LMFDB - Embedded newform 289.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, 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("289.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{16})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 2 $ x^4 - 4*x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.84776$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41421 q^{2} +1.08239 q^{3} +3.82843 q^{4} -0.765367 q^{5} +2.61313 q^{6} -2.61313 q^{7} +4.41421 q^{8} -1.82843 q^{9} +O(q^{10})$	\(q+2.41421 q^{2} +1.08239 q^{3} +3.82843 q^{4} -0.765367 q^{5} +2.61313 q^{6} -2.61313 q^{7} +4.41421 q^{8} -1.82843 q^{9} -1.84776 q^{10} +2.61313 q^{11} +4.14386 q^{12} +1.41421 q^{13} -6.30864 q^{14} -0.828427 q^{15} +3.00000 q^{16} -4.41421 q^{18} -0.828427 q^{19} -2.93015 q^{20} -2.82843 q^{21} +6.30864 q^{22} -4.77791 q^{23} +4.77791 q^{24} -4.41421 q^{25} +3.41421 q^{26} -5.22625 q^{27} -10.0042 q^{28} +0.317025 q^{29} -2.00000 q^{30} +7.83938 q^{31} -1.58579 q^{32} +2.82843 q^{33} +2.00000 q^{35} -7.00000 q^{36} +9.23880 q^{37} -2.00000 q^{38} +1.53073 q^{39} -3.37849 q^{40} +1.21371 q^{41} -6.82843 q^{42} +0.828427 q^{43} +10.0042 q^{44} +1.39942 q^{45} -11.5349 q^{46} +5.17157 q^{47} +3.24718 q^{48} -0.171573 q^{49} -10.6569 q^{50} +5.41421 q^{52} +1.41421 q^{53} -12.6173 q^{54} -2.00000 q^{55} -11.5349 q^{56} -0.896683 q^{57} +0.765367 q^{58} +6.00000 q^{59} -3.17157 q^{60} +3.82683 q^{61} +18.9259 q^{62} +4.77791 q^{63} -9.82843 q^{64} -1.08239 q^{65} +6.82843 q^{66} -1.17157 q^{67} -5.17157 q^{69} +4.82843 q^{70} -5.41196 q^{71} -8.07107 q^{72} -12.9343 q^{73} +22.3044 q^{74} -4.77791 q^{75} -3.17157 q^{76} -6.82843 q^{77} +3.69552 q^{78} -4.77791 q^{79} -2.29610 q^{80} -0.171573 q^{81} +2.93015 q^{82} +11.6569 q^{83} -10.8284 q^{84} +2.00000 q^{86} +0.343146 q^{87} +11.5349 q^{88} +6.58579 q^{89} +3.37849 q^{90} -3.69552 q^{91} -18.2919 q^{92} +8.48528 q^{93} +12.4853 q^{94} +0.634051 q^{95} -1.71644 q^{96} -10.3212 q^{97} -0.414214 q^{98} -4.77791 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{4} + 12 q^{8} + 4 q^{9} + 8 q^{15} + 12 q^{16} - 12 q^{18} + 8 q^{19} - 12 q^{25} + 8 q^{26} - 8 q^{30} - 12 q^{32} + 8 q^{35} - 28 q^{36} - 8 q^{38} - 16 q^{42} - 8 q^{43} + 32 q^{47} - 12 q^{49} - 20 q^{50} + 16 q^{52} - 8 q^{55} + 24 q^{59} - 24 q^{60} - 28 q^{64} + 16 q^{66} - 16 q^{67} - 32 q^{69} + 8 q^{70} - 4 q^{72} - 24 q^{76} - 16 q^{77} - 12 q^{81} + 24 q^{83} - 32 q^{84} + 8 q^{86} + 24 q^{87} + 32 q^{89} + 16 q^{94} + 4 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 + 4 * q^9 + 8 * q^15 + 12 * q^16 - 12 * q^18 + 8 * q^19 - 12 * q^25 + 8 * q^26 - 8 * q^30 - 12 * q^32 + 8 * q^35 - 28 * q^36 - 8 * q^38 - 16 * q^42 - 8 * q^43 + 32 * q^47 - 12 * q^49 - 20 * q^50 + 16 * q^52 - 8 * q^55 + 24 * q^59 - 24 * q^60 - 28 * q^64 + 16 * q^66 - 16 * q^67 - 32 * q^69 + 8 * q^70 - 4 * q^72 - 24 * q^76 - 16 * q^77 - 12 * q^81 + 24 * q^83 - 32 * q^84 + 8 * q^86 + 24 * q^87 + 32 * q^89 + 16 * q^94 + 4 * q^98

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 $

$2$	2.41421	1.70711	0.853553	−	0.521005i	$-0.174443\pi$
$2$	2.41421	1.70711	0.853553	+	0.521005i	$0.174443\pi$
$3$	1.08239	0.624919	0.312460	−	0.949931i	$-0.398847\pi$
$3$	1.08239	0.624919	0.312460	+	0.949931i	$0.398847\pi$
$4$	3.82843	1.91421
$5$	−0.765367	−0.342282	−0.171141	−	0.985247i	$-0.554745\pi$
$5$	−0.765367	−0.342282	−0.171141	+	0.985247i	$0.554745\pi$
$6$	2.61313	1.06680
$7$	−2.61313	−0.987669	−0.493834	−	0.869556i	$-0.664405\pi$
$7$	−2.61313	−0.987669	−0.493834	+	0.869556i	$0.664405\pi$
$8$	4.41421	1.56066
$9$	−1.82843	−0.609476
$10$	−1.84776	−0.584313
$11$	2.61313	0.787887	0.393944	−	0.919135i	$-0.371111\pi$
$11$	2.61313	0.787887	0.393944	+	0.919135i	$0.371111\pi$
$12$	4.14386	1.19623
$13$	1.41421	0.392232	0.196116	−	0.980581i	$-0.437167\pi$
$13$	1.41421	0.392232	0.196116	+	0.980581i	$0.437167\pi$
$14$	−6.30864	−1.68606
$15$	−0.828427	−0.213899
$16$	3.00000	0.750000
$17$	0	0
$17$	0	0
$18$	−4.41421	−1.04044
$19$	−0.828427	−0.190054	−0.0950271	−	0.995475i	$-0.530294\pi$
$19$	−0.828427	−0.190054	−0.0950271	+	0.995475i	$0.530294\pi$
$20$	−2.93015	−0.655202
$21$	−2.82843	−0.617213
$22$	6.30864	1.34501
$23$	−4.77791	−0.996263	−0.498132	−	0.867101i	$-0.665980\pi$
$23$	−4.77791	−0.996263	−0.498132	+	0.867101i	$0.665980\pi$
$24$	4.77791	0.975287
$25$	−4.41421	−0.882843
$26$	3.41421	0.669582
$27$	−5.22625	−1.00579
$28$	−10.0042	−1.89061
$29$	0.317025	0.0588701	0.0294351	−	0.999567i	$-0.490629\pi$
$29$	0.317025	0.0588701	0.0294351	+	0.999567i	$0.490629\pi$
$30$	−2.00000	−0.365148
$31$	7.83938	1.40799	0.703997	−	0.710203i	$-0.251397\pi$
$31$	7.83938	1.40799	0.703997	+	0.710203i	$0.251397\pi$
$32$	−1.58579	−0.280330
$33$	2.82843	0.492366
$34$	0	0
$35$	2.00000	0.338062
$36$	−7.00000	−1.16667
$37$	9.23880	1.51885	0.759424	−	0.650596i	$-0.225481\pi$
$37$	9.23880	1.51885	0.759424	+	0.650596i	$0.225481\pi$
$38$	−2.00000	−0.324443
$39$	1.53073	0.245114
$40$	−3.37849	−0.534187
$41$	1.21371	0.189549	0.0947747	−	0.995499i	$-0.469787\pi$
$41$	1.21371	0.189549	0.0947747	+	0.995499i	$0.469787\pi$
$42$	−6.82843	−1.05365
$43$	0.828427	0.126334	0.0631670	−	0.998003i	$-0.479880\pi$
$43$	0.828427	0.126334	0.0631670	+	0.998003i	$0.479880\pi$
$44$	10.0042	1.50818
$45$	1.39942	0.208613
$46$	−11.5349	−1.70073
$47$	5.17157	0.754351	0.377176	−	0.926142i	$-0.376895\pi$
$47$	5.17157	0.754351	0.377176	+	0.926142i	$0.376895\pi$
$48$	3.24718	0.468690
$49$	−0.171573	−0.0245104
$50$	−10.6569	−1.50711
$51$	0	0
$52$	5.41421	0.750816
$53$	1.41421	0.194257	0.0971286	−	0.995272i	$-0.469034\pi$
$53$	1.41421	0.194257	0.0971286	+	0.995272i	$0.469034\pi$
$54$	−12.6173	−1.71700
$55$	−2.00000	−0.269680
$56$	−11.5349	−1.54142
$57$	−0.896683	−0.118769
$58$	0.765367	0.100498
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	−3.17157	−0.409448
$61$	3.82683	0.489976	0.244988	−	0.969526i	$-0.421216\pi$
$61$	3.82683	0.489976	0.244988	+	0.969526i	$0.421216\pi$
$62$	18.9259	2.40360
$63$	4.77791	0.601960
$64$	−9.82843	−1.22855
$65$	−1.08239	−0.134254
$66$	6.82843	0.840521
$67$	−1.17157	−0.143130	−0.0715652	−	0.997436i	$-0.522799\pi$
$67$	−1.17157	−0.143130	−0.0715652	+	0.997436i	$0.522799\pi$
$68$	0	0
$69$	−5.17157	−0.622584
$70$	4.82843	0.577107
$71$	−5.41196	−0.642282	−0.321141	−	0.947031i	$-0.604066\pi$
$71$	−5.41196	−0.642282	−0.321141	+	0.947031i	$0.604066\pi$
$72$	−8.07107	−0.951184
$73$	−12.9343	−1.51385	−0.756923	−	0.653504i	$-0.773298\pi$
$73$	−12.9343	−1.51385	−0.756923	+	0.653504i	$0.773298\pi$
$74$	22.3044	2.59284
$75$	−4.77791	−0.551706
$76$	−3.17157	−0.363804
$77$	−6.82843	−0.778171
$78$	3.69552	0.418435
$79$	−4.77791	−0.537557	−0.268778	−	0.963202i	$-0.586620\pi$
$79$	−4.77791	−0.537557	−0.268778	+	0.963202i	$0.586620\pi$
$80$	−2.29610	−0.256712
$81$	−0.171573	−0.0190637
$82$	2.93015	0.323581
$83$	11.6569	1.27951	0.639753	−	0.768581i	$-0.279037\pi$
$83$	11.6569	1.27951	0.639753	+	0.768581i	$0.279037\pi$
$84$	−10.8284	−1.18148
$85$	0	0
$86$	2.00000	0.215666
$87$	0.343146	0.0367891
$88$	11.5349	1.22962
$89$	6.58579	0.698092	0.349046	−	0.937106i	$-0.386506\pi$
$89$	6.58579	0.698092	0.349046	+	0.937106i	$0.386506\pi$
$90$	3.37849	0.356124
$91$	−3.69552	−0.387396
$92$	−18.2919	−1.90706
$93$	8.48528	0.879883
$94$	12.4853	1.28776
$95$	0.634051	0.0650522
$96$	−1.71644	−0.175184
$97$	−10.3212	−1.04796	−0.523979	−	0.851731i	$-0.675553\pi$
$97$	−10.3212	−1.04796	−0.523979	+	0.851731i	$0.675553\pi$
$98$	−0.414214	−0.0418419
$99$	−4.77791	−0.480198
$100$	−16.8995	−1.68995
$101$	10.5858	1.05333	0.526663	−	0.850074i	$-0.323443\pi$
$101$	10.5858	1.05333	0.526663	+	0.850074i	$0.323443\pi$
$102$	0	0
$103$	12.4853	1.23021	0.615106	−	0.788445i	$-0.289113\pi$
$103$	12.4853	1.23021	0.615106	+	0.788445i	$0.289113\pi$
$104$	6.24264	0.612141
$105$	2.16478	0.211261
$106$	3.41421	0.331618
$107$	0.448342	0.0433428	0.0216714	−	0.999765i	$-0.493101\pi$
$107$	0.448342	0.0433428	0.0216714	+	0.999765i	$0.493101\pi$
$108$	−20.0083	−1.92530
$109$	15.5474	1.48917	0.744587	−	0.667525i	$-0.232646\pi$
$109$	15.5474	1.48917	0.744587	+	0.667525i	$0.232646\pi$
$110$	−4.82843	−0.460372
$111$	10.0000	0.949158
$112$	−7.83938	−0.740752
$113$	−13.1969	−1.24146	−0.620732	−	0.784023i	$-0.713165\pi$
$113$	−13.1969	−1.24146	−0.620732	+	0.784023i	$0.713165\pi$
$114$	−2.16478	−0.202751
$115$	3.65685	0.341003
$116$	1.21371	0.112690
$117$	−2.58579	−0.239056
$118$	14.4853	1.33348
$119$	0	0
$120$	−3.65685	−0.333824
$121$	−4.17157	−0.379234
$122$	9.23880	0.836441
$123$	1.31371	0.118453
$124$	30.0125	2.69520
$125$	7.20533	0.644464
$126$	11.5349	1.02761
$127$	−5.31371	−0.471515	−0.235758	−	0.971812i	$-0.575757\pi$
$127$	−5.31371	−0.471515	−0.235758	+	0.971812i	$0.575757\pi$
$128$	−20.5563	−1.81694
$129$	0.896683	0.0789485
$130$	−2.61313	−0.229186
$131$	15.2304	1.33069	0.665344	−	0.746537i	$-0.268285\pi$
$131$	15.2304	1.33069	0.665344	+	0.746537i	$0.268285\pi$
$132$	10.8284	0.942494
$133$	2.16478	0.187711
$134$	−2.82843	−0.244339
$135$	4.00000	0.344265
$136$	0	0
$137$	−16.7279	−1.42916	−0.714581	−	0.699552i	$-0.753383\pi$
$137$	−16.7279	−1.42916	−0.714581	+	0.699552i	$0.753383\pi$
$138$	−12.4853	−1.06282
$139$	−21.3533	−1.81117	−0.905584	−	0.424168i	$-0.860567\pi$
$139$	−21.3533	−1.81117	−0.905584	+	0.424168i	$0.860567\pi$
$140$	7.65685	0.647122
$141$	5.59767	0.471409
$142$	−13.0656	−1.09644
$143$	3.69552	0.309035
$144$	−5.48528	−0.457107
$145$	−0.242641	−0.0201502
$146$	−31.2262	−2.58430
$147$	−0.185709	−0.0153170
$148$	35.3701	2.90740
$149$	−16.9706	−1.39028	−0.695141	−	0.718873i	$-0.744658\pi$
$149$	−16.9706	−1.39028	−0.695141	+	0.718873i	$0.744658\pi$
$150$	−11.5349	−0.941820
$151$	7.17157	0.583614	0.291807	−	0.956477i	$-0.405743\pi$
$151$	7.17157	0.583614	0.291807	+	0.956477i	$0.405743\pi$
$152$	−3.65685	−0.296610
$153$	0	0
$154$	−16.4853	−1.32842
$155$	−6.00000	−0.481932
$156$	5.86030	0.469200
$157$	−9.65685	−0.770701	−0.385350	−	0.922770i	$-0.625919\pi$
$157$	−9.65685	−0.770701	−0.385350	+	0.922770i	$0.625919\pi$
$158$	−11.5349	−0.917667
$159$	1.53073	0.121395
$160$	1.21371	0.0959521
$161$	12.4853	0.983978
$162$	−0.414214	−0.0325437
$163$	8.47343	0.663690	0.331845	−	0.943334i	$-0.392329\pi$
$163$	8.47343	0.663690	0.331845	+	0.943334i	$0.392329\pi$
$164$	4.64659	0.362838
$165$	−2.16478	−0.168528
$166$	28.1421	2.18425
$167$	−1.97908	−0.153145	−0.0765727	−	0.997064i	$-0.524398\pi$
$167$	−1.97908	−0.153145	−0.0765727	+	0.997064i	$0.524398\pi$
$168$	−12.4853	−0.963260
$169$	−11.0000	−0.846154
$170$	0	0
$171$	1.51472	0.115833
$172$	3.17157	0.241830
$173$	2.93015	0.222775	0.111388	−	0.993777i	$-0.464470\pi$
$173$	2.93015	0.222775	0.111388	+	0.993777i	$0.464470\pi$
$174$	0.828427	0.0628029
$175$	11.5349	0.871956
$176$	7.83938	0.590915
$177$	6.49435	0.488145
$178$	15.8995	1.19172
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	5.35757	0.399330
$181$	11.6662	0.867143	0.433571	−	0.901119i	$-0.357253\pi$
$181$	11.6662	0.867143	0.433571	+	0.901119i	$0.357253\pi$
$182$	−8.92177	−0.661326
$183$	4.14214	0.306195
$184$	−21.0907	−1.55483
$185$	−7.07107	−0.519875
$186$	20.4853	1.50205
$187$	0	0
$188$	19.7990	1.44399
$189$	13.6569	0.993390
$190$	1.53073	0.111051
$191$	20.0000	1.44715	0.723575	−	0.690246i	$-0.242498\pi$
$191$	20.0000	1.44715	0.723575	+	0.690246i	$0.242498\pi$
$192$	−10.6382	−0.767747
$193$	2.29610	0.165277	0.0826385	−	0.996580i	$-0.473665\pi$
$193$	2.29610	0.165277	0.0826385	+	0.996580i	$0.473665\pi$
$194$	−24.9176	−1.78898
$195$	−1.17157	−0.0838981
$196$	−0.656854	−0.0469182
$197$	4.64659	0.331056	0.165528	−	0.986205i	$-0.447067\pi$
$197$	4.64659	0.331056	0.165528	+	0.986205i	$0.447067\pi$
$198$	−11.5349	−0.819749
$199$	−11.5349	−0.817687	−0.408844	−	0.912604i	$-0.634068\pi$
$199$	−11.5349	−0.817687	−0.408844	+	0.912604i	$0.634068\pi$
$200$	−19.4853	−1.37782
$201$	−1.26810	−0.0894450
$202$	25.5563	1.79814
$203$	−0.828427	−0.0581442
$204$	0	0
$205$	−0.928932	−0.0648794
$206$	30.1421	2.10010
$207$	8.73606	0.607198
$208$	4.24264	0.294174
$209$	−2.16478	−0.149741
$210$	5.22625	0.360646
$211$	−21.3533	−1.47003	−0.735013	−	0.678053i	$-0.762824\pi$
$211$	−21.3533	−1.47003	−0.735013	+	0.678053i	$0.762824\pi$
$212$	5.41421	0.371850
$213$	−5.85786	−0.401374
$214$	1.08239	0.0739908
$215$	−0.634051	−0.0432419
$216$	−23.0698	−1.56970
$217$	−20.4853	−1.39063
$218$	37.5348	2.54218
$219$	−14.0000	−0.946032
$220$	−7.65685	−0.516225
$221$	0	0
$222$	24.1421	1.62031
$223$	−4.82843	−0.323335	−0.161668	−	0.986845i	$-0.551687\pi$
$223$	−4.82843	−0.323335	−0.161668	+	0.986845i	$0.551687\pi$
$224$	4.14386	0.276873
$225$	8.07107	0.538071
$226$	−31.8602	−2.11931
$227$	17.3952	1.15456	0.577280	−	0.816546i	$-0.304114\pi$
$227$	17.3952	1.15456	0.577280	+	0.816546i	$0.304114\pi$
$228$	−3.43289	−0.227348
$229$	−17.1716	−1.13473	−0.567365	−	0.823467i	$-0.692037\pi$
$229$	−17.1716	−1.13473	−0.567365	+	0.823467i	$0.692037\pi$
$230$	8.82843	0.582129
$231$	−7.39104	−0.486294
$232$	1.39942	0.0918763
$233$	−8.79045	−0.575882	−0.287941	−	0.957648i	$-0.592971\pi$
$233$	−8.79045	−0.575882	−0.287941	+	0.957648i	$0.592971\pi$
$234$	−6.24264	−0.408094
$235$	−3.95815	−0.258201
$236$	22.9706	1.49526
$237$	−5.17157	−0.335930
$238$	0	0
$239$	14.8284	0.959171	0.479586	−	0.877495i	$-0.340787\pi$
$239$	14.8284	0.959171	0.479586	+	0.877495i	$0.340787\pi$
$240$	−2.48528	−0.160424
$241$	−3.56420	−0.229590	−0.114795	−	0.993389i	$-0.536621\pi$
$241$	−3.56420	−0.229590	−0.114795	+	0.993389i	$0.536621\pi$
$242$	−10.0711	−0.647393
$243$	15.4930	0.993879
$244$	14.6508	0.937919
$245$	0.131316	0.00838948
$246$	3.17157	0.202212
$247$	−1.17157	−0.0745454
$248$	34.6047	2.19740
$249$	12.6173	0.799588
$250$	17.3952	1.10017
$251$	20.4853	1.29302	0.646510	−	0.762906i	$-0.276228\pi$
$251$	20.4853	1.29302	0.646510	+	0.762906i	$0.276228\pi$
$252$	18.2919	1.15228
$253$	−12.4853	−0.784943
$254$	−12.8284	−0.804927
$255$	0	0
$256$	−29.9706	−1.87316
$257$	6.14214	0.383136	0.191568	−	0.981479i	$-0.438643\pi$
$257$	6.14214	0.383136	0.191568	+	0.981479i	$0.438643\pi$
$258$	2.16478	0.134774
$259$	−24.1421	−1.50012
$260$	−4.14386	−0.256991
$261$	−0.579658	−0.0358799
$262$	36.7695	2.27163
$263$	−10.4853	−0.646550	−0.323275	−	0.946305i	$-0.604784\pi$
$263$	−10.4853	−0.646550	−0.323275	+	0.946305i	$0.604784\pi$
$264$	12.4853	0.768416
$265$	−1.08239	−0.0664908
$266$	5.22625	0.320442
$267$	7.12840	0.436251
$268$	−4.48528	−0.273982
$269$	−26.4483	−1.61258	−0.806290	−	0.591520i	$-0.798528\pi$
$269$	−26.4483	−1.61258	−0.806290	+	0.591520i	$0.798528\pi$
$270$	9.65685	0.587697
$271$	−22.1421	−1.34504	−0.672519	−	0.740079i	$-0.734788\pi$
$271$	−22.1421	−1.34504	−0.672519	+	0.740079i	$0.734788\pi$
$272$	0	0
$273$	−4.00000	−0.242091
$274$	−40.3848	−2.43973
$275$	−11.5349	−0.695580
$276$	−19.7990	−1.19176
$277$	−19.9539	−1.19892	−0.599458	−	0.800406i	$-0.704617\pi$
$277$	−19.9539	−1.19892	−0.599458	+	0.800406i	$0.704617\pi$
$278$	−51.5515	−3.09186
$279$	−14.3337	−0.858138
$280$	8.82843	0.527599
$281$	1.89949	0.113314	0.0566572	−	0.998394i	$-0.481956\pi$
$281$	1.89949	0.113314	0.0566572	+	0.998394i	$0.481956\pi$
$282$	13.5140	0.804745
$283$	18.6633	1.10942	0.554709	−	0.832044i	$-0.312830\pi$
$283$	18.6633	1.10942	0.554709	+	0.832044i	$0.312830\pi$
$284$	−20.7193	−1.22946
$285$	0.686292	0.0406524
$286$	8.92177	0.527555
$287$	−3.17157	−0.187212
$288$	2.89949	0.170854
$289$	0	0
$290$	−0.585786	−0.0343986
$291$	−11.1716	−0.654889
$292$	−49.5181	−2.89783
$293$	−12.3431	−0.721094	−0.360547	−	0.932741i	$-0.617410\pi$
$293$	−12.3431	−0.721094	−0.360547	+	0.932741i	$0.617410\pi$
$294$	−0.448342	−0.0261478
$295$	−4.59220	−0.267368
$296$	40.7820	2.37041
$297$	−13.6569	−0.792451
$298$	−40.9706	−2.37336
$299$	−6.75699	−0.390767
$300$	−18.2919	−1.05608
$301$	−2.16478	−0.124776
$302$	17.3137	0.996292
$303$	11.4580	0.658243
$304$	−2.48528	−0.142541
$305$	−2.92893	−0.167710
$306$	0	0
$307$	−26.1421	−1.49201	−0.746005	−	0.665940i	$-0.768031\pi$
$307$	−26.1421	−1.49201	−0.746005	+	0.665940i	$0.768031\pi$
$308$	−26.1421	−1.48959
$309$	13.5140	0.768783
$310$	−14.4853	−0.822709
$311$	25.6829	1.45634	0.728172	−	0.685394i	$-0.240370\pi$
$311$	25.6829	1.45634	0.728172	+	0.685394i	$0.240370\pi$
$312$	6.75699	0.382539
$313$	−9.87285	−0.558046	−0.279023	−	0.960284i	$-0.590011\pi$
$313$	−9.87285	−0.558046	−0.279023	+	0.960284i	$0.590011\pi$
$314$	−23.3137	−1.31567
$315$	−3.65685	−0.206040
$316$	−18.2919	−1.02900
$317$	−19.2430	−1.08079	−0.540396	−	0.841411i	$-0.681726\pi$
$317$	−19.2430	−1.08079	−0.540396	+	0.841411i	$0.681726\pi$
$318$	3.69552	0.207234
$319$	0.828427	0.0463830
$320$	7.52235	0.420512
$321$	0.485281	0.0270858
$322$	30.1421	1.67976
$323$	0	0
$324$	−0.656854	−0.0364919
$325$	−6.24264	−0.346279
$326$	20.4567	1.13299
$327$	16.8284	0.930614
$328$	5.35757	0.295822
$329$	−13.5140	−0.745049
$330$	−5.22625	−0.287696
$331$	−21.7990	−1.19818	−0.599090	−	0.800681i	$-0.704471\pi$
$331$	−21.7990	−1.19818	−0.599090	+	0.800681i	$0.704471\pi$
$332$	44.6274	2.44925
$333$	−16.8925	−0.925701
$334$	−4.77791	−0.261436
$335$	0.896683	0.0489910
$336$	−8.48528	−0.462910
$337$	5.62020	0.306152	0.153076	−	0.988214i	$-0.451082\pi$
$337$	5.62020	0.306152	0.153076	+	0.988214i	$0.451082\pi$
$338$	−26.5563	−1.44447
$339$	−14.2843	−0.775815
$340$	0	0
$341$	20.4853	1.10934
$342$	3.65685	0.197740
$343$	18.7402	1.01188
$344$	3.65685	0.197164
$345$	3.95815	0.213100
$346$	7.07401	0.380301
$347$	16.7611	0.899786	0.449893	−	0.893083i	$-0.351462\pi$
$347$	16.7611	0.899786	0.449893	+	0.893083i	$0.351462\pi$
$348$	1.31371	0.0704222
$349$	−4.24264	−0.227103	−0.113552	−	0.993532i	$-0.536223\pi$
$349$	−4.24264	−0.227103	−0.113552	+	0.993532i	$0.536223\pi$
$350$	27.8477	1.48852
$351$	−7.39104	−0.394504
$352$	−4.14386	−0.220868
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	15.6788	0.833316
$355$	4.14214	0.219842
$356$	25.2132	1.33630
$357$	0	0
$358$	14.4853	0.765571
$359$	28.8284	1.52151	0.760753	−	0.649041i	$-0.224830\pi$
$359$	28.8284	1.52151	0.760753	+	0.649041i	$0.224830\pi$
$360$	6.17733	0.325574
$361$	−18.3137	−0.963879
$362$	28.1647	1.48031
$363$	−4.51528	−0.236991
$364$	−14.1480	−0.741558
$365$	9.89949	0.518163
$366$	10.0000	0.522708
$367$	4.40649	0.230017	0.115009	−	0.993365i	$-0.463310\pi$
$367$	4.40649	0.230017	0.115009	+	0.993365i	$0.463310\pi$
$368$	−14.3337	−0.747197
$369$	−2.21918	−0.115526
$370$	−17.0711	−0.887483
$371$	−3.69552	−0.191862
$372$	32.4853	1.68428
$373$	−11.5563	−0.598365	−0.299183	−	0.954196i	$-0.596714\pi$
$373$	−11.5563	−0.598365	−0.299183	+	0.954196i	$0.596714\pi$
$374$	0	0
$375$	7.79899	0.402738
$376$	22.8284	1.17729
$377$	0.448342	0.0230908
$378$	32.9706	1.69582
$379$	−2.61313	−0.134227	−0.0671136	−	0.997745i	$-0.521379\pi$
$379$	−2.61313	−0.134227	−0.0671136	+	0.997745i	$0.521379\pi$
$380$	2.42742	0.124524
$381$	−5.75152	−0.294659
$382$	48.2843	2.47044
$383$	22.4853	1.14894	0.574472	−	0.818524i	$-0.305207\pi$
$383$	22.4853	1.14894	0.574472	+	0.818524i	$0.305207\pi$
$384$	−22.2500	−1.13544
$385$	5.22625	0.266354
$386$	5.54328	0.282145
$387$	−1.51472	−0.0769975
$388$	−39.5139	−2.00602
$389$	−12.1421	−0.615631	−0.307815	−	0.951446i	$-0.599598\pi$
$389$	−12.1421	−0.615631	−0.307815	+	0.951446i	$0.599598\pi$
$390$	−2.82843	−0.143223
$391$	0	0
$392$	−0.757359	−0.0382524
$393$	16.4853	0.831572
$394$	11.2179	0.565148
$395$	3.65685	0.183996
$396$	−18.2919	−0.919202
$397$	17.7891	0.892812	0.446406	−	0.894831i	$-0.352704\pi$
$397$	17.7891	0.892812	0.446406	+	0.894831i	$0.352704\pi$
$398$	−27.8477	−1.39588
$399$	2.34315	0.117304
$400$	−13.2426	−0.662132
$401$	0.579658	0.0289467	0.0144734	−	0.999895i	$-0.495393\pi$
$401$	0.579658	0.0289467	0.0144734	+	0.999895i	$0.495393\pi$
$402$	−3.06147	−0.152692
$403$	11.0866	0.552261
$404$	40.5269	2.01629
$405$	0.131316	0.00652515
$406$	−2.00000	−0.0992583
$407$	24.1421	1.19668
$408$	0	0
$409$	−3.31371	−0.163852	−0.0819262	−	0.996638i	$-0.526107\pi$
$409$	−3.31371	−0.163852	−0.0819262	+	0.996638i	$0.526107\pi$
$410$	−2.24264	−0.110756
$411$	−18.1062	−0.893112
$412$	47.7990	2.35489
$413$	−15.6788	−0.771501
$414$	21.0907	1.03655
$415$	−8.92177	−0.437952
$416$	−2.24264	−0.109955
$417$	−23.1127	−1.13183
$418$	−5.22625	−0.255624
$419$	13.3283	0.651128	0.325564	−	0.945520i	$-0.394446\pi$
$419$	13.3283	0.651128	0.325564	+	0.945520i	$0.394446\pi$
$420$	8.28772	0.404399
$421$	14.5858	0.710868	0.355434	−	0.934701i	$-0.384333\pi$
$421$	14.5858	0.710868	0.355434	+	0.934701i	$0.384333\pi$
$422$	−51.5515	−2.50949
$423$	−9.45584	−0.459759
$424$	6.24264	0.303169
$425$	0	0
$426$	−14.1421	−0.685189
$427$	−10.0000	−0.483934
$428$	1.71644	0.0829674
$429$	4.00000	0.193122
$430$	−1.53073	−0.0738185
$431$	7.31411	0.352308	0.176154	−	0.984363i	$-0.443634\pi$
$431$	7.31411	0.352308	0.176154	+	0.984363i	$0.443634\pi$
$432$	−15.6788	−0.754344
$433$	20.8284	1.00095	0.500475	−	0.865751i	$-0.333159\pi$
$433$	20.8284	1.00095	0.500475	+	0.865751i	$0.333159\pi$
$434$	−49.4558	−2.37396
$435$	−0.262632	−0.0125923
$436$	59.5222	2.85060
$437$	3.95815	0.189344
$438$	−33.7990	−1.61498
$439$	10.6382	0.507734	0.253867	−	0.967239i	$-0.418297\pi$
$439$	10.6382	0.507734	0.253867	+	0.967239i	$0.418297\pi$
$440$	−8.82843	−0.420879
$441$	0.313708	0.0149385
$442$	0	0
$443$	−23.7990	−1.13072	−0.565362	−	0.824843i	$-0.691264\pi$
$443$	−23.7990	−1.13072	−0.565362	+	0.824843i	$0.691264\pi$
$444$	38.2843	1.81689
$445$	−5.04054	−0.238945
$446$	−11.6569	−0.551968
$447$	−18.3688	−0.868815
$448$	25.6829	1.21340
$449$	12.1146	0.571721	0.285861	−	0.958271i	$-0.407721\pi$
$449$	12.1146	0.571721	0.285861	+	0.958271i	$0.407721\pi$
$450$	19.4853	0.918545
$451$	3.17157	0.149344
$452$	−50.5235	−2.37643
$453$	7.76245	0.364712
$454$	41.9957	1.97096
$455$	2.82843	0.132599
$456$	−3.95815	−0.185357
$457$	13.1716	0.616140	0.308070	−	0.951364i	$-0.400317\pi$
$457$	13.1716	0.616140	0.308070	+	0.951364i	$0.400317\pi$
$458$	−41.4558	−1.93710
$459$	0	0
$460$	14.0000	0.652753
$461$	−24.0416	−1.11973	−0.559865	−	0.828584i	$-0.689147\pi$
$461$	−24.0416	−1.11973	−0.559865	+	0.828584i	$0.689147\pi$
$462$	−17.8435	−0.830157
$463$	14.6274	0.679794	0.339897	−	0.940463i	$-0.389608\pi$
$463$	14.6274	0.679794	0.339897	+	0.940463i	$0.389608\pi$
$464$	0.951076	0.0441526
$465$	−6.49435	−0.301168
$466$	−21.2220	−0.983092
$467$	32.6274	1.50982	0.754908	−	0.655830i	$-0.227681\pi$
$467$	32.6274	1.50982	0.754908	+	0.655830i	$0.227681\pi$
$468$	−9.89949	−0.457604
$469$	3.06147	0.141365
$470$	−9.55582	−0.440777
$471$	−10.4525	−0.481626
$472$	26.4853	1.21908
$473$	2.16478	0.0995369
$474$	−12.4853	−0.573468
$475$	3.65685	0.167788
$476$	0	0
$477$	−2.58579	−0.118395
$478$	35.7990	1.63741
$479$	5.14933	0.235279	0.117639	−	0.993056i	$-0.462467\pi$
$479$	5.14933	0.235279	0.117639	+	0.993056i	$0.462467\pi$
$480$	1.31371	0.0599623
$481$	13.0656	0.595741
$482$	−8.60474	−0.391935
$483$	13.5140	0.614907
$484$	−15.9706	−0.725935
$485$	7.89949	0.358698
$486$	37.4035	1.69666
$487$	−26.3170	−1.19254	−0.596268	−	0.802786i	$-0.703350\pi$
$487$	−26.3170	−1.19254	−0.596268	+	0.802786i	$0.703350\pi$
$488$	16.8925	0.764686
$489$	9.17157	0.414753
$490$	0.317025	0.0143217
$491$	37.1127	1.67487	0.837436	−	0.546535i	$-0.184053\pi$
$491$	37.1127	1.67487	0.837436	+	0.546535i	$0.184053\pi$
$492$	5.02944	0.226745
$493$	0	0
$494$	−2.82843	−0.127257
$495$	3.65685	0.164363
$496$	23.5181	1.05600
$497$	14.1421	0.634361
$498$	30.4608	1.36498
$499$	−21.4621	−0.960777	−0.480389	−	0.877056i	$-0.659504\pi$
$499$	−21.4621	−0.960777	−0.480389	+	0.877056i	$0.659504\pi$
$500$	27.5851	1.23364
$501$	−2.14214	−0.0957036
$502$	49.4558	2.20732
$503$	21.3533	0.952099	0.476049	−	0.879419i	$-0.342068\pi$
$503$	21.3533	0.952099	0.476049	+	0.879419i	$0.342068\pi$
$504$	21.0907	0.939455
$505$	−8.10201	−0.360535
$506$	−30.1421	−1.33998
$507$	−11.9063	−0.528778
$508$	−20.3431	−0.902581
$509$	36.9706	1.63869	0.819346	−	0.573300i	$-0.194337\pi$
$509$	36.9706	1.63869	0.819346	+	0.573300i	$0.194337\pi$
$510$	0	0
$511$	33.7990	1.49518
$512$	−31.2426	−1.38074
$513$	4.32957	0.191155
$514$	14.8284	0.654054
$515$	−9.55582	−0.421080
$516$	3.43289	0.151124
$517$	13.5140	0.594344
$518$	−58.2843	−2.56086
$519$	3.17157	0.139217
$520$	−4.77791	−0.209525
$521$	−18.6089	−0.815271	−0.407636	−	0.913145i	$-0.633647\pi$
$521$	−18.6089	−0.815271	−0.407636	+	0.913145i	$0.633647\pi$
$522$	−1.39942	−0.0612508
$523$	1.17157	0.0512293	0.0256147	−	0.999672i	$-0.491846\pi$
$523$	1.17157	0.0512293	0.0256147	+	0.999672i	$0.491846\pi$
$524$	58.3085	2.54722
$525$	12.4853	0.544902
$526$	−25.3137	−1.10373
$527$	0	0
$528$	8.48528	0.369274
$529$	−0.171573	−0.00745969
$530$	−2.61313	−0.113507
$531$	−10.9706	−0.476082
$532$	8.28772	0.359318
$533$	1.71644	0.0743474
$534$	17.2095	0.744727
$535$	−0.343146	−0.0148355
$536$	−5.17157	−0.223378
$537$	6.49435	0.280252
$538$	−63.8518	−2.75285
$539$	−0.448342	−0.0193114
$540$	15.3137	0.658997
$541$	18.4232	0.792075	0.396038	−	0.918234i	$-0.370385\pi$
$541$	18.4232	0.792075	0.396038	+	0.918234i	$0.370385\pi$
$542$	−53.4558	−2.29613
$543$	12.6274	0.541894
$544$	0	0
$545$	−11.8995	−0.509718
$546$	−9.65685	−0.413275
$547$	8.10201	0.346417	0.173208	−	0.984885i	$-0.444587\pi$
$547$	8.10201	0.346417	0.173208	+	0.984885i	$0.444587\pi$
$548$	−64.0416	−2.73572
$549$	−6.99709	−0.298628
$550$	−27.8477	−1.18743
$551$	−0.262632	−0.0111885
$552$	−22.8284	−0.971642
$553$	12.4853	0.530928
$554$	−48.1731	−2.04668
$555$	−7.65367	−0.324880
$556$	−81.7497	−3.46696
$557$	−19.7574	−0.837146	−0.418573	−	0.908183i	$-0.637470\pi$
$557$	−19.7574	−0.837146	−0.418573	+	0.908183i	$0.637470\pi$
$558$	−34.6047	−1.46493
$559$	1.17157	0.0495523
$560$	6.00000	0.253546
$561$	0	0
$562$	4.58579	0.193440
$563$	−34.7696	−1.46536	−0.732681	−	0.680572i	$-0.761731\pi$
$563$	−34.7696	−1.46536	−0.732681	+	0.680572i	$0.761731\pi$
$564$	21.4303	0.902377
$565$	10.1005	0.424931
$566$	45.0572	1.89390
$567$	0.448342	0.0188286
$568$	−23.8896	−1.00238
$569$	12.0416	0.504811	0.252406	−	0.967621i	$-0.418778\pi$
$569$	12.0416	0.504811	0.252406	+	0.967621i	$0.418778\pi$
$570$	1.65685	0.0693980
$571$	4.25265	0.177968	0.0889838	−	0.996033i	$-0.471638\pi$
$571$	4.25265	0.177968	0.0889838	+	0.996033i	$0.471638\pi$
$572$	14.1480	0.591559
$573$	21.6478	0.904352
$574$	−7.65685	−0.319591
$575$	21.0907	0.879544
$576$	17.9706	0.748773
$577$	27.0711	1.12698	0.563492	−	0.826122i	$-0.309458\pi$
$577$	27.0711	1.12698	0.563492	+	0.826122i	$0.309458\pi$
$578$	0	0
$579$	2.48528	0.103285
$580$	−0.928932	−0.0385718
$581$	−30.4608	−1.26373
$582$	−26.9706	−1.11797
$583$	3.69552	0.153053
$584$	−57.0948	−2.36260
$585$	1.97908	0.0818247
$586$	−29.7990	−1.23098
$587$	−45.3137	−1.87030	−0.935148	−	0.354256i	$-0.884734\pi$
$587$	−45.3137	−1.87030	−0.935148	+	0.354256i	$0.884734\pi$
$588$	−0.710974	−0.0293201
$589$	−6.49435	−0.267595
$590$	−11.0866	−0.456426
$591$	5.02944	0.206883
$592$	27.7164	1.13914
$593$	12.9289	0.530928	0.265464	−	0.964121i	$-0.414475\pi$
$593$	12.9289	0.530928	0.265464	+	0.964121i	$0.414475\pi$
$594$	−32.9706	−1.35280
$595$	0	0
$596$	−64.9706	−2.66130
$597$	−12.4853	−0.510989
$598$	−16.3128	−0.667080
$599$	−10.6274	−0.434224	−0.217112	−	0.976147i	$-0.569664\pi$
$599$	−10.6274	−0.434224	−0.217112	+	0.976147i	$0.569664\pi$
$600$	−21.0907	−0.861025
$601$	−8.41904	−0.343420	−0.171710	−	0.985148i	$-0.554929\pi$
$601$	−8.41904	−0.343420	−0.171710	+	0.985148i	$0.554929\pi$
$602$	−5.22625	−0.213006
$603$	2.14214	0.0872345
$604$	27.4558	1.11716
$605$	3.19278	0.129805
$606$	27.6620	1.12369
$607$	−16.3897	−0.665239	−0.332619	−	0.943061i	$-0.607932\pi$
$607$	−16.3897	−0.665239	−0.332619	+	0.943061i	$0.607932\pi$
$608$	1.31371	0.0532779
$609$	−0.896683	−0.0363354
$610$	−7.07107	−0.286299
$611$	7.31371	0.295881
$612$	0	0
$613$	5.31371	0.214619	0.107309	−	0.994226i	$-0.465776\pi$
$613$	5.31371	0.214619	0.107309	+	0.994226i	$0.465776\pi$
$614$	−63.1127	−2.54702
$615$	−1.00547	−0.0405444
$616$	−30.1421	−1.21446
$617$	−2.93015	−0.117963	−0.0589817	−	0.998259i	$-0.518785\pi$
$617$	−2.93015	−0.117963	−0.0589817	+	0.998259i	$0.518785\pi$
$618$	32.6256	1.31239
$619$	28.4818	1.14478	0.572389	−	0.819982i	$-0.306017\pi$
$619$	28.4818	1.14478	0.572389	+	0.819982i	$0.306017\pi$
$620$	−22.9706	−0.922520
$621$	24.9706	1.00203
$622$	62.0040	2.48614
$623$	−17.2095	−0.689484
$624$	4.59220	0.183835
$625$	16.5563	0.662254
$626$	−23.8352	−0.952645
$627$	−2.34315	−0.0935762
$628$	−36.9706	−1.47529
$629$	0	0
$630$	−8.82843	−0.351733
$631$	29.3137	1.16696	0.583480	−	0.812127i	$-0.301691\pi$
$631$	29.3137	1.16696	0.583480	+	0.812127i	$0.301691\pi$
$632$	−21.0907	−0.838944
$633$	−23.1127	−0.918647
$634$	−46.4566	−1.84503
$635$	4.06694	0.161391
$636$	5.86030	0.232376
$637$	−0.242641	−0.00961377
$638$	2.00000	0.0791808
$639$	9.89538	0.391455
$640$	15.7331	0.621907
$641$	41.4161	1.63584	0.817918	−	0.575335i	$-0.195128\pi$
$641$	41.4161	1.63584	0.817918	+	0.575335i	$0.195128\pi$
$642$	1.17157	0.0462383
$643$	−28.8532	−1.13786	−0.568929	−	0.822387i	$-0.692642\pi$
$643$	−28.8532	−1.13786	−0.568929	+	0.822387i	$0.692642\pi$
$644$	47.7990	1.88354
$645$	−0.686292	−0.0270227
$646$	0	0
$647$	−2.82843	−0.111197	−0.0555985	−	0.998453i	$-0.517707\pi$
$647$	−2.82843	−0.111197	−0.0555985	+	0.998453i	$0.517707\pi$
$648$	−0.757359	−0.0297519
$649$	15.6788	0.615445
$650$	−15.0711	−0.591136
$651$	−22.1731	−0.869033
$652$	32.4399	1.27044
$653$	9.50143	0.371820	0.185910	−	0.982567i	$-0.440477\pi$
$653$	9.50143	0.371820	0.185910	+	0.982567i	$0.440477\pi$
$654$	40.6274	1.58866
$655$	−11.6569	−0.455471
$656$	3.64113	0.142162
$657$	23.6494	0.922653
$658$	−32.6256	−1.27188
$659$	−8.48528	−0.330540	−0.165270	−	0.986248i	$-0.552849\pi$
$659$	−8.48528	−0.330540	−0.165270	+	0.986248i	$0.552849\pi$
$660$	−8.28772	−0.322599
$661$	1.21320	0.0471881	0.0235941	−	0.999722i	$-0.492489\pi$
$661$	1.21320	0.0471881	0.0235941	+	0.999722i	$0.492489\pi$
$662$	−52.6274	−2.04542
$663$	0	0
$664$	51.4558	1.99687
$665$	−1.65685	−0.0642501
$666$	−40.7820	−1.58027
$667$	−1.51472	−0.0586501
$668$	−7.57675	−0.293153
$669$	−5.22625	−0.202059
$670$	2.16478	0.0836329
$671$	10.0000	0.386046
$672$	4.48528	0.173023
$673$	−4.46088	−0.171954	−0.0859772	−	0.996297i	$-0.527401\pi$
$673$	−4.46088	−0.171954	−0.0859772	+	0.996297i	$0.527401\pi$
$674$	13.5684	0.522634
$675$	23.0698	0.887957
$676$	−42.1127	−1.61972
$677$	38.0920	1.46399	0.731997	−	0.681308i	$-0.238589\pi$
$677$	38.0920	1.46399	0.731997	+	0.681308i	$0.238589\pi$
$678$	−34.4853	−1.32440
$679$	26.9706	1.03504
$680$	0	0
$681$	18.8284	0.721507
$682$	49.4558	1.89376
$683$	−23.7808	−0.909946	−0.454973	−	0.890505i	$-0.650351\pi$
$683$	−23.7808	−0.909946	−0.454973	+	0.890505i	$0.650351\pi$
$684$	5.79899	0.221730
$685$	12.8030	0.489177
$686$	45.2429	1.72738
$687$	−18.5864	−0.709114
$688$	2.48528	0.0947505
$689$	2.00000	0.0761939
$690$	9.55582	0.363784
$691$	19.9314	0.758226	0.379113	−	0.925350i	$-0.376229\pi$
$691$	19.9314	0.758226	0.379113	+	0.925350i	$0.376229\pi$
$692$	11.2179	0.426439
$693$	12.4853	0.474277
$694$	40.4650	1.53603
$695$	16.3431	0.619931
$696$	1.51472	0.0574153
$697$	0	0
$698$	−10.2426	−0.387690
$699$	−9.51472	−0.359880
$700$	44.1605	1.66911
$701$	37.6985	1.42385	0.711926	−	0.702254i	$-0.247823\pi$
$701$	37.6985	1.42385	0.711926	+	0.702254i	$0.247823\pi$
$702$	−17.8435	−0.673461
$703$	−7.65367	−0.288664
$704$	−25.6829	−0.967961
$705$	−4.28427	−0.161355
$706$	−33.7990	−1.27204
$707$	−27.6620	−1.04034
$708$	24.8632	0.934415
$709$	−24.2835	−0.911986	−0.455993	−	0.889983i	$-0.650716\pi$
$709$	−24.2835	−0.911986	−0.455993	+	0.889983i	$0.650716\pi$
$710$	10.0000	0.375293
$711$	8.73606	0.327628
$712$	29.0711	1.08948
$713$	−37.4558	−1.40273
$714$	0	0
$715$	−2.82843	−0.105777
$716$	22.9706	0.858450
$717$	16.0502	0.599405
$718$	69.5980	2.59737
$719$	−33.9706	−1.26689	−0.633445	−	0.773787i	$-0.718360\pi$
$719$	−33.9706	−1.26689	−0.633445	+	0.773787i	$0.718360\pi$
$720$	4.19825	0.156460
$721$	−32.6256	−1.21504
$722$	−44.2132	−1.64545
$723$	−3.85786	−0.143476
$724$	44.6632	1.65990
$725$	−1.39942	−0.0519731
$726$	−10.9008	−0.404568
$727$	−43.1127	−1.59896	−0.799481	−	0.600692i	$-0.794892\pi$
$727$	−43.1127	−1.59896	−0.799481	+	0.600692i	$0.794892\pi$
$728$	−16.3128	−0.604593
$729$	17.2843	0.640158
$730$	23.8995	0.884560
$731$	0	0
$732$	15.8579	0.586124
$733$	36.0416	1.33123	0.665614	−	0.746296i	$-0.268170\pi$
$733$	36.0416	1.33123	0.665614	+	0.746296i	$0.268170\pi$
$734$	10.6382	0.392664
$735$	0.142136	0.00524275
$736$	7.57675	0.279283
$737$	−3.06147	−0.112771
$738$	−5.35757	−0.197215
$739$	22.2843	0.819740	0.409870	−	0.912144i	$-0.365574\pi$
$739$	22.2843	0.819740	0.409870	+	0.912144i	$0.365574\pi$
$740$	−27.0711	−0.995152
$741$	−1.26810	−0.0465849
$742$	−8.92177	−0.327528
$743$	−51.0263	−1.87197	−0.935986	−	0.352036i	$-0.885489\pi$
$743$	−51.0263	−1.87197	−0.935986	+	0.352036i	$0.885489\pi$
$744$	37.4558	1.37320
$745$	12.9887	0.475869
$746$	−27.8995	−1.02147
$747$	−21.3137	−0.779828
$748$	0	0
$749$	−1.17157	−0.0428083
$750$	18.8284	0.687517
$751$	47.5934	1.73671	0.868354	−	0.495945i	$-0.165178\pi$
$751$	47.5934	1.73671	0.868354	+	0.495945i	$0.165178\pi$
$752$	15.5147	0.565764
$753$	22.1731	0.808033
$754$	1.08239	0.0394184
$755$	−5.48888	−0.199761
$756$	52.2843	1.90156
$757$	2.54416	0.0924689	0.0462345	−	0.998931i	$-0.485278\pi$
$757$	2.54416	0.0924689	0.0462345	+	0.998931i	$0.485278\pi$
$758$	−6.30864	−0.229140
$759$	−13.5140	−0.490526
$760$	2.79884	0.101524
$761$	37.6985	1.36657	0.683285	−	0.730152i	$-0.260551\pi$
$761$	37.6985	1.36657	0.683285	+	0.730152i	$0.260551\pi$
$762$	−13.8854	−0.503015
$763$	−40.6274	−1.47081
$764$	76.5685	2.77015
$765$	0	0
$766$	54.2843	1.96137
$767$	8.48528	0.306386
$768$	−32.4399	−1.17057
$769$	12.7279	0.458981	0.229490	−	0.973311i	$-0.426294\pi$
$769$	12.7279	0.458981	0.229490	+	0.973311i	$0.426294\pi$
$770$	12.6173	0.454696
$771$	6.64820	0.239429
$772$	8.79045	0.316375
$773$	−0.828427	−0.0297965	−0.0148982	−	0.999889i	$-0.504742\pi$
$773$	−0.828427	−0.0297965	−0.0148982	+	0.999889i	$0.504742\pi$
$774$	−3.65685	−0.131443
$775$	−34.6047	−1.24304
$776$	−45.5599	−1.63551
$777$	−26.1313	−0.937454
$778$	−29.3137	−1.05095
$779$	−1.00547	−0.0360247
$780$	−4.48528	−0.160599
$781$	−14.1421	−0.506045
$782$	0	0
$783$	−1.65685	−0.0592111
$784$	−0.514719	−0.0183828
$785$	7.39104	0.263797
$786$	39.7990	1.41958
$787$	−20.5655	−0.733079	−0.366540	−	0.930402i	$-0.619458\pi$
$787$	−20.5655	−0.733079	−0.366540	+	0.930402i	$0.619458\pi$
$788$	17.7891	0.633712
$789$	−11.3492	−0.404042
$790$	8.82843	0.314101
$791$	34.4853	1.22616
$792$	−21.0907	−0.749426
$793$	5.41196	0.192184
$794$	42.9468	1.52412
$795$	−1.17157	−0.0415514
$796$	−44.1605	−1.56523
$797$	−25.2132	−0.893097	−0.446549	−	0.894759i	$-0.647347\pi$
$797$	−25.2132	−0.893097	−0.446549	+	0.894759i	$0.647347\pi$
$798$	5.65685	0.200250
$799$	0	0
$800$	7.00000	0.247487
$801$	−12.0416	−0.425470
$802$	1.39942	0.0494152
$803$	−33.7990	−1.19274
$804$	−4.85483	−0.171217
$805$	−9.55582	−0.336798
$806$	26.7653	0.942768
$807$	−28.6274	−1.00773
$808$	46.7279	1.64388
$809$	35.2931	1.24084	0.620420	−	0.784270i	$-0.286962\pi$
$809$	35.2931	1.24084	0.620420	+	0.784270i	$0.286962\pi$
$810$	0.317025	0.0111391
$811$	55.1383	1.93617	0.968083	−	0.250628i	$-0.0806372\pi$
$811$	55.1383	1.93617	0.968083	+	0.250628i	$0.0806372\pi$
$812$	−3.17157	−0.111300
$813$	−23.9665	−0.840541
$814$	58.2843	2.04286
$815$	−6.48528	−0.227169
$816$	0	0
$817$	−0.686292	−0.0240103
$818$	−8.00000	−0.279713
$819$	6.75699	0.236108
$820$	−3.55635	−0.124193
$821$	38.4315	1.34127	0.670635	−	0.741788i	$-0.266022\pi$
$821$	38.4315	1.34127	0.670635	+	0.741788i	$0.266022\pi$
$822$	−43.7122	−1.52464
$823$	9.74153	0.339568	0.169784	−	0.985481i	$-0.445693\pi$
$823$	9.74153	0.339568	0.169784	+	0.985481i	$0.445693\pi$
$824$	55.1127	1.91994
$825$	−12.4853	−0.434682
$826$	−37.8519	−1.31703
$827$	46.8506	1.62915	0.814577	−	0.580056i	$-0.196969\pi$
$827$	46.8506	1.62915	0.814577	+	0.580056i	$0.196969\pi$
$828$	33.4454	1.16231
$829$	53.9411	1.87345	0.936726	−	0.350062i	$-0.113840\pi$
$829$	53.9411	1.87345	0.936726	+	0.350062i	$0.113840\pi$
$830$	−21.5391	−0.747632
$831$	−21.5980	−0.749226
$832$	−13.8995	−0.481878
$833$	0	0
$834$	−55.7990	−1.93216
$835$	1.51472	0.0524190
$836$	−8.28772	−0.286637
$837$	−40.9706	−1.41615
$838$	32.1773	1.11155
$839$	−16.7611	−0.578659	−0.289330	−	0.957230i	$-0.593432\pi$
$839$	−16.7611	−0.578659	−0.289330	+	0.957230i	$0.593432\pi$
$840$	9.55582	0.329707
$841$	−28.8995	−0.996534
$842$	35.2132	1.21353
$843$	2.05600	0.0708123
$844$	−81.7497	−2.81394
$845$	8.41904	0.289624
$846$	−22.8284	−0.784857
$847$	10.9008	0.374557
$848$	4.24264	0.145693
$849$	20.2010	0.693297
$850$	0	0
$851$	−44.1421	−1.51317
$852$	−22.4264	−0.768316
$853$	−19.1660	−0.656233	−0.328116	−	0.944637i	$-0.606414\pi$
$853$	−19.1660	−0.656233	−0.328116	+	0.944637i	$0.606414\pi$
$854$	−24.1421	−0.826127
$855$	−1.15932	−0.0396478
$856$	1.97908	0.0676434
$857$	−9.23880	−0.315591	−0.157796	−	0.987472i	$-0.550439\pi$
$857$	−9.23880	−0.315591	−0.157796	+	0.987472i	$0.550439\pi$
$858$	9.65685	0.329680
$859$	−34.9706	−1.19318	−0.596590	−	0.802546i	$-0.703478\pi$
$859$	−34.9706	−1.19318	−0.596590	+	0.802546i	$0.703478\pi$
$860$	−2.42742	−0.0827742
$861$	−3.43289	−0.116992
$862$	17.6578	0.601428
$863$	−10.6274	−0.361761	−0.180881	−	0.983505i	$-0.557895\pi$
$863$	−10.6274	−0.361761	−0.180881	+	0.983505i	$0.557895\pi$
$864$	8.28772	0.281954
$865$	−2.24264	−0.0762521
$866$	50.2843	1.70873
$867$	0	0
$868$	−78.4264	−2.66197
$869$	−12.4853	−0.423534
$870$	−0.634051	−0.0214963
$871$	−1.65685	−0.0561404
$872$	68.6297	2.32410
$873$	18.8715	0.638705
$874$	9.55582	0.323230
$875$	−18.8284	−0.636517
$876$	−53.5980	−1.81091
$877$	−50.2291	−1.69611	−0.848057	−	0.529905i	$-0.822228\pi$
$877$	−50.2291	−1.69611	−0.848057	+	0.529905i	$0.822228\pi$
$878$	25.6829	0.866756
$879$	−13.3601	−0.450626
$880$	−6.00000	−0.202260
$881$	−33.6536	−1.13382	−0.566909	−	0.823780i	$-0.691861\pi$
$881$	−33.6536	−1.13382	−0.566909	+	0.823780i	$0.691861\pi$
$882$	0.757359	0.0255016
$883$	−8.00000	−0.269221	−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000	−0.269221	−0.134611	+	0.990899i	$0.542978\pi$
$884$	0	0
$885$	−4.97056	−0.167084
$886$	−57.4558	−1.93027
$887$	44.0517	1.47911	0.739556	−	0.673095i	$-0.235035\pi$
$887$	44.0517	1.47911	0.739556	+	0.673095i	$0.235035\pi$
$888$	44.1421	1.48131
$889$	13.8854	0.465701
$890$	−12.1689	−0.407904
$891$	−0.448342	−0.0150200
$892$	−18.4853	−0.618933
$893$	−4.28427	−0.143368
$894$	−44.3462	−1.48316
$895$	−4.59220	−0.153500
$896$	53.7163	1.79454
$897$	−7.31371	−0.244198
$898$	29.2471	0.975989
$899$	2.48528	0.0828888
$900$	30.8995	1.02998
$901$	0	0
$902$	7.65685	0.254945
$903$	−2.34315	−0.0779750
$904$	−58.2541	−1.93750
$905$	−8.92893	−0.296808
$906$	18.7402	0.622602
$907$	13.4370	0.446170	0.223085	−	0.974799i	$-0.428387\pi$
$907$	13.4370	0.446170	0.223085	+	0.974799i	$0.428387\pi$
$908$	66.5962	2.21007
$909$	−19.3553	−0.641976
$910$	6.82843	0.226360
$911$	−5.67459	−0.188008	−0.0940038	−	0.995572i	$-0.529967\pi$
$911$	−5.67459	−0.188008	−0.0940038	+	0.995572i	$0.529967\pi$
$912$	−2.69005	−0.0890764
$913$	30.4608	1.00811
$914$	31.7990	1.05182
$915$	−3.17025	−0.104805
$916$	−65.7401	−2.17211
$917$	−39.7990	−1.31428
$918$	0	0
$919$	19.3137	0.637100	0.318550	−	0.947906i	$-0.396804\pi$
$919$	19.3137	0.637100	0.318550	+	0.947906i	$0.396804\pi$
$920$	16.1421	0.532190
$921$	−28.2960	−0.932386
$922$	−58.0416	−1.91150
$923$	−7.65367	−0.251924
$924$	−28.2960	−0.930871
$925$	−40.7820	−1.34090
$926$	35.3137	1.16048
$927$	−22.8284	−0.749784
$928$	−0.502734	−0.0165031
$929$	−17.3408	−0.568933	−0.284467	−	0.958686i	$-0.591817\pi$
$929$	−17.3408	−0.568933	−0.284467	+	0.958686i	$0.591817\pi$
$930$	−15.6788	−0.514127
$931$	0.142136	0.00465831
$932$	−33.6536	−1.10236
$933$	27.7990	0.910098
$934$	78.7696	2.57742
$935$	0	0
$936$	−11.4142	−0.373085
$937$	−27.5563	−0.900227	−0.450113	−	0.892971i	$-0.648616\pi$
$937$	−27.5563	−0.900227	−0.450113	+	0.892971i	$0.648616\pi$
$938$	7.39104	0.241326
$939$	−10.6863	−0.348734
$940$	−15.1535	−0.494252
$941$	−39.8853	−1.30022	−0.650112	−	0.759838i	$-0.725278\pi$
$941$	−39.8853	−1.30022	−0.650112	+	0.759838i	$0.725278\pi$
$942$	−25.2346	−0.822187
$943$	−5.79899	−0.188841
$944$	18.0000	0.585850
$945$	−10.4525	−0.340020
$946$	5.22625	0.169920
$947$	−30.6465	−0.995879	−0.497939	−	0.867212i	$-0.665910\pi$
$947$	−30.6465	−0.995879	−0.497939	+	0.867212i	$0.665910\pi$
$948$	−19.7990	−0.643041
$949$	−18.2919	−0.593780
$950$	8.82843	0.286432
$951$	−20.8284	−0.675408
$952$	0	0
$953$	49.6985	1.60989	0.804946	−	0.593348i	$-0.202194\pi$
$953$	49.6985	1.60989	0.804946	+	0.593348i	$0.202194\pi$
$954$	−6.24264	−0.202113
$955$	−15.3073	−0.495334
$956$	56.7696	1.83606
$957$	0.896683	0.0289856
$958$	12.4316	0.401646
$959$	43.7122	1.41154
$960$	8.14214	0.262786
$961$	30.4558	0.982447
$962$	31.5432	1.01699
$963$	−0.819760	−0.0264164
$964$	−13.6453	−0.439485
$965$	−1.75736	−0.0565714
$966$	32.6256	1.04971
$967$	−43.6569	−1.40391	−0.701955	−	0.712221i	$-0.747689\pi$
$967$	−43.6569	−1.40391	−0.701955	+	0.712221i	$0.747689\pi$
$968$	−18.4142	−0.591855
$969$	0	0
$970$	19.0711	0.612335
$971$	51.7401	1.66042	0.830210	−	0.557451i	$-0.188221\pi$
$971$	51.7401	1.66042	0.830210	+	0.557451i	$0.188221\pi$
$972$	59.3140	1.90250
$973$	55.7990	1.78883
$974$	−63.5348	−2.03579
$975$	−6.75699	−0.216397
$976$	11.4805	0.367482
$977$	−38.3848	−1.22804	−0.614019	−	0.789291i	$-0.710448\pi$
$977$	−38.3848	−1.22804	−0.614019	+	0.789291i	$0.710448\pi$
$978$	22.1421	0.708027
$979$	17.2095	0.550018
$980$	0.502734	0.0160593
$981$	−28.4274	−0.907616
$982$	89.5980	2.85919
$983$	−9.74153	−0.310707	−0.155353	−	0.987859i	$-0.549652\pi$
$983$	−9.74153	−0.310707	−0.155353	+	0.987859i	$0.549652\pi$
$984$	5.79899	0.184865
$985$	−3.55635	−0.113315
$986$	0	0
$987$	−14.6274	−0.465596
$988$	−4.48528	−0.142696
$989$	−3.95815	−0.125862
$990$	8.82843	0.280586
$991$	40.8364	1.29721	0.648606	−	0.761125i	$-0.275352\pi$
$991$	40.8364	1.29721	0.648606	+	0.761125i	$0.275352\pi$
$992$	−12.4316	−0.394703
$993$	−23.5951	−0.748766
$994$	34.1421	1.08292
$995$	8.82843	0.279880
$996$	48.3044	1.53058
$997$	7.52235	0.238235	0.119118	−	0.992880i	$-0.461993\pi$
$997$	7.52235	0.238235	0.119118	+	0.992880i	$0.461993\pi$
$998$	−51.8142	−1.64015
$999$	−48.2843	−1.52765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.a.f.1.4		4
3.2	odd	2		2601.2.a.bb.1.2		4
4.3	odd	2		4624.2.a.bp.1.2		4
5.4	even	2		7225.2.a.u.1.1		4
17.2	even	8		289.2.c.c.38.4		8
17.3	odd	16		289.2.d.c.179.1		4
17.4	even	4		289.2.b.b.288.1		4
17.5	odd	16		289.2.d.a.110.1		4
17.6	odd	16		289.2.d.c.155.1		4
17.7	odd	16		289.2.d.a.134.1		4
17.8	even	8		289.2.c.c.251.1		8
17.9	even	8		289.2.c.c.251.2		8
17.10	odd	16		17.2.d.a.15.1	yes	4
17.11	odd	16		289.2.d.b.155.1		4
17.12	odd	16		17.2.d.a.8.1	✓	4
17.13	even	4		289.2.b.b.288.2		4
17.14	odd	16		289.2.d.b.179.1		4
17.15	even	8		289.2.c.c.38.3		8
17.16	even	2	inner	289.2.a.f.1.3		4
51.29	even	16		153.2.l.c.127.1		4
51.44	even	16		153.2.l.c.100.1		4
51.50	odd	2		2601.2.a.bb.1.1		4
68.27	even	16		272.2.v.d.49.1		4
68.63	even	16		272.2.v.d.161.1		4
68.67	odd	2		4624.2.a.bp.1.3		4
85.12	even	16		425.2.n.a.399.1		4
85.27	even	16		425.2.n.b.49.1		4
85.29	odd	16		425.2.m.a.76.1		4
85.44	odd	16		425.2.m.a.151.1		4
85.63	even	16		425.2.n.b.399.1		4
85.78	even	16		425.2.n.a.49.1		4
85.84	even	2		7225.2.a.u.1.2		4
119.10	even	48		833.2.v.a.814.1		8
119.12	even	48		833.2.v.a.263.1		8
119.27	even	16		833.2.l.a.491.1		4
119.44	odd	48		833.2.v.b.508.1		8
119.46	odd	48		833.2.v.b.569.1		8
119.61	even	48		833.2.v.a.508.1		8
119.80	even	48		833.2.v.a.569.1		8
119.95	odd	48		833.2.v.b.814.1		8
119.97	even	16		833.2.l.a.246.1		4
119.114	odd	48		833.2.v.b.263.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.8.1	✓	4	17.12	odd	16
17.2.d.a.15.1	yes	4	17.10	odd	16
153.2.l.c.100.1		4	51.44	even	16
153.2.l.c.127.1		4	51.29	even	16
272.2.v.d.49.1		4	68.27	even	16
272.2.v.d.161.1		4	68.63	even	16
289.2.a.f.1.3		4	17.16	even	2	inner
289.2.a.f.1.4		4	1.1	even	1	trivial
289.2.b.b.288.1		4	17.4	even	4
289.2.b.b.288.2		4	17.13	even	4
289.2.c.c.38.3		8	17.15	even	8
289.2.c.c.38.4		8	17.2	even	8
289.2.c.c.251.1		8	17.8	even	8
289.2.c.c.251.2		8	17.9	even	8
289.2.d.a.110.1		4	17.5	odd	16
289.2.d.a.134.1		4	17.7	odd	16
289.2.d.b.155.1		4	17.11	odd	16
289.2.d.b.179.1		4	17.14	odd	16
289.2.d.c.155.1		4	17.6	odd	16
289.2.d.c.179.1		4	17.3	odd	16
425.2.m.a.76.1		4	85.29	odd	16
425.2.m.a.151.1		4	85.44	odd	16
425.2.n.a.49.1		4	85.78	even	16
425.2.n.a.399.1		4	85.12	even	16
425.2.n.b.49.1		4	85.27	even	16
425.2.n.b.399.1		4	85.63	even	16
833.2.l.a.246.1		4	119.97	even	16
833.2.l.a.491.1		4	119.27	even	16
833.2.v.a.263.1		8	119.12	even	48
833.2.v.a.508.1		8	119.61	even	48
833.2.v.a.569.1		8	119.80	even	48
833.2.v.a.814.1		8	119.10	even	48
833.2.v.b.263.1		8	119.114	odd	48
833.2.v.b.508.1		8	119.44	odd	48
833.2.v.b.569.1		8	119.46	odd	48
833.2.v.b.814.1		8	119.95	odd	48
2601.2.a.bb.1.1		4	51.50	odd	2
2601.2.a.bb.1.2		4	3.2	odd	2
4624.2.a.bp.1.2		4	4.3	odd	2
4624.2.a.bp.1.3		4	68.67	odd	2
7225.2.a.u.1.1		4	5.4	even	2
7225.2.a.u.1.2		4	85.84	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41421 q^{2} +1.08239 q^{3} +3.82843 q^{4} -0.765367 q^{5} +2.61313 q^{6} -2.61313 q^{7} +4.41421 q^{8} -1.82843 q^{9} +O(q^{10})\)	\(q+2.41421 q^{2} +1.08239 q^{3} +3.82843 q^{4} -0.765367 q^{5} +2.61313 q^{6} -2.61313 q^{7} +4.41421 q^{8} -1.82843 q^{9} -1.84776 q^{10} +2.61313 q^{11} +4.14386 q^{12} +1.41421 q^{13} -6.30864 q^{14} -0.828427 q^{15} +3.00000 q^{16} -4.41421 q^{18} -0.828427 q^{19} -2.93015 q^{20} -2.82843 q^{21} +6.30864 q^{22} -4.77791 q^{23} +4.77791 q^{24} -4.41421 q^{25} +3.41421 q^{26} -5.22625 q^{27} -10.0042 q^{28} +0.317025 q^{29} -2.00000 q^{30} +7.83938 q^{31} -1.58579 q^{32} +2.82843 q^{33} +2.00000 q^{35} -7.00000 q^{36} +9.23880 q^{37} -2.00000 q^{38} +1.53073 q^{39} -3.37849 q^{40} +1.21371 q^{41} -6.82843 q^{42} +0.828427 q^{43} +10.0042 q^{44} +1.39942 q^{45} -11.5349 q^{46} +5.17157 q^{47} +3.24718 q^{48} -0.171573 q^{49} -10.6569 q^{50} +5.41421 q^{52} +1.41421 q^{53} -12.6173 q^{54} -2.00000 q^{55} -11.5349 q^{56} -0.896683 q^{57} +0.765367 q^{58} +6.00000 q^{59} -3.17157 q^{60} +3.82683 q^{61} +18.9259 q^{62} +4.77791 q^{63} -9.82843 q^{64} -1.08239 q^{65} +6.82843 q^{66} -1.17157 q^{67} -5.17157 q^{69} +4.82843 q^{70} -5.41196 q^{71} -8.07107 q^{72} -12.9343 q^{73} +22.3044 q^{74} -4.77791 q^{75} -3.17157 q^{76} -6.82843 q^{77} +3.69552 q^{78} -4.77791 q^{79} -2.29610 q^{80} -0.171573 q^{81} +2.93015 q^{82} +11.6569 q^{83} -10.8284 q^{84} +2.00000 q^{86} +0.343146 q^{87} +11.5349 q^{88} +6.58579 q^{89} +3.37849 q^{90} -3.69552 q^{91} -18.2919 q^{92} +8.48528 q^{93} +12.4853 q^{94} +0.634051 q^{95} -1.71644 q^{96} -10.3212 q^{97} -0.414214 q^{98} -4.77791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{4} + 12 q^{8} + 4 q^{9} + 8 q^{15} + 12 q^{16} - 12 q^{18} + 8 q^{19} - 12 q^{25} + 8 q^{26} - 8 q^{30} - 12 q^{32} + 8 q^{35} - 28 q^{36} - 8 q^{38} - 16 q^{42} - 8 q^{43} + 32 q^{47} - 12 q^{49} - 20 q^{50} + 16 q^{52} - 8 q^{55} + 24 q^{59} - 24 q^{60} - 28 q^{64} + 16 q^{66} - 16 q^{67} - 32 q^{69} + 8 q^{70} - 4 q^{72} - 24 q^{76} - 16 q^{77} - 12 q^{81} + 24 q^{83} - 32 q^{84} + 8 q^{86} + 24 q^{87} + 32 q^{89} + 16 q^{94} + 4 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 + 4 * q^9 + 8 * q^15 + 12 * q^16 - 12 * q^18 + 8 * q^19 - 12 * q^25 + 8 * q^26 - 8 * q^30 - 12 * q^32 + 8 * q^35 - 28 * q^36 - 8 * q^38 - 16 * q^42 - 8 * q^43 + 32 * q^47 - 12 * q^49 - 20 * q^50 + 16 * q^52 - 8 * q^55 + 24 * q^59 - 24 * q^60 - 28 * q^64 + 16 * q^66 - 16 * q^67 - 32 * q^69 + 8 * q^70 - 4 * q^72 - 24 * q^76 - 16 * q^77 - 12 * q^81 + 24 * q^83 - 32 * q^84 + 8 * q^86 + 24 * q^87 + 32 * q^89 + 16 * q^94 + 4 * q^98

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