LMFDB - Embedded newform 6018.2.a.ba.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 31 x^{10} + 111 x^{9} + 381 x^{8} - 1101 x^{7} - 2301 x^{6} + 4690 x^{5} + \cdots + 5653 $ x^12 - 4x^11 - 31x^10 + 111x^9 + 381x^8 - 1101x^7 - 2301x^6 + 4690x^5 + 6915x^4 - 8325x^3 - 10082x^2 + 5149*x + 5653
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			1.8
Root			$-1.11808$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.11808 q^{5} +1.00000 q^{6} +1.85275 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.11808 q^{5} +1.00000 q^{6} +1.85275 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.11808 q^{10} -0.995175 q^{11} +1.00000 q^{12} +4.79808 q^{13} +1.85275 q^{14} +2.11808 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +4.98131 q^{19} +2.11808 q^{20} +1.85275 q^{21} -0.995175 q^{22} -0.704010 q^{23} +1.00000 q^{24} -0.513749 q^{25} +4.79808 q^{26} +1.00000 q^{27} +1.85275 q^{28} -3.89769 q^{29} +2.11808 q^{30} -8.75624 q^{31} +1.00000 q^{32} -0.995175 q^{33} -1.00000 q^{34} +3.92427 q^{35} +1.00000 q^{36} +6.77580 q^{37} +4.98131 q^{38} +4.79808 q^{39} +2.11808 q^{40} +10.0025 q^{41} +1.85275 q^{42} +2.56650 q^{43} -0.995175 q^{44} +2.11808 q^{45} -0.704010 q^{46} -1.28850 q^{47} +1.00000 q^{48} -3.56730 q^{49} -0.513749 q^{50} -1.00000 q^{51} +4.79808 q^{52} +4.45878 q^{53} +1.00000 q^{54} -2.10786 q^{55} +1.85275 q^{56} +4.98131 q^{57} -3.89769 q^{58} +1.00000 q^{59} +2.11808 q^{60} -6.40474 q^{61} -8.75624 q^{62} +1.85275 q^{63} +1.00000 q^{64} +10.1627 q^{65} -0.995175 q^{66} -10.3643 q^{67} -1.00000 q^{68} -0.704010 q^{69} +3.92427 q^{70} -0.787298 q^{71} +1.00000 q^{72} -6.86869 q^{73} +6.77580 q^{74} -0.513749 q^{75} +4.98131 q^{76} -1.84381 q^{77} +4.79808 q^{78} +1.42408 q^{79} +2.11808 q^{80} +1.00000 q^{81} +10.0025 q^{82} +8.93027 q^{83} +1.85275 q^{84} -2.11808 q^{85} +2.56650 q^{86} -3.89769 q^{87} -0.995175 q^{88} +11.7078 q^{89} +2.11808 q^{90} +8.88967 q^{91} -0.704010 q^{92} -8.75624 q^{93} -1.28850 q^{94} +10.5508 q^{95} +1.00000 q^{96} -2.30503 q^{97} -3.56730 q^{98} -0.995175 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * 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
$5$	2.11808	0.947233	0.473616	−	0.880731i	$-0.342948\pi$
$5$	2.11808	0.947233	0.473616	+	0.880731i	$0.342948\pi$
$6$	1.00000	0.408248
$7$	1.85275	0.700275	0.350137	−	0.936698i	$-0.386135\pi$
$7$	1.85275	0.700275	0.350137	+	0.936698i	$0.386135\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.11808	0.669795
$11$	−0.995175	−0.300056	−0.150028	−	0.988682i	$-0.547936\pi$
$11$	−0.995175	−0.300056	−0.150028	+	0.988682i	$0.547936\pi$
$12$	1.00000	0.288675
$13$	4.79808	1.33075	0.665374	−	0.746510i	$-0.268272\pi$
$13$	4.79808	1.33075	0.665374	+	0.746510i	$0.268272\pi$
$14$	1.85275	0.495169
$15$	2.11808	0.546885
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	4.98131	1.14279	0.571396	−	0.820675i	$-0.306402\pi$
$19$	4.98131	1.14279	0.571396	+	0.820675i	$0.306402\pi$
$20$	2.11808	0.473616
$21$	1.85275	0.404304
$22$	−0.995175	−0.212172
$23$	−0.704010	−0.146796	−0.0733982	−	0.997303i	$-0.523384\pi$
$23$	−0.704010	−0.146796	−0.0733982	+	0.997303i	$0.523384\pi$
$24$	1.00000	0.204124
$25$	−0.513749	−0.102750
$26$	4.79808	0.940982
$27$	1.00000	0.192450
$28$	1.85275	0.350137
$29$	−3.89769	−0.723783	−0.361891	−	0.932220i	$-0.617869\pi$
$29$	−3.89769	−0.723783	−0.361891	+	0.932220i	$0.617869\pi$
$30$	2.11808	0.386706
$31$	−8.75624	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$31$	−8.75624	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$32$	1.00000	0.176777
$33$	−0.995175	−0.173238
$34$	−1.00000	−0.171499
$35$	3.92427	0.663324
$36$	1.00000	0.166667
$37$	6.77580	1.11394	0.556968	−	0.830534i	$-0.311965\pi$
$37$	6.77580	1.11394	0.556968	+	0.830534i	$0.311965\pi$
$38$	4.98131	0.808076
$39$	4.79808	0.768308
$40$	2.11808	0.334897
$41$	10.0025	1.56212	0.781061	−	0.624455i	$-0.214679\pi$
$41$	10.0025	1.56212	0.781061	+	0.624455i	$0.214679\pi$
$42$	1.85275	0.285886
$43$	2.56650	0.391388	0.195694	−	0.980665i	$-0.437304\pi$
$43$	2.56650	0.391388	0.195694	+	0.980665i	$0.437304\pi$
$44$	−0.995175	−0.150028
$45$	2.11808	0.315744
$46$	−0.704010	−0.103801
$47$	−1.28850	−0.187947	−0.0939733	−	0.995575i	$-0.529957\pi$
$47$	−1.28850	−0.187947	−0.0939733	+	0.995575i	$0.529957\pi$
$48$	1.00000	0.144338
$49$	−3.56730	−0.509615
$50$	−0.513749	−0.0726551
$51$	−1.00000	−0.140028
$52$	4.79808	0.665374
$53$	4.45878	0.612461	0.306231	−	0.951957i	$-0.400932\pi$
$53$	4.45878	0.612461	0.306231	+	0.951957i	$0.400932\pi$
$54$	1.00000	0.136083
$55$	−2.10786	−0.284223
$56$	1.85275	0.247585
$57$	4.98131	0.659791
$58$	−3.89769	−0.511792
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	2.11808	0.273443
$61$	−6.40474	−0.820043	−0.410021	−	0.912076i	$-0.634479\pi$
$61$	−6.40474	−0.820043	−0.410021	+	0.912076i	$0.634479\pi$
$62$	−8.75624	−1.11204
$63$	1.85275	0.233425
$64$	1.00000	0.125000
$65$	10.1627	1.26053
$66$	−0.995175	−0.122498
$67$	−10.3643	−1.26621	−0.633103	−	0.774068i	$-0.718219\pi$
$67$	−10.3643	−1.26621	−0.633103	+	0.774068i	$0.718219\pi$
$68$	−1.00000	−0.121268
$69$	−0.704010	−0.0847529
$70$	3.92427	0.469041
$71$	−0.787298	−0.0934350	−0.0467175	−	0.998908i	$-0.514876\pi$
$71$	−0.787298	−0.0934350	−0.0467175	+	0.998908i	$0.514876\pi$
$72$	1.00000	0.117851
$73$	−6.86869	−0.803919	−0.401960	−	0.915657i	$-0.631671\pi$
$73$	−6.86869	−0.803919	−0.401960	+	0.915657i	$0.631671\pi$
$74$	6.77580	0.787671
$75$	−0.513749	−0.0593226
$76$	4.98131	0.571396
$77$	−1.84381	−0.210122
$78$	4.79808	0.543276
$79$	1.42408	0.160221	0.0801106	−	0.996786i	$-0.474473\pi$
$79$	1.42408	0.160221	0.0801106	+	0.996786i	$0.474473\pi$
$80$	2.11808	0.236808
$81$	1.00000	0.111111
$82$	10.0025	1.10459
$83$	8.93027	0.980224	0.490112	−	0.871659i	$-0.336956\pi$
$83$	8.93027	0.980224	0.490112	+	0.871659i	$0.336956\pi$
$84$	1.85275	0.202152
$85$	−2.11808	−0.229738
$86$	2.56650	0.276753
$87$	−3.89769	−0.417876
$88$	−0.995175	−0.106086
$89$	11.7078	1.24103	0.620514	−	0.784195i	$-0.286924\pi$
$89$	11.7078	1.24103	0.620514	+	0.784195i	$0.286924\pi$
$90$	2.11808	0.223265
$91$	8.88967	0.931890
$92$	−0.704010	−0.0733982
$93$	−8.75624	−0.907980
$94$	−1.28850	−0.132898
$95$	10.5508	1.08249
$96$	1.00000	0.102062
$97$	−2.30503	−0.234040	−0.117020	−	0.993130i	$-0.537334\pi$
$97$	−2.30503	−0.234040	−0.117020	+	0.993130i	$0.537334\pi$
$98$	−3.56730	−0.360352
$99$	−0.995175	−0.100019
$100$	−0.513749	−0.0513749
$101$	−11.8041	−1.17455	−0.587274	−	0.809389i	$-0.699799\pi$
$101$	−11.8041	−1.17455	−0.587274	+	0.809389i	$0.699799\pi$
$102$	−1.00000	−0.0990148
$103$	−7.22800	−0.712196	−0.356098	−	0.934449i	$-0.615893\pi$
$103$	−7.22800	−0.712196	−0.356098	+	0.934449i	$0.615893\pi$
$104$	4.79808	0.470491
$105$	3.92427	0.382970
$106$	4.45878	0.433075
$107$	−12.4263	−1.20130	−0.600650	−	0.799512i	$-0.705092\pi$
$107$	−12.4263	−1.20130	−0.600650	+	0.799512i	$0.705092\pi$
$108$	1.00000	0.0962250
$109$	3.65506	0.350091	0.175046	−	0.984560i	$-0.443993\pi$
$109$	3.65506	0.350091	0.175046	+	0.984560i	$0.443993\pi$
$110$	−2.10786	−0.200976
$111$	6.77580	0.643131
$112$	1.85275	0.175069
$113$	15.1060	1.42105	0.710526	−	0.703671i	$-0.248457\pi$
$113$	15.1060	1.42105	0.710526	+	0.703671i	$0.248457\pi$
$114$	4.98131	0.466543
$115$	−1.49115	−0.139050
$116$	−3.89769	−0.361891
$117$	4.79808	0.443583
$118$	1.00000	0.0920575
$119$	−1.85275	−0.169842
$120$	2.11808	0.193353
$121$	−10.0096	−0.909966
$122$	−6.40474	−0.579858
$123$	10.0025	0.901892
$124$	−8.75624	−0.786334
$125$	−11.6785	−1.04456
$126$	1.85275	0.165056
$127$	−16.7083	−1.48263	−0.741313	−	0.671159i	$-0.765797\pi$
$127$	−16.7083	−1.48263	−0.741313	+	0.671159i	$0.765797\pi$
$128$	1.00000	0.0883883
$129$	2.56650	0.225968
$130$	10.1627	0.891329
$131$	20.3086	1.77437	0.887187	−	0.461409i	$-0.152656\pi$
$131$	20.3086	1.77437	0.887187	+	0.461409i	$0.152656\pi$
$132$	−0.995175	−0.0866188
$133$	9.22914	0.800268
$134$	−10.3643	−0.895342
$135$	2.11808	0.182295
$136$	−1.00000	−0.0857493
$137$	−6.33855	−0.541539	−0.270770	−	0.962644i	$-0.587278\pi$
$137$	−6.33855	−0.541539	−0.270770	+	0.962644i	$0.587278\pi$
$138$	−0.704010	−0.0599294
$139$	−13.0618	−1.10789	−0.553944	−	0.832554i	$-0.686878\pi$
$139$	−13.0618	−1.10789	−0.553944	+	0.832554i	$0.686878\pi$
$140$	3.92427	0.331662
$141$	−1.28850	−0.108511
$142$	−0.787298	−0.0660685
$143$	−4.77493	−0.399300
$144$	1.00000	0.0833333
$145$	−8.25561	−0.685591
$146$	−6.86869	−0.568457
$147$	−3.56730	−0.294226
$148$	6.77580	0.556968
$149$	−7.29411	−0.597557	−0.298778	−	0.954323i	$-0.596579\pi$
$149$	−7.29411	−0.597557	−0.298778	+	0.954323i	$0.596579\pi$
$150$	−0.513749	−0.0419474
$151$	−9.80168	−0.797650	−0.398825	−	0.917027i	$-0.630582\pi$
$151$	−9.80168	−0.797650	−0.398825	+	0.917027i	$0.630582\pi$
$152$	4.98131	0.404038
$153$	−1.00000	−0.0808452
$154$	−1.84381	−0.148579
$155$	−18.5464	−1.48968
$156$	4.79808	0.384154
$157$	13.6043	1.08574	0.542871	−	0.839816i	$-0.317337\pi$
$157$	13.6043	1.08574	0.542871	+	0.839816i	$0.317337\pi$
$158$	1.42408	0.113293
$159$	4.45878	0.353605
$160$	2.11808	0.167449
$161$	−1.30436	−0.102798
$162$	1.00000	0.0785674
$163$	−4.53377	−0.355113	−0.177556	−	0.984111i	$-0.556819\pi$
$163$	−4.53377	−0.355113	−0.177556	+	0.984111i	$0.556819\pi$
$164$	10.0025	0.781061
$165$	−2.10786	−0.164096
$166$	8.93027	0.693123
$167$	9.84395	0.761748	0.380874	−	0.924627i	$-0.375623\pi$
$167$	9.84395	0.761748	0.380874	+	0.924627i	$0.375623\pi$
$168$	1.85275	0.142943
$169$	10.0216	0.770893
$170$	−2.11808	−0.162449
$171$	4.98131	0.380931
$172$	2.56650	0.195694
$173$	8.46684	0.643722	0.321861	−	0.946787i	$-0.395692\pi$
$173$	8.46684	0.643722	0.321861	+	0.946787i	$0.395692\pi$
$174$	−3.89769	−0.295483
$175$	−0.951850	−0.0719531
$176$	−0.995175	−0.0750141
$177$	1.00000	0.0751646
$178$	11.7078	0.877539
$179$	−11.6338	−0.869555	−0.434777	−	0.900538i	$-0.643173\pi$
$179$	−11.6338	−0.869555	−0.434777	+	0.900538i	$0.643173\pi$
$180$	2.11808	0.157872
$181$	−10.7254	−0.797209	−0.398605	−	0.917123i	$-0.630505\pi$
$181$	−10.7254	−0.797209	−0.398605	+	0.917123i	$0.630505\pi$
$182$	8.88967	0.658946
$183$	−6.40474	−0.473452
$184$	−0.704010	−0.0519003
$185$	14.3517	1.05516
$186$	−8.75624	−0.642039
$187$	0.995175	0.0727744
$188$	−1.28850	−0.0939733
$189$	1.85275	0.134768
$190$	10.5508	0.765436
$191$	0.841466	0.0608863	0.0304432	−	0.999536i	$-0.490308\pi$
$191$	0.841466	0.0608863	0.0304432	+	0.999536i	$0.490308\pi$
$192$	1.00000	0.0721688
$193$	−3.94169	−0.283729	−0.141865	−	0.989886i	$-0.545310\pi$
$193$	−3.94169	−0.283729	−0.141865	+	0.989886i	$0.545310\pi$
$194$	−2.30503	−0.165491
$195$	10.1627	0.727767
$196$	−3.56730	−0.254807
$197$	21.7583	1.55021	0.775106	−	0.631831i	$-0.217696\pi$
$197$	21.7583	1.55021	0.775106	+	0.631831i	$0.217696\pi$
$198$	−0.995175	−0.0707240
$199$	26.7952	1.89946	0.949730	−	0.313071i	$-0.101358\pi$
$199$	26.7952	1.89946	0.949730	+	0.313071i	$0.101358\pi$
$200$	−0.513749	−0.0363275
$201$	−10.3643	−0.731044
$202$	−11.8041	−0.830530
$203$	−7.22146	−0.506847
$204$	−1.00000	−0.0700140
$205$	21.1860	1.47969
$206$	−7.22800	−0.503599
$207$	−0.704010	−0.0489321
$208$	4.79808	0.332687
$209$	−4.95728	−0.342902
$210$	3.92427	0.270801
$211$	22.8331	1.57189	0.785946	−	0.618295i	$-0.212176\pi$
$211$	22.8331	1.57189	0.785946	+	0.618295i	$0.212176\pi$
$212$	4.45878	0.306231
$213$	−0.787298	−0.0539447
$214$	−12.4263	−0.849448
$215$	5.43605	0.370735
$216$	1.00000	0.0680414
$217$	−16.2232	−1.10130
$218$	3.65506	0.247552
$219$	−6.86869	−0.464143
$220$	−2.10786	−0.142112
$221$	−4.79808	−0.322754
$222$	6.77580	0.454762
$223$	−3.83272	−0.256658	−0.128329	−	0.991732i	$-0.540961\pi$
$223$	−3.83272	−0.256658	−0.128329	+	0.991732i	$0.540961\pi$
$224$	1.85275	0.123792
$225$	−0.513749	−0.0342499
$226$	15.1060	1.00484
$227$	1.94283	0.128950	0.0644750	−	0.997919i	$-0.479463\pi$
$227$	1.94283	0.128950	0.0644750	+	0.997919i	$0.479463\pi$
$228$	4.98131	0.329896
$229$	2.17295	0.143593	0.0717963	−	0.997419i	$-0.477127\pi$
$229$	2.17295	0.143593	0.0717963	+	0.997419i	$0.477127\pi$
$230$	−1.49115	−0.0983234
$231$	−1.84381	−0.121314
$232$	−3.89769	−0.255896
$233$	22.0535	1.44477	0.722386	−	0.691490i	$-0.243046\pi$
$233$	22.0535	1.44477	0.722386	+	0.691490i	$0.243046\pi$
$234$	4.79808	0.313661
$235$	−2.72914	−0.178029
$236$	1.00000	0.0650945
$237$	1.42408	0.0925037
$238$	−1.85275	−0.120096
$239$	7.37723	0.477193	0.238597	−	0.971119i	$-0.423313\pi$
$239$	7.37723	0.477193	0.238597	+	0.971119i	$0.423313\pi$
$240$	2.11808	0.136721
$241$	8.63840	0.556448	0.278224	−	0.960516i	$-0.410254\pi$
$241$	8.63840	0.556448	0.278224	+	0.960516i	$0.410254\pi$
$242$	−10.0096	−0.643443
$243$	1.00000	0.0641500
$244$	−6.40474	−0.410021
$245$	−7.55583	−0.482724
$246$	10.0025	0.637734
$247$	23.9008	1.52077
$248$	−8.75624	−0.556022
$249$	8.93027	0.565933
$250$	−11.6785	−0.738616
$251$	−1.18407	−0.0747377	−0.0373689	−	0.999302i	$-0.511898\pi$
$251$	−1.18407	−0.0747377	−0.0373689	+	0.999302i	$0.511898\pi$
$252$	1.85275	0.116712
$253$	0.700613	0.0440472
$254$	−16.7083	−1.04838
$255$	−2.11808	−0.132639
$256$	1.00000	0.0625000
$257$	3.52679	0.219995	0.109997	−	0.993932i	$-0.464916\pi$
$257$	3.52679	0.219995	0.109997	+	0.993932i	$0.464916\pi$
$258$	2.56650	0.159783
$259$	12.5539	0.780061
$260$	10.1627	0.630265
$261$	−3.89769	−0.241261
$262$	20.3086	1.25467
$263$	−2.96129	−0.182601	−0.0913004	−	0.995823i	$-0.529102\pi$
$263$	−2.96129	−0.182601	−0.0913004	+	0.995823i	$0.529102\pi$
$264$	−0.995175	−0.0612488
$265$	9.44405	0.580143
$266$	9.22914	0.565875
$267$	11.7078	0.716508
$268$	−10.3643	−0.633103
$269$	−28.5630	−1.74151	−0.870757	−	0.491713i	$-0.836371\pi$
$269$	−28.5630	−1.74151	−0.870757	+	0.491713i	$0.836371\pi$
$270$	2.11808	0.128902
$271$	−17.2781	−1.04957	−0.524785	−	0.851235i	$-0.675854\pi$
$271$	−17.2781	−1.04957	−0.524785	+	0.851235i	$0.675854\pi$
$272$	−1.00000	−0.0606339
$273$	8.88967	0.538027
$274$	−6.33855	−0.382926
$275$	0.511270	0.0308307
$276$	−0.704010	−0.0423765
$277$	−27.4369	−1.64852	−0.824262	−	0.566209i	$-0.808409\pi$
$277$	−27.4369	−1.64852	−0.824262	+	0.566209i	$0.808409\pi$
$278$	−13.0618	−0.783395
$279$	−8.75624	−0.524222
$280$	3.92427	0.234520
$281$	−13.4653	−0.803273	−0.401637	−	0.915799i	$-0.631558\pi$
$281$	−13.4653	−0.803273	−0.401637	+	0.915799i	$0.631558\pi$
$282$	−1.28850	−0.0767289
$283$	−3.16806	−0.188322	−0.0941608	−	0.995557i	$-0.530017\pi$
$283$	−3.16806	−0.188322	−0.0941608	+	0.995557i	$0.530017\pi$
$284$	−0.787298	−0.0467175
$285$	10.5508	0.624976
$286$	−4.77493	−0.282348
$287$	18.5321	1.09392
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−8.25561	−0.484786
$291$	−2.30503	−0.135123
$292$	−6.86869	−0.401960
$293$	−20.8302	−1.21691	−0.608455	−	0.793588i	$-0.708211\pi$
$293$	−20.8302	−1.21691	−0.608455	+	0.793588i	$0.708211\pi$
$294$	−3.56730	−0.208049
$295$	2.11808	0.123319
$296$	6.77580	0.393836
$297$	−0.995175	−0.0577459
$298$	−7.29411	−0.422536
$299$	−3.37790	−0.195349
$300$	−0.513749	−0.0296613
$301$	4.75509	0.274079
$302$	−9.80168	−0.564023
$303$	−11.8041	−0.678125
$304$	4.98131	0.285698
$305$	−13.5657	−0.776772
$306$	−1.00000	−0.0571662
$307$	−26.0394	−1.48615	−0.743073	−	0.669210i	$-0.766633\pi$
$307$	−26.0394	−1.48615	−0.743073	+	0.669210i	$0.766633\pi$
$308$	−1.84381	−0.105061
$309$	−7.22800	−0.411187
$310$	−18.5464	−1.05336
$311$	9.96431	0.565024	0.282512	−	0.959264i	$-0.408832\pi$
$311$	9.96431	0.565024	0.282512	+	0.959264i	$0.408832\pi$
$312$	4.79808	0.271638
$313$	−17.6515	−0.997722	−0.498861	−	0.866682i	$-0.666248\pi$
$313$	−17.6515	−0.997722	−0.498861	+	0.866682i	$0.666248\pi$
$314$	13.6043	0.767735
$315$	3.92427	0.221108
$316$	1.42408	0.0801106
$317$	−17.1806	−0.964957	−0.482478	−	0.875908i	$-0.660263\pi$
$317$	−17.1806	−0.964957	−0.482478	+	0.875908i	$0.660263\pi$
$318$	4.45878	0.250036
$319$	3.87888	0.217176
$320$	2.11808	0.118404
$321$	−12.4263	−0.693571
$322$	−1.30436	−0.0726890
$323$	−4.98131	−0.277168
$324$	1.00000	0.0555556
$325$	−2.46501	−0.136734
$326$	−4.53377	−0.251102
$327$	3.65506	0.202125
$328$	10.0025	0.552294
$329$	−2.38727	−0.131614
$330$	−2.10786	−0.116034
$331$	21.4306	1.17793	0.588965	−	0.808158i	$-0.299535\pi$
$331$	21.4306	1.17793	0.588965	+	0.808158i	$0.299535\pi$
$332$	8.93027	0.490112
$333$	6.77580	0.371312
$334$	9.84395	0.538637
$335$	−21.9525	−1.19939
$336$	1.85275	0.101076
$337$	26.3403	1.43485	0.717423	−	0.696638i	$-0.245321\pi$
$337$	26.3403	1.43485	0.717423	+	0.696638i	$0.245321\pi$
$338$	10.0216	0.545103
$339$	15.1060	0.820445
$340$	−2.11808	−0.114869
$341$	8.71399	0.471889
$342$	4.98131	0.269359
$343$	−19.5786	−1.05715
$344$	2.56650	0.138376
$345$	−1.49115	−0.0802807
$346$	8.46684	0.455180
$347$	−32.6696	−1.75380	−0.876898	−	0.480676i	$-0.840391\pi$
$347$	−32.6696	−1.75380	−0.876898	+	0.480676i	$0.840391\pi$
$348$	−3.89769	−0.208938
$349$	23.0575	1.23424	0.617119	−	0.786870i	$-0.288300\pi$
$349$	23.0575	1.23424	0.617119	+	0.786870i	$0.288300\pi$
$350$	−0.951850	−0.0508785
$351$	4.79808	0.256103
$352$	−0.995175	−0.0530430
$353$	17.9142	0.953478	0.476739	−	0.879045i	$-0.341819\pi$
$353$	17.9142	0.953478	0.476739	+	0.879045i	$0.341819\pi$
$354$	1.00000	0.0531494
$355$	−1.66756	−0.0885047
$356$	11.7078	0.620514
$357$	−1.85275	−0.0980581
$358$	−11.6338	−0.614868
$359$	−18.4241	−0.972388	−0.486194	−	0.873851i	$-0.661615\pi$
$359$	−18.4241	−0.972388	−0.486194	+	0.873851i	$0.661615\pi$
$360$	2.11808	0.111632
$361$	5.81348	0.305973
$362$	−10.7254	−0.563712
$363$	−10.0096	−0.525369
$364$	8.88967	0.465945
$365$	−14.5484	−0.761499
$366$	−6.40474	−0.334781
$367$	−13.0476	−0.681079	−0.340540	−	0.940230i	$-0.610610\pi$
$367$	−13.0476	−0.681079	−0.340540	+	0.940230i	$0.610610\pi$
$368$	−0.704010	−0.0366991
$369$	10.0025	0.520707
$370$	14.3517	0.746108
$371$	8.26103	0.428891
$372$	−8.75624	−0.453990
$373$	−13.6098	−0.704688	−0.352344	−	0.935871i	$-0.614615\pi$
$373$	−13.6098	−0.704688	−0.352344	+	0.935871i	$0.614615\pi$
$374$	0.995175	0.0514593
$375$	−11.6785	−0.603078
$376$	−1.28850	−0.0664492
$377$	−18.7014	−0.963173
$378$	1.85275	0.0952954
$379$	4.23318	0.217444	0.108722	−	0.994072i	$-0.465324\pi$
$379$	4.23318	0.217444	0.108722	+	0.994072i	$0.465324\pi$
$380$	10.5508	0.541245
$381$	−16.7083	−0.855995
$382$	0.841466	0.0430531
$383$	18.7526	0.958214	0.479107	−	0.877756i	$-0.340961\pi$
$383$	18.7526	0.958214	0.479107	+	0.877756i	$0.340961\pi$
$384$	1.00000	0.0510310
$385$	−3.90534	−0.199034
$386$	−3.94169	−0.200627
$387$	2.56650	0.130463
$388$	−2.30503	−0.117020
$389$	25.9796	1.31722	0.658610	−	0.752484i	$-0.271145\pi$
$389$	25.9796	1.31722	0.658610	+	0.752484i	$0.271145\pi$
$390$	10.1627	0.514609
$391$	0.704010	0.0356033
$392$	−3.56730	−0.180176
$393$	20.3086	1.02444
$394$	21.7583	1.09617
$395$	3.01630	0.151767
$396$	−0.995175	−0.0500094
$397$	27.4749	1.37893	0.689463	−	0.724321i	$-0.257846\pi$
$397$	27.4749	1.37893	0.689463	+	0.724321i	$0.257846\pi$
$398$	26.7952	1.34312
$399$	9.22914	0.462035
$400$	−0.513749	−0.0256875
$401$	36.4019	1.81783	0.908913	−	0.416985i	$-0.136913\pi$
$401$	36.4019	1.81783	0.908913	+	0.416985i	$0.136913\pi$
$402$	−10.3643	−0.516926
$403$	−42.0132	−2.09283
$404$	−11.8041	−0.587274
$405$	2.11808	0.105248
$406$	−7.22146	−0.358395
$407$	−6.74311	−0.334243
$408$	−1.00000	−0.0495074
$409$	−3.84904	−0.190323	−0.0951614	−	0.995462i	$-0.530337\pi$
$409$	−3.84904	−0.190323	−0.0951614	+	0.995462i	$0.530337\pi$
$410$	21.1860	1.04630
$411$	−6.33855	−0.312658
$412$	−7.22800	−0.356098
$413$	1.85275	0.0911680
$414$	−0.704010	−0.0346002
$415$	18.9150	0.928500
$416$	4.79808	0.235245
$417$	−13.0618	−0.639639
$418$	−4.95728	−0.242468
$419$	−11.9526	−0.583922	−0.291961	−	0.956430i	$-0.594308\pi$
$419$	−11.9526	−0.583922	−0.291961	+	0.956430i	$0.594308\pi$
$420$	3.92427	0.191485
$421$	4.58796	0.223604	0.111802	−	0.993731i	$-0.464338\pi$
$421$	4.58796	0.223604	0.111802	+	0.993731i	$0.464338\pi$
$422$	22.8331	1.11150
$423$	−1.28850	−0.0626489
$424$	4.45878	0.216538
$425$	0.513749	0.0249205
$426$	−0.787298	−0.0381447
$427$	−11.8664	−0.574256
$428$	−12.4263	−0.600650
$429$	−4.77493	−0.230536
$430$	5.43605	0.262150
$431$	−19.2532	−0.927394	−0.463697	−	0.885994i	$-0.653477\pi$
$431$	−19.2532	−0.927394	−0.463697	+	0.885994i	$0.653477\pi$
$432$	1.00000	0.0481125
$433$	5.50629	0.264615	0.132308	−	0.991209i	$-0.457761\pi$
$433$	5.50629	0.264615	0.132308	+	0.991209i	$0.457761\pi$
$434$	−16.2232	−0.778736
$435$	−8.25561	−0.395826
$436$	3.65506	0.175046
$437$	−3.50690	−0.167758
$438$	−6.86869	−0.328199
$439$	17.0837	0.815360	0.407680	−	0.913125i	$-0.366338\pi$
$439$	17.0837	0.815360	0.407680	+	0.913125i	$0.366338\pi$
$440$	−2.10786	−0.100488
$441$	−3.56730	−0.169872
$442$	−4.79808	−0.228222
$443$	−39.4079	−1.87233	−0.936163	−	0.351567i	$-0.885649\pi$
$443$	−39.4079	−1.87233	−0.936163	+	0.351567i	$0.885649\pi$
$444$	6.77580	0.321565
$445$	24.7981	1.17554
$446$	−3.83272	−0.181484
$447$	−7.29411	−0.345000
$448$	1.85275	0.0875344
$449$	4.55668	0.215043	0.107521	−	0.994203i	$-0.465709\pi$
$449$	4.55668	0.215043	0.107521	+	0.994203i	$0.465709\pi$
$450$	−0.513749	−0.0242184
$451$	−9.95420	−0.468725
$452$	15.1060	0.710526
$453$	−9.80168	−0.460523
$454$	1.94283	0.0911814
$455$	18.8290	0.882717
$456$	4.98131	0.233271
$457$	−24.1775	−1.13098	−0.565488	−	0.824757i	$-0.691312\pi$
$457$	−24.1775	−1.13098	−0.565488	+	0.824757i	$0.691312\pi$
$458$	2.17295	0.101535
$459$	−1.00000	−0.0466760
$460$	−1.49115	−0.0695252
$461$	−1.90662	−0.0888002	−0.0444001	−	0.999014i	$-0.514138\pi$
$461$	−1.90662	−0.0888002	−0.0444001	+	0.999014i	$0.514138\pi$
$462$	−1.84381	−0.0857819
$463$	6.01033	0.279324	0.139662	−	0.990199i	$-0.455398\pi$
$463$	6.01033	0.279324	0.139662	+	0.990199i	$0.455398\pi$
$464$	−3.89769	−0.180946
$465$	−18.5464	−0.860069
$466$	22.0535	1.02161
$467$	18.9082	0.874969	0.437485	−	0.899226i	$-0.355869\pi$
$467$	18.9082	0.874969	0.437485	+	0.899226i	$0.355869\pi$
$468$	4.79808	0.221791
$469$	−19.2026	−0.886692
$470$	−2.72914	−0.125886
$471$	13.6043	0.626853
$472$	1.00000	0.0460287
$473$	−2.55412	−0.117438
$474$	1.42408	0.0654100
$475$	−2.55914	−0.117422
$476$	−1.85275	−0.0849208
$477$	4.45878	0.204154
$478$	7.37723	0.337427
$479$	−6.55927	−0.299701	−0.149850	−	0.988709i	$-0.547879\pi$
$479$	−6.55927	−0.299701	−0.149850	+	0.988709i	$0.547879\pi$
$480$	2.11808	0.0966766
$481$	32.5109	1.48237
$482$	8.63840	0.393468
$483$	−1.30436	−0.0593503
$484$	−10.0096	−0.454983
$485$	−4.88223	−0.221690
$486$	1.00000	0.0453609
$487$	20.6129	0.934061	0.467030	−	0.884241i	$-0.345324\pi$
$487$	20.6129	0.934061	0.467030	+	0.884241i	$0.345324\pi$
$488$	−6.40474	−0.289929
$489$	−4.53377	−0.205024
$490$	−7.55583	−0.341337
$491$	−15.5867	−0.703416	−0.351708	−	0.936110i	$-0.614399\pi$
$491$	−15.5867	−0.703416	−0.351708	+	0.936110i	$0.614399\pi$
$492$	10.0025	0.450946
$493$	3.89769	0.175543
$494$	23.9008	1.07535
$495$	−2.10786	−0.0947411
$496$	−8.75624	−0.393167
$497$	−1.45867	−0.0654302
$498$	8.93027	0.400175
$499$	7.96047	0.356360	0.178180	−	0.983998i	$-0.442979\pi$
$499$	7.96047	0.356360	0.178180	+	0.983998i	$0.442979\pi$
$500$	−11.6785	−0.522280
$501$	9.84395	0.439795
$502$	−1.18407	−0.0528476
$503$	36.4196	1.62387	0.811934	−	0.583749i	$-0.198415\pi$
$503$	36.4196	1.62387	0.811934	+	0.583749i	$0.198415\pi$
$504$	1.85275	0.0825282
$505$	−25.0019	−1.11257
$506$	0.700613	0.0311461
$507$	10.0216	0.445075
$508$	−16.7083	−0.741313
$509$	4.55045	0.201695	0.100848	−	0.994902i	$-0.467845\pi$
$509$	4.55045	0.201695	0.100848	+	0.994902i	$0.467845\pi$
$510$	−2.11808	−0.0937900
$511$	−12.7260	−0.562964
$512$	1.00000	0.0441942
$513$	4.98131	0.219930
$514$	3.52679	0.155560
$515$	−15.3095	−0.674616
$516$	2.56650	0.112984
$517$	1.28228	0.0563946
$518$	12.5539	0.551586
$519$	8.46684	0.371653
$520$	10.1627	0.445664
$521$	36.3282	1.59157	0.795784	−	0.605580i	$-0.207059\pi$
$521$	36.3282	1.59157	0.795784	+	0.605580i	$0.207059\pi$
$522$	−3.89769	−0.170597
$523$	−0.340485	−0.0148884	−0.00744418	−	0.999972i	$-0.502370\pi$
$523$	−0.340485	−0.0148884	−0.00744418	+	0.999972i	$0.502370\pi$
$524$	20.3086	0.887187
$525$	−0.951850	−0.0415422
$526$	−2.96129	−0.129118
$527$	8.75624	0.381428
$528$	−0.995175	−0.0433094
$529$	−22.5044	−0.978451
$530$	9.44405	0.410223
$531$	1.00000	0.0433963
$532$	9.22914	0.400134
$533$	47.9927	2.07879
$534$	11.7078	0.506648
$535$	−26.3200	−1.13791
$536$	−10.3643	−0.447671
$537$	−11.6338	−0.502038
$538$	−28.5630	−1.23144
$539$	3.55009	0.152913
$540$	2.11808	0.0911475
$541$	−1.19052	−0.0511845	−0.0255922	−	0.999672i	$-0.508147\pi$
$541$	−1.19052	−0.0511845	−0.0255922	+	0.999672i	$0.508147\pi$
$542$	−17.2781	−0.742158
$543$	−10.7254	−0.460269
$544$	−1.00000	−0.0428746
$545$	7.74170	0.331618
$546$	8.88967	0.380443
$547$	−24.2973	−1.03888	−0.519438	−	0.854508i	$-0.673859\pi$
$547$	−24.2973	−1.03888	−0.519438	+	0.854508i	$0.673859\pi$
$548$	−6.33855	−0.270770
$549$	−6.40474	−0.273348
$550$	0.511270	0.0218006
$551$	−19.4156	−0.827133
$552$	−0.704010	−0.0299647
$553$	2.63846	0.112199
$554$	−27.4369	−1.16568
$555$	14.3517	0.609195
$556$	−13.0618	−0.553944
$557$	−15.5428	−0.658569	−0.329285	−	0.944231i	$-0.606808\pi$
$557$	−15.5428	−0.658569	−0.329285	+	0.944231i	$0.606808\pi$
$558$	−8.75624	−0.370681
$559$	12.3143	0.520839
$560$	3.92427	0.165831
$561$	0.995175	0.0420163
$562$	−13.4653	−0.568000
$563$	−0.682048	−0.0287449	−0.0143724	−	0.999897i	$-0.504575\pi$
$563$	−0.682048	−0.0287449	−0.0143724	+	0.999897i	$0.504575\pi$
$564$	−1.28850	−0.0542555
$565$	31.9957	1.34607
$566$	−3.16806	−0.133164
$567$	1.85275	0.0778083
$568$	−0.787298	−0.0330343
$569$	13.2115	0.553853	0.276927	−	0.960891i	$-0.410684\pi$
$569$	13.2115	0.553853	0.276927	+	0.960891i	$0.410684\pi$
$570$	10.5508	0.441925
$571$	−29.4183	−1.23112	−0.615559	−	0.788091i	$-0.711070\pi$
$571$	−29.4183	−1.23112	−0.615559	+	0.788091i	$0.711070\pi$
$572$	−4.77493	−0.199650
$573$	0.841466	0.0351527
$574$	18.5321	0.773515
$575$	0.361685	0.0150833
$576$	1.00000	0.0416667
$577$	9.16246	0.381438	0.190719	−	0.981645i	$-0.438918\pi$
$577$	9.16246	0.381438	0.190719	+	0.981645i	$0.438918\pi$
$578$	1.00000	0.0415945
$579$	−3.94169	−0.163811
$580$	−8.25561	−0.342795
$581$	16.5456	0.686426
$582$	−2.30503	−0.0955464
$583$	−4.43727	−0.183773
$584$	−6.86869	−0.284228
$585$	10.1627	0.420176
$586$	−20.8302	−0.860486
$587$	23.6734	0.977107	0.488553	−	0.872534i	$-0.337525\pi$
$587$	23.6734	0.977107	0.488553	+	0.872534i	$0.337525\pi$
$588$	−3.56730	−0.147113
$589$	−43.6176	−1.79723
$590$	2.11808	0.0871999
$591$	21.7583	0.895016
$592$	6.77580	0.278484
$593$	19.5559	0.803065	0.401532	−	0.915845i	$-0.368478\pi$
$593$	19.5559	0.803065	0.401532	+	0.915845i	$0.368478\pi$
$594$	−0.995175	−0.0408325
$595$	−3.92427	−0.160880
$596$	−7.29411	−0.298778
$597$	26.7952	1.09665
$598$	−3.37790	−0.138133
$599$	−0.385521	−0.0157520	−0.00787599	−	0.999969i	$-0.502507\pi$
$599$	−0.385521	−0.0157520	−0.00787599	+	0.999969i	$0.502507\pi$
$600$	−0.513749	−0.0209737
$601$	−29.4588	−1.20165	−0.600824	−	0.799381i	$-0.705161\pi$
$601$	−29.4588	−1.20165	−0.600824	+	0.799381i	$0.705161\pi$
$602$	4.75509	0.193803
$603$	−10.3643	−0.422068
$604$	−9.80168	−0.398825
$605$	−21.2012	−0.861950
$606$	−11.8041	−0.479507
$607$	−5.18594	−0.210491	−0.105245	−	0.994446i	$-0.533563\pi$
$607$	−5.18594	−0.210491	−0.105245	+	0.994446i	$0.533563\pi$
$608$	4.98131	0.202019
$609$	−7.22146	−0.292628
$610$	−13.5657	−0.549260
$611$	−6.18232	−0.250110
$612$	−1.00000	−0.0404226
$613$	43.9068	1.77338	0.886689	−	0.462366i	$-0.152999\pi$
$613$	43.9068	1.77338	0.886689	+	0.462366i	$0.152999\pi$
$614$	−26.0394	−1.05086
$615$	21.1860	0.854301
$616$	−1.84381	−0.0742893
$617$	−36.0329	−1.45063	−0.725315	−	0.688417i	$-0.758306\pi$
$617$	−36.0329	−1.45063	−0.725315	+	0.688417i	$0.758306\pi$
$618$	−7.22800	−0.290753
$619$	−14.2859	−0.574199	−0.287099	−	0.957901i	$-0.592691\pi$
$619$	−14.2859	−0.574199	−0.287099	+	0.957901i	$0.592691\pi$
$620$	−18.5464	−0.744841
$621$	−0.704010	−0.0282510
$622$	9.96431	0.399533
$623$	21.6917	0.869061
$624$	4.79808	0.192077
$625$	−22.1673	−0.886693
$626$	−17.6515	−0.705496
$627$	−4.95728	−0.197975
$628$	13.6043	0.542871
$629$	−6.77580	−0.270169
$630$	3.92427	0.156347
$631$	20.7994	0.828012	0.414006	−	0.910274i	$-0.364129\pi$
$631$	20.7994	0.828012	0.414006	+	0.910274i	$0.364129\pi$
$632$	1.42408	0.0566467
$633$	22.8331	0.907532
$634$	−17.1806	−0.682328
$635$	−35.3896	−1.40439
$636$	4.45878	0.176802
$637$	−17.1162	−0.678170
$638$	3.87888	0.153566
$639$	−0.787298	−0.0311450
$640$	2.11808	0.0837244
$641$	15.2110	0.600798	0.300399	−	0.953814i	$-0.402880\pi$
$641$	15.2110	0.600798	0.300399	+	0.953814i	$0.402880\pi$
$642$	−12.4263	−0.490429
$643$	−27.1267	−1.06977	−0.534885	−	0.844925i	$-0.679645\pi$
$643$	−27.1267	−1.06977	−0.534885	+	0.844925i	$0.679645\pi$
$644$	−1.30436	−0.0513989
$645$	5.43605	0.214044
$646$	−4.98131	−0.195987
$647$	−49.5552	−1.94822	−0.974108	−	0.226083i	$-0.927408\pi$
$647$	−49.5552	−1.94822	−0.974108	+	0.226083i	$0.927408\pi$
$648$	1.00000	0.0392837
$649$	−0.995175	−0.0390640
$650$	−2.46501	−0.0966857
$651$	−16.2232	−0.635836
$652$	−4.53377	−0.177556
$653$	−0.679944	−0.0266082	−0.0133041	−	0.999911i	$-0.504235\pi$
$653$	−0.679944	−0.0266082	−0.0133041	+	0.999911i	$0.504235\pi$
$654$	3.65506	0.142924
$655$	43.0153	1.68075
$656$	10.0025	0.390531
$657$	−6.86869	−0.267973
$658$	−2.38727	−0.0930654
$659$	2.03111	0.0791209	0.0395605	−	0.999217i	$-0.487404\pi$
$659$	2.03111	0.0791209	0.0395605	+	0.999217i	$0.487404\pi$
$660$	−2.10786	−0.0820482
$661$	−18.3753	−0.714717	−0.357359	−	0.933967i	$-0.616323\pi$
$661$	−18.3753	−0.714717	−0.357359	+	0.933967i	$0.616323\pi$
$662$	21.4306	0.832923
$663$	−4.79808	−0.186342
$664$	8.93027	0.346562
$665$	19.5480	0.758041
$666$	6.77580	0.262557
$667$	2.74401	0.106249
$668$	9.84395	0.380874
$669$	−3.83272	−0.148181
$670$	−21.9525	−0.848098
$671$	6.37383	0.246059
$672$	1.85275	0.0714715
$673$	5.86779	0.226187	0.113093	−	0.993584i	$-0.463924\pi$
$673$	5.86779	0.226187	0.113093	+	0.993584i	$0.463924\pi$
$674$	26.3403	1.01459
$675$	−0.513749	−0.0197742
$676$	10.0216	0.385446
$677$	4.98281	0.191505	0.0957525	−	0.995405i	$-0.469474\pi$
$677$	4.98281	0.191505	0.0957525	+	0.995405i	$0.469474\pi$
$678$	15.1060	0.580142
$679$	−4.27065	−0.163892
$680$	−2.11808	−0.0812246
$681$	1.94283	0.0744493
$682$	8.71399	0.333676
$683$	15.2891	0.585022	0.292511	−	0.956262i	$-0.405509\pi$
$683$	15.2891	0.585022	0.292511	+	0.956262i	$0.405509\pi$
$684$	4.98131	0.190465
$685$	−13.4255	−0.512964
$686$	−19.5786	−0.747515
$687$	2.17295	0.0829032
$688$	2.56650	0.0978470
$689$	21.3936	0.815032
$690$	−1.49115	−0.0567671
$691$	−19.7546	−0.751502	−0.375751	−	0.926721i	$-0.622615\pi$
$691$	−19.7546	−0.751502	−0.375751	+	0.926721i	$0.622615\pi$
$692$	8.46684	0.321861
$693$	−1.84381	−0.0700407
$694$	−32.6696	−1.24012
$695$	−27.6659	−1.04943
$696$	−3.89769	−0.147742
$697$	−10.0025	−0.378870
$698$	23.0575	0.872738
$699$	22.0535	0.834139
$700$	−0.951850	−0.0359766
$701$	7.35353	0.277739	0.138870	−	0.990311i	$-0.455653\pi$
$701$	7.35353	0.277739	0.138870	+	0.990311i	$0.455653\pi$
$702$	4.79808	0.181092
$703$	33.7524	1.27300
$704$	−0.995175	−0.0375071
$705$	−2.72914	−0.102785
$706$	17.9142	0.674211
$707$	−21.8700	−0.822506
$708$	1.00000	0.0375823
$709$	30.8989	1.16043	0.580216	−	0.814463i	$-0.302968\pi$
$709$	30.8989	1.16043	0.580216	+	0.814463i	$0.302968\pi$
$710$	−1.66756	−0.0625823
$711$	1.42408	0.0534071
$712$	11.7078	0.438770
$713$	6.16449	0.230862
$714$	−1.85275	−0.0693376
$715$	−10.1137	−0.378230
$716$	−11.6338	−0.434777
$717$	7.37723	0.275508
$718$	−18.4241	−0.687582
$719$	49.2534	1.83684	0.918420	−	0.395606i	$-0.129466\pi$
$719$	49.2534	1.83684	0.918420	+	0.395606i	$0.129466\pi$
$720$	2.11808	0.0789361
$721$	−13.3917	−0.498733
$722$	5.81348	0.216355
$723$	8.63840	0.321266
$724$	−10.7254	−0.398605
$725$	2.00243	0.0743685
$726$	−10.0096	−0.371492
$727$	13.0536	0.484131	0.242065	−	0.970260i	$-0.422175\pi$
$727$	13.0536	0.484131	0.242065	+	0.970260i	$0.422175\pi$
$728$	8.88967	0.329473
$729$	1.00000	0.0370370
$730$	−14.5484	−0.538461
$731$	−2.56650	−0.0949255
$732$	−6.40474	−0.236726
$733$	−22.0851	−0.815733	−0.407866	−	0.913042i	$-0.633727\pi$
$733$	−22.0851	−0.815733	−0.407866	+	0.913042i	$0.633727\pi$
$734$	−13.0476	−0.481596
$735$	−7.55583	−0.278701
$736$	−0.704010	−0.0259502
$737$	10.3143	0.379933
$738$	10.0025	0.368196
$739$	−17.6210	−0.648200	−0.324100	−	0.946023i	$-0.605061\pi$
$739$	−17.6210	−0.648200	−0.324100	+	0.946023i	$0.605061\pi$
$740$	14.3517	0.527578
$741$	23.9008	0.878016
$742$	8.26103	0.303272
$743$	17.7838	0.652424	0.326212	−	0.945297i	$-0.394228\pi$
$743$	17.7838	0.652424	0.326212	+	0.945297i	$0.394228\pi$
$744$	−8.75624	−0.321019
$745$	−15.4495	−0.566025
$746$	−13.6098	−0.498289
$747$	8.93027	0.326741
$748$	0.995175	0.0363872
$749$	−23.0230	−0.841241
$750$	−11.6785	−0.426440
$751$	−23.7074	−0.865094	−0.432547	−	0.901611i	$-0.642385\pi$
$751$	−23.7074	−0.865094	−0.432547	+	0.901611i	$0.642385\pi$
$752$	−1.28850	−0.0469867
$753$	−1.18407	−0.0431499
$754$	−18.7014	−0.681066
$755$	−20.7607	−0.755560
$756$	1.85275	0.0673840
$757$	−10.4205	−0.378741	−0.189370	−	0.981906i	$-0.560645\pi$
$757$	−10.4205	−0.378741	−0.189370	+	0.981906i	$0.560645\pi$
$758$	4.23318	0.153756
$759$	0.700613	0.0254307
$760$	10.5508	0.382718
$761$	−4.85930	−0.176149	−0.0880747	−	0.996114i	$-0.528071\pi$
$761$	−4.85930	−0.176149	−0.0880747	+	0.996114i	$0.528071\pi$
$762$	−16.7083	−0.605280
$763$	6.77192	0.245160
$764$	0.841466	0.0304432
$765$	−2.11808	−0.0765792
$766$	18.7526	0.677560
$767$	4.79808	0.173249
$768$	1.00000	0.0360844
$769$	43.3963	1.56491	0.782455	−	0.622708i	$-0.213967\pi$
$769$	43.3963	1.56491	0.782455	+	0.622708i	$0.213967\pi$
$770$	−3.90534	−0.140739
$771$	3.52679	0.127014
$772$	−3.94169	−0.141865
$773$	−11.9574	−0.430077	−0.215038	−	0.976606i	$-0.568988\pi$
$773$	−11.9574	−0.430077	−0.215038	+	0.976606i	$0.568988\pi$
$774$	2.56650	0.0922510
$775$	4.49851	0.161591
$776$	−2.30503	−0.0827457
$777$	12.5539	0.450368
$778$	25.9796	0.931415
$779$	49.8254	1.78518
$780$	10.1627	0.363883
$781$	0.783499	0.0280358
$782$	0.704010	0.0251754
$783$	−3.89769	−0.139292
$784$	−3.56730	−0.127404
$785$	28.8150	1.02845
$786$	20.3086	0.724386
$787$	10.4769	0.373459	0.186730	−	0.982411i	$-0.440211\pi$
$787$	10.4769	0.373459	0.186730	+	0.982411i	$0.440211\pi$
$788$	21.7583	0.775106
$789$	−2.96129	−0.105425
$790$	3.01630	0.107315
$791$	27.9877	0.995127
$792$	−0.995175	−0.0353620
$793$	−30.7305	−1.09127
$794$	27.4749	0.975048
$795$	9.44405	0.334946
$796$	26.7952	0.949730
$797$	15.2615	0.540591	0.270295	−	0.962777i	$-0.412879\pi$
$797$	15.2615	0.540591	0.270295	+	0.962777i	$0.412879\pi$
$798$	9.22914	0.326708
$799$	1.28850	0.0455837
$800$	−0.513749	−0.0181638
$801$	11.7078	0.413676
$802$	36.4019	1.28540
$803$	6.83554	0.241221
$804$	−10.3643	−0.365522
$805$	−2.76273	−0.0973735
$806$	−42.0132	−1.47985
$807$	−28.5630	−1.00546
$808$	−11.8041	−0.415265
$809$	−52.3575	−1.84079	−0.920395	−	0.390989i	$-0.872133\pi$
$809$	−52.3575	−1.84079	−0.920395	+	0.390989i	$0.872133\pi$
$810$	2.11808	0.0744216
$811$	50.8669	1.78618	0.893090	−	0.449879i	$-0.148533\pi$
$811$	50.8669	1.78618	0.893090	+	0.449879i	$0.148533\pi$
$812$	−7.22146	−0.253423
$813$	−17.2781	−0.605970
$814$	−6.74311	−0.236346
$815$	−9.60288	−0.336374
$816$	−1.00000	−0.0350070
$817$	12.7845	0.447275
$818$	−3.84904	−0.134579
$819$	8.88967	0.310630
$820$	21.1860	0.739847
$821$	−0.128090	−0.00447038	−0.00223519	−	0.999998i	$-0.500711\pi$
$821$	−0.128090	−0.00447038	−0.00223519	+	0.999998i	$0.500711\pi$
$822$	−6.33855	−0.221082
$823$	−1.54763	−0.0539470	−0.0269735	−	0.999636i	$-0.508587\pi$
$823$	−1.54763	−0.0539470	−0.0269735	+	0.999636i	$0.508587\pi$
$824$	−7.22800	−0.251799
$825$	0.511270	0.0178001
$826$	1.85275	0.0644655
$827$	−15.4255	−0.536397	−0.268198	−	0.963364i	$-0.586428\pi$
$827$	−15.4255	−0.536397	−0.268198	+	0.963364i	$0.586428\pi$
$828$	−0.704010	−0.0244661
$829$	−39.9465	−1.38740	−0.693699	−	0.720265i	$-0.744020\pi$
$829$	−39.9465	−1.38740	−0.693699	+	0.720265i	$0.744020\pi$
$830$	18.9150	0.656549
$831$	−27.4369	−0.951775
$832$	4.79808	0.166344
$833$	3.56730	0.123600
$834$	−13.0618	−0.452293
$835$	20.8503	0.721553
$836$	−4.95728	−0.171451
$837$	−8.75624	−0.302660
$838$	−11.9526	−0.412895
$839$	19.0636	0.658148	0.329074	−	0.944304i	$-0.393263\pi$
$839$	19.0636	0.658148	0.329074	+	0.944304i	$0.393263\pi$
$840$	3.92427	0.135400
$841$	−13.8080	−0.476139
$842$	4.58796	0.158112
$843$	−13.4653	−0.463770
$844$	22.8331	0.785946
$845$	21.2265	0.730215
$846$	−1.28850	−0.0442994
$847$	−18.5454	−0.637227
$848$	4.45878	0.153115
$849$	−3.16806	−0.108728
$850$	0.513749	0.0176214
$851$	−4.77024	−0.163522
$852$	−0.787298	−0.0269724
$853$	−33.4062	−1.14381	−0.571903	−	0.820321i	$-0.693795\pi$
$853$	−33.4062	−1.14381	−0.571903	+	0.820321i	$0.693795\pi$
$854$	−11.8664	−0.406060
$855$	10.5508	0.360830
$856$	−12.4263	−0.424724
$857$	−48.1230	−1.64385	−0.821926	−	0.569594i	$-0.807100\pi$
$857$	−48.1230	−1.64385	−0.821926	+	0.569594i	$0.807100\pi$
$858$	−4.77493	−0.163013
$859$	−5.55853	−0.189655	−0.0948274	−	0.995494i	$-0.530230\pi$
$859$	−5.55853	−0.189655	−0.0948274	+	0.995494i	$0.530230\pi$
$860$	5.43605	0.185368
$861$	18.5321	0.631572
$862$	−19.2532	−0.655767
$863$	−40.5863	−1.38157	−0.690786	−	0.723059i	$-0.742736\pi$
$863$	−40.5863	−1.38157	−0.690786	+	0.723059i	$0.742736\pi$
$864$	1.00000	0.0340207
$865$	17.9334	0.609754
$866$	5.50629	0.187111
$867$	1.00000	0.0339618
$868$	−16.2232	−0.550650
$869$	−1.41721	−0.0480754
$870$	−8.25561	−0.279891
$871$	−49.7290	−1.68500
$872$	3.65506	0.123776
$873$	−2.30503	−0.0780133
$874$	−3.50690	−0.118623
$875$	−21.6375	−0.731480
$876$	−6.86869	−0.232071
$877$	41.8871	1.41443	0.707214	−	0.707000i	$-0.249952\pi$
$877$	41.8871	1.41443	0.707214	+	0.707000i	$0.249952\pi$
$878$	17.0837	0.576546
$879$	−20.8302	−0.702584
$880$	−2.10786	−0.0710558
$881$	−15.8135	−0.532771	−0.266386	−	0.963867i	$-0.585829\pi$
$881$	−15.8135	−0.532771	−0.266386	+	0.963867i	$0.585829\pi$
$882$	−3.56730	−0.120117
$883$	−6.64036	−0.223466	−0.111733	−	0.993738i	$-0.535640\pi$
$883$	−6.64036	−0.223466	−0.111733	+	0.993738i	$0.535640\pi$
$884$	−4.79808	−0.161377
$885$	2.11808	0.0711984
$886$	−39.4079	−1.32393
$887$	45.5316	1.52880	0.764401	−	0.644741i	$-0.223035\pi$
$887$	45.5316	1.52880	0.764401	+	0.644741i	$0.223035\pi$
$888$	6.77580	0.227381
$889$	−30.9565	−1.03825
$890$	24.7981	0.831234
$891$	−0.995175	−0.0333396
$892$	−3.83272	−0.128329
$893$	−6.41841	−0.214784
$894$	−7.29411	−0.243952
$895$	−24.6414	−0.823671
$896$	1.85275	0.0618961
$897$	−3.37790	−0.112785
$898$	4.55668	0.152058
$899$	34.1291	1.13827
$900$	−0.513749	−0.0171250
$901$	−4.45878	−0.148544
$902$	−9.95420	−0.331438
$903$	4.75509	0.158240
$904$	15.1060	0.502418
$905$	−22.7171	−0.755143
$906$	−9.80168	−0.325639
$907$	−52.2459	−1.73480	−0.867399	−	0.497614i	$-0.834210\pi$
$907$	−52.2459	−1.73480	−0.867399	+	0.497614i	$0.834210\pi$
$908$	1.94283	0.0644750
$909$	−11.8041	−0.391516
$910$	18.8290	0.624175
$911$	−16.3044	−0.540190	−0.270095	−	0.962834i	$-0.587055\pi$
$911$	−16.3044	−0.540190	−0.270095	+	0.962834i	$0.587055\pi$
$912$	4.98131	0.164948
$913$	−8.88717	−0.294123
$914$	−24.1775	−0.799721
$915$	−13.5657	−0.448469
$916$	2.17295	0.0717963
$917$	37.6269	1.24255
$918$	−1.00000	−0.0330049
$919$	−33.4098	−1.10209	−0.551043	−	0.834477i	$-0.685770\pi$
$919$	−33.4098	−1.10209	−0.551043	+	0.834477i	$0.685770\pi$
$920$	−1.49115	−0.0491617
$921$	−26.0394	−0.858027
$922$	−1.90662	−0.0627913
$923$	−3.77752	−0.124339
$924$	−1.84381	−0.0606570
$925$	−3.48106	−0.114457
$926$	6.01033	0.197512
$927$	−7.22800	−0.237399
$928$	−3.89769	−0.127948
$929$	−15.3357	−0.503148	−0.251574	−	0.967838i	$-0.580948\pi$
$929$	−15.3357	−0.503148	−0.251574	+	0.967838i	$0.580948\pi$
$930$	−18.5464	−0.608160
$931$	−17.7699	−0.582384
$932$	22.0535	0.722386
$933$	9.96431	0.326217
$934$	18.9082	0.618697
$935$	2.10786	0.0689343
$936$	4.79808	0.156830
$937$	41.8830	1.36826	0.684130	−	0.729360i	$-0.260182\pi$
$937$	41.8830	1.36826	0.684130	+	0.729360i	$0.260182\pi$
$938$	−19.2026	−0.626986
$939$	−17.6515	−0.576035
$940$	−2.72914	−0.0890146
$941$	−19.8238	−0.646237	−0.323119	−	0.946359i	$-0.604731\pi$
$941$	−19.8238	−0.646237	−0.323119	+	0.946359i	$0.604731\pi$
$942$	13.6043	0.443252
$943$	−7.04184	−0.229314
$944$	1.00000	0.0325472
$945$	3.92427	0.127657
$946$	−2.55412	−0.0830415
$947$	−33.6746	−1.09428	−0.547139	−	0.837042i	$-0.684283\pi$
$947$	−33.6746	−1.09428	−0.547139	+	0.837042i	$0.684283\pi$
$948$	1.42408	0.0462519
$949$	−32.9565	−1.06981
$950$	−2.55914	−0.0830296
$951$	−17.1806	−0.557118
$952$	−1.85275	−0.0600481
$953$	−13.6968	−0.443684	−0.221842	−	0.975083i	$-0.571207\pi$
$953$	−13.6968	−0.443684	−0.221842	+	0.975083i	$0.571207\pi$
$954$	4.45878	0.144358
$955$	1.78229	0.0576735
$956$	7.37723	0.238597
$957$	3.87888	0.125386
$958$	−6.55927	−0.211920
$959$	−11.7438	−0.379226
$960$	2.11808	0.0683606
$961$	45.6718	1.47328
$962$	32.5109	1.04819
$963$	−12.4263	−0.400434
$964$	8.63840	0.278224
$965$	−8.34881	−0.268758
$966$	−1.30436	−0.0419670
$967$	−23.6507	−0.760557	−0.380278	−	0.924872i	$-0.624172\pi$
$967$	−23.6507	−0.760557	−0.380278	+	0.924872i	$0.624172\pi$
$968$	−10.0096	−0.321722
$969$	−4.98131	−0.160023
$970$	−4.88223	−0.156759
$971$	43.4810	1.39537	0.697686	−	0.716404i	$-0.254213\pi$
$971$	43.4810	1.39537	0.697686	+	0.716404i	$0.254213\pi$
$972$	1.00000	0.0320750
$973$	−24.2003	−0.775826
$974$	20.6129	0.660481
$975$	−2.46501	−0.0789435
$976$	−6.40474	−0.205011
$977$	−42.5214	−1.36038	−0.680190	−	0.733036i	$-0.738103\pi$
$977$	−42.5214	−1.36038	−0.680190	+	0.733036i	$0.738103\pi$
$978$	−4.53377	−0.144974
$979$	−11.6513	−0.372378
$980$	−7.55583	−0.241362
$981$	3.65506	0.116697
$982$	−15.5867	−0.497390
$983$	24.3490	0.776612	0.388306	−	0.921530i	$-0.373060\pi$
$983$	24.3490	0.776612	0.388306	+	0.921530i	$0.373060\pi$
$984$	10.0025	0.318867
$985$	46.0857	1.46841
$986$	3.89769	0.124128
$987$	−2.38727	−0.0759876
$988$	23.9008	0.760384
$989$	−1.80684	−0.0574543
$990$	−2.10786	−0.0669921
$991$	−33.2694	−1.05684	−0.528419	−	0.848984i	$-0.677215\pi$
$991$	−33.2694	−1.05684	−0.528419	+	0.848984i	$0.677215\pi$
$992$	−8.75624	−0.278011
$993$	21.4306	0.680079
$994$	−1.45867	−0.0462662
$995$	56.7542	1.79923
$996$	8.93027	0.282966
$997$	−37.2751	−1.18051	−0.590257	−	0.807215i	$-0.700974\pi$
$997$	−37.2751	−1.18051	−0.590257	+	0.807215i	$0.700974\pi$
$998$	7.96047	0.251984
$999$	6.77580	0.214377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.ba.1.8	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.8	✓	12	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.11808 q^{5} +1.00000 q^{6} +1.85275 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.11808 q^{5} +1.00000 q^{6} +1.85275 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.11808 q^{10} -0.995175 q^{11} +1.00000 q^{12} +4.79808 q^{13} +1.85275 q^{14} +2.11808 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +4.98131 q^{19} +2.11808 q^{20} +1.85275 q^{21} -0.995175 q^{22} -0.704010 q^{23} +1.00000 q^{24} -0.513749 q^{25} +4.79808 q^{26} +1.00000 q^{27} +1.85275 q^{28} -3.89769 q^{29} +2.11808 q^{30} -8.75624 q^{31} +1.00000 q^{32} -0.995175 q^{33} -1.00000 q^{34} +3.92427 q^{35} +1.00000 q^{36} +6.77580 q^{37} +4.98131 q^{38} +4.79808 q^{39} +2.11808 q^{40} +10.0025 q^{41} +1.85275 q^{42} +2.56650 q^{43} -0.995175 q^{44} +2.11808 q^{45} -0.704010 q^{46} -1.28850 q^{47} +1.00000 q^{48} -3.56730 q^{49} -0.513749 q^{50} -1.00000 q^{51} +4.79808 q^{52} +4.45878 q^{53} +1.00000 q^{54} -2.10786 q^{55} +1.85275 q^{56} +4.98131 q^{57} -3.89769 q^{58} +1.00000 q^{59} +2.11808 q^{60} -6.40474 q^{61} -8.75624 q^{62} +1.85275 q^{63} +1.00000 q^{64} +10.1627 q^{65} -0.995175 q^{66} -10.3643 q^{67} -1.00000 q^{68} -0.704010 q^{69} +3.92427 q^{70} -0.787298 q^{71} +1.00000 q^{72} -6.86869 q^{73} +6.77580 q^{74} -0.513749 q^{75} +4.98131 q^{76} -1.84381 q^{77} +4.79808 q^{78} +1.42408 q^{79} +2.11808 q^{80} +1.00000 q^{81} +10.0025 q^{82} +8.93027 q^{83} +1.85275 q^{84} -2.11808 q^{85} +2.56650 q^{86} -3.89769 q^{87} -0.995175 q^{88} +11.7078 q^{89} +2.11808 q^{90} +8.88967 q^{91} -0.704010 q^{92} -8.75624 q^{93} -1.28850 q^{94} +10.5508 q^{95} +1.00000 q^{96} -2.30503 q^{97} -3.56730 q^{98} -0.995175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

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