LMFDB - Embedded newform 1014.2.e.g.991.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.g.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.267949 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.366025 + 0.633975i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.267949 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.366025 + 0.633975i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.133975 - 0.232051i) q^{10} +(-2.36603 - 4.09808i) q^{11} +1.00000 q^{12} +0.732051 q^{14} +(-0.133975 - 0.232051i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.13397 - 1.96410i) q^{17} +1.00000 q^{18} +(-0.633975 + 1.09808i) q^{19} +(-0.133975 + 0.232051i) q^{20} +0.732051 q^{21} +(-2.36603 + 4.09808i) q^{22} +(3.09808 + 5.36603i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.92820 q^{25} +1.00000 q^{27} +(-0.366025 - 0.633975i) q^{28} +(-1.23205 - 2.13397i) q^{29} +(-0.133975 + 0.232051i) q^{30} -5.46410 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.36603 + 4.09808i) q^{33} -2.26795 q^{34} +(-0.0980762 + 0.169873i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.23205 - 9.06218i) q^{37} +1.26795 q^{38} +0.267949 q^{40} +(-5.69615 - 9.86603i) q^{41} +(-0.366025 - 0.633975i) q^{42} +(-3.83013 + 6.63397i) q^{43} +4.73205 q^{44} +(-0.133975 + 0.232051i) q^{45} +(3.09808 - 5.36603i) q^{46} -8.19615 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.23205 + 5.59808i) q^{49} +(2.46410 + 4.26795i) q^{50} -2.26795 q^{51} +0.464102 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.633975 - 1.09808i) q^{55} +(-0.366025 + 0.633975i) q^{56} +1.26795 q^{57} +(-1.23205 + 2.13397i) q^{58} +(-4.00000 + 6.92820i) q^{59} +0.267949 q^{60} +(-0.598076 + 1.03590i) q^{61} +(2.73205 + 4.73205i) q^{62} +(-0.366025 - 0.633975i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(5.56218 + 9.63397i) q^{67} +(1.13397 + 1.96410i) q^{68} +(3.09808 - 5.36603i) q^{69} +0.196152 q^{70} +(-0.633975 + 1.09808i) q^{71} +(-0.500000 + 0.866025i) q^{72} -9.73205 q^{73} +(-5.23205 + 9.06218i) q^{74} +(2.46410 + 4.26795i) q^{75} +(-0.633975 - 1.09808i) q^{76} +3.46410 q^{77} -9.46410 q^{79} +(-0.133975 - 0.232051i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.69615 + 9.86603i) q^{82} +10.1962 q^{83} +(-0.366025 + 0.633975i) q^{84} +(0.303848 - 0.526279i) q^{85} +7.66025 q^{86} +(-1.23205 + 2.13397i) q^{87} +(-2.36603 - 4.09808i) q^{88} +(1.26795 + 2.19615i) q^{89} +0.267949 q^{90} -6.19615 q^{92} +(2.73205 + 4.73205i) q^{93} +(4.09808 + 7.09808i) q^{94} +(-0.169873 + 0.294229i) q^{95} +1.00000 q^{96} +(3.00000 - 5.19615i) q^{97} +(3.23205 - 5.59808i) q^{98} +4.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} - 4 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{21} - 6 q^{22} + 2 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{27} + 2 q^{28} + 2 q^{29} - 4 q^{30} - 8 q^{31} - 2 q^{32} - 6 q^{33} - 16 q^{34} + 10 q^{35} - 2 q^{36} - 14 q^{37} + 12 q^{38} + 8 q^{40} - 2 q^{41} + 2 q^{42} + 2 q^{43} + 12 q^{44} - 4 q^{45} + 2 q^{46} - 12 q^{47} - 2 q^{48} + 6 q^{49} - 4 q^{50} - 16 q^{51} - 12 q^{53} - 2 q^{54} - 6 q^{55} + 2 q^{56} + 12 q^{57} + 2 q^{58} - 16 q^{59} + 8 q^{60} + 8 q^{61} + 4 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 8 q^{68} + 2 q^{69} - 20 q^{70} - 6 q^{71} - 2 q^{72} - 32 q^{73} - 14 q^{74} - 4 q^{75} - 6 q^{76} - 24 q^{79} - 4 q^{80} - 2 q^{81} - 2 q^{82} + 20 q^{83} + 2 q^{84} + 22 q^{85} - 4 q^{86} + 2 q^{87} - 6 q^{88} + 12 q^{89} + 8 q^{90} - 4 q^{92} + 4 q^{93} + 6 q^{94} - 18 q^{95} + 4 q^{96} + 12 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 - 4 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^14 - 4 * q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 - 6 * q^19 - 4 * q^20 - 4 * q^21 - 6 * q^22 + 2 * q^23 - 2 * q^24 + 8 * q^25 + 4 * q^27 + 2 * q^28 + 2 * q^29 - 4 * q^30 - 8 * q^31 - 2 * q^32 - 6 * q^33 - 16 * q^34 + 10 * q^35 - 2 * q^36 - 14 * q^37 + 12 * q^38 + 8 * q^40 - 2 * q^41 + 2 * q^42 + 2 * q^43 + 12 * q^44 - 4 * q^45 + 2 * q^46 - 12 * q^47 - 2 * q^48 + 6 * q^49 - 4 * q^50 - 16 * q^51 - 12 * q^53 - 2 * q^54 - 6 * q^55 + 2 * q^56 + 12 * q^57 + 2 * q^58 - 16 * q^59 + 8 * q^60 + 8 * q^61 + 4 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^66 - 2 * q^67 + 8 * q^68 + 2 * q^69 - 20 * q^70 - 6 * q^71 - 2 * q^72 - 32 * q^73 - 14 * q^74 - 4 * q^75 - 6 * q^76 - 24 * q^79 - 4 * q^80 - 2 * q^81 - 2 * q^82 + 20 * q^83 + 2 * q^84 + 22 * q^85 - 4 * q^86 + 2 * q^87 - 6 * q^88 + 12 * q^89 + 8 * q^90 - 4 * q^92 + 4 * q^93 + 6 * q^94 - 18 * q^95 + 4 * q^96 + 12 * q^97 + 6 * q^98 + 12 * 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
$5$	0.267949			0.119831			0.0599153	−	0.998203i	$-0.480917\pi$
$5$	0.267949			0.119831			0.0599153	+	0.998203i	$0.480917\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.366025	+	0.633975i	−0.138345	+	0.239620i	−0.926870	−	0.375382i	$-0.877511\pi$
$7$	−0.366025	+	0.633975i	−0.138345	+	0.239620i	0.788526	+	0.615002i	$0.210845\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.133975	−	0.232051i	−0.0423665	−	0.0733809i
$11$	−2.36603	−	4.09808i	−0.713384	−	1.23562i	−0.963580	−	0.267421i	$-0.913828\pi$
$11$	−2.36603	−	4.09808i	−0.713384	−	1.23562i	0.250196	−	0.968195i	$-0.419505\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	0.732051			0.195649
$15$	−0.133975	−	0.232051i	−0.0345921	−	0.0599153i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.13397	−	1.96410i	0.275029	−	0.476365i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	1.13397	−	1.96410i	0.275029	−	0.476365i	0.970143	+	0.242536i	$0.0779791\pi$
$18$	1.00000			0.235702
$19$	−0.633975	+	1.09808i	−0.145444	+	0.251916i	−0.929538	−	0.368725i	$-0.879794\pi$
$19$	−0.633975	+	1.09808i	−0.145444	+	0.251916i	0.784095	+	0.620641i	$0.213128\pi$
$20$	−0.133975	+	0.232051i	−0.0299576	+	0.0518881i
$21$	0.732051			0.159747
$22$	−2.36603	+	4.09808i	−0.504438	+	0.873713i
$23$	3.09808	+	5.36603i	0.645994	+	1.11889i	0.984071	+	0.177775i	$0.0568901\pi$
$23$	3.09808	+	5.36603i	0.645994	+	1.11889i	−0.338078	+	0.941118i	$0.609777\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.92820			−0.985641
$26$		0			0
$27$	1.00000			0.192450
$28$	−0.366025	−	0.633975i	−0.0691723	−	0.119810i
$29$	−1.23205	−	2.13397i	−0.228786	−	0.396269i	0.728663	−	0.684873i	$-0.240142\pi$
$29$	−1.23205	−	2.13397i	−0.228786	−	0.396269i	−0.957449	+	0.288604i	$0.906809\pi$
$30$	−0.133975	+	0.232051i	−0.0244603	+	0.0423665i
$31$	−5.46410			−0.981382			−0.490691	−	0.871334i	$-0.663256\pi$
$31$	−5.46410			−0.981382			−0.490691	+	0.871334i	$0.663256\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.36603	+	4.09808i	−0.411872	+	0.713384i
$34$	−2.26795			−0.388950
$35$	−0.0980762	+	0.169873i	−0.0165779	+	0.0287138i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−5.23205	−	9.06218i	−0.860144	−	1.48981i	−0.871789	−	0.489881i	$-0.837040\pi$
$37$	−5.23205	−	9.06218i	−0.860144	−	1.48981i	0.0116456	−	0.999932i	$-0.496293\pi$
$38$	1.26795			0.205689
$39$		0			0
$40$	0.267949			0.0423665
$41$	−5.69615	−	9.86603i	−0.889590	−	1.54081i	−0.840361	−	0.542027i	$-0.817657\pi$
$41$	−5.69615	−	9.86603i	−0.889590	−	1.54081i	−0.0492283	−	0.998788i	$-0.515676\pi$
$42$	−0.366025	−	0.633975i	−0.0564789	−	0.0978244i
$43$	−3.83013	+	6.63397i	−0.584089	+	1.01167i	0.410899	+	0.911681i	$0.365215\pi$
$43$	−3.83013	+	6.63397i	−0.584089	+	1.01167i	−0.994988	+	0.0999910i	$0.968119\pi$
$44$	4.73205			0.713384
$45$	−0.133975	+	0.232051i	−0.0199718	+	0.0345921i
$46$	3.09808	−	5.36603i	0.456786	−	0.791177i
$47$	−8.19615			−1.19553			−0.597766	−	0.801671i	$-0.703945\pi$
$47$	−8.19615			−1.19553			−0.597766	+	0.801671i	$0.703945\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	3.23205	+	5.59808i	0.461722	+	0.799725i
$50$	2.46410	+	4.26795i	0.348477	+	0.603579i
$51$	−2.26795			−0.317576
$52$		0			0
$53$	0.464102			0.0637493			0.0318746	−	0.999492i	$-0.489852\pi$
$53$	0.464102			0.0637493			0.0318746	+	0.999492i	$0.489852\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−0.633975	−	1.09808i	−0.0854851	−	0.148065i
$56$	−0.366025	+	0.633975i	−0.0489122	+	0.0847184i
$57$	1.26795			0.167944
$58$	−1.23205	+	2.13397i	−0.161776	+	0.280205i
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$	0.267949			0.0345921
$61$	−0.598076	+	1.03590i	−0.0765758	+	0.132633i	−0.901770	−	0.432215i	$-0.857732\pi$
$61$	−0.598076	+	1.03590i	−0.0765758	+	0.132633i	0.825195	+	0.564848i	$0.191065\pi$
$62$	2.73205	+	4.73205i	0.346971	+	0.600971i
$63$	−0.366025	−	0.633975i	−0.0461149	−	0.0798733i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.73205			0.582475
$67$	5.56218	+	9.63397i	0.679528	+	1.17698i	0.975123	+	0.221664i	$0.0711488\pi$
$67$	5.56218	+	9.63397i	0.679528	+	1.17698i	−0.295595	+	0.955313i	$0.595518\pi$
$68$	1.13397	+	1.96410i	0.137515	+	0.238182i
$69$	3.09808	−	5.36603i	0.372965	−	0.645994i
$70$	0.196152			0.0234447
$71$	−0.633975	+	1.09808i	−0.0752389	+	0.130318i	−0.901190	−	0.433424i	$-0.857305\pi$
$71$	−0.633975	+	1.09808i	−0.0752389	+	0.130318i	0.825951	+	0.563742i	$0.190639\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−9.73205			−1.13905			−0.569525	−	0.821974i	$-0.692873\pi$
$73$	−9.73205			−1.13905			−0.569525	+	0.821974i	$0.692873\pi$
$74$	−5.23205	+	9.06218i	−0.608214	+	1.05346i
$75$	2.46410	+	4.26795i	0.284530	+	0.492820i
$76$	−0.633975	−	1.09808i	−0.0727219	−	0.125958i
$77$	3.46410			0.394771
$78$		0			0
$79$	−9.46410			−1.06479			−0.532397	−	0.846495i	$-0.678709\pi$
$79$	−9.46410			−1.06479			−0.532397	+	0.846495i	$0.678709\pi$
$80$	−0.133975	−	0.232051i	−0.0149788	−	0.0259441i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.69615	+	9.86603i	−0.629035	+	1.08952i
$83$	10.1962			1.11917			0.559587	−	0.828772i	$-0.310960\pi$
$83$	10.1962			1.11917			0.559587	+	0.828772i	$0.310960\pi$
$84$	−0.366025	+	0.633975i	−0.0399366	+	0.0691723i
$85$	0.303848	−	0.526279i	0.0329569	−	0.0570830i
$86$	7.66025			0.826026
$87$	−1.23205	+	2.13397i	−0.132090	+	0.228786i
$88$	−2.36603	−	4.09808i	−0.252219	−	0.436856i
$89$	1.26795	+	2.19615i	0.134402	+	0.232792i	0.925369	−	0.379068i	$-0.123755\pi$
$89$	1.26795	+	2.19615i	0.134402	+	0.232792i	−0.790967	+	0.611859i	$0.790422\pi$
$90$	0.267949			0.0282443
$91$		0			0
$92$	−6.19615			−0.645994
$93$	2.73205	+	4.73205i	0.283300	+	0.490691i
$94$	4.09808	+	7.09808i	0.422684	+	0.732111i
$95$	−0.169873	+	0.294229i	−0.0174286	+	0.0301872i
$96$	1.00000			0.102062
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	−0.672569	−	0.740034i	$-0.734809\pi$
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	0.977173	+	0.212445i	$0.0681426\pi$
$98$	3.23205	−	5.59808i	0.326486	−	0.565491i
$99$	4.73205			0.475589
$100$	2.46410	−	4.26795i	0.246410	−	0.426795i
$101$	5.96410	+	10.3301i	0.593450	+	1.02789i	0.993764	+	0.111508i	$0.0355680\pi$
$101$	5.96410	+	10.3301i	0.593450	+	1.02789i	−0.400313	+	0.916378i	$0.631099\pi$
$102$	1.13397	+	1.96410i	0.112280	+	0.194475i
$103$	−18.7321			−1.84572			−0.922862	−	0.385131i	$-0.874156\pi$
$103$	−18.7321			−1.84572			−0.922862	+	0.385131i	$0.874156\pi$
$104$		0			0
$105$	0.196152			0.0191425
$106$	−0.232051	−	0.401924i	−0.0225388	−	0.0390383i
$107$	0.0980762	+	0.169873i	0.00948139	+	0.0164222i	0.870727	−	0.491766i	$-0.163649\pi$
$107$	0.0980762	+	0.169873i	0.00948139	+	0.0164222i	−0.861246	+	0.508189i	$0.830315\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−5.46410			−0.523366			−0.261683	−	0.965154i	$-0.584277\pi$
$109$	−5.46410			−0.523366			−0.261683	+	0.965154i	$0.584277\pi$
$110$	−0.633975	+	1.09808i	−0.0604471	+	0.104697i
$111$	−5.23205	+	9.06218i	−0.496604	+	0.860144i
$112$	0.732051			0.0691723
$113$	9.33013	−	16.1603i	0.877705	−	1.52023i	0.0238510	−	0.999716i	$-0.492407\pi$
$113$	9.33013	−	16.1603i	0.877705	−	1.52023i	0.853854	−	0.520513i	$-0.174259\pi$
$114$	−0.633975	−	1.09808i	−0.0593772	−	0.102844i
$115$	0.830127	+	1.43782i	0.0774097	+	0.134078i
$116$	2.46410			0.228786
$117$		0			0
$118$	8.00000			0.736460
$119$	0.830127	+	1.43782i	0.0760976	+	0.131805i
$120$	−0.133975	−	0.232051i	−0.0122302	−	0.0211832i
$121$	−5.69615	+	9.86603i	−0.517832	+	0.896911i
$122$	1.19615			0.108295
$123$	−5.69615	+	9.86603i	−0.513605	+	0.889590i
$124$	2.73205	−	4.73205i	0.245345	−	0.424951i
$125$	−2.66025			−0.237940
$126$	−0.366025	+	0.633975i	−0.0326081	+	0.0564789i
$127$	−8.92820	−	15.4641i	−0.792250	−	1.37222i	−0.924571	−	0.381010i	$-0.875576\pi$
$127$	−8.92820	−	15.4641i	−0.792250	−	1.37222i	0.132321	−	0.991207i	$-0.457757\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	7.66025			0.674448
$130$		0			0
$131$	13.4641			1.17636			0.588182	−	0.808729i	$-0.299844\pi$
$131$	13.4641			1.17636			0.588182	+	0.808729i	$0.299844\pi$
$132$	−2.36603	−	4.09808i	−0.205936	−	0.356692i
$133$	−0.464102	−	0.803848i	−0.0402427	−	0.0697024i
$134$	5.56218	−	9.63397i	0.480499	−	0.832249i
$135$	0.267949			0.0230614
$136$	1.13397	−	1.96410i	0.0972375	−	0.168420i
$137$	0.964102	−	1.66987i	0.0823688	−	0.142667i	−0.821898	−	0.569634i	$-0.807085\pi$
$137$	0.964102	−	1.66987i	0.0823688	−	0.142667i	0.904267	+	0.426968i	$0.140418\pi$
$138$	−6.19615			−0.527452
$139$	4.92820	−	8.53590i	0.418005	−	0.724005i	−0.577734	−	0.816225i	$-0.696063\pi$
$139$	4.92820	−	8.53590i	0.418005	−	0.724005i	0.995739	+	0.0922197i	$0.0293962\pi$
$140$	−0.0980762	−	0.169873i	−0.00828895	−	0.0143569i
$141$	4.09808	+	7.09808i	0.345120	+	0.597766i
$142$	1.26795			0.106404
$143$		0			0
$144$	1.00000			0.0833333
$145$	−0.330127	−	0.571797i	−0.0274156	−	0.0474851i
$146$	4.86603	+	8.42820i	0.402715	+	0.697523i
$147$	3.23205	−	5.59808i	0.266575	−	0.461722i
$148$	10.4641			0.860144
$149$	−1.40192	+	2.42820i	−0.114850	+	0.198926i	−0.917720	−	0.397228i	$-0.869972\pi$
$149$	−1.40192	+	2.42820i	−0.114850	+	0.198926i	0.802870	+	0.596154i	$0.203305\pi$
$150$	2.46410	−	4.26795i	0.201193	−	0.348477i
$151$	3.26795			0.265942			0.132971	−	0.991120i	$-0.457548\pi$
$151$	3.26795			0.265942			0.132971	+	0.991120i	$0.457548\pi$
$152$	−0.633975	+	1.09808i	−0.0514221	+	0.0890657i
$153$	1.13397	+	1.96410i	0.0916764	+	0.158788i
$154$	−1.73205	−	3.00000i	−0.139573	−	0.241747i
$155$	−1.46410			−0.117599
$156$		0			0
$157$	−23.5885			−1.88256			−0.941282	−	0.337622i	$-0.890378\pi$
$157$	−23.5885			−1.88256			−0.941282	+	0.337622i	$0.890378\pi$
$158$	4.73205	+	8.19615i	0.376462	+	0.652051i
$159$	−0.232051	−	0.401924i	−0.0184028	−	0.0318746i
$160$	−0.133975	+	0.232051i	−0.0105916	+	0.0183452i
$161$	−4.53590			−0.357479
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	3.26795	−	5.66025i	0.255966	−	0.443345i	−0.709192	−	0.705016i	$-0.750940\pi$
$163$	3.26795	−	5.66025i	0.255966	−	0.443345i	0.965157	+	0.261670i	$0.0842733\pi$
$164$	11.3923			0.889590
$165$	−0.633975	+	1.09808i	−0.0493549	+	0.0854851i
$166$	−5.09808	−	8.83013i	−0.395687	−	0.685351i
$167$	1.26795	+	2.19615i	0.0981169	+	0.169943i	0.910905	−	0.412616i	$-0.135385\pi$
$167$	1.26795	+	2.19615i	0.0981169	+	0.169943i	−0.812788	+	0.582559i	$0.802051\pi$
$168$	0.732051			0.0564789
$169$		0			0
$170$	−0.607695			−0.0466081
$171$	−0.633975	−	1.09808i	−0.0484812	−	0.0839720i
$172$	−3.83013	−	6.63397i	−0.292044	−	0.505836i
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	−0.365755	−	0.930711i	$-0.619189\pi$
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	0.988897	−	0.148602i	$-0.0474774\pi$
$174$	2.46410			0.186803
$175$	1.80385	−	3.12436i	0.136358	−	0.236179i
$176$	−2.36603	+	4.09808i	−0.178346	+	0.308904i
$177$	8.00000			0.601317
$178$	1.26795	−	2.19615i	0.0950368	−	0.164609i
$179$	−11.0263	−	19.0981i	−0.824143	−	1.42746i	−0.902573	−	0.430538i	$-0.858324\pi$
$179$	−11.0263	−	19.0981i	−0.824143	−	1.42746i	0.0784298	−	0.996920i	$-0.475009\pi$
$180$	−0.133975	−	0.232051i	−0.00998588	−	0.0172960i
$181$	8.80385			0.654385			0.327192	−	0.944958i	$-0.393897\pi$
$181$	8.80385			0.654385			0.327192	+	0.944958i	$0.393897\pi$
$182$		0			0
$183$	1.19615			0.0884221
$184$	3.09808	+	5.36603i	0.228393	+	0.395589i
$185$	−1.40192	−	2.42820i	−0.103071	−	0.178525i
$186$	2.73205	−	4.73205i	0.200324	−	0.346971i
$187$	−10.7321			−0.784805
$188$	4.09808	−	7.09808i	0.298883	−	0.517680i
$189$	−0.366025	+	0.633975i	−0.0266244	+	0.0461149i
$190$	0.339746			0.0246478
$191$	−3.46410	+	6.00000i	−0.250654	+	0.434145i	−0.963706	−	0.266966i	$-0.913979\pi$
$191$	−3.46410	+	6.00000i	−0.250654	+	0.434145i	0.713052	+	0.701111i	$0.247312\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	4.13397	+	7.16025i	0.297570	+	0.515406i	0.975579	−	0.219647i	$-0.0704905\pi$
$193$	4.13397	+	7.16025i	0.297570	+	0.515406i	−0.678009	+	0.735053i	$0.737157\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	−6.46410			−0.461722
$197$	−4.92820	−	8.53590i	−0.351120	−	0.608158i	0.635326	−	0.772244i	$-0.280866\pi$
$197$	−4.92820	−	8.53590i	−0.351120	−	0.608158i	−0.986446	+	0.164086i	$0.947532\pi$
$198$	−2.36603	−	4.09808i	−0.168146	−	0.291238i
$199$	1.90192	−	3.29423i	0.134824	−	0.233522i	−0.790706	−	0.612196i	$-0.790286\pi$
$199$	1.90192	−	3.29423i	0.134824	−	0.233522i	0.925530	+	0.378674i	$0.123620\pi$
$200$	−4.92820			−0.348477
$201$	5.56218	−	9.63397i	0.392326	−	0.679528i
$202$	5.96410	−	10.3301i	0.419633	−	0.726825i
$203$	1.80385			0.126605
$204$	1.13397	−	1.96410i	0.0793941	−	0.137515i
$205$	−1.52628	−	2.64359i	−0.106600	−	0.184637i
$206$	9.36603	+	16.2224i	0.652562	+	1.13027i
$207$	−6.19615			−0.430662
$208$		0			0
$209$	6.00000			0.415029
$210$	−0.0980762	−	0.169873i	−0.00676790	−	0.0117223i
$211$	2.19615	+	3.80385i	0.151189	+	0.261868i	0.931665	−	0.363319i	$-0.118356\pi$
$211$	2.19615	+	3.80385i	0.151189	+	0.261868i	−0.780476	+	0.625186i	$0.785023\pi$
$212$	−0.232051	+	0.401924i	−0.0159373	+	0.0276042i
$213$	1.26795			0.0868784
$214$	0.0980762	−	0.169873i	0.00670435	−	0.0116123i
$215$	−1.02628	+	1.77757i	−0.0699917	+	0.121229i
$216$	1.00000			0.0680414
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$	2.73205	+	4.73205i	0.185038	+	0.320495i
$219$	4.86603	+	8.42820i	0.328816	+	0.569525i
$220$	1.26795			0.0854851
$221$		0			0
$222$	10.4641			0.702305
$223$	6.53590	+	11.3205i	0.437676	+	0.758077i	0.997510	−	0.0705277i	$-0.0224683\pi$
$223$	6.53590	+	11.3205i	0.437676	+	0.758077i	−0.559834	+	0.828605i	$0.689135\pi$
$224$	−0.366025	−	0.633975i	−0.0244561	−	0.0423592i
$225$	2.46410	−	4.26795i	0.164273	−	0.284530i
$226$	−18.6603			−1.24126
$227$	0.901924	−	1.56218i	0.0598628	−	0.103685i	−0.834541	−	0.550946i	$-0.814267\pi$
$227$	0.901924	−	1.56218i	0.0598628	−	0.103685i	0.894404	+	0.447261i	$0.147600\pi$
$228$	−0.633975	+	1.09808i	−0.0419860	+	0.0727219i
$229$	15.8564			1.04782			0.523910	−	0.851773i	$-0.324473\pi$
$229$	15.8564			1.04782			0.523910	+	0.851773i	$0.324473\pi$
$230$	0.830127	−	1.43782i	0.0547370	−	0.0948072i
$231$	−1.73205	−	3.00000i	−0.113961	−	0.197386i
$232$	−1.23205	−	2.13397i	−0.0808881	−	0.140102i
$233$	19.8564			1.30084			0.650418	−	0.759576i	$-0.274594\pi$
$233$	19.8564			1.30084			0.650418	+	0.759576i	$0.274594\pi$
$234$		0			0
$235$	−2.19615			−0.143261
$236$	−4.00000	−	6.92820i	−0.260378	−	0.450988i
$237$	4.73205	+	8.19615i	0.307380	+	0.532397i
$238$	0.830127	−	1.43782i	0.0538091	−	0.0932002i
$239$	−9.66025			−0.624870			−0.312435	−	0.949939i	$-0.601145\pi$
$239$	−9.66025			−0.624870			−0.312435	+	0.949939i	$0.601145\pi$
$240$	−0.133975	+	0.232051i	−0.00864802	+	0.0149788i
$241$	8.79423	−	15.2321i	0.566486	−	0.981183i	−0.430424	−	0.902627i	$-0.641636\pi$
$241$	8.79423	−	15.2321i	0.566486	−	0.981183i	0.996910	−	0.0785557i	$-0.0250308\pi$
$242$	11.3923			0.732325
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−0.598076	−	1.03590i	−0.0382879	−	0.0663166i
$245$	0.866025	+	1.50000i	0.0553283	+	0.0958315i
$246$	11.3923			0.726347
$247$		0			0
$248$	−5.46410			−0.346971
$249$	−5.09808	−	8.83013i	−0.323077	−	0.559587i
$250$	1.33013	+	2.30385i	0.0841246	+	0.145708i
$251$	−3.26795	+	5.66025i	−0.206271	+	0.357272i	−0.950537	−	0.310611i	$-0.899466\pi$
$251$	−3.26795	+	5.66025i	−0.206271	+	0.357272i	0.744266	+	0.667883i	$0.232800\pi$
$252$	0.732051			0.0461149
$253$	14.6603	−	25.3923i	0.921682	−	1.59640i
$254$	−8.92820	+	15.4641i	−0.560205	+	0.970304i
$255$	−0.607695			−0.0380553
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.3301	−	23.0885i	−0.831510	−	1.44022i	−0.896840	−	0.442355i	$-0.854143\pi$
$257$	−13.3301	−	23.0885i	−0.831510	−	1.44022i	0.0653297	−	0.997864i	$-0.479190\pi$
$258$	−3.83013	−	6.63397i	−0.238453	−	0.413013i
$259$	7.66025			0.475985
$260$		0			0
$261$	2.46410			0.152524
$262$	−6.73205	−	11.6603i	−0.415907	−	0.720373i
$263$	−14.0263	−	24.2942i	−0.864897	−	1.49805i	−0.867149	−	0.498049i	$-0.834050\pi$
$263$	−14.0263	−	24.2942i	−0.864897	−	1.49805i	0.00225153	−	0.999997i	$-0.499283\pi$
$264$	−2.36603	+	4.09808i	−0.145619	+	0.252219i
$265$	0.124356			0.00763911
$266$	−0.464102	+	0.803848i	−0.0284559	+	0.0492871i
$267$	1.26795	−	2.19615i	0.0775972	−	0.134402i
$268$	−11.1244			−0.679528
$269$	0.732051	−	1.26795i	0.0446339	−	0.0773082i	−0.842845	−	0.538156i	$-0.819121\pi$
$269$	0.732051	−	1.26795i	0.0446339	−	0.0773082i	0.887479	+	0.460848i	$0.152455\pi$
$270$	−0.133975	−	0.232051i	−0.00815343	−	0.0141222i
$271$	−2.92820	−	5.07180i	−0.177876	−	0.308090i	0.763277	−	0.646071i	$-0.223589\pi$
$271$	−2.92820	−	5.07180i	−0.177876	−	0.308090i	−0.941153	+	0.337982i	$0.890256\pi$
$272$	−2.26795			−0.137515
$273$		0			0
$274$	−1.92820			−0.116487
$275$	11.6603	+	20.1962i	0.703140	+	1.21787i
$276$	3.09808	+	5.36603i	0.186482	+	0.322997i
$277$	1.13397	−	1.96410i	0.0681339	−	0.118011i	−0.829946	−	0.557844i	$-0.811629\pi$
$277$	1.13397	−	1.96410i	0.0681339	−	0.118011i	0.898080	+	0.439832i	$0.144962\pi$
$278$	−9.85641			−0.591148
$279$	2.73205	−	4.73205i	0.163564	−	0.283300i
$280$	−0.0980762	+	0.169873i	−0.00586117	+	0.0101519i
$281$	−22.3205			−1.33153			−0.665765	−	0.746162i	$-0.731895\pi$
$281$	−22.3205			−1.33153			−0.665765	+	0.746162i	$0.731895\pi$
$282$	4.09808	−	7.09808i	0.244037	−	0.422684i
$283$	−4.16987	−	7.22243i	−0.247873	−	0.429329i	0.715062	−	0.699061i	$-0.246398\pi$
$283$	−4.16987	−	7.22243i	−0.247873	−	0.429329i	−0.962936	+	0.269732i	$0.913065\pi$
$284$	−0.633975	−	1.09808i	−0.0376195	−	0.0651588i
$285$	0.339746			0.0201248
$286$		0			0
$287$	8.33975			0.492280
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	5.92820	+	10.2679i	0.348718	+	0.603997i
$290$	−0.330127	+	0.571797i	−0.0193857	+	0.0335771i
$291$	−6.00000			−0.351726
$292$	4.86603	−	8.42820i	0.284763	−	0.493223i
$293$	7.25833	−	12.5718i	0.424036	−	0.734452i	−0.572294	−	0.820049i	$-0.693946\pi$
$293$	7.25833	−	12.5718i	0.424036	−	0.734452i	0.996330	+	0.0855965i	$0.0272796\pi$
$294$	−6.46410			−0.376994
$295$	−1.07180	+	1.85641i	−0.0624024	+	0.108084i
$296$	−5.23205	−	9.06218i	−0.304107	−	0.526728i
$297$	−2.36603	−	4.09808i	−0.137291	−	0.237795i
$298$	2.80385			0.162423
$299$		0			0
$300$	−4.92820			−0.284530
$301$	−2.80385	−	4.85641i	−0.161611	−	0.279919i
$302$	−1.63397	−	2.83013i	−0.0940247	−	0.162856i
$303$	5.96410	−	10.3301i	0.342629	−	0.593450i
$304$	1.26795			0.0727219
$305$	−0.160254	+	0.277568i	−0.00917612	+	0.0158935i
$306$	1.13397	−	1.96410i	0.0648250	−	0.112280i
$307$	8.58846			0.490169			0.245085	−	0.969502i	$-0.421184\pi$
$307$	8.58846			0.490169			0.245085	+	0.969502i	$0.421184\pi$
$308$	−1.73205	+	3.00000i	−0.0986928	+	0.170941i
$309$	9.36603	+	16.2224i	0.532815	+	0.922862i
$310$	0.732051	+	1.26795i	0.0415777	+	0.0720147i
$311$	15.6603			0.888012			0.444006	−	0.896024i	$-0.353557\pi$
$311$	15.6603			0.888012			0.444006	+	0.896024i	$0.353557\pi$
$312$		0			0
$313$	13.4641			0.761036			0.380518	−	0.924774i	$-0.375746\pi$
$313$	13.4641			0.761036			0.380518	+	0.924774i	$0.375746\pi$
$314$	11.7942	+	20.4282i	0.665587	+	1.15283i
$315$	−0.0980762	−	0.169873i	−0.00552597	−	0.00957126i
$316$	4.73205	−	8.19615i	0.266199	−	0.461070i
$317$	3.33975			0.187579			0.0937894	−	0.995592i	$-0.470102\pi$
$317$	3.33975			0.187579			0.0937894	+	0.995592i	$0.470102\pi$
$318$	−0.232051	+	0.401924i	−0.0130128	+	0.0225388i
$319$	−5.83013	+	10.0981i	−0.326424	+	0.565384i
$320$	0.267949			0.0149788
$321$	0.0980762	−	0.169873i	0.00547408	−	0.00948139i
$322$	2.26795	+	3.92820i	0.126388	+	0.218910i
$323$	1.43782	+	2.49038i	0.0800026	+	0.138569i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−6.53590			−0.361990
$327$	2.73205	+	4.73205i	0.151083	+	0.261683i
$328$	−5.69615	−	9.86603i	−0.314517	−	0.544760i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$	1.26795			0.0697983
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	−5.09808	+	8.83013i	−0.279793	+	0.484616i
$333$	10.4641			0.573429
$334$	1.26795	−	2.19615i	0.0693791	−	0.120168i
$335$	1.49038	+	2.58142i	0.0814282	+	0.141038i
$336$	−0.366025	−	0.633975i	−0.0199683	−	0.0345861i
$337$	6.85641			0.373492			0.186746	−	0.982408i	$-0.440206\pi$
$337$	6.85641			0.373492			0.186746	+	0.982408i	$0.440206\pi$
$338$		0			0
$339$	−18.6603			−1.01349
$340$	0.303848	+	0.526279i	0.0164784	+	0.0285415i
$341$	12.9282	+	22.3923i	0.700101	+	1.21261i
$342$	−0.633975	+	1.09808i	−0.0342814	+	0.0593772i
$343$	−9.85641			−0.532196
$344$	−3.83013	+	6.63397i	−0.206507	+	0.357680i
$345$	0.830127	−	1.43782i	0.0446925	−	0.0774097i
$346$	−16.3923			−0.881256
$347$	−4.43782	+	7.68653i	−0.238235	+	0.412635i	−0.960208	−	0.279286i	$-0.909902\pi$
$347$	−4.43782	+	7.68653i	−0.238235	+	0.412635i	0.721973	+	0.691921i	$0.243235\pi$
$348$	−1.23205	−	2.13397i	−0.0660449	−	0.114393i
$349$	9.66025	+	16.7321i	0.517102	+	0.895646i	0.999803	+	0.0198610i	$0.00632238\pi$
$349$	9.66025	+	16.7321i	0.517102	+	0.895646i	−0.482701	+	0.875785i	$0.660344\pi$
$350$	−3.60770			−0.192839
$351$		0			0
$352$	4.73205			0.252219
$353$	−9.89230	−	17.1340i	−0.526514	−	0.911949i	−0.999523	−	0.0308916i	$-0.990165\pi$
$353$	−9.89230	−	17.1340i	−0.526514	−	0.911949i	0.473008	−	0.881058i	$-0.343168\pi$
$354$	−4.00000	−	6.92820i	−0.212598	−	0.368230i
$355$	−0.169873	+	0.294229i	−0.00901592	+	0.0156160i
$356$	−2.53590			−0.134402
$357$	0.830127	−	1.43782i	0.0439350	−	0.0760976i
$358$	−11.0263	+	19.0981i	−0.582757	+	1.00936i
$359$	23.1244			1.22046			0.610228	−	0.792226i	$-0.291078\pi$
$359$	23.1244			1.22046			0.610228	+	0.792226i	$0.291078\pi$
$360$	−0.133975	+	0.232051i	−0.00706108	+	0.0122302i
$361$	8.69615	+	15.0622i	0.457692	+	0.792746i
$362$	−4.40192	−	7.62436i	−0.231360	−	0.400727i
$363$	11.3923			0.597941
$364$		0			0
$365$	−2.60770			−0.136493
$366$	−0.598076	−	1.03590i	−0.0312619	−	0.0541473i
$367$	7.36603	+	12.7583i	0.384503	+	0.665979i	0.991700	−	0.128572i	$-0.0410394\pi$
$367$	7.36603	+	12.7583i	0.384503	+	0.665979i	−0.607197	+	0.794551i	$0.707706\pi$
$368$	3.09808	−	5.36603i	0.161498	−	0.279723i
$369$	11.3923			0.593060
$370$	−1.40192	+	2.42820i	−0.0728825	+	0.126236i
$371$	−0.169873	+	0.294229i	−0.00881937	+	0.0152756i
$372$	−5.46410			−0.283300
$373$	5.13397	−	8.89230i	0.265827	−	0.460426i	−0.701953	−	0.712223i	$-0.747688\pi$
$373$	5.13397	−	8.89230i	0.265827	−	0.460426i	0.967780	+	0.251797i	$0.0810216\pi$
$374$	5.36603	+	9.29423i	0.277471	+	0.480593i
$375$	1.33013	+	2.30385i	0.0686875	+	0.118970i
$376$	−8.19615			−0.422684
$377$		0			0
$378$	0.732051			0.0376526
$379$	−0.732051	−	1.26795i	−0.0376029	−	0.0651302i	0.846611	−	0.532211i	$-0.178639\pi$
$379$	−0.732051	−	1.26795i	−0.0376029	−	0.0651302i	−0.884214	+	0.467081i	$0.845306\pi$
$380$	−0.169873	−	0.294229i	−0.00871430	−	0.0150936i
$381$	−8.92820	+	15.4641i	−0.457406	+	0.792250i
$382$	6.92820			0.354478
$383$	−2.73205	+	4.73205i	−0.139601	+	0.241797i	−0.927346	−	0.374206i	$-0.877915\pi$
$383$	−2.73205	+	4.73205i	−0.139601	+	0.241797i	0.787744	+	0.616002i	$0.211249\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	0.928203			0.0473056
$386$	4.13397	−	7.16025i	0.210414	−	0.364447i
$387$	−3.83013	−	6.63397i	−0.194696	−	0.337224i
$388$	3.00000	+	5.19615i	0.152302	+	0.263795i
$389$	−29.7846			−1.51014			−0.755070	−	0.655644i	$-0.772397\pi$
$389$	−29.7846			−1.51014			−0.755070	+	0.655644i	$0.772397\pi$
$390$		0			0
$391$	14.0526			0.710668
$392$	3.23205	+	5.59808i	0.163243	+	0.282746i
$393$	−6.73205	−	11.6603i	−0.339587	−	0.588182i
$394$	−4.92820	+	8.53590i	−0.248279	+	0.430032i
$395$	−2.53590			−0.127595
$396$	−2.36603	+	4.09808i	−0.118897	+	0.205936i
$397$	0.196152	−	0.339746i	0.00984461	−	0.0170514i	−0.861061	−	0.508501i	$-0.830200\pi$
$397$	0.196152	−	0.339746i	0.00984461	−	0.0170514i	0.870906	+	0.491450i	$0.163533\pi$
$398$	−3.80385			−0.190670
$399$	−0.464102	+	0.803848i	−0.0232341	+	0.0402427i
$400$	2.46410	+	4.26795i	0.123205	+	0.213397i
$401$	−10.9641	−	18.9904i	−0.547521	−	0.948334i	−0.998444	−	0.0557713i	$-0.982238\pi$
$401$	−10.9641	−	18.9904i	−0.547521	−	0.948334i	0.450922	−	0.892563i	$-0.351095\pi$
$402$	−11.1244			−0.554832
$403$		0			0
$404$	−11.9282			−0.593450
$405$	−0.133975	−	0.232051i	−0.00665725	−	0.0115307i
$406$	−0.901924	−	1.56218i	−0.0447617	−	0.0775296i
$407$	−24.7583	+	42.8827i	−1.22722	+	2.12562i
$408$	−2.26795			−0.112280
$409$	−7.13397	+	12.3564i	−0.352752	+	0.610985i	−0.986731	−	0.162366i	$-0.948088\pi$
$409$	−7.13397	+	12.3564i	−0.352752	+	0.610985i	0.633978	+	0.773351i	$0.281421\pi$
$410$	−1.52628	+	2.64359i	−0.0753776	+	0.130558i
$411$	−1.92820			−0.0951113
$412$	9.36603	−	16.2224i	0.461431	−	0.799222i
$413$	−2.92820	−	5.07180i	−0.144087	−	0.249567i
$414$	3.09808	+	5.36603i	0.152262	+	0.263726i
$415$	2.73205			0.134111
$416$		0			0
$417$	−9.85641			−0.482670
$418$	−3.00000	−	5.19615i	−0.146735	−	0.254152i
$419$	5.26795	+	9.12436i	0.257356	+	0.445754i	0.965533	−	0.260281i	$-0.0838153\pi$
$419$	5.26795	+	9.12436i	0.257356	+	0.445754i	−0.708177	+	0.706035i	$0.750482\pi$
$420$	−0.0980762	+	0.169873i	−0.00478563	+	0.00828895i
$421$	32.7128			1.59432			0.797162	−	0.603765i	$-0.206333\pi$
$421$	32.7128			1.59432			0.797162	+	0.603765i	$0.206333\pi$
$422$	2.19615	−	3.80385i	0.106907	−	0.185168i
$423$	4.09808	−	7.09808i	0.199255	−	0.345120i
$424$	0.464102			0.0225388
$425$	−5.58846	+	9.67949i	−0.271080	+	0.469524i
$426$	−0.633975	−	1.09808i	−0.0307162	−	0.0532020i
$427$	−0.437822	−	0.758330i	−0.0211877	−	0.0366982i
$428$	−0.196152			−0.00948139
$429$		0			0
$430$	2.05256			0.0989832
$431$	5.56218	+	9.63397i	0.267921	+	0.464052i	0.968325	−	0.249694i	$-0.0803302\pi$
$431$	5.56218	+	9.63397i	0.267921	+	0.464052i	−0.700404	+	0.713747i	$0.746997\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	7.42820	−	12.8660i	0.356977	−	0.618302i	−0.630478	−	0.776208i	$-0.717141\pi$
$433$	7.42820	−	12.8660i	0.356977	−	0.618302i	0.987454	+	0.157906i	$0.0504742\pi$
$434$	−4.00000			−0.192006
$435$	−0.330127	+	0.571797i	−0.0158284	+	0.0274156i
$436$	2.73205	−	4.73205i	0.130842	−	0.226624i
$437$	−7.85641			−0.375823
$438$	4.86603	−	8.42820i	0.232508	−	0.402715i
$439$	8.83013	+	15.2942i	0.421439	+	0.729954i	0.996080	−	0.0884515i	$-0.0281918\pi$
$439$	8.83013	+	15.2942i	0.421439	+	0.729954i	−0.574642	+	0.818405i	$0.694859\pi$
$440$	−0.633975	−	1.09808i	−0.0302236	−	0.0523487i
$441$	−6.46410			−0.307814
$442$		0			0
$443$	36.3923			1.72905			0.864525	−	0.502589i	$-0.167619\pi$
$443$	36.3923			1.72905			0.864525	+	0.502589i	$0.167619\pi$
$444$	−5.23205	−	9.06218i	−0.248302	−	0.430072i
$445$	0.339746	+	0.588457i	0.0161055	+	0.0278955i
$446$	6.53590	−	11.3205i	0.309484	−	0.536042i
$447$	2.80385			0.132617
$448$	−0.366025	+	0.633975i	−0.0172931	+	0.0299525i
$449$	11.6603	−	20.1962i	0.550281	−	0.953115i	−0.447973	−	0.894047i	$-0.647854\pi$
$449$	11.6603	−	20.1962i	0.550281	−	0.953115i	0.998254	−	0.0590680i	$-0.0188129\pi$
$450$	−4.92820			−0.232318
$451$	−26.9545	+	46.6865i	−1.26924	+	2.19838i
$452$	9.33013	+	16.1603i	0.438852	+	0.760114i
$453$	−1.63397	−	2.83013i	−0.0767708	−	0.132971i
$454$	−1.80385			−0.0846588
$455$		0			0
$456$	1.26795			0.0593772
$457$	−9.33013	−	16.1603i	−0.436445	−	0.755945i	0.560967	−	0.827838i	$-0.310429\pi$
$457$	−9.33013	−	16.1603i	−0.436445	−	0.755945i	−0.997412	+	0.0718931i	$0.977096\pi$
$458$	−7.92820	−	13.7321i	−0.370461	−	0.641657i
$459$	1.13397	−	1.96410i	0.0529294	−	0.0916764i
$460$	−1.66025			−0.0774097
$461$	−12.8660	+	22.2846i	−0.599231	+	1.03790i	0.393704	+	0.919237i	$0.371193\pi$
$461$	−12.8660	+	22.2846i	−0.599231	+	1.03790i	−0.992935	+	0.118661i	$0.962140\pi$
$462$	−1.73205	+	3.00000i	−0.0805823	+	0.139573i
$463$	−28.0526			−1.30371			−0.651856	−	0.758342i	$-0.726010\pi$
$463$	−28.0526			−1.30371			−0.651856	+	0.758342i	$0.726010\pi$
$464$	−1.23205	+	2.13397i	−0.0571965	+	0.0990673i
$465$	0.732051	+	1.26795i	0.0339480	+	0.0587997i
$466$	−9.92820	−	17.1962i	−0.459915	−	0.796596i
$467$	−12.5885			−0.582524			−0.291262	−	0.956643i	$-0.594075\pi$
$467$	−12.5885			−0.582524			−0.291262	+	0.956643i	$0.594075\pi$
$468$		0			0
$469$	−8.14359			−0.376036
$470$	1.09808	+	1.90192i	0.0506505	+	0.0877292i
$471$	11.7942	+	20.4282i	0.543449	+	0.941282i
$472$	−4.00000	+	6.92820i	−0.184115	+	0.318896i
$473$	36.2487			1.66672
$474$	4.73205	−	8.19615i	0.217350	−	0.376462i
$475$	3.12436	−	5.41154i	0.143355	−	0.248299i
$476$	−1.66025			−0.0760976
$477$	−0.232051	+	0.401924i	−0.0106249	+	0.0184028i
$478$	4.83013	+	8.36603i	0.220925	+	0.382653i
$479$	−13.2679	−	22.9808i	−0.606228	−	1.05002i	−0.991856	−	0.127363i	$-0.959349\pi$
$479$	−13.2679	−	22.9808i	−0.606228	−	1.05002i	0.385628	−	0.922654i	$-0.373985\pi$
$480$	0.267949			0.0122302
$481$		0			0
$482$	−17.5885			−0.801132
$483$	2.26795	+	3.92820i	0.103195	+	0.178739i
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	0.803848	−	1.39230i	0.0365008	−	0.0632213i
$486$	1.00000			0.0453609
$487$	−10.5622	+	18.2942i	−0.478618	+	0.828991i	−0.999699	−	0.0245163i	$-0.992195\pi$
$487$	−10.5622	+	18.2942i	−0.478618	+	0.828991i	0.521081	+	0.853507i	$0.325529\pi$
$488$	−0.598076	+	1.03590i	−0.0270736	+	0.0468929i
$489$	−6.53590			−0.295564
$490$	0.866025	−	1.50000i	0.0391230	−	0.0677631i
$491$	−2.63397	−	4.56218i	−0.118870	−	0.205888i	0.800450	−	0.599399i	$-0.204594\pi$
$491$	−2.63397	−	4.56218i	−0.118870	−	0.205888i	−0.919320	+	0.393511i	$0.871260\pi$
$492$	−5.69615	−	9.86603i	−0.256802	−	0.444795i
$493$	−5.58846			−0.251691
$494$		0			0
$495$	1.26795			0.0569901
$496$	2.73205	+	4.73205i	0.122673	+	0.212475i
$497$	−0.464102	−	0.803848i	−0.0208178	−	0.0360575i
$498$	−5.09808	+	8.83013i	−0.228450	+	0.395687i
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$	1.33013	−	2.30385i	0.0594851	−	0.103031i
$501$	1.26795	−	2.19615i	0.0566478	−	0.0981169i
$502$	6.53590			0.291711
$503$	5.49038	−	9.50962i	0.244804	−	0.424013i	−0.717272	−	0.696793i	$-0.754610\pi$
$503$	5.49038	−	9.50962i	0.244804	−	0.424013i	0.962076	+	0.272780i	$0.0879431\pi$
$504$	−0.366025	−	0.633975i	−0.0163041	−	0.0282395i
$505$	1.59808	+	2.76795i	0.0711135	+	0.123172i
$506$	−29.3205			−1.30346
$507$		0			0
$508$	17.8564			0.792250
$509$	−5.13397	−	8.89230i	−0.227559	−	0.394144i	0.729525	−	0.683954i	$-0.239741\pi$
$509$	−5.13397	−	8.89230i	−0.227559	−	0.394144i	−0.957084	+	0.289810i	$0.906408\pi$
$510$	0.303848	+	0.526279i	0.0134546	+	0.0233040i
$511$	3.56218	−	6.16987i	0.157581	−	0.272939i
$512$	1.00000			0.0441942
$513$	−0.633975	+	1.09808i	−0.0279907	+	0.0484812i
$514$	−13.3301	+	23.0885i	−0.587967	+	1.01839i
$515$	−5.01924			−0.221174
$516$	−3.83013	+	6.63397i	−0.168612	+	0.292044i
$517$	19.3923	+	33.5885i	0.852873	+	1.47722i
$518$	−3.83013	−	6.63397i	−0.168286	−	0.291480i
$519$	−16.3923			−0.719542
$520$		0			0
$521$	−17.4449			−0.764273			−0.382137	−	0.924106i	$-0.624812\pi$
$521$	−17.4449			−0.764273			−0.382137	+	0.924106i	$0.624812\pi$
$522$	−1.23205	−	2.13397i	−0.0539254	−	0.0934015i
$523$	−18.2224	−	31.5622i	−0.796811	−	1.38012i	−0.921683	−	0.387945i	$-0.873185\pi$
$523$	−18.2224	−	31.5622i	−0.796811	−	1.38012i	0.124871	−	0.992173i	$-0.460148\pi$
$524$	−6.73205	+	11.6603i	−0.294091	+	0.509381i
$525$	−3.60770			−0.157453
$526$	−14.0263	+	24.2942i	−0.611575	+	1.05928i
$527$	−6.19615	+	10.7321i	−0.269909	+	0.467495i
$528$	4.73205			0.205936
$529$	−7.69615	+	13.3301i	−0.334615	+	0.579571i
$530$	−0.0621778	−	0.107695i	−0.00270083	−	0.00467798i
$531$	−4.00000	−	6.92820i	−0.173585	−	0.300658i
$532$	0.928203			0.0402427
$533$		0			0
$534$	−2.53590			−0.109739
$535$	0.0262794	+	0.0455173i	0.00113616	+	0.00196789i
$536$	5.56218	+	9.63397i	0.240249	+	0.416124i
$537$	−11.0263	+	19.0981i	−0.475819	+	0.824143i
$538$	−1.46410			−0.0631219
$539$	15.2942	−	26.4904i	0.658769	−	1.14102i
$540$	−0.133975	+	0.232051i	−0.00576535	+	0.00998588i
$541$	40.3205			1.73351			0.866757	−	0.498731i	$-0.166200\pi$
$541$	40.3205			1.73351			0.866757	+	0.498731i	$0.166200\pi$
$542$	−2.92820	+	5.07180i	−0.125777	+	0.217852i
$543$	−4.40192	−	7.62436i	−0.188905	−	0.327192i
$544$	1.13397	+	1.96410i	0.0486188	+	0.0842102i
$545$	−1.46410			−0.0627152
$546$		0			0
$547$	6.19615			0.264928			0.132464	−	0.991188i	$-0.457711\pi$
$547$	6.19615			0.264928			0.132464	+	0.991188i	$0.457711\pi$
$548$	0.964102	+	1.66987i	0.0411844	+	0.0713334i
$549$	−0.598076	−	1.03590i	−0.0255253	−	0.0442111i
$550$	11.6603	−	20.1962i	0.497195	−	0.861167i
$551$	3.12436			0.133102
$552$	3.09808	−	5.36603i	0.131863	−	0.228393i
$553$	3.46410	−	6.00000i	0.147309	−	0.255146i
$554$	−2.26795			−0.0963559
$555$	−1.40192	+	2.42820i	−0.0595084	+	0.103071i
$556$	4.92820	+	8.53590i	0.209002	+	0.362003i
$557$	15.1865	+	26.3038i	0.643474	+	1.11453i	0.984652	+	0.174531i	$0.0558409\pi$
$557$	15.1865	+	26.3038i	0.643474	+	1.11453i	−0.341178	+	0.939999i	$0.610826\pi$
$558$	−5.46410			−0.231314
$559$		0			0
$560$	0.196152			0.00828895
$561$	5.36603	+	9.29423i	0.226554	+	0.392403i
$562$	11.1603	+	19.3301i	0.470767	+	0.815392i
$563$	−10.5359	+	18.2487i	−0.444035	+	0.769091i	−0.997984	−	0.0634589i	$-0.979787\pi$
$563$	−10.5359	+	18.2487i	−0.444035	+	0.769091i	0.553949	+	0.832550i	$0.313120\pi$
$564$	−8.19615			−0.345120
$565$	2.50000	−	4.33013i	0.105176	−	0.182170i
$566$	−4.16987	+	7.22243i	−0.175273	+	0.303581i
$567$	0.732051			0.0307432
$568$	−0.633975	+	1.09808i	−0.0266010	+	0.0460743i
$569$	19.3205	+	33.4641i	0.809958	+	1.40289i	0.912893	+	0.408200i	$0.133843\pi$
$569$	19.3205	+	33.4641i	0.809958	+	1.40289i	−0.102935	+	0.994688i	$0.532823\pi$
$570$	−0.169873	−	0.294229i	−0.00711520	−	0.0123239i
$571$	−24.0526			−1.00657			−0.503284	−	0.864121i	$-0.667875\pi$
$571$	−24.0526			−1.00657			−0.503284	+	0.864121i	$0.667875\pi$
$572$		0			0
$573$	6.92820			0.289430
$574$	−4.16987	−	7.22243i	−0.174047	−	0.301458i
$575$	−15.2679	−	26.4449i	−0.636717	−	1.10283i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	0.267949			0.0111549			0.00557744	−	0.999984i	$-0.498225\pi$
$577$	0.267949			0.0111549			0.00557744	+	0.999984i	$0.498225\pi$
$578$	5.92820	−	10.2679i	0.246581	−	0.427090i
$579$	4.13397	−	7.16025i	0.171802	−	0.297570i
$580$	0.660254			0.0274156
$581$	−3.73205	+	6.46410i	−0.154832	+	0.268176i
$582$	3.00000	+	5.19615i	0.124354	+	0.215387i
$583$	−1.09808	−	1.90192i	−0.0454777	−	0.0787696i
$584$	−9.73205			−0.402715
$585$		0			0
$586$	−14.5167			−0.599678
$587$	−8.00000	−	13.8564i	−0.330195	−	0.571915i	0.652355	−	0.757914i	$-0.273781\pi$
$587$	−8.00000	−	13.8564i	−0.330195	−	0.571915i	−0.982550	+	0.185999i	$0.940448\pi$
$588$	3.23205	+	5.59808i	0.133288	+	0.230861i
$589$	3.46410	−	6.00000i	0.142736	−	0.247226i
$590$	2.14359			0.0882503
$591$	−4.92820	+	8.53590i	−0.202719	+	0.351120i
$592$	−5.23205	+	9.06218i	−0.215036	+	0.372453i
$593$	−36.8564			−1.51351			−0.756756	−	0.653698i	$-0.773217\pi$
$593$	−36.8564			−1.51351			−0.756756	+	0.653698i	$0.773217\pi$
$594$	−2.36603	+	4.09808i	−0.0970792	+	0.168146i
$595$	0.222432	+	0.385263i	0.00911882	+	0.0157943i
$596$	−1.40192	−	2.42820i	−0.0574250	−	0.0994631i
$597$	−3.80385			−0.155681
$598$		0			0
$599$	−9.46410			−0.386693			−0.193346	−	0.981131i	$-0.561934\pi$
$599$	−9.46410			−0.386693			−0.193346	+	0.981131i	$0.561934\pi$
$600$	2.46410	+	4.26795i	0.100597	+	0.174238i
$601$	2.96410	+	5.13397i	0.120908	+	0.209419i	0.920126	−	0.391622i	$-0.128086\pi$
$601$	2.96410	+	5.13397i	0.120908	+	0.209419i	−0.799218	+	0.601041i	$0.794753\pi$
$602$	−2.80385	+	4.85641i	−0.114276	+	0.197932i
$603$	−11.1244			−0.453019
$604$	−1.63397	+	2.83013i	−0.0664855	+	0.115156i
$605$	−1.52628	+	2.64359i	−0.0620521	+	0.107477i
$606$	−11.9282			−0.484550
$607$	−0.392305	+	0.679492i	−0.0159232	+	0.0275797i	−0.873877	−	0.486147i	$-0.838402\pi$
$607$	−0.392305	+	0.679492i	−0.0159232	+	0.0275797i	0.857954	+	0.513726i	$0.171735\pi$
$608$	−0.633975	−	1.09808i	−0.0257111	−	0.0445329i
$609$	−0.901924	−	1.56218i	−0.0365478	−	0.0633026i
$610$	0.320508			0.0129770
$611$		0			0
$612$	−2.26795			−0.0916764
$613$	−5.69615	−	9.86603i	−0.230065	−	0.398485i	0.727762	−	0.685830i	$-0.240561\pi$
$613$	−5.69615	−	9.86603i	−0.230065	−	0.398485i	−0.957827	+	0.287345i	$0.907227\pi$
$614$	−4.29423	−	7.43782i	−0.173301	−	0.300166i
$615$	−1.52628	+	2.64359i	−0.0615455	+	0.106600i
$616$	3.46410			0.139573
$617$	−17.6244	+	30.5263i	−0.709530	+	1.22894i	0.255502	+	0.966809i	$0.417759\pi$
$617$	−17.6244	+	30.5263i	−0.709530	+	1.22894i	−0.965032	+	0.262133i	$0.915574\pi$
$618$	9.36603	−	16.2224i	0.376757	−	0.652562i
$619$	10.5359			0.423474			0.211737	−	0.977327i	$-0.432088\pi$
$619$	10.5359			0.423474			0.211737	+	0.977327i	$0.432088\pi$
$620$	0.732051	−	1.26795i	0.0293999	−	0.0509221i
$621$	3.09808	+	5.36603i	0.124322	+	0.215331i
$622$	−7.83013	−	13.5622i	−0.313959	−	0.543794i
$623$	−1.85641			−0.0743754
$624$		0			0
$625$	23.9282			0.957128
$626$	−6.73205	−	11.6603i	−0.269067	−	0.466037i
$627$	−3.00000	−	5.19615i	−0.119808	−	0.207514i
$628$	11.7942	−	20.4282i	0.470641	−	0.815174i
$629$	−23.7321			−0.946259
$630$	−0.0980762	+	0.169873i	−0.00390745	+	0.00676790i
$631$	−23.8564	+	41.3205i	−0.949709	+	1.64494i	−0.203671	+	0.979039i	$0.565287\pi$
$631$	−23.8564	+	41.3205i	−0.949709	+	1.64494i	−0.746037	+	0.665904i	$0.768046\pi$
$632$	−9.46410			−0.376462
$633$	2.19615	−	3.80385i	0.0872892	−	0.151189i
$634$	−1.66987	−	2.89230i	−0.0663191	−	0.114868i
$635$	−2.39230	−	4.14359i	−0.0949357	−	0.164433i
$636$	0.464102			0.0184028
$637$		0			0
$638$	11.6603			0.461634
$639$	−0.633975	−	1.09808i	−0.0250796	−	0.0434392i
$640$	−0.133975	−	0.232051i	−0.00529581	−	0.00917261i
$641$	−12.9904	+	22.5000i	−0.513089	+	0.888697i	0.486796	+	0.873516i	$0.338166\pi$
$641$	−12.9904	+	22.5000i	−0.513089	+	0.888697i	−0.999885	+	0.0151806i	$0.995168\pi$
$642$	−0.196152			−0.00774152
$643$	−6.92820	+	12.0000i	−0.273222	+	0.473234i	−0.969685	−	0.244359i	$-0.921423\pi$
$643$	−6.92820	+	12.0000i	−0.273222	+	0.473234i	0.696463	+	0.717592i	$0.254756\pi$
$644$	2.26795	−	3.92820i	0.0893697	−	0.154793i
$645$	2.05256			0.0808194
$646$	1.43782	−	2.49038i	0.0565704	−	0.0979827i
$647$	−13.1244	−	22.7321i	−0.515972	−	0.893689i	−0.999828	−	0.0185417i	$-0.994098\pi$
$647$	−13.1244	−	22.7321i	−0.515972	−	0.893689i	0.483856	−	0.875147i	$-0.339236\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	37.8564			1.48599
$650$		0			0
$651$	−4.00000			−0.156772
$652$	3.26795	+	5.66025i	0.127983	+	0.221673i
$653$	5.26795	+	9.12436i	0.206151	+	0.357064i	0.950499	−	0.310728i	$-0.100573\pi$
$653$	5.26795	+	9.12436i	0.206151	+	0.357064i	−0.744348	+	0.667792i	$0.767240\pi$
$654$	2.73205	−	4.73205i	0.106832	−	0.185038i
$655$	3.60770			0.140964
$656$	−5.69615	+	9.86603i	−0.222397	+	0.385204i
$657$	4.86603	−	8.42820i	0.189842	−	0.328816i
$658$	−6.00000			−0.233904
$659$	−19.1244	+	33.1244i	−0.744979	+	1.29034i	0.205225	+	0.978715i	$0.434207\pi$
$659$	−19.1244	+	33.1244i	−0.744979	+	1.29034i	−0.950205	+	0.311627i	$0.899126\pi$
$660$	−0.633975	−	1.09808i	−0.0246774	−	0.0427426i
$661$	4.69615	+	8.13397i	0.182659	+	0.316375i	0.942785	−	0.333401i	$-0.108196\pi$
$661$	4.69615	+	8.13397i	0.182659	+	0.316375i	−0.760126	+	0.649776i	$0.774863\pi$
$662$	20.0000			0.777322
$663$		0			0
$664$	10.1962			0.395687
$665$	−0.124356	−	0.215390i	−0.00482231	−	0.00835248i
$666$	−5.23205	−	9.06218i	−0.202738	−	0.351152i
$667$	7.63397	−	13.2224i	0.295589	−	0.511975i
$668$	−2.53590			−0.0981169
$669$	6.53590	−	11.3205i	0.252692	−	0.437676i
$670$	1.49038	−	2.58142i	0.0575784	−	0.0997288i
$671$	5.66025			0.218512
$672$	−0.366025	+	0.633975i	−0.0141197	+	0.0244561i
$673$	−7.03590	−	12.1865i	−0.271214	−	0.469756i	0.697959	−	0.716138i	$-0.254092\pi$
$673$	−7.03590	−	12.1865i	−0.271214	−	0.469756i	−0.969173	+	0.246381i	$0.920758\pi$
$674$	−3.42820	−	5.93782i	−0.132049	−	0.228716i
$675$	−4.92820			−0.189687
$676$		0			0
$677$	−38.5359			−1.48105			−0.740527	−	0.672026i	$-0.765424\pi$
$677$	−38.5359			−1.48105			−0.740527	+	0.672026i	$0.765424\pi$
$678$	9.33013	+	16.1603i	0.358321	+	0.620631i
$679$	2.19615	+	3.80385i	0.0842806	+	0.145978i
$680$	0.303848	−	0.526279i	0.0116520	−	0.0201819i
$681$	−1.80385			−0.0691236
$682$	12.9282	−	22.3923i	0.495046	−	0.857446i
$683$	18.9282	−	32.7846i	0.724268	−	1.25447i	−0.235007	−	0.971994i	$-0.575511\pi$
$683$	18.9282	−	32.7846i	0.724268	−	1.25447i	0.959275	−	0.282475i	$-0.0911553\pi$
$684$	1.26795			0.0484812
$685$	0.258330	−	0.447441i	0.00987029	−	0.0170958i
$686$	4.92820	+	8.53590i	0.188160	+	0.325902i
$687$	−7.92820	−	13.7321i	−0.302480	−	0.523910i
$688$	7.66025			0.292044
$689$		0			0
$690$	−1.66025			−0.0632048
$691$	−13.1699	−	22.8109i	−0.501006	−	0.867767i	−0.999999	−	0.00116153i	$-0.999630\pi$
$691$	−13.1699	−	22.8109i	−0.501006	−	0.867767i	0.498994	−	0.866606i	$-0.333703\pi$
$692$	8.19615	+	14.1962i	0.311571	+	0.539657i
$693$	−1.73205	+	3.00000i	−0.0657952	+	0.113961i
$694$	8.87564			0.336915
$695$	1.32051	−	2.28719i	0.0500897	−	0.0867580i
$696$	−1.23205	+	2.13397i	−0.0467008	+	0.0808881i
$697$	−25.8372			−0.978653
$698$	9.66025	−	16.7321i	0.365646	−	0.633317i
$699$	−9.92820	−	17.1962i	−0.375519	−	0.650418i
$700$	1.80385	+	3.12436i	0.0681790	+	0.118090i
$701$	31.3205			1.18296			0.591480	−	0.806320i	$-0.298544\pi$
$701$	31.3205			1.18296			0.591480	+	0.806320i	$0.298544\pi$
$702$		0			0
$703$	13.2679			0.500410
$704$	−2.36603	−	4.09808i	−0.0891729	−	0.154452i
$705$	1.09808	+	1.90192i	0.0413559	+	0.0716306i
$706$	−9.89230	+	17.1340i	−0.372302	+	0.644846i
$707$	−8.73205			−0.328403
$708$	−4.00000	+	6.92820i	−0.150329	+	0.260378i
$709$	−20.4282	+	35.3827i	−0.767197	+	1.32882i	0.171880	+	0.985118i	$0.445016\pi$
$709$	−20.4282	+	35.3827i	−0.767197	+	1.32882i	−0.939077	+	0.343707i	$0.888317\pi$
$710$	0.339746			0.0127504
$711$	4.73205	−	8.19615i	0.177466	−	0.307380i
$712$	1.26795	+	2.19615i	0.0475184	+	0.0823043i
$713$	−16.9282	−	29.3205i	−0.633966	−	1.09806i
$714$	−1.66025			−0.0621334
$715$		0			0
$716$	22.0526			0.824143
$717$	4.83013	+	8.36603i	0.180384	+	0.312435i
$718$	−11.5622	−	20.0263i	−0.431497	−	0.747374i
$719$	11.2679	−	19.5167i	0.420224	−	0.727849i	−0.575737	−	0.817635i	$-0.695285\pi$
$719$	11.2679	−	19.5167i	0.420224	−	0.727849i	0.995961	+	0.0897860i	$0.0286183\pi$
$720$	0.267949			0.00998588
$721$	6.85641	−	11.8756i	0.255346	−	0.442272i
$722$	8.69615	−	15.0622i	0.323637	−	0.560556i
$723$	−17.5885			−0.654122
$724$	−4.40192	+	7.62436i	−0.163596	+	0.283357i
$725$	6.07180	+	10.5167i	0.225501	+	0.390579i
$726$	−5.69615	−	9.86603i	−0.211404	−	0.366163i
$727$	20.9808			0.778133			0.389067	−	0.921210i	$-0.372798\pi$
$727$	20.9808			0.778133			0.389067	+	0.921210i	$0.372798\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	1.30385	+	2.25833i	0.0482576	+	0.0835846i
$731$	8.68653	+	15.0455i	0.321283	+	0.556479i
$732$	−0.598076	+	1.03590i	−0.0221055	+	0.0382879i
$733$	19.0000			0.701781			0.350891	−	0.936416i	$-0.385879\pi$
$733$	19.0000			0.701781			0.350891	+	0.936416i	$0.385879\pi$
$734$	7.36603	−	12.7583i	0.271885	−	0.470919i
$735$	0.866025	−	1.50000i	0.0319438	−	0.0553283i
$736$	−6.19615			−0.228393
$737$	26.3205	−	45.5885i	0.969528	−	1.67927i
$738$	−5.69615	−	9.86603i	−0.209678	−	0.363173i
$739$	5.46410	+	9.46410i	0.201000	+	0.348143i	0.948851	−	0.315724i	$-0.102247\pi$
$739$	5.46410	+	9.46410i	0.201000	+	0.348143i	−0.747851	+	0.663867i	$0.768914\pi$
$740$	2.80385			0.103071
$741$		0			0
$742$	0.339746			0.0124725
$743$	13.8038	+	23.9090i	0.506414	+	0.877135i	0.999972	+	0.00742221i	$0.00236259\pi$
$743$	13.8038	+	23.9090i	0.506414	+	0.877135i	−0.493558	+	0.869713i	$0.664304\pi$
$744$	2.73205	+	4.73205i	0.100162	+	0.173485i
$745$	−0.375644	+	0.650635i	−0.0137625	+	0.0238374i
$746$	−10.2679			−0.375936
$747$	−5.09808	+	8.83013i	−0.186529	+	0.323077i
$748$	5.36603	−	9.29423i	0.196201	−	0.339831i
$749$	−0.143594			−0.00524679
$750$	1.33013	−	2.30385i	0.0485694	−	0.0841246i
$751$	−7.95448	−	13.7776i	−0.290263	−	0.502751i	0.683609	−	0.729849i	$-0.260410\pi$
$751$	−7.95448	−	13.7776i	−0.290263	−	0.502751i	−0.973872	+	0.227098i	$0.927076\pi$
$752$	4.09808	+	7.09808i	0.149441	+	0.258840i
$753$	6.53590			0.238181
$754$		0			0
$755$	0.875644			0.0318680
$756$	−0.366025	−	0.633975i	−0.0133122	−	0.0230574i
$757$	−3.53590	−	6.12436i	−0.128514	−	0.222593i	0.794587	−	0.607151i	$-0.207688\pi$
$757$	−3.53590	−	6.12436i	−0.128514	−	0.222593i	−0.923101	+	0.384557i	$0.874354\pi$
$758$	−0.732051	+	1.26795i	−0.0265893	+	0.0460540i
$759$	−29.3205			−1.06427
$760$	−0.169873	+	0.294229i	−0.00616194	+	0.0106728i
$761$	11.6603	−	20.1962i	0.422684	−	0.732110i	−0.573517	−	0.819194i	$-0.694421\pi$
$761$	11.6603	−	20.1962i	0.422684	−	0.732110i	0.996201	+	0.0870836i	$0.0277547\pi$
$762$	17.8564			0.646869
$763$	2.00000	−	3.46410i	0.0724049	−	0.125409i
$764$	−3.46410	−	6.00000i	−0.125327	−	0.217072i
$765$	0.303848	+	0.526279i	0.0109856	+	0.0190277i
$766$	5.46410			0.197426
$767$		0			0
$768$	1.00000			0.0360844
$769$	8.07180	+	13.9808i	0.291076	+	0.504159i	0.974065	−	0.226270i	$-0.0726533\pi$
$769$	8.07180	+	13.9808i	0.291076	+	0.504159i	−0.682988	+	0.730429i	$0.739320\pi$
$770$	−0.464102	−	0.803848i	−0.0167251	−	0.0289687i
$771$	−13.3301	+	23.0885i	−0.480073	+	0.831510i
$772$	−8.26795			−0.297570
$773$	17.5359	−	30.3731i	0.630722	−	1.09244i	−0.356682	−	0.934226i	$-0.616092\pi$
$773$	17.5359	−	30.3731i	0.630722	−	1.09244i	0.987404	−	0.158217i	$-0.0505747\pi$
$774$	−3.83013	+	6.63397i	−0.137671	+	0.238453i
$775$	26.9282			0.967290
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	−3.83013	−	6.63397i	−0.137405	−	0.237993i
$778$	14.8923	+	25.7942i	0.533915	+	0.924768i
$779$	14.4449			0.517541
$780$		0			0
$781$	6.00000			0.214697
$782$	−7.02628	−	12.1699i	−0.251259	−	0.435194i
$783$	−1.23205	−	2.13397i	−0.0440299	−	0.0762620i
$784$	3.23205	−	5.59808i	0.115430	−	0.199931i
$785$	−6.32051			−0.225589
$786$	−6.73205	+	11.6603i	−0.240124	+	0.415907i
$787$	−19.6603	+	34.0526i	−0.700812	+	1.21384i	0.267369	+	0.963594i	$0.413846\pi$
$787$	−19.6603	+	34.0526i	−0.700812	+	1.21384i	−0.968182	+	0.250248i	$0.919488\pi$
$788$	9.85641			0.351120
$789$	−14.0263	+	24.2942i	−0.499349	+	0.864897i
$790$	1.26795	+	2.19615i	0.0451116	+	0.0781356i
$791$	6.83013	+	11.8301i	0.242851	+	0.420631i
$792$	4.73205			0.168146
$793$		0			0
$794$	−0.392305			−0.0139224
$795$	−0.0621778	−	0.107695i	−0.00220522	−	0.00381955i
$796$	1.90192	+	3.29423i	0.0674119	+	0.116761i
$797$	17.0000	−	29.4449i	0.602171	−	1.04299i	−0.390321	−	0.920679i	$-0.627636\pi$
$797$	17.0000	−	29.4449i	0.602171	−	1.04299i	0.992492	−	0.122312i	$-0.0390308\pi$
$798$	0.928203			0.0328580
$799$	−9.29423	+	16.0981i	−0.328806	+	0.569509i
$800$	2.46410	−	4.26795i	0.0871191	−	0.150895i
$801$	−2.53590			−0.0896016
$802$	−10.9641	+	18.9904i	−0.387156	+	0.670574i
$803$	23.0263	+	39.8827i	0.812580	+	1.40743i
$804$	5.56218	+	9.63397i	0.196163	+	0.339764i
$805$	−1.21539			−0.0428369
$806$		0			0
$807$	−1.46410			−0.0515388
$808$	5.96410	+	10.3301i	0.209816	+	0.363413i
$809$	11.2058	+	19.4090i	0.393974	+	0.682383i	0.992970	−	0.118369i	$-0.0377667\pi$
$809$	11.2058	+	19.4090i	0.393974	+	0.682383i	−0.598996	+	0.800752i	$0.704433\pi$
$810$	−0.133975	+	0.232051i	−0.00470739	+	0.00815343i
$811$	−45.1769			−1.58638			−0.793188	−	0.608977i	$-0.791580\pi$
$811$	−45.1769			−1.58638			−0.793188	+	0.608977i	$0.791580\pi$
$812$	−0.901924	+	1.56218i	−0.0316513	+	0.0548217i
$813$	−2.92820	+	5.07180i	−0.102697	+	0.177876i
$814$	49.5167			1.73556
$815$	0.875644	−	1.51666i	0.0306725	−	0.0531263i
$816$	1.13397	+	1.96410i	0.0396971	+	0.0687573i
$817$	−4.85641	−	8.41154i	−0.169904	−	0.294283i
$818$	14.2679			0.498867
$819$		0			0
$820$	3.05256			0.106600
$821$	−6.46410	−	11.1962i	−0.225599	−	0.390748i	0.730900	−	0.682484i	$-0.239100\pi$
$821$	−6.46410	−	11.1962i	−0.225599	−	0.390748i	−0.956499	+	0.291736i	$0.905767\pi$
$822$	0.964102	+	1.66987i	0.0336269	+	0.0582435i
$823$	20.7846	−	36.0000i	0.724506	−	1.25488i	−0.234671	−	0.972075i	$-0.575401\pi$
$823$	20.7846	−	36.0000i	0.724506	−	1.25488i	0.959177	−	0.282806i	$-0.0912654\pi$
$824$	−18.7321			−0.652562
$825$	11.6603	−	20.1962i	0.405958	−	0.703140i
$826$	−2.92820	+	5.07180i	−0.101885	+	0.176470i
$827$	33.4641			1.16366			0.581830	−	0.813310i	$-0.302337\pi$
$827$	33.4641			1.16366			0.581830	+	0.813310i	$0.302337\pi$
$828$	3.09808	−	5.36603i	0.107666	−	0.186482i
$829$	−6.06218	−	10.5000i	−0.210548	−	0.364680i	0.741338	−	0.671132i	$-0.234192\pi$
$829$	−6.06218	−	10.5000i	−0.210548	−	0.364680i	−0.951886	+	0.306452i	$0.900858\pi$
$830$	−1.36603	−	2.36603i	−0.0474154	−	0.0821259i
$831$	−2.26795			−0.0786743
$832$		0			0
$833$	14.6603			0.507948
$834$	4.92820	+	8.53590i	0.170650	+	0.295574i
$835$	0.339746	+	0.588457i	0.0117574	+	0.0203644i
$836$	−3.00000	+	5.19615i	−0.103757	+	0.179713i
$837$	−5.46410			−0.188867
$838$	5.26795	−	9.12436i	0.181978	−	0.315196i
$839$	−7.07180	+	12.2487i	−0.244146	+	0.422872i	−0.961891	−	0.273433i	$-0.911841\pi$
$839$	−7.07180	+	12.2487i	−0.244146	+	0.422872i	0.717745	+	0.696306i	$0.245174\pi$
$840$	0.196152			0.00676790
$841$	11.4641	−	19.8564i	0.395314	−	0.684704i
$842$	−16.3564	−	28.3301i	−0.563679	−	0.976321i
$843$	11.1603	+	19.3301i	0.384380	+	0.665765i
$844$	−4.39230			−0.151189
$845$		0			0
$846$	−8.19615			−0.281790
$847$	−4.16987	−	7.22243i	−0.143279	−	0.248166i
$848$	−0.232051	−	0.401924i	−0.00796866	−	0.0138021i
$849$	−4.16987	+	7.22243i	−0.143110	+	0.247873i
$850$	11.1769			0.383365
$851$	32.4186	−	56.1506i	1.11129	−	1.92482i
$852$	−0.633975	+	1.09808i	−0.0217196	+	0.0376195i
$853$	8.17691			0.279972			0.139986	−	0.990153i	$-0.455294\pi$
$853$	8.17691			0.279972			0.139986	+	0.990153i	$0.455294\pi$
$854$	−0.437822	+	0.758330i	−0.0149820	+	0.0259495i
$855$	−0.169873	−	0.294229i	−0.00580953	−	0.0100624i
$856$	0.0980762	+	0.169873i	0.00335218	+	0.00580614i
$857$	−19.4449			−0.664224			−0.332112	−	0.943240i	$-0.607761\pi$
$857$	−19.4449			−0.664224			−0.332112	+	0.943240i	$0.607761\pi$
$858$		0			0
$859$	−22.8756			−0.780507			−0.390253	−	0.920707i	$-0.627613\pi$
$859$	−22.8756			−0.780507			−0.390253	+	0.920707i	$0.627613\pi$
$860$	−1.02628	−	1.77757i	−0.0349958	−	0.0606146i
$861$	−4.16987	−	7.22243i	−0.142109	−	0.246140i
$862$	5.56218	−	9.63397i	0.189449	−	0.328134i
$863$	7.12436			0.242516			0.121258	−	0.992621i	$-0.461307\pi$
$863$	7.12436			0.242516			0.121258	+	0.992621i	$0.461307\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	2.19615	−	3.80385i	0.0746714	−	0.129335i
$866$	−14.8564			−0.504841
$867$	5.92820	−	10.2679i	0.201332	−	0.348718i
$868$	2.00000	+	3.46410i	0.0678844	+	0.117579i
$869$	22.3923	+	38.7846i	0.759607	+	1.31568i
$870$	0.660254			0.0223847
$871$		0			0
$872$	−5.46410			−0.185038
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$	3.92820	+	6.80385i	0.132873	+	0.230144i
$875$	0.973721	−	1.68653i	0.0329178	−	0.0570152i
$876$	−9.73205			−0.328816
$877$	−5.03590	+	8.72243i	−0.170050	+	0.294536i	−0.938437	−	0.345450i	$-0.887726\pi$
$877$	−5.03590	+	8.72243i	−0.170050	+	0.294536i	0.768387	+	0.639985i	$0.221060\pi$
$878$	8.83013	−	15.2942i	0.298002	−	0.516155i
$879$	−14.5167			−0.489635
$880$	−0.633975	+	1.09808i	−0.0213713	+	0.0370161i
$881$	−25.9186	−	44.8923i	−0.873219	−	1.51246i	−0.858648	−	0.512566i	$-0.828695\pi$
$881$	−25.9186	−	44.8923i	−0.873219	−	1.51246i	−0.0145717	−	0.999894i	$-0.504638\pi$
$882$	3.23205	+	5.59808i	0.108829	+	0.188497i
$883$	29.0718			0.978344			0.489172	−	0.872187i	$-0.337299\pi$
$883$	29.0718			0.978344			0.489172	+	0.872187i	$0.337299\pi$
$884$		0			0
$885$	2.14359			0.0720561
$886$	−18.1962	−	31.5167i	−0.611312	−	1.05882i
$887$	−5.07180	−	8.78461i	−0.170294	−	0.294958i	0.768228	−	0.640176i	$-0.221138\pi$
$887$	−5.07180	−	8.78461i	−0.170294	−	0.294958i	−0.938523	+	0.345217i	$0.887805\pi$
$888$	−5.23205	+	9.06218i	−0.175576	+	0.304107i
$889$	13.0718			0.438414
$890$	0.339746	−	0.588457i	0.0113883	−	0.0197251i
$891$	−2.36603	+	4.09808i	−0.0792648	+	0.137291i
$892$	−13.0718			−0.437676
$893$	5.19615	−	9.00000i	0.173883	−	0.301174i
$894$	−1.40192	−	2.42820i	−0.0468873	−	0.0812113i
$895$	−2.95448	−	5.11731i	−0.0987575	−	0.171053i
$896$	0.732051			0.0244561
$897$		0			0
$898$	−23.3205			−0.778215
$899$	6.73205	+	11.6603i	0.224526	+	0.388891i
$900$	2.46410	+	4.26795i	0.0821367	+	0.142265i
$901$	0.526279	−	0.911543i	0.0175329	−	0.0303679i
$902$	53.9090			1.79497
$903$	−2.80385	+	4.85641i	−0.0933062	+	0.161611i
$904$	9.33013	−	16.1603i	0.310315	−	0.537482i
$905$	2.35898			0.0784153
$906$	−1.63397	+	2.83013i	−0.0542852	+	0.0940247i
$907$	−7.80385	−	13.5167i	−0.259123	−	0.448813i	0.706885	−	0.707329i	$-0.250100\pi$
$907$	−7.80385	−	13.5167i	−0.259123	−	0.448813i	−0.966007	+	0.258516i	$0.916767\pi$
$908$	0.901924	+	1.56218i	0.0299314	+	0.0518427i
$909$	−11.9282			−0.395634
$910$		0			0
$911$	−9.46410			−0.313560			−0.156780	−	0.987634i	$-0.550111\pi$
$911$	−9.46410			−0.313560			−0.156780	+	0.987634i	$0.550111\pi$
$912$	−0.633975	−	1.09808i	−0.0209930	−	0.0363609i
$913$	−24.1244	−	41.7846i	−0.798400	−	1.38287i
$914$	−9.33013	+	16.1603i	−0.308613	+	0.534534i
$915$	0.320508			0.0105957
$916$	−7.92820	+	13.7321i	−0.261955	+	0.453720i
$917$	−4.92820	+	8.53590i	−0.162744	+	0.281880i
$918$	−2.26795			−0.0748535
$919$	28.9808	−	50.1962i	0.955987	−	1.65582i	0.223894	−	0.974613i	$-0.428123\pi$
$919$	28.9808	−	50.1962i	0.955987	−	1.65582i	0.732093	−	0.681205i	$-0.238544\pi$
$920$	0.830127	+	1.43782i	0.0273685	+	0.0474036i
$921$	−4.29423	−	7.43782i	−0.141500	−	0.245085i
$922$	25.7321			0.847440
$923$		0			0
$924$	3.46410			0.113961
$925$	25.7846	+	44.6603i	0.847793	+	1.46842i
$926$	14.0263	+	24.2942i	0.460932	+	0.798358i
$927$	9.36603	−	16.2224i	0.307621	−	0.532815i
$928$	2.46410			0.0808881
$929$	−4.62436	+	8.00962i	−0.151720	+	0.262787i	−0.931860	−	0.362818i	$-0.881815\pi$
$929$	−4.62436	+	8.00962i	−0.151720	+	0.262787i	0.780140	+	0.625605i	$0.215148\pi$
$930$	0.732051	−	1.26795i	0.0240049	−	0.0415777i
$931$	−8.19615			−0.268618
$932$	−9.92820	+	17.1962i	−0.325209	+	0.563279i
$933$	−7.83013	−	13.5622i	−0.256347	−	0.444006i
$934$	6.29423	+	10.9019i	0.205953	+	0.356722i
$935$	−2.87564			−0.0940436
$936$		0			0
$937$	43.2487			1.41287			0.706437	−	0.707776i	$-0.250301\pi$
$937$	43.2487			1.41287			0.706437	+	0.707776i	$0.250301\pi$
$938$	4.07180	+	7.05256i	0.132949	+	0.230274i
$939$	−6.73205	−	11.6603i	−0.219692	−	0.380518i
$940$	1.09808	−	1.90192i	0.0358153	−	0.0620339i
$941$	−56.6410			−1.84644			−0.923222	−	0.384267i	$-0.874454\pi$
$941$	−56.6410			−1.84644			−0.923222	+	0.384267i	$0.874454\pi$
$942$	11.7942	−	20.4282i	0.384277	−	0.665587i
$943$	35.2942	−	61.1314i	1.14934	−	1.99071i
$944$	8.00000			0.260378
$945$	−0.0980762	+	0.169873i	−0.00319042	+	0.00552597i
$946$	−18.1244	−	31.3923i	−0.589274	−	1.02065i
$947$	−17.4641	−	30.2487i	−0.567507	−	0.982951i	−0.996812	−	0.0797913i	$-0.974575\pi$
$947$	−17.4641	−	30.2487i	−0.567507	−	0.982951i	0.429305	−	0.903160i	$-0.358759\pi$
$948$	−9.46410			−0.307380
$949$		0			0
$950$	−6.24871			−0.202735
$951$	−1.66987	−	2.89230i	−0.0541493	−	0.0937894i
$952$	0.830127	+	1.43782i	0.0269046	+	0.0466001i
$953$	20.7846	−	36.0000i	0.673280	−	1.16615i	−0.303689	−	0.952771i	$-0.598218\pi$
$953$	20.7846	−	36.0000i	0.673280	−	1.16615i	0.976969	−	0.213383i	$-0.0684483\pi$
$954$	0.464102			0.0150258
$955$	−0.928203	+	1.60770i	−0.0300360	+	0.0520238i
$956$	4.83013	−	8.36603i	0.156217	−	0.270577i
$957$	11.6603			0.376922
$958$	−13.2679	+	22.9808i	−0.428668	+	0.742475i
$959$	0.705771	+	1.22243i	0.0227905	+	0.0394744i
$960$	−0.133975	−	0.232051i	−0.00432401	−	0.00748941i
$961$	−1.14359			−0.0368901
$962$		0			0
$963$	−0.196152			−0.00632092
$964$	8.79423	+	15.2321i	0.283243	+	0.490591i
$965$	1.10770	+	1.91858i	0.0356580	+	0.0617614i
$966$	2.26795	−	3.92820i	0.0729701	−	0.126388i
$967$	−18.8756			−0.607000			−0.303500	−	0.952831i	$-0.598155\pi$
$967$	−18.8756			−0.607000			−0.303500	+	0.952831i	$0.598155\pi$
$968$	−5.69615	+	9.86603i	−0.183081	+	0.317106i
$969$	1.43782	−	2.49038i	0.0461895	−	0.0800026i
$970$	−1.60770			−0.0516200
$971$	9.12436	−	15.8038i	0.292815	−	0.507170i	−0.681660	−	0.731669i	$-0.738741\pi$
$971$	9.12436	−	15.8038i	0.292815	−	0.507170i	0.974474	+	0.224500i	$0.0720748\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	3.60770	+	6.24871i	0.115657	+	0.200324i
$974$	21.1244			0.676868
$975$		0			0
$976$	1.19615			0.0382879
$977$	−16.0359	−	27.7750i	−0.513034	−	0.888601i	−0.999886	−	0.0151161i	$-0.995188\pi$
$977$	−16.0359	−	27.7750i	−0.513034	−	0.888601i	0.486852	−	0.873485i	$-0.338145\pi$
$978$	3.26795	+	5.66025i	0.104497	+	0.180995i
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$	−1.73205			−0.0553283
$981$	2.73205	−	4.73205i	0.0872277	−	0.151083i
$982$	−2.63397	+	4.56218i	−0.0840535	+	0.145585i
$983$	−20.7846			−0.662926			−0.331463	−	0.943468i	$-0.607542\pi$
$983$	−20.7846			−0.662926			−0.331463	+	0.943468i	$0.607542\pi$
$984$	−5.69615	+	9.86603i	−0.181587	+	0.314517i
$985$	−1.32051	−	2.28719i	−0.0420749	−	0.0728758i
$986$	2.79423	+	4.83975i	0.0889864	+	0.154129i
$987$	−6.00000			−0.190982
$988$		0			0
$989$	−47.4641			−1.50927
$990$	−0.633975	−	1.09808i	−0.0201490	−	0.0348992i
$991$	4.29423	+	7.43782i	0.136411	+	0.236270i	0.926135	−	0.377191i	$-0.123110\pi$
$991$	4.29423	+	7.43782i	0.136411	+	0.236270i	−0.789725	+	0.613461i	$0.789777\pi$
$992$	2.73205	−	4.73205i	0.0867427	−	0.150243i
$993$	20.0000			0.634681
$994$	−0.464102	+	0.803848i	−0.0147204	+	0.0254965i
$995$	0.509619	−	0.882686i	0.0161560	−	0.0279830i
$996$	10.1962			0.323077
$997$	−19.3301	+	33.4808i	−0.612191	+	1.06035i	0.378679	+	0.925528i	$0.376378\pi$
$997$	−19.3301	+	33.4808i	−0.612191	+	1.06035i	−0.990870	+	0.134818i	$0.956955\pi$
$998$	−16.0000	−	27.7128i	−0.506471	−	0.877234i
$999$	−5.23205	−	9.06218i	−0.165535	−	0.286715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.g.991.1		4
13.2	odd	12		1014.2.b.e.337.2		4
13.3	even	3		1014.2.a.k.1.1		2
13.4	even	6		1014.2.e.i.529.2		4
13.5	odd	4		1014.2.i.a.361.1		4
13.6	odd	12		78.2.i.a.43.2	✓	4
13.7	odd	12		1014.2.i.a.823.1		4
13.8	odd	4		78.2.i.a.49.2	yes	4
13.9	even	3	inner	1014.2.e.g.529.1		4
13.10	even	6		1014.2.a.i.1.2		2
13.11	odd	12		1014.2.b.e.337.3		4
13.12	even	2		1014.2.e.i.991.2		4
39.2	even	12		3042.2.b.i.1351.3		4
39.8	even	4		234.2.l.c.127.1		4
39.11	even	12		3042.2.b.i.1351.2		4
39.23	odd	6		3042.2.a.y.1.1		2
39.29	odd	6		3042.2.a.p.1.2		2
39.32	even	12		234.2.l.c.199.1		4
52.3	odd	6		8112.2.a.bp.1.1		2
52.19	even	12		624.2.bv.e.433.1		4
52.23	odd	6		8112.2.a.bj.1.2		2
52.47	even	4		624.2.bv.e.49.2		4
65.8	even	4		1950.2.y.b.49.2		4
65.19	odd	12		1950.2.bc.d.901.1		4
65.32	even	12		1950.2.y.b.199.2		4
65.34	odd	4		1950.2.bc.d.751.1		4
65.47	even	4		1950.2.y.g.49.1		4
65.58	even	12		1950.2.y.g.199.1		4
156.47	odd	4		1872.2.by.h.1297.1		4
156.71	odd	12		1872.2.by.h.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.2	✓	4	13.6	odd	12
78.2.i.a.49.2	yes	4	13.8	odd	4
234.2.l.c.127.1		4	39.8	even	4
234.2.l.c.199.1		4	39.32	even	12
624.2.bv.e.49.2		4	52.47	even	4
624.2.bv.e.433.1		4	52.19	even	12
1014.2.a.i.1.2		2	13.10	even	6
1014.2.a.k.1.1		2	13.3	even	3
1014.2.b.e.337.2		4	13.2	odd	12
1014.2.b.e.337.3		4	13.11	odd	12
1014.2.e.g.529.1		4	13.9	even	3	inner
1014.2.e.g.991.1		4	1.1	even	1	trivial
1014.2.e.i.529.2		4	13.4	even	6
1014.2.e.i.991.2		4	13.12	even	2
1014.2.i.a.361.1		4	13.5	odd	4
1014.2.i.a.823.1		4	13.7	odd	12
1872.2.by.h.433.2		4	156.71	odd	12
1872.2.by.h.1297.1		4	156.47	odd	4
1950.2.y.b.49.2		4	65.8	even	4
1950.2.y.b.199.2		4	65.32	even	12
1950.2.y.g.49.1		4	65.47	even	4
1950.2.y.g.199.1		4	65.58	even	12
1950.2.bc.d.751.1		4	65.34	odd	4
1950.2.bc.d.901.1		4	65.19	odd	12
3042.2.a.p.1.2		2	39.29	odd	6
3042.2.a.y.1.1		2	39.23	odd	6
3042.2.b.i.1351.2		4	39.11	even	12
3042.2.b.i.1351.3		4	39.2	even	12
8112.2.a.bj.1.2		2	52.23	odd	6
8112.2.a.bp.1.1		2	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.267949 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.366025 + 0.633975i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.267949 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.366025 + 0.633975i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.133975 - 0.232051i) q^{10} +(-2.36603 - 4.09808i) q^{11} +1.00000 q^{12} +0.732051 q^{14} +(-0.133975 - 0.232051i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.13397 - 1.96410i) q^{17} +1.00000 q^{18} +(-0.633975 + 1.09808i) q^{19} +(-0.133975 + 0.232051i) q^{20} +0.732051 q^{21} +(-2.36603 + 4.09808i) q^{22} +(3.09808 + 5.36603i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.92820 q^{25} +1.00000 q^{27} +(-0.366025 - 0.633975i) q^{28} +(-1.23205 - 2.13397i) q^{29} +(-0.133975 + 0.232051i) q^{30} -5.46410 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.36603 + 4.09808i) q^{33} -2.26795 q^{34} +(-0.0980762 + 0.169873i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.23205 - 9.06218i) q^{37} +1.26795 q^{38} +0.267949 q^{40} +(-5.69615 - 9.86603i) q^{41} +(-0.366025 - 0.633975i) q^{42} +(-3.83013 + 6.63397i) q^{43} +4.73205 q^{44} +(-0.133975 + 0.232051i) q^{45} +(3.09808 - 5.36603i) q^{46} -8.19615 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.23205 + 5.59808i) q^{49} +(2.46410 + 4.26795i) q^{50} -2.26795 q^{51} +0.464102 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.633975 - 1.09808i) q^{55} +(-0.366025 + 0.633975i) q^{56} +1.26795 q^{57} +(-1.23205 + 2.13397i) q^{58} +(-4.00000 + 6.92820i) q^{59} +0.267949 q^{60} +(-0.598076 + 1.03590i) q^{61} +(2.73205 + 4.73205i) q^{62} +(-0.366025 - 0.633975i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(5.56218 + 9.63397i) q^{67} +(1.13397 + 1.96410i) q^{68} +(3.09808 - 5.36603i) q^{69} +0.196152 q^{70} +(-0.633975 + 1.09808i) q^{71} +(-0.500000 + 0.866025i) q^{72} -9.73205 q^{73} +(-5.23205 + 9.06218i) q^{74} +(2.46410 + 4.26795i) q^{75} +(-0.633975 - 1.09808i) q^{76} +3.46410 q^{77} -9.46410 q^{79} +(-0.133975 - 0.232051i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.69615 + 9.86603i) q^{82} +10.1962 q^{83} +(-0.366025 + 0.633975i) q^{84} +(0.303848 - 0.526279i) q^{85} +7.66025 q^{86} +(-1.23205 + 2.13397i) q^{87} +(-2.36603 - 4.09808i) q^{88} +(1.26795 + 2.19615i) q^{89} +0.267949 q^{90} -6.19615 q^{92} +(2.73205 + 4.73205i) q^{93} +(4.09808 + 7.09808i) q^{94} +(-0.169873 + 0.294229i) q^{95} +1.00000 q^{96} +(3.00000 - 5.19615i) q^{97} +(3.23205 - 5.59808i) q^{98} +4.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} - 4 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{21} - 6 q^{22} + 2 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{27} + 2 q^{28} + 2 q^{29} - 4 q^{30} - 8 q^{31} - 2 q^{32} - 6 q^{33} - 16 q^{34} + 10 q^{35} - 2 q^{36} - 14 q^{37} + 12 q^{38} + 8 q^{40} - 2 q^{41} + 2 q^{42} + 2 q^{43} + 12 q^{44} - 4 q^{45} + 2 q^{46} - 12 q^{47} - 2 q^{48} + 6 q^{49} - 4 q^{50} - 16 q^{51} - 12 q^{53} - 2 q^{54} - 6 q^{55} + 2 q^{56} + 12 q^{57} + 2 q^{58} - 16 q^{59} + 8 q^{60} + 8 q^{61} + 4 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 8 q^{68} + 2 q^{69} - 20 q^{70} - 6 q^{71} - 2 q^{72} - 32 q^{73} - 14 q^{74} - 4 q^{75} - 6 q^{76} - 24 q^{79} - 4 q^{80} - 2 q^{81} - 2 q^{82} + 20 q^{83} + 2 q^{84} + 22 q^{85} - 4 q^{86} + 2 q^{87} - 6 q^{88} + 12 q^{89} + 8 q^{90} - 4 q^{92} + 4 q^{93} + 6 q^{94} - 18 q^{95} + 4 q^{96} + 12 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 8 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 - 4 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^14 - 4 * q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 - 6 * q^19 - 4 * q^20 - 4 * q^21 - 6 * q^22 + 2 * q^23 - 2 * q^24 + 8 * q^25 + 4 * q^27 + 2 * q^28 + 2 * q^29 - 4 * q^30 - 8 * q^31 - 2 * q^32 - 6 * q^33 - 16 * q^34 + 10 * q^35 - 2 * q^36 - 14 * q^37 + 12 * q^38 + 8 * q^40 - 2 * q^41 + 2 * q^42 + 2 * q^43 + 12 * q^44 - 4 * q^45 + 2 * q^46 - 12 * q^47 - 2 * q^48 + 6 * q^49 - 4 * q^50 - 16 * q^51 - 12 * q^53 - 2 * q^54 - 6 * q^55 + 2 * q^56 + 12 * q^57 + 2 * q^58 - 16 * q^59 + 8 * q^60 + 8 * q^61 + 4 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^66 - 2 * q^67 + 8 * q^68 + 2 * q^69 - 20 * q^70 - 6 * q^71 - 2 * q^72 - 32 * q^73 - 14 * q^74 - 4 * q^75 - 6 * q^76 - 24 * q^79 - 4 * q^80 - 2 * q^81 - 2 * q^82 + 20 * q^83 + 2 * q^84 + 22 * q^85 - 4 * q^86 + 2 * q^87 - 6 * q^88 + 12 * q^89 + 8 * q^90 - 4 * q^92 + 4 * q^93 + 6 * q^94 - 18 * q^95 + 4 * q^96 + 12 * q^97 + 6 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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