LMFDB - Embedded newform 507.2.k.i.80.2

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			80.2
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	507.80
Dual form			507.2.k.i.488.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.41421 - 1.41421i) q^{5} +(1.33195 + 1.10721i) q^{6} +(1.36603 - 0.366025i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.41421 - 1.41421i) q^{5} +(1.33195 + 1.10721i) q^{6} +(1.36603 - 0.366025i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-1.94949 - 2.28024i) q^{9} +(-1.73205 + 1.00000i) q^{10} +(3.86370 + 1.03528i) q^{11} +(-1.41421 + 1.00000i) q^{12} -1.41421i q^{14} +(3.24969 - 1.19980i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.70711 + 1.29289i) q^{18} +(-0.366025 - 1.36603i) q^{19} +(-0.517638 - 1.93185i) q^{20} +(-0.414214 + 2.41421i) q^{21} +(2.00000 - 3.46410i) q^{22} +(4.24264 + 7.34847i) q^{23} +(1.79970 + 4.87453i) q^{24} -1.00000i q^{25} +(5.00000 - 1.41421i) q^{27} +(1.36603 + 0.366025i) q^{28} +(2.44949 - 1.41421i) q^{29} +(-0.317837 - 3.44949i) q^{30} +(5.00000 - 5.00000i) q^{31} +(4.82963 - 1.29410i) q^{32} +(-4.42883 + 5.32780i) q^{33} +(-2.44949 - 1.41421i) q^{35} +(-0.548188 - 2.94949i) q^{36} +(-0.366025 + 1.36603i) q^{37} -1.41421 q^{38} -6.00000 q^{40} +(-0.517638 + 1.93185i) q^{41} +(2.22474 + 1.02494i) q^{42} +(5.19615 + 3.00000i) q^{43} +(2.82843 + 2.82843i) q^{44} +(-0.467750 + 5.98174i) q^{45} +(8.19615 - 2.19615i) q^{46} +(-2.82843 + 2.82843i) q^{47} +(1.72474 - 0.158919i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(-0.965926 - 0.258819i) q^{50} -5.65685i q^{53} +(-0.0719302 - 5.19565i) q^{54} +(-4.00000 - 6.92820i) q^{55} +(2.12132 - 3.67423i) q^{56} +(2.41421 + 0.414214i) q^{57} +(-0.732051 - 2.73205i) q^{58} +(-1.03528 - 3.86370i) q^{59} +(3.41421 + 0.585786i) q^{60} +(-4.00000 + 6.92820i) q^{61} +(-3.53553 - 6.12372i) q^{62} +(-3.49768 - 2.40130i) q^{63} -7.00000i q^{64} +(4.00000 + 5.65685i) q^{66} +(-6.83013 - 1.83013i) q^{67} +(-14.6349 + 1.34847i) q^{69} +(-2.00000 + 2.00000i) q^{70} +(-3.86370 + 1.03528i) q^{71} +(-8.97261 - 0.701625i) q^{72} +(-1.00000 - 1.00000i) q^{73} +(1.22474 + 0.707107i) q^{74} +(1.57313 + 0.724745i) q^{75} +(0.366025 - 1.36603i) q^{76} +5.65685 q^{77} -10.0000 q^{79} +(-0.517638 + 1.93185i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(1.73205 + 1.00000i) q^{82} +(-5.65685 - 5.65685i) q^{83} +(-1.56583 + 1.88366i) q^{84} +(4.24264 - 4.24264i) q^{86} +(0.449490 + 4.87832i) q^{87} +(10.3923 - 6.00000i) q^{88} +(-13.5230 - 3.62347i) q^{89} +(5.65685 + 2.00000i) q^{90} +8.48528i q^{92} +(4.24194 + 11.4894i) q^{93} +(2.00000 + 3.46410i) q^{94} +(-1.41421 + 2.44949i) q^{95} +(-1.46447 + 8.53553i) q^{96} +(-2.56218 - 9.56218i) q^{97} +(1.29410 + 4.82963i) q^{98} +(-5.17157 - 10.8284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 + 4 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.812035	−	0.583609i	$-0.801640\pi$
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i	0.995047	−	0.0994033i	$-0.0316934\pi$
$3$	−0.724745	+	1.57313i	−0.418432	+	0.908248i
$3$	−0.724745	+	1.57313i	−0.418432	+	0.908248i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.41421	−	1.41421i	−0.632456	−	0.632456i	0.316228	−	0.948683i	$-0.397584\pi$
$5$	−1.41421	−	1.41421i	−0.632456	−	0.632456i	−0.948683	+	0.316228i	$0.897584\pi$
$6$	1.33195	+	1.10721i	0.543767	+	0.452015i
$7$	1.36603	−	0.366025i	0.516309	−	0.138345i	0.00875026	−	0.999962i	$-0.497215\pi$
$7$	1.36603	−	0.366025i	0.516309	−	0.138345i	0.507559	+	0.861617i	$0.330548\pi$
$8$	2.12132	−	2.12132i	0.750000	−	0.750000i
$9$	−1.94949	−	2.28024i	−0.649830	−	0.760080i
$10$	−1.73205	+	1.00000i	−0.547723	+	0.316228i
$11$	3.86370	+	1.03528i	1.16495	+	0.312148i	0.788941	−	0.614468i	$-0.210630\pi$
$11$	3.86370	+	1.03528i	1.16495	+	0.312148i	0.376009	+	0.926616i	$0.377296\pi$
$12$	−1.41421	+	1.00000i	−0.408248	+	0.288675i
$13$		0			0
$13$		0			0
$14$		−	1.41421i		−	0.377964i
$15$	3.24969	−	1.19980i	0.839066	−	0.309787i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−2.70711	+	1.29289i	−0.638071	+	0.304738i
$19$	−0.366025	−	1.36603i	−0.0839720	−	0.313388i	0.911146	−	0.412085i	$-0.135199\pi$
$19$	−0.366025	−	1.36603i	−0.0839720	−	0.313388i	−0.995118	+	0.0986970i	$0.968533\pi$
$20$	−0.517638	−	1.93185i	−0.115747	−	0.431975i
$21$	−0.414214	+	2.41421i	−0.0903888	+	0.526825i
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$	4.24264	+	7.34847i	0.884652	+	1.53226i	0.846112	+	0.533005i	$0.178937\pi$
$23$	4.24264	+	7.34847i	0.884652	+	1.53226i	0.0385394	+	0.999257i	$0.487729\pi$
$24$	1.79970	+	4.87453i	0.367362	+	0.995010i
$25$		−	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	$-0.582082\pi$
$29$	2.44949	−	1.41421i	0.454859	−	0.262613i	0.709880	+	0.704323i	$0.248749\pi$
$30$	−0.317837	−	3.44949i	−0.0580289	−	0.629788i
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	−0.0972349	−	0.995261i	$-0.531000\pi$
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	0.995261	+	0.0972349i	$0.0309998\pi$
$32$	4.82963	−	1.29410i	0.853766	−	0.228766i
$33$	−4.42883	+	5.32780i	−0.770960	+	0.927452i
$34$		0			0
$35$	−2.44949	−	1.41421i	−0.414039	−	0.239046i
$36$	−0.548188	−	2.94949i	−0.0913647	−	0.491582i
$37$	−0.366025	+	1.36603i	−0.0601742	+	0.224573i	−0.989464	−	0.144778i	$-0.953753\pi$
$37$	−0.366025	+	1.36603i	−0.0601742	+	0.224573i	0.929290	+	0.369351i	$0.120420\pi$
$38$	−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	$-0.966583\pi$
$41$	−0.517638	+	1.93185i	−0.0808415	+	0.301705i	0.913653	+	0.406496i	$0.133249\pi$
$42$	2.22474	+	1.02494i	0.343286	+	0.158152i
$43$	5.19615	+	3.00000i	0.792406	+	0.457496i	0.840809	−	0.541332i	$-0.182080\pi$
$43$	5.19615	+	3.00000i	0.792406	+	0.457496i	−0.0484030	+	0.998828i	$0.515413\pi$
$44$	2.82843	+	2.82843i	0.426401	+	0.426401i
$45$	−0.467750	+	5.98174i	−0.0697281	+	0.891705i
$46$	8.19615	−	2.19615i	1.20846	−	0.323805i
$47$	−2.82843	+	2.82843i	−0.412568	+	0.412568i	−0.882632	−	0.470064i	$-0.844231\pi$
$47$	−2.82843	+	2.82843i	−0.412568	+	0.412568i	0.470064	+	0.882632i	$0.344231\pi$
$48$	1.72474	−	0.158919i	0.248945	−	0.0229379i
$49$	−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	$-0.127012\pi$
$54$	−0.0719302	−	5.19565i	−0.00978846	−	0.707039i
$55$	−4.00000	−	6.92820i	−0.539360	−	0.934199i
$56$	2.12132	−	3.67423i	0.283473	−	0.490990i
$57$	2.41421	+	0.414214i	0.319770	+	0.0548639i
$58$	−0.732051	−	2.73205i	−0.0961230	−	0.358736i
$59$	−1.03528	−	3.86370i	−0.134781	−	0.503011i	−0.999999	−	0.00161411i	$-0.999486\pi$
$59$	−1.03528	−	3.86370i	−0.134781	−	0.503011i	0.865217	−	0.501397i	$-0.167180\pi$
$60$	3.41421	+	0.585786i	0.440773	+	0.0756247i
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−3.53553	−	6.12372i	−0.449013	−	0.777714i
$63$	−3.49768	−	2.40130i	−0.440666	−	0.302536i
$64$		−	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	−0.183786	−	0.982966i	$-0.558835\pi$
$67$	−6.83013	−	1.83013i	−0.834433	−	0.223586i	−0.650647	+	0.759381i	$0.725502\pi$
$68$		0			0
$69$	−14.6349	+	1.34847i	−1.76184	+	0.162337i
$70$	−2.00000	+	2.00000i	−0.239046	+	0.239046i
$71$	−3.86370	+	1.03528i	−0.458537	+	0.122865i	−0.480691	−	0.876890i	$-0.659614\pi$
$71$	−3.86370	+	1.03528i	−0.458537	+	0.122865i	0.0221541	+	0.999755i	$0.492948\pi$
$72$	−8.97261	−	0.701625i	−1.05743	−	0.0826873i
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	0.646160	−	0.763202i	$-0.276374\pi$
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	−0.763202	+	0.646160i	$0.776374\pi$
$74$	1.22474	+	0.707107i	0.142374	+	0.0821995i
$75$	1.57313	+	0.724745i	0.181650	+	0.0836863i
$76$	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
$81$	−1.39898	+	8.89060i	−0.155442	+	0.987845i
$82$	1.73205	+	1.00000i	0.191273	+	0.110432i
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	0.324846	−	0.945767i	$-0.394687\pi$
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	−0.945767	+	0.324846i	$0.894687\pi$
$84$	−1.56583	+	1.88366i	−0.170846	+	0.205525i
$85$		0			0
$86$	4.24264	−	4.24264i	0.457496	−	0.457496i
$87$	0.449490	+	4.87832i	0.0481904	+	0.523010i
$88$	10.3923	−	6.00000i	1.10782	−	0.639602i
$89$	−13.5230	−	3.62347i	−1.43343	−	0.384087i	−0.543203	−	0.839601i	$-0.682789\pi$
$89$	−13.5230	−	3.62347i	−1.43343	−	0.384087i	−0.890228	+	0.455515i	$0.849455\pi$
$90$	5.65685	+	2.00000i	0.596285	+	0.210819i
$91$		0			0
$92$			8.48528i			0.884652i
$93$	4.24194	+	11.4894i	0.439868	+	1.19139i
$94$	2.00000	+	3.46410i	0.206284	+	0.357295i
$95$	−1.41421	+	2.44949i	−0.145095	+	0.251312i
$96$	−1.46447	+	8.53553i	−0.149466	+	0.871154i
$97$	−2.56218	−	9.56218i	−0.260150	−	0.970892i	−0.965153	−	0.261688i	$-0.915721\pi$
$97$	−2.56218	−	9.56218i	−0.260150	−	0.970892i	0.705003	−	0.709204i	$-0.250946\pi$
$98$	1.29410	+	4.82963i	0.130723	+	0.487866i
$99$	−5.17157	−	10.8284i	−0.519763	−	1.08830i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−4.24264	−	7.34847i	−0.422159	−	0.731200i	0.573992	−	0.818861i	$-0.305394\pi$
$101$	−4.24264	−	7.34847i	−0.422159	−	0.731200i	−0.996150	+	0.0876610i	$0.972061\pi$
$102$		0			0
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$		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	$-0.754826\pi$
$107$	−4.89898	+	2.82843i	−0.473602	+	0.273434i	0.244144	+	0.969739i	$0.421493\pi$
$108$	5.03723	+	1.27526i	0.484708	+	0.122711i
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	−0.753374	−	0.657592i	$-0.771575\pi$
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	0.657592	+	0.753374i	$0.271575\pi$
$110$	−7.72741	+	2.07055i	−0.736779	+	0.197419i
$111$	−1.88366	−	1.56583i	−0.178789	−	0.148622i
$112$	−1.00000	−	1.00000i	−0.0944911	−	0.0944911i
$113$	12.2474	+	7.07107i	1.15214	+	0.665190i	0.949409	−	0.314044i	$-0.101684\pi$
$113$	12.2474	+	7.07107i	1.15214	+	0.665190i	0.202735	+	0.979234i	$0.435017\pi$
$114$	1.02494	−	2.22474i	0.0959948	−	0.208366i
$115$	4.39230	−	16.3923i	0.409585	−	1.52859i
$116$	2.82843			0.262613
$117$		0			0
$118$	−4.00000			−0.368230
$119$		0			0
$120$	4.34847	−	9.43879i	0.396959	−	0.861640i
$121$	4.33013	+	2.50000i	0.393648	+	0.227273i
$122$	5.65685	+	5.65685i	0.512148	+	0.512148i
$123$	−2.66390	−	2.21441i	−0.240196	−	0.199667i
$124$	6.83013	−	1.83013i	0.613364	−	0.164350i
$125$	−8.48528	+	8.48528i	−0.758947	+	0.758947i
$126$	−3.22474	+	2.75699i	−0.287283	+	0.245613i
$127$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$127$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$128$	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	$0.835446\pi$
$132$	−6.49938	+	2.39960i	−0.565698	+	0.208859i
$133$	−1.00000	−	1.73205i	−0.0867110	−	0.150188i
$134$	−3.53553	+	6.12372i	−0.305424	+	0.529009i
$135$	−9.07107	−	5.07107i	−0.780713	−	0.436448i
$136$		0			0
$137$	3.62347	+	13.5230i	0.309574	+	1.15534i	0.928936	+	0.370240i	$0.120724\pi$
$137$	3.62347	+	13.5230i	0.309574	+	1.15534i	−0.619363	+	0.785105i	$0.712609\pi$
$138$	−2.48528	+	14.4853i	−0.211561	+	1.23307i
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	−1.41421	−	2.44949i	−0.119523	−	0.207020i
$141$	−2.39960	−	6.49938i	−0.202083	−	0.547346i
$142$			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
$147$	−0.794593	−	8.62372i	−0.0655369	−	0.711273i
$148$	−1.00000	+	1.00000i	−0.0821995	+	0.0821995i
$149$	1.93185	−	0.517638i	0.158263	−	0.0424066i	−0.178817	−	0.983882i	$-0.557227\pi$
$149$	1.93185	−	0.517638i	0.158263	−	0.0424066i	0.337081	+	0.941476i	$0.390560\pi$
$150$	1.10721	−	1.33195i	0.0904030	−	0.108753i
$151$	−1.00000	−	1.00000i	−0.0813788	−	0.0813788i	0.665246	−	0.746625i	$-0.268327\pi$
$151$	−1.00000	−	1.00000i	−0.0813788	−	0.0813788i	−0.746625	+	0.665246i	$0.768327\pi$
$152$	−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
$159$	8.89898	+	4.09978i	0.705735	+	0.325133i
$160$	−8.66025	−	5.00000i	−0.684653	−	0.395285i
$161$	8.48528	+	8.48528i	0.668734	+	0.668734i
$162$	8.22558	+	3.65237i	0.646263	+	0.286957i
$163$	1.36603	−	0.366025i	0.106995	−	0.0286693i	−0.204924	−	0.978778i	$-0.565695\pi$
$163$	1.36603	−	0.366025i	0.106995	−	0.0286693i	0.311919	+	0.950109i	$0.399028\pi$
$164$	−1.41421	+	1.41421i	−0.110432	+	0.110432i
$165$	13.7980	−	1.27135i	1.07417	−	0.0989744i
$166$	−6.92820	+	4.00000i	−0.537733	+	0.310460i
$167$	3.86370	+	1.03528i	0.298982	+	0.0801121i	0.405192	−	0.914232i	$-0.367205\pi$
$167$	3.86370	+	1.03528i	0.298982	+	0.0801121i	−0.106209	+	0.994344i	$0.533871\pi$
$168$	4.24264	+	6.00000i	0.327327	+	0.462910i
$169$		0			0
$170$		0			0
$171$	−2.40130	+	3.49768i	−0.183632	+	0.267474i
$172$	3.00000	+	5.19615i	0.228748	+	0.396203i
$173$	−4.24264	+	7.34847i	−0.322562	+	0.558694i	−0.981016	−	0.193927i	$-0.937877\pi$
$173$	−4.24264	+	7.34847i	−0.322562	+	0.558694i	0.658454	+	0.752621i	$0.271211\pi$
$174$	4.82843	+	0.828427i	0.366042	+	0.0628029i
$175$	−0.366025	−	1.36603i	−0.0276689	−	0.103262i
$176$	−1.03528	−	3.86370i	−0.0780369	−	0.291238i
$177$	6.82843	+	1.17157i	0.513256	+	0.0880608i
$178$	−7.00000	+	12.1244i	−0.524672	+	0.908759i
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	−3.39595	+	4.94646i	−0.253119	+	0.368688i
$181$		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
$186$	12.1958	−	1.12372i	0.894239	−	0.0823955i
$187$		0			0
$188$	−3.86370	+	1.03528i	−0.281790	+	0.0755053i
$189$	6.31249	−	3.76198i	0.459166	−	0.273644i
$190$	2.00000	+	2.00000i	0.145095	+	0.145095i
$191$	−2.44949	−	1.41421i	−0.177239	−	0.102329i	0.408756	−	0.912644i	$-0.365963\pi$
$191$	−2.44949	−	1.41421i	−0.177239	−	0.102329i	−0.585995	+	0.810315i	$0.699296\pi$
$192$	11.0119	+	5.07321i	0.794717	+	0.366128i
$193$	−6.95448	+	25.9545i	−0.500595	+	1.86824i	−0.00447566	+	0.999990i	$0.501425\pi$
$193$	−6.95448	+	25.9545i	−0.500595	+	1.86824i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	−9.89949			−0.710742
$195$		0			0
$196$	−5.00000			−0.357143
$197$	5.69402	−	21.2504i	0.405682	−	1.51403i	−0.397112	−	0.917770i	$-0.629988\pi$
$197$	5.69402	−	21.2504i	0.405682	−	1.51403i	0.802794	−	0.596256i	$-0.203346\pi$
$198$	−11.7980	+	2.19275i	−0.838444	+	0.155832i
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	−2.12132	−	2.12132i	−0.150000	−	0.150000i
$201$	7.82913	−	9.41832i	0.552224	−	0.664317i
$202$	−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
$210$	−1.69677	−	4.59575i	−0.117089	−	0.317137i
$211$	−7.00000	−	12.1244i	−0.481900	−	0.834675i	0.517884	−	0.855451i	$-0.326720\pi$
$211$	−7.00000	−	12.1244i	−0.481900	−	0.834675i	−0.999784	+	0.0207756i	$0.993386\pi$
$212$	2.82843	−	4.89898i	0.194257	−	0.336463i
$213$	1.17157	−	6.82843i	0.0802749	−	0.467876i
$214$	1.46410	+	5.46410i	0.100084	+	0.373518i
$215$	−3.10583	−	11.5911i	−0.211816	−	0.790507i
$216$	7.60660	−	13.6066i	0.517564	−	0.925812i
$217$	5.00000	−	8.66025i	0.339422	−	0.587896i
$218$	0.707107	+	1.22474i	0.0478913	+	0.0829502i
$219$	2.29788	−	0.848387i	0.155276	−	0.0573287i
$220$		−	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	−0.282179	−	0.959362i	$-0.591057\pi$
$223$	−15.0263	−	4.02628i	−1.00623	−	0.269620i	−0.724055	+	0.689742i	$0.757724\pi$
$224$	6.12372	−	3.53553i	0.409159	−	0.236228i
$225$	−2.28024	+	1.94949i	−0.152016	+	0.129966i
$226$	10.0000	−	10.0000i	0.665190	−	0.665190i
$227$	7.72741	−	2.07055i	0.512886	−	0.137427i	0.00691198	−	0.999976i	$-0.497800\pi$
$227$	7.72741	−	2.07055i	0.512886	−	0.137427i	0.505974	+	0.862549i	$0.331133\pi$
$228$	1.88366	+	1.56583i	0.124749	+	0.103699i
$229$	−1.00000	−	1.00000i	−0.0660819	−	0.0660819i	0.673293	−	0.739375i	$-0.264879\pi$
$229$	−1.00000	−	1.00000i	−0.0660819	−	0.0660819i	−0.739375	+	0.673293i	$0.764879\pi$
$230$	−14.6969	−	8.48528i	−0.969087	−	0.559503i
$231$	−4.09978	+	8.89898i	−0.269745	+	0.585510i
$232$	2.19615	−	8.19615i	0.144184	−	0.538104i
$233$	25.4558			1.66767			0.833834	−	0.552015i	$-0.186141\pi$
$233$	25.4558			1.66767			0.833834	+	0.552015i	$0.186141\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$	1.03528	−	3.86370i	0.0673907	−	0.251506i
$237$	7.24745	−	15.7313i	0.470772	−	1.02186i
$238$		0			0
$239$	−14.1421	−	14.1421i	−0.914779	−	0.914779i	0.0818647	−	0.996643i	$-0.473912\pi$
$239$	−14.1421	−	14.1421i	−0.914779	−	0.914779i	−0.996643	+	0.0818647i	$0.973912\pi$
$240$	−2.66390	−	2.21441i	−0.171954	−	0.142940i
$241$	−23.2224	+	6.22243i	−1.49589	+	0.400822i	−0.911721	−	0.410811i	$-0.865246\pi$
$241$	−23.2224	+	6.22243i	−1.49589	+	0.400822i	−0.584168	+	0.811633i	$0.698579\pi$
$242$	3.53553	−	3.53553i	0.227273	−	0.227273i
$243$	−12.9722	−	8.64420i	−0.832167	−	0.554526i
$244$	−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
$249$	12.9988	−	4.79920i	0.823763	−	0.304137i
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	12.7279	−	22.0454i	0.803379	−	1.39149i	−0.114000	−	0.993481i	$-0.536367\pi$
$251$	12.7279	−	22.0454i	0.803379	−	1.39149i	0.917380	−	0.398013i	$-0.130300\pi$
$252$	−1.82843	−	3.82843i	−0.115180	−	0.241168i
$253$	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	$-0.0814107\pi$
$257$	4.24264	+	7.34847i	0.264649	+	0.458385i	−0.702823	+	0.711365i	$0.748077\pi$
$258$	3.59940	+	9.74907i	0.224089	+	0.606950i
$259$			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	$-0.912430\pi$
$263$	−19.5959	+	11.3137i	−1.20834	+	0.697633i	−0.245940	+	0.969285i	$0.579097\pi$
$264$	1.90702	+	20.6969i	0.117369	+	1.27381i
$265$	−8.00000	+	8.00000i	−0.491436	+	0.491436i
$266$	−1.93185	+	0.517638i	−0.118449	+	0.0317384i
$267$	15.5009	−	18.6473i	0.948639	−	1.14120i
$268$	−5.00000	−	5.00000i	−0.305424	−	0.305424i
$269$	−17.1464	−	9.89949i	−1.04544	−	0.603583i	−0.124068	−	0.992274i	$-0.539594\pi$
$269$	−17.1464	−	9.89949i	−1.04544	−	0.603583i	−0.921368	+	0.388691i	$0.872927\pi$
$270$	−7.24604	+	7.44949i	−0.440980	+	0.453362i
$271$	−6.95448	+	25.9545i	−0.422455	+	1.57662i	0.346964	+	0.937878i	$0.387212\pi$
$271$	−6.95448	+	25.9545i	−0.422455	+	1.57662i	−0.769419	+	0.638744i	$0.779454\pi$
$272$		0			0
$273$		0			0
$274$	14.0000			0.845771
$275$	1.03528	−	3.86370i	0.0624295	−	0.232990i
$276$	−13.3485	−	6.14966i	−0.803483	−	0.370166i
$277$	−10.3923	−	6.00000i	−0.624413	−	0.360505i	0.154172	−	0.988044i	$-0.450729\pi$
$277$	−10.3923	−	6.00000i	−0.624413	−	0.360505i	−0.778585	+	0.627539i	$0.784062\pi$
$278$	−2.82843	−	2.82843i	−0.169638	−	0.169638i
$279$	−21.1486	−	1.65375i	−1.26614	−	0.0990072i
$280$	−8.19615	+	2.19615i	−0.489814	+	0.131245i
$281$	9.89949	−	9.89949i	0.590554	−	0.590554i	−0.347227	−	0.937781i	$-0.612877\pi$
$281$	9.89949	−	9.89949i	0.590554	−	0.590554i	0.937781	+	0.347227i	$0.112877\pi$
$282$	−6.89898	+	0.635674i	−0.410828	+	0.0378539i
$283$	−10.3923	+	6.00000i	−0.617758	+	0.356663i	−0.775996	−	0.630738i	$-0.782752\pi$
$283$	−10.3923	+	6.00000i	−0.617758	+	0.356663i	0.158237	+	0.987401i	$0.449419\pi$
$284$	−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
$288$	−12.3662	−	8.48988i	−0.728683	−	0.500271i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−2.82843	+	4.89898i	−0.166091	+	0.287678i
$291$	16.8995	+	2.89949i	0.990666	+	0.169971i
$292$	−0.366025	−	1.36603i	−0.0214200	−	0.0799406i
$293$	3.62347	+	13.5230i	0.211685	+	0.790020i	0.987307	+	0.158822i	$0.0507697\pi$
$293$	3.62347	+	13.5230i	0.211685	+	0.790020i	−0.775622	+	0.631198i	$0.782564\pi$
$294$	−8.53553	−	1.46447i	−0.497802	−	0.0854094i
$295$	−4.00000	+	6.92820i	−0.232889	+	0.403376i
$296$	2.12132	+	3.67423i	0.123299	+	0.213561i
$297$	20.7826	−	0.287721i	1.20593	−	0.0166952i
$298$		−	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
$303$	14.6349	−	1.34847i	0.840756	−	0.0774675i
$304$	−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	0.999570	−	0.0293286i	$-0.00933691\pi$
$307$	17.0000	+	17.0000i	0.970241	+	0.970241i	−0.0293286	+	0.999570i	$0.509337\pi$
$308$	4.89898	+	2.82843i	0.279145	+	0.161165i
$309$	−9.43879	−	4.34847i	−0.536954	−	0.247376i
$310$	−3.66025	+	13.6603i	−0.207888	+	0.775850i
$311$	−8.48528			−0.481156			−0.240578	−	0.970630i	$-0.577337\pi$
$311$	−8.48528			−0.481156			−0.240578	+	0.970630i	$0.577337\pi$
$312$		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
$315$	1.55051	+	8.34242i	0.0873614	+	0.470042i
$316$	−8.66025	−	5.00000i	−0.487177	−	0.281272i
$317$	7.07107	+	7.07107i	0.397151	+	0.397151i	0.877227	−	0.480076i	$-0.159391\pi$
$317$	7.07107	+	7.07107i	0.397151	+	0.397151i	−0.480076	+	0.877227i	$0.659391\pi$
$318$	6.26330	−	7.53465i	0.351229	−	0.422522i
$319$	10.9282	−	2.92820i	0.611862	−	0.163948i
$320$	−9.89949	+	9.89949i	−0.553399	+	0.553399i
$321$	−0.898979	−	9.75663i	−0.0501761	−	0.544562i
$322$	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
$327$	−0.848387	−	2.29788i	−0.0469159	−	0.127073i
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	−2.82843	+	4.89898i	−0.155936	+	0.270089i
$330$	2.34315	−	13.6569i	0.128986	−	0.751785i
$331$	−2.56218	−	9.56218i	−0.140830	−	0.525585i	−0.999906	−	0.0137361i	$-0.995628\pi$
$331$	−2.56218	−	9.56218i	−0.140830	−	0.525585i	0.859076	−	0.511849i	$-0.171039\pi$
$332$	−2.07055	−	7.72741i	−0.113636	−	0.424097i
$333$	3.82843	−	1.82843i	0.209797	−	0.100197i
$334$	2.00000	−	3.46410i	0.109435	−	0.189547i
$335$	7.07107	+	12.2474i	0.386334	+	0.669150i
$336$	2.29788	−	0.848387i	0.125359	−	0.0462833i
$337$			6.00000i			0.326841i	0.986557	+	0.163420i	$0.0522527\pi$
$337$			6.00000i			0.326841i	−0.986557	+	0.163420i	$0.947747\pi$
$338$		0			0
$339$	−20.0000	+	14.1421i	−1.08625	+	0.768095i
$340$		0			0
$341$	24.4949	−	14.1421i	1.32647	−	0.765840i
$342$	2.75699	+	3.22474i	0.149081	+	0.174374i
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	17.3867	−	4.65874i	0.937426	−	0.251183i
$345$	22.6040	+	18.7899i	1.21696	+	1.01162i
$346$	6.00000	+	6.00000i	0.322562	+	0.322562i
$347$	12.2474	+	7.07107i	0.657477	+	0.379595i	0.791315	−	0.611408i	$-0.209397\pi$
$347$	12.2474	+	7.07107i	0.657477	+	0.379595i	−0.133838	+	0.991003i	$0.542730\pi$
$348$	−2.04989	+	4.44949i	−0.109886	+	0.238518i
$349$	6.22243	−	23.2224i	0.333079	−	1.24307i	−0.572857	−	0.819655i	$-0.694165\pi$
$349$	6.22243	−	23.2224i	0.333079	−	1.24307i	0.905937	−	0.423413i	$-0.139168\pi$
$350$	−1.41421			−0.0755929
$351$		0			0
$352$	20.0000			1.06600
$353$	−6.72930	+	25.1141i	−0.358164	+	1.33669i	0.518291	+	0.855204i	$0.326568\pi$
$353$	−6.72930	+	25.1141i	−0.358164	+	1.33669i	−0.876455	+	0.481483i	$0.840098\pi$
$354$	2.89898	−	6.29253i	0.154079	−	0.334444i
$355$	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	$-0.783662\pi$
$359$	−2.82843	+	2.82843i	−0.149279	+	0.149279i	0.628517	+	0.777796i	$0.283662\pi$
$360$	11.6969	+	13.6814i	0.616483	+	0.721075i
$361$	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
$366$	−12.9988	+	4.79920i	−0.679456	+	0.250858i
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	4.24264	−	7.34847i	0.221163	−	0.383065i
$369$	5.41421	−	2.58579i	0.281853	−	0.134611i
$370$	−0.732051	−	2.73205i	−0.0380575	−	0.142033i
$371$	−2.07055	−	7.72741i	−0.107498	−	0.401187i
$372$	−2.07107	+	12.0711i	−0.107380	+	0.625856i
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$		0			0
$375$	−7.19881	−	19.4981i	−0.371745	−	1.00688i
$376$			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	0.853904	−	0.520430i	$-0.174228\pi$
$379$	25.9545	+	6.95448i	1.33319	+	0.357228i	0.479288	+	0.877658i	$0.340895\pi$
$380$	−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	$-0.717379\pi$
$383$	−15.4548	+	4.14110i	−0.789704	+	0.211601i	−0.158645	+	0.987336i	$0.550713\pi$
$384$	−3.32162	+	3.99585i	−0.169506	+	0.203913i
$385$	−8.00000	−	8.00000i	−0.407718	−	0.407718i
$386$	23.2702	+	13.4350i	1.18442	+	0.683825i
$387$	−3.28913	−	17.6969i	−0.167196	−	0.899586i
$388$	2.56218	−	9.56218i	0.130075	−	0.485446i
$389$	−16.9706			−0.860442			−0.430221	−	0.902724i	$-0.641564\pi$
$389$	−16.9706			−0.860442			−0.430221	+	0.902724i	$0.641564\pi$
$390$		0			0
$391$		0			0
$392$	−3.88229	+	14.4889i	−0.196085	+	0.731799i
$393$	−17.7980	−	8.19955i	−0.897788	−	0.413613i
$394$	−19.0526	−	11.0000i	−0.959854	−	0.554172i
$395$	14.1421	+	14.1421i	0.711568	+	0.711568i
$396$	0.935500	−	11.9635i	0.0470106	−	0.601187i
$397$	−23.2224	+	6.22243i	−1.16550	+	0.312295i	−0.789161	−	0.614187i	$-0.789484\pi$
$397$	−23.2224	+	6.22243i	−1.16550	+	0.312295i	−0.376340	+	0.926482i	$0.622817\pi$
$398$		0			0
$399$	3.44949	−	0.317837i	0.172690	−	0.0159118i
$400$	−0.866025	+	0.500000i	−0.0433013	+	0.0250000i
$401$	21.2504	+	5.69402i	1.06119	+	0.284346i	0.746870	−	0.664970i	$-0.231556\pi$
$401$	21.2504	+	5.69402i	1.06119	+	0.284346i	0.314323	+	0.949316i	$0.398223\pi$
$402$	−7.07107	−	10.0000i	−0.352673	−	0.498755i
$403$		0			0
$404$		−	8.48528i		−	0.422159i
$405$	14.5517	−	10.5948i	0.723078	−	0.526458i
$406$	−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	0.782274	+	0.622935i	$0.214060\pi$
$409$	8.41858	+	31.4186i	0.416272	+	1.55355i	−0.366002	+	0.930614i	$0.619274\pi$
$410$	−1.03528	−	3.86370i	−0.0511286	−	0.190815i
$411$	−23.8995	−	4.10051i	−1.17888	−	0.202263i
$412$	−3.00000	+	5.19615i	−0.147799	+	0.255996i
$413$	−2.82843	−	4.89898i	−0.139178	−	0.241063i
$414$	−20.9861	−	14.4078i	−1.03141	−	0.708105i
$415$			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	$-0.577540\pi$
$419$	9.79796	−	5.65685i	0.478662	−	0.276355i	0.719859	+	0.694121i	$0.244207\pi$
$420$	4.87832	−	0.449490i	0.238037	−	0.0219329i
$421$	−25.0000	+	25.0000i	−1.21843	+	1.21843i	−0.250242	+	0.968183i	$0.580510\pi$
$421$	−25.0000	+	25.0000i	−1.21843	+	1.21843i	−0.968183	+	0.250242i	$0.919490\pi$
$422$	−13.5230	+	3.62347i	−0.658287	+	0.176388i
$423$	11.9635	+	0.935500i	0.581684	+	0.0454856i
$424$	−12.0000	−	12.0000i	−0.582772	−	0.582772i
$425$		0			0
$426$	−6.29253	−	2.89898i	−0.304874	−	0.140456i
$427$	−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	0.416024	+	0.909353i	$0.363423\pi$
$431$	−8.28221	+	30.9096i	−0.398940	+	1.48886i	−0.814964	+	0.579511i	$0.803244\pi$
$432$	−3.72474	−	3.62302i	−0.179207	−	0.174313i
$433$	15.5885	+	9.00000i	0.749133	+	0.432512i	0.825381	−	0.564577i	$-0.190961\pi$
$433$	15.5885	+	9.00000i	0.749133	+	0.432512i	−0.0762473	+	0.997089i	$0.524294\pi$
$434$	−7.07107	−	7.07107i	−0.339422	−	0.339422i
$435$	6.26330	−	7.53465i	0.300302	−	0.361259i
$436$	−1.36603	+	0.366025i	−0.0654208	+	0.0175294i
$437$	8.48528	−	8.48528i	0.405906	−	0.405906i
$438$	−0.224745	−	2.43916i	−0.0107387	−	0.116547i
$439$	25.9808	−	15.0000i	1.23999	−	0.715911i	0.270901	−	0.962607i	$-0.412678\pi$
$439$	25.9808	−	15.0000i	1.23999	−	0.715911i	0.969093	+	0.246696i	$0.0793450\pi$
$440$	−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	$0.765473\pi$
$444$	−0.848387	−	2.29788i	−0.0402627	−	0.109052i
$445$	14.0000	+	24.2487i	0.663664	+	1.14950i
$446$	−7.77817	+	13.4722i	−0.368307	+	0.637927i
$447$	−0.585786	+	3.41421i	−0.0277067	+	0.161487i
$448$	−2.56218	−	9.56218i	−0.121052	−	0.451770i
$449$	−5.69402	−	21.2504i	−0.268717	−	1.00287i	−0.959936	−	0.280221i	$-0.909592\pi$
$449$	−5.69402	−	21.2504i	−0.268717	−	1.00287i	0.691218	−	0.722646i	$-0.257074\pi$
$450$	1.29289	+	2.70711i	0.0609476	+	0.127614i
$451$	−4.00000	+	6.92820i	−0.188353	+	0.326236i
$452$	7.07107	+	12.2474i	0.332595	+	0.576072i
$453$	2.29788	−	0.848387i	0.107964	−	0.0398607i
$454$		−	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	−0.853405	−	0.521249i	$-0.825466\pi$
$457$	−39.6147	−	10.6147i	−1.85310	−	0.496536i	−0.999695	+	0.0247126i	$0.992133\pi$
$458$	−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	$-0.658146\pi$
$461$	−9.65926	+	2.58819i	−0.449877	+	0.120544i	0.0267651	+	0.999642i	$0.491479\pi$
$462$	7.53465	+	6.26330i	0.350544	+	0.291395i
$463$	17.0000	+	17.0000i	0.790057	+	0.790057i	0.981503	−	0.191446i	$-0.0613177\pi$
$463$	17.0000	+	17.0000i	0.790057	+	0.790057i	−0.191446	+	0.981503i	$0.561318\pi$
$464$	−2.44949	−	1.41421i	−0.113715	−	0.0656532i
$465$	10.2494	−	22.2474i	0.475306	−	1.03170i
$466$	6.58846	−	24.5885i	0.305204	−	1.13904i
$467$	25.4558			1.17796			0.588978	−	0.808149i	$-0.299530\pi$
$467$	25.4558			1.17796			0.588978	+	0.808149i	$0.299530\pi$
$468$		0			0
$469$	−10.0000			−0.461757
$470$	2.07055	−	7.72741i	0.0955075	−	0.356439i
$471$	−10.1464	+	22.0239i	−0.467523	+	1.01481i
$472$	−10.3923	−	6.00000i	−0.478345	−	0.276172i
$473$	16.9706	+	16.9706i	0.780307	+	0.780307i
$474$	−13.3195	−	11.0721i	−0.611785	−	0.508557i
$475$	−1.36603	+	0.366025i	−0.0626775	+	0.0167944i
$476$		0			0
$477$	−12.8990	+	11.0280i	−0.590604	+	0.504936i
$478$	−17.3205	+	10.0000i	−0.792222	+	0.457389i
$479$	−30.9096	−	8.28221i	−1.41230	−	0.378424i	−0.529552	−	0.848277i	$-0.677640\pi$
$479$	−30.9096	−	8.28221i	−1.41230	−	0.378424i	−0.882744	+	0.469853i	$0.844307\pi$
$480$	14.1421	−	10.0000i	0.645497	−	0.456435i
$481$		0			0
$482$			24.0416i			1.09507i
$483$	−19.4981	+	7.19881i	−0.887196	+	0.327557i
$484$	2.50000	+	4.33013i	0.113636	+	0.196824i
$485$	−9.89949	+	17.1464i	−0.449513	+	0.778579i
$486$	−11.7071	+	10.2929i	−0.531045	+	0.466895i
$487$	−6.95448	−	25.9545i	−0.315138	−	1.17611i	−0.923861	−	0.382727i	$-0.874985\pi$
$487$	−6.95448	−	25.9545i	−0.315138	−	1.17611i	0.608724	−	0.793382i	$-0.291682\pi$
$488$	6.21166	+	23.1822i	0.281189	+	1.04941i
$489$	−0.414214	+	2.41421i	−0.0187314	+	0.109175i
$490$	5.00000	−	8.66025i	0.225877	−	0.391230i
$491$	−21.2132	−	36.7423i	−0.957338	−	1.65816i	−0.728924	−	0.684595i	$-0.759979\pi$
$491$	−21.2132	−	36.7423i	−0.957338	−	1.65816i	−0.228415	−	0.973564i	$-0.573354\pi$
$492$	−1.19980	−	3.24969i	−0.0540912	−	0.146507i
$493$		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
$498$	−1.27135	−	13.7980i	−0.0569705	−	0.618301i
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.0300737	−	0.999548i	$-0.490426\pi$
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.999548	−	0.0300737i	$-0.00957421\pi$
$500$	−11.5911	+	3.10583i	−0.518370	+	0.138897i
$501$	−4.42883	+	5.32780i	−0.197865	+	0.238029i
$502$	−18.0000	−	18.0000i	−0.803379	−	0.803379i
$503$	4.89898	+	2.82843i	0.218435	+	0.126113i	0.605225	−	0.796054i	$-0.293083\pi$
$503$	4.89898	+	2.82843i	0.218435	+	0.126113i	−0.386791	+	0.922168i	$0.626416\pi$
$504$	−12.5136	+	2.32577i	−0.557401	+	0.103598i
$505$	−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	−0.440010	−	0.897993i	$-0.645025\pi$
$509$	8.79985	−	32.8415i	0.390046	−	1.45567i	0.830056	−	0.557680i	$-0.188308\pi$
$510$		0			0
$511$	−1.73205	−	1.00000i	−0.0766214	−	0.0442374i
$512$	−7.77817	−	7.77817i	−0.343750	−	0.343750i
$513$	−3.76198	−	6.31249i	−0.166095	−	0.278703i
$514$	8.19615	−	2.19615i	0.361517	−	0.0968681i
$515$	8.48528	−	8.48528i	0.373906	−	0.373906i
$516$	−10.3485	+	0.953512i	−0.455566	+	0.0419760i
$517$	−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	$-0.238688\pi$
$522$	−4.80260	+	6.99536i	−0.210204	+	0.306178i
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$	−5.65685	+	9.79796i	−0.247121	+	0.428026i
$525$	2.41421	+	0.414214i	0.105365	+	0.0180778i
$526$	5.85641	+	21.8564i	0.255351	+	0.952985i
$527$		0			0
$528$	6.82843	+	1.17157i	0.297169	+	0.0509862i
$529$	−24.5000	+	42.4352i	−1.06522	+	1.84501i
$530$	5.65685	+	9.79796i	0.245718	+	0.425596i
$531$	−6.79191	+	9.89293i	−0.294744	+	0.429316i
$532$		−	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
$540$	−5.32024	−	8.92721i	−0.228947	−	0.384166i
$541$	−1.00000	−	1.00000i	−0.0429934	−	0.0429934i	0.685283	−	0.728277i	$-0.259678\pi$
$541$	−1.00000	−	1.00000i	−0.0429934	−	0.0429934i	−0.728277	+	0.685283i	$0.759678\pi$
$542$	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
$549$	23.5959	−	4.38551i	1.00705	−	0.187169i
$550$	−3.46410	−	2.00000i	−0.147710	−	0.0852803i
$551$	−2.82843	−	2.82843i	−0.120495	−	0.120495i
$552$	−28.1849	+	33.9059i	−1.19963	+	1.44313i
$553$	−13.6603	+	3.66025i	−0.580893	+	0.155650i
$554$	−8.48528	+	8.48528i	−0.360505	+	0.360505i
$555$	0.449490	+	4.87832i	0.0190798	+	0.207073i
$556$	3.46410	−	2.00000i	0.146911	−	0.0848189i
$557$	−13.5230	−	3.62347i	−0.572986	−	0.153531i	−0.0393204	−	0.999227i	$-0.512519\pi$
$557$	−13.5230	−	3.62347i	−0.572986	−	0.153531i	−0.533666	+	0.845695i	$0.679186\pi$
$558$	−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	−0.247649	−	0.968850i	$-0.579658\pi$
$563$	16.9706	−	29.3939i	0.715224	−	1.23880i	0.962873	−	0.269954i	$-0.0870086\pi$
$564$	1.17157	−	6.82843i	0.0493321	−	0.287529i
$565$	−7.32051	−	27.3205i	−0.307976	−	1.14938i
$566$	3.10583	+	11.5911i	0.130548	+	0.487211i
$567$	1.34315	+	12.6569i	0.0564068	+	0.531538i
$568$	−6.00000	+	10.3923i	−0.251754	+	0.436051i
$569$	−4.24264	−	7.34847i	−0.177861	−	0.308064i	0.763287	−	0.646060i	$-0.223584\pi$
$569$	−4.24264	−	7.34847i	−0.177861	−	0.308064i	−0.941148	+	0.337996i	$0.890251\pi$
$570$	−4.59575	+	1.69677i	−0.192495	+	0.0710701i
$571$		−	12.0000i		−	0.502184i	−0.967963	−	0.251092i	$-0.919210\pi$
$571$		−	12.0000i		−	0.502184i	0.967963	−	0.251092i	$-0.0807897\pi$
$572$		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
$576$	−15.9617	+	13.6464i	−0.665070	+	0.568601i
$577$	−1.00000	+	1.00000i	−0.0416305	+	0.0416305i	−0.727616	−	0.685985i	$-0.759372\pi$
$577$	−1.00000	+	1.00000i	−0.0416305	+	0.0416305i	0.685985	+	0.727616i	$0.259372\pi$
$578$	16.4207	−	4.39992i	0.683013	−	0.183013i
$579$	−35.7896	−	29.7507i	−1.48737	−	1.23640i
$580$	−4.00000	−	4.00000i	−0.166091	−	0.166091i
$581$	−9.79796	−	5.65685i	−0.406488	−	0.234686i
$582$	7.17461	−	15.5732i	0.297397	−	0.645530i
$583$	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	$-0.969461\pi$
$587$	−2.07055	+	7.72741i	−0.0854608	+	0.318944i	0.909940	+	0.414739i	$0.136127\pi$
$588$	3.62372	−	7.86566i	0.149440	−	0.324374i
$589$	−8.66025	−	5.00000i	−0.356840	−	0.206021i
$590$	5.65685	+	5.65685i	0.232889	+	0.232889i
$591$	29.3029	+	24.3585i	1.20536	+	1.00198i
$592$	1.36603	−	0.366025i	0.0561433	−	0.0150436i
$593$	9.89949	−	9.89949i	0.406524	−	0.406524i	−0.474001	−	0.880524i	$-0.657191\pi$
$593$	9.89949	−	9.89949i	0.406524	−	0.406524i	0.880524	+	0.474001i	$0.157191\pi$
$594$	5.10102	−	20.1489i	0.209297	−	0.826721i
$595$		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	$0.925757\pi$
$600$	4.87453	−	1.79970i	0.199002	−	0.0734725i
$601$	−4.00000	−	6.92820i	−0.163163	−	0.282607i	0.772838	−	0.634603i	$-0.218836\pi$
$601$	−4.00000	−	6.92820i	−0.163163	−	0.282607i	−0.936002	+	0.351996i	$0.885503\pi$
$602$	4.24264	−	7.34847i	0.172917	−	0.299501i
$603$	9.14214	+	19.1421i	0.372297	+	0.779528i
$604$	−0.366025	−	1.36603i	−0.0148934	−	0.0555828i
$605$	−2.58819	−	9.65926i	−0.105225	−	0.392705i
$606$	2.48528	−	14.4853i	0.100958	−	0.588424i
$607$	20.0000	−	34.6410i	0.811775	−	1.40604i	−0.0998457	−	0.995003i	$-0.531835\pi$
$607$	20.0000	−	34.6410i	0.811775	−	1.40604i	0.911621	−	0.411033i	$-0.134832\pi$
$608$	−3.53553	−	6.12372i	−0.143385	−	0.248350i
$609$	2.39960	+	6.49938i	0.0972368	+	0.263368i
$610$		−	16.0000i		−	0.647821i
$611$		0			0
$612$		0			0
$613$	1.36603	+	0.366025i	0.0551732	+	0.0147836i	0.286300	−	0.958140i	$-0.407575\pi$
$613$	1.36603	+	0.366025i	0.0551732	+	0.0147836i	−0.231127	+	0.972924i	$0.574241\pi$
$614$	20.8207	−	12.0208i	0.840254	−	0.485121i
$615$	0.635674	+	6.89898i	0.0256329	+	0.278194i
$616$	12.0000	−	12.0000i	0.483494	−	0.483494i
$617$	36.7052	−	9.83512i	1.47769	−	0.395947i	0.572133	−	0.820161i	$-0.306116\pi$
$617$	36.7052	−	9.83512i	1.47769	−	0.395947i	0.905562	+	0.424214i	$0.139449\pi$
$618$	−6.64324	+	7.99171i	−0.267230	+	0.321474i
$619$	−1.00000	−	1.00000i	−0.0401934	−	0.0401934i	0.686724	−	0.726918i	$-0.259048\pi$
$619$	−1.00000	−	1.00000i	−0.0401934	−	0.0401934i	−0.726918	+	0.686724i	$0.759048\pi$
$620$	−12.2474	−	7.07107i	−0.491869	−	0.283981i
$621$	31.6055	+	30.7423i	1.26829	+	1.23365i
$622$	−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
$627$	8.89898	+	4.09978i	0.355391	+	0.163729i
$628$	12.1244	+	7.00000i	0.483814	+	0.279330i
$629$		0			0
$630$	8.45946	+	0.661498i	0.337033	+	0.0263547i
$631$	25.9545	−	6.95448i	1.03323	−	0.276854i	0.297926	−	0.954589i	$-0.403705\pi$
$631$	25.9545	−	6.95448i	1.03323	−	0.276854i	0.735306	+	0.677735i	$0.237039\pi$
$632$	−21.2132	+	21.2132i	−0.843816	+	0.843816i
$633$	24.1464	−	2.22486i	0.959734	−	0.0884303i
$634$	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
$639$	9.89293	+	6.79191i	0.391358	+	0.268684i
$640$	−3.00000	−	5.19615i	−0.118585	−	0.205396i
$641$	8.48528	−	14.6969i	0.335148	−	0.580494i	−0.648365	−	0.761330i	$-0.724547\pi$
$641$	8.48528	−	14.6969i	0.335148	−	0.580494i	0.983513	+	0.180836i	$0.0578802\pi$
$642$	−9.65685	−	1.65685i	−0.381126	−	0.0653908i
$643$	1.83013	+	6.83013i	0.0721732	+	0.269354i	0.992577	−	0.121614i	$-0.0388070\pi$
$643$	1.83013	+	6.83013i	0.0721732	+	0.269354i	−0.920404	+	0.390968i	$0.872140\pi$
$644$	3.10583	+	11.5911i	0.122387	+	0.456754i
$645$	20.4853	+	3.51472i	0.806607	+	0.138392i
$646$		0			0
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$	15.8921	+	21.8275i	0.624302	+	0.857465i
$649$		−	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	$-0.755912\pi$
$653$	−12.2474	+	7.07107i	−0.479280	+	0.276712i	0.240837	+	0.970566i	$0.422578\pi$
$654$	−2.43916	+	0.224745i	−0.0953786	+	0.00878822i
$655$	16.0000	−	16.0000i	0.625172	−	0.625172i
$656$	1.93185	−	0.517638i	0.0754261	−	0.0202104i
$657$	−0.330749	+	4.22973i	−0.0129038	+	0.165017i
$658$	4.00000	+	4.00000i	0.155936	+	0.155936i
$659$	−2.44949	−	1.41421i	−0.0954186	−	0.0550899i	0.451531	−	0.892255i	$-0.350878\pi$
$659$	−2.44949	−	1.41421i	−0.0954186	−	0.0550899i	−0.546950	+	0.837165i	$0.684211\pi$
$660$	12.5851	+	5.79796i	0.489873	+	0.225685i
$661$	−0.366025	+	1.36603i	−0.0142367	+	0.0531322i	−0.972679	−	0.232155i	$-0.925422\pi$
$661$	−0.366025	+	1.36603i	−0.0142367	+	0.0531322i	0.958442	+	0.285287i	$0.0920890\pi$
$662$	−9.89949			−0.384755
$663$		0			0
$664$	−24.0000			−0.931381
$665$	−1.03528	+	3.86370i	−0.0401463	+	0.149828i
$666$	−0.775255	−	4.17121i	−0.0300405	−	0.161631i
$667$	20.7846	+	12.0000i	0.804783	+	0.464642i
$668$	2.82843	+	2.82843i	0.109435	+	0.109435i
$669$	17.2241	−	20.7203i	0.665922	−	0.801093i
$670$	13.6603	−	3.66025i	0.527742	−	0.141408i
$671$	−22.6274	+	22.6274i	−0.873522	+	0.873522i
$672$	1.12372	+	12.1958i	0.0433486	+	0.470463i
$673$	10.3923	−	6.00000i	0.400594	−	0.231283i	−0.286146	−	0.958186i	$-0.592374\pi$
$673$	10.3923	−	6.00000i	0.400594	−	0.231283i	0.686740	+	0.726903i	$0.259041\pi$
$674$	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	$-0.143188\pi$
$678$	8.48387	+	22.9788i	0.325821	+	0.882494i
$679$	−7.00000	−	12.1244i	−0.268635	−	0.465290i
$680$		0			0
$681$	−2.34315	+	13.6569i	−0.0897895	+	0.523332i
$682$	−7.32051	−	27.3205i	−0.280317	−	1.04616i
$683$	−1.03528	−	3.86370i	−0.0396137	−	0.147840i	0.943286	−	0.331980i	$-0.107717\pi$
$683$	−1.03528	−	3.86370i	−0.0396137	−	0.147840i	−0.982900	+	0.184140i	$0.941050\pi$
$684$	−3.82843	+	1.82843i	−0.146384	+	0.0699117i
$685$	14.0000	−	24.2487i	0.534913	−	0.926496i
$686$	8.48528	+	14.6969i	0.323970	+	0.561132i
$687$	2.29788	−	0.848387i	0.0876695	−	0.0323680i
$688$		−	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	−0.0385841	−	0.999255i	$-0.512285\pi$
$691$	−15.0263	−	4.02628i	−0.571627	−	0.153167i	−0.533042	+	0.846088i	$0.678951\pi$
$692$	−7.34847	+	4.24264i	−0.279347	+	0.161281i
$693$	−11.0280	−	12.8990i	−0.418918	−	0.489992i
$694$	10.0000	−	10.0000i	0.379595	−	0.379595i
$695$	−7.72741	+	2.07055i	−0.293117	+	0.0785405i
$696$	11.3020	+	9.39496i	0.428400	+	0.356115i
$697$		0			0
$698$	−20.8207	−	12.0208i	−0.788074	−	0.454995i
$699$	−18.4490	+	40.0454i	−0.697805	+	1.51466i
$700$	0.366025	−	1.36603i	0.0138345	−	0.0516309i
$701$	−50.9117			−1.92291			−0.961454	−	0.274966i	$-0.911333\pi$
$701$	−50.9117			−1.92291			−0.961454	+	0.274966i	$0.911333\pi$
$702$		0			0
$703$	2.00000			0.0754314
$704$	7.24693	−	27.0459i	0.273129	−	1.01933i
$705$	−5.79796	+	12.5851i	−0.218364	+	0.473981i
$706$	22.5167	+	13.0000i	0.847426	+	0.489261i
$707$	−8.48528	−	8.48528i	−0.319122	−	0.319122i
$708$	5.32780	+	4.42883i	0.200231	+	0.166445i
$709$	25.9545	−	6.95448i	0.974741	−	0.261181i	0.263913	−	0.964547i	$-0.414987\pi$
$709$	25.9545	−	6.95448i	0.974741	−	0.261181i	0.710828	+	0.703365i	$0.248320\pi$
$710$	5.65685	−	5.65685i	0.212298	−	0.212298i
$711$	19.4949	+	22.8024i	0.731116	+	0.855156i
$712$	−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
$717$	32.4969	−	11.9980i	1.21362	−	0.448074i
$718$	2.00000	+	3.46410i	0.0746393	+	0.129279i
$719$	−12.7279	+	22.0454i	−0.474671	+	0.822155i	−0.999579	−	0.0290041i	$-0.990766\pi$
$719$	−12.7279	+	22.0454i	−0.474671	+	0.822155i	0.524908	+	0.851159i	$0.324100\pi$
$720$	5.41421	−	2.58579i	0.201776	−	0.0963666i
$721$	2.19615	+	8.19615i	0.0817890	+	0.305241i
$722$	−4.39992	−	16.4207i	−0.163748	−	0.611117i
$723$	7.04163	−	41.0416i	0.261881	−	1.52635i
$724$		0			0
$725$	−1.41421	−	2.44949i	−0.0525226	−	0.0909718i
$726$	2.99950	+	8.12422i	0.111322	+	0.301518i
$727$			48.0000i			1.78022i	0.455744	+	0.890111i	$0.349373\pi$
$727$			48.0000i			1.78022i	−0.455744	+	0.890111i	$0.650627\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	2.73205	+	0.732051i	0.101118	+	0.0270944i
$731$		0			0
$732$	−1.27135	−	13.7980i	−0.0469904	−	0.509987i
$733$	5.00000	−	5.00000i	0.184679	−	0.184679i	−0.608712	−	0.793391i	$-0.708314\pi$
$733$	5.00000	−	5.00000i	0.184679	−	0.184679i	0.793391	+	0.608712i	$0.208314\pi$
$734$	−7.72741	+	2.07055i	−0.285224	+	0.0764255i
$735$	−11.0721	+	13.3195i	−0.408399	+	0.491298i
$736$	30.0000	+	30.0000i	1.10581	+	1.10581i
$737$	−24.4949	−	14.1421i	−0.902281	−	0.520932i
$738$	−1.09638	−	5.89898i	−0.0403582	−	0.217144i
$739$	−0.366025	+	1.36603i	−0.0134645	+	0.0502501i	−0.972331	−	0.233606i	$-0.924947\pi$
$739$	−0.366025	+	1.36603i	−0.0134645	+	0.0502501i	0.958867	+	0.283857i	$0.0916139\pi$
$740$	2.82843			0.103975
$741$		0			0
$742$	−8.00000			−0.293689
$743$	4.14110	−	15.4548i	0.151922	−	0.566982i	−0.847427	−	0.530912i	$-0.821849\pi$
$743$	4.14110	−	15.4548i	0.151922	−	0.566982i	0.999349	−	0.0360700i	$-0.0114839\pi$
$744$	33.3712	+	15.3742i	1.22345	+	0.563644i
$745$	−3.46410	−	2.00000i	−0.126915	−	0.0732743i
$746$	−2.82843	−	2.82843i	−0.103556	−	0.103556i
$747$	−1.87100	+	23.9270i	−0.0684563	+	0.875442i
$748$		0			0
$749$	−5.65685	+	5.65685i	−0.206697	+	0.206697i
$750$	−20.6969	+	1.90702i	−0.755745	+	0.0696347i
$751$	−25.9808	+	15.0000i	−0.948051	+	0.547358i	−0.892475	−	0.451097i	$-0.851033\pi$
$751$	−25.9808	+	15.0000i	−0.948051	+	0.547358i	−0.0555764	+	0.998454i	$0.517700\pi$
$752$	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
$756$	7.34777	−	0.101725i	0.267236	−	0.00369969i
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	0.973991	−	0.226587i	$-0.0727569\pi$
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	−0.683226	+	0.730207i	$0.739424\pi$
$758$	13.4350	−	23.2702i	0.487982	−	0.845210i
$759$	−57.9411	−	9.94113i	−2.10313	−	0.360840i
$760$	2.19615	+	8.19615i	0.0796628	+	0.297306i
$761$	12.9410	+	48.2963i	0.469109	+	1.75074i	0.642894	+	0.765955i	$0.277734\pi$
$761$	12.9410	+	48.2963i	0.469109	+	1.75074i	−0.173784	+	0.984784i	$0.555600\pi$
$762$		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	0.564376	−	0.825518i	$-0.309117\pi$
$769$	17.7583	+	4.75833i	0.640382	+	0.171590i	0.0760054	+	0.997107i	$0.475783\pi$
$770$	−9.79796	+	5.65685i	−0.353094	+	0.203859i
$771$	−14.6349	+	1.34847i	−0.527065	+	0.0485639i
$772$	−19.0000	+	19.0000i	−0.683825	+	0.683825i
$773$	13.5230	−	3.62347i	0.486387	−	0.130327i	−0.00728800	−	0.999973i	$-0.502320\pi$
$773$	13.5230	−	3.62347i	0.486387	−	0.130327i	0.493675	+	0.869646i	$0.335653\pi$
$774$	−17.9452	−	1.40325i	−0.645028	−	0.0504388i
$775$	−5.00000	−	5.00000i	−0.179605	−	0.179605i
$776$	−25.7196	−	14.8492i	−0.923281	−	0.533057i
$777$	−3.14626	−	1.44949i	−0.112872	−	0.0520002i
$778$	−4.39230	+	16.3923i	−0.157472	+	0.587693i
$779$	2.82843			0.101339
$780$		0			0
$781$	−16.0000			−0.572525
$782$		0			0
$783$	10.2474	−	10.5352i	0.366214	−	0.376496i
$784$	4.33013	+	2.50000i	0.154647	+	0.0892857i
$785$	−19.7990	−	19.7990i	−0.706656	−	0.706656i
$786$	−12.5266	+	15.0693i	−0.446809	+	0.537504i
$787$	25.9545	−	6.95448i	0.925177	−	0.247901i	0.235380	−	0.971903i	$-0.424366\pi$
$787$	25.9545	−	6.95448i	0.925177	−	0.247901i	0.689797	+	0.724003i	$0.257700\pi$
$788$	15.5563	−	15.5563i	0.554172	−	0.554172i
$789$	−3.59592	−	39.0265i	−0.128018	−	1.38938i
$790$	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
$795$	−6.78710	−	18.3830i	−0.240714	−	0.651978i
$796$		0			0
$797$	−8.48528	+	14.6969i	−0.300564	+	0.520592i	−0.976264	−	0.216585i	$-0.930508\pi$
$797$	−8.48528	+	14.6969i	−0.300564	+	0.520592i	0.675700	+	0.737177i	$0.263842\pi$
$798$	0.585786	−	3.41421i	0.0207366	−	0.120862i
$799$		0			0
$800$	−1.29410	−	4.82963i	−0.0457532	−	0.170753i
$801$	18.1005	+	37.8995i	0.639550	+	1.33911i
$802$	11.0000	−	19.0526i	0.388424	−	0.672769i
$803$	−2.82843	−	4.89898i	−0.0998130	−	0.172881i
$804$	11.4894	−	4.24194i	0.405199	−	0.149602i
$805$		−	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	$-0.850871\pi$
$809$	−26.9444	+	15.5563i	−0.947314	+	0.546932i	−0.0550686	+	0.998483i	$0.517538\pi$
$810$	−6.46750	−	16.7980i	−0.227245	−	0.590220i
$811$	−1.00000	+	1.00000i	−0.0351147	+	0.0351147i	−0.724446	−	0.689331i	$-0.757904\pi$
$811$	−1.00000	+	1.00000i	−0.0351147	+	0.0351147i	0.689331	+	0.724446i	$0.257904\pi$
$812$	3.86370	−	1.03528i	0.135589	−	0.0363311i
$813$	−35.7896	−	29.7507i	−1.25520	−	1.04340i
$814$	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	$-0.860835\pi$
$821$	2.58819	−	9.65926i	0.0903285	−	0.337110i	0.996270	+	0.0862928i	$0.0275020\pi$
$822$	−10.1464	+	22.0239i	−0.353897	+	0.768170i
$823$	25.9808	+	15.0000i	0.905632	+	0.522867i	0.879023	−	0.476779i	$-0.158196\pi$
$823$	25.9808	+	15.0000i	0.905632	+	0.522867i	0.0266091	+	0.999646i	$0.491529\pi$
$824$	12.7279	+	12.7279i	0.443398	+	0.443398i
$825$	5.32780	+	4.42883i	0.185490	+	0.154192i
$826$	−5.46410	+	1.46410i	−0.190120	+	0.0509426i
$827$	22.6274	−	22.6274i	0.786832	−	0.786832i	−0.194141	−	0.980974i	$-0.562192\pi$
$827$	22.6274	−	22.6274i	0.786832	−	0.786832i	0.980974	+	0.194141i	$0.0621920\pi$
$828$	19.3485	−	16.5420i	0.672406	−	0.574873i
$829$	−15.5885	+	9.00000i	−0.541409	+	0.312583i	−0.745650	−	0.666338i	$-0.767861\pi$
$829$	−15.5885	+	9.00000i	−0.541409	+	0.312583i	0.204240	+	0.978921i	$0.434528\pi$
$830$	15.4548	+	4.14110i	0.536444	+	0.143740i
$831$	16.9706	−	12.0000i	0.588702	−	0.416275i
$832$		0			0
$833$		0			0
$834$	6.49938	−	2.39960i	0.225055	−	0.0830914i
$835$	−4.00000	−	6.92820i	−0.138426	−	0.239760i
$836$	2.82843	−	4.89898i	0.0978232	−	0.169435i
$837$	17.9289	−	32.0711i	0.619715	−	1.10854i
$838$	−2.92820	−	10.9282i	−0.101153	−	0.377509i
$839$	−1.03528	−	3.86370i	−0.0357417	−	0.133390i	0.945750	−	0.324896i	$-0.105329\pi$
$839$	−1.03528	−	3.86370i	−0.0357417	−	0.133390i	−0.981491	+	0.191506i	$0.938663\pi$
$840$	2.48528	−	14.4853i	0.0857504	−	0.499790i
$841$	−10.5000	+	18.1865i	−0.362069	+	0.627122i
$842$	17.6777	+	30.6186i	0.609213	+	1.05519i
$843$	8.39861	+	22.7478i	0.289263	+	0.783477i
$844$		−	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
$849$	−1.90702	−	20.6969i	−0.0654489	−	0.710317i
$850$		0			0
$851$	−11.5911	+	3.10583i	−0.397338	+	0.106466i
$852$	4.42883	−	5.32780i	0.151729	−	0.182528i
$853$	−37.0000	−	37.0000i	−1.26686	−	1.26686i	−0.947703	−	0.319152i	$-0.896602\pi$
$853$	−37.0000	−	37.0000i	−1.26686	−	1.26686i	−0.319152	−	0.947703i	$-0.603398\pi$
$854$	9.79796	+	5.65685i	0.335279	+	0.193574i
$855$	8.34242	−	1.55051i	0.285305	−	0.0530263i
$856$	−4.39230	+	16.3923i	−0.150126	+	0.560277i
$857$	8.48528			0.289852			0.144926	−	0.989443i	$-0.453706\pi$
$857$	8.48528			0.289852			0.144926	+	0.989443i	$0.453706\pi$
$858$		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
$861$	−4.44949	−	2.04989i	−0.151638	−	0.0698600i
$862$	27.7128	+	16.0000i	0.943902	+	0.544962i
$863$	2.82843	+	2.82843i	0.0962808	+	0.0962808i	0.753607	−	0.657326i	$-0.228312\pi$
$863$	2.82843	+	2.82843i	0.0962808	+	0.0962808i	−0.657326	+	0.753607i	$0.728312\pi$
$864$	22.3180	−	13.3006i	0.759274	−	0.452496i
$865$	16.3923	−	4.39230i	0.557355	−	0.149343i
$866$	12.7279	−	12.7279i	0.432512	−	0.432512i
$867$	−29.3207	+	2.70162i	−0.995782	+	0.0917517i
$868$	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
$873$	−16.8091	+	24.4837i	−0.568902	+	0.828649i
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$	−8.48528	+	14.6969i	−0.286855	+	0.496847i
$876$	2.41421	+	0.414214i	0.0815687	+	0.0139950i
$877$	−4.75833	−	17.7583i	−0.160677	−	0.599656i	−0.998552	−	0.0537936i	$-0.982869\pi$
$877$	−4.75833	−	17.7583i	−0.160677	−	0.599656i	0.837875	−	0.545863i	$-0.183798\pi$
$878$	−7.76457	−	28.9778i	−0.262042	−	0.977953i
$879$	−23.8995	−	4.10051i	−0.806110	−	0.138307i
$880$	−4.00000	+	6.92820i	−0.134840	+	0.233550i
$881$	12.7279	+	22.0454i	0.428815	+	0.742729i	0.996768	−	0.0803319i	$-0.0255980\pi$
$881$	12.7279	+	22.0454i	0.428815	+	0.742729i	−0.567954	+	0.823061i	$0.692265\pi$
$882$	8.48988	−	12.3662i	0.285869	−	0.416390i
$883$		−	36.0000i		−	1.21150i	−0.795656	−	0.605748i	$-0.792874\pi$
$883$		−	36.0000i		−	1.21150i	0.795656	−	0.605748i	$-0.207126\pi$
$884$		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	$-0.742969\pi$
$887$	−12.2474	+	7.07107i	−0.411229	+	0.237423i	0.280089	+	0.959974i	$0.409636\pi$
$888$	−7.31747	+	0.674235i	−0.245558	+	0.0226258i
$889$		0			0
$890$	27.0459	−	7.24693i	0.906581	−	0.242918i
$891$	−14.6095	+	32.9023i	−0.489436	+	1.10227i
$892$	−11.0000	−	11.0000i	−0.368307	−	0.368307i
$893$	4.89898	+	2.82843i	0.163938	+	0.0946497i
$894$	3.14626	+	1.44949i	0.105227	+	0.0484782i
$895$		0			0
$896$	4.24264			0.141737
$897$		0			0
$898$	−22.0000			−0.734150
$899$	5.17638	−	19.3185i	0.172642	−	0.644309i
$900$	−2.94949	+	0.548188i	−0.0983163	+	0.0182729i
$901$		0			0
$902$	5.65685	+	5.65685i	0.188353	+	0.188353i
$903$	−9.39496	+	11.3020i	−0.312645	+	0.376106i
$904$	40.9808	−	10.9808i	1.36300	−	0.365215i
$905$		0			0
$906$	−0.224745	−	2.43916i	−0.00746665	−	0.0810356i
$907$	10.3923	−	6.00000i	0.345071	−	0.199227i	−0.317441	−	0.948278i	$-0.602824\pi$
$907$	10.3923	−	6.00000i	0.345071	−	0.199227i	0.662512	+	0.749051i	$0.269490\pi$
$908$	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	$-0.293336\pi$
$912$	−0.848387	−	2.29788i	−0.0280929	−	0.0760903i
$913$	−16.0000	−	27.7128i	−0.529523	−	0.917160i
$914$	−20.5061	+	35.5176i	−0.678281	+	1.17482i
$915$	−4.68629	+	27.3137i	−0.154924	+	0.902963i
$916$	−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	−0.436650	−	0.899631i	$-0.643835\pi$
$919$	17.0000	−	29.4449i	0.560778	−	0.971296i	0.997429	−	0.0716652i	$-0.0228313\pi$
$920$	−25.4558	−	44.0908i	−0.839254	−	1.45363i
$921$	−39.0639	+	14.4226i	−1.28720	+	0.475240i
$922$			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
$927$	13.6814	−	11.6969i	0.449357	−	0.384178i
$928$	10.0000	−	10.0000i	0.328266	−	0.328266i
$929$	−44.4326	+	11.9057i	−1.45779	+	0.390613i	−0.898725	−	0.438514i	$-0.855505\pi$
$929$	−44.4326	+	11.9057i	−1.45779	+	0.390613i	−0.559061	+	0.829126i	$0.688838\pi$
$930$	−18.8366	−	15.6583i	−0.617678	−	0.513455i
$931$	5.00000	+	5.00000i	0.163868	+	0.163868i
$932$	22.0454	+	12.7279i	0.722121	+	0.416917i
$933$	6.14966	−	13.3485i	0.201331	−	0.437009i
$934$	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
$939$	−5.79796	+	12.5851i	−0.189209	+	0.410698i
$940$	6.92820	+	4.00000i	0.225973	+	0.130466i
$941$	−26.8701	−	26.8701i	−0.875939	−	0.875939i	0.117173	−	0.993112i	$-0.462617\pi$
$941$	−26.8701	−	26.8701i	−0.875939	−	0.875939i	−0.993112	+	0.117173i	$0.962617\pi$
$942$	18.6473	+	15.5009i	0.607562	+	0.505046i
$943$	−16.3923	+	4.39230i	−0.533807	+	0.143033i
$944$	−2.82843	+	2.82843i	−0.0920575	+	0.0920575i
$945$	−14.2474	−	3.60697i	−0.463470	−	0.117335i
$946$	20.7846	−	12.0000i	0.675766	−	0.390154i
$947$	−30.9096	−	8.28221i	−1.00443	−	0.269136i	−0.281128	−	0.959670i	$-0.590709\pi$
$947$	−30.9096	−	8.28221i	−1.00443	−	0.269136i	−0.723299	+	0.690535i	$0.757375\pi$
$948$	14.1421	−	10.0000i	0.459315	−	0.324785i
$949$		0			0
$950$			1.41421i			0.0458831i
$951$	−16.2484	+	5.99900i	−0.526892	+	0.194531i
$952$		0			0
$953$	12.7279	−	22.0454i	0.412298	−	0.714121i	−0.582843	−	0.812585i	$-0.698060\pi$
$953$	12.7279	−	22.0454i	0.412298	−	0.714121i	0.995141	+	0.0984642i	$0.0313930\pi$
$954$	7.31371	+	15.3137i	0.236790	+	0.495800i
$955$	1.46410	+	5.46410i	0.0473772	+	0.176814i
$956$	−5.17638	−	19.3185i	−0.167416	−	0.624805i
$957$	−3.31371	+	19.3137i	−0.107117	+	0.624324i
$958$	−16.0000	+	27.7128i	−0.516937	+	0.895360i
$959$	9.89949	+	17.1464i	0.319671	+	0.553687i
$960$	−8.39861	−	22.7478i	−0.271064	−	0.734183i
$961$		−	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
$966$	1.90702	+	20.6969i	0.0613575	+	0.665913i
$967$	23.0000	−	23.0000i	0.739630	−	0.739630i	−0.232876	−	0.972506i	$-0.574814\pi$
$967$	23.0000	−	23.0000i	0.739630	−	0.739630i	0.972506	+	0.232876i	$0.0748137\pi$
$968$	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	$-0.166951\pi$
$971$	26.9444	+	15.5563i	0.864687	+	0.499227i	−0.000892350		1.00000i	$0.500284\pi$
$972$	−6.91215	−	13.9722i	−0.221707	−	0.448158i
$973$	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	0.609658	+	0.792664i	$0.291307\pi$
$977$	−9.83512	+	36.7052i	−0.314653	+	1.17430i	−0.924312	+	0.381638i	$0.875360\pi$
$978$	2.22474	+	1.02494i	0.0711395	+	0.0327741i
$979$	−48.4974	−	28.0000i	−1.54998	−	0.894884i
$980$	7.07107	+	7.07107i	0.225877	+	0.225877i
$981$	4.22973	+	0.330749i	0.135045	+	0.0105600i
$982$	−40.9808	+	10.9808i	−1.30775	+	0.350410i
$983$	−2.82843	+	2.82843i	−0.0902128	+	0.0902128i	−0.750773	−	0.660560i	$-0.770319\pi$
$983$	−2.82843	+	2.82843i	−0.0902128	+	0.0902128i	0.660560	+	0.750773i	$0.270319\pi$
$984$	−10.3485	+	0.953512i	−0.329897	+	0.0303968i
$985$	−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
$990$	19.7859	+	13.5838i	0.628836	+	0.431722i
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$	17.6777	−	30.6186i	0.561267	−	0.972142i
$993$	16.8995	+	2.89949i	0.536289	+	0.0920127i
$994$	1.46410	+	5.46410i	0.0464385	+	0.173311i
$995$		0			0
$996$	13.6569	+	2.34315i	0.432734	+	0.0742454i
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	−0.995077	−	0.0991016i	$-0.968403\pi$
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	0.583363	+	0.812211i	$0.301736\pi$
$998$	−16.2635	−	28.1691i	−0.514811	−	0.891678i
$999$	0.101725	+	7.34777i	0.00321842	+	0.232473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.i.80.2		8
3.2	odd	2	inner	507.2.k.i.80.1		8
13.2	odd	12		39.2.f.a.8.2	yes	4
13.3	even	3		507.2.f.a.239.2		4
13.4	even	6		507.2.k.j.188.2		8
13.5	odd	4		507.2.k.j.89.1		8
13.6	odd	12		507.2.k.j.488.2		8
13.7	odd	12	inner	507.2.k.i.488.1		8
13.8	odd	4	inner	507.2.k.i.89.2		8
13.9	even	3	inner	507.2.k.i.188.1		8
13.10	even	6		39.2.f.a.5.1	✓	4
13.11	odd	12		507.2.f.a.437.1		4
13.12	even	2		507.2.k.j.80.1		8
39.2	even	12		39.2.f.a.8.1	yes	4
39.5	even	4		507.2.k.j.89.2		8
39.8	even	4	inner	507.2.k.i.89.1		8
39.11	even	12		507.2.f.a.437.2		4
39.17	odd	6		507.2.k.j.188.1		8
39.20	even	12	inner	507.2.k.i.488.2		8
39.23	odd	6		39.2.f.a.5.2	yes	4
39.29	odd	6		507.2.f.a.239.1		4
39.32	even	12		507.2.k.j.488.1		8
39.35	odd	6	inner	507.2.k.i.188.2		8
39.38	odd	2		507.2.k.j.80.2		8
52.15	even	12		624.2.bf.d.593.2		4
52.23	odd	6		624.2.bf.d.161.2		4
65.2	even	12		975.2.n.d.749.2		4
65.23	odd	12		975.2.n.d.824.1		4
65.28	even	12		975.2.n.c.749.1		4
65.49	even	6		975.2.o.j.551.2		4
65.54	odd	12		975.2.o.j.476.1		4
65.62	odd	12		975.2.n.c.824.2		4
156.23	even	6		624.2.bf.d.161.1		4
156.119	odd	12		624.2.bf.d.593.1		4
195.2	odd	12		975.2.n.d.749.1		4
195.23	even	12		975.2.n.d.824.2		4
195.62	even	12		975.2.n.c.824.1		4
195.119	even	12		975.2.o.j.476.2		4
195.158	odd	12		975.2.n.c.749.2		4
195.179	odd	6		975.2.o.j.551.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.f.a.5.1	✓	4	13.10	even	6
39.2.f.a.5.2	yes	4	39.23	odd	6
39.2.f.a.8.1	yes	4	39.2	even	12
39.2.f.a.8.2	yes	4	13.2	odd	12
507.2.f.a.239.1		4	39.29	odd	6
507.2.f.a.239.2		4	13.3	even	3
507.2.f.a.437.1		4	13.11	odd	12
507.2.f.a.437.2		4	39.11	even	12
507.2.k.i.80.1		8	3.2	odd	2	inner
507.2.k.i.80.2		8	1.1	even	1	trivial
507.2.k.i.89.1		8	39.8	even	4	inner
507.2.k.i.89.2		8	13.8	odd	4	inner
507.2.k.i.188.1		8	13.9	even	3	inner
507.2.k.i.188.2		8	39.35	odd	6	inner
507.2.k.i.488.1		8	13.7	odd	12	inner
507.2.k.i.488.2		8	39.20	even	12	inner
507.2.k.j.80.1		8	13.12	even	2
507.2.k.j.80.2		8	39.38	odd	2
507.2.k.j.89.1		8	13.5	odd	4
507.2.k.j.89.2		8	39.5	even	4
507.2.k.j.188.1		8	39.17	odd	6
507.2.k.j.188.2		8	13.4	even	6
507.2.k.j.488.1		8	39.32	even	12
507.2.k.j.488.2		8	13.6	odd	12
624.2.bf.d.161.1		4	156.23	even	6
624.2.bf.d.161.2		4	52.23	odd	6
624.2.bf.d.593.1		4	156.119	odd	12
624.2.bf.d.593.2		4	52.15	even	12
975.2.n.c.749.1		4	65.28	even	12
975.2.n.c.749.2		4	195.158	odd	12
975.2.n.c.824.1		4	195.62	even	12
975.2.n.c.824.2		4	65.62	odd	12
975.2.n.d.749.1		4	195.2	odd	12
975.2.n.d.749.2		4	65.2	even	12
975.2.n.d.824.1		4	65.23	odd	12
975.2.n.d.824.2		4	195.23	even	12
975.2.o.j.476.1		4	65.54	odd	12
975.2.o.j.476.2		4	195.119	even	12
975.2.o.j.551.1		4	195.179	odd	6
975.2.o.j.551.2		4	65.49	even	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.41421 - 1.41421i) q^{5} +(1.33195 + 1.10721i) q^{6} +(1.36603 - 0.366025i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.41421 - 1.41421i) q^{5} +(1.33195 + 1.10721i) q^{6} +(1.36603 - 0.366025i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-1.94949 - 2.28024i) q^{9} +(-1.73205 + 1.00000i) q^{10} +(3.86370 + 1.03528i) q^{11} +(-1.41421 + 1.00000i) q^{12} -1.41421i q^{14} +(3.24969 - 1.19980i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.70711 + 1.29289i) q^{18} +(-0.366025 - 1.36603i) q^{19} +(-0.517638 - 1.93185i) q^{20} +(-0.414214 + 2.41421i) q^{21} +(2.00000 - 3.46410i) q^{22} +(4.24264 + 7.34847i) q^{23} +(1.79970 + 4.87453i) q^{24} -1.00000i q^{25} +(5.00000 - 1.41421i) q^{27} +(1.36603 + 0.366025i) q^{28} +(2.44949 - 1.41421i) q^{29} +(-0.317837 - 3.44949i) q^{30} +(5.00000 - 5.00000i) q^{31} +(4.82963 - 1.29410i) q^{32} +(-4.42883 + 5.32780i) q^{33} +(-2.44949 - 1.41421i) q^{35} +(-0.548188 - 2.94949i) q^{36} +(-0.366025 + 1.36603i) q^{37} -1.41421 q^{38} -6.00000 q^{40} +(-0.517638 + 1.93185i) q^{41} +(2.22474 + 1.02494i) q^{42} +(5.19615 + 3.00000i) q^{43} +(2.82843 + 2.82843i) q^{44} +(-0.467750 + 5.98174i) q^{45} +(8.19615 - 2.19615i) q^{46} +(-2.82843 + 2.82843i) q^{47} +(1.72474 - 0.158919i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(-0.965926 - 0.258819i) q^{50} -5.65685i q^{53} +(-0.0719302 - 5.19565i) q^{54} +(-4.00000 - 6.92820i) q^{55} +(2.12132 - 3.67423i) q^{56} +(2.41421 + 0.414214i) q^{57} +(-0.732051 - 2.73205i) q^{58} +(-1.03528 - 3.86370i) q^{59} +(3.41421 + 0.585786i) q^{60} +(-4.00000 + 6.92820i) q^{61} +(-3.53553 - 6.12372i) q^{62} +(-3.49768 - 2.40130i) q^{63} -7.00000i q^{64} +(4.00000 + 5.65685i) q^{66} +(-6.83013 - 1.83013i) q^{67} +(-14.6349 + 1.34847i) q^{69} +(-2.00000 + 2.00000i) q^{70} +(-3.86370 + 1.03528i) q^{71} +(-8.97261 - 0.701625i) q^{72} +(-1.00000 - 1.00000i) q^{73} +(1.22474 + 0.707107i) q^{74} +(1.57313 + 0.724745i) q^{75} +(0.366025 - 1.36603i) q^{76} +5.65685 q^{77} -10.0000 q^{79} +(-0.517638 + 1.93185i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(1.73205 + 1.00000i) q^{82} +(-5.65685 - 5.65685i) q^{83} +(-1.56583 + 1.88366i) q^{84} +(4.24264 - 4.24264i) q^{86} +(0.449490 + 4.87832i) q^{87} +(10.3923 - 6.00000i) q^{88} +(-13.5230 - 3.62347i) q^{89} +(5.65685 + 2.00000i) q^{90} +8.48528i q^{92} +(4.24194 + 11.4894i) q^{93} +(2.00000 + 3.46410i) q^{94} +(-1.41421 + 2.44949i) q^{95} +(-1.46447 + 8.53553i) q^{96} +(-2.56218 - 9.56218i) q^{97} +(1.29410 + 4.82963i) q^{98} +(-5.17157 - 10.8284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 + 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9} + 8 q^{15} - 4 q^{16} - 16 q^{18} + 4 q^{19} + 8 q^{21} + 16 q^{22} + 12 q^{24} + 40 q^{27} + 4 q^{28} + 40 q^{31} - 16 q^{33} + 4 q^{37} - 48 q^{40} + 8 q^{42} - 16 q^{45} + 24 q^{46} + 4 q^{48} - 4 q^{54} - 32 q^{55} + 8 q^{57} + 8 q^{58} + 16 q^{60} - 32 q^{61} - 4 q^{63} + 32 q^{66} - 20 q^{67} - 16 q^{70} - 24 q^{72} - 8 q^{73} - 4 q^{76} - 80 q^{79} + 28 q^{81} - 4 q^{84} - 16 q^{87} + 20 q^{93} + 16 q^{94} - 40 q^{96} + 28 q^{97} - 64 q^{99}+O(q^{100}) \) 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

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