LMFDB - Embedded newform 6042.2.a.bd.1.6

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:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 35 x^{9} + 77 x^{8} + 394 x^{7} - 994 x^{6} - 1477 x^{5} + 4683 x^{4} + 563 x^{3} + \cdots + 1534 $ x^11 - 2x^10 - 35x^9 + 77x^8 + 394x^7 - 994x^6 - 1477x^5 + 4683x^4 + 563x^3 - 6194x^2 + 1258x + 1534
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.864610$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.864610 q^{5} +1.00000 q^{6} +2.90002 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.864610 q^{5} +1.00000 q^{6} +2.90002 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.864610 q^{10} -1.74334 q^{11} -1.00000 q^{12} +4.31787 q^{13} -2.90002 q^{14} -0.864610 q^{15} +1.00000 q^{16} -3.14325 q^{17} -1.00000 q^{18} +1.00000 q^{19} +0.864610 q^{20} -2.90002 q^{21} +1.74334 q^{22} +2.44799 q^{23} +1.00000 q^{24} -4.25245 q^{25} -4.31787 q^{26} -1.00000 q^{27} +2.90002 q^{28} -4.86763 q^{29} +0.864610 q^{30} -7.65381 q^{31} -1.00000 q^{32} +1.74334 q^{33} +3.14325 q^{34} +2.50739 q^{35} +1.00000 q^{36} +9.48198 q^{37} -1.00000 q^{38} -4.31787 q^{39} -0.864610 q^{40} -6.40258 q^{41} +2.90002 q^{42} +4.11314 q^{43} -1.74334 q^{44} +0.864610 q^{45} -2.44799 q^{46} -9.98313 q^{47} -1.00000 q^{48} +1.41012 q^{49} +4.25245 q^{50} +3.14325 q^{51} +4.31787 q^{52} +1.00000 q^{53} +1.00000 q^{54} -1.50731 q^{55} -2.90002 q^{56} -1.00000 q^{57} +4.86763 q^{58} -13.8169 q^{59} -0.864610 q^{60} -10.8725 q^{61} +7.65381 q^{62} +2.90002 q^{63} +1.00000 q^{64} +3.73327 q^{65} -1.74334 q^{66} -10.8030 q^{67} -3.14325 q^{68} -2.44799 q^{69} -2.50739 q^{70} -2.93217 q^{71} -1.00000 q^{72} +4.34381 q^{73} -9.48198 q^{74} +4.25245 q^{75} +1.00000 q^{76} -5.05571 q^{77} +4.31787 q^{78} -4.78449 q^{79} +0.864610 q^{80} +1.00000 q^{81} +6.40258 q^{82} +8.79442 q^{83} -2.90002 q^{84} -2.71769 q^{85} -4.11314 q^{86} +4.86763 q^{87} +1.74334 q^{88} -13.0030 q^{89} -0.864610 q^{90} +12.5219 q^{91} +2.44799 q^{92} +7.65381 q^{93} +9.98313 q^{94} +0.864610 q^{95} +1.00000 q^{96} -11.8319 q^{97} -1.41012 q^{98} -1.74334 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9} - 2 q^{10} - 6 q^{11} - 11 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{15} + 11 q^{16} - 16 q^{17} - 11 q^{18} + 11 q^{19} + 2 q^{20} + 2 q^{21} + 6 q^{22} - 11 q^{23} + 11 q^{24} + 19 q^{25} + 7 q^{26} - 11 q^{27} - 2 q^{28} - 7 q^{29} + 2 q^{30} + 12 q^{31} - 11 q^{32} + 6 q^{33} + 16 q^{34} - 5 q^{35} + 11 q^{36} + 3 q^{37} - 11 q^{38} + 7 q^{39} - 2 q^{40} + 11 q^{41} - 2 q^{42} + 7 q^{43} - 6 q^{44} + 2 q^{45} + 11 q^{46} - 37 q^{47} - 11 q^{48} + 23 q^{49} - 19 q^{50} + 16 q^{51} - 7 q^{52} + 11 q^{53} + 11 q^{54} - 11 q^{55} + 2 q^{56} - 11 q^{57} + 7 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} - 12 q^{62} - 2 q^{63} + 11 q^{64} - 7 q^{65} - 6 q^{66} - 28 q^{67} - 16 q^{68} + 11 q^{69} + 5 q^{70} + 4 q^{71} - 11 q^{72} - 7 q^{73} - 3 q^{74} - 19 q^{75} + 11 q^{76} - 13 q^{77} - 7 q^{78} + 5 q^{79} + 2 q^{80} + 11 q^{81} - 11 q^{82} - 11 q^{83} + 2 q^{84} - 11 q^{85} - 7 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} - 2 q^{90} - 24 q^{91} - 11 q^{92} - 12 q^{93} + 37 q^{94} + 2 q^{95} + 11 q^{96} - 24 q^{97} - 23 q^{98} - 6 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9 - 2 * q^10 - 6 * q^11 - 11 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^15 + 11 * q^16 - 16 * q^17 - 11 * q^18 + 11 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 - 11 * q^23 + 11 * q^24 + 19 * q^25 + 7 * q^26 - 11 * q^27 - 2 * q^28 - 7 * q^29 + 2 * q^30 + 12 * q^31 - 11 * q^32 + 6 * q^33 + 16 * q^34 - 5 * q^35 + 11 * q^36 + 3 * q^37 - 11 * q^38 + 7 * q^39 - 2 * q^40 + 11 * q^41 - 2 * q^42 + 7 * q^43 - 6 * q^44 + 2 * q^45 + 11 * q^46 - 37 * q^47 - 11 * q^48 + 23 * q^49 - 19 * q^50 + 16 * q^51 - 7 * q^52 + 11 * q^53 + 11 * q^54 - 11 * q^55 + 2 * q^56 - 11 * q^57 + 7 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 - 12 * q^62 - 2 * q^63 + 11 * q^64 - 7 * q^65 - 6 * q^66 - 28 * q^67 - 16 * q^68 + 11 * q^69 + 5 * q^70 + 4 * q^71 - 11 * q^72 - 7 * q^73 - 3 * q^74 - 19 * q^75 + 11 * q^76 - 13 * q^77 - 7 * q^78 + 5 * q^79 + 2 * q^80 + 11 * q^81 - 11 * q^82 - 11 * q^83 + 2 * q^84 - 11 * q^85 - 7 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 - 2 * q^90 - 24 * q^91 - 11 * q^92 - 12 * q^93 + 37 * q^94 + 2 * q^95 + 11 * q^96 - 24 * q^97 - 23 * q^98 - 6 * 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
$5$	0.864610	0.386665	0.193333	−	0.981133i	$-0.438070\pi$
$5$	0.864610	0.386665	0.193333	+	0.981133i	$0.438070\pi$
$6$	1.00000	0.408248
$7$	2.90002	1.09610	0.548052	−	0.836444i	$-0.315369\pi$
$7$	2.90002	1.09610	0.548052	+	0.836444i	$0.315369\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.864610	−0.273414
$11$	−1.74334	−0.525636	−0.262818	−	0.964845i	$-0.584652\pi$
$11$	−1.74334	−0.525636	−0.262818	+	0.964845i	$0.584652\pi$
$12$	−1.00000	−0.288675
$13$	4.31787	1.19756	0.598781	−	0.800913i	$-0.295652\pi$
$13$	4.31787	1.19756	0.598781	+	0.800913i	$0.295652\pi$
$14$	−2.90002	−0.775063
$15$	−0.864610	−0.223241
$16$	1.00000	0.250000
$17$	−3.14325	−0.762351	−0.381175	−	0.924503i	$-0.624481\pi$
$17$	−3.14325	−0.762351	−0.381175	+	0.924503i	$0.624481\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.864610	0.193333
$21$	−2.90002	−0.632836
$22$	1.74334	0.371680
$23$	2.44799	0.510441	0.255220	−	0.966883i	$-0.417852\pi$
$23$	2.44799	0.510441	0.255220	+	0.966883i	$0.417852\pi$
$24$	1.00000	0.204124
$25$	−4.25245	−0.850490
$26$	−4.31787	−0.846805
$27$	−1.00000	−0.192450
$28$	2.90002	0.548052
$29$	−4.86763	−0.903897	−0.451948	−	0.892044i	$-0.649271\pi$
$29$	−4.86763	−0.903897	−0.451948	+	0.892044i	$0.649271\pi$
$30$	0.864610	0.157855
$31$	−7.65381	−1.37467	−0.687333	−	0.726343i	$-0.741219\pi$
$31$	−7.65381	−1.37467	−0.687333	+	0.726343i	$0.741219\pi$
$32$	−1.00000	−0.176777
$33$	1.74334	0.303476
$34$	3.14325	0.539063
$35$	2.50739	0.423826
$36$	1.00000	0.166667
$37$	9.48198	1.55883	0.779414	−	0.626509i	$-0.215517\pi$
$37$	9.48198	1.55883	0.779414	+	0.626509i	$0.215517\pi$
$38$	−1.00000	−0.162221
$39$	−4.31787	−0.691413
$40$	−0.864610	−0.136707
$41$	−6.40258	−0.999915	−0.499957	−	0.866050i	$-0.666651\pi$
$41$	−6.40258	−0.999915	−0.499957	+	0.866050i	$0.666651\pi$
$42$	2.90002	0.447483
$43$	4.11314	0.627247	0.313624	−	0.949547i	$-0.398457\pi$
$43$	4.11314	0.627247	0.313624	+	0.949547i	$0.398457\pi$
$44$	−1.74334	−0.262818
$45$	0.864610	0.128888
$46$	−2.44799	−0.360936
$47$	−9.98313	−1.45619	−0.728094	−	0.685477i	$-0.759594\pi$
$47$	−9.98313	−1.45619	−0.728094	+	0.685477i	$0.759594\pi$
$48$	−1.00000	−0.144338
$49$	1.41012	0.201446
$50$	4.25245	0.601387
$51$	3.14325	0.440143
$52$	4.31787	0.598781
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	−1.50731	−0.203245
$56$	−2.90002	−0.387532
$57$	−1.00000	−0.132453
$58$	4.86763	0.639152
$59$	−13.8169	−1.79881	−0.899404	−	0.437119i	$-0.855999\pi$
$59$	−13.8169	−1.79881	−0.899404	+	0.437119i	$0.855999\pi$
$60$	−0.864610	−0.111621
$61$	−10.8725	−1.39209	−0.696043	−	0.718000i	$-0.745058\pi$
$61$	−10.8725	−1.39209	−0.696043	+	0.718000i	$0.745058\pi$
$62$	7.65381	0.972035
$63$	2.90002	0.365368
$64$	1.00000	0.125000
$65$	3.73327	0.463056
$66$	−1.74334	−0.214590
$67$	−10.8030	−1.31979	−0.659897	−	0.751357i	$-0.729400\pi$
$67$	−10.8030	−1.31979	−0.659897	+	0.751357i	$0.729400\pi$
$68$	−3.14325	−0.381175
$69$	−2.44799	−0.294703
$70$	−2.50739	−0.299690
$71$	−2.93217	−0.347984	−0.173992	−	0.984747i	$-0.555667\pi$
$71$	−2.93217	−0.347984	−0.173992	+	0.984747i	$0.555667\pi$
$72$	−1.00000	−0.117851
$73$	4.34381	0.508405	0.254202	−	0.967151i	$-0.418187\pi$
$73$	4.34381	0.508405	0.254202	+	0.967151i	$0.418187\pi$
$74$	−9.48198	−1.10226
$75$	4.25245	0.491031
$76$	1.00000	0.114708
$77$	−5.05571	−0.576152
$78$	4.31787	0.488903
$79$	−4.78449	−0.538298	−0.269149	−	0.963099i	$-0.586742\pi$
$79$	−4.78449	−0.538298	−0.269149	+	0.963099i	$0.586742\pi$
$80$	0.864610	0.0966663
$81$	1.00000	0.111111
$82$	6.40258	0.707047
$83$	8.79442	0.965313	0.482656	−	0.875810i	$-0.339672\pi$
$83$	8.79442	0.965313	0.482656	+	0.875810i	$0.339672\pi$
$84$	−2.90002	−0.316418
$85$	−2.71769	−0.294774
$86$	−4.11314	−0.443531
$87$	4.86763	0.521865
$88$	1.74334	0.185840
$89$	−13.0030	−1.37832	−0.689158	−	0.724611i	$-0.742019\pi$
$89$	−13.0030	−1.37832	−0.689158	+	0.724611i	$0.742019\pi$
$90$	−0.864610	−0.0911378
$91$	12.5219	1.31265
$92$	2.44799	0.255220
$93$	7.65381	0.793663
$94$	9.98313	1.02968
$95$	0.864610	0.0887071
$96$	1.00000	0.102062
$97$	−11.8319	−1.20135	−0.600674	−	0.799494i	$-0.705101\pi$
$97$	−11.8319	−1.20135	−0.600674	+	0.799494i	$0.705101\pi$
$98$	−1.41012	−0.142444
$99$	−1.74334	−0.175212
$100$	−4.25245	−0.425245
$101$	3.58097	0.356320	0.178160	−	0.984002i	$-0.442986\pi$
$101$	3.58097	0.356320	0.178160	+	0.984002i	$0.442986\pi$
$102$	−3.14325	−0.311228
$103$	−11.1052	−1.09423	−0.547113	−	0.837059i	$-0.684273\pi$
$103$	−11.1052	−1.09423	−0.547113	+	0.837059i	$0.684273\pi$
$104$	−4.31787	−0.423402
$105$	−2.50739	−0.244696
$106$	−1.00000	−0.0971286
$107$	7.15731	0.691924	0.345962	−	0.938249i	$-0.387553\pi$
$107$	7.15731	0.691924	0.345962	+	0.938249i	$0.387553\pi$
$108$	−1.00000	−0.0962250
$109$	10.7045	1.02531	0.512653	−	0.858596i	$-0.328663\pi$
$109$	10.7045	1.02531	0.512653	+	0.858596i	$0.328663\pi$
$110$	1.50731	0.143716
$111$	−9.48198	−0.899990
$112$	2.90002	0.274026
$113$	−9.87778	−0.929223	−0.464612	−	0.885515i	$-0.653806\pi$
$113$	−9.87778	−0.929223	−0.464612	+	0.885515i	$0.653806\pi$
$114$	1.00000	0.0936586
$115$	2.11655	0.197370
$116$	−4.86763	−0.451948
$117$	4.31787	0.399188
$118$	13.8169	1.27195
$119$	−9.11550	−0.835616
$120$	0.864610	0.0789277
$121$	−7.96078	−0.723707
$122$	10.8725	0.984354
$123$	6.40258	0.577301
$124$	−7.65381	−0.687333
$125$	−7.99976	−0.715520
$126$	−2.90002	−0.258354
$127$	12.3988	1.10022	0.550110	−	0.835092i	$-0.314586\pi$
$127$	12.3988	1.10022	0.550110	+	0.835092i	$0.314586\pi$
$128$	−1.00000	−0.0883883
$129$	−4.11314	−0.362141
$130$	−3.73327	−0.327430
$131$	−6.48507	−0.566604	−0.283302	−	0.959031i	$-0.591430\pi$
$131$	−6.48507	−0.566604	−0.283302	+	0.959031i	$0.591430\pi$
$132$	1.74334	0.151738
$133$	2.90002	0.251464
$134$	10.8030	0.933235
$135$	−0.864610	−0.0744137
$136$	3.14325	0.269532
$137$	16.5214	1.41151	0.705757	−	0.708454i	$-0.250607\pi$
$137$	16.5214	1.41151	0.705757	+	0.708454i	$0.250607\pi$
$138$	2.44799	0.208387
$139$	−9.27726	−0.786887	−0.393443	−	0.919349i	$-0.628716\pi$
$139$	−9.27726	−0.786887	−0.393443	+	0.919349i	$0.628716\pi$
$140$	2.50739	0.211913
$141$	9.98313	0.840731
$142$	2.93217	0.246062
$143$	−7.52750	−0.629482
$144$	1.00000	0.0833333
$145$	−4.20860	−0.349505
$146$	−4.34381	−0.359496
$147$	−1.41012	−0.116305
$148$	9.48198	0.779414
$149$	18.8652	1.54550	0.772748	−	0.634712i	$-0.218881\pi$
$149$	18.8652	1.54550	0.772748	+	0.634712i	$0.218881\pi$
$150$	−4.25245	−0.347211
$151$	22.9955	1.87135	0.935675	−	0.352863i	$-0.114792\pi$
$151$	22.9955	1.87135	0.935675	+	0.352863i	$0.114792\pi$
$152$	−1.00000	−0.0811107
$153$	−3.14325	−0.254117
$154$	5.05571	0.407401
$155$	−6.61756	−0.531535
$156$	−4.31787	−0.345707
$157$	4.27863	0.341472	0.170736	−	0.985317i	$-0.445386\pi$
$157$	4.27863	0.341472	0.170736	+	0.985317i	$0.445386\pi$
$158$	4.78449	0.380634
$159$	−1.00000	−0.0793052
$160$	−0.864610	−0.0683534
$161$	7.09921	0.559496
$162$	−1.00000	−0.0785674
$163$	−1.36454	−0.106879	−0.0534396	−	0.998571i	$-0.517018\pi$
$163$	−1.36454	−0.106879	−0.0534396	+	0.998571i	$0.517018\pi$
$164$	−6.40258	−0.499957
$165$	1.50731	0.117344
$166$	−8.79442	−0.682579
$167$	−20.9727	−1.62292	−0.811459	−	0.584409i	$-0.801326\pi$
$167$	−20.9727	−1.62292	−0.811459	+	0.584409i	$0.801326\pi$
$168$	2.90002	0.223741
$169$	5.64403	0.434156
$170$	2.71769	0.208437
$171$	1.00000	0.0764719
$172$	4.11314	0.313624
$173$	18.5311	1.40890	0.704448	−	0.709756i	$-0.251195\pi$
$173$	18.5311	1.40890	0.704448	+	0.709756i	$0.251195\pi$
$174$	−4.86763	−0.369014
$175$	−12.3322	−0.932226
$176$	−1.74334	−0.131409
$177$	13.8169	1.03854
$178$	13.0030	0.974616
$179$	−0.823328	−0.0615384	−0.0307692	−	0.999527i	$-0.509796\pi$
$179$	−0.823328	−0.0615384	−0.0307692	+	0.999527i	$0.509796\pi$
$180$	0.864610	0.0644442
$181$	−16.9742	−1.26168	−0.630841	−	0.775912i	$-0.717290\pi$
$181$	−16.9742	−1.26168	−0.630841	+	0.775912i	$0.717290\pi$
$182$	−12.5219	−0.928187
$183$	10.8725	0.803722
$184$	−2.44799	−0.180468
$185$	8.19821	0.602745
$186$	−7.65381	−0.561205
$187$	5.47975	0.400719
$188$	−9.98313	−0.728094
$189$	−2.90002	−0.210945
$190$	−0.864610	−0.0627254
$191$	−19.6559	−1.42225	−0.711124	−	0.703067i	$-0.751814\pi$
$191$	−19.6559	−1.42225	−0.711124	+	0.703067i	$0.751814\pi$
$192$	−1.00000	−0.0721688
$193$	6.97298	0.501926	0.250963	−	0.967997i	$-0.419253\pi$
$193$	6.97298	0.501926	0.250963	+	0.967997i	$0.419253\pi$
$194$	11.8319	0.849481
$195$	−3.73327	−0.267345
$196$	1.41012	0.100723
$197$	−19.6949	−1.40320	−0.701602	−	0.712569i	$-0.747531\pi$
$197$	−19.6949	−1.40320	−0.701602	+	0.712569i	$0.747531\pi$
$198$	1.74334	0.123893
$199$	4.94883	0.350813	0.175406	−	0.984496i	$-0.443876\pi$
$199$	4.94883	0.350813	0.175406	+	0.984496i	$0.443876\pi$
$200$	4.25245	0.300694
$201$	10.8030	0.761983
$202$	−3.58097	−0.251956
$203$	−14.1162	−0.990766
$204$	3.14325	0.220072
$205$	−5.53573	−0.386632
$206$	11.1052	0.773734
$207$	2.44799	0.170147
$208$	4.31787	0.299391
$209$	−1.74334	−0.120589
$210$	2.50739	0.173026
$211$	19.8707	1.36796	0.683979	−	0.729502i	$-0.260248\pi$
$211$	19.8707	1.36796	0.683979	+	0.729502i	$0.260248\pi$
$212$	1.00000	0.0686803
$213$	2.93217	0.200909
$214$	−7.15731	−0.489264
$215$	3.55626	0.242535
$216$	1.00000	0.0680414
$217$	−22.1962	−1.50678
$218$	−10.7045	−0.725001
$219$	−4.34381	−0.293527
$220$	−1.50731	−0.101622
$221$	−13.5722	−0.912963
$222$	9.48198	0.636389
$223$	−13.4315	−0.899440	−0.449720	−	0.893170i	$-0.648476\pi$
$223$	−13.4315	−0.899440	−0.449720	+	0.893170i	$0.648476\pi$
$224$	−2.90002	−0.193766
$225$	−4.25245	−0.283497
$226$	9.87778	0.657060
$227$	−2.22110	−0.147419	−0.0737097	−	0.997280i	$-0.523484\pi$
$227$	−2.22110	−0.147419	−0.0737097	+	0.997280i	$0.523484\pi$
$228$	−1.00000	−0.0662266
$229$	−14.8688	−0.982555	−0.491277	−	0.871003i	$-0.663470\pi$
$229$	−14.8688	−0.982555	−0.491277	+	0.871003i	$0.663470\pi$
$230$	−2.11655	−0.139561
$231$	5.05571	0.332641
$232$	4.86763	0.319576
$233$	6.26646	0.410529	0.205265	−	0.978706i	$-0.434194\pi$
$233$	6.26646	0.410529	0.205265	+	0.978706i	$0.434194\pi$
$234$	−4.31787	−0.282268
$235$	−8.63151	−0.563057
$236$	−13.8169	−0.899404
$237$	4.78449	0.310786
$238$	9.11550	0.590870
$239$	19.4621	1.25890	0.629449	−	0.777042i	$-0.283281\pi$
$239$	19.4621	1.25890	0.629449	+	0.777042i	$0.283281\pi$
$240$	−0.864610	−0.0558103
$241$	12.6355	0.813922	0.406961	−	0.913446i	$-0.366588\pi$
$241$	12.6355	0.813922	0.406961	+	0.913446i	$0.366588\pi$
$242$	7.96078	0.511738
$243$	−1.00000	−0.0641500
$244$	−10.8725	−0.696043
$245$	1.21920	0.0778921
$246$	−6.40258	−0.408214
$247$	4.31787	0.274740
$248$	7.65381	0.486018
$249$	−8.79442	−0.557324
$250$	7.99976	0.505949
$251$	−8.74738	−0.552130	−0.276065	−	0.961139i	$-0.589030\pi$
$251$	−8.74738	−0.552130	−0.276065	+	0.961139i	$0.589030\pi$
$252$	2.90002	0.182684
$253$	−4.26766	−0.268306
$254$	−12.3988	−0.777973
$255$	2.71769	0.170188
$256$	1.00000	0.0625000
$257$	−12.2605	−0.764787	−0.382393	−	0.924000i	$-0.624900\pi$
$257$	−12.2605	−0.764787	−0.382393	+	0.924000i	$0.624900\pi$
$258$	4.11314	0.256073
$259$	27.4979	1.70864
$260$	3.73327	0.231528
$261$	−4.86763	−0.301299
$262$	6.48507	0.400649
$263$	21.1202	1.30233	0.651163	−	0.758938i	$-0.274281\pi$
$263$	21.1202	1.30233	0.651163	+	0.758938i	$0.274281\pi$
$264$	−1.74334	−0.107295
$265$	0.864610	0.0531125
$266$	−2.90002	−0.177812
$267$	13.0030	0.795771
$268$	−10.8030	−0.659897
$269$	10.5684	0.644366	0.322183	−	0.946677i	$-0.395583\pi$
$269$	10.5684	0.644366	0.322183	+	0.946677i	$0.395583\pi$
$270$	0.864610	0.0526185
$271$	22.8148	1.38590	0.692949	−	0.720987i	$-0.256311\pi$
$271$	22.8148	1.38590	0.692949	+	0.720987i	$0.256311\pi$
$272$	−3.14325	−0.190588
$273$	−12.5219	−0.757861
$274$	−16.5214	−0.998092
$275$	7.41345	0.447048
$276$	−2.44799	−0.147352
$277$	16.3373	0.981612	0.490806	−	0.871269i	$-0.336702\pi$
$277$	16.3373	0.981612	0.490806	+	0.871269i	$0.336702\pi$
$278$	9.27726	0.556413
$279$	−7.65381	−0.458222
$280$	−2.50739	−0.149845
$281$	7.31478	0.436363	0.218182	−	0.975908i	$-0.429987\pi$
$281$	7.31478	0.436363	0.218182	+	0.975908i	$0.429987\pi$
$282$	−9.98313	−0.594487
$283$	15.6198	0.928498	0.464249	−	0.885705i	$-0.346324\pi$
$283$	15.6198	0.928498	0.464249	+	0.885705i	$0.346324\pi$
$284$	−2.93217	−0.173992
$285$	−0.864610	−0.0512150
$286$	7.52750	0.445111
$287$	−18.5676	−1.09601
$288$	−1.00000	−0.0589256
$289$	−7.11997	−0.418821
$290$	4.20860	0.247138
$291$	11.8319	0.693599
$292$	4.34381	0.254202
$293$	−1.86089	−0.108715	−0.0543573	−	0.998522i	$-0.517311\pi$
$293$	−1.86089	−0.108715	−0.0543573	+	0.998522i	$0.517311\pi$
$294$	1.41012	0.0822400
$295$	−11.9462	−0.695536
$296$	−9.48198	−0.551129
$297$	1.74334	0.101159
$298$	−18.8652	−1.09283
$299$	10.5701	0.611285
$300$	4.25245	0.245515
$301$	11.9282	0.687529
$302$	−22.9955	−1.32324
$303$	−3.58097	−0.205721
$304$	1.00000	0.0573539
$305$	−9.40051	−0.538271
$306$	3.14325	0.179688
$307$	−26.1641	−1.49326	−0.746631	−	0.665239i	$-0.768330\pi$
$307$	−26.1641	−1.49326	−0.746631	+	0.665239i	$0.768330\pi$
$308$	−5.05571	−0.288076
$309$	11.1052	0.631752
$310$	6.61756	0.375852
$311$	9.77278	0.554163	0.277082	−	0.960846i	$-0.410633\pi$
$311$	9.77278	0.554163	0.277082	+	0.960846i	$0.410633\pi$
$312$	4.31787	0.244451
$313$	7.08022	0.400198	0.200099	−	0.979776i	$-0.435874\pi$
$313$	7.08022	0.400198	0.200099	+	0.979776i	$0.435874\pi$
$314$	−4.27863	−0.241457
$315$	2.50739	0.141275
$316$	−4.78449	−0.269149
$317$	−2.19198	−0.123114	−0.0615570	−	0.998104i	$-0.519607\pi$
$317$	−2.19198	−0.123114	−0.0615570	+	0.998104i	$0.519607\pi$
$318$	1.00000	0.0560772
$319$	8.48592	0.475120
$320$	0.864610	0.0483331
$321$	−7.15731	−0.399482
$322$	−7.09921	−0.395624
$323$	−3.14325	−0.174895
$324$	1.00000	0.0555556
$325$	−18.3615	−1.01852
$326$	1.36454	0.0755750
$327$	−10.7045	−0.591961
$328$	6.40258	0.353523
$329$	−28.9513	−1.59614
$330$	−1.50731	−0.0829744
$331$	−8.85033	−0.486458	−0.243229	−	0.969969i	$-0.578207\pi$
$331$	−8.85033	−0.486458	−0.243229	+	0.969969i	$0.578207\pi$
$332$	8.79442	0.482656
$333$	9.48198	0.519609
$334$	20.9727	1.14758
$335$	−9.34035	−0.510318
$336$	−2.90002	−0.158209
$337$	22.8213	1.24316	0.621578	−	0.783353i	$-0.286492\pi$
$337$	22.8213	1.24316	0.621578	+	0.783353i	$0.286492\pi$
$338$	−5.64403	−0.306995
$339$	9.87778	0.536487
$340$	−2.71769	−0.147387
$341$	13.3432	0.722573
$342$	−1.00000	−0.0540738
$343$	−16.2108	−0.875299
$344$	−4.11314	−0.221765
$345$	−2.11655	−0.113951
$346$	−18.5311	−0.996240
$347$	−28.4779	−1.52877	−0.764386	−	0.644759i	$-0.776958\pi$
$347$	−28.4779	−1.52877	−0.764386	+	0.644759i	$0.776958\pi$
$348$	4.86763	0.260933
$349$	−32.9964	−1.76626	−0.883129	−	0.469131i	$-0.844567\pi$
$349$	−32.9964	−1.76626	−0.883129	+	0.469131i	$0.844567\pi$
$350$	12.3322	0.659184
$351$	−4.31787	−0.230471
$352$	1.74334	0.0929201
$353$	30.1448	1.60445	0.802223	−	0.597025i	$-0.203651\pi$
$353$	30.1448	1.60445	0.802223	+	0.597025i	$0.203651\pi$
$354$	−13.8169	−0.734360
$355$	−2.53518	−0.134553
$356$	−13.0030	−0.689158
$357$	9.11550	0.482443
$358$	0.823328	0.0435142
$359$	15.8853	0.838392	0.419196	−	0.907896i	$-0.362312\pi$
$359$	15.8853	0.838392	0.419196	+	0.907896i	$0.362312\pi$
$360$	−0.864610	−0.0455689
$361$	1.00000	0.0526316
$362$	16.9742	0.892144
$363$	7.96078	0.417833
$364$	12.5219	0.656327
$365$	3.75570	0.196582
$366$	−10.8725	−0.568317
$367$	−22.1710	−1.15731	−0.578657	−	0.815571i	$-0.696423\pi$
$367$	−22.1710	−1.15731	−0.578657	+	0.815571i	$0.696423\pi$
$368$	2.44799	0.127610
$369$	−6.40258	−0.333305
$370$	−8.19821	−0.426205
$371$	2.90002	0.150562
$372$	7.65381	0.396832
$373$	−7.51665	−0.389197	−0.194599	−	0.980883i	$-0.562340\pi$
$373$	−7.51665	−0.389197	−0.194599	+	0.980883i	$0.562340\pi$
$374$	−5.47975	−0.283351
$375$	7.99976	0.413106
$376$	9.98313	0.514840
$377$	−21.0178	−1.08247
$378$	2.90002	0.149161
$379$	−29.4403	−1.51225	−0.756124	−	0.654428i	$-0.772909\pi$
$379$	−29.4403	−1.51225	−0.756124	+	0.654428i	$0.772909\pi$
$380$	0.864610	0.0443535
$381$	−12.3988	−0.635212
$382$	19.6559	1.00568
$383$	8.62893	0.440918	0.220459	−	0.975396i	$-0.429245\pi$
$383$	8.62893	0.440918	0.220459	+	0.975396i	$0.429245\pi$
$384$	1.00000	0.0510310
$385$	−4.37122	−0.222778
$386$	−6.97298	−0.354915
$387$	4.11314	0.209082
$388$	−11.8319	−0.600674
$389$	19.9894	1.01350	0.506750	−	0.862093i	$-0.330847\pi$
$389$	19.9894	1.01350	0.506750	+	0.862093i	$0.330847\pi$
$390$	3.73327	0.189042
$391$	−7.69464	−0.389135
$392$	−1.41012	−0.0712219
$393$	6.48507	0.327129
$394$	19.6949	0.992214
$395$	−4.13672	−0.208141
$396$	−1.74334	−0.0876059
$397$	16.3859	0.822386	0.411193	−	0.911548i	$-0.365112\pi$
$397$	16.3859	0.822386	0.411193	+	0.911548i	$0.365112\pi$
$398$	−4.94883	−0.248062
$399$	−2.90002	−0.145183
$400$	−4.25245	−0.212623
$401$	8.35977	0.417467	0.208733	−	0.977973i	$-0.433066\pi$
$401$	8.35977	0.417467	0.208733	+	0.977973i	$0.433066\pi$
$402$	−10.8030	−0.538803
$403$	−33.0482	−1.64625
$404$	3.58097	0.178160
$405$	0.864610	0.0429628
$406$	14.1162	0.700577
$407$	−16.5303	−0.819376
$408$	−3.14325	−0.155614
$409$	24.0429	1.18884	0.594422	−	0.804153i	$-0.297381\pi$
$409$	24.0429	1.18884	0.594422	+	0.804153i	$0.297381\pi$
$410$	5.53573	0.273390
$411$	−16.5214	−0.814938
$412$	−11.1052	−0.547113
$413$	−40.0693	−1.97168
$414$	−2.44799	−0.120312
$415$	7.60374	0.373253
$416$	−4.31787	−0.211701
$417$	9.27726	0.454309
$418$	1.74334	0.0852694
$419$	−4.25187	−0.207718	−0.103859	−	0.994592i	$-0.533119\pi$
$419$	−4.25187	−0.207718	−0.103859	+	0.994592i	$0.533119\pi$
$420$	−2.50739	−0.122348
$421$	7.68084	0.374341	0.187171	−	0.982327i	$-0.440068\pi$
$421$	7.68084	0.374341	0.187171	+	0.982327i	$0.440068\pi$
$422$	−19.8707	−0.967293
$423$	−9.98313	−0.485396
$424$	−1.00000	−0.0485643
$425$	13.3665	0.648372
$426$	−2.93217	−0.142064
$427$	−31.5306	−1.52587
$428$	7.15731	0.345962
$429$	7.52750	0.363431
$430$	−3.55626	−0.171498
$431$	−32.2853	−1.55513	−0.777564	−	0.628804i	$-0.783545\pi$
$431$	−32.2853	−1.55513	−0.777564	+	0.628804i	$0.783545\pi$
$432$	−1.00000	−0.0481125
$433$	−10.9186	−0.524713	−0.262356	−	0.964971i	$-0.584500\pi$
$433$	−10.9186	−0.524713	−0.262356	+	0.964971i	$0.584500\pi$
$434$	22.1962	1.06545
$435$	4.20860	0.201787
$436$	10.7045	0.512653
$437$	2.44799	0.117103
$438$	4.34381	0.207555
$439$	−18.3240	−0.874556	−0.437278	−	0.899326i	$-0.644057\pi$
$439$	−18.3240	−0.874556	−0.437278	+	0.899326i	$0.644057\pi$
$440$	1.50731	0.0718579
$441$	1.41012	0.0671487
$442$	13.5722	0.645562
$443$	14.1082	0.670301	0.335150	−	0.942165i	$-0.391213\pi$
$443$	14.1082	0.670301	0.335150	+	0.942165i	$0.391213\pi$
$444$	−9.48198	−0.449995
$445$	−11.2425	−0.532947
$446$	13.4315	0.636000
$447$	−18.8652	−0.892293
$448$	2.90002	0.137013
$449$	−2.59755	−0.122586	−0.0612929	−	0.998120i	$-0.519522\pi$
$449$	−2.59755	−0.122586	−0.0612929	+	0.998120i	$0.519522\pi$
$450$	4.25245	0.200462
$451$	11.1618	0.525591
$452$	−9.87778	−0.464612
$453$	−22.9955	−1.08042
$454$	2.22110	0.104241
$455$	10.8266	0.507558
$456$	1.00000	0.0468293
$457$	9.87647	0.462002	0.231001	−	0.972954i	$-0.425800\pi$
$457$	9.87647	0.462002	0.231001	+	0.972954i	$0.425800\pi$
$458$	14.8688	0.694771
$459$	3.14325	0.146714
$460$	2.11655	0.0986848
$461$	17.0797	0.795483	0.397741	−	0.917498i	$-0.369794\pi$
$461$	17.0797	0.795483	0.397741	+	0.917498i	$0.369794\pi$
$462$	−5.05571	−0.235213
$463$	−31.0474	−1.44289	−0.721447	−	0.692470i	$-0.756523\pi$
$463$	−31.0474	−1.44289	−0.721447	+	0.692470i	$0.756523\pi$
$464$	−4.86763	−0.225974
$465$	6.61756	0.306882
$466$	−6.26646	−0.290288
$467$	−7.16351	−0.331488	−0.165744	−	0.986169i	$-0.553002\pi$
$467$	−7.16351	−0.331488	−0.165744	+	0.986169i	$0.553002\pi$
$468$	4.31787	0.199594
$469$	−31.3288	−1.44663
$470$	8.63151	0.398142
$471$	−4.27863	−0.197149
$472$	13.8169	0.635974
$473$	−7.17058	−0.329704
$474$	−4.78449	−0.219759
$475$	−4.25245	−0.195116
$476$	−9.11550	−0.417808
$477$	1.00000	0.0457869
$478$	−19.4621	−0.890175
$479$	−27.8936	−1.27449	−0.637247	−	0.770660i	$-0.719927\pi$
$479$	−27.8936	−1.27449	−0.637247	+	0.770660i	$0.719927\pi$
$480$	0.864610	0.0394638
$481$	40.9420	1.86679
$482$	−12.6355	−0.575530
$483$	−7.09921	−0.323025
$484$	−7.96078	−0.361854
$485$	−10.2300	−0.464519
$486$	1.00000	0.0453609
$487$	−11.4312	−0.517997	−0.258998	−	0.965878i	$-0.583392\pi$
$487$	−11.4312	−0.517997	−0.258998	+	0.965878i	$0.583392\pi$
$488$	10.8725	0.492177
$489$	1.36454	0.0617067
$490$	−1.21920	−0.0550781
$491$	−30.1637	−1.36127	−0.680633	−	0.732624i	$-0.738295\pi$
$491$	−30.1637	−1.36127	−0.680633	+	0.732624i	$0.738295\pi$
$492$	6.40258	0.288651
$493$	15.3002	0.689086
$494$	−4.31787	−0.194270
$495$	−1.50731	−0.0677483
$496$	−7.65381	−0.343666
$497$	−8.50335	−0.381427
$498$	8.79442	0.394087
$499$	−1.49935	−0.0671201	−0.0335600	−	0.999437i	$-0.510684\pi$
$499$	−1.49935	−0.0671201	−0.0335600	+	0.999437i	$0.510684\pi$
$500$	−7.99976	−0.357760
$501$	20.9727	0.936992
$502$	8.74738	0.390415
$503$	−30.1530	−1.34446	−0.672228	−	0.740344i	$-0.734663\pi$
$503$	−30.1530	−1.34446	−0.672228	+	0.740344i	$0.734663\pi$
$504$	−2.90002	−0.129177
$505$	3.09614	0.137776
$506$	4.26766	0.189721
$507$	−5.64403	−0.250660
$508$	12.3988	0.550110
$509$	−36.5639	−1.62067	−0.810334	−	0.585968i	$-0.800714\pi$
$509$	−36.5639	−1.62067	−0.810334	+	0.585968i	$0.800714\pi$
$510$	−2.71769	−0.120341
$511$	12.5971	0.557265
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	12.2605	0.540786
$515$	−9.60164	−0.423099
$516$	−4.11314	−0.181071
$517$	17.4039	0.765425
$518$	−27.4979	−1.20819
$519$	−18.5311	−0.813426
$520$	−3.73327	−0.163715
$521$	1.89768	0.0831387	0.0415693	−	0.999136i	$-0.486764\pi$
$521$	1.89768	0.0831387	0.0415693	+	0.999136i	$0.486764\pi$
$522$	4.86763	0.213051
$523$	−20.9007	−0.913923	−0.456962	−	0.889486i	$-0.651062\pi$
$523$	−20.9007	−0.913923	−0.456962	+	0.889486i	$0.651062\pi$
$524$	−6.48507	−0.283302
$525$	12.3322	0.538221
$526$	−21.1202	−0.920884
$527$	24.0579	1.04798
$528$	1.74334	0.0758690
$529$	−17.0074	−0.739450
$530$	−0.864610	−0.0375562
$531$	−13.8169	−0.599602
$532$	2.90002	0.125732
$533$	−27.6455	−1.19746
$534$	−13.0030	−0.562695
$535$	6.18828	0.267543
$536$	10.8030	0.466617
$537$	0.823328	0.0355292
$538$	−10.5684	−0.455635
$539$	−2.45832	−0.105887
$540$	−0.864610	−0.0372069
$541$	−24.9565	−1.07296	−0.536482	−	0.843912i	$-0.680247\pi$
$541$	−24.9565	−1.07296	−0.536482	+	0.843912i	$0.680247\pi$
$542$	−22.8148	−0.979978
$543$	16.9742	0.728433
$544$	3.14325	0.134766
$545$	9.25523	0.396450
$546$	12.5219	0.535889
$547$	−19.6754	−0.841260	−0.420630	−	0.907232i	$-0.638191\pi$
$547$	−19.6754	−0.841260	−0.420630	+	0.907232i	$0.638191\pi$
$548$	16.5214	0.705757
$549$	−10.8725	−0.464029
$550$	−7.41345	−0.316111
$551$	−4.86763	−0.207368
$552$	2.44799	0.104193
$553$	−13.8751	−0.590031
$554$	−16.3373	−0.694104
$555$	−8.19821	−0.347995
$556$	−9.27726	−0.393443
$557$	2.36075	0.100028	0.0500142	−	0.998749i	$-0.484073\pi$
$557$	2.36075	0.100028	0.0500142	+	0.998749i	$0.484073\pi$
$558$	7.65381	0.324012
$559$	17.7600	0.751168
$560$	2.50739	0.105956
$561$	−5.47975	−0.231355
$562$	−7.31478	−0.308555
$563$	2.89196	0.121882	0.0609408	−	0.998141i	$-0.480590\pi$
$563$	2.89196	0.121882	0.0609408	+	0.998141i	$0.480590\pi$
$564$	9.98313	0.420365
$565$	−8.54042	−0.359298
$566$	−15.6198	−0.656547
$567$	2.90002	0.121789
$568$	2.93217	0.123031
$569$	5.51008	0.230995	0.115497	−	0.993308i	$-0.463154\pi$
$569$	5.51008	0.230995	0.115497	+	0.993308i	$0.463154\pi$
$570$	0.864610	0.0362145
$571$	7.08718	0.296589	0.148295	−	0.988943i	$-0.452622\pi$
$571$	7.08718	0.296589	0.148295	+	0.988943i	$0.452622\pi$
$572$	−7.52750	−0.314741
$573$	19.6559	0.821135
$574$	18.5676	0.774997
$575$	−10.4099	−0.434125
$576$	1.00000	0.0416667
$577$	11.9732	0.498451	0.249226	−	0.968445i	$-0.419824\pi$
$577$	11.9732	0.498451	0.249226	+	0.968445i	$0.419824\pi$
$578$	7.11997	0.296152
$579$	−6.97298	−0.289787
$580$	−4.20860	−0.174753
$581$	25.5040	1.05808
$582$	−11.8319	−0.490448
$583$	−1.74334	−0.0722016
$584$	−4.34381	−0.179748
$585$	3.73327	0.154352
$586$	1.86089	0.0768728
$587$	−9.49151	−0.391756	−0.195878	−	0.980628i	$-0.562756\pi$
$587$	−9.49151	−0.391756	−0.195878	+	0.980628i	$0.562756\pi$
$588$	−1.41012	−0.0581524
$589$	−7.65381	−0.315370
$590$	11.9462	0.491818
$591$	19.6949	0.810140
$592$	9.48198	0.389707
$593$	−0.310805	−0.0127632	−0.00638161	−	0.999980i	$-0.502031\pi$
$593$	−0.310805	−0.0127632	−0.00638161	+	0.999980i	$0.502031\pi$
$594$	−1.74334	−0.0715299
$595$	−7.88135	−0.323104
$596$	18.8652	0.772748
$597$	−4.94883	−0.202542
$598$	−10.5701	−0.432243
$599$	−11.3947	−0.465576	−0.232788	−	0.972528i	$-0.574785\pi$
$599$	−11.3947	−0.465576	−0.232788	+	0.972528i	$0.574785\pi$
$600$	−4.25245	−0.173606
$601$	14.8087	0.604060	0.302030	−	0.953298i	$-0.402336\pi$
$601$	14.8087	0.604060	0.302030	+	0.953298i	$0.402336\pi$
$602$	−11.9282	−0.486156
$603$	−10.8030	−0.439931
$604$	22.9955	0.935675
$605$	−6.88297	−0.279832
$606$	3.58097	0.145467
$607$	0.603813	0.0245080	0.0122540	−	0.999925i	$-0.496099\pi$
$607$	0.603813	0.0245080	0.0122540	+	0.999925i	$0.496099\pi$
$608$	−1.00000	−0.0405554
$609$	14.1162	0.572019
$610$	9.40051	0.380615
$611$	−43.1059	−1.74388
$612$	−3.14325	−0.127058
$613$	−11.6636	−0.471087	−0.235544	−	0.971864i	$-0.575687\pi$
$613$	−11.6636	−0.471087	−0.235544	+	0.971864i	$0.575687\pi$
$614$	26.1641	1.05590
$615$	5.53573	0.223222
$616$	5.05571	0.203700
$617$	−41.5718	−1.67362	−0.836810	−	0.547494i	$-0.815582\pi$
$617$	−41.5718	−1.67362	−0.836810	+	0.547494i	$0.815582\pi$
$618$	−11.1052	−0.446716
$619$	46.4693	1.86776	0.933880	−	0.357587i	$-0.116400\pi$
$619$	46.4693	1.86776	0.933880	+	0.357587i	$0.116400\pi$
$620$	−6.61756	−0.265768
$621$	−2.44799	−0.0982343
$622$	−9.77278	−0.391853
$623$	−37.7090	−1.51078
$624$	−4.31787	−0.172853
$625$	14.3456	0.573823
$626$	−7.08022	−0.282982
$627$	1.74334	0.0696221
$628$	4.27863	0.170736
$629$	−29.8043	−1.18837
$630$	−2.50739	−0.0998966
$631$	30.1429	1.19997	0.599985	−	0.800011i	$-0.295173\pi$
$631$	30.1429	1.19997	0.599985	+	0.800011i	$0.295173\pi$
$632$	4.78449	0.190317
$633$	−19.8707	−0.789791
$634$	2.19198	0.0870547
$635$	10.7202	0.425417
$636$	−1.00000	−0.0396526
$637$	6.08873	0.241244
$638$	−8.48592	−0.335961
$639$	−2.93217	−0.115995
$640$	−0.864610	−0.0341767
$641$	21.5609	0.851606	0.425803	−	0.904816i	$-0.359992\pi$
$641$	21.5609	0.851606	0.425803	+	0.904816i	$0.359992\pi$
$642$	7.15731	0.282477
$643$	36.1050	1.42384	0.711921	−	0.702260i	$-0.247825\pi$
$643$	36.1050	1.42384	0.711921	+	0.702260i	$0.247825\pi$
$644$	7.09921	0.279748
$645$	−3.55626	−0.140027
$646$	3.14325	0.123670
$647$	14.8713	0.584650	0.292325	−	0.956319i	$-0.405571\pi$
$647$	14.8713	0.584650	0.292325	+	0.956319i	$0.405571\pi$
$648$	−1.00000	−0.0392837
$649$	24.0875	0.945517
$650$	18.3615	0.720199
$651$	22.1962	0.869938
$652$	−1.36454	−0.0534396
$653$	0.0279784	0.00109488	0.000547440	−	1.00000i	$-0.499826\pi$
$653$	0.0279784	0.00109488	0.000547440		1.00000i	$0.499826\pi$
$654$	10.7045	0.418580
$655$	−5.60706	−0.219086
$656$	−6.40258	−0.249979
$657$	4.34381	0.169468
$658$	28.9513	1.12864
$659$	−17.6551	−0.687745	−0.343873	−	0.939016i	$-0.611739\pi$
$659$	−17.6551	−0.687745	−0.343873	+	0.939016i	$0.611739\pi$
$660$	1.50731	0.0586718
$661$	3.47304	0.135086	0.0675429	−	0.997716i	$-0.478484\pi$
$661$	3.47304	0.135086	0.0675429	+	0.997716i	$0.478484\pi$
$662$	8.85033	0.343978
$663$	13.5722	0.527099
$664$	−8.79442	−0.341290
$665$	2.50739	0.0972323
$666$	−9.48198	−0.367419
$667$	−11.9159	−0.461386
$668$	−20.9727	−0.811459
$669$	13.4315	0.519292
$670$	9.34035	0.360849
$671$	18.9545	0.731730
$672$	2.90002	0.111871
$673$	−11.6423	−0.448779	−0.224390	−	0.974499i	$-0.572039\pi$
$673$	−11.6423	−0.448779	−0.224390	+	0.974499i	$0.572039\pi$
$674$	−22.8213	−0.879043
$675$	4.25245	0.163677
$676$	5.64403	0.217078
$677$	−50.2718	−1.93210	−0.966052	−	0.258348i	$-0.916822\pi$
$677$	−50.2718	−1.93210	−0.966052	+	0.258348i	$0.916822\pi$
$678$	−9.87778	−0.379354
$679$	−34.3128	−1.31680
$680$	2.71769	0.104218
$681$	2.22110	0.0851127
$682$	−13.3432	−0.510936
$683$	−9.44375	−0.361355	−0.180677	−	0.983542i	$-0.557829\pi$
$683$	−9.44375	−0.361355	−0.180677	+	0.983542i	$0.557829\pi$
$684$	1.00000	0.0382360
$685$	14.2845	0.545783
$686$	16.2108	0.618930
$687$	14.8688	0.567278
$688$	4.11314	0.156812
$689$	4.31787	0.164498
$690$	2.11655	0.0805758
$691$	13.7970	0.524864	0.262432	−	0.964950i	$-0.415475\pi$
$691$	13.7970	0.524864	0.262432	+	0.964950i	$0.415475\pi$
$692$	18.5311	0.704448
$693$	−5.05571	−0.192051
$694$	28.4779	1.08101
$695$	−8.02121	−0.304262
$696$	−4.86763	−0.184507
$697$	20.1249	0.762286
$698$	32.9964	1.24893
$699$	−6.26646	−0.237019
$700$	−12.3322	−0.466113
$701$	−8.47621	−0.320142	−0.160071	−	0.987106i	$-0.551172\pi$
$701$	−8.47621	−0.320142	−0.160071	+	0.987106i	$0.551172\pi$
$702$	4.31787	0.162968
$703$	9.48198	0.357620
$704$	−1.74334	−0.0657045
$705$	8.63151	0.325081
$706$	−30.1448	−1.13451
$707$	10.3849	0.390564
$708$	13.8169	0.519271
$709$	17.7334	0.665992	0.332996	−	0.942928i	$-0.391940\pi$
$709$	17.7334	0.665992	0.332996	+	0.942928i	$0.391940\pi$
$710$	2.53518	0.0951436
$711$	−4.78449	−0.179433
$712$	13.0030	0.487308
$713$	−18.7364	−0.701685
$714$	−9.11550	−0.341139
$715$	−6.50835	−0.243399
$716$	−0.823328	−0.0307692
$717$	−19.4621	−0.726825
$718$	−15.8853	−0.592832
$719$	−32.9000	−1.22696	−0.613481	−	0.789710i	$-0.710231\pi$
$719$	−32.9000	−1.22696	−0.613481	+	0.789710i	$0.710231\pi$
$720$	0.864610	0.0322221
$721$	−32.2053	−1.19939
$722$	−1.00000	−0.0372161
$723$	−12.6355	−0.469918
$724$	−16.9742	−0.630841
$725$	20.6994	0.768755
$726$	−7.96078	−0.295452
$727$	−0.0763921	−0.00283323	−0.00141661	−	0.999999i	$-0.500451\pi$
$727$	−0.0763921	−0.00283323	−0.00141661	+	0.999999i	$0.500451\pi$
$728$	−12.5219	−0.464093
$729$	1.00000	0.0370370
$730$	−3.75570	−0.139005
$731$	−12.9286	−0.478182
$732$	10.8725	0.401861
$733$	8.59090	0.317312	0.158656	−	0.987334i	$-0.449284\pi$
$733$	8.59090	0.317312	0.158656	+	0.987334i	$0.449284\pi$
$734$	22.1710	0.818345
$735$	−1.21920	−0.0449710
$736$	−2.44799	−0.0902340
$737$	18.8332	0.693730
$738$	6.40258	0.235682
$739$	−16.5972	−0.610539	−0.305270	−	0.952266i	$-0.598747\pi$
$739$	−16.5972	−0.610539	−0.305270	+	0.952266i	$0.598747\pi$
$740$	8.19821	0.301372
$741$	−4.31787	−0.158621
$742$	−2.90002	−0.106463
$743$	−9.05641	−0.332247	−0.166124	−	0.986105i	$-0.553125\pi$
$743$	−9.05641	−0.332247	−0.166124	+	0.986105i	$0.553125\pi$
$744$	−7.65381	−0.280602
$745$	16.3110	0.597590
$746$	7.51665	0.275204
$747$	8.79442	0.321771
$748$	5.47975	0.200359
$749$	20.7564	0.758421
$750$	−7.99976	−0.292110
$751$	−42.7955	−1.56163	−0.780816	−	0.624762i	$-0.785196\pi$
$751$	−42.7955	−1.56163	−0.780816	+	0.624762i	$0.785196\pi$
$752$	−9.98313	−0.364047
$753$	8.74738	0.318772
$754$	21.0178	0.765424
$755$	19.8822	0.723586
$756$	−2.90002	−0.105473
$757$	35.4419	1.28816	0.644079	−	0.764959i	$-0.277241\pi$
$757$	35.4419	1.28816	0.644079	+	0.764959i	$0.277241\pi$
$758$	29.4403	1.06932
$759$	4.26766	0.154906
$760$	−0.864610	−0.0313627
$761$	−18.6256	−0.675179	−0.337589	−	0.941294i	$-0.609611\pi$
$761$	−18.6256	−0.675179	−0.337589	+	0.941294i	$0.609611\pi$
$762$	12.3988	0.449163
$763$	31.0433	1.12384
$764$	−19.6559	−0.711124
$765$	−2.71769	−0.0982581
$766$	−8.62893	−0.311776
$767$	−59.6596	−2.15418
$768$	−1.00000	−0.0360844
$769$	27.6772	0.998065	0.499033	−	0.866583i	$-0.333689\pi$
$769$	27.6772	0.998065	0.499033	+	0.866583i	$0.333689\pi$
$770$	4.37122	0.157528
$771$	12.2605	0.441550
$772$	6.97298	0.250963
$773$	−35.8210	−1.28839	−0.644196	−	0.764860i	$-0.722808\pi$
$773$	−35.8210	−1.28839	−0.644196	+	0.764860i	$0.722808\pi$
$774$	−4.11314	−0.147844
$775$	32.5475	1.16914
$776$	11.8319	0.424741
$777$	−27.4979	−0.986483
$778$	−19.9894	−0.716653
$779$	−6.40258	−0.229396
$780$	−3.73327	−0.133673
$781$	5.11175	0.182913
$782$	7.69464	0.275160
$783$	4.86763	0.173955
$784$	1.41012	0.0503615
$785$	3.69934	0.132035
$786$	−6.48507	−0.231315
$787$	44.2870	1.57866	0.789331	−	0.613968i	$-0.210428\pi$
$787$	44.2870	1.57866	0.789331	+	0.613968i	$0.210428\pi$
$788$	−19.6949	−0.701602
$789$	−21.1202	−0.751899
$790$	4.13672	0.147178
$791$	−28.6458	−1.01853
$792$	1.74334	0.0619467
$793$	−46.9463	−1.66711
$794$	−16.3859	−0.581515
$795$	−0.864610	−0.0306645
$796$	4.94883	0.175406
$797$	−47.1672	−1.67075	−0.835374	−	0.549682i	$-0.814749\pi$
$797$	−47.1672	−1.67075	−0.835374	+	0.549682i	$0.814749\pi$
$798$	2.90002	0.102660
$799$	31.3795	1.11013
$800$	4.25245	0.150347
$801$	−13.0030	−0.459439
$802$	−8.35977	−0.295194
$803$	−7.57272	−0.267236
$804$	10.8030	0.380991
$805$	6.13805	0.216338
$806$	33.0482	1.16407
$807$	−10.5684	−0.372025
$808$	−3.58097	−0.125978
$809$	16.5941	0.583418	0.291709	−	0.956507i	$-0.405776\pi$
$809$	16.5941	0.583418	0.291709	+	0.956507i	$0.405776\pi$
$810$	−0.864610	−0.0303793
$811$	−44.4007	−1.55912	−0.779561	−	0.626327i	$-0.784558\pi$
$811$	−44.4007	−1.55912	−0.779561	+	0.626327i	$0.784558\pi$
$812$	−14.1162	−0.495383
$813$	−22.8148	−0.800149
$814$	16.5303	0.579386
$815$	−1.17980	−0.0413265
$816$	3.14325	0.110036
$817$	4.11314	0.143900
$818$	−24.0429	−0.840639
$819$	12.5219	0.437551
$820$	−5.53573	−0.193316
$821$	43.7447	1.52670	0.763350	−	0.645985i	$-0.223553\pi$
$821$	43.7447	1.52670	0.763350	+	0.645985i	$0.223553\pi$
$822$	16.5214	0.576248
$823$	−10.6071	−0.369742	−0.184871	−	0.982763i	$-0.559187\pi$
$823$	−10.6071	−0.369742	−0.184871	+	0.982763i	$0.559187\pi$
$824$	11.1052	0.386867
$825$	−7.41345	−0.258103
$826$	40.0693	1.39419
$827$	49.1277	1.70834	0.854169	−	0.519996i	$-0.174067\pi$
$827$	49.1277	1.70834	0.854169	+	0.519996i	$0.174067\pi$
$828$	2.44799	0.0850734
$829$	8.96524	0.311376	0.155688	−	0.987806i	$-0.450241\pi$
$829$	8.96524	0.311376	0.155688	+	0.987806i	$0.450241\pi$
$830$	−7.60374	−0.263930
$831$	−16.3373	−0.566734
$832$	4.31787	0.149695
$833$	−4.43237	−0.153572
$834$	−9.27726	−0.321245
$835$	−18.1332	−0.627526
$836$	−1.74334	−0.0602945
$837$	7.65381	0.264554
$838$	4.25187	0.146878
$839$	−2.75915	−0.0952564	−0.0476282	−	0.998865i	$-0.515166\pi$
$839$	−2.75915	−0.0952564	−0.0476282	+	0.998865i	$0.515166\pi$
$840$	2.50739	0.0865130
$841$	−5.30614	−0.182970
$842$	−7.68084	−0.264699
$843$	−7.31478	−0.251934
$844$	19.8707	0.683979
$845$	4.87988	0.167873
$846$	9.98313	0.343227
$847$	−23.0864	−0.793259
$848$	1.00000	0.0343401
$849$	−15.6198	−0.536069
$850$	−13.3665	−0.458468
$851$	23.2118	0.795689
$852$	2.93217	0.100454
$853$	−40.4233	−1.38407	−0.692034	−	0.721865i	$-0.743285\pi$
$853$	−40.4233	−1.38407	−0.692034	+	0.721865i	$0.743285\pi$
$854$	31.5306	1.07896
$855$	0.864610	0.0295690
$856$	−7.15731	−0.244632
$857$	15.7195	0.536969	0.268484	−	0.963284i	$-0.413477\pi$
$857$	15.7195	0.536969	0.268484	+	0.963284i	$0.413477\pi$
$858$	−7.52750	−0.256985
$859$	−3.57136	−0.121853	−0.0609266	−	0.998142i	$-0.519406\pi$
$859$	−3.57136	−0.121853	−0.0609266	+	0.998142i	$0.519406\pi$
$860$	3.55626	0.121267
$861$	18.5676	0.632783
$862$	32.2853	1.09964
$863$	8.80719	0.299800	0.149900	−	0.988701i	$-0.452105\pi$
$863$	8.80719	0.299800	0.149900	+	0.988701i	$0.452105\pi$
$864$	1.00000	0.0340207
$865$	16.0222	0.544771
$866$	10.9186	0.371028
$867$	7.11997	0.241807
$868$	−22.1962	−0.753389
$869$	8.34098	0.282948
$870$	−4.20860	−0.142685
$871$	−46.6459	−1.58053
$872$	−10.7045	−0.362501
$873$	−11.8319	−0.400449
$874$	−2.44799	−0.0828044
$875$	−23.1995	−0.784285
$876$	−4.34381	−0.146764
$877$	1.68246	0.0568125	0.0284063	−	0.999596i	$-0.490957\pi$
$877$	1.68246	0.0568125	0.0284063	+	0.999596i	$0.490957\pi$
$878$	18.3240	0.618404
$879$	1.86089	0.0627663
$880$	−1.50731	−0.0508112
$881$	23.5730	0.794196	0.397098	−	0.917776i	$-0.370017\pi$
$881$	23.5730	0.794196	0.397098	+	0.917776i	$0.370017\pi$
$882$	−1.41012	−0.0474813
$883$	26.1955	0.881548	0.440774	−	0.897618i	$-0.354704\pi$
$883$	26.1955	0.881548	0.440774	+	0.897618i	$0.354704\pi$
$884$	−13.5722	−0.456481
$885$	11.9462	0.401568
$886$	−14.1082	−0.473974
$887$	−0.762587	−0.0256052	−0.0128026	−	0.999918i	$-0.504075\pi$
$887$	−0.762587	−0.0256052	−0.0128026	+	0.999918i	$0.504075\pi$
$888$	9.48198	0.318195
$889$	35.9569	1.20596
$890$	11.2425	0.376850
$891$	−1.74334	−0.0584040
$892$	−13.4315	−0.449720
$893$	−9.98313	−0.334073
$894$	18.8652	0.630946
$895$	−0.711857	−0.0237948
$896$	−2.90002	−0.0968829
$897$	−10.5701	−0.352925
$898$	2.59755	0.0866812
$899$	37.2560	1.24256
$900$	−4.25245	−0.141748
$901$	−3.14325	−0.104717
$902$	−11.1618	−0.371649
$903$	−11.9282	−0.396945
$904$	9.87778	0.328530
$905$	−14.6761	−0.487849
$906$	22.9955	0.763975
$907$	4.91961	0.163353	0.0816766	−	0.996659i	$-0.473973\pi$
$907$	4.91961	0.163353	0.0816766	+	0.996659i	$0.473973\pi$
$908$	−2.22110	−0.0737097
$909$	3.58097	0.118773
$910$	−10.8266	−0.358897
$911$	−22.3895	−0.741798	−0.370899	−	0.928673i	$-0.620950\pi$
$911$	−22.3895	−0.741798	−0.370899	+	0.928673i	$0.620950\pi$
$912$	−1.00000	−0.0331133
$913$	−15.3316	−0.507403
$914$	−9.87647	−0.326685
$915$	9.40051	0.310771
$916$	−14.8688	−0.491277
$917$	−18.8069	−0.621057
$918$	−3.14325	−0.103743
$919$	29.9405	0.987647	0.493823	−	0.869562i	$-0.335599\pi$
$919$	29.9405	0.987647	0.493823	+	0.869562i	$0.335599\pi$
$920$	−2.11655	−0.0697807
$921$	26.1641	0.862135
$922$	−17.0797	−0.562491
$923$	−12.6607	−0.416733
$924$	5.05571	0.166321
$925$	−40.3217	−1.32577
$926$	31.0474	1.02028
$927$	−11.1052	−0.364742
$928$	4.86763	0.159788
$929$	40.9162	1.34242	0.671209	−	0.741268i	$-0.265775\pi$
$929$	40.9162	1.34242	0.671209	+	0.741268i	$0.265775\pi$
$930$	−6.61756	−0.216998
$931$	1.41012	0.0462149
$932$	6.26646	0.205265
$933$	−9.77278	−0.319946
$934$	7.16351	0.234397
$935$	4.73784	0.154944
$936$	−4.31787	−0.141134
$937$	11.6618	0.380973	0.190487	−	0.981690i	$-0.438993\pi$
$937$	11.6618	0.380973	0.190487	+	0.981690i	$0.438993\pi$
$938$	31.3288	1.02292
$939$	−7.08022	−0.231054
$940$	−8.63151	−0.281529
$941$	−53.0317	−1.72878	−0.864392	−	0.502818i	$-0.832296\pi$
$941$	−53.0317	−1.72878	−0.864392	+	0.502818i	$0.832296\pi$
$942$	4.27863	0.139405
$943$	−15.6734	−0.510397
$944$	−13.8169	−0.449702
$945$	−2.50739	−0.0815653
$946$	7.17058	0.233136
$947$	8.08592	0.262757	0.131379	−	0.991332i	$-0.458060\pi$
$947$	8.08592	0.262757	0.131379	+	0.991332i	$0.458060\pi$
$948$	4.78449	0.155393
$949$	18.7560	0.608846
$950$	4.25245	0.137968
$951$	2.19198	0.0710799
$952$	9.11550	0.295435
$953$	16.1683	0.523741	0.261871	−	0.965103i	$-0.415661\pi$
$953$	16.1683	0.523741	0.261871	+	0.965103i	$0.415661\pi$
$954$	−1.00000	−0.0323762
$955$	−16.9946	−0.549934
$956$	19.4621	0.629449
$957$	−8.48592	−0.274311
$958$	27.8936	0.901203
$959$	47.9123	1.54717
$960$	−0.864610	−0.0279052
$961$	27.5808	0.889705
$962$	−40.9420	−1.32002
$963$	7.15731	0.230641
$964$	12.6355	0.406961
$965$	6.02891	0.194077
$966$	7.09921	0.228413
$967$	30.6731	0.986381	0.493191	−	0.869921i	$-0.335831\pi$
$967$	30.6731	0.986381	0.493191	+	0.869921i	$0.335831\pi$
$968$	7.96078	0.255869
$969$	3.14325	0.100976
$970$	10.2300	0.328465
$971$	−19.4710	−0.624853	−0.312427	−	0.949942i	$-0.601142\pi$
$971$	−19.4710	−0.624853	−0.312427	+	0.949942i	$0.601142\pi$
$972$	−1.00000	−0.0320750
$973$	−26.9042	−0.862511
$974$	11.4312	0.366279
$975$	18.3615	0.588040
$976$	−10.8725	−0.348022
$977$	42.7095	1.36640	0.683200	−	0.730232i	$-0.260588\pi$
$977$	42.7095	1.36640	0.683200	+	0.730232i	$0.260588\pi$
$978$	−1.36454	−0.0436333
$979$	22.6686	0.724492
$980$	1.21920	0.0389461
$981$	10.7045	0.341769
$982$	30.1637	0.962561
$983$	−56.0854	−1.78885	−0.894423	−	0.447222i	$-0.852413\pi$
$983$	−56.0854	−1.78885	−0.894423	+	0.447222i	$0.852413\pi$
$984$	−6.40258	−0.204107
$985$	−17.0284	−0.542570
$986$	−15.3002	−0.487258
$987$	28.9513	0.921529
$988$	4.31787	0.137370
$989$	10.0689	0.320173
$990$	1.50731	0.0479053
$991$	22.2051	0.705367	0.352683	−	0.935743i	$-0.385269\pi$
$991$	22.2051	0.705367	0.352683	+	0.935743i	$0.385269\pi$
$992$	7.65381	0.243009
$993$	8.85033	0.280857
$994$	8.50335	0.269710
$995$	4.27880	0.135647
$996$	−8.79442	−0.278662
$997$	12.9865	0.411287	0.205644	−	0.978627i	$-0.434071\pi$
$997$	12.9865	0.411287	0.205644	+	0.978627i	$0.434071\pi$
$998$	1.49935	0.0474610
$999$	−9.48198	−0.299997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bd.1.6	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bd.1.6	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.864610 q^{5} +1.00000 q^{6} +2.90002 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.864610 q^{5} +1.00000 q^{6} +2.90002 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.864610 q^{10} -1.74334 q^{11} -1.00000 q^{12} +4.31787 q^{13} -2.90002 q^{14} -0.864610 q^{15} +1.00000 q^{16} -3.14325 q^{17} -1.00000 q^{18} +1.00000 q^{19} +0.864610 q^{20} -2.90002 q^{21} +1.74334 q^{22} +2.44799 q^{23} +1.00000 q^{24} -4.25245 q^{25} -4.31787 q^{26} -1.00000 q^{27} +2.90002 q^{28} -4.86763 q^{29} +0.864610 q^{30} -7.65381 q^{31} -1.00000 q^{32} +1.74334 q^{33} +3.14325 q^{34} +2.50739 q^{35} +1.00000 q^{36} +9.48198 q^{37} -1.00000 q^{38} -4.31787 q^{39} -0.864610 q^{40} -6.40258 q^{41} +2.90002 q^{42} +4.11314 q^{43} -1.74334 q^{44} +0.864610 q^{45} -2.44799 q^{46} -9.98313 q^{47} -1.00000 q^{48} +1.41012 q^{49} +4.25245 q^{50} +3.14325 q^{51} +4.31787 q^{52} +1.00000 q^{53} +1.00000 q^{54} -1.50731 q^{55} -2.90002 q^{56} -1.00000 q^{57} +4.86763 q^{58} -13.8169 q^{59} -0.864610 q^{60} -10.8725 q^{61} +7.65381 q^{62} +2.90002 q^{63} +1.00000 q^{64} +3.73327 q^{65} -1.74334 q^{66} -10.8030 q^{67} -3.14325 q^{68} -2.44799 q^{69} -2.50739 q^{70} -2.93217 q^{71} -1.00000 q^{72} +4.34381 q^{73} -9.48198 q^{74} +4.25245 q^{75} +1.00000 q^{76} -5.05571 q^{77} +4.31787 q^{78} -4.78449 q^{79} +0.864610 q^{80} +1.00000 q^{81} +6.40258 q^{82} +8.79442 q^{83} -2.90002 q^{84} -2.71769 q^{85} -4.11314 q^{86} +4.86763 q^{87} +1.74334 q^{88} -13.0030 q^{89} -0.864610 q^{90} +12.5219 q^{91} +2.44799 q^{92} +7.65381 q^{93} +9.98313 q^{94} +0.864610 q^{95} +1.00000 q^{96} -11.8319 q^{97} -1.41012 q^{98} -1.74334 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9} - 2 q^{10} - 6 q^{11} - 11 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{15} + 11 q^{16} - 16 q^{17} - 11 q^{18} + 11 q^{19} + 2 q^{20} + 2 q^{21} + 6 q^{22} - 11 q^{23} + 11 q^{24} + 19 q^{25} + 7 q^{26} - 11 q^{27} - 2 q^{28} - 7 q^{29} + 2 q^{30} + 12 q^{31} - 11 q^{32} + 6 q^{33} + 16 q^{34} - 5 q^{35} + 11 q^{36} + 3 q^{37} - 11 q^{38} + 7 q^{39} - 2 q^{40} + 11 q^{41} - 2 q^{42} + 7 q^{43} - 6 q^{44} + 2 q^{45} + 11 q^{46} - 37 q^{47} - 11 q^{48} + 23 q^{49} - 19 q^{50} + 16 q^{51} - 7 q^{52} + 11 q^{53} + 11 q^{54} - 11 q^{55} + 2 q^{56} - 11 q^{57} + 7 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} - 12 q^{62} - 2 q^{63} + 11 q^{64} - 7 q^{65} - 6 q^{66} - 28 q^{67} - 16 q^{68} + 11 q^{69} + 5 q^{70} + 4 q^{71} - 11 q^{72} - 7 q^{73} - 3 q^{74} - 19 q^{75} + 11 q^{76} - 13 q^{77} - 7 q^{78} + 5 q^{79} + 2 q^{80} + 11 q^{81} - 11 q^{82} - 11 q^{83} + 2 q^{84} - 11 q^{85} - 7 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} - 2 q^{90} - 24 q^{91} - 11 q^{92} - 12 q^{93} + 37 q^{94} + 2 q^{95} + 11 q^{96} - 24 q^{97} - 23 q^{98} - 6 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9 - 2 * q^10 - 6 * q^11 - 11 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^15 + 11 * q^16 - 16 * q^17 - 11 * q^18 + 11 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 - 11 * q^23 + 11 * q^24 + 19 * q^25 + 7 * q^26 - 11 * q^27 - 2 * q^28 - 7 * q^29 + 2 * q^30 + 12 * q^31 - 11 * q^32 + 6 * q^33 + 16 * q^34 - 5 * q^35 + 11 * q^36 + 3 * q^37 - 11 * q^38 + 7 * q^39 - 2 * q^40 + 11 * q^41 - 2 * q^42 + 7 * q^43 - 6 * q^44 + 2 * q^45 + 11 * q^46 - 37 * q^47 - 11 * q^48 + 23 * q^49 - 19 * q^50 + 16 * q^51 - 7 * q^52 + 11 * q^53 + 11 * q^54 - 11 * q^55 + 2 * q^56 - 11 * q^57 + 7 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 - 12 * q^62 - 2 * q^63 + 11 * q^64 - 7 * q^65 - 6 * q^66 - 28 * q^67 - 16 * q^68 + 11 * q^69 + 5 * q^70 + 4 * q^71 - 11 * q^72 - 7 * q^73 - 3 * q^74 - 19 * q^75 + 11 * q^76 - 13 * q^77 - 7 * q^78 + 5 * q^79 + 2 * q^80 + 11 * q^81 - 11 * q^82 - 11 * q^83 + 2 * q^84 - 11 * q^85 - 7 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 - 2 * q^90 - 24 * q^91 - 11 * q^92 - 12 * q^93 + 37 * q^94 + 2 * q^95 + 11 * q^96 - 24 * q^97 - 23 * q^98 - 6 * q^99

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