LMFDB - Embedded newform 6018.2.a.s.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 17x^{6} + 37x^{5} + 105x^{4} - 117x^{3} - 238x^{2} + 42x + 90 $ x^8 - 3x^7 - 17x^6 + 37x^5 + 105x^4 - 117x^3 - 238x^2 + 42*x + 90
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.672052$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.462452 q^{5} +1.00000 q^{6} -3.09978 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.462452 q^{5} +1.00000 q^{6} -3.09978 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.462452 q^{10} +3.41974 q^{11} -1.00000 q^{12} -1.01430 q^{13} +3.09978 q^{14} +0.462452 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -5.41606 q^{19} -0.462452 q^{20} +3.09978 q^{21} -3.41974 q^{22} +4.54653 q^{23} +1.00000 q^{24} -4.78614 q^{25} +1.01430 q^{26} -1.00000 q^{27} -3.09978 q^{28} +5.48351 q^{29} -0.462452 q^{30} +0.993693 q^{31} -1.00000 q^{32} -3.41974 q^{33} +1.00000 q^{34} +1.43350 q^{35} +1.00000 q^{36} -2.00659 q^{37} +5.41606 q^{38} +1.01430 q^{39} +0.462452 q^{40} -9.32818 q^{41} -3.09978 q^{42} +4.96528 q^{43} +3.41974 q^{44} -0.462452 q^{45} -4.54653 q^{46} -9.79273 q^{47} -1.00000 q^{48} +2.60866 q^{49} +4.78614 q^{50} +1.00000 q^{51} -1.01430 q^{52} +11.4848 q^{53} +1.00000 q^{54} -1.58146 q^{55} +3.09978 q^{56} +5.41606 q^{57} -5.48351 q^{58} +1.00000 q^{59} +0.462452 q^{60} -6.11739 q^{61} -0.993693 q^{62} -3.09978 q^{63} +1.00000 q^{64} +0.469066 q^{65} +3.41974 q^{66} +12.5726 q^{67} -1.00000 q^{68} -4.54653 q^{69} -1.43350 q^{70} -9.59269 q^{71} -1.00000 q^{72} +13.2116 q^{73} +2.00659 q^{74} +4.78614 q^{75} -5.41606 q^{76} -10.6005 q^{77} -1.01430 q^{78} -12.8490 q^{79} -0.462452 q^{80} +1.00000 q^{81} +9.32818 q^{82} +12.6443 q^{83} +3.09978 q^{84} +0.462452 q^{85} -4.96528 q^{86} -5.48351 q^{87} -3.41974 q^{88} -16.7685 q^{89} +0.462452 q^{90} +3.14412 q^{91} +4.54653 q^{92} -0.993693 q^{93} +9.79273 q^{94} +2.50467 q^{95} +1.00000 q^{96} -13.7661 q^{97} -2.60866 q^{98} +3.41974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - q^5 + 8 * q^6 + 6 * q^7 - 8 * q^8 + 8 * q^9	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9} + q^{10} - 8 q^{12} + 6 q^{13} - 6 q^{14} + q^{15} + 8 q^{16} - 8 q^{17} - 8 q^{18} - 7 q^{19} - q^{20} - 6 q^{21} - 5 q^{23} + 8 q^{24} + 9 q^{25} - 6 q^{26} - 8 q^{27} + 6 q^{28} - 15 q^{29} - q^{30} + 21 q^{31} - 8 q^{32} + 8 q^{34} - 2 q^{35} + 8 q^{36} + 7 q^{37} + 7 q^{38} - 6 q^{39} + q^{40} - q^{41} + 6 q^{42} + 14 q^{43} - q^{45} + 5 q^{46} - 8 q^{47} - 8 q^{48} + 2 q^{49} - 9 q^{50} + 8 q^{51} + 6 q^{52} + 8 q^{53} + 8 q^{54} + 24 q^{55} - 6 q^{56} + 7 q^{57} + 15 q^{58} + 8 q^{59} + q^{60} - 21 q^{62} + 6 q^{63} + 8 q^{64} + 6 q^{65} + 15 q^{67} - 8 q^{68} + 5 q^{69} + 2 q^{70} - 22 q^{71} - 8 q^{72} + 13 q^{73} - 7 q^{74} - 9 q^{75} - 7 q^{76} - 6 q^{77} + 6 q^{78} + 26 q^{79} - q^{80} + 8 q^{81} + q^{82} + 30 q^{83} - 6 q^{84} + q^{85} - 14 q^{86} + 15 q^{87} - 6 q^{89} + q^{90} + 3 q^{91} - 5 q^{92} - 21 q^{93} + 8 q^{94} + 37 q^{95} + 8 q^{96} + 23 q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - q^5 + 8 * q^6 + 6 * q^7 - 8 * q^8 + 8 * q^9 + q^10 - 8 * q^12 + 6 * q^13 - 6 * q^14 + q^15 + 8 * q^16 - 8 * q^17 - 8 * q^18 - 7 * q^19 - q^20 - 6 * q^21 - 5 * q^23 + 8 * q^24 + 9 * q^25 - 6 * q^26 - 8 * q^27 + 6 * q^28 - 15 * q^29 - q^30 + 21 * q^31 - 8 * q^32 + 8 * q^34 - 2 * q^35 + 8 * q^36 + 7 * q^37 + 7 * q^38 - 6 * q^39 + q^40 - q^41 + 6 * q^42 + 14 * q^43 - q^45 + 5 * q^46 - 8 * q^47 - 8 * q^48 + 2 * q^49 - 9 * q^50 + 8 * q^51 + 6 * q^52 + 8 * q^53 + 8 * q^54 + 24 * q^55 - 6 * q^56 + 7 * q^57 + 15 * q^58 + 8 * q^59 + q^60 - 21 * q^62 + 6 * q^63 + 8 * q^64 + 6 * q^65 + 15 * q^67 - 8 * q^68 + 5 * q^69 + 2 * q^70 - 22 * q^71 - 8 * q^72 + 13 * q^73 - 7 * q^74 - 9 * q^75 - 7 * q^76 - 6 * q^77 + 6 * q^78 + 26 * q^79 - q^80 + 8 * q^81 + q^82 + 30 * q^83 - 6 * q^84 + q^85 - 14 * q^86 + 15 * q^87 - 6 * q^89 + q^90 + 3 * q^91 - 5 * q^92 - 21 * q^93 + 8 * q^94 + 37 * q^95 + 8 * q^96 + 23 * q^97 - 2 * q^98

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.462452	−0.206815	−0.103407	−	0.994639i	$-0.532975\pi$
$5$	−0.462452	−0.206815	−0.103407	+	0.994639i	$0.532975\pi$
$6$	1.00000	0.408248
$7$	−3.09978	−1.17161	−0.585804	−	0.810453i	$-0.699221\pi$
$7$	−3.09978	−1.17161	−0.585804	+	0.810453i	$0.699221\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.462452	0.146240
$11$	3.41974	1.03109	0.515545	−	0.856863i	$-0.327590\pi$
$11$	3.41974	1.03109	0.515545	+	0.856863i	$0.327590\pi$
$12$	−1.00000	−0.288675
$13$	−1.01430	−0.281317	−0.140658	−	0.990058i	$-0.544922\pi$
$13$	−1.01430	−0.281317	−0.140658	+	0.990058i	$0.544922\pi$
$14$	3.09978	0.828452
$15$	0.462452	0.119405
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−5.41606	−1.24253	−0.621265	−	0.783600i	$-0.713381\pi$
$19$	−5.41606	−1.24253	−0.621265	+	0.783600i	$0.713381\pi$
$20$	−0.462452	−0.103407
$21$	3.09978	0.676428
$22$	−3.41974	−0.729091
$23$	4.54653	0.948017	0.474008	−	0.880520i	$-0.342807\pi$
$23$	4.54653	0.948017	0.474008	+	0.880520i	$0.342807\pi$
$24$	1.00000	0.204124
$25$	−4.78614	−0.957228
$26$	1.01430	0.198921
$27$	−1.00000	−0.192450
$28$	−3.09978	−0.585804
$29$	5.48351	1.01826	0.509131	−	0.860689i	$-0.329967\pi$
$29$	5.48351	1.01826	0.509131	+	0.860689i	$0.329967\pi$
$30$	−0.462452	−0.0844318
$31$	0.993693	0.178473	0.0892363	−	0.996010i	$-0.471557\pi$
$31$	0.993693	0.178473	0.0892363	+	0.996010i	$0.471557\pi$
$32$	−1.00000	−0.176777
$33$	−3.41974	−0.595300
$34$	1.00000	0.171499
$35$	1.43350	0.242306
$36$	1.00000	0.166667
$37$	−2.00659	−0.329881	−0.164940	−	0.986304i	$-0.552743\pi$
$37$	−2.00659	−0.329881	−0.164940	+	0.986304i	$0.552743\pi$
$38$	5.41606	0.878602
$39$	1.01430	0.162418
$40$	0.462452	0.0731201
$41$	−9.32818	−1.45682	−0.728408	−	0.685143i	$-0.759740\pi$
$41$	−9.32818	−1.45682	−0.728408	+	0.685143i	$0.759740\pi$
$42$	−3.09978	−0.478307
$43$	4.96528	0.757198	0.378599	−	0.925561i	$-0.376406\pi$
$43$	4.96528	0.757198	0.378599	+	0.925561i	$0.376406\pi$
$44$	3.41974	0.515545
$45$	−0.462452	−0.0689383
$46$	−4.54653	−0.670349
$47$	−9.79273	−1.42842	−0.714208	−	0.699934i	$-0.753213\pi$
$47$	−9.79273	−1.42842	−0.714208	+	0.699934i	$0.753213\pi$
$48$	−1.00000	−0.144338
$49$	2.60866	0.372666
$50$	4.78614	0.676862
$51$	1.00000	0.140028
$52$	−1.01430	−0.140658
$53$	11.4848	1.57756	0.788779	−	0.614676i	$-0.210713\pi$
$53$	11.4848	1.57756	0.788779	+	0.614676i	$0.210713\pi$
$54$	1.00000	0.136083
$55$	−1.58146	−0.213245
$56$	3.09978	0.414226
$57$	5.41606	0.717375
$58$	−5.48351	−0.720020
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0.462452	0.0597023
$61$	−6.11739	−0.783252	−0.391626	−	0.920125i	$-0.628087\pi$
$61$	−6.11739	−0.783252	−0.391626	+	0.920125i	$0.628087\pi$
$62$	−0.993693	−0.126199
$63$	−3.09978	−0.390536
$64$	1.00000	0.125000
$65$	0.469066	0.0581804
$66$	3.41974	0.420941
$67$	12.5726	1.53599	0.767994	−	0.640457i	$-0.221255\pi$
$67$	12.5726	1.53599	0.767994	+	0.640457i	$0.221255\pi$
$68$	−1.00000	−0.121268
$69$	−4.54653	−0.547338
$70$	−1.43350	−0.171336
$71$	−9.59269	−1.13844	−0.569222	−	0.822184i	$-0.692755\pi$
$71$	−9.59269	−1.13844	−0.569222	+	0.822184i	$0.692755\pi$
$72$	−1.00000	−0.117851
$73$	13.2116	1.54630	0.773149	−	0.634224i	$-0.218680\pi$
$73$	13.2116	1.54630	0.773149	+	0.634224i	$0.218680\pi$
$74$	2.00659	0.233261
$75$	4.78614	0.552656
$76$	−5.41606	−0.621265
$77$	−10.6005	−1.20803
$78$	−1.01430	−0.114847
$79$	−12.8490	−1.44563	−0.722815	−	0.691042i	$-0.757152\pi$
$79$	−12.8490	−1.44563	−0.722815	+	0.691042i	$0.757152\pi$
$80$	−0.462452	−0.0517037
$81$	1.00000	0.111111
$82$	9.32818	1.03012
$83$	12.6443	1.38790	0.693948	−	0.720025i	$-0.255870\pi$
$83$	12.6443	1.38790	0.693948	+	0.720025i	$0.255870\pi$
$84$	3.09978	0.338214
$85$	0.462452	0.0501600
$86$	−4.96528	−0.535420
$87$	−5.48351	−0.587894
$88$	−3.41974	−0.364545
$89$	−16.7685	−1.77746	−0.888730	−	0.458431i	$-0.848412\pi$
$89$	−16.7685	−1.77746	−0.888730	+	0.458431i	$0.848412\pi$
$90$	0.462452	0.0487467
$91$	3.14412	0.329593
$92$	4.54653	0.474008
$93$	−0.993693	−0.103041
$94$	9.79273	1.01004
$95$	2.50467	0.256974
$96$	1.00000	0.102062
$97$	−13.7661	−1.39773	−0.698866	−	0.715253i	$-0.746311\pi$
$97$	−13.7661	−1.39773	−0.698866	+	0.715253i	$0.746311\pi$
$98$	−2.60866	−0.263515
$99$	3.41974	0.343697
$100$	−4.78614	−0.478614
$101$	7.37866	0.734204	0.367102	−	0.930181i	$-0.380350\pi$
$101$	7.37866	0.734204	0.367102	+	0.930181i	$0.380350\pi$
$102$	−1.00000	−0.0990148
$103$	−1.23565	−0.121752	−0.0608760	−	0.998145i	$-0.519389\pi$
$103$	−1.23565	−0.121752	−0.0608760	+	0.998145i	$0.519389\pi$
$104$	1.01430	0.0994604
$105$	−1.43350	−0.139895
$106$	−11.4848	−1.11550
$107$	−18.4087	−1.77963	−0.889817	−	0.456317i	$-0.849168\pi$
$107$	−18.4087	−1.77963	−0.889817	+	0.456317i	$0.849168\pi$
$108$	−1.00000	−0.0962250
$109$	9.03951	0.865828	0.432914	−	0.901435i	$-0.357485\pi$
$109$	9.03951	0.865828	0.432914	+	0.901435i	$0.357485\pi$
$110$	1.58146	0.150787
$111$	2.00659	0.190457
$112$	−3.09978	−0.292902
$113$	0.0679447	0.00639170	0.00319585	−	0.999995i	$-0.498983\pi$
$113$	0.0679447	0.00639170	0.00319585	+	0.999995i	$0.498983\pi$
$114$	−5.41606	−0.507261
$115$	−2.10255	−0.196064
$116$	5.48351	0.509131
$117$	−1.01430	−0.0937722
$118$	−1.00000	−0.0920575
$119$	3.09978	0.284157
$120$	−0.462452	−0.0422159
$121$	0.694607	0.0631461
$122$	6.11739	0.553842
$123$	9.32818	0.841093
$124$	0.993693	0.0892363
$125$	4.52562	0.404784
$126$	3.09978	0.276151
$127$	8.81446	0.782157	0.391078	−	0.920357i	$-0.372102\pi$
$127$	8.81446	0.782157	0.391078	+	0.920357i	$0.372102\pi$
$128$	−1.00000	−0.0883883
$129$	−4.96528	−0.437169
$130$	−0.469066	−0.0411398
$131$	−13.8890	−1.21349	−0.606745	−	0.794896i	$-0.707525\pi$
$131$	−13.8890	−1.21349	−0.606745	+	0.794896i	$0.707525\pi$
$132$	−3.41974	−0.297650
$133$	16.7886	1.45576
$134$	−12.5726	−1.08611
$135$	0.462452	0.0398015
$136$	1.00000	0.0857493
$137$	2.32950	0.199022	0.0995112	−	0.995036i	$-0.468272\pi$
$137$	2.32950	0.199022	0.0995112	+	0.995036i	$0.468272\pi$
$138$	4.54653	0.387026
$139$	17.2619	1.46414	0.732069	−	0.681231i	$-0.238555\pi$
$139$	17.2619	1.46414	0.732069	+	0.681231i	$0.238555\pi$
$140$	1.43350	0.121153
$141$	9.79273	0.824696
$142$	9.59269	0.805001
$143$	−3.46864	−0.290063
$144$	1.00000	0.0833333
$145$	−2.53586	−0.210592
$146$	−13.2116	−1.09340
$147$	−2.60866	−0.215159
$148$	−2.00659	−0.164940
$149$	−5.91926	−0.484925	−0.242462	−	0.970161i	$-0.577955\pi$
$149$	−5.91926	−0.484925	−0.242462	+	0.970161i	$0.577955\pi$
$150$	−4.78614	−0.390787
$151$	−3.06539	−0.249458	−0.124729	−	0.992191i	$-0.539806\pi$
$151$	−3.06539	−0.249458	−0.124729	+	0.992191i	$0.539806\pi$
$152$	5.41606	0.439301
$153$	−1.00000	−0.0808452
$154$	10.6005	0.854209
$155$	−0.459535	−0.0369108
$156$	1.01430	0.0812091
$157$	−2.92563	−0.233491	−0.116745	−	0.993162i	$-0.537246\pi$
$157$	−2.92563	−0.233491	−0.116745	+	0.993162i	$0.537246\pi$
$158$	12.8490	1.02221
$159$	−11.4848	−0.910804
$160$	0.462452	0.0365600
$161$	−14.0933	−1.11070
$162$	−1.00000	−0.0785674
$163$	18.3074	1.43394	0.716972	−	0.697102i	$-0.245528\pi$
$163$	18.3074	1.43394	0.716972	+	0.697102i	$0.245528\pi$
$164$	−9.32818	−0.728408
$165$	1.58146	0.123117
$166$	−12.6443	−0.981390
$167$	4.33129	0.335165	0.167582	−	0.985858i	$-0.446404\pi$
$167$	4.33129	0.335165	0.167582	+	0.985858i	$0.446404\pi$
$168$	−3.09978	−0.239154
$169$	−11.9712	−0.920861
$170$	−0.462452	−0.0354685
$171$	−5.41606	−0.414177
$172$	4.96528	0.378599
$173$	0.904961	0.0688029	0.0344015	−	0.999408i	$-0.489048\pi$
$173$	0.904961	0.0688029	0.0344015	+	0.999408i	$0.489048\pi$
$174$	5.48351	0.415704
$175$	14.8360	1.12150
$176$	3.41974	0.257772
$177$	−1.00000	−0.0751646
$178$	16.7685	1.25685
$179$	−6.53648	−0.488560	−0.244280	−	0.969705i	$-0.578552\pi$
$179$	−6.53648	−0.488560	−0.244280	+	0.969705i	$0.578552\pi$
$180$	−0.462452	−0.0344691
$181$	9.07582	0.674601	0.337300	−	0.941397i	$-0.390486\pi$
$181$	9.07582	0.674601	0.337300	+	0.941397i	$0.390486\pi$
$182$	−3.14412	−0.233057
$183$	6.11739	0.452210
$184$	−4.54653	−0.335174
$185$	0.927950	0.0682243
$186$	0.993693	0.0728611
$187$	−3.41974	−0.250076
$188$	−9.79273	−0.714208
$189$	3.09978	0.225476
$190$	−2.50467	−0.181708
$191$	4.65524	0.336841	0.168421	−	0.985715i	$-0.446133\pi$
$191$	4.65524	0.336841	0.168421	+	0.985715i	$0.446133\pi$
$192$	−1.00000	−0.0721688
$193$	19.2485	1.38554	0.692769	−	0.721160i	$-0.256391\pi$
$193$	19.2485	1.38554	0.692769	+	0.721160i	$0.256391\pi$
$194$	13.7661	0.988345
$195$	−0.469066	−0.0335905
$196$	2.60866	0.186333
$197$	−10.1618	−0.723997	−0.361998	−	0.932179i	$-0.617905\pi$
$197$	−10.1618	−0.723997	−0.361998	+	0.932179i	$0.617905\pi$
$198$	−3.41974	−0.243030
$199$	−17.3911	−1.23283	−0.616413	−	0.787423i	$-0.711415\pi$
$199$	−17.3911	−1.23283	−0.616413	+	0.787423i	$0.711415\pi$
$200$	4.78614	0.338431
$201$	−12.5726	−0.886803
$202$	−7.37866	−0.519161
$203$	−16.9977	−1.19300
$204$	1.00000	0.0700140
$205$	4.31383	0.301291
$206$	1.23565	0.0860917
$207$	4.54653	0.316006
$208$	−1.01430	−0.0703291
$209$	−18.5215	−1.28116
$210$	1.43350	0.0989210
$211$	21.8409	1.50359	0.751795	−	0.659397i	$-0.229188\pi$
$211$	21.8409	1.50359	0.751795	+	0.659397i	$0.229188\pi$
$212$	11.4848	0.788779
$213$	9.59269	0.657281
$214$	18.4087	1.25839
$215$	−2.29620	−0.156600
$216$	1.00000	0.0680414
$217$	−3.08023	−0.209100
$218$	−9.03951	−0.612233
$219$	−13.2116	−0.892756
$220$	−1.58146	−0.106622
$221$	1.01430	0.0682293
$222$	−2.00659	−0.134673
$223$	29.0515	1.94544	0.972718	−	0.231992i	$-0.0745244\pi$
$223$	29.0515	1.94544	0.972718	+	0.231992i	$0.0745244\pi$
$224$	3.09978	0.207113
$225$	−4.78614	−0.319076
$226$	−0.0679447	−0.00451961
$227$	7.98193	0.529780	0.264890	−	0.964279i	$-0.414664\pi$
$227$	7.98193	0.529780	0.264890	+	0.964279i	$0.414664\pi$
$228$	5.41606	0.358688
$229$	−18.3890	−1.21518	−0.607591	−	0.794250i	$-0.707864\pi$
$229$	−18.3890	−1.21518	−0.607591	+	0.794250i	$0.707864\pi$
$230$	2.10255	0.138638
$231$	10.6005	0.697458
$232$	−5.48351	−0.360010
$233$	8.00338	0.524319	0.262159	−	0.965025i	$-0.415565\pi$
$233$	8.00338	0.524319	0.262159	+	0.965025i	$0.415565\pi$
$234$	1.01430	0.0663070
$235$	4.52867	0.295418
$236$	1.00000	0.0650945
$237$	12.8490	0.834635
$238$	−3.09978	−0.200929
$239$	5.31462	0.343774	0.171887	−	0.985117i	$-0.445014\pi$
$239$	5.31462	0.343774	0.171887	+	0.985117i	$0.445014\pi$
$240$	0.462452	0.0298512
$241$	1.82462	0.117534	0.0587670	−	0.998272i	$-0.481283\pi$
$241$	1.82462	0.117534	0.0587670	+	0.998272i	$0.481283\pi$
$242$	−0.694607	−0.0446510
$243$	−1.00000	−0.0641500
$244$	−6.11739	−0.391626
$245$	−1.20638	−0.0770729
$246$	−9.32818	−0.594743
$247$	5.49352	0.349544
$248$	−0.993693	−0.0630996
$249$	−12.6443	−0.801302
$250$	−4.52562	−0.286225
$251$	8.87734	0.560333	0.280166	−	0.959951i	$-0.409610\pi$
$251$	8.87734	0.560333	0.280166	+	0.959951i	$0.409610\pi$
$252$	−3.09978	−0.195268
$253$	15.5479	0.977490
$254$	−8.81446	−0.553068
$255$	−0.462452	−0.0289599
$256$	1.00000	0.0625000
$257$	27.2737	1.70128	0.850642	−	0.525746i	$-0.176214\pi$
$257$	27.2737	1.70128	0.850642	+	0.525746i	$0.176214\pi$
$258$	4.96528	0.309125
$259$	6.21999	0.386491
$260$	0.469066	0.0290902
$261$	5.48351	0.339421
$262$	13.8890	0.858067
$263$	8.81776	0.543726	0.271863	−	0.962336i	$-0.412360\pi$
$263$	8.81776	0.543726	0.271863	+	0.962336i	$0.412360\pi$
$264$	3.41974	0.210470
$265$	−5.31117	−0.326263
$266$	−16.7886	−1.02938
$267$	16.7685	1.02622
$268$	12.5726	0.767994
$269$	15.3013	0.932938	0.466469	−	0.884538i	$-0.345526\pi$
$269$	15.3013	0.932938	0.466469	+	0.884538i	$0.345526\pi$
$270$	−0.462452	−0.0281439
$271$	10.9383	0.664454	0.332227	−	0.943199i	$-0.392200\pi$
$271$	10.9383	0.664454	0.332227	+	0.943199i	$0.392200\pi$
$272$	−1.00000	−0.0606339
$273$	−3.14412	−0.190291
$274$	−2.32950	−0.140730
$275$	−16.3673	−0.986988
$276$	−4.54653	−0.273669
$277$	7.08873	0.425921	0.212960	−	0.977061i	$-0.431689\pi$
$277$	7.08873	0.425921	0.212960	+	0.977061i	$0.431689\pi$
$278$	−17.2619	−1.03530
$279$	0.993693	0.0594908
$280$	−1.43350	−0.0856681
$281$	−11.3355	−0.676218	−0.338109	−	0.941107i	$-0.609787\pi$
$281$	−11.3355	−0.676218	−0.338109	+	0.941107i	$0.609787\pi$
$282$	−9.79273	−0.583148
$283$	−17.6373	−1.04843	−0.524216	−	0.851586i	$-0.675641\pi$
$283$	−17.6373	−1.04843	−0.524216	+	0.851586i	$0.675641\pi$
$284$	−9.59269	−0.569222
$285$	−2.50467	−0.148364
$286$	3.46864	0.205105
$287$	28.9153	1.70682
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	2.53586	0.148911
$291$	13.7661	0.806981
$292$	13.2116	0.773149
$293$	−12.7137	−0.742742	−0.371371	−	0.928485i	$-0.621112\pi$
$293$	−12.7137	−0.742742	−0.371371	+	0.928485i	$0.621112\pi$
$294$	2.60866	0.152140
$295$	−0.462452	−0.0269250
$296$	2.00659	0.116631
$297$	−3.41974	−0.198433
$298$	5.91926	0.342894
$299$	−4.61155	−0.266693
$300$	4.78614	0.276328
$301$	−15.3913	−0.887140
$302$	3.06539	0.176393
$303$	−7.37866	−0.423893
$304$	−5.41606	−0.310633
$305$	2.82900	0.161988
$306$	1.00000	0.0571662
$307$	6.40317	0.365448	0.182724	−	0.983164i	$-0.441508\pi$
$307$	6.40317	0.365448	0.182724	+	0.983164i	$0.441508\pi$
$308$	−10.6005	−0.604017
$309$	1.23565	0.0702936
$310$	0.459535	0.0260999
$311$	−24.3359	−1.37996	−0.689981	−	0.723827i	$-0.742381\pi$
$311$	−24.3359	−1.37996	−0.689981	+	0.723827i	$0.742381\pi$
$312$	−1.01430	−0.0574235
$313$	16.4654	0.930680	0.465340	−	0.885132i	$-0.345932\pi$
$313$	16.4654	0.930680	0.465340	+	0.885132i	$0.345932\pi$
$314$	2.92563	0.165103
$315$	1.43350	0.0807687
$316$	−12.8490	−0.722815
$317$	8.53893	0.479594	0.239797	−	0.970823i	$-0.422919\pi$
$317$	8.53893	0.479594	0.239797	+	0.970823i	$0.422919\pi$
$318$	11.4848	0.644036
$319$	18.7522	1.04992
$320$	−0.462452	−0.0258519
$321$	18.4087	1.02747
$322$	14.0933	0.785386
$323$	5.41606	0.301358
$324$	1.00000	0.0555556
$325$	4.85459	0.269284
$326$	−18.3074	−1.01395
$327$	−9.03951	−0.499886
$328$	9.32818	0.515062
$329$	30.3553	1.67354
$330$	−1.58146	−0.0870568
$331$	14.2573	0.783652	0.391826	−	0.920039i	$-0.371844\pi$
$331$	14.2573	0.783652	0.391826	+	0.920039i	$0.371844\pi$
$332$	12.6443	0.693948
$333$	−2.00659	−0.109960
$334$	−4.33129	−0.236997
$335$	−5.81423	−0.317665
$336$	3.09978	0.169107
$337$	17.4266	0.949289	0.474645	−	0.880178i	$-0.342577\pi$
$337$	17.4266	0.949289	0.474645	+	0.880178i	$0.342577\pi$
$338$	11.9712	0.651147
$339$	−0.0679447	−0.00369025
$340$	0.462452	0.0250800
$341$	3.39817	0.184021
$342$	5.41606	0.292867
$343$	13.6122	0.734989
$344$	−4.96528	−0.267710
$345$	2.10255	0.113198
$346$	−0.904961	−0.0486510
$347$	28.0199	1.50419	0.752094	−	0.659056i	$-0.229044\pi$
$347$	28.0199	1.50419	0.752094	+	0.659056i	$0.229044\pi$
$348$	−5.48351	−0.293947
$349$	−5.78440	−0.309632	−0.154816	−	0.987943i	$-0.549478\pi$
$349$	−5.78440	−0.309632	−0.154816	+	0.987943i	$0.549478\pi$
$350$	−14.8360	−0.793017
$351$	1.01430	0.0541394
$352$	−3.41974	−0.182273
$353$	−23.9682	−1.27570	−0.637851	−	0.770160i	$-0.720176\pi$
$353$	−23.9682	−1.27570	−0.637851	+	0.770160i	$0.720176\pi$
$354$	1.00000	0.0531494
$355$	4.43616	0.235447
$356$	−16.7685	−0.888730
$357$	−3.09978	−0.164058
$358$	6.53648	0.345464
$359$	23.6552	1.24847	0.624236	−	0.781236i	$-0.285410\pi$
$359$	23.6552	1.24847	0.624236	+	0.781236i	$0.285410\pi$
$360$	0.462452	0.0243734
$361$	10.3338	0.543882
$362$	−9.07582	−0.477015
$363$	−0.694607	−0.0364574
$364$	3.14412	0.164796
$365$	−6.10972	−0.319798
$366$	−6.11739	−0.319761
$367$	−4.28183	−0.223510	−0.111755	−	0.993736i	$-0.535647\pi$
$367$	−4.28183	−0.223510	−0.111755	+	0.993736i	$0.535647\pi$
$368$	4.54653	0.237004
$369$	−9.32818	−0.485605
$370$	−0.927950	−0.0482418
$371$	−35.6004	−1.84828
$372$	−0.993693	−0.0515206
$373$	−26.0004	−1.34625	−0.673125	−	0.739529i	$-0.735048\pi$
$373$	−26.0004	−1.34625	−0.673125	+	0.739529i	$0.735048\pi$
$374$	3.41974	0.176830
$375$	−4.52562	−0.233702
$376$	9.79273	0.505021
$377$	−5.56193	−0.286454
$378$	−3.09978	−0.159436
$379$	8.52503	0.437902	0.218951	−	0.975736i	$-0.429737\pi$
$379$	8.52503	0.437902	0.218951	+	0.975736i	$0.429737\pi$
$380$	2.50467	0.128487
$381$	−8.81446	−0.451579
$382$	−4.65524	−0.238183
$383$	14.5437	0.743146	0.371573	−	0.928404i	$-0.378819\pi$
$383$	14.5437	0.743146	0.371573	+	0.928404i	$0.378819\pi$
$384$	1.00000	0.0510310
$385$	4.90220	0.249839
$386$	−19.2485	−0.979723
$387$	4.96528	0.252399
$388$	−13.7661	−0.698866
$389$	10.8222	0.548706	0.274353	−	0.961629i	$-0.411536\pi$
$389$	10.8222	0.548706	0.274353	+	0.961629i	$0.411536\pi$
$390$	0.469066	0.0237521
$391$	−4.54653	−0.229928
$392$	−2.60866	−0.131757
$393$	13.8890	0.700609
$394$	10.1618	0.511943
$395$	5.94207	0.298978
$396$	3.41974	0.171848
$397$	−13.3029	−0.667653	−0.333826	−	0.942635i	$-0.608340\pi$
$397$	−13.3029	−0.667653	−0.333826	+	0.942635i	$0.608340\pi$
$398$	17.3911	0.871739
$399$	−16.7886	−0.840483
$400$	−4.78614	−0.239307
$401$	−5.21348	−0.260349	−0.130174	−	0.991491i	$-0.541554\pi$
$401$	−5.21348	−0.260349	−0.130174	+	0.991491i	$0.541554\pi$
$402$	12.5726	0.627064
$403$	−1.00790	−0.0502073
$404$	7.37866	0.367102
$405$	−0.462452	−0.0229794
$406$	16.9977	0.843582
$407$	−6.86200	−0.340137
$408$	−1.00000	−0.0495074
$409$	10.7249	0.530314	0.265157	−	0.964205i	$-0.414576\pi$
$409$	10.7249	0.530314	0.265157	+	0.964205i	$0.414576\pi$
$410$	−4.31383	−0.213045
$411$	−2.32950	−0.114906
$412$	−1.23565	−0.0608760
$413$	−3.09978	−0.152530
$414$	−4.54653	−0.223450
$415$	−5.84740	−0.287037
$416$	1.01430	0.0497302
$417$	−17.2619	−0.845320
$418$	18.5215	0.905917
$419$	33.2606	1.62489	0.812443	−	0.583041i	$-0.198137\pi$
$419$	33.2606	1.62489	0.812443	+	0.583041i	$0.198137\pi$
$420$	−1.43350	−0.0699477
$421$	−18.2718	−0.890514	−0.445257	−	0.895403i	$-0.646888\pi$
$421$	−18.2718	−0.890514	−0.445257	+	0.895403i	$0.646888\pi$
$422$	−21.8409	−1.06320
$423$	−9.79273	−0.476139
$424$	−11.4848	−0.557751
$425$	4.78614	0.232162
$426$	−9.59269	−0.464768
$427$	18.9626	0.917664
$428$	−18.4087	−0.889817
$429$	3.46864	0.167468
$430$	2.29620	0.110733
$431$	−30.4328	−1.46589	−0.732947	−	0.680285i	$-0.761856\pi$
$431$	−30.4328	−1.46589	−0.732947	+	0.680285i	$0.761856\pi$
$432$	−1.00000	−0.0481125
$433$	−16.5447	−0.795089	−0.397544	−	0.917583i	$-0.630138\pi$
$433$	−16.5447	−0.795089	−0.397544	+	0.917583i	$0.630138\pi$
$434$	3.08023	0.147856
$435$	2.53586	0.121585
$436$	9.03951	0.432914
$437$	−24.6243	−1.17794
$438$	13.2116	0.631274
$439$	21.2151	1.01254	0.506272	−	0.862374i	$-0.331023\pi$
$439$	21.2151	1.01254	0.506272	+	0.862374i	$0.331023\pi$
$440$	1.58146	0.0753934
$441$	2.60866	0.124222
$442$	−1.01430	−0.0482454
$443$	−0.353586	−0.0167994	−0.00839968	−	0.999965i	$-0.502674\pi$
$443$	−0.353586	−0.0167994	−0.00839968	+	0.999965i	$0.502674\pi$
$444$	2.00659	0.0952284
$445$	7.75464	0.367605
$446$	−29.0515	−1.37563
$447$	5.91926	0.279972
$448$	−3.09978	−0.146451
$449$	−9.52919	−0.449710	−0.224855	−	0.974392i	$-0.572191\pi$
$449$	−9.52919	−0.449710	−0.224855	+	0.974392i	$0.572191\pi$
$450$	4.78614	0.225621
$451$	−31.8999	−1.50211
$452$	0.0679447	0.00319585
$453$	3.06539	0.144025
$454$	−7.98193	−0.374611
$455$	−1.45400	−0.0681647
$456$	−5.41606	−0.253630
$457$	6.33962	0.296555	0.148277	−	0.988946i	$-0.452627\pi$
$457$	6.33962	0.296555	0.148277	+	0.988946i	$0.452627\pi$
$458$	18.3890	0.859264
$459$	1.00000	0.0466760
$460$	−2.10255	−0.0980320
$461$	0.746198	0.0347539	0.0173769	−	0.999849i	$-0.494468\pi$
$461$	0.746198	0.0347539	0.0173769	+	0.999849i	$0.494468\pi$
$462$	−10.6005	−0.493178
$463$	27.5147	1.27872	0.639358	−	0.768909i	$-0.279200\pi$
$463$	27.5147	1.27872	0.639358	+	0.768909i	$0.279200\pi$
$464$	5.48351	0.254566
$465$	0.459535	0.0213104
$466$	−8.00338	−0.370749
$467$	−12.4066	−0.574108	−0.287054	−	0.957914i	$-0.592676\pi$
$467$	−12.4066	−0.574108	−0.287054	+	0.957914i	$0.592676\pi$
$468$	−1.01430	−0.0468861
$469$	−38.9724	−1.79958
$470$	−4.52867	−0.208892
$471$	2.92563	0.134806
$472$	−1.00000	−0.0460287
$473$	16.9800	0.780739
$474$	−12.8490	−0.590176
$475$	25.9220	1.18938
$476$	3.09978	0.142078
$477$	11.4848	0.525853
$478$	−5.31462	−0.243085
$479$	12.2589	0.560124	0.280062	−	0.959982i	$-0.409645\pi$
$479$	12.2589	0.560124	0.280062	+	0.959982i	$0.409645\pi$
$480$	−0.462452	−0.0211080
$481$	2.03528	0.0928010
$482$	−1.82462	−0.0831091
$483$	14.0933	0.641265
$484$	0.694607	0.0315731
$485$	6.36614	0.289072
$486$	1.00000	0.0453609
$487$	39.2557	1.77885	0.889424	−	0.457084i	$-0.151106\pi$
$487$	39.2557	1.77885	0.889424	+	0.457084i	$0.151106\pi$
$488$	6.11739	0.276921
$489$	−18.3074	−0.827888
$490$	1.20638	0.0544988
$491$	37.4309	1.68923	0.844616	−	0.535372i	$-0.179829\pi$
$491$	37.4309	1.68923	0.844616	+	0.535372i	$0.179829\pi$
$492$	9.32818	0.420547
$493$	−5.48351	−0.246965
$494$	−5.49352	−0.247165
$495$	−1.58146	−0.0710816
$496$	0.993693	0.0446181
$497$	29.7353	1.33381
$498$	12.6443	0.566606
$499$	13.5140	0.604968	0.302484	−	0.953154i	$-0.402184\pi$
$499$	13.5140	0.604968	0.302484	+	0.953154i	$0.402184\pi$
$500$	4.52562	0.202392
$501$	−4.33129	−0.193508
$502$	−8.87734	−0.396215
$503$	21.0856	0.940160	0.470080	−	0.882624i	$-0.344225\pi$
$503$	21.0856	0.940160	0.470080	+	0.882624i	$0.344225\pi$
$504$	3.09978	0.138075
$505$	−3.41228	−0.151844
$506$	−15.5479	−0.691190
$507$	11.9712	0.531659
$508$	8.81446	0.391078
$509$	33.5985	1.48923	0.744614	−	0.667495i	$-0.232633\pi$
$509$	33.5985	1.48923	0.744614	+	0.667495i	$0.232633\pi$
$510$	0.462452	0.0204777
$511$	−40.9531	−1.81166
$512$	−1.00000	−0.0441942
$513$	5.41606	0.239125
$514$	−27.2737	−1.20299
$515$	0.571428	0.0251801
$516$	−4.96528	−0.218584
$517$	−33.4886	−1.47282
$518$	−6.21999	−0.273291
$519$	−0.904961	−0.0397234
$520$	−0.469066	−0.0205699
$521$	1.78620	0.0782550	0.0391275	−	0.999234i	$-0.487542\pi$
$521$	1.78620	0.0782550	0.0391275	+	0.999234i	$0.487542\pi$
$522$	−5.48351	−0.240007
$523$	0.682223	0.0298315	0.0149158	−	0.999889i	$-0.495252\pi$
$523$	0.682223	0.0298315	0.0149158	+	0.999889i	$0.495252\pi$
$524$	−13.8890	−0.606745
$525$	−14.8360	−0.647496
$526$	−8.81776	−0.384473
$527$	−0.993693	−0.0432859
$528$	−3.41974	−0.148825
$529$	−2.32908	−0.101265
$530$	5.31117	0.230703
$531$	1.00000	0.0433963
$532$	16.7886	0.727880
$533$	9.46158	0.409827
$534$	−16.7685	−0.725645
$535$	8.51313	0.368055
$536$	−12.5726	−0.543054
$537$	6.53648	0.282070
$538$	−15.3013	−0.659687
$539$	8.92095	0.384252
$540$	0.462452	0.0199008
$541$	11.3025	0.485933	0.242966	−	0.970035i	$-0.421880\pi$
$541$	11.3025	0.485933	0.242966	+	0.970035i	$0.421880\pi$
$542$	−10.9383	−0.469840
$543$	−9.07582	−0.389481
$544$	1.00000	0.0428746
$545$	−4.18034	−0.179066
$546$	3.14412	0.134556
$547$	−17.0550	−0.729220	−0.364610	−	0.931160i	$-0.618798\pi$
$547$	−17.0550	−0.729220	−0.364610	+	0.931160i	$0.618798\pi$
$548$	2.32950	0.0995112
$549$	−6.11739	−0.261084
$550$	16.3673	0.697906
$551$	−29.6990	−1.26522
$552$	4.54653	0.193513
$553$	39.8293	1.69371
$554$	−7.08873	−0.301171
$555$	−0.927950	−0.0393893
$556$	17.2619	0.732069
$557$	2.36442	0.100183	0.0500917	−	0.998745i	$-0.484049\pi$
$557$	2.36442	0.100183	0.0500917	+	0.998745i	$0.484049\pi$
$558$	−0.993693	−0.0420664
$559$	−5.03629	−0.213012
$560$	1.43350	0.0605765
$561$	3.41974	0.144381
$562$	11.3355	0.478158
$563$	15.3473	0.646811	0.323405	−	0.946261i	$-0.395172\pi$
$563$	15.3473	0.646811	0.323405	+	0.946261i	$0.395172\pi$
$564$	9.79273	0.412348
$565$	−0.0314212	−0.00132190
$566$	17.6373	0.741353
$567$	−3.09978	−0.130179
$568$	9.59269	0.402501
$569$	20.5880	0.863093	0.431546	−	0.902091i	$-0.357968\pi$
$569$	20.5880	0.863093	0.431546	+	0.902091i	$0.357968\pi$
$570$	2.50467	0.104909
$571$	44.0742	1.84445	0.922223	−	0.386658i	$-0.126371\pi$
$571$	44.0742	1.84445	0.922223	+	0.386658i	$0.126371\pi$
$572$	−3.46864	−0.145031
$573$	−4.65524	−0.194475
$574$	−28.9153	−1.20690
$575$	−21.7603	−0.907468
$576$	1.00000	0.0416667
$577$	13.4267	0.558963	0.279481	−	0.960151i	$-0.409837\pi$
$577$	13.4267	0.558963	0.279481	+	0.960151i	$0.409837\pi$
$578$	−1.00000	−0.0415945
$579$	−19.2485	−0.799940
$580$	−2.53586	−0.105296
$581$	−39.1947	−1.62607
$582$	−13.7661	−0.570621
$583$	39.2750	1.62660
$584$	−13.2116	−0.546699
$585$	0.469066	0.0193935
$586$	12.7137	0.525198
$587$	−10.2920	−0.424797	−0.212399	−	0.977183i	$-0.568128\pi$
$587$	−10.2920	−0.424797	−0.212399	+	0.977183i	$0.568128\pi$
$588$	−2.60866	−0.107579
$589$	−5.38191	−0.221758
$590$	0.462452	0.0190389
$591$	10.1618	0.418000
$592$	−2.00659	−0.0824702
$593$	−19.9966	−0.821162	−0.410581	−	0.911824i	$-0.634674\pi$
$593$	−19.9966	−0.821162	−0.410581	+	0.911824i	$0.634674\pi$
$594$	3.41974	0.140314
$595$	−1.43350	−0.0587678
$596$	−5.91926	−0.242462
$597$	17.3911	0.711772
$598$	4.61155	0.188580
$599$	6.49987	0.265578	0.132789	−	0.991144i	$-0.457607\pi$
$599$	6.49987	0.265578	0.132789	+	0.991144i	$0.457607\pi$
$600$	−4.78614	−0.195393
$601$	17.5412	0.715520	0.357760	−	0.933814i	$-0.383541\pi$
$601$	17.5412	0.715520	0.357760	+	0.933814i	$0.383541\pi$
$602$	15.3913	0.627302
$603$	12.5726	0.511996
$604$	−3.06539	−0.124729
$605$	−0.321223	−0.0130596
$606$	7.37866	0.299738
$607$	5.15727	0.209327	0.104664	−	0.994508i	$-0.466623\pi$
$607$	5.15727	0.209327	0.104664	+	0.994508i	$0.466623\pi$
$608$	5.41606	0.219650
$609$	16.9977	0.688782
$610$	−2.82900	−0.114543
$611$	9.93277	0.401837
$612$	−1.00000	−0.0404226
$613$	−14.9618	−0.604302	−0.302151	−	0.953260i	$-0.597705\pi$
$613$	−14.9618	−0.604302	−0.302151	+	0.953260i	$0.597705\pi$
$614$	−6.40317	−0.258411
$615$	−4.31383	−0.173951
$616$	10.6005	0.427104
$617$	7.11197	0.286317	0.143159	−	0.989700i	$-0.454274\pi$
$617$	7.11197	0.286317	0.143159	+	0.989700i	$0.454274\pi$
$618$	−1.23565	−0.0497051
$619$	−16.1014	−0.647171	−0.323586	−	0.946199i	$-0.604888\pi$
$619$	−16.1014	−0.647171	−0.323586	+	0.946199i	$0.604888\pi$
$620$	−0.459535	−0.0184554
$621$	−4.54653	−0.182446
$622$	24.3359	0.975780
$623$	51.9788	2.08249
$624$	1.01430	0.0406046
$625$	21.8378	0.873512
$626$	−16.4654	−0.658090
$627$	18.5215	0.739678
$628$	−2.92563	−0.116745
$629$	2.00659	0.0800079
$630$	−1.43350	−0.0571121
$631$	7.11143	0.283102	0.141551	−	0.989931i	$-0.454791\pi$
$631$	7.11143	0.283102	0.141551	+	0.989931i	$0.454791\pi$
$632$	12.8490	0.511107
$633$	−21.8409	−0.868098
$634$	−8.53893	−0.339124
$635$	−4.07627	−0.161762
$636$	−11.4848	−0.455402
$637$	−2.64597	−0.104837
$638$	−18.7522	−0.742405
$639$	−9.59269	−0.379481
$640$	0.462452	0.0182800
$641$	−27.6582	−1.09243	−0.546216	−	0.837644i	$-0.683932\pi$
$641$	−27.6582	−1.09243	−0.546216	+	0.837644i	$0.683932\pi$
$642$	−18.4087	−0.726533
$643$	30.9807	1.22176	0.610879	−	0.791724i	$-0.290816\pi$
$643$	30.9807	1.22176	0.610879	+	0.791724i	$0.290816\pi$
$644$	−14.0933	−0.555352
$645$	2.29620	0.0904129
$646$	−5.41606	−0.213092
$647$	2.65687	0.104452	0.0522261	−	0.998635i	$-0.483368\pi$
$647$	2.65687	0.104452	0.0522261	+	0.998635i	$0.483368\pi$
$648$	−1.00000	−0.0392837
$649$	3.41974	0.134236
$650$	−4.85459	−0.190413
$651$	3.08023	0.120724
$652$	18.3074	0.716972
$653$	31.4076	1.22907	0.614537	−	0.788888i	$-0.289343\pi$
$653$	31.4076	1.22907	0.614537	+	0.788888i	$0.289343\pi$
$654$	9.03951	0.353473
$655$	6.42301	0.250968
$656$	−9.32818	−0.364204
$657$	13.2116	0.515433
$658$	−30.3553	−1.18337
$659$	−8.30609	−0.323559	−0.161780	−	0.986827i	$-0.551723\pi$
$659$	−8.30609	−0.323559	−0.161780	+	0.986827i	$0.551723\pi$
$660$	1.58146	0.0615584
$661$	2.53525	0.0986097	0.0493048	−	0.998784i	$-0.484299\pi$
$661$	2.53525	0.0986097	0.0493048	+	0.998784i	$0.484299\pi$
$662$	−14.2573	−0.554126
$663$	−1.01430	−0.0393922
$664$	−12.6443	−0.490695
$665$	−7.76394	−0.301073
$666$	2.00659	0.0777537
$667$	24.9309	0.965330
$668$	4.33129	0.167582
$669$	−29.0515	−1.12320
$670$	5.81423	0.224623
$671$	−20.9199	−0.807603
$672$	−3.09978	−0.119577
$673$	27.7155	1.06835	0.534177	−	0.845372i	$-0.320621\pi$
$673$	27.7155	1.06835	0.534177	+	0.845372i	$0.320621\pi$
$674$	−17.4266	−0.671249
$675$	4.78614	0.184219
$676$	−11.9712	−0.460430
$677$	40.9931	1.57549	0.787746	−	0.616000i	$-0.211248\pi$
$677$	40.9931	1.57549	0.787746	+	0.616000i	$0.211248\pi$
$678$	0.0679447	0.00260940
$679$	42.6718	1.63759
$680$	−0.462452	−0.0177342
$681$	−7.98193	−0.305868
$682$	−3.39817	−0.130123
$683$	−33.5089	−1.28218	−0.641091	−	0.767465i	$-0.721518\pi$
$683$	−33.5089	−1.28218	−0.641091	+	0.767465i	$0.721518\pi$
$684$	−5.41606	−0.207088
$685$	−1.07728	−0.0411608
$686$	−13.6122	−0.519716
$687$	18.3890	0.701586
$688$	4.96528	0.189300
$689$	−11.6491	−0.443793
$690$	−2.10255	−0.0800428
$691$	41.5547	1.58082	0.790409	−	0.612580i	$-0.209868\pi$
$691$	41.5547	1.58082	0.790409	+	0.612580i	$0.209868\pi$
$692$	0.904961	0.0344015
$693$	−10.6005	−0.402678
$694$	−28.0199	−1.06362
$695$	−7.98281	−0.302805
$696$	5.48351	0.207852
$697$	9.32818	0.353330
$698$	5.78440	0.218943
$699$	−8.00338	−0.302716
$700$	14.8360	0.560748
$701$	9.70143	0.366418	0.183209	−	0.983074i	$-0.441352\pi$
$701$	9.70143	0.366418	0.183209	+	0.983074i	$0.441352\pi$
$702$	−1.01430	−0.0382823
$703$	10.8678	0.409887
$704$	3.41974	0.128886
$705$	−4.52867	−0.170559
$706$	23.9682	0.902057
$707$	−22.8723	−0.860200
$708$	−1.00000	−0.0375823
$709$	32.2494	1.21115	0.605575	−	0.795788i	$-0.292943\pi$
$709$	32.2494	1.21115	0.605575	+	0.795788i	$0.292943\pi$
$710$	−4.43616	−0.166486
$711$	−12.8490	−0.481877
$712$	16.7685	0.628427
$713$	4.51785	0.169195
$714$	3.09978	0.116007
$715$	1.60408	0.0599893
$716$	−6.53648	−0.244280
$717$	−5.31462	−0.198478
$718$	−23.6552	−0.882803
$719$	−43.3910	−1.61821	−0.809106	−	0.587662i	$-0.800048\pi$
$719$	−43.3910	−1.61821	−0.809106	+	0.587662i	$0.800048\pi$
$720$	−0.462452	−0.0172346
$721$	3.83024	0.142646
$722$	−10.3338	−0.384583
$723$	−1.82462	−0.0678583
$724$	9.07582	0.337300
$725$	−26.2448	−0.974709
$726$	0.694607	0.0257793
$727$	31.8128	1.17987	0.589936	−	0.807450i	$-0.299153\pi$
$727$	31.8128	1.17987	0.589936	+	0.807450i	$0.299153\pi$
$728$	−3.14412	−0.116529
$729$	1.00000	0.0370370
$730$	6.10972	0.226131
$731$	−4.96528	−0.183648
$732$	6.11739	0.226105
$733$	−29.9213	−1.10517	−0.552584	−	0.833457i	$-0.686358\pi$
$733$	−29.9213	−1.10517	−0.552584	+	0.833457i	$0.686358\pi$
$734$	4.28183	0.158045
$735$	1.20638	0.0444981
$736$	−4.54653	−0.167587
$737$	42.9950	1.58374
$738$	9.32818	0.343375
$739$	45.6857	1.68058	0.840288	−	0.542141i	$-0.182386\pi$
$739$	45.6857	1.68058	0.840288	+	0.542141i	$0.182386\pi$
$740$	0.927950	0.0341121
$741$	−5.49352	−0.201810
$742$	35.6004	1.30693
$743$	−1.96749	−0.0721804	−0.0360902	−	0.999349i	$-0.511490\pi$
$743$	−1.96749	−0.0721804	−0.0360902	+	0.999349i	$0.511490\pi$
$744$	0.993693	0.0364306
$745$	2.73738	0.100290
$746$	26.0004	0.951942
$747$	12.6443	0.462632
$748$	−3.41974	−0.125038
$749$	57.0630	2.08503
$750$	4.52562	0.165252
$751$	−10.5471	−0.384870	−0.192435	−	0.981310i	$-0.561638\pi$
$751$	−10.5471	−0.384870	−0.192435	+	0.981310i	$0.561638\pi$
$752$	−9.79273	−0.357104
$753$	−8.87734	−0.323508
$754$	5.56193	0.202554
$755$	1.41760	0.0515916
$756$	3.09978	0.112738
$757$	41.0400	1.49162	0.745812	−	0.666156i	$-0.232062\pi$
$757$	41.0400	1.49162	0.745812	+	0.666156i	$0.232062\pi$
$758$	−8.52503	−0.309643
$759$	−15.5479	−0.564354
$760$	−2.50467	−0.0908539
$761$	6.23599	0.226055	0.113027	−	0.993592i	$-0.463945\pi$
$761$	6.23599	0.226055	0.113027	+	0.993592i	$0.463945\pi$
$762$	8.81446	0.319314
$763$	−28.0205	−1.01441
$764$	4.65524	0.168421
$765$	0.462452	0.0167200
$766$	−14.5437	−0.525484
$767$	−1.01430	−0.0366243
$768$	−1.00000	−0.0360844
$769$	−24.5860	−0.886593	−0.443297	−	0.896375i	$-0.646191\pi$
$769$	−24.5860	−0.886593	−0.443297	+	0.896375i	$0.646191\pi$
$770$	−4.90220	−0.176663
$771$	−27.2737	−0.982237
$772$	19.2485	0.692769
$773$	4.43023	0.159344	0.0796721	−	0.996821i	$-0.474613\pi$
$773$	4.43023	0.159344	0.0796721	+	0.996821i	$0.474613\pi$
$774$	−4.96528	−0.178473
$775$	−4.75595	−0.170839
$776$	13.7661	0.494173
$777$	−6.21999	−0.223141
$778$	−10.8222	−0.387994
$779$	50.5220	1.81014
$780$	−0.469066	−0.0167952
$781$	−32.8045	−1.17384
$782$	4.54653	0.162584
$783$	−5.48351	−0.195965
$784$	2.60866	0.0931666
$785$	1.35297	0.0482894
$786$	−13.8890	−0.495405
$787$	−10.9536	−0.390452	−0.195226	−	0.980758i	$-0.562544\pi$
$787$	−10.9536	−0.390452	−0.195226	+	0.980758i	$0.562544\pi$
$788$	−10.1618	−0.361998
$789$	−8.81776	−0.313921
$790$	−5.94207	−0.211409
$791$	−0.210614	−0.00748857
$792$	−3.41974	−0.121515
$793$	6.20488	0.220342
$794$	13.3029	0.472102
$795$	5.31117	0.188368
$796$	−17.3911	−0.616413
$797$	−32.1260	−1.13796	−0.568981	−	0.822351i	$-0.692662\pi$
$797$	−32.1260	−1.13796	−0.568981	+	0.822351i	$0.692662\pi$
$798$	16.7886	0.594311
$799$	9.79273	0.346442
$800$	4.78614	0.169216
$801$	−16.7685	−0.592487
$802$	5.21348	0.184094
$803$	45.1801	1.59437
$804$	−12.5726	−0.443401
$805$	6.51746	0.229710
$806$	1.00790	0.0355019
$807$	−15.3013	−0.538632
$808$	−7.37866	−0.259580
$809$	27.9127	0.981359	0.490679	−	0.871340i	$-0.336749\pi$
$809$	27.9127	0.981359	0.490679	+	0.871340i	$0.336749\pi$
$810$	0.462452	0.0162489
$811$	−32.4750	−1.14035	−0.570177	−	0.821522i	$-0.693125\pi$
$811$	−32.4750	−1.14035	−0.570177	+	0.821522i	$0.693125\pi$
$812$	−16.9977	−0.596502
$813$	−10.9383	−0.383623
$814$	6.86200	0.240513
$815$	−8.46628	−0.296561
$816$	1.00000	0.0350070
$817$	−26.8923	−0.940842
$818$	−10.7249	−0.374989
$819$	3.14412	0.109864
$820$	4.31383	0.150646
$821$	47.2610	1.64942	0.824709	−	0.565557i	$-0.191339\pi$
$821$	47.2610	1.64942	0.824709	+	0.565557i	$0.191339\pi$
$822$	2.32950	0.0812506
$823$	50.3014	1.75339	0.876697	−	0.481042i	$-0.159742\pi$
$823$	50.3014	1.75339	0.876697	+	0.481042i	$0.159742\pi$
$824$	1.23565	0.0430459
$825$	16.3673	0.569838
$826$	3.09978	0.107855
$827$	−18.4992	−0.643281	−0.321640	−	0.946862i	$-0.604234\pi$
$827$	−18.4992	−0.643281	−0.321640	+	0.946862i	$0.604234\pi$
$828$	4.54653	0.158003
$829$	19.6735	0.683289	0.341645	−	0.939829i	$-0.389016\pi$
$829$	19.6735	0.683289	0.341645	+	0.939829i	$0.389016\pi$
$830$	5.84740	0.202966
$831$	−7.08873	−0.245905
$832$	−1.01430	−0.0351646
$833$	−2.60866	−0.0903848
$834$	17.2619	0.597732
$835$	−2.00301	−0.0693171
$836$	−18.5215	−0.640580
$837$	−0.993693	−0.0343471
$838$	−33.2606	−1.14897
$839$	10.3371	0.356875	0.178437	−	0.983951i	$-0.442896\pi$
$839$	10.3371	0.356875	0.178437	+	0.983951i	$0.442896\pi$
$840$	1.43350	0.0494605
$841$	1.06888	0.0368581
$842$	18.2718	0.629688
$843$	11.3355	0.390415
$844$	21.8409	0.751795
$845$	5.53610	0.190448
$846$	9.79273	0.336681
$847$	−2.15313	−0.0739825
$848$	11.4848	0.394390
$849$	17.6373	0.605312
$850$	−4.78614	−0.164163
$851$	−9.12300	−0.312733
$852$	9.59269	0.328640
$853$	3.55662	0.121776	0.0608882	−	0.998145i	$-0.480607\pi$
$853$	3.55662	0.121776	0.0608882	+	0.998145i	$0.480607\pi$
$854$	−18.9626	−0.648887
$855$	2.50467	0.0856579
$856$	18.4087	0.629196
$857$	20.7879	0.710100	0.355050	−	0.934847i	$-0.384464\pi$
$857$	20.7879	0.710100	0.355050	+	0.934847i	$0.384464\pi$
$858$	−3.46864	−0.118418
$859$	−24.8453	−0.847709	−0.423855	−	0.905730i	$-0.639323\pi$
$859$	−24.8453	−0.847709	−0.423855	+	0.905730i	$0.639323\pi$
$860$	−2.29620	−0.0782999
$861$	−28.9153	−0.985432
$862$	30.4328	1.03654
$863$	−53.2653	−1.81317	−0.906586	−	0.422022i	$-0.861320\pi$
$863$	−53.2653	−1.81317	−0.906586	+	0.422022i	$0.861320\pi$
$864$	1.00000	0.0340207
$865$	−0.418501	−0.0142295
$866$	16.5447	0.562213
$867$	−1.00000	−0.0339618
$868$	−3.08023	−0.104550
$869$	−43.9404	−1.49057
$870$	−2.53586	−0.0859737
$871$	−12.7524	−0.432099
$872$	−9.03951	−0.306116
$873$	−13.7661	−0.465910
$874$	24.6243	0.832929
$875$	−14.0284	−0.474248
$876$	−13.2116	−0.446378
$877$	−41.8997	−1.41485	−0.707426	−	0.706787i	$-0.750144\pi$
$877$	−41.8997	−1.41485	−0.707426	+	0.706787i	$0.750144\pi$
$878$	−21.2151	−0.715976
$879$	12.7137	0.428822
$880$	−1.58146	−0.0533112
$881$	11.2611	0.379396	0.189698	−	0.981843i	$-0.439249\pi$
$881$	11.2611	0.379396	0.189698	+	0.981843i	$0.439249\pi$
$882$	−2.60866	−0.0878383
$883$	9.31090	0.313337	0.156668	−	0.987651i	$-0.449925\pi$
$883$	9.31090	0.313337	0.156668	+	0.987651i	$0.449925\pi$
$884$	1.01430	0.0341146
$885$	0.462452	0.0155452
$886$	0.353586	0.0118789
$887$	19.7741	0.663949	0.331974	−	0.943288i	$-0.392285\pi$
$887$	19.7741	0.663949	0.331974	+	0.943288i	$0.392285\pi$
$888$	−2.00659	−0.0673367
$889$	−27.3229	−0.916382
$890$	−7.75464	−0.259936
$891$	3.41974	0.114566
$892$	29.0515	0.972718
$893$	53.0380	1.77485
$894$	−5.91926	−0.197970
$895$	3.02281	0.101041
$896$	3.09978	0.103557
$897$	4.61155	0.153975
$898$	9.52919	0.317993
$899$	5.44893	0.181732
$900$	−4.78614	−0.159538
$901$	−11.4848	−0.382614
$902$	31.8999	1.06215
$903$	15.3913	0.512190
$904$	−0.0679447	−0.00225981
$905$	−4.19713	−0.139517
$906$	−3.06539	−0.101841
$907$	−27.4968	−0.913018	−0.456509	−	0.889719i	$-0.650900\pi$
$907$	−27.4968	−0.913018	−0.456509	+	0.889719i	$0.650900\pi$
$908$	7.98193	0.264890
$909$	7.37866	0.244735
$910$	1.45400	0.0481997
$911$	41.6405	1.37961	0.689806	−	0.723994i	$-0.257696\pi$
$911$	41.6405	1.37961	0.689806	+	0.723994i	$0.257696\pi$
$912$	5.41606	0.179344
$913$	43.2403	1.43104
$914$	−6.33962	−0.209696
$915$	−2.82900	−0.0935238
$916$	−18.3890	−0.607591
$917$	43.0530	1.42174
$918$	−1.00000	−0.0330049
$919$	26.4162	0.871391	0.435695	−	0.900094i	$-0.356502\pi$
$919$	26.4162	0.871391	0.435695	+	0.900094i	$0.356502\pi$
$920$	2.10255	0.0693191
$921$	−6.40317	−0.210992
$922$	−0.746198	−0.0245747
$923$	9.72988	0.320263
$924$	10.6005	0.348729
$925$	9.60380	0.315771
$926$	−27.5147	−0.904189
$927$	−1.23565	−0.0405840
$928$	−5.48351	−0.180005
$929$	−42.1836	−1.38400	−0.692000	−	0.721897i	$-0.743270\pi$
$929$	−42.1836	−1.38400	−0.692000	+	0.721897i	$0.743270\pi$
$930$	−0.459535	−0.0150688
$931$	−14.1287	−0.463049
$932$	8.00338	0.262159
$933$	24.3359	0.796721
$934$	12.4066	0.405956
$935$	1.58146	0.0517194
$936$	1.01430	0.0331535
$937$	−4.18852	−0.136833	−0.0684166	−	0.997657i	$-0.521795\pi$
$937$	−4.18852	−0.136833	−0.0684166	+	0.997657i	$0.521795\pi$
$938$	38.9724	1.27249
$939$	−16.4654	−0.537328
$940$	4.52867	0.147709
$941$	−16.2725	−0.530468	−0.265234	−	0.964184i	$-0.585449\pi$
$941$	−16.2725	−0.530468	−0.265234	+	0.964184i	$0.585449\pi$
$942$	−2.92563	−0.0953223
$943$	−42.4108	−1.38109
$944$	1.00000	0.0325472
$945$	−1.43350	−0.0466318
$946$	−16.9800	−0.552066
$947$	−5.71774	−0.185802	−0.0929008	−	0.995675i	$-0.529614\pi$
$947$	−5.71774	−0.185802	−0.0929008	+	0.995675i	$0.529614\pi$
$948$	12.8490	0.417317
$949$	−13.4005	−0.434999
$950$	−25.9220	−0.841022
$951$	−8.53893	−0.276894
$952$	−3.09978	−0.100465
$953$	−22.9214	−0.742496	−0.371248	−	0.928534i	$-0.621070\pi$
$953$	−22.9214	−0.742496	−0.371248	+	0.928534i	$0.621070\pi$
$954$	−11.4848	−0.371834
$955$	−2.15283	−0.0696638
$956$	5.31462	0.171887
$957$	−18.7522	−0.606171
$958$	−12.2589	−0.396067
$959$	−7.22094	−0.233176
$960$	0.462452	0.0149256
$961$	−30.0126	−0.968148
$962$	−2.03528	−0.0656202
$963$	−18.4087	−0.593212
$964$	1.82462	0.0587670
$965$	−8.90151	−0.286550
$966$	−14.0933	−0.453443
$967$	57.8555	1.86051	0.930254	−	0.366916i	$-0.119586\pi$
$967$	57.8555	1.86051	0.930254	+	0.366916i	$0.119586\pi$
$968$	−0.694607	−0.0223255
$969$	−5.41606	−0.173989
$970$	−6.36614	−0.204404
$971$	−20.4848	−0.657387	−0.328694	−	0.944437i	$-0.606608\pi$
$971$	−20.4848	−0.657387	−0.328694	+	0.944437i	$0.606608\pi$
$972$	−1.00000	−0.0320750
$973$	−53.5083	−1.71540
$974$	−39.2557	−1.25784
$975$	−4.85459	−0.155471
$976$	−6.11739	−0.195813
$977$	−52.5707	−1.68189	−0.840943	−	0.541123i	$-0.817999\pi$
$977$	−52.5707	−1.68189	−0.840943	+	0.541123i	$0.817999\pi$
$978$	18.3074	0.585405
$979$	−57.3440	−1.83272
$980$	−1.20638	−0.0385365
$981$	9.03951	0.288609
$982$	−37.4309	−1.19447
$983$	29.4664	0.939834	0.469917	−	0.882711i	$-0.344284\pi$
$983$	29.4664	0.939834	0.469917	+	0.882711i	$0.344284\pi$
$984$	−9.32818	−0.297371
$985$	4.69934	0.149733
$986$	5.48351	0.174631
$987$	−30.3553	−0.966221
$988$	5.49352	0.174772
$989$	22.5748	0.717836
$990$	1.58146	0.0502623
$991$	33.6343	1.06843	0.534214	−	0.845349i	$-0.320608\pi$
$991$	33.6343	1.06843	0.534214	+	0.845349i	$0.320608\pi$
$992$	−0.993693	−0.0315498
$993$	−14.2573	−0.452442
$994$	−29.7353	−0.943146
$995$	8.04257	0.254967
$996$	−12.6443	−0.400651
$997$	−5.74935	−0.182084	−0.0910418	−	0.995847i	$-0.529020\pi$
$997$	−5.74935	−0.182084	−0.0910418	+	0.995847i	$0.529020\pi$
$998$	−13.5140	−0.427777
$999$	2.00659	0.0634856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.s.1.5	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.s.1.5	✓	8	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.462452 q^{5} +1.00000 q^{6} -3.09978 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.462452 q^{5} +1.00000 q^{6} -3.09978 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.462452 q^{10} +3.41974 q^{11} -1.00000 q^{12} -1.01430 q^{13} +3.09978 q^{14} +0.462452 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -5.41606 q^{19} -0.462452 q^{20} +3.09978 q^{21} -3.41974 q^{22} +4.54653 q^{23} +1.00000 q^{24} -4.78614 q^{25} +1.01430 q^{26} -1.00000 q^{27} -3.09978 q^{28} +5.48351 q^{29} -0.462452 q^{30} +0.993693 q^{31} -1.00000 q^{32} -3.41974 q^{33} +1.00000 q^{34} +1.43350 q^{35} +1.00000 q^{36} -2.00659 q^{37} +5.41606 q^{38} +1.01430 q^{39} +0.462452 q^{40} -9.32818 q^{41} -3.09978 q^{42} +4.96528 q^{43} +3.41974 q^{44} -0.462452 q^{45} -4.54653 q^{46} -9.79273 q^{47} -1.00000 q^{48} +2.60866 q^{49} +4.78614 q^{50} +1.00000 q^{51} -1.01430 q^{52} +11.4848 q^{53} +1.00000 q^{54} -1.58146 q^{55} +3.09978 q^{56} +5.41606 q^{57} -5.48351 q^{58} +1.00000 q^{59} +0.462452 q^{60} -6.11739 q^{61} -0.993693 q^{62} -3.09978 q^{63} +1.00000 q^{64} +0.469066 q^{65} +3.41974 q^{66} +12.5726 q^{67} -1.00000 q^{68} -4.54653 q^{69} -1.43350 q^{70} -9.59269 q^{71} -1.00000 q^{72} +13.2116 q^{73} +2.00659 q^{74} +4.78614 q^{75} -5.41606 q^{76} -10.6005 q^{77} -1.01430 q^{78} -12.8490 q^{79} -0.462452 q^{80} +1.00000 q^{81} +9.32818 q^{82} +12.6443 q^{83} +3.09978 q^{84} +0.462452 q^{85} -4.96528 q^{86} -5.48351 q^{87} -3.41974 q^{88} -16.7685 q^{89} +0.462452 q^{90} +3.14412 q^{91} +4.54653 q^{92} -0.993693 q^{93} +9.79273 q^{94} +2.50467 q^{95} +1.00000 q^{96} -13.7661 q^{97} -2.60866 q^{98} +3.41974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - q^5 + 8 * q^6 + 6 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9} + q^{10} - 8 q^{12} + 6 q^{13} - 6 q^{14} + q^{15} + 8 q^{16} - 8 q^{17} - 8 q^{18} - 7 q^{19} - q^{20} - 6 q^{21} - 5 q^{23} + 8 q^{24} + 9 q^{25} - 6 q^{26} - 8 q^{27} + 6 q^{28} - 15 q^{29} - q^{30} + 21 q^{31} - 8 q^{32} + 8 q^{34} - 2 q^{35} + 8 q^{36} + 7 q^{37} + 7 q^{38} - 6 q^{39} + q^{40} - q^{41} + 6 q^{42} + 14 q^{43} - q^{45} + 5 q^{46} - 8 q^{47} - 8 q^{48} + 2 q^{49} - 9 q^{50} + 8 q^{51} + 6 q^{52} + 8 q^{53} + 8 q^{54} + 24 q^{55} - 6 q^{56} + 7 q^{57} + 15 q^{58} + 8 q^{59} + q^{60} - 21 q^{62} + 6 q^{63} + 8 q^{64} + 6 q^{65} + 15 q^{67} - 8 q^{68} + 5 q^{69} + 2 q^{70} - 22 q^{71} - 8 q^{72} + 13 q^{73} - 7 q^{74} - 9 q^{75} - 7 q^{76} - 6 q^{77} + 6 q^{78} + 26 q^{79} - q^{80} + 8 q^{81} + q^{82} + 30 q^{83} - 6 q^{84} + q^{85} - 14 q^{86} + 15 q^{87} - 6 q^{89} + q^{90} + 3 q^{91} - 5 q^{92} - 21 q^{93} + 8 q^{94} + 37 q^{95} + 8 q^{96} + 23 q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - q^5 + 8 * q^6 + 6 * q^7 - 8 * q^8 + 8 * q^9 + q^10 - 8 * q^12 + 6 * q^13 - 6 * q^14 + q^15 + 8 * q^16 - 8 * q^17 - 8 * q^18 - 7 * q^19 - q^20 - 6 * q^21 - 5 * q^23 + 8 * q^24 + 9 * q^25 - 6 * q^26 - 8 * q^27 + 6 * q^28 - 15 * q^29 - q^30 + 21 * q^31 - 8 * q^32 + 8 * q^34 - 2 * q^35 + 8 * q^36 + 7 * q^37 + 7 * q^38 - 6 * q^39 + q^40 - q^41 + 6 * q^42 + 14 * q^43 - q^45 + 5 * q^46 - 8 * q^47 - 8 * q^48 + 2 * q^49 - 9 * q^50 + 8 * q^51 + 6 * q^52 + 8 * q^53 + 8 * q^54 + 24 * q^55 - 6 * q^56 + 7 * q^57 + 15 * q^58 + 8 * q^59 + q^60 - 21 * q^62 + 6 * q^63 + 8 * q^64 + 6 * q^65 + 15 * q^67 - 8 * q^68 + 5 * q^69 + 2 * q^70 - 22 * q^71 - 8 * q^72 + 13 * q^73 - 7 * q^74 - 9 * q^75 - 7 * q^76 - 6 * q^77 + 6 * q^78 + 26 * q^79 - q^80 + 8 * q^81 + q^82 + 30 * q^83 - 6 * q^84 + q^85 - 14 * q^86 + 15 * q^87 - 6 * q^89 + q^90 + 3 * q^91 - 5 * q^92 - 21 * q^93 + 8 * q^94 + 37 * q^95 + 8 * q^96 + 23 * q^97 - 2 * q^98

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