LMFDB - Embedded newform 6018.2.a.u.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$1$
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			1.5
Root			$-2.14979$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.03642 q^{5} +1.00000 q^{6} +2.58814 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.03642 q^{5} +1.00000 q^{6} +2.58814 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.03642 q^{10} +0.328441 q^{11} -1.00000 q^{12} -0.550837 q^{13} -2.58814 q^{14} +1.03642 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -0.668814 q^{19} -1.03642 q^{20} -2.58814 q^{21} -0.328441 q^{22} +2.85502 q^{23} +1.00000 q^{24} -3.92583 q^{25} +0.550837 q^{26} -1.00000 q^{27} +2.58814 q^{28} +4.26895 q^{29} -1.03642 q^{30} -1.05963 q^{31} -1.00000 q^{32} -0.328441 q^{33} -1.00000 q^{34} -2.68240 q^{35} +1.00000 q^{36} -10.8012 q^{37} +0.668814 q^{38} +0.550837 q^{39} +1.03642 q^{40} +0.525599 q^{41} +2.58814 q^{42} -5.46997 q^{43} +0.328441 q^{44} -1.03642 q^{45} -2.85502 q^{46} -3.44760 q^{47} -1.00000 q^{48} -0.301536 q^{49} +3.92583 q^{50} -1.00000 q^{51} -0.550837 q^{52} +7.70645 q^{53} +1.00000 q^{54} -0.340403 q^{55} -2.58814 q^{56} +0.668814 q^{57} -4.26895 q^{58} +1.00000 q^{59} +1.03642 q^{60} +4.66400 q^{61} +1.05963 q^{62} +2.58814 q^{63} +1.00000 q^{64} +0.570899 q^{65} +0.328441 q^{66} -1.71988 q^{67} +1.00000 q^{68} -2.85502 q^{69} +2.68240 q^{70} +1.62984 q^{71} -1.00000 q^{72} -15.3355 q^{73} +10.8012 q^{74} +3.92583 q^{75} -0.668814 q^{76} +0.850052 q^{77} -0.550837 q^{78} -2.43182 q^{79} -1.03642 q^{80} +1.00000 q^{81} -0.525599 q^{82} -10.0619 q^{83} -2.58814 q^{84} -1.03642 q^{85} +5.46997 q^{86} -4.26895 q^{87} -0.328441 q^{88} +2.38147 q^{89} +1.03642 q^{90} -1.42564 q^{91} +2.85502 q^{92} +1.05963 q^{93} +3.44760 q^{94} +0.693173 q^{95} +1.00000 q^{96} -6.24513 q^{97} +0.301536 q^{98} +0.328441 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.03642	−0.463502	−0.231751	−	0.972775i	$-0.574445\pi$
$5$	−1.03642	−0.463502	−0.231751	+	0.972775i	$0.574445\pi$
$6$	1.00000	0.408248
$7$	2.58814	0.978225	0.489112	−	0.872221i	$-0.337321\pi$
$7$	2.58814	0.978225	0.489112	+	0.872221i	$0.337321\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.03642	0.327745
$11$	0.328441	0.0990288	0.0495144	−	0.998773i	$-0.484233\pi$
$11$	0.328441	0.0990288	0.0495144	+	0.998773i	$0.484233\pi$
$12$	−1.00000	−0.288675
$13$	−0.550837	−0.152775	−0.0763873	−	0.997078i	$-0.524339\pi$
$13$	−0.550837	−0.152775	−0.0763873	+	0.997078i	$0.524339\pi$
$14$	−2.58814	−0.691709
$15$	1.03642	0.267603
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−0.668814	−0.153436	−0.0767182	−	0.997053i	$-0.524444\pi$
$19$	−0.668814	−0.153436	−0.0767182	+	0.997053i	$0.524444\pi$
$20$	−1.03642	−0.231751
$21$	−2.58814	−0.564778
$22$	−0.328441	−0.0700239
$23$	2.85502	0.595313	0.297657	−	0.954673i	$-0.403795\pi$
$23$	2.85502	0.595313	0.297657	+	0.954673i	$0.403795\pi$
$24$	1.00000	0.204124
$25$	−3.92583	−0.785166
$26$	0.550837	0.108028
$27$	−1.00000	−0.192450
$28$	2.58814	0.489112
$29$	4.26895	0.792724	0.396362	−	0.918094i	$-0.370273\pi$
$29$	4.26895	0.792724	0.396362	+	0.918094i	$0.370273\pi$
$30$	−1.03642	−0.189224
$31$	−1.05963	−0.190316	−0.0951579	−	0.995462i	$-0.530336\pi$
$31$	−1.05963	−0.190316	−0.0951579	+	0.995462i	$0.530336\pi$
$32$	−1.00000	−0.176777
$33$	−0.328441	−0.0571743
$34$	−1.00000	−0.171499
$35$	−2.68240	−0.453409
$36$	1.00000	0.166667
$37$	−10.8012	−1.77570	−0.887851	−	0.460131i	$-0.847802\pi$
$37$	−10.8012	−1.77570	−0.887851	+	0.460131i	$0.847802\pi$
$38$	0.668814	0.108496
$39$	0.550837	0.0882045
$40$	1.03642	0.163873
$41$	0.525599	0.0820848	0.0410424	−	0.999157i	$-0.486932\pi$
$41$	0.525599	0.0820848	0.0410424	+	0.999157i	$0.486932\pi$
$42$	2.58814	0.399359
$43$	−5.46997	−0.834162	−0.417081	−	0.908869i	$-0.636947\pi$
$43$	−5.46997	−0.834162	−0.417081	+	0.908869i	$0.636947\pi$
$44$	0.328441	0.0495144
$45$	−1.03642	−0.154501
$46$	−2.85502	−0.420950
$47$	−3.44760	−0.502885	−0.251442	−	0.967872i	$-0.580905\pi$
$47$	−3.44760	−0.502885	−0.251442	+	0.967872i	$0.580905\pi$
$48$	−1.00000	−0.144338
$49$	−0.301536	−0.0430765
$50$	3.92583	0.555196
$51$	−1.00000	−0.140028
$52$	−0.550837	−0.0763873
$53$	7.70645	1.05856	0.529281	−	0.848446i	$-0.322462\pi$
$53$	7.70645	1.05856	0.529281	+	0.848446i	$0.322462\pi$
$54$	1.00000	0.136083
$55$	−0.340403	−0.0459000
$56$	−2.58814	−0.345855
$57$	0.668814	0.0885866
$58$	−4.26895	−0.560540
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	1.03642	0.133801
$61$	4.66400	0.597164	0.298582	−	0.954384i	$-0.403486\pi$
$61$	4.66400	0.597164	0.298582	+	0.954384i	$0.403486\pi$
$62$	1.05963	0.134574
$63$	2.58814	0.326075
$64$	1.00000	0.125000
$65$	0.570899	0.0708113
$66$	0.328441	0.0404283
$67$	−1.71988	−0.210117	−0.105058	−	0.994466i	$-0.533503\pi$
$67$	−1.71988	−0.210117	−0.105058	+	0.994466i	$0.533503\pi$
$68$	1.00000	0.121268
$69$	−2.85502	−0.343704
$70$	2.68240	0.320608
$71$	1.62984	0.193427	0.0967134	−	0.995312i	$-0.469167\pi$
$71$	1.62984	0.193427	0.0967134	+	0.995312i	$0.469167\pi$
$72$	−1.00000	−0.117851
$73$	−15.3355	−1.79488	−0.897441	−	0.441134i	$-0.854576\pi$
$73$	−15.3355	−1.79488	−0.897441	+	0.441134i	$0.854576\pi$
$74$	10.8012	1.25561
$75$	3.92583	0.453316
$76$	−0.668814	−0.0767182
$77$	0.850052	0.0968724
$78$	−0.550837	−0.0623700
$79$	−2.43182	−0.273601	−0.136800	−	0.990599i	$-0.543682\pi$
$79$	−2.43182	−0.273601	−0.136800	+	0.990599i	$0.543682\pi$
$80$	−1.03642	−0.115875
$81$	1.00000	0.111111
$82$	−0.525599	−0.0580427
$83$	−10.0619	−1.10444	−0.552218	−	0.833700i	$-0.686218\pi$
$83$	−10.0619	−1.10444	−0.552218	+	0.833700i	$0.686218\pi$
$84$	−2.58814	−0.282389
$85$	−1.03642	−0.112416
$86$	5.46997	0.589842
$87$	−4.26895	−0.457679
$88$	−0.328441	−0.0350120
$89$	2.38147	0.252435	0.126218	−	0.992003i	$-0.459716\pi$
$89$	2.38147	0.252435	0.126218	+	0.992003i	$0.459716\pi$
$90$	1.03642	0.109248
$91$	−1.42564	−0.149448
$92$	2.85502	0.297657
$93$	1.05963	0.109879
$94$	3.44760	0.355593
$95$	0.693173	0.0711180
$96$	1.00000	0.102062
$97$	−6.24513	−0.634097	−0.317048	−	0.948409i	$-0.602692\pi$
$97$	−6.24513	−0.634097	−0.317048	+	0.948409i	$0.602692\pi$
$98$	0.301536	0.0304597
$99$	0.328441	0.0330096
$100$	−3.92583	−0.392583
$101$	11.5557	1.14983	0.574916	−	0.818212i	$-0.305035\pi$
$101$	11.5557	1.14983	0.574916	+	0.818212i	$0.305035\pi$
$102$	1.00000	0.0990148
$103$	12.9285	1.27388	0.636940	−	0.770913i	$-0.280200\pi$
$103$	12.9285	1.27388	0.636940	+	0.770913i	$0.280200\pi$
$104$	0.550837	0.0540140
$105$	2.68240	0.261776
$106$	−7.70645	−0.748517
$107$	16.3152	1.57725	0.788626	−	0.614874i	$-0.210793\pi$
$107$	16.3152	1.57725	0.788626	+	0.614874i	$0.210793\pi$
$108$	−1.00000	−0.0962250
$109$	−12.8397	−1.22982	−0.614910	−	0.788597i	$-0.710808\pi$
$109$	−12.8397	−1.22982	−0.614910	+	0.788597i	$0.710808\pi$
$110$	0.340403	0.0324562
$111$	10.8012	1.02520
$112$	2.58814	0.244556
$113$	−7.28064	−0.684905	−0.342453	−	0.939535i	$-0.611258\pi$
$113$	−7.28064	−0.684905	−0.342453	+	0.939535i	$0.611258\pi$
$114$	−0.668814	−0.0626402
$115$	−2.95900	−0.275929
$116$	4.26895	0.396362
$117$	−0.550837	−0.0509249
$118$	−1.00000	−0.0920575
$119$	2.58814	0.237254
$120$	−1.03642	−0.0946119
$121$	−10.8921	−0.990193
$122$	−4.66400	−0.422258
$123$	−0.525599	−0.0473917
$124$	−1.05963	−0.0951579
$125$	9.25092	0.827427
$126$	−2.58814	−0.230570
$127$	−5.99189	−0.531695	−0.265847	−	0.964015i	$-0.585652\pi$
$127$	−5.99189	−0.531695	−0.265847	+	0.964015i	$0.585652\pi$
$128$	−1.00000	−0.0883883
$129$	5.46997	0.481604
$130$	−0.570899	−0.0500711
$131$	−19.2336	−1.68045	−0.840224	−	0.542240i	$-0.817576\pi$
$131$	−19.2336	−1.68045	−0.840224	+	0.542240i	$0.817576\pi$
$132$	−0.328441	−0.0285871
$133$	−1.73098	−0.150095
$134$	1.71988	0.148575
$135$	1.03642	0.0892009
$136$	−1.00000	−0.0857493
$137$	11.8369	1.01129	0.505647	−	0.862741i	$-0.331254\pi$
$137$	11.8369	1.01129	0.505647	+	0.862741i	$0.331254\pi$
$138$	2.85502	0.243036
$139$	10.1241	0.858712	0.429356	−	0.903135i	$-0.358741\pi$
$139$	10.1241	0.858712	0.429356	+	0.903135i	$0.358741\pi$
$140$	−2.68240	−0.226704
$141$	3.44760	0.290341
$142$	−1.62984	−0.136773
$143$	−0.180918	−0.0151291
$144$	1.00000	0.0833333
$145$	−4.42443	−0.367429
$146$	15.3355	1.26917
$147$	0.301536	0.0248702
$148$	−10.8012	−0.887851
$149$	−2.04923	−0.167880	−0.0839399	−	0.996471i	$-0.526750\pi$
$149$	−2.04923	−0.167880	−0.0839399	+	0.996471i	$0.526750\pi$
$150$	−3.92583	−0.320543
$151$	−16.3006	−1.32652	−0.663261	−	0.748388i	$-0.730828\pi$
$151$	−16.3006	−1.32652	−0.663261	+	0.748388i	$0.730828\pi$
$152$	0.668814	0.0542480
$153$	1.00000	0.0808452
$154$	−0.850052	−0.0684991
$155$	1.09823	0.0882116
$156$	0.550837	0.0441022
$157$	3.98312	0.317888	0.158944	−	0.987288i	$-0.449191\pi$
$157$	3.98312	0.317888	0.158944	+	0.987288i	$0.449191\pi$
$158$	2.43182	0.193465
$159$	−7.70645	−0.611161
$160$	1.03642	0.0819363
$161$	7.38919	0.582350
$162$	−1.00000	−0.0785674
$163$	21.0239	1.64672	0.823359	−	0.567521i	$-0.192098\pi$
$163$	21.0239	1.64672	0.823359	+	0.567521i	$0.192098\pi$
$164$	0.525599	0.0410424
$165$	0.340403	0.0265004
$166$	10.0619	0.780955
$167$	−16.2720	−1.25916	−0.629581	−	0.776935i	$-0.716773\pi$
$167$	−16.2720	−1.25916	−0.629581	+	0.776935i	$0.716773\pi$
$168$	2.58814	0.199679
$169$	−12.6966	−0.976660
$170$	1.03642	0.0794899
$171$	−0.668814	−0.0511455
$172$	−5.46997	−0.417081
$173$	−10.0347	−0.762923	−0.381462	−	0.924385i	$-0.624579\pi$
$173$	−10.0347	−0.762923	−0.381462	+	0.924385i	$0.624579\pi$
$174$	4.26895	0.323628
$175$	−10.1606	−0.768069
$176$	0.328441	0.0247572
$177$	−1.00000	−0.0751646
$178$	−2.38147	−0.178499
$179$	10.2121	0.763286	0.381643	−	0.924310i	$-0.375358\pi$
$179$	10.2121	0.763286	0.381643	+	0.924310i	$0.375358\pi$
$180$	−1.03642	−0.0772503
$181$	9.52101	0.707691	0.353846	−	0.935304i	$-0.384874\pi$
$181$	9.52101	0.707691	0.353846	+	0.935304i	$0.384874\pi$
$182$	1.42564	0.105676
$183$	−4.66400	−0.344773
$184$	−2.85502	−0.210475
$185$	11.1946	0.823041
$186$	−1.05963	−0.0776961
$187$	0.328441	0.0240180
$188$	−3.44760	−0.251442
$189$	−2.58814	−0.188259
$190$	−0.693173	−0.0502881
$191$	8.89557	0.643661	0.321830	−	0.946797i	$-0.395702\pi$
$191$	8.89557	0.643661	0.321830	+	0.946797i	$0.395702\pi$
$192$	−1.00000	−0.0721688
$193$	−15.2739	−1.09944	−0.549719	−	0.835350i	$-0.685265\pi$
$193$	−15.2739	−1.09944	−0.549719	+	0.835350i	$0.685265\pi$
$194$	6.24513	0.448374
$195$	−0.570899	−0.0408829
$196$	−0.301536	−0.0215383
$197$	11.2776	0.803496	0.401748	−	0.915750i	$-0.368403\pi$
$197$	11.2776	0.803496	0.401748	+	0.915750i	$0.368403\pi$
$198$	−0.328441	−0.0233413
$199$	1.48477	0.105253	0.0526264	−	0.998614i	$-0.483241\pi$
$199$	1.48477	0.105253	0.0526264	+	0.998614i	$0.483241\pi$
$200$	3.92583	0.277598
$201$	1.71988	0.121311
$202$	−11.5557	−0.813055
$203$	11.0486	0.775462
$204$	−1.00000	−0.0700140
$205$	−0.544742	−0.0380464
$206$	−12.9285	−0.900769
$207$	2.85502	0.198438
$208$	−0.550837	−0.0381937
$209$	−0.219666	−0.0151946
$210$	−2.68240	−0.185103
$211$	−5.42501	−0.373473	−0.186737	−	0.982410i	$-0.559791\pi$
$211$	−5.42501	−0.373473	−0.186737	+	0.982410i	$0.559791\pi$
$212$	7.70645	0.529281
$213$	−1.62984	−0.111675
$214$	−16.3152	−1.11528
$215$	5.66919	0.386635
$216$	1.00000	0.0680414
$217$	−2.74248	−0.186172
$218$	12.8397	0.869615
$219$	15.3355	1.03628
$220$	−0.340403	−0.0229500
$221$	−0.550837	−0.0370533
$222$	−10.8012	−0.724927
$223$	21.1595	1.41695	0.708474	−	0.705737i	$-0.249384\pi$
$223$	21.1595	1.41695	0.708474	+	0.705737i	$0.249384\pi$
$224$	−2.58814	−0.172927
$225$	−3.92583	−0.261722
$226$	7.28064	0.484301
$227$	14.3490	0.952377	0.476189	−	0.879343i	$-0.342018\pi$
$227$	14.3490	0.952377	0.476189	+	0.879343i	$0.342018\pi$
$228$	0.668814	0.0442933
$229$	15.2853	1.01008	0.505042	−	0.863095i	$-0.331477\pi$
$229$	15.2853	1.01008	0.505042	+	0.863095i	$0.331477\pi$
$230$	2.95900	0.195111
$231$	−0.850052	−0.0559293
$232$	−4.26895	−0.280270
$233$	−25.3127	−1.65829	−0.829145	−	0.559034i	$-0.811172\pi$
$233$	−25.3127	−1.65829	−0.829145	+	0.559034i	$0.811172\pi$
$234$	0.550837	0.0360093
$235$	3.57317	0.233088
$236$	1.00000	0.0650945
$237$	2.43182	0.157963
$238$	−2.58814	−0.167764
$239$	21.1023	1.36499	0.682496	−	0.730890i	$-0.260895\pi$
$239$	21.1023	1.36499	0.682496	+	0.730890i	$0.260895\pi$
$240$	1.03642	0.0669007
$241$	26.8020	1.72647	0.863234	−	0.504804i	$-0.168435\pi$
$241$	26.8020	1.72647	0.863234	+	0.504804i	$0.168435\pi$
$242$	10.8921	0.700172
$243$	−1.00000	−0.0641500
$244$	4.66400	0.298582
$245$	0.312518	0.0199660
$246$	0.525599	0.0335110
$247$	0.368407	0.0234412
$248$	1.05963	0.0672868
$249$	10.0619	0.637647
$250$	−9.25092	−0.585079
$251$	−17.0612	−1.07689	−0.538446	−	0.842660i	$-0.680988\pi$
$251$	−17.0612	−1.07689	−0.538446	+	0.842660i	$0.680988\pi$
$252$	2.58814	0.163037
$253$	0.937707	0.0589531
$254$	5.99189	0.375965
$255$	1.03642	0.0649032
$256$	1.00000	0.0625000
$257$	−28.4862	−1.77692	−0.888460	−	0.458953i	$-0.848225\pi$
$257$	−28.4862	−1.77692	−0.888460	+	0.458953i	$0.848225\pi$
$258$	−5.46997	−0.340545
$259$	−27.9549	−1.73704
$260$	0.570899	0.0354056
$261$	4.26895	0.264241
$262$	19.2336	1.18826
$263$	−12.6911	−0.782569	−0.391284	−	0.920270i	$-0.627969\pi$
$263$	−12.6911	−0.782569	−0.391284	+	0.920270i	$0.627969\pi$
$264$	0.328441	0.0202142
$265$	−7.98713	−0.490645
$266$	1.73098	0.106133
$267$	−2.38147	−0.145744
$268$	−1.71988	−0.105058
$269$	−23.1876	−1.41377	−0.706886	−	0.707327i	$-0.749901\pi$
$269$	−23.1876	−1.41377	−0.706886	+	0.707327i	$0.749901\pi$
$270$	−1.03642	−0.0630746
$271$	−7.63277	−0.463658	−0.231829	−	0.972757i	$-0.574471\pi$
$271$	−7.63277	−0.463658	−0.231829	+	0.972757i	$0.574471\pi$
$272$	1.00000	0.0606339
$273$	1.42564	0.0862838
$274$	−11.8369	−0.715092
$275$	−1.28941	−0.0777541
$276$	−2.85502	−0.171852
$277$	16.4901	0.990796	0.495398	−	0.868666i	$-0.335022\pi$
$277$	16.4901	0.990796	0.495398	+	0.868666i	$0.335022\pi$
$278$	−10.1241	−0.607201
$279$	−1.05963	−0.0634386
$280$	2.68240	0.160304
$281$	−16.5257	−0.985838	−0.492919	−	0.870075i	$-0.664070\pi$
$281$	−16.5257	−0.985838	−0.492919	+	0.870075i	$0.664070\pi$
$282$	−3.44760	−0.205302
$283$	−22.5142	−1.33833	−0.669164	−	0.743115i	$-0.733348\pi$
$283$	−22.5142	−1.33833	−0.669164	+	0.743115i	$0.733348\pi$
$284$	1.62984	0.0967134
$285$	−0.693173	−0.0410600
$286$	0.180918	0.0106979
$287$	1.36032	0.0802973
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	4.42443	0.259811
$291$	6.24513	0.366096
$292$	−15.3355	−0.897441
$293$	25.7742	1.50575	0.752873	−	0.658166i	$-0.228668\pi$
$293$	25.7742	1.50575	0.752873	+	0.658166i	$0.228668\pi$
$294$	−0.301536	−0.0175859
$295$	−1.03642	−0.0603428
$296$	10.8012	0.627805
$297$	−0.328441	−0.0190581
$298$	2.04923	0.118709
$299$	−1.57265	−0.0909488
$300$	3.92583	0.226658
$301$	−14.1570	−0.815998
$302$	16.3006	0.937993
$303$	−11.5557	−0.663856
$304$	−0.668814	−0.0383591
$305$	−4.83386	−0.276786
$306$	−1.00000	−0.0571662
$307$	−21.8614	−1.24770	−0.623849	−	0.781545i	$-0.714432\pi$
$307$	−21.8614	−1.24770	−0.623849	+	0.781545i	$0.714432\pi$
$308$	0.850052	0.0484362
$309$	−12.9285	−0.735475
$310$	−1.09823	−0.0623750
$311$	−14.8414	−0.841576	−0.420788	−	0.907159i	$-0.638246\pi$
$311$	−14.8414	−0.841576	−0.420788	+	0.907159i	$0.638246\pi$
$312$	−0.550837	−0.0311850
$313$	2.76592	0.156339	0.0781696	−	0.996940i	$-0.475092\pi$
$313$	2.76592	0.156339	0.0781696	+	0.996940i	$0.475092\pi$
$314$	−3.98312	−0.224781
$315$	−2.68240	−0.151136
$316$	−2.43182	−0.136800
$317$	−4.05645	−0.227833	−0.113916	−	0.993490i	$-0.536340\pi$
$317$	−4.05645	−0.227833	−0.113916	+	0.993490i	$0.536340\pi$
$318$	7.70645	0.432156
$319$	1.40210	0.0785025
$320$	−1.03642	−0.0579377
$321$	−16.3152	−0.910626
$322$	−7.38919	−0.411784
$323$	−0.668814	−0.0372138
$324$	1.00000	0.0555556
$325$	2.16249	0.119953
$326$	−21.0239	−1.16441
$327$	12.8397	0.710037
$328$	−0.525599	−0.0290213
$329$	−8.92288	−0.491934
$330$	−0.340403	−0.0187386
$331$	11.3405	0.623328	0.311664	−	0.950192i	$-0.399114\pi$
$331$	11.3405	0.623328	0.311664	+	0.950192i	$0.399114\pi$
$332$	−10.0619	−0.552218
$333$	−10.8012	−0.591901
$334$	16.2720	0.890362
$335$	1.78252	0.0973893
$336$	−2.58814	−0.141195
$337$	−17.8392	−0.971761	−0.485880	−	0.874025i	$-0.661501\pi$
$337$	−17.8392	−0.971761	−0.485880	+	0.874025i	$0.661501\pi$
$338$	12.6966	0.690603
$339$	7.28064	0.395430
$340$	−1.03642	−0.0562078
$341$	−0.348027	−0.0188467
$342$	0.668814	0.0361653
$343$	−18.8974	−1.02036
$344$	5.46997	0.294921
$345$	2.95900	0.159307
$346$	10.0347	0.539468
$347$	6.47083	0.347372	0.173686	−	0.984801i	$-0.444432\pi$
$347$	6.47083	0.347372	0.173686	+	0.984801i	$0.444432\pi$
$348$	−4.26895	−0.228840
$349$	12.5865	0.673742	0.336871	−	0.941551i	$-0.390631\pi$
$349$	12.5865	0.673742	0.336871	+	0.941551i	$0.390631\pi$
$350$	10.1606	0.543107
$351$	0.550837	0.0294015
$352$	−0.328441	−0.0175060
$353$	−14.9803	−0.797324	−0.398662	−	0.917098i	$-0.630525\pi$
$353$	−14.9803	−0.797324	−0.398662	+	0.917098i	$0.630525\pi$
$354$	1.00000	0.0531494
$355$	−1.68920	−0.0896537
$356$	2.38147	0.126218
$357$	−2.58814	−0.136979
$358$	−10.2121	−0.539725
$359$	−30.6875	−1.61962	−0.809812	−	0.586690i	$-0.800431\pi$
$359$	−30.6875	−1.61962	−0.809812	+	0.586690i	$0.800431\pi$
$360$	1.03642	0.0546242
$361$	−18.5527	−0.976457
$362$	−9.52101	−0.500413
$363$	10.8921	0.571688
$364$	−1.42564	−0.0747240
$365$	15.8940	0.831931
$366$	4.66400	0.243791
$367$	−19.9254	−1.04010	−0.520050	−	0.854136i	$-0.674087\pi$
$367$	−19.9254	−1.04010	−0.520050	+	0.854136i	$0.674087\pi$
$368$	2.85502	0.148828
$369$	0.525599	0.0273616
$370$	−11.1946	−0.581978
$371$	19.9454	1.03551
$372$	1.05963	0.0549394
$373$	−21.3022	−1.10298	−0.551492	−	0.834180i	$-0.685941\pi$
$373$	−21.3022	−1.10298	−0.551492	+	0.834180i	$0.685941\pi$
$374$	−0.328441	−0.0169833
$375$	−9.25092	−0.477715
$376$	3.44760	0.177797
$377$	−2.35149	−0.121108
$378$	2.58814	0.133120
$379$	8.95772	0.460127	0.230064	−	0.973176i	$-0.426107\pi$
$379$	8.95772	0.460127	0.230064	+	0.973176i	$0.426107\pi$
$380$	0.693173	0.0355590
$381$	5.99189	0.306974
$382$	−8.89557	−0.455137
$383$	2.75199	0.140620	0.0703101	−	0.997525i	$-0.477601\pi$
$383$	2.75199	0.140620	0.0703101	+	0.997525i	$0.477601\pi$
$384$	1.00000	0.0510310
$385$	−0.881011	−0.0449005
$386$	15.2739	0.777420
$387$	−5.46997	−0.278054
$388$	−6.24513	−0.317048
$389$	−20.0517	−1.01666	−0.508330	−	0.861162i	$-0.669737\pi$
$389$	−20.0517	−1.01666	−0.508330	+	0.861162i	$0.669737\pi$
$390$	0.570899	0.0289086
$391$	2.85502	0.144385
$392$	0.301536	0.0152299
$393$	19.2336	0.970207
$394$	−11.2776	−0.568158
$395$	2.52038	0.126814
$396$	0.328441	0.0165048
$397$	8.78347	0.440830	0.220415	−	0.975406i	$-0.429259\pi$
$397$	8.78347	0.440830	0.220415	+	0.975406i	$0.429259\pi$
$398$	−1.48477	−0.0744249
$399$	1.73098	0.0866576
$400$	−3.92583	−0.196292
$401$	2.40824	0.120262	0.0601308	−	0.998191i	$-0.480848\pi$
$401$	2.40824	0.120262	0.0601308	+	0.998191i	$0.480848\pi$
$402$	−1.71988	−0.0857797
$403$	0.583685	0.0290754
$404$	11.5557	0.574916
$405$	−1.03642	−0.0515002
$406$	−11.0486	−0.548335
$407$	−3.54755	−0.175846
$408$	1.00000	0.0495074
$409$	26.4894	1.30982	0.654909	−	0.755708i	$-0.272707\pi$
$409$	26.4894	1.30982	0.654909	+	0.755708i	$0.272707\pi$
$410$	0.544742	0.0269029
$411$	−11.8369	−0.583870
$412$	12.9285	0.636940
$413$	2.58814	0.127354
$414$	−2.85502	−0.140317
$415$	10.4284	0.511908
$416$	0.550837	0.0270070
$417$	−10.1241	−0.495778
$418$	0.219666	0.0107442
$419$	−22.8269	−1.11517	−0.557583	−	0.830121i	$-0.688271\pi$
$419$	−22.8269	−1.11517	−0.557583	+	0.830121i	$0.688271\pi$
$420$	2.68240	0.130888
$421$	−26.9101	−1.31152	−0.655759	−	0.754970i	$-0.727651\pi$
$421$	−26.9101	−1.31152	−0.655759	+	0.754970i	$0.727651\pi$
$422$	5.42501	0.264086
$423$	−3.44760	−0.167628
$424$	−7.70645	−0.374258
$425$	−3.92583	−0.190431
$426$	1.62984	0.0789662
$427$	12.0711	0.584160
$428$	16.3152	0.788626
$429$	0.180918	0.00873478
$430$	−5.66919	−0.273393
$431$	−24.9651	−1.20253	−0.601263	−	0.799051i	$-0.705336\pi$
$431$	−24.9651	−1.20253	−0.601263	+	0.799051i	$0.705336\pi$
$432$	−1.00000	−0.0481125
$433$	−4.17199	−0.200493	−0.100247	−	0.994963i	$-0.531963\pi$
$433$	−4.17199	−0.200493	−0.100247	+	0.994963i	$0.531963\pi$
$434$	2.74248	0.131643
$435$	4.42443	0.212135
$436$	−12.8397	−0.614910
$437$	−1.90948	−0.0913428
$438$	−15.3355	−0.732758
$439$	−34.4803	−1.64566	−0.822828	−	0.568291i	$-0.807605\pi$
$439$	−34.4803	−1.64566	−0.822828	+	0.568291i	$0.807605\pi$
$440$	0.340403	0.0162281
$441$	−0.301536	−0.0143588
$442$	0.550837	0.0262006
$443$	−23.0099	−1.09323	−0.546617	−	0.837382i	$-0.684085\pi$
$443$	−23.0099	−1.09323	−0.546617	+	0.837382i	$0.684085\pi$
$444$	10.8012	0.512601
$445$	−2.46820	−0.117004
$446$	−21.1595	−1.00193
$447$	2.04923	0.0969254
$448$	2.58814	0.122278
$449$	−10.4492	−0.493129	−0.246564	−	0.969126i	$-0.579302\pi$
$449$	−10.4492	−0.493129	−0.246564	+	0.969126i	$0.579302\pi$
$450$	3.92583	0.185065
$451$	0.172628	0.00812875
$452$	−7.28064	−0.342453
$453$	16.3006	0.765868
$454$	−14.3490	−0.673432
$455$	1.47757	0.0692693
$456$	−0.668814	−0.0313201
$457$	36.1241	1.68981	0.844907	−	0.534914i	$-0.179656\pi$
$457$	36.1241	1.68981	0.844907	+	0.534914i	$0.179656\pi$
$458$	−15.2853	−0.714237
$459$	−1.00000	−0.0466760
$460$	−2.95900	−0.137964
$461$	40.3554	1.87954	0.939768	−	0.341812i	$-0.111041\pi$
$461$	40.3554	1.87954	0.939768	+	0.341812i	$0.111041\pi$
$462$	0.850052	0.0395480
$463$	4.06042	0.188704	0.0943519	−	0.995539i	$-0.469922\pi$
$463$	4.06042	0.188704	0.0943519	+	0.995539i	$0.469922\pi$
$464$	4.26895	0.198181
$465$	−1.09823	−0.0509290
$466$	25.3127	1.17259
$467$	−37.1361	−1.71845	−0.859226	−	0.511596i	$-0.829054\pi$
$467$	−37.1361	−1.71845	−0.859226	+	0.511596i	$0.829054\pi$
$468$	−0.550837	−0.0254624
$469$	−4.45128	−0.205541
$470$	−3.57317	−0.164818
$471$	−3.98312	−0.183533
$472$	−1.00000	−0.0460287
$473$	−1.79656	−0.0826061
$474$	−2.43182	−0.111697
$475$	2.62565	0.120473
$476$	2.58814	0.118627
$477$	7.70645	0.352854
$478$	−21.1023	−0.965195
$479$	−19.2776	−0.880816	−0.440408	−	0.897798i	$-0.645166\pi$
$479$	−19.2776	−0.880816	−0.440408	+	0.897798i	$0.645166\pi$
$480$	−1.03642	−0.0473059
$481$	5.94968	0.271282
$482$	−26.8020	−1.22080
$483$	−7.38919	−0.336220
$484$	−10.8921	−0.495097
$485$	6.47258	0.293905
$486$	1.00000	0.0453609
$487$	−9.52560	−0.431646	−0.215823	−	0.976432i	$-0.569243\pi$
$487$	−9.52560	−0.431646	−0.215823	+	0.976432i	$0.569243\pi$
$488$	−4.66400	−0.211129
$489$	−21.0239	−0.950733
$490$	−0.312518	−0.0141181
$491$	10.8049	0.487619	0.243810	−	0.969823i	$-0.421603\pi$
$491$	10.8049	0.487619	0.243810	+	0.969823i	$0.421603\pi$
$492$	−0.525599	−0.0236958
$493$	4.26895	0.192264
$494$	−0.368407	−0.0165754
$495$	−0.340403	−0.0153000
$496$	−1.05963	−0.0475789
$497$	4.21826	0.189215
$498$	−10.0619	−0.450884
$499$	25.4680	1.14010	0.570052	−	0.821609i	$-0.306923\pi$
$499$	25.4680	1.14010	0.570052	+	0.821609i	$0.306923\pi$
$500$	9.25092	0.413714
$501$	16.2720	0.726977
$502$	17.0612	0.761477
$503$	27.2165	1.21352	0.606761	−	0.794884i	$-0.292468\pi$
$503$	27.2165	1.21352	0.606761	+	0.794884i	$0.292468\pi$
$504$	−2.58814	−0.115285
$505$	−11.9765	−0.532949
$506$	−0.937707	−0.0416862
$507$	12.6966	0.563875
$508$	−5.99189	−0.265847
$509$	23.6190	1.04689	0.523446	−	0.852059i	$-0.324646\pi$
$509$	23.6190	1.04689	0.523446	+	0.852059i	$0.324646\pi$
$510$	−1.03642	−0.0458935
$511$	−39.6904	−1.75580
$512$	−1.00000	−0.0441942
$513$	0.668814	0.0295289
$514$	28.4862	1.25647
$515$	−13.3993	−0.590445
$516$	5.46997	0.240802
$517$	−1.13234	−0.0498001
$518$	27.9549	1.22827
$519$	10.0347	0.440474
$520$	−0.570899	−0.0250356
$521$	27.6475	1.21126	0.605630	−	0.795746i	$-0.292921\pi$
$521$	27.6475	1.21126	0.605630	+	0.795746i	$0.292921\pi$
$522$	−4.26895	−0.186847
$523$	−34.7234	−1.51835	−0.759175	−	0.650887i	$-0.774397\pi$
$523$	−34.7234	−1.51835	−0.759175	+	0.650887i	$0.774397\pi$
$524$	−19.2336	−0.840224
$525$	10.1606	0.443445
$526$	12.6911	0.553360
$527$	−1.05963	−0.0461583
$528$	−0.328441	−0.0142936
$529$	−14.8489	−0.645602
$530$	7.98713	0.346939
$531$	1.00000	0.0433963
$532$	−1.73098	−0.0750477
$533$	−0.289519	−0.0125405
$534$	2.38147	0.103056
$535$	−16.9094	−0.731058
$536$	1.71988	0.0742874
$537$	−10.2121	−0.440683
$538$	23.1876	0.999688
$539$	−0.0990368	−0.00426582
$540$	1.03642	0.0446005
$541$	−26.7090	−1.14831	−0.574156	−	0.818746i	$-0.694670\pi$
$541$	−26.7090	−1.14831	−0.574156	+	0.818746i	$0.694670\pi$
$542$	7.63277	0.327856
$543$	−9.52101	−0.408586
$544$	−1.00000	−0.0428746
$545$	13.3073	0.570024
$546$	−1.42564	−0.0610119
$547$	−9.15536	−0.391455	−0.195728	−	0.980658i	$-0.562707\pi$
$547$	−9.15536	−0.391455	−0.195728	+	0.980658i	$0.562707\pi$
$548$	11.8369	0.505647
$549$	4.66400	0.199055
$550$	1.28941	0.0549804
$551$	−2.85513	−0.121633
$552$	2.85502	0.121518
$553$	−6.29388	−0.267643
$554$	−16.4901	−0.700599
$555$	−11.1946	−0.475183
$556$	10.1241	0.429356
$557$	−38.3282	−1.62402	−0.812008	−	0.583646i	$-0.801626\pi$
$557$	−38.3282	−1.62402	−0.812008	+	0.583646i	$0.801626\pi$
$558$	1.05963	0.0448578
$559$	3.01306	0.127439
$560$	−2.68240	−0.113352
$561$	−0.328441	−0.0138668
$562$	16.5257	0.697093
$563$	10.5817	0.445966	0.222983	−	0.974822i	$-0.428421\pi$
$563$	10.5817	0.445966	0.222983	+	0.974822i	$0.428421\pi$
$564$	3.44760	0.145170
$565$	7.54581	0.317455
$566$	22.5142	0.946341
$567$	2.58814	0.108692
$568$	−1.62984	−0.0683867
$569$	5.49223	0.230246	0.115123	−	0.993351i	$-0.463274\pi$
$569$	5.49223	0.230246	0.115123	+	0.993351i	$0.463274\pi$
$570$	0.693173	0.0290338
$571$	−31.3251	−1.31091	−0.655457	−	0.755232i	$-0.727524\pi$
$571$	−31.3251	−1.31091	−0.655457	+	0.755232i	$0.727524\pi$
$572$	−0.180918	−0.00756454
$573$	−8.89557	−0.371618
$574$	−1.36032	−0.0567788
$575$	−11.2083	−0.467420
$576$	1.00000	0.0416667
$577$	−46.1827	−1.92261	−0.961305	−	0.275485i	$-0.911161\pi$
$577$	−46.1827	−1.92261	−0.961305	+	0.275485i	$0.911161\pi$
$578$	−1.00000	−0.0415945
$579$	15.2739	0.634761
$580$	−4.42443	−0.183714
$581$	−26.0416	−1.08039
$582$	−6.24513	−0.258869
$583$	2.53112	0.104828
$584$	15.3355	0.634587
$585$	0.570899	0.0236038
$586$	−25.7742	−1.06472
$587$	−40.6530	−1.67793	−0.838965	−	0.544185i	$-0.816839\pi$
$587$	−40.6530	−1.67793	−0.838965	+	0.544185i	$0.816839\pi$
$588$	0.301536	0.0124351
$589$	0.708698	0.0292014
$590$	1.03642	0.0426688
$591$	−11.2776	−0.463899
$592$	−10.8012	−0.443926
$593$	1.53525	0.0630452	0.0315226	−	0.999503i	$-0.489964\pi$
$593$	1.53525	0.0630452	0.0315226	+	0.999503i	$0.489964\pi$
$594$	0.328441	0.0134761
$595$	−2.68240	−0.109968
$596$	−2.04923	−0.0839399
$597$	−1.48477	−0.0607677
$598$	1.57265	0.0643105
$599$	−27.4789	−1.12276	−0.561378	−	0.827560i	$-0.689729\pi$
$599$	−27.4789	−1.12276	−0.561378	+	0.827560i	$0.689729\pi$
$600$	−3.92583	−0.160271
$601$	−9.76324	−0.398251	−0.199125	−	0.979974i	$-0.563810\pi$
$601$	−9.76324	−0.398251	−0.199125	+	0.979974i	$0.563810\pi$
$602$	14.1570	0.576998
$603$	−1.71988	−0.0700388
$604$	−16.3006	−0.663261
$605$	11.2888	0.458956
$606$	11.5557	0.469417
$607$	20.6299	0.837341	0.418671	−	0.908138i	$-0.362496\pi$
$607$	20.6299	0.837341	0.418671	+	0.908138i	$0.362496\pi$
$608$	0.668814	0.0271240
$609$	−11.0486	−0.447713
$610$	4.83386	0.195717
$611$	1.89907	0.0768280
$612$	1.00000	0.0404226
$613$	28.7830	1.16253	0.581267	−	0.813713i	$-0.302557\pi$
$613$	28.7830	1.16253	0.581267	+	0.813713i	$0.302557\pi$
$614$	21.8614	0.882256
$615$	0.544742	0.0219661
$616$	−0.850052	−0.0342496
$617$	31.0962	1.25189	0.625944	−	0.779868i	$-0.284714\pi$
$617$	31.0962	1.25189	0.625944	+	0.779868i	$0.284714\pi$
$618$	12.9285	0.520059
$619$	−15.4426	−0.620691	−0.310346	−	0.950624i	$-0.600445\pi$
$619$	−15.4426	−0.620691	−0.310346	+	0.950624i	$0.600445\pi$
$620$	1.09823	0.0441058
$621$	−2.85502	−0.114568
$622$	14.8414	0.595084
$623$	6.16357	0.246938
$624$	0.550837	0.0220511
$625$	10.0413	0.401653
$626$	−2.76592	−0.110548
$627$	0.219666	0.00877262
$628$	3.98312	0.158944
$629$	−10.8012	−0.430671
$630$	2.68240	0.106869
$631$	−31.2165	−1.24271	−0.621354	−	0.783530i	$-0.713417\pi$
$631$	−31.2165	−1.24271	−0.621354	+	0.783530i	$0.713417\pi$
$632$	2.43182	0.0967324
$633$	5.42501	0.215625
$634$	4.05645	0.161102
$635$	6.21012	0.246441
$636$	−7.70645	−0.305581
$637$	0.166097	0.00658100
$638$	−1.40210	−0.0555096
$639$	1.62984	0.0644756
$640$	1.03642	0.0409681
$641$	−0.703361	−0.0277811	−0.0138906	−	0.999904i	$-0.504422\pi$
$641$	−0.703361	−0.0277811	−0.0138906	+	0.999904i	$0.504422\pi$
$642$	16.3152	0.643910
$643$	38.4973	1.51819	0.759094	−	0.650982i	$-0.225643\pi$
$643$	38.4973	1.51819	0.759094	+	0.650982i	$0.225643\pi$
$644$	7.38919	0.291175
$645$	−5.66919	−0.223224
$646$	0.668814	0.0263141
$647$	−47.1976	−1.85553	−0.927764	−	0.373167i	$-0.878272\pi$
$647$	−47.1976	−1.85553	−0.927764	+	0.373167i	$0.878272\pi$
$648$	−1.00000	−0.0392837
$649$	0.328441	0.0128924
$650$	−2.16249	−0.0848199
$651$	2.74248	0.107486
$652$	21.0239	0.823359
$653$	−36.9305	−1.44520	−0.722601	−	0.691265i	$-0.757054\pi$
$653$	−36.9305	−1.44520	−0.722601	+	0.691265i	$0.757054\pi$
$654$	−12.8397	−0.502072
$655$	19.9341	0.778890
$656$	0.525599	0.0205212
$657$	−15.3355	−0.598294
$658$	8.92288	0.347850
$659$	−1.37589	−0.0535971	−0.0267986	−	0.999641i	$-0.508531\pi$
$659$	−1.37589	−0.0535971	−0.0267986	+	0.999641i	$0.508531\pi$
$660$	0.340403	0.0132502
$661$	13.3061	0.517547	0.258774	−	0.965938i	$-0.416682\pi$
$661$	13.3061	0.517547	0.258774	+	0.965938i	$0.416682\pi$
$662$	−11.3405	−0.440760
$663$	0.550837	0.0213927
$664$	10.0619	0.390477
$665$	1.79403	0.0695694
$666$	10.8012	0.418537
$667$	12.1879	0.471919
$668$	−16.2720	−0.629581
$669$	−21.1595	−0.818075
$670$	−1.78252	−0.0688647
$671$	1.53185	0.0591364
$672$	2.58814	0.0998396
$673$	−37.6570	−1.45157	−0.725786	−	0.687921i	$-0.758524\pi$
$673$	−37.6570	−1.45157	−0.725786	+	0.687921i	$0.758524\pi$
$674$	17.8392	0.687138
$675$	3.92583	0.151105
$676$	−12.6966	−0.488330
$677$	−25.4476	−0.978029	−0.489014	−	0.872276i	$-0.662643\pi$
$677$	−25.4476	−0.978029	−0.489014	+	0.872276i	$0.662643\pi$
$678$	−7.28064	−0.279611
$679$	−16.1633	−0.620289
$680$	1.03642	0.0397449
$681$	−14.3490	−0.549855
$682$	0.348027	0.0133267
$683$	51.0745	1.95431	0.977157	−	0.212520i	$-0.0681672\pi$
$683$	51.0745	1.95431	0.977157	+	0.212520i	$0.0681672\pi$
$684$	−0.668814	−0.0255727
$685$	−12.2680	−0.468736
$686$	18.8974	0.721506
$687$	−15.2853	−0.583172
$688$	−5.46997	−0.208541
$689$	−4.24500	−0.161722
$690$	−2.95900	−0.112647
$691$	27.7144	1.05430	0.527152	−	0.849771i	$-0.323260\pi$
$691$	27.7144	1.05430	0.527152	+	0.849771i	$0.323260\pi$
$692$	−10.0347	−0.381462
$693$	0.850052	0.0322908
$694$	−6.47083	−0.245629
$695$	−10.4928	−0.398014
$696$	4.26895	0.161814
$697$	0.525599	0.0199085
$698$	−12.5865	−0.476407
$699$	25.3127	0.957414
$700$	−10.1606	−0.384035
$701$	20.4898	0.773890	0.386945	−	0.922103i	$-0.373530\pi$
$701$	20.4898	0.773890	0.386945	+	0.922103i	$0.373530\pi$
$702$	−0.550837	−0.0207900
$703$	7.22398	0.272457
$704$	0.328441	0.0123786
$705$	−3.57317	−0.134573
$706$	14.9803	0.563793
$707$	29.9077	1.12479
$708$	−1.00000	−0.0375823
$709$	−37.3032	−1.40095	−0.700476	−	0.713676i	$-0.747029\pi$
$709$	−37.3032	−1.40095	−0.700476	+	0.713676i	$0.747029\pi$
$710$	1.68920	0.0633947
$711$	−2.43182	−0.0912002
$712$	−2.38147	−0.0892493
$713$	−3.02528	−0.113297
$714$	2.58814	0.0968587
$715$	0.187507	0.00701235
$716$	10.2121	0.381643
$717$	−21.1023	−0.788078
$718$	30.6875	1.14525
$719$	12.1722	0.453945	0.226972	−	0.973901i	$-0.427117\pi$
$719$	12.1722	0.453945	0.226972	+	0.973901i	$0.427117\pi$
$720$	−1.03642	−0.0386251
$721$	33.4607	1.24614
$722$	18.5527	0.690460
$723$	−26.8020	−0.996777
$724$	9.52101	0.353846
$725$	−16.7592	−0.622420
$726$	−10.8921	−0.404245
$727$	−14.0671	−0.521719	−0.260859	−	0.965377i	$-0.584006\pi$
$727$	−14.0671	−0.521719	−0.260859	+	0.965377i	$0.584006\pi$
$728$	1.42564	0.0528378
$729$	1.00000	0.0370370
$730$	−15.8940	−0.588264
$731$	−5.46997	−0.202314
$732$	−4.66400	−0.172386
$733$	41.5921	1.53624	0.768119	−	0.640307i	$-0.221193\pi$
$733$	41.5921	1.53624	0.768119	+	0.640307i	$0.221193\pi$
$734$	19.9254	0.735462
$735$	−0.312518	−0.0115274
$736$	−2.85502	−0.105237
$737$	−0.564879	−0.0208076
$738$	−0.525599	−0.0193476
$739$	−4.13980	−0.152285	−0.0761425	−	0.997097i	$-0.524260\pi$
$739$	−4.13980	−0.152285	−0.0761425	+	0.997097i	$0.524260\pi$
$740$	11.1946	0.411520
$741$	−0.368407	−0.0135338
$742$	−19.9454	−0.732218
$743$	19.5951	0.718876	0.359438	−	0.933169i	$-0.382968\pi$
$743$	19.5951	0.718876	0.359438	+	0.933169i	$0.382968\pi$
$744$	−1.05963	−0.0388480
$745$	2.12387	0.0778125
$746$	21.3022	0.779927
$747$	−10.0619	−0.368146
$748$	0.328441	0.0120090
$749$	42.2260	1.54291
$750$	9.25092	0.337796
$751$	0.815625	0.0297626	0.0148813	−	0.999889i	$-0.495263\pi$
$751$	0.815625	0.0297626	0.0148813	+	0.999889i	$0.495263\pi$
$752$	−3.44760	−0.125721
$753$	17.0612	0.621744
$754$	2.35149	0.0856364
$755$	16.8943	0.614845
$756$	−2.58814	−0.0941297
$757$	6.60362	0.240013	0.120006	−	0.992773i	$-0.461708\pi$
$757$	6.60362	0.240013	0.120006	+	0.992773i	$0.461708\pi$
$758$	−8.95772	−0.325359
$759$	−0.937707	−0.0340366
$760$	−0.693173	−0.0251440
$761$	30.5922	1.10897	0.554484	−	0.832194i	$-0.312916\pi$
$761$	30.5922	1.10897	0.554484	+	0.832194i	$0.312916\pi$
$762$	−5.99189	−0.217063
$763$	−33.2309	−1.20304
$764$	8.89557	0.321830
$765$	−1.03642	−0.0374719
$766$	−2.75199	−0.0994336
$767$	−0.550837	−0.0198896
$768$	−1.00000	−0.0360844
$769$	−4.82043	−0.173829	−0.0869146	−	0.996216i	$-0.527701\pi$
$769$	−4.82043	−0.173829	−0.0869146	+	0.996216i	$0.527701\pi$
$770$	0.881011	0.0317495
$771$	28.4862	1.02591
$772$	−15.2739	−0.549719
$773$	−47.9006	−1.72286	−0.861432	−	0.507873i	$-0.830432\pi$
$773$	−47.9006	−1.72286	−0.861432	+	0.507873i	$0.830432\pi$
$774$	5.46997	0.196614
$775$	4.15994	0.149430
$776$	6.24513	0.224187
$777$	27.9549	1.00288
$778$	20.0517	0.718888
$779$	−0.351528	−0.0125948
$780$	−0.570899	−0.0204415
$781$	0.535308	0.0191548
$782$	−2.85502	−0.102095
$783$	−4.26895	−0.152560
$784$	−0.301536	−0.0107691
$785$	−4.12819	−0.147341
$786$	−19.2336	−0.686040
$787$	−1.68498	−0.0600631	−0.0300316	−	0.999549i	$-0.509561\pi$
$787$	−1.68498	−0.0600631	−0.0300316	+	0.999549i	$0.509561\pi$
$788$	11.2776	0.401748
$789$	12.6911	0.451816
$790$	−2.52038	−0.0896712
$791$	−18.8433	−0.669991
$792$	−0.328441	−0.0116707
$793$	−2.56910	−0.0912314
$794$	−8.78347	−0.311714
$795$	7.98713	0.283274
$796$	1.48477	0.0526264
$797$	−21.3264	−0.755419	−0.377710	−	0.925924i	$-0.623288\pi$
$797$	−21.3264	−0.755419	−0.377710	+	0.925924i	$0.623288\pi$
$798$	−1.73098	−0.0612762
$799$	−3.44760	−0.121967
$800$	3.92583	0.138799
$801$	2.38147	0.0841451
$802$	−2.40824	−0.0850379
$803$	−5.03681	−0.177745
$804$	1.71988	0.0606554
$805$	−7.65831	−0.269920
$806$	−0.583685	−0.0205594
$807$	23.1876	0.816242
$808$	−11.5557	−0.406527
$809$	16.0214	0.563283	0.281642	−	0.959520i	$-0.409121\pi$
$809$	16.0214	0.563283	0.281642	+	0.959520i	$0.409121\pi$
$810$	1.03642	0.0364161
$811$	−45.8477	−1.60993	−0.804965	−	0.593322i	$-0.797816\pi$
$811$	−45.8477	−1.60993	−0.804965	+	0.593322i	$0.797816\pi$
$812$	11.0486	0.387731
$813$	7.63277	0.267693
$814$	3.54755	0.124342
$815$	−21.7896	−0.763256
$816$	−1.00000	−0.0350070
$817$	3.65839	0.127991
$818$	−26.4894	−0.926181
$819$	−1.42564	−0.0498160
$820$	−0.544742	−0.0190232
$821$	3.10196	0.108259	0.0541296	−	0.998534i	$-0.482762\pi$
$821$	3.10196	0.108259	0.0541296	+	0.998534i	$0.482762\pi$
$822$	11.8369	0.412859
$823$	−8.80778	−0.307020	−0.153510	−	0.988147i	$-0.549058\pi$
$823$	−8.80778	−0.307020	−0.153510	+	0.988147i	$0.549058\pi$
$824$	−12.9285	−0.450385
$825$	1.28941	0.0448913
$826$	−2.58814	−0.0900529
$827$	8.61291	0.299500	0.149750	−	0.988724i	$-0.452153\pi$
$827$	8.61291	0.299500	0.149750	+	0.988724i	$0.452153\pi$
$828$	2.85502	0.0992189
$829$	46.1638	1.60334	0.801668	−	0.597770i	$-0.203946\pi$
$829$	46.1638	1.60334	0.801668	+	0.597770i	$0.203946\pi$
$830$	−10.4284	−0.361974
$831$	−16.4901	−0.572036
$832$	−0.550837	−0.0190968
$833$	−0.301536	−0.0104476
$834$	10.1241	0.350568
$835$	16.8646	0.583623
$836$	−0.219666	−0.00759731
$837$	1.05963	0.0366263
$838$	22.8269	0.788542
$839$	−2.27098	−0.0784029	−0.0392014	−	0.999231i	$-0.512481\pi$
$839$	−2.27098	−0.0784029	−0.0392014	+	0.999231i	$0.512481\pi$
$840$	−2.68240	−0.0925516
$841$	−10.7761	−0.371589
$842$	26.9101	0.927383
$843$	16.5257	0.569174
$844$	−5.42501	−0.186737
$845$	13.1590	0.452683
$846$	3.44760	0.118531
$847$	−28.1903	−0.968632
$848$	7.70645	0.264641
$849$	22.5142	0.772684
$850$	3.92583	0.134655
$851$	−30.8376	−1.05710
$852$	−1.62984	−0.0558375
$853$	47.2041	1.61624	0.808118	−	0.589020i	$-0.200486\pi$
$853$	47.2041	1.61624	0.808118	+	0.589020i	$0.200486\pi$
$854$	−12.0711	−0.413064
$855$	0.693173	0.0237060
$856$	−16.3152	−0.557642
$857$	37.8605	1.29329	0.646645	−	0.762791i	$-0.276172\pi$
$857$	37.8605	1.29329	0.646645	+	0.762791i	$0.276172\pi$
$858$	−0.180918	−0.00617642
$859$	−5.19943	−0.177402	−0.0887012	−	0.996058i	$-0.528272\pi$
$859$	−5.19943	−0.177402	−0.0887012	+	0.996058i	$0.528272\pi$
$860$	5.66919	0.193318
$861$	−1.36032	−0.0463597
$862$	24.9651	0.850314
$863$	22.3597	0.761132	0.380566	−	0.924754i	$-0.375729\pi$
$863$	22.3597	0.761132	0.380566	+	0.924754i	$0.375729\pi$
$864$	1.00000	0.0340207
$865$	10.4002	0.353616
$866$	4.17199	0.141770
$867$	−1.00000	−0.0339618
$868$	−2.74248	−0.0930858
$869$	−0.798709	−0.0270943
$870$	−4.42443	−0.150002
$871$	0.947372	0.0321005
$872$	12.8397	0.434807
$873$	−6.24513	−0.211366
$874$	1.90948	0.0645891
$875$	23.9427	0.809410
$876$	15.3355	0.518138
$877$	1.27995	0.0432210	0.0216105	−	0.999766i	$-0.493121\pi$
$877$	1.27995	0.0432210	0.0216105	+	0.999766i	$0.493121\pi$
$878$	34.4803	1.16365
$879$	−25.7742	−0.869343
$880$	−0.340403	−0.0114750
$881$	−49.0833	−1.65366	−0.826829	−	0.562453i	$-0.809858\pi$
$881$	−49.0833	−1.65366	−0.826829	+	0.562453i	$0.809858\pi$
$882$	0.301536	0.0101532
$883$	8.00208	0.269291	0.134646	−	0.990894i	$-0.457010\pi$
$883$	8.00208	0.269291	0.134646	+	0.990894i	$0.457010\pi$
$884$	−0.550837	−0.0185266
$885$	1.03642	0.0348389
$886$	23.0099	0.773034
$887$	−5.45354	−0.183112	−0.0915560	−	0.995800i	$-0.529184\pi$
$887$	−5.45354	−0.183112	−0.0915560	+	0.995800i	$0.529184\pi$
$888$	−10.8012	−0.362464
$889$	−15.5079	−0.520117
$890$	2.46820	0.0827344
$891$	0.328441	0.0110032
$892$	21.1595	0.708474
$893$	2.30581	0.0771609
$894$	−2.04923	−0.0685366
$895$	−10.5840	−0.353784
$896$	−2.58814	−0.0864637
$897$	1.57265	0.0525093
$898$	10.4492	0.348695
$899$	−4.52352	−0.150868
$900$	−3.92583	−0.130861
$901$	7.70645	0.256739
$902$	−0.172628	−0.00574790
$903$	14.1570	0.471117
$904$	7.28064	0.242151
$905$	−9.86777	−0.328016
$906$	−16.3006	−0.541550
$907$	−38.1407	−1.26644	−0.633220	−	0.773972i	$-0.718267\pi$
$907$	−38.1407	−1.26644	−0.633220	+	0.773972i	$0.718267\pi$
$908$	14.3490	0.476189
$909$	11.5557	0.383278
$910$	−1.47757	−0.0489808
$911$	53.8433	1.78391	0.891953	−	0.452128i	$-0.149335\pi$
$911$	53.8433	1.78391	0.891953	+	0.452128i	$0.149335\pi$
$912$	0.668814	0.0221467
$913$	−3.30474	−0.109371
$914$	−36.1241	−1.19488
$915$	4.83386	0.159803
$916$	15.2853	0.505042
$917$	−49.7792	−1.64386
$918$	1.00000	0.0330049
$919$	−28.3433	−0.934958	−0.467479	−	0.884004i	$-0.654838\pi$
$919$	−28.3433	−0.934958	−0.467479	+	0.884004i	$0.654838\pi$
$920$	2.95900	0.0975555
$921$	21.8614	0.720359
$922$	−40.3554	−1.32903
$923$	−0.897778	−0.0295507
$924$	−0.850052	−0.0279647
$925$	42.4036	1.39422
$926$	−4.06042	−0.133434
$927$	12.9285	0.424627
$928$	−4.26895	−0.140135
$929$	29.4579	0.966484	0.483242	−	0.875487i	$-0.339459\pi$
$929$	29.4579	0.966484	0.483242	+	0.875487i	$0.339459\pi$
$930$	1.09823	0.0360122
$931$	0.201671	0.00660951
$932$	−25.3127	−0.829145
$933$	14.8414	0.485884
$934$	37.1361	1.21513
$935$	−0.340403	−0.0111324
$936$	0.550837	0.0180047
$937$	−32.6271	−1.06588	−0.532941	−	0.846153i	$-0.678913\pi$
$937$	−32.6271	−1.06588	−0.532941	+	0.846153i	$0.678913\pi$
$938$	4.45128	0.145340
$939$	−2.76592	−0.0902624
$940$	3.57317	0.116544
$941$	37.6241	1.22651	0.613255	−	0.789885i	$-0.289860\pi$
$941$	37.6241	1.22651	0.613255	+	0.789885i	$0.289860\pi$
$942$	3.98312	0.129777
$943$	1.50060	0.0488661
$944$	1.00000	0.0325472
$945$	2.68240	0.0872585
$946$	1.79656	0.0584113
$947$	−48.2651	−1.56840	−0.784202	−	0.620505i	$-0.786928\pi$
$947$	−48.2651	−1.56840	−0.784202	+	0.620505i	$0.786928\pi$
$948$	2.43182	0.0789817
$949$	8.44735	0.274212
$950$	−2.62565	−0.0851874
$951$	4.05645	0.131539
$952$	−2.58814	−0.0838821
$953$	9.60362	0.311092	0.155546	−	0.987829i	$-0.450286\pi$
$953$	9.60362	0.311092	0.155546	+	0.987829i	$0.450286\pi$
$954$	−7.70645	−0.249506
$955$	−9.21955	−0.298338
$956$	21.1023	0.682496
$957$	−1.40210	−0.0453234
$958$	19.2776	0.622831
$959$	30.6355	0.989272
$960$	1.03642	0.0334503
$961$	−29.8772	−0.963780
$962$	−5.94968	−0.191825
$963$	16.3152	0.525750
$964$	26.8020	0.863234
$965$	15.8302	0.509591
$966$	7.38919	0.237743
$967$	−38.0539	−1.22373	−0.611866	−	0.790961i	$-0.709581\pi$
$967$	−38.0539	−1.22373	−0.611866	+	0.790961i	$0.709581\pi$
$968$	10.8921	0.350086
$969$	0.668814	0.0214854
$970$	−6.47258	−0.207822
$971$	20.7233	0.665043	0.332521	−	0.943096i	$-0.392101\pi$
$971$	20.7233	0.665043	0.332521	+	0.943096i	$0.392101\pi$
$972$	−1.00000	−0.0320750
$973$	26.2025	0.840013
$974$	9.52560	0.305220
$975$	−2.16249	−0.0692552
$976$	4.66400	0.149291
$977$	−27.0974	−0.866922	−0.433461	−	0.901172i	$-0.642708\pi$
$977$	−27.0974	−0.866922	−0.433461	+	0.901172i	$0.642708\pi$
$978$	21.0239	0.672270
$979$	0.782173	0.0249984
$980$	0.312518	0.00998302
$981$	−12.8397	−0.409940
$982$	−10.8049	−0.344799
$983$	−15.5362	−0.495527	−0.247764	−	0.968821i	$-0.579696\pi$
$983$	−15.5362	−0.495527	−0.247764	+	0.968821i	$0.579696\pi$
$984$	0.525599	0.0167555
$985$	−11.6884	−0.372422
$986$	−4.26895	−0.135951
$987$	8.92288	0.284018
$988$	0.368407	0.0117206
$989$	−15.6169	−0.496588
$990$	0.340403	0.0108187
$991$	25.2340	0.801586	0.400793	−	0.916169i	$-0.368735\pi$
$991$	25.2340	0.801586	0.400793	+	0.916169i	$0.368735\pi$
$992$	1.05963	0.0336434
$993$	−11.3405	−0.359879
$994$	−4.21826	−0.133795
$995$	−1.53885	−0.0487848
$996$	10.0619	0.318823
$997$	−55.9970	−1.77344	−0.886721	−	0.462304i	$-0.847023\pi$
$997$	−55.9970	−1.77344	−0.886721	+	0.462304i	$0.847023\pi$
$998$	−25.4680	−0.806175
$999$	10.8012	0.341734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.u.1.5	✓	9

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.03642 q^{5} +1.00000 q^{6} +2.58814 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.03642 q^{5} +1.00000 q^{6} +2.58814 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.03642 q^{10} +0.328441 q^{11} -1.00000 q^{12} -0.550837 q^{13} -2.58814 q^{14} +1.03642 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -0.668814 q^{19} -1.03642 q^{20} -2.58814 q^{21} -0.328441 q^{22} +2.85502 q^{23} +1.00000 q^{24} -3.92583 q^{25} +0.550837 q^{26} -1.00000 q^{27} +2.58814 q^{28} +4.26895 q^{29} -1.03642 q^{30} -1.05963 q^{31} -1.00000 q^{32} -0.328441 q^{33} -1.00000 q^{34} -2.68240 q^{35} +1.00000 q^{36} -10.8012 q^{37} +0.668814 q^{38} +0.550837 q^{39} +1.03642 q^{40} +0.525599 q^{41} +2.58814 q^{42} -5.46997 q^{43} +0.328441 q^{44} -1.03642 q^{45} -2.85502 q^{46} -3.44760 q^{47} -1.00000 q^{48} -0.301536 q^{49} +3.92583 q^{50} -1.00000 q^{51} -0.550837 q^{52} +7.70645 q^{53} +1.00000 q^{54} -0.340403 q^{55} -2.58814 q^{56} +0.668814 q^{57} -4.26895 q^{58} +1.00000 q^{59} +1.03642 q^{60} +4.66400 q^{61} +1.05963 q^{62} +2.58814 q^{63} +1.00000 q^{64} +0.570899 q^{65} +0.328441 q^{66} -1.71988 q^{67} +1.00000 q^{68} -2.85502 q^{69} +2.68240 q^{70} +1.62984 q^{71} -1.00000 q^{72} -15.3355 q^{73} +10.8012 q^{74} +3.92583 q^{75} -0.668814 q^{76} +0.850052 q^{77} -0.550837 q^{78} -2.43182 q^{79} -1.03642 q^{80} +1.00000 q^{81} -0.525599 q^{82} -10.0619 q^{83} -2.58814 q^{84} -1.03642 q^{85} +5.46997 q^{86} -4.26895 q^{87} -0.328441 q^{88} +2.38147 q^{89} +1.03642 q^{90} -1.42564 q^{91} +2.85502 q^{92} +1.05963 q^{93} +3.44760 q^{94} +0.693173 q^{95} +1.00000 q^{96} -6.24513 q^{97} +0.301536 q^{98} +0.328441 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 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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