LMFDB - Embedded newform 6018.2.a.p.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:	$5$
Coefficient field:	5.5.1668357.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 11x^{3} + x^{2} + 17x - 2 $ x^5 - x^4 - 11x^3 + x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.53628$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.05778 q^{5} -1.00000 q^{6} +1.53628 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.05778 q^{5} -1.00000 q^{6} +1.53628 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.05778 q^{10} -3.38200 q^{11} +1.00000 q^{12} -1.02340 q^{13} -1.53628 q^{14} +3.05778 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.86050 q^{19} +3.05778 q^{20} +1.53628 q^{21} +3.38200 q^{22} +3.31561 q^{23} -1.00000 q^{24} +4.34999 q^{25} +1.02340 q^{26} +1.00000 q^{27} +1.53628 q^{28} +9.99843 q^{29} -3.05778 q^{30} -0.616436 q^{31} -1.00000 q^{32} -3.38200 q^{33} +1.00000 q^{34} +4.69761 q^{35} +1.00000 q^{36} +6.96745 q^{37} -3.86050 q^{38} -1.02340 q^{39} -3.05778 q^{40} +3.75695 q^{41} -1.53628 q^{42} -10.5037 q^{43} -3.38200 q^{44} +3.05778 q^{45} -3.31561 q^{46} +1.24801 q^{47} +1.00000 q^{48} -4.63983 q^{49} -4.34999 q^{50} -1.00000 q^{51} -1.02340 q^{52} -4.62844 q^{53} -1.00000 q^{54} -10.3414 q^{55} -1.53628 q^{56} +3.86050 q^{57} -9.99843 q^{58} -1.00000 q^{59} +3.05778 q^{60} -7.29167 q^{61} +0.616436 q^{62} +1.53628 q^{63} +1.00000 q^{64} -3.12932 q^{65} +3.38200 q^{66} +11.4731 q^{67} -1.00000 q^{68} +3.31561 q^{69} -4.69761 q^{70} +3.33520 q^{71} -1.00000 q^{72} -6.75436 q^{73} -6.96745 q^{74} +4.34999 q^{75} +3.86050 q^{76} -5.19570 q^{77} +1.02340 q^{78} +9.75174 q^{79} +3.05778 q^{80} +1.00000 q^{81} -3.75695 q^{82} +10.3190 q^{83} +1.53628 q^{84} -3.05778 q^{85} +10.5037 q^{86} +9.99843 q^{87} +3.38200 q^{88} +6.45613 q^{89} -3.05778 q^{90} -1.57223 q^{91} +3.31561 q^{92} -0.616436 q^{93} -1.24801 q^{94} +11.8046 q^{95} -1.00000 q^{96} +3.62504 q^{97} +4.63983 q^{98} -3.38200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} + q^{10} + 6 q^{11} + 5 q^{12} - 2 q^{13} + q^{14} - q^{15} + 5 q^{16} - 5 q^{17} - 5 q^{18} + 4 q^{19} - q^{20} - q^{21} - 6 q^{22} + 12 q^{23} - 5 q^{24} + 4 q^{25} + 2 q^{26} + 5 q^{27} - q^{28} + 19 q^{29} + q^{30} + 5 q^{31} - 5 q^{32} + 6 q^{33} + 5 q^{34} - 4 q^{35} + 5 q^{36} - 11 q^{37} - 4 q^{38} - 2 q^{39} + q^{40} + 6 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} - q^{45} - 12 q^{46} + 22 q^{47} + 5 q^{48} - 12 q^{49} - 4 q^{50} - 5 q^{51} - 2 q^{52} + 15 q^{53} - 5 q^{54} - 36 q^{55} + q^{56} + 4 q^{57} - 19 q^{58} - 5 q^{59} - q^{60} + 16 q^{61} - 5 q^{62} - q^{63} + 5 q^{64} - 2 q^{65} - 6 q^{66} + 25 q^{67} - 5 q^{68} + 12 q^{69} + 4 q^{70} - 5 q^{72} - 10 q^{73} + 11 q^{74} + 4 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 10 q^{79} - q^{80} + 5 q^{81} - 6 q^{82} + 19 q^{83} - q^{84} + q^{85} - 2 q^{86} + 19 q^{87} - 6 q^{88} + 23 q^{89} + q^{90} - 17 q^{91} + 12 q^{92} + 5 q^{93} - 22 q^{94} + q^{95} - 5 q^{96} + 8 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 + q^10 + 6 * q^11 + 5 * q^12 - 2 * q^13 + q^14 - q^15 + 5 * q^16 - 5 * q^17 - 5 * q^18 + 4 * q^19 - q^20 - q^21 - 6 * q^22 + 12 * q^23 - 5 * q^24 + 4 * q^25 + 2 * q^26 + 5 * q^27 - q^28 + 19 * q^29 + q^30 + 5 * q^31 - 5 * q^32 + 6 * q^33 + 5 * q^34 - 4 * q^35 + 5 * q^36 - 11 * q^37 - 4 * q^38 - 2 * q^39 + q^40 + 6 * q^41 + q^42 + 2 * q^43 + 6 * q^44 - q^45 - 12 * q^46 + 22 * q^47 + 5 * q^48 - 12 * q^49 - 4 * q^50 - 5 * q^51 - 2 * q^52 + 15 * q^53 - 5 * q^54 - 36 * q^55 + q^56 + 4 * q^57 - 19 * q^58 - 5 * q^59 - q^60 + 16 * q^61 - 5 * q^62 - q^63 + 5 * q^64 - 2 * q^65 - 6 * q^66 + 25 * q^67 - 5 * q^68 + 12 * q^69 + 4 * q^70 - 5 * q^72 - 10 * q^73 + 11 * q^74 + 4 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 10 * q^79 - q^80 + 5 * q^81 - 6 * q^82 + 19 * q^83 - q^84 + q^85 - 2 * q^86 + 19 * q^87 - 6 * q^88 + 23 * q^89 + q^90 - 17 * q^91 + 12 * q^92 + 5 * q^93 - 22 * q^94 + q^95 - 5 * q^96 + 8 * q^97 + 12 * q^98 + 6 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.05778	1.36748	0.683739	−	0.729726i	$-0.260353\pi$
$5$	3.05778	1.36748	0.683739	+	0.729726i	$0.260353\pi$
$6$	−1.00000	−0.408248
$7$	1.53628	0.580660	0.290330	−	0.956927i	$-0.406235\pi$
$7$	1.53628	0.580660	0.290330	+	0.956927i	$0.406235\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.05778	−0.966954
$11$	−3.38200	−1.01971	−0.509855	−	0.860260i	$-0.670301\pi$
$11$	−3.38200	−1.01971	−0.509855	+	0.860260i	$0.670301\pi$
$12$	1.00000	0.288675
$13$	−1.02340	−0.283840	−0.141920	−	0.989878i	$-0.545327\pi$
$13$	−1.02340	−0.283840	−0.141920	+	0.989878i	$0.545327\pi$
$14$	−1.53628	−0.410589
$15$	3.05778	0.789514
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	3.86050	0.885660	0.442830	−	0.896606i	$-0.353974\pi$
$19$	3.86050	0.885660	0.442830	+	0.896606i	$0.353974\pi$
$20$	3.05778	0.683739
$21$	1.53628	0.335244
$22$	3.38200	0.721044
$23$	3.31561	0.691353	0.345677	−	0.938354i	$-0.387649\pi$
$23$	3.31561	0.691353	0.345677	+	0.938354i	$0.387649\pi$
$24$	−1.00000	−0.204124
$25$	4.34999	0.869998
$26$	1.02340	0.200705
$27$	1.00000	0.192450
$28$	1.53628	0.290330
$29$	9.99843	1.85666	0.928331	−	0.371755i	$-0.121244\pi$
$29$	9.99843	1.85666	0.928331	+	0.371755i	$0.121244\pi$
$30$	−3.05778	−0.558271
$31$	−0.616436	−0.110715	−0.0553576	−	0.998467i	$-0.517630\pi$
$31$	−0.616436	−0.110715	−0.0553576	+	0.998467i	$0.517630\pi$
$32$	−1.00000	−0.176777
$33$	−3.38200	−0.588730
$34$	1.00000	0.171499
$35$	4.69761	0.794041
$36$	1.00000	0.166667
$37$	6.96745	1.14544	0.572721	−	0.819751i	$-0.305888\pi$
$37$	6.96745	1.14544	0.572721	+	0.819751i	$0.305888\pi$
$38$	−3.86050	−0.626256
$39$	−1.02340	−0.163875
$40$	−3.05778	−0.483477
$41$	3.75695	0.586737	0.293369	−	0.955999i	$-0.405224\pi$
$41$	3.75695	0.586737	0.293369	+	0.955999i	$0.405224\pi$
$42$	−1.53628	−0.237054
$43$	−10.5037	−1.60180	−0.800902	−	0.598795i	$-0.795646\pi$
$43$	−10.5037	−1.60180	−0.800902	+	0.598795i	$0.795646\pi$
$44$	−3.38200	−0.509855
$45$	3.05778	0.455826
$46$	−3.31561	−0.488861
$47$	1.24801	0.182041	0.0910204	−	0.995849i	$-0.470987\pi$
$47$	1.24801	0.182041	0.0910204	+	0.995849i	$0.470987\pi$
$48$	1.00000	0.144338
$49$	−4.63983	−0.662833
$50$	−4.34999	−0.615182
$51$	−1.00000	−0.140028
$52$	−1.02340	−0.141920
$53$	−4.62844	−0.635765	−0.317882	−	0.948130i	$-0.602972\pi$
$53$	−4.62844	−0.635765	−0.317882	+	0.948130i	$0.602972\pi$
$54$	−1.00000	−0.136083
$55$	−10.3414	−1.39443
$56$	−1.53628	−0.205294
$57$	3.86050	0.511336
$58$	−9.99843	−1.31286
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	3.05778	0.394757
$61$	−7.29167	−0.933602	−0.466801	−	0.884362i	$-0.654594\pi$
$61$	−7.29167	−0.933602	−0.466801	+	0.884362i	$0.654594\pi$
$62$	0.616436	0.0782874
$63$	1.53628	0.193553
$64$	1.00000	0.125000
$65$	−3.12932	−0.388145
$66$	3.38200	0.416295
$67$	11.4731	1.40167	0.700833	−	0.713326i	$-0.252812\pi$
$67$	11.4731	1.40167	0.700833	+	0.713326i	$0.252812\pi$
$68$	−1.00000	−0.121268
$69$	3.31561	0.399153
$70$	−4.69761	−0.561472
$71$	3.33520	0.395815	0.197908	−	0.980221i	$-0.436585\pi$
$71$	3.33520	0.395815	0.197908	+	0.980221i	$0.436585\pi$
$72$	−1.00000	−0.117851
$73$	−6.75436	−0.790539	−0.395269	−	0.918565i	$-0.629349\pi$
$73$	−6.75436	−0.790539	−0.395269	+	0.918565i	$0.629349\pi$
$74$	−6.96745	−0.809949
$75$	4.34999	0.502294
$76$	3.86050	0.442830
$77$	−5.19570	−0.592105
$78$	1.02340	0.115877
$79$	9.75174	1.09716	0.548578	−	0.836099i	$-0.315169\pi$
$79$	9.75174	1.09716	0.548578	+	0.836099i	$0.315169\pi$
$80$	3.05778	0.341870
$81$	1.00000	0.111111
$82$	−3.75695	−0.414886
$83$	10.3190	1.13266	0.566329	−	0.824179i	$-0.308363\pi$
$83$	10.3190	1.13266	0.566329	+	0.824179i	$0.308363\pi$
$84$	1.53628	0.167622
$85$	−3.05778	−0.331662
$86$	10.5037	1.13265
$87$	9.99843	1.07194
$88$	3.38200	0.360522
$89$	6.45613	0.684348	0.342174	−	0.939637i	$-0.388837\pi$
$89$	6.45613	0.684348	0.342174	+	0.939637i	$0.388837\pi$
$90$	−3.05778	−0.322318
$91$	−1.57223	−0.164814
$92$	3.31561	0.345677
$93$	−0.616436	−0.0639214
$94$	−1.24801	−0.128722
$95$	11.8046	1.21112
$96$	−1.00000	−0.102062
$97$	3.62504	0.368067	0.184034	−	0.982920i	$-0.441084\pi$
$97$	3.62504	0.368067	0.184034	+	0.982920i	$0.441084\pi$
$98$	4.63983	0.468694
$99$	−3.38200	−0.339903
$100$	4.34999	0.434999
$101$	2.67082	0.265756	0.132878	−	0.991132i	$-0.457578\pi$
$101$	2.67082	0.265756	0.132878	+	0.991132i	$0.457578\pi$
$102$	1.00000	0.0990148
$103$	1.34525	0.132551	0.0662755	−	0.997801i	$-0.478888\pi$
$103$	1.34525	0.132551	0.0662755	+	0.997801i	$0.478888\pi$
$104$	1.02340	0.100352
$105$	4.69761	0.458440
$106$	4.62844	0.449553
$107$	11.1785	1.08067	0.540335	−	0.841450i	$-0.318297\pi$
$107$	11.1785	1.08067	0.540335	+	0.841450i	$0.318297\pi$
$108$	1.00000	0.0962250
$109$	−7.90967	−0.757609	−0.378805	−	0.925477i	$-0.623665\pi$
$109$	−7.90967	−0.757609	−0.378805	+	0.925477i	$0.623665\pi$
$110$	10.3414	0.986012
$111$	6.96745	0.661321
$112$	1.53628	0.145165
$113$	−5.61589	−0.528298	−0.264149	−	0.964482i	$-0.585091\pi$
$113$	−5.61589	−0.528298	−0.264149	+	0.964482i	$0.585091\pi$
$114$	−3.86050	−0.361569
$115$	10.1384	0.945411
$116$	9.99843	0.928331
$117$	−1.02340	−0.0946132
$118$	1.00000	0.0920575
$119$	−1.53628	−0.140831
$120$	−3.05778	−0.279135
$121$	0.437896	0.0398087
$122$	7.29167	0.660157
$123$	3.75695	0.338753
$124$	−0.616436	−0.0553576
$125$	−1.98758	−0.177775
$126$	−1.53628	−0.136863
$127$	22.2111	1.97092	0.985458	−	0.169919i	$-0.0543505\pi$
$127$	22.2111	1.97092	0.985458	+	0.169919i	$0.0543505\pi$
$128$	−1.00000	−0.0883883
$129$	−10.5037	−0.924802
$130$	3.12932	0.274460
$131$	4.20710	0.367576	0.183788	−	0.982966i	$-0.441164\pi$
$131$	4.20710	0.367576	0.183788	+	0.982966i	$0.441164\pi$
$132$	−3.38200	−0.294365
$133$	5.93083	0.514268
$134$	−11.4731	−0.991127
$135$	3.05778	0.263171
$136$	1.00000	0.0857493
$137$	6.31269	0.539330	0.269665	−	0.962954i	$-0.413087\pi$
$137$	6.31269	0.539330	0.269665	+	0.962954i	$0.413087\pi$
$138$	−3.31561	−0.282244
$139$	10.5233	0.892576	0.446288	−	0.894889i	$-0.352746\pi$
$139$	10.5233	0.892576	0.446288	+	0.894889i	$0.352746\pi$
$140$	4.69761	0.397020
$141$	1.24801	0.105101
$142$	−3.33520	−0.279884
$143$	3.46113	0.289434
$144$	1.00000	0.0833333
$145$	30.5730	2.53895
$146$	6.75436	0.558995
$147$	−4.63983	−0.382687
$148$	6.96745	0.572721
$149$	−11.0906	−0.908576	−0.454288	−	0.890855i	$-0.650106\pi$
$149$	−11.0906	−0.908576	−0.454288	+	0.890855i	$0.650106\pi$
$150$	−4.34999	−0.355175
$151$	−3.05298	−0.248448	−0.124224	−	0.992254i	$-0.539644\pi$
$151$	−3.05298	−0.248448	−0.124224	+	0.992254i	$0.539644\pi$
$152$	−3.86050	−0.313128
$153$	−1.00000	−0.0808452
$154$	5.19570	0.418682
$155$	−1.88492	−0.151401
$156$	−1.02340	−0.0819374
$157$	1.96927	0.157165	0.0785823	−	0.996908i	$-0.474961\pi$
$157$	1.96927	0.157165	0.0785823	+	0.996908i	$0.474961\pi$
$158$	−9.75174	−0.775807
$159$	−4.62844	−0.367059
$160$	−3.05778	−0.241738
$161$	5.09372	0.401441
$162$	−1.00000	−0.0785674
$163$	−7.74059	−0.606290	−0.303145	−	0.952944i	$-0.598037\pi$
$163$	−7.74059	−0.606290	−0.303145	+	0.952944i	$0.598037\pi$
$164$	3.75695	0.293369
$165$	−10.3414	−0.805076
$166$	−10.3190	−0.800910
$167$	−11.9612	−0.925586	−0.462793	−	0.886466i	$-0.653153\pi$
$167$	−11.9612	−0.925586	−0.462793	+	0.886466i	$0.653153\pi$
$168$	−1.53628	−0.118527
$169$	−11.9527	−0.919435
$170$	3.05778	0.234521
$171$	3.86050	0.295220
$172$	−10.5037	−0.800902
$173$	9.90009	0.752690	0.376345	−	0.926480i	$-0.377181\pi$
$173$	9.90009	0.752690	0.376345	+	0.926480i	$0.377181\pi$
$174$	−9.99843	−0.757979
$175$	6.68282	0.505174
$176$	−3.38200	−0.254928
$177$	−1.00000	−0.0751646
$178$	−6.45613	−0.483907
$179$	11.8577	0.886287	0.443144	−	0.896451i	$-0.353863\pi$
$179$	11.8577	0.886287	0.443144	+	0.896451i	$0.353863\pi$
$180$	3.05778	0.227913
$181$	−8.80388	−0.654387	−0.327194	−	0.944957i	$-0.606103\pi$
$181$	−8.80388	−0.654387	−0.327194	+	0.944957i	$0.606103\pi$
$182$	1.57223	0.116541
$183$	−7.29167	−0.539016
$184$	−3.31561	−0.244430
$185$	21.3049	1.56637
$186$	0.616436	0.0451993
$187$	3.38200	0.247316
$188$	1.24801	0.0910204
$189$	1.53628	0.111748
$190$	−11.8046	−0.856392
$191$	3.26517	0.236260	0.118130	−	0.992998i	$-0.462310\pi$
$191$	3.26517	0.236260	0.118130	+	0.992998i	$0.462310\pi$
$192$	1.00000	0.0721688
$193$	−0.975034	−0.0701845	−0.0350922	−	0.999384i	$-0.511172\pi$
$193$	−0.975034	−0.0701845	−0.0350922	+	0.999384i	$0.511172\pi$
$194$	−3.62504	−0.260263
$195$	−3.12932	−0.224095
$196$	−4.63983	−0.331417
$197$	6.24305	0.444799	0.222399	−	0.974956i	$-0.428611\pi$
$197$	6.24305	0.444799	0.222399	+	0.974956i	$0.428611\pi$
$198$	3.38200	0.240348
$199$	−14.1931	−1.00612	−0.503060	−	0.864251i	$-0.667793\pi$
$199$	−14.1931	−1.00612	−0.503060	+	0.864251i	$0.667793\pi$
$200$	−4.34999	−0.307591
$201$	11.4731	0.809252
$202$	−2.67082	−0.187918
$203$	15.3604	1.07809
$204$	−1.00000	−0.0700140
$205$	11.4879	0.802351
$206$	−1.34525	−0.0937277
$207$	3.31561	0.230451
$208$	−1.02340	−0.0709599
$209$	−13.0562	−0.903117
$210$	−4.69761	−0.324166
$211$	1.85088	0.127420	0.0637098	−	0.997968i	$-0.479707\pi$
$211$	1.85088	0.127420	0.0637098	+	0.997968i	$0.479707\pi$
$212$	−4.62844	−0.317882
$213$	3.33520	0.228524
$214$	−11.1785	−0.764149
$215$	−32.1181	−2.19043
$216$	−1.00000	−0.0680414
$217$	−0.947020	−0.0642879
$218$	7.90967	0.535711
$219$	−6.75436	−0.456418
$220$	−10.3414	−0.697216
$221$	1.02340	0.0688412
$222$	−6.96745	−0.467624
$223$	−10.7496	−0.719848	−0.359924	−	0.932982i	$-0.617197\pi$
$223$	−10.7496	−0.719848	−0.359924	+	0.932982i	$0.617197\pi$
$224$	−1.53628	−0.102647
$225$	4.34999	0.289999
$226$	5.61589	0.373563
$227$	10.3425	0.686458	0.343229	−	0.939252i	$-0.388479\pi$
$227$	10.3425	0.686458	0.343229	+	0.939252i	$0.388479\pi$
$228$	3.86050	0.255668
$229$	6.28585	0.415381	0.207690	−	0.978195i	$-0.433405\pi$
$229$	6.28585	0.415381	0.207690	+	0.978195i	$0.433405\pi$
$230$	−10.1384	−0.668506
$231$	−5.19570	−0.341852
$232$	−9.99843	−0.656429
$233$	18.9550	1.24179	0.620893	−	0.783896i	$-0.286770\pi$
$233$	18.9550	1.24179	0.620893	+	0.783896i	$0.286770\pi$
$234$	1.02340	0.0669016
$235$	3.81613	0.248937
$236$	−1.00000	−0.0650945
$237$	9.75174	0.633444
$238$	1.53628	0.0995825
$239$	12.1587	0.786481	0.393241	−	0.919436i	$-0.371354\pi$
$239$	12.1587	0.786481	0.393241	+	0.919436i	$0.371354\pi$
$240$	3.05778	0.197379
$241$	12.7987	0.824434	0.412217	−	0.911086i	$-0.364754\pi$
$241$	12.7987	0.824434	0.412217	+	0.911086i	$0.364754\pi$
$242$	−0.437896	−0.0281490
$243$	1.00000	0.0641500
$244$	−7.29167	−0.466801
$245$	−14.1876	−0.906411
$246$	−3.75695	−0.239535
$247$	−3.95083	−0.251385
$248$	0.616436	0.0391437
$249$	10.3190	0.653940
$250$	1.98758	0.125706
$251$	−21.4380	−1.35315	−0.676576	−	0.736373i	$-0.736537\pi$
$251$	−21.4380	−1.35315	−0.676576	+	0.736373i	$0.736537\pi$
$252$	1.53628	0.0967767
$253$	−11.2134	−0.704980
$254$	−22.2111	−1.39365
$255$	−3.05778	−0.191485
$256$	1.00000	0.0625000
$257$	−1.26962	−0.0791968	−0.0395984	−	0.999216i	$-0.512608\pi$
$257$	−1.26962	−0.0791968	−0.0395984	+	0.999216i	$0.512608\pi$
$258$	10.5037	0.653934
$259$	10.7040	0.665113
$260$	−3.12932	−0.194072
$261$	9.99843	0.618887
$262$	−4.20710	−0.259916
$263$	−19.9569	−1.23059	−0.615296	−	0.788296i	$-0.710964\pi$
$263$	−19.9569	−1.23059	−0.615296	+	0.788296i	$0.710964\pi$
$264$	3.38200	0.208147
$265$	−14.1527	−0.869395
$266$	−5.93083	−0.363642
$267$	6.45613	0.395109
$268$	11.4731	0.700833
$269$	−13.9073	−0.847943	−0.423972	−	0.905676i	$-0.639364\pi$
$269$	−13.9073	−0.847943	−0.423972	+	0.905676i	$0.639364\pi$
$270$	−3.05778	−0.186090
$271$	13.8785	0.843060	0.421530	−	0.906814i	$-0.361493\pi$
$271$	13.8785	0.843060	0.421530	+	0.906814i	$0.361493\pi$
$272$	−1.00000	−0.0606339
$273$	−1.57223	−0.0951556
$274$	−6.31269	−0.381364
$275$	−14.7117	−0.887146
$276$	3.31561	0.199576
$277$	15.5930	0.936895	0.468447	−	0.883491i	$-0.344814\pi$
$277$	15.5930	0.936895	0.468447	+	0.883491i	$0.344814\pi$
$278$	−10.5233	−0.631147
$279$	−0.616436	−0.0369050
$280$	−4.69761	−0.280736
$281$	2.76080	0.164695	0.0823477	−	0.996604i	$-0.473758\pi$
$281$	2.76080	0.164695	0.0823477	+	0.996604i	$0.473758\pi$
$282$	−1.24801	−0.0743178
$283$	−30.9950	−1.84246	−0.921232	−	0.389014i	$-0.872816\pi$
$283$	−30.9950	−1.84246	−0.921232	+	0.389014i	$0.872816\pi$
$284$	3.33520	0.197908
$285$	11.8046	0.699241
$286$	−3.46113	−0.204661
$287$	5.77174	0.340695
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−30.5730	−1.79531
$291$	3.62504	0.212504
$292$	−6.75436	−0.395269
$293$	16.4014	0.958180	0.479090	−	0.877766i	$-0.340967\pi$
$293$	16.4014	0.958180	0.479090	+	0.877766i	$0.340967\pi$
$294$	4.63983	0.270601
$295$	−3.05778	−0.178031
$296$	−6.96745	−0.404975
$297$	−3.38200	−0.196243
$298$	11.0906	0.642460
$299$	−3.39319	−0.196233
$300$	4.34999	0.251147
$301$	−16.1367	−0.930104
$302$	3.05298	0.175679
$303$	2.67082	0.153434
$304$	3.86050	0.221415
$305$	−22.2963	−1.27668
$306$	1.00000	0.0571662
$307$	34.1464	1.94884	0.974419	−	0.224738i	$-0.0721525\pi$
$307$	34.1464	1.94884	0.974419	+	0.224738i	$0.0721525\pi$
$308$	−5.19570	−0.296053
$309$	1.34525	0.0765283
$310$	1.88492	0.107056
$311$	3.87360	0.219652	0.109826	−	0.993951i	$-0.464971\pi$
$311$	3.87360	0.219652	0.109826	+	0.993951i	$0.464971\pi$
$312$	1.02340	0.0579385
$313$	−17.8845	−1.01089	−0.505446	−	0.862858i	$-0.668672\pi$
$313$	−17.8845	−1.01089	−0.505446	+	0.862858i	$0.668672\pi$
$314$	−1.96927	−0.111132
$315$	4.69761	0.264680
$316$	9.75174	0.548578
$317$	−1.56824	−0.0880810	−0.0440405	−	0.999030i	$-0.514023\pi$
$317$	−1.56824	−0.0880810	−0.0440405	+	0.999030i	$0.514023\pi$
$318$	4.62844	0.259550
$319$	−33.8147	−1.89326
$320$	3.05778	0.170935
$321$	11.1785	0.623925
$322$	−5.09372	−0.283862
$323$	−3.86050	−0.214804
$324$	1.00000	0.0555556
$325$	−4.45177	−0.246940
$326$	7.74059	0.428712
$327$	−7.90967	−0.437406
$328$	−3.75695	−0.207443
$329$	1.91729	0.105704
$330$	10.3414	0.569274
$331$	8.06808	0.443462	0.221731	−	0.975108i	$-0.428829\pi$
$331$	8.06808	0.443462	0.221731	+	0.975108i	$0.428829\pi$
$332$	10.3190	0.566329
$333$	6.96745	0.381814
$334$	11.9612	0.654488
$335$	35.0822	1.91675
$336$	1.53628	0.0838111
$337$	−15.9269	−0.867593	−0.433796	−	0.901011i	$-0.642826\pi$
$337$	−15.9269	−0.867593	−0.433796	+	0.901011i	$0.642826\pi$
$338$	11.9527	0.650139
$339$	−5.61589	−0.305013
$340$	−3.05778	−0.165831
$341$	2.08478	0.112897
$342$	−3.86050	−0.208752
$343$	−17.8821	−0.965542
$344$	10.5037	0.566323
$345$	10.1384	0.545833
$346$	−9.90009	−0.532232
$347$	1.86486	0.100111	0.0500555	−	0.998746i	$-0.484060\pi$
$347$	1.86486	0.100111	0.0500555	+	0.998746i	$0.484060\pi$
$348$	9.99843	0.535972
$349$	−26.4402	−1.41531	−0.707655	−	0.706559i	$-0.750247\pi$
$349$	−26.4402	−1.41531	−0.707655	+	0.706559i	$0.750247\pi$
$350$	−6.68282	−0.357212
$351$	−1.02340	−0.0546249
$352$	3.38200	0.180261
$353$	20.1982	1.07504	0.537522	−	0.843250i	$-0.319361\pi$
$353$	20.1982	1.07504	0.537522	+	0.843250i	$0.319361\pi$
$354$	1.00000	0.0531494
$355$	10.1983	0.541269
$356$	6.45613	0.342174
$357$	−1.53628	−0.0813087
$358$	−11.8577	−0.626700
$359$	−16.8608	−0.889877	−0.444938	−	0.895561i	$-0.646774\pi$
$359$	−16.8608	−0.889877	−0.444938	+	0.895561i	$0.646774\pi$
$360$	−3.05778	−0.161159
$361$	−4.09651	−0.215606
$362$	8.80388	0.462722
$363$	0.437896	0.0229836
$364$	−1.57223	−0.0824072
$365$	−20.6533	−1.08104
$366$	7.29167	0.381142
$367$	−31.4836	−1.64343	−0.821714	−	0.569900i	$-0.806982\pi$
$367$	−31.4836	−1.64343	−0.821714	+	0.569900i	$0.806982\pi$
$368$	3.31561	0.172838
$369$	3.75695	0.195579
$370$	−21.3049	−1.10759
$371$	−7.11059	−0.369163
$372$	−0.616436	−0.0319607
$373$	−1.57431	−0.0815145	−0.0407572	−	0.999169i	$-0.512977\pi$
$373$	−1.57431	−0.0815145	−0.0407572	+	0.999169i	$0.512977\pi$
$374$	−3.38200	−0.174879
$375$	−1.98758	−0.102638
$376$	−1.24801	−0.0643611
$377$	−10.2324	−0.526994
$378$	−1.53628	−0.0790179
$379$	23.0239	1.18266	0.591328	−	0.806431i	$-0.298604\pi$
$379$	23.0239	1.18266	0.591328	+	0.806431i	$0.298604\pi$
$380$	11.8046	0.605561
$381$	22.2111	1.13791
$382$	−3.26517	−0.167061
$383$	9.17617	0.468880	0.234440	−	0.972131i	$-0.424674\pi$
$383$	9.17617	0.468880	0.234440	+	0.972131i	$0.424674\pi$
$384$	−1.00000	−0.0510310
$385$	−15.8873	−0.809692
$386$	0.975034	0.0496279
$387$	−10.5037	−0.533935
$388$	3.62504	0.184034
$389$	8.17625	0.414552	0.207276	−	0.978282i	$-0.433540\pi$
$389$	8.17625	0.414552	0.207276	+	0.978282i	$0.433540\pi$
$390$	3.12932	0.158459
$391$	−3.31561	−0.167678
$392$	4.63983	0.234347
$393$	4.20710	0.212220
$394$	−6.24305	−0.314520
$395$	29.8186	1.50034
$396$	−3.38200	−0.169952
$397$	−25.7166	−1.29068	−0.645341	−	0.763895i	$-0.723285\pi$
$397$	−25.7166	−1.29068	−0.645341	+	0.763895i	$0.723285\pi$
$398$	14.1931	0.711435
$399$	5.93083	0.296913
$400$	4.34999	0.217500
$401$	6.66798	0.332983	0.166491	−	0.986043i	$-0.446756\pi$
$401$	6.66798	0.332983	0.166491	+	0.986043i	$0.446756\pi$
$402$	−11.4731	−0.572228
$403$	0.630859	0.0314253
$404$	2.67082	0.132878
$405$	3.05778	0.151942
$406$	−15.3604	−0.762325
$407$	−23.5639	−1.16802
$408$	1.00000	0.0495074
$409$	−1.00352	−0.0496206	−0.0248103	−	0.999692i	$-0.507898\pi$
$409$	−1.00352	−0.0496206	−0.0248103	+	0.999692i	$0.507898\pi$
$410$	−11.4879	−0.567348
$411$	6.31269	0.311382
$412$	1.34525	0.0662755
$413$	−1.53628	−0.0755956
$414$	−3.31561	−0.162954
$415$	31.5532	1.54889
$416$	1.02340	0.0501762
$417$	10.5233	0.515329
$418$	13.0562	0.638600
$419$	−21.4897	−1.04984	−0.524919	−	0.851152i	$-0.675905\pi$
$419$	−21.4897	−1.04984	−0.524919	+	0.851152i	$0.675905\pi$
$420$	4.69761	0.229220
$421$	2.94777	0.143666	0.0718329	−	0.997417i	$-0.477115\pi$
$421$	2.94777	0.143666	0.0718329	+	0.997417i	$0.477115\pi$
$422$	−1.85088	−0.0900992
$423$	1.24801	0.0606803
$424$	4.62844	0.224777
$425$	−4.34999	−0.211006
$426$	−3.33520	−0.161591
$427$	−11.2021	−0.542106
$428$	11.1785	0.540335
$429$	3.46113	0.167105
$430$	32.1181	1.54887
$431$	34.9160	1.68185	0.840923	−	0.541155i	$-0.182013\pi$
$431$	34.9160	1.68185	0.840923	+	0.541155i	$0.182013\pi$
$432$	1.00000	0.0481125
$433$	−30.4654	−1.46407	−0.732037	−	0.681265i	$-0.761430\pi$
$433$	−30.4654	−1.46407	−0.732037	+	0.681265i	$0.761430\pi$
$434$	0.947020	0.0454584
$435$	30.5730	1.46586
$436$	−7.90967	−0.378805
$437$	12.7999	0.612304
$438$	6.75436	0.322736
$439$	25.7830	1.23055	0.615277	−	0.788311i	$-0.289044\pi$
$439$	25.7830	1.23055	0.615277	+	0.788311i	$0.289044\pi$
$440$	10.3414	0.493006
$441$	−4.63983	−0.220944
$442$	−1.02340	−0.0486781
$443$	22.9987	1.09270	0.546350	−	0.837557i	$-0.316017\pi$
$443$	22.9987	1.09270	0.546350	+	0.837557i	$0.316017\pi$
$444$	6.96745	0.330660
$445$	19.7414	0.935832
$446$	10.7496	0.509009
$447$	−11.0906	−0.524567
$448$	1.53628	0.0725826
$449$	16.8056	0.793104	0.396552	−	0.918012i	$-0.370207\pi$
$449$	16.8056	0.793104	0.396552	+	0.918012i	$0.370207\pi$
$450$	−4.34999	−0.205061
$451$	−12.7060	−0.598302
$452$	−5.61589	−0.264149
$453$	−3.05298	−0.143442
$454$	−10.3425	−0.485399
$455$	−4.80752	−0.225380
$456$	−3.86050	−0.180785
$457$	−6.66524	−0.311787	−0.155893	−	0.987774i	$-0.549826\pi$
$457$	−6.66524	−0.311787	−0.155893	+	0.987774i	$0.549826\pi$
$458$	−6.28585	−0.293719
$459$	−1.00000	−0.0466760
$460$	10.1384	0.472705
$461$	−8.84232	−0.411828	−0.205914	−	0.978570i	$-0.566017\pi$
$461$	−8.84232	−0.411828	−0.205914	+	0.978570i	$0.566017\pi$
$462$	5.19570	0.241726
$463$	−12.9431	−0.601516	−0.300758	−	0.953701i	$-0.597240\pi$
$463$	−12.9431	−0.601516	−0.300758	+	0.953701i	$0.597240\pi$
$464$	9.99843	0.464166
$465$	−1.88492	−0.0874112
$466$	−18.9550	−0.878075
$467$	34.7988	1.61030	0.805149	−	0.593072i	$-0.202085\pi$
$467$	34.7988	1.61030	0.805149	+	0.593072i	$0.202085\pi$
$468$	−1.02340	−0.0473066
$469$	17.6260	0.813892
$470$	−3.81613	−0.176025
$471$	1.96927	0.0907391
$472$	1.00000	0.0460287
$473$	35.5236	1.63338
$474$	−9.75174	−0.447912
$475$	16.7932	0.770523
$476$	−1.53628	−0.0704154
$477$	−4.62844	−0.211922
$478$	−12.1587	−0.556126
$479$	1.23920	0.0566205	0.0283103	−	0.999599i	$-0.490987\pi$
$479$	1.23920	0.0566205	0.0283103	+	0.999599i	$0.490987\pi$
$480$	−3.05778	−0.139568
$481$	−7.13047	−0.325122
$482$	−12.7987	−0.582963
$483$	5.09372	0.231772
$484$	0.437896	0.0199044
$485$	11.0846	0.503324
$486$	−1.00000	−0.0453609
$487$	23.1162	1.04750	0.523748	−	0.851873i	$-0.324533\pi$
$487$	23.1162	1.04750	0.523748	+	0.851873i	$0.324533\pi$
$488$	7.29167	0.330078
$489$	−7.74059	−0.350042
$490$	14.1876	0.640929
$491$	7.59394	0.342710	0.171355	−	0.985209i	$-0.445186\pi$
$491$	7.59394	0.342710	0.171355	+	0.985209i	$0.445186\pi$
$492$	3.75695	0.169377
$493$	−9.99843	−0.450307
$494$	3.95083	0.177756
$495$	−10.3414	−0.464811
$496$	−0.616436	−0.0276788
$497$	5.12381	0.229834
$498$	−10.3190	−0.462406
$499$	−5.98394	−0.267878	−0.133939	−	0.990990i	$-0.542763\pi$
$499$	−5.98394	−0.267878	−0.133939	+	0.990990i	$0.542763\pi$
$500$	−1.98758	−0.0888874
$501$	−11.9612	−0.534388
$502$	21.4380	0.956823
$503$	−17.8750	−0.797005	−0.398503	−	0.917167i	$-0.630470\pi$
$503$	−17.8750	−0.797005	−0.398503	+	0.917167i	$0.630470\pi$
$504$	−1.53628	−0.0684315
$505$	8.16676	0.363416
$506$	11.2134	0.498496
$507$	−11.9527	−0.530836
$508$	22.2111	0.985458
$509$	−18.2491	−0.808876	−0.404438	−	0.914566i	$-0.632533\pi$
$509$	−18.2491	−0.808876	−0.404438	+	0.914566i	$0.632533\pi$
$510$	3.05778	0.135401
$511$	−10.3766	−0.459034
$512$	−1.00000	−0.0441942
$513$	3.86050	0.170445
$514$	1.26962	0.0560006
$515$	4.11346	0.181261
$516$	−10.5037	−0.462401
$517$	−4.22076	−0.185629
$518$	−10.7040	−0.470306
$519$	9.90009	0.434566
$520$	3.12932	0.137230
$521$	−29.4612	−1.29072	−0.645359	−	0.763880i	$-0.723292\pi$
$521$	−29.4612	−1.29072	−0.645359	+	0.763880i	$0.723292\pi$
$522$	−9.99843	−0.437619
$523$	−1.39480	−0.0609901	−0.0304951	−	0.999535i	$-0.509708\pi$
$523$	−1.39480	−0.0609901	−0.0304951	+	0.999535i	$0.509708\pi$
$524$	4.20710	0.183788
$525$	6.68282	0.291662
$526$	19.9569	0.870160
$527$	0.616436	0.0268524
$528$	−3.38200	−0.147182
$529$	−12.0067	−0.522031
$530$	14.1527	0.614755
$531$	−1.00000	−0.0433963
$532$	5.93083	0.257134
$533$	−3.84486	−0.166539
$534$	−6.45613	−0.279384
$535$	34.1815	1.47779
$536$	−11.4731	−0.495564
$537$	11.8577	0.511698
$538$	13.9073	0.599586
$539$	15.6919	0.675898
$540$	3.05778	0.131586
$541$	−16.4269	−0.706249	−0.353124	−	0.935576i	$-0.614881\pi$
$541$	−16.4269	−0.706249	−0.353124	+	0.935576i	$0.614881\pi$
$542$	−13.8785	−0.596134
$543$	−8.80388	−0.377811
$544$	1.00000	0.0428746
$545$	−24.1860	−1.03601
$546$	1.57223	0.0672852
$547$	−14.7145	−0.629146	−0.314573	−	0.949233i	$-0.601861\pi$
$547$	−14.7145	−0.629146	−0.314573	+	0.949233i	$0.601861\pi$
$548$	6.31269	0.269665
$549$	−7.29167	−0.311201
$550$	14.7117	0.627307
$551$	38.5990	1.64437
$552$	−3.31561	−0.141122
$553$	14.9814	0.637075
$554$	−15.5930	−0.662485
$555$	21.3049	0.904342
$556$	10.5233	0.446288
$557$	−3.30447	−0.140015	−0.0700074	−	0.997546i	$-0.522302\pi$
$557$	−3.30447	−0.140015	−0.0700074	+	0.997546i	$0.522302\pi$
$558$	0.616436	0.0260958
$559$	10.7495	0.454655
$560$	4.69761	0.198510
$561$	3.38200	0.142788
$562$	−2.76080	−0.116457
$563$	−0.999402	−0.0421198	−0.0210599	−	0.999778i	$-0.506704\pi$
$563$	−0.999402	−0.0421198	−0.0210599	+	0.999778i	$0.506704\pi$
$564$	1.24801	0.0525506
$565$	−17.1721	−0.722437
$566$	30.9950	1.30282
$567$	1.53628	0.0645178
$568$	−3.33520	−0.139942
$569$	40.3931	1.69337	0.846684	−	0.532097i	$-0.178596\pi$
$569$	40.3931	1.69337	0.846684	+	0.532097i	$0.178596\pi$
$570$	−11.8046	−0.494438
$571$	11.4501	0.479171	0.239585	−	0.970875i	$-0.422989\pi$
$571$	11.4501	0.479171	0.239585	+	0.970875i	$0.422989\pi$
$572$	3.46113	0.144717
$573$	3.26517	0.136405
$574$	−5.77174	−0.240908
$575$	14.4229	0.601476
$576$	1.00000	0.0416667
$577$	−21.1757	−0.881556	−0.440778	−	0.897616i	$-0.645297\pi$
$577$	−21.1757	−0.881556	−0.440778	+	0.897616i	$0.645297\pi$
$578$	−1.00000	−0.0415945
$579$	−0.975034	−0.0405210
$580$	30.5730	1.26947
$581$	15.8529	0.657690
$582$	−3.62504	−0.150263
$583$	15.6534	0.648296
$584$	6.75436	0.279498
$585$	−3.12932	−0.129382
$586$	−16.4014	−0.677536
$587$	−12.9790	−0.535701	−0.267851	−	0.963460i	$-0.586313\pi$
$587$	−12.9790	−0.535701	−0.267851	+	0.963460i	$0.586313\pi$
$588$	−4.63983	−0.191344
$589$	−2.37975	−0.0980560
$590$	3.05778	0.125887
$591$	6.24305	0.256805
$592$	6.96745	0.286360
$593$	30.2200	1.24098	0.620492	−	0.784212i	$-0.286933\pi$
$593$	30.2200	1.24098	0.620492	+	0.784212i	$0.286933\pi$
$594$	3.38200	0.138765
$595$	−4.69761	−0.192583
$596$	−11.0906	−0.454288
$597$	−14.1931	−0.580884
$598$	3.39319	0.138758
$599$	1.20562	0.0492604	0.0246302	−	0.999697i	$-0.492159\pi$
$599$	1.20562	0.0492604	0.0246302	+	0.999697i	$0.492159\pi$
$600$	−4.34999	−0.177588
$601$	−35.4744	−1.44703	−0.723516	−	0.690307i	$-0.757475\pi$
$601$	−35.4744	−1.44703	−0.723516	+	0.690307i	$0.757475\pi$
$602$	16.1367	0.657683
$603$	11.4731	0.467222
$604$	−3.05298	−0.124224
$605$	1.33899	0.0544376
$606$	−2.67082	−0.108495
$607$	−14.3527	−0.582557	−0.291278	−	0.956638i	$-0.594081\pi$
$607$	−14.3527	−0.582557	−0.291278	+	0.956638i	$0.594081\pi$
$608$	−3.86050	−0.156564
$609$	15.3604	0.622436
$610$	22.2963	0.902750
$611$	−1.27721	−0.0516704
$612$	−1.00000	−0.0404226
$613$	−25.5760	−1.03301	−0.516503	−	0.856286i	$-0.672766\pi$
$613$	−25.5760	−1.03301	−0.516503	+	0.856286i	$0.672766\pi$
$614$	−34.1464	−1.37804
$615$	11.4879	0.463238
$616$	5.19570	0.209341
$617$	0.275470	0.0110900	0.00554500	−	0.999985i	$-0.498235\pi$
$617$	0.275470	0.0110900	0.00554500	+	0.999985i	$0.498235\pi$
$618$	−1.34525	−0.0541137
$619$	−7.83256	−0.314817	−0.157409	−	0.987534i	$-0.550314\pi$
$619$	−7.83256	−0.314817	−0.157409	+	0.987534i	$0.550314\pi$
$620$	−1.88492	−0.0757003
$621$	3.31561	0.133051
$622$	−3.87360	−0.155317
$623$	9.91845	0.397374
$624$	−1.02340	−0.0409687
$625$	−27.8275	−1.11310
$626$	17.8845	0.714809
$627$	−13.0562	−0.521415
$628$	1.96927	0.0785823
$629$	−6.96745	−0.277810
$630$	−4.69761	−0.187157
$631$	3.49029	0.138946	0.0694731	−	0.997584i	$-0.477868\pi$
$631$	3.49029	0.138946	0.0694731	+	0.997584i	$0.477868\pi$
$632$	−9.75174	−0.387903
$633$	1.85088	0.0735657
$634$	1.56824	0.0622827
$635$	67.9165	2.69519
$636$	−4.62844	−0.183529
$637$	4.74840	0.188138
$638$	33.8147	1.33873
$639$	3.33520	0.131938
$640$	−3.05778	−0.120869
$641$	4.58902	0.181255	0.0906276	−	0.995885i	$-0.471113\pi$
$641$	4.58902	0.181255	0.0906276	+	0.995885i	$0.471113\pi$
$642$	−11.1785	−0.441182
$643$	−29.3717	−1.15831	−0.579153	−	0.815219i	$-0.696617\pi$
$643$	−29.3717	−1.15831	−0.579153	+	0.815219i	$0.696617\pi$
$644$	5.09372	0.200721
$645$	−32.1181	−1.26465
$646$	3.86050	0.151889
$647$	−25.2818	−0.993929	−0.496964	−	0.867771i	$-0.665552\pi$
$647$	−25.2818	−0.993929	−0.496964	+	0.867771i	$0.665552\pi$
$648$	−1.00000	−0.0392837
$649$	3.38200	0.132755
$650$	4.45177	0.174613
$651$	−0.947020	−0.0371166
$652$	−7.74059	−0.303145
$653$	20.7127	0.810552	0.405276	−	0.914194i	$-0.367175\pi$
$653$	20.7127	0.810552	0.405276	+	0.914194i	$0.367175\pi$
$654$	7.90967	0.309293
$655$	12.8644	0.502653
$656$	3.75695	0.146684
$657$	−6.75436	−0.263513
$658$	−1.91729	−0.0747439
$659$	−38.2348	−1.48941	−0.744707	−	0.667391i	$-0.767411\pi$
$659$	−38.2348	−1.48941	−0.744707	+	0.667391i	$0.767411\pi$
$660$	−10.3414	−0.402538
$661$	−32.9603	−1.28201	−0.641004	−	0.767538i	$-0.721482\pi$
$661$	−32.9603	−1.28201	−0.641004	+	0.767538i	$0.721482\pi$
$662$	−8.06808	−0.313575
$663$	1.02340	0.0397455
$664$	−10.3190	−0.400455
$665$	18.1351	0.703250
$666$	−6.96745	−0.269983
$667$	33.1509	1.28361
$668$	−11.9612	−0.462793
$669$	−10.7496	−0.415604
$670$	−35.0822	−1.35535
$671$	24.6604	0.952004
$672$	−1.53628	−0.0592634
$673$	6.85541	0.264257	0.132128	−	0.991233i	$-0.457819\pi$
$673$	6.85541	0.264257	0.132128	+	0.991233i	$0.457819\pi$
$674$	15.9269	0.613481
$675$	4.34999	0.167431
$676$	−11.9527	−0.459718
$677$	42.2197	1.62263	0.811317	−	0.584607i	$-0.198751\pi$
$677$	42.2197	1.62263	0.811317	+	0.584607i	$0.198751\pi$
$678$	5.61589	0.215677
$679$	5.56909	0.213722
$680$	3.05778	0.117260
$681$	10.3425	0.396327
$682$	−2.08478	−0.0798305
$683$	−43.9874	−1.68313	−0.841565	−	0.540156i	$-0.818365\pi$
$683$	−43.9874	−1.68313	−0.841565	+	0.540156i	$0.818365\pi$
$684$	3.86050	0.147610
$685$	19.3028	0.737522
$686$	17.8821	0.682741
$687$	6.28585	0.239820
$688$	−10.5037	−0.400451
$689$	4.73673	0.180455
$690$	−10.1384	−0.385962
$691$	18.2747	0.695203	0.347601	−	0.937642i	$-0.386996\pi$
$691$	18.2747	0.695203	0.347601	+	0.937642i	$0.386996\pi$
$692$	9.90009	0.376345
$693$	−5.19570	−0.197368
$694$	−1.86486	−0.0707892
$695$	32.1779	1.22058
$696$	−9.99843	−0.378990
$697$	−3.75695	−0.142305
$698$	26.4402	1.00077
$699$	18.9550	0.716945
$700$	6.68282	0.252587
$701$	−37.1275	−1.40229	−0.701143	−	0.713020i	$-0.747327\pi$
$701$	−37.1275	−1.40229	−0.701143	+	0.713020i	$0.747327\pi$
$702$	1.02340	0.0386257
$703$	26.8979	1.01447
$704$	−3.38200	−0.127464
$705$	3.81613	0.143724
$706$	−20.1982	−0.760171
$707$	4.10313	0.154314
$708$	−1.00000	−0.0375823
$709$	4.42022	0.166005	0.0830025	−	0.996549i	$-0.473549\pi$
$709$	4.42022	0.166005	0.0830025	+	0.996549i	$0.473549\pi$
$710$	−10.1983	−0.382735
$711$	9.75174	0.365719
$712$	−6.45613	−0.241954
$713$	−2.04386	−0.0765433
$714$	1.53628	0.0574940
$715$	10.5834	0.395795
$716$	11.8577	0.443144
$717$	12.1587	0.454075
$718$	16.8608	0.629238
$719$	18.2091	0.679085	0.339543	−	0.940591i	$-0.389728\pi$
$719$	18.2091	0.679085	0.339543	+	0.940591i	$0.389728\pi$
$720$	3.05778	0.113957
$721$	2.06668	0.0769671
$722$	4.09651	0.152456
$723$	12.7987	0.475987
$724$	−8.80388	−0.327194
$725$	43.4931	1.61529
$726$	−0.437896	−0.0162518
$727$	22.8229	0.846453	0.423227	−	0.906024i	$-0.360897\pi$
$727$	22.8229	0.846453	0.423227	+	0.906024i	$0.360897\pi$
$728$	1.57223	0.0582707
$729$	1.00000	0.0370370
$730$	20.6533	0.764414
$731$	10.5037	0.388495
$732$	−7.29167	−0.269508
$733$	−14.8713	−0.549285	−0.274642	−	0.961546i	$-0.588559\pi$
$733$	−14.8713	−0.549285	−0.274642	+	0.961546i	$0.588559\pi$
$734$	31.4836	1.16208
$735$	−14.1876	−0.523316
$736$	−3.31561	−0.122215
$737$	−38.8021	−1.42929
$738$	−3.75695	−0.138295
$739$	29.3269	1.07881	0.539404	−	0.842047i	$-0.318649\pi$
$739$	29.3269	1.07881	0.539404	+	0.842047i	$0.318649\pi$
$740$	21.3049	0.783183
$741$	−3.95083	−0.145137
$742$	7.11059	0.261038
$743$	−52.6541	−1.93169	−0.965846	−	0.259115i	$-0.916569\pi$
$743$	−52.6541	−1.93169	−0.965846	+	0.259115i	$0.916569\pi$
$744$	0.616436	0.0225996
$745$	−33.9125	−1.24246
$746$	1.57431	0.0576394
$747$	10.3190	0.377553
$748$	3.38200	0.123658
$749$	17.1734	0.627503
$750$	1.98758	0.0725762
$751$	−38.6248	−1.40944	−0.704719	−	0.709486i	$-0.748927\pi$
$751$	−38.6248	−1.40944	−0.704719	+	0.709486i	$0.748927\pi$
$752$	1.24801	0.0455102
$753$	−21.4380	−0.781242
$754$	10.2324	0.372641
$755$	−9.33533	−0.339747
$756$	1.53628	0.0558741
$757$	41.6929	1.51536	0.757678	−	0.652629i	$-0.226334\pi$
$757$	41.6929	1.51536	0.757678	+	0.652629i	$0.226334\pi$
$758$	−23.0239	−0.836265
$759$	−11.2134	−0.407020
$760$	−11.8046	−0.428196
$761$	−9.92565	−0.359804	−0.179902	−	0.983684i	$-0.557578\pi$
$761$	−9.92565	−0.359804	−0.179902	+	0.983684i	$0.557578\pi$
$762$	−22.2111	−0.804623
$763$	−12.1515	−0.439914
$764$	3.26517	0.118130
$765$	−3.05778	−0.110554
$766$	−9.17617	−0.331548
$767$	1.02340	0.0369528
$768$	1.00000	0.0360844
$769$	10.0493	0.362387	0.181193	−	0.983447i	$-0.442004\pi$
$769$	10.0493	0.362387	0.181193	+	0.983447i	$0.442004\pi$
$770$	15.8873	0.572538
$771$	−1.26962	−0.0457243
$772$	−0.975034	−0.0350922
$773$	−17.5416	−0.630929	−0.315464	−	0.948937i	$-0.602160\pi$
$773$	−17.5416	−0.630929	−0.315464	+	0.948937i	$0.602160\pi$
$774$	10.5037	0.377549
$775$	−2.68149	−0.0963220
$776$	−3.62504	−0.130131
$777$	10.7040	0.384003
$778$	−8.17625	−0.293133
$779$	14.5037	0.519650
$780$	−3.12932	−0.112048
$781$	−11.2796	−0.403617
$782$	3.31561	0.118566
$783$	9.99843	0.357315
$784$	−4.63983	−0.165708
$785$	6.02158	0.214919
$786$	−4.20710	−0.150062
$787$	−18.3262	−0.653260	−0.326630	−	0.945152i	$-0.605913\pi$
$787$	−18.3262	−0.653260	−0.326630	+	0.945152i	$0.605913\pi$
$788$	6.24305	0.222399
$789$	−19.9569	−0.710483
$790$	−29.8186	−1.06090
$791$	−8.62760	−0.306762
$792$	3.38200	0.120174
$793$	7.46228	0.264993
$794$	25.7166	0.912650
$795$	−14.1527	−0.501945
$796$	−14.1931	−0.503060
$797$	7.85337	0.278181	0.139090	−	0.990280i	$-0.455582\pi$
$797$	7.85337	0.278181	0.139090	+	0.990280i	$0.455582\pi$
$798$	−5.93083	−0.209949
$799$	−1.24801	−0.0441514
$800$	−4.34999	−0.153795
$801$	6.45613	0.228116
$802$	−6.66798	−0.235454
$803$	22.8432	0.806120
$804$	11.4731	0.404626
$805$	15.5755	0.548963
$806$	−0.630859	−0.0222211
$807$	−13.9073	−0.489560
$808$	−2.67082	−0.0939590
$809$	2.33219	0.0819956	0.0409978	−	0.999159i	$-0.486946\pi$
$809$	2.33219	0.0819956	0.0409978	+	0.999159i	$0.486946\pi$
$810$	−3.05778	−0.107439
$811$	7.21354	0.253302	0.126651	−	0.991947i	$-0.459577\pi$
$811$	7.21354	0.253302	0.126651	+	0.991947i	$0.459577\pi$
$812$	15.3604	0.539045
$813$	13.8785	0.486741
$814$	23.5639	0.825914
$815$	−23.6690	−0.829089
$816$	−1.00000	−0.0350070
$817$	−40.5497	−1.41865
$818$	1.00352	0.0350871
$819$	−1.57223	−0.0549381
$820$	11.4879	0.401176
$821$	11.1461	0.389001	0.194500	−	0.980902i	$-0.437691\pi$
$821$	11.1461	0.389001	0.194500	+	0.980902i	$0.437691\pi$
$822$	−6.31269	−0.220180
$823$	34.9332	1.21769	0.608847	−	0.793288i	$-0.291632\pi$
$823$	34.9332	1.21769	0.608847	+	0.793288i	$0.291632\pi$
$824$	−1.34525	−0.0468639
$825$	−14.7117	−0.512194
$826$	1.53628	0.0534541
$827$	34.2325	1.19038	0.595189	−	0.803585i	$-0.297077\pi$
$827$	34.2325	1.19038	0.595189	+	0.803585i	$0.297077\pi$
$828$	3.31561	0.115226
$829$	−55.3841	−1.92357	−0.961784	−	0.273808i	$-0.911717\pi$
$829$	−55.3841	−1.92357	−0.961784	+	0.273808i	$0.911717\pi$
$830$	−31.5532	−1.09523
$831$	15.5930	0.540916
$832$	−1.02340	−0.0354799
$833$	4.63983	0.160761
$834$	−10.5233	−0.364393
$835$	−36.5747	−1.26572
$836$	−13.0562	−0.451558
$837$	−0.616436	−0.0213071
$838$	21.4897	0.742348
$839$	−13.6335	−0.470680	−0.235340	−	0.971913i	$-0.575620\pi$
$839$	−13.6335	−0.470680	−0.235340	+	0.971913i	$0.575620\pi$
$840$	−4.69761	−0.162083
$841$	70.9686	2.44719
$842$	−2.94777	−0.101587
$843$	2.76080	0.0950870
$844$	1.85088	0.0637098
$845$	−36.5485	−1.25731
$846$	−1.24801	−0.0429074
$847$	0.672732	0.0231154
$848$	−4.62844	−0.158941
$849$	−30.9950	−1.06375
$850$	4.34999	0.149203
$851$	23.1014	0.791905
$852$	3.33520	0.114262
$853$	−6.56804	−0.224885	−0.112443	−	0.993658i	$-0.535867\pi$
$853$	−6.56804	−0.224885	−0.112443	+	0.993658i	$0.535867\pi$
$854$	11.2021	0.383327
$855$	11.8046	0.403707
$856$	−11.1785	−0.382075
$857$	40.5970	1.38677	0.693384	−	0.720568i	$-0.256119\pi$
$857$	40.5970	1.38677	0.693384	+	0.720568i	$0.256119\pi$
$858$	−3.46113	−0.118161
$859$	−26.7597	−0.913028	−0.456514	−	0.889716i	$-0.650902\pi$
$859$	−26.7597	−0.913028	−0.456514	+	0.889716i	$0.650902\pi$
$860$	−32.1181	−1.09522
$861$	5.77174	0.196701
$862$	−34.9160	−1.18924
$863$	−25.3027	−0.861315	−0.430658	−	0.902515i	$-0.641718\pi$
$863$	−25.3027	−0.861315	−0.430658	+	0.902515i	$0.641718\pi$
$864$	−1.00000	−0.0340207
$865$	30.2723	1.02929
$866$	30.4654	1.03526
$867$	1.00000	0.0339618
$868$	−0.947020	−0.0321440
$869$	−32.9803	−1.11878
$870$	−30.5730	−1.03652
$871$	−11.7416	−0.397848
$872$	7.90967	0.267855
$873$	3.62504	0.122689
$874$	−12.7999	−0.432964
$875$	−3.05349	−0.103227
$876$	−6.75436	−0.228209
$877$	−24.1892	−0.816810	−0.408405	−	0.912801i	$-0.633915\pi$
$877$	−24.1892	−0.816810	−0.408405	+	0.912801i	$0.633915\pi$
$878$	−25.7830	−0.870133
$879$	16.4014	0.553206
$880$	−10.3414	−0.348608
$881$	17.6275	0.593884	0.296942	−	0.954895i	$-0.404033\pi$
$881$	17.6275	0.593884	0.296942	+	0.954895i	$0.404033\pi$
$882$	4.63983	0.156231
$883$	44.8845	1.51048	0.755242	−	0.655446i	$-0.227519\pi$
$883$	44.8845	1.51048	0.755242	+	0.655446i	$0.227519\pi$
$884$	1.02340	0.0344206
$885$	−3.05778	−0.102786
$886$	−22.9987	−0.772656
$887$	−16.9012	−0.567486	−0.283743	−	0.958900i	$-0.591576\pi$
$887$	−16.9012	−0.567486	−0.283743	+	0.958900i	$0.591576\pi$
$888$	−6.96745	−0.233812
$889$	34.1225	1.14443
$890$	−19.7414	−0.661733
$891$	−3.38200	−0.113301
$892$	−10.7496	−0.359924
$893$	4.81794	0.161226
$894$	11.0906	0.370925
$895$	36.2582	1.21198
$896$	−1.53628	−0.0513236
$897$	−3.39319	−0.113295
$898$	−16.8056	−0.560809
$899$	−6.16339	−0.205561
$900$	4.34999	0.145000
$901$	4.62844	0.154196
$902$	12.7060	0.423064
$903$	−16.1367	−0.536996
$904$	5.61589	0.186782
$905$	−26.9203	−0.894861
$906$	3.05298	0.101428
$907$	−42.9219	−1.42520	−0.712598	−	0.701572i	$-0.752482\pi$
$907$	−42.9219	−1.42520	−0.712598	+	0.701572i	$0.752482\pi$
$908$	10.3425	0.343229
$909$	2.67082	0.0885854
$910$	4.80752	0.159368
$911$	6.63455	0.219812	0.109906	−	0.993942i	$-0.464945\pi$
$911$	6.63455	0.219812	0.109906	+	0.993942i	$0.464945\pi$
$912$	3.86050	0.127834
$913$	−34.8988	−1.15498
$914$	6.66524	0.220466
$915$	−22.2963	−0.737092
$916$	6.28585	0.207690
$917$	6.46330	0.213437
$918$	1.00000	0.0330049
$919$	40.4623	1.33473	0.667364	−	0.744732i	$-0.267423\pi$
$919$	40.4623	1.33473	0.667364	+	0.744732i	$0.267423\pi$
$920$	−10.1384	−0.334253
$921$	34.1464	1.12516
$922$	8.84232	0.291206
$923$	−3.41324	−0.112348
$924$	−5.19570	−0.170926
$925$	30.3083	0.996532
$926$	12.9431	0.425336
$927$	1.34525	0.0441837
$928$	−9.99843	−0.328215
$929$	55.6656	1.82633	0.913165	−	0.407590i	$-0.133631\pi$
$929$	55.6656	1.82633	0.913165	+	0.407590i	$0.133631\pi$
$930$	1.88492	0.0618090
$931$	−17.9121	−0.587045
$932$	18.9550	0.620893
$933$	3.87360	0.126816
$934$	−34.7988	−1.13865
$935$	10.3414	0.338199
$936$	1.02340	0.0334508
$937$	5.06188	0.165364	0.0826821	−	0.996576i	$-0.473651\pi$
$937$	5.06188	0.165364	0.0826821	+	0.996576i	$0.473651\pi$
$938$	−17.6260	−0.575508
$939$	−17.8845	−0.583639
$940$	3.81613	0.124468
$941$	−10.2625	−0.334548	−0.167274	−	0.985910i	$-0.553496\pi$
$941$	−10.2625	−0.334548	−0.167274	+	0.985910i	$0.553496\pi$
$942$	−1.96927	−0.0641622
$943$	12.4566	0.405643
$944$	−1.00000	−0.0325472
$945$	4.69761	0.152813
$946$	−35.5236	−1.15497
$947$	2.01141	0.0653619	0.0326809	−	0.999466i	$-0.489595\pi$
$947$	2.01141	0.0653619	0.0326809	+	0.999466i	$0.489595\pi$
$948$	9.75174	0.316722
$949$	6.91240	0.224386
$950$	−16.7932	−0.544842
$951$	−1.56824	−0.0508536
$952$	1.53628	0.0497912
$953$	37.6195	1.21862	0.609308	−	0.792934i	$-0.291447\pi$
$953$	37.6195	1.21862	0.609308	+	0.792934i	$0.291447\pi$
$954$	4.62844	0.149851
$955$	9.98416	0.323080
$956$	12.1587	0.393241
$957$	−33.8147	−1.09307
$958$	−1.23920	−0.0400367
$959$	9.69808	0.313167
$960$	3.05778	0.0986893
$961$	−30.6200	−0.987742
$962$	7.13047	0.229896
$963$	11.1785	0.360223
$964$	12.7987	0.412217
$965$	−2.98143	−0.0959758
$966$	−5.09372	−0.163888
$967$	9.67552	0.311144	0.155572	−	0.987825i	$-0.450278\pi$
$967$	9.67552	0.311144	0.155572	+	0.987825i	$0.450278\pi$
$968$	−0.437896	−0.0140745
$969$	−3.86050	−0.124017
$970$	−11.0846	−0.355904
$971$	61.1703	1.96305	0.981524	−	0.191340i	$-0.0612832\pi$
$971$	61.1703	1.96305	0.981524	+	0.191340i	$0.0612832\pi$
$972$	1.00000	0.0320750
$973$	16.1668	0.518284
$974$	−23.1162	−0.740692
$975$	−4.45177	−0.142571
$976$	−7.29167	−0.233401
$977$	−11.6550	−0.372877	−0.186439	−	0.982467i	$-0.559695\pi$
$977$	−11.6550	−0.372877	−0.186439	+	0.982467i	$0.559695\pi$
$978$	7.74059	0.247517
$979$	−21.8346	−0.697837
$980$	−14.1876	−0.453205
$981$	−7.90967	−0.252536
$982$	−7.59394	−0.242332
$983$	−10.2688	−0.327525	−0.163762	−	0.986500i	$-0.552363\pi$
$983$	−10.2688	−0.327525	−0.163762	+	0.986500i	$0.552363\pi$
$984$	−3.75695	−0.119767
$985$	19.0898	0.608253
$986$	9.99843	0.318415
$987$	1.91729	0.0610282
$988$	−3.95083	−0.125693
$989$	−34.8263	−1.10741
$990$	10.3414	0.328671
$991$	7.99009	0.253814	0.126907	−	0.991915i	$-0.459495\pi$
$991$	7.99009	0.253814	0.126907	+	0.991915i	$0.459495\pi$
$992$	0.616436	0.0195719
$993$	8.06808	0.256033
$994$	−5.12381	−0.162517
$995$	−43.3993	−1.37585
$996$	10.3190	0.326970
$997$	−27.3092	−0.864892	−0.432446	−	0.901660i	$-0.642349\pi$
$997$	−27.3092	−0.864892	−0.432446	+	0.901660i	$0.642349\pi$
$998$	5.98394	0.189418
$999$	6.96745	0.220440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.p.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.p.1.5	✓	5	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.05778 q^{5} -1.00000 q^{6} +1.53628 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.05778 q^{5} -1.00000 q^{6} +1.53628 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.05778 q^{10} -3.38200 q^{11} +1.00000 q^{12} -1.02340 q^{13} -1.53628 q^{14} +3.05778 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.86050 q^{19} +3.05778 q^{20} +1.53628 q^{21} +3.38200 q^{22} +3.31561 q^{23} -1.00000 q^{24} +4.34999 q^{25} +1.02340 q^{26} +1.00000 q^{27} +1.53628 q^{28} +9.99843 q^{29} -3.05778 q^{30} -0.616436 q^{31} -1.00000 q^{32} -3.38200 q^{33} +1.00000 q^{34} +4.69761 q^{35} +1.00000 q^{36} +6.96745 q^{37} -3.86050 q^{38} -1.02340 q^{39} -3.05778 q^{40} +3.75695 q^{41} -1.53628 q^{42} -10.5037 q^{43} -3.38200 q^{44} +3.05778 q^{45} -3.31561 q^{46} +1.24801 q^{47} +1.00000 q^{48} -4.63983 q^{49} -4.34999 q^{50} -1.00000 q^{51} -1.02340 q^{52} -4.62844 q^{53} -1.00000 q^{54} -10.3414 q^{55} -1.53628 q^{56} +3.86050 q^{57} -9.99843 q^{58} -1.00000 q^{59} +3.05778 q^{60} -7.29167 q^{61} +0.616436 q^{62} +1.53628 q^{63} +1.00000 q^{64} -3.12932 q^{65} +3.38200 q^{66} +11.4731 q^{67} -1.00000 q^{68} +3.31561 q^{69} -4.69761 q^{70} +3.33520 q^{71} -1.00000 q^{72} -6.75436 q^{73} -6.96745 q^{74} +4.34999 q^{75} +3.86050 q^{76} -5.19570 q^{77} +1.02340 q^{78} +9.75174 q^{79} +3.05778 q^{80} +1.00000 q^{81} -3.75695 q^{82} +10.3190 q^{83} +1.53628 q^{84} -3.05778 q^{85} +10.5037 q^{86} +9.99843 q^{87} +3.38200 q^{88} +6.45613 q^{89} -3.05778 q^{90} -1.57223 q^{91} +3.31561 q^{92} -0.616436 q^{93} -1.24801 q^{94} +11.8046 q^{95} -1.00000 q^{96} +3.62504 q^{97} +4.63983 q^{98} -3.38200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} + q^{10} + 6 q^{11} + 5 q^{12} - 2 q^{13} + q^{14} - q^{15} + 5 q^{16} - 5 q^{17} - 5 q^{18} + 4 q^{19} - q^{20} - q^{21} - 6 q^{22} + 12 q^{23} - 5 q^{24} + 4 q^{25} + 2 q^{26} + 5 q^{27} - q^{28} + 19 q^{29} + q^{30} + 5 q^{31} - 5 q^{32} + 6 q^{33} + 5 q^{34} - 4 q^{35} + 5 q^{36} - 11 q^{37} - 4 q^{38} - 2 q^{39} + q^{40} + 6 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} - q^{45} - 12 q^{46} + 22 q^{47} + 5 q^{48} - 12 q^{49} - 4 q^{50} - 5 q^{51} - 2 q^{52} + 15 q^{53} - 5 q^{54} - 36 q^{55} + q^{56} + 4 q^{57} - 19 q^{58} - 5 q^{59} - q^{60} + 16 q^{61} - 5 q^{62} - q^{63} + 5 q^{64} - 2 q^{65} - 6 q^{66} + 25 q^{67} - 5 q^{68} + 12 q^{69} + 4 q^{70} - 5 q^{72} - 10 q^{73} + 11 q^{74} + 4 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 10 q^{79} - q^{80} + 5 q^{81} - 6 q^{82} + 19 q^{83} - q^{84} + q^{85} - 2 q^{86} + 19 q^{87} - 6 q^{88} + 23 q^{89} + q^{90} - 17 q^{91} + 12 q^{92} + 5 q^{93} - 22 q^{94} + q^{95} - 5 q^{96} + 8 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 + q^10 + 6 * q^11 + 5 * q^12 - 2 * q^13 + q^14 - q^15 + 5 * q^16 - 5 * q^17 - 5 * q^18 + 4 * q^19 - q^20 - q^21 - 6 * q^22 + 12 * q^23 - 5 * q^24 + 4 * q^25 + 2 * q^26 + 5 * q^27 - q^28 + 19 * q^29 + q^30 + 5 * q^31 - 5 * q^32 + 6 * q^33 + 5 * q^34 - 4 * q^35 + 5 * q^36 - 11 * q^37 - 4 * q^38 - 2 * q^39 + q^40 + 6 * q^41 + q^42 + 2 * q^43 + 6 * q^44 - q^45 - 12 * q^46 + 22 * q^47 + 5 * q^48 - 12 * q^49 - 4 * q^50 - 5 * q^51 - 2 * q^52 + 15 * q^53 - 5 * q^54 - 36 * q^55 + q^56 + 4 * q^57 - 19 * q^58 - 5 * q^59 - q^60 + 16 * q^61 - 5 * q^62 - q^63 + 5 * q^64 - 2 * q^65 - 6 * q^66 + 25 * q^67 - 5 * q^68 + 12 * q^69 + 4 * q^70 - 5 * q^72 - 10 * q^73 + 11 * q^74 + 4 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 10 * q^79 - q^80 + 5 * q^81 - 6 * q^82 + 19 * q^83 - q^84 + q^85 - 2 * q^86 + 19 * q^87 - 6 * q^88 + 23 * q^89 + q^90 - 17 * q^91 + 12 * q^92 + 5 * q^93 - 22 * q^94 + q^95 - 5 * q^96 + 8 * q^97 + 12 * q^98 + 6 * q^99

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