LMFDB - Embedded newform 6018.2.a.u.1.3

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 16x^{7} + 37x^{6} + 97x^{5} - 72x^{4} - 182x^{3} + 24x^{2} + 70x - 19 $ x^9 - 4x^8 - 16x^7 + 37x^6 + 97x^5 - 72x^4 - 182x^3 + 24x^2 + 70x - 19
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.85528$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.56975 q^{5} +1.00000 q^{6} +1.56796 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.56975 q^{5} +1.00000 q^{6} +1.56796 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.56975 q^{10} +4.42818 q^{11} -1.00000 q^{12} +5.02214 q^{13} -1.56796 q^{14} +1.56975 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -6.32128 q^{19} -1.56975 q^{20} -1.56796 q^{21} -4.42818 q^{22} +4.03574 q^{23} +1.00000 q^{24} -2.53590 q^{25} -5.02214 q^{26} -1.00000 q^{27} +1.56796 q^{28} -5.32046 q^{29} -1.56975 q^{30} -9.38160 q^{31} -1.00000 q^{32} -4.42818 q^{33} -1.00000 q^{34} -2.46130 q^{35} +1.00000 q^{36} +8.41088 q^{37} +6.32128 q^{38} -5.02214 q^{39} +1.56975 q^{40} -0.858061 q^{41} +1.56796 q^{42} -11.0451 q^{43} +4.42818 q^{44} -1.56975 q^{45} -4.03574 q^{46} -2.96300 q^{47} -1.00000 q^{48} -4.54151 q^{49} +2.53590 q^{50} -1.00000 q^{51} +5.02214 q^{52} +0.373013 q^{53} +1.00000 q^{54} -6.95112 q^{55} -1.56796 q^{56} +6.32128 q^{57} +5.32046 q^{58} +1.00000 q^{59} +1.56975 q^{60} -10.0519 q^{61} +9.38160 q^{62} +1.56796 q^{63} +1.00000 q^{64} -7.88348 q^{65} +4.42818 q^{66} -7.36553 q^{67} +1.00000 q^{68} -4.03574 q^{69} +2.46130 q^{70} -1.31956 q^{71} -1.00000 q^{72} +0.0349540 q^{73} -8.41088 q^{74} +2.53590 q^{75} -6.32128 q^{76} +6.94320 q^{77} +5.02214 q^{78} +3.92399 q^{79} -1.56975 q^{80} +1.00000 q^{81} +0.858061 q^{82} +8.34540 q^{83} -1.56796 q^{84} -1.56975 q^{85} +11.0451 q^{86} +5.32046 q^{87} -4.42818 q^{88} +9.55667 q^{89} +1.56975 q^{90} +7.87450 q^{91} +4.03574 q^{92} +9.38160 q^{93} +2.96300 q^{94} +9.92281 q^{95} +1.00000 q^{96} -11.4159 q^{97} +4.54151 q^{98} +4.42818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9} - 2 q^{10} - q^{11} - 9 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 7 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} + 4 q^{26} - 9 q^{27} - 5 q^{28} + 6 q^{29} + 2 q^{30} - 17 q^{31} - 9 q^{32} + q^{33} - 9 q^{34} + 10 q^{35} + 9 q^{36} + 2 q^{37} + 7 q^{38} + 4 q^{39} - 2 q^{40} + 14 q^{41} - 5 q^{42} - 27 q^{43} - q^{44} + 2 q^{45} + 8 q^{46} - 18 q^{47} - 9 q^{48} + 18 q^{49} - 5 q^{50} - 9 q^{51} - 4 q^{52} + 4 q^{53} + 9 q^{54} - 27 q^{55} + 5 q^{56} + 7 q^{57} - 6 q^{58} + 9 q^{59} - 2 q^{60} + 5 q^{61} + 17 q^{62} - 5 q^{63} + 9 q^{64} + 2 q^{65} - q^{66} - 22 q^{67} + 9 q^{68} + 8 q^{69} - 10 q^{70} + 16 q^{71} - 9 q^{72} - 12 q^{73} - 2 q^{74} - 5 q^{75} - 7 q^{76} + 6 q^{77} - 4 q^{78} - 9 q^{79} + 2 q^{80} + 9 q^{81} - 14 q^{82} + 10 q^{83} + 5 q^{84} + 2 q^{85} + 27 q^{86} - 6 q^{87} + q^{88} + 15 q^{89} - 2 q^{90} + 3 q^{91} - 8 q^{92} + 17 q^{93} + 18 q^{94} - 9 q^{95} + 9 q^{96} - 33 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9 - 2 * q^10 - q^11 - 9 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^15 + 9 * q^16 + 9 * q^17 - 9 * q^18 - 7 * q^19 + 2 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 9 * q^24 + 5 * q^25 + 4 * q^26 - 9 * q^27 - 5 * q^28 + 6 * q^29 + 2 * q^30 - 17 * q^31 - 9 * q^32 + q^33 - 9 * q^34 + 10 * q^35 + 9 * q^36 + 2 * q^37 + 7 * q^38 + 4 * q^39 - 2 * q^40 + 14 * q^41 - 5 * q^42 - 27 * q^43 - q^44 + 2 * q^45 + 8 * q^46 - 18 * q^47 - 9 * q^48 + 18 * q^49 - 5 * q^50 - 9 * q^51 - 4 * q^52 + 4 * q^53 + 9 * q^54 - 27 * q^55 + 5 * q^56 + 7 * q^57 - 6 * q^58 + 9 * q^59 - 2 * q^60 + 5 * q^61 + 17 * q^62 - 5 * q^63 + 9 * q^64 + 2 * q^65 - q^66 - 22 * q^67 + 9 * q^68 + 8 * q^69 - 10 * q^70 + 16 * q^71 - 9 * q^72 - 12 * q^73 - 2 * q^74 - 5 * q^75 - 7 * q^76 + 6 * q^77 - 4 * q^78 - 9 * q^79 + 2 * q^80 + 9 * q^81 - 14 * q^82 + 10 * q^83 + 5 * q^84 + 2 * q^85 + 27 * q^86 - 6 * q^87 + q^88 + 15 * q^89 - 2 * q^90 + 3 * q^91 - 8 * q^92 + 17 * q^93 + 18 * q^94 - 9 * q^95 + 9 * q^96 - 33 * q^97 - 18 * q^98 - 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
$5$	−1.56975	−0.702012	−0.351006	−	0.936373i	$-0.614160\pi$
$5$	−1.56975	−0.702012	−0.351006	+	0.936373i	$0.614160\pi$
$6$	1.00000	0.408248
$7$	1.56796	0.592632	0.296316	−	0.955090i	$-0.404242\pi$
$7$	1.56796	0.592632	0.296316	+	0.955090i	$0.404242\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.56975	0.496397
$11$	4.42818	1.33515	0.667573	−	0.744544i	$-0.267333\pi$
$11$	4.42818	1.33515	0.667573	+	0.744544i	$0.267333\pi$
$12$	−1.00000	−0.288675
$13$	5.02214	1.39289	0.696445	−	0.717610i	$-0.254764\pi$
$13$	5.02214	1.39289	0.696445	+	0.717610i	$0.254764\pi$
$14$	−1.56796	−0.419054
$15$	1.56975	0.405307
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−6.32128	−1.45020	−0.725101	−	0.688643i	$-0.758207\pi$
$19$	−6.32128	−1.45020	−0.725101	+	0.688643i	$0.758207\pi$
$20$	−1.56975	−0.351006
$21$	−1.56796	−0.342156
$22$	−4.42818	−0.944091
$23$	4.03574	0.841511	0.420755	−	0.907174i	$-0.361765\pi$
$23$	4.03574	0.841511	0.420755	+	0.907174i	$0.361765\pi$
$24$	1.00000	0.204124
$25$	−2.53590	−0.507179
$26$	−5.02214	−0.984922
$27$	−1.00000	−0.192450
$28$	1.56796	0.296316
$29$	−5.32046	−0.987984	−0.493992	−	0.869466i	$-0.664463\pi$
$29$	−5.32046	−0.987984	−0.493992	+	0.869466i	$0.664463\pi$
$30$	−1.56975	−0.286595
$31$	−9.38160	−1.68499	−0.842493	−	0.538707i	$-0.818913\pi$
$31$	−9.38160	−1.68499	−0.842493	+	0.538707i	$0.818913\pi$
$32$	−1.00000	−0.176777
$33$	−4.42818	−0.770847
$34$	−1.00000	−0.171499
$35$	−2.46130	−0.416035
$36$	1.00000	0.166667
$37$	8.41088	1.38274	0.691370	−	0.722501i	$-0.257007\pi$
$37$	8.41088	1.38274	0.691370	+	0.722501i	$0.257007\pi$
$38$	6.32128	1.02545
$39$	−5.02214	−0.804185
$40$	1.56975	0.248199
$41$	−0.858061	−0.134007	−0.0670033	−	0.997753i	$-0.521344\pi$
$41$	−0.858061	−0.134007	−0.0670033	+	0.997753i	$0.521344\pi$
$42$	1.56796	0.241941
$43$	−11.0451	−1.68436	−0.842180	−	0.539196i	$-0.818728\pi$
$43$	−11.0451	−1.68436	−0.842180	+	0.539196i	$0.818728\pi$
$44$	4.42818	0.667573
$45$	−1.56975	−0.234004
$46$	−4.03574	−0.595038
$47$	−2.96300	−0.432198	−0.216099	−	0.976371i	$-0.569333\pi$
$47$	−2.96300	−0.432198	−0.216099	+	0.976371i	$0.569333\pi$
$48$	−1.00000	−0.144338
$49$	−4.54151	−0.648787
$50$	2.53590	0.358630
$51$	−1.00000	−0.140028
$52$	5.02214	0.696445
$53$	0.373013	0.0512372	0.0256186	−	0.999672i	$-0.491844\pi$
$53$	0.373013	0.0512372	0.0256186	+	0.999672i	$0.491844\pi$
$54$	1.00000	0.136083
$55$	−6.95112	−0.937288
$56$	−1.56796	−0.209527
$57$	6.32128	0.837274
$58$	5.32046	0.698611
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	1.56975	0.202653
$61$	−10.0519	−1.28701	−0.643506	−	0.765441i	$-0.722521\pi$
$61$	−10.0519	−1.28701	−0.643506	+	0.765441i	$0.722521\pi$
$62$	9.38160	1.19146
$63$	1.56796	0.197544
$64$	1.00000	0.125000
$65$	−7.88348	−0.977825
$66$	4.42818	0.545071
$67$	−7.36553	−0.899843	−0.449921	−	0.893068i	$-0.648548\pi$
$67$	−7.36553	−0.899843	−0.449921	+	0.893068i	$0.648548\pi$
$68$	1.00000	0.121268
$69$	−4.03574	−0.485847
$70$	2.46130	0.294181
$71$	−1.31956	−0.156603	−0.0783013	−	0.996930i	$-0.524950\pi$
$71$	−1.31956	−0.156603	−0.0783013	+	0.996930i	$0.524950\pi$
$72$	−1.00000	−0.117851
$73$	0.0349540	0.00409105	0.00204553	−	0.999998i	$-0.499349\pi$
$73$	0.0349540	0.00409105	0.00204553	+	0.999998i	$0.499349\pi$
$74$	−8.41088	−0.977745
$75$	2.53590	0.292820
$76$	−6.32128	−0.725101
$77$	6.94320	0.791251
$78$	5.02214	0.568645
$79$	3.92399	0.441484	0.220742	−	0.975332i	$-0.429152\pi$
$79$	3.92399	0.441484	0.220742	+	0.975332i	$0.429152\pi$
$80$	−1.56975	−0.175503
$81$	1.00000	0.111111
$82$	0.858061	0.0947570
$83$	8.34540	0.916027	0.458014	−	0.888945i	$-0.348561\pi$
$83$	8.34540	0.916027	0.458014	+	0.888945i	$0.348561\pi$
$84$	−1.56796	−0.171078
$85$	−1.56975	−0.170263
$86$	11.0451	1.19102
$87$	5.32046	0.570413
$88$	−4.42818	−0.472045
$89$	9.55667	1.01301	0.506503	−	0.862238i	$-0.330938\pi$
$89$	9.55667	1.01301	0.506503	+	0.862238i	$0.330938\pi$
$90$	1.56975	0.165466
$91$	7.87450	0.825472
$92$	4.03574	0.420755
$93$	9.38160	0.972827
$94$	2.96300	0.305610
$95$	9.92281	1.01806
$96$	1.00000	0.102062
$97$	−11.4159	−1.15911	−0.579556	−	0.814933i	$-0.696774\pi$
$97$	−11.4159	−1.15911	−0.579556	+	0.814933i	$0.696774\pi$
$98$	4.54151	0.458762
$99$	4.42818	0.445049
$100$	−2.53590	−0.253590
$101$	4.44890	0.442683	0.221341	−	0.975196i	$-0.428957\pi$
$101$	4.44890	0.442683	0.221341	+	0.975196i	$0.428957\pi$
$102$	1.00000	0.0990148
$103$	0.173533	0.0170988	0.00854938	−	0.999963i	$-0.497279\pi$
$103$	0.173533	0.0170988	0.00854938	+	0.999963i	$0.497279\pi$
$104$	−5.02214	−0.492461
$105$	2.46130	0.240198
$106$	−0.373013	−0.0362302
$107$	−13.1523	−1.27148	−0.635742	−	0.771902i	$-0.719306\pi$
$107$	−13.1523	−1.27148	−0.635742	+	0.771902i	$0.719306\pi$
$108$	−1.00000	−0.0962250
$109$	2.31393	0.221634	0.110817	−	0.993841i	$-0.464653\pi$
$109$	2.31393	0.221634	0.110817	+	0.993841i	$0.464653\pi$
$110$	6.95112	0.662763
$111$	−8.41088	−0.798325
$112$	1.56796	0.148158
$113$	−3.29878	−0.310323	−0.155162	−	0.987889i	$-0.549590\pi$
$113$	−3.29878	−0.310323	−0.155162	+	0.987889i	$0.549590\pi$
$114$	−6.32128	−0.592042
$115$	−6.33510	−0.590751
$116$	−5.32046	−0.493992
$117$	5.02214	0.464297
$118$	−1.00000	−0.0920575
$119$	1.56796	0.143734
$120$	−1.56975	−0.143298
$121$	8.60876	0.782614
$122$	10.0519	0.910055
$123$	0.858061	0.0773688
$124$	−9.38160	−0.842493
$125$	11.8294	1.05806
$126$	−1.56796	−0.139685
$127$	11.1853	0.992531	0.496266	−	0.868171i	$-0.334704\pi$
$127$	11.1853	0.992531	0.496266	+	0.868171i	$0.334704\pi$
$128$	−1.00000	−0.0883883
$129$	11.0451	0.972466
$130$	7.88348	0.691427
$131$	3.43178	0.299836	0.149918	−	0.988698i	$-0.452099\pi$
$131$	3.43178	0.299836	0.149918	+	0.988698i	$0.452099\pi$
$132$	−4.42818	−0.385423
$133$	−9.91150	−0.859436
$134$	7.36553	0.636285
$135$	1.56975	0.135102
$136$	−1.00000	−0.0857493
$137$	−11.1705	−0.954360	−0.477180	−	0.878806i	$-0.658341\pi$
$137$	−11.1705	−0.954360	−0.477180	+	0.878806i	$0.658341\pi$
$138$	4.03574	0.343545
$139$	−13.3180	−1.12962	−0.564808	−	0.825222i	$-0.691050\pi$
$139$	−13.3180	−1.12962	−0.564808	+	0.825222i	$0.691050\pi$
$140$	−2.46130	−0.208017
$141$	2.96300	0.249530
$142$	1.31956	0.110735
$143$	22.2389	1.85971
$144$	1.00000	0.0833333
$145$	8.35177	0.693577
$146$	−0.0349540	−0.00289281
$147$	4.54151	0.374577
$148$	8.41088	0.691370
$149$	−4.05502	−0.332200	−0.166100	−	0.986109i	$-0.553117\pi$
$149$	−4.05502	−0.332200	−0.166100	+	0.986109i	$0.553117\pi$
$150$	−2.53590	−0.207055
$151$	12.4661	1.01447	0.507237	−	0.861807i	$-0.330667\pi$
$151$	12.4661	1.01447	0.507237	+	0.861807i	$0.330667\pi$
$152$	6.32128	0.512724
$153$	1.00000	0.0808452
$154$	−6.94320	−0.559499
$155$	14.7267	1.18288
$156$	−5.02214	−0.402093
$157$	14.3065	1.14178	0.570892	−	0.821025i	$-0.306597\pi$
$157$	14.3065	1.14178	0.570892	+	0.821025i	$0.306597\pi$
$158$	−3.92399	−0.312176
$159$	−0.373013	−0.0295818
$160$	1.56975	0.124099
$161$	6.32788	0.498707
$162$	−1.00000	−0.0785674
$163$	−10.6555	−0.834600	−0.417300	−	0.908769i	$-0.637024\pi$
$163$	−10.6555	−0.834600	−0.417300	+	0.908769i	$0.637024\pi$
$164$	−0.858061	−0.0670033
$165$	6.95112	0.541144
$166$	−8.34540	−0.647729
$167$	4.24036	0.328129	0.164065	−	0.986450i	$-0.447539\pi$
$167$	4.24036	0.328129	0.164065	+	0.986450i	$0.447539\pi$
$168$	1.56796	0.120971
$169$	12.2218	0.940142
$170$	1.56975	0.120394
$171$	−6.32128	−0.483400
$172$	−11.0451	−0.842180
$173$	19.2123	1.46068	0.730342	−	0.683082i	$-0.239361\pi$
$173$	19.2123	1.46068	0.730342	+	0.683082i	$0.239361\pi$
$174$	−5.32046	−0.403343
$175$	−3.97618	−0.300571
$176$	4.42818	0.333786
$177$	−1.00000	−0.0751646
$178$	−9.55667	−0.716303
$179$	1.20631	0.0901641	0.0450820	−	0.998983i	$-0.485645\pi$
$179$	1.20631	0.0901641	0.0450820	+	0.998983i	$0.485645\pi$
$180$	−1.56975	−0.117002
$181$	−9.88226	−0.734542	−0.367271	−	0.930114i	$-0.619708\pi$
$181$	−9.88226	−0.734542	−0.367271	+	0.930114i	$0.619708\pi$
$182$	−7.87450	−0.583697
$183$	10.0519	0.743057
$184$	−4.03574	−0.297519
$185$	−13.2030	−0.970700
$186$	−9.38160	−0.687893
$187$	4.42818	0.323820
$188$	−2.96300	−0.216099
$189$	−1.56796	−0.114052
$190$	−9.92281	−0.719876
$191$	−15.6635	−1.13337	−0.566684	−	0.823935i	$-0.691774\pi$
$191$	−15.6635	−1.13337	−0.566684	+	0.823935i	$0.691774\pi$
$192$	−1.00000	−0.0721688
$193$	−25.3029	−1.82135	−0.910673	−	0.413129i	$-0.864436\pi$
$193$	−25.3029	−1.82135	−0.910673	+	0.413129i	$0.864436\pi$
$194$	11.4159	0.819615
$195$	7.88348	0.564548
$196$	−4.54151	−0.324393
$197$	−22.5452	−1.60628	−0.803140	−	0.595790i	$-0.796839\pi$
$197$	−22.5452	−1.60628	−0.803140	+	0.595790i	$0.796839\pi$
$198$	−4.42818	−0.314697
$199$	−26.3825	−1.87021	−0.935104	−	0.354374i	$-0.884694\pi$
$199$	−26.3825	−1.87021	−0.935104	+	0.354374i	$0.884694\pi$
$200$	2.53590	0.179315
$201$	7.36553	0.519525
$202$	−4.44890	−0.313024
$203$	−8.34226	−0.585512
$204$	−1.00000	−0.0700140
$205$	1.34694	0.0940742
$206$	−0.173533	−0.0120906
$207$	4.03574	0.280504
$208$	5.02214	0.348222
$209$	−27.9918	−1.93623
$210$	−2.46130	−0.169846
$211$	−17.2927	−1.19048	−0.595238	−	0.803549i	$-0.702942\pi$
$211$	−17.2927	−1.19048	−0.595238	+	0.803549i	$0.702942\pi$
$212$	0.373013	0.0256186
$213$	1.31956	0.0904145
$214$	13.1523	0.899074
$215$	17.3380	1.18244
$216$	1.00000	0.0680414
$217$	−14.7100	−0.998577
$218$	−2.31393	−0.156719
$219$	−0.0349540	−0.00236197
$220$	−6.95112	−0.468644
$221$	5.02214	0.337825
$222$	8.41088	0.564501
$223$	−13.3305	−0.892678	−0.446339	−	0.894864i	$-0.647272\pi$
$223$	−13.3305	−0.892678	−0.446339	+	0.894864i	$0.647272\pi$
$224$	−1.56796	−0.104764
$225$	−2.53590	−0.169060
$226$	3.29878	0.219432
$227$	14.5838	0.967958	0.483979	−	0.875080i	$-0.339191\pi$
$227$	14.5838	0.967958	0.483979	+	0.875080i	$0.339191\pi$
$228$	6.32128	0.418637
$229$	8.63377	0.570536	0.285268	−	0.958448i	$-0.407917\pi$
$229$	8.63377	0.570536	0.285268	+	0.958448i	$0.407917\pi$
$230$	6.33510	0.417724
$231$	−6.94320	−0.456829
$232$	5.32046	0.349305
$233$	−12.4759	−0.817325	−0.408663	−	0.912685i	$-0.634005\pi$
$233$	−12.4759	−0.817325	−0.408663	+	0.912685i	$0.634005\pi$
$234$	−5.02214	−0.328307
$235$	4.65116	0.303408
$236$	1.00000	0.0650945
$237$	−3.92399	−0.254891
$238$	−1.56796	−0.101636
$239$	8.39307	0.542903	0.271451	−	0.962452i	$-0.412496\pi$
$239$	8.39307	0.542903	0.271451	+	0.962452i	$0.412496\pi$
$240$	1.56975	0.101327
$241$	3.52136	0.226831	0.113416	−	0.993548i	$-0.463821\pi$
$241$	3.52136	0.226831	0.113416	+	0.993548i	$0.463821\pi$
$242$	−8.60876	−0.553392
$243$	−1.00000	−0.0641500
$244$	−10.0519	−0.643506
$245$	7.12902	0.455456
$246$	−0.858061	−0.0547080
$247$	−31.7463	−2.01997
$248$	9.38160	0.595732
$249$	−8.34540	−0.528869
$250$	−11.8294	−0.748160
$251$	18.4166	1.16245	0.581224	−	0.813743i	$-0.302574\pi$
$251$	18.4166	1.16245	0.581224	+	0.813743i	$0.302574\pi$
$252$	1.56796	0.0987721
$253$	17.8710	1.12354
$254$	−11.1853	−0.701826
$255$	1.56975	0.0983013
$256$	1.00000	0.0625000
$257$	20.7618	1.29508	0.647541	−	0.762030i	$-0.275797\pi$
$257$	20.7618	1.29508	0.647541	+	0.762030i	$0.275797\pi$
$258$	−11.0451	−0.687637
$259$	13.1879	0.819457
$260$	−7.88348	−0.488913
$261$	−5.32046	−0.329328
$262$	−3.43178	−0.212016
$263$	−3.56931	−0.220093	−0.110046	−	0.993926i	$-0.535100\pi$
$263$	−3.56931	−0.220093	−0.110046	+	0.993926i	$0.535100\pi$
$264$	4.42818	0.272535
$265$	−0.585535	−0.0359692
$266$	9.91150	0.607713
$267$	−9.55667	−0.584859
$268$	−7.36553	−0.449921
$269$	−26.5567	−1.61919	−0.809595	−	0.586989i	$-0.800313\pi$
$269$	−26.5567	−1.61919	−0.809595	+	0.586989i	$0.800313\pi$
$270$	−1.56975	−0.0955317
$271$	−10.5286	−0.639568	−0.319784	−	0.947490i	$-0.603610\pi$
$271$	−10.5286	−0.639568	−0.319784	+	0.947490i	$0.603610\pi$
$272$	1.00000	0.0606339
$273$	−7.87450	−0.476586
$274$	11.1705	0.674835
$275$	−11.2294	−0.677158
$276$	−4.03574	−0.242923
$277$	10.0077	0.601306	0.300653	−	0.953734i	$-0.402795\pi$
$277$	10.0077	0.601306	0.300653	+	0.953734i	$0.402795\pi$
$278$	13.3180	0.798759
$279$	−9.38160	−0.561662
$280$	2.46130	0.147091
$281$	−15.9410	−0.950962	−0.475481	−	0.879726i	$-0.657726\pi$
$281$	−15.9410	−0.950962	−0.475481	+	0.879726i	$0.657726\pi$
$282$	−2.96300	−0.176444
$283$	20.6867	1.22970	0.614849	−	0.788645i	$-0.289217\pi$
$283$	20.6867	1.22970	0.614849	+	0.788645i	$0.289217\pi$
$284$	−1.31956	−0.0783013
$285$	−9.92281	−0.587776
$286$	−22.2389	−1.31501
$287$	−1.34540	−0.0794166
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−8.35177	−0.490433
$291$	11.4159	0.669213
$292$	0.0349540	0.00204553
$293$	−6.87410	−0.401589	−0.200795	−	0.979633i	$-0.564352\pi$
$293$	−6.87410	−0.401589	−0.200795	+	0.979633i	$0.564352\pi$
$294$	−4.54151	−0.264866
$295$	−1.56975	−0.0913942
$296$	−8.41088	−0.488873
$297$	−4.42818	−0.256949
$298$	4.05502	0.234901
$299$	20.2681	1.17213
$300$	2.53590	0.146410
$301$	−17.3182	−0.998206
$302$	−12.4661	−0.717341
$303$	−4.44890	−0.255583
$304$	−6.32128	−0.362550
$305$	15.7789	0.903498
$306$	−1.00000	−0.0571662
$307$	3.63772	0.207615	0.103808	−	0.994597i	$-0.466897\pi$
$307$	3.63772	0.207615	0.103808	+	0.994597i	$0.466897\pi$
$308$	6.94320	0.395625
$309$	−0.173533	−0.00987197
$310$	−14.7267	−0.836423
$311$	25.2771	1.43333	0.716666	−	0.697416i	$-0.245667\pi$
$311$	25.2771	1.43333	0.716666	+	0.697416i	$0.245667\pi$
$312$	5.02214	0.284322
$313$	13.2592	0.749453	0.374727	−	0.927135i	$-0.377737\pi$
$313$	13.2592	0.749453	0.374727	+	0.927135i	$0.377737\pi$
$314$	−14.3065	−0.807363
$315$	−2.46130	−0.138678
$316$	3.92399	0.220742
$317$	−18.4410	−1.03575	−0.517876	−	0.855456i	$-0.673277\pi$
$317$	−18.4410	−1.03575	−0.517876	+	0.855456i	$0.673277\pi$
$318$	0.373013	0.0209175
$319$	−23.5599	−1.31910
$320$	−1.56975	−0.0877515
$321$	13.1523	0.734091
$322$	−6.32788	−0.352639
$323$	−6.32128	−0.351725
$324$	1.00000	0.0555556
$325$	−12.7356	−0.706445
$326$	10.6555	0.590151
$327$	−2.31393	−0.127961
$328$	0.858061	0.0473785
$329$	−4.64586	−0.256135
$330$	−6.95112	−0.382646
$331$	−9.30779	−0.511602	−0.255801	−	0.966729i	$-0.582339\pi$
$331$	−9.30779	−0.511602	−0.255801	+	0.966729i	$0.582339\pi$
$332$	8.34540	0.458014
$333$	8.41088	0.460913
$334$	−4.24036	−0.232022
$335$	11.5620	0.631700
$336$	−1.56796	−0.0855391
$337$	7.42181	0.404292	0.202146	−	0.979355i	$-0.435208\pi$
$337$	7.42181	0.404292	0.202146	+	0.979355i	$0.435208\pi$
$338$	−12.2218	−0.664781
$339$	3.29878	0.179165
$340$	−1.56975	−0.0851315
$341$	−41.5434	−2.24970
$342$	6.32128	0.341816
$343$	−18.0966	−0.977124
$344$	11.0451	0.595511
$345$	6.33510	0.341070
$346$	−19.2123	−1.03286
$347$	−6.13873	−0.329544	−0.164772	−	0.986332i	$-0.552689\pi$
$347$	−6.13873	−0.329544	−0.164772	+	0.986332i	$0.552689\pi$
$348$	5.32046	0.285207
$349$	−16.9484	−0.907227	−0.453614	−	0.891198i	$-0.649865\pi$
$349$	−16.9484	−0.907227	−0.453614	+	0.891198i	$0.649865\pi$
$350$	3.97618	0.212536
$351$	−5.02214	−0.268062
$352$	−4.42818	−0.236023
$353$	4.63094	0.246480	0.123240	−	0.992377i	$-0.460672\pi$
$353$	4.63094	0.246480	0.123240	+	0.992377i	$0.460672\pi$
$354$	1.00000	0.0531494
$355$	2.07137	0.109937
$356$	9.55667	0.506503
$357$	−1.56796	−0.0829851
$358$	−1.20631	−0.0637556
$359$	−14.1063	−0.744502	−0.372251	−	0.928132i	$-0.621414\pi$
$359$	−14.1063	−0.744502	−0.372251	+	0.928132i	$0.621414\pi$
$360$	1.56975	0.0827329
$361$	20.9586	1.10308
$362$	9.88226	0.519400
$363$	−8.60876	−0.451843
$364$	7.87450	0.412736
$365$	−0.0548689	−0.00287197
$366$	−10.0519	−0.525420
$367$	18.2703	0.953701	0.476850	−	0.878984i	$-0.341778\pi$
$367$	18.2703	0.953701	0.476850	+	0.878984i	$0.341778\pi$
$368$	4.03574	0.210378
$369$	−0.858061	−0.0446689
$370$	13.2030	0.686389
$371$	0.584868	0.0303648
$372$	9.38160	0.486414
$373$	−20.0279	−1.03701	−0.518504	−	0.855075i	$-0.673511\pi$
$373$	−20.0279	−1.03701	−0.518504	+	0.855075i	$0.673511\pi$
$374$	−4.42818	−0.228976
$375$	−11.8294	−0.610870
$376$	2.96300	0.152805
$377$	−26.7201	−1.37615
$378$	1.56796	0.0806470
$379$	−1.50135	−0.0771193	−0.0385596	−	0.999256i	$-0.512277\pi$
$379$	−1.50135	−0.0771193	−0.0385596	+	0.999256i	$0.512277\pi$
$380$	9.92281	0.509029
$381$	−11.1853	−0.573038
$382$	15.6635	0.801413
$383$	−15.4324	−0.788558	−0.394279	−	0.918991i	$-0.629006\pi$
$383$	−15.4324	−0.788558	−0.394279	+	0.918991i	$0.629006\pi$
$384$	1.00000	0.0510310
$385$	−10.8991	−0.555467
$386$	25.3029	1.28789
$387$	−11.0451	−0.561453
$388$	−11.4159	−0.579556
$389$	−10.0620	−0.510164	−0.255082	−	0.966919i	$-0.582102\pi$
$389$	−10.0620	−0.510164	−0.255082	+	0.966919i	$0.582102\pi$
$390$	−7.88348	−0.399196
$391$	4.03574	0.204096
$392$	4.54151	0.229381
$393$	−3.43178	−0.173111
$394$	22.5452	1.13581
$395$	−6.15967	−0.309927
$396$	4.42818	0.222524
$397$	28.4292	1.42682	0.713410	−	0.700747i	$-0.247150\pi$
$397$	28.4292	1.42682	0.713410	+	0.700747i	$0.247150\pi$
$398$	26.3825	1.32244
$399$	9.91150	0.496196
$400$	−2.53590	−0.126795
$401$	−5.67523	−0.283407	−0.141704	−	0.989909i	$-0.545258\pi$
$401$	−5.67523	−0.283407	−0.141704	+	0.989909i	$0.545258\pi$
$402$	−7.36553	−0.367359
$403$	−47.1157	−2.34700
$404$	4.44890	0.221341
$405$	−1.56975	−0.0780013
$406$	8.34226	0.414019
$407$	37.2449	1.84616
$408$	1.00000	0.0495074
$409$	−18.1140	−0.895677	−0.447839	−	0.894114i	$-0.647806\pi$
$409$	−18.1140	−0.895677	−0.447839	+	0.894114i	$0.647806\pi$
$410$	−1.34694	−0.0665205
$411$	11.1705	0.551000
$412$	0.173533	0.00854938
$413$	1.56796	0.0771542
$414$	−4.03574	−0.198346
$415$	−13.1002	−0.643062
$416$	−5.02214	−0.246230
$417$	13.3180	0.652184
$418$	27.9918	1.36912
$419$	25.3939	1.24057	0.620287	−	0.784375i	$-0.287016\pi$
$419$	25.3939	1.24057	0.620287	+	0.784375i	$0.287016\pi$
$420$	2.46130	0.120099
$421$	38.0914	1.85646	0.928232	−	0.372003i	$-0.121329\pi$
$421$	38.0914	1.85646	0.928232	+	0.372003i	$0.121329\pi$
$422$	17.2927	0.841794
$423$	−2.96300	−0.144066
$424$	−0.373013	−0.0181151
$425$	−2.53590	−0.123009
$426$	−1.31956	−0.0639327
$427$	−15.7609	−0.762725
$428$	−13.1523	−0.635742
$429$	−22.2389	−1.07370
$430$	−17.3380	−0.836112
$431$	17.7075	0.852940	0.426470	−	0.904502i	$-0.359757\pi$
$431$	17.7075	0.852940	0.426470	+	0.904502i	$0.359757\pi$
$432$	−1.00000	−0.0481125
$433$	16.1988	0.778465	0.389232	−	0.921140i	$-0.372740\pi$
$433$	16.1988	0.778465	0.389232	+	0.921140i	$0.372740\pi$
$434$	14.7100	0.706101
$435$	−8.35177	−0.400437
$436$	2.31393	0.110817
$437$	−25.5111	−1.22036
$438$	0.0349540	0.00167017
$439$	29.1901	1.39317	0.696584	−	0.717476i	$-0.254702\pi$
$439$	29.1901	1.39317	0.696584	+	0.717476i	$0.254702\pi$
$440$	6.95112	0.331381
$441$	−4.54151	−0.216262
$442$	−5.02214	−0.238879
$443$	−8.54060	−0.405776	−0.202888	−	0.979202i	$-0.565033\pi$
$443$	−8.54060	−0.405776	−0.202888	+	0.979202i	$0.565033\pi$
$444$	−8.41088	−0.399163
$445$	−15.0016	−0.711142
$446$	13.3305	0.631219
$447$	4.05502	0.191796
$448$	1.56796	0.0740790
$449$	21.8035	1.02897	0.514485	−	0.857500i	$-0.327983\pi$
$449$	21.8035	1.02897	0.514485	+	0.857500i	$0.327983\pi$
$450$	2.53590	0.119543
$451$	−3.79965	−0.178918
$452$	−3.29878	−0.155162
$453$	−12.4661	−0.585706
$454$	−14.5838	−0.684450
$455$	−12.3610	−0.579491
$456$	−6.32128	−0.296021
$457$	−20.8093	−0.973419	−0.486709	−	0.873564i	$-0.661803\pi$
$457$	−20.8093	−0.973419	−0.486709	+	0.873564i	$0.661803\pi$
$458$	−8.63377	−0.403430
$459$	−1.00000	−0.0466760
$460$	−6.33510	−0.295375
$461$	35.7768	1.66629	0.833146	−	0.553053i	$-0.186537\pi$
$461$	35.7768	1.66629	0.833146	+	0.553053i	$0.186537\pi$
$462$	6.94320	0.323027
$463$	21.2430	0.987246	0.493623	−	0.869676i	$-0.335672\pi$
$463$	21.2430	0.987246	0.493623	+	0.869676i	$0.335672\pi$
$464$	−5.32046	−0.246996
$465$	−14.7267	−0.682936
$466$	12.4759	0.577936
$467$	−23.2909	−1.07777	−0.538887	−	0.842378i	$-0.681155\pi$
$467$	−23.2909	−1.07777	−0.538887	+	0.842378i	$0.681155\pi$
$468$	5.02214	0.232148
$469$	−11.5488	−0.533276
$470$	−4.65116	−0.214542
$471$	−14.3065	−0.659209
$472$	−1.00000	−0.0460287
$473$	−48.9096	−2.24887
$474$	3.92399	0.180235
$475$	16.0301	0.735512
$476$	1.56796	0.0718672
$477$	0.373013	0.0170791
$478$	−8.39307	−0.383890
$479$	−35.0581	−1.60184	−0.800922	−	0.598768i	$-0.795657\pi$
$479$	−35.0581	−1.60184	−0.800922	+	0.598768i	$0.795657\pi$
$480$	−1.56975	−0.0716488
$481$	42.2406	1.92600
$482$	−3.52136	−0.160394
$483$	−6.32788	−0.287928
$484$	8.60876	0.391307
$485$	17.9201	0.813710
$486$	1.00000	0.0453609
$487$	−38.1135	−1.72709	−0.863544	−	0.504274i	$-0.831760\pi$
$487$	−38.1135	−1.72709	−0.863544	+	0.504274i	$0.831760\pi$
$488$	10.0519	0.455027
$489$	10.6555	0.481857
$490$	−7.12902	−0.322056
$491$	−34.4388	−1.55420	−0.777101	−	0.629376i	$-0.783310\pi$
$491$	−34.4388	−1.55420	−0.777101	+	0.629376i	$0.783310\pi$
$492$	0.858061	0.0386844
$493$	−5.32046	−0.239621
$494$	31.7463	1.42833
$495$	−6.95112	−0.312429
$496$	−9.38160	−0.421246
$497$	−2.06901	−0.0928077
$498$	8.34540	0.373967
$499$	−19.8910	−0.890444	−0.445222	−	0.895420i	$-0.646875\pi$
$499$	−19.8910	−0.890444	−0.445222	+	0.895420i	$0.646875\pi$
$500$	11.8294	0.529029
$501$	−4.24036	−0.189445
$502$	−18.4166	−0.821975
$503$	7.06368	0.314954	0.157477	−	0.987523i	$-0.449664\pi$
$503$	7.06368	0.314954	0.157477	+	0.987523i	$0.449664\pi$
$504$	−1.56796	−0.0698424
$505$	−6.98365	−0.310768
$506$	−17.8710	−0.794463
$507$	−12.2218	−0.542791
$508$	11.1853	0.496266
$509$	3.79603	0.168256	0.0841281	−	0.996455i	$-0.473190\pi$
$509$	3.79603	0.168256	0.0841281	+	0.996455i	$0.473190\pi$
$510$	−1.56975	−0.0695095
$511$	0.0548064	0.00242449
$512$	−1.00000	−0.0441942
$513$	6.32128	0.279091
$514$	−20.7618	−0.915762
$515$	−0.272404	−0.0120035
$516$	11.0451	0.486233
$517$	−13.1207	−0.577047
$518$	−13.1879	−0.579443
$519$	−19.2123	−0.843326
$520$	7.88348	0.345713
$521$	−2.75381	−0.120647	−0.0603234	−	0.998179i	$-0.519213\pi$
$521$	−2.75381	−0.120647	−0.0603234	+	0.998179i	$0.519213\pi$
$522$	5.32046	0.232870
$523$	−29.9166	−1.30816	−0.654080	−	0.756426i	$-0.726944\pi$
$523$	−29.9166	−1.30816	−0.654080	+	0.756426i	$0.726944\pi$
$524$	3.43178	0.149918
$525$	3.97618	0.173535
$526$	3.56931	0.155629
$527$	−9.38160	−0.408669
$528$	−4.42818	−0.192712
$529$	−6.71277	−0.291859
$530$	0.585535	0.0254340
$531$	1.00000	0.0433963
$532$	−9.91150	−0.429718
$533$	−4.30930	−0.186656
$534$	9.55667	0.413558
$535$	20.6458	0.892596
$536$	7.36553	0.318143
$537$	−1.20631	−0.0520562
$538$	26.5567	1.14494
$539$	−20.1106	−0.866225
$540$	1.56975	0.0675511
$541$	42.5046	1.82741	0.913707	−	0.406374i	$-0.133207\pi$
$541$	42.5046	1.82741	0.913707	+	0.406374i	$0.133207\pi$
$542$	10.5286	0.452243
$543$	9.88226	0.424088
$544$	−1.00000	−0.0428746
$545$	−3.63228	−0.155590
$546$	7.87450	0.336997
$547$	−18.0279	−0.770817	−0.385408	−	0.922746i	$-0.625939\pi$
$547$	−18.0279	−0.770817	−0.385408	+	0.922746i	$0.625939\pi$
$548$	−11.1705	−0.477180
$549$	−10.0519	−0.429004
$550$	11.2294	0.478823
$551$	33.6321	1.43278
$552$	4.03574	0.171773
$553$	6.15265	0.261637
$554$	−10.0077	−0.425188
$555$	13.2030	0.560434
$556$	−13.3180	−0.564808
$557$	−12.7180	−0.538880	−0.269440	−	0.963017i	$-0.586839\pi$
$557$	−12.7180	−0.538880	−0.269440	+	0.963017i	$0.586839\pi$
$558$	9.38160	0.397155
$559$	−55.4699	−2.34613
$560$	−2.46130	−0.104009
$561$	−4.42818	−0.186958
$562$	15.9410	0.672432
$563$	11.1949	0.471807	0.235903	−	0.971777i	$-0.424195\pi$
$563$	11.1949	0.471807	0.235903	+	0.971777i	$0.424195\pi$
$564$	2.96300	0.124765
$565$	5.17825	0.217851
$566$	−20.6867	−0.869528
$567$	1.56796	0.0658480
$568$	1.31956	0.0553674
$569$	−19.5108	−0.817936	−0.408968	−	0.912549i	$-0.634111\pi$
$569$	−19.5108	−0.817936	−0.408968	+	0.912549i	$0.634111\pi$
$570$	9.92281	0.415621
$571$	29.6637	1.24139	0.620694	−	0.784053i	$-0.286851\pi$
$571$	29.6637	1.24139	0.620694	+	0.784053i	$0.286851\pi$
$572$	22.2389	0.929855
$573$	15.6635	0.654351
$574$	1.34540	0.0561560
$575$	−10.2342	−0.426797
$576$	1.00000	0.0416667
$577$	−11.9290	−0.496610	−0.248305	−	0.968682i	$-0.579873\pi$
$577$	−11.9290	−0.496610	−0.248305	+	0.968682i	$0.579873\pi$
$578$	−1.00000	−0.0415945
$579$	25.3029	1.05155
$580$	8.35177	0.346788
$581$	13.0852	0.542867
$582$	−11.4159	−0.473205
$583$	1.65177	0.0684092
$584$	−0.0349540	−0.00144641
$585$	−7.88348	−0.325942
$586$	6.87410	0.283966
$587$	−23.1181	−0.954188	−0.477094	−	0.878852i	$-0.658310\pi$
$587$	−23.1181	−0.954188	−0.477094	+	0.878852i	$0.658310\pi$
$588$	4.54151	0.187289
$589$	59.3037	2.44357
$590$	1.56975	0.0646254
$591$	22.5452	0.927386
$592$	8.41088	0.345685
$593$	−10.6787	−0.438523	−0.219262	−	0.975666i	$-0.570365\pi$
$593$	−10.6787	−0.438523	−0.219262	+	0.975666i	$0.570365\pi$
$594$	4.42818	0.181690
$595$	−2.46130	−0.100903
$596$	−4.05502	−0.166100
$597$	26.3825	1.07976
$598$	−20.2681	−0.828822
$599$	−6.05364	−0.247345	−0.123673	−	0.992323i	$-0.539467\pi$
$599$	−6.05364	−0.247345	−0.123673	+	0.992323i	$0.539467\pi$
$600$	−2.53590	−0.103528
$601$	14.7231	0.600567	0.300284	−	0.953850i	$-0.402919\pi$
$601$	14.7231	0.600567	0.300284	+	0.953850i	$0.402919\pi$
$602$	17.3182	0.705839
$603$	−7.36553	−0.299948
$604$	12.4661	0.507237
$605$	−13.5136	−0.549405
$606$	4.44890	0.180724
$607$	14.2004	0.576377	0.288188	−	0.957574i	$-0.406947\pi$
$607$	14.2004	0.576377	0.288188	+	0.957574i	$0.406947\pi$
$608$	6.32128	0.256362
$609$	8.34226	0.338045
$610$	−15.7789	−0.638869
$611$	−14.8806	−0.602004
$612$	1.00000	0.0404226
$613$	−21.3218	−0.861179	−0.430589	−	0.902548i	$-0.641694\pi$
$613$	−21.3218	−0.861179	−0.430589	+	0.902548i	$0.641694\pi$
$614$	−3.63772	−0.146806
$615$	−1.34694	−0.0543138
$616$	−6.94320	−0.279749
$617$	−0.0502364	−0.00202244	−0.00101122	−	0.999999i	$-0.500322\pi$
$617$	−0.0502364	−0.00202244	−0.00101122	+	0.999999i	$0.500322\pi$
$618$	0.173533	0.00698054
$619$	32.3130	1.29877	0.649384	−	0.760461i	$-0.275027\pi$
$619$	32.3130	1.29877	0.649384	+	0.760461i	$0.275027\pi$
$620$	14.7267	0.591440
$621$	−4.03574	−0.161949
$622$	−25.2771	−1.01352
$623$	14.9845	0.600340
$624$	−5.02214	−0.201046
$625$	−5.88975	−0.235590
$626$	−13.2592	−0.529944
$627$	27.9918	1.11788
$628$	14.3065	0.570892
$629$	8.41088	0.335364
$630$	2.46130	0.0980604
$631$	−16.4062	−0.653122	−0.326561	−	0.945176i	$-0.605890\pi$
$631$	−16.4062	−0.653122	−0.326561	+	0.945176i	$0.605890\pi$
$632$	−3.92399	−0.156088
$633$	17.2927	0.687322
$634$	18.4410	0.732387
$635$	−17.5580	−0.696769
$636$	−0.373013	−0.0147909
$637$	−22.8081	−0.903689
$638$	23.5599	0.932747
$639$	−1.31956	−0.0522009
$640$	1.56975	0.0620497
$641$	−8.15599	−0.322142	−0.161071	−	0.986943i	$-0.551495\pi$
$641$	−8.15599	−0.322142	−0.161071	+	0.986943i	$0.551495\pi$
$642$	−13.1523	−0.519081
$643$	−24.5983	−0.970063	−0.485032	−	0.874497i	$-0.661192\pi$
$643$	−24.5983	−0.970063	−0.485032	+	0.874497i	$0.661192\pi$
$644$	6.32788	0.249353
$645$	−17.3380	−0.682683
$646$	6.32128	0.248707
$647$	−24.3369	−0.956780	−0.478390	−	0.878147i	$-0.658780\pi$
$647$	−24.3369	−0.956780	−0.478390	+	0.878147i	$0.658780\pi$
$648$	−1.00000	−0.0392837
$649$	4.42818	0.173821
$650$	12.7356	0.499532
$651$	14.7100	0.576529
$652$	−10.6555	−0.417300
$653$	41.9761	1.64265	0.821325	−	0.570460i	$-0.193235\pi$
$653$	41.9761	1.64265	0.821325	+	0.570460i	$0.193235\pi$
$654$	2.31393	0.0904817
$655$	−5.38703	−0.210489
$656$	−0.858061	−0.0335017
$657$	0.0349540	0.00136368
$658$	4.64586	0.181114
$659$	−38.7798	−1.51065	−0.755323	−	0.655352i	$-0.772520\pi$
$659$	−38.7798	−1.51065	−0.755323	+	0.655352i	$0.772520\pi$
$660$	6.95112	0.270572
$661$	−36.2590	−1.41031	−0.705157	−	0.709052i	$-0.749123\pi$
$661$	−36.2590	−1.41031	−0.705157	+	0.709052i	$0.749123\pi$
$662$	9.30779	0.361757
$663$	−5.02214	−0.195044
$664$	−8.34540	−0.323865
$665$	15.5585	0.603334
$666$	−8.41088	−0.325915
$667$	−21.4720	−0.831400
$668$	4.24036	0.164065
$669$	13.3305	0.515388
$670$	−11.5620	−0.446680
$671$	−44.5115	−1.71835
$672$	1.56796	0.0604853
$673$	−41.8036	−1.61141	−0.805705	−	0.592317i	$-0.798213\pi$
$673$	−41.8036	−1.61141	−0.805705	+	0.592317i	$0.798213\pi$
$674$	−7.42181	−0.285877
$675$	2.53590	0.0976067
$676$	12.2218	0.470071
$677$	12.6939	0.487868	0.243934	−	0.969792i	$-0.421562\pi$
$677$	12.6939	0.487868	0.243934	+	0.969792i	$0.421562\pi$
$678$	−3.29878	−0.126689
$679$	−17.8997	−0.686927
$680$	1.56975	0.0601970
$681$	−14.5838	−0.558851
$682$	41.5434	1.59078
$683$	−26.7554	−1.02377	−0.511883	−	0.859055i	$-0.671052\pi$
$683$	−26.7554	−1.02377	−0.511883	+	0.859055i	$0.671052\pi$
$684$	−6.32128	−0.241700
$685$	17.5349	0.669972
$686$	18.0966	0.690931
$687$	−8.63377	−0.329399
$688$	−11.0451	−0.421090
$689$	1.87332	0.0713678
$690$	−6.33510	−0.241173
$691$	19.0999	0.726594	0.363297	−	0.931673i	$-0.381651\pi$
$691$	19.0999	0.726594	0.363297	+	0.931673i	$0.381651\pi$
$692$	19.2123	0.730342
$693$	6.94320	0.263750
$694$	6.13873	0.233023
$695$	20.9059	0.793004
$696$	−5.32046	−0.201671
$697$	−0.858061	−0.0325014
$698$	16.9484	0.641506
$699$	12.4759	0.471883
$700$	−3.97618	−0.150285
$701$	42.2524	1.59585	0.797925	−	0.602757i	$-0.205931\pi$
$701$	42.2524	1.59585	0.797925	+	0.602757i	$0.205931\pi$
$702$	5.02214	0.189548
$703$	−53.1675	−2.00525
$704$	4.42818	0.166893
$705$	−4.65116	−0.175173
$706$	−4.63094	−0.174288
$707$	6.97569	0.262348
$708$	−1.00000	−0.0375823
$709$	−6.92289	−0.259995	−0.129997	−	0.991514i	$-0.541497\pi$
$709$	−6.92289	−0.259995	−0.129997	+	0.991514i	$0.541497\pi$
$710$	−2.07137	−0.0777371
$711$	3.92399	0.147161
$712$	−9.55667	−0.358151
$713$	−37.8618	−1.41793
$714$	1.56796	0.0586793
$715$	−34.9094	−1.30554
$716$	1.20631	0.0450820
$717$	−8.39307	−0.313445
$718$	14.1063	0.526442
$719$	37.3731	1.39378	0.696890	−	0.717178i	$-0.254566\pi$
$719$	37.3731	1.39378	0.696890	+	0.717178i	$0.254566\pi$
$720$	−1.56975	−0.0585010
$721$	0.272093	0.0101333
$722$	−20.9586	−0.779998
$723$	−3.52136	−0.130961
$724$	−9.88226	−0.367271
$725$	13.4921	0.501085
$726$	8.60876	0.319501
$727$	−47.1650	−1.74925	−0.874627	−	0.484796i	$-0.838894\pi$
$727$	−47.1650	−1.74925	−0.874627	+	0.484796i	$0.838894\pi$
$728$	−7.87450	−0.291848
$729$	1.00000	0.0370370
$730$	0.0548689	0.00203079
$731$	−11.0451	−0.408517
$732$	10.0519	0.371528
$733$	−21.6421	−0.799370	−0.399685	−	0.916652i	$-0.630881\pi$
$733$	−21.6421	−0.799370	−0.399685	+	0.916652i	$0.630881\pi$
$734$	−18.2703	−0.674368
$735$	−7.12902	−0.262958
$736$	−4.03574	−0.148760
$737$	−32.6159	−1.20142
$738$	0.858061	0.0315857
$739$	−31.5759	−1.16154	−0.580769	−	0.814069i	$-0.697248\pi$
$739$	−31.5759	−1.16154	−0.580769	+	0.814069i	$0.697248\pi$
$740$	−13.2030	−0.485350
$741$	31.7463	1.16623
$742$	−0.584868	−0.0214712
$743$	−51.9752	−1.90679	−0.953393	−	0.301731i	$-0.902435\pi$
$743$	−51.9752	−1.90679	−0.953393	+	0.301731i	$0.902435\pi$
$744$	−9.38160	−0.343946
$745$	6.36535	0.233208
$746$	20.0279	0.733275
$747$	8.34540	0.305342
$748$	4.42818	0.161910
$749$	−20.6223	−0.753522
$750$	11.8294	0.431950
$751$	45.0086	1.64239	0.821194	−	0.570650i	$-0.193309\pi$
$751$	45.0086	1.64239	0.821194	+	0.570650i	$0.193309\pi$
$752$	−2.96300	−0.108050
$753$	−18.4166	−0.671140
$754$	26.7201	0.973087
$755$	−19.5685	−0.712172
$756$	−1.56796	−0.0570261
$757$	−8.79694	−0.319730	−0.159865	−	0.987139i	$-0.551106\pi$
$757$	−8.79694	−0.319730	−0.159865	+	0.987139i	$0.551106\pi$
$758$	1.50135	0.0545316
$759$	−17.8710	−0.648676
$760$	−9.92281	−0.359938
$761$	−6.50642	−0.235858	−0.117929	−	0.993022i	$-0.537625\pi$
$761$	−6.50642	−0.235858	−0.117929	+	0.993022i	$0.537625\pi$
$762$	11.1853	0.405199
$763$	3.62814	0.131348
$764$	−15.6635	−0.566684
$765$	−1.56975	−0.0567543
$766$	15.4324	0.557595
$767$	5.02214	0.181339
$768$	−1.00000	−0.0360844
$769$	−28.7458	−1.03660	−0.518300	−	0.855199i	$-0.673435\pi$
$769$	−28.7458	−1.03660	−0.518300	+	0.855199i	$0.673435\pi$
$770$	10.8991	0.392775
$771$	−20.7618	−0.747716
$772$	−25.3029	−0.910673
$773$	41.7232	1.50068	0.750340	−	0.661052i	$-0.229890\pi$
$773$	41.7232	1.50068	0.750340	+	0.661052i	$0.229890\pi$
$774$	11.0451	0.397008
$775$	23.7908	0.854590
$776$	11.4159	0.409808
$777$	−13.1879	−0.473113
$778$	10.0620	0.360740
$779$	5.42404	0.194337
$780$	7.88348	0.282274
$781$	−5.84323	−0.209087
$782$	−4.03574	−0.144318
$783$	5.32046	0.190138
$784$	−4.54151	−0.162197
$785$	−22.4576	−0.801546
$786$	3.43178	0.122408
$787$	18.7987	0.670101	0.335051	−	0.942200i	$-0.391247\pi$
$787$	18.7987	0.670101	0.335051	+	0.942200i	$0.391247\pi$
$788$	−22.5452	−0.803140
$789$	3.56931	0.127071
$790$	6.15967	0.219151
$791$	−5.17235	−0.183908
$792$	−4.42818	−0.157348
$793$	−50.4819	−1.79267
$794$	−28.4292	−1.00891
$795$	0.585535	0.0207668
$796$	−26.3825	−0.935104
$797$	10.6061	0.375689	0.187844	−	0.982199i	$-0.439850\pi$
$797$	10.6061	0.375689	0.187844	+	0.982199i	$0.439850\pi$
$798$	−9.91150	−0.350863
$799$	−2.96300	−0.104823
$800$	2.53590	0.0896575
$801$	9.55667	0.337668
$802$	5.67523	0.200399
$803$	0.154782	0.00546215
$804$	7.36553	0.259762
$805$	−9.93316	−0.350098
$806$	47.1157	1.65958
$807$	26.5567	0.934840
$808$	−4.44890	−0.156512
$809$	15.4536	0.543318	0.271659	−	0.962394i	$-0.412428\pi$
$809$	15.4536	0.543318	0.271659	+	0.962394i	$0.412428\pi$
$810$	1.56975	0.0551553
$811$	20.8835	0.733317	0.366659	−	0.930356i	$-0.380502\pi$
$811$	20.8835	0.733317	0.366659	+	0.930356i	$0.380502\pi$
$812$	−8.34226	−0.292756
$813$	10.5286	0.369255
$814$	−37.2449	−1.30543
$815$	16.7264	0.585899
$816$	−1.00000	−0.0350070
$817$	69.8191	2.44266
$818$	18.1140	0.633339
$819$	7.87450	0.275157
$820$	1.34694	0.0470371
$821$	27.0740	0.944890	0.472445	−	0.881360i	$-0.343371\pi$
$821$	27.0740	0.944890	0.472445	+	0.881360i	$0.343371\pi$
$822$	−11.1705	−0.389616
$823$	−49.5686	−1.72785	−0.863926	−	0.503618i	$-0.832002\pi$
$823$	−49.5686	−1.72785	−0.863926	+	0.503618i	$0.832002\pi$
$824$	−0.173533	−0.00604532
$825$	11.2294	0.390957
$826$	−1.56796	−0.0545562
$827$	50.1174	1.74275	0.871377	−	0.490614i	$-0.163228\pi$
$827$	50.1174	1.74275	0.871377	+	0.490614i	$0.163228\pi$
$828$	4.03574	0.140252
$829$	−20.4254	−0.709403	−0.354702	−	0.934980i	$-0.615418\pi$
$829$	−20.4254	−0.709403	−0.354702	+	0.934980i	$0.615418\pi$
$830$	13.1002	0.454714
$831$	−10.0077	−0.347164
$832$	5.02214	0.174111
$833$	−4.54151	−0.157354
$834$	−13.3180	−0.461164
$835$	−6.65630	−0.230351
$836$	−27.9918	−0.968115
$837$	9.38160	0.324276
$838$	−25.3939	−0.877219
$839$	−31.0610	−1.07234	−0.536172	−	0.844109i	$-0.680130\pi$
$839$	−31.0610	−1.07234	−0.536172	+	0.844109i	$0.680130\pi$
$840$	−2.46130	−0.0849228
$841$	−0.692715	−0.0238867
$842$	−38.0914	−1.31272
$843$	15.9410	0.549038
$844$	−17.2927	−0.595238
$845$	−19.1852	−0.659991
$846$	2.96300	0.101870
$847$	13.4982	0.463802
$848$	0.373013	0.0128093
$849$	−20.6867	−0.709967
$850$	2.53590	0.0869805
$851$	33.9442	1.16359
$852$	1.31956	0.0452073
$853$	24.8509	0.850879	0.425440	−	0.904987i	$-0.360119\pi$
$853$	24.8509	0.850879	0.425440	+	0.904987i	$0.360119\pi$
$854$	15.7609	0.539328
$855$	9.92281	0.339353
$856$	13.1523	0.449537
$857$	−31.5475	−1.07764	−0.538821	−	0.842420i	$-0.681130\pi$
$857$	−31.5475	−1.07764	−0.538821	+	0.842420i	$0.681130\pi$
$858$	22.2389	0.759224
$859$	18.7837	0.640893	0.320446	−	0.947267i	$-0.396167\pi$
$859$	18.7837	0.640893	0.320446	+	0.947267i	$0.396167\pi$
$860$	17.3380	0.591221
$861$	1.34540	0.0458512
$862$	−17.7075	−0.603119
$863$	23.9474	0.815179	0.407590	−	0.913165i	$-0.366369\pi$
$863$	23.9474	0.815179	0.407590	+	0.913165i	$0.366369\pi$
$864$	1.00000	0.0340207
$865$	−30.1584	−1.02542
$866$	−16.1988	−0.550458
$867$	−1.00000	−0.0339618
$868$	−14.7100	−0.499289
$869$	17.3761	0.589445
$870$	8.35177	0.283152
$871$	−36.9907	−1.25338
$872$	−2.31393	−0.0783595
$873$	−11.4159	−0.386370
$874$	25.5111	0.862925
$875$	18.5481	0.627039
$876$	−0.0349540	−0.00118099
$877$	−41.0595	−1.38648	−0.693240	−	0.720707i	$-0.743817\pi$
$877$	−41.0595	−1.38648	−0.693240	+	0.720707i	$0.743817\pi$
$878$	−29.1901	−0.985118
$879$	6.87410	0.231858
$880$	−6.95112	−0.234322
$881$	39.2815	1.32343	0.661714	−	0.749757i	$-0.269829\pi$
$881$	39.2815	1.32343	0.661714	+	0.749757i	$0.269829\pi$
$882$	4.54151	0.152921
$883$	−9.45275	−0.318110	−0.159055	−	0.987270i	$-0.550845\pi$
$883$	−9.45275	−0.318110	−0.159055	+	0.987270i	$0.550845\pi$
$884$	5.02214	0.168913
$885$	1.56975	0.0527665
$886$	8.54060	0.286927
$887$	−22.8709	−0.767930	−0.383965	−	0.923348i	$-0.625442\pi$
$887$	−22.8709	−0.767930	−0.383965	+	0.923348i	$0.625442\pi$
$888$	8.41088	0.282251
$889$	17.5380	0.588206
$890$	15.0016	0.502853
$891$	4.42818	0.148350
$892$	−13.3305	−0.446339
$893$	18.7300	0.626774
$894$	−4.05502	−0.135620
$895$	−1.89361	−0.0632962
$896$	−1.56796	−0.0523818
$897$	−20.2681	−0.676731
$898$	−21.8035	−0.727591
$899$	49.9144	1.66474
$900$	−2.53590	−0.0845299
$901$	0.373013	0.0124269
$902$	3.79965	0.126514
$903$	17.3182	0.576315
$904$	3.29878	0.109716
$905$	15.5126	0.515657
$906$	12.4661	0.414157
$907$	−11.9705	−0.397473	−0.198736	−	0.980053i	$-0.563684\pi$
$907$	−11.9705	−0.397473	−0.198736	+	0.980053i	$0.563684\pi$
$908$	14.5838	0.483979
$909$	4.44890	0.147561
$910$	12.3610	0.409762
$911$	5.21211	0.172685	0.0863425	−	0.996266i	$-0.472482\pi$
$911$	5.21211	0.172685	0.0863425	+	0.996266i	$0.472482\pi$
$912$	6.32128	0.209319
$913$	36.9549	1.22303
$914$	20.8093	0.688311
$915$	−15.7789	−0.521635
$916$	8.63377	0.285268
$917$	5.38089	0.177693
$918$	1.00000	0.0330049
$919$	−4.83798	−0.159590	−0.0797952	−	0.996811i	$-0.525427\pi$
$919$	−4.83798	−0.159590	−0.0797952	+	0.996811i	$0.525427\pi$
$920$	6.33510	0.208862
$921$	−3.63772	−0.119867
$922$	−35.7768	−1.17825
$923$	−6.62699	−0.218130
$924$	−6.94320	−0.228414
$925$	−21.3291	−0.701297
$926$	−21.2430	−0.698089
$927$	0.173533	0.00569959
$928$	5.32046	0.174653
$929$	−3.84123	−0.126027	−0.0630133	−	0.998013i	$-0.520071\pi$
$929$	−3.84123	−0.126027	−0.0630133	+	0.998013i	$0.520071\pi$
$930$	14.7267	0.482909
$931$	28.7081	0.940872
$932$	−12.4759	−0.408663
$933$	−25.2771	−0.827535
$934$	23.2909	0.762101
$935$	−6.95112	−0.227326
$936$	−5.02214	−0.164154
$937$	20.2336	0.661002	0.330501	−	0.943806i	$-0.392782\pi$
$937$	20.2336	0.661002	0.330501	+	0.943806i	$0.392782\pi$
$938$	11.5488	0.377083
$939$	−13.2592	−0.432697
$940$	4.65116	0.151704
$941$	48.1467	1.56954	0.784769	−	0.619788i	$-0.212781\pi$
$941$	48.1467	1.56954	0.784769	+	0.619788i	$0.212781\pi$
$942$	14.3065	0.466131
$943$	−3.46291	−0.112768
$944$	1.00000	0.0325472
$945$	2.46130	0.0800660
$946$	48.9096	1.59019
$947$	20.4616	0.664914	0.332457	−	0.943118i	$-0.392122\pi$
$947$	20.4616	0.664914	0.332457	+	0.943118i	$0.392122\pi$
$948$	−3.92399	−0.127445
$949$	0.175544	0.00569839
$950$	−16.0301	−0.520085
$951$	18.4410	0.597992
$952$	−1.56796	−0.0508178
$953$	41.6496	1.34916	0.674582	−	0.738200i	$-0.264324\pi$
$953$	41.6496	1.34916	0.674582	+	0.738200i	$0.264324\pi$
$954$	−0.373013	−0.0120767
$955$	24.5877	0.795638
$956$	8.39307	0.271451
$957$	23.5599	0.761585
$958$	35.0581	1.13268
$959$	−17.5149	−0.565585
$960$	1.56975	0.0506633
$961$	57.0145	1.83918
$962$	−42.2406	−1.36189
$963$	−13.1523	−0.423828
$964$	3.52136	0.113416
$965$	39.7192	1.27861
$966$	6.32788	0.203596
$967$	26.3480	0.847295	0.423648	−	0.905827i	$-0.360750\pi$
$967$	26.3480	0.847295	0.423648	+	0.905827i	$0.360750\pi$
$968$	−8.60876	−0.276696
$969$	6.32128	0.203069
$970$	−17.9201	−0.575380
$971$	−2.71713	−0.0871969	−0.0435984	−	0.999049i	$-0.513882\pi$
$971$	−2.71713	−0.0871969	−0.0435984	+	0.999049i	$0.513882\pi$
$972$	−1.00000	−0.0320750
$973$	−20.8820	−0.669447
$974$	38.1135	1.22124
$975$	12.7356	0.407866
$976$	−10.0519	−0.321753
$977$	−14.2246	−0.455084	−0.227542	−	0.973768i	$-0.573069\pi$
$977$	−14.2246	−0.455084	−0.227542	+	0.973768i	$0.573069\pi$
$978$	−10.6555	−0.340724
$979$	42.3186	1.35251
$980$	7.12902	0.227728
$981$	2.31393	0.0738780
$982$	34.4388	1.09899
$983$	−52.7224	−1.68158	−0.840792	−	0.541358i	$-0.817910\pi$
$983$	−52.7224	−1.68158	−0.840792	+	0.541358i	$0.817910\pi$
$984$	−0.858061	−0.0273540
$985$	35.3903	1.12763
$986$	5.32046	0.169438
$987$	4.64586	0.147879
$988$	−31.7463	−1.00999
$989$	−44.5752	−1.41741
$990$	6.95112	0.220921
$991$	25.5172	0.810580	0.405290	−	0.914188i	$-0.367170\pi$
$991$	25.5172	0.810580	0.405290	+	0.914188i	$0.367170\pi$
$992$	9.38160	0.297866
$993$	9.30779	0.295374
$994$	2.06901	0.0656250
$995$	41.4139	1.31291
$996$	−8.34540	−0.264434
$997$	−18.2407	−0.577688	−0.288844	−	0.957376i	$-0.593271\pi$
$997$	−18.2407	−0.577688	−0.288844	+	0.957376i	$0.593271\pi$
$998$	19.8910	0.629639
$999$	−8.41088	−0.266108

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.u.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.u.1.3	✓	9	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.56975 q^{5} +1.00000 q^{6} +1.56796 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.56975 q^{5} +1.00000 q^{6} +1.56796 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.56975 q^{10} +4.42818 q^{11} -1.00000 q^{12} +5.02214 q^{13} -1.56796 q^{14} +1.56975 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -6.32128 q^{19} -1.56975 q^{20} -1.56796 q^{21} -4.42818 q^{22} +4.03574 q^{23} +1.00000 q^{24} -2.53590 q^{25} -5.02214 q^{26} -1.00000 q^{27} +1.56796 q^{28} -5.32046 q^{29} -1.56975 q^{30} -9.38160 q^{31} -1.00000 q^{32} -4.42818 q^{33} -1.00000 q^{34} -2.46130 q^{35} +1.00000 q^{36} +8.41088 q^{37} +6.32128 q^{38} -5.02214 q^{39} +1.56975 q^{40} -0.858061 q^{41} +1.56796 q^{42} -11.0451 q^{43} +4.42818 q^{44} -1.56975 q^{45} -4.03574 q^{46} -2.96300 q^{47} -1.00000 q^{48} -4.54151 q^{49} +2.53590 q^{50} -1.00000 q^{51} +5.02214 q^{52} +0.373013 q^{53} +1.00000 q^{54} -6.95112 q^{55} -1.56796 q^{56} +6.32128 q^{57} +5.32046 q^{58} +1.00000 q^{59} +1.56975 q^{60} -10.0519 q^{61} +9.38160 q^{62} +1.56796 q^{63} +1.00000 q^{64} -7.88348 q^{65} +4.42818 q^{66} -7.36553 q^{67} +1.00000 q^{68} -4.03574 q^{69} +2.46130 q^{70} -1.31956 q^{71} -1.00000 q^{72} +0.0349540 q^{73} -8.41088 q^{74} +2.53590 q^{75} -6.32128 q^{76} +6.94320 q^{77} +5.02214 q^{78} +3.92399 q^{79} -1.56975 q^{80} +1.00000 q^{81} +0.858061 q^{82} +8.34540 q^{83} -1.56796 q^{84} -1.56975 q^{85} +11.0451 q^{86} +5.32046 q^{87} -4.42818 q^{88} +9.55667 q^{89} +1.56975 q^{90} +7.87450 q^{91} +4.03574 q^{92} +9.38160 q^{93} +2.96300 q^{94} +9.92281 q^{95} +1.00000 q^{96} -11.4159 q^{97} +4.54151 q^{98} +4.42818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9} - 2 q^{10} - q^{11} - 9 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 7 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} + 4 q^{26} - 9 q^{27} - 5 q^{28} + 6 q^{29} + 2 q^{30} - 17 q^{31} - 9 q^{32} + q^{33} - 9 q^{34} + 10 q^{35} + 9 q^{36} + 2 q^{37} + 7 q^{38} + 4 q^{39} - 2 q^{40} + 14 q^{41} - 5 q^{42} - 27 q^{43} - q^{44} + 2 q^{45} + 8 q^{46} - 18 q^{47} - 9 q^{48} + 18 q^{49} - 5 q^{50} - 9 q^{51} - 4 q^{52} + 4 q^{53} + 9 q^{54} - 27 q^{55} + 5 q^{56} + 7 q^{57} - 6 q^{58} + 9 q^{59} - 2 q^{60} + 5 q^{61} + 17 q^{62} - 5 q^{63} + 9 q^{64} + 2 q^{65} - q^{66} - 22 q^{67} + 9 q^{68} + 8 q^{69} - 10 q^{70} + 16 q^{71} - 9 q^{72} - 12 q^{73} - 2 q^{74} - 5 q^{75} - 7 q^{76} + 6 q^{77} - 4 q^{78} - 9 q^{79} + 2 q^{80} + 9 q^{81} - 14 q^{82} + 10 q^{83} + 5 q^{84} + 2 q^{85} + 27 q^{86} - 6 q^{87} + q^{88} + 15 q^{89} - 2 q^{90} + 3 q^{91} - 8 q^{92} + 17 q^{93} + 18 q^{94} - 9 q^{95} + 9 q^{96} - 33 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9 - 2 * q^10 - q^11 - 9 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^15 + 9 * q^16 + 9 * q^17 - 9 * q^18 - 7 * q^19 + 2 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 9 * q^24 + 5 * q^25 + 4 * q^26 - 9 * q^27 - 5 * q^28 + 6 * q^29 + 2 * q^30 - 17 * q^31 - 9 * q^32 + q^33 - 9 * q^34 + 10 * q^35 + 9 * q^36 + 2 * q^37 + 7 * q^38 + 4 * q^39 - 2 * q^40 + 14 * q^41 - 5 * q^42 - 27 * q^43 - q^44 + 2 * q^45 + 8 * q^46 - 18 * q^47 - 9 * q^48 + 18 * q^49 - 5 * q^50 - 9 * q^51 - 4 * q^52 + 4 * q^53 + 9 * q^54 - 27 * q^55 + 5 * q^56 + 7 * q^57 - 6 * q^58 + 9 * q^59 - 2 * q^60 + 5 * q^61 + 17 * q^62 - 5 * q^63 + 9 * q^64 + 2 * q^65 - q^66 - 22 * q^67 + 9 * q^68 + 8 * q^69 - 10 * q^70 + 16 * q^71 - 9 * q^72 - 12 * q^73 - 2 * q^74 - 5 * q^75 - 7 * q^76 + 6 * q^77 - 4 * q^78 - 9 * q^79 + 2 * q^80 + 9 * q^81 - 14 * q^82 + 10 * q^83 + 5 * q^84 + 2 * q^85 + 27 * q^86 - 6 * q^87 + q^88 + 15 * q^89 - 2 * q^90 + 3 * q^91 - 8 * q^92 + 17 * q^93 + 18 * q^94 - 9 * q^95 + 9 * q^96 - 33 * q^97 - 18 * q^98 - q^99

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