LMFDB - Embedded newform 6014.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.21269 q^{3} +1.00000 q^{4} -0.168256 q^{5} +3.21269 q^{6} +2.46391 q^{7} -1.00000 q^{8} +7.32140 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.21269 q^{3} +1.00000 q^{4} -0.168256 q^{5} +3.21269 q^{6} +2.46391 q^{7} -1.00000 q^{8} +7.32140 q^{9} +0.168256 q^{10} -1.60287 q^{11} -3.21269 q^{12} -3.41948 q^{13} -2.46391 q^{14} +0.540555 q^{15} +1.00000 q^{16} -7.07020 q^{17} -7.32140 q^{18} -4.86343 q^{19} -0.168256 q^{20} -7.91578 q^{21} +1.60287 q^{22} -8.15193 q^{23} +3.21269 q^{24} -4.97169 q^{25} +3.41948 q^{26} -13.8833 q^{27} +2.46391 q^{28} -0.180529 q^{29} -0.540555 q^{30} +1.00000 q^{31} -1.00000 q^{32} +5.14953 q^{33} +7.07020 q^{34} -0.414567 q^{35} +7.32140 q^{36} -5.75351 q^{37} +4.86343 q^{38} +10.9857 q^{39} +0.168256 q^{40} +2.81799 q^{41} +7.91578 q^{42} -8.62818 q^{43} -1.60287 q^{44} -1.23187 q^{45} +8.15193 q^{46} -1.16417 q^{47} -3.21269 q^{48} -0.929150 q^{49} +4.97169 q^{50} +22.7144 q^{51} -3.41948 q^{52} +0.317810 q^{53} +13.8833 q^{54} +0.269692 q^{55} -2.46391 q^{56} +15.6247 q^{57} +0.180529 q^{58} +4.26975 q^{59} +0.540555 q^{60} +7.59343 q^{61} -1.00000 q^{62} +18.0393 q^{63} +1.00000 q^{64} +0.575347 q^{65} -5.14953 q^{66} -10.8264 q^{67} -7.07020 q^{68} +26.1896 q^{69} +0.414567 q^{70} -2.37694 q^{71} -7.32140 q^{72} +1.68159 q^{73} +5.75351 q^{74} +15.9725 q^{75} -4.86343 q^{76} -3.94933 q^{77} -10.9857 q^{78} +1.41402 q^{79} -0.168256 q^{80} +22.6386 q^{81} -2.81799 q^{82} -3.80928 q^{83} -7.91578 q^{84} +1.18960 q^{85} +8.62818 q^{86} +0.579985 q^{87} +1.60287 q^{88} -0.520290 q^{89} +1.23187 q^{90} -8.42528 q^{91} -8.15193 q^{92} -3.21269 q^{93} +1.16417 q^{94} +0.818300 q^{95} +3.21269 q^{96} -1.00000 q^{97} +0.929150 q^{98} -11.7352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) $ 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * 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
$3$	−3.21269	−1.85485	−0.927425	−	0.374010i	$-0.877982\pi$
$3$	−3.21269	−1.85485	−0.927425	+	0.374010i	$0.877982\pi$
$4$	1.00000	0.500000
$5$	−0.168256	−0.0752463	−0.0376232	−	0.999292i	$-0.511979\pi$
$5$	−0.168256	−0.0752463	−0.0376232	+	0.999292i	$0.511979\pi$
$6$	3.21269	1.31158
$7$	2.46391	0.931270	0.465635	−	0.884977i	$-0.345826\pi$
$7$	2.46391	0.931270	0.465635	+	0.884977i	$0.345826\pi$
$8$	−1.00000	−0.353553
$9$	7.32140	2.44047
$10$	0.168256	0.0532072
$11$	−1.60287	−0.483284	−0.241642	−	0.970366i	$-0.577686\pi$
$11$	−1.60287	−0.483284	−0.241642	+	0.970366i	$0.577686\pi$
$12$	−3.21269	−0.927425
$13$	−3.41948	−0.948392	−0.474196	−	0.880419i	$-0.657261\pi$
$13$	−3.41948	−0.948392	−0.474196	+	0.880419i	$0.657261\pi$
$14$	−2.46391	−0.658508
$15$	0.540555	0.139571
$16$	1.00000	0.250000
$17$	−7.07020	−1.71477	−0.857387	−	0.514671i	$-0.827914\pi$
$17$	−7.07020	−1.71477	−0.857387	+	0.514671i	$0.827914\pi$
$18$	−7.32140	−1.72567
$19$	−4.86343	−1.11575	−0.557873	−	0.829926i	$-0.688383\pi$
$19$	−4.86343	−1.11575	−0.557873	+	0.829926i	$0.688383\pi$
$20$	−0.168256	−0.0376232
$21$	−7.91578	−1.72737
$22$	1.60287	0.341733
$23$	−8.15193	−1.69979	−0.849897	−	0.526949i	$-0.823336\pi$
$23$	−8.15193	−1.69979	−0.849897	+	0.526949i	$0.823336\pi$
$24$	3.21269	0.655788
$25$	−4.97169	−0.994338
$26$	3.41948	0.670614
$27$	−13.8833	−2.67185
$28$	2.46391	0.465635
$29$	−0.180529	−0.0335234	−0.0167617	−	0.999860i	$-0.505336\pi$
$29$	−0.180529	−0.0335234	−0.0167617	+	0.999860i	$0.505336\pi$
$30$	−0.540555	−0.0986913
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	5.14953	0.896418
$34$	7.07020	1.21253
$35$	−0.414567	−0.0700747
$36$	7.32140	1.22023
$37$	−5.75351	−0.945871	−0.472935	−	0.881097i	$-0.656806\pi$
$37$	−5.75351	−0.945871	−0.472935	+	0.881097i	$0.656806\pi$
$38$	4.86343	0.788952
$39$	10.9857	1.75912
$40$	0.168256	0.0266036
$41$	2.81799	0.440096	0.220048	−	0.975489i	$-0.429379\pi$
$41$	2.81799	0.440096	0.220048	+	0.975489i	$0.429379\pi$
$42$	7.91578	1.22143
$43$	−8.62818	−1.31579	−0.657893	−	0.753112i	$-0.728552\pi$
$43$	−8.62818	−1.31579	−0.657893	+	0.753112i	$0.728552\pi$
$44$	−1.60287	−0.241642
$45$	−1.23187	−0.183636
$46$	8.15193	1.20194
$47$	−1.16417	−0.169812	−0.0849060	−	0.996389i	$-0.527059\pi$
$47$	−1.16417	−0.169812	−0.0849060	+	0.996389i	$0.527059\pi$
$48$	−3.21269	−0.463712
$49$	−0.929150	−0.132736
$50$	4.97169	0.703103
$51$	22.7144	3.18065
$52$	−3.41948	−0.474196
$53$	0.317810	0.0436545	0.0218273	−	0.999762i	$-0.493052\pi$
$53$	0.317810	0.0436545	0.0218273	+	0.999762i	$0.493052\pi$
$54$	13.8833	1.88928
$55$	0.269692	0.0363653
$56$	−2.46391	−0.329254
$57$	15.6247	2.06954
$58$	0.180529	0.0237046
$59$	4.26975	0.555874	0.277937	−	0.960599i	$-0.410349\pi$
$59$	4.26975	0.555874	0.277937	+	0.960599i	$0.410349\pi$
$60$	0.540555	0.0697853
$61$	7.59343	0.972239	0.486119	−	0.873892i	$-0.338412\pi$
$61$	7.59343	0.972239	0.486119	+	0.873892i	$0.338412\pi$
$62$	−1.00000	−0.127000
$63$	18.0393	2.27273
$64$	1.00000	0.125000
$65$	0.575347	0.0713630
$66$	−5.14953	−0.633863
$67$	−10.8264	−1.32265	−0.661325	−	0.750099i	$-0.730006\pi$
$67$	−10.8264	−1.32265	−0.661325	+	0.750099i	$0.730006\pi$
$68$	−7.07020	−0.857387
$69$	26.1896	3.15286
$70$	0.414567	0.0495503
$71$	−2.37694	−0.282091	−0.141046	−	0.990003i	$-0.545046\pi$
$71$	−2.37694	−0.282091	−0.141046	+	0.990003i	$0.545046\pi$
$72$	−7.32140	−0.862835
$73$	1.68159	0.196815	0.0984073	−	0.995146i	$-0.468625\pi$
$73$	1.68159	0.196815	0.0984073	+	0.995146i	$0.468625\pi$
$74$	5.75351	0.668832
$75$	15.9725	1.84435
$76$	−4.86343	−0.557873
$77$	−3.94933	−0.450068
$78$	−10.9857	−1.24389
$79$	1.41402	0.159090	0.0795449	−	0.996831i	$-0.474653\pi$
$79$	1.41402	0.159090	0.0795449	+	0.996831i	$0.474653\pi$
$80$	−0.168256	−0.0188116
$81$	22.6386	2.51541
$82$	−2.81799	−0.311195
$83$	−3.80928	−0.418122	−0.209061	−	0.977903i	$-0.567041\pi$
$83$	−3.80928	−0.418122	−0.209061	+	0.977903i	$0.567041\pi$
$84$	−7.91578	−0.863683
$85$	1.18960	0.129031
$86$	8.62818	0.930401
$87$	0.579985	0.0621809
$88$	1.60287	0.170867
$89$	−0.520290	−0.0551507	−0.0275753	−	0.999620i	$-0.508779\pi$
$89$	−0.520290	−0.0551507	−0.0275753	+	0.999620i	$0.508779\pi$
$90$	1.23187	0.129850
$91$	−8.42528	−0.883209
$92$	−8.15193	−0.849897
$93$	−3.21269	−0.333141
$94$	1.16417	0.120075
$95$	0.818300	0.0839558
$96$	3.21269	0.327894
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	0.929150	0.0938583
$99$	−11.7352	−1.17944
$100$	−4.97169	−0.497169
$101$	−6.30628	−0.627498	−0.313749	−	0.949506i	$-0.601585\pi$
$101$	−6.30628	−0.627498	−0.313749	+	0.949506i	$0.601585\pi$
$102$	−22.7144	−2.24906
$103$	−0.543988	−0.0536008	−0.0268004	−	0.999641i	$-0.508532\pi$
$103$	−0.543988	−0.0536008	−0.0268004	+	0.999641i	$0.508532\pi$
$104$	3.41948	0.335307
$105$	1.33188	0.129978
$106$	−0.317810	−0.0308684
$107$	−8.91385	−0.861734	−0.430867	−	0.902415i	$-0.641792\pi$
$107$	−8.91385	−0.861734	−0.430867	+	0.902415i	$0.641792\pi$
$108$	−13.8833	−1.33592
$109$	17.6120	1.68693	0.843464	−	0.537186i	$-0.180513\pi$
$109$	17.6120	1.68693	0.843464	+	0.537186i	$0.180513\pi$
$110$	−0.269692	−0.0257142
$111$	18.4843	1.75445
$112$	2.46391	0.232818
$113$	15.1731	1.42736	0.713682	−	0.700470i	$-0.247026\pi$
$113$	15.1731	1.42736	0.713682	+	0.700470i	$0.247026\pi$
$114$	−15.6247	−1.46339
$115$	1.37161	0.127903
$116$	−0.180529	−0.0167617
$117$	−25.0353	−2.31452
$118$	−4.26975	−0.393062
$119$	−17.4203	−1.59692
$120$	−0.540555	−0.0493457
$121$	−8.43081	−0.766437
$122$	−7.59343	−0.687476
$123$	−9.05334	−0.816312
$124$	1.00000	0.0898027
$125$	1.67780	0.150067
$126$	−18.0393	−1.60706
$127$	10.7053	0.949945	0.474973	−	0.880001i	$-0.342458\pi$
$127$	10.7053	0.949945	0.474973	+	0.880001i	$0.342458\pi$
$128$	−1.00000	−0.0883883
$129$	27.7197	2.44058
$130$	−0.575347	−0.0504613
$131$	−20.0995	−1.75610	−0.878051	−	0.478566i	$-0.841157\pi$
$131$	−20.0995	−1.75610	−0.878051	+	0.478566i	$0.841157\pi$
$132$	5.14953	0.448209
$133$	−11.9830	−1.03906
$134$	10.8264	0.935255
$135$	2.33595	0.201047
$136$	7.07020	0.606264
$137$	−18.5117	−1.58156	−0.790782	−	0.612098i	$-0.790326\pi$
$137$	−18.5117	−1.58156	−0.790782	+	0.612098i	$0.790326\pi$
$138$	−26.1896	−2.22941
$139$	16.4193	1.39266	0.696332	−	0.717720i	$-0.254814\pi$
$139$	16.4193	1.39266	0.696332	+	0.717720i	$0.254814\pi$
$140$	−0.414567	−0.0350373
$141$	3.74013	0.314976
$142$	2.37694	0.199469
$143$	5.48098	0.458342
$144$	7.32140	0.610116
$145$	0.0303751	0.00252251
$146$	−1.68159	−0.139169
$147$	2.98507	0.246205
$148$	−5.75351	−0.472935
$149$	−20.0757	−1.64466	−0.822332	−	0.569008i	$-0.807328\pi$
$149$	−20.0757	−1.64466	−0.822332	+	0.569008i	$0.807328\pi$
$150$	−15.9725	−1.30415
$151$	−4.58760	−0.373333	−0.186667	−	0.982423i	$-0.559768\pi$
$151$	−4.58760	−0.373333	−0.186667	+	0.982423i	$0.559768\pi$
$152$	4.86343	0.394476
$153$	−51.7637	−4.18485
$154$	3.94933	0.318246
$155$	−0.168256	−0.0135146
$156$	10.9857	0.879562
$157$	22.0952	1.76339	0.881694	−	0.471821i	$-0.156403\pi$
$157$	22.0952	1.76339	0.881694	+	0.471821i	$0.156403\pi$
$158$	−1.41402	−0.112493
$159$	−1.02102	−0.0809725
$160$	0.168256	0.0133018
$161$	−20.0856	−1.58297
$162$	−22.6386	−1.77866
$163$	17.3801	1.36131	0.680656	−	0.732604i	$-0.261695\pi$
$163$	17.3801	1.36131	0.680656	+	0.732604i	$0.261695\pi$
$164$	2.81799	0.220048
$165$	−0.866439	−0.0674522
$166$	3.80928	0.295657
$167$	11.8284	0.915311	0.457655	−	0.889130i	$-0.348689\pi$
$167$	11.8284	0.915311	0.457655	+	0.889130i	$0.348689\pi$
$168$	7.91578	0.610716
$169$	−1.30719	−0.100553
$170$	−1.18960	−0.0912383
$171$	−35.6071	−2.72294
$172$	−8.62818	−0.657893
$173$	−1.92321	−0.146219	−0.0731096	−	0.997324i	$-0.523292\pi$
$173$	−1.92321	−0.146219	−0.0731096	+	0.997324i	$0.523292\pi$
$174$	−0.579985	−0.0439685
$175$	−12.2498	−0.925997
$176$	−1.60287	−0.120821
$177$	−13.7174	−1.03106
$178$	0.520290	0.0389974
$179$	−18.5729	−1.38820	−0.694100	−	0.719878i	$-0.744198\pi$
$179$	−18.5729	−1.38820	−0.694100	+	0.719878i	$0.744198\pi$
$180$	−1.23187	−0.0918180
$181$	−15.4633	−1.14938	−0.574690	−	0.818371i	$-0.694877\pi$
$181$	−15.4633	−1.14938	−0.574690	+	0.818371i	$0.694877\pi$
$182$	8.42528	0.624523
$183$	−24.3953	−1.80336
$184$	8.15193	0.600968
$185$	0.968062	0.0711733
$186$	3.21269	0.235566
$187$	11.3326	0.828723
$188$	−1.16417	−0.0849060
$189$	−34.2072	−2.48821
$190$	−0.818300	−0.0593657
$191$	9.26101	0.670103	0.335052	−	0.942200i	$-0.391246\pi$
$191$	9.26101	0.670103	0.335052	+	0.942200i	$0.391246\pi$
$192$	−3.21269	−0.231856
$193$	3.69562	0.266017	0.133008	−	0.991115i	$-0.457536\pi$
$193$	3.69562	0.266017	0.133008	+	0.991115i	$0.457536\pi$
$194$	1.00000	0.0717958
$195$	−1.84841	−0.132368
$196$	−0.929150	−0.0663679
$197$	−6.31010	−0.449576	−0.224788	−	0.974408i	$-0.572169\pi$
$197$	−6.31010	−0.449576	−0.224788	+	0.974408i	$0.572169\pi$
$198$	11.7352	0.833988
$199$	7.36903	0.522377	0.261188	−	0.965288i	$-0.415886\pi$
$199$	7.36903	0.522377	0.261188	+	0.965288i	$0.415886\pi$
$200$	4.97169	0.351552
$201$	34.7818	2.45332
$202$	6.30628	0.443708
$203$	−0.444807	−0.0312194
$204$	22.7144	1.59032
$205$	−0.474144	−0.0331156
$206$	0.543988	0.0379015
$207$	−59.6835	−4.14829
$208$	−3.41948	−0.237098
$209$	7.79544	0.539222
$210$	−1.33188	−0.0919083
$211$	10.5050	0.723192	0.361596	−	0.932335i	$-0.382232\pi$
$211$	10.5050	0.723192	0.361596	+	0.932335i	$0.382232\pi$
$212$	0.317810	0.0218273
$213$	7.63639	0.523237
$214$	8.91385	0.609338
$215$	1.45174	0.0990080
$216$	13.8833	0.944640
$217$	2.46391	0.167261
$218$	−17.6120	−1.19284
$219$	−5.40242	−0.365062
$220$	0.269692	0.0181827
$221$	24.1764	1.62628
$222$	−18.4843	−1.24058
$223$	−4.22573	−0.282976	−0.141488	−	0.989940i	$-0.545189\pi$
$223$	−4.22573	−0.282976	−0.141488	+	0.989940i	$0.545189\pi$
$224$	−2.46391	−0.164627
$225$	−36.3997	−2.42665
$226$	−15.1731	−1.00930
$227$	−10.9678	−0.727957	−0.363979	−	0.931407i	$-0.618582\pi$
$227$	−10.9678	−0.727957	−0.363979	+	0.931407i	$0.618582\pi$
$228$	15.6247	1.03477
$229$	9.27396	0.612841	0.306420	−	0.951896i	$-0.400869\pi$
$229$	9.27396	0.612841	0.306420	+	0.951896i	$0.400869\pi$
$230$	−1.37161	−0.0904413
$231$	12.6880	0.834808
$232$	0.180529	0.0118523
$233$	17.8950	1.17234	0.586169	−	0.810189i	$-0.300635\pi$
$233$	17.8950	1.17234	0.586169	+	0.810189i	$0.300635\pi$
$234$	25.0353	1.63661
$235$	0.195879	0.0127777
$236$	4.26975	0.277937
$237$	−4.54281	−0.295087
$238$	17.4203	1.12919
$239$	−10.4911	−0.678612	−0.339306	−	0.940676i	$-0.610192\pi$
$239$	−10.4911	−0.678612	−0.339306	+	0.940676i	$0.610192\pi$
$240$	0.540555	0.0348926
$241$	20.1762	1.29967	0.649833	−	0.760077i	$-0.274839\pi$
$241$	20.1762	1.29967	0.649833	+	0.760077i	$0.274839\pi$
$242$	8.43081	0.541953
$243$	−31.0811	−1.99385
$244$	7.59343	0.486119
$245$	0.156335	0.00998787
$246$	9.05334	0.577220
$247$	16.6304	1.05816
$248$	−1.00000	−0.0635001
$249$	12.2380	0.775554
$250$	−1.67780	−0.106113
$251$	−27.3234	−1.72464	−0.862320	−	0.506363i	$-0.830990\pi$
$251$	−27.3234	−1.72464	−0.862320	+	0.506363i	$0.830990\pi$
$252$	18.0393	1.13637
$253$	13.0665	0.821483
$254$	−10.7053	−0.671713
$255$	−3.82183	−0.239332
$256$	1.00000	0.0625000
$257$	−4.92004	−0.306904	−0.153452	−	0.988156i	$-0.549039\pi$
$257$	−4.92004	−0.306904	−0.153452	+	0.988156i	$0.549039\pi$
$258$	−27.7197	−1.72575
$259$	−14.1761	−0.880861
$260$	0.575347	0.0356815
$261$	−1.32172	−0.0818127
$262$	20.0995	1.24175
$263$	5.45197	0.336183	0.168091	−	0.985771i	$-0.446240\pi$
$263$	5.45197	0.336183	0.168091	+	0.985771i	$0.446240\pi$
$264$	−5.14953	−0.316932
$265$	−0.0534733	−0.00328484
$266$	11.9830	0.734728
$267$	1.67153	0.102296
$268$	−10.8264	−0.661325
$269$	−16.3988	−0.999855	−0.499927	−	0.866067i	$-0.666640\pi$
$269$	−16.3988	−0.999855	−0.499927	+	0.866067i	$0.666640\pi$
$270$	−2.33595	−0.142161
$271$	17.7179	1.07628	0.538142	−	0.842855i	$-0.319127\pi$
$271$	17.7179	1.07628	0.538142	+	0.842855i	$0.319127\pi$
$272$	−7.07020	−0.428694
$273$	27.0678	1.63822
$274$	18.5117	1.11833
$275$	7.96898	0.480547
$276$	26.1896	1.57643
$277$	16.2652	0.977279	0.488640	−	0.872486i	$-0.337493\pi$
$277$	16.2652	0.977279	0.488640	+	0.872486i	$0.337493\pi$
$278$	−16.4193	−0.984762
$279$	7.32140	0.438320
$280$	0.414567	0.0247751
$281$	8.02848	0.478939	0.239469	−	0.970904i	$-0.423027\pi$
$281$	8.02848	0.478939	0.239469	+	0.970904i	$0.423027\pi$
$282$	−3.74013	−0.222721
$283$	−31.9235	−1.89766	−0.948829	−	0.315791i	$-0.897730\pi$
$283$	−31.9235	−1.89766	−0.948829	+	0.315791i	$0.897730\pi$
$284$	−2.37694	−0.141046
$285$	−2.62895	−0.155725
$286$	−5.48098	−0.324097
$287$	6.94327	0.409849
$288$	−7.32140	−0.431417
$289$	32.9877	1.94045
$290$	−0.0303751	−0.00178369
$291$	3.21269	0.188331
$292$	1.68159	0.0984073
$293$	−4.79820	−0.280314	−0.140157	−	0.990129i	$-0.544761\pi$
$293$	−4.79820	−0.280314	−0.140157	+	0.990129i	$0.544761\pi$
$294$	−2.98507	−0.174093
$295$	−0.718411	−0.0418275
$296$	5.75351	0.334416
$297$	22.2532	1.29126
$298$	20.0757	1.16295
$299$	27.8753	1.61207
$300$	15.9725	0.922173
$301$	−21.2591	−1.22535
$302$	4.58760	0.263987
$303$	20.2601	1.16391
$304$	−4.86343	−0.278937
$305$	−1.27764	−0.0731574
$306$	51.7637	2.95913
$307$	8.40588	0.479749	0.239875	−	0.970804i	$-0.422894\pi$
$307$	8.40588	0.479749	0.239875	+	0.970804i	$0.422894\pi$
$308$	−3.94933	−0.225034
$309$	1.74767	0.0994213
$310$	0.168256	0.00955629
$311$	25.7794	1.46182	0.730908	−	0.682476i	$-0.239097\pi$
$311$	25.7794	1.46182	0.730908	+	0.682476i	$0.239097\pi$
$312$	−10.9857	−0.621944
$313$	10.7959	0.610223	0.305111	−	0.952317i	$-0.401306\pi$
$313$	10.7959	0.610223	0.305111	+	0.952317i	$0.401306\pi$
$314$	−22.0952	−1.24690
$315$	−3.03521	−0.171015
$316$	1.41402	0.0795449
$317$	1.37799	0.0773959	0.0386980	−	0.999251i	$-0.487679\pi$
$317$	1.37799	0.0773959	0.0386980	+	0.999251i	$0.487679\pi$
$318$	1.02102	0.0572562
$319$	0.289365	0.0162013
$320$	−0.168256	−0.00940579
$321$	28.6375	1.59839
$322$	20.0856	1.11933
$323$	34.3854	1.91325
$324$	22.6386	1.25770
$325$	17.0006	0.943022
$326$	−17.3801	−0.962592
$327$	−56.5821	−3.12900
$328$	−2.81799	−0.155598
$329$	−2.86841	−0.158141
$330$	0.866439	0.0476959
$331$	−27.0098	−1.48459	−0.742297	−	0.670071i	$-0.766264\pi$
$331$	−27.0098	−1.48459	−0.742297	+	0.670071i	$0.766264\pi$
$332$	−3.80928	−0.209061
$333$	−42.1237	−2.30837
$334$	−11.8284	−0.647222
$335$	1.82160	0.0995246
$336$	−7.91578	−0.431841
$337$	29.1414	1.58743	0.793717	−	0.608287i	$-0.208143\pi$
$337$	29.1414	1.58743	0.793717	+	0.608287i	$0.208143\pi$
$338$	1.30719	0.0711017
$339$	−48.7465	−2.64754
$340$	1.18960	0.0645153
$341$	−1.60287	−0.0868003
$342$	35.6071	1.92541
$343$	−19.5367	−1.05488
$344$	8.62818	0.465200
$345$	−4.40656	−0.237241
$346$	1.92321	0.103393
$347$	−31.2318	−1.67661	−0.838306	−	0.545200i	$-0.816454\pi$
$347$	−31.2318	−1.67661	−0.838306	+	0.545200i	$0.816454\pi$
$348$	0.579985	0.0310904
$349$	11.2345	0.601370	0.300685	−	0.953723i	$-0.402785\pi$
$349$	11.2345	0.601370	0.300685	+	0.953723i	$0.402785\pi$
$350$	12.2498	0.654779
$351$	47.4737	2.53396
$352$	1.60287	0.0854333
$353$	26.9324	1.43347	0.716734	−	0.697347i	$-0.245636\pi$
$353$	26.9324	1.43347	0.716734	+	0.697347i	$0.245636\pi$
$354$	13.7174	0.729071
$355$	0.399935	0.0212263
$356$	−0.520290	−0.0275753
$357$	55.9662	2.96204
$358$	18.5729	0.981606
$359$	−0.805458	−0.0425105	−0.0212552	−	0.999774i	$-0.506766\pi$
$359$	−0.805458	−0.0425105	−0.0212552	+	0.999774i	$0.506766\pi$
$360$	1.23187	0.0649251
$361$	4.65292	0.244891
$362$	15.4633	0.812734
$363$	27.0856	1.42162
$364$	−8.42528	−0.441605
$365$	−0.282937	−0.0148096
$366$	24.3953	1.27517
$367$	5.10873	0.266673	0.133337	−	0.991071i	$-0.457431\pi$
$367$	5.10873	0.266673	0.133337	+	0.991071i	$0.457431\pi$
$368$	−8.15193	−0.424948
$369$	20.6316	1.07404
$370$	−0.968062	−0.0503271
$371$	0.783054	0.0406542
$372$	−3.21269	−0.166570
$373$	−17.0128	−0.880890	−0.440445	−	0.897780i	$-0.645179\pi$
$373$	−17.0128	−0.880890	−0.440445	+	0.897780i	$0.645179\pi$
$374$	−11.3326	−0.585995
$375$	−5.39024	−0.278351
$376$	1.16417	0.0600376
$377$	0.617315	0.0317933
$378$	34.2072	1.75943
$379$	−31.8077	−1.63385	−0.816927	−	0.576741i	$-0.804324\pi$
$379$	−31.8077	−1.63385	−0.816927	+	0.576741i	$0.804324\pi$
$380$	0.818300	0.0419779
$381$	−34.3930	−1.76200
$382$	−9.26101	−0.473835
$383$	−19.6166	−1.00236	−0.501180	−	0.865343i	$-0.667101\pi$
$383$	−19.6166	−1.00236	−0.501180	+	0.865343i	$0.667101\pi$
$384$	3.21269	0.163947
$385$	0.664498	0.0338659
$386$	−3.69562	−0.188102
$387$	−63.1703	−3.21113
$388$	−1.00000	−0.0507673
$389$	9.07724	0.460235	0.230117	−	0.973163i	$-0.426089\pi$
$389$	9.07724	0.460235	0.230117	+	0.973163i	$0.426089\pi$
$390$	1.84841	0.0935980
$391$	57.6357	2.91476
$392$	0.929150	0.0469292
$393$	64.5736	3.25731
$394$	6.31010	0.317898
$395$	−0.237917	−0.0119709
$396$	−11.7352	−0.589718
$397$	−11.5233	−0.578336	−0.289168	−	0.957278i	$-0.593379\pi$
$397$	−11.5233	−0.578336	−0.289168	+	0.957278i	$0.593379\pi$
$398$	−7.36903	−0.369376
$399$	38.4978	1.92730
$400$	−4.97169	−0.248584
$401$	−37.8590	−1.89059	−0.945294	−	0.326221i	$-0.894225\pi$
$401$	−37.8590	−1.89059	−0.945294	+	0.326221i	$0.894225\pi$
$402$	−34.7818	−1.73476
$403$	−3.41948	−0.170336
$404$	−6.30628	−0.313749
$405$	−3.80909	−0.189275
$406$	0.444807	0.0220754
$407$	9.22213	0.457124
$408$	−22.7144	−1.12453
$409$	−8.93018	−0.441569	−0.220784	−	0.975323i	$-0.570862\pi$
$409$	−8.93018	−0.441569	−0.220784	+	0.975323i	$0.570862\pi$
$410$	0.474144	0.0234163
$411$	59.4725	2.93356
$412$	−0.543988	−0.0268004
$413$	10.5203	0.517669
$414$	59.6835	2.93328
$415$	0.640933	0.0314622
$416$	3.41948	0.167654
$417$	−52.7500	−2.58318
$418$	−7.79544	−0.381288
$419$	−4.48568	−0.219140	−0.109570	−	0.993979i	$-0.534947\pi$
$419$	−4.48568	−0.219140	−0.109570	+	0.993979i	$0.534947\pi$
$420$	1.33188	0.0649890
$421$	36.3332	1.77077	0.885386	−	0.464857i	$-0.153894\pi$
$421$	36.3332	1.77077	0.885386	+	0.464857i	$0.153894\pi$
$422$	−10.5050	−0.511374
$423$	−8.52336	−0.414420
$424$	−0.317810	−0.0154342
$425$	35.1508	1.70507
$426$	−7.63639	−0.369984
$427$	18.7095	0.905417
$428$	−8.91385	−0.430867
$429$	−17.6087	−0.850156
$430$	−1.45174	−0.0700092
$431$	−12.1978	−0.587550	−0.293775	−	0.955875i	$-0.594912\pi$
$431$	−12.1978	−0.587550	−0.293775	+	0.955875i	$0.594912\pi$
$432$	−13.8833	−0.667961
$433$	−16.0209	−0.769916	−0.384958	−	0.922934i	$-0.625784\pi$
$433$	−16.0209	−0.769916	−0.384958	+	0.922934i	$0.625784\pi$
$434$	−2.46391	−0.118271
$435$	−0.0975858	−0.00467888
$436$	17.6120	0.843464
$437$	39.6463	1.89654
$438$	5.40242	0.258138
$439$	−38.9387	−1.85844	−0.929222	−	0.369522i	$-0.879521\pi$
$439$	−38.9387	−1.85844	−0.929222	+	0.369522i	$0.879521\pi$
$440$	−0.269692	−0.0128571
$441$	−6.80268	−0.323937
$442$	−24.1764	−1.14995
$443$	8.24725	0.391839	0.195919	−	0.980620i	$-0.437231\pi$
$443$	8.24725	0.391839	0.195919	+	0.980620i	$0.437231\pi$
$444$	18.4843	0.877224
$445$	0.0875419	0.00414988
$446$	4.22573	0.200094
$447$	64.4970	3.05060
$448$	2.46391	0.116409
$449$	27.6400	1.30441	0.652206	−	0.758042i	$-0.273844\pi$
$449$	27.6400	1.30441	0.652206	+	0.758042i	$0.273844\pi$
$450$	36.3997	1.71590
$451$	−4.51687	−0.212691
$452$	15.1731	0.713682
$453$	14.7385	0.692477
$454$	10.9678	0.514744
$455$	1.41760	0.0664582
$456$	−15.6247	−0.731693
$457$	−16.7902	−0.785412	−0.392706	−	0.919664i	$-0.628461\pi$
$457$	−16.7902	−0.785412	−0.392706	+	0.919664i	$0.628461\pi$
$458$	−9.27396	−0.433344
$459$	98.1578	4.58161
$460$	1.37161	0.0639516
$461$	39.5708	1.84299	0.921497	−	0.388385i	$-0.126967\pi$
$461$	39.5708	1.84299	0.921497	+	0.388385i	$0.126967\pi$
$462$	−12.6880	−0.590298
$463$	10.0648	0.467750	0.233875	−	0.972267i	$-0.424859\pi$
$463$	10.0648	0.467750	0.233875	+	0.972267i	$0.424859\pi$
$464$	−0.180529	−0.00838085
$465$	0.540555	0.0250676
$466$	−17.8950	−0.828969
$467$	−26.8066	−1.24046	−0.620231	−	0.784419i	$-0.712961\pi$
$467$	−26.8066	−1.24046	−0.620231	+	0.784419i	$0.712961\pi$
$468$	−25.0353	−1.15726
$469$	−26.6752	−1.23175
$470$	−0.195879	−0.00903522
$471$	−70.9851	−3.27082
$472$	−4.26975	−0.196531
$473$	13.8299	0.635897
$474$	4.54281	0.208658
$475$	24.1795	1.10943
$476$	−17.4203	−0.798459
$477$	2.32681	0.106537
$478$	10.4911	0.479851
$479$	12.9915	0.593597	0.296798	−	0.954940i	$-0.404081\pi$
$479$	12.9915	0.593597	0.296798	+	0.954940i	$0.404081\pi$
$480$	−0.540555	−0.0246728
$481$	19.6740	0.897056
$482$	−20.1762	−0.919002
$483$	64.5289	2.93617
$484$	−8.43081	−0.383218
$485$	0.168256	0.00764011
$486$	31.0811	1.40987
$487$	0.249983	0.0113278	0.00566391	−	0.999984i	$-0.498197\pi$
$487$	0.249983	0.0113278	0.00566391	+	0.999984i	$0.498197\pi$
$488$	−7.59343	−0.343738
$489$	−55.8368	−2.52503
$490$	−0.156335	−0.00706249
$491$	−10.4225	−0.470359	−0.235179	−	0.971952i	$-0.575568\pi$
$491$	−10.4225	−0.470359	−0.235179	+	0.971952i	$0.575568\pi$
$492$	−9.05334	−0.408156
$493$	1.27638	0.0574851
$494$	−16.6304	−0.748236
$495$	1.97452	0.0887483
$496$	1.00000	0.0449013
$497$	−5.85658	−0.262703
$498$	−12.2380	−0.548399
$499$	14.2079	0.636031	0.318016	−	0.948085i	$-0.396984\pi$
$499$	14.2079	0.636031	0.318016	+	0.948085i	$0.396984\pi$
$500$	1.67780	0.0750333
$501$	−38.0011	−1.69776
$502$	27.3234	1.21951
$503$	20.8594	0.930076	0.465038	−	0.885291i	$-0.346041\pi$
$503$	20.8594	0.930076	0.465038	+	0.885291i	$0.346041\pi$
$504$	−18.0393	−0.803532
$505$	1.06107	0.0472169
$506$	−13.0665	−0.580876
$507$	4.19960	0.186511
$508$	10.7053	0.474973
$509$	−11.1372	−0.493646	−0.246823	−	0.969061i	$-0.579387\pi$
$509$	−11.1372	−0.493646	−0.246823	+	0.969061i	$0.579387\pi$
$510$	3.82183	0.169233
$511$	4.14327	0.183288
$512$	−1.00000	−0.0441942
$513$	67.5205	2.98110
$514$	4.92004	0.217014
$515$	0.0915292	0.00403326
$516$	27.7197	1.22029
$517$	1.86602	0.0820673
$518$	14.1761	0.622863
$519$	6.17869	0.271214
$520$	−0.575347	−0.0252306
$521$	6.68512	0.292880	0.146440	−	0.989220i	$-0.453218\pi$
$521$	6.68512	0.292880	0.146440	+	0.989220i	$0.453218\pi$
$522$	1.32172	0.0578503
$523$	−3.86489	−0.169000	−0.0844999	−	0.996423i	$-0.526929\pi$
$523$	−3.86489	−0.169000	−0.0844999	+	0.996423i	$0.526929\pi$
$524$	−20.0995	−0.878051
$525$	39.3548	1.71759
$526$	−5.45197	−0.237717
$527$	−7.07020	−0.307983
$528$	5.14953	0.224105
$529$	43.4539	1.88930
$530$	0.0534733	0.00232273
$531$	31.2605	1.35659
$532$	−11.9830	−0.519531
$533$	−9.63605	−0.417384
$534$	−1.67153	−0.0723343
$535$	1.49981	0.0648424
$536$	10.8264	0.467628
$537$	59.6689	2.57490
$538$	16.3988	0.707004
$539$	1.48931	0.0641490
$540$	2.33595	0.100523
$541$	23.6743	1.01784	0.508918	−	0.860815i	$-0.330046\pi$
$541$	23.6743	1.01784	0.508918	+	0.860815i	$0.330046\pi$
$542$	−17.7179	−0.761047
$543$	49.6789	2.13193
$544$	7.07020	0.303132
$545$	−2.96333	−0.126935
$546$	−27.0678	−1.15840
$547$	−9.00633	−0.385083	−0.192541	−	0.981289i	$-0.561673\pi$
$547$	−9.00633	−0.385083	−0.192541	+	0.981289i	$0.561673\pi$
$548$	−18.5117	−0.790782
$549$	55.5945	2.37271
$550$	−7.96898	−0.339798
$551$	0.877990	0.0374036
$552$	−26.1896	−1.11470
$553$	3.48402	0.148156
$554$	−16.2652	−0.691041
$555$	−3.11008	−0.132016
$556$	16.4193	0.696332
$557$	−2.40913	−0.102078	−0.0510390	−	0.998697i	$-0.516253\pi$
$557$	−2.40913	−0.102078	−0.0510390	+	0.998697i	$0.516253\pi$
$558$	−7.32140	−0.309939
$559$	29.5038	1.24788
$560$	−0.414567	−0.0175187
$561$	−36.4082	−1.53716
$562$	−8.02848	−0.338661
$563$	−6.77782	−0.285651	−0.142825	−	0.989748i	$-0.545619\pi$
$563$	−6.77782	−0.285651	−0.142825	+	0.989748i	$0.545619\pi$
$564$	3.74013	0.157488
$565$	−2.55296	−0.107404
$566$	31.9235	1.34185
$567$	55.7796	2.34252
$568$	2.37694	0.0997344
$569$	−38.7655	−1.62513	−0.812566	−	0.582869i	$-0.801930\pi$
$569$	−38.7655	−1.62513	−0.812566	+	0.582869i	$0.801930\pi$
$570$	2.62895	0.110114
$571$	−14.5793	−0.610125	−0.305063	−	0.952332i	$-0.598677\pi$
$571$	−14.5793	−0.610125	−0.305063	+	0.952332i	$0.598677\pi$
$572$	5.48098	0.229171
$573$	−29.7528	−1.24294
$574$	−6.94327	−0.289807
$575$	40.5288	1.69017
$576$	7.32140	0.305058
$577$	12.6516	0.526692	0.263346	−	0.964701i	$-0.415174\pi$
$577$	12.6516	0.526692	0.263346	+	0.964701i	$0.415174\pi$
$578$	−32.9877	−1.37211
$579$	−11.8729	−0.493421
$580$	0.0303751	0.00126126
$581$	−9.38571	−0.389385
$582$	−3.21269	−0.133170
$583$	−0.509408	−0.0210975
$584$	−1.68159	−0.0695845
$585$	4.21234	0.174159
$586$	4.79820	0.198212
$587$	−2.11177	−0.0871621	−0.0435810	−	0.999050i	$-0.513877\pi$
$587$	−2.11177	−0.0871621	−0.0435810	+	0.999050i	$0.513877\pi$
$588$	2.98507	0.123102
$589$	−4.86343	−0.200394
$590$	0.718411	0.0295765
$591$	20.2724	0.833896
$592$	−5.75351	−0.236468
$593$	36.0941	1.48221	0.741103	−	0.671392i	$-0.234303\pi$
$593$	36.0941	1.48221	0.741103	+	0.671392i	$0.234303\pi$
$594$	−22.2532	−0.913058
$595$	2.93107	0.120162
$596$	−20.0757	−0.822332
$597$	−23.6744	−0.968930
$598$	−27.8753	−1.13991
$599$	16.6804	0.681544	0.340772	−	0.940146i	$-0.389312\pi$
$599$	16.6804	0.681544	0.340772	+	0.940146i	$0.389312\pi$
$600$	−15.9725	−0.652075
$601$	27.1453	1.10728	0.553639	−	0.832756i	$-0.313239\pi$
$601$	27.1453	1.10728	0.553639	+	0.832756i	$0.313239\pi$
$602$	21.2591	0.866454
$603$	−79.2641	−3.22788
$604$	−4.58760	−0.186667
$605$	1.41853	0.0576716
$606$	−20.2601	−0.823012
$607$	−39.1281	−1.58816	−0.794079	−	0.607814i	$-0.792047\pi$
$607$	−39.1281	−1.58816	−0.794079	+	0.607814i	$0.792047\pi$
$608$	4.86343	0.197238
$609$	1.42903	0.0579072
$610$	1.27764	0.0517301
$611$	3.98086	0.161048
$612$	−51.7637	−2.09242
$613$	34.0566	1.37553	0.687767	−	0.725931i	$-0.258591\pi$
$613$	34.0566	1.37553	0.687767	+	0.725931i	$0.258591\pi$
$614$	−8.40588	−0.339234
$615$	1.52328	0.0614245
$616$	3.94933	0.159123
$617$	−39.3172	−1.58285	−0.791426	−	0.611265i	$-0.790661\pi$
$617$	−39.3172	−1.58285	−0.791426	+	0.611265i	$0.790661\pi$
$618$	−1.74767	−0.0703015
$619$	−8.06723	−0.324249	−0.162125	−	0.986770i	$-0.551835\pi$
$619$	−8.06723	−0.324249	−0.162125	+	0.986770i	$0.551835\pi$
$620$	−0.168256	−0.00675732
$621$	113.176	4.54159
$622$	−25.7794	−1.03366
$623$	−1.28195	−0.0513602
$624$	10.9857	0.439781
$625$	24.5762	0.983046
$626$	−10.7959	−0.431493
$627$	−25.0444	−1.00018
$628$	22.0952	0.881694
$629$	40.6784	1.62196
$630$	3.03521	0.120926
$631$	−24.2530	−0.965498	−0.482749	−	0.875759i	$-0.660362\pi$
$631$	−24.2530	−0.965498	−0.482749	+	0.875759i	$0.660362\pi$
$632$	−1.41402	−0.0562467
$633$	−33.7492	−1.34141
$634$	−1.37799	−0.0547272
$635$	−1.80124	−0.0714799
$636$	−1.02102	−0.0404863
$637$	3.17721	0.125885
$638$	−0.289365	−0.0114561
$639$	−17.4025	−0.688434
$640$	0.168256	0.00665090
$641$	−17.9617	−0.709443	−0.354721	−	0.934972i	$-0.615424\pi$
$641$	−17.9617	−0.709443	−0.354721	+	0.934972i	$0.615424\pi$
$642$	−28.6375	−1.13023
$643$	−11.3696	−0.448373	−0.224186	−	0.974546i	$-0.571972\pi$
$643$	−11.3696	−0.448373	−0.224186	+	0.974546i	$0.571972\pi$
$644$	−20.0856	−0.791484
$645$	−4.66400	−0.183645
$646$	−34.3854	−1.35288
$647$	−17.5097	−0.688378	−0.344189	−	0.938900i	$-0.611846\pi$
$647$	−17.5097	−0.688378	−0.344189	+	0.938900i	$0.611846\pi$
$648$	−22.6386	−0.889330
$649$	−6.84386	−0.268645
$650$	−17.0006	−0.666817
$651$	−7.91578	−0.310244
$652$	17.3801	0.680656
$653$	32.5069	1.27209	0.636046	−	0.771651i	$-0.280569\pi$
$653$	32.5069	1.27209	0.636046	+	0.771651i	$0.280569\pi$
$654$	56.5821	2.21253
$655$	3.38186	0.132140
$656$	2.81799	0.110024
$657$	12.3116	0.480319
$658$	2.86841	0.111822
$659$	−40.2455	−1.56774	−0.783871	−	0.620923i	$-0.786758\pi$
$659$	−40.2455	−1.56774	−0.783871	+	0.620923i	$0.786758\pi$
$660$	−0.866439	−0.0337261
$661$	−30.8491	−1.19989	−0.599946	−	0.800040i	$-0.704811\pi$
$661$	−30.8491	−1.19989	−0.599946	+	0.800040i	$0.704811\pi$
$662$	27.0098	1.04977
$663$	−77.6712	−3.01650
$664$	3.80928	0.147829
$665$	2.01622	0.0781856
$666$	42.1237	1.63226
$667$	1.47166	0.0569829
$668$	11.8284	0.457655
$669$	13.5760	0.524877
$670$	−1.82160	−0.0703745
$671$	−12.1713	−0.469867
$672$	7.91578	0.305358
$673$	2.90407	0.111944	0.0559719	−	0.998432i	$-0.482174\pi$
$673$	2.90407	0.111944	0.0559719	+	0.998432i	$0.482174\pi$
$674$	−29.1414	−1.12249
$675$	69.0235	2.65672
$676$	−1.30719	−0.0502765
$677$	9.50851	0.365442	0.182721	−	0.983165i	$-0.441510\pi$
$677$	9.50851	0.365442	0.182721	+	0.983165i	$0.441510\pi$
$678$	48.7465	1.87210
$679$	−2.46391	−0.0945562
$680$	−1.18960	−0.0456192
$681$	35.2361	1.35025
$682$	1.60287	0.0613771
$683$	4.73367	0.181129	0.0905645	−	0.995891i	$-0.471133\pi$
$683$	4.73367	0.181129	0.0905645	+	0.995891i	$0.471133\pi$
$684$	−35.6071	−1.36147
$685$	3.11471	0.119007
$686$	19.5367	0.745915
$687$	−29.7944	−1.13673
$688$	−8.62818	−0.328946
$689$	−1.08674	−0.0414016
$690$	4.40656	0.167755
$691$	15.2952	0.581858	0.290929	−	0.956745i	$-0.406036\pi$
$691$	15.2952	0.581858	0.290929	+	0.956745i	$0.406036\pi$
$692$	−1.92321	−0.0731096
$693$	−28.9146	−1.09837
$694$	31.2318	1.18554
$695$	−2.76264	−0.104793
$696$	−0.579985	−0.0219843
$697$	−19.9238	−0.754666
$698$	−11.2345	−0.425233
$699$	−57.4911	−2.17451
$700$	−12.2498	−0.462999
$701$	−8.80031	−0.332383	−0.166192	−	0.986093i	$-0.553147\pi$
$701$	−8.80031	−0.332383	−0.166192	+	0.986093i	$0.553147\pi$
$702$	−47.4737	−1.79178
$703$	27.9818	1.05535
$704$	−1.60287	−0.0604105
$705$	−0.629298	−0.0237008
$706$	−26.9324	−1.01361
$707$	−15.5381	−0.584370
$708$	−13.7174	−0.515531
$709$	−43.9778	−1.65162	−0.825811	−	0.563948i	$-0.809282\pi$
$709$	−43.9778	−1.65162	−0.825811	+	0.563948i	$0.809282\pi$
$710$	−0.399935	−0.0150093
$711$	10.3526	0.388253
$712$	0.520290	0.0194987
$713$	−8.15193	−0.305292
$714$	−55.9662	−2.09448
$715$	−0.922207	−0.0344886
$716$	−18.5729	−0.694100
$717$	33.7047	1.25872
$718$	0.805458	0.0300594
$719$	−50.5943	−1.88685	−0.943424	−	0.331588i	$-0.892416\pi$
$719$	−50.5943	−1.88685	−0.943424	+	0.331588i	$0.892416\pi$
$720$	−1.23187	−0.0459090
$721$	−1.34034	−0.0499168
$722$	−4.65292	−0.173164
$723$	−64.8200	−2.41068
$724$	−15.4633	−0.574690
$725$	0.897535	0.0333336
$726$	−27.0856	−1.00524
$727$	33.4312	1.23990	0.619948	−	0.784643i	$-0.287154\pi$
$727$	33.4312	1.23990	0.619948	+	0.784643i	$0.287154\pi$
$728$	8.42528	0.312262
$729$	31.9380	1.18289
$730$	0.282937	0.0104720
$731$	61.0029	2.25628
$732$	−24.3953	−0.901678
$733$	29.5206	1.09037	0.545184	−	0.838316i	$-0.316460\pi$
$733$	29.5206	1.09037	0.545184	+	0.838316i	$0.316460\pi$
$734$	−5.10873	−0.188567
$735$	−0.502256	−0.0185260
$736$	8.15193	0.300484
$737$	17.3533	0.639215
$738$	−20.6316	−0.759461
$739$	26.9881	0.992775	0.496387	−	0.868101i	$-0.334660\pi$
$739$	26.9881	0.992775	0.496387	+	0.868101i	$0.334660\pi$
$740$	0.968062	0.0355867
$741$	−53.4283	−1.96274
$742$	−0.783054	−0.0287468
$743$	−11.0415	−0.405075	−0.202537	−	0.979275i	$-0.564919\pi$
$743$	−11.0415	−0.405075	−0.202537	+	0.979275i	$0.564919\pi$
$744$	3.21269	0.117783
$745$	3.37785	0.123755
$746$	17.0128	0.622883
$747$	−27.8892	−1.02041
$748$	11.3326	0.414361
$749$	−21.9629	−0.802508
$750$	5.39024	0.196824
$751$	25.6701	0.936717	0.468358	−	0.883539i	$-0.344846\pi$
$751$	25.6701	0.936717	0.468358	+	0.883539i	$0.344846\pi$
$752$	−1.16417	−0.0424530
$753$	87.7818	3.19895
$754$	−0.617315	−0.0224813
$755$	0.771890	0.0280920
$756$	−34.2072	−1.24411
$757$	−2.24714	−0.0816736	−0.0408368	−	0.999166i	$-0.513002\pi$
$757$	−2.24714	−0.0816736	−0.0408368	+	0.999166i	$0.513002\pi$
$758$	31.8077	1.15531
$759$	−41.9786	−1.52373
$760$	−0.818300	−0.0296829
$761$	−6.48804	−0.235191	−0.117596	−	0.993062i	$-0.537519\pi$
$761$	−6.48804	−0.235191	−0.117596	+	0.993062i	$0.537519\pi$
$762$	34.3930	1.24593
$763$	43.3945	1.57099
$764$	9.26101	0.335052
$765$	8.70955	0.314894
$766$	19.6166	0.708776
$767$	−14.6003	−0.527186
$768$	−3.21269	−0.115928
$769$	5.71751	0.206179	0.103089	−	0.994672i	$-0.467127\pi$
$769$	5.71751	0.206179	0.103089	+	0.994672i	$0.467127\pi$
$770$	−0.664498	−0.0239468
$771$	15.8066	0.569260
$772$	3.69562	0.133008
$773$	−18.6023	−0.669078	−0.334539	−	0.942382i	$-0.608581\pi$
$773$	−18.6023	−0.669078	−0.334539	+	0.942382i	$0.608581\pi$
$774$	63.1703	2.27061
$775$	−4.97169	−0.178588
$776$	1.00000	0.0358979
$777$	45.5435	1.63387
$778$	−9.07724	−0.325435
$779$	−13.7051	−0.491036
$780$	−1.84841	−0.0661838
$781$	3.80993	0.136330
$782$	−57.6357	−2.06105
$783$	2.50634	0.0895694
$784$	−0.929150	−0.0331839
$785$	−3.71765	−0.132688
$786$	−64.5736	−2.30326
$787$	−19.7638	−0.704502	−0.352251	−	0.935906i	$-0.614584\pi$
$787$	−19.7638	−0.704502	−0.352251	+	0.935906i	$0.614584\pi$
$788$	−6.31010	−0.224788
$789$	−17.5155	−0.623568
$790$	0.237917	0.00846472
$791$	37.3851	1.32926
$792$	11.7352	0.416994
$793$	−25.9655	−0.922063
$794$	11.5233	0.408945
$795$	0.171793	0.00609289
$796$	7.36903	0.261188
$797$	46.6977	1.65412	0.827059	−	0.562115i	$-0.190012\pi$
$797$	46.6977	1.65412	0.827059	+	0.562115i	$0.190012\pi$
$798$	−38.4978	−1.36281
$799$	8.23093	0.291189
$800$	4.97169	0.175776
$801$	−3.80925	−0.134593
$802$	37.8590	1.33685
$803$	−2.69536	−0.0951173
$804$	34.7818	1.22666
$805$	3.37952	0.119112
$806$	3.41948	0.120446
$807$	52.6844	1.85458
$808$	6.30628	0.221854
$809$	27.6229	0.971168	0.485584	−	0.874190i	$-0.338607\pi$
$809$	27.6229	0.971168	0.485584	+	0.874190i	$0.338607\pi$
$810$	3.80909	0.133838
$811$	25.3229	0.889208	0.444604	−	0.895727i	$-0.353344\pi$
$811$	25.3229	0.889208	0.444604	+	0.895727i	$0.353344\pi$
$812$	−0.444807	−0.0156097
$813$	−56.9220	−1.99634
$814$	−9.22213	−0.323235
$815$	−2.92430	−0.102434
$816$	22.7144	0.795162
$817$	41.9625	1.46808
$818$	8.93018	0.312236
$819$	−61.6848	−2.15544
$820$	−0.474144	−0.0165578
$821$	52.3758	1.82793	0.913964	−	0.405794i	$-0.133005\pi$
$821$	52.3758	1.82793	0.913964	+	0.405794i	$0.133005\pi$
$822$	−59.4725	−2.07434
$823$	−38.9864	−1.35898	−0.679491	−	0.733684i	$-0.737799\pi$
$823$	−38.9864	−1.35898	−0.679491	+	0.733684i	$0.737799\pi$
$824$	0.543988	0.0189507
$825$	−25.6019	−0.891343
$826$	−10.5203	−0.366047
$827$	−13.9163	−0.483919	−0.241959	−	0.970286i	$-0.577790\pi$
$827$	−13.9163	−0.483919	−0.241959	+	0.970286i	$0.577790\pi$
$828$	−59.6835	−2.07414
$829$	−21.1920	−0.736030	−0.368015	−	0.929820i	$-0.619962\pi$
$829$	−21.1920	−0.736030	−0.368015	+	0.929820i	$0.619962\pi$
$830$	−0.640933	−0.0222471
$831$	−52.2550	−1.81271
$832$	−3.41948	−0.118549
$833$	6.56927	0.227612
$834$	52.7500	1.82658
$835$	−1.99020	−0.0688738
$836$	7.79544	0.269611
$837$	−13.8833	−0.479878
$838$	4.48568	0.154955
$839$	43.2638	1.49363	0.746817	−	0.665030i	$-0.231581\pi$
$839$	43.2638	1.49363	0.746817	+	0.665030i	$0.231581\pi$
$840$	−1.33188	−0.0459541
$841$	−28.9674	−0.998876
$842$	−36.3332	−1.25212
$843$	−25.7930	−0.888359
$844$	10.5050	0.361596
$845$	0.219942	0.00756625
$846$	8.52336	0.293039
$847$	−20.7727	−0.713760
$848$	0.317810	0.0109136
$849$	102.561	3.51987
$850$	−35.1508	−1.20566
$851$	46.9022	1.60779
$852$	7.63639	0.261618
$853$	22.6418	0.775241	0.387620	−	0.921819i	$-0.373297\pi$
$853$	22.6418	0.775241	0.387620	+	0.921819i	$0.373297\pi$
$854$	−18.7095	−0.640226
$855$	5.99110	0.204891
$856$	8.91385	0.304669
$857$	8.55754	0.292320	0.146160	−	0.989261i	$-0.453309\pi$
$857$	8.55754	0.292320	0.146160	+	0.989261i	$0.453309\pi$
$858$	17.6087	0.601151
$859$	−10.1397	−0.345962	−0.172981	−	0.984925i	$-0.555340\pi$
$859$	−10.1397	−0.345962	−0.172981	+	0.984925i	$0.555340\pi$
$860$	1.45174	0.0495040
$861$	−22.3066	−0.760207
$862$	12.1978	0.415460
$863$	0.694165	0.0236297	0.0118148	−	0.999930i	$-0.496239\pi$
$863$	0.694165	0.0236297	0.0118148	+	0.999930i	$0.496239\pi$
$864$	13.8833	0.472320
$865$	0.323592	0.0110025
$866$	16.0209	0.544413
$867$	−105.979	−3.59925
$868$	2.46391	0.0836305
$869$	−2.26649	−0.0768855
$870$	0.0975858	0.00330847
$871$	37.0205	1.25439
$872$	−17.6120	−0.596419
$873$	−7.32140	−0.247792
$874$	−39.6463	−1.34106
$875$	4.13394	0.139753
$876$	−5.40242	−0.182531
$877$	−55.6176	−1.87807	−0.939036	−	0.343820i	$-0.888279\pi$
$877$	−55.6176	−1.87807	−0.939036	+	0.343820i	$0.888279\pi$
$878$	38.9387	1.31412
$879$	15.4152	0.519940
$880$	0.269692	0.00909133
$881$	5.62108	0.189379	0.0946896	−	0.995507i	$-0.469814\pi$
$881$	5.62108	0.189379	0.0946896	+	0.995507i	$0.469814\pi$
$882$	6.80268	0.229058
$883$	24.2184	0.815014	0.407507	−	0.913202i	$-0.366398\pi$
$883$	24.2184	0.815014	0.407507	+	0.913202i	$0.366398\pi$
$884$	24.1764	0.813139
$885$	2.30803	0.0775837
$886$	−8.24725	−0.277072
$887$	42.0246	1.41105	0.705524	−	0.708686i	$-0.250712\pi$
$887$	42.0246	1.41105	0.705524	+	0.708686i	$0.250712\pi$
$888$	−18.4843	−0.620291
$889$	26.3770	0.884656
$890$	−0.0875419	−0.00293441
$891$	−36.2868	−1.21565
$892$	−4.22573	−0.141488
$893$	5.66187	0.189467
$894$	−64.4970	−2.15710
$895$	3.12499	0.104457
$896$	−2.46391	−0.0823134
$897$	−89.5548	−2.99015
$898$	−27.6400	−0.922358
$899$	−0.180529	−0.00602098
$900$	−36.3997	−1.21332
$901$	−2.24698	−0.0748577
$902$	4.51687	0.150395
$903$	68.2988	2.27284
$904$	−15.1731	−0.504649
$905$	2.60180	0.0864866
$906$	−14.7385	−0.489655
$907$	−50.4925	−1.67657	−0.838287	−	0.545229i	$-0.816443\pi$
$907$	−50.4925	−1.67657	−0.838287	+	0.545229i	$0.816443\pi$
$908$	−10.9678	−0.363979
$909$	−46.1708	−1.53139
$910$	−1.41760	−0.0469931
$911$	16.8224	0.557352	0.278676	−	0.960385i	$-0.410104\pi$
$911$	16.8224	0.557352	0.278676	+	0.960385i	$0.410104\pi$
$912$	15.6247	0.517385
$913$	6.10578	0.202072
$914$	16.7902	0.555370
$915$	4.10466	0.135696
$916$	9.27396	0.306420
$917$	−49.5234	−1.63541
$918$	−98.1578	−3.23969
$919$	0.439662	0.0145031	0.00725156	−	0.999974i	$-0.497692\pi$
$919$	0.439662	0.0145031	0.00725156	+	0.999974i	$0.497692\pi$
$920$	−1.37161	−0.0452206
$921$	−27.0055	−0.889862
$922$	−39.5708	−1.30319
$923$	8.12790	0.267533
$924$	12.6880	0.417404
$925$	28.6047	0.940515
$926$	−10.0648	−0.330749
$927$	−3.98275	−0.130811
$928$	0.180529	0.00592616
$929$	20.3908	0.669000	0.334500	−	0.942396i	$-0.391433\pi$
$929$	20.3908	0.669000	0.334500	+	0.942396i	$0.391433\pi$
$930$	−0.540555	−0.0177255
$931$	4.51885	0.148099
$932$	17.8950	0.586169
$933$	−82.8213	−2.71145
$934$	26.8066	0.877139
$935$	−1.90678	−0.0623583
$936$	25.0353	0.818305
$937$	59.0065	1.92766	0.963830	−	0.266519i	$-0.0858736\pi$
$937$	59.0065	1.92766	0.963830	+	0.266519i	$0.0858736\pi$
$938$	26.6752	0.870975
$939$	−34.6840	−1.13187
$940$	0.195879	0.00638886
$941$	−17.8872	−0.583105	−0.291552	−	0.956555i	$-0.594172\pi$
$941$	−17.8872	−0.583105	−0.291552	+	0.956555i	$0.594172\pi$
$942$	70.9851	2.31282
$943$	−22.9721	−0.748073
$944$	4.26975	0.138969
$945$	5.75557	0.187229
$946$	−13.8299	−0.449647
$947$	−41.3318	−1.34310	−0.671551	−	0.740958i	$-0.734372\pi$
$947$	−41.3318	−1.34310	−0.671551	+	0.740958i	$0.734372\pi$
$948$	−4.54281	−0.147544
$949$	−5.75014	−0.186657
$950$	−24.1795	−0.784485
$951$	−4.42707	−0.143558
$952$	17.4203	0.564596
$953$	−47.3464	−1.53370	−0.766850	−	0.641827i	$-0.778177\pi$
$953$	−47.3464	−1.53370	−0.766850	+	0.641827i	$0.778177\pi$
$954$	−2.32681	−0.0753333
$955$	−1.55822	−0.0504228
$956$	−10.4911	−0.339306
$957$	−0.929640	−0.0300510
$958$	−12.9915	−0.419736
$959$	−45.6112	−1.47286
$960$	0.540555	0.0174463
$961$	1.00000	0.0322581
$962$	−19.6740	−0.634315
$963$	−65.2618	−2.10303
$964$	20.1762	0.649833
$965$	−0.621810	−0.0200168
$966$	−64.5289	−2.07618
$967$	57.7767	1.85797	0.928986	−	0.370115i	$-0.120682\pi$
$967$	57.7767	1.85797	0.928986	+	0.370115i	$0.120682\pi$
$968$	8.43081	0.270976
$969$	−110.470	−3.54880
$970$	−0.168256	−0.00540237
$971$	19.8950	0.638462	0.319231	−	0.947677i	$-0.396575\pi$
$971$	19.8950	0.638462	0.319231	+	0.947677i	$0.396575\pi$
$972$	−31.0811	−0.996926
$973$	40.4556	1.29695
$974$	−0.249983	−0.00800998
$975$	−54.6176	−1.74916
$976$	7.59343	0.243060
$977$	−24.2832	−0.776887	−0.388444	−	0.921472i	$-0.626987\pi$
$977$	−24.2832	−0.776887	−0.388444	+	0.921472i	$0.626987\pi$
$978$	55.8368	1.78546
$979$	0.833958	0.0266534
$980$	0.156335	0.00499394
$981$	128.945	4.11689
$982$	10.4225	0.332594
$983$	52.5059	1.67468	0.837340	−	0.546683i	$-0.184110\pi$
$983$	52.5059	1.67468	0.837340	+	0.546683i	$0.184110\pi$
$984$	9.05334	0.288610
$985$	1.06171	0.0338290
$986$	−1.27638	−0.0406481
$987$	9.21534	0.293327
$988$	16.6304	0.529082
$989$	70.3363	2.23656
$990$	−1.97452	−0.0627545
$991$	7.82502	0.248570	0.124285	−	0.992247i	$-0.460336\pi$
$991$	7.82502	0.248570	0.124285	+	0.992247i	$0.460336\pi$
$992$	−1.00000	−0.0317500
$993$	86.7743	2.75370
$994$	5.85658	0.185759
$995$	−1.23988	−0.0393069
$996$	12.2380	0.387777
$997$	29.2442	0.926173	0.463087	−	0.886313i	$-0.346742\pi$
$997$	29.2442	0.926173	0.463087	+	0.886313i	$0.346742\pi$
$998$	−14.2079	−0.449742
$999$	79.8778	2.52722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.l.1.3	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.l.1.3	✓	38	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.21269 q^{3} +1.00000 q^{4} -0.168256 q^{5} +3.21269 q^{6} +2.46391 q^{7} -1.00000 q^{8} +7.32140 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.21269 q^{3} +1.00000 q^{4} -0.168256 q^{5} +3.21269 q^{6} +2.46391 q^{7} -1.00000 q^{8} +7.32140 q^{9} +0.168256 q^{10} -1.60287 q^{11} -3.21269 q^{12} -3.41948 q^{13} -2.46391 q^{14} +0.540555 q^{15} +1.00000 q^{16} -7.07020 q^{17} -7.32140 q^{18} -4.86343 q^{19} -0.168256 q^{20} -7.91578 q^{21} +1.60287 q^{22} -8.15193 q^{23} +3.21269 q^{24} -4.97169 q^{25} +3.41948 q^{26} -13.8833 q^{27} +2.46391 q^{28} -0.180529 q^{29} -0.540555 q^{30} +1.00000 q^{31} -1.00000 q^{32} +5.14953 q^{33} +7.07020 q^{34} -0.414567 q^{35} +7.32140 q^{36} -5.75351 q^{37} +4.86343 q^{38} +10.9857 q^{39} +0.168256 q^{40} +2.81799 q^{41} +7.91578 q^{42} -8.62818 q^{43} -1.60287 q^{44} -1.23187 q^{45} +8.15193 q^{46} -1.16417 q^{47} -3.21269 q^{48} -0.929150 q^{49} +4.97169 q^{50} +22.7144 q^{51} -3.41948 q^{52} +0.317810 q^{53} +13.8833 q^{54} +0.269692 q^{55} -2.46391 q^{56} +15.6247 q^{57} +0.180529 q^{58} +4.26975 q^{59} +0.540555 q^{60} +7.59343 q^{61} -1.00000 q^{62} +18.0393 q^{63} +1.00000 q^{64} +0.575347 q^{65} -5.14953 q^{66} -10.8264 q^{67} -7.07020 q^{68} +26.1896 q^{69} +0.414567 q^{70} -2.37694 q^{71} -7.32140 q^{72} +1.68159 q^{73} +5.75351 q^{74} +15.9725 q^{75} -4.86343 q^{76} -3.94933 q^{77} -10.9857 q^{78} +1.41402 q^{79} -0.168256 q^{80} +22.6386 q^{81} -2.81799 q^{82} -3.80928 q^{83} -7.91578 q^{84} +1.18960 q^{85} +8.62818 q^{86} +0.579985 q^{87} +1.60287 q^{88} -0.520290 q^{89} +1.23187 q^{90} -8.42528 q^{91} -8.15193 q^{92} -3.21269 q^{93} +1.16417 q^{94} +0.818300 q^{95} +3.21269 q^{96} -1.00000 q^{97} +0.929150 q^{98} -11.7352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * q^99

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