LMFDB - Embedded newform 507.2.k.i.488.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			488.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	507.488
Dual form			507.2.k.i.80.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 - 0.965926i) q^{2} +(1.72474 - 0.158919i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.41421 - 1.41421i) q^{5} +(-0.599900 - 1.62484i) q^{6} +(1.36603 + 0.366025i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(2.94949 - 0.548188i) q^{9} +(-1.73205 - 1.00000i) q^{10} +(-3.86370 + 1.03528i) q^{11} +(1.41421 - 1.00000i) q^{12} -1.41421i q^{14} +(2.21441 - 2.66390i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.29289 - 2.70711i) q^{18} +(-0.366025 + 1.36603i) q^{19} +(0.517638 - 1.93185i) q^{20} +(2.41421 + 0.414214i) q^{21} +(2.00000 + 3.46410i) q^{22} +(-4.24264 + 7.34847i) q^{23} +(-3.99585 - 3.32162i) q^{24} +1.00000i q^{25} +(5.00000 - 1.41421i) q^{27} +(1.36603 - 0.366025i) q^{28} +(-2.44949 - 1.41421i) q^{29} +(-3.14626 - 1.44949i) q^{30} +(5.00000 + 5.00000i) q^{31} +(-4.82963 - 1.29410i) q^{32} +(-6.49938 + 2.39960i) q^{33} +(2.44949 - 1.41421i) q^{35} +(2.28024 - 1.94949i) q^{36} +(-0.366025 - 1.36603i) q^{37} +1.41421 q^{38} -6.00000 q^{40} +(0.517638 + 1.93185i) q^{41} +(-0.224745 - 2.43916i) q^{42} +(5.19615 - 3.00000i) q^{43} +(-2.82843 + 2.82843i) q^{44} +(3.39595 - 4.94646i) q^{45} +(8.19615 + 2.19615i) q^{46} +(2.82843 + 2.82843i) q^{47} +(-0.724745 + 1.57313i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(0.965926 - 0.258819i) q^{50} -5.65685i q^{53} +(-2.66012 - 4.46360i) q^{54} +(-4.00000 + 6.92820i) q^{55} +(-2.12132 - 3.67423i) q^{56} +(-0.414214 + 2.41421i) q^{57} +(-0.732051 + 2.73205i) q^{58} +(1.03528 - 3.86370i) q^{59} +(0.585786 - 3.41421i) q^{60} +(-4.00000 - 6.92820i) q^{61} +(3.53553 - 6.12372i) q^{62} +(4.22973 + 0.330749i) q^{63} +7.00000i q^{64} +(4.00000 + 5.65685i) q^{66} +(-6.83013 + 1.83013i) q^{67} +(-6.14966 + 13.3485i) q^{69} +(-2.00000 - 2.00000i) q^{70} +(3.86370 + 1.03528i) q^{71} +(-7.41970 - 5.09393i) q^{72} +(-1.00000 + 1.00000i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(0.158919 + 1.72474i) q^{75} +(0.366025 + 1.36603i) q^{76} -5.65685 q^{77} -10.0000 q^{79} +(0.517638 + 1.93185i) q^{80} +(8.39898 - 3.23375i) q^{81} +(1.73205 - 1.00000i) q^{82} +(5.65685 - 5.65685i) q^{83} +(2.29788 - 0.848387i) q^{84} +(-4.24264 - 4.24264i) q^{86} +(-4.44949 - 2.04989i) q^{87} +(10.3923 + 6.00000i) q^{88} +(13.5230 - 3.62347i) q^{89} +(-5.65685 - 2.00000i) q^{90} +8.48528i q^{92} +(9.41832 + 7.82913i) q^{93} +(2.00000 - 3.46410i) q^{94} +(1.41421 + 2.44949i) q^{95} +(-8.53553 - 1.46447i) q^{96} +(-2.56218 + 9.56218i) q^{97} +(-1.29410 + 4.82963i) q^{98} +(-10.8284 + 5.17157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9} + 8 q^{15} - 4 q^{16} - 16 q^{18} + 4 q^{19} + 8 q^{21} + 16 q^{22} + 12 q^{24} + 40 q^{27} + 4 q^{28} + 40 q^{31} - 16 q^{33} + 4 q^{37} - 48 q^{40} + 8 q^{42}+ \cdots - 64 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 + 4 * q^9 + 8 * q^15 - 4 * q^16 - 16 * q^18 + 4 * q^19 + 8 * q^21 + 16 * q^22 + 12 * q^24 + 40 * q^27 + 4 * q^28 + 40 * q^31 - 16 * q^33 + 4 * q^37 - 48 * q^40 + 8 * q^42 - 16 * q^45 + 24 * q^46 + 4 * q^48 - 4 * q^54 - 32 * q^55 + 8 * q^57 + 8 * q^58 + 16 * q^60 - 32 * q^61 - 4 * q^63 + 32 * q^66 - 20 * q^67 - 16 * q^70 - 24 * q^72 - 8 * q^73 - 4 * q^76 - 80 * q^79 + 28 * q^81 - 4 * q^84 - 16 * q^87 + 20 * q^93 + 16 * q^94 - 40 * q^96 + 28 * q^97 - 64 * q^99

Character values

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

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i	−0.995047	−	0.0994033i	$-0.968307\pi$
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i	0.812035	−	0.583609i	$-0.198360\pi$
$3$	1.72474	−	0.158919i	0.995782	−	0.0917517i
$3$	1.72474	−	0.158919i	0.995782	−	0.0917517i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.41421	−	1.41421i	0.632456	−	0.632456i	−0.316228	−	0.948683i	$-0.602416\pi$
$5$	1.41421	−	1.41421i	0.632456	−	0.632456i	0.948683	+	0.316228i	$0.102416\pi$
$6$	−0.599900	−	1.62484i	−0.244908	−	0.663340i
$7$	1.36603	+	0.366025i	0.516309	+	0.138345i	0.507559	−	0.861617i	$-0.330548\pi$
$7$	1.36603	+	0.366025i	0.516309	+	0.138345i	0.00875026	+	0.999962i	$0.497215\pi$
$8$	−2.12132	−	2.12132i	−0.750000	−	0.750000i
$9$	2.94949	−	0.548188i	0.983163	−	0.182729i
$10$	−1.73205	−	1.00000i	−0.547723	−	0.316228i
$11$	−3.86370	+	1.03528i	−1.16495	+	0.312148i	−0.788941	−	0.614468i	$-0.789370\pi$
$11$	−3.86370	+	1.03528i	−1.16495	+	0.312148i	−0.376009	+	0.926616i	$0.622704\pi$
$12$	1.41421	−	1.00000i	0.408248	−	0.288675i
$13$		0			0
$13$		0			0
$14$		−	1.41421i		−	0.377964i
$15$	2.21441	−	2.66390i	0.571759	−	0.687817i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−1.29289	−	2.70711i	−0.304738	−	0.638071i
$19$	−0.366025	+	1.36603i	−0.0839720	+	0.313388i	−0.995118	−	0.0986970i	$-0.968533\pi$
$19$	−0.366025	+	1.36603i	−0.0839720	+	0.313388i	0.911146	+	0.412085i	$0.135199\pi$
$20$	0.517638	−	1.93185i	0.115747	−	0.431975i
$21$	2.41421	+	0.414214i	0.526825	+	0.0903888i
$22$	2.00000	+	3.46410i	0.426401	+	0.738549i
$23$	−4.24264	+	7.34847i	−0.884652	+	1.53226i	−0.0385394	+	0.999257i	$0.512271\pi$
$23$	−4.24264	+	7.34847i	−0.884652	+	1.53226i	−0.846112	+	0.533005i	$0.821063\pi$
$24$	−3.99585	−	3.32162i	−0.815650	−	0.678023i
$25$			1.00000i			0.200000i
$26$		0			0
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$	1.36603	−	0.366025i	0.258155	−	0.0691723i
$29$	−2.44949	−	1.41421i	−0.454859	−	0.262613i	0.255021	−	0.966935i	$-0.417918\pi$
$29$	−2.44949	−	1.41421i	−0.454859	−	0.262613i	−0.709880	+	0.704323i	$0.751251\pi$
$30$	−3.14626	−	1.44949i	−0.574427	−	0.264639i
$31$	5.00000	+	5.00000i	0.898027	+	0.898027i	0.995261	−	0.0972349i	$-0.0309998\pi$
$31$	5.00000	+	5.00000i	0.898027	+	0.898027i	−0.0972349	+	0.995261i	$0.531000\pi$
$32$	−4.82963	−	1.29410i	−0.853766	−	0.228766i
$33$	−6.49938	+	2.39960i	−1.13140	+	0.417717i
$34$		0			0
$35$	2.44949	−	1.41421i	0.414039	−	0.239046i
$36$	2.28024	−	1.94949i	0.380040	−	0.324915i
$37$	−0.366025	−	1.36603i	−0.0601742	−	0.224573i	0.929290	−	0.369351i	$-0.120420\pi$
$37$	−0.366025	−	1.36603i	−0.0601742	−	0.224573i	−0.989464	+	0.144778i	$0.953753\pi$
$38$	1.41421			0.229416
$39$		0			0
$40$	−6.00000			−0.948683
$41$	0.517638	+	1.93185i	0.0808415	+	0.301705i	0.994494	−	0.104791i	$-0.0334174\pi$
$41$	0.517638	+	1.93185i	0.0808415	+	0.301705i	−0.913653	+	0.406496i	$0.866751\pi$
$42$	−0.224745	−	2.43916i	−0.0346789	−	0.376370i
$43$	5.19615	−	3.00000i	0.792406	−	0.457496i	−0.0484030	−	0.998828i	$-0.515413\pi$
$43$	5.19615	−	3.00000i	0.792406	−	0.457496i	0.840809	+	0.541332i	$0.182080\pi$
$44$	−2.82843	+	2.82843i	−0.426401	+	0.426401i
$45$	3.39595	−	4.94646i	0.506239	−	0.737375i
$46$	8.19615	+	2.19615i	1.20846	+	0.323805i
$47$	2.82843	+	2.82843i	0.412568	+	0.412568i	0.882632	−	0.470064i	$-0.155769\pi$
$47$	2.82843	+	2.82843i	0.412568	+	0.412568i	−0.470064	+	0.882632i	$0.655769\pi$
$48$	−0.724745	+	1.57313i	−0.104608	+	0.227062i
$49$	−4.33013	−	2.50000i	−0.618590	−	0.357143i
$50$	0.965926	−	0.258819i	0.136603	−	0.0366025i
$51$		0			0
$52$		0			0
$53$		−	5.65685i		−	0.777029i	−0.921443	−	0.388514i	$-0.872988\pi$
$53$		−	5.65685i		−	0.777029i	0.921443	−	0.388514i	$-0.127012\pi$
$54$	−2.66012	−	4.46360i	−0.361997	−	0.607420i
$55$	−4.00000	+	6.92820i	−0.539360	+	0.934199i
$56$	−2.12132	−	3.67423i	−0.283473	−	0.490990i
$57$	−0.414214	+	2.41421i	−0.0548639	+	0.319770i
$58$	−0.732051	+	2.73205i	−0.0961230	+	0.358736i
$59$	1.03528	−	3.86370i	0.134781	−	0.503011i	−0.865217	−	0.501397i	$-0.832820\pi$
$59$	1.03528	−	3.86370i	0.134781	−	0.503011i	0.999999	−	0.00161411i	$-0.000513789\pi$
$60$	0.585786	−	3.41421i	0.0756247	−	0.440773i
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	3.53553	−	6.12372i	0.449013	−	0.777714i
$63$	4.22973	+	0.330749i	0.532896	+	0.0416705i
$64$			7.00000i			0.875000i
$65$		0			0
$66$	4.00000	+	5.65685i	0.492366	+	0.696311i
$67$	−6.83013	+	1.83013i	−0.834433	+	0.223586i	−0.650647	−	0.759381i	$-0.725502\pi$
$67$	−6.83013	+	1.83013i	−0.834433	+	0.223586i	−0.183786	+	0.982966i	$0.558835\pi$
$68$		0			0
$69$	−6.14966	+	13.3485i	−0.740333	+	1.60697i
$70$	−2.00000	−	2.00000i	−0.239046	−	0.239046i
$71$	3.86370	+	1.03528i	0.458537	+	0.122865i	0.480691	−	0.876890i	$-0.340386\pi$
$71$	3.86370	+	1.03528i	0.458537	+	0.122865i	−0.0221541	+	0.999755i	$0.507052\pi$
$72$	−7.41970	−	5.09393i	−0.874419	−	0.600325i
$73$	−1.00000	+	1.00000i	−0.117041	+	0.117041i	−0.763202	−	0.646160i	$-0.776374\pi$
$73$	−1.00000	+	1.00000i	−0.117041	+	0.117041i	0.646160	+	0.763202i	$0.276374\pi$
$74$	−1.22474	+	0.707107i	−0.142374	+	0.0821995i
$75$	0.158919	+	1.72474i	0.0183503	+	0.199156i
$76$	0.366025	+	1.36603i	0.0419860	+	0.156694i
$77$	−5.65685			−0.644658
$78$		0			0
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	0.517638	+	1.93185i	0.0578737	+	0.215988i
$81$	8.39898	−	3.23375i	0.933220	−	0.359306i
$82$	1.73205	−	1.00000i	0.191273	−	0.110432i
$83$	5.65685	−	5.65685i	0.620920	−	0.620920i	−0.324846	−	0.945767i	$-0.605313\pi$
$83$	5.65685	−	5.65685i	0.620920	−	0.620920i	0.945767	+	0.324846i	$0.105313\pi$
$84$	2.29788	−	0.848387i	0.250719	−	0.0925666i
$85$		0			0
$86$	−4.24264	−	4.24264i	−0.457496	−	0.457496i
$87$	−4.44949	−	2.04989i	−0.477035	−	0.219771i
$88$	10.3923	+	6.00000i	1.10782	+	0.639602i
$89$	13.5230	−	3.62347i	1.43343	−	0.384087i	0.543203	−	0.839601i	$-0.317211\pi$
$89$	13.5230	−	3.62347i	1.43343	−	0.384087i	0.890228	+	0.455515i	$0.150545\pi$
$90$	−5.65685	−	2.00000i	−0.596285	−	0.210819i
$91$		0			0
$92$			8.48528i			0.884652i
$93$	9.41832	+	7.82913i	0.976634	+	0.811843i
$94$	2.00000	−	3.46410i	0.206284	−	0.357295i
$95$	1.41421	+	2.44949i	0.145095	+	0.251312i
$96$	−8.53553	−	1.46447i	−0.871154	−	0.149466i
$97$	−2.56218	+	9.56218i	−0.260150	+	0.970892i	0.705003	+	0.709204i	$0.250946\pi$
$97$	−2.56218	+	9.56218i	−0.260150	+	0.970892i	−0.965153	+	0.261688i	$0.915721\pi$
$98$	−1.29410	+	4.82963i	−0.130723	+	0.487866i
$99$	−10.8284	+	5.17157i	−1.08830	+	0.519763i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	4.24264	−	7.34847i	0.422159	−	0.731200i	−0.573992	−	0.818861i	$-0.694606\pi$
$101$	4.24264	−	7.34847i	0.422159	−	0.731200i	0.996150	+	0.0876610i	$0.0279392\pi$
$102$		0			0
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$		0			0
$105$	4.00000	−	2.82843i	0.390360	−	0.276026i
$106$	−5.46410	+	1.46410i	−0.530720	+	0.142206i
$107$	4.89898	+	2.82843i	0.473602	+	0.273434i	0.717746	−	0.696305i	$-0.245174\pi$
$107$	4.89898	+	2.82843i	0.473602	+	0.273434i	−0.244144	+	0.969739i	$0.578507\pi$
$108$	3.62302	−	3.72474i	0.348625	−	0.358414i
$109$	−1.00000	−	1.00000i	−0.0957826	−	0.0957826i	0.657592	−	0.753374i	$-0.271575\pi$
$109$	−1.00000	−	1.00000i	−0.0957826	−	0.0957826i	−0.753374	+	0.657592i	$0.771575\pi$
$110$	7.72741	+	2.07055i	0.736779	+	0.197419i
$111$	−0.848387	−	2.29788i	−0.0805254	−	0.218105i
$112$	−1.00000	+	1.00000i	−0.0944911	+	0.0944911i
$113$	−12.2474	+	7.07107i	−1.15214	+	0.665190i	−0.949409	−	0.314044i	$-0.898316\pi$
$113$	−12.2474	+	7.07107i	−1.15214	+	0.665190i	−0.202735	+	0.979234i	$0.564983\pi$
$114$	2.43916	−	0.224745i	0.228448	−	0.0210493i
$115$	4.39230	+	16.3923i	0.409585	+	1.52859i
$116$	−2.82843			−0.262613
$117$		0			0
$118$	−4.00000			−0.368230
$119$		0			0
$120$	−10.3485	+	0.953512i	−0.944682	+	0.0870433i
$121$	4.33013	−	2.50000i	0.393648	−	0.227273i
$122$	−5.65685	+	5.65685i	−0.512148	+	0.512148i
$123$	1.19980	+	3.24969i	0.108182	+	0.293015i
$124$	6.83013	+	1.83013i	0.613364	+	0.164350i
$125$	8.48528	+	8.48528i	0.758947	+	0.758947i
$126$	−0.775255	−	4.17121i	−0.0690652	−	0.371601i
$127$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$127$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$128$	−2.89778	+	0.776457i	−0.256130	+	0.0686298i
$129$	8.48528	−	6.00000i	0.747087	−	0.528271i
$130$		0			0
$131$			11.3137i			0.988483i	0.869325	+	0.494242i	$0.164554\pi$
$131$			11.3137i			0.988483i	−0.869325	+	0.494242i	$0.835446\pi$
$132$	−4.42883	+	5.32780i	−0.385480	+	0.463726i
$133$	−1.00000	+	1.73205i	−0.0867110	+	0.150188i
$134$	3.53553	+	6.12372i	0.305424	+	0.529009i
$135$	5.07107	−	9.07107i	0.436448	−	0.780713i
$136$		0			0
$137$	−3.62347	+	13.5230i	−0.309574	+	1.15534i	0.619363	+	0.785105i	$0.287391\pi$
$137$	−3.62347	+	13.5230i	−0.309574	+	1.15534i	−0.928936	+	0.370240i	$0.879276\pi$
$138$	14.4853	+	2.48528i	1.23307	+	0.211561i
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$	1.41421	−	2.44949i	0.119523	−	0.207020i
$141$	5.32780	+	4.42883i	0.448682	+	0.372974i
$142$		−	4.00000i		−	0.335673i
$143$		0			0
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$	−5.46410	+	1.46410i	−0.453769	+	0.121587i
$146$	1.22474	+	0.707107i	0.101361	+	0.0585206i
$147$	−7.86566	−	3.62372i	−0.648749	−	0.298880i
$148$	−1.00000	−	1.00000i	−0.0821995	−	0.0821995i
$149$	−1.93185	−	0.517638i	−0.158263	−	0.0424066i	0.178817	−	0.983882i	$-0.442773\pi$
$149$	−1.93185	−	0.517638i	−0.158263	−	0.0424066i	−0.337081	+	0.941476i	$0.609440\pi$
$150$	1.62484	−	0.599900i	0.132668	−	0.0489817i
$151$	−1.00000	+	1.00000i	−0.0813788	+	0.0813788i	−0.746625	−	0.665246i	$-0.768327\pi$
$151$	−1.00000	+	1.00000i	−0.0813788	+	0.0813788i	0.665246	+	0.746625i	$0.268327\pi$
$152$	3.67423	−	2.12132i	0.298020	−	0.172062i
$153$		0			0
$154$	1.46410	+	5.46410i	0.117981	+	0.440310i
$155$	14.1421			1.13592
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	2.58819	+	9.65926i	0.205905	+	0.768449i
$159$	−0.898979	−	9.75663i	−0.0712937	−	0.773751i
$160$	−8.66025	+	5.00000i	−0.684653	+	0.395285i
$161$	−8.48528	+	8.48528i	−0.668734	+	0.668734i
$162$	−5.29738	−	7.27583i	−0.416201	−	0.571644i
$163$	1.36603	+	0.366025i	0.106995	+	0.0286693i	0.311919	−	0.950109i	$-0.399028\pi$
$163$	1.36603	+	0.366025i	0.106995	+	0.0286693i	−0.204924	+	0.978778i	$0.565695\pi$
$164$	1.41421	+	1.41421i	0.110432	+	0.110432i
$165$	−5.79796	+	12.5851i	−0.451370	+	0.979745i
$166$	−6.92820	−	4.00000i	−0.537733	−	0.310460i
$167$	−3.86370	+	1.03528i	−0.298982	+	0.0801121i	−0.405192	−	0.914232i	$-0.632795\pi$
$167$	−3.86370	+	1.03528i	−0.298982	+	0.0801121i	0.106209	+	0.994344i	$0.466129\pi$
$168$	−4.24264	−	6.00000i	−0.327327	−	0.462910i
$169$		0			0
$170$		0			0
$171$	−0.330749	+	4.22973i	−0.0252930	+	0.323455i
$172$	3.00000	−	5.19615i	0.228748	−	0.396203i
$173$	4.24264	+	7.34847i	0.322562	+	0.558694i	0.981016	−	0.193927i	$-0.0621226\pi$
$173$	4.24264	+	7.34847i	0.322562	+	0.558694i	−0.658454	+	0.752621i	$0.728789\pi$
$174$	−0.828427	+	4.82843i	−0.0628029	+	0.366042i
$175$	−0.366025	+	1.36603i	−0.0276689	+	0.103262i
$176$	1.03528	−	3.86370i	0.0780369	−	0.291238i
$177$	1.17157	−	6.82843i	0.0880608	−	0.513256i
$178$	−7.00000	−	12.1244i	−0.524672	−	0.908759i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	0.467750	−	5.98174i	0.0348640	−	0.445853i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	−8.00000	−	11.3137i	−0.591377	−	0.836333i
$184$	24.5885	−	6.58846i	1.81269	−	0.485708i
$185$	−2.44949	−	1.41421i	−0.180090	−	0.103975i
$186$	5.12472	−	11.1237i	0.375763	−	0.815631i
$187$		0			0
$188$	3.86370	+	1.03528i	0.281790	+	0.0755053i
$189$	7.34777	−	0.101725i	0.534471	−	0.00739938i
$190$	2.00000	−	2.00000i	0.145095	−	0.145095i
$191$	2.44949	−	1.41421i	0.177239	−	0.102329i	−0.408756	−	0.912644i	$-0.634037\pi$
$191$	2.44949	−	1.41421i	0.177239	−	0.102329i	0.585995	+	0.810315i	$0.300704\pi$
$192$	1.11243	+	12.0732i	0.0802827	+	0.871309i
$193$	−6.95448	−	25.9545i	−0.500595	−	1.86824i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	−6.95448	−	25.9545i	−0.500595	−	1.86824i	−0.00447566	−	0.999990i	$-0.501425\pi$
$194$	9.89949			0.710742
$195$		0			0
$196$	−5.00000			−0.357143
$197$	−5.69402	−	21.2504i	−0.405682	−	1.51403i	−0.802794	−	0.596256i	$-0.796654\pi$
$197$	−5.69402	−	21.2504i	−0.405682	−	1.51403i	0.397112	−	0.917770i	$-0.370012\pi$
$198$	7.79796	+	9.12096i	0.554177	+	0.648198i
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	2.12132	−	2.12132i	0.150000	−	0.150000i
$201$	−11.4894	+	4.24194i	−0.810399	+	0.299203i
$202$	−8.19615	−	2.19615i	−0.576679	−	0.154521i
$203$	−2.82843	−	2.82843i	−0.198517	−	0.198517i
$204$		0			0
$205$	3.46410	+	2.00000i	0.241943	+	0.139686i
$206$	−5.79555	+	1.55291i	−0.403795	+	0.108197i
$207$	−8.48528	+	24.0000i	−0.589768	+	1.66812i
$208$		0			0
$209$		−	5.65685i		−	0.391293i
$210$	−3.76733	−	3.13165i	−0.259970	−	0.216105i
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	−0.999784	−	0.0207756i	$-0.993386\pi$
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	0.517884	+	0.855451i	$0.326720\pi$
$212$	−2.82843	−	4.89898i	−0.194257	−	0.336463i
$213$	6.82843	+	1.17157i	0.467876	+	0.0802749i
$214$	1.46410	−	5.46410i	0.100084	−	0.373518i
$215$	3.10583	−	11.5911i	0.211816	−	0.790507i
$216$	−13.6066	−	7.60660i	−0.925812	−	0.517564i
$217$	5.00000	+	8.66025i	0.339422	+	0.587896i
$218$	−0.707107	+	1.22474i	−0.0478913	+	0.0829502i
$219$	−1.56583	+	1.88366i	−0.105809	+	0.127286i
$220$			8.00000i			0.539360i
$221$		0			0
$222$	−2.00000	+	1.41421i	−0.134231	+	0.0949158i
$223$	−15.0263	+	4.02628i	−1.00623	+	0.269620i	−0.724055	−	0.689742i	$-0.757724\pi$
$223$	−15.0263	+	4.02628i	−1.00623	+	0.269620i	−0.282179	+	0.959362i	$0.591057\pi$
$224$	−6.12372	−	3.53553i	−0.409159	−	0.236228i
$225$	0.548188	+	2.94949i	0.0365459	+	0.196633i
$226$	10.0000	+	10.0000i	0.665190	+	0.665190i
$227$	−7.72741	−	2.07055i	−0.512886	−	0.137427i	−0.00691198	−	0.999976i	$-0.502200\pi$
$227$	−7.72741	−	2.07055i	−0.512886	−	0.137427i	−0.505974	+	0.862549i	$0.668867\pi$
$228$	0.848387	+	2.29788i	0.0561858	+	0.152181i
$229$	−1.00000	+	1.00000i	−0.0660819	+	0.0660819i	−0.739375	−	0.673293i	$-0.764879\pi$
$229$	−1.00000	+	1.00000i	−0.0660819	+	0.0660819i	0.673293	+	0.739375i	$0.264879\pi$
$230$	14.6969	−	8.48528i	0.969087	−	0.559503i
$231$	−9.75663	+	0.898979i	−0.641939	+	0.0591485i
$232$	2.19615	+	8.19615i	0.144184	+	0.538104i
$233$	−25.4558			−1.66767			−0.833834	−	0.552015i	$-0.813859\pi$
$233$	−25.4558			−1.66767			−0.833834	+	0.552015i	$0.813859\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$	−1.03528	−	3.86370i	−0.0673907	−	0.251506i
$237$	−17.2474	+	1.58919i	−1.12034	+	0.103229i
$238$		0			0
$239$	14.1421	−	14.1421i	0.914779	−	0.914779i	−0.0818647	−	0.996643i	$-0.526088\pi$
$239$	14.1421	−	14.1421i	0.914779	−	0.914779i	0.996643	+	0.0818647i	$0.0260876\pi$
$240$	1.19980	+	3.24969i	0.0774468	+	0.209767i
$241$	−23.2224	−	6.22243i	−1.49589	−	0.400822i	−0.584168	−	0.811633i	$-0.698579\pi$
$241$	−23.2224	−	6.22243i	−1.49589	−	0.400822i	−0.911721	+	0.410811i	$0.865246\pi$
$242$	−3.53553	−	3.53553i	−0.227273	−	0.227273i
$243$	13.9722	−	6.91215i	0.896317	−	0.443415i
$244$	−6.92820	−	4.00000i	−0.443533	−	0.256074i
$245$	−9.65926	+	2.58819i	−0.617107	+	0.165353i
$246$	2.82843	−	2.00000i	0.180334	−	0.127515i
$247$		0			0
$248$		−	21.2132i		−	1.34704i
$249$	8.85765	−	10.6556i	0.561331	−	0.675272i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	−12.7279	−	22.0454i	−0.803379	−	1.39149i	−0.917380	−	0.398013i	$-0.869700\pi$
$251$	−12.7279	−	22.0454i	−0.803379	−	1.39149i	0.114000	−	0.993481i	$-0.463633\pi$
$252$	3.82843	−	1.82843i	0.241168	−	0.115180i
$253$	8.78461	−	32.7846i	0.552284	−	2.06115i
$254$		0			0
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−4.24264	+	7.34847i	−0.264649	+	0.458385i	−0.967472	−	0.252980i	$-0.918589\pi$
$257$	−4.24264	+	7.34847i	−0.264649	+	0.458385i	0.702823	+	0.711365i	$0.251923\pi$
$258$	−7.99171	−	6.64324i	−0.497542	−	0.413590i
$259$		−	2.00000i		−	0.124274i
$260$		0			0
$261$	−8.00000	−	2.82843i	−0.495188	−	0.175075i
$262$	10.9282	−	2.92820i	0.675147	−	0.180905i
$263$	19.5959	+	11.3137i	1.20834	+	0.697633i	0.962396	−	0.271652i	$-0.0875699\pi$
$263$	19.5959	+	11.3137i	1.20834	+	0.697633i	0.245940	+	0.969285i	$0.420903\pi$
$264$	18.8776	+	8.69694i	1.16184	+	0.535260i
$265$	−8.00000	−	8.00000i	−0.491436	−	0.491436i
$266$	1.93185	+	0.517638i	0.118449	+	0.0317384i
$267$	22.7478	−	8.39861i	1.39214	−	0.513986i
$268$	−5.00000	+	5.00000i	−0.305424	+	0.305424i
$269$	17.1464	−	9.89949i	1.04544	−	0.603583i	0.124068	−	0.992274i	$-0.460406\pi$
$269$	17.1464	−	9.89949i	1.04544	−	0.603583i	0.921368	+	0.388691i	$0.127073\pi$
$270$	−10.0745	−	2.55051i	−0.613113	−	0.155219i
$271$	−6.95448	−	25.9545i	−0.422455	−	1.57662i	−0.769419	−	0.638744i	$-0.779454\pi$
$271$	−6.95448	−	25.9545i	−0.422455	−	1.57662i	0.346964	−	0.937878i	$-0.387212\pi$
$272$		0			0
$273$		0			0
$274$	14.0000			0.845771
$275$	−1.03528	−	3.86370i	−0.0624295	−	0.232990i
$276$	1.34847	+	14.6349i	0.0811683	+	0.880920i
$277$	−10.3923	+	6.00000i	−0.624413	+	0.360505i	−0.778585	−	0.627539i	$-0.784062\pi$
$277$	−10.3923	+	6.00000i	−0.624413	+	0.360505i	0.154172	+	0.988044i	$0.450729\pi$
$278$	2.82843	−	2.82843i	0.169638	−	0.169638i
$279$	17.4884	+	12.0065i	1.04700	+	0.718811i
$280$	−8.19615	−	2.19615i	−0.489814	−	0.131245i
$281$	−9.89949	−	9.89949i	−0.590554	−	0.590554i	0.347227	−	0.937781i	$-0.387123\pi$
$281$	−9.89949	−	9.89949i	−0.590554	−	0.590554i	−0.937781	+	0.347227i	$0.887123\pi$
$282$	2.89898	−	6.29253i	0.172632	−	0.374715i
$283$	−10.3923	−	6.00000i	−0.617758	−	0.356663i	0.158237	−	0.987401i	$-0.449419\pi$
$283$	−10.3923	−	6.00000i	−0.617758	−	0.356663i	−0.775996	+	0.630738i	$0.782752\pi$
$284$	3.86370	−	1.03528i	0.229269	−	0.0614323i
$285$	2.82843	+	4.00000i	0.167542	+	0.236940i
$286$		0			0
$287$			2.82843i			0.166957i
$288$	−14.9543	−	1.16938i	−0.881193	−	0.0689061i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	2.82843	+	4.89898i	0.166091	+	0.287678i
$291$	−2.89949	+	16.8995i	−0.169971	+	0.990666i
$292$	−0.366025	+	1.36603i	−0.0214200	+	0.0799406i
$293$	−3.62347	+	13.5230i	−0.211685	+	0.790020i	0.775622	+	0.631198i	$0.217436\pi$
$293$	−3.62347	+	13.5230i	−0.211685	+	0.790020i	−0.987307	+	0.158822i	$0.949230\pi$
$294$	−1.46447	+	8.53553i	−0.0854094	+	0.497802i
$295$	−4.00000	−	6.92820i	−0.232889	−	0.403376i
$296$	−2.12132	+	3.67423i	−0.123299	+	0.213561i
$297$	−17.8544	+	10.6405i	−1.03602	+	0.617423i
$298$			2.00000i			0.115857i
$299$		0			0
$300$	1.00000	+	1.41421i	0.0577350	+	0.0816497i
$301$	8.19615	−	2.19615i	0.472418	−	0.126584i
$302$	1.22474	+	0.707107i	0.0704761	+	0.0406894i
$303$	6.14966	−	13.3485i	0.353289	−	0.766850i
$304$	−1.00000	−	1.00000i	−0.0573539	−	0.0573539i
$305$	−15.4548	−	4.14110i	−0.884940	−	0.237119i
$306$		0			0
$307$	17.0000	−	17.0000i	0.970241	−	0.970241i	−0.0293286	−	0.999570i	$-0.509337\pi$
$307$	17.0000	−	17.0000i	0.970241	−	0.970241i	0.999570	+	0.0293286i	$0.00933691\pi$
$308$	−4.89898	+	2.82843i	−0.279145	+	0.161165i
$309$	−0.953512	−	10.3485i	−0.0542434	−	0.588704i
$310$	−3.66025	−	13.6603i	−0.207888	−	0.775850i
$311$	8.48528			0.481156			0.240578	−	0.970630i	$-0.422663\pi$
$311$	8.48528			0.481156			0.240578	+	0.970630i	$0.422663\pi$
$312$		0			0
$313$	8.00000			0.452187			0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000			0.452187			0.226093	+	0.974106i	$0.427405\pi$
$314$	−3.62347	−	13.5230i	−0.204484	−	0.763145i
$315$	6.44949	−	5.51399i	0.363388	−	0.310678i
$316$	−8.66025	+	5.00000i	−0.487177	+	0.281272i
$317$	−7.07107	+	7.07107i	−0.397151	+	0.397151i	−0.877227	−	0.480076i	$-0.840609\pi$
$317$	−7.07107	+	7.07107i	−0.397151	+	0.397151i	0.480076	+	0.877227i	$0.340609\pi$
$318$	−9.19151	+	3.39355i	−0.515434	+	0.190301i
$319$	10.9282	+	2.92820i	0.611862	+	0.163948i
$320$	9.89949	+	9.89949i	0.553399	+	0.553399i
$321$	8.89898	+	4.09978i	0.496693	+	0.228827i
$322$	10.3923	+	6.00000i	0.579141	+	0.334367i
$323$		0			0
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$		0			0
$326$		−	1.41421i		−	0.0783260i
$327$	−1.88366	−	1.56583i	−0.104167	−	0.0865904i
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	2.82843	+	4.89898i	0.155936	+	0.270089i
$330$	13.6569	+	2.34315i	0.751785	+	0.128986i
$331$	−2.56218	+	9.56218i	−0.140830	+	0.525585i	0.859076	+	0.511849i	$0.171039\pi$
$331$	−2.56218	+	9.56218i	−0.140830	+	0.525585i	−0.999906	+	0.0137361i	$0.995628\pi$
$332$	2.07055	−	7.72741i	0.113636	−	0.424097i
$333$	−1.82843	−	3.82843i	−0.100197	−	0.209797i
$334$	2.00000	+	3.46410i	0.109435	+	0.189547i
$335$	−7.07107	+	12.2474i	−0.386334	+	0.669150i
$336$	−1.56583	+	1.88366i	−0.0854228	+	0.102762i
$337$		−	6.00000i		−	0.326841i	−0.986557	−	0.163420i	$-0.947747\pi$
$337$		−	6.00000i		−	0.326841i	0.986557	−	0.163420i	$-0.0522527\pi$
$338$		0			0
$339$	−20.0000	+	14.1421i	−1.08625	+	0.768095i
$340$		0			0
$341$	−24.4949	−	14.1421i	−1.32647	−	0.765840i
$342$	4.17121	−	0.775255i	0.225553	−	0.0419210i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	−17.3867	−	4.65874i	−0.937426	−	0.251183i
$345$	10.1806	+	27.5745i	0.548108	+	1.48456i
$346$	6.00000	−	6.00000i	0.322562	−	0.322562i
$347$	−12.2474	+	7.07107i	−0.657477	+	0.379595i	−0.791315	−	0.611408i	$-0.790603\pi$
$347$	−12.2474	+	7.07107i	−0.657477	+	0.379595i	0.133838	+	0.991003i	$0.457270\pi$
$348$	−4.87832	+	0.449490i	−0.261505	+	0.0240952i
$349$	6.22243	+	23.2224i	0.333079	+	1.24307i	0.905937	+	0.423413i	$0.139168\pi$
$349$	6.22243	+	23.2224i	0.333079	+	1.24307i	−0.572857	+	0.819655i	$0.694165\pi$
$350$	1.41421			0.0755929
$351$		0			0
$352$	20.0000			1.06600
$353$	6.72930	+	25.1141i	0.358164	+	1.33669i	0.876455	+	0.481483i	$0.159902\pi$
$353$	6.72930	+	25.1141i	0.358164	+	1.33669i	−0.518291	+	0.855204i	$0.673432\pi$
$354$	−6.89898	+	0.635674i	−0.366677	+	0.0337857i
$355$	6.92820	−	4.00000i	0.367711	−	0.212298i
$356$	9.89949	−	9.89949i	0.524672	−	0.524672i
$357$		0			0
$358$		0			0
$359$	2.82843	+	2.82843i	0.149279	+	0.149279i	0.777796	−	0.628517i	$-0.216338\pi$
$359$	2.82843	+	2.82843i	0.149279	+	0.149279i	−0.628517	+	0.777796i	$0.716338\pi$
$360$	−17.6969	+	3.28913i	−0.932711	+	0.173352i
$361$	14.7224	+	8.50000i	0.774865	+	0.447368i
$362$		0			0
$363$	7.07107	−	5.00000i	0.371135	−	0.262432i
$364$		0			0
$365$			2.82843i			0.148047i
$366$	−8.85765	+	10.6556i	−0.462997	+	0.556978i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	−4.24264	−	7.34847i	−0.221163	−	0.383065i
$369$	2.58579	+	5.41421i	0.134611	+	0.281853i
$370$	−0.732051	+	2.73205i	−0.0380575	+	0.142033i
$371$	2.07055	−	7.72741i	0.107498	−	0.401187i
$372$	12.0711	+	2.07107i	0.625856	+	0.107380i
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	15.9834	+	13.2865i	0.825380	+	0.686111i
$376$		−	12.0000i		−	0.618853i
$377$		0			0
$378$	−2.00000	−	7.07107i	−0.102869	−	0.363696i
$379$	25.9545	−	6.95448i	1.33319	−	0.357228i	0.479288	−	0.877658i	$-0.340895\pi$
$379$	25.9545	−	6.95448i	1.33319	−	0.357228i	0.853904	+	0.520430i	$0.174228\pi$
$380$	2.44949	+	1.41421i	0.125656	+	0.0725476i
$381$		0			0
$382$	−2.00000	−	2.00000i	−0.102329	−	0.102329i
$383$	15.4548	+	4.14110i	0.789704	+	0.211601i	0.631059	−	0.775735i	$-0.282621\pi$
$383$	15.4548	+	4.14110i	0.789704	+	0.211601i	0.158645	+	0.987336i	$0.449287\pi$
$384$	−4.87453	+	1.79970i	−0.248752	+	0.0918406i
$385$	−8.00000	+	8.00000i	−0.407718	+	0.407718i
$386$	−23.2702	+	13.4350i	−1.18442	+	0.683825i
$387$	13.6814	−	11.6969i	0.695466	−	0.594589i
$388$	2.56218	+	9.56218i	0.130075	+	0.485446i
$389$	16.9706			0.860442			0.430221	−	0.902724i	$-0.358436\pi$
$389$	16.9706			0.860442			0.430221	+	0.902724i	$0.358436\pi$
$390$		0			0
$391$		0			0
$392$	3.88229	+	14.4889i	0.196085	+	0.731799i
$393$	1.79796	+	19.5133i	0.0906950	+	0.984314i
$394$	−19.0526	+	11.0000i	−0.959854	+	0.554172i
$395$	−14.1421	+	14.1421i	−0.711568	+	0.711568i
$396$	−6.79191	+	9.89293i	−0.341306	+	0.497138i
$397$	−23.2224	−	6.22243i	−1.16550	−	0.312295i	−0.376340	−	0.926482i	$-0.622817\pi$
$397$	−23.2224	−	6.22243i	−1.16550	−	0.312295i	−0.789161	+	0.614187i	$0.789484\pi$
$398$		0			0
$399$	−1.44949	+	3.14626i	−0.0725653	+	0.157510i
$400$	−0.866025	−	0.500000i	−0.0433013	−	0.0250000i
$401$	−21.2504	+	5.69402i	−1.06119	+	0.284346i	−0.746870	−	0.664970i	$-0.768444\pi$
$401$	−21.2504	+	5.69402i	−1.06119	+	0.284346i	−0.314323	+	0.949316i	$0.601777\pi$
$402$	7.07107	+	10.0000i	0.352673	+	0.498755i
$403$		0			0
$404$		−	8.48528i		−	0.422159i
$405$	7.30474	−	16.4512i	0.362975	−	0.817465i
$406$	−2.00000	+	3.46410i	−0.0992583	+	0.171920i
$407$	2.82843	+	4.89898i	0.140200	+	0.242833i
$408$		0			0
$409$	8.41858	−	31.4186i	0.416272	−	1.55355i	−0.366002	−	0.930614i	$-0.619274\pi$
$409$	8.41858	−	31.4186i	0.416272	−	1.55355i	0.782274	−	0.622935i	$-0.214060\pi$
$410$	1.03528	−	3.86370i	0.0511286	−	0.190815i
$411$	−4.10051	+	23.8995i	−0.202263	+	1.17888i
$412$	−3.00000	−	5.19615i	−0.147799	−	0.255996i
$413$	2.82843	−	4.89898i	0.139178	−	0.241063i
$414$	25.3784	+	1.98450i	1.24728	+	0.0975326i
$415$		−	16.0000i		−	0.785409i
$416$		0			0
$417$	4.00000	+	5.65685i	0.195881	+	0.277017i
$418$	−5.46410	+	1.46410i	−0.267258	+	0.0716116i
$419$	−9.79796	−	5.65685i	−0.478662	−	0.276355i	0.241197	−	0.970476i	$-0.422460\pi$
$419$	−9.79796	−	5.65685i	−0.478662	−	0.276355i	−0.719859	+	0.694121i	$0.755793\pi$
$420$	2.04989	−	4.44949i	0.100024	−	0.217113i
$421$	−25.0000	−	25.0000i	−1.21843	−	1.21843i	−0.968183	−	0.250242i	$-0.919490\pi$
$421$	−25.0000	−	25.0000i	−1.21843	−	1.21843i	−0.250242	−	0.968183i	$-0.580510\pi$
$422$	13.5230	+	3.62347i	0.658287	+	0.176388i
$423$	9.89293	+	6.79191i	0.481011	+	0.330234i
$424$	−12.0000	+	12.0000i	−0.582772	+	0.582772i
$425$		0			0
$426$	−0.635674	−	6.89898i	−0.0307985	−	0.334257i
$427$	−2.92820	−	10.9282i	−0.141706	−	0.528853i
$428$	5.65685			0.273434
$429$		0			0
$430$	−12.0000			−0.578691
$431$	8.28221	+	30.9096i	0.398940	+	1.48886i	0.814964	+	0.579511i	$0.196756\pi$
$431$	8.28221	+	30.9096i	0.398940	+	1.48886i	−0.416024	+	0.909353i	$0.636577\pi$
$432$	−1.27526	+	5.03723i	−0.0613557	+	0.242354i
$433$	15.5885	−	9.00000i	0.749133	−	0.432512i	−0.0762473	−	0.997089i	$-0.524294\pi$
$433$	15.5885	−	9.00000i	0.749133	−	0.432512i	0.825381	+	0.564577i	$0.190961\pi$
$434$	7.07107	−	7.07107i	0.339422	−	0.339422i
$435$	−9.19151	+	3.39355i	−0.440699	+	0.162708i
$436$	−1.36603	−	0.366025i	−0.0654208	−	0.0175294i
$437$	−8.48528	−	8.48528i	−0.405906	−	0.405906i
$438$	2.22474	+	1.02494i	0.106302	+	0.0489737i
$439$	25.9808	+	15.0000i	1.23999	+	0.715911i	0.969093	−	0.246696i	$-0.0793450\pi$
$439$	25.9808	+	15.0000i	1.23999	+	0.715911i	0.270901	+	0.962607i	$0.412678\pi$
$440$	23.1822	−	6.21166i	1.10517	−	0.296129i
$441$	−14.1421	−	5.00000i	−0.673435	−	0.238095i
$442$		0			0
$443$			28.2843i			1.34383i	0.740630	+	0.671913i	$0.234527\pi$
$443$			28.2843i			1.34383i	−0.740630	+	0.671913i	$0.765473\pi$
$444$	−1.88366	−	1.56583i	−0.0893947	−	0.0743108i
$445$	14.0000	−	24.2487i	0.663664	−	1.14950i
$446$	7.77817	+	13.4722i	0.368307	+	0.637927i
$447$	−3.41421	−	0.585786i	−0.161487	−	0.0277067i
$448$	−2.56218	+	9.56218i	−0.121052	+	0.451770i
$449$	5.69402	−	21.2504i	0.268717	−	1.00287i	−0.691218	−	0.722646i	$-0.742926\pi$
$449$	5.69402	−	21.2504i	0.268717	−	1.00287i	0.959936	−	0.280221i	$-0.0904077\pi$
$450$	2.70711	−	1.29289i	0.127614	−	0.0609476i
$451$	−4.00000	−	6.92820i	−0.188353	−	0.326236i
$452$	−7.07107	+	12.2474i	−0.332595	+	0.576072i
$453$	−1.56583	+	1.88366i	−0.0735689	+	0.0885022i
$454$			8.00000i			0.375459i
$455$		0			0
$456$	6.00000	−	4.24264i	0.280976	−	0.198680i
$457$	−39.6147	+	10.6147i	−1.85310	+	0.496536i	−0.999695	−	0.0247126i	$-0.992133\pi$
$457$	−39.6147	+	10.6147i	−1.85310	+	0.496536i	−0.853405	+	0.521249i	$0.825466\pi$
$458$	1.22474	+	0.707107i	0.0572286	+	0.0330409i
$459$		0			0
$460$	12.0000	+	12.0000i	0.559503	+	0.559503i
$461$	9.65926	+	2.58819i	0.449877	+	0.120544i	0.476642	−	0.879098i	$-0.341854\pi$
$461$	9.65926	+	2.58819i	0.449877	+	0.120544i	−0.0267651	+	0.999642i	$0.508521\pi$
$462$	3.39355	+	9.19151i	0.157882	+	0.427628i
$463$	17.0000	−	17.0000i	0.790057	−	0.790057i	−0.191446	−	0.981503i	$-0.561318\pi$
$463$	17.0000	−	17.0000i	0.790057	−	0.790057i	0.981503	+	0.191446i	$0.0613177\pi$
$464$	2.44949	−	1.41421i	0.113715	−	0.0656532i
$465$	24.3916	−	2.24745i	1.13113	−	0.104223i
$466$	6.58846	+	24.5885i	0.305204	+	1.13904i
$467$	−25.4558			−1.17796			−0.588978	−	0.808149i	$-0.700470\pi$
$467$	−25.4558			−1.17796			−0.588978	+	0.808149i	$0.700470\pi$
$468$		0			0
$469$	−10.0000			−0.461757
$470$	−2.07055	−	7.72741i	−0.0955075	−	0.356439i
$471$	24.1464	−	2.22486i	1.11261	−	0.102516i
$472$	−10.3923	+	6.00000i	−0.478345	+	0.276172i
$473$	−16.9706	+	16.9706i	−0.780307	+	0.780307i
$474$	5.99900	+	16.2484i	0.275543	+	0.746316i
$475$	−1.36603	−	0.366025i	−0.0626775	−	0.0167944i
$476$		0			0
$477$	−3.10102	−	16.6848i	−0.141986	−	0.763946i
$478$	−17.3205	−	10.0000i	−0.792222	−	0.457389i
$479$	30.9096	−	8.28221i	1.41230	−	0.378424i	0.529552	−	0.848277i	$-0.322360\pi$
$479$	30.9096	−	8.28221i	1.41230	−	0.378424i	0.882744	+	0.469853i	$0.155693\pi$
$480$	−14.1421	+	10.0000i	−0.645497	+	0.456435i
$481$		0			0
$482$			24.0416i			1.09507i
$483$	−13.2865	+	15.9834i	−0.604556	+	0.727271i
$484$	2.50000	−	4.33013i	0.113636	−	0.196824i
$485$	9.89949	+	17.1464i	0.449513	+	0.778579i
$486$	−10.2929	−	11.7071i	−0.466895	−	0.531045i
$487$	−6.95448	+	25.9545i	−0.315138	+	1.17611i	0.608724	+	0.793382i	$0.291682\pi$
$487$	−6.95448	+	25.9545i	−0.315138	+	1.17611i	−0.923861	+	0.382727i	$0.874985\pi$
$488$	−6.21166	+	23.1822i	−0.281189	+	1.04941i
$489$	2.41421	+	0.414214i	0.109175	+	0.0187314i
$490$	5.00000	+	8.66025i	0.225877	+	0.391230i
$491$	21.2132	−	36.7423i	0.957338	−	1.65816i	0.228415	−	0.973564i	$-0.426646\pi$
$491$	21.2132	−	36.7423i	0.957338	−	1.65816i	0.728924	−	0.684595i	$-0.240021\pi$
$492$	2.66390	+	2.21441i	0.120098	+	0.0998334i
$493$		0			0
$494$		0			0
$495$	−8.00000	+	22.6274i	−0.359573	+	1.01703i
$496$	−6.83013	+	1.83013i	−0.306682	+	0.0821751i
$497$	4.89898	+	2.82843i	0.219749	+	0.126872i
$498$	−12.5851	−	5.79796i	−0.563950	−	0.259813i
$499$	23.0000	+	23.0000i	1.02962	+	1.02962i	0.999548	+	0.0300737i	$0.00957421\pi$
$499$	23.0000	+	23.0000i	1.02962	+	1.02962i	0.0300737	+	0.999548i	$0.490426\pi$
$500$	11.5911	+	3.10583i	0.518370	+	0.138897i
$501$	−6.49938	+	2.39960i	−0.290371	+	0.107206i
$502$	−18.0000	+	18.0000i	−0.803379	+	0.803379i
$503$	−4.89898	+	2.82843i	−0.218435	+	0.126113i	−0.605225	−	0.796054i	$-0.706917\pi$
$503$	−4.89898	+	2.82843i	−0.218435	+	0.126113i	0.386791	+	0.922168i	$0.373584\pi$
$504$	−8.27098	−	9.67423i	−0.368419	−	0.430925i
$505$	−4.39230	−	16.3923i	−0.195455	−	0.729448i
$506$	−33.9411			−1.50887
$507$		0			0
$508$		0			0
$509$	−8.79985	−	32.8415i	−0.390046	−	1.45567i	−0.830056	−	0.557680i	$-0.811692\pi$
$509$	−8.79985	−	32.8415i	−0.390046	−	1.45567i	0.440010	−	0.897993i	$-0.354975\pi$
$510$		0			0
$511$	−1.73205	+	1.00000i	−0.0766214	+	0.0442374i
$512$	7.77817	−	7.77817i	0.343750	−	0.343750i
$513$	0.101725	+	7.34777i	0.00449125	+	0.324412i
$514$	8.19615	+	2.19615i	0.361517	+	0.0968681i
$515$	−8.48528	−	8.48528i	−0.373906	−	0.373906i
$516$	4.34847	−	9.43879i	0.191431	−	0.415520i
$517$	−13.8564	−	8.00000i	−0.609404	−	0.351840i
$518$	−1.93185	+	0.517638i	−0.0848807	+	0.0227437i
$519$	8.48528	+	12.0000i	0.372463	+	0.526742i
$520$		0			0
$521$		−	31.1127i		−	1.36307i	−0.731785	−	0.681536i	$-0.761312\pi$
$521$		−	31.1127i		−	1.36307i	0.731785	−	0.681536i	$-0.238688\pi$
$522$	−0.661498	+	8.45946i	−0.0289530	+	0.370260i
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	5.65685	+	9.79796i	0.247121	+	0.428026i
$525$	−0.414214	+	2.41421i	−0.0180778	+	0.105365i
$526$	5.85641	−	21.8564i	0.255351	−	0.952985i
$527$		0			0
$528$	1.17157	−	6.82843i	0.0509862	−	0.297169i
$529$	−24.5000	−	42.4352i	−1.06522	−	1.84501i
$530$	−5.65685	+	9.79796i	−0.245718	+	0.425596i
$531$	0.935500	−	11.9635i	0.0405972	−	0.519171i
$532$			2.00000i			0.0867110i
$533$		0			0
$534$	−14.0000	−	19.7990i	−0.605839	−	0.856786i
$535$	10.9282	−	2.92820i	0.472467	−	0.126597i
$536$	18.3712	+	10.6066i	0.793514	+	0.458135i
$537$		0			0
$538$	−14.0000	−	14.0000i	−0.603583	−	0.603583i
$539$	19.3185	+	5.17638i	0.832107	+	0.222963i
$540$	−0.143860	−	10.3913i	−0.00619076	−	0.447171i
$541$	−1.00000	+	1.00000i	−0.0429934	+	0.0429934i	−0.728277	−	0.685283i	$-0.759678\pi$
$541$	−1.00000	+	1.00000i	−0.0429934	+	0.0429934i	0.685283	+	0.728277i	$0.259678\pi$
$542$	−23.2702	+	13.4350i	−0.999539	+	0.577084i
$543$		0			0
$544$		0			0
$545$	−2.82843			−0.121157
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	3.62347	+	13.5230i	0.154787	+	0.577672i
$549$	−15.5959	−	18.2419i	−0.665618	−	0.778546i
$550$	−3.46410	+	2.00000i	−0.147710	+	0.0852803i
$551$	2.82843	−	2.82843i	0.120495	−	0.120495i
$552$	41.3618	−	15.2710i	1.76047	−	0.649976i
$553$	−13.6603	−	3.66025i	−0.580893	−	0.155650i
$554$	8.48528	+	8.48528i	0.360505	+	0.360505i
$555$	−4.44949	−	2.04989i	−0.188870	−	0.0870129i
$556$	3.46410	+	2.00000i	0.146911	+	0.0848189i
$557$	13.5230	−	3.62347i	0.572986	−	0.153531i	0.0393204	−	0.999227i	$-0.487481\pi$
$557$	13.5230	−	3.62347i	0.572986	−	0.153531i	0.533666	+	0.845695i	$0.320814\pi$
$558$	7.07107	−	20.0000i	0.299342	−	0.846668i
$559$		0			0
$560$			2.82843i			0.119523i
$561$		0			0
$562$	−7.00000	+	12.1244i	−0.295277	+	0.511435i
$563$	−16.9706	−	29.3939i	−0.715224	−	1.23880i	−0.962873	−	0.269954i	$-0.912991\pi$
$563$	−16.9706	−	29.3939i	−0.715224	−	1.23880i	0.247649	−	0.968850i	$-0.420342\pi$
$564$	6.82843	+	1.17157i	0.287529	+	0.0493321i
$565$	−7.32051	+	27.3205i	−0.307976	+	1.14938i
$566$	−3.10583	+	11.5911i	−0.130548	+	0.487211i
$567$	12.6569	−	1.34315i	0.531538	−	0.0564068i
$568$	−6.00000	−	10.3923i	−0.251754	−	0.436051i
$569$	4.24264	−	7.34847i	0.177861	−	0.308064i	−0.763287	−	0.646060i	$-0.776416\pi$
$569$	4.24264	−	7.34847i	0.177861	−	0.308064i	0.941148	+	0.337996i	$0.109749\pi$
$570$	3.13165	−	3.76733i	0.131170	−	0.157796i
$571$			12.0000i			0.502184i	0.967963	+	0.251092i	$0.0807897\pi$
$571$			12.0000i			0.502184i	−0.967963	+	0.251092i	$0.919210\pi$
$572$		0			0
$573$	4.00000	−	2.82843i	0.167102	−	0.118159i
$574$	2.73205	−	0.732051i	0.114034	−	0.0305552i
$575$	−7.34847	−	4.24264i	−0.306452	−	0.176930i
$576$	3.83732	+	20.6464i	0.159888	+	0.860268i
$577$	−1.00000	−	1.00000i	−0.0416305	−	0.0416305i	0.685985	−	0.727616i	$-0.259372\pi$
$577$	−1.00000	−	1.00000i	−0.0416305	−	0.0416305i	−0.727616	+	0.685985i	$0.759372\pi$
$578$	−16.4207	−	4.39992i	−0.683013	−	0.183013i
$579$	−16.1194	−	43.6597i	−0.669898	−	1.81443i
$580$	−4.00000	+	4.00000i	−0.166091	+	0.166091i
$581$	9.79796	−	5.65685i	0.406488	−	0.234686i
$582$	17.0741	−	1.57321i	0.707744	−	0.0652118i
$583$	5.85641	+	21.8564i	0.242548	+	0.905200i
$584$	4.24264			0.175562
$585$		0			0
$586$	14.0000			0.578335
$587$	2.07055	+	7.72741i	0.0854608	+	0.318944i	0.995401	−	0.0957952i	$-0.0305394\pi$
$587$	2.07055	+	7.72741i	0.0854608	+	0.318944i	−0.909940	+	0.414739i	$0.863873\pi$
$588$	−8.62372	+	0.794593i	−0.355636	+	0.0327685i
$589$	−8.66025	+	5.00000i	−0.356840	+	0.206021i
$590$	−5.65685	+	5.65685i	−0.232889	+	0.232889i
$591$	−13.1978	−	35.7466i	−0.542885	−	1.47042i
$592$	1.36603	+	0.366025i	0.0561433	+	0.0150436i
$593$	−9.89949	−	9.89949i	−0.406524	−	0.406524i	0.474001	−	0.880524i	$-0.342809\pi$
$593$	−9.89949	−	9.89949i	−0.406524	−	0.406524i	−0.880524	+	0.474001i	$0.842809\pi$
$594$	14.8990	+	14.4921i	0.611313	+	0.594617i
$595$		0			0
$596$	−1.93185	+	0.517638i	−0.0791317	+	0.0212033i
$597$		0			0
$598$		0			0
$599$			11.3137i			0.462266i	0.972922	+	0.231133i	$0.0742432\pi$
$599$			11.3137i			0.462266i	−0.972922	+	0.231133i	$0.925757\pi$
$600$	3.32162	−	3.99585i	0.135605	−	0.163130i
$601$	−4.00000	+	6.92820i	−0.163163	+	0.282607i	−0.936002	−	0.351996i	$-0.885503\pi$
$601$	−4.00000	+	6.92820i	−0.163163	+	0.282607i	0.772838	+	0.634603i	$0.218836\pi$
$602$	−4.24264	−	7.34847i	−0.172917	−	0.299501i
$603$	−19.1421	+	9.14214i	−0.779528	+	0.372297i
$604$	−0.366025	+	1.36603i	−0.0148934	+	0.0555828i
$605$	2.58819	−	9.65926i	0.105225	−	0.392705i
$606$	−14.4853	−	2.48528i	−0.588424	−	0.100958i
$607$	20.0000	+	34.6410i	0.811775	+	1.40604i	0.911621	+	0.411033i	$0.134832\pi$
$607$	20.0000	+	34.6410i	0.811775	+	1.40604i	−0.0998457	+	0.995003i	$0.531835\pi$
$608$	3.53553	−	6.12372i	0.143385	−	0.248350i
$609$	−5.32780	−	4.42883i	−0.215894	−	0.179465i
$610$			16.0000i			0.647821i
$611$		0			0
$612$		0			0
$613$	1.36603	−	0.366025i	0.0551732	−	0.0147836i	−0.231127	−	0.972924i	$-0.574241\pi$
$613$	1.36603	−	0.366025i	0.0551732	−	0.0147836i	0.286300	+	0.958140i	$0.407575\pi$
$614$	−20.8207	−	12.0208i	−0.840254	−	0.485121i
$615$	6.29253	+	2.89898i	0.253739	+	0.116898i
$616$	12.0000	+	12.0000i	0.483494	+	0.483494i
$617$	−36.7052	−	9.83512i	−1.47769	−	0.395947i	−0.572133	−	0.820161i	$-0.693884\pi$
$617$	−36.7052	−	9.83512i	−1.47769	−	0.395947i	−0.905562	+	0.424214i	$0.860551\pi$
$618$	−9.74907	+	3.59940i	−0.392165	+	0.144789i
$619$	−1.00000	+	1.00000i	−0.0401934	+	0.0401934i	−0.726918	−	0.686724i	$-0.759048\pi$
$619$	−1.00000	+	1.00000i	−0.0401934	+	0.0401934i	0.686724	+	0.726918i	$0.259048\pi$
$620$	12.2474	−	7.07107i	0.491869	−	0.283981i
$621$	−10.8209	+	42.7423i	−0.434228	+	1.71519i
$622$	−2.19615	−	8.19615i	−0.0880577	−	0.328636i
$623$	19.7990			0.793230
$624$		0			0
$625$	19.0000			0.760000
$626$	−2.07055	−	7.72741i	−0.0827559	−	0.308849i
$627$	−0.898979	−	9.75663i	−0.0359018	−	0.389642i
$628$	12.1244	−	7.00000i	0.483814	−	0.279330i
$629$		0			0
$630$	−6.99536	−	4.80260i	−0.278702	−	0.191340i
$631$	25.9545	+	6.95448i	1.03323	+	0.276854i	0.735306	−	0.677735i	$-0.237039\pi$
$631$	25.9545	+	6.95448i	1.03323	+	0.276854i	0.297926	+	0.954589i	$0.403705\pi$
$632$	21.2132	+	21.2132i	0.843816	+	0.843816i
$633$	−10.1464	+	22.0239i	−0.403284	+	0.875369i
$634$	8.66025	+	5.00000i	0.343943	+	0.198575i
$635$		0			0
$636$	−5.65685	−	8.00000i	−0.224309	−	0.317221i
$637$		0			0
$638$		−	11.3137i		−	0.447914i
$639$	11.9635	+	0.935500i	0.473268	+	0.0370078i
$640$	−3.00000	+	5.19615i	−0.118585	+	0.205396i
$641$	−8.48528	−	14.6969i	−0.335148	−	0.580494i	0.648365	−	0.761330i	$-0.275453\pi$
$641$	−8.48528	−	14.6969i	−0.335148	−	0.580494i	−0.983513	+	0.180836i	$0.942120\pi$
$642$	1.65685	−	9.65685i	0.0653908	−	0.381126i
$643$	1.83013	−	6.83013i	0.0721732	−	0.269354i	−0.920404	−	0.390968i	$-0.872140\pi$
$643$	1.83013	−	6.83013i	0.0721732	−	0.269354i	0.992577	+	0.121614i	$0.0388070\pi$
$644$	−3.10583	+	11.5911i	−0.122387	+	0.456754i
$645$	3.51472	−	20.4853i	0.138392	−	0.806607i
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−24.6767	−	10.9571i	−0.969394	−	0.430436i
$649$			16.0000i			0.628055i
$650$		0			0
$651$	10.0000	+	14.1421i	0.391931	+	0.554274i
$652$	1.36603	−	0.366025i	0.0534977	−	0.0143347i
$653$	12.2474	+	7.07107i	0.479280	+	0.276712i	0.720116	−	0.693853i	$-0.244088\pi$
$653$	12.2474	+	7.07107i	0.479280	+	0.276712i	−0.240837	+	0.970566i	$0.577422\pi$
$654$	−1.02494	+	2.22474i	−0.0400785	+	0.0869944i
$655$	16.0000	+	16.0000i	0.625172	+	0.625172i
$656$	−1.93185	−	0.517638i	−0.0754261	−	0.0202104i
$657$	−2.40130	+	3.49768i	−0.0936837	+	0.136457i
$658$	4.00000	−	4.00000i	0.155936	−	0.155936i
$659$	2.44949	−	1.41421i	0.0954186	−	0.0550899i	−0.451531	−	0.892255i	$-0.649122\pi$
$659$	2.44949	−	1.41421i	0.0954186	−	0.0550899i	0.546950	+	0.837165i	$0.315789\pi$
$660$	1.27135	+	13.7980i	0.0494872	+	0.537085i
$661$	−0.366025	−	1.36603i	−0.0142367	−	0.0531322i	0.958442	−	0.285287i	$-0.0920890\pi$
$661$	−0.366025	−	1.36603i	−0.0142367	−	0.0531322i	−0.972679	+	0.232155i	$0.925422\pi$
$662$	9.89949			0.384755
$663$		0			0
$664$	−24.0000			−0.931381
$665$	1.03528	+	3.86370i	0.0401463	+	0.149828i
$666$	−3.22474	+	2.75699i	−0.124956	+	0.106831i
$667$	20.7846	−	12.0000i	0.804783	−	0.464642i
$668$	−2.82843	+	2.82843i	−0.109435	+	0.109435i
$669$	−25.2766	+	9.33226i	−0.977252	+	0.360806i
$670$	13.6603	+	3.66025i	0.527742	+	0.141408i
$671$	22.6274	+	22.6274i	0.873522	+	0.873522i
$672$	−11.1237	−	5.12472i	−0.429107	−	0.197690i
$673$	10.3923	+	6.00000i	0.400594	+	0.231283i	0.686740	−	0.726903i	$-0.259041\pi$
$673$	10.3923	+	6.00000i	0.400594	+	0.231283i	−0.286146	+	0.958186i	$0.592374\pi$
$674$	−5.79555	+	1.55291i	−0.223236	+	0.0598160i
$675$	1.41421	+	5.00000i	0.0544331	+	0.192450i
$676$		0			0
$677$		−	22.6274i		−	0.869642i	−0.900517	−	0.434821i	$-0.856812\pi$
$677$		−	22.6274i		−	0.869642i	0.900517	−	0.434821i	$-0.143188\pi$
$678$	18.8366	+	15.6583i	0.723417	+	0.601352i
$679$	−7.00000	+	12.1244i	−0.268635	+	0.465290i
$680$		0			0
$681$	−13.6569	−	2.34315i	−0.523332	−	0.0897895i
$682$	−7.32051	+	27.3205i	−0.280317	+	1.04616i
$683$	1.03528	−	3.86370i	0.0396137	−	0.147840i	−0.943286	−	0.331980i	$-0.892283\pi$
$683$	1.03528	−	3.86370i	0.0396137	−	0.147840i	0.982900	+	0.184140i	$0.0589499\pi$
$684$	1.82843	+	3.82843i	0.0699117	+	0.146384i
$685$	14.0000	+	24.2487i	0.534913	+	0.926496i
$686$	−8.48528	+	14.6969i	−0.323970	+	0.561132i
$687$	−1.56583	+	1.88366i	−0.0597400	+	0.0718662i
$688$			6.00000i			0.228748i
$689$		0			0
$690$	24.0000	−	16.9706i	0.913664	−	0.646058i
$691$	−15.0263	+	4.02628i	−0.571627	+	0.153167i	−0.533042	−	0.846088i	$-0.678951\pi$
$691$	−15.0263	+	4.02628i	−0.571627	+	0.153167i	−0.0385841	+	0.999255i	$0.512285\pi$
$692$	7.34847	+	4.24264i	0.279347	+	0.161281i
$693$	−16.6848	+	3.10102i	−0.633804	+	0.117798i
$694$	10.0000	+	10.0000i	0.379595	+	0.379595i
$695$	7.72741	+	2.07055i	0.293117	+	0.0785405i
$696$	5.09032	+	13.7873i	0.192948	+	0.522605i
$697$		0			0
$698$	20.8207	−	12.0208i	0.788074	−	0.454995i
$699$	−43.9048	+	4.04541i	−1.66063	+	0.153011i
$700$	0.366025	+	1.36603i	0.0138345	+	0.0516309i
$701$	50.9117			1.92291			0.961454	−	0.274966i	$-0.0886666\pi$
$701$	50.9117			1.92291			0.961454	+	0.274966i	$0.0886666\pi$
$702$		0			0
$703$	2.00000			0.0754314
$704$	−7.24693	−	27.0459i	−0.273129	−	1.01933i
$705$	13.7980	−	1.27135i	0.519661	−	0.0478818i
$706$	22.5167	−	13.0000i	0.847426	−	0.489261i
$707$	8.48528	−	8.48528i	0.319122	−	0.319122i
$708$	−2.39960	−	6.49938i	−0.0901826	−	0.244262i
$709$	25.9545	+	6.95448i	0.974741	+	0.261181i	0.710828	−	0.703365i	$-0.248320\pi$
$709$	25.9545	+	6.95448i	0.974741	+	0.261181i	0.263913	+	0.964547i	$0.414987\pi$
$710$	−5.65685	−	5.65685i	−0.212298	−	0.212298i
$711$	−29.4949	+	5.48188i	−1.10615	+	0.205587i
$712$	−36.3731	−	21.0000i	−1.36314	−	0.787008i
$713$	−57.9555	+	15.5291i	−2.17045	+	0.581571i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	22.1441	−	26.6390i	0.826988	−	0.994853i
$718$	2.00000	−	3.46410i	0.0746393	−	0.129279i
$719$	12.7279	+	22.0454i	0.474671	+	0.822155i	0.999579	−	0.0290041i	$-0.00923357\pi$
$719$	12.7279	+	22.0454i	0.474671	+	0.822155i	−0.524908	+	0.851159i	$0.675900\pi$
$720$	2.58579	+	5.41421i	0.0963666	+	0.201776i
$721$	2.19615	−	8.19615i	0.0817890	−	0.305241i
$722$	4.39992	−	16.4207i	0.163748	−	0.611117i
$723$	−41.0416	−	7.04163i	−1.52635	−	0.261881i
$724$		0			0
$725$	1.41421	−	2.44949i	0.0525226	−	0.0909718i
$726$	−6.65976	−	5.53603i	−0.247167	−	0.205461i
$727$		−	48.0000i		−	1.78022i	−0.455744	−	0.890111i	$-0.650627\pi$
$727$		−	48.0000i		−	1.78022i	0.455744	−	0.890111i	$-0.349373\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	2.73205	−	0.732051i	0.101118	−	0.0270944i
$731$		0			0
$732$	−12.5851	−	5.79796i	−0.465157	−	0.214299i
$733$	5.00000	+	5.00000i	0.184679	+	0.184679i	0.793391	−	0.608712i	$-0.208314\pi$
$733$	5.00000	+	5.00000i	0.184679	+	0.184679i	−0.608712	+	0.793391i	$0.708314\pi$
$734$	7.72741	+	2.07055i	0.285224	+	0.0764255i
$735$	−16.2484	+	5.99900i	−0.599333	+	0.221277i
$736$	30.0000	−	30.0000i	1.10581	−	1.10581i
$737$	24.4949	−	14.1421i	0.902281	−	0.520932i
$738$	4.56048	−	3.89898i	0.167874	−	0.143523i
$739$	−0.366025	−	1.36603i	−0.0134645	−	0.0502501i	0.958867	−	0.283857i	$-0.0916139\pi$
$739$	−0.366025	−	1.36603i	−0.0134645	−	0.0502501i	−0.972331	+	0.233606i	$0.924947\pi$
$740$	−2.82843			−0.103975
$741$		0			0
$742$	−8.00000			−0.293689
$743$	−4.14110	−	15.4548i	−0.151922	−	0.566982i	−0.999349	−	0.0360700i	$-0.988516\pi$
$743$	−4.14110	−	15.4548i	−0.151922	−	0.566982i	0.847427	−	0.530912i	$-0.178151\pi$
$744$	−3.37117	−	36.5874i	−0.123593	−	1.34136i
$745$	−3.46410	+	2.00000i	−0.126915	+	0.0732743i
$746$	2.82843	−	2.82843i	0.103556	−	0.103556i
$747$	13.5838	−	19.7859i	0.497006	−	0.723927i
$748$		0			0
$749$	5.65685	+	5.65685i	0.206697	+	0.206697i
$750$	8.69694	−	18.8776i	0.317567	−	0.689312i
$751$	−25.9808	−	15.0000i	−0.948051	−	0.547358i	−0.0555764	−	0.998454i	$-0.517700\pi$
$751$	−25.9808	−	15.0000i	−0.948051	−	0.547358i	−0.892475	+	0.451097i	$0.851033\pi$
$752$	−3.86370	+	1.03528i	−0.140895	+	0.0377526i
$753$	−25.4558	−	36.0000i	−0.927663	−	1.31191i
$754$		0			0
$755$			2.82843i			0.102937i
$756$	6.31249	−	3.76198i	0.229583	−	0.136822i
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	−0.683226	−	0.730207i	$-0.739424\pi$
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	0.973991	+	0.226587i	$0.0727569\pi$
$758$	−13.4350	−	23.2702i	−0.487982	−	0.845210i
$759$	9.94113	−	57.9411i	0.360840	−	2.10313i
$760$	2.19615	−	8.19615i	0.0796628	−	0.297306i
$761$	−12.9410	+	48.2963i	−0.469109	+	1.75074i	0.173784	+	0.984784i	$0.444400\pi$
$761$	−12.9410	+	48.2963i	−0.469109	+	1.75074i	−0.642894	+	0.765955i	$0.722266\pi$
$762$		0			0
$763$	−1.00000	−	1.73205i	−0.0362024	−	0.0627044i
$764$	1.41421	−	2.44949i	0.0511645	−	0.0886194i
$765$		0			0
$766$		−	16.0000i		−	0.578103i
$767$		0			0
$768$	17.0000	+	24.0416i	0.613435	+	0.867528i
$769$	17.7583	−	4.75833i	0.640382	−	0.171590i	0.0760054	−	0.997107i	$-0.475783\pi$
$769$	17.7583	−	4.75833i	0.640382	−	0.171590i	0.564376	+	0.825518i	$0.309117\pi$
$770$	9.79796	+	5.65685i	0.353094	+	0.203859i
$771$	−6.14966	+	13.3485i	−0.221475	+	0.480733i
$772$	−19.0000	−	19.0000i	−0.683825	−	0.683825i
$773$	−13.5230	−	3.62347i	−0.486387	−	0.130327i	0.00728800	−	0.999973i	$-0.497680\pi$
$773$	−13.5230	−	3.62347i	−0.486387	−	0.130327i	−0.493675	+	0.869646i	$0.664347\pi$
$774$	−14.8394	−	10.1879i	−0.533391	−	0.366195i
$775$	−5.00000	+	5.00000i	−0.179605	+	0.179605i
$776$	25.7196	−	14.8492i	0.923281	−	0.533057i
$777$	−0.317837	−	3.44949i	−0.0114023	−	0.123750i
$778$	−4.39230	−	16.3923i	−0.157472	−	0.587693i
$779$	−2.82843			−0.101339
$780$		0			0
$781$	−16.0000			−0.572525
$782$		0			0
$783$	−14.2474	−	3.60697i	−0.509162	−	0.128902i
$784$	4.33013	−	2.50000i	0.154647	−	0.0892857i
$785$	19.7990	−	19.7990i	0.706656	−	0.706656i
$786$	18.3830	−	6.78710i	0.655700	−	0.242088i
$787$	25.9545	+	6.95448i	0.925177	+	0.247901i	0.689797	−	0.724003i	$-0.257700\pi$
$787$	25.9545	+	6.95448i	0.925177	+	0.247901i	0.235380	+	0.971903i	$0.424366\pi$
$788$	−15.5563	−	15.5563i	−0.554172	−	0.554172i
$789$	35.5959	+	16.3991i	1.26725	+	0.583824i
$790$	17.3205	+	10.0000i	0.616236	+	0.355784i
$791$	−19.3185	+	5.17638i	−0.686887	+	0.184051i
$792$	33.9411	+	12.0000i	1.20605	+	0.426401i
$793$		0			0
$794$			24.0416i			0.853206i
$795$	−15.0693	−	12.5266i	−0.534453	−	0.444273i
$796$		0			0
$797$	8.48528	+	14.6969i	0.300564	+	0.520592i	0.976264	−	0.216585i	$-0.0694917\pi$
$797$	8.48528	+	14.6969i	0.300564	+	0.520592i	−0.675700	+	0.737177i	$0.736158\pi$
$798$	3.41421	+	0.585786i	0.120862	+	0.0207366i
$799$		0			0
$800$	1.29410	−	4.82963i	0.0457532	−	0.170753i
$801$	37.8995	−	18.1005i	1.33911	−	0.639550i
$802$	11.0000	+	19.0526i	0.388424	+	0.672769i
$803$	2.82843	−	4.89898i	0.0998130	−	0.172881i
$804$	−7.82913	+	9.41832i	−0.276112	+	0.332158i
$805$			24.0000i			0.845889i
$806$		0			0
$807$	28.0000	−	19.7990i	0.985647	−	0.696957i
$808$	−24.5885	+	6.58846i	−0.865019	+	0.231781i
$809$	26.9444	+	15.5563i	0.947314	+	0.546932i	0.892246	−	0.451550i	$-0.149129\pi$
$809$	26.9444	+	15.5563i	0.947314	+	0.546932i	0.0550686	+	0.998483i	$0.482462\pi$
$810$	−17.7812	−	2.79796i	−0.624768	−	0.0983103i
$811$	−1.00000	−	1.00000i	−0.0351147	−	0.0351147i	0.689331	−	0.724446i	$-0.257904\pi$
$811$	−1.00000	−	1.00000i	−0.0351147	−	0.0351147i	−0.724446	+	0.689331i	$0.757904\pi$
$812$	−3.86370	−	1.03528i	−0.135589	−	0.0363311i
$813$	−16.1194	−	43.6597i	−0.565331	−	1.53121i
$814$	4.00000	−	4.00000i	0.140200	−	0.140200i
$815$	2.44949	−	1.41421i	0.0858019	−	0.0495377i
$816$		0			0
$817$	2.19615	+	8.19615i	0.0768336	+	0.286747i
$818$	−32.5269			−1.13728
$819$		0			0
$820$	4.00000			0.139686
$821$	−2.58819	−	9.65926i	−0.0903285	−	0.337110i	0.905941	−	0.423403i	$-0.139165\pi$
$821$	−2.58819	−	9.65926i	−0.0903285	−	0.337110i	−0.996270	+	0.0862928i	$0.972498\pi$
$822$	24.1464	−	2.22486i	0.842203	−	0.0776009i
$823$	25.9808	−	15.0000i	0.905632	−	0.522867i	0.0266091	−	0.999646i	$-0.491529\pi$
$823$	25.9808	−	15.0000i	0.905632	−	0.522867i	0.879023	+	0.476779i	$0.158196\pi$
$824$	−12.7279	+	12.7279i	−0.443398	+	0.443398i
$825$	−2.39960	−	6.49938i	−0.0835434	−	0.226279i
$826$	−5.46410	−	1.46410i	−0.190120	−	0.0509426i
$827$	−22.6274	−	22.6274i	−0.786832	−	0.786832i	0.194141	−	0.980974i	$-0.437808\pi$
$827$	−22.6274	−	22.6274i	−0.786832	−	0.786832i	−0.980974	+	0.194141i	$0.937808\pi$
$828$	4.65153	+	25.0273i	0.161652	+	0.869757i
$829$	−15.5885	−	9.00000i	−0.541409	−	0.312583i	0.204240	−	0.978921i	$-0.434528\pi$
$829$	−15.5885	−	9.00000i	−0.541409	−	0.312583i	−0.745650	+	0.666338i	$0.767861\pi$
$830$	−15.4548	+	4.14110i	−0.536444	+	0.143740i
$831$	−16.9706	+	12.0000i	−0.588702	+	0.416275i
$832$		0			0
$833$		0			0
$834$	4.42883	−	5.32780i	0.153358	−	0.184487i
$835$	−4.00000	+	6.92820i	−0.138426	+	0.239760i
$836$	−2.82843	−	4.89898i	−0.0978232	−	0.169435i
$837$	32.0711	+	17.9289i	1.10854	+	0.619715i
$838$	−2.92820	+	10.9282i	−0.101153	+	0.377509i
$839$	1.03528	−	3.86370i	0.0357417	−	0.133390i	−0.945750	−	0.324896i	$-0.894671\pi$
$839$	1.03528	−	3.86370i	0.0357417	−	0.133390i	0.981491	+	0.191506i	$0.0613373\pi$
$840$	−14.4853	−	2.48528i	−0.499790	−	0.0857504i
$841$	−10.5000	−	18.1865i	−0.362069	−	0.627122i
$842$	−17.6777	+	30.6186i	−0.609213	+	1.05519i
$843$	−18.6473	−	15.5009i	−0.642248	−	0.533879i
$844$			14.0000i			0.481900i
$845$		0			0
$846$	4.00000	−	11.3137i	0.137523	−	0.388973i
$847$	6.83013	−	1.83013i	0.234686	−	0.0628839i
$848$	4.89898	+	2.82843i	0.168232	+	0.0971286i
$849$	−18.8776	−	8.69694i	−0.647877	−	0.298478i
$850$		0			0
$851$	11.5911	+	3.10583i	0.397338	+	0.106466i
$852$	6.49938	−	2.39960i	0.222665	−	0.0822090i
$853$	−37.0000	+	37.0000i	−1.26686	+	1.26686i	−0.319152	+	0.947703i	$0.603398\pi$
$853$	−37.0000	+	37.0000i	−1.26686	+	1.26686i	−0.947703	+	0.319152i	$0.896602\pi$
$854$	−9.79796	+	5.65685i	−0.335279	+	0.193574i
$855$	5.51399	+	6.44949i	0.188574	+	0.220568i
$856$	−4.39230	−	16.3923i	−0.150126	−	0.560277i
$857$	−8.48528			−0.289852			−0.144926	−	0.989443i	$-0.546294\pi$
$857$	−8.48528			−0.289852			−0.144926	+	0.989443i	$0.546294\pi$
$858$		0			0
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$	−3.10583	−	11.5911i	−0.105908	−	0.395254i
$861$	0.449490	+	4.87832i	0.0153186	+	0.166253i
$862$	27.7128	−	16.0000i	0.943902	−	0.544962i
$863$	−2.82843	+	2.82843i	−0.0962808	+	0.0962808i	−0.753607	−	0.657326i	$-0.771688\pi$
$863$	−2.82843	+	2.82843i	−0.0962808	+	0.0962808i	0.657326	+	0.753607i	$0.271688\pi$
$864$	−25.9783	+	0.359651i	−0.883799	+	0.0122356i
$865$	16.3923	+	4.39230i	0.557355	+	0.149343i
$866$	−12.7279	−	12.7279i	−0.432512	−	0.432512i
$867$	12.3207	−	26.7432i	0.418432	−	0.908248i
$868$	8.66025	+	5.00000i	0.293948	+	0.169711i
$869$	38.6370	−	10.3528i	1.31067	−	0.351193i
$870$	5.65685	+	8.00000i	0.191785	+	0.271225i
$871$		0			0
$872$			4.24264i			0.143674i
$873$	−2.31524	+	29.6081i	−0.0783592	+	1.00208i
$874$	−6.00000	+	10.3923i	−0.202953	+	0.351525i
$875$	8.48528	+	14.6969i	0.286855	+	0.496847i
$876$	−0.414214	+	2.41421i	−0.0139950	+	0.0815687i
$877$	−4.75833	+	17.7583i	−0.160677	+	0.599656i	0.837875	+	0.545863i	$0.183798\pi$
$877$	−4.75833	+	17.7583i	−0.160677	+	0.599656i	−0.998552	+	0.0537936i	$0.982869\pi$
$878$	7.76457	−	28.9778i	0.262042	−	0.977953i
$879$	−4.10051	+	23.8995i	−0.138307	+	0.806110i
$880$	−4.00000	−	6.92820i	−0.134840	−	0.233550i
$881$	−12.7279	+	22.0454i	−0.428815	+	0.742729i	−0.996768	−	0.0803319i	$-0.974402\pi$
$881$	−12.7279	+	22.0454i	−0.428815	+	0.742729i	0.567954	+	0.823061i	$0.307735\pi$
$882$	−1.16938	+	14.9543i	−0.0393749	+	0.503539i
$883$			36.0000i			1.21150i	0.795656	+	0.605748i	$0.207126\pi$
$883$			36.0000i			1.21150i	−0.795656	+	0.605748i	$0.792874\pi$
$884$		0			0
$885$	−8.00000	−	11.3137i	−0.268917	−	0.380306i
$886$	27.3205	−	7.32051i	0.917850	−	0.245937i
$887$	12.2474	+	7.07107i	0.411229	+	0.237423i	0.691318	−	0.722551i	$-0.257031\pi$
$887$	12.2474	+	7.07107i	0.411229	+	0.237423i	−0.280089	+	0.959974i	$0.590364\pi$
$888$	−3.07483	+	6.67423i	−0.103185	+	0.223973i
$889$		0			0
$890$	−27.0459	−	7.24693i	−0.906581	−	0.242918i
$891$	−29.1033	+	21.1895i	−0.974999	+	0.709876i
$892$	−11.0000	+	11.0000i	−0.368307	+	0.368307i
$893$	−4.89898	+	2.82843i	−0.163938	+	0.0946497i
$894$	0.317837	+	3.44949i	0.0106301	+	0.115368i
$895$		0			0
$896$	−4.24264			−0.141737
$897$		0			0
$898$	−22.0000			−0.734150
$899$	−5.17638	−	19.3185i	−0.172642	−	0.644309i
$900$	1.94949	+	2.28024i	0.0649830	+	0.0760080i
$901$		0			0
$902$	−5.65685	+	5.65685i	−0.188353	+	0.188353i
$903$	13.7873	−	5.09032i	0.458811	−	0.169395i
$904$	40.9808	+	10.9808i	1.36300	+	0.365215i
$905$		0			0
$906$	2.22474	+	1.02494i	0.0739122	+	0.0340515i
$907$	10.3923	+	6.00000i	0.345071	+	0.199227i	0.662512	−	0.749051i	$-0.269490\pi$
$907$	10.3923	+	6.00000i	0.345071	+	0.199227i	−0.317441	+	0.948278i	$0.602824\pi$
$908$	−7.72741	+	2.07055i	−0.256443	+	0.0687137i
$909$	8.48528	−	24.0000i	0.281439	−	0.796030i
$910$		0			0
$911$		−	48.0833i		−	1.59307i	−0.604593	−	0.796535i	$-0.706664\pi$
$911$		−	48.0833i		−	1.59307i	0.604593	−	0.796535i	$-0.293336\pi$
$912$	−1.88366	−	1.56583i	−0.0623743	−	0.0518497i
$913$	−16.0000	+	27.7128i	−0.529523	+	0.917160i
$914$	20.5061	+	35.5176i	0.678281	+	1.17482i
$915$	−27.3137	−	4.68629i	−0.902963	−	0.154924i
$916$	−0.366025	+	1.36603i	−0.0120938	+	0.0451347i
$917$	−4.14110	+	15.4548i	−0.136751	+	0.510363i
$918$		0			0
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	0.997429	+	0.0716652i	$0.0228313\pi$
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	−0.436650	+	0.899631i	$0.643835\pi$
$920$	25.4558	−	44.0908i	0.839254	−	1.45363i
$921$	26.6190	−	32.0223i	0.877127	−	1.05517i
$922$		−	10.0000i		−	0.329332i
$923$		0			0
$924$	−8.00000	+	5.65685i	−0.263181	+	0.186097i
$925$	1.36603	−	0.366025i	0.0449146	−	0.0120348i
$926$	−20.8207	−	12.0208i	−0.684209	−	0.395029i
$927$	−3.28913	−	17.6969i	−0.108029	−	0.581244i
$928$	10.0000	+	10.0000i	0.328266	+	0.328266i
$929$	44.4326	+	11.9057i	1.45779	+	0.390613i	0.898725	−	0.438514i	$-0.144495\pi$
$929$	44.4326	+	11.9057i	1.45779	+	0.390613i	0.559061	+	0.829126i	$0.311162\pi$
$930$	−8.48387	−	22.9788i	−0.278197	−	0.753504i
$931$	5.00000	−	5.00000i	0.163868	−	0.163868i
$932$	−22.0454	+	12.7279i	−0.722121	+	0.416917i
$933$	14.6349	−	1.34847i	0.479127	−	0.0441469i
$934$	6.58846	+	24.5885i	0.215581	+	0.804559i
$935$		0			0
$936$		0			0
$937$	−52.0000			−1.69877			−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000			−1.69877			−0.849383	+	0.527777i	$0.823026\pi$
$938$	2.58819	+	9.65926i	0.0845074	+	0.315386i
$939$	13.7980	−	1.27135i	0.450279	−	0.0414889i
$940$	6.92820	−	4.00000i	0.225973	−	0.130466i
$941$	26.8701	−	26.8701i	0.875939	−	0.875939i	−0.117173	−	0.993112i	$-0.537383\pi$
$941$	26.8701	−	26.8701i	0.875939	−	0.875939i	0.993112	+	0.117173i	$0.0373831\pi$
$942$	−8.39861	−	22.7478i	−0.273641	−	0.741164i
$943$	−16.3923	−	4.39230i	−0.533807	−	0.143033i
$944$	2.82843	+	2.82843i	0.0920575	+	0.0920575i
$945$	10.2474	−	10.5352i	0.333350	−	0.342709i
$946$	20.7846	+	12.0000i	0.675766	+	0.390154i
$947$	30.9096	−	8.28221i	1.00443	−	0.269136i	0.281128	−	0.959670i	$-0.409291\pi$
$947$	30.9096	−	8.28221i	1.00443	−	0.269136i	0.723299	+	0.690535i	$0.242625\pi$
$948$	−14.1421	+	10.0000i	−0.459315	+	0.324785i
$949$		0			0
$950$			1.41421i			0.0458831i
$951$	−11.0721	+	13.3195i	−0.359036	+	0.431915i
$952$		0			0
$953$	−12.7279	−	22.0454i	−0.412298	−	0.714121i	0.582843	−	0.812585i	$-0.301940\pi$
$953$	−12.7279	−	22.0454i	−0.412298	−	0.714121i	−0.995141	+	0.0984642i	$0.968607\pi$
$954$	−15.3137	+	7.31371i	−0.495800	+	0.236790i
$955$	1.46410	−	5.46410i	0.0473772	−	0.176814i
$956$	5.17638	−	19.3185i	0.167416	−	0.624805i
$957$	19.3137	+	3.31371i	0.624324	+	0.107117i
$958$	−16.0000	−	27.7128i	−0.516937	−	0.895360i
$959$	−9.89949	+	17.1464i	−0.319671	+	0.553687i
$960$	18.6473	+	15.5009i	0.601840	+	0.500289i
$961$			19.0000i			0.612903i
$962$		0			0
$963$	16.0000	+	5.65685i	0.515593	+	0.182290i
$964$	−23.2224	+	6.22243i	−0.747944	+	0.200411i
$965$	−46.5403	−	26.8701i	−1.49819	−	0.864978i
$966$	18.8776	+	8.69694i	0.607376	+	0.279819i
$967$	23.0000	+	23.0000i	0.739630	+	0.739630i	0.972506	−	0.232876i	$-0.0748137\pi$
$967$	23.0000	+	23.0000i	0.739630	+	0.739630i	−0.232876	+	0.972506i	$0.574814\pi$
$968$	−14.4889	−	3.88229i	−0.465690	−	0.124781i
$969$		0			0
$970$	14.0000	−	14.0000i	0.449513	−	0.449513i
$971$	−26.9444	+	15.5563i	−0.864687	+	0.499227i	−0.865579	−	0.500773i	$-0.833049\pi$
$971$	−26.9444	+	15.5563i	−0.864687	+	0.499227i	0.000892350		1.00000i	$0.499716\pi$
$972$	8.64420	−	12.9722i	0.277263	−	0.416083i
$973$	1.46410	+	5.46410i	0.0469369	+	0.175171i
$974$	26.8701			0.860972
$975$		0			0
$976$	8.00000			0.256074
$977$	9.83512	+	36.7052i	0.314653	+	1.17430i	0.924312	+	0.381638i	$0.124640\pi$
$977$	9.83512	+	36.7052i	0.314653	+	1.17430i	−0.609658	+	0.792664i	$0.708693\pi$
$978$	−0.224745	−	2.43916i	−0.00718655	−	0.0779957i
$979$	−48.4974	+	28.0000i	−1.54998	+	0.894884i
$980$	−7.07107	+	7.07107i	−0.225877	+	0.225877i
$981$	−3.49768	−	2.40130i	−0.111672	−	0.0766677i
$982$	−40.9808	−	10.9808i	−1.30775	−	0.350410i
$983$	2.82843	+	2.82843i	0.0902128	+	0.0902128i	0.750773	−	0.660560i	$-0.229681\pi$
$983$	2.82843	+	2.82843i	0.0902128	+	0.0902128i	−0.660560	+	0.750773i	$0.729681\pi$
$984$	4.34847	−	9.43879i	0.138624	−	0.300898i
$985$	−38.1051	−	22.0000i	−1.21413	−	0.700978i
$986$		0			0
$987$	5.65685	+	8.00000i	0.180060	+	0.254643i
$988$		0			0
$989$			50.9117i			1.61890i
$990$	23.9270	+	1.87100i	0.760449	+	0.0594643i
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	−17.6777	−	30.6186i	−0.561267	−	0.972142i
$993$	−2.89949	+	16.8995i	−0.0920127	+	0.536289i
$994$	1.46410	−	5.46410i	0.0464385	−	0.173311i
$995$		0			0
$996$	2.34315	−	13.6569i	0.0742454	−	0.432734i
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	16.2635	−	28.1691i	0.514811	−	0.891678i
$999$	−3.76198	−	6.31249i	−0.119024	−	0.199718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.i.488.1		8
3.2	odd	2	inner	507.2.k.i.488.2		8
13.2	odd	12	inner	507.2.k.i.80.2		8
13.3	even	3	inner	507.2.k.i.89.2		8
13.4	even	6		39.2.f.a.8.2	yes	4
13.5	odd	4	inner	507.2.k.i.188.1		8
13.6	odd	12		507.2.f.a.239.2		4
13.7	odd	12		39.2.f.a.5.1	✓	4
13.8	odd	4		507.2.k.j.188.2		8
13.9	even	3		507.2.f.a.437.1		4
13.10	even	6		507.2.k.j.89.1		8
13.11	odd	12		507.2.k.j.80.1		8
13.12	even	2		507.2.k.j.488.2		8
39.2	even	12	inner	507.2.k.i.80.1		8
39.5	even	4	inner	507.2.k.i.188.2		8
39.8	even	4		507.2.k.j.188.1		8
39.11	even	12		507.2.k.j.80.2		8
39.17	odd	6		39.2.f.a.8.1	yes	4
39.20	even	12		39.2.f.a.5.2	yes	4
39.23	odd	6		507.2.k.j.89.2		8
39.29	odd	6	inner	507.2.k.i.89.1		8
39.32	even	12		507.2.f.a.239.1		4
39.35	odd	6		507.2.f.a.437.2		4
39.38	odd	2		507.2.k.j.488.1		8
52.7	even	12		624.2.bf.d.161.2		4
52.43	odd	6		624.2.bf.d.593.2		4
65.4	even	6		975.2.o.j.476.1		4
65.7	even	12		975.2.n.c.824.2		4
65.17	odd	12		975.2.n.d.749.2		4
65.33	even	12		975.2.n.d.824.1		4
65.43	odd	12		975.2.n.c.749.1		4
65.59	odd	12		975.2.o.j.551.2		4
156.59	odd	12		624.2.bf.d.161.1		4
156.95	even	6		624.2.bf.d.593.1		4
195.17	even	12		975.2.n.d.749.1		4
195.59	even	12		975.2.o.j.551.1		4
195.98	odd	12		975.2.n.d.824.2		4
195.134	odd	6		975.2.o.j.476.2		4
195.137	odd	12		975.2.n.c.824.1		4
195.173	even	12		975.2.n.c.749.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.f.a.5.1	✓	4	13.7	odd	12
39.2.f.a.5.2	yes	4	39.20	even	12
39.2.f.a.8.1	yes	4	39.17	odd	6
39.2.f.a.8.2	yes	4	13.4	even	6
507.2.f.a.239.1		4	39.32	even	12
507.2.f.a.239.2		4	13.6	odd	12
507.2.f.a.437.1		4	13.9	even	3
507.2.f.a.437.2		4	39.35	odd	6
507.2.k.i.80.1		8	39.2	even	12	inner
507.2.k.i.80.2		8	13.2	odd	12	inner
507.2.k.i.89.1		8	39.29	odd	6	inner
507.2.k.i.89.2		8	13.3	even	3	inner
507.2.k.i.188.1		8	13.5	odd	4	inner
507.2.k.i.188.2		8	39.5	even	4	inner
507.2.k.i.488.1		8	1.1	even	1	trivial
507.2.k.i.488.2		8	3.2	odd	2	inner
507.2.k.j.80.1		8	13.11	odd	12
507.2.k.j.80.2		8	39.11	even	12
507.2.k.j.89.1		8	13.10	even	6
507.2.k.j.89.2		8	39.23	odd	6
507.2.k.j.188.1		8	39.8	even	4
507.2.k.j.188.2		8	13.8	odd	4
507.2.k.j.488.1		8	39.38	odd	2
507.2.k.j.488.2		8	13.12	even	2
624.2.bf.d.161.1		4	156.59	odd	12
624.2.bf.d.161.2		4	52.7	even	12
624.2.bf.d.593.1		4	156.95	even	6
624.2.bf.d.593.2		4	52.43	odd	6
975.2.n.c.749.1		4	65.43	odd	12
975.2.n.c.749.2		4	195.173	even	12
975.2.n.c.824.1		4	195.137	odd	12
975.2.n.c.824.2		4	65.7	even	12
975.2.n.d.749.1		4	195.17	even	12
975.2.n.d.749.2		4	65.17	odd	12
975.2.n.d.824.1		4	65.33	even	12
975.2.n.d.824.2		4	195.98	odd	12
975.2.o.j.476.1		4	65.4	even	6
975.2.o.j.476.2		4	195.134	odd	6
975.2.o.j.551.1		4	195.59	even	12
975.2.o.j.551.2		4	65.59	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.72474 - 0.158919i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.41421 - 1.41421i) q^{5} +(-0.599900 - 1.62484i) q^{6} +(1.36603 + 0.366025i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(2.94949 - 0.548188i) q^{9} +(-1.73205 - 1.00000i) q^{10} +(-3.86370 + 1.03528i) q^{11} +(1.41421 - 1.00000i) q^{12} -1.41421i q^{14} +(2.21441 - 2.66390i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.29289 - 2.70711i) q^{18} +(-0.366025 + 1.36603i) q^{19} +(0.517638 - 1.93185i) q^{20} +(2.41421 + 0.414214i) q^{21} +(2.00000 + 3.46410i) q^{22} +(-4.24264 + 7.34847i) q^{23} +(-3.99585 - 3.32162i) q^{24} +1.00000i q^{25} +(5.00000 - 1.41421i) q^{27} +(1.36603 - 0.366025i) q^{28} +(-2.44949 - 1.41421i) q^{29} +(-3.14626 - 1.44949i) q^{30} +(5.00000 + 5.00000i) q^{31} +(-4.82963 - 1.29410i) q^{32} +(-6.49938 + 2.39960i) q^{33} +(2.44949 - 1.41421i) q^{35} +(2.28024 - 1.94949i) q^{36} +(-0.366025 - 1.36603i) q^{37} +1.41421 q^{38} -6.00000 q^{40} +(0.517638 + 1.93185i) q^{41} +(-0.224745 - 2.43916i) q^{42} +(5.19615 - 3.00000i) q^{43} +(-2.82843 + 2.82843i) q^{44} +(3.39595 - 4.94646i) q^{45} +(8.19615 + 2.19615i) q^{46} +(2.82843 + 2.82843i) q^{47} +(-0.724745 + 1.57313i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(0.965926 - 0.258819i) q^{50} -5.65685i q^{53} +(-2.66012 - 4.46360i) q^{54} +(-4.00000 + 6.92820i) q^{55} +(-2.12132 - 3.67423i) q^{56} +(-0.414214 + 2.41421i) q^{57} +(-0.732051 + 2.73205i) q^{58} +(1.03528 - 3.86370i) q^{59} +(0.585786 - 3.41421i) q^{60} +(-4.00000 - 6.92820i) q^{61} +(3.53553 - 6.12372i) q^{62} +(4.22973 + 0.330749i) q^{63} +7.00000i q^{64} +(4.00000 + 5.65685i) q^{66} +(-6.83013 + 1.83013i) q^{67} +(-6.14966 + 13.3485i) q^{69} +(-2.00000 - 2.00000i) q^{70} +(3.86370 + 1.03528i) q^{71} +(-7.41970 - 5.09393i) q^{72} +(-1.00000 + 1.00000i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(0.158919 + 1.72474i) q^{75} +(0.366025 + 1.36603i) q^{76} -5.65685 q^{77} -10.0000 q^{79} +(0.517638 + 1.93185i) q^{80} +(8.39898 - 3.23375i) q^{81} +(1.73205 - 1.00000i) q^{82} +(5.65685 - 5.65685i) q^{83} +(2.29788 - 0.848387i) q^{84} +(-4.24264 - 4.24264i) q^{86} +(-4.44949 - 2.04989i) q^{87} +(10.3923 + 6.00000i) q^{88} +(13.5230 - 3.62347i) q^{89} +(-5.65685 - 2.00000i) q^{90} +8.48528i q^{92} +(9.41832 + 7.82913i) q^{93} +(2.00000 - 3.46410i) q^{94} +(1.41421 + 2.44949i) q^{95} +(-8.53553 - 1.46447i) q^{96} +(-2.56218 + 9.56218i) q^{97} +(-1.29410 + 4.82963i) q^{98} +(-10.8284 + 5.17157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9} + 8 q^{15} - 4 q^{16} - 16 q^{18} + 4 q^{19} + 8 q^{21} + 16 q^{22} + 12 q^{24} + 40 q^{27} + 4 q^{28} + 40 q^{31} - 16 q^{33} + 4 q^{37} - 48 q^{40} + 8 q^{42}+ \cdots - 64 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 + 4 * q^9 + 8 * q^15 - 4 * q^16 - 16 * q^18 + 4 * q^19 + 8 * q^21 + 16 * q^22 + 12 * q^24 + 40 * q^27 + 4 * q^28 + 40 * q^31 - 16 * q^33 + 4 * q^37 - 48 * q^40 + 8 * q^42 - 16 * q^45 + 24 * q^46 + 4 * q^48 - 4 * q^54 - 32 * q^55 + 8 * q^57 + 8 * q^58 + 16 * q^60 - 32 * q^61 - 4 * q^63 + 32 * q^66 - 20 * q^67 - 16 * q^70 - 24 * q^72 - 8 * q^73 - 4 * q^76 - 80 * q^79 + 28 * q^81 - 4 * q^84 - 16 * q^87 + 20 * q^93 + 16 * q^94 - 40 * q^96 + 28 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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