LMFDB - Embedded newform 802.2.e.b.45.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [802,2,Mod(45,802)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(802, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("802.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 802 = 2 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	802.e (of order $8$, degree $4$, 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:	$6.40400224211$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			45.5
Character	$\chi$	$=$	802.45
Dual form			802.2.e.b.303.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.62035 - 0.671173i) q^{3} +1.00000i q^{4} +2.02594 q^{5} +(-0.671173 - 1.62035i) q^{6} +(-1.35018 + 1.35018i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.0537565 + 0.0537565i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.62035 - 0.671173i) q^{3} +1.00000i q^{4} +2.02594 q^{5} +(-0.671173 - 1.62035i) q^{6} +(-1.35018 + 1.35018i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.0537565 + 0.0537565i) q^{9} +(1.43256 + 1.43256i) q^{10} +(1.87080 + 1.87080i) q^{11} +(0.671173 - 1.62035i) q^{12} +(-3.18501 + 1.31928i) q^{13} -1.90944 q^{14} +(-3.28275 - 1.35976i) q^{15} -1.00000 q^{16} +(-1.02889 + 0.426180i) q^{17} +0.0760232i q^{18} +(1.69429 + 4.09038i) q^{19} +2.02594i q^{20} +(3.09397 - 1.28156i) q^{21} +2.64571i q^{22} +(1.70992 + 4.12810i) q^{23} +(1.62035 - 0.671173i) q^{24} -0.895556 q^{25} +(-3.18501 - 1.31928i) q^{26} +(1.96249 + 4.73788i) q^{27} +(-1.35018 - 1.35018i) q^{28} +5.95604 q^{29} +(-1.35976 - 3.28275i) q^{30} +(-0.525422 - 1.26848i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.77573 - 4.28700i) q^{33} +(-1.02889 - 0.426180i) q^{34} +(-2.73538 + 2.73538i) q^{35} +(-0.0537565 + 0.0537565i) q^{36} +(-7.68292 - 3.18237i) q^{37} +(-1.69429 + 4.09038i) q^{38} +6.04631 q^{39} +(-1.43256 + 1.43256i) q^{40} -2.51293 q^{41} +(3.09397 + 1.28156i) q^{42} +(-3.49094 + 3.49094i) q^{43} +(-1.87080 + 1.87080i) q^{44} +(0.108908 + 0.108908i) q^{45} +(-1.70992 + 4.12810i) q^{46} +(7.49086 + 7.49086i) q^{47} +(1.62035 + 0.671173i) q^{48} +3.35405i q^{49} +(-0.633253 - 0.633253i) q^{50} +1.95321 q^{51} +(-1.31928 - 3.18501i) q^{52} +(-4.39872 + 10.6195i) q^{53} +(-1.96249 + 4.73788i) q^{54} +(3.79014 + 3.79014i) q^{55} -1.90944i q^{56} -7.76503i q^{57} +(4.21156 + 4.21156i) q^{58} +(-5.60253 + 2.32064i) q^{59} +(1.35976 - 3.28275i) q^{60} +(0.210842 + 0.509017i) q^{61} +(0.525422 - 1.26848i) q^{62} -0.145162 q^{63} -1.00000i q^{64} +(-6.45265 + 2.67278i) q^{65} +(1.77573 - 4.28700i) q^{66} +(0.542044 - 1.30861i) q^{67} +(-0.426180 - 1.02889i) q^{68} -7.83664i q^{69} -3.86841 q^{70} +(1.17551 - 2.83793i) q^{71} -0.0760232 q^{72} +(1.50131 - 1.50131i) q^{73} +(-3.18237 - 7.68292i) q^{74} +(1.45112 + 0.601073i) q^{75} +(-4.09038 + 1.69429i) q^{76} -5.05183 q^{77} +(4.27539 + 4.27539i) q^{78} +(0.957162 + 2.31079i) q^{79} -2.02594 q^{80} -9.22229i q^{81} +(-1.77691 - 1.77691i) q^{82} +4.03490 q^{83} +(1.28156 + 3.09397i) q^{84} +(-2.08447 + 0.863417i) q^{85} -4.93693 q^{86} +(-9.65090 - 3.99753i) q^{87} -2.64571 q^{88} +(12.1313 - 12.1313i) q^{89} +0.154019i q^{90} +(2.51907 - 6.08158i) q^{91} +(-4.12810 + 1.70992i) q^{92} +2.40804i q^{93} +10.5937i q^{94} +(3.43254 + 8.28688i) q^{95} +(0.671173 + 1.62035i) q^{96} +(-0.404086 - 0.975549i) q^{97} +(-2.37167 + 2.37167i) q^{98} +0.201136i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 68 * q + 4 * q^6 + 20 * q^9	$ 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) $ 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/802\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.62035	−	0.671173i	−0.935512	−	0.387502i	−0.137745	−	0.990468i	$-0.543986\pi$
$3$	−1.62035	−	0.671173i	−0.935512	−	0.387502i	−0.797767	+	0.602966i	$0.793986\pi$
$4$			1.00000i			0.500000i
$5$	2.02594			0.906029			0.453015	−	0.891503i	$-0.350349\pi$
$5$	2.02594			0.906029			0.453015	+	0.891503i	$0.350349\pi$
$6$	−0.671173	−	1.62035i	−0.274005	−	0.661507i
$7$	−1.35018	+	1.35018i	−0.510319	+	0.510319i	−0.914624	−	0.404305i	$-0.867513\pi$
$7$	−1.35018	+	1.35018i	−0.510319	+	0.510319i	0.404305	+	0.914624i	$0.367513\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.0537565	+	0.0537565i	0.0179188	+	0.0179188i
$10$	1.43256	+	1.43256i	0.453015	+	0.453015i
$11$	1.87080	+	1.87080i	0.564068	+	0.564068i	0.930460	−	0.366392i	$-0.119407\pi$
$11$	1.87080	+	1.87080i	0.564068	+	0.564068i	−0.366392	+	0.930460i	$0.619407\pi$
$12$	0.671173	−	1.62035i	0.193751	−	0.467756i
$13$	−3.18501	+	1.31928i	−0.883363	+	0.365901i	−0.777800	−	0.628512i	$-0.783664\pi$
$13$	−3.18501	+	1.31928i	−0.883363	+	0.365901i	−0.105563	+	0.994413i	$0.533664\pi$
$14$	−1.90944			−0.510319
$15$	−3.28275	−	1.35976i	−0.847601	−	0.351088i
$16$	−1.00000			−0.250000
$17$	−1.02889	+	0.426180i	−0.249542	+	0.103364i	−0.503949	−	0.863734i	$-0.668120\pi$
$17$	−1.02889	+	0.426180i	−0.249542	+	0.103364i	0.254406	+	0.967097i	$0.418120\pi$
$18$			0.0760232i			0.0179188i
$19$	1.69429	+	4.09038i	0.388697	+	0.938398i	0.990216	+	0.139540i	$0.0445623\pi$
$19$	1.69429	+	4.09038i	0.388697	+	0.938398i	−0.601519	+	0.798858i	$0.705438\pi$
$20$			2.02594i			0.453015i
$21$	3.09397	−	1.28156i	0.675159	−	0.279660i
$22$			2.64571i			0.564068i
$23$	1.70992	+	4.12810i	0.356542	+	0.860769i	0.995781	+	0.0917605i	$0.0292494\pi$
$23$	1.70992	+	4.12810i	0.356542	+	0.860769i	−0.639239	+	0.769008i	$0.720751\pi$
$24$	1.62035	−	0.671173i	0.330754	−	0.137003i
$25$	−0.895556			−0.179111
$26$	−3.18501	−	1.31928i	−0.624632	−	0.258731i
$27$	1.96249	+	4.73788i	0.377682	+	0.911805i
$28$	−1.35018	−	1.35018i	−0.255159	−	0.255159i
$29$	5.95604			1.10601			0.553005	−	0.833178i	$-0.313481\pi$
$29$	5.95604			1.10601			0.553005	+	0.833178i	$0.313481\pi$
$30$	−1.35976	−	3.28275i	−0.248257	−	0.599345i
$31$	−0.525422	−	1.26848i	−0.0943687	−	0.227826i	0.869646	−	0.493676i	$-0.164347\pi$
$31$	−0.525422	−	1.26848i	−0.0943687	−	0.227826i	−0.964014	+	0.265850i	$0.914347\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.77573	−	4.28700i	−0.309115	−	0.746270i
$34$	−1.02889	−	0.426180i	−0.176453	−	0.0730893i
$35$	−2.73538	+	2.73538i	−0.462364	+	0.462364i
$36$	−0.0537565	+	0.0537565i	−0.00895942	+	0.00895942i
$37$	−7.68292	−	3.18237i	−1.26306	−	0.523178i	−0.352215	−	0.935919i	$-0.614571\pi$
$37$	−7.68292	−	3.18237i	−1.26306	−	0.523178i	−0.910848	+	0.412741i	$0.864571\pi$
$38$	−1.69429	+	4.09038i	−0.274850	+	0.663548i
$39$	6.04631			0.968185
$40$	−1.43256	+	1.43256i	−0.226507	+	0.226507i
$41$	−2.51293			−0.392454			−0.196227	−	0.980559i	$-0.562869\pi$
$41$	−2.51293			−0.392454			−0.196227	+	0.980559i	$0.562869\pi$
$42$	3.09397	+	1.28156i	0.477409	+	0.197749i
$43$	−3.49094	+	3.49094i	−0.532363	+	0.532363i	−0.921275	−	0.388912i	$-0.872851\pi$
$43$	−3.49094	+	3.49094i	−0.532363	+	0.532363i	0.388912	+	0.921275i	$0.372851\pi$
$44$	−1.87080	+	1.87080i	−0.282034	+	0.282034i
$45$	0.108908	+	0.108908i	0.0162350	+	0.0162350i
$46$	−1.70992	+	4.12810i	−0.252113	+	0.608655i
$47$	7.49086	+	7.49086i	1.09265	+	1.09265i	0.995244	+	0.0974093i	$0.0310556\pi$
$47$	7.49086	+	7.49086i	1.09265	+	1.09265i	0.0974093	+	0.995244i	$0.468944\pi$
$48$	1.62035	+	0.671173i	0.233878	+	0.0968755i
$49$			3.35405i			0.479150i
$50$	−0.633253	−	0.633253i	−0.0895556	−	0.0895556i
$51$	1.95321			0.273504
$52$	−1.31928	−	3.18501i	−0.182951	−	0.441682i
$53$	−4.39872	+	10.6195i	−0.604211	+	1.45869i	0.264998	+	0.964249i	$0.414629\pi$
$53$	−4.39872	+	10.6195i	−0.604211	+	1.45869i	−0.869209	+	0.494446i	$0.835371\pi$
$54$	−1.96249	+	4.73788i	−0.267062	+	0.644744i
$55$	3.79014	+	3.79014i	0.511062	+	0.511062i
$56$		−	1.90944i		−	0.255159i
$57$		−	7.76503i		−	1.02850i
$58$	4.21156	+	4.21156i	0.553005	+	0.553005i
$59$	−5.60253	+	2.32064i	−0.729387	+	0.302122i	−0.716300	−	0.697792i	$-0.754166\pi$
$59$	−5.60253	+	2.32064i	−0.729387	+	0.302122i	−0.0130868	+	0.999914i	$0.504166\pi$
$60$	1.35976	−	3.28275i	0.175544	−	0.423801i
$61$	0.210842	+	0.509017i	0.0269955	+	0.0651730i	0.936802	−	0.349859i	$-0.113770\pi$
$61$	0.210842	+	0.509017i	0.0269955	+	0.0651730i	−0.909807	+	0.415032i	$0.863770\pi$
$62$	0.525422	−	1.26848i	0.0667287	−	0.161097i
$63$	−0.145162			−0.0182886
$64$		−	1.00000i		−	0.125000i
$65$	−6.45265	+	2.67278i	−0.800353	+	0.331517i
$66$	1.77573	−	4.28700i	0.218578	−	0.527693i
$67$	0.542044	−	1.30861i	0.0662212	−	0.159872i	−0.887304	−	0.461184i	$-0.847425\pi$
$67$	0.542044	−	1.30861i	0.0662212	−	0.159872i	0.953526	+	0.301312i	$0.0974247\pi$
$68$	−0.426180	−	1.02889i	−0.0516819	−	0.124771i
$69$		−	7.83664i		−	0.943420i
$70$	−3.86841			−0.462364
$71$	1.17551	−	2.83793i	0.139507	−	0.336801i	−0.838649	−	0.544673i	$-0.816654\pi$
$71$	1.17551	−	2.83793i	0.139507	−	0.336801i	0.978156	+	0.207872i	$0.0666538\pi$
$72$	−0.0760232			−0.00895942
$73$	1.50131	−	1.50131i	0.175714	−	0.175714i	−0.613770	−	0.789485i	$-0.710348\pi$
$73$	1.50131	−	1.50131i	0.175714	−	0.175714i	0.789485	+	0.613770i	$0.210348\pi$
$74$	−3.18237	−	7.68292i	−0.369943	−	0.893121i
$75$	1.45112	+	0.601073i	0.167561	+	0.0694059i
$76$	−4.09038	+	1.69429i	−0.469199	+	0.194349i
$77$	−5.05183			−0.575709
$78$	4.27539	+	4.27539i	0.484092	+	0.484092i
$79$	0.957162	+	2.31079i	0.107689	+	0.259985i	0.968533	−	0.248884i	$-0.0800639\pi$
$79$	0.957162	+	2.31079i	0.107689	+	0.259985i	−0.860844	+	0.508869i	$0.830064\pi$
$80$	−2.02594			−0.226507
$81$		−	9.22229i		−	1.02470i
$82$	−1.77691	−	1.77691i	−0.196227	−	0.196227i
$83$	4.03490			0.442888			0.221444	−	0.975173i	$-0.428923\pi$
$83$	4.03490			0.442888			0.221444	+	0.975173i	$0.428923\pi$
$84$	1.28156	+	3.09397i	0.139830	+	0.337579i
$85$	−2.08447	+	0.863417i	−0.226093	+	0.0936507i
$86$	−4.93693			−0.532363
$87$	−9.65090	−	3.99753i	−1.03469	−	0.428581i
$88$	−2.64571			−0.282034
$89$	12.1313	−	12.1313i	1.28592	−	1.28592i	0.348675	−	0.937244i	$-0.386632\pi$
$89$	12.1313	−	12.1313i	1.28592	−	1.28592i	0.937244	−	0.348675i	$-0.113368\pi$
$90$			0.154019i			0.0162350i
$91$	2.51907	−	6.08158i	0.264071	−	0.637523i
$92$	−4.12810	+	1.70992i	−0.430384	+	0.178271i
$93$			2.40804i			0.249702i
$94$			10.5937i			1.09265i
$95$	3.43254	+	8.28688i	0.352171	+	0.850216i
$96$	0.671173	+	1.62035i	0.0685013	+	0.165377i
$97$	−0.404086	−	0.975549i	−0.0410287	−	0.0990520i	0.902037	−	0.431659i	$-0.142072\pi$
$97$	−0.404086	−	0.975549i	−0.0410287	−	0.0990520i	−0.943065	+	0.332607i	$0.892072\pi$
$98$	−2.37167	+	2.37167i	−0.239575	+	0.239575i
$99$			0.201136i			0.0202149i
$100$		−	0.895556i		−	0.0895556i
$101$	5.54971	−	13.3982i	0.552217	−	1.33317i	−0.363594	−	0.931558i	$-0.618450\pi$
$101$	5.54971	−	13.3982i	0.552217	−	1.33317i	0.915810	−	0.401611i	$-0.131550\pi$
$102$	1.38113	+	1.38113i	0.136752	+	0.136752i
$103$	−2.07513	+	2.07513i	−0.204469	+	0.204469i	−0.801911	−	0.597443i	$-0.796183\pi$
$103$	−2.07513	+	2.07513i	−0.204469	+	0.204469i	0.597443	+	0.801911i	$0.296183\pi$
$104$	1.31928	−	3.18501i	0.129366	−	0.312316i
$105$	6.26820	−	2.59637i	0.611714	−	0.253380i
$106$	−10.6195	+	4.39872i	−1.03145	+	0.427242i
$107$	4.28006	−	1.77286i	0.413769	−	0.171389i	−0.166081	−	0.986112i	$-0.553111\pi$
$107$	4.28006	−	1.77286i	0.413769	−	0.171389i	0.579850	+	0.814723i	$0.303111\pi$
$108$	−4.73788	+	1.96249i	−0.455903	+	0.188841i
$109$	−2.15414	−	2.15414i	−0.206330	−	0.206330i	0.596376	−	0.802705i	$-0.296607\pi$
$109$	−2.15414	−	2.15414i	−0.206330	−	0.206330i	−0.802705	+	0.596376i	$0.796607\pi$
$110$			5.36007i			0.511062i
$111$	10.3131	+	10.3131i	0.978879	+	0.978879i
$112$	1.35018	−	1.35018i	0.127580	−	0.127580i
$113$		−	5.72573i		−	0.538631i	−0.963052	−	0.269315i	$-0.913203\pi$
$113$		−	5.72573i		−	0.538631i	0.963052	−	0.269315i	$-0.0867974\pi$
$114$	5.49071	−	5.49071i	0.514252	−	0.514252i
$115$	3.46419	+	8.36330i	0.323037	+	0.779881i
$116$			5.95604i			0.553005i
$117$	−0.242135	−	0.100295i	−0.0223854	−	0.00927232i
$118$	−5.60253	−	2.32064i	−0.515754	−	0.213632i
$119$	0.813765	−	1.96460i	0.0745977	−	0.180095i
$120$	3.28275	−	1.35976i	0.299672	−	0.124128i
$121$		−	4.00019i		−	0.363654i
$122$	−0.210842	+	0.509017i	−0.0190887	+	0.0460842i
$123$	4.07184	+	1.68661i	0.367145	+	0.152077i
$124$	1.26848	−	0.525422i	0.113913	−	0.0471843i
$125$	−11.9441			−1.06831
$126$	−0.102645	−	0.102645i	−0.00914432	−	0.00914432i
$127$	−0.714288	−	1.72444i	−0.0633828	−	0.153020i	0.889015	−	0.457879i	$-0.151391\pi$
$127$	−0.714288	−	1.72444i	−0.0633828	−	0.153020i	−0.952397	+	0.304859i	$0.901391\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	7.99958	−	3.31353i	0.704324	−	0.291740i
$130$	−6.45265	−	2.67278i	−0.565935	−	0.234418i
$131$	−1.70332	+	4.11218i	−0.148820	+	0.359283i	−0.980656	−	0.195738i	$-0.937290\pi$
$131$	−1.70332	+	4.11218i	−0.148820	+	0.359283i	0.831836	+	0.555021i	$0.187290\pi$
$132$	4.28700	−	1.77573i	0.373135	−	0.154558i
$133$	−7.81033	−	3.23514i	−0.677242	−	0.280523i
$134$	1.30861	−	0.542044i	0.113047	−	0.0468255i
$135$	3.97590	+	9.59867i	0.342191	+	0.826122i
$136$	0.426180	−	1.02889i	0.0365446	−	0.0882266i
$137$	7.42956	+	3.07742i	0.634750	+	0.262922i	0.676770	−	0.736195i	$-0.263379\pi$
$137$	7.42956	+	3.07742i	0.634750	+	0.262922i	−0.0420198	+	0.999117i	$0.513379\pi$
$138$	5.54134	−	5.54134i	0.471710	−	0.471710i
$139$	14.9805	−	6.20511i	1.27063	−	0.526310i	0.357471	−	0.933924i	$-0.383639\pi$
$139$	14.9805	−	6.20511i	1.27063	−	0.526310i	0.913154	+	0.407614i	$0.133639\pi$
$140$	−2.73538	−	2.73538i	−0.231182	−	0.231182i
$141$	−7.11019	−	17.1655i	−0.598786	−	1.44560i
$142$	2.83793	−	1.17551i	0.238154	−	0.0986466i
$143$	−8.42663	−	3.49043i	−0.704670	−	0.291884i
$144$	−0.0537565	−	0.0537565i	−0.00447971	−	0.00447971i
$145$	12.0666			1.00208
$146$	2.12317			0.175714
$147$	2.25115	−	5.43475i	0.185671	−	0.448250i
$148$	3.18237	−	7.68292i	0.261589	−	0.631532i
$149$		−	10.0651i		−	0.824564i	−0.911056	−	0.412282i	$-0.864732\pi$
$149$		−	10.0651i		−	0.824564i	0.911056	−	0.412282i	$-0.135268\pi$
$150$	0.601073	+	1.45112i	0.0490774	+	0.118483i
$151$	−0.303690	−	0.303690i	−0.0247139	−	0.0247139i	0.694642	−	0.719356i	$-0.255563\pi$
$151$	−0.303690	−	0.303690i	−0.0247139	−	0.0247139i	−0.719356	+	0.694642i	$0.755563\pi$
$152$	−4.09038	−	1.69429i	−0.331774	−	0.137425i
$153$	−0.0782195	−	0.0323996i	−0.00632367	−	0.00261935i
$154$	−3.57218	−	3.57218i	−0.287855	−	0.287855i
$155$	−1.06448	−	2.56987i	−0.0855008	−	0.206417i
$156$			6.04631i			0.484092i
$157$	21.5375	−	8.92113i	1.71888	−	0.711984i	0.719026	−	0.694984i	$-0.244588\pi$
$157$	21.5375	−	8.92113i	1.71888	−	0.711984i	0.999855	−	0.0170002i	$-0.00541159\pi$
$158$	−0.957162	+	2.31079i	−0.0761477	+	0.183837i
$159$	14.2550	−	14.2550i	1.13049	−	1.13049i
$160$	−1.43256	−	1.43256i	−0.113254	−	0.113254i
$161$	−7.88235	−	3.26498i	−0.621216	−	0.257316i
$162$	6.52114	−	6.52114i	0.512349	−	0.512349i
$163$	4.68944	−	1.94243i	0.367306	−	0.152143i	−0.191394	−	0.981513i	$-0.561301\pi$
$163$	4.68944	−	1.94243i	0.367306	−	0.152143i	0.558699	+	0.829370i	$0.311301\pi$
$164$		−	2.51293i		−	0.196227i
$165$	−3.59753	−	8.68521i	−0.280067	−	0.676143i
$166$	2.85311	+	2.85311i	0.221444	+	0.221444i
$167$	−9.55291	−	23.0628i	−0.739226	−	1.78465i	−0.609006	−	0.793165i	$-0.708432\pi$
$167$	−9.55291	−	23.0628i	−0.739226	−	1.78465i	−0.130220	−	0.991485i	$-0.541568\pi$
$168$	−1.28156	+	3.09397i	−0.0988747	+	0.238705i
$169$	−0.788574	+	0.788574i	−0.0606596	+	0.0606596i
$170$	−2.08447	−	0.863417i	−0.159872	−	0.0662210i
$171$	−0.128805	+	0.310964i	−0.00985000	+	0.0237800i
$172$	−3.49094	−	3.49094i	−0.266181	−	0.266181i
$173$	6.91667			0.525865			0.262932	−	0.964814i	$-0.415310\pi$
$173$	6.91667			0.525865			0.262932	+	0.964814i	$0.415310\pi$
$174$	−3.99753	−	9.65090i	−0.303052	−	0.731633i
$175$	1.20916	−	1.20916i	0.0914038	−	0.0914038i
$176$	−1.87080	−	1.87080i	−0.141017	−	0.141017i
$177$	10.6356			0.799423
$178$	17.1563			1.28592
$179$			11.5426i			0.862734i	0.902177	+	0.431367i	$0.141969\pi$
$179$			11.5426i			0.862734i	−0.902177	+	0.431367i	$0.858031\pi$
$180$	−0.108908	+	0.108908i	−0.00811749	+	0.00811749i
$181$	−1.24755	+	1.24755i	−0.0927296	+	0.0927296i	−0.751950	−	0.659220i	$-0.770886\pi$
$181$	−1.24755	+	1.24755i	−0.0927296	+	0.0927296i	0.659220	+	0.751950i	$0.270886\pi$
$182$	6.08158	−	2.51907i	0.450797	−	0.186726i
$183$		−	0.966300i		−	0.0714309i
$184$	−4.12810	−	1.70992i	−0.304328	−	0.126057i
$185$	−15.5651	−	6.44730i	−1.14437	−	0.474015i
$186$	−1.70274	+	1.70274i	−0.124851	+	0.124851i
$187$	−2.72215	−	1.12755i	−0.199063	−	0.0824547i
$188$	−7.49086	+	7.49086i	−0.546327	+	0.546327i
$189$	−9.04669	−	3.74726i	−0.658050	−	0.272573i
$190$	−3.43254	+	8.28688i	−0.249022	+	0.601193i
$191$	20.9205	+	8.66557i	1.51376	+	0.627018i	0.976329	−	0.216292i	$-0.0693962\pi$
$191$	20.9205	+	8.66557i	1.51376	+	0.627018i	0.537427	+	0.843310i	$0.319396\pi$
$192$	−0.671173	+	1.62035i	−0.0484377	+	0.116939i
$193$	−7.19885	+	2.98186i	−0.518185	+	0.214639i	−0.626419	−	0.779486i	$-0.715480\pi$
$193$	−7.19885	+	2.98186i	−0.518185	+	0.214639i	0.108235	+	0.994125i	$0.465480\pi$
$194$	0.404086	−	0.975549i	0.0290117	−	0.0700404i
$195$	12.2495			0.877204
$196$	−3.35405			−0.239575
$197$			6.83028i			0.486637i	0.969946	+	0.243319i	$0.0782360\pi$
$197$			6.83028i			0.486637i	−0.969946	+	0.243319i	$0.921764\pi$
$198$	−0.142224	+	0.142224i	−0.0101074	+	0.0101074i
$199$	−11.4872	+	4.75814i	−0.814304	+	0.337296i	−0.750670	−	0.660677i	$-0.770269\pi$
$199$	−11.4872	+	4.75814i	−0.814304	+	0.337296i	−0.0636344	+	0.997973i	$0.520269\pi$
$200$	0.633253	−	0.633253i	0.0447778	−	0.0447778i
$201$	−1.75661	+	1.75661i	−0.123901	+	0.123901i
$202$	13.3982	−	5.54971i	0.942693	−	0.390476i
$203$	−8.04171	+	8.04171i	−0.564417	+	0.564417i
$204$			1.95321i			0.136752i
$205$	−5.09105			−0.355575
$206$	−2.93468			−0.204469
$207$	−0.129993	+	0.313831i	−0.00903515	+	0.0218128i
$208$	3.18501	−	1.31928i	0.220841	−	0.0914753i
$209$	−4.48261	+	10.8220i	−0.310069	+	0.748572i
$210$	6.26820	+	2.59637i	0.432547	+	0.179167i
$211$	0.440524	−	1.06352i	0.0303269	−	0.0732156i	−0.907991	−	0.418991i	$-0.862384\pi$
$211$	0.440524	−	1.06352i	0.0303269	−	0.0732156i	0.938317	+	0.345775i	$0.112384\pi$
$212$	−10.6195	−	4.39872i	−0.729347	−	0.302106i
$213$	−3.80949	+	3.80949i	−0.261022	+	0.261022i
$214$	4.28006	+	1.77286i	0.292579	+	0.121190i
$215$	−7.07244	+	7.07244i	−0.482336	+	0.482336i
$216$	−4.73788	−	1.96249i	−0.322372	−	0.133531i
$217$	2.42209	+	1.00326i	0.164422	+	0.0681058i
$218$		−	3.04642i		−	0.206330i
$219$	−3.44028	+	1.42501i	−0.232473	+	0.0962934i
$220$	−3.79014	+	3.79014i	−0.255531	+	0.255531i
$221$	2.71478	−	2.71478i	0.182616	−	0.182616i
$222$			14.5850i			0.978879i
$223$	−4.97772			−0.333333			−0.166666	−	0.986013i	$-0.553300\pi$
$223$	−4.97772			−0.333333			−0.166666	+	0.986013i	$0.553300\pi$
$224$	1.90944			0.127580
$225$	−0.0481419	−	0.0481419i	−0.00320946	−	0.00320946i
$226$	4.04870	−	4.04870i	0.269315	−	0.269315i
$227$	−1.68040	−	4.05684i	−0.111532	−	0.269262i	0.858252	−	0.513229i	$-0.171551\pi$
$227$	−1.68040	−	4.05684i	−0.111532	−	0.269262i	−0.969783	+	0.243968i	$0.921551\pi$
$228$	7.76503			0.514252
$229$	16.5088	+	16.5088i	1.09093	+	1.09093i	0.995429	+	0.0954996i	$0.0304449\pi$
$229$	16.5088	+	16.5088i	1.09093	+	1.09093i	0.0954996	+	0.995429i	$0.469555\pi$
$230$	−3.46419	+	8.36330i	−0.228422	+	0.551459i
$231$	8.18575	+	3.39065i	0.538583	+	0.223088i
$232$	−4.21156	+	4.21156i	−0.276502	+	0.276502i
$233$	−10.0129	+	24.1734i	−0.655969	+	1.58365i	0.148005	+	0.988987i	$0.452715\pi$
$233$	−10.0129	+	24.1734i	−0.655969	+	1.58365i	−0.803975	+	0.594664i	$0.797285\pi$
$234$	−0.100295	−	0.242135i	−0.00655652	−	0.0158288i
$235$	15.1760	+	15.1760i	0.989976	+	0.989976i
$236$	−2.32064	−	5.60253i	−0.151061	−	0.364693i
$237$		−	4.38673i		−	0.284948i
$238$	1.96460	−	0.813765i	0.127346	−	0.0527485i
$239$	−6.60637	+	6.60637i	−0.427330	+	0.427330i	−0.887718	−	0.460388i	$-0.847710\pi$
$239$	−6.60637	+	6.60637i	−0.427330	+	0.427330i	0.460388	+	0.887718i	$0.347710\pi$
$240$	3.28275	+	1.35976i	0.211900	+	0.0877720i
$241$	−7.32494	−	7.32494i	−0.471841	−	0.471841i	0.430669	−	0.902510i	$-0.358278\pi$
$241$	−7.32494	−	7.32494i	−0.471841	−	0.471841i	−0.902510	+	0.430669i	$0.858278\pi$
$242$	2.82856	−	2.82856i	0.181827	−	0.181827i
$243$	−0.302269	+	0.729742i	−0.0193906	+	0.0468130i
$244$	−0.509017	+	0.210842i	−0.0325865	+	0.0134978i
$245$			6.79511i			0.434123i
$246$	1.68661	+	4.07184i	0.107534	+	0.259611i
$247$	−10.7927	−	10.7927i	−0.686722	−	0.686722i
$248$	1.26848	+	0.525422i	0.0805487	+	0.0333644i
$249$	−6.53797	−	2.70812i	−0.414327	−	0.171620i
$250$	−8.44572	−	8.44572i	−0.534155	−	0.534155i
$251$	−11.0562	−	26.6921i	−0.697862	−	1.68479i	−0.728307	−	0.685251i	$-0.759692\pi$
$251$	−11.0562	−	26.6921i	−0.697862	−	1.68479i	0.0304447	−	0.999536i	$-0.490308\pi$
$252$		−	0.145162i		−	0.00914432i
$253$	−4.52395	+	10.9218i	−0.284418	+	0.686646i
$254$	0.714288	−	1.72444i	0.0448184	−	0.108201i
$255$	3.95709			0.247802
$256$	1.00000			0.0625000
$257$	6.92825	+	6.92825i	0.432173	+	0.432173i	0.889367	−	0.457194i	$-0.151146\pi$
$257$	6.92825	+	6.92825i	0.432173	+	0.432173i	−0.457194	+	0.889367i	$0.651146\pi$
$258$	7.99958	+	3.31353i	0.498032	+	0.206292i
$259$	14.6701	−	6.07653i	0.911553	−	0.377577i
$260$	−2.67278	−	6.45265i	−0.165759	−	0.400176i
$261$	0.320176	+	0.320176i	0.0198184	+	0.0198184i
$262$	−4.11218	+	1.70332i	−0.254052	+	0.105232i
$263$	−11.5646	+	11.5646i	−0.713104	+	0.713104i	−0.967183	−	0.254080i	$-0.918227\pi$
$263$	−11.5646	+	11.5646i	−0.713104	+	0.713104i	0.254080	+	0.967183i	$0.418227\pi$
$264$	4.28700	+	1.77573i	0.263846	+	0.109289i
$265$	−8.91156	+	21.5144i	−0.547433	+	1.32162i
$266$	−3.23514	−	7.81033i	−0.198359	−	0.478882i
$267$	−27.7993	+	11.5148i	−1.70129	+	0.704697i
$268$	1.30861	+	0.542044i	0.0799360	+	0.0331106i
$269$	19.8157	−	8.20794i	1.20819	−	0.500447i	0.314551	−	0.949241i	$-0.398146\pi$
$269$	19.8157	−	8.20794i	1.20819	−	0.500447i	0.893635	+	0.448794i	$0.148146\pi$
$270$	−3.97590	+	9.59867i	−0.241966	+	0.584157i
$271$	10.3099	+	4.27051i	0.626283	+	0.259415i	0.673173	−	0.739485i	$-0.264931\pi$
$271$	10.3099	+	4.27051i	0.626283	+	0.259415i	−0.0468899	+	0.998900i	$0.514931\pi$
$272$	1.02889	−	0.426180i	0.0623856	−	0.0258410i
$273$	−8.16359	+	8.16359i	−0.494083	+	0.494083i
$274$	3.07742	+	7.42956i	0.185914	+	0.448836i
$275$	−1.67541	−	1.67541i	−0.101031	−	0.101031i
$276$	7.83664			0.471710
$277$	9.31108	−	3.85678i	0.559449	−	0.231731i	−0.0849971	−	0.996381i	$-0.527088\pi$
$277$	9.31108	−	3.85678i	0.559449	−	0.231731i	0.644446	+	0.764650i	$0.277088\pi$
$278$	14.9805	+	6.20511i	0.898468	+	0.372158i
$279$	0.0399443	−	0.0964340i	0.00239140	−	0.00577335i
$280$		−	3.86841i		−	0.231182i
$281$	−13.9975	+	5.79794i	−0.835018	+	0.345876i	−0.758887	−	0.651222i	$-0.774257\pi$
$281$	−13.9975	+	5.79794i	−0.835018	+	0.345876i	−0.0761309	+	0.997098i	$0.524257\pi$
$282$	7.11019	−	17.1655i	0.423405	−	1.02219i
$283$	21.5588	+	8.92995i	1.28154	+	0.530831i	0.916453	−	0.400143i	$-0.131040\pi$
$283$	21.5588	+	8.92995i	1.28154	+	0.530831i	0.365086	+	0.930974i	$0.381040\pi$
$284$	2.83793	+	1.17551i	0.168400	+	0.0697537i
$285$		−	15.7315i		−	0.931854i
$286$	−3.49043	−	8.42663i	−0.206393	−	0.498277i
$287$	3.39290	−	3.39290i	0.200277	−	0.200277i
$288$		−	0.0760232i		−	0.00447971i
$289$	−11.1438	+	11.1438i	−0.655519	+	0.655519i
$290$	8.53238	+	8.53238i	0.501038	+	0.501038i
$291$			1.85195i			0.108563i
$292$	1.50131	+	1.50131i	0.0878572	+	0.0878572i
$293$	−9.00783	+	3.73117i	−0.526243	+	0.217977i	−0.629957	−	0.776630i	$-0.716927\pi$
$293$	−9.00783	+	3.73117i	−0.526243	+	0.217977i	0.103714	+	0.994607i	$0.466927\pi$
$294$	5.43475	−	2.25115i	0.316961	−	0.131289i
$295$	−11.3504	+	4.70149i	−0.660846	+	0.273731i
$296$	7.68292	−	3.18237i	0.446560	−	0.184971i
$297$	−5.19220	+	12.5351i	−0.301282	+	0.727359i
$298$	7.11709	−	7.11709i	0.412282	−	0.412282i
$299$	−10.8922	−	10.8922i	−0.629912	−	0.629912i
$300$	−0.601073	+	1.45112i	−0.0347030	+	0.0837803i
$301$		−	9.42676i		−	0.543350i
$302$		−	0.429482i		−	0.0247139i
$303$	−17.9850	+	17.9850i	−1.03321	+	1.03321i
$304$	−1.69429	−	4.09038i	−0.0971743	−	0.234599i
$305$	0.427153	+	1.03124i	0.0244587	+	0.0590486i
$306$	−0.0323996	−	0.0782195i	−0.00185216	−	0.00447151i
$307$		−	3.46145i		−	0.197555i	−0.995110	−	0.0987776i	$-0.968507\pi$
$307$		−	3.46145i		−	0.197555i	0.995110	−	0.0987776i	$-0.0314932\pi$
$308$		−	5.05183i		−	0.287855i
$309$	4.75522	−	1.96967i	0.270515	−	0.112051i
$310$	1.06448	−	2.56987i	0.0604582	−	0.145959i
$311$			0.503088i			0.0285275i	0.999898	+	0.0142638i	$0.00454045\pi$
$311$			0.503088i			0.0285275i	−0.999898	+	0.0142638i	$0.995460\pi$
$312$	−4.27539	+	4.27539i	−0.242046	+	0.242046i
$313$	23.9909			1.35605			0.678024	−	0.735040i	$-0.262836\pi$
$313$	23.9909			1.35605			0.678024	+	0.735040i	$0.262836\pi$
$314$	21.5375	+	8.92113i	1.21543	+	0.503449i
$315$	−0.294089			−0.0165700
$316$	−2.31079	+	0.957162i	−0.129992	+	0.0538446i
$317$	−8.62758	−	20.8288i	−0.484573	−	1.16986i	−0.957415	−	0.288715i	$-0.906772\pi$
$317$	−8.62758	−	20.8288i	−0.484573	−	1.16986i	0.472842	−	0.881147i	$-0.343228\pi$
$318$	20.1596			1.13049
$319$	11.1426	+	11.1426i	0.623865	+	0.623865i
$320$		−	2.02594i		−	0.113254i
$321$	−8.12511			−0.453500
$322$	−3.26498	−	7.88235i	−0.181950	−	0.439266i
$323$	−3.48648	−	3.48648i	−0.193993	−	0.193993i
$324$	9.22229			0.512349
$325$	2.85236	−	1.18148i	0.158220	−	0.0655370i
$326$	4.68944	+	1.94243i	0.259724	+	0.107581i
$327$	2.04467	+	4.93628i	0.113071	+	0.272977i
$328$	1.77691	−	1.77691i	0.0981135	−	0.0981135i
$329$	−20.2280			−1.11520
$330$	3.59753	−	8.68521i	0.198038	−	0.478105i
$331$	12.9475			0.711659			0.355829	−	0.934551i	$-0.384198\pi$
$331$	12.9475			0.711659			0.355829	+	0.934551i	$0.384198\pi$
$332$			4.03490i			0.221444i
$333$	−0.241934	−	0.584080i	−0.0132579	−	0.0320074i
$334$	9.55291	−	23.0628i	0.522712	−	1.26194i
$335$	1.09815	−	2.65117i	0.0599983	−	0.144849i
$336$	−3.09397	+	1.28156i	−0.168790	+	0.0699150i
$337$			8.74531i			0.476387i	0.971218	+	0.238194i	$0.0765553\pi$
$337$			8.74531i			0.476387i	−0.971218	+	0.238194i	$0.923445\pi$
$338$	−1.11521			−0.0606596
$339$	−3.84295	+	9.27771i	−0.208721	+	0.503896i
$340$	−0.863417	−	2.08447i	−0.0468253	−	0.113046i
$341$	1.39012	−	3.35604i	0.0752791	−	0.181740i
$342$	−0.310964	+	0.128805i	−0.0168150	+	0.00696500i
$343$	−13.9798	−	13.9798i	−0.754838	−	0.754838i
$344$		−	4.93693i		−	0.266181i
$345$		−	15.8766i		−	0.854766i
$346$	4.89083	+	4.89083i	0.262932	+	0.262932i
$347$	−11.2883	+	27.2523i	−0.605986	+	1.46298i	0.261344	+	0.965246i	$0.415834\pi$
$347$	−11.2883	+	27.2523i	−0.605986	+	1.46298i	−0.867330	+	0.497734i	$0.834166\pi$
$348$	3.99753	−	9.65090i	0.214290	−	0.517343i
$349$	2.63380	+	6.35855i	0.140984	+	0.340365i	0.978562	−	0.205952i	$-0.0660292\pi$
$349$	2.63380	+	6.35855i	0.140984	+	0.340365i	−0.837578	+	0.546318i	$0.816029\pi$
$350$	1.71001			0.0914038
$351$	−12.5011	−	12.5011i	−0.667261	−	0.667261i
$352$		−	2.64571i		−	0.141017i
$353$	−20.7426	−	8.59187i	−1.10402	−	0.457299i	−0.245144	−	0.969487i	$-0.578835\pi$
$353$	−20.7426	−	8.59187i	−1.10402	−	0.457299i	−0.858874	+	0.512188i	$0.828835\pi$
$354$	7.52053	+	7.52053i	0.399712	+	0.399712i
$355$	2.38152	−	5.74949i	0.126398	−	0.305151i
$356$	12.1313	+	12.1313i	0.642959	+	0.642959i
$357$	−2.63717	+	2.63717i	−0.139574	+	0.139574i
$358$	−8.16185	+	8.16185i	−0.431367	+	0.431367i
$359$	−24.1144	−	9.98852i	−1.27271	−	0.527174i	−0.358923	−	0.933367i	$-0.616856\pi$
$359$	−24.1144	−	9.98852i	−1.27271	−	0.527174i	−0.913787	+	0.406193i	$0.866856\pi$
$360$	−0.154019			−0.00811749
$361$	−0.425571	+	0.425571i	−0.0223985	+	0.0223985i
$362$	−1.76430			−0.0927296
$363$	−2.68482	+	6.48173i	−0.140917	+	0.340203i
$364$	6.08158	+	2.51907i	0.318762	+	0.132035i
$365$	3.04156	−	3.04156i	0.159202	−	0.159202i
$366$	0.683277	−	0.683277i	0.0357155	−	0.0357155i
$367$	−19.5822	−	8.11119i	−1.02218	−	0.423401i	−0.192296	−	0.981337i	$-0.561593\pi$
$367$	−19.5822	−	8.11119i	−1.02218	−	0.423401i	−0.829884	+	0.557936i	$0.811593\pi$
$368$	−1.70992	−	4.12810i	−0.0891355	−	0.215192i
$369$	−0.135086	−	0.135086i	−0.00703232	−	0.00703232i
$370$	−6.44730	−	15.5651i	−0.335179	−	0.809193i
$371$	−8.39909	−	20.2772i	−0.436059	−	1.05274i
$372$	−2.40804			−0.124851
$373$	15.8422	+	15.8422i	0.820278	+	0.820278i	0.986148	−	0.165870i	$-0.0530431\pi$
$373$	15.8422	+	15.8422i	0.820278	+	0.820278i	−0.165870	+	0.986148i	$0.553043\pi$
$374$	−1.12755	−	2.72215i	−0.0583043	−	0.140759i
$375$	19.3536	+	8.01653i	0.999416	+	0.413972i
$376$	−10.5937			−0.546327
$377$	−18.9701	+	7.85766i	−0.977008	+	0.404690i
$378$	−3.74726	−	9.04669i	−0.192738	−	0.465311i
$379$			19.3913i			0.996065i	0.867158	+	0.498032i	$0.165944\pi$
$379$			19.3913i			0.996065i	−0.867158	+	0.498032i	$0.834056\pi$
$380$	−8.28688	+	3.43254i	−0.425108	+	0.176085i
$381$			3.27362i			0.167713i
$382$	8.66557	+	20.9205i	0.443369	+	1.07039i
$383$		−	0.972927i		−	0.0497142i	−0.999691	−	0.0248571i	$-0.992087\pi$
$383$		−	0.972927i		−	0.0497142i	0.999691	−	0.0248571i	$-0.00791308\pi$
$384$	−1.62035	+	0.671173i	−0.0826884	+	0.0342507i
$385$	−10.2347			−0.521609
$386$	−7.19885	−	2.98186i	−0.366412	−	0.151773i
$387$	−0.375321			−0.0190786
$388$	0.975549	−	0.404086i	0.0495260	−	0.0205143i
$389$	−0.611276	+	1.47575i	−0.0309929	+	0.0748235i	−0.938618	−	0.344958i	$-0.887893\pi$
$389$	−0.611276	+	1.47575i	−0.0309929	+	0.0748235i	0.907625	+	0.419781i	$0.137893\pi$
$390$	8.66169	+	8.66169i	0.438602	+	0.438602i
$391$	−3.51863	−	3.51863i	−0.177945	−	0.177945i
$392$	−2.37167	−	2.37167i	−0.119787	−	0.119787i
$393$	5.51997	−	5.51997i	0.278446	−	0.278446i
$394$	−4.82974	+	4.82974i	−0.243319	+	0.243319i
$395$	1.93916	+	4.68153i	0.0975695	+	0.235554i
$396$	−0.201136			−0.0101074
$397$		−	28.7598i		−	1.44341i	−0.692200	−	0.721706i	$-0.743358\pi$
$397$		−	28.7598i		−	1.44341i	0.692200	−	0.721706i	$-0.256642\pi$
$398$	−11.4872	−	4.75814i	−0.575800	−	0.238504i
$399$	10.4842	+	10.4842i	0.524865	+	0.524865i
$400$	0.895556			0.0447778
$401$	16.6358	+	11.1467i	0.830753	+	0.556641i
$401$	16.6358	+	11.1467i	0.830753	+	0.556641i
$402$	−2.48422			−0.123901
$403$	3.34695	+	3.34695i	0.166724	+	0.166724i
$404$	13.3982	+	5.54971i	0.666584	+	0.276108i
$405$		−	18.6838i		−	0.928407i
$406$	−11.3727			−0.564417
$407$	−8.41964	−	20.3268i	−0.417346	−	1.00756i
$408$	−1.38113	+	1.38113i	−0.0683759	+	0.0683759i
$409$	10.0118	−	10.0118i	0.495050	−	0.495050i	−0.414843	−	0.909893i	$-0.636164\pi$
$409$	10.0118	−	10.0118i	0.495050	−	0.495050i	0.909893	+	0.414843i	$0.136164\pi$
$410$	−3.59992	−	3.59992i	−0.177787	−	0.177787i
$411$	−9.97304	−	9.97304i	−0.491934	−	0.491934i
$412$	−2.07513	−	2.07513i	−0.102234	−	0.102234i
$413$	4.43112	−	10.6977i	0.218041	−	0.526398i
$414$	−0.313831	+	0.129993i	−0.0154240	+	0.00638882i
$415$	8.17448			0.401269
$416$	3.18501	+	1.31928i	0.156158	+	0.0646828i
$417$	−28.4384			−1.39263
$418$	−10.8220	+	4.48261i	−0.529320	+	0.219252i
$419$		−	12.8463i		−	0.627581i	−0.949492	−	0.313790i	$-0.898401\pi$
$419$		−	12.8463i		−	0.627581i	0.949492	−	0.313790i	$-0.101599\pi$
$420$	2.59637	+	6.26820i	0.126690	+	0.305857i
$421$		−	7.06982i		−	0.344562i	−0.985048	−	0.172281i	$-0.944886\pi$
$421$		−	7.06982i		−	0.344562i	0.985048	−	0.172281i	$-0.0551137\pi$
$422$	1.06352	−	0.440524i	0.0517712	−	0.0214444i
$423$			0.805364i			0.0391582i
$424$	−4.39872	−	10.6195i	−0.213621	−	0.515726i
$425$	0.921428	−	0.381668i	0.0446958	−	0.0185136i
$426$	−5.38743			−0.261022
$427$	−0.971937	−	0.402589i	−0.0470353	−	0.0194827i
$428$	1.77286	+	4.28006i	0.0856944	+	0.206885i
$429$	11.3115	+	11.3115i	0.546122	+	0.546122i
$430$	−10.0019			−0.482336
$431$	0.694027	+	1.67553i	0.0334301	+	0.0807074i	0.939713	−	0.341965i	$-0.111092\pi$
$431$	0.694027	+	1.67553i	0.0334301	+	0.0807074i	−0.906283	+	0.422672i	$0.861092\pi$
$432$	−1.96249	−	4.73788i	−0.0944205	−	0.227951i
$433$	23.8480	+	23.8480i	1.14606	+	1.14606i	0.987320	+	0.158742i	$0.0507439\pi$
$433$	23.8480	+	23.8480i	1.14606	+	1.14606i	0.158742	+	0.987320i	$0.449256\pi$
$434$	1.00326	+	2.42209i	0.0481581	+	0.116264i
$435$	−19.5522	−	8.09878i	−0.937455	−	0.388307i
$436$	2.15414	−	2.15414i	0.103165	−	0.103165i
$437$	−13.9884	+	13.9884i	−0.669157	+	0.669157i
$438$	−3.44028	−	1.42501i	−0.164383	−	0.0680897i
$439$	−1.65744	+	4.00140i	−0.0791051	+	0.190977i	−0.958484	−	0.285146i	$-0.907958\pi$
$439$	−1.65744	+	4.00140i	−0.0791051	+	0.190977i	0.879379	+	0.476122i	$0.157958\pi$
$440$	−5.36007			−0.255531
$441$	−0.180302	+	0.180302i	−0.00858580	+	0.00858580i
$442$	3.83928			0.182616
$443$	−19.1211	−	7.92024i	−0.908473	−	0.376302i	−0.121001	−	0.992652i	$-0.538610\pi$
$443$	−19.1211	−	7.92024i	−0.908473	−	0.376302i	−0.787472	+	0.616351i	$0.788610\pi$
$444$	−10.3131	+	10.3131i	−0.489440	+	0.489440i
$445$	24.5774	−	24.5774i	1.16508	−	1.16508i
$446$	−3.51978	−	3.51978i	−0.166666	−	0.166666i
$447$	−6.75541	+	16.3090i	−0.319520	+	0.771389i
$448$	1.35018	+	1.35018i	0.0637898	+	0.0637898i
$449$	−6.67658	−	2.76553i	−0.315087	−	0.130513i	0.219535	−	0.975605i	$-0.429546\pi$
$449$	−6.67658	−	2.76553i	−0.315087	−	0.130513i	−0.534622	+	0.845091i	$0.679546\pi$
$450$		−	0.0680830i		−	0.00320946i
$451$	−4.70120	−	4.70120i	−0.221371	−	0.221371i
$452$	5.72573			0.269315
$453$	0.288257	+	0.695914i	0.0135435	+	0.0326969i
$454$	1.68040	−	4.05684i	0.0788649	−	0.190397i
$455$	5.10350	−	12.3209i	0.239256	−	0.577615i
$456$	5.49071	+	5.49071i	0.257126	+	0.257126i
$457$		−	24.4525i		−	1.14384i	−0.820310	−	0.571919i	$-0.806199\pi$
$457$		−	24.4525i		−	1.14384i	0.820310	−	0.571919i	$-0.193801\pi$
$458$			23.3469i			1.09093i
$459$	−4.03838	−	4.03838i	−0.188495	−	0.188495i
$460$	−8.36330	+	3.46419i	−0.389941	+	0.161519i
$461$	−3.18445	+	7.68795i	−0.148315	+	0.358063i	−0.980524	−	0.196398i	$-0.937076\pi$
$461$	−3.18445	+	7.68795i	−0.148315	+	0.358063i	0.832210	+	0.554461i	$0.187076\pi$
$462$	3.39065	+	8.18575i	0.157747	+	0.380836i
$463$	−9.34407	+	22.5586i	−0.434256	+	1.04839i	0.543645	+	0.839315i	$0.317044\pi$
$463$	−9.34407	+	22.5586i	−0.434256	+	1.04839i	−0.977901	+	0.209071i	$0.932956\pi$
$464$	−5.95604			−0.276502
$465$			4.87855i			0.226237i
$466$	−24.1734	+	10.0129i	−1.11981	+	0.463840i
$467$	2.16651	−	5.23042i	0.100254	−	0.242035i	−0.865792	−	0.500404i	$-0.833185\pi$
$467$	2.16651	−	5.23042i	0.100254	−	0.242035i	0.966046	+	0.258369i	$0.0831849\pi$
$468$	0.100295	−	0.242135i	0.00463616	−	0.0111927i
$469$	1.03500	+	2.49871i	0.0477918	+	0.115380i
$470$			21.4622i			0.989976i
$471$	−40.8860			−1.88393
$472$	2.32064	−	5.60253i	0.106816	−	0.257877i
$473$	−13.0617			−0.600578
$474$	3.10188	−	3.10188i	0.142474	−	0.142474i
$475$	−1.51733	−	3.66316i	−0.0696200	−	0.168078i
$476$	1.96460	+	0.813765i	0.0900474	+	0.0372988i
$477$	−0.807325	+	0.334405i	−0.0369649	+	0.0153113i
$478$	−9.34282			−0.427330
$479$	24.9109	+	24.9109i	1.13821	+	1.13821i	0.988771	+	0.149439i	$0.0477468\pi$
$479$	24.9109	+	24.9109i	1.13821	+	1.13821i	0.149439	+	0.988771i	$0.452253\pi$
$480$	1.35976	+	3.28275i	0.0620642	+	0.149836i
$481$	28.6686			1.30718
$482$		−	10.3590i		−	0.471841i
$483$	10.5808	+	10.5808i	0.481445	+	0.481445i
$484$	4.00019			0.181827
$485$	−0.818655	−	1.97641i	−0.0371732	−	0.0897440i
$486$	−0.729742	+	0.302269i	−0.0331018	+	0.0137112i
$487$	23.8194			1.07936			0.539680	−	0.841871i	$-0.318545\pi$
$487$	23.8194			1.07936			0.539680	+	0.841871i	$0.318545\pi$
$488$	−0.509017	−	0.210842i	−0.0230421	−	0.00954436i
$489$	−8.90227			−0.402575
$490$	−4.80487	+	4.80487i	−0.217062	+	0.217062i
$491$			16.1208i			0.727523i	0.931492	+	0.363762i	$0.118508\pi$
$491$			16.1208i			0.727523i	−0.931492	+	0.363762i	$0.881492\pi$
$492$	−1.68661	+	4.07184i	−0.0760383	+	0.183573i
$493$	−6.12811	+	2.53835i	−0.275996	+	0.114321i
$494$		−	15.2632i		−	0.686722i
$495$			0.407489i			0.0183153i
$496$	0.525422	+	1.26848i	0.0235922	+	0.0569565i
$497$	2.24456	+	5.41886i	0.100682	+	0.243069i
$498$	−2.70812	−	6.53797i	−0.121354	−	0.292973i
$499$	−5.04568	+	5.04568i	−0.225876	+	0.225876i	−0.810967	−	0.585092i	$-0.801059\pi$
$499$	−5.04568	+	5.04568i	−0.225876	+	0.225876i	0.585092	+	0.810967i	$0.301059\pi$
$500$		−	11.9441i		−	0.534155i
$501$			43.7815i			1.95601i
$502$	11.0562	−	26.6921i	0.493463	−	1.19132i
$503$	14.0642	+	14.0642i	0.627093	+	0.627093i	0.947336	−	0.320243i	$-0.103764\pi$
$503$	14.0642	+	14.0642i	0.627093	+	0.627093i	−0.320243	+	0.947336i	$0.603764\pi$
$504$	0.102645	−	0.102645i	0.00457216	−	0.00457216i
$505$	11.2434	−	27.1439i	0.500324	−	1.20789i
$506$	−10.9218	+	4.52395i	−0.485532	+	0.201114i
$507$	1.80704	−	0.748500i	0.0802535	−	0.0332421i
$508$	1.72444	−	0.714288i	0.0765098	−	0.0316914i
$509$	23.4280	−	9.70420i	1.03843	−	0.430131i	0.202681	−	0.979245i	$-0.435035\pi$
$509$	23.4280	−	9.70420i	1.03843	−	0.430131i	0.835748	+	0.549114i	$0.185035\pi$
$510$	2.79808	+	2.79808i	0.123901	+	0.123901i
$511$			4.05405i			0.179341i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−16.0547	+	16.0547i	−0.708832	+	0.708832i
$514$			9.79803i			0.432173i
$515$	−4.20409	+	4.20409i	−0.185254	+	0.185254i
$516$	3.31353	+	7.99958i	0.145870	+	0.352162i
$517$			28.0278i			1.23266i
$518$	14.6701	+	6.07653i	0.644565	+	0.266988i
$519$	−11.2075	−	4.64228i	−0.491953	−	0.203774i
$520$	2.67278	−	6.45265i	0.117209	−	0.282968i
$521$	−1.55878	+	0.645668i	−0.0682914	+	0.0282872i	−0.416568	−	0.909105i	$-0.636767\pi$
$521$	−1.55878	+	0.645668i	−0.0682914	+	0.0282872i	0.348276	+	0.937392i	$0.386767\pi$
$522$			0.452797i			0.0198184i
$523$	−15.7669	+	38.0647i	−0.689439	+	1.66445i	0.0564703	+	0.998404i	$0.482015\pi$
$523$	−15.7669	+	38.0647i	−0.689439	+	1.66445i	−0.745909	+	0.666048i	$0.767985\pi$
$524$	−4.11218	−	1.70332i	−0.179642	−	0.0744100i
$525$	−2.77082	+	1.14771i	−0.120928	+	0.0500902i
$526$	−16.3548			−0.713104
$527$	1.08120	+	1.08120i	0.0470980	+	0.0470980i
$528$	1.77573	+	4.28700i	0.0772788	+	0.186568i
$529$	2.14605	−	2.14605i	0.0933064	−	0.0933064i
$530$	−21.5144	+	8.91156i	−0.934526	+	0.387094i
$531$	−0.425922	−	0.176423i	−0.0184834	−	0.00765609i
$532$	3.23514	−	7.81033i	0.140261	−	0.338621i
$533$	8.00372	−	3.31525i	0.346679	−	0.143599i
$534$	−27.7993	−	11.5148i	−1.20299	−	0.498296i
$535$	8.67116	−	3.59171i	0.374887	−	0.155283i
$536$	0.542044	+	1.30861i	0.0234127	+	0.0565233i
$537$	7.74708	−	18.7031i	0.334311	−	0.807098i
$538$	19.8157	+	8.20794i	0.854317	+	0.353870i
$539$	−6.27476	+	6.27476i	−0.270273	+	0.270273i
$540$	−9.59867	+	3.97590i	−0.413061	+	0.171096i
$541$	−6.00654	−	6.00654i	−0.258241	−	0.258241i	0.566097	−	0.824338i	$-0.308453\pi$
$541$	−6.00654	−	6.00654i	−0.258241	−	0.258241i	−0.824338	+	0.566097i	$0.808453\pi$
$542$	4.27051	+	10.3099i	0.183434	+	0.442849i
$543$	2.85879	−	1.18415i	0.122683	−	0.0508168i
$544$	1.02889	+	0.426180i	0.0441133	+	0.0182723i
$545$	−4.36417	−	4.36417i	−0.186941	−	0.186941i
$546$	−11.5451			−0.494083
$547$	11.7914			0.504162			0.252081	−	0.967706i	$-0.418885\pi$
$547$	11.7914			0.504162			0.252081	+	0.967706i	$0.418885\pi$
$548$	−3.07742	+	7.42956i	−0.131461	+	0.317375i
$549$	−0.0160289	+	0.0386971i	−0.000684095	+	0.00165155i
$550$		−	2.36938i		−	0.101031i
$551$	10.0913	+	24.3625i	0.429903	+	1.03788i
$552$	5.54134	+	5.54134i	0.235855	+	0.235855i
$553$	−4.41232	−	1.82764i	−0.187631	−	0.0777192i
$554$	9.31108	+	3.85678i	0.395590	+	0.163859i
$555$	20.8938	+	20.8938i	0.886893	+	0.886893i
$556$	6.20511	+	14.9805i	0.263155	+	0.635313i
$557$			5.41376i			0.229388i	0.993401	+	0.114694i	$0.0365888\pi$
$557$			5.41376i			0.229388i	−0.993401	+	0.114694i	$0.963411\pi$
$558$	0.0964340	−	0.0399443i	0.00408238	−	0.00169098i
$559$	6.51317	−	15.7242i	0.275478	−	0.665062i
$560$	2.73538	−	2.73538i	0.115591	−	0.115591i
$561$	3.65407	+	3.65407i	0.154275	+	0.154275i
$562$	−13.9975	−	5.79794i	−0.590447	−	0.244571i
$563$	5.23580	−	5.23580i	0.220662	−	0.220662i	−0.588115	−	0.808777i	$-0.700130\pi$
$563$	5.23580	−	5.23580i	0.220662	−	0.220662i	0.808777	+	0.588115i	$0.200130\pi$
$564$	17.1655	−	7.11019i	0.722798	−	0.299393i
$565$		−	11.6000i		−	0.488015i
$566$	8.92995	+	21.5588i	0.375354	+	0.906184i
$567$	12.4517	+	12.4517i	0.522923	+	0.522923i
$568$	1.17551	+	2.83793i	0.0493233	+	0.119077i
$569$	−5.36653	+	12.9560i	−0.224977	+	0.543142i	−0.995553	−	0.0942063i	$-0.969969\pi$
$569$	−5.36653	+	12.9560i	−0.224977	+	0.543142i	0.770576	+	0.637348i	$0.219969\pi$
$570$	11.1239	−	11.1239i	0.465927	−	0.465927i
$571$	36.7054	+	15.2039i	1.53607	+	0.636263i	0.980732	−	0.195358i	$-0.0625870\pi$
$571$	36.7054	+	15.2039i	1.53607	+	0.636263i	0.555343	+	0.831621i	$0.312587\pi$
$572$	3.49043	−	8.42663i	0.145942	−	0.352335i
$573$	−28.0826	−	28.0826i	−1.17317	−	1.17317i
$574$	4.79829			0.200277
$575$	−1.53132	−	3.69694i	−0.0638606	−	0.154173i
$576$	0.0537565	−	0.0537565i	0.00223985	−	0.00223985i
$577$	31.8716	+	31.8716i	1.32683	+	1.32683i	0.908117	+	0.418717i	$0.137520\pi$
$577$	31.8716	+	31.8716i	1.32683	+	1.32683i	0.418717	+	0.908117i	$0.362480\pi$
$578$	−15.7598			−0.655519
$579$	13.6660			0.567941
$580$			12.0666i			0.501038i
$581$	−5.44783	+	5.44783i	−0.226014	+	0.226014i
$582$	−1.30952	+	1.30952i	−0.0542815	+	0.0542815i
$583$	−28.0961	+	11.6378i	−1.16362	+	0.481987i
$584$			2.12317i			0.0878572i
$585$	−0.490551	−	0.203193i	−0.0202818	−	0.00840099i
$586$	−9.00783	−	3.73117i	−0.372110	−	0.154133i
$587$	31.7320	−	31.7320i	1.30972	−	1.30972i	0.388105	−	0.921615i	$-0.373130\pi$
$587$	31.7320	−	31.7320i	1.30972	−	1.30972i	0.921615	−	0.388105i	$-0.126870\pi$
$588$	5.43475	+	2.25115i	0.224125	+	0.0928357i
$589$	4.29836	−	4.29836i	0.177111	−	0.177111i
$590$	−11.3504	−	4.70149i	−0.467289	−	0.193557i
$591$	4.58430	−	11.0675i	0.188573	−	0.455255i
$592$	7.68292	+	3.18237i	0.315766	+	0.130795i
$593$	−11.9558	+	28.8638i	−0.490965	+	1.18529i	0.463265	+	0.886220i	$0.346678\pi$
$593$	−11.9558	+	28.8638i	−0.490965	+	1.18529i	−0.954230	+	0.299074i	$0.903322\pi$
$594$	−12.5351	+	5.19220i	−0.514321	+	0.213039i
$595$	1.64864	−	3.98017i	0.0675877	−	0.163171i
$596$	10.0651			0.412282
$597$	21.8068			0.892495
$598$		−	15.4039i		−	0.629912i
$599$	−8.88412	+	8.88412i	−0.362995	+	0.362995i	−0.864915	−	0.501919i	$-0.832627\pi$
$599$	−8.88412	+	8.88412i	−0.362995	+	0.362995i	0.501919	+	0.864915i	$0.332627\pi$
$600$	−1.45112	+	0.601073i	−0.0592416	+	0.0245387i
$601$	26.5946	−	26.5946i	1.08482	−	1.08482i	0.0887629	−	0.996053i	$-0.471709\pi$
$601$	26.5946	−	26.5946i	1.08482	−	1.08482i	0.996053	−	0.0887629i	$-0.0282913\pi$
$602$	6.66573	−	6.66573i	0.271675	−	0.271675i
$603$	0.0994846	−	0.0412079i	0.00405133	−	0.00167811i
$604$	0.303690	−	0.303690i	0.0123570	−	0.0123570i
$605$		−	8.10417i		−	0.329481i
$606$	−25.4346			−1.03321
$607$	−12.7842			−0.518896			−0.259448	−	0.965757i	$-0.583541\pi$
$607$	−12.7842			−0.518896			−0.259448	+	0.965757i	$0.583541\pi$
$608$	1.69429	−	4.09038i	0.0687126	−	0.165887i
$609$	18.4278	−	7.63304i	0.746732	−	0.309307i
$610$	−0.427153	+	1.03124i	−0.0172949	+	0.0417537i
$611$	−33.7410	−	13.9760i	−1.36501	−	0.565407i
$612$	0.0323996	−	0.0782195i	0.00130967	−	0.00316183i
$613$	22.7529	+	9.42456i	0.918981	+	0.380654i	0.791488	−	0.611185i	$-0.209307\pi$
$613$	22.7529	+	9.42456i	0.918981	+	0.380654i	0.127493	+	0.991839i	$0.459307\pi$
$614$	2.44761	−	2.44761i	0.0987776	−	0.0987776i
$615$	8.24932	+	3.41698i	0.332645	+	0.137786i
$616$	3.57218	−	3.57218i	0.143927	−	0.143927i
$617$	−11.1265	−	4.60873i	−0.447934	−	0.185540i	0.147301	−	0.989092i	$-0.452941\pi$
$617$	−11.1265	−	4.60873i	−0.447934	−	0.185540i	−0.595236	+	0.803551i	$0.702941\pi$
$618$	4.75522	+	1.96967i	0.191283	+	0.0792319i
$619$		−	1.97475i		−	0.0793720i	−0.999212	−	0.0396860i	$-0.987364\pi$
$619$		−	1.97475i		−	0.0793720i	0.999212	−	0.0396860i	$-0.0126358\pi$
$620$	2.56987	−	1.06448i	0.103209	−	0.0427504i
$621$	−16.2027	+	16.2027i	−0.650194	+	0.650194i
$622$	−0.355737	+	0.355737i	−0.0142638	+	0.0142638i
$623$			32.7589i			1.31246i
$624$	−6.04631			−0.242046
$625$	−19.7202			−0.788808
$626$	16.9642	+	16.9642i	0.678024	+	0.678024i
$627$	14.5268	−	14.5268i	0.580146	−	0.580146i
$628$	8.92113	+	21.5375i	0.355992	+	0.859441i
$629$	9.26114			0.369266
$630$	−0.207952	−	0.207952i	−0.00828502	−	0.00828502i
$631$	10.2397	−	24.7207i	0.407634	−	0.984116i	−0.578124	−	0.815949i	$-0.696215\pi$
$631$	10.2397	−	24.7207i	0.407634	−	0.984116i	0.985758	−	0.168168i	$-0.0537850\pi$
$632$	−2.31079	−	0.957162i	−0.0919184	−	0.0380739i
$633$	−1.42761	+	1.42761i	−0.0567424	+	0.0567424i
$634$	8.62758	−	20.8288i	0.342645	−	0.827218i
$635$	−1.44711	−	3.49363i	−0.0574267	−	0.138640i
$636$	14.2550	+	14.2550i	0.565247	+	0.565247i
$637$	−4.42491	−	10.6827i	−0.175321	−	0.423263i
$638$			15.7580i			0.623865i
$639$	0.215749	−	0.0893660i	0.00853488	−	0.00353526i
$640$	1.43256	−	1.43256i	0.0566268	−	0.0566268i
$641$	−6.06617	−	2.51269i	−0.239599	−	0.0992454i	0.259653	−	0.965702i	$-0.416392\pi$
$641$	−6.06617	−	2.51269i	−0.239599	−	0.0992454i	−0.499252	+	0.866457i	$0.666392\pi$
$642$	−5.74532	−	5.74532i	−0.226750	−	0.226750i
$643$	9.75894	−	9.75894i	0.384855	−	0.384855i	−0.487993	−	0.872848i	$-0.662271\pi$
$643$	9.75894	−	9.75894i	0.384855	−	0.384855i	0.872848	+	0.487993i	$0.162271\pi$
$644$	3.26498	−	7.88235i	0.128658	−	0.310608i
$645$	16.2067	−	6.71303i	0.638138	−	0.264325i
$646$		−	4.93063i		−	0.193993i
$647$	5.76909	+	13.9278i	0.226806	+	0.547559i	0.995785	−	0.0917152i	$-0.0292349\pi$
$647$	5.76909	+	13.9278i	0.226806	+	0.547559i	−0.768979	+	0.639274i	$0.779235\pi$
$648$	6.52114	+	6.52114i	0.256175	+	0.256175i
$649$	−14.8227	−	6.13976i	−0.581841	−	0.241007i
$650$	2.85236	+	1.18148i	0.111879	+	0.0463416i
$651$	−3.25128	−	3.25128i	−0.127428	−	0.127428i
$652$	1.94243	+	4.68944i	0.0760715	+	0.183653i
$653$		−	41.9720i		−	1.64249i	−0.570576	−	0.821245i	$-0.693280\pi$
$653$		−	41.9720i		−	1.64249i	0.570576	−	0.821245i	$-0.306720\pi$
$654$	−2.04467	+	4.93628i	−0.0799531	+	0.193024i
$655$	−3.45083	+	8.33105i	−0.134835	+	0.325521i
$656$	2.51293			0.0981135
$657$	0.161410			0.00629720
$658$	−14.3033	−	14.3033i	−0.557602	−	0.557602i
$659$	−2.27510	−	0.942376i	−0.0886252	−	0.0367098i	0.337930	−	0.941171i	$-0.390273\pi$
$659$	−2.27510	−	0.942376i	−0.0886252	−	0.0367098i	−0.426556	+	0.904461i	$0.640273\pi$
$660$	8.68521	−	3.59753i	0.338071	−	0.140034i
$661$	−2.16480	−	5.22629i	−0.0842010	−	0.203279i	0.876171	−	0.482000i	$-0.160090\pi$
$661$	−2.16480	−	5.22629i	−0.0842010	−	0.203279i	−0.960372	+	0.278721i	$0.910090\pi$
$662$	9.15526	+	9.15526i	0.355829	+	0.355829i
$663$	−6.22099	+	2.57682i	−0.241603	+	0.100075i
$664$	−2.85311	+	2.85311i	−0.110722	+	0.110722i
$665$	−15.8233	−	6.55422i	−0.613601	−	0.254162i
$666$	0.241934	−	0.584080i	0.00937474	−	0.0226326i
$667$	10.1843	+	24.5871i	0.394339	+	0.952018i
$668$	23.0628	−	9.55291i	0.892325	−	0.369613i
$669$	8.06568	+	3.34091i	0.311837	+	0.129167i
$670$	2.65117	−	1.09815i	0.102424	−	0.0424252i
$671$	−0.557827	+	1.34671i	−0.0215347	+	0.0519893i
$672$	−3.09397	−	1.28156i	−0.119352	−	0.0494374i
$673$	−43.1701	+	17.8816i	−1.66408	+	0.689287i	−0.998378	−	0.0569272i	$-0.981870\pi$
$673$	−43.1701	+	17.8816i	−1.66408	+	0.689287i	−0.665706	+	0.746214i	$0.731870\pi$
$674$	−6.18387	+	6.18387i	−0.238194	+	0.238194i
$675$	−1.75752	−	4.24304i	−0.0676471	−	0.163315i
$676$	−0.788574	−	0.788574i	−0.0303298	−	0.0303298i
$677$	−41.9974			−1.61409			−0.807046	−	0.590489i	$-0.798935\pi$
$677$	−41.9974			−1.61409			−0.807046	+	0.590489i	$0.798935\pi$
$678$	−9.27771	+	3.84295i	−0.356308	+	0.147588i
$679$	1.86275	+	0.771577i	0.0714858	+	0.0296104i
$680$	0.863417	−	2.08447i	0.0331105	−	0.0799359i
$681$			7.70135i			0.295116i
$682$	3.35604	−	1.39012i	0.128509	−	0.0532304i
$683$	−0.974236	+	2.35201i	−0.0372781	+	0.0899973i	−0.941422	−	0.337231i	$-0.890510\pi$
$683$	−0.974236	+	2.35201i	−0.0372781	+	0.0899973i	0.904144	+	0.427228i	$0.140510\pi$
$684$	−0.310964	−	0.128805i	−0.0118900	−	0.00492500i
$685$	15.0519	+	6.23468i	0.575102	+	0.238215i
$686$		−	19.7704i		−	0.754838i
$687$	−15.6698	−	37.8303i	−0.597840	−	1.44331i
$688$	3.49094	−	3.49094i	0.133091	−	0.133091i
$689$		−	39.6262i		−	1.50964i
$690$	11.2264	−	11.2264i	0.427383	−	0.427383i
$691$	−6.10778	−	6.10778i	−0.232351	−	0.232351i	0.581322	−	0.813673i	$-0.302536\pi$
$691$	−6.10778	−	6.10778i	−0.232351	−	0.232351i	−0.813673	+	0.581322i	$0.802536\pi$
$692$			6.91667i			0.262932i
$693$	−0.271569	−	0.271569i	−0.0103160	−	0.0103160i
$694$	−27.2523	+	11.2883i	−1.03448	+	0.428497i
$695$	30.3495	−	12.5712i	1.15122	−	0.476853i
$696$	9.65090	−	3.99753i	0.365817	−	0.151526i
$697$	2.58553	−	1.07096i	0.0979339	−	0.0405656i
$698$	−2.63380	+	6.35855i	−0.0996907	+	0.240675i
$699$	32.4490	−	32.4490i	1.22733	−	1.22733i
$700$	1.20916	+	1.20916i	0.0457019	+	0.0457019i
$701$	−0.803601	+	1.94006i	−0.0303516	+	0.0732752i	−0.938329	−	0.345745i	$-0.887626\pi$
$701$	−0.803601	+	1.94006i	−0.0303516	+	0.0732752i	0.907977	+	0.419020i	$0.137626\pi$
$702$		−	17.6793i		−	0.667261i
$703$		−	36.8179i		−	1.38861i
$704$	1.87080	−	1.87080i	0.0705085	−	0.0705085i
$705$	−14.4048	−	34.7763i	−0.542517	−	1.30975i
$706$	−8.59187	−	20.7426i	−0.323359	−	0.780658i
$707$	10.5968	+	25.5830i	0.398535	+	0.962148i
$708$			10.6356i			0.399712i
$709$		−	18.1229i		−	0.680622i	−0.940313	−	0.340311i	$-0.889468\pi$
$709$		−	18.1229i		−	0.680622i	0.940313	−	0.340311i	$-0.110532\pi$
$710$	5.74949	−	2.38152i	0.215774	−	0.0893767i
$711$	−0.0727665	+	0.175674i	−0.00272896	+	0.00658828i
$712$			17.1563i			0.642959i
$713$	4.33799	−	4.33799i	0.162459	−	0.162459i
$714$	−3.72953			−0.139574
$715$	−17.0719	−	7.07140i	−0.638452	−	0.264455i
$716$	−11.5426			−0.431367
$717$	15.1387	−	6.27065i	0.565364	−	0.234182i
$718$	−9.98852	−	24.1144i	−0.372768	−	0.899942i
$719$	−2.49405			−0.0930123			−0.0465062	−	0.998918i	$-0.514809\pi$
$719$	−2.49405			−0.0930123			−0.0465062	+	0.998918i	$0.514809\pi$
$720$	−0.108908	−	0.108908i	−0.00405875	−	0.00405875i
$721$		−	5.60358i		−	0.208688i
$722$	−0.601849			−0.0223985
$723$	6.95270	+	16.7853i	0.258574	+	0.624252i
$724$	−1.24755	−	1.24755i	−0.0463648	−	0.0463648i
$725$	−5.33397			−0.198099
$726$	−6.48173	+	2.68482i	−0.240560	+	0.0996431i
$727$	−5.16561	−	2.13967i	−0.191582	−	0.0793559i	0.284830	−	0.958578i	$-0.408063\pi$
$727$	−5.16561	−	2.13967i	−0.191582	−	0.0793559i	−0.476412	+	0.879222i	$0.658063\pi$
$728$	2.51907	+	6.08158i	0.0933631	+	0.225398i
$729$	−18.5839	+	18.5839i	−0.688291	+	0.688291i
$730$	4.30141			0.159202
$731$	2.10402	−	5.07956i	0.0778201	−	0.187874i
$732$	0.966300			0.0357155
$733$			2.82478i			0.104336i	0.998638	+	0.0521679i	$0.0166131\pi$
$733$			2.82478i			0.104336i	−0.998638	+	0.0521679i	$0.983387\pi$
$734$	−8.11119	−	19.5822i	−0.299390	−	0.722790i
$735$	4.56069	−	11.0105i	0.168224	−	0.406128i
$736$	1.70992	−	4.12810i	0.0630283	−	0.152164i
$737$	3.46221	−	1.43409i	0.127532	−	0.0528255i
$738$		−	0.191041i		−	0.00703232i
$739$	−14.8881			−0.547666			−0.273833	−	0.961777i	$-0.588292\pi$
$739$	−14.8881			−0.547666			−0.273833	+	0.961777i	$0.588292\pi$
$740$	6.44730	−	15.5651i	0.237007	−	0.572186i
$741$	10.2442	+	24.7317i	0.376331	+	0.908543i
$742$	8.39909	−	20.2772i	0.308340	−	0.744399i
$743$	−10.5456	+	4.36813i	−0.386881	+	0.160251i	−0.567641	−	0.823276i	$-0.692144\pi$
$743$	−10.5456	+	4.36813i	−0.386881	+	0.160251i	0.180761	+	0.983527i	$0.442144\pi$
$744$	−1.70274	−	1.70274i	−0.0624255	−	0.0624255i
$745$		−	20.3913i		−	0.747079i
$746$			22.4043i			0.820278i
$747$	0.216902	+	0.216902i	0.00793603	+	0.00793603i
$748$	1.12755	−	2.72215i	0.0412273	−	0.0995316i
$749$	−3.38517	+	8.17251i	−0.123691	+	0.298617i
$750$	8.01653	+	19.3536i	0.292722	+	0.706694i
$751$	−31.0038			−1.13134			−0.565672	−	0.824630i	$-0.691383\pi$
$751$	−31.0038			−1.13134			−0.565672	+	0.824630i	$0.691383\pi$
$752$	−7.49086	−	7.49086i	−0.273163	−	0.273163i
$753$			50.6712i			1.84656i
$754$	−18.9701	−	7.85766i	−0.690849	−	0.286159i
$755$	−0.615258	−	0.615258i	−0.0223915	−	0.0223915i
$756$	3.74726	−	9.04669i	0.136287	−	0.329025i
$757$	−8.02013	−	8.02013i	−0.291497	−	0.291497i	0.546175	−	0.837671i	$-0.316083\pi$
$757$	−8.02013	−	8.02013i	−0.291497	−	0.291497i	−0.837671	+	0.546175i	$0.816083\pi$
$758$	−13.7117	+	13.7117i	−0.498032	+	0.498032i
$759$	14.6608	−	14.6608i	0.532153	−	0.532153i
$760$	−8.28688	−	3.43254i	−0.300597	−	0.124511i
$761$	30.6130			1.10972			0.554859	−	0.831944i	$-0.312772\pi$
$761$	30.6130			1.10972			0.554859	+	0.831944i	$0.312772\pi$
$762$	−2.31480	+	2.31480i	−0.0838564	+	0.0838564i
$763$	5.81695			0.210588
$764$	−8.66557	+	20.9205i	−0.313509	+	0.756878i
$765$	−0.158468	−	0.0656397i	−0.00572943	−	0.00237321i
$766$	0.687963	−	0.687963i	0.0248571	−	0.0248571i
$767$	14.7825	−	14.7825i	0.533767	−	0.533767i
$768$	−1.62035	−	0.671173i	−0.0584695	−	0.0242189i
$769$	12.7039	+	30.6700i	0.458116	+	1.10599i	0.969159	+	0.246435i	$0.0792592\pi$
$769$	12.7039	+	30.6700i	0.458116	+	1.10599i	−0.511043	+	0.859555i	$0.670741\pi$
$770$	−7.23704	−	7.23704i	−0.260805	−	0.260805i
$771$	−6.57617	−	15.8763i	−0.236835	−	0.571770i
$772$	−2.98186	−	7.19885i	−0.107320	−	0.259092i
$773$	36.2025			1.30211			0.651056	−	0.759029i	$-0.274326\pi$
$773$	36.2025			1.30211			0.651056	+	0.759029i	$0.274326\pi$
$774$	−0.265392	−	0.265392i	−0.00953932	−	0.00953932i
$775$	0.470545	+	1.13600i	0.0169025	+	0.0408062i
$776$	0.975549	+	0.404086i	0.0350202	+	0.0145058i
$777$	−27.8491			−0.999081
$778$	−1.47575	+	0.611276i	−0.0529082	+	0.0219153i
$779$	−4.25764	−	10.2788i	−0.152546	−	0.368278i
$780$			12.2495i			0.438602i
$781$	7.50836	−	3.11006i	0.268670	−	0.111287i
$782$		−	4.97609i		−	0.177945i
$783$	11.6887	+	28.2190i	0.417720	+	1.00847i
$784$		−	3.35405i		−	0.119787i
$785$	43.6338	−	18.0737i	1.55736	−	0.645078i
$786$	7.80642			0.278446
$787$	21.6610	+	8.97229i	0.772132	+	0.319828i	0.733736	−	0.679435i	$-0.237775\pi$
$787$	21.6610	+	8.97229i	0.772132	+	0.319828i	0.0383964	+	0.999263i	$0.487775\pi$
$788$	−6.83028			−0.243319
$789$	26.5006	−	10.9769i	0.943446	−	0.390788i
$790$	−1.93916	+	4.68153i	−0.0689920	+	0.166562i
$791$	7.73074	+	7.73074i	0.274873	+	0.274873i
$792$	−0.142224	−	0.142224i	−0.00505372	−	0.00505372i
$793$	−1.34307	−	1.34307i	−0.0476937	−	0.0476937i
$794$	20.3362	−	20.3362i	0.721706	−	0.721706i
$795$	28.8798	−	28.8798i	1.02426	−	1.02426i
$796$	−4.75814	−	11.4872i	−0.168648	−	0.407152i
$797$	−20.8101			−0.737131			−0.368565	−	0.929602i	$-0.620151\pi$
$797$	−20.8101			−0.737131			−0.368565	+	0.929602i	$0.620151\pi$
$798$			14.8268i			0.524865i
$799$	−10.8997	−	4.51481i	−0.385604	−	0.159723i
$800$	0.633253	+	0.633253i	0.0223889	+	0.0223889i
$801$	1.30428			0.0460843
$802$	3.88138	+	19.6452i	0.137056	+	0.693697i
$803$	5.61729			0.198230
$804$	−1.75661	−	1.75661i	−0.0619507	−	0.0619507i
$805$	−15.9692	−	6.61466i	−0.562840	−	0.233136i
$806$			4.73331i			0.166724i
$807$	−37.6175			−1.32420
$808$	5.54971	+	13.3982i	0.195238	+	0.471346i
$809$	33.3650	−	33.3650i	1.17305	−	1.17305i	0.191573	−	0.981478i	$-0.438641\pi$
$809$	33.3650	−	33.3650i	1.17305	−	1.17305i	0.981478	−	0.191573i	$-0.0613588\pi$
$810$	13.2115	−	13.2115i	0.464204	−	0.464204i
$811$	37.6728	+	37.6728i	1.32287	+	1.32287i	0.911440	+	0.411432i	$0.134971\pi$
$811$	37.6728	+	37.6728i	1.32287	+	1.32287i	0.411432	+	0.911440i	$0.365029\pi$
$812$	−8.04171	−	8.04171i	−0.282209	−	0.282209i
$813$	−13.8395	−	13.8395i	−0.485372	−	0.485372i
$814$	8.41964	−	20.3268i	0.295108	−	0.712454i
$815$	9.50055	−	3.93525i	0.332790	−	0.137846i
$816$	−1.95321			−0.0683759
$817$	−20.1939	−	8.36460i	−0.706496	−	0.292640i
$818$	14.1588			0.495050
$819$	0.462341	−	0.191508i	0.0161555	−	0.00669183i
$820$		−	5.09105i		−	0.177787i
$821$	16.9168	+	40.8408i	0.590401	+	1.42535i	0.883116	+	0.469154i	$0.155441\pi$
$821$	16.9168	+	40.8408i	0.590401	+	1.42535i	−0.292715	+	0.956200i	$0.594559\pi$
$822$		−	14.1040i		−	0.491934i
$823$	−13.6053	+	5.63549i	−0.474250	+	0.196441i	−0.606989	−	0.794710i	$-0.707623\pi$
$823$	−13.6053	+	5.63549i	−0.474250	+	0.196441i	0.132739	+	0.991151i	$0.457623\pi$
$824$		−	2.93468i		−	0.102234i
$825$	1.59027	+	3.83924i	0.0553660	+	0.133665i
$826$	10.6977	−	4.43112i	0.372220	−	0.154178i
$827$	−1.39995			−0.0486810			−0.0243405	−	0.999704i	$-0.507749\pi$
$827$	−1.39995			−0.0486810			−0.0243405	+	0.999704i	$0.507749\pi$
$828$	−0.313831	−	0.129993i	−0.0109064	−	0.00451758i
$829$	−11.3416	−	27.3811i	−0.393911	−	0.950985i	−0.989079	−	0.147384i	$-0.952915\pi$
$829$	−11.3416	−	27.3811i	−0.393911	−	0.950985i	0.595168	−	0.803601i	$-0.297085\pi$
$830$	5.78023	+	5.78023i	0.200635	+	0.200635i
$831$	−17.6758			−0.613168
$832$	1.31928	+	3.18501i	0.0457376	+	0.110420i
$833$	−1.42943	−	3.45094i	−0.0495267	−	0.119568i
$834$	−20.1090	−	20.1090i	−0.696316	−	0.696316i
$835$	−19.3537	−	46.7238i	−0.669761	−	1.61695i
$836$	−10.8220	−	4.48261i	−0.374286	−	0.155034i
$837$	4.97878	−	4.97878i	0.172092	−	0.172092i
$838$	9.08368	−	9.08368i	0.313790	−	0.313790i
$839$	−49.8632	−	20.6540i	−1.72147	−	0.713056i	−0.999783	−	0.0208342i	$-0.993368\pi$
$839$	−49.8632	−	20.6540i	−1.72147	−	0.713056i	−0.721685	−	0.692221i	$-0.756632\pi$
$840$	−2.59637	+	6.26820i	−0.0895834	+	0.216273i
$841$	6.47444			0.223257
$842$	4.99912	−	4.99912i	0.172281	−	0.172281i
$843$	26.5723			0.915197
$844$	1.06352	+	0.440524i	0.0366078	+	0.0151634i
$845$	−1.59761	+	1.59761i	−0.0549593	+	0.0549593i
$846$	−0.569479	+	0.569479i	−0.0195791	+	0.0195791i
$847$	5.40097	+	5.40097i	0.185579	+	0.185579i
$848$	4.39872	−	10.6195i	0.151053	−	0.364674i
$849$	−28.9394	−	28.9394i	−0.993197	−	0.993197i
$850$	0.921428	+	0.381668i	0.0316047	+	0.0130911i
$851$		−	37.1574i		−	1.27374i
$852$	−3.80949	−	3.80949i	−0.130511	−	0.130511i
$853$	19.1788			0.656668			0.328334	−	0.944562i	$-0.393513\pi$
$853$	19.1788			0.656668			0.328334	+	0.944562i	$0.393513\pi$
$854$	−0.402589	−	0.971937i	−0.0137763	−	0.0332590i
$855$	−0.260952	+	0.629995i	−0.00892438	+	0.0215454i
$856$	−1.77286	+	4.28006i	−0.0605951	+	0.146289i
$857$	27.0787	+	27.0787i	0.924989	+	0.924989i	0.997377	−	0.0723872i	$-0.0230617\pi$
$857$	27.0787	+	27.0787i	0.924989	+	0.924989i	−0.0723872	+	0.997377i	$0.523062\pi$
$858$			15.9968i			0.546122i
$859$		−	0.0968166i		−	0.00330334i	−0.999999	−	0.00165167i	$-0.999474\pi$
$859$		−	0.0968166i		−	0.00330334i	0.999999	−	0.00165167i	$-0.000525743\pi$
$860$	−7.07244	−	7.07244i	−0.241168	−	0.241168i
$861$	−7.77493	+	3.22048i	−0.264969	+	0.109754i
$862$	−0.694027	+	1.67553i	−0.0236386	+	0.0570687i
$863$	−19.6347	−	47.4023i	−0.668372	−	1.61359i	−0.784334	−	0.620339i	$-0.786995\pi$
$863$	−19.6347	−	47.4023i	−0.668372	−	1.61359i	0.115962	−	0.993254i	$-0.463005\pi$
$864$	1.96249	−	4.73788i	0.0667654	−	0.161186i
$865$	14.0128			0.476449
$866$			33.7262i			1.14606i
$867$	25.5364	−	10.5775i	0.867262	−	0.359231i
$868$	−1.00326	+	2.42209i	−0.0340529	+	0.0822110i
$869$	−2.53238	+	6.11370i	−0.0859050	+	0.207393i
$870$	−8.09878	−	19.5522i	−0.274574	−	0.662881i
$871$			4.88304i			0.165456i
$872$	3.04642			0.103165
$873$	0.0307199	−	0.0741644i	0.00103971	−	0.00251008i
$874$	−19.7826			−0.669157
$875$	16.1266	−	16.1266i	0.545178	−	0.545178i
$876$	−1.42501	−	3.44028i	−0.0481467	−	0.116236i
$877$	1.90555	+	0.789303i	0.0643457	+	0.0266529i	0.414624	−	0.909993i	$-0.363913\pi$
$877$	1.90555	+	0.789303i	0.0643457	+	0.0266529i	−0.350278	+	0.936646i	$0.613913\pi$
$878$	−4.00140	+	1.65744i	−0.135041	+	0.0559357i
$879$	17.1001			0.576774
$880$	−3.79014	−	3.79014i	−0.127766	−	0.127766i
$881$	12.9821	+	31.3416i	0.437379	+	1.05593i	0.976851	+	0.213923i	$0.0686241\pi$
$881$	12.9821	+	31.3416i	0.437379	+	1.05593i	−0.539471	+	0.842004i	$0.681376\pi$
$882$	−0.254985			−0.00858580
$883$		−	26.7375i		−	0.899790i	−0.893082	−	0.449895i	$-0.851461\pi$
$883$		−	26.7375i		−	0.899790i	0.893082	−	0.449895i	$-0.148539\pi$
$884$	2.71478	+	2.71478i	0.0913079	+	0.0913079i
$885$	21.5472			0.724301
$886$	−7.92024	−	19.1211i	−0.266086	−	0.642387i
$887$	−30.0865	+	12.4623i	−1.01021	+	0.418441i	−0.825530	−	0.564358i	$-0.809124\pi$
$887$	−30.0865	+	12.4623i	−1.01021	+	0.418441i	−0.184677	+	0.982799i	$0.559124\pi$
$888$	−14.5850			−0.489440
$889$	3.29272	+	1.36389i	0.110434	+	0.0457434i
$890$	34.7577			1.16508
$891$	17.2531	−	17.2531i	0.578000	−	0.578000i
$892$		−	4.97772i		−	0.166666i
$893$	−17.9488	+	43.3322i	−0.600633	+	1.45006i
$894$	−16.3090	+	6.75541i	−0.545455	+	0.225935i
$895$			23.3846i			0.781662i
$896$			1.90944i			0.0637898i
$897$	10.3387	+	24.9598i	0.345199	+	0.833383i
$898$	−2.76553	−	6.67658i	−0.0922869	−	0.222800i
$899$	−3.12944	−	7.55513i	−0.104373	−	0.251978i
$900$	0.0481419	−	0.0481419i	0.00160473	−	0.00160473i
$901$		−	12.8009i		−	0.426460i
$902$		−	6.64850i		−	0.221371i
$903$	−6.32699	+	15.2747i	−0.210549	+	0.508310i
$904$	4.04870	+	4.04870i	0.134658	+	0.134658i
$905$	−2.52746	+	2.52746i	−0.0840157	+	0.0840157i
$906$	−0.288257	+	0.695914i	−0.00957670	+	0.0231202i
$907$	30.3327	−	12.5642i	1.00718	−	0.417189i	0.182756	−	0.983158i	$-0.441498\pi$
$907$	30.3327	−	12.5642i	1.00718	−	0.417189i	0.824426	+	0.565970i	$0.191498\pi$
$908$	4.05684	−	1.68040i	0.134631	−	0.0557659i
$909$	1.01857	−	0.421906i	0.0337839	−	0.0139938i
$910$	12.3209	−	5.10350i	0.408435	−	0.169179i
$911$	2.89837	+	2.89837i	0.0960274	+	0.0960274i	0.753489	−	0.657461i	$-0.228370\pi$
$911$	2.89837	+	2.89837i	0.0960274	+	0.0960274i	−0.657461	+	0.753489i	$0.728370\pi$
$912$			7.76503i			0.257126i
$913$	7.54850	+	7.54850i	0.249819	+	0.249819i
$914$	17.2905	−	17.2905i	0.571919	−	0.571919i
$915$		−	1.95767i		−	0.0647185i
$916$	−16.5088	+	16.5088i	−0.545465	+	0.545465i
$917$	−3.25239	−	7.85196i	−0.107403	−	0.259295i
$918$		−	5.71113i		−	0.188495i
$919$	−38.3604	−	15.8894i	−1.26539	−	0.524143i	−0.353832	−	0.935309i	$-0.615122\pi$
$919$	−38.3604	−	15.8894i	−1.26539	−	0.524143i	−0.911560	+	0.411166i	$0.865122\pi$
$920$	−8.36330	−	3.46419i	−0.275730	−	0.114211i
$921$	−2.32323	+	5.60877i	−0.0765530	+	0.184815i
$922$	−7.68795	+	3.18445i	−0.253189	+	0.104874i
$923$			10.5897i			0.348563i
$924$	−3.39065	+	8.18575i	−0.111544	+	0.269292i
$925$	6.88048	+	2.84999i	0.226229	+	0.0937070i
$926$	−22.5586	+	9.34407i	−0.741321	+	0.307065i
$927$	−0.223103			−0.00732767
$928$	−4.21156	−	4.21156i	−0.138251	−	0.138251i
$929$	−11.7309	−	28.3208i	−0.384877	−	0.929175i	−0.991007	−	0.133810i	$-0.957279\pi$
$929$	−11.7309	−	28.3208i	−0.384877	−	0.929175i	0.606130	−	0.795365i	$-0.292721\pi$
$930$	−3.44966	+	3.44966i	−0.113119	+	0.113119i
$931$	−13.7193	+	5.68273i	−0.449633	+	0.186244i
$932$	−24.1734	−	10.0129i	−0.791825	−	0.327985i
$933$	0.337659	−	0.815181i	0.0110545	−	0.0266878i
$934$	5.23042	−	2.16651i	0.171145	−	0.0708904i
$935$	−5.51492	−	2.28435i	−0.180357	−	0.0747064i
$936$	0.242135	−	0.100295i	0.00791442	−	0.00327826i
$937$	−2.97154	−	7.17394i	−0.0970761	−	0.234362i	0.867880	−	0.496774i	$-0.165482\pi$
$937$	−2.97154	−	7.17394i	−0.0970761	−	0.234362i	−0.964956	+	0.262412i	$0.915482\pi$
$938$	−1.03500	+	2.49871i	−0.0337939	+	0.0815857i
$939$	−38.8738	−	16.1021i	−1.26860	−	0.525471i
$940$	−15.1760	+	15.1760i	−0.494988	+	0.494988i
$941$	28.7075	−	11.8910i	0.935837	−	0.387636i	0.137947	−	0.990440i	$-0.455950\pi$
$941$	28.7075	−	11.8910i	0.935837	−	0.387636i	0.797890	+	0.602803i	$0.205950\pi$
$942$	−28.9108	−	28.9108i	−0.941965	−	0.941965i
$943$	−4.29690	−	10.3736i	−0.139926	−	0.337812i
$944$	5.60253	−	2.32064i	0.182347	−	0.0755305i
$945$	−18.3281	−	7.59174i	−0.596212	−	0.246959i
$946$	−9.23602	−	9.23602i	−0.300289	−	0.300289i
$947$	55.1899			1.79343			0.896715	−	0.442607i	$-0.145946\pi$
$947$	55.1899			1.79343			0.896715	+	0.442607i	$0.145946\pi$
$948$	4.38673			0.142474
$949$	−2.80104	+	6.76231i	−0.0909256	+	0.219514i
$950$	1.51733	−	3.66316i	0.0492288	−	0.118849i
$951$			39.5407i			1.28219i
$952$	0.813765	+	1.96460i	0.0263743	+	0.0636731i
$953$	3.59645	+	3.59645i	0.116500	+	0.116500i	0.762954	−	0.646453i	$-0.223748\pi$
$953$	3.59645	+	3.59645i	0.116500	+	0.116500i	−0.646453	+	0.762954i	$0.723748\pi$
$954$	−0.807325	−	0.334405i	−0.0261381	−	0.0108268i
$955$	42.3838	+	17.5559i	1.37151	+	0.568097i
$956$	−6.60637	−	6.60637i	−0.213665	−	0.213665i
$957$	−10.5763	−	25.5335i	−0.341884	−	0.825382i
$958$			35.2294i			1.13821i
$959$	−14.1863	+	5.87615i	−0.458099	+	0.189751i
$960$	−1.35976	+	3.28275i	−0.0438860	+	0.105950i
$961$	20.5873	−	20.5873i	0.664108	−	0.664108i
$962$	20.2718	+	20.2718i	0.653588	+	0.653588i
$963$	0.325384	+	0.134778i	0.0104853	+	0.00434317i
$964$	7.32494	−	7.32494i	0.235921	−	0.235921i
$965$	−14.5845	+	6.04108i	−0.469491	+	0.194469i
$966$			14.9636i			0.481445i
$967$	−7.43940	−	17.9603i	−0.239235	−	0.577564i	0.757969	−	0.652290i	$-0.226192\pi$
$967$	−7.43940	−	17.9603i	−0.239235	−	0.577564i	−0.997204	+	0.0747263i	$0.976192\pi$
$968$	2.82856	+	2.82856i	0.0909135	+	0.0909135i
$969$	3.30930	+	7.98936i	0.106310	+	0.256655i
$970$	0.818655	−	1.97641i	0.0262854	−	0.0634586i
$971$	15.0597	−	15.0597i	0.483288	−	0.483288i	−0.422892	−	0.906180i	$-0.638985\pi$
$971$	15.0597	−	15.0597i	0.483288	−	0.483288i	0.906180	+	0.422892i	$0.138985\pi$
$972$	−0.729742	−	0.302269i	−0.0234065	−	0.00969529i
$973$	−11.8483	+	28.6043i	−0.379838	+	0.917010i
$974$	16.8428	+	16.8428i	0.539680	+	0.539680i
$975$	−5.41481			−0.173413
$976$	−0.210842	−	0.509017i	−0.00674888	−	0.0162932i
$977$	12.7954	−	12.7954i	0.409360	−	0.409360i	−0.472156	−	0.881515i	$-0.656524\pi$
$977$	12.7954	−	12.7954i	0.409360	−	0.409360i	0.881515	+	0.472156i	$0.156524\pi$
$978$	−6.29486	−	6.29486i	−0.201287	−	0.201287i
$979$	45.3907			1.45069
$980$	−6.79511			−0.217062
$981$		−	0.231598i		−	0.00739437i
$982$	−11.3992	+	11.3992i	−0.363762	+	0.363762i
$983$	−6.82032	+	6.82032i	−0.217534	+	0.217534i	−0.807459	−	0.589924i	$-0.799158\pi$
$983$	−6.82032	+	6.82032i	−0.217534	+	0.217534i	0.589924	+	0.807459i	$0.299158\pi$
$984$	−4.07184	+	1.68661i	−0.129806	+	0.0537672i
$985$			13.8378i			0.440907i
$986$	−6.12811	−	2.53835i	−0.195159	−	0.0808374i
$987$	32.7765	+	13.5765i	1.04329	+	0.432143i
$988$	10.7927	−	10.7927i	0.343361	−	0.343361i
$989$	−20.3801	−	8.44173i	−0.648051	−	0.268432i
$990$	−0.288138	+	0.288138i	−0.00915764	+	0.00915764i
$991$	−2.32800	−	0.964287i	−0.0739512	−	0.0306316i	0.345401	−	0.938455i	$-0.387743\pi$
$991$	−2.32800	−	0.964287i	−0.0739512	−	0.0306316i	−0.419352	+	0.907824i	$0.637743\pi$
$992$	−0.525422	+	1.26848i	−0.0166822	+	0.0402743i
$993$	−20.9795	−	8.69001i	−0.665765	−	0.275769i
$994$	−2.24456	+	5.41886i	−0.0711932	+	0.171876i
$995$	−23.2724	+	9.63973i	−0.737784	+	0.305600i
$996$	2.70812	−	6.53797i	0.0858099	−	0.207164i
$997$	35.4039			1.12125			0.560627	−	0.828069i	$-0.310560\pi$
$997$	35.4039			1.12125			0.560627	+	0.828069i	$0.310560\pi$
$998$	−7.13567			−0.225876
$999$		−	42.6461i		−	1.34926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	802.2.e.b.45.5	✓	68
401.303	even	8	inner	802.2.e.b.303.5	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
802.2.e.b.45.5	✓	68	1.1	even	1	trivial
802.2.e.b.303.5	yes	68	401.303	even	8	inner

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:	\( N \)	\(=\)	\( 802 = 2 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	802.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.62035 - 0.671173i) q^{3} +1.00000i q^{4} +2.02594 q^{5} +(-0.671173 - 1.62035i) q^{6} +(-1.35018 + 1.35018i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.0537565 + 0.0537565i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.62035 - 0.671173i) q^{3} +1.00000i q^{4} +2.02594 q^{5} +(-0.671173 - 1.62035i) q^{6} +(-1.35018 + 1.35018i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.0537565 + 0.0537565i) q^{9} +(1.43256 + 1.43256i) q^{10} +(1.87080 + 1.87080i) q^{11} +(0.671173 - 1.62035i) q^{12} +(-3.18501 + 1.31928i) q^{13} -1.90944 q^{14} +(-3.28275 - 1.35976i) q^{15} -1.00000 q^{16} +(-1.02889 + 0.426180i) q^{17} +0.0760232i q^{18} +(1.69429 + 4.09038i) q^{19} +2.02594i q^{20} +(3.09397 - 1.28156i) q^{21} +2.64571i q^{22} +(1.70992 + 4.12810i) q^{23} +(1.62035 - 0.671173i) q^{24} -0.895556 q^{25} +(-3.18501 - 1.31928i) q^{26} +(1.96249 + 4.73788i) q^{27} +(-1.35018 - 1.35018i) q^{28} +5.95604 q^{29} +(-1.35976 - 3.28275i) q^{30} +(-0.525422 - 1.26848i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.77573 - 4.28700i) q^{33} +(-1.02889 - 0.426180i) q^{34} +(-2.73538 + 2.73538i) q^{35} +(-0.0537565 + 0.0537565i) q^{36} +(-7.68292 - 3.18237i) q^{37} +(-1.69429 + 4.09038i) q^{38} +6.04631 q^{39} +(-1.43256 + 1.43256i) q^{40} -2.51293 q^{41} +(3.09397 + 1.28156i) q^{42} +(-3.49094 + 3.49094i) q^{43} +(-1.87080 + 1.87080i) q^{44} +(0.108908 + 0.108908i) q^{45} +(-1.70992 + 4.12810i) q^{46} +(7.49086 + 7.49086i) q^{47} +(1.62035 + 0.671173i) q^{48} +3.35405i q^{49} +(-0.633253 - 0.633253i) q^{50} +1.95321 q^{51} +(-1.31928 - 3.18501i) q^{52} +(-4.39872 + 10.6195i) q^{53} +(-1.96249 + 4.73788i) q^{54} +(3.79014 + 3.79014i) q^{55} -1.90944i q^{56} -7.76503i q^{57} +(4.21156 + 4.21156i) q^{58} +(-5.60253 + 2.32064i) q^{59} +(1.35976 - 3.28275i) q^{60} +(0.210842 + 0.509017i) q^{61} +(0.525422 - 1.26848i) q^{62} -0.145162 q^{63} -1.00000i q^{64} +(-6.45265 + 2.67278i) q^{65} +(1.77573 - 4.28700i) q^{66} +(0.542044 - 1.30861i) q^{67} +(-0.426180 - 1.02889i) q^{68} -7.83664i q^{69} -3.86841 q^{70} +(1.17551 - 2.83793i) q^{71} -0.0760232 q^{72} +(1.50131 - 1.50131i) q^{73} +(-3.18237 - 7.68292i) q^{74} +(1.45112 + 0.601073i) q^{75} +(-4.09038 + 1.69429i) q^{76} -5.05183 q^{77} +(4.27539 + 4.27539i) q^{78} +(0.957162 + 2.31079i) q^{79} -2.02594 q^{80} -9.22229i q^{81} +(-1.77691 - 1.77691i) q^{82} +4.03490 q^{83} +(1.28156 + 3.09397i) q^{84} +(-2.08447 + 0.863417i) q^{85} -4.93693 q^{86} +(-9.65090 - 3.99753i) q^{87} -2.64571 q^{88} +(12.1313 - 12.1313i) q^{89} +0.154019i q^{90} +(2.51907 - 6.08158i) q^{91} +(-4.12810 + 1.70992i) q^{92} +2.40804i q^{93} +10.5937i q^{94} +(3.43254 + 8.28688i) q^{95} +(0.671173 + 1.62035i) q^{96} +(-0.404086 - 0.975549i) q^{97} +(-2.37167 + 2.37167i) q^{98} +0.201136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 68 * q + 4 * q^6 + 20 * q^9	\( 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) \) 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

Introduction

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