LMFDB - Embedded newform 2738.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.37902897.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 15x^{4} - x^{3} + 60x^{2} - 64 $ x^6 - 15x^4 - x^3 + 60x^2 - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.14945$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.14945 q^{3} +1.00000 q^{4} +1.53209 q^{5} -3.14945 q^{6} -4.82524 q^{7} +1.00000 q^{8} +6.91903 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.14945 q^{3} +1.00000 q^{4} +1.53209 q^{5} -3.14945 q^{6} -4.82524 q^{7} +1.00000 q^{8} +6.91903 q^{9} +1.53209 q^{10} -1.09379 q^{11} -3.14945 q^{12} +1.76958 q^{13} -4.82524 q^{14} -4.82524 q^{15} +1.00000 q^{16} +2.94585 q^{17} +6.91903 q^{18} -0.825235 q^{19} +1.53209 q^{20} +15.1968 q^{21} -1.09379 q^{22} -0.243241 q^{23} -3.14945 q^{24} -2.65270 q^{25} +1.76958 q^{26} -12.3428 q^{27} -4.82524 q^{28} -5.57173 q^{29} -4.82524 q^{30} -5.73495 q^{31} +1.00000 q^{32} +3.44484 q^{33} +2.94585 q^{34} -7.39269 q^{35} +6.91903 q^{36} -0.825235 q^{38} -5.57320 q^{39} +1.53209 q^{40} +2.91194 q^{41} +15.1968 q^{42} +4.37987 q^{43} -1.09379 q^{44} +10.6006 q^{45} -0.243241 q^{46} +2.26498 q^{47} -3.14945 q^{48} +16.2829 q^{49} -2.65270 q^{50} -9.27780 q^{51} +1.76958 q^{52} +6.14945 q^{53} -12.3428 q^{54} -1.67579 q^{55} -4.82524 q^{56} +2.59904 q^{57} -5.57173 q^{58} +8.82524 q^{59} -4.82524 q^{60} -11.7522 q^{61} -5.73495 q^{62} -33.3859 q^{63} +1.00000 q^{64} +2.71115 q^{65} +3.44484 q^{66} +8.98400 q^{67} +2.94585 q^{68} +0.766075 q^{69} -7.39269 q^{70} -1.21864 q^{71} +6.91903 q^{72} +8.79418 q^{73} +8.35455 q^{75} -0.825235 q^{76} +5.27780 q^{77} -5.57320 q^{78} +2.15367 q^{79} +1.53209 q^{80} +18.1159 q^{81} +2.91194 q^{82} +5.09379 q^{83} +15.1968 q^{84} +4.51330 q^{85} +4.37987 q^{86} +17.5479 q^{87} -1.09379 q^{88} +8.97619 q^{89} +10.6006 q^{90} -8.53863 q^{91} -0.243241 q^{92} +18.0619 q^{93} +2.26498 q^{94} -1.26433 q^{95} -3.14945 q^{96} +4.35907 q^{97} +16.2829 q^{98} -7.56798 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 3 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^7 + 6 * q^8 + 12 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - 3 q^{7} + 6 q^{8} + 12 q^{9} - 3 q^{11} - 3 q^{14} - 3 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} + 21 q^{19} + 6 q^{21} - 3 q^{22} + 21 q^{23} - 18 q^{25} - 3 q^{27} - 3 q^{28} - 6 q^{29} - 3 q^{30} + 21 q^{31} + 6 q^{32} - 3 q^{33} + 3 q^{34} - 3 q^{35} + 12 q^{36} + 21 q^{38} + 27 q^{39} + 18 q^{41} + 6 q^{42} + 18 q^{43} - 3 q^{44} + 6 q^{45} + 21 q^{46} - 9 q^{47} + 15 q^{49} - 18 q^{50} + 18 q^{53} - 3 q^{54} - 3 q^{55} - 3 q^{56} + 6 q^{57} - 6 q^{58} + 27 q^{59} - 3 q^{60} - 24 q^{61} + 21 q^{62} - 36 q^{63} + 6 q^{64} + 3 q^{65} - 3 q^{66} + 9 q^{67} + 3 q^{68} + 27 q^{69} - 3 q^{70} + 12 q^{72} + 27 q^{73} - 3 q^{75} + 21 q^{76} - 24 q^{77} + 27 q^{78} + 21 q^{79} - 6 q^{81} + 18 q^{82} + 27 q^{83} + 6 q^{84} - 3 q^{85} + 18 q^{86} - 3 q^{88} - 21 q^{89} + 6 q^{90} - 24 q^{91} + 21 q^{92} + 54 q^{93} - 9 q^{94} - 3 q^{95} + 42 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^7 + 6 * q^8 + 12 * q^9 - 3 * q^11 - 3 * q^14 - 3 * q^15 + 6 * q^16 + 3 * q^17 + 12 * q^18 + 21 * q^19 + 6 * q^21 - 3 * q^22 + 21 * q^23 - 18 * q^25 - 3 * q^27 - 3 * q^28 - 6 * q^29 - 3 * q^30 + 21 * q^31 + 6 * q^32 - 3 * q^33 + 3 * q^34 - 3 * q^35 + 12 * q^36 + 21 * q^38 + 27 * q^39 + 18 * q^41 + 6 * q^42 + 18 * q^43 - 3 * q^44 + 6 * q^45 + 21 * q^46 - 9 * q^47 + 15 * q^49 - 18 * q^50 + 18 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 + 6 * q^57 - 6 * q^58 + 27 * q^59 - 3 * q^60 - 24 * q^61 + 21 * q^62 - 36 * q^63 + 6 * q^64 + 3 * q^65 - 3 * q^66 + 9 * q^67 + 3 * q^68 + 27 * q^69 - 3 * q^70 + 12 * q^72 + 27 * q^73 - 3 * q^75 + 21 * q^76 - 24 * q^77 + 27 * q^78 + 21 * q^79 - 6 * q^81 + 18 * q^82 + 27 * q^83 + 6 * q^84 - 3 * q^85 + 18 * q^86 - 3 * q^88 - 21 * q^89 + 6 * q^90 - 24 * q^91 + 21 * q^92 + 54 * q^93 - 9 * q^94 - 3 * q^95 + 42 * q^97 + 15 * q^98 - 36 * 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
$3$	−3.14945	−1.81834	−0.909168	−	0.416431i	$-0.863281\pi$
$3$	−3.14945	−1.81834	−0.909168	+	0.416431i	$0.863281\pi$
$4$	1.00000	0.500000
$5$	1.53209	0.685171	0.342585	−	0.939487i	$-0.388697\pi$
$5$	1.53209	0.685171	0.342585	+	0.939487i	$0.388697\pi$
$6$	−3.14945	−1.28576
$7$	−4.82524	−1.82377	−0.911884	−	0.410448i	$-0.865372\pi$
$7$	−4.82524	−1.82377	−0.911884	+	0.410448i	$0.865372\pi$
$8$	1.00000	0.353553
$9$	6.91903	2.30634
$10$	1.53209	0.484489
$11$	−1.09379	−0.329791	−0.164895	−	0.986311i	$-0.552729\pi$
$11$	−1.09379	−0.329791	−0.164895	+	0.986311i	$0.552729\pi$
$12$	−3.14945	−0.909168
$13$	1.76958	0.490793	0.245396	−	0.969423i	$-0.421082\pi$
$13$	1.76958	0.490793	0.245396	+	0.969423i	$0.421082\pi$
$14$	−4.82524	−1.28960
$15$	−4.82524	−1.24587
$16$	1.00000	0.250000
$17$	2.94585	0.714474	0.357237	−	0.934014i	$-0.383719\pi$
$17$	2.94585	0.714474	0.357237	+	0.934014i	$0.383719\pi$
$18$	6.91903	1.63083
$19$	−0.825235	−0.189322	−0.0946610	−	0.995510i	$-0.530177\pi$
$19$	−0.825235	−0.189322	−0.0946610	+	0.995510i	$0.530177\pi$
$20$	1.53209	0.342585
$21$	15.1968	3.31622
$22$	−1.09379	−0.233197
$23$	−0.243241	−0.0507192	−0.0253596	−	0.999678i	$-0.508073\pi$
$23$	−0.243241	−0.0507192	−0.0253596	+	0.999678i	$0.508073\pi$
$24$	−3.14945	−0.642879
$25$	−2.65270	−0.530541
$26$	1.76958	0.347043
$27$	−12.3428	−2.37537
$28$	−4.82524	−0.911884
$29$	−5.57173	−1.03464	−0.517322	−	0.855791i	$-0.673071\pi$
$29$	−5.57173	−1.03464	−0.517322	+	0.855791i	$0.673071\pi$
$30$	−4.82524	−0.880963
$31$	−5.73495	−1.03003	−0.515013	−	0.857182i	$-0.672213\pi$
$31$	−5.73495	−1.03003	−0.515013	+	0.857182i	$0.672213\pi$
$32$	1.00000	0.176777
$33$	3.44484	0.599670
$34$	2.94585	0.505209
$35$	−7.39269	−1.24959
$36$	6.91903	1.15317
$37$	0	0
$37$	0	0
$38$	−0.825235	−0.133871
$39$	−5.57320	−0.892426
$40$	1.53209	0.242245
$41$	2.91194	0.454768	0.227384	−	0.973805i	$-0.426983\pi$
$41$	2.91194	0.454768	0.227384	+	0.973805i	$0.426983\pi$
$42$	15.1968	2.34492
$43$	4.37987	0.667924	0.333962	−	0.942587i	$-0.391614\pi$
$43$	4.37987	0.667924	0.333962	+	0.942587i	$0.391614\pi$
$44$	−1.09379	−0.164895
$45$	10.6006	1.58024
$46$	−0.243241	−0.0358639
$47$	2.26498	0.330382	0.165191	−	0.986262i	$-0.447176\pi$
$47$	2.26498	0.330382	0.165191	+	0.986262i	$0.447176\pi$
$48$	−3.14945	−0.454584
$49$	16.2829	2.32613
$50$	−2.65270	−0.375149
$51$	−9.27780	−1.29915
$52$	1.76958	0.245396
$53$	6.14945	0.844692	0.422346	−	0.906435i	$-0.361207\pi$
$53$	6.14945	0.844692	0.422346	+	0.906435i	$0.361207\pi$
$54$	−12.3428	−1.67964
$55$	−1.67579	−0.225963
$56$	−4.82524	−0.644799
$57$	2.59904	0.344251
$58$	−5.57173	−0.731604
$59$	8.82524	1.14895	0.574474	−	0.818523i	$-0.305207\pi$
$59$	8.82524	1.14895	0.574474	+	0.818523i	$0.305207\pi$
$60$	−4.82524	−0.622935
$61$	−11.7522	−1.50472	−0.752360	−	0.658752i	$-0.771085\pi$
$61$	−11.7522	−1.50472	−0.752360	+	0.658752i	$0.771085\pi$
$62$	−5.73495	−0.728339
$63$	−33.3859	−4.20623
$64$	1.00000	0.125000
$65$	2.71115	0.336277
$66$	3.44484	0.424031
$67$	8.98400	1.09757	0.548785	−	0.835963i	$-0.315091\pi$
$67$	8.98400	1.09757	0.548785	+	0.835963i	$0.315091\pi$
$68$	2.94585	0.357237
$69$	0.766075	0.0922245
$70$	−7.39269	−0.883595
$71$	−1.21864	−0.144626	−0.0723132	−	0.997382i	$-0.523038\pi$
$71$	−1.21864	−0.144626	−0.0723132	+	0.997382i	$0.523038\pi$
$72$	6.91903	0.815415
$73$	8.79418	1.02928	0.514640	−	0.857406i	$-0.327925\pi$
$73$	8.79418	1.02928	0.514640	+	0.857406i	$0.327925\pi$
$74$	0	0
$75$	8.35455	0.964701
$76$	−0.825235	−0.0946610
$77$	5.27780	0.601462
$78$	−5.57320	−0.631040
$79$	2.15367	0.242307	0.121153	−	0.992634i	$-0.461341\pi$
$79$	2.15367	0.242307	0.121153	+	0.992634i	$0.461341\pi$
$80$	1.53209	0.171293
$81$	18.1159	2.01287
$82$	2.91194	0.321570
$83$	5.09379	0.559116	0.279558	−	0.960129i	$-0.409812\pi$
$83$	5.09379	0.559116	0.279558	+	0.960129i	$0.409812\pi$
$84$	15.1968	1.65811
$85$	4.51330	0.489537
$86$	4.37987	0.472294
$87$	17.5479	1.88133
$88$	−1.09379	−0.116599
$89$	8.97619	0.951474	0.475737	−	0.879587i	$-0.342181\pi$
$89$	8.97619	0.951474	0.475737	+	0.879587i	$0.342181\pi$
$90$	10.6006	1.11740
$91$	−8.53863	−0.895092
$92$	−0.243241	−0.0253596
$93$	18.0619	1.87293
$94$	2.26498	0.233615
$95$	−1.26433	−0.129718
$96$	−3.14945	−0.321439
$97$	4.35907	0.442597	0.221298	−	0.975206i	$-0.428971\pi$
$97$	4.35907	0.442597	0.221298	+	0.975206i	$0.428971\pi$
$98$	16.2829	1.64482
$99$	−7.56798	−0.760610
$100$	−2.65270	−0.265270
$101$	−4.38889	−0.436711	−0.218355	−	0.975869i	$-0.570069\pi$
$101$	−4.38889	−0.436711	−0.218355	+	0.975869i	$0.570069\pi$
$102$	−9.27780	−0.918640
$103$	12.6452	1.24597	0.622987	−	0.782233i	$-0.285919\pi$
$103$	12.6452	1.24597	0.622987	+	0.782233i	$0.285919\pi$
$104$	1.76958	0.173521
$105$	23.2829	2.27218
$106$	6.14945	0.597287
$107$	18.8597	1.82323	0.911616	−	0.411042i	$-0.134835\pi$
$107$	18.8597	1.82323	0.911616	+	0.411042i	$0.134835\pi$
$108$	−12.3428	−1.18768
$109$	−8.41432	−0.805946	−0.402973	−	0.915212i	$-0.632023\pi$
$109$	−8.41432	−0.805946	−0.402973	+	0.915212i	$0.632023\pi$
$110$	−1.67579	−0.159780
$111$	0	0
$112$	−4.82524	−0.455942
$113$	−6.38461	−0.600614	−0.300307	−	0.953843i	$-0.597089\pi$
$113$	−6.38461	−0.600614	−0.300307	+	0.953843i	$0.597089\pi$
$114$	2.59904	0.243422
$115$	−0.372667	−0.0347513
$116$	−5.57173	−0.517322
$117$	12.2438	1.13194
$118$	8.82524	0.812429
$119$	−14.2144	−1.30303
$120$	−4.82524	−0.440482
$121$	−9.80362	−0.891238
$122$	−11.7522	−1.06400
$123$	−9.17100	−0.826921
$124$	−5.73495	−0.515013
$125$	−11.7246	−1.04868
$126$	−33.3859	−2.97426
$127$	−4.75254	−0.421719	−0.210860	−	0.977516i	$-0.567626\pi$
$127$	−4.75254	−0.421719	−0.210860	+	0.977516i	$0.567626\pi$
$128$	1.00000	0.0883883
$129$	−13.7942	−1.21451
$130$	2.71115	0.237784
$131$	17.9870	1.57153	0.785765	−	0.618525i	$-0.212270\pi$
$131$	17.9870	1.57153	0.785765	+	0.618525i	$0.212270\pi$
$132$	3.44484	0.299835
$133$	3.98196	0.345279
$134$	8.98400	0.776099
$135$	−18.9102	−1.62753
$136$	2.94585	0.252605
$137$	22.1091	1.88891	0.944456	−	0.328639i	$-0.106590\pi$
$137$	22.1091	1.88891	0.944456	+	0.328639i	$0.106590\pi$
$138$	0.766075	0.0652126
$139$	−2.66547	−0.226082	−0.113041	−	0.993590i	$-0.536059\pi$
$139$	−2.66547	−0.226082	−0.113041	+	0.993590i	$0.536059\pi$
$140$	−7.39269	−0.624796
$141$	−7.13345	−0.600745
$142$	−1.21864	−0.102266
$143$	−1.93555	−0.161859
$144$	6.91903	0.576586
$145$	−8.53639	−0.708908
$146$	8.79418	0.727811
$147$	−51.2822	−4.22968
$148$	0	0
$149$	6.13622	0.502699	0.251349	−	0.967896i	$-0.419126\pi$
$149$	6.13622	0.502699	0.251349	+	0.967896i	$0.419126\pi$
$150$	8.35455	0.682146
$151$	−0.436768	−0.0355437	−0.0177719	−	0.999842i	$-0.505657\pi$
$151$	−0.436768	−0.0355437	−0.0177719	+	0.999842i	$0.505657\pi$
$152$	−0.825235	−0.0669354
$153$	20.3824	1.64782
$154$	5.27780	0.425298
$155$	−8.78645	−0.705745
$156$	−5.57320	−0.446213
$157$	6.06139	0.483751	0.241876	−	0.970307i	$-0.422237\pi$
$157$	6.06139	0.483751	0.241876	+	0.970307i	$0.422237\pi$
$158$	2.15367	0.171337
$159$	−19.3674	−1.53593
$160$	1.53209	0.121122
$161$	1.17369	0.0925001
$162$	18.1159	1.42332
$163$	13.7349	1.07580	0.537902	−	0.843007i	$-0.319217\pi$
$163$	13.7349	1.07580	0.537902	+	0.843007i	$0.319217\pi$
$164$	2.91194	0.227384
$165$	5.27780	0.410877
$166$	5.09379	0.395355
$167$	23.8199	1.84324	0.921621	−	0.388091i	$-0.126865\pi$
$167$	23.8199	1.84324	0.921621	+	0.388091i	$0.126865\pi$
$168$	15.1968	1.17246
$169$	−9.86859	−0.759122
$170$	4.51330	0.346155
$171$	−5.70983	−0.436641
$172$	4.37987	0.333962
$173$	21.4452	1.63045	0.815223	−	0.579147i	$-0.196614\pi$
$173$	21.4452	1.63045	0.815223	+	0.579147i	$0.196614\pi$
$174$	17.5479	1.33030
$175$	12.7999	0.967583
$176$	−1.09379	−0.0824477
$177$	−27.7946	−2.08917
$178$	8.97619	0.672794
$179$	11.5247	0.861400	0.430700	−	0.902495i	$-0.358267\pi$
$179$	11.5247	0.861400	0.430700	+	0.902495i	$0.358267\pi$
$180$	10.6006	0.790119
$181$	−17.7689	−1.32075	−0.660374	−	0.750937i	$-0.729602\pi$
$181$	−17.7689	−1.32075	−0.660374	+	0.750937i	$0.729602\pi$
$182$	−8.53863	−0.632926
$183$	37.0131	2.73609
$184$	−0.243241	−0.0179320
$185$	0	0
$186$	18.0619	1.32436
$187$	−3.22215	−0.235627
$188$	2.26498	0.165191
$189$	59.5568	4.33212
$190$	−1.26433	−0.0917244
$191$	−25.9113	−1.87487	−0.937437	−	0.348155i	$-0.886808\pi$
$191$	−25.9113	−1.87487	−0.937437	+	0.348155i	$0.886808\pi$
$192$	−3.14945	−0.227292
$193$	10.9030	0.784813	0.392407	−	0.919792i	$-0.371643\pi$
$193$	10.9030	0.784813	0.392407	+	0.919792i	$0.371643\pi$
$194$	4.35907	0.312963
$195$	−8.53863	−0.611464
$196$	16.2829	1.16306
$197$	−6.44314	−0.459055	−0.229527	−	0.973302i	$-0.573718\pi$
$197$	−6.44314	−0.459055	−0.229527	+	0.973302i	$0.573718\pi$
$198$	−7.56798	−0.537833
$199$	18.8556	1.33664	0.668318	−	0.743876i	$-0.267014\pi$
$199$	18.8556	1.33664	0.668318	+	0.743876i	$0.267014\pi$
$200$	−2.65270	−0.187574
$201$	−28.2946	−1.99575
$202$	−4.38889	−0.308801
$203$	26.8849	1.88695
$204$	−9.27780	−0.649576
$205$	4.46135	0.311594
$206$	12.6452	0.881036
$207$	−1.68299	−0.116976
$208$	1.76958	0.122698
$209$	0.902636	0.0624366
$210$	23.2829	1.60667
$211$	−1.41450	−0.0973783	−0.0486891	−	0.998814i	$-0.515504\pi$
$211$	−1.41450	−0.0973783	−0.0486891	+	0.998814i	$0.515504\pi$
$212$	6.14945	0.422346
$213$	3.83806	0.262979
$214$	18.8597	1.28922
$215$	6.71035	0.457642
$216$	−12.3428	−0.839820
$217$	27.6725	1.87853
$218$	−8.41432	−0.569890
$219$	−27.6968	−1.87158
$220$	−1.67579	−0.112982
$221$	5.21291	0.350659
$222$	0	0
$223$	−12.1750	−0.815302	−0.407651	−	0.913138i	$-0.633652\pi$
$223$	−12.1750	−0.815302	−0.407651	+	0.913138i	$0.633652\pi$
$224$	−4.82524	−0.322400
$225$	−18.3541	−1.22361
$226$	−6.38461	−0.424698
$227$	−21.2999	−1.41373	−0.706863	−	0.707350i	$-0.749890\pi$
$227$	−21.2999	−1.41373	−0.706863	+	0.707350i	$0.749890\pi$
$228$	2.59904	0.172125
$229$	−2.84960	−0.188307	−0.0941535	−	0.995558i	$-0.530014\pi$
$229$	−2.84960	−0.188307	−0.0941535	+	0.995558i	$0.530014\pi$
$230$	−0.372667	−0.0245729
$231$	−16.6222	−1.09366
$232$	−5.57173	−0.365802
$233$	23.5165	1.54062	0.770310	−	0.637670i	$-0.220101\pi$
$233$	23.5165	1.54062	0.770310	+	0.637670i	$0.220101\pi$
$234$	12.2438	0.800400
$235$	3.47016	0.226368
$236$	8.82524	0.574474
$237$	−6.78288	−0.440595
$238$	−14.2144	−0.921384
$239$	8.03813	0.519943	0.259972	−	0.965616i	$-0.416287\pi$
$239$	8.03813	0.519943	0.259972	+	0.965616i	$0.416287\pi$
$240$	−4.82524	−0.311468
$241$	18.4519	1.18859	0.594294	−	0.804248i	$-0.297432\pi$
$241$	18.4519	1.18859	0.594294	+	0.804248i	$0.297432\pi$
$242$	−9.80362	−0.630200
$243$	−20.0266	−1.28471
$244$	−11.7522	−0.752360
$245$	24.9468	1.59380
$246$	−9.17100	−0.584721
$247$	−1.46032	−0.0929179
$248$	−5.73495	−0.364170
$249$	−16.0426	−1.01666
$250$	−11.7246	−0.741530
$251$	23.2945	1.47033	0.735167	−	0.677886i	$-0.237104\pi$
$251$	23.2945	1.47033	0.735167	+	0.677886i	$0.237104\pi$
$252$	−33.3859	−2.10312
$253$	0.266055	0.0167267
$254$	−4.75254	−0.298201
$255$	−14.2144	−0.890142
$256$	1.00000	0.0625000
$257$	−4.25683	−0.265534	−0.132767	−	0.991147i	$-0.542386\pi$
$257$	−4.25683	−0.265534	−0.132767	+	0.991147i	$0.542386\pi$
$258$	−13.7942	−0.858788
$259$	0	0
$260$	2.71115	0.168139
$261$	−38.5510	−2.38624
$262$	17.9870	1.11124
$263$	−6.88547	−0.424576	−0.212288	−	0.977207i	$-0.568092\pi$
$263$	−6.88547	−0.424576	−0.212288	+	0.977207i	$0.568092\pi$
$264$	3.44484	0.212015
$265$	9.42150	0.578758
$266$	3.98196	0.244149
$267$	−28.2701	−1.73010
$268$	8.98400	0.548785
$269$	9.67565	0.589935	0.294968	−	0.955507i	$-0.404691\pi$
$269$	9.67565	0.589935	0.294968	+	0.955507i	$0.404691\pi$
$270$	−18.9102	−1.15084
$271$	7.66277	0.465480	0.232740	−	0.972539i	$-0.425231\pi$
$271$	7.66277	0.465480	0.232740	+	0.972539i	$0.425231\pi$
$272$	2.94585	0.178618
$273$	26.8920	1.62758
$274$	22.1091	1.33566
$275$	2.90151	0.174967
$276$	0.766075	0.0461123
$277$	4.01957	0.241513	0.120756	−	0.992682i	$-0.461468\pi$
$277$	4.01957	0.241513	0.120756	+	0.992682i	$0.461468\pi$
$278$	−2.66547	−0.159864
$279$	−39.6803	−2.37560
$280$	−7.39269	−0.441798
$281$	−6.99927	−0.417542	−0.208771	−	0.977965i	$-0.566946\pi$
$281$	−6.99927	−0.417542	−0.208771	+	0.977965i	$0.566946\pi$
$282$	−7.13345	−0.424791
$283$	−4.70460	−0.279660	−0.139830	−	0.990176i	$-0.544656\pi$
$283$	−4.70460	−0.279660	−0.139830	+	0.990176i	$0.544656\pi$
$284$	−1.21864	−0.0723132
$285$	3.98196	0.235871
$286$	−1.93555	−0.114452
$287$	−14.0508	−0.829392
$288$	6.91903	0.407708
$289$	−8.32197	−0.489527
$290$	−8.53639	−0.501274
$291$	−13.7287	−0.804790
$292$	8.79418	0.514640
$293$	−14.2310	−0.831384	−0.415692	−	0.909505i	$-0.636461\pi$
$293$	−14.2310	−0.831384	−0.415692	+	0.909505i	$0.636461\pi$
$294$	−51.2822	−2.99084
$295$	13.5210	0.787226
$296$	0	0
$297$	13.5004	0.783374
$298$	6.13622	0.355462
$299$	−0.430434	−0.0248926
$300$	8.35455	0.482350
$301$	−21.1339	−1.21814
$302$	−0.436768	−0.0251332
$303$	13.8226	0.794086
$304$	−0.825235	−0.0473305
$305$	−18.0055	−1.03099
$306$	20.3824	1.16519
$307$	0.802616	0.0458077	0.0229039	−	0.999738i	$-0.492709\pi$
$307$	0.802616	0.0458077	0.0229039	+	0.999738i	$0.492709\pi$
$308$	5.27780	0.300731
$309$	−39.8256	−2.26560
$310$	−8.78645	−0.499037
$311$	−2.46944	−0.140029	−0.0700145	−	0.997546i	$-0.522305\pi$
$311$	−2.46944	−0.140029	−0.0700145	+	0.997546i	$0.522305\pi$
$312$	−5.57320	−0.315520
$313$	−17.8439	−1.00860	−0.504298	−	0.863530i	$-0.668249\pi$
$313$	−17.8439	−1.00860	−0.504298	+	0.863530i	$0.668249\pi$
$314$	6.06139	0.342064
$315$	−51.1502	−2.88199
$316$	2.15367	0.121153
$317$	3.53955	0.198801	0.0994006	−	0.995047i	$-0.468307\pi$
$317$	3.53955	0.198801	0.0994006	+	0.995047i	$0.468307\pi$
$318$	−19.3674	−1.08607
$319$	6.09432	0.341216
$320$	1.53209	0.0856464
$321$	−59.3976	−3.31525
$322$	1.17369	0.0654074
$323$	−2.43102	−0.135266
$324$	18.1159	1.00644
$325$	−4.69417	−0.260386
$326$	13.7349	0.760708
$327$	26.5005	1.46548
$328$	2.91194	0.160785
$329$	−10.9291	−0.602540
$330$	5.27780	0.290534
$331$	3.82628	0.210311	0.105156	−	0.994456i	$-0.466466\pi$
$331$	3.82628	0.210311	0.105156	+	0.994456i	$0.466466\pi$
$332$	5.09379	0.279558
$333$	0	0
$334$	23.8199	1.30337
$335$	13.7643	0.752023
$336$	15.1968	0.829055
$337$	−21.3962	−1.16553	−0.582764	−	0.812641i	$-0.698029\pi$
$337$	−21.3962	−1.16553	−0.582764	+	0.812641i	$0.698029\pi$
$338$	−9.86859	−0.536781
$339$	20.1080	1.09212
$340$	4.51330	0.244768
$341$	6.27284	0.339693
$342$	−5.70983	−0.308752
$343$	−44.7922	−2.41855
$344$	4.37987	0.236147
$345$	1.17369	0.0631896
$346$	21.4452	1.15290
$347$	−25.6363	−1.37623	−0.688113	−	0.725603i	$-0.741561\pi$
$347$	−25.6363	−1.37623	−0.688113	+	0.725603i	$0.741561\pi$
$348$	17.5479	0.940665
$349$	15.5352	0.831578	0.415789	−	0.909461i	$-0.363505\pi$
$349$	15.5352	0.831578	0.415789	+	0.909461i	$0.363505\pi$
$350$	12.7999	0.684184
$351$	−21.8415	−1.16581
$352$	−1.09379	−0.0582993
$353$	−1.35631	−0.0721890	−0.0360945	−	0.999348i	$-0.511492\pi$
$353$	−1.35631	−0.0721890	−0.0360945	+	0.999348i	$0.511492\pi$
$354$	−27.7946	−1.47727
$355$	−1.86707	−0.0990938
$356$	8.97619	0.475737
$357$	44.7676	2.36935
$358$	11.5247	0.609102
$359$	−22.3147	−1.17772	−0.588862	−	0.808233i	$-0.700424\pi$
$359$	−22.3147	−1.17772	−0.588862	+	0.808233i	$0.700424\pi$
$360$	10.6006	0.558699
$361$	−18.3190	−0.964157
$362$	−17.7689	−0.933910
$363$	30.8760	1.62057
$364$	−8.53863	−0.447546
$365$	13.4735	0.705233
$366$	37.0131	1.93470
$367$	7.22844	0.377321	0.188661	−	0.982042i	$-0.439585\pi$
$367$	7.22844	0.377321	0.188661	+	0.982042i	$0.439585\pi$
$368$	−0.243241	−0.0126798
$369$	20.1478	1.04885
$370$	0	0
$371$	−29.6725	−1.54052
$372$	18.0619	0.936467
$373$	−11.7328	−0.607504	−0.303752	−	0.952751i	$-0.598239\pi$
$373$	−11.7328	−0.607504	−0.303752	+	0.952751i	$0.598239\pi$
$374$	−3.22215	−0.166613
$375$	36.9261	1.90686
$376$	2.26498	0.116808
$377$	−9.85962	−0.507796
$378$	59.5568	3.06327
$379$	−2.76782	−0.142173	−0.0710866	−	0.997470i	$-0.522647\pi$
$379$	−2.76782	−0.142173	−0.0710866	+	0.997470i	$0.522647\pi$
$380$	−1.26433	−0.0648590
$381$	14.9679	0.766827
$382$	−25.9113	−1.32574
$383$	19.4717	0.994955	0.497478	−	0.867477i	$-0.334260\pi$
$383$	19.4717	0.994955	0.497478	+	0.867477i	$0.334260\pi$
$384$	−3.14945	−0.160720
$385$	8.08607	0.412104
$386$	10.9030	0.554947
$387$	30.3044	1.54046
$388$	4.35907	0.221298
$389$	−2.34776	−0.119036	−0.0595181	−	0.998227i	$-0.518956\pi$
$389$	−2.34776	−0.119036	−0.0595181	+	0.998227i	$0.518956\pi$
$390$	−8.53863	−0.432371
$391$	−0.716551	−0.0362375
$392$	16.2829	0.822411
$393$	−56.6491	−2.85757
$394$	−6.44314	−0.324601
$395$	3.29962	0.166022
$396$	−7.56798	−0.380305
$397$	2.27548	0.114203	0.0571015	−	0.998368i	$-0.481814\pi$
$397$	2.27548	0.114203	0.0571015	+	0.998368i	$0.481814\pi$
$398$	18.8556	0.945145
$399$	−12.5410	−0.627834
$400$	−2.65270	−0.132635
$401$	17.5482	0.876316	0.438158	−	0.898898i	$-0.355631\pi$
$401$	17.5482	0.876316	0.438158	+	0.898898i	$0.355631\pi$
$402$	−28.2946	−1.41121
$403$	−10.1484	−0.505530
$404$	−4.38889	−0.218355
$405$	27.7551	1.37916
$406$	26.8849	1.33428
$407$	0	0
$408$	−9.27780	−0.459320
$409$	22.6789	1.12140	0.560699	−	0.828020i	$-0.310532\pi$
$409$	22.6789	1.12140	0.560699	+	0.828020i	$0.310532\pi$
$410$	4.46135	0.220330
$411$	−69.6316	−3.43467
$412$	12.6452	0.622987
$413$	−42.5838	−2.09541
$414$	−1.68299	−0.0827145
$415$	7.80414	0.383090
$416$	1.76958	0.0867607
$417$	8.39476	0.411093
$418$	0.902636	0.0441494
$419$	18.8213	0.919483	0.459741	−	0.888053i	$-0.347942\pi$
$419$	18.8213	0.919483	0.459741	+	0.888053i	$0.347942\pi$
$420$	23.2829	1.13609
$421$	−17.9266	−0.873689	−0.436844	−	0.899537i	$-0.643904\pi$
$421$	−17.9266	−0.873689	−0.436844	+	0.899537i	$0.643904\pi$
$422$	−1.41450	−0.0688568
$423$	15.6715	0.761974
$424$	6.14945	0.298644
$425$	−7.81447	−0.379057
$426$	3.83806	0.185954
$427$	56.7073	2.74426
$428$	18.8597	0.911616
$429$	6.09592	0.294314
$430$	6.71035	0.323602
$431$	12.2609	0.590585	0.295293	−	0.955407i	$-0.404583\pi$
$431$	12.2609	0.590585	0.295293	+	0.955407i	$0.404583\pi$
$432$	−12.3428	−0.593842
$433$	21.1146	1.01470	0.507351	−	0.861740i	$-0.330625\pi$
$433$	21.1146	1.01470	0.507351	+	0.861740i	$0.330625\pi$
$434$	27.6725	1.32832
$435$	26.8849	1.28903
$436$	−8.41432	−0.402973
$437$	0.200731	0.00960226
$438$	−27.6968	−1.32340
$439$	−24.0926	−1.14988	−0.574938	−	0.818197i	$-0.694974\pi$
$439$	−24.0926	−1.14988	−0.574938	+	0.818197i	$0.694974\pi$
$440$	−1.67579	−0.0798900
$441$	112.662	5.36485
$442$	5.21291	0.247953
$443$	19.2348	0.913871	0.456936	−	0.889500i	$-0.348947\pi$
$443$	19.2348	0.913871	0.456936	+	0.889500i	$0.348947\pi$
$444$	0	0
$445$	13.7523	0.651923
$446$	−12.1750	−0.576505
$447$	−19.3257	−0.914075
$448$	−4.82524	−0.227971
$449$	−6.58735	−0.310876	−0.155438	−	0.987846i	$-0.549679\pi$
$449$	−6.58735	−0.310876	−0.155438	+	0.987846i	$0.549679\pi$
$450$	−18.3541	−0.865222
$451$	−3.18505	−0.149978
$452$	−6.38461	−0.300307
$453$	1.37558	0.0646304
$454$	−21.2999	−0.999656
$455$	−13.0819	−0.613291
$456$	2.59904	0.121711
$457$	−28.9912	−1.35615	−0.678075	−	0.734992i	$-0.737186\pi$
$457$	−28.9912	−1.35615	−0.678075	+	0.734992i	$0.737186\pi$
$458$	−2.84960	−0.133153
$459$	−36.3600	−1.69714
$460$	−0.372667	−0.0173757
$461$	35.8514	1.66977	0.834883	−	0.550428i	$-0.185535\pi$
$461$	35.8514	1.66977	0.834883	+	0.550428i	$0.185535\pi$
$462$	−16.6222	−0.773334
$463$	−18.5824	−0.863599	−0.431800	−	0.901970i	$-0.642121\pi$
$463$	−18.5824	−0.863599	−0.431800	+	0.901970i	$0.642121\pi$
$464$	−5.57173	−0.258661
$465$	27.6725	1.28328
$466$	23.5165	1.08938
$467$	−1.64625	−0.0761795	−0.0380898	−	0.999274i	$-0.512127\pi$
$467$	−1.64625	−0.0761795	−0.0380898	+	0.999274i	$0.512127\pi$
$468$	12.2438	0.565968
$469$	−43.3499	−2.00171
$470$	3.47016	0.160066
$471$	−19.0900	−0.879622
$472$	8.82524	0.406214
$473$	−4.79067	−0.220275
$474$	−6.78288	−0.311548
$475$	2.18911	0.100443
$476$	−14.2144	−0.651517
$477$	42.5482	1.94815
$478$	8.03813	0.367656
$479$	−34.0714	−1.55676	−0.778381	−	0.627792i	$-0.783959\pi$
$479$	−34.0714	−1.55676	−0.778381	+	0.627792i	$0.783959\pi$
$480$	−4.82524	−0.220241
$481$	0	0
$482$	18.4519	0.840459
$483$	−3.69649	−0.168196
$484$	−9.80362	−0.445619
$485$	6.67849	0.303255
$486$	−20.0266	−0.908427
$487$	−31.0898	−1.40881	−0.704407	−	0.709796i	$-0.748787\pi$
$487$	−31.0898	−1.40881	−0.704407	+	0.709796i	$0.748787\pi$
$488$	−11.7522	−0.531999
$489$	−43.2575	−1.95617
$490$	24.9468	1.12698
$491$	35.0539	1.58196	0.790981	−	0.611841i	$-0.209571\pi$
$491$	35.0539	1.58196	0.790981	+	0.611841i	$0.209571\pi$
$492$	−9.17100	−0.413461
$493$	−16.4135	−0.739226
$494$	−1.46032	−0.0657029
$495$	−11.5948	−0.521148
$496$	−5.73495	−0.257507
$497$	5.88024	0.263765
$498$	−16.0426	−0.718888
$499$	−35.1712	−1.57448	−0.787239	−	0.616648i	$-0.788490\pi$
$499$	−35.1712	−1.57448	−0.787239	+	0.616648i	$0.788490\pi$
$500$	−11.7246	−0.524341
$501$	−75.0197	−3.35163
$502$	23.2945	1.03968
$503$	4.63236	0.206547	0.103273	−	0.994653i	$-0.467068\pi$
$503$	4.63236	0.206547	0.103273	+	0.994653i	$0.467068\pi$
$504$	−33.3859	−1.48713
$505$	−6.72417	−0.299221
$506$	0.266055	0.0118276
$507$	31.0806	1.38034
$508$	−4.75254	−0.210860
$509$	−23.8507	−1.05716	−0.528581	−	0.848883i	$-0.677276\pi$
$509$	−23.8507	−1.05716	−0.528581	+	0.848883i	$0.677276\pi$
$510$	−14.2144	−0.629425
$511$	−42.4340	−1.87717
$512$	1.00000	0.0441942
$513$	10.1857	0.449709
$514$	−4.25683	−0.187761
$515$	19.3736	0.853705
$516$	−13.7942	−0.607255
$517$	−2.47742	−0.108957
$518$	0	0
$519$	−67.5405	−2.96470
$520$	2.71115	0.118892
$521$	19.3996	0.849912	0.424956	−	0.905214i	$-0.360290\pi$
$521$	19.3996	0.849912	0.424956	+	0.905214i	$0.360290\pi$
$522$	−38.5510	−1.68733
$523$	1.93995	0.0848283	0.0424141	−	0.999100i	$-0.486495\pi$
$523$	1.93995	0.0848283	0.0424141	+	0.999100i	$0.486495\pi$
$524$	17.9870	0.785765
$525$	−40.3127	−1.75939
$526$	−6.88547	−0.300221
$527$	−16.8943	−0.735927
$528$	3.44484	0.149918
$529$	−22.9408	−0.997428
$530$	9.42150	0.409244
$531$	61.0620	2.64987
$532$	3.98196	0.172640
$533$	5.15290	0.223197
$534$	−28.2701	−1.22336
$535$	28.8947	1.24923
$536$	8.98400	0.388050
$537$	−36.2966	−1.56631
$538$	9.67565	0.417147
$539$	−17.8101	−0.767135
$540$	−18.9102	−0.813767
$541$	−4.31210	−0.185392	−0.0926958	−	0.995694i	$-0.529548\pi$
$541$	−4.31210	−0.185392	−0.0926958	+	0.995694i	$0.529548\pi$
$542$	7.66277	0.329144
$543$	55.9621	2.40156
$544$	2.94585	0.126302
$545$	−12.8915	−0.552211
$546$	26.8920	1.15087
$547$	17.5166	0.748956	0.374478	−	0.927236i	$-0.377822\pi$
$547$	17.5166	0.748956	0.374478	+	0.927236i	$0.377822\pi$
$548$	22.1091	0.944456
$549$	−81.3141	−3.47040
$550$	2.90151	0.123721
$551$	4.59799	0.195881
$552$	0.766075	0.0326063
$553$	−10.3920	−0.441912
$554$	4.01957	0.170775
$555$	0	0
$556$	−2.66547	−0.113041
$557$	22.8107	0.966521	0.483261	−	0.875477i	$-0.339452\pi$
$557$	22.8107	0.966521	0.483261	+	0.875477i	$0.339452\pi$
$558$	−39.6803	−1.67980
$559$	7.75052	0.327812
$560$	−7.39269	−0.312398
$561$	10.1480	0.428448
$562$	−6.99927	−0.295247
$563$	−26.5842	−1.12039	−0.560195	−	0.828361i	$-0.689274\pi$
$563$	−26.5842	−1.12039	−0.560195	+	0.828361i	$0.689274\pi$
$564$	−7.13345	−0.300373
$565$	−9.78179	−0.411523
$566$	−4.70460	−0.197749
$567$	−87.4133	−3.67101
$568$	−1.21864	−0.0511331
$569$	−13.9698	−0.585646	−0.292823	−	0.956167i	$-0.594595\pi$
$569$	−13.9698	−0.585646	−0.292823	+	0.956167i	$0.594595\pi$
$570$	3.98196	0.166786
$571$	21.9636	0.919148	0.459574	−	0.888140i	$-0.348002\pi$
$571$	21.9636	0.919148	0.459574	+	0.888140i	$0.348002\pi$
$572$	−1.93555	−0.0809295
$573$	81.6062	3.40915
$574$	−14.0508	−0.586468
$575$	0.645246	0.0269086
$576$	6.91903	0.288293
$577$	31.5119	1.31186	0.655929	−	0.754823i	$-0.272277\pi$
$577$	31.5119	1.31186	0.655929	+	0.754823i	$0.272277\pi$
$578$	−8.32197	−0.346148
$579$	−34.3384	−1.42705
$580$	−8.53639	−0.354454
$581$	−24.5787	−1.01970
$582$	−13.7287	−0.569072
$583$	−6.72622	−0.278572
$584$	8.79418	0.363906
$585$	18.7585	0.775570
$586$	−14.2310	−0.587877
$587$	−41.8748	−1.72836	−0.864179	−	0.503185i	$-0.832161\pi$
$587$	−41.8748	−1.72836	−0.864179	+	0.503185i	$0.832161\pi$
$588$	−51.2822	−2.11484
$589$	4.73268	0.195007
$590$	13.5210	0.556653
$591$	20.2923	0.834715
$592$	0	0
$593$	−30.7471	−1.26263	−0.631316	−	0.775525i	$-0.717485\pi$
$593$	−30.7471	−1.26263	−0.631316	+	0.775525i	$0.717485\pi$
$594$	13.5004	0.553929
$595$	−21.7778	−0.892801
$596$	6.13622	0.251349
$597$	−59.3847	−2.43045
$598$	−0.430434	−0.0176017
$599$	30.0843	1.22921	0.614605	−	0.788835i	$-0.289315\pi$
$599$	30.0843	1.22921	0.614605	+	0.788835i	$0.289315\pi$
$600$	8.35455	0.341073
$601$	30.3518	1.23808	0.619038	−	0.785361i	$-0.287523\pi$
$601$	30.3518	1.23808	0.619038	+	0.785361i	$0.287523\pi$
$602$	−21.1339	−0.861354
$603$	62.1605	2.53137
$604$	−0.436768	−0.0177719
$605$	−15.0200	−0.610650
$606$	13.8226	0.561504
$607$	−1.15032	−0.0466902	−0.0233451	−	0.999727i	$-0.507432\pi$
$607$	−1.15032	−0.0466902	−0.0233451	+	0.999727i	$0.507432\pi$
$608$	−0.825235	−0.0334677
$609$	−84.6727	−3.43111
$610$	−18.0055	−0.729020
$611$	4.00807	0.162149
$612$	20.3824	0.823910
$613$	−15.4606	−0.624448	−0.312224	−	0.950008i	$-0.601074\pi$
$613$	−15.4606	−0.624448	−0.312224	+	0.950008i	$0.601074\pi$
$614$	0.802616	0.0323910
$615$	−14.0508	−0.566582
$616$	5.27780	0.212649
$617$	20.9822	0.844711	0.422356	−	0.906430i	$-0.361203\pi$
$617$	20.9822	0.844711	0.422356	+	0.906430i	$0.361203\pi$
$618$	−39.8256	−1.60202
$619$	30.8550	1.24017	0.620084	−	0.784535i	$-0.287098\pi$
$619$	30.8550	1.24017	0.620084	+	0.784535i	$0.287098\pi$
$620$	−8.78645	−0.352872
$621$	3.00227	0.120477
$622$	−2.46944	−0.0990155
$623$	−43.3122	−1.73527
$624$	−5.57320	−0.223106
$625$	−4.69965	−0.187986
$626$	−17.8439	−0.713185
$627$	−2.84281	−0.113531
$628$	6.06139	0.241876
$629$	0	0
$630$	−51.1502	−2.03787
$631$	5.84354	0.232628	0.116314	−	0.993213i	$-0.462892\pi$
$631$	5.84354	0.232628	0.116314	+	0.993213i	$0.462892\pi$
$632$	2.15367	0.0856684
$633$	4.45490	0.177066
$634$	3.53955	0.140574
$635$	−7.28131	−0.288950
$636$	−19.3674	−0.767966
$637$	28.8139	1.14165
$638$	6.09432	0.241276
$639$	−8.43183	−0.333558
$640$	1.53209	0.0605611
$641$	29.8415	1.17867	0.589334	−	0.807889i	$-0.299390\pi$
$641$	29.8415	1.17867	0.589334	+	0.807889i	$0.299390\pi$
$642$	−59.3976	−2.34423
$643$	14.3623	0.566396	0.283198	−	0.959062i	$-0.408605\pi$
$643$	14.3623	0.566396	0.283198	+	0.959062i	$0.408605\pi$
$644$	1.17369	0.0462500
$645$	−21.1339	−0.832147
$646$	−2.43102	−0.0956472
$647$	9.29257	0.365329	0.182664	−	0.983175i	$-0.441528\pi$
$647$	9.29257	0.365329	0.182664	+	0.983175i	$0.441528\pi$
$648$	18.1159	0.711658
$649$	−9.65297	−0.378912
$650$	−4.69417	−0.184120
$651$	−87.1530	−3.41580
$652$	13.7349	0.537902
$653$	−42.5566	−1.66537	−0.832684	−	0.553748i	$-0.813197\pi$
$653$	−42.5566	−1.66537	−0.832684	+	0.553748i	$0.813197\pi$
$654$	26.5005	1.03625
$655$	27.5577	1.07677
$656$	2.91194	0.113692
$657$	60.8471	2.37387
$658$	−10.9291	−0.426060
$659$	10.9819	0.427794	0.213897	−	0.976856i	$-0.431384\pi$
$659$	10.9819	0.427794	0.213897	+	0.976856i	$0.431384\pi$
$660$	5.27780	0.205438
$661$	33.5295	1.30415	0.652073	−	0.758156i	$-0.273900\pi$
$661$	33.5295	1.30415	0.652073	+	0.758156i	$0.273900\pi$
$662$	3.82628	0.148712
$663$	−16.4178	−0.637615
$664$	5.09379	0.197677
$665$	6.10071	0.236575
$666$	0	0
$667$	1.35527	0.0524764
$668$	23.8199	0.921621
$669$	38.3447	1.48249
$670$	13.7643	0.531761
$671$	12.8545	0.496243
$672$	15.1968	0.586231
$673$	−43.8179	−1.68905	−0.844527	−	0.535513i	$-0.820118\pi$
$673$	−43.8179	−1.68905	−0.844527	+	0.535513i	$0.820118\pi$
$674$	−21.3962	−0.824153
$675$	32.7417	1.26023
$676$	−9.86859	−0.379561
$677$	−2.17579	−0.0836225	−0.0418113	−	0.999126i	$-0.513313\pi$
$677$	−2.17579	−0.0836225	−0.0418113	+	0.999126i	$0.513313\pi$
$678$	20.1080	0.772243
$679$	−21.0336	−0.807194
$680$	4.51330	0.173077
$681$	67.0831	2.57063
$682$	6.27284	0.240199
$683$	−31.7054	−1.21317	−0.606586	−	0.795018i	$-0.707462\pi$
$683$	−31.7054	−1.21317	−0.606586	+	0.795018i	$0.707462\pi$
$684$	−5.70983	−0.218321
$685$	33.8732	1.29423
$686$	−44.7922	−1.71017
$687$	8.97468	0.342405
$688$	4.37987	0.166981
$689$	10.8819	0.414569
$690$	1.17369	0.0446818
$691$	25.4909	0.969718	0.484859	−	0.874592i	$-0.338871\pi$
$691$	25.4909	0.969718	0.484859	+	0.874592i	$0.338871\pi$
$692$	21.4452	0.815223
$693$	36.5173	1.38718
$694$	−25.6363	−0.973139
$695$	−4.08374	−0.154905
$696$	17.5479	0.665151
$697$	8.57813	0.324920
$698$	15.5352	0.588015
$699$	−74.0642	−2.80136
$700$	12.7999	0.483791
$701$	−17.9887	−0.679426	−0.339713	−	0.940529i	$-0.610330\pi$
$701$	−17.9887	−0.679426	−0.339713	+	0.940529i	$0.610330\pi$
$702$	−21.8415	−0.824355
$703$	0	0
$704$	−1.09379	−0.0412238
$705$	−10.9291	−0.411613
$706$	−1.35631	−0.0510453
$707$	21.1774	0.796459
$708$	−27.7946	−1.04459
$709$	27.8902	1.04744	0.523719	−	0.851891i	$-0.324544\pi$
$709$	27.8902	1.04744	0.523719	+	0.851891i	$0.324544\pi$
$710$	−1.86707	−0.0700699
$711$	14.9013	0.558843
$712$	8.97619	0.336397
$713$	1.39497	0.0522422
$714$	44.7676	1.67538
$715$	−2.96544	−0.110901
$716$	11.5247	0.430700
$717$	−25.3157	−0.945431
$718$	−22.3147	−0.832777
$719$	−27.4295	−1.02295	−0.511474	−	0.859299i	$-0.670900\pi$
$719$	−27.4295	−1.02295	−0.511474	+	0.859299i	$0.670900\pi$
$720$	10.6006	0.395060
$721$	−61.0163	−2.27237
$722$	−18.3190	−0.681762
$723$	−58.1132	−2.16125
$724$	−17.7689	−0.660374
$725$	14.7802	0.548921
$726$	30.8760	1.14592
$727$	10.1833	0.377679	0.188839	−	0.982008i	$-0.439527\pi$
$727$	10.1833	0.377679	0.188839	+	0.982008i	$0.439527\pi$
$728$	−8.53863	−0.316463
$729$	8.72530	0.323159
$730$	13.4735	0.498675
$731$	12.9024	0.477214
$732$	37.0131	1.36804
$733$	−35.2114	−1.30056	−0.650282	−	0.759693i	$-0.725349\pi$
$733$	−35.2114	−1.30056	−0.650282	+	0.759693i	$0.725349\pi$
$734$	7.22844	0.266807
$735$	−78.5688	−2.89805
$736$	−0.243241	−0.00896598
$737$	−9.82663	−0.361968
$738$	20.1478	0.741650
$739$	−8.78122	−0.323022	−0.161511	−	0.986871i	$-0.551637\pi$
$739$	−8.78122	−0.323022	−0.161511	+	0.986871i	$0.551637\pi$
$740$	0	0
$741$	4.59920	0.168956
$742$	−29.6725	−1.08931
$743$	14.7448	0.540935	0.270467	−	0.962729i	$-0.412822\pi$
$743$	14.7448	0.540935	0.270467	+	0.962729i	$0.412822\pi$
$744$	18.0619	0.662182
$745$	9.40123	0.344434
$746$	−11.7328	−0.429570
$747$	35.2441	1.28951
$748$	−3.22215	−0.117813
$749$	−91.0023	−3.32515
$750$	36.9261	1.34835
$751$	−34.8856	−1.27299	−0.636496	−	0.771280i	$-0.719617\pi$
$751$	−34.8856	−1.27299	−0.636496	+	0.771280i	$0.719617\pi$
$752$	2.26498	0.0825955
$753$	−73.3648	−2.67356
$754$	−9.85962	−0.359066
$755$	−0.669168	−0.0243535
$756$	59.5568	2.16606
$757$	52.0167	1.89058	0.945289	−	0.326233i	$-0.105780\pi$
$757$	52.0167	1.89058	0.945289	+	0.326233i	$0.105780\pi$
$758$	−2.76782	−0.100532
$759$	−0.837926	−0.0304148
$760$	−1.26433	−0.0458622
$761$	5.96409	0.216198	0.108099	−	0.994140i	$-0.465524\pi$
$761$	5.96409	0.216198	0.108099	+	0.994140i	$0.465524\pi$
$762$	14.9679	0.542229
$763$	40.6011	1.46986
$764$	−25.9113	−0.937437
$765$	31.2277	1.12904
$766$	19.4717	0.703540
$767$	15.6169	0.563895
$768$	−3.14945	−0.113646
$769$	37.0902	1.33751	0.668753	−	0.743484i	$-0.266828\pi$
$769$	37.0902	1.33751	0.668753	+	0.743484i	$0.266828\pi$
$770$	8.08607	0.291402
$771$	13.4067	0.482830
$772$	10.9030	0.392407
$773$	−3.17969	−0.114366	−0.0571828	−	0.998364i	$-0.518212\pi$
$773$	−3.17969	−0.114366	−0.0571828	+	0.998364i	$0.518212\pi$
$774$	30.3044	1.08927
$775$	15.2131	0.546471
$776$	4.35907	0.156482
$777$	0	0
$778$	−2.34776	−0.0841713
$779$	−2.40303	−0.0860976
$780$	−8.53863	−0.305732
$781$	1.33294	0.0476964
$782$	−0.716551	−0.0256238
$783$	68.7706	2.45766
$784$	16.2829	0.581532
$785$	9.28658	0.331452
$786$	−56.6491	−2.02061
$787$	−5.25051	−0.187160	−0.0935802	−	0.995612i	$-0.529831\pi$
$787$	−5.25051	−0.187160	−0.0935802	+	0.995612i	$0.529831\pi$
$788$	−6.44314	−0.229527
$789$	21.6854	0.772022
$790$	3.29962	0.117395
$791$	30.8073	1.09538
$792$	−7.56798	−0.268916
$793$	−20.7965	−0.738506
$794$	2.27548	0.0807536
$795$	−29.6725	−1.05238
$796$	18.8556	0.668318
$797$	26.6310	0.943319	0.471660	−	0.881781i	$-0.343655\pi$
$797$	26.6310	0.943319	0.471660	+	0.881781i	$0.343655\pi$
$798$	−12.5410	−0.443945
$799$	6.67231	0.236049
$800$	−2.65270	−0.0937872
$801$	62.1065	2.19443
$802$	17.5482	0.619649
$803$	−9.61900	−0.339447
$804$	−28.2946	−0.997875
$805$	1.79820	0.0633784
$806$	−10.1484	−0.357464
$807$	−30.4730	−1.07270
$808$	−4.38889	−0.154401
$809$	−15.5185	−0.545600	−0.272800	−	0.962071i	$-0.587950\pi$
$809$	−15.5185	−0.545600	−0.272800	+	0.962071i	$0.587950\pi$
$810$	27.7551	0.975215
$811$	32.7418	1.14972	0.574860	−	0.818252i	$-0.305056\pi$
$811$	32.7418	1.14972	0.574860	+	0.818252i	$0.305056\pi$
$812$	26.8849	0.943476
$813$	−24.1335	−0.846399
$814$	0	0
$815$	21.0432	0.737110
$816$	−9.27780	−0.324788
$817$	−3.61442	−0.126453
$818$	22.6789	0.792948
$819$	−59.0790	−2.06439
$820$	4.46135	0.155797
$821$	−12.1639	−0.424521	−0.212261	−	0.977213i	$-0.568083\pi$
$821$	−12.1639	−0.424521	−0.212261	+	0.977213i	$0.568083\pi$
$822$	−69.6316	−2.42868
$823$	21.8103	0.760259	0.380130	−	0.924933i	$-0.375879\pi$
$823$	21.8103	0.760259	0.380130	+	0.924933i	$0.375879\pi$
$824$	12.6452	0.440518
$825$	−9.13815	−0.318149
$826$	−42.5838	−1.48168
$827$	−11.5278	−0.400860	−0.200430	−	0.979708i	$-0.564234\pi$
$827$	−11.5278	−0.400860	−0.200430	+	0.979708i	$0.564234\pi$
$828$	−1.68299	−0.0584879
$829$	−10.4937	−0.364461	−0.182230	−	0.983256i	$-0.558332\pi$
$829$	−10.4937	−0.364461	−0.182230	+	0.983256i	$0.558332\pi$
$830$	7.80414	0.270886
$831$	−12.6594	−0.439151
$832$	1.76958	0.0613491
$833$	47.9670	1.66196
$834$	8.39476	0.290687
$835$	36.4943	1.26294
$836$	0.902636	0.0312183
$837$	70.7852	2.44669
$838$	18.8213	0.650172
$839$	−27.6168	−0.953436	−0.476718	−	0.879056i	$-0.658174\pi$
$839$	−27.6168	−0.953436	−0.476718	+	0.879056i	$0.658174\pi$
$840$	23.2829	0.803336
$841$	2.04419	0.0704893
$842$	−17.9266	−0.617791
$843$	22.0439	0.759231
$844$	−1.41450	−0.0486891
$845$	−15.1196	−0.520129
$846$	15.6715	0.538797
$847$	47.3048	1.62541
$848$	6.14945	0.211173
$849$	14.8169	0.508515
$850$	−7.81447	−0.268034
$851$	0	0
$852$	3.83806	0.131490
$853$	20.6389	0.706661	0.353330	−	0.935499i	$-0.385049\pi$
$853$	20.6389	0.706661	0.353330	+	0.935499i	$0.385049\pi$
$854$	56.7073	1.94048
$855$	−8.74796	−0.299174
$856$	18.8597	0.644610
$857$	31.3189	1.06983	0.534917	−	0.844905i	$-0.320343\pi$
$857$	31.3189	1.06983	0.534917	+	0.844905i	$0.320343\pi$
$858$	6.09592	0.208111
$859$	45.5472	1.55405	0.777025	−	0.629469i	$-0.216728\pi$
$859$	45.5472	1.55405	0.777025	+	0.629469i	$0.216728\pi$
$860$	6.71035	0.228821
$861$	44.2522	1.50811
$862$	12.2609	0.417607
$863$	−50.2043	−1.70897	−0.854487	−	0.519473i	$-0.826128\pi$
$863$	−50.2043	−1.70897	−0.854487	+	0.519473i	$0.826128\pi$
$864$	−12.3428	−0.419910
$865$	32.8559	1.11713
$866$	21.1146	0.717503
$867$	26.2096	0.890125
$868$	27.6725	0.939265
$869$	−2.35567	−0.0799106
$870$	26.8849	0.911484
$871$	15.8979	0.538680
$872$	−8.41432	−0.284945
$873$	30.1606	1.02078
$874$	0.200731	0.00678983
$875$	56.5741	1.91255
$876$	−27.6968	−0.935788
$877$	31.7132	1.07088	0.535439	−	0.844574i	$-0.320146\pi$
$877$	31.7132	1.07088	0.535439	+	0.844574i	$0.320146\pi$
$878$	−24.0926	−0.813086
$879$	44.8198	1.51173
$880$	−1.67579	−0.0564908
$881$	29.7084	1.00090	0.500450	−	0.865765i	$-0.333168\pi$
$881$	29.7084	1.00090	0.500450	+	0.865765i	$0.333168\pi$
$882$	112.662	3.79352
$883$	15.5877	0.524569	0.262285	−	0.964991i	$-0.415524\pi$
$883$	15.5877	0.524569	0.262285	+	0.964991i	$0.415524\pi$
$884$	5.21291	0.175329
$885$	−42.5838	−1.43144
$886$	19.2348	0.646205
$887$	−39.8038	−1.33648	−0.668240	−	0.743946i	$-0.732952\pi$
$887$	−39.8038	−1.33648	−0.668240	+	0.743946i	$0.732952\pi$
$888$	0	0
$889$	22.9321	0.769118
$890$	13.7523	0.460979
$891$	−19.8150	−0.663827
$892$	−12.1750	−0.407651
$893$	−1.86915	−0.0625486
$894$	−19.3257	−0.646348
$895$	17.6569	0.590206
$896$	−4.82524	−0.161200
$897$	1.35563	0.0452631
$898$	−6.58735	−0.219823
$899$	31.9536	1.06571
$900$	−18.3541	−0.611804
$901$	18.1154	0.603510
$902$	−3.18505	−0.106051
$903$	66.5601	2.21498
$904$	−6.38461	−0.212349
$905$	−27.2235	−0.904938
$906$	1.37558	0.0457006
$907$	44.9605	1.49289	0.746444	−	0.665448i	$-0.231760\pi$
$907$	44.9605	1.49289	0.746444	+	0.665448i	$0.231760\pi$
$908$	−21.2999	−0.706863
$909$	−30.3668	−1.00720
$910$	−13.0819	−0.433662
$911$	−14.2042	−0.470607	−0.235304	−	0.971922i	$-0.575608\pi$
$911$	−14.2042	−0.470607	−0.235304	+	0.971922i	$0.575608\pi$
$912$	2.59904	0.0860627
$913$	−5.57155	−0.184391
$914$	−28.9912	−0.958943
$915$	56.7073	1.87469
$916$	−2.84960	−0.0941535
$917$	−86.7914	−2.86611
$918$	−36.3600	−1.20006
$919$	46.2177	1.52458	0.762291	−	0.647235i	$-0.224075\pi$
$919$	46.2177	1.52458	0.762291	+	0.647235i	$0.224075\pi$
$920$	−0.372667	−0.0122865
$921$	−2.52780	−0.0832938
$922$	35.8514	1.18070
$923$	−2.15649	−0.0709816
$924$	−16.6222	−0.546829
$925$	0	0
$926$	−18.5824	−0.610657
$927$	87.4928	2.87364
$928$	−5.57173	−0.182901
$929$	−53.7917	−1.76485	−0.882424	−	0.470455i	$-0.844090\pi$
$929$	−53.7917	−1.76485	−0.882424	+	0.470455i	$0.844090\pi$
$930$	27.6725	0.907416
$931$	−13.4372	−0.440387
$932$	23.5165	0.770310
$933$	7.77737	0.254620
$934$	−1.64625	−0.0538671
$935$	−4.93662	−0.161445
$936$	12.2438	0.400200
$937$	−40.2307	−1.31428	−0.657140	−	0.753768i	$-0.728234\pi$
$937$	−40.2307	−1.31428	−0.657140	+	0.753768i	$0.728234\pi$
$938$	−43.3499	−1.41542
$939$	56.1984	1.83397
$940$	3.47016	0.113184
$941$	−1.75799	−0.0573087	−0.0286544	−	0.999589i	$-0.509122\pi$
$941$	−1.75799	−0.0573087	−0.0286544	+	0.999589i	$0.509122\pi$
$942$	−19.0900	−0.621987
$943$	−0.708302	−0.0230655
$944$	8.82524	0.287237
$945$	91.2463	2.96824
$946$	−4.79067	−0.155758
$947$	50.7742	1.64994	0.824971	−	0.565176i	$-0.191192\pi$
$947$	50.7742	1.64994	0.824971	+	0.565176i	$0.191192\pi$
$948$	−6.78288	−0.220298
$949$	15.5620	0.505163
$950$	2.18911	0.0710239
$951$	−11.1476	−0.361487
$952$	−14.2144	−0.460692
$953$	24.6652	0.798983	0.399492	−	0.916737i	$-0.369187\pi$
$953$	24.6652	0.798983	0.399492	+	0.916737i	$0.369187\pi$
$954$	42.5482	1.37755
$955$	−39.6984	−1.28461
$956$	8.03813	0.259972
$957$	−19.1937	−0.620445
$958$	−34.0714	−1.10080
$959$	−106.682	−3.44494
$960$	−4.82524	−0.155734
$961$	1.88962	0.0609556
$962$	0	0
$963$	130.491	4.20500
$964$	18.4519	0.594294
$965$	16.7043	0.537731
$966$	−3.69649	−0.118933
$967$	−31.1092	−1.00040	−0.500202	−	0.865909i	$-0.666741\pi$
$967$	−31.1092	−1.00040	−0.500202	+	0.865909i	$0.666741\pi$
$968$	−9.80362	−0.315100
$969$	7.65637	0.245958
$970$	6.67849	0.214433
$971$	20.7251	0.665099	0.332550	−	0.943086i	$-0.392091\pi$
$971$	20.7251	0.665099	0.332550	+	0.943086i	$0.392091\pi$
$972$	−20.0266	−0.642355
$973$	12.8615	0.412321
$974$	−31.0898	−0.996182
$975$	14.7840	0.473468
$976$	−11.7522	−0.376180
$977$	−27.6243	−0.883778	−0.441889	−	0.897070i	$-0.645692\pi$
$977$	−27.6243	−0.883778	−0.441889	+	0.897070i	$0.645692\pi$
$978$	−43.2575	−1.38322
$979$	−9.81809	−0.313787
$980$	24.9468	0.796898
$981$	−58.2189	−1.85879
$982$	35.0539	1.11862
$983$	−31.8355	−1.01539	−0.507697	−	0.861536i	$-0.669503\pi$
$983$	−31.8355	−1.01539	−0.507697	+	0.861536i	$0.669503\pi$
$984$	−9.17100	−0.292361
$985$	−9.87146	−0.314531
$986$	−16.4135	−0.522712
$987$	34.4206	1.09562
$988$	−1.46032	−0.0464589
$989$	−1.06536	−0.0338766
$990$	−11.5948	−0.368507
$991$	0.0903272	0.00286934	0.00143467	−	0.999999i	$-0.499543\pi$
$991$	0.0903272	0.00286934	0.00143467	+	0.999999i	$0.499543\pi$
$992$	−5.73495	−0.182085
$993$	−12.0507	−0.382416
$994$	5.88024	0.186510
$995$	28.8884	0.915824
$996$	−16.0426	−0.508330
$997$	46.6956	1.47886	0.739432	−	0.673231i	$-0.235094\pi$
$997$	46.6956	1.47886	0.739432	+	0.673231i	$0.235094\pi$
$998$	−35.1712	−1.11332
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.t.1.1		6
37.7	even	9		74.2.f.b.49.1	✓	12
37.16	even	9		74.2.f.b.71.1	yes	12
37.36	even	2		2738.2.a.q.1.1		6
111.44	odd	18		666.2.x.g.271.2		12
111.53	odd	18		666.2.x.g.145.2		12
148.7	odd	18		592.2.bc.d.49.2		12
148.127	odd	18		592.2.bc.d.145.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.49.1	✓	12	37.7	even	9
74.2.f.b.71.1	yes	12	37.16	even	9
592.2.bc.d.49.2		12	148.7	odd	18
592.2.bc.d.145.2		12	148.127	odd	18
666.2.x.g.145.2		12	111.53	odd	18
666.2.x.g.271.2		12	111.44	odd	18
2738.2.a.q.1.1		6	37.36	even	2
2738.2.a.t.1.1		6	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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.14945 q^{3} +1.00000 q^{4} +1.53209 q^{5} -3.14945 q^{6} -4.82524 q^{7} +1.00000 q^{8} +6.91903 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.14945 q^{3} +1.00000 q^{4} +1.53209 q^{5} -3.14945 q^{6} -4.82524 q^{7} +1.00000 q^{8} +6.91903 q^{9} +1.53209 q^{10} -1.09379 q^{11} -3.14945 q^{12} +1.76958 q^{13} -4.82524 q^{14} -4.82524 q^{15} +1.00000 q^{16} +2.94585 q^{17} +6.91903 q^{18} -0.825235 q^{19} +1.53209 q^{20} +15.1968 q^{21} -1.09379 q^{22} -0.243241 q^{23} -3.14945 q^{24} -2.65270 q^{25} +1.76958 q^{26} -12.3428 q^{27} -4.82524 q^{28} -5.57173 q^{29} -4.82524 q^{30} -5.73495 q^{31} +1.00000 q^{32} +3.44484 q^{33} +2.94585 q^{34} -7.39269 q^{35} +6.91903 q^{36} -0.825235 q^{38} -5.57320 q^{39} +1.53209 q^{40} +2.91194 q^{41} +15.1968 q^{42} +4.37987 q^{43} -1.09379 q^{44} +10.6006 q^{45} -0.243241 q^{46} +2.26498 q^{47} -3.14945 q^{48} +16.2829 q^{49} -2.65270 q^{50} -9.27780 q^{51} +1.76958 q^{52} +6.14945 q^{53} -12.3428 q^{54} -1.67579 q^{55} -4.82524 q^{56} +2.59904 q^{57} -5.57173 q^{58} +8.82524 q^{59} -4.82524 q^{60} -11.7522 q^{61} -5.73495 q^{62} -33.3859 q^{63} +1.00000 q^{64} +2.71115 q^{65} +3.44484 q^{66} +8.98400 q^{67} +2.94585 q^{68} +0.766075 q^{69} -7.39269 q^{70} -1.21864 q^{71} +6.91903 q^{72} +8.79418 q^{73} +8.35455 q^{75} -0.825235 q^{76} +5.27780 q^{77} -5.57320 q^{78} +2.15367 q^{79} +1.53209 q^{80} +18.1159 q^{81} +2.91194 q^{82} +5.09379 q^{83} +15.1968 q^{84} +4.51330 q^{85} +4.37987 q^{86} +17.5479 q^{87} -1.09379 q^{88} +8.97619 q^{89} +10.6006 q^{90} -8.53863 q^{91} -0.243241 q^{92} +18.0619 q^{93} +2.26498 q^{94} -1.26433 q^{95} -3.14945 q^{96} +4.35907 q^{97} +16.2829 q^{98} -7.56798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 3 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^7 + 6 * q^8 + 12 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - 3 q^{7} + 6 q^{8} + 12 q^{9} - 3 q^{11} - 3 q^{14} - 3 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} + 21 q^{19} + 6 q^{21} - 3 q^{22} + 21 q^{23} - 18 q^{25} - 3 q^{27} - 3 q^{28} - 6 q^{29} - 3 q^{30} + 21 q^{31} + 6 q^{32} - 3 q^{33} + 3 q^{34} - 3 q^{35} + 12 q^{36} + 21 q^{38} + 27 q^{39} + 18 q^{41} + 6 q^{42} + 18 q^{43} - 3 q^{44} + 6 q^{45} + 21 q^{46} - 9 q^{47} + 15 q^{49} - 18 q^{50} + 18 q^{53} - 3 q^{54} - 3 q^{55} - 3 q^{56} + 6 q^{57} - 6 q^{58} + 27 q^{59} - 3 q^{60} - 24 q^{61} + 21 q^{62} - 36 q^{63} + 6 q^{64} + 3 q^{65} - 3 q^{66} + 9 q^{67} + 3 q^{68} + 27 q^{69} - 3 q^{70} + 12 q^{72} + 27 q^{73} - 3 q^{75} + 21 q^{76} - 24 q^{77} + 27 q^{78} + 21 q^{79} - 6 q^{81} + 18 q^{82} + 27 q^{83} + 6 q^{84} - 3 q^{85} + 18 q^{86} - 3 q^{88} - 21 q^{89} + 6 q^{90} - 24 q^{91} + 21 q^{92} + 54 q^{93} - 9 q^{94} - 3 q^{95} + 42 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 3 * q^7 + 6 * q^8 + 12 * q^9 - 3 * q^11 - 3 * q^14 - 3 * q^15 + 6 * q^16 + 3 * q^17 + 12 * q^18 + 21 * q^19 + 6 * q^21 - 3 * q^22 + 21 * q^23 - 18 * q^25 - 3 * q^27 - 3 * q^28 - 6 * q^29 - 3 * q^30 + 21 * q^31 + 6 * q^32 - 3 * q^33 + 3 * q^34 - 3 * q^35 + 12 * q^36 + 21 * q^38 + 27 * q^39 + 18 * q^41 + 6 * q^42 + 18 * q^43 - 3 * q^44 + 6 * q^45 + 21 * q^46 - 9 * q^47 + 15 * q^49 - 18 * q^50 + 18 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 + 6 * q^57 - 6 * q^58 + 27 * q^59 - 3 * q^60 - 24 * q^61 + 21 * q^62 - 36 * q^63 + 6 * q^64 + 3 * q^65 - 3 * q^66 + 9 * q^67 + 3 * q^68 + 27 * q^69 - 3 * q^70 + 12 * q^72 + 27 * q^73 - 3 * q^75 + 21 * q^76 - 24 * q^77 + 27 * q^78 + 21 * q^79 - 6 * q^81 + 18 * q^82 + 27 * q^83 + 6 * q^84 - 3 * q^85 + 18 * q^86 - 3 * q^88 - 21 * q^89 + 6 * q^90 - 24 * q^91 + 21 * q^92 + 54 * q^93 - 9 * q^94 - 3 * q^95 + 42 * q^97 + 15 * q^98 - 36 * q^99

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