LMFDB - Embedded newform 243.3.f.a.26.5

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)

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")

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);

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			26.5
Character	$\chi$	$=$	243.26
Dual form			243.3.f.a.215.5

$q$-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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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	0.777904	−	0.628383i	$-0.216283\pi$
$2$	2.58795	+	0.456325i	1.29397	+	0.228163i	0.516071	+	0.856546i	$0.327394\pi$
$3$		0			0
$3$		0			0
$4$	2.73048	+	0.993814i	0.682620	+	0.248453i
$5$	4.01814	+	4.78863i	0.803627	+	0.957726i	0.999739	−	0.0228560i	$-0.00727592\pi$
$5$	4.01814	+	4.78863i	0.803627	+	0.957726i	−0.196112	+	0.980582i	$0.562831\pi$
$6$		0			0
$7$	7.62807	−	2.77639i	1.08972	−	0.396627i	0.266206	−	0.963916i	$-0.414230\pi$
$7$	7.62807	−	2.77639i	1.08972	−	0.396627i	0.823519	+	0.567289i	$0.192008\pi$
$8$	−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	−0.949109	−	0.314948i	$-0.898013\pi$
$11$	−5.21549	+	6.21558i	−0.474135	+	0.565052i	0.474974	+	0.880000i	$0.342458\pi$
$12$		0			0
$13$	1.68605	+	9.56207i	0.129696	+	0.735544i	0.978407	+	0.206687i	$0.0662681\pi$
$13$	1.68605	+	9.56207i	0.129696	+	0.735544i	−0.848711	+	0.528857i	$0.822621\pi$
$14$	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	−0.0657372	−	0.997837i	$-0.520940\pi$
$17$	13.0143	−	7.51380i	0.765546	−	0.441988i	0.831284	+	0.555849i	$0.187607\pi$
$18$		0			0
$19$	8.93226	−	15.4711i	0.470119	−	0.814270i	−0.529297	−	0.848437i	$-0.677544\pi$
$19$	8.93226	−	15.4711i	0.470119	−	0.814270i	0.999416	+	0.0341664i	$0.0108776\pi$
$20$	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	0.574685	+	0.818375i	$0.305125\pi$
$23$	−9.00658	+	24.7454i	−0.391590	+	1.07589i	−0.966275	+	0.257511i	$0.917098\pi$
$24$		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	0.425211	−	0.905094i	$-0.360200\pi$
$29$	14.9413	+	2.63456i	0.515218	+	0.0908468i	0.0900069	+	0.995941i	$0.471311\pi$
$30$		0			0
$31$	−30.7596	−	11.1956i	−0.992246	−	0.361148i	−0.205656	−	0.978624i	$-0.565933\pi$
$31$	−30.7596	−	11.1956i	−0.992246	−	0.361148i	−0.786589	+	0.617476i	$0.788155\pi$
$32$	−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	0.569344	−	0.822100i	$-0.307197\pi$
$37$	−15.8096	−	27.3831i	−0.427287	−	0.740083i	−0.996631	+	0.0820163i	$0.973864\pi$
$38$	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	0.0283154	−	0.999599i	$-0.490986\pi$
$41$	16.2691	−	2.86867i	0.396806	−	0.0699677i	0.368491	+	0.929631i	$0.379875\pi$
$42$		0			0
$43$	−64.2129	−	53.8810i	−1.49332	−	1.25305i	−0.890342	−	0.455292i	$-0.849535\pi$
$43$	−64.2129	−	53.8810i	−1.49332	−	1.25305i	−0.602982	−	0.797755i	$-0.706021\pi$
$44$	−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	0.882504	−	0.470305i	$-0.155856\pi$
$47$	−4.50446	−	12.3759i	−0.0958397	−	0.263317i	−0.978344	+	0.206988i	$0.933634\pi$
$48$		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	$-0.922005\pi$
$53$		−	25.7140i		−	0.485169i	0.970130	−	0.242585i	$-0.0779952\pi$
$54$		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	0.628007	−	0.778208i	$-0.283871\pi$
$59$	−14.5984	−	17.3977i	−0.247430	−	0.294875i	−0.875437	+	0.483332i	$0.839426\pi$
$60$		0			0
$61$	−32.0325	+	11.6589i	−0.525123	+	0.191129i	−0.590959	−	0.806701i	$-0.701251\pi$
$61$	−32.0325	+	11.6589i	−0.525123	+	0.191129i	0.0658363	+	0.997830i	$0.479028\pi$
$62$	−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	0.993507	−	0.113768i	$-0.0362922\pi$
$67$	1.40732	+	7.98130i	0.0210048	+	0.119124i	−0.972503	+	0.232892i	$0.925181\pi$
$68$	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	−0.730199	−	0.683234i	$-0.760573\pi$
$71$	−35.7557	+	20.6436i	−0.503601	+	0.290754i	0.226598	+	0.973988i	$0.427240\pi$
$72$		0			0
$73$	40.4046	−	69.9827i	0.553487	−	0.958668i	−0.444532	−	0.895763i	$-0.646630\pi$
$73$	40.4046	−	69.9827i	0.553487	−	0.958668i	0.998020	−	0.0629050i	$-0.0200365\pi$
$74$	−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	0.939263	+	0.343199i	$0.111510\pi$
$79$	−4.79818	+	27.2118i	−0.0607365	+	0.344454i	−0.999999	+	0.00125471i	$0.999601\pi$
$80$		−	119.894i		−	1.49868i
$81$		0			0
$82$	43.4126			0.529421
$83$	−17.3226	−	3.05444i	−0.208706	−	0.0368004i	0.0683177	−	0.997664i	$-0.478237\pi$
$83$	−17.3226	−	3.05444i	−0.208706	−	0.0368004i	−0.277023	+	0.960863i	$0.589348\pi$
$84$		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	0.356013	−	0.934481i	$-0.384136\pi$
$89$	−24.4986	−	14.1443i	−0.275265	−	0.158924i	−0.631278	+	0.775557i	$0.717469\pi$
$90$		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	0.983667	+	0.179996i	$0.0576083\pi$
$97$	129.179	+	108.394i	1.33174	+	1.11746i	0.348073	+	0.937467i	$0.386836\pi$
$98$	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	0.999992	+	0.00390224i	$0.00124213\pi$
$101$	23.8827	+	65.6171i	0.236462	+	0.649674i	−0.763530	+	0.645772i	$0.776536\pi$
$102$		0			0
$103$	53.5180	−	44.9069i	0.519592	−	0.435989i	−0.344898	−	0.938640i	$-0.612086\pi$
$103$	53.5180	−	44.9069i	0.519592	−	0.435989i	0.864489	+	0.502651i	$0.167642\pi$
$104$	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	$0.192065\pi$
$107$			121.432i			1.13488i	−0.823416	+	0.567438i	$0.807935\pi$
$108$		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	0.993345	−	0.115174i	$-0.0367425\pi$
$113$	79.9394	+	95.2681i	0.707429	+	0.843081i	−0.285917	+	0.958254i	$0.592298\pi$
$114$		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	−0.536641	−	0.843811i	$-0.680307\pi$
$127$	58.7300	−	101.723i	0.462441	−	0.800971i	0.999082	+	0.0428396i	$0.0136404\pi$
$128$	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	−0.945693	−	0.325062i	$-0.894615\pi$
$131$	−1.61188	+	4.42859i	−0.0123044	+	0.0338060i	0.933388	+	0.358868i	$0.116837\pi$
$132$		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	0.896393	−	0.443260i	$-0.146178\pi$
$137$	217.436	+	38.3398i	1.58712	+	0.279853i	0.690730	+	0.723113i	$0.257289\pi$
$138$		0			0
$139$	33.6086	+	12.2325i	0.241788	+	0.0880038i	0.460072	−	0.887882i	$-0.347824\pi$
$139$	33.6086	+	12.2325i	0.241788	+	0.0880038i	−0.218284	+	0.975885i	$0.570046\pi$
$140$	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	−0.697849	−	0.716245i	$-0.745860\pi$
$149$	−165.188	+	29.1271i	−1.10864	+	0.195484i	−0.410794	+	0.911728i	$0.634748\pi$
$150$		0			0
$151$	−64.1318	−	53.8130i	−0.424714	−	0.356377i	0.405239	−	0.914211i	$-0.367188\pi$
$151$	−64.1318	−	53.8130i	−0.424714	−	0.356377i	−0.829953	+	0.557834i	$0.811633\pi$
$152$	−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	−0.806078	−	0.591810i	$-0.798414\pi$
$157$	−57.0276	+	47.8518i	−0.363233	+	0.304789i	0.442845	+	0.896598i	$0.353969\pi$
$158$	−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	0.368944	−	0.929452i	$-0.379719\pi$
$167$	−101.946	−	121.494i	−0.610454	−	0.727510i	−0.979398	+	0.201941i	$0.935275\pi$
$168$		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	−0.164809	+	0.986325i	$0.552701\pi$
$173$	−191.603	+	228.343i	−1.10753	+	1.31990i	−0.942722	+	0.333579i	$0.891744\pi$
$174$		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	−0.569268	−	0.822152i	$-0.692773\pi$
$179$	−25.3997	+	14.6645i	−0.141898	+	0.0819248i	0.427370	+	0.904077i	$0.359440\pi$
$180$		0			0
$181$	−41.7019	+	72.2299i	−0.230397	+	0.399060i	−0.957925	−	0.287018i	$-0.907336\pi$
$181$	−41.7019	+	72.2299i	−0.230397	+	0.399060i	0.727528	+	0.686078i	$0.240669\pi$
$182$	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	0.562934	−	0.826502i	$-0.309673\pi$
$191$	154.565	+	27.2539i	0.809238	+	0.142691i	0.246305	+	0.969192i	$0.420784\pi$
$192$		0			0
$193$	38.9684	+	14.1833i	0.201909	+	0.0734888i	0.440995	−	0.897510i	$-0.354626\pi$
$193$	38.9684	+	14.1833i	0.201909	+	0.0734888i	−0.239086	+	0.970998i	$0.576848\pi$
$194$	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	0.885568	−	0.464510i	$-0.153770\pi$
$197$	182.437	+	105.330i	0.926074	+	0.534669i	0.0405063	+	0.999179i	$0.487103\pi$
$198$		0			0
$199$	87.7654	+	152.014i	0.441032	+	0.763890i	0.997766	−	0.0668004i	$-0.0212791\pi$
$199$	87.7654	+	152.014i	0.441032	+	0.763890i	−0.556734	+	0.830691i	$0.687946\pi$
$200$	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	−0.978797	−	0.204833i	$-0.934335\pi$
$211$	−199.826	+	167.674i	−0.947042	+	0.794662i	0.0317552	+	0.999496i	$0.489890\pi$
$212$	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	0.653051	−	0.757314i	$-0.273489\pi$
$223$	365.744	−	133.120i	1.64011	−	0.596951i	0.987058	+	0.160364i	$0.0512666\pi$
$224$	−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	−0.00222294	+	0.999998i	$0.500708\pi$
$227$	−223.968	+	266.914i	−0.986642	+	1.17583i	−0.984419	+	0.175837i	$0.943737\pi$
$228$		0			0
$229$	−63.2989	−	358.986i	−0.276415	−	1.56762i	−0.734433	−	0.678682i	$-0.762552\pi$
$229$	−63.2989	−	358.986i	−0.276415	−	1.56762i	0.458018	−	0.888943i	$-0.348560\pi$
$230$	−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	−0.809198	−	0.587536i	$-0.800098\pi$
$233$	−164.260	+	94.8353i	−0.704976	+	0.407018i	0.104222	+	0.994554i	$0.466765\pi$
$234$		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	−0.502723	−	0.864448i	$-0.667668\pi$
$239$	104.692	−	287.639i	0.438042	−	1.20351i	0.940764	−	0.339062i	$-0.110110\pi$
$240$		0			0
$241$	−51.2098	+	290.425i	−0.212489	+	1.20508i	0.672723	+	0.739894i	$0.265125\pi$
$241$	−51.2098	+	290.425i	−0.212489	+	1.20508i	−0.885212	+	0.465189i	$0.845987\pi$
$242$			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	0.150083	−	0.988673i	$-0.452046\pi$
$251$	−158.404	−	91.4547i	−0.631092	−	0.364361i	−0.781175	+	0.624312i	$0.785379\pi$
$252$		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	−0.662278	−	0.749258i	$-0.730410\pi$
$257$	−264.287	+	46.6009i	−1.02835	+	0.181327i	−0.366076	+	0.930585i	$0.619299\pi$
$258$		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	−0.927171	−	0.374638i	$-0.877767\pi$
$263$	−120.383	−	330.749i	−0.457730	−	1.25760i	0.469441	−	0.882964i	$-0.344455\pi$
$264$		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	$0.0987518\pi$
$269$			164.243i			0.610570i	−0.952261	+	0.305285i	$0.901248\pi$
$270$		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	−0.584006	−	0.811749i	$-0.698516\pi$
$277$	−141.159	+	51.3776i	−0.509598	+	0.185479i	0.0744078	+	0.997228i	$0.476293\pi$
$278$	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	0.0891220	−	0.996021i	$-0.471594\pi$
$281$	296.324	−	353.146i	1.05454	−	1.25675i	0.965413	−	0.260725i	$-0.0839617\pi$
$282$		0			0
$283$	−11.9570	−	67.8114i	−0.0422508	−	0.239616i	0.956367	−	0.292166i	$-0.0943761\pi$
$283$	−11.9570	−	67.8114i	−0.0422508	−	0.239616i	−0.998618	+	0.0525503i	$0.983265\pi$
$284$	−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	0.162519	+	0.986705i	$0.448038\pi$
$293$	−174.692	+	479.963i	−0.596220	+	1.63810i	−0.758739	+	0.651395i	$0.774184\pi$
$294$		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	0.820005	−	0.572357i	$-0.193971\pi$
$307$	−26.3017	−	45.5559i	−0.0856734	−	0.148391i	−0.905678	+	0.423966i	$0.860637\pi$
$308$	−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	−0.704414	−	0.709789i	$-0.748790\pi$
$311$	−349.435	+	61.6148i	−1.12358	+	0.198118i	−0.419170	+	0.907908i	$0.637679\pi$
$312$		0			0
$313$	128.886	+	108.148i	0.411776	+	0.345521i	0.825024	−	0.565097i	$-0.191161\pi$
$313$	128.886	+	108.148i	0.411776	+	0.345521i	−0.413248	+	0.910618i	$0.635606\pi$
$314$	−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	−0.833383	−	0.552696i	$-0.813599\pi$
$317$	−174.426	−	479.232i	−0.550241	−	1.51177i	0.283142	−	0.959078i	$-0.408623\pi$
$318$		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	0.188020	−	0.982165i	$-0.439793\pi$
$331$	318.877	−	116.062i	0.963375	−	0.350640i	0.775355	+	0.631526i	$0.217571\pi$
$332$	−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	0.962167	−	0.272461i	$-0.0878376\pi$
$337$	−11.8494	−	67.2013i	−0.0351614	−	0.199410i	−0.997328	+	0.0730508i	$0.976726\pi$
$338$	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	−0.824687	−	0.565589i	$-0.808649\pi$
$347$	59.2029	−	162.659i	0.170613	−	0.468757i	0.995301	+	0.0968324i	$0.0308711\pi$
$348$		0			0
$349$	79.8055	−	452.600i	0.228669	−	1.29685i	−0.626876	−	0.779119i	$-0.715667\pi$
$349$	79.8055	−	452.600i	0.228669	−	1.29685i	0.855545	−	0.517728i	$-0.173222\pi$
$350$			300.278i			0.857939i
$351$		0			0
$352$	315.623			0.896655
$353$	−396.139	−	69.8500i	−1.12221	−	0.197875i	−0.418397	−	0.908264i	$-0.637408\pi$
$353$	−396.139	−	69.8500i	−1.12221	−	0.197875i	−0.703809	+	0.710389i	$0.748519\pi$
$354$		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	0.748896	−	0.662688i	$-0.230584\pi$
$359$	197.249	+	113.882i	0.549439	+	0.317219i	−0.199457	+	0.979907i	$0.563918\pi$
$360$		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	0.363068	−	0.931763i	$-0.381729\pi$
$367$	−180.378	−	151.355i	−0.491493	−	0.412412i	−0.854561	+	0.519351i	$0.826174\pi$
$368$	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	0.359105	−	0.933297i	$-0.383082\pi$
$373$	500.037	−	419.581i	1.34058	−	1.12488i	0.981476	−	0.191584i	$-0.0613623\pi$
$374$	−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	0.848001	−	0.529994i	$-0.177806\pi$
$383$	68.4823	+	81.6140i	0.178805	+	0.213091i	−0.669196	+	0.743086i	$0.733361\pi$
$384$		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	0.00468714	+	0.999989i	$0.498508\pi$
$389$	−381.579	+	454.749i	−0.980924	+	1.16902i	−0.985611	+	0.169030i	$0.945936\pi$
$390$		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	−0.999489	−	0.0319623i	$-0.989824\pi$
$397$	−187.410	+	324.603i	−0.472064	+	0.817640i	0.527425	+	0.849602i	$0.323158\pi$
$398$	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	−0.765954	−	0.642895i	$-0.777733\pi$
$401$	93.8523	−	257.857i	0.234046	−	0.643035i	1.00000		0.000140039i	$-4.45758e-5\pi$
$402$		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	0.886123	−	0.463450i	$-0.153389\pi$
$409$	518.216	+	188.615i	1.26703	+	0.461162i	0.380909	+	0.924612i	$0.375611\pi$
$410$	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	−0.275629	−	0.961264i	$-0.588886\pi$
$419$	−86.2570	+	15.2094i	−0.205864	+	0.0362994i	0.0697651	+	0.997563i	$0.477775\pi$
$420$		0			0
$421$	226.948	+	190.432i	0.539069	+	0.452332i	0.871219	−	0.490894i	$-0.163330\pi$
$421$	226.948	+	190.432i	0.539069	+	0.452332i	−0.332151	+	0.943226i	$0.607774\pi$
$422$	−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	$-0.761972\pi$
$431$		−	586.175i		−	1.36003i	0.733196	−	0.680017i	$-0.238028\pi$
$432$		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	−0.674101	−	0.738639i	$-0.735469\pi$
$439$	−314.194	+	114.357i	−0.715704	+	0.260495i	−0.0416031	+	0.999134i	$0.513247\pi$
$440$	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	−0.331380	−	0.943497i	$-0.607514\pi$
$443$	290.310	−	345.978i	0.655327	−	0.780988i	0.986707	+	0.162509i	$0.0519588\pi$
$444$		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	−0.304346	−	0.952562i	$-0.598438\pi$
$449$	165.422	−	95.5067i	0.368424	−	0.212710i	0.672770	+	0.739852i	$0.265104\pi$
$450$		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	0.819512	+	0.573062i	$0.194244\pi$
$457$	−66.9852	+	379.892i	−0.146576	+	0.831274i	−0.966088	+	0.258212i	$0.916867\pi$
$458$		−	957.923i		−	2.09153i
$459$		0			0
$460$	−478.320			−1.03983
$461$	426.474	+	75.1990i	0.925107	+	0.163121i	0.615856	−	0.787859i	$-0.288810\pi$
$461$	426.474	+	75.1990i	0.925107	+	0.163121i	0.309252	+	0.950980i	$0.399921\pi$
$462$		0			0
$463$	−519.515	−	189.088i	−1.12206	−	0.408397i	−0.286658	−	0.958033i	$-0.592544\pi$
$463$	−519.515	−	189.088i	−1.12206	−	0.408397i	−0.835405	+	0.549635i	$0.814767\pi$
$464$	−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	0.686176	−	0.727436i	$-0.259288\pi$
$467$	186.467	+	107.657i	0.399286	+	0.230528i	−0.286890	+	0.957964i	$0.592621\pi$
$468$		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	0.993914	−	0.110163i	$-0.0351371\pi$
$479$	77.4641	+	212.831i	0.161721	+	0.444323i	−0.832193	+	0.554486i	$0.812915\pi$
$480$		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	−0.998790	−	0.0491885i	$-0.984336\pi$
$491$	−429.032	−	511.301i	−0.873793	−	1.04135i	0.124997	−	0.992157i	$-0.460108\pi$
$492$		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	0.973171	−	0.230084i	$-0.0739003\pi$
$499$	−9.98207	−	56.6112i	−0.0200042	−	0.113449i	−0.993175	+	0.116635i	$0.962789\pi$
$500$	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	−0.857725	−	0.514109i	$-0.828123\pi$
$503$	−423.202	+	244.336i	−0.841356	+	0.485757i	0.0163686	+	0.999866i	$0.494789\pi$
$504$		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	−0.997818	−	0.0660300i	$-0.978967\pi$
$509$	−97.2199	+	267.109i	−0.191002	+	0.524773i	0.806816	+	0.590803i	$0.201189\pi$
$510$		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	0.465842	−	0.884868i	$-0.345752\pi$
$521$	−35.1966	−	20.3207i	−0.0675558	−	0.0390033i	−0.533397	+	0.845865i	$0.679085\pi$
$522$		0			0
$523$	−174.951	−	303.024i	−0.334514	−	0.579395i	0.648877	−	0.760893i	$-0.275239\pi$
$523$	−174.951	−	303.024i	−0.334514	−	0.579395i	−0.983391	+	0.181498i	$0.941905\pi$
$524$	−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	−0.723889	−	0.689917i	$-0.757647\pi$
$547$	−456.718	+	166.232i	−0.834950	+	0.303897i	−0.111061	+	0.993814i	$0.535425\pi$
$548$	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	−0.502537	−	0.864556i	$-0.667600\pi$
$557$	−2.82805	+	1.63278i	−0.00507730	+	0.00293138i	0.497459	+	0.867487i	$0.334266\pi$
$558$		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	−0.556545	−	0.830817i	$-0.687873\pi$
$563$	227.357	−	624.659i	0.403832	−	1.10952i	0.960378	−	0.278702i	$-0.0899043\pi$
$564$		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	0.238974	−	0.971026i	$-0.423189\pi$
$569$	74.7814	+	13.1860i	0.131426	+	0.0231739i	−0.107548	+	0.994200i	$0.534300\pi$
$570$		0			0
$571$	276.356	+	100.585i	0.483985	+	0.176156i	0.572477	−	0.819921i	$-0.305983\pi$
$571$	276.356	+	100.585i	0.483985	+	0.176156i	−0.0884919	+	0.996077i	$0.528205\pi$
$572$	−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	−0.803461	−	0.595357i	$-0.797011\pi$
$577$	−529.296	−	916.768i	−0.917325	−	1.58885i	−0.113864	−	0.993496i	$-0.536323\pi$
$578$	−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	0.892626	−	0.450798i	$-0.148860\pi$
$587$	−47.5072	−	130.525i	−0.0809322	−	0.222359i	−0.973558	+	0.228438i	$0.926638\pi$
$588$		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	$-0.960902\pi$
$593$		−	145.309i		−	0.245040i	0.992466	−	0.122520i	$-0.0390975\pi$
$594$		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	0.753578	−	0.657359i	$-0.228326\pi$
$599$	−14.7665	−	17.5980i	−0.0246518	−	0.0293789i	−0.778230	+	0.627980i	$0.783882\pi$
$600$		0			0
$601$	871.442	−	317.179i	1.44999	−	0.527752i	0.507399	−	0.861711i	$-0.330607\pi$
$601$	871.442	−	317.179i	1.44999	−	0.527752i	0.942588	+	0.333959i	$0.108385\pi$
$602$	−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	0.963305	+	0.268410i	$0.0864981\pi$
$607$	90.9868	+	516.012i	0.149896	+	0.850102i	−0.813409	+	0.581692i	$0.802391\pi$
$608$	−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	−0.893223	−	0.449614i	$-0.851562\pi$
$613$	−35.0848	+	60.7687i	−0.0572346	+	0.0991333i	0.835988	+	0.548747i	$0.184895\pi$
$614$	−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	0.607591	+	0.794250i	$0.292136\pi$
$617$	−227.293	+	624.483i	−0.368385	+	1.01213i	−0.975976	+	0.217879i	$0.930086\pi$
$618$		0			0
$619$	−168.570	+	956.006i	−0.272326	+	1.54444i	0.475005	+	0.879983i	$0.342446\pi$
$619$	−168.570	+	956.006i	−0.272326	+	1.54444i	−0.747330	+	0.664453i	$0.768665\pi$
$620$		−	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	0.931232	−	0.364426i	$-0.118735\pi$
$631$	94.6588	+	163.954i	0.150014	+	0.259832i	−0.781218	+	0.624258i	$0.785401\pi$
$632$	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	0.975511	+	0.219952i	$0.0705901\pi$
$641$	236.919	+	650.930i	0.369609	+	1.01549i	−0.605902	+	0.795539i	$0.707188\pi$
$642$		0			0
$643$	815.534	−	684.314i	1.26833	−	1.06425i	0.273584	−	0.961848i	$-0.411791\pi$
$643$	815.534	−	684.314i	1.26833	−	1.06425i	0.994743	−	0.102404i	$-0.0326535\pi$
$644$	−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	$-0.912114\pi$
$647$		−	352.755i		−	0.545217i	0.962125	−	0.272608i	$-0.0878863\pi$
$648$		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	0.945626	−	0.325255i	$-0.105450\pi$
$653$	301.103	+	358.840i	0.461107	+	0.549526i	−0.484520	+	0.874780i	$0.661006\pi$
$654$		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	−0.806327	−	0.591470i	$-0.798548\pi$
$659$	−55.2415	+	65.8343i	−0.0838262	+	0.0999002i	0.722501	+	0.691370i	$0.242992\pi$
$660$		0			0
$661$	21.3782	+	121.242i	0.0323422	+	0.183422i	0.996699	−	0.0811828i	$-0.0258698\pi$
$661$	21.3782	+	121.242i	0.0323422	+	0.183422i	−0.964357	+	0.264604i	$0.914759\pi$
$662$	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	0.785565	+	0.618779i	$0.212373\pi$
$673$	−110.547	+	626.942i	−0.164260	+	0.931563i	−0.949824	+	0.312784i	$0.898739\pi$
$674$		−	179.321i		−	0.266054i
$675$		0			0
$676$	217.127			0.321194
$677$	162.798	+	28.7056i	0.240469	+	0.0424012i	0.292584	−	0.956240i	$-0.405485\pi$
$677$	162.798	+	28.7056i	0.240469	+	0.0424012i	−0.0521144	+	0.998641i	$0.516596\pi$
$678$		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	0.975468	+	0.220142i	$0.0706522\pi$
$683$	1129.58	+	652.163i	1.65385	+	0.954851i	0.678383	+	0.734709i	$0.262681\pi$
$684$		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	0.419812	−	0.907611i	$-0.362096\pi$
$691$	−277.168	−	232.571i	−0.401111	−	0.336572i	−0.820923	+	0.571039i	$0.806540\pi$
$692$	−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	$0.219904\pi$
$701$			893.344i			1.27438i	−0.770705	+	0.637192i	$0.780096\pi$
$702$		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	0.158947	−	0.987287i	$-0.449190\pi$
$709$	648.964	−	236.203i	0.915323	−	0.333150i	0.756376	+	0.654137i	$0.226968\pi$
$710$	−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	−0.761403	−	0.648279i	$-0.775489\pi$
$719$	−417.508	+	241.049i	−0.580679	+	0.335255i	0.180724	+	0.983534i	$0.442156\pi$
$720$		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	−0.915472	−	0.402382i	$-0.868182\pi$
$727$	59.9144	−	339.791i	0.0824132	−	0.467388i	0.997885	−	0.0650059i	$-0.0207066\pi$
$728$		−	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	−0.0276307	−	0.999618i	$-0.508796\pi$
$733$	−506.752	−	184.443i	−0.691339	−	0.251627i	−0.663709	+	0.747991i	$0.731018\pi$
$734$	−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	0.501032	−	0.865429i	$-0.332954\pi$
$739$	−368.737	−	638.671i	−0.498968	−	0.864237i	−0.999999	+	0.00119161i	$0.999621\pi$
$740$	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	−0.813950	−	0.580935i	$-0.802687\pi$
$743$	−1025.43	+	180.811i	−1.38012	+	0.243353i	−0.566171	+	0.824288i	$0.691576\pi$
$744$		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	−0.511525	−	0.859269i	$-0.670919\pi$
$751$	184.644	−	154.935i	0.245864	−	0.206305i	0.757389	+	0.652964i	$0.226475\pi$
$752$	−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	0.883864	−	0.467743i	$-0.154933\pi$
$761$	205.276	+	244.639i	0.269746	+	0.321470i	−0.614119	+	0.789214i	$0.710488\pi$
$762$		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	−0.990179	−	0.139809i	$-0.955351\pi$
$769$	−82.6925	−	468.973i	−0.107533	−	0.609847i	0.882646	−	0.470038i	$-0.155760\pi$
$770$	−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	−0.998611	−	0.0526817i	$-0.983223\pi$
$773$	−1122.62	+	648.147i	−1.45229	+	0.838482i	−0.453682	+	0.891164i	$0.649890\pi$
$774$		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	−0.227677	−	0.973737i	$-0.573113\pi$
$787$	−809.031	−	294.463i	−1.02799	−	0.374159i	−0.800317	+	0.599577i	$0.795335\pi$
$788$	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	−0.520154	−	0.854073i	$-0.674125\pi$
$797$	−571.312	+	100.738i	−0.716828	+	0.126396i	−0.196675	+	0.980469i	$0.563014\pi$
$798$		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	$-0.865972\pi$
$809$		−	661.323i		−	0.817457i	0.912656	−	0.408729i	$-0.134028\pi$
$810$		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	−0.703436	−	0.710759i	$-0.748352\pi$
$821$	97.4327	−	116.116i	0.118676	−	0.141432i	0.822111	+	0.569327i	$0.192796\pi$
$822$		0			0
$823$	39.0398	+	221.406i	0.0474360	+	0.269023i	0.999296	−	0.0375092i	$-0.0119424\pi$
$823$	39.0398	+	221.406i	0.0474360	+	0.269023i	−0.951860	+	0.306532i	$0.900831\pi$
$824$	−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	−0.666497	−	0.745508i	$-0.732207\pi$
$827$	−292.855	+	169.080i	−0.354117	+	0.204449i	0.312380	+	0.949957i	$0.398874\pi$
$828$		0			0
$829$	401.806	−	695.949i	0.484688	−	0.839504i	−0.515157	−	0.857096i	$-0.672267\pi$
$829$	401.806	−	695.949i	0.484688	−	0.839504i	0.999845	+	0.0175917i	$0.00559990\pi$
$830$	−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	0.650654	−	0.759374i	$-0.274495\pi$
$839$	840.969	+	148.286i	1.00235	+	0.176741i	0.351693	+	0.936115i	$0.385606\pi$
$840$		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	0.209082	−	0.977898i	$-0.432952\pi$
$853$	−612.158	−	513.661i	−0.717653	−	0.602182i	−0.926735	+	0.375716i	$0.877397\pi$
$854$	−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	−0.707256	−	0.706958i	$-0.750067\pi$
$857$	−531.246	−	1459.59i	−0.619890	−	1.70313i	0.0873655	−	0.996176i	$-0.472155\pi$
$858$		0			0
$859$	−21.6423	+	18.1601i	−0.0251948	+	0.0211409i	−0.655298	−	0.755370i	$-0.727457\pi$
$859$	−21.6423	+	18.1601i	−0.0251948	+	0.0211409i	0.630103	+	0.776511i	$0.283013\pi$
$860$	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	$0.185869\pi$
$863$			951.550i			1.10261i	−0.834305	+	0.551304i	$0.814131\pi$
$864$		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	0.953847	−	0.300294i	$-0.0970849\pi$
$877$	−39.6252	−	224.726i	−0.0451827	−	0.256244i	−0.999029	+	0.0440504i	$0.985974\pi$
$878$	−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	0.525250	−	0.850948i	$-0.323972\pi$
$881$	1343.36	−	775.592i	1.52482	−	0.880354i	0.999568	−	0.0294054i	$-0.00936139\pi$
$882$		0			0
$883$	−781.794	+	1354.11i	−0.885384	+	1.53353i	−0.0401121	+	0.999195i	$0.512772\pi$
$883$	−781.794	+	1354.11i	−0.885384	+	1.53353i	−0.845272	+	0.534336i	$0.820562\pi$
$884$	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	0.727578	+	0.686025i	$0.240646\pi$
$887$	−240.153	+	659.815i	−0.270748	+	0.743873i	−0.998325	+	0.0578478i	$0.981576\pi$
$888$		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	0.974851	+	0.222858i	$0.0715387\pi$
$907$	1236.79	+	1037.79i	1.36360	+	1.14420i	0.388754	+	0.921342i	$0.372906\pi$
$908$	−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	0.999982	−	0.00595016i	$-0.00189401\pi$
$911$	209.645	+	575.996i	0.230127	+	0.632268i	−0.769856	+	0.638218i	$0.779672\pi$
$912$		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	−0.131748	−	0.991283i	$-0.542059\pi$
$929$	805.771	−	960.281i	0.867354	−	1.03367i	0.999101	−	0.0423885i	$-0.0134967\pi$
$930$		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	−0.508878	−	0.860839i	$-0.669939\pi$
$937$	460.132	−	796.972i	0.491070	−	0.850557i	0.999947	+	0.0102815i	$0.00327275\pi$
$938$	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	−0.751335	−	0.659921i	$-0.770590\pi$
$941$	233.754	−	642.234i	0.248410	−	0.682502i	0.999745	−	0.0225805i	$-0.00718822\pi$
$942$		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	−0.282141	−	0.959373i	$-0.591044\pi$
$947$	−828.995	−	146.174i	−0.875391	−	0.154355i	−0.593250	+	0.805018i	$0.702156\pi$
$948$		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	−0.353640	−	0.935382i	$-0.615056\pi$
$953$	−1277.52	−	737.576i	−1.34052	−	0.773952i	−0.986884	+	0.161430i	$0.948390\pi$
$954$		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	−0.505030	−	0.863102i	$-0.668519\pi$
$967$	248.771	−	208.744i	0.257261	−	0.215868i	0.762291	+	0.647234i	$0.224074\pi$
$968$	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	$-0.787272\pi$
$971$		−	1203.37i		−	1.23931i	0.784873	−	0.619657i	$-0.212728\pi$
$972$		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	0.824722	−	0.565539i	$-0.191332\pi$
$977$	121.698	+	145.034i	0.124563	+	0.148448i	−0.700159	+	0.713987i	$0.746887\pi$
$978$		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	0.173009	+	0.984920i	$0.444651\pi$
$983$	−812.932	+	968.815i	−0.826991	+	0.985570i	−1.00000		0.000649412i	$0.999793\pi$
$984$		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	−0.263589	−	0.964635i	$-0.584906\pi$
$991$	697.271	−	1207.71i	0.703604	−	1.21868i	0.967193	−	0.254043i	$-0.0817603\pi$
$992$	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	−0.761658	−	0.647980i	$-0.775614\pi$
$997$	175.161	−	993.390i	0.175689	−	0.996379i	0.937346	−	0.348399i	$-0.113275\pi$
$998$		−	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.26.5		30
3.2	odd	2		243.3.f.d.26.1		30
9.2	odd	6		27.3.f.a.20.5	✓	30
9.4	even	3		243.3.f.b.107.1		30
9.5	odd	6		243.3.f.c.107.5		30
9.7	even	3		81.3.f.a.62.1		30
27.4	even	9		243.3.f.c.134.5		30
27.5	odd	18		81.3.f.a.17.1		30
27.11	odd	18		729.3.b.a.728.5		30
27.13	even	9		243.3.f.d.215.1		30
27.14	odd	18	inner	243.3.f.a.215.5		30
27.16	even	9		729.3.b.a.728.26		30
27.22	even	9		27.3.f.a.23.5	yes	30
27.23	odd	18		243.3.f.b.134.1		30
36.11	even	6		432.3.bc.a.209.5		30
108.103	odd	18		432.3.bc.a.401.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.20.5	✓	30	9.2	odd	6
27.3.f.a.23.5	yes	30	27.22	even	9
81.3.f.a.17.1		30	27.5	odd	18
81.3.f.a.62.1		30	9.7	even	3
243.3.f.a.26.5		30	1.1	even	1	trivial
243.3.f.a.215.5		30	27.14	odd	18	inner
243.3.f.b.107.1		30	9.4	even	3
243.3.f.b.134.1		30	27.23	odd	18
243.3.f.c.107.5		30	9.5	odd	6
243.3.f.c.134.5		30	27.4	even	9
243.3.f.d.26.1		30	3.2	odd	2
243.3.f.d.215.1		30	27.13	even	9
432.3.bc.a.209.5		30	36.11	even	6
432.3.bc.a.401.5		30	108.103	odd	18
729.3.b.a.728.5		30	27.11	odd	18
729.3.b.a.728.26		30	27.16	even	9

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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