−0.211067
$977$	−21.0622	−0.673840	−0.336920	−	0.941533i	$-0.609385\pi$
$977$	−21.0622	−0.673840	−0.336920	+	0.941533i	$0.609385\pi$
$978$	−9.89725	−0.316479
$979$	66.2451	2.11720
$980$	8.35121	0.266770
$981$	4.90716	0.156674
$982$	−9.69531	−0.309390
$983$	−33.6243	−1.07245	−0.536224	−	0.844076i	$-0.680150\pi$
$983$	−33.6243	−1.07245	−0.536224	+	0.844076i	$0.680150\pi$
$984$	19.2020	0.612138
$985$	−36.6476	−1.16769
$986$	150.239	4.78460
$987$	6.32987	0.201482
$988$	−15.6340	−0.497383
$989$	−20.4514	−0.650316
$990$	52.7211	1.67559
$991$	43.5186	1.38241	0.691207	−	0.722657i	$-0.257079\pi$
$991$	43.5186	1.38241	0.691207	+	0.722657i	$0.257079\pi$
$992$	−11.8710	−0.376906
$993$	−6.69712	−0.212527
$994$	−78.4923	−2.48963
$995$	24.8251	0.787010
$996$	−7.60683	−0.241032
$997$	−47.2702	−1.49706	−0.748531	−	0.663100i	$-0.769240\pi$
$997$	−47.2702	−1.49706	−0.748531	+	0.663100i	$0.769240\pi$
$998$	−19.7004	−0.623605
$999$	−16.1536	−0.511078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.11	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.39631 q^{2} -0.467815 q^{3} +3.74231 q^{4} +2.01057 q^{5} +1.12103 q^{6} -2.84779 q^{7} -4.17511 q^{8} -2.78115 q^{9} +O(q^{10})\)	\(q-2.39631 q^{2} -0.467815 q^{3} +3.74231 q^{4} +2.01057 q^{5} +1.12103 q^{6} -2.84779 q^{7} -4.17511 q^{8} -2.78115 q^{9} -4.81795 q^{10} +3.93458 q^{11} -1.75071 q^{12} -1.00000 q^{13} +6.82420 q^{14} -0.940573 q^{15} +2.52025 q^{16} +6.24553 q^{17} +6.66450 q^{18} +4.17763 q^{19} +7.52416 q^{20} +1.33224 q^{21} -9.42848 q^{22} +2.17631 q^{23} +1.95318 q^{24} -0.957616 q^{25} +2.39631 q^{26} +2.70451 q^{27} -10.6573 q^{28} -10.0386 q^{29} +2.25391 q^{30} -5.13693 q^{31} +2.31092 q^{32} -1.84065 q^{33} -14.9662 q^{34} -5.72568 q^{35} -10.4079 q^{36} -5.97286 q^{37} -10.0109 q^{38} +0.467815 q^{39} -8.39434 q^{40} +9.83118 q^{41} -3.19246 q^{42} -9.39726 q^{43} +14.7244 q^{44} -5.59169 q^{45} -5.21512 q^{46} +4.75131 q^{47} -1.17901 q^{48} +1.10992 q^{49} +2.29475 q^{50} -2.92175 q^{51} -3.74231 q^{52} +4.79505 q^{53} -6.48084 q^{54} +7.91074 q^{55} +11.8898 q^{56} -1.95436 q^{57} +24.0555 q^{58} -10.1207 q^{59} -3.51991 q^{60} -2.61639 q^{61} +12.3097 q^{62} +7.92014 q^{63} -10.5782 q^{64} -2.01057 q^{65} +4.41078 q^{66} +7.15184 q^{67} +23.3727 q^{68} -1.01811 q^{69} +13.7205 q^{70} -11.5021 q^{71} +11.6116 q^{72} -13.4207 q^{73} +14.3128 q^{74} +0.447987 q^{75} +15.6340 q^{76} -11.2049 q^{77} -1.12103 q^{78} +2.13610 q^{79} +5.06713 q^{80} +7.07824 q^{81} -23.5586 q^{82} +4.34501 q^{83} +4.98565 q^{84} +12.5571 q^{85} +22.5188 q^{86} +4.69619 q^{87} -16.4273 q^{88} +16.8366 q^{89} +13.3994 q^{90} +2.84779 q^{91} +8.14443 q^{92} +2.40313 q^{93} -11.3856 q^{94} +8.39942 q^{95} -1.08108 q^{96} -0.381896 q^{97} -2.65971 q^{98} -10.9427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 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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