LMFDB - Embedded newform 243.3.f.a.215.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,3,Mod(26,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.26"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	243.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [30,-3,0,3,-21] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.62127042396$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			215.5
Character	$\chi$	$=$	243.215
Dual form			243.3.f.a.26.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.58795 - 0.456325i) q^{2} +(2.73048 - 0.993814i) q^{4} +(4.01814 - 4.78863i) q^{5} +(7.62807 + 2.77639i) q^{7} +(-2.49037 + 1.43782i) q^{8} +(8.21356 - 14.2263i) q^{10} +(-5.21549 - 6.21558i) q^{11} +(1.68605 - 9.56207i) q^{13} +(21.0080 + 3.70428i) q^{14} +(-14.6925 + 12.3285i) q^{16} +(13.0143 + 7.51380i) q^{17} +(8.93226 + 15.4711i) q^{19} +(6.21244 - 17.0685i) q^{20} +(-16.3337 - 13.7056i) q^{22} +(-9.00658 - 24.7454i) q^{23} +(-2.44434 - 13.8625i) q^{25} -25.5156i q^{26} +23.5875 q^{28} +(14.9413 - 2.63456i) q^{29} +(-30.7596 + 11.1956i) q^{31} +(-25.0039 + 29.7985i) q^{32} +(37.1091 + 13.5066i) q^{34} +(43.9457 - 25.3721i) q^{35} +(-15.8096 + 27.3831i) q^{37} +(30.1761 + 35.9625i) q^{38} +(-3.12149 + 17.7028i) q^{40} +(16.2691 + 2.86867i) q^{41} +(-64.2129 + 53.8810i) q^{43} +(-20.4179 - 11.7883i) q^{44} +(-34.6005 - 59.9298i) q^{46} +(-4.50446 + 12.3759i) q^{47} +(12.9430 + 10.8604i) q^{49} +(-12.6516 - 34.7601i) q^{50} +(-4.89919 - 27.7847i) q^{52} +25.7140i q^{53} -50.7206 q^{55} +(-22.9887 + 4.05353i) q^{56} +(37.4652 - 13.6362i) q^{58} +(-14.5984 + 17.3977i) q^{59} +(-32.0325 - 11.6589i) q^{61} +(-74.4955 + 43.0100i) q^{62} +(-12.7517 + 22.0867i) q^{64} +(-39.0144 - 46.4956i) q^{65} +(1.40732 - 7.98130i) q^{67} +(43.0026 + 7.58252i) q^{68} +(102.151 - 85.7152i) q^{70} +(-35.7557 - 20.6436i) q^{71} +(40.4046 + 69.9827i) q^{73} +(-28.4189 + 78.0804i) q^{74} +(39.7648 + 33.3666i) q^{76} +(-22.5272 - 61.8931i) q^{77} +(-4.79818 - 27.2118i) q^{79} +119.894i q^{80} +43.4126 q^{82} +(-17.3226 + 3.05444i) q^{83} +(88.2740 - 32.1291i) q^{85} +(-141.593 + 168.743i) q^{86} +(21.9254 + 7.98019i) q^{88} +(-24.4986 + 14.1443i) q^{89} +(39.4094 - 68.2590i) q^{91} +(-49.1846 - 58.6159i) q^{92} +(-6.00988 + 34.0837i) q^{94} +(109.977 + 19.3918i) q^{95} +(129.179 - 108.394i) q^{97} +(38.4516 + 22.2000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} - 57 q^{11} + 3 q^{13} + 114 q^{14} + 27 q^{16} + 9 q^{17} - 3 q^{19} + 183 q^{20} + 75 q^{22} - 48 q^{23} + 21 q^{25} - 12 q^{28} + 78 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) $ 30 * q - 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 - 57 * q^11 + 3 * q^13 + 114 * q^14 + 27 * q^16 + 9 * q^17 - 3 * q^19 + 183 * q^20 + 75 * q^22 - 48 * q^23 + 21 * q^25 - 12 * q^28 + 78 * q^29 - 87 * q^31 - 243 * q^32 - 153 * q^34 + 252 * q^35 - 3 * q^37 - 321 * q^38 - 168 * q^40 + 357 * q^41 - 87 * q^43 - 639 * q^44 - 3 * q^46 + 51 * q^47 - 69 * q^49 - 168 * q^50 - 36 * q^52 - 12 * q^55 + 177 * q^56 + 138 * q^58 - 48 * q^59 + 147 * q^61 + 900 * q^62 - 51 * q^64 - 624 * q^65 + 12 * q^67 + 477 * q^68 - 6 * q^70 - 315 * q^71 - 66 * q^73 + 480 * q^74 - 57 * q^76 - 453 * q^77 - 15 * q^79 - 12 * q^82 + 591 * q^83 + 243 * q^85 - 669 * q^86 + 591 * q^88 - 72 * q^89 + 96 * q^91 - 564 * q^92 + 957 * q^94 + 606 * q^95 + 696 * q^97 - 882 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	2.58795	−	0.456325i	1.29397	−	0.228163i	0.516071	−	0.856546i	$-0.327394\pi$
$2$	2.58795	−	0.456325i	1.29397	−	0.228163i	0.777904	+	0.628383i	$0.216283\pi$
$3$		0			0
$3$		0			0
$4$	2.73048	−	0.993814i	0.682620	−	0.248453i
$5$	4.01814	−	4.78863i	0.803627	−	0.957726i	−0.196112	−	0.980582i	$-0.562831\pi$
$5$	4.01814	−	4.78863i	0.803627	−	0.957726i	0.999739	+	0.0228560i	$0.00727592\pi$
$6$		0			0
$7$	7.62807	+	2.77639i	1.08972	+	0.396627i	0.823519	−	0.567289i	$-0.192008\pi$
$7$	7.62807	+	2.77639i	1.08972	+	0.396627i	0.266206	+	0.963916i	$0.414230\pi$
$8$	−2.49037	+	1.43782i	−0.311297	+	0.179727i
$9$		0			0
$10$	8.21356	−	14.2263i	0.821356	−	1.42263i
$11$	−5.21549	−	6.21558i	−0.474135	−	0.565052i	0.474974	−	0.880000i	$-0.342458\pi$
$11$	−5.21549	−	6.21558i	−0.474135	−	0.565052i	−0.949109	+	0.314948i	$0.898013\pi$
$12$		0			0
$13$	1.68605	−	9.56207i	0.129696	−	0.735544i	−0.848711	−	0.528857i	$-0.822621\pi$
$13$	1.68605	−	9.56207i	0.129696	−	0.735544i	0.978407	−	0.206687i	$-0.0662681\pi$
$14$	21.0080	+	3.70428i	1.50057	+	0.264591i
$15$		0			0
$16$	−14.6925	+	12.3285i	−0.918280	+	0.770529i
$17$	13.0143	+	7.51380i	0.765546	+	0.441988i	0.831284	−	0.555849i	$-0.187607\pi$
$17$	13.0143	+	7.51380i	0.765546	+	0.441988i	−0.0657372	+	0.997837i	$0.520940\pi$
$18$		0			0
$19$	8.93226	+	15.4711i	0.470119	+	0.814270i	0.999416	−	0.0341664i	$-0.0108776\pi$
$19$	8.93226	+	15.4711i	0.470119	+	0.814270i	−0.529297	+	0.848437i	$0.677544\pi$
$20$	6.21244	−	17.0685i	0.310622	−	0.853427i
$21$		0			0
$22$	−16.3337	−	13.7056i	−0.742443	−	0.622984i
$23$	−9.00658	−	24.7454i	−0.391590	−	1.07589i	−0.966275	−	0.257511i	$-0.917098\pi$
$23$	−9.00658	−	24.7454i	−0.391590	−	1.07589i	0.574685	−	0.818375i	$-0.305125\pi$
$24$		0			0
$25$	−2.44434	−	13.8625i	−0.0977735	−	0.554501i
$26$		−	25.5156i		−	0.981367i
$27$		0			0
$28$	23.5875			0.842411
$29$	14.9413	−	2.63456i	0.515218	−	0.0908468i	0.0900069	−	0.995941i	$-0.471311\pi$
$29$	14.9413	−	2.63456i	0.515218	−	0.0908468i	0.425211	+	0.905094i	$0.360200\pi$
$30$		0			0
$31$	−30.7596	+	11.1956i	−0.992246	+	0.361148i	−0.786589	−	0.617476i	$-0.788155\pi$
$31$	−30.7596	+	11.1956i	−0.992246	+	0.361148i	−0.205656	+	0.978624i	$0.565933\pi$
$32$	−25.0039	+	29.7985i	−0.781373	+	0.931204i
$33$		0			0
$34$	37.1091	+	13.5066i	1.09144	+	0.397253i
$35$	43.9457	−	25.3721i	1.25559	−	0.724917i
$36$		0			0
$37$	−15.8096	+	27.3831i	−0.427287	+	0.740083i	−0.996631	−	0.0820163i	$-0.973864\pi$
$37$	−15.8096	+	27.3831i	−0.427287	+	0.740083i	0.569344	+	0.822100i	$0.307197\pi$
$38$	30.1761	+	35.9625i	0.794108	+	0.946382i
$39$		0			0
$40$	−3.12149	+	17.7028i	−0.0780371	+	0.442571i
$41$	16.2691	+	2.86867i	0.396806	+	0.0699677i	0.368491	−	0.929631i	$-0.379875\pi$
$41$	16.2691	+	2.86867i	0.396806	+	0.0699677i	0.0283154	+	0.999599i	$0.490986\pi$
$42$		0			0
$43$	−64.2129	+	53.8810i	−1.49332	+	1.25305i	−0.602982	+	0.797755i	$0.706021\pi$
$43$	−64.2129	+	53.8810i	−1.49332	+	1.25305i	−0.890342	+	0.455292i	$0.849535\pi$
$44$	−20.4179	−	11.7883i	−0.464044	−	0.267916i
$45$		0			0
$46$	−34.6005	−	59.9298i	−0.752185	−	1.30282i
$47$	−4.50446	+	12.3759i	−0.0958397	+	0.263317i	−0.978344	−	0.206988i	$-0.933634\pi$
$47$	−4.50446	+	12.3759i	−0.0958397	+	0.263317i	0.882504	+	0.470305i	$0.155856\pi$
$48$		0			0
$49$	12.9430	+	10.8604i	0.264142	+	0.221641i
$50$	−12.6516	−	34.7601i	−0.253033	−	0.695202i
$51$		0			0
$52$	−4.89919	−	27.7847i	−0.0942152	−	0.534321i
$53$			25.7140i			0.485169i	0.970130	+	0.242585i	$0.0779952\pi$
$53$			25.7140i			0.485169i	−0.970130	+	0.242585i	$0.922005\pi$
$54$		0			0
$55$	−50.7206			−0.922193
$56$	−22.9887	+	4.05353i	−0.410512	+	0.0723844i
$57$		0			0
$58$	37.4652	−	13.6362i	0.645951	−	0.235107i
$59$	−14.5984	+	17.3977i	−0.247430	+	0.294875i	−0.875437	−	0.483332i	$-0.839426\pi$
$59$	−14.5984	+	17.3977i	−0.247430	+	0.294875i	0.628007	+	0.778208i	$0.283871\pi$
$60$		0			0
$61$	−32.0325	−	11.6589i	−0.525123	−	0.191129i	0.0658363	−	0.997830i	$-0.479028\pi$
$61$	−32.0325	−	11.6589i	−0.525123	−	0.191129i	−0.590959	+	0.806701i	$0.701251\pi$
$62$	−74.4955	+	43.0100i	−1.20154	+	0.693710i
$63$		0			0
$64$	−12.7517	+	22.0867i	−0.199246	+	0.345104i
$65$	−39.0144	−	46.4956i	−0.600222	−	0.715317i
$66$		0			0
$67$	1.40732	−	7.98130i	0.0210048	−	0.119124i	−0.972503	−	0.232892i	$-0.925181\pi$
$67$	1.40732	−	7.98130i	0.0210048	−	0.119124i	0.993507	+	0.113768i	$0.0362922\pi$
$68$	43.0026	+	7.58252i	0.632391	+	0.111508i
$69$		0			0
$70$	102.151	−	85.7152i	1.45931	−	1.22450i
$71$	−35.7557	−	20.6436i	−0.503601	−	0.290754i	0.226598	−	0.973988i	$-0.427240\pi$
$71$	−35.7557	−	20.6436i	−0.503601	−	0.290754i	−0.730199	+	0.683234i	$0.760573\pi$
$72$		0			0
$73$	40.4046	+	69.9827i	0.553487	+	0.958668i	0.998020	+	0.0629050i	$0.0200365\pi$
$73$	40.4046	+	69.9827i	0.553487	+	0.958668i	−0.444532	+	0.895763i	$0.646630\pi$
$74$	−28.4189	+	78.0804i	−0.384040	+	1.05514i
$75$		0			0
$76$	39.7648	+	33.3666i	0.523221	+	0.439035i
$77$	−22.5272	−	61.8931i	−0.292562	−	0.803806i
$78$		0			0
$79$	−4.79818	−	27.2118i	−0.0607365	−	0.344454i	−0.999999	−	0.00125471i	$-0.999601\pi$
$79$	−4.79818	−	27.2118i	−0.0607365	−	0.344454i	0.939263	−	0.343199i	$-0.111510\pi$
$80$			119.894i			1.49868i
$81$		0			0
$82$	43.4126			0.529421
$83$	−17.3226	+	3.05444i	−0.208706	+	0.0368004i	−0.277023	−	0.960863i	$-0.589348\pi$
$83$	−17.3226	+	3.05444i	−0.208706	+	0.0368004i	0.0683177	+	0.997664i	$0.478237\pi$
$84$		0			0
$85$	88.2740	−	32.1291i	1.03852	−	0.377989i
$86$	−141.593	+	168.743i	−1.64642	+	1.96213i
$87$		0			0
$88$	21.9254	+	7.98019i	0.249152	+	0.0906839i
$89$	−24.4986	+	14.1443i	−0.275265	+	0.158924i	−0.631278	−	0.775557i	$-0.717469\pi$
$89$	−24.4986	+	14.1443i	−0.275265	+	0.158924i	0.356013	+	0.934481i	$0.384136\pi$
$90$		0			0
$91$	39.4094	−	68.2590i	0.433070	−	0.750099i
$92$	−49.1846	−	58.6159i	−0.534615	−	0.637129i
$93$		0			0
$94$	−6.00988	+	34.0837i	−0.0639349	+	0.362593i
$95$	109.977	+	19.3918i	1.15765	+	0.204125i
$96$		0			0
$97$	129.179	−	108.394i	1.33174	−	1.11746i	0.348073	−	0.937467i	$-0.386836\pi$
$97$	129.179	−	108.394i	1.33174	−	1.11746i	0.983667	−	0.179996i	$-0.0576083\pi$
$98$	38.4516	+	22.2000i	0.392363	+	0.226531i
$99$		0			0
$100$	−20.4510	−	35.4221i	−0.204510	−	0.354221i
$101$	23.8827	−	65.6171i	0.236462	−	0.649674i	−0.763530	−	0.645772i	$-0.776536\pi$
$101$	23.8827	−	65.6171i	0.236462	−	0.649674i	0.999992	−	0.00390224i	$-0.00124213\pi$
$102$		0			0
$103$	53.5180	+	44.9069i	0.519592	+	0.435989i	0.864489	−	0.502651i	$-0.167642\pi$
$103$	53.5180	+	44.9069i	0.519592	+	0.435989i	−0.344898	+	0.938640i	$0.612086\pi$
$104$	9.54962	+	26.2374i	0.0918233	+	0.252282i
$105$		0			0
$106$	11.7339	+	66.5464i	0.110697	+	0.627797i
$107$		−	121.432i		−	1.13488i	−0.823416	−	0.567438i	$-0.807935\pi$
$107$		−	121.432i		−	1.13488i	0.823416	−	0.567438i	$-0.192065\pi$
$108$		0			0
$109$	−119.633			−1.09755			−0.548777	−	0.835969i	$-0.684907\pi$
$109$	−119.633			−1.09755			−0.548777	+	0.835969i	$0.684907\pi$
$110$	−131.262	+	23.1451i	−1.19329	+	0.210410i
$111$		0			0
$112$	−146.304	+	53.2503i	−1.30629	+	0.475449i
$113$	79.9394	−	95.2681i	0.707429	−	0.843081i	−0.285917	−	0.958254i	$-0.592298\pi$
$113$	79.9394	−	95.2681i	0.707429	−	0.843081i	0.993345	+	0.115174i	$0.0367425\pi$
$114$		0			0
$115$	−154.686	−	56.3011i	−1.34510	−	0.489575i
$116$	38.1787	−	22.0425i	0.329127	−	0.190021i
$117$		0			0
$118$	−29.8408	+	51.6859i	−0.252889	+	0.438016i
$119$	78.4127	+	93.4486i	0.658930	+	0.785282i
$120$		0			0
$121$	9.57936	−	54.3272i	0.0791682	−	0.448985i
$122$	−88.2188	−	15.5554i	−0.723105	−	0.127503i
$123$		0			0
$124$	−72.8622	+	61.1387i	−0.587599	+	0.493054i
$125$	59.1363	+	34.1424i	0.473091	+	0.273139i
$126$		0			0
$127$	58.7300	+	101.723i	0.462441	+	0.800971i	0.999082	−	0.0428396i	$-0.0136404\pi$
$127$	58.7300	+	101.723i	0.462441	+	0.800971i	−0.536641	+	0.843811i	$0.680307\pi$
$128$	30.2951	−	83.2351i	0.236680	−	0.650274i
$129$		0			0
$130$	−122.184	−	102.525i	−0.939881	−	0.788654i
$131$	−1.61188	−	4.42859i	−0.0123044	−	0.0338060i	0.933388	−	0.358868i	$-0.116837\pi$
$131$	−1.61188	−	4.42859i	−0.0123044	−	0.0338060i	−0.945693	+	0.325062i	$0.894615\pi$
$132$		0			0
$133$	25.1820	+	142.814i	0.189339	+	1.07379i
$134$		−	21.2974i		−	0.158936i
$135$		0			0
$136$	−43.2139			−0.317749
$137$	217.436	−	38.3398i	1.58712	−	0.279853i	0.690730	−	0.723113i	$-0.257289\pi$
$137$	217.436	−	38.3398i	1.58712	−	0.279853i	0.896393	+	0.443260i	$0.146178\pi$
$138$		0			0
$139$	33.6086	−	12.2325i	0.241788	−	0.0880038i	−0.218284	−	0.975885i	$-0.570046\pi$
$139$	33.6086	−	12.2325i	0.241788	−	0.0880038i	0.460072	+	0.887882i	$0.347824\pi$
$140$	94.7779	−	112.952i	0.676985	−	0.806799i
$141$		0			0
$142$	−101.954	−	37.1083i	−0.717986	−	0.261326i
$143$	−68.2274	+	39.3911i	−0.477114	+	0.275462i
$144$		0			0
$145$	47.4203	−	82.1344i	0.327037	−	0.566444i
$146$	136.500	+	162.674i	0.934931	+	1.11421i
$147$		0			0
$148$	−15.9542	+	90.4808i	−0.107799	+	0.611357i
$149$	−165.188	−	29.1271i	−1.10864	−	0.195484i	−0.410794	−	0.911728i	$-0.634748\pi$
$149$	−165.188	−	29.1271i	−1.10864	−	0.195484i	−0.697849	+	0.716245i	$0.745860\pi$
$150$		0			0
$151$	−64.1318	+	53.8130i	−0.424714	+	0.356377i	−0.829953	−	0.557834i	$-0.811633\pi$
$151$	−64.1318	+	53.8130i	−0.424714	+	0.356377i	0.405239	+	0.914211i	$0.367188\pi$
$152$	−44.4893	−	25.6859i	−0.292693	−	0.168986i
$153$		0			0
$154$	−86.5428	−	149.896i	−0.561966	−	0.973354i
$155$	−69.9848	+	192.282i	−0.451515	+	1.24053i
$156$		0			0
$157$	−57.0276	−	47.8518i	−0.363233	−	0.304789i	0.442845	−	0.896598i	$-0.353969\pi$
$157$	−57.0276	−	47.8518i	−0.363233	−	0.304789i	−0.806078	+	0.591810i	$0.798414\pi$
$158$	−24.8349	−	68.2333i	−0.157183	−	0.431857i
$159$		0			0
$160$	42.2249	+	239.469i	0.263905	+	1.49668i
$161$		−	213.765i		−	1.32773i
$162$		0			0
$163$	254.830			1.56337			0.781687	−	0.623670i	$-0.214359\pi$
$163$	254.830			1.56337			0.781687	+	0.623670i	$0.214359\pi$
$164$	47.2733	−	8.33555i	0.288252	−	0.0508266i
$165$		0			0
$166$	−43.4361	+	15.8095i	−0.261663	+	0.0952377i
$167$	−101.946	+	121.494i	−0.610454	+	0.727510i	−0.979398	−	0.201941i	$-0.935275\pi$
$167$	−101.946	+	121.494i	−0.610454	+	0.727510i	0.368944	+	0.929452i	$0.379719\pi$
$168$		0			0
$169$	70.2176	+	25.5571i	0.415489	+	0.151226i
$170$	213.787	−	123.430i	1.25757	−	0.726060i
$171$		0			0
$172$	−121.784	+	210.937i	−0.708049	+	1.22638i
$173$	−191.603	−	228.343i	−1.10753	−	1.31990i	−0.942722	−	0.333579i	$-0.891744\pi$
$173$	−191.603	−	228.343i	−1.10753	−	1.31990i	−0.164809	−	0.986325i	$-0.552701\pi$
$174$		0			0
$175$	19.8422	−	112.531i	0.113384	−	0.643033i
$176$	153.257	+	27.0233i	0.870778	+	0.153542i
$177$		0			0
$178$	−56.9467	+	47.7840i	−0.319925	+	0.268449i
$179$	−25.3997	−	14.6645i	−0.141898	−	0.0819248i	0.427370	−	0.904077i	$-0.359440\pi$
$179$	−25.3997	−	14.6645i	−0.141898	−	0.0819248i	−0.569268	+	0.822152i	$0.692773\pi$
$180$		0			0
$181$	−41.7019	−	72.2299i	−0.230397	−	0.399060i	0.727528	−	0.686078i	$-0.240669\pi$
$181$	−41.7019	−	72.2299i	−0.230397	−	0.399060i	−0.957925	+	0.287018i	$0.907336\pi$
$182$	70.8411	−	194.634i	0.389237	−	1.06942i
$183$		0			0
$184$	58.0091	+	48.6754i	0.315267	+	0.264540i
$185$	67.6021	+	185.735i	0.365417	+	1.00398i
$186$		0			0
$187$	−21.1732	−	120.079i	−0.113226	−	0.642136i
$188$			38.2688i			0.203557i
$189$		0			0
$190$	293.463			1.54454
$191$	154.565	−	27.2539i	0.809238	−	0.142691i	0.246305	−	0.969192i	$-0.420784\pi$
$191$	154.565	−	27.2539i	0.809238	−	0.142691i	0.562934	+	0.826502i	$0.309673\pi$
$192$		0			0
$193$	38.9684	−	14.1833i	0.201909	−	0.0734888i	−0.239086	−	0.970998i	$-0.576848\pi$
$193$	38.9684	−	14.1833i	0.201909	−	0.0734888i	0.440995	+	0.897510i	$0.354626\pi$
$194$	284.845	−	339.466i	1.46828	−	1.74982i
$195$		0			0
$196$	46.1337	+	16.7913i	0.235376	+	0.0856699i
$197$	182.437	−	105.330i	0.926074	−	0.534669i	0.0405063	−	0.999179i	$-0.487103\pi$
$197$	182.437	−	105.330i	0.926074	−	0.534669i	0.885568	+	0.464510i	$0.153770\pi$
$198$		0			0
$199$	87.7654	−	152.014i	0.441032	−	0.763890i	−0.556734	−	0.830691i	$-0.687946\pi$
$199$	87.7654	−	152.014i	0.441032	−	0.763890i	0.997766	+	0.0668004i	$0.0212791\pi$
$200$	26.0191	+	31.0084i	0.130096	+	0.155042i
$201$		0			0
$202$	31.8644	−	180.712i	0.157745	−	0.894614i
$203$	121.288	+	21.3863i	0.597478	+	0.105351i
$204$		0			0
$205$	79.1083	−	66.3797i	0.385894	−	0.323804i
$206$	158.994	+	91.7952i	0.771815	+	0.445608i
$207$		0			0
$208$	93.1133	+	161.277i	0.447660	+	0.775370i
$209$	49.5759	−	136.209i	0.237205	−	0.651716i
$210$		0			0
$211$	−199.826	−	167.674i	−0.947042	−	0.794662i	0.0317552	−	0.999496i	$-0.489890\pi$
$211$	−199.826	−	167.674i	−0.947042	−	0.794662i	−0.978797	+	0.204833i	$0.934335\pi$
$212$	25.5549	+	70.2115i	0.120542	+	0.331186i
$213$		0			0
$214$	−55.4123	−	314.259i	−0.258936	−	1.46850i
$215$			523.993i			2.43718i
$216$		0			0
$217$	−265.720			−1.22452
$218$	−309.605	+	54.5918i	−1.42021	+	0.250421i
$219$		0			0
$220$	−138.492	+	50.4069i	−0.629508	+	0.229122i
$221$	93.7903	−	111.775i	0.424390	−	0.505769i
$222$		0			0
$223$	365.744	+	133.120i	1.64011	+	0.596951i	0.987058	−	0.160364i	$-0.0512666\pi$
$223$	365.744	+	133.120i	1.64011	+	0.596951i	0.653051	+	0.757314i	$0.273489\pi$
$224$	−273.464	+	157.885i	−1.22082	+	0.704842i
$225$		0			0
$226$	163.406	−	283.027i	0.723035	−	1.25233i
$227$	−223.968	−	266.914i	−0.986642	−	1.17583i	−0.984419	−	0.175837i	$-0.943737\pi$
$227$	−223.968	−	266.914i	−0.986642	−	1.17583i	−0.00222294	−	0.999998i	$-0.500708\pi$
$228$		0			0
$229$	−63.2989	+	358.986i	−0.276415	+	1.56762i	0.458018	+	0.888943i	$0.348560\pi$
$229$	−63.2989	+	358.986i	−0.276415	+	1.56762i	−0.734433	+	0.678682i	$0.762552\pi$
$230$	−426.011	−	75.1173i	−1.85222	−	0.326597i
$231$		0			0
$232$	−33.4214	+	28.0439i	−0.144058	+	0.120879i
$233$	−164.260	−	94.8353i	−0.704976	−	0.407018i	0.104222	−	0.994554i	$-0.466765\pi$
$233$	−164.260	−	94.8353i	−0.704976	−	0.407018i	−0.809198	+	0.587536i	$0.800098\pi$
$234$		0			0
$235$	41.1641	+	71.2983i	0.175166	+	0.303397i
$236$	−22.5705	+	62.0120i	−0.0956378	+	0.262763i
$237$		0			0
$238$	245.571	+	206.059i	1.03181	+	0.865792i
$239$	104.692	+	287.639i	0.438042	+	1.20351i	0.940764	+	0.339062i	$0.110110\pi$
$239$	104.692	+	287.639i	0.438042	+	1.20351i	−0.502723	+	0.864448i	$0.667668\pi$
$240$		0			0
$241$	−51.2098	−	290.425i	−0.212489	−	1.20508i	−0.885212	−	0.465189i	$-0.845987\pi$
$241$	−51.2098	−	290.425i	−0.212489	−	1.20508i	0.672723	−	0.739894i	$-0.265125\pi$
$242$		−	144.967i		−	0.599039i
$243$		0			0
$244$	−99.0509			−0.405946
$245$	104.013	−	18.3403i	0.424543	−	0.0748584i
$246$		0			0
$247$	162.996	−	59.3258i	0.659904	−	0.240185i
$248$	60.5057	−	72.1079i	0.243975	−	0.290758i
$249$		0			0
$250$	168.622	+	61.3734i	0.674488	+	0.245493i
$251$	−158.404	+	91.4547i	−0.631092	+	0.364361i	−0.781175	−	0.624312i	$-0.785379\pi$
$251$	−158.404	+	91.4547i	−0.631092	+	0.364361i	0.150083	+	0.988673i	$0.452046\pi$
$252$		0			0
$253$	−106.833	+	185.040i	−0.422265	+	0.731384i
$254$	198.409	+	236.455i	0.781138	+	0.930925i
$255$		0			0
$256$	58.1344	−	329.697i	0.227088	−	1.28788i
$257$	−264.287	−	46.6009i	−1.02835	−	0.181327i	−0.366076	−	0.930585i	$-0.619299\pi$
$257$	−264.287	−	46.6009i	−1.02835	−	0.181327i	−0.662278	+	0.749258i	$0.730410\pi$
$258$		0			0
$259$	−196.623	+	164.986i	−0.759163	+	0.637013i
$260$	−152.736	−	88.1822i	−0.587447	−	0.339162i
$261$		0			0
$262$	−6.19233	−	10.7254i	−0.0236348	−	0.0409368i
$263$	−120.383	+	330.749i	−0.457730	+	1.25760i	0.469441	+	0.882964i	$0.344455\pi$
$263$	−120.383	+	330.749i	−0.457730	+	1.25760i	−0.927171	+	0.374638i	$0.877767\pi$
$264$		0			0
$265$	123.135	+	103.322i	0.464659	+	0.389895i
$266$	130.340	+	358.105i	0.489999	+	1.34626i
$267$		0			0
$268$	−4.08927	−	23.1914i	−0.0152585	−	0.0865351i
$269$		−	164.243i		−	0.610570i	−0.952261	−	0.305285i	$-0.901248\pi$
$269$		−	164.243i		−	0.610570i	0.952261	−	0.305285i	$-0.0987518\pi$
$270$		0			0
$271$	−128.850			−0.475462			−0.237731	−	0.971331i	$-0.576404\pi$
$271$	−128.850			−0.475462			−0.237731	+	0.971331i	$0.576404\pi$
$272$	−283.846	+	50.0497i	−1.04355	+	0.184006i
$273$		0			0
$274$	545.218	−	198.443i	1.98985	−	0.724245i
$275$	−73.4152	+	87.4928i	−0.266964	+	0.318156i
$276$		0			0
$277$	−141.159	−	51.3776i	−0.509598	−	0.185479i	0.0744078	−	0.997228i	$-0.476293\pi$
$277$	−141.159	−	51.3776i	−0.509598	−	0.185479i	−0.584006	+	0.811749i	$0.698516\pi$
$278$	81.3953	−	46.9936i	0.292789	−	0.169042i
$279$		0			0
$280$	−72.9609	+	126.372i	−0.260575	+	0.451328i
$281$	296.324	+	353.146i	1.05454	+	1.25675i	0.965413	+	0.260725i	$0.0839617\pi$
$281$	296.324	+	353.146i	1.05454	+	1.25675i	0.0891220	+	0.996021i	$0.471594\pi$
$282$		0			0
$283$	−11.9570	+	67.8114i	−0.0422508	+	0.239616i	−0.998618	−	0.0525503i	$-0.983265\pi$
$283$	−11.9570	+	67.8114i	−0.0422508	+	0.239616i	0.956367	+	0.292166i	$0.0943761\pi$
$284$	−118.146	−	20.8323i	−0.416007	−	0.0733533i
$285$		0			0
$286$	−158.594	+	133.076i	−0.554524	+	0.465301i
$287$	116.137	+	67.0517i	0.404658	+	0.233630i
$288$		0			0
$289$	−31.5856	−	54.7078i	−0.109293	−	0.189300i
$290$	85.2414	−	234.199i	0.293936	−	0.807582i
$291$		0			0
$292$	179.874	+	150.932i	0.616006	+	0.516890i
$293$	−174.692	−	479.963i	−0.596220	−	1.63810i	−0.758739	−	0.651395i	$-0.774184\pi$
$293$	−174.692	−	479.963i	−0.596220	−	1.63810i	0.162519	−	0.986705i	$-0.448038\pi$
$294$		0			0
$295$	24.6527	+	139.812i	0.0835684	+	0.473940i
$296$		−	90.9255i		−	0.307181i
$297$		0			0
$298$	−440.789			−1.47916
$299$	−251.803	+	44.3996i	−0.842149	+	0.148494i
$300$		0			0
$301$	−639.416	+	232.728i	−2.12430	+	0.773184i
$302$	−141.414	+	168.530i	−0.468257	+	0.558047i
$303$		0			0
$304$	−321.972	−	117.188i	−1.05912	−	0.385488i
$305$	−184.541	+	106.545i	−0.605053	+	0.349327i
$306$		0			0
$307$	−26.3017	+	45.5559i	−0.0856734	+	0.148391i	−0.905678	−	0.423966i	$-0.860637\pi$
$307$	−26.3017	+	45.5559i	−0.0856734	+	0.148391i	0.820005	+	0.572357i	$0.193971\pi$
$308$	−123.020	−	146.610i	−0.399417	−	0.476007i
$309$		0			0
$310$	−93.3742	+	529.551i	−0.301207	+	1.70823i
$311$	−349.435	−	61.6148i	−1.12358	−	0.198118i	−0.419170	−	0.907908i	$-0.637679\pi$
$311$	−349.435	−	61.6148i	−1.12358	−	0.198118i	−0.704414	+	0.709789i	$0.748790\pi$
$312$		0			0
$313$	128.886	−	108.148i	0.411776	−	0.345521i	−0.413248	−	0.910618i	$-0.635606\pi$
$313$	128.886	−	108.148i	0.411776	−	0.345521i	0.825024	+	0.565097i	$0.191161\pi$
$314$	−169.421	−	97.8150i	−0.539556	−	0.311513i
$315$		0			0
$316$	−40.1448	−	69.5329i	−0.127041	−	0.220041i
$317$	−174.426	+	479.232i	−0.550241	+	1.51177i	0.283142	+	0.959078i	$0.408623\pi$
$317$	−174.426	+	479.232i	−0.550241	+	1.51177i	−0.833383	+	0.552696i	$0.813599\pi$
$318$		0			0
$319$	−94.3015	−	79.1284i	−0.295616	−	0.248051i
$320$	54.5266	+	149.811i	0.170396	+	0.468158i
$321$		0			0
$322$	−97.5465	−	553.214i	−0.302939	−	1.71805i
$323$			268.461i			0.831149i
$324$		0			0
$325$	−136.676			−0.420541
$326$	659.488	−	116.285i	2.02297	−	0.356704i
$327$		0			0
$328$	−44.6407	+	16.2479i	−0.136100	+	0.0495362i
$329$	−68.7207	+	81.8982i	−0.208878	+	0.248931i
$330$		0			0
$331$	318.877	+	116.062i	0.963375	+	0.350640i	0.775355	−	0.631526i	$-0.217571\pi$
$331$	318.877	+	116.062i	0.963375	+	0.350640i	0.188020	+	0.982165i	$0.439793\pi$
$332$	−44.2634	+	25.5555i	−0.133324	+	0.0769744i
$333$		0			0
$334$	−208.390	+	360.941i	−0.623921	+	1.08066i
$335$	−32.5647	−	38.8091i	−0.0972080	−	0.115848i
$336$		0			0
$337$	−11.8494	+	67.2013i	−0.0351614	+	0.199410i	−0.997328	−	0.0730508i	$-0.976726\pi$
$337$	−11.8494	+	67.2013i	−0.0351614	+	0.199410i	0.962167	+	0.272461i	$0.0878376\pi$
$338$	193.382	+	34.0985i	0.572136	+	0.100883i
$339$		0			0
$340$	209.100	−	175.456i	0.615000	−	0.516046i
$341$	230.013	+	132.798i	0.674526	+	0.389438i
$342$		0			0
$343$	−130.305	−	225.695i	−0.379897	−	0.658002i
$344$	82.4431	−	226.510i	0.239660	−	0.658461i
$345$		0			0
$346$	−600.058	−	503.508i	−1.73427	−	1.45523i
$347$	59.2029	+	162.659i	0.170613	+	0.468757i	0.995301	−	0.0968324i	$-0.0308711\pi$
$347$	59.2029	+	162.659i	0.170613	+	0.468757i	−0.824687	+	0.565589i	$0.808649\pi$
$348$		0			0
$349$	79.8055	+	452.600i	0.228669	+	1.29685i	0.855545	+	0.517728i	$0.173222\pi$
$349$	79.8055	+	452.600i	0.228669	+	1.29685i	−0.626876	+	0.779119i	$0.715667\pi$
$350$		−	300.278i		−	0.857939i
$351$		0			0
$352$	315.623			0.896655
$353$	−396.139	+	69.8500i	−1.12221	+	0.197875i	−0.703809	−	0.710389i	$-0.748519\pi$
$353$	−396.139	+	69.8500i	−1.12221	+	0.197875i	−0.418397	+	0.908264i	$0.637408\pi$
$354$		0			0
$355$	−242.525	+	88.2721i	−0.683170	+	0.248654i
$356$	−52.8361	+	62.9677i	−0.148416	+	0.176875i
$357$		0			0
$358$	−72.4250	−	26.3605i	−0.202304	−	0.0736328i
$359$	197.249	−	113.882i	0.549439	−	0.317219i	−0.199457	−	0.979907i	$-0.563918\pi$
$359$	197.249	−	113.882i	0.549439	−	0.317219i	0.748896	+	0.662688i	$0.230584\pi$
$360$		0			0
$361$	20.9294	−	36.2507i	0.0579761	−	0.100418i
$362$	−140.883	−	167.898i	−0.389179	−	0.463806i
$363$		0			0
$364$	39.7698	−	225.546i	0.109258	−	0.619631i
$365$	497.472	+	87.7178i	1.36294	+	0.240323i
$366$		0			0
$367$	−180.378	+	151.355i	−0.491493	+	0.412412i	−0.854561	−	0.519351i	$-0.826174\pi$
$367$	−180.378	+	151.355i	−0.491493	+	0.412412i	0.363068	+	0.931763i	$0.381729\pi$
$368$	437.401	+	252.534i	1.18859	+	0.686233i
$369$		0			0
$370$	259.707	+	449.825i	0.701910	+	1.21574i
$371$	−71.3920	+	196.148i	−0.192431	+	0.528701i
$372$		0			0
$373$	500.037	+	419.581i	1.34058	+	1.12488i	0.981476	+	0.191584i	$0.0613623\pi$
$373$	500.037	+	419.581i	1.34058	+	1.12488i	0.359105	+	0.933297i	$0.383082\pi$
$374$	−109.591	−	301.098i	−0.293023	−	0.805074i
$375$		0			0
$376$	−6.57651	−	37.2973i	−0.0174907	−	0.0991948i
$377$		−	147.312i		−	0.390748i
$378$		0			0
$379$	625.053			1.64922			0.824608	−	0.565705i	$-0.191396\pi$
$379$	625.053			1.64922			0.824608	+	0.565705i	$0.191396\pi$
$380$	319.561	−	56.3472i	0.840949	−	0.148282i
$381$		0			0
$382$	387.569	−	141.063i	1.01458	−	0.369276i
$383$	68.4823	−	81.6140i	0.178805	−	0.213091i	−0.669196	−	0.743086i	$-0.733361\pi$
$383$	68.4823	−	81.6140i	0.178805	−	0.213091i	0.848001	+	0.529994i	$0.177806\pi$
$384$		0			0
$385$	−386.901	−	140.820i	−1.00494	−	0.365767i
$386$	94.3760	−	54.4880i	0.244497	−	0.141161i
$387$		0			0
$388$	244.997	−	424.347i	0.631436	−	1.09368i
$389$	−381.579	−	454.749i	−0.980924	−	1.16902i	−0.985611	−	0.169030i	$-0.945936\pi$
$389$	−381.579	−	454.749i	−0.980924	−	1.16902i	0.00468714	−	0.999989i	$-0.498508\pi$
$390$		0			0
$391$	68.7176	−	389.717i	0.175748	−	0.996719i
$392$	−47.8481	−	8.43691i	−0.122061	−	0.0215227i
$393$		0			0
$394$	424.072	−	355.839i	1.07633	−	0.903144i
$395$	−149.587	−	86.3642i	−0.378702	−	0.218643i
$396$		0			0
$397$	−187.410	−	324.603i	−0.472064	−	0.817640i	0.527425	−	0.849602i	$-0.323158\pi$
$397$	−187.410	−	324.603i	−0.472064	−	0.817640i	−0.999489	+	0.0319623i	$0.989824\pi$
$398$	157.765	−	433.455i	0.396393	−	1.08908i
$399$		0			0
$400$	206.817	+	173.540i	0.517042	+	0.433850i
$401$	93.8523	+	257.857i	0.234046	+	0.643035i	1.00000		0.000140039i	$4.45758e-5\pi$
$401$	93.8523	+	257.857i	0.234046	+	0.643035i	−0.765954	+	0.642895i	$0.777733\pi$
$402$		0			0
$403$	55.1907	+	313.002i	0.136950	+	0.776680i
$404$		−	202.901i		−	0.502231i
$405$		0			0
$406$	323.646			0.797158
$407$	252.657	−	44.5502i	0.620778	−	0.109460i
$408$		0			0
$409$	518.216	−	188.615i	1.26703	−	0.461162i	0.380909	−	0.924612i	$-0.375611\pi$
$409$	518.216	−	188.615i	1.26703	−	0.461162i	0.886123	+	0.463450i	$0.153389\pi$
$410$	174.438	−	207.887i	0.425457	−	0.507040i
$411$		0			0
$412$	190.759	+	69.4305i	0.463007	+	0.168521i
$413$	−159.660	+	92.1798i	−0.386586	+	0.223196i
$414$		0			0
$415$	−54.9779	+	95.2245i	−0.132477	+	0.229457i
$416$	242.778	+	289.331i	0.583600	+	0.695508i
$417$		0			0
$418$	66.1445	−	375.124i	0.158240	−	0.897426i
$419$	−86.2570	−	15.2094i	−0.205864	−	0.0362994i	0.0697651	−	0.997563i	$-0.477775\pi$
$419$	−86.2570	−	15.2094i	−0.205864	−	0.0362994i	−0.275629	+	0.961264i	$0.588886\pi$
$420$		0			0
$421$	226.948	−	190.432i	0.539069	−	0.452332i	−0.332151	−	0.943226i	$-0.607774\pi$
$421$	226.948	−	190.432i	0.539069	−	0.452332i	0.871219	+	0.490894i	$0.163330\pi$
$422$	−593.653	−	342.746i	−1.40676	−	0.812194i
$423$		0			0
$424$	−36.9720	−	64.0374i	−0.0871981	−	0.151032i
$425$	72.3490	−	198.777i	0.170233	−	0.467711i
$426$		0			0
$427$	−211.977	−	177.870i	−0.496433	−	0.416556i
$428$	−120.680	−	331.567i	−0.281964	−	0.774689i
$429$		0			0
$430$	239.111	+	1356.07i	0.556073	+	3.15365i
$431$			586.175i			1.36003i	0.733196	+	0.680017i	$0.238028\pi$
$431$			586.175i			1.36003i	−0.733196	+	0.680017i	$0.761972\pi$
$432$		0			0
$433$	415.367			0.959277			0.479639	−	0.877466i	$-0.340768\pi$
$433$	415.367			0.959277			0.479639	+	0.877466i	$0.340768\pi$
$434$	−687.670	+	121.255i	−1.58449	+	0.279389i
$435$		0			0
$436$	−326.657	+	118.893i	−0.749213	+	0.272691i
$437$	302.390	−	360.374i	0.691967	−	0.824655i
$438$		0			0
$439$	−314.194	−	114.357i	−0.715704	−	0.260495i	−0.0416031	−	0.999134i	$-0.513247\pi$
$439$	−314.194	−	114.357i	−0.715704	−	0.260495i	−0.674101	+	0.738639i	$0.735469\pi$
$440$	126.313	−	72.9270i	0.287076	−	0.165743i
$441$		0			0
$442$	191.719	−	332.067i	0.433753	−	0.751282i
$443$	290.310	+	345.978i	0.655327	+	0.780988i	0.986707	−	0.162509i	$-0.0519588\pi$
$443$	290.310	+	345.978i	0.655327	+	0.780988i	−0.331380	+	0.943497i	$0.607514\pi$
$444$		0			0
$445$	−30.7070	+	174.148i	−0.0690045	+	0.391344i
$446$	1007.27	+	177.610i	2.25846	+	0.398228i
$447$		0			0
$448$	−158.592	+	133.075i	−0.354001	+	0.297042i
$449$	165.422	+	95.5067i	0.368424	+	0.212710i	0.672770	−	0.739852i	$-0.265104\pi$
$449$	165.422	+	95.5067i	0.368424	+	0.212710i	−0.304346	+	0.952562i	$0.598438\pi$
$450$		0			0
$451$	−67.0206	−	116.083i	−0.148604	−	0.257390i
$452$	123.594	−	339.573i	0.273439	−	0.751267i
$453$		0			0
$454$	−701.417	−	588.559i	−1.54497	−	1.29639i
$455$	−168.515	−	462.991i	−0.370362	−	1.01756i
$456$		0			0
$457$	−66.9852	−	379.892i	−0.146576	−	0.831274i	−0.966088	−	0.258212i	$-0.916867\pi$
$457$	−66.9852	−	379.892i	−0.146576	−	0.831274i	0.819512	−	0.573062i	$-0.194244\pi$
$458$			957.923i			2.09153i
$459$		0			0
$460$	−478.320			−1.03983
$461$	426.474	−	75.1990i	0.925107	−	0.163121i	0.309252	−	0.950980i	$-0.399921\pi$
$461$	426.474	−	75.1990i	0.925107	−	0.163121i	0.615856	+	0.787859i	$0.288810\pi$
$462$		0			0
$463$	−519.515	+	189.088i	−1.12206	+	0.408397i	−0.835405	−	0.549635i	$-0.814767\pi$
$463$	−519.515	+	189.088i	−1.12206	+	0.408397i	−0.286658	+	0.958033i	$0.592544\pi$
$464$	−187.045	+	222.912i	−0.403114	+	0.480413i
$465$		0			0
$466$	−468.371	−	170.473i	−1.00509	−	0.365822i
$467$	186.467	−	107.657i	0.399286	−	0.230528i	−0.286890	−	0.957964i	$-0.592621\pi$
$467$	186.467	−	107.657i	0.399286	−	0.230528i	0.686176	+	0.727436i	$0.259288\pi$
$468$		0			0
$469$	32.8943	−	56.9747i	0.0701372	−	0.121481i
$470$	139.066	+	165.732i	0.295885	+	0.352622i
$471$		0			0
$472$	11.3407	−	64.3165i	0.0240270	−	0.136264i
$473$	669.803	+	118.104i	1.41607	+	0.249692i
$474$		0			0
$475$	192.635	−	161.640i	0.405548	−	0.340296i
$476$	306.975	+	177.232i	0.644905	+	0.372336i
$477$		0			0
$478$	402.194	+	696.621i	0.841411	+	1.45737i
$479$	77.4641	−	212.831i	0.161721	−	0.444323i	−0.832193	−	0.554486i	$-0.812915\pi$
$479$	77.4641	−	212.831i	0.161721	−	0.444323i	0.993914	+	0.110163i	$0.0351371\pi$
$480$		0			0
$481$	235.183	+	197.342i	0.488946	+	0.410275i
$482$	−265.057	−	728.237i	−0.549910	−	1.51087i
$483$		0			0
$484$	−27.8349	−	157.860i	−0.0575101	−	0.326156i
$485$		−	1054.13i		−	2.17347i
$486$		0			0
$487$	−443.130			−0.909919			−0.454959	−	0.890512i	$-0.650346\pi$
$487$	−443.130			−0.909919			−0.454959	+	0.890512i	$0.650346\pi$
$488$	96.5363	−	17.0220i	0.197820	−	0.0348810i
$489$		0			0
$490$	260.812	−	94.9276i	0.532268	−	0.193730i
$491$	−429.032	+	511.301i	−0.873793	+	1.04135i	0.124997	+	0.992157i	$0.460108\pi$
$491$	−429.032	+	511.301i	−0.873793	+	1.04135i	−0.998790	+	0.0491885i	$0.984336\pi$
$492$		0			0
$493$	214.246	+	77.9792i	0.434576	+	0.158173i
$494$	394.754	−	227.912i	0.799098	−	0.461360i
$495$		0			0
$496$	313.911	−	543.710i	0.632885	−	1.09619i
$497$	−215.432	−	256.742i	−0.433465	−	0.516584i
$498$		0			0
$499$	−9.98207	+	56.6112i	−0.0200042	+	0.113449i	−0.993175	−	0.116635i	$-0.962789\pi$
$499$	−9.98207	+	56.6112i	−0.0200042	+	0.113449i	0.973171	+	0.230084i	$0.0739003\pi$
$500$	195.402	+	34.4546i	0.390804	+	0.0689092i
$501$		0			0
$502$	−368.209	+	308.964i	−0.733484	+	0.615466i
$503$	−423.202	−	244.336i	−0.841356	−	0.485757i	0.0163686	−	0.999866i	$-0.494789\pi$
$503$	−423.202	−	244.336i	−0.841356	−	0.485757i	−0.857725	+	0.514109i	$0.828123\pi$
$504$		0			0
$505$	−218.252	−	378.024i	−0.432182	−	0.748562i
$506$	−192.040	+	527.625i	−0.379526	+	1.04274i
$507$		0			0
$508$	261.455	+	219.387i	0.514675	+	0.431864i
$509$	−97.2199	−	267.109i	−0.191002	−	0.524773i	0.806816	−	0.590803i	$-0.201189\pi$
$509$	−97.2199	−	267.109i	−0.191002	−	0.524773i	−0.997818	+	0.0660300i	$0.978967\pi$
$510$		0			0
$511$	113.909	+	646.012i	0.222915	+	1.26421i
$512$		−	525.459i		−	1.02629i
$513$		0			0
$514$	−705.227			−1.37204
$515$	430.085	−	75.8356i	0.835116	−	0.147254i
$516$		0			0
$517$	100.416	−	36.5486i	0.194229	−	0.0706936i
$518$	−433.563	+	516.701i	−0.836995	+	0.997492i
$519$		0			0
$520$	164.013	+	59.6957i	0.315409	+	0.114799i
$521$	−35.1966	+	20.3207i	−0.0675558	+	0.0390033i	−0.533397	−	0.845865i	$-0.679085\pi$
$521$	−35.1966	+	20.3207i	−0.0675558	+	0.0390033i	0.465842	+	0.884868i	$0.345752\pi$
$522$		0			0
$523$	−174.951	+	303.024i	−0.334514	+	0.579395i	−0.983391	−	0.181498i	$-0.941905\pi$
$523$	−174.951	+	303.024i	−0.334514	+	0.579395i	0.648877	+	0.760893i	$0.275239\pi$
$524$	−8.80239	−	10.4903i	−0.0167985	−	0.0200196i
$525$		0			0
$526$	−160.616	+	910.896i	−0.305353	+	1.73174i
$527$	−484.436	−	85.4191i	−0.919233	−	0.162086i
$528$		0			0
$529$	−125.977	+	105.708i	−0.238142	+	0.199825i
$530$	365.815	+	211.203i	0.690216	+	0.398497i
$531$		0			0
$532$	210.690	+	364.926i	0.396034	+	0.685951i
$533$	54.8609	−	150.729i	0.102929	−	0.282794i
$534$		0			0
$535$	−581.491	−	487.929i	−1.08690	−	0.912017i
$536$	7.97091	+	21.8999i	0.0148711	+	0.0408580i
$537$		0			0
$538$	−74.9484	−	425.054i	−0.139309	−	0.790063i
$539$		−	137.090i		−	0.254342i
$540$		0			0
$541$	145.531			0.269003			0.134501	−	0.990913i	$-0.457057\pi$
$541$	145.531			0.269003			0.134501	+	0.990913i	$0.457057\pi$
$542$	−333.458	+	58.7976i	−0.615236	+	0.108483i
$543$		0			0
$544$	−549.309	+	199.932i	−1.00976	+	0.367522i
$545$	−480.704	+	572.880i	−0.882025	+	1.05116i
$546$		0			0
$547$	−456.718	−	166.232i	−0.834950	−	0.303897i	−0.111061	−	0.993814i	$-0.535425\pi$
$547$	−456.718	−	166.232i	−0.834950	−	0.303897i	−0.723889	+	0.689917i	$0.757647\pi$
$548$	555.602	−	320.777i	1.01387	−	0.585359i
$549$		0			0
$550$	−150.070	+	259.928i	−0.272854	+	0.472597i
$551$	174.219	+	207.626i	0.316187	+	0.376818i
$552$		0			0
$553$	38.9498	−	220.895i	0.0704337	−	0.399449i
$554$	−388.757	−	68.5483i	−0.701727	−	0.123733i
$555$		0			0
$556$	79.6107	−	66.8013i	0.143185	−	0.120146i
$557$	−2.82805	−	1.63278i	−0.00507730	−	0.00293138i	0.497459	−	0.867487i	$-0.334266\pi$
$557$	−2.82805	−	1.63278i	−0.00507730	−	0.00293138i	−0.502537	+	0.864556i	$0.667600\pi$
$558$		0			0
$559$	406.948	+	704.855i	0.727993	+	1.26092i
$560$	−332.873	+	914.562i	−0.594417	+	1.63315i
$561$		0			0
$562$	928.022	+	778.703i	1.65128	+	1.38559i
$563$	227.357	+	624.659i	0.403832	+	1.10952i	0.960378	+	0.278702i	$0.0899043\pi$
$563$	227.357	+	624.659i	0.403832	+	1.10952i	−0.556545	+	0.830817i	$0.687873\pi$
$564$		0			0
$565$	−134.996	−	765.600i	−0.238931	−	1.35505i
$566$			180.949i			0.319697i
$567$		0			0
$568$	118.727			0.209026
$569$	74.7814	−	13.1860i	0.131426	−	0.0231739i	−0.107548	−	0.994200i	$-0.534300\pi$
$569$	74.7814	−	13.1860i	0.131426	−	0.0231739i	0.238974	+	0.971026i	$0.423189\pi$
$570$		0			0
$571$	276.356	−	100.585i	0.483985	−	0.176156i	−0.0884919	−	0.996077i	$-0.528205\pi$
$571$	276.356	−	100.585i	0.483985	−	0.176156i	0.572477	+	0.819921i	$0.305983\pi$
$572$	−147.146	+	175.362i	−0.257248	+	0.306577i
$573$		0			0
$574$	331.154	+	120.530i	0.576923	+	0.209983i
$575$	−321.018	+	185.340i	−0.558292	+	0.322330i
$576$		0			0
$577$	−529.296	+	916.768i	−0.917325	+	1.58885i	−0.113864	+	0.993496i	$0.536323\pi$
$577$	−529.296	+	916.768i	−0.917325	+	1.58885i	−0.803461	+	0.595357i	$0.797011\pi$
$578$	−106.706	−	127.168i	−0.184613	−	0.220013i
$579$		0			0
$580$	47.8540	−	271.393i	0.0825069	−	0.467920i
$581$	−140.618	−	24.7948i	−0.242028	−	0.0426760i
$582$		0			0
$583$	159.827	−	134.111i	0.274146	−	0.230036i
$584$	−201.245	−	116.189i	−0.344597	−	0.198953i
$585$		0			0
$586$	−671.115	−	1162.40i	−1.14525	−	1.98363i
$587$	−47.5072	+	130.525i	−0.0809322	+	0.222359i	−0.973558	−	0.228438i	$-0.926638\pi$
$587$	−47.5072	+	130.525i	−0.0809322	+	0.222359i	0.892626	+	0.450798i	$0.148860\pi$
$588$		0			0
$589$	−447.961	−	375.884i	−0.760546	−	0.638173i
$590$	127.600	+	350.578i	0.216271	+	0.594199i
$591$		0			0
$592$	−105.308	−	597.234i	−0.177886	−	1.00884i
$593$			145.309i			0.245040i	0.992466	+	0.122520i	$0.0390975\pi$
$593$			145.309i			0.245040i	−0.992466	+	0.122520i	$0.960902\pi$
$594$		0			0
$595$	762.563			1.28162
$596$	−479.989	+	84.6350i	−0.805351	+	0.142005i
$597$		0			0
$598$	−631.392	+	229.808i	−1.05584	+	0.384294i
$599$	−14.7665	+	17.5980i	−0.0246518	+	0.0293789i	−0.778230	−	0.627980i	$-0.783882\pi$
$599$	−14.7665	+	17.5980i	−0.0246518	+	0.0293789i	0.753578	+	0.657359i	$0.228326\pi$
$600$		0			0
$601$	871.442	+	317.179i	1.44999	+	0.527752i	0.942588	−	0.333959i	$-0.108385\pi$
$601$	871.442	+	317.179i	1.44999	+	0.527752i	0.507399	+	0.861711i	$0.330607\pi$
$602$	−1548.58	+	894.071i	−2.57238	+	1.48517i
$603$		0			0
$604$	−121.631	+	210.670i	−0.201375	+	0.348792i
$605$	−221.662	−	264.166i	−0.366383	−	0.436638i
$606$		0			0
$607$	90.9868	−	516.012i	0.149896	−	0.850102i	−0.813409	−	0.581692i	$-0.802391\pi$
$607$	90.9868	−	516.012i	0.149896	−	0.850102i	0.963305	−	0.268410i	$-0.0864981\pi$
$608$	−684.359	−	120.671i	−1.12559	−	0.198472i
$609$		0			0
$610$	−428.964	+	359.943i	−0.703219	+	0.590071i
$611$	110.745	+	63.9384i	0.181251	+	0.104646i
$612$		0			0
$613$	−35.0848	−	60.7687i	−0.0572346	−	0.0991333i	0.835988	−	0.548747i	$-0.184895\pi$
$613$	−35.0848	−	60.7687i	−0.0572346	−	0.0991333i	−0.893223	+	0.449614i	$0.851562\pi$
$614$	−47.2792	+	129.899i	−0.0770020	+	0.211561i
$615$		0			0
$616$	145.092	+	121.747i	0.235539	+	0.197641i
$617$	−227.293	−	624.483i	−0.368385	−	1.01213i	−0.975976	−	0.217879i	$-0.930086\pi$
$617$	−227.293	−	624.483i	−0.368385	−	1.01213i	0.607591	−	0.794250i	$-0.292136\pi$
$618$		0			0
$619$	−168.570	−	956.006i	−0.272326	−	1.54444i	−0.747330	−	0.664453i	$-0.768665\pi$
$619$	−168.570	−	956.006i	−0.272326	−	1.54444i	0.475005	−	0.879983i	$-0.342446\pi$
$620$			594.574i			0.958990i
$621$		0			0
$622$	−932.436			−1.49909
$623$	−226.147	+	39.8758i	−0.362997	+	0.0640061i
$624$		0			0
$625$	731.800	−	266.353i	1.17088	−	0.426165i
$626$	284.200	−	338.696i	0.453993	−	0.541048i
$627$		0			0
$628$	−203.269	−	73.9837i	−0.323676	−	0.117808i
$629$	−411.502	+	237.581i	−0.654216	+	0.377712i
$630$		0			0
$631$	94.6588	−	163.954i	0.150014	−	0.259832i	−0.781218	−	0.624258i	$-0.785401\pi$
$631$	94.6588	−	163.954i	0.150014	−	0.259832i	0.931232	+	0.364426i	$0.118735\pi$
$632$	51.0749	+	60.8687i	0.0808148	+	0.0963113i
$633$		0			0
$634$	−232.721	+	1319.82i	−0.367067	+	2.08174i
$635$	723.100	+	127.502i	1.13874	+	0.200791i
$636$		0			0
$637$	125.671	−	105.450i	0.197285	−	0.165542i
$638$	−280.156	−	161.748i	−0.439116	−	0.253524i
$639$		0			0
$640$	−276.852	−	479.522i	−0.432581	−	0.749253i
$641$	236.919	−	650.930i	0.369609	−	1.01549i	−0.605902	−	0.795539i	$-0.707188\pi$
$641$	236.919	−	650.930i	0.369609	−	1.01549i	0.975511	−	0.219952i	$-0.0705901\pi$
$642$		0			0
$643$	815.534	+	684.314i	1.26833	+	1.06425i	0.994743	+	0.102404i	$0.0326535\pi$
$643$	815.534	+	684.314i	1.26833	+	1.06425i	0.273584	+	0.961848i	$0.411791\pi$
$644$	−212.443	−	583.682i	−0.329880	−	0.906338i
$645$		0			0
$646$	122.506	+	694.764i	0.189637	+	1.07549i
$647$			352.755i			0.545217i	0.962125	+	0.272608i	$0.0878863\pi$
$647$			352.755i			0.545217i	−0.962125	+	0.272608i	$0.912114\pi$
$648$		0			0
$649$	184.274			0.283935
$650$	−353.710	+	62.3686i	−0.544169	+	0.0959517i
$651$		0			0
$652$	695.809	−	253.254i	1.06719	−	0.388426i
$653$	301.103	−	358.840i	0.461107	−	0.549526i	−0.484520	−	0.874780i	$-0.661006\pi$
$653$	301.103	−	358.840i	0.461107	−	0.549526i	0.945626	+	0.325255i	$0.105450\pi$
$654$		0			0
$655$	−27.6836	−	10.0760i	−0.0422650	−	0.0153832i
$656$	−274.399	+	158.424i	−0.418291	+	0.241501i
$657$		0			0
$658$	−140.474	+	243.307i	−0.213486	+	0.369768i
$659$	−55.2415	−	65.8343i	−0.0838262	−	0.0999002i	0.722501	−	0.691370i	$-0.242992\pi$
$659$	−55.2415	−	65.8343i	−0.0838262	−	0.0999002i	−0.806327	+	0.591470i	$0.798548\pi$
$660$		0			0
$661$	21.3782	−	121.242i	0.0323422	−	0.183422i	−0.964357	−	0.264604i	$-0.914759\pi$
$661$	21.3782	−	121.242i	0.0323422	−	0.183422i	0.996699	+	0.0811828i	$0.0258698\pi$
$662$	878.200	+	154.850i	1.32659	+	0.233913i
$663$		0			0
$664$	38.7480	−	32.5134i	0.0583554	−	0.0489660i
$665$	785.070	+	453.260i	1.18056	+	0.681594i
$666$		0			0
$667$	−199.763	−	346.000i	−0.299495	−	0.518741i
$668$	−157.618	+	433.053i	−0.235956	+	0.648283i
$669$		0			0
$670$	−101.985	−	85.5759i	−0.152217	−	0.127725i
$671$	94.5985	+	259.907i	0.140981	+	0.387343i
$672$		0			0
$673$	−110.547	−	626.942i	−0.164260	−	0.931563i	−0.949824	−	0.312784i	$-0.898739\pi$
$673$	−110.547	−	626.942i	−0.164260	−	0.931563i	0.785565	−	0.618779i	$-0.212373\pi$
$674$			179.321i			0.266054i
$675$		0			0
$676$	217.127			0.321194
$677$	162.798	−	28.7056i	0.240469	−	0.0424012i	−0.0521144	−	0.998641i	$-0.516596\pi$
$677$	162.798	−	28.7056i	0.240469	−	0.0424012i	0.292584	+	0.956240i	$0.405485\pi$
$678$		0			0
$679$	1286.33	−	468.186i	1.89445	−	0.689522i
$680$	−173.639	+	206.935i	−0.255352	+	0.304317i
$681$		0			0
$682$	655.862	+	238.714i	0.961675	+	0.350021i
$683$	1129.58	−	652.163i	1.65385	−	0.954851i	0.678383	−	0.734709i	$-0.262681\pi$
$683$	1129.58	−	652.163i	1.65385	−	0.954851i	0.975468	−	0.220142i	$-0.0706522\pi$
$684$		0			0
$685$	690.092	−	1195.27i	1.00743	−	1.74493i
$686$	−440.212	−	524.625i	−0.641709	−	0.764759i
$687$		0			0
$688$	279.177	−	1583.29i	0.405781	−	2.30130i
$689$	245.879	+	43.3551i	0.356863	+	0.0629246i
$690$		0			0
$691$	−277.168	+	232.571i	−0.401111	+	0.336572i	−0.820923	−	0.571039i	$-0.806540\pi$
$691$	−277.168	+	232.571i	−0.401111	+	0.336572i	0.419812	+	0.907611i	$0.362096\pi$
$692$	−750.099	−	433.070i	−1.08396	−	0.625824i
$693$		0			0
$694$	227.439	+	393.936i	0.327722	+	0.567632i
$695$	76.4668	−	210.091i	0.110024	−	0.302289i
$696$		0			0
$697$	190.176	+	159.576i	0.272849	+	0.228947i
$698$	413.066	+	1134.89i	0.591784	+	1.62591i
$699$		0			0
$700$	−57.6559	−	326.983i	−0.0823655	−	0.467118i
$701$		−	893.344i		−	1.27438i	−0.770705	−	0.637192i	$-0.780096\pi$
$701$		−	893.344i		−	1.27438i	0.770705	−	0.637192i	$-0.219904\pi$
$702$		0			0
$703$	−564.863			−0.803504
$704$	203.788	−	35.9333i	0.289472	−	0.0510416i
$705$		0			0
$706$	−993.313	+	361.537i	−1.40696	+	0.512091i
$707$	364.357	−	434.224i	0.515357	−	0.614179i
$708$		0			0
$709$	648.964	+	236.203i	0.915323	+	0.333150i	0.756376	−	0.654137i	$-0.226968\pi$
$709$	648.964	+	236.203i	0.915323	+	0.333150i	0.158947	+	0.987287i	$0.449190\pi$
$710$	−587.363	+	339.114i	−0.827272	+	0.477626i
$711$		0			0
$712$	40.6737	−	70.4490i	0.0571260	−	0.0989452i
$713$	554.078	+	660.324i	0.777108	+	0.926121i
$714$		0			0
$715$	−85.5176	+	484.994i	−0.119605	+	0.678314i
$716$	−83.9273	−	14.7986i	−0.117217	−	0.0206685i
$717$		0			0
$718$	458.502	−	384.729i	0.638583	−	0.535834i
$719$	−417.508	−	241.049i	−0.580679	−	0.335255i	0.180724	−	0.983534i	$-0.442156\pi$
$719$	−417.508	−	241.049i	−0.580679	−	0.335255i	−0.761403	+	0.648279i	$0.775489\pi$
$720$		0			0
$721$	283.560	+	491.140i	0.393287	+	0.681192i
$722$	37.6220	−	103.366i	0.0521081	−	0.143166i
$723$		0			0
$724$	−185.649	−	155.778i	−0.256422	−	0.215163i
$725$	−73.0432	−	200.685i	−0.100749	−	0.276806i
$726$		0			0
$727$	59.9144	+	339.791i	0.0824132	+	0.467388i	0.997885	+	0.0650059i	$0.0207066\pi$
$727$	59.9144	+	339.791i	0.0824132	+	0.467388i	−0.915472	+	0.402382i	$0.868182\pi$
$728$			226.654i			0.311338i
$729$		0			0
$730$	1327.46			1.81844
$731$	−1240.54	+	218.740i	−1.69704	+	0.299234i
$732$		0			0
$733$	−506.752	+	184.443i	−0.691339	+	0.251627i	−0.663709	−	0.747991i	$-0.731018\pi$
$733$	−506.752	+	184.443i	−0.691339	+	0.251627i	−0.0276307	+	0.999618i	$0.508796\pi$
$734$	−397.742	+	474.011i	−0.541883	+	0.645791i
$735$		0			0
$736$	962.575	+	350.349i	1.30785	+	0.476017i
$737$	−56.9482	+	32.8791i	−0.0772704	+	0.0446121i
$738$		0			0
$739$	−368.737	+	638.671i	−0.498968	+	0.864237i	−0.999999	−	0.00119161i	$-0.999621\pi$
$739$	−368.737	+	638.671i	−0.498968	+	0.864237i	0.501032	+	0.865429i	$0.332954\pi$
$740$	369.173	+	439.963i	0.498882	+	0.594545i
$741$		0			0
$742$	−95.2517	+	540.199i	−0.128372	+	0.728031i
$743$	−1025.43	−	180.811i	−1.38012	−	0.243353i	−0.566171	−	0.824288i	$-0.691576\pi$
$743$	−1025.43	−	180.811i	−1.38012	−	0.243353i	−0.813950	+	0.580935i	$0.802687\pi$
$744$		0			0
$745$	−803.226	+	673.987i	−1.07816	+	0.904680i
$746$	1485.54	+	857.674i	1.99133	+	1.14970i
$747$		0			0
$748$	−177.150	−	306.832i	−0.236831	−	0.410204i
$749$	337.142	−	926.289i	0.450122	−	1.23670i
$750$		0			0
$751$	184.644	+	154.935i	0.245864	+	0.206305i	0.757389	−	0.652964i	$-0.226475\pi$
$751$	184.644	+	154.935i	0.245864	+	0.206305i	−0.511525	+	0.859269i	$0.670919\pi$
$752$	−86.3942	−	237.366i	−0.114886	−	0.315646i
$753$		0			0
$754$	−67.2222	−	381.236i	−0.0891541	−	0.505618i
$755$			523.331i			0.693154i
$756$		0			0
$757$	32.7615			0.0432781			0.0216391	−	0.999766i	$-0.493112\pi$
$757$	32.7615			0.0432781			0.0216391	+	0.999766i	$0.493112\pi$
$758$	1617.60	−	285.227i	2.13404	−	0.376289i
$759$		0			0
$760$	−301.765	+	109.833i	−0.397059	+	0.144518i
$761$	205.276	−	244.639i	0.269746	−	0.321470i	−0.614119	−	0.789214i	$-0.710488\pi$
$761$	205.276	−	244.639i	0.269746	−	0.321470i	0.883864	+	0.467743i	$0.154933\pi$
$762$		0			0
$763$	−912.573	−	332.149i	−1.19603	−	0.435320i
$764$	394.950	−	228.025i	0.516951	−	0.298462i
$765$		0			0
$766$	139.986	−	242.463i	0.182750	−	0.316531i
$767$	141.744	+	168.924i	0.184803	+	0.220240i
$768$		0			0
$769$	−82.6925	+	468.973i	−0.107533	+	0.609847i	0.882646	+	0.470038i	$0.155760\pi$
$769$	−82.6925	+	468.973i	−0.107533	+	0.609847i	−0.990179	+	0.139809i	$0.955351\pi$
$770$	−1065.54	−	187.883i	−1.38382	−	0.244004i
$771$		0			0
$772$	92.3069	−	77.4546i	0.119568	−	0.100330i
$773$	−1122.62	−	648.147i	−1.45229	−	0.838482i	−0.453682	−	0.891164i	$-0.649890\pi$
$773$	−1122.62	−	648.147i	−1.45229	−	0.838482i	−0.998611	+	0.0526817i	$0.983223\pi$
$774$		0			0
$775$	230.386	+	399.040i	0.297272	+	0.514890i
$776$	−165.853	+	455.677i	−0.213728	+	0.587213i
$777$		0			0
$778$	−1195.02	−	1002.74i	−1.53602	−	1.28887i
$779$	100.938	+	277.324i	0.129574	+	0.356001i
$780$		0			0
$781$	58.1717	+	329.908i	0.0744837	+	0.422418i
$782$		−	1039.93i		−	1.32983i
$783$		0			0
$784$	−324.056			−0.413337
$785$	−458.289	+	80.8088i	−0.583808	+	0.102941i
$786$		0			0
$787$	−809.031	+	294.463i	−1.02799	+	0.374159i	−0.800317	−	0.599577i	$-0.795335\pi$
$787$	−809.031	+	294.463i	−1.02799	+	0.374159i	−0.227677	+	0.973737i	$0.573113\pi$
$788$	393.461	−	468.909i	0.499317	−	0.595062i
$789$		0			0
$790$	−426.534	−	155.246i	−0.539917	−	0.196514i
$791$	874.285	−	504.769i	1.10529	−	0.638140i
$792$		0			0
$793$	−165.492	+	286.640i	−0.208690	+	0.361462i
$794$	−633.131	−	754.536i	−0.797394	−	0.950298i
$795$		0			0
$796$	88.5680	−	502.294i	0.111266	−	0.631023i
$797$	−571.312	−	100.738i	−0.716828	−	0.126396i	−0.196675	−	0.980469i	$-0.563014\pi$
$797$	−571.312	−	100.738i	−0.716828	−	0.126396i	−0.520154	+	0.854073i	$0.674125\pi$
$798$		0			0
$799$	−151.613	+	127.218i	−0.189753	+	0.159222i
$800$	474.201	+	273.780i	0.592751	+	0.342225i
$801$		0			0
$802$	360.552	+	624.494i	0.449566	+	0.778671i
$803$	224.254	−	616.132i	0.279270	−	0.767287i
$804$		0			0
$805$	−1023.64	−	858.938i	−1.27161	−	1.06700i
$806$	285.661	+	784.849i	0.354419	+	0.973757i
$807$		0			0
$808$	34.8687	+	197.750i	0.0431543	+	0.244740i
$809$			661.323i			0.817457i	0.912656	+	0.408729i	$0.134028\pi$
$809$			661.323i			0.817457i	−0.912656	+	0.408729i	$0.865972\pi$
$810$		0			0
$811$	−168.725			−0.208045			−0.104023	−	0.994575i	$-0.533171\pi$
$811$	−168.725			−0.208045			−0.104023	+	0.994575i	$0.533171\pi$
$812$	352.429	−	62.1427i	0.434025	−	0.0765304i
$813$		0			0
$814$	633.533	−	230.587i	0.778296	−	0.283277i
$815$	1023.94	−	1220.29i	1.25637	−	1.49728i
$816$		0			0
$817$	−1407.17	−	512.167i	−1.72236	−	0.626887i
$818$	1255.05	−	724.602i	1.53429	−	0.885822i
$819$		0			0
$820$	150.035	−	259.868i	0.182969	−	0.316912i
$821$	97.4327	+	116.116i	0.118676	+	0.141432i	0.822111	−	0.569327i	$-0.192796\pi$
$821$	97.4327	+	116.116i	0.118676	+	0.141432i	−0.703436	+	0.710759i	$0.748352\pi$
$822$		0			0
$823$	39.0398	−	221.406i	0.0474360	−	0.269023i	−0.951860	−	0.306532i	$-0.900831\pi$
$823$	39.0398	−	221.406i	0.0474360	−	0.269023i	0.999296	+	0.0375092i	$0.0119424\pi$
$824$	−197.848	−	34.8859i	−0.240106	−	0.0423372i
$825$		0			0
$826$	−371.128	+	311.414i	−0.449308	+	0.377014i
$827$	−292.855	−	169.080i	−0.354117	−	0.204449i	0.312380	−	0.949957i	$-0.398874\pi$
$827$	−292.855	−	169.080i	−0.354117	−	0.204449i	−0.666497	+	0.745508i	$0.732207\pi$
$828$		0			0
$829$	401.806	+	695.949i	0.484688	+	0.839504i	0.999845	−	0.0175917i	$-0.00559990\pi$
$829$	401.806	+	695.949i	0.484688	+	0.839504i	−0.515157	+	0.857096i	$0.672267\pi$
$830$	−98.8267	+	271.524i	−0.119068	+	0.327137i
$831$		0			0
$832$	189.694	+	159.172i	0.227998	+	0.191313i
$833$	86.8402	+	238.591i	0.104250	+	0.286424i
$834$		0			0
$835$	172.159	+	976.361i	0.206178	+	1.16929i
$836$		−	421.184i		−	0.503809i
$837$		0			0
$838$	−230.169			−0.274665
$839$	840.969	−	148.286i	1.00235	−	0.176741i	0.351693	−	0.936115i	$-0.385606\pi$
$839$	840.969	−	148.286i	1.00235	−	0.176741i	0.650654	+	0.759374i	$0.274495\pi$
$840$		0			0
$841$	−573.980	+	208.911i	−0.682496	+	0.248408i
$842$	500.431	−	596.390i	0.594336	−	0.708302i
$843$		0			0
$844$	−712.257	−	259.240i	−0.843906	−	0.307157i
$845$	404.527	−	233.554i	0.478731	−	0.276395i
$846$		0			0
$847$	223.906	−	387.816i	0.264351	−	0.457870i
$848$	−317.013	−	377.802i	−0.373837	−	0.445521i
$849$		0			0
$850$	96.5284	−	547.440i	0.113563	−	0.644047i
$851$	819.995	+	144.587i	0.963567	+	0.169903i
$852$		0			0
$853$	−612.158	+	513.661i	−0.717653	+	0.602182i	−0.926735	−	0.375716i	$-0.877397\pi$
$853$	−612.158	+	513.661i	−0.717653	+	0.602182i	0.209082	+	0.977898i	$0.432952\pi$
$854$	−629.751	−	363.587i	−0.737414	−	0.425746i
$855$		0			0
$856$	174.597	+	302.410i	0.203968	+	0.353283i
$857$	−531.246	+	1459.59i	−0.619890	+	1.70313i	0.0873655	+	0.996176i	$0.472155\pi$
$857$	−531.246	+	1459.59i	−0.619890	+	1.70313i	−0.707256	+	0.706958i	$0.750067\pi$
$858$		0			0
$859$	−21.6423	−	18.1601i	−0.0251948	−	0.0211409i	0.630103	−	0.776511i	$-0.283013\pi$
$859$	−21.6423	−	18.1601i	−0.0251948	−	0.0211409i	−0.655298	+	0.755370i	$0.727457\pi$
$860$	520.752	+	1430.75i	0.605525	+	1.66367i
$861$		0			0
$862$	267.487	+	1516.99i	0.310309	+	1.75985i
$863$		−	951.550i		−	1.10261i	−0.834305	−	0.551304i	$-0.814131\pi$
$863$		−	951.550i		−	1.10261i	0.834305	−	0.551304i	$-0.185869\pi$
$864$		0			0
$865$	−1863.34			−2.15415
$866$	1074.95	−	189.543i	1.24128	−	0.218871i
$867$		0			0
$868$	−725.543	+	264.076i	−0.835879	+	0.304235i
$869$	−144.112	+	171.746i	−0.165837	+	0.197637i
$870$		0			0
$871$	−73.9450	−	26.9138i	−0.0848967	−	0.0308999i
$872$	297.932	−	172.011i	0.341665	−	0.197260i
$873$		0			0
$874$	618.122	−	1070.62i	0.707233	−	1.22496i
$875$	356.304	+	424.626i	0.407204	+	0.485287i
$876$		0			0
$877$	−39.6252	+	224.726i	−0.0451827	+	0.256244i	−0.999029	−	0.0440504i	$-0.985974\pi$
$877$	−39.6252	+	224.726i	−0.0451827	+	0.256244i	0.953847	+	0.300294i	$0.0970849\pi$
$878$	−865.303	−	152.576i	−0.985538	−	0.173777i
$879$		0			0
$880$	745.212	−	625.307i	0.846832	−	0.710576i
$881$	1343.36	+	775.592i	1.52482	+	0.880354i	0.999568	+	0.0294054i	$0.00936139\pi$
$881$	1343.36	+	775.592i	1.52482	+	0.880354i	0.525250	+	0.850948i	$0.323972\pi$
$882$		0			0
$883$	−781.794	−	1354.11i	−0.885384	−	1.53353i	−0.845272	−	0.534336i	$-0.820562\pi$
$883$	−781.794	−	1354.11i	−0.885384	−	1.53353i	−0.0401121	−	0.999195i	$-0.512772\pi$
$884$	145.009	−	398.409i	0.164037	−	0.450689i
$885$		0			0
$886$	909.185	+	762.897i	1.02617	+	0.861058i
$887$	−240.153	−	659.815i	−0.270748	−	0.743873i	−0.998325	−	0.0578478i	$-0.981576\pi$
$887$	−240.153	−	659.815i	−0.270748	−	0.743873i	0.727578	−	0.686025i	$-0.240646\pi$
$888$		0			0
$889$	165.573	+	939.010i	0.186246	+	1.05625i
$890$			464.699i			0.522134i
$891$		0			0
$892$	1130.95			1.26789
$893$	−231.704	+	40.8557i	−0.259467	+	0.0457511i
$894$		0			0
$895$	−172.283	+	62.7057i	−0.192494	+	0.0700622i
$896$	462.186	−	550.812i	0.515833	−	0.614746i
$897$		0			0
$898$	471.687	+	171.680i	0.525264	+	0.191180i
$899$	−430.094	+	248.315i	−0.478413	+	0.276212i
$900$		0			0
$901$	−193.210	+	334.649i	−0.214439	+	0.371419i
$902$	−226.418	−	269.834i	−0.251017	−	0.299151i
$903$		0			0
$904$	−62.1009	+	352.192i	−0.0686957	+	0.389592i
$905$	−513.446	−	90.5344i	−0.567344	−	0.100038i
$906$		0			0
$907$	1236.79	−	1037.79i	1.36360	−	1.14420i	0.388754	−	0.921342i	$-0.372906\pi$
$907$	1236.79	−	1037.79i	1.36360	−	1.14420i	0.974851	−	0.222858i	$-0.0715387\pi$
$908$	−876.803	−	506.222i	−0.965642	−	0.557514i
$909$		0			0
$910$	−647.383	−	1121.30i	−0.711410	−	1.23220i
$911$	209.645	−	575.996i	0.230127	−	0.632268i	−0.769856	−	0.638218i	$-0.779672\pi$
$911$	209.645	−	575.996i	0.230127	−	0.632268i	0.999982	+	0.00595016i	$0.00189401\pi$
$912$		0			0
$913$	109.331	+	91.7394i	0.119749	+	0.100481i
$914$	−346.709	−	952.574i	−0.379331	−	1.04220i
$915$		0			0
$916$	183.929	+	1043.11i	0.200796	+	1.13877i
$917$		−	38.2568i		−	0.0417195i
$918$		0			0
$919$	628.091			0.683451			0.341725	−	0.939800i	$-0.388989\pi$
$919$	628.091			0.683451			0.341725	+	0.939800i	$0.388989\pi$
$920$	466.177	−	82.1995i	0.506714	−	0.0893473i
$921$		0			0
$922$	1069.38	−	389.222i	1.15985	−	0.422150i
$923$	−257.681	+	307.092i	−0.279178	+	0.332711i
$924$		0			0
$925$	418.243	+	152.228i	0.452154	+	0.164571i
$926$	−1258.19	+	726.418i	−1.35874	+	0.784469i
$927$		0			0
$928$	−295.086	+	511.103i	−0.317980	+	0.550758i
$929$	805.771	+	960.281i	0.867354	+	1.03367i	0.999101	+	0.0423885i	$0.0134967\pi$
$929$	805.771	+	960.281i	0.867354	+	1.03367i	−0.131748	+	0.991283i	$0.542059\pi$
$930$		0			0
$931$	−52.4133	+	297.250i	−0.0562978	+	0.319281i
$932$	−542.756	−	95.7025i	−0.582356	−	0.102685i
$933$		0			0
$934$	433.440	−	363.700i	0.464069	−	0.389400i
$935$	−660.093	−	381.105i	−0.705981	−	0.407599i
$936$		0			0
$937$	460.132	+	796.972i	0.491070	+	0.850557i	0.999947	−	0.0102815i	$-0.00327275\pi$
$937$	460.132	+	796.972i	0.491070	+	0.850557i	−0.508878	+	0.860839i	$0.669939\pi$
$938$	59.1299	−	162.458i	0.0630383	−	0.173196i
$939$		0			0
$940$	183.255	+	153.769i	0.194952	+	0.163584i
$941$	233.754	+	642.234i	0.248410	+	0.682502i	0.999745	+	0.0225805i	$0.00718822\pi$
$941$	233.754	+	642.234i	0.248410	+	0.682502i	−0.751335	+	0.659921i	$0.770590\pi$
$942$		0			0
$943$	−75.5421	−	428.421i	−0.0801083	−	0.454317i
$944$		−	435.590i		−	0.461430i
$945$		0			0
$946$	1787.31			1.88934
$947$	−828.995	+	146.174i	−0.875391	+	0.154355i	−0.593250	−	0.805018i	$-0.702156\pi$
$947$	−828.995	+	146.174i	−0.875391	+	0.154355i	−0.282141	+	0.959373i	$0.591044\pi$
$948$		0			0
$949$	737.304	−	268.357i	0.776928	−	0.282779i
$950$	424.770	−	506.222i	0.447127	−	0.532865i
$951$		0			0
$952$	−329.639	−	119.979i	−0.346259	−	0.126028i
$953$	−1277.52	+	737.576i	−1.34052	+	0.773952i	−0.986884	−	0.161430i	$-0.948390\pi$
$953$	−1277.52	+	737.576i	−1.34052	+	0.773952i	−0.353640	+	0.935382i	$0.615056\pi$
$954$		0			0
$955$	490.553	−	849.662i	0.513668	−	0.889698i
$956$	571.719	+	681.348i	0.598032	+	0.712707i
$957$		0			0
$958$	103.353	−	586.145i	0.107884	−	0.611842i
$959$	1765.06	+	311.228i	1.84052	+	0.324534i
$960$		0			0
$961$	84.6440	−	71.0248i	0.0880791	−	0.0739072i
$962$	698.694	+	403.391i	0.726294	+	0.419326i
$963$		0			0
$964$	−428.456	−	742.107i	−0.444456	−	0.769821i
$965$	88.6616	−	243.596i	0.0918773	−	0.252431i
$966$		0			0
$967$	248.771	+	208.744i	0.257261	+	0.215868i	0.762291	−	0.647234i	$-0.224074\pi$
$967$	248.771	+	208.744i	0.257261	+	0.215868i	−0.505030	+	0.863102i	$0.668519\pi$
$968$	54.2565	+	149.068i	0.0560501	+	0.153996i
$969$		0			0
$970$	−481.027	−	2728.04i	−0.495904	−	2.81241i
$971$			1203.37i			1.23931i	0.784873	+	0.619657i	$0.212728\pi$
$971$			1203.37i			1.23931i	−0.784873	+	0.619657i	$0.787272\pi$
$972$		0			0
$973$	290.331			0.298387
$974$	−1146.80	+	202.212i	−1.17741	+	0.207609i
$975$		0			0
$976$	614.373	−	223.614i	0.629481	−	0.229112i
$977$	121.698	−	145.034i	0.124563	−	0.148448i	−0.700159	−	0.713987i	$-0.746887\pi$
$977$	121.698	−	145.034i	0.124563	−	0.148448i	0.824722	+	0.565539i	$0.191332\pi$
$978$		0			0
$979$	215.687	+	78.5036i	0.220313	+	0.0801875i
$980$	265.779	−	153.448i	0.271203	−	0.156579i
$981$		0			0
$982$	−876.994	+	1519.00i	−0.893070	+	1.54684i
$983$	−812.932	−	968.815i	−0.826991	−	0.985570i	−1.00000		0.000649412i	$-0.999793\pi$
$983$	−812.932	−	968.815i	−0.826991	−	0.985570i	0.173009	−	0.984920i	$-0.444651\pi$
$984$		0			0
$985$	228.670	−	1296.85i	0.232152	−	1.31660i
$986$	590.042	+	104.040i	0.598420	+	0.105518i
$987$		0			0
$988$	386.100	−	323.976i	0.390789	−	0.327911i
$989$	1911.64	+	1103.69i	1.93291	+	1.11596i
$990$		0			0
$991$	697.271	+	1207.71i	0.703604	+	1.21868i	0.967193	+	0.254043i	$0.0817603\pi$
$991$	697.271	+	1207.71i	0.703604	+	1.21868i	−0.263589	+	0.964635i	$0.584906\pi$
$992$	435.499	−	1196.52i	0.439011	−	1.20617i
$993$		0			0
$994$	−674.686	−	566.129i	−0.678759	−	0.569546i
$995$	−375.286	−	1031.09i	−0.377172	−	1.03627i
$996$		0			0
$997$	175.161	+	993.390i	0.175689	+	0.996379i	0.937346	+	0.348399i	$0.113275\pi$
$997$	175.161	+	993.390i	0.175689	+	0.996379i	−0.761658	+	0.647980i	$0.775614\pi$
$998$			151.062i			0.151365i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.3.f.a.215.5		30
3.2	odd	2		243.3.f.d.215.1		30
9.2	odd	6		243.3.f.c.134.5		30
9.4	even	3		81.3.f.a.17.1		30
9.5	odd	6		27.3.f.a.23.5	yes	30
9.7	even	3		243.3.f.b.134.1		30
27.2	odd	18	inner	243.3.f.a.26.5		30
27.5	odd	18		729.3.b.a.728.26		30
27.7	even	9		243.3.f.c.107.5		30
27.11	odd	18		81.3.f.a.62.1		30
27.16	even	9		27.3.f.a.20.5	✓	30
27.20	odd	18		243.3.f.b.107.1		30
27.22	even	9		729.3.b.a.728.5		30
27.25	even	9		243.3.f.d.26.1		30
36.23	even	6		432.3.bc.a.401.5		30
108.43	odd	18		432.3.bc.a.209.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.20.5	✓	30	27.16	even	9
27.3.f.a.23.5	yes	30	9.5	odd	6
81.3.f.a.17.1		30	9.4	even	3
81.3.f.a.62.1		30	27.11	odd	18
243.3.f.a.26.5		30	27.2	odd	18	inner
243.3.f.a.215.5		30	1.1	even	1	trivial
243.3.f.b.107.1		30	27.20	odd	18
243.3.f.b.134.1		30	9.7	even	3
243.3.f.c.107.5		30	27.7	even	9
243.3.f.c.134.5		30	9.2	odd	6
243.3.f.d.26.1		30	27.25	even	9
243.3.f.d.215.1		30	3.2	odd	2
432.3.bc.a.209.5		30	108.43	odd	18
432.3.bc.a.401.5		30	36.23	even	6
729.3.b.a.728.5		30	27.22	even	9
729.3.b.a.728.26		30	27.5	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	243.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.58795 - 0.456325i) q^{2} +(2.73048 - 0.993814i) q^{4} +(4.01814 - 4.78863i) q^{5} +(7.62807 + 2.77639i) q^{7} +(-2.49037 + 1.43782i) q^{8} +(8.21356 - 14.2263i) q^{10} +(-5.21549 - 6.21558i) q^{11} +(1.68605 - 9.56207i) q^{13} +(21.0080 + 3.70428i) q^{14} +(-14.6925 + 12.3285i) q^{16} +(13.0143 + 7.51380i) q^{17} +(8.93226 + 15.4711i) q^{19} +(6.21244 - 17.0685i) q^{20} +(-16.3337 - 13.7056i) q^{22} +(-9.00658 - 24.7454i) q^{23} +(-2.44434 - 13.8625i) q^{25} -25.5156i q^{26} +23.5875 q^{28} +(14.9413 - 2.63456i) q^{29} +(-30.7596 + 11.1956i) q^{31} +(-25.0039 + 29.7985i) q^{32} +(37.1091 + 13.5066i) q^{34} +(43.9457 - 25.3721i) q^{35} +(-15.8096 + 27.3831i) q^{37} +(30.1761 + 35.9625i) q^{38} +(-3.12149 + 17.7028i) q^{40} +(16.2691 + 2.86867i) q^{41} +(-64.2129 + 53.8810i) q^{43} +(-20.4179 - 11.7883i) q^{44} +(-34.6005 - 59.9298i) q^{46} +(-4.50446 + 12.3759i) q^{47} +(12.9430 + 10.8604i) q^{49} +(-12.6516 - 34.7601i) q^{50} +(-4.89919 - 27.7847i) q^{52} +25.7140i q^{53} -50.7206 q^{55} +(-22.9887 + 4.05353i) q^{56} +(37.4652 - 13.6362i) q^{58} +(-14.5984 + 17.3977i) q^{59} +(-32.0325 - 11.6589i) q^{61} +(-74.4955 + 43.0100i) q^{62} +(-12.7517 + 22.0867i) q^{64} +(-39.0144 - 46.4956i) q^{65} +(1.40732 - 7.98130i) q^{67} +(43.0026 + 7.58252i) q^{68} +(102.151 - 85.7152i) q^{70} +(-35.7557 - 20.6436i) q^{71} +(40.4046 + 69.9827i) q^{73} +(-28.4189 + 78.0804i) q^{74} +(39.7648 + 33.3666i) q^{76} +(-22.5272 - 61.8931i) q^{77} +(-4.79818 - 27.2118i) q^{79} +119.894i q^{80} +43.4126 q^{82} +(-17.3226 + 3.05444i) q^{83} +(88.2740 - 32.1291i) q^{85} +(-141.593 + 168.743i) q^{86} +(21.9254 + 7.98019i) q^{88} +(-24.4986 + 14.1443i) q^{89} +(39.4094 - 68.2590i) q^{91} +(-49.1846 - 58.6159i) q^{92} +(-6.00988 + 34.0837i) q^{94} +(109.977 + 19.3918i) q^{95} +(129.179 - 108.394i) q^{97} +(38.4516 + 22.2000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} - 57 q^{11} + 3 q^{13} + 114 q^{14} + 27 q^{16} + 9 q^{17} - 3 q^{19} + 183 q^{20} + 75 q^{22} - 48 q^{23} + 21 q^{25} - 12 q^{28} + 78 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 - 57 * q^11 + 3 * q^13 + 114 * q^14 + 27 * q^16 + 9 * q^17 - 3 * q^19 + 183 * q^20 + 75 * q^22 - 48 * q^23 + 21 * q^25 - 12 * q^28 + 78 * q^29 - 87 * q^31 - 243 * q^32 - 153 * q^34 + 252 * q^35 - 3 * q^37 - 321 * q^38 - 168 * q^40 + 357 * q^41 - 87 * q^43 - 639 * q^44 - 3 * q^46 + 51 * q^47 - 69 * q^49 - 168 * q^50 - 36 * q^52 - 12 * q^55 + 177 * q^56 + 138 * q^58 - 48 * q^59 + 147 * q^61 + 900 * q^62 - 51 * q^64 - 624 * q^65 + 12 * q^67 + 477 * q^68 - 6 * q^70 - 315 * q^71 - 66 * q^73 + 480 * q^74 - 57 * q^76 - 453 * q^77 - 15 * q^79 - 12 * q^82 + 591 * q^83 + 243 * q^85 - 669 * q^86 + 591 * q^88 - 72 * q^89 + 96 * q^91 - 564 * q^92 + 957 * q^94 + 606 * q^95 + 696 * q^97 - 882 * q^98

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