LMFDB - Embedded newform 6042.2.a.bh.1.3

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			1.3
Root			$-2.34301$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.34301 q^{5} +1.00000 q^{6} +4.92290 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.34301 q^{5} +1.00000 q^{6} +4.92290 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.34301 q^{10} +0.147355 q^{11} +1.00000 q^{12} -3.88581 q^{13} +4.92290 q^{14} -2.34301 q^{15} +1.00000 q^{16} +7.05730 q^{17} +1.00000 q^{18} +1.00000 q^{19} -2.34301 q^{20} +4.92290 q^{21} +0.147355 q^{22} +2.33985 q^{23} +1.00000 q^{24} +0.489694 q^{25} -3.88581 q^{26} +1.00000 q^{27} +4.92290 q^{28} -0.861761 q^{29} -2.34301 q^{30} -1.37440 q^{31} +1.00000 q^{32} +0.147355 q^{33} +7.05730 q^{34} -11.5344 q^{35} +1.00000 q^{36} +11.3128 q^{37} +1.00000 q^{38} -3.88581 q^{39} -2.34301 q^{40} +4.12566 q^{41} +4.92290 q^{42} -9.14475 q^{43} +0.147355 q^{44} -2.34301 q^{45} +2.33985 q^{46} -12.6928 q^{47} +1.00000 q^{48} +17.2350 q^{49} +0.489694 q^{50} +7.05730 q^{51} -3.88581 q^{52} -1.00000 q^{53} +1.00000 q^{54} -0.345254 q^{55} +4.92290 q^{56} +1.00000 q^{57} -0.861761 q^{58} +11.6526 q^{59} -2.34301 q^{60} +1.78247 q^{61} -1.37440 q^{62} +4.92290 q^{63} +1.00000 q^{64} +9.10450 q^{65} +0.147355 q^{66} +0.00540667 q^{67} +7.05730 q^{68} +2.33985 q^{69} -11.5344 q^{70} +6.38625 q^{71} +1.00000 q^{72} +8.90858 q^{73} +11.3128 q^{74} +0.489694 q^{75} +1.00000 q^{76} +0.725414 q^{77} -3.88581 q^{78} +3.67761 q^{79} -2.34301 q^{80} +1.00000 q^{81} +4.12566 q^{82} -13.7085 q^{83} +4.92290 q^{84} -16.5353 q^{85} -9.14475 q^{86} -0.861761 q^{87} +0.147355 q^{88} -13.9349 q^{89} -2.34301 q^{90} -19.1295 q^{91} +2.33985 q^{92} -1.37440 q^{93} -12.6928 q^{94} -2.34301 q^{95} +1.00000 q^{96} +11.9850 q^{97} +17.2350 q^{98} +0.147355 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.34301	−1.04783	−0.523913	−	0.851772i	$-0.675528\pi$
$5$	−2.34301	−1.04783	−0.523913	+	0.851772i	$0.675528\pi$
$6$	1.00000	0.408248
$7$	4.92290	1.86068	0.930342	−	0.366694i	$-0.119510\pi$
$7$	4.92290	1.86068	0.930342	+	0.366694i	$0.119510\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.34301	−0.740925
$11$	0.147355	0.0444292	0.0222146	−	0.999753i	$-0.492928\pi$
$11$	0.147355	0.0444292	0.0222146	+	0.999753i	$0.492928\pi$
$12$	1.00000	0.288675
$13$	−3.88581	−1.07773	−0.538865	−	0.842392i	$-0.681147\pi$
$13$	−3.88581	−1.07773	−0.538865	+	0.842392i	$0.681147\pi$
$14$	4.92290	1.31570
$15$	−2.34301	−0.604962
$16$	1.00000	0.250000
$17$	7.05730	1.71165	0.855823	−	0.517268i	$-0.173051\pi$
$17$	7.05730	1.71165	0.855823	+	0.517268i	$0.173051\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.34301	−0.523913
$21$	4.92290	1.07427
$22$	0.147355	0.0314162
$23$	2.33985	0.487892	0.243946	−	0.969789i	$-0.421558\pi$
$23$	2.33985	0.487892	0.243946	+	0.969789i	$0.421558\pi$
$24$	1.00000	0.204124
$25$	0.489694	0.0979387
$26$	−3.88581	−0.762071
$27$	1.00000	0.192450
$28$	4.92290	0.930342
$29$	−0.861761	−0.160025	−0.0800125	−	0.996794i	$-0.525496\pi$
$29$	−0.861761	−0.160025	−0.0800125	+	0.996794i	$0.525496\pi$
$30$	−2.34301	−0.427773
$31$	−1.37440	−0.246850	−0.123425	−	0.992354i	$-0.539388\pi$
$31$	−1.37440	−0.246850	−0.123425	+	0.992354i	$0.539388\pi$
$32$	1.00000	0.176777
$33$	0.147355	0.0256512
$34$	7.05730	1.21032
$35$	−11.5344	−1.94967
$36$	1.00000	0.166667
$37$	11.3128	1.85981	0.929905	−	0.367800i	$-0.119889\pi$
$37$	11.3128	1.85981	0.929905	+	0.367800i	$0.119889\pi$
$38$	1.00000	0.162221
$39$	−3.88581	−0.622228
$40$	−2.34301	−0.370462
$41$	4.12566	0.644319	0.322160	−	0.946685i	$-0.395591\pi$
$41$	4.12566	0.644319	0.322160	+	0.946685i	$0.395591\pi$
$42$	4.92290	0.759621
$43$	−9.14475	−1.39456	−0.697280	−	0.716799i	$-0.745607\pi$
$43$	−9.14475	−1.39456	−0.697280	+	0.716799i	$0.745607\pi$
$44$	0.147355	0.0222146
$45$	−2.34301	−0.349275
$46$	2.33985	0.344992
$47$	−12.6928	−1.85143	−0.925715	−	0.378221i	$-0.876536\pi$
$47$	−12.6928	−1.85143	−0.925715	+	0.378221i	$0.876536\pi$
$48$	1.00000	0.144338
$49$	17.2350	2.46214
$50$	0.489694	0.0692531
$51$	7.05730	0.988220
$52$	−3.88581	−0.538865
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.00000	0.136083
$55$	−0.345254	−0.0465540
$56$	4.92290	0.657851
$57$	1.00000	0.132453
$58$	−0.861761	−0.113155
$59$	11.6526	1.51704	0.758522	−	0.651648i	$-0.225922\pi$
$59$	11.6526	1.51704	0.758522	+	0.651648i	$0.225922\pi$
$60$	−2.34301	−0.302481
$61$	1.78247	0.228222	0.114111	−	0.993468i	$-0.463598\pi$
$61$	1.78247	0.228222	0.114111	+	0.993468i	$0.463598\pi$
$62$	−1.37440	−0.174549
$63$	4.92290	0.620228
$64$	1.00000	0.125000
$65$	9.10450	1.12927
$66$	0.147355	0.0181381
$67$	0.00540667	0.000660530 0	0.000330265	−	1.00000i	$-0.499895\pi$
$67$	0.00540667	0.000660530 0	0.000330265		1.00000i	$0.499895\pi$
$68$	7.05730	0.855823
$69$	2.33985	0.281685
$70$	−11.5344	−1.37863
$71$	6.38625	0.757908	0.378954	−	0.925415i	$-0.376284\pi$
$71$	6.38625	0.757908	0.378954	+	0.925415i	$0.376284\pi$
$72$	1.00000	0.117851
$73$	8.90858	1.04267	0.521335	−	0.853352i	$-0.325434\pi$
$73$	8.90858	1.04267	0.521335	+	0.853352i	$0.325434\pi$
$74$	11.3128	1.31508
$75$	0.489694	0.0565449
$76$	1.00000	0.114708
$77$	0.725414	0.0826686
$78$	−3.88581	−0.439982
$79$	3.67761	0.413763	0.206882	−	0.978366i	$-0.433668\pi$
$79$	3.67761	0.413763	0.206882	+	0.978366i	$0.433668\pi$
$80$	−2.34301	−0.261956
$81$	1.00000	0.111111
$82$	4.12566	0.455603
$83$	−13.7085	−1.50470	−0.752351	−	0.658763i	$-0.771080\pi$
$83$	−13.7085	−1.50470	−0.752351	+	0.658763i	$0.771080\pi$
$84$	4.92290	0.537133
$85$	−16.5353	−1.79351
$86$	−9.14475	−0.986103
$87$	−0.861761	−0.0923905
$88$	0.147355	0.0157081
$89$	−13.9349	−1.47709	−0.738546	−	0.674203i	$-0.764487\pi$
$89$	−13.9349	−1.47709	−0.738546	+	0.674203i	$0.764487\pi$
$90$	−2.34301	−0.246975
$91$	−19.1295	−2.00532
$92$	2.33985	0.243946
$93$	−1.37440	−0.142519
$94$	−12.6928	−1.30916
$95$	−2.34301	−0.240388
$96$	1.00000	0.102062
$97$	11.9850	1.21689	0.608444	−	0.793597i	$-0.291794\pi$
$97$	11.9850	1.21689	0.608444	+	0.793597i	$0.291794\pi$
$98$	17.2350	1.74100
$99$	0.147355	0.0148097
$100$	0.489694	0.0489694
$101$	3.93792	0.391838	0.195919	−	0.980620i	$-0.437231\pi$
$101$	3.93792	0.391838	0.195919	+	0.980620i	$0.437231\pi$
$102$	7.05730	0.698777
$103$	8.00908	0.789158	0.394579	−	0.918862i	$-0.370890\pi$
$103$	8.00908	0.789158	0.394579	+	0.918862i	$0.370890\pi$
$104$	−3.88581	−0.381035
$105$	−11.5344	−1.12564
$106$	−1.00000	−0.0971286
$107$	−17.2139	−1.66413	−0.832063	−	0.554681i	$-0.812840\pi$
$107$	−17.2139	−1.66413	−0.832063	+	0.554681i	$0.812840\pi$
$108$	1.00000	0.0962250
$109$	−14.1920	−1.35934	−0.679672	−	0.733517i	$-0.737878\pi$
$109$	−14.1920	−1.35934	−0.679672	+	0.733517i	$0.737878\pi$
$110$	−0.345254	−0.0329187
$111$	11.3128	1.07376
$112$	4.92290	0.465171
$113$	13.5779	1.27731	0.638653	−	0.769495i	$-0.279492\pi$
$113$	13.5779	1.27731	0.638653	+	0.769495i	$0.279492\pi$
$114$	1.00000	0.0936586
$115$	−5.48228	−0.511226
$116$	−0.861761	−0.0800125
$117$	−3.88581	−0.359244
$118$	11.6526	1.07271
$119$	34.7424	3.18483
$120$	−2.34301	−0.213887
$121$	−10.9783	−0.998026
$122$	1.78247	0.161377
$123$	4.12566	0.371998
$124$	−1.37440	−0.123425
$125$	10.5677	0.945203
$126$	4.92290	0.438567
$127$	11.9281	1.05845	0.529223	−	0.848483i	$-0.322483\pi$
$127$	11.9281	1.05845	0.529223	+	0.848483i	$0.322483\pi$
$128$	1.00000	0.0883883
$129$	−9.14475	−0.805150
$130$	9.10450	0.798517
$131$	−9.73109	−0.850209	−0.425104	−	0.905144i	$-0.639763\pi$
$131$	−9.73109	−0.850209	−0.425104	+	0.905144i	$0.639763\pi$
$132$	0.147355	0.0128256
$133$	4.92290	0.426870
$134$	0.00540667	0.000467065 0
$135$	−2.34301	−0.201654
$136$	7.05730	0.605159
$137$	−0.770416	−0.0658211	−0.0329105	−	0.999458i	$-0.510478\pi$
$137$	−0.770416	−0.0658211	−0.0329105	+	0.999458i	$0.510478\pi$
$138$	2.33985	0.199181
$139$	8.17197	0.693138	0.346569	−	0.938025i	$-0.387347\pi$
$139$	8.17197	0.693138	0.346569	+	0.938025i	$0.387347\pi$
$140$	−11.5344	−0.974836
$141$	−12.6928	−1.06892
$142$	6.38625	0.535922
$143$	−0.572594	−0.0478827
$144$	1.00000	0.0833333
$145$	2.01911	0.167678
$146$	8.90858	0.737280
$147$	17.2350	1.42152
$148$	11.3128	0.929905
$149$	15.7470	1.29005	0.645023	−	0.764163i	$-0.276848\pi$
$149$	15.7470	1.29005	0.645023	+	0.764163i	$0.276848\pi$
$150$	0.489694	0.0399833
$151$	11.0970	0.903064	0.451532	−	0.892255i	$-0.350878\pi$
$151$	11.0970	0.903064	0.451532	+	0.892255i	$0.350878\pi$
$152$	1.00000	0.0811107
$153$	7.05730	0.570549
$154$	0.725414	0.0584555
$155$	3.22023	0.258655
$156$	−3.88581	−0.311114
$157$	7.60704	0.607108	0.303554	−	0.952814i	$-0.401827\pi$
$157$	7.60704	0.607108	0.303554	+	0.952814i	$0.401827\pi$
$158$	3.67761	0.292575
$159$	−1.00000	−0.0793052
$160$	−2.34301	−0.185231
$161$	11.5188	0.907812
$162$	1.00000	0.0785674
$163$	14.1951	1.11184	0.555922	−	0.831235i	$-0.312365\pi$
$163$	14.1951	1.11184	0.555922	+	0.831235i	$0.312365\pi$
$164$	4.12566	0.322160
$165$	−0.345254	−0.0268780
$166$	−13.7085	−1.06398
$167$	−1.11876	−0.0865722	−0.0432861	−	0.999063i	$-0.513783\pi$
$167$	−1.11876	−0.0865722	−0.0432861	+	0.999063i	$0.513783\pi$
$168$	4.92290	0.379810
$169$	2.09955	0.161504
$170$	−16.5353	−1.26820
$171$	1.00000	0.0764719
$172$	−9.14475	−0.697280
$173$	3.10366	0.235967	0.117983	−	0.993016i	$-0.462357\pi$
$173$	3.10366	0.235967	0.117983	+	0.993016i	$0.462357\pi$
$174$	−0.861761	−0.0653300
$175$	2.41071	0.182233
$176$	0.147355	0.0111073
$177$	11.6526	0.875865
$178$	−13.9349	−1.04446
$179$	−22.4844	−1.68057	−0.840283	−	0.542148i	$-0.817611\pi$
$179$	−22.4844	−1.68057	−0.840283	+	0.542148i	$0.817611\pi$
$180$	−2.34301	−0.174638
$181$	−6.64731	−0.494091	−0.247046	−	0.969004i	$-0.579460\pi$
$181$	−6.64731	−0.494091	−0.247046	+	0.969004i	$0.579460\pi$
$182$	−19.1295	−1.41797
$183$	1.78247	0.131764
$184$	2.33985	0.172496
$185$	−26.5060	−1.94876
$186$	−1.37440	−0.100776
$187$	1.03993	0.0760471
$188$	−12.6928	−0.925715
$189$	4.92290	0.358089
$190$	−2.34301	−0.169980
$191$	5.88726	0.425987	0.212994	−	0.977054i	$-0.431679\pi$
$191$	5.88726	0.425987	0.212994	+	0.977054i	$0.431679\pi$
$192$	1.00000	0.0721688
$193$	25.0147	1.80060	0.900298	−	0.435275i	$-0.143349\pi$
$193$	25.0147	1.80060	0.900298	+	0.435275i	$0.143349\pi$
$194$	11.9850	0.860470
$195$	9.10450	0.651987
$196$	17.2350	1.23107
$197$	−18.7543	−1.33619	−0.668095	−	0.744076i	$-0.732890\pi$
$197$	−18.7543	−1.33619	−0.668095	+	0.744076i	$0.732890\pi$
$198$	0.147355	0.0104721
$199$	13.9720	0.990450	0.495225	−	0.868765i	$-0.335086\pi$
$199$	13.9720	0.990450	0.495225	+	0.868765i	$0.335086\pi$
$200$	0.489694	0.0346266
$201$	0.00540667	0.000381357 0
$202$	3.93792	0.277071
$203$	−4.24237	−0.297756
$204$	7.05730	0.494110
$205$	−9.66645	−0.675134
$206$	8.00908	0.558019
$207$	2.33985	0.162631
$208$	−3.88581	−0.269433
$209$	0.147355	0.0101928
$210$	−11.5344	−0.795950
$211$	−20.6913	−1.42444	−0.712222	−	0.701954i	$-0.752311\pi$
$211$	−20.6913	−1.42444	−0.712222	+	0.701954i	$0.752311\pi$
$212$	−1.00000	−0.0686803
$213$	6.38625	0.437579
$214$	−17.2139	−1.17672
$215$	21.4262	1.46126
$216$	1.00000	0.0680414
$217$	−6.76604	−0.459309
$218$	−14.1920	−0.961201
$219$	8.90858	0.601986
$220$	−0.345254	−0.0232770
$221$	−27.4234	−1.84469
$222$	11.3128	0.759264
$223$	−3.70739	−0.248265	−0.124133	−	0.992266i	$-0.539615\pi$
$223$	−3.70739	−0.248265	−0.124133	+	0.992266i	$0.539615\pi$
$224$	4.92290	0.328925
$225$	0.489694	0.0326462
$226$	13.5779	0.903192
$227$	12.1558	0.806806	0.403403	−	0.915022i	$-0.367827\pi$
$227$	12.1558	0.806806	0.403403	+	0.915022i	$0.367827\pi$
$228$	1.00000	0.0662266
$229$	11.0978	0.733360	0.366680	−	0.930347i	$-0.380494\pi$
$229$	11.0978	0.733360	0.366680	+	0.930347i	$0.380494\pi$
$230$	−5.48228	−0.361491
$231$	0.725414	0.0477288
$232$	−0.861761	−0.0565774
$233$	−22.5811	−1.47934	−0.739670	−	0.672970i	$-0.765018\pi$
$233$	−22.5811	−1.47934	−0.739670	+	0.672970i	$0.765018\pi$
$234$	−3.88581	−0.254024
$235$	29.7393	1.93998
$236$	11.6526	0.758522
$237$	3.67761	0.238886
$238$	34.7424	2.25202
$239$	−24.9397	−1.61321	−0.806607	−	0.591089i	$-0.798698\pi$
$239$	−24.9397	−1.61321	−0.806607	+	0.591089i	$0.798698\pi$
$240$	−2.34301	−0.151241
$241$	−9.93150	−0.639744	−0.319872	−	0.947461i	$-0.603640\pi$
$241$	−9.93150	−0.639744	−0.319872	+	0.947461i	$0.603640\pi$
$242$	−10.9783	−0.705711
$243$	1.00000	0.0641500
$244$	1.78247	0.114111
$245$	−40.3818	−2.57990
$246$	4.12566	0.263042
$247$	−3.88581	−0.247248
$248$	−1.37440	−0.0872745
$249$	−13.7085	−0.868740
$250$	10.5677	0.668359
$251$	−6.51281	−0.411085	−0.205542	−	0.978648i	$-0.565896\pi$
$251$	−6.51281	−0.411085	−0.205542	+	0.978648i	$0.565896\pi$
$252$	4.92290	0.310114
$253$	0.344788	0.0216766
$254$	11.9281	0.748435
$255$	−16.5353	−1.03548
$256$	1.00000	0.0625000
$257$	−12.8633	−0.802388	−0.401194	−	0.915993i	$-0.631405\pi$
$257$	−12.8633	−0.802388	−0.401194	+	0.915993i	$0.631405\pi$
$258$	−9.14475	−0.569327
$259$	55.6917	3.46052
$260$	9.10450	0.564637
$261$	−0.861761	−0.0533417
$262$	−9.73109	−0.601188
$263$	22.3403	1.37756	0.688780	−	0.724970i	$-0.258147\pi$
$263$	22.3403	1.37756	0.688780	+	0.724970i	$0.258147\pi$
$264$	0.147355	0.00906907
$265$	2.34301	0.143930
$266$	4.92290	0.301843
$267$	−13.9349	−0.852800
$268$	0.00540667	0.000330265 0
$269$	−23.2857	−1.41975	−0.709876	−	0.704327i	$-0.751249\pi$
$269$	−23.2857	−1.41975	−0.709876	+	0.704327i	$0.751249\pi$
$270$	−2.34301	−0.142591
$271$	29.9595	1.81991	0.909957	−	0.414704i	$-0.136115\pi$
$271$	29.9595	1.81991	0.909957	+	0.414704i	$0.136115\pi$
$272$	7.05730	0.427912
$273$	−19.1295	−1.15777
$274$	−0.770416	−0.0465425
$275$	0.0721588	0.00435134
$276$	2.33985	0.140842
$277$	3.66005	0.219911	0.109956	−	0.993936i	$-0.464929\pi$
$277$	3.66005	0.219911	0.109956	+	0.993936i	$0.464929\pi$
$278$	8.17197	0.490122
$279$	−1.37440	−0.0822832
$280$	−11.5344	−0.689313
$281$	−6.98531	−0.416709	−0.208354	−	0.978053i	$-0.566811\pi$
$281$	−6.98531	−0.416709	−0.208354	+	0.978053i	$0.566811\pi$
$282$	−12.6928	−0.755843
$283$	12.7038	0.755163	0.377581	−	0.925976i	$-0.376756\pi$
$283$	12.7038	0.755163	0.377581	+	0.925976i	$0.376756\pi$
$284$	6.38625	0.378954
$285$	−2.34301	−0.138788
$286$	−0.572594	−0.0338582
$287$	20.3102	1.19887
$288$	1.00000	0.0589256
$289$	32.8055	1.92974
$290$	2.01911	0.118567
$291$	11.9850	0.702570
$292$	8.90858	0.521335
$293$	23.3389	1.36347	0.681737	−	0.731598i	$-0.261225\pi$
$293$	23.3389	1.36347	0.681737	+	0.731598i	$0.261225\pi$
$294$	17.2350	1.00517
$295$	−27.3022	−1.58960
$296$	11.3128	0.657542
$297$	0.147355	0.00855040
$298$	15.7470	0.912200
$299$	−9.09221	−0.525816
$300$	0.489694	0.0282725
$301$	−45.0187	−2.59484
$302$	11.0970	0.638563
$303$	3.93792	0.226228
$304$	1.00000	0.0573539
$305$	−4.17634	−0.239137
$306$	7.05730	0.403439
$307$	12.9783	0.740711	0.370356	−	0.928890i	$-0.379236\pi$
$307$	12.9783	0.740711	0.370356	+	0.928890i	$0.379236\pi$
$308$	0.725414	0.0413343
$309$	8.00908	0.455621
$310$	3.22023	0.182897
$311$	−26.9396	−1.52760	−0.763802	−	0.645450i	$-0.776670\pi$
$311$	−26.9396	−1.52760	−0.763802	+	0.645450i	$0.776670\pi$
$312$	−3.88581	−0.219991
$313$	−2.84262	−0.160675	−0.0803373	−	0.996768i	$-0.525600\pi$
$313$	−2.84262	−0.160675	−0.0803373	+	0.996768i	$0.525600\pi$
$314$	7.60704	0.429290
$315$	−11.5344	−0.649891
$316$	3.67761	0.206882
$317$	−16.5580	−0.929992	−0.464996	−	0.885313i	$-0.653944\pi$
$317$	−16.5580	−0.929992	−0.464996	+	0.885313i	$0.653944\pi$
$318$	−1.00000	−0.0560772
$319$	−0.126985	−0.00710978
$320$	−2.34301	−0.130978
$321$	−17.2139	−0.960784
$322$	11.5188	0.641920
$323$	7.05730	0.392679
$324$	1.00000	0.0555556
$325$	−1.90286	−0.105552
$326$	14.1951	0.786192
$327$	−14.1920	−0.784817
$328$	4.12566	0.227801
$329$	−62.4853	−3.44493
$330$	−0.345254	−0.0190056
$331$	−22.3490	−1.22841	−0.614206	−	0.789146i	$-0.710523\pi$
$331$	−22.3490	−1.22841	−0.614206	+	0.789146i	$0.710523\pi$
$332$	−13.7085	−0.752351
$333$	11.3128	0.619937
$334$	−1.11876	−0.0612158
$335$	−0.0126679	−0.000692120 0
$336$	4.92290	0.268566
$337$	−14.4755	−0.788531	−0.394266	−	0.918997i	$-0.629001\pi$
$337$	−14.4755	−0.788531	−0.394266	+	0.918997i	$0.629001\pi$
$338$	2.09955	0.114200
$339$	13.5779	0.737453
$340$	−16.5353	−0.896754
$341$	−0.202525	−0.0109673
$342$	1.00000	0.0540738
$343$	50.3859	2.72058
$344$	−9.14475	−0.493052
$345$	−5.48228	−0.295156
$346$	3.10366	0.166854
$347$	−7.13933	−0.383259	−0.191630	−	0.981467i	$-0.561377\pi$
$347$	−7.13933	−0.383259	−0.191630	+	0.981467i	$0.561377\pi$
$348$	−0.861761	−0.0461953
$349$	29.0252	1.55369	0.776843	−	0.629695i	$-0.216820\pi$
$349$	29.0252	1.55369	0.776843	+	0.629695i	$0.216820\pi$
$350$	2.41071	0.128858
$351$	−3.88581	−0.207409
$352$	0.147355	0.00785404
$353$	−26.5837	−1.41491	−0.707455	−	0.706758i	$-0.750157\pi$
$353$	−26.5837	−1.41491	−0.707455	+	0.706758i	$0.750157\pi$
$354$	11.6526	0.619330
$355$	−14.9630	−0.794156
$356$	−13.9349	−0.738546
$357$	34.7424	1.83876
$358$	−22.4844	−1.18834
$359$	−14.0787	−0.743045	−0.371523	−	0.928424i	$-0.621164\pi$
$359$	−14.0787	−0.743045	−0.371523	+	0.928424i	$0.621164\pi$
$360$	−2.34301	−0.123487
$361$	1.00000	0.0526316
$362$	−6.64731	−0.349375
$363$	−10.9783	−0.576211
$364$	−19.1295	−1.00266
$365$	−20.8729	−1.09254
$366$	1.78247	0.0931711
$367$	27.0255	1.41072	0.705360	−	0.708850i	$-0.250786\pi$
$367$	27.0255	1.41072	0.705360	+	0.708850i	$0.250786\pi$
$368$	2.33985	0.121973
$369$	4.12566	0.214773
$370$	−26.5060	−1.37798
$371$	−4.92290	−0.255584
$372$	−1.37440	−0.0712594
$373$	30.5998	1.58440	0.792198	−	0.610265i	$-0.208937\pi$
$373$	30.5998	1.58440	0.792198	+	0.610265i	$0.208937\pi$
$374$	1.03993	0.0537734
$375$	10.5677	0.545713
$376$	−12.6928	−0.654579
$377$	3.34864	0.172464
$378$	4.92290	0.253207
$379$	−30.4944	−1.56639	−0.783195	−	0.621776i	$-0.786412\pi$
$379$	−30.4944	−1.56639	−0.783195	+	0.621776i	$0.786412\pi$
$380$	−2.34301	−0.120194
$381$	11.9281	0.611094
$382$	5.88726	0.301219
$383$	19.7608	1.00973	0.504864	−	0.863199i	$-0.331543\pi$
$383$	19.7608	1.00973	0.504864	+	0.863199i	$0.331543\pi$
$384$	1.00000	0.0510310
$385$	−1.69965	−0.0866223
$386$	25.0147	1.27321
$387$	−9.14475	−0.464854
$388$	11.9850	0.608444
$389$	33.0443	1.67541	0.837705	−	0.546122i	$-0.183897\pi$
$389$	33.0443	1.67541	0.837705	+	0.546122i	$0.183897\pi$
$390$	9.10450	0.461024
$391$	16.5130	0.835099
$392$	17.2350	0.870499
$393$	−9.73109	−0.490868
$394$	−18.7543	−0.944829
$395$	−8.61667	−0.433552
$396$	0.147355	0.00740486
$397$	−25.4655	−1.27808	−0.639039	−	0.769175i	$-0.720668\pi$
$397$	−25.4655	−1.27808	−0.639039	+	0.769175i	$0.720668\pi$
$398$	13.9720	0.700354
$399$	4.92290	0.246454
$400$	0.489694	0.0244847
$401$	29.6649	1.48139	0.740697	−	0.671839i	$-0.234495\pi$
$401$	29.6649	1.48139	0.740697	+	0.671839i	$0.234495\pi$
$402$	0.00540667	0.000269660 0
$403$	5.34066	0.266037
$404$	3.93792	0.195919
$405$	−2.34301	−0.116425
$406$	−4.24237	−0.210545
$407$	1.66699	0.0826298
$408$	7.05730	0.349388
$409$	22.4338	1.10928	0.554639	−	0.832091i	$-0.312856\pi$
$409$	22.4338	1.10928	0.554639	+	0.832091i	$0.312856\pi$
$410$	−9.66645	−0.477392
$411$	−0.770416	−0.0380018
$412$	8.00908	0.394579
$413$	57.3648	2.82274
$414$	2.33985	0.114997
$415$	32.1191	1.57667
$416$	−3.88581	−0.190518
$417$	8.17197	0.400183
$418$	0.147355	0.00720736
$419$	0.928448	0.0453577	0.0226788	−	0.999743i	$-0.492780\pi$
$419$	0.928448	0.0453577	0.0226788	+	0.999743i	$0.492780\pi$
$420$	−11.5344	−0.562822
$421$	−19.0809	−0.929947	−0.464973	−	0.885325i	$-0.653936\pi$
$421$	−19.0809	−0.929947	−0.464973	+	0.885325i	$0.653936\pi$
$422$	−20.6913	−1.00723
$423$	−12.6928	−0.617143
$424$	−1.00000	−0.0485643
$425$	3.45592	0.167637
$426$	6.38625	0.309415
$427$	8.77493	0.424648
$428$	−17.2139	−0.832063
$429$	−0.572594	−0.0276451
$430$	21.4262	1.03326
$431$	−15.6720	−0.754895	−0.377448	−	0.926031i	$-0.623198\pi$
$431$	−15.6720	−0.754895	−0.377448	+	0.926031i	$0.623198\pi$
$432$	1.00000	0.0481125
$433$	−32.1557	−1.54530	−0.772652	−	0.634830i	$-0.781070\pi$
$433$	−32.1557	−1.54530	−0.772652	+	0.634830i	$0.781070\pi$
$434$	−6.76604	−0.324780
$435$	2.01911	0.0968092
$436$	−14.1920	−0.679672
$437$	2.33985	0.111930
$438$	8.90858	0.425669
$439$	15.1068	0.721011	0.360505	−	0.932757i	$-0.382604\pi$
$439$	15.1068	0.721011	0.360505	+	0.932757i	$0.382604\pi$
$440$	−0.345254	−0.0164593
$441$	17.2350	0.820714
$442$	−27.4234	−1.30440
$443$	−1.65980	−0.0788594	−0.0394297	−	0.999222i	$-0.512554\pi$
$443$	−1.65980	−0.0788594	−0.0394297	+	0.999222i	$0.512554\pi$
$444$	11.3128	0.536881
$445$	32.6495	1.54774
$446$	−3.70739	−0.175550
$447$	15.7470	0.744809
$448$	4.92290	0.232585
$449$	20.8624	0.984559	0.492280	−	0.870437i	$-0.336164\pi$
$449$	20.8624	0.984559	0.492280	+	0.870437i	$0.336164\pi$
$450$	0.489694	0.0230844
$451$	0.607936	0.0286266
$452$	13.5779	0.638653
$453$	11.0970	0.521384
$454$	12.1558	0.570498
$455$	44.8206	2.10122
$456$	1.00000	0.0468293
$457$	−38.7857	−1.81432	−0.907160	−	0.420786i	$-0.861754\pi$
$457$	−38.7857	−1.81432	−0.907160	+	0.420786i	$0.861754\pi$
$458$	11.0978	0.518564
$459$	7.05730	0.329407
$460$	−5.48228	−0.255613
$461$	−3.80779	−0.177346	−0.0886732	−	0.996061i	$-0.528263\pi$
$461$	−3.80779	−0.177346	−0.0886732	+	0.996061i	$0.528263\pi$
$462$	0.725414	0.0337493
$463$	−34.7302	−1.61405	−0.807025	−	0.590518i	$-0.798924\pi$
$463$	−34.7302	−1.61405	−0.807025	+	0.590518i	$0.798924\pi$
$464$	−0.861761	−0.0400063
$465$	3.22023	0.149335
$466$	−22.5811	−1.04605
$467$	−24.2279	−1.12113	−0.560566	−	0.828110i	$-0.689416\pi$
$467$	−24.2279	−1.12113	−0.560566	+	0.828110i	$0.689416\pi$
$468$	−3.88581	−0.179622
$469$	0.0266165	0.00122904
$470$	29.7393	1.37177
$471$	7.60704	0.350514
$472$	11.6526	0.536356
$473$	−1.34752	−0.0619592
$474$	3.67761	0.168918
$475$	0.489694	0.0224687
$476$	34.7424	1.59242
$477$	−1.00000	−0.0457869
$478$	−24.9397	−1.14071
$479$	−29.3361	−1.34040	−0.670199	−	0.742181i	$-0.733791\pi$
$479$	−29.3361	−1.34040	−0.670199	+	0.742181i	$0.733791\pi$
$480$	−2.34301	−0.106943
$481$	−43.9594	−2.00437
$482$	−9.93150	−0.452368
$483$	11.5188	0.524126
$484$	−10.9783	−0.499013
$485$	−28.0809	−1.27509
$486$	1.00000	0.0453609
$487$	−16.0875	−0.728994	−0.364497	−	0.931205i	$-0.618759\pi$
$487$	−16.0875	−0.728994	−0.364497	+	0.931205i	$0.618759\pi$
$488$	1.78247	0.0806886
$489$	14.1951	0.641923
$490$	−40.3818	−1.82426
$491$	27.6286	1.24686	0.623432	−	0.781878i	$-0.285738\pi$
$491$	27.6286	1.24686	0.623432	+	0.781878i	$0.285738\pi$
$492$	4.12566	0.185999
$493$	−6.08171	−0.273906
$494$	−3.88581	−0.174831
$495$	−0.345254	−0.0155180
$496$	−1.37440	−0.0617124
$497$	31.4389	1.41023
$498$	−13.7085	−0.614292
$499$	32.2700	1.44460	0.722302	−	0.691578i	$-0.243084\pi$
$499$	32.2700	1.44460	0.722302	+	0.691578i	$0.243084\pi$
$500$	10.5677	0.472602
$501$	−1.11876	−0.0499825
$502$	−6.51281	−0.290681
$503$	−25.6014	−1.14151	−0.570756	−	0.821120i	$-0.693350\pi$
$503$	−25.6014	−1.14151	−0.570756	+	0.821120i	$0.693350\pi$
$504$	4.92290	0.219284
$505$	−9.22659	−0.410578
$506$	0.344788	0.0153277
$507$	2.09955	0.0932441
$508$	11.9281	0.529223
$509$	20.2036	0.895510	0.447755	−	0.894156i	$-0.352224\pi$
$509$	20.2036	0.895510	0.447755	+	0.894156i	$0.352224\pi$
$510$	−16.5353	−0.732196
$511$	43.8561	1.94008
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−12.8633	−0.567374
$515$	−18.7654	−0.826900
$516$	−9.14475	−0.402575
$517$	−1.87034	−0.0822575
$518$	55.6917	2.44695
$519$	3.10366	0.136235
$520$	9.10450	0.399259
$521$	−8.51070	−0.372861	−0.186430	−	0.982468i	$-0.559692\pi$
$521$	−8.51070	−0.372861	−0.186430	+	0.982468i	$0.559692\pi$
$522$	−0.861761	−0.0377183
$523$	−17.0611	−0.746029	−0.373015	−	0.927825i	$-0.621676\pi$
$523$	−17.0611	−0.746029	−0.373015	+	0.927825i	$0.621676\pi$
$524$	−9.73109	−0.425104
$525$	2.41071	0.105212
$526$	22.3403	0.974082
$527$	−9.69956	−0.422519
$528$	0.147355	0.00641280
$529$	−17.5251	−0.761962
$530$	2.34301	0.101774
$531$	11.6526	0.505681
$532$	4.92290	0.213435
$533$	−16.0315	−0.694403
$534$	−13.9349	−0.603020
$535$	40.3322	1.74371
$536$	0.00540667	0.000233532 0
$537$	−22.4844	−0.970275
$538$	−23.2857	−1.00392
$539$	2.53966	0.109391
$540$	−2.34301	−0.100827
$541$	21.7437	0.934837	0.467418	−	0.884036i	$-0.345184\pi$
$541$	21.7437	0.934837	0.467418	+	0.884036i	$0.345184\pi$
$542$	29.9595	1.28687
$543$	−6.64731	−0.285264
$544$	7.05730	0.302579
$545$	33.2519	1.42435
$546$	−19.1295	−0.818667
$547$	−28.0123	−1.19772	−0.598859	−	0.800854i	$-0.704379\pi$
$547$	−28.0123	−1.19772	−0.598859	+	0.800854i	$0.704379\pi$
$548$	−0.770416	−0.0329105
$549$	1.78247	0.0760739
$550$	0.0721588	0.00307686
$551$	−0.861761	−0.0367123
$552$	2.33985	0.0995905
$553$	18.1045	0.769882
$554$	3.66005	0.155501
$555$	−26.5060	−1.12512
$556$	8.17197	0.346569
$557$	−37.6832	−1.59669	−0.798344	−	0.602201i	$-0.794291\pi$
$557$	−37.6832	−1.59669	−0.798344	+	0.602201i	$0.794291\pi$
$558$	−1.37440	−0.0581830
$559$	35.5348	1.50296
$560$	−11.5344	−0.487418
$561$	1.03993	0.0439058
$562$	−6.98531	−0.294658
$563$	18.8688	0.795226	0.397613	−	0.917553i	$-0.369839\pi$
$563$	18.8688	0.795226	0.397613	+	0.917553i	$0.369839\pi$
$564$	−12.6928	−0.534462
$565$	−31.8133	−1.33839
$566$	12.7038	0.533981
$567$	4.92290	0.206743
$568$	6.38625	0.267961
$569$	−0.681242	−0.0285592	−0.0142796	−	0.999898i	$-0.504545\pi$
$569$	−0.681242	−0.0285592	−0.0142796	+	0.999898i	$0.504545\pi$
$570$	−2.34301	−0.0981379
$571$	37.8082	1.58223	0.791113	−	0.611670i	$-0.209502\pi$
$571$	37.8082	1.58223	0.791113	+	0.611670i	$0.209502\pi$
$572$	−0.572594	−0.0239413
$573$	5.88726	0.245944
$574$	20.3102	0.847732
$575$	1.14581	0.0477835
$576$	1.00000	0.0416667
$577$	4.18137	0.174073	0.0870363	−	0.996205i	$-0.472260\pi$
$577$	4.18137	0.174073	0.0870363	+	0.996205i	$0.472260\pi$
$578$	32.8055	1.36453
$579$	25.0147	1.03957
$580$	2.01911	0.0838392
$581$	−67.4856	−2.79977
$582$	11.9850	0.496792
$583$	−0.147355	−0.00610282
$584$	8.90858	0.368640
$585$	9.10450	0.376425
$586$	23.3389	0.964121
$587$	−38.8629	−1.60404	−0.802021	−	0.597296i	$-0.796242\pi$
$587$	−38.8629	−1.60404	−0.802021	+	0.597296i	$0.796242\pi$
$588$	17.2350	0.710759
$589$	−1.37440	−0.0566312
$590$	−27.3022	−1.12401
$591$	−18.7543	−0.771450
$592$	11.3128	0.464952
$593$	36.9911	1.51904	0.759521	−	0.650483i	$-0.225433\pi$
$593$	36.9911	1.51904	0.759521	+	0.650483i	$0.225433\pi$
$594$	0.147355	0.00604605
$595$	−81.4018	−3.33715
$596$	15.7470	0.645023
$597$	13.9720	0.571837
$598$	−9.09221	−0.371808
$599$	−21.7123	−0.887141	−0.443571	−	0.896239i	$-0.646288\pi$
$599$	−21.7123	−0.887141	−0.443571	+	0.896239i	$0.646288\pi$
$600$	0.489694	0.0199917
$601$	−4.00890	−0.163527	−0.0817633	−	0.996652i	$-0.526055\pi$
$601$	−4.00890	−0.163527	−0.0817633	+	0.996652i	$0.526055\pi$
$602$	−45.0187	−1.83483
$603$	0.00540667	0.000220177 0
$604$	11.0970	0.451532
$605$	25.7222	1.04576
$606$	3.93792	0.159967
$607$	−24.6822	−1.00182	−0.500910	−	0.865500i	$-0.667001\pi$
$607$	−24.6822	−1.00182	−0.500910	+	0.865500i	$0.667001\pi$
$608$	1.00000	0.0405554
$609$	−4.24237	−0.171909
$610$	−4.17634	−0.169095
$611$	49.3217	1.99534
$612$	7.05730	0.285274
$613$	−17.6240	−0.711827	−0.355914	−	0.934519i	$-0.615830\pi$
$613$	−17.6240	−0.711827	−0.355914	+	0.934519i	$0.615830\pi$
$614$	12.9783	0.523762
$615$	−9.66645	−0.389789
$616$	0.725414	0.0292278
$617$	−14.6777	−0.590900	−0.295450	−	0.955358i	$-0.595470\pi$
$617$	−14.6777	−0.590900	−0.295450	+	0.955358i	$0.595470\pi$
$618$	8.00908	0.322172
$619$	−14.6219	−0.587706	−0.293853	−	0.955851i	$-0.594938\pi$
$619$	−14.6219	−0.587706	−0.293853	+	0.955851i	$0.594938\pi$
$620$	3.22023	0.129328
$621$	2.33985	0.0938948
$622$	−26.9396	−1.08018
$623$	−68.6000	−2.74840
$624$	−3.88581	−0.155557
$625$	−27.2087	−1.08835
$626$	−2.84262	−0.113614
$627$	0.147355	0.00588479
$628$	7.60704	0.303554
$629$	79.8377	3.18334
$630$	−11.5344	−0.459542
$631$	3.29837	0.131306	0.0656531	−	0.997843i	$-0.479087\pi$
$631$	3.29837	0.131306	0.0656531	+	0.997843i	$0.479087\pi$
$632$	3.67761	0.146287
$633$	−20.6913	−0.822403
$634$	−16.5580	−0.657604
$635$	−27.9476	−1.10907
$636$	−1.00000	−0.0396526
$637$	−66.9720	−2.65353
$638$	−0.126985	−0.00502737
$639$	6.38625	0.252636
$640$	−2.34301	−0.0926156
$641$	5.80346	0.229223	0.114612	−	0.993410i	$-0.463438\pi$
$641$	5.80346	0.229223	0.114612	+	0.993410i	$0.463438\pi$
$642$	−17.2139	−0.679377
$643$	−9.51611	−0.375279	−0.187639	−	0.982238i	$-0.560084\pi$
$643$	−9.51611	−0.375279	−0.187639	+	0.982238i	$0.560084\pi$
$644$	11.5188	0.453906
$645$	21.4262	0.843657
$646$	7.05730	0.277666
$647$	24.9067	0.979184	0.489592	−	0.871952i	$-0.337146\pi$
$647$	24.9067	0.979184	0.489592	+	0.871952i	$0.337146\pi$
$648$	1.00000	0.0392837
$649$	1.71707	0.0674010
$650$	−1.90286	−0.0746362
$651$	−6.76604	−0.265182
$652$	14.1951	0.555922
$653$	−11.4570	−0.448349	−0.224174	−	0.974549i	$-0.571969\pi$
$653$	−11.4570	−0.448349	−0.224174	+	0.974549i	$0.571969\pi$
$654$	−14.1920	−0.554950
$655$	22.8000	0.890871
$656$	4.12566	0.161080
$657$	8.90858	0.347557
$658$	−62.4853	−2.43593
$659$	8.42596	0.328229	0.164114	−	0.986441i	$-0.447523\pi$
$659$	8.42596	0.328229	0.164114	+	0.986441i	$0.447523\pi$
$660$	−0.345254	−0.0134390
$661$	32.7846	1.27517	0.637586	−	0.770379i	$-0.279933\pi$
$661$	32.7846	1.27517	0.637586	+	0.770379i	$0.279933\pi$
$662$	−22.3490	−0.868618
$663$	−27.4234	−1.06503
$664$	−13.7085	−0.531992
$665$	−11.5344	−0.447285
$666$	11.3128	0.438361
$667$	−2.01639	−0.0780749
$668$	−1.11876	−0.0432861
$669$	−3.70739	−0.143336
$670$	−0.0126679	−0.000489403 0
$671$	0.262656	0.0101397
$672$	4.92290	0.189905
$673$	−23.1945	−0.894082	−0.447041	−	0.894513i	$-0.647522\pi$
$673$	−23.1945	−0.894082	−0.447041	+	0.894513i	$0.647522\pi$
$674$	−14.4755	−0.557576
$675$	0.489694	0.0188483
$676$	2.09955	0.0807518
$677$	−11.8591	−0.455784	−0.227892	−	0.973686i	$-0.573183\pi$
$677$	−11.8591	−0.455784	−0.227892	+	0.973686i	$0.573183\pi$
$678$	13.5779	0.521458
$679$	59.0008	2.26424
$680$	−16.5353	−0.634101
$681$	12.1558	0.465810
$682$	−0.202525	−0.00775507
$683$	20.4292	0.781701	0.390850	−	0.920454i	$-0.372181\pi$
$683$	20.4292	0.781701	0.390850	+	0.920454i	$0.372181\pi$
$684$	1.00000	0.0382360
$685$	1.80509	0.0689690
$686$	50.3859	1.92374
$687$	11.0978	0.423406
$688$	−9.14475	−0.348640
$689$	3.88581	0.148038
$690$	−5.48228	−0.208707
$691$	−40.2269	−1.53030	−0.765152	−	0.643850i	$-0.777336\pi$
$691$	−40.2269	−1.53030	−0.765152	+	0.643850i	$0.777336\pi$
$692$	3.10366	0.117983
$693$	0.725414	0.0275562
$694$	−7.13933	−0.271005
$695$	−19.1470	−0.726288
$696$	−0.861761	−0.0326650
$697$	29.1160	1.10285
$698$	29.0252	1.09862
$699$	−22.5811	−0.854097
$700$	2.41071	0.0911165
$701$	−43.2922	−1.63512	−0.817561	−	0.575842i	$-0.804674\pi$
$701$	−43.2922	−1.63512	−0.817561	+	0.575842i	$0.804674\pi$
$702$	−3.88581	−0.146661
$703$	11.3128	0.426670
$704$	0.147355	0.00555365
$705$	29.7393	1.12005
$706$	−26.5837	−1.00049
$707$	19.3860	0.729087
$708$	11.6526	0.437933
$709$	−30.2718	−1.13688	−0.568440	−	0.822724i	$-0.692453\pi$
$709$	−30.2718	−1.13688	−0.568440	+	0.822724i	$0.692453\pi$
$710$	−14.9630	−0.561553
$711$	3.67761	0.137921
$712$	−13.9349	−0.522231
$713$	−3.21589	−0.120436
$714$	34.7424	1.30020
$715$	1.34159	0.0501727
$716$	−22.4844	−0.840283
$717$	−24.9397	−0.931389
$718$	−14.0787	−0.525412
$719$	24.7562	0.923250	0.461625	−	0.887075i	$-0.347267\pi$
$719$	24.7562	0.923250	0.461625	+	0.887075i	$0.347267\pi$
$720$	−2.34301	−0.0873188
$721$	39.4279	1.46837
$722$	1.00000	0.0372161
$723$	−9.93150	−0.369357
$724$	−6.64731	−0.247046
$725$	−0.421999	−0.0156726
$726$	−10.9783	−0.407442
$727$	−13.8089	−0.512145	−0.256073	−	0.966658i	$-0.582429\pi$
$727$	−13.8089	−0.512145	−0.256073	+	0.966658i	$0.582429\pi$
$728$	−19.1295	−0.708986
$729$	1.00000	0.0370370
$730$	−20.8729	−0.772541
$731$	−64.5372	−2.38700
$732$	1.78247	0.0658819
$733$	−8.92523	−0.329661	−0.164830	−	0.986322i	$-0.552708\pi$
$733$	−8.92523	−0.329661	−0.164830	+	0.986322i	$0.552708\pi$
$734$	27.0255	0.997529
$735$	−40.3818	−1.48950
$736$	2.33985	0.0862479
$737$	0.000796699 0	2.93468e−5 0
$738$	4.12566	0.151868
$739$	45.1773	1.66188	0.830938	−	0.556365i	$-0.187805\pi$
$739$	45.1773	1.66188	0.830938	+	0.556365i	$0.187805\pi$
$740$	−26.5060	−0.974378
$741$	−3.88581	−0.142749
$742$	−4.92290	−0.180726
$743$	−16.1231	−0.591500	−0.295750	−	0.955265i	$-0.595569\pi$
$743$	−16.1231	−0.591500	−0.295750	+	0.955265i	$0.595569\pi$
$744$	−1.37440	−0.0503880
$745$	−36.8954	−1.35174
$746$	30.5998	1.12034
$747$	−13.7085	−0.501567
$748$	1.03993	0.0380235
$749$	−84.7422	−3.09641
$750$	10.5677	0.385878
$751$	−37.3184	−1.36177	−0.680884	−	0.732391i	$-0.738404\pi$
$751$	−37.3184	−1.36177	−0.680884	+	0.732391i	$0.738404\pi$
$752$	−12.6928	−0.462858
$753$	−6.51281	−0.237340
$754$	3.34864	0.121950
$755$	−26.0005	−0.946254
$756$	4.92290	0.179044
$757$	−41.1123	−1.49425	−0.747126	−	0.664683i	$-0.768567\pi$
$757$	−41.1123	−1.49425	−0.747126	+	0.664683i	$0.768567\pi$
$758$	−30.4944	−1.10761
$759$	0.344788	0.0125150
$760$	−2.34301	−0.0849899
$761$	−41.8573	−1.51732	−0.758662	−	0.651484i	$-0.774147\pi$
$761$	−41.8573	−1.51732	−0.758662	+	0.651484i	$0.774147\pi$
$762$	11.9281	0.432109
$763$	−69.8657	−2.52931
$764$	5.88726	0.212994
$765$	−16.5353	−0.597836
$766$	19.7608	0.713986
$767$	−45.2799	−1.63496
$768$	1.00000	0.0360844
$769$	−0.737447	−0.0265930	−0.0132965	−	0.999912i	$-0.504233\pi$
$769$	−0.737447	−0.0265930	−0.0132965	+	0.999912i	$0.504233\pi$
$770$	−1.69965	−0.0612512
$771$	−12.8633	−0.463259
$772$	25.0147	0.900298
$773$	8.02860	0.288769	0.144384	−	0.989522i	$-0.453880\pi$
$773$	8.02860	0.288769	0.144384	+	0.989522i	$0.453880\pi$
$774$	−9.14475	−0.328701
$775$	−0.673035	−0.0241761
$776$	11.9850	0.430235
$777$	55.6917	1.99793
$778$	33.0443	1.18469
$779$	4.12566	0.147817
$780$	9.10450	0.325993
$781$	0.941045	0.0336732
$782$	16.5130	0.590504
$783$	−0.861761	−0.0307968
$784$	17.2350	0.615535
$785$	−17.8234	−0.636143
$786$	−9.73109	−0.347096
$787$	−6.26041	−0.223159	−0.111580	−	0.993755i	$-0.535591\pi$
$787$	−6.26041	−0.223159	−0.111580	+	0.993755i	$0.535591\pi$
$788$	−18.7543	−0.668095
$789$	22.3403	0.795335
$790$	−8.61667	−0.306567
$791$	66.8429	2.37666
$792$	0.147355	0.00523603
$793$	−6.92634	−0.245962
$794$	−25.4655	−0.903737
$795$	2.34301	0.0830980
$796$	13.9720	0.495225
$797$	39.4088	1.39593	0.697965	−	0.716132i	$-0.254089\pi$
$797$	39.4088	1.39593	0.697965	+	0.716132i	$0.254089\pi$
$798$	4.92290	0.174269
$799$	−89.5767	−3.16900
$800$	0.489694	0.0173133
$801$	−13.9349	−0.492364
$802$	29.6649	1.04750
$803$	1.31272	0.0463250
$804$	0.00540667	0.000190678 0
$805$	−26.9888	−0.951229
$806$	5.34066	0.188117
$807$	−23.2857	−0.819694
$808$	3.93792	0.138536
$809$	41.5425	1.46056	0.730278	−	0.683150i	$-0.239391\pi$
$809$	41.5425	1.46056	0.730278	+	0.683150i	$0.239391\pi$
$810$	−2.34301	−0.0823250
$811$	−5.82999	−0.204719	−0.102359	−	0.994747i	$-0.532639\pi$
$811$	−5.82999	−0.204719	−0.102359	+	0.994747i	$0.532639\pi$
$812$	−4.24237	−0.148878
$813$	29.9595	1.05073
$814$	1.66699	0.0584281
$815$	−33.2592	−1.16502
$816$	7.05730	0.247055
$817$	−9.14475	−0.319934
$818$	22.4338	0.784378
$819$	−19.1295	−0.668438
$820$	−9.66645	−0.337567
$821$	22.3791	0.781038	0.390519	−	0.920595i	$-0.372296\pi$
$821$	22.3791	0.781038	0.390519	+	0.920595i	$0.372296\pi$
$822$	−0.770416	−0.0268714
$823$	−36.7821	−1.28214	−0.641071	−	0.767482i	$-0.721510\pi$
$823$	−36.7821	−1.28214	−0.641071	+	0.767482i	$0.721510\pi$
$824$	8.00908	0.279010
$825$	0.0721588	0.00251225
$826$	57.3648	1.99598
$827$	27.4241	0.953631	0.476816	−	0.879003i	$-0.341791\pi$
$827$	27.4241	0.953631	0.476816	+	0.879003i	$0.341791\pi$
$828$	2.33985	0.0813153
$829$	−28.5700	−0.992276	−0.496138	−	0.868244i	$-0.665249\pi$
$829$	−28.5700	−0.992276	−0.496138	+	0.868244i	$0.665249\pi$
$830$	32.1191	1.11487
$831$	3.66005	0.126966
$832$	−3.88581	−0.134716
$833$	121.633	4.21432
$834$	8.17197	0.282972
$835$	2.62126	0.0907126
$836$	0.147355	0.00509638
$837$	−1.37440	−0.0475062
$838$	0.928448	0.0320727
$839$	−50.3820	−1.73938	−0.869690	−	0.493599i	$-0.835681\pi$
$839$	−50.3820	−1.73938	−0.869690	+	0.493599i	$0.835681\pi$
$840$	−11.5344	−0.397975
$841$	−28.2574	−0.974392
$842$	−19.0809	−0.657572
$843$	−6.98531	−0.240587
$844$	−20.6913	−0.712222
$845$	−4.91926	−0.169228
$846$	−12.6928	−0.436386
$847$	−54.0451	−1.85701
$848$	−1.00000	−0.0343401
$849$	12.7038	0.435994
$850$	3.45592	0.118537
$851$	26.4702	0.907386
$852$	6.38625	0.218789
$853$	−36.0865	−1.23558	−0.617789	−	0.786344i	$-0.711971\pi$
$853$	−36.0865	−1.23558	−0.617789	+	0.786344i	$0.711971\pi$
$854$	8.77493	0.300272
$855$	−2.34301	−0.0801292
$856$	−17.2139	−0.588358
$857$	27.7354	0.947424	0.473712	−	0.880680i	$-0.342914\pi$
$857$	27.7354	0.947424	0.473712	+	0.880680i	$0.342914\pi$
$858$	−0.572594	−0.0195480
$859$	41.6076	1.41963	0.709817	−	0.704386i	$-0.248778\pi$
$859$	41.6076	1.41963	0.709817	+	0.704386i	$0.248778\pi$
$860$	21.4262	0.730628
$861$	20.3102	0.692170
$862$	−15.6720	−0.533792
$863$	10.9087	0.371335	0.185668	−	0.982613i	$-0.440555\pi$
$863$	10.9087	0.371335	0.185668	+	0.982613i	$0.440555\pi$
$864$	1.00000	0.0340207
$865$	−7.27189	−0.247252
$866$	−32.1557	−1.09270
$867$	32.8055	1.11413
$868$	−6.76604	−0.229654
$869$	0.541914	0.0183832
$870$	2.01911	0.0684544
$871$	−0.0210093	−0.000711873 0
$872$	−14.1920	−0.480600
$873$	11.9850	0.405629
$874$	2.33985	0.0791465
$875$	52.0237	1.75872
$876$	8.90858	0.300993
$877$	7.08699	0.239311	0.119655	−	0.992815i	$-0.461821\pi$
$877$	7.08699	0.239311	0.119655	+	0.992815i	$0.461821\pi$
$878$	15.1068	0.509831
$879$	23.3389	0.787202
$880$	−0.345254	−0.0116385
$881$	−43.6537	−1.47073	−0.735366	−	0.677670i	$-0.762990\pi$
$881$	−43.6537	−1.47073	−0.735366	+	0.677670i	$0.762990\pi$
$882$	17.2350	0.580332
$883$	−8.27401	−0.278443	−0.139221	−	0.990261i	$-0.544460\pi$
$883$	−8.27401	−0.278443	−0.139221	+	0.990261i	$0.544460\pi$
$884$	−27.4234	−0.922347
$885$	−27.3022	−0.917754
$886$	−1.65980	−0.0557620
$887$	−15.1912	−0.510070	−0.255035	−	0.966932i	$-0.582087\pi$
$887$	−15.1912	−0.510070	−0.255035	+	0.966932i	$0.582087\pi$
$888$	11.3128	0.379632
$889$	58.7208	1.96943
$890$	32.6495	1.09441
$891$	0.147355	0.00493658
$892$	−3.70739	−0.124133
$893$	−12.6928	−0.424747
$894$	15.7470	0.526659
$895$	52.6813	1.76094
$896$	4.92290	0.164463
$897$	−9.09221	−0.303580
$898$	20.8624	0.696189
$899$	1.18441	0.0395021
$900$	0.489694	0.0163231
$901$	−7.05730	−0.235113
$902$	0.607936	0.0202421
$903$	−45.0187	−1.49813
$904$	13.5779	0.451596
$905$	15.5747	0.517721
$906$	11.0970	0.368674
$907$	−56.5975	−1.87929	−0.939644	−	0.342153i	$-0.888844\pi$
$907$	−56.5975	−1.87929	−0.939644	+	0.342153i	$0.888844\pi$
$908$	12.1558	0.403403
$909$	3.93792	0.130613
$910$	44.8206	1.48579
$911$	50.8777	1.68565	0.842826	−	0.538186i	$-0.180890\pi$
$911$	50.8777	1.68565	0.842826	+	0.538186i	$0.180890\pi$
$912$	1.00000	0.0331133
$913$	−2.02001	−0.0668527
$914$	−38.7857	−1.28292
$915$	−4.17634	−0.138066
$916$	11.0978	0.366680
$917$	−47.9052	−1.58197
$918$	7.05730	0.232926
$919$	−29.1060	−0.960117	−0.480058	−	0.877237i	$-0.659385\pi$
$919$	−29.1060	−0.960117	−0.480058	+	0.877237i	$0.659385\pi$
$920$	−5.48228	−0.180746
$921$	12.9783	0.427650
$922$	−3.80779	−0.125403
$923$	−24.8158	−0.816821
$924$	0.725414	0.0238644
$925$	5.53980	0.182147
$926$	−34.7302	−1.14131
$927$	8.00908	0.263053
$928$	−0.861761	−0.0282887
$929$	31.5508	1.03515	0.517574	−	0.855639i	$-0.326835\pi$
$929$	31.5508	1.03515	0.517574	+	0.855639i	$0.326835\pi$
$930$	3.22023	0.105596
$931$	17.2350	0.564854
$932$	−22.5811	−0.739670
$933$	−26.9396	−0.881963
$934$	−24.2279	−0.792760
$935$	−2.43656	−0.0796841
$936$	−3.88581	−0.127012
$937$	−19.4293	−0.634728	−0.317364	−	0.948304i	$-0.602798\pi$
$937$	−19.4293	−0.634728	−0.317364	+	0.948304i	$0.602798\pi$
$938$	0.0266165	0.000869060 0
$939$	−2.84262	−0.0927655
$940$	29.7393	0.969988
$941$	−43.9857	−1.43389	−0.716947	−	0.697128i	$-0.754461\pi$
$941$	−43.9857	−1.43389	−0.716947	+	0.697128i	$0.754461\pi$
$942$	7.60704	0.247851
$943$	9.65341	0.314358
$944$	11.6526	0.379261
$945$	−11.5344	−0.375214
$946$	−1.34752	−0.0438118
$947$	−19.2413	−0.625259	−0.312629	−	0.949875i	$-0.601210\pi$
$947$	−19.2413	−0.625259	−0.312629	+	0.949875i	$0.601210\pi$
$948$	3.67761	0.119443
$949$	−34.6171	−1.12372
$950$	0.489694	0.0158878
$951$	−16.5580	−0.536931
$952$	34.7424	1.12601
$953$	−44.7407	−1.44929	−0.724647	−	0.689120i	$-0.757997\pi$
$953$	−44.7407	−1.44929	−0.724647	+	0.689120i	$0.757997\pi$
$954$	−1.00000	−0.0323762
$955$	−13.7939	−0.446361
$956$	−24.9397	−0.806607
$957$	−0.126985	−0.00410483
$958$	−29.3361	−0.947805
$959$	−3.79269	−0.122472
$960$	−2.34301	−0.0756203
$961$	−29.1110	−0.939065
$962$	−43.9594	−1.41731
$963$	−17.2139	−0.554709
$964$	−9.93150	−0.319872
$965$	−58.6096	−1.88671
$966$	11.5188	0.370613
$967$	2.97832	0.0957764	0.0478882	−	0.998853i	$-0.484751\pi$
$967$	2.97832	0.0957764	0.0478882	+	0.998853i	$0.484751\pi$
$968$	−10.9783	−0.352855
$969$	7.05730	0.226713
$970$	−28.0809	−0.901622
$971$	−26.8948	−0.863094	−0.431547	−	0.902090i	$-0.642032\pi$
$971$	−26.8948	−0.863094	−0.431547	+	0.902090i	$0.642032\pi$
$972$	1.00000	0.0320750
$973$	40.2299	1.28971
$974$	−16.0875	−0.515476
$975$	−1.90286	−0.0609402
$976$	1.78247	0.0570554
$977$	39.9167	1.27705	0.638524	−	0.769602i	$-0.279545\pi$
$977$	39.9167	1.27705	0.638524	+	0.769602i	$0.279545\pi$
$978$	14.1951	0.453908
$979$	−2.05337	−0.0656260
$980$	−40.3818	−1.28995
$981$	−14.1920	−0.453114
$982$	27.6286	0.881665
$983$	38.4862	1.22752	0.613760	−	0.789493i	$-0.289656\pi$
$983$	38.4862	1.22752	0.613760	+	0.789493i	$0.289656\pi$
$984$	4.12566	0.131521
$985$	43.9415	1.40009
$986$	−6.08171	−0.193681
$987$	−62.4853	−1.98893
$988$	−3.88581	−0.123624
$989$	−21.3973	−0.680395
$990$	−0.345254	−0.0109729
$991$	32.7197	1.03937	0.519687	−	0.854357i	$-0.326049\pi$
$991$	32.7197	1.03937	0.519687	+	0.854357i	$0.326049\pi$
$992$	−1.37440	−0.0436373
$993$	−22.3490	−0.709223
$994$	31.4389	0.997181
$995$	−32.7366	−1.03782
$996$	−13.7085	−0.434370
$997$	−1.62511	−0.0514676	−0.0257338	−	0.999669i	$-0.508192\pi$
$997$	−1.62511	−0.0514676	−0.0257338	+	0.999669i	$0.508192\pi$
$998$	32.2700	1.02149
$999$	11.3128	0.357921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bh.1.3	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bh.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.34301 q^{5} +1.00000 q^{6} +4.92290 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.34301 q^{5} +1.00000 q^{6} +4.92290 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.34301 q^{10} +0.147355 q^{11} +1.00000 q^{12} -3.88581 q^{13} +4.92290 q^{14} -2.34301 q^{15} +1.00000 q^{16} +7.05730 q^{17} +1.00000 q^{18} +1.00000 q^{19} -2.34301 q^{20} +4.92290 q^{21} +0.147355 q^{22} +2.33985 q^{23} +1.00000 q^{24} +0.489694 q^{25} -3.88581 q^{26} +1.00000 q^{27} +4.92290 q^{28} -0.861761 q^{29} -2.34301 q^{30} -1.37440 q^{31} +1.00000 q^{32} +0.147355 q^{33} +7.05730 q^{34} -11.5344 q^{35} +1.00000 q^{36} +11.3128 q^{37} +1.00000 q^{38} -3.88581 q^{39} -2.34301 q^{40} +4.12566 q^{41} +4.92290 q^{42} -9.14475 q^{43} +0.147355 q^{44} -2.34301 q^{45} +2.33985 q^{46} -12.6928 q^{47} +1.00000 q^{48} +17.2350 q^{49} +0.489694 q^{50} +7.05730 q^{51} -3.88581 q^{52} -1.00000 q^{53} +1.00000 q^{54} -0.345254 q^{55} +4.92290 q^{56} +1.00000 q^{57} -0.861761 q^{58} +11.6526 q^{59} -2.34301 q^{60} +1.78247 q^{61} -1.37440 q^{62} +4.92290 q^{63} +1.00000 q^{64} +9.10450 q^{65} +0.147355 q^{66} +0.00540667 q^{67} +7.05730 q^{68} +2.33985 q^{69} -11.5344 q^{70} +6.38625 q^{71} +1.00000 q^{72} +8.90858 q^{73} +11.3128 q^{74} +0.489694 q^{75} +1.00000 q^{76} +0.725414 q^{77} -3.88581 q^{78} +3.67761 q^{79} -2.34301 q^{80} +1.00000 q^{81} +4.12566 q^{82} -13.7085 q^{83} +4.92290 q^{84} -16.5353 q^{85} -9.14475 q^{86} -0.861761 q^{87} +0.147355 q^{88} -13.9349 q^{89} -2.34301 q^{90} -19.1295 q^{91} +2.33985 q^{92} -1.37440 q^{93} -12.6928 q^{94} -2.34301 q^{95} +1.00000 q^{96} +11.9850 q^{97} +17.2350 q^{98} +0.147355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 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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