LMFDB - Embedded newform 6010.2.a.g.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.60467 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.60467 q^{6} -3.11642 q^{7} -1.00000 q^{8} -0.425041 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.60467 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.60467 q^{6} -3.11642 q^{7} -1.00000 q^{8} -0.425041 q^{9} -1.00000 q^{10} -0.687301 q^{11} +1.60467 q^{12} +0.929339 q^{13} +3.11642 q^{14} +1.60467 q^{15} +1.00000 q^{16} -2.78141 q^{17} +0.425041 q^{18} -2.69070 q^{19} +1.00000 q^{20} -5.00083 q^{21} +0.687301 q^{22} -7.77406 q^{23} -1.60467 q^{24} +1.00000 q^{25} -0.929339 q^{26} -5.49605 q^{27} -3.11642 q^{28} +2.75384 q^{29} -1.60467 q^{30} +8.25125 q^{31} -1.00000 q^{32} -1.10289 q^{33} +2.78141 q^{34} -3.11642 q^{35} -0.425041 q^{36} -2.56950 q^{37} +2.69070 q^{38} +1.49128 q^{39} -1.00000 q^{40} +10.1783 q^{41} +5.00083 q^{42} -6.09157 q^{43} -0.687301 q^{44} -0.425041 q^{45} +7.77406 q^{46} +8.18377 q^{47} +1.60467 q^{48} +2.71210 q^{49} -1.00000 q^{50} -4.46324 q^{51} +0.929339 q^{52} -1.76255 q^{53} +5.49605 q^{54} -0.687301 q^{55} +3.11642 q^{56} -4.31768 q^{57} -2.75384 q^{58} +13.6431 q^{59} +1.60467 q^{60} +10.1664 q^{61} -8.25125 q^{62} +1.32461 q^{63} +1.00000 q^{64} +0.929339 q^{65} +1.10289 q^{66} +5.82525 q^{67} -2.78141 q^{68} -12.4748 q^{69} +3.11642 q^{70} +3.66284 q^{71} +0.425041 q^{72} +7.51309 q^{73} +2.56950 q^{74} +1.60467 q^{75} -2.69070 q^{76} +2.14192 q^{77} -1.49128 q^{78} +5.39395 q^{79} +1.00000 q^{80} -7.54422 q^{81} -10.1783 q^{82} +14.3621 q^{83} -5.00083 q^{84} -2.78141 q^{85} +6.09157 q^{86} +4.41899 q^{87} +0.687301 q^{88} +2.01565 q^{89} +0.425041 q^{90} -2.89622 q^{91} -7.77406 q^{92} +13.2405 q^{93} -8.18377 q^{94} -2.69070 q^{95} -1.60467 q^{96} -0.940044 q^{97} -2.71210 q^{98} +0.292131 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * 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
$3$	1.60467	0.926455	0.463228	−	0.886239i	$-0.346691\pi$
$3$	1.60467	0.926455	0.463228	+	0.886239i	$0.346691\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.60467	−0.655103
$7$	−3.11642	−1.17790	−0.588949	−	0.808170i	$-0.700458\pi$
$7$	−3.11642	−1.17790	−0.588949	+	0.808170i	$0.700458\pi$
$8$	−1.00000	−0.353553
$9$	−0.425041	−0.141680
$10$	−1.00000	−0.316228
$11$	−0.687301	−0.207229	−0.103615	−	0.994618i	$-0.533041\pi$
$11$	−0.687301	−0.207229	−0.103615	+	0.994618i	$0.533041\pi$
$12$	1.60467	0.463228
$13$	0.929339	0.257752	0.128876	−	0.991661i	$-0.458863\pi$
$13$	0.929339	0.257752	0.128876	+	0.991661i	$0.458863\pi$
$14$	3.11642	0.832899
$15$	1.60467	0.414323
$16$	1.00000	0.250000
$17$	−2.78141	−0.674591	−0.337295	−	0.941399i	$-0.609512\pi$
$17$	−2.78141	−0.674591	−0.337295	+	0.941399i	$0.609512\pi$
$18$	0.425041	0.100183
$19$	−2.69070	−0.617288	−0.308644	−	0.951178i	$-0.599875\pi$
$19$	−2.69070	−0.617288	−0.308644	+	0.951178i	$0.599875\pi$
$20$	1.00000	0.223607
$21$	−5.00083	−1.09127
$22$	0.687301	0.146533
$23$	−7.77406	−1.62100	−0.810502	−	0.585736i	$-0.800805\pi$
$23$	−7.77406	−1.62100	−0.810502	+	0.585736i	$0.800805\pi$
$24$	−1.60467	−0.327551
$25$	1.00000	0.200000
$26$	−0.929339	−0.182258
$27$	−5.49605	−1.05772
$28$	−3.11642	−0.588949
$29$	2.75384	0.511374	0.255687	−	0.966760i	$-0.417698\pi$
$29$	2.75384	0.511374	0.255687	+	0.966760i	$0.417698\pi$
$30$	−1.60467	−0.292971
$31$	8.25125	1.48197	0.740984	−	0.671522i	$-0.234359\pi$
$31$	8.25125	1.48197	0.740984	+	0.671522i	$0.234359\pi$
$32$	−1.00000	−0.176777
$33$	−1.10289	−0.191989
$34$	2.78141	0.477008
$35$	−3.11642	−0.526772
$36$	−0.425041	−0.0708402
$37$	−2.56950	−0.422422	−0.211211	−	0.977440i	$-0.567741\pi$
$37$	−2.56950	−0.422422	−0.211211	+	0.977440i	$0.567741\pi$
$38$	2.69070	0.436489
$39$	1.49128	0.238796
$40$	−1.00000	−0.158114
$41$	10.1783	1.58958	0.794790	−	0.606884i	$-0.207581\pi$
$41$	10.1783	1.58958	0.794790	+	0.606884i	$0.207581\pi$
$42$	5.00083	0.771644
$43$	−6.09157	−0.928956	−0.464478	−	0.885585i	$-0.653758\pi$
$43$	−6.09157	−0.928956	−0.464478	+	0.885585i	$0.653758\pi$
$44$	−0.687301	−0.103615
$45$	−0.425041	−0.0633614
$46$	7.77406	1.14622
$47$	8.18377	1.19373	0.596863	−	0.802343i	$-0.296414\pi$
$47$	8.18377	1.19373	0.596863	+	0.802343i	$0.296414\pi$
$48$	1.60467	0.231614
$49$	2.71210	0.387443
$50$	−1.00000	−0.141421
$51$	−4.46324	−0.624978
$52$	0.929339	0.128876
$53$	−1.76255	−0.242105	−0.121052	−	0.992646i	$-0.538627\pi$
$53$	−1.76255	−0.242105	−0.121052	+	0.992646i	$0.538627\pi$
$54$	5.49605	0.747918
$55$	−0.687301	−0.0926757
$56$	3.11642	0.416450
$57$	−4.31768	−0.571890
$58$	−2.75384	−0.361596
$59$	13.6431	1.77618	0.888090	−	0.459669i	$-0.152032\pi$
$59$	13.6431	1.77618	0.888090	+	0.459669i	$0.152032\pi$
$60$	1.60467	0.207162
$61$	10.1664	1.30168	0.650839	−	0.759216i	$-0.274417\pi$
$61$	10.1664	1.30168	0.650839	+	0.759216i	$0.274417\pi$
$62$	−8.25125	−1.04791
$63$	1.32461	0.166885
$64$	1.00000	0.125000
$65$	0.929339	0.115270
$66$	1.10289	0.135756
$67$	5.82525	0.711667	0.355834	−	0.934549i	$-0.384197\pi$
$67$	5.82525	0.711667	0.355834	+	0.934549i	$0.384197\pi$
$68$	−2.78141	−0.337295
$69$	−12.4748	−1.50179
$70$	3.11642	0.372484
$71$	3.66284	0.434699	0.217349	−	0.976094i	$-0.430259\pi$
$71$	3.66284	0.434699	0.217349	+	0.976094i	$0.430259\pi$
$72$	0.425041	0.0500916
$73$	7.51309	0.879340	0.439670	−	0.898159i	$-0.355095\pi$
$73$	7.51309	0.879340	0.439670	+	0.898159i	$0.355095\pi$
$74$	2.56950	0.298698
$75$	1.60467	0.185291
$76$	−2.69070	−0.308644
$77$	2.14192	0.244095
$78$	−1.49128	−0.168854
$79$	5.39395	0.606867	0.303433	−	0.952853i	$-0.401867\pi$
$79$	5.39395	0.606867	0.303433	+	0.952853i	$0.401867\pi$
$80$	1.00000	0.111803
$81$	−7.54422	−0.838246
$82$	−10.1783	−1.12400
$83$	14.3621	1.57645	0.788225	−	0.615388i	$-0.211001\pi$
$83$	14.3621	1.57645	0.788225	+	0.615388i	$0.211001\pi$
$84$	−5.00083	−0.545635
$85$	−2.78141	−0.301686
$86$	6.09157	0.656871
$87$	4.41899	0.473766
$88$	0.687301	0.0732666
$89$	2.01565	0.213658	0.106829	−	0.994277i	$-0.465930\pi$
$89$	2.01565	0.213658	0.106829	+	0.994277i	$0.465930\pi$
$90$	0.425041	0.0448033
$91$	−2.89622	−0.303606
$92$	−7.77406	−0.810502
$93$	13.2405	1.37298
$94$	−8.18377	−0.844092
$95$	−2.69070	−0.276060
$96$	−1.60467	−0.163776
$97$	−0.940044	−0.0954470	−0.0477235	−	0.998861i	$-0.515197\pi$
$97$	−0.940044	−0.0954470	−0.0477235	+	0.998861i	$0.515197\pi$
$98$	−2.71210	−0.273964
$99$	0.292131	0.0293603
$100$	1.00000	0.100000
$101$	−9.37203	−0.932552	−0.466276	−	0.884639i	$-0.654405\pi$
$101$	−9.37203	−0.932552	−0.466276	+	0.884639i	$0.654405\pi$
$102$	4.46324	0.441926
$103$	8.96135	0.882988	0.441494	−	0.897264i	$-0.354449\pi$
$103$	8.96135	0.882988	0.441494	+	0.897264i	$0.354449\pi$
$104$	−0.929339	−0.0911292
$105$	−5.00083	−0.488031
$106$	1.76255	0.171194
$107$	8.59311	0.830727	0.415364	−	0.909655i	$-0.363654\pi$
$107$	8.59311	0.830727	0.415364	+	0.909655i	$0.363654\pi$
$108$	−5.49605	−0.528858
$109$	3.71733	0.356055	0.178028	−	0.984025i	$-0.443028\pi$
$109$	3.71733	0.356055	0.178028	+	0.984025i	$0.443028\pi$
$110$	0.687301	0.0655316
$111$	−4.12319	−0.391356
$112$	−3.11642	−0.294474
$113$	−3.37517	−0.317509	−0.158754	−	0.987318i	$-0.550748\pi$
$113$	−3.37517	−0.317509	−0.158754	+	0.987318i	$0.550748\pi$
$114$	4.31768	0.404387
$115$	−7.77406	−0.724935
$116$	2.75384	0.255687
$117$	−0.395007	−0.0365184
$118$	−13.6431	−1.25595
$119$	8.66805	0.794599
$120$	−1.60467	−0.146485
$121$	−10.5276	−0.957056
$122$	−10.1664	−0.920425
$123$	16.3328	1.47268
$124$	8.25125	0.740984
$125$	1.00000	0.0894427
$126$	−1.32461	−0.118005
$127$	9.32108	0.827112	0.413556	−	0.910479i	$-0.364287\pi$
$127$	9.32108	0.827112	0.413556	+	0.910479i	$0.364287\pi$
$128$	−1.00000	−0.0883883
$129$	−9.77495	−0.860636
$130$	−0.929339	−0.0815085
$131$	7.23720	0.632317	0.316158	−	0.948706i	$-0.397607\pi$
$131$	7.23720	0.632317	0.316158	+	0.948706i	$0.397607\pi$
$132$	−1.10289	−0.0959943
$133$	8.38535	0.727102
$134$	−5.82525	−0.503225
$135$	−5.49605	−0.473025
$136$	2.78141	0.238504
$137$	−10.5113	−0.898037	−0.449019	−	0.893522i	$-0.648226\pi$
$137$	−10.5113	−0.898037	−0.449019	+	0.893522i	$0.648226\pi$
$138$	12.4748	1.06192
$139$	1.62939	0.138203	0.0691014	−	0.997610i	$-0.477987\pi$
$139$	1.62939	0.138203	0.0691014	+	0.997610i	$0.477987\pi$
$140$	−3.11642	−0.263386
$141$	13.1322	1.10593
$142$	−3.66284	−0.307378
$143$	−0.638736	−0.0534138
$144$	−0.425041	−0.0354201
$145$	2.75384	0.228694
$146$	−7.51309	−0.621787
$147$	4.35202	0.358949
$148$	−2.56950	−0.211211
$149$	−6.26425	−0.513187	−0.256594	−	0.966519i	$-0.582600\pi$
$149$	−6.26425	−0.513187	−0.256594	+	0.966519i	$0.582600\pi$
$150$	−1.60467	−0.131021
$151$	0.0233969	0.00190401	0.000952007	−	1.00000i	$-0.499697\pi$
$151$	0.0233969	0.00190401	0.000952007		1.00000i	$0.499697\pi$
$152$	2.69070	0.218244
$153$	1.18221	0.0955763
$154$	−2.14192	−0.172601
$155$	8.25125	0.662757
$156$	1.49128	0.119398
$157$	−20.0262	−1.59827	−0.799134	−	0.601153i	$-0.794708\pi$
$157$	−20.0262	−1.59827	−0.799134	+	0.601153i	$0.794708\pi$
$158$	−5.39395	−0.429119
$159$	−2.82831	−0.224299
$160$	−1.00000	−0.0790569
$161$	24.2273	1.90938
$162$	7.54422	0.592730
$163$	15.8054	1.23797	0.618985	−	0.785402i	$-0.287544\pi$
$163$	15.8054	1.23797	0.618985	+	0.785402i	$0.287544\pi$
$164$	10.1783	0.794790
$165$	−1.10289	−0.0858599
$166$	−14.3621	−1.11472
$167$	−9.40287	−0.727616	−0.363808	−	0.931474i	$-0.618524\pi$
$167$	−9.40287	−0.727616	−0.363808	+	0.931474i	$0.618524\pi$
$168$	5.00083	0.385822
$169$	−12.1363	−0.933564
$170$	2.78141	0.213324
$171$	1.14366	0.0874576
$172$	−6.09157	−0.464478
$173$	18.9532	1.44099	0.720494	−	0.693461i	$-0.243915\pi$
$173$	18.9532	1.44099	0.720494	+	0.693461i	$0.243915\pi$
$174$	−4.41899	−0.335003
$175$	−3.11642	−0.235580
$176$	−0.687301	−0.0518073
$177$	21.8926	1.64555
$178$	−2.01565	−0.151079
$179$	−4.09628	−0.306170	−0.153085	−	0.988213i	$-0.548921\pi$
$179$	−4.09628	−0.306170	−0.153085	+	0.988213i	$0.548921\pi$
$180$	−0.425041	−0.0316807
$181$	8.46873	0.629476	0.314738	−	0.949179i	$-0.398083\pi$
$181$	8.46873	0.629476	0.314738	+	0.949179i	$0.398083\pi$
$182$	2.89622	0.214682
$183$	16.3137	1.20595
$184$	7.77406	0.573111
$185$	−2.56950	−0.188913
$186$	−13.2405	−0.970842
$187$	1.91167	0.139795
$188$	8.18377	0.596863
$189$	17.1280	1.24588
$190$	2.69070	0.195204
$191$	−3.44231	−0.249077	−0.124538	−	0.992215i	$-0.539745\pi$
$191$	−3.44231	−0.249077	−0.124538	+	0.992215i	$0.539745\pi$
$192$	1.60467	0.115807
$193$	20.2128	1.45495	0.727474	−	0.686135i	$-0.240694\pi$
$193$	20.2128	1.45495	0.727474	+	0.686135i	$0.240694\pi$
$194$	0.940044	0.0674912
$195$	1.49128	0.106793
$196$	2.71210	0.193722
$197$	−14.6494	−1.04373	−0.521865	−	0.853028i	$-0.674764\pi$
$197$	−14.6494	−1.04373	−0.521865	+	0.853028i	$0.674764\pi$
$198$	−0.292131	−0.0207609
$199$	−5.34395	−0.378823	−0.189411	−	0.981898i	$-0.560658\pi$
$199$	−5.34395	−0.378823	−0.189411	+	0.981898i	$0.560658\pi$
$200$	−1.00000	−0.0707107
$201$	9.34759	0.659328
$202$	9.37203	0.659414
$203$	−8.58212	−0.602347
$204$	−4.46324	−0.312489
$205$	10.1783	0.710882
$206$	−8.96135	−0.624367
$207$	3.30429	0.229664
$208$	0.929339	0.0644381
$209$	1.84932	0.127920
$210$	5.00083	0.345090
$211$	12.3024	0.846929	0.423464	−	0.905913i	$-0.360814\pi$
$211$	12.3024	0.846929	0.423464	+	0.905913i	$0.360814\pi$
$212$	−1.76255	−0.121052
$213$	5.87764	0.402729
$214$	−8.59311	−0.587413
$215$	−6.09157	−0.415442
$216$	5.49605	0.373959
$217$	−25.7144	−1.74561
$218$	−3.71733	−0.251769
$219$	12.0560	0.814669
$220$	−0.687301	−0.0463379
$221$	−2.58487	−0.173877
$222$	4.12319	0.276730
$223$	14.5047	0.971309	0.485655	−	0.874151i	$-0.338581\pi$
$223$	14.5047	0.971309	0.485655	+	0.874151i	$0.338581\pi$
$224$	3.11642	0.208225
$225$	−0.425041	−0.0283361
$226$	3.37517	0.224513
$227$	9.83217	0.652584	0.326292	−	0.945269i	$-0.394201\pi$
$227$	9.83217	0.652584	0.326292	+	0.945269i	$0.394201\pi$
$228$	−4.31768	−0.285945
$229$	−0.432323	−0.0285687	−0.0142844	−	0.999898i	$-0.504547\pi$
$229$	−0.432323	−0.0285687	−0.0142844	+	0.999898i	$0.504547\pi$
$230$	7.77406	0.512606
$231$	3.43707	0.226143
$232$	−2.75384	−0.180798
$233$	28.3649	1.85825	0.929124	−	0.369769i	$-0.120563\pi$
$233$	28.3649	1.85825	0.929124	+	0.369769i	$0.120563\pi$
$234$	0.395007	0.0258224
$235$	8.18377	0.533850
$236$	13.6431	0.888090
$237$	8.65549	0.562235
$238$	−8.66805	−0.561866
$239$	8.24447	0.533290	0.266645	−	0.963795i	$-0.414085\pi$
$239$	8.24447	0.533290	0.266645	+	0.963795i	$0.414085\pi$
$240$	1.60467	0.103581
$241$	−23.8891	−1.53883	−0.769416	−	0.638749i	$-0.779452\pi$
$241$	−23.8891	−1.53883	−0.769416	+	0.638749i	$0.779452\pi$
$242$	10.5276	0.676741
$243$	4.38220	0.281118
$244$	10.1664	0.650839
$245$	2.71210	0.173270
$246$	−16.3328	−1.04134
$247$	−2.50057	−0.159108
$248$	−8.25125	−0.523955
$249$	23.0465	1.46051
$250$	−1.00000	−0.0632456
$251$	2.64188	0.166754	0.0833769	−	0.996518i	$-0.473429\pi$
$251$	2.64188	0.166754	0.0833769	+	0.996518i	$0.473429\pi$
$252$	1.32461	0.0834425
$253$	5.34312	0.335919
$254$	−9.32108	−0.584857
$255$	−4.46324	−0.279499
$256$	1.00000	0.0625000
$257$	−0.420643	−0.0262390	−0.0131195	−	0.999914i	$-0.504176\pi$
$257$	−0.420643	−0.0262390	−0.0131195	+	0.999914i	$0.504176\pi$
$258$	9.77495	0.608562
$259$	8.00764	0.497570
$260$	0.929339	0.0576352
$261$	−1.17049	−0.0724517
$262$	−7.23720	−0.447116
$263$	−4.11820	−0.253939	−0.126969	−	0.991907i	$-0.540525\pi$
$263$	−4.11820	−0.253939	−0.126969	+	0.991907i	$0.540525\pi$
$264$	1.10289	0.0678782
$265$	−1.76255	−0.108273
$266$	−8.38535	−0.514139
$267$	3.23444	0.197945
$268$	5.82525	0.355834
$269$	30.2056	1.84167	0.920835	−	0.389953i	$-0.127509\pi$
$269$	30.2056	1.84167	0.920835	+	0.389953i	$0.127509\pi$
$270$	5.49605	0.334479
$271$	12.3327	0.749158	0.374579	−	0.927195i	$-0.377787\pi$
$271$	12.3327	0.749158	0.374579	+	0.927195i	$0.377787\pi$
$272$	−2.78141	−0.168648
$273$	−4.64747	−0.281277
$274$	10.5113	0.635008
$275$	−0.687301	−0.0414458
$276$	−12.4748	−0.750894
$277$	17.2256	1.03499	0.517494	−	0.855687i	$-0.326865\pi$
$277$	17.2256	1.03499	0.517494	+	0.855687i	$0.326865\pi$
$278$	−1.62939	−0.0977242
$279$	−3.50712	−0.209966
$280$	3.11642	0.186242
$281$	−17.9215	−1.06911	−0.534554	−	0.845135i	$-0.679520\pi$
$281$	−17.9215	−1.06911	−0.534554	+	0.845135i	$0.679520\pi$
$282$	−13.1322	−0.782013
$283$	−31.8066	−1.89070	−0.945352	−	0.326050i	$-0.894282\pi$
$283$	−31.8066	−1.89070	−0.945352	+	0.326050i	$0.894282\pi$
$284$	3.66284	0.217349
$285$	−4.31768	−0.255757
$286$	0.638736	0.0377693
$287$	−31.7198	−1.87236
$288$	0.425041	0.0250458
$289$	−9.26376	−0.544927
$290$	−2.75384	−0.161711
$291$	−1.50846	−0.0884274
$292$	7.51309	0.439670
$293$	0.184708	0.0107907	0.00539537	−	0.999985i	$-0.498283\pi$
$293$	0.184708	0.0107907	0.00539537	+	0.999985i	$0.498283\pi$
$294$	−4.35202	−0.253815
$295$	13.6431	0.794332
$296$	2.56950	0.149349
$297$	3.77745	0.219190
$298$	6.26425	0.362878
$299$	−7.22474	−0.417818
$300$	1.60467	0.0926455
$301$	18.9839	1.09421
$302$	−0.0233969	−0.00134634
$303$	−15.0390	−0.863968
$304$	−2.69070	−0.154322
$305$	10.1664	0.582128
$306$	−1.18221	−0.0675826
$307$	−21.7285	−1.24011	−0.620055	−	0.784558i	$-0.712890\pi$
$307$	−21.7285	−1.24011	−0.620055	+	0.784558i	$0.712890\pi$
$308$	2.14192	0.122047
$309$	14.3800	0.818049
$310$	−8.25125	−0.468640
$311$	5.38313	0.305249	0.152625	−	0.988284i	$-0.451227\pi$
$311$	5.38313	0.305249	0.152625	+	0.988284i	$0.451227\pi$
$312$	−1.49128	−0.0844272
$313$	−34.8758	−1.97130	−0.985649	−	0.168805i	$-0.946009\pi$
$313$	−34.8758	−1.97130	−0.985649	+	0.168805i	$0.946009\pi$
$314$	20.0262	1.13015
$315$	1.32461	0.0746332
$316$	5.39395	0.303433
$317$	−22.6062	−1.26969	−0.634846	−	0.772639i	$-0.718936\pi$
$317$	−22.6062	−1.26969	−0.634846	+	0.772639i	$0.718936\pi$
$318$	2.82831	0.158604
$319$	−1.89272	−0.105972
$320$	1.00000	0.0559017
$321$	13.7891	0.769632
$322$	−24.2273	−1.35013
$323$	7.48393	0.416417
$324$	−7.54422	−0.419123
$325$	0.929339	0.0515505
$326$	−15.8054	−0.875378
$327$	5.96507	0.329869
$328$	−10.1783	−0.562002
$329$	−25.5041	−1.40609
$330$	1.10289	0.0607121
$331$	32.8876	1.80767	0.903833	−	0.427884i	$-0.140741\pi$
$331$	32.8876	1.80767	0.903833	+	0.427884i	$0.140741\pi$
$332$	14.3621	0.788225
$333$	1.09214	0.0598489
$334$	9.40287	0.514502
$335$	5.82525	0.318267
$336$	−5.00083	−0.272817
$337$	10.1958	0.555401	0.277700	−	0.960668i	$-0.410428\pi$
$337$	10.1958	0.555401	0.277700	+	0.960668i	$0.410428\pi$
$338$	12.1363	0.660129
$339$	−5.41602	−0.294158
$340$	−2.78141	−0.150843
$341$	−5.67110	−0.307107
$342$	−1.14366	−0.0618419
$343$	13.3629	0.721529
$344$	6.09157	0.328435
$345$	−12.4748	−0.671620
$346$	−18.9532	−1.01893
$347$	−19.1016	−1.02543	−0.512713	−	0.858560i	$-0.671359\pi$
$347$	−19.1016	−1.02543	−0.512713	+	0.858560i	$0.671359\pi$
$348$	4.41899	0.236883
$349$	−4.08509	−0.218670	−0.109335	−	0.994005i	$-0.534872\pi$
$349$	−4.08509	−0.218670	−0.109335	+	0.994005i	$0.534872\pi$
$350$	3.11642	0.166580
$351$	−5.10770	−0.272629
$352$	0.687301	0.0366333
$353$	−6.61409	−0.352033	−0.176016	−	0.984387i	$-0.556321\pi$
$353$	−6.61409	−0.352033	−0.176016	+	0.984387i	$0.556321\pi$
$354$	−21.8926	−1.16358
$355$	3.66284	0.194403
$356$	2.01565	0.106829
$357$	13.9093	0.736161
$358$	4.09628	0.216495
$359$	36.4850	1.92560	0.962802	−	0.270207i	$-0.0870921\pi$
$359$	36.4850	1.92560	0.962802	+	0.270207i	$0.0870921\pi$
$360$	0.425041	0.0224016
$361$	−11.7601	−0.618955
$362$	−8.46873	−0.445107
$363$	−16.8933	−0.886670
$364$	−2.89622	−0.151803
$365$	7.51309	0.393253
$366$	−16.3137	−0.852733
$367$	−36.3714	−1.89857	−0.949285	−	0.314416i	$-0.898191\pi$
$367$	−36.3714	−1.89857	−0.949285	+	0.314416i	$0.898191\pi$
$368$	−7.77406	−0.405251
$369$	−4.32619	−0.225212
$370$	2.56950	0.133582
$371$	5.49285	0.285175
$372$	13.2405	0.686489
$373$	−25.9846	−1.34543	−0.672716	−	0.739901i	$-0.734873\pi$
$373$	−25.9846	−1.34543	−0.672716	+	0.739901i	$0.734873\pi$
$374$	−1.91167	−0.0988499
$375$	1.60467	0.0828647
$376$	−8.18377	−0.422046
$377$	2.55925	0.131808
$378$	−17.1280	−0.880971
$379$	−4.86214	−0.249751	−0.124876	−	0.992172i	$-0.539853\pi$
$379$	−4.86214	−0.249751	−0.124876	+	0.992172i	$0.539853\pi$
$380$	−2.69070	−0.138030
$381$	14.9572	0.766282
$382$	3.44231	0.176124
$383$	−34.5934	−1.76764	−0.883819	−	0.467828i	$-0.845037\pi$
$383$	−34.5934	−1.76764	−0.883819	+	0.467828i	$0.845037\pi$
$384$	−1.60467	−0.0818879
$385$	2.14192	0.109163
$386$	−20.2128	−1.02880
$387$	2.58917	0.131615
$388$	−0.940044	−0.0477235
$389$	−11.8172	−0.599154	−0.299577	−	0.954072i	$-0.596846\pi$
$389$	−11.8172	−0.599154	−0.299577	+	0.954072i	$0.596846\pi$
$390$	−1.49128	−0.0755140
$391$	21.6228	1.09351
$392$	−2.71210	−0.136982
$393$	11.6133	0.585813
$394$	14.6494	0.738029
$395$	5.39395	0.271399
$396$	0.292131	0.0146802
$397$	−11.0646	−0.555318	−0.277659	−	0.960680i	$-0.589558\pi$
$397$	−11.0646	−0.555318	−0.277659	+	0.960680i	$0.589558\pi$
$398$	5.34395	0.267868
$399$	13.4557	0.673628
$400$	1.00000	0.0500000
$401$	−14.7306	−0.735609	−0.367805	−	0.929903i	$-0.619891\pi$
$401$	−14.7306	−0.735609	−0.367805	+	0.929903i	$0.619891\pi$
$402$	−9.34759	−0.466215
$403$	7.66821	0.381981
$404$	−9.37203	−0.466276
$405$	−7.54422	−0.374875
$406$	8.58212	0.425923
$407$	1.76602	0.0875382
$408$	4.46324	0.220963
$409$	−32.0559	−1.58506	−0.792531	−	0.609831i	$-0.791237\pi$
$409$	−32.0559	−1.58506	−0.792531	+	0.609831i	$0.791237\pi$
$410$	−10.1783	−0.502670
$411$	−16.8671	−0.831992
$412$	8.96135	0.441494
$413$	−42.5177	−2.09216
$414$	−3.30429	−0.162397
$415$	14.3621	0.705009
$416$	−0.929339	−0.0455646
$417$	2.61463	0.128039
$418$	−1.84932	−0.0904532
$419$	−13.5834	−0.663593	−0.331797	−	0.943351i	$-0.607655\pi$
$419$	−13.5834	−0.663593	−0.331797	+	0.943351i	$0.607655\pi$
$420$	−5.00083	−0.244015
$421$	25.3061	1.23335	0.616673	−	0.787220i	$-0.288480\pi$
$421$	25.3061	1.23335	0.616673	+	0.787220i	$0.288480\pi$
$422$	−12.3024	−0.598869
$423$	−3.47844	−0.169127
$424$	1.76255	0.0855969
$425$	−2.78141	−0.134918
$426$	−5.87764	−0.284772
$427$	−31.6829	−1.53324
$428$	8.59311	0.415364
$429$	−1.02496	−0.0494855
$430$	6.09157	0.293762
$431$	−11.6280	−0.560099	−0.280050	−	0.959985i	$-0.590351\pi$
$431$	−11.6280	−0.560099	−0.280050	+	0.959985i	$0.590351\pi$
$432$	−5.49605	−0.264429
$433$	34.0219	1.63499	0.817495	−	0.575935i	$-0.195362\pi$
$433$	34.0219	1.63499	0.817495	+	0.575935i	$0.195362\pi$
$434$	25.7144	1.23433
$435$	4.41899	0.211874
$436$	3.71733	0.178028
$437$	20.9176	1.00063
$438$	−12.0560	−0.576058
$439$	−9.89151	−0.472096	−0.236048	−	0.971741i	$-0.575852\pi$
$439$	−9.89151	−0.472096	−0.236048	+	0.971741i	$0.575852\pi$
$440$	0.687301	0.0327658
$441$	−1.15275	−0.0548931
$442$	2.58487	0.122950
$443$	−8.53644	−0.405578	−0.202789	−	0.979222i	$-0.565001\pi$
$443$	−8.53644	−0.405578	−0.202789	+	0.979222i	$0.565001\pi$
$444$	−4.12319	−0.195678
$445$	2.01565	0.0955508
$446$	−14.5047	−0.686819
$447$	−10.0520	−0.475445
$448$	−3.11642	−0.147237
$449$	38.0657	1.79643	0.898215	−	0.439555i	$-0.144864\pi$
$449$	38.0657	1.79643	0.898215	+	0.439555i	$0.144864\pi$
$450$	0.425041	0.0200366
$451$	−6.99555	−0.329407
$452$	−3.37517	−0.158754
$453$	0.0375443	0.00176398
$454$	−9.83217	−0.461447
$455$	−2.89622	−0.135777
$456$	4.31768	0.202194
$457$	−29.0974	−1.36112	−0.680560	−	0.732692i	$-0.738264\pi$
$457$	−29.0974	−1.36112	−0.680560	+	0.732692i	$0.738264\pi$
$458$	0.432323	0.0202011
$459$	15.2868	0.713526
$460$	−7.77406	−0.362467
$461$	6.16790	0.287268	0.143634	−	0.989631i	$-0.454121\pi$
$461$	6.16790	0.287268	0.143634	+	0.989631i	$0.454121\pi$
$462$	−3.43707	−0.159907
$463$	25.1005	1.16652	0.583260	−	0.812286i	$-0.301777\pi$
$463$	25.1005	1.16652	0.583260	+	0.812286i	$0.301777\pi$
$464$	2.75384	0.127844
$465$	13.2405	0.614014
$466$	−28.3649	−1.31398
$467$	22.4315	1.03801	0.519004	−	0.854772i	$-0.326303\pi$
$467$	22.4315	1.03801	0.519004	+	0.854772i	$0.326303\pi$
$468$	−0.395007	−0.0182592
$469$	−18.1539	−0.838271
$470$	−8.18377	−0.377489
$471$	−32.1355	−1.48072
$472$	−13.6431	−0.627975
$473$	4.18674	0.192507
$474$	−8.65549	−0.397560
$475$	−2.69070	−0.123458
$476$	8.66805	0.397300
$477$	0.749156	0.0343015
$478$	−8.24447	−0.377093
$479$	10.8241	0.494566	0.247283	−	0.968943i	$-0.420462\pi$
$479$	10.8241	0.494566	0.247283	+	0.968943i	$0.420462\pi$
$480$	−1.60467	−0.0732427
$481$	−2.38793	−0.108880
$482$	23.8891	1.08812
$483$	38.8767	1.76895
$484$	−10.5276	−0.478528
$485$	−0.940044	−0.0426852
$486$	−4.38220	−0.198781
$487$	1.76668	0.0800558	0.0400279	−	0.999199i	$-0.487255\pi$
$487$	1.76668	0.0800558	0.0400279	+	0.999199i	$0.487255\pi$
$488$	−10.1664	−0.460213
$489$	25.3623	1.14692
$490$	−2.71210	−0.122520
$491$	17.6313	0.795688	0.397844	−	0.917453i	$-0.369759\pi$
$491$	17.6313	0.795688	0.397844	+	0.917453i	$0.369759\pi$
$492$	16.3328	0.736338
$493$	−7.65954	−0.344969
$494$	2.50057	0.112506
$495$	0.292131	0.0131303
$496$	8.25125	0.370492
$497$	−11.4150	−0.512031
$498$	−23.0465	−1.03274
$499$	22.1347	0.990887	0.495443	−	0.868640i	$-0.335006\pi$
$499$	22.1347	0.990887	0.495443	+	0.868640i	$0.335006\pi$
$500$	1.00000	0.0447214
$501$	−15.0885	−0.674103
$502$	−2.64188	−0.117913
$503$	35.1572	1.56758	0.783791	−	0.621025i	$-0.213284\pi$
$503$	35.1572	1.56758	0.783791	+	0.621025i	$0.213284\pi$
$504$	−1.32461	−0.0590027
$505$	−9.37203	−0.417050
$506$	−5.34312	−0.237531
$507$	−19.4748	−0.864905
$508$	9.32108	0.413556
$509$	−36.5797	−1.62137	−0.810683	−	0.585486i	$-0.800904\pi$
$509$	−36.5797	−1.62137	−0.810683	+	0.585486i	$0.800904\pi$
$510$	4.46324	0.197636
$511$	−23.4140	−1.03577
$512$	−1.00000	−0.0441942
$513$	14.7882	0.652916
$514$	0.420643	0.0185538
$515$	8.96135	0.394884
$516$	−9.77495	−0.430318
$517$	−5.62472	−0.247375
$518$	−8.00764	−0.351835
$519$	30.4137	1.33501
$520$	−0.929339	−0.0407542
$521$	−20.2230	−0.885984	−0.442992	−	0.896526i	$-0.646083\pi$
$521$	−20.2230	−0.885984	−0.442992	+	0.896526i	$0.646083\pi$
$522$	1.17049	0.0512311
$523$	15.2692	0.667674	0.333837	−	0.942631i	$-0.391656\pi$
$523$	15.2692	0.667674	0.333837	+	0.942631i	$0.391656\pi$
$524$	7.23720	0.316158
$525$	−5.00083	−0.218254
$526$	4.11820	0.179562
$527$	−22.9501	−0.999723
$528$	−1.10289	−0.0479971
$529$	37.4360	1.62765
$530$	1.76255	0.0765602
$531$	−5.79888	−0.251650
$532$	8.38535	0.363551
$533$	9.45908	0.409718
$534$	−3.23444	−0.139968
$535$	8.59311	0.371513
$536$	−5.82525	−0.251612
$537$	−6.57317	−0.283653
$538$	−30.2056	−1.30226
$539$	−1.86403	−0.0802895
$540$	−5.49605	−0.236512
$541$	28.4806	1.22448	0.612238	−	0.790673i	$-0.290269\pi$
$541$	28.4806	1.22448	0.612238	+	0.790673i	$0.290269\pi$
$542$	−12.3327	−0.529734
$543$	13.5895	0.583181
$544$	2.78141	0.119252
$545$	3.71733	0.159233
$546$	4.64747	0.198893
$547$	−14.7971	−0.632679	−0.316339	−	0.948646i	$-0.602454\pi$
$547$	−14.7971	−0.632679	−0.316339	+	0.948646i	$0.602454\pi$
$548$	−10.5113	−0.449019
$549$	−4.32115	−0.184422
$550$	0.687301	0.0293066
$551$	−7.40974	−0.315665
$552$	12.4748	0.530962
$553$	−16.8098	−0.714827
$554$	−17.2256	−0.731846
$555$	−4.12319	−0.175020
$556$	1.62939	0.0691014
$557$	6.88225	0.291610	0.145805	−	0.989313i	$-0.453423\pi$
$557$	6.88225	0.291610	0.145805	+	0.989313i	$0.453423\pi$
$558$	3.50712	0.148468
$559$	−5.66114	−0.239441
$560$	−3.11642	−0.131693
$561$	3.06759	0.129514
$562$	17.9215	0.755973
$563$	−6.40626	−0.269992	−0.134996	−	0.990846i	$-0.543102\pi$
$563$	−6.40626	−0.269992	−0.134996	+	0.990846i	$0.543102\pi$
$564$	13.1322	0.552967
$565$	−3.37517	−0.141994
$566$	31.8066	1.33693
$567$	23.5110	0.987368
$568$	−3.66284	−0.153689
$569$	43.6770	1.83104	0.915518	−	0.402277i	$-0.131781\pi$
$569$	43.6770	1.83104	0.915518	+	0.402277i	$0.131781\pi$
$570$	4.31768	0.180848
$571$	43.5949	1.82439	0.912196	−	0.409755i	$-0.134386\pi$
$571$	43.5949	1.82439	0.912196	+	0.409755i	$0.134386\pi$
$572$	−0.638736	−0.0267069
$573$	−5.52376	−0.230758
$574$	31.7198	1.32396
$575$	−7.77406	−0.324201
$576$	−0.425041	−0.0177100
$577$	26.8066	1.11597	0.557987	−	0.829850i	$-0.311574\pi$
$577$	26.8066	1.11597	0.557987	+	0.829850i	$0.311574\pi$
$578$	9.26376	0.385322
$579$	32.4348	1.34794
$580$	2.75384	0.114347
$581$	−44.7585	−1.85690
$582$	1.50846	0.0625276
$583$	1.21140	0.0501712
$584$	−7.51309	−0.310894
$585$	−0.395007	−0.0163315
$586$	−0.184708	−0.00763021
$587$	−3.75873	−0.155139	−0.0775697	−	0.996987i	$-0.524716\pi$
$587$	−3.75873	−0.155139	−0.0775697	+	0.996987i	$0.524716\pi$
$588$	4.35202	0.179474
$589$	−22.2016	−0.914802
$590$	−13.6431	−0.561678
$591$	−23.5075	−0.966969
$592$	−2.56950	−0.105606
$593$	39.9221	1.63941	0.819703	−	0.572789i	$-0.194139\pi$
$593$	39.9221	1.63941	0.819703	+	0.572789i	$0.194139\pi$
$594$	−3.77745	−0.154990
$595$	8.66805	0.355356
$596$	−6.26425	−0.256594
$597$	−8.57527	−0.350962
$598$	7.22474	0.295442
$599$	−17.4137	−0.711506	−0.355753	−	0.934580i	$-0.615776\pi$
$599$	−17.4137	−0.711506	−0.355753	+	0.934580i	$0.615776\pi$
$600$	−1.60467	−0.0655103
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−18.9839	−0.773727
$603$	−2.47597	−0.100829
$604$	0.0233969	0.000952007 0
$605$	−10.5276	−0.428008
$606$	15.0390	0.610918
$607$	17.6817	0.717676	0.358838	−	0.933400i	$-0.383173\pi$
$607$	17.6817	0.717676	0.358838	+	0.933400i	$0.383173\pi$
$608$	2.69070	0.109122
$609$	−13.7715	−0.558047
$610$	−10.1664	−0.411627
$611$	7.60550	0.307686
$612$	1.18221	0.0477881
$613$	20.3473	0.821819	0.410910	−	0.911676i	$-0.365211\pi$
$613$	20.3473	0.821819	0.410910	+	0.911676i	$0.365211\pi$
$614$	21.7285	0.876890
$615$	16.3328	0.658601
$616$	−2.14192	−0.0863005
$617$	15.5233	0.624943	0.312471	−	0.949927i	$-0.398843\pi$
$617$	15.5233	0.624943	0.312471	+	0.949927i	$0.398843\pi$
$618$	−14.3800	−0.578448
$619$	15.8071	0.635340	0.317670	−	0.948201i	$-0.397100\pi$
$619$	15.8071	0.635340	0.317670	+	0.948201i	$0.397100\pi$
$620$	8.25125	0.331378
$621$	42.7266	1.71456
$622$	−5.38313	−0.215844
$623$	−6.28161	−0.251667
$624$	1.49128	0.0596990
$625$	1.00000	0.0400000
$626$	34.8758	1.39392
$627$	2.96754	0.118512
$628$	−20.0262	−0.799134
$629$	7.14682	0.284962
$630$	−1.32461	−0.0527737
$631$	−8.29079	−0.330051	−0.165026	−	0.986289i	$-0.552771\pi$
$631$	−8.29079	−0.330051	−0.165026	+	0.986289i	$0.552771\pi$
$632$	−5.39395	−0.214560
$633$	19.7412	0.784642
$634$	22.6062	0.897808
$635$	9.32108	0.369896
$636$	−2.82831	−0.112150
$637$	2.52046	0.0998644
$638$	1.89272	0.0749333
$639$	−1.55686	−0.0615883
$640$	−1.00000	−0.0395285
$641$	10.9551	0.432702	0.216351	−	0.976316i	$-0.430584\pi$
$641$	10.9551	0.432702	0.216351	+	0.976316i	$0.430584\pi$
$642$	−13.7891	−0.544212
$643$	10.4590	0.412463	0.206232	−	0.978503i	$-0.433880\pi$
$643$	10.4590	0.412463	0.206232	+	0.978503i	$0.433880\pi$
$644$	24.2273	0.954688
$645$	−9.77495	−0.384888
$646$	−7.48393	−0.294451
$647$	−12.3046	−0.483743	−0.241872	−	0.970308i	$-0.577761\pi$
$647$	−12.3046	−0.483743	−0.241872	+	0.970308i	$0.577761\pi$
$648$	7.54422	0.296365
$649$	−9.37692	−0.368076
$650$	−0.929339	−0.0364517
$651$	−41.2631	−1.61723
$652$	15.8054	0.618985
$653$	41.2597	1.61462	0.807309	−	0.590129i	$-0.200923\pi$
$653$	41.2597	1.61462	0.807309	+	0.590129i	$0.200923\pi$
$654$	−5.96507	−0.233253
$655$	7.23720	0.282781
$656$	10.1783	0.397395
$657$	−3.19337	−0.124585
$658$	25.5041	0.994253
$659$	24.0085	0.935237	0.467619	−	0.883930i	$-0.345112\pi$
$659$	24.0085	0.935237	0.467619	+	0.883930i	$0.345112\pi$
$660$	−1.10289	−0.0429300
$661$	−35.2124	−1.36960	−0.684802	−	0.728729i	$-0.740111\pi$
$661$	−35.2124	−1.36960	−0.684802	+	0.728729i	$0.740111\pi$
$662$	−32.8876	−1.27821
$663$	−4.14786	−0.161090
$664$	−14.3621	−0.557359
$665$	8.38535	0.325170
$666$	−1.09214	−0.0423196
$667$	−21.4085	−0.828940
$668$	−9.40287	−0.363808
$669$	23.2753	0.899875
$670$	−5.82525	−0.225049
$671$	−6.98740	−0.269746
$672$	5.00083	0.192911
$673$	−12.4679	−0.480601	−0.240301	−	0.970699i	$-0.577246\pi$
$673$	−12.4679	−0.480601	−0.240301	+	0.970699i	$0.577246\pi$
$674$	−10.1958	−0.392728
$675$	−5.49605	−0.211543
$676$	−12.1363	−0.466782
$677$	23.5415	0.904772	0.452386	−	0.891822i	$-0.350573\pi$
$677$	23.5415	0.904772	0.452386	+	0.891822i	$0.350573\pi$
$678$	5.41602	0.208001
$679$	2.92958	0.112427
$680$	2.78141	0.106662
$681$	15.7774	0.604590
$682$	5.67110	0.217158
$683$	16.4451	0.629256	0.314628	−	0.949215i	$-0.398120\pi$
$683$	16.4451	0.629256	0.314628	+	0.949215i	$0.398120\pi$
$684$	1.14366	0.0437288
$685$	−10.5113	−0.401615
$686$	−13.3629	−0.510198
$687$	−0.693736	−0.0264677
$688$	−6.09157	−0.232239
$689$	−1.63801	−0.0624031
$690$	12.4748	0.474907
$691$	21.7475	0.827314	0.413657	−	0.910433i	$-0.364251\pi$
$691$	21.7475	0.827314	0.413657	+	0.910433i	$0.364251\pi$
$692$	18.9532	0.720494
$693$	−0.910405	−0.0345834
$694$	19.1016	0.725085
$695$	1.62939	0.0618062
$696$	−4.41899	−0.167501
$697$	−28.3100	−1.07232
$698$	4.08509	0.154623
$699$	45.5163	1.72158
$700$	−3.11642	−0.117790
$701$	37.5534	1.41837	0.709187	−	0.705021i	$-0.249062\pi$
$701$	37.5534	1.41837	0.709187	+	0.705021i	$0.249062\pi$
$702$	5.10770	0.192778
$703$	6.91373	0.260756
$704$	−0.687301	−0.0259036
$705$	13.1322	0.494589
$706$	6.61409	0.248925
$707$	29.2072	1.09845
$708$	21.8926	0.822776
$709$	28.5152	1.07091	0.535456	−	0.844563i	$-0.320140\pi$
$709$	28.5152	1.07091	0.535456	+	0.844563i	$0.320140\pi$
$710$	−3.66284	−0.137464
$711$	−2.29265	−0.0859811
$712$	−2.01565	−0.0755395
$713$	−64.1457	−2.40228
$714$	−13.9093	−0.520544
$715$	−0.638736	−0.0238874
$716$	−4.09628	−0.153085
$717$	13.2296	0.494070
$718$	−36.4850	−1.36161
$719$	20.4274	0.761814	0.380907	−	0.924613i	$-0.375612\pi$
$719$	20.4274	0.761814	0.380907	+	0.924613i	$0.375612\pi$
$720$	−0.425041	−0.0158403
$721$	−27.9274	−1.04007
$722$	11.7601	0.437667
$723$	−38.3340	−1.42566
$724$	8.46873	0.314738
$725$	2.75384	0.102275
$726$	16.8933	0.626970
$727$	−10.0606	−0.373128	−0.186564	−	0.982443i	$-0.559735\pi$
$727$	−10.0606	−0.373128	−0.186564	+	0.982443i	$0.559735\pi$
$728$	2.89622	0.107341
$729$	29.6646	1.09869
$730$	−7.51309	−0.278072
$731$	16.9432	0.626665
$732$	16.3137	0.602973
$733$	−28.2666	−1.04405	−0.522025	−	0.852930i	$-0.674823\pi$
$733$	−28.2666	−1.04405	−0.522025	+	0.852930i	$0.674823\pi$
$734$	36.3714	1.34249
$735$	4.35202	0.160527
$736$	7.77406	0.286556
$737$	−4.00370	−0.147478
$738$	4.32619	0.159249
$739$	−42.0674	−1.54747	−0.773737	−	0.633507i	$-0.781615\pi$
$739$	−42.0674	−1.54747	−0.773737	+	0.633507i	$0.781615\pi$
$740$	−2.56950	−0.0944565
$741$	−4.01259	−0.147406
$742$	−5.49285	−0.201649
$743$	41.5891	1.52576	0.762878	−	0.646543i	$-0.223786\pi$
$743$	41.5891	1.52576	0.762878	+	0.646543i	$0.223786\pi$
$744$	−13.2405	−0.485421
$745$	−6.26425	−0.229504
$746$	25.9846	0.951364
$747$	−6.10450	−0.223352
$748$	1.91167	0.0698975
$749$	−26.7798	−0.978512
$750$	−1.60467	−0.0585942
$751$	22.3675	0.816202	0.408101	−	0.912937i	$-0.366191\pi$
$751$	22.3675	0.816202	0.408101	+	0.912937i	$0.366191\pi$
$752$	8.18377	0.298431
$753$	4.23934	0.154490
$754$	−2.55925	−0.0932023
$755$	0.0233969	0.000851501 0
$756$	17.1280	0.622941
$757$	−15.9125	−0.578348	−0.289174	−	0.957277i	$-0.593381\pi$
$757$	−15.9125	−0.578348	−0.289174	+	0.957277i	$0.593381\pi$
$758$	4.86214	0.176601
$759$	8.57394	0.311214
$760$	2.69070	0.0976018
$761$	−11.0925	−0.402105	−0.201052	−	0.979581i	$-0.564436\pi$
$761$	−11.0925	−0.402105	−0.201052	+	0.979581i	$0.564436\pi$
$762$	−14.9572	−0.541844
$763$	−11.5848	−0.419397
$764$	−3.44231	−0.124538
$765$	1.18221	0.0427430
$766$	34.5934	1.24991
$767$	12.6791	0.457815
$768$	1.60467	0.0579035
$769$	25.9818	0.936929	0.468464	−	0.883482i	$-0.344807\pi$
$769$	25.9818	0.936929	0.468464	+	0.883482i	$0.344807\pi$
$770$	−2.14192	−0.0771895
$771$	−0.674992	−0.0243092
$772$	20.2128	0.727474
$773$	−50.4160	−1.81334	−0.906669	−	0.421843i	$-0.861383\pi$
$773$	−50.4160	−1.81334	−0.906669	+	0.421843i	$0.861383\pi$
$774$	−2.58917	−0.0930657
$775$	8.25125	0.296394
$776$	0.940044	0.0337456
$777$	12.8496	0.460977
$778$	11.8172	0.423666
$779$	−27.3867	−0.981229
$780$	1.49128	0.0533964
$781$	−2.51747	−0.0900823
$782$	−21.6228	−0.773231
$783$	−15.1352	−0.540889
$784$	2.71210	0.0968608
$785$	−20.0262	−0.714767
$786$	−11.6133	−0.414233
$787$	−25.0249	−0.892041	−0.446020	−	0.895023i	$-0.647159\pi$
$787$	−25.0249	−0.892041	−0.446020	+	0.895023i	$0.647159\pi$
$788$	−14.6494	−0.521865
$789$	−6.60834	−0.235263
$790$	−5.39395	−0.191908
$791$	10.5184	0.373993
$792$	−0.292131	−0.0103804
$793$	9.44806	0.335511
$794$	11.0646	0.392669
$795$	−2.82831	−0.100310
$796$	−5.34395	−0.189411
$797$	−38.1229	−1.35038	−0.675191	−	0.737643i	$-0.735939\pi$
$797$	−38.1229	−1.35038	−0.675191	+	0.737643i	$0.735939\pi$
$798$	−13.4557	−0.476327
$799$	−22.7624	−0.805276
$800$	−1.00000	−0.0353553
$801$	−0.856732	−0.0302711
$802$	14.7306	0.520154
$803$	−5.16375	−0.182225
$804$	9.34759	0.329664
$805$	24.2273	0.853899
$806$	−7.66821	−0.270101
$807$	48.4700	1.70622
$808$	9.37203	0.329707
$809$	15.7869	0.555039	0.277520	−	0.960720i	$-0.410488\pi$
$809$	15.7869	0.555039	0.277520	+	0.960720i	$0.410488\pi$
$810$	7.54422	0.265077
$811$	−38.9831	−1.36888	−0.684442	−	0.729068i	$-0.739954\pi$
$811$	−38.9831	−1.36888	−0.684442	+	0.729068i	$0.739954\pi$
$812$	−8.58212	−0.301173
$813$	19.7899	0.694061
$814$	−1.76602	−0.0618989
$815$	15.8054	0.553637
$816$	−4.46324	−0.156245
$817$	16.3906	0.573433
$818$	32.0559	1.12081
$819$	1.23101	0.0430150
$820$	10.1783	0.355441
$821$	22.2432	0.776294	0.388147	−	0.921598i	$-0.373115\pi$
$821$	22.2432	0.776294	0.388147	+	0.921598i	$0.373115\pi$
$822$	16.8671	0.588307
$823$	44.2080	1.54100	0.770498	−	0.637443i	$-0.220008\pi$
$823$	44.2080	1.54100	0.770498	+	0.637443i	$0.220008\pi$
$824$	−8.96135	−0.312183
$825$	−1.10289	−0.0383977
$826$	42.5177	1.47938
$827$	5.06233	0.176034	0.0880172	−	0.996119i	$-0.471947\pi$
$827$	5.06233	0.176034	0.0880172	+	0.996119i	$0.471947\pi$
$828$	3.30429	0.114832
$829$	−24.4554	−0.849373	−0.424686	−	0.905341i	$-0.639616\pi$
$829$	−24.4554	−0.849373	−0.424686	+	0.905341i	$0.639616\pi$
$830$	−14.3621	−0.498517
$831$	27.6414	0.958869
$832$	0.929339	0.0322190
$833$	−7.54347	−0.261366
$834$	−2.61463	−0.0905371
$835$	−9.40287	−0.325400
$836$	1.84932	0.0639601
$837$	−45.3493	−1.56750
$838$	13.5834	0.469231
$839$	−46.9607	−1.62126	−0.810631	−	0.585557i	$-0.800876\pi$
$839$	−46.9607	−1.62126	−0.810631	+	0.585557i	$0.800876\pi$
$840$	5.00083	0.172545
$841$	−21.4164	−0.738496
$842$	−25.3061	−0.872107
$843$	−28.7581	−0.990480
$844$	12.3024	0.423464
$845$	−12.1363	−0.417502
$846$	3.47844	0.119591
$847$	32.8085	1.12731
$848$	−1.76255	−0.0605262
$849$	−51.0390	−1.75165
$850$	2.78141	0.0954016
$851$	19.9754	0.684748
$852$	5.87764	0.201365
$853$	−29.5993	−1.01346	−0.506730	−	0.862105i	$-0.669146\pi$
$853$	−29.5993	−1.01346	−0.506730	+	0.862105i	$0.669146\pi$
$854$	31.6829	1.08417
$855$	1.14366	0.0391122
$856$	−8.59311	−0.293706
$857$	17.1682	0.586453	0.293227	−	0.956043i	$-0.405271\pi$
$857$	17.1682	0.586453	0.293227	+	0.956043i	$0.405271\pi$
$858$	1.02496	0.0349915
$859$	−7.96399	−0.271728	−0.135864	−	0.990728i	$-0.543381\pi$
$859$	−7.96399	−0.271728	−0.135864	+	0.990728i	$0.543381\pi$
$860$	−6.09157	−0.207721
$861$	−50.8998	−1.73466
$862$	11.6280	0.396050
$863$	25.7201	0.875521	0.437760	−	0.899092i	$-0.355772\pi$
$863$	25.7201	0.875521	0.437760	+	0.899092i	$0.355772\pi$
$864$	5.49605	0.186980
$865$	18.9532	0.644430
$866$	−34.0219	−1.15611
$867$	−14.8653	−0.504851
$868$	−25.7144	−0.872804
$869$	−3.70727	−0.125760
$870$	−4.41899	−0.149818
$871$	5.41363	0.183434
$872$	−3.71733	−0.125885
$873$	0.399557	0.0135230
$874$	−20.9176	−0.707550
$875$	−3.11642	−0.105354
$876$	12.0560	0.407335
$877$	−28.3501	−0.957314	−0.478657	−	0.878002i	$-0.658876\pi$
$877$	−28.3501	−0.957314	−0.478657	+	0.878002i	$0.658876\pi$
$878$	9.89151	0.333822
$879$	0.296395	0.00999714
$880$	−0.687301	−0.0231689
$881$	12.2507	0.412738	0.206369	−	0.978474i	$-0.433835\pi$
$881$	12.2507	0.412738	0.206369	+	0.978474i	$0.433835\pi$
$882$	1.15275	0.0388153
$883$	30.3544	1.02151	0.510754	−	0.859727i	$-0.329366\pi$
$883$	30.3544	1.02151	0.510754	+	0.859727i	$0.329366\pi$
$884$	−2.58487	−0.0869387
$885$	21.8926	0.735913
$886$	8.53644	0.286787
$887$	30.9037	1.03765	0.518823	−	0.854882i	$-0.326370\pi$
$887$	30.9037	1.03765	0.518823	+	0.854882i	$0.326370\pi$
$888$	4.12319	0.138365
$889$	−29.0484	−0.974253
$890$	−2.01565	−0.0675646
$891$	5.18515	0.173709
$892$	14.5047	0.485655
$893$	−22.0200	−0.736873
$894$	10.0520	0.336191
$895$	−4.09628	−0.136924
$896$	3.11642	0.104112
$897$	−11.5933	−0.387089
$898$	−38.0657	−1.27027
$899$	22.7226	0.757841
$900$	−0.425041	−0.0141680
$901$	4.90237	0.163322
$902$	6.99555	0.232926
$903$	30.4629	1.01374
$904$	3.37517	0.112256
$905$	8.46873	0.281510
$906$	−0.0375443	−0.00124733
$907$	17.4869	0.580643	0.290322	−	0.956929i	$-0.406238\pi$
$907$	17.4869	0.580643	0.290322	+	0.956929i	$0.406238\pi$
$908$	9.83217	0.326292
$909$	3.98350	0.132124
$910$	2.89622	0.0960086
$911$	16.3782	0.542632	0.271316	−	0.962490i	$-0.412541\pi$
$911$	16.3782	0.542632	0.271316	+	0.962490i	$0.412541\pi$
$912$	−4.31768	−0.142973
$913$	−9.87112	−0.326686
$914$	29.0974	0.962458
$915$	16.3137	0.539316
$916$	−0.432323	−0.0142844
$917$	−22.5542	−0.744805
$918$	−15.2868	−0.504539
$919$	−32.2299	−1.06317	−0.531583	−	0.847006i	$-0.678402\pi$
$919$	−32.2299	−1.06317	−0.531583	+	0.847006i	$0.678402\pi$
$920$	7.77406	0.256303
$921$	−34.8670	−1.14891
$922$	−6.16790	−0.203129
$923$	3.40402	0.112045
$924$	3.43707	0.113071
$925$	−2.56950	−0.0844845
$926$	−25.1005	−0.824854
$927$	−3.80894	−0.125102
$928$	−2.75384	−0.0903991
$929$	39.7688	1.30477	0.652386	−	0.757887i	$-0.273768\pi$
$929$	39.7688	1.30477	0.652386	+	0.757887i	$0.273768\pi$
$930$	−13.2405	−0.434174
$931$	−7.29744	−0.239164
$932$	28.3649	0.929124
$933$	8.63814	0.282800
$934$	−22.4315	−0.733982
$935$	1.91167	0.0625182
$936$	0.395007	0.0129112
$937$	49.8188	1.62751	0.813754	−	0.581209i	$-0.197420\pi$
$937$	49.8188	1.62751	0.813754	+	0.581209i	$0.197420\pi$
$938$	18.1539	0.592747
$939$	−55.9641	−1.82632
$940$	8.18377	0.266925
$941$	−34.7070	−1.13142	−0.565708	−	0.824606i	$-0.691397\pi$
$941$	−34.7070	−1.13142	−0.565708	+	0.824606i	$0.691397\pi$
$942$	32.1355	1.04703
$943$	−79.1266	−2.57672
$944$	13.6431	0.444045
$945$	17.1280	0.557175
$946$	−4.18674	−0.136123
$947$	−41.4740	−1.34772	−0.673862	−	0.738857i	$-0.735366\pi$
$947$	−41.4740	−1.34772	−0.673862	+	0.738857i	$0.735366\pi$
$948$	8.65549	0.281117
$949$	6.98221	0.226652
$950$	2.69070	0.0872977
$951$	−36.2755	−1.17631
$952$	−8.66805	−0.280933
$953$	−1.77497	−0.0574969	−0.0287485	−	0.999587i	$-0.509152\pi$
$953$	−1.77497	−0.0574969	−0.0287485	+	0.999587i	$0.509152\pi$
$954$	−0.749156	−0.0242548
$955$	−3.44231	−0.111390
$956$	8.24447	0.266645
$957$	−3.03718	−0.0981781
$958$	−10.8241	−0.349711
$959$	32.7575	1.05780
$960$	1.60467	0.0517904
$961$	37.0832	1.19623
$962$	2.38793	0.0769901
$963$	−3.65242	−0.117698
$964$	−23.8891	−0.769416
$965$	20.2128	0.650672
$966$	−38.8767	−1.25084
$967$	−34.7974	−1.11901	−0.559505	−	0.828827i	$-0.689009\pi$
$967$	−34.7974	−1.11901	−0.559505	+	0.828827i	$0.689009\pi$
$968$	10.5276	0.338370
$969$	12.0092	0.385792
$970$	0.940044	0.0301830
$971$	−45.9590	−1.47489	−0.737447	−	0.675405i	$-0.763969\pi$
$971$	−45.9590	−1.47489	−0.737447	+	0.675405i	$0.763969\pi$
$972$	4.38220	0.140559
$973$	−5.07786	−0.162789
$974$	−1.76668	−0.0566080
$975$	1.49128	0.0477592
$976$	10.1664	0.325419
$977$	15.6542	0.500823	0.250412	−	0.968139i	$-0.419434\pi$
$977$	15.6542	0.500823	0.250412	+	0.968139i	$0.419434\pi$
$978$	−25.3623	−0.810998
$979$	−1.38536	−0.0442762
$980$	2.71210	0.0866349
$981$	−1.58002	−0.0504460
$982$	−17.6313	−0.562636
$983$	41.1776	1.31336	0.656681	−	0.754168i	$-0.271960\pi$
$983$	41.1776	1.31336	0.656681	+	0.754168i	$0.271960\pi$
$984$	−16.3328	−0.520669
$985$	−14.6494	−0.466770
$986$	7.65954	0.243930
$987$	−40.9256	−1.30268
$988$	−2.50057	−0.0795538
$989$	47.3562	1.50584
$990$	−0.292131	−0.00928454
$991$	−14.5380	−0.461813	−0.230907	−	0.972976i	$-0.574169\pi$
$991$	−14.5380	−0.461813	−0.230907	+	0.972976i	$0.574169\pi$
$992$	−8.25125	−0.261978
$993$	52.7737	1.67472
$994$	11.4150	0.362060
$995$	−5.34395	−0.169415
$996$	23.0465	0.730255
$997$	22.2575	0.704901	0.352450	−	0.935830i	$-0.385349\pi$
$997$	22.2575	0.704901	0.352450	+	0.935830i	$0.385349\pi$
$998$	−22.1347	−0.700663
$999$	14.1221	0.446803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.g.1.19	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.g.1.19	✓	27	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.60467 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.60467 q^{6} -3.11642 q^{7} -1.00000 q^{8} -0.425041 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.60467 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.60467 q^{6} -3.11642 q^{7} -1.00000 q^{8} -0.425041 q^{9} -1.00000 q^{10} -0.687301 q^{11} +1.60467 q^{12} +0.929339 q^{13} +3.11642 q^{14} +1.60467 q^{15} +1.00000 q^{16} -2.78141 q^{17} +0.425041 q^{18} -2.69070 q^{19} +1.00000 q^{20} -5.00083 q^{21} +0.687301 q^{22} -7.77406 q^{23} -1.60467 q^{24} +1.00000 q^{25} -0.929339 q^{26} -5.49605 q^{27} -3.11642 q^{28} +2.75384 q^{29} -1.60467 q^{30} +8.25125 q^{31} -1.00000 q^{32} -1.10289 q^{33} +2.78141 q^{34} -3.11642 q^{35} -0.425041 q^{36} -2.56950 q^{37} +2.69070 q^{38} +1.49128 q^{39} -1.00000 q^{40} +10.1783 q^{41} +5.00083 q^{42} -6.09157 q^{43} -0.687301 q^{44} -0.425041 q^{45} +7.77406 q^{46} +8.18377 q^{47} +1.60467 q^{48} +2.71210 q^{49} -1.00000 q^{50} -4.46324 q^{51} +0.929339 q^{52} -1.76255 q^{53} +5.49605 q^{54} -0.687301 q^{55} +3.11642 q^{56} -4.31768 q^{57} -2.75384 q^{58} +13.6431 q^{59} +1.60467 q^{60} +10.1664 q^{61} -8.25125 q^{62} +1.32461 q^{63} +1.00000 q^{64} +0.929339 q^{65} +1.10289 q^{66} +5.82525 q^{67} -2.78141 q^{68} -12.4748 q^{69} +3.11642 q^{70} +3.66284 q^{71} +0.425041 q^{72} +7.51309 q^{73} +2.56950 q^{74} +1.60467 q^{75} -2.69070 q^{76} +2.14192 q^{77} -1.49128 q^{78} +5.39395 q^{79} +1.00000 q^{80} -7.54422 q^{81} -10.1783 q^{82} +14.3621 q^{83} -5.00083 q^{84} -2.78141 q^{85} +6.09157 q^{86} +4.41899 q^{87} +0.687301 q^{88} +2.01565 q^{89} +0.425041 q^{90} -2.89622 q^{91} -7.77406 q^{92} +13.2405 q^{93} -8.18377 q^{94} -2.69070 q^{95} -1.60467 q^{96} -0.940044 q^{97} -2.71210 q^{98} +0.292131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * q^99

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