LMFDB - Embedded newform 1638.2.m.g.1621.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(289,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("1638.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.m (of order $3$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.4
Root			$1.26359 + 0.635098i$ of defining polynomial
Character	$\chi$	$=$	1638.1621
Dual form			1638.2.m.g.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(1.97513 + 3.42102i) q^{5} +(-1.15207 - 2.38175i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.97513 + 3.42102i) q^{5} +(-1.15207 - 2.38175i) q^{7} -1.00000 q^{8} +(-1.97513 - 3.42102i) q^{10} +(2.45689 + 4.25545i) q^{11} +(-3.39335 + 1.21869i) q^{13} +(1.15207 + 2.38175i) q^{14} +1.00000 q^{16} -0.140571 q^{17} +(0.388481 - 0.672870i) q^{19} +(1.97513 + 3.42102i) q^{20} +(-2.45689 - 4.25545i) q^{22} -9.53690 q^{23} +(-5.30226 + 9.18378i) q^{25} +(3.39335 - 1.21869i) q^{26} +(-1.15207 - 2.38175i) q^{28} +(0.629759 - 1.09077i) q^{29} +(-1.67992 + 2.90971i) q^{31} -1.00000 q^{32} +0.140571 q^{34} +(5.87254 - 8.64551i) q^{35} +11.1368 q^{37} +(-0.388481 + 0.672870i) q^{38} +(-1.97513 - 3.42102i) q^{40} +(-4.65505 + 8.06279i) q^{41} +(-0.541233 - 0.937443i) q^{43} +(2.45689 + 4.25545i) q^{44} +9.53690 q^{46} +(-3.33199 - 5.77118i) q^{47} +(-4.34548 + 5.48788i) q^{49} +(5.30226 - 9.18378i) q^{50} +(-3.39335 + 1.21869i) q^{52} +(-5.53204 + 9.58177i) q^{53} +(-9.70533 + 16.8101i) q^{55} +(1.15207 + 2.38175i) q^{56} +(-0.629759 + 1.09077i) q^{58} -0.431218 q^{59} +(4.14057 - 7.17168i) q^{61} +(1.67992 - 2.90971i) q^{62} +1.00000 q^{64} +(-10.8715 - 9.20163i) q^{65} +(-4.09814 - 7.09819i) q^{67} -0.140571 q^{68} +(-5.87254 + 8.64551i) q^{70} +(-1.93865 - 3.35783i) q^{71} +(-0.0817820 + 0.141650i) q^{73} -11.1368 q^{74} +(0.388481 - 0.672870i) q^{76} +(7.30493 - 10.7543i) q^{77} +(2.17517 + 3.76751i) q^{79} +(1.97513 + 3.42102i) q^{80} +(4.65505 - 8.06279i) q^{82} +10.5220 q^{83} +(-0.277647 - 0.480898i) q^{85} +(0.541233 + 0.937443i) q^{86} +(-2.45689 - 4.25545i) q^{88} +1.07274 q^{89} +(6.81198 + 6.67809i) q^{91} -9.53690 q^{92} +(3.33199 + 5.77118i) q^{94} +3.06920 q^{95} +(-6.54097 - 11.3293i) q^{97} +(4.34548 - 5.48788i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} + 2 q^{10} + 6 q^{11} - 11 q^{13} + 3 q^{14} + 8 q^{16} + 8 q^{17} + 6 q^{19} - 2 q^{20} - 6 q^{22} - 20 q^{23} - 18 q^{25} + 11 q^{26} - 3 q^{28} - 2 q^{29} + 6 q^{31} - 8 q^{32} - 8 q^{34} + 18 q^{35} + 56 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} + 20 q^{46} - q^{47} + 5 q^{49} + 18 q^{50} - 11 q^{52} - 7 q^{53} + q^{55} + 3 q^{56} + 2 q^{58} + 4 q^{59} + 24 q^{61} - 6 q^{62} + 8 q^{64} - 22 q^{65} - 15 q^{67} + 8 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} - 56 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} - 2 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} - 6 q^{88} + 50 q^{89} - 8 q^{91} - 20 q^{92} + q^{94} - 16 q^{95} - q^{97} - 5 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8 + 2 * q^10 + 6 * q^11 - 11 * q^13 + 3 * q^14 + 8 * q^16 + 8 * q^17 + 6 * q^19 - 2 * q^20 - 6 * q^22 - 20 * q^23 - 18 * q^25 + 11 * q^26 - 3 * q^28 - 2 * q^29 + 6 * q^31 - 8 * q^32 - 8 * q^34 + 18 * q^35 + 56 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 + 20 * q^46 - q^47 + 5 * q^49 + 18 * q^50 - 11 * q^52 - 7 * q^53 + q^55 + 3 * q^56 + 2 * q^58 + 4 * q^59 + 24 * q^61 - 6 * q^62 + 8 * q^64 - 22 * q^65 - 15 * q^67 + 8 * q^68 - 18 * q^70 - 6 * q^71 + q^73 - 56 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 - 2 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 - 6 * q^88 + 50 * q^89 - 8 * q^91 - 20 * q^92 + q^94 - 16 * q^95 - q^97 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.97513	+	3.42102i	0.883304	+	1.52993i	0.847646	+	0.530563i	$0.178019\pi$
$5$	1.97513	+	3.42102i	0.883304	+	1.52993i	0.0356582	+	0.999364i	$0.488647\pi$
$6$		0			0
$7$	−1.15207	−	2.38175i	−0.435441	−	0.900217i
$7$	−1.15207	−	2.38175i	−0.435441	−	0.900217i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.97513	−	3.42102i	−0.624590	−	1.08182i
$11$	2.45689	+	4.25545i	0.740779	+	1.28307i	0.952141	+	0.305659i	$0.0988769\pi$
$11$	2.45689	+	4.25545i	0.740779	+	1.28307i	−0.211362	+	0.977408i	$0.567790\pi$
$12$		0			0
$13$	−3.39335	+	1.21869i	−0.941145	+	0.338004i
$13$	−3.39335	+	1.21869i	−0.941145	+	0.338004i
$14$	1.15207	+	2.38175i	0.307903	+	0.636550i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.140571			−0.0340936			−0.0170468	−	0.999855i	$-0.505426\pi$
$17$	−0.140571			−0.0340936			−0.0170468	+	0.999855i	$0.505426\pi$
$18$		0			0
$19$	0.388481	−	0.672870i	0.0891238	−	0.154367i	−0.818017	−	0.575194i	$-0.804927\pi$
$19$	0.388481	−	0.672870i	0.0891238	−	0.154367i	0.907141	+	0.420827i	$0.138260\pi$
$20$	1.97513	+	3.42102i	0.441652	+	0.764963i
$21$		0			0
$22$	−2.45689	−	4.25545i	−0.523810	−	0.907266i
$23$	−9.53690			−1.98858			−0.994291	−	0.106706i	$-0.965970\pi$
$23$	−9.53690			−1.98858			−0.994291	+	0.106706i	$0.965970\pi$
$24$		0			0
$25$	−5.30226	+	9.18378i	−1.06045	+	1.83676i
$26$	3.39335	−	1.21869i	0.665490	−	0.239005i
$27$		0			0
$28$	−1.15207	−	2.38175i	−0.217720	−	0.450109i
$29$	0.629759	−	1.09077i	0.116943	−	0.202552i	−0.801612	−	0.597845i	$-0.796024\pi$
$29$	0.629759	−	1.09077i	0.116943	−	0.202552i	0.918555	+	0.395293i	$0.129357\pi$
$30$		0			0
$31$	−1.67992	+	2.90971i	−0.301723	+	0.522600i	−0.976526	−	0.215398i	$-0.930895\pi$
$31$	−1.67992	+	2.90971i	−0.301723	+	0.522600i	0.674803	+	0.737998i	$0.264229\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	0.140571			0.0241078
$35$	5.87254	−	8.64551i	0.992641	−	1.46136i
$36$		0			0
$37$	11.1368			1.83088			0.915440	−	0.402454i	$-0.131843\pi$
$37$	11.1368			1.83088			0.915440	+	0.402454i	$0.131843\pi$
$38$	−0.388481	+	0.672870i	−0.0630200	+	0.109154i
$39$		0			0
$40$	−1.97513	−	3.42102i	−0.312295	−	0.540911i
$41$	−4.65505	+	8.06279i	−0.726997	+	1.25920i	0.231150	+	0.972918i	$0.425751\pi$
$41$	−4.65505	+	8.06279i	−0.726997	+	1.25920i	−0.958147	+	0.286277i	$0.907582\pi$
$42$		0			0
$43$	−0.541233	−	0.937443i	−0.0825372	−	0.142959i	0.821802	−	0.569773i	$-0.192969\pi$
$43$	−0.541233	−	0.937443i	−0.0825372	−	0.142959i	−0.904339	+	0.426815i	$0.859636\pi$
$44$	2.45689	+	4.25545i	0.370390	+	0.641534i
$45$		0			0
$46$	9.53690			1.40614
$47$	−3.33199	−	5.77118i	−0.486021	−	0.841813i	0.513850	−	0.857880i	$-0.328219\pi$
$47$	−3.33199	−	5.77118i	−0.486021	−	0.841813i	−0.999871	+	0.0160671i	$0.994885\pi$
$48$		0			0
$49$	−4.34548	+	5.48788i	−0.620783	+	0.783983i
$50$	5.30226	−	9.18378i	0.749852	−	1.29878i
$51$		0			0
$52$	−3.39335	+	1.21869i	−0.470572	+	0.169002i
$53$	−5.53204	+	9.58177i	−0.759884	+	1.31616i	0.183026	+	0.983108i	$0.441411\pi$
$53$	−5.53204	+	9.58177i	−0.759884	+	1.31616i	−0.942910	+	0.333049i	$0.891923\pi$
$54$		0			0
$55$	−9.70533	+	16.8101i	−1.30867	+	2.26668i
$56$	1.15207	+	2.38175i	0.153952	+	0.318275i
$57$		0			0
$58$	−0.629759	+	1.09077i	−0.0826914	+	0.143226i
$59$	−0.431218			−0.0561399			−0.0280699	−	0.999606i	$-0.508936\pi$
$59$	−0.431218			−0.0561399			−0.0280699	+	0.999606i	$0.508936\pi$
$60$		0			0
$61$	4.14057	−	7.17168i	0.530146	−	0.918240i	−0.469236	−	0.883073i	$-0.655470\pi$
$61$	4.14057	−	7.17168i	0.530146	−	0.918240i	0.999381	−	0.0351665i	$-0.0111962\pi$
$62$	1.67992	−	2.90971i	0.213351	−	0.369534i
$63$		0			0
$64$	1.00000			0.125000
$65$	−10.8715	−	9.20163i	−1.34844	−	1.14132i
$66$		0			0
$67$	−4.09814	−	7.09819i	−0.500668	−	0.867182i	−1.00000		0.000771201i	$-0.999755\pi$
$67$	−4.09814	−	7.09819i	−0.500668	−	0.867182i	0.499332	−	0.866411i	$-0.333579\pi$
$68$	−0.140571			−0.0170468
$69$		0			0
$70$	−5.87254	+	8.64551i	−0.701903	+	1.03334i
$71$	−1.93865	−	3.35783i	−0.230075	−	0.398502i	0.727755	−	0.685837i	$-0.240564\pi$
$71$	−1.93865	−	3.35783i	−0.230075	−	0.398502i	−0.957830	+	0.287336i	$0.907230\pi$
$72$		0			0
$73$	−0.0817820	+	0.141650i	−0.00957185	+	0.0165789i	−0.870772	−	0.491688i	$-0.836380\pi$
$73$	−0.0817820	+	0.141650i	−0.00957185	+	0.0165789i	0.861200	+	0.508267i	$0.169714\pi$
$74$	−11.1368			−1.29463
$75$		0			0
$76$	0.388481	−	0.672870i	0.0445619	−	0.0771834i
$77$	7.30493	−	10.7543i	0.832474	−	1.22556i
$78$		0			0
$79$	2.17517	+	3.76751i	0.244726	+	0.423878i	0.962055	−	0.272857i	$-0.0879687\pi$
$79$	2.17517	+	3.76751i	0.244726	+	0.423878i	−0.717329	+	0.696735i	$0.754635\pi$
$80$	1.97513	+	3.42102i	0.220826	+	0.382482i
$81$		0			0
$82$	4.65505	−	8.06279i	0.514064	−	0.890386i
$83$	10.5220			1.15494			0.577472	−	0.816410i	$-0.304039\pi$
$83$	10.5220			1.15494			0.577472	+	0.816410i	$0.304039\pi$
$84$		0			0
$85$	−0.277647	−	0.480898i	−0.0301150	−	0.0521607i
$86$	0.541233	+	0.937443i	0.0583626	+	0.101087i
$87$		0			0
$88$	−2.45689	−	4.25545i	−0.261905	−	0.453633i
$89$	1.07274			0.113710			0.0568550	−	0.998382i	$-0.481893\pi$
$89$	1.07274			0.113710			0.0568550	+	0.998382i	$0.481893\pi$
$90$		0			0
$91$	6.81198	+	6.67809i	0.714090	+	0.700054i
$92$	−9.53690			−0.994291
$93$		0			0
$94$	3.33199	+	5.77118i	0.343669	+	0.595252i
$95$	3.06920			0.314893
$96$		0			0
$97$	−6.54097	−	11.3293i	−0.664135	−	1.15032i	−0.979519	−	0.201351i	$-0.935467\pi$
$97$	−6.54097	−	11.3293i	−0.664135	−	1.15032i	0.315384	−	0.948964i	$-0.397867\pi$
$98$	4.34548	−	5.48788i	0.438960	−	0.554359i
$99$		0			0
$100$	−5.30226	+	9.18378i	−0.530226	+	0.918378i
$101$	3.69262	+	6.39580i	0.367429	+	0.636406i	0.989163	−	0.146823i	$-0.0469047\pi$
$101$	3.69262	+	6.39580i	0.367429	+	0.636406i	−0.621734	+	0.783229i	$0.713571\pi$
$102$		0			0
$103$	−1.99107	−	3.44863i	−0.196186	−	0.339804i	0.751103	−	0.660185i	$-0.229522\pi$
$103$	−1.99107	−	3.44863i	−0.196186	−	0.339804i	−0.947289	+	0.320382i	$0.896189\pi$
$104$	3.39335	−	1.21869i	0.332745	−	0.119502i
$105$		0			0
$106$	5.53204	−	9.58177i	0.537319	−	0.930664i
$107$	7.07358			0.683828			0.341914	−	0.939731i	$-0.388925\pi$
$107$	7.07358			0.683828			0.341914	+	0.939731i	$0.388925\pi$
$108$		0			0
$109$	−7.42350	+	12.8579i	−0.711042	+	1.23156i	0.253424	+	0.967355i	$0.418443\pi$
$109$	−7.42350	+	12.8579i	−0.711042	+	1.23156i	−0.964466	+	0.264206i	$0.914890\pi$
$110$	9.70533	−	16.8101i	0.925367	−	1.60278i
$111$		0			0
$112$	−1.15207	−	2.38175i	−0.108860	−	0.225054i
$113$	0.785895	+	1.36121i	0.0739308	+	0.128052i	0.900621	−	0.434606i	$-0.143112\pi$
$113$	0.785895	+	1.36121i	0.0739308	+	0.128052i	−0.826690	+	0.562658i	$0.809779\pi$
$114$		0			0
$115$	−18.8366	−	32.6259i	−1.75652	−	3.04238i
$116$	0.629759	−	1.09077i	0.0584717	−	0.101276i
$117$		0			0
$118$	0.431218			0.0396969
$119$	0.161948	+	0.334806i	0.0148457	+	0.0306916i
$120$		0			0
$121$	−6.57259	+	11.3841i	−0.597508	+	1.03491i
$122$	−4.14057	+	7.17168i	−0.374870	+	0.649293i
$123$		0			0
$124$	−1.67992	+	2.90971i	−0.150862	+	0.261300i
$125$	−22.1392			−1.98019
$126$		0			0
$127$	−5.42757	+	9.40083i	−0.481619	+	0.834188i	−0.999777	−	0.0210962i	$-0.993284\pi$
$127$	−5.42757	+	9.40083i	−0.481619	+	0.834188i	0.518159	+	0.855285i	$0.326618\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	10.8715	+	9.20163i	0.953490	+	0.807037i
$131$	0.961751	+	1.66580i	0.0840285	+	0.145542i	0.904977	−	0.425461i	$-0.139888\pi$
$131$	0.961751	+	1.66580i	0.0840285	+	0.145542i	−0.820948	+	0.571003i	$0.806555\pi$
$132$		0			0
$133$	−2.05016	−	0.150075i	−0.177772	−	0.0130131i
$134$	4.09814	+	7.09819i	0.354026	+	0.613190i
$135$		0			0
$136$	0.140571			0.0120539
$137$	−15.8821			−1.35690			−0.678450	−	0.734646i	$-0.737348\pi$
$137$	−15.8821			−1.35690			−0.678450	+	0.734646i	$0.737348\pi$
$138$		0			0
$139$	2.94351	+	5.09831i	0.249665	+	0.432433i	0.963433	−	0.267950i	$-0.0863461\pi$
$139$	2.94351	+	5.09831i	0.249665	+	0.432433i	−0.713768	+	0.700383i	$0.753013\pi$
$140$	5.87254	−	8.64551i	0.496320	−	0.730679i
$141$		0			0
$142$	1.93865	+	3.35783i	0.162688	+	0.281783i
$143$	−13.5231	−	11.4460i	−1.13086	−	0.957165i
$144$		0			0
$145$	4.97542			0.413186
$146$	0.0817820	−	0.141650i	0.00676832	−	0.0117231i
$147$		0			0
$148$	11.1368			0.915440
$149$	−6.63504	+	11.4922i	−0.543564	+	0.941480i	0.455132	+	0.890424i	$0.349592\pi$
$149$	−6.63504	+	11.4922i	−0.543564	+	0.941480i	−0.998696	+	0.0510562i	$0.983741\pi$
$150$		0			0
$151$	−8.06783	+	13.9739i	−0.656551	+	1.13718i	0.324952	+	0.945731i	$0.394652\pi$
$151$	−8.06783	+	13.9739i	−0.656551	+	1.13718i	−0.981503	+	0.191449i	$0.938681\pi$
$152$	−0.388481	+	0.672870i	−0.0315100	+	0.0545769i
$153$		0			0
$154$	−7.30493	+	10.7543i	−0.588648	+	0.866603i
$155$	−13.2723			−1.06605
$156$		0			0
$157$	−8.85322	+	15.3342i	−0.706564	+	1.22380i	0.259561	+	0.965727i	$0.416422\pi$
$157$	−8.85322	+	15.3342i	−0.706564	+	1.22380i	−0.966124	+	0.258077i	$0.916911\pi$
$158$	−2.17517	−	3.76751i	−0.173047	−	0.299727i
$159$		0			0
$160$	−1.97513	−	3.42102i	−0.156148	−	0.270455i
$161$	10.9872	+	22.7145i	0.865909	+	1.79016i
$162$		0			0
$163$	−1.63571	+	2.83313i	−0.128119	+	0.221908i	−0.922948	−	0.384926i	$-0.874227\pi$
$163$	−1.63571	+	2.83313i	−0.128119	+	0.221908i	0.794829	+	0.606833i	$0.207560\pi$
$164$	−4.65505	+	8.06279i	−0.363498	+	0.629598i
$165$		0			0
$166$	−10.5220			−0.816669
$167$	4.42914	−	7.67150i	0.342737	−	0.593638i	−0.642203	−	0.766535i	$-0.721979\pi$
$167$	4.42914	−	7.67150i	0.342737	−	0.593638i	0.984940	+	0.172896i	$0.0553126\pi$
$168$		0			0
$169$	10.0296	−	8.27088i	0.771506	−	0.636221i
$170$	0.277647	+	0.480898i	0.0212945	+	0.0368832i
$171$		0			0
$172$	−0.541233	−	0.937443i	−0.0412686	−	0.0714793i
$173$	−7.47486	+	12.9468i	−0.568303	+	0.984330i	0.428431	+	0.903575i	$0.359067\pi$
$173$	−7.47486	+	12.9468i	−0.568303	+	0.984330i	−0.996734	+	0.0807555i	$0.974267\pi$
$174$		0			0
$175$	27.9820	+	2.04832i	2.11524	+	0.154839i
$176$	2.45689	+	4.25545i	0.185195	+	0.320767i
$177$		0			0
$178$	−1.07274			−0.0804051
$179$	−11.6034	−	20.0977i	−0.867281	−	1.50217i	−0.864765	−	0.502177i	$-0.832532\pi$
$179$	−11.6034	−	20.0977i	−0.867281	−	1.50217i	−0.00251612	−	0.999997i	$-0.500801\pi$
$180$		0			0
$181$	19.4618			1.44658			0.723291	−	0.690543i	$-0.242629\pi$
$181$	19.4618			1.44658			0.723291	+	0.690543i	$0.242629\pi$
$182$	−6.81198	−	6.67809i	−0.504938	−	0.495013i
$183$		0			0
$184$	9.53690			0.703070
$185$	21.9966	+	38.0993i	1.61722	+	2.80111i
$186$		0			0
$187$	−0.345368	−	0.598195i	−0.0252558	−	0.0437444i
$188$	−3.33199	−	5.77118i	−0.243010	−	0.420906i
$189$		0			0
$190$	−3.06920			−0.222663
$191$	−7.29819	+	12.6408i	−0.528078	+	0.914658i	0.471386	+	0.881927i	$0.343754\pi$
$191$	−7.29819	+	12.6408i	−0.528078	+	0.914658i	−0.999464	+	0.0327313i	$0.989579\pi$
$192$		0			0
$193$	0.884301	+	1.53165i	0.0636534	+	0.110251i	0.896096	−	0.443861i	$-0.146391\pi$
$193$	0.884301	+	1.53165i	0.0636534	+	0.110251i	−0.832442	+	0.554111i	$0.813058\pi$
$194$	6.54097	+	11.3293i	0.469614	+	0.813396i
$195$		0			0
$196$	−4.34548	+	5.48788i	−0.310391	+	0.391991i
$197$	−2.92757	+	5.07070i	−0.208581	+	0.361272i	−0.951268	−	0.308366i	$-0.900218\pi$
$197$	−2.92757	+	5.07070i	−0.208581	+	0.361272i	0.742687	+	0.669639i	$0.233551\pi$
$198$		0			0
$199$	13.9227			0.986958			0.493479	−	0.869758i	$-0.335725\pi$
$199$	13.9227			0.986958			0.493479	+	0.869758i	$0.335725\pi$
$200$	5.30226	−	9.18378i	0.374926	−	0.649391i
$201$		0			0
$202$	−3.69262	−	6.39580i	−0.259812	−	0.450007i
$203$	−3.32348	−	0.243283i	−0.233262	−	0.0170751i
$204$		0			0
$205$	−36.7773			−2.56864
$206$	1.99107	+	3.44863i	0.138724	+	0.240277i
$207$		0			0
$208$	−3.39335	+	1.21869i	−0.235286	+	0.0845010i
$209$	3.81782			0.264084
$210$		0			0
$211$	3.35399	−	5.80929i	0.230898	−	0.399928i	−0.727174	−	0.686453i	$-0.759167\pi$
$211$	3.35399	−	5.80929i	0.230898	−	0.399928i	0.958073	+	0.286525i	$0.0925002\pi$
$212$	−5.53204	+	9.58177i	−0.379942	+	0.658079i
$213$		0			0
$214$	−7.07358			−0.483540
$215$	2.13801	−	3.70314i	0.145811	−	0.252552i
$216$		0			0
$217$	8.86560	+	0.648974i	0.601836	+	0.0440552i
$218$	7.42350	−	12.8579i	0.502783	−	0.870846i
$219$		0			0
$220$	−9.70533	+	16.8101i	−0.654333	+	1.13334i
$221$	0.477008	−	0.171313i	0.0320870	−	0.0115238i
$222$		0			0
$223$	−1.02744	+	1.77957i	−0.0688023	+	0.119169i	−0.898374	−	0.439231i	$-0.855251\pi$
$223$	−1.02744	+	1.77957i	−0.0688023	+	0.119169i	0.829572	+	0.558400i	$0.188584\pi$
$224$	1.15207	+	2.38175i	0.0769758	+	0.159137i
$225$		0			0
$226$	−0.785895	−	1.36121i	−0.0522770	−	0.0905463i
$227$	25.8298			1.71438			0.857190	−	0.515000i	$-0.172208\pi$
$227$	25.8298			1.71438			0.857190	+	0.515000i	$0.172208\pi$
$228$		0			0
$229$	5.39496	+	9.34435i	0.356509	+	0.617492i	0.987375	−	0.158400i	$-0.0506336\pi$
$229$	5.39496	+	9.34435i	0.356509	+	0.617492i	−0.630866	+	0.775892i	$0.717300\pi$
$230$	18.8366	+	32.6259i	1.24205	+	2.15129i
$231$		0			0
$232$	−0.629759	+	1.09077i	−0.0413457	+	0.0716129i
$233$	1.92109	+	3.32742i	0.125855	+	0.217987i	0.922067	−	0.387031i	$-0.126499\pi$
$233$	1.92109	+	3.32742i	0.125855	+	0.217987i	−0.796212	+	0.605018i	$0.793166\pi$
$234$		0			0
$235$	13.1622	−	22.7976i	0.858608	−	1.48715i
$236$	−0.431218			−0.0280699
$237$		0			0
$238$	−0.161948	−	0.334806i	−0.0104975	−	0.0217023i
$239$	−10.2560			−0.663404			−0.331702	−	0.943384i	$-0.607623\pi$
$239$	−10.2560			−0.663404			−0.331702	+	0.943384i	$0.607623\pi$
$240$		0			0
$241$	−0.632854			−0.0407657			−0.0203829	−	0.999792i	$-0.506489\pi$
$241$	−0.632854			−0.0407657			−0.0203829	+	0.999792i	$0.506489\pi$
$242$	6.57259	−	11.3841i	0.422502	−	0.731795i
$243$		0			0
$244$	4.14057	−	7.17168i	0.265073	−	0.459120i
$245$	−27.3570	−	4.02672i	−1.74778	−	0.257258i
$246$		0			0
$247$	−0.498231	+	2.75672i	−0.0317017	+	0.175406i
$248$	1.67992	−	2.90971i	0.106675	−	0.184767i
$249$		0			0
$250$	22.1392			1.40021
$251$	−7.53648	−	13.0536i	−0.475698	−	0.823934i	0.523914	−	0.851771i	$-0.324471\pi$
$251$	−7.53648	−	13.0536i	−0.475698	−	0.823934i	−0.999612	+	0.0278373i	$0.991138\pi$
$252$		0			0
$253$	−23.4311	−	40.5838i	−1.47310	−	2.55148i
$254$	5.42757	−	9.40083i	0.340556	−	0.589860i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−11.1382			−0.694780			−0.347390	−	0.937721i	$-0.612932\pi$
$257$	−11.1382			−0.694780			−0.347390	+	0.937721i	$0.612932\pi$
$258$		0			0
$259$	−12.8304	−	26.5251i	−0.797240	−	1.64819i
$260$	−10.8715	−	9.20163i	−0.674219	−	0.570661i
$261$		0			0
$262$	−0.961751	−	1.66580i	−0.0594172	−	0.102914i
$263$	8.58528	+	14.8701i	0.529391	+	0.916932i	0.999412	+	0.0342770i	$0.0109128\pi$
$263$	8.58528	+	14.8701i	0.529391	+	0.916932i	−0.470021	+	0.882655i	$0.655754\pi$
$264$		0			0
$265$	−43.7059			−2.68483
$266$	2.05016	+	0.150075i	0.125704	+	0.00920168i
$267$		0			0
$268$	−4.09814	−	7.09819i	−0.250334	−	0.433591i
$269$	−3.28711			−0.200419			−0.100209	−	0.994966i	$-0.531951\pi$
$269$	−3.28711			−0.200419			−0.100209	+	0.994966i	$0.531951\pi$
$270$		0			0
$271$	14.7261			0.894545			0.447273	−	0.894398i	$-0.352395\pi$
$271$	14.7261			0.894545			0.447273	+	0.894398i	$0.352395\pi$
$272$	−0.140571			−0.00852340
$273$		0			0
$274$	15.8821			0.959474
$275$	−52.1082			−3.14224
$276$		0			0
$277$	18.5004			1.11158			0.555791	−	0.831322i	$-0.312415\pi$
$277$	18.5004			1.11158			0.555791	+	0.831322i	$0.312415\pi$
$278$	−2.94351	−	5.09831i	−0.176540	−	0.305776i
$279$		0			0
$280$	−5.87254	+	8.64551i	−0.350951	+	0.516668i
$281$	31.3463			1.86996			0.934981	−	0.354698i	$-0.115416\pi$
$281$	31.3463			1.86996			0.934981	+	0.354698i	$0.115416\pi$
$282$		0			0
$283$	7.35985	+	12.7476i	0.437498	+	0.757768i	0.997496	−	0.0707258i	$-0.0225315\pi$
$283$	7.35985	+	12.7476i	0.437498	+	0.757768i	−0.559998	+	0.828494i	$0.689198\pi$
$284$	−1.93865	−	3.35783i	−0.115037	−	0.199251i
$285$		0			0
$286$	13.5231	+	11.4460i	0.799640	+	0.676818i
$287$	24.5665	+	1.79830i	1.45011	+	0.106150i
$288$		0			0
$289$	−16.9802			−0.998838
$290$	−4.97542			−0.292167
$291$		0			0
$292$	−0.0817820	+	0.141650i	−0.00478593	+	0.00828947i
$293$	−8.39523	−	14.5410i	−0.490454	−	0.849492i	0.509485	−	0.860479i	$-0.329836\pi$
$293$	−8.39523	−	14.5410i	−0.490454	−	0.849492i	−0.999940	+	0.0109876i	$0.996502\pi$
$294$		0			0
$295$	−0.851711	−	1.47521i	−0.0495886	−	0.0858899i
$296$	−11.1368			−0.647314
$297$		0			0
$298$	6.63504	−	11.4922i	0.384358	−	0.665727i
$299$	32.3620	−	11.6225i	1.87154	−	0.672149i
$300$		0			0
$301$	−1.60922	+	2.36908i	−0.0927538	+	0.136551i
$302$	8.06783	−	13.9739i	0.464252	−	0.804107i
$303$		0			0
$304$	0.388481	−	0.672870i	0.0222809	−	0.0385917i
$305$	32.7126			1.87312
$306$		0			0
$307$	5.69511			0.325037			0.162519	−	0.986705i	$-0.448038\pi$
$307$	5.69511			0.325037			0.162519	+	0.986705i	$0.448038\pi$
$308$	7.30493	−	10.7543i	0.416237	−	0.612781i
$309$		0			0
$310$	13.2723			0.753813
$311$	−0.183797	+	0.318345i	−0.0104221	+	0.0180517i	−0.871189	−	0.490947i	$-0.836651\pi$
$311$	−0.183797	+	0.318345i	−0.0104221	+	0.0180517i	0.860767	+	0.508999i	$0.169984\pi$
$312$		0			0
$313$	−2.95742	−	5.12240i	−0.167163	−	0.289535i	0.770258	−	0.637732i	$-0.220127\pi$
$313$	−2.95742	−	5.12240i	−0.167163	−	0.289535i	−0.937421	+	0.348197i	$0.886794\pi$
$314$	8.85322	−	15.3342i	0.499616	−	0.865360i
$315$		0			0
$316$	2.17517	+	3.76751i	0.122363	+	0.211939i
$317$	4.28899	+	7.42875i	0.240894	+	0.417240i	0.960969	−	0.276656i	$-0.0892262\pi$
$317$	4.28899	+	7.42875i	0.240894	+	0.417240i	−0.720075	+	0.693896i	$0.755893\pi$
$318$		0			0
$319$	6.18899			0.346517
$320$	1.97513	+	3.42102i	0.110413	+	0.191241i
$321$		0			0
$322$	−10.9872	−	22.7145i	−0.612290	−	1.26583i
$323$	−0.0546094	+	0.0945863i	−0.00303855	+	0.00526292i
$324$		0			0
$325$	6.80020	−	37.6255i	0.377207	−	2.08709i
$326$	1.63571	−	2.83313i	0.0905935	−	0.156912i
$327$		0			0
$328$	4.65505	−	8.06279i	0.257032	−	0.445193i
$329$	−9.90683	+	14.5848i	−0.546181	+	0.804084i
$330$		0			0
$331$	2.07489	−	3.59381i	0.114046	−	0.197533i	−0.803352	−	0.595504i	$-0.796952\pi$
$331$	2.07489	−	3.59381i	0.114046	−	0.197533i	0.917398	+	0.397971i	$0.130286\pi$
$332$	10.5220			0.577472
$333$		0			0
$334$	−4.42914	+	7.67150i	−0.242352	+	0.419766i
$335$	16.1887	−	28.0397i	0.884483	−	1.53197i
$336$		0			0
$337$	18.5391			1.00989			0.504945	−	0.863152i	$-0.331513\pi$
$337$	18.5391			1.00989			0.504945	+	0.863152i	$0.331513\pi$
$338$	−10.0296	+	8.27088i	−0.545537	+	0.449877i
$339$		0			0
$340$	−0.277647	−	0.480898i	−0.0150575	−	0.0260804i
$341$	−16.5095			−0.894041
$342$		0			0
$343$	18.0770	+	4.02745i	0.976069	+	0.217462i
$344$	0.541233	+	0.937443i	0.0291813	+	0.0505435i
$345$		0			0
$346$	7.47486	−	12.9468i	0.401851	−	0.696027i
$347$	22.9868			1.23400			0.616999	−	0.786964i	$-0.288348\pi$
$347$	22.9868			1.23400			0.616999	+	0.786964i	$0.288348\pi$
$348$		0			0
$349$	7.29494	−	12.6352i	0.390489	−	0.676347i	−0.602025	−	0.798477i	$-0.705639\pi$
$349$	7.29494	−	12.6352i	0.390489	−	0.676347i	0.992514	+	0.122130i	$0.0389726\pi$
$350$	−27.9820	−	2.04832i	−1.49570	−	0.109487i
$351$		0			0
$352$	−2.45689	−	4.25545i	−0.130953	−	0.226816i
$353$	−9.86522	−	17.0871i	−0.525073	−	0.909453i	−0.999574	−	0.0291979i	$-0.990705\pi$
$353$	−9.86522	−	17.0871i	−0.525073	−	0.909453i	0.474501	−	0.880255i	$-0.342629\pi$
$354$		0			0
$355$	7.65815	−	13.2643i	0.406452	−	0.703996i
$356$	1.07274			0.0568550
$357$		0			0
$358$	11.6034	+	20.0977i	0.613260	+	1.06220i
$359$	−18.8344	−	32.6222i	−0.994044	−	1.72173i	−0.591401	−	0.806378i	$-0.701425\pi$
$359$	−18.8344	−	32.6222i	−0.994044	−	1.72173i	−0.402644	−	0.915357i	$-0.631909\pi$
$360$		0			0
$361$	9.19816	+	15.9317i	0.484114	+	0.838510i
$362$	−19.4618			−1.02289
$363$		0			0
$364$	6.81198	+	6.67809i	0.357045	+	0.350027i
$365$	−0.646119			−0.0338194
$366$		0			0
$367$	−1.25141	−	2.16750i	−0.0653229	−	0.113143i	0.831514	−	0.555503i	$-0.187474\pi$
$367$	−1.25141	−	2.16750i	−0.0653229	−	0.113143i	−0.896837	+	0.442361i	$0.854141\pi$
$368$	−9.53690			−0.497145
$369$		0			0
$370$	−21.9966	−	38.0993i	−1.14355	−	1.98069i
$371$	29.1947	+	2.13709i	1.51571	+	0.110952i
$372$		0			0
$373$	6.58371	−	11.4033i	0.340891	−	0.590441i	−0.643707	−	0.765272i	$-0.722605\pi$
$373$	6.58371	−	11.4033i	0.340891	−	0.590441i	0.984598	+	0.174831i	$0.0559378\pi$
$374$	0.345368	+	0.598195i	0.0178586	+	0.0309319i
$375$		0			0
$376$	3.33199	+	5.77118i	0.171834	+	0.297626i
$377$	−0.807672	+	4.46886i	−0.0415972	+	0.230158i
$378$		0			0
$379$	−5.93228	+	10.2750i	−0.304721	+	0.527792i	−0.977199	−	0.212325i	$-0.931896\pi$
$379$	−5.93228	+	10.2750i	−0.304721	+	0.527792i	0.672478	+	0.740117i	$0.265230\pi$
$380$	3.06920			0.157447
$381$		0			0
$382$	7.29819	−	12.6408i	0.373408	−	0.646761i
$383$	8.21139	−	14.2225i	0.419582	−	0.726738i	−0.576315	−	0.817228i	$-0.695510\pi$
$383$	8.21139	−	14.2225i	0.419582	−	0.726738i	0.995897	+	0.0904897i	$0.0288432\pi$
$384$		0			0
$385$	51.2187	+	3.74928i	2.61035	+	0.191081i
$386$	−0.884301	−	1.53165i	−0.0450098	−	0.0779592i
$387$		0			0
$388$	−6.54097	−	11.3293i	−0.332067	−	0.575158i
$389$	−9.03721	+	15.6529i	−0.458205	+	0.793634i	−0.998866	−	0.0476065i	$-0.984841\pi$
$389$	−9.03721	+	15.6529i	−0.458205	+	0.793634i	0.540662	+	0.841240i	$0.318174\pi$
$390$		0			0
$391$	1.34062			0.0677979
$392$	4.34548	−	5.48788i	0.219480	−	0.277180i
$393$		0			0
$394$	2.92757	−	5.07070i	0.147489	−	0.255458i
$395$	−8.59248	+	14.8826i	−0.432335	+	0.748826i
$396$		0			0
$397$	1.20491	−	2.08696i	0.0604726	−	0.104742i	−0.834204	−	0.551456i	$-0.814073\pi$
$397$	1.20491	−	2.08696i	0.0604726	−	0.104742i	0.894677	+	0.446714i	$0.147406\pi$
$398$	−13.9227			−0.697884
$399$		0			0
$400$	−5.30226	+	9.18378i	−0.265113	+	0.459189i
$401$	24.9243			1.24466			0.622331	−	0.782754i	$-0.286186\pi$
$401$	24.9243			1.24466			0.622331	+	0.782754i	$0.286186\pi$
$402$		0			0
$403$	2.15452	−	11.9210i	0.107324	−	0.593826i
$404$	3.69262	+	6.39580i	0.183715	+	0.318203i
$405$		0			0
$406$	3.32348	+	0.243283i	0.164941	+	0.0120739i
$407$	27.3619	+	47.3922i	1.35628	+	2.34914i
$408$		0			0
$409$	27.4769			1.35865			0.679323	−	0.733840i	$-0.262274\pi$
$409$	27.4769			1.35865			0.679323	+	0.733840i	$0.262274\pi$
$410$	36.7773			1.81630
$411$		0			0
$412$	−1.99107	−	3.44863i	−0.0980929	−	0.169902i
$413$	0.496793	+	1.02706i	0.0244456	+	0.0505381i
$414$		0			0
$415$	20.7824	+	35.9961i	1.02017	+	1.76698i
$416$	3.39335	−	1.21869i	0.166372	−	0.0597512i
$417$		0			0
$418$	−3.81782			−0.186736
$419$	5.16655	−	8.94872i	0.252402	−	0.437174i	−0.711784	−	0.702398i	$-0.752113\pi$
$419$	5.16655	−	8.94872i	0.252402	−	0.437174i	0.964187	+	0.265224i	$0.0854460\pi$
$420$		0			0
$421$	−16.8702			−0.822204			−0.411102	−	0.911589i	$-0.634856\pi$
$421$	−16.8702			−0.822204			−0.411102	+	0.911589i	$0.634856\pi$
$422$	−3.35399	+	5.80929i	−0.163270	+	0.282792i
$423$		0			0
$424$	5.53204	−	9.58177i	0.268659	−	0.465332i
$425$	0.745346	−	1.29098i	0.0361546	−	0.0626216i
$426$		0			0
$427$	−21.8514	−	1.59955i	−1.05746	−	0.0774077i
$428$	7.07358			0.341914
$429$		0			0
$430$	−2.13801	+	3.70314i	−0.103104	+	0.178581i
$431$	12.1718	+	21.0822i	0.586294	+	1.01549i	0.994713	+	0.102697i	$0.0327471\pi$
$431$	12.1718	+	21.0822i	0.586294	+	1.01549i	−0.408418	+	0.912795i	$0.633920\pi$
$432$		0			0
$433$	0.984059	+	1.70444i	0.0472909	+	0.0819102i	0.888702	−	0.458485i	$-0.151608\pi$
$433$	0.984059	+	1.70444i	0.0472909	+	0.0819102i	−0.841411	+	0.540396i	$0.818275\pi$
$434$	−8.86560	−	0.648974i	−0.425562	−	0.0311518i
$435$		0			0
$436$	−7.42350	+	12.8579i	−0.355521	+	0.615781i
$437$	−3.70491	+	6.41709i	−0.177230	+	0.306971i
$438$		0			0
$439$	20.2636			0.967128			0.483564	−	0.875309i	$-0.339342\pi$
$439$	20.2636			0.967128			0.483564	+	0.875309i	$0.339342\pi$
$440$	9.70533	−	16.8101i	0.462683	−	0.801391i
$441$		0			0
$442$	−0.477008	+	0.171313i	−0.0226889	+	0.00814854i
$443$	14.2707	+	24.7177i	0.678024	+	1.17437i	0.975575	+	0.219666i	$0.0704967\pi$
$443$	14.2707	+	24.7177i	0.678024	+	1.17437i	−0.297551	+	0.954706i	$0.596170\pi$
$444$		0			0
$445$	2.11879	+	3.66986i	0.100440	+	0.173968i
$446$	1.02744	−	1.77957i	0.0486505	−	0.0842652i
$447$		0			0
$448$	−1.15207	−	2.38175i	−0.0544301	−	0.112527i
$449$	−12.1517	−	21.0474i	−0.573475	−	0.993287i	−0.996206	−	0.0870320i	$-0.972262\pi$
$449$	−12.1517	−	21.0474i	−0.573475	−	0.993287i	0.422731	−	0.906255i	$-0.361072\pi$
$450$		0			0
$451$	−45.7477			−2.15418
$452$	0.785895	+	1.36121i	0.0369654	+	0.0640259i
$453$		0			0
$454$	−25.8298			−1.21225
$455$	−9.39135	+	36.4940i	−0.440273	+	1.71087i
$456$		0			0
$457$	−6.25302			−0.292504			−0.146252	−	0.989247i	$-0.546721\pi$
$457$	−6.25302			−0.292504			−0.146252	+	0.989247i	$0.546721\pi$
$458$	−5.39496	−	9.34435i	−0.252090	−	0.436633i
$459$		0			0
$460$	−18.8366	−	32.6259i	−0.878261	−	1.52119i
$461$	−9.65625	−	16.7251i	−0.449736	−	0.778966i	0.548632	−	0.836064i	$-0.315149\pi$
$461$	−9.65625	−	16.7251i	−0.449736	−	0.778966i	−0.998369	+	0.0570976i	$0.981815\pi$
$462$		0			0
$463$	21.4480			0.996772			0.498386	−	0.866955i	$-0.333926\pi$
$463$	21.4480			0.996772			0.498386	+	0.866955i	$0.333926\pi$
$464$	0.629759	−	1.09077i	0.0292358	−	0.0506379i
$465$		0			0
$466$	−1.92109	−	3.32742i	−0.0889928	−	0.154140i
$467$	−2.39255	−	4.14402i	−0.110714	−	0.191762i	0.805344	−	0.592807i	$-0.201980\pi$
$467$	−2.39255	−	4.14402i	−0.110714	−	0.191762i	−0.916058	+	0.401045i	$0.868647\pi$
$468$		0			0
$469$	−12.1848	+	17.9384i	−0.562641	+	0.828316i
$470$	−13.1622	+	22.7976i	−0.607128	+	1.05158i
$471$		0			0
$472$	0.431218			0.0198484
$473$	2.65950	−	4.60638i	0.122284	−	0.211802i
$474$		0			0
$475$	4.11966	+	7.13545i	0.189023	+	0.327397i
$476$	0.161948	+	0.334806i	0.00742287	+	0.0153458i
$477$		0			0
$478$	10.2560			0.469098
$479$	−5.85660	−	10.1439i	−0.267595	−	0.463488i	0.700645	−	0.713510i	$-0.252896\pi$
$479$	−5.85660	−	10.1439i	−0.267595	−	0.463488i	−0.968240	+	0.250022i	$0.919562\pi$
$480$		0			0
$481$	−37.7910	+	13.5723i	−1.72312	+	0.618845i
$482$	0.632854			0.0288257
$483$		0			0
$484$	−6.57259	+	11.3841i	−0.298754	+	0.517457i
$485$	25.8385	−	44.7536i	1.17327	−	2.03216i
$486$		0			0
$487$	−25.7570			−1.16716			−0.583581	−	0.812055i	$-0.698349\pi$
$487$	−25.7570			−1.16716			−0.583581	+	0.812055i	$0.698349\pi$
$488$	−4.14057	+	7.17168i	−0.187435	+	0.324647i
$489$		0			0
$490$	27.3570	+	4.02672i	1.23586	+	0.181909i
$491$	−2.35012	+	4.07053i	−0.106059	+	0.183700i	−0.914171	−	0.405330i	$-0.867157\pi$
$491$	−2.35012	+	4.07053i	−0.106059	+	0.183700i	0.808111	+	0.589030i	$0.200490\pi$
$492$		0			0
$493$	−0.0885262	+	0.153332i	−0.00398702	+	0.00690572i
$494$	0.498231	−	2.75672i	0.0224165	−	0.124031i
$495$		0			0
$496$	−1.67992	+	2.90971i	−0.0754308	+	0.130650i
$497$	−5.76407	+	8.48583i	−0.258554	+	0.380641i
$498$		0			0
$499$	16.3247	+	28.2752i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941832\pi$
$499$	16.3247	+	28.2752i	0.730794	+	1.26577i	−0.225751	+	0.974185i	$0.572483\pi$
$500$	−22.1392			−0.990097
$501$		0			0
$502$	7.53648	+	13.0536i	0.336370	+	0.582609i
$503$	−7.49164	−	12.9759i	−0.334036	−	0.578567i	0.649263	−	0.760564i	$-0.275077\pi$
$503$	−7.49164	−	12.9759i	−0.334036	−	0.578567i	−0.983299	+	0.181997i	$0.941744\pi$
$504$		0			0
$505$	−14.5868	+	25.2650i	−0.649103	+	1.12428i
$506$	23.4311	+	40.5838i	1.04164	+	1.80417i
$507$		0			0
$508$	−5.42757	+	9.40083i	−0.240809	+	0.417094i
$509$	0.420876			0.0186550			0.00932749	−	0.999956i	$-0.497031\pi$
$509$	0.420876			0.0186550			0.00932749	+	0.999956i	$0.497031\pi$
$510$		0			0
$511$	0.431595	+	0.0315933i	0.0190926	+	0.00139761i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	11.1382			0.491284
$515$	7.86522	−	13.6230i	0.346583	−	0.600300i
$516$		0			0
$517$	16.3727	−	28.3583i	0.720068	−	1.24720i
$518$	12.8304	+	26.5251i	0.563734	+	1.16545i
$519$		0			0
$520$	10.8715	+	9.20163i	0.476745	+	0.403518i
$521$	15.5914	−	27.0050i	0.683070	−	1.18311i	−0.290969	−	0.956732i	$-0.593978\pi$
$521$	15.5914	−	27.0050i	0.683070	−	1.18311i	0.974039	−	0.226379i	$-0.0726888\pi$
$522$		0			0
$523$	14.3638			0.628087			0.314043	−	0.949409i	$-0.398316\pi$
$523$	14.3638			0.628087			0.314043	+	0.949409i	$0.398316\pi$
$524$	0.961751	+	1.66580i	0.0420143	+	0.0727709i
$525$		0			0
$526$	−8.58528	−	14.8701i	−0.374336	−	0.648369i
$527$	0.236149	−	0.409023i	0.0102868	−	0.0178173i
$528$		0			0
$529$	67.9525			2.95446
$530$	43.7059			1.89846
$531$		0			0
$532$	−2.05016	−	0.150075i	−0.0888859	−	0.00650657i
$533$	5.97015	−	33.0329i	0.258596	−	1.43081i
$534$		0			0
$535$	13.9712	+	24.1989i	0.604028	+	1.04621i
$536$	4.09814	+	7.09819i	0.177013	+	0.306595i
$537$		0			0
$538$	3.28711			0.141717
$539$	−34.0298	−	5.00889i	−1.46577	−	0.215748i
$540$		0			0
$541$	4.68698	+	8.11808i	0.201509	+	0.349024i	0.949015	−	0.315232i	$-0.102082\pi$
$541$	4.68698	+	8.11808i	0.201509	+	0.349024i	−0.747506	+	0.664255i	$0.768749\pi$
$542$	−14.7261			−0.632539
$543$		0			0
$544$	0.140571			0.00602695
$545$	−58.6494			−2.51227
$546$		0			0
$547$	17.7829			0.760343			0.380172	−	0.924916i	$-0.375865\pi$
$547$	17.7829			0.760343			0.380172	+	0.924916i	$0.375865\pi$
$548$	−15.8821			−0.678450
$549$		0			0
$550$	52.1082			2.22190
$551$	−0.489299	−	0.847491i	−0.0208449	−	0.0361043i
$552$		0			0
$553$	6.46732	−	9.52114i	0.275019	−	0.404880i
$554$	−18.5004			−0.786008
$555$		0			0
$556$	2.94351	+	5.09831i	0.124833	+	0.216216i
$557$	6.68207	+	11.5737i	0.283128	+	0.490393i	0.972154	−	0.234345i	$-0.0752944\pi$
$557$	6.68207	+	11.5737i	0.283128	+	0.490393i	−0.689025	+	0.724737i	$0.741961\pi$
$558$		0			0
$559$	2.97904	+	2.52147i	0.126000	+	0.106647i
$560$	5.87254	−	8.64551i	0.248160	−	0.365339i
$561$		0			0
$562$	−31.3463			−1.32226
$563$	27.3883			1.15428			0.577139	−	0.816646i	$-0.304169\pi$
$563$	27.3883			1.15428			0.577139	+	0.816646i	$0.304169\pi$
$564$		0			0
$565$	−3.10449	+	5.37713i	−0.130607	+	0.226217i
$566$	−7.35985	−	12.7476i	−0.309357	−	0.535823i
$567$		0			0
$568$	1.93865	+	3.35783i	0.0813438	+	0.140892i
$569$	10.9762			0.460145			0.230072	−	0.973173i	$-0.426104\pi$
$569$	10.9762			0.460145			0.230072	+	0.973173i	$0.426104\pi$
$570$		0			0
$571$	−14.5552	+	25.2103i	−0.609115	+	1.05502i	0.382271	+	0.924050i	$0.375142\pi$
$571$	−14.5552	+	25.2103i	−0.609115	+	1.05502i	−0.991387	+	0.130969i	$0.958191\pi$
$572$	−13.5231	−	11.4460i	−0.565431	−	0.478583i
$573$		0			0
$574$	−24.5665	−	1.79830i	−1.02539	−	0.0750596i
$575$	50.5671	−	87.5847i	2.10879	−	3.65254i
$576$		0			0
$577$	−10.0317	+	17.3753i	−0.417623	+	0.723345i	−0.995700	−	0.0926375i	$-0.970470\pi$
$577$	−10.0317	+	17.3753i	−0.417623	+	0.723345i	0.578076	+	0.815983i	$0.303804\pi$
$578$	16.9802			0.706285
$579$		0			0
$580$	4.97542			0.206593
$581$	−12.1221	−	25.0609i	−0.502910	−	1.03970i
$582$		0			0
$583$	−54.3663			−2.25162
$584$	0.0817820	−	0.141650i	0.00338416	−	0.00586154i
$585$		0			0
$586$	8.39523	+	14.5410i	0.346804	+	0.600681i
$587$	−16.0113	+	27.7323i	−0.660855	+	1.14463i	0.319536	+	0.947574i	$0.396473\pi$
$587$	−16.0113	+	27.7323i	−0.660855	+	1.14463i	−0.980391	+	0.197060i	$0.936860\pi$
$588$		0			0
$589$	1.30524	+	2.26074i	0.0537814	+	0.0931521i
$590$	0.851711	+	1.47521i	0.0350644	+	0.0607333i
$591$		0			0
$592$	11.1368			0.457720
$593$	−12.2192	−	21.1643i	−0.501784	−	0.869115i	−0.999998	−	0.00206106i	$-0.999344\pi$
$593$	−12.2192	−	21.1643i	−0.501784	−	0.869115i	0.498214	−	0.867054i	$-0.333989\pi$
$594$		0			0
$595$	−0.825512	+	1.21531i	−0.0338427	+	0.0498229i
$596$	−6.63504	+	11.4922i	−0.271782	+	0.470740i
$597$		0			0
$598$	−32.3620	+	11.6225i	−1.32338	+	0.475281i
$599$	7.93636	−	13.7462i	0.324271	−	0.561654i	−0.657093	−	0.753809i	$-0.728214\pi$
$599$	7.93636	−	13.7462i	0.324271	−	0.561654i	0.981365	+	0.192155i	$0.0615477\pi$
$600$		0			0
$601$	−0.0246085	+	0.0426231i	−0.00100380	+	0.00173863i	−0.866527	−	0.499130i	$-0.833653\pi$
$601$	−0.0246085	+	0.0426231i	−0.00100380	+	0.00173863i	0.865523	+	0.500869i	$0.166986\pi$
$602$	1.60922	−	2.36908i	0.0655869	−	0.0965565i
$603$		0			0
$604$	−8.06783	+	13.9739i	−0.328275	+	0.568590i
$605$	−51.9268			−2.11112
$606$		0			0
$607$	−6.61325	+	11.4545i	−0.268423	+	0.464923i	−0.968455	−	0.249189i	$-0.919836\pi$
$607$	−6.61325	+	11.4545i	−0.268423	+	0.464923i	0.700031	+	0.714112i	$0.253169\pi$
$608$	−0.388481	+	0.672870i	−0.0157550	+	0.0272885i
$609$		0			0
$610$	−32.7126			−1.32450
$611$	18.3399	+	15.5229i	0.741952	+	0.627991i
$612$		0			0
$613$	1.17548	+	2.03599i	0.0474772	+	0.0822329i	0.888787	−	0.458320i	$-0.151549\pi$
$613$	1.17548	+	2.03599i	0.0474772	+	0.0822329i	−0.841310	+	0.540553i	$0.818215\pi$
$614$	−5.69511			−0.229836
$615$		0			0
$616$	−7.30493	+	10.7543i	−0.294324	+	0.433302i
$617$	16.1133	+	27.9090i	0.648697	+	1.12358i	0.983434	+	0.181264i	$0.0580189\pi$
$617$	16.1133	+	27.9090i	0.648697	+	1.12358i	−0.334738	+	0.942311i	$0.608648\pi$
$618$		0			0
$619$	9.49745	−	16.4501i	0.381735	−	0.661184i	−0.609575	−	0.792728i	$-0.708660\pi$
$619$	9.49745	−	16.4501i	0.381735	−	0.661184i	0.991310	+	0.131544i	$0.0419934\pi$
$620$	−13.2723			−0.533027
$621$		0			0
$622$	0.183797	−	0.318345i	0.00736957	−	0.0127645i
$623$	−1.23587	−	2.55500i	−0.0495140	−	0.102364i
$624$		0			0
$625$	−17.2165	−	29.8199i	−0.688662	−	1.19280i
$626$	2.95742	+	5.12240i	0.118202	+	0.204732i
$627$		0			0
$628$	−8.85322	+	15.3342i	−0.353282	+	0.611902i
$629$	−1.56552			−0.0624213
$630$		0			0
$631$	−11.7271	−	20.3119i	−0.466849	−	0.808606i	0.532434	−	0.846471i	$-0.321277\pi$
$631$	−11.7271	−	20.3119i	−0.466849	−	0.808606i	−0.999283	+	0.0378658i	$0.987944\pi$
$632$	−2.17517	−	3.76751i	−0.0865237	−	0.149863i
$633$		0			0
$634$	−4.28899	−	7.42875i	−0.170338	−	0.295033i
$635$	−42.8806			−1.70166
$636$		0			0
$637$	8.05769	−	23.9181i	0.319257	−	0.947668i
$638$	−6.18899			−0.245024
$639$		0			0
$640$	−1.97513	−	3.42102i	−0.0780738	−	0.135228i
$641$	−5.60442			−0.221361			−0.110681	−	0.993856i	$-0.535303\pi$
$641$	−5.60442			−0.221361			−0.110681	+	0.993856i	$0.535303\pi$
$642$		0			0
$643$	11.5626	+	20.0270i	0.455983	+	0.789786i	0.998744	−	0.0501012i	$-0.0159544\pi$
$643$	11.5626	+	20.0270i	0.455983	+	0.789786i	−0.542761	+	0.839887i	$0.682621\pi$
$644$	10.9872	+	22.7145i	0.432955	+	0.895078i
$645$		0			0
$646$	0.0546094	−	0.0945863i	0.00214858	−	0.00372145i
$647$	8.88782	+	15.3941i	0.349416	+	0.605206i	0.986146	−	0.165881i	$-0.0530466\pi$
$647$	8.88782	+	15.3941i	0.349416	+	0.605206i	−0.636730	+	0.771087i	$0.719713\pi$
$648$		0			0
$649$	−1.05945	−	1.83503i	−0.0415872	−	0.0720312i
$650$	−6.80020	+	37.6255i	−0.266726	+	1.47579i
$651$		0			0
$652$	−1.63571	+	2.83313i	−0.0640593	+	0.110954i
$653$	−2.50502			−0.0980290			−0.0490145	−	0.998798i	$-0.515608\pi$
$653$	−2.50502			−0.0980290			−0.0490145	+	0.998798i	$0.515608\pi$
$654$		0			0
$655$	−3.79916	+	6.58034i	−0.148445	+	0.257115i
$656$	−4.65505	+	8.06279i	−0.181749	+	0.314799i
$657$		0			0
$658$	9.90683	−	14.5848i	0.386209	−	0.568573i
$659$	15.8598	+	27.4700i	0.617810	+	1.07008i	0.989884	+	0.141876i	$0.0453134\pi$
$659$	15.8598	+	27.4700i	0.617810	+	1.07008i	−0.372074	+	0.928203i	$0.621353\pi$
$660$		0			0
$661$	−11.3573	−	19.6714i	−0.441747	−	0.765128i	0.556072	−	0.831134i	$-0.312308\pi$
$661$	−11.3573	−	19.6714i	−0.441747	−	0.765128i	−0.997819	+	0.0660056i	$0.978974\pi$
$662$	−2.07489	+	3.59381i	−0.0806427	+	0.139677i
$663$		0			0
$664$	−10.5220			−0.408335
$665$	−3.53593	−	7.31007i	−0.137117	−	0.283473i
$666$		0			0
$667$	−6.00595	+	10.4026i	−0.232551	+	0.402791i
$668$	4.42914	−	7.67150i	0.171369	−	0.296819i
$669$		0			0
$670$	−16.1887	+	28.0397i	−0.625424	+	1.08327i
$671$	40.6917			1.57088
$672$		0			0
$673$	−2.56027	+	4.43452i	−0.0986911	+	0.170938i	−0.911143	−	0.412090i	$-0.864799\pi$
$673$	−2.56027	+	4.43452i	−0.0986911	+	0.170938i	0.812452	+	0.583028i	$0.198132\pi$
$674$	−18.5391			−0.714100
$675$		0			0
$676$	10.0296	−	8.27088i	0.385753	−	0.318111i
$677$	−1.02921	−	1.78264i	−0.0395556	−	0.0685123i	0.845570	−	0.533865i	$-0.179261\pi$
$677$	−1.02921	−	1.78264i	−0.0395556	−	0.0685123i	−0.885125	+	0.465353i	$0.845928\pi$
$678$		0			0
$679$	−19.4479	+	28.6311i	−0.746342	+	1.09876i
$680$	0.277647	+	0.480898i	0.0106473	+	0.0184416i
$681$		0			0
$682$	16.5095			0.632183
$683$	26.9289			1.03040			0.515202	−	0.857069i	$-0.327717\pi$
$683$	26.9289			1.03040			0.515202	+	0.857069i	$0.327717\pi$
$684$		0			0
$685$	−31.3692	−	54.3330i	−1.19856	−	2.07596i
$686$	−18.0770	−	4.02745i	−0.690185	−	0.153769i
$687$		0			0
$688$	−0.541233	−	0.937443i	−0.0206343	−	0.0357397i
$689$	7.09489	−	39.2561i	0.270294	−	1.49554i
$690$		0			0
$691$	51.2761			1.95063			0.975316	−	0.220812i	$-0.0708706\pi$
$691$	51.2761			1.95063			0.975316	+	0.220812i	$0.0708706\pi$
$692$	−7.47486	+	12.9468i	−0.284152	+	0.492165i
$693$		0			0
$694$	−22.9868			−0.872568
$695$	−11.6276	+	20.1396i	−0.441061	+	0.763939i
$696$		0			0
$697$	0.654367	−	1.13340i	0.0247859	−	0.0429305i
$698$	−7.29494	+	12.6352i	−0.276118	+	0.478250i
$699$		0			0
$700$	27.9820	+	2.04832i	1.05762	+	0.0774193i
$701$	26.2809			0.992617			0.496308	−	0.868146i	$-0.334689\pi$
$701$	26.2809			0.992617			0.496308	+	0.868146i	$0.334689\pi$
$702$		0			0
$703$	4.32644	−	7.49362i	0.163175	−	0.282627i
$704$	2.45689	+	4.25545i	0.0925974	+	0.160383i
$705$		0			0
$706$	9.86522	+	17.0871i	0.371283	+	0.643080i
$707$	10.9791	−	16.1633i	0.412910	−	0.607883i
$708$		0			0
$709$	−4.37966	+	7.58580i	−0.164482	+	0.284891i	−0.936471	−	0.350745i	$-0.885928\pi$
$709$	−4.37966	+	7.58580i	−0.164482	+	0.284891i	0.771989	+	0.635635i	$0.219262\pi$
$710$	−7.65815	+	13.2643i	−0.287405	+	0.497800i
$711$		0			0
$712$	−1.07274			−0.0402026
$713$	16.0213	−	27.7496i	0.600001	−	1.03923i
$714$		0			0
$715$	12.4472	−	68.8703i	0.465498	−	2.57560i
$716$	−11.6034	−	20.0977i	−0.433640	−	0.751087i
$717$		0			0
$718$	18.8344	+	32.6222i	0.702895	+	1.21745i
$719$	−1.13801	+	1.97109i	−0.0424405	+	0.0735091i	−0.886465	−	0.462795i	$-0.846847\pi$
$719$	−1.13801	+	1.97109i	−0.0424405	+	0.0735091i	0.844025	+	0.536304i	$0.180180\pi$
$720$		0			0
$721$	−5.91994	+	8.71528i	−0.220470	+	0.324574i
$722$	−9.19816	−	15.9317i	−0.342320	−	0.592916i
$723$		0			0
$724$	19.4618			0.723291
$725$	6.67829	+	11.5671i	0.248025	+	0.429592i
$726$		0			0
$727$	−39.8719			−1.47877			−0.739383	−	0.673285i	$-0.764883\pi$
$727$	−39.8719			−1.47877			−0.739383	+	0.673285i	$0.764883\pi$
$728$	−6.81198	−	6.67809i	−0.252469	−	0.247506i
$729$		0			0
$730$	0.646119			0.0239139
$731$	0.0760819	+	0.131778i	0.00281399	+	0.00487398i
$732$		0			0
$733$	−12.8845	−	22.3167i	−0.475901	−	0.824284i	0.523718	−	0.851892i	$-0.324545\pi$
$733$	−12.8845	−	22.3167i	−0.475901	−	0.824284i	−0.999619	+	0.0276073i	$0.991211\pi$
$734$	1.25141	+	2.16750i	0.0461903	+	0.0800039i
$735$		0			0
$736$	9.53690			0.351535
$737$	20.1373	−	34.8789i	0.741769	−	1.28478i
$738$		0			0
$739$	−6.40893	−	11.1006i	−0.235756	−	0.408342i	0.723736	−	0.690077i	$-0.242423\pi$
$739$	−6.40893	−	11.1006i	−0.235756	−	0.408342i	−0.959492	+	0.281735i	$0.909090\pi$
$740$	21.9966	+	38.0993i	0.808612	+	1.40056i
$741$		0			0
$742$	−29.1947	−	2.13709i	−1.07177	−	0.0784551i
$743$	10.1715	−	17.6176i	0.373156	−	0.646326i	−0.616893	−	0.787047i	$-0.711609\pi$
$743$	10.1715	−	17.6176i	0.373156	−	0.646326i	0.990049	+	0.140721i	$0.0449422\pi$
$744$		0			0
$745$	−52.4202			−1.92053
$746$	−6.58371	+	11.4033i	−0.241047	+	0.417505i
$747$		0			0
$748$	−0.345368	−	0.598195i	−0.0126279	−	0.0218722i
$749$	−8.14924	−	16.8475i	−0.297767	−	0.615594i
$750$		0			0
$751$	−30.4741			−1.11202			−0.556008	−	0.831177i	$-0.687668\pi$
$751$	−30.4741			−1.11202			−0.556008	+	0.831177i	$0.687668\pi$
$752$	−3.33199	−	5.77118i	−0.121505	−	0.210453i
$753$		0			0
$754$	0.807672	−	4.46886i	0.0294137	−	0.162746i
$755$	−63.7400			−2.31974
$756$		0			0
$757$	10.7264	−	18.5787i	0.389859	−	0.675256i	−0.602571	−	0.798065i	$-0.705857\pi$
$757$	10.7264	−	18.5787i	0.389859	−	0.675256i	0.992430	+	0.122809i	$0.0391904\pi$
$758$	5.93228	−	10.2750i	0.215470	−	0.373205i
$759$		0			0
$760$	−3.06920			−0.111332
$761$	−25.0238	+	43.3425i	−0.907112	+	1.57116i	−0.0890544	+	0.996027i	$0.528385\pi$
$761$	−25.0238	+	43.3425i	−0.907112	+	1.57116i	−0.818057	+	0.575137i	$0.804949\pi$
$762$		0			0
$763$	39.1767	+	2.86779i	1.41829	+	0.103821i
$764$	−7.29819	+	12.6408i	−0.264039	+	0.457329i
$765$		0			0
$766$	−8.21139	+	14.2225i	−0.296690	+	0.513881i
$767$	1.46327	−	0.525522i	0.0528357	−	0.0189755i
$768$		0			0
$769$	25.3820	−	43.9629i	0.915298	−	1.58534i	0.108833	−	0.994060i	$-0.465289\pi$
$769$	25.3820	−	43.9629i	0.915298	−	1.58534i	0.806465	−	0.591282i	$-0.201378\pi$
$770$	−51.2187	−	3.74928i	−1.84579	−	0.135115i
$771$		0			0
$772$	0.884301	+	1.53165i	0.0318267	+	0.0551255i
$773$	−14.2845			−0.513778			−0.256889	−	0.966441i	$-0.582697\pi$
$773$	−14.2845			−0.513778			−0.256889	+	0.966441i	$0.582697\pi$
$774$		0			0
$775$	−17.8148	−	30.8561i	−0.639925	−	1.10838i
$776$	6.54097	+	11.3293i	0.234807	+	0.406698i
$777$		0			0
$778$	9.03721	−	15.6529i	0.324000	−	0.561184i
$779$	3.61680	+	6.26448i	0.129585	+	0.224448i
$780$		0			0
$781$	9.52607	−	16.4996i	0.340870	−	0.590403i
$782$	−1.34062			−0.0479403
$783$		0			0
$784$	−4.34548	+	5.48788i	−0.155196	+	0.195996i
$785$	−69.9449			−2.49644
$786$		0			0
$787$	−6.53995			−0.233124			−0.116562	−	0.993183i	$-0.537187\pi$
$787$	−6.53995			−0.233124			−0.116562	+	0.993183i	$0.537187\pi$
$788$	−2.92757	+	5.07070i	−0.104290	+	0.180636i
$789$		0			0
$790$	8.59248	−	14.8826i	0.305707	−	0.529500i
$791$	2.33666	−	3.44001i	0.0830821	−	0.122313i
$792$		0			0
$793$	−5.31033	+	29.3821i	−0.188575	+	1.04339i
$794$	−1.20491	+	2.08696i	−0.0427606	+	0.0740635i
$795$		0			0
$796$	13.9227			0.493479
$797$	24.2958	+	42.0815i	0.860601	+	1.49060i	0.871350	+	0.490662i	$0.163245\pi$
$797$	24.2958	+	42.0815i	0.860601	+	1.49060i	−0.0107495	+	0.999942i	$0.503422\pi$
$798$		0			0
$799$	0.468383	+	0.811263i	0.0165702	+	0.0287004i
$800$	5.30226	−	9.18378i	0.187463	−	0.324695i
$801$		0			0
$802$	−24.9243			−0.880109
$803$	−0.803716			−0.0283625
$804$		0			0
$805$	−56.0058	+	82.4514i	−1.97395	+	2.90603i
$806$	−2.15452	+	11.9210i	−0.0758897	+	0.419898i
$807$		0			0
$808$	−3.69262	−	6.39580i	−0.129906	−	0.225003i
$809$	20.8592	+	36.1291i	0.733369	+	1.27023i	0.955435	+	0.295201i	$0.0953866\pi$
$809$	20.8592	+	36.1291i	0.733369	+	1.27023i	−0.222066	+	0.975032i	$0.571280\pi$
$810$		0			0
$811$	2.40508			0.0844538			0.0422269	−	0.999108i	$-0.486555\pi$
$811$	2.40508			0.0844538			0.0422269	+	0.999108i	$0.486555\pi$
$812$	−3.32348	−	0.243283i	−0.116631	−	0.00853757i
$813$		0			0
$814$	−27.3619	−	47.3922i	−0.959034	−	1.66109i
$815$	−12.9229			−0.452670
$816$		0			0
$817$	−0.841036			−0.0294241
$818$	−27.4769			−0.960707
$819$		0			0
$820$	−36.7773			−1.28432
$821$	0.453291			0.0158200			0.00790998	−	0.999969i	$-0.497482\pi$
$821$	0.453291			0.0158200			0.00790998	+	0.999969i	$0.497482\pi$
$822$		0			0
$823$	−4.19063			−0.146076			−0.0730380	−	0.997329i	$-0.523269\pi$
$823$	−4.19063			−0.146076			−0.0730380	+	0.997329i	$0.523269\pi$
$824$	1.99107	+	3.44863i	0.0693621	+	0.120139i
$825$		0			0
$826$	−0.496793	−	1.02706i	−0.0172856	−	0.0357358i
$827$	−1.35282			−0.0470421			−0.0235211	−	0.999723i	$-0.507488\pi$
$827$	−1.35282			−0.0470421			−0.0235211	+	0.999723i	$0.507488\pi$
$828$		0			0
$829$	24.1081	+	41.7564i	0.837309	+	1.45026i	0.892137	+	0.451765i	$0.149206\pi$
$829$	24.1081	+	41.7564i	0.837309	+	1.45026i	−0.0548281	+	0.998496i	$0.517461\pi$
$830$	−20.7824	−	35.9961i	−0.721367	−	1.24944i
$831$		0			0
$832$	−3.39335	+	1.21869i	−0.117643	+	0.0422505i
$833$	0.610851	−	0.771439i	0.0211647	−	0.0267288i
$834$		0			0
$835$	34.9925			1.21096
$836$	3.81782			0.132042
$837$		0			0
$838$	−5.16655	+	8.94872i	−0.178475	+	0.309128i
$839$	−14.1093	−	24.4380i	−0.487107	−	0.843694i	0.512783	−	0.858518i	$-0.328614\pi$
$839$	−14.1093	−	24.4380i	−0.487107	−	0.843694i	−0.999890	+	0.0148244i	$0.995281\pi$
$840$		0			0
$841$	13.7068	+	23.7409i	0.472649	+	0.818651i
$842$	16.8702			0.581386
$843$		0			0
$844$	3.35399	−	5.80929i	0.115449	−	0.199964i
$845$	48.1046	+	17.9754i	1.65485	+	0.618372i
$846$		0			0
$847$	34.6860	+	2.53907i	1.19183	+	0.0872434i
$848$	−5.53204	+	9.58177i	−0.189971	+	0.329039i
$849$		0			0
$850$	−0.745346	+	1.29098i	−0.0255652	+	0.0442801i
$851$	−106.211			−3.64085
$852$		0			0
$853$	−3.29308			−0.112753			−0.0563764	−	0.998410i	$-0.517955\pi$
$853$	−3.29308			−0.112753			−0.0563764	+	0.998410i	$0.517955\pi$
$854$	21.8514	+	1.59955i	0.747739	+	0.0547355i
$855$		0			0
$856$	−7.07358			−0.241770
$857$	−16.7918	+	29.0842i	−0.573596	+	0.993497i	0.422597	+	0.906318i	$0.361119\pi$
$857$	−16.7918	+	29.0842i	−0.573596	+	0.993497i	−0.996193	+	0.0871794i	$0.972215\pi$
$858$		0			0
$859$	−13.6075	−	23.5688i	−0.464280	−	0.804157i	0.534888	−	0.844923i	$-0.320354\pi$
$859$	−13.6075	−	23.5688i	−0.464280	−	0.804157i	−0.999169	+	0.0407656i	$0.987020\pi$
$860$	2.13801	−	3.70314i	0.0729054	−	0.126276i
$861$		0			0
$862$	−12.1718	−	21.0822i	−0.414573	−	0.718061i
$863$	7.05959	+	12.2276i	0.240311	+	0.416231i	0.960803	−	0.277232i	$-0.0894172\pi$
$863$	7.05959	+	12.2276i	0.240311	+	0.416231i	−0.720492	+	0.693463i	$0.756084\pi$
$864$		0			0
$865$	−59.0552			−2.00794
$866$	−0.984059	−	1.70444i	−0.0334397	−	0.0579193i
$867$		0			0
$868$	8.86560	+	0.648974i	0.300918	+	0.0220276i
$869$	−10.6883	+	18.5127i	−0.362576	+	0.628000i
$870$		0			0
$871$	22.5569	+	19.0922i	0.764312	+	0.646916i
$872$	7.42350	−	12.8579i	0.251391	−	0.435423i
$873$		0			0
$874$	3.70491	−	6.41709i	0.125320	−	0.217061i
$875$	25.5059	+	52.7302i	0.862257	+	1.78261i
$876$		0			0
$877$	4.00956	−	6.94476i	0.135393	−	0.234508i	−0.790354	−	0.612650i	$-0.790104\pi$
$877$	4.00956	−	6.94476i	0.135393	−	0.234508i	0.925748	+	0.378142i	$0.123437\pi$
$878$	−20.2636			−0.683863
$879$		0			0
$880$	−9.70533	+	16.8101i	−0.327167	+	0.566669i
$881$	−13.1358	+	22.7519i	−0.442558	+	0.766532i	−0.997878	−	0.0651039i	$-0.979262\pi$
$881$	−13.1358	+	22.7519i	−0.442558	+	0.766532i	0.555321	+	0.831636i	$0.312595\pi$
$882$		0			0
$883$	−18.7341			−0.630452			−0.315226	−	0.949017i	$-0.602080\pi$
$883$	−18.7341			−0.630452			−0.315226	+	0.949017i	$0.602080\pi$
$884$	0.477008	−	0.171313i	0.0160435	−	0.00576189i
$885$		0			0
$886$	−14.2707	−	24.7177i	−0.479435	−	0.830406i
$887$	12.2377			0.410901			0.205450	−	0.978668i	$-0.434134\pi$
$887$	12.2377			0.410901			0.205450	+	0.978668i	$0.434134\pi$
$888$		0			0
$889$	28.6434	+	2.09673i	0.960667	+	0.0703222i
$890$	−2.11879	−	3.66986i	−0.0710221	−	0.123014i
$891$		0			0
$892$	−1.02744	+	1.77957i	−0.0344011	+	0.0595845i
$893$	−5.17767			−0.173264
$894$		0			0
$895$	45.8365	−	79.3911i	1.53214	−	2.65375i
$896$	1.15207	+	2.38175i	0.0384879	+	0.0795687i
$897$		0			0
$898$	12.1517	+	21.0474i	0.405508	+	0.702360i
$899$	2.11589	+	3.66484i	0.0705690	+	0.122229i
$900$		0			0
$901$	0.777647	−	1.34692i	0.0259072	−	0.0448725i
$902$	45.7477			1.52323
$903$		0			0
$904$	−0.785895	−	1.36121i	−0.0261385	−	0.0452732i
$905$	38.4395	+	66.5791i	1.27777	+	2.21316i
$906$		0			0
$907$	11.4450	+	19.8233i	0.380024	+	0.658221i	0.991065	−	0.133378i	$-0.0425824\pi$
$907$	11.4450	+	19.8233i	0.380024	+	0.658221i	−0.611041	+	0.791599i	$0.709249\pi$
$908$	25.8298			0.857190
$909$		0			0
$910$	9.39135	−	36.4940i	0.311320	−	1.20976i
$911$	−22.0074			−0.729139			−0.364570	−	0.931176i	$-0.618784\pi$
$911$	−22.0074			−0.729139			−0.364570	+	0.931176i	$0.618784\pi$
$912$		0			0
$913$	25.8515	+	44.7761i	0.855559	+	1.48187i
$914$	6.25302			0.206832
$915$		0			0
$916$	5.39496	+	9.34435i	0.178255	+	0.308746i
$917$	2.85952	−	4.20977i	0.0944297	−	0.139019i
$918$		0			0
$919$	−24.9601	+	43.2322i	−0.823358	+	1.42610i	0.0798091	+	0.996810i	$0.474569\pi$
$919$	−24.9601	+	43.2322i	−0.823358	+	1.42610i	−0.903167	+	0.429288i	$0.858764\pi$
$920$	18.8366	+	32.6259i	0.621024	+	1.07565i
$921$		0			0
$922$	9.65625	+	16.7251i	0.318012	+	0.550812i
$923$	10.6707	+	9.03168i	0.351229	+	0.297281i
$924$		0			0
$925$	−59.0502	+	102.278i	−1.94156	+	3.36288i
$926$	−21.4480			−0.704824
$927$		0			0
$928$	−0.629759	+	1.09077i	−0.0206729	+	0.0358064i
$929$	4.50148	−	7.79679i	0.147689	−	0.255804i	−0.782684	−	0.622419i	$-0.786150\pi$
$929$	4.50148	−	7.79679i	0.147689	−	0.255804i	0.930373	+	0.366615i	$0.119483\pi$
$930$		0			0
$931$	2.00449	+	5.05588i	0.0656944	+	0.165700i
$932$	1.92109	+	3.32742i	0.0629274	+	0.108993i
$933$		0			0
$934$	2.39255	+	4.14402i	0.0782866	+	0.135596i
$935$	1.36429	−	2.36302i	0.0446171	−	0.0772791i
$936$		0			0
$937$	−42.4359			−1.38632			−0.693159	−	0.720784i	$-0.743782\pi$
$937$	−42.4359			−1.38632			−0.693159	+	0.720784i	$0.743782\pi$
$938$	12.1848	−	17.9384i	0.397847	−	0.585708i
$939$		0			0
$940$	13.1622	−	22.7976i	0.429304	−	0.743577i
$941$	4.68568	−	8.11583i	0.152749	−	0.264569i	−0.779488	−	0.626417i	$-0.784521\pi$
$941$	4.68568	−	8.11583i	0.152749	−	0.264569i	0.932237	+	0.361848i	$0.117854\pi$
$942$		0			0
$943$	44.3948	−	76.8940i	1.44569	−	2.50401i
$944$	−0.431218			−0.0140350
$945$		0			0
$946$	−2.65950	+	4.60638i	−0.0864677	+	0.149766i
$947$	36.2822			1.17901			0.589507	−	0.807764i	$-0.299322\pi$
$947$	36.2822			1.17901			0.589507	+	0.807764i	$0.299322\pi$
$948$		0			0
$949$	0.104886	−	0.580336i	0.00340475	−	0.0188385i
$950$	−4.11966	−	7.13545i	−0.133659	−	0.231505i
$951$		0			0
$952$	−0.161948	−	0.334806i	−0.00524876	−	0.0108511i
$953$	−9.41368	−	16.3050i	−0.304939	−	0.528170i	0.672309	−	0.740271i	$-0.265303\pi$
$953$	−9.41368	−	16.3050i	−0.304939	−	0.528170i	−0.977248	+	0.212101i	$0.931969\pi$
$954$		0			0
$955$	−57.6594			−1.86581
$956$	−10.2560			−0.331702
$957$		0			0
$958$	5.85660	+	10.1439i	0.189218	+	0.327735i
$959$	18.2973	+	37.8273i	0.590850	+	1.22151i
$960$		0			0
$961$	9.85571	+	17.0706i	0.317926	+	0.550664i
$962$	37.7910	−	13.5723i	1.21843	−	0.437590i
$963$		0			0
$964$	−0.632854			−0.0203829
$965$	−3.49322	+	6.05043i	−0.112451	+	0.194770i
$966$		0			0
$967$	−9.63971			−0.309992			−0.154996	−	0.987915i	$-0.549536\pi$
$967$	−9.63971			−0.309992			−0.154996	+	0.987915i	$0.549536\pi$
$968$	6.57259	−	11.3841i	0.211251	−	0.365897i
$969$		0			0
$970$	−25.8385	+	44.7536i	−0.829624	+	1.43695i
$971$	9.13666	−	15.8252i	0.293209	−	0.507853i	−0.681357	−	0.731951i	$-0.738610\pi$
$971$	9.13666	−	15.8252i	0.293209	−	0.507853i	0.974567	+	0.224097i	$0.0719434\pi$
$972$		0			0
$973$	8.75178	−	12.8843i	0.280569	−	0.413052i
$974$	25.7570			0.825308
$975$		0			0
$976$	4.14057	−	7.17168i	0.132536	−	0.229560i
$977$	16.0432	+	27.7877i	0.513268	+	0.889007i	0.999882	+	0.0153892i	$0.00489873\pi$
$977$	16.0432	+	27.7877i	0.513268	+	0.889007i	−0.486613	+	0.873617i	$0.661768\pi$
$978$		0			0
$979$	2.63560	+	4.56499i	0.0842340	+	0.145898i
$980$	−27.3570	−	4.02672i	−0.873888	−	0.128629i
$981$		0			0
$982$	2.35012	−	4.07053i	0.0749954	−	0.129896i
$983$	11.7559	−	20.3618i	0.374955	−	0.649442i	−0.615365	−	0.788242i	$-0.710991\pi$
$983$	11.7559	−	20.3618i	0.374955	−	0.649442i	0.990320	+	0.138801i	$0.0443247\pi$
$984$		0			0
$985$	−23.1293			−0.736960
$986$	0.0885262	−	0.153332i	0.00281925	−	0.00488308i
$987$		0			0
$988$	−0.498231	+	2.75672i	−0.0158509	+	0.0877029i
$989$	5.16168	+	8.94030i	0.164132	+	0.284285i
$990$		0			0
$991$	−12.5930	−	21.8117i	−0.400029	−	0.692870i	0.593700	−	0.804686i	$-0.297667\pi$
$991$	−12.5930	−	21.8117i	−0.400029	−	0.692870i	−0.993729	+	0.111816i	$0.964333\pi$
$992$	1.67992	−	2.90971i	0.0533376	−	0.0923835i
$993$		0			0
$994$	5.76407	−	8.48583i	0.182825	−	0.269154i
$995$	27.4992	+	47.6300i	0.871783	+	1.50997i
$996$		0			0
$997$	14.9958			0.474921			0.237461	−	0.971397i	$-0.423685\pi$
$997$	14.9958			0.474921			0.237461	+	0.971397i	$0.423685\pi$
$998$	−16.3247	−	28.2752i	−0.516749	−	0.895036i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.m.g.1621.4		8
3.2	odd	2		546.2.j.d.529.1	yes	8
7.2	even	3		1638.2.p.i.919.4		8
13.3	even	3		1638.2.p.i.991.4		8
21.2	odd	6		546.2.k.b.373.1	yes	8
39.29	odd	6		546.2.k.b.445.1	yes	8
91.16	even	3	inner	1638.2.m.g.289.4		8
273.107	odd	6		546.2.j.d.289.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.1	✓	8	273.107	odd	6
546.2.j.d.529.1	yes	8	3.2	odd	2
546.2.k.b.373.1	yes	8	21.2	odd	6
546.2.k.b.445.1	yes	8	39.29	odd	6
1638.2.m.g.289.4		8	91.16	even	3	inner
1638.2.m.g.1621.4		8	1.1	even	1	trivial
1638.2.p.i.919.4		8	7.2	even	3
1638.2.p.i.991.4		8	13.3	even	3

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.m (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.97513 + 3.42102i) q^{5} +(-1.15207 - 2.38175i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.97513 + 3.42102i) q^{5} +(-1.15207 - 2.38175i) q^{7} -1.00000 q^{8} +(-1.97513 - 3.42102i) q^{10} +(2.45689 + 4.25545i) q^{11} +(-3.39335 + 1.21869i) q^{13} +(1.15207 + 2.38175i) q^{14} +1.00000 q^{16} -0.140571 q^{17} +(0.388481 - 0.672870i) q^{19} +(1.97513 + 3.42102i) q^{20} +(-2.45689 - 4.25545i) q^{22} -9.53690 q^{23} +(-5.30226 + 9.18378i) q^{25} +(3.39335 - 1.21869i) q^{26} +(-1.15207 - 2.38175i) q^{28} +(0.629759 - 1.09077i) q^{29} +(-1.67992 + 2.90971i) q^{31} -1.00000 q^{32} +0.140571 q^{34} +(5.87254 - 8.64551i) q^{35} +11.1368 q^{37} +(-0.388481 + 0.672870i) q^{38} +(-1.97513 - 3.42102i) q^{40} +(-4.65505 + 8.06279i) q^{41} +(-0.541233 - 0.937443i) q^{43} +(2.45689 + 4.25545i) q^{44} +9.53690 q^{46} +(-3.33199 - 5.77118i) q^{47} +(-4.34548 + 5.48788i) q^{49} +(5.30226 - 9.18378i) q^{50} +(-3.39335 + 1.21869i) q^{52} +(-5.53204 + 9.58177i) q^{53} +(-9.70533 + 16.8101i) q^{55} +(1.15207 + 2.38175i) q^{56} +(-0.629759 + 1.09077i) q^{58} -0.431218 q^{59} +(4.14057 - 7.17168i) q^{61} +(1.67992 - 2.90971i) q^{62} +1.00000 q^{64} +(-10.8715 - 9.20163i) q^{65} +(-4.09814 - 7.09819i) q^{67} -0.140571 q^{68} +(-5.87254 + 8.64551i) q^{70} +(-1.93865 - 3.35783i) q^{71} +(-0.0817820 + 0.141650i) q^{73} -11.1368 q^{74} +(0.388481 - 0.672870i) q^{76} +(7.30493 - 10.7543i) q^{77} +(2.17517 + 3.76751i) q^{79} +(1.97513 + 3.42102i) q^{80} +(4.65505 - 8.06279i) q^{82} +10.5220 q^{83} +(-0.277647 - 0.480898i) q^{85} +(0.541233 + 0.937443i) q^{86} +(-2.45689 - 4.25545i) q^{88} +1.07274 q^{89} +(6.81198 + 6.67809i) q^{91} -9.53690 q^{92} +(3.33199 + 5.77118i) q^{94} +3.06920 q^{95} +(-6.54097 - 11.3293i) q^{97} +(4.34548 - 5.48788i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} + 2 q^{10} + 6 q^{11} - 11 q^{13} + 3 q^{14} + 8 q^{16} + 8 q^{17} + 6 q^{19} - 2 q^{20} - 6 q^{22} - 20 q^{23} - 18 q^{25} + 11 q^{26} - 3 q^{28} - 2 q^{29} + 6 q^{31} - 8 q^{32} - 8 q^{34} + 18 q^{35} + 56 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} + 20 q^{46} - q^{47} + 5 q^{49} + 18 q^{50} - 11 q^{52} - 7 q^{53} + q^{55} + 3 q^{56} + 2 q^{58} + 4 q^{59} + 24 q^{61} - 6 q^{62} + 8 q^{64} - 22 q^{65} - 15 q^{67} + 8 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} - 56 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} - 2 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} - 6 q^{88} + 50 q^{89} - 8 q^{91} - 20 q^{92} + q^{94} - 16 q^{95} - q^{97} - 5 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8 + 2 * q^10 + 6 * q^11 - 11 * q^13 + 3 * q^14 + 8 * q^16 + 8 * q^17 + 6 * q^19 - 2 * q^20 - 6 * q^22 - 20 * q^23 - 18 * q^25 + 11 * q^26 - 3 * q^28 - 2 * q^29 + 6 * q^31 - 8 * q^32 - 8 * q^34 + 18 * q^35 + 56 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 + 20 * q^46 - q^47 + 5 * q^49 + 18 * q^50 - 11 * q^52 - 7 * q^53 + q^55 + 3 * q^56 + 2 * q^58 + 4 * q^59 + 24 * q^61 - 6 * q^62 + 8 * q^64 - 22 * q^65 - 15 * q^67 + 8 * q^68 - 18 * q^70 - 6 * q^71 + q^73 - 56 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 - 2 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 - 6 * q^88 + 50 * q^89 - 8 * q^91 - 20 * q^92 + q^94 - 16 * q^95 - q^97 - 5 * q^98

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