LMFDB - Embedded newform 507.2.j.f.316.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	507.316
Dual form			507.2.j.f.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.09077 - 1.20711i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.91421 + 3.31552i) q^{4} -2.82843i q^{5} +(2.09077 - 1.20711i) q^{6} +(-2.44949 + 1.41421i) q^{7} -4.41421i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.09077 - 1.20711i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.91421 + 3.31552i) q^{4} -2.82843i q^{5} +(2.09077 - 1.20711i) q^{6} +(-2.44949 + 1.41421i) q^{7} -4.41421i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.41421 + 5.91359i) q^{10} +(1.73205 + 1.00000i) q^{11} -3.82843 q^{12} +6.82843 q^{14} +(2.44949 + 1.41421i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(-1.82843 - 3.16693i) q^{17} +2.41421i q^{18} +(-2.44949 + 1.41421i) q^{19} +(9.37769 - 5.41421i) q^{20} -2.82843i q^{21} +(-2.41421 - 4.18154i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(3.82282 + 2.20711i) q^{24} -3.00000 q^{25} +1.00000 q^{27} +(-9.37769 - 5.41421i) q^{28} +(-1.00000 + 1.73205i) q^{29} +(-3.41421 - 5.91359i) q^{30} +6.82843i q^{31} +(-1.37333 + 0.792893i) q^{32} +(-1.73205 + 1.00000i) q^{33} +8.82843i q^{34} +(4.00000 + 6.92820i) q^{35} +(1.91421 - 3.31552i) q^{36} +(-3.16693 - 1.82843i) q^{37} +6.82843 q^{38} -12.4853 q^{40} +(9.37769 + 5.41421i) q^{41} +(-3.41421 + 5.91359i) q^{42} +(4.82843 + 8.36308i) q^{43} +7.65685i q^{44} +(-2.44949 + 1.41421i) q^{45} +(8.36308 - 4.82843i) q^{46} -0.343146i q^{47} +(-1.50000 - 2.59808i) q^{48} +(0.500000 - 0.866025i) q^{49} +(6.27231 + 3.62132i) q^{50} +3.65685 q^{51} -2.00000 q^{53} +(-2.09077 - 1.20711i) q^{54} +(2.82843 - 4.89898i) q^{55} +(6.24264 + 10.8126i) q^{56} -2.82843i q^{57} +(4.18154 - 2.41421i) q^{58} +(-3.16693 + 1.82843i) q^{59} +10.8284i q^{60} +(4.65685 + 8.06591i) q^{61} +(8.24264 - 14.2767i) q^{62} +(2.44949 + 1.41421i) q^{63} +9.82843 q^{64} +4.82843 q^{66} +(1.01461 + 0.585786i) q^{67} +(7.00000 - 12.1244i) q^{68} +(-2.00000 - 3.46410i) q^{69} -19.3137i q^{70} +(-1.73205 + 1.00000i) q^{71} +(-3.82282 + 2.20711i) q^{72} +11.6569i q^{73} +(4.41421 + 7.64564i) q^{74} +(1.50000 - 2.59808i) q^{75} +(-9.37769 - 5.41421i) q^{76} -5.65685 q^{77} +11.3137 q^{79} +(7.34847 + 4.24264i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-13.0711 - 22.6398i) q^{82} +7.65685i q^{83} +(9.37769 - 5.41421i) q^{84} +(-8.95743 + 5.17157i) q^{85} -23.3137i q^{86} +(-1.00000 - 1.73205i) q^{87} +(4.41421 - 7.64564i) q^{88} +(-7.94282 - 4.58579i) q^{89} +6.82843 q^{90} -15.3137 q^{92} +(-5.91359 - 3.41421i) q^{93} +(-0.414214 + 0.717439i) q^{94} +(4.00000 + 6.92820i) q^{95} -1.58579i q^{96} +(6.63103 - 3.82843i) q^{97} +(-2.09077 + 1.20711i) q^{98} -2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 16 q^{10} - 8 q^{12} + 32 q^{14} - 12 q^{16} + 8 q^{17} - 8 q^{22} - 16 q^{23} - 24 q^{25} + 8 q^{27} - 8 q^{29} - 16 q^{30} + 32 q^{35} + 4 q^{36} + 32 q^{38} - 32 q^{40} - 16 q^{42} + 16 q^{43} - 12 q^{48} + 4 q^{49} - 16 q^{51} - 16 q^{53} + 16 q^{56} - 8 q^{61} + 32 q^{62} + 56 q^{64} + 16 q^{66} + 56 q^{68} - 16 q^{69} + 24 q^{74} + 12 q^{75} - 4 q^{81} - 48 q^{82} - 8 q^{87} + 24 q^{88} + 32 q^{90} - 32 q^{92} + 8 q^{94} + 32 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 16 * q^10 - 8 * q^12 + 32 * q^14 - 12 * q^16 + 8 * q^17 - 8 * q^22 - 16 * q^23 - 24 * q^25 + 8 * q^27 - 8 * q^29 - 16 * q^30 + 32 * q^35 + 4 * q^36 + 32 * q^38 - 32 * q^40 - 16 * q^42 + 16 * q^43 - 12 * q^48 + 4 * q^49 - 16 * q^51 - 16 * q^53 + 16 * q^56 - 8 * q^61 + 32 * q^62 + 56 * q^64 + 16 * q^66 + 56 * q^68 - 16 * q^69 + 24 * q^74 + 12 * q^75 - 4 * q^81 - 48 * q^82 - 8 * q^87 + 24 * q^88 + 32 * q^90 - 32 * q^92 + 8 * q^94 + 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.09077	−	1.20711i	−1.47840	−	0.853553i	−0.478696	−	0.877981i	$-0.658890\pi$
$2$	−2.09077	−	1.20711i	−1.47840	−	0.853553i	−0.999702	+	0.0244272i	$0.992224\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.91421	+	3.31552i	0.957107	+	1.65776i
$5$		−	2.82843i		−	1.26491i	−0.774597	−	0.632456i	$-0.782047\pi$
$5$		−	2.82843i		−	1.26491i	0.774597	−	0.632456i	$-0.217953\pi$
$6$	2.09077	−	1.20711i	0.853553	−	0.492799i
$7$	−2.44949	+	1.41421i	−0.925820	+	0.534522i	−0.885487	−	0.464664i	$-0.846175\pi$
$7$	−2.44949	+	1.41421i	−0.925820	+	0.534522i	−0.0403329	+	0.999186i	$0.512842\pi$
$8$		−	4.41421i		−	1.56066i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−3.41421	+	5.91359i	−1.07967	+	1.87004i
$11$	1.73205	+	1.00000i	0.522233	+	0.301511i	0.737848	−	0.674967i	$-0.235842\pi$
$11$	1.73205	+	1.00000i	0.522233	+	0.301511i	−0.215615	+	0.976478i	$0.569176\pi$
$12$	−3.82843			−1.10517
$13$		0			0
$13$		0			0
$14$	6.82843			1.82497
$15$	2.44949	+	1.41421i	0.632456	+	0.365148i
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−1.82843	−	3.16693i	−0.443459	−	0.768093i	0.554485	−	0.832194i	$-0.312915\pi$
$17$	−1.82843	−	3.16693i	−0.443459	−	0.768093i	−0.997943	+	0.0641009i	$0.979582\pi$
$18$			2.41421i			0.569036i
$19$	−2.44949	+	1.41421i	−0.561951	+	0.324443i	−0.753928	−	0.656957i	$-0.771843\pi$
$19$	−2.44949	+	1.41421i	−0.561951	+	0.324443i	0.191977	+	0.981399i	$0.438510\pi$
$20$	9.37769	−	5.41421i	2.09692	−	1.21065i
$21$		−	2.82843i		−	0.617213i
$22$	−2.41421	−	4.18154i	−0.514712	−	0.891507i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$	3.82282	+	2.20711i	0.780330	+	0.450524i
$25$	−3.00000			−0.600000
$26$		0			0
$27$	1.00000			0.192450
$28$	−9.37769	−	5.41421i	−1.77222	−	1.02319i
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	−0.943811	−	0.330487i	$-0.892787\pi$
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	0.758115	+	0.652121i	$0.226120\pi$
$30$	−3.41421	−	5.91359i	−0.623347	−	1.07967i
$31$			6.82843i			1.22642i	0.789919	+	0.613211i	$0.210122\pi$
$31$			6.82843i			1.22642i	−0.789919	+	0.613211i	$0.789878\pi$
$32$	−1.37333	+	0.792893i	−0.242773	+	0.140165i
$33$	−1.73205	+	1.00000i	−0.301511	+	0.174078i
$34$			8.82843i			1.51406i
$35$	4.00000	+	6.92820i	0.676123	+	1.17108i
$36$	1.91421	−	3.31552i	0.319036	−	0.552586i
$37$	−3.16693	−	1.82843i	−0.520640	−	0.300592i	0.216557	−	0.976270i	$-0.430517\pi$
$37$	−3.16693	−	1.82843i	−0.520640	−	0.300592i	−0.737196	+	0.675679i	$0.763851\pi$
$38$	6.82843			1.10772
$39$		0			0
$40$	−12.4853			−1.97410
$41$	9.37769	+	5.41421i	1.46455	+	0.845558i	0.999217	−	0.0395775i	$-0.0126012\pi$
$41$	9.37769	+	5.41421i	1.46455	+	0.845558i	0.465333	+	0.885136i	$0.345935\pi$
$42$	−3.41421	+	5.91359i	−0.526825	+	0.912487i
$43$	4.82843	+	8.36308i	0.736328	+	1.27536i	0.954138	+	0.299367i	$0.0967754\pi$
$43$	4.82843	+	8.36308i	0.736328	+	1.27536i	−0.217810	+	0.975991i	$0.569891\pi$
$44$			7.65685i			1.15431i
$45$	−2.44949	+	1.41421i	−0.365148	+	0.210819i
$46$	8.36308	−	4.82843i	1.23307	−	0.711913i
$47$		−	0.343146i		−	0.0500530i	−0.999687	−	0.0250265i	$-0.992033\pi$
$47$		−	0.343146i		−	0.0500530i	0.999687	−	0.0250265i	$-0.00796701\pi$
$48$	−1.50000	−	2.59808i	−0.216506	−	0.375000i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	6.27231	+	3.62132i	0.887039	+	0.512132i
$51$	3.65685			0.512062
$52$		0			0
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$	−2.09077	−	1.20711i	−0.284518	−	0.164266i
$55$	2.82843	−	4.89898i	0.381385	−	0.660578i
$56$	6.24264	+	10.8126i	0.834208	+	1.44489i
$57$		−	2.82843i		−	0.374634i
$58$	4.18154	−	2.41421i	0.549063	−	0.317002i
$59$	−3.16693	+	1.82843i	−0.412299	+	0.238041i	−0.691777	−	0.722111i	$-0.743172\pi$
$59$	−3.16693	+	1.82843i	−0.412299	+	0.238041i	0.279478	+	0.960152i	$0.409839\pi$
$60$			10.8284i			1.39794i
$61$	4.65685	+	8.06591i	0.596249	+	1.03273i	0.993369	+	0.114967i	$0.0366763\pi$
$61$	4.65685	+	8.06591i	0.596249	+	1.03273i	−0.397120	+	0.917767i	$0.629990\pi$
$62$	8.24264	−	14.2767i	1.04682	−	1.81314i
$63$	2.44949	+	1.41421i	0.308607	+	0.178174i
$64$	9.82843			1.22855
$65$		0			0
$66$	4.82843			0.594338
$67$	1.01461	+	0.585786i	0.123955	+	0.0715652i	0.560695	−	0.828022i	$-0.310534\pi$
$67$	1.01461	+	0.585786i	0.123955	+	0.0715652i	−0.436741	+	0.899587i	$0.643867\pi$
$68$	7.00000	−	12.1244i	0.848875	−	1.47029i
$69$	−2.00000	−	3.46410i	−0.240772	−	0.417029i
$70$		−	19.3137i		−	2.30843i
$71$	−1.73205	+	1.00000i	−0.205557	+	0.118678i	−0.599245	−	0.800566i	$-0.704532\pi$
$71$	−1.73205	+	1.00000i	−0.205557	+	0.118678i	0.393688	+	0.919244i	$0.371199\pi$
$72$	−3.82282	+	2.20711i	−0.450524	+	0.260110i
$73$			11.6569i			1.36433i	0.731198	+	0.682166i	$0.238962\pi$
$73$			11.6569i			1.36433i	−0.731198	+	0.682166i	$0.761038\pi$
$74$	4.41421	+	7.64564i	0.513142	+	0.888788i
$75$	1.50000	−	2.59808i	0.173205	−	0.300000i
$76$	−9.37769	−	5.41421i	−1.07570	−	0.621053i
$77$	−5.65685			−0.644658
$78$		0			0
$79$	11.3137			1.27289			0.636446	−	0.771321i	$-0.280404\pi$
$79$	11.3137			1.27289			0.636446	+	0.771321i	$0.280404\pi$
$80$	7.34847	+	4.24264i	0.821584	+	0.474342i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−13.0711	−	22.6398i	−1.44346	−	2.50014i
$83$			7.65685i			0.840449i	0.907420	+	0.420224i	$0.138049\pi$
$83$			7.65685i			0.840449i	−0.907420	+	0.420224i	$0.861951\pi$
$84$	9.37769	−	5.41421i	1.02319	−	0.590739i
$85$	−8.95743	+	5.17157i	−0.971569	+	0.560936i
$86$		−	23.3137i		−	2.51398i
$87$	−1.00000	−	1.73205i	−0.107211	−	0.185695i
$88$	4.41421	−	7.64564i	0.470557	−	0.815028i
$89$	−7.94282	−	4.58579i	−0.841937	−	0.486092i	0.0159854	−	0.999872i	$-0.494911\pi$
$89$	−7.94282	−	4.58579i	−0.841937	−	0.486092i	−0.857922	+	0.513780i	$0.828245\pi$
$90$	6.82843			0.719779
$91$		0			0
$92$	−15.3137			−1.59656
$93$	−5.91359	−	3.41421i	−0.613211	−	0.354037i
$94$	−0.414214	+	0.717439i	−0.0427229	+	0.0739982i
$95$	4.00000	+	6.92820i	0.410391	+	0.710819i
$96$		−	1.58579i		−	0.161849i
$97$	6.63103	−	3.82843i	0.673279	−	0.388718i	−0.124039	−	0.992277i	$-0.539585\pi$
$97$	6.63103	−	3.82843i	0.673279	−	0.388718i	0.797318	+	0.603559i	$0.206251\pi$
$98$	−2.09077	+	1.20711i	−0.211200	+	0.121936i
$99$		−	2.00000i		−	0.201008i
$100$	−5.74264	−	9.94655i	−0.574264	−	0.994655i
$101$	−1.82843	+	3.16693i	−0.181935	+	0.315121i	−0.942540	−	0.334095i	$-0.891569\pi$
$101$	−1.82843	+	3.16693i	−0.181935	+	0.315121i	0.760604	+	0.649216i	$0.224903\pi$
$102$	−7.64564	−	4.41421i	−0.757031	−	0.437072i
$103$	−13.6569			−1.34565			−0.672825	−	0.739802i	$-0.734919\pi$
$103$	−13.6569			−1.34565			−0.672825	+	0.739802i	$0.734919\pi$
$104$		0			0
$105$	−8.00000			−0.780720
$106$	4.18154	+	2.41421i	0.406147	+	0.234489i
$107$	−5.65685	+	9.79796i	−0.546869	+	0.947204i	0.451618	+	0.892211i	$0.350847\pi$
$107$	−5.65685	+	9.79796i	−0.546869	+	0.947204i	−0.998487	+	0.0549930i	$0.982486\pi$
$108$	1.91421	+	3.31552i	0.184195	+	0.319036i
$109$			17.3137i			1.65835i	0.558987	+	0.829176i	$0.311190\pi$
$109$			17.3137i			1.65835i	−0.558987	+	0.829176i	$0.688810\pi$
$110$	−11.8272	+	6.82843i	−1.12768	+	0.651065i
$111$	3.16693	−	1.82843i	0.300592	−	0.173547i
$112$		−	8.48528i		−	0.801784i
$113$	−8.65685	−	14.9941i	−0.814368	−	1.41053i	−0.909781	−	0.415090i	$-0.863750\pi$
$113$	−8.65685	−	14.9941i	−0.814368	−	1.41053i	0.0954122	−	0.995438i	$-0.469583\pi$
$114$	−3.41421	+	5.91359i	−0.319770	+	0.553859i
$115$	9.79796	+	5.65685i	0.913664	+	0.527504i
$116$	−7.65685			−0.710921
$117$		0			0
$118$	8.82843			0.812723
$119$	8.95743	+	5.17157i	0.821126	+	0.474077i
$120$	6.24264	−	10.8126i	0.569873	−	0.987048i
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$		−	22.4853i		−	2.03572i
$123$	−9.37769	+	5.41421i	−0.845558	+	0.488183i
$124$	−22.6398	+	13.0711i	−2.03311	+	1.17382i
$125$		−	5.65685i		−	0.505964i
$126$	−3.41421	−	5.91359i	−0.304162	−	0.526825i
$127$	−2.82843	+	4.89898i	−0.250982	+	0.434714i	−0.963797	−	0.266639i	$-0.914087\pi$
$127$	−2.82843	+	4.89898i	−0.250982	+	0.434714i	0.712814	+	0.701353i	$0.247420\pi$
$128$	−17.8023	−	10.2782i	−1.57352	−	0.908471i
$129$	−9.65685			−0.850239
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$	−6.63103	−	3.82843i	−0.577157	−	0.333222i
$133$	4.00000	−	6.92820i	0.346844	−	0.600751i
$134$	−1.41421	−	2.44949i	−0.122169	−	0.211604i
$135$		−	2.82843i		−	0.243432i
$136$	−13.9795	+	8.07107i	−1.19873	+	0.692088i
$137$	−4.47871	+	2.58579i	−0.382642	+	0.220919i	−0.678967	−	0.734169i	$-0.737572\pi$
$137$	−4.47871	+	2.58579i	−0.382642	+	0.220919i	0.296325	+	0.955087i	$0.404239\pi$
$138$			9.65685i			0.822046i
$139$	−7.65685	−	13.2621i	−0.649446	−	1.12487i	−0.983255	−	0.182233i	$-0.941668\pi$
$139$	−7.65685	−	13.2621i	−0.649446	−	1.12487i	0.333810	−	0.942641i	$-0.391666\pi$
$140$	−15.3137	+	26.5241i	−1.29424	+	2.24170i
$141$	0.297173	+	0.171573i	0.0250265	+	0.0144490i
$142$	4.82843			0.405193
$143$		0			0
$144$	3.00000			0.250000
$145$	4.89898	+	2.82843i	0.406838	+	0.234888i
$146$	14.0711	−	24.3718i	1.16453	−	2.01702i
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$		−	14.0000i		−	1.15079i
$149$	12.8418	−	7.41421i	1.05204	−	0.607396i	0.128821	−	0.991668i	$-0.458881\pi$
$149$	12.8418	−	7.41421i	1.05204	−	0.607396i	0.923220	+	0.384272i	$0.125547\pi$
$150$	−6.27231	+	3.62132i	−0.512132	+	0.295680i
$151$		−	20.4853i		−	1.66707i	−0.552468	−	0.833534i	$-0.686314\pi$
$151$		−	20.4853i		−	1.66707i	0.552468	−	0.833534i	$-0.313686\pi$
$152$	6.24264	+	10.8126i	0.506345	+	0.877015i
$153$	−1.82843	+	3.16693i	−0.147820	+	0.256031i
$154$	11.8272	+	6.82843i	0.953062	+	0.550250i
$155$	19.3137			1.55131
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	−23.6544	−	13.6569i	−1.88184	−	1.08648i
$159$	1.00000	−	1.73205i	0.0793052	−	0.137361i
$160$	2.24264	+	3.88437i	0.177296	+	0.307086i
$161$		−	11.3137i		−	0.891645i
$162$	2.09077	−	1.20711i	0.164266	−	0.0948393i
$163$	11.4069	−	6.58579i	0.893459	−	0.515839i	0.0183864	−	0.999831i	$-0.494147\pi$
$163$	11.4069	−	6.58579i	0.893459	−	0.515839i	0.875072	+	0.483992i	$0.160814\pi$
$164$			41.4558i			3.23716i
$165$	2.82843	+	4.89898i	0.220193	+	0.381385i
$166$	9.24264	−	16.0087i	0.717368	−	1.24252i
$167$	−6.63103	−	3.82843i	−0.513125	−	0.296253i	0.220993	−	0.975275i	$-0.429070\pi$
$167$	−6.63103	−	3.82843i	−0.513125	−	0.296253i	−0.734117	+	0.679023i	$0.762404\pi$
$168$	−12.4853			−0.963260
$169$		0			0
$170$	24.9706			1.91515
$171$	2.44949	+	1.41421i	0.187317	+	0.108148i
$172$	−18.4853	+	32.0174i	−1.40949	+	2.44131i
$173$	−0.171573	−	0.297173i	−0.0130444	−	0.0225936i	0.859429	−	0.511254i	$-0.170819\pi$
$173$	−0.171573	−	0.297173i	−0.0130444	−	0.0225936i	−0.872474	+	0.488661i	$0.837486\pi$
$174$			4.82843i			0.366042i
$175$	7.34847	−	4.24264i	0.555492	−	0.320713i
$176$	−5.19615	+	3.00000i	−0.391675	+	0.226134i
$177$		−	3.65685i		−	0.274866i
$178$	11.0711	+	19.1757i	0.829812	+	1.43728i
$179$	−0.343146	+	0.594346i	−0.0256479	+	0.0444235i	−0.878564	−	0.477624i	$-0.841498\pi$
$179$	−0.343146	+	0.594346i	−0.0256479	+	0.0444235i	0.852917	+	0.522047i	$0.174832\pi$
$180$	−9.37769	−	5.41421i	−0.698972	−	0.403552i
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$	−9.31371			−0.688489
$184$	15.2913	+	8.82843i	1.12729	+	0.650840i
$185$	−5.17157	+	8.95743i	−0.380222	+	0.658563i
$186$	8.24264	+	14.2767i	0.604380	+	1.04682i
$187$		−	7.31371i		−	0.534831i
$188$	1.13770	−	0.656854i	0.0829757	−	0.0479060i
$189$	−2.44949	+	1.41421i	−0.178174	+	0.102869i
$190$		−	19.3137i		−	1.40116i
$191$	9.65685	+	16.7262i	0.698745	+	1.21026i	0.968902	+	0.247446i	$0.0795913\pi$
$191$	9.65685	+	16.7262i	0.698745	+	1.21026i	−0.270156	+	0.962817i	$0.587075\pi$
$192$	−4.91421	+	8.51167i	−0.354653	+	0.614277i
$193$	14.9941	+	8.65685i	1.07930	+	0.623134i	0.930707	−	0.365765i	$-0.119192\pi$
$193$	14.9941	+	8.65685i	1.07930	+	0.623134i	0.148592	+	0.988899i	$0.452526\pi$
$194$	−18.4853			−1.32717
$195$		0			0
$196$	3.82843			0.273459
$197$	−14.2767	−	8.24264i	−1.01717	−	0.587264i	−0.103888	−	0.994589i	$-0.533128\pi$
$197$	−14.2767	−	8.24264i	−1.01717	−	0.587264i	−0.913283	+	0.407325i	$0.866462\pi$
$198$	−2.41421	+	4.18154i	−0.171571	+	0.297169i
$199$	5.17157	+	8.95743i	0.366603	+	0.634975i	0.989032	−	0.147701i	$-0.0471874\pi$
$199$	5.17157	+	8.95743i	0.366603	+	0.634975i	−0.622429	+	0.782676i	$0.713854\pi$
$200$			13.2426i			0.936396i
$201$	−1.01461	+	0.585786i	−0.0715652	+	0.0413182i
$202$	7.64564	−	4.41421i	0.537946	−	0.310583i
$203$		−	5.65685i		−	0.397033i
$204$	7.00000	+	12.1244i	0.490098	+	0.848875i
$205$	15.3137	−	26.5241i	1.06956	−	1.85252i
$206$	28.5533	+	16.4853i	1.98941	+	1.14858i
$207$	4.00000			0.278019
$208$		0			0
$209$	−5.65685			−0.391293
$210$	16.7262	+	9.65685i	1.15421	+	0.666386i
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	−0.582165	−	0.813070i	$-0.697794\pi$
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	0.995222	+	0.0976347i	$0.0311277\pi$
$212$	−3.82843	−	6.63103i	−0.262937	−	0.455421i
$213$		−	2.00000i		−	0.137038i
$214$	23.6544	−	13.6569i	1.61698	−	0.933563i
$215$	23.6544	−	13.6569i	1.61321	−	0.931390i
$216$		−	4.41421i		−	0.300349i
$217$	−9.65685	−	16.7262i	−0.655550	−	1.13545i
$218$	20.8995	−	36.1990i	1.41549	−	2.45170i
$219$	−10.0951	−	5.82843i	−0.682166	−	0.393849i
$220$	21.6569			1.46010
$221$		0			0
$222$	−8.82843			−0.592525
$223$	3.88437	+	2.24264i	0.260116	+	0.150178i	0.624388	−	0.781115i	$-0.285349\pi$
$223$	3.88437	+	2.24264i	0.260116	+	0.150178i	−0.364271	+	0.931293i	$0.618682\pi$
$224$	2.24264	−	3.88437i	0.149843	−	0.259535i
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$			41.7990i			2.78043i
$227$	−4.60181	+	2.65685i	−0.305433	+	0.176342i	−0.644881	−	0.764283i	$-0.723093\pi$
$227$	−4.60181	+	2.65685i	−0.305433	+	0.176342i	0.339448	+	0.940625i	$0.389760\pi$
$228$	9.37769	−	5.41421i	0.621053	−	0.358565i
$229$			21.3137i			1.40845i	0.709977	+	0.704225i	$0.248705\pi$
$229$			21.3137i			1.40845i	−0.709977	+	0.704225i	$0.751295\pi$
$230$	−13.6569	−	23.6544i	−0.900506	−	1.55972i
$231$	2.82843	−	4.89898i	0.186097	−	0.322329i
$232$	7.64564	+	4.41421i	0.501961	+	0.289807i
$233$	26.9706			1.76690			0.883450	−	0.468525i	$-0.155214\pi$
$233$	26.9706			1.76690			0.883450	+	0.468525i	$0.155214\pi$
$234$		0			0
$235$	−0.970563			−0.0633125
$236$	−12.1244	−	7.00000i	−0.789228	−	0.455661i
$237$	−5.65685	+	9.79796i	−0.367452	+	0.636446i
$238$	−12.4853	−	21.6251i	−0.809301	−	1.40175i
$239$		−	2.00000i		−	0.129369i	−0.997906	−	0.0646846i	$-0.979396\pi$
$239$		−	2.00000i		−	0.129369i	0.997906	−	0.0646846i	$-0.0206041\pi$
$240$	−7.34847	+	4.24264i	−0.474342	+	0.273861i
$241$	10.0951	−	5.82843i	0.650285	−	0.375442i	−0.138281	−	0.990393i	$-0.544158\pi$
$241$	10.0951	−	5.82843i	0.650285	−	0.375442i	0.788565	+	0.614951i	$0.210824\pi$
$242$			16.8995i			1.08634i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−17.8284	+	30.8797i	−1.14135	+	1.97687i
$245$	−2.44949	−	1.41421i	−0.156492	−	0.0903508i
$246$	26.1421			1.66676
$247$		0			0
$248$	30.1421			1.91403
$249$	−6.63103	−	3.82843i	−0.420224	−	0.242617i
$250$	−6.82843	+	11.8272i	−0.431868	+	0.748017i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$			10.8284i			0.682127i
$253$	−6.92820	+	4.00000i	−0.435572	+	0.251478i
$254$	11.8272	−	6.82843i	0.742103	−	0.428454i
$255$		−	10.3431i		−	0.647713i
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	−7.82843	+	13.5592i	−0.488324	+	0.845802i	−0.999910	−	0.0134304i	$-0.995725\pi$
$257$	−7.82843	+	13.5592i	−0.488324	+	0.845802i	0.511586	+	0.859232i	$0.329058\pi$
$258$	20.1903	+	11.6569i	1.25699	+	0.725724i
$259$	10.3431			0.642692
$260$		0			0
$261$	2.00000			0.123797
$262$	16.7262	+	9.65685i	1.03335	+	0.596602i
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	−0.989561	−	0.144112i	$-0.953967\pi$
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	0.619586	+	0.784929i	$0.287301\pi$
$264$	4.41421	+	7.64564i	0.271676	+	0.470557i
$265$			5.65685i			0.347498i
$266$	−16.7262	+	9.65685i	−1.02555	+	0.592100i
$267$	7.94282	−	4.58579i	0.486092	−	0.280646i
$268$			4.48528i			0.273982i
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$	−3.41421	+	5.91359i	−0.207782	+	0.359890i
$271$	−10.2182	−	5.89949i	−0.620713	−	0.358369i	0.156434	−	0.987688i	$-0.450000\pi$
$271$	−10.2182	−	5.89949i	−0.620713	−	0.358369i	−0.777147	+	0.629320i	$0.783334\pi$
$272$	10.9706			0.665188
$273$		0			0
$274$	12.4853			0.754263
$275$	−5.19615	−	3.00000i	−0.313340	−	0.180907i
$276$	7.65685	−	13.2621i	0.460888	−	0.798282i
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$			36.9706i			2.21735i
$279$	5.91359	−	3.41421i	0.354037	−	0.204404i
$280$	30.5826	−	17.6569i	1.82766	−	1.05520i
$281$			26.8284i			1.60045i	0.599700	+	0.800225i	$0.295287\pi$
$281$			26.8284i			1.60045i	−0.599700	+	0.800225i	$0.704713\pi$
$282$	−0.414214	−	0.717439i	−0.0246661	−	0.0427229i
$283$	−2.48528	+	4.30463i	−0.147735	+	0.255884i	−0.930390	−	0.366572i	$-0.880531\pi$
$283$	−2.48528	+	4.30463i	−0.147735	+	0.255884i	0.782655	+	0.622455i	$0.213865\pi$
$284$	−6.63103	−	3.82843i	−0.393479	−	0.227175i
$285$	−8.00000			−0.473879
$286$		0			0
$287$	−30.6274			−1.80788
$288$	1.37333	+	0.792893i	0.0809243	+	0.0467217i
$289$	1.81371	−	3.14144i	0.106689	−	0.184790i
$290$	−6.82843	−	11.8272i	−0.400979	−	0.694516i
$291$			7.65685i			0.448853i
$292$	−38.6485	+	22.3137i	−2.26173	+	1.30581i
$293$	−22.6398	+	13.0711i	−1.32263	+	0.763620i	−0.984147	−	0.177353i	$-0.943247\pi$
$293$	−22.6398	+	13.0711i	−1.32263	+	0.763620i	−0.338481	+	0.940973i	$0.609913\pi$
$294$		−	2.41421i		−	0.140800i
$295$	5.17157	+	8.95743i	0.301101	+	0.521522i
$296$	−8.07107	+	13.9795i	−0.469121	+	0.812542i
$297$	1.73205	+	1.00000i	0.100504	+	0.0580259i
$298$	−35.7990			−2.07378
$299$		0			0
$300$	11.4853			0.663103
$301$	−23.6544	−	13.6569i	−1.36341	−	0.787168i
$302$	−24.7279	+	42.8300i	−1.42293	+	2.46459i
$303$	−1.82843	−	3.16693i	−0.105040	−	0.181935i
$304$		−	8.48528i		−	0.486664i
$305$	22.8138	−	13.1716i	1.30632	−	0.754202i
$306$	7.64564	−	4.41421i	0.437072	−	0.252344i
$307$		−	17.1716i		−	0.980033i	−0.871713	−	0.490017i	$-0.836991\pi$
$307$		−	17.1716i		−	0.980033i	0.871713	−	0.490017i	$-0.163009\pi$
$308$	−10.8284	−	18.7554i	−0.617007	−	1.06869i
$309$	6.82843	−	11.8272i	0.388456	−	0.672825i
$310$	−40.3805	−	23.3137i	−2.29346	−	1.32413i
$311$	−34.6274			−1.96354			−0.981770	−	0.190071i	$-0.939128\pi$
$311$	−34.6274			−1.96354			−0.981770	+	0.190071i	$0.939128\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	20.9077	+	12.0711i	1.17989	+	0.681210i
$315$	4.00000	−	6.92820i	0.225374	−	0.390360i
$316$	21.6569	+	37.5108i	1.21829	+	2.11015i
$317$			8.48528i			0.476581i	0.971194	+	0.238290i	$0.0765870\pi$
$317$			8.48528i			0.476581i	−0.971194	+	0.238290i	$0.923413\pi$
$318$	−4.18154	+	2.41421i	−0.234489	+	0.135382i
$319$	−3.46410	+	2.00000i	−0.193952	+	0.111979i
$320$		−	27.7990i		−	1.55401i
$321$	−5.65685	−	9.79796i	−0.315735	−	0.546869i
$322$	−13.6569	+	23.6544i	−0.761067	+	1.31821i
$323$	8.95743	+	5.17157i	0.498405	+	0.287754i
$324$	−3.82843			−0.212690
$325$		0			0
$326$	−31.7990			−1.76118
$327$	−14.9941	−	8.65685i	−0.829176	−	0.478725i
$328$	23.8995	−	41.3951i	1.31963	−	2.28566i
$329$	0.485281	+	0.840532i	0.0267544	+	0.0463400i
$330$		−	13.6569i		−	0.751785i
$331$	1.85514	−	1.07107i	0.101968	−	0.0588712i	−0.448149	−	0.893959i	$-0.647917\pi$
$331$	1.85514	−	1.07107i	0.101968	−	0.0588712i	0.550117	+	0.835088i	$0.314583\pi$
$332$	−25.3864	+	14.6569i	−1.39326	+	0.804399i
$333$			3.65685i			0.200394i
$334$	9.24264	+	16.0087i	0.505735	+	0.875958i
$335$	1.65685	−	2.86976i	0.0905236	−	0.156792i
$336$	7.34847	+	4.24264i	0.400892	+	0.231455i
$337$	13.3137			0.725244			0.362622	−	0.931936i	$-0.381882\pi$
$337$	13.3137			0.725244			0.362622	+	0.931936i	$0.381882\pi$
$338$		0			0
$339$	17.3137			0.940352
$340$	−34.2929	−	19.7990i	−1.85979	−	1.07375i
$341$	−6.82843	+	11.8272i	−0.369780	+	0.640478i
$342$	−3.41421	−	5.91359i	−0.184620	−	0.319770i
$343$		−	16.9706i		−	0.916324i
$344$	36.9164	−	21.3137i	1.99040	−	1.14916i
$345$	−9.79796	+	5.65685i	−0.527504	+	0.304555i
$346$			0.828427i			0.0445365i
$347$	15.6569	+	27.1185i	0.840504	+	1.45580i	0.889469	+	0.456995i	$0.151074\pi$
$347$	15.6569	+	27.1185i	0.840504	+	1.45580i	−0.0489652	+	0.998800i	$0.515592\pi$
$348$	3.82843	−	6.63103i	0.205225	−	0.355461i
$349$	6.63103	+	3.82843i	0.354951	+	0.204931i	0.666864	−	0.745180i	$-0.267636\pi$
$349$	6.63103	+	3.82843i	0.354951	+	0.204931i	−0.311913	+	0.950111i	$0.600970\pi$
$350$	−20.4853			−1.09498
$351$		0			0
$352$	−3.17157			−0.169045
$353$	15.1172	+	8.72792i	0.804608	+	0.464540i	0.845080	−	0.534640i	$-0.179553\pi$
$353$	15.1172	+	8.72792i	0.804608	+	0.464540i	−0.0404722	+	0.999181i	$0.512886\pi$
$354$	−4.41421	+	7.64564i	−0.234613	+	0.406361i
$355$	2.82843	+	4.89898i	0.150117	+	0.260011i
$356$		−	35.1127i		−	1.86097i
$357$	−8.95743	+	5.17157i	−0.474077	+	0.273709i
$358$	1.43488	−	0.828427i	0.0758357	−	0.0437837i
$359$			1.02944i			0.0543316i	0.999631	+	0.0271658i	$0.00864821\pi$
$359$			1.02944i			0.0543316i	−0.999631	+	0.0271658i	$0.991352\pi$
$360$	6.24264	+	10.8126i	0.329016	+	0.569873i
$361$	−5.50000	+	9.52628i	−0.289474	+	0.501383i
$362$	29.2708	+	16.8995i	1.53844	+	0.888218i
$363$	7.00000			0.367405
$364$		0			0
$365$	32.9706			1.72576
$366$	19.4728	+	11.2426i	1.01786	+	0.587662i
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	−0.361874	−	0.932227i	$-0.617863\pi$
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	0.988269	−	0.152721i	$-0.0488036\pi$
$368$	−6.00000	−	10.3923i	−0.312772	−	0.541736i
$369$		−	10.8284i		−	0.563705i
$370$	21.6251	−	12.4853i	1.12424	−	0.649079i
$371$	4.89898	−	2.82843i	0.254342	−	0.146845i
$372$		−	26.1421i		−	1.35541i
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	0.707055	−	0.707159i	$-0.250023\pi$
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	−0.965945	+	0.258748i	$0.916690\pi$
$374$	−8.82843	+	15.2913i	−0.456507	+	0.790693i
$375$	4.89898	+	2.82843i	0.252982	+	0.146059i
$376$	−1.51472			−0.0781156
$377$		0			0
$378$	6.82843			0.351216
$379$	−14.2767	−	8.24264i	−0.733343	−	0.423396i	0.0863007	−	0.996269i	$-0.472495\pi$
$379$	−14.2767	−	8.24264i	−0.733343	−	0.423396i	−0.819644	+	0.572873i	$0.805829\pi$
$380$	−15.3137	+	26.5241i	−0.785577	+	1.36066i
$381$	−2.82843	−	4.89898i	−0.144905	−	0.250982i
$382$		−	46.6274i		−	2.38567i
$383$	2.57258	−	1.48528i	0.131453	−	0.0758943i	−0.432832	−	0.901475i	$-0.642485\pi$
$383$	2.57258	−	1.48528i	0.131453	−	0.0758943i	0.564284	+	0.825581i	$0.309152\pi$
$384$	17.8023	−	10.2782i	0.908471	−	0.524506i
$385$			16.0000i			0.815436i
$386$	−20.8995	−	36.1990i	−1.06376	−	1.84248i
$387$	4.82843	−	8.36308i	0.245443	−	0.425119i
$388$	25.3864	+	14.6569i	1.28880	+	0.744089i
$389$	−6.97056			−0.353422			−0.176711	−	0.984263i	$-0.556546\pi$
$389$	−6.97056			−0.353422			−0.176711	+	0.984263i	$0.556546\pi$
$390$		0			0
$391$	14.6274			0.739740
$392$	−3.82282	−	2.20711i	−0.193082	−	0.111476i
$393$	4.00000	−	6.92820i	0.201773	−	0.349482i
$394$	19.8995	+	34.4669i	1.00252	+	1.73642i
$395$		−	32.0000i		−	1.61009i
$396$	6.63103	−	3.82843i	0.333222	−	0.192386i
$397$	−2.57258	+	1.48528i	−0.129114	+	0.0745441i	−0.563166	−	0.826344i	$-0.690417\pi$
$397$	−2.57258	+	1.48528i	−0.129114	+	0.0745441i	0.434052	+	0.900888i	$0.357083\pi$
$398$		−	24.9706i		−	1.25166i
$399$	4.00000	+	6.92820i	0.200250	+	0.346844i
$400$	4.50000	−	7.79423i	0.225000	−	0.389711i
$401$	1.85514	+	1.07107i	0.0926415	+	0.0534866i	0.545605	−	0.838042i	$-0.316300\pi$
$401$	1.85514	+	1.07107i	0.0926415	+	0.0534866i	−0.452964	+	0.891529i	$0.649633\pi$
$402$	2.82843			0.141069
$403$		0			0
$404$	−14.0000			−0.696526
$405$	2.44949	+	1.41421i	0.121716	+	0.0702728i
$406$	−6.82843	+	11.8272i	−0.338889	+	0.586973i
$407$	−3.65685	−	6.33386i	−0.181264	−	0.313958i
$408$		−	16.1421i		−	0.799155i
$409$	0.891519	−	0.514719i	0.0440828	−	0.0254512i	−0.477797	−	0.878470i	$-0.658564\pi$
$409$	0.891519	−	0.514719i	0.0440828	−	0.0254512i	0.521879	+	0.853019i	$0.325231\pi$
$410$	−64.0349	+	36.9706i	−3.16246	+	1.82585i
$411$		−	5.17157i		−	0.255095i
$412$	−26.1421	−	45.2795i	−1.28793	−	2.23076i
$413$	5.17157	−	8.95743i	0.254476	−	0.440766i
$414$	−8.36308	−	4.82843i	−0.411023	−	0.237304i
$415$	21.6569			1.06309
$416$		0			0
$417$	15.3137			0.749916
$418$	11.8272	+	6.82843i	0.578486	+	0.333989i
$419$	15.3137	−	26.5241i	0.748124	−	1.29579i	−0.200597	−	0.979674i	$-0.564288\pi$
$419$	15.3137	−	26.5241i	0.748124	−	1.29579i	0.948721	−	0.316114i	$-0.102378\pi$
$420$	−15.3137	−	26.5241i	−0.747232	−	1.29424i
$421$		−	14.6863i		−	0.715766i	−0.933766	−	0.357883i	$-0.883499\pi$
$421$		−	14.6863i		−	0.715766i	0.933766	−	0.357883i	$-0.116501\pi$
$422$	−25.0892	+	14.4853i	−1.22133	+	0.705132i
$423$	−0.297173	+	0.171573i	−0.0144490	+	0.00834216i
$424$			8.82843i			0.428746i
$425$	5.48528	+	9.50079i	0.266075	+	0.460856i
$426$	−2.41421	+	4.18154i	−0.116969	+	0.202596i
$427$	−22.8138	−	13.1716i	−1.10404	−	0.637417i
$428$	−43.3137			−2.09365
$429$		0			0
$430$	−65.9411			−3.17996
$431$	17.0233	+	9.82843i	0.819985	+	0.473419i	0.850411	−	0.526118i	$-0.176353\pi$
$431$	17.0233	+	9.82843i	0.819985	+	0.473419i	−0.0304262	+	0.999537i	$0.509686\pi$
$432$	−1.50000	+	2.59808i	−0.0721688	+	0.125000i
$433$	0.656854	+	1.13770i	0.0315664	+	0.0546746i	0.881377	−	0.472414i	$-0.156617\pi$
$433$	0.656854	+	1.13770i	0.0315664	+	0.0546746i	−0.849811	+	0.527088i	$0.823284\pi$
$434$			46.6274i			2.23819i
$435$	−4.89898	+	2.82843i	−0.234888	+	0.135613i
$436$	−57.4039	+	33.1421i	−2.74915	+	1.58722i
$437$		−	11.3137i		−	0.541208i
$438$	14.0711	+	24.3718i	0.672342	+	1.16453i
$439$	−8.48528	+	14.6969i	−0.404980	+	0.701447i	−0.994319	−	0.106439i	$-0.966055\pi$
$439$	−8.48528	+	14.6969i	−0.404980	+	0.701447i	0.589339	+	0.807886i	$0.299388\pi$
$440$	−21.6251	−	12.4853i	−1.03094	−	0.595212i
$441$	−1.00000			−0.0476190
$442$		0			0
$443$	41.9411			1.99268			0.996342	−	0.0854611i	$-0.0272364\pi$
$443$	41.9411			1.99268			0.996342	+	0.0854611i	$0.0272364\pi$
$444$	12.1244	+	7.00000i	0.575396	+	0.332205i
$445$	−12.9706	+	22.4657i	−0.614864	+	1.06498i
$446$	−5.41421	−	9.37769i	−0.256370	−	0.444047i
$447$			14.8284i			0.701361i
$448$	−24.0746	+	13.8995i	−1.13742	+	0.656689i
$449$	6.75412	−	3.89949i	0.318747	−	0.184029i	−0.332087	−	0.943249i	$-0.607753\pi$
$449$	6.75412	−	3.89949i	0.318747	−	0.184029i	0.650834	+	0.759220i	$0.274419\pi$
$450$		−	7.24264i		−	0.341421i
$451$	10.8284	+	18.7554i	0.509891	+	0.883157i
$452$	33.1421	−	57.4039i	1.55887	−	2.70005i
$453$	17.7408	+	10.2426i	0.833534	+	0.481241i
$454$	12.8284			0.602068
$455$		0			0
$456$	−12.4853			−0.584677
$457$	3.16693	+	1.82843i	0.148143	+	0.0855302i	0.572239	−	0.820087i	$-0.306075\pi$
$457$	3.16693	+	1.82843i	0.148143	+	0.0855302i	−0.424096	+	0.905617i	$0.639408\pi$
$458$	25.7279	−	44.5621i	1.20219	−	2.08225i
$459$	−1.82843	−	3.16693i	−0.0853437	−	0.147820i
$460$			43.3137i			2.01951i
$461$	−9.37769	+	5.41421i	−0.436763	+	0.252165i	−0.702223	−	0.711957i	$-0.747809\pi$
$461$	−9.37769	+	5.41421i	−0.436763	+	0.252165i	0.265461	+	0.964122i	$0.414476\pi$
$462$	−11.8272	+	6.82843i	−0.550250	+	0.317687i
$463$		−	7.51472i		−	0.349239i	−0.984636	−	0.174619i	$-0.944131\pi$
$463$		−	7.51472i		−	0.349239i	0.984636	−	0.174619i	$-0.0558695\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$	−9.65685	+	16.7262i	−0.447826	+	0.775657i
$466$	−56.3893	−	32.5563i	−2.61218	−	1.50814i
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	−3.31371			−0.153013
$470$	2.02922	+	1.17157i	0.0936011	+	0.0540406i
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$	8.07107	+	13.9795i	0.371501	+	0.643459i
$473$			19.3137i			0.888045i
$474$	23.6544	−	13.6569i	1.08648	−	0.627280i
$475$	7.34847	−	4.24264i	0.337171	−	0.194666i
$476$			39.5980i			1.81497i
$477$	1.00000	+	1.73205i	0.0457869	+	0.0793052i
$478$	−2.41421	+	4.18154i	−0.110424	+	0.191259i
$479$	−2.32640	−	1.34315i	−0.106296	−	0.0613699i	0.445910	−	0.895078i	$-0.352880\pi$
$479$	−2.32640	−	1.34315i	−0.106296	−	0.0613699i	−0.552205	+	0.833708i	$0.686214\pi$
$480$	−4.48528			−0.204724
$481$		0			0
$482$	−28.1421			−1.28184
$483$	9.79796	+	5.65685i	0.445823	+	0.257396i
$484$	13.3995	−	23.2086i	0.609068	−	1.05494i
$485$	−10.8284	−	18.7554i	−0.491694	−	0.851638i
$486$			2.41421i			0.109511i
$487$	−27.5387	+	15.8995i	−1.24790	+	0.720475i	−0.970690	−	0.240335i	$-0.922743\pi$
$487$	−27.5387	+	15.8995i	−1.24790	+	0.720475i	−0.277209	+	0.960810i	$0.589409\pi$
$488$	35.6046	−	20.5563i	1.61175	−	0.930542i
$489$			13.1716i			0.595639i
$490$	3.41421	+	5.91359i	0.154238	+	0.267149i
$491$	−7.31371	+	12.6677i	−0.330063	+	0.571686i	−0.982524	−	0.186136i	$-0.940403\pi$
$491$	−7.31371	+	12.6677i	−0.330063	+	0.571686i	0.652461	+	0.757822i	$0.273737\pi$
$492$	−35.9018	−	20.7279i	−1.61858	−	0.934487i
$493$	7.31371			0.329393
$494$		0			0
$495$	−5.65685			−0.254257
$496$	−17.7408	−	10.2426i	−0.796584	−	0.459908i
$497$	2.82843	−	4.89898i	0.126872	−	0.219749i
$498$	9.24264	+	16.0087i	0.414173	+	0.717368i
$499$			2.14214i			0.0958952i	0.998850	+	0.0479476i	$0.0152680\pi$
$499$			2.14214i			0.0958952i	−0.998850	+	0.0479476i	$0.984732\pi$
$500$	18.7554	−	10.8284i	0.838766	−	0.484262i
$501$	6.63103	−	3.82843i	0.296253	−	0.171042i
$502$		0			0
$503$	−7.65685	−	13.2621i	−0.341402	−	0.591326i	0.643291	−	0.765622i	$-0.277569\pi$
$503$	−7.65685	−	13.2621i	−0.341402	−	0.591326i	−0.984693	+	0.174296i	$0.944235\pi$
$504$	6.24264	−	10.8126i	0.278069	−	0.481630i
$505$	8.95743	+	5.17157i	0.398600	+	0.230132i
$506$	19.3137			0.858599
$507$		0			0
$508$	−21.6569			−0.960868
$509$	−24.0746	−	13.8995i	−1.06709	−	0.616084i	−0.139705	−	0.990193i	$-0.544615\pi$
$509$	−24.0746	−	13.8995i	−1.06709	−	0.616084i	−0.927385	+	0.374109i	$0.877949\pi$
$510$	−12.4853	+	21.6251i	−0.552858	+	0.957577i
$511$	−16.4853	−	28.5533i	−0.729266	−	1.26313i
$512$		−	31.2426i		−	1.38074i
$513$	−2.44949	+	1.41421i	−0.108148	+	0.0624391i
$514$	32.7349	−	18.8995i	1.44387	−	0.833621i
$515$			38.6274i			1.70213i
$516$	−18.4853	−	32.0174i	−0.813769	−	1.40949i
$517$	0.343146	−	0.594346i	0.0150915	−	0.0261393i
$518$	−21.6251	−	12.4853i	−0.950154	−	0.548572i
$519$	0.343146			0.0150624
$520$		0			0
$521$	2.68629			0.117689			0.0588443	−	0.998267i	$-0.481258\pi$
$521$	2.68629			0.117689			0.0588443	+	0.998267i	$0.481258\pi$
$522$	−4.18154	−	2.41421i	−0.183021	−	0.105667i
$523$	−3.65685	+	6.33386i	−0.159903	+	0.276960i	−0.934834	−	0.355086i	$-0.884452\pi$
$523$	−3.65685	+	6.33386i	−0.159903	+	0.276960i	0.774930	+	0.632046i	$0.217785\pi$
$524$	−15.3137	−	26.5241i	−0.668982	−	1.15871i
$525$			8.48528i			0.370328i
$526$	25.0892	−	14.4853i	1.09394	−	0.631588i
$527$	21.6251	−	12.4853i	0.942006	−	0.543867i
$528$		−	6.00000i		−	0.261116i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	6.82843	−	11.8272i	0.296608	−	0.513740i
$531$	3.16693	+	1.82843i	0.137433	+	0.0793470i
$532$	30.6274			1.32787
$533$		0			0
$534$	−22.1421			−0.958184
$535$	27.7128	+	16.0000i	1.19813	+	0.691740i
$536$	2.58579	−	4.47871i	0.111689	−	0.193451i
$537$	−0.343146	−	0.594346i	−0.0148078	−	0.0256479i
$538$			43.4558i			1.87351i
$539$	1.73205	−	1.00000i	0.0746047	−	0.0430730i
$540$	9.37769	−	5.41421i	0.403552	−	0.232991i
$541$			10.0000i			0.429934i	0.976621	+	0.214967i	$0.0689643\pi$
$541$			10.0000i			0.429934i	−0.976621	+	0.214967i	$0.931036\pi$
$542$	14.2426	+	24.6690i	0.611774	+	1.05962i
$543$	7.00000	−	12.1244i	0.300399	−	0.520306i
$544$	5.02207	+	2.89949i	0.215320	+	0.124315i
$545$	48.9706			2.09767
$546$		0			0
$547$	0.686292			0.0293437			0.0146719	−	0.999892i	$-0.495330\pi$
$547$	0.686292			0.0293437			0.0146719	+	0.999892i	$0.495330\pi$
$548$	−17.1464	−	9.89949i	−0.732459	−	0.422885i
$549$	4.65685	−	8.06591i	0.198750	−	0.344245i
$550$	7.24264	+	12.5446i	0.308827	+	0.534904i
$551$		−	5.65685i		−	0.240990i
$552$	−15.2913	+	8.82843i	−0.650840	+	0.375763i
$553$	−27.7128	+	16.0000i	−1.17847	+	0.680389i
$554$			4.82843i			0.205140i
$555$	−5.17157	−	8.95743i	−0.219521	−	0.380222i
$556$	29.3137	−	50.7728i	1.24318	−	2.15325i
$557$	−27.5387	−	15.8995i	−1.16685	−	0.673683i	−0.213917	−	0.976852i	$-0.568622\pi$
$557$	−27.5387	−	15.8995i	−1.16685	−	0.673683i	−0.952937	+	0.303169i	$0.901955\pi$
$558$	−16.4853			−0.697878
$559$		0			0
$560$	−24.0000			−1.01419
$561$	6.33386	+	3.65685i	0.267416	+	0.154393i
$562$	32.3848	−	56.0921i	1.36607	−	2.36610i
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	0.905088	−	0.425223i	$-0.139804\pi$
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	−0.820798	+	0.571218i	$0.806471\pi$
$564$			1.31371i			0.0553171i
$565$	−42.4098	+	24.4853i	−1.78419	+	1.03010i
$566$	10.3923	−	6.00000i	0.436821	−	0.252199i
$567$		−	2.82843i		−	0.118783i
$568$	4.41421	+	7.64564i	0.185216	+	0.320804i
$569$	−4.51472	+	7.81972i	−0.189267	+	0.327820i	−0.945006	−	0.327053i	$-0.893944\pi$
$569$	−4.51472	+	7.81972i	−0.189267	+	0.327820i	0.755739	+	0.654873i	$0.227278\pi$
$570$	16.7262	+	9.65685i	0.700582	+	0.404481i
$571$	−20.9706			−0.877591			−0.438795	−	0.898587i	$-0.644595\pi$
$571$	−20.9706			−0.877591			−0.438795	+	0.898587i	$0.644595\pi$
$572$		0			0
$573$	−19.3137			−0.806842
$574$	64.0349	+	36.9706i	2.67276	+	1.54312i
$575$	6.00000	−	10.3923i	0.250217	−	0.433389i
$576$	−4.91421	−	8.51167i	−0.204759	−	0.354653i
$577$		−	35.9411i		−	1.49625i	−0.663559	−	0.748124i	$-0.730955\pi$
$577$		−	35.9411i		−	1.49625i	0.663559	−	0.748124i	$-0.269045\pi$
$578$	−7.58410	+	4.37868i	−0.315457	+	0.182129i
$579$	−14.9941	+	8.65685i	−0.623134	+	0.359767i
$580$			21.6569i			0.899252i
$581$	−10.8284	−	18.7554i	−0.449239	−	0.778105i
$582$	9.24264	−	16.0087i	0.383120	−	0.663583i
$583$	−3.46410	−	2.00000i	−0.143468	−	0.0828315i
$584$	51.4558			2.12926
$585$		0			0
$586$	63.1127			2.60716
$587$	19.8931	+	11.4853i	0.821076	+	0.474048i	0.850787	−	0.525510i	$-0.176126\pi$
$587$	19.8931	+	11.4853i	0.821076	+	0.474048i	−0.0297116	+	0.999559i	$0.509459\pi$
$588$	−1.91421	+	3.31552i	−0.0789408	+	0.136730i
$589$	−9.65685	−	16.7262i	−0.397904	−	0.689190i
$590$		−	24.9706i		−	1.02802i
$591$	14.2767	−	8.24264i	0.587264	−	0.339057i
$592$	9.50079	−	5.48528i	0.390480	−	0.225444i
$593$		−	3.51472i		−	0.144332i	−0.997393	−	0.0721661i	$-0.977009\pi$
$593$		−	3.51472i		−	0.144332i	0.997393	−	0.0721661i	$-0.0229912\pi$
$594$	−2.41421	−	4.18154i	−0.0990564	−	0.171571i
$595$	14.6274	−	25.3354i	0.599666	−	1.03865i
$596$	49.1639	+	28.3848i	2.01383	+	1.16269i
$597$	−10.3431			−0.423317
$598$		0			0
$599$	−0.686292			−0.0280411			−0.0140206	−	0.999902i	$-0.504463\pi$
$599$	−0.686292			−0.0280411			−0.0140206	+	0.999902i	$0.504463\pi$
$600$	−11.4685	−	6.62132i	−0.468198	−	0.270314i
$601$	−22.3137	+	38.6485i	−0.910195	+	1.57650i	−0.0964075	+	0.995342i	$0.530735\pi$
$601$	−22.3137	+	38.6485i	−0.910195	+	1.57650i	−0.813788	+	0.581162i	$0.802598\pi$
$602$	32.9706	+	57.1067i	1.34378	+	2.32749i
$603$		−	1.17157i		−	0.0477101i
$604$	67.9193	−	39.2132i	2.76360	−	1.59556i
$605$	−17.1464	+	9.89949i	−0.697101	+	0.402472i
$606$			8.82843i			0.358630i
$607$	12.9706	+	22.4657i	0.526459	+	0.911854i	0.999525	+	0.0308265i	$0.00981393\pi$
$607$	12.9706	+	22.4657i	0.526459	+	0.911854i	−0.473066	+	0.881027i	$0.656853\pi$
$608$	2.24264	−	3.88437i	0.0909511	−	0.157532i
$609$	4.89898	+	2.82843i	0.198517	+	0.114614i
$610$	−63.5980			−2.57501
$611$		0			0
$612$	−14.0000			−0.565916
$613$	−31.4741	−	18.1716i	−1.27123	−	0.733943i	−0.296008	−	0.955186i	$-0.595655\pi$
$613$	−31.4741	−	18.1716i	−1.27123	−	0.733943i	−0.975219	+	0.221243i	$0.928989\pi$
$614$	−20.7279	+	35.9018i	−0.836511	+	1.44888i
$615$	15.3137	+	26.5241i	0.617508	+	1.06956i
$616$			24.9706i			1.00609i
$617$	25.2633	−	14.5858i	1.01706	−	0.587202i	0.103811	−	0.994597i	$-0.466896\pi$
$617$	25.2633	−	14.5858i	1.01706	−	0.587202i	0.913252	+	0.407395i	$0.133563\pi$
$618$	−28.5533	+	16.4853i	−1.14858	+	0.663135i
$619$		−	15.7990i		−	0.635015i	−0.948256	−	0.317508i	$-0.897154\pi$
$619$		−	15.7990i		−	0.635015i	0.948256	−	0.317508i	$-0.102846\pi$
$620$	36.9706	+	64.0349i	1.48477	+	2.57170i
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$	72.3980	+	41.7990i	2.90289	+	1.67599i
$623$	25.9411			1.03931
$624$		0			0
$625$	−31.0000			−1.24000
$626$	−12.5446	−	7.24264i	−0.501384	−	0.289474i
$627$	2.82843	−	4.89898i	0.112956	−	0.195646i
$628$	−19.1421	−	33.1552i	−0.763854	−	1.32303i
$629$			13.3726i			0.533200i
$630$	−16.7262	+	9.65685i	−0.666386	+	0.384738i
$631$	−16.5521	+	9.55635i	−0.658928	+	0.380432i	−0.791868	−	0.610692i	$-0.790891\pi$
$631$	−16.5521	+	9.55635i	−0.658928	+	0.380432i	0.132940	+	0.991124i	$0.457558\pi$
$632$		−	49.9411i		−	1.98655i
$633$	6.00000	+	10.3923i	0.238479	+	0.413057i
$634$	10.2426	−	17.7408i	0.406787	−	0.704576i
$635$	13.8564	+	8.00000i	0.549875	+	0.317470i
$636$	7.65685			0.303614
$637$		0			0
$638$	9.65685			0.382319
$639$	1.73205	+	1.00000i	0.0685189	+	0.0395594i
$640$	−29.0711	+	50.3526i	−1.14913	+	1.99036i
$641$	−13.1421	−	22.7628i	−0.519083	−	0.899078i	−0.999754	−	0.0221773i	$-0.992940\pi$
$641$	−13.1421	−	22.7628i	−0.519083	−	0.899078i	0.480671	−	0.876901i	$-0.340393\pi$
$642$			27.3137i			1.07799i
$643$	−14.8710	+	8.58579i	−0.586456	+	0.338590i	−0.763695	−	0.645577i	$-0.776617\pi$
$643$	−14.8710	+	8.58579i	−0.586456	+	0.338590i	0.177239	+	0.984168i	$0.443283\pi$
$644$	37.5108	−	21.6569i	1.47813	−	0.853400i
$645$			27.3137i			1.07548i
$646$	−12.4853	−	21.6251i	−0.491227	−	0.850830i
$647$	−5.65685	+	9.79796i	−0.222394	+	0.385198i	−0.955534	−	0.294880i	$-0.904720\pi$
$647$	−5.65685	+	9.79796i	−0.222394	+	0.385198i	0.733140	+	0.680077i	$0.238054\pi$
$648$	3.82282	+	2.20711i	0.150175	+	0.0867033i
$649$	−7.31371			−0.287088
$650$		0			0
$651$	19.3137			0.756964
$652$	43.6705	+	25.2132i	1.71027	+	0.987425i
$653$	1.34315	−	2.32640i	0.0525614	−	0.0910389i	−0.838548	−	0.544828i	$-0.816595\pi$
$653$	1.34315	−	2.32640i	0.0525614	−	0.0910389i	0.891109	+	0.453789i	$0.149928\pi$
$654$	20.8995	+	36.1990i	0.817235	+	1.41549i
$655$			22.6274i			0.884126i
$656$	−28.1331	+	16.2426i	−1.09841	+	0.634169i
$657$	10.0951	−	5.82843i	0.393849	−	0.227389i
$658$		−	2.34315i		−	0.0913453i
$659$	12.3431	+	21.3790i	0.480821	+	0.832806i	0.999758	−	0.0220065i	$-0.00700546\pi$
$659$	12.3431	+	21.3790i	0.480821	+	0.832806i	−0.518937	+	0.854812i	$0.673672\pi$
$660$	−10.8284	+	18.7554i	−0.421496	+	0.730052i
$661$	0.891519	+	0.514719i	0.0346761	+	0.0200202i	0.517238	−	0.855842i	$-0.326960\pi$
$661$	0.891519	+	0.514719i	0.0346761	+	0.0200202i	−0.482562	+	0.875862i	$0.660294\pi$
$662$	−5.17157			−0.200999
$663$		0			0
$664$	33.7990			1.31166
$665$	−19.5959	−	11.3137i	−0.759897	−	0.438727i
$666$	4.41421	−	7.64564i	0.171047	−	0.296263i
$667$	−4.00000	−	6.92820i	−0.154881	−	0.268261i
$668$		−	29.3137i		−	1.13418i
$669$	−3.88437	+	2.24264i	−0.150178	+	0.0867055i
$670$	−6.92820	+	4.00000i	−0.267660	+	0.154533i
$671$			18.6274i			0.719103i
$672$	2.24264	+	3.88437i	0.0865117	+	0.149843i
$673$	−14.3137	+	24.7921i	−0.551753	+	0.955664i	0.446395	+	0.894836i	$0.352708\pi$
$673$	−14.3137	+	24.7921i	−0.551753	+	0.955664i	−0.998148	+	0.0608282i	$0.980626\pi$
$674$	−27.8359	−	16.0711i	−1.07220	−	0.619034i
$675$	−3.00000			−0.115470
$676$		0			0
$677$	49.3137			1.89528			0.947640	−	0.319341i	$-0.103462\pi$
$677$	49.3137			1.89528			0.947640	+	0.319341i	$0.103462\pi$
$678$	−36.1990	−	20.8995i	−1.39021	−	0.802640i
$679$	−10.8284	+	18.7554i	−0.415557	+	0.719766i
$680$	22.8284	+	39.5400i	0.875430	+	1.51629i
$681$		−	5.31371i		−	0.203622i
$682$	28.5533	−	16.4853i	1.09336	−	0.631254i
$683$	−17.2695	+	9.97056i	−0.660800	+	0.381513i	−0.792582	−	0.609766i	$-0.791264\pi$
$683$	−17.2695	+	9.97056i	−0.660800	+	0.381513i	0.131782	+	0.991279i	$0.457930\pi$
$684$			10.8284i			0.414035i
$685$	7.31371	+	12.6677i	0.279442	+	0.484008i
$686$	−20.4853	+	35.4815i	−0.782132	+	1.35469i
$687$	−18.4582	−	10.6569i	−0.704225	−	0.406584i
$688$	−28.9706			−1.10449
$689$		0			0
$690$	27.3137			1.03982
$691$	−29.5680	−	17.0711i	−1.12482	−	0.649414i	−0.182192	−	0.983263i	$-0.558319\pi$
$691$	−29.5680	−	17.0711i	−1.12482	−	0.649414i	−0.942627	+	0.333849i	$0.891652\pi$
$692$	0.656854	−	1.13770i	0.0249699	−	0.0432491i
$693$	2.82843	+	4.89898i	0.107443	+	0.186097i
$694$		−	75.5980i		−	2.86966i
$695$	−37.5108	+	21.6569i	−1.42286	+	0.821491i
$696$	−7.64564	+	4.41421i	−0.289807	+	0.167320i
$697$		−	39.5980i		−	1.49988i
$698$	−9.24264	−	16.0087i	−0.349839	−	0.605939i
$699$	−13.4853	+	23.3572i	−0.510060	+	0.883450i
$700$	28.1331	+	16.2426i	1.06333	+	0.613914i
$701$	−38.9706			−1.47190			−0.735949	−	0.677037i	$-0.763264\pi$
$701$	−38.9706			−1.47190			−0.735949	+	0.677037i	$0.763264\pi$
$702$		0			0
$703$	10.3431			0.390099
$704$	17.0233	+	9.82843i	0.641591	+	0.370423i
$705$	0.485281	−	0.840532i	0.0182768	−	0.0316563i
$706$	−21.0711	−	36.4962i	−0.793020	−	1.37355i
$707$		−	10.3431i		−	0.388994i
$708$	12.1244	−	7.00000i	0.455661	−	0.263076i
$709$	35.1844	−	20.3137i	1.32138	−	0.762897i	0.337429	−	0.941351i	$-0.390443\pi$
$709$	35.1844	−	20.3137i	1.32138	−	0.762897i	0.983948	+	0.178454i	$0.0571095\pi$
$710$		−	13.6569i		−	0.512533i
$711$	−5.65685	−	9.79796i	−0.212149	−	0.367452i
$712$	−20.2426	+	35.0613i	−0.758625	+	1.31398i
$713$	−23.6544	−	13.6569i	−0.885863	−	0.511453i
$714$	24.9706			0.934500
$715$		0			0
$716$	−2.62742			−0.0981912
$717$	1.73205	+	1.00000i	0.0646846	+	0.0373457i
$718$	1.24264	−	2.15232i	0.0463749	−	0.0803237i
$719$	18.9706	+	32.8580i	0.707483	+	1.22540i	0.965788	+	0.259333i	$0.0835026\pi$
$719$	18.9706	+	32.8580i	0.707483	+	1.22540i	−0.258305	+	0.966063i	$0.583164\pi$
$720$		−	8.48528i		−	0.316228i
$721$	33.4523	−	19.3137i	1.24583	−	0.719280i
$722$	22.9985	−	13.2782i	0.855915	−	0.494162i
$723$			11.6569i			0.433523i
$724$	−26.7990	−	46.4172i	−0.995977	−	1.72508i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	−14.6354	−	8.44975i	−0.543170	−	0.313600i
$727$	21.6569			0.803208			0.401604	−	0.915813i	$-0.368453\pi$
$727$	21.6569			0.803208			0.401604	+	0.915813i	$0.368453\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−68.9339	−	39.7990i	−2.55136	−	1.47303i
$731$	17.6569	−	30.5826i	0.653062	−	1.13114i
$732$	−17.8284	−	30.8797i	−0.658958	−	1.14135i
$733$		−	8.62742i		−	0.318661i	−0.987225	−	0.159330i	$-0.949066\pi$
$733$		−	8.62742i		−	0.318661i	0.987225	−	0.159330i	$-0.0509335\pi$
$734$	−50.1785	+	28.9706i	−1.85212	+	1.06932i
$735$	2.44949	−	1.41421i	0.0903508	−	0.0521641i
$736$		−	6.34315i		−	0.233811i
$737$	1.17157	+	2.02922i	0.0431554	+	0.0747474i
$738$	−13.0711	+	22.6398i	−0.481153	+	0.833381i
$739$	−8.78335	−	5.07107i	−0.323101	−	0.186542i	0.329673	−	0.944095i	$-0.393061\pi$
$739$	−8.78335	−	5.07107i	−0.323101	−	0.186542i	−0.652774	+	0.757553i	$0.726395\pi$
$740$	−39.5980			−1.45565
$741$		0			0
$742$	−13.6569			−0.501359
$743$	1.73205	+	1.00000i	0.0635428	+	0.0366864i	0.531435	−	0.847099i	$-0.321653\pi$
$743$	1.73205	+	1.00000i	0.0635428	+	0.0366864i	−0.467892	+	0.883786i	$0.654986\pi$
$744$	−15.0711	+	26.1039i	−0.552532	+	0.957014i
$745$	−20.9706	−	36.3221i	−0.768302	−	1.33074i
$746$			24.1421i			0.883906i
$747$	6.63103	−	3.82843i	0.242617	−	0.140075i
$748$	24.2487	−	14.0000i	0.886621	−	0.511891i
$749$		−	32.0000i		−	1.16925i
$750$	−6.82843	−	11.8272i	−0.249339	−	0.431868i
$751$	16.4853	−	28.5533i	0.601556	−	1.04193i	−0.391029	−	0.920378i	$-0.627881\pi$
$751$	16.4853	−	28.5533i	0.601556	−	1.04193i	0.992586	−	0.121548i	$-0.0387858\pi$
$752$	0.891519	+	0.514719i	0.0325103	+	0.0187699i
$753$		0			0
$754$		0			0
$755$	−57.9411			−2.10869
$756$	−9.37769	−	5.41421i	−0.341063	−	0.196913i
$757$	7.97056	−	13.8054i	0.289695	−	0.501767i	−0.684042	−	0.729443i	$-0.739779\pi$
$757$	7.97056	−	13.8054i	0.289695	−	0.501767i	0.973737	+	0.227676i	$0.0731128\pi$
$758$	19.8995	+	34.4669i	0.722782	+	1.25190i
$759$		−	8.00000i		−	0.290382i
$760$	30.5826	−	17.6569i	1.10935	−	0.640481i
$761$	13.4361	−	7.75736i	0.487060	−	0.281204i	−0.236294	−	0.971682i	$-0.575933\pi$
$761$	13.4361	−	7.75736i	0.487060	−	0.281204i	0.723354	+	0.690478i	$0.242600\pi$
$762$			13.6569i			0.494736i
$763$	−24.4853	−	42.4098i	−0.886427	−	1.53534i
$764$	−36.9706	+	64.0349i	−1.33755	+	2.31670i
$765$	8.95743	+	5.17157i	0.323856	+	0.186979i
$766$	−7.17157			−0.259119
$767$		0			0
$768$	−29.9706			−1.08147
$769$	36.3731	+	21.0000i	1.31165	+	0.757279i	0.982369	−	0.186954i	$-0.0598615\pi$
$769$	36.3731	+	21.0000i	1.31165	+	0.757279i	0.329278	+	0.944233i	$0.393195\pi$
$770$	19.3137	−	33.4523i	0.696018	−	1.20554i
$771$	−7.82843	−	13.5592i	−0.281934	−	0.488324i
$772$			66.2843i			2.38562i
$773$	−5.07306	+	2.92893i	−0.182465	+	0.105346i	−0.588450	−	0.808533i	$-0.700262\pi$
$773$	−5.07306	+	2.92893i	−0.182465	+	0.105346i	0.405985	+	0.913880i	$0.366928\pi$
$774$	−20.1903	+	11.6569i	−0.725724	+	0.418997i
$775$		−	20.4853i		−	0.735853i
$776$	−16.8995	−	29.2708i	−0.606657	−	1.05076i
$777$	−5.17157	+	8.95743i	−0.185529	+	0.321346i
$778$	14.5738	+	8.41421i	0.522498	+	0.301664i
$779$	−30.6274			−1.09734
$780$		0			0
$781$	−4.00000			−0.143131
$782$	−30.5826	−	17.6569i	−1.09363	−	0.631408i
$783$	−1.00000	+	1.73205i	−0.0357371	+	0.0618984i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$			28.2843i			1.00951i
$786$	−16.7262	+	9.65685i	−0.596602	+	0.344449i
$787$	28.3793	−	16.3848i	1.01161	−	0.584054i	0.0999484	−	0.994993i	$-0.468132\pi$
$787$	28.3793	−	16.3848i	1.01161	−	0.584054i	0.911663	+	0.410938i	$0.134799\pi$
$788$		−	63.1127i		−	2.24830i
$789$	−6.00000	−	10.3923i	−0.213606	−	0.369976i
$790$	−38.6274	+	66.9046i	−1.37430	+	2.38036i
$791$	42.4098	+	24.4853i	1.50792	+	0.870596i
$792$	−8.82843			−0.313704
$793$		0			0
$794$	7.17157			0.254510
$795$	−4.89898	−	2.82843i	−0.173749	−	0.100314i
$796$	−19.7990	+	34.2929i	−0.701757	+	1.21548i
$797$	17.8284	+	30.8797i	0.631515	+	1.09382i	0.987242	+	0.159227i	$0.0509000\pi$
$797$	17.8284	+	30.8797i	0.631515	+	1.09382i	−0.355727	+	0.934590i	$0.615767\pi$
$798$		−	19.3137i		−	0.683698i
$799$	−1.08672	+	0.627417i	−0.0384453	+	0.0221964i
$800$	4.11999	−	2.37868i	0.145664	−	0.0840990i
$801$			9.17157i			0.324062i
$802$	−2.58579	−	4.47871i	−0.0913073	−	0.158149i
$803$	−11.6569	+	20.1903i	−0.411361	+	0.712499i
$804$	−3.88437	−	2.24264i	−0.136991	−	0.0790918i
$805$	−32.0000			−1.12785
$806$		0			0
$807$	18.0000			0.633630
$808$	13.9795	+	8.07107i	0.491797	+	0.283939i
$809$	−20.6569	+	35.7787i	−0.726256	+	1.25791i	0.232198	+	0.972668i	$0.425408\pi$
$809$	−20.6569	+	35.7787i	−0.726256	+	1.25791i	−0.958455	+	0.285244i	$0.907925\pi$
$810$	−3.41421	−	5.91359i	−0.119963	−	0.207782i
$811$			1.85786i			0.0652384i	0.999468	+	0.0326192i	$0.0103849\pi$
$811$			1.85786i			0.0652384i	−0.999468	+	0.0326192i	$0.989615\pi$
$812$	18.7554	−	10.8284i	0.658185	−	0.380003i
$813$	10.2182	−	5.89949i	0.358369	−	0.206904i
$814$			17.6569i			0.618872i
$815$	−18.6274	−	32.2636i	−0.652490	−	1.13015i
$816$	−5.48528	+	9.50079i	−0.192023	+	0.332594i
$817$	−23.6544	−	13.6569i	−0.827561	−	0.477793i
$818$	−2.48528			−0.0868958
$819$		0			0
$820$	117.255			4.09472
$821$	13.6823	+	7.89949i	0.477516	+	0.275694i	0.719381	−	0.694616i	$-0.244426\pi$
$821$	13.6823	+	7.89949i	0.477516	+	0.275694i	−0.241864	+	0.970310i	$0.577759\pi$
$822$	−6.24264	+	10.8126i	−0.217737	+	0.377132i
$823$	24.4853	+	42.4098i	0.853503	+	1.47831i	0.878027	+	0.478612i	$0.158860\pi$
$823$	24.4853	+	42.4098i	0.853503	+	1.47831i	−0.0245234	+	0.999699i	$0.507807\pi$
$824$			60.2843i			2.10010i
$825$	5.19615	−	3.00000i	0.180907	−	0.104447i
$826$	−21.6251	+	12.4853i	−0.752435	+	0.434418i
$827$		−	26.0000i		−	0.904109i	−0.891990	−	0.452054i	$-0.850691\pi$
$827$		−	26.0000i		−	0.904109i	0.891990	−	0.452054i	$-0.149309\pi$
$828$	7.65685	+	13.2621i	0.266094	+	0.460888i
$829$	2.65685	−	4.60181i	0.0922764	−	0.159827i	−0.816192	−	0.577780i	$-0.803919\pi$
$829$	2.65685	−	4.60181i	0.0922764	−	0.159827i	0.908469	+	0.417953i	$0.137252\pi$
$830$	−45.2795	−	26.1421i	−1.57167	−	0.907407i
$831$	2.00000			0.0693792
$832$		0			0
$833$	−3.65685			−0.126702
$834$	−32.0174	−	18.4853i	−1.10867	−	0.640093i
$835$	−10.8284	+	18.7554i	−0.374733	+	0.649057i
$836$	−10.8284	−	18.7554i	−0.374509	−	0.648669i
$837$			6.82843i			0.236025i
$838$	−64.0349	+	36.9706i	−2.21205	+	1.27713i
$839$	−40.9239	+	23.6274i	−1.41285	+	0.815709i	−0.995656	−	0.0931087i	$-0.970320\pi$
$839$	−40.9239	+	23.6274i	−1.41285	+	0.815709i	−0.417194	+	0.908818i	$0.636986\pi$
$840$			35.3137i			1.21844i
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−17.7279	+	30.7057i	−0.610945	+	1.05819i
$843$	−23.2341	−	13.4142i	−0.800225	−	0.462010i
$844$	45.9411			1.58136
$845$		0			0
$846$	0.828427			0.0284819
$847$	17.1464	+	9.89949i	0.589158	+	0.340151i
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$	−2.48528	−	4.30463i	−0.0852946	−	0.147735i
$850$		−	26.4853i		−	0.908438i
$851$	12.6677	−	7.31371i	0.434244	−	0.250711i
$852$	6.63103	−	3.82843i	0.227175	−	0.131160i
$853$		−	7.65685i		−	0.262166i	−0.991371	−	0.131083i	$-0.958155\pi$
$853$		−	7.65685i		−	0.262166i	0.991371	−	0.131083i	$-0.0418454\pi$
$854$	31.7990	+	55.0775i	1.08814	+	1.88471i
$855$	4.00000	−	6.92820i	0.136797	−	0.236940i
$856$	43.2503	+	24.9706i	1.47826	+	0.853476i
$857$	−29.5980			−1.01105			−0.505524	−	0.862813i	$-0.668701\pi$
$857$	−29.5980			−1.01105			−0.505524	+	0.862813i	$0.668701\pi$
$858$		0			0
$859$	−23.3137			−0.795453			−0.397727	−	0.917504i	$-0.630201\pi$
$859$	−23.3137			−0.795453			−0.397727	+	0.917504i	$0.630201\pi$
$860$	90.5590	+	52.2843i	3.08804	+	1.78288i
$861$	15.3137	−	26.5241i	0.521890	−	0.903940i
$862$	−23.7279	−	41.0980i	−0.808176	−	1.39980i
$863$			39.6569i			1.34994i	0.737847	+	0.674968i	$0.235842\pi$
$863$			39.6569i			1.34994i	−0.737847	+	0.674968i	$0.764158\pi$
$864$	−1.37333	+	0.792893i	−0.0467217	+	0.0269748i
$865$	−0.840532	+	0.485281i	−0.0285789	+	0.0165001i
$866$		−	3.17157i		−	0.107774i
$867$	1.81371	+	3.14144i	0.0615968	+	0.106689i
$868$	36.9706	−	64.0349i	1.25486	−	2.17349i
$869$	19.5959	+	11.3137i	0.664746	+	0.383791i
$870$	13.6569			0.463011
$871$		0			0
$872$	76.4264			2.58812
$873$	−6.63103	−	3.82843i	−0.224426	−	0.129573i
$874$	−13.6569	+	23.6544i	−0.461950	+	0.800121i
$875$	8.00000	+	13.8564i	0.270449	+	0.468432i
$876$		−	44.6274i		−	1.50782i
$877$	12.3705	−	7.14214i	0.417724	−	0.241173i	−0.276379	−	0.961049i	$-0.589135\pi$
$877$	12.3705	−	7.14214i	0.417724	−	0.241173i	0.694103	+	0.719876i	$0.255801\pi$
$878$	35.4815	−	20.4853i	1.19744	−	0.691345i
$879$		−	26.1421i		−	0.881752i
$880$	8.48528	+	14.6969i	0.286039	+	0.495434i
$881$	26.7990	−	46.4172i	0.902881	−	1.56384i	0.0791441	−	0.996863i	$-0.474781\pi$
$881$	26.7990	−	46.4172i	0.902881	−	1.56384i	0.823737	−	0.566972i	$-0.191885\pi$
$882$	2.09077	+	1.20711i	0.0703999	+	0.0406454i
$883$	51.5980			1.73641			0.868205	−	0.496205i	$-0.165274\pi$
$883$	51.5980			1.73641			0.868205	+	0.496205i	$0.165274\pi$
$884$		0			0
$885$	−10.3431			−0.347681
$886$	−87.6893	−	50.6274i	−2.94598	−	1.70086i
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	−0.791026	−	0.611783i	$-0.790453\pi$
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	0.925332	+	0.379157i	$0.123786\pi$
$888$	−8.07107	−	13.9795i	−0.270847	−	0.469121i
$889$		−	16.0000i		−	0.536623i
$890$	54.2369	−	31.3137i	1.81803	−	1.04964i
$891$	−1.73205	+	1.00000i	−0.0580259	+	0.0335013i
$892$			17.1716i			0.574947i
$893$	0.485281	+	0.840532i	0.0162393	+	0.0281273i
$894$	17.8995	−	31.0028i	0.598649	−	1.03689i
$895$	1.68106	+	0.970563i	0.0561918	+	0.0324423i
$896$	58.1421			1.94239
$897$		0			0
$898$	−18.8284			−0.628313
$899$	−11.8272	−	6.82843i	−0.394459	−	0.227741i
$900$	−5.74264	+	9.94655i	−0.191421	+	0.331552i
$901$	3.65685	+	6.33386i	0.121827	+	0.211011i
$902$		−	52.2843i		−	1.74088i
$903$	23.6544	−	13.6569i	0.787168	−	0.454472i
$904$	−66.1872	+	38.2132i	−2.20135	+	1.27095i
$905$			39.5980i			1.31628i
$906$	−24.7279	−	42.8300i	−0.821530	−	1.42293i
$907$	10.4853	−	18.1610i	0.348158	−	0.603027i	−0.637764	−	0.770232i	$-0.720141\pi$
$907$	10.4853	−	18.1610i	0.348158	−	0.603027i	0.985922	+	0.167204i	$0.0534739\pi$
$908$	−17.6177	−	10.1716i	−0.584663	−	0.337556i
$909$	3.65685			0.121290
$910$		0			0
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$	7.34847	+	4.24264i	0.243332	+	0.140488i
$913$	−7.65685	+	13.2621i	−0.253405	+	0.438910i
$914$	−4.41421	−	7.64564i	−0.146009	−	0.252895i
$915$			26.3431i			0.870878i
$916$	−70.6659	+	40.7990i	−2.33487	+	1.34804i
$917$	19.5959	−	11.3137i	0.647114	−	0.373612i
$918$			8.82843i			0.291382i
$919$	9.65685	+	16.7262i	0.318550	+	0.551745i	0.980186	−	0.198080i	$-0.0634707\pi$
$919$	9.65685	+	16.7262i	0.318550	+	0.551745i	−0.661636	+	0.749826i	$0.730137\pi$
$920$	24.9706	−	43.2503i	0.823255	−	1.42592i
$921$	14.8710	+	8.58579i	0.490017	+	0.282911i
$922$	26.1421			0.860945
$923$		0			0
$924$	21.6569			0.712458
$925$	9.50079	+	5.48528i	0.312384	+	0.180355i
$926$	−9.07107	+	15.7116i	−0.298094	+	0.516314i
$927$	6.82843	+	11.8272i	0.224275	+	0.388456i
$928$		−	3.17157i		−	0.104112i
$929$	24.0746	−	13.8995i	0.789863	−	0.456028i	−0.0500513	−	0.998747i	$-0.515938\pi$
$929$	24.0746	−	13.8995i	0.789863	−	0.456028i	0.839914	+	0.542719i	$0.182605\pi$
$930$	40.3805	−	23.3137i	1.32413	−	0.764487i
$931$			2.82843i			0.0926980i
$932$	51.6274	+	89.4213i	1.69111	+	2.92909i
$933$	17.3137	−	29.9882i	0.566825	−	0.981770i
$934$	−16.7262	−	9.65685i	−0.547297	−	0.315982i
$935$	−20.6863			−0.676514
$936$		0			0
$937$	1.31371			0.0429170			0.0214585	−	0.999770i	$-0.493169\pi$
$937$	1.31371			0.0429170			0.0214585	+	0.999770i	$0.493169\pi$
$938$	6.92820	+	4.00000i	0.226214	+	0.130605i
$939$	−3.00000	+	5.19615i	−0.0979013	+	0.169570i
$940$	−1.85786	−	3.21792i	−0.0605969	−	0.104957i
$941$		−	5.85786i		−	0.190961i	−0.995431	−	0.0954805i	$-0.969561\pi$
$941$		−	5.85786i		−	0.190961i	0.995431	−	0.0954805i	$-0.0304387\pi$
$942$	−20.9077	+	12.0711i	−0.681210	+	0.393297i
$943$	−37.5108	+	21.6569i	−1.22152	+	0.705244i
$944$		−	10.9706i		−	0.357061i
$945$	4.00000	+	6.92820i	0.130120	+	0.225374i
$946$	23.3137	−	40.3805i	0.757994	−	1.31288i
$947$	47.6059	+	27.4853i	1.54698	+	0.893152i	0.998370	+	0.0570760i	$0.0181777\pi$
$947$	47.6059	+	27.4853i	1.54698	+	0.893152i	0.548614	+	0.836076i	$0.315156\pi$
$948$	−43.3137			−1.40676
$949$		0			0
$950$	−20.4853			−0.664630
$951$	−7.34847	−	4.24264i	−0.238290	−	0.137577i
$952$	22.8284	−	39.5400i	0.739874	−	1.28150i
$953$	25.8284	+	44.7361i	0.836665	+	1.44915i	0.892668	+	0.450715i	$0.148831\pi$
$953$	25.8284	+	44.7361i	0.836665	+	1.44915i	−0.0560029	+	0.998431i	$0.517836\pi$
$954$		−	4.82843i		−	0.156326i
$955$	47.3087	−	27.3137i	1.53087	−	0.883851i
$956$	6.63103	−	3.82843i	0.214463	−	0.123820i
$957$		−	4.00000i		−	0.129302i
$958$	3.24264	+	5.61642i	0.104765	+	0.181458i
$959$	7.31371	−	12.6677i	0.236172	−	0.409062i
$960$	24.0746	+	13.8995i	0.777005	+	0.448604i
$961$	−15.6274			−0.504110
$962$		0			0
$963$	11.3137			0.364579
$964$	38.6485	+	22.3137i	1.24478	+	0.718676i
$965$	24.4853	−	42.4098i	0.788209	−	1.36522i
$966$	−13.6569	−	23.6544i	−0.439402	−	0.761067i
$967$			10.1421i			0.326149i	0.986614	+	0.163075i	$0.0521411\pi$
$967$			10.1421i			0.326149i	−0.986614	+	0.163075i	$0.947859\pi$
$968$	−26.7597	+	15.4497i	−0.860091	+	0.496574i
$969$	−8.95743	+	5.17157i	−0.287754	+	0.166135i
$970$			52.2843i			1.67875i
$971$	−3.65685	−	6.33386i	−0.117354	−	0.203263i	0.801364	−	0.598177i	$-0.204108\pi$
$971$	−3.65685	−	6.33386i	−0.117354	−	0.203263i	−0.918718	+	0.394913i	$0.870775\pi$
$972$	1.91421	−	3.31552i	0.0613984	−	0.106345i
$973$	37.5108	+	21.6569i	1.20254	+	0.694287i
$974$	76.7696			2.45986
$975$		0			0
$976$	−27.9411			−0.894374
$977$	12.0013	+	6.92893i	0.383954	+	0.221676i	0.679537	−	0.733641i	$-0.262181\pi$
$977$	12.0013	+	6.92893i	0.383954	+	0.221676i	−0.295583	+	0.955317i	$0.595514\pi$
$978$	15.8995	−	27.5387i	0.508410	−	0.880592i
$979$	−9.17157	−	15.8856i	−0.293125	−	0.507707i
$980$		−	10.8284i		−	0.345901i
$981$	14.9941	−	8.65685i	0.478725	−	0.276392i
$982$	30.5826	−	17.6569i	0.975929	−	0.563453i
$983$			2.68629i			0.0856794i	0.999082	+	0.0428397i	$0.0136405\pi$
$983$			2.68629i			0.0856794i	−0.999082	+	0.0428397i	$0.986360\pi$
$984$	23.8995	+	41.3951i	0.761888	+	1.31963i
$985$	−23.3137	+	40.3805i	−0.742837	+	1.28663i
$986$	−15.2913	−	8.82843i	−0.486974	−	0.281154i
$987$	−0.970563			−0.0308934
$988$		0			0
$989$	−38.6274			−1.22828
$990$	11.8272	+	6.82843i	0.375893	+	0.217022i
$991$	−13.6569	+	23.6544i	−0.433824	+	0.751406i	−0.997199	−	0.0747959i	$-0.976169\pi$
$991$	−13.6569	+	23.6544i	−0.433824	+	0.751406i	0.563375	+	0.826202i	$0.309503\pi$
$992$	−5.41421	−	9.37769i	−0.171901	−	0.297742i
$993$			2.14214i			0.0679786i
$994$	−11.8272	+	6.82843i	−0.375135	+	0.216585i
$995$	25.3354	−	14.6274i	0.803187	−	0.463720i
$996$		−	29.3137i		−	0.928840i
$997$	−25.6274	−	44.3880i	−0.811628	−	1.40578i	−0.911724	−	0.410804i	$-0.865248\pi$
$997$	−25.6274	−	44.3880i	−0.811628	−	1.40578i	0.100095	−	0.994978i	$-0.468085\pi$
$998$	2.58579	−	4.47871i	0.0818516	−	0.141771i
$999$	−3.16693	−	1.82843i	−0.100197	−	0.0578489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.f.316.1		8
13.2	odd	12		507.2.e.d.484.1		4
13.3	even	3	inner	507.2.j.f.361.4		8
13.4	even	6		507.2.b.e.337.1		4
13.5	odd	4		507.2.e.d.22.1		4
13.6	odd	12		507.2.a.h.1.2		2
13.7	odd	12		39.2.a.b.1.1	✓	2
13.8	odd	4		507.2.e.h.22.2		4
13.9	even	3		507.2.b.e.337.4		4
13.10	even	6	inner	507.2.j.f.361.1		8
13.11	odd	12		507.2.e.h.484.2		4
13.12	even	2	inner	507.2.j.f.316.4		8
39.17	odd	6		1521.2.b.j.1351.4		4
39.20	even	12		117.2.a.c.1.2		2
39.32	even	12		1521.2.a.f.1.1		2
39.35	odd	6		1521.2.b.j.1351.1		4
52.7	even	12		624.2.a.k.1.2		2
52.19	even	12		8112.2.a.bm.1.1		2
65.7	even	12		975.2.c.h.274.1		4
65.33	even	12		975.2.c.h.274.4		4
65.59	odd	12		975.2.a.l.1.2		2
91.20	even	12		1911.2.a.h.1.1		2
104.59	even	12		2496.2.a.bi.1.1		2
104.85	odd	12		2496.2.a.bf.1.1		2
117.7	odd	12		1053.2.e.m.352.2		4
117.20	even	12		1053.2.e.e.352.1		4
117.59	even	12		1053.2.e.e.703.1		4
117.85	odd	12		1053.2.e.m.703.2		4
143.98	even	12		4719.2.a.p.1.2		2
156.59	odd	12		1872.2.a.w.1.1		2
195.59	even	12		2925.2.a.v.1.1		2
195.98	odd	12		2925.2.c.u.2224.1		4
195.137	odd	12		2925.2.c.u.2224.4		4
273.20	odd	12		5733.2.a.u.1.2		2
312.59	odd	12		7488.2.a.co.1.2		2
312.293	even	12		7488.2.a.cl.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.a.b.1.1	✓	2	13.7	odd	12
117.2.a.c.1.2		2	39.20	even	12
507.2.a.h.1.2		2	13.6	odd	12
507.2.b.e.337.1		4	13.4	even	6
507.2.b.e.337.4		4	13.9	even	3
507.2.e.d.22.1		4	13.5	odd	4
507.2.e.d.484.1		4	13.2	odd	12
507.2.e.h.22.2		4	13.8	odd	4
507.2.e.h.484.2		4	13.11	odd	12
507.2.j.f.316.1		8	1.1	even	1	trivial
507.2.j.f.316.4		8	13.12	even	2	inner
507.2.j.f.361.1		8	13.10	even	6	inner
507.2.j.f.361.4		8	13.3	even	3	inner
624.2.a.k.1.2		2	52.7	even	12
975.2.a.l.1.2		2	65.59	odd	12
975.2.c.h.274.1		4	65.7	even	12
975.2.c.h.274.4		4	65.33	even	12
1053.2.e.e.352.1		4	117.20	even	12
1053.2.e.e.703.1		4	117.59	even	12
1053.2.e.m.352.2		4	117.7	odd	12
1053.2.e.m.703.2		4	117.85	odd	12
1521.2.a.f.1.1		2	39.32	even	12
1521.2.b.j.1351.1		4	39.35	odd	6
1521.2.b.j.1351.4		4	39.17	odd	6
1872.2.a.w.1.1		2	156.59	odd	12
1911.2.a.h.1.1		2	91.20	even	12
2496.2.a.bf.1.1		2	104.85	odd	12
2496.2.a.bi.1.1		2	104.59	even	12
2925.2.a.v.1.1		2	195.59	even	12
2925.2.c.u.2224.1		4	195.98	odd	12
2925.2.c.u.2224.4		4	195.137	odd	12
4719.2.a.p.1.2		2	143.98	even	12
5733.2.a.u.1.2		2	273.20	odd	12
7488.2.a.cl.1.2		2	312.293	even	12
7488.2.a.co.1.2		2	312.59	odd	12
8112.2.a.bm.1.1		2	52.19	even	12

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.09077 - 1.20711i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.91421 + 3.31552i) q^{4} -2.82843i q^{5} +(2.09077 - 1.20711i) q^{6} +(-2.44949 + 1.41421i) q^{7} -4.41421i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.09077 - 1.20711i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.91421 + 3.31552i) q^{4} -2.82843i q^{5} +(2.09077 - 1.20711i) q^{6} +(-2.44949 + 1.41421i) q^{7} -4.41421i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.41421 + 5.91359i) q^{10} +(1.73205 + 1.00000i) q^{11} -3.82843 q^{12} +6.82843 q^{14} +(2.44949 + 1.41421i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(-1.82843 - 3.16693i) q^{17} +2.41421i q^{18} +(-2.44949 + 1.41421i) q^{19} +(9.37769 - 5.41421i) q^{20} -2.82843i q^{21} +(-2.41421 - 4.18154i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(3.82282 + 2.20711i) q^{24} -3.00000 q^{25} +1.00000 q^{27} +(-9.37769 - 5.41421i) q^{28} +(-1.00000 + 1.73205i) q^{29} +(-3.41421 - 5.91359i) q^{30} +6.82843i q^{31} +(-1.37333 + 0.792893i) q^{32} +(-1.73205 + 1.00000i) q^{33} +8.82843i q^{34} +(4.00000 + 6.92820i) q^{35} +(1.91421 - 3.31552i) q^{36} +(-3.16693 - 1.82843i) q^{37} +6.82843 q^{38} -12.4853 q^{40} +(9.37769 + 5.41421i) q^{41} +(-3.41421 + 5.91359i) q^{42} +(4.82843 + 8.36308i) q^{43} +7.65685i q^{44} +(-2.44949 + 1.41421i) q^{45} +(8.36308 - 4.82843i) q^{46} -0.343146i q^{47} +(-1.50000 - 2.59808i) q^{48} +(0.500000 - 0.866025i) q^{49} +(6.27231 + 3.62132i) q^{50} +3.65685 q^{51} -2.00000 q^{53} +(-2.09077 - 1.20711i) q^{54} +(2.82843 - 4.89898i) q^{55} +(6.24264 + 10.8126i) q^{56} -2.82843i q^{57} +(4.18154 - 2.41421i) q^{58} +(-3.16693 + 1.82843i) q^{59} +10.8284i q^{60} +(4.65685 + 8.06591i) q^{61} +(8.24264 - 14.2767i) q^{62} +(2.44949 + 1.41421i) q^{63} +9.82843 q^{64} +4.82843 q^{66} +(1.01461 + 0.585786i) q^{67} +(7.00000 - 12.1244i) q^{68} +(-2.00000 - 3.46410i) q^{69} -19.3137i q^{70} +(-1.73205 + 1.00000i) q^{71} +(-3.82282 + 2.20711i) q^{72} +11.6569i q^{73} +(4.41421 + 7.64564i) q^{74} +(1.50000 - 2.59808i) q^{75} +(-9.37769 - 5.41421i) q^{76} -5.65685 q^{77} +11.3137 q^{79} +(7.34847 + 4.24264i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-13.0711 - 22.6398i) q^{82} +7.65685i q^{83} +(9.37769 - 5.41421i) q^{84} +(-8.95743 + 5.17157i) q^{85} -23.3137i q^{86} +(-1.00000 - 1.73205i) q^{87} +(4.41421 - 7.64564i) q^{88} +(-7.94282 - 4.58579i) q^{89} +6.82843 q^{90} -15.3137 q^{92} +(-5.91359 - 3.41421i) q^{93} +(-0.414214 + 0.717439i) q^{94} +(4.00000 + 6.92820i) q^{95} -1.58579i q^{96} +(6.63103 - 3.82843i) q^{97} +(-2.09077 + 1.20711i) q^{98} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 16 q^{10} - 8 q^{12} + 32 q^{14} - 12 q^{16} + 8 q^{17} - 8 q^{22} - 16 q^{23} - 24 q^{25} + 8 q^{27} - 8 q^{29} - 16 q^{30} + 32 q^{35} + 4 q^{36} + 32 q^{38} - 32 q^{40} - 16 q^{42} + 16 q^{43} - 12 q^{48} + 4 q^{49} - 16 q^{51} - 16 q^{53} + 16 q^{56} - 8 q^{61} + 32 q^{62} + 56 q^{64} + 16 q^{66} + 56 q^{68} - 16 q^{69} + 24 q^{74} + 12 q^{75} - 4 q^{81} - 48 q^{82} - 8 q^{87} + 24 q^{88} + 32 q^{90} - 32 q^{92} + 8 q^{94} + 32 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 16 * q^10 - 8 * q^12 + 32 * q^14 - 12 * q^16 + 8 * q^17 - 8 * q^22 - 16 * q^23 - 24 * q^25 + 8 * q^27 - 8 * q^29 - 16 * q^30 + 32 * q^35 + 4 * q^36 + 32 * q^38 - 32 * q^40 - 16 * q^42 + 16 * q^43 - 12 * q^48 + 4 * q^49 - 16 * q^51 - 16 * q^53 + 16 * q^56 - 8 * q^61 + 32 * q^62 + 56 * q^64 + 16 * q^66 + 56 * q^68 - 16 * q^69 + 24 * q^74 + 12 * q^75 - 4 * q^81 - 48 * q^82 - 8 * q^87 + 24 * q^88 + 32 * q^90 - 32 * q^92 + 8 * q^94 + 32 * q^95

Introduction

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