LMFDB - Embedded newform 6018.2.a.y.1.7

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 33x^{8} + 53x^{7} + 356x^{6} - 433x^{5} - 1296x^{4} + 1135x^{3} + 930x^{2} - 186x - 104 $ x^10 - 2x^9 - 33x^8 + 53x^7 + 356x^6 - 433x^5 - 1296x^4 + 1135x^3 + 930x^2 - 186*x - 104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.556815$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.556815 q^{5} -1.00000 q^{6} +0.727556 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.556815 q^{5} -1.00000 q^{6} +0.727556 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.556815 q^{10} +4.53073 q^{11} +1.00000 q^{12} -2.52269 q^{13} -0.727556 q^{14} +0.556815 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -7.07185 q^{19} +0.556815 q^{20} +0.727556 q^{21} -4.53073 q^{22} -0.184722 q^{23} -1.00000 q^{24} -4.68996 q^{25} +2.52269 q^{26} +1.00000 q^{27} +0.727556 q^{28} -8.45781 q^{29} -0.556815 q^{30} +3.98591 q^{31} -1.00000 q^{32} +4.53073 q^{33} +1.00000 q^{34} +0.405114 q^{35} +1.00000 q^{36} +1.09215 q^{37} +7.07185 q^{38} -2.52269 q^{39} -0.556815 q^{40} -4.34727 q^{41} -0.727556 q^{42} +2.87701 q^{43} +4.53073 q^{44} +0.556815 q^{45} +0.184722 q^{46} +3.17173 q^{47} +1.00000 q^{48} -6.47066 q^{49} +4.68996 q^{50} -1.00000 q^{51} -2.52269 q^{52} -11.9287 q^{53} -1.00000 q^{54} +2.52277 q^{55} -0.727556 q^{56} -7.07185 q^{57} +8.45781 q^{58} +1.00000 q^{59} +0.556815 q^{60} -15.1576 q^{61} -3.98591 q^{62} +0.727556 q^{63} +1.00000 q^{64} -1.40467 q^{65} -4.53073 q^{66} +3.20865 q^{67} -1.00000 q^{68} -0.184722 q^{69} -0.405114 q^{70} +3.53239 q^{71} -1.00000 q^{72} -12.2252 q^{73} -1.09215 q^{74} -4.68996 q^{75} -7.07185 q^{76} +3.29636 q^{77} +2.52269 q^{78} -6.38902 q^{79} +0.556815 q^{80} +1.00000 q^{81} +4.34727 q^{82} -12.2390 q^{83} +0.727556 q^{84} -0.556815 q^{85} -2.87701 q^{86} -8.45781 q^{87} -4.53073 q^{88} -14.3230 q^{89} -0.556815 q^{90} -1.83540 q^{91} -0.184722 q^{92} +3.98591 q^{93} -3.17173 q^{94} -3.93771 q^{95} -1.00000 q^{96} +8.31606 q^{97} +6.47066 q^{98} +4.53073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * 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
$5$	0.556815	0.249015	0.124508	−	0.992219i	$-0.460265\pi$
$5$	0.556815	0.249015	0.124508	+	0.992219i	$0.460265\pi$
$6$	−1.00000	−0.408248
$7$	0.727556	0.274990	0.137495	−	0.990502i	$-0.456095\pi$
$7$	0.727556	0.274990	0.137495	+	0.990502i	$0.456095\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.556815	−0.176080
$11$	4.53073	1.36607	0.683033	−	0.730388i	$-0.260661\pi$
$11$	4.53073	1.36607	0.683033	+	0.730388i	$0.260661\pi$
$12$	1.00000	0.288675
$13$	−2.52269	−0.699669	−0.349835	−	0.936812i	$-0.613762\pi$
$13$	−2.52269	−0.699669	−0.349835	+	0.936812i	$0.613762\pi$
$14$	−0.727556	−0.194448
$15$	0.556815	0.143769
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−7.07185	−1.62239	−0.811196	−	0.584774i	$-0.801183\pi$
$19$	−7.07185	−1.62239	−0.811196	+	0.584774i	$0.801183\pi$
$20$	0.556815	0.124508
$21$	0.727556	0.158766
$22$	−4.53073	−0.965954
$23$	−0.184722	−0.0385172	−0.0192586	−	0.999815i	$-0.506131\pi$
$23$	−0.184722	−0.0385172	−0.0192586	+	0.999815i	$0.506131\pi$
$24$	−1.00000	−0.204124
$25$	−4.68996	−0.937991
$26$	2.52269	0.494741
$27$	1.00000	0.192450
$28$	0.727556	0.137495
$29$	−8.45781	−1.57058	−0.785288	−	0.619130i	$-0.787485\pi$
$29$	−8.45781	−1.57058	−0.785288	+	0.619130i	$0.787485\pi$
$30$	−0.556815	−0.101660
$31$	3.98591	0.715891	0.357946	−	0.933742i	$-0.383477\pi$
$31$	3.98591	0.715891	0.357946	+	0.933742i	$0.383477\pi$
$32$	−1.00000	−0.176777
$33$	4.53073	0.788698
$34$	1.00000	0.171499
$35$	0.405114	0.0684768
$36$	1.00000	0.166667
$37$	1.09215	0.179548	0.0897741	−	0.995962i	$-0.471385\pi$
$37$	1.09215	0.179548	0.0897741	+	0.995962i	$0.471385\pi$
$38$	7.07185	1.14720
$39$	−2.52269	−0.403954
$40$	−0.556815	−0.0880401
$41$	−4.34727	−0.678929	−0.339465	−	0.940619i	$-0.610246\pi$
$41$	−4.34727	−0.678929	−0.339465	+	0.940619i	$0.610246\pi$
$42$	−0.727556	−0.112264
$43$	2.87701	0.438740	0.219370	−	0.975642i	$-0.429600\pi$
$43$	2.87701	0.438740	0.219370	+	0.975642i	$0.429600\pi$
$44$	4.53073	0.683033
$45$	0.556815	0.0830050
$46$	0.184722	0.0272358
$47$	3.17173	0.462644	0.231322	−	0.972877i	$-0.425695\pi$
$47$	3.17173	0.462644	0.231322	+	0.972877i	$0.425695\pi$
$48$	1.00000	0.144338
$49$	−6.47066	−0.924380
$50$	4.68996	0.663260
$51$	−1.00000	−0.140028
$52$	−2.52269	−0.349835
$53$	−11.9287	−1.63854	−0.819269	−	0.573409i	$-0.805621\pi$
$53$	−11.9287	−1.63854	−0.819269	+	0.573409i	$0.805621\pi$
$54$	−1.00000	−0.136083
$55$	2.52277	0.340171
$56$	−0.727556	−0.0972238
$57$	−7.07185	−0.936689
$58$	8.45781	1.11057
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0.556815	0.0718845
$61$	−15.1576	−1.94073	−0.970363	−	0.241653i	$-0.922311\pi$
$61$	−15.1576	−1.94073	−0.970363	+	0.241653i	$0.922311\pi$
$62$	−3.98591	−0.506212
$63$	0.727556	0.0916635
$64$	1.00000	0.125000
$65$	−1.40467	−0.174228
$66$	−4.53073	−0.557694
$67$	3.20865	0.391998	0.195999	−	0.980604i	$-0.437205\pi$
$67$	3.20865	0.391998	0.195999	+	0.980604i	$0.437205\pi$
$68$	−1.00000	−0.121268
$69$	−0.184722	−0.0222379
$70$	−0.405114	−0.0484204
$71$	3.53239	0.419217	0.209609	−	0.977785i	$-0.432781\pi$
$71$	3.53239	0.419217	0.209609	+	0.977785i	$0.432781\pi$
$72$	−1.00000	−0.117851
$73$	−12.2252	−1.43085	−0.715423	−	0.698691i	$-0.753766\pi$
$73$	−12.2252	−1.43085	−0.715423	+	0.698691i	$0.753766\pi$
$74$	−1.09215	−0.126960
$75$	−4.68996	−0.541550
$76$	−7.07185	−0.811196
$77$	3.29636	0.375655
$78$	2.52269	0.285639
$79$	−6.38902	−0.718821	−0.359410	−	0.933180i	$-0.617022\pi$
$79$	−6.38902	−0.718821	−0.359410	+	0.933180i	$0.617022\pi$
$80$	0.556815	0.0622538
$81$	1.00000	0.111111
$82$	4.34727	0.480075
$83$	−12.2390	−1.34341	−0.671704	−	0.740820i	$-0.734437\pi$
$83$	−12.2390	−1.34341	−0.671704	+	0.740820i	$0.734437\pi$
$84$	0.727556	0.0793829
$85$	−0.556815	−0.0603950
$86$	−2.87701	−0.310236
$87$	−8.45781	−0.906773
$88$	−4.53073	−0.482977
$89$	−14.3230	−1.51823	−0.759117	−	0.650954i	$-0.774369\pi$
$89$	−14.3230	−1.51823	−0.759117	+	0.650954i	$0.774369\pi$
$90$	−0.556815	−0.0586934
$91$	−1.83540	−0.192402
$92$	−0.184722	−0.0192586
$93$	3.98591	0.413320
$94$	−3.17173	−0.327139
$95$	−3.93771	−0.404000
$96$	−1.00000	−0.102062
$97$	8.31606	0.844368	0.422184	−	0.906510i	$-0.361264\pi$
$97$	8.31606	0.844368	0.422184	+	0.906510i	$0.361264\pi$
$98$	6.47066	0.653636
$99$	4.53073	0.455355
$100$	−4.68996	−0.468996
$101$	6.06297	0.603288	0.301644	−	0.953421i	$-0.402465\pi$
$101$	6.06297	0.603288	0.301644	+	0.953421i	$0.402465\pi$
$102$	1.00000	0.0990148
$103$	17.2773	1.70238	0.851192	−	0.524855i	$-0.175880\pi$
$103$	17.2773	1.70238	0.851192	+	0.524855i	$0.175880\pi$
$104$	2.52269	0.247370
$105$	0.405114	0.0395351
$106$	11.9287	1.15862
$107$	−11.7625	−1.13712	−0.568560	−	0.822642i	$-0.692499\pi$
$107$	−11.7625	−1.13712	−0.568560	+	0.822642i	$0.692499\pi$
$108$	1.00000	0.0962250
$109$	5.36322	0.513703	0.256852	−	0.966451i	$-0.417315\pi$
$109$	5.36322	0.513703	0.256852	+	0.966451i	$0.417315\pi$
$110$	−2.52277	−0.240537
$111$	1.09215	0.103662
$112$	0.727556	0.0687476
$113$	−4.36168	−0.410313	−0.205156	−	0.978729i	$-0.565770\pi$
$113$	−4.36168	−0.410313	−0.205156	+	0.978729i	$0.565770\pi$
$114$	7.07185	0.662339
$115$	−0.102856	−0.00959136
$116$	−8.45781	−0.785288
$117$	−2.52269	−0.233223
$118$	−1.00000	−0.0920575
$119$	−0.727556	−0.0666950
$120$	−0.556815	−0.0508300
$121$	9.52748	0.866135
$122$	15.1576	1.37230
$123$	−4.34727	−0.391980
$124$	3.98591	0.357946
$125$	−5.39551	−0.482589
$126$	−0.727556	−0.0648159
$127$	9.35619	0.830228	0.415114	−	0.909769i	$-0.363742\pi$
$127$	9.35619	0.830228	0.415114	+	0.909769i	$0.363742\pi$
$128$	−1.00000	−0.0883883
$129$	2.87701	0.253307
$130$	1.40467	0.123198
$131$	20.2038	1.76521	0.882605	−	0.470115i	$-0.155787\pi$
$131$	20.2038	1.76521	0.882605	+	0.470115i	$0.155787\pi$
$132$	4.53073	0.394349
$133$	−5.14517	−0.446142
$134$	−3.20865	−0.277185
$135$	0.556815	0.0479230
$136$	1.00000	0.0857493
$137$	6.34305	0.541923	0.270962	−	0.962590i	$-0.412658\pi$
$137$	6.34305	0.541923	0.270962	+	0.962590i	$0.412658\pi$
$138$	0.184722	0.0157246
$139$	7.39186	0.626970	0.313485	−	0.949593i	$-0.398504\pi$
$139$	7.39186	0.626970	0.313485	+	0.949593i	$0.398504\pi$
$140$	0.405114	0.0342384
$141$	3.17173	0.267108
$142$	−3.53239	−0.296431
$143$	−11.4296	−0.955794
$144$	1.00000	0.0833333
$145$	−4.70943	−0.391097
$146$	12.2252	1.01176
$147$	−6.47066	−0.533691
$148$	1.09215	0.0897741
$149$	−8.91020	−0.729952	−0.364976	−	0.931017i	$-0.618923\pi$
$149$	−8.91020	−0.729952	−0.364976	+	0.931017i	$0.618923\pi$
$150$	4.68996	0.382933
$151$	−16.1476	−1.31408	−0.657038	−	0.753858i	$-0.728191\pi$
$151$	−16.1476	−1.31408	−0.657038	+	0.753858i	$0.728191\pi$
$152$	7.07185	0.573602
$153$	−1.00000	−0.0808452
$154$	−3.29636	−0.265628
$155$	2.21942	0.178268
$156$	−2.52269	−0.201977
$157$	3.17083	0.253060	0.126530	−	0.991963i	$-0.459616\pi$
$157$	3.17083	0.253060	0.126530	+	0.991963i	$0.459616\pi$
$158$	6.38902	0.508283
$159$	−11.9287	−0.946011
$160$	−0.556815	−0.0440201
$161$	−0.134396	−0.0105919
$162$	−1.00000	−0.0785674
$163$	2.80623	0.219801	0.109901	−	0.993943i	$-0.464947\pi$
$163$	2.80623	0.219801	0.109901	+	0.993943i	$0.464947\pi$
$164$	−4.34727	−0.339465
$165$	2.52277	0.196398
$166$	12.2390	0.949933
$167$	−23.2163	−1.79653	−0.898267	−	0.439450i	$-0.855174\pi$
$167$	−23.2163	−1.79653	−0.898267	+	0.439450i	$0.855174\pi$
$168$	−0.727556	−0.0561322
$169$	−6.63602	−0.510463
$170$	0.556815	0.0427057
$171$	−7.07185	−0.540798
$172$	2.87701	0.219370
$173$	6.57794	0.500112	0.250056	−	0.968231i	$-0.419551\pi$
$173$	6.57794	0.500112	0.250056	+	0.968231i	$0.419551\pi$
$174$	8.45781	0.641185
$175$	−3.41221	−0.257939
$176$	4.53073	0.341516
$177$	1.00000	0.0751646
$178$	14.3230	1.07355
$179$	19.0412	1.42321	0.711603	−	0.702582i	$-0.247969\pi$
$179$	19.0412	1.42321	0.711603	+	0.702582i	$0.247969\pi$
$180$	0.556815	0.0415025
$181$	9.19753	0.683647	0.341824	−	0.939764i	$-0.388955\pi$
$181$	9.19753	0.683647	0.341824	+	0.939764i	$0.388955\pi$
$182$	1.83540	0.136049
$183$	−15.1576	−1.12048
$184$	0.184722	0.0136179
$185$	0.608125	0.0447102
$186$	−3.98591	−0.292261
$187$	−4.53073	−0.331320
$188$	3.17173	0.231322
$189$	0.727556	0.0529219
$190$	3.93771	0.285671
$191$	−9.74626	−0.705215	−0.352607	−	0.935771i	$-0.614705\pi$
$191$	−9.74626	−0.705215	−0.352607	+	0.935771i	$0.614705\pi$
$192$	1.00000	0.0721688
$193$	10.5626	0.760312	0.380156	−	0.924922i	$-0.375870\pi$
$193$	10.5626	0.760312	0.380156	+	0.924922i	$0.375870\pi$
$194$	−8.31606	−0.597059
$195$	−1.40467	−0.100591
$196$	−6.47066	−0.462190
$197$	14.7874	1.05356	0.526780	−	0.850002i	$-0.323399\pi$
$197$	14.7874	1.05356	0.526780	+	0.850002i	$0.323399\pi$
$198$	−4.53073	−0.321985
$199$	14.8207	1.05061	0.525305	−	0.850914i	$-0.323951\pi$
$199$	14.8207	1.05061	0.525305	+	0.850914i	$0.323951\pi$
$200$	4.68996	0.331630
$201$	3.20865	0.226320
$202$	−6.06297	−0.426589
$203$	−6.15354	−0.431894
$204$	−1.00000	−0.0700140
$205$	−2.42062	−0.169064
$206$	−17.2773	−1.20377
$207$	−0.184722	−0.0128391
$208$	−2.52269	−0.174917
$209$	−32.0406	−2.21629
$210$	−0.405114	−0.0279555
$211$	−10.2870	−0.708185	−0.354092	−	0.935210i	$-0.615210\pi$
$211$	−10.2870	−0.708185	−0.354092	+	0.935210i	$0.615210\pi$
$212$	−11.9287	−0.819269
$213$	3.53239	0.242035
$214$	11.7625	0.804066
$215$	1.60196	0.109253
$216$	−1.00000	−0.0680414
$217$	2.89998	0.196863
$218$	−5.36322	−0.363243
$219$	−12.2252	−0.826100
$220$	2.52277	0.170085
$221$	2.52269	0.169695
$222$	−1.09215	−0.0733002
$223$	18.1422	1.21489	0.607447	−	0.794360i	$-0.292194\pi$
$223$	18.1422	1.21489	0.607447	+	0.794360i	$0.292194\pi$
$224$	−0.727556	−0.0486119
$225$	−4.68996	−0.312664
$226$	4.36168	0.290135
$227$	1.83958	0.122097	0.0610485	−	0.998135i	$-0.480556\pi$
$227$	1.83958	0.122097	0.0610485	+	0.998135i	$0.480556\pi$
$228$	−7.07185	−0.468344
$229$	−2.39025	−0.157952	−0.0789760	−	0.996877i	$-0.525165\pi$
$229$	−2.39025	−0.157952	−0.0789760	+	0.996877i	$0.525165\pi$
$230$	0.102856	0.00678211
$231$	3.29636	0.216884
$232$	8.45781	0.555283
$233$	13.5052	0.884756	0.442378	−	0.896829i	$-0.354135\pi$
$233$	13.5052	0.884756	0.442378	+	0.896829i	$0.354135\pi$
$234$	2.52269	0.164914
$235$	1.76606	0.115205
$236$	1.00000	0.0650945
$237$	−6.38902	−0.415011
$238$	0.727556	0.0471605
$239$	−28.3102	−1.83124	−0.915618	−	0.402049i	$-0.868298\pi$
$239$	−28.3102	−1.83124	−0.915618	+	0.402049i	$0.868298\pi$
$240$	0.556815	0.0359422
$241$	18.4711	1.18983	0.594915	−	0.803789i	$-0.297186\pi$
$241$	18.4711	1.18983	0.594915	+	0.803789i	$0.297186\pi$
$242$	−9.52748	−0.612450
$243$	1.00000	0.0641500
$244$	−15.1576	−0.970363
$245$	−3.60296	−0.230185
$246$	4.34727	0.277172
$247$	17.8401	1.13514
$248$	−3.98591	−0.253106
$249$	−12.2390	−0.775617
$250$	5.39551	0.341242
$251$	−4.08294	−0.257713	−0.128857	−	0.991663i	$-0.541131\pi$
$251$	−4.08294	−0.257713	−0.128857	+	0.991663i	$0.541131\pi$
$252$	0.727556	0.0458317
$253$	−0.836924	−0.0526170
$254$	−9.35619	−0.587060
$255$	−0.556815	−0.0348691
$256$	1.00000	0.0625000
$257$	−24.7228	−1.54217	−0.771084	−	0.636734i	$-0.780285\pi$
$257$	−24.7228	−1.54217	−0.771084	+	0.636734i	$0.780285\pi$
$258$	−2.87701	−0.179115
$259$	0.794600	0.0493740
$260$	−1.40467	−0.0871141
$261$	−8.45781	−0.523526
$262$	−20.2038	−1.24819
$263$	−28.5865	−1.76272	−0.881361	−	0.472444i	$-0.843372\pi$
$263$	−28.5865	−1.76272	−0.881361	+	0.472444i	$0.843372\pi$
$264$	−4.53073	−0.278847
$265$	−6.64210	−0.408021
$266$	5.14517	0.315470
$267$	−14.3230	−0.876553
$268$	3.20865	0.195999
$269$	−2.43595	−0.148523	−0.0742614	−	0.997239i	$-0.523660\pi$
$269$	−2.43595	−0.148523	−0.0742614	+	0.997239i	$0.523660\pi$
$270$	−0.556815	−0.0338867
$271$	20.1234	1.22241	0.611206	−	0.791472i	$-0.290685\pi$
$271$	20.1234	1.22241	0.611206	+	0.791472i	$0.290685\pi$
$272$	−1.00000	−0.0606339
$273$	−1.83540	−0.111084
$274$	−6.34305	−0.383198
$275$	−21.2489	−1.28136
$276$	−0.184722	−0.0111190
$277$	5.30586	0.318798	0.159399	−	0.987214i	$-0.449044\pi$
$277$	5.30586	0.318798	0.159399	+	0.987214i	$0.449044\pi$
$278$	−7.39186	−0.443335
$279$	3.98591	0.238630
$280$	−0.405114	−0.0242102
$281$	3.68578	0.219875	0.109938	−	0.993938i	$-0.464935\pi$
$281$	3.68578	0.219875	0.109938	+	0.993938i	$0.464935\pi$
$282$	−3.17173	−0.188874
$283$	12.2697	0.729359	0.364680	−	0.931133i	$-0.381178\pi$
$283$	12.2697	0.729359	0.364680	+	0.931133i	$0.381178\pi$
$284$	3.53239	0.209609
$285$	−3.93771	−0.233250
$286$	11.4296	0.675848
$287$	−3.16288	−0.186699
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	4.70943	0.276548
$291$	8.31606	0.487496
$292$	−12.2252	−0.715423
$293$	−2.57594	−0.150488	−0.0752439	−	0.997165i	$-0.523974\pi$
$293$	−2.57594	−0.150488	−0.0752439	+	0.997165i	$0.523974\pi$
$294$	6.47066	0.377377
$295$	0.556815	0.0324190
$296$	−1.09215	−0.0634799
$297$	4.53073	0.262899
$298$	8.91020	0.516154
$299$	0.465997	0.0269493
$300$	−4.68996	−0.270775
$301$	2.09319	0.120649
$302$	16.1476	0.929192
$303$	6.06297	0.348309
$304$	−7.07185	−0.405598
$305$	−8.43995	−0.483270
$306$	1.00000	0.0571662
$307$	8.68684	0.495784	0.247892	−	0.968788i	$-0.420262\pi$
$307$	8.68684	0.495784	0.247892	+	0.968788i	$0.420262\pi$
$308$	3.29636	0.187827
$309$	17.2773	0.982872
$310$	−2.21942	−0.126054
$311$	8.99505	0.510063	0.255031	−	0.966933i	$-0.417914\pi$
$311$	8.99505	0.510063	0.255031	+	0.966933i	$0.417914\pi$
$312$	2.52269	0.142819
$313$	−10.0722	−0.569315	−0.284657	−	0.958629i	$-0.591880\pi$
$313$	−10.0722	−0.569315	−0.284657	+	0.958629i	$0.591880\pi$
$314$	−3.17083	−0.178940
$315$	0.405114	0.0228256
$316$	−6.38902	−0.359410
$317$	−16.3971	−0.920954	−0.460477	−	0.887672i	$-0.652322\pi$
$317$	−16.3971	−0.920954	−0.460477	+	0.887672i	$0.652322\pi$
$318$	11.9287	0.668931
$319$	−38.3200	−2.14551
$320$	0.556815	0.0311269
$321$	−11.7625	−0.656517
$322$	0.134396	0.00748957
$323$	7.07185	0.393488
$324$	1.00000	0.0555556
$325$	11.8313	0.656284
$326$	−2.80623	−0.155423
$327$	5.36322	0.296587
$328$	4.34727	0.240038
$329$	2.30761	0.127223
$330$	−2.52277	−0.138874
$331$	7.11007	0.390805	0.195402	−	0.980723i	$-0.437399\pi$
$331$	7.11007	0.390805	0.195402	+	0.980723i	$0.437399\pi$
$332$	−12.2390	−0.671704
$333$	1.09215	0.0598494
$334$	23.2163	1.27034
$335$	1.78662	0.0976135
$336$	0.727556	0.0396915
$337$	3.44704	0.187772	0.0938862	−	0.995583i	$-0.470071\pi$
$337$	3.44704	0.187772	0.0938862	+	0.995583i	$0.470071\pi$
$338$	6.63602	0.360952
$339$	−4.36168	−0.236894
$340$	−0.556815	−0.0301975
$341$	18.0591	0.977955
$342$	7.07185	0.382402
$343$	−9.80067	−0.529186
$344$	−2.87701	−0.155118
$345$	−0.102856	−0.00553757
$346$	−6.57794	−0.353632
$347$	−0.159048	−0.00853813	−0.00426906	−	0.999991i	$-0.501359\pi$
$347$	−0.159048	−0.00853813	−0.00426906	+	0.999991i	$0.501359\pi$
$348$	−8.45781	−0.453386
$349$	−5.25727	−0.281415	−0.140708	−	0.990051i	$-0.544938\pi$
$349$	−5.25727	−0.281415	−0.140708	+	0.990051i	$0.544938\pi$
$350$	3.41221	0.182390
$351$	−2.52269	−0.134651
$352$	−4.53073	−0.241489
$353$	−20.1464	−1.07229	−0.536143	−	0.844127i	$-0.680119\pi$
$353$	−20.1464	−1.07229	−0.536143	+	0.844127i	$0.680119\pi$
$354$	−1.00000	−0.0531494
$355$	1.96688	0.104391
$356$	−14.3230	−0.759117
$357$	−0.727556	−0.0385064
$358$	−19.0412	−1.00636
$359$	3.01999	0.159389	0.0796944	−	0.996819i	$-0.474606\pi$
$359$	3.01999	0.159389	0.0796944	+	0.996819i	$0.474606\pi$
$360$	−0.556815	−0.0293467
$361$	31.0110	1.63216
$362$	−9.19753	−0.483412
$363$	9.52748	0.500063
$364$	−1.83540	−0.0962012
$365$	−6.80715	−0.356302
$366$	15.1576	0.792298
$367$	29.5906	1.54462	0.772310	−	0.635246i	$-0.219101\pi$
$367$	29.5906	1.54462	0.772310	+	0.635246i	$0.219101\pi$
$368$	−0.184722	−0.00962930
$369$	−4.34727	−0.226310
$370$	−0.608125	−0.0316149
$371$	−8.67883	−0.450583
$372$	3.98591	0.206660
$373$	−18.9667	−0.982058	−0.491029	−	0.871143i	$-0.663379\pi$
$373$	−18.9667	−0.982058	−0.491029	+	0.871143i	$0.663379\pi$
$374$	4.53073	0.234278
$375$	−5.39551	−0.278623
$376$	−3.17173	−0.163569
$377$	21.3365	1.09888
$378$	−0.727556	−0.0374215
$379$	15.0100	0.771010	0.385505	−	0.922706i	$-0.374027\pi$
$379$	15.0100	0.771010	0.385505	+	0.922706i	$0.374027\pi$
$380$	−3.93771	−0.202000
$381$	9.35619	0.479332
$382$	9.74626	0.498662
$383$	−23.9175	−1.22213	−0.611064	−	0.791581i	$-0.709258\pi$
$383$	−23.9175	−1.22213	−0.611064	+	0.791581i	$0.709258\pi$
$384$	−1.00000	−0.0510310
$385$	1.83546	0.0935437
$386$	−10.5626	−0.537622
$387$	2.87701	0.146247
$388$	8.31606	0.422184
$389$	14.3949	0.729850	0.364925	−	0.931037i	$-0.381095\pi$
$389$	14.3949	0.729850	0.364925	+	0.931037i	$0.381095\pi$
$390$	1.40467	0.0711283
$391$	0.184722	0.00934179
$392$	6.47066	0.326818
$393$	20.2038	1.01914
$394$	−14.7874	−0.744979
$395$	−3.55750	−0.178997
$396$	4.53073	0.227678
$397$	−6.29385	−0.315879	−0.157940	−	0.987449i	$-0.550485\pi$
$397$	−6.29385	−0.315879	−0.157940	+	0.987449i	$0.550485\pi$
$398$	−14.8207	−0.742893
$399$	−5.14517	−0.257580
$400$	−4.68996	−0.234498
$401$	30.8031	1.53823	0.769116	−	0.639109i	$-0.220697\pi$
$401$	30.8031	1.53823	0.769116	+	0.639109i	$0.220697\pi$
$402$	−3.20865	−0.160033
$403$	−10.0552	−0.500887
$404$	6.06297	0.301644
$405$	0.556815	0.0276683
$406$	6.15354	0.305395
$407$	4.94823	0.245275
$408$	1.00000	0.0495074
$409$	−31.8845	−1.57659	−0.788293	−	0.615300i	$-0.789035\pi$
$409$	−31.8845	−1.57659	−0.788293	+	0.615300i	$0.789035\pi$
$410$	2.42062	0.119546
$411$	6.34305	0.312880
$412$	17.2773	0.851192
$413$	0.727556	0.0358007
$414$	0.184722	0.00907859
$415$	−6.81487	−0.334529
$416$	2.52269	0.123685
$417$	7.39186	0.361981
$418$	32.0406	1.56716
$419$	6.97628	0.340814	0.170407	−	0.985374i	$-0.445492\pi$
$419$	6.97628	0.340814	0.170407	+	0.985374i	$0.445492\pi$
$420$	0.405114	0.0197675
$421$	10.4242	0.508043	0.254021	−	0.967199i	$-0.418247\pi$
$421$	10.4242	0.508043	0.254021	+	0.967199i	$0.418247\pi$
$422$	10.2870	0.500762
$423$	3.17173	0.154215
$424$	11.9287	0.579311
$425$	4.68996	0.227496
$426$	−3.53239	−0.171145
$427$	−11.0280	−0.533681
$428$	−11.7625	−0.568560
$429$	−11.4296	−0.551828
$430$	−1.60196	−0.0772535
$431$	24.4816	1.17924	0.589618	−	0.807682i	$-0.299278\pi$
$431$	24.4816	1.17924	0.589618	+	0.807682i	$0.299278\pi$
$432$	1.00000	0.0481125
$433$	−22.7883	−1.09514	−0.547568	−	0.836761i	$-0.684446\pi$
$433$	−22.7883	−1.09514	−0.547568	+	0.836761i	$0.684446\pi$
$434$	−2.89998	−0.139203
$435$	−4.70943	−0.225800
$436$	5.36322	0.256852
$437$	1.30632	0.0624900
$438$	12.2252	0.584141
$439$	3.64730	0.174076	0.0870381	−	0.996205i	$-0.472260\pi$
$439$	3.64730	0.174076	0.0870381	+	0.996205i	$0.472260\pi$
$440$	−2.52277	−0.120269
$441$	−6.47066	−0.308127
$442$	−2.52269	−0.119992
$443$	−15.0337	−0.714274	−0.357137	−	0.934052i	$-0.616247\pi$
$443$	−15.0337	−0.714274	−0.357137	+	0.934052i	$0.616247\pi$
$444$	1.09215	0.0518311
$445$	−7.97525	−0.378063
$446$	−18.1422	−0.859060
$447$	−8.91020	−0.421438
$448$	0.727556	0.0343738
$449$	−23.6239	−1.11488	−0.557441	−	0.830217i	$-0.688217\pi$
$449$	−23.6239	−1.11488	−0.557441	+	0.830217i	$0.688217\pi$
$450$	4.68996	0.221087
$451$	−19.6963	−0.927462
$452$	−4.36168	−0.205156
$453$	−16.1476	−0.758682
$454$	−1.83958	−0.0863356
$455$	−1.02198	−0.0479111
$456$	7.07185	0.331170
$457$	−36.6981	−1.71667	−0.858333	−	0.513093i	$-0.828500\pi$
$457$	−36.6981	−1.71667	−0.858333	+	0.513093i	$0.828500\pi$
$458$	2.39025	0.111689
$459$	−1.00000	−0.0466760
$460$	−0.102856	−0.00479568
$461$	−28.3825	−1.32190	−0.660951	−	0.750429i	$-0.729847\pi$
$461$	−28.3825	−1.32190	−0.660951	+	0.750429i	$0.729847\pi$
$462$	−3.29636	−0.153360
$463$	−0.789581	−0.0366949	−0.0183475	−	0.999832i	$-0.505841\pi$
$463$	−0.789581	−0.0366949	−0.0183475	+	0.999832i	$0.505841\pi$
$464$	−8.45781	−0.392644
$465$	2.21942	0.102923
$466$	−13.5052	−0.625617
$467$	2.20236	0.101913	0.0509566	−	0.998701i	$-0.483773\pi$
$467$	2.20236	0.101913	0.0509566	+	0.998701i	$0.483773\pi$
$468$	−2.52269	−0.116612
$469$	2.33447	0.107796
$470$	−1.76606	−0.0814625
$471$	3.17083	0.146104
$472$	−1.00000	−0.0460287
$473$	13.0350	0.599348
$474$	6.38902	0.293457
$475$	33.1667	1.52179
$476$	−0.727556	−0.0333475
$477$	−11.9287	−0.546180
$478$	28.3102	1.29488
$479$	−10.5683	−0.482880	−0.241440	−	0.970416i	$-0.577620\pi$
$479$	−10.5683	−0.482880	−0.241440	+	0.970416i	$0.577620\pi$
$480$	−0.556815	−0.0254150
$481$	−2.75516	−0.125624
$482$	−18.4711	−0.841336
$483$	−0.134396	−0.00611521
$484$	9.52748	0.433067
$485$	4.63051	0.210260
$486$	−1.00000	−0.0453609
$487$	−12.1501	−0.550575	−0.275288	−	0.961362i	$-0.588773\pi$
$487$	−12.1501	−0.550575	−0.275288	+	0.961362i	$0.588773\pi$
$488$	15.1576	0.686150
$489$	2.80623	0.126902
$490$	3.60296	0.162765
$491$	34.2121	1.54397	0.771985	−	0.635641i	$-0.219264\pi$
$491$	34.2121	1.54397	0.771985	+	0.635641i	$0.219264\pi$
$492$	−4.34727	−0.195990
$493$	8.45781	0.380921
$494$	−17.8401	−0.802664
$495$	2.52277	0.113390
$496$	3.98591	0.178973
$497$	2.57001	0.115281
$498$	12.2390	0.548444
$499$	16.3962	0.733996	0.366998	−	0.930222i	$-0.380385\pi$
$499$	16.3962	0.733996	0.366998	+	0.930222i	$0.380385\pi$
$500$	−5.39551	−0.241295
$501$	−23.2163	−1.03723
$502$	4.08294	0.182231
$503$	−27.6603	−1.23331	−0.616657	−	0.787232i	$-0.711513\pi$
$503$	−27.6603	−1.23331	−0.616657	+	0.787232i	$0.711513\pi$
$504$	−0.727556	−0.0324079
$505$	3.37595	0.150228
$506$	0.836924	0.0372058
$507$	−6.63602	−0.294716
$508$	9.35619	0.415114
$509$	3.05246	0.135298	0.0676490	−	0.997709i	$-0.478450\pi$
$509$	3.05246	0.135298	0.0676490	+	0.997709i	$0.478450\pi$
$510$	0.556815	0.0246562
$511$	−8.89449	−0.393469
$512$	−1.00000	−0.0441942
$513$	−7.07185	−0.312230
$514$	24.7228	1.09048
$515$	9.62026	0.423919
$516$	2.87701	0.126653
$517$	14.3702	0.632002
$518$	−0.794600	−0.0349127
$519$	6.57794	0.288740
$520$	1.40467	0.0615989
$521$	20.0225	0.877202	0.438601	−	0.898682i	$-0.355474\pi$
$521$	20.0225	0.877202	0.438601	+	0.898682i	$0.355474\pi$
$522$	8.45781	0.370188
$523$	43.3271	1.89456	0.947281	−	0.320405i	$-0.103819\pi$
$523$	43.3271	1.89456	0.947281	+	0.320405i	$0.103819\pi$
$524$	20.2038	0.882605
$525$	−3.41221	−0.148921
$526$	28.5865	1.24643
$527$	−3.98591	−0.173629
$528$	4.53073	0.197175
$529$	−22.9659	−0.998516
$530$	6.64210	0.288514
$531$	1.00000	0.0433963
$532$	−5.14517	−0.223071
$533$	10.9668	0.475026
$534$	14.3230	0.619816
$535$	−6.54951	−0.283160
$536$	−3.20865	−0.138592
$537$	19.0412	0.821688
$538$	2.43595	0.105021
$539$	−29.3168	−1.26276
$540$	0.556815	0.0239615
$541$	5.86864	0.252313	0.126156	−	0.992010i	$-0.459736\pi$
$541$	5.86864	0.252313	0.126156	+	0.992010i	$0.459736\pi$
$542$	−20.1234	−0.864376
$543$	9.19753	0.394704
$544$	1.00000	0.0428746
$545$	2.98632	0.127920
$546$	1.83540	0.0785479
$547$	−20.0022	−0.855230	−0.427615	−	0.903961i	$-0.640646\pi$
$547$	−20.0022	−0.855230	−0.427615	+	0.903961i	$0.640646\pi$
$548$	6.34305	0.270962
$549$	−15.1576	−0.646909
$550$	21.2489	0.906057
$551$	59.8124	2.54809
$552$	0.184722	0.00786229
$553$	−4.64837	−0.197669
$554$	−5.30586	−0.225425
$555$	0.608125	0.0258134
$556$	7.39186	0.313485
$557$	−39.0434	−1.65432	−0.827162	−	0.561964i	$-0.810046\pi$
$557$	−39.0434	−1.65432	−0.827162	+	0.561964i	$0.810046\pi$
$558$	−3.98591	−0.168737
$559$	−7.25782	−0.306973
$560$	0.405114	0.0171192
$561$	−4.53073	−0.191287
$562$	−3.68578	−0.155475
$563$	−8.51830	−0.359003	−0.179502	−	0.983758i	$-0.557449\pi$
$563$	−8.51830	−0.359003	−0.179502	+	0.983758i	$0.557449\pi$
$564$	3.17173	0.133554
$565$	−2.42865	−0.102174
$566$	−12.2697	−0.515735
$567$	0.727556	0.0305545
$568$	−3.53239	−0.148216
$569$	10.4497	0.438074	0.219037	−	0.975717i	$-0.429708\pi$
$569$	10.4497	0.438074	0.219037	+	0.975717i	$0.429708\pi$
$570$	3.93771	0.164932
$571$	−1.02766	−0.0430061	−0.0215031	−	0.999769i	$-0.506845\pi$
$571$	−1.02766	−0.0430061	−0.0215031	+	0.999769i	$0.506845\pi$
$572$	−11.4296	−0.477897
$573$	−9.74626	−0.407156
$574$	3.16288	0.132016
$575$	0.866338	0.0361288
$576$	1.00000	0.0416667
$577$	−39.5656	−1.64714	−0.823569	−	0.567215i	$-0.808021\pi$
$577$	−39.5656	−1.64714	−0.823569	+	0.567215i	$0.808021\pi$
$578$	−1.00000	−0.0415945
$579$	10.5626	0.438966
$580$	−4.70943	−0.195549
$581$	−8.90458	−0.369424
$582$	−8.31606	−0.344712
$583$	−54.0459	−2.23835
$584$	12.2252	0.505881
$585$	−1.40467	−0.0580760
$586$	2.57594	0.106411
$587$	−43.1650	−1.78161	−0.890805	−	0.454387i	$-0.849858\pi$
$587$	−43.1650	−1.78161	−0.890805	+	0.454387i	$0.849858\pi$
$588$	−6.47066	−0.266846
$589$	−28.1878	−1.16146
$590$	−0.556815	−0.0229237
$591$	14.7874	0.608273
$592$	1.09215	0.0448870
$593$	15.5747	0.639578	0.319789	−	0.947489i	$-0.396388\pi$
$593$	15.5747	0.639578	0.319789	+	0.947489i	$0.396388\pi$
$594$	−4.53073	−0.185898
$595$	−0.405114	−0.0166081
$596$	−8.91020	−0.364976
$597$	14.8207	0.606570
$598$	−0.465997	−0.0190560
$599$	31.9373	1.30492	0.652462	−	0.757822i	$-0.273736\pi$
$599$	31.9373	1.30492	0.652462	+	0.757822i	$0.273736\pi$
$600$	4.68996	0.191467
$601$	11.2085	0.457203	0.228602	−	0.973520i	$-0.426585\pi$
$601$	11.2085	0.457203	0.228602	+	0.973520i	$0.426585\pi$
$602$	−2.09319	−0.0853120
$603$	3.20865	0.130666
$604$	−16.1476	−0.657038
$605$	5.30504	0.215681
$606$	−6.06297	−0.246291
$607$	21.5682	0.875425	0.437712	−	0.899115i	$-0.355789\pi$
$607$	21.5682	0.875425	0.437712	+	0.899115i	$0.355789\pi$
$608$	7.07185	0.286801
$609$	−6.15354	−0.249354
$610$	8.43995	0.341723
$611$	−8.00129	−0.323698
$612$	−1.00000	−0.0404226
$613$	−13.7089	−0.553698	−0.276849	−	0.960913i	$-0.589290\pi$
$613$	−13.7089	−0.553698	−0.276849	+	0.960913i	$0.589290\pi$
$614$	−8.68684	−0.350572
$615$	−2.42062	−0.0976089
$616$	−3.29636	−0.132814
$617$	−2.28828	−0.0921228	−0.0460614	−	0.998939i	$-0.514667\pi$
$617$	−2.28828	−0.0921228	−0.0460614	+	0.998939i	$0.514667\pi$
$618$	−17.2773	−0.694995
$619$	6.13229	0.246477	0.123239	−	0.992377i	$-0.460672\pi$
$619$	6.13229	0.246477	0.123239	+	0.992377i	$0.460672\pi$
$620$	2.21942	0.0891339
$621$	−0.184722	−0.00741264
$622$	−8.99505	−0.360669
$623$	−10.4208	−0.417500
$624$	−2.52269	−0.100989
$625$	20.4455	0.817820
$626$	10.0722	0.402566
$627$	−32.0406	−1.27958
$628$	3.17083	0.126530
$629$	−1.09215	−0.0435468
$630$	−0.405114	−0.0161401
$631$	−41.7045	−1.66023	−0.830114	−	0.557593i	$-0.811725\pi$
$631$	−41.7045	−1.66023	−0.830114	+	0.557593i	$0.811725\pi$
$632$	6.38902	0.254141
$633$	−10.2870	−0.408871
$634$	16.3971	0.651213
$635$	5.20966	0.206739
$636$	−11.9287	−0.473005
$637$	16.3235	0.646760
$638$	38.3200	1.51710
$639$	3.53239	0.139739
$640$	−0.556815	−0.0220100
$641$	26.3236	1.03972	0.519859	−	0.854252i	$-0.325984\pi$
$641$	26.3236	1.03972	0.519859	+	0.854252i	$0.325984\pi$
$642$	11.7625	0.464228
$643$	−19.2145	−0.757747	−0.378874	−	0.925448i	$-0.623688\pi$
$643$	−19.2145	−0.757747	−0.378874	+	0.925448i	$0.623688\pi$
$644$	−0.134396	−0.00529593
$645$	1.60196	0.0630772
$646$	−7.07185	−0.278238
$647$	−15.1523	−0.595698	−0.297849	−	0.954613i	$-0.596269\pi$
$647$	−15.1523	−0.595698	−0.297849	+	0.954613i	$0.596269\pi$
$648$	−1.00000	−0.0392837
$649$	4.53073	0.177847
$650$	−11.8313	−0.464063
$651$	2.89998	0.113659
$652$	2.80623	0.109901
$653$	−15.2969	−0.598615	−0.299308	−	0.954157i	$-0.596756\pi$
$653$	−15.2969	−0.598615	−0.299308	+	0.954157i	$0.596756\pi$
$654$	−5.36322	−0.209718
$655$	11.2497	0.439564
$656$	−4.34727	−0.169732
$657$	−12.2252	−0.476949
$658$	−2.30761	−0.0899600
$659$	9.62638	0.374990	0.187495	−	0.982266i	$-0.439963\pi$
$659$	9.62638	0.374990	0.187495	+	0.982266i	$0.439963\pi$
$660$	2.52277	0.0981989
$661$	−29.3777	−1.14266	−0.571330	−	0.820720i	$-0.693572\pi$
$661$	−29.3777	−1.14266	−0.571330	+	0.820720i	$0.693572\pi$
$662$	−7.11007	−0.276341
$663$	2.52269	0.0979733
$664$	12.2390	0.474966
$665$	−2.86490	−0.111096
$666$	−1.09215	−0.0423199
$667$	1.56234	0.0604942
$668$	−23.2163	−0.898267
$669$	18.1422	0.701420
$670$	−1.78662	−0.0690232
$671$	−68.6747	−2.65116
$672$	−0.727556	−0.0280661
$673$	−5.27171	−0.203210	−0.101605	−	0.994825i	$-0.532398\pi$
$673$	−5.27171	−0.203210	−0.101605	+	0.994825i	$0.532398\pi$
$674$	−3.44704	−0.132775
$675$	−4.68996	−0.180517
$676$	−6.63602	−0.255232
$677$	−7.47823	−0.287412	−0.143706	−	0.989620i	$-0.545902\pi$
$677$	−7.47823	−0.287412	−0.143706	+	0.989620i	$0.545902\pi$
$678$	4.36168	0.167509
$679$	6.05040	0.232193
$680$	0.556815	0.0213529
$681$	1.83958	0.0704927
$682$	−18.0591	−0.691518
$683$	34.8078	1.33188	0.665941	−	0.746004i	$-0.268030\pi$
$683$	34.8078	1.33188	0.665941	+	0.746004i	$0.268030\pi$
$684$	−7.07185	−0.270399
$685$	3.53190	0.134947
$686$	9.80067	0.374191
$687$	−2.39025	−0.0911936
$688$	2.87701	0.109685
$689$	30.0925	1.14643
$690$	0.102856	0.00391566
$691$	3.79401	0.144331	0.0721655	−	0.997393i	$-0.477009\pi$
$691$	3.79401	0.144331	0.0721655	+	0.997393i	$0.477009\pi$
$692$	6.57794	0.250056
$693$	3.29636	0.125218
$694$	0.159048	0.00603737
$695$	4.11590	0.156125
$696$	8.45781	0.320593
$697$	4.34727	0.164665
$698$	5.25727	0.198991
$699$	13.5052	0.510814
$700$	−3.41221	−0.128969
$701$	−28.7902	−1.08739	−0.543696	−	0.839282i	$-0.682975\pi$
$701$	−28.7902	−1.08739	−0.543696	+	0.839282i	$0.682975\pi$
$702$	2.52269	0.0952129
$703$	−7.72351	−0.291298
$704$	4.53073	0.170758
$705$	1.76606	0.0665138
$706$	20.1464	0.758221
$707$	4.41115	0.165899
$708$	1.00000	0.0375823
$709$	31.2676	1.17428	0.587140	−	0.809486i	$-0.300254\pi$
$709$	31.2676	1.17428	0.587140	+	0.809486i	$0.300254\pi$
$710$	−1.96688	−0.0738158
$711$	−6.38902	−0.239607
$712$	14.3230	0.536777
$713$	−0.736286	−0.0275741
$714$	0.727556	0.0272281
$715$	−6.36418	−0.238007
$716$	19.0412	0.711603
$717$	−28.3102	−1.05726
$718$	−3.01999	−0.112705
$719$	−8.55997	−0.319233	−0.159616	−	0.987179i	$-0.551026\pi$
$719$	−8.55997	−0.319233	−0.159616	+	0.987179i	$0.551026\pi$
$720$	0.556815	0.0207513
$721$	12.5702	0.468139
$722$	−31.0110	−1.15411
$723$	18.4711	0.686948
$724$	9.19753	0.341824
$725$	39.6668	1.47319
$726$	−9.52748	−0.353598
$727$	−24.9322	−0.924683	−0.462342	−	0.886702i	$-0.652991\pi$
$727$	−24.9322	−0.924683	−0.462342	+	0.886702i	$0.652991\pi$
$728$	1.83540	0.0680245
$729$	1.00000	0.0370370
$730$	6.80715	0.251944
$731$	−2.87701	−0.106410
$732$	−15.1576	−0.560239
$733$	−27.5030	−1.01585	−0.507924	−	0.861402i	$-0.669587\pi$
$733$	−27.5030	−1.01585	−0.507924	+	0.861402i	$0.669587\pi$
$734$	−29.5906	−1.09221
$735$	−3.60296	−0.132897
$736$	0.184722	0.00680894
$737$	14.5375	0.535496
$738$	4.34727	0.160025
$739$	−31.2257	−1.14866	−0.574329	−	0.818625i	$-0.694737\pi$
$739$	−31.2257	−1.14866	−0.574329	+	0.818625i	$0.694737\pi$
$740$	0.608125	0.0223551
$741$	17.8401	0.655372
$742$	8.67883	0.318610
$743$	−42.0672	−1.54330	−0.771648	−	0.636050i	$-0.780567\pi$
$743$	−42.0672	−1.54330	−0.771648	+	0.636050i	$0.780567\pi$
$744$	−3.98591	−0.146131
$745$	−4.96133	−0.181769
$746$	18.9667	0.694420
$747$	−12.2390	−0.447803
$748$	−4.53073	−0.165660
$749$	−8.55786	−0.312697
$750$	5.39551	0.197016
$751$	50.4787	1.84199	0.920996	−	0.389571i	$-0.127377\pi$
$751$	50.4787	1.84199	0.920996	+	0.389571i	$0.127377\pi$
$752$	3.17173	0.115661
$753$	−4.08294	−0.148791
$754$	−21.3365	−0.777028
$755$	−8.99124	−0.327225
$756$	0.727556	0.0264610
$757$	−13.3679	−0.485866	−0.242933	−	0.970043i	$-0.578110\pi$
$757$	−13.3679	−0.485866	−0.242933	+	0.970043i	$0.578110\pi$
$758$	−15.0100	−0.545186
$759$	−0.836924	−0.0303784
$760$	3.93771	0.142836
$761$	16.4010	0.594535	0.297267	−	0.954794i	$-0.403925\pi$
$761$	16.4010	0.594535	0.297267	+	0.954794i	$0.403925\pi$
$762$	−9.35619	−0.338939
$763$	3.90204	0.141263
$764$	−9.74626	−0.352607
$765$	−0.556815	−0.0201317
$766$	23.9175	0.864175
$767$	−2.52269	−0.0910891
$768$	1.00000	0.0360844
$769$	53.8744	1.94276	0.971380	−	0.237529i	$-0.0763375\pi$
$769$	53.8744	1.94276	0.971380	+	0.237529i	$0.0763375\pi$
$770$	−1.83546	−0.0661454
$771$	−24.7228	−0.890371
$772$	10.5626	0.380156
$773$	41.6383	1.49762	0.748812	−	0.662782i	$-0.230624\pi$
$773$	41.6383	1.49762	0.748812	+	0.662782i	$0.230624\pi$
$774$	−2.87701	−0.103412
$775$	−18.6938	−0.671500
$776$	−8.31606	−0.298529
$777$	0.794600	0.0285061
$778$	−14.3949	−0.516082
$779$	30.7432	1.10149
$780$	−1.40467	−0.0502953
$781$	16.0043	0.572678
$782$	−0.184722	−0.00660564
$783$	−8.45781	−0.302258
$784$	−6.47066	−0.231095
$785$	1.76556	0.0630157
$786$	−20.2038	−0.720644
$787$	37.7304	1.34494	0.672472	−	0.740123i	$-0.265233\pi$
$787$	37.7304	1.34494	0.672472	+	0.740123i	$0.265233\pi$
$788$	14.7874	0.526780
$789$	−28.5865	−1.01771
$790$	3.55750	0.126570
$791$	−3.17337	−0.112832
$792$	−4.53073	−0.160992
$793$	38.2378	1.35787
$794$	6.29385	0.223360
$795$	−6.64210	−0.235571
$796$	14.8207	0.525305
$797$	−27.7615	−0.983365	−0.491682	−	0.870775i	$-0.663618\pi$
$797$	−27.7615	−0.983365	−0.491682	+	0.870775i	$0.663618\pi$
$798$	5.14517	0.182137
$799$	−3.17173	−0.112208
$800$	4.68996	0.165815
$801$	−14.3230	−0.506078
$802$	−30.8031	−1.08769
$803$	−55.3889	−1.95463
$804$	3.20865	0.113160
$805$	−0.0748334	−0.00263753
$806$	10.0552	0.354181
$807$	−2.43595	−0.0857497
$808$	−6.06297	−0.213295
$809$	−22.0325	−0.774621	−0.387310	−	0.921949i	$-0.626596\pi$
$809$	−22.0325	−0.774621	−0.387310	+	0.921949i	$0.626596\pi$
$810$	−0.556815	−0.0195645
$811$	−8.42903	−0.295983	−0.147992	−	0.988989i	$-0.547281\pi$
$811$	−8.42903	−0.295983	−0.147992	+	0.988989i	$0.547281\pi$
$812$	−6.15354	−0.215947
$813$	20.1234	0.705760
$814$	−4.94823	−0.173435
$815$	1.56255	0.0547338
$816$	−1.00000	−0.0350070
$817$	−20.3458	−0.711809
$818$	31.8845	1.11481
$819$	−1.83540	−0.0641341
$820$	−2.42062	−0.0845318
$821$	−14.8318	−0.517635	−0.258817	−	0.965926i	$-0.583333\pi$
$821$	−14.8318	−0.517635	−0.258817	+	0.965926i	$0.583333\pi$
$822$	−6.34305	−0.221239
$823$	−45.7402	−1.59440	−0.797202	−	0.603713i	$-0.793687\pi$
$823$	−45.7402	−1.59440	−0.797202	+	0.603713i	$0.793687\pi$
$824$	−17.2773	−0.601884
$825$	−21.2489	−0.739792
$826$	−0.727556	−0.0253149
$827$	−31.7970	−1.10569	−0.552844	−	0.833285i	$-0.686458\pi$
$827$	−31.7970	−1.10569	−0.552844	+	0.833285i	$0.686458\pi$
$828$	−0.184722	−0.00641953
$829$	0.596329	0.0207114	0.0103557	−	0.999946i	$-0.496704\pi$
$829$	0.596329	0.0207114	0.0103557	+	0.999946i	$0.496704\pi$
$830$	6.81487	0.236548
$831$	5.30586	0.184058
$832$	−2.52269	−0.0874586
$833$	6.47066	0.224195
$834$	−7.39186	−0.255959
$835$	−12.9272	−0.447364
$836$	−32.0406	−1.10815
$837$	3.98591	0.137773
$838$	−6.97628	−0.240992
$839$	18.0766	0.624072	0.312036	−	0.950070i	$-0.398989\pi$
$839$	18.0766	0.624072	0.312036	+	0.950070i	$0.398989\pi$
$840$	−0.405114	−0.0139778
$841$	42.5346	1.46671
$842$	−10.4242	−0.359240
$843$	3.68578	0.126945
$844$	−10.2870	−0.354092
$845$	−3.69503	−0.127113
$846$	−3.17173	−0.109046
$847$	6.93178	0.238179
$848$	−11.9287	−0.409635
$849$	12.2697	0.421096
$850$	−4.68996	−0.160864
$851$	−0.201744	−0.00691569
$852$	3.53239	0.121018
$853$	15.8635	0.543155	0.271578	−	0.962417i	$-0.412455\pi$
$853$	15.8635	0.543155	0.271578	+	0.962417i	$0.412455\pi$
$854$	11.0280	0.377369
$855$	−3.93771	−0.134667
$856$	11.7625	0.402033
$857$	−17.3927	−0.594125	−0.297062	−	0.954858i	$-0.596007\pi$
$857$	−17.3927	−0.594125	−0.297062	+	0.954858i	$0.596007\pi$
$858$	11.4296	0.390201
$859$	−19.8118	−0.675971	−0.337986	−	0.941151i	$-0.609746\pi$
$859$	−19.8118	−0.675971	−0.337986	+	0.941151i	$0.609746\pi$
$860$	1.60196	0.0546265
$861$	−3.16288	−0.107791
$862$	−24.4816	−0.833846
$863$	−39.4009	−1.34122	−0.670612	−	0.741809i	$-0.733968\pi$
$863$	−39.4009	−1.34122	−0.670612	+	0.741809i	$0.733968\pi$
$864$	−1.00000	−0.0340207
$865$	3.66270	0.124535
$866$	22.7883	0.774378
$867$	1.00000	0.0339618
$868$	2.89998	0.0984317
$869$	−28.9469	−0.981956
$870$	4.70943	0.159665
$871$	−8.09443	−0.274269
$872$	−5.36322	−0.181622
$873$	8.31606	0.281456
$874$	−1.30632	−0.0441871
$875$	−3.92554	−0.132707
$876$	−12.2252	−0.413050
$877$	57.8470	1.95335	0.976677	−	0.214713i	$-0.0688817\pi$
$877$	57.8470	1.95335	0.976677	+	0.214713i	$0.0688817\pi$
$878$	−3.64730	−0.123090
$879$	−2.57594	−0.0868842
$880$	2.52277	0.0850427
$881$	6.65276	0.224137	0.112069	−	0.993700i	$-0.464252\pi$
$881$	6.65276	0.224137	0.112069	+	0.993700i	$0.464252\pi$
$882$	6.47066	0.217879
$883$	4.61515	0.155312	0.0776561	−	0.996980i	$-0.475256\pi$
$883$	4.61515	0.155312	0.0776561	+	0.996980i	$0.475256\pi$
$884$	2.52269	0.0848473
$885$	0.556815	0.0187171
$886$	15.0337	0.505068
$887$	−36.5812	−1.22828	−0.614138	−	0.789198i	$-0.710496\pi$
$887$	−36.5812	−1.22828	−0.614138	+	0.789198i	$0.710496\pi$
$888$	−1.09215	−0.0366501
$889$	6.80716	0.228305
$890$	7.97525	0.267331
$891$	4.53073	0.151785
$892$	18.1422	0.607447
$893$	−22.4300	−0.750590
$894$	8.91020	0.298002
$895$	10.6024	0.354400
$896$	−0.727556	−0.0243060
$897$	0.465997	0.0155592
$898$	23.6239	0.788340
$899$	−33.7121	−1.12436
$900$	−4.68996	−0.156332
$901$	11.9287	0.397404
$902$	19.6963	0.655814
$903$	2.09319	0.0696570
$904$	4.36168	0.145067
$905$	5.12132	0.170238
$906$	16.1476	0.536469
$907$	−11.4676	−0.380775	−0.190388	−	0.981709i	$-0.560974\pi$
$907$	−11.4676	−0.380775	−0.190388	+	0.981709i	$0.560974\pi$
$908$	1.83958	0.0610485
$909$	6.06297	0.201096
$910$	1.02198	0.0338782
$911$	−8.87475	−0.294034	−0.147017	−	0.989134i	$-0.546967\pi$
$911$	−8.87475	−0.294034	−0.147017	+	0.989134i	$0.546967\pi$
$912$	−7.07185	−0.234172
$913$	−55.4517	−1.83518
$914$	36.6981	1.21387
$915$	−8.43995	−0.279016
$916$	−2.39025	−0.0789760
$917$	14.6994	0.485416
$918$	1.00000	0.0330049
$919$	−1.22425	−0.0403841	−0.0201921	−	0.999796i	$-0.506428\pi$
$919$	−1.22425	−0.0403841	−0.0201921	+	0.999796i	$0.506428\pi$
$920$	0.102856	0.00339106
$921$	8.68684	0.286241
$922$	28.3825	0.934726
$923$	−8.91112	−0.293313
$924$	3.29636	0.108442
$925$	−5.12213	−0.168415
$926$	0.789581	0.0259472
$927$	17.2773	0.567461
$928$	8.45781	0.277641
$929$	18.1845	0.596615	0.298307	−	0.954470i	$-0.403578\pi$
$929$	18.1845	0.596615	0.298307	+	0.954470i	$0.403578\pi$
$930$	−2.21942	−0.0727775
$931$	45.7595	1.49971
$932$	13.5052	0.442378
$933$	8.99505	0.294485
$934$	−2.20236	−0.0720635
$935$	−2.52277	−0.0825036
$936$	2.52269	0.0824568
$937$	28.1864	0.920808	0.460404	−	0.887709i	$-0.347705\pi$
$937$	28.1864	0.920808	0.460404	+	0.887709i	$0.347705\pi$
$938$	−2.33447	−0.0762232
$939$	−10.0722	−0.328694
$940$	1.76606	0.0576027
$941$	6.98702	0.227770	0.113885	−	0.993494i	$-0.463670\pi$
$941$	6.98702	0.227770	0.113885	+	0.993494i	$0.463670\pi$
$942$	−3.17083	−0.103311
$943$	0.803036	0.0261504
$944$	1.00000	0.0325472
$945$	0.405114	0.0131784
$946$	−13.0350	−0.423803
$947$	38.0176	1.23541	0.617703	−	0.786412i	$-0.288064\pi$
$947$	38.0176	1.23541	0.617703	+	0.786412i	$0.288064\pi$
$948$	−6.38902	−0.207506
$949$	30.8403	1.00112
$950$	−33.1667	−1.07607
$951$	−16.3971	−0.531713
$952$	0.727556	0.0235802
$953$	−35.3336	−1.14457	−0.572284	−	0.820055i	$-0.693943\pi$
$953$	−35.3336	−1.14457	−0.572284	+	0.820055i	$0.693943\pi$
$954$	11.9287	0.386207
$955$	−5.42686	−0.175609
$956$	−28.3102	−0.915618
$957$	−38.3200	−1.23871
$958$	10.5683	0.341448
$959$	4.61493	0.149024
$960$	0.556815	0.0179711
$961$	−15.1125	−0.487499
$962$	2.75516	0.0888298
$963$	−11.7625	−0.379040
$964$	18.4711	0.594915
$965$	5.88141	0.189329
$966$	0.134396	0.00432411
$967$	−9.19886	−0.295815	−0.147908	−	0.989001i	$-0.547254\pi$
$967$	−9.19886	−0.295815	−0.147908	+	0.989001i	$0.547254\pi$
$968$	−9.52748	−0.306225
$969$	7.07185	0.227180
$970$	−4.63051	−0.148677
$971$	37.0612	1.18935	0.594676	−	0.803966i	$-0.297280\pi$
$971$	37.0612	1.18935	0.594676	+	0.803966i	$0.297280\pi$
$972$	1.00000	0.0320750
$973$	5.37800	0.172411
$974$	12.1501	0.389315
$975$	11.8313	0.378906
$976$	−15.1576	−0.485181
$977$	−2.53254	−0.0810231	−0.0405116	−	0.999179i	$-0.512899\pi$
$977$	−2.53254	−0.0810231	−0.0405116	+	0.999179i	$0.512899\pi$
$978$	−2.80623	−0.0897334
$979$	−64.8936	−2.07401
$980$	−3.60296	−0.115092
$981$	5.36322	0.171234
$982$	−34.2121	−1.09175
$983$	−37.9931	−1.21179	−0.605895	−	0.795544i	$-0.707185\pi$
$983$	−37.9931	−1.21179	−0.605895	+	0.795544i	$0.707185\pi$
$984$	4.34727	0.138586
$985$	8.23385	0.262352
$986$	−8.45781	−0.269352
$987$	2.30761	0.0734521
$988$	17.8401	0.567569
$989$	−0.531447	−0.0168990
$990$	−2.52277	−0.0801790
$991$	−22.4659	−0.713654	−0.356827	−	0.934171i	$-0.616141\pi$
$991$	−22.4659	−0.713654	−0.356827	+	0.934171i	$0.616141\pi$
$992$	−3.98591	−0.126553
$993$	7.11007	0.225631
$994$	−2.57001	−0.0815158
$995$	8.25237	0.261618
$996$	−12.2390	−0.387808
$997$	45.4875	1.44060	0.720301	−	0.693662i	$-0.244004\pi$
$997$	45.4875	1.44060	0.720301	+	0.693662i	$0.244004\pi$
$998$	−16.3962	−0.519014
$999$	1.09215	0.0345541

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.y.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.y.1.7	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.556815 q^{5} -1.00000 q^{6} +0.727556 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.556815 q^{5} -1.00000 q^{6} +0.727556 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.556815 q^{10} +4.53073 q^{11} +1.00000 q^{12} -2.52269 q^{13} -0.727556 q^{14} +0.556815 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -7.07185 q^{19} +0.556815 q^{20} +0.727556 q^{21} -4.53073 q^{22} -0.184722 q^{23} -1.00000 q^{24} -4.68996 q^{25} +2.52269 q^{26} +1.00000 q^{27} +0.727556 q^{28} -8.45781 q^{29} -0.556815 q^{30} +3.98591 q^{31} -1.00000 q^{32} +4.53073 q^{33} +1.00000 q^{34} +0.405114 q^{35} +1.00000 q^{36} +1.09215 q^{37} +7.07185 q^{38} -2.52269 q^{39} -0.556815 q^{40} -4.34727 q^{41} -0.727556 q^{42} +2.87701 q^{43} +4.53073 q^{44} +0.556815 q^{45} +0.184722 q^{46} +3.17173 q^{47} +1.00000 q^{48} -6.47066 q^{49} +4.68996 q^{50} -1.00000 q^{51} -2.52269 q^{52} -11.9287 q^{53} -1.00000 q^{54} +2.52277 q^{55} -0.727556 q^{56} -7.07185 q^{57} +8.45781 q^{58} +1.00000 q^{59} +0.556815 q^{60} -15.1576 q^{61} -3.98591 q^{62} +0.727556 q^{63} +1.00000 q^{64} -1.40467 q^{65} -4.53073 q^{66} +3.20865 q^{67} -1.00000 q^{68} -0.184722 q^{69} -0.405114 q^{70} +3.53239 q^{71} -1.00000 q^{72} -12.2252 q^{73} -1.09215 q^{74} -4.68996 q^{75} -7.07185 q^{76} +3.29636 q^{77} +2.52269 q^{78} -6.38902 q^{79} +0.556815 q^{80} +1.00000 q^{81} +4.34727 q^{82} -12.2390 q^{83} +0.727556 q^{84} -0.556815 q^{85} -2.87701 q^{86} -8.45781 q^{87} -4.53073 q^{88} -14.3230 q^{89} -0.556815 q^{90} -1.83540 q^{91} -0.184722 q^{92} +3.98591 q^{93} -3.17173 q^{94} -3.93771 q^{95} -1.00000 q^{96} +8.31606 q^{97} +6.47066 q^{98} +4.53073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * q^99

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