LMFDB - Embedded newform 4019.2.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$0$
Dimension:	$186$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67918 q^{2} +1.79491 q^{3} +5.17799 q^{4} +3.40719 q^{5} -4.80888 q^{6} +4.24264 q^{7} -8.51439 q^{8} +0.221695 q^{9} +O(q^{10})$	\(q-2.67918 q^{2} +1.79491 q^{3} +5.17799 q^{4} +3.40719 q^{5} -4.80888 q^{6} +4.24264 q^{7} -8.51439 q^{8} +0.221695 q^{9} -9.12846 q^{10} +2.35460 q^{11} +9.29401 q^{12} -0.771756 q^{13} -11.3668 q^{14} +6.11559 q^{15} +12.4556 q^{16} -0.943428 q^{17} -0.593959 q^{18} +0.177774 q^{19} +17.6424 q^{20} +7.61515 q^{21} -6.30838 q^{22} +4.24430 q^{23} -15.2825 q^{24} +6.60893 q^{25} +2.06767 q^{26} -4.98680 q^{27} +21.9683 q^{28} -3.76412 q^{29} -16.3847 q^{30} +1.56412 q^{31} -16.3419 q^{32} +4.22628 q^{33} +2.52761 q^{34} +14.4555 q^{35} +1.14793 q^{36} -4.89927 q^{37} -0.476289 q^{38} -1.38523 q^{39} -29.0101 q^{40} +5.04113 q^{41} -20.4023 q^{42} +2.14408 q^{43} +12.1921 q^{44} +0.755355 q^{45} -11.3712 q^{46} -2.93352 q^{47} +22.3566 q^{48} +11.0000 q^{49} -17.7065 q^{50} -1.69337 q^{51} -3.99614 q^{52} -5.59078 q^{53} +13.3605 q^{54} +8.02255 q^{55} -36.1235 q^{56} +0.319089 q^{57} +10.0847 q^{58} -10.0882 q^{59} +31.6664 q^{60} +4.00902 q^{61} -4.19056 q^{62} +0.940570 q^{63} +18.8717 q^{64} -2.62952 q^{65} -11.3230 q^{66} -5.93967 q^{67} -4.88506 q^{68} +7.61813 q^{69} -38.7288 q^{70} +0.981034 q^{71} -1.88759 q^{72} +12.6623 q^{73} +13.1260 q^{74} +11.8624 q^{75} +0.920513 q^{76} +9.98970 q^{77} +3.71128 q^{78} +8.26770 q^{79} +42.4385 q^{80} -9.61594 q^{81} -13.5061 q^{82} +2.07952 q^{83} +39.4311 q^{84} -3.21444 q^{85} -5.74437 q^{86} -6.75625 q^{87} -20.0479 q^{88} +10.1165 q^{89} -2.02373 q^{90} -3.27428 q^{91} +21.9769 q^{92} +2.80746 q^{93} +7.85941 q^{94} +0.605711 q^{95} -29.3322 q^{96} +6.37714 q^{97} -29.4709 q^{98} +0.522001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) $ 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * 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 $

$2$	−2.67918	−1.89446	−0.947232	−	0.320549i	$-0.896133\pi$
$2$	−2.67918	−1.89446	−0.947232	+	0.320549i	$0.896133\pi$
$3$	1.79491	1.03629	0.518145	−	0.855293i	$-0.326623\pi$
$3$	1.79491	1.03629	0.518145	+	0.855293i	$0.326623\pi$
$4$	5.17799	2.58899
$5$	3.40719	1.52374	0.761870	−	0.647729i	$-0.224281\pi$
$5$	3.40719	1.52374	0.761870	+	0.647729i	$0.224281\pi$
$6$	−4.80888	−1.96322
$7$	4.24264	1.60357	0.801784	−	0.597615i	$-0.203885\pi$
$7$	4.24264	1.60357	0.801784	+	0.597615i	$0.203885\pi$
$8$	−8.51439	−3.01029
$9$	0.221695	0.0738982
$10$	−9.12846	−2.88667
$11$	2.35460	0.709937	0.354969	−	0.934878i	$-0.384492\pi$
$11$	2.35460	0.709937	0.354969	+	0.934878i	$0.384492\pi$
$12$	9.29401	2.68295
$13$	−0.771756	−0.214047	−0.107023	−	0.994257i	$-0.534132\pi$
$13$	−0.771756	−0.214047	−0.107023	+	0.994257i	$0.534132\pi$
$14$	−11.3668	−3.03790
$15$	6.11559	1.57904
$16$	12.4556	3.11389
$17$	−0.943428	−0.228815	−0.114407	−	0.993434i	$-0.536497\pi$
$17$	−0.943428	−0.228815	−0.114407	+	0.993434i	$0.536497\pi$
$18$	−0.593959	−0.139997
$19$	0.177774	0.0407842	0.0203921	−	0.999792i	$-0.493509\pi$
$19$	0.177774	0.0407842	0.0203921	+	0.999792i	$0.493509\pi$
$20$	17.6424	3.94496
$21$	7.61515	1.66176
$22$	−6.30838	−1.34495
$23$	4.24430	0.884998	0.442499	−	0.896769i	$-0.354092\pi$
$23$	4.24430	0.884998	0.442499	+	0.896769i	$0.354092\pi$
$24$	−15.2825	−3.11954
$25$	6.60893	1.32179
$26$	2.06767	0.405504
$27$	−4.98680	−0.959711
$28$	21.9683	4.15163
$29$	−3.76412	−0.698979	−0.349490	−	0.936940i	$-0.613645\pi$
$29$	−3.76412	−0.698979	−0.349490	+	0.936940i	$0.613645\pi$
$30$	−16.3847	−2.99143
$31$	1.56412	0.280925	0.140462	−	0.990086i	$-0.455141\pi$
$31$	1.56412	0.280925	0.140462	+	0.990086i	$0.455141\pi$
$32$	−16.3419	−2.88887
$33$	4.22628	0.735701
$34$	2.52761	0.433481
$35$	14.4555	2.44342
$36$	1.14793	0.191322
$37$	−4.89927	−0.805435	−0.402718	−	0.915324i	$-0.631934\pi$
$37$	−4.89927	−0.805435	−0.402718	+	0.915324i	$0.631934\pi$
$38$	−0.476289	−0.0772642
$39$	−1.38523	−0.221815
$40$	−29.0101	−4.58690
$41$	5.04113	0.787293	0.393646	−	0.919262i	$-0.371213\pi$
$41$	5.04113	0.787293	0.393646	+	0.919262i	$0.371213\pi$
$42$	−20.4023	−3.14815
$43$	2.14408	0.326969	0.163485	−	0.986546i	$-0.447727\pi$
$43$	2.14408	0.326969	0.163485	+	0.986546i	$0.447727\pi$
$44$	12.1921	1.83802
$45$	0.755355	0.112602
$46$	−11.3712	−1.67660
$47$	−2.93352	−0.427897	−0.213949	−	0.976845i	$-0.568632\pi$
$47$	−2.93352	−0.427897	−0.213949	+	0.976845i	$0.568632\pi$
$48$	22.3566	3.22690
$49$	11.0000	1.57143
$50$	−17.7065	−2.50408
$51$	−1.69337	−0.237119
$52$	−3.99614	−0.554165
$53$	−5.59078	−0.767953	−0.383977	−	0.923343i	$-0.625446\pi$
$53$	−5.59078	−0.767953	−0.383977	+	0.923343i	$0.625446\pi$
$54$	13.3605	1.81814
$55$	8.02255	1.08176
$56$	−36.1235	−4.82720
$57$	0.319089	0.0422643
$58$	10.0847	1.32419
$59$	−10.0882	−1.31337	−0.656683	−	0.754167i	$-0.728041\pi$
$59$	−10.0882	−1.31337	−0.656683	+	0.754167i	$0.728041\pi$
$60$	31.6664	4.08812
$61$	4.00902	0.513303	0.256651	−	0.966504i	$-0.417381\pi$
$61$	4.00902	0.513303	0.256651	+	0.966504i	$0.417381\pi$
$62$	−4.19056	−0.532202
$63$	0.940570	0.118501
$64$	18.8717	2.35897
$65$	−2.62952	−0.326152
$66$	−11.3230	−1.39376
$67$	−5.93967	−0.725646	−0.362823	−	0.931858i	$-0.618187\pi$
$67$	−5.93967	−0.725646	−0.362823	+	0.931858i	$0.618187\pi$
$68$	−4.88506	−0.592400
$69$	7.61813	0.917115
$70$	−38.7288	−4.62897
$71$	0.981034	0.116427	0.0582137	−	0.998304i	$-0.481460\pi$
$71$	0.981034	0.116427	0.0582137	+	0.998304i	$0.481460\pi$
$72$	−1.88759	−0.222455
$73$	12.6623	1.48200	0.741002	−	0.671502i	$-0.234351\pi$
$73$	12.6623	1.48200	0.741002	+	0.671502i	$0.234351\pi$
$74$	13.1260	1.52587
$75$	11.8624	1.36975
$76$	0.920513	0.105590
$77$	9.98970	1.13843
$78$	3.71128	0.420220
$79$	8.26770	0.930189	0.465094	−	0.885261i	$-0.346020\pi$
$79$	8.26770	0.930189	0.465094	+	0.885261i	$0.346020\pi$
$80$	42.4385	4.74477
$81$	−9.61594	−1.06844
$82$	−13.5061	−1.49150
$83$	2.07952	0.228257	0.114129	−	0.993466i	$-0.463592\pi$
$83$	2.07952	0.228257	0.114129	+	0.993466i	$0.463592\pi$
$84$	39.4311	4.30229
$85$	−3.21444	−0.348654
$86$	−5.74437	−0.619432
$87$	−6.75625	−0.724346
$88$	−20.0479	−2.13712
$89$	10.1165	1.07235	0.536176	−	0.844106i	$-0.319868\pi$
$89$	10.1165	1.07235	0.536176	+	0.844106i	$0.319868\pi$
$90$	−2.02373	−0.213320
$91$	−3.27428	−0.343238
$92$	21.9769	2.29125
$93$	2.80746	0.291120
$94$	7.85941	0.810636
$95$	0.605711	0.0621446
$96$	−29.3322	−2.99371
$97$	6.37714	0.647500	0.323750	−	0.946143i	$-0.395056\pi$
$97$	6.37714	0.647500	0.323750	+	0.946143i	$0.395056\pi$
$98$	−29.4709	−2.97701
$99$	0.522001	0.0524631
$100$	34.2210	3.42210
$101$	3.74303	0.372446	0.186223	−	0.982508i	$-0.440375\pi$
$101$	3.74303	0.372446	0.186223	+	0.982508i	$0.440375\pi$
$102$	4.53683	0.449213
$103$	15.4160	1.51898	0.759491	−	0.650518i	$-0.225448\pi$
$103$	15.4160	1.51898	0.759491	+	0.650518i	$0.225448\pi$
$104$	6.57103	0.644343
$105$	25.9462	2.53209
$106$	14.9787	1.45486
$107$	9.38689	0.907465	0.453733	−	0.891138i	$-0.350092\pi$
$107$	9.38689	0.907465	0.453733	+	0.891138i	$0.350092\pi$
$108$	−25.8216	−2.48468
$109$	6.78692	0.650069	0.325035	−	0.945702i	$-0.394624\pi$
$109$	6.78692	0.650069	0.325035	+	0.945702i	$0.394624\pi$
$110$	−21.4938	−2.04936
$111$	−8.79374	−0.834665
$112$	52.8445	4.99334
$113$	−12.7958	−1.20373	−0.601865	−	0.798598i	$-0.705576\pi$
$113$	−12.7958	−1.20373	−0.601865	+	0.798598i	$0.705576\pi$
$114$	−0.854895	−0.0800682
$115$	14.4611	1.34851
$116$	−19.4906	−1.80965
$117$	−0.171094	−0.0158177
$118$	27.0279	2.48812
$119$	−4.00262	−0.366920
$120$	−52.0705	−4.75337
$121$	−5.45588	−0.495989
$122$	−10.7409	−0.972433
$123$	9.04837	0.815864
$124$	8.09901	0.727313
$125$	5.48193	0.490319
$126$	−2.51995	−0.224495
$127$	16.2045	1.43791	0.718957	−	0.695055i	$-0.244620\pi$
$127$	16.2045	1.43791	0.718957	+	0.695055i	$0.244620\pi$
$128$	−17.8768	−1.58010
$129$	3.84843	0.338835
$130$	7.04494	0.617882
$131$	−11.4044	−0.996411	−0.498205	−	0.867059i	$-0.666007\pi$
$131$	−11.4044	−0.996411	−0.498205	+	0.867059i	$0.666007\pi$
$132$	21.8836	1.90473
$133$	0.754232	0.0654002
$134$	15.9134	1.37471
$135$	−16.9910	−1.46235
$136$	8.03271	0.688799
$137$	−10.4134	−0.889674	−0.444837	−	0.895612i	$-0.646738\pi$
$137$	−10.4134	−0.889674	−0.444837	+	0.895612i	$0.646738\pi$
$138$	−20.4103	−1.73744
$139$	22.2147	1.88422	0.942111	−	0.335301i	$-0.108838\pi$
$139$	22.2147	1.88422	0.942111	+	0.335301i	$0.108838\pi$
$140$	74.8503	6.32600
$141$	−5.26539	−0.443426
$142$	−2.62836	−0.220567
$143$	−1.81717	−0.151960
$144$	2.76133	0.230111
$145$	−12.8251	−1.06506
$146$	−33.9244	−2.80760
$147$	19.7440	1.62846
$148$	−25.3684	−2.08527
$149$	18.7095	1.53274	0.766370	−	0.642399i	$-0.222061\pi$
$149$	18.7095	1.53274	0.766370	+	0.642399i	$0.222061\pi$
$150$	−31.7815	−2.59495
$151$	−9.87583	−0.803683	−0.401842	−	0.915709i	$-0.631630\pi$
$151$	−9.87583	−0.803683	−0.401842	+	0.915709i	$0.631630\pi$
$152$	−1.51364	−0.122772
$153$	−0.209153	−0.0169090
$154$	−26.7642	−2.15672
$155$	5.32926	0.428057
$156$	−7.17271	−0.574276
$157$	−4.99671	−0.398781	−0.199390	−	0.979920i	$-0.563896\pi$
$157$	−4.99671	−0.398781	−0.199390	+	0.979920i	$0.563896\pi$
$158$	−22.1506	−1.76221
$159$	−10.0349	−0.795823
$160$	−55.6800	−4.40189
$161$	18.0070	1.41915
$162$	25.7628	2.02412
$163$	17.3381	1.35802	0.679012	−	0.734127i	$-0.262408\pi$
$163$	17.3381	1.35802	0.679012	+	0.734127i	$0.262408\pi$
$164$	26.1029	2.03830
$165$	14.3997	1.12102
$166$	−5.57141	−0.432425
$167$	11.9365	0.923673	0.461836	−	0.886965i	$-0.347191\pi$
$167$	11.9365	0.923673	0.461836	+	0.886965i	$0.347191\pi$
$168$	−64.8383	−5.00239
$169$	−12.4044	−0.954184
$170$	8.61204	0.660513
$171$	0.0394116	0.00301388
$172$	11.1020	0.846522
$173$	−11.1659	−0.848925	−0.424462	−	0.905446i	$-0.639537\pi$
$173$	−11.1659	−0.848925	−0.424462	+	0.905446i	$0.639537\pi$
$174$	18.1012	1.37225
$175$	28.0393	2.11957
$176$	29.3279	2.21067
$177$	−18.1073	−1.36103
$178$	−27.1040	−2.03153
$179$	−21.7682	−1.62703	−0.813517	−	0.581541i	$-0.802450\pi$
$179$	−21.7682	−1.62703	−0.813517	+	0.581541i	$0.802450\pi$
$180$	3.91122	0.291525
$181$	−18.6499	−1.38624	−0.693118	−	0.720824i	$-0.743764\pi$
$181$	−18.6499	−1.38624	−0.693118	+	0.720824i	$0.743764\pi$
$182$	8.77238	0.650252
$183$	7.19582	0.531931
$184$	−36.1376	−2.66410
$185$	−16.6927	−1.22727
$186$	−7.52167	−0.551516
$187$	−2.22139	−0.162444
$188$	−15.1897	−1.10782
$189$	−21.1572	−1.53896
$190$	−1.62281	−0.117731
$191$	23.1125	1.67236	0.836179	−	0.548456i	$-0.184784\pi$
$191$	23.1125	1.67236	0.836179	+	0.548456i	$0.184784\pi$
$192$	33.8730	2.44457
$193$	−4.25147	−0.306027	−0.153014	−	0.988224i	$-0.548898\pi$
$193$	−4.25147	−0.306027	−0.153014	+	0.988224i	$0.548898\pi$
$194$	−17.0855	−1.22667
$195$	−4.71974	−0.337988
$196$	56.9578	4.06842
$197$	−12.7225	−0.906444	−0.453222	−	0.891398i	$-0.649726\pi$
$197$	−12.7225	−0.906444	−0.453222	+	0.891398i	$0.649726\pi$
$198$	−1.39853	−0.0993894
$199$	5.39041	0.382116	0.191058	−	0.981579i	$-0.438808\pi$
$199$	5.39041	0.382116	0.191058	+	0.981579i	$0.438808\pi$
$200$	−56.2710	−3.97896
$201$	−10.6612	−0.751980
$202$	−10.0282	−0.705585
$203$	−15.9698	−1.12086
$204$	−8.76823	−0.613899
$205$	17.1761	1.19963
$206$	−41.3021	−2.87766
$207$	0.940938	0.0653997
$208$	−9.61267	−0.666519
$209$	0.418587	0.0289542
$210$	−69.5146	−4.79696
$211$	13.0974	0.901665	0.450833	−	0.892609i	$-0.351127\pi$
$211$	13.0974	0.901665	0.450833	+	0.892609i	$0.351127\pi$
$212$	−28.9490	−1.98823
$213$	1.76087	0.120653
$214$	−25.1491	−1.71916
$215$	7.30529	0.498217
$216$	42.4596	2.88901
$217$	6.63601	0.450482
$218$	−18.1834	−1.23153
$219$	22.7276	1.53579
$220$	41.5407	2.80067
$221$	0.728096	0.0489770
$222$	23.5600	1.58124
$223$	−8.97763	−0.601187	−0.300593	−	0.953752i	$-0.597185\pi$
$223$	−8.97763	−0.601187	−0.300593	+	0.953752i	$0.597185\pi$
$224$	−69.3329	−4.63250
$225$	1.46516	0.0976776
$226$	34.2823	2.28042
$227$	−9.42563	−0.625601	−0.312801	−	0.949819i	$-0.601267\pi$
$227$	−9.42563	−0.625601	−0.312801	+	0.949819i	$0.601267\pi$
$228$	1.65224	0.109422
$229$	11.2643	0.744366	0.372183	−	0.928159i	$-0.378609\pi$
$229$	11.2643	0.744366	0.372183	+	0.928159i	$0.378609\pi$
$230$	−38.7439	−2.55470
$231$	17.9306	1.17975
$232$	32.0492	2.10413
$233$	−7.74021	−0.507078	−0.253539	−	0.967325i	$-0.581595\pi$
$233$	−7.74021	−0.507078	−0.253539	+	0.967325i	$0.581595\pi$
$234$	0.458391	0.0299660
$235$	−9.99504	−0.652004
$236$	−52.2363	−3.40030
$237$	14.8398	0.963946
$238$	10.7237	0.695117
$239$	−19.7048	−1.27460	−0.637299	−	0.770617i	$-0.719948\pi$
$239$	−19.7048	−1.27460	−0.637299	+	0.770617i	$0.719948\pi$
$240$	76.1732	4.91696
$241$	−22.2796	−1.43515	−0.717577	−	0.696480i	$-0.754749\pi$
$241$	−22.2796	−1.43515	−0.717577	+	0.696480i	$0.754749\pi$
$242$	14.6173	0.939633
$243$	−2.29931	−0.147501
$244$	20.7587	1.32894
$245$	37.4790	2.39445
$246$	−24.2422	−1.54562
$247$	−0.137198	−0.00872973
$248$	−13.3176	−0.845666
$249$	3.73255	0.236541
$250$	−14.6871	−0.928892
$251$	7.14696	0.451112	0.225556	−	0.974230i	$-0.427580\pi$
$251$	7.14696	0.451112	0.225556	+	0.974230i	$0.427580\pi$
$252$	4.87026	0.306798
$253$	9.99361	0.628293
$254$	−43.4146	−2.72408
$255$	−5.76962	−0.361307
$256$	10.1518	0.634486
$257$	−27.7660	−1.73200	−0.865999	−	0.500046i	$-0.833317\pi$
$257$	−27.7660	−1.73200	−0.865999	+	0.500046i	$0.833317\pi$
$258$	−10.3106	−0.641911
$259$	−20.7858	−1.29157
$260$	−13.6156	−0.844404
$261$	−0.834485	−0.0516533
$262$	30.5545	1.88766
$263$	−10.3906	−0.640714	−0.320357	−	0.947297i	$-0.603803\pi$
$263$	−10.3906	−0.640714	−0.320357	+	0.947297i	$0.603803\pi$
$264$	−35.9842	−2.21468
$265$	−19.0488	−1.17016
$266$	−2.02072	−0.123898
$267$	18.1583	1.11127
$268$	−30.7555	−1.87869
$269$	6.80874	0.415136	0.207568	−	0.978221i	$-0.433445\pi$
$269$	6.80874	0.415136	0.207568	+	0.978221i	$0.433445\pi$
$270$	45.5218	2.77037
$271$	−18.4643	−1.12163	−0.560813	−	0.827942i	$-0.689512\pi$
$271$	−18.4643	−1.12163	−0.560813	+	0.827942i	$0.689512\pi$
$272$	−11.7509	−0.712505
$273$	−5.87704	−0.355694
$274$	27.8992	1.68545
$275$	15.5614	0.938385
$276$	39.4466	2.37440
$277$	21.1513	1.27086	0.635428	−	0.772160i	$-0.280824\pi$
$277$	21.1513	1.27086	0.635428	+	0.772160i	$0.280824\pi$
$278$	−59.5170	−3.56959
$279$	0.346758	0.0207598
$280$	−123.080	−7.35541
$281$	−1.12876	−0.0673359	−0.0336680	−	0.999433i	$-0.510719\pi$
$281$	−1.12876	−0.0673359	−0.0336680	+	0.999433i	$0.510719\pi$
$282$	14.1069	0.840054
$283$	8.47831	0.503983	0.251992	−	0.967729i	$-0.418914\pi$
$283$	8.47831	0.503983	0.251992	+	0.967729i	$0.418914\pi$
$284$	5.07978	0.301430
$285$	1.08719	0.0643999
$286$	4.86853	0.287882
$287$	21.3877	1.26248
$288$	−3.62291	−0.213482
$289$	−16.1099	−0.947644
$290$	34.3606	2.01772
$291$	11.4464	0.670998
$292$	65.5650	3.83690
$293$	−31.1792	−1.82151	−0.910755	−	0.412948i	$-0.864499\pi$
$293$	−31.1792	−1.82151	−0.910755	+	0.412948i	$0.864499\pi$
$294$	−52.8976	−3.08505
$295$	−34.3722	−2.00123
$296$	41.7143	2.42459
$297$	−11.7419	−0.681334
$298$	−50.1260	−2.90372
$299$	−3.27556	−0.189431
$300$	61.4235	3.54629
$301$	9.09656	0.524317
$302$	26.4591	1.52255
$303$	6.71840	0.385962
$304$	2.21428	0.126998
$305$	13.6595	0.782140
$306$	0.560357	0.0320335
$307$	−1.98032	−0.113023	−0.0565113	−	0.998402i	$-0.517998\pi$
$307$	−1.98032	−0.113023	−0.0565113	+	0.998402i	$0.517998\pi$
$308$	51.7265	2.94739
$309$	27.6703	1.57411
$310$	−14.2780	−0.810938
$311$	6.38578	0.362104	0.181052	−	0.983474i	$-0.442050\pi$
$311$	6.38578	0.362104	0.181052	+	0.983474i	$0.442050\pi$
$312$	11.7944	0.667726
$313$	−1.87494	−0.105978	−0.0529889	−	0.998595i	$-0.516875\pi$
$313$	−1.87494	−0.105978	−0.0529889	+	0.998595i	$0.516875\pi$
$314$	13.3871	0.755475
$315$	3.20470	0.180564
$316$	42.8100	2.40825
$317$	−27.5822	−1.54917	−0.774586	−	0.632469i	$-0.782042\pi$
$317$	−27.5822	−1.54917	−0.774586	+	0.632469i	$0.782042\pi$
$318$	26.8854	1.50766
$319$	−8.86298	−0.496232
$320$	64.2995	3.59445
$321$	16.8486	0.940398
$322$	−48.2440	−2.68854
$323$	−0.167717	−0.00933203
$324$	−49.7912	−2.76618
$325$	−5.10048	−0.282924
$326$	−46.4518	−2.57273
$327$	12.1819	0.673661
$328$	−42.9222	−2.36998
$329$	−12.4458	−0.686162
$330$	−38.5794	−2.12373
$331$	−4.17007	−0.229208	−0.114604	−	0.993411i	$-0.536560\pi$
$331$	−4.17007	−0.229208	−0.114604	+	0.993411i	$0.536560\pi$
$332$	10.7677	0.590957
$333$	−1.08614	−0.0595202
$334$	−31.9799	−1.74986
$335$	−20.2376	−1.10570
$336$	94.8511	5.17455
$337$	−21.6223	−1.17784	−0.588922	−	0.808190i	$-0.700447\pi$
$337$	−21.6223	−1.17784	−0.588922	+	0.808190i	$0.700447\pi$
$338$	33.2336	1.80767
$339$	−22.9673	−1.24741
$340$	−16.6443	−0.902664
$341$	3.68288	0.199439
$342$	−0.105591	−0.00570969
$343$	16.9705	0.916322
$344$	−18.2555	−0.984273
$345$	25.9564	1.39745
$346$	29.9153	1.60826
$347$	29.2605	1.57079	0.785393	−	0.618997i	$-0.212461\pi$
$347$	29.2605	1.57079	0.785393	+	0.618997i	$0.212461\pi$
$348$	−34.9838	−1.87533
$349$	9.16072	0.490362	0.245181	−	0.969477i	$-0.421153\pi$
$349$	9.16072	0.490362	0.245181	+	0.969477i	$0.421153\pi$
$350$	−75.1223	−4.01545
$351$	3.84860	0.205423
$352$	−38.4786	−2.05092
$353$	6.04329	0.321652	0.160826	−	0.986983i	$-0.448584\pi$
$353$	6.04329	0.321652	0.160826	+	0.986983i	$0.448584\pi$
$354$	48.5127	2.57842
$355$	3.34257	0.177405
$356$	52.3834	2.77631
$357$	−7.18434	−0.380236
$358$	58.3209	3.08236
$359$	6.32835	0.333997	0.166999	−	0.985957i	$-0.446592\pi$
$359$	6.32835	0.333997	0.166999	+	0.985957i	$0.446592\pi$
$360$	−6.43139	−0.338964
$361$	−18.9684	−0.998337
$362$	49.9664	2.62618
$363$	−9.79280	−0.513989
$364$	−16.9542	−0.888641
$365$	43.1427	2.25819
$366$	−19.2789	−1.00772
$367$	−22.5970	−1.17955	−0.589777	−	0.807566i	$-0.700784\pi$
$367$	−22.5970	−1.17955	−0.589777	+	0.807566i	$0.700784\pi$
$368$	52.8652	2.75579
$369$	1.11759	0.0581795
$370$	44.7228	2.32503
$371$	−23.7197	−1.23146
$372$	14.5370	0.753707
$373$	34.0143	1.76119	0.880597	−	0.473867i	$-0.157142\pi$
$373$	34.0143	1.76119	0.880597	+	0.473867i	$0.157142\pi$
$374$	5.95150	0.307745
$375$	9.83956	0.508113
$376$	24.9771	1.28810
$377$	2.90498	0.149614
$378$	56.6839	2.91550
$379$	5.66019	0.290745	0.145372	−	0.989377i	$-0.453562\pi$
$379$	5.66019	0.290745	0.145372	+	0.989377i	$0.453562\pi$
$380$	3.13636	0.160892
$381$	29.0855	1.49010
$382$	−61.9223	−3.16822
$383$	−6.25319	−0.319523	−0.159762	−	0.987156i	$-0.551073\pi$
$383$	−6.25319	−0.319523	−0.159762	+	0.987156i	$0.551073\pi$
$384$	−32.0873	−1.63745
$385$	34.0368	1.73468
$386$	11.3904	0.579758
$387$	0.475331	0.0241624
$388$	33.0207	1.67637
$389$	−8.86145	−0.449294	−0.224647	−	0.974440i	$-0.572123\pi$
$389$	−8.86145	−0.449294	−0.224647	+	0.974440i	$0.572123\pi$
$390$	12.6450	0.640306
$391$	−4.00419	−0.202501
$392$	−93.6582	−4.73045
$393$	−20.4699	−1.03257
$394$	34.0860	1.71723
$395$	28.1696	1.41737
$396$	2.70291	0.135827
$397$	−20.3659	−1.02213	−0.511067	−	0.859541i	$-0.670750\pi$
$397$	−20.3659	−1.02213	−0.511067	+	0.859541i	$0.670750\pi$
$398$	−14.4419	−0.723906
$399$	1.35378	0.0677737
$400$	82.3181	4.11590
$401$	19.5051	0.974037	0.487018	−	0.873392i	$-0.338084\pi$
$401$	19.5051	0.974037	0.487018	+	0.873392i	$0.338084\pi$
$402$	28.5631	1.42460
$403$	−1.20712	−0.0601310
$404$	19.3814	0.964259
$405$	−32.7633	−1.62802
$406$	42.7859	2.12343
$407$	−11.5358	−0.571808
$408$	14.4180	0.713796
$409$	2.21382	0.109466	0.0547331	−	0.998501i	$-0.482569\pi$
$409$	2.21382	0.109466	0.0547331	+	0.998501i	$0.482569\pi$
$410$	−46.0178	−2.27266
$411$	−18.6910	−0.921960
$412$	79.8238	3.93263
$413$	−42.8004	−2.10607
$414$	−2.52094	−0.123897
$415$	7.08532	0.347805
$416$	12.6120	0.618353
$417$	39.8733	1.95260
$418$	−1.12147	−0.0548528
$419$	12.9430	0.632308	0.316154	−	0.948708i	$-0.397608\pi$
$419$	12.9430	0.632308	0.316154	+	0.948708i	$0.397608\pi$
$420$	134.349	6.55558
$421$	−23.5801	−1.14923	−0.574613	−	0.818425i	$-0.694847\pi$
$421$	−23.5801	−1.14923	−0.574613	+	0.818425i	$0.694847\pi$
$422$	−35.0904	−1.70817
$423$	−0.650344	−0.0316208
$424$	47.6021	2.31176
$425$	−6.23505	−0.302444
$426$	−4.71767	−0.228572
$427$	17.0088	0.823115
$428$	48.6052	2.34942
$429$	−3.26166	−0.157474
$430$	−19.5722	−0.943853
$431$	−18.4420	−0.888321	−0.444160	−	0.895947i	$-0.646498\pi$
$431$	−18.4420	−0.888321	−0.444160	+	0.895947i	$0.646498\pi$
$432$	−62.1135	−2.98844
$433$	25.9151	1.24540	0.622700	−	0.782461i	$-0.286036\pi$
$433$	25.9151	1.24540	0.622700	+	0.782461i	$0.286036\pi$
$434$	−17.7790	−0.853422
$435$	−23.0198	−1.10372
$436$	35.1426	1.68303
$437$	0.754528	0.0360940
$438$	−60.8912	−2.90949
$439$	−28.6625	−1.36799	−0.683994	−	0.729488i	$-0.739759\pi$
$439$	−28.6625	−1.36799	−0.683994	+	0.729488i	$0.739759\pi$
$440$	−68.3071	−3.25641
$441$	2.43864	0.116126
$442$	−1.95070	−0.0927852
$443$	−7.73283	−0.367398	−0.183699	−	0.982983i	$-0.558807\pi$
$443$	−7.73283	−0.367398	−0.183699	+	0.982983i	$0.558807\pi$
$444$	−45.5339	−2.16094
$445$	34.4690	1.63399
$446$	24.0527	1.13893
$447$	33.5818	1.58836
$448$	80.0659	3.78276
$449$	3.24019	0.152914	0.0764571	−	0.997073i	$-0.475639\pi$
$449$	3.24019	0.152914	0.0764571	+	0.997073i	$0.475639\pi$
$450$	−3.92543	−0.185047
$451$	11.8698	0.558928
$452$	−66.2567	−3.11645
$453$	−17.7262	−0.832849
$454$	25.2529	1.18518
$455$	−11.1561	−0.523006
$456$	−2.71684	−0.127228
$457$	−34.2988	−1.60443	−0.802214	−	0.597036i	$-0.796345\pi$
$457$	−34.2988	−1.60443	−0.802214	+	0.597036i	$0.796345\pi$
$458$	−30.1791	−1.41018
$459$	4.70469	0.219596
$460$	74.8796	3.49128
$461$	−25.7584	−1.19969	−0.599843	−	0.800118i	$-0.704770\pi$
$461$	−25.7584	−1.19969	−0.599843	+	0.800118i	$0.704770\pi$
$462$	−48.0392	−2.23499
$463$	0.610424	0.0283688	0.0141844	−	0.999899i	$-0.495485\pi$
$463$	0.610424	0.0283688	0.0141844	+	0.999899i	$0.495485\pi$
$464$	−46.8843	−2.17655
$465$	9.56554	0.443591
$466$	20.7374	0.960641
$467$	−39.9655	−1.84938	−0.924691	−	0.380718i	$-0.875677\pi$
$467$	−39.9655	−1.84938	−0.924691	+	0.380718i	$0.875677\pi$
$468$	−0.885923	−0.0409518
$469$	−25.1999	−1.16362
$470$	26.7785	1.23520
$471$	−8.96863	−0.413252
$472$	85.8945	3.95361
$473$	5.04844	0.232128
$474$	−39.7583	−1.82616
$475$	1.17490	0.0539080
$476$	−20.7255	−0.949953
$477$	−1.23945	−0.0567503
$478$	52.7926	2.41468
$479$	11.6561	0.532580	0.266290	−	0.963893i	$-0.414202\pi$
$479$	11.6561	0.532580	0.266290	+	0.963893i	$0.414202\pi$
$480$	−99.9404	−4.56164
$481$	3.78104	0.172401
$482$	59.6909	2.71885
$483$	32.3210	1.47066
$484$	−28.2505	−1.28411
$485$	21.7281	0.986622
$486$	6.16026	0.279435
$487$	15.2904	0.692873	0.346437	−	0.938073i	$-0.387392\pi$
$487$	15.2904	0.692873	0.346437	+	0.938073i	$0.387392\pi$
$488$	−34.1344	−1.54519
$489$	31.1203	1.40731
$490$	−100.413	−4.53620
$491$	11.1860	0.504816	0.252408	−	0.967621i	$-0.418777\pi$
$491$	11.1860	0.504816	0.252408	+	0.967621i	$0.418777\pi$
$492$	46.8523	2.11227
$493$	3.55117	0.159937
$494$	0.367579	0.0165382
$495$	1.77856	0.0799401
$496$	19.4821	0.874770
$497$	4.16217	0.186699
$498$	−10.0002	−0.448118
$499$	21.6594	0.969608	0.484804	−	0.874623i	$-0.338891\pi$
$499$	21.6594	0.969608	0.484804	+	0.874623i	$0.338891\pi$
$500$	28.3854	1.26943
$501$	21.4249	0.957193
$502$	−19.1480	−0.854616
$503$	−34.8968	−1.55597	−0.777986	−	0.628282i	$-0.783758\pi$
$503$	−34.8968	−1.55597	−0.777986	+	0.628282i	$0.783758\pi$
$504$	−8.00838	−0.356722
$505$	12.7532	0.567511
$506$	−26.7747	−1.19028
$507$	−22.2647	−0.988812
$508$	83.9065	3.72275
$509$	1.90425	0.0844043	0.0422021	−	0.999109i	$-0.486563\pi$
$509$	1.90425	0.0844043	0.0422021	+	0.999109i	$0.486563\pi$
$510$	15.4578	0.684484
$511$	53.7214	2.37649
$512$	8.55527	0.378093
$513$	−0.886525	−0.0391411
$514$	74.3901	3.28121
$515$	52.5251	2.31453
$516$	19.9271	0.877242
$517$	−6.90724	−0.303780
$518$	55.6889	2.44683
$519$	−20.0417	−0.879733
$520$	22.3887	0.981811
$521$	−9.02708	−0.395484	−0.197742	−	0.980254i	$-0.563361\pi$
$521$	−9.02708	−0.395484	−0.197742	+	0.980254i	$0.563361\pi$
$522$	2.23573	0.0978553
$523$	30.9607	1.35382	0.676908	−	0.736068i	$-0.263320\pi$
$523$	30.9607	1.35382	0.676908	+	0.736068i	$0.263320\pi$
$524$	−59.0521	−2.57970
$525$	50.3280	2.19649
$526$	27.8384	1.21381
$527$	−1.47564	−0.0642798
$528$	52.6408	2.29090
$529$	−4.98591	−0.216779
$530$	51.0352	2.21683
$531$	−2.23649	−0.0970553
$532$	3.90541	0.169321
$533$	−3.89052	−0.168517
$534$	−48.6492	−2.10526
$535$	31.9829	1.38274
$536$	50.5727	2.18441
$537$	−39.0720	−1.68608
$538$	−18.2418	−0.786461
$539$	25.9005	1.11562
$540$	−87.9791	−3.78602
$541$	−28.6160	−1.23030	−0.615148	−	0.788411i	$-0.710904\pi$
$541$	−28.6160	−1.23030	−0.615148	+	0.788411i	$0.710904\pi$
$542$	49.4691	2.12488
$543$	−33.4749	−1.43654
$544$	15.4174	0.661016
$545$	23.1243	0.990537
$546$	15.7456	0.673850
$547$	6.72599	0.287582	0.143791	−	0.989608i	$-0.454071\pi$
$547$	6.72599	0.287582	0.143791	+	0.989608i	$0.454071\pi$
$548$	−53.9203	−2.30336
$549$	0.888778	0.0379321
$550$	−41.6916	−1.77774
$551$	−0.669164	−0.0285073
$552$	−64.8637	−2.76078
$553$	35.0769	1.49162
$554$	−56.6680	−2.40759
$555$	−29.9619	−1.27181
$556$	115.027	4.87824
$557$	−15.6976	−0.665127	−0.332564	−	0.943081i	$-0.607914\pi$
$557$	−15.6976	−0.665127	−0.332564	+	0.943081i	$0.607914\pi$
$558$	−0.929025	−0.0393288
$559$	−1.65471	−0.0699867
$560$	180.051	7.60856
$561$	−3.98719	−0.168339
$562$	3.02414	0.127565
$563$	8.44214	0.355794	0.177897	−	0.984049i	$-0.443071\pi$
$563$	8.44214	0.355794	0.177897	+	0.984049i	$0.443071\pi$
$564$	−27.2641	−1.14803
$565$	−43.5978	−1.83417
$566$	−22.7149	−0.954778
$567$	−40.7969	−1.71331
$568$	−8.35291	−0.350480
$569$	32.6999	1.37085	0.685425	−	0.728144i	$-0.259617\pi$
$569$	32.6999	1.37085	0.685425	+	0.728144i	$0.259617\pi$
$570$	−2.91279	−0.122003
$571$	10.7769	0.451000	0.225500	−	0.974243i	$-0.427598\pi$
$571$	10.7769	0.451000	0.225500	+	0.974243i	$0.427598\pi$
$572$	−9.40930	−0.393423
$573$	41.4847	1.73305
$574$	−57.3014	−2.39172
$575$	28.0503	1.16978
$576$	4.18376	0.174323
$577$	11.9981	0.499487	0.249744	−	0.968312i	$-0.419654\pi$
$577$	11.9981	0.499487	0.249744	+	0.968312i	$0.419654\pi$
$578$	43.1614	1.79528
$579$	−7.63099	−0.317133
$580$	−66.4080	−2.75744
$581$	8.82266	0.366026
$582$	−30.6669	−1.27118
$583$	−13.1640	−0.545199
$584$	−107.811	−4.46127
$585$	−0.582950	−0.0241020
$586$	83.5346	3.45078
$587$	28.4798	1.17549	0.587744	−	0.809047i	$-0.300016\pi$
$587$	28.4798	1.17549	0.587744	+	0.809047i	$0.300016\pi$
$588$	102.234	4.21606
$589$	0.278061	0.0114573
$590$	92.0893	3.79126
$591$	−22.8358	−0.939339
$592$	−61.0232	−2.50804
$593$	−35.1838	−1.44483	−0.722413	−	0.691462i	$-0.756967\pi$
$593$	−35.1838	−1.44483	−0.722413	+	0.691462i	$0.756967\pi$
$594$	31.4586	1.29076
$595$	−13.6377	−0.559091
$596$	96.8775	3.96826
$597$	9.67530	0.395984
$598$	8.77582	0.358870
$599$	−8.77130	−0.358385	−0.179193	−	0.983814i	$-0.557349\pi$
$599$	−8.77130	−0.358385	−0.179193	+	0.983814i	$0.557349\pi$
$600$	−101.001	−4.12336
$601$	13.2025	0.538539	0.269270	−	0.963065i	$-0.413218\pi$
$601$	13.2025	0.538539	0.269270	+	0.963065i	$0.413218\pi$
$602$	−24.3713	−0.993300
$603$	−1.31679	−0.0536239
$604$	−51.1369	−2.08073
$605$	−18.5892	−0.755759
$606$	−17.9998	−0.731191
$607$	−23.3907	−0.949399	−0.474699	−	0.880148i	$-0.657443\pi$
$607$	−23.3907	−0.949399	−0.474699	+	0.880148i	$0.657443\pi$
$608$	−2.90517	−0.117820
$609$	−28.6643	−1.16154
$610$	−36.5962	−1.48174
$611$	2.26396	0.0915899
$612$	−1.08299	−0.0437773
$613$	−2.94124	−0.118796	−0.0593978	−	0.998234i	$-0.518918\pi$
$613$	−2.94124	−0.118796	−0.0593978	+	0.998234i	$0.518918\pi$
$614$	5.30562	0.214117
$615$	30.8295	1.24317
$616$	−85.0562	−3.42701
$617$	4.69305	0.188935	0.0944675	−	0.995528i	$-0.469885\pi$
$617$	4.69305	0.188935	0.0944675	+	0.995528i	$0.469885\pi$
$618$	−74.1335	−2.98209
$619$	18.4708	0.742404	0.371202	−	0.928552i	$-0.378946\pi$
$619$	18.4708	0.742404	0.371202	+	0.928552i	$0.378946\pi$
$620$	27.5949	1.10824
$621$	−21.1655	−0.849342
$622$	−17.1086	−0.685993
$623$	42.9209	1.71959
$624$	−17.2539	−0.690707
$625$	−14.3667	−0.574667
$626$	5.02330	0.200771
$627$	0.751324	0.0300050
$628$	−25.8729	−1.03244
$629$	4.62211	0.184295
$630$	−8.58596	−0.342073
$631$	−31.2103	−1.24246	−0.621232	−	0.783627i	$-0.713367\pi$
$631$	−31.2103	−1.24246	−0.621232	+	0.783627i	$0.713367\pi$
$632$	−70.3944	−2.80014
$633$	23.5087	0.934387
$634$	73.8976	2.93485
$635$	55.2117	2.19101
$636$	−51.9608	−2.06038
$637$	−8.48931	−0.336359
$638$	23.7455	0.940093
$639$	0.217490	0.00860377
$640$	−60.9098	−2.40767
$641$	10.4899	0.414327	0.207164	−	0.978306i	$-0.433577\pi$
$641$	10.4899	0.414327	0.207164	+	0.978306i	$0.433577\pi$
$642$	−45.1404	−1.78155
$643$	9.94229	0.392086	0.196043	−	0.980595i	$-0.437191\pi$
$643$	9.94229	0.392086	0.196043	+	0.980595i	$0.437191\pi$
$644$	93.2402	3.67418
$645$	13.1123	0.516297
$646$	0.449344	0.0176792
$647$	−22.1163	−0.869481	−0.434740	−	0.900556i	$-0.643160\pi$
$647$	−22.1163	−0.869481	−0.434740	+	0.900556i	$0.643160\pi$
$648$	81.8738	3.21631
$649$	−23.7535	−0.932407
$650$	13.6651	0.535989
$651$	11.9110	0.466830
$652$	89.7764	3.51591
$653$	26.4649	1.03565	0.517825	−	0.855486i	$-0.326742\pi$
$653$	26.4649	1.03565	0.517825	+	0.855486i	$0.326742\pi$
$654$	−32.6375	−1.27623
$655$	−38.8571	−1.51827
$656$	62.7902	2.45155
$657$	2.80715	0.109517
$658$	33.3446	1.29991
$659$	41.2127	1.60542	0.802710	−	0.596370i	$-0.203391\pi$
$659$	41.2127	1.60542	0.802710	+	0.596370i	$0.203391\pi$
$660$	74.5617	2.90231
$661$	35.0407	1.36293	0.681463	−	0.731853i	$-0.261344\pi$
$661$	35.0407	1.36293	0.681463	+	0.731853i	$0.261344\pi$
$662$	11.1724	0.434226
$663$	1.30687	0.0507544
$664$	−17.7059	−0.687121
$665$	2.56981	0.0996530
$666$	2.90996	0.112759
$667$	−15.9761	−0.618595
$668$	61.8070	2.39138
$669$	−16.1140	−0.623004
$670$	54.2200	2.09470
$671$	9.43962	0.364413
$672$	−124.446	−4.80061
$673$	12.9361	0.498649	0.249325	−	0.968420i	$-0.419791\pi$
$673$	12.9361	0.498649	0.249325	+	0.968420i	$0.419791\pi$
$674$	57.9300	2.23138
$675$	−32.9574	−1.26853
$676$	−64.2298	−2.47038
$677$	−23.0474	−0.885785	−0.442892	−	0.896575i	$-0.646048\pi$
$677$	−23.0474	−0.885785	−0.442892	+	0.896575i	$0.646048\pi$
$678$	61.5336	2.36318
$679$	27.0559	1.03831
$680$	27.3690	1.04955
$681$	−16.9181	−0.648305
$682$	−9.86708	−0.377830
$683$	−12.7869	−0.489279	−0.244639	−	0.969614i	$-0.578670\pi$
$683$	−12.7869	−0.489279	−0.244639	+	0.969614i	$0.578670\pi$
$684$	0.204073	0.00780292
$685$	−35.4803	−1.35563
$686$	−45.4670	−1.73594
$687$	20.2184	0.771380
$688$	26.7058	1.01815
$689$	4.31472	0.164378
$690$	−69.5418	−2.64741
$691$	−7.55565	−0.287430	−0.143715	−	0.989619i	$-0.545905\pi$
$691$	−7.55565	−0.287430	−0.143715	+	0.989619i	$0.545905\pi$
$692$	−57.8167	−2.19786
$693$	2.21466	0.0841281
$694$	−78.3941	−2.97580
$695$	75.6895	2.87107
$696$	57.5253	2.18049
$697$	−4.75594	−0.180144
$698$	−24.5432	−0.928973
$699$	−13.8930	−0.525480
$700$	145.187	5.48756
$701$	47.9056	1.80937	0.904686	−	0.426080i	$-0.140106\pi$
$701$	47.9056	1.80937	0.904686	+	0.426080i	$0.140106\pi$
$702$	−10.3111	−0.389166
$703$	−0.870964	−0.0328490
$704$	44.4353	1.67472
$705$	−17.9402	−0.675666
$706$	−16.1910	−0.609358
$707$	15.8803	0.597241
$708$	−93.7594	−3.52369
$709$	−2.30619	−0.0866106	−0.0433053	−	0.999062i	$-0.513789\pi$
$709$	−2.30619	−0.0866106	−0.0433053	+	0.999062i	$0.513789\pi$
$710$	−8.95533	−0.336087
$711$	1.83290	0.0687392
$712$	−86.1362	−3.22809
$713$	6.63861	0.248618
$714$	19.2481	0.720343
$715$	−6.19145	−0.231547
$716$	−112.716	−4.21238
$717$	−35.3683	−1.32085
$718$	−16.9548	−0.632746
$719$	−38.3734	−1.43109	−0.715543	−	0.698569i	$-0.753821\pi$
$719$	−38.3734	−1.43109	−0.715543	+	0.698569i	$0.753821\pi$
$720$	9.40838	0.350630
$721$	65.4045	2.43579
$722$	50.8197	1.89131
$723$	−39.9898	−1.48724
$724$	−96.5690	−3.58896
$725$	−24.8768	−0.923901
$726$	26.2366	0.973733
$727$	−30.0976	−1.11626	−0.558130	−	0.829754i	$-0.688481\pi$
$727$	−30.0976	−1.11626	−0.558130	+	0.829754i	$0.688481\pi$
$728$	27.8785	1.03325
$729$	24.7208	0.915583
$730$	−115.587	−4.27806
$731$	−2.02279	−0.0748154
$732$	37.2599	1.37716
$733$	−7.95287	−0.293746	−0.146873	−	0.989155i	$-0.546921\pi$
$733$	−7.95287	−0.293746	−0.146873	+	0.989155i	$0.546921\pi$
$734$	60.5413	2.23462
$735$	67.2714	2.48134
$736$	−69.3600	−2.55664
$737$	−13.9855	−0.515163
$738$	−2.99423	−0.110219
$739$	−21.4214	−0.788000	−0.394000	−	0.919110i	$-0.628909\pi$
$739$	−21.4214	−0.788000	−0.394000	+	0.919110i	$0.628909\pi$
$740$	−86.4348	−3.17741
$741$	−0.246259	−0.00904653
$742$	63.5492	2.33296
$743$	−36.8867	−1.35324	−0.676620	−	0.736332i	$-0.736556\pi$
$743$	−36.8867	−1.35324	−0.676620	+	0.736332i	$0.736556\pi$
$744$	−23.9038	−0.876355
$745$	63.7467	2.33550
$746$	−91.1303	−3.33652
$747$	0.461019	0.0168678
$748$	−11.5023	−0.420567
$749$	39.8252	1.45518
$750$	−26.3619	−0.962602
$751$	−16.0621	−0.586116	−0.293058	−	0.956095i	$-0.594673\pi$
$751$	−16.0621	−0.586116	−0.293058	+	0.956095i	$0.594673\pi$
$752$	−36.5386	−1.33243
$753$	12.8281	0.467483
$754$	−7.78296	−0.283439
$755$	−33.6488	−1.22461
$756$	−109.552	−3.98436
$757$	−16.3826	−0.595437	−0.297719	−	0.954654i	$-0.596226\pi$
$757$	−16.3826	−0.595437	−0.297719	+	0.954654i	$0.596226\pi$
$758$	−15.1647	−0.550805
$759$	17.9376	0.651094
$760$	−5.15726	−0.187073
$761$	−1.60901	−0.0583266	−0.0291633	−	0.999575i	$-0.509284\pi$
$761$	−1.60901	−0.0583266	−0.0291633	+	0.999575i	$0.509284\pi$
$762$	−77.9253	−2.82293
$763$	28.7945	1.04243
$764$	119.676	4.32973
$765$	−0.712623	−0.0257649
$766$	16.7534	0.605325
$767$	7.78559	0.281122
$768$	18.2215	0.657512
$769$	−13.9207	−0.501992	−0.250996	−	0.967988i	$-0.580758\pi$
$769$	−13.9207	−0.501992	−0.250996	+	0.967988i	$0.580758\pi$
$770$	−91.1906	−3.28628
$771$	−49.8375	−1.79485
$772$	−22.0140	−0.792303
$773$	−24.9483	−0.897327	−0.448663	−	0.893701i	$-0.648100\pi$
$773$	−24.9483	−0.897327	−0.448663	+	0.893701i	$0.648100\pi$
$774$	−1.27350	−0.0457749
$775$	10.3372	0.371323
$776$	−54.2974	−1.94916
$777$	−37.3087	−1.33844
$778$	23.7414	0.851170
$779$	0.896184	0.0321091
$780$	−24.4388	−0.875048
$781$	2.30994	0.0826561
$782$	10.7279	0.383630
$783$	18.7709	0.670818
$784$	137.011	4.89326
$785$	−17.0247	−0.607638
$786$	54.8426	1.95617
$787$	−40.5409	−1.44513	−0.722564	−	0.691304i	$-0.757037\pi$
$787$	−40.5409	−1.44513	−0.722564	+	0.691304i	$0.757037\pi$
$788$	−65.8772	−2.34678
$789$	−18.6502	−0.663966
$790$	−75.4713	−2.68515
$791$	−54.2881	−1.93026
$792$	−4.44452	−0.157929
$793$	−3.09399	−0.109871
$794$	54.5638	1.93640
$795$	−34.1909	−1.21263
$796$	27.9115	0.989297
$797$	−5.18440	−0.183641	−0.0918205	−	0.995776i	$-0.529269\pi$
$797$	−5.18440	−0.183641	−0.0918205	+	0.995776i	$0.529269\pi$
$798$	−3.62701	−0.128395
$799$	2.76756	0.0979092
$800$	−108.003	−3.81847
$801$	2.24278	0.0792449
$802$	−52.2575	−1.84528
$803$	29.8145	1.05213
$804$	−55.2033	−1.94687
$805$	61.3534	2.16242
$806$	3.23409	0.113916
$807$	12.2211	0.430202
$808$	−31.8696	−1.12117
$809$	40.8795	1.43725	0.718624	−	0.695399i	$-0.244772\pi$
$809$	40.8795	1.43725	0.718624	+	0.695399i	$0.244772\pi$
$810$	87.7787	3.08423
$811$	−12.7566	−0.447944	−0.223972	−	0.974596i	$-0.571902\pi$
$811$	−12.7566	−0.447944	−0.223972	+	0.974596i	$0.571902\pi$
$812$	−82.6914	−2.90190
$813$	−33.1417	−1.16233
$814$	30.9064	1.08327
$815$	59.0741	2.06928
$816$	−21.0919	−0.738362
$817$	0.381163	0.0133352
$818$	−5.93120	−0.207380
$819$	−0.725891	−0.0253647
$820$	88.9376	3.10583
$821$	−24.2367	−0.845865	−0.422933	−	0.906161i	$-0.638999\pi$
$821$	−24.2367	−0.845865	−0.422933	+	0.906161i	$0.638999\pi$
$822$	50.0766	1.74662
$823$	−50.0340	−1.74408	−0.872039	−	0.489437i	$-0.837202\pi$
$823$	−50.0340	−1.74408	−0.872039	+	0.489437i	$0.837202\pi$
$824$	−131.258	−4.57258
$825$	27.9312	0.972440
$826$	114.670	3.98987
$827$	6.53424	0.227218	0.113609	−	0.993526i	$-0.463759\pi$
$827$	6.53424	0.227218	0.113609	+	0.993526i	$0.463759\pi$
$828$	4.87217	0.169319
$829$	12.4686	0.433052	0.216526	−	0.976277i	$-0.430527\pi$
$829$	12.4686	0.433052	0.216526	+	0.976277i	$0.430527\pi$
$830$	−18.9828	−0.658904
$831$	37.9646	1.31698
$832$	−14.5644	−0.504929
$833$	−10.3777	−0.359566
$834$	−106.827	−3.69913
$835$	40.6698	1.40744
$836$	2.16744	0.0749624
$837$	−7.79997	−0.269607
$838$	−34.6766	−1.19788
$839$	3.46998	0.119797	0.0598985	−	0.998204i	$-0.480922\pi$
$839$	3.46998	0.119797	0.0598985	+	0.998204i	$0.480922\pi$
$840$	−220.916	−7.62234
$841$	−14.8314	−0.511428
$842$	63.1754	2.17717
$843$	−2.02601	−0.0697796
$844$	67.8184	2.33441
$845$	−42.2641	−1.45393
$846$	1.74239	0.0599045
$847$	−23.1473	−0.795352
$848$	−69.6364	−2.39132
$849$	15.2178	0.522273
$850$	16.7048	0.572970
$851$	−20.7940	−0.712808
$852$	9.11774	0.312369
$853$	18.7247	0.641120	0.320560	−	0.947228i	$-0.396129\pi$
$853$	18.7247	0.641120	0.320560	+	0.947228i	$0.396129\pi$
$854$	−45.5697	−1.55936
$855$	0.134283	0.00459237
$856$	−79.9237	−2.73173
$857$	−11.2670	−0.384872	−0.192436	−	0.981310i	$-0.561639\pi$
$857$	−11.2670	−0.384872	−0.192436	+	0.981310i	$0.561639\pi$
$858$	8.73856	0.298330
$859$	16.5295	0.563978	0.281989	−	0.959418i	$-0.409006\pi$
$859$	16.5295	0.563978	0.281989	+	0.959418i	$0.409006\pi$
$860$	37.8267	1.28988
$861$	38.3890	1.30829
$862$	49.4094	1.68289
$863$	−56.9291	−1.93789	−0.968944	−	0.247279i	$-0.920464\pi$
$863$	−56.9291	−1.93789	−0.968944	+	0.247279i	$0.920464\pi$
$864$	81.4939	2.77248
$865$	−38.0442	−1.29354
$866$	−69.4311	−2.35936
$867$	−28.9159	−0.982034
$868$	34.3612	1.16629
$869$	19.4671	0.660376
$870$	61.6741	2.09095
$871$	4.58398	0.155322
$872$	−57.7865	−1.95690
$873$	1.41378	0.0478491
$874$	−2.02151	−0.0683787
$875$	23.2579	0.786259
$876$	117.683	3.97614
$877$	45.8775	1.54917	0.774587	−	0.632468i	$-0.217958\pi$
$877$	45.8775	1.54917	0.774587	+	0.632468i	$0.217958\pi$
$878$	76.7920	2.59160
$879$	−55.9638	−1.88761
$880$	99.9255	3.36849
$881$	24.1818	0.814706	0.407353	−	0.913271i	$-0.366452\pi$
$881$	24.1818	0.814706	0.407353	+	0.913271i	$0.366452\pi$
$882$	−6.53354	−0.219996
$883$	−46.3884	−1.56109	−0.780547	−	0.625097i	$-0.785059\pi$
$883$	−46.3884	−1.56109	−0.780547	+	0.625097i	$0.785059\pi$
$884$	3.77007	0.126801
$885$	−61.6950	−2.07385
$886$	20.7176	0.696022
$887$	−50.3969	−1.69216	−0.846082	−	0.533053i	$-0.821045\pi$
$887$	−50.3969	−1.69216	−0.846082	+	0.533053i	$0.821045\pi$
$888$	74.8733	2.51258
$889$	68.7497	2.30579
$890$	−92.3485	−3.09553
$891$	−22.6416	−0.758523
$892$	−46.4861	−1.55647
$893$	−0.521504	−0.0174515
$894$	−89.9716	−3.00910
$895$	−74.1685	−2.47918
$896$	−75.8450	−2.53380
$897$	−5.87934	−0.196305
$898$	−8.68105	−0.289690
$899$	−5.88755	−0.196361
$900$	7.58660	0.252887
$901$	5.27450	0.175719
$902$	−31.8014	−1.05887
$903$	16.3275	0.543345
$904$	108.949	3.62358
$905$	−63.5438	−2.11227
$906$	47.4916	1.57780
$907$	19.3106	0.641199	0.320600	−	0.947215i	$-0.396116\pi$
$907$	19.3106	0.641199	0.320600	+	0.947215i	$0.396116\pi$
$908$	−48.8058	−1.61968
$909$	0.829810	0.0275231
$910$	29.8892	0.990816
$911$	43.9721	1.45686	0.728430	−	0.685121i	$-0.240250\pi$
$911$	43.9721	1.45686	0.728430	+	0.685121i	$0.240250\pi$
$912$	3.97443	0.131607
$913$	4.89643	0.162048
$914$	91.8924	3.03953
$915$	24.5175	0.810524
$916$	58.3264	1.92716
$917$	−48.3849	−1.59781
$918$	−12.6047	−0.416017
$919$	19.0386	0.628024	0.314012	−	0.949419i	$-0.398327\pi$
$919$	19.0386	0.628024	0.314012	+	0.949419i	$0.398327\pi$
$920$	−123.128	−4.05940
$921$	−3.55449	−0.117124
$922$	69.0112	2.27276
$923$	−0.757119	−0.0249209
$924$	92.8444	3.05436
$925$	−32.3789	−1.06461
$926$	−1.63543	−0.0537437
$927$	3.41764	0.112250
$928$	61.5129	2.01926
$929$	14.1864	0.465442	0.232721	−	0.972544i	$-0.425237\pi$
$929$	14.1864	0.465442	0.232721	+	0.972544i	$0.425237\pi$
$930$	−25.6278	−0.840367
$931$	1.95552	0.0640895
$932$	−40.0787	−1.31282
$933$	11.4619	0.375245
$934$	107.075	3.50359
$935$	−7.56870	−0.247523
$936$	1.45676	0.0476158
$937$	−4.35334	−0.142217	−0.0711086	−	0.997469i	$-0.522654\pi$
$937$	−4.35334	−0.142217	−0.0711086	+	0.997469i	$0.522654\pi$
$938$	67.5149	2.20444
$939$	−3.36535	−0.109824
$940$	−51.7542	−1.68804
$941$	47.0485	1.53374	0.766869	−	0.641803i	$-0.221813\pi$
$941$	47.0485	1.53374	0.766869	+	0.641803i	$0.221813\pi$
$942$	24.0285	0.782892
$943$	21.3961	0.696752
$944$	−125.654	−4.08968
$945$	−72.0866	−2.34498
$946$	−13.5257	−0.439758
$947$	−50.1049	−1.62819	−0.814096	−	0.580730i	$-0.802767\pi$
$947$	−50.1049	−1.62819	−0.814096	+	0.580730i	$0.802767\pi$
$948$	76.8401	2.49565
$949$	−9.77217	−0.317218
$950$	−3.14776	−0.102127
$951$	−49.5076	−1.60539
$952$	34.0799	1.10454
$953$	−51.4249	−1.66582	−0.832908	−	0.553411i	$-0.813326\pi$
$953$	−51.4249	−1.66582	−0.832908	+	0.553411i	$0.813326\pi$
$954$	3.32069	0.107511
$955$	78.7485	2.54824
$956$	−102.031	−3.29993
$957$	−15.9082	−0.514240
$958$	−31.2287	−1.00895
$959$	−44.1801	−1.42665
$960$	115.412	3.72490
$961$	−28.5535	−0.921081
$962$	−10.1301	−0.326607
$963$	2.08102	0.0670600
$964$	−115.363	−3.71560
$965$	−14.4856	−0.466306
$966$	−86.5936	−2.78610
$967$	−40.2974	−1.29588	−0.647938	−	0.761693i	$-0.724369\pi$
$967$	−40.2974	−1.29588	−0.647938	+	0.761693i	$0.724369\pi$
$968$	46.4535	1.49307
$969$	−0.301037	−0.00967070
$970$	−58.2134	−1.86912
$971$	15.5865	0.500195	0.250097	−	0.968221i	$-0.419537\pi$
$971$	15.5865	0.500195	0.250097	+	0.968221i	$0.419537\pi$
$972$	−11.9058	−0.381879
$973$	94.2488	3.02148
$974$	−40.9656	−1.31262
$975$	−9.15490	−0.293191
$976$	49.9347	1.59837
$977$	26.5625	0.849810	0.424905	−	0.905238i	$-0.360307\pi$
$977$	26.5625	0.849810	0.424905	+	0.905238i	$0.360307\pi$
$978$	−83.3767	−2.66609
$979$	23.8204	0.761303
$980$	194.066	6.19921
$981$	1.50462	0.0480389
$982$	−29.9692	−0.956356
$983$	56.0787	1.78863	0.894316	−	0.447436i	$-0.147663\pi$
$983$	56.0787	1.78863	0.894316	+	0.447436i	$0.147663\pi$
$984$	−77.0413	−2.45599
$985$	−43.3481	−1.38119
$986$	−9.51422	−0.302995
$987$	−22.3392	−0.711063
$988$	−0.710412	−0.0226012
$989$	9.10013	0.289367
$990$	−4.76507	−0.151444
$991$	14.5768	0.463048	0.231524	−	0.972829i	$-0.425629\pi$
$991$	14.5768	0.463048	0.231524	+	0.972829i	$0.425629\pi$
$992$	−25.5608	−0.811555
$993$	−7.48489	−0.237526
$994$	−11.1512	−0.353695
$995$	18.3662	0.582246
$996$	19.3271	0.612403
$997$	−55.2501	−1.74979	−0.874894	−	0.484314i	$-0.839069\pi$
$997$	−55.2501	−1.74979	−0.874894	+	0.484314i	$0.839069\pi$
$998$	−58.0294	−1.83689
$999$	24.4317	0.772985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.8	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.8	✓	186	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67918 q^{2} +1.79491 q^{3} +5.17799 q^{4} +3.40719 q^{5} -4.80888 q^{6} +4.24264 q^{7} -8.51439 q^{8} +0.221695 q^{9} +O(q^{10})\)	\(q-2.67918 q^{2} +1.79491 q^{3} +5.17799 q^{4} +3.40719 q^{5} -4.80888 q^{6} +4.24264 q^{7} -8.51439 q^{8} +0.221695 q^{9} -9.12846 q^{10} +2.35460 q^{11} +9.29401 q^{12} -0.771756 q^{13} -11.3668 q^{14} +6.11559 q^{15} +12.4556 q^{16} -0.943428 q^{17} -0.593959 q^{18} +0.177774 q^{19} +17.6424 q^{20} +7.61515 q^{21} -6.30838 q^{22} +4.24430 q^{23} -15.2825 q^{24} +6.60893 q^{25} +2.06767 q^{26} -4.98680 q^{27} +21.9683 q^{28} -3.76412 q^{29} -16.3847 q^{30} +1.56412 q^{31} -16.3419 q^{32} +4.22628 q^{33} +2.52761 q^{34} +14.4555 q^{35} +1.14793 q^{36} -4.89927 q^{37} -0.476289 q^{38} -1.38523 q^{39} -29.0101 q^{40} +5.04113 q^{41} -20.4023 q^{42} +2.14408 q^{43} +12.1921 q^{44} +0.755355 q^{45} -11.3712 q^{46} -2.93352 q^{47} +22.3566 q^{48} +11.0000 q^{49} -17.7065 q^{50} -1.69337 q^{51} -3.99614 q^{52} -5.59078 q^{53} +13.3605 q^{54} +8.02255 q^{55} -36.1235 q^{56} +0.319089 q^{57} +10.0847 q^{58} -10.0882 q^{59} +31.6664 q^{60} +4.00902 q^{61} -4.19056 q^{62} +0.940570 q^{63} +18.8717 q^{64} -2.62952 q^{65} -11.3230 q^{66} -5.93967 q^{67} -4.88506 q^{68} +7.61813 q^{69} -38.7288 q^{70} +0.981034 q^{71} -1.88759 q^{72} +12.6623 q^{73} +13.1260 q^{74} +11.8624 q^{75} +0.920513 q^{76} +9.98970 q^{77} +3.71128 q^{78} +8.26770 q^{79} +42.4385 q^{80} -9.61594 q^{81} -13.5061 q^{82} +2.07952 q^{83} +39.4311 q^{84} -3.21444 q^{85} -5.74437 q^{86} -6.75625 q^{87} -20.0479 q^{88} +10.1165 q^{89} -2.02373 q^{90} -3.27428 q^{91} +21.9769 q^{92} +2.80746 q^{93} +7.85941 q^{94} +0.605711 q^{95} -29.3322 q^{96} +6.37714 q^{97} -29.4709 q^{98} +0.522001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * q^99

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