LMFDB - Embedded newform 2738.2.a.t.1.3

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			1.3
Root			$1.37564$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.37564 q^{3} +1.00000 q^{4} +0.347296 q^{5} -1.37564 q^{6} -0.477756 q^{7} +1.00000 q^{8} -1.10761 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.37564 q^{3} +1.00000 q^{4} +0.347296 q^{5} -1.37564 q^{6} -0.477756 q^{7} +1.00000 q^{8} -1.10761 q^{9} +0.347296 q^{10} +2.58536 q^{11} -1.37564 q^{12} -4.48325 q^{13} -0.477756 q^{14} -0.477756 q^{15} +1.00000 q^{16} +2.00984 q^{17} -1.10761 q^{18} +3.52224 q^{19} +0.347296 q^{20} +0.657221 q^{21} +2.58536 q^{22} +5.20972 q^{23} -1.37564 q^{24} -4.87939 q^{25} -4.48325 q^{26} +5.65060 q^{27} -0.477756 q^{28} +0.228222 q^{29} -0.477756 q^{30} -6.74658 q^{31} +1.00000 q^{32} -3.55654 q^{33} +2.00984 q^{34} -0.165923 q^{35} -1.10761 q^{36} +3.52224 q^{38} +6.16735 q^{39} +0.347296 q^{40} +10.7164 q^{41} +0.657221 q^{42} +8.85889 q^{43} +2.58536 q^{44} -0.384668 q^{45} +5.20972 q^{46} +7.45780 q^{47} -1.37564 q^{48} -6.77175 q^{49} -4.87939 q^{50} -2.76483 q^{51} -4.48325 q^{52} +4.37564 q^{53} +5.65060 q^{54} +0.897887 q^{55} -0.477756 q^{56} -4.84535 q^{57} +0.228222 q^{58} +4.47776 q^{59} -0.477756 q^{60} -1.43851 q^{61} -6.74658 q^{62} +0.529166 q^{63} +1.00000 q^{64} -1.55702 q^{65} -3.55654 q^{66} -10.5230 q^{67} +2.00984 q^{68} -7.16671 q^{69} -0.165923 q^{70} +8.87964 q^{71} -1.10761 q^{72} +7.18667 q^{73} +6.71229 q^{75} +3.52224 q^{76} -1.23517 q^{77} +6.16735 q^{78} +3.53579 q^{79} +0.347296 q^{80} -4.45039 q^{81} +10.7164 q^{82} +1.41464 q^{83} +0.657221 q^{84} +0.698012 q^{85} +8.85889 q^{86} -0.313952 q^{87} +2.58536 q^{88} +3.82425 q^{89} -0.384668 q^{90} +2.14190 q^{91} +5.20972 q^{92} +9.28089 q^{93} +7.45780 q^{94} +1.22326 q^{95} -1.37564 q^{96} +18.4835 q^{97} -6.77175 q^{98} -2.86357 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.37564	−0.794228	−0.397114	−	0.917769i	$-0.629988\pi$
$3$	−1.37564	−0.794228	−0.397114	+	0.917769i	$0.629988\pi$
$4$	1.00000	0.500000
$5$	0.347296	0.155316	0.0776578	−	0.996980i	$-0.475256\pi$
$5$	0.347296	0.155316	0.0776578	+	0.996980i	$0.475256\pi$
$6$	−1.37564	−0.561604
$7$	−0.477756	−0.180575	−0.0902873	−	0.995916i	$-0.528779\pi$
$7$	−0.477756	−0.180575	−0.0902873	+	0.995916i	$0.528779\pi$
$8$	1.00000	0.353553
$9$	−1.10761	−0.369202
$10$	0.347296	0.109825
$11$	2.58536	0.779516	0.389758	−	0.920917i	$-0.372559\pi$
$11$	2.58536	0.779516	0.389758	+	0.920917i	$0.372559\pi$
$12$	−1.37564	−0.397114
$13$	−4.48325	−1.24343	−0.621715	−	0.783244i	$-0.713564\pi$
$13$	−4.48325	−1.24343	−0.621715	+	0.783244i	$0.713564\pi$
$14$	−0.477756	−0.127686
$15$	−0.477756	−0.123356
$16$	1.00000	0.250000
$17$	2.00984	0.487459	0.243729	−	0.969843i	$-0.421629\pi$
$17$	2.00984	0.487459	0.243729	+	0.969843i	$0.421629\pi$
$18$	−1.10761	−0.261065
$19$	3.52224	0.808058	0.404029	−	0.914746i	$-0.367609\pi$
$19$	3.52224	0.808058	0.404029	+	0.914746i	$0.367609\pi$
$20$	0.347296	0.0776578
$21$	0.657221	0.143417
$22$	2.58536	0.551201
$23$	5.20972	1.08630	0.543151	−	0.839635i	$-0.317231\pi$
$23$	5.20972	1.08630	0.543151	+	0.839635i	$0.317231\pi$
$24$	−1.37564	−0.280802
$25$	−4.87939	−0.975877
$26$	−4.48325	−0.879238
$27$	5.65060	1.08746
$28$	−0.477756	−0.0902873
$29$	0.228222	0.0423797	0.0211899	−	0.999775i	$-0.493255\pi$
$29$	0.228222	0.0423797	0.0211899	+	0.999775i	$0.493255\pi$
$30$	−0.477756	−0.0872259
$31$	−6.74658	−1.21172	−0.605861	−	0.795571i	$-0.707171\pi$
$31$	−6.74658	−1.21172	−0.605861	+	0.795571i	$0.707171\pi$
$32$	1.00000	0.176777
$33$	−3.55654	−0.619113
$34$	2.00984	0.344686
$35$	−0.165923	−0.0280461
$36$	−1.10761	−0.184601
$37$	0	0
$37$	0	0
$38$	3.52224	0.571383
$39$	6.16735	0.987566
$40$	0.347296	0.0549124
$41$	10.7164	1.67361	0.836807	−	0.547498i	$-0.184420\pi$
$41$	10.7164	1.67361	0.836807	+	0.547498i	$0.184420\pi$
$42$	0.657221	0.101411
$43$	8.85889	1.35097	0.675484	−	0.737374i	$-0.263935\pi$
$43$	8.85889	1.35097	0.675484	+	0.737374i	$0.263935\pi$
$44$	2.58536	0.389758
$45$	−0.384668	−0.0573429
$46$	5.20972	0.768131
$47$	7.45780	1.08783	0.543916	−	0.839140i	$-0.316941\pi$
$47$	7.45780	1.08783	0.543916	+	0.839140i	$0.316941\pi$
$48$	−1.37564	−0.198557
$49$	−6.77175	−0.967393
$50$	−4.87939	−0.690049
$51$	−2.76483	−0.387153
$52$	−4.48325	−0.621715
$53$	4.37564	0.601041	0.300520	−	0.953775i	$-0.402840\pi$
$53$	4.37564	0.601041	0.300520	+	0.953775i	$0.402840\pi$
$54$	5.65060	0.768949
$55$	0.897887	0.121071
$56$	−0.477756	−0.0638428
$57$	−4.84535	−0.641782
$58$	0.228222	0.0299670
$59$	4.47776	0.582954	0.291477	−	0.956578i	$-0.405853\pi$
$59$	4.47776	0.582954	0.291477	+	0.956578i	$0.405853\pi$
$60$	−0.477756	−0.0616780
$61$	−1.43851	−0.184182	−0.0920909	−	0.995751i	$-0.529355\pi$
$61$	−1.43851	−0.184182	−0.0920909	+	0.995751i	$0.529355\pi$
$62$	−6.74658	−0.856817
$63$	0.529166	0.0666686
$64$	1.00000	0.125000
$65$	−1.55702	−0.193124
$66$	−3.55654	−0.437779
$67$	−10.5230	−1.28559	−0.642797	−	0.766037i	$-0.722226\pi$
$67$	−10.5230	−1.28559	−0.642797	+	0.766037i	$0.722226\pi$
$68$	2.00984	0.243729
$69$	−7.16671	−0.862771
$70$	−0.165923	−0.0198316
$71$	8.87964	1.05382	0.526910	−	0.849921i	$-0.323351\pi$
$71$	8.87964	1.05382	0.526910	+	0.849921i	$0.323351\pi$
$72$	−1.10761	−0.130533
$73$	7.18667	0.841136	0.420568	−	0.907261i	$-0.361831\pi$
$73$	7.18667	0.841136	0.420568	+	0.907261i	$0.361831\pi$
$74$	0	0
$75$	6.71229	0.775069
$76$	3.52224	0.404029
$77$	−1.23517	−0.140761
$78$	6.16735	0.698315
$79$	3.53579	0.397807	0.198904	−	0.980019i	$-0.436262\pi$
$79$	3.53579	0.397807	0.198904	+	0.980019i	$0.436262\pi$
$80$	0.347296	0.0388289
$81$	−4.45039	−0.494487
$82$	10.7164	1.18342
$83$	1.41464	0.155277	0.0776383	−	0.996982i	$-0.475262\pi$
$83$	1.41464	0.155277	0.0776383	+	0.996982i	$0.475262\pi$
$84$	0.657221	0.0717087
$85$	0.698012	0.0757100
$86$	8.85889	0.955279
$87$	−0.313952	−0.0336591
$88$	2.58536	0.275601
$89$	3.82425	0.405370	0.202685	−	0.979244i	$-0.435033\pi$
$89$	3.82425	0.405370	0.202685	+	0.979244i	$0.435033\pi$
$90$	−0.384668	−0.0405476
$91$	2.14190	0.224532
$92$	5.20972	0.543151
$93$	9.28089	0.962383
$94$	7.45780	0.769213
$95$	1.22326	0.125504
$96$	−1.37564	−0.140401
$97$	18.4835	1.87672	0.938358	−	0.345665i	$-0.112347\pi$
$97$	18.4835	1.87672	0.938358	+	0.345665i	$0.112347\pi$
$98$	−6.77175	−0.684050
$99$	−2.86357	−0.287799
$100$	−4.87939	−0.487939
$101$	17.1286	1.70436	0.852180	−	0.523248i	$-0.175280\pi$
$101$	17.1286	1.70436	0.852180	+	0.523248i	$0.175280\pi$
$102$	−2.76483	−0.273759
$103$	−13.4202	−1.32233	−0.661167	−	0.750238i	$-0.729939\pi$
$103$	−13.4202	−1.32233	−0.661167	+	0.750238i	$0.729939\pi$
$104$	−4.48325	−0.439619
$105$	0.228251	0.0222750
$106$	4.37564	0.425000
$107$	−20.4600	−1.97794	−0.988972	−	0.148101i	$-0.952684\pi$
$107$	−20.4600	−1.97794	−0.988972	+	0.148101i	$0.952684\pi$
$108$	5.65060	0.543729
$109$	10.6587	1.02092	0.510461	−	0.859901i	$-0.329475\pi$
$109$	10.6587	1.02092	0.510461	+	0.859901i	$0.329475\pi$
$110$	0.897887	0.0856102
$111$	0	0
$112$	−0.477756	−0.0451437
$113$	12.2122	1.14883	0.574415	−	0.818564i	$-0.305230\pi$
$113$	12.2122	1.14883	0.574415	+	0.818564i	$0.305230\pi$
$114$	−4.84535	−0.453809
$115$	1.80932	0.168720
$116$	0.228222	0.0211899
$117$	4.96568	0.459077
$118$	4.47776	0.412211
$119$	−0.960215	−0.0880227
$120$	−0.477756	−0.0436129
$121$	−4.31590	−0.392355
$122$	−1.43851	−0.130236
$123$	−14.7419	−1.32923
$124$	−6.74658	−0.605861
$125$	−3.43107	−0.306885
$126$	0.529166	0.0471418
$127$	−7.04958	−0.625549	−0.312774	−	0.949827i	$-0.601258\pi$
$127$	−7.04958	−0.625549	−0.312774	+	0.949827i	$0.601258\pi$
$128$	1.00000	0.0883883
$129$	−12.1867	−1.07298
$130$	−1.55702	−0.136559
$131$	1.98503	0.173433	0.0867164	−	0.996233i	$-0.472363\pi$
$131$	1.98503	0.173433	0.0867164	+	0.996233i	$0.472363\pi$
$132$	−3.55654	−0.309557
$133$	−1.68277	−0.145915
$134$	−10.5230	−0.909052
$135$	1.96243	0.168899
$136$	2.00984	0.172343
$137$	17.3979	1.48641	0.743203	−	0.669065i	$-0.233305\pi$
$137$	17.3979	1.48641	0.743203	+	0.669065i	$0.233305\pi$
$138$	−7.16671	−0.610071
$139$	0.737051	0.0625159	0.0312579	−	0.999511i	$-0.490049\pi$
$139$	0.737051	0.0625159	0.0312579	+	0.999511i	$0.490049\pi$
$140$	−0.165923	−0.0140230
$141$	−10.2593	−0.863986
$142$	8.87964	0.745163
$143$	−11.5908	−0.969274
$144$	−1.10761	−0.0923006
$145$	0.0792606	0.00658223
$146$	7.18667	0.594773
$147$	9.31551	0.768330
$148$	0	0
$149$	−19.0346	−1.55938	−0.779689	−	0.626167i	$-0.784623\pi$
$149$	−19.0346	−1.55938	−0.779689	+	0.626167i	$0.784623\pi$
$150$	6.71229	0.548056
$151$	−6.47198	−0.526682	−0.263341	−	0.964703i	$-0.584824\pi$
$151$	−6.47198	−0.526682	−0.263341	+	0.964703i	$0.584824\pi$
$152$	3.52224	0.285692
$153$	−2.22612	−0.179971
$154$	−1.23517	−0.0995330
$155$	−2.34306	−0.188199
$156$	6.16735	0.493783
$157$	12.0920	0.965047	0.482523	−	0.875883i	$-0.339720\pi$
$157$	12.0920	0.965047	0.482523	+	0.875883i	$0.339720\pi$
$158$	3.53579	0.281292
$159$	−6.01932	−0.477363
$160$	0.347296	0.0274562
$161$	−2.48897	−0.196159
$162$	−4.45039	−0.349655
$163$	14.7466	1.15504	0.577521	−	0.816376i	$-0.304020\pi$
$163$	14.7466	1.15504	0.577521	+	0.816376i	$0.304020\pi$
$164$	10.7164	0.836807
$165$	−1.23517	−0.0961580
$166$	1.41464	0.109797
$167$	8.30639	0.642768	0.321384	−	0.946949i	$-0.395852\pi$
$167$	8.30639	0.642768	0.321384	+	0.946949i	$0.395852\pi$
$168$	0.657221	0.0507057
$169$	7.09953	0.546118
$170$	0.698012	0.0535351
$171$	−3.90126	−0.298337
$172$	8.85889	0.675484
$173$	−6.61273	−0.502757	−0.251378	−	0.967889i	$-0.580884\pi$
$173$	−6.61273	−0.502757	−0.251378	+	0.967889i	$0.580884\pi$
$174$	−0.313952	−0.0238006
$175$	2.33115	0.176219
$176$	2.58536	0.194879
$177$	−6.15979	−0.462998
$178$	3.82425	0.286640
$179$	4.53985	0.339325	0.169662	−	0.985502i	$-0.445732\pi$
$179$	4.53985	0.339325	0.169662	+	0.985502i	$0.445732\pi$
$180$	−0.384668	−0.0286715
$181$	−1.56373	−0.116231	−0.0581154	−	0.998310i	$-0.518509\pi$
$181$	−1.56373	−0.116231	−0.0581154	+	0.998310i	$0.518509\pi$
$182$	2.14190	0.158768
$183$	1.97887	0.146282
$184$	5.20972	0.384066
$185$	0	0
$186$	9.28089	0.680508
$187$	5.19618	0.379982
$188$	7.45780	0.543916
$189$	−2.69961	−0.196367
$190$	1.22326	0.0887448
$191$	23.0183	1.66555	0.832773	−	0.553615i	$-0.186752\pi$
$191$	23.0183	1.66555	0.832773	+	0.553615i	$0.186752\pi$
$192$	−1.37564	−0.0992785
$193$	−10.5541	−0.759701	−0.379851	−	0.925048i	$-0.624025\pi$
$193$	−10.5541	−0.759701	−0.379851	+	0.925048i	$0.624025\pi$
$194$	18.4835	1.32704
$195$	2.14190	0.153385
$196$	−6.77175	−0.483696
$197$	4.82867	0.344028	0.172014	−	0.985094i	$-0.444973\pi$
$197$	4.82867	0.344028	0.172014	+	0.985094i	$0.444973\pi$
$198$	−2.86357	−0.203505
$199$	10.2922	0.729592	0.364796	−	0.931087i	$-0.381139\pi$
$199$	10.2922	0.729592	0.364796	+	0.931087i	$0.381139\pi$
$200$	−4.87939	−0.345025
$201$	14.4759	1.02105
$202$	17.1286	1.20516
$203$	−0.109034	−0.00765270
$204$	−2.76483	−0.193577
$205$	3.72175	0.259938
$206$	−13.4202	−0.935032
$207$	−5.77032	−0.401065
$208$	−4.48325	−0.310857
$209$	9.10628	0.629894
$210$	0.228251	0.0157508
$211$	1.37094	0.0943794	0.0471897	−	0.998886i	$-0.484973\pi$
$211$	1.37094	0.0943794	0.0471897	+	0.998886i	$0.484973\pi$
$212$	4.37564	0.300520
$213$	−12.2152	−0.836973
$214$	−20.4600	−1.39862
$215$	3.07666	0.209827
$216$	5.65060	0.384475
$217$	3.22322	0.218806
$218$	10.6587	0.721900
$219$	−9.88629	−0.668054
$220$	0.897887	0.0605355
$221$	−9.01064	−0.606121
$222$	0	0
$223$	−29.2612	−1.95947	−0.979736	−	0.200292i	$-0.935811\pi$
$223$	−29.2612	−1.95947	−0.979736	+	0.200292i	$0.935811\pi$
$224$	−0.477756	−0.0319214
$225$	5.40444	0.360296
$226$	12.2122	0.812345
$227$	10.3046	0.683939	0.341969	−	0.939711i	$-0.388906\pi$
$227$	10.3046	0.683939	0.341969	+	0.939711i	$0.388906\pi$
$228$	−4.84535	−0.320891
$229$	15.6678	1.03536	0.517678	−	0.855576i	$-0.326797\pi$
$229$	15.6678	1.03536	0.517678	+	0.855576i	$0.326797\pi$
$230$	1.80932	0.119303
$231$	1.69916	0.111796
$232$	0.228222	0.0149835
$233$	7.20404	0.471952	0.235976	−	0.971759i	$-0.424171\pi$
$233$	7.20404	0.471952	0.235976	+	0.971759i	$0.424171\pi$
$234$	4.96568	0.324617
$235$	2.59007	0.168957
$236$	4.47776	0.291477
$237$	−4.86398	−0.315949
$238$	−0.960215	−0.0622415
$239$	−21.9530	−1.42002	−0.710012	−	0.704190i	$-0.751310\pi$
$239$	−21.9530	−1.42002	−0.710012	+	0.704190i	$0.751310\pi$
$240$	−0.477756	−0.0308390
$241$	14.8104	0.954021	0.477011	−	0.878898i	$-0.341720\pi$
$241$	14.8104	0.954021	0.477011	+	0.878898i	$0.341720\pi$
$242$	−4.31590	−0.277437
$243$	−10.8297	−0.694723
$244$	−1.43851	−0.0920909
$245$	−2.35180	−0.150251
$246$	−14.7419	−0.939908
$247$	−15.7911	−1.00476
$248$	−6.74658	−0.428408
$249$	−1.94604	−0.123325
$250$	−3.43107	−0.217000
$251$	13.2899	0.838849	0.419424	−	0.907790i	$-0.362232\pi$
$251$	13.2899	0.838849	0.419424	+	0.907790i	$0.362232\pi$
$252$	0.529166	0.0333343
$253$	13.4690	0.846790
$254$	−7.04958	−0.442330
$255$	−0.960215	−0.0601310
$256$	1.00000	0.0625000
$257$	17.5025	1.09178	0.545889	−	0.837857i	$-0.316192\pi$
$257$	17.5025	1.09178	0.545889	+	0.837857i	$0.316192\pi$
$258$	−12.1867	−0.758709
$259$	0	0
$260$	−1.55702	−0.0965621
$261$	−0.252780	−0.0156467
$262$	1.98503	0.122636
$263$	−14.1334	−0.871505	−0.435753	−	0.900066i	$-0.643518\pi$
$263$	−14.1334	−0.871505	−0.435753	+	0.900066i	$0.643518\pi$
$264$	−3.55654	−0.218890
$265$	1.51964	0.0933510
$266$	−1.68277	−0.103177
$267$	−5.26080	−0.321956
$268$	−10.5230	−0.642797
$269$	−26.8102	−1.63465	−0.817324	−	0.576179i	$-0.804543\pi$
$269$	−26.8102	−1.63465	−0.817324	+	0.576179i	$0.804543\pi$
$270$	1.96243	0.119430
$271$	−10.9129	−0.662909	−0.331454	−	0.943471i	$-0.607539\pi$
$271$	−10.9129	−0.662909	−0.331454	+	0.943471i	$0.607539\pi$
$272$	2.00984	0.121865
$273$	−2.94649	−0.178329
$274$	17.3979	1.05105
$275$	−12.6150	−0.760712
$276$	−7.16671	−0.431385
$277$	6.14345	0.369124	0.184562	−	0.982821i	$-0.440913\pi$
$277$	6.14345	0.369124	0.184562	+	0.982821i	$0.440913\pi$
$278$	0.737051	0.0442054
$279$	7.47256	0.447371
$280$	−0.165923	−0.00991579
$281$	2.95302	0.176163	0.0880813	−	0.996113i	$-0.471926\pi$
$281$	2.95302	0.176163	0.0880813	+	0.996113i	$0.471926\pi$
$282$	−10.2593	−0.610930
$283$	14.4745	0.860419	0.430209	−	0.902729i	$-0.358440\pi$
$283$	14.4745	0.860419	0.430209	+	0.902729i	$0.358440\pi$
$284$	8.87964	0.526910
$285$	−1.68277	−0.0996788
$286$	−11.5908	−0.685380
$287$	−5.11980	−0.302212
$288$	−1.10761	−0.0652664
$289$	−12.9605	−0.762384
$290$	0.0792606	0.00465434
$291$	−25.4267	−1.49054
$292$	7.18667	0.420568
$293$	−12.5821	−0.735055	−0.367528	−	0.930013i	$-0.619796\pi$
$293$	−12.5821	−0.735055	−0.367528	+	0.930013i	$0.619796\pi$
$294$	9.31551	0.543291
$295$	1.55511	0.0905419
$296$	0	0
$297$	14.6089	0.847691
$298$	−19.0346	−1.10265
$299$	−23.3565	−1.35074
$300$	6.71229	0.387534
$301$	−4.23239	−0.243951
$302$	−6.47198	−0.372420
$303$	−23.5629	−1.35365
$304$	3.52224	0.202015
$305$	−0.499588	−0.0286063
$306$	−2.22612	−0.127259
$307$	−18.8997	−1.07866	−0.539331	−	0.842094i	$-0.681323\pi$
$307$	−18.8997	−1.07866	−0.539331	+	0.842094i	$0.681323\pi$
$308$	−1.23517	−0.0703804
$309$	18.4614	1.05023
$310$	−2.34306	−0.133077
$311$	−0.113386	−0.00642951	−0.00321475	−	0.999995i	$-0.501023\pi$
$311$	−0.113386	−0.00642951	−0.00321475	+	0.999995i	$0.501023\pi$
$312$	6.16735	0.349157
$313$	9.18109	0.518946	0.259473	−	0.965750i	$-0.416451\pi$
$313$	9.18109	0.518946	0.259473	+	0.965750i	$0.416451\pi$
$314$	12.0920	0.682391
$315$	0.183777	0.0103547
$316$	3.53579	0.198904
$317$	26.2646	1.47517	0.737583	−	0.675256i	$-0.235967\pi$
$317$	26.2646	1.47517	0.737583	+	0.675256i	$0.235967\pi$
$318$	−6.01932	−0.337547
$319$	0.590036	0.0330357
$320$	0.347296	0.0194145
$321$	28.1457	1.57094
$322$	−2.48897	−0.138705
$323$	7.07916	0.393895
$324$	−4.45039	−0.247244
$325$	21.8755	1.21343
$326$	14.7466	0.816738
$327$	−14.6626	−0.810844
$328$	10.7164	0.591712
$329$	−3.56301	−0.196435
$330$	−1.23517	−0.0679940
$331$	−28.5781	−1.57079	−0.785397	−	0.618992i	$-0.787541\pi$
$331$	−28.5781	−1.57079	−0.785397	+	0.618992i	$0.787541\pi$
$332$	1.41464	0.0776383
$333$	0	0
$334$	8.30639	0.454506
$335$	−3.65461	−0.199673
$336$	0.657221	0.0358544
$337$	−9.77285	−0.532361	−0.266181	−	0.963923i	$-0.585762\pi$
$337$	−9.77285	−0.532361	−0.266181	+	0.963923i	$0.585762\pi$
$338$	7.09953	0.386163
$339$	−16.7997	−0.912432
$340$	0.698012	0.0378550
$341$	−17.4424	−0.944557
$342$	−3.90126	−0.210956
$343$	6.57953	0.355261
$344$	8.85889	0.477639
$345$	−2.48897	−0.134002
$346$	−6.61273	−0.355503
$347$	16.5763	0.889864	0.444932	−	0.895564i	$-0.353228\pi$
$347$	16.5763	0.889864	0.444932	+	0.895564i	$0.353228\pi$
$348$	−0.313952	−0.0168296
$349$	18.6888	1.00039	0.500194	−	0.865913i	$-0.333262\pi$
$349$	18.6888	1.00039	0.500194	+	0.865913i	$0.333262\pi$
$350$	2.33115	0.124605
$351$	−25.3331	−1.35218
$352$	2.58536	0.137800
$353$	5.40403	0.287628	0.143814	−	0.989605i	$-0.454063\pi$
$353$	5.40403	0.287628	0.143814	+	0.989605i	$0.454063\pi$
$354$	−6.15979	−0.327389
$355$	3.08387	0.163675
$356$	3.82425	0.202685
$357$	1.32091	0.0699101
$358$	4.53985	0.239939
$359$	−10.5664	−0.557672	−0.278836	−	0.960339i	$-0.589949\pi$
$359$	−10.5664	−0.557672	−0.278836	+	0.960339i	$0.589949\pi$
$360$	−0.384668	−0.0202738
$361$	−6.59380	−0.347042
$362$	−1.56373	−0.0821876
$363$	5.93714	0.311619
$364$	2.14190	0.112266
$365$	2.49590	0.130642
$366$	1.97887	0.103437
$367$	−0.215875	−0.0112686	−0.00563430	−	0.999984i	$-0.501793\pi$
$367$	−0.215875	−0.0112686	−0.00563430	+	0.999984i	$0.501793\pi$
$368$	5.20972	0.271575
$369$	−11.8695	−0.617902
$370$	0	0
$371$	−2.09049	−0.108533
$372$	9.28089	0.481192
$373$	−19.8047	−1.02545	−0.512725	−	0.858553i	$-0.671364\pi$
$373$	−19.8047	−1.02545	−0.512725	+	0.858553i	$0.671364\pi$
$374$	5.19618	0.268688
$375$	4.71993	0.243736
$376$	7.45780	0.384607
$377$	−1.02318	−0.0526962
$378$	−2.69961	−0.138853
$379$	−23.0959	−1.18636	−0.593179	−	0.805071i	$-0.702127\pi$
$379$	−23.0959	−1.18636	−0.593179	+	0.805071i	$0.702127\pi$
$380$	1.22326	0.0627520
$381$	9.69770	0.496828
$382$	23.0183	1.17772
$383$	−5.08602	−0.259883	−0.129942	−	0.991522i	$-0.541479\pi$
$383$	−5.08602	−0.259883	−0.129942	+	0.991522i	$0.541479\pi$
$384$	−1.37564	−0.0702005
$385$	−0.428971	−0.0218624
$386$	−10.5541	−0.537190
$387$	−9.81217	−0.498781
$388$	18.4835	0.938358
$389$	−29.1473	−1.47783	−0.738914	−	0.673800i	$-0.764661\pi$
$389$	−29.1473	−1.47783	−0.738914	+	0.673800i	$0.764661\pi$
$390$	2.14190	0.108459
$391$	10.4707	0.529527
$392$	−6.77175	−0.342025
$393$	−2.73069	−0.137745
$394$	4.82867	0.243265
$395$	1.22797	0.0617857
$396$	−2.86357	−0.143900
$397$	−15.9925	−0.802640	−0.401320	−	0.915938i	$-0.631448\pi$
$397$	−15.9925	−0.802640	−0.401320	+	0.915938i	$0.631448\pi$
$398$	10.2922	0.515899
$399$	2.31489	0.115890
$400$	−4.87939	−0.243969
$401$	−5.43983	−0.271652	−0.135826	−	0.990733i	$-0.543369\pi$
$401$	−5.43983	−0.271652	−0.135826	+	0.990733i	$0.543369\pi$
$402$	14.4759	0.721994
$403$	30.2466	1.50669
$404$	17.1286	0.852180
$405$	−1.54560	−0.0768016
$406$	−0.109034	−0.00541128
$407$	0	0
$408$	−2.76483	−0.136879
$409$	−37.7243	−1.86535	−0.932674	−	0.360721i	$-0.882531\pi$
$409$	−37.7243	−1.86535	−0.932674	+	0.360721i	$0.882531\pi$
$410$	3.72175	0.183804
$411$	−23.9334	−1.18055
$412$	−13.4202	−0.661167
$413$	−2.13927	−0.105267
$414$	−5.77032	−0.283596
$415$	0.491298	0.0241169
$416$	−4.48325	−0.219809
$417$	−1.01392	−0.0496518
$418$	9.10628	0.445403
$419$	6.19173	0.302486	0.151243	−	0.988497i	$-0.451672\pi$
$419$	6.19173	0.302486	0.151243	+	0.988497i	$0.451672\pi$
$420$	0.228251	0.0111375
$421$	−10.1086	−0.492664	−0.246332	−	0.969185i	$-0.579225\pi$
$421$	−10.1086	−0.492664	−0.246332	+	0.969185i	$0.579225\pi$
$422$	1.37094	0.0667363
$423$	−8.26031	−0.401630
$424$	4.37564	0.212500
$425$	−9.80681	−0.475700
$426$	−12.2152	−0.591829
$427$	0.687254	0.0332586
$428$	−20.4600	−0.988972
$429$	15.9448	0.769824
$430$	3.07666	0.148370
$431$	−34.1782	−1.64631	−0.823153	−	0.567820i	$-0.807787\pi$
$431$	−34.1782	−1.64631	−0.823153	+	0.567820i	$0.807787\pi$
$432$	5.65060	0.271865
$433$	−0.686319	−0.0329824	−0.0164912	−	0.999864i	$-0.505250\pi$
$433$	−0.686319	−0.0329824	−0.0164912	+	0.999864i	$0.505250\pi$
$434$	3.22322	0.154719
$435$	−0.109034	−0.00522779
$436$	10.6587	0.510461
$437$	18.3499	0.877795
$438$	−9.88629	−0.472385
$439$	21.5089	1.02656	0.513282	−	0.858220i	$-0.328430\pi$
$439$	21.5089	1.02656	0.513282	+	0.858220i	$0.328430\pi$
$440$	0.897887	0.0428051
$441$	7.50044	0.357164
$442$	−9.01064	−0.428592
$443$	−28.5971	−1.35869	−0.679344	−	0.733820i	$-0.737736\pi$
$443$	−28.5971	−1.35869	−0.679344	+	0.733820i	$0.737736\pi$
$444$	0	0
$445$	1.32815	0.0629602
$446$	−29.2612	−1.38556
$447$	26.1849	1.23850
$448$	−0.477756	−0.0225718
$449$	−34.5689	−1.63141	−0.815703	−	0.578471i	$-0.803650\pi$
$449$	−34.5689	−1.63141	−0.815703	+	0.578471i	$0.803650\pi$
$450$	5.40444	0.254768
$451$	27.7057	1.30461
$452$	12.2122	0.574415
$453$	8.90313	0.418305
$454$	10.3046	0.483618
$455$	0.743873	0.0348733
$456$	−4.84535	−0.226904
$457$	32.9084	1.53939	0.769695	−	0.638411i	$-0.220408\pi$
$457$	32.9084	1.53939	0.769695	+	0.638411i	$0.220408\pi$
$458$	15.6678	0.732107
$459$	11.3568	0.530091
$460$	1.80932	0.0843598
$461$	−18.1394	−0.844838	−0.422419	−	0.906401i	$-0.638819\pi$
$461$	−18.1394	−0.844838	−0.422419	+	0.906401i	$0.638819\pi$
$462$	1.69916	0.0790519
$463$	0.339403	0.0157734	0.00788671	−	0.999969i	$-0.497490\pi$
$463$	0.339403	0.0157734	0.00788671	+	0.999969i	$0.497490\pi$
$464$	0.228222	0.0105949
$465$	3.22322	0.149473
$466$	7.20404	0.333721
$467$	−14.2020	−0.657191	−0.328596	−	0.944471i	$-0.606575\pi$
$467$	−14.2020	−0.657191	−0.328596	+	0.944471i	$0.606575\pi$
$468$	4.96568	0.229539
$469$	5.02744	0.232146
$470$	2.59007	0.119471
$471$	−16.6343	−0.766467
$472$	4.47776	0.206105
$473$	22.9035	1.05310
$474$	−4.86398	−0.223410
$475$	−17.1864	−0.788566
$476$	−0.960215	−0.0440114
$477$	−4.84649	−0.221906
$478$	−21.9530	−1.00411
$479$	−33.9805	−1.55261	−0.776304	−	0.630359i	$-0.782908\pi$
$479$	−33.9805	−1.55261	−0.776304	+	0.630359i	$0.782908\pi$
$480$	−0.477756	−0.0218065
$481$	0	0
$482$	14.8104	0.674595
$483$	3.42394	0.155795
$484$	−4.31590	−0.196177
$485$	6.41925	0.291483
$486$	−10.8297	−0.491243
$487$	−25.3330	−1.14795	−0.573974	−	0.818874i	$-0.694599\pi$
$487$	−25.3330	−1.14795	−0.573974	+	0.818874i	$0.694599\pi$
$488$	−1.43851	−0.0651181
$489$	−20.2860	−0.917366
$490$	−2.35180	−0.106244
$491$	21.2687	0.959844	0.479922	−	0.877311i	$-0.340665\pi$
$491$	21.2687	0.959844	0.479922	+	0.877311i	$0.340665\pi$
$492$	−14.7419	−0.664615
$493$	0.458690	0.0206584
$494$	−15.7911	−0.710475
$495$	−0.994506	−0.0446997
$496$	−6.74658	−0.302930
$497$	−4.24230	−0.190293
$498$	−1.94604	−0.0872039
$499$	16.4306	0.735534	0.367767	−	0.929918i	$-0.380122\pi$
$499$	16.4306	0.735534	0.367767	+	0.929918i	$0.380122\pi$
$500$	−3.43107	−0.153442
$501$	−11.4266	−0.510504
$502$	13.2899	0.593155
$503$	20.8838	0.931162	0.465581	−	0.885005i	$-0.345845\pi$
$503$	20.8838	0.931162	0.465581	+	0.885005i	$0.345845\pi$
$504$	0.529166	0.0235709
$505$	5.94870	0.264714
$506$	13.4690	0.598771
$507$	−9.76641	−0.433742
$508$	−7.04958	−0.312774
$509$	40.0925	1.77707	0.888534	−	0.458811i	$-0.151725\pi$
$509$	40.0925	1.77707	0.888534	+	0.458811i	$0.151725\pi$
$510$	−0.960215	−0.0425190
$511$	−3.43347	−0.151888
$512$	1.00000	0.0441942
$513$	19.9028	0.878730
$514$	17.5025	0.772004
$515$	−4.66080	−0.205379
$516$	−12.1867	−0.536488
$517$	19.2811	0.847982
$518$	0	0
$519$	9.09676	0.399303
$520$	−1.55702	−0.0682797
$521$	9.16686	0.401608	0.200804	−	0.979631i	$-0.435645\pi$
$521$	9.16686	0.401608	0.200804	+	0.979631i	$0.435645\pi$
$522$	−0.252780	−0.0110639
$523$	29.6446	1.29627	0.648135	−	0.761525i	$-0.275549\pi$
$523$	29.6446	1.29627	0.648135	+	0.761525i	$0.275549\pi$
$524$	1.98503	0.0867164
$525$	−3.20684	−0.139958
$526$	−14.1334	−0.616247
$527$	−13.5596	−0.590665
$528$	−3.55654	−0.154778
$529$	4.14118	0.180051
$530$	1.51964	0.0660092
$531$	−4.95959	−0.215228
$532$	−1.68277	−0.0729574
$533$	−48.0441	−2.08102
$534$	−5.26080	−0.227657
$535$	−7.10569	−0.307206
$536$	−10.5230	−0.454526
$537$	−6.24522	−0.269501
$538$	−26.8102	−1.15587
$539$	−17.5074	−0.754098
$540$	1.96243	0.0844497
$541$	28.9861	1.24621	0.623104	−	0.782139i	$-0.285871\pi$
$541$	28.9861	1.24621	0.623104	+	0.782139i	$0.285871\pi$
$542$	−10.9129	−0.468747
$543$	2.15113	0.0923138
$544$	2.00984	0.0861714
$545$	3.70174	0.158565
$546$	−2.94649	−0.126098
$547$	5.36609	0.229437	0.114719	−	0.993398i	$-0.463403\pi$
$547$	5.36609	0.229437	0.114719	+	0.993398i	$0.463403\pi$
$548$	17.3979	0.743203
$549$	1.59330	0.0680003
$550$	−12.6150	−0.537905
$551$	0.803853	0.0342453
$552$	−7.16671	−0.305036
$553$	−1.68924	−0.0718339
$554$	6.14345	0.261010
$555$	0	0
$556$	0.737051	0.0312579
$557$	−11.7348	−0.497222	−0.248611	−	0.968603i	$-0.579974\pi$
$557$	−11.7348	−0.497222	−0.248611	+	0.968603i	$0.579974\pi$
$558$	7.47256	0.316339
$559$	−39.7166	−1.67983
$560$	−0.165923	−0.00701152
$561$	−7.14808	−0.301792
$562$	2.95302	0.124566
$563$	18.9186	0.797323	0.398662	−	0.917098i	$-0.369475\pi$
$563$	18.9186	0.797323	0.398662	+	0.917098i	$0.369475\pi$
$564$	−10.2593	−0.431993
$565$	4.24126	0.178431
$566$	14.4745	0.608408
$567$	2.12620	0.0892919
$568$	8.87964	0.372581
$569$	−21.6147	−0.906136	−0.453068	−	0.891476i	$-0.649671\pi$
$569$	−21.6147	−0.906136	−0.453068	+	0.891476i	$0.649671\pi$
$570$	−1.68277	−0.0704836
$571$	−35.0999	−1.46888	−0.734442	−	0.678671i	$-0.762556\pi$
$571$	−35.0999	−1.46888	−0.734442	+	0.678671i	$0.762556\pi$
$572$	−11.5908	−0.484637
$573$	−31.6649	−1.32282
$574$	−5.11980	−0.213696
$575$	−25.4202	−1.06010
$576$	−1.10761	−0.0461503
$577$	−43.0837	−1.79360	−0.896799	−	0.442439i	$-0.854113\pi$
$577$	−43.0837	−1.79360	−0.896799	+	0.442439i	$0.854113\pi$
$578$	−12.9605	−0.539087
$579$	14.5187	0.603376
$580$	0.0792606	0.00329112
$581$	−0.675851	−0.0280390
$582$	−25.4267	−1.05397
$583$	11.3126	0.468521
$584$	7.18667	0.297387
$585$	1.72456	0.0713019
$586$	−12.5821	−0.519762
$587$	−20.4247	−0.843019	−0.421509	−	0.906824i	$-0.638500\pi$
$587$	−20.4247	−0.843019	−0.421509	+	0.906824i	$0.638500\pi$
$588$	9.31551	0.384165
$589$	−23.7631	−0.979142
$590$	1.55511	0.0640228
$591$	−6.64252	−0.273237
$592$	0	0
$593$	−0.908005	−0.0372873	−0.0186436	−	0.999826i	$-0.505935\pi$
$593$	−0.908005	−0.0372873	−0.0186436	+	0.999826i	$0.505935\pi$
$594$	14.6089	0.599408
$595$	−0.333479	−0.0136713
$596$	−19.0346	−0.779689
$597$	−14.1583	−0.579462
$598$	−23.3565	−0.955117
$599$	−12.3235	−0.503526	−0.251763	−	0.967789i	$-0.581010\pi$
$599$	−12.3235	−0.503526	−0.251763	+	0.967789i	$0.581010\pi$
$600$	6.71229	0.274028
$601$	−34.3189	−1.39990	−0.699948	−	0.714194i	$-0.746793\pi$
$601$	−34.3189	−1.39990	−0.699948	+	0.714194i	$0.746793\pi$
$602$	−4.23239	−0.172499
$603$	11.6554	0.474644
$604$	−6.47198	−0.263341
$605$	−1.49890	−0.0609388
$606$	−23.5629	−0.957175
$607$	−4.08558	−0.165829	−0.0829143	−	0.996557i	$-0.526423\pi$
$607$	−4.08558	−0.165829	−0.0829143	+	0.996557i	$0.526423\pi$
$608$	3.52224	0.142846
$609$	0.149992	0.00607799
$610$	−0.499588	−0.0202277
$611$	−33.4352	−1.35264
$612$	−2.22612	−0.0899855
$613$	19.8782	0.802873	0.401437	−	0.915887i	$-0.368511\pi$
$613$	19.8782	0.802873	0.401437	+	0.915887i	$0.368511\pi$
$614$	−18.8997	−0.762730
$615$	−5.11980	−0.206450
$616$	−1.23517	−0.0497665
$617$	3.82536	0.154003	0.0770016	−	0.997031i	$-0.475465\pi$
$617$	3.82536	0.154003	0.0770016	+	0.997031i	$0.475465\pi$
$618$	18.4614	0.742628
$619$	−11.9503	−0.480324	−0.240162	−	0.970733i	$-0.577201\pi$
$619$	−11.9503	−0.480324	−0.240162	+	0.970733i	$0.577201\pi$
$620$	−2.34306	−0.0940997
$621$	29.4380	1.18131
$622$	−0.113386	−0.00454635
$623$	−1.82706	−0.0731995
$624$	6.16735	0.246892
$625$	23.2053	0.928213
$626$	9.18109	0.366950
$627$	−12.5270	−0.500280
$628$	12.0920	0.482523
$629$	0	0
$630$	0.183777	0.00732186
$631$	−20.1492	−0.802128	−0.401064	−	0.916050i	$-0.631360\pi$
$631$	−20.1492	−0.802128	−0.401064	+	0.916050i	$0.631360\pi$
$632$	3.53579	0.140646
$633$	−1.88592	−0.0749587
$634$	26.2646	1.04310
$635$	−2.44829	−0.0971575
$636$	−6.01932	−0.238682
$637$	30.3594	1.20288
$638$	0.590036	0.0233597
$639$	−9.83515	−0.389073
$640$	0.347296	0.0137281
$641$	30.1490	1.19081	0.595406	−	0.803425i	$-0.296991\pi$
$641$	30.1490	1.19081	0.595406	+	0.803425i	$0.296991\pi$
$642$	28.1457	1.11082
$643$	−13.0551	−0.514844	−0.257422	−	0.966299i	$-0.582873\pi$
$643$	−13.0551	−0.514844	−0.257422	+	0.966299i	$0.582873\pi$
$644$	−2.48897	−0.0980793
$645$	−4.23239	−0.166650
$646$	7.07916	0.278526
$647$	47.0424	1.84943	0.924715	−	0.380661i	$-0.124304\pi$
$647$	47.0424	1.84943	0.924715	+	0.380661i	$0.124304\pi$
$648$	−4.45039	−0.174828
$649$	11.5766	0.454422
$650$	21.8755	0.858028
$651$	−4.43400	−0.173782
$652$	14.7466	0.577521
$653$	−27.6191	−1.08082	−0.540409	−	0.841403i	$-0.681730\pi$
$653$	−27.6191	−1.08082	−0.540409	+	0.841403i	$0.681730\pi$
$654$	−14.6626	−0.573353
$655$	0.689394	0.0269368
$656$	10.7164	0.418403
$657$	−7.96001	−0.310549
$658$	−3.56301	−0.138900
$659$	35.9283	1.39957	0.699783	−	0.714355i	$-0.253280\pi$
$659$	35.9283	1.39957	0.699783	+	0.714355i	$0.253280\pi$
$660$	−1.23517	−0.0480790
$661$	39.4234	1.53339	0.766696	−	0.642010i	$-0.221899\pi$
$661$	39.4234	1.53339	0.766696	+	0.642010i	$0.221899\pi$
$662$	−28.5781	−1.11072
$663$	12.3954	0.481398
$664$	1.41464	0.0548986
$665$	−0.584421	−0.0226629
$666$	0	0
$667$	1.18897	0.0460372
$668$	8.30639	0.321384
$669$	40.2529	1.55627
$670$	−3.65461	−0.141190
$671$	−3.71906	−0.143573
$672$	0.657221	0.0253529
$673$	15.2554	0.588054	0.294027	−	0.955797i	$-0.405005\pi$
$673$	15.2554	0.588054	0.294027	+	0.955797i	$0.405005\pi$
$674$	−9.77285	−0.376436
$675$	−27.5715	−1.06123
$676$	7.09953	0.273059
$677$	21.4058	0.822691	0.411345	−	0.911480i	$-0.365059\pi$
$677$	21.4058	0.822691	0.411345	+	0.911480i	$0.365059\pi$
$678$	−16.7997	−0.645187
$679$	−8.83060	−0.338887
$680$	0.698012	0.0267675
$681$	−14.1754	−0.543203
$682$	−17.4424	−0.667903
$683$	12.6272	0.483168	0.241584	−	0.970380i	$-0.422333\pi$
$683$	12.6272	0.483168	0.241584	+	0.970380i	$0.422333\pi$
$684$	−3.90126	−0.149168
$685$	6.04224	0.230862
$686$	6.57953	0.251208
$687$	−21.5533	−0.822308
$688$	8.85889	0.337742
$689$	−19.6171	−0.747352
$690$	−2.48897	−0.0947536
$691$	−3.43270	−0.130586	−0.0652930	−	0.997866i	$-0.520798\pi$
$691$	−3.43270	−0.130586	−0.0652930	+	0.997866i	$0.520798\pi$
$692$	−6.61273	−0.251378
$693$	1.36808	0.0519692
$694$	16.5763	0.629229
$695$	0.255975	0.00970970
$696$	−0.313952	−0.0119003
$697$	21.5382	0.815818
$698$	18.6888	0.707382
$699$	−9.91019	−0.374838
$700$	2.33115	0.0881093
$701$	0.187492	0.00708148	0.00354074	−	0.999994i	$-0.498873\pi$
$701$	0.187492	0.00708148	0.00354074	+	0.999994i	$0.498873\pi$
$702$	−25.3331	−0.956134
$703$	0	0
$704$	2.58536	0.0974395
$705$	−3.56301	−0.134191
$706$	5.40403	0.203384
$707$	−8.18329	−0.307764
$708$	−6.15979	−0.231499
$709$	−48.4114	−1.81813	−0.909064	−	0.416656i	$-0.863202\pi$
$709$	−48.4114	−1.81813	−0.909064	+	0.416656i	$0.863202\pi$
$710$	3.08387	0.115735
$711$	−3.91626	−0.146871
$712$	3.82425	0.143320
$713$	−35.1478	−1.31630
$714$	1.32091	0.0494339
$715$	−4.02545	−0.150543
$716$	4.53985	0.169662
$717$	30.1995	1.12782
$718$	−10.5664	−0.394334
$719$	−45.5785	−1.69979	−0.849896	−	0.526951i	$-0.823335\pi$
$719$	−45.5785	−1.69979	−0.849896	+	0.526951i	$0.823335\pi$
$720$	−0.384668	−0.0143357
$721$	6.41159	0.238780
$722$	−6.59380	−0.245396
$723$	−20.3738	−0.757710
$724$	−1.56373	−0.0581154
$725$	−1.11358	−0.0413574
$726$	5.93714	0.220348
$727$	41.9406	1.55549	0.777745	−	0.628580i	$-0.216363\pi$
$727$	41.9406	1.55549	0.777745	+	0.628580i	$0.216363\pi$
$728$	2.14190	0.0793840
$729$	28.2489	1.04626
$730$	2.49590	0.0923776
$731$	17.8050	0.658542
$732$	1.97887	0.0731411
$733$	17.6149	0.650622	0.325311	−	0.945607i	$-0.394531\pi$
$733$	17.6149	0.650622	0.325311	+	0.945607i	$0.394531\pi$
$734$	−0.215875	−0.00796811
$735$	3.23524	0.119334
$736$	5.20972	0.192033
$737$	−27.2059	−1.00214
$738$	−11.8695	−0.436923
$739$	39.4393	1.45080	0.725400	−	0.688328i	$-0.241655\pi$
$739$	39.4393	1.45080	0.725400	+	0.688328i	$0.241655\pi$
$740$	0	0
$741$	21.7229	0.798011
$742$	−2.09049	−0.0767442
$743$	13.1159	0.481176	0.240588	−	0.970627i	$-0.422660\pi$
$743$	13.1159	0.481176	0.240588	+	0.970627i	$0.422660\pi$
$744$	9.28089	0.340254
$745$	−6.61066	−0.242196
$746$	−19.8047	−0.725102
$747$	−1.56686	−0.0573285
$748$	5.19618	0.189991
$749$	9.77489	0.357167
$750$	4.71993	0.172348
$751$	−39.9787	−1.45884	−0.729421	−	0.684065i	$-0.760211\pi$
$751$	−39.9787	−1.45884	−0.729421	+	0.684065i	$0.760211\pi$
$752$	7.45780	0.271958
$753$	−18.2821	−0.666237
$754$	−1.02318	−0.0372618
$755$	−2.24769	−0.0818020
$756$	−2.69961	−0.0981837
$757$	27.9721	1.01666	0.508332	−	0.861161i	$-0.330262\pi$
$757$	27.9721	1.01666	0.508332	+	0.861161i	$0.330262\pi$
$758$	−23.0959	−0.838882
$759$	−18.5286	−0.672544
$760$	1.22326	0.0443724
$761$	−2.17669	−0.0789049	−0.0394525	−	0.999221i	$-0.512561\pi$
$761$	−2.17669	−0.0789049	−0.0394525	+	0.999221i	$0.512561\pi$
$762$	9.69770	0.351311
$763$	−5.09227	−0.184353
$764$	23.0183	0.832773
$765$	−0.773123	−0.0279523
$766$	−5.08602	−0.183765
$767$	−20.0749	−0.724863
$768$	−1.37564	−0.0496392
$769$	−41.3810	−1.49224	−0.746118	−	0.665814i	$-0.768084\pi$
$769$	−41.3810	−1.49224	−0.746118	+	0.665814i	$0.768084\pi$
$770$	−0.428971	−0.0154590
$771$	−24.0772	−0.867121
$772$	−10.5541	−0.379851
$773$	−12.2869	−0.441930	−0.220965	−	0.975282i	$-0.570921\pi$
$773$	−12.2869	−0.441930	−0.220965	+	0.975282i	$0.570921\pi$
$774$	−9.81217	−0.352691
$775$	32.9192	1.18249
$776$	18.4835	0.663519
$777$	0	0
$778$	−29.1473	−1.04498
$779$	37.7456	1.35238
$780$	2.14190	0.0766923
$781$	22.9571	0.821469
$782$	10.4707	0.374432
$783$	1.28959	0.0460862
$784$	−6.77175	−0.241848
$785$	4.19951	0.149887
$786$	−2.73069	−0.0974006
$787$	24.1525	0.860945	0.430473	−	0.902604i	$-0.358347\pi$
$787$	24.1525	0.860945	0.430473	+	0.902604i	$0.358347\pi$
$788$	4.82867	0.172014
$789$	19.4426	0.692174
$790$	1.22797	0.0436891
$791$	−5.83446	−0.207449
$792$	−2.86357	−0.101752
$793$	6.44918	0.229017
$794$	−15.9925	−0.567552
$795$	−2.09049	−0.0741420
$796$	10.2922	0.364796
$797$	−32.9521	−1.16722	−0.583611	−	0.812033i	$-0.698361\pi$
$797$	−32.9521	−1.16722	−0.583611	+	0.812033i	$0.698361\pi$
$798$	2.31489	0.0819463
$799$	14.9890	0.530273
$800$	−4.87939	−0.172512
$801$	−4.23576	−0.149663
$802$	−5.43983	−0.192087
$803$	18.5802	0.655679
$804$	14.4759	0.510527
$805$	−0.864411	−0.0304665
$806$	30.2466	1.06539
$807$	36.8813	1.29828
$808$	17.1286	0.602582
$809$	35.6899	1.25479	0.627395	−	0.778701i	$-0.284121\pi$
$809$	35.6899	1.25479	0.627395	+	0.778701i	$0.284121\pi$
$810$	−1.54560	−0.0543069
$811$	33.8803	1.18970	0.594848	−	0.803838i	$-0.297212\pi$
$811$	33.8803	1.18970	0.594848	+	0.803838i	$0.297212\pi$
$812$	−0.109034	−0.00382635
$813$	15.0122	0.526501
$814$	0	0
$815$	5.12143	0.179396
$816$	−2.76483	−0.0967883
$817$	31.2032	1.09166
$818$	−37.7243	−1.31900
$819$	−2.37238	−0.0828977
$820$	3.72175	0.129969
$821$	−23.7121	−0.827557	−0.413778	−	0.910378i	$-0.635791\pi$
$821$	−23.7121	−0.827557	−0.413778	+	0.910378i	$0.635791\pi$
$822$	−23.9334	−0.834772
$823$	24.8087	0.864777	0.432389	−	0.901687i	$-0.357671\pi$
$823$	24.8087	0.864777	0.432389	+	0.901687i	$0.357671\pi$
$824$	−13.4202	−0.467516
$825$	17.3537	0.604179
$826$	−2.13927	−0.0744348
$827$	53.0663	1.84530	0.922648	−	0.385643i	$-0.126020\pi$
$827$	53.0663	1.84530	0.922648	+	0.385643i	$0.126020\pi$
$828$	−5.77032	−0.200533
$829$	−6.24877	−0.217029	−0.108514	−	0.994095i	$-0.534609\pi$
$829$	−6.24877	−0.217029	−0.108514	+	0.994095i	$0.534609\pi$
$830$	0.491298	0.0170532
$831$	−8.45120	−0.293169
$832$	−4.48325	−0.155429
$833$	−13.6102	−0.471564
$834$	−1.01392	−0.0351092
$835$	2.88478	0.0998319
$836$	9.10628	0.314947
$837$	−38.1222	−1.31770
$838$	6.19173	0.213890
$839$	11.3762	0.392749	0.196375	−	0.980529i	$-0.437083\pi$
$839$	11.3762	0.392749	0.196375	+	0.980529i	$0.437083\pi$
$840$	0.228251	0.00787539
$841$	−28.9479	−0.998204
$842$	−10.1086	−0.348366
$843$	−4.06231	−0.139913
$844$	1.37094	0.0471897
$845$	2.46564	0.0848206
$846$	−8.26031	−0.283995
$847$	2.06195	0.0708493
$848$	4.37564	0.150260
$849$	−19.9117	−0.683368
$850$	−9.80681	−0.336371
$851$	0	0
$852$	−12.2152	−0.418486
$853$	−0.933850	−0.0319744	−0.0159872	−	0.999872i	$-0.505089\pi$
$853$	−0.933850	−0.0319744	−0.0159872	+	0.999872i	$0.505089\pi$
$854$	0.687254	0.0235174
$855$	−1.35489	−0.0463364
$856$	−20.4600	−0.699309
$857$	34.2745	1.17080	0.585398	−	0.810746i	$-0.300938\pi$
$857$	34.2745	1.17080	0.585398	+	0.810746i	$0.300938\pi$
$858$	15.9448	0.544348
$859$	−16.0621	−0.548031	−0.274016	−	0.961725i	$-0.588352\pi$
$859$	−16.0621	−0.548031	−0.274016	+	0.961725i	$0.588352\pi$
$860$	3.07666	0.104913
$861$	7.04302	0.240025
$862$	−34.1782	−1.16411
$863$	−6.42690	−0.218774	−0.109387	−	0.993999i	$-0.534889\pi$
$863$	−6.42690	−0.218774	−0.109387	+	0.993999i	$0.534889\pi$
$864$	5.65060	0.192237
$865$	−2.29658	−0.0780860
$866$	−0.686319	−0.0233221
$867$	17.8291	0.605506
$868$	3.22322	0.109403
$869$	9.14129	0.310097
$870$	−0.109034	−0.00369661
$871$	47.1774	1.59855
$872$	10.6587	0.360950
$873$	−20.4725	−0.692888
$874$	18.3499	0.620695
$875$	1.63922	0.0554156
$876$	−9.88629	−0.334027
$877$	43.8656	1.48124	0.740619	−	0.671926i	$-0.234533\pi$
$877$	43.8656	1.48124	0.740619	+	0.671926i	$0.234533\pi$
$878$	21.5089	0.725890
$879$	17.3085	0.583801
$880$	0.897887	0.0302678
$881$	−23.8174	−0.802428	−0.401214	−	0.915984i	$-0.631412\pi$
$881$	−23.8174	−0.802428	−0.401214	+	0.915984i	$0.631412\pi$
$882$	7.50044	0.252553
$883$	7.83196	0.263566	0.131783	−	0.991279i	$-0.457930\pi$
$883$	7.83196	0.263566	0.131783	+	0.991279i	$0.457930\pi$
$884$	−9.01064	−0.303060
$885$	−2.13927	−0.0719109
$886$	−28.5971	−0.960738
$887$	−37.5492	−1.26078	−0.630389	−	0.776280i	$-0.717104\pi$
$887$	−37.5492	−1.26078	−0.630389	+	0.776280i	$0.717104\pi$
$888$	0	0
$889$	3.36798	0.112958
$890$	1.32815	0.0445196
$891$	−11.5059	−0.385461
$892$	−29.2612	−0.979736
$893$	26.2682	0.879031
$894$	26.1849	0.875752
$895$	1.57667	0.0527024
$896$	−0.477756	−0.0159607
$897$	32.1302	1.07280
$898$	−34.5689	−1.15358
$899$	−1.53972	−0.0513524
$900$	5.40444	0.180148
$901$	8.79436	0.292983
$902$	27.7057	0.922498
$903$	5.82225	0.193752
$904$	12.2122	0.406172
$905$	−0.543077	−0.0180525
$906$	8.90313	0.295787
$907$	32.7999	1.08910	0.544551	−	0.838728i	$-0.316700\pi$
$907$	32.7999	1.08910	0.544551	+	0.838728i	$0.316700\pi$
$908$	10.3046	0.341969
$909$	−18.9718	−0.629254
$910$	0.743873	0.0246592
$911$	33.6227	1.11397	0.556985	−	0.830522i	$-0.311958\pi$
$911$	33.6227	1.11397	0.556985	+	0.830522i	$0.311958\pi$
$912$	−4.84535	−0.160446
$913$	3.65735	0.121041
$914$	32.9084	1.08851
$915$	0.687254	0.0227199
$916$	15.6678	0.517678
$917$	−0.948359	−0.0313176
$918$	11.3568	0.374831
$919$	−29.1313	−0.960954	−0.480477	−	0.877007i	$-0.659536\pi$
$919$	−29.1313	−0.960954	−0.480477	+	0.877007i	$0.659536\pi$
$920$	1.80932	0.0596514
$921$	25.9992	0.856704
$922$	−18.1394	−0.597391
$923$	−39.8096	−1.31035
$924$	1.69916	0.0558981
$925$	0	0
$926$	0.339403	0.0111535
$927$	14.8643	0.488209
$928$	0.228222	0.00749175
$929$	30.8607	1.01251	0.506254	−	0.862385i	$-0.331030\pi$
$929$	30.8607	1.01251	0.506254	+	0.862385i	$0.331030\pi$
$930$	3.22322	0.105693
$931$	−23.8518	−0.781710
$932$	7.20404	0.235976
$933$	0.155978	0.00510649
$934$	−14.2020	−0.464704
$935$	1.80461	0.0590172
$936$	4.96568	0.162308
$937$	7.32810	0.239399	0.119699	−	0.992810i	$-0.461807\pi$
$937$	7.32810	0.239399	0.119699	+	0.992810i	$0.461807\pi$
$938$	5.02744	0.164152
$939$	−12.6299	−0.412161
$940$	2.59007	0.0844786
$941$	42.1918	1.37541	0.687707	−	0.725989i	$-0.258618\pi$
$941$	42.1918	1.37541	0.687707	+	0.725989i	$0.258618\pi$
$942$	−16.6343	−0.541974
$943$	55.8292	1.81805
$944$	4.47776	0.145739
$945$	−0.937563	−0.0304989
$946$	22.9035	0.744655
$947$	−39.0961	−1.27045	−0.635227	−	0.772326i	$-0.719093\pi$
$947$	−39.0961	−1.27045	−0.635227	+	0.772326i	$0.719093\pi$
$948$	−4.86398	−0.157975
$949$	−32.2196	−1.04589
$950$	−17.1864	−0.557600
$951$	−36.1307	−1.17162
$952$	−0.960215	−0.0311207
$953$	−1.21858	−0.0394738	−0.0197369	−	0.999805i	$-0.506283\pi$
$953$	−1.21858	−0.0394738	−0.0197369	+	0.999805i	$0.506283\pi$
$954$	−4.84649	−0.156911
$955$	7.99417	0.258685
$956$	−21.9530	−0.710012
$957$	−0.811679	−0.0262378
$958$	−33.9805	−1.09786
$959$	−8.31197	−0.268407
$960$	−0.477756	−0.0154195
$961$	14.5164	0.468270
$962$	0	0
$963$	22.6617	0.730262
$964$	14.8104	0.477011
$965$	−3.66540	−0.117994
$966$	3.42394	0.110163
$967$	12.6894	0.408065	0.204032	−	0.978964i	$-0.434595\pi$
$967$	12.6894	0.408065	0.204032	+	0.978964i	$0.434595\pi$
$968$	−4.31590	−0.138718
$969$	−9.73840	−0.312842
$970$	6.41925	0.206110
$971$	0.880539	0.0282578	0.0141289	−	0.999900i	$-0.495502\pi$
$971$	0.880539	0.0282578	0.0141289	+	0.999900i	$0.495502\pi$
$972$	−10.8297	−0.347361
$973$	−0.352131	−0.0112888
$974$	−25.3330	−0.811721
$975$	−30.0929	−0.963743
$976$	−1.43851	−0.0460454
$977$	46.8109	1.49761	0.748806	−	0.662789i	$-0.230627\pi$
$977$	46.8109	1.49761	0.748806	+	0.662789i	$0.230627\pi$
$978$	−20.2860	−0.648676
$979$	9.88707	0.315992
$980$	−2.35180	−0.0751256
$981$	−11.8057	−0.376927
$982$	21.2687	0.678712
$983$	−34.5213	−1.10106	−0.550529	−	0.834816i	$-0.685574\pi$
$983$	−34.5213	−1.10106	−0.550529	+	0.834816i	$0.685574\pi$
$984$	−14.7419	−0.469954
$985$	1.67698	0.0534330
$986$	0.458690	0.0146077
$987$	4.90142	0.156014
$988$	−15.7911	−0.502382
$989$	46.1523	1.46756
$990$	−0.994506	−0.0316075
$991$	−47.5403	−1.51017	−0.755083	−	0.655629i	$-0.772404\pi$
$991$	−47.5403	−1.51017	−0.755083	+	0.655629i	$0.772404\pi$
$992$	−6.74658	−0.214204
$993$	39.3133	1.24757
$994$	−4.24230	−0.134558
$995$	3.57443	0.113317
$996$	−1.94604	−0.0616625
$997$	53.6409	1.69882	0.849412	−	0.527731i	$-0.176957\pi$
$997$	53.6409	1.69882	0.849412	+	0.527731i	$0.176957\pi$
$998$	16.4306	0.520101
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.t.1.3		6
37.12	even	9		74.2.f.b.33.1	yes	12
37.34	even	9		74.2.f.b.9.1	✓	12
37.36	even	2		2738.2.a.q.1.3		6
111.71	odd	18		666.2.x.g.379.1		12
111.86	odd	18		666.2.x.g.181.1		12
148.71	odd	18		592.2.bc.d.305.2		12
148.123	odd	18		592.2.bc.d.33.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.9.1	✓	12	37.34	even	9
74.2.f.b.33.1	yes	12	37.12	even	9
592.2.bc.d.33.2		12	148.123	odd	18
592.2.bc.d.305.2		12	148.71	odd	18
666.2.x.g.181.1		12	111.86	odd	18
666.2.x.g.379.1		12	111.71	odd	18
2738.2.a.q.1.3		6	37.36	even	2
2738.2.a.t.1.3		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.37564 q^{3} +1.00000 q^{4} +0.347296 q^{5} -1.37564 q^{6} -0.477756 q^{7} +1.00000 q^{8} -1.10761 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.37564 q^{3} +1.00000 q^{4} +0.347296 q^{5} -1.37564 q^{6} -0.477756 q^{7} +1.00000 q^{8} -1.10761 q^{9} +0.347296 q^{10} +2.58536 q^{11} -1.37564 q^{12} -4.48325 q^{13} -0.477756 q^{14} -0.477756 q^{15} +1.00000 q^{16} +2.00984 q^{17} -1.10761 q^{18} +3.52224 q^{19} +0.347296 q^{20} +0.657221 q^{21} +2.58536 q^{22} +5.20972 q^{23} -1.37564 q^{24} -4.87939 q^{25} -4.48325 q^{26} +5.65060 q^{27} -0.477756 q^{28} +0.228222 q^{29} -0.477756 q^{30} -6.74658 q^{31} +1.00000 q^{32} -3.55654 q^{33} +2.00984 q^{34} -0.165923 q^{35} -1.10761 q^{36} +3.52224 q^{38} +6.16735 q^{39} +0.347296 q^{40} +10.7164 q^{41} +0.657221 q^{42} +8.85889 q^{43} +2.58536 q^{44} -0.384668 q^{45} +5.20972 q^{46} +7.45780 q^{47} -1.37564 q^{48} -6.77175 q^{49} -4.87939 q^{50} -2.76483 q^{51} -4.48325 q^{52} +4.37564 q^{53} +5.65060 q^{54} +0.897887 q^{55} -0.477756 q^{56} -4.84535 q^{57} +0.228222 q^{58} +4.47776 q^{59} -0.477756 q^{60} -1.43851 q^{61} -6.74658 q^{62} +0.529166 q^{63} +1.00000 q^{64} -1.55702 q^{65} -3.55654 q^{66} -10.5230 q^{67} +2.00984 q^{68} -7.16671 q^{69} -0.165923 q^{70} +8.87964 q^{71} -1.10761 q^{72} +7.18667 q^{73} +6.71229 q^{75} +3.52224 q^{76} -1.23517 q^{77} +6.16735 q^{78} +3.53579 q^{79} +0.347296 q^{80} -4.45039 q^{81} +10.7164 q^{82} +1.41464 q^{83} +0.657221 q^{84} +0.698012 q^{85} +8.85889 q^{86} -0.313952 q^{87} +2.58536 q^{88} +3.82425 q^{89} -0.384668 q^{90} +2.14190 q^{91} +5.20972 q^{92} +9.28089 q^{93} +7.45780 q^{94} +1.22326 q^{95} -1.37564 q^{96} +18.4835 q^{97} -6.77175 q^{98} -2.86357 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 3 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 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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