LMFDB - Embedded newform 6018.2.a.n.1.4

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:	$4$
Coefficient field:	4.4.2525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 5 $ x^4 - 2x^3 - 4x^2 + 5*x + 5
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			1.4
Root			$-1.46673$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.99126 q^{5} -1.00000 q^{6} +0.711544 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.99126 q^{5} -1.00000 q^{6} +0.711544 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.99126 q^{10} -1.46673 q^{11} -1.00000 q^{12} -5.85410 q^{13} +0.711544 q^{14} -2.99126 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -5.93346 q^{19} +2.99126 q^{20} -0.711544 q^{21} -1.46673 q^{22} -7.43642 q^{23} -1.00000 q^{24} +3.94761 q^{25} -5.85410 q^{26} -1.00000 q^{27} +0.711544 q^{28} +2.76059 q^{29} -2.99126 q^{30} +4.05779 q^{31} +1.00000 q^{32} +1.46673 q^{33} +1.00000 q^{34} +2.12841 q^{35} +1.00000 q^{36} -8.03238 q^{37} -5.93346 q^{38} +5.85410 q^{39} +2.99126 q^{40} -5.32083 q^{41} -0.711544 q^{42} +4.83121 q^{43} -1.46673 q^{44} +2.99126 q^{45} -7.43642 q^{46} -3.35907 q^{47} -1.00000 q^{48} -6.49371 q^{49} +3.94761 q^{50} -1.00000 q^{51} -5.85410 q^{52} -13.1251 q^{53} -1.00000 q^{54} -4.38737 q^{55} +0.711544 q^{56} +5.93346 q^{57} +2.76059 q^{58} -1.00000 q^{59} -2.99126 q^{60} -11.0133 q^{61} +4.05779 q^{62} +0.711544 q^{63} +1.00000 q^{64} -17.5111 q^{65} +1.46673 q^{66} +5.57307 q^{67} +1.00000 q^{68} +7.43642 q^{69} +2.12841 q^{70} -5.52068 q^{71} +1.00000 q^{72} -0.395297 q^{73} -8.03238 q^{74} -3.94761 q^{75} -5.93346 q^{76} -1.04364 q^{77} +5.85410 q^{78} -0.307503 q^{79} +2.99126 q^{80} +1.00000 q^{81} -5.32083 q^{82} +16.5918 q^{83} -0.711544 q^{84} +2.99126 q^{85} +4.83121 q^{86} -2.76059 q^{87} -1.46673 q^{88} -13.5507 q^{89} +2.99126 q^{90} -4.16545 q^{91} -7.43642 q^{92} -4.05779 q^{93} -3.35907 q^{94} -17.7485 q^{95} -1.00000 q^{96} +7.09017 q^{97} -6.49371 q^{98} -1.46673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} - 10 q^{13} + q^{14} + 3 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 8 q^{19} - 3 q^{20} - q^{21} + 2 q^{22} - 10 q^{23} - 4 q^{24} + 5 q^{25} - 10 q^{26} - 4 q^{27} + q^{28} - 5 q^{29} + 3 q^{30} + 17 q^{31} + 4 q^{32} - 2 q^{33} + 4 q^{34} - 8 q^{35} + 4 q^{36} - 9 q^{37} - 8 q^{38} + 10 q^{39} - 3 q^{40} - q^{42} - 14 q^{43} + 2 q^{44} - 3 q^{45} - 10 q^{46} + 2 q^{47} - 4 q^{48} - 5 q^{49} + 5 q^{50} - 4 q^{51} - 10 q^{52} - 11 q^{53} - 4 q^{54} - 12 q^{55} + q^{56} + 8 q^{57} - 5 q^{58} - 4 q^{59} + 3 q^{60} - 28 q^{61} + 17 q^{62} + q^{63} + 4 q^{64} - 2 q^{66} - q^{67} + 4 q^{68} + 10 q^{69} - 8 q^{70} + 12 q^{71} + 4 q^{72} + 10 q^{73} - 9 q^{74} - 5 q^{75} - 8 q^{76} + 10 q^{78} + 4 q^{79} - 3 q^{80} + 4 q^{81} + 17 q^{83} - q^{84} - 3 q^{85} - 14 q^{86} + 5 q^{87} + 2 q^{88} - 13 q^{89} - 3 q^{90} - 25 q^{91} - 10 q^{92} - 17 q^{93} + 2 q^{94} - 15 q^{95} - 4 q^{96} + 6 q^{97} - 5 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 - 10 * q^13 + q^14 + 3 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 8 * q^19 - 3 * q^20 - q^21 + 2 * q^22 - 10 * q^23 - 4 * q^24 + 5 * q^25 - 10 * q^26 - 4 * q^27 + q^28 - 5 * q^29 + 3 * q^30 + 17 * q^31 + 4 * q^32 - 2 * q^33 + 4 * q^34 - 8 * q^35 + 4 * q^36 - 9 * q^37 - 8 * q^38 + 10 * q^39 - 3 * q^40 - q^42 - 14 * q^43 + 2 * q^44 - 3 * q^45 - 10 * q^46 + 2 * q^47 - 4 * q^48 - 5 * q^49 + 5 * q^50 - 4 * q^51 - 10 * q^52 - 11 * q^53 - 4 * q^54 - 12 * q^55 + q^56 + 8 * q^57 - 5 * q^58 - 4 * q^59 + 3 * q^60 - 28 * q^61 + 17 * q^62 + q^63 + 4 * q^64 - 2 * q^66 - q^67 + 4 * q^68 + 10 * q^69 - 8 * q^70 + 12 * q^71 + 4 * q^72 + 10 * q^73 - 9 * q^74 - 5 * q^75 - 8 * q^76 + 10 * q^78 + 4 * q^79 - 3 * q^80 + 4 * q^81 + 17 * q^83 - q^84 - 3 * q^85 - 14 * q^86 + 5 * q^87 + 2 * q^88 - 13 * q^89 - 3 * q^90 - 25 * q^91 - 10 * q^92 - 17 * q^93 + 2 * q^94 - 15 * q^95 - 4 * q^96 + 6 * q^97 - 5 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.99126	1.33773	0.668865	−	0.743384i	$-0.266780\pi$
$5$	2.99126	1.33773	0.668865	+	0.743384i	$0.266780\pi$
$6$	−1.00000	−0.408248
$7$	0.711544	0.268938	0.134469	−	0.990918i	$-0.457067\pi$
$7$	0.711544	0.268938	0.134469	+	0.990918i	$0.457067\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.99126	0.945918
$11$	−1.46673	−0.442236	−0.221118	−	0.975247i	$-0.570971\pi$
$11$	−1.46673	−0.442236	−0.221118	+	0.975247i	$0.570971\pi$
$12$	−1.00000	−0.288675
$13$	−5.85410	−1.62364	−0.811818	−	0.583911i	$-0.801522\pi$
$13$	−5.85410	−1.62364	−0.811818	+	0.583911i	$0.801522\pi$
$14$	0.711544	0.190168
$15$	−2.99126	−0.772339
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−5.93346	−1.36123	−0.680615	−	0.732641i	$-0.738287\pi$
$19$	−5.93346	−1.36123	−0.680615	+	0.732641i	$0.738287\pi$
$20$	2.99126	0.668865
$21$	−0.711544	−0.155272
$22$	−1.46673	−0.312708
$23$	−7.43642	−1.55060	−0.775300	−	0.631593i	$-0.782401\pi$
$23$	−7.43642	−1.55060	−0.775300	+	0.631593i	$0.782401\pi$
$24$	−1.00000	−0.204124
$25$	3.94761	0.789522
$26$	−5.85410	−1.14808
$27$	−1.00000	−0.192450
$28$	0.711544	0.134469
$29$	2.76059	0.512629	0.256315	−	0.966593i	$-0.417492\pi$
$29$	2.76059	0.512629	0.256315	+	0.966593i	$0.417492\pi$
$30$	−2.99126	−0.546126
$31$	4.05779	0.728801	0.364401	−	0.931242i	$-0.381274\pi$
$31$	4.05779	0.728801	0.364401	+	0.931242i	$0.381274\pi$
$32$	1.00000	0.176777
$33$	1.46673	0.255325
$34$	1.00000	0.171499
$35$	2.12841	0.359767
$36$	1.00000	0.166667
$37$	−8.03238	−1.32051	−0.660257	−	0.751039i	$-0.729553\pi$
$37$	−8.03238	−1.32051	−0.660257	+	0.751039i	$0.729553\pi$
$38$	−5.93346	−0.962535
$39$	5.85410	0.937407
$40$	2.99126	0.472959
$41$	−5.32083	−0.830975	−0.415487	−	0.909599i	$-0.636389\pi$
$41$	−5.32083	−0.830975	−0.415487	+	0.909599i	$0.636389\pi$
$42$	−0.711544	−0.109794
$43$	4.83121	0.736753	0.368376	−	0.929677i	$-0.379914\pi$
$43$	4.83121	0.736753	0.368376	+	0.929677i	$0.379914\pi$
$44$	−1.46673	−0.221118
$45$	2.99126	0.445910
$46$	−7.43642	−1.09644
$47$	−3.35907	−0.489971	−0.244986	−	0.969527i	$-0.578783\pi$
$47$	−3.35907	−0.489971	−0.244986	+	0.969527i	$0.578783\pi$
$48$	−1.00000	−0.144338
$49$	−6.49371	−0.927672
$50$	3.94761	0.558277
$51$	−1.00000	−0.140028
$52$	−5.85410	−0.811818
$53$	−13.1251	−1.80287	−0.901434	−	0.432918i	$-0.857484\pi$
$53$	−13.1251	−1.80287	−0.901434	+	0.432918i	$0.857484\pi$
$54$	−1.00000	−0.136083
$55$	−4.38737	−0.591593
$56$	0.711544	0.0950841
$57$	5.93346	0.785906
$58$	2.76059	0.362483
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−2.99126	−0.386169
$61$	−11.0133	−1.41011	−0.705056	−	0.709151i	$-0.749078\pi$
$61$	−11.0133	−1.41011	−0.705056	+	0.709151i	$0.749078\pi$
$62$	4.05779	0.515340
$63$	0.711544	0.0896461
$64$	1.00000	0.125000
$65$	−17.5111	−2.17199
$66$	1.46673	0.180542
$67$	5.57307	0.680858	0.340429	−	0.940270i	$-0.389428\pi$
$67$	5.57307	0.680858	0.340429	+	0.940270i	$0.389428\pi$
$68$	1.00000	0.121268
$69$	7.43642	0.895240
$70$	2.12841	0.254394
$71$	−5.52068	−0.655184	−0.327592	−	0.944819i	$-0.606237\pi$
$71$	−5.52068	−0.655184	−0.327592	+	0.944819i	$0.606237\pi$
$72$	1.00000	0.117851
$73$	−0.395297	−0.0462660	−0.0231330	−	0.999732i	$-0.507364\pi$
$73$	−0.395297	−0.0462660	−0.0231330	+	0.999732i	$0.507364\pi$
$74$	−8.03238	−0.933745
$75$	−3.94761	−0.455831
$76$	−5.93346	−0.680615
$77$	−1.04364	−0.118934
$78$	5.85410	0.662847
$79$	−0.307503	−0.0345968	−0.0172984	−	0.999850i	$-0.505507\pi$
$79$	−0.307503	−0.0345968	−0.0172984	+	0.999850i	$0.505507\pi$
$80$	2.99126	0.334433
$81$	1.00000	0.111111
$82$	−5.32083	−0.587588
$83$	16.5918	1.82119	0.910593	−	0.413303i	$-0.135625\pi$
$83$	16.5918	1.82119	0.910593	+	0.413303i	$0.135625\pi$
$84$	−0.711544	−0.0776358
$85$	2.99126	0.324447
$86$	4.83121	0.520963
$87$	−2.76059	−0.295967
$88$	−1.46673	−0.156354
$89$	−13.5507	−1.43637	−0.718185	−	0.695853i	$-0.755027\pi$
$89$	−13.5507	−1.43637	−0.718185	+	0.695853i	$0.755027\pi$
$90$	2.99126	0.315306
$91$	−4.16545	−0.436658
$92$	−7.43642	−0.775300
$93$	−4.05779	−0.420773
$94$	−3.35907	−0.346462
$95$	−17.7485	−1.82096
$96$	−1.00000	−0.102062
$97$	7.09017	0.719898	0.359949	−	0.932972i	$-0.382794\pi$
$97$	7.09017	0.719898	0.359949	+	0.932972i	$0.382794\pi$
$98$	−6.49371	−0.655963
$99$	−1.46673	−0.147412
$100$	3.94761	0.394761
$101$	8.11714	0.807686	0.403843	−	0.914828i	$-0.367674\pi$
$101$	8.11714	0.807686	0.403843	+	0.914828i	$0.367674\pi$
$102$	−1.00000	−0.0990148
$103$	0.172872	0.0170335	0.00851677	−	0.999964i	$-0.497289\pi$
$103$	0.172872	0.0170335	0.00851677	+	0.999964i	$0.497289\pi$
$104$	−5.85410	−0.574042
$105$	−2.12841	−0.207712
$106$	−13.1251	−1.27482
$107$	1.03778	0.100326	0.0501631	−	0.998741i	$-0.484026\pi$
$107$	1.03778	0.100326	0.0501631	+	0.998741i	$0.484026\pi$
$108$	−1.00000	−0.0962250
$109$	12.4626	1.19370	0.596849	−	0.802354i	$-0.296419\pi$
$109$	12.4626	1.19370	0.596849	+	0.802354i	$0.296419\pi$
$110$	−4.38737	−0.418319
$111$	8.03238	0.762400
$112$	0.711544	0.0672346
$113$	−7.38403	−0.694631	−0.347316	−	0.937748i	$-0.612907\pi$
$113$	−7.38403	−0.694631	−0.347316	+	0.937748i	$0.612907\pi$
$114$	5.93346	0.555720
$115$	−22.2442	−2.07429
$116$	2.76059	0.256315
$117$	−5.85410	−0.541212
$118$	−1.00000	−0.0920575
$119$	0.711544	0.0652271
$120$	−2.99126	−0.273063
$121$	−8.84870	−0.804427
$122$	−11.0133	−0.997100
$123$	5.32083	0.479763
$124$	4.05779	0.364401
$125$	−3.14796	−0.281562
$126$	0.711544	0.0633894
$127$	7.59721	0.674143	0.337072	−	0.941479i	$-0.390564\pi$
$127$	7.59721	0.674143	0.337072	+	0.941479i	$0.390564\pi$
$128$	1.00000	0.0883883
$129$	−4.83121	−0.425364
$130$	−17.5111	−1.53583
$131$	−4.07144	−0.355723	−0.177861	−	0.984056i	$-0.556918\pi$
$131$	−4.07144	−0.355723	−0.177861	+	0.984056i	$0.556918\pi$
$132$	1.46673	0.127663
$133$	−4.22192	−0.366087
$134$	5.57307	0.481440
$135$	−2.99126	−0.257446
$136$	1.00000	0.0857493
$137$	−2.16879	−0.185292	−0.0926461	−	0.995699i	$-0.529533\pi$
$137$	−2.16879	−0.185292	−0.0926461	+	0.995699i	$0.529533\pi$
$138$	7.43642	0.633030
$139$	5.55402	0.471086	0.235543	−	0.971864i	$-0.424313\pi$
$139$	5.55402	0.471086	0.235543	+	0.971864i	$0.424313\pi$
$140$	2.12841	0.179883
$141$	3.35907	0.282885
$142$	−5.52068	−0.463285
$143$	8.58640	0.718031
$144$	1.00000	0.0833333
$145$	8.25764	0.685759
$146$	−0.395297	−0.0327150
$147$	6.49371	0.535592
$148$	−8.03238	−0.660257
$149$	9.25636	0.758311	0.379155	−	0.925333i	$-0.376215\pi$
$149$	9.25636	0.758311	0.379155	+	0.925333i	$0.376215\pi$
$150$	−3.94761	−0.322321
$151$	21.8016	1.77419	0.887096	−	0.461585i	$-0.152719\pi$
$151$	21.8016	1.77419	0.887096	+	0.461585i	$0.152719\pi$
$152$	−5.93346	−0.481267
$153$	1.00000	0.0808452
$154$	−1.04364	−0.0840992
$155$	12.1379	0.974939
$156$	5.85410	0.468703
$157$	−3.44547	−0.274979	−0.137489	−	0.990503i	$-0.543903\pi$
$157$	−3.44547	−0.274979	−0.137489	+	0.990503i	$0.543903\pi$
$158$	−0.307503	−0.0244636
$159$	13.1251	1.04089
$160$	2.99126	0.236480
$161$	−5.29134	−0.417016
$162$	1.00000	0.0785674
$163$	0.776757	0.0608403	0.0304202	−	0.999537i	$-0.490315\pi$
$163$	0.776757	0.0608403	0.0304202	+	0.999537i	$0.490315\pi$
$164$	−5.32083	−0.415487
$165$	4.38737	0.341556
$166$	16.5918	1.28777
$167$	12.8798	0.996665	0.498333	−	0.866986i	$-0.333946\pi$
$167$	12.8798	0.996665	0.498333	+	0.866986i	$0.333946\pi$
$168$	−0.711544	−0.0548968
$169$	21.2705	1.63619
$170$	2.99126	0.229419
$171$	−5.93346	−0.453743
$172$	4.83121	0.368376
$173$	−2.73230	−0.207733	−0.103866	−	0.994591i	$-0.533121\pi$
$173$	−2.73230	−0.207733	−0.103866	+	0.994591i	$0.533121\pi$
$174$	−2.76059	−0.209280
$175$	2.80890	0.212333
$176$	−1.46673	−0.110559
$177$	1.00000	0.0751646
$178$	−13.5507	−1.01567
$179$	9.00459	0.673034	0.336517	−	0.941677i	$-0.390751\pi$
$179$	9.00459	0.673034	0.336517	+	0.941677i	$0.390751\pi$
$180$	2.99126	0.222955
$181$	14.4966	1.07752	0.538761	−	0.842458i	$-0.318892\pi$
$181$	14.4966	1.07752	0.538761	+	0.842458i	$0.318892\pi$
$182$	−4.16545	−0.308764
$183$	11.0133	0.814129
$184$	−7.43642	−0.548220
$185$	−24.0269	−1.76649
$186$	−4.05779	−0.297532
$187$	−1.46673	−0.107258
$188$	−3.35907	−0.244986
$189$	−0.711544	−0.0517572
$190$	−17.7485	−1.28761
$191$	−6.56867	−0.475293	−0.237646	−	0.971352i	$-0.576376\pi$
$191$	−6.56867	−0.475293	−0.237646	+	0.971352i	$0.576376\pi$
$192$	−1.00000	−0.0721688
$193$	−19.5373	−1.40633	−0.703165	−	0.711027i	$-0.748230\pi$
$193$	−19.5373	−1.40633	−0.703165	+	0.711027i	$0.748230\pi$
$194$	7.09017	0.509045
$195$	17.5111	1.25400
$196$	−6.49371	−0.463836
$197$	−15.2494	−1.08647	−0.543237	−	0.839579i	$-0.682802\pi$
$197$	−15.2494	−1.08647	−0.543237	+	0.839579i	$0.682802\pi$
$198$	−1.46673	−0.104236
$199$	3.28512	0.232876	0.116438	−	0.993198i	$-0.462852\pi$
$199$	3.28512	0.232876	0.116438	+	0.993198i	$0.462852\pi$
$200$	3.94761	0.279138
$201$	−5.57307	−0.393094
$202$	8.11714	0.571120
$203$	1.96428	0.137866
$204$	−1.00000	−0.0700140
$205$	−15.9160	−1.11162
$206$	0.172872	0.0120445
$207$	−7.43642	−0.516867
$208$	−5.85410	−0.405909
$209$	8.70280	0.601985
$210$	−2.12841	−0.146874
$211$	−4.77423	−0.328672	−0.164336	−	0.986404i	$-0.552548\pi$
$211$	−4.77423	−0.328672	−0.164336	+	0.986404i	$0.552548\pi$
$212$	−13.1251	−0.901434
$213$	5.52068	0.378271
$214$	1.03778	0.0709413
$215$	14.4514	0.985576
$216$	−1.00000	−0.0680414
$217$	2.88730	0.196003
$218$	12.4626	0.844072
$219$	0.395297	0.0267117
$220$	−4.38737	−0.295796
$221$	−5.85410	−0.393790
$222$	8.03238	0.539098
$223$	28.5356	1.91088	0.955441	−	0.295181i	$-0.0953798\pi$
$223$	28.5356	1.91088	0.955441	+	0.295181i	$0.0953798\pi$
$224$	0.711544	0.0475420
$225$	3.94761	0.263174
$226$	−7.38403	−0.491178
$227$	20.1528	1.33759	0.668794	−	0.743448i	$-0.266811\pi$
$227$	20.1528	1.33759	0.668794	+	0.743448i	$0.266811\pi$
$228$	5.93346	0.392953
$229$	−8.61803	−0.569496	−0.284748	−	0.958602i	$-0.591910\pi$
$229$	−8.61803	−0.569496	−0.284748	+	0.958602i	$0.591910\pi$
$230$	−22.2442	−1.46674
$231$	1.04364	0.0686667
$232$	2.76059	0.181242
$233$	28.7164	1.88127	0.940636	−	0.339417i	$-0.110230\pi$
$233$	28.7164	1.88127	0.940636	+	0.339417i	$0.110230\pi$
$234$	−5.85410	−0.382695
$235$	−10.0478	−0.655449
$236$	−1.00000	−0.0650945
$237$	0.307503	0.0199745
$238$	0.711544	0.0461225
$239$	5.75807	0.372459	0.186229	−	0.982506i	$-0.440373\pi$
$239$	5.75807	0.372459	0.186229	+	0.982506i	$0.440373\pi$
$240$	−2.99126	−0.193085
$241$	−0.110998	−0.00715002	−0.00357501	−	0.999994i	$-0.501138\pi$
$241$	−0.110998	−0.00715002	−0.00357501	+	0.999994i	$0.501138\pi$
$242$	−8.84870	−0.568816
$243$	−1.00000	−0.0641500
$244$	−11.0133	−0.705056
$245$	−19.4243	−1.24098
$246$	5.32083	0.339244
$247$	34.7351	2.21014
$248$	4.05779	0.257670
$249$	−16.5918	−1.05146
$250$	−3.14796	−0.199095
$251$	6.17205	0.389577	0.194788	−	0.980845i	$-0.437598\pi$
$251$	6.17205	0.389577	0.194788	+	0.980845i	$0.437598\pi$
$252$	0.711544	0.0448231
$253$	10.9072	0.685732
$254$	7.59721	0.476691
$255$	−2.99126	−0.187320
$256$	1.00000	0.0625000
$257$	−6.47598	−0.403961	−0.201980	−	0.979390i	$-0.564738\pi$
$257$	−6.47598	−0.403961	−0.201980	+	0.979390i	$0.564738\pi$
$258$	−4.83121	−0.300778
$259$	−5.71539	−0.355137
$260$	−17.5111	−1.08599
$261$	2.76059	0.170876
$262$	−4.07144	−0.251534
$263$	−20.4978	−1.26395	−0.631974	−	0.774990i	$-0.717755\pi$
$263$	−20.4978	−1.26395	−0.631974	+	0.774990i	$0.717755\pi$
$264$	1.46673	0.0902711
$265$	−39.2604	−2.41175
$266$	−4.22192	−0.258863
$267$	13.5507	0.829288
$268$	5.57307	0.340429
$269$	−12.4313	−0.757947	−0.378973	−	0.925408i	$-0.623723\pi$
$269$	−12.4313	−0.757947	−0.378973	+	0.925408i	$0.623723\pi$
$270$	−2.99126	−0.182042
$271$	−17.9712	−1.09168	−0.545838	−	0.837891i	$-0.683788\pi$
$271$	−17.9712	−1.09168	−0.545838	+	0.837891i	$0.683788\pi$
$272$	1.00000	0.0606339
$273$	4.16545	0.252105
$274$	−2.16879	−0.131021
$275$	−5.79009	−0.349155
$276$	7.43642	0.447620
$277$	−20.6142	−1.23859	−0.619293	−	0.785160i	$-0.712581\pi$
$277$	−20.6142	−1.23859	−0.619293	+	0.785160i	$0.712581\pi$
$278$	5.55402	0.333108
$279$	4.05779	0.242934
$280$	2.12841	0.127197
$281$	−15.3216	−0.914009	−0.457004	−	0.889465i	$-0.651078\pi$
$281$	−15.3216	−0.914009	−0.457004	+	0.889465i	$0.651078\pi$
$282$	3.35907	0.200030
$283$	−29.2003	−1.73578	−0.867888	−	0.496760i	$-0.834523\pi$
$283$	−29.2003	−1.73578	−0.867888	+	0.496760i	$0.834523\pi$
$284$	−5.52068	−0.327592
$285$	17.7485	1.05133
$286$	8.58640	0.507724
$287$	−3.78601	−0.223481
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	8.25764	0.484905
$291$	−7.09017	−0.415633
$292$	−0.395297	−0.0231330
$293$	−8.53075	−0.498371	−0.249186	−	0.968456i	$-0.580163\pi$
$293$	−8.53075	−0.498371	−0.249186	+	0.968456i	$0.580163\pi$
$294$	6.49371	0.378721
$295$	−2.99126	−0.174158
$296$	−8.03238	−0.466872
$297$	1.46673	0.0851084
$298$	9.25636	0.536207
$299$	43.5336	2.51761
$300$	−3.94761	−0.227915
$301$	3.43762	0.198141
$302$	21.8016	1.25454
$303$	−8.11714	−0.466318
$304$	−5.93346	−0.340307
$305$	−32.9437	−1.88635
$306$	1.00000	0.0571662
$307$	−24.5831	−1.40303	−0.701515	−	0.712655i	$-0.747492\pi$
$307$	−24.5831	−1.40303	−0.701515	+	0.712655i	$0.747492\pi$
$308$	−1.04364	−0.0594671
$309$	−0.172872	−0.00983432
$310$	12.1379	0.689386
$311$	24.8569	1.40950	0.704752	−	0.709454i	$-0.251058\pi$
$311$	24.8569	1.40950	0.704752	+	0.709454i	$0.251058\pi$
$312$	5.85410	0.331423
$313$	11.2312	0.634823	0.317412	−	0.948288i	$-0.397186\pi$
$313$	11.2312	0.634823	0.317412	+	0.948288i	$0.397186\pi$
$314$	−3.44547	−0.194439
$315$	2.12841	0.119922
$316$	−0.307503	−0.0172984
$317$	12.7193	0.714388	0.357194	−	0.934030i	$-0.383733\pi$
$317$	12.7193	0.714388	0.357194	+	0.934030i	$0.383733\pi$
$318$	13.1251	0.736017
$319$	−4.04905	−0.226703
$320$	2.99126	0.167216
$321$	−1.03778	−0.0579233
$322$	−5.29134	−0.294875
$323$	−5.93346	−0.330147
$324$	1.00000	0.0555556
$325$	−23.1097	−1.28190
$326$	0.776757	0.0430206
$327$	−12.4626	−0.689182
$328$	−5.32083	−0.293794
$329$	−2.39013	−0.131772
$330$	4.38737	0.241517
$331$	−16.8703	−0.927274	−0.463637	−	0.886025i	$-0.653456\pi$
$331$	−16.8703	−0.927274	−0.463637	+	0.886025i	$0.653456\pi$
$332$	16.5918	0.910593
$333$	−8.03238	−0.440172
$334$	12.8798	0.704749
$335$	16.6705	0.910805
$336$	−0.711544	−0.0388179
$337$	3.28814	0.179117	0.0895583	−	0.995982i	$-0.471454\pi$
$337$	3.28814	0.179117	0.0895583	+	0.995982i	$0.471454\pi$
$338$	21.2705	1.15696
$339$	7.38403	0.401045
$340$	2.99126	0.162224
$341$	−5.95169	−0.322302
$342$	−5.93346	−0.320845
$343$	−9.60136	−0.518425
$344$	4.83121	0.260481
$345$	22.2442	1.19759
$346$	−2.73230	−0.146889
$347$	−31.5381	−1.69306	−0.846528	−	0.532344i	$-0.821311\pi$
$347$	−31.5381	−1.69306	−0.846528	+	0.532344i	$0.821311\pi$
$348$	−2.76059	−0.147983
$349$	15.3388	0.821065	0.410532	−	0.911846i	$-0.365343\pi$
$349$	15.3388	0.821065	0.410532	+	0.911846i	$0.365343\pi$
$350$	2.80890	0.150142
$351$	5.85410	0.312469
$352$	−1.46673	−0.0781771
$353$	21.0272	1.11917	0.559583	−	0.828775i	$-0.310961\pi$
$353$	21.0272	1.11917	0.559583	+	0.828775i	$0.310961\pi$
$354$	1.00000	0.0531494
$355$	−16.5138	−0.876460
$356$	−13.5507	−0.718185
$357$	−0.711544	−0.0376589
$358$	9.00459	0.475907
$359$	−11.2044	−0.591347	−0.295674	−	0.955289i	$-0.595544\pi$
$359$	−11.2044	−0.591347	−0.295674	+	0.955289i	$0.595544\pi$
$360$	2.99126	0.157653
$361$	16.2060	0.852947
$362$	14.4966	0.761924
$363$	8.84870	0.464436
$364$	−4.16545	−0.218329
$365$	−1.18243	−0.0618914
$366$	11.0133	0.575676
$367$	−34.9113	−1.82236	−0.911178	−	0.412013i	$-0.864826\pi$
$367$	−34.9113	−1.82236	−0.911178	+	0.412013i	$0.864826\pi$
$368$	−7.43642	−0.387650
$369$	−5.32083	−0.276992
$370$	−24.0269	−1.24910
$371$	−9.33906	−0.484860
$372$	−4.05779	−0.210387
$373$	13.0888	0.677715	0.338857	−	0.940838i	$-0.389960\pi$
$373$	13.0888	0.677715	0.338857	+	0.940838i	$0.389960\pi$
$374$	−1.46673	−0.0758429
$375$	3.14796	0.162560
$376$	−3.35907	−0.173231
$377$	−16.1608	−0.832323
$378$	−0.711544	−0.0365979
$379$	10.6969	0.549465	0.274732	−	0.961521i	$-0.411411\pi$
$379$	10.6969	0.549465	0.274732	+	0.961521i	$0.411411\pi$
$380$	−17.7485	−0.910479
$381$	−7.59721	−0.389217
$382$	−6.56867	−0.336083
$383$	−2.90937	−0.148662	−0.0743310	−	0.997234i	$-0.523682\pi$
$383$	−2.90937	−0.148662	−0.0743310	+	0.997234i	$0.523682\pi$
$384$	−1.00000	−0.0510310
$385$	−3.12181	−0.159102
$386$	−19.5373	−0.994425
$387$	4.83121	0.245584
$388$	7.09017	0.359949
$389$	11.4035	0.578182	0.289091	−	0.957302i	$-0.406647\pi$
$389$	11.4035	0.578182	0.289091	+	0.957302i	$0.406647\pi$
$390$	17.5111	0.886710
$391$	−7.43642	−0.376076
$392$	−6.49371	−0.327982
$393$	4.07144	0.205377
$394$	−15.2494	−0.768254
$395$	−0.919821	−0.0462812
$396$	−1.46673	−0.0737060
$397$	−15.5656	−0.781214	−0.390607	−	0.920558i	$-0.627735\pi$
$397$	−15.5656	−0.781214	−0.390607	+	0.920558i	$0.627735\pi$
$398$	3.28512	0.164668
$399$	4.22192	0.211360
$400$	3.94761	0.197381
$401$	−30.1923	−1.50773	−0.753867	−	0.657027i	$-0.771814\pi$
$401$	−30.1923	−1.50773	−0.753867	+	0.657027i	$0.771814\pi$
$402$	−5.57307	−0.277959
$403$	−23.7547	−1.18331
$404$	8.11714	0.403843
$405$	2.99126	0.148637
$406$	1.96428	0.0974857
$407$	11.7813	0.583980
$408$	−1.00000	−0.0495074
$409$	11.5256	0.569903	0.284952	−	0.958542i	$-0.408022\pi$
$409$	11.5256	0.569903	0.284952	+	0.958542i	$0.408022\pi$
$410$	−15.9160	−0.786034
$411$	2.16879	0.106979
$412$	0.172872	0.00851677
$413$	−0.711544	−0.0350128
$414$	−7.43642	−0.365480
$415$	49.6303	2.43626
$416$	−5.85410	−0.287021
$417$	−5.55402	−0.271982
$418$	8.70280	0.425668
$419$	3.45088	0.168586	0.0842932	−	0.996441i	$-0.473137\pi$
$419$	3.45088	0.168586	0.0842932	+	0.996441i	$0.473137\pi$
$420$	−2.12841	−0.103856
$421$	3.36498	0.163999	0.0819996	−	0.996632i	$-0.473869\pi$
$421$	3.36498	0.163999	0.0819996	+	0.996632i	$0.473869\pi$
$422$	−4.77423	−0.232406
$423$	−3.35907	−0.163324
$424$	−13.1251	−0.637410
$425$	3.94761	0.191487
$426$	5.52068	0.267478
$427$	−7.83647	−0.379233
$428$	1.03778	0.0501631
$429$	−8.58640	−0.414555
$430$	14.4514	0.696908
$431$	29.3637	1.41440	0.707199	−	0.707015i	$-0.249959\pi$
$431$	29.3637	1.41440	0.707199	+	0.707015i	$0.249959\pi$
$432$	−1.00000	−0.0481125
$433$	13.4966	0.648605	0.324302	−	0.945953i	$-0.394870\pi$
$433$	13.4966	0.648605	0.324302	+	0.945953i	$0.394870\pi$
$434$	2.88730	0.138595
$435$	−8.25764	−0.395923
$436$	12.4626	0.596849
$437$	44.1237	2.11072
$438$	0.395297	0.0188880
$439$	−2.09402	−0.0999419	−0.0499709	−	0.998751i	$-0.515913\pi$
$439$	−2.09402	−0.0999419	−0.0499709	+	0.998751i	$0.515913\pi$
$440$	−4.38737	−0.209160
$441$	−6.49371	−0.309224
$442$	−5.85410	−0.278451
$443$	−33.3472	−1.58437	−0.792187	−	0.610278i	$-0.791058\pi$
$443$	−33.3472	−1.58437	−0.792187	+	0.610278i	$0.791058\pi$
$444$	8.03238	0.381200
$445$	−40.5336	−1.92147
$446$	28.5356	1.35120
$447$	−9.25636	−0.437811
$448$	0.711544	0.0336173
$449$	−32.2808	−1.52343	−0.761713	−	0.647915i	$-0.775641\pi$
$449$	−32.2808	−1.52343	−0.761713	+	0.647915i	$0.775641\pi$
$450$	3.94761	0.186092
$451$	7.80424	0.367487
$452$	−7.38403	−0.347316
$453$	−21.8016	−1.02433
$454$	20.1528	0.945817
$455$	−12.4599	−0.584130
$456$	5.93346	0.277860
$457$	−8.94939	−0.418635	−0.209317	−	0.977848i	$-0.567124\pi$
$457$	−8.94939	−0.418635	−0.209317	+	0.977848i	$0.567124\pi$
$458$	−8.61803	−0.402694
$459$	−1.00000	−0.0466760
$460$	−22.2442	−1.03714
$461$	−31.0675	−1.44696	−0.723479	−	0.690346i	$-0.757458\pi$
$461$	−31.0675	−1.44696	−0.723479	+	0.690346i	$0.757458\pi$
$462$	1.04364	0.0485547
$463$	13.5687	0.630590	0.315295	−	0.948994i	$-0.397897\pi$
$463$	13.5687	0.630590	0.315295	+	0.948994i	$0.397897\pi$
$464$	2.76059	0.128157
$465$	−12.1379	−0.562881
$466$	28.7164	1.33026
$467$	−29.0779	−1.34557	−0.672783	−	0.739840i	$-0.734901\pi$
$467$	−29.0779	−1.34557	−0.672783	+	0.739840i	$0.734901\pi$
$468$	−5.85410	−0.270606
$469$	3.96548	0.183109
$470$	−10.0478	−0.463473
$471$	3.44547	0.158759
$472$	−1.00000	−0.0460287
$473$	−7.08609	−0.325819
$474$	0.307503	0.0141241
$475$	−23.4230	−1.07472
$476$	0.711544	0.0326136
$477$	−13.1251	−0.600956
$478$	5.75807	0.263368
$479$	41.9376	1.91618	0.958089	−	0.286472i	$-0.0924824\pi$
$479$	41.9376	1.91618	0.958089	+	0.286472i	$0.0924824\pi$
$480$	−2.99126	−0.136532
$481$	47.0224	2.14403
$482$	−0.110998	−0.00505582
$483$	5.29134	0.240764
$484$	−8.84870	−0.402214
$485$	21.2085	0.963029
$486$	−1.00000	−0.0453609
$487$	−42.7506	−1.93721	−0.968607	−	0.248598i	$-0.920030\pi$
$487$	−42.7506	−1.93721	−0.968607	+	0.248598i	$0.920030\pi$
$488$	−11.0133	−0.498550
$489$	−0.776757	−0.0351262
$490$	−19.4243	−0.877502
$491$	16.4633	0.742979	0.371490	−	0.928437i	$-0.378847\pi$
$491$	16.4633	0.742979	0.371490	+	0.928437i	$0.378847\pi$
$492$	5.32083	0.239882
$493$	2.76059	0.124331
$494$	34.7351	1.56281
$495$	−4.38737	−0.197198
$496$	4.05779	0.182200
$497$	−3.92821	−0.176204
$498$	−16.5918	−0.743496
$499$	−4.77800	−0.213893	−0.106946	−	0.994265i	$-0.534107\pi$
$499$	−4.77800	−0.213893	−0.106946	+	0.994265i	$0.534107\pi$
$500$	−3.14796	−0.140781
$501$	−12.8798	−0.575425
$502$	6.17205	0.275472
$503$	−7.24178	−0.322895	−0.161448	−	0.986881i	$-0.551616\pi$
$503$	−7.24178	−0.322895	−0.161448	+	0.986881i	$0.551616\pi$
$504$	0.711544	0.0316947
$505$	24.2805	1.08047
$506$	10.9072	0.484886
$507$	−21.2705	−0.944657
$508$	7.59721	0.337072
$509$	14.8733	0.659247	0.329624	−	0.944112i	$-0.393078\pi$
$509$	14.8733	0.659247	0.329624	+	0.944112i	$0.393078\pi$
$510$	−2.99126	−0.132455
$511$	−0.281271	−0.0124427
$512$	1.00000	0.0441942
$513$	5.93346	0.261969
$514$	−6.47598	−0.285643
$515$	0.517103	0.0227863
$516$	−4.83121	−0.212682
$517$	4.92686	0.216683
$518$	−5.71539	−0.251120
$519$	2.73230	0.119934
$520$	−17.5111	−0.767913
$521$	6.22200	0.272591	0.136295	−	0.990668i	$-0.456480\pi$
$521$	6.22200	0.272591	0.136295	+	0.990668i	$0.456480\pi$
$522$	2.76059	0.120828
$523$	−21.5012	−0.940181	−0.470090	−	0.882618i	$-0.655779\pi$
$523$	−21.5012	−0.940181	−0.470090	+	0.882618i	$0.655779\pi$
$524$	−4.07144	−0.177861
$525$	−2.80890	−0.122590
$526$	−20.4978	−0.893746
$527$	4.05779	0.176760
$528$	1.46673	0.0638313
$529$	32.3003	1.40436
$530$	−39.2604	−1.70536
$531$	−1.00000	−0.0433963
$532$	−4.22192	−0.183043
$533$	31.1487	1.34920
$534$	13.5507	0.586395
$535$	3.10427	0.134209
$536$	5.57307	0.240720
$537$	−9.00459	−0.388577
$538$	−12.4313	−0.535949
$539$	9.52452	0.410250
$540$	−2.99126	−0.128723
$541$	−4.41192	−0.189683	−0.0948416	−	0.995492i	$-0.530234\pi$
$541$	−4.41192	−0.189683	−0.0948416	+	0.995492i	$0.530234\pi$
$542$	−17.9712	−0.771931
$543$	−14.4966	−0.622108
$544$	1.00000	0.0428746
$545$	37.2787	1.59685
$546$	4.16545	0.178265
$547$	4.65659	0.199101	0.0995506	−	0.995032i	$-0.468259\pi$
$547$	4.65659	0.199101	0.0995506	+	0.995032i	$0.468259\pi$
$548$	−2.16879	−0.0926461
$549$	−11.0133	−0.470037
$550$	−5.79009	−0.246890
$551$	−16.3799	−0.697806
$552$	7.43642	0.316515
$553$	−0.218802	−0.00930441
$554$	−20.6142	−0.875813
$555$	24.0269	1.01988
$556$	5.55402	0.235543
$557$	−10.3728	−0.439508	−0.219754	−	0.975555i	$-0.570525\pi$
$557$	−10.3728	−0.439508	−0.219754	+	0.975555i	$0.570525\pi$
$558$	4.05779	0.171780
$559$	−28.2824	−1.19622
$560$	2.12841	0.0899417
$561$	1.46673	0.0619255
$562$	−15.3216	−0.646302
$563$	−27.3450	−1.15245	−0.576227	−	0.817289i	$-0.695476\pi$
$563$	−27.3450	−1.15245	−0.576227	+	0.817289i	$0.695476\pi$
$564$	3.35907	0.141443
$565$	−22.0875	−0.929229
$566$	−29.2003	−1.22738
$567$	0.711544	0.0298820
$568$	−5.52068	−0.231643
$569$	34.5141	1.44691	0.723454	−	0.690372i	$-0.242553\pi$
$569$	34.5141	1.44691	0.723454	+	0.690372i	$0.242553\pi$
$570$	17.7485	0.743403
$571$	2.03439	0.0851368	0.0425684	−	0.999094i	$-0.486446\pi$
$571$	2.03439	0.0851368	0.0425684	+	0.999094i	$0.486446\pi$
$572$	8.58640	0.359015
$573$	6.56867	0.274410
$574$	−3.78601	−0.158025
$575$	−29.3561	−1.22423
$576$	1.00000	0.0416667
$577$	27.8086	1.15769	0.578844	−	0.815439i	$-0.303504\pi$
$577$	27.8086	1.15769	0.578844	+	0.815439i	$0.303504\pi$
$578$	1.00000	0.0415945
$579$	19.5373	0.811945
$580$	8.25764	0.342880
$581$	11.8058	0.489787
$582$	−7.09017	−0.293897
$583$	19.2510	0.797293
$584$	−0.395297	−0.0163575
$585$	−17.5111	−0.723996
$586$	−8.53075	−0.352402
$587$	−36.5946	−1.51042	−0.755211	−	0.655482i	$-0.772465\pi$
$587$	−36.5946	−1.51042	−0.755211	+	0.655482i	$0.772465\pi$
$588$	6.49371	0.267796
$589$	−24.0768	−0.992066
$590$	−2.99126	−0.123148
$591$	15.2494	0.627276
$592$	−8.03238	−0.330129
$593$	−27.3370	−1.12260	−0.561299	−	0.827613i	$-0.689698\pi$
$593$	−27.3370	−1.12260	−0.561299	+	0.827613i	$0.689698\pi$
$594$	1.46673	0.0601807
$595$	2.12841	0.0872563
$596$	9.25636	0.379155
$597$	−3.28512	−0.134451
$598$	43.5336	1.78022
$599$	33.9062	1.38537	0.692685	−	0.721241i	$-0.256428\pi$
$599$	33.9062	1.38537	0.692685	+	0.721241i	$0.256428\pi$
$600$	−3.94761	−0.161161
$601$	17.7460	0.723874	0.361937	−	0.932203i	$-0.382116\pi$
$601$	17.7460	0.723874	0.361937	+	0.932203i	$0.382116\pi$
$602$	3.43762	0.140107
$603$	5.57307	0.226953
$604$	21.8016	0.887096
$605$	−26.4687	−1.07611
$606$	−8.11714	−0.329736
$607$	5.74423	0.233151	0.116576	−	0.993182i	$-0.462808\pi$
$607$	5.74423	0.233151	0.116576	+	0.993182i	$0.462808\pi$
$608$	−5.93346	−0.240634
$609$	−1.96428	−0.0795967
$610$	−32.9437	−1.33385
$611$	19.6644	0.795535
$612$	1.00000	0.0404226
$613$	−25.7710	−1.04088	−0.520441	−	0.853897i	$-0.674233\pi$
$613$	−25.7710	−1.04088	−0.520441	+	0.853897i	$0.674233\pi$
$614$	−24.5831	−0.992091
$615$	15.9160	0.641794
$616$	−1.04364	−0.0420496
$617$	26.8541	1.08111	0.540553	−	0.841310i	$-0.318215\pi$
$617$	26.8541	1.08111	0.540553	+	0.841310i	$0.318215\pi$
$618$	−0.172872	−0.00695391
$619$	17.3013	0.695397	0.347699	−	0.937606i	$-0.386963\pi$
$619$	17.3013	0.695397	0.347699	+	0.937606i	$0.386963\pi$
$620$	12.1379	0.487470
$621$	7.43642	0.298413
$622$	24.8569	0.996669
$623$	−9.64190	−0.386295
$624$	5.85410	0.234352
$625$	−29.1544	−1.16618
$626$	11.2312	0.448888
$627$	−8.70280	−0.347556
$628$	−3.44547	−0.137489
$629$	−8.03238	−0.320272
$630$	2.12841	0.0847979
$631$	19.2737	0.767275	0.383637	−	0.923484i	$-0.374671\pi$
$631$	19.2737	0.767275	0.383637	+	0.923484i	$0.374671\pi$
$632$	−0.307503	−0.0122318
$633$	4.77423	0.189759
$634$	12.7193	0.505149
$635$	22.7252	0.901822
$636$	13.1251	0.520443
$637$	38.0148	1.50620
$638$	−4.04905	−0.160303
$639$	−5.52068	−0.218395
$640$	2.99126	0.118240
$641$	−43.3656	−1.71284	−0.856419	−	0.516282i	$-0.827316\pi$
$641$	−43.3656	−1.71284	−0.856419	+	0.516282i	$0.827316\pi$
$642$	−1.03778	−0.0409580
$643$	28.2659	1.11470	0.557350	−	0.830278i	$-0.311818\pi$
$643$	28.2659	1.11470	0.557350	+	0.830278i	$0.311818\pi$
$644$	−5.29134	−0.208508
$645$	−14.4514	−0.569023
$646$	−5.93346	−0.233449
$647$	16.2145	0.637458	0.318729	−	0.947846i	$-0.396744\pi$
$647$	16.2145	0.637458	0.318729	+	0.947846i	$0.396744\pi$
$648$	1.00000	0.0392837
$649$	1.46673	0.0575743
$650$	−23.1097	−0.906438
$651$	−2.88730	−0.113162
$652$	0.776757	0.0304202
$653$	9.51175	0.372223	0.186112	−	0.982529i	$-0.440411\pi$
$653$	9.51175	0.372223	0.186112	+	0.982529i	$0.440411\pi$
$654$	−12.4626	−0.487325
$655$	−12.1787	−0.475861
$656$	−5.32083	−0.207744
$657$	−0.395297	−0.0154220
$658$	−2.39013	−0.0931769
$659$	−4.87788	−0.190015	−0.0950076	−	0.995477i	$-0.530288\pi$
$659$	−4.87788	−0.190015	−0.0950076	+	0.995477i	$0.530288\pi$
$660$	4.38737	0.170778
$661$	−26.3709	−1.02571	−0.512855	−	0.858475i	$-0.671412\pi$
$661$	−26.3709	−1.02571	−0.512855	+	0.858475i	$0.671412\pi$
$662$	−16.8703	−0.655682
$663$	5.85410	0.227354
$664$	16.5918	0.643887
$665$	−12.6288	−0.489725
$666$	−8.03238	−0.311248
$667$	−20.5289	−0.794883
$668$	12.8798	0.498333
$669$	−28.5356	−1.10325
$670$	16.6705	0.644036
$671$	16.1536	0.623603
$672$	−0.711544	−0.0274484
$673$	37.8497	1.45900	0.729499	−	0.683982i	$-0.239753\pi$
$673$	37.8497	1.45900	0.729499	+	0.683982i	$0.239753\pi$
$674$	3.28814	0.126655
$675$	−3.94761	−0.151944
$676$	21.2705	0.818097
$677$	42.1869	1.62138	0.810688	−	0.585478i	$-0.199093\pi$
$677$	42.1869	1.62138	0.810688	+	0.585478i	$0.199093\pi$
$678$	7.38403	0.283582
$679$	5.04497	0.193608
$680$	2.99126	0.114709
$681$	−20.1528	−0.772256
$682$	−5.95169	−0.227902
$683$	8.10641	0.310183	0.155092	−	0.987900i	$-0.450433\pi$
$683$	8.10641	0.310183	0.155092	+	0.987900i	$0.450433\pi$
$684$	−5.93346	−0.226872
$685$	−6.48741	−0.247871
$686$	−9.60136	−0.366582
$687$	8.61803	0.328799
$688$	4.83121	0.184188
$689$	76.8355	2.92720
$690$	22.2442	0.846823
$691$	38.5519	1.46658	0.733292	−	0.679914i	$-0.237983\pi$
$691$	38.5519	1.46658	0.733292	+	0.679914i	$0.237983\pi$
$692$	−2.73230	−0.103866
$693$	−1.04364	−0.0396448
$694$	−31.5381	−1.19717
$695$	16.6135	0.630186
$696$	−2.76059	−0.104640
$697$	−5.32083	−0.201541
$698$	15.3388	0.580580
$699$	−28.7164	−1.08615
$700$	2.80890	0.106166
$701$	16.9838	0.641471	0.320735	−	0.947169i	$-0.396070\pi$
$701$	16.9838	0.641471	0.320735	+	0.947169i	$0.396070\pi$
$702$	5.85410	0.220949
$703$	47.6598	1.79752
$704$	−1.46673	−0.0552795
$705$	10.0478	0.378424
$706$	21.0272	0.791369
$707$	5.77570	0.217218
$708$	1.00000	0.0375823
$709$	1.10055	0.0413320	0.0206660	−	0.999786i	$-0.493421\pi$
$709$	1.10055	0.0413320	0.0206660	+	0.999786i	$0.493421\pi$
$710$	−16.5138	−0.619750
$711$	−0.307503	−0.0115323
$712$	−13.5507	−0.507833
$713$	−30.1754	−1.13008
$714$	−0.711544	−0.0266289
$715$	25.6841	0.960531
$716$	9.00459	0.336517
$717$	−5.75807	−0.215039
$718$	−11.2044	−0.418146
$719$	2.40673	0.0897559	0.0448779	−	0.998992i	$-0.485710\pi$
$719$	2.40673	0.0897559	0.0448779	+	0.998992i	$0.485710\pi$
$720$	2.99126	0.111478
$721$	0.123006	0.00458097
$722$	16.2060	0.603125
$723$	0.110998	0.00412806
$724$	14.4966	0.538761
$725$	10.8977	0.404732
$726$	8.84870	0.328406
$727$	−17.2223	−0.638742	−0.319371	−	0.947630i	$-0.603472\pi$
$727$	−17.2223	−0.638742	−0.319371	+	0.947630i	$0.603472\pi$
$728$	−4.16545	−0.154382
$729$	1.00000	0.0370370
$730$	−1.18243	−0.0437638
$731$	4.83121	0.178689
$732$	11.0133	0.407064
$733$	−32.4741	−1.19946	−0.599729	−	0.800203i	$-0.704725\pi$
$733$	−32.4741	−1.19946	−0.599729	+	0.800203i	$0.704725\pi$
$734$	−34.9113	−1.28860
$735$	19.4243	0.716477
$736$	−7.43642	−0.274110
$737$	−8.17419	−0.301100
$738$	−5.32083	−0.195863
$739$	−22.1035	−0.813092	−0.406546	−	0.913630i	$-0.633267\pi$
$739$	−22.1035	−0.813092	−0.406546	+	0.913630i	$0.633267\pi$
$740$	−24.0269	−0.883246
$741$	−34.7351	−1.27603
$742$	−9.33906	−0.342848
$743$	32.9016	1.20704	0.603521	−	0.797347i	$-0.293764\pi$
$743$	32.9016	1.20704	0.603521	+	0.797347i	$0.293764\pi$
$744$	−4.05779	−0.148766
$745$	27.6881	1.01442
$746$	13.0888	0.479217
$747$	16.5918	0.607062
$748$	−1.46673	−0.0536290
$749$	0.738427	0.0269815
$750$	3.14796	0.114947
$751$	−15.8264	−0.577512	−0.288756	−	0.957403i	$-0.593242\pi$
$751$	−15.8264	−0.577512	−0.288756	+	0.957403i	$0.593242\pi$
$752$	−3.35907	−0.122493
$753$	−6.17205	−0.224922
$754$	−16.1608	−0.588541
$755$	65.2143	2.37339
$756$	−0.711544	−0.0258786
$757$	−11.6002	−0.421618	−0.210809	−	0.977527i	$-0.567610\pi$
$757$	−11.6002	−0.421618	−0.210809	+	0.977527i	$0.567610\pi$
$758$	10.6969	0.388530
$759$	−10.9072	−0.395907
$760$	−17.7485	−0.643806
$761$	−10.1296	−0.367197	−0.183599	−	0.983001i	$-0.558775\pi$
$761$	−10.1296	−0.367197	−0.183599	+	0.983001i	$0.558775\pi$
$762$	−7.59721	−0.275218
$763$	8.86767	0.321031
$764$	−6.56867	−0.237646
$765$	2.99126	0.108149
$766$	−2.90937	−0.105120
$767$	5.85410	0.211379
$768$	−1.00000	−0.0360844
$769$	−15.2619	−0.550357	−0.275178	−	0.961393i	$-0.588737\pi$
$769$	−15.2619	−0.550357	−0.275178	+	0.961393i	$0.588737\pi$
$770$	−3.12181	−0.112502
$771$	6.47598	0.233227
$772$	−19.5373	−0.703165
$773$	−39.6475	−1.42602	−0.713010	−	0.701154i	$-0.752669\pi$
$773$	−39.6475	−1.42602	−0.713010	+	0.701154i	$0.752669\pi$
$774$	4.83121	0.173654
$775$	16.0186	0.575405
$776$	7.09017	0.254522
$777$	5.71539	0.205038
$778$	11.4035	0.408837
$779$	31.5710	1.13115
$780$	17.5111	0.626999
$781$	8.09736	0.289746
$782$	−7.43642	−0.265926
$783$	−2.76059	−0.0986555
$784$	−6.49371	−0.231918
$785$	−10.3063	−0.367848
$786$	4.07144	0.145223
$787$	−51.0652	−1.82028	−0.910139	−	0.414302i	$-0.864026\pi$
$787$	−51.0652	−1.82028	−0.910139	+	0.414302i	$0.864026\pi$
$788$	−15.2494	−0.543237
$789$	20.4978	0.729741
$790$	−0.919821	−0.0327258
$791$	−5.25406	−0.186813
$792$	−1.46673	−0.0521180
$793$	64.4732	2.28951
$794$	−15.5656	−0.552401
$795$	39.2604	1.39242
$796$	3.28512	0.116438
$797$	52.4143	1.85661	0.928305	−	0.371819i	$-0.121266\pi$
$797$	52.4143	1.85661	0.928305	+	0.371819i	$0.121266\pi$
$798$	4.22192	0.149454
$799$	−3.35907	−0.118835
$800$	3.94761	0.139569
$801$	−13.5507	−0.478790
$802$	−30.1923	−1.06613
$803$	0.579794	0.0204605
$804$	−5.57307	−0.196547
$805$	−15.8277	−0.557855
$806$	−23.7547	−0.836725
$807$	12.4313	0.437601
$808$	8.11714	0.285560
$809$	20.9984	0.738265	0.369132	−	0.929377i	$-0.379655\pi$
$809$	20.9984	0.738265	0.369132	+	0.929377i	$0.379655\pi$
$810$	2.99126	0.105102
$811$	−8.89086	−0.312200	−0.156100	−	0.987741i	$-0.549892\pi$
$811$	−8.89086	−0.312200	−0.156100	+	0.987741i	$0.549892\pi$
$812$	1.96428	0.0689328
$813$	17.9712	0.630279
$814$	11.7813	0.412936
$815$	2.32348	0.0813879
$816$	−1.00000	−0.0350070
$817$	−28.6658	−1.00289
$818$	11.5256	0.402982
$819$	−4.16545	−0.145553
$820$	−15.9160	−0.555810
$821$	−49.7065	−1.73477	−0.867384	−	0.497639i	$-0.834200\pi$
$821$	−49.7065	−1.73477	−0.867384	+	0.497639i	$0.834200\pi$
$822$	2.16879	0.0756453
$823$	−9.15768	−0.319217	−0.159608	−	0.987180i	$-0.551023\pi$
$823$	−9.15768	−0.319217	−0.159608	+	0.987180i	$0.551023\pi$
$824$	0.172872	0.00602227
$825$	5.79009	0.201585
$826$	−0.711544	−0.0247578
$827$	−27.5344	−0.957465	−0.478732	−	0.877961i	$-0.658904\pi$
$827$	−27.5344	−0.957465	−0.478732	+	0.877961i	$0.658904\pi$
$828$	−7.43642	−0.258433
$829$	−28.7360	−0.998041	−0.499021	−	0.866590i	$-0.666307\pi$
$829$	−28.7360	−0.998041	−0.499021	+	0.866590i	$0.666307\pi$
$830$	49.6303	1.72269
$831$	20.6142	0.715098
$832$	−5.85410	−0.202954
$833$	−6.49371	−0.224994
$834$	−5.55402	−0.192320
$835$	38.5266	1.33327
$836$	8.70280	0.300993
$837$	−4.05779	−0.140258
$838$	3.45088	0.119209
$839$	6.37788	0.220189	0.110095	−	0.993921i	$-0.464885\pi$
$839$	6.37788	0.220189	0.110095	+	0.993921i	$0.464885\pi$
$840$	−2.12841	−0.0734371
$841$	−21.3791	−0.737211
$842$	3.36498	0.115965
$843$	15.3216	0.527703
$844$	−4.77423	−0.164336
$845$	63.6255	2.18879
$846$	−3.35907	−0.115487
$847$	−6.29624	−0.216341
$848$	−13.1251	−0.450717
$849$	29.2003	1.00215
$850$	3.94761	0.135402
$851$	59.7321	2.04759
$852$	5.52068	0.189135
$853$	6.53493	0.223752	0.111876	−	0.993722i	$-0.464314\pi$
$853$	6.53493	0.223752	0.111876	+	0.993722i	$0.464314\pi$
$854$	−7.83647	−0.268158
$855$	−17.7485	−0.606986
$856$	1.03778	0.0354707
$857$	54.1070	1.84826	0.924130	−	0.382078i	$-0.124792\pi$
$857$	54.1070	1.84826	0.924130	+	0.382078i	$0.124792\pi$
$858$	−8.58640	−0.293135
$859$	−3.73739	−0.127518	−0.0637590	−	0.997965i	$-0.520309\pi$
$859$	−3.73739	−0.127518	−0.0637590	+	0.997965i	$0.520309\pi$
$860$	14.4514	0.492788
$861$	3.78601	0.129027
$862$	29.3637	1.00013
$863$	−7.34173	−0.249915	−0.124958	−	0.992162i	$-0.539880\pi$
$863$	−7.34173	−0.249915	−0.124958	+	0.992162i	$0.539880\pi$
$864$	−1.00000	−0.0340207
$865$	−8.17300	−0.277890
$866$	13.4966	0.458633
$867$	−1.00000	−0.0339618
$868$	2.88730	0.0980013
$869$	0.451025	0.0153000
$870$	−8.25764	−0.279960
$871$	−32.6253	−1.10547
$872$	12.4626	0.422036
$873$	7.09017	0.239966
$874$	44.1237	1.49251
$875$	−2.23991	−0.0757229
$876$	0.395297	0.0133558
$877$	23.0261	0.777535	0.388768	−	0.921336i	$-0.372901\pi$
$877$	23.0261	0.777535	0.388768	+	0.921336i	$0.372901\pi$
$878$	−2.09402	−0.0706696
$879$	8.53075	0.287735
$880$	−4.38737	−0.147898
$881$	−2.69836	−0.0909100	−0.0454550	−	0.998966i	$-0.514474\pi$
$881$	−2.69836	−0.0909100	−0.0454550	+	0.998966i	$0.514474\pi$
$882$	−6.49371	−0.218654
$883$	−4.67162	−0.157213	−0.0786063	−	0.996906i	$-0.525047\pi$
$883$	−4.67162	−0.157213	−0.0786063	+	0.996906i	$0.525047\pi$
$884$	−5.85410	−0.196895
$885$	2.99126	0.100550
$886$	−33.3472	−1.12032
$887$	−6.85713	−0.230240	−0.115120	−	0.993352i	$-0.536725\pi$
$887$	−6.85713	−0.230240	−0.115120	+	0.993352i	$0.536725\pi$
$888$	8.03238	0.269549
$889$	5.40575	0.181303
$890$	−40.5336	−1.35869
$891$	−1.46673	−0.0491374
$892$	28.5356	0.955441
$893$	19.9309	0.666964
$894$	−9.25636	−0.309579
$895$	26.9350	0.900339
$896$	0.711544	0.0237710
$897$	−43.5336	−1.45354
$898$	−32.2808	−1.07722
$899$	11.2019	0.373605
$900$	3.94761	0.131587
$901$	−13.1251	−0.437259
$902$	7.80424	0.259853
$903$	−3.43762	−0.114397
$904$	−7.38403	−0.245589
$905$	43.3630	1.44143
$906$	−21.8016	−0.724311
$907$	10.3181	0.342608	0.171304	−	0.985218i	$-0.445202\pi$
$907$	10.3181	0.342608	0.171304	+	0.985218i	$0.445202\pi$
$908$	20.1528	0.668794
$909$	8.11714	0.269229
$910$	−12.4599	−0.413043
$911$	−5.12562	−0.169819	−0.0849097	−	0.996389i	$-0.527060\pi$
$911$	−5.12562	−0.169819	−0.0849097	+	0.996389i	$0.527060\pi$
$912$	5.93346	0.196477
$913$	−24.3357	−0.805395
$914$	−8.94939	−0.296020
$915$	32.9437	1.08908
$916$	−8.61803	−0.284748
$917$	−2.89700	−0.0956675
$918$	−1.00000	−0.0330049
$919$	−1.45585	−0.0480240	−0.0240120	−	0.999712i	$-0.507644\pi$
$919$	−1.45585	−0.0480240	−0.0240120	+	0.999712i	$0.507644\pi$
$920$	−22.2442	−0.733371
$921$	24.5831	0.810039
$922$	−31.0675	−1.02315
$923$	32.3186	1.06378
$924$	1.04364	0.0343334
$925$	−31.7087	−1.04258
$926$	13.5687	0.445894
$927$	0.172872	0.00567785
$928$	2.76059	0.0906209
$929$	12.0635	0.395791	0.197895	−	0.980223i	$-0.436589\pi$
$929$	12.0635	0.395791	0.197895	+	0.980223i	$0.436589\pi$
$930$	−12.1379	−0.398017
$931$	38.5302	1.26278
$932$	28.7164	0.940636
$933$	−24.8569	−0.813777
$934$	−29.0779	−0.951459
$935$	−4.38737	−0.143482
$936$	−5.85410	−0.191347
$937$	−18.1223	−0.592030	−0.296015	−	0.955183i	$-0.595658\pi$
$937$	−18.1223	−0.592030	−0.296015	+	0.955183i	$0.595658\pi$
$938$	3.96548	0.129478
$939$	−11.2312	−0.366515
$940$	−10.0478	−0.327725
$941$	−4.34598	−0.141675	−0.0708374	−	0.997488i	$-0.522567\pi$
$941$	−4.34598	−0.141675	−0.0708374	+	0.997488i	$0.522567\pi$
$942$	3.44547	0.112260
$943$	39.5679	1.28851
$944$	−1.00000	−0.0325472
$945$	−2.12841	−0.0692372
$946$	−7.08609	−0.230389
$947$	−30.5398	−0.992409	−0.496205	−	0.868206i	$-0.665273\pi$
$947$	−30.5398	−0.992409	−0.496205	+	0.868206i	$0.665273\pi$
$948$	0.307503	0.00998724
$949$	2.31411	0.0751191
$950$	−23.4230	−0.759943
$951$	−12.7193	−0.412452
$952$	0.711544	0.0230613
$953$	−53.6683	−1.73849	−0.869244	−	0.494383i	$-0.835394\pi$
$953$	−53.6683	−1.73849	−0.869244	+	0.494383i	$0.835394\pi$
$954$	−13.1251	−0.424940
$955$	−19.6486	−0.635813
$956$	5.75807	0.186229
$957$	4.04905	0.130887
$958$	41.9376	1.35494
$959$	−1.54319	−0.0498322
$960$	−2.99126	−0.0965424
$961$	−14.5343	−0.468849
$962$	47.0224	1.51606
$963$	1.03778	0.0334421
$964$	−0.110998	−0.00357501
$965$	−58.4412	−1.88129
$966$	5.29134	0.170246
$967$	−25.4155	−0.817306	−0.408653	−	0.912690i	$-0.634001\pi$
$967$	−25.4155	−0.817306	−0.408653	+	0.912690i	$0.634001\pi$
$968$	−8.84870	−0.284408
$969$	5.93346	0.190610
$970$	21.2085	0.680964
$971$	17.2934	0.554970	0.277485	−	0.960730i	$-0.410499\pi$
$971$	17.2934	0.554970	0.277485	+	0.960730i	$0.410499\pi$
$972$	−1.00000	−0.0320750
$973$	3.95193	0.126693
$974$	−42.7506	−1.36982
$975$	23.1097	0.740103
$976$	−11.0133	−0.352528
$977$	−36.0197	−1.15237	−0.576186	−	0.817318i	$-0.695460\pi$
$977$	−36.0197	−1.15237	−0.576186	+	0.817318i	$0.695460\pi$
$978$	−0.776757	−0.0248380
$979$	19.8752	0.635215
$980$	−19.4243	−0.620488
$981$	12.4626	0.397899
$982$	16.4633	0.525366
$983$	54.5578	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$983$	54.5578	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$984$	5.32083	0.169622
$985$	−45.6149	−1.45341
$986$	2.76059	0.0879152
$987$	2.39013	0.0760786
$988$	34.7351	1.10507
$989$	−35.9269	−1.14241
$990$	−4.38737	−0.139440
$991$	−53.2078	−1.69020	−0.845101	−	0.534607i	$-0.820460\pi$
$991$	−53.2078	−1.69020	−0.845101	+	0.534607i	$0.820460\pi$
$992$	4.05779	0.128835
$993$	16.8703	0.535362
$994$	−3.92821	−0.124595
$995$	9.82662	0.311525
$996$	−16.5918	−0.525731
$997$	−34.2298	−1.08407	−0.542034	−	0.840357i	$-0.682346\pi$
$997$	−34.2298	−1.08407	−0.542034	+	0.840357i	$0.682346\pi$
$998$	−4.77800	−0.151245
$999$	8.03238	0.254133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.n.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.n.1.4	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.99126 q^{5} -1.00000 q^{6} +0.711544 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.99126 q^{5} -1.00000 q^{6} +0.711544 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.99126 q^{10} -1.46673 q^{11} -1.00000 q^{12} -5.85410 q^{13} +0.711544 q^{14} -2.99126 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -5.93346 q^{19} +2.99126 q^{20} -0.711544 q^{21} -1.46673 q^{22} -7.43642 q^{23} -1.00000 q^{24} +3.94761 q^{25} -5.85410 q^{26} -1.00000 q^{27} +0.711544 q^{28} +2.76059 q^{29} -2.99126 q^{30} +4.05779 q^{31} +1.00000 q^{32} +1.46673 q^{33} +1.00000 q^{34} +2.12841 q^{35} +1.00000 q^{36} -8.03238 q^{37} -5.93346 q^{38} +5.85410 q^{39} +2.99126 q^{40} -5.32083 q^{41} -0.711544 q^{42} +4.83121 q^{43} -1.46673 q^{44} +2.99126 q^{45} -7.43642 q^{46} -3.35907 q^{47} -1.00000 q^{48} -6.49371 q^{49} +3.94761 q^{50} -1.00000 q^{51} -5.85410 q^{52} -13.1251 q^{53} -1.00000 q^{54} -4.38737 q^{55} +0.711544 q^{56} +5.93346 q^{57} +2.76059 q^{58} -1.00000 q^{59} -2.99126 q^{60} -11.0133 q^{61} +4.05779 q^{62} +0.711544 q^{63} +1.00000 q^{64} -17.5111 q^{65} +1.46673 q^{66} +5.57307 q^{67} +1.00000 q^{68} +7.43642 q^{69} +2.12841 q^{70} -5.52068 q^{71} +1.00000 q^{72} -0.395297 q^{73} -8.03238 q^{74} -3.94761 q^{75} -5.93346 q^{76} -1.04364 q^{77} +5.85410 q^{78} -0.307503 q^{79} +2.99126 q^{80} +1.00000 q^{81} -5.32083 q^{82} +16.5918 q^{83} -0.711544 q^{84} +2.99126 q^{85} +4.83121 q^{86} -2.76059 q^{87} -1.46673 q^{88} -13.5507 q^{89} +2.99126 q^{90} -4.16545 q^{91} -7.43642 q^{92} -4.05779 q^{93} -3.35907 q^{94} -17.7485 q^{95} -1.00000 q^{96} +7.09017 q^{97} -6.49371 q^{98} -1.46673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} - 10 q^{13} + q^{14} + 3 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 8 q^{19} - 3 q^{20} - q^{21} + 2 q^{22} - 10 q^{23} - 4 q^{24} + 5 q^{25} - 10 q^{26} - 4 q^{27} + q^{28} - 5 q^{29} + 3 q^{30} + 17 q^{31} + 4 q^{32} - 2 q^{33} + 4 q^{34} - 8 q^{35} + 4 q^{36} - 9 q^{37} - 8 q^{38} + 10 q^{39} - 3 q^{40} - q^{42} - 14 q^{43} + 2 q^{44} - 3 q^{45} - 10 q^{46} + 2 q^{47} - 4 q^{48} - 5 q^{49} + 5 q^{50} - 4 q^{51} - 10 q^{52} - 11 q^{53} - 4 q^{54} - 12 q^{55} + q^{56} + 8 q^{57} - 5 q^{58} - 4 q^{59} + 3 q^{60} - 28 q^{61} + 17 q^{62} + q^{63} + 4 q^{64} - 2 q^{66} - q^{67} + 4 q^{68} + 10 q^{69} - 8 q^{70} + 12 q^{71} + 4 q^{72} + 10 q^{73} - 9 q^{74} - 5 q^{75} - 8 q^{76} + 10 q^{78} + 4 q^{79} - 3 q^{80} + 4 q^{81} + 17 q^{83} - q^{84} - 3 q^{85} - 14 q^{86} + 5 q^{87} + 2 q^{88} - 13 q^{89} - 3 q^{90} - 25 q^{91} - 10 q^{92} - 17 q^{93} + 2 q^{94} - 15 q^{95} - 4 q^{96} + 6 q^{97} - 5 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 - 10 * q^13 + q^14 + 3 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 8 * q^19 - 3 * q^20 - q^21 + 2 * q^22 - 10 * q^23 - 4 * q^24 + 5 * q^25 - 10 * q^26 - 4 * q^27 + q^28 - 5 * q^29 + 3 * q^30 + 17 * q^31 + 4 * q^32 - 2 * q^33 + 4 * q^34 - 8 * q^35 + 4 * q^36 - 9 * q^37 - 8 * q^38 + 10 * q^39 - 3 * q^40 - q^42 - 14 * q^43 + 2 * q^44 - 3 * q^45 - 10 * q^46 + 2 * q^47 - 4 * q^48 - 5 * q^49 + 5 * q^50 - 4 * q^51 - 10 * q^52 - 11 * q^53 - 4 * q^54 - 12 * q^55 + q^56 + 8 * q^57 - 5 * q^58 - 4 * q^59 + 3 * q^60 - 28 * q^61 + 17 * q^62 + q^63 + 4 * q^64 - 2 * q^66 - q^67 + 4 * q^68 + 10 * q^69 - 8 * q^70 + 12 * q^71 + 4 * q^72 + 10 * q^73 - 9 * q^74 - 5 * q^75 - 8 * q^76 + 10 * q^78 + 4 * q^79 - 3 * q^80 + 4 * q^81 + 17 * q^83 - q^84 - 3 * q^85 - 14 * q^86 + 5 * q^87 + 2 * q^88 - 13 * q^89 - 3 * q^90 - 25 * q^91 - 10 * q^92 - 17 * q^93 + 2 * q^94 - 15 * q^95 - 4 * q^96 + 6 * q^97 - 5 * q^98 + 2 * q^99

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