LMFDB - Embedded newform 729.2.e.a.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:	$1$
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			82.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.a.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	$-0.897518\pi$
$2$	−0.233956	−	1.32683i	−0.165432	−	0.938209i	0.783187	−	0.621786i	$-0.213593\pi$
$3$		0			0
$3$		0			0
$4$	0.173648	−	0.0632028i	0.0868241	−	0.0316014i
$5$	−1.26604	−	1.06234i	−0.566192	−	0.475092i	0.314188	−	0.949361i	$-0.398268\pi$
$5$	−1.26604	−	1.06234i	−0.566192	−	0.475092i	−0.880380	+	0.474269i	$0.842712\pi$
$6$		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	$0.631336\pi$
$11$	−4.55303	+	3.82045i	−1.37279	+	1.15191i	−0.971795	+	0.235829i	$0.924219\pi$
$12$		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	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		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	−0.613896	−	0.789387i	$-0.710399\pi$
$23$	−2.76604	+	1.00676i	−0.576760	+	0.209924i	0.0371361	+	0.999310i	$0.488176\pi$
$24$		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	0.998521	−	0.0543640i	$-0.0173131\pi$
$29$	0.224155	+	1.27125i	0.0416246	+	0.236065i	−0.956897	+	0.290429i	$0.906202\pi$
$30$		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	$-0.819419\pi$
$41$	0.851167	−	4.82721i	0.132930	−	0.753883i	0.976279	−	0.216517i	$-0.0694696\pi$
$42$		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	0.0729991	−	0.997332i	$-0.476743\pi$
$47$	−3.51114	−	1.27795i	−0.512153	−	0.186408i	−0.585152	+	0.810924i	$0.698965\pi$
$48$		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	0.930880	−	0.365326i	$-0.119042\pi$
$59$	5.62836	+	4.72275i	0.732749	+	0.614850i	−0.198130	+	0.980176i	$0.563487\pi$
$60$		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	−0.981936	−	0.189212i	$-0.939407\pi$
$71$	−2.75624	+	4.77396i	−0.327106	+	0.566564i	0.654830	+	0.755776i	$0.272740\pi$
$72$		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	$-0.985364\pi$
$83$	−0.692066	−	3.92490i	−0.0759642	−	0.430814i	0.922979	−	0.384850i	$-0.125747\pi$
$84$		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	0.997044	−	0.0768323i	$-0.0244806\pi$
$89$	4.07532	+	7.05866i	0.431983	+	0.748217i	−0.565061	+	0.825049i	$0.691147\pi$
$90$		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	0.801495	−	0.598001i	$-0.204038\pi$
$101$	10.3623	+	3.77157i	1.03109	+	0.375286i	0.229593	+	0.973287i	$0.426260\pi$
$102$		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	$-0.459298\pi$
$107$	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	−0.148231	−	0.988953i	$-0.547358\pi$
$113$	−12.2023	−	10.2390i	−1.14790	−	0.963202i	−0.999668	+	0.0257512i	$0.991802\pi$
$114$		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	−0.943650	−	0.330946i	$-0.892632\pi$
$131$	−16.6395	+	6.05628i	−1.45380	+	0.529140i	−0.510150	+	0.860085i	$0.670410\pi$
$132$		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	0.999983	−	0.00589552i	$-0.00187661\pi$
$137$	0.682266	+	3.86932i	0.0582899	+	0.330579i	−0.941693	+	0.336474i	$0.890766\pi$
$138$		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	$0.373440\pi$
$149$	−3.56418	+	20.2135i	−0.291989	+	1.65595i	−0.679195	+	0.733958i	$0.737671\pi$
$150$		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	0.506690	−	0.862128i	$-0.330869\pi$
$167$	−3.28699	−	2.75811i	−0.254355	−	0.213429i	−0.761045	+	0.648699i	$0.775313\pi$
$168$		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	−0.746523	−	0.665359i	$-0.768278\pi$
$173$	−2.90554	+	2.43804i	−0.220904	+	0.185361i	0.525619	+	0.850720i	$0.323834\pi$
$174$		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	−0.668909	−	0.743344i	$-0.733239\pi$
$179$	4.13816	−	7.16750i	0.309300	−	0.535724i	0.978209	+	0.207620i	$0.0665718\pi$
$180$		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	$0.00251378\pi$
$191$	0.870767	+	4.93837i	0.0630065	+	0.357328i	−0.936962	+	0.349430i	$0.886375\pi$
$192$		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	0.878628	−	0.477507i	$-0.158460\pi$
$197$	0.361844	+	0.626733i	0.0257803	+	0.0446529i	−0.852847	+	0.522160i	$0.825126\pi$
$198$		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	−0.0851707	−	0.996366i	$-0.527144\pi$
$227$	13.2777	−	11.1413i	0.881269	−	0.739472i	0.966440	+	0.256894i	$0.0826991\pi$
$228$		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	$-0.647986\pi$
$233$	8.39440	−	14.5395i	0.549935	−	0.952516i	0.998278	−	0.0586545i	$-0.0186810\pi$
$234$		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	−0.461555	−	0.887111i	$-0.652708\pi$
$239$	−3.78611	+	1.37803i	−0.244903	+	0.0891375i	0.216652	+	0.976249i	$0.430486\pi$
$240$		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	$-0.905894\pi$
$251$	−11.5753	−	20.0490i	−0.730628	−	1.26548i	0.225987	−	0.974130i	$-0.427439\pi$
$252$		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	$0.177799\pi$
$257$	−2.08600	+	11.8303i	−0.130121	+	0.737953i	−0.978134	+	0.207977i	$0.933312\pi$
$258$		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	0.781587	−	0.623796i	$-0.214410\pi$
$263$	15.8824	+	5.78071i	0.979349	+	0.356454i	0.197762	+	0.980250i	$0.436633\pi$
$264$		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	−0.538409	−	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	−0.0956121	−	0.995419i	$-0.530481\pi$
$281$	14.5517	−	12.2103i	0.868081	−	0.728406i	0.963693	+	0.267012i	$0.0860364\pi$
$282$		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	0.249251	−	0.968439i	$-0.419815\pi$
$293$	18.1903	−	6.62073i	1.06269	−	0.386787i	0.813438	+	0.581652i	$0.197593\pi$
$294$		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	$-0.846659\pi$
$311$	1.85204	−	10.5035i	0.105020	−	0.595597i	0.991212	−	0.132280i	$-0.0422297\pi$
$312$		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	0.926027	−	0.377458i	$-0.123202\pi$
$317$	24.7977	+	9.02563i	1.39278	+	0.506930i	0.466752	+	0.884388i	$0.345424\pi$
$318$		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	0.211091	−	0.977466i	$-0.432298\pi$
$347$	18.6484	−	6.78747i	1.00110	−	0.364371i	0.790009	+	0.613096i	$0.210076\pi$
$348$		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	0.995178	−	0.0980859i	$-0.0312720\pi$
$353$	0.497312	+	2.82039i	0.0264692	+	0.150114i	−0.968709	+	0.248200i	$0.920161\pi$
$354$		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	$0.107991\pi$
$359$	14.3944	+	24.9318i	0.759707	+	1.31585i	−0.183292	+	0.983058i	$0.558676\pi$
$360$		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	0.719693	−	0.694292i	$-0.244283\pi$
$383$	3.14930	+	2.64258i	0.160922	+	0.135029i	−0.558771	+	0.829322i	$0.688727\pi$
$384$		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	−0.911265	−	0.411822i	$-0.864893\pi$
$389$	−13.0949	+	10.9879i	−0.663939	+	0.557111i	0.247326	+	0.968932i	$0.420448\pi$
$390$		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	−0.660676	−	0.750671i	$-0.729730\pi$
$401$	−13.7023	+	4.98724i	−0.684262	+	0.249051i	−0.0235855	+	0.999722i	$0.507508\pi$
$402$		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	$0.207971\pi$
$419$	−3.27538	+	18.5756i	−0.160013	+	0.907477i	−0.954059	+	0.299619i	$0.903140\pi$
$420$		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	$-0.809662\pi$
$431$	−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	0.805205	−	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	−0.564695	−	0.825299i	$-0.691006\pi$
$443$	3.15729	−	2.64928i	0.150007	−	0.125871i	0.714703	+	0.699428i	$0.246562\pi$
$444$		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	−0.564320	−	0.825556i	$-0.690862\pi$
$449$	9.17071	−	15.8841i	0.432793	−	0.749619i	0.997113	+	0.0759373i	$0.0241949\pi$
$450$		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	$-0.831910\pi$
$461$	−4.81861	−	27.3277i	−0.224425	−	1.27278i	0.639356	−	0.768911i	$-0.279201\pi$
$462$		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	$0.0751309\pi$
$467$	14.8819	+	25.7762i	0.688653	+	1.19278i	−0.283621	+	0.958936i	$0.591536\pi$
$468$		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	−0.634710	−	0.772750i	$-0.718880\pi$
$479$	−35.4038	−	12.8859i	−1.61764	−	0.588773i	−0.982930	+	0.183977i	$0.941103\pi$
$480$		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	0.651354	−	0.758774i	$-0.274201\pi$
$491$	0.381445	+	0.320070i	0.0172144	+	0.0144446i	−0.634140	+	0.773218i	$0.718646\pi$
$492$		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	−0.585461	−	0.810701i	$-0.699086\pi$
$503$	9.18092	−	15.9018i	0.409357	−	0.709027i	0.994818	+	0.101673i	$0.0324197\pi$
$504$		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	−0.856790	−	0.515666i	$-0.827544\pi$
$509$	−26.6596	+	9.70329i	−1.18166	+	0.430091i	−0.324875	+	0.945757i	$0.605322\pi$
$510$		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	$-0.913115\pi$
$521$	−16.3191	−	28.2655i	−0.714952	−	1.23833i	0.248026	−	0.968753i	$-0.420218\pi$
$522$		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	$-0.619287\pi$
$557$	14.7010	−	25.4629i	0.622901	−	1.07890i	0.988943	−	0.148298i	$-0.0473794\pi$
$558$		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	−0.539107	−	0.842237i	$-0.681238\pi$
$563$	−9.74510	+	3.54693i	−0.410707	+	0.149485i	0.128400	+	0.991722i	$0.459016\pi$
$564$		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	$0.187305\pi$
$569$	5.72503	+	32.4683i	0.240006	+	1.36114i	−0.591805	+	0.806081i	$0.701584\pi$
$570$		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	−0.361485	−	0.932378i	$-0.617730\pi$
$587$	−29.9876	−	10.9146i	−1.23772	−	0.450493i	−0.876234	+	0.481885i	$0.839952\pi$
$588$		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	0.818602	−	0.574361i	$-0.194749\pi$
$599$	9.67024	+	8.11430i	0.395115	+	0.331541i	−0.423487	+	0.905902i	$0.639194\pi$
$600$		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	−0.779298	−	0.626653i	$-0.784424\pi$
$617$	−24.1805	+	8.80099i	−0.973471	+	0.354314i	−0.194172	+	0.980967i	$0.562202\pi$
$618$		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	0.566612	−	0.823985i	$-0.308254\pi$
$641$	11.9251	+	4.34040i	0.471015	+	0.171435i	−0.0955971	+	0.995420i	$0.530476\pi$
$642$		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	$-0.570341\pi$
$647$	−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	−0.982444	−	0.186558i	$-0.940267\pi$
$653$	−34.1596	−	28.6633i	−1.33677	−	1.12168i	−0.354323	−	0.935123i	$-0.615289\pi$
$654$		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	−0.407758	−	0.913090i	$-0.633689\pi$
$659$	10.7986	−	9.06110i	0.420654	−	0.352970i	0.828412	+	0.560120i	$0.189245\pi$
$660$		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	$-0.819282\pi$
$677$	−6.10829	−	34.6418i	−0.234761	−	1.33139i	0.608357	−	0.793664i	$-0.291829\pi$
$678$		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	0.644549	−	0.764563i	$-0.277045\pi$
$683$	−8.88191	−	15.3839i	−0.339857	−	0.588649i	−0.984406	+	0.175914i	$0.943712\pi$
$684$		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	$-0.307512\pi$
$701$	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	0.739384	−	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	$0.468353\pi$
$719$	−21.7763	+	37.7177i	−0.812119	+	1.40663i	−0.911378	+	0.411570i	$0.864980\pi$
$720$		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	$0.226311\pi$
$743$	−4.83821	+	27.4389i	−0.177497	+	1.00663i	−0.935222	+	0.354061i	$0.884801\pi$
$744$		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	$0.0297256\pi$
$761$	34.7688	+	29.1745i	1.26037	+	1.05757i	0.264725	+	0.964324i	$0.414719\pi$
$762$		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	$0.562286\pi$
$773$	−26.3214	+	45.5899i	−0.946713	+	1.63976i	−0.752284	+	0.658839i	$0.771048\pi$
$774$		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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