LMFDB - Embedded newform 1014.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(1,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, 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("1014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	1014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.356896 q^{5} -1.00000 q^{6} -4.04892 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.356896 q^{5} -1.00000 q^{6} -4.04892 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.356896 q^{10} +0.911854 q^{11} +1.00000 q^{12} +4.04892 q^{14} -0.356896 q^{15} +1.00000 q^{16} -2.09783 q^{17} -1.00000 q^{18} +4.98792 q^{19} -0.356896 q^{20} -4.04892 q^{21} -0.911854 q^{22} +8.49396 q^{23} -1.00000 q^{24} -4.87263 q^{25} +1.00000 q^{27} -4.04892 q^{28} +8.51573 q^{29} +0.356896 q^{30} +10.7899 q^{31} -1.00000 q^{32} +0.911854 q^{33} +2.09783 q^{34} +1.44504 q^{35} +1.00000 q^{36} +0.615957 q^{37} -4.98792 q^{38} +0.356896 q^{40} +7.60388 q^{41} +4.04892 q^{42} -6.27413 q^{43} +0.911854 q^{44} -0.356896 q^{45} -8.49396 q^{46} -1.78017 q^{47} +1.00000 q^{48} +9.39373 q^{49} +4.87263 q^{50} -2.09783 q^{51} +10.4112 q^{53} -1.00000 q^{54} -0.325437 q^{55} +4.04892 q^{56} +4.98792 q^{57} -8.51573 q^{58} +6.04892 q^{59} -0.356896 q^{60} -3.10992 q^{61} -10.7899 q^{62} -4.04892 q^{63} +1.00000 q^{64} -0.911854 q^{66} -13.5797 q^{67} -2.09783 q^{68} +8.49396 q^{69} -1.44504 q^{70} -11.4819 q^{71} -1.00000 q^{72} -0.533188 q^{73} -0.615957 q^{74} -4.87263 q^{75} +4.98792 q^{76} -3.69202 q^{77} -11.7071 q^{79} -0.356896 q^{80} +1.00000 q^{81} -7.60388 q^{82} +6.49934 q^{83} -4.04892 q^{84} +0.748709 q^{85} +6.27413 q^{86} +8.51573 q^{87} -0.911854 q^{88} +6.49396 q^{89} +0.356896 q^{90} +8.49396 q^{92} +10.7899 q^{93} +1.78017 q^{94} -1.78017 q^{95} -1.00000 q^{96} +1.96077 q^{97} -9.39373 q^{98} +0.911854 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - q^{11} + 3 q^{12} + 3 q^{14} + 3 q^{15} + 3 q^{16} + 12 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} - 3 q^{21} + q^{22} + 16 q^{23} - 3 q^{24} + 2 q^{25} + 3 q^{27} - 3 q^{28} + 13 q^{29} - 3 q^{30} + 9 q^{31} - 3 q^{32} - q^{33} - 12 q^{34} + 4 q^{35} + 3 q^{36} + 12 q^{37} + 4 q^{38} - 3 q^{40} + 14 q^{41} + 3 q^{42} - 8 q^{43} - q^{44} + 3 q^{45} - 16 q^{46} - 4 q^{47} + 3 q^{48} - 4 q^{49} - 2 q^{50} + 12 q^{51} + 15 q^{53} - 3 q^{54} - 22 q^{55} + 3 q^{56} - 4 q^{57} - 13 q^{58} + 9 q^{59} + 3 q^{60} - 10 q^{61} - 9 q^{62} - 3 q^{63} + 3 q^{64} + q^{66} + 6 q^{67} + 12 q^{68} + 16 q^{69} - 4 q^{70} - 6 q^{71} - 3 q^{72} - 5 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 6 q^{77} - 5 q^{79} + 3 q^{80} + 3 q^{81} - 14 q^{82} + 7 q^{83} - 3 q^{84} + 26 q^{85} + 8 q^{86} + 13 q^{87} + q^{88} + 10 q^{89} - 3 q^{90} + 16 q^{92} + 9 q^{93} + 4 q^{94} - 4 q^{95} - 3 q^{96} - 7 q^{97} + 4 q^{98} - q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - q^11 + 3 * q^12 + 3 * q^14 + 3 * q^15 + 3 * q^16 + 12 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 - 3 * q^21 + q^22 + 16 * q^23 - 3 * q^24 + 2 * q^25 + 3 * q^27 - 3 * q^28 + 13 * q^29 - 3 * q^30 + 9 * q^31 - 3 * q^32 - q^33 - 12 * q^34 + 4 * q^35 + 3 * q^36 + 12 * q^37 + 4 * q^38 - 3 * q^40 + 14 * q^41 + 3 * q^42 - 8 * q^43 - q^44 + 3 * q^45 - 16 * q^46 - 4 * q^47 + 3 * q^48 - 4 * q^49 - 2 * q^50 + 12 * q^51 + 15 * q^53 - 3 * q^54 - 22 * q^55 + 3 * q^56 - 4 * q^57 - 13 * q^58 + 9 * q^59 + 3 * q^60 - 10 * q^61 - 9 * q^62 - 3 * q^63 + 3 * q^64 + q^66 + 6 * q^67 + 12 * q^68 + 16 * q^69 - 4 * q^70 - 6 * q^71 - 3 * q^72 - 5 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 6 * q^77 - 5 * q^79 + 3 * q^80 + 3 * q^81 - 14 * q^82 + 7 * q^83 - 3 * q^84 + 26 * q^85 + 8 * q^86 + 13 * q^87 + q^88 + 10 * q^89 - 3 * q^90 + 16 * q^92 + 9 * q^93 + 4 * q^94 - 4 * q^95 - 3 * q^96 - 7 * q^97 + 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.356896	−0.159609	−0.0798043	−	0.996811i	$-0.525430\pi$
$5$	−0.356896	−0.159609	−0.0798043	+	0.996811i	$0.525430\pi$
$6$	−1.00000	−0.408248
$7$	−4.04892	−1.53035	−0.765173	−	0.643824i	$-0.777347\pi$
$7$	−4.04892	−1.53035	−0.765173	+	0.643824i	$0.777347\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.356896	0.112860
$11$	0.911854	0.274934	0.137467	−	0.990506i	$-0.456104\pi$
$11$	0.911854	0.274934	0.137467	+	0.990506i	$0.456104\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	4.04892	1.08212
$15$	−0.356896	−0.0921501
$16$	1.00000	0.250000
$17$	−2.09783	−0.508800	−0.254400	−	0.967099i	$-0.581878\pi$
$17$	−2.09783	−0.508800	−0.254400	+	0.967099i	$0.581878\pi$
$18$	−1.00000	−0.235702
$19$	4.98792	1.14431	0.572153	−	0.820147i	$-0.306108\pi$
$19$	4.98792	1.14431	0.572153	+	0.820147i	$0.306108\pi$
$20$	−0.356896	−0.0798043
$21$	−4.04892	−0.883546
$22$	−0.911854	−0.194408
$23$	8.49396	1.77111	0.885556	−	0.464532i	$-0.153777\pi$
$23$	8.49396	1.77111	0.885556	+	0.464532i	$0.153777\pi$
$24$	−1.00000	−0.204124
$25$	−4.87263	−0.974525
$26$	0	0
$27$	1.00000	0.192450
$28$	−4.04892	−0.765173
$29$	8.51573	1.58133	0.790666	−	0.612248i	$-0.209735\pi$
$29$	8.51573	1.58133	0.790666	+	0.612248i	$0.209735\pi$
$30$	0.356896	0.0651600
$31$	10.7899	1.93792	0.968958	−	0.247227i	$-0.0795192\pi$
$31$	10.7899	1.93792	0.968958	+	0.247227i	$0.0795192\pi$
$32$	−1.00000	−0.176777
$33$	0.911854	0.158733
$34$	2.09783	0.359776
$35$	1.44504	0.244257
$36$	1.00000	0.166667
$37$	0.615957	0.101263	0.0506314	−	0.998717i	$-0.483877\pi$
$37$	0.615957	0.101263	0.0506314	+	0.998717i	$0.483877\pi$
$38$	−4.98792	−0.809147
$39$	0	0
$40$	0.356896	0.0564302
$41$	7.60388	1.18753	0.593763	−	0.804640i	$-0.297642\pi$
$41$	7.60388	1.18753	0.593763	+	0.804640i	$0.297642\pi$
$42$	4.04892	0.624762
$43$	−6.27413	−0.956795	−0.478398	−	0.878143i	$-0.658782\pi$
$43$	−6.27413	−0.956795	−0.478398	+	0.878143i	$0.658782\pi$
$44$	0.911854	0.137467
$45$	−0.356896	−0.0532029
$46$	−8.49396	−1.25237
$47$	−1.78017	−0.259664	−0.129832	−	0.991536i	$-0.541444\pi$
$47$	−1.78017	−0.259664	−0.129832	+	0.991536i	$0.541444\pi$
$48$	1.00000	0.144338
$49$	9.39373	1.34196
$50$	4.87263	0.689093
$51$	−2.09783	−0.293756
$52$	0	0
$53$	10.4112	1.43009	0.715043	−	0.699080i	$-0.246407\pi$
$53$	10.4112	1.43009	0.715043	+	0.699080i	$0.246407\pi$
$54$	−1.00000	−0.136083
$55$	−0.325437	−0.0438819
$56$	4.04892	0.541059
$57$	4.98792	0.660666
$58$	−8.51573	−1.11817
$59$	6.04892	0.787502	0.393751	−	0.919217i	$-0.371177\pi$
$59$	6.04892	0.787502	0.393751	+	0.919217i	$0.371177\pi$
$60$	−0.356896	−0.0460751
$61$	−3.10992	−0.398184	−0.199092	−	0.979981i	$-0.563799\pi$
$61$	−3.10992	−0.398184	−0.199092	+	0.979981i	$0.563799\pi$
$62$	−10.7899	−1.37031
$63$	−4.04892	−0.510116
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.911854	−0.112241
$67$	−13.5797	−1.65903	−0.829513	−	0.558487i	$-0.811382\pi$
$67$	−13.5797	−1.65903	−0.829513	+	0.558487i	$0.811382\pi$
$68$	−2.09783	−0.254400
$69$	8.49396	1.02255
$70$	−1.44504	−0.172716
$71$	−11.4819	−1.36265	−0.681324	−	0.731982i	$-0.738596\pi$
$71$	−11.4819	−1.36265	−0.681324	+	0.731982i	$0.738596\pi$
$72$	−1.00000	−0.117851
$73$	−0.533188	−0.0624049	−0.0312025	−	0.999513i	$-0.509934\pi$
$73$	−0.533188	−0.0624049	−0.0312025	+	0.999513i	$0.509934\pi$
$74$	−0.615957	−0.0716036
$75$	−4.87263	−0.562642
$76$	4.98792	0.572153
$77$	−3.69202	−0.420745
$78$	0	0
$79$	−11.7071	−1.31715	−0.658575	−	0.752515i	$-0.728841\pi$
$79$	−11.7071	−1.31715	−0.658575	+	0.752515i	$0.728841\pi$
$80$	−0.356896	−0.0399022
$81$	1.00000	0.111111
$82$	−7.60388	−0.839708
$83$	6.49934	0.713395	0.356697	−	0.934220i	$-0.383903\pi$
$83$	6.49934	0.713395	0.356697	+	0.934220i	$0.383903\pi$
$84$	−4.04892	−0.441773
$85$	0.748709	0.0812088
$86$	6.27413	0.676556
$87$	8.51573	0.912982
$88$	−0.911854	−0.0972040
$89$	6.49396	0.688358	0.344179	−	0.938904i	$-0.388157\pi$
$89$	6.49396	0.688358	0.344179	+	0.938904i	$0.388157\pi$
$90$	0.356896	0.0376201
$91$	0	0
$92$	8.49396	0.885556
$93$	10.7899	1.11886
$94$	1.78017	0.183610
$95$	−1.78017	−0.182641
$96$	−1.00000	−0.102062
$97$	1.96077	0.199086	0.0995431	−	0.995033i	$-0.468262\pi$
$97$	1.96077	0.199086	0.0995431	+	0.995033i	$0.468262\pi$
$98$	−9.39373	−0.948910
$99$	0.911854	0.0916448
$100$	−4.87263	−0.487263
$101$	6.98254	0.694789	0.347394	−	0.937719i	$-0.387067\pi$
$101$	6.98254	0.694789	0.347394	+	0.937719i	$0.387067\pi$
$102$	2.09783	0.207717
$103$	4.94869	0.487609	0.243804	−	0.969824i	$-0.421604\pi$
$103$	4.94869	0.487609	0.243804	+	0.969824i	$0.421604\pi$
$104$	0	0
$105$	1.44504	0.141022
$106$	−10.4112	−1.01122
$107$	−4.26875	−0.412676	−0.206338	−	0.978481i	$-0.566155\pi$
$107$	−4.26875	−0.412676	−0.206338	+	0.978481i	$0.566155\pi$
$108$	1.00000	0.0962250
$109$	6.21983	0.595752	0.297876	−	0.954605i	$-0.403722\pi$
$109$	6.21983	0.595752	0.297876	+	0.954605i	$0.403722\pi$
$110$	0.325437	0.0310292
$111$	0.615957	0.0584641
$112$	−4.04892	−0.382587
$113$	12.9879	1.22180	0.610900	−	0.791708i	$-0.290808\pi$
$113$	12.9879	1.22180	0.610900	+	0.791708i	$0.290808\pi$
$114$	−4.98792	−0.467161
$115$	−3.03146	−0.282685
$116$	8.51573	0.790666
$117$	0	0
$118$	−6.04892	−0.556848
$119$	8.49396	0.778640
$120$	0.356896	0.0325800
$121$	−10.1685	−0.924411
$122$	3.10992	0.281559
$123$	7.60388	0.685618
$124$	10.7899	0.968958
$125$	3.52350	0.315151
$126$	4.04892	0.360706
$127$	9.22282	0.818393	0.409196	−	0.912446i	$-0.365809\pi$
$127$	9.22282	0.818393	0.409196	+	0.912446i	$0.365809\pi$
$128$	−1.00000	−0.0883883
$129$	−6.27413	−0.552406
$130$	0	0
$131$	−14.5526	−1.27146	−0.635732	−	0.771910i	$-0.719302\pi$
$131$	−14.5526	−1.27146	−0.635732	+	0.771910i	$0.719302\pi$
$132$	0.911854	0.0793667
$133$	−20.1957	−1.75119
$134$	13.5797	1.17311
$135$	−0.356896	−0.0307167
$136$	2.09783	0.179888
$137$	15.4034	1.31600	0.658002	−	0.753017i	$-0.271402\pi$
$137$	15.4034	1.31600	0.658002	+	0.753017i	$0.271402\pi$
$138$	−8.49396	−0.723054
$139$	2.71379	0.230181	0.115090	−	0.993355i	$-0.463284\pi$
$139$	2.71379	0.230181	0.115090	+	0.993355i	$0.463284\pi$
$140$	1.44504	0.122128
$141$	−1.78017	−0.149917
$142$	11.4819	0.963538
$143$	0	0
$144$	1.00000	0.0833333
$145$	−3.03923	−0.252394
$146$	0.533188	0.0441269
$147$	9.39373	0.774782
$148$	0.615957	0.0506314
$149$	14.7356	1.20718	0.603592	−	0.797293i	$-0.293736\pi$
$149$	14.7356	1.20718	0.603592	+	0.797293i	$0.293736\pi$
$150$	4.87263	0.397848
$151$	15.8213	1.28752	0.643760	−	0.765227i	$-0.277373\pi$
$151$	15.8213	1.28752	0.643760	+	0.765227i	$0.277373\pi$
$152$	−4.98792	−0.404574
$153$	−2.09783	−0.169600
$154$	3.69202	0.297512
$155$	−3.85086	−0.309308
$156$	0	0
$157$	−4.27413	−0.341112	−0.170556	−	0.985348i	$-0.554556\pi$
$157$	−4.27413	−0.341112	−0.170556	+	0.985348i	$0.554556\pi$
$158$	11.7071	0.931366
$159$	10.4112	0.825661
$160$	0.356896	0.0282151
$161$	−34.3913	−2.71042
$162$	−1.00000	−0.0785674
$163$	0.317667	0.0248816	0.0124408	−	0.999923i	$-0.496040\pi$
$163$	0.317667	0.0248816	0.0124408	+	0.999923i	$0.496040\pi$
$164$	7.60388	0.593763
$165$	−0.325437	−0.0253352
$166$	−6.49934	−0.504446
$167$	−12.3612	−0.956539	−0.478269	−	0.878213i	$-0.658736\pi$
$167$	−12.3612	−0.956539	−0.478269	+	0.878213i	$0.658736\pi$
$168$	4.04892	0.312381
$169$	0	0
$170$	−0.748709	−0.0574233
$171$	4.98792	0.381436
$172$	−6.27413	−0.478398
$173$	−17.0640	−1.29735	−0.648675	−	0.761065i	$-0.724677\pi$
$173$	−17.0640	−1.29735	−0.648675	+	0.761065i	$0.724677\pi$
$174$	−8.51573	−0.645576
$175$	19.7289	1.49136
$176$	0.911854	0.0687336
$177$	6.04892	0.454664
$178$	−6.49396	−0.486743
$179$	−24.9681	−1.86620	−0.933100	−	0.359616i	$-0.882908\pi$
$179$	−24.9681	−1.86620	−0.933100	+	0.359616i	$0.882908\pi$
$180$	−0.356896	−0.0266014
$181$	5.26205	0.391125	0.195562	−	0.980691i	$-0.437347\pi$
$181$	5.26205	0.391125	0.195562	+	0.980691i	$0.437347\pi$
$182$	0	0
$183$	−3.10992	−0.229892
$184$	−8.49396	−0.626183
$185$	−0.219833	−0.0161624
$186$	−10.7899	−0.791151
$187$	−1.91292	−0.139886
$188$	−1.78017	−0.129832
$189$	−4.04892	−0.294515
$190$	1.78017	0.129147
$191$	10.5375	0.762467	0.381233	−	0.924479i	$-0.375499\pi$
$191$	10.5375	0.762467	0.381233	+	0.924479i	$0.375499\pi$
$192$	1.00000	0.0721688
$193$	−3.42758	−0.246723	−0.123361	−	0.992362i	$-0.539367\pi$
$193$	−3.42758	−0.246723	−0.123361	+	0.992362i	$0.539367\pi$
$194$	−1.96077	−0.140775
$195$	0	0
$196$	9.39373	0.670981
$197$	−3.77479	−0.268943	−0.134471	−	0.990917i	$-0.542934\pi$
$197$	−3.77479	−0.268943	−0.134471	+	0.990917i	$0.542934\pi$
$198$	−0.911854	−0.0648026
$199$	17.9541	1.27273	0.636365	−	0.771388i	$-0.280437\pi$
$199$	17.9541	1.27273	0.636365	+	0.771388i	$0.280437\pi$
$200$	4.87263	0.344547
$201$	−13.5797	−0.957839
$202$	−6.98254	−0.491290
$203$	−34.4795	−2.41999
$204$	−2.09783	−0.146878
$205$	−2.71379	−0.189539
$206$	−4.94869	−0.344792
$207$	8.49396	0.590371
$208$	0	0
$209$	4.54825	0.314609
$210$	−1.44504	−0.0997174
$211$	−12.5375	−0.863117	−0.431559	−	0.902085i	$-0.642036\pi$
$211$	−12.5375	−0.863117	−0.431559	+	0.902085i	$0.642036\pi$
$212$	10.4112	0.715043
$213$	−11.4819	−0.786725
$214$	4.26875	0.291806
$215$	2.23921	0.152713
$216$	−1.00000	−0.0680414
$217$	−43.6872	−2.96568
$218$	−6.21983	−0.421260
$219$	−0.533188	−0.0360295
$220$	−0.325437	−0.0219410
$221$	0	0
$222$	−0.615957	−0.0413403
$223$	−5.42758	−0.363458	−0.181729	−	0.983349i	$-0.558169\pi$
$223$	−5.42758	−0.363458	−0.181729	+	0.983349i	$0.558169\pi$
$224$	4.04892	0.270530
$225$	−4.87263	−0.324842
$226$	−12.9879	−0.863943
$227$	−16.5767	−1.10024	−0.550118	−	0.835087i	$-0.685417\pi$
$227$	−16.5767	−1.10024	−0.550118	+	0.835087i	$0.685417\pi$
$228$	4.98792	0.330333
$229$	23.8780	1.57790	0.788951	−	0.614456i	$-0.210624\pi$
$229$	23.8780	1.57790	0.788951	+	0.614456i	$0.210624\pi$
$230$	3.03146	0.199888
$231$	−3.69202	−0.242917
$232$	−8.51573	−0.559085
$233$	13.9952	0.916857	0.458428	−	0.888731i	$-0.348413\pi$
$233$	13.9952	0.916857	0.458428	+	0.888731i	$0.348413\pi$
$234$	0	0
$235$	0.635334	0.0414446
$236$	6.04892	0.393751
$237$	−11.7071	−0.760457
$238$	−8.49396	−0.550582
$239$	−13.2862	−0.859413	−0.429707	−	0.902969i	$-0.641383\pi$
$239$	−13.2862	−0.859413	−0.429707	+	0.902969i	$0.641383\pi$
$240$	−0.356896	−0.0230375
$241$	−10.4789	−0.675005	−0.337502	−	0.941325i	$-0.609582\pi$
$241$	−10.4789	−0.675005	−0.337502	+	0.941325i	$0.609582\pi$
$242$	10.1685	0.653657
$243$	1.00000	0.0641500
$244$	−3.10992	−0.199092
$245$	−3.35258	−0.214189
$246$	−7.60388	−0.484805
$247$	0	0
$248$	−10.7899	−0.685157
$249$	6.49934	0.411879
$250$	−3.52350	−0.222846
$251$	3.48725	0.220114	0.110057	−	0.993925i	$-0.464897\pi$
$251$	3.48725	0.220114	0.110057	+	0.993925i	$0.464897\pi$
$252$	−4.04892	−0.255058
$253$	7.74525	0.486940
$254$	−9.22282	−0.578691
$255$	0.748709	0.0468859
$256$	1.00000	0.0625000
$257$	6.53750	0.407798	0.203899	−	0.978992i	$-0.434639\pi$
$257$	6.53750	0.407798	0.203899	+	0.978992i	$0.434639\pi$
$258$	6.27413	0.390610
$259$	−2.49396	−0.154967
$260$	0	0
$261$	8.51573	0.527110
$262$	14.5526	0.899060
$263$	8.01938	0.494496	0.247248	−	0.968952i	$-0.420474\pi$
$263$	8.01938	0.494496	0.247248	+	0.968952i	$0.420474\pi$
$264$	−0.911854	−0.0561207
$265$	−3.71571	−0.228254
$266$	20.1957	1.23828
$267$	6.49396	0.397424
$268$	−13.5797	−0.829513
$269$	−27.6732	−1.68727	−0.843633	−	0.536920i	$-0.819588\pi$
$269$	−27.6732	−1.68727	−0.843633	+	0.536920i	$0.819588\pi$
$270$	0.356896	0.0217200
$271$	−14.7289	−0.894714	−0.447357	−	0.894355i	$-0.647635\pi$
$271$	−14.7289	−0.894714	−0.447357	+	0.894355i	$0.647635\pi$
$272$	−2.09783	−0.127200
$273$	0	0
$274$	−15.4034	−0.930555
$275$	−4.44312	−0.267930
$276$	8.49396	0.511276
$277$	3.26205	0.195997	0.0979986	−	0.995187i	$-0.468756\pi$
$277$	3.26205	0.195997	0.0979986	+	0.995187i	$0.468756\pi$
$278$	−2.71379	−0.162762
$279$	10.7899	0.645972
$280$	−1.44504	−0.0863578
$281$	−7.72587	−0.460887	−0.230443	−	0.973086i	$-0.574018\pi$
$281$	−7.72587	−0.460887	−0.230443	+	0.973086i	$0.574018\pi$
$282$	1.78017	0.106007
$283$	−19.7802	−1.17581	−0.587904	−	0.808930i	$-0.700047\pi$
$283$	−19.7802	−1.17581	−0.587904	+	0.808930i	$0.700047\pi$
$284$	−11.4819	−0.681324
$285$	−1.78017	−0.105448
$286$	0	0
$287$	−30.7875	−1.81733
$288$	−1.00000	−0.0589256
$289$	−12.5991	−0.741123
$290$	3.03923	0.178470
$291$	1.96077	0.114942
$292$	−0.533188	−0.0312025
$293$	12.9119	0.754319	0.377159	−	0.926148i	$-0.376901\pi$
$293$	12.9119	0.754319	0.377159	+	0.926148i	$0.376901\pi$
$294$	−9.39373	−0.547854
$295$	−2.15883	−0.125692
$296$	−0.615957	−0.0358018
$297$	0.911854	0.0529111
$298$	−14.7356	−0.853608
$299$	0	0
$300$	−4.87263	−0.281321
$301$	25.4034	1.46423
$302$	−15.8213	−0.910414
$303$	6.98254	0.401137
$304$	4.98792	0.286077
$305$	1.10992	0.0635536
$306$	2.09783	0.119925
$307$	−19.9651	−1.13947	−0.569734	−	0.821829i	$-0.692954\pi$
$307$	−19.9651	−1.13947	−0.569734	+	0.821829i	$0.692954\pi$
$308$	−3.69202	−0.210372
$309$	4.94869	0.281521
$310$	3.85086	0.218714
$311$	13.4819	0.764487	0.382244	−	0.924062i	$-0.375152\pi$
$311$	13.4819	0.764487	0.382244	+	0.924062i	$0.375152\pi$
$312$	0	0
$313$	12.9245	0.730537	0.365269	−	0.930902i	$-0.380977\pi$
$313$	12.9245	0.730537	0.365269	+	0.930902i	$0.380977\pi$
$314$	4.27413	0.241203
$315$	1.44504	0.0814189
$316$	−11.7071	−0.658575
$317$	11.8726	0.666833	0.333417	−	0.942780i	$-0.391798\pi$
$317$	11.8726	0.666833	0.333417	+	0.942780i	$0.391798\pi$
$318$	−10.4112	−0.583831
$319$	7.76510	0.434762
$320$	−0.356896	−0.0199511
$321$	−4.26875	−0.238258
$322$	34.3913	1.91655
$323$	−10.4638	−0.582223
$324$	1.00000	0.0555556
$325$	0	0
$326$	−0.317667	−0.0175940
$327$	6.21983	0.343958
$328$	−7.60388	−0.419854
$329$	7.20775	0.397376
$330$	0.325437	0.0179147
$331$	−10.2392	−0.562798	−0.281399	−	0.959591i	$-0.590798\pi$
$331$	−10.2392	−0.562798	−0.281399	+	0.959591i	$0.590798\pi$
$332$	6.49934	0.356697
$333$	0.615957	0.0337542
$334$	12.3612	0.676375
$335$	4.84654	0.264795
$336$	−4.04892	−0.220887
$337$	1.44935	0.0789513	0.0394757	−	0.999221i	$-0.487431\pi$
$337$	1.44935	0.0789513	0.0394757	+	0.999221i	$0.487431\pi$
$338$	0	0
$339$	12.9879	0.705407
$340$	0.748709	0.0406044
$341$	9.83877	0.532799
$342$	−4.98792	−0.269716
$343$	−9.69202	−0.523320
$344$	6.27413	0.338278
$345$	−3.03146	−0.163208
$346$	17.0640	0.917365
$347$	6.84117	0.367253	0.183627	−	0.982996i	$-0.441216\pi$
$347$	6.84117	0.367253	0.183627	+	0.982996i	$0.441216\pi$
$348$	8.51573	0.456491
$349$	34.3370	1.83802	0.919010	−	0.394234i	$-0.128990\pi$
$349$	34.3370	1.83802	0.919010	+	0.394234i	$0.128990\pi$
$350$	−19.7289	−1.05455
$351$	0	0
$352$	−0.911854	−0.0486020
$353$	−26.0495	−1.38648	−0.693238	−	0.720709i	$-0.743816\pi$
$353$	−26.0495	−1.38648	−0.693238	+	0.720709i	$0.743816\pi$
$354$	−6.04892	−0.321496
$355$	4.09783	0.217490
$356$	6.49396	0.344179
$357$	8.49396	0.449548
$358$	24.9681	1.31960
$359$	−8.49396	−0.448294	−0.224147	−	0.974555i	$-0.571960\pi$
$359$	−8.49396	−0.448294	−0.224147	+	0.974555i	$0.571960\pi$
$360$	0.356896	0.0188101
$361$	5.87933	0.309438
$362$	−5.26205	−0.276567
$363$	−10.1685	−0.533709
$364$	0	0
$365$	0.190293	0.00996037
$366$	3.10992	0.162558
$367$	27.4523	1.43300	0.716500	−	0.697587i	$-0.245743\pi$
$367$	27.4523	1.43300	0.716500	+	0.697587i	$0.245743\pi$
$368$	8.49396	0.442778
$369$	7.60388	0.395842
$370$	0.219833	0.0114285
$371$	−42.1540	−2.18853
$372$	10.7899	0.559428
$373$	26.6219	1.37843	0.689216	−	0.724556i	$-0.257955\pi$
$373$	26.6219	1.37843	0.689216	+	0.724556i	$0.257955\pi$
$374$	1.91292	0.0989147
$375$	3.52350	0.181953
$376$	1.78017	0.0918051
$377$	0	0
$378$	4.04892	0.208254
$379$	−11.6474	−0.598288	−0.299144	−	0.954208i	$-0.596701\pi$
$379$	−11.6474	−0.598288	−0.299144	+	0.954208i	$0.596701\pi$
$380$	−1.78017	−0.0913207
$381$	9.22282	0.472499
$382$	−10.5375	−0.539145
$383$	−10.5181	−0.537451	−0.268725	−	0.963217i	$-0.586602\pi$
$383$	−10.5181	−0.537451	−0.268725	+	0.963217i	$0.586602\pi$
$384$	−1.00000	−0.0510310
$385$	1.31767	0.0671545
$386$	3.42758	0.174459
$387$	−6.27413	−0.318932
$388$	1.96077	0.0995431
$389$	−9.25965	−0.469483	−0.234742	−	0.972058i	$-0.575424\pi$
$389$	−9.25965	−0.469483	−0.234742	+	0.972058i	$0.575424\pi$
$390$	0	0
$391$	−17.8189	−0.901142
$392$	−9.39373	−0.474455
$393$	−14.5526	−0.734080
$394$	3.77479	0.190171
$395$	4.17821	0.210229
$396$	0.911854	0.0458224
$397$	−14.5133	−0.728403	−0.364202	−	0.931320i	$-0.618658\pi$
$397$	−14.5133	−0.728403	−0.364202	+	0.931320i	$0.618658\pi$
$398$	−17.9541	−0.899956
$399$	−20.1957	−1.01105
$400$	−4.87263	−0.243631
$401$	38.8418	1.93966	0.969832	−	0.243773i	$-0.0783851\pi$
$401$	38.8418	1.93966	0.969832	+	0.243773i	$0.0783851\pi$
$402$	13.5797	0.677294
$403$	0	0
$404$	6.98254	0.347394
$405$	−0.356896	−0.0177343
$406$	34.4795	1.71119
$407$	0.561663	0.0278406
$408$	2.09783	0.103858
$409$	−33.9221	−1.67734	−0.838671	−	0.544639i	$-0.816667\pi$
$409$	−33.9221	−1.67734	−0.838671	+	0.544639i	$0.816667\pi$
$410$	2.71379	0.134025
$411$	15.4034	0.759795
$412$	4.94869	0.243804
$413$	−24.4916	−1.20515
$414$	−8.49396	−0.417455
$415$	−2.31959	−0.113864
$416$	0	0
$417$	2.71379	0.132895
$418$	−4.54825	−0.222462
$419$	0.955395	0.0466741	0.0233370	−	0.999728i	$-0.492571\pi$
$419$	0.955395	0.0466741	0.0233370	+	0.999728i	$0.492571\pi$
$420$	1.44504	0.0705108
$421$	−5.68233	−0.276940	−0.138470	−	0.990367i	$-0.544218\pi$
$421$	−5.68233	−0.276940	−0.138470	+	0.990367i	$0.544218\pi$
$422$	12.5375	0.610316
$423$	−1.78017	−0.0865547
$424$	−10.4112	−0.505612
$425$	10.2220	0.495838
$426$	11.4819	0.556299
$427$	12.5918	0.609360
$428$	−4.26875	−0.206338
$429$	0	0
$430$	−2.23921	−0.107984
$431$	−14.8465	−0.715133	−0.357566	−	0.933888i	$-0.616393\pi$
$431$	−14.8465	−0.715133	−0.357566	+	0.933888i	$0.616393\pi$
$432$	1.00000	0.0481125
$433$	−26.1497	−1.25668	−0.628338	−	0.777940i	$-0.716265\pi$
$433$	−26.1497	−1.25668	−0.628338	+	0.777940i	$0.716265\pi$
$434$	43.6872	2.09705
$435$	−3.03923	−0.145720
$436$	6.21983	0.297876
$437$	42.3672	2.02670
$438$	0.533188	0.0254767
$439$	−23.5502	−1.12399	−0.561994	−	0.827141i	$-0.689966\pi$
$439$	−23.5502	−1.12399	−0.561994	+	0.827141i	$0.689966\pi$
$440$	0.325437	0.0155146
$441$	9.39373	0.447321
$442$	0	0
$443$	21.9433	1.04256	0.521279	−	0.853386i	$-0.325455\pi$
$443$	21.9433	1.04256	0.521279	+	0.853386i	$0.325455\pi$
$444$	0.615957	0.0292320
$445$	−2.31767	−0.109868
$446$	5.42758	0.257004
$447$	14.7356	0.696968
$448$	−4.04892	−0.191293
$449$	11.4034	0.538161	0.269080	−	0.963118i	$-0.413280\pi$
$449$	11.4034	0.538161	0.269080	+	0.963118i	$0.413280\pi$
$450$	4.87263	0.229698
$451$	6.93362	0.326492
$452$	12.9879	0.610900
$453$	15.8213	0.743350
$454$	16.5767	0.777984
$455$	0	0
$456$	−4.98792	−0.233581
$457$	7.66919	0.358749	0.179375	−	0.983781i	$-0.442593\pi$
$457$	7.66919	0.358749	0.179375	+	0.983781i	$0.442593\pi$
$458$	−23.8780	−1.11575
$459$	−2.09783	−0.0979185
$460$	−3.03146	−0.141343
$461$	−28.5080	−1.32775	−0.663874	−	0.747844i	$-0.731089\pi$
$461$	−28.5080	−1.32775	−0.663874	+	0.747844i	$0.731089\pi$
$462$	3.69202	0.171768
$463$	−14.3284	−0.665898	−0.332949	−	0.942945i	$-0.608044\pi$
$463$	−14.3284	−0.665898	−0.332949	+	0.942945i	$0.608044\pi$
$464$	8.51573	0.395333
$465$	−3.85086	−0.178579
$466$	−13.9952	−0.648316
$467$	33.3207	1.54190	0.770948	−	0.636898i	$-0.219783\pi$
$467$	33.3207	1.54190	0.770948	+	0.636898i	$0.219783\pi$
$468$	0	0
$469$	54.9831	2.53889
$470$	−0.635334	−0.0293058
$471$	−4.27413	−0.196941
$472$	−6.04892	−0.278424
$473$	−5.72109	−0.263056
$474$	11.7071	0.537724
$475$	−24.3043	−1.11516
$476$	8.49396	0.389320
$477$	10.4112	0.476696
$478$	13.2862	0.607697
$479$	−22.1280	−1.01105	−0.505526	−	0.862811i	$-0.668702\pi$
$479$	−22.1280	−1.01105	−0.505526	+	0.862811i	$0.668702\pi$
$480$	0.356896	0.0162900
$481$	0	0
$482$	10.4789	0.477301
$483$	−34.3913	−1.56486
$484$	−10.1685	−0.462206
$485$	−0.699791	−0.0317759
$486$	−1.00000	−0.0453609
$487$	−0.126310	−0.00572364	−0.00286182	−	0.999996i	$-0.500911\pi$
$487$	−0.126310	−0.00572364	−0.00286182	+	0.999996i	$0.500911\pi$
$488$	3.10992	0.140779
$489$	0.317667	0.0143654
$490$	3.35258	0.151454
$491$	13.9433	0.629253	0.314626	−	0.949216i	$-0.398121\pi$
$491$	13.9433	0.629253	0.314626	+	0.949216i	$0.398121\pi$
$492$	7.60388	0.342809
$493$	−17.8646	−0.804581
$494$	0	0
$495$	−0.325437	−0.0146273
$496$	10.7899	0.484479
$497$	46.4892	2.08532
$498$	−6.49934	−0.291242
$499$	28.3913	1.27097	0.635485	−	0.772113i	$-0.280800\pi$
$499$	28.3913	1.27097	0.635485	+	0.772113i	$0.280800\pi$
$500$	3.52350	0.157576
$501$	−12.3612	−0.552258
$502$	−3.48725	−0.155644
$503$	12.5676	0.560363	0.280181	−	0.959947i	$-0.409605\pi$
$503$	12.5676	0.560363	0.280181	+	0.959947i	$0.409605\pi$
$504$	4.04892	0.180353
$505$	−2.49204	−0.110894
$506$	−7.74525	−0.344318
$507$	0	0
$508$	9.22282	0.409196
$509$	4.37675	0.193996	0.0969980	−	0.995285i	$-0.469076\pi$
$509$	4.37675	0.193996	0.0969980	+	0.995285i	$0.469076\pi$
$510$	−0.748709	−0.0331534
$511$	2.15883	0.0955012
$512$	−1.00000	−0.0441942
$513$	4.98792	0.220222
$514$	−6.53750	−0.288357
$515$	−1.76617	−0.0778266
$516$	−6.27413	−0.276203
$517$	−1.62325	−0.0713906
$518$	2.49396	0.109578
$519$	−17.0640	−0.749026
$520$	0	0
$521$	−23.2707	−1.01951	−0.509753	−	0.860321i	$-0.670263\pi$
$521$	−23.2707	−1.01951	−0.509753	+	0.860321i	$0.670263\pi$
$522$	−8.51573	−0.372723
$523$	37.9952	1.66141	0.830707	−	0.556709i	$-0.187936\pi$
$523$	37.9952	1.66141	0.830707	+	0.556709i	$0.187936\pi$
$524$	−14.5526	−0.635732
$525$	19.7289	0.861038
$526$	−8.01938	−0.349661
$527$	−22.6353	−0.986011
$528$	0.911854	0.0396834
$529$	49.1473	2.13684
$530$	3.71571	0.161400
$531$	6.04892	0.262501
$532$	−20.1957	−0.875593
$533$	0	0
$534$	−6.49396	−0.281021
$535$	1.52350	0.0658666
$536$	13.5797	0.586554
$537$	−24.9681	−1.07745
$538$	27.6732	1.19308
$539$	8.56571	0.368951
$540$	−0.356896	−0.0153584
$541$	3.16421	0.136040	0.0680200	−	0.997684i	$-0.478332\pi$
$541$	3.16421	0.136040	0.0680200	+	0.997684i	$0.478332\pi$
$542$	14.7289	0.632659
$543$	5.26205	0.225816
$544$	2.09783	0.0899439
$545$	−2.21983	−0.0950872
$546$	0	0
$547$	7.56033	0.323257	0.161628	−	0.986852i	$-0.448325\pi$
$547$	7.56033	0.323257	0.161628	+	0.986852i	$0.448325\pi$
$548$	15.4034	0.658002
$549$	−3.10992	−0.132728
$550$	4.44312	0.189455
$551$	42.4758	1.80953
$552$	−8.49396	−0.361527
$553$	47.4010	2.01570
$554$	−3.26205	−0.138591
$555$	−0.219833	−0.00933137
$556$	2.71379	0.115090
$557$	−0.415502	−0.0176054	−0.00880269	−	0.999961i	$-0.502802\pi$
$557$	−0.415502	−0.0176054	−0.00880269	+	0.999961i	$0.502802\pi$
$558$	−10.7899	−0.456771
$559$	0	0
$560$	1.44504	0.0610642
$561$	−1.91292	−0.0807635
$562$	7.72587	0.325896
$563$	−29.0465	−1.22417	−0.612083	−	0.790794i	$-0.709668\pi$
$563$	−29.0465	−1.22417	−0.612083	+	0.790794i	$0.709668\pi$
$564$	−1.78017	−0.0749586
$565$	−4.63533	−0.195010
$566$	19.7802	0.831422
$567$	−4.04892	−0.170039
$568$	11.4819	0.481769
$569$	39.6862	1.66373	0.831865	−	0.554977i	$-0.187273\pi$
$569$	39.6862	1.66373	0.831865	+	0.554977i	$0.187273\pi$
$570$	1.78017	0.0745630
$571$	−7.09651	−0.296980	−0.148490	−	0.988914i	$-0.547441\pi$
$571$	−7.09651	−0.296980	−0.148490	+	0.988914i	$0.547441\pi$
$572$	0	0
$573$	10.5375	0.440210
$574$	30.7875	1.28504
$575$	−41.3879	−1.72599
$576$	1.00000	0.0416667
$577$	−8.78687	−0.365802	−0.182901	−	0.983131i	$-0.558549\pi$
$577$	−8.78687	−0.365802	−0.182901	+	0.983131i	$0.558549\pi$
$578$	12.5991	0.524053
$579$	−3.42758	−0.142446
$580$	−3.03923	−0.126197
$581$	−26.3153	−1.09174
$582$	−1.96077	−0.0812766
$583$	9.49349	0.393180
$584$	0.533188	0.0220635
$585$	0	0
$586$	−12.9119	−0.533384
$587$	−36.7066	−1.51504	−0.757522	−	0.652810i	$-0.773590\pi$
$587$	−36.7066	−1.51504	−0.757522	+	0.652810i	$0.773590\pi$
$588$	9.39373	0.387391
$589$	53.8189	2.21757
$590$	2.15883	0.0888778
$591$	−3.77479	−0.155274
$592$	0.615957	0.0253157
$593$	−10.8310	−0.444776	−0.222388	−	0.974958i	$-0.571385\pi$
$593$	−10.8310	−0.444776	−0.222388	+	0.974958i	$0.571385\pi$
$594$	−0.911854	−0.0374138
$595$	−3.03146	−0.124278
$596$	14.7356	0.603592
$597$	17.9541	0.734811
$598$	0	0
$599$	23.5254	0.961223	0.480611	−	0.876934i	$-0.340415\pi$
$599$	23.5254	0.961223	0.480611	+	0.876934i	$0.340415\pi$
$600$	4.87263	0.198924
$601$	27.8213	1.13486	0.567428	−	0.823423i	$-0.307939\pi$
$601$	27.8213	1.13486	0.567428	+	0.823423i	$0.307939\pi$
$602$	−25.4034	−1.03537
$603$	−13.5797	−0.553009
$604$	15.8213	0.643760
$605$	3.62910	0.147544
$606$	−6.98254	−0.283646
$607$	0.0972437	0.00394700	0.00197350	−	0.999998i	$-0.499372\pi$
$607$	0.0972437	0.00394700	0.00197350	+	0.999998i	$0.499372\pi$
$608$	−4.98792	−0.202287
$609$	−34.4795	−1.39718
$610$	−1.10992	−0.0449392
$611$	0	0
$612$	−2.09783	−0.0847999
$613$	8.06505	0.325744	0.162872	−	0.986647i	$-0.447924\pi$
$613$	8.06505	0.325744	0.162872	+	0.986647i	$0.447924\pi$
$614$	19.9651	0.805725
$615$	−2.71379	−0.109431
$616$	3.69202	0.148756
$617$	−19.2185	−0.773708	−0.386854	−	0.922141i	$-0.626438\pi$
$617$	−19.2185	−0.773708	−0.386854	+	0.922141i	$0.626438\pi$
$618$	−4.94869	−0.199065
$619$	12.3827	0.497703	0.248852	−	0.968542i	$-0.419947\pi$
$619$	12.3827	0.497703	0.248852	+	0.968542i	$0.419947\pi$
$620$	−3.85086	−0.154654
$621$	8.49396	0.340851
$622$	−13.4819	−0.540574
$623$	−26.2935	−1.05343
$624$	0	0
$625$	23.1056	0.924224
$626$	−12.9245	−0.516568
$627$	4.54825	0.181640
$628$	−4.27413	−0.170556
$629$	−1.29218	−0.0515224
$630$	−1.44504	−0.0575718
$631$	−4.74333	−0.188829	−0.0944145	−	0.995533i	$-0.530098\pi$
$631$	−4.74333	−0.188829	−0.0944145	+	0.995533i	$0.530098\pi$
$632$	11.7071	0.465683
$633$	−12.5375	−0.498321
$634$	−11.8726	−0.471522
$635$	−3.29159	−0.130623
$636$	10.4112	0.412831
$637$	0	0
$638$	−7.76510	−0.307423
$639$	−11.4819	−0.454216
$640$	0.356896	0.0141075
$641$	−16.4456	−0.649563	−0.324782	−	0.945789i	$-0.605291\pi$
$641$	−16.4456	−0.649563	−0.324782	+	0.945789i	$0.605291\pi$
$642$	4.26875	0.168474
$643$	1.74525	0.0688260	0.0344130	−	0.999408i	$-0.489044\pi$
$643$	1.74525	0.0688260	0.0344130	+	0.999408i	$0.489044\pi$
$644$	−34.3913	−1.35521
$645$	2.23921	0.0881688
$646$	10.4638	0.411694
$647$	28.7633	1.13080	0.565401	−	0.824816i	$-0.308721\pi$
$647$	28.7633	1.13080	0.565401	+	0.824816i	$0.308721\pi$
$648$	−1.00000	−0.0392837
$649$	5.51573	0.216511
$650$	0	0
$651$	−43.6872	−1.71224
$652$	0.317667	0.0124408
$653$	−16.1661	−0.632630	−0.316315	−	0.948654i	$-0.602446\pi$
$653$	−16.1661	−0.632630	−0.316315	+	0.948654i	$0.602446\pi$
$654$	−6.21983	−0.243215
$655$	5.19375	0.202937
$656$	7.60388	0.296881
$657$	−0.533188	−0.0208016
$658$	−7.20775	−0.280987
$659$	−16.3558	−0.637133	−0.318566	−	0.947901i	$-0.603201\pi$
$659$	−16.3558	−0.637133	−0.318566	+	0.947901i	$0.603201\pi$
$660$	−0.325437	−0.0126676
$661$	−33.1159	−1.28806	−0.644029	−	0.765001i	$-0.722739\pi$
$661$	−33.1159	−1.28806	−0.644029	+	0.765001i	$0.722739\pi$
$662$	10.2392	0.397958
$663$	0	0
$664$	−6.49934	−0.252223
$665$	7.20775	0.279505
$666$	−0.615957	−0.0238679
$667$	72.3323	2.80072
$668$	−12.3612	−0.478269
$669$	−5.42758	−0.209843
$670$	−4.84654	−0.187238
$671$	−2.83579	−0.109474
$672$	4.04892	0.156190
$673$	−35.1540	−1.35509	−0.677544	−	0.735482i	$-0.736956\pi$
$673$	−35.1540	−1.35509	−0.677544	+	0.735482i	$0.736956\pi$
$674$	−1.44935	−0.0558270
$675$	−4.87263	−0.187547
$676$	0	0
$677$	23.7855	0.914153	0.457076	−	0.889427i	$-0.348897\pi$
$677$	23.7855	0.914153	0.457076	+	0.889427i	$0.348897\pi$
$678$	−12.9879	−0.498798
$679$	−7.93900	−0.304671
$680$	−0.748709	−0.0287117
$681$	−16.5767	−0.635222
$682$	−9.83877	−0.376746
$683$	2.99223	0.114495	0.0572473	−	0.998360i	$-0.481768\pi$
$683$	2.99223	0.114495	0.0572473	+	0.998360i	$0.481768\pi$
$684$	4.98792	0.190718
$685$	−5.49742	−0.210046
$686$	9.69202	0.370043
$687$	23.8780	0.911003
$688$	−6.27413	−0.239199
$689$	0	0
$690$	3.03146	0.115406
$691$	11.6233	0.442169	0.221085	−	0.975255i	$-0.429040\pi$
$691$	11.6233	0.442169	0.221085	+	0.975255i	$0.429040\pi$
$692$	−17.0640	−0.648675
$693$	−3.69202	−0.140248
$694$	−6.84117	−0.259687
$695$	−0.968541	−0.0367389
$696$	−8.51573	−0.322788
$697$	−15.9517	−0.604213
$698$	−34.3370	−1.29968
$699$	13.9952	0.529348
$700$	19.7289	0.745681
$701$	−33.8431	−1.27824	−0.639118	−	0.769109i	$-0.720700\pi$
$701$	−33.8431	−1.27824	−0.639118	+	0.769109i	$0.720700\pi$
$702$	0	0
$703$	3.07234	0.115876
$704$	0.911854	0.0343668
$705$	0.635334	0.0239281
$706$	26.0495	0.980386
$707$	−28.2717	−1.06327
$708$	6.04892	0.227332
$709$	−26.1909	−0.983619	−0.491810	−	0.870703i	$-0.663664\pi$
$709$	−26.1909	−0.983619	−0.491810	+	0.870703i	$0.663664\pi$
$710$	−4.09783	−0.153789
$711$	−11.7071	−0.439050
$712$	−6.49396	−0.243371
$713$	91.6486	3.43227
$714$	−8.49396	−0.317878
$715$	0	0
$716$	−24.9681	−0.933100
$717$	−13.2862	−0.496183
$718$	8.49396	0.316992
$719$	−21.7345	−0.810560	−0.405280	−	0.914193i	$-0.632826\pi$
$719$	−21.7345	−0.810560	−0.405280	+	0.914193i	$0.632826\pi$
$720$	−0.356896	−0.0133007
$721$	−20.0368	−0.746211
$722$	−5.87933	−0.218806
$723$	−10.4789	−0.389714
$724$	5.26205	0.195562
$725$	−41.4940	−1.54105
$726$	10.1685	0.377389
$727$	−2.01400	−0.0746951	−0.0373476	−	0.999302i	$-0.511891\pi$
$727$	−2.01400	−0.0746951	−0.0373476	+	0.999302i	$0.511891\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.190293	−0.00704304
$731$	13.1621	0.486817
$732$	−3.10992	−0.114946
$733$	13.5013	0.498680	0.249340	−	0.968416i	$-0.419786\pi$
$733$	13.5013	0.498680	0.249340	+	0.968416i	$0.419786\pi$
$734$	−27.4523	−1.01328
$735$	−3.35258	−0.123662
$736$	−8.49396	−0.313091
$737$	−12.3827	−0.456123
$738$	−7.60388	−0.279903
$739$	−16.5918	−0.610339	−0.305170	−	0.952298i	$-0.598713\pi$
$739$	−16.5918	−0.610339	−0.305170	+	0.952298i	$0.598713\pi$
$740$	−0.219833	−0.00808120
$741$	0	0
$742$	42.1540	1.54752
$743$	−19.8479	−0.728148	−0.364074	−	0.931370i	$-0.618614\pi$
$743$	−19.8479	−0.728148	−0.364074	+	0.931370i	$0.618614\pi$
$744$	−10.7899	−0.395575
$745$	−5.25906	−0.192677
$746$	−26.6219	−0.974698
$747$	6.49934	0.237798
$748$	−1.91292	−0.0699432
$749$	17.2838	0.631537
$750$	−3.52350	−0.128660
$751$	27.9347	1.01935	0.509676	−	0.860367i	$-0.329765\pi$
$751$	27.9347	1.01935	0.509676	+	0.860367i	$0.329765\pi$
$752$	−1.78017	−0.0649160
$753$	3.48725	0.127083
$754$	0	0
$755$	−5.64656	−0.205499
$756$	−4.04892	−0.147258
$757$	−0.548253	−0.0199266	−0.00996330	−	0.999950i	$-0.503171\pi$
$757$	−0.548253	−0.0199266	−0.00996330	+	0.999950i	$0.503171\pi$
$758$	11.6474	0.423053
$759$	7.74525	0.281135
$760$	1.78017	0.0645735
$761$	1.97584	0.0716240	0.0358120	−	0.999359i	$-0.488598\pi$
$761$	1.97584	0.0716240	0.0358120	+	0.999359i	$0.488598\pi$
$762$	−9.22282	−0.334107
$763$	−25.1836	−0.911707
$764$	10.5375	0.381233
$765$	0.748709	0.0270696
$766$	10.5181	0.380035
$767$	0	0
$768$	1.00000	0.0360844
$769$	28.6112	1.03175	0.515873	−	0.856665i	$-0.327468\pi$
$769$	28.6112	1.03175	0.515873	+	0.856665i	$0.327468\pi$
$770$	−1.31767	−0.0474854
$771$	6.53750	0.235442
$772$	−3.42758	−0.123361
$773$	52.5080	1.88858	0.944290	−	0.329114i	$-0.106750\pi$
$773$	52.5080	1.88858	0.944290	+	0.329114i	$0.106750\pi$
$774$	6.27413	0.225519
$775$	−52.5749	−1.88855
$776$	−1.96077	−0.0703876
$777$	−2.49396	−0.0894703
$778$	9.25965	0.331975
$779$	37.9275	1.35889
$780$	0	0
$781$	−10.4698	−0.374639
$782$	17.8189	0.637203
$783$	8.51573	0.304327
$784$	9.39373	0.335490
$785$	1.52542	0.0544445
$786$	14.5526	0.519073
$787$	23.6426	0.842769	0.421384	−	0.906882i	$-0.361544\pi$
$787$	23.6426	0.842769	0.421384	+	0.906882i	$0.361544\pi$
$788$	−3.77479	−0.134471
$789$	8.01938	0.285497
$790$	−4.17821	−0.148654
$791$	−52.5870	−1.86978
$792$	−0.911854	−0.0324013
$793$	0	0
$794$	14.5133	0.515059
$795$	−3.71571	−0.131783
$796$	17.9541	0.636365
$797$	41.6558	1.47552	0.737762	−	0.675061i	$-0.235883\pi$
$797$	41.6558	1.47552	0.737762	+	0.675061i	$0.235883\pi$
$798$	20.1957	0.714919
$799$	3.73450	0.132117
$800$	4.87263	0.172273
$801$	6.49396	0.229453
$802$	−38.8418	−1.37155
$803$	−0.486189	−0.0171573
$804$	−13.5797	−0.478920
$805$	12.2741	0.432606
$806$	0	0
$807$	−27.6732	−0.974144
$808$	−6.98254	−0.245645
$809$	−44.2392	−1.55537	−0.777684	−	0.628656i	$-0.783606\pi$
$809$	−44.2392	−1.55537	−0.777684	+	0.628656i	$0.783606\pi$
$810$	0.356896	0.0125400
$811$	−52.3913	−1.83971	−0.919854	−	0.392260i	$-0.871693\pi$
$811$	−52.3913	−1.83971	−0.919854	+	0.392260i	$0.871693\pi$
$812$	−34.4795	−1.20999
$813$	−14.7289	−0.516564
$814$	−0.561663	−0.0196863
$815$	−0.113374	−0.00397132
$816$	−2.09783	−0.0734389
$817$	−31.2948	−1.09487
$818$	33.9221	1.18606
$819$	0	0
$820$	−2.71379	−0.0947697
$821$	25.6276	0.894408	0.447204	−	0.894432i	$-0.352420\pi$
$821$	25.6276	0.894408	0.447204	+	0.894432i	$0.352420\pi$
$822$	−15.4034	−0.537256
$823$	−40.2553	−1.40321	−0.701606	−	0.712565i	$-0.747534\pi$
$823$	−40.2553	−1.40321	−0.701606	+	0.712565i	$0.747534\pi$
$824$	−4.94869	−0.172396
$825$	−4.44312	−0.154690
$826$	24.4916	0.852171
$827$	18.0519	0.627726	0.313863	−	0.949468i	$-0.398377\pi$
$827$	18.0519	0.627726	0.313863	+	0.949468i	$0.398377\pi$
$828$	8.49396	0.295185
$829$	22.6655	0.787204	0.393602	−	0.919281i	$-0.371229\pi$
$829$	22.6655	0.787204	0.393602	+	0.919281i	$0.371229\pi$
$830$	2.31959	0.0805140
$831$	3.26205	0.113159
$832$	0	0
$833$	−19.7065	−0.682790
$834$	−2.71379	−0.0939709
$835$	4.41166	0.152672
$836$	4.54825	0.157305
$837$	10.7899	0.372952
$838$	−0.955395	−0.0330036
$839$	−22.0823	−0.762365	−0.381183	−	0.924500i	$-0.624483\pi$
$839$	−22.0823	−0.762365	−0.381183	+	0.924500i	$0.624483\pi$
$840$	−1.44504	−0.0498587
$841$	43.5176	1.50061
$842$	5.68233	0.195826
$843$	−7.72587	−0.266093
$844$	−12.5375	−0.431559
$845$	0	0
$846$	1.78017	0.0612034
$847$	41.1715	1.41467
$848$	10.4112	0.357522
$849$	−19.7802	−0.678854
$850$	−10.2220	−0.350610
$851$	5.23191	0.179348
$852$	−11.4819	−0.393363
$853$	−28.9831	−0.992364	−0.496182	−	0.868219i	$-0.665265\pi$
$853$	−28.9831	−0.992364	−0.496182	+	0.868219i	$0.665265\pi$
$854$	−12.5918	−0.430882
$855$	−1.78017	−0.0608804
$856$	4.26875	0.145903
$857$	−42.9047	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$857$	−42.9047	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$858$	0	0
$859$	−47.0616	−1.60572	−0.802860	−	0.596167i	$-0.796690\pi$
$859$	−47.0616	−1.60572	−0.802860	+	0.596167i	$0.796690\pi$
$860$	2.23921	0.0763564
$861$	−30.7875	−1.04923
$862$	14.8465	0.505675
$863$	−42.6064	−1.45034	−0.725169	−	0.688571i	$-0.758238\pi$
$863$	−42.6064	−1.45034	−0.725169	+	0.688571i	$0.758238\pi$
$864$	−1.00000	−0.0340207
$865$	6.09006	0.207068
$866$	26.1497	0.888604
$867$	−12.5991	−0.427888
$868$	−43.6872	−1.48284
$869$	−10.6752	−0.362130
$870$	3.03923	0.103040
$871$	0	0
$872$	−6.21983	−0.210630
$873$	1.96077	0.0663621
$874$	−42.3672	−1.43309
$875$	−14.2664	−0.482291
$876$	−0.533188	−0.0180147
$877$	27.4082	0.925509	0.462755	−	0.886486i	$-0.346861\pi$
$877$	27.4082	0.925509	0.462755	+	0.886486i	$0.346861\pi$
$878$	23.5502	0.794780
$879$	12.9119	0.435506
$880$	−0.325437	−0.0109705
$881$	24.3177	0.819283	0.409642	−	0.912247i	$-0.365654\pi$
$881$	24.3177	0.819283	0.409642	+	0.912247i	$0.365654\pi$
$882$	−9.39373	−0.316303
$883$	−32.2306	−1.08465	−0.542323	−	0.840170i	$-0.682455\pi$
$883$	−32.2306	−1.08465	−0.542323	+	0.840170i	$0.682455\pi$
$884$	0	0
$885$	−2.15883	−0.0725684
$886$	−21.9433	−0.737200
$887$	−35.1642	−1.18070	−0.590349	−	0.807148i	$-0.701010\pi$
$887$	−35.1642	−1.18070	−0.590349	+	0.807148i	$0.701010\pi$
$888$	−0.615957	−0.0206702
$889$	−37.3424	−1.25242
$890$	2.31767	0.0776884
$891$	0.911854	0.0305483
$892$	−5.42758	−0.181729
$893$	−8.87933	−0.297135
$894$	−14.7356	−0.492831
$895$	8.91100	0.297862
$896$	4.04892	0.135265
$897$	0	0
$898$	−11.4034	−0.380537
$899$	91.8835	3.06449
$900$	−4.87263	−0.162421
$901$	−21.8410	−0.727628
$902$	−6.93362	−0.230864
$903$	25.4034	0.845373
$904$	−12.9879	−0.431972
$905$	−1.87800	−0.0624269
$906$	−15.8213	−0.525628
$907$	−13.1207	−0.435665	−0.217832	−	0.975986i	$-0.569899\pi$
$907$	−13.1207	−0.435665	−0.217832	+	0.975986i	$0.569899\pi$
$908$	−16.5767	−0.550118
$909$	6.98254	0.231596
$910$	0	0
$911$	45.7453	1.51561	0.757804	−	0.652482i	$-0.226272\pi$
$911$	45.7453	1.51561	0.757804	+	0.652482i	$0.226272\pi$
$912$	4.98792	0.165166
$913$	5.92645	0.196137
$914$	−7.66919	−0.253674
$915$	1.10992	0.0366927
$916$	23.8780	0.788951
$917$	58.9221	1.94578
$918$	2.09783	0.0692389
$919$	17.9849	0.593268	0.296634	−	0.954991i	$-0.404136\pi$
$919$	17.9849	0.593268	0.296634	+	0.954991i	$0.404136\pi$
$920$	3.03146	0.0999442
$921$	−19.9651	−0.657872
$922$	28.5080	0.938860
$923$	0	0
$924$	−3.69202	−0.121459
$925$	−3.00133	−0.0986831
$926$	14.3284	0.470861
$927$	4.94869	0.162536
$928$	−8.51573	−0.279543
$929$	31.6883	1.03966	0.519830	−	0.854270i	$-0.325995\pi$
$929$	31.6883	1.03966	0.519830	+	0.854270i	$0.325995\pi$
$930$	3.85086	0.126275
$931$	46.8552	1.53562
$932$	13.9952	0.458428
$933$	13.4819	0.441377
$934$	−33.3207	−1.09029
$935$	0.682713	0.0223271
$936$	0	0
$937$	−53.0484	−1.73302	−0.866509	−	0.499162i	$-0.833641\pi$
$937$	−53.0484	−1.73302	−0.866509	+	0.499162i	$0.833641\pi$
$938$	−54.9831	−1.79526
$939$	12.9245	0.421776
$940$	0.635334	0.0207223
$941$	21.9433	0.715332	0.357666	−	0.933850i	$-0.383573\pi$
$941$	21.9433	0.715332	0.357666	+	0.933850i	$0.383573\pi$
$942$	4.27413	0.139259
$943$	64.5870	2.10324
$944$	6.04892	0.196875
$945$	1.44504	0.0470072
$946$	5.72109	0.186009
$947$	12.2241	0.397231	0.198616	−	0.980077i	$-0.436355\pi$
$947$	12.2241	0.397231	0.198616	+	0.980077i	$0.436355\pi$
$948$	−11.7071	−0.380229
$949$	0	0
$950$	24.3043	0.788534
$951$	11.8726	0.384996
$952$	−8.49396	−0.275291
$953$	−3.85862	−0.124993	−0.0624966	−	0.998045i	$-0.519906\pi$
$953$	−3.85862	−0.124993	−0.0624966	+	0.998045i	$0.519906\pi$
$954$	−10.4112	−0.337075
$955$	−3.76079	−0.121696
$956$	−13.2862	−0.429707
$957$	7.76510	0.251010
$958$	22.1280	0.714922
$959$	−62.3672	−2.01394
$960$	−0.356896	−0.0115188
$961$	85.4210	2.75552
$962$	0	0
$963$	−4.26875	−0.137559
$964$	−10.4789	−0.337502
$965$	1.22329	0.0393791
$966$	34.3913	1.10652
$967$	−0.613564	−0.0197309	−0.00986545	−	0.999951i	$-0.503140\pi$
$967$	−0.613564	−0.0197309	−0.00986545	+	0.999951i	$0.503140\pi$
$968$	10.1685	0.326829
$969$	−10.4638	−0.336147
$970$	0.699791	0.0224689
$971$	−12.9769	−0.416449	−0.208224	−	0.978081i	$-0.566768\pi$
$971$	−12.9769	−0.416449	−0.208224	+	0.978081i	$0.566768\pi$
$972$	1.00000	0.0320750
$973$	−10.9879	−0.352256
$974$	0.126310	0.00404722
$975$	0	0
$976$	−3.10992	−0.0995460
$977$	−37.0616	−1.18571	−0.592853	−	0.805311i	$-0.701998\pi$
$977$	−37.0616	−1.18571	−0.592853	+	0.805311i	$0.701998\pi$
$978$	−0.317667	−0.0101579
$979$	5.92154	0.189253
$980$	−3.35258	−0.107094
$981$	6.21983	0.198584
$982$	−13.9433	−0.444949
$983$	−14.1193	−0.450337	−0.225169	−	0.974320i	$-0.572293\pi$
$983$	−14.1193	−0.450337	−0.225169	+	0.974320i	$0.572293\pi$
$984$	−7.60388	−0.242403
$985$	1.34721	0.0429256
$986$	17.8646	0.568925
$987$	7.20775	0.229425
$988$	0	0
$989$	−53.2922	−1.69459
$990$	0.325437	0.0103431
$991$	28.5392	0.906576	0.453288	−	0.891364i	$-0.350251\pi$
$991$	28.5392	0.906576	0.453288	+	0.891364i	$0.350251\pi$
$992$	−10.7899	−0.342578
$993$	−10.2392	−0.324932
$994$	−46.4892	−1.47455
$995$	−6.40773	−0.203139
$996$	6.49934	0.205939
$997$	−18.8853	−0.598103	−0.299052	−	0.954237i	$-0.596670\pi$
$997$	−18.8853	−0.598103	−0.299052	+	0.954237i	$0.596670\pi$
$998$	−28.3913	−0.898712
$999$	0.615957	0.0194880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.a.m.1.2	✓	3
3.2	odd	2		3042.2.a.be.1.2		3
4.3	odd	2		8112.2.a.ce.1.2		3
13.2	odd	12		1014.2.i.g.823.2		12
13.3	even	3		1014.2.e.m.529.2		6
13.4	even	6		1014.2.e.k.991.2		6
13.5	odd	4		1014.2.b.g.337.5		6
13.6	odd	12		1014.2.i.g.361.5		12
13.7	odd	12		1014.2.i.g.361.2		12
13.8	odd	4		1014.2.b.g.337.2		6
13.9	even	3		1014.2.e.m.991.2		6
13.10	even	6		1014.2.e.k.529.2		6
13.11	odd	12		1014.2.i.g.823.5		12
13.12	even	2		1014.2.a.o.1.2	yes	3
39.5	even	4		3042.2.b.r.1351.2		6
39.8	even	4		3042.2.b.r.1351.5		6
39.38	odd	2		3042.2.a.bd.1.2		3
52.51	odd	2		8112.2.a.bz.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.m.1.2	✓	3	1.1	even	1	trivial
1014.2.a.o.1.2	yes	3	13.12	even	2
1014.2.b.g.337.2		6	13.8	odd	4
1014.2.b.g.337.5		6	13.5	odd	4
1014.2.e.k.529.2		6	13.10	even	6
1014.2.e.k.991.2		6	13.4	even	6
1014.2.e.m.529.2		6	13.3	even	3
1014.2.e.m.991.2		6	13.9	even	3
1014.2.i.g.361.2		12	13.7	odd	12
1014.2.i.g.361.5		12	13.6	odd	12
1014.2.i.g.823.2		12	13.2	odd	12
1014.2.i.g.823.5		12	13.11	odd	12
3042.2.a.bd.1.2		3	39.38	odd	2
3042.2.a.be.1.2		3	3.2	odd	2
3042.2.b.r.1351.2		6	39.5	even	4
3042.2.b.r.1351.5		6	39.8	even	4
8112.2.a.bz.1.2		3	52.51	odd	2
8112.2.a.ce.1.2		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.356896 q^{5} -1.00000 q^{6} -4.04892 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.356896 q^{5} -1.00000 q^{6} -4.04892 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.356896 q^{10} +0.911854 q^{11} +1.00000 q^{12} +4.04892 q^{14} -0.356896 q^{15} +1.00000 q^{16} -2.09783 q^{17} -1.00000 q^{18} +4.98792 q^{19} -0.356896 q^{20} -4.04892 q^{21} -0.911854 q^{22} +8.49396 q^{23} -1.00000 q^{24} -4.87263 q^{25} +1.00000 q^{27} -4.04892 q^{28} +8.51573 q^{29} +0.356896 q^{30} +10.7899 q^{31} -1.00000 q^{32} +0.911854 q^{33} +2.09783 q^{34} +1.44504 q^{35} +1.00000 q^{36} +0.615957 q^{37} -4.98792 q^{38} +0.356896 q^{40} +7.60388 q^{41} +4.04892 q^{42} -6.27413 q^{43} +0.911854 q^{44} -0.356896 q^{45} -8.49396 q^{46} -1.78017 q^{47} +1.00000 q^{48} +9.39373 q^{49} +4.87263 q^{50} -2.09783 q^{51} +10.4112 q^{53} -1.00000 q^{54} -0.325437 q^{55} +4.04892 q^{56} +4.98792 q^{57} -8.51573 q^{58} +6.04892 q^{59} -0.356896 q^{60} -3.10992 q^{61} -10.7899 q^{62} -4.04892 q^{63} +1.00000 q^{64} -0.911854 q^{66} -13.5797 q^{67} -2.09783 q^{68} +8.49396 q^{69} -1.44504 q^{70} -11.4819 q^{71} -1.00000 q^{72} -0.533188 q^{73} -0.615957 q^{74} -4.87263 q^{75} +4.98792 q^{76} -3.69202 q^{77} -11.7071 q^{79} -0.356896 q^{80} +1.00000 q^{81} -7.60388 q^{82} +6.49934 q^{83} -4.04892 q^{84} +0.748709 q^{85} +6.27413 q^{86} +8.51573 q^{87} -0.911854 q^{88} +6.49396 q^{89} +0.356896 q^{90} +8.49396 q^{92} +10.7899 q^{93} +1.78017 q^{94} -1.78017 q^{95} -1.00000 q^{96} +1.96077 q^{97} -9.39373 q^{98} +0.911854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - q^{11} + 3 q^{12} + 3 q^{14} + 3 q^{15} + 3 q^{16} + 12 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} - 3 q^{21} + q^{22} + 16 q^{23} - 3 q^{24} + 2 q^{25} + 3 q^{27} - 3 q^{28} + 13 q^{29} - 3 q^{30} + 9 q^{31} - 3 q^{32} - q^{33} - 12 q^{34} + 4 q^{35} + 3 q^{36} + 12 q^{37} + 4 q^{38} - 3 q^{40} + 14 q^{41} + 3 q^{42} - 8 q^{43} - q^{44} + 3 q^{45} - 16 q^{46} - 4 q^{47} + 3 q^{48} - 4 q^{49} - 2 q^{50} + 12 q^{51} + 15 q^{53} - 3 q^{54} - 22 q^{55} + 3 q^{56} - 4 q^{57} - 13 q^{58} + 9 q^{59} + 3 q^{60} - 10 q^{61} - 9 q^{62} - 3 q^{63} + 3 q^{64} + q^{66} + 6 q^{67} + 12 q^{68} + 16 q^{69} - 4 q^{70} - 6 q^{71} - 3 q^{72} - 5 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 6 q^{77} - 5 q^{79} + 3 q^{80} + 3 q^{81} - 14 q^{82} + 7 q^{83} - 3 q^{84} + 26 q^{85} + 8 q^{86} + 13 q^{87} + q^{88} + 10 q^{89} - 3 q^{90} + 16 q^{92} + 9 q^{93} + 4 q^{94} - 4 q^{95} - 3 q^{96} - 7 q^{97} + 4 q^{98} - q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - q^11 + 3 * q^12 + 3 * q^14 + 3 * q^15 + 3 * q^16 + 12 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 - 3 * q^21 + q^22 + 16 * q^23 - 3 * q^24 + 2 * q^25 + 3 * q^27 - 3 * q^28 + 13 * q^29 - 3 * q^30 + 9 * q^31 - 3 * q^32 - q^33 - 12 * q^34 + 4 * q^35 + 3 * q^36 + 12 * q^37 + 4 * q^38 - 3 * q^40 + 14 * q^41 + 3 * q^42 - 8 * q^43 - q^44 + 3 * q^45 - 16 * q^46 - 4 * q^47 + 3 * q^48 - 4 * q^49 - 2 * q^50 + 12 * q^51 + 15 * q^53 - 3 * q^54 - 22 * q^55 + 3 * q^56 - 4 * q^57 - 13 * q^58 + 9 * q^59 + 3 * q^60 - 10 * q^61 - 9 * q^62 - 3 * q^63 + 3 * q^64 + q^66 + 6 * q^67 + 12 * q^68 + 16 * q^69 - 4 * q^70 - 6 * q^71 - 3 * q^72 - 5 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 6 * q^77 - 5 * q^79 + 3 * q^80 + 3 * q^81 - 14 * q^82 + 7 * q^83 - 3 * q^84 + 26 * q^85 + 8 * q^86 + 13 * q^87 + q^88 + 10 * q^89 - 3 * q^90 + 16 * q^92 + 9 * q^93 + 4 * q^94 - 4 * q^95 - 3 * q^96 - 7 * q^97 + 4 * q^98 - q^99

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