LMFDB - Embedded newform 729.2.e.i.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			82.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.i.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.233956 + 1.32683i) q^{2} +(0.173648 - 0.0632028i) q^{4} +(1.26604 + 1.06234i) q^{5} +(-2.26604 - 0.824773i) q^{7} +(1.47178 + 2.54920i) q^{8} +O(q^{10})$	\(q+(0.233956 + 1.32683i) q^{2} +(0.173648 - 0.0632028i) q^{4} +(1.26604 + 1.06234i) q^{5} +(-2.26604 - 0.824773i) q^{7} +(1.47178 + 2.54920i) q^{8} +(-1.11334 + 1.92836i) q^{10} +(4.55303 - 3.82045i) q^{11} +(-0.560307 + 3.17766i) q^{13} +(0.564178 - 3.19961i) q^{14} +(-2.75490 + 2.31164i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(3.31908 + 5.74881i) q^{19} +(0.286989 + 0.104455i) q^{20} +(6.13429 + 5.14728i) q^{22} +(2.76604 - 1.00676i) q^{23} +(-0.393933 - 2.23411i) q^{25} -4.34730 q^{26} -0.445622 q^{28} +(-0.224155 - 1.27125i) q^{29} +(0.553033 - 0.201288i) q^{31} +(0.798133 + 0.669713i) q^{32} +(-3.79813 - 1.38241i) q^{34} +(-1.99273 - 3.45150i) q^{35} +(-0.0209445 + 0.0362770i) q^{37} +(-6.85117 + 5.74881i) q^{38} +(-0.844770 + 4.79093i) q^{40} +(-0.851167 + 4.82721i) q^{41} +(-3.97178 + 3.33272i) q^{43} +(0.549163 - 0.951178i) q^{44} +(1.98293 + 3.43453i) q^{46} +(3.51114 + 1.27795i) q^{47} +(-0.907604 - 0.761570i) q^{49} +(2.87211 - 1.04536i) q^{50} +(0.103541 + 0.587208i) q^{52} +11.6382 q^{53} +9.82295 q^{55} +(-1.23261 - 6.99049i) q^{56} +(1.63429 - 0.594831i) q^{58} +(-5.62836 - 4.72275i) q^{59} +(-10.3833 - 3.77920i) q^{61} +(0.396459 + 0.686688i) q^{62} +(-4.29813 + 7.44459i) q^{64} +(-4.08512 + 3.42782i) q^{65} +(0.322481 - 1.82888i) q^{67} +(-0.0962667 + 0.545955i) q^{68} +(4.11334 - 3.45150i) q^{70} +(2.75624 - 4.77396i) q^{71} +(-2.77719 - 4.81023i) q^{73} +(-0.0530334 - 0.0193026i) q^{74} +(0.939693 + 0.788496i) q^{76} +(-13.4684 + 4.90209i) q^{77} +(-0.656574 - 3.72362i) q^{79} -5.94356 q^{80} -6.60401 q^{82} +(0.692066 + 3.92490i) q^{83} +(-4.65910 + 1.69577i) q^{85} +(-5.35117 - 4.49016i) q^{86} +(16.4402 + 5.98373i) q^{88} +(-4.07532 - 7.05866i) q^{89} +(3.89053 - 6.73859i) q^{91} +(0.416689 - 0.349643i) q^{92} +(-0.874171 + 4.95767i) q^{94} +(-1.90508 + 10.8042i) q^{95} +(0.199807 - 0.167658i) q^{97} +(0.798133 - 1.38241i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 3 * q^5 - 9 * q^7 - 6 * q^8	$ 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8} + 15 q^{11} - 9 q^{13} - 15 q^{14} - 18 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} + 27 q^{22} + 12 q^{23} - 27 q^{25} - 24 q^{26} - 24 q^{28} - 3 q^{29} - 9 q^{31} - 9 q^{32} - 9 q^{34} + 6 q^{35} + 3 q^{37} - 15 q^{38} - 18 q^{40} + 21 q^{41} - 9 q^{43} + 15 q^{44} - 9 q^{46} + 15 q^{47} - 9 q^{49} - 12 q^{50} - 9 q^{52} + 36 q^{53} + 18 q^{55} - 21 q^{56} + 3 q^{59} - 27 q^{61} + 12 q^{62} - 12 q^{64} - 3 q^{65} + 27 q^{67} + 27 q^{68} + 18 q^{70} + 9 q^{71} - 6 q^{73} + 12 q^{74} - 24 q^{77} + 18 q^{79} - 6 q^{80} + 36 q^{82} + 15 q^{83} + 9 q^{85} - 6 q^{86} + 27 q^{88} + 6 q^{91} - 51 q^{92} - 27 q^{94} - 30 q^{95} - 36 q^{97} - 9 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 3 * q^5 - 9 * q^7 - 6 * q^8 + 15 * q^11 - 9 * q^13 - 15 * q^14 - 18 * q^16 - 9 * q^17 + 3 * q^19 - 6 * q^20 + 27 * q^22 + 12 * q^23 - 27 * q^25 - 24 * q^26 - 24 * q^28 - 3 * q^29 - 9 * q^31 - 9 * q^32 - 9 * q^34 + 6 * q^35 + 3 * q^37 - 15 * q^38 - 18 * q^40 + 21 * q^41 - 9 * q^43 + 15 * q^44 - 9 * q^46 + 15 * q^47 - 9 * q^49 - 12 * q^50 - 9 * q^52 + 36 * q^53 + 18 * q^55 - 21 * q^56 + 3 * q^59 - 27 * q^61 + 12 * q^62 - 12 * q^64 - 3 * q^65 + 27 * q^67 + 27 * q^68 + 18 * q^70 + 9 * q^71 - 6 * q^73 + 12 * q^74 - 24 * q^77 + 18 * q^79 - 6 * q^80 + 36 * q^82 + 15 * q^83 + 9 * q^85 - 6 * q^86 + 27 * q^88 + 6 * q^91 - 51 * q^92 - 27 * q^94 - 30 * q^95 - 36 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.233956	+	1.32683i	0.165432	+	0.938209i	0.948618	+	0.316423i	$0.102482\pi$
$2$	0.233956	+	1.32683i	0.165432	+	0.938209i	−0.783187	+	0.621786i	$0.786407\pi$
$3$		0			0
$3$		0			0
$4$	0.173648	−	0.0632028i	0.0868241	−	0.0316014i
$5$	1.26604	+	1.06234i	0.566192	+	0.475092i	0.880380	−	0.474269i	$-0.157288\pi$
$5$	1.26604	+	1.06234i	0.566192	+	0.475092i	−0.314188	+	0.949361i	$0.601732\pi$
$6$		0			0
$7$	−2.26604	−	0.824773i	−0.856484	−	0.311735i	−0.123803	−	0.992307i	$-0.539509\pi$
$7$	−2.26604	−	0.824773i	−0.856484	−	0.311735i	−0.732681	+	0.680572i	$0.761731\pi$
$8$	1.47178	+	2.54920i	0.520353	+	0.901278i
$9$		0			0
$10$	−1.11334	+	1.92836i	−0.352069	+	0.609802i
$11$	4.55303	−	3.82045i	1.37279	−	1.15191i	0.400997	−	0.916080i	$-0.368664\pi$
$11$	4.55303	−	3.82045i	1.37279	−	1.15191i	0.971795	−	0.235829i	$-0.0757806\pi$
$12$		0			0
$13$	−0.560307	+	3.17766i	−0.155401	+	0.881325i	0.803017	+	0.595957i	$0.203227\pi$
$13$	−0.560307	+	3.17766i	−0.155401	+	0.881325i	−0.958418	+	0.285368i	$0.907884\pi$
$14$	0.564178	−	3.19961i	0.150783	−	0.855132i
$15$		0			0
$16$	−2.75490	+	2.31164i	−0.688725	+	0.577909i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	3.31908	+	5.74881i	0.761449	+	1.31887i	0.942104	+	0.335321i	$0.108845\pi$
$19$	3.31908	+	5.74881i	0.761449	+	1.31887i	−0.180655	+	0.983547i	$0.557822\pi$
$20$	0.286989	+	0.104455i	0.0641727	+	0.0233569i
$21$		0			0
$22$	6.13429	+	5.14728i	1.30783	+	1.09740i
$23$	2.76604	−	1.00676i	0.576760	−	0.209924i	−0.0371361	−	0.999310i	$-0.511824\pi$
$23$	2.76604	−	1.00676i	0.576760	−	0.209924i	0.613896	+	0.789387i	$0.289601\pi$
$24$		0			0
$25$	−0.393933	−	2.23411i	−0.0787866	−	0.446821i
$26$	−4.34730			−0.852575
$27$		0			0
$28$	−0.445622			−0.0842147
$29$	−0.224155	−	1.27125i	−0.0416246	−	0.236065i	0.956897	−	0.290429i	$-0.0937980\pi$
$29$	−0.224155	−	1.27125i	−0.0416246	−	0.236065i	−0.998521	+	0.0543640i	$0.982687\pi$
$30$		0			0
$31$	0.553033	−	0.201288i	0.0993277	−	0.0361523i	−0.291878	−	0.956455i	$-0.594280\pi$
$31$	0.553033	−	0.201288i	0.0993277	−	0.0361523i	0.391206	+	0.920303i	$0.372058\pi$
$32$	0.798133	+	0.669713i	0.141091	+	0.118390i
$33$		0			0
$34$	−3.79813	−	1.38241i	−0.651374	−	0.237081i
$35$	−1.99273	−	3.45150i	−0.336832	−	0.583410i
$36$		0			0
$37$	−0.0209445	+	0.0362770i	−0.00344326	+	0.00596390i	−0.867742	−	0.497015i	$-0.834429\pi$
$37$	−0.0209445	+	0.0362770i	−0.00344326	+	0.00596390i	0.864299	+	0.502979i	$0.167763\pi$
$38$	−6.85117	+	5.74881i	−1.11141	+	0.932580i
$39$		0			0
$40$	−0.844770	+	4.79093i	−0.133570	+	0.757512i
$41$	−0.851167	+	4.82721i	−0.132930	+	0.753883i	0.843349	+	0.537366i	$0.180581\pi$
$41$	−0.851167	+	4.82721i	−0.132930	+	0.753883i	−0.976279	+	0.216517i	$0.930530\pi$
$42$		0			0
$43$	−3.97178	+	3.33272i	−0.605691	+	0.508235i	−0.893269	−	0.449522i	$-0.851594\pi$
$43$	−3.97178	+	3.33272i	−0.605691	+	0.508235i	0.287578	+	0.957757i	$0.407150\pi$
$44$	0.549163	−	0.951178i	0.0827894	−	0.143396i
$45$		0			0
$46$	1.98293	+	3.43453i	0.292366	+	0.506394i
$47$	3.51114	+	1.27795i	0.512153	+	0.186408i	0.585152	−	0.810924i	$-0.301035\pi$
$47$	3.51114	+	1.27795i	0.512153	+	0.186408i	−0.0729991	+	0.997332i	$0.523257\pi$
$48$		0			0
$49$	−0.907604	−	0.761570i	−0.129658	−	0.108796i
$50$	2.87211	−	1.04536i	0.406178	−	0.147837i
$51$		0			0
$52$	0.103541	+	0.587208i	0.0143585	+	0.0814311i
$53$	11.6382			1.59862			0.799312	−	0.600916i	$-0.205198\pi$
$53$	11.6382			1.59862			0.799312	+	0.600916i	$0.205198\pi$
$54$		0			0
$55$	9.82295			1.32453
$56$	−1.23261	−	6.99049i	−0.164715	−	0.934143i
$57$		0			0
$58$	1.63429	−	0.594831i	0.214592	−	0.0781052i
$59$	−5.62836	−	4.72275i	−0.732749	−	0.614850i	0.198130	−	0.980176i	$-0.436513\pi$
$59$	−5.62836	−	4.72275i	−0.732749	−	0.614850i	−0.930880	+	0.365326i	$0.880958\pi$
$60$		0			0
$61$	−10.3833	−	3.77920i	−1.32944	−	0.483876i	−0.422969	−	0.906144i	$-0.639012\pi$
$61$	−10.3833	−	3.77920i	−1.32944	−	0.483876i	−0.906471	+	0.422268i	$0.861234\pi$
$62$	0.396459	+	0.686688i	0.0503504	+	0.0872094i
$63$		0			0
$64$	−4.29813	+	7.44459i	−0.537267	+	0.930573i
$65$	−4.08512	+	3.42782i	−0.506697	+	0.425169i
$66$		0			0
$67$	0.322481	−	1.82888i	0.0393974	−	0.223434i	−0.958752	−	0.284244i	$-0.908257\pi$
$67$	0.322481	−	1.82888i	0.0393974	−	0.223434i	0.998149	+	0.0608104i	$0.0193685\pi$
$68$	−0.0962667	+	0.545955i	−0.0116740	+	0.0662068i
$69$		0			0
$70$	4.11334	−	3.45150i	0.491638	−	0.412533i
$71$	2.75624	−	4.77396i	0.327106	−	0.566564i	−0.654830	−	0.755776i	$-0.727260\pi$
$71$	2.75624	−	4.77396i	0.327106	−	0.566564i	0.981936	+	0.189212i	$0.0605932\pi$
$72$		0			0
$73$	−2.77719	−	4.81023i	−0.325045	−	0.562995i	0.656476	−	0.754347i	$-0.272046\pi$
$73$	−2.77719	−	4.81023i	−0.325045	−	0.562995i	−0.981522	+	0.191352i	$0.938713\pi$
$74$	−0.0530334	−	0.0193026i	−0.00616501	−	0.00224388i
$75$		0			0
$76$	0.939693	+	0.788496i	0.107790	+	0.0904467i
$77$	−13.4684	+	4.90209i	−1.53486	+	0.558645i
$78$		0			0
$79$	−0.656574	−	3.72362i	−0.0738704	−	0.418940i	−0.999208	−	0.0397952i	$-0.987329\pi$
$79$	−0.656574	−	3.72362i	−0.0738704	−	0.418940i	0.925338	−	0.379144i	$-0.123782\pi$
$80$	−5.94356			−0.664511
$81$		0			0
$82$	−6.60401			−0.729291
$83$	0.692066	+	3.92490i	0.0759642	+	0.430814i	0.998943	+	0.0459637i	$0.0146359\pi$
$83$	0.692066	+	3.92490i	0.0759642	+	0.430814i	−0.922979	+	0.384850i	$0.874253\pi$
$84$		0			0
$85$	−4.65910	+	1.69577i	−0.505350	+	0.183932i
$86$	−5.35117	−	4.49016i	−0.577031	−	0.484187i
$87$		0			0
$88$	16.4402	+	5.98373i	1.75253	+	0.637868i
$89$	−4.07532	−	7.05866i	−0.431983	−	0.748217i	0.565061	−	0.825049i	$-0.308853\pi$
$89$	−4.07532	−	7.05866i	−0.431983	−	0.748217i	−0.997044	+	0.0768323i	$0.975519\pi$
$90$		0			0
$91$	3.89053	−	6.73859i	0.407838	−	0.706397i
$92$	0.416689	−	0.349643i	0.0434428	−	0.0364528i
$93$		0			0
$94$	−0.874171	+	4.95767i	−0.0901638	+	0.511344i
$95$	−1.90508	+	10.8042i	−0.195457	+	1.10849i
$96$		0			0
$97$	0.199807	−	0.167658i	0.0202874	−	0.0170231i	−0.632588	−	0.774489i	$-0.718007\pi$
$97$	0.199807	−	0.167658i	0.0202874	−	0.0170231i	0.652875	+	0.757466i	$0.273563\pi$
$98$	0.798133	−	1.38241i	0.0806236	−	0.139644i
$99$		0			0
$100$	−0.209607	−	0.363051i	−0.0209607	−	0.0363051i
$101$	−10.3623	−	3.77157i	−1.03109	−	0.375286i	−0.229593	−	0.973287i	$-0.573740\pi$
$101$	−10.3623	−	3.77157i	−1.03109	−	0.375286i	−0.801495	+	0.598001i	$0.795962\pi$
$102$		0			0
$103$	−2.99273	−	2.51120i	−0.294882	−	0.247435i	0.483328	−	0.875439i	$-0.339428\pi$
$103$	−2.99273	−	2.51120i	−0.294882	−	0.247435i	−0.778210	+	0.628004i	$0.783872\pi$
$104$	−8.92514	+	3.24849i	−0.875182	+	0.318540i
$105$		0			0
$106$	2.72281	+	15.4418i	0.264463	+	1.49984i
$107$	−2.63816			−0.255040			−0.127520	−	0.991836i	$-0.540702\pi$
$107$	−2.63816			−0.255040			−0.127520	+	0.991836i	$0.540702\pi$
$108$		0			0
$109$	−8.95811			−0.858031			−0.429016	−	0.903297i	$-0.641140\pi$
$109$	−8.95811			−0.858031			−0.429016	+	0.903297i	$0.641140\pi$
$110$	2.29813	+	13.0334i	0.219118	+	1.24268i
$111$		0			0
$112$	8.14930	−	2.96610i	0.770036	−	0.280270i
$113$	12.2023	+	10.2390i	1.14790	+	0.963202i	0.999668	−	0.0257512i	$-0.00819777\pi$
$113$	12.2023	+	10.2390i	1.14790	+	0.963202i	0.148231	+	0.988953i	$0.452642\pi$
$114$		0			0
$115$	4.57145	+	1.66387i	0.426290	+	0.155157i
$116$	−0.119271	−	0.206583i	−0.0110740	−	0.0191807i
$117$		0			0
$118$	4.94949	−	8.57277i	0.455638	−	0.789188i
$119$	5.54189	−	4.65020i	0.508024	−	0.426283i
$120$		0			0
$121$	4.22416	−	23.9564i	0.384014	−	2.17785i
$122$	2.58512	−	14.6610i	0.234046	−	1.32734i
$123$		0			0
$124$	0.0833113	−	0.0699065i	0.00748158	−	0.00627779i
$125$	6.00640	−	10.4034i	0.537228	−	0.930507i
$126$		0			0
$127$	−1.79813	−	3.11446i	−0.159559	−	0.276363i	0.775151	−	0.631776i	$-0.217674\pi$
$127$	−1.79813	−	3.11446i	−0.159559	−	0.276363i	−0.934710	+	0.355412i	$0.884340\pi$
$128$	−8.92514	−	3.24849i	−0.788879	−	0.287128i
$129$		0			0
$130$	−5.50387	−	4.61830i	−0.482721	−	0.405051i
$131$	16.6395	−	6.05628i	1.45380	−	0.529140i	0.510150	−	0.860085i	$-0.329590\pi$
$131$	16.6395	−	6.05628i	1.45380	−	0.529140i	0.943650	+	0.330946i	$0.107368\pi$
$132$		0			0
$133$	−2.77972	−	15.7645i	−0.241032	−	1.36696i
$134$	2.50206			0.216145
$135$		0			0
$136$	−8.83069			−0.757225
$137$	−0.682266	−	3.86932i	−0.0582899	−	0.330579i	0.941693	−	0.336474i	$-0.109234\pi$
$137$	−0.682266	−	3.86932i	−0.0582899	−	0.330579i	−0.999983	+	0.00589552i	$0.998123\pi$
$138$		0			0
$139$	−11.2442	+	4.09256i	−0.953723	+	0.347127i	−0.771571	−	0.636144i	$-0.780529\pi$
$139$	−11.2442	+	4.09256i	−0.953723	+	0.347127i	−0.182152	+	0.983270i	$0.558306\pi$
$140$	−0.564178	−	0.473401i	−0.0476817	−	0.0400097i
$141$		0			0
$142$	6.97906	+	2.54017i	0.585669	+	0.213166i
$143$	9.58899	+	16.6086i	0.801872	+	1.38888i
$144$		0			0
$145$	1.06670	−	1.84759i	0.0885849	−	0.153434i
$146$	5.73261	−	4.81023i	0.474434	−	0.398098i
$147$		0			0
$148$	−0.00134417	+	0.00762319i	−0.000110490	+	0.000626622i
$149$	3.56418	−	20.2135i	0.291989	−	1.65595i	−0.387206	−	0.921993i	$-0.626560\pi$
$149$	3.56418	−	20.2135i	0.291989	−	1.65595i	0.679195	−	0.733958i	$-0.262329\pi$
$150$		0			0
$151$	12.2626	−	10.2896i	0.997920	−	0.837354i	0.0112247	−	0.999937i	$-0.496427\pi$
$151$	12.2626	−	10.2896i	0.997920	−	0.837354i	0.986695	+	0.162583i	$0.0519825\pi$
$152$	−9.76991	+	16.9220i	−0.792445	+	1.37255i
$153$		0			0
$154$	−9.65523	−	16.7233i	−0.778041	−	1.34761i
$155$	0.914000	+	0.332669i	0.0734143	+	0.0267206i
$156$		0			0
$157$	−16.8327	−	14.1244i	−1.34340	−	1.12725i	−0.980739	−	0.195325i	$-0.937424\pi$
$157$	−16.8327	−	14.1244i	−1.34340	−	1.12725i	−0.362661	−	0.931921i	$-0.618132\pi$
$158$	4.78699	−	1.74232i	0.380832	−	0.138612i
$159$		0			0
$160$	0.299011	+	1.69577i	0.0236389	+	0.134063i
$161$	−7.09833			−0.559426
$162$		0			0
$163$	20.5107			1.60652			0.803262	−	0.595625i	$-0.203096\pi$
$163$	20.5107			1.60652			0.803262	+	0.595625i	$0.203096\pi$
$164$	0.157289	+	0.892032i	0.0122822	+	0.0696560i
$165$		0			0
$166$	−5.04576	+	1.83651i	−0.391627	+	0.142541i
$167$	3.28699	+	2.75811i	0.254355	+	0.213429i	0.761045	−	0.648699i	$-0.224687\pi$
$167$	3.28699	+	2.75811i	0.254355	+	0.213429i	−0.506690	+	0.862128i	$0.669131\pi$
$168$		0			0
$169$	2.43242	+	0.885328i	0.187109	+	0.0681022i
$170$	−3.34002	−	5.78509i	−0.256168	−	0.443696i
$171$		0			0
$172$	−0.479055	+	0.829748i	−0.0365276	+	0.0632677i
$173$	2.90554	−	2.43804i	0.220904	−	0.185361i	−0.525619	−	0.850720i	$-0.676166\pi$
$173$	2.90554	−	2.43804i	0.220904	−	0.185361i	0.746523	+	0.665359i	$0.231722\pi$
$174$		0			0
$175$	−0.949960	+	5.38749i	−0.0718102	+	0.407256i
$176$	−3.71167	+	21.0499i	−0.279777	+	1.58670i
$177$		0			0
$178$	8.41219	−	7.05866i	0.630520	−	0.529069i
$179$	−4.13816	+	7.16750i	−0.309300	+	0.535724i	−0.978209	−	0.207620i	$-0.933428\pi$
$179$	−4.13816	+	7.16750i	−0.309300	+	0.535724i	0.668909	+	0.743344i	$0.266761\pi$
$180$		0			0
$181$	−3.36097	−	5.82137i	−0.249819	−	0.432699i	0.713657	−	0.700496i	$-0.247038\pi$
$181$	−3.36097	−	5.82137i	−0.249819	−	0.432699i	−0.963475	+	0.267797i	$0.913704\pi$
$182$	9.85117	+	3.58553i	0.730217	+	0.265777i
$183$		0			0
$184$	6.63744	+	5.56947i	0.489319	+	0.410587i
$185$	−0.0650551	+	0.0236781i	−0.00478295	+	0.00174085i
$186$		0			0
$187$	3.09627	+	17.5598i	0.226421	+	1.28410i
$188$	0.690474			0.0503580
$189$		0			0
$190$	−14.7811			−1.07233
$191$	−0.870767	−	4.93837i	−0.0630065	−	0.357328i	−0.999969	−	0.00789719i	$-0.997486\pi$
$191$	−0.870767	−	4.93837i	−0.0630065	−	0.357328i	0.936962	−	0.349430i	$-0.113625\pi$
$192$		0			0
$193$	16.7875	−	6.11013i	1.20839	−	0.439817i	0.342243	−	0.939611i	$-0.388813\pi$
$193$	16.7875	−	6.11013i	1.20839	−	0.439817i	0.866144	+	0.499794i	$0.166591\pi$
$194$	0.269200	+	0.225885i	0.0193274	+	0.0162176i
$195$		0			0
$196$	−0.205737	−	0.0748822i	−0.0146955	−	0.00534873i
$197$	−0.361844	−	0.626733i	−0.0257803	−	0.0446529i	0.852847	−	0.522160i	$-0.174874\pi$
$197$	−0.361844	−	0.626733i	−0.0257803	−	0.0446529i	−0.878628	+	0.477507i	$0.841540\pi$
$198$		0			0
$199$	5.09627	−	8.82699i	0.361265	−	0.625729i	−0.626905	−	0.779096i	$-0.715678\pi$
$199$	5.09627	−	8.82699i	0.361265	−	0.625729i	0.988169	+	0.153367i	$0.0490117\pi$
$200$	5.11540	−	4.29233i	0.361713	−	0.303514i
$201$		0			0
$202$	2.57991	−	14.6314i	0.181522	−	1.02946i
$203$	−0.540545	+	3.06558i	−0.0379388	+	0.215162i
$204$		0			0
$205$	−6.20574	+	5.20723i	−0.433427	+	0.363689i
$206$	2.63176	−	4.55834i	0.183363	−	0.317595i
$207$		0			0
$208$	−5.80200	−	10.0494i	−0.402297	−	0.696798i
$209$	37.0749	+	13.4942i	2.56453	+	0.933411i
$210$		0			0
$211$	−11.3871	−	9.55493i	−0.783922	−	0.657789i	0.160311	−	0.987067i	$-0.448750\pi$
$211$	−11.3871	−	9.55493i	−0.783922	−	0.657789i	−0.944233	+	0.329278i	$0.893195\pi$
$212$	2.02094	−	0.735564i	0.138799	−	0.0505187i
$213$		0			0
$214$	−0.617211	−	3.50038i	−0.0421917	−	0.239281i
$215$	−8.56893			−0.584396
$216$		0			0
$217$	−1.41921			−0.0963426
$218$	−2.09580	−	11.8859i	−0.141945	−	0.805013i
$219$		0			0
$220$	1.70574	−	0.620838i	0.115001	−	0.0418569i
$221$	−7.41534	−	6.22221i	−0.498810	−	0.418551i
$222$		0			0
$223$	10.2883	+	3.74465i	0.688958	+	0.250760i	0.662689	−	0.748895i	$-0.269415\pi$
$223$	10.2883	+	3.74465i	0.688958	+	0.250760i	0.0262688	+	0.999655i	$0.491637\pi$
$224$	−1.25624	−	2.17588i	−0.0839364	−	0.145382i
$225$		0			0
$226$	−10.7306	+	18.5859i	−0.713786	+	1.23631i
$227$	−13.2777	+	11.1413i	−0.881269	+	0.739472i	−0.966440	−	0.256894i	$-0.917301\pi$
$227$	−13.2777	+	11.1413i	−0.881269	+	0.739472i	0.0851707	+	0.996366i	$0.472856\pi$
$228$		0			0
$229$	0.271259	−	1.53839i	0.0179253	−	0.101659i	−0.974532	−	0.224246i	$-0.928008\pi$
$229$	0.271259	−	1.53839i	0.0179253	−	0.101659i	0.992458	+	0.122587i	$0.0391191\pi$
$230$	−1.13816	+	6.45480i	−0.0750478	+	0.425617i
$231$		0			0
$232$	2.91076	−	2.44242i	0.191101	−	0.160353i
$233$	−8.39440	+	14.5395i	−0.549935	+	0.952516i	0.448343	+	0.893862i	$0.352014\pi$
$233$	−8.39440	+	14.5395i	−0.549935	+	0.952516i	−0.998278	+	0.0586545i	$0.981319\pi$
$234$		0			0
$235$	3.08765	+	5.34796i	0.201416	+	0.348863i
$236$	−1.27584	−	0.464369i	−0.0830504	−	0.0302279i
$237$		0			0
$238$	7.46657	+	6.26519i	0.483986	+	0.406112i
$239$	3.78611	−	1.37803i	0.244903	−	0.0891375i	−0.216652	−	0.976249i	$-0.569514\pi$
$239$	3.78611	−	1.37803i	0.244903	−	0.0891375i	0.461555	+	0.887111i	$0.347292\pi$
$240$		0			0
$241$	−0.582129	−	3.30142i	−0.0374982	−	0.212663i	0.960301	−	0.278965i	$-0.0899912\pi$
$241$	−0.582129	−	3.30142i	−0.0374982	−	0.212663i	−0.997800	+	0.0663015i	$0.978880\pi$
$242$	32.7743			2.10681
$243$		0			0
$244$	−2.04189			−0.130719
$245$	−0.340022	−	1.92836i	−0.0217232	−	0.123199i
$246$		0			0
$247$	−20.1275	+	7.32580i	−1.28068	+	0.466130i
$248$	1.32707	+	1.11354i	0.0842688	+	0.0707100i
$249$		0			0
$250$	15.2087	+	5.53553i	0.961885	+	0.350097i
$251$	11.5753	+	20.0490i	0.730628	+	1.26548i	0.956615	+	0.291354i	$0.0941059\pi$
$251$	11.5753	+	20.0490i	0.730628	+	1.26548i	−0.225987	+	0.974130i	$0.572561\pi$
$252$		0			0
$253$	8.74763	−	15.1513i	0.549959	−	0.952556i
$254$	3.71167	−	3.11446i	0.232891	−	0.195418i
$255$		0			0
$256$	−0.763356	+	4.32921i	−0.0477098	+	0.270575i
$257$	2.08600	−	11.8303i	0.130121	−	0.737953i	−0.848013	−	0.529976i	$-0.822201\pi$
$257$	2.08600	−	11.8303i	0.130121	−	0.737953i	0.978134	−	0.207977i	$-0.0666880\pi$
$258$		0			0
$259$	0.0773815	−	0.0649308i	0.00480825	−	0.00403460i
$260$	−0.492726	+	0.853427i	−0.0305576	+	0.0529273i
$261$		0			0
$262$	11.9285	+	20.6609i	0.736948	+	1.27643i
$263$	−15.8824	−	5.78071i	−0.979349	−	0.356454i	−0.197762	−	0.980250i	$-0.563367\pi$
$263$	−15.8824	−	5.78071i	−0.979349	−	0.356454i	−0.781587	+	0.623796i	$0.785590\pi$
$264$		0			0
$265$	14.7344	+	12.3636i	0.905128	+	0.759493i
$266$	20.2665	−	7.37641i	1.24262	−	0.452277i
$267$		0			0
$268$	−0.0595922	−	0.337964i	−0.00364017	−	0.0206444i
$269$	−7.91447			−0.482554			−0.241277	−	0.970456i	$-0.577566\pi$
$269$	−7.91447			−0.482554			−0.241277	+	0.970456i	$0.577566\pi$
$270$		0			0
$271$	−17.2344			−1.04692			−0.523458	−	0.852051i	$-0.675358\pi$
$271$	−17.2344			−1.04692			−0.523458	+	0.852051i	$0.675358\pi$
$272$	−1.87346	−	10.6249i	−0.113595	−	0.644229i
$273$		0			0
$274$	4.97431	−	1.81050i	0.300509	−	0.109376i
$275$	−10.3289	−	8.66696i	−0.622855	−	0.522637i
$276$		0			0
$277$	−24.8405	−	9.04120i	−1.49252	−	0.543233i	−0.538409	−	0.842684i	$-0.680974\pi$
$277$	−24.8405	−	9.04120i	−1.49252	−	0.543233i	−0.954112	+	0.299451i	$0.903197\pi$
$278$	−8.06077	−	13.9617i	−0.483453	−	0.837365i
$279$		0			0
$280$	5.86571	−	10.1597i	0.350543	−	0.607159i
$281$	−14.5517	+	12.2103i	−0.868081	+	0.728406i	−0.963693	−	0.267012i	$-0.913964\pi$
$281$	−14.5517	+	12.2103i	−0.868081	+	0.728406i	0.0956121	+	0.995419i	$0.469519\pi$
$282$		0			0
$283$	−2.88026	+	16.3348i	−0.171214	+	0.971002i	0.771210	+	0.636581i	$0.219652\pi$
$283$	−2.88026	+	16.3348i	−0.171214	+	0.971002i	−0.942424	+	0.334421i	$0.891459\pi$
$284$	0.176890	−	1.00319i	0.0104965	−	0.0595284i
$285$		0			0
$286$	−19.7934	+	16.6086i	−1.17041	+	0.982088i
$287$	5.91013	−	10.2366i	0.348864	−	0.604250i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	2.70099	+	0.983080i	0.158608	+	0.0577284i
$291$		0			0
$292$	−0.786274	−	0.659762i	−0.0460132	−	0.0386097i
$293$	−18.1903	+	6.62073i	−1.06269	+	0.386787i	−0.813438	−	0.581652i	$-0.802407\pi$
$293$	−18.1903	+	6.62073i	−1.06269	+	0.386787i	−0.249251	+	0.968439i	$0.580185\pi$
$294$		0			0
$295$	−2.10859	−	11.9584i	−0.122767	−	0.696246i
$296$	−0.123303			−0.00716685
$297$		0			0
$298$	27.6536			1.60193
$299$	1.64930	+	9.35365i	0.0953815	+	0.540935i
$300$		0			0
$301$	11.7490	−	4.27628i	0.677199	−	0.246480i
$302$	16.5214	+	13.8631i	0.950700	+	0.797732i
$303$		0			0
$304$	−22.4329	−	8.16490i	−1.28661	−	0.468289i
$305$	−9.13088	−	15.8152i	−0.522833	−	0.905573i
$306$		0			0
$307$	−10.4029	+	18.0183i	−0.593722	+	1.02836i	0.400003	+	0.916514i	$0.369009\pi$
$307$	−10.4029	+	18.0183i	−0.593722	+	1.02836i	−0.993726	+	0.111844i	$0.964324\pi$
$308$	−2.02893	+	1.70248i	−0.115609	+	0.0970077i
$309$		0			0
$310$	−0.227559	+	1.29055i	−0.0129245	+	0.0732984i
$311$	−1.85204	+	10.5035i	−0.105020	+	0.595597i	0.886193	+	0.463317i	$0.153341\pi$
$311$	−1.85204	+	10.5035i	−0.105020	+	0.595597i	−0.991212	+	0.132280i	$0.957770\pi$
$312$		0			0
$313$	2.92262	−	2.45237i	0.165196	−	0.138616i	−0.556442	−	0.830886i	$-0.687834\pi$
$313$	2.92262	−	2.45237i	0.165196	−	0.138616i	0.721638	+	0.692270i	$0.243389\pi$
$314$	14.8025	−	25.6386i	0.835352	−	1.44687i
$315$		0			0
$316$	−0.349356	−	0.605102i	−0.0196528	−	0.0340396i
$317$	−24.7977	−	9.02563i	−1.39278	−	0.506930i	−0.466752	−	0.884388i	$-0.654576\pi$
$317$	−24.7977	−	9.02563i	−1.39278	−	0.506930i	−0.926027	+	0.377458i	$0.876798\pi$
$318$		0			0
$319$	−5.87733	−	4.93166i	−0.329067	−	0.276120i
$320$	−13.3503	+	4.85911i	−0.746304	+	0.271632i
$321$		0			0
$322$	−1.66069	−	9.41826i	−0.0925468	−	0.524859i
$323$	−19.9145			−1.10807
$324$		0			0
$325$	7.31996			0.406038
$326$	4.79860	+	27.2142i	0.265770	+	1.50726i
$327$		0			0
$328$	−13.5582	+	4.93480i	−0.748629	+	0.272479i
$329$	−6.90239	−	5.79179i	−0.380541	−	0.319312i
$330$		0			0
$331$	1.47683	+	0.537524i	0.0811741	+	0.0295450i	0.382288	−	0.924043i	$-0.375136\pi$
$331$	1.47683	+	0.537524i	0.0811741	+	0.0295450i	−0.301114	+	0.953588i	$0.597358\pi$
$332$	0.368241	+	0.637812i	0.0202098	+	0.0350045i
$333$		0			0
$334$	−2.89053	+	5.00654i	−0.158163	+	0.273946i
$335$	2.35117	−	1.97286i	0.128458	−	0.107789i
$336$		0			0
$337$	−1.39187	+	7.89371i	−0.0758202	+	0.429998i	0.923142	+	0.384458i	$0.125612\pi$
$337$	−1.39187	+	7.89371i	−0.0758202	+	0.429998i	−0.998963	+	0.0455394i	$0.985499\pi$
$338$	−0.605600	+	3.43453i	−0.0329403	+	0.186814i
$339$		0			0
$340$	−0.701867	+	0.588936i	−0.0380641	+	0.0319395i
$341$	1.74897	−	3.02931i	0.0947121	−	0.164046i
$342$		0			0
$343$	9.86871	+	17.0931i	0.532860	+	0.922941i
$344$	−14.3414	−	5.21983i	−0.773235	−	0.281434i
$345$		0			0
$346$	3.91463	+	3.28476i	0.210452	+	0.176590i
$347$	−18.6484	+	6.78747i	−1.00110	+	0.364371i	−0.790009	−	0.613096i	$-0.789924\pi$
$347$	−18.6484	+	6.78747i	−1.00110	+	0.364371i	−0.211091	+	0.977466i	$0.567702\pi$
$348$		0			0
$349$	1.92633	+	10.9247i	0.103114	+	0.584788i	0.991957	+	0.126576i	$0.0403988\pi$
$349$	1.92633	+	10.9247i	0.103114	+	0.584788i	−0.888843	+	0.458212i	$0.848490\pi$
$350$	−7.37052			−0.393971
$351$		0			0
$352$	6.19253			0.330063
$353$	−0.497312	−	2.82039i	−0.0264692	−	0.150114i	0.968709	−	0.248200i	$-0.0798391\pi$
$353$	−0.497312	−	2.82039i	−0.0264692	−	0.150114i	−0.995178	+	0.0980859i	$0.968728\pi$
$354$		0			0
$355$	8.56108	−	3.11598i	0.454375	−	0.165379i
$356$	−1.15380	−	0.968153i	−0.0611512	−	0.0513120i
$357$		0			0
$358$	−10.4782	−	3.81374i	−0.553789	−	0.201563i
$359$	−14.3944	−	24.9318i	−0.759707	−	1.31585i	−0.943000	−	0.332793i	$-0.892009\pi$
$359$	−14.3944	−	24.9318i	−0.759707	−	1.31585i	0.183292	−	0.983058i	$-0.441324\pi$
$360$		0			0
$361$	−12.5326	+	21.7070i	−0.659608	+	1.14247i
$362$	6.93763	−	5.82137i	0.364634	−	0.305964i
$363$		0			0
$364$	0.249686	−	1.41604i	0.0130871	−	0.0742205i
$365$	1.59405	−	9.04028i	0.0834361	−	0.473190i
$366$		0			0
$367$	−8.42056	+	7.06569i	−0.439550	+	0.368826i	−0.835541	−	0.549428i	$-0.814846\pi$
$367$	−8.42056	+	7.06569i	−0.439550	+	0.368826i	0.395991	+	0.918254i	$0.370401\pi$
$368$	−5.29292	+	9.16760i	−0.275912	+	0.477894i
$369$		0			0
$370$	−0.0466368	−	0.0807773i	−0.00242453	−	0.00419941i
$371$	−26.3726	−	9.59883i	−1.36920	−	0.498347i
$372$		0			0
$373$	25.5933	+	21.4754i	1.32517	+	1.11195i	0.985180	+	0.171523i	$0.0548689\pi$
$373$	25.5933	+	21.4754i	1.32517	+	1.11195i	0.339992	+	0.940428i	$0.389576\pi$
$374$	−22.5744	+	8.21643i	−1.16730	+	0.424861i
$375$		0			0
$376$	1.90988	+	10.8315i	0.0984946	+	0.558591i
$377$	4.16519			0.214518
$378$		0			0
$379$	20.9394			1.07559			0.537794	−	0.843077i	$-0.319258\pi$
$379$	20.9394			1.07559			0.537794	+	0.843077i	$0.319258\pi$
$380$	0.352044	+	1.99654i	0.0180595	+	0.102420i
$381$		0			0
$382$	6.34864	−	2.31072i	0.324825	−	0.118227i
$383$	−3.14930	−	2.64258i	−0.160922	−	0.135029i	0.558771	−	0.829322i	$-0.311273\pi$
$383$	−3.14930	−	2.64258i	−0.160922	−	0.135029i	−0.719693	+	0.694292i	$0.755717\pi$
$384$		0			0
$385$	−22.2592	−	8.10170i	−1.13444	−	0.412901i
$386$	12.0346	+	20.8446i	0.612546	+	1.06096i
$387$		0			0
$388$	0.0240997	−	0.0417419i	0.00122348	−	0.00211912i
$389$	13.0949	−	10.9879i	0.663939	−	0.557111i	−0.247326	−	0.968932i	$-0.579552\pi$
$389$	13.0949	−	10.9879i	0.663939	−	0.557111i	0.911265	+	0.411822i	$0.135107\pi$
$390$		0			0
$391$	−1.53343	+	8.69653i	−0.0775490	+	0.439802i
$392$	0.605600	−	3.43453i	0.0305874	−	0.173470i
$393$		0			0
$394$	0.746911	−	0.626733i	0.0376288	−	0.0315743i
$395$	3.12449	−	5.41177i	0.157210	−	0.272296i
$396$		0			0
$397$	−11.2010	−	19.4007i	−0.562162	−	0.973692i	−0.997308	−	0.0733324i	$-0.976637\pi$
$397$	−11.2010	−	19.4007i	−0.562162	−	0.973692i	0.435146	−	0.900360i	$-0.356697\pi$
$398$	12.9042	+	4.69674i	0.646829	+	0.235427i
$399$		0			0
$400$	6.24969	+	5.24411i	0.312484	+	0.262205i
$401$	13.7023	−	4.98724i	0.684262	−	0.249051i	0.0235855	−	0.999722i	$-0.492492\pi$
$401$	13.7023	−	4.98724i	0.684262	−	0.249051i	0.660676	+	0.750671i	$0.270270\pi$
$402$		0			0
$403$	0.329755	+	1.87014i	0.0164263	+	0.0931581i
$404$	−2.03777			−0.101383
$405$		0			0
$406$	−4.19396			−0.208143
$407$	0.0432332	+	0.245188i	0.00214299	+	0.0121535i
$408$		0			0
$409$	16.4474	−	5.98638i	0.813273	−	0.296007i	0.0982980	−	0.995157i	$-0.468660\pi$
$409$	16.4474	−	5.98638i	0.813273	−	0.296007i	0.714975	+	0.699150i	$0.246438\pi$
$410$	−8.36097	−	7.01568i	−0.412919	−	0.346480i
$411$		0			0
$412$	−0.678396	−	0.246916i	−0.0334222	−	0.0121647i
$413$	8.85891	+	15.3441i	0.435918	+	0.755033i
$414$		0			0
$415$	−3.29339	+	5.70431i	−0.161666	+	0.280014i
$416$	−2.57532	+	2.16095i	−0.126266	+	0.105949i
$417$		0			0
$418$	−9.23055	+	52.3491i	−0.451481	+	2.56048i
$419$	3.27538	−	18.5756i	0.160013	−	0.907477i	−0.794046	−	0.607858i	$-0.792029\pi$
$419$	3.27538	−	18.5756i	0.160013	−	0.907477i	0.954059	−	0.299619i	$-0.0968597\pi$
$420$		0			0
$421$	−24.7690	+	20.7837i	−1.20717	+	1.01294i	−0.207773	+	0.978177i	$0.566622\pi$
$421$	−24.7690	+	20.7837i	−1.20717	+	1.01294i	−0.999396	+	0.0347581i	$0.988934\pi$
$422$	10.0137	−	17.3442i	0.487458	−	0.844302i
$423$		0			0
$424$	17.1288	+	29.6680i	0.831849	+	1.44080i
$425$	6.39528	+	2.32769i	0.310217	+	0.112910i
$426$		0			0
$427$	20.4119	+	17.1277i	0.987803	+	0.828865i
$428$	−0.458111	+	0.166739i	−0.0221436	+	0.00805962i
$429$		0			0
$430$	−2.00475	−	11.3695i	−0.0966775	−	0.548285i
$431$	34.3164			1.65297			0.826483	−	0.562962i	$-0.190338\pi$
$431$	34.3164			1.65297			0.826483	+	0.562962i	$0.190338\pi$
$432$		0			0
$433$	−25.0669			−1.20464			−0.602318	−	0.798256i	$-0.705756\pi$
$433$	−25.0669			−1.20464			−0.602318	+	0.798256i	$0.705756\pi$
$434$	−0.332033	−	1.88305i	−0.0159381	−	0.0903895i
$435$		0			0
$436$	−1.55556	+	0.566177i	−0.0744978	+	0.0271150i
$437$	14.9684	+	12.5600i	0.716035	+	0.600824i
$438$		0			0
$439$	21.8084	+	7.93761i	1.04086	+	0.378841i	0.805205	−	0.592996i	$-0.202055\pi$
$439$	21.8084	+	7.93761i	1.04086	+	0.378841i	0.235653	+	0.971837i	$0.424277\pi$
$440$	14.4572	+	25.0407i	0.689222	+	1.19377i
$441$		0			0
$442$	6.52094	−	11.2946i	0.310170	−	0.537230i
$443$	−3.15729	+	2.64928i	−0.150007	+	0.125871i	−0.714703	−	0.699428i	$-0.753438\pi$
$443$	−3.15729	+	2.64928i	−0.150007	+	0.125871i	0.564695	+	0.825299i	$0.308994\pi$
$444$		0			0
$445$	2.33915	−	13.2660i	0.110886	−	0.628866i
$446$	−2.56149	+	14.5269i	−0.121290	+	0.687870i
$447$		0			0
$448$	15.8799	−	13.3248i	0.750252	−	0.629537i
$449$	−9.17071	+	15.8841i	−0.432793	+	0.749619i	−0.997113	−	0.0759373i	$-0.975805\pi$
$449$	−9.17071	+	15.8841i	−0.432793	+	0.749619i	0.564320	+	0.825556i	$0.309138\pi$
$450$		0			0
$451$	14.5667	+	25.2303i	0.685919	+	1.18805i
$452$	2.76604	+	1.00676i	0.130104	+	0.0473539i
$453$		0			0
$454$	−17.8889	−	15.0106i	−0.839569	−	0.704482i
$455$	12.0842	−	4.39831i	0.566518	−	0.206196i
$456$		0			0
$457$	−3.37939	−	19.1654i	−0.158081	−	0.896522i	−0.955915	−	0.293644i	$-0.905132\pi$
$457$	−3.37939	−	19.1654i	−0.158081	−	0.896522i	0.797834	−	0.602877i	$-0.205979\pi$
$458$	2.10464			0.0983432
$459$		0			0
$460$	0.898986			0.0419154
$461$	4.81861	+	27.3277i	0.224425	+	1.27278i	0.863781	+	0.503867i	$0.168090\pi$
$461$	4.81861	+	27.3277i	0.224425	+	1.27278i	−0.639356	+	0.768911i	$0.720799\pi$
$462$		0			0
$463$	−36.3530	+	13.2314i	−1.68947	+	0.614915i	−0.994558	−	0.104183i	$-0.966777\pi$
$463$	−36.3530	+	13.2314i	−1.68947	+	0.614915i	−0.694908	+	0.719099i	$0.744555\pi$
$464$	3.55619	+	2.98400i	0.165092	+	0.138529i
$465$		0			0
$466$	−21.2554	−	7.73632i	−0.984636	−	0.358378i
$467$	−14.8819	−	25.7762i	−0.688653	−	1.19278i	−0.972274	−	0.233845i	$-0.924869\pi$
$467$	−14.8819	−	25.7762i	−0.688653	−	1.19278i	0.283621	−	0.958936i	$-0.408464\pi$
$468$		0			0
$469$	−2.23917	+	3.87836i	−0.103395	+	0.179086i
$470$	−6.37346	+	5.34796i	−0.293986	+	0.246683i
$471$		0			0
$472$	3.75553	−	21.2987i	0.172862	−	0.980350i
$473$	−5.35117	+	30.3480i	−0.246047	+	1.39540i
$474$		0			0
$475$	11.5360	−	9.67982i	0.529306	−	0.444141i
$476$	0.668434	−	1.15776i	0.0306376	−	0.0530659i
$477$		0			0
$478$	2.71419	+	4.70112i	0.124144	+	0.215024i
$479$	35.4038	+	12.8859i	1.61764	+	0.588773i	0.982930	−	0.183977i	$-0.0588973\pi$
$479$	35.4038	+	12.8859i	1.61764	+	0.588773i	0.634710	+	0.772750i	$0.281120\pi$
$480$		0			0
$481$	−0.103541	−	0.0868809i	−0.00472105	−	0.00396143i
$482$	4.24422	−	1.54477i	0.193319	−	0.0703624i
$483$		0			0
$484$	−0.780592	−	4.42696i	−0.0354815	−	0.201225i
$485$	0.431074			0.0195741
$486$		0			0
$487$	−0.763823			−0.0346121			−0.0173061	−	0.999850i	$-0.505509\pi$
$487$	−0.763823			−0.0346121			−0.0173061	+	0.999850i	$0.505509\pi$
$488$	−5.64796	−	32.0311i	−0.255671	−	1.44998i
$489$		0			0
$490$	2.47906	−	0.902302i	0.111992	−	0.0407619i
$491$	−0.381445	−	0.320070i	−0.0172144	−	0.0144446i	0.634140	−	0.773218i	$-0.281354\pi$
$491$	−0.381445	−	0.320070i	−0.0172144	−	0.0144446i	−0.651354	+	0.758774i	$0.725799\pi$
$492$		0			0
$493$	3.63903	+	1.32450i	0.163894	+	0.0596525i
$494$	−14.4290	−	24.9918i	−0.649192	−	1.12443i
$495$		0			0
$496$	−1.05825	+	1.83294i	−0.0475167	+	0.0823014i
$497$	−10.1832	+	8.54472i	−0.456779	+	0.383283i
$498$		0			0
$499$	1.55690	−	8.82964i	0.0696966	−	0.395269i	−0.929925	−	0.367750i	$-0.880128\pi$
$499$	1.55690	−	8.82964i	0.0696966	−	0.395269i	0.999621	−	0.0275190i	$-0.00876067\pi$
$500$	0.385477	−	2.18615i	0.0172391	−	0.0977676i
$501$		0			0
$502$	−23.8935	+	20.0490i	−1.06642	+	0.894833i
$503$	−9.18092	+	15.9018i	−0.409357	+	0.709027i	−0.994818	−	0.101673i	$-0.967580\pi$
$503$	−9.18092	+	15.9018i	−0.409357	+	0.709027i	0.585461	+	0.810701i	$0.300914\pi$
$504$		0			0
$505$	−9.11246	−	15.7832i	−0.405499	−	0.702345i
$506$	22.1498	+	8.06186i	0.984677	+	0.358393i
$507$		0			0
$508$	−0.509085	−	0.427173i	−0.0225870	−	0.0189527i
$509$	26.6596	−	9.70329i	1.18166	−	0.430091i	0.324875	−	0.945757i	$-0.394678\pi$
$509$	26.6596	−	9.70329i	1.18166	−	0.430091i	0.856790	+	0.515666i	$0.172456\pi$
$510$		0			0
$511$	2.32588	+	13.1907i	0.102891	+	0.583524i
$512$	−24.9186			−1.10126
$513$		0			0
$514$	16.1848			0.713881
$515$	−1.12119	−	6.35857i	−0.0494054	−	0.280192i
$516$		0			0
$517$	20.8687	−	7.59559i	0.917805	−	0.334054i
$518$	0.104256	+	0.0874810i	0.00458074	+	0.00384370i
$519$		0			0
$520$	−14.7506	−	5.36879i	−0.646857	−	0.235437i
$521$	16.3191	+	28.2655i	0.714952	+	1.23833i	0.962978	+	0.269580i	$0.0868847\pi$
$521$	16.3191	+	28.2655i	0.714952	+	1.23833i	−0.248026	+	0.968753i	$0.579782\pi$
$522$		0			0
$523$	11.0116	−	19.0727i	0.481504	−	0.833990i	−0.518271	−	0.855217i	$-0.673424\pi$
$523$	11.0116	−	19.0727i	0.481504	−	0.833990i	0.999775	+	0.0212271i	$0.00675730\pi$
$524$	2.50665	−	2.10332i	0.109503	−	0.0918842i
$525$		0			0
$526$	3.95424	−	22.4256i	0.172413	−	0.977803i
$527$	−0.306589	+	1.73875i	−0.0133552	+	0.0757413i
$528$		0			0
$529$	−10.9816	+	9.21464i	−0.477460	+	0.400637i
$530$	−12.9572	+	22.4426i	−0.562826	+	0.974844i
$531$		0			0
$532$	−1.47906	−	2.56180i	−0.0641252	−	0.111068i
$533$	−14.8623	−	5.40944i	−0.643758	−	0.234309i
$534$		0			0
$535$	−3.34002	−	2.80261i	−0.144402	−	0.121167i
$536$	5.13681	−	1.86965i	0.221876	−	0.0807564i
$537$		0			0
$538$	−1.85163	−	10.5011i	−0.0798296	−	0.452736i
$539$	−7.04189			−0.303316
$540$		0			0
$541$	−15.7870			−0.678738			−0.339369	−	0.940653i	$-0.610214\pi$
$541$	−15.7870			−0.678738			−0.339369	+	0.940653i	$0.610214\pi$
$542$	−4.03209	−	22.8671i	−0.173193	−	0.982227i
$543$		0			0
$544$	−2.93717	+	1.06904i	−0.125930	+	0.0458348i
$545$	−11.3414	−	9.51654i	−0.485811	−	0.407644i
$546$		0			0
$547$	25.7656	+	9.37792i	1.10166	+	0.400971i	0.827928	−	0.560835i	$-0.189520\pi$
$547$	25.7656	+	9.37792i	1.10166	+	0.400971i	0.273731	+	0.961806i	$0.411742\pi$
$548$	−0.363026	−	0.628780i	−0.0155077	−	0.0268602i
$549$		0			0
$550$	9.08306	−	15.7323i	0.387303	−	0.670829i
$551$	6.56418	−	5.50800i	0.279643	−	0.234649i
$552$		0			0
$553$	−1.58331	+	8.97940i	−0.0673292	+	0.381843i
$554$	6.18454	−	35.0743i	0.262756	−	1.49016i
$555$		0			0
$556$	−1.69388	+	1.42133i	−0.0718364	+	0.0602779i
$557$	−14.7010	+	25.4629i	−0.622901	+	1.07890i	0.366042	+	0.930598i	$0.380713\pi$
$557$	−14.7010	+	25.4629i	−0.622901	+	1.07890i	−0.988943	+	0.148298i	$0.952621\pi$
$558$		0			0
$559$	−8.36484	−	14.4883i	−0.353795	−	0.612791i
$560$	13.4684	+	4.90209i	0.569143	+	0.207151i
$561$		0			0
$562$	−19.6054	−	16.4509i	−0.827005	−	0.693940i
$563$	9.74510	−	3.54693i	0.410707	−	0.149485i	−0.128400	−	0.991722i	$-0.540984\pi$
$563$	9.74510	−	3.54693i	0.410707	−	0.149485i	0.539107	+	0.842237i	$0.318762\pi$
$564$		0			0
$565$	4.57145	+	25.9260i	0.192322	+	1.09071i
$566$	−22.3473			−0.939327
$567$		0			0
$568$	16.2264			0.680843
$569$	−5.72503	−	32.4683i	−0.240006	−	1.36114i	−0.831811	−	0.555060i	$-0.812695\pi$
$569$	−5.72503	−	32.4683i	−0.240006	−	1.36114i	0.591805	−	0.806081i	$-0.298416\pi$
$570$		0			0
$571$	0.692944	−	0.252211i	0.0289988	−	0.0105547i	−0.327480	−	0.944858i	$-0.606199\pi$
$571$	0.692944	−	0.252211i	0.0289988	−	0.0105547i	0.356479	+	0.934303i	$0.383977\pi$
$572$	2.71482	+	2.27801i	0.113512	+	0.0952482i
$573$		0			0
$574$	14.9650	+	5.44681i	0.624626	+	0.227345i
$575$	−3.33884	−	5.78304i	−0.139239	−	0.241169i
$576$		0			0
$577$	−9.67159	+	16.7517i	−0.402634	+	0.697382i	−0.994043	−	0.108990i	$-0.965238\pi$
$577$	−9.67159	+	16.7517i	−0.402634	+	0.697382i	0.591409	+	0.806371i	$0.298572\pi$
$578$	−8.25671	+	6.92820i	−0.343434	+	0.288175i
$579$		0			0
$580$	0.0684587	−	0.388249i	0.00284259	−	0.0161211i
$581$	1.66890	−	9.46480i	0.0692377	−	0.392666i
$582$		0			0
$583$	52.9889	−	44.4630i	2.19458	−	1.84147i
$584$	8.17483	−	14.1592i	0.338277	−	0.585913i
$585$		0			0
$586$	−13.0403	−	22.5865i	−0.538690	−	0.933038i
$587$	29.9876	+	10.9146i	1.23772	+	0.450493i	0.876234	−	0.481885i	$-0.160048\pi$
$587$	29.9876	+	10.9146i	1.23772	+	0.450493i	0.361485	+	0.932378i	$0.382270\pi$
$588$		0			0
$589$	2.99273	+	2.51120i	0.123313	+	0.103472i
$590$	15.3735	−	5.59548i	0.632915	−	0.230362i
$591$		0			0
$592$	−0.0261591	−	0.148356i	−0.00107513	−	0.00609738i
$593$	31.6783			1.30087			0.650436	−	0.759561i	$-0.274586\pi$
$593$	31.6783			1.30087			0.650436	+	0.759561i	$0.274586\pi$
$594$		0			0
$595$	11.9564			0.490163
$596$	−0.658633	−	3.73530i	−0.0269787	−	0.153004i
$597$		0			0
$598$	−12.0248	+	4.37667i	−0.491731	+	0.178976i
$599$	−9.67024	−	8.11430i	−0.395115	−	0.331541i	0.423487	−	0.905902i	$-0.360806\pi$
$599$	−9.67024	−	8.11430i	−0.395115	−	0.331541i	−0.818602	+	0.574361i	$0.805251\pi$
$600$		0			0
$601$	8.37123	+	3.04688i	0.341470	+	0.124285i	0.507062	−	0.861909i	$-0.330731\pi$
$601$	8.37123	+	3.04688i	0.341470	+	0.124285i	−0.165592	+	0.986194i	$0.552954\pi$
$602$	8.42262	+	14.5884i	0.343280	+	0.594579i
$603$		0			0
$604$	1.47906	−	2.56180i	0.0601819	−	0.104238i
$605$	30.7977	−	25.8424i	1.25211	−	1.05064i
$606$		0			0
$607$	−5.75196	+	32.6210i	−0.233465	+	1.32405i	0.612357	+	0.790581i	$0.290221\pi$
$607$	−5.75196	+	32.6210i	−0.233465	+	1.32405i	−0.845822	+	0.533465i	$0.820890\pi$
$608$	−1.20099	+	6.81115i	−0.0487065	+	0.276229i
$609$		0			0
$610$	18.8478	−	15.8152i	0.763124	−	0.640337i
$611$	−6.02822	+	10.4412i	−0.243876	+	0.422405i
$612$		0			0
$613$	−8.84002	−	15.3114i	−0.357045	−	0.618420i	0.630421	−	0.776254i	$-0.282882\pi$
$613$	−8.84002	−	15.3114i	−0.357045	−	0.618420i	−0.987466	+	0.157833i	$0.949549\pi$
$614$	−26.3410	−	9.58732i	−1.06303	−	0.386913i
$615$		0			0
$616$	−32.3189	−	27.1188i	−1.30217	−	1.09265i
$617$	24.1805	−	8.80099i	0.973471	−	0.354314i	0.194172	−	0.980967i	$-0.437798\pi$
$617$	24.1805	−	8.80099i	0.973471	−	0.354314i	0.779298	+	0.626653i	$0.215576\pi$
$618$		0			0
$619$	4.82651	+	27.3725i	0.193994	+	1.10019i	0.913844	+	0.406065i	$0.133099\pi$
$619$	4.82651	+	27.3725i	0.193994	+	1.10019i	−0.719850	+	0.694129i	$0.755790\pi$
$620$	0.179740			0.00721854
$621$		0			0
$622$	−14.3696			−0.576168
$623$	3.41307	+	19.3565i	0.136742	+	0.775500i
$624$		0			0
$625$	7.99747	−	2.91084i	0.319899	−	0.116434i
$626$	3.93763	+	3.30407i	0.157379	+	0.132057i
$627$		0			0
$628$	−3.81567	−	1.38879i	−0.152262	−	0.0554188i
$629$	−0.0628336	−	0.108831i	−0.00250534	−	0.00433938i
$630$		0			0
$631$	−13.4069	+	23.2214i	−0.533720	+	0.924430i	0.465504	+	0.885046i	$0.345873\pi$
$631$	−13.4069	+	23.2214i	−0.533720	+	0.924430i	−0.999224	+	0.0393842i	$0.987460\pi$
$632$	8.52591	−	7.15409i	0.339143	−	0.284574i
$633$		0			0
$634$	6.17390	−	35.0139i	0.245197	−	1.39058i
$635$	1.03209	−	5.85327i	0.0409572	−	0.232280i
$636$		0			0
$637$	2.92855	−	2.45734i	0.116033	−	0.0973635i
$638$	5.16843	−	8.95199i	0.204620	−	0.354413i
$639$		0			0
$640$	−7.84864	−	13.5942i	−0.310245	−	0.537360i
$641$	−11.9251	−	4.34040i	−0.471015	−	0.171435i	0.0955971	−	0.995420i	$-0.469524\pi$
$641$	−11.9251	−	4.34040i	−0.471015	−	0.171435i	−0.566612	+	0.823985i	$0.691746\pi$
$642$		0			0
$643$	11.8558	+	9.94816i	0.467545	+	0.392317i	0.845898	−	0.533344i	$-0.179065\pi$
$643$	11.8558	+	9.94816i	0.467545	+	0.392317i	−0.378353	+	0.925661i	$0.623509\pi$
$644$	−1.23261	+	0.448634i	−0.0485717	+	0.0176787i
$645$		0			0
$646$	−4.65910	−	26.4231i	−0.183310	−	1.03960i
$647$	11.1506			0.438377			0.219189	−	0.975683i	$-0.429659\pi$
$647$	11.1506			0.438377			0.219189	+	0.975683i	$0.429659\pi$
$648$		0			0
$649$	−43.6691			−1.71416
$650$	1.71254	+	9.71232i	0.0671715	+	0.380949i
$651$		0			0
$652$	3.56165	−	1.29634i	0.139485	−	0.0507684i
$653$	34.1596	+	28.6633i	1.33677	+	1.12168i	0.982444	+	0.186558i	$0.0597332\pi$
$653$	34.1596	+	28.6633i	1.33677	+	1.12168i	0.354323	+	0.935123i	$0.384711\pi$
$654$		0			0
$655$	27.5002	+	10.0092i	1.07452	+	0.391093i
$656$	−8.81386	−	15.2661i	−0.344124	−	0.596039i
$657$		0			0
$658$	6.06986	−	10.5133i	0.236628	−	0.409851i
$659$	−10.7986	+	9.06110i	−0.420654	+	0.352970i	−0.828412	−	0.560120i	$-0.810755\pi$
$659$	−10.7986	+	9.06110i	−0.420654	+	0.352970i	0.407758	+	0.913090i	$0.366311\pi$
$660$		0			0
$661$	6.27126	−	35.5661i	0.243924	−	1.38336i	−0.579055	−	0.815288i	$-0.696578\pi$
$661$	6.27126	−	35.5661i	0.243924	−	1.38336i	0.822979	−	0.568072i	$-0.192310\pi$
$662$	−0.367688	+	2.08526i	−0.0142906	+	0.0810460i
$663$		0			0
$664$	−8.98680	+	7.54082i	−0.348755	+	0.292640i
$665$	13.2280	−	22.9116i	0.512961	−	0.888474i
$666$		0			0
$667$	−1.89986	−	3.29066i	−0.0735630	−	0.127415i
$668$	0.745100	+	0.271194i	0.0288288	+	0.0104928i
$669$		0			0
$670$	3.16772	+	2.65803i	0.122380	+	0.102689i
$671$	−61.7135	+	22.4619i	−2.38242	+	0.867132i
$672$		0			0
$673$	0.389348	+	2.20810i	0.0150082	+	0.0851160i	0.991392	−	0.130928i	$-0.0417957\pi$
$673$	0.389348	+	2.20810i	0.0150082	+	0.0851160i	−0.976384	+	0.216044i	$0.930685\pi$
$674$	−10.7992			−0.415971
$675$		0			0
$676$	0.478340			0.0183977
$677$	6.10829	+	34.6418i	0.234761	+	1.33139i	0.843117	+	0.537730i	$0.180718\pi$
$677$	6.10829	+	34.6418i	0.234761	+	1.33139i	−0.608357	+	0.793664i	$0.708171\pi$
$678$		0			0
$679$	−0.591052	+	0.215125i	−0.0226825	+	0.00825575i
$680$	−11.1800	−	9.38117i	−0.428735	−	0.359752i
$681$		0			0
$682$	4.42855	+	1.61186i	0.169578	+	0.0617213i
$683$	8.88191	+	15.3839i	0.339857	+	0.588649i	0.984406	−	0.175914i	$-0.0562880\pi$
$683$	8.88191	+	15.3839i	0.339857	+	0.588649i	−0.644549	+	0.764563i	$0.722955\pi$
$684$		0			0
$685$	3.24675	−	5.62353i	0.124052	−	0.214864i
$686$	−20.3708	+	17.0931i	−0.777760	+	0.652618i
$687$		0			0
$688$	3.23783	−	18.3626i	0.123441	−	0.700068i
$689$	−6.52094	+	36.9821i	−0.248428	+	1.40891i
$690$		0			0
$691$	−33.7294	+	28.3023i	−1.28313	+	1.07667i	−0.290323	+	0.956929i	$0.593763\pi$
$691$	−33.7294	+	28.3023i	−1.28313	+	1.07667i	−0.992805	+	0.119743i	$0.961793\pi$
$692$	0.350452	−	0.607000i	0.0133222	−	0.0230747i
$693$		0			0
$694$	−13.3687	−	23.1553i	−0.507469	−	0.878962i
$695$	−18.5834	−	6.76379i	−0.704907	−	0.256565i
$696$		0			0
$697$	−11.2647	−	9.45221i	−0.426681	−	0.358028i
$698$	−14.0446	+	5.11181i	−0.531595	+	0.193485i
$699$		0			0
$700$	0.175545	+	0.995568i	0.00663499	+	0.0376289i
$701$	−30.1052			−1.13706			−0.568530	−	0.822663i	$-0.692488\pi$
$701$	−30.1052			−1.13706			−0.568530	+	0.822663i	$0.692488\pi$
$702$		0			0
$703$	−0.278066			−0.0104875
$704$	8.87211	+	50.3162i	0.334380	+	1.89636i
$705$		0			0
$706$	3.62583	−	1.31969i	0.136460	−	0.0496673i
$707$	20.3708	+	17.0931i	0.766122	+	0.642852i
$708$		0			0
$709$	23.2456	+	8.46069i	0.873006	+	0.317748i	0.739384	−	0.673284i	$-0.235117\pi$
$709$	23.2456	+	8.46069i	0.873006	+	0.317748i	0.133622	+	0.991032i	$0.457339\pi$
$710$	6.13728	+	10.6301i	0.230328	+	0.398940i
$711$		0			0
$712$	11.9960	−	20.7776i	0.449568	−	0.778674i
$713$	1.32707	−	1.11354i	0.0496991	−	0.0417025i
$714$		0			0
$715$	−5.50387	+	31.2140i	−0.205833	+	1.16734i
$716$	−0.265578	+	1.50617i	−0.00992510	+	0.0562880i
$717$		0			0
$718$	29.7126	−	24.9318i	1.10886	−	0.930448i
$719$	21.7763	−	37.7177i	0.812119	−	1.40663i	−0.0992586	−	0.995062i	$-0.531647\pi$
$719$	21.7763	−	37.7177i	0.812119	−	1.40663i	0.911378	−	0.411570i	$-0.135020\pi$
$720$		0			0
$721$	4.71048	+	8.15880i	0.175428	+	0.303850i
$722$	−31.7335	−	11.5501i	−1.18100	−	0.429849i
$723$		0			0
$724$	−0.951552	−	0.798447i	−0.0353642	−	0.0296741i
$725$	−2.75180	+	1.00157i	−0.102199	+	0.0371975i
$726$		0			0
$727$	3.56624	+	20.2251i	0.132264	+	0.750109i	0.976726	+	0.214492i	$0.0688096\pi$
$727$	3.56624	+	20.2251i	0.132264	+	0.750109i	−0.844461	+	0.535617i	$0.820079\pi$
$728$	22.9040			0.848880
$729$		0			0
$730$	12.3678			0.457754
$731$	−2.70099	−	15.3181i	−0.0998997	−	0.566559i
$732$		0			0
$733$	−13.1613	+	4.79033i	−0.486125	+	0.176935i	−0.573443	−	0.819246i	$-0.694393\pi$
$733$	−13.1613	+	4.79033i	−0.486125	+	0.176935i	0.0873183	+	0.996180i	$0.472170\pi$
$734$	−11.3450	−	9.51958i	−0.418751	−	0.351374i
$735$		0			0
$736$	2.88191	+	1.04893i	0.106229	+	0.0386641i
$737$	−5.51889	−	9.55899i	−0.203291	−	0.352110i
$738$		0			0
$739$	20.9907	−	36.3569i	0.772154	−	1.33741i	−0.164226	−	0.986423i	$-0.552513\pi$
$739$	20.9907	−	36.3569i	0.772154	−	1.33741i	0.936380	−	0.350987i	$-0.114154\pi$
$740$	−0.00980018	+	0.00822333i	−0.000360262	+	0.000302296i
$741$		0			0
$742$	6.56599	−	37.2376i	0.241045	−	1.36703i
$743$	4.83821	−	27.4389i	0.177497	−	1.00663i	−0.757726	−	0.652573i	$-0.773689\pi$
$743$	4.83821	−	27.4389i	0.177497	−	1.00663i	0.935222	−	0.354061i	$-0.115199\pi$
$744$		0			0
$745$	25.9859	−	21.8048i	0.952050	−	0.798865i
$746$	−22.5064	+	38.9822i	−0.824018	+	1.42724i
$747$		0			0
$748$	1.64749	+	2.85353i	0.0602382	+	0.104336i
$749$	5.97818	+	2.17588i	0.218438	+	0.0795049i
$750$		0			0
$751$	−40.5276	−	34.0067i	−1.47887	−	1.24092i	−0.907379	−	0.420314i	$-0.861920\pi$
$751$	−40.5276	−	34.0067i	−1.47887	−	1.24092i	−0.571493	−	0.820607i	$-0.693635\pi$
$752$	−12.6270	+	4.59586i	−0.460460	+	0.167594i
$753$		0			0
$754$	0.974470	+	5.52649i	0.0354881	+	0.201263i
$755$	26.4561			0.962834
$756$		0			0
$757$	−41.4858			−1.50783			−0.753913	−	0.656975i	$-0.771836\pi$
$757$	−41.4858			−1.50783			−0.753913	+	0.656975i	$0.771836\pi$
$758$	4.89890	+	27.7830i	0.177936	+	1.00913i
$759$		0			0
$760$	−30.3460	+	11.0450i	−1.10077	+	0.400646i
$761$	−34.7688	−	29.1745i	−1.26037	−	1.05757i	−0.995643	−	0.0932500i	$-0.970274\pi$
$761$	−34.7688	−	29.1745i	−1.26037	−	1.05757i	−0.264725	−	0.964324i	$-0.585281\pi$
$762$		0			0
$763$	20.2995	+	7.38841i	0.734890	+	0.267478i
$764$	−0.463326	−	0.802503i	−0.0167625	−	0.0290336i
$765$		0			0
$766$	2.76945	−	4.79682i	0.100064	−	0.173316i
$767$	18.1609	−	15.2388i	0.655752	−	0.550242i
$768$		0			0
$769$	0.888470	−	5.03876i	0.0320391	−	0.181703i	−0.964589	−	0.263759i	$-0.915038\pi$
$769$	0.888470	−	5.03876i	0.0320391	−	0.181703i	0.996628	+	0.0820564i	$0.0261488\pi$
$770$	5.54189	−	31.4296i	0.199716	−	1.13264i
$771$		0			0
$772$	2.52893	−	2.12203i	0.0910183	−	0.0763734i
$773$	26.3214	−	45.5899i	0.946713	−	1.63976i	0.194430	−	0.980916i	$-0.437714\pi$
$773$	26.3214	−	45.5899i	0.946713	−	1.63976i	0.752284	−	0.658839i	$-0.228952\pi$
$774$		0			0
$775$	−0.667556	−	1.15624i	−0.0239793	−	0.0415334i
$776$	0.721467	+	0.262593i	0.0258992	+	0.00942652i
$777$		0			0
$778$	17.6427	+	14.8040i	0.632523	+	0.530750i
$779$	−30.5758	+	11.1287i	−1.09549	+	0.398726i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.233956 + 1.32683i) q^{2} +(0.173648 - 0.0632028i) q^{4} +(1.26604 + 1.06234i) q^{5} +(-2.26604 - 0.824773i) q^{7} +(1.47178 + 2.54920i) q^{8} +O(q^{10})\)	\(q+(0.233956 + 1.32683i) q^{2} +(0.173648 - 0.0632028i) q^{4} +(1.26604 + 1.06234i) q^{5} +(-2.26604 - 0.824773i) q^{7} +(1.47178 + 2.54920i) q^{8} +(-1.11334 + 1.92836i) q^{10} +(4.55303 - 3.82045i) q^{11} +(-0.560307 + 3.17766i) q^{13} +(0.564178 - 3.19961i) q^{14} +(-2.75490 + 2.31164i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(3.31908 + 5.74881i) q^{19} +(0.286989 + 0.104455i) q^{20} +(6.13429 + 5.14728i) q^{22} +(2.76604 - 1.00676i) q^{23} +(-0.393933 - 2.23411i) q^{25} -4.34730 q^{26} -0.445622 q^{28} +(-0.224155 - 1.27125i) q^{29} +(0.553033 - 0.201288i) q^{31} +(0.798133 + 0.669713i) q^{32} +(-3.79813 - 1.38241i) q^{34} +(-1.99273 - 3.45150i) q^{35} +(-0.0209445 + 0.0362770i) q^{37} +(-6.85117 + 5.74881i) q^{38} +(-0.844770 + 4.79093i) q^{40} +(-0.851167 + 4.82721i) q^{41} +(-3.97178 + 3.33272i) q^{43} +(0.549163 - 0.951178i) q^{44} +(1.98293 + 3.43453i) q^{46} +(3.51114 + 1.27795i) q^{47} +(-0.907604 - 0.761570i) q^{49} +(2.87211 - 1.04536i) q^{50} +(0.103541 + 0.587208i) q^{52} +11.6382 q^{53} +9.82295 q^{55} +(-1.23261 - 6.99049i) q^{56} +(1.63429 - 0.594831i) q^{58} +(-5.62836 - 4.72275i) q^{59} +(-10.3833 - 3.77920i) q^{61} +(0.396459 + 0.686688i) q^{62} +(-4.29813 + 7.44459i) q^{64} +(-4.08512 + 3.42782i) q^{65} +(0.322481 - 1.82888i) q^{67} +(-0.0962667 + 0.545955i) q^{68} +(4.11334 - 3.45150i) q^{70} +(2.75624 - 4.77396i) q^{71} +(-2.77719 - 4.81023i) q^{73} +(-0.0530334 - 0.0193026i) q^{74} +(0.939693 + 0.788496i) q^{76} +(-13.4684 + 4.90209i) q^{77} +(-0.656574 - 3.72362i) q^{79} -5.94356 q^{80} -6.60401 q^{82} +(0.692066 + 3.92490i) q^{83} +(-4.65910 + 1.69577i) q^{85} +(-5.35117 - 4.49016i) q^{86} +(16.4402 + 5.98373i) q^{88} +(-4.07532 - 7.05866i) q^{89} +(3.89053 - 6.73859i) q^{91} +(0.416689 - 0.349643i) q^{92} +(-0.874171 + 4.95767i) q^{94} +(-1.90508 + 10.8042i) q^{95} +(0.199807 - 0.167658i) q^{97} +(0.798133 - 1.38241i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 3 * q^5 - 9 * q^7 - 6 * q^8	\( 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8} + 15 q^{11} - 9 q^{13} - 15 q^{14} - 18 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} + 27 q^{22} + 12 q^{23} - 27 q^{25} - 24 q^{26} - 24 q^{28} - 3 q^{29} - 9 q^{31} - 9 q^{32} - 9 q^{34} + 6 q^{35} + 3 q^{37} - 15 q^{38} - 18 q^{40} + 21 q^{41} - 9 q^{43} + 15 q^{44} - 9 q^{46} + 15 q^{47} - 9 q^{49} - 12 q^{50} - 9 q^{52} + 36 q^{53} + 18 q^{55} - 21 q^{56} + 3 q^{59} - 27 q^{61} + 12 q^{62} - 12 q^{64} - 3 q^{65} + 27 q^{67} + 27 q^{68} + 18 q^{70} + 9 q^{71} - 6 q^{73} + 12 q^{74} - 24 q^{77} + 18 q^{79} - 6 q^{80} + 36 q^{82} + 15 q^{83} + 9 q^{85} - 6 q^{86} + 27 q^{88} + 6 q^{91} - 51 q^{92} - 27 q^{94} - 30 q^{95} - 36 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 3 * q^5 - 9 * q^7 - 6 * q^8 + 15 * q^11 - 9 * q^13 - 15 * q^14 - 18 * q^16 - 9 * q^17 + 3 * q^19 - 6 * q^20 + 27 * q^22 + 12 * q^23 - 27 * q^25 - 24 * q^26 - 24 * q^28 - 3 * q^29 - 9 * q^31 - 9 * q^32 - 9 * q^34 + 6 * q^35 + 3 * q^37 - 15 * q^38 - 18 * q^40 + 21 * q^41 - 9 * q^43 + 15 * q^44 - 9 * q^46 + 15 * q^47 - 9 * q^49 - 12 * q^50 - 9 * q^52 + 36 * q^53 + 18 * q^55 - 21 * q^56 + 3 * q^59 - 27 * q^61 + 12 * q^62 - 12 * q^64 - 3 * q^65 + 27 * q^67 + 27 * q^68 + 18 * q^70 + 9 * q^71 - 6 * q^73 + 12 * q^74 - 24 * q^77 + 18 * q^79 - 6 * q^80 + 36 * q^82 + 15 * q^83 + 9 * q^85 - 6 * q^86 + 27 * q^88 + 6 * q^91 - 51 * q^92 - 27 * q^94 - 30 * q^95 - 36 * q^97 - 9 * q^98

Introduction

L-functions

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