LMFDB - Embedded newform 729.2.c.c.487.5

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			487.5
Root			$-0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.c.244.5

$q$-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	−0.544141	−	0.838994i	$-0.683144\pi$
$2$	0.642788	−	1.11334i	0.454519	−	0.787251i	0.998660	+	0.0517430i	$0.0164777\pi$
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.300767i	0.0868241	+	0.150384i
$5$	0.223238	+	0.386659i	0.0998350	+	0.172919i	0.911616	−	0.411042i	$-0.134835\pi$
$5$	0.223238	+	0.386659i	0.0998350	+	0.172919i	−0.811781	+	0.583962i	$0.801502\pi$
$6$		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	−0.995850	−	0.0910078i	$-0.970991\pi$
$11$	−1.39003	+	2.40760i	−0.419110	+	0.725920i	0.576740	+	0.816928i	$0.304325\pi$
$12$		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	$-0.174385\pi$
$17$	7.03936			1.70730			0.853648	+	0.520850i	$0.174385\pi$
$18$		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	$0.107485\pi$
$23$	3.63846	+	6.30200i	0.758672	+	1.31406i	−0.184856	+	0.982766i	$0.559182\pi$
$24$		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	−0.647652	−	0.761937i	$-0.724249\pi$
$29$	1.80958	−	3.13429i	0.336031	−	0.582022i	0.983682	+	0.179914i	$0.0575821\pi$
$30$		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	0.611432	−	0.791297i	$-0.290594\pi$
$41$	−2.43042	−	4.20961i	−0.379568	−	0.657430i	−0.990999	+	0.133867i	$0.957261\pi$
$42$		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	−0.734750	−	0.678338i	$-0.762701\pi$
$47$	1.50881	−	2.61334i	0.220083	−	0.381195i	0.954833	+	0.297143i	$0.0960338\pi$
$48$		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	$-0.705798\pi$
$53$	−8.77141			−1.20485			−0.602423	+	0.798177i	$0.705798\pi$
$54$		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	0.946218	−	0.323529i	$-0.104869\pi$
$59$	1.48189	+	2.56670i	0.192925	+	0.334156i	−0.753293	+	0.657685i	$0.771536\pi$
$60$		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	$-0.601981\pi$
$71$	−5.30731			−0.629862			−0.314931	+	0.949115i	$0.601981\pi$
$72$		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	$0.517529\pi$
$83$	−8.12863	+	14.0792i	−0.892233	+	1.54539i	−0.837193	+	0.546908i	$0.815805\pi$
$84$		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	$-0.930955\pi$
$89$	−18.4258			−1.95313			−0.976567	+	0.215214i	$0.930955\pi$
$90$		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	−0.913134	−	0.407661i	$-0.866345\pi$
$101$	−1.04039	+	1.80200i	−0.103522	+	0.179306i	0.809611	+	0.586967i	$0.199678\pi$
$102$		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	$-0.465532\pi$
$107$	2.23583			0.216146			0.108073	+	0.994143i	$0.465532\pi$
$108$		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	0.902993	−	0.429655i	$-0.141365\pi$
$113$	0.844075	+	1.46198i	0.0794039	+	0.137532i	−0.823589	+	0.567187i	$0.808032\pi$
$114$		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	0.795174	−	0.606382i	$-0.207380\pi$
$131$	−1.45994	−	2.52869i	−0.127555	−	0.220932i	−0.922729	+	0.385450i	$0.874046\pi$
$132$		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	−0.948187	−	0.317712i	$-0.897085\pi$
$137$	−2.32861	+	4.03327i	−0.198947	+	0.344586i	0.749241	+	0.662298i	$0.230419\pi$
$138$		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	$0.143801\pi$
$149$	10.1059	+	17.5039i	0.827905	+	1.43397i	−0.0717743	+	0.997421i	$0.522866\pi$
$150$		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	0.633394	−	0.773829i	$-0.281661\pi$
$167$	−4.56769	−	7.91147i	−0.353459	−	0.612208i	−0.986853	+	0.161621i	$0.948328\pi$
$168$		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	−0.958071	−	0.286530i	$-0.907498\pi$
$173$	−3.03693	+	5.26011i	−0.230893	+	0.399919i	0.727178	+	0.686449i	$0.240832\pi$
$174$		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	$-0.374469\pi$
$179$	10.2811			0.768449			0.384224	+	0.923240i	$0.374469\pi$
$180$		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	$0.344758\pi$
$191$	−7.33515	+	12.7049i	−0.530753	+	0.919291i	−0.999356	+	0.0358825i	$0.988576\pi$
$192$		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	$-0.604220\pi$
$197$	−9.02768			−0.643196			−0.321598	+	0.946876i	$0.604220\pi$
$198$		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	−0.635861	−	0.771804i	$-0.719355\pi$
$227$	5.28039	−	9.14590i	0.350472	−	0.607034i	0.986332	+	0.164769i	$0.0526880\pi$
$228$		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	$-0.363423\pi$
$233$	12.7007			0.832050			0.416025	+	0.909353i	$0.363423\pi$
$234$		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	0.945001	−	0.327067i	$-0.106060\pi$
$239$	2.92577	+	5.06758i	0.189252	+	0.327795i	−0.755749	+	0.654862i	$0.772727\pi$
$240$		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	$-0.568414\pi$
$251$	−6.75790			−0.426555			−0.213277	+	0.976992i	$0.568414\pi$
$252$		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	0.802859	−	0.596169i	$-0.203311\pi$
$257$	−1.84148	−	3.18954i	−0.114868	−	0.198958i	−0.917727	+	0.397211i	$0.869978\pi$
$258$		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	−0.916641	−	0.399712i	$-0.869110\pi$
$263$	−1.81893	+	3.15048i	−0.112160	+	0.194267i	0.804481	+	0.593979i	$0.202444\pi$
$264$		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	$-0.569315\pi$
$269$	−7.08672			−0.432085			−0.216042	+	0.976384i	$0.569315\pi$
$270$		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	$0.396114\pi$
$281$	−11.0637	+	19.1630i	−0.660008	+	1.14317i	−0.980613	+	0.195954i	$0.937220\pi$
$282$		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	$-0.983769\pi$
$293$	−9.30304	−	16.1133i	−0.543489	−	0.941351i	0.455211	−	0.890384i	$-0.349564\pi$
$294$		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	$-0.970509\pi$
$311$	−10.1927	−	17.6544i	−0.577978	−	1.00109i	0.417734	−	0.908570i	$-0.362825\pi$
$312$		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	−0.920250	−	0.391331i	$-0.872015\pi$
$317$	−2.15830	+	3.73829i	−0.121222	+	0.209963i	0.799028	+	0.601294i	$0.205348\pi$
$318$		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	0.884880	−	0.465819i	$-0.154240\pi$
$347$	0.727021	+	1.25924i	0.0390285	+	0.0675994i	−0.845851	+	0.533419i	$0.820907\pi$
$348$		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	−0.971455	−	0.237225i	$-0.923762\pi$
$353$	−5.26606	+	9.12108i	−0.280284	+	0.485466i	0.691171	+	0.722692i	$0.257095\pi$
$354$		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	$-0.373145\pi$
$359$	14.7055			0.776124			0.388062	+	0.921633i	$0.373145\pi$
$360$		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	$0.305532\pi$
$383$	19.4958	+	33.7677i	0.996188	+	1.72545i	0.422550	+	0.906339i	$0.361135\pi$
$384$		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	−0.965944	−	0.258752i	$-0.916689\pi$
$389$	−5.10602	+	8.84389i	−0.258886	+	0.448403i	0.707058	+	0.707156i	$0.250022\pi$
$390$		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	$0.00487632\pi$
$401$	10.2770	+	17.8002i	0.513208	+	0.888902i	−0.486675	+	0.873583i	$0.661790\pi$
$402$		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	$-0.828220\pi$
$419$	−17.8892	−	30.9850i	−0.873946	−	1.51372i	−0.0160641	−	0.999871i	$-0.505114\pi$
$420$		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	$-0.426645\pi$
$431$	9.48411			0.456833			0.228417	+	0.973563i	$0.426645\pi$
$432$		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	−0.669428	−	0.742877i	$-0.733461\pi$
$443$	6.49605	−	11.2515i	0.308637	−	0.534575i	0.978064	+	0.208303i	$0.0667939\pi$
$444$		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	$-0.534835\pi$
$449$	−4.62857			−0.218436			−0.109218	+	0.994018i	$0.534835\pi$
$450$		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	$-0.547629\pi$
$461$	16.7862	−	29.0746i	0.781813	−	1.35414i	0.930885	−	0.365313i	$-0.119038\pi$
$462$		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	$-0.315865\pi$
$467$	23.6307			1.09350			0.546750	+	0.837296i	$0.315865\pi$
$468$		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	−0.791007	−	0.611807i	$-0.790443\pi$
$479$	2.94010	−	5.09240i	0.134336	−	0.232678i	0.925344	+	0.379129i	$0.123776\pi$
$480$		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	$0.155573\pi$
$491$	18.7921	+	32.5489i	0.848077	+	1.46891i	−0.0348455	+	0.999393i	$0.511094\pi$
$492$		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	$-0.636975\pi$
$503$	−18.7119			−0.834324			−0.417162	+	0.908832i	$0.636975\pi$
$504$		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	0.517368	−	0.855763i	$-0.326912\pi$
$509$	−10.8841	−	18.8518i	−0.482429	−	0.835591i	−0.999797	+	0.0201720i	$0.993579\pi$
$510$		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	$-0.545311\pi$
$521$	−6.47643			−0.283738			−0.141869	+	0.989885i	$0.545311\pi$
$522$		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	$-0.335185\pi$
$557$	23.3627			0.989908			0.494954	+	0.868919i	$0.335185\pi$
$558$		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	$-0.915414\pi$
$563$	−16.8439	−	29.1744i	−0.709884	−	1.22956i	0.255016	−	0.966937i	$-0.417919\pi$
$564$		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	$-0.609976\pi$
$569$	15.3979	−	26.6700i	0.645515	−	1.11806i	0.984182	−	0.177158i	$-0.0566905\pi$
$570$		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	−0.936232	−	0.351382i	$-0.885712\pi$
$587$	−3.96880	+	6.87417i	−0.163810	+	0.283727i	0.772422	+	0.635110i	$0.219045\pi$
$588$		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	$-0.232533\pi$
$593$	36.2753			1.48965			0.744824	+	0.667261i	$0.232533\pi$
$594$		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	$-0.925441\pi$
$599$	−16.8225	−	29.1374i	−0.687349	−	1.19052i	0.285343	−	0.958425i	$-0.407892\pi$
$600$		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	0.967061	−	0.254545i	$-0.0819256\pi$
$617$	6.53498	+	11.3189i	0.263088	+	0.455682i	−0.703973	+	0.710227i	$0.748592\pi$
$618$		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	−0.898568	−	0.438834i	$-0.855392\pi$
$641$	−1.75308	+	3.03643i	−0.0692426	+	0.119932i	0.829326	+	0.558766i	$0.188725\pi$
$642$		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	$-0.519072\pi$
$647$	−3.04628			−0.119762			−0.0598808	+	0.998206i	$0.519072\pi$
$648$		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	$0.0387326\pi$
$653$	15.3687	+	26.6193i	0.601423	+	1.04169i	−0.391183	+	0.920313i	$0.627934\pi$
$654$		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	$-0.609636\pi$
$659$	16.5920	−	28.7381i	0.646331	−	1.11948i	0.983992	−	0.178211i	$-0.0570309\pi$
$660$		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	−0.711022	−	0.703170i	$-0.751767\pi$
$677$	6.59461	−	11.4222i	0.253452	−	0.438991i	0.964474	+	0.264178i	$0.0851008\pi$
$678$		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	$-0.520587\pi$
$683$	−3.37814			−0.129261			−0.0646305	+	0.997909i	$0.520587\pi$
$684$		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	$-0.170926\pi$
$701$	45.5001			1.71852			0.859258	+	0.511543i	$0.170926\pi$
$702$		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	$-0.871511\pi$
$719$	−49.3182			−1.83926			−0.919630	+	0.392786i	$0.871511\pi$
$720$		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	$0.168997\pi$
$743$	23.7053	+	41.0588i	0.869663	+	1.50630i	0.00732129	+	0.999973i	$0.497670\pi$
$744$		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	0.920255	−	0.391320i	$-0.127981\pi$
$761$	3.34440	+	5.79267i	0.121234	+	0.209984i	−0.799020	+	0.601304i	$0.794648\pi$
$762$		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	$-0.558979\pi$
$773$	−10.2442			−0.368457			−0.184228	+	0.982883i	$0.558979\pi$
$774$		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
$787$	−0.473841	−	0.820717i	−0.0168906	−	0.0292554i	0.857457	−	0.514556i	$-0.172043\pi$
$787$	−0.473841	−	0.820717i	−0.0168906	−	0.0292554i	−0.874347	+	0.485301i	$0.838710\pi$
$788$	−1.56764	−	2.71523i	−0.0558449	−	0.0967262i
$789$		0			0
$790$	3.41565	−	5.91608i	0.121523	−	0.210485i
$791$	5.96270			0.212009
$792$		0			0
$793$	25.9554			0.921704
$794$	−0.734644	+	1.27244i	−0.0260715	+	0.0451572i
$795$		0			0
$796$	0.452181	+	0.783201i	0.0160271	+	0.0277598i
$797$	−3.50535	−	6.07145i	−0.124166	−	0.215062i	0.797241	−	0.603662i	$-0.206292\pi$
$797$	−3.50535	−	6.07145i	−0.124166	−	0.215062i	−0.921407	+	0.388600i	$0.872959\pi$
$798$		0			0
$799$	10.6211	−	18.3963i	0.375747	−	0.650813i
$800$	9.31790			0.329437
$801$		0			0
$802$	26.4237			0.933052
$803$	2.16063	−	3.74233i	0.0762471	−	0.132064i
$804$		0			0
$805$	5.73783	+	9.93821i	0.202232	+	0.350276i
$806$	−4.09489	−	7.09256i	−0.144236	−	0.249825i
$807$		0			0
$808$	−3.13950	+	5.43777i	−0.110447	+	0.191300i
$809$	−45.1028			−1.58573			−0.792866	−	0.609396i	$-0.791412\pi$
$809$	−45.1028			−1.58573			−0.792866	+	0.609396i	$0.791412\pi$
$810$		0			0
$811$	8.07285			0.283476			0.141738	−	0.989904i	$-0.454731\pi$
$811$	8.07285			0.283476			0.141738	+	0.989904i	$0.454731\pi$
$812$	2.21978	−	3.84477i	0.0778990	−	0.134925i
$813$		0			0
$814$	−5.76604	−	9.98708i	−0.202100	−	0.350047i
$815$	0.851698	+	1.47519i	0.0298337	+	0.0516735i
$816$		0			0
$817$	−14.9290	+	25.8578i	−0.522300	+	0.904650i
$818$	10.4496			0.365362
$819$		0			0
$820$	0.753718			0.0263210
$821$	−3.13468	+	5.42943i	−0.109401	+	0.189488i	−0.915528	−	0.402255i	$-0.868227\pi$
$821$	−3.13468	+	5.42943i	−0.109401	+	0.189488i	0.806127	+	0.591743i	$0.201560\pi$
$822$		0			0
$823$	9.89646	+	17.1412i	0.344969	+	0.597504i	0.985348	−	0.170555i	$-0.0545561\pi$
$823$	9.89646	+	17.1412i	0.344969	+	0.597504i	−0.640379	+	0.768059i	$0.721223\pi$
$824$	2.18523	+	3.78493i	0.0761261	+	0.131854i
$825$		0			0
$826$	6.72890	−	11.6548i	0.234128	−	0.405522i
$827$	−41.8003			−1.45354			−0.726769	−	0.686882i	$-0.758979\pi$
$827$	−41.8003			−1.45354			−0.726769	+	0.686882i	$0.758979\pi$
$828$		0			0
$829$	33.7279			1.17142			0.585710	−	0.810521i	$-0.300816\pi$
$829$	33.7279			1.17142			0.585710	+	0.810521i	$0.300816\pi$
$830$	−4.66565	+	8.08115i	−0.161947	+	0.280501i
$831$		0			0
$832$	−14.5865	−	25.2645i	−0.505695	−	0.875889i
$833$	−19.2725	−	33.3810i	−0.667754	−	1.15658i
$834$		0			0
$835$	2.03936	−	3.53228i	0.0705751	−	0.122240i
$836$	5.00594			0.173134
$837$		0			0
$838$	−45.9959			−1.58890
$839$	−14.6434	+	25.3631i	−0.505546	+	0.875631i	0.494434	+	0.869215i	$0.335375\pi$
$839$	−14.6434	+	25.3631i	−0.505546	+	0.875631i	−0.999979	+	0.00641552i	$0.997958\pi$
$840$		0			0
$841$	7.95084	+	13.7713i	0.274167	+	0.474871i
$842$	−8.43264	−	14.6058i	−0.290608	−	0.503348i
$843$		0			0
$844$	−2.84002	+	4.91906i	−0.0977576	+	0.169321i
$845$	0.968961			0.0333333
$846$		0			0
$847$	11.5544			0.397013
$848$	−13.9676	+	24.1925i	−0.479648	+	0.830775i
$849$		0			0
$850$	−21.7221	−	37.6238i	−0.745062	−	1.29048i
$851$	−11.7402	−	20.3346i	−0.402448	−	0.697060i
$852$		0			0
$853$	−18.7991	+	32.5609i	−0.643668	+	1.11487i	0.340940	+	0.940085i	$0.389255\pi$
$853$	−18.7991	+	32.5609i	−0.643668	+	1.11487i	−0.984607	+	0.174780i	$0.944079\pi$
$854$	35.8136			1.22552
$855$		0			0
$856$	6.74691			0.230605
$857$	−14.5050	+	25.1234i	−0.495481	+	0.858198i	−0.999986	−	0.00521069i	$-0.998341\pi$
$857$	−14.5050	+	25.1234i	−0.495481	+	0.858198i	0.504506	+	0.863408i	$0.331675\pi$
$858$		0			0
$859$	12.4338	+	21.5359i	0.424235	+	0.734796i	0.996349	−	0.0853783i	$-0.0272099\pi$
$859$	12.4338	+	21.5359i	0.424235	+	0.734796i	−0.572114	+	0.820174i	$0.693877\pi$
$860$	0.446476	+	0.773318i	0.0152247	+	0.0263699i
$861$		0			0
$862$	6.09627	−	10.5590i	0.207640	−	0.359642i
$863$	−42.4018			−1.44337			−0.721687	−	0.692219i	$-0.756633\pi$
$863$	−42.4018			−1.44337			−0.721687	+	0.692219i	$0.756633\pi$
$864$		0			0
$865$	−2.71183			−0.0922050
$866$	11.3534	−	19.6647i	0.385805	−	0.668235i
$867$		0			0
$868$	1.18732	+	2.05650i	0.0403002	+	0.0698020i
$869$	16.5437	+	28.6545i	0.561206	+	0.972038i
$870$		0			0
$871$	15.5309	−	26.9003i	0.526245	−	0.911483i
$872$	−34.7117			−1.17549
$873$		0			0
$874$	−48.5039			−1.64067
$875$	7.72778	−	13.3849i	0.261247	−	0.452492i
$876$		0			0
$877$	−6.02734	−	10.4397i	−0.203529	−	0.352522i	0.746134	−	0.665796i	$-0.231908\pi$
$877$	−6.02734	−	10.4397i	−0.203529	−	0.352522i	−0.949663	+	0.313273i	$0.898574\pi$
$878$	−11.3552	−	19.6677i	−0.383218	−	0.663753i
$879$		0			0
$880$	−1.97653	+	3.42345i	−0.0666288	+	0.115404i
$881$	14.7827			0.498041			0.249020	−	0.968498i	$-0.419891\pi$
$881$	14.7827			0.498041			0.249020	+	0.968498i	$0.419891\pi$
$882$		0			0
$883$	−25.8462			−0.869793			−0.434896	−	0.900480i	$-0.643215\pi$
$883$	−25.8462			−0.869793			−0.434896	+	0.900480i	$0.643215\pi$
$884$	4.02266	−	6.96744i	0.135297	−	0.234341i
$885$		0			0
$886$	−8.35117	−	14.4646i	−0.280563	−	0.485949i
$887$	22.9280	+	39.7124i	0.769846	+	1.33341i	0.937646	+	0.347592i	$0.113001\pi$
$887$	22.9280	+	39.7124i	0.769846	+	1.33341i	−0.167799	+	0.985821i	$0.553666\pi$
$888$		0			0
$889$	−4.71941	+	8.17425i	−0.158284	+	0.274156i
$890$	−10.5760			−0.354509
$891$		0			0
$892$	−1.28581			−0.0430520
$893$	−7.82288	+	13.5496i	−0.261783	+	0.453421i
$894$		0			0
$895$	2.29514	+	3.97530i	0.0767181	+	0.132880i
$896$	−13.2709	−	22.9859i	−0.443351	−	0.767906i
$897$		0			0
$898$	−2.97519	+	5.15317i	−0.0992832	+	0.171964i
$899$	7.00605			0.233665
$900$		0			0
$901$	−61.7452			−2.05703
$902$	8.68626	−	15.0450i	0.289221	−	0.500945i
$903$		0			0
$904$	2.54710	+	4.41171i	0.0847154	+	0.146731i
$905$	−5.16598	−	8.94774i	−0.171723	−	0.297433i
$906$		0			0
$907$	5.84998	−	10.1325i	0.194246	−	0.336443i	−0.752407	−	0.658698i	$-0.771107\pi$
$907$	5.84998	−	10.1325i	0.194246	−	0.336443i	0.946653	+	0.322255i	$0.104441\pi$
$908$	3.66772			0.121717
$909$		0			0
$910$	−6.67169			−0.221165
$911$	14.3376	−	24.8335i	0.475027	−	0.822771i	−0.524564	−	0.851371i	$-0.675772\pi$
$911$	14.3376	−	24.8335i	0.475027	−	0.822771i	0.999591	+	0.0285999i	$0.00910489\pi$
$912$		0			0
$913$	−22.5981	−	39.1410i	−0.747887	−	1.29538i
$914$	13.2203	+	22.8983i	0.437289	+	0.757407i
$915$		0			0
$916$	2.34864	−	4.06796i	0.0776013	−	0.134409i
$917$	−10.3133			−0.340574
$918$		0			0
$919$	4.33511			0.143002			0.0715011	−	0.997441i	$-0.477221\pi$
$919$	4.33511			0.143002			0.0715011	+	0.997441i	$0.477221\pi$
$920$	−4.90209	+	8.49067i	−0.161617	+	0.279929i
$921$		0			0
$922$	−21.5800	−	37.3776i	−0.710698	−	1.23097i
$923$	8.73281	+	15.1257i	0.287444	+	0.497867i
$924$		0			0
$925$	−7.74510	+	13.4149i	−0.254657	+	0.441079i
$926$	−16.8809			−0.554742
$927$		0			0
$928$	7.02465			0.230596
$929$	−6.44545	+	11.1638i	−0.211468	+	0.366274i	−0.952174	−	0.305555i	$-0.901158\pi$
$929$	−6.44545	+	11.1638i	−0.211468	+	0.366274i	0.740706	+	0.671829i	$0.234491\pi$
$930$		0			0
$931$	14.1951	+	24.5866i	0.465224	+	0.805792i
$932$	2.20545	+	3.81996i	0.0722420	+	0.125127i
$933$		0			0
$934$	15.1895	−	26.3091i	0.497017	−	0.860859i
$935$	−8.73746			−0.285746
$936$		0			0
$937$	−53.2080			−1.73823			−0.869115	−	0.494610i	$-0.835311\pi$
$937$	−53.2080			−1.73823			−0.869115	+	0.494610i	$0.835311\pi$
$938$	21.4297	−	37.1174i	0.699705	−	1.21193i
$939$		0			0
$940$	0.233956	+	0.405223i	0.00763079	+	0.0132169i
$941$	16.7037	+	28.9317i	0.544526	+	0.943147i	0.998637	+	0.0522013i	$0.0166237\pi$
$941$	16.7037	+	28.9317i	0.544526	+	0.943147i	−0.454111	+	0.890945i	$0.650043\pi$
$942$		0			0
$943$	17.6860	−	30.6330i	0.575935	−	0.997548i
$944$	9.43901			0.307214
$945$		0			0
$946$	20.5817			0.669169
$947$	7.75238	−	13.4275i	0.251918	−	0.436335i	−0.712136	−	0.702042i	$-0.752272\pi$
$947$	7.75238	−	13.4275i	0.251918	−	0.436335i	0.964054	+	0.265707i	$0.0856052\pi$
$948$		0			0
$949$	2.55762	+	4.42993i	0.0830238	+	0.143801i
$950$	15.9993	+	27.7115i	0.519084	+	0.899081i
$951$		0			0
$952$	37.5146	−	64.9772i	1.21586	−	2.10592i
$953$	22.5049			0.729004			0.364502	−	0.931203i	$-0.381239\pi$
$953$	22.5049			0.729004			0.364502	+	0.931203i	$0.381239\pi$
$954$		0			0
$955$	−6.54993			−0.211951
$956$	−1.01611	+	1.75995i	−0.0328633	+	0.0569209i
$957$		0			0
$958$	−3.77972	−	6.54666i	−0.122117	−	0.211513i
$959$	8.22486	+	14.2459i	0.265595	+	0.460023i
$960$		0			0
$961$	13.6263	−	23.6014i	0.439558	−	0.761337i
$962$	13.6510			0.440124
$963$		0			0
$964$	2.96585			0.0955237
$965$	5.23303	−	9.06387i	0.168457	−	0.291776i
$966$		0			0
$967$	20.9042	+	36.2071i	0.672234	+	1.16434i	0.977269	+	0.212002i	$0.0679983\pi$
$967$	20.9042	+	36.2071i	0.672234	+	1.16434i	−0.305035	+	0.952341i	$0.598668\pi$
$968$	4.93572	+	8.54891i	0.158640	+	0.274773i
$969$		0			0
$970$	−2.90255	+	5.02737i	−0.0931953	+	0.161419i
$971$	35.8662			1.15100			0.575501	−	0.817801i	$-0.304807\pi$
$971$	35.8662			1.15100			0.575501	+	0.817801i	$0.304807\pi$
$972$		0			0
$973$	28.2662			0.906173
$974$	24.9379	−	43.1938i	0.799063	−	1.38402i
$975$		0			0
$976$	12.5594	+	21.7536i	0.402018	+	0.696315i
$977$	−7.02504	−	12.1677i	−0.224751	−	0.389280i	0.731494	−	0.681848i	$-0.238823\pi$
$977$	−7.02504	−	12.1677i	−0.224751	−	0.389280i	−0.956245	+	0.292568i	$0.905490\pi$
$978$		0			0
$979$	25.6125	−	44.3621i	0.818578	−	1.41782i
$980$	0.849051			0.0271219
$981$		0			0
$982$	48.3174			1.54187
$983$	8.84457	−	15.3192i	0.282098	−	0.488608i	−0.689803	−	0.723997i	$-0.742303\pi$
$983$	8.84457	−	15.3192i	0.282098	−	0.488608i	0.971901	+	0.235389i	$0.0756364\pi$
$984$		0			0
$985$	−2.01532	−	3.49064i	−0.0642134	−	0.111221i
$986$	−16.3760	−	28.3641i	−0.521519	−	0.903298i
$987$		0			0
$988$	−2.96286	+	5.13182i	−0.0942611	+	0.163265i
$989$	41.9062			1.33254
$990$		0			0
$991$	32.8958			1.04497			0.522485	−	0.852649i	$-0.325005\pi$
$991$	32.8958			1.04497			0.522485	+	0.852649i	$0.325005\pi$
$992$	−1.87868	+	3.25397i	−0.0596481	+	0.103314i
$993$		0			0
$994$	12.0496	+	20.8706i	0.382191	+	0.661974i
$995$	0.581313	+	1.00686i	0.0184289	+	0.0319197i
$996$		0			0
$997$	−10.0034	+	17.3264i	−0.316811	+	0.548733i	−0.979821	−	0.199878i	$-0.935945\pi$
$997$	−10.0034	+	17.3264i	−0.316811	+	0.548733i	0.663010	+	0.748611i	$0.269279\pi$
$998$	−43.3907			−1.37351
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.c.487.5		12
3.2	odd	2	inner	729.2.c.c.487.2		12
9.2	odd	6		729.2.a.c.1.5	yes	6
9.4	even	3	inner	729.2.c.c.244.5		12
9.5	odd	6	inner	729.2.c.c.244.2		12
9.7	even	3		729.2.a.c.1.2	✓	6
27.2	odd	18		729.2.e.m.325.2		12
27.4	even	9		729.2.e.q.163.2		12
27.5	odd	18		729.2.e.m.406.2		12
27.7	even	9		729.2.e.r.82.1		12
27.11	odd	18		729.2.e.q.568.1		12
27.13	even	9		729.2.e.r.649.1		12
27.14	odd	18		729.2.e.r.649.2		12
27.16	even	9		729.2.e.q.568.2		12
27.20	odd	18		729.2.e.r.82.2		12
27.22	even	9		729.2.e.m.406.1		12
27.23	odd	18		729.2.e.q.163.1		12
27.25	even	9		729.2.e.m.325.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.c.1.2	✓	6	9.7	even	3
729.2.a.c.1.5	yes	6	9.2	odd	6
729.2.c.c.244.2		12	9.5	odd	6	inner
729.2.c.c.244.5		12	9.4	even	3	inner
729.2.c.c.487.2		12	3.2	odd	2	inner
729.2.c.c.487.5		12	1.1	even	1	trivial
729.2.e.m.325.1		12	27.25	even	9
729.2.e.m.325.2		12	27.2	odd	18
729.2.e.m.406.1		12	27.22	even	9
729.2.e.m.406.2		12	27.5	odd	18
729.2.e.q.163.1		12	27.23	odd	18
729.2.e.q.163.2		12	27.4	even	9
729.2.e.q.568.1		12	27.11	odd	18
729.2.e.q.568.2		12	27.16	even	9
729.2.e.r.82.1		12	27.7	even	9
729.2.e.r.82.2		12	27.20	odd	18
729.2.e.r.649.1		12	27.13	even	9
729.2.e.r.649.2		12	27.14	odd	18

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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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