LMFDB - Embedded newform 6042.2.a.be.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 36 x^{10} + 105 x^{9} + 465 x^{8} - 1287 x^{7} - 2668 x^{6} + 6443 x^{5} + \cdots + 1496 $ x^12 - 3x^11 - 36x^10 + 105x^9 + 465x^8 - 1287x^7 - 2668x^6 + 6443x^5 + 7140x^4 - 10858x^3 - 10086x^2 + 2072*x + 1496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-3.06562$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.06562 q^{5} +1.00000 q^{6} -0.702849 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.06562 q^{5} +1.00000 q^{6} -0.702849 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.06562 q^{10} +1.81002 q^{11} -1.00000 q^{12} -6.14263 q^{13} +0.702849 q^{14} -3.06562 q^{15} +1.00000 q^{16} -3.70788 q^{17} -1.00000 q^{18} -1.00000 q^{19} +3.06562 q^{20} +0.702849 q^{21} -1.81002 q^{22} -6.68548 q^{23} +1.00000 q^{24} +4.39803 q^{25} +6.14263 q^{26} -1.00000 q^{27} -0.702849 q^{28} +8.71256 q^{29} +3.06562 q^{30} +3.96049 q^{31} -1.00000 q^{32} -1.81002 q^{33} +3.70788 q^{34} -2.15467 q^{35} +1.00000 q^{36} +10.8355 q^{37} +1.00000 q^{38} +6.14263 q^{39} -3.06562 q^{40} +3.89267 q^{41} -0.702849 q^{42} -4.71436 q^{43} +1.81002 q^{44} +3.06562 q^{45} +6.68548 q^{46} +11.4458 q^{47} -1.00000 q^{48} -6.50600 q^{49} -4.39803 q^{50} +3.70788 q^{51} -6.14263 q^{52} -1.00000 q^{53} +1.00000 q^{54} +5.54883 q^{55} +0.702849 q^{56} +1.00000 q^{57} -8.71256 q^{58} -8.72958 q^{59} -3.06562 q^{60} -10.0199 q^{61} -3.96049 q^{62} -0.702849 q^{63} +1.00000 q^{64} -18.8310 q^{65} +1.81002 q^{66} +3.97282 q^{67} -3.70788 q^{68} +6.68548 q^{69} +2.15467 q^{70} +6.35010 q^{71} -1.00000 q^{72} -13.0764 q^{73} -10.8355 q^{74} -4.39803 q^{75} -1.00000 q^{76} -1.27217 q^{77} -6.14263 q^{78} -10.8122 q^{79} +3.06562 q^{80} +1.00000 q^{81} -3.89267 q^{82} -4.59380 q^{83} +0.702849 q^{84} -11.3670 q^{85} +4.71436 q^{86} -8.71256 q^{87} -1.81002 q^{88} +9.95545 q^{89} -3.06562 q^{90} +4.31734 q^{91} -6.68548 q^{92} -3.96049 q^{93} -11.4458 q^{94} -3.06562 q^{95} +1.00000 q^{96} +4.27886 q^{97} +6.50600 q^{98} +1.81002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 12 q^{3} + 12 q^{4} - 3 q^{5} + 12 q^{6} - q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 12 * q^3 + 12 * q^4 - 3 * q^5 + 12 * q^6 - q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} - 12 q^{3} + 12 q^{4} - 3 q^{5} + 12 q^{6} - q^{7} - 12 q^{8} + 12 q^{9} + 3 q^{10} - 7 q^{11} - 12 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} + 12 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{19} - 3 q^{20} + q^{21} + 7 q^{22} - 18 q^{23} + 12 q^{24} + 21 q^{25} - 4 q^{26} - 12 q^{27} - q^{28} + 10 q^{29} - 3 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} + 4 q^{34} - 19 q^{35} + 12 q^{36} + 14 q^{37} + 12 q^{38} - 4 q^{39} + 3 q^{40} - 9 q^{41} - q^{42} - 4 q^{43} - 7 q^{44} - 3 q^{45} + 18 q^{46} - 14 q^{47} - 12 q^{48} + 37 q^{49} - 21 q^{50} + 4 q^{51} + 4 q^{52} - 12 q^{53} + 12 q^{54} - 4 q^{55} + q^{56} + 12 q^{57} - 10 q^{58} - 18 q^{59} + 3 q^{60} - 7 q^{61} - 14 q^{62} - q^{63} + 12 q^{64} + 3 q^{65} - 7 q^{66} + 8 q^{67} - 4 q^{68} + 18 q^{69} + 19 q^{70} - q^{71} - 12 q^{72} - 31 q^{73} - 14 q^{74} - 21 q^{75} - 12 q^{76} - 25 q^{77} + 4 q^{78} - 3 q^{80} + 12 q^{81} + 9 q^{82} - 48 q^{83} + q^{84} + 4 q^{85} + 4 q^{86} - 10 q^{87} + 7 q^{88} + 13 q^{89} + 3 q^{90} + 9 q^{91} - 18 q^{92} - 14 q^{93} + 14 q^{94} + 3 q^{95} + 12 q^{96} + 25 q^{97} - 37 q^{98} - 7 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 12 * q^3 + 12 * q^4 - 3 * q^5 + 12 * q^6 - q^7 - 12 * q^8 + 12 * q^9 + 3 * q^10 - 7 * q^11 - 12 * q^12 + 4 * q^13 + q^14 + 3 * q^15 + 12 * q^16 - 4 * q^17 - 12 * q^18 - 12 * q^19 - 3 * q^20 + q^21 + 7 * q^22 - 18 * q^23 + 12 * q^24 + 21 * q^25 - 4 * q^26 - 12 * q^27 - q^28 + 10 * q^29 - 3 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 + 4 * q^34 - 19 * q^35 + 12 * q^36 + 14 * q^37 + 12 * q^38 - 4 * q^39 + 3 * q^40 - 9 * q^41 - q^42 - 4 * q^43 - 7 * q^44 - 3 * q^45 + 18 * q^46 - 14 * q^47 - 12 * q^48 + 37 * q^49 - 21 * q^50 + 4 * q^51 + 4 * q^52 - 12 * q^53 + 12 * q^54 - 4 * q^55 + q^56 + 12 * q^57 - 10 * q^58 - 18 * q^59 + 3 * q^60 - 7 * q^61 - 14 * q^62 - q^63 + 12 * q^64 + 3 * q^65 - 7 * q^66 + 8 * q^67 - 4 * q^68 + 18 * q^69 + 19 * q^70 - q^71 - 12 * q^72 - 31 * q^73 - 14 * q^74 - 21 * q^75 - 12 * q^76 - 25 * q^77 + 4 * q^78 - 3 * q^80 + 12 * q^81 + 9 * q^82 - 48 * q^83 + q^84 + 4 * q^85 + 4 * q^86 - 10 * q^87 + 7 * q^88 + 13 * q^89 + 3 * q^90 + 9 * q^91 - 18 * q^92 - 14 * q^93 + 14 * q^94 + 3 * q^95 + 12 * q^96 + 25 * q^97 - 37 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.06562	1.37099	0.685494	−	0.728079i	$-0.259586\pi$
$5$	3.06562	1.37099	0.685494	+	0.728079i	$0.259586\pi$
$6$	1.00000	0.408248
$7$	−0.702849	−0.265652	−0.132826	−	0.991139i	$-0.542405\pi$
$7$	−0.702849	−0.265652	−0.132826	+	0.991139i	$0.542405\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.06562	−0.969434
$11$	1.81002	0.545741	0.272870	−	0.962051i	$-0.412027\pi$
$11$	1.81002	0.545741	0.272870	+	0.962051i	$0.412027\pi$
$12$	−1.00000	−0.288675
$13$	−6.14263	−1.70366	−0.851830	−	0.523819i	$-0.824507\pi$
$13$	−6.14263	−1.70366	−0.851830	+	0.523819i	$0.824507\pi$
$14$	0.702849	0.187844
$15$	−3.06562	−0.791540
$16$	1.00000	0.250000
$17$	−3.70788	−0.899293	−0.449646	−	0.893207i	$-0.648450\pi$
$17$	−3.70788	−0.899293	−0.449646	+	0.893207i	$0.648450\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.06562	0.685494
$21$	0.702849	0.153374
$22$	−1.81002	−0.385897
$23$	−6.68548	−1.39402	−0.697010	−	0.717061i	$-0.745487\pi$
$23$	−6.68548	−1.39402	−0.697010	+	0.717061i	$0.745487\pi$
$24$	1.00000	0.204124
$25$	4.39803	0.879606
$26$	6.14263	1.20467
$27$	−1.00000	−0.192450
$28$	−0.702849	−0.132826
$29$	8.71256	1.61788	0.808941	−	0.587890i	$-0.200041\pi$
$29$	8.71256	1.61788	0.808941	+	0.587890i	$0.200041\pi$
$30$	3.06562	0.559703
$31$	3.96049	0.711325	0.355663	−	0.934614i	$-0.384255\pi$
$31$	3.96049	0.711325	0.355663	+	0.934614i	$0.384255\pi$
$32$	−1.00000	−0.176777
$33$	−1.81002	−0.315084
$34$	3.70788	0.635896
$35$	−2.15467	−0.364205
$36$	1.00000	0.166667
$37$	10.8355	1.78134	0.890670	−	0.454650i	$-0.150236\pi$
$37$	10.8355	1.78134	0.890670	+	0.454650i	$0.150236\pi$
$38$	1.00000	0.162221
$39$	6.14263	0.983608
$40$	−3.06562	−0.484717
$41$	3.89267	0.607933	0.303967	−	0.952683i	$-0.401689\pi$
$41$	3.89267	0.607933	0.303967	+	0.952683i	$0.401689\pi$
$42$	−0.702849	−0.108452
$43$	−4.71436	−0.718934	−0.359467	−	0.933158i	$-0.617041\pi$
$43$	−4.71436	−0.718934	−0.359467	+	0.933158i	$0.617041\pi$
$44$	1.81002	0.272870
$45$	3.06562	0.456996
$46$	6.68548	0.985721
$47$	11.4458	1.66955	0.834774	−	0.550593i	$-0.185598\pi$
$47$	11.4458	1.66955	0.834774	+	0.550593i	$0.185598\pi$
$48$	−1.00000	−0.144338
$49$	−6.50600	−0.929429
$50$	−4.39803	−0.621975
$51$	3.70788	0.519207
$52$	−6.14263	−0.851830
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.00000	0.136083
$55$	5.54883	0.748204
$56$	0.702849	0.0939221
$57$	1.00000	0.132453
$58$	−8.71256	−1.14402
$59$	−8.72958	−1.13649	−0.568247	−	0.822858i	$-0.692378\pi$
$59$	−8.72958	−1.13649	−0.568247	+	0.822858i	$0.692378\pi$
$60$	−3.06562	−0.395770
$61$	−10.0199	−1.28292	−0.641459	−	0.767157i	$-0.721671\pi$
$61$	−10.0199	−1.28292	−0.641459	+	0.767157i	$0.721671\pi$
$62$	−3.96049	−0.502983
$63$	−0.702849	−0.0885506
$64$	1.00000	0.125000
$65$	−18.8310	−2.33570
$66$	1.81002	0.222798
$67$	3.97282	0.485357	0.242678	−	0.970107i	$-0.421974\pi$
$67$	3.97282	0.485357	0.242678	+	0.970107i	$0.421974\pi$
$68$	−3.70788	−0.449646
$69$	6.68548	0.804838
$70$	2.15467	0.257532
$71$	6.35010	0.753618	0.376809	−	0.926291i	$-0.377021\pi$
$71$	6.35010	0.753618	0.376809	+	0.926291i	$0.377021\pi$
$72$	−1.00000	−0.117851
$73$	−13.0764	−1.53047	−0.765237	−	0.643748i	$-0.777378\pi$
$73$	−13.0764	−1.53047	−0.765237	+	0.643748i	$0.777378\pi$
$74$	−10.8355	−1.25960
$75$	−4.39803	−0.507841
$76$	−1.00000	−0.114708
$77$	−1.27217	−0.144977
$78$	−6.14263	−0.695516
$79$	−10.8122	−1.21647	−0.608235	−	0.793757i	$-0.708122\pi$
$79$	−10.8122	−1.21647	−0.608235	+	0.793757i	$0.708122\pi$
$80$	3.06562	0.342747
$81$	1.00000	0.111111
$82$	−3.89267	−0.429874
$83$	−4.59380	−0.504235	−0.252118	−	0.967697i	$-0.581127\pi$
$83$	−4.59380	−0.504235	−0.252118	+	0.967697i	$0.581127\pi$
$84$	0.702849	0.0766871
$85$	−11.3670	−1.23292
$86$	4.71436	0.508363
$87$	−8.71256	−0.934085
$88$	−1.81002	−0.192949
$89$	9.95545	1.05528	0.527638	−	0.849469i	$-0.323078\pi$
$89$	9.95545	1.05528	0.527638	+	0.849469i	$0.323078\pi$
$90$	−3.06562	−0.323145
$91$	4.31734	0.452580
$92$	−6.68548	−0.697010
$93$	−3.96049	−0.410684
$94$	−11.4458	−1.18055
$95$	−3.06562	−0.314526
$96$	1.00000	0.102062
$97$	4.27886	0.434452	0.217226	−	0.976121i	$-0.430299\pi$
$97$	4.27886	0.434452	0.217226	+	0.976121i	$0.430299\pi$
$98$	6.50600	0.657206
$99$	1.81002	0.181914
$100$	4.39803	0.439803
$101$	−3.21153	−0.319559	−0.159780	−	0.987153i	$-0.551078\pi$
$101$	−3.21153	−0.319559	−0.159780	+	0.987153i	$0.551078\pi$
$102$	−3.70788	−0.367135
$103$	−19.5787	−1.92914	−0.964571	−	0.263823i	$-0.915017\pi$
$103$	−19.5787	−1.92914	−0.964571	+	0.263823i	$0.915017\pi$
$104$	6.14263	0.602335
$105$	2.15467	0.210274
$106$	1.00000	0.0971286
$107$	−5.20707	−0.503386	−0.251693	−	0.967807i	$-0.580987\pi$
$107$	−5.20707	−0.503386	−0.251693	+	0.967807i	$0.580987\pi$
$108$	−1.00000	−0.0962250
$109$	11.4620	1.09786	0.548931	−	0.835868i	$-0.315035\pi$
$109$	11.4620	1.09786	0.548931	+	0.835868i	$0.315035\pi$
$110$	−5.54883	−0.529060
$111$	−10.8355	−1.02846
$112$	−0.702849	−0.0664130
$113$	−5.52149	−0.519418	−0.259709	−	0.965687i	$-0.583627\pi$
$113$	−5.52149	−0.519418	−0.259709	+	0.965687i	$0.583627\pi$
$114$	−1.00000	−0.0936586
$115$	−20.4952	−1.91118
$116$	8.71256	0.808941
$117$	−6.14263	−0.567886
$118$	8.72958	0.803623
$119$	2.60608	0.238899
$120$	3.06562	0.279852
$121$	−7.72384	−0.702167
$122$	10.0199	0.907160
$123$	−3.89267	−0.350990
$124$	3.96049	0.355663
$125$	−1.84541	−0.165059
$126$	0.702849	0.0626147
$127$	13.2362	1.17453	0.587263	−	0.809396i	$-0.300205\pi$
$127$	13.2362	1.17453	0.587263	+	0.809396i	$0.300205\pi$
$128$	−1.00000	−0.0883883
$129$	4.71436	0.415077
$130$	18.8310	1.65159
$131$	0.991300	0.0866103	0.0433052	−	0.999062i	$-0.486211\pi$
$131$	0.991300	0.0866103	0.0433052	+	0.999062i	$0.486211\pi$
$132$	−1.81002	−0.157542
$133$	0.702849	0.0609447
$134$	−3.97282	−0.343199
$135$	−3.06562	−0.263847
$136$	3.70788	0.317948
$137$	5.45522	0.466071	0.233036	−	0.972468i	$-0.425134\pi$
$137$	5.45522	0.466071	0.233036	+	0.972468i	$0.425134\pi$
$138$	−6.68548	−0.569106
$139$	−10.9764	−0.931005	−0.465503	−	0.885046i	$-0.654126\pi$
$139$	−10.9764	−0.931005	−0.465503	+	0.885046i	$0.654126\pi$
$140$	−2.15467	−0.182103
$141$	−11.4458	−0.963914
$142$	−6.35010	−0.532888
$143$	−11.1183	−0.929756
$144$	1.00000	0.0833333
$145$	26.7094	2.21810
$146$	13.0764	1.08221
$147$	6.50600	0.536606
$148$	10.8355	0.890670
$149$	−1.00010	−0.0819314	−0.0409657	−	0.999161i	$-0.513043\pi$
$149$	−1.00010	−0.0819314	−0.0409657	+	0.999161i	$0.513043\pi$
$150$	4.39803	0.359098
$151$	−14.6434	−1.19167	−0.595833	−	0.803109i	$-0.703178\pi$
$151$	−14.6434	−1.19167	−0.595833	+	0.803109i	$0.703178\pi$
$152$	1.00000	0.0811107
$153$	−3.70788	−0.299764
$154$	1.27217	0.102514
$155$	12.1414	0.975218
$156$	6.14263	0.491804
$157$	18.4677	1.47388	0.736940	−	0.675958i	$-0.236270\pi$
$157$	18.4677	1.47388	0.736940	+	0.675958i	$0.236270\pi$
$158$	10.8122	0.860174
$159$	1.00000	0.0793052
$160$	−3.06562	−0.242359
$161$	4.69888	0.370324
$162$	−1.00000	−0.0785674
$163$	−2.73543	−0.214255	−0.107128	−	0.994245i	$-0.534165\pi$
$163$	−2.73543	−0.214255	−0.107128	+	0.994245i	$0.534165\pi$
$164$	3.89267	0.303967
$165$	−5.54883	−0.431976
$166$	4.59380	0.356548
$167$	−19.0933	−1.47748	−0.738740	−	0.673990i	$-0.764579\pi$
$167$	−19.0933	−1.47748	−0.738740	+	0.673990i	$0.764579\pi$
$168$	−0.702849	−0.0542260
$169$	24.7319	1.90245
$170$	11.3670	0.871805
$171$	−1.00000	−0.0764719
$172$	−4.71436	−0.359467
$173$	−24.2138	−1.84094	−0.920471	−	0.390812i	$-0.872194\pi$
$173$	−24.2138	−1.84094	−0.920471	+	0.390812i	$0.872194\pi$
$174$	8.71256	0.660498
$175$	−3.09115	−0.233669
$176$	1.81002	0.136435
$177$	8.72958	0.656156
$178$	−9.95545	−0.746193
$179$	6.41946	0.479813	0.239906	−	0.970796i	$-0.422883\pi$
$179$	6.41946	0.479813	0.239906	+	0.970796i	$0.422883\pi$
$180$	3.06562	0.228498
$181$	−16.4907	−1.22575	−0.612873	−	0.790181i	$-0.709986\pi$
$181$	−16.4907	−1.22575	−0.612873	+	0.790181i	$0.709986\pi$
$182$	−4.31734	−0.320023
$183$	10.0199	0.740693
$184$	6.68548	0.492860
$185$	33.2174	2.44219
$186$	3.96049	0.290397
$187$	−6.71133	−0.490781
$188$	11.4458	0.834774
$189$	0.702849	0.0511247
$190$	3.06562	0.222404
$191$	−23.2381	−1.68145	−0.840725	−	0.541462i	$-0.817871\pi$
$191$	−23.2381	−1.68145	−0.840725	+	0.541462i	$0.817871\pi$
$192$	−1.00000	−0.0721688
$193$	2.24702	0.161744	0.0808721	−	0.996724i	$-0.474229\pi$
$193$	2.24702	0.161744	0.0808721	+	0.996724i	$0.474229\pi$
$194$	−4.27886	−0.307204
$195$	18.8310	1.34851
$196$	−6.50600	−0.464715
$197$	−27.0039	−1.92395	−0.961975	−	0.273139i	$-0.911938\pi$
$197$	−27.0039	−1.92395	−0.961975	+	0.273139i	$0.911938\pi$
$198$	−1.81002	−0.128632
$199$	−5.70253	−0.404242	−0.202121	−	0.979361i	$-0.564783\pi$
$199$	−5.70253	−0.404242	−0.202121	+	0.979361i	$0.564783\pi$
$200$	−4.39803	−0.310988
$201$	−3.97282	−0.280221
$202$	3.21153	0.225963
$203$	−6.12361	−0.429793
$204$	3.70788	0.259603
$205$	11.9335	0.833468
$206$	19.5787	1.36411
$207$	−6.68548	−0.464673
$208$	−6.14263	−0.425915
$209$	−1.81002	−0.125202
$210$	−2.15467	−0.148686
$211$	18.6064	1.28092	0.640459	−	0.767992i	$-0.278744\pi$
$211$	18.6064	1.28092	0.640459	+	0.767992i	$0.278744\pi$
$212$	−1.00000	−0.0686803
$213$	−6.35010	−0.435102
$214$	5.20707	0.355948
$215$	−14.4525	−0.985649
$216$	1.00000	0.0680414
$217$	−2.78363	−0.188965
$218$	−11.4620	−0.776305
$219$	13.0764	0.883620
$220$	5.54883	0.374102
$221$	22.7761	1.53209
$222$	10.8355	0.727229
$223$	−16.9465	−1.13482	−0.567410	−	0.823435i	$-0.692055\pi$
$223$	−16.9465	−1.13482	−0.567410	+	0.823435i	$0.692055\pi$
$224$	0.702849	0.0469611
$225$	4.39803	0.293202
$226$	5.52149	0.367284
$227$	−18.3370	−1.21707	−0.608535	−	0.793527i	$-0.708242\pi$
$227$	−18.3370	−1.21707	−0.608535	+	0.793527i	$0.708242\pi$
$228$	1.00000	0.0662266
$229$	13.2114	0.873036	0.436518	−	0.899695i	$-0.356211\pi$
$229$	13.2114	0.873036	0.436518	+	0.899695i	$0.356211\pi$
$230$	20.4952	1.35141
$231$	1.27217	0.0837025
$232$	−8.71256	−0.572008
$233$	−26.8200	−1.75704	−0.878518	−	0.477710i	$-0.841467\pi$
$233$	−26.8200	−1.75704	−0.878518	+	0.477710i	$0.841467\pi$
$234$	6.14263	0.401556
$235$	35.0886	2.28893
$236$	−8.72958	−0.568247
$237$	10.8122	0.702329
$238$	−2.60608	−0.168927
$239$	−11.5584	−0.747649	−0.373824	−	0.927499i	$-0.621954\pi$
$239$	−11.5584	−0.747649	−0.373824	+	0.927499i	$0.621954\pi$
$240$	−3.06562	−0.197885
$241$	3.30329	0.212783	0.106392	−	0.994324i	$-0.466070\pi$
$241$	3.30329	0.212783	0.106392	+	0.994324i	$0.466070\pi$
$242$	7.72384	0.496507
$243$	−1.00000	−0.0641500
$244$	−10.0199	−0.641459
$245$	−19.9449	−1.27424
$246$	3.89267	0.248188
$247$	6.14263	0.390846
$248$	−3.96049	−0.251491
$249$	4.59380	0.291120
$250$	1.84541	0.116714
$251$	2.46616	0.155662	0.0778312	−	0.996967i	$-0.475200\pi$
$251$	2.46616	0.155662	0.0778312	+	0.996967i	$0.475200\pi$
$252$	−0.702849	−0.0442753
$253$	−12.1008	−0.760774
$254$	−13.2362	−0.830515
$255$	11.3670	0.711826
$256$	1.00000	0.0625000
$257$	26.0219	1.62320	0.811601	−	0.584213i	$-0.198597\pi$
$257$	26.0219	1.62320	0.811601	+	0.584213i	$0.198597\pi$
$258$	−4.71436	−0.293504
$259$	−7.61569	−0.473216
$260$	−18.8310	−1.16785
$261$	8.71256	0.539294
$262$	−0.991300	−0.0612427
$263$	−3.95505	−0.243879	−0.121939	−	0.992538i	$-0.538911\pi$
$263$	−3.95505	−0.243879	−0.121939	+	0.992538i	$0.538911\pi$
$264$	1.81002	0.111399
$265$	−3.06562	−0.188320
$266$	−0.702849	−0.0430944
$267$	−9.95545	−0.609264
$268$	3.97282	0.242678
$269$	8.40098	0.512217	0.256108	−	0.966648i	$-0.417560\pi$
$269$	8.40098	0.512217	0.256108	+	0.966648i	$0.417560\pi$
$270$	3.06562	0.186568
$271$	−1.75752	−0.106762	−0.0533808	−	0.998574i	$-0.517000\pi$
$271$	−1.75752	−0.106762	−0.0533808	+	0.998574i	$0.517000\pi$
$272$	−3.70788	−0.224823
$273$	−4.31734	−0.261297
$274$	−5.45522	−0.329562
$275$	7.96051	0.480037
$276$	6.68548	0.402419
$277$	28.0502	1.68538	0.842688	−	0.538402i	$-0.180972\pi$
$277$	28.0502	1.68538	0.842688	+	0.538402i	$0.180972\pi$
$278$	10.9764	0.658320
$279$	3.96049	0.237108
$280$	2.15467	0.128766
$281$	18.1580	1.08321	0.541607	−	0.840632i	$-0.317816\pi$
$281$	18.1580	1.08321	0.541607	+	0.840632i	$0.317816\pi$
$282$	11.4458	0.681590
$283$	−7.27926	−0.432707	−0.216354	−	0.976315i	$-0.569416\pi$
$283$	−7.27926	−0.432707	−0.216354	+	0.976315i	$0.569416\pi$
$284$	6.35010	0.376809
$285$	3.06562	0.181592
$286$	11.1183	0.657437
$287$	−2.73596	−0.161499
$288$	−1.00000	−0.0589256
$289$	−3.25163	−0.191272
$290$	−26.7094	−1.56843
$291$	−4.27886	−0.250831
$292$	−13.0764	−0.765237
$293$	−9.66547	−0.564663	−0.282331	−	0.959317i	$-0.591108\pi$
$293$	−9.66547	−0.564663	−0.282331	+	0.959317i	$0.591108\pi$
$294$	−6.50600	−0.379438
$295$	−26.7616	−1.55812
$296$	−10.8355	−0.629799
$297$	−1.81002	−0.105028
$298$	1.00010	0.0579343
$299$	41.0665	2.37493
$300$	−4.39803	−0.253920
$301$	3.31349	0.190986
$302$	14.6434	0.842634
$303$	3.21153	0.184498
$304$	−1.00000	−0.0573539
$305$	−30.7172	−1.75886
$306$	3.70788	0.211965
$307$	−7.60327	−0.433941	−0.216971	−	0.976178i	$-0.569618\pi$
$307$	−7.60327	−0.433941	−0.216971	+	0.976178i	$0.569618\pi$
$308$	−1.27217	−0.0724885
$309$	19.5787	1.11379
$310$	−12.1414	−0.689583
$311$	−9.52249	−0.539971	−0.269985	−	0.962864i	$-0.587019\pi$
$311$	−9.52249	−0.539971	−0.269985	+	0.962864i	$0.587019\pi$
$312$	−6.14263	−0.347758
$313$	27.9479	1.57971	0.789855	−	0.613293i	$-0.210156\pi$
$313$	27.9479	1.57971	0.789855	+	0.613293i	$0.210156\pi$
$314$	−18.4677	−1.04219
$315$	−2.15467	−0.121402
$316$	−10.8122	−0.608235
$317$	−27.1141	−1.52288	−0.761439	−	0.648236i	$-0.775507\pi$
$317$	−27.1141	−1.52288	−0.761439	+	0.648236i	$0.775507\pi$
$318$	−1.00000	−0.0560772
$319$	15.7699	0.882944
$320$	3.06562	0.171373
$321$	5.20707	0.290630
$322$	−4.69888	−0.261859
$323$	3.70788	0.206312
$324$	1.00000	0.0555556
$325$	−27.0155	−1.49855
$326$	2.73543	0.151501
$327$	−11.4620	−0.633850
$328$	−3.89267	−0.214937
$329$	−8.04470	−0.443519
$330$	5.54883	0.305453
$331$	20.8071	1.14366	0.571832	−	0.820371i	$-0.306233\pi$
$331$	20.8071	1.14366	0.571832	+	0.820371i	$0.306233\pi$
$332$	−4.59380	−0.252118
$333$	10.8355	0.593780
$334$	19.0933	1.04474
$335$	12.1792	0.665418
$336$	0.702849	0.0383435
$337$	0.368760	0.0200876	0.0100438	−	0.999950i	$-0.496803\pi$
$337$	0.368760	0.0200876	0.0100438	+	0.999950i	$0.496803\pi$
$338$	−24.7319	−1.34524
$339$	5.52149	0.299886
$340$	−11.3670	−0.616460
$341$	7.16856	0.388199
$342$	1.00000	0.0540738
$343$	9.49268	0.512556
$344$	4.71436	0.254182
$345$	20.4952	1.10342
$346$	24.2138	1.30174
$347$	−12.7108	−0.682351	−0.341175	−	0.940000i	$-0.610825\pi$
$347$	−12.7108	−0.682351	−0.341175	+	0.940000i	$0.610825\pi$
$348$	−8.71256	−0.467042
$349$	−5.04459	−0.270031	−0.135015	−	0.990844i	$-0.543108\pi$
$349$	−5.04459	−0.270031	−0.135015	+	0.990844i	$0.543108\pi$
$350$	3.09115	0.165229
$351$	6.14263	0.327869
$352$	−1.81002	−0.0964743
$353$	−25.3361	−1.34850	−0.674252	−	0.738501i	$-0.735534\pi$
$353$	−25.3361	−1.34850	−0.674252	+	0.738501i	$0.735534\pi$
$354$	−8.72958	−0.463972
$355$	19.4670	1.03320
$356$	9.95545	0.527638
$357$	−2.60608	−0.137928
$358$	−6.41946	−0.339279
$359$	−3.77883	−0.199439	−0.0997194	−	0.995016i	$-0.531795\pi$
$359$	−3.77883	−0.199439	−0.0997194	+	0.995016i	$0.531795\pi$
$360$	−3.06562	−0.161572
$361$	1.00000	0.0526316
$362$	16.4907	0.866734
$363$	7.72384	0.405396
$364$	4.31734	0.226290
$365$	−40.0872	−2.09826
$366$	−10.0199	−0.523749
$367$	−16.2915	−0.850407	−0.425204	−	0.905098i	$-0.639798\pi$
$367$	−16.2915	−0.850407	−0.425204	+	0.905098i	$0.639798\pi$
$368$	−6.68548	−0.348505
$369$	3.89267	0.202644
$370$	−33.2174	−1.72689
$371$	0.702849	0.0364901
$372$	−3.96049	−0.205342
$373$	−2.35628	−0.122004	−0.0610018	−	0.998138i	$-0.519430\pi$
$373$	−2.35628	−0.122004	−0.0610018	+	0.998138i	$0.519430\pi$
$374$	6.71133	0.347034
$375$	1.84541	0.0952966
$376$	−11.4458	−0.590274
$377$	−53.5181	−2.75632
$378$	−0.702849	−0.0361506
$379$	22.2547	1.14315	0.571575	−	0.820550i	$-0.306333\pi$
$379$	22.2547	1.14315	0.571575	+	0.820550i	$0.306333\pi$
$380$	−3.06562	−0.157263
$381$	−13.2362	−0.678113
$382$	23.2381	1.18896
$383$	−16.5412	−0.845218	−0.422609	−	0.906312i	$-0.638886\pi$
$383$	−16.5412	−0.845218	−0.422609	+	0.906312i	$0.638886\pi$
$384$	1.00000	0.0510310
$385$	−3.89999	−0.198762
$386$	−2.24702	−0.114370
$387$	−4.71436	−0.239645
$388$	4.27886	0.217226
$389$	−11.6489	−0.590621	−0.295310	−	0.955401i	$-0.595423\pi$
$389$	−11.6489	−0.590621	−0.295310	+	0.955401i	$0.595423\pi$
$390$	−18.8310	−0.953544
$391$	24.7890	1.25363
$392$	6.50600	0.328603
$393$	−0.991300	−0.0500045
$394$	27.0039	1.36044
$395$	−33.1462	−1.66776
$396$	1.81002	0.0909568
$397$	29.7700	1.49412	0.747058	−	0.664759i	$-0.231466\pi$
$397$	29.7700	1.49412	0.747058	+	0.664759i	$0.231466\pi$
$398$	5.70253	0.285842
$399$	−0.702849	−0.0351864
$400$	4.39803	0.219902
$401$	7.30647	0.364868	0.182434	−	0.983218i	$-0.441602\pi$
$401$	7.30647	0.364868	0.182434	+	0.983218i	$0.441602\pi$
$402$	3.97282	0.198146
$403$	−24.3278	−1.21186
$404$	−3.21153	−0.159780
$405$	3.06562	0.152332
$406$	6.12361	0.303910
$407$	19.6124	0.972150
$408$	−3.70788	−0.183567
$409$	−23.0819	−1.14133	−0.570663	−	0.821185i	$-0.693314\pi$
$409$	−23.0819	−1.14133	−0.570663	+	0.821185i	$0.693314\pi$
$410$	−11.9335	−0.589351
$411$	−5.45522	−0.269086
$412$	−19.5787	−0.964571
$413$	6.13558	0.301912
$414$	6.68548	0.328574
$415$	−14.0829	−0.691300
$416$	6.14263	0.301167
$417$	10.9764	0.537516
$418$	1.81002	0.0885309
$419$	−29.9593	−1.46361	−0.731803	−	0.681516i	$-0.761321\pi$
$419$	−29.9593	−1.46361	−0.731803	+	0.681516i	$0.761321\pi$
$420$	2.15467	0.105137
$421$	4.25915	0.207578	0.103789	−	0.994599i	$-0.466903\pi$
$421$	4.25915	0.207578	0.103789	+	0.994599i	$0.466903\pi$
$422$	−18.6064	−0.905746
$423$	11.4458	0.556516
$424$	1.00000	0.0485643
$425$	−16.3074	−0.791023
$426$	6.35010	0.307663
$427$	7.04248	0.340810
$428$	−5.20707	−0.251693
$429$	11.1183	0.536795
$430$	14.4525	0.696959
$431$	−32.5517	−1.56796	−0.783979	−	0.620787i	$-0.786813\pi$
$431$	−32.5517	−1.56796	−0.783979	+	0.620787i	$0.786813\pi$
$432$	−1.00000	−0.0481125
$433$	−0.282725	−0.0135869	−0.00679346	−	0.999977i	$-0.502162\pi$
$433$	−0.282725	−0.0135869	−0.00679346	+	0.999977i	$0.502162\pi$
$434$	2.78363	0.133618
$435$	−26.7094	−1.28062
$436$	11.4620	0.548931
$437$	6.68548	0.319810
$438$	−13.0764	−0.624814
$439$	32.5360	1.55286	0.776429	−	0.630205i	$-0.217029\pi$
$439$	32.5360	1.55286	0.776429	+	0.630205i	$0.217029\pi$
$440$	−5.54883	−0.264530
$441$	−6.50600	−0.309810
$442$	−22.7761	−1.08335
$443$	32.2431	1.53192	0.765958	−	0.642891i	$-0.222265\pi$
$443$	32.2431	1.53192	0.765958	+	0.642891i	$0.222265\pi$
$444$	−10.8355	−0.514229
$445$	30.5196	1.44677
$446$	16.9465	0.802439
$447$	1.00010	0.0473031
$448$	−0.702849	−0.0332065
$449$	−27.7628	−1.31021	−0.655104	−	0.755538i	$-0.727375\pi$
$449$	−27.7628	−1.31021	−0.655104	+	0.755538i	$0.727375\pi$
$450$	−4.39803	−0.207325
$451$	7.04580	0.331774
$452$	−5.52149	−0.259709
$453$	14.6434	0.688008
$454$	18.3370	0.860598
$455$	13.2353	0.620482
$456$	−1.00000	−0.0468293
$457$	4.10220	0.191893	0.0959464	−	0.995386i	$-0.469412\pi$
$457$	4.10220	0.191893	0.0959464	+	0.995386i	$0.469412\pi$
$458$	−13.2114	−0.617330
$459$	3.70788	0.173069
$460$	−20.4952	−0.955592
$461$	−0.635941	−0.0296187	−0.0148094	−	0.999890i	$-0.504714\pi$
$461$	−0.635941	−0.0296187	−0.0148094	+	0.999890i	$0.504714\pi$
$462$	−1.27217	−0.0591866
$463$	0.0871142	0.00404854	0.00202427	−	0.999998i	$-0.499356\pi$
$463$	0.0871142	0.00404854	0.00202427	+	0.999998i	$0.499356\pi$
$464$	8.71256	0.404471
$465$	−12.1414	−0.563042
$466$	26.8200	1.24241
$467$	8.91128	0.412365	0.206182	−	0.978514i	$-0.433896\pi$
$467$	8.91128	0.412365	0.206182	+	0.978514i	$0.433896\pi$
$468$	−6.14263	−0.283943
$469$	−2.79229	−0.128936
$470$	−35.0886	−1.61852
$471$	−18.4677	−0.850945
$472$	8.72958	0.401812
$473$	−8.53308	−0.392352
$474$	−10.8122	−0.496622
$475$	−4.39803	−0.201795
$476$	2.60608	0.119449
$477$	−1.00000	−0.0457869
$478$	11.5584	0.528668
$479$	−8.54588	−0.390471	−0.195236	−	0.980756i	$-0.562547\pi$
$479$	−8.54588	−0.390471	−0.195236	+	0.980756i	$0.562547\pi$
$480$	3.06562	0.139926
$481$	−66.5583	−3.03480
$482$	−3.30329	−0.150461
$483$	−4.69888	−0.213807
$484$	−7.72384	−0.351083
$485$	13.1174	0.595629
$486$	1.00000	0.0453609
$487$	−39.4348	−1.78696	−0.893481	−	0.449101i	$-0.851744\pi$
$487$	−39.4348	−1.78696	−0.893481	+	0.449101i	$0.851744\pi$
$488$	10.0199	0.453580
$489$	2.73543	0.123700
$490$	19.9449	0.901021
$491$	5.53940	0.249990	0.124995	−	0.992157i	$-0.460109\pi$
$491$	5.53940	0.249990	0.124995	+	0.992157i	$0.460109\pi$
$492$	−3.89267	−0.175495
$493$	−32.3051	−1.45495
$494$	−6.14263	−0.276370
$495$	5.54883	0.249401
$496$	3.96049	0.177831
$497$	−4.46316	−0.200200
$498$	−4.59380	−0.205853
$499$	−19.5274	−0.874167	−0.437083	−	0.899421i	$-0.643989\pi$
$499$	−19.5274	−0.874167	−0.437083	+	0.899421i	$0.643989\pi$
$500$	−1.84541	−0.0825293
$501$	19.0933	0.853024
$502$	−2.46616	−0.110070
$503$	35.4998	1.58286	0.791428	−	0.611262i	$-0.209338\pi$
$503$	35.4998	1.58286	0.791428	+	0.611262i	$0.209338\pi$
$504$	0.702849	0.0313074
$505$	−9.84534	−0.438112
$506$	12.1008	0.537948
$507$	−24.7319	−1.09838
$508$	13.2362	0.587263
$509$	−16.0349	−0.710734	−0.355367	−	0.934727i	$-0.615644\pi$
$509$	−16.0349	−0.710734	−0.355367	+	0.934727i	$0.615644\pi$
$510$	−11.3670	−0.503337
$511$	9.19072	0.406573
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−26.0219	−1.14778
$515$	−60.0207	−2.64483
$516$	4.71436	0.207538
$517$	20.7172	0.911141
$518$	7.61569	0.334614
$519$	24.2138	1.06287
$520$	18.8310	0.825793
$521$	38.3097	1.67838	0.839188	−	0.543841i	$-0.183031\pi$
$521$	38.3097	1.67838	0.839188	+	0.543841i	$0.183031\pi$
$522$	−8.71256	−0.381339
$523$	25.2315	1.10330	0.551649	−	0.834077i	$-0.313999\pi$
$523$	25.2315	1.10330	0.551649	+	0.834077i	$0.313999\pi$
$524$	0.991300	0.0433052
$525$	3.09115	0.134909
$526$	3.95505	0.172448
$527$	−14.6850	−0.639690
$528$	−1.81002	−0.0787709
$529$	21.6957	0.943291
$530$	3.06562	0.133162
$531$	−8.72958	−0.378832
$532$	0.702849	0.0304724
$533$	−23.9112	−1.03571
$534$	9.95545	0.430815
$535$	−15.9629	−0.690136
$536$	−3.97282	−0.171600
$537$	−6.41946	−0.277020
$538$	−8.40098	−0.362192
$539$	−11.7760	−0.507227
$540$	−3.06562	−0.131923
$541$	32.7778	1.40923	0.704614	−	0.709591i	$-0.251120\pi$
$541$	32.7778	1.40923	0.704614	+	0.709591i	$0.251120\pi$
$542$	1.75752	0.0754919
$543$	16.4907	0.707685
$544$	3.70788	0.158974
$545$	35.1382	1.50515
$546$	4.31734	0.184765
$547$	0.179174	0.00766091	0.00383046	−	0.999993i	$-0.498781\pi$
$547$	0.179174	0.00766091	0.00383046	+	0.999993i	$0.498781\pi$
$548$	5.45522	0.233036
$549$	−10.0199	−0.427639
$550$	−7.96051	−0.339437
$551$	−8.71256	−0.371168
$552$	−6.68548	−0.284553
$553$	7.59935	0.323157
$554$	−28.0502	−1.19174
$555$	−33.2174	−1.41000
$556$	−10.9764	−0.465503
$557$	10.6469	0.451122	0.225561	−	0.974229i	$-0.427578\pi$
$557$	10.6469	0.451122	0.225561	+	0.974229i	$0.427578\pi$
$558$	−3.96049	−0.167661
$559$	28.9586	1.22482
$560$	−2.15467	−0.0910513
$561$	6.71133	0.283352
$562$	−18.1580	−0.765948
$563$	7.93615	0.334469	0.167234	−	0.985917i	$-0.446516\pi$
$563$	7.93615	0.334469	0.167234	+	0.985917i	$0.446516\pi$
$564$	−11.4458	−0.481957
$565$	−16.9268	−0.712116
$566$	7.27926	0.305970
$567$	−0.702849	−0.0295169
$568$	−6.35010	−0.266444
$569$	36.9536	1.54918	0.774588	−	0.632466i	$-0.217957\pi$
$569$	36.9536	1.54918	0.774588	+	0.632466i	$0.217957\pi$
$570$	−3.06562	−0.128405
$571$	−40.4322	−1.69203	−0.846017	−	0.533156i	$-0.821006\pi$
$571$	−40.4322	−1.69203	−0.846017	+	0.533156i	$0.821006\pi$
$572$	−11.1183	−0.464878
$573$	23.2381	0.970786
$574$	2.73596	0.114197
$575$	−29.4030	−1.22619
$576$	1.00000	0.0416667
$577$	−17.5657	−0.731272	−0.365636	−	0.930758i	$-0.619148\pi$
$577$	−17.5657	−0.731272	−0.365636	+	0.930758i	$0.619148\pi$
$578$	3.25163	0.135250
$579$	−2.24702	−0.0933831
$580$	26.7094	1.10905
$581$	3.22875	0.133951
$582$	4.27886	0.177364
$583$	−1.81002	−0.0749633
$584$	13.0764	0.541105
$585$	−18.8310	−0.778565
$586$	9.66547	0.399277
$587$	−31.8133	−1.31308	−0.656538	−	0.754293i	$-0.727980\pi$
$587$	−31.8133	−1.31308	−0.656538	+	0.754293i	$0.727980\pi$
$588$	6.50600	0.268303
$589$	−3.96049	−0.163189
$590$	26.7616	1.10176
$591$	27.0039	1.11079
$592$	10.8355	0.445335
$593$	−22.5672	−0.926724	−0.463362	−	0.886169i	$-0.653357\pi$
$593$	−22.5672	−0.926724	−0.463362	+	0.886169i	$0.653357\pi$
$594$	1.81002	0.0742659
$595$	7.98925	0.327527
$596$	−1.00010	−0.0409657
$597$	5.70253	0.233389
$598$	−41.0665	−1.67933
$599$	−22.0129	−0.899424	−0.449712	−	0.893174i	$-0.648473\pi$
$599$	−22.0129	−0.899424	−0.449712	+	0.893174i	$0.648473\pi$
$600$	4.39803	0.179549
$601$	−6.71741	−0.274009	−0.137004	−	0.990570i	$-0.543747\pi$
$601$	−6.71741	−0.274009	−0.137004	+	0.990570i	$0.543747\pi$
$602$	−3.31349	−0.135048
$603$	3.97282	0.161786
$604$	−14.6434	−0.595833
$605$	−23.6784	−0.962662
$606$	−3.21153	−0.130460
$607$	−11.2265	−0.455669	−0.227834	−	0.973700i	$-0.573164\pi$
$607$	−11.2265	−0.455669	−0.227834	+	0.973700i	$0.573164\pi$
$608$	1.00000	0.0405554
$609$	6.12361	0.248141
$610$	30.7172	1.24370
$611$	−70.3076	−2.84434
$612$	−3.70788	−0.149882
$613$	−39.8397	−1.60911	−0.804556	−	0.593877i	$-0.797597\pi$
$613$	−39.8397	−1.60911	−0.804556	+	0.593877i	$0.797597\pi$
$614$	7.60327	0.306843
$615$	−11.9335	−0.481203
$616$	1.27217	0.0512571
$617$	22.0247	0.886680	0.443340	−	0.896354i	$-0.353794\pi$
$617$	22.0247	0.886680	0.443340	+	0.896354i	$0.353794\pi$
$618$	−19.5787	−0.787569
$619$	−34.3130	−1.37916	−0.689578	−	0.724211i	$-0.742204\pi$
$619$	−34.3130	−1.37916	−0.689578	+	0.724211i	$0.742204\pi$
$620$	12.1414	0.487609
$621$	6.68548	0.268279
$622$	9.52249	0.381817
$623$	−6.99718	−0.280336
$624$	6.14263	0.245902
$625$	−27.6475	−1.10590
$626$	−27.9479	−1.11702
$627$	1.81002	0.0722851
$628$	18.4677	0.736940
$629$	−40.1766	−1.60195
$630$	2.15467	0.0858440
$631$	−14.6582	−0.583534	−0.291767	−	0.956489i	$-0.594243\pi$
$631$	−14.6582	−0.583534	−0.291767	+	0.956489i	$0.594243\pi$
$632$	10.8122	0.430087
$633$	−18.6064	−0.739538
$634$	27.1141	1.07684
$635$	40.5773	1.61026
$636$	1.00000	0.0396526
$637$	39.9640	1.58343
$638$	−15.7699	−0.624336
$639$	6.35010	0.251206
$640$	−3.06562	−0.121179
$641$	19.3608	0.764705	0.382352	−	0.924017i	$-0.375114\pi$
$641$	19.3608	0.764705	0.382352	+	0.924017i	$0.375114\pi$
$642$	−5.20707	−0.205507
$643$	25.1327	0.991135	0.495568	−	0.868569i	$-0.334960\pi$
$643$	25.1327	0.991135	0.495568	+	0.868569i	$0.334960\pi$
$644$	4.69888	0.185162
$645$	14.4525	0.569065
$646$	−3.70788	−0.145885
$647$	−16.7659	−0.659137	−0.329569	−	0.944132i	$-0.606903\pi$
$647$	−16.7659	−0.659137	−0.329569	+	0.944132i	$0.606903\pi$
$648$	−1.00000	−0.0392837
$649$	−15.8007	−0.620232
$650$	27.0155	1.05963
$651$	2.78363	0.109099
$652$	−2.73543	−0.107128
$653$	23.2484	0.909779	0.454889	−	0.890548i	$-0.349679\pi$
$653$	23.2484	0.909779	0.454889	+	0.890548i	$0.349679\pi$
$654$	11.4620	0.448200
$655$	3.03895	0.118742
$656$	3.89267	0.151983
$657$	−13.0764	−0.510158
$658$	8.04470	0.313615
$659$	5.89945	0.229810	0.114905	−	0.993376i	$-0.463344\pi$
$659$	5.89945	0.229810	0.114905	+	0.993376i	$0.463344\pi$
$660$	−5.54883	−0.215988
$661$	10.3397	0.402167	0.201084	−	0.979574i	$-0.435554\pi$
$661$	10.3397	0.402167	0.201084	+	0.979574i	$0.435554\pi$
$662$	−20.8071	−0.808692
$663$	−22.7761	−0.884552
$664$	4.59380	0.178274
$665$	2.15467	0.0835544
$666$	−10.8355	−0.419866
$667$	−58.2477	−2.25536
$668$	−19.0933	−0.738740
$669$	16.9465	0.655189
$670$	−12.1792	−0.470522
$671$	−18.1362	−0.700141
$672$	−0.702849	−0.0271130
$673$	−7.14905	−0.275576	−0.137788	−	0.990462i	$-0.543999\pi$
$673$	−7.14905	−0.275576	−0.137788	+	0.990462i	$0.543999\pi$
$674$	−0.368760	−0.0142041
$675$	−4.39803	−0.169280
$676$	24.7319	0.951227
$677$	−23.8394	−0.916222	−0.458111	−	0.888895i	$-0.651474\pi$
$677$	−23.8394	−0.916222	−0.458111	+	0.888895i	$0.651474\pi$
$678$	−5.52149	−0.212052
$679$	−3.00739	−0.115413
$680$	11.3670	0.435903
$681$	18.3370	0.702675
$682$	−7.16856	−0.274498
$683$	−2.20830	−0.0844983	−0.0422491	−	0.999107i	$-0.513452\pi$
$683$	−2.20830	−0.0844983	−0.0422491	+	0.999107i	$0.513452\pi$
$684$	−1.00000	−0.0382360
$685$	16.7236	0.638977
$686$	−9.49268	−0.362432
$687$	−13.2114	−0.504048
$688$	−4.71436	−0.179733
$689$	6.14263	0.234016
$690$	−20.4952	−0.780237
$691$	−48.5529	−1.84704	−0.923520	−	0.383549i	$-0.874702\pi$
$691$	−48.5529	−1.84704	−0.923520	+	0.383549i	$0.874702\pi$
$692$	−24.2138	−0.920471
$693$	−1.27217	−0.0483257
$694$	12.7108	0.482495
$695$	−33.6495	−1.27640
$696$	8.71256	0.330249
$697$	−14.4336	−0.546710
$698$	5.04459	0.190940
$699$	26.8200	1.01442
$700$	−3.09115	−0.116834
$701$	46.6463	1.76181	0.880904	−	0.473296i	$-0.156936\pi$
$701$	46.6463	1.76181	0.880904	+	0.473296i	$0.156936\pi$
$702$	−6.14263	−0.231839
$703$	−10.8355	−0.408667
$704$	1.81002	0.0682176
$705$	−35.0886	−1.32151
$706$	25.3361	0.953537
$707$	2.25722	0.0848916
$708$	8.72958	0.328078
$709$	−47.8603	−1.79743	−0.898715	−	0.438533i	$-0.855498\pi$
$709$	−47.8603	−1.79743	−0.898715	+	0.438533i	$0.855498\pi$
$710$	−19.4670	−0.730583
$711$	−10.8122	−0.405490
$712$	−9.95545	−0.373096
$713$	−26.4778	−0.991602
$714$	2.60608	0.0975300
$715$	−34.0844	−1.27468
$716$	6.41946	0.239906
$717$	11.5584	0.431655
$718$	3.77883	0.141025
$719$	−14.8801	−0.554932	−0.277466	−	0.960735i	$-0.589495\pi$
$719$	−14.8801	−0.554932	−0.277466	+	0.960735i	$0.589495\pi$
$720$	3.06562	0.114249
$721$	13.7608	0.512480
$722$	−1.00000	−0.0372161
$723$	−3.30329	−0.122851
$724$	−16.4907	−0.612873
$725$	38.3181	1.42310
$726$	−7.72384	−0.286658
$727$	−17.9215	−0.664671	−0.332336	−	0.943161i	$-0.607837\pi$
$727$	−17.9215	−0.664671	−0.332336	+	0.943161i	$0.607837\pi$
$728$	−4.31734	−0.160011
$729$	1.00000	0.0370370
$730$	40.0872	1.48369
$731$	17.4803	0.646532
$732$	10.0199	0.370347
$733$	47.0350	1.73728	0.868639	−	0.495446i	$-0.164995\pi$
$733$	47.0350	1.73728	0.868639	+	0.495446i	$0.164995\pi$
$734$	16.2915	0.601329
$735$	19.9449	0.735680
$736$	6.68548	0.246430
$737$	7.19087	0.264879
$738$	−3.89267	−0.143291
$739$	29.4777	1.08435	0.542177	−	0.840264i	$-0.317600\pi$
$739$	29.4777	1.08435	0.542177	+	0.840264i	$0.317600\pi$
$740$	33.2174	1.22110
$741$	−6.14263	−0.225655
$742$	−0.702849	−0.0258024
$743$	−4.71709	−0.173053	−0.0865265	−	0.996250i	$-0.527577\pi$
$743$	−4.71709	−0.173053	−0.0865265	+	0.996250i	$0.527577\pi$
$744$	3.96049	0.145199
$745$	−3.06593	−0.112327
$746$	2.35628	0.0862696
$747$	−4.59380	−0.168078
$748$	−6.71133	−0.245390
$749$	3.65978	0.133725
$750$	−1.84541	−0.0673849
$751$	34.5710	1.26151	0.630756	−	0.775981i	$-0.282745\pi$
$751$	34.5710	1.26151	0.630756	+	0.775981i	$0.282745\pi$
$752$	11.4458	0.417387
$753$	−2.46616	−0.0898717
$754$	53.5181	1.94901
$755$	−44.8912	−1.63376
$756$	0.702849	0.0255624
$757$	12.4986	0.454269	0.227135	−	0.973863i	$-0.427064\pi$
$757$	12.4986	0.454269	0.227135	+	0.973863i	$0.427064\pi$
$758$	−22.2547	−0.808329
$759$	12.1008	0.439233
$760$	3.06562	0.111202
$761$	−21.3783	−0.774963	−0.387482	−	0.921877i	$-0.626655\pi$
$761$	−21.3783	−0.774963	−0.387482	+	0.921877i	$0.626655\pi$
$762$	13.2362	0.479498
$763$	−8.05606	−0.291649
$764$	−23.2381	−0.840725
$765$	−11.3670	−0.410973
$766$	16.5412	0.597659
$767$	53.6226	1.93620
$768$	−1.00000	−0.0360844
$769$	18.5756	0.669854	0.334927	−	0.942244i	$-0.391288\pi$
$769$	18.5756	0.669854	0.334927	+	0.942244i	$0.391288\pi$
$770$	3.89999	0.140546
$771$	−26.0219	−0.937156
$772$	2.24702	0.0808721
$773$	8.02226	0.288541	0.144270	−	0.989538i	$-0.453917\pi$
$773$	8.02226	0.288541	0.144270	+	0.989538i	$0.453917\pi$
$774$	4.71436	0.169454
$775$	17.4184	0.625686
$776$	−4.27886	−0.153602
$777$	7.61569	0.273212
$778$	11.6489	0.417632
$779$	−3.89267	−0.139469
$780$	18.8310	0.674257
$781$	11.4938	0.411280
$782$	−24.7890	−0.886452
$783$	−8.71256	−0.311362
$784$	−6.50600	−0.232357
$785$	56.6149	2.02067
$786$	0.991300	0.0353585
$787$	3.18809	0.113643	0.0568215	−	0.998384i	$-0.481903\pi$
$787$	3.18809	0.113643	0.0568215	+	0.998384i	$0.481903\pi$
$788$	−27.0039	−0.961975
$789$	3.95505	0.140803
$790$	33.1462	1.17929
$791$	3.88077	0.137984
$792$	−1.81002	−0.0643162
$793$	61.5486	2.18566
$794$	−29.7700	−1.05650
$795$	3.06562	0.108726
$796$	−5.70253	−0.202121
$797$	−48.0099	−1.70060	−0.850299	−	0.526299i	$-0.823579\pi$
$797$	−48.0099	−1.70060	−0.850299	+	0.526299i	$0.823579\pi$
$798$	0.702849	0.0248806
$799$	−42.4398	−1.50141
$800$	−4.39803	−0.155494
$801$	9.95545	0.351759
$802$	−7.30647	−0.258000
$803$	−23.6685	−0.835243
$804$	−3.97282	−0.140110
$805$	14.4050	0.507709
$806$	24.3278	0.856912
$807$	−8.40098	−0.295728
$808$	3.21153	0.112981
$809$	−10.8968	−0.383109	−0.191555	−	0.981482i	$-0.561353\pi$
$809$	−10.8968	−0.383109	−0.191555	+	0.981482i	$0.561353\pi$
$810$	−3.06562	−0.107715
$811$	−38.2849	−1.34436	−0.672182	−	0.740386i	$-0.734643\pi$
$811$	−38.2849	−1.34436	−0.672182	+	0.740386i	$0.734643\pi$
$812$	−6.12361	−0.214897
$813$	1.75752	0.0616389
$814$	−19.6124	−0.687414
$815$	−8.38579	−0.293741
$816$	3.70788	0.129802
$817$	4.71436	0.164935
$818$	23.0819	0.807039
$819$	4.31734	0.150860
$820$	11.9335	0.416734
$821$	−6.44840	−0.225051	−0.112525	−	0.993649i	$-0.535894\pi$
$821$	−6.44840	−0.225051	−0.112525	+	0.993649i	$0.535894\pi$
$822$	5.45522	0.190273
$823$	11.2027	0.390503	0.195251	−	0.980753i	$-0.437448\pi$
$823$	11.2027	0.390503	0.195251	+	0.980753i	$0.437448\pi$
$824$	19.5787	0.682055
$825$	−7.96051	−0.277149
$826$	−6.13558	−0.213484
$827$	31.5793	1.09812	0.549060	−	0.835783i	$-0.314986\pi$
$827$	31.5793	1.09812	0.549060	+	0.835783i	$0.314986\pi$
$828$	−6.68548	−0.232337
$829$	48.6272	1.68889	0.844446	−	0.535640i	$-0.179930\pi$
$829$	48.6272	1.68889	0.844446	+	0.535640i	$0.179930\pi$
$830$	14.0829	0.488823
$831$	−28.0502	−0.973052
$832$	−6.14263	−0.212957
$833$	24.1235	0.835829
$834$	−10.9764	−0.380081
$835$	−58.5327	−2.02561
$836$	−1.81002	−0.0626008
$837$	−3.96049	−0.136895
$838$	29.9593	1.03493
$839$	22.9301	0.791635	0.395817	−	0.918329i	$-0.370461\pi$
$839$	22.9301	0.791635	0.395817	+	0.918329i	$0.370461\pi$
$840$	−2.15467	−0.0743431
$841$	46.9087	1.61754
$842$	−4.25915	−0.146780
$843$	−18.1580	−0.625394
$844$	18.6064	0.640459
$845$	75.8187	2.60824
$846$	−11.4458	−0.393516
$847$	5.42869	0.186532
$848$	−1.00000	−0.0343401
$849$	7.27926	0.249824
$850$	16.3074	0.559338
$851$	−72.4404	−2.48322
$852$	−6.35010	−0.217551
$853$	−32.2852	−1.10542	−0.552712	−	0.833372i	$-0.686407\pi$
$853$	−32.2852	−1.10542	−0.552712	+	0.833372i	$0.686407\pi$
$854$	−7.04248	−0.240989
$855$	−3.06562	−0.104842
$856$	5.20707	0.177974
$857$	53.1645	1.81607	0.908033	−	0.418899i	$-0.137584\pi$
$857$	53.1645	1.81607	0.908033	+	0.418899i	$0.137584\pi$
$858$	−11.1183	−0.379571
$859$	−44.7399	−1.52651	−0.763253	−	0.646100i	$-0.776399\pi$
$859$	−44.7399	−1.52651	−0.763253	+	0.646100i	$0.776399\pi$
$860$	−14.4525	−0.492825
$861$	2.73596	0.0932412
$862$	32.5517	1.10871
$863$	−16.3368	−0.556112	−0.278056	−	0.960565i	$-0.589690\pi$
$863$	−16.3368	−0.556112	−0.278056	+	0.960565i	$0.589690\pi$
$864$	1.00000	0.0340207
$865$	−74.2303	−2.52391
$866$	0.282725	0.00960740
$867$	3.25163	0.110431
$868$	−2.78363	−0.0944824
$869$	−19.5703	−0.663877
$870$	26.7094	0.905534
$871$	−24.4036	−0.826883
$872$	−11.4620	−0.388153
$873$	4.27886	0.144817
$874$	−6.68548	−0.226140
$875$	1.29704	0.0438481
$876$	13.0764	0.441810
$877$	33.7809	1.14070	0.570351	−	0.821401i	$-0.306807\pi$
$877$	33.7809	1.14070	0.570351	+	0.821401i	$0.306807\pi$
$878$	−32.5360	−1.09804
$879$	9.66547	0.326008
$880$	5.54883	0.187051
$881$	−28.1037	−0.946836	−0.473418	−	0.880838i	$-0.656980\pi$
$881$	−28.1037	−0.946836	−0.473418	+	0.880838i	$0.656980\pi$
$882$	6.50600	0.219069
$883$	3.78910	0.127514	0.0637568	−	0.997965i	$-0.479692\pi$
$883$	3.78910	0.127514	0.0637568	+	0.997965i	$0.479692\pi$
$884$	22.7761	0.766044
$885$	26.7616	0.899581
$886$	−32.2431	−1.08323
$887$	−21.3743	−0.717680	−0.358840	−	0.933399i	$-0.616828\pi$
$887$	−21.3743	−0.717680	−0.358840	+	0.933399i	$0.616828\pi$
$888$	10.8355	0.363614
$889$	−9.30307	−0.312015
$890$	−30.5196	−1.02302
$891$	1.81002	0.0606379
$892$	−16.9465	−0.567410
$893$	−11.4458	−0.383021
$894$	−1.00010	−0.0334484
$895$	19.6796	0.657817
$896$	0.702849	0.0234805
$897$	−41.0665	−1.37117
$898$	27.7628	0.926457
$899$	34.5060	1.15084
$900$	4.39803	0.146601
$901$	3.70788	0.123527
$902$	−7.04580	−0.234600
$903$	−3.31349	−0.110266
$904$	5.52149	0.183642
$905$	−50.5543	−1.68048
$906$	−14.6434	−0.486495
$907$	−21.8726	−0.726269	−0.363134	−	0.931737i	$-0.618293\pi$
$907$	−21.8726	−0.726269	−0.363134	+	0.931737i	$0.618293\pi$
$908$	−18.3370	−0.608535
$909$	−3.21153	−0.106520
$910$	−13.2353	−0.438747
$911$	−9.31069	−0.308477	−0.154238	−	0.988034i	$-0.549292\pi$
$911$	−9.31069	−0.308477	−0.154238	+	0.988034i	$0.549292\pi$
$912$	1.00000	0.0331133
$913$	−8.31487	−0.275182
$914$	−4.10220	−0.135689
$915$	30.7172	1.01548
$916$	13.2114	0.436518
$917$	−0.696734	−0.0230082
$918$	−3.70788	−0.122378
$919$	42.2107	1.39240	0.696201	−	0.717847i	$-0.254872\pi$
$919$	42.2107	1.39240	0.696201	+	0.717847i	$0.254872\pi$
$920$	20.4952	0.675705
$921$	7.60327	0.250536
$922$	0.635941	0.0209436
$923$	−39.0063	−1.28391
$924$	1.27217	0.0418513
$925$	47.6547	1.56688
$926$	−0.0871142	−0.00286275
$927$	−19.5787	−0.643047
$928$	−8.71256	−0.286004
$929$	40.6973	1.33524	0.667618	−	0.744504i	$-0.267314\pi$
$929$	40.6973	1.33524	0.667618	+	0.744504i	$0.267314\pi$
$930$	12.1414	0.398131
$931$	6.50600	0.213226
$932$	−26.8200	−0.878518
$933$	9.52249	0.311752
$934$	−8.91128	−0.291586
$935$	−20.5744	−0.672854
$936$	6.14263	0.200778
$937$	39.2116	1.28099	0.640493	−	0.767964i	$-0.278730\pi$
$937$	39.2116	1.28099	0.640493	+	0.767964i	$0.278730\pi$
$938$	2.79229	0.0911715
$939$	−27.9479	−0.912046
$940$	35.0886	1.14446
$941$	4.17222	0.136011	0.0680053	−	0.997685i	$-0.478337\pi$
$941$	4.17222	0.136011	0.0680053	+	0.997685i	$0.478337\pi$
$942$	18.4677	0.601709
$943$	−26.0244	−0.847471
$944$	−8.72958	−0.284124
$945$	2.15467	0.0700913
$946$	8.53308	0.277434
$947$	33.0156	1.07286	0.536431	−	0.843944i	$-0.319772\pi$
$947$	33.0156	1.07286	0.536431	+	0.843944i	$0.319772\pi$
$948$	10.8122	0.351165
$949$	80.3234	2.60741
$950$	4.39803	0.142691
$951$	27.1141	0.879234
$952$	−2.60608	−0.0844635
$953$	23.0507	0.746685	0.373342	−	0.927694i	$-0.378212\pi$
$953$	23.0507	0.746685	0.373342	+	0.927694i	$0.378212\pi$
$954$	1.00000	0.0323762
$955$	−71.2392	−2.30525
$956$	−11.5584	−0.373824
$957$	−15.7699	−0.509768
$958$	8.54588	0.276105
$959$	−3.83420	−0.123813
$960$	−3.06562	−0.0989425
$961$	−15.3145	−0.494016
$962$	66.5583	2.14592
$963$	−5.20707	−0.167795
$964$	3.30329	0.106392
$965$	6.88852	0.221749
$966$	4.69888	0.151184
$967$	−19.3924	−0.623618	−0.311809	−	0.950145i	$-0.600935\pi$
$967$	−19.3924	−0.623618	−0.311809	+	0.950145i	$0.600935\pi$
$968$	7.72384	0.248253
$969$	−3.70788	−0.119114
$970$	−13.1174	−0.421173
$971$	43.6197	1.39982	0.699912	−	0.714229i	$-0.253222\pi$
$971$	43.6197	1.39982	0.699912	+	0.714229i	$0.253222\pi$
$972$	−1.00000	−0.0320750
$973$	7.71474	0.247323
$974$	39.4348	1.26357
$975$	27.0155	0.865188
$976$	−10.0199	−0.320729
$977$	34.8862	1.11611	0.558054	−	0.829805i	$-0.311548\pi$
$977$	34.8862	1.11611	0.558054	+	0.829805i	$0.311548\pi$
$978$	−2.73543	−0.0874694
$979$	18.0195	0.575907
$980$	−19.9449	−0.637118
$981$	11.4620	0.365954
$982$	−5.53940	−0.176769
$983$	37.9705	1.21107	0.605536	−	0.795818i	$-0.292959\pi$
$983$	37.9705	1.21107	0.605536	+	0.795818i	$0.292959\pi$
$984$	3.89267	0.124094
$985$	−82.7838	−2.63771
$986$	32.3051	1.02881
$987$	8.04470	0.256066
$988$	6.14263	0.195423
$989$	31.5178	1.00221
$990$	−5.54883	−0.176353
$991$	7.05199	0.224014	0.112007	−	0.993707i	$-0.464272\pi$
$991$	7.05199	0.224014	0.112007	+	0.993707i	$0.464272\pi$
$992$	−3.96049	−0.125746
$993$	−20.8071	−0.660295
$994$	4.46316	0.141563
$995$	−17.4818	−0.554211
$996$	4.59380	0.145560
$997$	−2.03416	−0.0644225	−0.0322113	−	0.999481i	$-0.510255\pi$
$997$	−2.03416	−0.0644225	−0.0322113	+	0.999481i	$0.510255\pi$
$998$	19.5274	0.618129
$999$	−10.8355	−0.342819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.be.1.11	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.be.1.11	✓	12	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.06562 q^{5} +1.00000 q^{6} -0.702849 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.06562 q^{5} +1.00000 q^{6} -0.702849 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.06562 q^{10} +1.81002 q^{11} -1.00000 q^{12} -6.14263 q^{13} +0.702849 q^{14} -3.06562 q^{15} +1.00000 q^{16} -3.70788 q^{17} -1.00000 q^{18} -1.00000 q^{19} +3.06562 q^{20} +0.702849 q^{21} -1.81002 q^{22} -6.68548 q^{23} +1.00000 q^{24} +4.39803 q^{25} +6.14263 q^{26} -1.00000 q^{27} -0.702849 q^{28} +8.71256 q^{29} +3.06562 q^{30} +3.96049 q^{31} -1.00000 q^{32} -1.81002 q^{33} +3.70788 q^{34} -2.15467 q^{35} +1.00000 q^{36} +10.8355 q^{37} +1.00000 q^{38} +6.14263 q^{39} -3.06562 q^{40} +3.89267 q^{41} -0.702849 q^{42} -4.71436 q^{43} +1.81002 q^{44} +3.06562 q^{45} +6.68548 q^{46} +11.4458 q^{47} -1.00000 q^{48} -6.50600 q^{49} -4.39803 q^{50} +3.70788 q^{51} -6.14263 q^{52} -1.00000 q^{53} +1.00000 q^{54} +5.54883 q^{55} +0.702849 q^{56} +1.00000 q^{57} -8.71256 q^{58} -8.72958 q^{59} -3.06562 q^{60} -10.0199 q^{61} -3.96049 q^{62} -0.702849 q^{63} +1.00000 q^{64} -18.8310 q^{65} +1.81002 q^{66} +3.97282 q^{67} -3.70788 q^{68} +6.68548 q^{69} +2.15467 q^{70} +6.35010 q^{71} -1.00000 q^{72} -13.0764 q^{73} -10.8355 q^{74} -4.39803 q^{75} -1.00000 q^{76} -1.27217 q^{77} -6.14263 q^{78} -10.8122 q^{79} +3.06562 q^{80} +1.00000 q^{81} -3.89267 q^{82} -4.59380 q^{83} +0.702849 q^{84} -11.3670 q^{85} +4.71436 q^{86} -8.71256 q^{87} -1.81002 q^{88} +9.95545 q^{89} -3.06562 q^{90} +4.31734 q^{91} -6.68548 q^{92} -3.96049 q^{93} -11.4458 q^{94} -3.06562 q^{95} +1.00000 q^{96} +4.27886 q^{97} +6.50600 q^{98} +1.81002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 12 q^{3} + 12 q^{4} - 3 q^{5} + 12 q^{6} - q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 12 * q^3 + 12 * q^4 - 3 * q^5 + 12 * q^6 - q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} - 12 q^{3} + 12 q^{4} - 3 q^{5} + 12 q^{6} - q^{7} - 12 q^{8} + 12 q^{9} + 3 q^{10} - 7 q^{11} - 12 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} + 12 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{19} - 3 q^{20} + q^{21} + 7 q^{22} - 18 q^{23} + 12 q^{24} + 21 q^{25} - 4 q^{26} - 12 q^{27} - q^{28} + 10 q^{29} - 3 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} + 4 q^{34} - 19 q^{35} + 12 q^{36} + 14 q^{37} + 12 q^{38} - 4 q^{39} + 3 q^{40} - 9 q^{41} - q^{42} - 4 q^{43} - 7 q^{44} - 3 q^{45} + 18 q^{46} - 14 q^{47} - 12 q^{48} + 37 q^{49} - 21 q^{50} + 4 q^{51} + 4 q^{52} - 12 q^{53} + 12 q^{54} - 4 q^{55} + q^{56} + 12 q^{57} - 10 q^{58} - 18 q^{59} + 3 q^{60} - 7 q^{61} - 14 q^{62} - q^{63} + 12 q^{64} + 3 q^{65} - 7 q^{66} + 8 q^{67} - 4 q^{68} + 18 q^{69} + 19 q^{70} - q^{71} - 12 q^{72} - 31 q^{73} - 14 q^{74} - 21 q^{75} - 12 q^{76} - 25 q^{77} + 4 q^{78} - 3 q^{80} + 12 q^{81} + 9 q^{82} - 48 q^{83} + q^{84} + 4 q^{85} + 4 q^{86} - 10 q^{87} + 7 q^{88} + 13 q^{89} + 3 q^{90} + 9 q^{91} - 18 q^{92} - 14 q^{93} + 14 q^{94} + 3 q^{95} + 12 q^{96} + 25 q^{97} - 37 q^{98} - 7 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 12 * q^3 + 12 * q^4 - 3 * q^5 + 12 * q^6 - q^7 - 12 * q^8 + 12 * q^9 + 3 * q^10 - 7 * q^11 - 12 * q^12 + 4 * q^13 + q^14 + 3 * q^15 + 12 * q^16 - 4 * q^17 - 12 * q^18 - 12 * q^19 - 3 * q^20 + q^21 + 7 * q^22 - 18 * q^23 + 12 * q^24 + 21 * q^25 - 4 * q^26 - 12 * q^27 - q^28 + 10 * q^29 - 3 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 + 4 * q^34 - 19 * q^35 + 12 * q^36 + 14 * q^37 + 12 * q^38 - 4 * q^39 + 3 * q^40 - 9 * q^41 - q^42 - 4 * q^43 - 7 * q^44 - 3 * q^45 + 18 * q^46 - 14 * q^47 - 12 * q^48 + 37 * q^49 - 21 * q^50 + 4 * q^51 + 4 * q^52 - 12 * q^53 + 12 * q^54 - 4 * q^55 + q^56 + 12 * q^57 - 10 * q^58 - 18 * q^59 + 3 * q^60 - 7 * q^61 - 14 * q^62 - q^63 + 12 * q^64 + 3 * q^65 - 7 * q^66 + 8 * q^67 - 4 * q^68 + 18 * q^69 + 19 * q^70 - q^71 - 12 * q^72 - 31 * q^73 - 14 * q^74 - 21 * q^75 - 12 * q^76 - 25 * q^77 + 4 * q^78 - 3 * q^80 + 12 * q^81 + 9 * q^82 - 48 * q^83 + q^84 + 4 * q^85 + 4 * q^86 - 10 * q^87 + 7 * q^88 + 13 * q^89 + 3 * q^90 + 9 * q^91 - 18 * q^92 - 14 * q^93 + 14 * q^94 + 3 * q^95 + 12 * q^96 + 25 * q^97 - 37 * q^98 - 7 * q^99

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