LMFDB - Embedded newform 1530.2.n.o.829.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(829,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1530.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.n (of order $4$, 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:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1530.829
Dual form			1530.2.n.o.1279.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} +1.00000 q^{8} +(2.12132 - 0.707107i) q^{10} +(1.58579 - 1.58579i) q^{11} +3.00000i q^{13} +(1.00000 + 1.00000i) q^{14} +1.00000 q^{16} +(2.12132 + 3.53553i) q^{17} +7.24264i q^{19} +(2.12132 - 0.707107i) q^{20} +(1.58579 - 1.58579i) q^{22} +(-2.82843 - 2.82843i) q^{23} +(4.00000 - 3.00000i) q^{25} +3.00000i q^{26} +(1.00000 + 1.00000i) q^{28} +(-0.707107 - 0.707107i) q^{29} +(-5.36396 - 5.36396i) q^{31} +1.00000 q^{32} +(2.12132 + 3.53553i) q^{34} +(2.82843 + 1.41421i) q^{35} +(5.24264 - 5.24264i) q^{37} +7.24264i q^{38} +(2.12132 - 0.707107i) q^{40} +(-4.41421 + 4.41421i) q^{41} +3.75736 q^{43} +(1.58579 - 1.58579i) q^{44} +(-2.82843 - 2.82843i) q^{46} +1.58579i q^{47} -5.00000i q^{49} +(4.00000 - 3.00000i) q^{50} +3.00000i q^{52} +3.00000 q^{53} +(2.24264 - 4.48528i) q^{55} +(1.00000 + 1.00000i) q^{56} +(-0.707107 - 0.707107i) q^{58} -12.8995i q^{59} +(6.12132 - 6.12132i) q^{61} +(-5.36396 - 5.36396i) q^{62} +1.00000 q^{64} +(2.12132 + 6.36396i) q^{65} +14.4853i q^{67} +(2.12132 + 3.53553i) q^{68} +(2.82843 + 1.41421i) q^{70} +(-3.70711 - 3.70711i) q^{71} +(-8.36396 + 8.36396i) q^{73} +(5.24264 - 5.24264i) q^{74} +7.24264i q^{76} +3.17157 q^{77} +(-0.242641 + 0.242641i) q^{79} +(2.12132 - 0.707107i) q^{80} +(-4.41421 + 4.41421i) q^{82} -4.24264 q^{83} +(7.00000 + 6.00000i) q^{85} +3.75736 q^{86} +(1.58579 - 1.58579i) q^{88} -11.4853 q^{89} +(-3.00000 + 3.00000i) q^{91} +(-2.82843 - 2.82843i) q^{92} +1.58579i q^{94} +(5.12132 + 15.3640i) q^{95} +(0.121320 - 0.121320i) q^{97} -5.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8	$ 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8} + 12 q^{11} + 4 q^{14} + 4 q^{16} + 12 q^{22} + 16 q^{25} + 4 q^{28} + 4 q^{31} + 4 q^{32} + 4 q^{37} - 12 q^{41} + 32 q^{43} + 12 q^{44} + 16 q^{50} + 12 q^{53} - 8 q^{55} + 4 q^{56} + 16 q^{61} + 4 q^{62} + 4 q^{64} - 12 q^{71} - 8 q^{73} + 4 q^{74} + 24 q^{77} + 16 q^{79} - 12 q^{82} + 28 q^{85} + 32 q^{86} + 12 q^{88} - 12 q^{89} - 12 q^{91} + 12 q^{95} - 8 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8 + 12 * q^11 + 4 * q^14 + 4 * q^16 + 12 * q^22 + 16 * q^25 + 4 * q^28 + 4 * q^31 + 4 * q^32 + 4 * q^37 - 12 * q^41 + 32 * q^43 + 12 * q^44 + 16 * q^50 + 12 * q^53 - 8 * q^55 + 4 * q^56 + 16 * q^61 + 4 * q^62 + 4 * q^64 - 12 * q^71 - 8 * q^73 + 4 * q^74 + 24 * q^77 + 16 * q^79 - 12 * q^82 + 28 * q^85 + 32 * q^86 + 12 * q^88 - 12 * q^89 - 12 * q^91 + 12 * q^95 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$6$		0			0
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	0.870367	−	0.492403i	$-0.163881\pi$
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	−0.492403	+	0.870367i	$0.663881\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	2.12132	−	0.707107i	0.670820	−	0.223607i
$11$	1.58579	−	1.58579i	0.478133	−	0.478133i	−0.426401	−	0.904534i	$-0.640219\pi$
$11$	1.58579	−	1.58579i	0.478133	−	0.478133i	0.904534	+	0.426401i	$0.140219\pi$
$12$		0			0
$13$			3.00000i			0.832050i	0.909353	+	0.416025i	$0.136577\pi$
$13$			3.00000i			0.832050i	−0.909353	+	0.416025i	$0.863423\pi$
$14$	1.00000	+	1.00000i	0.267261	+	0.267261i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.12132	+	3.53553i	0.514496	+	0.857493i
$17$	2.12132	+	3.53553i	0.514496	+	0.857493i
$18$		0			0
$19$			7.24264i			1.66158i	0.556589	+	0.830788i	$0.312110\pi$
$19$			7.24264i			1.66158i	−0.556589	+	0.830788i	$0.687890\pi$
$20$	2.12132	−	0.707107i	0.474342	−	0.158114i
$21$		0			0
$22$	1.58579	−	1.58579i	0.338091	−	0.338091i
$23$	−2.82843	−	2.82843i	−0.589768	−	0.589768i	0.347801	−	0.937568i	$-0.386929\pi$
$23$	−2.82843	−	2.82843i	−0.589768	−	0.589768i	−0.937568	+	0.347801i	$0.886929\pi$
$24$		0			0
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$			3.00000i			0.588348i
$27$		0			0
$28$	1.00000	+	1.00000i	0.188982	+	0.188982i
$29$	−0.707107	−	0.707107i	−0.131306	−	0.131306i	0.638399	−	0.769706i	$-0.279597\pi$
$29$	−0.707107	−	0.707107i	−0.131306	−	0.131306i	−0.769706	+	0.638399i	$0.779597\pi$
$30$		0			0
$31$	−5.36396	−	5.36396i	−0.963396	−	0.963396i	0.0359575	−	0.999353i	$-0.488552\pi$
$31$	−5.36396	−	5.36396i	−0.963396	−	0.963396i	−0.999353	+	0.0359575i	$0.988552\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	2.12132	+	3.53553i	0.363803	+	0.606339i
$35$	2.82843	+	1.41421i	0.478091	+	0.239046i
$36$		0			0
$37$	5.24264	−	5.24264i	0.861885	−	0.861885i	−0.129672	−	0.991557i	$-0.541392\pi$
$37$	5.24264	−	5.24264i	0.861885	−	0.861885i	0.991557	+	0.129672i	$0.0413925\pi$
$38$			7.24264i			1.17491i
$39$		0			0
$40$	2.12132	−	0.707107i	0.335410	−	0.111803i
$41$	−4.41421	+	4.41421i	−0.689384	+	0.689384i	−0.962096	−	0.272712i	$-0.912080\pi$
$41$	−4.41421	+	4.41421i	−0.689384	+	0.689384i	0.272712	+	0.962096i	$0.412080\pi$
$42$		0			0
$43$	3.75736			0.572992			0.286496	−	0.958081i	$-0.407509\pi$
$43$	3.75736			0.572992			0.286496	+	0.958081i	$0.407509\pi$
$44$	1.58579	−	1.58579i	0.239066	−	0.239066i
$45$		0			0
$46$	−2.82843	−	2.82843i	−0.417029	−	0.417029i
$47$			1.58579i			0.231311i	0.993289	+	0.115655i	$0.0368968\pi$
$47$			1.58579i			0.231311i	−0.993289	+	0.115655i	$0.963103\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$		0			0
$52$			3.00000i			0.416025i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$		0			0
$55$	2.24264	−	4.48528i	0.302398	−	0.604795i
$56$	1.00000	+	1.00000i	0.133631	+	0.133631i
$57$		0			0
$58$	−0.707107	−	0.707107i	−0.0928477	−	0.0928477i
$59$		−	12.8995i		−	1.67937i	−0.543073	−	0.839686i	$-0.682739\pi$
$59$		−	12.8995i		−	1.67937i	0.543073	−	0.839686i	$-0.317261\pi$
$60$		0			0
$61$	6.12132	−	6.12132i	0.783755	−	0.783755i	−0.196707	−	0.980462i	$-0.563025\pi$
$61$	6.12132	−	6.12132i	0.783755	−	0.783755i	0.980462	+	0.196707i	$0.0630249\pi$
$62$	−5.36396	−	5.36396i	−0.681224	−	0.681224i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.12132	+	6.36396i	0.263117	+	0.789352i
$66$		0			0
$67$			14.4853i			1.76966i	0.465915	+	0.884829i	$0.345725\pi$
$67$			14.4853i			1.76966i	−0.465915	+	0.884829i	$0.654275\pi$
$68$	2.12132	+	3.53553i	0.257248	+	0.428746i
$69$		0			0
$70$	2.82843	+	1.41421i	0.338062	+	0.169031i
$71$	−3.70711	−	3.70711i	−0.439953	−	0.439953i	0.452043	−	0.891996i	$-0.350695\pi$
$71$	−3.70711	−	3.70711i	−0.439953	−	0.439953i	−0.891996	+	0.452043i	$0.850695\pi$
$72$		0			0
$73$	−8.36396	+	8.36396i	−0.978928	+	0.978928i	−0.999783	−	0.0208549i	$-0.993361\pi$
$73$	−8.36396	+	8.36396i	−0.978928	+	0.978928i	0.0208549	+	0.999783i	$0.493361\pi$
$74$	5.24264	−	5.24264i	0.609445	−	0.609445i
$75$		0			0
$76$			7.24264i			0.830788i
$77$	3.17157			0.361434
$78$		0			0
$79$	−0.242641	+	0.242641i	−0.0272992	+	0.0272992i	−0.720625	−	0.693325i	$-0.756145\pi$
$79$	−0.242641	+	0.242641i	−0.0272992	+	0.0272992i	0.693325	+	0.720625i	$0.256145\pi$
$80$	2.12132	−	0.707107i	0.237171	−	0.0790569i
$81$		0			0
$82$	−4.41421	+	4.41421i	−0.487468	+	0.487468i
$83$	−4.24264			−0.465690			−0.232845	−	0.972514i	$-0.574804\pi$
$83$	−4.24264			−0.465690			−0.232845	+	0.972514i	$0.574804\pi$
$84$		0			0
$85$	7.00000	+	6.00000i	0.759257	+	0.650791i
$86$	3.75736			0.405166
$87$		0			0
$88$	1.58579	−	1.58579i	0.169045	−	0.169045i
$89$	−11.4853			−1.21744			−0.608719	−	0.793386i	$-0.708316\pi$
$89$	−11.4853			−1.21744			−0.608719	+	0.793386i	$0.708316\pi$
$90$		0			0
$91$	−3.00000	+	3.00000i	−0.314485	+	0.314485i
$92$	−2.82843	−	2.82843i	−0.294884	−	0.294884i
$93$		0			0
$94$			1.58579i			0.163561i
$95$	5.12132	+	15.3640i	0.525436	+	1.57631i
$96$		0			0
$97$	0.121320	−	0.121320i	0.0123182	−	0.0123182i	−0.700921	−	0.713239i	$-0.747227\pi$
$97$	0.121320	−	0.121320i	0.0123182	−	0.0123182i	0.713239	+	0.700921i	$0.247227\pi$
$98$		−	5.00000i		−	0.505076i
$99$		0			0
$100$	4.00000	−	3.00000i	0.400000	−	0.300000i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$			3.00000i			0.294174i
$105$		0			0
$106$	3.00000			0.291386
$107$	2.82843	−	2.82843i	0.273434	−	0.273434i	−0.557047	−	0.830481i	$-0.688066\pi$
$107$	2.82843	−	2.82843i	0.273434	−	0.273434i	0.830481	+	0.557047i	$0.188066\pi$
$108$		0			0
$109$	8.60660	−	8.60660i	0.824363	−	0.824363i	−0.162367	−	0.986730i	$-0.551913\pi$
$109$	8.60660	−	8.60660i	0.824363	−	0.824363i	0.986730	+	0.162367i	$0.0519130\pi$
$110$	2.24264	−	4.48528i	0.213827	−	0.427655i
$111$		0			0
$112$	1.00000	+	1.00000i	0.0944911	+	0.0944911i
$113$	−2.46447	−	2.46447i	−0.231837	−	0.231837i	0.581622	−	0.813459i	$-0.302418\pi$
$113$	−2.46447	−	2.46447i	−0.231837	−	0.231837i	−0.813459	+	0.581622i	$0.802418\pi$
$114$		0			0
$115$	−8.00000	−	4.00000i	−0.746004	−	0.373002i
$116$	−0.707107	−	0.707107i	−0.0656532	−	0.0656532i
$117$		0			0
$118$		−	12.8995i		−	1.18749i
$119$	−1.41421	+	5.65685i	−0.129641	+	0.518563i
$120$		0			0
$121$			5.97056i			0.542778i
$122$	6.12132	−	6.12132i	0.554198	−	0.554198i
$123$		0			0
$124$	−5.36396	−	5.36396i	−0.481698	−	0.481698i
$125$	6.36396	−	9.19239i	0.569210	−	0.822192i
$126$		0			0
$127$	17.7279			1.57310			0.786549	−	0.617527i	$-0.211866\pi$
$127$	17.7279			1.57310			0.786549	+	0.617527i	$0.211866\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	2.12132	+	6.36396i	0.186052	+	0.558156i
$131$	−7.58579	−	7.58579i	−0.662773	−	0.662773i	0.293260	−	0.956033i	$-0.405260\pi$
$131$	−7.58579	−	7.58579i	−0.662773	−	0.662773i	−0.956033	+	0.293260i	$0.905260\pi$
$132$		0			0
$133$	−7.24264	+	7.24264i	−0.628017	+	0.628017i
$134$			14.4853i			1.25134i
$135$		0			0
$136$	2.12132	+	3.53553i	0.181902	+	0.303170i
$137$			4.58579i			0.391790i	0.980625	+	0.195895i	$0.0627612\pi$
$137$			4.58579i			0.391790i	−0.980625	+	0.195895i	$0.937239\pi$
$138$		0			0
$139$	−11.0000	−	11.0000i	−0.933008	−	0.933008i	0.0648849	−	0.997893i	$-0.479332\pi$
$139$	−11.0000	−	11.0000i	−0.933008	−	0.933008i	−0.997893	+	0.0648849i	$0.979332\pi$
$140$	2.82843	+	1.41421i	0.239046	+	0.119523i
$141$		0			0
$142$	−3.70711	−	3.70711i	−0.311093	−	0.311093i
$143$	4.75736	+	4.75736i	0.397830	+	0.397830i
$144$		0			0
$145$	−2.00000	−	1.00000i	−0.166091	−	0.0830455i
$146$	−8.36396	+	8.36396i	−0.692206	+	0.692206i
$147$		0			0
$148$	5.24264	−	5.24264i	0.430942	−	0.430942i
$149$	12.7279			1.04271			0.521356	−	0.853339i	$-0.325426\pi$
$149$	12.7279			1.04271			0.521356	+	0.853339i	$0.325426\pi$
$150$		0			0
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$			7.24264i			0.587456i
$153$		0			0
$154$	3.17157			0.255573
$155$	−15.1716	−	7.58579i	−1.21861	−	0.609305i
$156$		0			0
$157$		−	12.0000i		−	0.957704i	−0.877896	−	0.478852i	$-0.841053\pi$
$157$		−	12.0000i		−	0.957704i	0.877896	−	0.478852i	$-0.158947\pi$
$158$	−0.242641	+	0.242641i	−0.0193035	+	0.0193035i
$159$		0			0
$160$	2.12132	−	0.707107i	0.167705	−	0.0559017i
$161$		−	5.65685i		−	0.445823i
$162$		0			0
$163$	−4.48528	−	4.48528i	−0.351314	−	0.351314i	0.509284	−	0.860598i	$-0.329910\pi$
$163$	−4.48528	−	4.48528i	−0.351314	−	0.351314i	−0.860598	+	0.509284i	$0.829910\pi$
$164$	−4.41421	+	4.41421i	−0.344692	+	0.344692i
$165$		0			0
$166$	−4.24264			−0.329293
$167$	1.07107	−	1.07107i	0.0828817	−	0.0828817i	−0.664451	−	0.747332i	$-0.731334\pi$
$167$	1.07107	−	1.07107i	0.0828817	−	0.0828817i	0.747332	+	0.664451i	$0.231334\pi$
$168$		0			0
$169$	4.00000			0.307692
$170$	7.00000	+	6.00000i	0.536875	+	0.460179i
$171$		0			0
$172$	3.75736			0.286496
$173$	−17.6569	+	17.6569i	−1.34243	+	1.34243i	−0.448787	+	0.893639i	$0.648144\pi$
$173$	−17.6569	+	17.6569i	−1.34243	+	1.34243i	−0.893639	+	0.448787i	$0.851856\pi$
$174$		0			0
$175$	7.00000	+	1.00000i	0.529150	+	0.0755929i
$176$	1.58579	−	1.58579i	0.119533	−	0.119533i
$177$		0			0
$178$	−11.4853			−0.860858
$179$		−	0.686292i		−	0.0512958i	−0.999671	−	0.0256479i	$-0.991835\pi$
$179$		−	0.686292i		−	0.0512958i	0.999671	−	0.0256479i	$-0.00816488\pi$
$180$		0			0
$181$	−14.0000	+	14.0000i	−1.04061	+	1.04061i	−0.0414721	+	0.999140i	$0.513205\pi$
$181$	−14.0000	+	14.0000i	−1.04061	+	1.04061i	−0.999140	+	0.0414721i	$0.986795\pi$
$182$	−3.00000	+	3.00000i	−0.222375	+	0.222375i
$183$		0			0
$184$	−2.82843	−	2.82843i	−0.208514	−	0.208514i
$185$	7.41421	−	14.8284i	0.545104	−	1.09021i
$186$		0			0
$187$	8.97056	+	2.24264i	0.655993	+	0.163998i
$188$			1.58579i			0.115655i
$189$		0			0
$190$	5.12132	+	15.3640i	0.371540	+	1.11462i
$191$	−21.2132			−1.53493			−0.767467	−	0.641089i	$-0.778483\pi$
$191$	−21.2132			−1.53493			−0.767467	+	0.641089i	$0.778483\pi$
$192$		0			0
$193$	18.4853	+	18.4853i	1.33060	+	1.33060i	0.904833	+	0.425767i	$0.139996\pi$
$193$	18.4853	+	18.4853i	1.33060	+	1.33060i	0.425767	+	0.904833i	$0.360004\pi$
$194$	0.121320	−	0.121320i	0.00871029	−	0.00871029i
$195$		0			0
$196$		−	5.00000i		−	0.357143i
$197$	−3.34315	−	3.34315i	−0.238189	−	0.238189i	0.577911	−	0.816100i	$-0.303868\pi$
$197$	−3.34315	−	3.34315i	−0.238189	−	0.238189i	−0.816100	+	0.577911i	$0.803868\pi$
$198$		0			0
$199$	−7.12132	−	7.12132i	−0.504817	−	0.504817i	0.408114	−	0.912931i	$-0.366187\pi$
$199$	−7.12132	−	7.12132i	−0.504817	−	0.504817i	−0.912931	+	0.408114i	$0.866187\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$		0			0
$202$		0			0
$203$		−	1.41421i		−	0.0992583i
$204$		0			0
$205$	−6.24264	+	12.4853i	−0.436005	+	0.872010i
$206$		0			0
$207$		0			0
$208$			3.00000i			0.208013i
$209$	11.4853	+	11.4853i	0.794454	+	0.794454i
$210$		0			0
$211$	−8.00000	+	8.00000i	−0.550743	+	0.550743i	−0.926655	−	0.375912i	$-0.877329\pi$
$211$	−8.00000	+	8.00000i	−0.550743	+	0.550743i	0.375912	+	0.926655i	$0.377329\pi$
$212$	3.00000			0.206041
$213$		0			0
$214$	2.82843	−	2.82843i	0.193347	−	0.193347i
$215$	7.97056	−	2.65685i	0.543588	−	0.181196i
$216$		0			0
$217$		−	10.7279i		−	0.728259i
$218$	8.60660	−	8.60660i	0.582913	−	0.582913i
$219$		0			0
$220$	2.24264	−	4.48528i	0.151199	−	0.302398i
$221$	−10.6066	+	6.36396i	−0.713477	+	0.428086i
$222$		0			0
$223$	−23.2426			−1.55644			−0.778221	−	0.627990i	$-0.783878\pi$
$223$	−23.2426			−1.55644			−0.778221	+	0.627990i	$0.783878\pi$
$224$	1.00000	+	1.00000i	0.0668153	+	0.0668153i
$225$		0			0
$226$	−2.46447	−	2.46447i	−0.163934	−	0.163934i
$227$	4.05025	+	4.05025i	0.268825	+	0.268825i	0.828627	−	0.559802i	$-0.189123\pi$
$227$	4.05025	+	4.05025i	0.268825	+	0.268825i	−0.559802	+	0.828627i	$0.689123\pi$
$228$		0			0
$229$			7.75736i			0.512621i	0.966595	+	0.256310i	$0.0825069\pi$
$229$			7.75736i			0.512621i	−0.966595	+	0.256310i	$0.917493\pi$
$230$	−8.00000	−	4.00000i	−0.527504	−	0.263752i
$231$		0			0
$232$	−0.707107	−	0.707107i	−0.0464238	−	0.0464238i
$233$	10.9497	−	10.9497i	0.717342	−	0.717342i	−0.250718	−	0.968060i	$-0.580667\pi$
$233$	10.9497	−	10.9497i	0.717342	−	0.717342i	0.968060	+	0.250718i	$0.0806668\pi$
$234$		0			0
$235$	1.12132	+	3.36396i	0.0731469	+	0.219441i
$236$		−	12.8995i		−	0.839686i
$237$		0			0
$238$	−1.41421	+	5.65685i	−0.0916698	+	0.366679i
$239$	−22.2426			−1.43876			−0.719378	−	0.694618i	$-0.755573\pi$
$239$	−22.2426			−1.43876			−0.719378	+	0.694618i	$0.755573\pi$
$240$		0			0
$241$	2.75736	+	2.75736i	0.177617	+	0.177617i	0.790316	−	0.612699i	$-0.209916\pi$
$241$	2.75736	+	2.75736i	0.177617	+	0.177617i	−0.612699	+	0.790316i	$0.709916\pi$
$242$			5.97056i			0.383802i
$243$		0			0
$244$	6.12132	−	6.12132i	0.391877	−	0.391877i
$245$	−3.53553	−	10.6066i	−0.225877	−	0.677631i
$246$		0			0
$247$	−21.7279			−1.38251
$248$	−5.36396	−	5.36396i	−0.340612	−	0.340612i
$249$		0			0
$250$	6.36396	−	9.19239i	0.402492	−	0.581378i
$251$	−20.4853			−1.29302			−0.646510	−	0.762906i	$-0.723772\pi$
$251$	−20.4853			−1.29302			−0.646510	+	0.762906i	$0.723772\pi$
$252$		0			0
$253$	−8.97056			−0.563974
$254$	17.7279			1.11235
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.72792			−0.419676			−0.209838	−	0.977736i	$-0.567294\pi$
$257$	−6.72792			−0.419676			−0.209838	+	0.977736i	$0.567294\pi$
$258$		0			0
$259$	10.4853			0.651524
$260$	2.12132	+	6.36396i	0.131559	+	0.394676i
$261$		0			0
$262$	−7.58579	−	7.58579i	−0.468651	−	0.468651i
$263$	−4.75736			−0.293351			−0.146676	−	0.989185i	$-0.546857\pi$
$263$	−4.75736			−0.293351			−0.146676	+	0.989185i	$0.546857\pi$
$264$		0			0
$265$	6.36396	−	2.12132i	0.390935	−	0.130312i
$266$	−7.24264	+	7.24264i	−0.444075	+	0.444075i
$267$		0			0
$268$			14.4853i			0.884829i
$269$	11.2929	+	11.2929i	0.688540	+	0.688540i	0.961909	−	0.273369i	$-0.0881381\pi$
$269$	11.2929	+	11.2929i	0.688540	+	0.688540i	−0.273369	+	0.961909i	$0.588138\pi$
$270$		0			0
$271$	−6.48528			−0.393953			−0.196976	−	0.980408i	$-0.563112\pi$
$271$	−6.48528			−0.393953			−0.196976	+	0.980408i	$0.563112\pi$
$272$	2.12132	+	3.53553i	0.128624	+	0.214373i
$273$		0			0
$274$			4.58579i			0.277037i
$275$	1.58579	−	11.1005i	0.0956265	−	0.669386i
$276$		0			0
$277$	8.24264	−	8.24264i	0.495252	−	0.495252i	−0.414704	−	0.909956i	$-0.636115\pi$
$277$	8.24264	−	8.24264i	0.495252	−	0.495252i	0.909956	+	0.414704i	$0.136115\pi$
$278$	−11.0000	−	11.0000i	−0.659736	−	0.659736i
$279$		0			0
$280$	2.82843	+	1.41421i	0.169031	+	0.0845154i
$281$			3.34315i			0.199435i	0.995016	+	0.0997177i	$0.0317940\pi$
$281$			3.34315i			0.199435i	−0.995016	+	0.0997177i	$0.968206\pi$
$282$		0			0
$283$	−19.1213	−	19.1213i	−1.13664	−	1.13664i	−0.989048	−	0.147597i	$-0.952846\pi$
$283$	−19.1213	−	19.1213i	−1.13664	−	1.13664i	−0.147597	−	0.989048i	$-0.547154\pi$
$284$	−3.70711	−	3.70711i	−0.219976	−	0.219976i
$285$		0			0
$286$	4.75736	+	4.75736i	0.281309	+	0.281309i
$287$	−8.82843			−0.521126
$288$		0			0
$289$	−8.00000	+	15.0000i	−0.470588	+	0.882353i
$290$	−2.00000	−	1.00000i	−0.117444	−	0.0587220i
$291$		0			0
$292$	−8.36396	+	8.36396i	−0.489464	+	0.489464i
$293$		−	20.6569i		−	1.20679i	−0.797444	−	0.603393i	$-0.793815\pi$
$293$		−	20.6569i		−	1.20679i	0.797444	−	0.603393i	$-0.206185\pi$
$294$		0			0
$295$	−9.12132	−	27.3640i	−0.531064	−	1.59319i
$296$	5.24264	−	5.24264i	0.304722	−	0.304722i
$297$		0			0
$298$	12.7279			0.737309
$299$	8.48528	−	8.48528i	0.490716	−	0.490716i
$300$		0			0
$301$	3.75736	+	3.75736i	0.216571	+	0.216571i
$302$		−	12.0000i		−	0.690522i
$303$		0			0
$304$			7.24264i			0.415394i
$305$	8.65685	−	17.3137i	0.495690	−	0.991380i
$306$		0			0
$307$			33.2132i			1.89558i	0.318899	+	0.947789i	$0.396687\pi$
$307$			33.2132i			1.89558i	−0.318899	+	0.947789i	$0.603313\pi$
$308$	3.17157			0.180717
$309$		0			0
$310$	−15.1716	−	7.58579i	−0.861687	−	0.430844i
$311$	1.41421	+	1.41421i	0.0801927	+	0.0801927i	0.746065	−	0.665873i	$-0.231941\pi$
$311$	1.41421	+	1.41421i	0.0801927	+	0.0801927i	−0.665873	+	0.746065i	$0.731941\pi$
$312$		0			0
$313$	−22.4853	−	22.4853i	−1.27094	−	1.27094i	−0.945594	−	0.325349i	$-0.894518\pi$
$313$	−22.4853	−	22.4853i	−1.27094	−	1.27094i	−0.325349	−	0.945594i	$-0.605482\pi$
$314$		−	12.0000i		−	0.677199i
$315$		0			0
$316$	−0.242641	+	0.242641i	−0.0136496	+	0.0136496i
$317$	14.1421	+	14.1421i	0.794301	+	0.794301i	0.982190	−	0.187889i	$-0.0601645\pi$
$317$	14.1421	+	14.1421i	0.794301	+	0.794301i	−0.187889	+	0.982190i	$0.560164\pi$
$318$		0			0
$319$	−2.24264			−0.125564
$320$	2.12132	−	0.707107i	0.118585	−	0.0395285i
$321$		0			0
$322$		−	5.65685i		−	0.315244i
$323$	−25.6066	+	15.3640i	−1.42479	+	0.854874i
$324$		0			0
$325$	9.00000	+	12.0000i	0.499230	+	0.665640i
$326$	−4.48528	−	4.48528i	−0.248417	−	0.248417i
$327$		0			0
$328$	−4.41421	+	4.41421i	−0.243734	+	0.243734i
$329$	−1.58579	+	1.58579i	−0.0874272	+	0.0874272i
$330$		0			0
$331$		−	15.7279i		−	0.864485i	−0.901757	−	0.432242i	$-0.857722\pi$
$331$		−	15.7279i		−	0.864485i	0.901757	−	0.432242i	$-0.142278\pi$
$332$	−4.24264			−0.232845
$333$		0			0
$334$	1.07107	−	1.07107i	0.0586062	−	0.0586062i
$335$	10.2426	+	30.7279i	0.559615	+	1.67885i
$336$		0			0
$337$	12.8492	−	12.8492i	0.699943	−	0.699943i	−0.264455	−	0.964398i	$-0.585192\pi$
$337$	12.8492	−	12.8492i	0.699943	−	0.699943i	0.964398	+	0.264455i	$0.0851921\pi$
$338$	4.00000			0.217571
$339$		0			0
$340$	7.00000	+	6.00000i	0.379628	+	0.325396i
$341$	−17.0122			−0.921262
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	3.75736			0.202583
$345$		0			0
$346$	−17.6569	+	17.6569i	−0.949238	+	0.949238i
$347$	−15.7071	−	15.7071i	−0.843202	−	0.843202i	0.146072	−	0.989274i	$-0.453337\pi$
$347$	−15.7071	−	15.7071i	−0.843202	−	0.843202i	−0.989274	+	0.146072i	$0.953337\pi$
$348$		0			0
$349$			10.9706i			0.587241i	0.955922	+	0.293620i	$0.0948602\pi$
$349$			10.9706i			0.587241i	−0.955922	+	0.293620i	$0.905140\pi$
$350$	7.00000	+	1.00000i	0.374166	+	0.0534522i
$351$		0			0
$352$	1.58579	−	1.58579i	0.0845227	−	0.0845227i
$353$			11.3137i			0.602168i	0.953598	+	0.301084i	$0.0973484\pi$
$353$			11.3137i			0.602168i	−0.953598	+	0.301084i	$0.902652\pi$
$354$		0			0
$355$	−10.4853	−	5.24264i	−0.556501	−	0.278250i
$356$	−11.4853			−0.608719
$357$		0			0
$358$		−	0.686292i		−	0.0362716i
$359$			7.07107i			0.373197i	0.982436	+	0.186598i	$0.0597463\pi$
$359$			7.07107i			0.373197i	−0.982436	+	0.186598i	$0.940254\pi$
$360$		0			0
$361$	−33.4558			−1.76083
$362$	−14.0000	+	14.0000i	−0.735824	+	0.735824i
$363$		0			0
$364$	−3.00000	+	3.00000i	−0.157243	+	0.157243i
$365$	−11.8284	+	23.6569i	−0.619128	+	1.23826i
$366$		0			0
$367$	−18.2426	−	18.2426i	−0.952258	−	0.952258i	0.0466531	−	0.998911i	$-0.485144\pi$
$367$	−18.2426	−	18.2426i	−0.952258	−	0.952258i	−0.998911	+	0.0466531i	$0.985144\pi$
$368$	−2.82843	−	2.82843i	−0.147442	−	0.147442i
$369$		0			0
$370$	7.41421	−	14.8284i	0.385447	−	0.770893i
$371$	3.00000	+	3.00000i	0.155752	+	0.155752i
$372$		0			0
$373$		−	32.4853i		−	1.68202i	−0.541016	−	0.841012i	$-0.681960\pi$
$373$		−	32.4853i		−	1.68202i	0.541016	−	0.841012i	$-0.318040\pi$
$374$	8.97056	+	2.24264i	0.463857	+	0.115964i
$375$		0			0
$376$			1.58579i			0.0817807i
$377$	2.12132	−	2.12132i	0.109254	−	0.109254i
$378$		0			0
$379$	0.485281	+	0.485281i	0.0249272	+	0.0249272i	0.719461	−	0.694533i	$-0.244389\pi$
$379$	0.485281	+	0.485281i	0.0249272	+	0.0249272i	−0.694533	+	0.719461i	$0.744389\pi$
$380$	5.12132	+	15.3640i	0.262718	+	0.788155i
$381$		0			0
$382$	−21.2132			−1.08536
$383$	13.2426			0.676667			0.338334	−	0.941026i	$-0.390137\pi$
$383$	13.2426			0.676667			0.338334	+	0.941026i	$0.390137\pi$
$384$		0			0
$385$	6.72792	−	2.24264i	0.342887	−	0.114296i
$386$	18.4853	+	18.4853i	0.940876	+	0.940876i
$387$		0			0
$388$	0.121320	−	0.121320i	0.00615911	−	0.00615911i
$389$		−	16.6274i		−	0.843044i	−0.906818	−	0.421522i	$-0.861496\pi$
$389$		−	16.6274i		−	0.843044i	0.906818	−	0.421522i	$-0.138504\pi$
$390$		0			0
$391$	4.00000	−	16.0000i	0.202289	−	0.809155i
$392$		−	5.00000i		−	0.252538i
$393$		0			0
$394$	−3.34315	−	3.34315i	−0.168425	−	0.168425i
$395$	−0.343146	+	0.686292i	−0.0172655	+	0.0345311i
$396$		0			0
$397$	4.72792	+	4.72792i	0.237288	+	0.237288i	0.815726	−	0.578438i	$-0.196338\pi$
$397$	4.72792	+	4.72792i	0.237288	+	0.237288i	−0.578438	+	0.815726i	$0.696338\pi$
$398$	−7.12132	−	7.12132i	−0.356960	−	0.356960i
$399$		0			0
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$	2.10051	−	2.10051i	0.104894	−	0.104894i	−0.652712	−	0.757606i	$-0.726369\pi$
$401$	2.10051	−	2.10051i	0.104894	−	0.104894i	0.757606	+	0.652712i	$0.226369\pi$
$402$		0			0
$403$	16.0919	−	16.0919i	0.801594	−	0.801594i
$404$		0			0
$405$		0			0
$406$		−	1.41421i		−	0.0701862i
$407$		−	16.6274i		−	0.824190i
$408$		0			0
$409$	25.4853			1.26017			0.630083	−	0.776528i	$-0.283021\pi$
$409$	25.4853			1.26017			0.630083	+	0.776528i	$0.283021\pi$
$410$	−6.24264	+	12.4853i	−0.308302	+	0.616604i
$411$		0			0
$412$		0			0
$413$	12.8995	−	12.8995i	0.634743	−	0.634743i
$414$		0			0
$415$	−9.00000	+	3.00000i	−0.441793	+	0.147264i
$416$			3.00000i			0.147087i
$417$		0			0
$418$	11.4853	+	11.4853i	0.561763	+	0.561763i
$419$	11.3137	−	11.3137i	0.552711	−	0.552711i	−0.374511	−	0.927222i	$-0.622190\pi$
$419$	11.3137	−	11.3137i	0.552711	−	0.552711i	0.927222	+	0.374511i	$0.122190\pi$
$420$		0			0
$421$	−19.2132			−0.936394			−0.468197	−	0.883624i	$-0.655096\pi$
$421$	−19.2132			−0.936394			−0.468197	+	0.883624i	$0.655096\pi$
$422$	−8.00000	+	8.00000i	−0.389434	+	0.389434i
$423$		0			0
$424$	3.00000			0.145693
$425$	19.0919	+	7.77817i	0.926092	+	0.377297i
$426$		0			0
$427$	12.2426			0.592463
$428$	2.82843	−	2.82843i	0.136717	−	0.136717i
$429$		0			0
$430$	7.97056	−	2.65685i	0.384375	−	0.128125i
$431$	−17.6569	+	17.6569i	−0.850501	+	0.850501i	−0.990195	−	0.139694i	$-0.955388\pi$
$431$	−17.6569	+	17.6569i	−0.850501	+	0.850501i	0.139694	+	0.990195i	$0.455388\pi$
$432$		0			0
$433$	−5.75736			−0.276681			−0.138341	−	0.990385i	$-0.544177\pi$
$433$	−5.75736			−0.276681			−0.138341	+	0.990385i	$0.544177\pi$
$434$		−	10.7279i		−	0.514957i
$435$		0			0
$436$	8.60660	−	8.60660i	0.412181	−	0.412181i
$437$	20.4853	−	20.4853i	0.979944	−	0.979944i
$438$		0			0
$439$	20.9706	+	20.9706i	1.00087	+	1.00087i	1.00000		0.000870732i	$0.000277162\pi$
$439$	20.9706	+	20.9706i	1.00087	+	1.00087i	0.000870732		1.00000i	$0.499723\pi$
$440$	2.24264	−	4.48528i	0.106914	−	0.213827i
$441$		0			0
$442$	−10.6066	+	6.36396i	−0.504505	+	0.302703i
$443$			37.7990i			1.79588i	0.440114	+	0.897942i	$0.354938\pi$
$443$			37.7990i			1.79588i	−0.440114	+	0.897942i	$0.645062\pi$
$444$		0			0
$445$	−24.3640	+	8.12132i	−1.15496	+	0.384988i
$446$	−23.2426			−1.10057
$447$		0			0
$448$	1.00000	+	1.00000i	0.0472456	+	0.0472456i
$449$	28.7990	−	28.7990i	1.35911	−	1.35911i	0.484090	−	0.875018i	$-0.339151\pi$
$449$	28.7990	−	28.7990i	1.35911	−	1.35911i	0.875018	−	0.484090i	$-0.160849\pi$
$450$		0			0
$451$			14.0000i			0.659234i
$452$	−2.46447	−	2.46447i	−0.115919	−	0.115919i
$453$		0			0
$454$	4.05025	+	4.05025i	0.190088	+	0.190088i
$455$	−4.24264	+	8.48528i	−0.198898	+	0.397796i
$456$		0			0
$457$	−2.24264			−0.104906			−0.0524532	−	0.998623i	$-0.516704\pi$
$457$	−2.24264			−0.104906			−0.0524532	+	0.998623i	$0.516704\pi$
$458$			7.75736i			0.362478i
$459$		0			0
$460$	−8.00000	−	4.00000i	−0.373002	−	0.186501i
$461$			40.2843i			1.87623i	0.346330	+	0.938113i	$0.387428\pi$
$461$			40.2843i			1.87623i	−0.346330	+	0.938113i	$0.612572\pi$
$462$		0			0
$463$			25.2426i			1.17312i	0.809904	+	0.586562i	$0.199519\pi$
$463$			25.2426i			1.17312i	−0.809904	+	0.586562i	$0.800481\pi$
$464$	−0.707107	−	0.707107i	−0.0328266	−	0.0328266i
$465$		0			0
$466$	10.9497	−	10.9497i	0.507237	−	0.507237i
$467$	18.7279			0.866625			0.433312	−	0.901244i	$-0.357345\pi$
$467$	18.7279			0.866625			0.433312	+	0.901244i	$0.357345\pi$
$468$		0			0
$469$	−14.4853	+	14.4853i	−0.668868	+	0.668868i
$470$	1.12132	+	3.36396i	0.0517227	+	0.155168i
$471$		0			0
$472$		−	12.8995i		−	0.593747i
$473$	5.95837	−	5.95837i	0.273966	−	0.273966i
$474$		0			0
$475$	21.7279	+	28.9706i	0.996945	+	1.32926i
$476$	−1.41421	+	5.65685i	−0.0648204	+	0.259281i
$477$		0			0
$478$	−22.2426			−1.01735
$479$	10.0503	+	10.0503i	0.459208	+	0.459208i	0.898395	−	0.439188i	$-0.144734\pi$
$479$	10.0503	+	10.0503i	0.459208	+	0.459208i	−0.439188	+	0.898395i	$0.644734\pi$
$480$		0			0
$481$	15.7279	+	15.7279i	0.717132	+	0.717132i
$482$	2.75736	+	2.75736i	0.125594	+	0.125594i
$483$		0			0
$484$			5.97056i			0.271389i
$485$	0.171573	−	0.343146i	0.00779072	−	0.0155814i
$486$		0			0
$487$	11.2426	+	11.2426i	0.509453	+	0.509453i	0.914358	−	0.404906i	$-0.132696\pi$
$487$	11.2426	+	11.2426i	0.509453	+	0.509453i	−0.404906	+	0.914358i	$0.632696\pi$
$488$	6.12132	−	6.12132i	0.277099	−	0.277099i
$489$		0			0
$490$	−3.53553	−	10.6066i	−0.159719	−	0.479157i
$491$		−	6.89949i		−	0.311370i	−0.987807	−	0.155685i	$-0.950242\pi$
$491$		−	6.89949i		−	0.311370i	0.987807	−	0.155685i	$-0.0497585\pi$
$492$		0			0
$493$	1.00000	−	4.00000i	0.0450377	−	0.180151i
$494$	−21.7279			−0.977585
$495$		0			0
$496$	−5.36396	−	5.36396i	−0.240849	−	0.240849i
$497$		−	7.41421i		−	0.332573i
$498$		0			0
$499$	−8.51472	+	8.51472i	−0.381171	+	0.381171i	−0.871524	−	0.490353i	$-0.836868\pi$
$499$	−8.51472	+	8.51472i	−0.381171	+	0.381171i	0.490353	+	0.871524i	$0.336868\pi$
$500$	6.36396	−	9.19239i	0.284605	−	0.411096i
$501$		0			0
$502$	−20.4853			−0.914303
$503$	−13.0711	−	13.0711i	−0.582810	−	0.582810i	0.352864	−	0.935674i	$-0.385208\pi$
$503$	−13.0711	−	13.0711i	−0.582810	−	0.582810i	−0.935674	+	0.352864i	$0.885208\pi$
$504$		0			0
$505$		0			0
$506$	−8.97056			−0.398790
$507$		0			0
$508$	17.7279			0.786549
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$	−16.7279			−0.740000
$512$	1.00000			0.0441942
$513$		0			0
$514$	−6.72792			−0.296756
$515$		0			0
$516$		0			0
$517$	2.51472	+	2.51472i	0.110597	+	0.110597i
$518$	10.4853			0.460697
$519$		0			0
$520$	2.12132	+	6.36396i	0.0930261	+	0.279078i
$521$	11.3137	−	11.3137i	0.495663	−	0.495663i	−0.414422	−	0.910085i	$-0.636016\pi$
$521$	11.3137	−	11.3137i	0.495663	−	0.495663i	0.910085	+	0.414422i	$0.136016\pi$
$522$		0			0
$523$			26.4853i			1.15812i	0.815285	+	0.579060i	$0.196580\pi$
$523$			26.4853i			1.15812i	−0.815285	+	0.579060i	$0.803420\pi$
$524$	−7.58579	−	7.58579i	−0.331387	−	0.331387i
$525$		0			0
$526$	−4.75736			−0.207431
$527$	7.58579	−	30.3431i	0.330442	−	1.32177i
$528$		0			0
$529$		−	7.00000i		−	0.304348i
$530$	6.36396	−	2.12132i	0.276433	−	0.0921443i
$531$		0			0
$532$	−7.24264	+	7.24264i	−0.314008	+	0.314008i
$533$	−13.2426	−	13.2426i	−0.573602	−	0.573602i
$534$		0			0
$535$	4.00000	−	8.00000i	0.172935	−	0.345870i
$536$			14.4853i			0.625669i
$537$		0			0
$538$	11.2929	+	11.2929i	0.486871	+	0.486871i
$539$	−7.92893	−	7.92893i	−0.341523	−	0.341523i
$540$		0			0
$541$	20.9706	+	20.9706i	0.901595	+	0.901595i	0.995574	−	0.0939792i	$-0.0299587\pi$
$541$	20.9706	+	20.9706i	0.901595	+	0.901595i	−0.0939792	+	0.995574i	$0.529959\pi$
$542$	−6.48528			−0.278567
$543$		0			0
$544$	2.12132	+	3.53553i	0.0909509	+	0.151585i
$545$	12.1716	−	24.3431i	0.521373	−	1.04275i
$546$		0			0
$547$	2.39340	−	2.39340i	0.102334	−	0.102334i	−0.654086	−	0.756420i	$-0.726947\pi$
$547$	2.39340	−	2.39340i	0.102334	−	0.102334i	0.756420	+	0.654086i	$0.226947\pi$
$548$			4.58579i			0.195895i
$549$		0			0
$550$	1.58579	−	11.1005i	0.0676182	−	0.473327i
$551$	5.12132	−	5.12132i	0.218176	−	0.218176i
$552$		0			0
$553$	−0.485281			−0.0206363
$554$	8.24264	−	8.24264i	0.350196	−	0.350196i
$555$		0			0
$556$	−11.0000	−	11.0000i	−0.466504	−	0.466504i
$557$			34.7990i			1.47448i	0.675631	+	0.737240i	$0.263871\pi$
$557$			34.7990i			1.47448i	−0.675631	+	0.737240i	$0.736129\pi$
$558$		0			0
$559$			11.2721i			0.476758i
$560$	2.82843	+	1.41421i	0.119523	+	0.0597614i
$561$		0			0
$562$			3.34315i			0.141022i
$563$	45.9411			1.93619			0.968094	−	0.250588i	$-0.0806240\pi$
$563$	45.9411			1.93619			0.968094	+	0.250588i	$0.0806240\pi$
$564$		0			0
$565$	−6.97056	−	3.48528i	−0.293254	−	0.146627i
$566$	−19.1213	−	19.1213i	−0.803729	−	0.803729i
$567$		0			0
$568$	−3.70711	−	3.70711i	−0.155547	−	0.155547i
$569$			20.3137i			0.851595i	0.904818	+	0.425797i	$0.140006\pi$
$569$			20.3137i			0.851595i	−0.904818	+	0.425797i	$0.859994\pi$
$570$		0			0
$571$	−20.2132	+	20.2132i	−0.845896	+	0.845896i	−0.989618	−	0.143722i	$-0.954093\pi$
$571$	−20.2132	+	20.2132i	−0.845896	+	0.845896i	0.143722	+	0.989618i	$0.454093\pi$
$572$	4.75736	+	4.75736i	0.198915	+	0.198915i
$573$		0			0
$574$	−8.82843			−0.368491
$575$	−19.7990	−	2.82843i	−0.825675	−	0.117954i
$576$		0			0
$577$		−	4.97056i		−	0.206927i	−0.994633	−	0.103464i	$-0.967007\pi$
$577$		−	4.97056i		−	0.206927i	0.994633	−	0.103464i	$-0.0329925\pi$
$578$	−8.00000	+	15.0000i	−0.332756	+	0.623918i
$579$		0			0
$580$	−2.00000	−	1.00000i	−0.0830455	−	0.0415227i
$581$	−4.24264	−	4.24264i	−0.176014	−	0.176014i
$582$		0			0
$583$	4.75736	−	4.75736i	0.197030	−	0.197030i
$584$	−8.36396	+	8.36396i	−0.346103	+	0.346103i
$585$		0			0
$586$		−	20.6569i		−	0.853327i
$587$	−24.0000			−0.990586			−0.495293	−	0.868726i	$-0.664939\pi$
$587$	−24.0000			−0.990586			−0.495293	+	0.868726i	$0.664939\pi$
$588$		0			0
$589$	38.8492	−	38.8492i	1.60076	−	1.60076i
$590$	−9.12132	−	27.3640i	−0.375519	−	1.12656i
$591$		0			0
$592$	5.24264	−	5.24264i	0.215471	−	0.215471i
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$		0			0
$595$	1.00000	+	13.0000i	0.0409960	+	0.532948i
$596$	12.7279			0.521356
$597$		0			0
$598$	8.48528	−	8.48528i	0.346989	−	0.346989i
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$		0			0
$601$	28.7279	−	28.7279i	1.17184	−	1.17184i	0.190065	−	0.981772i	$-0.439130\pi$
$601$	28.7279	−	28.7279i	1.17184	−	1.17184i	0.981772	−	0.190065i	$-0.0608698\pi$
$602$	3.75736	+	3.75736i	0.153139	+	0.153139i
$603$		0			0
$604$		−	12.0000i		−	0.488273i
$605$	4.22183	+	12.6655i	0.171642	+	0.514925i
$606$		0			0
$607$	26.4558	−	26.4558i	1.07381	−	1.07381i	0.0767600	−	0.997050i	$-0.475542\pi$
$607$	26.4558	−	26.4558i	1.07381	−	1.07381i	0.997050	−	0.0767600i	$-0.0244575\pi$
$608$			7.24264i			0.293728i
$609$		0			0
$610$	8.65685	−	17.3137i	0.350506	−	0.701012i
$611$	−4.75736			−0.192462
$612$		0			0
$613$		−	4.02944i		−	0.162747i	−0.996684	−	0.0813737i	$-0.974069\pi$
$613$		−	4.02944i		−	0.162747i	0.996684	−	0.0813737i	$-0.0259307\pi$
$614$			33.2132i			1.34038i
$615$		0			0
$616$	3.17157			0.127786
$617$	19.4350	−	19.4350i	0.782425	−	0.782425i	−0.197815	−	0.980239i	$-0.563384\pi$
$617$	19.4350	−	19.4350i	0.782425	−	0.782425i	0.980239	+	0.197815i	$0.0633844\pi$
$618$		0			0
$619$	5.75736	−	5.75736i	0.231408	−	0.231408i	−0.581872	−	0.813280i	$-0.697680\pi$
$619$	5.75736	−	5.75736i	0.231408	−	0.231408i	0.813280	+	0.581872i	$0.197680\pi$
$620$	−15.1716	−	7.58579i	−0.609305	−	0.304653i
$621$		0			0
$622$	1.41421	+	1.41421i	0.0567048	+	0.0567048i
$623$	−11.4853	−	11.4853i	−0.460148	−	0.460148i
$624$		0			0
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$	−22.4853	−	22.4853i	−0.898693	−	0.898693i
$627$		0			0
$628$		−	12.0000i		−	0.478852i
$629$	29.6569	+	7.41421i	1.18250	+	0.295624i
$630$		0			0
$631$		−	2.48528i		−	0.0989375i	−0.998776	−	0.0494687i	$-0.984247\pi$
$631$		−	2.48528i		−	0.0989375i	0.998776	−	0.0494687i	$-0.0157528\pi$
$632$	−0.242641	+	0.242641i	−0.00965173	+	0.00965173i
$633$		0			0
$634$	14.1421	+	14.1421i	0.561656	+	0.561656i
$635$	37.6066	−	12.5355i	1.49237	−	0.497457i
$636$		0			0
$637$	15.0000			0.594322
$638$	−2.24264			−0.0887870
$639$		0			0
$640$	2.12132	−	0.707107i	0.0838525	−	0.0279508i
$641$	−3.55635	−	3.55635i	−0.140467	−	0.140467i	0.633376	−	0.773844i	$-0.281668\pi$
$641$	−3.55635	−	3.55635i	−0.140467	−	0.140467i	−0.773844	+	0.633376i	$0.781668\pi$
$642$		0			0
$643$	−3.75736	+	3.75736i	−0.148176	+	0.148176i	−0.777303	−	0.629127i	$-0.783413\pi$
$643$	−3.75736	+	3.75736i	−0.148176	+	0.148176i	0.629127	+	0.777303i	$0.283413\pi$
$644$		−	5.65685i		−	0.222911i
$645$		0			0
$646$	−25.6066	+	15.3640i	−1.00748	+	0.604487i
$647$			47.5269i			1.86848i	0.356651	+	0.934238i	$0.383919\pi$
$647$			47.5269i			1.86848i	−0.356651	+	0.934238i	$0.616081\pi$
$648$		0			0
$649$	−20.4558	−	20.4558i	−0.802962	−	0.802962i
$650$	9.00000	+	12.0000i	0.353009	+	0.470679i
$651$		0			0
$652$	−4.48528	−	4.48528i	−0.175657	−	0.175657i
$653$	−4.79899	−	4.79899i	−0.187799	−	0.187799i	0.606945	−	0.794744i	$-0.292395\pi$
$653$	−4.79899	−	4.79899i	−0.187799	−	0.187799i	−0.794744	+	0.606945i	$0.792395\pi$
$654$		0			0
$655$	−21.4558	−	10.7279i	−0.838349	−	0.419175i
$656$	−4.41421	+	4.41421i	−0.172346	+	0.172346i
$657$		0			0
$658$	−1.58579	+	1.58579i	−0.0618204	+	0.0618204i
$659$	−30.2132			−1.17694			−0.588470	−	0.808519i	$-0.700269\pi$
$659$	−30.2132			−1.17694			−0.588470	+	0.808519i	$0.700269\pi$
$660$		0			0
$661$		−	12.0000i		−	0.466746i	−0.972387	−	0.233373i	$-0.925024\pi$
$661$		−	12.0000i		−	0.466746i	0.972387	−	0.233373i	$-0.0749763\pi$
$662$		−	15.7279i		−	0.611283i
$663$		0			0
$664$	−4.24264			−0.164646
$665$	−10.2426	+	20.4853i	−0.397193	+	0.794385i
$666$		0			0
$667$			4.00000i			0.154881i
$668$	1.07107	−	1.07107i	0.0414409	−	0.0414409i
$669$		0			0
$670$	10.2426	+	30.7279i	0.395708	+	1.18712i
$671$		−	19.4142i		−	0.749477i
$672$		0			0
$673$	25.8787	+	25.8787i	0.997550	+	0.997550i	0.999997	−	0.00244721i	$-0.000778973\pi$
$673$	25.8787	+	25.8787i	0.997550	+	0.997550i	−0.00244721	+	0.999997i	$0.500779\pi$
$674$	12.8492	−	12.8492i	0.494934	−	0.494934i
$675$		0			0
$676$	4.00000			0.153846
$677$	−22.4142	+	22.4142i	−0.861448	+	0.861448i	−0.991506	−	0.130058i	$-0.958484\pi$
$677$	−22.4142	+	22.4142i	−0.861448	+	0.861448i	0.130058	+	0.991506i	$0.458484\pi$
$678$		0			0
$679$	0.242641			0.00931169
$680$	7.00000	+	6.00000i	0.268438	+	0.230089i
$681$		0			0
$682$	−17.0122			−0.651431
$683$	−24.5355	+	24.5355i	−0.938826	+	0.938826i	−0.998234	−	0.0594077i	$-0.981079\pi$
$683$	−24.5355	+	24.5355i	−0.938826	+	0.938826i	0.0594077	+	0.998234i	$0.481079\pi$
$684$		0			0
$685$	3.24264	+	9.72792i	0.123895	+	0.371685i
$686$	12.0000	−	12.0000i	0.458162	−	0.458162i
$687$		0			0
$688$	3.75736			0.143248
$689$			9.00000i			0.342873i
$690$		0			0
$691$	9.48528	−	9.48528i	0.360837	−	0.360837i	−0.503284	−	0.864121i	$-0.667875\pi$
$691$	9.48528	−	9.48528i	0.360837	−	0.360837i	0.864121	+	0.503284i	$0.167875\pi$
$692$	−17.6569	+	17.6569i	−0.671213	+	0.671213i
$693$		0			0
$694$	−15.7071	−	15.7071i	−0.596234	−	0.596234i
$695$	−31.1127	−	15.5563i	−1.18017	−	0.590086i
$696$		0			0
$697$	−24.9706	−	6.24264i	−0.945828	−	0.236457i
$698$			10.9706i			0.415242i
$699$		0			0
$700$	7.00000	+	1.00000i	0.264575	+	0.0377964i
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$		0			0
$703$	37.9706	+	37.9706i	1.43209	+	1.43209i
$704$	1.58579	−	1.58579i	0.0597666	−	0.0597666i
$705$		0			0
$706$			11.3137i			0.425797i
$707$		0			0
$708$		0			0
$709$	2.60660	+	2.60660i	0.0978930	+	0.0978930i	0.754357	−	0.656464i	$-0.227949\pi$
$709$	2.60660	+	2.60660i	0.0978930	+	0.0978930i	−0.656464	+	0.754357i	$0.727949\pi$
$710$	−10.4853	−	5.24264i	−0.393506	−	0.196753i
$711$		0			0
$712$	−11.4853			−0.430429
$713$			30.3431i			1.13636i
$714$		0			0
$715$	13.4558	+	6.72792i	0.503220	+	0.251610i
$716$		−	0.686292i		−	0.0256479i
$717$		0			0
$718$			7.07107i			0.263890i
$719$	27.7487	+	27.7487i	1.03485	+	1.03485i	0.999370	+	0.0354830i	$0.0112970\pi$
$719$	27.7487	+	27.7487i	1.03485	+	1.03485i	0.0354830	+	0.999370i	$0.488703\pi$
$720$		0			0
$721$		0			0
$722$	−33.4558			−1.24510
$723$		0			0
$724$	−14.0000	+	14.0000i	−0.520306	+	0.520306i
$725$	−4.94975	−	0.707107i	−0.183829	−	0.0262613i
$726$		0			0
$727$			16.7574i			0.621496i	0.950492	+	0.310748i	$0.100580\pi$
$727$			16.7574i			0.621496i	−0.950492	+	0.310748i	$0.899420\pi$
$728$	−3.00000	+	3.00000i	−0.111187	+	0.111187i
$729$		0			0
$730$	−11.8284	+	23.6569i	−0.437790	+	0.875579i
$731$	7.97056	+	13.2843i	0.294802	+	0.491337i
$732$		0			0
$733$	−32.9706			−1.21780			−0.608898	−	0.793249i	$-0.708388\pi$
$733$	−32.9706			−1.21780			−0.608898	+	0.793249i	$0.708388\pi$
$734$	−18.2426	−	18.2426i	−0.673348	−	0.673348i
$735$		0			0
$736$	−2.82843	−	2.82843i	−0.104257	−	0.104257i
$737$	22.9706	+	22.9706i	0.846132	+	0.846132i
$738$		0			0
$739$		−	35.1838i		−	1.29426i	−0.762381	−	0.647128i	$-0.775970\pi$
$739$		−	35.1838i		−	1.29426i	0.762381	−	0.647128i	$-0.224030\pi$
$740$	7.41421	−	14.8284i	0.272552	−	0.545104i
$741$		0			0
$742$	3.00000	+	3.00000i	0.110133	+	0.110133i
$743$	17.8284	−	17.8284i	0.654062	−	0.654062i	−0.299907	−	0.953968i	$-0.596956\pi$
$743$	17.8284	−	17.8284i	0.654062	−	0.654062i	0.953968	+	0.299907i	$0.0969556\pi$
$744$		0			0
$745$	27.0000	−	9.00000i	0.989203	−	0.329734i
$746$		−	32.4853i		−	1.18937i
$747$		0			0
$748$	8.97056	+	2.24264i	0.327996	+	0.0819991i
$749$	5.65685			0.206697
$750$		0			0
$751$	19.3640	+	19.3640i	0.706601	+	0.706601i	0.965819	−	0.259218i	$-0.0834648\pi$
$751$	19.3640	+	19.3640i	0.706601	+	0.706601i	−0.259218	+	0.965819i	$0.583465\pi$
$752$			1.58579i			0.0578277i
$753$		0			0
$754$	2.12132	−	2.12132i	0.0772539	−	0.0772539i
$755$	−8.48528	−	25.4558i	−0.308811	−	0.926433i
$756$		0			0
$757$	32.9411			1.19727			0.598633	−	0.801024i	$-0.295711\pi$
$757$	32.9411			1.19727			0.598633	+	0.801024i	$0.295711\pi$
$758$	0.485281	+	0.485281i	0.0176262	+	0.0176262i
$759$		0			0
$760$	5.12132	+	15.3640i	0.185770	+	0.557309i
$761$	−20.4853			−0.742591			−0.371295	−	0.928515i	$-0.621086\pi$
$761$	−20.4853			−0.742591			−0.371295	+	0.928515i	$0.621086\pi$
$762$		0			0
$763$	17.2132			0.623160
$764$	−21.2132			−0.767467
$765$		0			0
$766$	13.2426			0.478476
$767$	38.6985			1.39732
$768$		0			0
$769$	−14.4558			−0.521291			−0.260646	−	0.965435i	$-0.583935\pi$
$769$	−14.4558			−0.521291			−0.260646	+	0.965435i	$0.583935\pi$
$770$	6.72792	−	2.24264i	0.242457	−	0.0808192i
$771$		0			0
$772$	18.4853	+	18.4853i	0.665300	+	0.665300i
$773$	32.4853			1.16841			0.584207	−	0.811605i	$-0.301406\pi$
$773$	32.4853			1.16841			0.584207	+	0.811605i	$0.301406\pi$
$774$		0			0
$775$	−37.5477	−	5.36396i	−1.34875	−	0.192679i
$776$	0.121320	−	0.121320i	0.00435515	−	0.00435515i
$777$		0			0
$778$		−	16.6274i		−	0.596122i
$779$	−31.9706	−	31.9706i	−1.14546	−	1.14546i
$780$		0			0
$781$	−11.7574			−0.420711
$782$	4.00000	−	16.0000i	0.143040	−	0.572159i
$783$		0			0
$784$		−	5.00000i		−	0.178571i
$785$	−8.48528	−	25.4558i	−0.302853	−	0.908558i
$786$		0			0
$787$	1.36396	−	1.36396i	0.0486200	−	0.0486200i	−0.682379	−	0.730999i	$-0.739055\pi$
$787$	1.36396	−	1.36396i	0.0486200	−	0.0486200i	0.730999	+	0.682379i	$0.239055\pi$
$788$	−3.34315	−	3.34315i	−0.119095	−	0.119095i
$789$		0			0
$790$	−0.343146	+	0.686292i	−0.0122086	+	0.0244172i
$791$		−	4.92893i		−	0.175253i
$792$		0			0
$793$	18.3640	+	18.3640i	0.652123	+	0.652123i
$794$	4.72792	+	4.72792i	0.167788	+	0.167788i
$795$		0			0
$796$	−7.12132	−	7.12132i	−0.252409	−	0.252409i
$797$	28.9706			1.02619			0.513095	−	0.858332i	$-0.328499\pi$
$797$	28.9706			1.02619			0.513095	+	0.858332i	$0.328499\pi$
$798$		0			0
$799$	−5.60660	+	3.36396i	−0.198347	+	0.119008i
$800$	4.00000	−	3.00000i	0.141421	−	0.106066i
$801$		0			0
$802$	2.10051	−	2.10051i	0.0741714	−	0.0741714i
$803$			26.5269i			0.936114i
$804$		0			0
$805$	−4.00000	−	12.0000i	−0.140981	−	0.422944i
$806$	16.0919	−	16.0919i	0.566812	−	0.566812i
$807$		0			0
$808$		0			0
$809$	−35.1421	+	35.1421i	−1.23553	+	1.23553i	−0.273723	+	0.961809i	$0.588255\pi$
$809$	−35.1421	+	35.1421i	−1.23553	+	1.23553i	−0.961809	+	0.273723i	$0.911745\pi$
$810$		0			0
$811$	9.48528	+	9.48528i	0.333073	+	0.333073i	0.853752	−	0.520679i	$-0.174321\pi$
$811$	9.48528	+	9.48528i	0.333073	+	0.333073i	−0.520679	+	0.853752i	$0.674321\pi$
$812$		−	1.41421i		−	0.0496292i
$813$		0			0
$814$		−	16.6274i		−	0.582791i
$815$	−12.6863	−	6.34315i	−0.444381	−	0.222191i
$816$		0			0
$817$			27.2132i			0.952069i
$818$	25.4853			0.891072
$819$		0			0
$820$	−6.24264	+	12.4853i	−0.218002	+	0.436005i
$821$	18.0208	+	18.0208i	0.628931	+	0.628931i	0.947799	−	0.318868i	$-0.103303\pi$
$821$	18.0208	+	18.0208i	0.628931	+	0.628931i	−0.318868	+	0.947799i	$0.603303\pi$
$822$		0			0
$823$	10.7279	+	10.7279i	0.373952	+	0.373952i	0.868914	−	0.494962i	$-0.164818\pi$
$823$	10.7279	+	10.7279i	0.373952	+	0.373952i	−0.494962	+	0.868914i	$0.664818\pi$
$824$		0			0
$825$		0			0
$826$	12.8995	−	12.8995i	0.448831	−	0.448831i
$827$	−5.31371	−	5.31371i	−0.184776	−	0.184776i	0.608657	−	0.793433i	$-0.291708\pi$
$827$	−5.31371	−	5.31371i	−0.184776	−	0.184776i	−0.793433	+	0.608657i	$0.791708\pi$
$828$		0			0
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$	−9.00000	+	3.00000i	−0.312395	+	0.104132i
$831$		0			0
$832$			3.00000i			0.104006i
$833$	17.6777	−	10.6066i	0.612495	−	0.367497i
$834$		0			0
$835$	1.51472	−	3.02944i	0.0524190	−	0.104838i
$836$	11.4853	+	11.4853i	0.397227	+	0.397227i
$837$		0			0
$838$	11.3137	−	11.3137i	0.390826	−	0.390826i
$839$	2.97918	−	2.97918i	0.102853	−	0.102853i	−0.653808	−	0.756661i	$-0.726830\pi$
$839$	2.97918	−	2.97918i	0.102853	−	0.102853i	0.756661	+	0.653808i	$0.226830\pi$
$840$		0			0
$841$		−	28.0000i		−	0.965517i
$842$	−19.2132			−0.662131
$843$		0			0
$844$	−8.00000	+	8.00000i	−0.275371	+	0.275371i
$845$	8.48528	−	2.82843i	0.291903	−	0.0973009i
$846$		0			0
$847$	−5.97056	+	5.97056i	−0.205151	+	0.205151i
$848$	3.00000			0.103020
$849$		0			0
$850$	19.0919	+	7.77817i	0.654846	+	0.266789i
$851$	−29.6569			−1.01662
$852$		0			0
$853$	−8.51472	+	8.51472i	−0.291538	+	0.291538i	−0.837688	−	0.546149i	$-0.816093\pi$
$853$	−8.51472	+	8.51472i	−0.291538	+	0.291538i	0.546149	+	0.837688i	$0.316093\pi$
$854$	12.2426			0.418935
$855$		0			0
$856$	2.82843	−	2.82843i	0.0966736	−	0.0966736i
$857$	−25.4350	−	25.4350i	−0.868844	−	0.868844i	0.123500	−	0.992345i	$-0.460588\pi$
$857$	−25.4350	−	25.4350i	−0.868844	−	0.868844i	−0.992345	+	0.123500i	$0.960588\pi$
$858$		0			0
$859$		−	45.7279i		−	1.56022i	−0.625645	−	0.780108i	$-0.715164\pi$
$859$		−	45.7279i		−	1.56022i	0.625645	−	0.780108i	$-0.284836\pi$
$860$	7.97056	−	2.65685i	0.271794	−	0.0905980i
$861$		0			0
$862$	−17.6569	+	17.6569i	−0.601395	+	0.601395i
$863$		−	55.1127i		−	1.87606i	−0.346557	−	0.938029i	$-0.612649\pi$
$863$		−	55.1127i		−	1.87606i	0.346557	−	0.938029i	$-0.387351\pi$
$864$		0			0
$865$	−24.9706	+	49.9411i	−0.849025	+	1.69805i
$866$	−5.75736			−0.195643
$867$		0			0
$868$		−	10.7279i		−	0.364129i
$869$			0.769553i			0.0261053i
$870$		0			0
$871$	−43.4558			−1.47245
$872$	8.60660	−	8.60660i	0.291456	−	0.291456i
$873$		0			0
$874$	20.4853	−	20.4853i	0.692925	−	0.692925i
$875$	15.5563	−	2.82843i	0.525901	−	0.0956183i
$876$		0			0
$877$	−8.51472	−	8.51472i	−0.287522	−	0.287522i	0.548578	−	0.836099i	$-0.315169\pi$
$877$	−8.51472	−	8.51472i	−0.287522	−	0.287522i	−0.836099	+	0.548578i	$0.815169\pi$
$878$	20.9706	+	20.9706i	0.707722	+	0.707722i
$879$		0			0
$880$	2.24264	−	4.48528i	0.0755994	−	0.151199i
$881$	8.44365	+	8.44365i	0.284474	+	0.284474i	0.834890	−	0.550416i	$-0.185531\pi$
$881$	8.44365	+	8.44365i	0.284474	+	0.284474i	−0.550416	+	0.834890i	$0.685531\pi$
$882$		0			0
$883$		−	18.7279i		−	0.630245i	−0.949051	−	0.315122i	$-0.897954\pi$
$883$		−	18.7279i		−	0.630245i	0.949051	−	0.315122i	$-0.102046\pi$
$884$	−10.6066	+	6.36396i	−0.356739	+	0.214043i
$885$		0			0
$886$			37.7990i			1.26988i
$887$	19.5858	−	19.5858i	0.657626	−	0.657626i	−0.297192	−	0.954818i	$-0.596050\pi$
$887$	19.5858	−	19.5858i	0.657626	−	0.657626i	0.954818	+	0.297192i	$0.0960500\pi$
$888$		0			0
$889$	17.7279	+	17.7279i	0.594575	+	0.594575i
$890$	−24.3640	+	8.12132i	−0.816682	+	0.272227i
$891$		0			0
$892$	−23.2426			−0.778221
$893$	−11.4853			−0.384340
$894$		0			0
$895$	−0.485281	−	1.45584i	−0.0162212	−	0.0486635i
$896$	1.00000	+	1.00000i	0.0334077	+	0.0334077i
$897$		0			0
$898$	28.7990	−	28.7990i	0.961035	−	0.961035i
$899$			7.58579i			0.253000i
$900$		0			0
$901$	6.36396	+	10.6066i	0.212014	+	0.353357i
$902$			14.0000i			0.466149i
$903$		0			0
$904$	−2.46447	−	2.46447i	−0.0819669	−	0.0819669i
$905$	−19.7990	+	39.5980i	−0.658141	+	1.31628i
$906$		0			0
$907$	−7.84924	−	7.84924i	−0.260630	−	0.260630i	0.564680	−	0.825310i	$-0.309000\pi$
$907$	−7.84924	−	7.84924i	−0.260630	−	0.260630i	−0.825310	+	0.564680i	$0.809000\pi$
$908$	4.05025	+	4.05025i	0.134412	+	0.134412i
$909$		0			0
$910$	−4.24264	+	8.48528i	−0.140642	+	0.281284i
$911$	35.3137	−	35.3137i	1.17000	−	1.17000i	0.187785	−	0.982210i	$-0.439869\pi$
$911$	35.3137	−	35.3137i	1.17000	−	1.17000i	0.982210	−	0.187785i	$-0.0601309\pi$
$912$		0			0
$913$	−6.72792	+	6.72792i	−0.222662	+	0.222662i
$914$	−2.24264			−0.0741800
$915$		0			0
$916$			7.75736i			0.256310i
$917$		−	15.1716i		−	0.501009i
$918$		0			0
$919$	−31.2132			−1.02963			−0.514814	−	0.857302i	$-0.672139\pi$
$919$	−31.2132			−1.02963			−0.514814	+	0.857302i	$0.672139\pi$
$920$	−8.00000	−	4.00000i	−0.263752	−	0.131876i
$921$		0			0
$922$			40.2843i			1.32669i
$923$	11.1213	−	11.1213i	0.366063	−	0.366063i
$924$		0			0
$925$	5.24264	−	36.6985i	0.172377	−	1.20664i
$926$			25.2426i			0.829525i
$927$		0			0
$928$	−0.707107	−	0.707107i	−0.0232119	−	0.0232119i
$929$	15.3431	−	15.3431i	0.503392	−	0.503392i	−0.409098	−	0.912490i	$-0.634157\pi$
$929$	15.3431	−	15.3431i	0.503392	−	0.503392i	0.912490	+	0.409098i	$0.134157\pi$
$930$		0			0
$931$	36.2132			1.18684
$932$	10.9497	−	10.9497i	0.358671	−	0.358671i
$933$		0			0
$934$	18.7279			0.612796
$935$	20.6152	−	1.58579i	0.674190	−	0.0518608i
$936$		0			0
$937$	47.2132			1.54239			0.771194	−	0.636600i	$-0.219660\pi$
$937$	47.2132			1.54239			0.771194	+	0.636600i	$0.219660\pi$
$938$	−14.4853	+	14.4853i	−0.472961	+	0.472961i
$939$		0			0
$940$	1.12132	+	3.36396i	0.0365734	+	0.109720i
$941$	−14.8076	+	14.8076i	−0.482714	+	0.482714i	−0.905997	−	0.423283i	$-0.860878\pi$
$941$	−14.8076	+	14.8076i	−0.482714	+	0.482714i	0.423283	+	0.905997i	$0.360878\pi$
$942$		0			0
$943$	24.9706			0.813153
$944$		−	12.8995i		−	0.419843i
$945$		0			0
$946$	5.95837	−	5.95837i	0.193723	−	0.193723i
$947$	−26.2929	+	26.2929i	−0.854404	+	0.854404i	−0.990672	−	0.136268i	$-0.956489\pi$
$947$	−26.2929	+	26.2929i	−0.854404	+	0.854404i	0.136268	+	0.990672i	$0.456489\pi$
$948$		0			0
$949$	−25.0919	−	25.0919i	−0.814517	−	0.814517i
$950$	21.7279	+	28.9706i	0.704947	+	0.939929i
$951$		0			0
$952$	−1.41421	+	5.65685i	−0.0458349	+	0.183340i
$953$			4.58579i			0.148548i	0.997238	+	0.0742741i	$0.0236640\pi$
$953$			4.58579i			0.148548i	−0.997238	+	0.0742741i	$0.976336\pi$
$954$		0			0
$955$	−45.0000	+	15.0000i	−1.45617	+	0.485389i
$956$	−22.2426			−0.719378
$957$		0			0
$958$	10.0503	+	10.0503i	0.324709	+	0.324709i
$959$	−4.58579	+	4.58579i	−0.148083	+	0.148083i
$960$		0			0
$961$			26.5442i			0.856263i
$962$	15.7279	+	15.7279i	0.507089	+	0.507089i
$963$		0			0
$964$	2.75736	+	2.75736i	0.0888086	+	0.0888086i
$965$	52.2843	+	26.1421i	1.68309	+	0.841545i
$966$		0			0
$967$	30.9706			0.995946			0.497973	−	0.867192i	$-0.334078\pi$
$967$	30.9706			0.995946			0.497973	+	0.867192i	$0.334078\pi$
$968$			5.97056i			0.191901i
$969$		0			0
$970$	0.171573	−	0.343146i	0.00550887	−	0.0110177i
$971$			30.5563i			0.980600i	0.871554	+	0.490300i	$0.163113\pi$
$971$			30.5563i			0.980600i	−0.871554	+	0.490300i	$0.836887\pi$
$972$		0			0
$973$		−	22.0000i		−	0.705288i
$974$	11.2426	+	11.2426i	0.360237	+	0.360237i
$975$		0			0
$976$	6.12132	−	6.12132i	0.195939	−	0.195939i
$977$	−0.727922			−0.0232883			−0.0116441	−	0.999932i	$-0.503707\pi$
$977$	−0.727922			−0.0232883			−0.0116441	+	0.999932i	$0.503707\pi$
$978$		0			0
$979$	−18.2132	+	18.2132i	−0.582097	+	0.582097i
$980$	−3.53553	−	10.6066i	−0.112938	−	0.338815i
$981$		0			0
$982$		−	6.89949i		−	0.220172i
$983$	44.0122	−	44.0122i	1.40377	−	1.40377i	0.616114	−	0.787657i	$-0.288706\pi$
$983$	44.0122	−	44.0122i	1.40377	−	1.40377i	0.787657	−	0.616114i	$-0.211294\pi$
$984$		0			0
$985$	−9.45584	−	4.72792i	−0.301288	−	0.150644i
$986$	1.00000	−	4.00000i	0.0318465	−	0.127386i
$987$		0			0
$988$	−21.7279			−0.691257
$989$	−10.6274	−	10.6274i	−0.337932	−	0.337932i
$990$		0			0
$991$	21.1213	+	21.1213i	0.670941	+	0.670941i	0.957933	−	0.286992i	$-0.0926553\pi$
$991$	21.1213	+	21.1213i	0.670941	+	0.670941i	−0.286992	+	0.957933i	$0.592655\pi$
$992$	−5.36396	−	5.36396i	−0.170306	−	0.170306i
$993$		0			0
$994$		−	7.41421i		−	0.235165i
$995$	−20.1421	−	10.0711i	−0.638549	−	0.319274i
$996$		0			0
$997$	30.6985	+	30.6985i	0.972231	+	0.972231i	0.999625	−	0.0273939i	$-0.00872086\pi$
$997$	30.6985	+	30.6985i	0.972231	+	0.972231i	−0.0273939	+	0.999625i	$0.508721\pi$
$998$	−8.51472	+	8.51472i	−0.269529	+	0.269529i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.n.o.829.2		4
3.2	odd	2		170.2.g.e.149.2	yes	4
5.4	even	2		1530.2.n.j.829.1		4
15.2	even	4		850.2.h.k.251.1		4
15.8	even	4		850.2.h.h.251.2		4
15.14	odd	2		170.2.g.f.149.1	yes	4
17.4	even	4		1530.2.n.j.1279.1		4
51.38	odd	4		170.2.g.f.89.1	yes	4
85.4	even	4	inner	1530.2.n.o.1279.2		4
255.38	even	4		850.2.h.h.701.2		4
255.89	odd	4		170.2.g.e.89.2	✓	4
255.242	even	4		850.2.h.k.701.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.g.e.89.2	✓	4	255.89	odd	4
170.2.g.e.149.2	yes	4	3.2	odd	2
170.2.g.f.89.1	yes	4	51.38	odd	4
170.2.g.f.149.1	yes	4	15.14	odd	2
850.2.h.h.251.2		4	15.8	even	4
850.2.h.h.701.2		4	255.38	even	4
850.2.h.k.251.1		4	15.2	even	4
850.2.h.k.701.1		4	255.242	even	4
1530.2.n.j.829.1		4	5.4	even	2
1530.2.n.j.1279.1		4	17.4	even	4
1530.2.n.o.829.2		4	1.1	even	1	trivial
1530.2.n.o.1279.2		4	85.4	even	4	inner

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:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} +1.00000 q^{8} +(2.12132 - 0.707107i) q^{10} +(1.58579 - 1.58579i) q^{11} +3.00000i q^{13} +(1.00000 + 1.00000i) q^{14} +1.00000 q^{16} +(2.12132 + 3.53553i) q^{17} +7.24264i q^{19} +(2.12132 - 0.707107i) q^{20} +(1.58579 - 1.58579i) q^{22} +(-2.82843 - 2.82843i) q^{23} +(4.00000 - 3.00000i) q^{25} +3.00000i q^{26} +(1.00000 + 1.00000i) q^{28} +(-0.707107 - 0.707107i) q^{29} +(-5.36396 - 5.36396i) q^{31} +1.00000 q^{32} +(2.12132 + 3.53553i) q^{34} +(2.82843 + 1.41421i) q^{35} +(5.24264 - 5.24264i) q^{37} +7.24264i q^{38} +(2.12132 - 0.707107i) q^{40} +(-4.41421 + 4.41421i) q^{41} +3.75736 q^{43} +(1.58579 - 1.58579i) q^{44} +(-2.82843 - 2.82843i) q^{46} +1.58579i q^{47} -5.00000i q^{49} +(4.00000 - 3.00000i) q^{50} +3.00000i q^{52} +3.00000 q^{53} +(2.24264 - 4.48528i) q^{55} +(1.00000 + 1.00000i) q^{56} +(-0.707107 - 0.707107i) q^{58} -12.8995i q^{59} +(6.12132 - 6.12132i) q^{61} +(-5.36396 - 5.36396i) q^{62} +1.00000 q^{64} +(2.12132 + 6.36396i) q^{65} +14.4853i q^{67} +(2.12132 + 3.53553i) q^{68} +(2.82843 + 1.41421i) q^{70} +(-3.70711 - 3.70711i) q^{71} +(-8.36396 + 8.36396i) q^{73} +(5.24264 - 5.24264i) q^{74} +7.24264i q^{76} +3.17157 q^{77} +(-0.242641 + 0.242641i) q^{79} +(2.12132 - 0.707107i) q^{80} +(-4.41421 + 4.41421i) q^{82} -4.24264 q^{83} +(7.00000 + 6.00000i) q^{85} +3.75736 q^{86} +(1.58579 - 1.58579i) q^{88} -11.4853 q^{89} +(-3.00000 + 3.00000i) q^{91} +(-2.82843 - 2.82843i) q^{92} +1.58579i q^{94} +(5.12132 + 15.3640i) q^{95} +(0.121320 - 0.121320i) q^{97} -5.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8	\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8} + 12 q^{11} + 4 q^{14} + 4 q^{16} + 12 q^{22} + 16 q^{25} + 4 q^{28} + 4 q^{31} + 4 q^{32} + 4 q^{37} - 12 q^{41} + 32 q^{43} + 12 q^{44} + 16 q^{50} + 12 q^{53} - 8 q^{55} + 4 q^{56} + 16 q^{61} + 4 q^{62} + 4 q^{64} - 12 q^{71} - 8 q^{73} + 4 q^{74} + 24 q^{77} + 16 q^{79} - 12 q^{82} + 28 q^{85} + 32 q^{86} + 12 q^{88} - 12 q^{89} - 12 q^{91} + 12 q^{95} - 8 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8 + 12 * q^11 + 4 * q^14 + 4 * q^16 + 12 * q^22 + 16 * q^25 + 4 * q^28 + 4 * q^31 + 4 * q^32 + 4 * q^37 - 12 * q^41 + 32 * q^43 + 12 * q^44 + 16 * q^50 + 12 * q^53 - 8 * q^55 + 4 * q^56 + 16 * q^61 + 4 * q^62 + 4 * q^64 - 12 * q^71 - 8 * q^73 + 4 * q^74 + 24 * q^77 + 16 * q^79 - 12 * q^82 + 28 * q^85 + 32 * q^86 + 12 * q^88 - 12 * q^89 - 12 * q^91 + 12 * q^95 - 8 * q^97

Introduction

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