LMFDB - Embedded newform 5290.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.4752.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 4x + 1 $ x^4 - 2x^3 - 3x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.21969$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.33225 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.33225 q^{6} -1.33225 q^{7} +1.00000 q^{8} +2.43937 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.33225 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.33225 q^{6} -1.33225 q^{7} +1.00000 q^{8} +2.43937 q^{9} +1.00000 q^{10} +2.43937 q^{11} -2.33225 q^{12} +6.66449 q^{13} -1.33225 q^{14} -2.33225 q^{15} +1.00000 q^{16} +1.60020 q^{17} +2.43937 q^{18} +7.95717 q^{19} +1.00000 q^{20} +3.10713 q^{21} +2.43937 q^{22} -2.33225 q^{24} +1.00000 q^{25} +6.66449 q^{26} +1.30752 q^{27} -1.33225 q^{28} -6.21099 q^{29} -2.33225 q^{30} +3.33225 q^{31} +1.00000 q^{32} -5.68922 q^{33} +1.60020 q^{34} -1.33225 q^{35} +2.43937 q^{36} -0.664493 q^{37} +7.95717 q^{38} -15.5432 q^{39} +1.00000 q^{40} -2.17566 q^{41} +3.10713 q^{42} -9.46508 q^{43} +2.43937 q^{44} +2.43937 q^{45} -7.77162 q^{47} -2.33225 q^{48} -5.22512 q^{49} +1.00000 q^{50} -3.73205 q^{51} +6.66449 q^{52} +4.66775 q^{53} +1.30752 q^{54} +2.43937 q^{55} -1.33225 q^{56} -18.5581 q^{57} -6.21099 q^{58} +11.5680 q^{59} -2.33225 q^{60} +12.1286 q^{61} +3.33225 q^{62} -3.24985 q^{63} +1.00000 q^{64} +6.66449 q^{65} -5.68922 q^{66} -12.0222 q^{67} +1.60020 q^{68} -1.33225 q^{70} +3.59596 q^{71} +2.43937 q^{72} +1.48318 q^{73} -0.664493 q^{74} -2.33225 q^{75} +7.95717 q^{76} -3.24985 q^{77} -15.5432 q^{78} -3.77162 q^{79} +1.00000 q^{80} -10.3676 q^{81} -2.17566 q^{82} -2.96777 q^{83} +3.10713 q^{84} +1.60020 q^{85} -9.46508 q^{86} +14.4856 q^{87} +2.43937 q^{88} -6.51851 q^{89} +2.43937 q^{90} -8.87875 q^{91} -7.77162 q^{93} -7.77162 q^{94} +7.95717 q^{95} -2.33225 q^{96} +6.92820 q^{97} -5.22512 q^{98} +5.95054 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{14} + 2 q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{18} + 8 q^{19} + 4 q^{20} + 18 q^{21} + 4 q^{22} + 2 q^{24} + 4 q^{25} + 4 q^{26} + 2 q^{27} + 6 q^{28} - 2 q^{29} + 2 q^{30} + 2 q^{31} + 4 q^{32} + 8 q^{33} + 2 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} + 8 q^{38} - 28 q^{39} + 4 q^{40} - 8 q^{41} + 18 q^{42} - 2 q^{43} + 4 q^{44} + 4 q^{45} - 14 q^{47} + 2 q^{48} - 4 q^{49} + 4 q^{50} - 8 q^{51} + 4 q^{52} + 30 q^{53} + 2 q^{54} + 4 q^{55} + 6 q^{56} - 38 q^{57} - 2 q^{58} + 4 q^{59} + 2 q^{60} + 12 q^{61} + 2 q^{62} + 12 q^{63} + 4 q^{64} + 4 q^{65} + 8 q^{66} + 2 q^{67} + 2 q^{68} + 6 q^{70} - 2 q^{71} + 4 q^{72} + 2 q^{73} + 20 q^{74} + 2 q^{75} + 8 q^{76} + 12 q^{77} - 28 q^{78} + 2 q^{79} + 4 q^{80} - 8 q^{81} - 8 q^{82} + 26 q^{83} + 18 q^{84} + 2 q^{85} - 2 q^{86} + 2 q^{87} + 4 q^{88} + 4 q^{90} - 24 q^{91} - 14 q^{93} - 14 q^{94} + 8 q^{95} + 2 q^{96} - 4 q^{98} + 40 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 4 * q^11 + 2 * q^12 + 4 * q^13 + 6 * q^14 + 2 * q^15 + 4 * q^16 + 2 * q^17 + 4 * q^18 + 8 * q^19 + 4 * q^20 + 18 * q^21 + 4 * q^22 + 2 * q^24 + 4 * q^25 + 4 * q^26 + 2 * q^27 + 6 * q^28 - 2 * q^29 + 2 * q^30 + 2 * q^31 + 4 * q^32 + 8 * q^33 + 2 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 + 8 * q^38 - 28 * q^39 + 4 * q^40 - 8 * q^41 + 18 * q^42 - 2 * q^43 + 4 * q^44 + 4 * q^45 - 14 * q^47 + 2 * q^48 - 4 * q^49 + 4 * q^50 - 8 * q^51 + 4 * q^52 + 30 * q^53 + 2 * q^54 + 4 * q^55 + 6 * q^56 - 38 * q^57 - 2 * q^58 + 4 * q^59 + 2 * q^60 + 12 * q^61 + 2 * q^62 + 12 * q^63 + 4 * q^64 + 4 * q^65 + 8 * q^66 + 2 * q^67 + 2 * q^68 + 6 * q^70 - 2 * q^71 + 4 * q^72 + 2 * q^73 + 20 * q^74 + 2 * q^75 + 8 * q^76 + 12 * q^77 - 28 * q^78 + 2 * q^79 + 4 * q^80 - 8 * q^81 - 8 * q^82 + 26 * q^83 + 18 * q^84 + 2 * q^85 - 2 * q^86 + 2 * q^87 + 4 * q^88 + 4 * q^90 - 24 * q^91 - 14 * q^93 - 14 * q^94 + 8 * q^95 + 2 * q^96 - 4 * q^98 + 40 * 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
$3$	−2.33225	−1.34652	−0.673262	−	0.739404i	$-0.735107\pi$
$3$	−2.33225	−1.34652	−0.673262	+	0.739404i	$0.735107\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.33225	−0.952136
$7$	−1.33225	−0.503542	−0.251771	−	0.967787i	$-0.581013\pi$
$7$	−1.33225	−0.503542	−0.251771	+	0.967787i	$0.581013\pi$
$8$	1.00000	0.353553
$9$	2.43937	0.813125
$10$	1.00000	0.316228
$11$	2.43937	0.735499	0.367749	−	0.929925i	$-0.380128\pi$
$11$	2.43937	0.735499	0.367749	+	0.929925i	$0.380128\pi$
$12$	−2.33225	−0.673262
$13$	6.66449	1.84840	0.924199	−	0.381912i	$-0.124734\pi$
$13$	6.66449	1.84840	0.924199	+	0.381912i	$0.124734\pi$
$14$	−1.33225	−0.356058
$15$	−2.33225	−0.602183
$16$	1.00000	0.250000
$17$	1.60020	0.388104	0.194052	−	0.980991i	$-0.437837\pi$
$17$	1.60020	0.388104	0.194052	+	0.980991i	$0.437837\pi$
$18$	2.43937	0.574966
$19$	7.95717	1.82550	0.912750	−	0.408519i	$-0.133954\pi$
$19$	7.95717	1.82550	0.912750	+	0.408519i	$0.133954\pi$
$20$	1.00000	0.223607
$21$	3.10713	0.678031
$22$	2.43937	0.520076
$23$	0	0
$23$	0	0
$24$	−2.33225	−0.476068
$25$	1.00000	0.200000
$26$	6.66449	1.30701
$27$	1.30752	0.251632
$28$	−1.33225	−0.251771
$29$	−6.21099	−1.15335	−0.576676	−	0.816973i	$-0.695651\pi$
$29$	−6.21099	−1.15335	−0.576676	+	0.816973i	$0.695651\pi$
$30$	−2.33225	−0.425808
$31$	3.33225	0.598489	0.299245	−	0.954176i	$-0.403265\pi$
$31$	3.33225	0.598489	0.299245	+	0.954176i	$0.403265\pi$
$32$	1.00000	0.176777
$33$	−5.68922	−0.990366
$34$	1.60020	0.274431
$35$	−1.33225	−0.225191
$36$	2.43937	0.406562
$37$	−0.664493	−0.109242	−0.0546210	−	0.998507i	$-0.517395\pi$
$37$	−0.664493	−0.109242	−0.0546210	+	0.998507i	$0.517395\pi$
$38$	7.95717	1.29082
$39$	−15.5432	−2.48891
$40$	1.00000	0.158114
$41$	−2.17566	−0.339782	−0.169891	−	0.985463i	$-0.554341\pi$
$41$	−2.17566	−0.339782	−0.169891	+	0.985463i	$0.554341\pi$
$42$	3.10713	0.479440
$43$	−9.46508	−1.44341	−0.721706	−	0.692200i	$-0.756642\pi$
$43$	−9.46508	−1.44341	−0.721706	+	0.692200i	$0.756642\pi$
$44$	2.43937	0.367749
$45$	2.43937	0.363640
$46$	0	0
$47$	−7.77162	−1.13361	−0.566804	−	0.823853i	$-0.691820\pi$
$47$	−7.77162	−1.13361	−0.566804	+	0.823853i	$0.691820\pi$
$48$	−2.33225	−0.336631
$49$	−5.22512	−0.746446
$50$	1.00000	0.141421
$51$	−3.73205	−0.522592
$52$	6.66449	0.924199
$53$	4.66775	0.641165	0.320583	−	0.947221i	$-0.396121\pi$
$53$	4.66775	0.641165	0.320583	+	0.947221i	$0.396121\pi$
$54$	1.30752	0.177931
$55$	2.43937	0.328925
$56$	−1.33225	−0.178029
$57$	−18.5581	−2.45808
$58$	−6.21099	−0.815543
$59$	11.5680	1.50602	0.753011	−	0.658008i	$-0.228601\pi$
$59$	11.5680	1.50602	0.753011	+	0.658008i	$0.228601\pi$
$60$	−2.33225	−0.301092
$61$	12.1286	1.55291	0.776454	−	0.630174i	$-0.217017\pi$
$61$	12.1286	1.55291	0.776454	+	0.630174i	$0.217017\pi$
$62$	3.33225	0.423196
$63$	−3.24985	−0.409442
$64$	1.00000	0.125000
$65$	6.66449	0.826629
$66$	−5.68922	−0.700295
$67$	−12.0222	−1.46874	−0.734372	−	0.678747i	$-0.762523\pi$
$67$	−12.0222	−1.46874	−0.734372	+	0.678747i	$0.762523\pi$
$68$	1.60020	0.194052
$69$	0	0
$70$	−1.33225	−0.159234
$71$	3.59596	0.426762	0.213381	−	0.976969i	$-0.431553\pi$
$71$	3.59596	0.426762	0.213381	+	0.976969i	$0.431553\pi$
$72$	2.43937	0.287483
$73$	1.48318	0.173593	0.0867967	−	0.996226i	$-0.472337\pi$
$73$	1.48318	0.173593	0.0867967	+	0.996226i	$0.472337\pi$
$74$	−0.664493	−0.0772457
$75$	−2.33225	−0.269305
$76$	7.95717	0.912750
$77$	−3.24985	−0.370354
$78$	−15.5432	−1.75993
$79$	−3.77162	−0.424340	−0.212170	−	0.977233i	$-0.568053\pi$
$79$	−3.77162	−0.424340	−0.212170	+	0.977233i	$0.568053\pi$
$80$	1.00000	0.111803
$81$	−10.3676	−1.15195
$82$	−2.17566	−0.240262
$83$	−2.96777	−0.325755	−0.162878	−	0.986646i	$-0.552078\pi$
$83$	−2.96777	−0.325755	−0.162878	+	0.986646i	$0.552078\pi$
$84$	3.10713	0.339015
$85$	1.60020	0.173566
$86$	−9.46508	−1.02065
$87$	14.4856	1.55302
$88$	2.43937	0.260038
$89$	−6.51851	−0.690961	−0.345480	−	0.938426i	$-0.612284\pi$
$89$	−6.51851	−0.690961	−0.345480	+	0.938426i	$0.612284\pi$
$90$	2.43937	0.257133
$91$	−8.87875	−0.930746
$92$	0	0
$93$	−7.77162	−0.805879
$94$	−7.77162	−0.801581
$95$	7.95717	0.816388
$96$	−2.33225	−0.238034
$97$	6.92820	0.703452	0.351726	−	0.936103i	$-0.385595\pi$
$97$	6.92820	0.703452	0.351726	+	0.936103i	$0.385595\pi$
$98$	−5.22512	−0.527817
$99$	5.95054	0.598052
$100$	1.00000	0.100000
$101$	6.40078	0.636902	0.318451	−	0.947939i	$-0.396837\pi$
$101$	6.40078	0.636902	0.318451	+	0.947939i	$0.396837\pi$
$102$	−3.73205	−0.369528
$103$	−5.38496	−0.530596	−0.265298	−	0.964166i	$-0.585470\pi$
$103$	−5.38496	−0.530596	−0.265298	+	0.964166i	$0.585470\pi$
$104$	6.66449	0.653507
$105$	3.10713	0.303225
$106$	4.66775	0.453372
$107$	9.60117	0.928181	0.464090	−	0.885788i	$-0.346381\pi$
$107$	9.60117	0.928181	0.464090	+	0.885788i	$0.346381\pi$
$108$	1.30752	0.125816
$109$	6.67862	0.639696	0.319848	−	0.947469i	$-0.396368\pi$
$109$	6.67862	0.639696	0.319848	+	0.947469i	$0.396368\pi$
$110$	2.43937	0.232585
$111$	1.54976	0.147097
$112$	−1.33225	−0.125885
$113$	20.7041	1.94767	0.973837	−	0.227247i	$-0.0729724\pi$
$113$	20.7041	1.94767	0.973837	+	0.227247i	$0.0729724\pi$
$114$	−18.5581	−1.73812
$115$	0	0
$116$	−6.21099	−0.576676
$117$	16.2572	1.50298
$118$	11.5680	1.06492
$119$	−2.13186	−0.195427
$120$	−2.33225	−0.212904
$121$	−5.04946	−0.459041
$122$	12.1286	1.09807
$123$	5.07418	0.457524
$124$	3.33225	0.299245
$125$	1.00000	0.0894427
$126$	−3.24985	−0.289519
$127$	−16.0353	−1.42291	−0.711453	−	0.702734i	$-0.751962\pi$
$127$	−16.0353	−1.42291	−0.711453	+	0.702734i	$0.751962\pi$
$128$	1.00000	0.0883883
$129$	22.0749	1.94359
$130$	6.66449	0.584515
$131$	−15.1112	−1.32027	−0.660136	−	0.751146i	$-0.729501\pi$
$131$	−15.1112	−1.32027	−0.660136	+	0.751146i	$0.729501\pi$
$132$	−5.68922	−0.495183
$133$	−10.6009	−0.919216
$134$	−12.0222	−1.03856
$135$	1.30752	0.112533
$136$	1.60020	0.137216
$137$	21.1369	1.80585	0.902924	−	0.429800i	$-0.141416\pi$
$137$	21.1369	1.80585	0.902924	+	0.429800i	$0.141416\pi$
$138$	0	0
$139$	18.6332	1.58045	0.790226	−	0.612816i	$-0.209963\pi$
$139$	18.6332	1.58045	0.790226	+	0.612816i	$0.209963\pi$
$140$	−1.33225	−0.112595
$141$	18.1253	1.52643
$142$	3.59596	0.301766
$143$	16.2572	1.35949
$144$	2.43937	0.203281
$145$	−6.21099	−0.515795
$146$	1.48318	0.122749
$147$	12.1863	1.00511
$148$	−0.664493	−0.0546210
$149$	16.7790	1.37459	0.687293	−	0.726380i	$-0.258799\pi$
$149$	16.7790	1.37459	0.687293	+	0.726380i	$0.258799\pi$
$150$	−2.33225	−0.190427
$151$	−6.93668	−0.564499	−0.282250	−	0.959341i	$-0.591081\pi$
$151$	−6.93668	−0.564499	−0.282250	+	0.959341i	$0.591081\pi$
$152$	7.95717	0.645412
$153$	3.90348	0.315577
$154$	−3.24985	−0.261880
$155$	3.33225	0.267652
$156$	−15.5432	−1.24446
$157$	2.27219	0.181340	0.0906702	−	0.995881i	$-0.471099\pi$
$157$	2.27219	0.181340	0.0906702	+	0.995881i	$0.471099\pi$
$158$	−3.77162	−0.300054
$159$	−10.8864	−0.863344
$160$	1.00000	0.0790569
$161$	0	0
$162$	−10.3676	−0.814554
$163$	9.14246	0.716093	0.358046	−	0.933704i	$-0.383443\pi$
$163$	9.14246	0.716093	0.358046	+	0.933704i	$0.383443\pi$
$164$	−2.17566	−0.169891
$165$	−5.68922	−0.442905
$166$	−2.96777	−0.230344
$167$	−3.24224	−0.250892	−0.125446	−	0.992100i	$-0.540036\pi$
$167$	−3.24224	−0.250892	−0.125446	+	0.992100i	$0.540036\pi$
$168$	3.10713	0.239720
$169$	31.4155	2.41657
$170$	1.60020	0.122729
$171$	19.4105	1.48436
$172$	−9.46508	−0.721706
$173$	−0.0353305	−0.00268613	−0.00134306	−	0.999999i	$-0.500428\pi$
$173$	−0.0353305	−0.00268613	−0.00134306	+	0.999999i	$0.500428\pi$
$174$	14.4856	1.09815
$175$	−1.33225	−0.100708
$176$	2.43937	0.183875
$177$	−26.9794	−2.02789
$178$	−6.51851	−0.488583
$179$	18.0459	1.34882	0.674408	−	0.738359i	$-0.264399\pi$
$179$	18.0459	1.34882	0.674408	+	0.738359i	$0.264399\pi$
$180$	2.43937	0.181820
$181$	16.5591	1.23083	0.615413	−	0.788205i	$-0.288989\pi$
$181$	16.5591	1.23083	0.615413	+	0.788205i	$0.288989\pi$
$182$	−8.87875	−0.658137
$183$	−28.2869	−2.09103
$184$	0	0
$185$	−0.664493	−0.0488545
$186$	−7.77162	−0.569843
$187$	3.90348	0.285450
$188$	−7.77162	−0.566804
$189$	−1.74194	−0.126707
$190$	7.95717	0.577274
$191$	1.95619	0.141545	0.0707725	−	0.997492i	$-0.477454\pi$
$191$	1.95619	0.141545	0.0707725	+	0.997492i	$0.477454\pi$
$192$	−2.33225	−0.168315
$193$	5.43611	0.391300	0.195650	−	0.980674i	$-0.437318\pi$
$193$	5.43611	0.391300	0.195650	+	0.980674i	$0.437318\pi$
$194$	6.92820	0.497416
$195$	−15.5432	−1.11307
$196$	−5.22512	−0.373223
$197$	−2.45024	−0.174572	−0.0872861	−	0.996183i	$-0.527819\pi$
$197$	−2.45024	−0.174572	−0.0872861	+	0.996183i	$0.527819\pi$
$198$	5.95054	0.422887
$199$	−12.4361	−0.881573	−0.440786	−	0.897612i	$-0.645300\pi$
$199$	−12.4361	−0.881573	−0.440786	+	0.897612i	$0.645300\pi$
$200$	1.00000	0.0707107
$201$	28.0387	1.97770
$202$	6.40078	0.450358
$203$	8.27458	0.580761
$204$	−3.73205	−0.261296
$205$	−2.17566	−0.151955
$206$	−5.38496	−0.375188
$207$	0	0
$208$	6.66449	0.462099
$209$	19.4105	1.34265
$210$	3.10713	0.214412
$211$	−24.2151	−1.66703	−0.833517	−	0.552493i	$-0.813676\pi$
$211$	−24.2151	−1.66703	−0.833517	+	0.552493i	$0.813676\pi$
$212$	4.66775	0.320583
$213$	−8.38666	−0.574644
$214$	9.60117	0.656323
$215$	−9.46508	−0.645513
$216$	1.30752	0.0889654
$217$	−4.43937	−0.301364
$218$	6.67862	0.452333
$219$	−3.45915	−0.233747
$220$	2.43937	0.164463
$221$	10.6645	0.717371
$222$	1.54976	0.104013
$223$	−24.8637	−1.66500	−0.832500	−	0.554025i	$-0.813091\pi$
$223$	−24.8637	−1.66500	−0.832500	+	0.554025i	$0.813091\pi$
$224$	−1.33225	−0.0890145
$225$	2.43937	0.162625
$226$	20.7041	1.37721
$227$	4.47894	0.297278	0.148639	−	0.988892i	$-0.452511\pi$
$227$	4.47894	0.297278	0.148639	+	0.988892i	$0.452511\pi$
$228$	−18.5581	−1.22904
$229$	2.11447	0.139728	0.0698640	−	0.997557i	$-0.477743\pi$
$229$	2.11447	0.139728	0.0698640	+	0.997557i	$0.477743\pi$
$230$	0	0
$231$	7.57944	0.498691
$232$	−6.21099	−0.407772
$233$	−26.7156	−1.75020	−0.875100	−	0.483942i	$-0.839205\pi$
$233$	−26.7156	−1.75020	−0.875100	+	0.483942i	$0.839205\pi$
$234$	16.2572	1.06277
$235$	−7.77162	−0.506965
$236$	11.5680	0.753011
$237$	8.79635	0.571384
$238$	−2.13186	−0.138188
$239$	−2.31317	−0.149626	−0.0748131	−	0.997198i	$-0.523836\pi$
$239$	−2.31317	−0.149626	−0.0748131	+	0.997198i	$0.523836\pi$
$240$	−2.33225	−0.150546
$241$	5.99772	0.386347	0.193173	−	0.981165i	$-0.438122\pi$
$241$	5.99772	0.386347	0.193173	+	0.981165i	$0.438122\pi$
$242$	−5.04946	−0.324591
$243$	20.2572	1.29950
$244$	12.1286	0.776454
$245$	−5.22512	−0.333821
$246$	5.07418	0.323518
$247$	53.0305	3.37425
$248$	3.33225	0.211598
$249$	6.92158	0.438637
$250$	1.00000	0.0632456
$251$	23.0907	1.45747	0.728737	−	0.684794i	$-0.240108\pi$
$251$	23.0907	1.45747	0.728737	+	0.684794i	$0.240108\pi$
$252$	−3.24985	−0.204721
$253$	0	0
$254$	−16.0353	−1.00615
$255$	−3.73205	−0.233710
$256$	1.00000	0.0625000
$257$	−17.8176	−1.11143	−0.555714	−	0.831373i	$-0.687555\pi$
$257$	−17.8176	−1.11143	−0.555714	+	0.831373i	$0.687555\pi$
$258$	22.0749	1.37432
$259$	0.885268	0.0550079
$260$	6.66449	0.413314
$261$	−15.1509	−0.937819
$262$	−15.1112	−0.933574
$263$	−11.2711	−0.695003	−0.347501	−	0.937679i	$-0.612970\pi$
$263$	−11.2711	−0.695003	−0.347501	+	0.937679i	$0.612970\pi$
$264$	−5.68922	−0.350147
$265$	4.66775	0.286738
$266$	−10.6009	−0.649984
$267$	15.2028	0.930395
$268$	−12.0222	−0.734372
$269$	21.6159	1.31794	0.658971	−	0.752168i	$-0.270992\pi$
$269$	21.6159	1.31794	0.658971	+	0.752168i	$0.270992\pi$
$270$	1.30752	0.0795730
$271$	−25.7001	−1.56117	−0.780585	−	0.625050i	$-0.785078\pi$
$271$	−25.7001	−1.56117	−0.780585	+	0.625050i	$0.785078\pi$
$272$	1.60020	0.0970261
$273$	20.7074	1.25327
$274$	21.1369	1.27693
$275$	2.43937	0.147100
$276$	0	0
$277$	−21.1289	−1.26951	−0.634755	−	0.772713i	$-0.718899\pi$
$277$	−21.1289	−1.26951	−0.634755	+	0.772713i	$0.718899\pi$
$278$	18.6332	1.11755
$279$	8.12859	0.486646
$280$	−1.33225	−0.0796170
$281$	−24.5058	−1.46189	−0.730947	−	0.682435i	$-0.760921\pi$
$281$	−24.5058	−1.46189	−0.730947	+	0.682435i	$0.760921\pi$
$282$	18.1253	1.07935
$283$	−11.7782	−0.700144	−0.350072	−	0.936723i	$-0.613843\pi$
$283$	−11.7782	−0.700144	−0.350072	+	0.936723i	$0.613843\pi$
$284$	3.59596	0.213381
$285$	−18.5581	−1.09929
$286$	16.2572	0.961308
$287$	2.89852	0.171094
$288$	2.43937	0.143741
$289$	−14.4394	−0.849375
$290$	−6.21099	−0.364722
$291$	−16.1583	−0.947215
$292$	1.48318	0.0867967
$293$	17.2498	1.00775	0.503873	−	0.863778i	$-0.331908\pi$
$293$	17.2498	1.00775	0.503873	+	0.863778i	$0.331908\pi$
$294$	12.1863	0.710717
$295$	11.5680	0.673513
$296$	−0.664493	−0.0386229
$297$	3.18953	0.185075
$298$	16.7790	0.971979
$299$	0	0
$300$	−2.33225	−0.134652
$301$	12.6098	0.726818
$302$	−6.93668	−0.399161
$303$	−14.9282	−0.857603
$304$	7.95717	0.456375
$305$	12.1286	0.694481
$306$	3.90348	0.223147
$307$	−14.0126	−0.799739	−0.399870	−	0.916572i	$-0.630945\pi$
$307$	−14.0126	−0.799739	−0.399870	+	0.916572i	$0.630945\pi$
$308$	−3.24985	−0.185177
$309$	12.5591	0.714460
$310$	3.33225	0.189259
$311$	−15.7740	−0.894462	−0.447231	−	0.894419i	$-0.647590\pi$
$311$	−15.7740	−0.894462	−0.447231	+	0.894419i	$0.647590\pi$
$312$	−15.5432	−0.879963
$313$	9.77586	0.552564	0.276282	−	0.961077i	$-0.410898\pi$
$313$	9.77586	0.552564	0.276282	+	0.961077i	$0.410898\pi$
$314$	2.27219	0.128227
$315$	−3.24985	−0.183108
$316$	−3.77162	−0.212170
$317$	19.5489	1.09797	0.548987	−	0.835831i	$-0.315013\pi$
$317$	19.5489	1.09797	0.548987	+	0.835831i	$0.315013\pi$
$318$	−10.8864	−0.610476
$319$	−15.1509	−0.848290
$320$	1.00000	0.0559017
$321$	−22.3923	−1.24982
$322$	0	0
$323$	12.7330	0.708485
$324$	−10.3676	−0.575976
$325$	6.66449	0.369680
$326$	9.14246	0.506354
$327$	−15.5762	−0.861365
$328$	−2.17566	−0.120131
$329$	10.3537	0.570819
$330$	−5.68922	−0.313181
$331$	12.9915	0.714079	0.357039	−	0.934089i	$-0.383786\pi$
$331$	12.9915	0.714079	0.357039	+	0.934089i	$0.383786\pi$
$332$	−2.96777	−0.162878
$333$	−1.62095	−0.0888273
$334$	−3.24224	−0.177408
$335$	−12.0222	−0.656842
$336$	3.10713	0.169508
$337$	−19.9242	−1.08534	−0.542671	−	0.839945i	$-0.682587\pi$
$337$	−19.9242	−1.08534	−0.542671	+	0.839945i	$0.682587\pi$
$338$	31.4155	1.70878
$339$	−48.2870	−2.62259
$340$	1.60020	0.0867828
$341$	8.12859	0.440188
$342$	19.4105	1.04960
$343$	16.2869	0.879408
$344$	−9.46508	−0.510323
$345$	0	0
$346$	−0.0353305	−0.00189938
$347$	−22.7736	−1.22255	−0.611275	−	0.791418i	$-0.709343\pi$
$347$	−22.7736	−1.22255	−0.611275	+	0.791418i	$0.709343\pi$
$348$	14.4856	0.776508
$349$	12.0876	0.647035	0.323518	−	0.946222i	$-0.395134\pi$
$349$	12.0876	0.647035	0.323518	+	0.946222i	$0.395134\pi$
$350$	−1.33225	−0.0712116
$351$	8.71395	0.465116
$352$	2.43937	0.130019
$353$	24.6068	1.30969	0.654844	−	0.755764i	$-0.272734\pi$
$353$	24.6068	1.30969	0.654844	+	0.755764i	$0.272734\pi$
$354$	−26.9794	−1.43394
$355$	3.59596	0.190854
$356$	−6.51851	−0.345480
$357$	4.97201	0.263147
$358$	18.0459	0.953757
$359$	28.9867	1.52986	0.764930	−	0.644114i	$-0.222774\pi$
$359$	28.9867	1.52986	0.764930	+	0.644114i	$0.222774\pi$
$360$	2.43937	0.128566
$361$	44.3166	2.33245
$362$	16.5591	0.870325
$363$	11.7766	0.618110
$364$	−8.87875	−0.465373
$365$	1.48318	0.0776333
$366$	−28.2869	−1.47858
$367$	−12.9829	−0.677701	−0.338850	−	0.940840i	$-0.610038\pi$
$367$	−12.9829	−0.677701	−0.338850	+	0.940840i	$0.610038\pi$
$368$	0	0
$369$	−5.30726	−0.276285
$370$	−0.664493	−0.0345453
$371$	−6.21860	−0.322854
$372$	−7.77162	−0.402940
$373$	14.1234	0.731281	0.365640	−	0.930756i	$-0.380850\pi$
$373$	14.1234	0.731281	0.365640	+	0.930756i	$0.380850\pi$
$374$	3.90348	0.201844
$375$	−2.33225	−0.120437
$376$	−7.77162	−0.400791
$377$	−41.3931	−2.13185
$378$	−1.74194	−0.0895956
$379$	−2.85330	−0.146564	−0.0732822	−	0.997311i	$-0.523347\pi$
$379$	−2.85330	−0.146564	−0.0732822	+	0.997311i	$0.523347\pi$
$380$	7.95717	0.408194
$381$	37.3983	1.91598
$382$	1.95619	0.100087
$383$	5.94207	0.303625	0.151813	−	0.988409i	$-0.451489\pi$
$383$	5.94207	0.303625	0.151813	+	0.988409i	$0.451489\pi$
$384$	−2.33225	−0.119017
$385$	−3.24985	−0.165628
$386$	5.43611	0.276691
$387$	−23.0889	−1.17367
$388$	6.92820	0.351726
$389$	21.4364	1.08687	0.543434	−	0.839452i	$-0.317124\pi$
$389$	21.4364	1.08687	0.543434	+	0.839452i	$0.317124\pi$
$390$	−15.5432	−0.787063
$391$	0	0
$392$	−5.22512	−0.263908
$393$	35.2431	1.77778
$394$	−2.45024	−0.123441
$395$	−3.77162	−0.189771
$396$	5.95054	0.299026
$397$	21.7368	1.09094	0.545471	−	0.838130i	$-0.316351\pi$
$397$	21.7368	1.09094	0.545471	+	0.838130i	$0.316351\pi$
$398$	−12.4361	−0.623366
$399$	24.7239	1.23775
$400$	1.00000	0.0500000
$401$	29.1208	1.45423	0.727113	−	0.686518i	$-0.240862\pi$
$401$	29.1208	1.45423	0.727113	+	0.686518i	$0.240862\pi$
$402$	28.0387	1.39844
$403$	22.2077	1.10625
$404$	6.40078	0.318451
$405$	−10.3676	−0.515169
$406$	8.27458	0.410660
$407$	−1.62095	−0.0803473
$408$	−3.73205	−0.184764
$409$	−5.86136	−0.289826	−0.144913	−	0.989444i	$-0.546290\pi$
$409$	−5.86136	−0.289826	−0.144913	+	0.989444i	$0.546290\pi$
$410$	−2.17566	−0.107448
$411$	−49.2965	−2.43162
$412$	−5.38496	−0.265298
$413$	−15.4114	−0.758345
$414$	0	0
$415$	−2.96777	−0.145682
$416$	6.66449	0.326754
$417$	−43.4573	−2.12811
$418$	19.4105	0.949399
$419$	23.5127	1.14867	0.574335	−	0.818620i	$-0.305261\pi$
$419$	23.5127	1.14867	0.574335	+	0.818620i	$0.305261\pi$
$420$	3.10713	0.151612
$421$	21.1713	1.03182	0.515912	−	0.856641i	$-0.327453\pi$
$421$	21.1713	1.03182	0.515912	+	0.856641i	$0.327453\pi$
$422$	−24.2151	−1.17877
$423$	−18.9579	−0.921764
$424$	4.66775	0.226686
$425$	1.60020	0.0776209
$426$	−8.38666	−0.406335
$427$	−16.1583	−0.781954
$428$	9.60117	0.464090
$429$	−37.9158	−1.83059
$430$	−9.46508	−0.456447
$431$	−0.0296831	−0.00142979	−0.000714893	−	1.00000i	$-0.500228\pi$
$431$	−0.0296831	−0.00142979	−0.000714893		1.00000i	$0.500228\pi$
$432$	1.30752	0.0629080
$433$	20.0815	0.965057	0.482528	−	0.875880i	$-0.339719\pi$
$433$	20.0815	0.965057	0.482528	+	0.875880i	$0.339719\pi$
$434$	−4.43937	−0.213097
$435$	14.4856	0.694530
$436$	6.67862	0.319848
$437$	0	0
$438$	−3.45915	−0.165284
$439$	28.4385	1.35730	0.678648	−	0.734464i	$-0.262566\pi$
$439$	28.4385	1.35730	0.678648	+	0.734464i	$0.262566\pi$
$440$	2.43937	0.116293
$441$	−12.7460	−0.606953
$442$	10.6645	0.507258
$443$	−5.04620	−0.239752	−0.119876	−	0.992789i	$-0.538250\pi$
$443$	−5.04620	−0.239752	−0.119876	+	0.992789i	$0.538250\pi$
$444$	1.54976	0.0735484
$445$	−6.51851	−0.309007
$446$	−24.8637	−1.17733
$447$	−39.1327	−1.85091
$448$	−1.33225	−0.0629427
$449$	−30.6455	−1.44625	−0.723126	−	0.690716i	$-0.757296\pi$
$449$	−30.6455	−1.44625	−0.723126	+	0.690716i	$0.757296\pi$
$450$	2.43937	0.114993
$451$	−5.30726	−0.249909
$452$	20.7041	0.973837
$453$	16.1781	0.760111
$454$	4.47894	0.210207
$455$	−8.87875	−0.416242
$456$	−18.5581	−0.869062
$457$	7.09300	0.331797	0.165898	−	0.986143i	$-0.446948\pi$
$457$	7.09300	0.331797	0.165898	+	0.986143i	$0.446948\pi$
$458$	2.11447	0.0988027
$459$	2.09229	0.0976595
$460$	0	0
$461$	34.3151	1.59821	0.799107	−	0.601188i	$-0.205306\pi$
$461$	34.3151	1.59821	0.799107	+	0.601188i	$0.205306\pi$
$462$	7.57944	0.352628
$463$	24.5294	1.13998	0.569988	−	0.821653i	$-0.306948\pi$
$463$	24.5294	1.13998	0.569988	+	0.821653i	$0.306948\pi$
$464$	−6.21099	−0.288338
$465$	−7.77162	−0.360400
$466$	−26.7156	−1.23758
$467$	−37.4788	−1.73431	−0.867156	−	0.498037i	$-0.834054\pi$
$467$	−37.4788	−1.73431	−0.867156	+	0.498037i	$0.834054\pi$
$468$	16.2572	0.751489
$469$	16.0165	0.739574
$470$	−7.77162	−0.358478
$471$	−5.29930	−0.244179
$472$	11.5680	0.532459
$473$	−23.0889	−1.06163
$474$	8.79635	0.404030
$475$	7.95717	0.365100
$476$	−2.13186	−0.0977134
$477$	11.3864	0.521347
$478$	−2.31317	−0.105802
$479$	−10.8929	−0.497708	−0.248854	−	0.968541i	$-0.580054\pi$
$479$	−10.8929	−0.497708	−0.248854	+	0.968541i	$0.580054\pi$
$480$	−2.33225	−0.106452
$481$	−4.42851	−0.201923
$482$	5.99772	0.273189
$483$	0	0
$484$	−5.04946	−0.229521
$485$	6.92820	0.314594
$486$	20.2572	0.918885
$487$	−38.7866	−1.75759	−0.878794	−	0.477202i	$-0.841651\pi$
$487$	−38.7866	−1.75759	−0.878794	+	0.477202i	$0.841651\pi$
$488$	12.1286	0.549036
$489$	−21.3225	−0.964235
$490$	−5.22512	−0.236047
$491$	−6.76950	−0.305503	−0.152752	−	0.988265i	$-0.548813\pi$
$491$	−6.76950	−0.305503	−0.152752	+	0.988265i	$0.548813\pi$
$492$	5.07418	0.228762
$493$	−9.93881	−0.447621
$494$	53.0305	2.38596
$495$	5.95054	0.267457
$496$	3.33225	0.149622
$497$	−4.79070	−0.214892
$498$	6.92158	0.310163
$499$	27.2206	1.21856	0.609280	−	0.792955i	$-0.291459\pi$
$499$	27.2206	1.21856	0.609280	+	0.792955i	$0.291459\pi$
$500$	1.00000	0.0447214
$501$	7.56171	0.337832
$502$	23.0907	1.03059
$503$	6.87027	0.306330	0.153165	−	0.988201i	$-0.451053\pi$
$503$	6.87027	0.306330	0.153165	+	0.988201i	$0.451053\pi$
$504$	−3.24985	−0.144760
$505$	6.40078	0.284831
$506$	0	0
$507$	−73.2686	−3.25397
$508$	−16.0353	−0.711453
$509$	13.6474	0.604909	0.302455	−	0.953164i	$-0.402194\pi$
$509$	13.6474	0.604909	0.302455	+	0.953164i	$0.402194\pi$
$510$	−3.73205	−0.165258
$511$	−1.97596	−0.0874115
$512$	1.00000	0.0441942
$513$	10.4041	0.459354
$514$	−17.8176	−0.785899
$515$	−5.38496	−0.237290
$516$	22.0749	0.971793
$517$	−18.9579	−0.833767
$518$	0.885268	0.0388965
$519$	0.0823994	0.00361693
$520$	6.66449	0.292257
$521$	−12.9475	−0.567242	−0.283621	−	0.958936i	$-0.591536\pi$
$521$	−12.9475	−0.567242	−0.283621	+	0.958936i	$0.591536\pi$
$522$	−15.1509	−0.663138
$523$	−10.8208	−0.473161	−0.236581	−	0.971612i	$-0.576027\pi$
$523$	−10.8208	−0.473161	−0.236581	+	0.971612i	$0.576027\pi$
$524$	−15.1112	−0.660136
$525$	3.10713	0.135606
$526$	−11.2711	−0.491441
$527$	5.33225	0.232276
$528$	−5.68922	−0.247592
$529$	0	0
$530$	4.66775	0.202754
$531$	28.2186	1.22458
$532$	−10.6009	−0.459608
$533$	−14.4997	−0.628051
$534$	15.2028	0.657889
$535$	9.60117	0.415095
$536$	−12.0222	−0.519279
$537$	−42.0876	−1.81621
$538$	21.6159	0.931926
$539$	−12.7460	−0.549010
$540$	1.30752	0.0562666
$541$	27.8744	1.19841	0.599206	−	0.800595i	$-0.295483\pi$
$541$	27.8744	1.19841	0.599206	+	0.800595i	$0.295483\pi$
$542$	−25.7001	−1.10391
$543$	−38.6198	−1.65733
$544$	1.60020	0.0686078
$545$	6.67862	0.286081
$546$	20.7074	0.886196
$547$	6.79918	0.290712	0.145356	−	0.989379i	$-0.453567\pi$
$547$	6.79918	0.290712	0.145356	+	0.989379i	$0.453567\pi$
$548$	21.1369	0.902924
$549$	29.5862	1.26271
$550$	2.43937	0.104015
$551$	−49.4219	−2.10545
$552$	0	0
$553$	5.02473	0.213673
$554$	−21.1289	−0.897679
$555$	1.54976	0.0657837
$556$	18.6332	0.790226
$557$	−29.4133	−1.24628	−0.623142	−	0.782109i	$-0.714144\pi$
$557$	−29.4133	−1.24628	−0.623142	+	0.782109i	$0.714144\pi$
$558$	8.12859	0.344111
$559$	−63.0800	−2.66800
$560$	−1.33225	−0.0562977
$561$	−9.10387	−0.384366
$562$	−24.5058	−1.03371
$563$	7.08364	0.298540	0.149270	−	0.988796i	$-0.452308\pi$
$563$	7.08364	0.298540	0.149270	+	0.988796i	$0.452308\pi$
$564$	18.1253	0.763214
$565$	20.7041	0.871026
$566$	−11.7782	−0.495077
$567$	13.8122	0.580057
$568$	3.59596	0.150883
$569$	−15.9586	−0.669019	−0.334510	−	0.942392i	$-0.608571\pi$
$569$	−15.9586	−0.669019	−0.334510	+	0.942392i	$0.608571\pi$
$570$	−18.5581	−0.777313
$571$	5.39159	0.225631	0.112815	−	0.993616i	$-0.464013\pi$
$571$	5.39159	0.225631	0.112815	+	0.993616i	$0.464013\pi$
$572$	16.2572	0.679747
$573$	−4.56232	−0.190594
$574$	2.89852	0.120982
$575$	0	0
$576$	2.43937	0.101641
$577$	−36.9581	−1.53859	−0.769294	−	0.638895i	$-0.779392\pi$
$577$	−36.9581	−1.53859	−0.769294	+	0.638895i	$0.779392\pi$
$578$	−14.4394	−0.600599
$579$	−12.6784	−0.526894
$580$	−6.21099	−0.257897
$581$	3.95380	0.164031
$582$	−16.1583	−0.669782
$583$	11.3864	0.471576
$584$	1.48318	0.0613745
$585$	16.2572	0.672152
$586$	17.2498	0.712585
$587$	−1.05033	−0.0433517	−0.0216759	−	0.999765i	$-0.506900\pi$
$587$	−1.05033	−0.0433517	−0.0216759	+	0.999765i	$0.506900\pi$
$588$	12.1863	0.502553
$589$	26.5153	1.09254
$590$	11.5680	0.476246
$591$	5.71456	0.235066
$592$	−0.664493	−0.0273105
$593$	9.37622	0.385035	0.192518	−	0.981294i	$-0.438335\pi$
$593$	9.37622	0.385035	0.192518	+	0.981294i	$0.438335\pi$
$594$	3.18953	0.130868
$595$	−2.13186	−0.0873975
$596$	16.7790	0.687293
$597$	29.0041	1.18706
$598$	0	0
$599$	18.9264	0.773311	0.386655	−	0.922224i	$-0.373630\pi$
$599$	18.9264	0.773311	0.386655	+	0.922224i	$0.373630\pi$
$600$	−2.33225	−0.0952136
$601$	−30.3981	−1.23996	−0.619982	−	0.784616i	$-0.712860\pi$
$601$	−30.3981	−1.23996	−0.619982	+	0.784616i	$0.712860\pi$
$602$	12.6098	0.513938
$603$	−29.3266	−1.19427
$604$	−6.93668	−0.282250
$605$	−5.04946	−0.205290
$606$	−14.9282	−0.606417
$607$	22.0203	0.893778	0.446889	−	0.894589i	$-0.352532\pi$
$607$	22.0203	0.893778	0.446889	+	0.894589i	$0.352532\pi$
$608$	7.95717	0.322706
$609$	−19.2983	−0.782009
$610$	12.1286	0.491072
$611$	−51.7939	−2.09536
$612$	3.90348	0.157789
$613$	−41.6686	−1.68298	−0.841489	−	0.540274i	$-0.818320\pi$
$613$	−41.6686	−1.68298	−0.841489	+	0.540274i	$0.818320\pi$
$614$	−14.0126	−0.565501
$615$	5.07418	0.204611
$616$	−3.24985	−0.130940
$617$	4.86234	0.195750	0.0978752	−	0.995199i	$-0.468795\pi$
$617$	4.86234	0.195750	0.0978752	+	0.995199i	$0.468795\pi$
$618$	12.5591	0.505200
$619$	−33.9826	−1.36588	−0.682938	−	0.730476i	$-0.739298\pi$
$619$	−33.9826	−1.36588	−0.682938	+	0.730476i	$0.739298\pi$
$620$	3.33225	0.133826
$621$	0	0
$622$	−15.7740	−0.632480
$623$	8.68427	0.347928
$624$	−15.5432	−0.622228
$625$	1.00000	0.0400000
$626$	9.77586	0.390722
$627$	−45.2701	−1.80791
$628$	2.27219	0.0906702
$629$	−1.06332	−0.0423973
$630$	−3.24985	−0.129477
$631$	19.9689	0.794950	0.397475	−	0.917613i	$-0.369887\pi$
$631$	19.9689	0.794950	0.397475	+	0.917613i	$0.369887\pi$
$632$	−3.77162	−0.150027
$633$	56.4755	2.24470
$634$	19.5489	0.776386
$635$	−16.0353	−0.636343
$636$	−10.8864	−0.431672
$637$	−34.8228	−1.37973
$638$	−15.1509	−0.599831
$639$	8.77188	0.347010
$640$	1.00000	0.0395285
$641$	−10.3321	−0.408093	−0.204046	−	0.978961i	$-0.565409\pi$
$641$	−10.3321	−0.408093	−0.204046	+	0.978961i	$0.565409\pi$
$642$	−22.3923	−0.883754
$643$	20.2487	0.798531	0.399266	−	0.916835i	$-0.369265\pi$
$643$	20.2487	0.798531	0.399266	+	0.916835i	$0.369265\pi$
$644$	0	0
$645$	22.0749	0.869198
$646$	12.7330	0.500974
$647$	2.23742	0.0879619	0.0439810	−	0.999032i	$-0.485996\pi$
$647$	2.23742	0.0879619	0.0439810	+	0.999032i	$0.485996\pi$
$648$	−10.3676	−0.407277
$649$	28.2186	1.10768
$650$	6.66449	0.261403
$651$	10.3537	0.405794
$652$	9.14246	0.358046
$653$	−41.7566	−1.63406	−0.817031	−	0.576593i	$-0.804382\pi$
$653$	−41.7566	−1.63406	−0.817031	+	0.576593i	$0.804382\pi$
$654$	−15.5762	−0.609077
$655$	−15.1112	−0.590444
$656$	−2.17566	−0.0849454
$657$	3.61804	0.141153
$658$	10.3537	0.403630
$659$	6.17142	0.240405	0.120202	−	0.992749i	$-0.461646\pi$
$659$	6.17142	0.240405	0.120202	+	0.992749i	$0.461646\pi$
$660$	−5.68922	−0.221453
$661$	10.5430	0.410074	0.205037	−	0.978754i	$-0.434268\pi$
$661$	10.5430	0.410074	0.205037	+	0.978754i	$0.434268\pi$
$662$	12.9915	0.504930
$663$	−24.8722	−0.965957
$664$	−2.96777	−0.115172
$665$	−10.6009	−0.411086
$666$	−1.62095	−0.0628104
$667$	0	0
$668$	−3.24224	−0.125446
$669$	57.9884	2.24196
$670$	−12.0222	−0.464457
$671$	29.5862	1.14216
$672$	3.10713	0.119860
$673$	37.2064	1.43420	0.717101	−	0.696969i	$-0.245469\pi$
$673$	37.2064	1.43420	0.717101	+	0.696969i	$0.245469\pi$
$674$	−19.9242	−0.767453
$675$	1.30752	0.0503264
$676$	31.4155	1.20829
$677$	22.8246	0.877221	0.438610	−	0.898677i	$-0.355471\pi$
$677$	22.8246	0.877221	0.438610	+	0.898677i	$0.355471\pi$
$678$	−48.2870	−1.85445
$679$	−9.23007	−0.354218
$680$	1.60020	0.0613647
$681$	−10.4460	−0.400292
$682$	8.12859	0.311260
$683$	−34.5123	−1.32057	−0.660287	−	0.751013i	$-0.729566\pi$
$683$	−34.5123	−1.32057	−0.660287	+	0.751013i	$0.729566\pi$
$684$	19.4105	0.742179
$685$	21.1369	0.807600
$686$	16.2869	0.621836
$687$	−4.93146	−0.188147
$688$	−9.46508	−0.360853
$689$	31.1082	1.18513
$690$	0	0
$691$	12.3093	0.468270	0.234135	−	0.972204i	$-0.424774\pi$
$691$	12.3093	0.468270	0.234135	+	0.972204i	$0.424774\pi$
$692$	−0.0353305	−0.00134306
$693$	−7.92759	−0.301144
$694$	−22.7736	−0.864473
$695$	18.6332	0.706799
$696$	14.4856	0.549074
$697$	−3.48149	−0.131871
$698$	12.0876	0.457523
$699$	62.3075	2.35668
$700$	−1.33225	−0.0503542
$701$	−8.02881	−0.303244	−0.151622	−	0.988439i	$-0.548450\pi$
$701$	−8.02881	−0.303244	−0.151622	+	0.988439i	$0.548450\pi$
$702$	8.71395	0.328887
$703$	−5.28748	−0.199421
$704$	2.43937	0.0919374
$705$	18.1253	0.682640
$706$	24.6068	0.926090
$707$	−8.52742	−0.320707
$708$	−26.9794	−1.01395
$709$	−30.3222	−1.13877	−0.569387	−	0.822070i	$-0.692819\pi$
$709$	−30.3222	−1.13877	−0.569387	+	0.822070i	$0.692819\pi$
$710$	3.59596	0.134954
$711$	−9.20039	−0.345042
$712$	−6.51851	−0.244292
$713$	0	0
$714$	4.97201	0.186073
$715$	16.2572	0.607984
$716$	18.0459	0.674408
$717$	5.39487	0.201475
$718$	28.9867	1.08177
$719$	15.7627	0.587850	0.293925	−	0.955828i	$-0.405038\pi$
$719$	15.7627	0.587850	0.293925	+	0.955828i	$0.405038\pi$
$720$	2.43937	0.0909101
$721$	7.17410	0.267177
$722$	44.3166	1.64929
$723$	−13.9882	−0.520225
$724$	16.5591	0.615413
$725$	−6.21099	−0.230671
$726$	11.7766	0.437070
$727$	−34.3171	−1.27275	−0.636375	−	0.771380i	$-0.719567\pi$
$727$	−34.3171	−1.27275	−0.636375	+	0.771380i	$0.719567\pi$
$728$	−8.87875	−0.329068
$729$	−16.1420	−0.597853
$730$	1.48318	0.0548950
$731$	−15.1460	−0.560194
$732$	−28.2869	−1.04551
$733$	−30.7121	−1.13438	−0.567189	−	0.823588i	$-0.691969\pi$
$733$	−30.7121	−1.13438	−0.567189	+	0.823588i	$0.691969\pi$
$734$	−12.9829	−0.479207
$735$	12.1863	0.449497
$736$	0	0
$737$	−29.3266	−1.08026
$738$	−5.30726	−0.195363
$739$	−11.0162	−0.405239	−0.202620	−	0.979258i	$-0.564946\pi$
$739$	−11.0162	−0.405239	−0.202620	+	0.979258i	$0.564946\pi$
$740$	−0.664493	−0.0244272
$741$	−123.680	−4.54351
$742$	−6.21860	−0.228292
$743$	49.9851	1.83378	0.916888	−	0.399144i	$-0.130693\pi$
$743$	49.9851	1.83378	0.916888	+	0.399144i	$0.130693\pi$
$744$	−7.77162	−0.284921
$745$	16.7790	0.614734
$746$	14.1234	0.517094
$747$	−7.23951	−0.264880
$748$	3.90348	0.142725
$749$	−12.7911	−0.467378
$750$	−2.33225	−0.0851616
$751$	51.6950	1.88638	0.943189	−	0.332258i	$-0.107810\pi$
$751$	51.6950	1.88638	0.943189	+	0.332258i	$0.107810\pi$
$752$	−7.77162	−0.283402
$753$	−53.8533	−1.96252
$754$	−41.3931	−1.50745
$755$	−6.93668	−0.252452
$756$	−1.74194	−0.0633536
$757$	−8.04620	−0.292444	−0.146222	−	0.989252i	$-0.546711\pi$
$757$	−8.04620	−0.292444	−0.146222	+	0.989252i	$0.546711\pi$
$758$	−2.85330	−0.103637
$759$	0	0
$760$	7.95717	0.288637
$761$	−37.1409	−1.34636	−0.673178	−	0.739480i	$-0.735071\pi$
$761$	−37.1409	−1.34636	−0.673178	+	0.739480i	$0.735071\pi$
$762$	37.3983	1.35480
$763$	−8.89757	−0.322114
$764$	1.95619	0.0707725
$765$	3.90348	0.141130
$766$	5.94207	0.214696
$767$	77.0946	2.78373
$768$	−2.33225	−0.0841577
$769$	−16.6669	−0.601023	−0.300512	−	0.953778i	$-0.597157\pi$
$769$	−16.6669	−0.601023	−0.300512	+	0.953778i	$0.597157\pi$
$770$	−3.24985	−0.117116
$771$	41.5549	1.49656
$772$	5.43611	0.195650
$773$	−53.9375	−1.94000	−0.969999	−	0.243111i	$-0.921832\pi$
$773$	−53.9375	−1.94000	−0.969999	+	0.243111i	$0.921832\pi$
$774$	−23.0889	−0.829912
$775$	3.33225	0.119698
$776$	6.92820	0.248708
$777$	−2.06466	−0.0740694
$778$	21.4364	0.768531
$779$	−17.3121	−0.620271
$780$	−15.5432	−0.556537
$781$	8.77188	0.313883
$782$	0	0
$783$	−8.12099	−0.290221
$784$	−5.22512	−0.186611
$785$	2.27219	0.0810979
$786$	35.2431	1.25708
$787$	20.6594	0.736427	0.368214	−	0.929741i	$-0.379969\pi$
$787$	20.6594	0.736427	0.368214	+	0.929741i	$0.379969\pi$
$788$	−2.45024	−0.0872861
$789$	26.2869	0.935837
$790$	−3.77162	−0.134188
$791$	−27.5829	−0.980736
$792$	5.95054	0.211443
$793$	80.8309	2.87039
$794$	21.7368	0.771412
$795$	−10.8864	−0.386099
$796$	−12.4361	−0.440786
$797$	−43.8744	−1.55411	−0.777055	−	0.629433i	$-0.783287\pi$
$797$	−43.8744	−1.55411	−0.777055	+	0.629433i	$0.783287\pi$
$798$	24.7239	0.875218
$799$	−12.4361	−0.439958
$800$	1.00000	0.0353553
$801$	−15.9011	−0.561837
$802$	29.1208	1.02829
$803$	3.61804	0.127678
$804$	28.0387	0.988849
$805$	0	0
$806$	22.2077	0.782234
$807$	−50.4135	−1.77464
$808$	6.40078	0.225179
$809$	26.5476	0.933363	0.466682	−	0.884425i	$-0.345449\pi$
$809$	26.5476	0.933363	0.466682	+	0.884425i	$0.345449\pi$
$810$	−10.3676	−0.364280
$811$	−31.8143	−1.11715	−0.558575	−	0.829454i	$-0.688652\pi$
$811$	−31.8143	−1.11715	−0.558575	+	0.829454i	$0.688652\pi$
$812$	8.27458	0.290381
$813$	59.9389	2.10215
$814$	−1.62095	−0.0568142
$815$	9.14246	0.320246
$816$	−3.73205	−0.130648
$817$	−75.3153	−2.63495
$818$	−5.86136	−0.204938
$819$	−21.6586	−0.756812
$820$	−2.17566	−0.0759775
$821$	21.1128	0.736841	0.368420	−	0.929659i	$-0.379899\pi$
$821$	21.1128	0.736841	0.368420	+	0.929659i	$0.379899\pi$
$822$	−49.2965	−1.71941
$823$	35.3940	1.23376	0.616879	−	0.787058i	$-0.288397\pi$
$823$	35.3940	1.23376	0.616879	+	0.787058i	$0.288397\pi$
$824$	−5.38496	−0.187594
$825$	−5.68922	−0.198073
$826$	−15.4114	−0.536231
$827$	28.2839	0.983529	0.491764	−	0.870728i	$-0.336352\pi$
$827$	28.2839	0.983529	0.491764	+	0.870728i	$0.336352\pi$
$828$	0	0
$829$	−16.7586	−0.582051	−0.291026	−	0.956715i	$-0.593997\pi$
$829$	−16.7586	−0.582051	−0.291026	+	0.956715i	$0.593997\pi$
$830$	−2.96777	−0.103013
$831$	49.2777	1.70942
$832$	6.66449	0.231050
$833$	−8.36121	−0.289699
$834$	−43.4573	−1.50480
$835$	−3.24224	−0.112202
$836$	19.4105	0.671327
$837$	4.35697	0.150599
$838$	23.5127	0.812233
$839$	35.3482	1.22036	0.610178	−	0.792264i	$-0.291098\pi$
$839$	35.3482	1.22036	0.610178	+	0.792264i	$0.291098\pi$
$840$	3.10713	0.107206
$841$	9.57645	0.330222
$842$	21.1713	0.729610
$843$	57.1536	1.96847
$844$	−24.2151	−0.833517
$845$	31.4155	1.08072
$846$	−18.9579	−0.651786
$847$	6.72712	0.231147
$848$	4.66775	0.160291
$849$	27.4698	0.942760
$850$	1.60020	0.0548863
$851$	0	0
$852$	−8.38666	−0.287322
$853$	−52.3312	−1.79179	−0.895894	−	0.444268i	$-0.853464\pi$
$853$	−52.3312	−1.79179	−0.895894	+	0.444268i	$0.853464\pi$
$854$	−16.1583	−0.552925
$855$	19.4105	0.663825
$856$	9.60117	0.328161
$857$	24.7491	0.845415	0.422707	−	0.906266i	$-0.361080\pi$
$857$	24.7491	0.845415	0.422707	+	0.906266i	$0.361080\pi$
$858$	−37.9158	−1.29442
$859$	33.4239	1.14041	0.570205	−	0.821502i	$-0.306864\pi$
$859$	33.4239	1.14041	0.570205	+	0.821502i	$0.306864\pi$
$860$	−9.46508	−0.322757
$861$	−6.76006	−0.230382
$862$	−0.0296831	−0.00101101
$863$	−10.4573	−0.355971	−0.177986	−	0.984033i	$-0.556958\pi$
$863$	−10.4573	−0.355971	−0.177986	+	0.984033i	$0.556958\pi$
$864$	1.30752	0.0444827
$865$	−0.0353305	−0.00120127
$866$	20.0815	0.682398
$867$	33.6762	1.14370
$868$	−4.43937	−0.150682
$869$	−9.20039	−0.312102
$870$	14.4856	0.491107
$871$	−80.1218	−2.71482
$872$	6.67862	0.226167
$873$	16.9005	0.571994
$874$	0	0
$875$	−1.33225	−0.0450382
$876$	−3.45915	−0.116874
$877$	−41.2993	−1.39458	−0.697289	−	0.716790i	$-0.745611\pi$
$877$	−41.2993	−1.39458	−0.697289	+	0.716790i	$0.745611\pi$
$878$	28.4385	0.959753
$879$	−40.2309	−1.35695
$880$	2.43937	0.0822313
$881$	7.85402	0.264609	0.132304	−	0.991209i	$-0.457762\pi$
$881$	7.85402	0.264609	0.132304	+	0.991209i	$0.457762\pi$
$882$	−12.7460	−0.429181
$883$	28.1628	0.947753	0.473877	−	0.880591i	$-0.342854\pi$
$883$	28.1628	0.947753	0.473877	+	0.880591i	$0.342854\pi$
$884$	10.6645	0.358686
$885$	−26.9794	−0.906901
$886$	−5.04620	−0.169530
$887$	−23.1990	−0.778946	−0.389473	−	0.921038i	$-0.627343\pi$
$887$	−23.1990	−0.778946	−0.389473	+	0.921038i	$0.627343\pi$
$888$	1.54976	0.0520066
$889$	21.3630	0.716492
$890$	−6.51851	−0.218501
$891$	−25.2904	−0.847260
$892$	−24.8637	−0.832500
$893$	−61.8401	−2.06940
$894$	−39.1327	−1.30879
$895$	18.0459	0.603209
$896$	−1.33225	−0.0445072
$897$	0	0
$898$	−30.6455	−1.02265
$899$	−20.6966	−0.690269
$900$	2.43937	0.0813125
$901$	7.46932	0.248839
$902$	−5.30726	−0.176712
$903$	−29.4092	−0.978677
$904$	20.7041	0.688607
$905$	16.5591	0.550442
$906$	16.1781	0.537480
$907$	−30.0316	−0.997183	−0.498592	−	0.866837i	$-0.666149\pi$
$907$	−30.0316	−0.997183	−0.498592	+	0.866837i	$0.666149\pi$
$908$	4.47894	0.148639
$909$	15.6139	0.517880
$910$	−8.87875	−0.294328
$911$	−27.1410	−0.899222	−0.449611	−	0.893224i	$-0.648437\pi$
$911$	−27.1410	−0.899222	−0.449611	+	0.893224i	$0.648437\pi$
$912$	−18.5581	−0.614520
$913$	−7.23951	−0.239593
$914$	7.09300	0.234616
$915$	−28.2869	−0.935135
$916$	2.11447	0.0698640
$917$	20.1319	0.664812
$918$	2.09229	0.0690557
$919$	−17.4844	−0.576758	−0.288379	−	0.957516i	$-0.593116\pi$
$919$	−17.4844	−0.576758	−0.288379	+	0.957516i	$0.593116\pi$
$920$	0	0
$921$	32.6807	1.07687
$922$	34.3151	1.13011
$923$	23.9652	0.788825
$924$	7.57944	0.249345
$925$	−0.664493	−0.0218484
$926$	24.5294	0.806085
$927$	−13.1359	−0.431441
$928$	−6.21099	−0.203886
$929$	−39.3931	−1.29245	−0.646223	−	0.763148i	$-0.723653\pi$
$929$	−39.3931	−1.29245	−0.646223	+	0.763148i	$0.723653\pi$
$930$	−7.77162	−0.254841
$931$	−41.5772	−1.36264
$932$	−26.7156	−0.875100
$933$	36.7889	1.20441
$934$	−37.4788	−1.22634
$935$	3.90348	0.127657
$936$	16.2572	0.531383
$937$	−49.5500	−1.61873	−0.809364	−	0.587307i	$-0.800188\pi$
$937$	−49.5500	−1.61873	−0.809364	+	0.587307i	$0.800188\pi$
$938$	16.0165	0.522958
$939$	−22.7997	−0.744041
$940$	−7.77162	−0.253482
$941$	−35.1172	−1.14479	−0.572395	−	0.819978i	$-0.693985\pi$
$941$	−35.1172	−1.14479	−0.572395	+	0.819978i	$0.693985\pi$
$942$	−5.29930	−0.172661
$943$	0	0
$944$	11.5680	0.376505
$945$	−1.74194	−0.0566652
$946$	−23.0889	−0.750684
$947$	−8.68357	−0.282178	−0.141089	−	0.989997i	$-0.545060\pi$
$947$	−8.68357	−0.282178	−0.141089	+	0.989997i	$0.545060\pi$
$948$	8.79635	0.285692
$949$	9.88466	0.320870
$950$	7.95717	0.258165
$951$	−45.5928	−1.47845
$952$	−2.13186	−0.0690938
$953$	−33.3931	−1.08171	−0.540855	−	0.841116i	$-0.681899\pi$
$953$	−33.3931	−1.08171	−0.540855	+	0.841116i	$0.681899\pi$
$954$	11.3864	0.368648
$955$	1.95619	0.0633009
$956$	−2.31317	−0.0748131
$957$	35.3357	1.14224
$958$	−10.8929	−0.351933
$959$	−28.1596	−0.909320
$960$	−2.33225	−0.0752729
$961$	−19.8961	−0.641811
$962$	−4.42851	−0.142781
$963$	23.4209	0.754726
$964$	5.99772	0.193173
$965$	5.43611	0.174995
$966$	0	0
$967$	29.8646	0.960380	0.480190	−	0.877165i	$-0.340568\pi$
$967$	29.8646	0.960380	0.480190	+	0.877165i	$0.340568\pi$
$968$	−5.04946	−0.162296
$969$	−29.6966	−0.953991
$970$	6.92820	0.222451
$971$	−41.6695	−1.33724	−0.668618	−	0.743606i	$-0.733114\pi$
$971$	−41.6695	−1.33724	−0.668618	+	0.743606i	$0.733114\pi$
$972$	20.2572	0.649750
$973$	−24.8241	−0.795823
$974$	−38.7866	−1.24280
$975$	−15.5432	−0.497782
$976$	12.1286	0.388227
$977$	39.9935	1.27950	0.639752	−	0.768581i	$-0.279037\pi$
$977$	39.9935	1.27950	0.639752	+	0.768581i	$0.279037\pi$
$978$	−21.3225	−0.681817
$979$	−15.9011	−0.508201
$980$	−5.22512	−0.166910
$981$	16.2916	0.520152
$982$	−6.76950	−0.216023
$983$	9.51499	0.303481	0.151741	−	0.988420i	$-0.451512\pi$
$983$	9.51499	0.303481	0.151741	+	0.988420i	$0.451512\pi$
$984$	5.07418	0.161759
$985$	−2.45024	−0.0780711
$986$	−9.93881	−0.316516
$987$	−24.1474	−0.768621
$988$	53.0305	1.68713
$989$	0	0
$990$	5.95054	0.189121
$991$	−4.87027	−0.154709	−0.0773546	−	0.997004i	$-0.524647\pi$
$991$	−4.87027	−0.154709	−0.0773546	+	0.997004i	$0.524647\pi$
$992$	3.33225	0.105799
$993$	−30.2994	−0.961523
$994$	−4.79070	−0.151952
$995$	−12.4361	−0.394251
$996$	6.92158	0.219319
$997$	−25.6911	−0.813645	−0.406822	−	0.913507i	$-0.633363\pi$
$997$	−25.6911	−0.813645	−0.406822	+	0.913507i	$0.633363\pi$
$998$	27.2206	0.861652
$999$	−0.868837	−0.0274888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bb.1.1	yes	4
23.22	odd	2		5290.2.a.ba.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.ba.1.1	✓	4	23.22	odd	2
5290.2.a.bb.1.1	yes	4	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.33225 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.33225 q^{6} -1.33225 q^{7} +1.00000 q^{8} +2.43937 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.33225 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.33225 q^{6} -1.33225 q^{7} +1.00000 q^{8} +2.43937 q^{9} +1.00000 q^{10} +2.43937 q^{11} -2.33225 q^{12} +6.66449 q^{13} -1.33225 q^{14} -2.33225 q^{15} +1.00000 q^{16} +1.60020 q^{17} +2.43937 q^{18} +7.95717 q^{19} +1.00000 q^{20} +3.10713 q^{21} +2.43937 q^{22} -2.33225 q^{24} +1.00000 q^{25} +6.66449 q^{26} +1.30752 q^{27} -1.33225 q^{28} -6.21099 q^{29} -2.33225 q^{30} +3.33225 q^{31} +1.00000 q^{32} -5.68922 q^{33} +1.60020 q^{34} -1.33225 q^{35} +2.43937 q^{36} -0.664493 q^{37} +7.95717 q^{38} -15.5432 q^{39} +1.00000 q^{40} -2.17566 q^{41} +3.10713 q^{42} -9.46508 q^{43} +2.43937 q^{44} +2.43937 q^{45} -7.77162 q^{47} -2.33225 q^{48} -5.22512 q^{49} +1.00000 q^{50} -3.73205 q^{51} +6.66449 q^{52} +4.66775 q^{53} +1.30752 q^{54} +2.43937 q^{55} -1.33225 q^{56} -18.5581 q^{57} -6.21099 q^{58} +11.5680 q^{59} -2.33225 q^{60} +12.1286 q^{61} +3.33225 q^{62} -3.24985 q^{63} +1.00000 q^{64} +6.66449 q^{65} -5.68922 q^{66} -12.0222 q^{67} +1.60020 q^{68} -1.33225 q^{70} +3.59596 q^{71} +2.43937 q^{72} +1.48318 q^{73} -0.664493 q^{74} -2.33225 q^{75} +7.95717 q^{76} -3.24985 q^{77} -15.5432 q^{78} -3.77162 q^{79} +1.00000 q^{80} -10.3676 q^{81} -2.17566 q^{82} -2.96777 q^{83} +3.10713 q^{84} +1.60020 q^{85} -9.46508 q^{86} +14.4856 q^{87} +2.43937 q^{88} -6.51851 q^{89} +2.43937 q^{90} -8.87875 q^{91} -7.77162 q^{93} -7.77162 q^{94} +7.95717 q^{95} -2.33225 q^{96} +6.92820 q^{97} -5.22512 q^{98} +5.95054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 6 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{14} + 2 q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{18} + 8 q^{19} + 4 q^{20} + 18 q^{21} + 4 q^{22} + 2 q^{24} + 4 q^{25} + 4 q^{26} + 2 q^{27} + 6 q^{28} - 2 q^{29} + 2 q^{30} + 2 q^{31} + 4 q^{32} + 8 q^{33} + 2 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} + 8 q^{38} - 28 q^{39} + 4 q^{40} - 8 q^{41} + 18 q^{42} - 2 q^{43} + 4 q^{44} + 4 q^{45} - 14 q^{47} + 2 q^{48} - 4 q^{49} + 4 q^{50} - 8 q^{51} + 4 q^{52} + 30 q^{53} + 2 q^{54} + 4 q^{55} + 6 q^{56} - 38 q^{57} - 2 q^{58} + 4 q^{59} + 2 q^{60} + 12 q^{61} + 2 q^{62} + 12 q^{63} + 4 q^{64} + 4 q^{65} + 8 q^{66} + 2 q^{67} + 2 q^{68} + 6 q^{70} - 2 q^{71} + 4 q^{72} + 2 q^{73} + 20 q^{74} + 2 q^{75} + 8 q^{76} + 12 q^{77} - 28 q^{78} + 2 q^{79} + 4 q^{80} - 8 q^{81} - 8 q^{82} + 26 q^{83} + 18 q^{84} + 2 q^{85} - 2 q^{86} + 2 q^{87} + 4 q^{88} + 4 q^{90} - 24 q^{91} - 14 q^{93} - 14 q^{94} + 8 q^{95} + 2 q^{96} - 4 q^{98} + 40 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 6 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 4 * q^11 + 2 * q^12 + 4 * q^13 + 6 * q^14 + 2 * q^15 + 4 * q^16 + 2 * q^17 + 4 * q^18 + 8 * q^19 + 4 * q^20 + 18 * q^21 + 4 * q^22 + 2 * q^24 + 4 * q^25 + 4 * q^26 + 2 * q^27 + 6 * q^28 - 2 * q^29 + 2 * q^30 + 2 * q^31 + 4 * q^32 + 8 * q^33 + 2 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 + 8 * q^38 - 28 * q^39 + 4 * q^40 - 8 * q^41 + 18 * q^42 - 2 * q^43 + 4 * q^44 + 4 * q^45 - 14 * q^47 + 2 * q^48 - 4 * q^49 + 4 * q^50 - 8 * q^51 + 4 * q^52 + 30 * q^53 + 2 * q^54 + 4 * q^55 + 6 * q^56 - 38 * q^57 - 2 * q^58 + 4 * q^59 + 2 * q^60 + 12 * q^61 + 2 * q^62 + 12 * q^63 + 4 * q^64 + 4 * q^65 + 8 * q^66 + 2 * q^67 + 2 * q^68 + 6 * q^70 - 2 * q^71 + 4 * q^72 + 2 * q^73 + 20 * q^74 + 2 * q^75 + 8 * q^76 + 12 * q^77 - 28 * q^78 + 2 * q^79 + 4 * q^80 - 8 * q^81 - 8 * q^82 + 26 * q^83 + 18 * q^84 + 2 * q^85 - 2 * q^86 + 2 * q^87 + 4 * q^88 + 4 * q^90 - 24 * q^91 - 14 * q^93 - 14 * q^94 + 8 * q^95 + 2 * q^96 - 4 * q^98 + 40 * q^99

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