LMFDB - Embedded newform 1014.2.e.l.991.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(529,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1014.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.2
Root			$0.222521 + 0.385418i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.l.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.13706 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.0244587 - 0.0423637i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.13706 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.0244587 - 0.0423637i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.06853 - 1.85075i) q^{10} +(-3.14795 - 5.45241i) q^{11} -1.00000 q^{12} -0.0489173 q^{14} +(1.06853 + 1.85075i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.44504 - 2.50289i) q^{17} +1.00000 q^{18} +(3.60388 - 6.24210i) q^{19} +(-1.06853 + 1.85075i) q^{20} +0.0489173 q^{21} +(-3.14795 + 5.45241i) q^{22} +(-1.35690 - 2.35021i) q^{23} +(0.500000 + 0.866025i) q^{24} -0.432960 q^{25} -1.00000 q^{27} +(0.0244587 + 0.0423637i) q^{28} +(-2.45593 - 4.25379i) q^{29} +(1.06853 - 1.85075i) q^{30} +9.00969 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.14795 - 5.45241i) q^{33} -2.89008 q^{34} +(0.0522697 - 0.0905338i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.0881460 + 0.152673i) q^{37} -7.20775 q^{38} +2.13706 q^{40} +(4.29590 + 7.44071i) q^{41} +(-0.0244587 - 0.0423637i) q^{42} +(-3.35690 + 5.81431i) q^{43} +6.29590 q^{44} +(-1.06853 + 1.85075i) q^{45} +(-1.35690 + 2.35021i) q^{46} +7.20775 q^{47} +(0.500000 - 0.866025i) q^{48} +(3.49880 + 6.06011i) q^{49} +(0.216480 + 0.374955i) q^{50} +2.89008 q^{51} +9.34481 q^{53} +(0.500000 + 0.866025i) q^{54} +(-6.72737 - 11.6521i) q^{55} +(0.0244587 - 0.0423637i) q^{56} +7.20775 q^{57} +(-2.45593 + 4.25379i) q^{58} +(2.13437 - 3.69685i) q^{59} -2.13706 q^{60} +(-3.55496 + 6.15737i) q^{61} +(-4.50484 - 7.80262i) q^{62} +(0.0244587 + 0.0423637i) q^{63} +1.00000 q^{64} -6.29590 q^{66} +(-2.69202 - 4.66272i) q^{67} +(1.44504 + 2.50289i) q^{68} +(1.35690 - 2.35021i) q^{69} -0.104539 q^{70} +(4.35690 - 7.54637i) q^{71} +(-0.500000 + 0.866025i) q^{72} -14.9487 q^{73} +(0.0881460 - 0.152673i) q^{74} +(-0.216480 - 0.374955i) q^{75} +(3.60388 + 6.24210i) q^{76} -0.307979 q^{77} +13.8291 q^{79} +(-1.06853 - 1.85075i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.29590 - 7.44071i) q^{82} -11.1347 q^{83} +(-0.0244587 + 0.0423637i) q^{84} +(3.08815 - 5.34883i) q^{85} +6.71379 q^{86} +(2.45593 - 4.25379i) q^{87} +(-3.14795 - 5.45241i) q^{88} +(-1.96077 - 3.39616i) q^{89} +2.13706 q^{90} +2.71379 q^{92} +(4.50484 + 7.80262i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(7.70171 - 13.3398i) q^{95} -1.00000 q^{96} +(1.23945 - 2.14678i) q^{97} +(3.49880 - 6.06011i) q^{98} +6.29590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^7 + 6 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{7} + 6 q^{8} - 3 q^{9} - q^{10} - 5 q^{11} - 6 q^{12} + 18 q^{14} + q^{15} - 3 q^{16} + 8 q^{17} + 6 q^{18} + 4 q^{19} - q^{20} - 18 q^{21} - 5 q^{22} + 3 q^{24} + 36 q^{25} - 6 q^{27} - 9 q^{28} - 11 q^{29} + q^{30} + 10 q^{31} - 3 q^{32} + 5 q^{33} - 16 q^{34} + 4 q^{35} - 3 q^{36} + 8 q^{37} - 8 q^{38} + 2 q^{40} - 2 q^{41} + 9 q^{42} - 12 q^{43} + 10 q^{44} - q^{45} + 8 q^{47} + 3 q^{48} - 20 q^{49} - 18 q^{50} + 16 q^{51} + 10 q^{53} + 3 q^{54} - 18 q^{55} - 9 q^{56} + 8 q^{57} - 11 q^{58} + 5 q^{59} - 2 q^{60} - 22 q^{61} - 5 q^{62} - 9 q^{63} + 6 q^{64} - 10 q^{66} - 6 q^{67} + 8 q^{68} - 8 q^{70} + 18 q^{71} - 3 q^{72} - 26 q^{73} + 8 q^{74} + 18 q^{75} + 4 q^{76} - 12 q^{77} + 62 q^{79} - q^{80} - 3 q^{81} - 2 q^{82} + 26 q^{83} + 9 q^{84} + 26 q^{85} + 24 q^{86} + 11 q^{87} - 5 q^{88} + 14 q^{89} + 2 q^{90} + 5 q^{93} - 4 q^{94} - 8 q^{95} - 6 q^{96} + 23 q^{97} - 20 q^{98} + 10 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^7 + 6 * q^8 - 3 * q^9 - q^10 - 5 * q^11 - 6 * q^12 + 18 * q^14 + q^15 - 3 * q^16 + 8 * q^17 + 6 * q^18 + 4 * q^19 - q^20 - 18 * q^21 - 5 * q^22 + 3 * q^24 + 36 * q^25 - 6 * q^27 - 9 * q^28 - 11 * q^29 + q^30 + 10 * q^31 - 3 * q^32 + 5 * q^33 - 16 * q^34 + 4 * q^35 - 3 * q^36 + 8 * q^37 - 8 * q^38 + 2 * q^40 - 2 * q^41 + 9 * q^42 - 12 * q^43 + 10 * q^44 - q^45 + 8 * q^47 + 3 * q^48 - 20 * q^49 - 18 * q^50 + 16 * q^51 + 10 * q^53 + 3 * q^54 - 18 * q^55 - 9 * q^56 + 8 * q^57 - 11 * q^58 + 5 * q^59 - 2 * q^60 - 22 * q^61 - 5 * q^62 - 9 * q^63 + 6 * q^64 - 10 * q^66 - 6 * q^67 + 8 * q^68 - 8 * q^70 + 18 * q^71 - 3 * q^72 - 26 * q^73 + 8 * q^74 + 18 * q^75 + 4 * q^76 - 12 * q^77 + 62 * q^79 - q^80 - 3 * q^81 - 2 * q^82 + 26 * q^83 + 9 * q^84 + 26 * q^85 + 24 * q^86 + 11 * q^87 - 5 * q^88 + 14 * q^89 + 2 * q^90 + 5 * q^93 - 4 * q^94 - 8 * q^95 - 6 * q^96 + 23 * q^97 - 20 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.13706			0.955724			0.477862	−	0.878435i	$-0.341412\pi$
$5$	2.13706			0.955724			0.477862	+	0.878435i	$0.341412\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	0.0244587	−	0.0423637i	0.00924451	−	0.0160120i	−0.861366	−	0.507985i	$-0.830391\pi$
$7$	0.0244587	−	0.0423637i	0.00924451	−	0.0160120i	0.870611	+	0.491973i	$0.163724\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.06853	−	1.85075i	−0.337899	−	0.585259i
$11$	−3.14795	−	5.45241i	−0.949142	−	1.64396i	−0.747237	−	0.664557i	$-0.768620\pi$
$11$	−3.14795	−	5.45241i	−0.949142	−	1.64396i	−0.201905	−	0.979405i	$-0.564713\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	−0.0489173			−0.0130737
$15$	1.06853	+	1.85075i	0.275894	+	0.477862i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.44504	−	2.50289i	0.350474	−	0.607039i	−0.635858	−	0.771806i	$-0.719354\pi$
$17$	1.44504	−	2.50289i	0.350474	−	0.607039i	0.986333	+	0.164767i	$0.0526871\pi$
$18$	1.00000			0.235702
$19$	3.60388	−	6.24210i	0.826786	−	1.43203i	−0.0737611	−	0.997276i	$-0.523500\pi$
$19$	3.60388	−	6.24210i	0.826786	−	1.43203i	0.900547	−	0.434759i	$-0.143166\pi$
$20$	−1.06853	+	1.85075i	−0.238931	+	0.413841i
$21$	0.0489173			0.0106746
$22$	−3.14795	+	5.45241i	−0.671145	+	1.16246i
$23$	−1.35690	−	2.35021i	−0.282932	−	0.490053i	0.689173	−	0.724597i	$-0.257974\pi$
$23$	−1.35690	−	2.35021i	−0.282932	−	0.490053i	−0.972106	+	0.234543i	$0.924641\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.432960			−0.0865921
$26$		0			0
$27$	−1.00000			−0.192450
$28$	0.0244587	+	0.0423637i	0.00462225	+	0.00800598i
$29$	−2.45593	−	4.25379i	−0.456054	−	0.789909i	0.542694	−	0.839931i	$-0.317404\pi$
$29$	−2.45593	−	4.25379i	−0.456054	−	0.789909i	−0.998748	+	0.0500215i	$0.984071\pi$
$30$	1.06853	−	1.85075i	0.195086	−	0.337899i
$31$	9.00969			1.61819			0.809094	−	0.587679i	$-0.199958\pi$
$31$	9.00969			1.61819			0.809094	+	0.587679i	$0.199958\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.14795	−	5.45241i	0.547987	−	0.949142i
$34$	−2.89008			−0.495645
$35$	0.0522697	−	0.0905338i	0.00883520	−	0.0153030i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	0.0881460	+	0.152673i	0.0144911	+	0.0250993i	0.873180	−	0.487398i	$-0.162054\pi$
$37$	0.0881460	+	0.152673i	0.0144911	+	0.0250993i	−0.858689	+	0.512497i	$0.828721\pi$
$38$	−7.20775			−1.16925
$39$		0			0
$40$	2.13706			0.337899
$41$	4.29590	+	7.44071i	0.670906	+	1.16204i	0.977647	+	0.210251i	$0.0674281\pi$
$41$	4.29590	+	7.44071i	0.670906	+	1.16204i	−0.306741	+	0.951793i	$0.599239\pi$
$42$	−0.0244587	−	0.0423637i	−0.00377405	−	0.00653685i
$43$	−3.35690	+	5.81431i	−0.511922	+	0.886675i	0.487983	+	0.872853i	$0.337733\pi$
$43$	−3.35690	+	5.81431i	−0.511922	+	0.886675i	−0.999904	+	0.0138213i	$0.995600\pi$
$44$	6.29590			0.949142
$45$	−1.06853	+	1.85075i	−0.159287	+	0.275894i
$46$	−1.35690	+	2.35021i	−0.200063	+	0.346520i
$47$	7.20775			1.05136			0.525679	−	0.850683i	$-0.323811\pi$
$47$	7.20775			1.05136			0.525679	+	0.850683i	$0.323811\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	3.49880	+	6.06011i	0.499829	+	0.865729i
$50$	0.216480	+	0.374955i	0.0306149	+	0.0530266i
$51$	2.89008			0.404693
$52$		0			0
$53$	9.34481			1.28361			0.641804	−	0.766868i	$-0.278186\pi$
$53$	9.34481			1.28361			0.641804	+	0.766868i	$0.278186\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−6.72737	−	11.6521i	−0.907118	−	1.57117i
$56$	0.0244587	−	0.0423637i	0.00326843	−	0.00566108i
$57$	7.20775			0.954690
$58$	−2.45593	+	4.25379i	−0.322479	+	0.558550i
$59$	2.13437	−	3.69685i	0.277872	−	0.481288i	−0.692984	−	0.720953i	$-0.743704\pi$
$59$	2.13437	−	3.69685i	0.277872	−	0.481288i	0.970856	+	0.239665i	$0.0770376\pi$
$60$	−2.13706			−0.275894
$61$	−3.55496	+	6.15737i	−0.455166	+	0.788370i	−0.998698	−	0.0510183i	$-0.983753\pi$
$61$	−3.55496	+	6.15737i	−0.455166	+	0.788370i	0.543532	+	0.839388i	$0.317087\pi$
$62$	−4.50484	−	7.80262i	−0.572116	−	0.990934i
$63$	0.0244587	+	0.0423637i	0.00308150	+	0.00533732i
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.29590			−0.774971
$67$	−2.69202	−	4.66272i	−0.328883	−	0.569642i	0.653408	−	0.757006i	$-0.273339\pi$
$67$	−2.69202	−	4.66272i	−0.328883	−	0.569642i	−0.982290	+	0.187365i	$0.940005\pi$
$68$	1.44504	+	2.50289i	0.175237	+	0.303520i
$69$	1.35690	−	2.35021i	0.163351	−	0.282932i
$70$	−0.104539			−0.0124949
$71$	4.35690	−	7.54637i	0.517068	−	0.895589i	−0.482735	−	0.875766i	$-0.660357\pi$
$71$	4.35690	−	7.54637i	0.517068	−	0.895589i	0.999804	−	0.0198223i	$-0.00631006\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−14.9487			−1.74961			−0.874806	−	0.484474i	$-0.839011\pi$
$73$	−14.9487			−1.74961			−0.874806	+	0.484474i	$0.839011\pi$
$74$	0.0881460	−	0.152673i	0.0102468	−	0.0177479i
$75$	−0.216480	−	0.374955i	−0.0249970	−	0.0432960i
$76$	3.60388	+	6.24210i	0.413393	+	0.716017i
$77$	−0.307979			−0.0350974
$78$		0			0
$79$	13.8291			1.55589			0.777947	−	0.628330i	$-0.216261\pi$
$79$	13.8291			1.55589			0.777947	+	0.628330i	$0.216261\pi$
$80$	−1.06853	−	1.85075i	−0.119465	−	0.206920i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.29590	−	7.44071i	0.474402	−	0.821689i
$83$	−11.1347			−1.22219			−0.611094	−	0.791558i	$-0.709270\pi$
$83$	−11.1347			−1.22219			−0.611094	+	0.791558i	$0.709270\pi$
$84$	−0.0244587	+	0.0423637i	−0.00266866	+	0.00462225i
$85$	3.08815	−	5.34883i	0.334956	−	0.580162i
$86$	6.71379			0.723967
$87$	2.45593	−	4.25379i	0.263303	−	0.456054i
$88$	−3.14795	−	5.45241i	−0.335572	−	0.581229i
$89$	−1.96077	−	3.39616i	−0.207841	−	0.359992i	0.743193	−	0.669077i	$-0.233310\pi$
$89$	−1.96077	−	3.39616i	−0.207841	−	0.359992i	−0.951034	+	0.309085i	$0.899977\pi$
$90$	2.13706			0.225266
$91$		0			0
$92$	2.71379			0.282932
$93$	4.50484	+	7.80262i	0.467131	+	0.809094i
$94$	−3.60388	−	6.24210i	−0.371711	−	0.643823i
$95$	7.70171	−	13.3398i	0.790179	−	1.36863i
$96$	−1.00000			−0.102062
$97$	1.23945	−	2.14678i	0.125847	−	0.217973i	−0.796217	−	0.605011i	$-0.793169\pi$
$97$	1.23945	−	2.14678i	0.125847	−	0.217973i	0.922064	+	0.387038i	$0.126502\pi$
$98$	3.49880	−	6.06011i	0.353433	−	0.612163i
$99$	6.29590			0.632761
$100$	0.216480	−	0.374955i	0.0216480	−	0.0374955i
$101$	−0.826396	−	1.43136i	−0.0822295	−	0.142426i	0.821978	−	0.569520i	$-0.192871\pi$
$101$	−0.826396	−	1.43136i	−0.0822295	−	0.142426i	−0.904207	+	0.427094i	$0.859537\pi$
$102$	−1.44504	−	2.50289i	−0.143080	−	0.247823i
$103$	−8.23490			−0.811409			−0.405704	−	0.914004i	$-0.632974\pi$
$103$	−8.23490			−0.811409			−0.405704	+	0.914004i	$0.632974\pi$
$104$		0			0
$105$	0.104539			0.0102020
$106$	−4.67241	−	8.09285i	−0.453824	−	0.786047i
$107$	4.18329	+	7.24567i	0.404414	+	0.700466i	0.994253	−	0.107055i	$-0.0341421\pi$
$107$	4.18329	+	7.24567i	0.404414	+	0.700466i	−0.589839	+	0.807521i	$0.700809\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−17.4276			−1.66926			−0.834630	−	0.550811i	$-0.814318\pi$
$109$	−17.4276			−1.66926			−0.834630	+	0.550811i	$0.814318\pi$
$110$	−6.72737	+	11.6521i	−0.641429	+	1.11099i
$111$	−0.0881460	+	0.152673i	−0.00836645	+	0.0144911i
$112$	−0.0489173			−0.00462225
$113$	6.98792	−	12.1034i	0.657368	−	1.13859i	−0.323926	−	0.946082i	$-0.605003\pi$
$113$	6.98792	−	12.1034i	0.657368	−	1.13859i	0.981294	−	0.192513i	$-0.0616636\pi$
$114$	−3.60388	−	6.24210i	−0.337534	−	0.584626i
$115$	−2.89977	−	5.02255i	−0.270405	−	0.468355i
$116$	4.91185			0.456054
$117$		0			0
$118$	−4.26875			−0.392970
$119$	−0.0706876	−	0.122435i	−0.00647992	−	0.0112236i
$120$	1.06853	+	1.85075i	0.0975431	+	0.168950i
$121$	−14.3192	+	24.8015i	−1.30174	+	2.25468i
$122$	7.10992			0.643702
$123$	−4.29590	+	7.44071i	−0.387348	+	0.670906i
$124$	−4.50484	+	7.80262i	−0.404547	+	0.700696i
$125$	−11.6106			−1.03848
$126$	0.0244587	−	0.0423637i	0.00217895	−	0.00377405i
$127$	3.76055	+	6.51347i	0.333695	+	0.577977i	0.983233	−	0.182352i	$-0.0583711\pi$
$127$	3.76055	+	6.51347i	0.333695	+	0.577977i	−0.649538	+	0.760329i	$0.725038\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−6.71379			−0.591116
$130$		0			0
$131$	5.12498			0.447772			0.223886	−	0.974615i	$-0.428126\pi$
$131$	5.12498			0.447772			0.223886	+	0.974615i	$0.428126\pi$
$132$	3.14795	+	5.45241i	0.273994	+	0.474571i
$133$	−0.176292	−	0.305347i	−0.0152865	−	0.0264769i
$134$	−2.69202	+	4.66272i	−0.232555	+	0.402797i
$135$	−2.13706			−0.183929
$136$	1.44504	−	2.50289i	0.123911	−	0.214621i
$137$	2.00000	−	3.46410i	0.170872	−	0.295958i	−0.767853	−	0.640626i	$-0.778675\pi$
$137$	2.00000	−	3.46410i	0.170872	−	0.295958i	0.938725	+	0.344668i	$0.112008\pi$
$138$	−2.71379			−0.231013
$139$	−4.34481	+	7.52544i	−0.368522	+	0.638299i	−0.989335	−	0.145660i	$-0.953470\pi$
$139$	−4.34481	+	7.52544i	−0.368522	+	0.638299i	0.620812	+	0.783959i	$0.286803\pi$
$140$	0.0522697	+	0.0905338i	0.00441760	+	0.00765150i
$141$	3.60388	+	6.24210i	0.303501	+	0.525679i
$142$	−8.71379			−0.731245
$143$		0			0
$144$	1.00000			0.0833333
$145$	−5.24847	−	9.09062i	−0.435862	−	0.754935i
$146$	7.47434	+	12.9459i	0.618581	+	1.07141i
$147$	−3.49880	+	6.06011i	−0.288576	+	0.499829i
$148$	−0.176292			−0.0144911
$149$	2.43416	−	4.21608i	0.199414	−	0.345395i	−0.748925	−	0.662655i	$-0.769430\pi$
$149$	2.43416	−	4.21608i	0.199414	−	0.345395i	0.948339	+	0.317260i	$0.102763\pi$
$150$	−0.216480	+	0.374955i	−0.0176755	+	0.0306149i
$151$	14.7463			1.20004			0.600019	−	0.799986i	$-0.295160\pi$
$151$	14.7463			1.20004			0.600019	+	0.799986i	$0.295160\pi$
$152$	3.60388	−	6.24210i	0.292313	−	0.506301i
$153$	1.44504	+	2.50289i	0.116825	+	0.202346i
$154$	0.153989	+	0.266717i	0.0124088	+	0.0214927i
$155$	19.2543			1.54654
$156$		0			0
$157$	−16.7138			−1.33391			−0.666953	−	0.745100i	$-0.732402\pi$
$157$	−16.7138			−1.33391			−0.666953	+	0.745100i	$0.732402\pi$
$158$	−6.91454	−	11.9763i	−0.550091	−	0.952786i
$159$	4.67241	+	8.09285i	0.370546	+	0.641804i
$160$	−1.06853	+	1.85075i	−0.0844748	+	0.146315i
$161$	−0.132751			−0.0104623
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−2.77479	+	4.80608i	−0.217338	+	0.376441i	−0.953993	−	0.299828i	$-0.903071\pi$
$163$	−2.77479	+	4.80608i	−0.217338	+	0.376441i	0.736655	+	0.676269i	$0.236404\pi$
$164$	−8.59179			−0.670906
$165$	6.72737	−	11.6521i	0.523725	−	0.907118i
$166$	5.56734	+	9.64291i	0.432109	+	0.748435i
$167$	1.96077	+	3.39616i	0.151729	+	0.262802i	0.931863	−	0.362810i	$-0.118183\pi$
$167$	1.96077	+	3.39616i	0.151729	+	0.262802i	−0.780134	+	0.625612i	$0.784849\pi$
$168$	0.0489173			0.00377405
$169$		0			0
$170$	−6.17629			−0.473700
$171$	3.60388	+	6.24210i	0.275595	+	0.477345i
$172$	−3.35690	−	5.81431i	−0.255961	−	0.443337i
$173$	1.74214	−	3.01747i	0.132452	−	0.229414i	−0.792169	−	0.610302i	$-0.791048\pi$
$173$	1.74214	−	3.01747i	0.132452	−	0.229414i	0.924621	+	0.380888i	$0.124382\pi$
$174$	−4.91185			−0.372367
$175$	−0.0105896	+	0.0183418i	−0.000800501	+	0.00138651i
$176$	−3.14795	+	5.45241i	−0.237286	+	0.410991i
$177$	4.26875			0.320859
$178$	−1.96077	+	3.39616i	−0.146966	+	0.254553i
$179$	−1.79440	−	3.10800i	−0.134120	−	0.232303i	0.791141	−	0.611634i	$-0.209487\pi$
$179$	−1.79440	−	3.10800i	−0.134120	−	0.232303i	−0.925261	+	0.379331i	$0.876154\pi$
$180$	−1.06853	−	1.85075i	−0.0796436	−	0.137947i
$181$	5.50604			0.409261			0.204630	−	0.978839i	$-0.434401\pi$
$181$	5.50604			0.409261			0.204630	+	0.978839i	$0.434401\pi$
$182$		0			0
$183$	−7.10992			−0.525580
$184$	−1.35690	−	2.35021i	−0.100032	−	0.173260i
$185$	0.188374	+	0.326273i	0.0138495	+	0.0239880i
$186$	4.50484	−	7.80262i	0.330311	−	0.572116i
$187$	−18.1957			−1.33060
$188$	−3.60388	+	6.24210i	−0.262840	+	0.455252i
$189$	−0.0244587	+	0.0423637i	−0.00177911	+	0.00308150i
$190$	−15.4034			−1.11748
$191$	2.82908	−	4.90012i	0.204705	−	0.354560i	−0.745333	−	0.666692i	$-0.767710\pi$
$191$	2.82908	−	4.90012i	0.204705	−	0.354560i	0.950039	+	0.312132i	$0.101043\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	6.70171	+	11.6077i	0.482400	+	0.835541i	0.999796	−	0.0202053i	$-0.00643197\pi$
$193$	6.70171	+	11.6077i	0.482400	+	0.835541i	−0.517396	+	0.855746i	$0.673099\pi$
$194$	−2.47889			−0.177974
$195$		0			0
$196$	−6.99761			−0.499829
$197$	9.99061	+	17.3042i	0.711801	+	1.23288i	0.964180	+	0.265248i	$0.0854537\pi$
$197$	9.99061	+	17.3042i	0.711801	+	1.23288i	−0.252379	+	0.967628i	$0.581213\pi$
$198$	−3.14795	−	5.45241i	−0.223715	−	0.387486i
$199$	3.12080	−	5.40539i	0.221228	−	0.383178i	−0.733953	−	0.679200i	$-0.762327\pi$
$199$	3.12080	−	5.40539i	0.221228	−	0.383178i	0.955181	+	0.296022i	$0.0956603\pi$
$200$	−0.432960			−0.0306149
$201$	2.69202	−	4.66272i	0.189881	−	0.328883i
$202$	−0.826396	+	1.43136i	−0.0581450	+	0.100710i
$203$	−0.240275			−0.0168640
$204$	−1.44504	+	2.50289i	−0.101173	+	0.175237i
$205$	9.18060	+	15.9013i	0.641201	+	1.11059i
$206$	4.11745	+	7.13163i	0.286876	+	0.496884i
$207$	2.71379			0.188622
$208$		0			0
$209$	−45.3793			−3.13895
$210$	−0.0522697	−	0.0905338i	−0.00360695	−	0.00624743i
$211$	2.54288	+	4.40439i	0.175059	+	0.303211i	0.940182	−	0.340674i	$-0.110655\pi$
$211$	2.54288	+	4.40439i	0.175059	+	0.303211i	−0.765123	+	0.643884i	$0.777322\pi$
$212$	−4.67241	+	8.09285i	−0.320902	+	0.555819i
$213$	8.71379			0.597059
$214$	4.18329	−	7.24567i	0.285964	−	0.495304i
$215$	−7.17390	+	12.4256i	−0.489256	+	0.847416i
$216$	−1.00000			−0.0680414
$217$	0.220365	−	0.381683i	0.0149594	−	0.0259104i
$218$	8.71379	+	15.0927i	0.590172	+	1.02221i
$219$	−7.47434	−	12.9459i	−0.505069	−	0.874806i
$220$	13.4547			0.907118
$221$		0			0
$222$	0.176292			0.0118319
$223$	−10.2741	−	17.7953i	−0.688006	−	1.19166i	−0.972482	−	0.232979i	$-0.925153\pi$
$223$	−10.2741	−	17.7953i	−0.688006	−	1.19166i	0.284475	−	0.958683i	$-0.408181\pi$
$224$	0.0244587	+	0.0423637i	0.00163421	+	0.00283054i
$225$	0.216480	−	0.374955i	0.0144320	−	0.0249970i
$226$	−13.9758			−0.929659
$227$	2.20560	−	3.82020i	0.146390	−	0.253556i	−0.783500	−	0.621391i	$-0.786568\pi$
$227$	2.20560	−	3.82020i	0.146390	−	0.253556i	0.929891	+	0.367836i	$0.119901\pi$
$228$	−3.60388	+	6.24210i	−0.238672	+	0.413393i
$229$	−0.230586			−0.0152376			−0.00761878	−	0.999971i	$-0.502425\pi$
$229$	−0.230586			−0.0152376			−0.00761878	+	0.999971i	$0.502425\pi$
$230$	−2.89977	+	5.02255i	−0.191205	+	0.331177i
$231$	−0.153989	−	0.266717i	−0.0101317	−	0.0175487i
$232$	−2.45593	−	4.25379i	−0.161240	−	0.279275i
$233$	−7.82371			−0.512548			−0.256274	−	0.966604i	$-0.582495\pi$
$233$	−7.82371			−0.512548			−0.256274	+	0.966604i	$0.582495\pi$
$234$		0			0
$235$	15.4034			1.00481
$236$	2.13437	+	3.69685i	0.138936	+	0.240644i
$237$	6.91454	+	11.9763i	0.449148	+	0.777947i
$238$	−0.0706876	+	0.122435i	−0.00458200	+	0.00793625i
$239$	−11.1535			−0.721457			−0.360729	−	0.932671i	$-0.617472\pi$
$239$	−11.1535			−0.721457			−0.360729	+	0.932671i	$0.617472\pi$
$240$	1.06853	−	1.85075i	0.0689734	−	0.119465i
$241$	−1.77263	+	3.07029i	−0.114185	+	0.197775i	−0.917454	−	0.397842i	$-0.869759\pi$
$241$	−1.77263	+	3.07029i	−0.114185	+	0.197775i	0.803268	+	0.595617i	$0.203092\pi$
$242$	28.6383			1.84094
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.55496	−	6.15737i	−0.227583	−	0.394185i
$245$	7.47716	+	12.9508i	0.477699	+	0.827398i
$246$	8.59179			0.547793
$247$		0			0
$248$	9.00969			0.572116
$249$	−5.56734	−	9.64291i	−0.352816	−	0.611094i
$250$	5.80529	+	10.0551i	0.367159	+	0.635938i
$251$	2.08546	−	3.61212i	0.131633	−	0.227995i	−0.792673	−	0.609647i	$-0.791311\pi$
$251$	2.08546	−	3.61212i	0.131633	−	0.227995i	0.924306	+	0.381652i	$0.124645\pi$
$252$	−0.0489173			−0.00308150
$253$	−8.54288	+	14.7967i	−0.537086	+	0.930260i
$254$	3.76055	−	6.51347i	0.235958	−	0.408691i
$255$	6.17629			0.386774
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.44504	+	9.43109i	0.339652	+	0.588295i	0.984367	−	0.176128i	$-0.0563572\pi$
$257$	5.44504	+	9.43109i	0.339652	+	0.588295i	−0.644715	+	0.764423i	$0.723024\pi$
$258$	3.35690	+	5.81431i	0.208991	+	0.361983i
$259$	0.00862374			0.000535853
$260$		0			0
$261$	4.91185			0.304036
$262$	−2.56249	−	4.43836i	−0.158311	−	0.274203i
$263$	15.6136	+	27.0435i	0.962774	+	1.66757i	0.715481	+	0.698632i	$0.246207\pi$
$263$	15.6136	+	27.0435i	0.962774	+	1.66757i	0.247292	+	0.968941i	$0.420459\pi$
$264$	3.14795	−	5.45241i	0.193743	−	0.335572i
$265$	19.9705			1.22678
$266$	−0.176292	+	0.305347i	−0.0108092	+	0.0187220i
$267$	1.96077	−	3.39616i	0.119997	−	0.207841i
$268$	5.38404			0.328883
$269$	−7.95862	+	13.7847i	−0.485245	+	0.840470i	−0.999856	−	0.0169542i	$-0.994603\pi$
$269$	−7.95862	+	13.7847i	−0.485245	+	0.840470i	0.514611	+	0.857424i	$0.327936\pi$
$270$	1.06853	+	1.85075i	0.0650288	+	0.112633i
$271$	1.76055	+	3.04937i	0.106946	+	0.185236i	0.914532	−	0.404514i	$-0.132559\pi$
$271$	1.76055	+	3.04937i	0.106946	+	0.185236i	−0.807586	+	0.589750i	$0.799226\pi$
$272$	−2.89008			−0.175237
$273$		0			0
$274$	−4.00000			−0.241649
$275$	1.36294	+	2.36068i	0.0821882	+	0.142354i
$276$	1.35690	+	2.35021i	0.0816755	+	0.141466i
$277$	4.29052	−	7.43140i	0.257792	−	0.446509i	−0.707858	−	0.706355i	$-0.750338\pi$
$277$	4.29052	−	7.43140i	0.257792	−	0.446509i	0.965650	+	0.259845i	$0.0836716\pi$
$278$	8.68963			0.521169
$279$	−4.50484	+	7.80262i	−0.269698	+	0.467131i
$280$	0.0522697	−	0.0905338i	0.00312371	−	0.00541043i
$281$	8.07846			0.481920			0.240960	−	0.970535i	$-0.422538\pi$
$281$	8.07846			0.481920			0.240960	+	0.970535i	$0.422538\pi$
$282$	3.60388	−	6.24210i	0.214608	−	0.371711i
$283$	8.70171	+	15.0718i	0.517263	+	0.895926i	0.999799	+	0.0200496i	$0.00638242\pi$
$283$	8.70171	+	15.0718i	0.517263	+	0.895926i	−0.482536	+	0.875876i	$0.660284\pi$
$284$	4.35690	+	7.54637i	0.258534	+	0.447794i
$285$	15.4034			0.912420
$286$		0			0
$287$	0.420288			0.0248088
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	4.32371	+	7.48888i	0.254336	+	0.440522i
$290$	−5.24847	+	9.09062i	−0.308201	+	0.533820i
$291$	2.47889			0.145315
$292$	7.47434	−	12.9459i	0.437403	−	0.757604i
$293$	−9.68545	+	16.7757i	−0.565830	+	0.980046i	0.431142	+	0.902284i	$0.358111\pi$
$293$	−9.68545	+	16.7757i	−0.565830	+	0.980046i	−0.996972	+	0.0777621i	$0.975223\pi$
$294$	6.99761			0.408109
$295$	4.56129	−	7.90039i	0.265569	−	0.459979i
$296$	0.0881460	+	0.152673i	0.00512338	+	0.00887396i
$297$	3.14795	+	5.45241i	0.182662	+	0.316381i
$298$	−4.86831			−0.282014
$299$		0			0
$300$	0.432960			0.0249970
$301$	0.164210	+	0.284421i	0.00946493	+	0.0163937i
$302$	−7.37316	−	12.7707i	−0.424278	−	0.734870i
$303$	0.826396	−	1.43136i	0.0474752	−	0.0822295i
$304$	−7.20775			−0.413393
$305$	−7.59717	+	13.1587i	−0.435013	+	0.753464i
$306$	1.44504	−	2.50289i	0.0826075	−	0.143080i
$307$	12.4263			0.709204			0.354602	−	0.935017i	$-0.384616\pi$
$307$	12.4263			0.709204			0.354602	+	0.935017i	$0.384616\pi$
$308$	0.153989	−	0.266717i	0.00877435	−	0.0151976i
$309$	−4.11745	−	7.13163i	−0.234233	−	0.405704i
$310$	−9.62714	−	16.6747i	−0.546785	−	0.947059i
$311$	2.71379			0.153885			0.0769425	−	0.997036i	$-0.475484\pi$
$311$	2.71379			0.153885			0.0769425	+	0.997036i	$0.475484\pi$
$312$		0			0
$313$	15.3884			0.869801			0.434901	−	0.900478i	$-0.356783\pi$
$313$	15.3884			0.869801			0.434901	+	0.900478i	$0.356783\pi$
$314$	8.35690	+	14.4746i	0.471607	+	0.816847i
$315$	0.0522697	+	0.0905338i	0.00294507	+	0.00510100i
$316$	−6.91454	+	11.9763i	−0.388973	+	0.673722i
$317$	−25.6528			−1.44080			−0.720402	−	0.693557i	$-0.756043\pi$
$317$	−25.6528			−1.44080			−0.720402	+	0.693557i	$0.756043\pi$
$318$	4.67241	−	8.09285i	0.262016	−	0.453824i
$319$	−15.4623	+	26.7814i	−0.865721	+	1.49947i
$320$	2.13706			0.119465
$321$	−4.18329	+	7.24567i	−0.233489	+	0.404414i
$322$	0.0663757	+	0.114966i	0.00369898	+	0.00640681i
$323$	−10.4155	−	18.0402i	−0.579534	−	1.00378i
$324$	1.00000			0.0555556
$325$		0			0
$326$	5.54958			0.307363
$327$	−8.71379	−	15.0927i	−0.481874	−	0.834630i
$328$	4.29590	+	7.44071i	0.237201	+	0.410845i
$329$	0.176292	−	0.305347i	0.00971929	−	0.0168343i
$330$	−13.4547			−0.740659
$331$	−1.91185	+	3.31143i	−0.105085	+	0.182013i	−0.913773	−	0.406225i	$-0.866845\pi$
$331$	−1.91185	+	3.31143i	−0.105085	+	0.182013i	0.808688	+	0.588238i	$0.200178\pi$
$332$	5.56734	−	9.64291i	0.305547	−	0.529223i
$333$	−0.176292			−0.00966074
$334$	1.96077	−	3.39616i	0.107289	−	0.185829i
$335$	−5.75302	−	9.96452i	−0.314321	−	0.544420i
$336$	−0.0244587	−	0.0423637i	−0.00133433	−	0.00231113i
$337$	20.1304			1.09657			0.548285	−	0.836291i	$-0.315281\pi$
$337$	20.1304			1.09657			0.548285	+	0.836291i	$0.315281\pi$
$338$		0			0
$339$	13.9758			0.759063
$340$	3.08815	+	5.34883i	0.167478	+	0.290081i
$341$	−28.3620	−	49.1245i	−1.53589	−	2.66024i
$342$	3.60388	−	6.24210i	0.194875	−	0.337534i
$343$	0.684726			0.0369717
$344$	−3.35690	+	5.81431i	−0.180992	+	0.313487i
$345$	2.89977	−	5.02255i	0.156118	−	0.270405i
$346$	−3.48427			−0.187316
$347$	−1.46950	+	2.54525i	−0.0788869	+	0.136636i	−0.902770	−	0.430124i	$-0.858470\pi$
$347$	−1.46950	+	2.54525i	−0.0788869	+	0.136636i	0.823883	+	0.566760i	$0.191803\pi$
$348$	2.45593	+	4.25379i	0.131652	+	0.228027i
$349$	3.68664	+	6.38546i	0.197342	+	0.341806i	0.947666	−	0.319265i	$-0.103436\pi$
$349$	3.68664	+	6.38546i	0.197342	+	0.341806i	−0.750324	+	0.661070i	$0.770103\pi$
$350$	0.0211793			0.00113208
$351$		0			0
$352$	6.29590			0.335572
$353$	−1.00538	−	1.74136i	−0.0535108	−	0.0926834i	0.838029	−	0.545625i	$-0.183708\pi$
$353$	−1.00538	−	1.74136i	−0.0535108	−	0.0926834i	−0.891540	+	0.452942i	$0.850374\pi$
$354$	−2.13437	−	3.69685i	−0.113441	−	0.196485i
$355$	9.31096	−	16.1271i	0.494175	−	0.855935i
$356$	3.92154			0.207841
$357$	0.0706876	−	0.122435i	0.00374118	−	0.00647992i
$358$	−1.79440	+	3.10800i	−0.0948373	+	0.164263i
$359$	−31.4577			−1.66027			−0.830137	−	0.557559i	$-0.811738\pi$
$359$	−31.4577			−1.66027			−0.830137	+	0.557559i	$0.811738\pi$
$360$	−1.06853	+	1.85075i	−0.0563166	+	0.0975431i
$361$	−16.4758	−	28.5370i	−0.867149	−	1.50195i
$362$	−2.75302	−	4.76837i	−0.144696	−	0.250620i
$363$	−28.6383			−1.50312
$364$		0			0
$365$	−31.9463			−1.67215
$366$	3.55496	+	6.15737i	0.185821	+	0.321851i
$367$	2.24967	+	3.89654i	0.117432	+	0.203398i	0.918749	−	0.394842i	$-0.129201\pi$
$367$	2.24967	+	3.89654i	0.117432	+	0.203398i	−0.801317	+	0.598239i	$0.795867\pi$
$368$	−1.35690	+	2.35021i	−0.0707331	+	0.122513i
$369$	−8.59179			−0.447271
$370$	0.188374	−	0.326273i	0.00979308	−	0.0169621i
$371$	0.228562	−	0.395881i	0.0118663	−	0.0205531i
$372$	−9.00969			−0.467131
$373$	−18.9148	+	32.7615i	−0.979373	+	1.69632i	−0.314698	+	0.949192i	$0.601903\pi$
$373$	−18.9148	+	32.7615i	−0.979373	+	1.69632i	−0.664676	+	0.747132i	$0.731430\pi$
$374$	9.09783	+	15.7579i	0.470438	+	0.814822i
$375$	−5.80529	−	10.0551i	−0.299784	−	0.519241i
$376$	7.20775			0.371711
$377$		0			0
$378$	0.0489173			0.00251604
$379$	−4.21983	−	7.30896i	−0.216758	−	0.375436i	0.737057	−	0.675831i	$-0.236215\pi$
$379$	−4.21983	−	7.30896i	−0.216758	−	0.375436i	−0.953815	+	0.300395i	$0.902882\pi$
$380$	7.70171	+	13.3398i	0.395089	+	0.684315i
$381$	−3.76055	+	6.51347i	−0.192659	+	0.333695i
$382$	−5.65817			−0.289497
$383$	0.643104	−	1.11389i	0.0328611	−	0.0569171i	−0.849127	−	0.528188i	$-0.822871\pi$
$383$	0.643104	−	1.11389i	0.0328611	−	0.0569171i	0.881988	+	0.471271i	$0.156205\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−0.658170			−0.0335434
$386$	6.70171	−	11.6077i	0.341108	−	0.590817i
$387$	−3.35690	−	5.81431i	−0.170641	−	0.295558i
$388$	1.23945	+	2.14678i	0.0629234	+	0.108986i
$389$	23.3924			1.18604			0.593021	−	0.805187i	$-0.297935\pi$
$389$	23.3924			1.18604			0.593021	+	0.805187i	$0.297935\pi$
$390$		0			0
$391$	−7.84309			−0.396642
$392$	3.49880	+	6.06011i	0.176716	+	0.306082i
$393$	2.56249	+	4.43836i	0.129261	+	0.223886i
$394$	9.99061	−	17.3042i	0.503320	−	0.871775i
$395$	29.5536			1.48700
$396$	−3.14795	+	5.45241i	−0.158190	+	0.273994i
$397$	18.5429	−	32.1172i	0.930640	−	1.61192i	0.148411	−	0.988926i	$-0.452584\pi$
$397$	18.5429	−	32.1172i	0.930640	−	1.61192i	0.782229	−	0.622990i	$-0.214082\pi$
$398$	−6.24160			−0.312863
$399$	0.176292	−	0.305347i	0.00882564	−	0.0152865i
$400$	0.216480	+	0.374955i	0.0108240	+	0.0187477i
$401$	2.43296	+	4.21401i	0.121496	+	0.210438i	0.920358	−	0.391077i	$-0.127897\pi$
$401$	2.43296	+	4.21401i	0.121496	+	0.210438i	−0.798862	+	0.601515i	$0.794564\pi$
$402$	−5.38404			−0.268532
$403$		0			0
$404$	1.65279			0.0822295
$405$	−1.06853	−	1.85075i	−0.0530958	−	0.0919646i
$406$	0.120137	+	0.208084i	0.00596232	+	0.0103270i
$407$	0.554958	−	0.961216i	0.0275083	−	0.0476457i
$408$	2.89008			0.143080
$409$	−0.222521	+	0.385418i	−0.0110030	+	0.0190577i	−0.871474	−	0.490441i	$-0.836836\pi$
$409$	−0.222521	+	0.385418i	−0.0110030	+	0.0190577i	0.860472	+	0.509499i	$0.170169\pi$
$410$	9.18060	−	15.9013i	0.453398	−	0.785308i
$411$	4.00000			0.197305
$412$	4.11745	−	7.13163i	0.202852	−	0.351350i
$413$	−0.104408	−	0.180840i	−0.00513758	−	0.00889855i
$414$	−1.35690	−	2.35021i	−0.0666878	−	0.115507i
$415$	−23.7955			−1.16807
$416$		0			0
$417$	−8.68963			−0.425533
$418$	22.6896	+	39.2996i	1.10979	+	1.92221i
$419$	−8.99343	−	15.5771i	−0.439358	−	0.760990i	0.558282	−	0.829651i	$-0.311461\pi$
$419$	−8.99343	−	15.5771i	−0.439358	−	0.760990i	−0.997640	+	0.0686612i	$0.978127\pi$
$420$	−0.0522697	+	0.0905338i	−0.00255050	+	0.00441760i
$421$	21.2814			1.03719			0.518597	−	0.855019i	$-0.326455\pi$
$421$	21.2814			1.03719			0.518597	+	0.855019i	$0.326455\pi$
$422$	2.54288	−	4.40439i	0.123785	−	0.214402i
$423$	−3.60388	+	6.24210i	−0.175226	+	0.303501i
$424$	9.34481			0.453824
$425$	−0.625646	+	1.08365i	−0.0303483	+	0.0525648i
$426$	−4.35690	−	7.54637i	−0.211092	−	0.365623i
$427$	0.173899	+	0.301202i	0.00841557	+	0.0145762i
$428$	−8.36658			−0.404414
$429$		0			0
$430$	14.3478			0.691912
$431$	−12.3569	−	21.4028i	−0.595211	−	1.03094i	−0.993517	−	0.113683i	$-0.963735\pi$
$431$	−12.3569	−	21.4028i	−0.595211	−	1.03094i	0.398306	−	0.917252i	$-0.369598\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−16.1087	+	27.9011i	−0.774136	+	1.34084i	0.161143	+	0.986931i	$0.448482\pi$
$433$	−16.1087	+	27.9011i	−0.774136	+	1.34084i	−0.935279	+	0.353911i	$0.884851\pi$
$434$	−0.440730			−0.0211557
$435$	5.24847	−	9.09062i	0.251645	−	0.435862i
$436$	8.71379	−	15.0927i	0.417315	−	0.722811i
$437$	−19.5603			−0.935698
$438$	−7.47434	+	12.9459i	−0.357138	+	0.618581i
$439$	−16.0438	−	27.7887i	−0.765731	−	1.32628i	−0.939859	−	0.341561i	$-0.889044\pi$
$439$	−16.0438	−	27.7887i	−0.765731	−	1.32628i	0.174129	−	0.984723i	$-0.444289\pi$
$440$	−6.72737	−	11.6521i	−0.320715	−	0.555494i
$441$	−6.99761			−0.333219
$442$		0			0
$443$	20.5109			0.974504			0.487252	−	0.873261i	$-0.337999\pi$
$443$	20.5109			0.974504			0.487252	+	0.873261i	$0.337999\pi$
$444$	−0.0881460	−	0.152673i	−0.00418322	−	0.00724556i
$445$	−4.19029	−	7.25780i	−0.198639	−	0.344053i
$446$	−10.2741	+	17.7953i	−0.486494	+	0.842632i
$447$	4.86831			0.230263
$448$	0.0244587	−	0.0423637i	0.00115556	−	0.00200149i
$449$	7.65817	−	13.2643i	0.361411	−	0.625983i	−0.626782	−	0.779195i	$-0.715628\pi$
$449$	7.65817	−	13.2643i	0.361411	−	0.625983i	0.988193	+	0.153212i	$0.0489617\pi$
$450$	−0.432960			−0.0204099
$451$	27.0465	−	46.8460i	1.27357	−	2.20589i
$452$	6.98792	+	12.1034i	0.328684	+	0.569297i
$453$	7.37316	+	12.7707i	0.346421	+	0.600019i
$454$	−4.41119			−0.207027
$455$		0			0
$456$	7.20775			0.337534
$457$	9.59299	+	16.6155i	0.448741	+	0.777242i	0.998304	−	0.0582096i	$-0.0185392\pi$
$457$	9.59299	+	16.6155i	0.448741	+	0.777242i	−0.549563	+	0.835452i	$0.685206\pi$
$458$	0.115293	+	0.199693i	0.00538729	+	0.00933106i
$459$	−1.44504	+	2.50289i	−0.0674488	+	0.116825i
$460$	5.79954			0.270405
$461$	−4.15615	+	7.19865i	−0.193571	+	0.335275i	−0.946431	−	0.322906i	$-0.895340\pi$
$461$	−4.15615	+	7.19865i	−0.193571	+	0.335275i	0.752860	+	0.658181i	$0.228674\pi$
$462$	−0.153989	+	0.266717i	−0.00716423	+	0.0124088i
$463$	−6.32842			−0.294107			−0.147053	−	0.989129i	$-0.546979\pi$
$463$	−6.32842			−0.294107			−0.147053	+	0.989129i	$0.546979\pi$
$464$	−2.45593	+	4.25379i	−0.114014	+	0.197477i
$465$	9.62714	+	16.6747i	0.446448	+	0.773270i
$466$	3.91185	+	6.77553i	0.181213	+	0.313870i
$467$	−31.1879			−1.44320			−0.721602	−	0.692308i	$-0.756594\pi$
$467$	−31.1879			−1.44320			−0.721602	+	0.692308i	$0.756594\pi$
$468$		0			0
$469$	−0.263373			−0.0121614
$470$	−7.70171	−	13.3398i	−0.355253	−	0.615317i
$471$	−8.35690	−	14.4746i	−0.385065	−	0.666953i
$472$	2.13437	−	3.69685i	0.0982426	−	0.170161i
$473$	42.2693			1.94355
$474$	6.91454	−	11.9763i	0.317595	−	0.550091i
$475$	−1.56033	+	2.70258i	−0.0715931	+	0.124003i
$476$	0.141375			0.00647992
$477$	−4.67241	+	8.09285i	−0.213935	+	0.370546i
$478$	5.57673	+	9.65918i	0.255074	+	0.441800i
$479$	8.96615	+	15.5298i	0.409674	+	0.709576i	0.994853	−	0.101328i	$-0.0323092\pi$
$479$	8.96615	+	15.5298i	0.409674	+	0.709576i	−0.585179	+	0.810904i	$0.698976\pi$
$480$	−2.13706			−0.0975431
$481$		0			0
$482$	3.54527			0.161483
$483$	−0.0663757	−	0.114966i	−0.00302020	−	0.00523114i
$484$	−14.3192	−	24.8015i	−0.650871	−	1.12734i
$485$	2.64878	−	4.58782i	0.120275	−	0.208322i
$486$	−1.00000			−0.0453609
$487$	−15.1640	+	26.2648i	−0.687145	+	1.19017i	0.285612	+	0.958345i	$0.407803\pi$
$487$	−15.1640	+	26.2648i	−0.687145	+	1.19017i	−0.972757	+	0.231825i	$0.925530\pi$
$488$	−3.55496	+	6.15737i	−0.160925	+	0.278731i
$489$	−5.54958			−0.250961
$490$	7.47716	−	12.9508i	0.337784	−	0.585059i
$491$	−15.0477	−	26.0634i	−0.679094	−	1.17623i	−0.975254	−	0.221087i	$-0.929039\pi$
$491$	−15.0477	−	26.0634i	−0.679094	−	1.17623i	0.296160	−	0.955138i	$-0.404294\pi$
$492$	−4.29590	−	7.44071i	−0.193674	−	0.335453i
$493$	−14.1957			−0.639341
$494$		0			0
$495$	13.4547			0.604745
$496$	−4.50484	−	7.80262i	−0.202273	−	0.350348i
$497$	−0.213128	−	0.369148i	−0.00956009	−	0.0165586i
$498$	−5.56734	+	9.64291i	−0.249478	+	0.432109i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	5.80529	−	10.0551i	0.259620	−	0.449676i
$501$	−1.96077	+	3.39616i	−0.0876008	+	0.151729i
$502$	−4.17092			−0.186157
$503$	−16.8756	+	29.2294i	−0.752446	+	1.30328i	0.194188	+	0.980964i	$0.437793\pi$
$503$	−16.8756	+	29.2294i	−0.752446	+	1.30328i	−0.946634	+	0.322311i	$0.895540\pi$
$504$	0.0244587	+	0.0423637i	0.00108948	+	0.00188703i
$505$	−1.76606	−	3.05891i	−0.0785887	−	0.136120i
$506$	17.0858			0.759554
$507$		0			0
$508$	−7.52111			−0.333695
$509$	7.37196	+	12.7686i	0.326756	+	0.565959i	0.981866	−	0.189575i	$-0.0607110\pi$
$509$	7.37196	+	12.7686i	0.326756	+	0.565959i	−0.655110	+	0.755534i	$0.727378\pi$
$510$	−3.08815	−	5.34883i	−0.136745	−	0.236850i
$511$	−0.365625	+	0.633281i	−0.0161743	+	0.0280147i
$512$	1.00000			0.0441942
$513$	−3.60388	+	6.24210i	−0.159115	+	0.275595i
$514$	5.44504	−	9.43109i	0.240171	−	0.415988i
$515$	−17.5985			−0.775483
$516$	3.35690	−	5.81431i	0.147779	−	0.255961i
$517$	−22.6896	−	39.2996i	−0.997889	−	1.72839i
$518$	−0.00431187	−	0.00746837i	−0.000189453	−	0.000328142i
$519$	3.48427			0.152943
$520$		0			0
$521$	22.1086			0.968595			0.484297	−	0.874903i	$-0.339075\pi$
$521$	22.1086			0.968595			0.484297	+	0.874903i	$0.339075\pi$
$522$	−2.45593	−	4.25379i	−0.107493	−	0.186183i
$523$	8.67994	+	15.0341i	0.379547	+	0.657395i	0.990996	−	0.133889i	$-0.0427464\pi$
$523$	8.67994	+	15.0341i	0.379547	+	0.657395i	−0.611449	+	0.791284i	$0.709413\pi$
$524$	−2.56249	+	4.43836i	−0.111943	+	0.193891i
$525$	−0.0211793			−0.000924339
$526$	15.6136	−	27.0435i	0.680784	−	1.17915i
$527$	13.0194	−	22.5502i	0.567133	−	0.982303i
$528$	−6.29590			−0.273994
$529$	7.81767	−	13.5406i	0.339899	−	0.588722i
$530$	−9.98523	−	17.2949i	−0.433731	−	0.751244i
$531$	2.13437	+	3.69685i	0.0926240	+	0.160429i
$532$	0.352584			0.0152865
$533$		0			0
$534$	−3.92154			−0.169702
$535$	8.93996	+	15.4845i	0.386508	+	0.669452i
$536$	−2.69202	−	4.66272i	−0.116278	−	0.201399i
$537$	1.79440	−	3.10800i	0.0774343	−	0.134120i
$538$	15.9172			0.686241
$539$	22.0281	−	38.1538i	0.948818	−	1.64340i
$540$	1.06853	−	1.85075i	0.0459823	−	0.0796436i
$541$	−8.83579			−0.379880			−0.189940	−	0.981796i	$-0.560829\pi$
$541$	−8.83579			−0.379880			−0.189940	+	0.981796i	$0.560829\pi$
$542$	1.76055	−	3.04937i	0.0756222	−	0.130982i
$543$	2.75302	+	4.76837i	0.118143	+	0.204630i
$544$	1.44504	+	2.50289i	0.0619557	+	0.107310i
$545$	−37.2438			−1.59535
$546$		0			0
$547$	−8.10859			−0.346698			−0.173349	−	0.984860i	$-0.555459\pi$
$547$	−8.10859			−0.346698			−0.173349	+	0.984860i	$0.555459\pi$
$548$	2.00000	+	3.46410i	0.0854358	+	0.147979i
$549$	−3.55496	−	6.15737i	−0.151722	−	0.262790i
$550$	1.36294	−	2.36068i	0.0581158	−	0.100660i
$551$	−35.4034			−1.50824
$552$	1.35690	−	2.35021i	0.0577533	−	0.100032i
$553$	0.338241	−	0.585851i	0.0143835	−	0.0249129i
$554$	−8.58104			−0.364573
$555$	−0.188374	+	0.326273i	−0.00799601	+	0.0138495i
$556$	−4.34481	−	7.52544i	−0.184261	−	0.319150i
$557$	4.78017	+	8.27949i	0.202542	+	0.350813i	0.949347	−	0.314230i	$-0.101746\pi$
$557$	4.78017	+	8.27949i	0.202542	+	0.350813i	−0.746805	+	0.665043i	$0.768413\pi$
$558$	9.00969			0.381411
$559$		0			0
$560$	−0.104539			−0.00441760
$561$	−9.09783	−	15.7579i	−0.384111	−	0.665300i
$562$	−4.03923	−	6.99615i	−0.170385	−	0.295115i
$563$	22.5819	−	39.1129i	0.951712	−	1.64841i	0.209994	−	0.977703i	$-0.432656\pi$
$563$	22.5819	−	39.1129i	0.951712	−	1.64841i	0.741719	−	0.670711i	$-0.234011\pi$
$564$	−7.20775			−0.303501
$565$	14.9336	−	25.8658i	0.628262	−	1.08818i
$566$	8.70171	−	15.0718i	0.365760	−	0.633515i
$567$	−0.0489173			−0.00205434
$568$	4.35690	−	7.54637i	0.182811	−	0.316638i
$569$	1.60388	+	2.77799i	0.0672380	+	0.116460i	0.897685	−	0.440639i	$-0.145248\pi$
$569$	1.60388	+	2.77799i	0.0672380	+	0.116460i	−0.830447	+	0.557098i	$0.811915\pi$
$570$	−7.70171	−	13.3398i	−0.322589	−	0.558741i
$571$	0.0241632			0.00101120			0.000505599	−	1.00000i	$-0.499839\pi$
$571$	0.0241632			0.00101120			0.000505599		1.00000i	$0.499839\pi$
$572$		0			0
$573$	5.65817			0.236373
$574$	−0.210144	−	0.363980i	−0.00877123	−	0.0151922i
$575$	0.587482	+	1.01755i	0.0244997	+	0.0424347i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	46.0200			1.91584			0.957918	−	0.287041i	$-0.0926717\pi$
$577$	46.0200			1.91584			0.957918	+	0.287041i	$0.0926717\pi$
$578$	4.32371	−	7.48888i	0.179843	−	0.311496i
$579$	−6.70171	+	11.6077i	−0.278514	+	0.482400i
$580$	10.4969			0.435862
$581$	−0.272339	+	0.471705i	−0.0112985	+	0.0195696i
$582$	−1.23945	−	2.14678i	−0.0513767	−	0.0889871i
$583$	−29.4170	−	50.9517i	−1.21833	−	2.11020i
$584$	−14.9487			−0.618581
$585$		0			0
$586$	19.3709			0.800204
$587$	−12.9693	−	22.4634i	−0.535299	−	0.927165i	−0.999149	−	0.0412510i	$-0.986866\pi$
$587$	−12.9693	−	22.4634i	−0.535299	−	0.927165i	0.463850	−	0.885914i	$-0.346468\pi$
$588$	−3.49880	−	6.06011i	−0.144288	−	0.249915i
$589$	32.4698	−	56.2393i	1.33789	−	2.31730i
$590$	−9.12259			−0.375571
$591$	−9.99061	+	17.3042i	−0.410959	+	0.711801i
$592$	0.0881460	−	0.152673i	0.00362278	−	0.00627484i
$593$	8.30691			0.341124			0.170562	−	0.985347i	$-0.445442\pi$
$593$	8.30691			0.341124			0.170562	+	0.985347i	$0.445442\pi$
$594$	3.14795	−	5.45241i	0.129162	−	0.223715i
$595$	−0.151064	−	0.261650i	−0.00619302	−	0.0107266i
$596$	2.43416	+	4.21608i	0.0997069	+	0.172697i
$597$	6.24160			0.255452
$598$		0			0
$599$	37.1702			1.51873			0.759366	−	0.650664i	$-0.225509\pi$
$599$	37.1702			1.51873			0.759366	+	0.650664i	$0.225509\pi$
$600$	−0.216480	−	0.374955i	−0.00883776	−	0.0153075i
$601$	6.28501	+	10.8860i	0.256371	+	0.444048i	0.965267	−	0.261265i	$-0.0841398\pi$
$601$	6.28501	+	10.8860i	0.256371	+	0.444048i	−0.708896	+	0.705313i	$0.750806\pi$
$602$	0.164210	−	0.284421i	0.00669272	−	0.0115921i
$603$	5.38404			0.219255
$604$	−7.37316	+	12.7707i	−0.300010	+	0.519632i
$605$	−30.6010	+	53.0024i	−1.24411	+	2.15485i
$606$	−1.65279			−0.0671401
$607$	−4.02446	+	6.97057i	−0.163348	+	0.282927i	−0.936067	−	0.351821i	$-0.885563\pi$
$607$	−4.02446	+	6.97057i	−0.163348	+	0.282927i	0.772720	+	0.634748i	$0.218896\pi$
$608$	3.60388	+	6.24210i	0.146156	+	0.253150i
$609$	−0.120137	−	0.208084i	−0.00486821	−	0.00843199i
$610$	15.1943			0.615201
$611$		0			0
$612$	−2.89008			−0.116825
$613$	15.2295	+	26.3783i	0.615115	+	1.06541i	0.990364	+	0.138486i	$0.0442236\pi$
$613$	15.2295	+	26.3783i	0.615115	+	1.06541i	−0.375250	+	0.926924i	$0.622443\pi$
$614$	−6.21313	−	10.7615i	−0.250741	−	0.434297i
$615$	−9.18060	+	15.9013i	−0.370198	+	0.641201i
$616$	−0.307979			−0.0124088
$617$	2.36658	−	4.09904i	0.0952751	−	0.165021i	−0.814448	−	0.580236i	$-0.802960\pi$
$617$	2.36658	−	4.09904i	0.0952751	−	0.165021i	0.909723	+	0.415215i	$0.136294\pi$
$618$	−4.11745	+	7.13163i	−0.165628	+	0.286876i
$619$	24.9095			1.00120			0.500598	−	0.865680i	$-0.333114\pi$
$619$	24.9095			1.00120			0.500598	+	0.865680i	$0.333114\pi$
$620$	−9.62714	+	16.6747i	−0.386635	+	0.669672i
$621$	1.35690	+	2.35021i	0.0544504	+	0.0943108i
$622$	−1.35690	−	2.35021i	−0.0544066	−	0.0942349i
$623$	−0.191831			−0.00768556
$624$		0			0
$625$	−22.6477			−0.905910
$626$	−7.69418	−	13.3267i	−0.307521	−	0.532642i
$627$	−22.6896	−	39.2996i	−0.906136	−	1.56947i
$628$	8.35690	−	14.4746i	0.333476	−	0.577598i
$629$	0.509499			0.0203150
$630$	0.0522697	−	0.0905338i	0.00208248	−	0.00360695i
$631$	12.2148	−	21.1566i	0.486262	−	0.842230i	−0.513614	−	0.858022i	$-0.671694\pi$
$631$	12.2148	−	21.1566i	0.486262	−	0.842230i	0.999875	+	0.0157918i	$0.00502689\pi$
$632$	13.8291			0.550091
$633$	−2.54288	+	4.40439i	−0.101070	+	0.175059i
$634$	12.8264	+	22.2160i	0.509401	+	0.882309i
$635$	8.03654	+	13.9197i	0.318920	+	0.552386i
$636$	−9.34481			−0.370546
$637$		0			0
$638$	30.9245			1.22431
$639$	4.35690	+	7.54637i	0.172356	+	0.298530i
$640$	−1.06853	−	1.85075i	−0.0422374	−	0.0731574i
$641$	−24.3991	+	42.2605i	−0.963707	+	1.66919i	−0.250657	+	0.968076i	$0.580647\pi$
$641$	−24.3991	+	42.2605i	−0.963707	+	1.66919i	−0.713050	+	0.701113i	$0.752687\pi$
$642$	8.36658			0.330203
$643$	−14.1347	+	24.4820i	−0.557417	+	0.965475i	0.440294	+	0.897854i	$0.354874\pi$
$643$	−14.1347	+	24.4820i	−0.557417	+	0.965475i	−0.997711	+	0.0676209i	$0.978459\pi$
$644$	0.0663757	−	0.114966i	0.00261557	−	0.00453030i
$645$	−14.3478			−0.564944
$646$	−10.4155	+	18.0402i	−0.409792	+	0.709781i
$647$	−17.4480	−	30.2209i	−0.685953	−	1.18810i	−0.973136	−	0.230229i	$-0.926052\pi$
$647$	−17.4480	−	30.2209i	−0.685953	−	1.18810i	0.287184	−	0.957876i	$-0.407281\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−26.8756			−1.05496
$650$		0			0
$651$	0.440730			0.0172736
$652$	−2.77479	−	4.80608i	−0.108669	−	0.188221i
$653$	5.85786	+	10.1461i	0.229236	+	0.397048i	0.957582	−	0.288162i	$-0.0930440\pi$
$653$	5.85786	+	10.1461i	0.229236	+	0.397048i	−0.728346	+	0.685209i	$0.759711\pi$
$654$	−8.71379	+	15.0927i	−0.340736	+	0.590172i
$655$	10.9524			0.427946
$656$	4.29590	−	7.44071i	0.167727	−	0.290511i
$657$	7.47434	−	12.9459i	0.291602	−	0.505069i
$658$	−0.352584			−0.0137452
$659$	3.56734	−	6.17881i	0.138964	−	0.240692i	−0.788141	−	0.615495i	$-0.788956\pi$
$659$	3.56734	−	6.17881i	0.138964	−	0.240692i	0.927105	+	0.374803i	$0.122290\pi$
$660$	6.72737	+	11.6521i	0.261862	+	0.453559i
$661$	−4.26444	−	7.38622i	−0.165867	−	0.287291i	0.771096	−	0.636719i	$-0.219709\pi$
$661$	−4.26444	−	7.38622i	−0.165867	−	0.287291i	−0.936963	+	0.349429i	$0.886376\pi$
$662$	3.82371			0.148613
$663$		0			0
$664$	−11.1347			−0.432109
$665$	−0.376747	−	0.652545i	−0.0146096	−	0.0253046i
$666$	0.0881460	+	0.152673i	0.00341559	+	0.00591597i
$667$	−6.66487	+	11.5439i	−0.258065	+	0.446982i
$668$	−3.92154			−0.151729
$669$	10.2741	−	17.7953i	0.397221	−	0.688006i
$670$	−5.75302	+	9.96452i	−0.222259	+	0.384963i
$671$	44.7633			1.72807
$672$	−0.0244587	+	0.0423637i	−0.000943514	+	0.00163421i
$673$	15.7969	+	27.3610i	0.608924	+	1.05469i	0.991418	+	0.130729i	$0.0417319\pi$
$673$	15.7969	+	27.3610i	0.608924	+	1.05469i	−0.382494	+	0.923958i	$0.624935\pi$
$674$	−10.0652	−	17.4334i	−0.387696	−	0.671510i
$675$	0.432960			0.0166646
$676$		0			0
$677$	−17.3002			−0.664901			−0.332451	−	0.943121i	$-0.607875\pi$
$677$	−17.3002			−0.664901			−0.332451	+	0.943121i	$0.607875\pi$
$678$	−6.98792	−	12.1034i	−0.268369	−	0.464829i
$679$	−0.0606304	−	0.105015i	−0.00232678	−	0.00403011i
$680$	3.08815	−	5.34883i	0.118425	−	0.205118i
$681$	4.41119			0.169037
$682$	−28.3620	+	49.1245i	−1.08604	+	1.88107i
$683$	15.1978	−	26.3234i	0.581529	−	1.00724i	−0.413770	−	0.910382i	$-0.635788\pi$
$683$	15.1978	−	26.3234i	0.581529	−	1.00724i	0.995298	−	0.0968556i	$-0.0308785\pi$
$684$	−7.20775			−0.275595
$685$	4.27413	−	7.40300i	0.163306	−	0.282854i
$686$	−0.342363	−	0.592990i	−0.0130715	−	0.0226405i
$687$	−0.115293	−	0.199693i	−0.00439871	−	0.00761878i
$688$	6.71379			0.255961
$689$		0			0
$690$	−5.79954			−0.220785
$691$	17.8659	+	30.9447i	0.679652	+	1.17719i	0.975086	+	0.221828i	$0.0712024\pi$
$691$	17.8659	+	30.9447i	0.679652	+	1.17719i	−0.295434	+	0.955363i	$0.595464\pi$
$692$	1.74214	+	3.01747i	0.0662260	+	0.114707i
$693$	0.153989	−	0.266717i	0.00584957	−	0.0101317i
$694$	2.93900			0.111563
$695$	−9.28514	+	16.0823i	−0.352206	+	0.610038i
$696$	2.45593	−	4.25379i	0.0930917	−	0.161240i
$697$	24.8310			0.940541
$698$	3.68664	−	6.38546i	0.139542	−	0.241693i
$699$	−3.91185	−	6.77553i	−0.147960	−	0.256274i
$700$	−0.0105896	−	0.0183418i	−0.000400250	−	0.000693254i
$701$	20.1328			0.760404			0.380202	−	0.924904i	$-0.375855\pi$
$701$	20.1328			0.760404			0.380202	+	0.924904i	$0.375855\pi$
$702$		0			0
$703$	1.27067			0.0479242
$704$	−3.14795	−	5.45241i	−0.118643	−	0.205495i
$705$	7.70171	+	13.3398i	0.290063	+	0.502404i
$706$	−1.00538	+	1.74136i	−0.0378379	+	0.0655371i
$707$	−0.0808502			−0.00304069
$708$	−2.13437	+	3.69685i	−0.0802147	+	0.138936i
$709$	8.30798	−	14.3898i	0.312013	−	0.540422i	−0.666785	−	0.745250i	$-0.732330\pi$
$709$	8.30798	−	14.3898i	0.312013	−	0.540422i	0.978798	+	0.204828i	$0.0656635\pi$
$710$	−18.6219			−0.698868
$711$	−6.91454	+	11.9763i	−0.259316	+	0.449148i
$712$	−1.96077	−	3.39616i	−0.0734830	−	0.127276i
$713$	−12.2252	−	21.1747i	−0.457838	−	0.792998i
$714$	−0.141375			−0.00529083
$715$		0			0
$716$	3.58881			0.134120
$717$	−5.57673	−	9.65918i	−0.208267	−	0.360729i
$718$	15.7289	+	27.2432i	0.586996	+	1.01671i
$719$	−1.02416	+	1.77390i	−0.0381948	+	0.0661554i	−0.884491	−	0.466557i	$-0.845494\pi$
$719$	−1.02416	+	1.77390i	−0.0381948	+	0.0661554i	0.846296	+	0.532713i	$0.178827\pi$
$720$	2.13706			0.0796436
$721$	−0.201415	+	0.348860i	−0.00750107	+	0.0129922i
$722$	−16.4758	+	28.5370i	−0.613167	+	1.06204i
$723$	−3.54527			−0.131850
$724$	−2.75302	+	4.76837i	−0.102315	+	0.177215i
$725$	1.06332	+	1.84172i	0.0394907	+	0.0683998i
$726$	14.3192	+	24.8015i	0.531434	+	0.920470i
$727$	29.9377			1.11033			0.555163	−	0.831741i	$-0.312656\pi$
$727$	29.9377			1.11033			0.555163	+	0.831741i	$0.312656\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	15.9731	+	27.6663i	0.591193	+	1.02398i
$731$	9.70171	+	16.8039i	0.358831	+	0.621513i
$732$	3.55496	−	6.15737i	0.131395	−	0.227583i
$733$	1.46250			0.0540187			0.0270093	−	0.999635i	$-0.491402\pi$
$733$	1.46250			0.0540187			0.0270093	+	0.999635i	$0.491402\pi$
$734$	2.24967	−	3.89654i	0.0830368	−	0.143824i
$735$	−7.47716	+	12.9508i	−0.275799	+	0.477699i
$736$	2.71379			0.100032
$737$	−16.9487	+	29.3560i	−0.624313	+	1.08134i
$738$	4.29590	+	7.44071i	0.158134	+	0.273896i
$739$	20.1933	+	34.9758i	0.742822	+	1.28660i	0.951206	+	0.308558i	$0.0998463\pi$
$739$	20.1933	+	34.9758i	0.742822	+	1.28660i	−0.208384	+	0.978047i	$0.566820\pi$
$740$	−0.376747			−0.0138495
$741$		0			0
$742$	−0.457123			−0.0167815
$743$	−4.88769	−	8.46573i	−0.179312	−	0.310577i	0.762333	−	0.647185i	$-0.224054\pi$
$743$	−4.88769	−	8.46573i	−0.179312	−	0.310577i	−0.941645	+	0.336607i	$0.890720\pi$
$744$	4.50484	+	7.80262i	0.165156	+	0.286058i
$745$	5.20195	−	9.01004i	0.190585	−	0.330102i
$746$	37.8297			1.38504
$747$	5.56734	−	9.64291i	0.203698	−	0.352816i
$748$	9.09783	−	15.7579i	0.332650	−	0.576166i
$749$	0.409271			0.0149544
$750$	−5.80529	+	10.0551i	−0.211979	+	0.367159i
$751$	−17.2729	−	29.9176i	−0.630298	−	1.09171i	−0.987491	−	0.157678i	$-0.949599\pi$
$751$	−17.2729	−	29.9176i	−0.630298	−	1.09171i	0.357192	−	0.934031i	$-0.383734\pi$
$752$	−3.60388	−	6.24210i	−0.131420	−	0.227626i
$753$	4.17092			0.151997
$754$		0			0
$755$	31.5138			1.14690
$756$	−0.0244587	−	0.0423637i	−0.000889553	−	0.00154075i
$757$	2.57242	+	4.45556i	0.0934961	+	0.161940i	0.908980	−	0.416840i	$-0.136862\pi$
$757$	2.57242	+	4.45556i	0.0934961	+	0.161940i	−0.815484	+	0.578780i	$0.803529\pi$
$758$	−4.21983	+	7.30896i	−0.153271	+	0.265474i
$759$	−17.0858			−0.620174
$760$	7.70171	−	13.3398i	0.279370	−	0.483884i
$761$	−9.75600	+	16.8979i	−0.353655	+	0.612548i	−0.986887	−	0.161414i	$-0.948395\pi$
$761$	−9.75600	+	16.8979i	−0.353655	+	0.612548i	0.633232	+	0.773962i	$0.281728\pi$
$762$	7.52111			0.272461
$763$	−0.426256	+	0.738296i	−0.0154315	+	0.0267281i
$764$	2.82908	+	4.90012i	0.102353	+	0.177280i
$765$	3.08815	+	5.34883i	0.111652	+	0.193387i
$766$	−1.28621			−0.0464726
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	2.87800	+	4.98485i	0.103783	+	0.179758i	0.913241	−	0.407421i	$-0.133572\pi$
$769$	2.87800	+	4.98485i	0.103783	+	0.179758i	−0.809457	+	0.587179i	$0.800238\pi$
$770$	0.329085	+	0.569992i	0.0118594	+	0.0205411i
$771$	−5.44504	+	9.43109i	−0.196098	+	0.339652i
$772$	−13.4034			−0.482400
$773$	−2.06369	+	3.57441i	−0.0742257	+	0.128563i	−0.900749	−	0.434339i	$-0.856982\pi$
$773$	−2.06369	+	3.57441i	−0.0742257	+	0.128563i	0.826524	+	0.562902i	$0.190315\pi$
$774$	−3.35690	+	5.81431i	−0.120661	+	0.208991i
$775$	−3.90084			−0.140122
$776$	1.23945	−	2.14678i	0.0444935	−	0.0770651i
$777$	0.00431187	+	0.00746837i	0.000154687	+	0.000267926i
$778$	−11.6962	−	20.2584i	−0.419329	−	0.726299i
$779$	61.9275			2.21878
$780$		0			0
$781$	−54.8611			−1.96309
$782$	3.92154	+	6.79231i	0.140234	+	0.242893i
$783$	2.45593	+	4.25379i	0.0877677	+	0.152018i
$784$	3.49880	−	6.06011i	0.124957	−	0.216432i
$785$	−35.7184			−1.27485
$786$	2.56249	−	4.43836i	0.0914010	−	0.158311i
$787$	−8.11960	+	14.0636i	−0.289433	+	0.501312i	−0.973674	−	0.227943i	$-0.926800\pi$
$787$	−8.11960	+	14.0636i	−0.289433	+	0.501312i	0.684242	+	0.729255i	$0.260133\pi$
$788$	−19.9812			−0.711801
$789$	−15.6136	+	27.0435i	−0.555858	+	0.962774i
$790$	−14.7768	−	25.5942i	−0.525735	−	0.910601i
$791$	−0.341830	−	0.592068i	−0.0121541	−	0.0210515i
$792$	6.29590			0.223715
$793$		0			0
$794$	−37.0858			−1.31612
$795$	9.98523	+	17.2949i	0.354140	+	0.613388i
$796$	3.12080	+	5.40539i	0.110614	+	0.191589i
$797$	−8.05741	+	13.9558i	−0.285408	+	0.494341i	−0.972708	−	0.232032i	$-0.925462\pi$
$797$	−8.05741	+	13.9558i	−0.285408	+	0.494341i	0.687300	+	0.726374i	$0.258796\pi$
$798$	−0.352584			−0.0124813
$799$	10.4155	−	18.0402i	0.368474	−	0.638216i
$800$	0.216480	−	0.374955i	0.00765373	−	0.0132566i
$801$	3.92154			0.138561
$802$	2.43296	−	4.21401i	0.0859108	−	0.148802i
$803$	47.0577	+	81.5063i	1.66063	+	2.87630i
$804$	2.69202	+	4.66272i	0.0949403	+	0.164441i
$805$	−0.283698			−0.00999905
$806$		0			0
$807$	−15.9172			−0.560313
$808$	−0.826396	−	1.43136i	−0.0290725	−	0.0503551i
$809$	−20.0761	−	34.7728i	−0.705837	−	1.22255i	−0.966389	−	0.257085i	$-0.917238\pi$
$809$	−20.0761	−	34.7728i	−0.705837	−	1.22255i	0.260552	−	0.965460i	$-0.416096\pi$
$810$	−1.06853	+	1.85075i	−0.0375444	+	0.0650288i
$811$	−39.8646			−1.39984			−0.699918	−	0.714224i	$-0.746780\pi$
$811$	−39.8646			−1.39984			−0.699918	+	0.714224i	$0.746780\pi$
$812$	0.120137	−	0.208084i	0.00421600	−	0.00730232i
$813$	−1.76055	+	3.04937i	−0.0617453	+	0.106946i
$814$	−1.10992			−0.0389025
$815$	−5.92990	+	10.2709i	−0.207715	+	0.359774i
$816$	−1.44504	−	2.50289i	−0.0505866	−	0.0876185i
$817$	24.1957	+	41.9081i	0.846499	+	1.46618i
$818$	0.445042			0.0155605
$819$		0			0
$820$	−18.3612			−0.641201
$821$	−3.12714	−	5.41636i	−0.109138	−	0.189032i	0.806283	−	0.591529i	$-0.201476\pi$
$821$	−3.12714	−	5.41636i	−0.109138	−	0.189032i	−0.915421	+	0.402497i	$0.868142\pi$
$822$	−2.00000	−	3.46410i	−0.0697580	−	0.120824i
$823$	2.37167	−	4.10785i	0.0826711	−	0.143191i	−0.821725	−	0.569884i	$-0.806988\pi$
$823$	2.37167	−	4.10785i	0.0826711	−	0.143191i	0.904396	+	0.426693i	$0.140322\pi$
$824$	−8.23490			−0.286876
$825$	−1.36294	+	2.36068i	−0.0474514	+	0.0821882i
$826$	−0.104408	+	0.180840i	−0.00363282	+	0.00629222i
$827$	0.716185			0.0249042			0.0124521	−	0.999922i	$-0.496036\pi$
$827$	0.716185			0.0249042			0.0124521	+	0.999922i	$0.496036\pi$
$828$	−1.35690	+	2.35021i	−0.0471554	+	0.0816755i
$829$	18.0030	+	31.1821i	0.625269	+	1.08300i	0.988489	+	0.151295i	$0.0483443\pi$
$829$	18.0030	+	31.1821i	0.625269	+	1.08300i	−0.363219	+	0.931704i	$0.618322\pi$
$830$	11.8977	+	20.6075i	0.412977	+	0.715297i
$831$	8.58104			0.297673
$832$		0			0
$833$	20.2237			0.700709
$834$	4.34481	+	7.52544i	0.150449	+	0.260585i
$835$	4.19029	+	7.25780i	0.145011	+	0.251167i
$836$	22.6896	−	39.2996i	0.784737	−	1.35920i
$837$	−9.00969			−0.311420
$838$	−8.99343	+	15.5771i	−0.310673	+	0.538101i
$839$	−10.7778	+	18.6677i	−0.372090	+	0.644479i	−0.989887	−	0.141859i	$-0.954692\pi$
$839$	−10.7778	+	18.6677i	−0.372090	+	0.644479i	0.617797	+	0.786338i	$0.288025\pi$
$840$	0.104539			0.00360695
$841$	2.43685	−	4.22074i	0.0840291	−	0.145543i
$842$	−10.6407	−	18.4303i	−0.366703	−	0.635148i
$843$	4.03923	+	6.99615i	0.139118	+	0.240960i
$844$	−5.08575			−0.175059
$845$		0			0
$846$	7.20775			0.247808
$847$	0.700455	+	1.21322i	0.0240679	+	0.0416869i
$848$	−4.67241	−	8.09285i	−0.160451	−	0.277909i
$849$	−8.70171	+	15.0718i	−0.298642	+	0.517263i
$850$	1.25129			0.0429189
$851$	0.239210	−	0.414324i	0.00820001	−	0.0142028i
$852$	−4.35690	+	7.54637i	−0.149265	+	0.258534i
$853$	−37.8237			−1.29506			−0.647530	−	0.762040i	$-0.724198\pi$
$853$	−37.8237			−1.29506			−0.647530	+	0.762040i	$0.724198\pi$
$854$	0.173899	−	0.301202i	0.00595070	−	0.0103069i
$855$	7.70171	+	13.3398i	0.263393	+	0.456210i
$856$	4.18329	+	7.24567i	0.142982	+	0.247652i
$857$	−6.58317			−0.224877			−0.112438	−	0.993659i	$-0.535866\pi$
$857$	−6.58317			−0.224877			−0.112438	+	0.993659i	$0.535866\pi$
$858$		0			0
$859$	−20.6246			−0.703702			−0.351851	−	0.936056i	$-0.614448\pi$
$859$	−20.6246			−0.703702			−0.351851	+	0.936056i	$0.614448\pi$
$860$	−7.17390	−	12.4256i	−0.244628	−	0.423708i
$861$	0.210144	+	0.363980i	0.00716168	+	0.0124044i
$862$	−12.3569	+	21.4028i	−0.420878	+	0.728981i
$863$	15.9081			0.541519			0.270760	−	0.962647i	$-0.412725\pi$
$863$	15.9081			0.541519			0.270760	+	0.962647i	$0.412725\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	3.72305	−	6.44852i	0.126588	−	0.219256i
$866$	32.2174			1.09479
$867$	−4.32371	+	7.48888i	−0.146841	+	0.254336i
$868$	0.220365	+	0.381683i	0.00747968	+	0.0129552i
$869$	−43.5332	−	75.4018i	−1.47676	−	2.55783i
$870$	−10.4969			−0.355880
$871$		0			0
$872$	−17.4276			−0.590172
$873$	1.23945	+	2.14678i	0.0419489	+	0.0726577i
$874$	9.78017	+	16.9397i	0.330819	+	0.572995i
$875$	−0.283979	+	0.491867i	−0.00960025	+	0.0166281i
$876$	14.9487			0.505069
$877$	7.80194	−	13.5134i	0.263453	−	0.456313i	−0.703704	−	0.710493i	$-0.748472\pi$
$877$	7.80194	−	13.5134i	0.263453	−	0.456313i	0.967157	+	0.254179i	$0.0818054\pi$
$878$	−16.0438	+	27.7887i	−0.541453	+	0.937825i
$879$	−19.3709			−0.653364
$880$	−6.72737	+	11.6521i	−0.226779	+	0.392794i
$881$	7.12737	+	12.3450i	0.240127	+	0.415913i	0.960750	−	0.277414i	$-0.0894775\pi$
$881$	7.12737	+	12.3450i	0.240127	+	0.415913i	−0.720623	+	0.693327i	$0.756144\pi$
$882$	3.49880	+	6.06011i	0.117811	+	0.204054i
$883$	1.65817			0.0558019			0.0279009	−	0.999611i	$-0.491118\pi$
$883$	1.65817			0.0558019			0.0279009	+	0.999611i	$0.491118\pi$
$884$		0			0
$885$	9.12259			0.306652
$886$	−10.2555	−	17.7630i	−0.344539	−	0.596760i
$887$	9.60148	+	16.6303i	0.322386	+	0.558389i	0.980980	−	0.194109i	$-0.0621817\pi$
$887$	9.60148	+	16.6303i	0.322386	+	0.558389i	−0.658594	+	0.752499i	$0.728848\pi$
$888$	−0.0881460	+	0.152673i	−0.00295799	+	0.00512338i
$889$	0.367913			0.0123394
$890$	−4.19029	+	7.25780i	−0.140459	+	0.243282i
$891$	−3.14795	+	5.45241i	−0.105460	+	0.182662i
$892$	20.5483			0.688006
$893$	25.9758	−	44.9915i	0.869248	−	1.50558i
$894$	−2.43416	−	4.21608i	−0.0814104	−	0.141007i
$895$	−3.83476	−	6.64199i	−0.128182	−	0.222017i
$896$	−0.0489173			−0.00163421
$897$		0			0
$898$	−15.3163			−0.511113
$899$	−22.1271	−	38.3253i	−0.737981	−	1.27822i
$900$	0.216480	+	0.374955i	0.00721600	+	0.0124985i
$901$	13.5036	−	23.3890i	0.449872	−	0.779201i
$902$	−54.0930			−1.80110
$903$	−0.164210	+	0.284421i	−0.00546458	+	0.00946493i
$904$	6.98792	−	12.1034i	0.232415	−	0.402554i
$905$	11.7668			0.391140
$906$	7.37316	−	12.7707i	0.244957	−	0.424278i
$907$	16.1836	+	28.0308i	0.537367	+	0.930747i	0.999045	+	0.0436995i	$0.0139144\pi$
$907$	16.1836	+	28.0308i	0.537367	+	0.930747i	−0.461678	+	0.887048i	$0.652752\pi$
$908$	2.20560	+	3.82020i	0.0731952	+	0.126778i
$909$	1.65279			0.0548197
$910$		0			0
$911$	−33.9624			−1.12523			−0.562613	−	0.826721i	$-0.690204\pi$
$911$	−33.9624			−1.12523			−0.562613	+	0.826721i	$0.690204\pi$
$912$	−3.60388	−	6.24210i	−0.119336	−	0.206696i
$913$	35.0514	+	60.7108i	1.16003	+	2.00923i
$914$	9.59299	−	16.6155i	0.317308	−	0.549593i
$915$	−15.1943			−0.502309
$916$	0.115293	−	0.199693i	0.00380939	−	0.00659806i
$917$	0.125350	−	0.217113i	0.00413943	−	0.00716970i
$918$	2.89008			0.0953870
$919$	10.0390	−	17.3880i	0.331156	−	0.573579i	−0.651583	−	0.758577i	$-0.725895\pi$
$919$	10.0390	−	17.3880i	0.331156	−	0.573579i	0.982739	+	0.184999i	$0.0592281\pi$
$920$	−2.89977	−	5.02255i	−0.0956027	−	0.165589i
$921$	6.21313	+	10.7615i	0.204730	+	0.354602i
$922$	8.31229			0.273751
$923$		0			0
$924$	0.307979			0.0101317
$925$	−0.0381637	−	0.0661015i	−0.00125482	−	0.00217340i
$926$	3.16421	+	5.48057i	0.103982	+	0.180103i
$927$	4.11745	−	7.13163i	0.135235	−	0.234233i
$928$	4.91185			0.161240
$929$	−28.0640	+	48.6082i	−0.920749	+	1.59478i	−0.122491	+	0.992470i	$0.539088\pi$
$929$	−28.0640	+	48.6082i	−0.920749	+	1.59478i	−0.798258	+	0.602315i	$0.794245\pi$
$930$	9.62714	−	16.6747i	0.315686	−	0.546785i
$931$	50.4370			1.65301
$932$	3.91185	−	6.77553i	0.128137	−	0.221940i
$933$	1.35690	+	2.35021i	0.0444228	+	0.0769425i
$934$	15.5939	+	27.0095i	0.510250	+	0.883778i
$935$	−38.8853			−1.27169
$936$		0			0
$937$	27.0291			0.883001			0.441501	−	0.897261i	$-0.354446\pi$
$937$	27.0291			0.883001			0.441501	+	0.897261i	$0.354446\pi$
$938$	0.131687	+	0.228088i	0.00429972	+	0.00744733i
$939$	7.69418	+	13.3267i	0.251090	+	0.434901i
$940$	−7.70171	+	13.3398i	−0.251202	+	0.435095i
$941$	−24.0277			−0.783282			−0.391641	−	0.920118i	$-0.628092\pi$
$941$	−24.0277			−0.783282			−0.391641	+	0.920118i	$0.628092\pi$
$942$	−8.35690	+	14.4746i	−0.272282	+	0.471607i
$943$	11.6582	−	20.1925i	0.379642	−	0.657560i
$944$	−4.26875			−0.138936
$945$	−0.0522697	+	0.0905338i	−0.00170033	+	0.00294507i
$946$	−21.1347	−	36.6063i	−0.687147	−	1.19017i
$947$	13.3983	+	23.2065i	0.435386	+	0.754110i	0.997327	−	0.0730670i	$-0.0232787\pi$
$947$	13.3983	+	23.2065i	0.435386	+	0.754110i	−0.561941	+	0.827177i	$0.689945\pi$
$948$	−13.8291			−0.449148
$949$		0			0
$950$	3.12067			0.101248
$951$	−12.8264	−	22.2160i	−0.415924	−	0.720402i
$952$	−0.0706876	−	0.122435i	−0.00229100	−	0.00396813i
$953$	−17.2107	+	29.8099i	−0.557510	+	0.965636i	0.440193	+	0.897903i	$0.354910\pi$
$953$	−17.2107	+	29.8099i	−0.557510	+	0.965636i	−0.997703	+	0.0677332i	$0.978423\pi$
$954$	9.34481			0.302550
$955$	6.04593	−	10.4719i	0.195642	−	0.338862i
$956$	5.57673	−	9.65918i	0.180364	−	0.312400i
$957$	−30.9245			−0.999648
$958$	8.96615	−	15.5298i	0.289683	−	0.501746i
$959$	−0.0978347	−	0.169455i	−0.00315925	−	0.00547198i
$960$	1.06853	+	1.85075i	0.0344867	+	0.0597327i
$961$	50.1745			1.61853
$962$		0			0
$963$	−8.36658			−0.269609
$964$	−1.77263	−	3.07029i	−0.0570927	−	0.0988875i
$965$	14.3220	+	24.8064i	0.461041	+	0.798546i
$966$	−0.0663757	+	0.114966i	−0.00213560	+	0.00369898i
$967$	26.2631			0.844565			0.422282	−	0.906464i	$-0.361229\pi$
$967$	26.2631			0.844565			0.422282	+	0.906464i	$0.361229\pi$
$968$	−14.3192	+	24.8015i	−0.460235	+	0.797151i
$969$	10.4155	−	18.0402i	0.334594	−	0.579534i
$970$	−5.29755			−0.170094
$971$	19.9921	−	34.6273i	0.641577	−	1.11124i	−0.343504	−	0.939151i	$-0.611614\pi$
$971$	19.9921	−	34.6273i	0.641577	−	1.11124i	0.985081	−	0.172093i	$-0.0550528\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	0.212537	+	0.368124i	0.00681362	+	0.0118015i
$974$	30.3279			0.971770
$975$		0			0
$976$	7.10992			0.227583
$977$	−2.29159	−	3.96914i	−0.0733143	−	0.126984i	0.827038	−	0.562146i	$-0.190024\pi$
$977$	−2.29159	−	3.96914i	−0.0733143	−	0.126984i	−0.900352	+	0.435162i	$0.856691\pi$
$978$	2.77479	+	4.80608i	0.0887280	+	0.153681i
$979$	−12.3448	+	21.3818i	−0.394542	+	0.683367i
$980$	−14.9543			−0.477699
$981$	8.71379	−	15.0927i	0.278210	−	0.481874i
$982$	−15.0477	+	26.0634i	−0.480192	+	0.831717i
$983$	−10.6848			−0.340794			−0.170397	−	0.985376i	$-0.554505\pi$
$983$	−10.6848			−0.340794			−0.170397	+	0.985376i	$0.554505\pi$
$984$	−4.29590	+	7.44071i	−0.136948	+	0.237201i
$985$	21.3506	+	36.9803i	0.680285	+	1.17829i
$986$	7.09783	+	12.2938i	0.226041	+	0.391515i
$987$	0.352584			0.0112229
$988$		0			0
$989$	18.2198			0.579357
$990$	−6.72737	−	11.6521i	−0.213810	−	0.370329i
$991$	−25.3010	−	43.8227i	−0.803714	−	1.39207i	−0.917156	−	0.398529i	$-0.869521\pi$
$991$	−25.3010	−	43.8227i	−0.803714	−	1.39207i	0.113442	−	0.993545i	$-0.463812\pi$
$992$	−4.50484	+	7.80262i	−0.143029	+	0.247733i
$993$	−3.82371			−0.121342
$994$	−0.213128	+	0.369148i	−0.00676000	+	0.0117087i
$995$	6.66935	−	11.5517i	0.211433	−	0.366212i
$996$	11.1347			0.352816
$997$	17.9801	−	31.1425i	0.569437	−	0.986294i	−0.427185	−	0.904164i	$-0.640495\pi$
$997$	17.9801	−	31.1425i	0.569437	−	0.986294i	0.996622	−	0.0821294i	$-0.0261721\pi$
$998$		0			0
$999$	−0.0881460	−	0.152673i	−0.00278882	−	0.00483037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.l.991.2		6
13.2	odd	12		1014.2.b.f.337.2		6
13.3	even	3		1014.2.a.n.1.2	yes	3
13.4	even	6		1014.2.e.n.529.2		6
13.5	odd	4		1014.2.i.h.361.2		12
13.6	odd	12		1014.2.i.h.823.5		12
13.7	odd	12		1014.2.i.h.823.2		12
13.8	odd	4		1014.2.i.h.361.5		12
13.9	even	3	inner	1014.2.e.l.529.2		6
13.10	even	6		1014.2.a.l.1.2	✓	3
13.11	odd	12		1014.2.b.f.337.5		6
13.12	even	2		1014.2.e.n.991.2		6
39.2	even	12		3042.2.b.o.1351.5		6
39.11	even	12		3042.2.b.o.1351.2		6
39.23	odd	6		3042.2.a.bh.1.2		3
39.29	odd	6		3042.2.a.ba.1.2		3
52.3	odd	6		8112.2.a.cm.1.2		3
52.23	odd	6		8112.2.a.cj.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.l.1.2	✓	3	13.10	even	6
1014.2.a.n.1.2	yes	3	13.3	even	3
1014.2.b.f.337.2		6	13.2	odd	12
1014.2.b.f.337.5		6	13.11	odd	12
1014.2.e.l.529.2		6	13.9	even	3	inner
1014.2.e.l.991.2		6	1.1	even	1	trivial
1014.2.e.n.529.2		6	13.4	even	6
1014.2.e.n.991.2		6	13.12	even	2
1014.2.i.h.361.2		12	13.5	odd	4
1014.2.i.h.361.5		12	13.8	odd	4
1014.2.i.h.823.2		12	13.7	odd	12
1014.2.i.h.823.5		12	13.6	odd	12
3042.2.a.ba.1.2		3	39.29	odd	6
3042.2.a.bh.1.2		3	39.23	odd	6
3042.2.b.o.1351.2		6	39.11	even	12
3042.2.b.o.1351.5		6	39.2	even	12
8112.2.a.cj.1.2		3	52.23	odd	6
8112.2.a.cm.1.2		3	52.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.13706 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.0244587 - 0.0423637i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.13706 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.0244587 - 0.0423637i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.06853 - 1.85075i) q^{10} +(-3.14795 - 5.45241i) q^{11} -1.00000 q^{12} -0.0489173 q^{14} +(1.06853 + 1.85075i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.44504 - 2.50289i) q^{17} +1.00000 q^{18} +(3.60388 - 6.24210i) q^{19} +(-1.06853 + 1.85075i) q^{20} +0.0489173 q^{21} +(-3.14795 + 5.45241i) q^{22} +(-1.35690 - 2.35021i) q^{23} +(0.500000 + 0.866025i) q^{24} -0.432960 q^{25} -1.00000 q^{27} +(0.0244587 + 0.0423637i) q^{28} +(-2.45593 - 4.25379i) q^{29} +(1.06853 - 1.85075i) q^{30} +9.00969 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.14795 - 5.45241i) q^{33} -2.89008 q^{34} +(0.0522697 - 0.0905338i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.0881460 + 0.152673i) q^{37} -7.20775 q^{38} +2.13706 q^{40} +(4.29590 + 7.44071i) q^{41} +(-0.0244587 - 0.0423637i) q^{42} +(-3.35690 + 5.81431i) q^{43} +6.29590 q^{44} +(-1.06853 + 1.85075i) q^{45} +(-1.35690 + 2.35021i) q^{46} +7.20775 q^{47} +(0.500000 - 0.866025i) q^{48} +(3.49880 + 6.06011i) q^{49} +(0.216480 + 0.374955i) q^{50} +2.89008 q^{51} +9.34481 q^{53} +(0.500000 + 0.866025i) q^{54} +(-6.72737 - 11.6521i) q^{55} +(0.0244587 - 0.0423637i) q^{56} +7.20775 q^{57} +(-2.45593 + 4.25379i) q^{58} +(2.13437 - 3.69685i) q^{59} -2.13706 q^{60} +(-3.55496 + 6.15737i) q^{61} +(-4.50484 - 7.80262i) q^{62} +(0.0244587 + 0.0423637i) q^{63} +1.00000 q^{64} -6.29590 q^{66} +(-2.69202 - 4.66272i) q^{67} +(1.44504 + 2.50289i) q^{68} +(1.35690 - 2.35021i) q^{69} -0.104539 q^{70} +(4.35690 - 7.54637i) q^{71} +(-0.500000 + 0.866025i) q^{72} -14.9487 q^{73} +(0.0881460 - 0.152673i) q^{74} +(-0.216480 - 0.374955i) q^{75} +(3.60388 + 6.24210i) q^{76} -0.307979 q^{77} +13.8291 q^{79} +(-1.06853 - 1.85075i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.29590 - 7.44071i) q^{82} -11.1347 q^{83} +(-0.0244587 + 0.0423637i) q^{84} +(3.08815 - 5.34883i) q^{85} +6.71379 q^{86} +(2.45593 - 4.25379i) q^{87} +(-3.14795 - 5.45241i) q^{88} +(-1.96077 - 3.39616i) q^{89} +2.13706 q^{90} +2.71379 q^{92} +(4.50484 + 7.80262i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(7.70171 - 13.3398i) q^{95} -1.00000 q^{96} +(1.23945 - 2.14678i) q^{97} +(3.49880 - 6.06011i) q^{98} +6.29590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{7} + 6 q^{8} - 3 q^{9} - q^{10} - 5 q^{11} - 6 q^{12} + 18 q^{14} + q^{15} - 3 q^{16} + 8 q^{17} + 6 q^{18} + 4 q^{19} - q^{20} - 18 q^{21} - 5 q^{22} + 3 q^{24} + 36 q^{25} - 6 q^{27} - 9 q^{28} - 11 q^{29} + q^{30} + 10 q^{31} - 3 q^{32} + 5 q^{33} - 16 q^{34} + 4 q^{35} - 3 q^{36} + 8 q^{37} - 8 q^{38} + 2 q^{40} - 2 q^{41} + 9 q^{42} - 12 q^{43} + 10 q^{44} - q^{45} + 8 q^{47} + 3 q^{48} - 20 q^{49} - 18 q^{50} + 16 q^{51} + 10 q^{53} + 3 q^{54} - 18 q^{55} - 9 q^{56} + 8 q^{57} - 11 q^{58} + 5 q^{59} - 2 q^{60} - 22 q^{61} - 5 q^{62} - 9 q^{63} + 6 q^{64} - 10 q^{66} - 6 q^{67} + 8 q^{68} - 8 q^{70} + 18 q^{71} - 3 q^{72} - 26 q^{73} + 8 q^{74} + 18 q^{75} + 4 q^{76} - 12 q^{77} + 62 q^{79} - q^{80} - 3 q^{81} - 2 q^{82} + 26 q^{83} + 9 q^{84} + 26 q^{85} + 24 q^{86} + 11 q^{87} - 5 q^{88} + 14 q^{89} + 2 q^{90} + 5 q^{93} - 4 q^{94} - 8 q^{95} - 6 q^{96} + 23 q^{97} - 20 q^{98} + 10 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^7 + 6 * q^8 - 3 * q^9 - q^10 - 5 * q^11 - 6 * q^12 + 18 * q^14 + q^15 - 3 * q^16 + 8 * q^17 + 6 * q^18 + 4 * q^19 - q^20 - 18 * q^21 - 5 * q^22 + 3 * q^24 + 36 * q^25 - 6 * q^27 - 9 * q^28 - 11 * q^29 + q^30 + 10 * q^31 - 3 * q^32 + 5 * q^33 - 16 * q^34 + 4 * q^35 - 3 * q^36 + 8 * q^37 - 8 * q^38 + 2 * q^40 - 2 * q^41 + 9 * q^42 - 12 * q^43 + 10 * q^44 - q^45 + 8 * q^47 + 3 * q^48 - 20 * q^49 - 18 * q^50 + 16 * q^51 + 10 * q^53 + 3 * q^54 - 18 * q^55 - 9 * q^56 + 8 * q^57 - 11 * q^58 + 5 * q^59 - 2 * q^60 - 22 * q^61 - 5 * q^62 - 9 * q^63 + 6 * q^64 - 10 * q^66 - 6 * q^67 + 8 * q^68 - 8 * q^70 + 18 * q^71 - 3 * q^72 - 26 * q^73 + 8 * q^74 + 18 * q^75 + 4 * q^76 - 12 * q^77 + 62 * q^79 - q^80 - 3 * q^81 - 2 * q^82 + 26 * q^83 + 9 * q^84 + 26 * q^85 + 24 * q^86 + 11 * q^87 - 5 * q^88 + 14 * q^89 + 2 * q^90 + 5 * q^93 - 4 * q^94 - 8 * q^95 - 6 * q^96 + 23 * q^97 - 20 * q^98 + 10 * q^99

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