LMFDB - Embedded newform 1323.2.g.f.667.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.g (of order $3$, degree $2$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.2
Root			$0.920620 + 1.59456i$ of defining polynomial
Character	$\chi$	$=$	1323.667
Dual form			1323.2.g.f.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.920620 - 1.59456i) q^{2} +(-0.695084 + 1.20392i) q^{4} +1.33475 q^{5} -1.12285 q^{8} +O(q^{10})$	\(q+(-0.920620 - 1.59456i) q^{2} +(-0.695084 + 1.20392i) q^{4} +1.33475 q^{5} -1.12285 q^{8} +(-1.22880 - 2.12835i) q^{10} -1.51302 q^{11} +(2.58800 + 4.48254i) q^{13} +(2.42388 + 4.19829i) q^{16} +(0.774463 + 1.34141i) q^{17} +(1.25211 - 2.16872i) q^{19} +(-0.927765 + 1.60694i) q^{20} +(1.39291 + 2.41260i) q^{22} +7.36079 q^{23} -3.21843 q^{25} +(4.76513 - 8.25344i) q^{26} +(0.0309713 - 0.0536439i) q^{29} +(-1.92388 + 3.33227i) q^{31} +(3.34011 - 5.78523i) q^{32} +(1.42597 - 2.46986i) q^{34} +(-0.281608 + 0.487760i) q^{37} -4.61087 q^{38} -1.49873 q^{40} +(4.51188 + 7.81481i) q^{41} +(5.09988 - 8.83325i) q^{43} +(1.05167 - 1.82155i) q^{44} +(-6.77649 - 11.7372i) q^{46} +(4.75925 + 8.24327i) q^{47} +(2.96296 + 5.13199i) q^{50} -7.19550 q^{52} +(-0.755374 - 1.30835i) q^{53} -2.01950 q^{55} -0.114051 q^{58} +(4.22166 - 7.31212i) q^{59} +(1.61958 + 2.80520i) q^{61} +7.08467 q^{62} -2.60434 q^{64} +(3.45434 + 5.98309i) q^{65} +(-3.46670 + 6.00449i) q^{67} -2.15327 q^{68} +12.3304 q^{71} +(1.37936 + 2.38912i) q^{73} +1.03702 q^{74} +(1.74064 + 3.01488i) q^{76} +(2.95969 + 5.12633i) q^{79} +(3.23529 + 5.60368i) q^{80} +(8.30746 - 14.3889i) q^{82} +(2.80111 - 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} -18.7802 q^{86} +1.69889 q^{88} +(0.703287 - 1.21813i) q^{89} +(-5.11636 + 8.86180i) q^{92} +(8.76293 - 15.1778i) q^{94} +(1.67126 - 2.89470i) q^{95} +(6.09713 - 10.5605i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} - 8 q^{5} + 6 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^4 - 8 * q^5 + 6 * q^8	$ 10 q - 2 q^{2} - 4 q^{4} - 8 q^{5} + 6 q^{8} + 7 q^{10} + 8 q^{11} + 8 q^{13} + 2 q^{16} + 12 q^{17} - q^{19} + 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} + 11 q^{26} - 7 q^{29} + 3 q^{31} + 2 q^{32} - 3 q^{34} - 40 q^{38} - 6 q^{40} + 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 27 q^{47} - 19 q^{50} - 20 q^{52} + 21 q^{53} - 4 q^{55} + 20 q^{58} + 30 q^{59} + 14 q^{61} - 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 54 q^{68} + 6 q^{71} - 15 q^{73} - 72 q^{74} - 5 q^{76} - 4 q^{79} + 20 q^{80} + 5 q^{82} + 9 q^{83} - 6 q^{85} - 16 q^{86} + 36 q^{88} + 28 q^{89} - 27 q^{92} + 3 q^{94} + 14 q^{95} + 12 q^{97}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 - 8 * q^5 + 6 * q^8 + 7 * q^10 + 8 * q^11 + 8 * q^13 + 2 * q^16 + 12 * q^17 - q^19 + 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 + 11 * q^26 - 7 * q^29 + 3 * q^31 + 2 * q^32 - 3 * q^34 - 40 * q^38 - 6 * q^40 + 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 27 * q^47 - 19 * q^50 - 20 * q^52 + 21 * q^53 - 4 * q^55 + 20 * q^58 + 30 * q^59 + 14 * q^61 - 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 54 * q^68 + 6 * q^71 - 15 * q^73 - 72 * q^74 - 5 * q^76 - 4 * q^79 + 20 * q^80 + 5 * q^82 + 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 + 28 * q^89 - 27 * q^92 + 3 * q^94 + 14 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.920620	−	1.59456i	−0.650977	−	1.12753i	−0.982886	−	0.184214i	$-0.941026\pi$
$2$	−0.920620	−	1.59456i	−0.650977	−	1.12753i	0.331909	−	0.943311i	$-0.392307\pi$
$3$		0			0
$3$		0			0
$4$	−0.695084	+	1.20392i	−0.347542	+	0.601960i
$5$	1.33475			0.596920			0.298460	−	0.954422i	$-0.403527\pi$
$5$	1.33475			0.596920			0.298460	+	0.954422i	$0.403527\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.12285			−0.396987
$9$		0			0
$10$	−1.22880	−	2.12835i	−0.388581	−	0.673042i
$11$	−1.51302			−0.456192			−0.228096	−	0.973639i	$-0.573250\pi$
$11$	−1.51302			−0.456192			−0.228096	+	0.973639i	$0.573250\pi$
$12$		0			0
$13$	2.58800	+	4.48254i	0.717781	+	1.24323i	0.961877	+	0.273482i	$0.0881755\pi$
$13$	2.58800	+	4.48254i	0.717781	+	1.24323i	−0.244096	+	0.969751i	$0.578491\pi$
$14$		0			0
$15$		0			0
$16$	2.42388	+	4.19829i	0.605971	+	1.04957i
$17$	0.774463	+	1.34141i	0.187835	+	0.325340i	0.944528	−	0.328430i	$-0.106520\pi$
$17$	0.774463	+	1.34141i	0.187835	+	0.325340i	−0.756693	+	0.653770i	$0.773186\pi$
$18$		0			0
$19$	1.25211	−	2.16872i	0.287254	−	0.497538i	−0.685900	−	0.727696i	$-0.740591\pi$
$19$	1.25211	−	2.16872i	0.287254	−	0.497538i	0.973153	+	0.230158i	$0.0739244\pi$
$20$	−0.927765	+	1.60694i	−0.207455	+	0.359322i
$21$		0			0
$22$	1.39291	+	2.41260i	0.296970	+	0.514367i
$23$	7.36079			1.53483			0.767415	−	0.641151i	$-0.221543\pi$
$23$	7.36079			1.53483			0.767415	+	0.641151i	$0.221543\pi$
$24$		0			0
$25$	−3.21843			−0.643687
$26$	4.76513	−	8.25344i	0.934518	−	1.61863i
$27$		0			0
$28$		0			0
$29$	0.0309713	−	0.0536439i	0.00575123	−	0.00996143i	−0.863135	−	0.504972i	$-0.831503\pi$
$29$	0.0309713	−	0.0536439i	0.00575123	−	0.00996143i	0.868887	+	0.495011i	$0.164836\pi$
$30$		0			0
$31$	−1.92388	+	3.33227i	−0.345540	+	0.598493i	−0.985452	−	0.169956i	$-0.945638\pi$
$31$	−1.92388	+	3.33227i	−0.345540	+	0.598493i	0.639912	+	0.768448i	$0.278971\pi$
$32$	3.34011	−	5.78523i	0.590453	−	1.02269i
$33$		0			0
$34$	1.42597	−	2.46986i	0.244552	−	0.423577i
$35$		0			0
$36$		0			0
$37$	−0.281608	+	0.487760i	−0.0462961	+	0.0801872i	−0.888245	−	0.459370i	$-0.848075\pi$
$37$	−0.281608	+	0.487760i	−0.0462961	+	0.0801872i	0.841949	+	0.539557i	$0.181408\pi$
$38$	−4.61087			−0.747982
$39$		0			0
$40$	−1.49873			−0.236969
$41$	4.51188	+	7.81481i	0.704638	+	1.22047i	0.966822	+	0.255450i	$0.0822237\pi$
$41$	4.51188	+	7.81481i	0.704638	+	1.22047i	−0.262185	+	0.965018i	$0.584443\pi$
$42$		0			0
$43$	5.09988	−	8.83325i	0.777724	−	1.34706i	−0.155526	−	0.987832i	$-0.549707\pi$
$43$	5.09988	−	8.83325i	0.777724	−	1.34706i	0.933251	−	0.359226i	$-0.116959\pi$
$44$	1.05167	−	1.82155i	0.158546	−	0.274609i
$45$		0			0
$46$	−6.77649	−	11.7372i	−0.999139	−	1.73056i
$47$	4.75925	+	8.24327i	0.694209	+	1.20240i	0.970447	+	0.241315i	$0.0775788\pi$
$47$	4.75925	+	8.24327i	0.694209	+	1.20240i	−0.276238	+	0.961089i	$0.589088\pi$
$48$		0			0
$49$		0			0
$50$	2.96296	+	5.13199i	0.419025	+	0.725773i
$51$		0			0
$52$	−7.19550			−0.997836
$53$	−0.755374	−	1.30835i	−0.103759	−	0.179715i	0.809472	−	0.587159i	$-0.199754\pi$
$53$	−0.755374	−	1.30835i	−0.103759	−	0.179715i	−0.913230	+	0.407444i	$0.866420\pi$
$54$		0			0
$55$	−2.01950			−0.272310
$56$		0			0
$57$		0			0
$58$	−0.114051			−0.0149757
$59$	4.22166	−	7.31212i	0.549613	−	0.951957i	−0.448688	−	0.893688i	$-0.648109\pi$
$59$	4.22166	−	7.31212i	0.549613	−	0.951957i	0.998301	−	0.0582689i	$-0.0185581\pi$
$60$		0			0
$61$	1.61958	+	2.80520i	0.207367	+	0.359169i	0.950884	−	0.309547i	$-0.100177\pi$
$61$	1.61958	+	2.80520i	0.207367	+	0.359169i	−0.743518	+	0.668716i	$0.766844\pi$
$62$	7.08467			0.899754
$63$		0			0
$64$	−2.60434			−0.325543
$65$	3.45434	+	5.98309i	0.428458	+	0.742111i
$66$		0			0
$67$	−3.46670	+	6.00449i	−0.423524	+	0.733566i	−0.996281	−	0.0861595i	$-0.972541\pi$
$67$	−3.46670	+	6.00449i	−0.423524	+	0.733566i	0.572757	+	0.819725i	$0.305874\pi$
$68$	−2.15327			−0.261122
$69$		0			0
$70$		0			0
$71$	12.3304			1.46335			0.731673	−	0.681656i	$-0.238740\pi$
$71$	12.3304			1.46335			0.731673	+	0.681656i	$0.238740\pi$
$72$		0			0
$73$	1.37936	+	2.38912i	0.161442	+	0.279625i	0.935386	−	0.353629i	$-0.115052\pi$
$73$	1.37936	+	2.38912i	0.161442	+	0.279625i	−0.773944	+	0.633254i	$0.781719\pi$
$74$	1.03702			0.120551
$75$		0			0
$76$	1.74064	+	3.01488i	0.199665	+	0.345830i
$77$		0			0
$78$		0			0
$79$	2.95969	+	5.12633i	0.332991	+	0.576758i	0.983097	−	0.183086i	$-0.0586087\pi$
$79$	2.95969	+	5.12633i	0.332991	+	0.576758i	−0.650106	+	0.759844i	$0.725275\pi$
$80$	3.23529	+	5.60368i	0.361716	+	0.626511i
$81$		0			0
$82$	8.30746	−	14.3889i	0.917406	−	1.58899i
$83$	2.80111	−	4.85167i	0.307462	−	0.532540i	−0.670344	−	0.742050i	$-0.733854\pi$
$83$	2.80111	−	4.85167i	0.307462	−	0.532540i	0.977806	+	0.209510i	$0.0671870\pi$
$84$		0			0
$85$	1.03372	+	1.79045i	0.112122	+	0.194202i
$86$	−18.7802			−2.02512
$87$		0			0
$88$	1.69889			0.181102
$89$	0.703287	−	1.21813i	0.0745483	−	0.129121i	−0.826341	−	0.563169i	$-0.809582\pi$
$89$	0.703287	−	1.21813i	0.0745483	−	0.129121i	0.900890	+	0.434048i	$0.142915\pi$
$90$		0			0
$91$		0			0
$92$	−5.11636	+	8.86180i	−0.533418	+	0.923906i
$93$		0			0
$94$	8.76293	−	15.1778i	0.903827	−	1.56548i
$95$	1.67126	−	2.89470i	0.171467	−	0.296990i
$96$		0			0
$97$	6.09713	−	10.5605i	0.619070	−	1.07226i	−0.370586	−	0.928798i	$-0.620843\pi$
$97$	6.09713	−	10.5605i	0.619070	−	1.07226i	0.989656	−	0.143462i	$-0.0458236\pi$
$98$		0			0
$99$		0			0
$100$	2.23708	−	3.87474i	0.223708	−	0.387474i
$101$	1.11867			0.111312			0.0556560	−	0.998450i	$-0.482275\pi$
$101$	1.11867			0.111312			0.0556560	+	0.998450i	$0.482275\pi$
$102$		0			0
$103$	−1.93045			−0.190213			−0.0951063	−	0.995467i	$-0.530319\pi$
$103$	−1.93045			−0.190213			−0.0951063	+	0.995467i	$0.530319\pi$
$104$	−2.90593	−	5.03322i	−0.284950	−	0.493548i
$105$		0			0
$106$	−1.39082	+	2.40898i	−0.135089	+	0.233981i
$107$	−2.88969	+	5.00509i	−0.279357	+	0.483860i	−0.971225	−	0.238163i	$-0.923455\pi$
$107$	−2.88969	+	5.00509i	−0.279357	+	0.483860i	0.691868	+	0.722024i	$0.256788\pi$
$108$		0			0
$109$	−4.12106	−	7.13788i	−0.394726	−	0.683685i	0.598340	−	0.801242i	$-0.295827\pi$
$109$	−4.12106	−	7.13788i	−0.394726	−	0.683685i	−0.993066	+	0.117557i	$0.962494\pi$
$110$	1.85920	+	3.22022i	0.177267	+	0.307036i
$111$		0			0
$112$		0			0
$113$	−7.25105	−	12.5592i	−0.682121	−	1.18147i	−0.974332	−	0.225115i	$-0.927724\pi$
$113$	−7.25105	−	12.5592i	−0.682121	−	1.18147i	0.292211	−	0.956354i	$-0.405609\pi$
$114$		0			0
$115$	9.82483			0.916170
$116$	0.0430553	+	0.0745740i	0.00399759	+	0.00692403i
$117$		0			0
$118$	−15.5462			−1.43114
$119$		0			0
$120$		0			0
$121$	−8.71078			−0.791889
$122$	2.98204	−	5.16505i	0.269982	−	0.467622i
$123$		0			0
$124$	−2.67452	−	4.63241i	−0.240179	−	0.416002i
$125$	−10.9696			−0.981149
$126$		0			0
$127$	8.50004			0.754257			0.377128	−	0.926161i	$-0.376912\pi$
$127$	8.50004			0.754257			0.377128	+	0.926161i	$0.376912\pi$
$128$	−4.28260	−	7.41769i	−0.378532	−	0.655637i
$129$		0			0
$130$	6.36027	−	11.0163i	0.557832	−	0.966194i
$131$	−2.01346			−0.175917			−0.0879585	−	0.996124i	$-0.528034\pi$
$131$	−2.01346			−0.175917			−0.0879585	+	0.996124i	$0.528034\pi$
$132$		0			0
$133$		0			0
$134$	12.7660			1.10282
$135$		0			0
$136$	−0.869605	−	1.50620i	−0.0745680	−	0.129156i
$137$	−2.21740			−0.189445			−0.0947225	−	0.995504i	$-0.530196\pi$
$137$	−2.21740			−0.189445			−0.0947225	+	0.995504i	$0.530196\pi$
$138$		0			0
$139$	−0.377669	−	0.654143i	−0.0320335	−	0.0554836i	0.849564	−	0.527485i	$-0.176865\pi$
$139$	−0.377669	−	0.654143i	−0.0320335	−	0.0554836i	−0.881598	+	0.472002i	$0.843532\pi$
$140$		0			0
$141$		0			0
$142$	−11.3516	−	19.6615i	−0.952604	−	1.64996i
$143$	−3.91568	−	6.78216i	−0.327446	−	0.567153i
$144$		0			0
$145$	0.0413391	−	0.0716014i	0.00343303	−	0.00594618i
$146$	2.53973	−	4.39894i	0.210189	−	0.364059i
$147$		0			0
$148$	−0.391482	−	0.678068i	−0.0321797	−	0.0557368i
$149$	−6.58499			−0.539463			−0.269732	−	0.962936i	$-0.586935\pi$
$149$	−6.58499			−0.539463			−0.269732	+	0.962936i	$0.586935\pi$
$150$		0			0
$151$	12.6671			1.03083			0.515417	−	0.856939i	$-0.327637\pi$
$151$	12.6671			1.03083			0.515417	+	0.856939i	$0.327637\pi$
$152$	−1.40593	+	2.43514i	−0.114036	+	0.197516i
$153$		0			0
$154$		0			0
$155$	−2.56791	+	4.44775i	−0.206260	+	0.357252i
$156$		0			0
$157$	−8.65372	+	14.9887i	−0.690642	+	1.19623i	0.280986	+	0.959712i	$0.409338\pi$
$157$	−8.65372	+	14.9887i	−0.690642	+	1.19623i	−0.971628	+	0.236515i	$0.923995\pi$
$158$	5.44950	−	9.43882i	0.433539	−	0.750912i
$159$		0			0
$160$	4.45822	−	7.72186i	0.352453	−	0.610467i
$161$		0			0
$162$		0			0
$163$	6.10963	−	10.5822i	0.478543	−	0.828861i	−0.521154	−	0.853463i	$-0.674498\pi$
$163$	6.10963	−	10.5822i	0.478543	−	0.828861i	0.999697	+	0.0246014i	$0.00783167\pi$
$164$	−12.5445			−0.979564
$165$		0			0
$166$	−10.3150			−0.800602
$167$	1.76248	+	3.05270i	0.136385	+	0.236225i	0.926126	−	0.377215i	$-0.123118\pi$
$167$	1.76248	+	3.05270i	0.136385	+	0.236225i	−0.789741	+	0.613440i	$0.789785\pi$
$168$		0			0
$169$	−6.89546	+	11.9433i	−0.530420	+	0.918714i
$170$	1.90332	−	3.29665i	0.145978	−	0.252842i
$171$		0			0
$172$	7.08968	+	12.2797i	0.540583	+	0.936318i
$173$	−5.07046	−	8.78229i	−0.385500	−	0.667705i	0.606339	−	0.795206i	$-0.292638\pi$
$173$	−5.07046	−	8.78229i	−0.385500	−	0.667705i	−0.991838	+	0.127502i	$0.959304\pi$
$174$		0			0
$175$		0			0
$176$	−3.66738	−	6.35208i	−0.276439	−	0.478806i
$177$		0			0
$178$	−2.58984			−0.194117
$179$	−0.850579	−	1.47325i	−0.0635752	−	0.110116i	0.832486	−	0.554046i	$-0.186917\pi$
$179$	−0.850579	−	1.47325i	−0.0635752	−	0.110116i	−0.896061	+	0.443931i	$0.853584\pi$
$180$		0			0
$181$	16.9941			1.26316			0.631581	−	0.775310i	$-0.282406\pi$
$181$	16.9941			1.26316			0.631581	+	0.775310i	$0.282406\pi$
$182$		0			0
$183$		0			0
$184$	−8.26505			−0.609308
$185$	−0.375877	+	0.651039i	−0.0276351	+	0.0478653i
$186$		0			0
$187$	−1.17178	−	2.02957i	−0.0856887	−	0.148417i
$188$	−13.2323			−0.965066
$189$		0			0
$190$	−6.15437			−0.446485
$191$	11.3470	+	19.6535i	0.821038	+	1.42208i	0.904910	+	0.425603i	$0.139938\pi$
$191$	11.3470	+	19.6535i	0.821038	+	1.42208i	−0.0838717	+	0.996477i	$0.526729\pi$
$192$		0			0
$193$	−3.09349	+	5.35808i	−0.222674	+	0.385683i	−0.955619	−	0.294605i	$-0.904812\pi$
$193$	−3.09349	+	5.35808i	−0.222674	+	0.385683i	0.732945	+	0.680288i	$0.238145\pi$
$194$	−22.4526			−1.61200
$195$		0			0
$196$		0			0
$197$	−9.77010			−0.696091			−0.348045	−	0.937478i	$-0.613154\pi$
$197$	−9.77010			−0.696091			−0.348045	+	0.937478i	$0.613154\pi$
$198$		0			0
$199$	4.33973	+	7.51664i	0.307636	+	0.532840i	0.977845	−	0.209332i	$-0.0671289\pi$
$199$	4.33973	+	7.51664i	0.307636	+	0.532840i	−0.670209	+	0.742172i	$0.733796\pi$
$200$	3.61381			0.255535
$201$		0			0
$202$	−1.02987	−	1.78379i	−0.0724615	−	0.125507i
$203$		0			0
$204$		0			0
$205$	6.02225	+	10.4308i	0.420612	+	0.728522i
$206$	1.77721	+	3.07822i	0.123824	+	0.214470i
$207$		0			0
$208$	−12.5460	+	21.7303i	−0.869909	+	1.50673i
$209$	−1.89446	+	3.28130i	−0.131043	+	0.226973i
$210$		0			0
$211$	−2.84219	−	4.92283i	−0.195665	−	0.338901i	0.751453	−	0.659786i	$-0.229353\pi$
$211$	−2.84219	−	4.92283i	−0.195665	−	0.338901i	−0.947118	+	0.320885i	$0.896020\pi$
$212$	2.10019			0.144242
$213$		0			0
$214$	10.6412			0.727420
$215$	6.80708	−	11.7902i	0.464239	−	0.804086i
$216$		0			0
$217$		0			0
$218$	−7.58786	+	13.1426i	−0.513915	+	0.890126i
$219$		0			0
$220$	1.40372	−	2.43132i	0.0946390	−	0.163920i
$221$	−4.00862	+	6.94313i	−0.269649	+	0.467045i
$222$		0			0
$223$	−5.86133	+	10.1521i	−0.392503	+	0.679836i	−0.992779	−	0.119957i	$-0.961724\pi$
$223$	−5.86133	+	10.1521i	−0.392503	+	0.679836i	0.600276	+	0.799793i	$0.295058\pi$
$224$		0			0
$225$		0			0
$226$	−13.3509	+	23.1245i	−0.888091	+	1.53822i
$227$	11.1831			0.742247			0.371123	−	0.928584i	$-0.378973\pi$
$227$	11.1831			0.742247			0.371123	+	0.928584i	$0.378973\pi$
$228$		0			0
$229$	9.65647			0.638118			0.319059	−	0.947735i	$-0.396633\pi$
$229$	9.65647			0.638118			0.319059	+	0.947735i	$0.396633\pi$
$230$	−9.04494	−	15.6663i	−0.596406	−	1.03301i
$231$		0			0
$232$	−0.0347761	+	0.0602340i	−0.00228317	+	0.00395456i
$233$	9.64492	−	16.7055i	0.631860	−	1.09441i	−0.355311	−	0.934748i	$-0.615625\pi$
$233$	9.64492	−	16.7055i	0.631860	−	1.09441i	0.987171	−	0.159666i	$-0.0510416\pi$
$234$		0			0
$235$	6.35243	+	11.0027i	0.414387	+	0.717739i
$236$	5.86881	+	10.1651i	0.382027	+	0.661690i
$237$		0			0
$238$		0			0
$239$	0.194641	+	0.337128i	0.0125903	+	0.0218070i	0.872252	−	0.489057i	$-0.162659\pi$
$239$	0.194641	+	0.337128i	0.0125903	+	0.0218070i	−0.859662	+	0.510864i	$0.829326\pi$
$240$		0			0
$241$	−10.6361			−0.685134			−0.342567	−	0.939493i	$-0.611296\pi$
$241$	−10.6361			−0.685134			−0.342567	+	0.939493i	$0.611296\pi$
$242$	8.01932	+	13.8899i	0.515502	+	0.892875i
$243$		0			0
$244$	−4.50299			−0.288274
$245$		0			0
$246$		0			0
$247$	12.9618			0.824741
$248$	2.16023	−	3.74163i	0.137175	−	0.237594i
$249$		0			0
$250$	10.0988	+	17.4917i	0.638705	+	1.10627i
$251$	−3.26628			−0.206166			−0.103083	−	0.994673i	$-0.532871\pi$
$251$	−3.26628			−0.206166			−0.103083	+	0.994673i	$0.532871\pi$
$252$		0			0
$253$	−11.1370			−0.700176
$254$	−7.82531	−	13.5538i	−0.491004	−	0.850443i
$255$		0			0
$256$	−10.4896	+	18.1686i	−0.655603	+	1.13554i
$257$	−4.69573			−0.292912			−0.146456	−	0.989217i	$-0.546787\pi$
$257$	−4.69573			−0.292912			−0.146456	+	0.989217i	$0.546787\pi$
$258$		0			0
$259$		0			0
$260$	−9.60421			−0.595628
$261$		0			0
$262$	1.85363	+	3.21059i	0.114518	+	0.198351i
$263$	−19.5498			−1.20549			−0.602747	−	0.797932i	$-0.705927\pi$
$263$	−19.5498			−1.20549			−0.602747	+	0.797932i	$0.705927\pi$
$264$		0			0
$265$	−1.00824	−	1.74632i	−0.0619355	−	0.107276i
$266$		0			0
$267$		0			0
$268$	−4.81929	−	8.34725i	−0.294385	−	0.509890i
$269$	7.88365	+	13.6549i	0.480675	+	0.832553i	0.999754	−	0.0221730i	$-0.00705846\pi$
$269$	7.88365	+	13.6549i	0.480675	+	0.832553i	−0.519079	+	0.854726i	$0.673725\pi$
$270$		0			0
$271$	−7.39882	+	12.8151i	−0.449446	+	0.778464i	−0.998350	−	0.0574218i	$-0.981712\pi$
$271$	−7.39882	+	12.8151i	−0.449446	+	0.778464i	0.548904	+	0.835886i	$0.315045\pi$
$272$	−3.75442	+	6.50285i	−0.227645	+	0.394293i
$273$		0			0
$274$	2.04138	+	3.53578i	0.123324	+	0.213604i
$275$	4.86954			0.293644
$276$		0			0
$277$	−7.45122			−0.447701			−0.223850	−	0.974624i	$-0.571863\pi$
$277$	−7.45122			−0.447701			−0.223850	+	0.974624i	$0.571863\pi$
$278$	−0.695380	+	1.20443i	−0.0417061	+	0.0722371i
$279$		0			0
$280$		0			0
$281$	12.9938	−	22.5060i	0.775146	−	1.34259i	−0.159566	−	0.987187i	$-0.551009\pi$
$281$	12.9938	−	22.5060i	0.775146	−	1.34259i	0.934712	−	0.355406i	$-0.115657\pi$
$282$		0			0
$283$	9.37768	−	16.2426i	0.557445	−	0.965524i	−0.440263	−	0.897869i	$-0.645115\pi$
$283$	9.37768	−	16.2426i	0.557445	−	0.965524i	0.997709	−	0.0676550i	$-0.0215517\pi$
$284$	−8.57064	+	14.8448i	−0.508574	+	0.880876i
$285$		0			0
$286$	−7.20971	+	12.4876i	−0.426319	+	0.738406i
$287$		0			0
$288$		0			0
$289$	7.30041	−	12.6447i	0.429436	−	0.743805i
$290$	−0.152230			−0.00893928
$291$		0			0
$292$	−3.83507			−0.224431
$293$	−1.23089	−	2.13196i	−0.0719093	−	0.124551i	0.827829	−	0.560981i	$-0.189576\pi$
$293$	−1.23089	−	2.13196i	−0.0719093	−	0.124551i	−0.899738	+	0.436430i	$0.856243\pi$
$294$		0			0
$295$	5.63487	−	9.75988i	0.328075	−	0.568242i
$296$	0.316203	−	0.547680i	0.0183790	−	0.0318333i
$297$		0			0
$298$	6.06227	+	10.5002i	0.351178	+	0.608258i
$299$	19.0497	+	32.9950i	1.10167	+	1.90815i
$300$		0			0
$301$		0			0
$302$	−11.6616	−	20.1985i	−0.671050	−	1.16229i
$303$		0			0
$304$	12.1399			0.696270
$305$	2.16175	+	3.74425i	0.123781	+	0.214395i
$306$		0			0
$307$	4.66277			0.266118			0.133059	−	0.991108i	$-0.457520\pi$
$307$	4.66277			0.266118			0.133059	+	0.991108i	$0.457520\pi$
$308$		0			0
$309$		0			0
$310$	9.45629			0.537081
$311$	−13.7410	+	23.8002i	−0.779183	+	1.34958i	0.153231	+	0.988190i	$0.451032\pi$
$311$	−13.7410	+	23.8002i	−0.779183	+	1.34958i	−0.932413	+	0.361393i	$0.882301\pi$
$312$		0			0
$313$	2.74666	+	4.75735i	0.155250	+	0.268901i	0.933150	−	0.359487i	$-0.117048\pi$
$313$	2.74666	+	4.75735i	0.155250	+	0.268901i	−0.777900	+	0.628388i	$0.783715\pi$
$314$	31.8671			1.79837
$315$		0			0
$316$	−8.22893			−0.462914
$317$	4.93879	+	8.55424i	0.277390	+	0.480454i	0.970735	−	0.240152i	$-0.0771972\pi$
$317$	4.93879	+	8.55424i	0.277390	+	0.480454i	−0.693345	+	0.720606i	$0.743864\pi$
$318$		0			0
$319$	−0.0468601	+	0.0811641i	−0.00262366	+	0.00454432i
$320$	−3.47615			−0.194323
$321$		0			0
$322$		0			0
$323$	3.87885			0.215825
$324$		0			0
$325$	−8.32930	−	14.4268i	−0.462026	−	0.800253i
$326$	−22.4986			−1.24608
$327$		0			0
$328$	−5.06616	−	8.77485i	−0.279732	−	0.484510i
$329$		0			0
$330$		0			0
$331$	10.3471	+	17.9217i	0.568729	+	0.985067i	0.996692	+	0.0812710i	$0.0258979\pi$
$331$	10.3471	+	17.9217i	0.568729	+	0.985067i	−0.427963	+	0.903796i	$0.640769\pi$
$332$	3.89401	+	6.74463i	0.213712	+	0.370160i
$333$		0			0
$334$	3.24514	−	5.62076i	0.177566	−	0.307554i
$335$	−4.62718	+	8.01452i	−0.252810	+	0.437880i
$336$		0			0
$337$	0.748747	+	1.29687i	0.0407869	+	0.0706449i	0.885698	−	0.464261i	$-0.153680\pi$
$337$	0.748747	+	1.29687i	0.0407869	+	0.0706449i	−0.844911	+	0.534906i	$0.820347\pi$
$338$	25.3924			1.38116
$339$		0			0
$340$	−2.87408			−0.155869
$341$	2.91087	−	5.04177i	0.157632	−	0.273027i
$342$		0			0
$343$		0			0
$344$	−5.72639	+	9.91840i	−0.308746	+	0.534764i
$345$		0			0
$346$	−9.33593	+	16.1703i	−0.501903	+	0.869321i
$347$	−14.7694	+	25.5813i	−0.792862	+	1.37328i	0.131326	+	0.991339i	$0.458077\pi$
$347$	−14.7694	+	25.5813i	−0.792862	+	1.37328i	−0.924188	+	0.381938i	$0.875257\pi$
$348$		0			0
$349$	−18.0006	+	31.1780i	−0.963551	+	1.66892i	−0.250094	+	0.968222i	$0.580461\pi$
$349$	−18.0006	+	31.1780i	−0.963551	+	1.66892i	−0.713458	+	0.700698i	$0.752872\pi$
$350$		0			0
$351$		0			0
$352$	−5.05363	+	8.75315i	−0.269360	+	0.466545i
$353$	−29.4930			−1.56975			−0.784877	−	0.619652i	$-0.787274\pi$
$353$	−29.4930			−1.56975			−0.784877	+	0.619652i	$0.787274\pi$
$354$		0			0
$355$	16.4580			0.873500
$356$	0.977687	+	1.69340i	0.0518173	+	0.0897502i
$357$		0			0
$358$	−1.56612	+	2.71260i	−0.0827720	+	0.143365i
$359$	−2.70535	+	4.68580i	−0.142783	+	0.247307i	−0.928544	−	0.371224i	$-0.878938\pi$
$359$	−2.70535	+	4.68580i	−0.142783	+	0.247307i	0.785761	+	0.618531i	$0.212272\pi$
$360$		0			0
$361$	6.36444	+	11.0235i	0.334971	+	0.580186i
$362$	−15.6451	−	27.0981i	−0.822289	−	1.42425i
$363$		0			0
$364$		0			0
$365$	1.84110	+	3.18888i	0.0963676	+	0.166914i
$366$		0			0
$367$	23.0843			1.20499			0.602496	−	0.798122i	$-0.294173\pi$
$367$	23.0843			1.20499			0.602496	+	0.798122i	$0.294173\pi$
$368$	17.8417	+	30.9027i	0.930063	+	1.61092i
$369$		0			0
$370$	1.38416			0.0719591
$371$		0			0
$372$		0			0
$373$	21.5030			1.11338			0.556692	−	0.830719i	$-0.312070\pi$
$373$	21.5030			1.11338			0.556692	+	0.830719i	$0.312070\pi$
$374$	−2.15752	+	3.73694i	−0.111563	+	0.193232i
$375$		0			0
$376$	−5.34392	−	9.25595i	−0.275592	−	0.477339i
$377$	0.320615			0.0165125
$378$		0			0
$379$	5.72168			0.293903			0.146952	−	0.989144i	$-0.453054\pi$
$379$	5.72168			0.293903			0.146952	+	0.989144i	$0.453054\pi$
$380$	2.32333	+	4.02412i	0.119184	+	0.206433i
$381$		0			0
$382$	20.8925	−	36.1869i	1.06895	−	1.85148i
$383$	−34.9209			−1.78437			−0.892187	−	0.451666i	$-0.850830\pi$
$383$	−34.9209			−1.78437			−0.892187	+	0.451666i	$0.850830\pi$
$384$		0			0
$385$		0			0
$386$	11.3917			0.579823
$387$		0			0
$388$	8.47603	+	14.6809i	0.430305	+	0.745311i
$389$	28.8822			1.46438			0.732192	−	0.681098i	$-0.238497\pi$
$389$	28.8822			1.46438			0.732192	+	0.681098i	$0.238497\pi$
$390$		0			0
$391$	5.70066	+	9.87383i	0.288295	+	0.499341i
$392$		0			0
$393$		0			0
$394$	8.99455	+	15.5790i	0.453139	+	0.784860i
$395$	3.95046	+	6.84239i	0.198769	+	0.344278i
$396$		0			0
$397$	−5.59226	+	9.68607i	−0.280667	+	0.486130i	−0.971549	−	0.236838i	$-0.923889\pi$
$397$	−5.59226	+	9.68607i	−0.280667	+	0.486130i	0.690882	+	0.722968i	$0.257222\pi$
$398$	7.99049	−	13.8399i	0.400527	−	0.693734i
$399$		0			0
$400$	−7.80111	−	13.5119i	−0.390056	−	0.675596i
$401$	1.08212			0.0540386			0.0270193	−	0.999635i	$-0.491398\pi$
$401$	1.08212			0.0540386			0.0270193	+	0.999635i	$0.491398\pi$
$402$		0			0
$403$	−19.9160			−0.992088
$404$	−0.777570	+	1.34679i	−0.0386856	+	0.0670054i
$405$		0			0
$406$		0			0
$407$	0.426078	−	0.737988i	0.0211199	−	0.0365807i
$408$		0			0
$409$	−10.8674	+	18.8229i	−0.537360	+	0.930735i	0.461685	+	0.887044i	$0.347245\pi$
$409$	−10.8674	+	18.8229i	−0.537360	+	0.930735i	−0.999045	+	0.0436908i	$0.986088\pi$
$410$	11.0884	−	19.2057i	0.547618	−	0.948501i
$411$		0			0
$412$	1.34182	−	2.32410i	0.0661069	−	0.114500i
$413$		0			0
$414$		0			0
$415$	3.73879	−	6.47578i	0.183530	−	0.317884i
$416$	34.5767			1.69526
$417$		0			0
$418$	6.97632			0.341223
$419$	12.5906	+	21.8075i	0.615090	+	1.06537i	0.990369	+	0.138455i	$0.0442135\pi$
$419$	12.5906	+	21.8075i	0.615090	+	1.06537i	−0.375279	+	0.926912i	$0.622453\pi$
$420$		0			0
$421$	−14.8304	+	25.6869i	−0.722788	+	1.25191i	0.237090	+	0.971488i	$0.423806\pi$
$421$	−14.8304	+	25.6869i	−0.722788	+	1.25191i	−0.959878	+	0.280418i	$0.909527\pi$
$422$	−5.23316	+	9.06411i	−0.254746	+	0.441234i
$423$		0			0
$424$	0.848171	+	1.46907i	0.0411908	+	0.0713446i
$425$	−2.49256	−	4.31724i	−0.120907	−	0.209417i
$426$		0			0
$427$		0			0
$428$	−4.01715	−	6.95791i	−0.194176	−	0.336323i
$429$		0			0
$430$	−25.0669			−1.20884
$431$	−2.44517	−	4.23516i	−0.117780	−	0.204000i	0.801108	−	0.598520i	$-0.204244\pi$
$431$	−2.44517	−	4.23516i	−0.117780	−	0.204000i	−0.918887	+	0.394520i	$0.870911\pi$
$432$		0			0
$433$	−9.71430			−0.466839			−0.233420	−	0.972376i	$-0.574992\pi$
$433$	−9.71430			−0.466839			−0.233420	+	0.972376i	$0.574992\pi$
$434$		0			0
$435$		0			0
$436$	11.4579			0.548735
$437$	9.21651	−	15.9635i	0.440885	−	0.763636i
$438$		0			0
$439$	−7.41176	−	12.8375i	−0.353744	−	0.612703i	0.633158	−	0.774022i	$-0.281758\pi$
$439$	−7.41176	−	12.8375i	−0.353744	−	0.612703i	−0.986902	+	0.161320i	$0.948425\pi$
$440$	2.26760			0.108103
$441$		0			0
$442$	14.7617			0.702141
$443$	−10.9510	−	18.9676i	−0.520297	−	0.901180i	−0.999722	−	0.0235972i	$-0.992488\pi$
$443$	−10.9510	−	18.9676i	−0.520297	−	0.901180i	0.479425	−	0.877583i	$-0.340845\pi$
$444$		0			0
$445$	0.938715	−	1.62590i	0.0444994	−	0.0770751i
$446$	21.5842			1.02204
$447$		0			0
$448$		0			0
$449$	−21.4952			−1.01442			−0.507212	−	0.861822i	$-0.669324\pi$
$449$	−21.4952			−1.01442			−0.507212	+	0.861822i	$0.669324\pi$
$450$		0			0
$451$	−6.82655	−	11.8239i	−0.321450	−	0.556767i
$452$	20.1603			0.948263
$453$		0			0
$454$	−10.2954	−	17.8321i	−0.483185	−	0.836902i
$455$		0			0
$456$		0			0
$457$	−20.3128	−	35.1827i	−0.950190	−	1.64578i	−0.745009	−	0.667054i	$-0.767555\pi$
$457$	−20.3128	−	35.1827i	−0.950190	−	1.64578i	−0.205181	−	0.978724i	$-0.565778\pi$
$458$	−8.88995	−	15.3978i	−0.415400	−	0.719494i
$459$		0			0
$460$	−6.82908	+	11.8283i	−0.318408	+	0.551498i
$461$	1.41541	−	2.45155i	0.0659220	−	0.114180i	−0.831181	−	0.556003i	$-0.812334\pi$
$461$	1.41541	−	2.45155i	0.0659220	−	0.114180i	0.897103	+	0.441822i	$0.145668\pi$
$462$		0			0
$463$	−13.9324	−	24.1317i	−0.647494	−	1.12149i	−0.983719	−	0.179711i	$-0.942484\pi$
$463$	−13.9324	−	24.1317i	−0.647494	−	1.12149i	0.336225	−	0.941782i	$-0.390850\pi$
$464$	0.300284			0.0139403
$465$		0			0
$466$	−35.5173			−1.64531
$467$	−13.3219	+	23.0742i	−0.616464	+	1.06775i	0.373661	+	0.927565i	$0.378102\pi$
$467$	−13.3219	+	23.0742i	−0.616464	+	1.06775i	−0.990126	+	0.140182i	$0.955231\pi$
$468$		0			0
$469$		0			0
$470$	11.6964	−	20.2587i	0.539513	−	0.934463i
$471$		0			0
$472$	−4.74028	+	8.21041i	−0.218189	+	0.377915i
$473$	−7.71620	+	13.3648i	−0.354791	+	0.614516i
$474$		0			0
$475$	−4.02983	+	6.97987i	−0.184901	+	0.320258i
$476$		0			0
$477$		0			0
$478$	0.358381	−	0.620734i	0.0163920	−	0.0283917i
$479$	−31.5791			−1.44289			−0.721443	−	0.692474i	$-0.756521\pi$
$479$	−31.5791			−1.44289			−0.721443	+	0.692474i	$0.756521\pi$
$480$		0			0
$481$	−2.91520			−0.132922
$482$	9.79185	+	16.9600i	0.446007	+	0.772506i
$483$		0			0
$484$	6.05472	−	10.4871i	0.275215	−	0.476686i
$485$	8.13817	−	14.0957i	0.369535	−	0.640054i
$486$		0			0
$487$	−0.153087	−	0.265154i	−0.00693703	−	0.0120153i	0.862536	−	0.505996i	$-0.168875\pi$
$487$	−0.153087	−	0.265154i	−0.00693703	−	0.0120153i	−0.869473	+	0.493980i	$0.835541\pi$
$488$	−1.81855	−	3.14982i	−0.0823218	−	0.142586i
$489$		0			0
$490$		0			0
$491$	9.06981	+	15.7094i	0.409315	+	0.708954i	0.994813	−	0.101720i	$-0.0324345\pi$
$491$	9.06981	+	15.7094i	0.409315	+	0.708954i	−0.585498	+	0.810674i	$0.699101\pi$
$492$		0			0
$493$	0.0959447			0.00432113
$494$	−11.9329	−	20.6684i	−0.536887	−	0.929916i
$495$		0			0
$496$	−18.6531			−0.837549
$497$		0			0
$498$		0			0
$499$	−21.3091			−0.953928			−0.476964	−	0.878923i	$-0.658263\pi$
$499$	−21.3091			−0.953928			−0.476964	+	0.878923i	$0.658263\pi$
$500$	7.62478	−	13.2065i	0.340990	−	0.590613i
$501$		0			0
$502$	3.00701	+	5.20829i	0.134209	+	0.232457i
$503$	−17.0738			−0.761285			−0.380642	−	0.924722i	$-0.624297\pi$
$503$	−17.0738			−0.761285			−0.380642	+	0.924722i	$0.624297\pi$
$504$		0			0
$505$	1.49315			0.0664443
$506$	10.2529	+	17.7586i	0.455799	+	0.789466i
$507$		0			0
$508$	−5.90824	+	10.2334i	−0.262136	+	0.454032i
$509$	36.7735			1.62996			0.814979	−	0.579490i	$-0.196748\pi$
$509$	36.7735			1.62996			0.814979	+	0.579490i	$0.196748\pi$
$510$		0			0
$511$		0			0
$512$	21.4975			0.950065
$513$		0			0
$514$	4.32299	+	7.48764i	0.190679	+	0.330265i
$515$	−2.57667			−0.113542
$516$		0			0
$517$	−7.20083	−	12.4722i	−0.316692	−	0.548527i
$518$		0			0
$519$		0			0
$520$	−3.87870	−	6.71810i	−0.170092	−	0.294608i
$521$	−9.57535	−	16.5850i	−0.419504	−	0.726602i	0.576386	−	0.817178i	$-0.304463\pi$
$521$	−9.57535	−	16.5850i	−0.419504	−	0.726602i	−0.995890	+	0.0905758i	$0.971129\pi$
$522$		0			0
$523$	20.9715	−	36.3236i	0.917018	−	1.58832i	0.113097	−	0.993584i	$-0.463923\pi$
$523$	20.9715	−	36.3236i	0.917018	−	1.58832i	0.803920	−	0.594737i	$-0.202744\pi$
$524$	1.39952	−	2.42405i	0.0611385	−	0.105895i
$525$		0			0
$526$	17.9980	+	31.1734i	0.784749	+	1.35922i
$527$	−5.95991			−0.259618
$528$		0			0
$529$	31.1812			1.35570
$530$	−1.85641	+	3.21539i	−0.0806372	+	0.139668i
$531$		0			0
$532$		0			0
$533$	−23.3535	+	40.4494i	−1.01155	+	1.75206i
$534$		0			0
$535$	−3.85702	+	6.68056i	−0.166754	+	0.288826i
$536$	3.89258	−	6.74214i	0.168134	−	0.291216i
$537$		0			0
$538$	14.5157	−	25.1419i	0.625816	−	1.08395i
$539$		0			0
$540$		0			0
$541$	−1.44272	+	2.49886i	−0.0620273	+	0.107434i	−0.895371	−	0.445320i	$-0.853090\pi$
$541$	−1.44272	+	2.49886i	−0.0620273	+	0.107434i	0.833344	+	0.552754i	$0.186423\pi$
$542$	27.2460			1.17032
$543$		0			0
$544$	10.3472			0.443631
$545$	−5.50059	−	9.52731i	−0.235620	−	0.408105i
$546$		0			0
$547$	1.38738	−	2.40301i	0.0593201	−	0.102745i	−0.834840	−	0.550492i	$-0.814440\pi$
$547$	1.38738	−	2.40301i	0.0593201	−	0.102745i	0.894160	+	0.447747i	$0.147773\pi$
$548$	1.54128	−	2.66957i	0.0658401	−	0.114038i
$549$		0			0
$550$	−4.48300	−	7.76478i	−0.191156	−	0.331091i
$551$	−0.0775590	−	0.134336i	−0.00330413	−	0.00572291i
$552$		0			0
$553$		0			0
$554$	6.85975	+	11.8814i	0.291443	+	0.504794i
$555$		0			0
$556$	1.05005			0.0445319
$557$	−15.5344	−	26.9064i	−0.658214	−	1.14006i	−0.981078	−	0.193614i	$-0.937979\pi$
$557$	−15.5344	−	26.9064i	−0.658214	−	1.14006i	0.322864	−	0.946445i	$-0.395354\pi$
$558$		0			0
$559$	52.7939			2.23294
$560$		0			0
$561$		0			0
$562$	−47.8495			−2.01841
$563$	−0.144020	+	0.249451i	−0.00606973	+	0.0105131i	−0.869044	−	0.494734i	$-0.835265\pi$
$563$	−0.144020	+	0.249451i	−0.00606973	+	0.0105131i	0.862975	+	0.505247i	$0.168599\pi$
$564$		0			0
$565$	−9.67836	−	16.7634i	−0.407172	−	0.705242i
$566$	−34.5331			−1.45154
$567$		0			0
$568$	−13.8451			−0.580929
$569$	−8.04004	−	13.9258i	−0.337056	−	0.583798i	0.646821	−	0.762641i	$-0.276098\pi$
$569$	−8.04004	−	13.9258i	−0.337056	−	0.583798i	−0.983878	+	0.178843i	$0.942765\pi$
$570$		0			0
$571$	7.64289	−	13.2379i	0.319845	−	0.553988i	−0.660610	−	0.750729i	$-0.729702\pi$
$571$	7.64289	−	13.2379i	0.319845	−	0.553988i	0.980456	+	0.196741i	$0.0630358\pi$
$572$	10.8869			0.455204
$573$		0			0
$574$		0			0
$575$	−23.6902			−0.987950
$576$		0			0
$577$	−12.0812	−	20.9253i	−0.502949	−	0.871133i	−0.999994	−	0.00340833i	$-0.998915\pi$
$577$	−12.0812	−	20.9253i	−0.502949	−	0.871133i	0.497045	−	0.867725i	$-0.334418\pi$
$578$	−26.8836			−1.11821
$579$		0			0
$580$	0.0574683	+	0.0995380i	0.00238624	+	0.00413309i
$581$		0			0
$582$		0			0
$583$	1.14289	+	1.97955i	0.0473338	+	0.0819845i
$584$	−1.54881	−	2.68262i	−0.0640902	−	0.111007i
$585$		0			0
$586$	−2.26636	+	3.92546i	−0.0936226	+	0.162159i
$587$	18.0145	−	31.2020i	0.743537	−	1.28784i	−0.207339	−	0.978269i	$-0.566480\pi$
$587$	18.0145	−	31.2020i	0.743537	−	1.28784i	0.950875	−	0.309574i	$-0.100186\pi$
$588$		0			0
$589$	4.81783	+	8.34472i	0.198515	+	0.343838i
$590$	−20.7503			−0.854276
$591$		0			0
$592$	−2.73034			−0.112216
$593$	12.4668	−	21.5932i	0.511951	−	0.886726i	−0.487953	−	0.872870i	$-0.662256\pi$
$593$	12.4668	−	21.5932i	0.511951	−	0.886726i	0.999904	−	0.0138558i	$-0.00441057\pi$
$594$		0			0
$595$		0			0
$596$	4.57712	−	7.92780i	0.187486	−	0.324735i
$597$		0			0
$598$	35.0751	−	60.7518i	1.43433	−	2.48433i
$599$	19.7642	−	34.2325i	0.807542	−	1.39870i	−0.107019	−	0.994257i	$-0.534131\pi$
$599$	19.7642	−	34.2325i	0.807542	−	1.39870i	0.914561	−	0.404447i	$-0.132536\pi$
$600$		0			0
$601$	−1.86447	+	3.22936i	−0.0760534	+	0.131728i	−0.901544	−	0.432688i	$-0.857565\pi$
$601$	−1.86447	+	3.22936i	−0.0760534	+	0.131728i	0.825490	+	0.564416i	$0.190899\pi$
$602$		0			0
$603$		0			0
$604$	−8.80470	+	15.2502i	−0.358258	+	0.620521i
$605$	−11.6267			−0.472694
$606$		0			0
$607$	−23.6528			−0.960036			−0.480018	−	0.877259i	$-0.659370\pi$
$607$	−23.6528			−0.960036			−0.480018	+	0.877259i	$0.659370\pi$
$608$	−8.36436	−	14.4875i	−0.339219	−	0.587545i
$609$		0			0
$610$	3.98029	−	6.89407i	0.161157	−	0.279133i
$611$	−24.6339	+	42.6671i	−0.996580	+	1.72613i
$612$		0			0
$613$	1.89952	+	3.29006i	0.0767208	+	0.132884i	0.901833	−	0.432084i	$-0.142222\pi$
$613$	1.89952	+	3.29006i	0.0767208	+	0.132884i	−0.825113	+	0.564968i	$0.808888\pi$
$614$	−4.29264	−	7.43507i	−0.173237	−	0.300055i
$615$		0			0
$616$		0			0
$617$	17.5615	+	30.4174i	0.706999	+	1.22456i	0.965965	+	0.258672i	$0.0832849\pi$
$617$	17.5615	+	30.4174i	0.706999	+	1.22456i	−0.258966	+	0.965886i	$0.583382\pi$
$618$		0			0
$619$	21.1632			0.850622			0.425311	−	0.905047i	$-0.360165\pi$
$619$	21.1632			0.850622			0.425311	+	0.905047i	$0.360165\pi$
$620$	−3.56983	−	6.18312i	−0.143368	−	0.248320i
$621$		0			0
$622$	50.6011			2.02892
$623$		0			0
$624$		0			0
$625$	1.45048			0.0580192
$626$	5.05726	−	8.75943i	0.202129	−	0.350097i
$627$		0			0
$628$	−12.0301	−	20.8368i	−0.480054	−	0.831477i
$629$	−0.872381			−0.0347841
$630$		0			0
$631$	4.74845			0.189033			0.0945164	−	0.995523i	$-0.469870\pi$
$631$	4.74845			0.189033			0.0945164	+	0.995523i	$0.469870\pi$
$632$	−3.32329	−	5.75610i	−0.132193	−	0.228965i
$633$		0			0
$634$	9.09350	−	15.7504i	0.361149	−	0.625529i
$635$	11.3455			0.450231
$636$		0			0
$637$		0			0
$638$	0.172562			0.00683178
$639$		0			0
$640$	−5.71622	−	9.90078i	−0.225953	−	0.391363i
$641$	9.87469			0.390027			0.195013	−	0.980801i	$-0.437525\pi$
$641$	9.87469			0.390027			0.195013	+	0.980801i	$0.437525\pi$
$642$		0			0
$643$	−21.9748	−	38.0615i	−0.866602	−	1.50100i	−0.865448	−	0.501000i	$-0.832966\pi$
$643$	−21.9748	−	38.0615i	−0.866602	−	1.50100i	−0.00115462	−	0.999999i	$-0.500368\pi$
$644$		0			0
$645$		0			0
$646$	−3.57095	−	6.18507i	−0.140497	−	0.243348i
$647$	22.1936	+	38.4404i	0.872521	+	1.51125i	0.859381	+	0.511336i	$0.170849\pi$
$647$	22.1936	+	38.4404i	0.872521	+	1.51125i	0.0131398	+	0.999914i	$0.495817\pi$
$648$		0			0
$649$	−6.38743	+	11.0634i	−0.250729	+	0.434275i
$650$	−15.3362	+	26.5631i	−0.601537	+	1.04189i
$651$		0			0
$652$	8.49341	+	14.7110i	0.332628	+	0.576128i
$653$	−41.9912			−1.64324			−0.821622	−	0.570033i	$-0.806930\pi$
$653$	−41.9912			−1.64324			−0.821622	+	0.570033i	$0.806930\pi$
$654$		0			0
$655$	−2.68748			−0.105008
$656$	−21.8726	+	37.8844i	−0.853980	+	1.47914i
$657$		0			0
$658$		0			0
$659$	19.6365	−	34.0114i	0.764928	−	1.32489i	−0.175356	−	0.984505i	$-0.556108\pi$
$659$	19.6365	−	34.0114i	0.764928	−	1.32489i	0.940284	−	0.340390i	$-0.110559\pi$
$660$		0			0
$661$	−0.0933694	+	0.161721i	−0.00363165	+	0.00629020i	−0.867836	−	0.496852i	$-0.834489\pi$
$661$	−0.0933694	+	0.161721i	−0.00363165	+	0.00629020i	0.864204	+	0.503142i	$0.167823\pi$
$662$	19.0515	−	32.9982i	0.740459	−	1.28251i
$663$		0			0
$664$	−3.14522	+	5.44769i	−0.122058	+	0.211411i
$665$		0			0
$666$		0			0
$667$	0.227973	−	0.394862i	0.00882717	−	0.0152891i
$668$	−4.90028			−0.189597
$669$		0			0
$670$	17.0395			0.658294
$671$	−2.45046	−	4.24432i	−0.0945989	−	0.163850i
$672$		0			0
$673$	−5.43382	+	9.41166i	−0.209458	+	0.362793i	−0.951544	−	0.307512i	$-0.900503\pi$
$673$	−5.43382	+	9.41166i	−0.209458	+	0.362793i	0.742086	+	0.670305i	$0.233837\pi$
$674$	1.37862	−	2.38785i	0.0531026	−	0.0919764i
$675$		0			0
$676$	−9.58584	−	16.6032i	−0.368686	−	0.638583i
$677$	−14.1950	−	24.5865i	−0.545560	−	0.944937i	−0.998571	−	0.0534326i	$-0.982984\pi$
$677$	−14.1950	−	24.5865i	−0.545560	−	0.944937i	0.453012	−	0.891505i	$-0.350350\pi$
$678$		0			0
$679$		0			0
$680$	−1.16071	−	2.01041i	−0.0445111	−	0.0770956i
$681$		0			0
$682$	−10.7192			−0.410460
$683$	−5.92034	−	10.2543i	−0.226536	−	0.392371i	0.730243	−	0.683187i	$-0.239407\pi$
$683$	−5.92034	−	10.2543i	−0.226536	−	0.392371i	−0.956779	+	0.290816i	$0.906073\pi$
$684$		0			0
$685$	−2.95968			−0.113083
$686$		0			0
$687$		0			0
$688$	49.4461			1.88511
$689$	3.90981	−	6.77199i	0.148952	−	0.257992i
$690$		0			0
$691$	5.95416	+	10.3129i	0.226507	+	0.392321i	0.956770	−	0.290844i	$-0.0939361\pi$
$691$	5.95416	+	10.3129i	0.226507	+	0.392321i	−0.730264	+	0.683165i	$0.760603\pi$
$692$	14.0976			0.535909
$693$		0			0
$694$	54.3880			2.06454
$695$	−0.504096	−	0.873119i	−0.0191214	−	0.0331193i
$696$		0			0
$697$	−6.98857	+	12.1046i	−0.264711	+	0.458493i
$698$	66.2870			2.50900
$699$		0			0
$700$		0			0
$701$	31.3902			1.18559			0.592795	−	0.805353i	$-0.298024\pi$
$701$	31.3902			1.18559			0.592795	+	0.805353i	$0.298024\pi$
$702$		0			0
$703$	0.705208	+	1.22146i	0.0265974	+	0.0460681i
$704$	3.94041			0.148510
$705$		0			0
$706$	27.1518	+	47.0284i	1.02187	+	1.76994i
$707$		0			0
$708$		0			0
$709$	−0.312609	−	0.541455i	−0.0117403	−	0.0203348i	0.860096	−	0.510133i	$-0.170404\pi$
$709$	−0.312609	−	0.541455i	−0.0117403	−	0.0203348i	−0.871836	+	0.489798i	$0.837070\pi$
$710$	−15.1516	−	26.2433i	−0.568628	−	0.984893i
$711$		0			0
$712$	−0.789685	+	1.36777i	−0.0295947	+	0.0512595i
$713$	−14.1613	+	24.5281i	−0.530345	+	0.918584i
$714$		0			0
$715$	−5.22647	−	9.05251i	−0.195459	−	0.338545i
$716$	2.36489			0.0883802
$717$		0			0
$718$	9.96239			0.371793
$719$	12.1969	−	21.1257i	0.454869	−	0.787857i	−0.543811	−	0.839208i	$-0.683019\pi$
$719$	12.1969	−	21.1257i	0.454869	−	0.787857i	0.998681	+	0.0513506i	$0.0163526\pi$
$720$		0			0
$721$		0			0
$722$	11.7185	−	20.2970i	0.436116	−	0.755376i
$723$		0			0
$724$	−11.8123	+	20.4595i	−0.439002	+	0.760373i
$725$	−0.0996792	+	0.172649i	−0.00370199	+	0.00641204i
$726$		0			0
$727$	18.9253	−	32.7796i	0.701900	−	1.21573i	−0.265899	−	0.964001i	$-0.585669\pi$
$727$	18.9253	−	32.7796i	0.701900	−	1.21573i	0.967799	−	0.251726i	$-0.0809980\pi$
$728$		0			0
$729$		0			0
$730$	3.38991	−	5.87150i	0.125466	−	0.217314i
$731$	15.7987			0.584335
$732$		0			0
$733$	−2.40155			−0.0887033			−0.0443516	−	0.999016i	$-0.514122\pi$
$733$	−2.40155			−0.0887033			−0.0443516	+	0.999016i	$0.514122\pi$
$734$	−21.2519	−	36.8093i	−0.784421	−	1.35866i
$735$		0			0
$736$	24.5858	−	42.5839i	0.906245	−	1.56966i
$737$	5.24517	−	9.08490i	0.193208	−	0.334646i
$738$		0			0
$739$	−15.1940	−	26.3167i	−0.558920	−	0.968077i	−0.997587	−	0.0694277i	$-0.977883\pi$
$739$	−15.1940	−	26.3167i	−0.558920	−	0.968077i	0.438667	−	0.898650i	$-0.355451\pi$
$740$	−0.522533	−	0.905053i	−0.0192087	−	0.0332704i
$741$		0			0
$742$		0			0
$743$	2.54785	+	4.41300i	0.0934715	+	0.161897i	0.908970	−	0.416862i	$-0.136870\pi$
$743$	2.54785	+	4.41300i	0.0934715	+	0.161897i	−0.815498	+	0.578760i	$0.803537\pi$
$744$		0			0
$745$	−8.78934			−0.322016
$746$	−19.7961	−	34.2879i	−0.724787	−	1.25537i
$747$		0			0
$748$	3.25793			0.119122
$749$		0			0
$750$		0			0
$751$	−0.975011			−0.0355787			−0.0177893	−	0.999842i	$-0.505663\pi$
$751$	−0.975011			−0.0355787			−0.0177893	+	0.999842i	$0.505663\pi$
$752$	−23.0718	+	39.9615i	−0.841341	+	1.45724i
$753$		0			0
$754$	−0.295165	−	0.511240i	−0.0107493	−	0.0186183i
$755$	16.9075			0.615326
$756$		0			0
$757$	11.6346			0.422865			0.211433	−	0.977393i	$-0.432187\pi$
$757$	11.6346			0.422865			0.211433	+	0.977393i	$0.432187\pi$
$758$	−5.26750	−	9.12357i	−0.191324	−	0.331383i
$759$		0			0
$760$	−1.87657	+	3.25031i	−0.0680703	+	0.117901i
$761$	−54.1749			−1.96384			−0.981920	−	0.189298i	$-0.939379\pi$
$761$	−54.1749			−1.96384			−0.981920	+	0.189298i	$0.939379\pi$
$762$		0			0
$763$		0			0
$764$	−31.5484			−1.14138
$765$		0			0
$766$	32.1489	+	55.6835i	1.16159	+	2.01193i
$767$	43.7025			1.57801
$768$		0			0
$769$	10.4326	+	18.0698i	0.376208	+	0.651612i	0.990507	−	0.137462i	$-0.0438943\pi$
$769$	10.4326	+	18.0698i	0.376208	+	0.651612i	−0.614299	+	0.789074i	$0.710561\pi$
$770$		0			0
$771$		0			0
$772$	−4.30047	−	7.44863i	−0.154777	−	0.268082i
$773$	−27.4972	−	47.6266i	−0.989007	−	1.71301i	−0.622561	−	0.782572i	$-0.713908\pi$
$773$	−27.4972	−	47.6266i	−0.989007	−	1.71301i	−0.366447	−	0.930439i	$-0.619426\pi$
$774$		0			0
$775$	6.19189	−	10.7247i	0.222419	−	0.385242i
$776$	−6.84616	+	11.8579i	−0.245763	+	0.425674i
$777$		0			0
$778$	−26.5895	−	46.0544i	−0.953281	−	1.65113i
$779$	22.5975			0.809639
$780$		0			0
$781$	−18.6560			−0.667566
$782$	10.4963	−	18.1801i	0.375346	−	0.650119i
$783$		0			0
$784$		0			0
$785$	−11.5506	+	20.0062i	−0.412258	+	0.714051i
$786$		0			0
$787$	4.59475	−	7.95833i	0.163785	−	0.283684i	−0.772438	−	0.635090i	$-0.780963\pi$
$787$	4.59475	−	7.95833i	0.163785	−	0.283684i	0.936223	+	0.351406i	$0.114296\pi$
$788$	6.79103	−	11.7624i	0.241921	−	0.419019i
$789$		0			0
$790$	7.27374	−	12.5985i	0.258788	−	0.448234i
$791$		0			0
$792$		0			0
$793$	−8.38296	+	14.5197i	−0.297688	+	0.515610i
$794$	20.5934			0.730832
$795$		0			0
$796$	−12.0659			−0.427665
$797$	3.53774	+	6.12754i	0.125313	+	0.217049i	0.921855	−	0.387534i	$-0.126673\pi$
$797$	3.53774	+	6.12754i	0.125313	+	0.217049i	−0.796542	+	0.604583i	$0.793340\pi$
$798$		0			0
$799$	−7.37174	+	12.7682i	−0.260793	+	0.451707i
$800$	−10.7499	+	18.6194i	−0.380067	+	0.658295i
$801$		0			0
$802$	−0.996224	−	1.72551i	−0.0351779	−	0.0609299i
$803$	−2.08699	−	3.61477i	−0.0736483	−	0.127563i
$804$		0			0
$805$		0			0
$806$	18.3351	+	31.7573i	0.645827	+	1.11860i
$807$		0			0
$808$	−1.25610			−0.0441894
$809$	2.97060	+	5.14522i	0.104441	+	0.180896i	0.913510	−	0.406817i	$-0.133361\pi$
$809$	2.97060	+	5.14522i	0.104441	+	0.180896i	−0.809069	+	0.587714i	$0.800028\pi$
$810$		0			0
$811$	−44.4139			−1.55958			−0.779791	−	0.626039i	$-0.784675\pi$
$811$	−44.4139			−1.55958			−0.779791	+	0.626039i	$0.784675\pi$
$812$		0			0
$813$		0			0
$814$	−1.56902			−0.0549942
$815$	8.15485	−	14.1246i	0.285652	−	0.494764i
$816$		0			0
$817$	−12.7712	−	22.1204i	−0.446808	−	0.773894i
$818$	40.0191			1.39924
$819$		0			0
$820$	−16.7439			−0.584721
$821$	3.17761	+	5.50378i	0.110899	+	0.192083i	0.916133	−	0.400874i	$-0.131294\pi$
$821$	3.17761	+	5.50378i	0.110899	+	0.192083i	−0.805234	+	0.592958i	$0.797960\pi$
$822$		0			0
$823$	4.73216	−	8.19635i	0.164953	−	0.285707i	−0.771686	−	0.636004i	$-0.780586\pi$
$823$	4.73216	−	8.19635i	0.164953	−	0.285707i	0.936639	+	0.350297i	$0.113919\pi$
$824$	2.16760			0.0755120
$825$		0			0
$826$		0			0
$827$	4.86261			0.169090			0.0845448	−	0.996420i	$-0.473056\pi$
$827$	4.86261			0.169090			0.0845448	+	0.996420i	$0.473056\pi$
$828$		0			0
$829$	−20.3926	−	35.3211i	−0.708266	−	1.22675i	−0.965500	−	0.260403i	$-0.916145\pi$
$829$	−20.3926	−	35.3211i	−0.708266	−	1.22675i	0.257234	−	0.966349i	$-0.417189\pi$
$830$	−13.7680			−0.477896
$831$		0			0
$832$	−6.74003	−	11.6741i	−0.233668	−	0.404725i
$833$		0			0
$834$		0			0
$835$	2.35247	+	4.07460i	0.0814107	+	0.141007i
$836$	−2.63362	−	4.56156i	−0.0910856	−	0.157765i
$837$		0			0
$838$	23.1823	−	40.1529i	0.800818	−	1.38706i
$839$	9.60171	−	16.6307i	0.331488	−	0.574154i	−0.651316	−	0.758807i	$-0.725783\pi$
$839$	9.60171	−	16.6307i	0.331488	−	0.574154i	0.982804	+	0.184653i	$0.0591161\pi$
$840$		0			0
$841$	14.4981	+	25.1114i	0.499934	+	0.865911i
$842$	54.6126			1.88207
$843$		0			0
$844$	7.90225			0.272007
$845$	−9.20374	+	15.9413i	−0.316618	+	0.548399i
$846$		0			0
$847$		0			0
$848$	3.66188	−	6.34256i	0.125749	−	0.217804i
$849$		0			0
$850$	−4.58940	+	7.94907i	−0.157415	+	0.272651i
$851$	−2.07286	+	3.59029i	−0.0710566	+	0.123074i
$852$		0			0
$853$	6.95055	−	12.0387i	0.237982	−	0.412198i	−0.722153	−	0.691734i	$-0.756847\pi$
$853$	6.95055	−	12.0387i	0.237982	−	0.412198i	0.960135	+	0.279536i	$0.0901806\pi$
$854$		0			0
$855$		0			0
$856$	3.24469	−	5.61996i	0.110901	−	0.192086i
$857$	56.9838			1.94653			0.973265	−	0.229686i	$-0.0737700\pi$
$857$	56.9838			1.94653			0.973265	+	0.229686i	$0.0737700\pi$
$858$		0			0
$859$	20.1002			0.685810			0.342905	−	0.939370i	$-0.388589\pi$
$859$	20.1002			0.685810			0.342905	+	0.939370i	$0.388589\pi$
$860$	9.46298	+	16.3904i	0.322685	+	0.558907i
$861$		0			0
$862$	−4.50214	+	7.79794i	−0.153344	+	0.265599i
$863$	3.08893	−	5.35018i	0.105148	−	0.182122i	−0.808650	−	0.588289i	$-0.799802\pi$
$863$	3.08893	−	5.35018i	0.105148	−	0.182122i	0.913799	+	0.406167i	$0.133135\pi$
$864$		0			0
$865$	−6.76781	−	11.7222i	−0.230112	−	0.398566i
$866$	8.94318	+	15.4900i	0.303902	+	0.526373i
$867$		0			0
$868$		0			0
$869$	−4.47806	−	7.75623i	−0.151908	−	0.263112i
$870$		0			0
$871$	−35.8872			−1.21599
$872$	4.62732	+	8.01476i	0.156701	+	0.271414i
$873$		0			0
$874$	−33.9396			−1.14802
$875$		0			0
$876$		0			0
$877$	−37.2574			−1.25809			−0.629046	−	0.777368i	$-0.716554\pi$
$877$	−37.2574			−1.25809			−0.629046	+	0.777368i	$0.716554\pi$
$878$	−13.6468	+	23.6370i	−0.460558	+	0.797710i
$879$		0			0
$880$	−4.89504	−	8.47846i	−0.165012	−	0.285809i
$881$	−11.7848			−0.397041			−0.198520	−	0.980097i	$-0.563614\pi$
$881$	−11.7848			−0.397041			−0.198520	+	0.980097i	$0.563614\pi$
$882$		0			0
$883$	−29.2308			−0.983693			−0.491847	−	0.870682i	$-0.663678\pi$
$883$	−29.2308			−0.983693			−0.491847	+	0.870682i	$0.663678\pi$
$884$	−5.57265	−	9.65211i	−0.187428	−	0.324636i
$885$		0			0
$886$	−20.1634	+	34.9240i	−0.677402	+	1.17329i
$887$	28.5161			0.957479			0.478739	−	0.877957i	$-0.341094\pi$
$887$	28.5161			0.957479			0.478739	+	0.877957i	$0.341094\pi$
$888$		0			0
$889$		0			0
$890$	−3.45680			−0.115872
$891$		0			0
$892$	−8.14822	−	14.1131i	−0.272823	−	0.472543i
$893$	23.8364			0.797656
$894$		0			0
$895$	−1.13531	−	1.96642i	−0.0379493	−	0.0657301i
$896$		0			0
$897$		0			0
$898$	19.7890	+	34.2755i	0.660366	+	1.14379i
$899$	0.119171	+	0.206410i	0.00397456	+	0.00688414i
$900$		0			0
$901$	1.17002	−	2.02653i	0.0389790	−	0.0675135i
$902$	−12.5693	+	21.7707i	−0.418513	+	0.724885i
$903$		0			0
$904$	8.14183	+	14.1021i	0.270793	+	0.469028i
$905$	22.6829			0.754006
$906$		0			0
$907$	−7.89155			−0.262035			−0.131017	−	0.991380i	$-0.541824\pi$
$907$	−7.89155			−0.262035			−0.131017	+	0.991380i	$0.541824\pi$
$908$	−7.77317	+	13.4635i	−0.257962	+	0.446803i
$909$		0			0
$910$		0			0
$911$	14.2206	−	24.6308i	0.471150	−	0.816055i	−0.528306	−	0.849054i	$-0.677173\pi$
$911$	14.2206	−	24.6308i	0.471150	−	0.816055i	0.999455	+	0.0329991i	$0.0105058\pi$
$912$		0			0
$913$	−4.23813	+	7.34065i	−0.140262	+	0.242940i
$914$	−37.4007	+	64.7798i	−1.23710	+	2.14273i
$915$		0			0
$916$	−6.71206	+	11.6256i	−0.221773	+	0.384121i
$917$		0			0
$918$		0			0
$919$	3.99271	−	6.91558i	0.131707	−	0.228124i	−0.792627	−	0.609706i	$-0.791287\pi$
$919$	3.99271	−	6.91558i	0.131707	−	0.228124i	0.924335	+	0.381582i	$0.124621\pi$
$920$	−11.0318			−0.363708
$921$		0			0
$922$	−5.21221			−0.171655
$923$	31.9110	+	55.2714i	1.05036	+	1.81928i
$924$		0			0
$925$	0.906337	−	1.56982i	0.0298002	−	0.0516154i
$926$	−25.6529	+	44.4322i	−0.843008	+	1.46013i
$927$		0			0
$928$	−0.206895	−	0.358353i	−0.00679167	−	0.0117635i
$929$	−9.40031	−	16.2818i	−0.308414	−	0.534189i	0.669601	−	0.742721i	$-0.266465\pi$
$929$	−9.40031	−	16.2818i	−0.308414	−	0.534189i	−0.978016	+	0.208531i	$0.933132\pi$
$930$		0			0
$931$		0			0
$932$	13.4081	+	23.2234i	0.439196	+	0.760709i
$933$		0			0
$934$	49.0577			1.60522
$935$	−1.56403	−	2.70898i	−0.0511493	−	0.0885932i
$936$		0			0
$937$	−48.5788			−1.58700			−0.793500	−	0.608570i	$-0.791744\pi$
$937$	−48.5788			−1.58700			−0.793500	+	0.608570i	$0.791744\pi$
$938$		0			0
$939$		0			0
$940$	−17.6619			−0.576067
$941$	−10.2425	+	17.7406i	−0.333898	+	0.578328i	−0.983272	−	0.182141i	$-0.941697\pi$
$941$	−10.2425	+	17.7406i	−0.333898	+	0.578328i	0.649375	+	0.760468i	$0.275031\pi$
$942$		0			0
$943$	33.2110	+	57.5231i	1.08150	+	1.87321i
$944$	40.9312			1.33220
$945$		0			0
$946$	28.4148			0.923843
$947$	−7.42524	−	12.8609i	−0.241288	−	0.417923i	0.719793	−	0.694188i	$-0.244236\pi$
$947$	−7.42524	−	12.8609i	−0.241288	−	0.417923i	−0.961081	+	0.276265i	$0.910903\pi$
$948$		0			0
$949$	−7.13954	+	12.3661i	−0.231759	+	0.401419i
$950$	14.8398			0.481466
$951$		0			0
$952$		0			0
$953$	−46.4678			−1.50524			−0.752620	−	0.658456i	$-0.771210\pi$
$953$	−46.4678			−1.50524			−0.752620	+	0.658456i	$0.771210\pi$
$954$		0			0
$955$	15.1454	+	26.2326i	0.490094	+	0.848868i
$956$	−0.541167			−0.0175026
$957$		0			0
$958$	29.0724	+	50.3548i	0.939285	+	1.62689i
$959$		0			0
$960$		0			0
$961$	8.09733	+	14.0250i	0.261204	+	0.452419i
$962$	2.68380	+	4.64847i	0.0865291	+	0.149873i
$963$		0			0
$964$	7.39301	−	12.8051i	0.238113	−	0.412423i
$965$	−4.12905	+	7.15172i	−0.132919	+	0.230222i
$966$		0			0
$967$	0.863670	+	1.49592i	0.0277738	+	0.0481056i	0.879578	−	0.475754i	$-0.157825\pi$
$967$	0.863670	+	1.49592i	0.0277738	+	0.0481056i	−0.851804	+	0.523860i	$0.824492\pi$
$968$	9.78089			0.314370
$969$		0			0
$970$	−29.9687			−0.962235
$971$	−3.78085	+	6.54863i	−0.121333	+	0.210156i	−0.920294	−	0.391228i	$-0.872050\pi$
$971$	−3.78085	+	6.54863i	−0.121333	+	0.210156i	0.798960	+	0.601384i	$0.205384\pi$
$972$		0			0
$973$		0			0
$974$	−0.281870	+	0.488213i	−0.00903169	+	0.0156434i
$975$		0			0
$976$	−7.85137	+	13.5990i	−0.251316	+	0.435293i
$977$	−28.3101	+	49.0345i	−0.905721	+	1.56875i	−0.0857737	+	0.996315i	$0.527336\pi$
$977$	−28.3101	+	49.0345i	−0.905721	+	1.56875i	−0.819947	+	0.572440i	$0.805997\pi$
$978$		0			0
$979$	−1.06408	+	1.84305i	−0.0340083	+	0.0589041i
$980$		0			0
$981$		0			0
$982$	16.6997	−	28.9247i	0.532909	−	0.923025i
$983$	32.2972			1.03012			0.515061	−	0.857154i	$-0.327769\pi$
$983$	32.2972			1.03012			0.515061	+	0.857154i	$0.327769\pi$
$984$		0			0
$985$	−13.0407			−0.415510
$986$	−0.0883286	−	0.152990i	−0.00281296	−	0.00487218i
$987$		0			0
$988$	−9.00955	+	15.6050i	−0.286632	+	0.496461i
$989$	37.5391	−	65.0197i	1.19367	−	2.06750i
$990$		0			0
$991$	−7.15502	−	12.3929i	−0.227287	−	0.393672i	0.729716	−	0.683750i	$-0.239652\pi$
$991$	−7.15502	−	12.3929i	−0.227287	−	0.393672i	−0.957003	+	0.290078i	$0.906319\pi$
$992$	12.8520	+	22.2602i	0.408050	+	0.706764i
$993$		0			0
$994$		0			0
$995$	5.79247	+	10.0329i	0.183634	+	0.318063i
$996$		0			0
$997$	−56.2524			−1.78153			−0.890765	−	0.454463i	$-0.849831\pi$
$997$	−56.2524			−1.78153			−0.890765	+	0.454463i	$0.849831\pi$
$998$	19.6176	+	33.9787i	0.620985	+	1.07558i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.g.f.667.2		10
3.2	odd	2		441.2.g.f.79.4		10
7.2	even	3		1323.2.f.f.883.2		10
7.3	odd	6		189.2.h.b.46.4		10
7.4	even	3		1323.2.h.f.802.4		10
7.5	odd	6		1323.2.f.e.883.2		10
7.6	odd	2		189.2.g.b.100.2		10
9.4	even	3		1323.2.h.f.226.4		10
9.5	odd	6		441.2.h.f.373.2		10
21.2	odd	6		441.2.f.f.295.4		10
21.5	even	6		441.2.f.e.295.4		10
21.11	odd	6		441.2.h.f.214.2		10
21.17	even	6		63.2.h.b.25.2	yes	10
21.20	even	2		63.2.g.b.16.4	yes	10
28.3	even	6		3024.2.q.i.2881.4		10
28.27	even	2		3024.2.t.i.289.2		10
63.2	odd	6		3969.2.a.ba.1.2		5
63.4	even	3	inner	1323.2.g.f.361.2		10
63.5	even	6		441.2.f.e.148.4		10
63.13	odd	6		189.2.h.b.37.4		10
63.16	even	3		3969.2.a.bb.1.4		5
63.20	even	6		567.2.e.f.163.4		10
63.23	odd	6		441.2.f.f.148.4		10
63.31	odd	6		189.2.g.b.172.2		10
63.32	odd	6		441.2.g.f.67.4		10
63.34	odd	6		567.2.e.e.163.2		10
63.38	even	6		567.2.e.f.487.4		10
63.40	odd	6		1323.2.f.e.442.2		10
63.41	even	6		63.2.h.b.58.2	yes	10
63.47	even	6		3969.2.a.z.1.2		5
63.52	odd	6		567.2.e.e.487.2		10
63.58	even	3		1323.2.f.f.442.2		10
63.59	even	6		63.2.g.b.4.4	✓	10
63.61	odd	6		3969.2.a.bc.1.4		5
84.59	odd	6		1008.2.q.i.529.2		10
84.83	odd	2		1008.2.t.i.961.5		10
252.31	even	6		3024.2.t.i.1873.2		10
252.59	odd	6		1008.2.t.i.193.5		10
252.139	even	6		3024.2.q.i.2305.4		10
252.167	odd	6		1008.2.q.i.625.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	63.59	even	6
63.2.g.b.16.4	yes	10	21.20	even	2
63.2.h.b.25.2	yes	10	21.17	even	6
63.2.h.b.58.2	yes	10	63.41	even	6
189.2.g.b.100.2		10	7.6	odd	2
189.2.g.b.172.2		10	63.31	odd	6
189.2.h.b.37.4		10	63.13	odd	6
189.2.h.b.46.4		10	7.3	odd	6
441.2.f.e.148.4		10	63.5	even	6
441.2.f.e.295.4		10	21.5	even	6
441.2.f.f.148.4		10	63.23	odd	6
441.2.f.f.295.4		10	21.2	odd	6
441.2.g.f.67.4		10	63.32	odd	6
441.2.g.f.79.4		10	3.2	odd	2
441.2.h.f.214.2		10	21.11	odd	6
441.2.h.f.373.2		10	9.5	odd	6
567.2.e.e.163.2		10	63.34	odd	6
567.2.e.e.487.2		10	63.52	odd	6
567.2.e.f.163.4		10	63.20	even	6
567.2.e.f.487.4		10	63.38	even	6
1008.2.q.i.529.2		10	84.59	odd	6
1008.2.q.i.625.2		10	252.167	odd	6
1008.2.t.i.193.5		10	252.59	odd	6
1008.2.t.i.961.5		10	84.83	odd	2
1323.2.f.e.442.2		10	63.40	odd	6
1323.2.f.e.883.2		10	7.5	odd	6
1323.2.f.f.442.2		10	63.58	even	3
1323.2.f.f.883.2		10	7.2	even	3
1323.2.g.f.361.2		10	63.4	even	3	inner
1323.2.g.f.667.2		10	1.1	even	1	trivial
1323.2.h.f.226.4		10	9.4	even	3
1323.2.h.f.802.4		10	7.4	even	3
3024.2.q.i.2305.4		10	252.139	even	6
3024.2.q.i.2881.4		10	28.3	even	6
3024.2.t.i.289.2		10	28.27	even	2
3024.2.t.i.1873.2		10	252.31	even	6
3969.2.a.z.1.2		5	63.47	even	6
3969.2.a.ba.1.2		5	63.2	odd	6
3969.2.a.bb.1.4		5	63.16	even	3
3969.2.a.bc.1.4		5	63.61	odd	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.920620 - 1.59456i) q^{2} +(-0.695084 + 1.20392i) q^{4} +1.33475 q^{5} -1.12285 q^{8} +O(q^{10})\)	\(q+(-0.920620 - 1.59456i) q^{2} +(-0.695084 + 1.20392i) q^{4} +1.33475 q^{5} -1.12285 q^{8} +(-1.22880 - 2.12835i) q^{10} -1.51302 q^{11} +(2.58800 + 4.48254i) q^{13} +(2.42388 + 4.19829i) q^{16} +(0.774463 + 1.34141i) q^{17} +(1.25211 - 2.16872i) q^{19} +(-0.927765 + 1.60694i) q^{20} +(1.39291 + 2.41260i) q^{22} +7.36079 q^{23} -3.21843 q^{25} +(4.76513 - 8.25344i) q^{26} +(0.0309713 - 0.0536439i) q^{29} +(-1.92388 + 3.33227i) q^{31} +(3.34011 - 5.78523i) q^{32} +(1.42597 - 2.46986i) q^{34} +(-0.281608 + 0.487760i) q^{37} -4.61087 q^{38} -1.49873 q^{40} +(4.51188 + 7.81481i) q^{41} +(5.09988 - 8.83325i) q^{43} +(1.05167 - 1.82155i) q^{44} +(-6.77649 - 11.7372i) q^{46} +(4.75925 + 8.24327i) q^{47} +(2.96296 + 5.13199i) q^{50} -7.19550 q^{52} +(-0.755374 - 1.30835i) q^{53} -2.01950 q^{55} -0.114051 q^{58} +(4.22166 - 7.31212i) q^{59} +(1.61958 + 2.80520i) q^{61} +7.08467 q^{62} -2.60434 q^{64} +(3.45434 + 5.98309i) q^{65} +(-3.46670 + 6.00449i) q^{67} -2.15327 q^{68} +12.3304 q^{71} +(1.37936 + 2.38912i) q^{73} +1.03702 q^{74} +(1.74064 + 3.01488i) q^{76} +(2.95969 + 5.12633i) q^{79} +(3.23529 + 5.60368i) q^{80} +(8.30746 - 14.3889i) q^{82} +(2.80111 - 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} -18.7802 q^{86} +1.69889 q^{88} +(0.703287 - 1.21813i) q^{89} +(-5.11636 + 8.86180i) q^{92} +(8.76293 - 15.1778i) q^{94} +(1.67126 - 2.89470i) q^{95} +(6.09713 - 10.5605i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} - 8 q^{5} + 6 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^4 - 8 * q^5 + 6 * q^8	\( 10 q - 2 q^{2} - 4 q^{4} - 8 q^{5} + 6 q^{8} + 7 q^{10} + 8 q^{11} + 8 q^{13} + 2 q^{16} + 12 q^{17} - q^{19} + 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} + 11 q^{26} - 7 q^{29} + 3 q^{31} + 2 q^{32} - 3 q^{34} - 40 q^{38} - 6 q^{40} + 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 27 q^{47} - 19 q^{50} - 20 q^{52} + 21 q^{53} - 4 q^{55} + 20 q^{58} + 30 q^{59} + 14 q^{61} - 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 54 q^{68} + 6 q^{71} - 15 q^{73} - 72 q^{74} - 5 q^{76} - 4 q^{79} + 20 q^{80} + 5 q^{82} + 9 q^{83} - 6 q^{85} - 16 q^{86} + 36 q^{88} + 28 q^{89} - 27 q^{92} + 3 q^{94} + 14 q^{95} + 12 q^{97}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 - 8 * q^5 + 6 * q^8 + 7 * q^10 + 8 * q^11 + 8 * q^13 + 2 * q^16 + 12 * q^17 - q^19 + 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 + 11 * q^26 - 7 * q^29 + 3 * q^31 + 2 * q^32 - 3 * q^34 - 40 * q^38 - 6 * q^40 + 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 27 * q^47 - 19 * q^50 - 20 * q^52 + 21 * q^53 - 4 * q^55 + 20 * q^58 + 30 * q^59 + 14 * q^61 - 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 54 * q^68 + 6 * q^71 - 15 * q^73 - 72 * q^74 - 5 * q^76 - 4 * q^79 + 20 * q^80 + 5 * q^82 + 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 + 28 * q^89 - 27 * q^92 + 3 * q^94 + 14 * q^95 + 12 * q^97

Introduction

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