LMFDB - Embedded newform 243.2.c.e.82.1

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			82.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	243.82
Dual form			243.2.c.e.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26604 - 2.19285i) q^{2} +(-2.20574 + 3.82045i) q^{4} +(-0.233956 + 0.405223i) q^{5} +(1.61334 + 2.79439i) q^{7} +6.10607 q^{8} +O(q^{10})$	\(q+(-1.26604 - 2.19285i) q^{2} +(-2.20574 + 3.82045i) q^{4} +(-0.233956 + 0.405223i) q^{5} +(1.61334 + 2.79439i) q^{7} +6.10607 q^{8} +1.18479 q^{10} +(1.55303 + 2.68993i) q^{11} +(1.09240 - 1.89209i) q^{13} +(4.08512 - 7.07564i) q^{14} +(-3.31908 - 5.74881i) q^{16} +3.00000 q^{17} +0.0418891 q^{19} +(-1.03209 - 1.78763i) q^{20} +(3.93242 - 6.81115i) q^{22} +(-3.05303 + 5.28801i) q^{23} +(2.39053 + 4.14052i) q^{25} -5.53209 q^{26} -14.2344 q^{28} +(-3.28699 - 5.69323i) q^{29} +(3.11334 - 5.39246i) q^{31} +(-2.29813 + 3.98048i) q^{32} +(-3.79813 - 6.57856i) q^{34} -1.50980 q^{35} +3.59627 q^{37} +(-0.0530334 - 0.0918566i) q^{38} +(-1.42855 + 2.47432i) q^{40} +(-3.85117 + 6.67042i) q^{41} +(0.294263 + 0.509678i) q^{43} -13.7023 q^{44} +15.4611 q^{46} +(4.83022 + 8.36619i) q^{47} +(-1.70574 + 2.95442i) q^{49} +(6.05303 - 10.4842i) q^{50} +(4.81908 + 8.34689i) q^{52} +4.95811 q^{53} -1.45336 q^{55} +(9.85117 + 17.0627i) q^{56} +(-8.32295 + 14.4158i) q^{58} +(4.26604 - 7.38901i) q^{59} +(0.634285 + 1.09861i) q^{61} -15.7665 q^{62} -1.63816 q^{64} +(0.511144 + 0.885328i) q^{65} +(-5.00387 + 8.66696i) q^{67} +(-6.61721 + 11.4613i) q^{68} +(1.91147 + 3.31077i) q^{70} +11.8307 q^{71} -8.23442 q^{73} +(-4.55303 - 7.88609i) q^{74} +(-0.0923963 + 0.160035i) q^{76} +(-5.01114 + 8.67956i) q^{77} +(-5.52481 - 9.56926i) q^{79} +3.10607 q^{80} +19.5030 q^{82} +(0.754900 + 1.30753i) q^{83} +(-0.701867 + 1.21567i) q^{85} +(0.745100 - 1.29055i) q^{86} +(9.48293 + 16.4249i) q^{88} -15.8726 q^{89} +7.04963 q^{91} +(-13.4684 - 23.3279i) q^{92} +(12.2306 - 21.1839i) q^{94} +(-0.00980018 + 0.0169744i) q^{95} +(-9.32295 - 16.1478i) q^{97} +8.63816 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.26604	−	2.19285i	−0.895229	−	1.55058i	−0.833521	−	0.552487i	$-0.813679\pi$
$2$	−1.26604	−	2.19285i	−0.895229	−	1.55058i	−0.0617072	−	0.998094i	$-0.519654\pi$
$3$		0			0
$3$		0			0
$4$	−2.20574	+	3.82045i	−1.10287	+	1.91022i
$5$	−0.233956	+	0.405223i	−0.104628	+	0.181221i	−0.913586	−	0.406645i	$-0.866699\pi$
$5$	−0.233956	+	0.405223i	−0.104628	+	0.181221i	0.808958	+	0.587866i	$0.200032\pi$
$6$		0			0
$7$	1.61334	+	2.79439i	0.609786	+	1.05618i	0.991275	+	0.131806i	$0.0420778\pi$
$7$	1.61334	+	2.79439i	0.609786	+	1.05618i	−0.381490	+	0.924373i	$0.624589\pi$
$8$	6.10607			2.15882
$9$		0			0
$10$	1.18479			0.374664
$11$	1.55303	+	2.68993i	0.468257	+	0.811045i	0.999342	−	0.0362735i	$-0.0115487\pi$
$11$	1.55303	+	2.68993i	0.468257	+	0.811045i	−0.531085	+	0.847319i	$0.678215\pi$
$12$		0			0
$13$	1.09240	−	1.89209i	0.302976	−	0.524770i	−0.673832	−	0.738884i	$-0.735353\pi$
$13$	1.09240	−	1.89209i	0.302976	−	0.524770i	0.976809	+	0.214114i	$0.0686864\pi$
$14$	4.08512	−	7.07564i	1.09179	−	1.89104i
$15$		0			0
$16$	−3.31908	−	5.74881i	−0.829769	−	1.43720i
$17$	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
$19$	0.0418891			0.00961001			0.00480501	−	0.999988i	$-0.498471\pi$
$19$	0.0418891			0.00961001			0.00480501	+	0.999988i	$0.498471\pi$
$20$	−1.03209	−	1.78763i	−0.230782	−	0.399726i
$21$		0			0
$22$	3.93242	−	6.81115i	0.838394	−	1.45214i
$23$	−3.05303	+	5.28801i	−0.636601	+	1.10263i	0.349572	+	0.936910i	$0.386327\pi$
$23$	−3.05303	+	5.28801i	−0.636601	+	1.10263i	−0.986173	+	0.165717i	$0.947006\pi$
$24$		0			0
$25$	2.39053	+	4.14052i	0.478106	+	0.828104i
$26$	−5.53209			−1.08493
$27$		0			0
$28$	−14.2344			−2.69005
$29$	−3.28699	−	5.69323i	−0.610379	−	1.05721i	−0.991177	−	0.132548i	$-0.957684\pi$
$29$	−3.28699	−	5.69323i	−0.610379	−	1.05721i	0.380798	−	0.924658i	$-0.375649\pi$
$30$		0			0
$31$	3.11334	−	5.39246i	0.559173	−	0.968515i	−0.438393	−	0.898783i	$-0.644452\pi$
$31$	3.11334	−	5.39246i	0.559173	−	0.968515i	0.997566	−	0.0697319i	$-0.0222144\pi$
$32$	−2.29813	+	3.98048i	−0.406256	+	0.703657i
$33$		0			0
$34$	−3.79813	−	6.57856i	−0.651374	−	1.12821i
$35$	−1.50980			−0.255203
$36$		0			0
$37$	3.59627			0.591223			0.295611	−	0.955308i	$-0.404477\pi$
$37$	3.59627			0.591223			0.295611	+	0.955308i	$0.404477\pi$
$38$	−0.0530334	−	0.0918566i	−0.00860316	−	0.0149011i
$39$		0			0
$40$	−1.42855	+	2.47432i	−0.225873	+	0.391224i
$41$	−3.85117	+	6.67042i	−0.601451	+	1.04174i	0.391150	+	0.920327i	$0.372077\pi$
$41$	−3.85117	+	6.67042i	−0.601451	+	1.04174i	−0.992602	+	0.121417i	$0.961256\pi$
$42$		0			0
$43$	0.294263	+	0.509678i	0.0448747	+	0.0777252i	0.887590	−	0.460634i	$-0.152378\pi$
$43$	0.294263	+	0.509678i	0.0448747	+	0.0777252i	−0.842716	+	0.538359i	$0.819044\pi$
$44$	−13.7023			−2.06570
$45$		0			0
$46$	15.4611			2.27962
$47$	4.83022	+	8.36619i	0.704560	+	1.22033i	0.966850	+	0.255345i	$0.0821891\pi$
$47$	4.83022	+	8.36619i	0.704560	+	1.22033i	−0.262290	+	0.964989i	$0.584478\pi$
$48$		0			0
$49$	−1.70574	+	2.95442i	−0.243677	+	0.422060i
$50$	6.05303	−	10.4842i	0.856028	−	1.48268i
$51$		0			0
$52$	4.81908	+	8.34689i	0.668286	+	1.15751i
$53$	4.95811			0.681049			0.340524	−	0.940236i	$-0.389395\pi$
$53$	4.95811			0.681049			0.340524	+	0.940236i	$0.389395\pi$
$54$		0			0
$55$	−1.45336			−0.195971
$56$	9.85117	+	17.0627i	1.31642	+	2.28010i
$57$		0			0
$58$	−8.32295	+	14.4158i	−1.09286	+	1.89288i
$59$	4.26604	−	7.38901i	0.555392	−	0.961967i	−0.442481	−	0.896778i	$-0.645902\pi$
$59$	4.26604	−	7.38901i	0.555392	−	0.961967i	0.997873	−	0.0651889i	$-0.0207650\pi$
$60$		0			0
$61$	0.634285	+	1.09861i	0.0812119	+	0.140663i	0.903771	−	0.428017i	$-0.140788\pi$
$61$	0.634285	+	1.09861i	0.0812119	+	0.140663i	−0.822559	+	0.568680i	$0.807454\pi$
$62$	−15.7665			−2.00235
$63$		0			0
$64$	−1.63816			−0.204769
$65$	0.511144	+	0.885328i	0.0633997	+	0.109811i
$66$		0			0
$67$	−5.00387	+	8.66696i	−0.611320	+	1.05884i	0.379698	+	0.925110i	$0.376028\pi$
$67$	−5.00387	+	8.66696i	−0.611320	+	1.05884i	−0.991018	+	0.133727i	$0.957305\pi$
$68$	−6.61721	+	11.4613i	−0.802455	+	1.38989i
$69$		0			0
$70$	1.91147	+	3.31077i	0.228465	+	0.395713i
$71$	11.8307			1.40404			0.702022	−	0.712155i	$-0.252281\pi$
$71$	11.8307			1.40404			0.702022	+	0.712155i	$0.252281\pi$
$72$		0			0
$73$	−8.23442			−0.963766			−0.481883	−	0.876236i	$-0.660047\pi$
$73$	−8.23442			−0.963766			−0.481883	+	0.876236i	$0.660047\pi$
$74$	−4.55303	−	7.88609i	−0.529279	−	0.916739i
$75$		0			0
$76$	−0.0923963	+	0.160035i	−0.0105986	+	0.0183573i
$77$	−5.01114	+	8.67956i	−0.571073	+	0.989127i
$78$		0			0
$79$	−5.52481	−	9.56926i	−0.621590	−	1.07663i	−0.989190	−	0.146642i	$-0.953154\pi$
$79$	−5.52481	−	9.56926i	−0.621590	−	1.07663i	0.367599	−	0.929984i	$-0.380180\pi$
$80$	3.10607			0.347269
$81$		0			0
$82$	19.5030			2.15375
$83$	0.754900	+	1.30753i	0.0828610	+	0.143520i	0.904478	−	0.426521i	$-0.140261\pi$
$83$	0.754900	+	1.30753i	0.0828610	+	0.143520i	−0.821617	+	0.570040i	$0.806928\pi$
$84$		0			0
$85$	−0.701867	+	1.21567i	−0.0761281	+	0.131858i
$86$	0.745100	−	1.29055i	0.0803462	−	0.139164i
$87$		0			0
$88$	9.48293	+	16.4249i	1.01088	+	1.75090i
$89$	−15.8726			−1.68249			−0.841245	−	0.540654i	$-0.818177\pi$
$89$	−15.8726			−1.68249			−0.841245	+	0.540654i	$0.818177\pi$
$90$		0			0
$91$	7.04963			0.739002
$92$	−13.4684	−	23.3279i	−1.40418	−	2.43210i
$93$		0			0
$94$	12.2306	−	21.1839i	1.26149	−	2.18496i
$95$	−0.00980018	+	0.0169744i	−0.00100548	+	0.00174154i
$96$		0			0
$97$	−9.32295	−	16.1478i	−0.946602	−	1.63956i	−0.752512	−	0.658579i	$-0.771158\pi$
$97$	−9.32295	−	16.1478i	−0.946602	−	1.63956i	−0.194090	−	0.980984i	$-0.562176\pi$
$98$	8.63816			0.872585
$99$		0			0
$100$	−21.0915			−2.10915
$101$	−4.54323	−	7.86911i	−0.452069	−	0.783006i	0.546446	−	0.837494i	$-0.315980\pi$
$101$	−4.54323	−	7.86911i	−0.452069	−	0.783006i	−0.998514	+	0.0544887i	$0.982647\pi$
$102$		0			0
$103$	−0.130415	+	0.225885i	−0.0128502	+	0.0222571i	−0.872379	−	0.488830i	$-0.837424\pi$
$103$	−0.130415	+	0.225885i	−0.0128502	+	0.0222571i	0.859529	+	0.511087i	$0.170757\pi$
$104$	6.67024	−	11.5532i	0.654071	−	1.13288i
$105$		0			0
$106$	−6.27719	−	10.8724i	−0.609694	−	1.05602i
$107$	4.04189			0.390744			0.195372	−	0.980729i	$-0.437409\pi$
$107$	4.04189			0.390744			0.195372	+	0.980729i	$0.437409\pi$
$108$		0			0
$109$	−5.40373			−0.517584			−0.258792	−	0.965933i	$-0.583324\pi$
$109$	−5.40373			−0.517584			−0.258792	+	0.965933i	$0.583324\pi$
$110$	1.84002	+	3.18701i	0.175439	+	0.303870i
$111$		0			0
$112$	10.7096	−	18.5496i	1.01196	−	1.75277i
$113$	−0.692066	+	1.19869i	−0.0651041	+	0.112764i	−0.896740	−	0.442557i	$-0.854071\pi$
$113$	−0.692066	+	1.19869i	−0.0651041	+	0.112764i	0.831636	+	0.555321i	$0.187405\pi$
$114$		0			0
$115$	−1.42855	−	2.47432i	−0.133213	−	0.230731i
$116$	29.0009			2.69267
$117$		0			0
$118$	−21.6040			−1.98881
$119$	4.84002	+	8.38316i	0.443684	+	0.768483i
$120$		0			0
$121$	0.676174	−	1.17117i	0.0614704	−	0.106470i
$122$	1.60607	−	2.78179i	0.145406	−	0.251851i
$123$		0			0
$124$	13.7344	+	23.7887i	1.23339	+	2.13629i
$125$	−4.57667			−0.409349
$126$		0			0
$127$	−6.63816			−0.589041			−0.294521	−	0.955645i	$-0.595160\pi$
$127$	−6.63816			−0.589041			−0.294521	+	0.955645i	$0.595160\pi$
$128$	6.67024	+	11.5532i	0.589572	+	1.02117i
$129$		0			0
$130$	1.29426	−	2.24173i	0.113514	−	0.196613i
$131$	6.32042	−	10.9473i	0.552218	−	0.956469i	−0.445896	−	0.895085i	$-0.647115\pi$
$131$	6.32042	−	10.9473i	0.552218	−	0.956469i	0.998114	−	0.0613847i	$-0.0195517\pi$
$132$		0			0
$133$	0.0675813	+	0.117054i	0.00586005	+	0.0101499i
$134$	25.3405			2.18908
$135$		0			0
$136$	18.3182			1.57077
$137$	−5.30793	−	9.19361i	−0.453487	−	0.785463i	0.545112	−	0.838363i	$-0.316487\pi$
$137$	−5.30793	−	9.19361i	−0.453487	−	0.785463i	−0.998600	+	0.0528998i	$0.983154\pi$
$138$		0			0
$139$	3.73055	−	6.46151i	0.316421	−	0.548058i	−0.663317	−	0.748338i	$-0.730852\pi$
$139$	3.73055	−	6.46151i	0.316421	−	0.548058i	0.979739	+	0.200281i	$0.0641853\pi$
$140$	3.33022	−	5.76811i	0.281455	−	0.487495i
$141$		0			0
$142$	−14.9782	−	25.9430i	−1.25694	−	2.17709i
$143$	6.78611			0.567483
$144$		0			0
$145$	3.07604			0.255451
$146$	10.4251	+	18.0569i	0.862791	+	1.49440i
$147$		0			0
$148$	−7.93242	+	13.7394i	−0.652041	+	1.12937i
$149$	2.12701	−	3.68409i	0.174252	−	0.301813i	−0.765650	−	0.643257i	$-0.777583\pi$
$149$	2.12701	−	3.68409i	0.174252	−	0.301813i	0.939902	+	0.341444i	$0.110916\pi$
$150$		0			0
$151$	−0.0675813	−	0.117054i	−0.00549969	−	0.00952574i	0.863262	−	0.504755i	$-0.168417\pi$
$151$	−0.0675813	−	0.117054i	−0.00549969	−	0.00952574i	−0.868762	+	0.495230i	$0.835084\pi$
$152$	0.255777			0.0207463
$153$		0			0
$154$	25.3773			2.04496
$155$	1.45677	+	2.52319i	0.117010	+	0.202668i
$156$		0			0
$157$	−6.66297	+	11.5406i	−0.531763	+	0.921040i	0.467550	+	0.883967i	$0.345137\pi$
$157$	−6.66297	+	11.5406i	−0.531763	+	0.921040i	−0.999313	+	0.0370736i	$0.988196\pi$
$158$	−13.9893	+	24.2302i	−1.11293	+	1.92765i
$159$		0			0
$160$	−1.07532	−	1.86251i	−0.0850117	−	0.147245i
$161$	−19.7023			−1.55276
$162$		0			0
$163$	−9.76382			−0.764762			−0.382381	−	0.924005i	$-0.624896\pi$
$163$	−9.76382			−0.764762			−0.382381	+	0.924005i	$0.624896\pi$
$164$	−16.9893	−	29.4264i	−1.32664	−	2.29781i
$165$		0			0
$166$	1.91147	−	3.31077i	0.148359	−	0.256966i
$167$	1.78699	−	3.09516i	0.138281	−	0.239510i	−0.788565	−	0.614952i	$-0.789176\pi$
$167$	1.78699	−	3.09516i	0.138281	−	0.239510i	0.926846	+	0.375441i	$0.122509\pi$
$168$		0			0
$169$	4.11334	+	7.12452i	0.316411	+	0.548040i
$170$	3.55438			0.272608
$171$		0			0
$172$	−2.59627			−0.197963
$173$	−9.38326	−	16.2523i	−0.713396	−	1.23564i	−0.963575	−	0.267438i	$-0.913823\pi$
$173$	−9.38326	−	16.2523i	−0.713396	−	1.23564i	0.250179	−	0.968200i	$-0.419510\pi$
$174$		0			0
$175$	−7.71348	+	13.3601i	−0.583084	+	1.00993i
$176$	10.3093	−	17.8562i	0.777091	−	1.34596i
$177$		0			0
$178$	20.0954	+	34.8062i	1.50621	+	2.60884i
$179$	−5.08378			−0.379979			−0.189990	−	0.981786i	$-0.560845\pi$
$179$	−5.08378			−0.379979			−0.189990	+	0.981786i	$0.560845\pi$
$180$		0			0
$181$	7.15064			0.531503			0.265752	−	0.964042i	$-0.414380\pi$
$181$	7.15064			0.531503			0.265752	+	0.964042i	$0.414380\pi$
$182$	−8.92514	−	15.4588i	−0.661576	−	1.14588i
$183$		0			0
$184$	−18.6420	+	32.2889i	−1.37431	+	2.38037i
$185$	−0.841367	+	1.45729i	−0.0618585	+	0.107142i
$186$		0			0
$187$	4.65910	+	8.06980i	0.340707	+	0.590122i
$188$	−42.6168			−3.10815
$189$		0			0
$190$	0.0496299			0.00360053
$191$	5.25490	+	9.10175i	0.380231	+	0.658580i	0.991095	−	0.133156i	$-0.0425111\pi$
$191$	5.25490	+	9.10175i	0.380231	+	0.658580i	−0.610864	+	0.791736i	$0.709178\pi$
$192$		0			0
$193$	5.07145	−	8.78401i	0.365051	−	0.632287i	−0.623733	−	0.781637i	$-0.714385\pi$
$193$	5.07145	−	8.78401i	0.365051	−	0.632287i	0.988784	+	0.149350i	$0.0477182\pi$
$194$	−23.6065	+	40.8877i	−1.69485	+	2.93557i
$195$		0			0
$196$	−7.52481	−	13.0334i	−0.537487	−	0.930954i
$197$	14.0838			1.00343			0.501714	−	0.865034i	$-0.332703\pi$
$197$	14.0838			1.00343			0.501714	+	0.865034i	$0.332703\pi$
$198$		0			0
$199$	10.2763			0.728468			0.364234	−	0.931307i	$-0.381331\pi$
$199$	10.2763			0.728468			0.364234	+	0.931307i	$0.381331\pi$
$200$	14.5967	+	25.2823i	1.03214	+	1.78773i
$201$		0			0
$202$	−11.5039	+	19.9253i	−0.809409	+	1.40194i
$203$	10.6061	−	18.3702i	0.744400	−	1.28934i
$204$		0			0
$205$	−1.80200	−	3.12116i	−0.125857	−	0.217991i
$206$	0.660444			0.0460153
$207$		0			0
$208$	−14.5030			−1.00560
$209$	0.0650551	+	0.112679i	0.00449996	+	0.00779415i
$210$		0			0
$211$	3.57145	−	6.18594i	0.245869	−	0.425857i	−0.716507	−	0.697580i	$-0.754260\pi$
$211$	3.57145	−	6.18594i	0.245869	−	0.425857i	0.962376	+	0.271723i	$0.0875934\pi$
$212$	−10.9363	+	18.9422i	−0.751107	+	1.30096i
$213$		0			0
$214$	−5.11721	−	8.86327i	−0.349805	−	0.605881i
$215$	−0.275378			−0.0187806
$216$		0			0
$217$	20.0915			1.36390
$218$	6.84137	+	11.8496i	0.463356	+	0.802556i
$219$		0			0
$220$	3.20574	−	5.55250i	0.216131	−	0.374349i
$221$	3.27719	−	5.67626i	0.220448	−	0.381826i
$222$		0			0
$223$	5.16772	+	8.95075i	0.346056	+	0.599387i	0.985545	−	0.169414i	$-0.0541874\pi$
$223$	5.16772	+	8.95075i	0.346056	+	0.599387i	−0.639489	+	0.768800i	$0.720854\pi$
$224$	−14.8307			−0.990917
$225$		0			0
$226$	3.50475			0.233132
$227$	6.51114	+	11.2776i	0.432160	+	0.748523i	0.997059	−	0.0766371i	$-0.0244183\pi$
$227$	6.51114	+	11.2776i	0.432160	+	0.748523i	−0.564899	+	0.825160i	$0.691085\pi$
$228$		0			0
$229$	14.0496	−	24.3347i	0.928426	−	1.60808i	0.142469	−	0.989799i	$-0.454496\pi$
$229$	14.0496	−	24.3347i	0.928426	−	1.60808i	0.785957	−	0.618281i	$-0.212171\pi$
$230$	−3.61721	+	6.26519i	−0.238512	+	0.413115i
$231$		0			0
$232$	−20.0706	−	34.7633i	−1.31770	−	2.28232i
$233$	−13.9145			−0.911567			−0.455784	−	0.890091i	$-0.650641\pi$
$233$	−13.9145			−0.911567			−0.455784	+	0.890091i	$0.650641\pi$
$234$		0			0
$235$	−4.52023			−0.294867
$236$	18.8195	+	32.5964i	1.22505	+	2.12185i
$237$		0			0
$238$	12.2554	−	21.2269i	0.794397	−	1.37594i
$239$	7.50980	−	13.0074i	0.485769	−	0.841376i	−0.514098	−	0.857732i	$-0.671873\pi$
$239$	7.50980	−	13.0074i	0.485769	−	0.841376i	0.999866	+	0.0163558i	$0.00520644\pi$
$240$		0			0
$241$	6.48680	+	11.2355i	0.417851	+	0.723740i	0.995723	−	0.0923879i	$-0.0294500\pi$
$241$	6.48680	+	11.2355i	0.417851	+	0.723740i	−0.577872	+	0.816128i	$0.696117\pi$
$242$	−3.42427			−0.220120
$243$		0			0
$244$	−5.59627			−0.358264
$245$	−0.798133	−	1.38241i	−0.0509909	−	0.0883188i
$246$		0			0
$247$	0.0457595	−	0.0792577i	0.00291160	−	0.00504305i
$248$	19.0103	−	32.9267i	1.20715	−	2.09085i
$249$		0			0
$250$	5.79426	+	10.0360i	0.366461	+	0.634730i
$251$	0.872578			0.0550766			0.0275383	−	0.999621i	$-0.491233\pi$
$251$	0.872578			0.0550766			0.0275383	+	0.999621i	$0.491233\pi$
$252$		0			0
$253$	−18.9659			−1.19237
$254$	8.40420	+	14.5565i	0.527326	+	0.913356i
$255$		0			0
$256$	15.2515	−	26.4164i	0.953219	−	1.65102i
$257$	−2.28833	+	3.96351i	−0.142742	+	0.247237i	−0.928528	−	0.371261i	$-0.878925\pi$
$257$	−2.28833	+	3.96351i	−0.142742	+	0.247237i	0.785786	+	0.618498i	$0.212259\pi$
$258$		0			0
$259$	5.80200	+	10.0494i	0.360519	+	0.624437i
$260$	−4.50980			−0.279686
$261$		0			0
$262$	−32.0077			−1.97744
$263$	−2.14883	−	3.72189i	−0.132503	−	0.229501i	0.792138	−	0.610342i	$-0.208968\pi$
$263$	−2.14883	−	3.72189i	−0.132503	−	0.229501i	−0.924641	+	0.380841i	$0.875635\pi$
$264$		0			0
$265$	−1.15998	+	2.00914i	−0.0712569	+	0.123420i
$266$	0.171122	−	0.296392i	0.0104922	−	0.0181730i
$267$		0			0
$268$	−22.0744	−	38.2341i	−1.34841	−	2.33552i
$269$	12.1257			0.739315			0.369657	−	0.929168i	$-0.379475\pi$
$269$	12.1257			0.739315			0.369657	+	0.929168i	$0.379475\pi$
$270$		0			0
$271$	−0.319955			−0.0194359			−0.00971795	−	0.999953i	$-0.503093\pi$
$271$	−0.319955			−0.0194359			−0.00971795	+	0.999953i	$0.503093\pi$
$272$	−9.95723	−	17.2464i	−0.603746	−	1.04572i
$273$		0			0
$274$	−13.4402	+	23.2790i	−0.811950	+	1.40634i
$275$	−7.42514	+	12.8607i	−0.447753	+	0.775531i
$276$		0			0
$277$	13.4106	+	23.2278i	0.805765	+	1.39563i	0.915774	+	0.401695i	$0.131579\pi$
$277$	13.4106	+	23.2278i	0.805765	+	1.39563i	−0.110009	+	0.993931i	$0.535088\pi$
$278$	−18.8922			−1.13308
$279$		0			0
$280$	−9.21894			−0.550937
$281$	−13.3405	−	23.1064i	−0.795827	−	1.37841i	−0.922313	−	0.386444i	$-0.873703\pi$
$281$	−13.3405	−	23.1064i	−0.795827	−	1.37841i	0.126486	−	0.991968i	$-0.459630\pi$
$282$		0			0
$283$	4.64677	−	8.04845i	0.276222	−	0.478431i	−0.694221	−	0.719762i	$-0.744251\pi$
$283$	4.64677	−	8.04845i	0.276222	−	0.478431i	0.970443	+	0.241332i	$0.0775842\pi$
$284$	−26.0954	+	45.1985i	−1.54848	+	2.68204i
$285$		0			0
$286$	−8.59152	−	14.8809i	−0.508027	−	0.879929i
$287$	−24.8530			−1.46702
$288$		0			0
$289$	−8.00000			−0.470588
$290$	−3.89440	−	6.74530i	−0.228687	−	0.396098i
$291$		0			0
$292$	18.1630	−	31.4592i	1.06291	−	1.84101i
$293$	9.81954	−	17.0080i	0.573664	−	0.993615i	−0.422521	−	0.906353i	$-0.638855\pi$
$293$	9.81954	−	17.0080i	0.573664	−	0.993615i	0.996185	−	0.0872621i	$-0.0278118\pi$
$294$		0			0
$295$	1.99613	+	3.45740i	0.116219	+	0.201297i
$296$	21.9590			1.27634
$297$		0			0
$298$	−10.7716			−0.623980
$299$	6.67024	+	11.5532i	0.385750	+	0.668139i
$300$		0			0
$301$	−0.949493	+	1.64457i	−0.0547279	+	0.0947914i
$302$	−0.171122	+	0.296392i	−0.00984696	+	0.0170554i
$303$		0			0
$304$	−0.139033	−	0.240812i	−0.00797409	−	0.0138115i
$305$	−0.593578			−0.0339882
$306$		0			0
$307$	28.3432			1.61763			0.808815	−	0.588063i	$-0.200109\pi$
$307$	28.3432			1.61763			0.808815	+	0.588063i	$0.200109\pi$
$308$	−22.1065	−	38.2896i	−1.25964	−	2.18175i
$309$		0			0
$310$	3.68866	−	6.38895i	0.209502	−	0.362868i
$311$	1.02229	−	1.77066i	0.0579687	−	0.100405i	−0.835585	−	0.549362i	$-0.814871\pi$
$311$	1.02229	−	1.77066i	0.0579687	−	0.100405i	0.893553	+	0.448957i	$0.148204\pi$
$312$		0			0
$313$	−4.20574	−	7.28455i	−0.237722	−	0.411747i	0.722338	−	0.691540i	$-0.243067\pi$
$313$	−4.20574	−	7.28455i	−0.237722	−	0.411747i	−0.960060	+	0.279793i	$0.909734\pi$
$314$	33.7425			1.90420
$315$		0			0
$316$	48.7452			2.74213
$317$	−15.5642	−	26.9579i	−0.874171	−	1.51411i	−0.857643	−	0.514246i	$-0.828072\pi$
$317$	−15.5642	−	26.9579i	−0.874171	−	1.51411i	−0.0165284	−	0.999863i	$-0.505261\pi$
$318$		0			0
$319$	10.2096	−	17.6836i	0.571628	−	0.990089i
$320$	0.383256	−	0.663818i	0.0214246	−	0.0371086i
$321$		0			0
$322$	24.9440	+	43.2043i	1.39008	+	2.40768i
$323$	0.125667			0.00699231
$324$		0			0
$325$	10.4456			0.579419
$326$	12.3614	+	21.4106i	0.684636	+	1.18583i
$327$		0			0
$328$	−23.5155	+	40.7300i	−1.29843	+	2.24894i
$329$	−15.5856	+	26.9950i	−0.859261	+	1.48828i
$330$		0			0
$331$	−15.5155	−	26.8736i	−0.852808	−	1.47711i	−0.878664	−	0.477441i	$-0.841564\pi$
$331$	−15.5155	−	26.8736i	−0.852808	−	1.47711i	0.0258558	−	0.999666i	$-0.491769\pi$
$332$	−6.66044			−0.365539
$333$		0			0
$334$	−9.04963			−0.495174
$335$	−2.34137	−	4.05537i	−0.127923	−	0.221568i
$336$		0			0
$337$	−11.8648	+	20.5505i	−0.646319	+	1.11946i	0.337676	+	0.941262i	$0.390359\pi$
$337$	−11.8648	+	20.5505i	−0.646319	+	1.11946i	−0.983995	+	0.178195i	$0.942974\pi$
$338$	10.4153	−	18.0399i	0.566520	−	0.981242i
$339$		0			0
$340$	−3.09627	−	5.36289i	−0.167919	−	0.290844i
$341$	19.3405			1.04735
$342$		0			0
$343$	11.5790			0.625209
$344$	1.79679	+	3.11213i	0.0968764	+	0.167795i
$345$		0			0
$346$	−23.7592	+	41.1522i	−1.27730	+	2.21236i
$347$	0.904200	−	1.56612i	0.0485400	−	0.0840738i	−0.840735	−	0.541447i	$-0.817876\pi$
$347$	0.904200	−	1.56612i	0.0485400	−	0.0840738i	0.889275	+	0.457374i	$0.151210\pi$
$348$		0			0
$349$	−7.63041	−	13.2163i	−0.408447	−	0.707451i	0.586269	−	0.810116i	$-0.300596\pi$
$349$	−7.63041	−	13.2163i	−0.408447	−	0.707451i	−0.994716	+	0.102666i	$0.967263\pi$
$350$	39.0624			2.08797
$351$		0			0
$352$	−14.2763			−0.760930
$353$	16.1912	+	28.0440i	0.861770	+	1.49263i	0.870219	+	0.492665i	$0.163977\pi$
$353$	16.1912	+	28.0440i	0.861770	+	1.49263i	−0.00844890	+	0.999964i	$0.502689\pi$
$354$		0			0
$355$	−2.76786	+	4.79407i	−0.146903	+	0.254443i
$356$	35.0107	−	60.6404i	1.85557	−	3.21393i
$357$		0			0
$358$	6.43629	+	11.1480i	0.340168	+	0.589189i
$359$	−1.91447			−0.101042			−0.0505209	−	0.998723i	$-0.516088\pi$
$359$	−1.91447			−0.101042			−0.0505209	+	0.998723i	$0.516088\pi$
$360$		0			0
$361$	−18.9982			−0.999908
$362$	−9.05303	−	15.6803i	−0.475817	−	0.824139i
$363$		0			0
$364$	−15.5496	+	26.9327i	−0.815022	+	1.41166i
$365$	1.92649	−	3.33678i	0.100837	−	0.174655i
$366$		0			0
$367$	13.4324	+	23.2656i	0.701167	+	1.21446i	0.968057	+	0.250729i	$0.0806704\pi$
$367$	13.4324	+	23.2656i	0.701167	+	1.21446i	−0.266891	+	0.963727i	$0.585996\pi$
$368$	40.5330			2.11293
$369$		0			0
$370$	4.26083			0.221510
$371$	7.99912	+	13.8549i	0.415294	+	0.719310i
$372$		0			0
$373$	−7.42009	+	12.8520i	−0.384198	+	0.665450i	−0.991658	−	0.128900i	$-0.958855\pi$
$373$	−7.42009	+	12.8520i	−0.384198	+	0.665450i	0.607460	+	0.794350i	$0.292189\pi$
$374$	11.7973	−	20.4334i	0.610022	−	1.05659i
$375$		0			0
$376$	29.4937	+	51.0845i	1.52102	+	2.63448i
$377$	−14.3628			−0.739721
$378$		0			0
$379$	−33.7870			−1.73552			−0.867762	−	0.496980i	$-0.834442\pi$
$379$	−33.7870			−1.73552			−0.867762	+	0.496980i	$0.834442\pi$
$380$	−0.0432332	−	0.0748822i	−0.00221782	−	0.00384137i
$381$		0			0
$382$	13.3059	−	23.0465i	0.680788	−	1.17916i
$383$	4.63950	−	8.03585i	0.237067	−	0.410613i	−0.722804	−	0.691053i	$-0.757147\pi$
$383$	4.63950	−	8.03585i	0.237067	−	0.410613i	0.959871	+	0.280440i	$0.0904805\pi$
$384$		0			0
$385$	−2.34477	−	4.06126i	−0.119501	−	0.206981i
$386$	−25.6827			−1.30722
$387$		0			0
$388$	82.2559			4.17591
$389$	7.98932	+	13.8379i	0.405075	+	0.701610i	0.994330	−	0.106337i	$-0.0339122\pi$
$389$	7.98932	+	13.8379i	0.405075	+	0.701610i	−0.589255	+	0.807947i	$0.700579\pi$
$390$		0			0
$391$	−9.15910	+	15.8640i	−0.463196	+	0.802278i
$392$	−10.4153	+	18.0399i	−0.526054	+	0.911153i
$393$		0			0
$394$	−17.8307	−	30.8837i	−0.898297	−	1.55590i
$395$	5.17024			0.260143
$396$		0			0
$397$	19.7050			0.988967			0.494483	−	0.869187i	$-0.335357\pi$
$397$	19.7050			0.988967			0.494483	+	0.869187i	$0.335357\pi$
$398$	−13.0103	−	22.5344i	−0.652146	−	1.12955i
$399$		0			0
$400$	15.8687	−	27.4854i	0.793435	−	1.37427i
$401$	−0.573978	+	0.994159i	−0.0286631	+	0.0496459i	−0.880001	−	0.474972i	$-0.842458\pi$
$401$	−0.573978	+	0.994159i	−0.0286631	+	0.0496459i	0.851338	+	0.524618i	$0.175792\pi$
$402$		0			0
$403$	−6.80200	−	11.7814i	−0.338832	−	0.586874i
$404$	40.0847			1.99429
$405$		0			0
$406$	−53.7110			−2.66563
$407$	5.58512	+	9.67372i	0.276844	+	0.479508i
$408$		0			0
$409$	1.55051	−	2.68556i	0.0766676	−	0.132792i	−0.825143	−	0.564924i	$-0.808905\pi$
$409$	1.55051	−	2.68556i	0.0766676	−	0.132792i	0.901810	+	0.432132i	$0.142239\pi$
$410$	−4.56283	+	7.90306i	−0.225342	+	0.390304i
$411$		0			0
$412$	−0.575322	−	0.996487i	−0.0283441	−	0.0490934i
$413$	27.5303			1.35468
$414$		0			0
$415$	−0.706452			−0.0346784
$416$	5.02094	+	8.69653i	0.246172	+	0.426383i
$417$		0			0
$418$	0.164725	−	0.285313i	0.00805698	−	0.0139551i
$419$	−17.7246	+	30.6999i	−0.865904	+	1.49979i	0.000241841		1.00000i	$0.499923\pi$
$419$	−17.7246	+	30.6999i	−0.865904	+	1.49979i	−0.866146	+	0.499791i	$0.833410\pi$
$420$		0			0
$421$	−4.60859	−	7.98232i	−0.224609	−	0.389034i	0.731593	−	0.681742i	$-0.238777\pi$
$421$	−4.60859	−	7.98232i	−0.224609	−	0.389034i	−0.956202	+	0.292707i	$0.905444\pi$
$422$	−18.0865			−0.880435
$423$		0			0
$424$	30.2746			1.47026
$425$	7.17159	+	12.4216i	0.347873	+	0.602534i
$426$		0			0
$427$	−2.04664	+	3.54488i	−0.0990437	+	0.171549i
$428$	−8.91534	+	15.4418i	−0.430939	+	0.746409i
$429$		0			0
$430$	0.348641	+	0.603863i	0.0168129	+	0.0291209i
$431$	11.5794			0.557758			0.278879	−	0.960326i	$-0.410037\pi$
$431$	11.5794			0.557758			0.278879	+	0.960326i	$0.410037\pi$
$432$		0			0
$433$	6.06511			0.291471			0.145735	−	0.989324i	$-0.453445\pi$
$433$	6.06511			0.291471			0.145735	+	0.989324i	$0.453445\pi$
$434$	−25.4368	−	44.0578i	−1.22100	−	2.11484i
$435$		0			0
$436$	11.9192	−	20.6447i	0.570827	−	0.988701i
$437$	−0.127889	+	0.221510i	−0.00611775	+	0.0105962i
$438$		0			0
$439$	−14.5030	−	25.1199i	−0.692190	−	1.19891i	−0.971119	−	0.238597i	$-0.923313\pi$
$439$	−14.5030	−	25.1199i	−0.692190	−	1.19891i	0.278929	−	0.960312i	$-0.410021\pi$
$440$	−8.87433			−0.423067
$441$		0			0
$442$	−16.5963			−0.789404
$443$	−15.4461	−	26.7534i	−0.733866	−	1.27109i	−0.955219	−	0.295899i	$-0.904381\pi$
$443$	−15.4461	−	26.7534i	−0.733866	−	1.27109i	0.221353	−	0.975194i	$-0.428953\pi$
$444$		0			0
$445$	3.71348	−	6.43193i	0.176036	−	0.304903i
$446$	13.0851	−	22.6641i	0.619598	−	1.07318i
$447$		0			0
$448$	−2.64290	−	4.57764i	−0.124865	−	0.216273i
$449$	−39.0820			−1.84439			−0.922197	−	0.386720i	$-0.873608\pi$
$449$	−39.0820			−1.84439			−0.922197	+	0.386720i	$0.873608\pi$
$450$		0			0
$451$	−23.9240			−1.12654
$452$	−3.05303	−	5.28801i	−0.143603	−	0.248727i
$453$		0			0
$454$	16.4868	−	28.5560i	0.773764	−	1.34020i
$455$	−1.64930	+	2.85667i	−0.0773204	+	0.133923i
$456$		0			0
$457$	0.752374	+	1.30315i	0.0351946	+	0.0609588i	0.883086	−	0.469211i	$-0.155462\pi$
$457$	0.752374	+	1.30315i	0.0351946	+	0.0609588i	−0.847892	+	0.530170i	$0.822128\pi$
$458$	−71.1498			−3.32461
$459$		0			0
$460$	12.6040			0.587665
$461$	−13.1186	−	22.7220i	−0.610992	−	1.05827i	−0.991074	−	0.133316i	$-0.957437\pi$
$461$	−13.1186	−	22.7220i	−0.610992	−	1.05827i	0.380082	−	0.924953i	$-0.375896\pi$
$462$		0			0
$463$	−3.37820	+	5.85122i	−0.156998	+	0.271929i	−0.933785	−	0.357835i	$-0.883515\pi$
$463$	−3.37820	+	5.85122i	−0.156998	+	0.271929i	0.776786	+	0.629764i	$0.216848\pi$
$464$	−21.8195	+	37.7926i	−1.01295	+	1.75448i
$465$		0			0
$466$	17.6163	+	30.5124i	0.816061	+	1.41346i
$467$	33.7469			1.56162			0.780810	−	0.624768i	$-0.214806\pi$
$467$	33.7469			1.56162			0.780810	+	0.624768i	$0.214806\pi$
$468$		0			0
$469$	−32.2918			−1.49110
$470$	5.72281	+	9.91220i	0.263974	+	0.457216i
$471$		0			0
$472$	26.0488	−	45.1178i	1.19899	−	2.07671i
$473$	−0.914000	+	1.58310i	−0.0420258	+	0.0727908i
$474$		0			0
$475$	0.100137	+	0.173442i	0.00459460	+	0.00795809i
$476$	−42.7033			−1.95730
$477$		0			0
$478$	−38.0310			−1.73950
$479$	−5.56330	−	9.63592i	−0.254194	−	0.440276i	0.710483	−	0.703715i	$-0.248477\pi$
$479$	−5.56330	−	9.63592i	−0.254194	−	0.440276i	−0.964676	+	0.263438i	$0.915143\pi$
$480$		0			0
$481$	3.92855	−	6.80445i	0.179126	−	0.310256i
$482$	16.4251	−	28.4492i	0.748145	−	1.29582i
$483$		0			0
$484$	2.98293	+	5.16658i	0.135588	+	0.234845i
$485$	8.72462			0.396165
$486$		0			0
$487$	−4.74691			−0.215103			−0.107552	−	0.994200i	$-0.534301\pi$
$487$	−4.74691			−0.215103			−0.107552	+	0.994200i	$0.534301\pi$
$488$	3.87299	+	6.70821i	0.175322	+	0.303667i
$489$		0			0
$490$	−2.02094	+	3.50038i	−0.0912970	+	0.158131i
$491$	−11.1702	+	19.3474i	−0.504106	+	0.873137i	0.495883	+	0.868390i	$0.334845\pi$
$491$	−11.1702	+	19.3474i	−0.504106	+	0.873137i	−0.999989	+	0.00474780i	$0.998489\pi$
$492$		0			0
$493$	−9.86097	−	17.0797i	−0.444116	−	0.769231i
$494$	−0.231734			−0.0104262
$495$		0			0
$496$	−41.3337			−1.85594
$497$	19.0869	+	33.0595i	0.856166	+	1.48292i
$498$		0			0
$499$	5.23055	−	9.05958i	0.234152	−	0.405563i	−0.724874	−	0.688881i	$-0.758102\pi$
$499$	5.23055	−	9.05958i	0.234152	−	0.405563i	0.959026	+	0.283319i	$0.0914354\pi$
$500$	10.0949	−	17.4849i	0.451459	−	0.781949i
$501$		0			0
$502$	−1.10472	−	1.91344i	−0.0493062	−	0.0854008i
$503$	25.0419			1.11656			0.558281	−	0.829652i	$-0.311461\pi$
$503$	25.0419			1.11656			0.558281	+	0.829652i	$0.311461\pi$
$504$		0			0
$505$	4.25166			0.189196
$506$	24.0116	+	41.5893i	1.06745	+	1.84887i
$507$		0			0
$508$	14.6420	−	25.3607i	0.649635	−	1.12520i
$509$	−9.03121	+	15.6425i	−0.400301	+	0.693342i	−0.993762	−	0.111521i	$-0.964428\pi$
$509$	−9.03121	+	15.6425i	−0.400301	+	0.693342i	0.593461	+	0.804863i	$0.297761\pi$
$510$		0			0
$511$	−13.2849	−	23.0102i	−0.587691	−	1.01791i
$512$	−50.5553			−2.23425
$513$		0			0
$514$	11.5885			0.511148
$515$	−0.0610226	−	0.105694i	−0.00268898	−	0.00465744i
$516$		0			0
$517$	−15.0030	+	25.9859i	−0.659831	+	1.14286i
$518$	14.6912	−	25.4459i	0.645494	−	1.11803i
$519$		0			0
$520$	3.12108	+	5.40587i	0.136868	+	0.237063i
$521$	−25.9581			−1.13725			−0.568623	−	0.822598i	$-0.692524\pi$
$521$	−25.9581			−1.13725			−0.568623	+	0.822598i	$0.692524\pi$
$522$		0			0
$523$	25.5945			1.11917			0.559585	−	0.828773i	$-0.310961\pi$
$523$	25.5945			1.11917			0.559585	+	0.828773i	$0.310961\pi$
$524$	27.8824	+	48.2937i	1.21805	+	2.10972i
$525$		0			0
$526$	−5.44104	+	9.42415i	−0.237240	+	0.410913i
$527$	9.34002	−	16.1774i	0.406858	−	0.704698i
$528$		0			0
$529$	−7.14203	−	12.3704i	−0.310523	−	0.537841i
$530$	5.87433			0.255165
$531$		0			0
$532$	−0.596267			−0.0258514
$533$	8.41400	+	14.5735i	0.364451	+	0.631247i
$534$		0			0
$535$	−0.945622	+	1.63787i	−0.0408828	+	0.0708111i
$536$	−30.5540	+	52.9210i	−1.31973	+	2.28584i
$537$		0			0
$538$	−15.3516	−	26.5898i	−0.661856	−	1.14637i
$539$	−10.5963			−0.456414
$540$		0			0
$541$	27.8476			1.19726			0.598631	−	0.801025i	$-0.295712\pi$
$541$	27.8476			1.19726			0.598631	+	0.801025i	$0.295712\pi$
$542$	0.405078	+	0.701615i	0.0173996	+	0.0301369i
$543$		0			0
$544$	−6.89440	+	11.9415i	−0.295595	+	0.511985i
$545$	1.26423	−	2.18972i	0.0541538	−	0.0937972i
$546$		0			0
$547$	2.95424	+	5.11689i	0.126314	+	0.218783i	0.922246	−	0.386604i	$-0.126352\pi$
$547$	2.95424	+	5.11689i	0.126314	+	0.218783i	−0.795932	+	0.605386i	$0.793019\pi$
$548$	46.8316			2.00055
$549$		0			0
$550$	37.6023			1.60337
$551$	−0.137689	−	0.238484i	−0.00586574	−	0.0101598i
$552$		0			0
$553$	17.8268	−	30.8770i	0.758073	−	1.31302i
$554$	33.9568	−	58.8149i	1.44269	−	2.49881i
$555$		0			0
$556$	16.4572	+	28.5048i	0.697942	+	1.20887i
$557$	26.7050			1.13153			0.565764	−	0.824567i	$-0.308581\pi$
$557$	26.7050			1.13153			0.565764	+	0.824567i	$0.308581\pi$
$558$		0			0
$559$	1.28581			0.0543838
$560$	5.01114	+	8.67956i	0.211759	+	0.366778i
$561$		0			0
$562$	−33.7793	+	58.5075i	−1.42489	+	2.46799i
$563$	−18.0312	+	31.2310i	−0.759925	+	1.31623i	0.182963	+	0.983120i	$0.441431\pi$
$563$	−18.0312	+	31.2310i	−0.759925	+	1.31623i	−0.942888	+	0.333109i	$0.891902\pi$
$564$		0			0
$565$	−0.323826	−	0.560882i	−0.0136234	−	0.0235965i
$566$	−23.5321			−0.989127
$567$		0			0
$568$	72.2390			3.03108
$569$	4.52363	+	7.83516i	0.189641	+	0.328467i	0.945130	−	0.326693i	$-0.105934\pi$
$569$	4.52363	+	7.83516i	0.189641	+	0.328467i	−0.755490	+	0.655160i	$0.772601\pi$
$570$		0			0
$571$	−15.2895	+	26.4822i	−0.639846	+	1.10825i	0.345620	+	0.938375i	$0.387669\pi$
$571$	−15.2895	+	26.4822i	−0.639846	+	1.10825i	−0.985466	+	0.169872i	$0.945665\pi$
$572$	−14.9684	+	25.9260i	−0.625859	+	1.08402i
$573$		0			0
$574$	31.4650	+	54.4989i	1.31332	+	2.27474i
$575$	−29.1935			−1.21745
$576$		0			0
$577$	−25.1489			−1.04696			−0.523481	−	0.852037i	$-0.675367\pi$
$577$	−25.1489			−1.04696			−0.523481	+	0.852037i	$0.675367\pi$
$578$	10.1284	+	17.5428i	0.421284	+	0.729685i
$579$		0			0
$580$	−6.78493	+	11.7518i	−0.281729	+	0.487969i
$581$	−2.43582	+	4.21897i	−0.101055	+	0.175032i
$582$		0			0
$583$	7.70011	+	13.3370i	0.318906	+	0.552361i
$584$	−50.2799			−2.08060
$585$		0			0
$586$	−49.7279			−2.05424
$587$	−10.4368	−	18.0770i	−0.430771	−	0.746117i	0.566169	−	0.824289i	$-0.308425\pi$
$587$	−10.4368	−	18.0770i	−0.430771	−	0.746117i	−0.996940	+	0.0781720i	$0.975092\pi$
$588$		0			0
$589$	0.130415	−	0.225885i	0.00537365	−	0.00930744i
$590$	5.05438	−	8.75444i	0.208085	−	0.360415i
$591$		0			0
$592$	−11.9363	−	20.6743i	−0.490578	−	0.849707i
$593$	15.6212			0.641488			0.320744	−	0.947166i	$-0.396067\pi$
$593$	15.6212			0.641488			0.320744	+	0.947166i	$0.396067\pi$
$594$		0			0
$595$	−4.52940			−0.185687
$596$	9.38326	+	16.2523i	0.384353	+	0.665719i
$597$		0			0
$598$	16.8897	−	29.2537i	0.690669	−	1.19627i
$599$	0.224155	−	0.388249i	0.00915874	−	0.0158634i	−0.861410	−	0.507911i	$-0.830418\pi$
$599$	0.224155	−	0.388249i	0.00915874	−	0.0158634i	0.870568	+	0.492047i	$0.163751\pi$
$600$		0			0
$601$	8.83615	+	15.3047i	0.360434	+	0.624290i	0.988032	−	0.154247i	$-0.0492952\pi$
$601$	8.83615	+	15.3047i	0.360434	+	0.624290i	−0.627598	+	0.778537i	$0.715962\pi$
$602$	4.80840			0.195976
$603$		0			0
$604$	0.596267			0.0242617
$605$	0.316390	+	0.548003i	0.0128631	+	0.0222795i
$606$		0			0
$607$	−13.0993	+	22.6886i	−0.531683	+	0.920901i	0.467634	+	0.883922i	$0.345107\pi$
$607$	−13.0993	+	22.6886i	−0.531683	+	0.920901i	−0.999316	+	0.0369787i	$0.988227\pi$
$608$	−0.0962667	+	0.166739i	−0.00390413	+	0.00676215i
$609$		0			0
$610$	0.751497	+	1.30163i	0.0304272	+	0.0527015i
$611$	21.1061			0.853860
$612$		0			0
$613$	14.5544			0.587846			0.293923	−	0.955829i	$-0.405039\pi$
$613$	14.5544			0.587846			0.293923	+	0.955829i	$0.405039\pi$
$614$	−35.8837	−	62.1524i	−1.44815	−	2.50827i
$615$		0			0
$616$	−30.5984	+	52.9980i	−1.23284	+	2.13535i
$617$	−7.01027	+	12.1421i	−0.282223	+	0.488824i	−0.971932	−	0.235262i	$-0.924405\pi$
$617$	−7.01027	+	12.1421i	−0.282223	+	0.488824i	0.689709	+	0.724087i	$0.257738\pi$
$618$		0			0
$619$	15.8562	+	27.4638i	0.637315	+	1.10386i	0.986020	+	0.166630i	$0.0532884\pi$
$619$	15.8562	+	27.4638i	0.637315	+	1.10386i	−0.348704	+	0.937233i	$0.613378\pi$
$620$	−12.8530			−0.516188
$621$		0			0
$622$	−5.17705			−0.207581
$623$	−25.6079	−	44.3541i	−1.02596	−	1.77701i
$624$		0			0
$625$	−10.8819	+	18.8480i	−0.435276	+	0.753921i
$626$	−10.6493	+	18.4451i	−0.425632	+	0.737216i
$627$		0			0
$628$	−29.3935	−	50.9111i	−1.17293	−	2.03157i
$629$	10.7888			0.430178
$630$		0			0
$631$	−38.5758			−1.53568			−0.767840	−	0.640642i	$-0.778668\pi$
$631$	−38.5758			−1.53568			−0.767840	+	0.640642i	$0.778668\pi$
$632$	−33.7349	−	58.4305i	−1.34190	−	2.32424i
$633$		0			0
$634$	−39.4099	+	68.2599i	−1.56517	+	2.71095i
$635$	1.55303	−	2.68993i	0.0616303	−	0.106747i
$636$		0			0
$637$	3.72668	+	6.45480i	0.147657	+	0.255749i
$638$	−51.7033			−2.04695
$639$		0			0
$640$	−6.24216			−0.246743
$641$	15.3084	+	26.5149i	0.604645	+	1.04728i	0.992107	+	0.125391i	$0.0400185\pi$
$641$	15.3084	+	26.5149i	0.604645	+	1.04728i	−0.387462	+	0.921886i	$0.626648\pi$
$642$		0			0
$643$	17.1125	−	29.6397i	0.674850	−	1.16887i	−0.301663	−	0.953415i	$-0.597542\pi$
$643$	17.1125	−	29.6397i	0.674850	−	1.16887i	0.976513	−	0.215459i	$-0.0691249\pi$
$644$	43.4582	−	75.2718i	1.71249	−	2.96612i
$645$		0			0
$646$	−0.159100	−	0.275570i	−0.00625972	−	0.0108421i
$647$	−12.8726			−0.506073			−0.253037	−	0.967457i	$-0.581429\pi$
$647$	−12.8726			−0.506073			−0.253037	+	0.967457i	$0.581429\pi$
$648$		0			0
$649$	26.5012			1.04026
$650$	−13.2246	−	22.9057i	−0.518712	−	0.898436i
$651$		0			0
$652$	21.5364	−	37.3022i	0.843432	−	1.46087i
$653$	5.65957	−	9.80266i	0.221476	−	0.383608i	−0.733780	−	0.679387i	$-0.762246\pi$
$653$	5.65957	−	9.80266i	0.221476	−	0.383608i	0.955256	+	0.295779i	$0.0955792\pi$
$654$		0			0
$655$	2.95740	+	5.12236i	0.115555	+	0.200147i
$656$	51.1293			1.99626
$657$		0			0
$658$	78.9282			3.07694
$659$	6.88460	+	11.9245i	0.268186	+	0.464512i	0.968393	−	0.249428i	$-0.0802425\pi$
$659$	6.88460	+	11.9245i	0.268186	+	0.464512i	−0.700207	+	0.713939i	$0.746909\pi$
$660$		0			0
$661$	10.1334	−	17.5516i	0.394144	−	0.682677i	−0.598848	−	0.800863i	$-0.704374\pi$
$661$	10.1334	−	17.5516i	0.394144	−	0.682677i	0.992992	+	0.118186i	$0.0377078\pi$
$662$	−39.2866	+	68.0463i	−1.52692	+	2.64470i
$663$		0			0
$664$	4.60947	+	7.98384i	0.178882	+	0.309833i
$665$	−0.0632441			−0.00245250
$666$		0			0
$667$	40.1411			1.55427
$668$	7.88326	+	13.6542i	0.305012	+	0.528297i
$669$		0			0
$670$	−5.92855	+	10.2685i	−0.229040	+	0.396709i
$671$	−1.97013	+	3.41237i	−0.0760561	+	0.131733i
$672$		0			0
$673$	15.2724	+	26.4526i	0.588709	+	1.01967i	0.994402	+	0.105665i	$0.0336971\pi$
$673$	15.2724	+	26.4526i	0.588709	+	1.01967i	−0.405692	+	0.914010i	$0.632970\pi$
$674$	60.0856			2.31441
$675$		0			0
$676$	−36.2918			−1.39584
$677$	1.85962	+	3.22096i	0.0714711	+	0.123792i	0.899546	−	0.436826i	$-0.143897\pi$
$677$	1.85962	+	3.22096i	0.0714711	+	0.123792i	−0.828075	+	0.560617i	$0.810564\pi$
$678$		0			0
$679$	30.0822	−	52.1039i	1.15445	−	1.99956i
$680$	−4.28564	+	7.42295i	−0.164347	+	0.284657i
$681$		0			0
$682$	−24.4859	−	42.4109i	−0.937614	−	1.62400i
$683$	−21.7469			−0.832122			−0.416061	−	0.909337i	$-0.636590\pi$
$683$	−21.7469			−0.832122			−0.416061	+	0.909337i	$0.636590\pi$
$684$		0			0
$685$	4.96728			0.189790
$686$	−14.6596	−	25.3911i	−0.559705	−	0.969437i
$687$		0			0
$688$	1.95336	−	3.38332i	0.0744713	−	0.128988i
$689$	5.41622	−	9.38117i	0.206342	−	0.357394i
$690$		0			0
$691$	18.7974	+	32.5581i	0.715087	+	1.23857i	0.962926	+	0.269766i	$0.0869465\pi$
$691$	18.7974	+	32.5581i	0.715087	+	1.23857i	−0.247838	+	0.968801i	$0.579720\pi$
$692$	82.7880			3.14713
$693$		0			0
$694$	−4.57903			−0.173818
$695$	1.74557	+	3.02341i	0.0662131	+	0.114684i
$696$		0			0
$697$	−11.5535	+	20.0112i	−0.437620	+	0.757980i
$698$	−19.3209	+	33.4648i	−0.731306	+	1.26666i
$699$		0			0
$700$	−34.0278	−	58.9379i	−1.28613	−	2.22764i
$701$	23.3351			0.881355			0.440678	−	0.897665i	$-0.354738\pi$
$701$	23.3351			0.881355			0.440678	+	0.897665i	$0.354738\pi$
$702$		0			0
$703$	0.150644			0.00568166
$704$	−2.54411	−	4.40653i	−0.0958848	−	0.166077i
$705$		0			0
$706$	40.9975	−	71.0098i	1.54296	−	2.67249i
$707$	14.6596	−	25.3911i	0.551330	−	0.954931i
$708$		0			0
$709$	−3.28952	−	5.69761i	−0.123540	−	0.213978i	0.797621	−	0.603159i	$-0.206091\pi$
$709$	−3.28952	−	5.69761i	−0.123540	−	0.213978i	−0.921161	+	0.389181i	$0.872758\pi$
$710$	14.0169			0.526045
$711$		0			0
$712$	−96.9190			−3.63219
$713$	19.0103	+	32.9267i	0.711940	+	1.23312i
$714$		0			0
$715$	−1.58765	+	2.74989i	−0.0593747	+	0.102840i
$716$	11.2135	−	19.4223i	0.419067	−	0.725846i
$717$		0			0
$718$	2.42380	+	4.19815i	0.0904554	+	0.156673i
$719$	−16.8324			−0.627744			−0.313872	−	0.949465i	$-0.601626\pi$
$719$	−16.8324			−0.627744			−0.313872	+	0.949465i	$0.601626\pi$
$720$		0			0
$721$	−0.841615			−0.0313434
$722$	24.0526	+	41.6604i	0.895146	+	1.55044i
$723$		0			0
$724$	−15.7724	+	27.3187i	−0.586178	+	1.01529i
$725$	15.7153	−	27.2197i	0.583651	−	1.01091i
$726$		0			0
$727$	−12.7811	−	22.1374i	−0.474023	−	0.821032i	0.525534	−	0.850772i	$-0.323865\pi$
$727$	−12.7811	−	22.1374i	−0.474023	−	0.821032i	−0.999558	+	0.0297400i	$0.990532\pi$
$728$	43.0455			1.59537
$729$		0			0
$730$	−9.75608			−0.361089
$731$	0.882789	+	1.52904i	0.0326511	+	0.0565534i
$732$		0			0
$733$	7.39899	−	12.8154i	0.273288	−	0.473348i	−0.696414	−	0.717640i	$-0.745222\pi$
$733$	7.39899	−	12.8154i	0.273288	−	0.473348i	0.969702	+	0.244292i	$0.0785555\pi$
$734$	34.0121	−	58.9106i	1.25541	−	2.17443i
$735$		0			0
$736$	−14.0326	−	24.3051i	−0.517247	−	0.895898i
$737$	−31.0847			−1.14502
$738$		0			0
$739$	9.19078			0.338088			0.169044	−	0.985608i	$-0.445932\pi$
$739$	9.19078			0.338088			0.169044	+	0.985608i	$0.445932\pi$
$740$	−3.71167	−	6.42880i	−0.136444	−	0.236327i
$741$		0			0
$742$	20.2545	−	35.0818i	0.743566	−	1.28789i
$743$	−22.2246	+	38.4942i	−0.815342	+	1.41221i	0.0937395	+	0.995597i	$0.470118\pi$
$743$	−22.2246	+	38.4942i	−0.815342	+	1.41221i	−0.909082	+	0.416618i	$0.863215\pi$
$744$		0			0
$745$	0.995252	+	1.72383i	0.0364632	+	0.0631562i
$746$	37.5767			1.37578
$747$		0			0
$748$	−41.1070			−1.50302
$749$	6.52094	+	11.2946i	0.238270	+	0.412696i
$750$		0			0
$751$	17.9030	−	31.0089i	0.653290	−	1.13153i	−0.329029	−	0.944320i	$-0.606721\pi$
$751$	17.9030	−	31.0089i	0.653290	−	1.13153i	0.982319	−	0.187212i	$-0.0599453\pi$
$752$	32.0638	−	55.5361i	1.16925	−	2.02519i
$753$		0			0
$754$	18.1839	+	31.4955i	0.662219	+	1.14700i
$755$	0.0632441			0.00230169
$756$		0			0
$757$	−45.8976			−1.66818			−0.834088	−	0.551632i	$-0.814005\pi$
$757$	−45.8976			−1.66818			−0.834088	+	0.551632i	$0.814005\pi$
$758$	42.7759	+	74.0900i	1.55369	+	2.69107i
$759$		0			0
$760$	−0.0598406	+	0.103647i	−0.00217064	+	0.00375967i
$761$	18.5976	−	32.2120i	0.674163	−	1.16768i	−0.302550	−	0.953134i	$-0.597838\pi$
$761$	18.5976	−	32.2120i	0.674163	−	1.16768i	0.976713	−	0.214551i	$-0.0688288\pi$
$762$		0			0
$763$	−8.71806	−	15.1001i	−0.315615	−	0.546661i
$764$	−46.3637			−1.67738
$765$		0			0
$766$	−23.4953			−0.848918
$767$	−9.32042	−	16.1434i	−0.336541	−	0.582906i
$768$		0			0
$769$	19.1668	−	33.1979i	0.691174	−	1.19715i	−0.280280	−	0.959918i	$-0.590427\pi$
$769$	19.1668	−	33.1979i	0.691174	−	1.19715i	0.971454	−	0.237230i	$-0.0762395\pi$
$770$	−5.93717	+	10.2835i	−0.213961	+	0.370591i
$771$		0			0
$772$	22.3726	+	38.7504i	0.805207	+	1.39466i
$773$	52.8272			1.90006			0.950031	−	0.312156i	$-0.101051\pi$
$773$	52.8272			1.90006			0.950031	+	0.312156i	$0.101051\pi$
$774$		0			0
$775$	29.7701			1.06937
$776$	−56.9265	−	98.5997i	−2.04354	−	3.53952i
$777$		0			0
$778$	20.2297	−	35.0388i	0.725269	−	1.25620i
$779$	−0.161322	+	0.279418i	−0.00577995	+	0.0100112i
$780$		0			0
$781$	18.3735	+	31.8238i	0.657454	+	1.13874i
$782$	46.3833			1.65866
$783$		0			0
$784$	22.6459			0.808782
$785$	−3.11768	−	5.39998i	−0.111275	−	0.192733i
$786$		0			0
$787$	−22.6202	+	39.1793i	−0.806323	+	1.39659i	0.109071	+	0.994034i	$0.465212\pi$
$787$	−22.6202	+	39.1793i	−0.806323	+	1.39659i	−0.915394	+	0.402559i	$0.868121\pi$
$788$	−31.0651	+	53.8064i	−1.10665	+	1.91677i
$789$		0			0
$790$	−6.54576	−	11.3376i	−0.232888	−	0.403373i
$791$	−4.46616			−0.158798
$792$		0			0
$793$	2.77156			0.0984211
$794$	−24.9474	−	43.2102i	−0.885351	−	1.53347i
$795$		0			0
$796$	−22.6668	+	39.2601i	−0.803405	+	1.39154i
$797$	8.45946	−	14.6522i	0.299649	−	0.519008i	−0.676406	−	0.736529i	$-0.736464\pi$
$797$	8.45946	−	14.6522i	0.299649	−	0.519008i	0.976056	+	0.217521i	$0.0697970\pi$
$798$		0			0
$799$	14.4907	+	25.0986i	0.512643	+	0.887924i
$800$	−21.9750			−0.776934
$801$		0			0
$802$	2.90673			0.102640
$803$	−12.7883	−	22.1500i	−0.451290	−	0.781658i
$804$		0			0
$805$	4.60947	−	7.98384i	0.162462	−	0.281393i
$806$	−17.2233	+	29.8316i	−0.606664	+	1.05077i
$807$		0			0
$808$	−27.7413	−	48.0493i	−0.975935	−	1.69037i
$809$	−34.9145			−1.22753			−0.613764	−	0.789490i	$-0.710345\pi$
$809$	−34.9145			−1.22753			−0.613764	+	0.789490i	$0.710345\pi$
$810$		0			0
$811$	18.0419			0.633536			0.316768	−	0.948503i	$-0.397402\pi$
$811$	18.0419			0.633536			0.316768	+	0.948503i	$0.397402\pi$
$812$	46.7884	+	81.0399i	1.64195	+	2.84394i
$813$		0			0
$814$	14.1420	−	24.4947i	0.495678	−	0.858539i
$815$	2.28430	−	3.95652i	0.0800156	−	0.138591i
$816$		0			0
$817$	0.0123264	+	0.0213500i	0.000431246	+	0.000746940i
$818$	−7.85204			−0.274540
$819$		0			0
$820$	15.8990			0.555217
$821$	−20.3195	−	35.1945i	−0.709157	−	1.22830i	−0.965170	−	0.261623i	$-0.915742\pi$
$821$	−20.3195	−	35.1945i	−0.709157	−	1.22830i	0.256013	−	0.966673i	$-0.417591\pi$
$822$		0			0
$823$	−13.0248	+	22.5596i	−0.454017	+	0.786380i	−0.998631	−	0.0523068i	$-0.983343\pi$
$823$	−13.0248	+	22.5596i	−0.454017	+	0.786380i	0.544615	+	0.838686i	$0.316676\pi$
$824$	−0.796322	+	1.37927i	−0.0277412	+	0.0480492i
$825$		0			0
$826$	−34.8546	−	60.3700i	−1.21275	−	2.10054i
$827$	−37.6195			−1.30816			−0.654079	−	0.756426i	$-0.726944\pi$
$827$	−37.6195			−1.30816			−0.654079	+	0.756426i	$0.726944\pi$
$828$		0			0
$829$	−35.0215			−1.21635			−0.608173	−	0.793805i	$-0.708097\pi$
$829$	−35.0215			−1.21635			−0.608173	+	0.793805i	$0.708097\pi$
$830$	0.894400	+	1.54915i	0.0310451	+	0.0537717i
$831$		0			0
$832$	−1.78952	+	3.09953i	−0.0620403	+	0.107457i
$833$	−5.11721	+	8.86327i	−0.177301	+	0.307094i
$834$		0			0
$835$	0.836152	+	1.44826i	0.0289362	+	0.0501190i
$836$	−0.573978			−0.0198514
$837$		0			0
$838$	89.7606			3.10073
$839$	−13.3071	−	23.0485i	−0.459411	−	0.795722i	0.539519	−	0.841973i	$-0.318606\pi$
$839$	−13.3071	−	23.0485i	−0.459411	−	0.795722i	−0.998930	+	0.0462508i	$0.985273\pi$
$840$		0			0
$841$	−7.10859	+	12.3124i	−0.245124	+	0.424567i
$842$	−11.6694	+	20.2119i	−0.402153	+	0.696549i
$843$		0			0
$844$	15.7554	+	27.2891i	0.542322	+	0.939329i
$845$	−3.84936			−0.132422
$846$		0			0
$847$	4.36360			0.149935
$848$	−16.4564	−	28.5032i	−0.565114	−	0.978805i
$849$		0			0
$850$	18.1591	−	31.4525i	0.622852	−	1.07881i
$851$	−10.9795	+	19.0171i	−0.376373	+	0.651897i
$852$		0			0
$853$	−1.22756	−	2.12619i	−0.0420308	−	0.0727995i	0.844245	−	0.535958i	$-0.180049\pi$
$853$	−1.22756	−	2.12619i	−0.0420308	−	0.0727995i	−0.886276	+	0.463158i	$0.846716\pi$
$854$	10.3645			0.354667
$855$		0			0
$856$	24.6800			0.843547
$857$	4.91488	+	8.51282i	0.167889	+	0.290792i	0.937677	−	0.347507i	$-0.112972\pi$
$857$	4.91488	+	8.51282i	0.167889	+	0.290792i	−0.769788	+	0.638299i	$0.779638\pi$
$858$		0			0
$859$	−4.40848	+	7.63571i	−0.150415	+	0.260527i	−0.931380	−	0.364048i	$-0.881394\pi$
$859$	−4.40848	+	7.63571i	−0.150415	+	0.260527i	0.780965	+	0.624575i	$0.214728\pi$
$860$	0.607411	−	1.05207i	0.0207125	−	0.0358752i
$861$		0			0
$862$	−14.6600	−	25.3918i	−0.499321	−	0.864849i
$863$	−6.62124			−0.225390			−0.112695	−	0.993630i	$-0.535948\pi$
$863$	−6.62124			−0.225390			−0.112695	+	0.993630i	$0.535948\pi$
$864$		0			0
$865$	8.78106			0.298565
$866$	−7.67870	−	13.2999i	−0.260933	−	0.451949i
$867$		0			0
$868$	−44.3166	+	76.7586i	−1.50420	+	2.60536i
$869$	17.1604	−	29.7228i	0.582128	−	1.00828i
$870$		0			0
$871$	10.9324	+	18.9355i	0.370431	+	0.641605i
$872$	−32.9956			−1.11737
$873$		0			0
$874$	0.647651			0.0219071
$875$	−7.38372	−	12.7890i	−0.249615	−	0.432347i
$876$		0			0
$877$	2.03802	−	3.52995i	0.0688190	−	0.119198i	−0.829563	−	0.558414i	$-0.811410\pi$
$877$	2.03802	−	3.52995i	0.0688190	−	0.119198i	0.898382	+	0.439216i	$0.144744\pi$
$878$	−36.7229	+	63.6059i	−1.23934	+	2.14659i
$879$		0			0
$880$	4.82383	+	8.35511i	0.162611	+	0.281651i
$881$	9.25133			0.311685			0.155843	−	0.987782i	$-0.450191\pi$
$881$	9.25133			0.311685			0.155843	+	0.987782i	$0.450191\pi$
$882$		0			0
$883$	−37.7701			−1.27107			−0.635533	−	0.772074i	$-0.719220\pi$
$883$	−37.7701			−1.27107			−0.635533	+	0.772074i	$0.719220\pi$
$884$	14.4572	+	25.0407i	0.486249	+	0.842209i
$885$		0			0
$886$	−39.1109	+	67.7420i	−1.31396	+	2.27584i
$887$	−9.48932	+	16.4360i	−0.318620	+	0.551866i	−0.980200	−	0.198008i	$-0.936553\pi$
$887$	−9.48932	+	16.4360i	−0.318620	+	0.551866i	0.661580	+	0.749874i	$0.269886\pi$
$888$		0			0
$889$	−10.7096	−	18.5496i	−0.359189	−	0.622133i
$890$	−18.8057			−0.630369
$891$		0			0
$892$	−45.5945			−1.52662
$893$	0.202333	+	0.350452i	0.00677083	+	0.0117274i
$894$		0			0
$895$	1.18938	−	2.06006i	0.0397565	−	0.0688603i
$896$	−21.5228	+	37.2785i	−0.719025	+	1.24539i
$897$		0			0
$898$	49.4796	+	85.7011i	1.65115	+	2.85988i
$899$	−40.9341			−1.36523
$900$		0			0
$901$	14.8743			0.495536
$902$	30.2888	+	52.4617i	1.00851	+	1.74678i
$903$		0			0
$904$	−4.22580	+	7.31931i	−0.140548	+	0.243437i
$905$	−1.67293	+	2.89760i	−0.0556102	+	0.0963196i
$906$		0			0
$907$	−4.82295	−	8.35359i	−0.160143	−	0.277376i	0.774777	−	0.632235i	$-0.217862\pi$
$907$	−4.82295	−	8.35359i	−0.160143	−	0.277376i	−0.934920	+	0.354859i	$0.884529\pi$
$908$	−57.4475			−1.90646
$909$		0			0
$910$	8.35235			0.276878
$911$	3.26739	+	5.65928i	0.108253	+	0.187500i	0.915063	−	0.403311i	$-0.132141\pi$
$911$	3.26739	+	5.65928i	0.108253	+	0.187500i	−0.806809	+	0.590812i	$0.798808\pi$
$912$		0			0
$913$	−2.34477	+	4.06126i	−0.0776006	+	0.134408i
$914$	1.90508	−	3.29969i	0.0630144	−	0.109144i
$915$		0			0
$916$	61.9796	+	107.352i	2.04786	+	3.54700i
$917$	40.7880			1.34694
$918$		0			0
$919$	3.89124			0.128360			0.0641802	−	0.997938i	$-0.479557\pi$
$919$	3.89124			0.128360			0.0641802	+	0.997938i	$0.479557\pi$
$920$	−8.72281	−	15.1084i	−0.287583	−	0.498108i
$921$		0			0
$922$	−33.2173	+	57.5341i	−1.09396	+	1.89479i
$923$	12.9238	−	22.3847i	0.425392	−	0.736801i
$924$		0			0
$925$	8.59698	+	14.8904i	0.282667	+	0.489594i
$926$	17.1078			0.562198
$927$		0			0
$928$	30.2158			0.991881
$929$	19.9265	+	34.5137i	0.653767	+	1.13236i	0.982201	+	0.187831i	$0.0601456\pi$
$929$	19.9265	+	34.5137i	0.653767	+	1.13236i	−0.328435	+	0.944527i	$0.606521\pi$
$930$		0			0
$931$	−0.0714517	+	0.123758i	−0.00234174	+	0.00405601i
$932$	30.6917	−	53.1595i	1.00534	−	1.74130i
$933$		0			0
$934$	−42.7251	−	74.0020i	−1.39801	−	2.42142i
$935$	−4.36009			−0.142590
$936$		0			0
$937$	33.0651			1.08019			0.540095	−	0.841604i	$-0.318388\pi$
$937$	33.0651			1.08019			0.540095	+	0.841604i	$0.318388\pi$
$938$	40.8828	+	70.8112i	1.33487	+	2.31207i
$939$		0			0
$940$	9.97044	−	17.2693i	0.325200	−	0.563263i
$941$	26.9033	−	46.5979i	0.877023	−	1.51905i	0.0224315	−	0.999748i	$-0.492859\pi$
$941$	26.9033	−	46.5979i	0.877023	−	1.51905i	0.854592	−	0.519300i	$-0.173807\pi$
$942$		0			0
$943$	−23.5155	−	40.7300i	−0.765769	−	1.32635i
$944$	−56.6373			−1.84339
$945$		0			0
$946$	4.62866			0.150491
$947$	−21.1177	−	36.5769i	−0.686232	−	1.18859i	−0.973048	−	0.230603i	$-0.925930\pi$
$947$	−21.1177	−	36.5769i	−0.686232	−	1.18859i	0.286815	−	0.957986i	$-0.407403\pi$
$948$		0			0
$949$	−8.99525	+	15.5802i	−0.291998	+	0.505756i
$950$	0.253556	−	0.439172i	0.00822644	−	0.0142486i
$951$		0			0
$952$	29.5535	+	51.1882i	0.957834	+	1.65902i
$953$	24.5776			0.796147			0.398073	−	0.917354i	$-0.369679\pi$
$953$	24.5776			0.796147			0.398073	+	0.917354i	$0.369679\pi$
$954$		0			0
$955$	−4.91765			−0.159131
$956$	33.1293	+	57.3816i	1.07148	+	1.85585i
$957$		0			0
$958$	−14.0868	+	24.3990i	−0.455123	+	0.788296i
$959$	17.1270	−	29.6649i	0.553060	−	0.957928i
$960$		0			0
$961$	−3.88578	−	6.73037i	−0.125348	−	0.217109i
$962$	−19.8949			−0.641436
$963$		0			0
$964$	−57.2327			−1.84334
$965$	2.37299	+	4.11014i	0.0763892	+	0.132310i
$966$		0			0
$967$	−2.23601	+	3.87289i	−0.0719054	+	0.124544i	−0.899736	−	0.436434i	$-0.856241\pi$
$967$	−2.23601	+	3.87289i	−0.0719054	+	0.124544i	0.827831	+	0.560978i	$0.189575\pi$
$968$	4.12877	−	7.15123i	0.132704	−	0.229849i
$969$		0			0
$970$	−11.0458	−	19.1318i	−0.354658	−	0.614286i
$971$	−4.61949			−0.148246			−0.0741232	−	0.997249i	$-0.523616\pi$
$971$	−4.61949			−0.148246			−0.0741232	+	0.997249i	$0.523616\pi$
$972$		0			0
$973$	24.0746			0.771796
$974$	6.00980	+	10.4093i	0.192566	+	0.333535i
$975$		0			0
$976$	4.21048	−	7.29277i	0.134774	−	0.233436i
$977$	5.64038	−	9.76942i	0.180452	−	0.312551i	−0.761583	−	0.648068i	$-0.775577\pi$
$977$	5.64038	−	9.76942i	0.180452	−	0.312551i	0.942034	+	0.335516i	$0.108911\pi$
$978$		0			0
$979$	−24.6506	−	42.6962i	−0.787838	−	1.36458i
$980$	7.04189			0.224945
$981$		0			0
$982$	56.5681			1.80516
$983$	8.53209	+	14.7780i	0.272131	+	0.471345i	0.969407	−	0.245457i	$-0.0789381\pi$
$983$	8.53209	+	14.7780i	0.272131	+	0.471345i	−0.697276	+	0.716803i	$0.745605\pi$
$984$		0			0
$985$	−3.29498	+	5.70707i	−0.104987	+	0.181842i
$986$	−24.9688	+	43.2473i	−0.795170	+	1.37727i
$987$		0			0
$988$	0.201867	+	0.349643i	0.00642223	+	0.0111236i
$989$	−3.59358			−0.114269
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	14.3097	+	24.7852i	0.454335	+	0.786931i
$993$		0			0
$994$	48.3298	−	83.7097i	1.53293	−	2.65511i
$995$	−2.40420	+	4.16420i	−0.0762183	+	0.132014i
$996$		0			0
$997$	−11.1924	−	19.3858i	−0.354466	−	0.613953i	0.632560	−	0.774511i	$-0.282004\pi$
$997$	−11.1924	−	19.3858i	−0.354466	−	0.613953i	−0.987026	+	0.160558i	$0.948671\pi$
$998$	−26.4884			−0.838477
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.c.e.82.1		6
3.2	odd	2		243.2.c.f.82.3		6
9.2	odd	6		243.2.c.f.163.3		6
9.4	even	3		243.2.a.f.1.3	yes	3
9.5	odd	6		243.2.a.e.1.1	✓	3
9.7	even	3	inner	243.2.c.e.163.1		6
27.2	odd	18		729.2.e.g.82.1		6
27.4	even	9		729.2.e.b.649.1		6
27.5	odd	18		729.2.e.h.163.1		6
27.7	even	9		729.2.e.c.568.1		6
27.11	odd	18		729.2.e.a.325.1		6
27.13	even	9		729.2.e.i.406.1		6
27.14	odd	18		729.2.e.a.406.1		6
27.16	even	9		729.2.e.i.325.1		6
27.20	odd	18		729.2.e.h.568.1		6
27.22	even	9		729.2.e.c.163.1		6
27.23	odd	18		729.2.e.g.649.1		6
27.25	even	9		729.2.e.b.82.1		6
36.23	even	6		3888.2.a.bd.1.3		3
36.31	odd	6		3888.2.a.bk.1.1		3
45.4	even	6		6075.2.a.bq.1.1		3
45.14	odd	6		6075.2.a.bv.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.1	✓	3	9.5	odd	6
243.2.a.f.1.3	yes	3	9.4	even	3
243.2.c.e.82.1		6	1.1	even	1	trivial
243.2.c.e.163.1		6	9.7	even	3	inner
243.2.c.f.82.3		6	3.2	odd	2
243.2.c.f.163.3		6	9.2	odd	6
729.2.e.a.325.1		6	27.11	odd	18
729.2.e.a.406.1		6	27.14	odd	18
729.2.e.b.82.1		6	27.25	even	9
729.2.e.b.649.1		6	27.4	even	9
729.2.e.c.163.1		6	27.22	even	9
729.2.e.c.568.1		6	27.7	even	9
729.2.e.g.82.1		6	27.2	odd	18
729.2.e.g.649.1		6	27.23	odd	18
729.2.e.h.163.1		6	27.5	odd	18
729.2.e.h.568.1		6	27.20	odd	18
729.2.e.i.325.1		6	27.16	even	9
729.2.e.i.406.1		6	27.13	even	9
3888.2.a.bd.1.3		3	36.23	even	6
3888.2.a.bk.1.1		3	36.31	odd	6
6075.2.a.bq.1.1		3	45.4	even	6
6075.2.a.bv.1.3		3	45.14	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)

\(f(q)\)	\(=\)	\(q+(-1.26604 - 2.19285i) q^{2} +(-2.20574 + 3.82045i) q^{4} +(-0.233956 + 0.405223i) q^{5} +(1.61334 + 2.79439i) q^{7} +6.10607 q^{8} +O(q^{10})\)	\(q+(-1.26604 - 2.19285i) q^{2} +(-2.20574 + 3.82045i) q^{4} +(-0.233956 + 0.405223i) q^{5} +(1.61334 + 2.79439i) q^{7} +6.10607 q^{8} +1.18479 q^{10} +(1.55303 + 2.68993i) q^{11} +(1.09240 - 1.89209i) q^{13} +(4.08512 - 7.07564i) q^{14} +(-3.31908 - 5.74881i) q^{16} +3.00000 q^{17} +0.0418891 q^{19} +(-1.03209 - 1.78763i) q^{20} +(3.93242 - 6.81115i) q^{22} +(-3.05303 + 5.28801i) q^{23} +(2.39053 + 4.14052i) q^{25} -5.53209 q^{26} -14.2344 q^{28} +(-3.28699 - 5.69323i) q^{29} +(3.11334 - 5.39246i) q^{31} +(-2.29813 + 3.98048i) q^{32} +(-3.79813 - 6.57856i) q^{34} -1.50980 q^{35} +3.59627 q^{37} +(-0.0530334 - 0.0918566i) q^{38} +(-1.42855 + 2.47432i) q^{40} +(-3.85117 + 6.67042i) q^{41} +(0.294263 + 0.509678i) q^{43} -13.7023 q^{44} +15.4611 q^{46} +(4.83022 + 8.36619i) q^{47} +(-1.70574 + 2.95442i) q^{49} +(6.05303 - 10.4842i) q^{50} +(4.81908 + 8.34689i) q^{52} +4.95811 q^{53} -1.45336 q^{55} +(9.85117 + 17.0627i) q^{56} +(-8.32295 + 14.4158i) q^{58} +(4.26604 - 7.38901i) q^{59} +(0.634285 + 1.09861i) q^{61} -15.7665 q^{62} -1.63816 q^{64} +(0.511144 + 0.885328i) q^{65} +(-5.00387 + 8.66696i) q^{67} +(-6.61721 + 11.4613i) q^{68} +(1.91147 + 3.31077i) q^{70} +11.8307 q^{71} -8.23442 q^{73} +(-4.55303 - 7.88609i) q^{74} +(-0.0923963 + 0.160035i) q^{76} +(-5.01114 + 8.67956i) q^{77} +(-5.52481 - 9.56926i) q^{79} +3.10607 q^{80} +19.5030 q^{82} +(0.754900 + 1.30753i) q^{83} +(-0.701867 + 1.21567i) q^{85} +(0.745100 - 1.29055i) q^{86} +(9.48293 + 16.4249i) q^{88} -15.8726 q^{89} +7.04963 q^{91} +(-13.4684 - 23.3279i) q^{92} +(12.2306 - 21.1839i) q^{94} +(-0.00980018 + 0.0169744i) q^{95} +(-9.32295 - 16.1478i) q^{97} +8.63816 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 3 q^{7} + 12 q^{8}+O(q^{10}) \) 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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