LMFDB - Embedded newform 729.2.c.c.487.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, not minimal)

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:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.2
Root			$0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.c.244.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 + 1.11334i) q^{2} +(0.173648 + 0.300767i) q^{4} +(-0.223238 - 0.386659i) q^{5} +(1.76604 - 3.05888i) q^{7} -3.01763 q^{8} +O(q^{10})$	\(q+(-0.642788 + 1.11334i) q^{2} +(0.173648 + 0.300767i) q^{4} +(-0.223238 - 0.386659i) q^{5} +(1.76604 - 3.05888i) q^{7} -3.01763 q^{8} +0.573978 q^{10} +(1.39003 - 2.40760i) q^{11} +(-1.64543 - 2.84997i) q^{13} +(2.27038 + 3.93242i) q^{14} +(1.59240 - 2.75811i) q^{16} -7.03936 q^{17} -5.18479 q^{19} +(0.0775297 - 0.134285i) q^{20} +(1.78699 + 3.09516i) q^{22} +(-3.63846 - 6.30200i) q^{23} +(2.40033 - 4.15749i) q^{25} +4.23065 q^{26} +1.22668 q^{28} +(-1.80958 + 3.13429i) q^{29} +(0.967911 + 1.67647i) q^{31} +(-0.970481 - 1.68092i) q^{32} +(4.52481 - 7.83721i) q^{34} -1.57699 q^{35} -3.22668 q^{37} +(3.33272 - 5.77244i) q^{38} +(0.673648 + 1.16679i) q^{40} +(2.43042 + 4.20961i) q^{41} +(2.87939 - 4.98724i) q^{43} +0.965505 q^{44} +9.35504 q^{46} +(-1.50881 + 2.61334i) q^{47} +(-2.73783 - 4.74205i) q^{49} +(3.08580 + 5.34477i) q^{50} +(0.571452 - 0.989783i) q^{52} +8.77141 q^{53} -1.24123 q^{55} +(-5.32926 + 9.23055i) q^{56} +(-2.32635 - 4.02936i) q^{58} +(-1.48189 - 2.56670i) q^{59} +(-3.94356 + 6.83045i) q^{61} -2.48865 q^{62} +8.86484 q^{64} +(-0.734644 + 1.27244i) q^{65} +(4.71941 + 8.17425i) q^{67} +(-1.22237 - 2.11721i) q^{68} +(1.01367 - 1.75573i) q^{70} +5.30731 q^{71} -1.55438 q^{73} +(2.07407 - 3.59240i) q^{74} +(-0.900330 - 1.55942i) q^{76} +(-4.90971 - 8.50387i) q^{77} +(5.95084 - 10.3072i) q^{79} -1.42193 q^{80} -6.24897 q^{82} +(8.12863 - 14.0792i) q^{83} +(1.57145 + 2.72183i) q^{85} +(3.70167 + 6.41147i) q^{86} +(-4.19459 + 7.26525i) q^{88} +18.4258 q^{89} -11.6236 q^{91} +(1.26363 - 2.18866i) q^{92} +(-1.93969 - 3.35965i) q^{94} +(1.15744 + 2.00475i) q^{95} +(-5.05690 + 8.75881i) q^{97} +7.03936 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{7}+O(q^{10}) $ 12 * q + 12 * q^7	$ 12 q + 12 q^{7} - 24 q^{10} + 12 q^{13} + 12 q^{16} - 48 q^{19} + 6 q^{22} - 12 q^{28} + 30 q^{31} - 12 q^{37} + 6 q^{40} + 12 q^{43} + 12 q^{46} + 6 q^{49} + 6 q^{52} - 60 q^{55} - 30 q^{58} + 12 q^{61} + 12 q^{64} - 6 q^{67} - 30 q^{70} + 24 q^{73} + 18 q^{76} + 48 q^{79} - 24 q^{82} + 18 q^{85} - 42 q^{88} - 12 q^{94} + 12 q^{97}+O(q^{100}) $ 12 * q + 12 * q^7 - 24 * q^10 + 12 * q^13 + 12 * q^16 - 48 * q^19 + 6 * q^22 - 12 * q^28 + 30 * q^31 - 12 * q^37 + 6 * q^40 + 12 * q^43 + 12 * q^46 + 6 * q^49 + 6 * q^52 - 60 * q^55 - 30 * q^58 + 12 * q^61 + 12 * q^64 - 6 * q^67 - 30 * q^70 + 24 * q^73 + 18 * q^76 + 48 * q^79 - 24 * q^82 + 18 * q^85 - 42 * q^88 - 12 * q^94 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.642788	+	1.11334i	−0.454519	+	0.787251i	−0.998660	−	0.0517430i	$-0.983522\pi$
$2$	−0.642788	+	1.11334i	−0.454519	+	0.787251i	0.544141	+	0.838994i	$0.316856\pi$
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.300767i	0.0868241	+	0.150384i
$5$	−0.223238	−	0.386659i	−0.0998350	−	0.172919i	0.811781	−	0.583962i	$-0.198498\pi$
$5$	−0.223238	−	0.386659i	−0.0998350	−	0.172919i	−0.911616	+	0.411042i	$0.865165\pi$
$6$		0			0
$7$	1.76604	−	3.05888i	0.667502	−	1.15615i	−0.311098	−	0.950378i	$-0.600697\pi$
$7$	1.76604	−	3.05888i	0.667502	−	1.15615i	0.978600	−	0.205770i	$-0.0659698\pi$
$8$	−3.01763			−1.06689
$9$		0			0
$10$	0.573978			0.181508
$11$	1.39003	−	2.40760i	0.419110	−	0.725920i	−0.576740	−	0.816928i	$-0.695675\pi$
$11$	1.39003	−	2.40760i	0.419110	−	0.725920i	0.995850	+	0.0910078i	$0.0290088\pi$
$12$		0			0
$13$	−1.64543	−	2.84997i	−0.456360	−	0.790439i	0.542405	−	0.840117i	$-0.317514\pi$
$13$	−1.64543	−	2.84997i	−0.456360	−	0.790439i	−0.998765	+	0.0496782i	$0.984180\pi$
$14$	2.27038	+	3.93242i	0.606785	+	1.05098i
$15$		0			0
$16$	1.59240	−	2.75811i	0.398099	−	0.689528i
$17$	−7.03936			−1.70730			−0.853648	−	0.520850i	$-0.825615\pi$
$17$	−7.03936			−1.70730			−0.853648	+	0.520850i	$0.825615\pi$
$18$		0			0
$19$	−5.18479			−1.18947			−0.594736	−	0.803921i	$-0.702744\pi$
$19$	−5.18479			−1.18947			−0.594736	+	0.803921i	$0.702744\pi$
$20$	0.0775297	−	0.134285i	0.0173362	−	0.0300271i
$21$		0			0
$22$	1.78699	+	3.09516i	0.380987	+	0.659889i
$23$	−3.63846	−	6.30200i	−0.758672	−	1.31406i	−0.943528	−	0.331293i	$-0.892515\pi$
$23$	−3.63846	−	6.30200i	−0.758672	−	1.31406i	0.184856	−	0.982766i	$-0.440818\pi$
$24$		0			0
$25$	2.40033	−	4.15749i	0.480066	−	0.831499i
$26$	4.23065			0.829698
$27$		0			0
$28$	1.22668			0.231821
$29$	−1.80958	+	3.13429i	−0.336031	+	0.582022i	−0.983682	−	0.179914i	$-0.942418\pi$
$29$	−1.80958	+	3.13429i	−0.336031	+	0.582022i	0.647652	+	0.761937i	$0.275751\pi$
$30$		0			0
$31$	0.967911	+	1.67647i	0.173842	+	0.301103i	0.939760	−	0.341835i	$-0.111048\pi$
$31$	0.967911	+	1.67647i	0.173842	+	0.301103i	−0.765918	+	0.642938i	$0.777715\pi$
$32$	−0.970481	−	1.68092i	−0.171558	−	0.297148i
$33$		0			0
$34$	4.52481	−	7.83721i	0.775999	−	1.34407i
$35$	−1.57699			−0.266560
$36$		0			0
$37$	−3.22668			−0.530463			−0.265232	−	0.964185i	$-0.585448\pi$
$37$	−3.22668			−0.530463			−0.265232	+	0.964185i	$0.585448\pi$
$38$	3.33272	−	5.77244i	0.540639	−	0.936414i
$39$		0			0
$40$	0.673648	+	1.16679i	0.106513	+	0.184486i
$41$	2.43042	+	4.20961i	0.379568	+	0.657430i	0.990999	−	0.133867i	$-0.0427395\pi$
$41$	2.43042	+	4.20961i	0.379568	+	0.657430i	−0.611432	+	0.791297i	$0.709406\pi$
$42$		0			0
$43$	2.87939	−	4.98724i	0.439102	−	0.760547i	−0.558518	−	0.829492i	$-0.688630\pi$
$43$	2.87939	−	4.98724i	0.439102	−	0.760547i	0.997620	+	0.0689450i	$0.0219633\pi$
$44$	0.965505			0.145555
$45$		0			0
$46$	9.35504			1.37932
$47$	−1.50881	+	2.61334i	−0.220083	+	0.381195i	−0.954833	−	0.297143i	$-0.903966\pi$
$47$	−1.50881	+	2.61334i	−0.220083	+	0.381195i	0.734750	+	0.678338i	$0.237299\pi$
$48$		0			0
$49$	−2.73783	−	4.74205i	−0.391118	−	0.677436i
$50$	3.08580	+	5.34477i	0.436399	+	0.755865i
$51$		0			0
$52$	0.571452	−	0.989783i	0.0792461	−	0.137258i
$53$	8.77141			1.20485			0.602423	−	0.798177i	$-0.294202\pi$
$53$	8.77141			1.20485			0.602423	+	0.798177i	$0.294202\pi$
$54$		0			0
$55$	−1.24123			−0.167367
$56$	−5.32926	+	9.23055i	−0.712153	+	1.23348i
$57$		0			0
$58$	−2.32635	−	4.02936i	−0.305465	−	0.529081i
$59$	−1.48189	−	2.56670i	−0.192925	−	0.334156i	0.753293	−	0.657685i	$-0.228464\pi$
$59$	−1.48189	−	2.56670i	−0.192925	−	0.334156i	−0.946218	+	0.323529i	$0.895131\pi$
$60$		0			0
$61$	−3.94356	+	6.83045i	−0.504922	+	0.874550i	0.495062	+	0.868857i	$0.335145\pi$
$61$	−3.94356	+	6.83045i	−0.504922	+	0.874550i	−0.999984	+	0.00569222i	$0.998188\pi$
$62$	−2.48865			−0.316058
$63$		0			0
$64$	8.86484			1.10810
$65$	−0.734644	+	1.27244i	−0.0911214	+	0.157827i
$66$		0			0
$67$	4.71941	+	8.17425i	0.576567	+	0.998644i	0.995869	+	0.0907972i	$0.0289415\pi$
$67$	4.71941	+	8.17425i	0.576567	+	0.998644i	−0.419302	+	0.907847i	$0.637725\pi$
$68$	−1.22237	−	2.11721i	−0.148234	−	0.256750i
$69$		0			0
$70$	1.01367	−	1.75573i	0.121157	−	0.209850i
$71$	5.30731			0.629862			0.314931	−	0.949115i	$-0.398019\pi$
$71$	5.30731			0.629862			0.314931	+	0.949115i	$0.398019\pi$
$72$		0			0
$73$	−1.55438			−0.181926			−0.0909631	−	0.995854i	$-0.528995\pi$
$73$	−1.55438			−0.181926			−0.0909631	+	0.995854i	$0.528995\pi$
$74$	2.07407	−	3.59240i	0.241106	−	0.417608i
$75$		0			0
$76$	−0.900330	−	1.55942i	−0.103275	−	0.178877i
$77$	−4.90971	−	8.50387i	−0.559514	−	0.969106i
$78$		0			0
$79$	5.95084	−	10.3072i	0.669521	−	1.15965i	−0.308517	−	0.951219i	$-0.599833\pi$
$79$	5.95084	−	10.3072i	0.669521	−	1.15965i	0.978038	−	0.208426i	$-0.0668341\pi$
$80$	−1.42193			−0.158977
$81$		0			0
$82$	−6.24897			−0.690083
$83$	8.12863	−	14.0792i	0.892233	−	1.54539i	0.0550399	−	0.998484i	$-0.482471\pi$
$83$	8.12863	−	14.0792i	0.892233	−	1.54539i	0.837193	−	0.546908i	$-0.184195\pi$
$84$		0			0
$85$	1.57145	+	2.72183i	0.170448	+	0.295224i
$86$	3.70167	+	6.41147i	0.399161	+	0.691367i
$87$		0			0
$88$	−4.19459	+	7.26525i	−0.447145	+	0.774478i
$89$	18.4258			1.95313			0.976567	−	0.215214i	$-0.0690450\pi$
$89$	18.4258			1.95313			0.976567	+	0.215214i	$0.0690450\pi$
$90$		0			0
$91$	−11.6236			−1.21849
$92$	1.26363	−	2.18866i	0.131742	−	0.228184i
$93$		0			0
$94$	−1.93969	−	3.35965i	−0.200064	−	0.346521i
$95$	1.15744	+	2.00475i	0.118751	+	0.205683i
$96$		0			0
$97$	−5.05690	+	8.75881i	−0.513451	+	0.889323i	0.486427	+	0.873721i	$0.338300\pi$
$97$	−5.05690	+	8.75881i	−0.513451	+	0.889323i	−0.999878	+	0.0156019i	$0.995034\pi$
$98$	7.03936			0.711083
$99$		0			0
$100$	1.66725			0.166725
$101$	1.04039	−	1.80200i	0.103522	−	0.179306i	−0.809611	−	0.586967i	$-0.800322\pi$
$101$	1.04039	−	1.80200i	0.103522	−	0.179306i	0.913134	+	0.407661i	$0.133655\pi$
$102$		0			0
$103$	0.724155	+	1.25427i	0.0713531	+	0.123587i	0.899495	−	0.436932i	$-0.143935\pi$
$103$	0.724155	+	1.25427i	0.0713531	+	0.123587i	−0.828141	+	0.560519i	$0.810602\pi$
$104$	4.96529	+	8.60014i	0.486887	+	0.843313i
$105$		0			0
$106$	−5.63816	+	9.76557i	−0.547626	+	0.948516i
$107$	−2.23583			−0.216146			−0.108073	−	0.994143i	$-0.534468\pi$
$107$	−2.23583			−0.216146			−0.108073	+	0.994143i	$0.534468\pi$
$108$		0			0
$109$	−11.5030			−1.10179			−0.550893	−	0.834576i	$-0.685713\pi$
$109$	−11.5030			−1.10179			−0.550893	+	0.834576i	$0.685713\pi$
$110$	0.797847	−	1.38191i	0.0760717	−	0.131760i
$111$		0			0
$112$	−5.62449	−	9.74189i	−0.531464	−	0.920522i
$113$	−0.844075	−	1.46198i	−0.0794039	−	0.137532i	0.823589	−	0.567187i	$-0.191968\pi$
$113$	−0.844075	−	1.46198i	−0.0794039	−	0.137532i	−0.902993	+	0.429655i	$0.858635\pi$
$114$		0			0
$115$	−1.62449	+	2.81369i	−0.151484	+	0.262378i
$116$	−1.25692			−0.116702
$117$		0			0
$118$	3.81016			0.350753
$119$	−12.4318	+	21.5326i	−1.13962	+	1.97389i
$120$		0			0
$121$	1.63563	+	2.83299i	0.148694	+	0.257545i
$122$	−5.06975	−	8.78106i	−0.458993	−	0.795000i
$123$		0			0
$124$	−0.336152	+	0.582232i	−0.0301873	+	0.0522860i
$125$	−4.37576			−0.391379
$126$		0			0
$127$	−2.67230			−0.237129			−0.118564	−	0.992946i	$-0.537829\pi$
$127$	−2.67230			−0.237129			−0.118564	+	0.992946i	$0.537829\pi$
$128$	−3.75725	+	6.50774i	−0.332097	+	0.575208i
$129$		0			0
$130$	−0.944440	−	1.63582i	−0.0828329	−	0.143471i
$131$	1.45994	+	2.52869i	0.127555	+	0.220932i	0.922729	−	0.385450i	$-0.125954\pi$
$131$	1.45994	+	2.52869i	0.127555	+	0.220932i	−0.795174	+	0.606382i	$0.792620\pi$
$132$		0			0
$133$	−9.15657	+	15.8597i	−0.793976	+	1.37521i
$134$	−12.1343			−1.04824
$135$		0			0
$136$	21.2422			1.82150
$137$	2.32861	−	4.03327i	0.198947	−	0.344586i	−0.749241	−	0.662298i	$-0.769581\pi$
$137$	2.32861	−	4.03327i	0.198947	−	0.344586i	0.948187	+	0.317712i	$0.102915\pi$
$138$		0			0
$139$	4.00134	+	6.93053i	0.339390	+	0.587840i	0.984318	−	0.176403i	$-0.0564462\pi$
$139$	4.00134	+	6.93053i	0.339390	+	0.587840i	−0.644928	+	0.764243i	$0.723113\pi$
$140$	−0.273842	−	0.474308i	−0.0231438	−	0.0400863i
$141$		0			0
$142$	−3.41147	+	5.90885i	−0.286285	+	0.495859i
$143$	−9.14879			−0.765060
$144$		0			0
$145$	1.61587			0.134190
$146$	0.999135	−	1.73055i	0.0826890	−	0.143222i
$147$		0			0
$148$	−0.560307	−	0.970481i	−0.0460570	−	0.0797730i
$149$	−10.1059	−	17.5039i	−0.827905	−	1.43397i	−0.899679	−	0.436552i	$-0.856199\pi$
$149$	−10.1059	−	17.5039i	−0.827905	−	1.43397i	0.0717743	−	0.997421i	$-0.477134\pi$
$150$		0			0
$151$	−3.35117	+	5.80439i	−0.272714	+	0.472355i	−0.969556	−	0.244870i	$-0.921255\pi$
$151$	−3.35117	+	5.80439i	−0.272714	+	0.472355i	0.696842	+	0.717225i	$0.254588\pi$
$152$	15.6458			1.26904
$153$		0			0
$154$	12.6236			1.01724
$155$	0.432149	−	0.748503i	0.0347110	−	0.0601212i
$156$		0			0
$157$	−2.66250	−	4.61159i	−0.212491	−	0.368045i	0.740003	−	0.672604i	$-0.234824\pi$
$157$	−2.66250	−	4.61159i	−0.212491	−	0.368045i	−0.952493	+	0.304559i	$0.901491\pi$
$158$	7.65025	+	13.2506i	0.608621	+	1.05416i
$159$		0			0
$160$	−0.433296	+	0.750491i	−0.0342551	+	0.0593315i
$161$	−25.7028			−2.02566
$162$		0			0
$163$	3.81521			0.298830			0.149415	−	0.988775i	$-0.452261\pi$
$163$	3.81521			0.298830			0.149415	+	0.988775i	$0.452261\pi$
$164$	−0.844075	+	1.46198i	−0.0659112	+	0.114162i
$165$		0			0
$166$	10.4500	+	18.0999i	0.811074	+	1.40482i
$167$	4.56769	+	7.91147i	0.353459	+	0.612208i	0.986853	−	0.161621i	$-0.0516722\pi$
$167$	4.56769	+	7.91147i	0.353459	+	0.612208i	−0.633394	+	0.773829i	$0.718339\pi$
$168$		0			0
$169$	1.08512	−	1.87949i	0.0834709	−	0.144576i
$170$	−4.04044			−0.309888
$171$		0			0
$172$	2.00000			0.152499
$173$	3.03693	−	5.26011i	0.230893	−	0.399919i	−0.727178	−	0.686449i	$-0.759168\pi$
$173$	3.03693	−	5.26011i	0.230893	−	0.399919i	0.958071	+	0.286530i	$0.0925018\pi$
$174$		0			0
$175$	−8.47818	−	14.6846i	−0.640890	−	1.11005i
$176$	−4.42696	−	7.66772i	−0.333695	−	0.577976i
$177$		0			0
$178$	−11.8439	+	20.5142i	−0.887737	+	1.53761i
$179$	−10.2811			−0.768449			−0.384224	−	0.923240i	$-0.625531\pi$
$179$	−10.2811			−0.768449			−0.384224	+	0.923240i	$0.625531\pi$
$180$		0			0
$181$	−23.1411			−1.72007			−0.860034	−	0.510237i	$-0.829558\pi$
$181$	−23.1411			−1.72007			−0.860034	+	0.510237i	$0.829558\pi$
$182$	7.47151	−	12.9410i	0.553825	−	0.959253i
$183$		0			0
$184$	10.9795	+	19.0171i	0.809421	+	1.40196i
$185$	0.720317	+	1.24763i	0.0529588	+	0.0917273i
$186$		0			0
$187$	−9.78493	+	16.9480i	−0.715545	+	1.23936i
$188$	−1.04801			−0.0764340
$189$		0			0
$190$	−2.97596			−0.215899
$191$	7.33515	−	12.7049i	0.530753	−	0.919291i	−0.468603	−	0.883409i	$-0.655242\pi$
$191$	7.33515	−	12.7049i	0.530753	−	0.919291i	0.999356	−	0.0358825i	$-0.0114242\pi$
$192$		0			0
$193$	−11.7208	−	20.3009i	−0.843678	−	1.46129i	−0.886764	−	0.462222i	$-0.847052\pi$
$193$	−11.7208	−	20.3009i	−0.843678	−	1.46129i	0.0430860	−	0.999071i	$-0.486281\pi$
$194$	−6.50103	−	11.2601i	−0.466747	−	0.808429i
$195$		0			0
$196$	0.950837	−	1.64690i	0.0679169	−	0.117636i
$197$	9.02768			0.643196			0.321598	−	0.946876i	$-0.395780\pi$
$197$	9.02768			0.643196			0.321598	+	0.946876i	$0.395780\pi$
$198$		0			0
$199$	2.60401			0.184593			0.0922966	−	0.995732i	$-0.470579\pi$
$199$	2.60401			0.184593			0.0922966	+	0.995732i	$0.470579\pi$
$200$	−7.24330	+	12.5458i	−0.512178	+	0.887119i
$201$		0			0
$202$	1.33750	+	2.31661i	0.0941059	+	0.162996i
$203$	6.39160	+	11.0706i	0.448602	+	0.777002i
$204$		0			0
$205$	1.08512	−	1.87949i	0.0757882	−	0.131269i
$206$	−1.86191			−0.129726
$207$		0			0
$208$	−10.4807			−0.726706
$209$	−7.20702	+	12.4829i	−0.498520	+	0.863462i
$210$		0			0
$211$	8.17752	+	14.1639i	0.562964	+	0.975082i	0.997236	+	0.0742999i	$0.0236722\pi$
$211$	8.17752	+	14.1639i	0.562964	+	0.975082i	−0.434272	+	0.900782i	$0.642994\pi$
$212$	1.52314	+	2.63816i	0.104610	+	0.181189i
$213$		0			0
$214$	1.43717	−	2.48925i	0.0982427	−	0.170161i
$215$	−2.57115			−0.175351
$216$		0			0
$217$	6.83750			0.464159
$218$	7.39398	−	12.8068i	0.500784	−	0.867383i
$219$		0			0
$220$	−0.215537	−	0.373321i	−0.0145315	−	0.0251693i
$221$	11.5828	+	20.0620i	0.779142	+	1.34951i
$222$		0			0
$223$	−1.85117	+	3.20631i	−0.123963	+	0.214711i	−0.921327	−	0.388788i	$-0.872894\pi$
$223$	−1.85117	+	3.20631i	−0.123963	+	0.214711i	0.797364	+	0.603499i	$0.206227\pi$
$224$	−6.85565			−0.458062
$225$		0			0
$226$	2.17024			0.144363
$227$	−5.28039	+	9.14590i	−0.350472	+	0.607034i	−0.986332	−	0.164769i	$-0.947312\pi$
$227$	−5.28039	+	9.14590i	−0.350472	+	0.607034i	0.635861	+	0.771804i	$0.280645\pi$
$228$		0			0
$229$	−6.76264	−	11.7132i	−0.446888	−	0.774033i	0.551294	−	0.834311i	$-0.314134\pi$
$229$	−6.76264	−	11.7132i	−0.446888	−	0.774033i	−0.998182	+	0.0602787i	$0.980801\pi$
$230$	−2.08840	−	3.61721i	−0.137705	−	0.238512i
$231$		0			0
$232$	5.46064	−	9.45810i	0.358508	−	0.620955i
$233$	−12.7007			−0.832050			−0.416025	−	0.909353i	$-0.636577\pi$
$233$	−12.7007			−0.832050			−0.416025	+	0.909353i	$0.636577\pi$
$234$		0			0
$235$	1.34730			0.0878879
$236$	0.514654	−	0.891407i	0.0335011	−	0.0580256i
$237$		0			0
$238$	−15.9820	−	27.6817i	−1.03596	−	1.79434i
$239$	−2.92577	−	5.06758i	−0.189252	−	0.327795i	0.755749	−	0.654862i	$-0.227273\pi$
$239$	−2.92577	−	5.06758i	−0.189252	−	0.327795i	−0.945001	+	0.327067i	$0.893940\pi$
$240$		0			0
$241$	4.26991	−	7.39571i	0.275049	−	0.476400i	−0.695098	−	0.718915i	$-0.744639\pi$
$241$	4.26991	−	7.39571i	0.275049	−	0.476400i	0.970148	+	0.242515i	$0.0779725\pi$
$242$	−4.20545			−0.270337
$243$		0			0
$244$	−2.73917			−0.175357
$245$	−1.22237	+	2.11721i	−0.0780945	+	0.135264i
$246$		0			0
$247$	8.53121	+	14.7765i	0.542828	+	0.940206i
$248$	−2.92079	−	5.05896i	−0.185471	−	0.321244i
$249$		0			0
$250$	2.81268	−	4.87171i	0.177890	−	0.308114i
$251$	6.75790			0.426555			0.213277	−	0.976992i	$-0.431586\pi$
$251$	6.75790			0.426555			0.213277	+	0.976992i	$0.431586\pi$
$252$		0			0
$253$	−20.2303			−1.27187
$254$	1.71772	−	2.97519i	0.107780	−	0.186680i
$255$		0			0
$256$	4.03462	+	6.98816i	0.252163	+	0.436760i
$257$	1.84148	+	3.18954i	0.114868	+	0.198958i	0.917727	−	0.397211i	$-0.130022\pi$
$257$	1.84148	+	3.18954i	0.114868	+	0.198958i	−0.802859	+	0.596169i	$0.796689\pi$
$258$		0			0
$259$	−5.69846	+	9.87003i	−0.354085	+	0.613294i
$260$	−0.510278			−0.0316461
$261$		0			0
$262$	−3.75372			−0.231905
$263$	1.81893	−	3.15048i	0.112160	−	0.194267i	−0.804481	−	0.593979i	$-0.797556\pi$
$263$	1.81893	−	3.15048i	0.112160	−	0.194267i	0.916641	+	0.399712i	$0.130890\pi$
$264$		0			0
$265$	−1.95811	−	3.39155i	−0.120286	−	0.208341i
$266$	−11.7715	−	20.3888i	−0.721755	−	1.25012i
$267$		0			0
$268$	−1.63903	+	2.83889i	−0.100120	+	0.173413i
$269$	7.08672			0.432085			0.216042	−	0.976384i	$-0.430685\pi$
$269$	7.08672			0.432085			0.216042	+	0.976384i	$0.430685\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	−11.2095	+	19.4153i	−0.679673	+	1.17723i
$273$		0			0
$274$	2.99360	+	5.18507i	0.180850	+	0.313242i
$275$	−6.67306	−	11.5581i	−0.402401	−	0.696979i
$276$		0			0
$277$	6.94609	−	12.0310i	0.417350	−	0.722871i	−0.578322	−	0.815809i	$-0.696292\pi$
$277$	6.94609	−	12.0310i	0.417350	−	0.722871i	0.995672	+	0.0929372i	$0.0296256\pi$
$278$	−10.2881			−0.617037
$279$		0			0
$280$	4.75877			0.284391
$281$	11.0637	−	19.1630i	0.660008	−	1.14317i	−0.320605	−	0.947213i	$-0.603886\pi$
$281$	11.0637	−	19.1630i	0.660008	−	1.14317i	0.980613	−	0.195954i	$-0.0627804\pi$
$282$		0			0
$283$	11.8662	+	20.5528i	0.705371	+	1.22174i	0.966557	+	0.256450i	$0.0825530\pi$
$283$	11.8662	+	20.5528i	0.705371	+	1.22174i	−0.261186	+	0.965288i	$0.584114\pi$
$284$	0.921605	+	1.59627i	0.0546872	+	0.0947210i
$285$		0			0
$286$	5.88073	−	10.1857i	0.347735	−	0.602294i
$287$	17.1689			1.01345
$288$		0			0
$289$	32.5526			1.91486
$290$	−1.03866	+	1.79901i	−0.0609922	+	0.105642i
$291$		0			0
$292$	−0.269915	−	0.467506i	−0.0157956	−	0.0273587i
$293$	9.30304	+	16.1133i	0.543489	+	0.941351i	0.998700	+	0.0509677i	$0.0162306\pi$
$293$	9.30304	+	16.1133i	0.543489	+	0.941351i	−0.455211	+	0.890384i	$0.650436\pi$
$294$		0			0
$295$	−0.661626	+	1.14597i	−0.0385214	+	0.0667210i
$296$	9.73692			0.565947
$297$		0			0
$298$	25.9837			1.50520
$299$	−11.9737	+	20.7390i	−0.692455	+	1.19937i
$300$		0			0
$301$	−10.1702	−	17.6154i	−0.586203	−	1.01533i
$302$	−4.30818	−	7.46198i	−0.247908	−	0.429389i
$303$		0			0
$304$	−8.25624	+	14.3002i	−0.473528	+	0.820175i
$305$	3.52141			0.201635
$306$		0			0
$307$	20.7469			1.18409			0.592044	−	0.805905i	$-0.298321\pi$
$307$	20.7469			1.18409			0.592044	+	0.805905i	$0.298321\pi$
$308$	1.70513	−	2.95336i	0.0971585	−	0.168283i
$309$		0			0
$310$	0.555560	+	0.962258i	0.0315537	+	0.0546526i
$311$	10.1927	+	17.6544i	0.577978	+	1.00109i	0.995711	+	0.0925169i	$0.0294912\pi$
$311$	10.1927	+	17.6544i	0.577978	+	1.00109i	−0.417734	+	0.908570i	$0.637175\pi$
$312$		0			0
$313$	14.9204	−	25.8429i	0.843351	−	1.46073i	−0.0436951	−	0.999045i	$-0.513913\pi$
$313$	14.9204	−	25.8429i	0.843351	−	1.46073i	0.887046	−	0.461681i	$-0.152754\pi$
$314$	6.84570			0.386325
$315$		0			0
$316$	4.13341			0.232522
$317$	2.15830	−	3.73829i	0.121222	−	0.209963i	−0.799028	−	0.601294i	$-0.794652\pi$
$317$	2.15830	−	3.73829i	0.121222	−	0.209963i	0.920250	+	0.391331i	$0.127985\pi$
$318$		0			0
$319$	5.03074	+	8.71351i	0.281668	+	0.487863i
$320$	−1.97897	−	3.42767i	−0.110628	−	0.191613i
$321$		0			0
$322$	16.5214	−	28.6159i	0.920702	−	1.59470i
$323$	36.4976			2.03078
$324$		0			0
$325$	−15.7983			−0.876332
$326$	−2.45237	+	4.24763i	−0.135824	+	0.235254i
$327$		0			0
$328$	−7.33409	−	12.7030i	−0.404958	−	0.701407i
$329$	5.32926	+	9.23055i	0.293812	+	0.508897i
$330$		0			0
$331$	1.45946	−	2.52785i	0.0802189	−	0.138943i	−0.823125	−	0.567860i	$-0.807771\pi$
$331$	1.45946	−	2.52785i	0.0802189	−	0.138943i	0.903344	+	0.428917i	$0.141105\pi$
$332$	5.64608			0.309869
$333$		0			0
$334$	−11.7442			−0.642615
$335$	2.10710	−	3.64960i	0.115123	−	0.199399i
$336$		0			0
$337$	−7.22075	−	12.5067i	−0.393339	−	0.681284i	0.599548	−	0.800339i	$-0.295347\pi$
$337$	−7.22075	−	12.5067i	−0.393339	−	0.681284i	−0.992888	+	0.119055i	$0.962014\pi$
$338$	1.39501	+	2.41622i	0.0758783	+	0.131425i
$339$		0			0
$340$	−0.545759	+	0.945283i	−0.0295980	+	0.0512652i
$341$	5.38170			0.291436
$342$		0			0
$343$	5.38413			0.290716
$344$	−8.68891	+	15.0496i	−0.468475	+	0.811422i
$345$		0			0
$346$	3.90420	+	6.76227i	0.209891	+	0.363542i
$347$	−0.727021	−	1.25924i	−0.0390285	−	0.0675994i	0.845851	−	0.533419i	$-0.179093\pi$
$347$	−0.727021	−	1.25924i	−0.0390285	−	0.0675994i	−0.884880	+	0.465819i	$0.845760\pi$
$348$		0			0
$349$	13.7909	−	23.8865i	0.738208	−	1.27861i	−0.215094	−	0.976593i	$-0.569006\pi$
$349$	13.7909	−	23.8865i	0.738208	−	1.27861i	0.953302	−	0.302020i	$-0.0976609\pi$
$350$	21.7987			1.16519
$351$		0			0
$352$	−5.39599			−0.287607
$353$	5.26606	−	9.12108i	0.280284	−	0.485466i	−0.691171	−	0.722692i	$-0.742905\pi$
$353$	5.26606	−	9.12108i	0.280284	−	0.485466i	0.971455	+	0.237225i	$0.0762380\pi$
$354$		0			0
$355$	−1.18479	−	2.05212i	−0.0628823	−	0.108915i
$356$	3.19961	+	5.54189i	0.169579	+	0.293720i
$357$		0			0
$358$	6.60859	−	11.4464i	0.349275	−	0.604962i
$359$	−14.7055			−0.776124			−0.388062	−	0.921633i	$-0.626855\pi$
$359$	−14.7055			−0.776124			−0.388062	+	0.921633i	$0.626855\pi$
$360$		0			0
$361$	7.88207			0.414846
$362$	14.8748	−	25.7640i	0.781804	−	1.35412i
$363$		0			0
$364$	−2.01842	−	3.49600i	−0.105794	−	0.183240i
$365$	0.346996	+	0.601014i	0.0181626	+	0.0314585i
$366$		0			0
$367$	10.6814	−	18.5007i	0.557564	−	0.965729i	−0.440135	−	0.897932i	$-0.645069\pi$
$367$	10.6814	−	18.5007i	0.557564	−	0.965729i	0.997699	−	0.0677976i	$-0.0215972\pi$
$368$	−23.1755			−1.20811
$369$		0			0
$370$	−1.85204			−0.0962832
$371$	15.4907	−	26.8307i	0.804237	−	1.39298i
$372$		0			0
$373$	−11.3123	−	19.5934i	−0.585727	−	1.01451i	−0.994784	−	0.102000i	$-0.967476\pi$
$373$	−11.3123	−	19.5934i	−0.585727	−	1.01451i	0.409057	−	0.912509i	$-0.365858\pi$
$374$	−12.5793	−	21.7879i	−0.650458	−	1.12663i
$375$		0			0
$376$	4.55303	−	7.88609i	0.234805	−	0.406694i
$377$	11.9101			0.613404
$378$		0			0
$379$	−17.0743			−0.877047			−0.438523	−	0.898720i	$-0.644498\pi$
$379$	−17.0743			−0.877047			−0.438523	+	0.898720i	$0.644498\pi$
$380$	−0.401975	+	0.696242i	−0.0206209	+	0.0357164i
$381$		0			0
$382$	9.42989	+	16.3331i	0.482475	+	0.835672i
$383$	−19.4958	−	33.7677i	−0.996188	−	1.72545i	−0.573638	−	0.819109i	$-0.694468\pi$
$383$	−19.4958	−	33.7677i	−0.996188	−	1.72545i	−0.422550	−	0.906339i	$-0.638865\pi$
$384$		0			0
$385$	−2.19207	+	3.79677i	−0.111718	+	0.193501i
$386$	30.1358			1.53387
$387$		0			0
$388$	−3.51249			−0.178320
$389$	5.10602	−	8.84389i	0.258886	−	0.448403i	−0.707058	−	0.707156i	$-0.749978\pi$
$389$	5.10602	−	8.84389i	0.258886	−	0.448403i	0.965944	+	0.258752i	$0.0833114\pi$
$390$		0			0
$391$	25.6125	+	44.3621i	1.29528	+	2.24349i
$392$	8.26173	+	14.3097i	0.417281	+	0.722751i
$393$		0			0
$394$	−5.80288	+	10.0509i	−0.292345	+	0.506356i
$395$	−5.31381			−0.267367
$396$		0			0
$397$	−1.14290			−0.0573607			−0.0286803	−	0.999589i	$-0.509130\pi$
$397$	−1.14290			−0.0573607			−0.0286803	+	0.999589i	$0.509130\pi$
$398$	−1.67382	+	2.89915i	−0.0839012	+	0.145321i
$399$		0			0
$400$	−7.64455	−	13.2408i	−0.382228	−	0.662038i
$401$	−10.2770	−	17.8002i	−0.513208	−	0.888902i	−0.999883	−	0.0153188i	$-0.995124\pi$
$401$	−10.2770	−	17.8002i	−0.513208	−	0.888902i	0.486675	−	0.873583i	$-0.338210\pi$
$402$		0			0
$403$	3.18526	−	5.51703i	0.158669	−	0.274823i
$404$	0.722645			0.0359530
$405$		0			0
$406$	−16.4338			−0.815594
$407$	−4.48519	+	7.76857i	−0.222322	+	0.385074i
$408$		0			0
$409$	4.06418	+	7.03936i	0.200961	+	0.348074i	0.948838	−	0.315763i	$-0.102260\pi$
$409$	4.06418	+	7.03936i	0.200961	+	0.348074i	−0.747878	+	0.663837i	$0.768927\pi$
$410$	1.39501	+	2.41622i	0.0688945	+	0.119329i
$411$		0			0
$412$	−0.251497	+	0.435605i	−0.0123903	+	0.0214607i
$413$	−10.4683			−0.515112
$414$		0			0
$415$	−7.25847			−0.356304
$416$	−3.19372	+	5.53168i	−0.156585	+	0.271213i
$417$		0			0
$418$	−9.26517	−	16.0477i	−0.453174	−	0.784921i
$419$	17.8892	+	30.9850i	0.873946	+	1.51372i	0.857882	+	0.513847i	$0.171780\pi$
$419$	17.8892	+	30.9850i	0.873946	+	1.51372i	0.0160641	+	0.999871i	$0.494886\pi$
$420$		0			0
$421$	6.55943	−	11.3613i	0.319687	−	0.553714i	−0.660736	−	0.750619i	$-0.729756\pi$
$421$	6.55943	−	11.3613i	0.319687	−	0.553714i	0.980423	+	0.196904i	$0.0630889\pi$
$422$	−21.0256			−1.02351
$423$		0			0
$424$	−26.4688			−1.28544
$425$	−16.8968	+	29.2661i	−0.819615	+	1.41961i
$426$		0			0
$427$	13.9290	+	24.1258i	0.674072	+	1.16753i
$428$	−0.388249	−	0.672466i	−0.0187667	−	0.0325049i
$429$		0			0
$430$	1.65270	−	2.86257i	0.0797004	−	0.138045i
$431$	−9.48411			−0.456833			−0.228417	−	0.973563i	$-0.573355\pi$
$431$	−9.48411			−0.456833			−0.228417	+	0.973563i	$0.573355\pi$
$432$		0			0
$433$	17.6628			0.848820			0.424410	−	0.905470i	$-0.360481\pi$
$433$	17.6628			0.848820			0.424410	+	0.905470i	$0.360481\pi$
$434$	−4.39506	+	7.61246i	−0.210970	+	0.365410i
$435$		0			0
$436$	−1.99747	−	3.45973i	−0.0956616	−	0.165691i
$437$	18.8647	+	32.6746i	0.902420	+	1.56304i
$438$		0			0
$439$	8.83275	−	15.2988i	0.421564	−	0.730170i	−0.574529	−	0.818485i	$-0.694815\pi$
$439$	8.83275	−	15.2988i	0.421564	−	0.730170i	0.996093	+	0.0883141i	$0.0281479\pi$
$440$	3.74557			0.178563
$441$		0			0
$442$	−29.7811			−1.41654
$443$	−6.49605	+	11.2515i	−0.308637	+	0.534575i	−0.978064	−	0.208303i	$-0.933206\pi$
$443$	−6.49605	+	11.2515i	−0.308637	+	0.534575i	0.669428	+	0.742877i	$0.266539\pi$
$444$		0			0
$445$	−4.11334	−	7.12452i	−0.194991	−	0.337734i
$446$	−2.37981	−	4.12196i	−0.112687	−	0.195180i
$447$		0			0
$448$	15.6557	−	27.1165i	0.739662	−	1.28113i
$449$	4.62857			0.218436			0.109218	−	0.994018i	$-0.465165\pi$
$449$	4.62857			0.218436			0.109218	+	0.994018i	$0.465165\pi$
$450$		0			0
$451$	13.5134			0.636322
$452$	0.293144	−	0.507741i	0.0137883	−	0.0238821i
$453$		0			0
$454$	−6.78833	−	11.7577i	−0.318592	−	0.551818i
$455$	2.59483	+	4.49437i	0.121647	+	0.210700i
$456$		0			0
$457$	−10.2836	+	17.8117i	−0.481046	+	0.833196i	−0.999763	−	0.0217498i	$-0.993076\pi$
$457$	−10.2836	+	17.8117i	−0.481046	+	0.833196i	0.518718	+	0.854946i	$0.326410\pi$
$458$	17.3878			0.812477
$459$		0			0
$460$	−1.12836			−0.0526098
$461$	−16.7862	+	29.0746i	−0.781813	+	1.35414i	0.149072	+	0.988826i	$0.452371\pi$
$461$	−16.7862	+	29.0746i	−0.781813	+	1.35414i	−0.930885	+	0.365313i	$0.880962\pi$
$462$		0			0
$463$	−6.56552	−	11.3718i	−0.305126	−	0.528493i	0.672164	−	0.740403i	$-0.265365\pi$
$463$	−6.56552	−	11.3718i	−0.305126	−	0.528493i	−0.977289	+	0.211909i	$0.932032\pi$
$464$	5.76314	+	9.98205i	0.267547	+	0.463405i
$465$		0			0
$466$	8.16385	−	14.1402i	0.378183	−	0.655032i
$467$	−23.6307			−1.09350			−0.546750	−	0.837296i	$-0.684135\pi$
$467$	−23.6307			−1.09350			−0.546750	+	0.837296i	$0.684135\pi$
$468$		0			0
$469$	33.3387			1.53944
$470$	−0.866025	+	1.50000i	−0.0399468	+	0.0691898i
$471$		0			0
$472$	4.47178	+	7.74535i	0.205830	+	0.356509i
$473$	−8.00487	−	13.8648i	−0.368064	−	0.637506i
$474$		0			0
$475$	−12.4452	+	21.5557i	−0.571025	+	0.989045i
$476$	−8.63506			−0.395787
$477$		0			0
$478$	7.52259			0.344075
$479$	−2.94010	+	5.09240i	−0.134336	+	0.232678i	−0.925344	−	0.379129i	$-0.876224\pi$
$479$	−2.94010	+	5.09240i	−0.134336	+	0.232678i	0.791007	+	0.611807i	$0.209557\pi$
$480$		0			0
$481$	5.30928	+	9.19594i	0.242082	+	0.419299i
$482$	5.48930	+	9.50774i	0.250031	+	0.433066i
$483$		0			0
$484$	−0.568048	+	0.983888i	−0.0258204	+	0.0447222i
$485$	4.51557			0.205041
$486$		0			0
$487$	38.7965			1.75804			0.879020	−	0.476786i	$-0.158198\pi$
$487$	38.7965			1.75804			0.879020	+	0.476786i	$0.158198\pi$
$488$	11.9002	−	20.6117i	0.538697	−	0.933050i
$489$		0			0
$490$	−1.57145	−	2.72183i	−0.0709910	−	0.122960i
$491$	−18.7921	−	32.5489i	−0.848077	−	1.46891i	−0.882922	−	0.469519i	$-0.844427\pi$
$491$	−18.7921	−	32.5489i	−0.848077	−	1.46891i	0.0348455	−	0.999393i	$-0.488906\pi$
$492$		0			0
$493$	12.7383	−	22.0634i	0.573704	−	0.993684i
$494$	−21.9350			−0.986904
$495$		0			0
$496$	6.16519			0.276825
$497$	9.37295	−	16.2344i	0.420434	−	0.728213i
$498$		0			0
$499$	−16.8760	−	29.2301i	−0.755473	−	1.30852i	−0.945139	−	0.326668i	$-0.894074\pi$
$499$	−16.8760	−	29.2301i	−0.755473	−	1.30852i	0.189666	−	0.981849i	$-0.439259\pi$
$500$	−0.759842	−	1.31608i	−0.0339812	−	0.0588571i
$501$		0			0
$502$	−4.34389	+	7.52384i	−0.193877	+	0.335806i
$503$	18.7119			0.834324			0.417162	−	0.908832i	$-0.363025\pi$
$503$	18.7119			0.834324			0.417162	+	0.908832i	$0.363025\pi$
$504$		0			0
$505$	−0.929015			−0.0413406
$506$	13.0038	−	22.5232i	0.578089	−	1.00128i
$507$		0			0
$508$	−0.464041	−	0.803742i	−0.0205885	−	0.0356603i
$509$	10.8841	+	18.8518i	0.482429	+	0.835591i	0.999797	−	0.0201720i	$-0.00642139\pi$
$509$	10.8841	+	18.8518i	0.482429	+	0.835591i	−0.517368	+	0.855763i	$0.673088\pi$
$510$		0			0
$511$	−2.74510	+	4.75465i	−0.121436	+	0.210333i
$512$	−25.4026			−1.12265
$513$		0			0
$514$	−4.73473			−0.208840
$515$	0.323318	−	0.560003i	0.0142471	−	0.0246767i
$516$		0			0
$517$	4.19459	+	7.26525i	0.184478	+	0.319525i
$518$	−7.32580	−	12.6887i	−0.321877	−	0.557508i
$519$		0			0
$520$	2.21688	−	3.83975i	0.0972167	−	0.168384i
$521$	6.47643			0.283738			0.141869	−	0.989885i	$-0.454689\pi$
$521$	6.47643			0.283738			0.141869	+	0.989885i	$0.454689\pi$
$522$		0			0
$523$	−10.8726			−0.475425			−0.237712	−	0.971336i	$-0.576398\pi$
$523$	−10.8726			−0.475425			−0.237712	+	0.971336i	$0.576398\pi$
$524$	−0.507031	+	0.878203i	−0.0221497	+	0.0383645i
$525$		0			0
$526$	2.33837	+	4.05018i	0.101958	+	0.176596i
$527$	−6.81348	−	11.8013i	−0.296800	−	0.514072i
$528$		0			0
$529$	−14.9768	+	25.9406i	−0.651167	+	1.12785i
$530$	5.03460			0.218689
$531$		0			0
$532$	−6.36009			−0.275745
$533$	7.99816	−	13.8532i	0.346439	−	0.600050i
$534$		0			0
$535$	0.499123	+	0.864506i	0.0215790	+	0.0373758i
$536$	−14.2414	−	24.6668i	−0.615135	−	1.06545i
$537$		0			0
$538$	−4.55525	+	7.88993i	−0.196391	+	0.340159i
$539$	−15.2226			−0.655686
$540$		0			0
$541$	24.6459			1.05961			0.529805	−	0.848120i	$-0.322265\pi$
$541$	24.6459			1.05961			0.529805	+	0.848120i	$0.322265\pi$
$542$	12.2130	−	21.1535i	0.524592	−	0.908620i
$543$		0			0
$544$	6.83157	+	11.8326i	0.292901	+	0.507319i
$545$	2.56790	+	4.44774i	0.109997	+	0.190520i
$546$		0			0
$547$	−15.4636	+	26.7838i	−0.661177	+	1.14519i	0.319130	+	0.947711i	$0.396609\pi$
$547$	−15.4636	+	26.7838i	−0.661177	+	1.14519i	−0.980307	+	0.197481i	$0.936724\pi$
$548$	1.61744			0.0690934
$549$		0			0
$550$	17.1575			0.731596
$551$	9.38230	−	16.2506i	0.399699	−	0.692300i
$552$		0			0
$553$	−21.0189	−	36.4058i	−0.893814	−	1.54813i
$554$	8.92972	+	15.4667i	0.379387	+	0.657118i
$555$		0			0
$556$	−1.38965	+	2.40695i	−0.0589344	+	0.102077i
$557$	−23.3627			−0.989908			−0.494954	−	0.868919i	$-0.664815\pi$
$557$	−23.3627			−0.989908			−0.494954	+	0.868919i	$0.664815\pi$
$558$		0			0
$559$	−18.9513			−0.801555
$560$	−2.51120	+	4.34952i	−0.106117	+	0.183801i
$561$		0			0
$562$	14.2233	+	24.6354i	0.599973	+	1.03918i
$563$	16.8439	+	29.1744i	0.709884	+	1.22956i	0.964900	+	0.262618i	$0.0845860\pi$
$563$	16.8439	+	29.1744i	0.709884	+	1.22956i	−0.255016	+	0.966937i	$0.582081\pi$
$564$		0			0
$565$	−0.376859	+	0.652739i	−0.0158546	+	0.0274609i
$566$	−30.5097			−1.28242
$567$		0			0
$568$	−16.0155			−0.671995
$569$	−15.3979	+	26.6700i	−0.645515	+	1.11806i	0.338668	+	0.940906i	$0.390024\pi$
$569$	−15.3979	+	26.6700i	−0.645515	+	1.11806i	−0.984182	+	0.177158i	$0.943310\pi$
$570$		0			0
$571$	14.9376	+	25.8727i	0.625120	+	1.08274i	0.988518	+	0.151106i	$0.0482835\pi$
$571$	14.9376	+	25.8727i	0.625120	+	1.08274i	−0.363397	+	0.931634i	$0.618383\pi$
$572$	−1.58867	−	2.75166i	−0.0664257	−	0.115053i
$573$		0			0
$574$	−11.0360	+	19.1148i	−0.460632	+	0.797838i
$575$	−34.9340			−1.45685
$576$		0			0
$577$	4.80747			0.200137			0.100069	−	0.994981i	$-0.468094\pi$
$577$	4.80747			0.200137			0.100069	+	0.994981i	$0.468094\pi$
$578$	−20.9244	+	36.2422i	−0.870341	+	1.50748i
$579$		0			0
$580$	0.280592	+	0.486000i	0.0116510	+	0.0201801i
$581$	−28.7110	−	49.7290i	−1.19113	−	2.06310i
$582$		0			0
$583$	12.1925	−	21.1181i	0.504963	−	0.874622i
$584$	4.69053			0.194096
$585$		0			0
$586$	−23.9195			−0.988106
$587$	3.96880	−	6.87417i	0.163810	−	0.283727i	−0.772422	−	0.635110i	$-0.780955\pi$
$587$	3.96880	−	6.87417i	0.163810	−	0.283727i	0.936232	+	0.351382i	$0.114288\pi$
$588$		0			0
$589$	−5.01842	−	8.69216i	−0.206780	−	0.358154i
$590$	−0.850571	−	1.47323i	−0.0350174	−	0.0606520i
$591$		0			0
$592$	−5.13816	+	8.89955i	−0.211177	+	0.365769i
$593$	−36.2753			−1.48965			−0.744824	−	0.667261i	$-0.767467\pi$
$593$	−36.2753			−1.48965			−0.744824	+	0.667261i	$0.767467\pi$
$594$		0			0
$595$	11.1010			0.455097
$596$	3.50973	−	6.07903i	0.143764	−	0.249007i
$597$		0			0
$598$	−15.3931	−	26.6616i	−0.629469	−	1.09027i
$599$	16.8225	+	29.1374i	0.687349	+	1.19052i	0.972692	+	0.232098i	$0.0745591\pi$
$599$	16.8225	+	29.1374i	0.687349	+	1.19052i	−0.285343	+	0.958425i	$0.592108\pi$
$600$		0			0
$601$	1.48886	−	2.57877i	0.0607317	−	0.105190i	−0.834061	−	0.551672i	$-0.813990\pi$
$601$	1.48886	−	2.57877i	0.0607317	−	0.105190i	0.894793	+	0.446482i	$0.147323\pi$
$602$	26.1492			1.06576
$603$		0			0
$604$	−2.32770			−0.0947126
$605$	0.730269	−	1.26486i	0.0296896	−	0.0514240i
$606$		0			0
$607$	7.82429	+	13.5521i	0.317578	+	0.550062i	0.979982	−	0.199085i	$-0.0637971\pi$
$607$	7.82429	+	13.5521i	0.317578	+	0.550062i	−0.662404	+	0.749147i	$0.730464\pi$
$608$	5.03174	+	8.71523i	0.204064	+	0.353449i
$609$		0			0
$610$	−2.26352	+	3.92053i	−0.0916472	+	0.158738i
$611$	9.93058			0.401748
$612$		0			0
$613$	−1.06687			−0.0430903			−0.0215452	−	0.999768i	$-0.506859\pi$
$613$	−1.06687			−0.0430903			−0.0215452	+	0.999768i	$0.506859\pi$
$614$	−13.3359	+	23.0984i	−0.538191	+	0.932175i
$615$		0			0
$616$	14.8157	+	25.6615i	0.596941	+	1.03393i
$617$	−6.53498	−	11.3189i	−0.263088	−	0.455682i	0.703973	−	0.710227i	$-0.251408\pi$
$617$	−6.53498	−	11.3189i	−0.263088	−	0.455682i	−0.967061	+	0.254545i	$0.918074\pi$
$618$		0			0
$619$	−10.2588	+	17.7687i	−0.412335	+	0.714185i	−0.995145	−	0.0984238i	$-0.968620\pi$
$619$	−10.2588	+	17.7687i	−0.412335	+	0.714185i	0.582810	+	0.812609i	$0.301953\pi$
$620$	0.300167			0.0120550
$621$		0			0
$622$	−26.2071			−1.05081
$623$	32.5408	−	56.3624i	1.30372	−	2.25811i
$624$		0			0
$625$	−11.0248	−	19.0955i	−0.440993	−	0.763822i
$626$	19.1813	+	33.2230i	0.766639	+	1.32786i
$627$		0			0
$628$	0.924678	−	1.60159i	0.0368987	−	0.0639104i
$629$	22.7138			0.905658
$630$		0			0
$631$	−10.3122			−0.410523			−0.205261	−	0.978707i	$-0.565804\pi$
$631$	−10.3122			−0.410523			−0.205261	+	0.978707i	$0.565804\pi$
$632$	−17.9574	+	31.1031i	−0.714307	+	1.23722i
$633$		0			0
$634$	2.77466	+	4.80586i	0.110196	+	0.190865i
$635$	0.596559	+	1.03327i	0.0236737	+	0.0410041i
$636$		0			0
$637$	−9.00980	+	15.6054i	−0.356981	+	0.618310i
$638$	−12.9348			−0.512094
$639$		0			0
$640$	3.35504			0.132619
$641$	1.75308	−	3.03643i	0.0692426	−	0.119932i	−0.829326	−	0.558766i	$-0.811275\pi$
$641$	1.75308	−	3.03643i	0.0692426	−	0.119932i	0.898568	+	0.438834i	$0.144608\pi$
$642$		0			0
$643$	−15.7758	−	27.3246i	−0.622139	−	1.07758i	−0.989087	−	0.147334i	$-0.952931\pi$
$643$	−15.7758	−	27.3246i	−0.622139	−	1.07758i	0.366948	−	0.930241i	$-0.380403\pi$
$644$	−4.46324	−	7.73055i	−0.175876	−	0.304626i
$645$		0			0
$646$	−23.4602	+	40.6343i	−0.923030	+	1.59874i
$647$	3.04628			0.119762			0.0598808	−	0.998206i	$-0.480928\pi$
$647$	3.04628			0.119762			0.0598808	+	0.998206i	$0.480928\pi$
$648$		0			0
$649$	−8.23947			−0.323428
$650$	10.1549	−	17.5889i	0.398310	−	0.689893i
$651$		0			0
$652$	0.662504	+	1.14749i	0.0259457	+	0.0449392i
$653$	−15.3687	−	26.6193i	−0.601423	−	1.04169i	−0.992606	−	0.121382i	$-0.961267\pi$
$653$	−15.3687	−	26.6193i	−0.601423	−	1.04169i	0.391183	−	0.920313i	$-0.372066\pi$
$654$		0			0
$655$	0.651826	−	1.12900i	0.0254690	−	0.0441135i
$656$	15.4808			0.604422
$657$		0			0
$658$	−13.7023			−0.534173
$659$	−16.5920	+	28.7381i	−0.646331	+	1.11948i	0.337661	+	0.941268i	$0.390364\pi$
$659$	−16.5920	+	28.7381i	−0.646331	+	1.11948i	−0.983992	+	0.178211i	$0.942969\pi$
$660$		0			0
$661$	7.45383	+	12.9104i	0.289920	+	0.502157i	0.973790	−	0.227447i	$-0.0730378\pi$
$661$	7.45383	+	12.9104i	0.289920	+	0.502157i	−0.683870	+	0.729604i	$0.739705\pi$
$662$	1.87624	+	3.24974i	0.0729221	+	0.126305i
$663$		0			0
$664$	−24.5292	+	42.4857i	−0.951916	+	1.64877i
$665$	8.17637			0.317066
$666$		0			0
$667$	26.3364			1.01975
$668$	−1.58634	+	2.74763i	−0.0613774	+	0.106309i
$669$		0			0
$670$	2.70884	+	4.69184i	0.104651	+	0.181262i
$671$	10.9633	+	18.9891i	0.423235	+	0.733065i
$672$		0			0
$673$	−3.44444	+	5.96595i	−0.132773	+	0.229970i	−0.924745	−	0.380588i	$-0.875722\pi$
$673$	−3.44444	+	5.96595i	−0.132773	+	0.229970i	0.791971	+	0.610558i	$0.209055\pi$
$674$	18.5656			0.715122
$675$		0			0
$676$	0.753718			0.0289892
$677$	−6.59461	+	11.4222i	−0.253452	+	0.438991i	−0.964474	−	0.264178i	$-0.914899\pi$
$677$	−6.59461	+	11.4222i	−0.253452	+	0.438991i	0.711022	+	0.703170i	$0.248233\pi$
$678$		0			0
$679$	17.8614	+	30.9369i	0.685459	+	1.18725i
$680$	−4.74205	−	8.21348i	−0.181849	−	0.314972i
$681$		0			0
$682$	−3.45929	+	5.99167i	−0.132463	+	0.229433i
$683$	3.37814			0.129261			0.0646305	−	0.997909i	$-0.479413\pi$
$683$	3.37814			0.129261			0.0646305	+	0.997909i	$0.479413\pi$
$684$		0			0
$685$	−2.07934			−0.0794473
$686$	−3.46085	+	5.99437i	−0.132136	+	0.228866i
$687$		0			0
$688$	−9.17024	−	15.8833i	−0.349612	−	0.605546i
$689$	−14.4327	−	24.9982i	−0.549844	−	0.952357i
$690$		0			0
$691$	−11.7075	+	20.2781i	−0.445376	+	0.771414i	−0.998078	−	0.0619648i	$-0.980263\pi$
$691$	−11.7075	+	20.2781i	−0.445376	+	0.771414i	0.552702	+	0.833379i	$0.313597\pi$
$692$	2.10943			0.0801884
$693$		0			0
$694$	1.86928			0.0709569
$695$	1.78650	−	3.09431i	0.0677659	−	0.117374i
$696$		0			0
$697$	−17.1086	−	29.6330i	−0.648034	−	1.12243i
$698$	17.7292	+	30.7079i	0.671060	+	1.16231i
$699$		0			0
$700$	2.94444	−	5.09992i	0.111289	−	0.192759i
$701$	−45.5001			−1.71852			−0.859258	−	0.511543i	$-0.829074\pi$
$701$	−45.5001			−1.71852			−0.859258	+	0.511543i	$0.829074\pi$
$702$		0			0
$703$	16.7297			0.630972
$704$	12.3224	−	21.3430i	0.464418	−	0.804395i
$705$		0			0
$706$	6.76991	+	11.7258i	0.254789	+	0.441308i
$707$	−3.67474	−	6.36484i	−0.138203	−	0.239374i
$708$		0			0
$709$	−19.3084	+	33.4431i	−0.725142	+	1.25598i	0.233773	+	0.972291i	$0.424893\pi$
$709$	−19.3084	+	33.4431i	−0.725142	+	1.25598i	−0.958915	+	0.283692i	$0.908441\pi$
$710$	3.04628			0.114325
$711$		0			0
$712$	−55.6023			−2.08378
$713$	7.04342	−	12.1996i	0.263778	−	0.456877i
$714$		0			0
$715$	2.04236	+	3.53746i	0.0763798	+	0.132294i
$716$	−1.78530	−	3.09223i	−0.0667199	−	0.115562i
$717$		0			0
$718$	9.45249	−	16.3722i	0.352764	−	0.611005i
$719$	49.3182			1.83926			0.919630	−	0.392786i	$-0.128489\pi$
$719$	49.3182			1.83926			0.919630	+	0.392786i	$0.128489\pi$
$720$		0			0
$721$	5.11556			0.190513
$722$	−5.06650	+	8.77543i	−0.188556	+	0.326588i
$723$		0			0
$724$	−4.01842	−	6.96010i	−0.149343	−	0.258670i
$725$	8.68718	+	15.0466i	0.322634	+	0.558818i
$726$		0			0
$727$	16.1472	−	27.9678i	0.598868	−	1.03727i	−0.394120	−	0.919059i	$-0.628951\pi$
$727$	16.1472	−	27.9678i	0.598868	−	1.03727i	0.992988	−	0.118211i	$-0.0377159\pi$
$728$	35.0757			1.29999
$729$		0			0
$730$	−0.892178			−0.0330210
$731$	−20.2690	+	35.1070i	−0.749677	+	1.29848i
$732$		0			0
$733$	−19.7331	−	34.1787i	−0.728858	−	1.26242i	−0.957366	−	0.288877i	$-0.906718\pi$
$733$	−19.7331	−	34.1787i	−0.728858	−	1.26242i	0.228508	−	0.973542i	$-0.426615\pi$
$734$	13.7317	+	23.7841i	0.506847	+	0.877885i
$735$		0			0
$736$	−7.06212	+	12.2319i	−0.260313	+	0.450876i
$737$	26.2405			0.966581
$738$		0			0
$739$	35.3090			1.29886			0.649432	−	0.760420i	$-0.275007\pi$
$739$	35.3090			1.29886			0.649432	+	0.760420i	$0.275007\pi$
$740$	−0.250164	+	0.433296i	−0.00919620	+	0.0159283i
$741$		0			0
$742$	19.9145	+	34.4929i	0.731083	+	1.26627i
$743$	−23.7053	−	41.0588i	−0.869663	−	1.50630i	−0.862342	−	0.506327i	$-0.831003\pi$
$743$	−23.7053	−	41.0588i	−0.869663	−	1.50630i	−0.00732129	−	0.999973i	$-0.502330\pi$
$744$		0			0
$745$	−4.51202	+	7.81505i	−0.165308	+	0.286321i
$746$	29.0855			1.06490
$747$		0			0
$748$	−6.79654			−0.248506
$749$	−3.94858	+	6.83915i	−0.144278	+	0.249897i
$750$		0			0
$751$	4.46404	+	7.73195i	0.162895	+	0.282143i	0.935906	−	0.352250i	$-0.114583\pi$
$751$	4.46404	+	7.73195i	0.162895	+	0.282143i	−0.773011	+	0.634393i	$0.781250\pi$
$752$	4.80526	+	8.32295i	0.175230	+	0.303507i
$753$		0			0
$754$	−7.65570	+	13.2601i	−0.278804	+	0.482903i
$755$	2.99243			0.108906
$756$		0			0
$757$	−3.63816			−0.132231			−0.0661155	−	0.997812i	$-0.521061\pi$
$757$	−3.63816			−0.132231			−0.0661155	+	0.997812i	$0.521061\pi$
$758$	10.9751	−	19.0095i	0.398635	−	0.690456i
$759$		0			0
$760$	−3.49273	−	6.04958i	−0.126694	−	0.219441i
$761$	−3.34440	−	5.79267i	−0.121234	−	0.209984i	0.799020	−	0.601304i	$-0.205352\pi$
$761$	−3.34440	−	5.79267i	−0.121234	−	0.209984i	−0.920255	+	0.391320i	$0.872019\pi$
$762$		0			0
$763$	−20.3148	+	35.1863i	−0.735445	+	1.27383i
$764$	5.09494			0.184329
$765$		0			0
$766$	50.1266			1.81115
$767$	−4.87668	+	8.44666i	−0.176087	+	0.304991i
$768$		0			0
$769$	10.7356	+	18.5946i	0.387136	+	0.670539i	0.992063	−	0.125742i	$-0.0401311\pi$
$769$	10.7356	+	18.5946i	0.387136	+	0.670539i	−0.604927	+	0.796281i	$0.706798\pi$
$770$	−2.81807	−	4.88103i	−0.101556	−	0.175900i
$771$		0			0
$772$	4.07057	−	7.05044i	0.146503	−	0.253751i
$773$	10.2442			0.368457			0.184228	−	0.982883i	$-0.441021\pi$
$773$	10.2442			0.368457			0.184228	+	0.982883i	$0.441021\pi$
$774$		0			0
$775$	9.29322			0.333822
$776$	15.2598	−	26.4308i	0.547796	−	0.948811i
$777$		0			0
$778$	6.56418	+	11.3695i	0.235337	+	0.407616i
$779$	−12.6012	−	21.8259i	−0.451485	−	0.781996i
$780$		0			0
$781$	7.37733	−	12.7779i	0.263981	−	0.457229i
$782$	−65.8535			−2.35492
$783$		0			0
$784$	−17.4388			−0.622815
$785$	−1.18874	+	2.05896i	−0.0424281	+	0.0734875i
$786$		0			0
$787$

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 1.11334i) q^{2} +(0.173648 + 0.300767i) q^{4} +(-0.223238 - 0.386659i) q^{5} +(1.76604 - 3.05888i) q^{7} -3.01763 q^{8} +O(q^{10})\)	\(q+(-0.642788 + 1.11334i) q^{2} +(0.173648 + 0.300767i) q^{4} +(-0.223238 - 0.386659i) q^{5} +(1.76604 - 3.05888i) q^{7} -3.01763 q^{8} +0.573978 q^{10} +(1.39003 - 2.40760i) q^{11} +(-1.64543 - 2.84997i) q^{13} +(2.27038 + 3.93242i) q^{14} +(1.59240 - 2.75811i) q^{16} -7.03936 q^{17} -5.18479 q^{19} +(0.0775297 - 0.134285i) q^{20} +(1.78699 + 3.09516i) q^{22} +(-3.63846 - 6.30200i) q^{23} +(2.40033 - 4.15749i) q^{25} +4.23065 q^{26} +1.22668 q^{28} +(-1.80958 + 3.13429i) q^{29} +(0.967911 + 1.67647i) q^{31} +(-0.970481 - 1.68092i) q^{32} +(4.52481 - 7.83721i) q^{34} -1.57699 q^{35} -3.22668 q^{37} +(3.33272 - 5.77244i) q^{38} +(0.673648 + 1.16679i) q^{40} +(2.43042 + 4.20961i) q^{41} +(2.87939 - 4.98724i) q^{43} +0.965505 q^{44} +9.35504 q^{46} +(-1.50881 + 2.61334i) q^{47} +(-2.73783 - 4.74205i) q^{49} +(3.08580 + 5.34477i) q^{50} +(0.571452 - 0.989783i) q^{52} +8.77141 q^{53} -1.24123 q^{55} +(-5.32926 + 9.23055i) q^{56} +(-2.32635 - 4.02936i) q^{58} +(-1.48189 - 2.56670i) q^{59} +(-3.94356 + 6.83045i) q^{61} -2.48865 q^{62} +8.86484 q^{64} +(-0.734644 + 1.27244i) q^{65} +(4.71941 + 8.17425i) q^{67} +(-1.22237 - 2.11721i) q^{68} +(1.01367 - 1.75573i) q^{70} +5.30731 q^{71} -1.55438 q^{73} +(2.07407 - 3.59240i) q^{74} +(-0.900330 - 1.55942i) q^{76} +(-4.90971 - 8.50387i) q^{77} +(5.95084 - 10.3072i) q^{79} -1.42193 q^{80} -6.24897 q^{82} +(8.12863 - 14.0792i) q^{83} +(1.57145 + 2.72183i) q^{85} +(3.70167 + 6.41147i) q^{86} +(-4.19459 + 7.26525i) q^{88} +18.4258 q^{89} -11.6236 q^{91} +(1.26363 - 2.18866i) q^{92} +(-1.93969 - 3.35965i) q^{94} +(1.15744 + 2.00475i) q^{95} +(-5.05690 + 8.75881i) q^{97} +7.03936 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{7}+O(q^{10}) \) 12 * q + 12 * q^7	\( 12 q + 12 q^{7} - 24 q^{10} + 12 q^{13} + 12 q^{16} - 48 q^{19} + 6 q^{22} - 12 q^{28} + 30 q^{31} - 12 q^{37} + 6 q^{40} + 12 q^{43} + 12 q^{46} + 6 q^{49} + 6 q^{52} - 60 q^{55} - 30 q^{58} + 12 q^{61} + 12 q^{64} - 6 q^{67} - 30 q^{70} + 24 q^{73} + 18 q^{76} + 48 q^{79} - 24 q^{82} + 18 q^{85} - 42 q^{88} - 12 q^{94} + 12 q^{97}+O(q^{100}) \) 12 * q + 12 * q^7 - 24 * q^10 + 12 * q^13 + 12 * q^16 - 48 * q^19 + 6 * q^22 - 12 * q^28 + 30 * q^31 - 12 * q^37 + 6 * q^40 + 12 * q^43 + 12 * q^46 + 6 * q^49 + 6 * q^52 - 60 * q^55 - 30 * q^58 + 12 * q^61 + 12 * q^64 - 6 * q^67 - 30 * q^70 + 24 * q^73 + 18 * q^76 + 48 * q^79 - 24 * q^82 + 18 * q^85 - 42 * q^88 - 12 * q^94 + 12 * q^97

Introduction

L-functions

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