LMFDB - Embedded newform 729.2.e.i.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:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			649.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.i.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	$-0.786407\pi$
$2$	0.233956	−	1.32683i	0.165432	−	0.938209i	0.948618	−	0.316423i	$-0.102482\pi$
$3$		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	$-0.601732\pi$
$5$	1.26604	−	1.06234i	0.566192	−	0.475092i	0.880380	+	0.474269i	$0.157288\pi$
$6$		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	$0.0757806\pi$
$11$	4.55303	+	3.82045i	1.37279	+	1.15191i	0.400997	+	0.916080i	$0.368664\pi$
$12$		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	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		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	0.613896	−	0.789387i	$-0.289601\pi$
$23$	2.76604	+	1.00676i	0.576760	+	0.209924i	−0.0371361	+	0.999310i	$0.511824\pi$
$24$		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	$-0.982687\pi$
$29$	−0.224155	+	1.27125i	−0.0416246	+	0.236065i	0.956897	+	0.290429i	$0.0937980\pi$
$30$		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	$-0.930530\pi$
$41$	−0.851167	−	4.82721i	−0.132930	−	0.753883i	0.843349	−	0.537366i	$-0.180581\pi$
$42$		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	−0.0729991	−	0.997332i	$-0.523257\pi$
$47$	3.51114	−	1.27795i	0.512153	−	0.186408i	0.585152	+	0.810924i	$0.301035\pi$
$48$		0			0
$49$	−0.907604	+	0.761570i	−0.129658	+	0.108796i
$50$	2.87211	+	1.04536i	0.406178	+	0.147837i
$51$		0			0
$52$	0.103541	−	0.587208i	0.0143585	−	0.0814311i
$53$	11.6382			1.59862			0.799312	−	0.600916i	$-0.205198\pi$
$53$	11.6382			1.59862			0.799312	+	0.600916i	$0.205198\pi$
$54$		0			0
$55$	9.82295			1.32453
$56$	−1.23261	+	6.99049i	−0.164715	+	0.934143i
$57$		0			0
$58$	1.63429	+	0.594831i	0.214592	+	0.0781052i
$59$	−5.62836	+	4.72275i	−0.732749	+	0.614850i	−0.930880	−	0.365326i	$-0.880958\pi$
$59$	−5.62836	+	4.72275i	−0.732749	+	0.614850i	0.198130	+	0.980176i	$0.436513\pi$
$60$		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	0.981936	−	0.189212i	$-0.0605932\pi$
$71$	2.75624	+	4.77396i	0.327106	+	0.566564i	−0.654830	+	0.755776i	$0.727260\pi$
$72$		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	$-0.874253\pi$
$83$	0.692066	−	3.92490i	0.0759642	−	0.430814i	0.998943	−	0.0459637i	$-0.0146359\pi$
$84$		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	$-0.975519\pi$
$89$	−4.07532	+	7.05866i	−0.431983	+	0.748217i	0.565061	+	0.825049i	$0.308853\pi$
$90$		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	−0.801495	−	0.598001i	$-0.795962\pi$
$101$	−10.3623	+	3.77157i	−1.03109	+	0.375286i	−0.229593	+	0.973287i	$0.573740\pi$
$102$		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	$-0.540702\pi$
$107$	−2.63816			−0.255040			−0.127520	+	0.991836i	$0.540702\pi$
$108$		0			0
$109$	−8.95811			−0.858031			−0.429016	−	0.903297i	$-0.641140\pi$
$109$	−8.95811			−0.858031			−0.429016	+	0.903297i	$0.641140\pi$
$110$	2.29813	−	13.0334i	0.219118	−	1.24268i
$111$		0			0
$112$	8.14930	+	2.96610i	0.770036	+	0.280270i
$113$	12.2023	−	10.2390i	1.14790	−	0.963202i	0.148231	−	0.988953i	$-0.452642\pi$
$113$	12.2023	−	10.2390i	1.14790	−	0.963202i	0.999668	+	0.0257512i	$0.00819777\pi$
$114$		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	0.943650	−	0.330946i	$-0.107368\pi$
$131$	16.6395	+	6.05628i	1.45380	+	0.529140i	0.510150	+	0.860085i	$0.329590\pi$
$132$		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	$-0.998123\pi$
$137$	−0.682266	+	3.86932i	−0.0582899	+	0.330579i	0.941693	+	0.336474i	$0.109234\pi$
$138$		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	$0.262329\pi$
$149$	3.56418	+	20.2135i	0.291989	+	1.65595i	−0.387206	+	0.921993i	$0.626560\pi$
$150$		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	−0.506690	−	0.862128i	$-0.669131\pi$
$167$	3.28699	−	2.75811i	0.254355	−	0.213429i	0.761045	+	0.648699i	$0.224687\pi$
$168$		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	$-0.231722\pi$
$173$	2.90554	+	2.43804i	0.220904	+	0.185361i	−0.525619	+	0.850720i	$0.676166\pi$
$174$		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	$-0.266761\pi$
$179$	−4.13816	−	7.16750i	−0.309300	−	0.535724i	−0.978209	+	0.207620i	$0.933428\pi$
$180$		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	$0.113625\pi$
$191$	−0.870767	+	4.93837i	−0.0630065	+	0.357328i	−0.999969	+	0.00789719i	$0.997486\pi$
$192$		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	−0.878628	−	0.477507i	$-0.841540\pi$
$197$	−0.361844	+	0.626733i	−0.0257803	+	0.0446529i	0.852847	+	0.522160i	$0.174874\pi$
$198$		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	0.0851707	−	0.996366i	$-0.472856\pi$
$227$	−13.2777	−	11.1413i	−0.881269	−	0.739472i	−0.966440	+	0.256894i	$0.917301\pi$
$228$		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	$-0.981319\pi$
$233$	−8.39440	−	14.5395i	−0.549935	−	0.952516i	0.448343	−	0.893862i	$-0.352014\pi$
$234$		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	$-0.347292\pi$
$239$	3.78611	+	1.37803i	0.244903	+	0.0891375i	−0.216652	+	0.976249i	$0.569514\pi$
$240$		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	$-0.572561\pi$
$251$	11.5753	−	20.0490i	0.730628	−	1.26548i	0.956615	−	0.291354i	$-0.0941059\pi$
$252$		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	$0.0666880\pi$
$257$	2.08600	+	11.8303i	0.130121	+	0.737953i	−0.848013	+	0.529976i	$0.822201\pi$
$258$		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	$-0.785590\pi$
$263$	−15.8824	+	5.78071i	−0.979349	+	0.356454i	−0.197762	+	0.980250i	$0.563367\pi$
$264$		0			0
$265$	14.7344	−	12.3636i	0.905128	−	0.759493i
$266$	20.2665	+	7.37641i	1.24262	+	0.452277i
$267$		0			0
$268$	−0.0595922	+	0.337964i	−0.00364017	+	0.0206444i
$269$	−7.91447			−0.482554			−0.241277	−	0.970456i	$-0.577566\pi$
$269$	−7.91447			−0.482554			−0.241277	+	0.970456i	$0.577566\pi$
$270$		0			0
$271$	−17.2344			−1.04692			−0.523458	−	0.852051i	$-0.675358\pi$
$271$	−17.2344			−1.04692			−0.523458	+	0.852051i	$0.675358\pi$
$272$	−1.87346	+	10.6249i	−0.113595	+	0.644229i
$273$		0			0
$274$	4.97431	+	1.81050i	0.300509	+	0.109376i
$275$	−10.3289	+	8.66696i	−0.622855	+	0.522637i
$276$		0			0
$277$	−24.8405	+	9.04120i	−1.49252	+	0.543233i	−0.954112	−	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	0.0956121	−	0.995419i	$-0.469519\pi$
$281$	−14.5517	−	12.2103i	−0.868081	−	0.728406i	−0.963693	+	0.267012i	$0.913964\pi$
$282$		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	−0.249251	−	0.968439i	$-0.580185\pi$
$293$	−18.1903	−	6.62073i	−1.06269	−	0.386787i	−0.813438	+	0.581652i	$0.802407\pi$
$294$		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	$-0.957770\pi$
$311$	−1.85204	−	10.5035i	−0.105020	−	0.595597i	0.886193	−	0.463317i	$-0.153341\pi$
$312$		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	−0.926027	−	0.377458i	$-0.876798\pi$
$317$	−24.7977	+	9.02563i	−1.39278	+	0.506930i	−0.466752	+	0.884388i	$0.654576\pi$
$318$		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	−0.211091	−	0.977466i	$-0.567702\pi$
$347$	−18.6484	−	6.78747i	−1.00110	−	0.364371i	−0.790009	+	0.613096i	$0.789924\pi$
$348$		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	−0.995178	−	0.0980859i	$-0.968728\pi$
$353$	−0.497312	+	2.82039i	−0.0264692	+	0.150114i	0.968709	+	0.248200i	$0.0798391\pi$
$354$		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	$0.441324\pi$
$359$	−14.3944	+	24.9318i	−0.759707	+	1.31585i	−0.943000	+	0.332793i	$0.892009\pi$
$360$		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	−0.719693	−	0.694292i	$-0.755717\pi$
$383$	−3.14930	+	2.64258i	−0.160922	+	0.135029i	0.558771	+	0.829322i	$0.311273\pi$
$384$		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	$-0.135107\pi$
$389$	13.0949	+	10.9879i	0.663939	+	0.557111i	−0.247326	+	0.968932i	$0.579552\pi$
$390$		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	0.660676	−	0.750671i	$-0.270270\pi$
$401$	13.7023	+	4.98724i	0.684262	+	0.249051i	0.0235855	+	0.999722i	$0.492492\pi$
$402$		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	$0.0968597\pi$
$419$	3.27538	+	18.5756i	0.160013	+	0.907477i	−0.794046	+	0.607858i	$0.792029\pi$
$420$		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	$-0.190338\pi$
$431$	34.3164			1.65297			0.826483	+	0.562962i	$0.190338\pi$
$432$		0			0
$433$	−25.0669			−1.20464			−0.602318	−	0.798256i	$-0.705756\pi$
$433$	−25.0669			−1.20464			−0.602318	+	0.798256i	$0.705756\pi$
$434$	−0.332033	+	1.88305i	−0.0159381	+	0.0903895i
$435$		0			0
$436$	−1.55556	−	0.566177i	−0.0744978	−	0.0271150i
$437$	14.9684	−	12.5600i	0.716035	−	0.600824i
$438$		0			0
$439$	21.8084	−	7.93761i	1.04086	−	0.378841i	0.235653	−	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	0.564695	−	0.825299i	$-0.308994\pi$
$443$	−3.15729	−	2.64928i	−0.150007	−	0.125871i	−0.714703	+	0.699428i	$0.753438\pi$
$444$		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	$-0.309138\pi$
$449$	−9.17071	−	15.8841i	−0.432793	−	0.749619i	−0.997113	+	0.0759373i	$0.975805\pi$
$450$		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	$-0.720799\pi$
$461$	4.81861	−	27.3277i	0.224425	−	1.27278i	0.863781	−	0.503867i	$-0.168090\pi$
$462$		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	$0.408464\pi$
$467$	−14.8819	+	25.7762i	−0.688653	+	1.19278i	−0.972274	+	0.233845i	$0.924869\pi$
$468$		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	$-0.281120\pi$
$479$	35.4038	−	12.8859i	1.61764	−	0.588773i	0.982930	+	0.183977i	$0.0588973\pi$
$480$		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	$-0.725799\pi$
$491$	−0.381445	+	0.320070i	−0.0172144	+	0.0144446i	0.634140	+	0.773218i	$0.281354\pi$
$492$		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	0.585461	−	0.810701i	$-0.300914\pi$
$503$	−9.18092	−	15.9018i	−0.409357	−	0.709027i	−0.994818	+	0.101673i	$0.967580\pi$
$504$		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	$-0.172456\pi$
$509$	26.6596	+	9.70329i	1.18166	+	0.430091i	0.324875	+	0.945757i	$0.394678\pi$
$510$		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	$-0.579782\pi$
$521$	16.3191	−	28.2655i	0.714952	−	1.23833i	0.962978	−	0.269580i	$-0.0868847\pi$
$522$		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	$-0.952621\pi$
$557$	−14.7010	−	25.4629i	−0.622901	−	1.07890i	0.366042	−	0.930598i	$-0.380713\pi$
$558$		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	$-0.318762\pi$
$563$	9.74510	+	3.54693i	0.410707	+	0.149485i	−0.128400	+	0.991722i	$0.540984\pi$
$564$		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	$0.298416\pi$
$569$	−5.72503	+	32.4683i	−0.240006	+	1.36114i	−0.831811	+	0.555060i	$0.812695\pi$
$570$		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	0.361485	−	0.932378i	$-0.382270\pi$
$587$	29.9876	−	10.9146i	1.23772	−	0.450493i	0.876234	+	0.481885i	$0.160048\pi$
$588$		0			0
$589$	2.99273	−	2.51120i	0.123313	−	0.103472i
$590$	15.3735	+	5.59548i	0.632915	+	0.230362i
$591$		0			0
$592$	−0.0261591	+	0.148356i	−0.00107513	+	0.00609738i
$593$	31.6783			1.30087			0.650436	−	0.759561i	$-0.274586\pi$
$593$	31.6783			1.30087			0.650436	+	0.759561i	$0.274586\pi$
$594$		0			0
$595$	11.9564			0.490163
$596$	−0.658633	+	3.73530i	−0.0269787	+	0.153004i
$597$		0			0
$598$	−12.0248	−	4.37667i	−0.491731	−	0.178976i
$599$	−9.67024	+	8.11430i	−0.395115	+	0.331541i	−0.818602	−	0.574361i	$-0.805251\pi$
$599$	−9.67024	+	8.11430i	−0.395115	+	0.331541i	0.423487	+	0.905902i	$0.360806\pi$
$600$		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	0.779298	−	0.626653i	$-0.215576\pi$
$617$	24.1805	+	8.80099i	0.973471	+	0.354314i	0.194172	+	0.980967i	$0.437798\pi$
$618$		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	−0.566612	−	0.823985i	$-0.691746\pi$
$641$	−11.9251	+	4.34040i	−0.471015	+	0.171435i	0.0955971	+	0.995420i	$0.469524\pi$
$642$		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	$-0.429659\pi$
$647$	11.1506			0.438377			0.219189	+	0.975683i	$0.429659\pi$
$648$		0			0
$649$	−43.6691			−1.71416
$650$	1.71254	−	9.71232i	0.0671715	−	0.380949i
$651$		0			0
$652$	3.56165	+	1.29634i	0.139485	+	0.0507684i
$653$	34.1596	−	28.6633i	1.33677	−	1.12168i	0.354323	−	0.935123i	$-0.384711\pi$
$653$	34.1596	−	28.6633i	1.33677	−	1.12168i	0.982444	−	0.186558i	$-0.0597332\pi$
$654$		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	$-0.366311\pi$
$659$	−10.7986	−	9.06110i	−0.420654	−	0.352970i	−0.828412	+	0.560120i	$0.810755\pi$
$660$		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	$-0.708171\pi$
$677$	6.10829	−	34.6418i	0.234761	−	1.33139i	0.843117	−	0.537730i	$-0.180718\pi$
$678$		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	$-0.722955\pi$
$683$	8.88191	−	15.3839i	0.339857	−	0.588649i	0.984406	+	0.175914i	$0.0562880\pi$
$684$		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	$-0.692488\pi$
$701$	−30.1052			−1.13706			−0.568530	+	0.822663i	$0.692488\pi$
$702$		0			0
$703$	−0.278066			−0.0104875
$704$	8.87211	−	50.3162i	0.334380	−	1.89636i
$705$		0			0
$706$	3.62583	+	1.31969i	0.136460	+	0.0496673i
$707$	20.3708	−	17.0931i	0.766122	−	0.642852i
$708$		0			0
$709$	23.2456	−	8.46069i	0.873006	−	0.317748i	0.133622	−	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	$0.135020\pi$
$719$	21.7763	+	37.7177i	0.812119	+	1.40663i	−0.0992586	+	0.995062i	$0.531647\pi$
$720$		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	$0.115199\pi$
$743$	4.83821	+	27.4389i	0.177497	+	1.00663i	−0.757726	+	0.652573i	$0.773689\pi$
$744$		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	$0.585281\pi$
$761$	−34.7688	+	29.1745i	−1.26037	+	1.05757i	−0.995643	+	0.0932500i	$0.970274\pi$
$762$		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	$0.228952\pi$
$773$	26.3214	+	45.5899i	0.946713	+	1.63976i	0.194430	+	0.980916i	$0.437714\pi$
$774$		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
$780$		0			0
$781$	−5.68938	+	32.2661i	−0.203582	+	1.15457i
$782$	−11.8976			−0.425456
$783$		0			0
$784$	4.26083			0.152172
$785$	−6.30618	+	35.7641i	−0.225077	+	1.27648i
$786$		0			0
$787$	19.5103	+	7.10116i	0.695466	+	0.253129i	0.665474	−	0.746421i	$-0.268230\pi$
$787$	19.5103	+	7.10116i	0.695466	+	0.253129i	0.0299921	+	0.999550i	$0.490452\pi$
$788$	−0.102445	+	0.0859614i	−0.00364945	+	0.00306225i
$789$		0			0
$790$	7.91147	−	2.87954i	0.281478	−	0.102449i
$791$	−19.2062	+	33.2661i	−0.682894	+	1.18281i
$792$		0			0
$793$	17.8268	+	30.8770i	0.633049	+	1.09647i
$794$	23.1208	+	19.4007i	0.820528	+	0.688504i
$795$		0			0
$796$	0.327067	+	1.85489i	0.0115926	+	0.0657448i
$797$	−7.91488	−	44.8875i	−0.280359	−	1.59000i	−0.721406	−	0.692513i	$-0.756504\pi$
$797$	−7.91488	−	44.8875i	−0.280359	−	1.59000i	0.441046	−	0.897484i	$-0.354607\pi$
$798$		0			0
$799$	−8.58693	−	7.20529i	−0.303784	−	0.254905i
$800$	1.18180	+	2.04694i	0.0417829	+	0.0723701i
$801$		0			0
$802$	9.82295	−	17.0138i	0.346860	−	0.600780i
$803$	−31.0219	+	11.2910i	−1.09474	+	0.398452i
$804$		0			0
$805$	−8.98680	+	7.54082i	−0.316743	+	0.265779i
$806$	−2.40420	−	0.875057i	−0.0846843	−	0.0308226i
$807$		0			0
$808$	−5.63656	+	31.9665i	−0.198294	+	1.12458i
$809$	−4.21120			−0.148058			−0.0740290	−	0.997256i	$-0.523586\pi$
$809$	−4.21120			−0.148058			−0.0740290	+	0.997256i	$0.523586\pi$
$810$		0			0
$811$	11.3618			0.398968			0.199484	−	0.979901i	$-0.436073\pi$
$811$	11.3618			0.398968			0.199484	+	0.979901i	$0.436073\pi$
$812$	0.0998887	−	0.566497i	0.00350540	−	0.0198801i
$813$		0			0
$814$	−0.315207	−	0.114726i	−0.0110480	−	0.00402115i
$815$	25.9675	−	21.7893i	0.909602	−	0.763247i
$816$		0			0
$817$	−32.3418	+	11.7715i	−1.13150	+	0.411831i
$818$	11.7909	−	20.4224i	0.412258	−	0.714051i
$819$		0			0
$820$	−0.748503	−	1.29645i	−0.0261389	−	0.0452739i
$821$	1.25806	+	1.05563i	0.0439064	+	0.0368419i	0.664477	−	0.747309i	$-0.268654\pi$
$821$	1.25806	+	1.05563i	0.0439064	+	0.0368419i	−0.620570	+	0.784151i	$0.713099\pi$
$822$		0			0
$823$	1.94815	+	11.0485i	0.0679082	+	0.385126i	0.999752	+	0.0222670i	$0.00708839\pi$
$823$	1.94815	+	11.0485i	0.0679082	+	0.385126i	−0.931844	+	0.362859i	$0.881800\pi$
$824$	1.99690	+	11.3250i	0.0695653	+	0.394525i
$825$		0			0
$826$	−18.2864	−	15.3441i	−0.636264	−	0.533889i
$827$	4.80659	+	8.32526i	0.167141	+	0.289498i	0.937414	−	0.348218i	$-0.113213\pi$
$827$	4.80659	+	8.32526i	0.167141	+	0.289498i	−0.770272	+	0.637715i	$0.779880\pi$
$828$		0			0
$829$	−16.7469	+	29.0065i	−0.581644	+	1.00744i	0.413640	+	0.910440i	$0.364257\pi$
$829$	−16.7469	+	29.0065i	−0.581644	+	1.00744i	−0.995285	+	0.0969971i	$0.969076\pi$
$830$	−8.33915	+	3.03520i	−0.289456	+	0.105353i
$831$		0			0
$832$	−21.2481	+	17.8293i	−0.736645	+	0.618119i
$833$	3.34002	+	1.21567i	0.115725	+	0.0421204i
$834$		0			0
$835$	1.23143	−	6.98378i	0.0426154	−	0.241684i
$836$	7.29086			0.252160
$837$		0			0
$838$	25.4129			0.877874
$839$	−5.55572	+	31.5081i	−0.191805	+	1.08778i	0.725091	+	0.688653i	$0.241798\pi$
$839$	−5.55572	+	31.5081i	−0.191805	+	1.08778i	−0.916896	+	0.399126i	$0.869314\pi$
$840$		0			0
$841$	25.6853	+	9.34867i	0.885699	+	0.322368i
$842$	−33.3712	+	28.0018i	−1.15005	+	0.965005i
$843$		0			0
$844$	−2.58125	+	0.939499i	−0.0888504	+	0.0323389i
$845$	2.13903	−	3.70491i	0.0735850	−	0.127453i
$846$		0			0
$847$	−29.3307	−	50.8022i	−1.00781	−	1.74559i
$848$	−32.0620	−	26.9032i	−1.10101	−	0.923859i
$849$		0			0
$850$	−1.59223	−	9.03001i	−0.0546132	−	0.309727i
$851$	−0.0214114	−	0.121430i	−0.000733972	−	0.00416256i
$852$		0			0
$853$	26.9971	+	22.6532i	0.924362	+	0.775632i	0.974797	−	0.223096i	$-0.0716162\pi$
$853$	26.9971	+	22.6532i	0.924362	+	0.775632i	−0.0504347	+	0.998727i	$0.516061\pi$
$854$	−17.9500	−	31.0902i	−0.614235	−	1.06389i
$855$		0			0
$856$	−3.88279	+	6.72519i	−0.132711	+	0.229862i
$857$	19.9675	−	7.26758i	0.682077	−	0.248256i	0.0223378	−	0.999750i	$-0.492889\pi$
$857$	19.9675	−	7.26758i	0.682077	−	0.248256i	0.659739	+	0.751495i	$0.270667\pi$
$858$		0			0
$859$	39.7105	−	33.3211i	1.35491	−	1.13690i	0.377387	−	0.926056i	$-0.376823\pi$
$859$	39.7105	−	33.3211i	1.35491	−	1.13690i	0.977519	−	0.210846i	$-0.0676217\pi$
$860$	−1.48798	−	0.541580i	−0.0507396	−	0.0184677i
$861$		0			0
$862$	8.02852	−	45.5320i	0.273453	−	1.55083i
$863$	−22.6783			−0.771978			−0.385989	−	0.922503i	$-0.626140\pi$
$863$	−22.6783			−0.771978			−0.385989	+	0.922503i	$0.626140\pi$
$864$		0			0
$865$	6.26857			0.213138
$866$	−5.86453	+	33.2594i	−0.199285	+	1.13020i
$867$		0			0
$868$	−0.246444	−	0.0896983i	−0.00836486	−	0.00304456i
$869$	−17.2153	+	14.4453i	−0.583989	+	0.490025i
$870$		0			0
$871$	5.63088	−	2.04947i	0.190795	−	0.0694438i
$872$	−13.1844	+	22.8360i	−0.446480	+	0.773325i
$873$		0			0
$874$	−13.1630	−	22.7989i	−0.445244	−	0.771185i
$875$	−22.1912	−	18.6206i	−0.750199	−	0.629492i
$876$		0			0
$877$	0.196814	+	1.11619i	0.00664594	+	0.0376910i	0.987950	−	0.154771i	$-0.0494639\pi$
$877$	0.196814	+	1.11619i	0.00664594	+	0.0376910i	−0.981304	+	0.192462i	$0.938353\pi$
$878$	−5.42964	−	30.7930i	−0.183242	−	1.03921i
$879$		0			0
$880$	−27.0612	−	22.7071i	−0.912234	−	0.765455i
$881$	15.4145	+	26.6986i	0.519327	+	0.899500i	0.999748	+	0.0224621i	$0.00715051\pi$
$881$	15.4145	+	26.6986i	0.519327	+	0.899500i	−0.480421	+	0.877038i	$0.659516\pi$
$882$		0			0
$883$	4.66756	−	8.08444i	0.157076	−	0.272063i	−0.776737	−	0.629825i	$-0.783127\pi$
$883$	4.66756	−	8.08444i	0.157076	−	0.272063i	0.933813	+	0.357762i	$0.116460\pi$
$884$	−1.68092	+	0.611806i	−0.0565355	+	0.0205772i
$885$		0			0
$886$	−4.25380	+	3.56937i	−0.142909	+	0.119915i
$887$	13.2442	+	4.82050i	0.444697	+	0.161857i	0.554656	−	0.832079i	$-0.312850\pi$
$887$	13.2442	+	4.82050i	0.444697	+	0.161857i	−0.109959	+	0.993936i	$0.535072\pi$
$888$		0			0
$889$	1.50593	−	8.54055i	0.0505073	−	0.286441i
$890$	18.1489			0.608352
$891$		0			0
$892$	2.02322			0.0677425
$893$	4.30706	−	24.4265i	0.144130	−	0.817403i
$894$		0			0
$895$	−12.8534	−	4.67825i	−0.429641	−	0.156377i
$896$	17.5455	−	14.7224i	0.586154	−	0.491842i
$897$		0			0
$898$	−23.2211	+	8.45177i	−0.774897	+	0.282039i
$899$	−0.379852	+	0.657923i	−0.0126688	+	0.0219430i
$900$		0			0
$901$	−17.4572	−	30.2368i	−0.581585	−	1.00733i
$902$	−30.0683	−	25.2303i	−1.00116	−	0.840076i
$903$		0			0
$904$	−8.14203	−	46.1757i	−0.270800	−	1.53578i
$905$	1.92912	+	10.9406i	0.0641261	+	0.363677i
$906$		0			0
$907$	−6.69459	−	5.61743i	−0.222290	−	0.186524i	0.524841	−	0.851200i	$-0.324125\pi$
$907$	−6.69459	−	5.61743i	−0.222290	−	0.186524i	−0.747131	+	0.664677i	$0.768569\pi$
$908$	−1.60148	−	2.77385i	−0.0531470	−	0.0920533i
$909$		0			0
$910$	8.66297	−	15.0047i	0.287175	−	0.497401i
$911$	19.4055	−	7.06304i	0.642934	−	0.234009i	8.31009e−5	−	1.00000i	$-0.499974\pi$
$911$	19.4055	−	7.06304i	0.642934	−	0.234009i	0.642851	+	0.765991i	$0.277751\pi$
$912$		0			0
$913$	18.1459	−	15.2262i	0.600542	−	0.503914i
$914$	24.6386	+	8.96773i	0.814973	+	0.296626i
$915$		0			0
$916$	−0.0501266	+	0.284282i	−0.00165623	+	0.00939295i
$917$	−42.7009			−1.41011
$918$		0			0
$919$	−2.36009			−0.0778522			−0.0389261	−	0.999242i	$-0.512394\pi$
$919$	−2.36009			−0.0778522			−0.0389261	+	0.999242i	$0.512394\pi$
$920$	2.48663	−	14.1024i	0.0819819	−	0.464942i
$921$		0			0
$922$	−35.1318	−	12.7869i	−1.15700	−	0.421115i
$923$	13.6257	−	11.4333i	0.448494	−	0.376331i
$924$		0			0
$925$	0.0892974	−	0.0325016i	0.00293608	−	0.00106865i
$926$	−26.0608	+	45.1386i	−0.856410	+	1.48335i
$927$		0			0
$928$	0.672466	+	1.16475i	0.0220748	+	0.0382346i
$929$	−20.5455	−	17.2397i	−0.674076	−	0.565617i	0.240192	−	0.970725i	$-0.422789\pi$
$929$	−20.5455	−	17.2397i	−0.674076	−	0.565617i	−0.914269	+	0.405108i	$0.867234\pi$
$930$		0			0
$931$	1.36571	+	7.74535i	0.0447595	+	0.253844i
$932$	−0.538734	−	3.05531i	−0.0176468	−	0.100080i
$933$		0			0
$934$	30.7189	+	25.7762i	1.00515	+	0.843424i
$935$	−14.7344	−	25.5208i	−0.481867	−	0.834618i
$936$		0			0
$937$	−0.966567	+	1.67414i	−0.0315764	+	0.0546919i	−0.881382	−	0.472405i	$-0.843386\pi$
$937$	−0.966567	+	1.67414i	−0.0315764	+	0.0546919i	0.849805	+	0.527097i	$0.176719\pi$
$938$	−5.66978	+	2.06363i	−0.185125	+	0.0673799i
$939$		0			0
$940$	0.874171	−	0.733516i	0.0285123	−	0.0239247i
$941$	−11.1921	−	4.07358i	−0.364851	−	0.132795i	0.153088	−	0.988213i	$-0.451078\pi$
$941$	−11.1921	−	4.07358i	−0.364851	−	0.132795i	−0.517939	+	0.855418i	$0.673300\pi$
$942$		0			0
$943$	2.50546	−	14.2092i	0.0815891	−	0.462715i
$944$	26.4228			0.859990
$945$		0			0
$946$	−41.5185			−1.34988
$947$	−0.0548444	+	0.311038i	−0.00178220	+	0.0101074i	−0.985686	−	0.168592i	$-0.946078\pi$
$947$	−0.0548444	+	0.311038i	−0.00178220	+	0.0101074i	0.983904	+	0.178700i	$0.0571890\pi$
$948$		0			0
$949$	16.8414	+	6.12976i	0.546694	+	0.198980i
$950$	15.5424	−	13.0416i	0.504261	−	0.423125i
$951$		0			0
$952$	20.0107	−	7.28331i	0.648552	−	0.236053i
$953$	−1.62567	+	2.81574i	−0.0526605	+	0.0912107i	−0.891154	−	0.453701i	$-0.850103\pi$
$953$	−1.62567	+	2.81574i	−0.0526605	+	0.0912107i	0.838494	+	0.544912i	$0.183437\pi$
$954$		0			0
$955$	4.14378	+	7.17724i	0.134090	+	0.232250i
$956$	0.570356	+	0.478585i	0.0184466	+	0.0154786i
$957$		0			0
$958$	−8.81449	−	49.9895i	−0.284783	−	1.61509i
$959$	−1.64527	−	9.33078i	−0.0531285	−	0.301306i
$960$		0			0
$961$	−23.4820	−	19.7038i	−0.757485	−	0.635606i
$962$	0.0910521	+	0.157707i	0.00293564	+	0.00508467i
$963$		0			0
$964$	−0.309745	+	0.536493i	−0.00997620	+	0.0172793i
$965$	27.7447	−	10.0982i	0.893133	−	0.325074i
$966$		0			0
$967$	8.40167	−	7.04984i	0.270180	−	0.226708i	−0.497624	−	0.867393i	$-0.665794\pi$
$967$	8.40167	−	7.04984i	0.270180	−	0.226708i	0.767804	+	0.640685i	$0.221350\pi$
$968$	67.2866	+	24.4903i	2.16267	+	0.787149i
$969$		0			0
$970$	0.100852	−	0.571962i	0.00323817	−	0.0183646i
$971$	23.3868			0.750519			0.375259	−	0.926920i	$-0.377554\pi$
$971$	23.3868			0.750519			0.375259	+	0.926920i	$0.377554\pi$
$972$		0			0
$973$	28.8553			0.925060
$974$	−0.178701	+	1.01346i	−0.00572594	+	0.0324734i
$975$		0			0
$976$	37.3410	+	13.5910i	1.19525	+	0.435037i
$977$	−38.4372	+	32.2527i	−1.22972	+	1.03185i	−0.231458	+	0.972845i	$0.574350\pi$
$977$	−38.4372	+	32.2527i	−1.22972	+	1.03185i	−0.998257	+	0.0590092i	$0.981206\pi$
$978$		0			0
$979$	−45.5223	+	16.5688i	−1.45490	+	0.529540i
$980$	−0.180922	+	0.313366i	−0.00577935	+	0.0100101i
$981$		0			0
$982$	0.335437	+	0.580994i	0.0107042	+	0.0185402i
$983$	−11.2567	−	9.44550i	−0.359033	−	0.301265i	0.445372	−	0.895346i	$-0.353071\pi$
$983$	−11.2567	−	9.44550i	−0.359033	−	0.301265i	−0.804405	+	0.594081i	$0.797516\pi$
$984$		0			0
$985$	0.207691	+	1.17787i	0.00661757	+	0.0375301i
$986$	−0.906011	−	5.13824i	−0.0288533	−	0.163635i
$987$		0			0
$988$	−3.03209	−	2.54422i	−0.0964636	−	0.0809426i
$989$	−7.63088	−	13.2171i	−0.242648	−	0.420279i
$990$		0			0
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$	0.576199	−	0.209719i	0.0182944	−	0.00665860i
$993$		0			0
$994$	−13.7198	+	11.5123i	−0.435165	+	0.365147i
$995$	15.8293	+	5.76141i	0.501824	+	0.182649i
$996$		0			0
$997$	−7.96807	+	45.1892i	−0.252351	+	1.43116i	0.550429	+	0.834882i	$0.314464\pi$
$997$	−7.96807	+	45.1892i	−0.252351	+	1.43116i	−0.802781	+	0.596274i	$0.796647\pi$
$998$	12.0797			0.382375
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.i.649.1		6
3.2	odd	2		729.2.e.a.649.1		6
9.2	odd	6		729.2.e.g.163.1		6
9.4	even	3		729.2.e.c.406.1		6
9.5	odd	6		729.2.e.h.406.1		6
9.7	even	3		729.2.e.b.163.1		6
27.2	odd	18		243.2.c.f.163.2		6
27.4	even	9		729.2.e.c.325.1		6
27.5	odd	18		729.2.e.g.568.1		6
27.7	even	9		243.2.c.e.82.2		6
27.11	odd	18		243.2.a.e.1.2	✓	3
27.13	even	9	inner	729.2.e.i.82.1		6
27.14	odd	18		729.2.e.a.82.1		6
27.16	even	9		243.2.a.f.1.2	yes	3
27.20	odd	18		243.2.c.f.82.2		6
27.22	even	9		729.2.e.b.568.1		6
27.23	odd	18		729.2.e.h.325.1		6
27.25	even	9		243.2.c.e.163.2		6
108.11	even	18		3888.2.a.bd.1.2		3
108.43	odd	18		3888.2.a.bk.1.2		3
135.119	odd	18		6075.2.a.bv.1.2		3
135.124	even	18		6075.2.a.bq.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.2	✓	3	27.11	odd	18
243.2.a.f.1.2	yes	3	27.16	even	9
243.2.c.e.82.2		6	27.7	even	9
243.2.c.e.163.2		6	27.25	even	9
243.2.c.f.82.2		6	27.20	odd	18
243.2.c.f.163.2		6	27.2	odd	18
729.2.e.a.82.1		6	27.14	odd	18
729.2.e.a.649.1		6	3.2	odd	2
729.2.e.b.163.1		6	9.7	even	3
729.2.e.b.568.1		6	27.22	even	9
729.2.e.c.325.1		6	27.4	even	9
729.2.e.c.406.1		6	9.4	even	3
729.2.e.g.163.1		6	9.2	odd	6
729.2.e.g.568.1		6	27.5	odd	18
729.2.e.h.325.1		6	27.23	odd	18
729.2.e.h.406.1		6	9.5	odd	6
729.2.e.i.82.1		6	27.13	even	9	inner
729.2.e.i.649.1		6	1.1	even	1	trivial
3888.2.a.bd.1.2		3	108.11	even	18
3888.2.a.bk.1.2		3	108.43	odd	18
6075.2.a.bq.1.2		3	135.124	even	18
6075.2.a.bv.1.2		3	135.119	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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