LMFDB - Embedded newform 648.2.n.a.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(109,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.109"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$648 = 2^{3} \cdot 3^{4}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	648.n (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-4,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{2} + 1$ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	648.109
Dual form			648.2.n.a.541.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-3.23205 - 1.86603i) q^{5} +(0.366025 + 0.633975i) q^{7} +(2.00000 - 2.00000i) q^{8} +(1.36603 + 5.09808i) q^{10} +(4.09808 - 2.36603i) q^{11} +(-2.13397 - 1.23205i) q^{13} +(0.267949 - 1.00000i) q^{14} -4.00000 q^{16} -3.73205 q^{17} -3.26795i q^{19} +(3.73205 - 6.46410i) q^{20} +(-6.46410 - 1.73205i) q^{22} +(-4.36603 + 7.56218i) q^{23} +(4.46410 + 7.73205i) q^{25} +(0.901924 + 3.36603i) q^{26} +(-1.26795 + 0.732051i) q^{28} +(-4.50000 + 2.59808i) q^{29} +(-1.00000 + 1.73205i) q^{31} +(4.00000 + 4.00000i) q^{32} +(3.73205 + 3.73205i) q^{34} -2.73205i q^{35} +5.00000i q^{37} +(-3.26795 + 3.26795i) q^{38} +(-10.1962 + 2.73205i) q^{40} +(-2.26795 + 3.92820i) q^{41} +(-8.36603 + 4.83013i) q^{43} +(4.73205 + 8.19615i) q^{44} +(11.9282 - 3.19615i) q^{46} +(-1.73205 - 3.00000i) q^{47} +(3.23205 - 5.59808i) q^{49} +(3.26795 - 12.1962i) q^{50} +(2.46410 - 4.26795i) q^{52} -0.928203i q^{53} -17.6603 q^{55} +(2.00000 + 0.535898i) q^{56} +(7.09808 + 1.90192i) q^{58} +(-7.26795 - 4.19615i) q^{59} +(-7.79423 + 4.50000i) q^{61} +(2.73205 - 0.732051i) q^{62} -8.00000i q^{64} +(4.59808 + 7.96410i) q^{65} +(4.09808 + 2.36603i) q^{67} -7.46410i q^{68} +(-2.73205 + 2.73205i) q^{70} +5.66025 q^{71} +9.00000 q^{73} +(5.00000 - 5.00000i) q^{74} +6.53590 q^{76} +(3.00000 + 1.73205i) q^{77} +(-2.63397 - 4.56218i) q^{79} +(12.9282 + 7.46410i) q^{80} +(6.19615 - 1.66025i) q^{82} +(-12.1244 + 7.00000i) q^{83} +(12.0622 + 6.96410i) q^{85} +(13.1962 + 3.53590i) q^{86} +(3.46410 - 12.9282i) q^{88} -11.7321 q^{89} -1.80385i q^{91} +(-15.1244 - 8.73205i) q^{92} +(-1.26795 + 4.73205i) q^{94} +(-6.09808 + 10.5622i) q^{95} +(4.00000 + 6.92820i) q^{97} +(-8.83013 + 2.36603i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 4 q^{2} - 6 q^{5} - 2 q^{7} + 8 q^{8} + 2 q^{10} + 6 q^{11} - 12 q^{13} + 8 q^{14} - 16 q^{16} - 8 q^{17} + 8 q^{20} - 12 q^{22} - 14 q^{23} + 4 q^{25} + 14 q^{26} - 12 q^{28} - 18 q^{29} - 4 q^{31}+ \cdots - 18 q^{98}+O(q^{100})$ 4 * q - 4 * q^2 - 6 * q^5 - 2 * q^7 + 8 * q^8 + 2 * q^10 + 6 * q^11 - 12 * q^13 + 8 * q^14 - 16 * q^16 - 8 * q^17 + 8 * q^20 - 12 * q^22 - 14 * q^23 + 4 * q^25 + 14 * q^26 - 12 * q^28 - 18 * q^29 - 4 * q^31 + 16 * q^32 + 8 * q^34 - 20 * q^38 - 20 * q^40 - 16 * q^41 - 30 * q^43 + 12 * q^44 + 20 * q^46 + 6 * q^49 + 20 * q^50 - 4 * q^52 - 36 * q^55 + 8 * q^56 + 18 * q^58 - 36 * q^59 + 4 * q^62 + 8 * q^65 + 6 * q^67 - 4 * q^70 - 12 * q^71 + 36 * q^73 + 20 * q^74 + 40 * q^76 + 12 * q^77 - 14 * q^79 + 24 * q^80 + 4 * q^82 + 24 * q^85 + 32 * q^86 - 40 * q^89 - 12 * q^92 - 12 * q^94 - 14 * q^95 + 16 * q^97 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$ .

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$		0			0
$3$		0			0
$4$			2.00000i			1.00000i
$5$	−3.23205	−	1.86603i	−1.44542	−	0.834512i	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−3.23205	−	1.86603i	−1.44542	−	0.834512i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$	0.366025	+	0.633975i	0.138345	+	0.239620i	0.926870	−	0.375382i	$-0.122489\pi$
$7$	0.366025	+	0.633975i	0.138345	+	0.239620i	−0.788526	+	0.615002i	$0.789155\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$	1.36603	+	5.09808i	0.431975	+	1.61215i
$11$	4.09808	−	2.36603i	1.23562	−	0.713384i	0.267421	−	0.963580i	$-0.413828\pi$
$11$	4.09808	−	2.36603i	1.23562	−	0.713384i	0.968195	+	0.250196i	$0.0804951\pi$
$12$		0			0
$13$	−2.13397	−	1.23205i	−0.591858	−	0.341709i	0.173974	−	0.984750i	$-0.444339\pi$
$13$	−2.13397	−	1.23205i	−0.591858	−	0.341709i	−0.765832	+	0.643041i	$0.777673\pi$
$14$	0.267949	−	1.00000i	0.0716124	−	0.267261i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	−3.73205			−0.905155			−0.452578	−	0.891725i	$-0.649495\pi$
$17$	−3.73205			−0.905155			−0.452578	+	0.891725i	$0.649495\pi$
$18$		0			0
$19$		−	3.26795i		−	0.749719i	−0.927082	−	0.374859i	$-0.877691\pi$
$19$		−	3.26795i		−	0.749719i	0.927082	−	0.374859i	$-0.122309\pi$
$20$	3.73205	−	6.46410i	0.834512	−	1.44542i
$21$		0			0
$22$	−6.46410	−	1.73205i	−1.37815	−	0.369274i
$23$	−4.36603	+	7.56218i	−0.910379	+	1.57682i	−0.0968500	+	0.995299i	$0.530877\pi$
$23$	−4.36603	+	7.56218i	−0.910379	+	1.57682i	−0.813529	+	0.581524i	$0.802457\pi$
$24$		0			0
$25$	4.46410	+	7.73205i	0.892820	+	1.54641i
$26$	0.901924	+	3.36603i	0.176882	+	0.660132i
$27$		0			0
$28$	−1.26795	+	0.732051i	−0.239620	+	0.138345i
$29$	−4.50000	+	2.59808i	−0.835629	+	0.482451i	−0.855776	−	0.517346i	$-0.826920\pi$
$29$	−4.50000	+	2.59808i	−0.835629	+	0.482451i	0.0201471	+	0.999797i	$0.493587\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$		0			0
$34$	3.73205	+	3.73205i	0.640041	+	0.640041i
$35$		−	2.73205i		−	0.461801i
$36$		0			0
$37$			5.00000i			0.821995i	0.911636	+	0.410997i	$0.134819\pi$
$37$			5.00000i			0.821995i	−0.911636	+	0.410997i	$0.865181\pi$
$38$	−3.26795	+	3.26795i	−0.530131	+	0.530131i
$39$		0			0
$40$	−10.1962	+	2.73205i	−1.61215	+	0.431975i
$41$	−2.26795	+	3.92820i	−0.354194	+	0.613482i	−0.986980	−	0.160845i	$-0.948578\pi$
$41$	−2.26795	+	3.92820i	−0.354194	+	0.613482i	0.632786	+	0.774327i	$0.281911\pi$
$42$		0			0
$43$	−8.36603	+	4.83013i	−1.27581	+	0.736587i	−0.976075	−	0.217436i	$-0.930231\pi$
$43$	−8.36603	+	4.83013i	−1.27581	+	0.736587i	−0.299732	+	0.954023i	$0.596897\pi$
$44$	4.73205	+	8.19615i	0.713384	+	1.23562i
$45$		0			0
$46$	11.9282	−	3.19615i	1.75872	−	0.471247i
$47$	−1.73205	−	3.00000i	−0.252646	−	0.437595i	0.711608	−	0.702577i	$-0.247967\pi$
$47$	−1.73205	−	3.00000i	−0.252646	−	0.437595i	−0.964253	+	0.264982i	$0.914634\pi$
$48$		0			0
$49$	3.23205	−	5.59808i	0.461722	−	0.799725i
$50$	3.26795	−	12.1962i	0.462158	−	1.72480i
$51$		0			0
$52$	2.46410	−	4.26795i	0.341709	−	0.591858i
$53$		−	0.928203i		−	0.127499i	−0.997966	−	0.0637493i	$-0.979694\pi$
$53$		−	0.928203i		−	0.127499i	0.997966	−	0.0637493i	$-0.0203058\pi$
$54$		0			0
$55$	−17.6603			−2.38131
$56$	2.00000	+	0.535898i	0.267261	+	0.0716124i
$57$		0			0
$58$	7.09808	+	1.90192i	0.932023	+	0.249735i
$59$	−7.26795	−	4.19615i	−0.946206	−	0.546293i	−0.0543060	−	0.998524i	$-0.517295\pi$
$59$	−7.26795	−	4.19615i	−0.946206	−	0.546293i	−0.891900	+	0.452232i	$0.850628\pi$
$60$		0			0
$61$	−7.79423	+	4.50000i	−0.997949	+	0.576166i	−0.907641	−	0.419748i	$-0.862118\pi$
$61$	−7.79423	+	4.50000i	−0.997949	+	0.576166i	−0.0903080	+	0.995914i	$0.528785\pi$
$62$	2.73205	−	0.732051i	0.346971	−	0.0929705i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	4.59808	+	7.96410i	0.570321	+	0.987825i
$66$		0			0
$67$	4.09808	+	2.36603i	0.500660	+	0.289056i	0.728986	−	0.684529i	$-0.239992\pi$
$67$	4.09808	+	2.36603i	0.500660	+	0.289056i	−0.228326	+	0.973585i	$0.573325\pi$
$68$		−	7.46410i		−	0.905155i
$69$		0			0
$70$	−2.73205	+	2.73205i	−0.326543	+	0.326543i
$71$	5.66025			0.671749			0.335874	−	0.941907i	$-0.390968\pi$
$71$	5.66025			0.671749			0.335874	+	0.941907i	$0.390968\pi$
$72$		0			0
$73$	9.00000			1.05337			0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000			1.05337			0.526685	+	0.850060i	$0.323435\pi$
$74$	5.00000	−	5.00000i	0.581238	−	0.581238i
$75$		0			0
$76$	6.53590			0.749719
$77$	3.00000	+	1.73205i	0.341882	+	0.197386i
$78$		0			0
$79$	−2.63397	−	4.56218i	−0.296345	−	0.513285i	0.678952	−	0.734183i	$-0.262435\pi$
$79$	−2.63397	−	4.56218i	−0.296345	−	0.513285i	−0.975297	+	0.220898i	$0.929101\pi$
$80$	12.9282	+	7.46410i	1.44542	+	0.834512i
$81$		0			0
$82$	6.19615	−	1.66025i	0.684251	−	0.183344i
$83$	−12.1244	+	7.00000i	−1.33082	+	0.768350i	−0.985426	−	0.170107i	$-0.945589\pi$
$83$	−12.1244	+	7.00000i	−1.33082	+	0.768350i	−0.345395	+	0.938457i	$0.612255\pi$
$84$		0			0
$85$	12.0622	+	6.96410i	1.30833	+	0.755363i
$86$	13.1962	+	3.53590i	1.42298	+	0.381286i
$87$		0			0
$88$	3.46410	−	12.9282i	0.369274	−	1.37815i
$89$	−11.7321			−1.24359			−0.621797	−	0.783178i	$-0.713597\pi$
$89$	−11.7321			−1.24359			−0.621797	+	0.783178i	$0.713597\pi$
$90$		0			0
$91$		−	1.80385i		−	0.189095i
$92$	−15.1244	−	8.73205i	−1.57682	−	0.910379i
$93$		0			0
$94$	−1.26795	+	4.73205i	−0.130779	+	0.488074i
$95$	−6.09808	+	10.5622i	−0.625649	+	1.08366i
$96$		0			0
$97$	4.00000	+	6.92820i	0.406138	+	0.703452i	0.994453	−	0.105180i	$-0.0335417\pi$
$97$	4.00000	+	6.92820i	0.406138	+	0.703452i	−0.588315	+	0.808632i	$0.700208\pi$
$98$	−8.83013	+	2.36603i	−0.891978	+	0.239005i
$99$		0			0
$100$	−15.4641	+	8.92820i	−1.54641	+	0.892820i
$101$	6.92820	−	4.00000i	0.689382	−	0.398015i	−0.113998	−	0.993481i	$-0.536366\pi$
$101$	6.92820	−	4.00000i	0.689382	−	0.398015i	0.803380	+	0.595466i	$0.203033\pi$
$102$		0			0
$103$	1.73205	−	3.00000i	0.170664	−	0.295599i	−0.767988	−	0.640464i	$-0.778742\pi$
$103$	1.73205	−	3.00000i	0.170664	−	0.295599i	0.938652	+	0.344865i	$0.112075\pi$
$104$	−6.73205	+	1.80385i	−0.660132	+	0.176882i
$105$		0			0
$106$	−0.928203	+	0.928203i	−0.0901551	+	0.0901551i
$107$			10.3923i			1.00466i	0.864675	+	0.502331i	$0.167524\pi$
$107$			10.3923i			1.00466i	−0.864675	+	0.502331i	$0.832476\pi$
$108$		0			0
$109$		−	12.8564i		−	1.23142i	−0.787973	−	0.615710i	$-0.788869\pi$
$109$		−	12.8564i		−	1.23142i	0.787973	−	0.615710i	$-0.211131\pi$
$110$	17.6603	+	17.6603i	1.68384	+	1.68384i
$111$		0			0
$112$	−1.46410	−	2.53590i	−0.138345	−	0.239620i
$113$	3.86603	−	6.69615i	0.363685	−	0.629921i	−0.624879	−	0.780721i	$-0.714852\pi$
$113$	3.86603	−	6.69615i	0.363685	−	0.629921i	0.988564	+	0.150800i	$0.0481851\pi$
$114$		0			0
$115$	28.2224	−	16.2942i	2.63176	−	1.51944i
$116$	−5.19615	−	9.00000i	−0.482451	−	0.835629i
$117$		0			0
$118$	3.07180	+	11.4641i	0.282782	+	1.05536i
$119$	−1.36603	−	2.36603i	−0.125223	−	0.216893i
$120$		0			0
$121$	5.69615	−	9.86603i	0.517832	−	0.896911i
$122$	12.2942	+	3.29423i	1.11307	+	0.298245i
$123$		0			0
$124$	−3.46410	−	2.00000i	−0.311086	−	0.179605i
$125$		−	14.6603i		−	1.31125i
$126$		0			0
$127$	−13.6603			−1.21215			−0.606076	−	0.795407i	$-0.707257\pi$
$127$	−13.6603			−1.21215			−0.606076	+	0.795407i	$0.707257\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$		0			0
$130$	3.36603	−	12.5622i	0.295220	−	1.10178i
$131$	−0.169873	−	0.0980762i	−0.0148419	−	0.00856896i	0.492561	−	0.870278i	$-0.336061\pi$
$131$	−0.169873	−	0.0980762i	−0.0148419	−	0.00856896i	−0.507403	+	0.861709i	$0.669394\pi$
$132$		0			0
$133$	2.07180	−	1.19615i	0.179648	−	0.103720i
$134$	−1.73205	−	6.46410i	−0.149626	−	0.558413i
$135$		0			0
$136$	−7.46410	+	7.46410i	−0.640041	+	0.640041i
$137$	8.59808	+	14.8923i	0.734583	+	1.27234i	0.954906	+	0.296908i	$0.0959556\pi$
$137$	8.59808	+	14.8923i	0.734583	+	1.27234i	−0.220323	+	0.975427i	$0.570711\pi$
$138$		0			0
$139$	−16.8564	−	9.73205i	−1.42974	−	0.825462i	−0.432642	−	0.901566i	$-0.642419\pi$
$139$	−16.8564	−	9.73205i	−1.42974	−	0.825462i	−0.997100	+	0.0761041i	$0.975752\pi$
$140$	5.46410			0.461801
$141$		0			0
$142$	−5.66025	−	5.66025i	−0.474998	−	0.474998i
$143$	−11.6603			−0.975079
$144$		0			0
$145$	19.3923			1.61044
$146$	−9.00000	−	9.00000i	−0.744845	−	0.744845i
$147$		0			0
$148$	−10.0000			−0.821995
$149$	4.50000	+	2.59808i	0.368654	+	0.212843i	0.672870	−	0.739760i	$-0.265061\pi$
$149$	4.50000	+	2.59808i	0.368654	+	0.212843i	−0.304216	+	0.952603i	$0.598394\pi$
$150$		0			0
$151$	−6.92820	−	12.0000i	−0.563809	−	0.976546i	−0.997159	−	0.0753205i	$-0.976002\pi$
$151$	−6.92820	−	12.0000i	−0.563809	−	0.976546i	0.433350	−	0.901226i	$-0.357331\pi$
$152$	−6.53590	−	6.53590i	−0.530131	−	0.530131i
$153$		0			0
$154$	−1.26795	−	4.73205i	−0.102174	−	0.381320i
$155$	6.46410	−	3.73205i	0.519209	−	0.299766i
$156$		0			0
$157$	−2.13397	−	1.23205i	−0.170310	−	0.0983284i	0.412422	−	0.910993i	$-0.364683\pi$
$157$	−2.13397	−	1.23205i	−0.170310	−	0.0983284i	−0.582732	+	0.812664i	$0.698016\pi$
$158$	−1.92820	+	7.19615i	−0.153400	+	0.572495i
$159$		0			0
$160$	−5.46410	−	20.3923i	−0.431975	−	1.61215i
$161$	−6.39230			−0.503784
$162$		0			0
$163$		−	6.53590i		−	0.511931i	−0.966686	−	0.255966i	$-0.917607\pi$
$163$		−	6.53590i		−	0.511931i	0.966686	−	0.255966i	$-0.0823934\pi$
$164$	−7.85641	−	4.53590i	−0.613482	−	0.354194i
$165$		0			0
$166$	19.1244	+	5.12436i	1.48434	+	0.397727i
$167$	7.36603	−	12.7583i	0.570000	−	0.987269i	−0.426565	−	0.904457i	$-0.640276\pi$
$167$	7.36603	−	12.7583i	0.570000	−	0.987269i	0.996565	−	0.0828123i	$-0.0263902\pi$
$168$		0			0
$169$	−3.46410	−	6.00000i	−0.266469	−	0.461538i
$170$	−5.09808	−	19.0263i	−0.391005	−	1.45925i
$171$		0			0
$172$	−9.66025	−	16.7321i	−0.736587	−	1.27581i
$173$	1.50000	−	0.866025i	0.114043	−	0.0658427i	−0.441894	−	0.897067i	$-0.645693\pi$
$173$	1.50000	−	0.866025i	0.114043	−	0.0658427i	0.555936	+	0.831225i	$0.312360\pi$
$174$		0			0
$175$	−3.26795	+	5.66025i	−0.247034	+	0.427875i
$176$	−16.3923	+	9.46410i	−1.23562	+	0.713384i
$177$		0			0
$178$	11.7321	+	11.7321i	0.879354	+	0.879354i
$179$		−	14.0000i		−	1.04641i	−0.852207	−	0.523205i	$-0.824736\pi$
$179$		−	14.0000i		−	1.04641i	0.852207	−	0.523205i	$-0.175264\pi$
$180$		0			0
$181$			6.53590i			0.485810i	0.970050	+	0.242905i	$0.0781002\pi$
$181$			6.53590i			0.485810i	−0.970050	+	0.242905i	$0.921900\pi$
$182$	−1.80385	+	1.80385i	−0.133710	+	0.133710i
$183$		0			0
$184$	6.39230	+	23.8564i	0.471247	+	1.75872i
$185$	9.33013	−	16.1603i	0.685965	−	1.18813i
$186$		0			0
$187$	−15.2942	+	8.83013i	−1.11842	+	0.645723i
$188$	6.00000	−	3.46410i	0.437595	−	0.252646i
$189$		0			0
$190$	16.6603	−	4.46410i	1.20866	−	0.323860i
$191$	−8.29423	−	14.3660i	−0.600149	−	1.03949i	−0.992798	−	0.119801i	$-0.961774\pi$
$191$	−8.29423	−	14.3660i	−0.600149	−	1.03949i	0.392649	−	0.919689i	$-0.371559\pi$
$192$		0			0
$193$	−5.42820	+	9.40192i	−0.390731	+	0.676765i	−0.992546	−	0.121870i	$-0.961111\pi$
$193$	−5.42820	+	9.40192i	−0.390731	+	0.676765i	0.601815	+	0.798635i	$0.294444\pi$
$194$	2.92820	−	10.9282i	0.210233	−	0.784599i
$195$		0			0
$196$	11.1962	+	6.46410i	0.799725	+	0.461722i
$197$			4.12436i			0.293848i	0.989148	+	0.146924i	$0.0469373\pi$
$197$			4.12436i			0.293848i	−0.989148	+	0.146924i	$0.953063\pi$
$198$		0			0
$199$	2.39230			0.169586			0.0847930	−	0.996399i	$-0.472977\pi$
$199$	2.39230			0.169586			0.0847930	+	0.996399i	$0.472977\pi$
$200$	24.3923	+	6.53590i	1.72480	+	0.462158i
$201$		0			0
$202$	−10.9282	−	2.92820i	−0.768906	−	0.206028i
$203$	−3.29423	−	1.90192i	−0.231210	−	0.133489i
$204$		0			0
$205$	14.6603	−	8.46410i	1.02392	−	0.591158i
$206$	−4.73205	+	1.26795i	−0.329698	+	0.0883422i
$207$		0			0
$208$	8.53590	+	4.92820i	0.591858	+	0.341709i
$209$	−7.73205	−	13.3923i	−0.534837	−	0.926365i
$210$		0			0
$211$	22.5622	+	13.0263i	1.55324	+	0.896766i	0.997875	+	0.0651625i	$0.0207566\pi$
$211$	22.5622	+	13.0263i	1.55324	+	0.896766i	0.555370	+	0.831604i	$0.312577\pi$
$212$	1.85641			0.127499
$213$		0			0
$214$	10.3923	−	10.3923i	0.710403	−	0.710403i
$215$	36.0526			2.45876
$216$		0			0
$217$	−1.46410			−0.0993897
$218$	−12.8564	+	12.8564i	−0.870746	+	0.870746i
$219$		0			0
$220$		−	35.3205i		−	2.38131i
$221$	7.96410	+	4.59808i	0.535723	+	0.309300i
$222$		0			0
$223$	−11.5622	−	20.0263i	−0.774261	−	1.34106i	−0.935209	−	0.354096i	$-0.884789\pi$
$223$	−11.5622	−	20.0263i	−0.774261	−	1.34106i	0.160948	−	0.986963i	$-0.448545\pi$
$224$	−1.07180	+	4.00000i	−0.0716124	+	0.267261i
$225$		0			0
$226$	−10.5622	+	2.83013i	−0.702586	+	0.188257i
$227$	5.83013	−	3.36603i	0.386959	−	0.223411i	−0.293883	−	0.955842i	$-0.594947\pi$
$227$	5.83013	−	3.36603i	0.386959	−	0.223411i	0.680842	+	0.732431i	$0.261614\pi$
$228$		0			0
$229$	−9.86603	−	5.69615i	−0.651965	−	0.376412i	0.137243	−	0.990537i	$-0.456176\pi$
$229$	−9.86603	−	5.69615i	−0.651965	−	0.376412i	−0.789209	+	0.614125i	$0.789509\pi$
$230$	−44.5167	−	11.9282i	−2.93534	−	0.786522i
$231$		0			0
$232$	−3.80385	+	14.1962i	−0.249735	+	0.932023i
$233$	3.73205			0.244495			0.122247	−	0.992500i	$-0.460990\pi$
$233$	3.73205			0.244495			0.122247	+	0.992500i	$0.460990\pi$
$234$		0			0
$235$			12.9282i			0.843343i
$236$	8.39230	−	14.5359i	0.546293	−	0.946206i
$237$		0			0
$238$	−1.00000	+	3.73205i	−0.0648204	+	0.241913i
$239$	−3.92820	+	6.80385i	−0.254094	+	0.440104i	−0.964649	−	0.263538i	$-0.915111\pi$
$239$	−3.92820	+	6.80385i	−0.254094	+	0.440104i	0.710555	+	0.703642i	$0.248444\pi$
$240$		0			0
$241$	2.23205	+	3.86603i	0.143779	+	0.249033i	0.928917	−	0.370289i	$-0.120741\pi$
$241$	2.23205	+	3.86603i	0.143779	+	0.249033i	−0.785138	+	0.619321i	$0.787408\pi$
$242$	−15.5622	+	4.16987i	−1.00037	+	0.268050i
$243$		0			0
$244$	−9.00000	−	15.5885i	−0.576166	−	0.997949i
$245$	−20.8923	+	12.0622i	−1.33476	+	0.770624i
$246$		0			0
$247$	−4.02628	+	6.97372i	−0.256186	+	0.443727i
$248$	1.46410	+	5.46410i	0.0929705	+	0.346971i
$249$		0			0
$250$	−14.6603	+	14.6603i	−0.927196	+	0.927196i
$251$			7.26795i			0.458749i	0.973338	+	0.229374i	$0.0736680\pi$
$251$			7.26795i			0.458749i	−0.973338	+	0.229374i	$0.926332\pi$
$252$		0			0
$253$			41.3205i			2.59780i
$254$	13.6603	+	13.6603i	0.857121	+	0.857121i
$255$		0			0
$256$	16.0000			1.00000
$257$	1.66987	−	2.89230i	0.104164	−	0.180417i	−0.809232	−	0.587489i	$-0.800117\pi$
$257$	1.66987	−	2.89230i	0.104164	−	0.180417i	0.913396	+	0.407072i	$0.133450\pi$
$258$		0			0
$259$	−3.16987	+	1.83013i	−0.196966	+	0.113719i
$260$	−15.9282	+	9.19615i	−0.987825	+	0.570321i
$261$		0			0
$262$	0.0717968	+	0.267949i	0.00443562	+	0.0165540i
$263$	8.12436	+	14.0718i	0.500969	+	0.867704i	0.999999	+	0.00111953i	$0.000356359\pi$
$263$	8.12436	+	14.0718i	0.500969	+	0.867704i	−0.499030	+	0.866585i	$0.666310\pi$
$264$		0			0
$265$	−1.73205	+	3.00000i	−0.106399	+	0.184289i
$266$	−3.26795	−	0.875644i	−0.200371	−	0.0536892i
$267$		0			0
$268$	−4.73205	+	8.19615i	−0.289056	+	0.500660i
$269$			25.7321i			1.56891i	0.620185	+	0.784455i	$0.287057\pi$
$269$			25.7321i			1.56891i	−0.620185	+	0.784455i	$0.712943\pi$
$270$		0			0
$271$	10.7321			0.651926			0.325963	−	0.945383i	$-0.394312\pi$
$271$	10.7321			0.651926			0.325963	+	0.945383i	$0.394312\pi$
$272$	14.9282			0.905155
$273$		0			0
$274$	6.29423	−	23.4904i	0.380248	−	1.41911i
$275$	36.5885	+	21.1244i	2.20637	+	1.27385i
$276$		0			0
$277$	−8.53590	+	4.92820i	−0.512872	+	0.296107i	−0.734014	−	0.679135i	$-0.762355\pi$
$277$	−8.53590	+	4.92820i	−0.512872	+	0.296107i	0.221141	+	0.975242i	$0.429022\pi$
$278$	7.12436	+	26.5885i	0.427290	+	1.59467i
$279$		0			0
$280$	−5.46410	−	5.46410i	−0.326543	−	0.326543i
$281$	−6.86603	−	11.8923i	−0.409593	−	0.709435i	0.585251	−	0.810852i	$-0.300996\pi$
$281$	−6.86603	−	11.8923i	−0.409593	−	0.709435i	−0.994844	+	0.101417i	$0.967663\pi$
$282$		0			0
$283$	−5.53590	−	3.19615i	−0.329075	−	0.189992i	0.326355	−	0.945247i	$-0.394179\pi$
$283$	−5.53590	−	3.19615i	−0.329075	−	0.189992i	−0.655430	+	0.755256i	$0.727513\pi$
$284$			11.3205i			0.671749i
$285$		0			0
$286$	11.6603	+	11.6603i	0.689485	+	0.689485i
$287$	−3.32051			−0.196003
$288$		0			0
$289$	−3.07180			−0.180694
$290$	−19.3923	−	19.3923i	−1.13876	−	1.13876i
$291$		0			0
$292$			18.0000i			1.05337i
$293$	−2.89230	−	1.66987i	−0.168970	−	0.0975550i	0.413130	−	0.910672i	$-0.364436\pi$
$293$	−2.89230	−	1.66987i	−0.168970	−	0.0975550i	−0.582100	+	0.813117i	$0.697769\pi$
$294$		0			0
$295$	15.6603	+	27.1244i	0.911775	+	1.57924i
$296$	10.0000	+	10.0000i	0.581238	+	0.581238i
$297$		0			0
$298$	−1.90192	−	7.09808i	−0.110175	−	0.411181i
$299$	18.6340	−	10.7583i	1.07763	−	0.622170i
$300$		0			0
$301$	−6.12436	−	3.53590i	−0.353002	−	0.203806i
$302$	−5.07180	+	18.9282i	−0.291849	+	1.08920i
$303$		0			0
$304$			13.0718i			0.749719i
$305$	33.5885			1.92327
$306$		0			0
$307$		−	14.7846i		−	0.843802i	−0.906642	−	0.421901i	$-0.861363\pi$
$307$		−	14.7846i		−	0.843802i	0.906642	−	0.421901i	$-0.138637\pi$
$308$	−3.46410	+	6.00000i	−0.197386	+	0.341882i
$309$		0			0
$310$	−10.1962	−	2.73205i	−0.579103	−	0.155170i
$311$	9.66025	−	16.7321i	0.547783	−	0.948788i	−0.450643	−	0.892704i	$-0.648805\pi$
$311$	9.66025	−	16.7321i	0.547783	−	0.948788i	0.998426	−	0.0560835i	$-0.0178613\pi$
$312$		0			0
$313$	−1.23205	−	2.13397i	−0.0696396	−	0.120619i	0.829103	−	0.559096i	$-0.188852\pi$
$313$	−1.23205	−	2.13397i	−0.0696396	−	0.120619i	−0.898743	+	0.438476i	$0.855518\pi$
$314$	0.901924	+	3.36603i	0.0508985	+	0.189956i
$315$		0			0
$316$	9.12436	−	5.26795i	0.513285	−	0.296345i
$317$	1.03590	−	0.598076i	0.0581818	−	0.0335913i	−0.470627	−	0.882332i	$-0.655972\pi$
$317$	1.03590	−	0.598076i	0.0581818	−	0.0335913i	0.528809	+	0.848741i	$0.322639\pi$
$318$		0			0
$319$	−12.2942	+	21.2942i	−0.688345	+	1.19225i
$320$	−14.9282	+	25.8564i	−0.834512	+	1.44542i
$321$		0			0
$322$	6.39230	+	6.39230i	0.356229	+	0.356229i
$323$			12.1962i			0.678612i
$324$		0			0
$325$		−	22.0000i		−	1.22034i
$326$	−6.53590	+	6.53590i	−0.361990	+	0.361990i
$327$		0			0
$328$	3.32051	+	12.3923i	0.183344	+	0.684251i
$329$	1.26795	−	2.19615i	0.0699043	−	0.121078i
$330$		0			0
$331$	−11.3660	+	6.56218i	−0.624733	+	0.360690i	−0.778710	−	0.627385i	$-0.784125\pi$
$331$	−11.3660	+	6.56218i	−0.624733	+	0.360690i	0.153976	+	0.988075i	$0.450792\pi$
$332$	−14.0000	−	24.2487i	−0.768350	−	1.33082i
$333$		0			0
$334$	−20.1244	+	5.39230i	−1.10116	+	0.295054i
$335$	−8.83013	−	15.2942i	−0.482441	−	0.835613i
$336$		0			0
$337$	−2.00000	+	3.46410i	−0.108947	+	0.188702i	−0.915344	−	0.402673i	$-0.868081\pi$
$337$	−2.00000	+	3.46410i	−0.108947	+	0.188702i	0.806397	+	0.591375i	$0.201415\pi$
$338$	−2.53590	+	9.46410i	−0.137935	+	0.514779i
$339$		0			0
$340$	−13.9282	+	24.1244i	−0.755363	+	1.30833i
$341$			9.46410i			0.512510i
$342$		0			0
$343$	9.85641			0.532196
$344$	−7.07180	+	26.3923i	−0.381286	+	1.42298i
$345$		0			0
$346$	−2.36603	−	0.633975i	−0.127198	−	0.0340827i
$347$	−5.83013	−	3.36603i	−0.312978	−	0.180698i	0.335281	−	0.942118i	$-0.391169\pi$
$347$	−5.83013	−	3.36603i	−0.312978	−	0.180698i	−0.648258	+	0.761421i	$0.724502\pi$
$348$		0			0
$349$	−10.2679	+	5.92820i	−0.549631	+	0.317329i	−0.748973	−	0.662600i	$-0.769453\pi$
$349$	−10.2679	+	5.92820i	−0.549631	+	0.317329i	0.199342	+	0.979930i	$0.436119\pi$
$350$	8.92820	−	2.39230i	0.477233	−	0.127874i
$351$		0			0
$352$	25.8564	+	6.92820i	1.37815	+	0.369274i
$353$	3.46410	+	6.00000i	0.184376	+	0.319348i	0.943366	−	0.331754i	$-0.107640\pi$
$353$	3.46410	+	6.00000i	0.184376	+	0.319348i	−0.758990	+	0.651102i	$0.774307\pi$
$354$		0			0
$355$	−18.2942	−	10.5622i	−0.970957	−	0.560582i
$356$		−	23.4641i		−	1.24359i
$357$		0			0
$358$	−14.0000	+	14.0000i	−0.739923	+	0.739923i
$359$	1.12436			0.0593412			0.0296706	−	0.999560i	$-0.490554\pi$
$359$	1.12436			0.0593412			0.0296706	+	0.999560i	$0.490554\pi$
$360$		0			0
$361$	8.32051			0.437921
$362$	6.53590	−	6.53590i	0.343519	−	0.343519i
$363$		0			0
$364$	3.60770			0.189095
$365$	−29.0885	−	16.7942i	−1.52256	−	0.879050i
$366$		0			0
$367$	−1.26795	−	2.19615i	−0.0661864	−	0.114638i	0.831033	−	0.556223i	$-0.187750\pi$
$367$	−1.26795	−	2.19615i	−0.0661864	−	0.114638i	−0.897220	+	0.441585i	$0.854417\pi$
$368$	17.4641	−	30.2487i	0.910379	−	1.57682i
$369$		0			0
$370$	−25.4904	+	6.83013i	−1.32518	+	0.355081i
$371$	0.588457	−	0.339746i	0.0305512	−	0.0176387i
$372$		0			0
$373$	−19.8564	−	11.4641i	−1.02813	−	0.593589i	−0.111679	−	0.993744i	$-0.535623\pi$
$373$	−19.8564	−	11.4641i	−1.02813	−	0.593589i	−0.916447	+	0.400156i	$0.868956\pi$
$374$	24.1244	+	6.46410i	1.24744	+	0.334251i
$375$		0			0
$376$	−9.46410	−	2.53590i	−0.488074	−	0.130779i
$377$	12.8038			0.659432
$378$		0			0
$379$			10.0000i			0.513665i	0.966456	+	0.256833i	$0.0826790\pi$
$379$			10.0000i			0.513665i	−0.966456	+	0.256833i	$0.917321\pi$
$380$	−21.1244	−	12.1962i	−1.08366	−	0.625649i
$381$		0			0
$382$	−6.07180	+	22.6603i	−0.310660	+	1.15940i
$383$	10.0981	−	17.4904i	0.515988	−	0.893717i	−0.483840	−	0.875156i	$-0.660758\pi$
$383$	10.0981	−	17.4904i	0.515988	−	0.893717i	0.999828	−	0.0185603i	$-0.00590828\pi$
$384$		0			0
$385$	−6.46410	−	11.1962i	−0.329441	−	0.570609i
$386$	14.8301	−	3.97372i	0.754834	−	0.202257i
$387$		0			0
$388$	−13.8564	+	8.00000i	−0.703452	+	0.406138i
$389$	14.6603	−	8.46410i	0.743304	−	0.429147i	−0.0799651	−	0.996798i	$-0.525481\pi$
$389$	14.6603	−	8.46410i	0.743304	−	0.429147i	0.823270	+	0.567651i	$0.192148\pi$
$390$		0			0
$391$	16.2942	−	28.2224i	0.824035	−	1.42727i
$392$	−4.73205	−	17.6603i	−0.239005	−	0.891978i
$393$		0			0
$394$	4.12436	−	4.12436i	0.207782	−	0.207782i
$395$			19.6603i			0.989215i
$396$		0			0
$397$		−	32.4641i		−	1.62933i	−0.579934	−	0.814663i	$-0.696922\pi$
$397$		−	32.4641i		−	1.62933i	0.579934	−	0.814663i	$-0.303078\pi$
$398$	−2.39230	−	2.39230i	−0.119915	−	0.119915i
$399$		0			0
$400$	−17.8564	−	30.9282i	−0.892820	−	1.54641i
$401$	4.79423	−	8.30385i	0.239412	−	0.414674i	−0.721133	−	0.692796i	$-0.756379\pi$
$401$	4.79423	−	8.30385i	0.239412	−	0.414674i	0.960546	+	0.278122i	$0.0897119\pi$
$402$		0			0
$403$	4.26795	−	2.46410i	0.212602	−	0.122746i
$404$	8.00000	+	13.8564i	0.398015	+	0.689382i
$405$		0			0
$406$	1.39230	+	5.19615i	0.0690989	+	0.257881i
$407$	11.8301	+	20.4904i	0.586398	+	1.01567i
$408$		0			0
$409$	−14.3564	+	24.8660i	−0.709879	+	1.22955i	0.255023	+	0.966935i	$0.417917\pi$
$409$	−14.3564	+	24.8660i	−0.709879	+	1.22955i	−0.964902	+	0.262611i	$0.915416\pi$
$410$	−23.1244	−	6.19615i	−1.14203	−	0.306006i
$411$		0			0
$412$	6.00000	+	3.46410i	0.295599	+	0.170664i
$413$		−	6.14359i		−	0.302306i
$414$		0			0
$415$	52.2487			2.56479
$416$	−3.60770	−	13.4641i	−0.176882	−	0.660132i
$417$		0			0
$418$	−5.66025	+	21.1244i	−0.276852	+	1.03323i
$419$	−18.5885	−	10.7321i	−0.908106	−	0.524295i	−0.0282844	−	0.999600i	$-0.509004\pi$
$419$	−18.5885	−	10.7321i	−0.908106	−	0.524295i	−0.879821	+	0.475305i	$0.842338\pi$
$420$		0			0
$421$	11.2583	−	6.50000i	0.548697	−	0.316791i	−0.199899	−	0.979817i	$-0.564061\pi$
$421$	11.2583	−	6.50000i	0.548697	−	0.316791i	0.748596	+	0.663026i	$0.230728\pi$
$422$	−9.53590	−	35.5885i	−0.464200	−	1.73242i
$423$		0			0
$424$	−1.85641	−	1.85641i	−0.0901551	−	0.0901551i
$425$	−16.6603	−	28.8564i	−0.808141	−	1.39974i
$426$		0			0
$427$	−5.70577	−	3.29423i	−0.276122	−	0.159419i
$428$	−20.7846			−1.00466
$429$		0			0
$430$	−36.0526	−	36.0526i	−1.73861	−	1.73861i
$431$	−21.7128			−1.04587			−0.522935	−	0.852373i	$-0.675163\pi$
$431$	−21.7128			−1.04587			−0.522935	+	0.852373i	$0.675163\pi$
$432$		0			0
$433$	−21.7846			−1.04690			−0.523451	−	0.852056i	$-0.675356\pi$
$433$	−21.7846			−1.04690			−0.523451	+	0.852056i	$0.675356\pi$
$434$	1.46410	+	1.46410i	0.0702791	+	0.0702791i
$435$		0			0
$436$	25.7128			1.23142
$437$	24.7128	+	14.2679i	1.18217	+	0.682529i
$438$		0			0
$439$	15.0000	+	25.9808i	0.715911	+	1.23999i	0.962607	+	0.270901i	$0.0873217\pi$
$439$	15.0000	+	25.9808i	0.715911	+	1.23999i	−0.246696	+	0.969093i	$0.579345\pi$
$440$	−35.3205	+	35.3205i	−1.68384	+	1.68384i
$441$		0			0
$442$	−3.36603	−	12.5622i	−0.160106	−	0.597522i
$443$	−25.3923	+	14.6603i	−1.20642	+	0.696530i	−0.961976	−	0.273133i	$-0.911940\pi$
$443$	−25.3923	+	14.6603i	−1.20642	+	0.696530i	−0.244448	+	0.969662i	$0.578607\pi$
$444$		0			0
$445$	37.9186	+	21.8923i	1.79751	+	1.03779i
$446$	−8.46410	+	31.5885i	−0.400787	+	1.49576i
$447$		0			0
$448$	5.07180	−	2.92820i	0.239620	−	0.138345i
$449$	−24.9282			−1.17643			−0.588217	−	0.808703i	$-0.700170\pi$
$449$	−24.9282			−1.17643			−0.588217	+	0.808703i	$0.700170\pi$
$450$		0			0
$451$			21.4641i			1.01071i
$452$	13.3923	+	7.73205i	0.629921	+	0.363685i
$453$		0			0
$454$	−9.19615	−	2.46410i	−0.431597	−	0.115646i
$455$	−3.36603	+	5.83013i	−0.157802	+	0.273321i
$456$		0			0
$457$	3.16025	+	5.47372i	0.147830	+	0.256050i	0.930425	−	0.366481i	$-0.119438\pi$
$457$	3.16025	+	5.47372i	0.147830	+	0.256050i	−0.782595	+	0.622531i	$0.786104\pi$
$458$	4.16987	+	15.5622i	0.194845	+	0.727173i
$459$		0			0
$460$	32.5885	+	56.4449i	1.51944	+	2.63176i
$461$	35.7846	−	20.6603i	1.66666	−	0.962244i	0.697233	−	0.716844i	$-0.254414\pi$
$461$	35.7846	−	20.6603i	1.66666	−	0.962244i	0.969422	−	0.245400i	$-0.0789193\pi$
$462$		0			0
$463$	−6.73205	+	11.6603i	−0.312865	+	0.541898i	−0.978981	−	0.203950i	$-0.934622\pi$
$463$	−6.73205	+	11.6603i	−0.312865	+	0.541898i	0.666116	+	0.745848i	$0.267955\pi$
$464$	18.0000	−	10.3923i	0.835629	−	0.482451i
$465$		0			0
$466$	−3.73205	−	3.73205i	−0.172884	−	0.172884i
$467$		−	24.7846i		−	1.14689i	−0.819242	−	0.573447i	$-0.805606\pi$
$467$		−	24.7846i		−	1.14689i	0.819242	−	0.573447i	$-0.194394\pi$
$468$		0			0
$469$			3.46410i			0.159957i
$470$	12.9282	−	12.9282i	0.596334	−	0.596334i
$471$		0			0
$472$	−22.9282	+	6.14359i	−1.05536	+	0.282782i
$473$	−22.8564	+	39.5885i	−1.05094	+	1.82028i
$474$		0			0
$475$	25.2679	−	14.5885i	1.15937	−	0.669364i
$476$	4.73205	−	2.73205i	0.216893	−	0.125223i
$477$		0			0
$478$	10.7321	−	2.87564i	0.490873	−	0.131529i
$479$	−0.830127	−	1.43782i	−0.0379295	−	0.0656958i	0.846437	−	0.532488i	$-0.178743\pi$
$479$	−0.830127	−	1.43782i	−0.0379295	−	0.0656958i	−0.884367	+	0.466792i	$0.845410\pi$
$480$		0			0
$481$	6.16025	−	10.6699i	0.280883	−	0.486504i
$482$	1.63397	−	6.09808i	0.0744255	−	0.277760i
$483$		0			0
$484$	19.7321	+	11.3923i	0.896911	+	0.517832i
$485$		−	29.8564i		−	1.35571i
$486$		0			0
$487$	−25.7128			−1.16516			−0.582579	−	0.812774i	$-0.697956\pi$
$487$	−25.7128			−1.16516			−0.582579	+	0.812774i	$0.697956\pi$
$488$	−6.58846	+	24.5885i	−0.298245	+	1.11307i
$489$		0			0
$490$	32.9545	+	8.83013i	1.48873	+	0.398904i
$491$	−11.9545	−	6.90192i	−0.539498	−	0.311479i	0.205377	−	0.978683i	$-0.434158\pi$
$491$	−11.9545	−	6.90192i	−0.539498	−	0.311479i	−0.744876	+	0.667203i	$0.767491\pi$
$492$		0			0
$493$	16.7942	−	9.69615i	0.756374	−	0.436693i
$494$	11.0000	−	2.94744i	0.494913	−	0.132612i
$495$		0			0
$496$	4.00000	−	6.92820i	0.179605	−	0.311086i
$497$	2.07180	+	3.58846i	0.0929328	+	0.160964i
$498$		0			0
$499$	7.09808	+	4.09808i	0.317754	+	0.183455i	0.650391	−	0.759600i	$-0.274605\pi$
$499$	7.09808	+	4.09808i	0.317754	+	0.183455i	−0.332637	+	0.943055i	$0.607938\pi$
$500$	29.3205			1.31125
$501$		0			0
$502$	7.26795	−	7.26795i	0.324384	−	0.324384i
$503$	−0.679492			−0.0302970			−0.0151485	−	0.999885i	$-0.504822\pi$
$503$	−0.679492			−0.0302970			−0.0151485	+	0.999885i	$0.504822\pi$
$504$		0			0
$505$	−29.8564			−1.32859
$506$	41.3205	−	41.3205i	1.83692	−	1.83692i
$507$		0			0
$508$		−	27.3205i		−	1.21215i
$509$	25.3923	+	14.6603i	1.12549	+	0.649804i	0.942798	−	0.333365i	$-0.108184\pi$
$509$	25.3923	+	14.6603i	1.12549	+	0.649804i	0.182696	+	0.983169i	$0.441517\pi$
$510$		0			0
$511$	3.29423	+	5.70577i	0.145728	+	0.252408i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	−4.56218	+	1.22243i	−0.201229	+	0.0539192i
$515$	−11.1962	+	6.46410i	−0.493361	+	0.284842i
$516$		0			0
$517$	−14.1962	−	8.19615i	−0.624346	−	0.360466i
$518$	5.00000	+	1.33975i	0.219687	+	0.0588651i
$519$		0			0
$520$	25.1244	+	6.73205i	1.10178	+	0.295220i
$521$	26.7846			1.17346			0.586728	−	0.809784i	$-0.300416\pi$
$521$	26.7846			1.17346			0.586728	+	0.809784i	$0.300416\pi$
$522$		0			0
$523$			13.2679i			0.580167i	0.957001	+	0.290083i	$0.0936831\pi$
$523$			13.2679i			0.580167i	−0.957001	+	0.290083i	$0.906317\pi$
$524$	0.196152	−	0.339746i	0.00856896	−	0.0148419i
$525$		0			0
$526$	5.94744	−	22.1962i	0.259321	−	0.967798i
$527$	3.73205	−	6.46410i	0.162571	−	0.281581i
$528$		0			0
$529$	−26.6244	−	46.1147i	−1.15758	−	2.00499i
$530$	4.73205	−	1.26795i	0.205547	−	0.0550762i
$531$		0			0
$532$	2.39230	+	4.14359i	0.103720	+	0.179648i
$533$	9.67949	−	5.58846i	0.419265	−	0.242063i
$534$		0			0
$535$	19.3923	−	33.5885i	0.838402	−	1.45216i
$536$	12.9282	−	3.46410i	0.558413	−	0.149626i
$537$		0			0
$538$	25.7321	−	25.7321i	1.10939	−	1.10939i
$539$		−	30.5885i		−	1.31754i
$540$		0			0
$541$			24.1769i			1.03945i	0.854335	+	0.519723i	$0.173965\pi$
$541$			24.1769i			1.03945i	−0.854335	+	0.519723i	$0.826035\pi$
$542$	−10.7321	−	10.7321i	−0.460981	−	0.460981i
$543$		0			0
$544$	−14.9282	−	14.9282i	−0.640041	−	0.640041i
$545$	−23.9904	+	41.5526i	−1.02764	+	1.77992i
$546$		0			0
$547$	−22.5167	+	13.0000i	−0.962743	+	0.555840i	−0.897016	−	0.441998i	$-0.854270\pi$
$547$	−22.5167	+	13.0000i	−0.962743	+	0.555840i	−0.0657267	+	0.997838i	$0.520937\pi$
$548$	−29.7846	+	17.1962i	−1.27234	+	0.734583i
$549$		0			0
$550$	−15.4641	−	57.7128i	−0.659392	−	2.46088i
$551$	8.49038	+	14.7058i	0.361702	+	0.626487i
$552$		0			0
$553$	1.92820	−	3.33975i	0.0819955	−	0.142020i
$554$	13.4641	+	3.60770i	0.572035	+	0.153276i
$555$		0			0
$556$	19.4641	−	33.7128i	0.825462	−	1.42974i
$557$			13.0526i			0.553055i	0.961006	+	0.276527i	$0.0891836\pi$
$557$			13.0526i			0.553055i	−0.961006	+	0.276527i	$0.910816\pi$
$558$		0			0
$559$	23.8038			1.00680
$560$			10.9282i			0.461801i
$561$		0			0
$562$	−5.02628	+	18.7583i	−0.212021	+	0.791272i
$563$	−21.0000	−	12.1244i	−0.885044	−	0.510981i	−0.0127261	−	0.999919i	$-0.504051\pi$
$563$	−21.0000	−	12.1244i	−0.885044	−	0.510981i	−0.872318	+	0.488938i	$0.837384\pi$
$564$		0			0
$565$	−24.9904	+	14.4282i	−1.05135	+	0.606999i
$566$	2.33975	+	8.73205i	0.0983469	+	0.367035i
$567$		0			0
$568$	11.3205	−	11.3205i	0.474998	−	0.474998i
$569$	16.7942	+	29.0885i	0.704051	+	1.21945i	0.967033	+	0.254651i	$0.0819606\pi$
$569$	16.7942	+	29.0885i	0.704051	+	1.21945i	−0.262982	+	0.964801i	$0.584706\pi$
$570$		0			0
$571$	22.7321	+	13.1244i	0.951307	+	0.549237i	0.893487	−	0.449090i	$-0.148252\pi$
$571$	22.7321	+	13.1244i	0.951307	+	0.549237i	0.0578201	+	0.998327i	$0.481585\pi$
$572$		−	23.3205i		−	0.975079i
$573$		0			0
$574$	3.32051	+	3.32051i	0.138595	+	0.138595i
$575$	−77.9615			−3.25122
$576$		0			0
$577$	−45.2487			−1.88373			−0.941864	−	0.335994i	$-0.890928\pi$
$577$	−45.2487			−1.88373			−0.941864	+	0.335994i	$0.890928\pi$
$578$	3.07180	+	3.07180i	0.127770	+	0.127770i
$579$		0			0
$580$			38.7846i			1.61044i
$581$	−8.87564	−	5.12436i	−0.368224	−	0.212594i
$582$		0			0
$583$	−2.19615	−	3.80385i	−0.0909553	−	0.157539i
$584$	18.0000	−	18.0000i	0.744845	−	0.744845i
$585$		0			0
$586$	1.22243	+	4.56218i	0.0504982	+	0.188462i
$587$	−36.6340	+	21.1506i	−1.51205	+	0.872980i	−0.512145	+	0.858899i	$0.671149\pi$
$587$	−36.6340	+	21.1506i	−1.51205	+	0.872980i	−0.999901	+	0.0140812i	$0.995518\pi$
$588$		0			0
$589$	5.66025	+	3.26795i	0.233227	+	0.134654i
$590$	11.4641	−	42.7846i	0.471970	−	1.76141i
$591$		0			0
$592$		−	20.0000i		−	0.821995i
$593$	−14.4115			−0.591811			−0.295906	−	0.955217i	$-0.595621\pi$
$593$	−14.4115			−0.591811			−0.295906	+	0.955217i	$0.595621\pi$
$594$		0			0
$595$			10.1962i			0.418001i
$596$	−5.19615	+	9.00000i	−0.212843	+	0.368654i
$597$		0			0
$598$	−29.3923	−	7.87564i	−1.20194	−	0.322059i
$599$	4.12436	−	7.14359i	0.168517	−	0.291879i	−0.769382	−	0.638789i	$-0.779436\pi$
$599$	4.12436	−	7.14359i	0.168517	−	0.291879i	0.937899	+	0.346910i	$0.112769\pi$
$600$		0			0
$601$	−8.62436	−	14.9378i	−0.351795	−	0.609326i	0.634769	−	0.772702i	$-0.281095\pi$
$601$	−8.62436	−	14.9378i	−0.351795	−	0.609326i	−0.986564	+	0.163375i	$0.947762\pi$
$602$	2.58846	+	9.66025i	0.105498	+	0.393723i
$603$		0			0
$604$	24.0000	−	13.8564i	0.976546	−	0.563809i
$605$	−36.8205	+	21.2583i	−1.49697	+	0.864274i
$606$		0			0
$607$	12.9545	−	22.4378i	0.525806	−	0.910723i	−0.473742	−	0.880664i	$-0.657097\pi$
$607$	12.9545	−	22.4378i	0.525806	−	0.910723i	0.999548	−	0.0300594i	$-0.00956963\pi$
$608$	13.0718	−	13.0718i	0.530131	−	0.530131i
$609$		0			0
$610$	−33.5885	−	33.5885i	−1.35996	−	1.35996i
$611$			8.53590i			0.345325i
$612$		0			0
$613$		−	24.3923i		−	0.985196i	−0.870257	−	0.492598i	$-0.836047\pi$
$613$		−	24.3923i		−	0.985196i	0.870257	−	0.492598i	$-0.163953\pi$
$614$	−14.7846	+	14.7846i	−0.596658	+	0.596658i
$615$		0			0
$616$	9.46410	−	2.53590i	0.381320	−	0.102174i
$617$	13.0622	−	22.6244i	0.525863	−	0.910822i	−0.473683	−	0.880696i	$-0.657076\pi$
$617$	13.0622	−	22.6244i	0.525863	−	0.910822i	0.999546	−	0.0301266i	$-0.00959106\pi$
$618$		0			0
$619$	5.41154	−	3.12436i	0.217508	−	0.125578i	−0.387288	−	0.921959i	$-0.626588\pi$
$619$	5.41154	−	3.12436i	0.217508	−	0.125578i	0.604796	+	0.796380i	$0.293255\pi$
$620$	7.46410	+	12.9282i	0.299766	+	0.519209i
$621$		0			0
$622$	−26.3923	+	7.07180i	−1.05824	+	0.283553i
$623$	−4.29423	−	7.43782i	−0.172045	−	0.297990i
$624$		0			0
$625$	−5.03590	+	8.72243i	−0.201436	+	0.348897i
$626$	−0.901924	+	3.36603i	−0.0360481	+	0.134533i
$627$		0			0
$628$	2.46410	−	4.26795i	0.0983284	−	0.170310i
$629$		−	18.6603i		−	0.744033i
$630$		0			0
$631$	0.784610			0.0312348			0.0156174	−	0.999878i	$-0.495029\pi$
$631$	0.784610			0.0312348			0.0156174	+	0.999878i	$0.495029\pi$
$632$	−14.3923	−	3.85641i	−0.572495	−	0.153400i
$633$		0			0
$634$	−1.63397	−	0.437822i	−0.0648934	−	0.0173881i
$635$	44.1506	+	25.4904i	1.75206	+	1.01155i
$636$		0			0
$637$	−13.7942	+	7.96410i	−0.546547	+	0.315549i
$638$	33.5885	−	9.00000i	1.32978	−	0.356313i
$639$		0			0
$640$	40.7846	−	10.9282i	1.61215	−	0.431975i
$641$	−11.5263	−	19.9641i	−0.455261	−	0.788535i	0.543442	−	0.839446i	$-0.317121\pi$
$641$	−11.5263	−	19.9641i	−0.455261	−	0.788535i	−0.998703	+	0.0509118i	$0.983787\pi$
$642$		0			0
$643$	−5.53590	−	3.19615i	−0.218315	−	0.126044i	0.386855	−	0.922141i	$-0.373561\pi$
$643$	−5.53590	−	3.19615i	−0.218315	−	0.126044i	−0.605170	+	0.796097i	$0.706895\pi$
$644$		−	12.7846i		−	0.503784i
$645$		0			0
$646$	12.1962	−	12.1962i	0.479851	−	0.479851i
$647$	49.7654			1.95648			0.978239	−	0.207480i	$-0.0665261\pi$
$647$	49.7654			1.95648			0.978239	+	0.207480i	$0.0665261\pi$
$648$		0			0
$649$	−39.7128			−1.55886
$650$	−22.0000	+	22.0000i	−0.862911	+	0.862911i
$651$		0			0
$652$	13.0718			0.511931
$653$	−30.8038	−	17.7846i	−1.20545	−	0.695966i	−0.243686	−	0.969854i	$-0.578357\pi$
$653$	−30.8038	−	17.7846i	−1.20545	−	0.695966i	−0.961761	+	0.273889i	$0.911690\pi$
$654$		0			0
$655$	0.366025	+	0.633975i	0.0143018	+	0.0247714i
$656$	9.07180	−	15.7128i	0.354194	−	0.613482i
$657$		0			0
$658$	−3.46410	+	0.928203i	−0.135045	+	0.0361851i
$659$	8.70577	−	5.02628i	0.339129	−	0.195796i	−0.320758	−	0.947161i	$-0.603938\pi$
$659$	8.70577	−	5.02628i	0.339129	−	0.195796i	0.659887	+	0.751365i	$0.270604\pi$
$660$		0			0
$661$	27.8660	+	16.0885i	1.08386	+	0.625768i	0.931936	−	0.362623i	$-0.118119\pi$
$661$	27.8660	+	16.0885i	1.08386	+	0.625768i	0.151927	+	0.988392i	$0.451452\pi$
$662$	17.9282	+	4.80385i	0.696799	+	0.186707i
$663$		0			0
$664$	−10.2487	+	38.2487i	−0.397727	+	1.48434i
$665$	−8.92820			−0.346221
$666$		0			0
$667$		−	45.3731i		−	1.75685i
$668$	25.5167	+	14.7321i	0.987269	+	0.570000i
$669$		0			0
$670$	−6.46410	+	24.1244i	−0.249730	+	0.932005i
$671$	−21.2942	+	36.8827i	−0.822055	+	1.42384i
$672$		0			0
$673$	18.6244	+	32.2583i	0.717916	+	1.24347i	0.961824	+	0.273669i	$0.0882372\pi$
$673$	18.6244	+	32.2583i	0.717916	+	1.24347i	−0.243908	+	0.969798i	$0.578429\pi$
$674$	5.46410	−	1.46410i	0.210469	−	0.0563951i
$675$		0			0
$676$	12.0000	−	6.92820i	0.461538	−	0.266469i
$677$	−25.3923	+	14.6603i	−0.975906	+	0.563439i	−0.901031	−	0.433754i	$-0.857189\pi$
$677$	−25.3923	+	14.6603i	−0.975906	+	0.563439i	−0.0748741	+	0.997193i	$0.523855\pi$
$678$		0			0
$679$	−2.92820	+	5.07180i	−0.112374	+	0.194638i
$680$	38.0526	−	10.1962i	1.45925	−	0.391005i
$681$		0			0
$682$	9.46410	−	9.46410i	0.362399	−	0.362399i
$683$		−	34.1051i		−	1.30500i	−0.757790	−	0.652498i	$-0.773721\pi$
$683$		−	34.1051i		−	1.30500i	0.757790	−	0.652498i	$-0.226279\pi$
$684$		0			0
$685$		−	64.1769i		−	2.45207i
$686$	−9.85641	−	9.85641i	−0.376319	−	0.376319i
$687$		0			0
$688$	33.4641	−	19.3205i	1.27581	−	0.736587i
$689$	−1.14359	+	1.98076i	−0.0435674	+	0.0754610i
$690$		0			0
$691$	−11.0263	+	6.36603i	−0.419459	+	0.242175i	−0.694846	−	0.719159i	$-0.744527\pi$
$691$	−11.0263	+	6.36603i	−0.419459	+	0.242175i	0.275387	+	0.961334i	$0.411194\pi$
$692$	1.73205	+	3.00000i	0.0658427	+	0.114043i
$693$		0			0
$694$	2.46410	+	9.19615i	0.0935360	+	0.349081i
$695$	36.3205	+	62.9090i	1.37772	+	2.38627i
$696$		0			0
$697$	8.46410	−	14.6603i	0.320601	−	0.555297i
$698$	16.1962	+	4.33975i	0.613033	+	0.164262i
$699$		0			0
$700$	−11.3205	−	6.53590i	−0.427875	−	0.247034i
$701$		−	10.1244i		−	0.382392i	−0.981552	−	0.191196i	$-0.938763\pi$
$701$		−	10.1244i		−	0.382392i	0.981552	−	0.191196i	$-0.0612365\pi$
$702$		0			0
$703$	16.3397			0.616265
$704$	−18.9282	−	32.7846i	−0.713384	−	1.23562i
$705$		0			0
$706$	2.53590	−	9.46410i	0.0954398	−	0.356186i
$707$	5.07180	+	2.92820i	0.190745	+	0.110126i
$708$		0			0
$709$	41.0429	−	23.6962i	1.54140	−	0.889928i	0.542649	−	0.839959i	$-0.317421\pi$
$709$	41.0429	−	23.6962i	1.54140	−	0.889928i	0.998751	−	0.0499682i	$-0.0159120\pi$
$710$	7.73205	+	28.8564i	0.290179	+	1.08296i
$711$		0			0
$712$	−23.4641	+	23.4641i	−0.879354	+	0.879354i
$713$	−8.73205	−	15.1244i	−0.327018	−	0.566412i
$714$		0			0
$715$	37.6865	+	21.7583i	1.40940	+	0.813715i
$716$	28.0000			1.04641
$717$		0			0
$718$	−1.12436	−	1.12436i	−0.0419606	−	0.0419606i
$719$	−48.0526			−1.79206			−0.896029	−	0.443995i	$-0.853561\pi$
$719$	−48.0526			−1.79206			−0.896029	+	0.443995i	$0.853561\pi$
$720$		0			0
$721$	2.53590			0.0944418
$722$	−8.32051	−	8.32051i	−0.309657	−	0.309657i
$723$		0			0
$724$	−13.0718			−0.485810
$725$	−40.1769	−	23.1962i	−1.49213	−	0.861483i
$726$		0			0
$727$	24.7583	+	42.8827i	0.918236	+	1.59043i	0.802094	+	0.597198i	$0.203719\pi$
$727$	24.7583	+	42.8827i	0.918236	+	1.59043i	0.116142	+	0.993233i	$0.462947\pi$
$728$	−3.60770	−	3.60770i	−0.133710	−	0.133710i
$729$		0			0
$730$	12.2942	+	45.8827i	0.455030	+	1.69819i
$731$	31.2224	−	18.0263i	1.15480	−	0.666726i
$732$		0			0
$733$	−25.5167	−	14.7321i	−0.942479	−	0.544141i	−0.0517427	−	0.998660i	$-0.516478\pi$
$733$	−25.5167	−	14.7321i	−0.942479	−	0.544141i	−0.890737	+	0.454520i	$0.849811\pi$
$734$	−0.928203	+	3.46410i	−0.0342606	+	0.127862i
$735$		0			0
$736$	−47.7128	+	12.7846i	−1.75872	+	0.471247i
$737$	22.3923			0.824831
$738$		0			0
$739$			9.60770i			0.353425i	0.984263	+	0.176712i	$0.0565462\pi$
$739$			9.60770i			0.353425i	−0.984263	+	0.176712i	$0.943454\pi$
$740$	32.3205	+	18.6603i	1.18813	+	0.685965i
$741$		0			0
$742$	−0.928203	−	0.248711i	−0.0340754	−	0.00913048i
$743$	15.3923	−	26.6603i	0.564689	−	0.978070i	−0.432390	−	0.901687i	$-0.642329\pi$
$743$	15.3923	−	26.6603i	0.564689	−	0.978070i	0.997079	−	0.0763830i	$-0.0243372\pi$
$744$		0			0
$745$	−9.69615	−	16.7942i	−0.355240	−	0.615293i
$746$	8.39230	+	31.3205i	0.307264	+	1.14673i
$747$		0			0
$748$	−17.6603	−	30.5885i	−0.645723	−	1.11842i
$749$	−6.58846	+	3.80385i	−0.240737	+	0.138990i
$750$		0			0
$751$	8.75833	−	15.1699i	0.319596	−	0.553557i	−0.660808	−	0.750555i	$-0.729786\pi$
$751$	8.75833	−	15.1699i	0.319596	−	0.553557i	0.980404	+	0.196999i	$0.0631195\pi$
$752$	6.92820	+	12.0000i	0.252646	+	0.437595i
$753$		0			0
$754$	−12.8038	−	12.8038i	−0.466289	−	0.466289i
$755$			51.7128i			1.88202i
$756$		0			0
$757$			18.2487i			0.663261i	0.943409	+	0.331630i	$0.107599\pi$
$757$			18.2487i			0.663261i	−0.943409	+	0.331630i	$0.892401\pi$
$758$	10.0000	−	10.0000i	0.363216	−	0.363216i
$759$		0			0
$760$	8.92820	+	33.3205i	0.323860	+	1.20866i
$761$	−17.9904	+	31.1603i	−0.652151	+	1.12956i	0.330449	+	0.943824i	$0.392800\pi$
$761$	−17.9904	+	31.1603i	−0.652151	+	1.12956i	−0.982600	+	0.185735i	$0.940534\pi$
$762$		0			0
$763$	8.15064	−	4.70577i	0.295073	−	0.170360i
$764$	28.7321	−	16.5885i	1.03949	−	0.600149i
$765$		0			0
$766$	−27.5885	+	7.39230i	−0.996811	+	0.267095i
$767$	10.3397	+	17.9090i	0.373347	+	0.646655i
$768$		0			0
$769$	19.6962	−	34.1147i	0.710261	−	1.23021i	−0.254497	−	0.967073i	$-0.581910\pi$
$769$	19.6962	−	34.1147i	0.710261	−	1.23021i	0.964759	−	0.263135i	$-0.0847566\pi$
$770$	−4.73205	+	17.6603i	−0.170531	+	0.636431i
$771$		0			0
$772$	−18.8038	−	10.8564i	−0.676765	−	0.390731i
$773$			40.6603i			1.46245i	0.682138	+	0.731224i	$0.261051\pi$
$773$			40.6603i			1.46245i	−0.682138	+	0.731224i	$0.738949\pi$
$774$		0			0
$775$	−17.8564			−0.641421
$776$	21.8564	+	5.85641i	0.784599	+	0.210233i
$777$		0			0
$778$	−23.1244	−	6.19615i	−0.829048	−	0.222143i
$779$	12.8372	+	7.41154i	0.459939	+	0.265546i
$780$		0			0
$781$	23.1962	−	13.3923i	0.830024	−	0.479214i
$782$	−44.5167	+	11.9282i	−1.59191	+	0.426552i
$783$		0			0
$784$	−12.9282	+	22.3923i	−0.461722	+	0.799725i
$785$	4.59808	+	7.96410i	0.164112	+	0.284251i
$786$		0			0
$787$	−12.5096	−	7.22243i	−0.445920	−	0.257452i	0.260186	−	0.965559i	$-0.416216\pi$
$787$	−12.5096	−	7.22243i	−0.445920	−	0.257452i	−0.706105	+	0.708107i	$0.749550\pi$
$788$	−8.24871			−0.293848
$789$		0			0
$790$	19.6603	−	19.6603i	0.699480	−	0.699480i
$791$	5.66025			0.201255
$792$		0			0
$793$	22.1769			0.787525
$794$	−32.4641	+	32.4641i	−1.15211	+	1.15211i
$795$		0			0
$796$			4.78461i			0.169586i
$797$	10.6244	+	6.13397i	0.376334	+	0.217277i	0.676222	−	0.736698i	$-0.263616\pi$
$797$	10.6244	+	6.13397i	0.376334	+	0.217277i	−0.299888	+	0.953974i	$0.596949\pi$
$798$		0			0
$799$	6.46410	+	11.1962i	0.228683	+	0.396091i
$800$	−13.0718	+	48.7846i	−0.462158	+	1.72480i
$801$		0			0
$802$	−13.0981	+	3.50962i	−0.462509	+	0.123929i
$803$	36.8827	−	21.2942i	1.30156	−	0.751457i
$804$		0			0
$805$	20.6603	+	11.9282i	0.728178	+	0.420414i
$806$	−6.73205	−	1.80385i	−0.237126	−	0.0635378i
$807$		0			0
$808$	5.85641	−	21.8564i	0.206028	−	0.768906i
$809$	−49.0526			−1.72460			−0.862298	−	0.506401i	$-0.830976\pi$
$809$	−49.0526			−1.72460			−0.862298	+	0.506401i	$0.830976\pi$
$810$		0			0
$811$		−	48.7846i		−	1.71306i	−0.516098	−	0.856530i	$-0.672616\pi$
$811$		−	48.7846i		−	1.71306i	0.516098	−	0.856530i	$-0.327384\pi$
$812$	3.80385	−	6.58846i	0.133489	−	0.231210i
$813$		0			0
$814$	8.66025	−	32.3205i	0.303542	−	1.13283i
$815$	−12.1962	+	21.1244i	−0.427213	+	0.739954i
$816$		0			0
$817$	15.7846	+	27.3397i	0.552234	+	0.956497i
$818$	39.2224	−	10.5096i	1.37138	−	0.367460i
$819$		0			0
$820$	16.9282	+	29.3205i	0.591158	+	1.02392i
$821$	−1.37564	+	0.794229i	−0.0480103	+	0.0277188i	−0.523813	−	0.851833i	$-0.675491\pi$
$821$	−1.37564	+	0.794229i	−0.0480103	+	0.0277188i	0.475803	+	0.879552i	$0.342158\pi$
$822$		0			0
$823$	8.80385	−	15.2487i	0.306883	−	0.531537i	−0.670796	−	0.741642i	$-0.734047\pi$
$823$	8.80385	−	15.2487i	0.306883	−	0.531537i	0.977679	+	0.210105i	$0.0673807\pi$
$824$	−2.53590	−	9.46410i	−0.0883422	−	0.329698i
$825$		0			0
$826$	−6.14359	+	6.14359i	−0.213763	+	0.213763i
$827$		−	12.3397i		−	0.429095i	−0.976714	−	0.214548i	$-0.931172\pi$
$827$		−	12.3397i		−	0.429095i	0.976714	−	0.214548i	$-0.0688277\pi$
$828$		0			0
$829$			53.1769i			1.84691i	0.383706	+	0.923455i	$0.374648\pi$
$829$			53.1769i			1.84691i	−0.383706	+	0.923455i	$0.625352\pi$
$830$	−52.2487	−	52.2487i	−1.81358	−	1.81358i
$831$		0			0
$832$	−9.85641	+	17.0718i	−0.341709	+	0.591858i
$833$	−12.0622	+	20.8923i	−0.417930	+	0.723875i
$834$		0			0
$835$	−47.6147	+	27.4904i	−1.64778	+	0.951344i
$836$	26.7846	−	15.4641i	0.926365	−	0.534837i
$837$		0			0
$838$	7.85641	+	29.3205i	0.271395	+	1.01286i
$839$	−20.9019	−	36.2032i	−0.721615	−	1.24987i	−0.960352	−	0.278789i	$-0.910067\pi$
$839$	−20.9019	−	36.2032i	−0.721615	−	1.24987i	0.238738	−	0.971084i	$-0.423266\pi$
$840$		0			0
$841$	−1.00000	+	1.73205i	−0.0344828	+	0.0597259i
$842$	−17.7583	−	4.75833i	−0.611992	−	0.163983i
$843$		0			0
$844$	−26.0526	+	45.1244i	−0.896766	+	1.55324i
$845$			25.8564i			0.889487i
$846$		0			0
$847$	8.33975			0.286557
$848$			3.71281i			0.127499i
$849$		0			0
$850$	−12.1962	+	45.5167i	−0.418325	+	1.56121i
$851$	−37.8109	−	21.8301i	−1.29614	−	0.748327i
$852$		0			0
$853$	−4.39230	+	2.53590i	−0.150390	+	0.0868275i	−0.573307	−	0.819341i	$-0.694340\pi$
$853$	−4.39230	+	2.53590i	−0.150390	+	0.0868275i	0.422917	+	0.906168i	$0.361006\pi$
$854$	2.41154	+	9.00000i	0.0825213	+	0.307974i
$855$		0			0
$856$	20.7846	+	20.7846i	0.710403	+	0.710403i
$857$	−0.0621778	−	0.107695i	−0.00212395	−	0.00367880i	0.864961	−	0.501838i	$-0.167343\pi$
$857$	−0.0621778	−	0.107695i	−0.00212395	−	0.00367880i	−0.867085	+	0.498159i	$0.834009\pi$
$858$		0			0
$859$	−1.73205	−	1.00000i	−0.0590968	−	0.0341196i	0.470160	−	0.882581i	$-0.344196\pi$
$859$	−1.73205	−	1.00000i	−0.0590968	−	0.0341196i	−0.529257	+	0.848461i	$0.677529\pi$
$860$			72.1051i			2.45876i
$861$		0			0
$862$	21.7128	+	21.7128i	0.739541	+	0.739541i
$863$	−25.5167			−0.868597			−0.434299	−	0.900769i	$-0.643004\pi$
$863$	−25.5167			−0.868597			−0.434299	+	0.900769i	$0.643004\pi$
$864$		0			0
$865$	−6.46410			−0.219786
$866$	21.7846	+	21.7846i	0.740271	+	0.740271i
$867$		0			0
$868$		−	2.92820i		−	0.0993897i
$869$	−21.5885	−	12.4641i	−0.732338	−	0.422816i
$870$		0			0
$871$	−5.83013	−	10.0981i	−0.197546	−	0.342160i
$872$	−25.7128	−	25.7128i	−0.870746	−	0.870746i
$873$		0			0
$874$	−10.4449	−	38.9808i	−0.353303	−	1.31854i
$875$	9.29423	−	5.36603i	0.314202	−	0.181405i
$876$		0			0
$877$	−49.4545	−	28.5526i	−1.66996	−	0.964151i	−0.967656	−	0.252274i	$-0.918822\pi$
$877$	−49.4545	−	28.5526i	−1.66996	−	0.964151i	−0.702303	−	0.711878i	$-0.747845\pi$
$878$	10.9808	−	40.9808i	0.370583	−	1.38303i
$879$		0			0
$880$	70.6410			2.38131
$881$	27.8564			0.938506			0.469253	−	0.883064i	$-0.344523\pi$
$881$	27.8564			0.938506			0.469253	+	0.883064i	$0.344523\pi$
$882$		0			0
$883$			1.32051i			0.0444386i	0.999753	+	0.0222193i	$0.00707321\pi$
$883$			1.32051i			0.0444386i	−0.999753	+	0.0222193i	$0.992927\pi$
$884$	−9.19615	+	15.9282i	−0.309300	+	0.535723i
$885$		0			0
$886$	40.0526	+	10.7321i	1.34559	+	0.360550i
$887$	−1.09808	+	1.90192i	−0.0368698	+	0.0638604i	−0.883871	−	0.467730i	$-0.845072\pi$
$887$	−1.09808	+	1.90192i	−0.0368698	+	0.0638604i	0.847002	+	0.531590i	$0.178405\pi$
$888$		0			0
$889$	−5.00000	−	8.66025i	−0.167695	−	0.290456i
$890$	−16.0263	−	59.8109i	−0.537202	−	2.00487i
$891$		0			0
$892$	40.0526	−	23.1244i	1.34106	−	0.774261i
$893$	−9.80385	+	5.66025i	−0.328073	+	0.189413i
$894$		0			0
$895$	−26.1244	+	45.2487i	−0.873241	+	1.51250i
$896$	−8.00000	−	2.14359i	−0.267261	−	0.0716124i
$897$		0			0
$898$	24.9282	+	24.9282i	0.831865	+	0.831865i
$899$		−	10.3923i		−	0.346603i
$900$		0			0
$901$			3.46410i			0.115406i
$902$	21.4641	−	21.4641i	0.714676	−	0.714676i
$903$		0			0
$904$	−5.66025	−	21.1244i	−0.188257	−	0.702586i
$905$	12.1962	−	21.1244i	0.405414	−	0.702197i
$906$		0			0
$907$	28.0526	−	16.1962i	0.931470	−	0.537784i	0.0441938	−	0.999023i	$-0.485928\pi$
$907$	28.0526	−	16.1962i	0.931470	−	0.537784i	0.887276	+	0.461239i	$0.152595\pi$
$908$	6.73205	+	11.6603i	0.223411	+	0.386959i
$909$		0			0
$910$	9.19615	−	2.46410i	0.304849	−	0.0816842i
$911$	−8.36603	−	14.4904i	−0.277179	−	0.480088i	0.693504	−	0.720453i	$-0.256066\pi$
$911$	−8.36603	−	14.4904i	−0.277179	−	0.480088i	−0.970683	+	0.240365i	$0.922733\pi$
$912$		0			0
$913$	−33.1244	+	57.3731i	−1.09626	+	1.89877i
$914$	2.31347	−	8.63397i	0.0765227	−	0.285586i
$915$		0			0
$916$	11.3923	−	19.7321i	0.376412	−	0.651965i
$917$		−	0.143594i		−	0.00474188i
$918$		0			0
$919$	16.9808			0.560144			0.280072	−	0.959979i	$-0.409642\pi$
$919$	16.9808			0.560144			0.280072	+	0.959979i	$0.409642\pi$
$920$	23.8564	−	89.0333i	0.786522	−	2.93534i
$921$		0			0
$922$	−56.4449	−	15.1244i	−1.85891	−	0.498094i
$923$	−12.0788	−	6.97372i	−0.397580	−	0.229543i
$924$		0			0
$925$	−38.6603	+	22.3205i	−1.27114	+	0.733894i
$926$	18.3923	−	4.92820i	0.604409	−	0.161951i
$927$		0			0
$928$	−28.3923	−	7.60770i	−0.932023	−	0.249735i
$929$	0.258330	+	0.447441i	0.00847554	+	0.0146801i	0.870232	−	0.492642i	$-0.163969\pi$
$929$	0.258330	+	0.447441i	0.00847554	+	0.0146801i	−0.861757	+	0.507322i	$0.830635\pi$
$930$		0			0
$931$	−18.2942	−	10.5622i	−0.599569	−	0.346161i
$932$			7.46410i			0.244495i
$933$		0			0
$934$	−24.7846	+	24.7846i	−0.810977	+	0.810977i
$935$	65.9090			2.15545
$936$		0			0
$937$	−7.24871			−0.236805			−0.118403	−	0.992966i	$-0.537777\pi$
$937$	−7.24871			−0.236805			−0.118403	+	0.992966i	$0.537777\pi$
$938$	3.46410	−	3.46410i	0.113107	−	0.113107i
$939$		0			0
$940$	−25.8564			−0.843343
$941$	15.9115	+	9.18653i	0.518701	+	0.299472i	0.736403	−	0.676543i	$-0.236523\pi$
$941$	15.9115	+	9.18653i	0.518701	+	0.299472i	−0.217702	+	0.976015i	$0.569856\pi$
$942$		0			0
$943$	−19.8038	−	34.3013i	−0.644902	−	1.11700i
$944$	29.0718	+	16.7846i	0.946206	+	0.546293i
$945$		0			0
$946$	62.4449	−	16.7321i	2.03026	−	0.544006i
$947$	−17.4904	+	10.0981i	−0.568361	+	0.328143i	−0.756494	−	0.654000i	$-0.773090\pi$
$947$	−17.4904	+	10.0981i	−0.568361	+	0.328143i	0.188133	+	0.982143i	$0.439756\pi$
$948$		0			0
$949$	−19.2058	−	11.0885i	−0.623446	−	0.359947i
$950$	−39.8564	−	10.6795i	−1.29311	−	0.346488i
$951$		0			0
$952$	−7.46410	−	2.00000i	−0.241913	−	0.0648204i
$953$	26.6603			0.863610			0.431805	−	0.901967i	$-0.357877\pi$
$953$	26.6603			0.863610			0.431805	+	0.901967i	$0.357877\pi$
$954$		0			0
$955$			61.9090i			2.00333i
$956$	−13.6077	−	7.85641i	−0.440104	−	0.254094i
$957$		0			0
$958$	−0.607695	+	2.26795i	−0.0196337	+	0.0732741i
$959$	−6.29423	+	10.9019i	−0.203251	+	0.352041i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	−16.8301	+	4.50962i	−0.542625	+	0.145396i
$963$		0			0
$964$	−7.73205	+	4.46410i	−0.249033	+	0.143779i
$965$	35.0885	−	20.2583i	1.12954	−	0.652139i
$966$		0			0
$967$	−5.09808	+	8.83013i	−0.163943	+	0.283958i	−0.936279	−	0.351256i	$-0.885755\pi$
$967$	−5.09808	+	8.83013i	−0.163943	+	0.283958i	0.772336	+	0.635214i	$0.219088\pi$
$968$	−8.33975	−	31.1244i	−0.268050	−	1.00037i
$969$		0			0
$970$	−29.8564	+	29.8564i	−0.958631	+	0.958631i
$971$		−	51.1244i		−	1.64066i	−0.571891	−	0.820329i	$-0.693790\pi$
$971$		−	51.1244i		−	1.64066i	0.571891	−	0.820329i	$-0.306210\pi$
$972$		0			0
$973$		−	14.2487i		−	0.456793i
$974$	25.7128	+	25.7128i	0.823892	+	0.823892i
$975$		0			0
$976$	31.1769	−	18.0000i	0.997949	−	0.576166i
$977$	11.3923	−	19.7321i	0.364472	−	0.631284i	−0.624219	−	0.781249i	$-0.714583\pi$
$977$	11.3923	−	19.7321i	0.364472	−	0.631284i	0.988691	+	0.149965i	$0.0479161\pi$
$978$		0			0
$979$	−48.0788	+	27.7583i	−1.53661	+	0.887160i
$980$	−24.1244	−	41.7846i	−0.770624	−	1.33476i
$981$		0			0
$982$	5.05256	+	18.8564i	0.161234	+	0.601732i
$983$	0.732051	+	1.26795i	0.0233488	+	0.0404413i	0.877464	−	0.479643i	$-0.159234\pi$
$983$	0.732051	+	1.26795i	0.0233488	+	0.0404413i	−0.854115	+	0.520084i	$0.825901\pi$
$984$		0			0
$985$	7.69615	−	13.3301i	0.245220	−	0.424733i
$986$	−26.4904	−	7.09808i	−0.843626	−	0.226049i
$987$		0			0
$988$	−13.9474	−	8.05256i	−0.443727	−	0.256186i
$989$		−	84.3538i		−	2.68230i
$990$		0			0
$991$	2.58846			0.0822251			0.0411125	−	0.999155i	$-0.486910\pi$
$991$	2.58846			0.0822251			0.0411125	+	0.999155i	$0.486910\pi$
$992$	−10.9282	+	2.92820i	−0.346971	+	0.0929705i
$993$		0			0
$994$	1.51666	−	5.66025i	0.0481055	−	0.179532i
$995$	−7.73205	−	4.46410i	−0.245122	−	0.141522i
$996$		0			0
$997$	−24.1865	+	13.9641i	−0.765995	+	0.442248i	−0.831444	−	0.555608i	$-0.812485\pi$
$997$	−24.1865	+	13.9641i	−0.765995	+	0.442248i	0.0654489	+	0.997856i	$0.479152\pi$
$998$	−3.00000	−	11.1962i	−0.0949633	−	0.354408i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.n.a.109.1		4
3.2	odd	2		648.2.n.m.109.2		4
4.3	odd	2		2592.2.r.a.433.1		4
8.3	odd	2		2592.2.r.k.433.2		4
8.5	even	2		648.2.n.l.109.1		4
9.2	odd	6		648.2.n.b.541.2		4
9.4	even	3		648.2.d.i.325.3	yes	4
9.5	odd	6		648.2.d.e.325.2	yes	4
9.7	even	3		648.2.n.l.541.1		4
12.11	even	2		2592.2.r.j.433.2		4
24.5	odd	2		648.2.n.b.109.2		4
24.11	even	2		2592.2.r.b.433.1		4
36.7	odd	6		2592.2.r.k.2161.2		4
36.11	even	6		2592.2.r.b.2161.1		4
36.23	even	6		2592.2.d.h.1297.1		4
36.31	odd	6		2592.2.d.g.1297.4		4
72.5	odd	6		648.2.d.e.325.1	✓	4
72.11	even	6		2592.2.r.j.2161.2		4
72.13	even	6		648.2.d.i.325.4	yes	4
72.29	odd	6		648.2.n.m.541.1		4
72.43	odd	6		2592.2.r.a.2161.1		4
72.59	even	6		2592.2.d.h.1297.4		4
72.61	even	6	inner	648.2.n.a.541.2		4
72.67	odd	6		2592.2.d.g.1297.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
648.2.d.e.325.1	✓	4	72.5	odd	6
648.2.d.e.325.2	yes	4	9.5	odd	6
648.2.d.i.325.3	yes	4	9.4	even	3
648.2.d.i.325.4	yes	4	72.13	even	6
648.2.n.a.109.1		4	1.1	even	1	trivial
648.2.n.a.541.2		4	72.61	even	6	inner
648.2.n.b.109.2		4	24.5	odd	2
648.2.n.b.541.2		4	9.2	odd	6
648.2.n.l.109.1		4	8.5	even	2
648.2.n.l.541.1		4	9.7	even	3
648.2.n.m.109.2		4	3.2	odd	2
648.2.n.m.541.1		4	72.29	odd	6
2592.2.d.g.1297.1		4	72.67	odd	6
2592.2.d.g.1297.4		4	36.31	odd	6
2592.2.d.h.1297.1		4	36.23	even	6
2592.2.d.h.1297.4		4	72.59	even	6
2592.2.r.a.433.1		4	4.3	odd	2
2592.2.r.a.2161.1		4	72.43	odd	6
2592.2.r.b.433.1		4	24.11	even	2
2592.2.r.b.2161.1		4	36.11	even	6
2592.2.r.j.433.2		4	12.11	even	2
2592.2.r.j.2161.2		4	72.11	even	6
2592.2.r.k.433.2		4	8.3	odd	2
2592.2.r.k.2161.2		4	36.7	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	648.2.n.a.109.1

Level	$648$
Weight	$2$
Character	648.109
Analytic conductor	$5.174$
Analytic rank	$1$
Dimension	$4$
Inner twists	$2$