LMFDB - Embedded newform 6042.2.a.bh.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 40 x^{11} + 123 x^{10} + 537 x^{9} - 1707 x^{8} - 2914 x^{7} + 9639 x^{6} + \cdots + 1200 $ x^13 - 3x^12 - 40x^11 + 123x^10 + 537x^9 - 1707x^8 - 2914x^7 + 9639x^6 + 6938x^5 - 22200x^4 - 9466x^3 + 16812x^2 + 9304x + 1200
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.48443$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.48443 q^{5} +1.00000 q^{6} +3.12498 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.48443 q^{5} +1.00000 q^{6} +3.12498 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.48443 q^{10} -5.11950 q^{11} +1.00000 q^{12} -0.205621 q^{13} +3.12498 q^{14} +2.48443 q^{15} +1.00000 q^{16} -2.50123 q^{17} +1.00000 q^{18} +1.00000 q^{19} +2.48443 q^{20} +3.12498 q^{21} -5.11950 q^{22} +6.16430 q^{23} +1.00000 q^{24} +1.17239 q^{25} -0.205621 q^{26} +1.00000 q^{27} +3.12498 q^{28} +3.57299 q^{29} +2.48443 q^{30} +3.57447 q^{31} +1.00000 q^{32} -5.11950 q^{33} -2.50123 q^{34} +7.76379 q^{35} +1.00000 q^{36} -4.19788 q^{37} +1.00000 q^{38} -0.205621 q^{39} +2.48443 q^{40} -1.86196 q^{41} +3.12498 q^{42} -3.23362 q^{43} -5.11950 q^{44} +2.48443 q^{45} +6.16430 q^{46} +11.3263 q^{47} +1.00000 q^{48} +2.76549 q^{49} +1.17239 q^{50} -2.50123 q^{51} -0.205621 q^{52} -1.00000 q^{53} +1.00000 q^{54} -12.7190 q^{55} +3.12498 q^{56} +1.00000 q^{57} +3.57299 q^{58} -0.0335822 q^{59} +2.48443 q^{60} +12.7311 q^{61} +3.57447 q^{62} +3.12498 q^{63} +1.00000 q^{64} -0.510851 q^{65} -5.11950 q^{66} +8.55473 q^{67} -2.50123 q^{68} +6.16430 q^{69} +7.76379 q^{70} +15.0639 q^{71} +1.00000 q^{72} +12.3811 q^{73} -4.19788 q^{74} +1.17239 q^{75} +1.00000 q^{76} -15.9983 q^{77} -0.205621 q^{78} -3.91819 q^{79} +2.48443 q^{80} +1.00000 q^{81} -1.86196 q^{82} +1.25650 q^{83} +3.12498 q^{84} -6.21413 q^{85} -3.23362 q^{86} +3.57299 q^{87} -5.11950 q^{88} -10.4800 q^{89} +2.48443 q^{90} -0.642562 q^{91} +6.16430 q^{92} +3.57447 q^{93} +11.3263 q^{94} +2.48443 q^{95} +1.00000 q^{96} +0.0148062 q^{97} +2.76549 q^{98} -5.11950 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 4 q^{11} + 13 q^{12} + 18 q^{13} + 12 q^{14} + 3 q^{15} + 13 q^{16} + 3 q^{17} + 13 q^{18} + 13 q^{19} + 3 q^{20} + 12 q^{21} + 4 q^{22} + 8 q^{23} + 13 q^{24} + 24 q^{25} + 18 q^{26} + 13 q^{27} + 12 q^{28} + 11 q^{29} + 3 q^{30} + 2 q^{31} + 13 q^{32} + 4 q^{33} + 3 q^{34} - 6 q^{35} + 13 q^{36} + 26 q^{37} + 13 q^{38} + 18 q^{39} + 3 q^{40} + 3 q^{41} + 12 q^{42} + 24 q^{43} + 4 q^{44} + 3 q^{45} + 8 q^{46} + 4 q^{47} + 13 q^{48} + 41 q^{49} + 24 q^{50} + 3 q^{51} + 18 q^{52} - 13 q^{53} + 13 q^{54} + 23 q^{55} + 12 q^{56} + 13 q^{57} + 11 q^{58} + 8 q^{59} + 3 q^{60} + 29 q^{61} + 2 q^{62} + 12 q^{63} + 13 q^{64} + 13 q^{65} + 4 q^{66} - 5 q^{67} + 3 q^{68} + 8 q^{69} - 6 q^{70} + 29 q^{71} + 13 q^{72} + 15 q^{73} + 26 q^{74} + 24 q^{75} + 13 q^{76} + 3 q^{77} + 18 q^{78} + 15 q^{79} + 3 q^{80} + 13 q^{81} + 3 q^{82} + 4 q^{83} + 12 q^{84} - q^{85} + 24 q^{86} + 11 q^{87} + 4 q^{88} + 3 q^{89} + 3 q^{90} - 29 q^{91} + 8 q^{92} + 2 q^{93} + 4 q^{94} + 3 q^{95} + 13 q^{96} + 50 q^{97} + 41 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 4 * q^11 + 13 * q^12 + 18 * q^13 + 12 * q^14 + 3 * q^15 + 13 * q^16 + 3 * q^17 + 13 * q^18 + 13 * q^19 + 3 * q^20 + 12 * q^21 + 4 * q^22 + 8 * q^23 + 13 * q^24 + 24 * q^25 + 18 * q^26 + 13 * q^27 + 12 * q^28 + 11 * q^29 + 3 * q^30 + 2 * q^31 + 13 * q^32 + 4 * q^33 + 3 * q^34 - 6 * q^35 + 13 * q^36 + 26 * q^37 + 13 * q^38 + 18 * q^39 + 3 * q^40 + 3 * q^41 + 12 * q^42 + 24 * q^43 + 4 * q^44 + 3 * q^45 + 8 * q^46 + 4 * q^47 + 13 * q^48 + 41 * q^49 + 24 * q^50 + 3 * q^51 + 18 * q^52 - 13 * q^53 + 13 * q^54 + 23 * q^55 + 12 * q^56 + 13 * q^57 + 11 * q^58 + 8 * q^59 + 3 * q^60 + 29 * q^61 + 2 * q^62 + 12 * q^63 + 13 * q^64 + 13 * q^65 + 4 * q^66 - 5 * q^67 + 3 * q^68 + 8 * q^69 - 6 * q^70 + 29 * q^71 + 13 * q^72 + 15 * q^73 + 26 * q^74 + 24 * q^75 + 13 * q^76 + 3 * q^77 + 18 * q^78 + 15 * q^79 + 3 * q^80 + 13 * q^81 + 3 * q^82 + 4 * q^83 + 12 * q^84 - q^85 + 24 * q^86 + 11 * q^87 + 4 * q^88 + 3 * q^89 + 3 * q^90 - 29 * q^91 + 8 * q^92 + 2 * q^93 + 4 * q^94 + 3 * q^95 + 13 * q^96 + 50 * q^97 + 41 * q^98 + 4 * 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
$5$	2.48443	1.11107	0.555535	−	0.831493i	$-0.312513\pi$
$5$	2.48443	1.11107	0.555535	+	0.831493i	$0.312513\pi$
$6$	1.00000	0.408248
$7$	3.12498	1.18113	0.590566	−	0.806990i	$-0.298905\pi$
$7$	3.12498	1.18113	0.590566	+	0.806990i	$0.298905\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.48443	0.785646
$11$	−5.11950	−1.54359	−0.771793	−	0.635874i	$-0.780640\pi$
$11$	−5.11950	−1.54359	−0.771793	+	0.635874i	$0.780640\pi$
$12$	1.00000	0.288675
$13$	−0.205621	−0.0570290	−0.0285145	−	0.999593i	$-0.509078\pi$
$13$	−0.205621	−0.0570290	−0.0285145	+	0.999593i	$0.509078\pi$
$14$	3.12498	0.835186
$15$	2.48443	0.641477
$16$	1.00000	0.250000
$17$	−2.50123	−0.606638	−0.303319	−	0.952889i	$-0.598095\pi$
$17$	−2.50123	−0.606638	−0.303319	+	0.952889i	$0.598095\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.48443	0.555535
$21$	3.12498	0.681926
$22$	−5.11950	−1.09148
$23$	6.16430	1.28535	0.642673	−	0.766141i	$-0.277826\pi$
$23$	6.16430	1.28535	0.642673	+	0.766141i	$0.277826\pi$
$24$	1.00000	0.204124
$25$	1.17239	0.234478
$26$	−0.205621	−0.0403256
$27$	1.00000	0.192450
$28$	3.12498	0.590566
$29$	3.57299	0.663487	0.331744	−	0.943370i	$-0.392363\pi$
$29$	3.57299	0.663487	0.331744	+	0.943370i	$0.392363\pi$
$30$	2.48443	0.453593
$31$	3.57447	0.641993	0.320997	−	0.947080i	$-0.395982\pi$
$31$	3.57447	0.641993	0.320997	+	0.947080i	$0.395982\pi$
$32$	1.00000	0.176777
$33$	−5.11950	−0.891190
$34$	−2.50123	−0.428958
$35$	7.76379	1.31232
$36$	1.00000	0.166667
$37$	−4.19788	−0.690128	−0.345064	−	0.938579i	$-0.612143\pi$
$37$	−4.19788	−0.690128	−0.345064	+	0.938579i	$0.612143\pi$
$38$	1.00000	0.162221
$39$	−0.205621	−0.0329257
$40$	2.48443	0.392823
$41$	−1.86196	−0.290790	−0.145395	−	0.989374i	$-0.546445\pi$
$41$	−1.86196	−0.290790	−0.145395	+	0.989374i	$0.546445\pi$
$42$	3.12498	0.482195
$43$	−3.23362	−0.493123	−0.246561	−	0.969127i	$-0.579301\pi$
$43$	−3.23362	−0.493123	−0.246561	+	0.969127i	$0.579301\pi$
$44$	−5.11950	−0.771793
$45$	2.48443	0.370357
$46$	6.16430	0.908876
$47$	11.3263	1.65211	0.826053	−	0.563593i	$-0.190581\pi$
$47$	11.3263	1.65211	0.826053	+	0.563593i	$0.190581\pi$
$48$	1.00000	0.144338
$49$	2.76549	0.395070
$50$	1.17239	0.165801
$51$	−2.50123	−0.350242
$52$	−0.205621	−0.0285145
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.00000	0.136083
$55$	−12.7190	−1.71503
$56$	3.12498	0.417593
$57$	1.00000	0.132453
$58$	3.57299	0.469156
$59$	−0.0335822	−0.00437202	−0.00218601	−	0.999998i	$-0.500696\pi$
$59$	−0.0335822	−0.00437202	−0.00218601	+	0.999998i	$0.500696\pi$
$60$	2.48443	0.320739
$61$	12.7311	1.63005	0.815026	−	0.579424i	$-0.196723\pi$
$61$	12.7311	1.63005	0.815026	+	0.579424i	$0.196723\pi$
$62$	3.57447	0.453958
$63$	3.12498	0.393710
$64$	1.00000	0.125000
$65$	−0.510851	−0.0633633
$66$	−5.11950	−0.630167
$67$	8.55473	1.04513	0.522563	−	0.852600i	$-0.324976\pi$
$67$	8.55473	1.04513	0.522563	+	0.852600i	$0.324976\pi$
$68$	−2.50123	−0.303319
$69$	6.16430	0.742094
$70$	7.76379	0.927951
$71$	15.0639	1.78775	0.893876	−	0.448314i	$-0.147975\pi$
$71$	15.0639	1.78775	0.893876	+	0.448314i	$0.147975\pi$
$72$	1.00000	0.117851
$73$	12.3811	1.44910	0.724548	−	0.689224i	$-0.242049\pi$
$73$	12.3811	1.44910	0.724548	+	0.689224i	$0.242049\pi$
$74$	−4.19788	−0.487994
$75$	1.17239	0.135376
$76$	1.00000	0.114708
$77$	−15.9983	−1.82318
$78$	−0.205621	−0.0232820
$79$	−3.91819	−0.440830	−0.220415	−	0.975406i	$-0.570741\pi$
$79$	−3.91819	−0.440830	−0.220415	+	0.975406i	$0.570741\pi$
$80$	2.48443	0.277768
$81$	1.00000	0.111111
$82$	−1.86196	−0.205619
$83$	1.25650	0.137919	0.0689595	−	0.997619i	$-0.478032\pi$
$83$	1.25650	0.137919	0.0689595	+	0.997619i	$0.478032\pi$
$84$	3.12498	0.340963
$85$	−6.21413	−0.674017
$86$	−3.23362	−0.348691
$87$	3.57299	0.383065
$88$	−5.11950	−0.545740
$89$	−10.4800	−1.11088	−0.555441	−	0.831556i	$-0.687451\pi$
$89$	−10.4800	−1.11088	−0.555441	+	0.831556i	$0.687451\pi$
$90$	2.48443	0.261882
$91$	−0.642562	−0.0673588
$92$	6.16430	0.642673
$93$	3.57447	0.370655
$94$	11.3263	1.16821
$95$	2.48443	0.254897
$96$	1.00000	0.102062
$97$	0.0148062	0.00150334	0.000751670	−	1.00000i	$-0.499761\pi$
$97$	0.0148062	0.00150334	0.000751670		1.00000i	$0.499761\pi$
$98$	2.76549	0.279357
$99$	−5.11950	−0.514529
$100$	1.17239	0.117239
$101$	−13.3301	−1.32639	−0.663197	−	0.748445i	$-0.730801\pi$
$101$	−13.3301	−1.32639	−0.663197	+	0.748445i	$0.730801\pi$
$102$	−2.50123	−0.247659
$103$	−4.82699	−0.475618	−0.237809	−	0.971312i	$-0.576429\pi$
$103$	−4.82699	−0.475618	−0.237809	+	0.971312i	$0.576429\pi$
$104$	−0.205621	−0.0201628
$105$	7.76379	0.757668
$106$	−1.00000	−0.0971286
$107$	−8.50351	−0.822066	−0.411033	−	0.911621i	$-0.634832\pi$
$107$	−8.50351	−0.822066	−0.411033	+	0.911621i	$0.634832\pi$
$108$	1.00000	0.0962250
$109$	16.6190	1.59181	0.795905	−	0.605421i	$-0.206995\pi$
$109$	16.6190	1.59181	0.795905	+	0.605421i	$0.206995\pi$
$110$	−12.7190	−1.21271
$111$	−4.19788	−0.398445
$112$	3.12498	0.295283
$113$	1.23917	0.116571	0.0582855	−	0.998300i	$-0.481437\pi$
$113$	1.23917	0.116571	0.0582855	+	0.998300i	$0.481437\pi$
$114$	1.00000	0.0936586
$115$	15.3148	1.42811
$116$	3.57299	0.331744
$117$	−0.205621	−0.0190097
$118$	−0.0335822	−0.00309149
$119$	−7.81630	−0.716519
$120$	2.48443	0.226796
$121$	15.2093	1.38266
$122$	12.7311	1.15262
$123$	−1.86196	−0.167888
$124$	3.57447	0.320997
$125$	−9.50942	−0.850549
$126$	3.12498	0.278395
$127$	7.86960	0.698314	0.349157	−	0.937064i	$-0.386468\pi$
$127$	7.86960	0.698314	0.349157	+	0.937064i	$0.386468\pi$
$128$	1.00000	0.0883883
$129$	−3.23362	−0.284705
$130$	−0.510851	−0.0448046
$131$	−5.26449	−0.459961	−0.229980	−	0.973195i	$-0.573866\pi$
$131$	−5.26449	−0.459961	−0.229980	+	0.973195i	$0.573866\pi$
$132$	−5.11950	−0.445595
$133$	3.12498	0.270970
$134$	8.55473	0.739016
$135$	2.48443	0.213826
$136$	−2.50123	−0.214479
$137$	10.2032	0.871714	0.435857	−	0.900016i	$-0.356445\pi$
$137$	10.2032	0.871714	0.435857	+	0.900016i	$0.356445\pi$
$138$	6.16430	0.524740
$139$	16.1919	1.37338	0.686690	−	0.726951i	$-0.259063\pi$
$139$	16.1919	1.37338	0.686690	+	0.726951i	$0.259063\pi$
$140$	7.76379	0.656160
$141$	11.3263	0.953844
$142$	15.0639	1.26413
$143$	1.05268	0.0880293
$144$	1.00000	0.0833333
$145$	8.87684	0.737181
$146$	12.3811	1.02467
$147$	2.76549	0.228094
$148$	−4.19788	−0.345064
$149$	−3.61546	−0.296190	−0.148095	−	0.988973i	$-0.547314\pi$
$149$	−3.61546	−0.296190	−0.148095	+	0.988973i	$0.547314\pi$
$150$	1.17239	0.0957254
$151$	−16.5934	−1.35035	−0.675177	−	0.737655i	$-0.735933\pi$
$151$	−16.5934	−1.35035	−0.675177	+	0.737655i	$0.735933\pi$
$152$	1.00000	0.0811107
$153$	−2.50123	−0.202213
$154$	−15.9983	−1.28918
$155$	8.88051	0.713300
$156$	−0.205621	−0.0164629
$157$	−24.2076	−1.93198	−0.965989	−	0.258583i	$-0.916744\pi$
$157$	−24.2076	−1.93198	−0.965989	+	0.258583i	$0.916744\pi$
$158$	−3.91819	−0.311714
$159$	−1.00000	−0.0793052
$160$	2.48443	0.196411
$161$	19.2633	1.51816
$162$	1.00000	0.0785674
$163$	−3.55923	−0.278781	−0.139390	−	0.990238i	$-0.544514\pi$
$163$	−3.55923	−0.278781	−0.139390	+	0.990238i	$0.544514\pi$
$164$	−1.86196	−0.145395
$165$	−12.7190	−0.990175
$166$	1.25650	0.0975235
$167$	4.50016	0.348233	0.174117	−	0.984725i	$-0.444293\pi$
$167$	4.50016	0.348233	0.174117	+	0.984725i	$0.444293\pi$
$168$	3.12498	0.241097
$169$	−12.9577	−0.996748
$170$	−6.21413	−0.476602
$171$	1.00000	0.0764719
$172$	−3.23362	−0.246561
$173$	−9.29037	−0.706334	−0.353167	−	0.935560i	$-0.614895\pi$
$173$	−9.29037	−0.706334	−0.353167	+	0.935560i	$0.614895\pi$
$174$	3.57299	0.270868
$175$	3.66370	0.276950
$176$	−5.11950	−0.385897
$177$	−0.0335822	−0.00252419
$178$	−10.4800	−0.785512
$179$	−15.5291	−1.16070	−0.580349	−	0.814368i	$-0.697084\pi$
$179$	−15.5291	−1.16070	−0.580349	+	0.814368i	$0.697084\pi$
$180$	2.48443	0.185178
$181$	−5.81330	−0.432099	−0.216050	−	0.976382i	$-0.569317\pi$
$181$	−5.81330	−0.432099	−0.216050	+	0.976382i	$0.569317\pi$
$182$	−0.642562	−0.0476298
$183$	12.7311	0.941111
$184$	6.16430	0.454438
$185$	−10.4293	−0.766781
$186$	3.57447	0.262093
$187$	12.8050	0.936398
$188$	11.3263	0.826053
$189$	3.12498	0.227309
$190$	2.48443	0.180239
$191$	−23.8329	−1.72449	−0.862244	−	0.506494i	$-0.830941\pi$
$191$	−23.8329	−1.72449	−0.862244	+	0.506494i	$0.830941\pi$
$192$	1.00000	0.0721688
$193$	6.95830	0.500870	0.250435	−	0.968133i	$-0.419426\pi$
$193$	6.95830	0.500870	0.250435	+	0.968133i	$0.419426\pi$
$194$	0.0148062	0.00106302
$195$	−0.510851	−0.0365828
$196$	2.76549	0.197535
$197$	−17.2946	−1.23219	−0.616093	−	0.787673i	$-0.711285\pi$
$197$	−17.2946	−1.23219	−0.616093	+	0.787673i	$0.711285\pi$
$198$	−5.11950	−0.363827
$199$	−20.4320	−1.44838	−0.724192	−	0.689599i	$-0.757787\pi$
$199$	−20.4320	−1.44838	−0.724192	+	0.689599i	$0.757787\pi$
$200$	1.17239	0.0829006
$201$	8.55473	0.603404
$202$	−13.3301	−0.937902
$203$	11.1655	0.783665
$204$	−2.50123	−0.175121
$205$	−4.62592	−0.323088
$206$	−4.82699	−0.336312
$207$	6.16430	0.428448
$208$	−0.205621	−0.0142573
$209$	−5.11950	−0.354123
$210$	7.76379	0.535752
$211$	−21.6657	−1.49153	−0.745763	−	0.666212i	$-0.767915\pi$
$211$	−21.6657	−1.49153	−0.745763	+	0.666212i	$0.767915\pi$
$212$	−1.00000	−0.0686803
$213$	15.0639	1.03216
$214$	−8.50351	−0.581288
$215$	−8.03371	−0.547895
$216$	1.00000	0.0680414
$217$	11.1701	0.758278
$218$	16.6190	1.12558
$219$	12.3811	0.836636
$220$	−12.7190	−0.857517
$221$	0.514306	0.0345960
$222$	−4.19788	−0.281743
$223$	−5.79946	−0.388360	−0.194180	−	0.980966i	$-0.562205\pi$
$223$	−5.79946	−0.388360	−0.194180	+	0.980966i	$0.562205\pi$
$224$	3.12498	0.208796
$225$	1.17239	0.0781595
$226$	1.23917	0.0824281
$227$	−2.76882	−0.183773	−0.0918865	−	0.995769i	$-0.529290\pi$
$227$	−2.76882	−0.183773	−0.0918865	+	0.995769i	$0.529290\pi$
$228$	1.00000	0.0662266
$229$	21.6718	1.43212	0.716058	−	0.698041i	$-0.245945\pi$
$229$	21.6718	1.43212	0.716058	+	0.698041i	$0.245945\pi$
$230$	15.3148	1.00983
$231$	−15.9983	−1.05261
$232$	3.57299	0.234578
$233$	−25.6133	−1.67798	−0.838991	−	0.544145i	$-0.816854\pi$
$233$	−25.6133	−1.67798	−0.838991	+	0.544145i	$0.816854\pi$
$234$	−0.205621	−0.0134419
$235$	28.1393	1.83561
$236$	−0.0335822	−0.00218601
$237$	−3.91819	−0.254514
$238$	−7.81630	−0.506655
$239$	−16.6250	−1.07538	−0.537691	−	0.843142i	$-0.680703\pi$
$239$	−16.6250	−1.07538	−0.537691	+	0.843142i	$0.680703\pi$
$240$	2.48443	0.160369
$241$	13.6577	0.879771	0.439886	−	0.898054i	$-0.355019\pi$
$241$	13.6577	0.879771	0.439886	+	0.898054i	$0.355019\pi$
$242$	15.2093	0.977688
$243$	1.00000	0.0641500
$244$	12.7311	0.815026
$245$	6.87067	0.438951
$246$	−1.86196	−0.118714
$247$	−0.205621	−0.0130834
$248$	3.57447	0.226979
$249$	1.25650	0.0796276
$250$	−9.50942	−0.601429
$251$	−27.9579	−1.76468	−0.882342	−	0.470609i	$-0.844034\pi$
$251$	−27.9579	−1.76468	−0.882342	+	0.470609i	$0.844034\pi$
$252$	3.12498	0.196855
$253$	−31.5581	−1.98404
$254$	7.86960	0.493782
$255$	−6.21413	−0.389144
$256$	1.00000	0.0625000
$257$	−5.24628	−0.327254	−0.163627	−	0.986522i	$-0.552319\pi$
$257$	−5.24628	−0.327254	−0.163627	+	0.986522i	$0.552319\pi$
$258$	−3.23362	−0.201317
$259$	−13.1183	−0.815131
$260$	−0.510851	−0.0316817
$261$	3.57299	0.221162
$262$	−5.26449	−0.325241
$263$	−7.07094	−0.436013	−0.218006	−	0.975947i	$-0.569955\pi$
$263$	−7.07094	−0.436013	−0.218006	+	0.975947i	$0.569955\pi$
$264$	−5.11950	−0.315083
$265$	−2.48443	−0.152617
$266$	3.12498	0.191605
$267$	−10.4800	−0.641368
$268$	8.55473	0.522563
$269$	5.58588	0.340577	0.170289	−	0.985394i	$-0.445530\pi$
$269$	5.58588	0.340577	0.170289	+	0.985394i	$0.445530\pi$
$270$	2.48443	0.151198
$271$	5.22274	0.317259	0.158629	−	0.987338i	$-0.449292\pi$
$271$	5.22274	0.317259	0.158629	+	0.987338i	$0.449292\pi$
$272$	−2.50123	−0.151659
$273$	−0.642562	−0.0388896
$274$	10.2032	0.616395
$275$	−6.00206	−0.361938
$276$	6.16430	0.371047
$277$	−12.3692	−0.743191	−0.371596	−	0.928395i	$-0.621189\pi$
$277$	−12.3692	−0.743191	−0.371596	+	0.928395i	$0.621189\pi$
$278$	16.1919	0.971126
$279$	3.57447	0.213998
$280$	7.76379	0.463975
$281$	29.8136	1.77853	0.889265	−	0.457393i	$-0.151217\pi$
$281$	29.8136	1.77853	0.889265	+	0.457393i	$0.151217\pi$
$282$	11.3263	0.674469
$283$	−23.6526	−1.40600	−0.702999	−	0.711191i	$-0.748156\pi$
$283$	−23.6526	−1.40600	−0.702999	+	0.711191i	$0.748156\pi$
$284$	15.0639	0.893876
$285$	2.48443	0.147165
$286$	1.05268	0.0622461
$287$	−5.81859	−0.343461
$288$	1.00000	0.0589256
$289$	−10.7438	−0.631991
$290$	8.87684	0.521266
$291$	0.0148062	0.000867953 0
$292$	12.3811	0.724548
$293$	−6.90290	−0.403272	−0.201636	−	0.979461i	$-0.564626\pi$
$293$	−6.90290	−0.403272	−0.201636	+	0.979461i	$0.564626\pi$
$294$	2.76549	0.161287
$295$	−0.0834325	−0.00485763
$296$	−4.19788	−0.243997
$297$	−5.11950	−0.297063
$298$	−3.61546	−0.209438
$299$	−1.26751	−0.0733020
$300$	1.17239	0.0676881
$301$	−10.1050	−0.582443
$302$	−16.5934	−0.954845
$303$	−13.3301	−0.765794
$304$	1.00000	0.0573539
$305$	31.6296	1.81110
$306$	−2.50123	−0.142986
$307$	13.1228	0.748960	0.374480	−	0.927235i	$-0.377821\pi$
$307$	13.1228	0.748960	0.374480	+	0.927235i	$0.377821\pi$
$308$	−15.9983	−0.911589
$309$	−4.82699	−0.274598
$310$	8.88051	0.504379
$311$	−13.2498	−0.751330	−0.375665	−	0.926756i	$-0.622586\pi$
$311$	−13.2498	−0.751330	−0.375665	+	0.926756i	$0.622586\pi$
$312$	−0.205621	−0.0116410
$313$	22.6548	1.28053	0.640264	−	0.768155i	$-0.278825\pi$
$313$	22.6548	1.28053	0.640264	+	0.768155i	$0.278825\pi$
$314$	−24.2076	−1.36611
$315$	7.76379	0.437440
$316$	−3.91819	−0.220415
$317$	12.7278	0.714866	0.357433	−	0.933939i	$-0.383652\pi$
$317$	12.7278	0.714866	0.357433	+	0.933939i	$0.383652\pi$
$318$	−1.00000	−0.0560772
$319$	−18.2919	−1.02415
$320$	2.48443	0.138884
$321$	−8.50351	−0.474620
$322$	19.2633	1.07350
$323$	−2.50123	−0.139172
$324$	1.00000	0.0555556
$325$	−0.241069	−0.0133721
$326$	−3.55923	−0.197128
$327$	16.6190	0.919032
$328$	−1.86196	−0.102810
$329$	35.3943	1.95135
$330$	−12.7190	−0.700160
$331$	−18.1038	−0.995075	−0.497538	−	0.867442i	$-0.665762\pi$
$331$	−18.1038	−0.995075	−0.497538	+	0.867442i	$0.665762\pi$
$332$	1.25650	0.0689595
$333$	−4.19788	−0.230043
$334$	4.50016	0.246238
$335$	21.2536	1.16121
$336$	3.12498	0.170482
$337$	−29.5543	−1.60992	−0.804962	−	0.593326i	$-0.797815\pi$
$337$	−29.5543	−1.60992	−0.804962	+	0.593326i	$0.797815\pi$
$338$	−12.9577	−0.704807
$339$	1.23917	0.0673023
$340$	−6.21413	−0.337009
$341$	−18.2995	−0.990972
$342$	1.00000	0.0540738
$343$	−13.2327	−0.714501
$344$	−3.23362	−0.174345
$345$	15.3148	0.824520
$346$	−9.29037	−0.499453
$347$	28.2176	1.51480	0.757401	−	0.652950i	$-0.226469\pi$
$347$	28.2176	1.51480	0.757401	+	0.652950i	$0.226469\pi$
$348$	3.57299	0.191532
$349$	−18.0071	−0.963898	−0.481949	−	0.876199i	$-0.660071\pi$
$349$	−18.0071	−0.963898	−0.481949	+	0.876199i	$0.660071\pi$
$350$	3.66370	0.195833
$351$	−0.205621	−0.0109752
$352$	−5.11950	−0.272870
$353$	3.91736	0.208500	0.104250	−	0.994551i	$-0.466756\pi$
$353$	3.91736	0.208500	0.104250	+	0.994551i	$0.466756\pi$
$354$	−0.0335822	−0.00178487
$355$	37.4251	1.98632
$356$	−10.4800	−0.555441
$357$	−7.81630	−0.413682
$358$	−15.5291	−0.820738
$359$	1.33449	0.0704315	0.0352157	−	0.999380i	$-0.488788\pi$
$359$	1.33449	0.0704315	0.0352157	+	0.999380i	$0.488788\pi$
$360$	2.48443	0.130941
$361$	1.00000	0.0526316
$362$	−5.81330	−0.305540
$363$	15.2093	0.798279
$364$	−0.642562	−0.0336794
$365$	30.7599	1.61005
$366$	12.7311	0.665466
$367$	−25.9999	−1.35718	−0.678592	−	0.734516i	$-0.737409\pi$
$367$	−25.9999	−1.35718	−0.678592	+	0.734516i	$0.737409\pi$
$368$	6.16430	0.321336
$369$	−1.86196	−0.0969299
$370$	−10.4293	−0.542196
$371$	−3.12498	−0.162241
$372$	3.57447	0.185327
$373$	17.1347	0.887202	0.443601	−	0.896224i	$-0.353701\pi$
$373$	17.1347	0.887202	0.443601	+	0.896224i	$0.353701\pi$
$374$	12.8050	0.662133
$375$	−9.50942	−0.491065
$376$	11.3263	0.584107
$377$	−0.734682	−0.0378380
$378$	3.12498	0.160732
$379$	29.1281	1.49621	0.748104	−	0.663582i	$-0.230965\pi$
$379$	29.1281	1.49621	0.748104	+	0.663582i	$0.230965\pi$
$380$	2.48443	0.127449
$381$	7.86960	0.403172
$382$	−23.8329	−1.21940
$383$	−9.84728	−0.503173	−0.251586	−	0.967835i	$-0.580952\pi$
$383$	−9.84728	−0.503173	−0.251586	+	0.967835i	$0.580952\pi$
$384$	1.00000	0.0510310
$385$	−39.7467	−2.02568
$386$	6.95830	0.354168
$387$	−3.23362	−0.164374
$388$	0.0148062	0.000751670 0
$389$	17.7678	0.900863	0.450431	−	0.892811i	$-0.351270\pi$
$389$	17.7678	0.900863	0.450431	+	0.892811i	$0.351270\pi$
$390$	−0.510851	−0.0258680
$391$	−15.4183	−0.779739
$392$	2.76549	0.139678
$393$	−5.26449	−0.265558
$394$	−17.2946	−0.871287
$395$	−9.73446	−0.489794
$396$	−5.11950	−0.257264
$397$	−14.9004	−0.747830	−0.373915	−	0.927463i	$-0.621985\pi$
$397$	−14.9004	−0.747830	−0.373915	+	0.927463i	$0.621985\pi$
$398$	−20.4320	−1.02416
$399$	3.12498	0.156445
$400$	1.17239	0.0586196
$401$	−3.91125	−0.195318	−0.0976592	−	0.995220i	$-0.531136\pi$
$401$	−3.91125	−0.195318	−0.0976592	+	0.995220i	$0.531136\pi$
$402$	8.55473	0.426671
$403$	−0.734986	−0.0366123
$404$	−13.3301	−0.663197
$405$	2.48443	0.123452
$406$	11.1655	0.554135
$407$	21.4910	1.06527
$408$	−2.50123	−0.123829
$409$	37.0720	1.83309	0.916547	−	0.399928i	$-0.130965\pi$
$409$	37.0720	1.83309	0.916547	+	0.399928i	$0.130965\pi$
$410$	−4.62592	−0.228458
$411$	10.2032	0.503285
$412$	−4.82699	−0.237809
$413$	−0.104944	−0.00516393
$414$	6.16430	0.302959
$415$	3.12169	0.153238
$416$	−0.205621	−0.0100814
$417$	16.1919	0.792921
$418$	−5.11950	−0.250403
$419$	−27.2496	−1.33123	−0.665616	−	0.746295i	$-0.731831\pi$
$419$	−27.2496	−1.33123	−0.665616	+	0.746295i	$0.731831\pi$
$420$	7.76379	0.378834
$421$	20.6950	1.00861	0.504306	−	0.863525i	$-0.331748\pi$
$421$	20.6950	1.00861	0.504306	+	0.863525i	$0.331748\pi$
$422$	−21.6657	−1.05467
$423$	11.3263	0.550702
$424$	−1.00000	−0.0485643
$425$	−2.93242	−0.142243
$426$	15.0639	0.729847
$427$	39.7845	1.92531
$428$	−8.50351	−0.411033
$429$	1.05268	0.0508237
$430$	−8.03371	−0.387420
$431$	−10.6675	−0.513835	−0.256917	−	0.966433i	$-0.582707\pi$
$431$	−10.6675	−0.513835	−0.256917	+	0.966433i	$0.582707\pi$
$432$	1.00000	0.0481125
$433$	20.0675	0.964380	0.482190	−	0.876067i	$-0.339841\pi$
$433$	20.0675	0.964380	0.482190	+	0.876067i	$0.339841\pi$
$434$	11.1701	0.536184
$435$	8.87684	0.425612
$436$	16.6190	0.795905
$437$	6.16430	0.294878
$438$	12.3811	0.591591
$439$	−11.4656	−0.547222	−0.273611	−	0.961840i	$-0.588218\pi$
$439$	−11.4656	−0.547222	−0.273611	+	0.961840i	$0.588218\pi$
$440$	−12.7190	−0.606356
$441$	2.76549	0.131690
$442$	0.514306	0.0244630
$443$	−22.0400	−1.04715	−0.523576	−	0.851979i	$-0.675402\pi$
$443$	−22.0400	−1.04715	−0.523576	+	0.851979i	$0.675402\pi$
$444$	−4.19788	−0.199223
$445$	−26.0369	−1.23427
$446$	−5.79946	−0.274612
$447$	−3.61546	−0.171005
$448$	3.12498	0.147641
$449$	−18.6553	−0.880399	−0.440200	−	0.897900i	$-0.645092\pi$
$449$	−18.6553	−0.880399	−0.440200	+	0.897900i	$0.645092\pi$
$450$	1.17239	0.0552671
$451$	9.53231	0.448859
$452$	1.23917	0.0582855
$453$	−16.5934	−0.779628
$454$	−2.76882	−0.129947
$455$	−1.59640	−0.0748404
$456$	1.00000	0.0468293
$457$	8.64888	0.404578	0.202289	−	0.979326i	$-0.435162\pi$
$457$	8.64888	0.404578	0.202289	+	0.979326i	$0.435162\pi$
$458$	21.6718	1.01266
$459$	−2.50123	−0.116747
$460$	15.3148	0.714055
$461$	39.5876	1.84378	0.921890	−	0.387451i	$-0.126644\pi$
$461$	39.5876	1.84378	0.921890	+	0.387451i	$0.126644\pi$
$462$	−15.9983	−0.744309
$463$	31.8426	1.47985	0.739924	−	0.672690i	$-0.234861\pi$
$463$	31.8426	1.47985	0.739924	+	0.672690i	$0.234861\pi$
$464$	3.57299	0.165872
$465$	8.88051	0.411824
$466$	−25.6133	−1.18651
$467$	−1.66839	−0.0772038	−0.0386019	−	0.999255i	$-0.512290\pi$
$467$	−1.66839	−0.0772038	−0.0386019	+	0.999255i	$0.512290\pi$
$468$	−0.205621	−0.00950484
$469$	26.7334	1.23443
$470$	28.1393	1.29797
$471$	−24.2076	−1.11543
$472$	−0.0335822	−0.00154574
$473$	16.5545	0.761178
$474$	−3.91819	−0.179968
$475$	1.17239	0.0537930
$476$	−7.81630	−0.358259
$477$	−1.00000	−0.0457869
$478$	−16.6250	−0.760411
$479$	11.9699	0.546918	0.273459	−	0.961884i	$-0.411832\pi$
$479$	11.9699	0.546918	0.273459	+	0.961884i	$0.411832\pi$
$480$	2.48443	0.113398
$481$	0.863173	0.0393573
$482$	13.6577	0.622092
$483$	19.2633	0.876511
$484$	15.2093	0.691330
$485$	0.0367849	0.00167032
$486$	1.00000	0.0453609
$487$	41.1234	1.86348	0.931739	−	0.363128i	$-0.118291\pi$
$487$	41.1234	1.86348	0.931739	+	0.363128i	$0.118291\pi$
$488$	12.7311	0.576311
$489$	−3.55923	−0.160954
$490$	6.87067	0.310385
$491$	−20.9796	−0.946797	−0.473399	−	0.880848i	$-0.656973\pi$
$491$	−20.9796	−0.946797	−0.473399	+	0.880848i	$0.656973\pi$
$492$	−1.86196	−0.0839438
$493$	−8.93687	−0.402496
$494$	−0.205621	−0.00925133
$495$	−12.7190	−0.571678
$496$	3.57447	0.160498
$497$	47.0743	2.11157
$498$	1.25650	0.0563052
$499$	10.1204	0.453051	0.226526	−	0.974005i	$-0.427263\pi$
$499$	10.1204	0.453051	0.226526	+	0.974005i	$0.427263\pi$
$500$	−9.50942	−0.425274
$501$	4.50016	0.201053
$502$	−27.9579	−1.24782
$503$	−10.2783	−0.458286	−0.229143	−	0.973393i	$-0.573592\pi$
$503$	−10.2783	−0.458286	−0.229143	+	0.973393i	$0.573592\pi$
$504$	3.12498	0.139198
$505$	−33.1177	−1.47372
$506$	−31.5581	−1.40293
$507$	−12.9577	−0.575473
$508$	7.86960	0.349157
$509$	−33.7802	−1.49728	−0.748640	−	0.662977i	$-0.769293\pi$
$509$	−33.7802	−1.49728	−0.748640	+	0.662977i	$0.769293\pi$
$510$	−6.21413	−0.275166
$511$	38.6906	1.71157
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−5.24628	−0.231404
$515$	−11.9923	−0.528445
$516$	−3.23362	−0.142352
$517$	−57.9848	−2.55017
$518$	−13.1183	−0.576385
$519$	−9.29037	−0.407802
$520$	−0.510851	−0.0224023
$521$	4.03874	0.176941	0.0884703	−	0.996079i	$-0.471802\pi$
$521$	4.03874	0.176941	0.0884703	+	0.996079i	$0.471802\pi$
$522$	3.57299	0.156385
$523$	−43.0330	−1.88170	−0.940852	−	0.338818i	$-0.889973\pi$
$523$	−43.0330	−1.88170	−0.940852	+	0.338818i	$0.889973\pi$
$524$	−5.26449	−0.229980
$525$	3.66370	0.159897
$526$	−7.07094	−0.308308
$527$	−8.94057	−0.389457
$528$	−5.11950	−0.222798
$529$	14.9986	0.652113
$530$	−2.48443	−0.107917
$531$	−0.0335822	−0.00145734
$532$	3.12498	0.135485
$533$	0.382859	0.0165835
$534$	−10.4800	−0.453516
$535$	−21.1264	−0.913373
$536$	8.55473	0.369508
$537$	−15.5291	−0.670130
$538$	5.58588	0.240824
$539$	−14.1579	−0.609825
$540$	2.48443	0.106913
$541$	−0.0524443	−0.00225476	−0.00112738	−	0.999999i	$-0.500359\pi$
$541$	−0.0524443	−0.00225476	−0.00112738	+	0.999999i	$0.500359\pi$
$542$	5.22274	0.224336
$543$	−5.81330	−0.249473
$544$	−2.50123	−0.107239
$545$	41.2887	1.76861
$546$	−0.642562	−0.0274991
$547$	−26.8168	−1.14660	−0.573301	−	0.819345i	$-0.694337\pi$
$547$	−26.8168	−1.14660	−0.573301	+	0.819345i	$0.694337\pi$
$548$	10.2032	0.435857
$549$	12.7311	0.543351
$550$	−6.00206	−0.255929
$551$	3.57299	0.152214
$552$	6.16430	0.262370
$553$	−12.2443	−0.520679
$554$	−12.3692	−0.525516
$555$	−10.4293	−0.442701
$556$	16.1919	0.686690
$557$	37.7320	1.59876	0.799379	−	0.600828i	$-0.205162\pi$
$557$	37.7320	1.59876	0.799379	+	0.600828i	$0.205162\pi$
$558$	3.57447	0.151319
$559$	0.664901	0.0281223
$560$	7.76379	0.328080
$561$	12.8050	0.540630
$562$	29.8136	1.25761
$563$	−13.8009	−0.581637	−0.290818	−	0.956778i	$-0.593928\pi$
$563$	−13.8009	−0.581637	−0.290818	+	0.956778i	$0.593928\pi$
$564$	11.3263	0.476922
$565$	3.07862	0.129519
$566$	−23.6526	−0.994191
$567$	3.12498	0.131237
$568$	15.0639	0.632066
$569$	16.2593	0.681625	0.340813	−	0.940131i	$-0.389298\pi$
$569$	16.2593	0.681625	0.340813	+	0.940131i	$0.389298\pi$
$570$	2.48443	0.104061
$571$	9.70873	0.406298	0.203149	−	0.979148i	$-0.434882\pi$
$571$	9.70873	0.406298	0.203149	+	0.979148i	$0.434882\pi$
$572$	1.05268	0.0440146
$573$	−23.8329	−0.995633
$574$	−5.81859	−0.242863
$575$	7.22697	0.301386
$576$	1.00000	0.0416667
$577$	20.6899	0.861333	0.430667	−	0.902511i	$-0.358278\pi$
$577$	20.6899	0.861333	0.430667	+	0.902511i	$0.358278\pi$
$578$	−10.7438	−0.446885
$579$	6.95830	0.289177
$580$	8.87684	0.368591
$581$	3.92654	0.162900
$582$	0.0148062	0.000613736 0
$583$	5.11950	0.212028
$584$	12.3811	0.512333
$585$	−0.510851	−0.0211211
$586$	−6.90290	−0.285156
$587$	28.2740	1.16699	0.583496	−	0.812116i	$-0.301684\pi$
$587$	28.2740	1.16699	0.583496	+	0.812116i	$0.301684\pi$
$588$	2.76549	0.114047
$589$	3.57447	0.147283
$590$	−0.0834325	−0.00343486
$591$	−17.2946	−0.711403
$592$	−4.19788	−0.172532
$593$	−33.3598	−1.36992	−0.684960	−	0.728580i	$-0.740181\pi$
$593$	−33.3598	−1.36992	−0.684960	+	0.728580i	$0.740181\pi$
$594$	−5.11950	−0.210056
$595$	−19.4190	−0.796103
$596$	−3.61546	−0.148095
$597$	−20.4320	−0.836224
$598$	−1.26751	−0.0518323
$599$	12.9397	0.528702	0.264351	−	0.964427i	$-0.414842\pi$
$599$	12.9397	0.528702	0.264351	+	0.964427i	$0.414842\pi$
$600$	1.17239	0.0478627
$601$	46.6549	1.90309	0.951546	−	0.307507i	$-0.0994948\pi$
$601$	46.6549	1.90309	0.951546	+	0.307507i	$0.0994948\pi$
$602$	−10.1050	−0.411849
$603$	8.55473	0.348376
$604$	−16.5934	−0.675177
$605$	37.7863	1.53623
$606$	−13.3301	−0.541498
$607$	−35.2070	−1.42901	−0.714504	−	0.699631i	$-0.753348\pi$
$607$	−35.2070	−1.42901	−0.714504	+	0.699631i	$0.753348\pi$
$608$	1.00000	0.0405554
$609$	11.1655	0.452449
$610$	31.6296	1.28064
$611$	−2.32892	−0.0942180
$612$	−2.50123	−0.101106
$613$	12.7581	0.515293	0.257647	−	0.966239i	$-0.417053\pi$
$613$	12.7581	0.515293	0.257647	+	0.966239i	$0.417053\pi$
$614$	13.1228	0.529595
$615$	−4.62592	−0.186535
$616$	−15.9983	−0.644591
$617$	13.9363	0.561052	0.280526	−	0.959846i	$-0.409491\pi$
$617$	13.9363	0.561052	0.280526	+	0.959846i	$0.409491\pi$
$618$	−4.82699	−0.194170
$619$	39.1082	1.57189	0.785946	−	0.618295i	$-0.212176\pi$
$619$	39.1082	1.57189	0.785946	+	0.618295i	$0.212176\pi$
$620$	8.88051	0.356650
$621$	6.16430	0.247365
$622$	−13.2498	−0.531270
$623$	−32.7499	−1.31210
$624$	−0.205621	−0.00823143
$625$	−29.4875	−1.17950
$626$	22.6548	0.905470
$627$	−5.11950	−0.204453
$628$	−24.2076	−0.965989
$629$	10.4999	0.418657
$630$	7.76379	0.309317
$631$	31.2542	1.24421	0.622105	−	0.782934i	$-0.286278\pi$
$631$	31.2542	1.24421	0.622105	+	0.782934i	$0.286278\pi$
$632$	−3.91819	−0.155857
$633$	−21.6657	−0.861133
$634$	12.7278	0.505486
$635$	19.5515	0.775876
$636$	−1.00000	−0.0396526
$637$	−0.568644	−0.0225305
$638$	−18.2919	−0.724183
$639$	15.0639	0.595917
$640$	2.48443	0.0982057
$641$	−9.09174	−0.359102	−0.179551	−	0.983749i	$-0.557465\pi$
$641$	−9.09174	−0.359102	−0.179551	+	0.983749i	$0.557465\pi$
$642$	−8.50351	−0.335607
$643$	24.4566	0.964474	0.482237	−	0.876041i	$-0.339824\pi$
$643$	24.4566	0.964474	0.482237	+	0.876041i	$0.339824\pi$
$644$	19.2633	0.759081
$645$	−8.03371	−0.316327
$646$	−2.50123	−0.0984096
$647$	5.21169	0.204893	0.102446	−	0.994739i	$-0.467333\pi$
$647$	5.21169	0.204893	0.102446	+	0.994739i	$0.467333\pi$
$648$	1.00000	0.0392837
$649$	0.171924	0.00674860
$650$	−0.241069	−0.00945549
$651$	11.1701	0.437792
$652$	−3.55923	−0.139390
$653$	−0.844341	−0.0330416	−0.0165208	−	0.999864i	$-0.505259\pi$
$653$	−0.844341	−0.0330416	−0.0165208	+	0.999864i	$0.505259\pi$
$654$	16.6190	0.649854
$655$	−13.0793	−0.511049
$656$	−1.86196	−0.0726974
$657$	12.3811	0.483032
$658$	35.3943	1.37981
$659$	21.4982	0.837452	0.418726	−	0.908113i	$-0.362477\pi$
$659$	21.4982	0.837452	0.418726	+	0.908113i	$0.362477\pi$
$660$	−12.7190	−0.495088
$661$	−41.8826	−1.62904	−0.814522	−	0.580132i	$-0.803001\pi$
$661$	−41.8826	−1.62904	−0.814522	+	0.580132i	$0.803001\pi$
$662$	−18.1038	−0.703624
$663$	0.514306	0.0199740
$664$	1.25650	0.0487617
$665$	7.76379	0.301067
$666$	−4.19788	−0.162665
$667$	22.0250	0.852810
$668$	4.50016	0.174117
$669$	−5.79946	−0.224220
$670$	21.2536	0.821099
$671$	−65.1769	−2.51613
$672$	3.12498	0.120549
$673$	6.12223	0.235994	0.117997	−	0.993014i	$-0.462353\pi$
$673$	6.12223	0.235994	0.117997	+	0.993014i	$0.462353\pi$
$674$	−29.5543	−1.13839
$675$	1.17239	0.0451254
$676$	−12.9577	−0.498374
$677$	33.1459	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$677$	33.1459	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$678$	1.23917	0.0475899
$679$	0.0462690	0.00177564
$680$	−6.21413	−0.238301
$681$	−2.76882	−0.106101
$682$	−18.2995	−0.700723
$683$	10.7811	0.412526	0.206263	−	0.978497i	$-0.433870\pi$
$683$	10.7811	0.412526	0.206263	+	0.978497i	$0.433870\pi$
$684$	1.00000	0.0382360
$685$	25.3490	0.968536
$686$	−13.2327	−0.505229
$687$	21.6718	0.826832
$688$	−3.23362	−0.123281
$689$	0.205621	0.00783354
$690$	15.3148	0.583023
$691$	−48.6252	−1.84979	−0.924894	−	0.380224i	$-0.875847\pi$
$691$	−48.6252	−1.84979	−0.924894	+	0.380224i	$0.875847\pi$
$692$	−9.29037	−0.353167
$693$	−15.9983	−0.607726
$694$	28.2176	1.07113
$695$	40.2277	1.52592
$696$	3.57299	0.135434
$697$	4.65720	0.176404
$698$	−18.0071	−0.681579
$699$	−25.6133	−0.968783
$700$	3.66370	0.138475
$701$	−15.3877	−0.581185	−0.290592	−	0.956847i	$-0.593852\pi$
$701$	−15.3877	−0.581185	−0.290592	+	0.956847i	$0.593852\pi$
$702$	−0.205621	−0.00776067
$703$	−4.19788	−0.158326
$704$	−5.11950	−0.192948
$705$	28.1393	1.05979
$706$	3.91736	0.147432
$707$	−41.6563	−1.56664
$708$	−0.0335822	−0.00126209
$709$	−20.7840	−0.780561	−0.390280	−	0.920696i	$-0.627622\pi$
$709$	−20.7840	−0.780561	−0.390280	+	0.920696i	$0.627622\pi$
$710$	37.4251	1.40454
$711$	−3.91819	−0.146943
$712$	−10.4800	−0.392756
$713$	22.0341	0.825183
$714$	−7.81630	−0.292518
$715$	2.61530	0.0978067
$716$	−15.5291	−0.580349
$717$	−16.6250	−0.620873
$718$	1.33449	0.0498026
$719$	−10.2105	−0.380789	−0.190395	−	0.981708i	$-0.560977\pi$
$719$	−10.2105	−0.380789	−0.190395	+	0.981708i	$0.560977\pi$
$720$	2.48443	0.0925892
$721$	−15.0842	−0.561767
$722$	1.00000	0.0372161
$723$	13.6577	0.507936
$724$	−5.81330	−0.216050
$725$	4.18894	0.155573
$726$	15.2093	0.564468
$727$	39.4893	1.46458	0.732288	−	0.680995i	$-0.238453\pi$
$727$	39.4893	1.46458	0.732288	+	0.680995i	$0.238453\pi$
$728$	−0.642562	−0.0238149
$729$	1.00000	0.0370370
$730$	30.7599	1.13848
$731$	8.08804	0.299147
$732$	12.7311	0.470556
$733$	22.9148	0.846378	0.423189	−	0.906041i	$-0.360911\pi$
$733$	22.9148	0.846378	0.423189	+	0.906041i	$0.360911\pi$
$734$	−25.9999	−0.959674
$735$	6.87067	0.253429
$736$	6.16430	0.227219
$737$	−43.7959	−1.61324
$738$	−1.86196	−0.0685398
$739$	37.2318	1.36959	0.684797	−	0.728734i	$-0.259891\pi$
$739$	37.2318	1.36959	0.684797	+	0.728734i	$0.259891\pi$
$740$	−10.4293	−0.383390
$741$	−0.205621	−0.00755368
$742$	−3.12498	−0.114722
$743$	−21.0338	−0.771657	−0.385829	−	0.922571i	$-0.626084\pi$
$743$	−21.0338	−0.771657	−0.385829	+	0.922571i	$0.626084\pi$
$744$	3.57447	0.131046
$745$	−8.98235	−0.329088
$746$	17.1347	0.627347
$747$	1.25650	0.0459730
$748$	12.8050	0.468199
$749$	−26.5733	−0.970967
$750$	−9.50942	−0.347235
$751$	22.8875	0.835178	0.417589	−	0.908636i	$-0.362875\pi$
$751$	22.8875	0.835178	0.417589	+	0.908636i	$0.362875\pi$
$752$	11.3263	0.413026
$753$	−27.9579	−1.01884
$754$	−0.734682	−0.0267555
$755$	−41.2252	−1.50034
$756$	3.12498	0.113654
$757$	20.5229	0.745918	0.372959	−	0.927848i	$-0.378343\pi$
$757$	20.5229	0.745918	0.372959	+	0.927848i	$0.378343\pi$
$758$	29.1281	1.05798
$759$	−31.5581	−1.14549
$760$	2.48443	0.0901197
$761$	−12.8149	−0.464541	−0.232270	−	0.972651i	$-0.574615\pi$
$761$	−12.8149	−0.464541	−0.232270	+	0.972651i	$0.574615\pi$
$762$	7.86960	0.285085
$763$	51.9340	1.88014
$764$	−23.8329	−0.862244
$765$	−6.21413	−0.224672
$766$	−9.84728	−0.355797
$767$	0.00690520	0.000249332 0
$768$	1.00000	0.0360844
$769$	39.6972	1.43152	0.715759	−	0.698347i	$-0.246081\pi$
$769$	39.6972	1.43152	0.715759	+	0.698347i	$0.246081\pi$
$770$	−39.7467	−1.43237
$771$	−5.24628	−0.188940
$772$	6.95830	0.250435
$773$	−34.6764	−1.24722	−0.623612	−	0.781734i	$-0.714336\pi$
$773$	−34.6764	−1.24722	−0.623612	+	0.781734i	$0.714336\pi$
$774$	−3.23362	−0.116230
$775$	4.19068	0.150534
$776$	0.0148062	0.000531511 0
$777$	−13.1183	−0.470616
$778$	17.7678	0.637006
$779$	−1.86196	−0.0667117
$780$	−0.510851	−0.0182914
$781$	−77.1194	−2.75955
$782$	−15.4183	−0.551359
$783$	3.57299	0.127688
$784$	2.76549	0.0987676
$785$	−60.1421	−2.14656
$786$	−5.26449	−0.187778
$787$	−43.3170	−1.54408	−0.772041	−	0.635572i	$-0.780764\pi$
$787$	−43.3170	−1.54408	−0.772041	+	0.635572i	$0.780764\pi$
$788$	−17.2946	−0.616093
$789$	−7.07094	−0.251732
$790$	−9.73446	−0.346337
$791$	3.87237	0.137686
$792$	−5.11950	−0.181913
$793$	−2.61779	−0.0929603
$794$	−14.9004	−0.528796
$795$	−2.48443	−0.0881136
$796$	−20.4320	−0.724192
$797$	−31.9863	−1.13301	−0.566507	−	0.824057i	$-0.691706\pi$
$797$	−31.9863	−1.13301	−0.566507	+	0.824057i	$0.691706\pi$
$798$	3.12498	0.110623
$799$	−28.3296	−1.00223
$800$	1.17239	0.0414503
$801$	−10.4800	−0.370294
$802$	−3.91125	−0.138111
$803$	−63.3849	−2.23680
$804$	8.55473	0.301702
$805$	47.8583	1.68678
$806$	−0.734986	−0.0258888
$807$	5.58588	0.196632
$808$	−13.3301	−0.468951
$809$	−34.8426	−1.22500	−0.612500	−	0.790470i	$-0.709836\pi$
$809$	−34.8426	−1.22500	−0.612500	+	0.790470i	$0.709836\pi$
$810$	2.48443	0.0872940
$811$	−19.1274	−0.671653	−0.335827	−	0.941924i	$-0.609016\pi$
$811$	−19.1274	−0.671653	−0.335827	+	0.941924i	$0.609016\pi$
$812$	11.1655	0.391833
$813$	5.22274	0.183170
$814$	21.4910	0.753261
$815$	−8.84266	−0.309745
$816$	−2.50123	−0.0875606
$817$	−3.23362	−0.113130
$818$	37.0720	1.29619
$819$	−0.642562	−0.0224529
$820$	−4.62592	−0.161544
$821$	−4.04364	−0.141124	−0.0705620	−	0.997507i	$-0.522479\pi$
$821$	−4.04364	−0.141124	−0.0705620	+	0.997507i	$0.522479\pi$
$822$	10.2032	0.355876
$823$	−6.55242	−0.228403	−0.114201	−	0.993458i	$-0.536431\pi$
$823$	−6.55242	−0.228403	−0.114201	+	0.993458i	$0.536431\pi$
$824$	−4.82699	−0.168156
$825$	−6.00206	−0.208965
$826$	−0.104944	−0.00365145
$827$	−35.6180	−1.23856	−0.619279	−	0.785171i	$-0.712575\pi$
$827$	−35.6180	−1.23856	−0.619279	+	0.785171i	$0.712575\pi$
$828$	6.16430	0.214224
$829$	−17.8431	−0.619716	−0.309858	−	0.950783i	$-0.600282\pi$
$829$	−17.8431	−0.619716	−0.309858	+	0.950783i	$0.600282\pi$
$830$	3.12169	0.108355
$831$	−12.3692	−0.429082
$832$	−0.205621	−0.00712863
$833$	−6.91714	−0.239665
$834$	16.1919	0.560680
$835$	11.1803	0.386912
$836$	−5.11950	−0.177062
$837$	3.57447	0.123552
$838$	−27.2496	−0.941323
$839$	7.20559	0.248765	0.124382	−	0.992234i	$-0.460305\pi$
$839$	7.20559	0.248765	0.124382	+	0.992234i	$0.460305\pi$
$840$	7.76379	0.267876
$841$	−16.2338	−0.559785
$842$	20.6950	0.713196
$843$	29.8136	1.02683
$844$	−21.6657	−0.745763
$845$	−32.1925	−1.10746
$846$	11.3263	0.389405
$847$	47.5286	1.63310
$848$	−1.00000	−0.0343401
$849$	−23.6526	−0.811753
$850$	−2.93242	−0.100581
$851$	−25.8770	−0.887052
$852$	15.0639	0.516080
$853$	−18.6238	−0.637665	−0.318833	−	0.947811i	$-0.603291\pi$
$853$	−18.6238	−0.637665	−0.318833	+	0.947811i	$0.603291\pi$
$854$	39.7845	1.36140
$855$	2.48443	0.0849657
$856$	−8.50351	−0.290644
$857$	28.5559	0.975452	0.487726	−	0.872997i	$-0.337827\pi$
$857$	28.5559	0.975452	0.487726	+	0.872997i	$0.337827\pi$
$858$	1.05268	0.0359378
$859$	48.5241	1.65562	0.827811	−	0.561008i	$-0.189586\pi$
$859$	48.5241	1.65562	0.827811	+	0.561008i	$0.189586\pi$
$860$	−8.03371	−0.273947
$861$	−5.81859	−0.198297
$862$	−10.6675	−0.363336
$863$	8.62556	0.293618	0.146809	−	0.989165i	$-0.453100\pi$
$863$	8.62556	0.293618	0.146809	+	0.989165i	$0.453100\pi$
$864$	1.00000	0.0340207
$865$	−23.0813	−0.784787
$866$	20.0675	0.681920
$867$	−10.7438	−0.364880
$868$	11.1701	0.379139
$869$	20.0591	0.680460
$870$	8.87684	0.300953
$871$	−1.75903	−0.0596026
$872$	16.6190	0.562790
$873$	0.0148062	0.000501113 0
$874$	6.16430	0.208511
$875$	−29.7167	−1.00461
$876$	12.3811	0.418318
$877$	−35.8350	−1.21006	−0.605031	−	0.796202i	$-0.706839\pi$
$877$	−35.8350	−1.21006	−0.605031	+	0.796202i	$0.706839\pi$
$878$	−11.4656	−0.386944
$879$	−6.90290	−0.232829
$880$	−12.7190	−0.428758
$881$	0.474716	0.0159936	0.00799679	−	0.999968i	$-0.497455\pi$
$881$	0.474716	0.0159936	0.00799679	+	0.999968i	$0.497455\pi$
$882$	2.76549	0.0931190
$883$	4.51128	0.151817	0.0759083	−	0.997115i	$-0.475814\pi$
$883$	4.51128	0.151817	0.0759083	+	0.997115i	$0.475814\pi$
$884$	0.514306	0.0172980
$885$	−0.0834325	−0.00280455
$886$	−22.0400	−0.740449
$887$	0.452304	0.0151869	0.00759344	−	0.999971i	$-0.497583\pi$
$887$	0.452304	0.0151869	0.00759344	+	0.999971i	$0.497583\pi$
$888$	−4.19788	−0.140872
$889$	24.5923	0.824800
$890$	−26.0369	−0.872760
$891$	−5.11950	−0.171510
$892$	−5.79946	−0.194180
$893$	11.3263	0.379019
$894$	−3.61546	−0.120919
$895$	−38.5809	−1.28962
$896$	3.12498	0.104398
$897$	−1.26751	−0.0423209
$898$	−18.6553	−0.622536
$899$	12.7715	0.425954
$900$	1.17239	0.0390797
$901$	2.50123	0.0833281
$902$	9.53231	0.317391
$903$	−10.1050	−0.336274
$904$	1.23917	0.0412141
$905$	−14.4427	−0.480093
$906$	−16.5934	−0.551280
$907$	−30.8581	−1.02462	−0.512312	−	0.858799i	$-0.671211\pi$
$907$	−30.8581	−1.02462	−0.512312	+	0.858799i	$0.671211\pi$
$908$	−2.76882	−0.0918865
$909$	−13.3301	−0.442131
$910$	−1.59640	−0.0529201
$911$	28.1310	0.932023	0.466011	−	0.884779i	$-0.345691\pi$
$911$	28.1310	0.932023	0.466011	+	0.884779i	$0.345691\pi$
$912$	1.00000	0.0331133
$913$	−6.43266	−0.212890
$914$	8.64888	0.286080
$915$	31.6296	1.04564
$916$	21.6718	0.716058
$917$	−16.4514	−0.543274
$918$	−2.50123	−0.0825529
$919$	−16.2952	−0.537529	−0.268765	−	0.963206i	$-0.586615\pi$
$919$	−16.2952	−0.537529	−0.268765	+	0.963206i	$0.586615\pi$
$920$	15.3148	0.504913
$921$	13.1228	0.432412
$922$	39.5876	1.30375
$923$	−3.09745	−0.101954
$924$	−15.9983	−0.526306
$925$	−4.92156	−0.161820
$926$	31.8426	1.04641
$927$	−4.82699	−0.158539
$928$	3.57299	0.117289
$929$	−17.8996	−0.587268	−0.293634	−	0.955918i	$-0.594865\pi$
$929$	−17.8996	−0.587268	−0.293634	+	0.955918i	$0.594865\pi$
$930$	8.88051	0.291203
$931$	2.76549	0.0906354
$932$	−25.6133	−0.838991
$933$	−13.2498	−0.433780
$934$	−1.66839	−0.0545913
$935$	31.8132	1.04040
$936$	−0.205621	−0.00672094
$937$	44.3886	1.45011	0.725056	−	0.688689i	$-0.241814\pi$
$937$	44.3886	1.45011	0.725056	+	0.688689i	$0.241814\pi$
$938$	26.7334	0.872875
$939$	22.6548	0.739313
$940$	28.1393	0.917803
$941$	22.5182	0.734074	0.367037	−	0.930206i	$-0.380372\pi$
$941$	22.5182	0.734074	0.367037	+	0.930206i	$0.380372\pi$
$942$	−24.2076	−0.788727
$943$	−11.4777	−0.373765
$944$	−0.0335822	−0.00109301
$945$	7.76379	0.252556
$946$	16.5545	0.538234
$947$	−54.4391	−1.76903	−0.884517	−	0.466508i	$-0.845512\pi$
$947$	−54.4391	−1.76903	−0.884517	+	0.466508i	$0.845512\pi$
$948$	−3.91819	−0.127257
$949$	−2.54581	−0.0826405
$950$	1.17239	0.0380374
$951$	12.7278	0.412728
$952$	−7.81630	−0.253328
$953$	−36.7869	−1.19164	−0.595822	−	0.803117i	$-0.703174\pi$
$953$	−36.7869	−1.19164	−0.595822	+	0.803117i	$0.703174\pi$
$954$	−1.00000	−0.0323762
$955$	−59.2111	−1.91603
$956$	−16.6250	−0.537691
$957$	−18.2919	−0.591293
$958$	11.9699	0.386729
$959$	31.8846	1.02961
$960$	2.48443	0.0801846
$961$	−18.2232	−0.587845
$962$	0.863173	0.0278298
$963$	−8.50351	−0.274022
$964$	13.6577	0.439886
$965$	17.2874	0.556502
$966$	19.2633	0.619787
$967$	35.2201	1.13260	0.566301	−	0.824199i	$-0.308374\pi$
$967$	35.2201	1.13260	0.566301	+	0.824199i	$0.308374\pi$
$968$	15.2093	0.488844
$969$	−2.50123	−0.0803511
$970$	0.0367849	0.00118109
$971$	50.3544	1.61595	0.807974	−	0.589218i	$-0.200564\pi$
$971$	50.3544	1.61595	0.807974	+	0.589218i	$0.200564\pi$
$972$	1.00000	0.0320750
$973$	50.5994	1.62214
$974$	41.1234	1.31768
$975$	−0.241069	−0.00772037
$976$	12.7311	0.407513
$977$	−4.45082	−0.142394	−0.0711972	−	0.997462i	$-0.522682\pi$
$977$	−4.45082	−0.142394	−0.0711972	+	0.997462i	$0.522682\pi$
$978$	−3.55923	−0.113812
$979$	53.6526	1.71474
$980$	6.87067	0.219476
$981$	16.6190	0.530604
$982$	−20.9796	−0.669487
$983$	−33.4134	−1.06572	−0.532862	−	0.846202i	$-0.678883\pi$
$983$	−33.4134	−1.06572	−0.532862	+	0.846202i	$0.678883\pi$
$984$	−1.86196	−0.0593572
$985$	−42.9671	−1.36905
$986$	−8.93687	−0.284608
$987$	35.3943	1.12661
$988$	−0.205621	−0.00654168
$989$	−19.9330	−0.633833
$990$	−12.7190	−0.404237
$991$	24.8029	0.787891	0.393945	−	0.919134i	$-0.371110\pi$
$991$	24.8029	0.787891	0.393945	+	0.919134i	$0.371110\pi$
$992$	3.57447	0.113489
$993$	−18.1038	−0.574507
$994$	47.0743	1.49310
$995$	−50.7618	−1.60926
$996$	1.25650	0.0398138
$997$	1.33066	0.0421424	0.0210712	−	0.999778i	$-0.493292\pi$
$997$	1.33066	0.0421424	0.0210712	+	0.999778i	$0.493292\pi$
$998$	10.1204	0.320356
$999$	−4.19788	−0.132815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bh.1.11	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bh.1.11	✓	13	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.48443 q^{5} +1.00000 q^{6} +3.12498 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.48443 q^{5} +1.00000 q^{6} +3.12498 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.48443 q^{10} -5.11950 q^{11} +1.00000 q^{12} -0.205621 q^{13} +3.12498 q^{14} +2.48443 q^{15} +1.00000 q^{16} -2.50123 q^{17} +1.00000 q^{18} +1.00000 q^{19} +2.48443 q^{20} +3.12498 q^{21} -5.11950 q^{22} +6.16430 q^{23} +1.00000 q^{24} +1.17239 q^{25} -0.205621 q^{26} +1.00000 q^{27} +3.12498 q^{28} +3.57299 q^{29} +2.48443 q^{30} +3.57447 q^{31} +1.00000 q^{32} -5.11950 q^{33} -2.50123 q^{34} +7.76379 q^{35} +1.00000 q^{36} -4.19788 q^{37} +1.00000 q^{38} -0.205621 q^{39} +2.48443 q^{40} -1.86196 q^{41} +3.12498 q^{42} -3.23362 q^{43} -5.11950 q^{44} +2.48443 q^{45} +6.16430 q^{46} +11.3263 q^{47} +1.00000 q^{48} +2.76549 q^{49} +1.17239 q^{50} -2.50123 q^{51} -0.205621 q^{52} -1.00000 q^{53} +1.00000 q^{54} -12.7190 q^{55} +3.12498 q^{56} +1.00000 q^{57} +3.57299 q^{58} -0.0335822 q^{59} +2.48443 q^{60} +12.7311 q^{61} +3.57447 q^{62} +3.12498 q^{63} +1.00000 q^{64} -0.510851 q^{65} -5.11950 q^{66} +8.55473 q^{67} -2.50123 q^{68} +6.16430 q^{69} +7.76379 q^{70} +15.0639 q^{71} +1.00000 q^{72} +12.3811 q^{73} -4.19788 q^{74} +1.17239 q^{75} +1.00000 q^{76} -15.9983 q^{77} -0.205621 q^{78} -3.91819 q^{79} +2.48443 q^{80} +1.00000 q^{81} -1.86196 q^{82} +1.25650 q^{83} +3.12498 q^{84} -6.21413 q^{85} -3.23362 q^{86} +3.57299 q^{87} -5.11950 q^{88} -10.4800 q^{89} +2.48443 q^{90} -0.642562 q^{91} +6.16430 q^{92} +3.57447 q^{93} +11.3263 q^{94} +2.48443 q^{95} +1.00000 q^{96} +0.0148062 q^{97} +2.76549 q^{98} -5.11950 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 4 q^{11} + 13 q^{12} + 18 q^{13} + 12 q^{14} + 3 q^{15} + 13 q^{16} + 3 q^{17} + 13 q^{18} + 13 q^{19} + 3 q^{20} + 12 q^{21} + 4 q^{22} + 8 q^{23} + 13 q^{24} + 24 q^{25} + 18 q^{26} + 13 q^{27} + 12 q^{28} + 11 q^{29} + 3 q^{30} + 2 q^{31} + 13 q^{32} + 4 q^{33} + 3 q^{34} - 6 q^{35} + 13 q^{36} + 26 q^{37} + 13 q^{38} + 18 q^{39} + 3 q^{40} + 3 q^{41} + 12 q^{42} + 24 q^{43} + 4 q^{44} + 3 q^{45} + 8 q^{46} + 4 q^{47} + 13 q^{48} + 41 q^{49} + 24 q^{50} + 3 q^{51} + 18 q^{52} - 13 q^{53} + 13 q^{54} + 23 q^{55} + 12 q^{56} + 13 q^{57} + 11 q^{58} + 8 q^{59} + 3 q^{60} + 29 q^{61} + 2 q^{62} + 12 q^{63} + 13 q^{64} + 13 q^{65} + 4 q^{66} - 5 q^{67} + 3 q^{68} + 8 q^{69} - 6 q^{70} + 29 q^{71} + 13 q^{72} + 15 q^{73} + 26 q^{74} + 24 q^{75} + 13 q^{76} + 3 q^{77} + 18 q^{78} + 15 q^{79} + 3 q^{80} + 13 q^{81} + 3 q^{82} + 4 q^{83} + 12 q^{84} - q^{85} + 24 q^{86} + 11 q^{87} + 4 q^{88} + 3 q^{89} + 3 q^{90} - 29 q^{91} + 8 q^{92} + 2 q^{93} + 4 q^{94} + 3 q^{95} + 13 q^{96} + 50 q^{97} + 41 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 4 * q^11 + 13 * q^12 + 18 * q^13 + 12 * q^14 + 3 * q^15 + 13 * q^16 + 3 * q^17 + 13 * q^18 + 13 * q^19 + 3 * q^20 + 12 * q^21 + 4 * q^22 + 8 * q^23 + 13 * q^24 + 24 * q^25 + 18 * q^26 + 13 * q^27 + 12 * q^28 + 11 * q^29 + 3 * q^30 + 2 * q^31 + 13 * q^32 + 4 * q^33 + 3 * q^34 - 6 * q^35 + 13 * q^36 + 26 * q^37 + 13 * q^38 + 18 * q^39 + 3 * q^40 + 3 * q^41 + 12 * q^42 + 24 * q^43 + 4 * q^44 + 3 * q^45 + 8 * q^46 + 4 * q^47 + 13 * q^48 + 41 * q^49 + 24 * q^50 + 3 * q^51 + 18 * q^52 - 13 * q^53 + 13 * q^54 + 23 * q^55 + 12 * q^56 + 13 * q^57 + 11 * q^58 + 8 * q^59 + 3 * q^60 + 29 * q^61 + 2 * q^62 + 12 * q^63 + 13 * q^64 + 13 * q^65 + 4 * q^66 - 5 * q^67 + 3 * q^68 + 8 * q^69 - 6 * q^70 + 29 * q^71 + 13 * q^72 + 15 * q^73 + 26 * q^74 + 24 * q^75 + 13 * q^76 + 3 * q^77 + 18 * q^78 + 15 * q^79 + 3 * q^80 + 13 * q^81 + 3 * q^82 + 4 * q^83 + 12 * q^84 - q^85 + 24 * q^86 + 11 * q^87 + 4 * q^88 + 3 * q^89 + 3 * q^90 - 29 * q^91 + 8 * q^92 + 2 * q^93 + 4 * q^94 + 3 * q^95 + 13 * q^96 + 50 * q^97 + 41 * q^98 + 4 * q^99

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