LMFDB - Embedded newform 6018.2.a.y.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 33x^{8} + 53x^{7} + 356x^{6} - 433x^{5} - 1296x^{4} + 1135x^{3} + 930x^{2} - 186x - 104 $ x^10 - 2x^9 - 33x^8 + 53x^7 + 356x^6 - 433x^5 - 1296x^4 + 1135x^3 + 930x^2 - 186*x - 104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.94189$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.94189 q^{5} -1.00000 q^{6} -4.15692 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.94189 q^{5} -1.00000 q^{6} -4.15692 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.94189 q^{10} +0.498663 q^{11} +1.00000 q^{12} -1.50384 q^{13} +4.15692 q^{14} -3.94189 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +5.53020 q^{19} -3.94189 q^{20} -4.15692 q^{21} -0.498663 q^{22} -1.40276 q^{23} -1.00000 q^{24} +10.5385 q^{25} +1.50384 q^{26} +1.00000 q^{27} -4.15692 q^{28} -0.951830 q^{29} +3.94189 q^{30} +7.82563 q^{31} -1.00000 q^{32} +0.498663 q^{33} +1.00000 q^{34} +16.3861 q^{35} +1.00000 q^{36} -6.18139 q^{37} -5.53020 q^{38} -1.50384 q^{39} +3.94189 q^{40} +2.21944 q^{41} +4.15692 q^{42} +7.51232 q^{43} +0.498663 q^{44} -3.94189 q^{45} +1.40276 q^{46} +2.58146 q^{47} +1.00000 q^{48} +10.2800 q^{49} -10.5385 q^{50} -1.00000 q^{51} -1.50384 q^{52} -2.76796 q^{53} -1.00000 q^{54} -1.96567 q^{55} +4.15692 q^{56} +5.53020 q^{57} +0.951830 q^{58} +1.00000 q^{59} -3.94189 q^{60} -1.40709 q^{61} -7.82563 q^{62} -4.15692 q^{63} +1.00000 q^{64} +5.92795 q^{65} -0.498663 q^{66} +5.89786 q^{67} -1.00000 q^{68} -1.40276 q^{69} -16.3861 q^{70} -1.28420 q^{71} -1.00000 q^{72} -5.94314 q^{73} +6.18139 q^{74} +10.5385 q^{75} +5.53020 q^{76} -2.07291 q^{77} +1.50384 q^{78} -0.338386 q^{79} -3.94189 q^{80} +1.00000 q^{81} -2.21944 q^{82} +11.1030 q^{83} -4.15692 q^{84} +3.94189 q^{85} -7.51232 q^{86} -0.951830 q^{87} -0.498663 q^{88} -4.18127 q^{89} +3.94189 q^{90} +6.25134 q^{91} -1.40276 q^{92} +7.82563 q^{93} -2.58146 q^{94} -21.7994 q^{95} -1.00000 q^{96} -5.63340 q^{97} -10.2800 q^{98} +0.498663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.94189	−1.76287	−0.881433	−	0.472310i	$-0.843420\pi$
$5$	−3.94189	−1.76287	−0.881433	+	0.472310i	$0.843420\pi$
$6$	−1.00000	−0.408248
$7$	−4.15692	−1.57117	−0.785585	−	0.618754i	$-0.787638\pi$
$7$	−4.15692	−1.57117	−0.785585	+	0.618754i	$0.787638\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.94189	1.24653
$11$	0.498663	0.150353	0.0751763	−	0.997170i	$-0.476048\pi$
$11$	0.498663	0.150353	0.0751763	+	0.997170i	$0.476048\pi$
$12$	1.00000	0.288675
$13$	−1.50384	−0.417089	−0.208545	−	0.978013i	$-0.566873\pi$
$13$	−1.50384	−0.417089	−0.208545	+	0.978013i	$0.566873\pi$
$14$	4.15692	1.11098
$15$	−3.94189	−1.01779
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	5.53020	1.26872	0.634358	−	0.773039i	$-0.281265\pi$
$19$	5.53020	1.26872	0.634358	+	0.773039i	$0.281265\pi$
$20$	−3.94189	−0.881433
$21$	−4.15692	−0.907115
$22$	−0.498663	−0.106315
$23$	−1.40276	−0.292496	−0.146248	−	0.989248i	$-0.546720\pi$
$23$	−1.40276	−0.292496	−0.146248	+	0.989248i	$0.546720\pi$
$24$	−1.00000	−0.204124
$25$	10.5385	2.10769
$26$	1.50384	0.294927
$27$	1.00000	0.192450
$28$	−4.15692	−0.785585
$29$	−0.951830	−0.176750	−0.0883752	−	0.996087i	$-0.528167\pi$
$29$	−0.951830	−0.176750	−0.0883752	+	0.996087i	$0.528167\pi$
$30$	3.94189	0.719687
$31$	7.82563	1.40553	0.702763	−	0.711424i	$-0.251950\pi$
$31$	7.82563	1.40553	0.702763	+	0.711424i	$0.251950\pi$
$32$	−1.00000	−0.176777
$33$	0.498663	0.0868061
$34$	1.00000	0.171499
$35$	16.3861	2.76976
$36$	1.00000	0.166667
$37$	−6.18139	−1.01621	−0.508107	−	0.861294i	$-0.669655\pi$
$37$	−6.18139	−1.01621	−0.508107	+	0.861294i	$0.669655\pi$
$38$	−5.53020	−0.897118
$39$	−1.50384	−0.240807
$40$	3.94189	0.623267
$41$	2.21944	0.346618	0.173309	−	0.984868i	$-0.444554\pi$
$41$	2.21944	0.346618	0.173309	+	0.984868i	$0.444554\pi$
$42$	4.15692	0.641427
$43$	7.51232	1.14562	0.572809	−	0.819689i	$-0.305854\pi$
$43$	7.51232	1.14562	0.572809	+	0.819689i	$0.305854\pi$
$44$	0.498663	0.0751763
$45$	−3.94189	−0.587622
$46$	1.40276	0.206826
$47$	2.58146	0.376545	0.188272	−	0.982117i	$-0.439711\pi$
$47$	2.58146	0.376545	0.188272	+	0.982117i	$0.439711\pi$
$48$	1.00000	0.144338
$49$	10.2800	1.46857
$50$	−10.5385	−1.49036
$51$	−1.00000	−0.140028
$52$	−1.50384	−0.208545
$53$	−2.76796	−0.380209	−0.190104	−	0.981764i	$-0.560883\pi$
$53$	−2.76796	−0.380209	−0.190104	+	0.981764i	$0.560883\pi$
$54$	−1.00000	−0.136083
$55$	−1.96567	−0.265051
$56$	4.15692	0.555492
$57$	5.53020	0.732493
$58$	0.951830	0.124981
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−3.94189	−0.508895
$61$	−1.40709	−0.180160	−0.0900800	−	0.995935i	$-0.528712\pi$
$61$	−1.40709	−0.180160	−0.0900800	+	0.995935i	$0.528712\pi$
$62$	−7.82563	−0.993857
$63$	−4.15692	−0.523723
$64$	1.00000	0.125000
$65$	5.92795	0.735272
$66$	−0.498663	−0.0613812
$67$	5.89786	0.720539	0.360269	−	0.932848i	$-0.382685\pi$
$67$	5.89786	0.720539	0.360269	+	0.932848i	$0.382685\pi$
$68$	−1.00000	−0.121268
$69$	−1.40276	−0.168873
$70$	−16.3861	−1.95852
$71$	−1.28420	−0.152407	−0.0762035	−	0.997092i	$-0.524280\pi$
$71$	−1.28420	−0.152407	−0.0762035	+	0.997092i	$0.524280\pi$
$72$	−1.00000	−0.117851
$73$	−5.94314	−0.695592	−0.347796	−	0.937570i	$-0.613070\pi$
$73$	−5.94314	−0.695592	−0.347796	+	0.937570i	$0.613070\pi$
$74$	6.18139	0.718572
$75$	10.5385	1.21688
$76$	5.53020	0.634358
$77$	−2.07291	−0.236230
$78$	1.50384	0.170276
$79$	−0.338386	−0.0380714	−0.0190357	−	0.999819i	$-0.506060\pi$
$79$	−0.338386	−0.0380714	−0.0190357	+	0.999819i	$0.506060\pi$
$80$	−3.94189	−0.440716
$81$	1.00000	0.111111
$82$	−2.21944	−0.245096
$83$	11.1030	1.21871	0.609356	−	0.792897i	$-0.291428\pi$
$83$	11.1030	1.21871	0.609356	+	0.792897i	$0.291428\pi$
$84$	−4.15692	−0.453558
$85$	3.94189	0.427558
$86$	−7.51232	−0.810074
$87$	−0.951830	−0.102047
$88$	−0.498663	−0.0531577
$89$	−4.18127	−0.443214	−0.221607	−	0.975136i	$-0.571130\pi$
$89$	−4.18127	−0.443214	−0.221607	+	0.975136i	$0.571130\pi$
$90$	3.94189	0.415511
$91$	6.25134	0.655318
$92$	−1.40276	−0.146248
$93$	7.82563	0.811480
$94$	−2.58146	−0.266257
$95$	−21.7994	−2.23657
$96$	−1.00000	−0.102062
$97$	−5.63340	−0.571985	−0.285993	−	0.958232i	$-0.592323\pi$
$97$	−5.63340	−0.571985	−0.285993	+	0.958232i	$0.592323\pi$
$98$	−10.2800	−1.03844
$99$	0.498663	0.0501175
$100$	10.5385	1.05385
$101$	−12.0184	−1.19588	−0.597939	−	0.801542i	$-0.704013\pi$
$101$	−12.0184	−1.19588	−0.597939	+	0.801542i	$0.704013\pi$
$102$	1.00000	0.0990148
$103$	−4.10334	−0.404314	−0.202157	−	0.979353i	$-0.564795\pi$
$103$	−4.10334	−0.404314	−0.202157	+	0.979353i	$0.564795\pi$
$104$	1.50384	0.147463
$105$	16.3861	1.59912
$106$	2.76796	0.268848
$107$	−9.44296	−0.912885	−0.456443	−	0.889753i	$-0.650877\pi$
$107$	−9.44296	−0.912885	−0.456443	+	0.889753i	$0.650877\pi$
$108$	1.00000	0.0962250
$109$	4.29439	0.411328	0.205664	−	0.978623i	$-0.434065\pi$
$109$	4.29439	0.411328	0.205664	+	0.978623i	$0.434065\pi$
$110$	1.96567	0.187420
$111$	−6.18139	−0.586712
$112$	−4.15692	−0.392792
$113$	−3.82370	−0.359704	−0.179852	−	0.983694i	$-0.557562\pi$
$113$	−3.82370	−0.359704	−0.179852	+	0.983694i	$0.557562\pi$
$114$	−5.53020	−0.517951
$115$	5.52953	0.515632
$116$	−0.951830	−0.0883752
$117$	−1.50384	−0.139030
$118$	−1.00000	−0.0920575
$119$	4.15692	0.381065
$120$	3.94189	0.359843
$121$	−10.7513	−0.977394
$122$	1.40709	0.127392
$123$	2.21944	0.200120
$124$	7.82563	0.702763
$125$	−21.8320	−1.95271
$126$	4.15692	0.370328
$127$	7.54136	0.669188	0.334594	−	0.942362i	$-0.391401\pi$
$127$	7.54136	0.669188	0.334594	+	0.942362i	$0.391401\pi$
$128$	−1.00000	−0.0883883
$129$	7.51232	0.661423
$130$	−5.92795	−0.519916
$131$	−1.89804	−0.165833	−0.0829164	−	0.996557i	$-0.526423\pi$
$131$	−1.89804	−0.165833	−0.0829164	+	0.996557i	$0.526423\pi$
$132$	0.498663	0.0434031
$133$	−22.9886	−1.99337
$134$	−5.89786	−0.509498
$135$	−3.94189	−0.339264
$136$	1.00000	0.0857493
$137$	14.5703	1.24483	0.622414	−	0.782688i	$-0.286152\pi$
$137$	14.5703	1.24483	0.622414	+	0.782688i	$0.286152\pi$
$138$	1.40276	0.119411
$139$	3.31377	0.281070	0.140535	−	0.990076i	$-0.455118\pi$
$139$	3.31377	0.281070	0.140535	+	0.990076i	$0.455118\pi$
$140$	16.3861	1.38488
$141$	2.58146	0.217398
$142$	1.28420	0.107768
$143$	−0.749908	−0.0627105
$144$	1.00000	0.0833333
$145$	3.75200	0.311587
$146$	5.94314	0.491858
$147$	10.2800	0.847882
$148$	−6.18139	−0.508107
$149$	22.1026	1.81072	0.905358	−	0.424650i	$-0.139603\pi$
$149$	22.1026	1.81072	0.905358	+	0.424650i	$0.139603\pi$
$150$	−10.5385	−0.860462
$151$	1.38851	0.112995	0.0564977	−	0.998403i	$-0.482007\pi$
$151$	1.38851	0.112995	0.0564977	+	0.998403i	$0.482007\pi$
$152$	−5.53020	−0.448559
$153$	−1.00000	−0.0808452
$154$	2.07291	0.167040
$155$	−30.8478	−2.47775
$156$	−1.50384	−0.120403
$157$	−5.78310	−0.461542	−0.230771	−	0.973008i	$-0.574125\pi$
$157$	−5.78310	−0.461542	−0.230771	+	0.973008i	$0.574125\pi$
$158$	0.338386	0.0269205
$159$	−2.76796	−0.219514
$160$	3.94189	0.311633
$161$	5.83118	0.459561
$162$	−1.00000	−0.0785674
$163$	21.2108	1.66136	0.830681	−	0.556749i	$-0.187951\pi$
$163$	21.2108	1.66136	0.830681	+	0.556749i	$0.187951\pi$
$164$	2.21944	0.173309
$165$	−1.96567	−0.153028
$166$	−11.1030	−0.861760
$167$	11.6389	0.900645	0.450323	−	0.892866i	$-0.351309\pi$
$167$	11.6389	0.900645	0.450323	+	0.892866i	$0.351309\pi$
$168$	4.15692	0.320714
$169$	−10.7385	−0.826037
$170$	−3.94189	−0.302329
$171$	5.53020	0.422905
$172$	7.51232	0.572809
$173$	−16.7116	−1.27056	−0.635278	−	0.772284i	$-0.719114\pi$
$173$	−16.7116	−1.27056	−0.635278	+	0.772284i	$0.719114\pi$
$174$	0.951830	0.0721580
$175$	−43.8076	−3.31154
$176$	0.498663	0.0375882
$177$	1.00000	0.0751646
$178$	4.18127	0.313399
$179$	−8.52772	−0.637392	−0.318696	−	0.947857i	$-0.603245\pi$
$179$	−8.52772	−0.637392	−0.318696	+	0.947857i	$0.603245\pi$
$180$	−3.94189	−0.293811
$181$	2.38605	0.177354	0.0886770	−	0.996060i	$-0.471736\pi$
$181$	2.38605	0.177354	0.0886770	+	0.996060i	$0.471736\pi$
$182$	−6.25134	−0.463380
$183$	−1.40709	−0.104015
$184$	1.40276	0.103413
$185$	24.3663	1.79145
$186$	−7.82563	−0.573803
$187$	−0.498663	−0.0364659
$188$	2.58146	0.188272
$189$	−4.15692	−0.302372
$190$	21.7994	1.58150
$191$	3.23671	0.234200	0.117100	−	0.993120i	$-0.462640\pi$
$191$	3.23671	0.234200	0.117100	+	0.993120i	$0.462640\pi$
$192$	1.00000	0.0721688
$193$	−3.26683	−0.235152	−0.117576	−	0.993064i	$-0.537512\pi$
$193$	−3.26683	−0.235152	−0.117576	+	0.993064i	$0.537512\pi$
$194$	5.63340	0.404455
$195$	5.92795	0.424510
$196$	10.2800	0.734287
$197$	−21.7155	−1.54716	−0.773581	−	0.633698i	$-0.781536\pi$
$197$	−21.7155	−1.54716	−0.773581	+	0.633698i	$0.781536\pi$
$198$	−0.498663	−0.0354385
$199$	4.55946	0.323211	0.161606	−	0.986855i	$-0.448333\pi$
$199$	4.55946	0.323211	0.161606	+	0.986855i	$0.448333\pi$
$200$	−10.5385	−0.745182
$201$	5.89786	0.416003
$202$	12.0184	0.845613
$203$	3.95668	0.277705
$204$	−1.00000	−0.0700140
$205$	−8.74877	−0.611041
$206$	4.10334	0.285893
$207$	−1.40276	−0.0974988
$208$	−1.50384	−0.104272
$209$	2.75771	0.190755
$210$	−16.3861	−1.13075
$211$	−13.5622	−0.933661	−0.466831	−	0.884347i	$-0.654604\pi$
$211$	−13.5622	−0.933661	−0.466831	+	0.884347i	$0.654604\pi$
$212$	−2.76796	−0.190104
$213$	−1.28420	−0.0879922
$214$	9.44296	0.645507
$215$	−29.6127	−2.01957
$216$	−1.00000	−0.0680414
$217$	−32.5306	−2.20832
$218$	−4.29439	−0.290853
$219$	−5.94314	−0.401600
$220$	−1.96567	−0.132526
$221$	1.50384	0.101159
$222$	6.18139	0.414868
$223$	−20.9059	−1.39996	−0.699981	−	0.714161i	$-0.746808\pi$
$223$	−20.9059	−1.39996	−0.699981	+	0.714161i	$0.746808\pi$
$224$	4.15692	0.277746
$225$	10.5385	0.702564
$226$	3.82370	0.254349
$227$	−22.7966	−1.51306	−0.756532	−	0.653957i	$-0.773108\pi$
$227$	−22.7966	−1.51306	−0.756532	+	0.653957i	$0.773108\pi$
$228$	5.53020	0.366247
$229$	−2.76690	−0.182842	−0.0914211	−	0.995812i	$-0.529141\pi$
$229$	−2.76690	−0.182842	−0.0914211	+	0.995812i	$0.529141\pi$
$230$	−5.52953	−0.364607
$231$	−2.07291	−0.136387
$232$	0.951830	0.0624907
$233$	−24.4763	−1.60350	−0.801749	−	0.597661i	$-0.796097\pi$
$233$	−24.4763	−1.60350	−0.801749	+	0.597661i	$0.796097\pi$
$234$	1.50384	0.0983089
$235$	−10.1758	−0.663798
$236$	1.00000	0.0650945
$237$	−0.338386	−0.0219805
$238$	−4.15692	−0.269453
$239$	−26.3324	−1.70330	−0.851652	−	0.524108i	$-0.824399\pi$
$239$	−26.3324	−1.70330	−0.851652	+	0.524108i	$0.824399\pi$
$240$	−3.94189	−0.254448
$241$	22.7724	1.46690	0.733448	−	0.679746i	$-0.237910\pi$
$241$	22.7724	1.46690	0.733448	+	0.679746i	$0.237910\pi$
$242$	10.7513	0.691122
$243$	1.00000	0.0641500
$244$	−1.40709	−0.0900800
$245$	−40.5227	−2.58890
$246$	−2.21944	−0.141506
$247$	−8.31653	−0.529168
$248$	−7.82563	−0.496928
$249$	11.1030	0.703624
$250$	21.8320	1.38078
$251$	−18.9842	−1.19827	−0.599137	−	0.800647i	$-0.704489\pi$
$251$	−18.9842	−1.19827	−0.599137	+	0.800647i	$0.704489\pi$
$252$	−4.15692	−0.261862
$253$	−0.699506	−0.0439776
$254$	−7.54136	−0.473187
$255$	3.94189	0.246850
$256$	1.00000	0.0625000
$257$	−24.9891	−1.55878	−0.779388	−	0.626542i	$-0.784470\pi$
$257$	−24.9891	−1.55878	−0.779388	+	0.626542i	$0.784470\pi$
$258$	−7.51232	−0.467697
$259$	25.6956	1.59665
$260$	5.92795	0.367636
$261$	−0.951830	−0.0589168
$262$	1.89804	0.117261
$263$	−2.12162	−0.130825	−0.0654125	−	0.997858i	$-0.520836\pi$
$263$	−2.12162	−0.130825	−0.0654125	+	0.997858i	$0.520836\pi$
$264$	−0.498663	−0.0306906
$265$	10.9110	0.670257
$266$	22.9886	1.40952
$267$	−4.18127	−0.255889
$268$	5.89786	0.360269
$269$	−3.47081	−0.211619	−0.105810	−	0.994386i	$-0.533743\pi$
$269$	−3.47081	−0.211619	−0.105810	+	0.994386i	$0.533743\pi$
$270$	3.94189	0.239896
$271$	30.2685	1.83868	0.919340	−	0.393463i	$-0.128723\pi$
$271$	30.2685	1.83868	0.919340	+	0.393463i	$0.128723\pi$
$272$	−1.00000	−0.0606339
$273$	6.25134	0.378348
$274$	−14.5703	−0.880226
$275$	5.25515	0.316897
$276$	−1.40276	−0.0844364
$277$	−7.55172	−0.453739	−0.226870	−	0.973925i	$-0.572849\pi$
$277$	−7.55172	−0.453739	−0.226870	+	0.973925i	$0.572849\pi$
$278$	−3.31377	−0.198747
$279$	7.82563	0.468508
$280$	−16.3861	−0.979258
$281$	15.1341	0.902823	0.451411	−	0.892316i	$-0.350921\pi$
$281$	15.1341	0.902823	0.451411	+	0.892316i	$0.350921\pi$
$282$	−2.58146	−0.153724
$283$	−23.2461	−1.38183	−0.690917	−	0.722934i	$-0.742793\pi$
$283$	−23.2461	−1.38183	−0.690917	+	0.722934i	$0.742793\pi$
$284$	−1.28420	−0.0762035
$285$	−21.7994	−1.29129
$286$	0.749908	0.0443430
$287$	−9.22604	−0.544596
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−3.75200	−0.220325
$291$	−5.63340	−0.330236
$292$	−5.94314	−0.347796
$293$	−1.25275	−0.0731866	−0.0365933	−	0.999330i	$-0.511651\pi$
$293$	−1.25275	−0.0731866	−0.0365933	+	0.999330i	$0.511651\pi$
$294$	−10.2800	−0.599543
$295$	−3.94189	−0.229505
$296$	6.18139	0.359286
$297$	0.498663	0.0289354
$298$	−22.1026	−1.28037
$299$	2.10953	0.121997
$300$	10.5385	0.608439
$301$	−31.2281	−1.79996
$302$	−1.38851	−0.0798998
$303$	−12.0184	−0.690440
$304$	5.53020	0.317179
$305$	5.54661	0.317598
$306$	1.00000	0.0571662
$307$	15.8570	0.905006	0.452503	−	0.891763i	$-0.350531\pi$
$307$	15.8570	0.905006	0.452503	+	0.891763i	$0.350531\pi$
$308$	−2.07291	−0.118115
$309$	−4.10334	−0.233431
$310$	30.8478	1.75203
$311$	−27.3982	−1.55361	−0.776805	−	0.629741i	$-0.783161\pi$
$311$	−27.3982	−1.55361	−0.776805	+	0.629741i	$0.783161\pi$
$312$	1.50384	0.0851380
$313$	13.8140	0.780813	0.390407	−	0.920643i	$-0.372334\pi$
$313$	13.8140	0.780813	0.390407	+	0.920643i	$0.372334\pi$
$314$	5.78310	0.326359
$315$	16.3861	0.923254
$316$	−0.338386	−0.0190357
$317$	−0.452225	−0.0253995	−0.0126997	−	0.999919i	$-0.504043\pi$
$317$	−0.452225	−0.0253995	−0.0126997	+	0.999919i	$0.504043\pi$
$318$	2.76796	0.155220
$319$	−0.474643	−0.0265749
$320$	−3.94189	−0.220358
$321$	−9.44296	−0.527054
$322$	−5.83118	−0.324959
$323$	−5.53020	−0.307709
$324$	1.00000	0.0555556
$325$	−15.8481	−0.879096
$326$	−21.2108	−1.17476
$327$	4.29439	0.237480
$328$	−2.21944	−0.122548
$329$	−10.7309	−0.591616
$330$	1.96567	0.108207
$331$	2.42899	0.133509	0.0667546	−	0.997769i	$-0.478736\pi$
$331$	2.42899	0.133509	0.0667546	+	0.997769i	$0.478736\pi$
$332$	11.1030	0.609356
$333$	−6.18139	−0.338738
$334$	−11.6389	−0.636852
$335$	−23.2487	−1.27021
$336$	−4.15692	−0.226779
$337$	−18.2783	−0.995683	−0.497842	−	0.867268i	$-0.665874\pi$
$337$	−18.2783	−0.995683	−0.497842	+	0.867268i	$0.665874\pi$
$338$	10.7385	0.584096
$339$	−3.82370	−0.207675
$340$	3.94189	0.213779
$341$	3.90236	0.211324
$342$	−5.53020	−0.299039
$343$	−13.6348	−0.736211
$344$	−7.51232	−0.405037
$345$	5.52953	0.297700
$346$	16.7116	0.898419
$347$	−22.7612	−1.22189	−0.610944	−	0.791674i	$-0.709210\pi$
$347$	−22.7612	−1.22189	−0.610944	+	0.791674i	$0.709210\pi$
$348$	−0.951830	−0.0510234
$349$	20.3696	1.09036	0.545179	−	0.838320i	$-0.316462\pi$
$349$	20.3696	1.09036	0.545179	+	0.838320i	$0.316462\pi$
$350$	43.8076	2.34162
$351$	−1.50384	−0.0802689
$352$	−0.498663	−0.0265788
$353$	11.2316	0.597798	0.298899	−	0.954285i	$-0.403381\pi$
$353$	11.2316	0.597798	0.298899	+	0.954285i	$0.403381\pi$
$354$	−1.00000	−0.0531494
$355$	5.06219	0.268673
$356$	−4.18127	−0.221607
$357$	4.15692	0.220008
$358$	8.52772	0.450704
$359$	−11.0162	−0.581413	−0.290706	−	0.956812i	$-0.593890\pi$
$359$	−11.0162	−0.581413	−0.290706	+	0.956812i	$0.593890\pi$
$360$	3.94189	0.207756
$361$	11.5832	0.609640
$362$	−2.38605	−0.125408
$363$	−10.7513	−0.564299
$364$	6.25134	0.327659
$365$	23.4272	1.22623
$366$	1.40709	0.0735500
$367$	24.3809	1.27267	0.636336	−	0.771412i	$-0.280449\pi$
$367$	24.3809	1.27267	0.636336	+	0.771412i	$0.280449\pi$
$368$	−1.40276	−0.0731241
$369$	2.21944	0.115539
$370$	−24.3663	−1.26675
$371$	11.5062	0.597373
$372$	7.82563	0.405740
$373$	16.8690	0.873445	0.436722	−	0.899596i	$-0.356139\pi$
$373$	16.8690	0.873445	0.436722	+	0.899596i	$0.356139\pi$
$374$	0.498663	0.0257853
$375$	−21.8320	−1.12740
$376$	−2.58146	−0.133129
$377$	1.43140	0.0737207
$378$	4.15692	0.213809
$379$	24.1425	1.24011	0.620057	−	0.784557i	$-0.287109\pi$
$379$	24.1425	1.24011	0.620057	+	0.784557i	$0.287109\pi$
$380$	−21.7994	−1.11829
$381$	7.54136	0.386356
$382$	−3.23671	−0.165604
$383$	−31.5959	−1.61448	−0.807238	−	0.590227i	$-0.799038\pi$
$383$	−31.5959	−1.61448	−0.807238	+	0.590227i	$0.799038\pi$
$384$	−1.00000	−0.0510310
$385$	8.17116	0.416441
$386$	3.26683	0.166277
$387$	7.51232	0.381873
$388$	−5.63340	−0.285993
$389$	30.5279	1.54782	0.773912	−	0.633293i	$-0.218297\pi$
$389$	30.5279	1.54782	0.773912	+	0.633293i	$0.218297\pi$
$390$	−5.92795	−0.300174
$391$	1.40276	0.0709408
$392$	−10.2800	−0.519220
$393$	−1.89804	−0.0957436
$394$	21.7155	1.09401
$395$	1.33388	0.0671148
$396$	0.498663	0.0250588
$397$	11.1233	0.558261	0.279131	−	0.960253i	$-0.409954\pi$
$397$	11.1233	0.558261	0.279131	+	0.960253i	$0.409954\pi$
$398$	−4.55946	−0.228545
$399$	−22.9886	−1.15087
$400$	10.5385	0.526923
$401$	7.50926	0.374995	0.187497	−	0.982265i	$-0.439962\pi$
$401$	7.50926	0.374995	0.187497	+	0.982265i	$0.439962\pi$
$402$	−5.89786	−0.294159
$403$	−11.7685	−0.586230
$404$	−12.0184	−0.597939
$405$	−3.94189	−0.195874
$406$	−3.95668	−0.196367
$407$	−3.08243	−0.152791
$408$	1.00000	0.0495074
$409$	11.2784	0.557680	0.278840	−	0.960338i	$-0.410050\pi$
$409$	11.2784	0.557680	0.278840	+	0.960338i	$0.410050\pi$
$410$	8.74877	0.432071
$411$	14.5703	0.718702
$412$	−4.10334	−0.202157
$413$	−4.15692	−0.204549
$414$	1.40276	0.0689420
$415$	−43.7667	−2.14843
$416$	1.50384	0.0737317
$417$	3.31377	0.162276
$418$	−2.75771	−0.134884
$419$	1.29791	0.0634070	0.0317035	−	0.999497i	$-0.489907\pi$
$419$	1.29791	0.0634070	0.0317035	+	0.999497i	$0.489907\pi$
$420$	16.3861	0.799561
$421$	−20.1220	−0.980688	−0.490344	−	0.871529i	$-0.663129\pi$
$421$	−20.1220	−0.980688	−0.490344	+	0.871529i	$0.663129\pi$
$422$	13.5622	0.660198
$423$	2.58146	0.125515
$424$	2.76796	0.134424
$425$	−10.5385	−0.511191
$426$	1.28420	0.0622199
$427$	5.84919	0.283062
$428$	−9.44296	−0.456443
$429$	−0.749908	−0.0362059
$430$	29.6127	1.42805
$431$	−3.84667	−0.185288	−0.0926438	−	0.995699i	$-0.529532\pi$
$431$	−3.84667	−0.185288	−0.0926438	+	0.995699i	$0.529532\pi$
$432$	1.00000	0.0481125
$433$	−35.2352	−1.69329	−0.846647	−	0.532154i	$-0.821383\pi$
$433$	−35.2352	−1.69329	−0.846647	+	0.532154i	$0.821383\pi$
$434$	32.5306	1.56152
$435$	3.75200	0.179895
$436$	4.29439	0.205664
$437$	−7.75757	−0.371095
$438$	5.94314	0.283974
$439$	20.4457	0.975821	0.487910	−	0.872894i	$-0.337759\pi$
$439$	20.4457	0.975821	0.487910	+	0.872894i	$0.337759\pi$
$440$	1.96567	0.0937098
$441$	10.2800	0.489525
$442$	−1.50384	−0.0715302
$443$	28.8660	1.37147	0.685733	−	0.727853i	$-0.259482\pi$
$443$	28.8660	1.37147	0.685733	+	0.727853i	$0.259482\pi$
$444$	−6.18139	−0.293356
$445$	16.4821	0.781326
$446$	20.9059	0.989923
$447$	22.1026	1.04542
$448$	−4.15692	−0.196396
$449$	−20.9032	−0.986483	−0.493241	−	0.869892i	$-0.664188\pi$
$449$	−20.9032	−0.986483	−0.493241	+	0.869892i	$0.664188\pi$
$450$	−10.5385	−0.496788
$451$	1.10675	0.0521149
$452$	−3.82370	−0.179852
$453$	1.38851	0.0652379
$454$	22.7966	1.06990
$455$	−24.6421	−1.15524
$456$	−5.53020	−0.258976
$457$	2.29892	0.107539	0.0537694	−	0.998553i	$-0.482876\pi$
$457$	2.29892	0.107539	0.0537694	+	0.998553i	$0.482876\pi$
$458$	2.76690	0.129289
$459$	−1.00000	−0.0466760
$460$	5.52953	0.257816
$461$	0.701928	0.0326920	0.0163460	−	0.999866i	$-0.494797\pi$
$461$	0.701928	0.0326920	0.0163460	+	0.999866i	$0.494797\pi$
$462$	2.07291	0.0964403
$463$	−13.7307	−0.638122	−0.319061	−	0.947734i	$-0.603367\pi$
$463$	−13.7307	−0.638122	−0.319061	+	0.947734i	$0.603367\pi$
$464$	−0.951830	−0.0441876
$465$	−30.8478	−1.43053
$466$	24.4763	1.13384
$467$	31.5561	1.46024	0.730122	−	0.683317i	$-0.239463\pi$
$467$	31.5561	1.46024	0.730122	+	0.683317i	$0.239463\pi$
$468$	−1.50384	−0.0695149
$469$	−24.5170	−1.13209
$470$	10.1758	0.469376
$471$	−5.78310	−0.266471
$472$	−1.00000	−0.0460287
$473$	3.74612	0.172247
$474$	0.338386	0.0155426
$475$	58.2799	2.67406
$476$	4.15692	0.190532
$477$	−2.76796	−0.126736
$478$	26.3324	1.20442
$479$	16.7993	0.767579	0.383790	−	0.923421i	$-0.374619\pi$
$479$	16.7993	0.767579	0.383790	+	0.923421i	$0.374619\pi$
$480$	3.94189	0.179922
$481$	9.29581	0.423852
$482$	−22.7724	−1.03725
$483$	5.83118	0.265328
$484$	−10.7513	−0.488697
$485$	22.2062	1.00833
$486$	−1.00000	−0.0453609
$487$	11.7486	0.532381	0.266190	−	0.963921i	$-0.414235\pi$
$487$	11.7486	0.532381	0.266190	+	0.963921i	$0.414235\pi$
$488$	1.40709	0.0636962
$489$	21.2108	0.959188
$490$	40.5227	1.83063
$491$	−27.1704	−1.22618	−0.613091	−	0.790012i	$-0.710074\pi$
$491$	−27.1704	−1.22618	−0.613091	+	0.790012i	$0.710074\pi$
$492$	2.21944	0.100060
$493$	0.951830	0.0428683
$494$	8.31653	0.374178
$495$	−1.96567	−0.0883505
$496$	7.82563	0.351381
$497$	5.33834	0.239457
$498$	−11.1030	−0.497537
$499$	13.5465	0.606427	0.303213	−	0.952923i	$-0.401941\pi$
$499$	13.5465	0.606427	0.303213	+	0.952923i	$0.401941\pi$
$500$	−21.8320	−0.976357
$501$	11.6389	0.519988
$502$	18.9842	0.847307
$503$	5.34380	0.238268	0.119134	−	0.992878i	$-0.461988\pi$
$503$	5.34380	0.238268	0.119134	+	0.992878i	$0.461988\pi$
$504$	4.15692	0.185164
$505$	47.3753	2.10817
$506$	0.699506	0.0310969
$507$	−10.7385	−0.476912
$508$	7.54136	0.334594
$509$	−16.2169	−0.718803	−0.359402	−	0.933183i	$-0.617019\pi$
$509$	−16.2169	−0.718803	−0.359402	+	0.933183i	$0.617019\pi$
$510$	−3.94189	−0.174550
$511$	24.7052	1.09289
$512$	−1.00000	−0.0441942
$513$	5.53020	0.244164
$514$	24.9891	1.10222
$515$	16.1749	0.712751
$516$	7.51232	0.330711
$517$	1.28728	0.0566145
$518$	−25.6956	−1.12900
$519$	−16.7116	−0.733556
$520$	−5.92795	−0.259958
$521$	−17.9280	−0.785441	−0.392720	−	0.919658i	$-0.628466\pi$
$521$	−17.9280	−0.785441	−0.392720	+	0.919658i	$0.628466\pi$
$522$	0.951830	0.0416605
$523$	10.1573	0.444147	0.222073	−	0.975030i	$-0.428718\pi$
$523$	10.1573	0.444147	0.222073	+	0.975030i	$0.428718\pi$
$524$	−1.89804	−0.0829164
$525$	−43.8076	−1.91192
$526$	2.12162	0.0925072
$527$	−7.82563	−0.340890
$528$	0.498663	0.0217015
$529$	−21.0323	−0.914446
$530$	−10.9110	−0.473943
$531$	1.00000	0.0433963
$532$	−22.9886	−0.996684
$533$	−3.33767	−0.144571
$534$	4.18127	0.180941
$535$	37.2231	1.60929
$536$	−5.89786	−0.254749
$537$	−8.52772	−0.367998
$538$	3.47081	0.149637
$539$	5.12627	0.220804
$540$	−3.94189	−0.169632
$541$	9.31203	0.400355	0.200178	−	0.979760i	$-0.435848\pi$
$541$	9.31203	0.400355	0.200178	+	0.979760i	$0.435848\pi$
$542$	−30.2685	−1.30014
$543$	2.38605	0.102395
$544$	1.00000	0.0428746
$545$	−16.9280	−0.725115
$546$	−6.25134	−0.267533
$547$	−16.7678	−0.716940	−0.358470	−	0.933541i	$-0.616702\pi$
$547$	−16.7678	−0.716940	−0.358470	+	0.933541i	$0.616702\pi$
$548$	14.5703	0.622414
$549$	−1.40709	−0.0600533
$550$	−5.25515	−0.224080
$551$	−5.26381	−0.224246
$552$	1.40276	0.0597056
$553$	1.40665	0.0598166
$554$	7.55172	0.320842
$555$	24.3663	1.03429
$556$	3.31377	0.140535
$557$	−22.3494	−0.946976	−0.473488	−	0.880800i	$-0.657005\pi$
$557$	−22.3494	−0.946976	−0.473488	+	0.880800i	$0.657005\pi$
$558$	−7.82563	−0.331286
$559$	−11.2973	−0.477825
$560$	16.3861	0.692440
$561$	−0.498663	−0.0210536
$562$	−15.1341	−0.638392
$563$	−0.888753	−0.0374565	−0.0187282	−	0.999825i	$-0.505962\pi$
$563$	−0.888753	−0.0374565	−0.0187282	+	0.999825i	$0.505962\pi$
$564$	2.58146	0.108699
$565$	15.0726	0.634109
$566$	23.2461	0.977105
$567$	−4.15692	−0.174574
$568$	1.28420	0.0538840
$569$	−9.71946	−0.407461	−0.203730	−	0.979027i	$-0.565307\pi$
$569$	−9.71946	−0.407461	−0.203730	+	0.979027i	$0.565307\pi$
$570$	21.7994	0.913078
$571$	−12.4264	−0.520028	−0.260014	−	0.965605i	$-0.583727\pi$
$571$	−12.4264	−0.520028	−0.260014	+	0.965605i	$0.583727\pi$
$572$	−0.749908	−0.0313552
$573$	3.23671	0.135215
$574$	9.22604	0.385087
$575$	−14.7830	−0.616493
$576$	1.00000	0.0416667
$577$	17.8013	0.741078	0.370539	−	0.928817i	$-0.379173\pi$
$577$	17.8013	0.741078	0.370539	+	0.928817i	$0.379173\pi$
$578$	−1.00000	−0.0415945
$579$	−3.26683	−0.135765
$580$	3.75200	0.155794
$581$	−46.1543	−1.91480
$582$	5.63340	0.233512
$583$	−1.38028	−0.0571654
$584$	5.94314	0.245929
$585$	5.92795	0.245091
$586$	1.25275	0.0517507
$587$	15.7385	0.649596	0.324798	−	0.945783i	$-0.394704\pi$
$587$	15.7385	0.649596	0.324798	+	0.945783i	$0.394704\pi$
$588$	10.2800	0.423941
$589$	43.2774	1.78321
$590$	3.94189	0.162285
$591$	−21.7155	−0.893254
$592$	−6.18139	−0.254054
$593$	−24.4389	−1.00359	−0.501793	−	0.864988i	$-0.667326\pi$
$593$	−24.4389	−1.00359	−0.501793	+	0.864988i	$0.667326\pi$
$594$	−0.498663	−0.0204604
$595$	−16.3861	−0.671766
$596$	22.1026	0.905358
$597$	4.55946	0.186606
$598$	−2.10953	−0.0862650
$599$	4.01786	0.164165	0.0820826	−	0.996626i	$-0.473843\pi$
$599$	4.01786	0.164165	0.0820826	+	0.996626i	$0.473843\pi$
$600$	−10.5385	−0.430231
$601$	−27.6449	−1.12766	−0.563829	−	0.825892i	$-0.690672\pi$
$601$	−27.6449	−1.12766	−0.563829	+	0.825892i	$0.690672\pi$
$602$	31.2281	1.27276
$603$	5.89786	0.240180
$604$	1.38851	0.0564977
$605$	42.3805	1.72301
$606$	12.0184	0.488215
$607$	−13.0087	−0.528009	−0.264004	−	0.964521i	$-0.585043\pi$
$607$	−13.0087	−0.528009	−0.264004	+	0.964521i	$0.585043\pi$
$608$	−5.53020	−0.224279
$609$	3.95668	0.160333
$610$	−5.54661	−0.224576
$611$	−3.88210	−0.157053
$612$	−1.00000	−0.0404226
$613$	−17.1424	−0.692375	−0.346188	−	0.938165i	$-0.612524\pi$
$613$	−17.1424	−0.692375	−0.346188	+	0.938165i	$0.612524\pi$
$614$	−15.8570	−0.639936
$615$	−8.74877	−0.352785
$616$	2.07291	0.0835198
$617$	4.35336	0.175260	0.0876298	−	0.996153i	$-0.472071\pi$
$617$	4.35336	0.175260	0.0876298	+	0.996153i	$0.472071\pi$
$618$	4.10334	0.165061
$619$	23.2469	0.934372	0.467186	−	0.884159i	$-0.345268\pi$
$619$	23.2469	0.934372	0.467186	+	0.884159i	$0.345268\pi$
$620$	−30.8478	−1.23888
$621$	−1.40276	−0.0562909
$622$	27.3982	1.09857
$623$	17.3812	0.696364
$624$	−1.50384	−0.0602017
$625$	33.3669	1.33468
$626$	−13.8140	−0.552118
$627$	2.75771	0.110132
$628$	−5.78310	−0.230771
$629$	6.18139	0.246468
$630$	−16.3861	−0.652839
$631$	−43.8505	−1.74566	−0.872831	−	0.488023i	$-0.837718\pi$
$631$	−43.8505	−1.74566	−0.872831	+	0.488023i	$0.837718\pi$
$632$	0.338386	0.0134603
$633$	−13.5622	−0.539050
$634$	0.452225	0.0179601
$635$	−29.7272	−1.17969
$636$	−2.76796	−0.109757
$637$	−15.4595	−0.612527
$638$	0.474643	0.0187913
$639$	−1.28420	−0.0508023
$640$	3.94189	0.155817
$641$	29.0630	1.14792	0.573959	−	0.818884i	$-0.305407\pi$
$641$	29.0630	1.14792	0.573959	+	0.818884i	$0.305407\pi$
$642$	9.44296	0.372684
$643$	−36.4625	−1.43794	−0.718970	−	0.695041i	$-0.755386\pi$
$643$	−36.4625	−1.43794	−0.718970	+	0.695041i	$0.755386\pi$
$644$	5.83118	0.229781
$645$	−29.6127	−1.16600
$646$	5.53020	0.217583
$647$	36.5252	1.43595	0.717977	−	0.696066i	$-0.245068\pi$
$647$	36.5252	1.43595	0.717977	+	0.696066i	$0.245068\pi$
$648$	−1.00000	−0.0392837
$649$	0.498663	0.0195742
$650$	15.8481	0.621615
$651$	−32.5306	−1.27497
$652$	21.2108	0.830681
$653$	4.06149	0.158938	0.0794691	−	0.996837i	$-0.474677\pi$
$653$	4.06149	0.158938	0.0794691	+	0.996837i	$0.474677\pi$
$654$	−4.29439	−0.167924
$655$	7.48187	0.292341
$656$	2.21944	0.0866545
$657$	−5.94314	−0.231864
$658$	10.7309	0.418336
$659$	2.96343	0.115439	0.0577195	−	0.998333i	$-0.481617\pi$
$659$	2.96343	0.115439	0.0577195	+	0.998333i	$0.481617\pi$
$660$	−1.96567	−0.0765138
$661$	−37.2128	−1.44741	−0.723704	−	0.690110i	$-0.757562\pi$
$661$	−37.2128	−1.44741	−0.723704	+	0.690110i	$0.757562\pi$
$662$	−2.42899	−0.0944052
$663$	1.50384	0.0584042
$664$	−11.1030	−0.430880
$665$	90.6186	3.51404
$666$	6.18139	0.239524
$667$	1.33519	0.0516988
$668$	11.6389	0.450323
$669$	−20.9059	−0.808269
$670$	23.2487	0.898176
$671$	−0.701667	−0.0270875
$672$	4.15692	0.160357
$673$	24.8134	0.956488	0.478244	−	0.878227i	$-0.341273\pi$
$673$	24.8134	0.956488	0.478244	+	0.878227i	$0.341273\pi$
$674$	18.2783	0.704055
$675$	10.5385	0.405626
$676$	−10.7385	−0.413018
$677$	27.3139	1.04976	0.524879	−	0.851177i	$-0.324111\pi$
$677$	27.3139	1.04976	0.524879	+	0.851177i	$0.324111\pi$
$678$	3.82370	0.146848
$679$	23.4176	0.898686
$680$	−3.94189	−0.151164
$681$	−22.7966	−0.873568
$682$	−3.90236	−0.149429
$683$	−5.73788	−0.219554	−0.109777	−	0.993956i	$-0.535014\pi$
$683$	−5.73788	−0.219554	−0.109777	+	0.993956i	$0.535014\pi$
$684$	5.53020	0.211453
$685$	−57.4346	−2.19446
$686$	13.6348	0.520580
$687$	−2.76690	−0.105564
$688$	7.51232	0.286405
$689$	4.16256	0.158581
$690$	−5.52953	−0.210506
$691$	19.7151	0.749996	0.374998	−	0.927026i	$-0.377643\pi$
$691$	19.7151	0.749996	0.374998	+	0.927026i	$0.377643\pi$
$692$	−16.7116	−0.635278
$693$	−2.07291	−0.0787432
$694$	22.7612	0.864005
$695$	−13.0625	−0.495489
$696$	0.951830	0.0360790
$697$	−2.21944	−0.0840672
$698$	−20.3696	−0.771000
$699$	−24.4763	−0.925780
$700$	−43.8076	−1.65577
$701$	−26.9130	−1.01649	−0.508245	−	0.861212i	$-0.669706\pi$
$701$	−26.9130	−1.01649	−0.508245	+	0.861212i	$0.669706\pi$
$702$	1.50384	0.0567587
$703$	−34.1844	−1.28929
$704$	0.498663	0.0187941
$705$	−10.1758	−0.383244
$706$	−11.2316	−0.422707
$707$	49.9597	1.87893
$708$	1.00000	0.0375823
$709$	20.3950	0.765950	0.382975	−	0.923759i	$-0.374900\pi$
$709$	20.3950	0.765950	0.382975	+	0.923759i	$0.374900\pi$
$710$	−5.06219	−0.189980
$711$	−0.338386	−0.0126905
$712$	4.18127	0.156700
$713$	−10.9775	−0.411111
$714$	−4.15692	−0.155569
$715$	2.95605	0.110550
$716$	−8.52772	−0.318696
$717$	−26.3324	−0.983403
$718$	11.0162	0.411121
$719$	44.6821	1.66636	0.833181	−	0.553000i	$-0.186517\pi$
$719$	44.6821	1.66636	0.833181	+	0.553000i	$0.186517\pi$
$720$	−3.94189	−0.146905
$721$	17.0573	0.635246
$722$	−11.5832	−0.431081
$723$	22.7724	0.846913
$724$	2.38605	0.0886770
$725$	−10.0308	−0.372535
$726$	10.7513	0.399019
$727$	−9.79608	−0.363317	−0.181658	−	0.983362i	$-0.558146\pi$
$727$	−9.79608	−0.363317	−0.181658	+	0.983362i	$0.558146\pi$
$728$	−6.25134	−0.231690
$729$	1.00000	0.0370370
$730$	−23.4272	−0.867079
$731$	−7.51232	−0.277853
$732$	−1.40709	−0.0520077
$733$	−21.7235	−0.802376	−0.401188	−	0.915996i	$-0.631403\pi$
$733$	−21.7235	−0.802376	−0.401188	+	0.915996i	$0.631403\pi$
$734$	−24.3809	−0.899915
$735$	−40.5227	−1.49470
$736$	1.40276	0.0517065
$737$	2.94105	0.108335
$738$	−2.21944	−0.0816986
$739$	−19.2383	−0.707694	−0.353847	−	0.935303i	$-0.615127\pi$
$739$	−19.2383	−0.707694	−0.353847	+	0.935303i	$0.615127\pi$
$740$	24.3663	0.895725
$741$	−8.31653	−0.305515
$742$	−11.5062	−0.422406
$743$	16.3722	0.600637	0.300318	−	0.953839i	$-0.402907\pi$
$743$	16.3722	0.600637	0.300318	+	0.953839i	$0.402907\pi$
$744$	−7.82563	−0.286902
$745$	−87.1259	−3.19205
$746$	−16.8690	−0.617619
$747$	11.1030	0.406237
$748$	−0.498663	−0.0182329
$749$	39.2537	1.43430
$750$	21.8320	0.797192
$751$	29.1864	1.06503	0.532513	−	0.846422i	$-0.321248\pi$
$751$	29.1864	1.06503	0.532513	+	0.846422i	$0.321248\pi$
$752$	2.58146	0.0941362
$753$	−18.9842	−0.691823
$754$	−1.43140	−0.0521284
$755$	−5.47335	−0.199196
$756$	−4.15692	−0.151186
$757$	−46.2138	−1.67967	−0.839834	−	0.542844i	$-0.817348\pi$
$757$	−46.2138	−1.67967	−0.839834	+	0.542844i	$0.817348\pi$
$758$	−24.1425	−0.876893
$759$	−0.699506	−0.0253905
$760$	21.7994	0.790749
$761$	0.704492	0.0255378	0.0127689	−	0.999918i	$-0.495935\pi$
$761$	0.704492	0.0255378	0.0127689	+	0.999918i	$0.495935\pi$
$762$	−7.54136	−0.273195
$763$	−17.8515	−0.646266
$764$	3.23671	0.117100
$765$	3.94189	0.142519
$766$	31.5959	1.14161
$767$	−1.50384	−0.0543004
$768$	1.00000	0.0360844
$769$	−52.2220	−1.88318	−0.941588	−	0.336768i	$-0.890666\pi$
$769$	−52.2220	−1.88318	−0.941588	+	0.336768i	$0.890666\pi$
$770$	−8.17116	−0.294468
$771$	−24.9891	−0.899959
$772$	−3.26683	−0.117576
$773$	−25.1829	−0.905764	−0.452882	−	0.891570i	$-0.649604\pi$
$773$	−25.1829	−0.905764	−0.452882	+	0.891570i	$0.649604\pi$
$774$	−7.51232	−0.270025
$775$	82.4702	2.96242
$776$	5.63340	0.202227
$777$	25.6956	0.921824
$778$	−30.5279	−1.09448
$779$	12.2739	0.439760
$780$	5.92795	0.212255
$781$	−0.640385	−0.0229148
$782$	−1.40276	−0.0501627
$783$	−0.951830	−0.0340156
$784$	10.2800	0.367144
$785$	22.7963	0.813636
$786$	1.89804	0.0677009
$787$	−7.60915	−0.271237	−0.135618	−	0.990761i	$-0.543302\pi$
$787$	−7.60915	−0.271237	−0.135618	+	0.990761i	$0.543302\pi$
$788$	−21.7155	−0.773581
$789$	−2.12162	−0.0755318
$790$	−1.33388	−0.0474573
$791$	15.8948	0.565156
$792$	−0.498663	−0.0177192
$793$	2.11604	0.0751428
$794$	−11.1233	−0.394750
$795$	10.9110	0.386973
$796$	4.55946	0.161606
$797$	42.9104	1.51996	0.759982	−	0.649944i	$-0.225208\pi$
$797$	42.9104	1.51996	0.759982	+	0.649944i	$0.225208\pi$
$798$	22.9886	0.813789
$799$	−2.58146	−0.0913255
$800$	−10.5385	−0.372591
$801$	−4.18127	−0.147738
$802$	−7.50926	−0.265161
$803$	−2.96363	−0.104584
$804$	5.89786	0.208002
$805$	−22.9859	−0.810145
$806$	11.7685	0.414527
$807$	−3.47081	−0.122178
$808$	12.0184	0.422807
$809$	−32.8067	−1.15342	−0.576711	−	0.816948i	$-0.695664\pi$
$809$	−32.8067	−1.15342	−0.576711	+	0.816948i	$0.695664\pi$
$810$	3.94189	0.138504
$811$	−10.6872	−0.375279	−0.187639	−	0.982238i	$-0.560084\pi$
$811$	−10.6872	−0.375279	−0.187639	+	0.982238i	$0.560084\pi$
$812$	3.95668	0.138852
$813$	30.2685	1.06156
$814$	3.08243	0.108039
$815$	−83.6107	−2.92876
$816$	−1.00000	−0.0350070
$817$	41.5447	1.45346
$818$	−11.2784	−0.394339
$819$	6.25134	0.218439
$820$	−8.74877	−0.305520
$821$	29.0217	1.01286	0.506431	−	0.862280i	$-0.330964\pi$
$821$	29.0217	1.01286	0.506431	+	0.862280i	$0.330964\pi$
$822$	−14.5703	−0.508199
$823$	−34.4951	−1.20242	−0.601212	−	0.799090i	$-0.705315\pi$
$823$	−34.4951	−1.20242	−0.601212	+	0.799090i	$0.705315\pi$
$824$	4.10334	0.142947
$825$	5.25515	0.182961
$826$	4.15692	0.144638
$827$	−8.00747	−0.278447	−0.139224	−	0.990261i	$-0.544461\pi$
$827$	−8.00747	−0.278447	−0.139224	+	0.990261i	$0.544461\pi$
$828$	−1.40276	−0.0487494
$829$	12.8577	0.446567	0.223283	−	0.974754i	$-0.428322\pi$
$829$	12.8577	0.446567	0.223283	+	0.974754i	$0.428322\pi$
$830$	43.7667	1.51917
$831$	−7.55172	−0.261966
$832$	−1.50384	−0.0521362
$833$	−10.2800	−0.356182
$834$	−3.31377	−0.114746
$835$	−45.8792	−1.58772
$836$	2.75771	0.0953774
$837$	7.82563	0.270493
$838$	−1.29791	−0.0448355
$839$	−19.6180	−0.677288	−0.338644	−	0.940914i	$-0.609968\pi$
$839$	−19.6180	−0.677288	−0.338644	+	0.940914i	$0.609968\pi$
$840$	−16.3861	−0.565375
$841$	−28.0940	−0.968759
$842$	20.1220	0.693451
$843$	15.1341	0.521245
$844$	−13.5622	−0.466831
$845$	42.3298	1.45619
$846$	−2.58146	−0.0887525
$847$	44.6925	1.53565
$848$	−2.76796	−0.0950522
$849$	−23.2461	−0.797802
$850$	10.5385	0.361466
$851$	8.67103	0.297239
$852$	−1.28420	−0.0439961
$853$	−56.0982	−1.92076	−0.960382	−	0.278687i	$-0.910101\pi$
$853$	−56.0982	−1.92076	−0.960382	+	0.278687i	$0.910101\pi$
$854$	−5.84919	−0.200155
$855$	−21.7994	−0.745525
$856$	9.44296	0.322754
$857$	−36.9979	−1.26382	−0.631911	−	0.775041i	$-0.717729\pi$
$857$	−36.9979	−1.26382	−0.631911	+	0.775041i	$0.717729\pi$
$858$	0.749908	0.0256014
$859$	−5.69995	−0.194480	−0.0972399	−	0.995261i	$-0.531001\pi$
$859$	−5.69995	−0.194480	−0.0972399	+	0.995261i	$0.531001\pi$
$860$	−29.6127	−1.00979
$861$	−9.22604	−0.314422
$862$	3.84667	0.131018
$863$	−27.5457	−0.937668	−0.468834	−	0.883286i	$-0.655326\pi$
$863$	−27.5457	−0.937668	−0.468834	+	0.883286i	$0.655326\pi$
$864$	−1.00000	−0.0340207
$865$	65.8750	2.23982
$866$	35.2352	1.19734
$867$	1.00000	0.0339618
$868$	−32.5306	−1.10416
$869$	−0.168741	−0.00572414
$870$	−3.75200	−0.127205
$871$	−8.86943	−0.300529
$872$	−4.29439	−0.145426
$873$	−5.63340	−0.190662
$874$	7.75757	0.262404
$875$	90.7540	3.06805
$876$	−5.94314	−0.200800
$877$	−45.2181	−1.52691	−0.763453	−	0.645863i	$-0.776498\pi$
$877$	−45.2181	−1.52691	−0.763453	+	0.645863i	$0.776498\pi$
$878$	−20.4457	−0.690010
$879$	−1.25275	−0.0422543
$880$	−1.96567	−0.0662629
$881$	6.59805	0.222294	0.111147	−	0.993804i	$-0.464548\pi$
$881$	6.59805	0.222294	0.111147	+	0.993804i	$0.464548\pi$
$882$	−10.2800	−0.346146
$883$	−11.5376	−0.388271	−0.194136	−	0.980975i	$-0.562190\pi$
$883$	−11.5376	−0.388271	−0.194136	+	0.980975i	$0.562190\pi$
$884$	1.50384	0.0505795
$885$	−3.94189	−0.132505
$886$	−28.8660	−0.969773
$887$	10.1090	0.339428	0.169714	−	0.985493i	$-0.445716\pi$
$887$	10.1090	0.339428	0.169714	+	0.985493i	$0.445716\pi$
$888$	6.18139	0.207434
$889$	−31.3489	−1.05141
$890$	−16.4821	−0.552481
$891$	0.498663	0.0167058
$892$	−20.9059	−0.699981
$893$	14.2760	0.477728
$894$	−22.1026	−0.739221
$895$	33.6153	1.12364
$896$	4.15692	0.138873
$897$	2.10953	0.0704351
$898$	20.9032	0.697549
$899$	−7.44867	−0.248427
$900$	10.5385	0.351282
$901$	2.76796	0.0922142
$902$	−1.10675	−0.0368508
$903$	−31.2281	−1.03921
$904$	3.82370	0.127174
$905$	−9.40555	−0.312651
$906$	−1.38851	−0.0461301
$907$	−0.586820	−0.0194850	−0.00974252	−	0.999953i	$-0.503101\pi$
$907$	−0.586820	−0.0194850	−0.00974252	+	0.999953i	$0.503101\pi$
$908$	−22.7966	−0.756532
$909$	−12.0184	−0.398626
$910$	24.6421	0.816876
$911$	29.8518	0.989034	0.494517	−	0.869168i	$-0.335345\pi$
$911$	29.8518	0.989034	0.494517	+	0.869168i	$0.335345\pi$
$912$	5.53020	0.183123
$913$	5.53666	0.183237
$914$	−2.29892	−0.0760415
$915$	5.54661	0.183365
$916$	−2.76690	−0.0914211
$917$	7.89002	0.260551
$918$	1.00000	0.0330049
$919$	50.2728	1.65835	0.829173	−	0.558992i	$-0.188812\pi$
$919$	50.2728	1.65835	0.829173	+	0.558992i	$0.188812\pi$
$920$	−5.52953	−0.182303
$921$	15.8570	0.522505
$922$	−0.701928	−0.0231168
$923$	1.93123	0.0635673
$924$	−2.07291	−0.0681936
$925$	−65.1424	−2.14187
$926$	13.7307	0.451220
$927$	−4.10334	−0.134771
$928$	0.951830	0.0312453
$929$	−19.8873	−0.652481	−0.326240	−	0.945287i	$-0.605782\pi$
$929$	−19.8873	−0.652481	−0.326240	+	0.945287i	$0.605782\pi$
$930$	30.8478	1.01154
$931$	56.8506	1.86320
$932$	−24.4763	−0.801749
$933$	−27.3982	−0.896978
$934$	−31.5561	−1.03255
$935$	1.96567	0.0642844
$936$	1.50384	0.0491544
$937$	−9.75972	−0.318836	−0.159418	−	0.987211i	$-0.550962\pi$
$937$	−9.75972	−0.318836	−0.159418	+	0.987211i	$0.550962\pi$
$938$	24.5170	0.800508
$939$	13.8140	0.450803
$940$	−10.1758	−0.331899
$941$	44.8098	1.46076	0.730380	−	0.683041i	$-0.239343\pi$
$941$	44.8098	1.46076	0.730380	+	0.683041i	$0.239343\pi$
$942$	5.78310	0.188424
$943$	−3.11335	−0.101384
$944$	1.00000	0.0325472
$945$	16.3861	0.533041
$946$	−3.74612	−0.121797
$947$	6.54741	0.212762	0.106381	−	0.994325i	$-0.466074\pi$
$947$	6.54741	0.212762	0.106381	+	0.994325i	$0.466074\pi$
$948$	−0.338386	−0.0109903
$949$	8.93751	0.290124
$950$	−58.2799	−1.89085
$951$	−0.452225	−0.0146644
$952$	−4.15692	−0.134727
$953$	47.0221	1.52320	0.761598	−	0.648050i	$-0.224415\pi$
$953$	47.0221	1.52320	0.761598	+	0.648050i	$0.224415\pi$
$954$	2.76796	0.0896161
$955$	−12.7587	−0.412863
$956$	−26.3324	−0.851652
$957$	−0.474643	−0.0153430
$958$	−16.7993	−0.542760
$959$	−60.5678	−1.95584
$960$	−3.94189	−0.127224
$961$	30.2406	0.975502
$962$	−9.29581	−0.299709
$963$	−9.44296	−0.304295
$964$	22.7724	0.733448
$965$	12.8775	0.414541
$966$	−5.83118	−0.187615
$967$	31.8194	1.02324	0.511622	−	0.859211i	$-0.329045\pi$
$967$	31.8194	1.02324	0.511622	+	0.859211i	$0.329045\pi$
$968$	10.7513	0.345561
$969$	−5.53020	−0.177656
$970$	−22.2062	−0.712999
$971$	−8.89877	−0.285575	−0.142788	−	0.989753i	$-0.545607\pi$
$971$	−8.89877	−0.285575	−0.142788	+	0.989753i	$0.545607\pi$
$972$	1.00000	0.0320750
$973$	−13.7751	−0.441609
$974$	−11.7486	−0.376450
$975$	−15.8481	−0.507546
$976$	−1.40709	−0.0450400
$977$	−20.2006	−0.646273	−0.323137	−	0.946352i	$-0.604737\pi$
$977$	−20.2006	−0.646273	−0.323137	+	0.946352i	$0.604737\pi$
$978$	−21.2108	−0.678248
$979$	−2.08505	−0.0666383
$980$	−40.5227	−1.29445
$981$	4.29439	0.137109
$982$	27.1704	0.867041
$983$	24.2799	0.774408	0.387204	−	0.921994i	$-0.373441\pi$
$983$	24.2799	0.774408	0.387204	+	0.921994i	$0.373441\pi$
$984$	−2.21944	−0.0707531
$985$	85.5998	2.72744
$986$	−0.951830	−0.0303124
$987$	−10.7309	−0.341570
$988$	−8.31653	−0.264584
$989$	−10.5380	−0.335089
$990$	1.96567	0.0624732
$991$	−23.6797	−0.752212	−0.376106	−	0.926577i	$-0.622737\pi$
$991$	−23.6797	−0.752212	−0.376106	+	0.926577i	$0.622737\pi$
$992$	−7.82563	−0.248464
$993$	2.42899	0.0770815
$994$	−5.33834	−0.169322
$995$	−17.9729	−0.569778
$996$	11.1030	0.351812
$997$	−17.1151	−0.542040	−0.271020	−	0.962574i	$-0.587361\pi$
$997$	−17.1151	−0.542040	−0.271020	+	0.962574i	$0.587361\pi$
$998$	−13.5465	−0.428808
$999$	−6.18139	−0.195571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.y.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.y.1.2	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.94189 q^{5} -1.00000 q^{6} -4.15692 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.94189 q^{5} -1.00000 q^{6} -4.15692 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.94189 q^{10} +0.498663 q^{11} +1.00000 q^{12} -1.50384 q^{13} +4.15692 q^{14} -3.94189 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +5.53020 q^{19} -3.94189 q^{20} -4.15692 q^{21} -0.498663 q^{22} -1.40276 q^{23} -1.00000 q^{24} +10.5385 q^{25} +1.50384 q^{26} +1.00000 q^{27} -4.15692 q^{28} -0.951830 q^{29} +3.94189 q^{30} +7.82563 q^{31} -1.00000 q^{32} +0.498663 q^{33} +1.00000 q^{34} +16.3861 q^{35} +1.00000 q^{36} -6.18139 q^{37} -5.53020 q^{38} -1.50384 q^{39} +3.94189 q^{40} +2.21944 q^{41} +4.15692 q^{42} +7.51232 q^{43} +0.498663 q^{44} -3.94189 q^{45} +1.40276 q^{46} +2.58146 q^{47} +1.00000 q^{48} +10.2800 q^{49} -10.5385 q^{50} -1.00000 q^{51} -1.50384 q^{52} -2.76796 q^{53} -1.00000 q^{54} -1.96567 q^{55} +4.15692 q^{56} +5.53020 q^{57} +0.951830 q^{58} +1.00000 q^{59} -3.94189 q^{60} -1.40709 q^{61} -7.82563 q^{62} -4.15692 q^{63} +1.00000 q^{64} +5.92795 q^{65} -0.498663 q^{66} +5.89786 q^{67} -1.00000 q^{68} -1.40276 q^{69} -16.3861 q^{70} -1.28420 q^{71} -1.00000 q^{72} -5.94314 q^{73} +6.18139 q^{74} +10.5385 q^{75} +5.53020 q^{76} -2.07291 q^{77} +1.50384 q^{78} -0.338386 q^{79} -3.94189 q^{80} +1.00000 q^{81} -2.21944 q^{82} +11.1030 q^{83} -4.15692 q^{84} +3.94189 q^{85} -7.51232 q^{86} -0.951830 q^{87} -0.498663 q^{88} -4.18127 q^{89} +3.94189 q^{90} +6.25134 q^{91} -1.40276 q^{92} +7.82563 q^{93} -2.58146 q^{94} -21.7994 q^{95} -1.00000 q^{96} -5.63340 q^{97} -10.2800 q^{98} +0.498663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * q^99

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