LMFDB - Embedded newform 243.2.c.e.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(82,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, 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("243.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.2
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	243.163
Dual form			243.2.c.e.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.673648 + 1.16679i) q^{2} +(0.0923963 + 0.160035i) q^{4} +(-0.826352 - 1.43128i) q^{5} +(-1.20574 + 2.08840i) q^{7} -2.94356 q^{8} +O(q^{10})$	\(q+(-0.673648 + 1.16679i) q^{2} +(0.0923963 + 0.160035i) q^{4} +(-0.826352 - 1.43128i) q^{5} +(-1.20574 + 2.08840i) q^{7} -2.94356 q^{8} +2.22668 q^{10} +(-2.97178 + 5.14728i) q^{11} +(1.61334 + 2.79439i) q^{13} +(-1.62449 - 2.81369i) q^{14} +(1.79813 - 3.11446i) q^{16} +3.00000 q^{17} -6.63816 q^{19} +(0.152704 - 0.264490i) q^{20} +(-4.00387 - 6.93491i) q^{22} +(1.47178 + 2.54920i) q^{23} +(1.13429 - 1.96464i) q^{25} -4.34730 q^{26} -0.445622 q^{28} +(0.645430 - 1.11792i) q^{29} +(0.294263 + 0.509678i) q^{31} +(-0.520945 - 0.902302i) q^{32} +(-2.02094 + 3.50038i) q^{34} +3.98545 q^{35} +0.0418891 q^{37} +(4.47178 - 7.74535i) q^{38} +(2.43242 + 4.21307i) q^{40} +(2.45084 + 4.24497i) q^{41} +(2.59240 - 4.49016i) q^{43} -1.09833 q^{44} -3.96585 q^{46} +(1.86824 - 3.23589i) q^{47} +(0.592396 + 1.02606i) q^{49} +(1.52822 + 2.64695i) q^{50} +(-0.298133 + 0.516382i) q^{52} +11.6382 q^{53} +9.82295 q^{55} +(3.54916 - 6.14733i) q^{56} +(0.869585 + 1.50617i) q^{58} +(3.67365 + 6.36295i) q^{59} +(-5.52481 + 9.56926i) q^{61} -0.792919 q^{62} +8.59627 q^{64} +(2.66637 - 4.61830i) q^{65} +(-0.928548 - 1.60829i) q^{67} +(0.277189 + 0.480105i) q^{68} +(-2.68479 + 4.65020i) q^{70} -5.51249 q^{71} +5.55438 q^{73} +(-0.0282185 + 0.0488759i) q^{74} +(-0.613341 - 1.06234i) q^{76} +(-7.16637 - 12.4125i) q^{77} +(1.89053 - 3.27449i) q^{79} -5.94356 q^{80} -6.60401 q^{82} +(-1.99273 + 3.45150i) q^{83} +(-2.47906 - 4.29385i) q^{85} +(3.49273 + 6.04958i) q^{86} +(8.74763 - 15.1513i) q^{88} +8.15064 q^{89} -7.78106 q^{91} +(-0.271974 + 0.471073i) q^{92} +(2.51707 + 4.35970i) q^{94} +(5.48545 + 9.50108i) q^{95} +(-0.130415 + 0.225885i) q^{97} -1.59627 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 3 q^{7} + 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 3 * q^7 + 12 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 3 q^{7} + 12 q^{8} - 3 q^{11} + 3 q^{13} + 3 q^{14} - 3 q^{16} + 18 q^{17} - 6 q^{19} + 3 q^{20} - 6 q^{23} - 3 q^{25} - 24 q^{26} - 24 q^{28} - 12 q^{29} + 12 q^{31} - 9 q^{34} - 12 q^{35} - 6 q^{37} + 12 q^{38} - 9 q^{40} + 3 q^{41} + 12 q^{43} - 30 q^{44} + 18 q^{46} + 6 q^{47} + 24 q^{50} + 12 q^{52} + 36 q^{53} + 18 q^{55} + 33 q^{56} - 9 q^{58} + 21 q^{59} - 6 q^{61} - 24 q^{62} + 24 q^{64} - 3 q^{65} - 6 q^{67} - 9 q^{68} - 9 q^{70} - 18 q^{71} + 12 q^{73} - 15 q^{74} + 3 q^{76} - 24 q^{77} - 6 q^{79} - 6 q^{80} + 36 q^{82} + 6 q^{83} - 18 q^{85} + 3 q^{86} + 36 q^{88} - 12 q^{91} - 24 q^{92} + 36 q^{94} - 3 q^{95} - 15 q^{97} + 18 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 3 * q^7 + 12 * q^8 - 3 * q^11 + 3 * q^13 + 3 * q^14 - 3 * q^16 + 18 * q^17 - 6 * q^19 + 3 * q^20 - 6 * q^23 - 3 * q^25 - 24 * q^26 - 24 * q^28 - 12 * q^29 + 12 * q^31 - 9 * q^34 - 12 * q^35 - 6 * q^37 + 12 * q^38 - 9 * q^40 + 3 * q^41 + 12 * q^43 - 30 * q^44 + 18 * q^46 + 6 * q^47 + 24 * q^50 + 12 * q^52 + 36 * q^53 + 18 * q^55 + 33 * q^56 - 9 * q^58 + 21 * q^59 - 6 * q^61 - 24 * q^62 + 24 * q^64 - 3 * q^65 - 6 * q^67 - 9 * q^68 - 9 * q^70 - 18 * q^71 + 12 * q^73 - 15 * q^74 + 3 * q^76 - 24 * q^77 - 6 * q^79 - 6 * q^80 + 36 * q^82 + 6 * q^83 - 18 * q^85 + 3 * q^86 + 36 * q^88 - 12 * q^91 - 24 * q^92 + 36 * q^94 - 3 * q^95 - 15 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.673648	+	1.16679i	−0.476341	+	0.825047i	−0.999633	−	0.0271067i	$-0.991371\pi$
$2$	−0.673648	+	1.16679i	−0.476341	+	0.825047i	0.523291	+	0.852154i	$0.324704\pi$
$3$		0			0
$3$		0			0
$4$	0.0923963	+	0.160035i	0.0461981	+	0.0800175i
$5$	−0.826352	−	1.43128i	−0.369556	−	0.640089i	0.619940	−	0.784649i	$-0.287157\pi$
$5$	−0.826352	−	1.43128i	−0.369556	−	0.640089i	−0.989496	+	0.144560i	$0.953823\pi$
$6$		0			0
$7$	−1.20574	+	2.08840i	−0.455726	+	0.789340i	−0.998730	−	0.0503900i	$-0.983954\pi$
$7$	−1.20574	+	2.08840i	−0.455726	+	0.789340i	0.543004	+	0.839730i	$0.317287\pi$
$8$	−2.94356			−1.04071
$9$		0			0
$10$	2.22668			0.704139
$11$	−2.97178	+	5.14728i	−0.896026	+	1.55196i	−0.0634960	+	0.997982i	$0.520225\pi$
$11$	−2.97178	+	5.14728i	−0.896026	+	1.55196i	−0.832530	+	0.553980i	$0.813108\pi$
$12$		0			0
$13$	1.61334	+	2.79439i	0.447460	+	0.775024i	0.998220	−	0.0596400i	$-0.0189953\pi$
$13$	1.61334	+	2.79439i	0.447460	+	0.775024i	−0.550760	+	0.834664i	$0.685662\pi$
$14$	−1.62449	−	2.81369i	−0.434162	−	0.751991i
$15$		0			0
$16$	1.79813	−	3.11446i	0.449533	−	0.778615i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		0			0
$19$	−6.63816			−1.52290			−0.761449	−	0.648225i	$-0.775512\pi$
$19$	−6.63816			−1.52290			−0.761449	+	0.648225i	$0.775512\pi$
$20$	0.152704	−	0.264490i	0.0341456	−	0.0591419i
$21$		0			0
$22$	−4.00387	−	6.93491i	−0.853628	−	1.47853i
$23$	1.47178	+	2.54920i	0.306888	+	0.531545i	0.977680	−	0.210100i	$-0.0673791\pi$
$23$	1.47178	+	2.54920i	0.306888	+	0.531545i	−0.670792	+	0.741645i	$0.734046\pi$
$24$		0			0
$25$	1.13429	−	1.96464i	0.226857	−	0.392928i
$26$	−4.34730			−0.852575
$27$		0			0
$28$	−0.445622			−0.0842147
$29$	0.645430	−	1.11792i	0.119853	−	0.207592i	−0.799856	−	0.600192i	$-0.795091\pi$
$29$	0.645430	−	1.11792i	0.119853	−	0.207592i	0.919709	+	0.392600i	$0.128424\pi$
$30$		0			0
$31$	0.294263	+	0.509678i	0.0528512	+	0.0915409i	0.891241	−	0.453531i	$-0.149836\pi$
$31$	0.294263	+	0.509678i	0.0528512	+	0.0915409i	−0.838389	+	0.545072i	$0.816502\pi$
$32$	−0.520945	−	0.902302i	−0.0920909	−	0.159506i
$33$		0			0
$34$	−2.02094	+	3.50038i	−0.346589	+	0.600310i
$35$	3.98545			0.673664
$36$		0			0
$37$	0.0418891			0.00688652			0.00344326	−	0.999994i	$-0.498904\pi$
$37$	0.0418891			0.00688652			0.00344326	+	0.999994i	$0.498904\pi$
$38$	4.47178	−	7.74535i	0.725419	−	1.25646i
$39$		0			0
$40$	2.43242	+	4.21307i	0.384599	+	0.666145i
$41$	2.45084	+	4.24497i	0.382756	+	0.662954i	0.991455	−	0.130448i	$-0.0416415\pi$
$41$	2.45084	+	4.24497i	0.382756	+	0.662954i	−0.608699	+	0.793401i	$0.708308\pi$
$42$		0			0
$43$	2.59240	−	4.49016i	0.395337	−	0.684743i	−0.597807	−	0.801640i	$-0.703961\pi$
$43$	2.59240	−	4.49016i	0.395337	−	0.684743i	0.993144	+	0.116896i	$0.0372946\pi$
$44$	−1.09833			−0.165579
$45$		0			0
$46$	−3.96585			−0.584733
$47$	1.86824	−	3.23589i	0.272511	−	0.472003i	−0.696993	−	0.717078i	$-0.745479\pi$
$47$	1.86824	−	3.23589i	0.272511	−	0.472003i	0.969504	+	0.245075i	$0.0788126\pi$
$48$		0			0
$49$	0.592396	+	1.02606i	0.0846280	+	0.146580i
$50$	1.52822	+	2.64695i	0.216123	+	0.374336i
$51$		0			0
$52$	−0.298133	+	0.516382i	−0.0413437	+	0.0716093i
$53$	11.6382			1.59862			0.799312	−	0.600916i	$-0.205198\pi$
$53$	11.6382			1.59862			0.799312	+	0.600916i	$0.205198\pi$
$54$		0			0
$55$	9.82295			1.32453
$56$	3.54916	−	6.14733i	0.474277	−	0.821472i
$57$		0			0
$58$	0.869585	+	1.50617i	0.114182	+	0.197769i
$59$	3.67365	+	6.36295i	0.478268	+	0.828385i	0.999690	−	0.0249144i	$-0.00793133\pi$
$59$	3.67365	+	6.36295i	0.478268	+	0.828385i	−0.521421	+	0.853299i	$0.674598\pi$
$60$		0			0
$61$	−5.52481	+	9.56926i	−0.707380	+	1.22522i	0.258446	+	0.966026i	$0.416790\pi$
$61$	−5.52481	+	9.56926i	−0.707380	+	1.22522i	−0.965826	+	0.259192i	$0.916544\pi$
$62$	−0.792919			−0.100701
$63$		0			0
$64$	8.59627			1.07453
$65$	2.66637	−	4.61830i	0.330723	−	0.572829i
$66$		0			0
$67$	−0.928548	−	1.60829i	−0.113440	−	0.196484i	0.803715	−	0.595015i	$-0.202854\pi$
$67$	−0.928548	−	1.60829i	−0.113440	−	0.196484i	−0.917155	+	0.398530i	$0.869520\pi$
$68$	0.277189	+	0.480105i	0.0336141	+	0.0582213i
$69$		0			0
$70$	−2.68479	+	4.65020i	−0.320894	+	0.555805i
$71$	−5.51249			−0.654212			−0.327106	−	0.944988i	$-0.606073\pi$
$71$	−5.51249			−0.654212			−0.327106	+	0.944988i	$0.606073\pi$
$72$		0			0
$73$	5.55438			0.650091			0.325045	−	0.945698i	$-0.394620\pi$
$73$	5.55438			0.650091			0.325045	+	0.945698i	$0.394620\pi$
$74$	−0.0282185	+	0.0488759i	−0.00328033	+	0.00568170i
$75$		0			0
$76$	−0.613341	−	1.06234i	−0.0703550	−	0.121858i
$77$	−7.16637	−	12.4125i	−0.816684	−	1.41454i
$78$		0			0
$79$	1.89053	−	3.27449i	0.212701	−	0.368409i	−0.739858	−	0.672763i	$-0.765107\pi$
$79$	1.89053	−	3.27449i	0.212701	−	0.368409i	0.952559	+	0.304354i	$0.0984406\pi$
$80$	−5.94356			−0.664511
$81$		0			0
$82$	−6.60401			−0.729291
$83$	−1.99273	+	3.45150i	−0.218730	+	0.378852i	−0.954420	−	0.298467i	$-0.903525\pi$
$83$	−1.99273	+	3.45150i	−0.218730	+	0.378852i	0.735690	+	0.677319i	$0.236858\pi$
$84$		0			0
$85$	−2.47906	−	4.29385i	−0.268891	−	0.465733i
$86$	3.49273	+	6.04958i	0.376630	+	0.652343i
$87$		0			0
$88$	8.74763	−	15.1513i	0.932500	−	1.61514i
$89$	8.15064			0.863967			0.431983	−	0.901882i	$-0.357814\pi$
$89$	8.15064			0.863967			0.431983	+	0.901882i	$0.357814\pi$
$90$		0			0
$91$	−7.78106			−0.815677
$92$	−0.271974	+	0.471073i	−0.0283553	+	0.0491128i
$93$		0			0
$94$	2.51707	+	4.35970i	0.259616	+	0.449669i
$95$	5.48545	+	9.50108i	0.562796	+	0.974790i
$96$		0			0
$97$	−0.130415	+	0.225885i	−0.0132416	+	0.0229352i	−0.872570	−	0.488489i	$-0.837548\pi$
$97$	−0.130415	+	0.225885i	−0.0132416	+	0.0229352i	0.859329	+	0.511424i	$0.170882\pi$
$98$	−1.59627			−0.161247
$99$		0			0
$100$	0.419215			0.0419215
$101$	−5.51367	+	9.54996i	−0.548631	+	0.950256i	0.449738	+	0.893161i	$0.351517\pi$
$101$	−5.51367	+	9.54996i	−0.548631	+	0.950256i	−0.998369	+	0.0570958i	$0.981816\pi$
$102$		0			0
$103$	1.95336	+	3.38332i	0.192471	+	0.333369i	0.946068	−	0.323967i	$-0.105017\pi$
$103$	1.95336	+	3.38332i	0.192471	+	0.333369i	−0.753598	+	0.657336i	$0.771683\pi$
$104$	−4.74897	−	8.22546i	−0.465675	−	0.806573i
$105$		0			0
$106$	−7.84002	+	13.5793i	−0.761490	+	1.31894i
$107$	−2.63816			−0.255040			−0.127520	−	0.991836i	$-0.540702\pi$
$107$	−2.63816			−0.255040			−0.127520	+	0.991836i	$0.540702\pi$
$108$		0			0
$109$	−8.95811			−0.858031			−0.429016	−	0.903297i	$-0.641140\pi$
$109$	−8.95811			−0.858031			−0.429016	+	0.903297i	$0.641140\pi$
$110$	−6.61721	+	11.4613i	−0.630926	+	1.09280i
$111$		0			0
$112$	4.33615	+	7.51044i	0.409728	+	0.709669i
$113$	−7.96451	−	13.7949i	−0.749238	−	1.29772i	−0.948188	−	0.317708i	$-0.897087\pi$
$113$	−7.96451	−	13.7949i	−0.749238	−	1.29772i	0.198951	−	0.980010i	$-0.436247\pi$
$114$		0			0
$115$	2.43242	−	4.21307i	0.226824	−	0.392871i
$116$	0.238541			0.0221480
$117$		0			0
$118$	−9.89899			−0.911275
$119$	−3.61721	+	6.26519i	−0.331589	+	0.574329i
$120$		0			0
$121$	−12.1630	−	21.0669i	−1.10572	−	1.91517i
$122$	−7.44356	−	12.8926i	−0.673909	−	1.16724i
$123$		0			0
$124$	−0.0543776	+	0.0941848i	−0.00488325	+	0.00845804i
$125$	−12.0128			−1.07446
$126$		0			0
$127$	3.59627			0.319117			0.159559	−	0.987188i	$-0.448993\pi$
$127$	3.59627			0.319117			0.159559	+	0.987188i	$0.448993\pi$
$128$	−4.74897	+	8.22546i	−0.419754	+	0.727035i
$129$		0			0
$130$	3.59240	+	6.22221i	0.315074	+	0.545724i
$131$	8.85369	+	15.3350i	0.773551	+	1.33983i	0.935605	+	0.353047i	$0.114855\pi$
$131$	8.85369	+	15.3350i	0.773551	+	1.33983i	−0.162055	+	0.986782i	$0.551812\pi$
$132$		0			0
$133$	8.00387	−	13.8631i	0.694024	−	1.20208i
$134$	2.50206			0.216145
$135$		0			0
$136$	−8.83069			−0.757225
$137$	1.96451	−	3.40263i	0.167839	−	0.290706i	−0.769821	−	0.638260i	$-0.779654\pi$
$137$	1.96451	−	3.40263i	0.167839	−	0.290706i	0.937660	+	0.347554i	$0.112988\pi$
$138$		0			0
$139$	−5.98293	−	10.3627i	−0.507465	−	0.878955i	−0.999963	−	0.00864157i	$-0.997249\pi$
$139$	−5.98293	−	10.3627i	−0.507465	−	0.878955i	0.492498	−	0.870314i	$-0.336084\pi$
$140$	0.368241	+	0.637812i	0.0311220	+	0.0539049i
$141$		0			0
$142$	3.71348	−	6.43193i	0.311628	−	0.539756i
$143$	−19.1780			−1.60374
$144$		0			0
$145$	−2.13341			−0.177170
$146$	−3.74170	+	6.48081i	−0.309665	+	0.536356i
$147$		0			0
$148$	0.00387039	+	0.00670372i	0.000318144	+	0.000551042i
$149$	−10.2626	−	17.7754i	−0.840748	−	1.45622i	−0.889263	−	0.457396i	$-0.848782\pi$
$149$	−10.2626	−	17.7754i	−0.840748	−	1.45622i	0.0485147	−	0.998822i	$-0.484551\pi$
$150$		0			0
$151$	−8.00387	+	13.8631i	−0.651346	+	1.12816i	0.331451	+	0.943472i	$0.392462\pi$
$151$	−8.00387	+	13.8631i	−0.651346	+	1.12816i	−0.982797	+	0.184691i	$0.940871\pi$
$152$	19.5398			1.58489
$153$		0			0
$154$	19.3105			1.55608
$155$	0.486329	−	0.842347i	0.0390629	−	0.0676590i
$156$		0			0
$157$	10.9868	+	19.0297i	0.876842	+	1.51873i	0.854788	+	0.518978i	$0.173687\pi$
$157$	10.9868	+	19.0297i	0.876842	+	1.51873i	0.0220541	+	0.999757i	$0.492979\pi$
$158$	2.54710	+	4.41171i	0.202637	+	0.350977i
$159$		0			0
$160$	−0.860967	+	1.49124i	−0.0680654	+	0.117893i
$161$	−7.09833			−0.559426
$162$		0			0
$163$	20.5107			1.60652			0.803262	−	0.595625i	$-0.203096\pi$
$163$	20.5107			1.60652			0.803262	+	0.595625i	$0.203096\pi$
$164$	−0.452896	+	0.784440i	−0.0353653	+	0.0612544i
$165$		0			0
$166$	−2.68479	−	4.65020i	−0.208380	−	0.360925i
$167$	−2.14543	−	3.71599i	−0.166018	−	0.287552i	0.770998	−	0.636837i	$-0.219758\pi$
$167$	−2.14543	−	3.71599i	−0.166018	−	0.287552i	−0.937016	+	0.349285i	$0.886424\pi$
$168$		0			0
$169$	1.29426	−	2.24173i	0.0995587	−	0.172441i
$170$	6.68004			0.512336
$171$		0			0
$172$	0.958111			0.0730553
$173$	−1.89646	+	3.28476i	−0.144185	+	0.249736i	−0.929069	−	0.369907i	$-0.879389\pi$
$173$	−1.89646	+	3.28476i	−0.144185	+	0.249736i	0.784884	+	0.619643i	$0.212723\pi$
$174$		0			0
$175$	2.73530	+	4.73768i	0.206769	+	0.358135i
$176$	10.6873	+	18.5110i	0.805587	+	1.39532i
$177$		0			0
$178$	−5.49067	+	9.51011i	−0.411543	+	0.712813i
$179$	8.27631			0.618601			0.309300	−	0.950964i	$-0.399905\pi$
$179$	8.27631			0.618601			0.309300	+	0.950964i	$0.399905\pi$
$180$		0			0
$181$	6.72193			0.499637			0.249819	−	0.968293i	$-0.419629\pi$
$181$	6.72193			0.499637			0.249819	+	0.968293i	$0.419629\pi$
$182$	5.24170	−	9.07888i	0.388540	−	0.672972i
$183$		0			0
$184$	−4.33228	−	7.50373i	−0.319380	−	0.553182i
$185$	−0.0346151	−	0.0599551i	−0.00254495	−	0.00440799i
$186$		0			0
$187$	−8.91534	+	15.4418i	−0.651955	+	1.12922i
$188$	0.690474			0.0503580
$189$		0			0
$190$	−14.7811			−1.07233
$191$	2.50727	−	4.34273i	0.181420	−	0.314229i	−0.760944	−	0.648817i	$-0.775264\pi$
$191$	2.50727	−	4.34273i	0.181420	−	0.314229i	0.942364	+	0.334589i	$0.108597\pi$
$192$		0			0
$193$	8.93242	+	15.4714i	0.642970	+	1.11366i	0.984766	+	0.173882i	$0.0556312\pi$
$193$	8.93242	+	15.4714i	0.642970	+	1.11366i	−0.341797	+	0.939774i	$0.611035\pi$
$194$	−0.175708	−	0.304334i	−0.0126151	−	0.0218499i
$195$		0			0
$196$	−0.109470	+	0.189608i	−0.00781931	+	0.0135435i
$197$	0.723689			0.0515607			0.0257803	−	0.999668i	$-0.491793\pi$
$197$	0.723689			0.0515607			0.0257803	+	0.999668i	$0.491793\pi$
$198$		0			0
$199$	−10.1925			−0.722530			−0.361265	−	0.932463i	$-0.617655\pi$
$199$	−10.1925			−0.722530			−0.361265	+	0.932463i	$0.617655\pi$
$200$	−3.33884	+	5.78304i	−0.236092	+	0.408923i
$201$		0			0
$202$	−7.42855	−	12.8666i	−0.522671	−	0.905292i
$203$	1.55644	+	2.69583i	0.109240	+	0.189210i
$204$		0			0
$205$	4.05051	−	7.01568i	0.282900	−	0.489997i
$206$	−5.26352			−0.366727
$207$		0			0
$208$	11.6040			0.804593
$209$	19.7271	−	34.1684i	1.36456	−	2.36348i
$210$		0			0
$211$	7.43242	+	12.8733i	0.511669	+	0.886236i	0.999909	+	0.0135268i	$0.00430584\pi$
$211$	7.43242	+	12.8733i	0.511669	+	0.886236i	−0.488240	+	0.872710i	$0.662361\pi$
$212$	1.07532	+	1.86251i	0.0738534	+	0.127918i
$213$		0			0
$214$	1.77719	−	3.07818i	0.121486	−	0.210420i
$215$	−8.56893			−0.584396
$216$		0			0
$217$	−1.41921			−0.0963426
$218$	6.03462	−	10.4523i	0.408716	−	0.707916i
$219$		0			0
$220$	0.907604	+	1.57202i	0.0611906	+	0.105985i
$221$	4.84002	+	8.38316i	0.325575	+	0.563913i
$222$		0			0
$223$	5.47431	−	9.48178i	0.366587	−	0.634947i	−0.622443	−	0.782665i	$-0.713860\pi$
$223$	5.47431	−	9.48178i	0.366587	−	0.634947i	0.989029	+	0.147718i	$0.0471930\pi$
$224$	2.51249			0.167873
$225$		0			0
$226$	21.4611			1.42757
$227$	8.66637	−	15.0106i	0.575207	−	0.996289i	−0.420812	−	0.907148i	$-0.638255\pi$
$227$	8.66637	−	15.0106i	0.575207	−	0.996289i	0.996019	−	0.0891405i	$-0.0284120\pi$
$228$		0			0
$229$	−0.781059	−	1.35283i	−0.0516138	−	0.0893978i	0.839064	−	0.544032i	$-0.183103\pi$
$229$	−0.781059	−	1.35283i	−0.0516138	−	0.0893978i	−0.890678	+	0.454635i	$0.849770\pi$
$230$	3.27719	+	5.67626i	0.216091	+	0.374281i
$231$		0			0
$232$	−1.89986	+	3.29066i	−0.124732	+	0.216042i
$233$	16.7888			1.09987			0.549935	−	0.835207i	$-0.314652\pi$
$233$	16.7888			1.09987			0.549935	+	0.835207i	$0.314652\pi$
$234$		0			0
$235$	−6.17530			−0.402832
$236$	−0.678863	+	1.17582i	−0.0441902	+	0.0765397i
$237$		0			0
$238$	−4.87346	−	8.44107i	−0.315899	−	0.547153i
$239$	2.01455	+	3.48930i	0.130310	+	0.225704i	0.923796	−	0.382885i	$-0.125069\pi$
$239$	2.01455	+	3.48930i	0.130310	+	0.225704i	−0.793486	+	0.608589i	$0.791736\pi$
$240$		0			0
$241$	1.67617	−	2.90322i	0.107972	−	0.187013i	−0.806977	−	0.590583i	$-0.798898\pi$
$241$	1.67617	−	2.90322i	0.107972	−	0.187013i	0.914949	+	0.403571i	$0.132231\pi$
$242$	32.7743			2.10681
$243$		0			0
$244$	−2.04189			−0.130719
$245$	0.979055	−	1.69577i	0.0625496	−	0.108339i
$246$		0			0
$247$	−10.7096	−	18.5496i	−0.681436	−	1.18028i
$248$	−0.866181	−	1.50027i	−0.0550026	−	0.0952673i
$249$		0			0
$250$	8.09240	−	14.0164i	0.511808	−	0.886478i
$251$	−23.1506			−1.46126			−0.730628	−	0.682776i	$-0.760773\pi$
$251$	−23.1506			−1.46126			−0.730628	+	0.682776i	$0.760773\pi$
$252$		0			0
$253$	−17.4953			−1.09992
$254$	−2.42262	+	4.19610i	−0.152009	+	0.263287i
$255$		0			0
$256$	2.19800	+	3.80704i	0.137375	+	0.237940i
$257$	−6.00640	−	10.4034i	−0.374669	−	0.648945i	0.615609	−	0.788052i	$-0.288910\pi$
$257$	−6.00640	−	10.4034i	−0.374669	−	0.648945i	−0.990277	+	0.139107i	$0.955577\pi$
$258$		0			0
$259$	−0.0505072	+	0.0874810i	−0.00313836	+	0.00543581i
$260$	0.985452			0.0611151
$261$		0			0
$262$	−23.8571			−1.47390
$263$	−8.45084	+	14.6373i	−0.521101	+	0.902573i	0.478598	+	0.878034i	$0.341145\pi$
$263$	−8.45084	+	14.6373i	−0.521101	+	0.902573i	−0.999699	+	0.0245391i	$0.992188\pi$
$264$		0			0
$265$	−9.61721	−	16.6575i	−0.590781	−	1.02326i
$266$	10.7836	+	18.6777i	0.661184	+	1.14520i
$267$		0			0
$268$	0.171589	−	0.297200i	0.0104815	−	0.0181544i
$269$	−7.91447			−0.482554			−0.241277	−	0.970456i	$-0.577566\pi$
$269$	−7.91447			−0.482554			−0.241277	+	0.970456i	$0.577566\pi$
$270$		0			0
$271$	−17.2344			−1.04692			−0.523458	−	0.852051i	$-0.675358\pi$
$271$	−17.2344			−1.04692			−0.523458	+	0.852051i	$0.675358\pi$
$272$	5.39440	−	9.34337i	0.327084	−	0.566525i
$273$		0			0
$274$	2.64677	+	4.58435i	0.159897	+	0.276951i
$275$	6.74170	+	11.6770i	0.406540	+	0.704147i
$276$		0			0
$277$	−13.2173	+	22.8931i	−0.794153	+	1.37551i	0.129222	+	0.991616i	$0.458752\pi$
$277$	−13.2173	+	22.8931i	−0.794153	+	1.37551i	−0.923375	+	0.383898i	$0.874581\pi$
$278$	16.1215			0.966906
$279$		0			0
$280$	−11.7314			−0.701087
$281$	9.49794	−	16.4509i	0.566600	−	0.981379i	−0.430299	−	0.902686i	$-0.641592\pi$
$281$	9.49794	−	16.4509i	0.566600	−	0.981379i	0.996899	−	0.0786931i	$-0.0250747\pi$
$282$		0			0
$283$	8.29339	+	14.3646i	0.492991	+	0.853885i	0.999967	−	0.00807493i	$-0.00257036\pi$
$283$	8.29339	+	14.3646i	0.492991	+	0.853885i	−0.506977	+	0.861960i	$0.669237\pi$
$284$	−0.509333	−	0.882191i	−0.0302234	−	0.0523484i
$285$		0			0
$286$	12.9192	−	22.3767i	0.763929	−	1.32316i
$287$	−11.8203			−0.697728
$288$		0			0
$289$	−8.00000			−0.470588
$290$	1.43717	−	2.48925i	0.0843933	−	0.146174i
$291$		0			0
$292$	0.513204	+	0.888895i	0.0300330	+	0.0520186i
$293$	−9.67886	−	16.7643i	−0.565445	−	0.979380i	−0.997008	−	0.0772970i	$-0.975371\pi$
$293$	−9.67886	−	16.7643i	−0.565445	−	0.979380i	0.431563	−	0.902083i	$-0.357962\pi$
$294$		0			0
$295$	6.07145	−	10.5161i	0.353494	−	0.612269i
$296$	−0.123303			−0.00716685
$297$		0			0
$298$	27.6536			1.60193
$299$	−4.74897	+	8.22546i	−0.274640	+	0.475691i
$300$		0			0
$301$	6.25150	+	10.8279i	0.360330	+	0.624110i
$302$	−10.7836	−	18.6777i	−0.620526	−	1.07478i
$303$		0			0
$304$	−11.9363	+	20.6743i	−0.684593	+	1.18575i
$305$	18.2618			1.04567
$306$		0			0
$307$	20.8057			1.18744			0.593722	−	0.804670i	$-0.297658\pi$
$307$	20.8057			1.18744			0.593722	+	0.804670i	$0.297658\pi$
$308$	1.32429	−	2.29374i	0.0754586	−	0.130698i
$309$		0			0
$310$	0.655230	+	1.13489i	0.0372146	+	0.0644575i
$311$	5.33275	+	9.23659i	0.302392	+	0.523759i	0.976677	−	0.214712i	$-0.0688814\pi$
$311$	5.33275	+	9.23659i	0.302392	+	0.523759i	−0.674285	+	0.738471i	$0.735548\pi$
$312$		0			0
$313$	−1.90760	+	3.30407i	−0.107824	+	0.186757i	−0.914889	−	0.403707i	$-0.867722\pi$
$313$	−1.90760	+	3.30407i	−0.107824	+	0.186757i	0.807064	+	0.590463i	$0.201055\pi$
$314$	−29.6049			−1.67070
$315$		0			0
$316$	0.698711			0.0393056
$317$	−13.1946	+	22.8537i	−0.741082	+	1.28359i	0.210921	+	0.977503i	$0.432354\pi$
$317$	−13.1946	+	22.8537i	−0.741082	+	1.28359i	−0.952003	+	0.306089i	$0.900980\pi$
$318$		0			0
$319$	3.83615	+	6.64441i	0.214783	+	0.372016i
$320$	−7.10354	−	12.3037i	−0.397100	−	0.687797i
$321$		0			0
$322$	4.78177	−	8.28228i	0.266478	−	0.461553i
$323$	−19.9145			−1.10807
$324$		0			0
$325$	7.31996			0.406038
$326$	−13.8170	+	23.9318i	−0.765254	+	1.32546i
$327$		0			0
$328$	−7.21419	−	12.4953i	−0.398337	−	0.689940i
$329$	4.50521	+	7.80326i	0.248381	+	0.430208i
$330$		0			0
$331$	0.785807	−	1.36106i	0.0431919	−	0.0748105i	−0.843621	−	0.536939i	$-0.819581\pi$
$331$	0.785807	−	1.36106i	0.0431919	−	0.0748105i	0.886813	+	0.462128i	$0.152914\pi$
$332$	−0.736482			−0.0404197
$333$		0			0
$334$	5.78106			0.316325
$335$	−1.53462	+	2.65803i	−0.0838450	+	0.145224i
$336$		0			0
$337$	4.00774	+	6.94161i	0.218316	+	0.378134i	0.954293	−	0.298872i	$-0.0966105\pi$
$337$	4.00774	+	6.94161i	0.218316	+	0.378134i	−0.735978	+	0.677006i	$0.763277\pi$
$338$	1.74376	+	3.02027i	0.0948478	+	0.164281i
$339$		0			0
$340$	0.458111	−	0.793471i	0.0248446	−	0.0430320i
$341$	−3.49794			−0.189424
$342$		0			0
$343$	−19.7374			−1.06572
$344$	−7.63088	+	13.2171i	−0.411430	+	0.712617i
$345$		0			0
$346$	−2.55509	−	4.42555i	−0.137363	−	0.237919i
$347$	−9.92262	−	17.1865i	−0.532674	−	0.922619i	−0.999272	−	0.0381490i	$-0.987854\pi$
$347$	−9.92262	−	17.1865i	−0.532674	−	0.922619i	0.466598	−	0.884470i	$-0.345479\pi$
$348$		0			0
$349$	−5.54664	+	9.60706i	−0.296905	+	0.514254i	−0.975426	−	0.220327i	$-0.929288\pi$
$349$	−5.54664	+	9.60706i	−0.296905	+	0.514254i	0.678522	+	0.734581i	$0.262621\pi$
$350$	−7.37052			−0.393971
$351$		0			0
$352$	6.19253			0.330063
$353$	1.43195	−	2.48021i	0.0762151	−	0.132008i	−0.825399	−	0.564550i	$-0.809050\pi$
$353$	1.43195	−	2.48021i	0.0762151	−	0.132008i	0.901614	+	0.432541i	$0.142383\pi$
$354$		0			0
$355$	4.55525	+	7.88993i	0.241768	+	0.418754i
$356$	0.753089	+	1.30439i	0.0399136	+	0.0691325i
$357$		0			0
$358$	−5.57532	+	9.65674i	−0.294665	+	0.510375i
$359$	28.7888			1.51941			0.759707	−	0.650265i	$-0.225342\pi$
$359$	28.7888			1.51941			0.759707	+	0.650265i	$0.225342\pi$
$360$		0			0
$361$	25.0651			1.31922
$362$	−4.52822	+	7.84310i	−0.237998	+	0.412224i
$363$		0			0
$364$	−0.718941	−	1.24524i	−0.0376827	−	0.0652684i
$365$	−4.58987	−	7.94989i	−0.240245	−	0.416116i
$366$		0			0
$367$	5.49613	−	9.51958i	0.286896	−	0.496918i	−0.686171	−	0.727440i	$-0.740710\pi$
$367$	5.49613	−	9.51958i	0.286896	−	0.496918i	0.973067	+	0.230522i	$0.0740434\pi$
$368$	10.5858			0.551825
$369$		0			0
$370$	0.0932736			0.00484906
$371$	−14.0326	+	24.3051i	−0.728534	+	1.26186i
$372$		0			0
$373$	−16.7049	−	28.9337i	−0.864945	−	1.49813i	−0.867102	−	0.498131i	$-0.834020\pi$
$373$	−16.7049	−	28.9337i	−0.864945	−	1.49813i	0.00215708	−	0.999998i	$-0.499313\pi$
$374$	−12.0116	−	20.8047i	−0.621106	−	1.07579i
$375$		0			0
$376$	−5.49928	+	9.52504i	−0.283604	+	0.491216i
$377$	4.16519			0.214518
$378$		0			0
$379$	20.9394			1.07559			0.537794	−	0.843077i	$-0.319258\pi$
$379$	20.9394			1.07559			0.537794	+	0.843077i	$0.319258\pi$
$380$	−1.01367	+	1.75573i	−0.0520002	+	0.0900670i
$381$		0			0
$382$	3.37804	+	5.85094i	0.172836	+	0.299360i
$383$	2.05556	+	3.56033i	0.105034	+	0.181925i	0.913752	−	0.406272i	$-0.133171\pi$
$383$	2.05556	+	3.56033i	0.105034	+	0.181925i	−0.808718	+	0.588197i	$0.799838\pi$
$384$		0			0
$385$	−11.8439	+	20.5142i	−0.603621	+	1.04550i
$386$	−24.0692			−1.22509
$387$		0			0
$388$	−0.0481994			−0.00244695
$389$	−8.54710	+	14.8040i	−0.433355	+	0.750593i	−0.997160	−	0.0753148i	$-0.976004\pi$
$389$	−8.54710	+	14.8040i	−0.433355	+	0.750593i	0.563804	+	0.825908i	$0.309337\pi$
$390$		0			0
$391$	4.41534	+	7.64760i	0.223294	+	0.386756i
$392$	−1.74376	−	3.02027i	−0.0880730	−	0.152547i
$393$		0			0
$394$	−0.487511	+	0.844395i	−0.0245605	+	0.0425400i
$395$	−6.24897			−0.314420
$396$		0			0
$397$	22.4020			1.12432			0.562162	−	0.827027i	$-0.309970\pi$
$397$	22.4020			1.12432			0.562162	+	0.827027i	$0.309970\pi$
$398$	6.86618	−	11.8926i	0.344171	−	0.596121i
$399$		0			0
$400$	−4.07919	−	7.06537i	−0.203960	−	0.353268i
$401$	7.29086	+	12.6281i	0.364088	+	0.630619i	0.988629	−	0.150373i	$-0.0480474\pi$
$401$	7.29086	+	12.6281i	0.364088	+	0.630619i	−0.624541	+	0.780992i	$0.714714\pi$
$402$		0			0
$403$	−0.949493	+	1.64457i	−0.0472976	+	0.0819219i
$404$	−2.03777			−0.101383
$405$		0			0
$406$	−4.19396			−0.208143
$407$	−0.124485	+	0.215615i	−0.00617050	+	0.0106876i
$408$		0			0
$409$	8.75150	+	15.1580i	0.432734	+	0.749517i	0.997108	−	0.0760026i	$-0.0242157\pi$
$409$	8.75150	+	15.1580i	0.432734	+	0.749517i	−0.564374	+	0.825519i	$0.690882\pi$
$410$	5.45723	+	9.45221i	0.269514	+	0.466811i
$411$		0			0
$412$	−0.360967	+	0.625213i	−0.0177836	+	0.0308020i
$413$	−17.7178			−0.871837
$414$		0			0
$415$	6.58677			0.323332
$416$	1.68092	−	2.91144i	0.0824140	−	0.142745i
$417$		0			0
$418$	26.5783	+	46.0350i	1.29999	+	2.25165i
$419$	−9.43107	−	16.3351i	−0.460738	−	0.798022i	0.538260	−	0.842779i	$-0.319082\pi$
$419$	−9.43107	−	16.3351i	−0.460738	−	0.798022i	−0.998998	+	0.0447571i	$0.985749\pi$
$420$		0			0
$421$	16.1668	−	28.0018i	0.787924	−	1.36472i	−0.139313	−	0.990248i	$-0.544489\pi$
$421$	16.1668	−	28.0018i	0.787924	−	1.36472i	0.927237	−	0.374475i	$-0.122177\pi$
$422$	−20.0273			−0.974916
$423$		0			0
$424$	−34.2576			−1.66370
$425$	3.40286	−	5.89392i	0.165063	−	0.285897i
$426$		0			0
$427$	−13.3229	−	23.0760i	−0.644743	−	1.11673i
$428$	−0.243756	−	0.422197i	−0.0117824	−	0.0204077i
$429$		0			0
$430$	5.77244	−	9.99816i	0.278372	−	0.482154i
$431$	34.3164			1.65297			0.826483	−	0.562962i	$-0.190338\pi$
$431$	34.3164			1.65297			0.826483	+	0.562962i	$0.190338\pi$
$432$		0			0
$433$	−25.0669			−1.20464			−0.602318	−	0.798256i	$-0.705756\pi$
$433$	−25.0669			−1.20464			−0.602318	+	0.798256i	$0.705756\pi$
$434$	0.956052	−	1.65593i	0.0458919	−	0.0794872i
$435$		0			0
$436$	−0.827696	−	1.43361i	−0.0396394	−	0.0686575i
$437$	−9.76991	−	16.9220i	−0.467358	−	0.809489i
$438$		0			0
$439$	11.6040	−	20.0987i	0.553829	−	0.959260i	−0.444165	−	0.895945i	$-0.646499\pi$
$439$	11.6040	−	20.0987i	0.553829	−	0.959260i	0.997994	−	0.0633148i	$-0.0201672\pi$
$440$	−28.9145			−1.37844
$441$		0			0
$442$	−13.0419			−0.620339
$443$	2.06077	−	3.56937i	0.0979103	−	0.169586i	−0.812909	−	0.582390i	$-0.802117\pi$
$443$	2.06077	−	3.56937i	0.0979103	−	0.169586i	0.910820	+	0.412805i	$0.135451\pi$
$444$		0			0
$445$	−6.73530	−	11.6659i	−0.319284	−	0.553016i
$446$	7.37551	+	12.7748i	0.349241	+	0.604903i
$447$		0			0
$448$	−10.3648	+	17.9524i	−0.489693	+	0.848172i
$449$	18.3414			0.865585			0.432793	−	0.901494i	$-0.357528\pi$
$449$	18.3414			0.865585			0.432793	+	0.901494i	$0.357528\pi$
$450$		0			0
$451$	−29.1334			−1.37184
$452$	1.47178	−	2.54920i	0.0692268	−	0.119904i
$453$		0			0
$454$	11.6762	+	20.2237i	0.547990	+	0.949147i
$455$	6.42989	+	11.1369i	0.301438	+	0.522106i
$456$		0			0
$457$	9.73055	−	16.8538i	0.455176	−	0.788388i	−0.543522	−	0.839395i	$-0.682910\pi$
$457$	9.73055	−	16.8538i	0.455176	−	0.788388i	0.998698	+	0.0510067i	$0.0162430\pi$
$458$	2.10464			0.0983432
$459$		0			0
$460$	0.898986			0.0419154
$461$	−13.8746	+	24.0316i	−0.646206	+	1.11926i	0.337815	+	0.941212i	$0.390312\pi$
$461$	−13.8746	+	24.0316i	−0.646206	+	1.11926i	−0.984022	+	0.178050i	$0.943021\pi$
$462$		0			0
$463$	−19.3430	−	33.5031i	−0.898946	−	1.55702i	−0.828843	−	0.559481i	$-0.811001\pi$
$463$	−19.3430	−	33.5031i	−0.898946	−	1.55702i	−0.0701028	−	0.997540i	$-0.522333\pi$
$464$	−2.32114	−	4.02033i	−0.107756	−	0.186639i
$465$		0			0
$466$	−11.3097	+	19.5891i	−0.523914	+	0.907445i
$467$	29.7638			1.37731			0.688653	−	0.725091i	$-0.258202\pi$
$467$	29.7638			1.37731			0.688653	+	0.725091i	$0.258202\pi$
$468$		0			0
$469$	4.47834			0.206791
$470$	4.15998	−	7.20529i	0.191885	−	0.332355i
$471$		0			0
$472$	−10.8136	−	18.7297i	−0.497737	−	0.862106i
$473$	15.4081	+	26.6876i	0.708464	+	1.22710i
$474$		0			0
$475$	−7.52956	+	13.0416i	−0.345480	+	0.598389i
$476$	−1.33687			−0.0612752
$477$		0			0
$478$	−5.42839			−0.248289
$479$	18.8380	−	32.6283i	0.860728	−	1.49083i	−0.0104984	−	0.999945i	$-0.503342\pi$
$479$	18.8380	−	32.6283i	0.860728	−	1.49083i	0.871227	−	0.490881i	$-0.163325\pi$
$480$		0			0
$481$	0.0675813	+	0.117054i	0.00308144	+	0.00533722i
$482$	2.25830	+	3.91150i	0.102863	+	0.178164i
$483$		0			0
$484$	2.24763	−	3.89300i	0.102165	−	0.176955i
$485$	0.431074			0.0195741
$486$		0			0
$487$	−0.763823			−0.0346121			−0.0173061	−	0.999850i	$-0.505509\pi$
$487$	−0.763823			−0.0346121			−0.0173061	+	0.999850i	$0.505509\pi$
$488$	16.2626	−	28.1677i	0.736175	−	1.27509i
$489$		0			0
$490$	1.31908	+	2.28471i	0.0595899	+	0.103213i
$491$	0.248970	+	0.431229i	0.0112359	+	0.0194611i	0.871589	−	0.490238i	$-0.163090\pi$
$491$	0.248970	+	0.431229i	0.0112359	+	0.0194611i	−0.860353	+	0.509699i	$0.829757\pi$
$492$		0			0
$493$	1.93629	−	3.35375i	0.0872061	−	0.151045i
$494$	28.8580			1.29838
$495$		0			0
$496$	2.11650			0.0950335
$497$	6.64661	−	11.5123i	0.298141	−	0.516396i
$498$		0			0
$499$	−4.48293	−	7.76466i	−0.200683	−	0.347594i	0.748065	−	0.663625i	$-0.230983\pi$
$499$	−4.48293	−	7.76466i	−0.200683	−	0.347594i	−0.948749	+	0.316031i	$0.897650\pi$
$500$	−1.10994	−	1.92247i	−0.0496379	−	0.0859754i
$501$		0			0
$502$	15.5954	−	27.0120i	0.696056	−	1.20560i
$503$	18.3618			0.818714			0.409357	−	0.912374i	$-0.365753\pi$
$503$	18.3618			0.818714			0.409357	+	0.912374i	$0.365753\pi$
$504$		0			0
$505$	18.2249			0.810999
$506$	11.7856	−	20.4133i	0.523936	−	0.907483i
$507$		0			0
$508$	0.332282	+	0.575529i	0.0147426	+	0.0255350i
$509$	14.1853	+	24.5696i	0.628751	+	1.08903i	0.987803	+	0.155710i	$0.0497667\pi$
$509$	14.1853	+	24.5696i	0.628751	+	1.08903i	−0.359052	+	0.933317i	$0.616900\pi$
$510$		0			0
$511$	−6.69712	+	11.5998i	−0.296263	+	0.513143i
$512$	−24.9186			−1.10126
$513$		0			0
$514$	16.1848			0.713881
$515$	3.22833	−	5.59163i	0.142257	−	0.246397i
$516$		0			0
$517$	11.1040	+	19.2327i	0.488354	+	0.845853i
$518$	−0.0680482	−	0.117863i	−0.00298986	−	0.00517860i
$519$		0			0
$520$	−7.84864	+	13.5942i	−0.344186	+	0.596147i
$521$	−32.6382			−1.42990			−0.714952	−	0.699174i	$-0.753551\pi$
$521$	−32.6382			−1.42990			−0.714952	+	0.699174i	$0.753551\pi$
$522$		0			0
$523$	−22.0232			−0.963008			−0.481504	−	0.876444i	$-0.659909\pi$
$523$	−22.0232			−0.963008			−0.481504	+	0.876444i	$0.659909\pi$
$524$	−1.63610	+	2.83380i	−0.0714732	+	0.123795i
$525$		0			0
$526$	−11.3858	−	19.7208i	−0.496444	−	0.859866i
$527$	0.882789	+	1.52904i	0.0384549	+	0.0666058i
$528$		0			0
$529$	7.16772	−	12.4149i	0.311640	−	0.539776i
$530$	25.9145			1.12565
$531$		0			0
$532$	2.95811			0.128250
$533$	−7.90807	+	13.6972i	−0.342537	+	0.593291i
$534$		0			0
$535$	2.18004	+	3.77595i	0.0942516	+	0.163248i
$536$	2.73324	+	4.73411i	0.118058	+	0.204482i
$537$		0			0
$538$	5.33157	−	9.23454i	0.229860	−	0.398129i
$539$	−7.04189			−0.303316
$540$		0			0
$541$	−15.7870			−0.678738			−0.339369	−	0.940653i	$-0.610214\pi$
$541$	−15.7870			−0.678738			−0.339369	+	0.940653i	$0.610214\pi$
$542$	11.6099	−	20.1090i	0.498690	−	0.863756i
$543$		0			0
$544$	−1.56283	−	2.70691i	−0.0670059	−	0.116058i
$545$	7.40255	+	12.8216i	0.317090	+	0.549217i
$546$		0			0
$547$	13.7096	−	23.7457i	0.586180	−	1.01529i	−0.408547	−	0.912737i	$-0.633964\pi$
$547$	13.7096	−	23.7457i	0.586180	−	1.01529i	0.994727	−	0.102557i	$-0.0327024\pi$
$548$	0.726053			0.0310154
$549$		0			0
$550$	−18.1661			−0.774606
$551$	−4.28446	+	7.42091i	−0.182524	+	0.316141i
$552$		0			0
$553$	4.55896	+	7.89636i	0.193867	+	0.335787i
$554$	−17.8077	−	30.8438i	−0.756576	−	1.31043i
$555$		0			0
$556$	1.10560	−	1.91496i	0.0468879	−	0.0812122i
$557$	29.4020			1.24580			0.622901	−	0.782301i	$-0.285954\pi$
$557$	29.4020			1.24580			0.622901	+	0.782301i	$0.285954\pi$
$558$		0			0
$559$	16.7297			0.707590
$560$	7.16637	−	12.4125i	0.302835	−	0.524525i
$561$		0			0
$562$	12.7965	+	22.1643i	0.539789	+	0.934943i
$563$	5.18526	+	8.98113i	0.218533	+	0.378510i	0.954360	−	0.298660i	$-0.0965397\pi$
$563$	5.18526	+	8.98113i	0.218533	+	0.378510i	−0.735827	+	0.677170i	$0.763206\pi$
$564$		0			0
$565$	−13.1630	+	22.7989i	−0.553770	+	0.959158i
$566$	−22.3473			−0.939327
$567$		0			0
$568$	16.2264			0.680843
$569$	16.4846	−	28.5521i	0.691069	−	1.19697i	−0.280419	−	0.959878i	$-0.590473\pi$
$569$	16.4846	−	28.5521i	0.691069	−	1.19697i	0.971488	−	0.237089i	$-0.0761934\pi$
$570$		0			0
$571$	0.368708	+	0.638620i	0.0154299	+	0.0267254i	0.873637	−	0.486578i	$-0.161755\pi$
$571$	0.368708	+	0.638620i	0.0154299	+	0.0267254i	−0.858207	+	0.513303i	$0.828422\pi$
$572$	−1.77197	−	3.06915i	−0.0740900	−	0.128328i
$573$		0			0
$574$	7.96270	−	13.7918i	0.332357	−	0.575658i
$575$	6.67768			0.278479
$576$		0			0
$577$	19.3432			0.805267			0.402634	−	0.915361i	$-0.368095\pi$
$577$	19.3432			0.805267			0.402634	+	0.915361i	$0.368095\pi$
$578$	5.38919	−	9.33434i	0.224161	−	0.388257i
$579$		0			0
$580$	−0.197119	−	0.341420i	−0.00818492	−	0.0141767i
$581$	−4.80541	−	8.32321i	−0.199362	−	0.345305i
$582$		0			0
$583$	−34.5861	+	59.9048i	−1.43241	+	2.48100i
$584$	−16.3497			−0.676554
$585$		0			0
$586$	26.0806			1.07738
$587$	15.9561	−	27.6367i	0.658577	−	1.14069i	−0.322408	−	0.946601i	$-0.604492\pi$
$587$	15.9561	−	27.6367i	0.658577	−	1.14069i	0.980984	−	0.194087i	$-0.0621745\pi$
$588$		0			0
$589$	−1.95336	−	3.38332i	−0.0804869	−	0.139407i
$590$	8.18004	+	14.1683i	0.336767	+	0.583298i
$591$		0			0
$592$	0.0753221	−	0.130462i	0.00309572	−	0.00536194i
$593$	31.6783			1.30087			0.650436	−	0.759561i	$-0.274586\pi$
$593$	31.6783			1.30087			0.650436	+	0.759561i	$0.274586\pi$
$594$		0			0
$595$	11.9564			0.490163
$596$	1.89646	−	3.28476i	0.0776820	−	0.134549i
$597$		0			0
$598$	−6.39827	−	11.0821i	−0.261645	−	0.453182i
$599$	6.31180	+	10.9324i	0.257893	+	0.446684i	0.965677	−	0.259745i	$-0.0836384\pi$
$599$	6.31180	+	10.9324i	0.257893	+	0.446684i	−0.707784	+	0.706429i	$0.750305\pi$
$600$		0			0
$601$	4.45424	−	7.71497i	0.181692	−	0.314700i	−0.760765	−	0.649028i	$-0.775176\pi$
$601$	4.45424	−	7.71497i	0.181692	−	0.314700i	0.942457	+	0.334328i	$0.108509\pi$
$602$	−16.8452			−0.686561
$603$		0			0
$604$	−2.95811			−0.120364
$605$	−20.1018	+	34.8173i	−0.817254	+	1.41553i
$606$		0			0
$607$	16.5621	+	28.6864i	0.672236	+	1.16435i	0.977269	+	0.212005i	$0.0679992\pi$
$607$	16.5621	+	28.6864i	0.672236	+	1.16435i	−0.305033	+	0.952342i	$0.598668\pi$
$608$	3.45811	+	5.98962i	0.140245	+	0.242911i
$609$		0			0
$610$	−12.3020	+	21.3077i	−0.498094	+	0.862723i
$611$	12.0564			0.487751
$612$		0			0
$613$	17.6800			0.714090			0.357045	−	0.934087i	$-0.383784\pi$
$613$	17.6800			0.714090			0.357045	+	0.934087i	$0.383784\pi$
$614$	−14.0157	+	24.2760i	−0.565629	+	0.979698i
$615$		0			0
$616$	21.0947	+	36.5370i	0.849929	+	1.47212i
$617$	12.8662	+	22.2849i	0.517973	+	0.897155i	0.999782	+	0.0208793i	$0.00664655\pi$
$617$	12.8662	+	22.2849i	0.517973	+	0.897155i	−0.481809	+	0.876276i	$0.660020\pi$
$618$		0			0
$619$	−13.8974	+	24.0710i	−0.558583	+	0.967495i	0.439032	+	0.898472i	$0.355322\pi$
$619$	−13.8974	+	24.0710i	−0.558583	+	0.967495i	−0.997615	+	0.0690232i	$0.978012\pi$
$620$	0.179740			0.00721854
$621$		0			0
$622$	−14.3696			−0.576168
$623$	−9.82753	+	17.0218i	−0.393732	+	0.681964i
$624$		0			0
$625$	4.25537	+	7.37051i	0.170215	+	0.294820i
$626$	−2.57011	−	4.45156i	−0.102722	−	0.177920i
$627$		0			0
$628$	−2.03028	+	3.51654i	−0.0810169	+	0.140325i
$629$	0.125667			0.00501068
$630$		0			0
$631$	26.8138			1.06744			0.533720	−	0.845661i	$-0.320794\pi$
$631$	26.8138			1.06744			0.533720	+	0.845661i	$0.320794\pi$
$632$	−5.56489	+	9.63868i	−0.221360	+	0.383406i
$633$		0			0
$634$	−17.7770	−	30.7907i	−0.706016	−	1.22286i
$635$	−2.97178	−	5.14728i	−0.117932	−	0.204263i
$636$		0			0
$637$	−1.91147	+	3.31077i	−0.0757354	+	0.131177i
$638$	−10.3369			−0.409240
$639$		0			0
$640$	15.6973			0.620490
$641$	−6.34524	+	10.9903i	−0.250622	+	0.434090i	−0.963697	−	0.266998i	$-0.913968\pi$
$641$	−6.34524	+	10.9903i	−0.250622	+	0.434090i	0.713075	+	0.701087i	$0.247302\pi$
$642$		0			0
$643$	−7.73829	−	13.4031i	−0.305168	−	0.528567i	0.672130	−	0.740433i	$-0.265379\pi$
$643$	−7.73829	−	13.4031i	−0.305168	−	0.528567i	−0.977299	+	0.211866i	$0.932046\pi$
$644$	−0.655859	−	1.13598i	−0.0258445	−	0.0447639i
$645$		0			0
$646$	13.4153	−	23.2361i	0.527820	−	0.914210i
$647$	11.1506			0.438377			0.219189	−	0.975683i	$-0.429659\pi$
$647$	11.1506			0.438377			0.219189	+	0.975683i	$0.429659\pi$
$648$		0			0
$649$	−43.6691			−1.71416
$650$	−4.93107	+	8.54087i	−0.193413	+	0.335001i
$651$		0			0
$652$	1.89512	+	3.28244i	0.0742184	+	0.128550i
$653$	−22.2961	−	38.6179i	−0.872513	−	1.51124i	−0.859389	−	0.511323i	$-0.829156\pi$
$653$	−22.2961	−	38.6179i	−0.872513	−	1.51124i	−0.0131240	−	0.999914i	$-0.504178\pi$
$654$		0			0
$655$	14.6325	−	25.3443i	0.571740	−	0.990283i
$656$	17.6277			0.688247
$657$		0			0
$658$	−12.1397			−0.473255
$659$	7.04829	−	12.2080i	0.274562	−	0.475556i	−0.695462	−	0.718563i	$-0.744800\pi$
$659$	7.04829	−	12.2080i	0.274562	−	0.475556i	0.970025	+	0.243007i	$0.0781337\pi$
$660$		0			0
$661$	−18.0574	−	31.2763i	−0.702350	−	1.21651i	−0.967639	−	0.252337i	$-0.918801\pi$
$661$	−18.0574	−	31.2763i	−0.702350	−	1.21651i	0.265289	−	0.964169i	$-0.414533\pi$
$662$	1.05871	+	1.83375i	0.0411481	+	0.0712706i
$663$		0			0
$664$	5.86571	−	10.1597i	0.227634	−	0.394273i
$665$	−26.4561			−1.02592
$666$		0			0
$667$	3.79973			0.147126
$668$	0.396459	−	0.686688i	0.0153395	−	0.0265687i
$669$		0			0
$670$	−2.06758	−	3.58116i	−0.0798776	−	0.138352i
$671$	−32.8371	−	56.8755i	−1.26766	−	2.19565i
$672$		0			0
$673$	−1.12108	+	1.94177i	−0.0432145	+	0.0748497i	−0.886824	−	0.462108i	$-0.847093\pi$
$673$	−1.12108	+	1.94177i	−0.0432145	+	0.0748497i	0.843609	+	0.536958i	$0.180427\pi$
$674$	−10.7992			−0.415971
$675$		0			0
$676$	0.478340			0.0183977
$677$	−17.5881	+	30.4635i	−0.675966	+	1.17081i	0.300219	+	0.953870i	$0.402940\pi$
$677$	−17.5881	+	30.4635i	−0.675966	+	1.17081i	−0.976185	+	0.216938i	$0.930393\pi$
$678$		0			0
$679$	−0.314492	−	0.544717i	−0.0120691	−	0.0209043i
$680$	7.29726	+	12.6392i	0.279837	+	0.484692i
$681$		0			0
$682$	2.35638	−	4.08137i	0.0902305	−	0.156284i
$683$	−17.7638			−0.679714			−0.339857	−	0.940477i	$-0.610379\pi$
$683$	−17.7638			−0.679714			−0.339857	+	0.940477i	$0.610379\pi$
$684$		0			0
$685$	−6.49350			−0.248104
$686$	13.2961	−	23.0295i	0.507646	−	0.879269i
$687$		0			0
$688$	−9.32295	−	16.1478i	−0.355434	−	0.615630i
$689$	18.7763	+	32.5215i	0.715320	+	1.23897i
$690$		0			0
$691$	22.0153	−	38.1317i	0.837502	−	1.45060i	−0.0544745	−	0.998515i	$-0.517348\pi$
$691$	22.0153	−	38.1317i	0.837502	−	1.45060i	0.891977	−	0.452081i	$-0.149318\pi$
$692$	−0.700903			−0.0266443
$693$		0			0
$694$	26.7374			1.01494
$695$	−9.88800	+	17.1265i	−0.375073	+	0.649646i
$696$		0			0
$697$	7.35251	+	12.7349i	0.278496	+	0.482370i
$698$	−7.47296	−	12.9436i	−0.282856	−	0.489921i
$699$		0			0
$700$	−0.505463	+	0.875488i	−0.0191047	+	0.0330903i
$701$	−30.1052			−1.13706			−0.568530	−	0.822663i	$-0.692488\pi$
$701$	−30.1052			−1.13706			−0.568530	+	0.822663i	$0.692488\pi$
$702$		0			0
$703$	−0.278066			−0.0104875
$704$	−25.5462	+	44.2474i	−0.962810	+	1.66764i
$705$		0			0
$706$	1.92926	+	3.34158i	0.0726088	+	0.125762i
$707$	−13.2961	−	23.0295i	−0.500050	−	0.866113i
$708$		0			0
$709$	12.3687	−	21.4232i	0.464517	−	0.804566i	−0.534663	−	0.845065i	$-0.679561\pi$
$709$	12.3687	−	21.4232i	0.464517	−	0.804566i	0.999180	+	0.0404991i	$0.0128948\pi$
$710$	−12.2746			−0.460656
$711$		0			0
$712$	−23.9919			−0.899136
$713$	−0.866181	+	1.50027i	−0.0324388	+	0.0561856i
$714$		0			0
$715$	15.8478	+	27.4491i	0.592673	+	1.02654i
$716$	0.764700	+	1.32450i	0.0285782	+	0.0494989i
$717$		0			0
$718$	−19.3935	+	33.5906i	−0.723760	+	1.25359i
$719$	−43.5526			−1.62424			−0.812119	−	0.583491i	$-0.801686\pi$
$719$	−43.5526			−1.62424			−0.812119	+	0.583491i	$0.801686\pi$
$720$		0			0
$721$	−9.42097			−0.350855
$722$	−16.8851	+	29.2458i	−0.628397	+	1.08842i
$723$		0			0
$724$	0.621082	+	1.07574i	0.0230823	+	0.0399797i
$725$	−1.46420	−	2.53607i	−0.0543791	−	0.0941874i
$726$		0			0
$727$	−10.2686	+	17.7857i	−0.380840	+	0.659635i	−0.991183	−	0.132503i	$-0.957699\pi$
$727$	−10.2686	+	17.7857i	−0.380840	+	0.659635i	0.610342	+	0.792138i	$0.291032\pi$
$728$	22.9040			0.848880
$729$		0			0
$730$	12.3678			0.457754
$731$	7.77719	−	13.4705i	0.287650	−	0.498224i
$732$		0			0
$733$	−7.00299	−	12.1295i	−0.258661	−	0.448015i	0.707222	−	0.706991i	$-0.249948\pi$
$733$	−7.00299	−	12.1295i	−0.258661	−	0.448015i	−0.965884	+	0.258977i	$0.916615\pi$
$734$	7.40492	+	12.8257i	0.273320	+	0.473405i
$735$		0			0
$736$	1.53343	−	2.65598i	0.0565231	−	0.0979009i
$737$	11.0378			0.406581
$738$		0			0
$739$	−41.9813			−1.54431			−0.772154	−	0.635435i	$-0.780821\pi$
$739$	−41.9813			−1.54431			−0.772154	+	0.635435i	$0.780821\pi$
$740$	0.00639661	−	0.0110793i	0.000235144	−	0.000407282i
$741$		0			0
$742$	−18.9060	−	32.7462i	−0.694062	−	1.20215i
$743$	−13.9311	−	24.1293i	−0.511082	−	0.885219i	−0.999918	−	0.0128435i	$-0.995912\pi$
$743$	−13.9311	−	24.1293i	−0.511082	−	0.885219i	0.488836	−	0.872376i	$-0.337422\pi$
$744$		0			0
$745$	−16.9611	+	29.3775i	−0.621407	+	1.07631i
$746$	45.0128			1.64804
$747$		0			0
$748$	−3.29498			−0.120476
$749$	3.18092	−	5.50952i	0.116228	−	0.201313i
$750$		0			0
$751$	26.4525	+	45.8170i	0.965265	+	1.67189i	0.708902	+	0.705307i	$0.249191\pi$
$751$	26.4525	+	45.8170i	0.965265	+	1.67189i	0.256363	+	0.966580i	$0.417476\pi$
$752$	−6.71869	−	11.6371i	−0.245006	−	0.424362i
$753$		0			0
$754$	−2.80587	+	4.85992i	−0.102184	+	0.176988i
$755$	26.4561			0.962834
$756$		0			0
$757$	−41.4858			−1.50783			−0.753913	−	0.656975i	$-0.771836\pi$
$757$	−41.4858			−1.50783			−0.753913	+	0.656975i	$0.771836\pi$
$758$	−14.1058	+	24.4320i	−0.512346	+	0.887410i
$759$		0			0
$760$	−16.1468	−	27.9670i	−0.585705	−	1.01447i
$761$	22.6937	+	39.3067i	0.822647	+	1.42487i	0.903705	+	0.428156i	$0.140837\pi$
$761$	22.6937	+	39.3067i	0.822647	+	1.42487i	−0.0810582	+	0.996709i	$0.525830\pi$
$762$		0			0
$763$	10.8011	−	18.7081i	0.391027	−	0.677279i
$764$	0.926651			0.0335251
$765$		0			0
$766$	−5.53890			−0.200128
$767$	−11.8537	+	20.5312i	−0.428012	+	0.741339i
$768$		0			0
$769$	−2.55825	−	4.43102i	−0.0922528	−	0.159787i	0.816206	−	0.577761i	$-0.196073\pi$
$769$	−2.55825	−	4.43102i	−0.0922528	−	0.159787i	−0.908459	+	0.417975i	$0.862740\pi$
$770$	−15.9572	−	27.6387i	−0.575059	−	0.996031i
$771$		0			0
$772$	−1.65064	+	2.85900i	−0.0594080	+	0.102898i
$773$	−52.6427			−1.89343			−0.946713	−	0.322077i	$-0.895619\pi$
$773$	−52.6427			−1.89343			−0.946713	+	0.322077i	$0.895619\pi$
$774$		0			0
$775$	1.33511			0.0479587
$776$	0.383885	−	0.664908i	0.0137807	−	0.0238688i
$777$		0			0
$778$	−11.5155	−	19.9454i	−0.412850	−	0.715077i
$779$	−16.2690	−	28.1788i	−0.582899	−	1.00961i
$780$		0			0
$781$	16.3819	−	28.3743i	0.586191	−	1.01531i
$782$	−11.8976			−0.425456
$783$		0			0
$784$	4.26083			0.152172
$785$	18.1579	−	31.4504i	0.648084	−	1.12251i
$786$		0			0
$787$	10.3812	+	17.9808i	0.370050	+	0.640945i	0.989573	−	0.144034i	$-0.0460073\pi$
$787$	10.3812	+	17.9808i	0.370050	+	0.640945i	−0.619523	+	0.784978i	$0.712674\pi$
$788$	0.0668661	+	0.115816i	0.00238201	+	0.00412576i
$789$		0			0
$790$	4.20961	−	7.29125i	0.149771	−	0.259411i
$791$	38.4124			1.36579
$792$		0			0
$793$	−35.6536			−1.26610
$794$	−15.0911	+	26.1385i	−0.535561	+	0.927620i
$795$		0			0
$796$	−0.941752	−	1.63116i	−0.0333795	−	0.0578150i
$797$	22.7900	+	39.4734i	0.807263	+	1.39822i	0.914753	+	0.404014i	$0.132385\pi$
$797$	22.7900	+	39.4734i	0.807263	+	1.39822i	−0.107490	+	0.994206i	$0.534281\pi$
$798$		0			0
$799$	5.60472	−	9.70766i	0.198281	−	0.343432i
$800$	−2.36360			−0.0835658
$801$		0			0
$802$	−19.6459			−0.693721
$803$	−16.5064	+	28.5899i	−0.582498	+	1.00892i
$804$		0			0
$805$	5.86571	+	10.1597i	0.206739	+	0.358083i
$806$	−1.27925	−	2.21572i	−0.0450596	−	0.0780455i
$807$		0			0
$808$	16.2298	−	28.1109i	0.570964	−	0.988938i
$809$	−4.21120			−0.148058			−0.0740290	−	0.997256i	$-0.523586\pi$
$809$	−4.21120			−0.148058			−0.0740290	+	0.997256i	$0.523586\pi$
$810$		0			0
$811$	11.3618			0.398968			0.199484	−	0.979901i	$-0.436073\pi$
$811$	11.3618			0.398968			0.199484	+	0.979901i	$0.436073\pi$
$812$	−0.287618	+	0.498169i	−0.0100934	+	0.0174823i
$813$		0			0
$814$	−0.167718	−	0.290497i	−0.00587853	−	0.0101819i
$815$	−16.9491	−	29.3567i	−0.593700	−	1.02832i
$816$		0			0
$817$	−17.2087	+	29.8064i	−0.602057	+	1.04279i
$818$	−23.5817			−0.824515
$819$		0			0
$820$	1.49701			0.0522778
$821$	−0.821137	+	1.42225i	−0.0286579	+	0.0496369i	−0.879999	−	0.474976i	$-0.842457\pi$
$821$	−0.821137	+	1.42225i	−0.0286579	+	0.0496369i	0.851341	+	0.524613i	$0.175790\pi$
$822$		0			0
$823$	−5.60947	−	9.71589i	−0.195534	−	0.338675i	0.751542	−	0.659686i	$-0.229311\pi$
$823$	−5.60947	−	9.71589i	−0.195534	−	0.338675i	−0.947075	+	0.321011i	$0.895977\pi$
$824$	−5.74985	−	9.95903i	−0.200305	−	0.346939i
$825$		0			0
$826$	11.9356	−	20.6730i	0.415292	−	0.719306i
$827$	−9.61318			−0.334283			−0.167141	−	0.985933i	$-0.553454\pi$
$827$	−9.61318			−0.334283			−0.167141	+	0.985933i	$0.553454\pi$
$828$		0			0
$829$	33.4938			1.16329			0.581644	−	0.813443i	$-0.302410\pi$
$829$	33.4938			1.16329			0.581644	+	0.813443i	$0.302410\pi$
$830$	−4.43717	+	7.68540i	−0.154016	+	0.266764i
$831$		0			0
$832$	13.8687	+	24.0213i	0.480811	+	0.832789i
$833$	1.77719	+	3.07818i	0.0615759	+	0.106653i
$834$		0			0
$835$	−3.54576	+	6.14144i	−0.122706	+	0.212533i
$836$	7.29086			0.252160
$837$		0			0
$838$	25.4129			0.877874
$839$	15.9971	−	27.7077i	0.552280	−	0.956577i	−0.445830	−	0.895118i	$-0.647091\pi$
$839$	15.9971	−	27.7077i	0.552280	−	0.956577i	0.998110	−	0.0614591i	$-0.0195754\pi$
$840$		0			0
$841$	13.6668	+	23.6717i	0.471270	+	0.816264i
$842$	21.7815	+	37.7267i	0.750641	+	1.30015i
$843$		0			0
$844$	−1.37346	+	2.37889i	−0.0472763	+	0.0818849i
$845$	−4.27807			−0.147170
$846$		0			0
$847$	58.6614			2.01563
$848$	20.9270	−	36.2466i	0.718635	−	1.24471i
$849$		0			0
$850$	4.58466	+	7.94086i	0.157252	+	0.272369i
$851$	0.0616516	+	0.106784i	0.00211339	+	0.00366050i
$852$		0			0
$853$	−17.6211	+	30.5206i	−0.603334	+	1.04501i	0.388978	+	0.921247i	$0.372828\pi$
$853$	−17.6211	+	30.5206i	−0.603334	+	1.04501i	−0.992312	+	0.123759i	$0.960505\pi$
$854$	35.8999			1.22847
$855$		0			0
$856$	7.76558			0.265422
$857$	10.6245	−	18.4021i	0.362925	−	0.628605i	−0.625515	−	0.780212i	$-0.715111\pi$
$857$	10.6245	−	18.4021i	0.362925	−	0.628605i	0.988441	+	0.151606i	$0.0484446\pi$
$858$		0			0
$859$	−25.9192	−	44.8934i	−0.884352	−	1.53174i	−0.846454	−	0.532461i	$-0.821267\pi$
$859$	−25.9192	−	44.8934i	−0.884352	−	1.53174i	−0.0378979	−	0.999282i	$-0.512066\pi$
$860$	−0.791737	−	1.37133i	−0.0269980	−	0.0467619i
$861$		0			0
$862$	−23.1172	+	40.0402i	−0.787375	+	1.36377i
$863$	−22.6783			−0.771978			−0.385989	−	0.922503i	$-0.626140\pi$
$863$	−22.6783			−0.771978			−0.385989	+	0.922503i	$0.626140\pi$
$864$		0			0
$865$	6.26857			0.213138
$866$	16.8862	−	29.2478i	0.573818	−	0.993882i
$867$		0			0
$868$	−0.131130	−	0.227124i	−0.00445085	−	0.00770909i
$869$	11.2365	+	19.4622i	0.381172	+	0.660208i
$870$		0			0
$871$	2.99613	−	5.18945i	0.101520	−	0.175838i
$872$	26.3688			0.892959
$873$		0			0
$874$	26.3259			0.890488
$875$	14.4843	−	25.0875i	0.489658	−	0.848112i
$876$		0			0
$877$	−0.566704	−	0.981560i	−0.0191362	−	0.0331449i	0.856299	−	0.516481i	$-0.172758\pi$
$877$	−0.566704	−	0.981560i	−0.0191362	−	0.0331449i	−0.875435	+	0.483336i	$0.839425\pi$
$878$	15.6340	+	27.0789i	0.527623	+	0.913870i
$879$		0			0
$880$	17.6630	−	30.5932i	0.595419	−	1.03130i
$881$	−30.8289			−1.03865			−0.519327	−	0.854576i	$-0.673817\pi$
$881$	−30.8289			−1.03865			−0.519327	+	0.854576i	$0.673817\pi$
$882$		0			0
$883$	−9.33511			−0.314152			−0.157076	−	0.987587i	$-0.550207\pi$
$883$	−9.33511			−0.314152			−0.157076	+	0.987587i	$0.550207\pi$
$884$	−0.894400	+	1.54915i	−0.0300819	+	0.0521034i
$885$		0			0
$886$	2.77647	+	4.80899i	0.0932775	+	0.161561i
$887$	7.04710	+	12.2059i	0.236619	+	0.409835i	0.959742	−	0.280884i	$-0.0906275\pi$
$887$	7.04710	+	12.2059i	0.236619	+	0.409835i	−0.723123	+	0.690719i	$0.757294\pi$
$888$		0			0
$889$	−4.33615	+	7.51044i	−0.145430	+	0.251892i
$890$	18.1489			0.608352
$891$		0			0
$892$	2.02322			0.0677425
$893$	−12.4017	+	21.4803i	−0.415006	+	0.718812i
$894$		0			0
$895$	−6.83915	−	11.8457i	−0.228607	−	0.395960i
$896$	−11.4520	−	19.8355i	−0.382585	−	0.662657i
$897$		0			0
$898$	−12.3557	+	21.4006i	−0.412314	+	0.714149i
$899$	0.759704			0.0253376
$900$		0			0
$901$	34.9145			1.16317
$902$	19.6257	−	33.9927i	0.653463	−	1.13183i
$903$		0			0
$904$	23.4440	+	40.6063i	0.779737	+	1.35054i
$905$	−5.55468	−	9.62099i	−0.184644	−	0.319813i
$906$		0			0
$907$	4.36959	−	7.56834i	0.145090	−	0.251303i	−0.784317	−	0.620361i	$-0.786986\pi$
$907$	4.36959	−	7.56834i	0.145090	−	0.251303i	0.929406	+	0.369058i	$0.120320\pi$
$908$	3.20296			0.106294
$909$		0			0
$910$	−17.3259			−0.574349
$911$	10.3255	−	17.8842i	0.342098	−	0.592532i	−0.642724	−	0.766098i	$-0.722196\pi$
$911$	10.3255	−	17.8842i	0.342098	−	0.592532i	0.984822	+	0.173566i	$0.0555291\pi$
$912$		0			0
$913$	−11.8439	−	20.5142i	−0.391976	−	0.678922i
$914$	13.1099	+	22.7071i	0.433638	+	0.751083i
$915$		0			0
$916$	0.144334	−	0.249994i	0.00476893	−	0.00826002i
$917$	−42.7009			−1.41011
$918$		0			0
$919$	−2.36009			−0.0778522			−0.0389261	−	0.999242i	$-0.512394\pi$
$919$	−2.36009			−0.0778522			−0.0389261	+	0.999242i	$0.512394\pi$
$920$	−7.15998	+	12.4014i	−0.236057	+	0.408864i
$921$		0			0
$922$	−18.6932	−	32.3777i	−0.615629	−	1.06630i
$923$	−8.89352	−	15.4040i	−0.292734	−	0.507030i
$924$		0			0
$925$	0.0475142	−	0.0822969i	0.00156226	−	0.00270591i
$926$	52.1215			1.71282
$927$		0			0
$928$	−1.34493			−0.0441496
$929$	13.4101	−	23.2270i	0.439972	−	0.762054i	−0.557715	−	0.830033i	$-0.688322\pi$
$929$	13.4101	−	23.2270i	0.439972	−	0.762054i	0.997687	+	0.0679787i	$0.0216550\pi$
$930$		0			0
$931$	−3.93242	−	6.81115i	−0.128880	−	0.223226i
$932$	1.55122	+	2.68680i	0.0508120	+	0.0880089i
$933$		0			0
$934$	−20.0503	+	34.7282i	−0.656067	+	1.13634i
$935$	29.4688			0.963734
$936$		0			0
$937$	1.93313			0.0631527			0.0315764	−	0.999501i	$-0.489947\pi$
$937$	1.93313			0.0631527			0.0315764	+	0.999501i	$0.489947\pi$
$938$	−3.01683	+	5.22530i	−0.0985029	+	0.170612i
$939$		0			0
$940$	−0.570574	−	0.988264i	−0.0186101	−	0.0322336i
$941$	−5.95517	−	10.3147i	−0.194133	−	0.336248i	0.752483	−	0.658612i	$-0.228856\pi$
$941$	−5.95517	−	10.3147i	−0.194133	−	0.336248i	−0.946616	+	0.322363i	$0.895523\pi$
$942$		0			0
$943$	−7.21419	+	12.4953i	−0.234926	+	0.406905i
$944$	26.4228			0.859990
$945$		0			0
$946$	−41.5185			−1.34988
$947$	0.157918	−	0.273522i	0.00513165	−	0.00888828i	−0.863448	−	0.504438i	$-0.831700\pi$
$947$	0.157918	−	0.273522i	0.00513165	−	0.00888828i	0.868580	+	0.495549i	$0.165033\pi$
$948$		0			0
$949$	8.96110	+	15.5211i	0.290890	+	0.503836i
$950$	−10.1446	−	17.5709i	−0.329133	−	0.570075i
$951$		0			0
$952$	10.6475	−	18.4420i	0.345087	−	0.597708i
$953$	3.25133			0.105321			0.0526605	−	0.998612i	$-0.483230\pi$
$953$	3.25133			0.105321			0.0526605	+	0.998612i	$0.483230\pi$
$954$		0			0
$955$	−8.28756			−0.268179
$956$	−0.372273	+	0.644796i	−0.0120402	+	0.0208542i
$957$		0			0
$958$	25.3803	+	43.9600i	0.820001	+	1.42028i
$959$	4.73736	+	8.20535i	0.152977	+	0.264964i
$960$		0			0
$961$	15.3268	−	26.5468i	0.494414	−	0.856349i
$962$	−0.182104			−0.00587127
$963$		0			0
$964$	0.619489			0.0199524
$965$	14.7626	−	25.5696i	0.475226	−	0.823116i
$966$		0			0
$967$	−5.48380	−	9.49823i	−0.176347	−	0.305442i	0.764279	−	0.644885i	$-0.223095\pi$
$967$	−5.48380	−	9.49823i	−0.176347	−	0.305442i	−0.940627	+	0.339443i	$0.889761\pi$
$968$	35.8025	+	62.0117i	1.15073	+	1.99313i
$969$		0			0
$970$	−0.290393	+	0.502975i	−0.00932394	+	0.0161495i
$971$	23.3868			0.750519			0.375259	−	0.926920i	$-0.377554\pi$
$971$	23.3868			0.750519			0.375259	+	0.926920i	$0.377554\pi$
$972$		0			0
$973$	28.8553			0.925060
$974$	0.514548	−	0.891223i	0.0164872	−	0.0285566i
$975$		0			0
$976$	19.8687	+	34.4136i	0.635982	+	1.10155i
$977$	25.0881	+	43.4539i	0.802640	+	1.39021i	0.917873	+	0.396875i	$0.129905\pi$
$977$	25.0881	+	43.4539i	0.802640	+	1.39021i	−0.115233	+	0.993339i	$0.536761\pi$
$978$		0			0
$979$	−24.2219	+	41.9536i	−0.774136	+	1.34084i
$980$	0.361844			0.0115587
$981$		0			0
$982$	−0.670874			−0.0214084
$983$	7.34730	−	12.7259i	0.234342	−	0.405893i	−0.724739	−	0.689024i	$-0.758040\pi$
$983$	7.34730	−	12.7259i	0.234342	−	0.405893i	0.959081	+	0.283131i	$0.0913730\pi$
$984$		0			0
$985$	−0.598021	−	1.03580i	−0.0190545	−	0.0330034i
$986$	2.60876	+	4.51850i	0.0830797	+	0.143898i
$987$		0			0
$988$	1.97906	−	3.42782i	0.0629621	−	0.109054i
$989$	15.2618			0.485296
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	0.306589	−	0.531028i	0.00973422	−	0.0168602i
$993$		0			0
$994$	8.95496	+	15.5104i	0.284034	+	0.491961i
$995$	8.42262	+	14.5884i	0.267015	+	0.462483i
$996$		0			0
$997$	22.9432	−	39.7387i	0.726617	−	1.25854i	−0.231688	−	0.972790i	$-0.574425\pi$
$997$	22.9432	−	39.7387i	0.726617	−	1.25854i	0.958305	−	0.285747i	$-0.0922418\pi$
$998$	12.0797			0.382375
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.c.e.163.2		6
3.2	odd	2		243.2.c.f.163.2		6
9.2	odd	6		243.2.a.e.1.2	✓	3
9.4	even	3	inner	243.2.c.e.82.2		6
9.5	odd	6		243.2.c.f.82.2		6
9.7	even	3		243.2.a.f.1.2	yes	3
27.2	odd	18		729.2.e.h.325.1		6
27.4	even	9		729.2.e.b.163.1		6
27.5	odd	18		729.2.e.h.406.1		6
27.7	even	9		729.2.e.i.82.1		6
27.11	odd	18		729.2.e.g.568.1		6
27.13	even	9		729.2.e.i.649.1		6
27.14	odd	18		729.2.e.a.649.1		6
27.16	even	9		729.2.e.b.568.1		6
27.20	odd	18		729.2.e.a.82.1		6
27.22	even	9		729.2.e.c.406.1		6
27.23	odd	18		729.2.e.g.163.1		6
27.25	even	9		729.2.e.c.325.1		6
36.7	odd	6		3888.2.a.bk.1.2		3
36.11	even	6		3888.2.a.bd.1.2		3
45.29	odd	6		6075.2.a.bv.1.2		3
45.34	even	6		6075.2.a.bq.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.2	✓	3	9.2	odd	6
243.2.a.f.1.2	yes	3	9.7	even	3
243.2.c.e.82.2		6	9.4	even	3	inner
243.2.c.e.163.2		6	1.1	even	1	trivial
243.2.c.f.82.2		6	9.5	odd	6
243.2.c.f.163.2		6	3.2	odd	2
729.2.e.a.82.1		6	27.20	odd	18
729.2.e.a.649.1		6	27.14	odd	18
729.2.e.b.163.1		6	27.4	even	9
729.2.e.b.568.1		6	27.16	even	9
729.2.e.c.325.1		6	27.25	even	9
729.2.e.c.406.1		6	27.22	even	9
729.2.e.g.163.1		6	27.23	odd	18
729.2.e.g.568.1		6	27.11	odd	18
729.2.e.h.325.1		6	27.2	odd	18
729.2.e.h.406.1		6	27.5	odd	18
729.2.e.i.82.1		6	27.7	even	9
729.2.e.i.649.1		6	27.13	even	9
3888.2.a.bd.1.2		3	36.11	even	6
3888.2.a.bk.1.2		3	36.7	odd	6
6075.2.a.bq.1.2		3	45.34	even	6
6075.2.a.bv.1.2		3	45.29	odd	6

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.673648 + 1.16679i) q^{2} +(0.0923963 + 0.160035i) q^{4} +(-0.826352 - 1.43128i) q^{5} +(-1.20574 + 2.08840i) q^{7} -2.94356 q^{8} +O(q^{10})\)	\(q+(-0.673648 + 1.16679i) q^{2} +(0.0923963 + 0.160035i) q^{4} +(-0.826352 - 1.43128i) q^{5} +(-1.20574 + 2.08840i) q^{7} -2.94356 q^{8} +2.22668 q^{10} +(-2.97178 + 5.14728i) q^{11} +(1.61334 + 2.79439i) q^{13} +(-1.62449 - 2.81369i) q^{14} +(1.79813 - 3.11446i) q^{16} +3.00000 q^{17} -6.63816 q^{19} +(0.152704 - 0.264490i) q^{20} +(-4.00387 - 6.93491i) q^{22} +(1.47178 + 2.54920i) q^{23} +(1.13429 - 1.96464i) q^{25} -4.34730 q^{26} -0.445622 q^{28} +(0.645430 - 1.11792i) q^{29} +(0.294263 + 0.509678i) q^{31} +(-0.520945 - 0.902302i) q^{32} +(-2.02094 + 3.50038i) q^{34} +3.98545 q^{35} +0.0418891 q^{37} +(4.47178 - 7.74535i) q^{38} +(2.43242 + 4.21307i) q^{40} +(2.45084 + 4.24497i) q^{41} +(2.59240 - 4.49016i) q^{43} -1.09833 q^{44} -3.96585 q^{46} +(1.86824 - 3.23589i) q^{47} +(0.592396 + 1.02606i) q^{49} +(1.52822 + 2.64695i) q^{50} +(-0.298133 + 0.516382i) q^{52} +11.6382 q^{53} +9.82295 q^{55} +(3.54916 - 6.14733i) q^{56} +(0.869585 + 1.50617i) q^{58} +(3.67365 + 6.36295i) q^{59} +(-5.52481 + 9.56926i) q^{61} -0.792919 q^{62} +8.59627 q^{64} +(2.66637 - 4.61830i) q^{65} +(-0.928548 - 1.60829i) q^{67} +(0.277189 + 0.480105i) q^{68} +(-2.68479 + 4.65020i) q^{70} -5.51249 q^{71} +5.55438 q^{73} +(-0.0282185 + 0.0488759i) q^{74} +(-0.613341 - 1.06234i) q^{76} +(-7.16637 - 12.4125i) q^{77} +(1.89053 - 3.27449i) q^{79} -5.94356 q^{80} -6.60401 q^{82} +(-1.99273 + 3.45150i) q^{83} +(-2.47906 - 4.29385i) q^{85} +(3.49273 + 6.04958i) q^{86} +(8.74763 - 15.1513i) q^{88} +8.15064 q^{89} -7.78106 q^{91} +(-0.271974 + 0.471073i) q^{92} +(2.51707 + 4.35970i) q^{94} +(5.48545 + 9.50108i) q^{95} +(-0.130415 + 0.225885i) q^{97} -1.59627 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 3 q^{7} + 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 3 * q^7 + 12 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 3 q^{7} + 12 q^{8} - 3 q^{11} + 3 q^{13} + 3 q^{14} - 3 q^{16} + 18 q^{17} - 6 q^{19} + 3 q^{20} - 6 q^{23} - 3 q^{25} - 24 q^{26} - 24 q^{28} - 12 q^{29} + 12 q^{31} - 9 q^{34} - 12 q^{35} - 6 q^{37} + 12 q^{38} - 9 q^{40} + 3 q^{41} + 12 q^{43} - 30 q^{44} + 18 q^{46} + 6 q^{47} + 24 q^{50} + 12 q^{52} + 36 q^{53} + 18 q^{55} + 33 q^{56} - 9 q^{58} + 21 q^{59} - 6 q^{61} - 24 q^{62} + 24 q^{64} - 3 q^{65} - 6 q^{67} - 9 q^{68} - 9 q^{70} - 18 q^{71} + 12 q^{73} - 15 q^{74} + 3 q^{76} - 24 q^{77} - 6 q^{79} - 6 q^{80} + 36 q^{82} + 6 q^{83} - 18 q^{85} + 3 q^{86} + 36 q^{88} - 12 q^{91} - 24 q^{92} + 36 q^{94} - 3 q^{95} - 15 q^{97} + 18 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 3 * q^7 + 12 * q^8 - 3 * q^11 + 3 * q^13 + 3 * q^14 - 3 * q^16 + 18 * q^17 - 6 * q^19 + 3 * q^20 - 6 * q^23 - 3 * q^25 - 24 * q^26 - 24 * q^28 - 12 * q^29 + 12 * q^31 - 9 * q^34 - 12 * q^35 - 6 * q^37 + 12 * q^38 - 9 * q^40 + 3 * q^41 + 12 * q^43 - 30 * q^44 + 18 * q^46 + 6 * q^47 + 24 * q^50 + 12 * q^52 + 36 * q^53 + 18 * q^55 + 33 * q^56 - 9 * q^58 + 21 * q^59 - 6 * q^61 - 24 * q^62 + 24 * q^64 - 3 * q^65 - 6 * q^67 - 9 * q^68 - 9 * q^70 - 18 * q^71 + 12 * q^73 - 15 * q^74 + 3 * q^76 - 24 * q^77 - 6 * q^79 - 6 * q^80 + 36 * q^82 + 6 * q^83 - 18 * q^85 + 3 * q^86 + 36 * q^88 - 12 * q^91 - 24 * q^92 + 36 * q^94 - 3 * q^95 - 15 * q^97 + 18 * q^98

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