LMFDB - Embedded newform 729.2.e.a.649.1

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:	$1$
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			649.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.a.82.1

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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	0.783187	+	0.621786i	$0.213593\pi$
$2$	−0.233956	+	1.32683i	−0.165432	+	0.938209i	−0.948618	+	0.316423i	$0.897518\pi$
$3$		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	$-0.842712\pi$
$5$	−1.26604	+	1.06234i	−0.566192	+	0.475092i	0.314188	+	0.949361i	$0.398268\pi$
$6$		0			0
$7$	−2.26604	+	0.824773i	−0.856484	+	0.311735i	−0.732681	−	0.680572i	$-0.761731\pi$
$7$	−2.26604	+	0.824773i	−0.856484	+	0.311735i	−0.123803	+	0.992307i	$0.539509\pi$
$8$	−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	−0.971795	−	0.235829i	$-0.924219\pi$
$11$	−4.55303	−	3.82045i	−1.37279	−	1.15191i	−0.400997	−	0.916080i	$-0.631336\pi$
$12$		0			0
$13$	−0.560307	−	3.17766i	−0.155401	−	0.881325i	−0.958418	−	0.285368i	$-0.907884\pi$
$13$	−0.560307	−	3.17766i	−0.155401	−	0.881325i	0.803017	−	0.595957i	$-0.203227\pi$
$14$	−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	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	3.31908	−	5.74881i	0.761449	−	1.31887i	−0.180655	−	0.983547i	$-0.557822\pi$
$19$	3.31908	−	5.74881i	0.761449	−	1.31887i	0.942104	−	0.335321i	$-0.108845\pi$
$20$	−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	$-0.488176\pi$
$23$	−2.76604	−	1.00676i	−0.576760	−	0.209924i	−0.613896	+	0.789387i	$0.710399\pi$
$24$		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	$-0.906202\pi$
$29$	0.224155	−	1.27125i	0.0416246	−	0.236065i	0.998521	+	0.0543640i	$0.0173131\pi$
$30$		0			0
$31$	0.553033	+	0.201288i	0.0993277	+	0.0361523i	0.391206	−	0.920303i	$-0.372058\pi$
$31$	0.553033	+	0.201288i	0.0993277	+	0.0361523i	−0.291878	+	0.956455i	$0.594280\pi$
$32$	−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	0.864299	−	0.502979i	$-0.167763\pi$
$37$	−0.0209445	−	0.0362770i	−0.00344326	−	0.00596390i	−0.867742	+	0.497015i	$0.834429\pi$
$38$	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	0.976279	+	0.216517i	$0.0694696\pi$
$41$	0.851167	+	4.82721i	0.132930	+	0.753883i	−0.843349	+	0.537366i	$0.819419\pi$
$42$		0			0
$43$	−3.97178	−	3.33272i	−0.605691	−	0.508235i	0.287578	−	0.957757i	$-0.407150\pi$
$43$	−3.97178	−	3.33272i	−0.605691	−	0.508235i	−0.893269	+	0.449522i	$0.851594\pi$
$44$	−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	$-0.698965\pi$
$47$	−3.51114	+	1.27795i	−0.512153	+	0.186408i	0.0729991	+	0.997332i	$0.476743\pi$
$48$		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	$-0.794802\pi$
$53$	−11.6382			−1.59862			−0.799312	+	0.600916i	$0.794802\pi$
$54$		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	$-0.563487\pi$
$59$	5.62836	−	4.72275i	0.732749	−	0.614850i	0.930880	+	0.365326i	$0.119042\pi$
$60$		0			0
$61$	−10.3833	+	3.77920i	−1.32944	+	0.483876i	−0.906471	−	0.422268i	$-0.861234\pi$
$61$	−10.3833	+	3.77920i	−1.32944	+	0.483876i	−0.422969	+	0.906144i	$0.639012\pi$
$62$	−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	0.998149	−	0.0608104i	$-0.0193685\pi$
$67$	0.322481	+	1.82888i	0.0393974	+	0.223434i	−0.958752	+	0.284244i	$0.908257\pi$
$68$	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	$-0.272740\pi$
$71$	−2.75624	−	4.77396i	−0.327106	−	0.566564i	−0.981936	+	0.189212i	$0.939407\pi$
$72$		0			0
$73$	−2.77719	+	4.81023i	−0.325045	+	0.562995i	−0.981522	−	0.191352i	$-0.938713\pi$
$73$	−2.77719	+	4.81023i	−0.325045	+	0.562995i	0.656476	+	0.754347i	$0.272046\pi$
$74$	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	0.925338	+	0.379144i	$0.123782\pi$
$79$	−0.656574	+	3.72362i	−0.0738704	+	0.418940i	−0.999208	+	0.0397952i	$0.987329\pi$
$80$	5.94356			0.664511
$81$		0			0
$82$	−6.60401			−0.729291
$83$	−0.692066	+	3.92490i	−0.0759642	+	0.430814i	0.922979	+	0.384850i	$0.125747\pi$
$83$	−0.692066	+	3.92490i	−0.0759642	+	0.430814i	−0.998943	+	0.0459637i	$0.985364\pi$
$84$		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	$-0.691147\pi$
$89$	4.07532	−	7.05866i	0.431983	−	0.748217i	0.997044	+	0.0768323i	$0.0244806\pi$
$90$		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	0.652875	−	0.757466i	$-0.273563\pi$
$97$	0.199807	+	0.167658i	0.0202874	+	0.0170231i	−0.632588	+	0.774489i	$0.718007\pi$
$98$	−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	$-0.426260\pi$
$101$	10.3623	−	3.77157i	1.03109	−	0.375286i	0.801495	+	0.598001i	$0.204038\pi$
$102$		0			0
$103$	−2.99273	+	2.51120i	−0.294882	+	0.247435i	−0.778210	−	0.628004i	$-0.783872\pi$
$103$	−2.99273	+	2.51120i	−0.294882	+	0.247435i	0.483328	+	0.875439i	$0.339428\pi$
$104$	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	$-0.459298\pi$
$107$	2.63816			0.255040			0.127520	+	0.991836i	$0.459298\pi$
$108$		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	$-0.991802\pi$
$113$	−12.2023	+	10.2390i	−1.14790	+	0.963202i	−0.148231	+	0.988953i	$0.547358\pi$
$114$		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	−0.934710	−	0.355412i	$-0.884340\pi$
$127$	−1.79813	+	3.11446i	−0.159559	+	0.276363i	0.775151	+	0.631776i	$0.217674\pi$
$128$	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	$-0.670410\pi$
$131$	−16.6395	−	6.05628i	−1.45380	−	0.529140i	−0.943650	+	0.330946i	$0.892632\pi$
$132$		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	$-0.890766\pi$
$137$	0.682266	−	3.86932i	0.0582899	−	0.330579i	0.999983	+	0.00589552i	$0.00187661\pi$
$138$		0			0
$139$	−11.2442	−	4.09256i	−0.953723	−	0.347127i	−0.182152	−	0.983270i	$-0.558306\pi$
$139$	−11.2442	−	4.09256i	−0.953723	−	0.347127i	−0.771571	+	0.636144i	$0.780529\pi$
$140$	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	−0.679195	−	0.733958i	$-0.737671\pi$
$149$	−3.56418	−	20.2135i	−0.291989	−	1.65595i	0.387206	−	0.921993i	$-0.373440\pi$
$150$		0			0
$151$	12.2626	+	10.2896i	0.997920	+	0.837354i	0.986695	−	0.162583i	$-0.0519825\pi$
$151$	12.2626	+	10.2896i	0.997920	+	0.837354i	0.0112247	+	0.999937i	$0.496427\pi$
$152$	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	−0.362661	+	0.931921i	$0.618132\pi$
$157$	−16.8327	+	14.1244i	−1.34340	+	1.12725i	−0.980739	+	0.195325i	$0.937424\pi$
$158$	−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	$-0.775313\pi$
$167$	−3.28699	+	2.75811i	−0.254355	+	0.213429i	0.506690	+	0.862128i	$0.330869\pi$
$168$		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	$-0.323834\pi$
$173$	−2.90554	−	2.43804i	−0.220904	−	0.185361i	−0.746523	+	0.665359i	$0.768278\pi$
$174$		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	$-0.0665718\pi$
$179$	4.13816	+	7.16750i	0.309300	+	0.535724i	−0.668909	+	0.743344i	$0.733239\pi$
$180$		0			0
$181$	−3.36097	+	5.82137i	−0.249819	+	0.432699i	−0.963475	−	0.267797i	$-0.913704\pi$
$181$	−3.36097	+	5.82137i	−0.249819	+	0.432699i	0.713657	+	0.700496i	$0.247038\pi$
$182$	−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	−0.936962	−	0.349430i	$-0.886375\pi$
$191$	0.870767	−	4.93837i	0.0630065	−	0.357328i	0.999969	−	0.00789719i	$-0.00251378\pi$
$192$		0			0
$193$	16.7875	+	6.11013i	1.20839	+	0.439817i	0.866144	−	0.499794i	$-0.166591\pi$
$193$	16.7875	+	6.11013i	1.20839	+	0.439817i	0.342243	+	0.939611i	$0.388813\pi$
$194$	−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	$-0.825126\pi$
$197$	0.361844	−	0.626733i	0.0257803	−	0.0446529i	0.878628	+	0.477507i	$0.158460\pi$
$198$		0			0
$199$	5.09627	+	8.82699i	0.361265	+	0.625729i	0.988169	−	0.153367i	$-0.0490117\pi$
$199$	5.09627	+	8.82699i	0.361265	+	0.625729i	−0.626905	+	0.779096i	$0.715678\pi$
$200$	−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	−0.944233	−	0.329278i	$-0.893195\pi$
$211$	−11.3871	+	9.55493i	−0.783922	+	0.657789i	0.160311	+	0.987067i	$0.448750\pi$
$212$	−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	0.0262688	−	0.999655i	$-0.491637\pi$
$223$	10.2883	−	3.74465i	0.688958	−	0.250760i	0.662689	+	0.748895i	$0.269415\pi$
$224$	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	$-0.0826991\pi$
$227$	13.2777	+	11.1413i	0.881269	+	0.739472i	−0.0851707	+	0.996366i	$0.527144\pi$
$228$		0			0
$229$	0.271259	+	1.53839i	0.0179253	+	0.101659i	0.992458	−	0.122587i	$-0.0391191\pi$
$229$	0.271259	+	1.53839i	0.0179253	+	0.101659i	−0.974532	+	0.224246i	$0.928008\pi$
$230$	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	0.998278	+	0.0586545i	$0.0186810\pi$
$233$	8.39440	+	14.5395i	0.549935	+	0.952516i	−0.448343	+	0.893862i	$0.647986\pi$
$234$		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	$-0.430486\pi$
$239$	−3.78611	−	1.37803i	−0.244903	−	0.0891375i	−0.461555	+	0.887111i	$0.652708\pi$
$240$		0			0
$241$	−0.582129	+	3.30142i	−0.0374982	+	0.212663i	−0.997800	−	0.0663015i	$-0.978880\pi$
$241$	−0.582129	+	3.30142i	−0.0374982	+	0.212663i	0.960301	+	0.278965i	$0.0899912\pi$
$242$	−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	0.225987	+	0.974130i	$0.427439\pi$
$251$	−11.5753	+	20.0490i	−0.730628	+	1.26548i	−0.956615	+	0.291354i	$0.905894\pi$
$252$		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	−0.978134	−	0.207977i	$-0.933312\pi$
$257$	−2.08600	−	11.8303i	−0.130121	−	0.737953i	0.848013	−	0.529976i	$-0.177799\pi$
$258$		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	$-0.436633\pi$
$263$	15.8824	−	5.78071i	0.979349	−	0.356454i	0.781587	+	0.623796i	$0.214410\pi$
$264$		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	$-0.422434\pi$
$269$	7.91447			0.482554			0.241277	+	0.970456i	$0.422434\pi$
$270$		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	−0.954112	−	0.299451i	$-0.903197\pi$
$277$	−24.8405	+	9.04120i	−1.49252	+	0.543233i	−0.538409	+	0.842684i	$0.680974\pi$
$278$	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	$-0.0860364\pi$
$281$	14.5517	+	12.2103i	0.868081	+	0.728406i	−0.0956121	+	0.995419i	$0.530481\pi$
$282$		0			0
$283$	−2.88026	−	16.3348i	−0.171214	−	0.971002i	−0.942424	−	0.334421i	$-0.891459\pi$
$283$	−2.88026	−	16.3348i	−0.171214	−	0.971002i	0.771210	−	0.636581i	$-0.219652\pi$
$284$	−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	$-0.197593\pi$
$293$	18.1903	+	6.62073i	1.06269	+	0.386787i	0.249251	+	0.968439i	$0.419815\pi$
$294$		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	−0.993726	−	0.111844i	$-0.964324\pi$
$307$	−10.4029	−	18.0183i	−0.593722	−	1.02836i	0.400003	−	0.916514i	$-0.369009\pi$
$308$	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	0.991212	+	0.132280i	$0.0422297\pi$
$311$	1.85204	+	10.5035i	0.105020	+	0.595597i	−0.886193	+	0.463317i	$0.846659\pi$
$312$		0			0
$313$	2.92262	+	2.45237i	0.165196	+	0.138616i	0.721638	−	0.692270i	$-0.243389\pi$
$313$	2.92262	+	2.45237i	0.165196	+	0.138616i	−0.556442	+	0.830886i	$0.687834\pi$
$314$	−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	$-0.345424\pi$
$317$	24.7977	−	9.02563i	1.39278	−	0.506930i	0.926027	+	0.377458i	$0.123202\pi$
$318$		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	−0.301114	−	0.953588i	$-0.597358\pi$
$331$	1.47683	−	0.537524i	0.0811741	−	0.0295450i	0.382288	+	0.924043i	$0.375136\pi$
$332$	−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	−0.998963	−	0.0455394i	$-0.985499\pi$
$337$	−1.39187	−	7.89371i	−0.0758202	−	0.429998i	0.923142	−	0.384458i	$-0.125612\pi$
$338$	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	$-0.210076\pi$
$347$	18.6484	+	6.78747i	1.00110	+	0.364371i	0.211091	+	0.977466i	$0.432298\pi$
$348$		0			0
$349$	1.92633	−	10.9247i	0.103114	−	0.584788i	−0.888843	−	0.458212i	$-0.848490\pi$
$349$	1.92633	−	10.9247i	0.103114	−	0.584788i	0.991957	−	0.126576i	$-0.0403988\pi$
$350$	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	$-0.920161\pi$
$353$	0.497312	−	2.82039i	0.0264692	−	0.150114i	0.995178	+	0.0980859i	$0.0312720\pi$
$354$		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	−0.183292	−	0.983058i	$-0.558676\pi$
$359$	14.3944	−	24.9318i	0.759707	−	1.31585i	0.943000	−	0.332793i	$-0.107991\pi$
$360$		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	0.395991	−	0.918254i	$-0.370401\pi$
$367$	−8.42056	−	7.06569i	−0.439550	−	0.368826i	−0.835541	+	0.549428i	$0.814846\pi$
$368$	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	0.339992	−	0.940428i	$-0.389576\pi$
$373$	25.5933	−	21.4754i	1.32517	−	1.11195i	0.985180	−	0.171523i	$-0.0548689\pi$
$374$	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	$-0.688727\pi$
$383$	3.14930	−	2.64258i	0.160922	−	0.135029i	0.719693	+	0.694292i	$0.244283\pi$
$384$		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	$-0.420448\pi$
$389$	−13.0949	−	10.9879i	−0.663939	−	0.557111i	−0.911265	+	0.411822i	$0.864893\pi$
$390$		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	0.435146	+	0.900360i	$0.356697\pi$
$397$	−11.2010	+	19.4007i	−0.562162	+	0.973692i	−0.997308	+	0.0733324i	$0.976637\pi$
$398$	−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	$-0.507508\pi$
$401$	−13.7023	−	4.98724i	−0.684262	−	0.249051i	−0.660676	+	0.750671i	$0.729730\pi$
$402$		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	0.714975	−	0.699150i	$-0.246438\pi$
$409$	16.4474	+	5.98638i	0.813273	+	0.296007i	0.0982980	+	0.995157i	$0.468660\pi$
$410$	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	−0.954059	−	0.299619i	$-0.903140\pi$
$419$	−3.27538	−	18.5756i	−0.160013	−	0.907477i	0.794046	−	0.607858i	$-0.207971\pi$
$420$		0			0
$421$	−24.7690	−	20.7837i	−1.20717	−	1.01294i	−0.999396	−	0.0347581i	$-0.988934\pi$
$421$	−24.7690	−	20.7837i	−1.20717	−	1.01294i	−0.207773	−	0.978177i	$-0.566622\pi$
$422$	−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	$-0.809662\pi$
$431$	−34.3164			−1.65297			−0.826483	+	0.562962i	$0.809662\pi$
$432$		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	0.235653	−	0.971837i	$-0.424277\pi$
$439$	21.8084	−	7.93761i	1.04086	−	0.378841i	0.805205	+	0.592996i	$0.202055\pi$
$440$	−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	$-0.246562\pi$
$443$	3.15729	+	2.64928i	0.150007	+	0.125871i	−0.564695	+	0.825299i	$0.691006\pi$
$444$		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	$-0.0241949\pi$
$449$	9.17071	+	15.8841i	0.432793	+	0.749619i	−0.564320	+	0.825556i	$0.690862\pi$
$450$		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	0.797834	+	0.602877i	$0.205979\pi$
$457$	−3.37939	+	19.1654i	−0.158081	+	0.896522i	−0.955915	+	0.293644i	$0.905132\pi$
$458$	−2.10464			−0.0983432
$459$		0			0
$460$	0.898986			0.0419154
$461$	−4.81861	+	27.3277i	−0.224425	+	1.27278i	0.639356	+	0.768911i	$0.279201\pi$
$461$	−4.81861	+	27.3277i	−0.224425	+	1.27278i	−0.863781	+	0.503867i	$0.831910\pi$
$462$		0			0
$463$	−36.3530	−	13.2314i	−1.68947	−	0.614915i	−0.694908	−	0.719099i	$-0.744555\pi$
$463$	−36.3530	−	13.2314i	−1.68947	−	0.614915i	−0.994558	+	0.104183i	$0.966777\pi$
$464$	−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	−0.283621	−	0.958936i	$-0.591536\pi$
$467$	14.8819	−	25.7762i	0.688653	−	1.19278i	0.972274	−	0.233845i	$-0.0751309\pi$
$468$		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	$-0.941103\pi$
$479$	−35.4038	+	12.8859i	−1.61764	+	0.588773i	−0.634710	+	0.772750i	$0.718880\pi$
$480$		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	$-0.718646\pi$
$491$	0.381445	−	0.320070i	0.0172144	−	0.0144446i	0.651354	+	0.758774i	$0.274201\pi$
$492$		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	0.999621	+	0.0275190i	$0.00876067\pi$
$499$	1.55690	+	8.82964i	0.0696966	+	0.395269i	−0.929925	+	0.367750i	$0.880128\pi$
$500$	−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	$-0.0324197\pi$
$503$	9.18092	+	15.9018i	0.409357	+	0.709027i	−0.585461	+	0.810701i	$0.699086\pi$
$504$		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	$-0.605322\pi$
$509$	−26.6596	−	9.70329i	−1.18166	−	0.430091i	−0.856790	+	0.515666i	$0.827544\pi$
$510$		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	0.248026	+	0.968753i	$0.420218\pi$
$521$	−16.3191	+	28.2655i	−0.714952	+	1.23833i	−0.962978	+	0.269580i	$0.913115\pi$
$522$		0			0
$523$	11.0116	+	19.0727i	0.481504	+	0.833990i	0.999775	−	0.0212271i	$-0.00675730\pi$
$523$	11.0116	+	19.0727i	0.481504	+	0.833990i	−0.518271	+	0.855217i	$0.673424\pi$
$524$	−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	0.273731	−	0.961806i	$-0.411742\pi$
$547$	25.7656	−	9.37792i	1.10166	−	0.400971i	0.827928	+	0.560835i	$0.189520\pi$
$548$	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	0.988943	+	0.148298i	$0.0473794\pi$
$557$	14.7010	+	25.4629i	0.622901	+	1.07890i	−0.366042	+	0.930598i	$0.619287\pi$
$558$		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	$-0.459016\pi$
$563$	−9.74510	−	3.54693i	−0.410707	−	0.149485i	−0.539107	+	0.842237i	$0.681238\pi$
$564$		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	−0.591805	−	0.806081i	$-0.701584\pi$
$569$	5.72503	−	32.4683i	0.240006	−	1.36114i	0.831811	−	0.555060i	$-0.187305\pi$
$570$		0			0
$571$	0.692944	+	0.252211i	0.0289988	+	0.0105547i	0.356479	−	0.934303i	$-0.383977\pi$
$571$	0.692944	+	0.252211i	0.0289988	+	0.0105547i	−0.327480	+	0.944858i	$0.606199\pi$
$572$	−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	0.591409	−	0.806371i	$-0.298572\pi$
$577$	−9.67159	−	16.7517i	−0.402634	−	0.697382i	−0.994043	+	0.108990i	$0.965238\pi$
$578$	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	$-0.839952\pi$
$587$	−29.9876	+	10.9146i	−1.23772	+	0.450493i	−0.361485	+	0.932378i	$0.617730\pi$
$588$		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	$-0.725414\pi$
$593$	−31.6783			−1.30087			−0.650436	+	0.759561i	$0.725414\pi$
$594$		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	$-0.639194\pi$
$599$	9.67024	−	8.11430i	0.395115	−	0.331541i	0.818602	+	0.574361i	$0.194749\pi$
$600$		0			0
$601$	8.37123	−	3.04688i	0.341470	−	0.124285i	−0.165592	−	0.986194i	$-0.552954\pi$
$601$	8.37123	−	3.04688i	0.341470	−	0.124285i	0.507062	+	0.861909i	$0.330731\pi$
$602$	−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	−0.845822	−	0.533465i	$-0.820890\pi$
$607$	−5.75196	−	32.6210i	−0.233465	−	1.32405i	0.612357	−	0.790581i	$-0.290221\pi$
$608$	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	−0.987466	−	0.157833i	$-0.949549\pi$
$613$	−8.84002	+	15.3114i	−0.357045	+	0.618420i	0.630421	+	0.776254i	$0.282882\pi$
$614$	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	$-0.562202\pi$
$617$	−24.1805	−	8.80099i	−0.973471	−	0.354314i	−0.779298	+	0.626653i	$0.784424\pi$
$618$		0			0
$619$	4.82651	−	27.3725i	0.193994	−	1.10019i	−0.719850	−	0.694129i	$-0.755790\pi$
$619$	4.82651	−	27.3725i	0.193994	−	1.10019i	0.913844	−	0.406065i	$-0.133099\pi$
$620$	−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	−0.999224	−	0.0393842i	$-0.987460\pi$
$631$	−13.4069	−	23.2214i	−0.533720	−	0.924430i	0.465504	−	0.885046i	$-0.345873\pi$
$632$	−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	$-0.530476\pi$
$641$	11.9251	−	4.34040i	0.471015	−	0.171435i	0.566612	+	0.823985i	$0.308254\pi$
$642$		0			0
$643$	11.8558	−	9.94816i	0.467545	−	0.392317i	−0.378353	−	0.925661i	$-0.623509\pi$
$643$	11.8558	−	9.94816i	0.467545	−	0.392317i	0.845898	+	0.533344i	$0.179065\pi$
$644$	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	$-0.570341\pi$
$647$	−11.1506			−0.438377			−0.219189	+	0.975683i	$0.570341\pi$
$648$		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	−0.354323	+	0.935123i	$0.615289\pi$
$653$	−34.1596	+	28.6633i	−1.33677	+	1.12168i	−0.982444	+	0.186558i	$0.940267\pi$
$654$		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	$-0.189245\pi$
$659$	10.7986	+	9.06110i	0.420654	+	0.352970i	−0.407758	+	0.913090i	$0.633689\pi$
$660$		0			0
$661$	6.27126	+	35.5661i	0.243924	+	1.38336i	0.822979	+	0.568072i	$0.192310\pi$
$661$	6.27126	+	35.5661i	0.243924	+	1.38336i	−0.579055	+	0.815288i	$0.696578\pi$
$662$	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	−0.976384	−	0.216044i	$-0.930685\pi$
$673$	0.389348	−	2.20810i	0.0150082	−	0.0851160i	0.991392	+	0.130928i	$0.0417957\pi$
$674$	10.7992			0.415971
$675$		0			0
$676$	0.478340			0.0183977
$677$	−6.10829	+	34.6418i	−0.234761	+	1.33139i	0.608357	+	0.793664i	$0.291829\pi$
$677$	−6.10829	+	34.6418i	−0.234761	+	1.33139i	−0.843117	+	0.537730i	$0.819282\pi$
$678$		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	$-0.943712\pi$
$683$	−8.88191	+	15.3839i	−0.339857	+	0.588649i	0.644549	+	0.764563i	$0.277045\pi$
$684$		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	−0.992805	−	0.119743i	$-0.961793\pi$
$691$	−33.7294	−	28.3023i	−1.28313	−	1.07667i	−0.290323	−	0.956929i	$-0.593763\pi$
$692$	−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	$-0.307512\pi$
$701$	30.1052			1.13706			0.568530	+	0.822663i	$0.307512\pi$
$702$		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	0.133622	−	0.991032i	$-0.457339\pi$
$709$	23.2456	−	8.46069i	0.873006	−	0.317748i	0.739384	+	0.673284i	$0.235117\pi$
$710$	−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	−0.911378	−	0.411570i	$-0.864980\pi$
$719$	−21.7763	−	37.7177i	−0.812119	−	1.40663i	0.0992586	−	0.995062i	$-0.468353\pi$
$720$		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	−0.844461	−	0.535617i	$-0.820079\pi$
$727$	3.56624	−	20.2251i	0.132264	−	0.750109i	0.976726	−	0.214492i	$-0.0688096\pi$
$728$	−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	0.0873183	−	0.996180i	$-0.472170\pi$
$733$	−13.1613	−	4.79033i	−0.486125	−	0.176935i	−0.573443	+	0.819246i	$0.694393\pi$
$734$	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	0.936380	+	0.350987i	$0.114154\pi$
$739$	20.9907	+	36.3569i	0.772154	+	1.33741i	−0.164226	+	0.986423i	$0.552513\pi$
$740$	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	−0.935222	−	0.354061i	$-0.884801\pi$
$743$	−4.83821	−	27.4389i	−0.177497	−	1.00663i	0.757726	−	0.652573i	$-0.226311\pi$
$744$		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	−0.571493	+	0.820607i	$0.693635\pi$
$751$	−40.5276	+	34.0067i	−1.47887	+	1.24092i	−0.907379	+	0.420314i	$0.861920\pi$
$752$	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	0.264725	−	0.964324i	$-0.414719\pi$
$761$	34.7688	−	29.1745i	1.26037	−	1.05757i	0.995643	−	0.0932500i	$-0.0297256\pi$
$762$		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	0.996628	−	0.0820564i	$-0.0261488\pi$
$769$	0.888470	+	5.03876i	0.0320391	+	0.181703i	−0.964589	+	0.263759i	$0.915038\pi$
$770$	−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	−0.752284	−	0.658839i	$-0.771048\pi$
$773$	−26.3214	−	45.5899i	−0.946713	−	1.63976i	−0.194430	−	0.980916i	$-0.562286\pi$
$774$		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
$780$

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

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