LMFDB - Embedded newform 666.2.k.a.175.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.10
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(0.0965604 + 1.72936i) q^{3} -1.00000 q^{4} -2.20312i q^{5} +(1.72936 - 0.0965604i) q^{6} +(-0.875783 + 1.51690i) q^{7} +1.00000i q^{8} +(-2.98135 + 0.333975i) q^{9} -2.20312 q^{10} +(-2.89341 - 5.01153i) q^{11} +(-0.0965604 - 1.72936i) q^{12} +1.73401i q^{13} +(1.51690 + 0.875783i) q^{14} +(3.80998 - 0.212734i) q^{15} +1.00000 q^{16} +(-1.78280 - 1.02930i) q^{17} +(0.333975 + 2.98135i) q^{18} +(-2.49642 + 1.44131i) q^{19} +2.20312i q^{20} +(-2.70783 - 1.36807i) q^{21} +(-5.01153 + 2.89341i) q^{22} +(-4.24050 - 2.44826i) q^{23} +(-1.72936 + 0.0965604i) q^{24} +0.146254 q^{25} +1.73401 q^{26} +(-0.865442 - 5.12357i) q^{27} +(0.875783 - 1.51690i) q^{28} +(-3.02653 + 1.74737i) q^{29} +(-0.212734 - 3.80998i) q^{30} +(-5.00602 - 2.89022i) q^{31} -1.00000i q^{32} +(8.38734 - 5.48765i) q^{33} +(-1.02930 + 1.78280i) q^{34} +(3.34192 + 1.92946i) q^{35} +(2.98135 - 0.333975i) q^{36} +(2.05548 - 5.72495i) q^{37} +(1.44131 + 2.49642i) q^{38} +(-2.99873 + 0.167437i) q^{39} +2.20312 q^{40} -0.153407 q^{41} +(-1.36807 + 2.70783i) q^{42} +(-1.67257 + 0.965660i) q^{43} +(2.89341 + 5.01153i) q^{44} +(0.735787 + 6.56828i) q^{45} +(-2.44826 + 4.24050i) q^{46} +(-2.21426 - 3.83521i) q^{47} +(0.0965604 + 1.72936i) q^{48} +(1.96601 + 3.40523i) q^{49} -0.146254i q^{50} +(1.60788 - 3.18249i) q^{51} -1.73401i q^{52} +(3.36414 - 5.82685i) q^{53} +(-5.12357 + 0.865442i) q^{54} +(-11.0410 + 6.37453i) q^{55} +(-1.51690 - 0.875783i) q^{56} +(-2.73359 - 4.17802i) q^{57} +(1.74737 + 3.02653i) q^{58} +(-3.26980 + 1.88782i) q^{59} +(-3.80998 + 0.212734i) q^{60} +(-5.05840 - 2.92047i) q^{61} +(-2.89022 + 5.00602i) q^{62} +(2.10441 - 4.81490i) q^{63} -1.00000 q^{64} +3.82024 q^{65} +(-5.48765 - 8.38734i) q^{66} -11.9957 q^{67} +(1.78280 + 1.02930i) q^{68} +(3.82444 - 7.56975i) q^{69} +(1.92946 - 3.34192i) q^{70} +(4.20433 + 7.28212i) q^{71} +(-0.333975 - 2.98135i) q^{72} -8.77691 q^{73} +(-5.72495 - 2.05548i) q^{74} +(0.0141223 + 0.252925i) q^{75} +(2.49642 - 1.44131i) q^{76} +10.1360 q^{77} +(0.167437 + 2.99873i) q^{78} +(8.51800 + 4.91787i) q^{79} -2.20312i q^{80} +(8.77692 - 1.99139i) q^{81} +0.153407i q^{82} -5.50705 q^{83} +(2.70783 + 1.36807i) q^{84} +(-2.26768 + 3.92773i) q^{85} +(0.965660 + 1.67257i) q^{86} +(-3.31406 - 5.06522i) q^{87} +(5.01153 - 2.89341i) q^{88} +(12.2455 + 7.06992i) q^{89} +(6.56828 - 0.735787i) q^{90} +(-2.63032 - 1.51862i) q^{91} +(4.24050 + 2.44826i) q^{92} +(4.51485 - 8.93627i) q^{93} +(-3.83521 + 2.21426i) q^{94} +(3.17537 + 5.49991i) q^{95} +(1.72936 - 0.0965604i) q^{96} +(10.6935 - 6.17388i) q^{97} +(3.40523 - 1.96601i) q^{98} +(10.3000 + 13.9748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.0965604	+	1.72936i	0.0557492	+	0.998445i
$3$	0.0965604	+	1.72936i	0.0557492	+	0.998445i
$4$	−1.00000			−0.500000
$5$		−	2.20312i		−	0.985266i	−0.870237	−	0.492633i	$-0.836034\pi$
$5$		−	2.20312i		−	0.985266i	0.870237	−	0.492633i	$-0.163966\pi$
$6$	1.72936	−	0.0965604i	0.706007	−	0.0394206i
$7$	−0.875783	+	1.51690i	−0.331015	+	0.573334i	−0.982711	−	0.185146i	$-0.940724\pi$
$7$	−0.875783	+	1.51690i	−0.331015	+	0.573334i	0.651696	+	0.758480i	$0.274058\pi$
$8$			1.00000i			0.353553i
$9$	−2.98135	+	0.333975i	−0.993784	+	0.111325i
$10$	−2.20312			−0.696688
$11$	−2.89341	−	5.01153i	−0.872396	−	1.51103i	−0.859511	−	0.511117i	$-0.829232\pi$
$11$	−2.89341	−	5.01153i	−0.872396	−	1.51103i	−0.0128842	−	0.999917i	$-0.504101\pi$
$12$	−0.0965604	−	1.72936i	−0.0278746	−	0.499222i
$13$			1.73401i			0.480928i	0.970658	+	0.240464i	$0.0772996\pi$
$13$			1.73401i			0.480928i	−0.970658	+	0.240464i	$0.922700\pi$
$14$	1.51690	+	0.875783i	0.405409	+	0.234063i
$15$	3.80998	−	0.212734i	0.983734	−	0.0549278i
$16$	1.00000			0.250000
$17$	−1.78280	−	1.02930i	−0.432393	−	0.249642i	0.267973	−	0.963427i	$-0.413646\pi$
$17$	−1.78280	−	1.02930i	−0.432393	−	0.249642i	−0.700366	+	0.713784i	$0.746980\pi$
$18$	0.333975	+	2.98135i	0.0787186	+	0.702711i
$19$	−2.49642	+	1.44131i	−0.572717	+	0.330658i	−0.758234	−	0.651983i	$-0.773937\pi$
$19$	−2.49642	+	1.44131i	−0.572717	+	0.330658i	0.185517	+	0.982641i	$0.440604\pi$
$20$			2.20312i			0.492633i
$21$	−2.70783	−	1.36807i	−0.590896	−	0.298537i
$22$	−5.01153	+	2.89341i	−1.06846	+	0.616877i
$23$	−4.24050	−	2.44826i	−0.884206	−	0.510497i	−0.0121633	−	0.999926i	$-0.503872\pi$
$23$	−4.24050	−	2.44826i	−0.884206	−	0.510497i	−0.872043	+	0.489429i	$0.837205\pi$
$24$	−1.72936	+	0.0965604i	−0.353004	+	0.0197103i
$25$	0.146254			0.0292508
$26$	1.73401			0.340068
$27$	−0.865442	−	5.12357i	−0.166554	−	0.986032i
$28$	0.875783	−	1.51690i	0.165507	−	0.286667i
$29$	−3.02653	+	1.74737i	−0.562012	+	0.324478i	−0.753953	−	0.656929i	$-0.771855\pi$
$29$	−3.02653	+	1.74737i	−0.562012	+	0.324478i	0.191941	+	0.981406i	$0.438522\pi$
$30$	−0.212734	−	3.80998i	−0.0388398	−	0.695605i
$31$	−5.00602	−	2.89022i	−0.899107	−	0.519100i	−0.0221966	−	0.999754i	$-0.507066\pi$
$31$	−5.00602	−	2.89022i	−0.899107	−	0.519100i	−0.876910	+	0.480654i	$0.840399\pi$
$32$		−	1.00000i		−	0.176777i
$33$	8.38734	−	5.48765i	1.46005	−	0.955278i
$34$	−1.02930	+	1.78280i	−0.176524	+	0.305748i
$35$	3.34192	+	1.92946i	0.564887	+	0.326138i
$36$	2.98135	−	0.333975i	0.496892	−	0.0556625i
$37$	2.05548	−	5.72495i	0.337918	−	0.941175i
$37$	2.05548	−	5.72495i	0.337918	−	0.941175i
$38$	1.44131	+	2.49642i	0.233811	+	0.404972i
$39$	−2.99873	+	0.167437i	−0.480180	+	0.0268114i
$40$	2.20312			0.348344
$41$	−0.153407			−0.0239582			−0.0119791	−	0.999928i	$-0.503813\pi$
$41$	−0.153407			−0.0239582			−0.0119791	+	0.999928i	$0.503813\pi$
$42$	−1.36807	+	2.70783i	−0.211098	+	0.417827i
$43$	−1.67257	+	0.965660i	−0.255065	+	0.147262i	−0.622081	−	0.782953i	$-0.713713\pi$
$43$	−1.67257	+	0.965660i	−0.255065	+	0.147262i	0.367016	+	0.930214i	$0.380379\pi$
$44$	2.89341	+	5.01153i	0.436198	+	0.755517i
$45$	0.735787	+	6.56828i	0.109685	+	0.979142i
$46$	−2.44826	+	4.24050i	−0.360976	+	0.625228i
$47$	−2.21426	−	3.83521i	−0.322983	−	0.559422i	0.658119	−	0.752914i	$-0.271352\pi$
$47$	−2.21426	−	3.83521i	−0.322983	−	0.559422i	−0.981102	+	0.193491i	$0.938019\pi$
$48$	0.0965604	+	1.72936i	0.0139373	+	0.249611i
$49$	1.96601	+	3.40523i	0.280859	+	0.486461i
$50$		−	0.146254i		−	0.0206834i
$51$	1.60788	−	3.18249i	0.225148	−	0.445638i
$52$		−	1.73401i		−	0.240464i
$53$	3.36414	−	5.82685i	0.462100	−	0.800380i	−0.536966	−	0.843604i	$-0.680430\pi$
$53$	3.36414	−	5.82685i	0.462100	−	0.800380i	0.999065	+	0.0432241i	$0.0137629\pi$
$54$	−5.12357	+	0.865442i	−0.697230	+	0.117772i
$55$	−11.0410	+	6.37453i	−1.48877	+	0.859542i
$56$	−1.51690	−	0.875783i	−0.202704	−	0.117031i
$57$	−2.73359	−	4.17802i	−0.362073	−	0.553392i
$58$	1.74737	+	3.02653i	0.229440	+	0.397402i
$59$	−3.26980	+	1.88782i	−0.425692	+	0.245773i	−0.697510	−	0.716575i	$-0.745709\pi$
$59$	−3.26980	+	1.88782i	−0.425692	+	0.245773i	0.271818	+	0.962349i	$0.412375\pi$
$60$	−3.80998	+	0.212734i	−0.491867	+	0.0274639i
$61$	−5.05840	−	2.92047i	−0.647662	−	0.373928i	0.139898	−	0.990166i	$-0.455323\pi$
$61$	−5.05840	−	2.92047i	−0.647662	−	0.373928i	−0.787560	+	0.616238i	$0.788656\pi$
$62$	−2.89022	+	5.00602i	−0.367059	+	0.635765i
$63$	2.10441	−	4.81490i	0.265131	−	0.606621i
$64$	−1.00000			−0.125000
$65$	3.82024			0.473842
$66$	−5.48765	−	8.38734i	−0.675483	−	1.03241i
$67$	−11.9957			−1.46551			−0.732753	−	0.680494i	$-0.761765\pi$
$67$	−11.9957			−1.46551			−0.732753	+	0.680494i	$0.761765\pi$
$68$	1.78280	+	1.02930i	0.216196	+	0.124821i
$69$	3.82444	−	7.56975i	0.460409	−	0.911291i
$70$	1.92946	−	3.34192i	0.230614	−	0.399435i
$71$	4.20433	+	7.28212i	0.498963	+	0.864229i	0.999999	−	0.00119744i	$-0.000381157\pi$
$71$	4.20433	+	7.28212i	0.498963	+	0.864229i	−0.501037	+	0.865426i	$0.667048\pi$
$72$	−0.333975	−	2.98135i	−0.0393593	−	0.351356i
$73$	−8.77691			−1.02726			−0.513630	−	0.858012i	$-0.671700\pi$
$73$	−8.77691			−1.02726			−0.513630	+	0.858012i	$0.671700\pi$
$74$	−5.72495	−	2.05548i	−0.665512	−	0.238944i
$75$	0.0141223	+	0.252925i	0.00163071	+	0.0292053i
$76$	2.49642	−	1.44131i	0.286359	−	0.165329i
$77$	10.1360			1.15510
$78$	0.167437	+	2.99873i	0.0189585	+	0.339539i
$79$	8.51800	+	4.91787i	0.958350	+	0.553303i	0.895665	−	0.444730i	$-0.146700\pi$
$79$	8.51800	+	4.91787i	0.958350	+	0.553303i	0.0626850	+	0.998033i	$0.480034\pi$
$80$		−	2.20312i		−	0.246317i
$81$	8.77692	−	1.99139i	0.975214	−	0.221266i
$82$			0.153407i			0.0169410i
$83$	−5.50705			−0.604477			−0.302239	−	0.953232i	$-0.597734\pi$
$83$	−5.50705			−0.604477			−0.302239	+	0.953232i	$0.597734\pi$
$84$	2.70783	+	1.36807i	0.295448	+	0.149269i
$85$	−2.26768	+	3.92773i	−0.245964	+	0.426022i
$86$	0.965660	+	1.67257i	0.104130	+	0.180358i
$87$	−3.31406	−	5.06522i	−0.355305	−	0.543048i
$88$	5.01153	−	2.89341i	0.534231	−	0.308438i
$89$	12.2455	+	7.06992i	1.29802	+	0.749410i	0.980061	−	0.198696i	$-0.0636706\pi$
$89$	12.2455	+	7.06992i	1.29802	+	0.749410i	0.317955	+	0.948106i	$0.397004\pi$
$90$	6.56828	−	0.735787i	0.692358	−	0.0775588i
$91$	−2.63032	−	1.51862i	−0.275733	−	0.159194i
$92$	4.24050	+	2.44826i	0.442103	+	0.255248i
$93$	4.51485	−	8.93627i	0.468168	−	0.926648i
$94$	−3.83521	+	2.21426i	−0.395571	+	0.228383i
$95$	3.17537	+	5.49991i	0.325786	+	0.564279i
$96$	1.72936	−	0.0965604i	0.176502	−	0.00985516i
$97$	10.6935	−	6.17388i	1.08576	−	0.626862i	0.153314	−	0.988178i	$-0.451005\pi$
$97$	10.6935	−	6.17388i	1.08576	−	0.626862i	0.932444	+	0.361315i	$0.117672\pi$
$98$	3.40523	−	1.96601i	0.343980	−	0.198597i
$99$	10.3000	+	13.9748i	1.03519	+	1.40452i
$100$	−0.146254			−0.0146254
$101$	0.0734513	+	0.127221i	0.00730867	+	0.0126590i	0.869657	−	0.493657i	$-0.164340\pi$
$101$	0.0734513	+	0.127221i	0.00730867	+	0.0126590i	−0.862348	+	0.506316i	$0.831007\pi$
$102$	−3.18249	−	1.60788i	−0.315114	−	0.159204i
$103$	−2.98986	−	1.72620i	−0.294600	−	0.170087i	0.345415	−	0.938450i	$-0.387738\pi$
$103$	−2.98986	−	1.72620i	−0.294600	−	0.170087i	−0.640014	+	0.768363i	$0.721072\pi$
$104$	−1.73401			−0.170034
$105$	−3.01402	+	5.96567i	−0.294138	+	0.582190i
$106$	−5.82685	−	3.36414i	−0.565954	−	0.326754i
$107$	0.964265	+	1.67016i	0.0932191	+	0.161460i	0.908864	−	0.417093i	$-0.136951\pi$
$107$	0.964265	+	1.67016i	0.0932191	+	0.161460i	−0.815645	+	0.578553i	$0.803618\pi$
$108$	0.865442	+	5.12357i	0.0832772	+	0.493016i
$109$	13.3766	+	7.72301i	1.28125	+	0.739730i	0.977077	−	0.212887i	$-0.0682866\pi$
$109$	13.3766	+	7.72301i	1.28125	+	0.739730i	0.304173	+	0.952617i	$0.401620\pi$
$110$	6.37453	+	11.0410i	0.607788	+	1.05272i
$111$	10.0990	+	3.00185i	0.958550	+	0.284923i
$112$	−0.875783	+	1.51690i	−0.0827537	+	0.143334i
$113$	6.88099	−	3.97274i	0.647309	−	0.373724i	−0.140116	−	0.990135i	$-0.544747\pi$
$113$	6.88099	−	3.97274i	0.647309	−	0.373724i	0.787424	+	0.616411i	$0.211414\pi$
$114$	−4.17802	+	2.73359i	−0.391308	+	0.256024i
$115$	−5.39381	+	9.34235i	−0.502975	+	0.871178i
$116$	3.02653	−	1.74737i	0.281006	−	0.162239i
$117$	−0.579116	−	5.16970i	−0.0535393	−	0.477939i
$118$	1.88782	+	3.26980i	0.173788	+	0.301010i
$119$	3.12269	−	1.80289i	0.286257	−	0.165270i
$120$	0.212734	+	3.80998i	0.0194199	+	0.347802i
$121$	−11.2436	+	19.4745i	−1.02215	+	1.77041i
$122$	−2.92047	+	5.05840i	−0.264407	+	0.457966i
$123$	−0.0148130	−	0.265296i	−0.00133565	−	0.0239209i
$124$	5.00602	+	2.89022i	0.449553	+	0.259550i
$125$		−	11.3378i		−	1.01409i
$126$	−4.81490	−	2.10441i	−0.428946	−	0.187476i
$127$	−2.22085	+	3.84662i	−0.197068	+	0.341333i	−0.947577	−	0.319529i	$-0.896475\pi$
$127$	−2.22085	+	3.84662i	−0.197068	+	0.341333i	0.750508	+	0.660861i	$0.229809\pi$
$128$			1.00000i			0.0883883i
$129$	−1.83148	−	2.79923i	−0.161252	−	0.246458i
$130$		−	3.82024i		−	0.335057i
$131$	1.21427	−	0.701057i	0.106091	−	0.0612516i	−0.446016	−	0.895025i	$-0.647157\pi$
$131$	1.21427	−	0.701057i	0.106091	−	0.0612516i	0.552107	+	0.833774i	$0.313824\pi$
$132$	−8.38734	+	5.48765i	−0.730024	+	0.477639i
$133$		−	5.04908i		−	0.437811i
$134$			11.9957i			1.03627i
$135$	−11.2879	+	1.90668i	−0.971504	+	0.164100i
$136$	1.02930	−	1.78280i	0.0882618	−	0.152874i
$137$	1.57528	+	2.72847i	0.134585	+	0.233109i	0.925439	−	0.378897i	$-0.123696\pi$
$137$	1.57528	+	2.72847i	0.134585	+	0.233109i	−0.790854	+	0.612005i	$0.790363\pi$
$138$	−7.56975	−	3.82444i	−0.644380	−	0.325558i
$139$	−5.97008	−	10.3405i	−0.506376	−	0.877068i	−0.999973	−	0.00737771i	$-0.997652\pi$
$139$	−5.97008	−	10.3405i	−0.506376	−	0.877068i	0.493597	−	0.869691i	$-0.335682\pi$
$140$	−3.34192	−	1.92946i	−0.282443	−	0.163069i
$141$	6.41863	−	4.19957i	0.540546	−	0.353668i
$142$	7.28212	−	4.20433i	0.611102	−	0.352820i
$143$	8.69005	−	5.01720i	0.726699	−	0.419560i
$144$	−2.98135	+	0.333975i	−0.248446	+	0.0278312i
$145$	3.84966	+	6.66780i	0.319697	+	0.553731i
$146$			8.77691i			0.726382i
$147$	−5.69902	+	3.72874i	−0.470047	+	0.307542i
$148$	−2.05548	+	5.72495i	−0.168959	+	0.470588i
$149$	−11.0723	+	19.1778i	−0.907080	+	1.57111i	−0.0889792	+	0.996033i	$0.528360\pi$
$149$	−11.0723	+	19.1778i	−0.907080	+	1.57111i	−0.818101	+	0.575075i	$0.804973\pi$
$150$	0.252925	−	0.0141223i	0.0206513	−	0.00115308i
$151$	3.85413	−	6.67555i	0.313645	−	0.543248i	−0.665504	−	0.746394i	$-0.731783\pi$
$151$	3.85413	−	6.67555i	0.313645	−	0.543248i	0.979148	+	0.203146i	$0.0651166\pi$
$152$	−1.44131	−	2.49642i	−0.116905	−	0.202486i
$153$	5.65892	+	2.47330i	0.457497	+	0.199954i
$154$		−	10.1360i		−	0.816781i
$155$	−6.36752	+	11.0289i	−0.511451	+	0.885860i
$156$	2.99873	−	0.167437i	0.240090	−	0.0134057i
$157$	−7.31390	−	12.6681i	−0.583713	−	1.01102i	−0.995035	−	0.0995303i	$-0.968266\pi$
$157$	−7.31390	−	12.6681i	−0.583713	−	1.01102i	0.411321	−	0.911490i	$-0.365067\pi$
$158$	4.91787	−	8.51800i	0.391245	−	0.677656i
$159$	10.4016	+	5.25515i	0.824897	+	0.416760i
$160$	−2.20312			−0.174172
$161$	7.42752	−	4.28828i	0.585371	−	0.337964i
$162$	−1.99139	−	8.77692i	−0.156459	−	0.689580i
$163$	19.1986	+	11.0843i	1.50375	+	0.868189i	0.999991	+	0.00434303i	$0.00138244\pi$
$163$	19.1986	+	11.0843i	1.50375	+	0.868189i	0.503756	+	0.863846i	$0.331951\pi$
$164$	0.153407			0.0119791
$165$	−12.0900	−	18.4783i	−0.941203	−	1.43854i
$166$			5.50705i			0.427430i
$167$		−	0.159969i		−	0.0123788i	−0.999981	−	0.00618939i	$-0.998030\pi$
$167$		−	0.159969i		−	0.0123788i	0.999981	−	0.00618939i	$-0.00197016\pi$
$168$	1.36807	−	2.70783i	0.105549	−	0.208913i
$169$	9.99320			0.768708
$170$	3.92773	+	2.26768i	0.301243	+	0.173923i
$171$	6.96134	−	5.13078i	0.532347	−	0.392361i
$172$	1.67257	−	0.965660i	0.127532	−	0.0736309i
$173$	23.2333			1.76639			0.883196	−	0.469004i	$-0.155387\pi$
$173$	23.2333			1.76639			0.883196	+	0.469004i	$0.155387\pi$
$174$	−5.06522	+	3.31406i	−0.383993	+	0.251238i
$175$	−0.128087	+	0.221853i	−0.00968244	+	0.0167705i
$176$	−2.89341	−	5.01153i	−0.218099	−	0.377758i
$177$	−3.58045	−	5.47236i	−0.269123	−	0.411328i
$178$	7.06992	−	12.2455i	0.529913	−	0.917836i
$179$		−	22.3023i		−	1.66695i	−0.552558	−	0.833474i	$-0.686348\pi$
$179$		−	22.3023i		−	1.66695i	0.552558	−	0.833474i	$-0.313652\pi$
$180$	−0.735787	−	6.56828i	−0.0548424	−	0.489571i
$181$	−7.02806	−	12.1730i	−0.522392	−	0.904809i	−0.999661	−	0.0260516i	$-0.991707\pi$
$181$	−7.02806	−	12.1730i	−0.522392	−	0.904809i	0.477269	−	0.878757i	$-0.341627\pi$
$182$	−1.51862	+	2.63032i	−0.112567	+	0.194972i
$183$	4.56209	−	9.02979i	0.337240	−	0.667501i
$184$	2.44826	−	4.24050i	0.180488	−	0.312614i
$185$	−12.6128	−	4.52846i	−0.927308	−	0.332939i
$186$	−8.93627	−	4.51485i	−0.655239	−	0.331045i
$187$			11.9128i			0.871147i
$188$	2.21426	+	3.83521i	0.161491	+	0.279711i
$189$	8.52989	+	3.17435i	0.620458	+	0.230900i
$190$	5.49991	−	3.17537i	0.399005	−	0.230366i
$191$	9.55824	−	5.51845i	0.691610	−	0.399301i	−0.112605	−	0.993640i	$-0.535919\pi$
$191$	9.55824	−	5.51845i	0.691610	−	0.399301i	0.804215	+	0.594339i	$0.202586\pi$
$192$	−0.0965604	−	1.72936i	−0.00696865	−	0.124806i
$193$	−18.3424	−	10.5900i	−1.32032	−	0.762286i	−0.336539	−	0.941669i	$-0.609256\pi$
$193$	−18.3424	−	10.5900i	−1.32032	−	0.762286i	−0.983779	+	0.179383i	$0.942590\pi$
$194$	−6.17388	−	10.6935i	−0.443259	−	0.767747i
$195$	0.368884	+	6.60656i	0.0264163	+	0.473105i
$196$	−1.96601	−	3.40523i	−0.140429	−	0.243231i
$197$	−5.82548	+	10.0900i	−0.415048	+	0.718884i	−0.995433	−	0.0954576i	$-0.969569\pi$
$197$	−5.82548	+	10.0900i	−0.415048	+	0.718884i	0.580385	+	0.814342i	$0.302902\pi$
$198$	13.9748	−	10.3000i	0.993147	−	0.731989i
$199$			3.66930i			0.260110i	0.991507	+	0.130055i	$0.0415154\pi$
$199$			3.66930i			0.260110i	−0.991507	+	0.130055i	$0.958485\pi$
$200$			0.146254i			0.0103417i
$201$	−1.15831	−	20.7448i	−0.0817008	−	1.46323i
$202$	0.127221	−	0.0734513i	0.00895126	−	0.00516801i
$203$		−	6.12125i		−	0.429627i
$204$	−1.60788	+	3.18249i	−0.112574	+	0.222819i
$205$			0.337974i			0.0236052i
$206$	−1.72620	+	2.98986i	−0.120270	+	0.208314i
$207$	13.4601	+	5.88289i	0.935541	+	0.408889i
$208$			1.73401i			0.120232i
$209$	14.4463	+	8.34058i	0.999272	+	0.576930i
$210$	5.96567	+	3.01402i	0.411671	+	0.207987i
$211$	−0.696105	+	1.20569i	−0.0479218	+	0.0830030i	−0.888991	−	0.457924i	$-0.848593\pi$
$211$	−0.696105	+	1.20569i	−0.0479218	+	0.0830030i	0.841070	+	0.540927i	$0.181926\pi$
$212$	−3.36414	+	5.82685i	−0.231050	+	0.400190i
$213$	−12.1874	+	7.97396i	−0.835068	+	0.546367i
$214$	1.67016	−	0.964265i	0.114170	−	0.0659158i
$215$	2.12747	+	3.68488i	0.145092	+	0.251307i
$216$	5.12357	−	0.865442i	0.348615	−	0.0588859i
$217$	8.76836	−	5.06242i	0.595235	−	0.343659i
$218$	7.72301	−	13.3766i	0.523068	−	0.905980i
$219$	−0.847502	−	15.1784i	−0.0572689	−	1.02566i
$220$	11.0410	−	6.37453i	0.744385	−	0.429771i
$221$	1.78482	−	3.09140i	0.120060	−	0.207950i
$222$	3.00185	−	10.0990i	0.201471	−	0.677798i
$223$	8.33456	+	14.4359i	0.558123	+	0.966698i	0.997653	+	0.0684698i	$0.0218117\pi$
$223$	8.33456	+	14.4359i	0.558123	+	0.966698i	−0.439530	+	0.898228i	$0.644855\pi$
$224$	1.51690	+	0.875783i	0.101352	+	0.0585157i
$225$	−0.436034	+	0.0488451i	−0.0290690	+	0.00325634i
$226$	−3.97274	−	6.88099i	−0.264263	−	0.457716i
$227$	−18.3649	−	10.6030i	−1.21892	−	0.703744i	−0.254233	−	0.967143i	$-0.581823\pi$
$227$	−18.3649	−	10.6030i	−1.21892	−	0.703744i	−0.964687	+	0.263399i	$0.915156\pi$
$228$	2.73359	+	4.17802i	0.181036	+	0.276696i
$229$	7.52806			0.497468			0.248734	−	0.968572i	$-0.419986\pi$
$229$	7.52806			0.497468			0.248734	+	0.968572i	$0.419986\pi$
$230$	9.34235	+	5.39381i	0.616016	+	0.355657i
$231$	0.978735	+	17.5287i	0.0643961	+	1.15331i
$232$	−1.74737	−	3.02653i	−0.114720	−	0.198701i
$233$	−28.0205			−1.83568			−0.917841	−	0.396948i	$-0.870069\pi$
$233$	−28.0205			−1.83568			−0.917841	+	0.396948i	$0.870069\pi$
$234$	−5.16970	+	0.579116i	−0.337954	+	0.0378580i
$235$	−8.44943	+	4.87828i	−0.551180	+	0.318224i
$236$	3.26980	−	1.88782i	0.212846	−	0.122887i
$237$	−7.68225	+	15.2055i	−0.499016	+	0.987705i
$238$	−1.80289	−	3.12269i	−0.116864	−	0.202414i
$239$	−0.704600	+	0.406801i	−0.0455768	+	0.0263138i	−0.522615	−	0.852569i	$-0.675044\pi$
$239$	−0.704600	+	0.406801i	−0.0455768	+	0.0263138i	0.477038	+	0.878882i	$0.341710\pi$
$240$	3.80998	−	0.212734i	0.245933	−	0.0137319i
$241$	−9.61383	−	5.55055i	−0.619281	−	0.357542i	0.157308	−	0.987550i	$-0.449719\pi$
$241$	−9.61383	−	5.55055i	−0.619281	−	0.357542i	−0.776589	+	0.630007i	$0.783052\pi$
$242$	19.4745	+	11.2436i	1.25187	+	0.722768i
$243$	4.29133	+	14.9861i	0.275289	+	0.961361i
$244$	5.05840	+	2.92047i	0.323831	+	0.186964i
$245$	7.50213	−	4.33136i	0.479294	−	0.276720i
$246$	−0.265296	+	0.0148130i	−0.0169146	+	0.000944446i
$247$	−2.49924	−	4.32881i	−0.159023	−	0.275436i
$248$	2.89022	−	5.00602i	0.183529	−	0.317882i
$249$	−0.531763	−	9.52366i	−0.0336991	−	0.603537i
$250$	−11.3378			−0.717067
$251$		−	0.696263i		−	0.0439477i	−0.999759	−	0.0219739i	$-0.993005\pi$
$251$		−	0.696263i		−	0.0439477i	0.999759	−	0.0219739i	$-0.00699506\pi$
$252$	−2.10441	+	4.81490i	−0.132565	+	0.303310i
$253$			28.3352i			1.78142i
$254$	3.84662	+	2.22085i	0.241359	+	0.139348i
$255$	−7.01141	−	3.54236i	−0.439072	−	0.221831i
$256$	1.00000			0.0625000
$257$	−10.5165	+	6.07173i	−0.656004	+	0.378744i	−0.790753	−	0.612136i	$-0.790311\pi$
$257$	−10.5165	+	6.07173i	−0.656004	+	0.378744i	0.134749	+	0.990880i	$0.456977\pi$
$258$	−2.79923	+	1.83148i	−0.174272	+	0.114023i
$259$	6.88402	+	8.13176i	0.427752	+	0.505283i
$260$	−3.82024			−0.236921
$261$	8.43956	−	6.22029i	0.522396	−	0.385027i
$262$	−0.701057	−	1.21427i	−0.0433114	−	0.0750176i
$263$	−3.51835	+	6.09396i	−0.216951	+	0.375770i	−0.953874	−	0.300206i	$-0.902944\pi$
$263$	−3.51835	+	6.09396i	−0.216951	+	0.375770i	0.736924	+	0.675976i	$0.236278\pi$
$264$	5.48765	+	8.38734i	0.337742	+	0.516205i
$265$	−12.8373	−	7.41160i	−0.788587	−	0.455291i
$266$	−5.04908			−0.309579
$267$	−11.0440	+	21.8594i	−0.675881	+	1.33778i
$268$	11.9957			0.732753
$269$	−30.3419			−1.84998			−0.924990	−	0.379991i	$-0.875927\pi$
$269$	−30.3419			−1.84998			−0.924990	+	0.379991i	$0.875927\pi$
$270$	1.90668	+	11.2879i	0.116037	+	0.686957i
$271$	−9.19451	+	15.9254i	−0.558527	+	0.967397i	0.439093	+	0.898442i	$0.355300\pi$
$271$	−9.19451	+	15.9254i	−0.558527	+	0.967397i	−0.997620	+	0.0689552i	$0.978033\pi$
$272$	−1.78280	−	1.02930i	−0.108098	−	0.0624105i
$273$	2.37225	−	4.69540i	0.143575	−	0.284179i
$274$	2.72847	−	1.57528i	0.164833	−	0.0951662i
$275$	−0.423172	−	0.732956i	−0.0255182	−	0.0441989i
$276$	−3.82444	+	7.56975i	−0.230205	+	0.455645i
$277$	−2.67442	−	1.54407i	−0.160690	−	0.0927745i	0.417499	−	0.908678i	$-0.362907\pi$
$277$	−2.67442	−	1.54407i	−0.160690	−	0.0927745i	−0.578189	+	0.815903i	$0.696240\pi$
$278$	−10.3405	+	5.97008i	−0.620181	+	0.358062i
$279$	15.8900	+	6.94489i	0.951307	+	0.415780i
$280$	−1.92946	+	3.34192i	−0.115307	+	0.199718i
$281$		−	31.1901i		−	1.86064i	−0.366744	−	0.930322i	$-0.619528\pi$
$281$		−	31.1901i		−	1.86064i	0.366744	−	0.930322i	$-0.380472\pi$
$282$	−4.19957	−	6.41863i	−0.250081	−	0.382224i
$283$		−	18.6244i		−	1.10711i	−0.832814	−	0.553553i	$-0.813272\pi$
$283$		−	18.6244i		−	1.10711i	0.832814	−	0.553553i	$-0.186728\pi$
$284$	−4.20433	−	7.28212i	−0.249481	−	0.432114i
$285$	−9.20469	+	6.02243i	−0.545239	+	0.356738i
$286$	−5.01720	−	8.69005i	−0.296674	−	0.513854i
$287$	0.134351	−	0.232703i	0.00793050	−	0.0137360i
$288$	0.333975	+	2.98135i	0.0196797	+	0.175678i
$289$	−6.38108	−	11.0524i	−0.375358	−	0.650138i
$290$	6.66780	−	3.84966i	0.391547	−	0.226060i
$291$	11.7094	+	17.8967i	0.686418	+	1.04912i
$292$	8.77691			0.513630
$293$	8.32950			0.486614			0.243307	−	0.969949i	$-0.421768\pi$
$293$	8.32950			0.486614			0.243307	+	0.969949i	$0.421768\pi$
$294$	3.72874	+	5.69902i	0.217465	+	0.332373i
$295$	4.15910	+	7.20377i	0.242152	+	0.419420i
$296$	5.72495	+	2.05548i	0.332756	+	0.119472i
$297$	−23.1729	+	19.1618i	−1.34463	+	1.11188i
$298$	19.1778	+	11.0723i	1.11094	+	0.641402i
$299$	4.24530	−	7.35308i	0.245512	−	0.425240i
$300$	−0.0141223	−	0.252925i	−0.000815353	−	0.0146026i
$301$		−	3.38283i		−	0.194983i
$302$	−6.67555	−	3.85413i	−0.384135	−	0.221780i
$303$	−0.212919	+	0.139308i	−0.0122319	+	0.00800304i
$304$	−2.49642	+	1.44131i	−0.143179	+	0.0826646i
$305$	−6.43415	+	11.1443i	−0.368418	+	0.638119i
$306$	2.47330	−	5.65892i	0.141389	−	0.323499i
$307$	18.2501			1.04159			0.520795	−	0.853682i	$-0.325636\pi$
$307$	18.2501			1.04159			0.520795	+	0.853682i	$0.325636\pi$
$308$	−10.1360			−0.577552
$309$	2.69651	−	5.33722i	0.153399	−	0.303624i
$310$	11.0289	+	6.36752i	0.626397	+	0.361651i
$311$	−19.7794	+	11.4196i	−1.12159	+	0.647548i	−0.941805	−	0.336159i	$-0.890872\pi$
$311$	−19.7794	+	11.4196i	−1.12159	+	0.647548i	−0.179780	+	0.983707i	$0.557539\pi$
$312$	−0.167437	−	2.99873i	−0.00947925	−	0.169769i
$313$		−	22.8223i		−	1.29000i	−0.764185	−	0.644998i	$-0.776858\pi$
$313$		−	22.8223i		−	1.29000i	0.764185	−	0.644998i	$-0.223142\pi$
$314$	−12.6681	+	7.31390i	−0.714900	+	0.412747i
$315$	−10.6078	−	4.63627i	−0.597683	−	0.261224i
$316$	−8.51800	−	4.91787i	−0.479175	−	0.276652i
$317$	−18.9208			−1.06270			−0.531350	−	0.847152i	$-0.678315\pi$
$317$	−18.9208			−1.06270			−0.531350	+	0.847152i	$0.678315\pi$
$318$	5.25515	−	10.4016i	0.294694	−	0.583290i
$319$	17.5140	+	10.1117i	0.980593	+	0.566146i
$320$			2.20312i			0.123158i
$321$	−2.79519	+	1.82883i	−0.156012	+	0.102075i
$322$	−4.28828	−	7.42752i	−0.238977	−	0.413920i
$323$	5.93415			0.330185
$324$	−8.77692	+	1.99139i	−0.487607	+	0.110633i
$325$			0.253606i			0.0140675i
$326$	11.0843	−	19.1986i	0.613902	−	1.06331i
$327$	−12.0642	+	23.8787i	−0.667151	+	1.32050i
$328$		−	0.153407i		−	0.00847049i
$329$	7.75683			0.427648
$330$	−18.4783	+	12.0900i	−1.01720	+	0.665531i
$331$		−	2.21942i		−	0.121990i	−0.998138	−	0.0609951i	$-0.980573\pi$
$331$		−	2.21942i		−	0.121990i	0.998138	−	0.0609951i	$-0.0194274\pi$
$332$	5.50705			0.302239
$333$	−4.21611	+	17.7546i	−0.231041	+	0.972944i
$334$	−0.159969			−0.00875311
$335$			26.4280i			1.44391i
$336$	−2.70783	−	1.36807i	−0.147724	−	0.0746343i
$337$	−31.2364			−1.70156			−0.850778	−	0.525525i	$-0.823869\pi$
$337$	−31.2364			−1.70156			−0.850778	+	0.525525i	$0.823869\pi$
$338$		−	9.99320i		−	0.543559i
$339$	7.53472	+	11.5161i	0.409230	+	0.625467i
$340$	2.26768	−	3.92773i	0.122982	−	0.213011i
$341$			33.4504i			1.81144i
$342$	−5.13078	−	6.96134i	−0.277441	−	0.376426i
$343$	−19.1481			−1.03390
$344$	−0.965660	−	1.67257i	−0.0520649	−	0.0901790i
$345$	−16.6771	−	8.42572i	−0.897864	−	0.453625i
$346$		−	23.2333i		−	1.24903i
$347$	−16.9135	−	9.76501i	−0.907964	−	0.524213i	−0.0281883	−	0.999603i	$-0.508974\pi$
$347$	−16.9135	−	9.76501i	−0.907964	−	0.524213i	−0.879775	+	0.475390i	$0.842307\pi$
$348$	3.31406	+	5.06522i	0.177652	+	0.271524i
$349$	2.40768			0.128880			0.0644401	−	0.997922i	$-0.479474\pi$
$349$	2.40768			0.128880			0.0644401	+	0.997922i	$0.479474\pi$
$350$	0.221853	+	0.128087i	0.0118585	+	0.00684652i
$351$	8.88434	−	1.50069i	0.474211	−	0.0801008i
$352$	−5.01153	+	2.89341i	−0.267116	+	0.154219i
$353$		−	4.40051i		−	0.234215i	−0.993119	−	0.117108i	$-0.962638\pi$
$353$		−	4.40051i		−	0.234215i	0.993119	−	0.117108i	$-0.0373623\pi$
$354$	−5.47236	+	3.58045i	−0.290853	+	0.190299i
$355$	16.0434	−	9.26266i	0.851495	−	0.491611i
$356$	−12.2455	−	7.06992i	−0.649008	−	0.374705i
$357$	3.41937	+	5.22617i	0.180972	+	0.276598i
$358$	−22.3023			−1.17871
$359$	−6.84944			−0.361500			−0.180750	−	0.983529i	$-0.557852\pi$
$359$	−6.84944			−0.361500			−0.180750	+	0.983529i	$0.557852\pi$
$360$	−6.56828	+	0.735787i	−0.346179	+	0.0387794i
$361$	−5.34527	+	9.25828i	−0.281330	+	0.487278i
$362$	−12.1730	+	7.02806i	−0.639797	+	0.369387i
$363$	−34.7641	−	17.5638i	−1.82464	−	0.921860i
$364$	2.63032	+	1.51862i	0.137866	+	0.0795972i
$365$			19.3366i			1.01212i
$366$	−9.02979	−	4.56209i	−0.471994	−	0.238464i
$367$	−7.84129	+	13.5815i	−0.409312	+	0.708949i	−0.994813	−	0.101723i	$-0.967564\pi$
$367$	−7.84129	+	13.5815i	−0.409312	+	0.708949i	0.585501	+	0.810672i	$0.300898\pi$
$368$	−4.24050	−	2.44826i	−0.221052	−	0.127624i
$369$	0.457360	−	0.0512341i	0.0238092	−	0.00266714i
$370$	−4.52846	+	12.6128i	−0.235424	+	0.655706i
$371$	5.89250	+	10.2061i	0.305924	+	0.529875i
$372$	−4.51485	+	8.93627i	−0.234084	+	0.463324i
$373$	37.7648			1.95539			0.977693	−	0.210040i	$-0.0673594\pi$
$373$	37.7648			1.95539			0.977693	+	0.210040i	$0.0673594\pi$
$374$	11.9128			0.615994
$375$	19.6071	−	1.09479i	1.01251	−	0.0565345i
$376$	3.83521	−	2.21426i	0.197786	−	0.114192i
$377$	−3.02995	−	5.24803i	−0.156050	−	0.270287i
$378$	3.17435	−	8.52989i	0.163271	−	0.438730i
$379$	3.26005	−	5.64658i	0.167458	−	0.290045i	−0.770068	−	0.637962i	$-0.779778\pi$
$379$	3.26005	−	5.64658i	0.167458	−	0.290045i	0.937525	+	0.347917i	$0.113111\pi$
$380$	−3.17537	−	5.49991i	−0.162893	−	0.282139i
$381$	−6.86663	−	3.46921i	−0.351788	−	0.177733i
$382$	−5.51845	−	9.55824i	−0.282349	−	0.489042i
$383$			5.51754i			0.281933i	0.990014	+	0.140966i	$0.0450210\pi$
$383$			5.51754i			0.281933i	−0.990014	+	0.140966i	$0.954979\pi$
$384$	−1.72936	+	0.0965604i	−0.0882509	+	0.00492758i
$385$		−	22.3308i		−	1.13808i
$386$	−10.5900	+	18.3424i	−0.539018	+	0.933606i
$387$	4.66402	−	3.43757i	0.237085	−	0.174741i
$388$	−10.6935	+	6.17388i	−0.542879	+	0.313431i
$389$	−3.11248	−	1.79699i	−0.157809	−	0.0911110i	0.419016	−	0.907979i	$-0.362375\pi$
$389$	−3.11248	−	1.79699i	−0.157809	−	0.0911110i	−0.576825	+	0.816868i	$0.695708\pi$
$390$	6.60656	−	0.368884i	0.334536	−	0.0186792i
$391$	5.03999	+	8.72951i	0.254883	+	0.441470i
$392$	−3.40523	+	1.96601i	−0.171990	+	0.0992985i
$393$	1.32963	+	2.03220i	0.0670708	+	0.102511i
$394$	10.0900	+	5.82548i	0.508328	+	0.293483i
$395$	10.8347	−	18.7662i	0.545151	−	0.944229i
$396$	−10.3000	−	13.9748i	−0.517594	−	0.702261i
$397$	39.1325			1.96401			0.982003	−	0.188868i	$-0.0604817\pi$
$397$	39.1325			1.96401			0.982003	+	0.188868i	$0.0604817\pi$
$398$	3.66930			0.183925
$399$	8.73167	−	0.487542i	0.437130	−	0.0244076i
$400$	0.146254			0.00731269
$401$	26.7562	+	15.4477i	1.33614	+	0.771422i	0.986233	−	0.165361i	$-0.0528789\pi$
$401$	26.7562	+	15.4477i	1.33614	+	0.771422i	0.349910	+	0.936783i	$0.386212\pi$
$402$	−20.7448	+	1.15831i	−1.03466	+	0.0577712i
$403$	5.01168	−	8.68049i	0.249650	−	0.432406i
$404$	−0.0734513	−	0.127221i	−0.00365434	−	0.00632950i
$405$	−4.38728	−	19.3366i	−0.218006	−	0.960845i
$406$	−6.12125			−0.303792
$407$	−34.6381	+	6.26353i	−1.71695	+	0.310472i
$408$	3.18249	+	1.60788i	0.157557	+	0.0796020i
$409$	−12.3156	+	7.11043i	−0.608969	+	0.351588i	−0.772562	−	0.634940i	$-0.781025\pi$
$409$	−12.3156	+	7.11043i	−0.608969	+	0.351588i	0.163593	+	0.986528i	$0.447692\pi$
$410$	0.337974			0.0166914
$411$	−4.56638	+	2.98768i	−0.225243	+	0.147372i
$412$	2.98986	+	1.72620i	0.147300	+	0.0850436i
$413$		−	6.61328i		−	0.325418i
$414$	5.88289	−	13.4601i	0.289128	−	0.661527i
$415$			12.1327i			0.595571i
$416$	1.73401			0.0850169
$417$	17.3059	−	11.3229i	0.847474	−	0.554484i
$418$	8.34058	−	14.4463i	0.407951	−	0.706592i
$419$	−10.7299	−	18.5847i	−0.524189	−	0.907922i	−0.999603	−	0.0281603i	$-0.991035\pi$
$419$	−10.7299	−	18.5847i	−0.524189	−	0.907922i	0.475414	−	0.879762i	$-0.342298\pi$
$420$	3.01402	−	5.96567i	0.147069	−	0.291095i
$421$	12.8185	−	7.40075i	0.624734	−	0.360690i	−0.153976	−	0.988075i	$-0.549208\pi$
$421$	12.8185	−	7.40075i	0.624734	−	0.360690i	0.778710	+	0.627384i	$0.215874\pi$
$422$	1.20569	+	0.696105i	0.0586920	+	0.0338858i
$423$	7.88234	+	10.6946i	0.383253	+	0.519989i
$424$	5.82685	+	3.36414i	0.282977	+	0.163377i
$425$	−0.260742	−	0.150539i	−0.0126478	−	0.00730223i
$426$	7.97396	+	12.1874i	0.386340	+	0.590482i
$427$	8.86012	−	5.11539i	0.428771	−	0.247551i
$428$	−0.964265	−	1.67016i	−0.0466095	−	0.0807301i
$429$	9.51565	+	14.5437i	0.459420	+	0.702178i
$430$	3.68488	−	2.12747i	0.177701	−	0.102596i
$431$	11.6393	−	6.71993i	0.560644	−	0.323688i	−0.192760	−	0.981246i	$-0.561744\pi$
$431$	11.6393	−	6.71993i	0.560644	−	0.323688i	0.753404	+	0.657558i	$0.228411\pi$
$432$	−0.865442	−	5.12357i	−0.0416386	−	0.246508i
$433$	−9.82764			−0.472286			−0.236143	−	0.971718i	$-0.575883\pi$
$433$	−9.82764			−0.472286			−0.236143	+	0.971718i	$0.575883\pi$
$434$	−5.06242	−	8.76836i	−0.243004	−	0.420895i
$435$	−11.1593	+	7.30128i	−0.535047	+	0.350070i
$436$	−13.3766	−	7.72301i	−0.640625	−	0.369865i
$437$	14.1148			0.675200
$438$	−15.1784	+	0.847502i	−0.725253	+	0.0404952i
$439$	−26.5054	−	15.3029i	−1.26503	−	0.730367i	−0.290989	−	0.956727i	$-0.593984\pi$
$439$	−26.5054	−	15.3029i	−1.26503	−	0.730367i	−0.974044	+	0.226360i	$0.927317\pi$
$440$	−6.37453	−	11.0410i	−0.303894	−	0.526360i
$441$	−6.99863	−	9.49559i	−0.333268	−	0.452171i
$442$	−3.09140	−	1.78482i	−0.147043	−	0.0848952i
$443$	−19.1041	−	33.0893i	−0.907664	−	1.57212i	−0.817301	−	0.576211i	$-0.804531\pi$
$443$	−19.1041	−	33.0893i	−0.907664	−	1.57212i	−0.0903624	−	0.995909i	$-0.528803\pi$
$444$	−10.0990	−	3.00185i	−0.479275	−	0.142461i
$445$	15.5759	−	26.9782i	0.738368	−	1.27889i
$446$	14.4359	−	8.33456i	0.683559	−	0.394653i
$447$	−34.2345	−	17.2962i	−1.61923	−	0.818081i
$448$	0.875783	−	1.51690i	0.0413768	−	0.0716668i
$449$	21.1587	−	12.2160i	0.998541	−	0.576508i	0.0907244	−	0.995876i	$-0.471082\pi$
$449$	21.1587	−	12.2160i	0.998541	−	0.576508i	0.907816	+	0.419368i	$0.137748\pi$
$450$	0.0488451	+	0.436034i	0.00230258	+	0.0205549i
$451$	0.443869	+	0.768804i	0.0209010	+	0.0362016i
$452$	−6.88099	+	3.97274i	−0.323654	+	0.186862i
$453$	11.9166	+	6.02057i	0.559889	+	0.282871i
$454$	−10.6030	+	18.3649i	−0.497622	+	0.861907i
$455$	−3.34570	+	5.79492i	−0.156849	+	0.271670i
$456$	4.17802	−	2.73359i	0.195654	−	0.128012i
$457$	34.6280	+	19.9925i	1.61983	+	0.935209i	0.986963	+	0.160947i	$0.0514550\pi$
$457$	34.6280	+	19.9925i	1.61983	+	0.935209i	0.632866	+	0.774261i	$0.281878\pi$
$458$		−	7.52806i		−	0.351763i
$459$	−3.73079	+	10.0251i	−0.174138	+	0.467932i
$460$	5.39381	−	9.34235i	0.251488	−	0.435589i
$461$		−	20.4189i		−	0.951001i	−0.879715	−	0.475501i	$-0.842267\pi$
$461$		−	20.4189i		−	0.951001i	0.879715	−	0.475501i	$-0.157733\pi$
$462$	17.5287	−	0.978735i	0.815511	−	0.0455349i
$463$			30.4512i			1.41519i	0.706620	+	0.707593i	$0.250219\pi$
$463$			30.4512i			1.41519i	−0.706620	+	0.707593i	$0.749781\pi$
$464$	−3.02653	+	1.74737i	−0.140503	+	0.0811194i
$465$	−19.6877	−	9.94676i	−0.912995	−	0.461270i
$466$			28.0205i			1.29802i
$467$		−	32.7226i		−	1.51422i	−0.653286	−	0.757111i	$-0.726610\pi$
$467$		−	32.7226i		−	1.51422i	0.653286	−	0.757111i	$-0.273390\pi$
$468$	0.579116	+	5.16970i	0.0267697	+	0.238969i
$469$	10.5056	−	18.1963i	0.485104	−	0.840225i
$470$	4.87828	+	8.44943i	0.225018	+	0.389743i
$471$	21.2014	−	13.8716i	0.976907	−	0.639169i
$472$	−1.88782	−	3.26980i	−0.0868940	−	0.150505i
$473$	9.67887	+	5.58810i	0.445035	+	0.256941i
$474$	15.2055	+	7.68225i	0.698413	+	0.352857i
$475$	−0.365111	+	0.210797i	−0.0167524	+	0.00967201i
$476$	−3.12269	+	1.80289i	−0.143128	+	0.0826352i
$477$	−8.08365	+	18.4954i	−0.370125	+	0.846848i
$478$	0.406801	+	0.704600i	0.0186067	+	0.0322277i
$479$			9.24633i			0.422476i	0.977435	+	0.211238i	$0.0677494\pi$
$479$			9.24633i			0.422476i	−0.977435	+	0.211238i	$0.932251\pi$
$480$	−0.212734	−	3.80998i	−0.00970995	−	0.173901i
$481$	9.92712	+	3.56422i	0.452638	+	0.162514i
$482$	−5.55055	+	9.61383i	−0.252821	+	0.437898i
$483$	8.13317	+	12.4308i	0.370072	+	0.565619i
$484$	11.2436	−	19.4745i	0.511074	−	0.885206i
$485$	−13.6018	−	23.5590i	−0.617626	−	1.06976i
$486$	14.9861	−	4.29133i	0.679785	−	0.194659i
$487$			3.90658i			0.177024i	0.996075	+	0.0885121i	$0.0282112\pi$
$487$			3.90658i			0.177024i	−0.996075	+	0.0885121i	$0.971789\pi$
$488$	2.92047	−	5.05840i	0.132203	−	0.228983i
$489$	−17.3149	+	34.2715i	−0.783006	+	1.54981i
$490$	−4.33136	−	7.50213i	−0.195671	−	0.338912i
$491$	2.34173	−	4.05599i	0.105681	−	0.183044i	−0.808335	−	0.588722i	$-0.799631\pi$
$491$	2.34173	−	4.05599i	0.105681	−	0.183044i	0.914016	+	0.405678i	$0.132965\pi$
$492$	0.0148130	+	0.265296i	0.000667824	+	0.0119604i
$493$	7.19426			0.324013
$494$	−4.32881	+	2.49924i	−0.194763	+	0.112446i
$495$	30.7882	−	22.6921i	1.38383	−	1.01994i
$496$	−5.00602	−	2.89022i	−0.224777	−	0.129775i
$497$	−14.7283			−0.660656
$498$	−9.52366	+	0.531763i	−0.426765	+	0.0238289i
$499$		−	8.75225i		−	0.391805i	−0.980623	−	0.195902i	$-0.937236\pi$
$499$		−	8.75225i		−	0.391805i	0.980623	−	0.195902i	$-0.0627635\pi$
$500$			11.3378i			0.507043i
$501$	0.276644	−	0.0154467i	0.0123595	−	0.000690106i
$502$	−0.696263			−0.0310757
$503$	−27.9553	−	16.1400i	−1.24647	−	0.719648i	−0.276064	−	0.961139i	$-0.589030\pi$
$503$	−27.9553	−	16.1400i	−1.24647	−	0.719648i	−0.970403	+	0.241491i	$0.922364\pi$
$504$	4.81490	+	2.10441i	0.214473	+	0.0937379i
$505$	0.280284	−	0.161822i	0.0124725	−	0.00720099i
$506$	28.3352			1.25965
$507$	0.964948	+	17.2818i	0.0428548	+	0.767513i
$508$	2.22085	−	3.84662i	0.0985342	−	0.170666i
$509$	11.0421	+	19.1255i	0.489433	+	0.847723i	0.999926	−	0.0121588i	$-0.00387036\pi$
$509$	11.0421	+	19.1255i	0.489433	+	0.847723i	−0.510493	+	0.859882i	$0.670537\pi$
$510$	−3.54236	+	7.01141i	−0.156858	+	0.310471i
$511$	7.68667	−	13.3137i	0.340038	−	0.588963i
$512$		−	1.00000i		−	0.0441942i
$513$	9.54514	+	11.5432i	0.421428	+	0.509645i
$514$	6.07173	+	10.5165i	0.267813	+	0.463865i
$515$	−3.80302	+	6.58703i	−0.167581	+	0.290259i
$516$	1.83148	+	2.79923i	0.0806262	+	0.123229i
$517$	−12.8135	+	22.1936i	−0.563537	+	0.976075i
$518$	8.13176	−	6.88402i	0.357289	−	0.302467i
$519$	2.24341	+	40.1786i	0.0984749	+	1.76364i
$520$			3.82024i			0.167529i
$521$	−19.9127	−	34.4899i	−0.872393	−	1.51103i	−0.859514	−	0.511112i	$-0.829234\pi$
$521$	−19.9127	−	34.4899i	−0.872393	−	1.51103i	−0.0128791	−	0.999917i	$-0.504100\pi$
$522$	−6.22029	−	8.43956i	−0.272255	−	0.369390i
$523$	−28.5295	+	16.4715i	−1.24751	+	0.720249i	−0.970612	−	0.240651i	$-0.922639\pi$
$523$	−28.5295	+	16.4715i	−1.24751	+	0.720249i	−0.276895	+	0.960900i	$0.589306\pi$
$524$	−1.21427	+	0.701057i	−0.0530454	+	0.0306258i
$525$	−0.396030	−	0.200085i	−0.0172842	−	0.00873244i
$526$	6.09396	+	3.51835i	0.265709	+	0.153407i
$527$	5.94982	+	10.3054i	0.259178	+	0.448910i
$528$	8.38734	−	5.48765i	0.365012	−	0.238819i
$529$	0.487918	+	0.845098i	0.0212138	+	0.0367434i
$530$	−7.41160	+	12.8373i	−0.321939	+	0.557615i
$531$	9.11794	−	6.72029i	0.395685	−	0.291636i
$532$			5.04908i			0.218906i
$533$		−	0.266010i		−	0.0115222i
$534$	21.8594	+	11.0440i	0.945951	+	0.477920i
$535$	3.67956	−	2.12439i	0.159081	−	0.0918456i
$536$		−	11.9957i		−	0.518135i
$537$	38.5686	−	2.15351i	1.66436	−	0.0929310i
$538$			30.3419i			1.30813i
$539$	11.3769	−	19.7054i	0.490039	−	0.848773i
$540$	11.2879	−	1.90668i	0.485752	−	0.0820502i
$541$		−	23.1297i		−	0.994423i	−0.867629	−	0.497212i	$-0.834357\pi$
$541$		−	23.1297i		−	0.994423i	0.867629	−	0.497212i	$-0.165643\pi$
$542$	15.9254	+	9.19451i	0.684053	+	0.394938i
$543$	20.3728	−	13.3295i	0.874279	−	0.572022i
$544$	−1.02930	+	1.78280i	−0.0441309	+	0.0764370i
$545$	17.0147	−	29.4704i	0.728831	−	1.26237i
$546$	−4.69540	−	2.37225i	−0.200945	−	0.101523i
$547$	−3.08246	+	1.77966i	−0.131796	+	0.0760927i	−0.564449	−	0.825468i	$-0.690911\pi$
$547$	−3.08246	+	1.77966i	−0.131796	+	0.0760927i	0.432652	+	0.901561i	$0.357578\pi$
$548$	−1.57528	−	2.72847i	−0.0672926	−	0.116554i
$549$	16.0562	+	7.01757i	0.685264	+	0.299503i
$550$	−0.732956	+	0.423172i	−0.0312533	+	0.0180441i
$551$	5.03698	−	8.72430i	0.214582	−	0.371668i
$552$	7.56975	+	3.82444i	0.322190	+	0.162779i
$553$	−14.9198	+	8.61397i	−0.634456	+	0.366303i
$554$	−1.54407	+	2.67442i	−0.0656015	+	0.113625i
$555$	6.61344	−	22.2492i	0.280725	−	0.944427i
$556$	5.97008	+	10.3405i	0.253188	+	0.438534i
$557$	−12.1779	−	7.03089i	−0.515993	−	0.297909i	0.219301	−	0.975657i	$-0.429622\pi$
$557$	−12.1779	−	7.03089i	−0.515993	−	0.297909i	−0.735294	+	0.677749i	$0.762956\pi$
$558$	6.94489	−	15.8900i	0.294001	−	0.672676i
$559$	−1.67447	−	2.90026i	−0.0708223	−	0.122668i
$560$	3.34192	+	1.92946i	0.141222	+	0.0815344i
$561$	−20.6014	+	1.15030i	−0.869792	+	0.0485657i
$562$	−31.1901			−1.31567
$563$	14.7402	+	8.51026i	0.621226	+	0.358665i	0.777346	−	0.629073i	$-0.216565\pi$
$563$	14.7402	+	8.51026i	0.621226	+	0.358665i	−0.156120	+	0.987738i	$0.549899\pi$
$564$	−6.41863	+	4.19957i	−0.270273	+	0.176834i
$565$	−8.75243	−	15.1597i	−0.368218	−	0.637771i
$566$	−18.6244			−0.782842
$567$	−4.66593	+	15.0577i	−0.195951	+	0.632366i
$568$	−7.28212	+	4.20433i	−0.305551	+	0.176410i
$569$	−25.2893	+	14.6008i	−1.06018	+	0.612097i	−0.925483	−	0.378790i	$-0.876340\pi$
$569$	−25.2893	+	14.6008i	−1.06018	+	0.612097i	−0.134700	+	0.990886i	$0.543007\pi$
$570$	6.02243	+	9.20469i	0.252252	+	0.385542i
$571$	11.3047	+	19.5803i	0.473086	+	0.819409i	0.999525	−	0.0308034i	$-0.00980656\pi$
$571$	11.3047	+	19.5803i	0.473086	+	0.819409i	−0.526439	+	0.850213i	$0.676473\pi$
$572$	−8.69005	+	5.01720i	−0.363349	+	0.209780i
$573$	10.4663	+	15.9967i	0.437237	+	0.668274i
$574$	−0.232703	−	0.134351i	−0.00971284	−	0.00560771i
$575$	−0.620190	−	0.358067i	−0.0258637	−	0.0149324i
$576$	2.98135	−	0.333975i	0.124223	−	0.0139156i
$577$	−2.79510	−	1.61375i	−0.116361	−	0.0671813i	0.440690	−	0.897659i	$-0.354734\pi$
$577$	−2.79510	−	1.61375i	−0.116361	−	0.0671813i	−0.557051	+	0.830478i	$0.688067\pi$
$578$	−11.0524	+	6.38108i	−0.459717	+	0.265418i
$579$	16.5428	−	32.7432i	0.687494	−	1.36076i
$580$	−3.84966	−	6.66780i	−0.159848	−	0.276865i
$581$	4.82298	−	8.35364i	0.200091	−	0.346568i
$582$	17.8967	−	11.7094i	0.741841	−	0.485371i
$583$	−38.9353			−1.61253
$584$		−	8.77691i		−	0.363191i
$585$	−11.3895	+	1.27586i	−0.470897	+	0.0527505i
$586$		−	8.32950i		−	0.344088i
$587$	−9.59856	−	5.54173i	−0.396175	−	0.228732i	0.288657	−	0.957432i	$-0.406791\pi$
$587$	−9.59856	−	5.54173i	−0.396175	−	0.228732i	−0.684832	+	0.728701i	$0.740125\pi$
$588$	5.69902	−	3.72874i	0.235024	−	0.153771i
$589$	16.6628			0.686579
$590$	7.20377	−	4.15910i	0.296574	−	0.171227i
$591$	−18.0118	−	9.10003i	−0.740905	−	0.374325i
$592$	2.05548	−	5.72495i	0.0844796	−	0.235294i
$593$	−28.0728			−1.15281			−0.576406	−	0.817163i	$-0.695545\pi$
$593$	−28.0728			−1.15281			−0.576406	+	0.817163i	$0.695545\pi$
$594$	19.1618	+	23.1729i	0.786218	+	0.950794i
$595$	−3.97198	−	6.87967i	−0.162835	−	0.282039i
$596$	11.0723	−	19.1778i	0.453540	−	0.785554i
$597$	−6.34553	+	0.354309i	−0.259705	+	0.0145009i
$598$	−7.35308	−	4.24530i	−0.300690	−	0.173603i
$599$	17.7473			0.725136			0.362568	−	0.931957i	$-0.381900\pi$
$599$	17.7473			0.725136			0.362568	+	0.931957i	$0.381900\pi$
$600$	−0.252925	+	0.0141223i	−0.0103256	+	0.000576542i
$601$	−15.5751			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$601$	−15.5751			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$602$	−3.38283			−0.137874
$603$	35.7634	−	4.00626i	1.45640	−	0.163147i
$604$	−3.85413	+	6.67555i	−0.156822	+	0.271624i
$605$	42.9048	+	24.7711i	1.74433	+	1.00709i
$606$	0.139308	+	0.212919i	0.00565900	+	0.00864923i
$607$	26.0932	−	15.0649i	1.05909	−	0.611467i	0.133911	−	0.990993i	$-0.457246\pi$
$607$	26.0932	−	15.0649i	1.05909	−	0.611467i	0.925181	+	0.379526i	$0.123913\pi$
$608$	1.44131	+	2.49642i	0.0584527	+	0.101243i
$609$	10.5858	−	0.591070i	0.428959	−	0.0239514i
$610$	11.1443	+	6.43415i	0.451219	+	0.260511i
$611$	6.65029	−	3.83955i	0.269042	−	0.155331i
$612$	−5.65892	−	2.47330i	−0.228748	−	0.0999771i
$613$	13.3762	−	23.1683i	0.540260	−	0.935757i	−0.458629	−	0.888628i	$-0.651659\pi$
$613$	13.3762	−	23.1683i	0.540260	−	0.935757i	0.998889	−	0.0471293i	$-0.0150073\pi$
$614$		−	18.2501i		−	0.736516i
$615$	−0.584479	+	0.0326350i	−0.0235684	+	0.00131597i
$616$			10.1360i			0.408391i
$617$	−9.14876	−	15.8461i	−0.368315	−	0.637940i	0.620987	−	0.783821i	$-0.286732\pi$
$617$	−9.14876	−	15.8461i	−0.368315	−	0.637940i	−0.989302	+	0.145880i	$0.953399\pi$
$618$	−5.33722	−	2.69651i	−0.214695	−	0.108470i
$619$	1.29247	+	2.23862i	0.0519487	+	0.0899777i	0.890830	−	0.454336i	$-0.150123\pi$
$619$	1.29247	+	2.23862i	0.0519487	+	0.0899777i	−0.838882	+	0.544314i	$0.816790\pi$
$620$	6.36752	−	11.0289i	0.255726	−	0.442930i
$621$	−8.87391	+	23.8454i	−0.356098	+	0.956881i
$622$	11.4196	+	19.7794i	0.457885	+	0.793081i
$623$	−21.4487	+	12.3834i	−0.859325	+	0.496131i
$624$	−2.99873	+	0.167437i	−0.120045	+	0.00670284i
$625$	−24.2473			−0.969894
$626$	−22.8223			−0.912164
$627$	−13.0289	+	25.7882i	−0.520324	+	1.02988i
$628$	7.31390	+	12.6681i	0.291857	+	0.505510i
$629$	−9.55720	+	8.09074i	−0.381071	+	0.322599i
$630$	−4.63627	+	10.6078i	−0.184713	+	0.422626i
$631$	40.8780	+	23.6009i	1.62733	+	0.939538i	0.984886	+	0.173203i	$0.0554118\pi$
$631$	40.8780	+	23.6009i	1.62733	+	0.939538i	0.642442	+	0.766335i	$0.277922\pi$
$632$	−4.91787	+	8.51800i	−0.195622	+	0.338828i
$633$	−2.15228	−	1.08739i	−0.0855455	−	0.0432199i
$634$			18.9208i			0.751442i
$635$	8.47458	+	4.89280i	0.336303	+	0.194165i
$636$	−10.4016	−	5.25515i	−0.412448	−	0.208380i
$637$	−5.90471	+	3.40908i	−0.233953	+	0.135073i
$638$	10.1117	−	17.5140i	0.400325	−	0.693384i
$639$	−14.9666	−	20.3064i	−0.592071	−	0.803310i
$640$	2.20312			0.0870860
$641$	−24.5408			−0.969303			−0.484651	−	0.874707i	$-0.661054\pi$
$641$	−24.5408			−0.969303			−0.484651	+	0.874707i	$0.661054\pi$
$642$	1.82883	+	2.79519i	0.0721782	+	0.110317i
$643$	−19.7635	−	11.4105i	−0.779397	−	0.449985i	0.0568194	−	0.998384i	$-0.481904\pi$
$643$	−19.7635	−	11.4105i	−0.779397	−	0.449985i	−0.836217	+	0.548399i	$0.815237\pi$
$644$	−7.42752	+	4.28828i	−0.292685	+	0.168982i
$645$	−6.16704	+	4.03496i	−0.242827	+	0.158877i
$646$		−	5.93415i		−	0.233476i
$647$	19.6465	−	11.3429i	0.772385	−	0.445937i	−0.0613400	−	0.998117i	$-0.519537\pi$
$647$	19.6465	−	11.3429i	0.772385	−	0.445937i	0.833725	+	0.552180i	$0.186204\pi$
$648$	1.99139	+	8.77692i	0.0782293	+	0.344790i
$649$	18.9217	+	10.9245i	0.742743	+	0.428823i
$650$	0.253606			0.00994724
$651$	9.60140	+	14.6748i	0.376309	+	0.575151i
$652$	−19.1986	−	11.0843i	−0.751874	−	0.434094i
$653$		−	22.4319i		−	0.877828i	−0.898529	−	0.438914i	$-0.855363\pi$
$653$		−	22.4319i		−	0.877828i	0.898529	−	0.438914i	$-0.144637\pi$
$654$	23.8787	+	12.0642i	0.933732	+	0.471747i
$655$	−1.54451	−	2.67518i	−0.0603491	−	0.104528i
$656$	−0.153407			−0.00598954
$657$	26.1671	−	2.93127i	1.02087	−	0.114360i
$658$		−	7.75683i		−	0.302393i
$659$	12.1547	−	21.0525i	0.473478	−	0.820088i	−0.526061	−	0.850447i	$-0.676332\pi$
$659$	12.1547	−	21.0525i	0.473478	−	0.820088i	0.999539	+	0.0303585i	$0.00966491\pi$
$660$	12.0900	+	18.4783i	0.470601	+	0.719268i
$661$		−	23.1018i		−	0.898556i	−0.893392	−	0.449278i	$-0.851681\pi$
$661$		−	23.1018i		−	0.898556i	0.893392	−	0.449278i	$-0.148319\pi$
$662$	−2.21942			−0.0862601
$663$	5.51848	+	2.78808i	0.214320	+	0.108280i
$664$		−	5.50705i		−	0.213715i
$665$	−11.1237			−0.431360
$666$	17.7546	+	4.21611i	0.687975	+	0.163371i
$667$	17.1120			0.662579
$668$			0.159969i			0.00618939i
$669$	−24.1600	+	15.8074i	−0.934079	+	0.611148i
$670$	26.4280			1.02100
$671$			33.8005i			1.30485i
$672$	−1.36807	+	2.70783i	−0.0527744	+	0.104457i
$673$	0.903856	−	1.56552i	0.0348411	−	0.0603465i	−0.848079	−	0.529870i	$-0.822241\pi$
$673$	0.903856	−	1.56552i	0.0348411	−	0.0603465i	0.882920	+	0.469523i	$0.155574\pi$
$674$			31.2364i			1.20318i
$675$	−0.126574	−	0.749343i	−0.00487185	−	0.0288422i
$676$	−9.99320			−0.384354
$677$	−6.82025	−	11.8130i	−0.262123	−	0.454011i	0.704683	−	0.709523i	$-0.251089\pi$
$677$	−6.82025	−	11.8130i	−0.262123	−	0.454011i	−0.966806	+	0.255512i	$0.917756\pi$
$678$	11.5161	−	7.53472i	0.442272	−	0.289369i
$679$			21.6279i			0.830003i
$680$	−3.92773	−	2.26768i	−0.150622	−	0.0869614i
$681$	16.5630	−	32.7833i	0.634696	−	1.25626i
$682$	33.4504			1.28088
$683$	28.9161	+	16.6947i	1.10644	+	0.638806i	0.937906	−	0.346889i	$-0.112762\pi$
$683$	28.9161	+	16.6947i	1.10644	+	0.638806i	0.168538	+	0.985695i	$0.446095\pi$
$684$	−6.96134	+	5.13078i	−0.266173	+	0.196180i
$685$	6.01114	−	3.47053i	0.229674	−	0.132602i
$686$			19.1481i			0.731080i
$687$	0.726912	+	13.0187i	0.0277334	+	0.496694i
$688$	−1.67257	+	0.965660i	−0.0637662	+	0.0368154i
$689$	10.1038	+	5.83345i	0.384925	+	0.222237i
$690$	−8.42572	+	16.6771i	−0.320762	+	0.634886i
$691$	8.71948			0.331705			0.165852	−	0.986151i	$-0.446963\pi$
$691$	8.71948			0.331705			0.165852	+	0.986151i	$0.446963\pi$
$692$	−23.2333			−0.883196
$693$	−30.2190	+	3.38517i	−1.14792	+	0.128592i
$694$	−9.76501	+	16.9135i	−0.370675	+	0.642027i
$695$	−22.7813	+	13.1528i	−0.864146	+	0.498915i
$696$	5.06522	−	3.31406i	0.191997	−	0.125619i
$697$	0.273494	+	0.157902i	0.0103593	+	0.00598097i
$698$		−	2.40768i		−	0.0911321i
$699$	−2.70567	−	48.4574i	−0.102338	−	1.83283i
$700$	0.128087	−	0.221853i	0.00484122	−	0.00838524i
$701$	39.8291	+	22.9954i	1.50433	+	0.868523i	0.999987	+	0.00501701i	$0.00159697\pi$
$701$	39.8291	+	22.9954i	1.50433	+	0.868523i	0.504339	+	0.863506i	$0.331736\pi$
$702$	−1.50069	−	8.88434i	−0.0566398	−	0.335318i
$703$	3.12008	+	17.2544i	0.117676	+	0.650763i
$704$	2.89341	+	5.01153i	0.109049	+	0.188879i
$705$	−9.25217	−	14.1410i	−0.348457	−	0.532582i
$706$	−4.40051			−0.165615
$707$	−0.257309			−0.00967711
$708$	3.58045	+	5.47236i	0.134562	+	0.205664i
$709$	19.8841	−	11.4801i	0.746765	−	0.431145i	−0.0777589	−	0.996972i	$-0.524776\pi$
$709$	19.8841	−	11.4801i	0.746765	−	0.431145i	0.824524	+	0.565827i	$0.191443\pi$
$710$	−9.26266	−	16.0434i	−0.347621	−	0.602098i
$711$	−27.0376	−	11.8171i	−1.01399	−	0.443176i
$712$	−7.06992	+	12.2455i	−0.264956	+	0.458918i
$713$	14.1520	+	24.5120i	0.529997	+	0.917982i
$714$	5.22617	−	3.41937i	0.195584	−	0.127967i
$715$	−11.0535	−	19.1452i	−0.413378	−	0.715992i
$716$			22.3023i			0.833474i
$717$	−0.771541	−	1.17922i	−0.0288137	−	0.0440390i
$718$			6.84944i			0.255619i
$719$	−14.5957	+	25.2804i	−0.544326	+	0.942800i	0.454323	+	0.890837i	$0.349881\pi$
$719$	−14.5957	+	25.2804i	−0.544326	+	0.942800i	−0.998649	+	0.0519633i	$0.983452\pi$
$720$	0.735787	+	6.56828i	0.0274212	+	0.244785i
$721$	5.23694	−	3.02355i	0.195034	−	0.112603i
$722$	9.25828	+	5.34527i	0.344558	+	0.198930i
$723$	8.67057	−	17.1617i	0.322462	−	0.638251i
$724$	7.02806	+	12.1730i	0.261196	+	0.452404i
$725$	−0.442641	+	0.255559i	−0.0164393	+	0.00949122i
$726$	−17.5638	+	34.7641i	−0.651853	+	1.29022i
$727$	−30.4635	−	17.5881i	−1.12983	−	0.652307i	−0.185937	−	0.982562i	$-0.559532\pi$
$727$	−30.4635	−	17.5881i	−1.12983	−	0.652307i	−0.943892	+	0.330254i	$0.892865\pi$
$728$	1.51862	−	2.63032i	0.0562837	−	0.0974862i
$729$	−25.5020	+	8.86832i	−0.944519	+	0.328456i
$730$	19.3366			0.715680
$731$	3.97582			0.147051
$732$	−4.56209	+	9.02979i	−0.168620	+	0.333750i
$733$	30.1172			1.11240			0.556202	−	0.831047i	$-0.312258\pi$
$733$	30.1172			1.11240			0.556202	+	0.831047i	$0.312258\pi$
$734$	13.5815	+	7.84129i	0.501303	+	0.289427i
$735$	8.21487	+	12.5556i	0.303010	+	0.463121i
$736$	−2.44826	+	4.24050i	−0.0902439	+	0.156307i
$737$	34.7084	+	60.1168i	1.27850	+	2.21443i
$738$	−0.0512341	−	0.457360i	−0.00188595	−	0.0168357i
$739$	−25.0573			−0.921749			−0.460875	−	0.887465i	$-0.652464\pi$
$739$	−25.0573			−0.921749			−0.460875	+	0.887465i	$0.652464\pi$
$740$	12.6128	+	4.52846i	0.463654	+	0.166470i
$741$	7.24474	−	4.74007i	0.266142	−	0.174131i
$742$	10.2061	−	5.89250i	0.374678	−	0.216321i
$743$	7.85138			0.288039			0.144020	−	0.989575i	$-0.453997\pi$
$743$	7.85138			0.288039			0.144020	+	0.989575i	$0.453997\pi$
$744$	8.93627	+	4.51485i	0.327620	+	0.165522i
$745$	42.2511	+	24.3937i	1.54796	+	0.893715i
$746$		−	37.7648i		−	1.38267i
$747$	16.4185	−	1.83922i	0.600720	−	0.0672934i
$748$		−	11.9128i		−	0.435573i
$749$	−3.37795			−0.123428
$750$	−1.09479	−	19.6071i	−0.0399759	−	0.715952i
$751$	10.1458	−	17.5730i	0.370225	−	0.641248i	−0.619375	−	0.785095i	$-0.712614\pi$
$751$	10.1458	−	17.5730i	0.370225	−	0.641248i	0.989600	+	0.143847i	$0.0459473\pi$
$752$	−2.21426	−	3.83521i	−0.0807457	−	0.139856i
$753$	1.20409	−	0.0672314i	0.0438794	−	0.00245005i
$754$	−5.24803	+	3.02995i	−0.191122	+	0.110344i
$755$	−14.7070	−	8.49112i	−0.535244	−	0.309023i
$756$	−8.52989	−	3.17435i	−0.310229	−	0.115450i
$757$	−11.5579	−	6.67293i	−0.420078	−	0.242532i	0.275033	−	0.961435i	$-0.411311\pi$
$757$	−11.5579	−	6.67293i	−0.420078	−	0.242532i	−0.695111	+	0.718903i	$0.744645\pi$
$758$	−5.64658	−	3.26005i	−0.205093	−	0.118411i
$759$	−49.0017	+	2.73606i	−1.77865	+	0.0993127i
$760$	−5.49991	+	3.17537i	−0.199503	+	0.115183i
$761$	21.9602	+	38.0361i	0.796056	+	1.37881i	0.922167	+	0.386793i	$0.126417\pi$
$761$	21.9602	+	38.0361i	0.796056	+	1.37881i	−0.126111	+	0.992016i	$0.540250\pi$
$762$	−3.46921	+	6.86663i	−0.125676	+	0.248752i
$763$	−23.4301	+	13.5274i	−0.848225	+	0.489723i
$764$	−9.55824	+	5.51845i	−0.345805	+	0.199651i
$765$	5.44898	−	12.4673i	0.197008	−	0.450756i
$766$	5.51754			0.199357
$767$	−3.27350	−	5.66987i	−0.118199	−	0.204727i
$768$	0.0965604	+	1.72936i	0.00348432	+	0.0624028i
$769$	−8.44465	−	4.87552i	−0.304522	−	0.175816i	0.339951	−	0.940443i	$-0.389590\pi$
$769$	−8.44465	−	4.87552i	−0.304522	−	0.175816i	−0.644472	+	0.764628i	$0.722923\pi$
$770$	−22.3308			−0.804747
$771$	−11.5157	−	17.6006i	−0.414727	−	0.633869i
$772$	18.3424	+	10.5900i	0.660159	+	0.381143i
$773$	6.62325	+	11.4718i	0.238222	+	0.412612i	0.960204	−	0.279299i	$-0.0901022\pi$
$773$	6.62325	+	11.4718i	0.238222	+	0.412612i	−0.721982	+	0.691911i	$0.756769\pi$
$774$	−3.43757	−	4.66402i	−0.123561	−	0.167645i
$775$	−0.732149	−	0.422707i	−0.0262996	−	0.0151841i
$776$	6.17388	+	10.6935i	0.221629	+	0.383873i
$777$	−13.3980	+	12.6901i	−0.480650	+	0.455256i
$778$	−1.79699	+	3.11248i	−0.0644252	+	0.111588i
$779$	0.382968	−	0.221107i	0.0137212	−	0.00792197i
$780$	−0.368884	−	6.60656i	−0.0132082	−	0.236553i
$781$	24.3297	−	42.1403i	0.870586	−	1.50790i
$782$	8.72951	−	5.03999i	0.312167	−	0.180230i
$783$	11.5720	+	13.9944i	0.413551	+	0.500118i
$784$	1.96601	+	3.40523i	0.0702146	+	0.121615i
$785$	−27.9093	+	16.1134i	−0.996124	+	0.575113i
$786$	2.03220	−	1.32963i	0.0724863	−	0.0474262i
$787$	−12.9258	+	22.3881i	−0.460754	+	0.798049i	−0.998999	−	0.0447392i	$-0.985754\pi$
$787$	−12.9258	+	22.3881i	−0.460754	+	0.798049i	0.538245	+	0.842789i	$0.319088\pi$
$788$	5.82548	−	10.0900i	0.207524	−	0.359442i
$789$	−10.8784	−	5.49605i	−0.387280	−	0.195665i
$790$	−18.7662	−	10.8347i	−0.667671	−	0.385480i
$791$			13.9170i			0.494833i
$792$	−13.9748	+	10.3000i	−0.496573	+	0.365994i
$793$	5.06413	−	8.77133i	0.179832	−	0.311479i
$794$		−	39.1325i		−	1.38876i
$795$	11.5777	−	22.9159i	0.410620	−	0.812743i
$796$		−	3.66930i		−	0.130055i
$797$	−24.9761	+	14.4200i	−0.884700	+	0.510782i	−0.872205	−	0.489140i	$-0.837311\pi$
$797$	−24.9761	+	14.4200i	−0.884700	+	0.510782i	−0.0124951	+	0.999922i	$0.503977\pi$
$798$	−0.487542	−	8.73167i	−0.0172588	−	0.309098i
$799$			9.11655i			0.322520i
$800$		−	0.146254i		−	0.00517086i
$801$	−38.8692	−	16.9882i	−1.37338	−	0.600250i
$802$	15.4477	−	26.7562i	0.545478	−	0.944796i
$803$	25.3952	+	43.9858i	0.896177	+	1.55222i
$804$	1.15831	+	20.7448i	0.0408504	+	0.731614i
$805$	−9.44761	−	16.3637i	−0.332984	−	0.576746i
$806$	−8.68049	−	5.01168i	−0.305757	−	0.176529i
$807$	−2.92983	−	52.4720i	−0.103135	−	1.84710i
$808$	−0.127221	+	0.0734513i	−0.00447563	+	0.00258401i
$809$	22.8265	−	13.1789i	0.802538	−	0.463346i	−0.0418197	−	0.999125i	$-0.513316\pi$
$809$	22.8265	−	13.1789i	0.802538	−	0.463346i	0.844358	+	0.535780i	$0.179982\pi$
$810$	−19.3366	+	4.38728i	−0.679420	+	0.154153i
$811$	4.23218	+	7.33035i	0.148612	+	0.257403i	0.930715	−	0.365746i	$-0.119186\pi$
$811$	4.23218	+	7.33035i	0.148612	+	0.257403i	−0.782103	+	0.623149i	$0.785853\pi$
$812$			6.12125i			0.214814i
$813$	−28.4285	−	14.3628i	−0.997030	−	0.503727i
$814$	6.26353	+	34.6381i	0.219537	+	1.21406i
$815$	24.4200	−	42.2968i	0.855397	−	1.48159i
$816$	1.60788	−	3.18249i	0.0562871	−	0.111409i
$817$	2.78362	−	4.82138i	0.0973867	−	0.168679i
$818$	7.11043	+	12.3156i	0.248610	+	0.430606i
$819$	8.34910	+	3.64907i	0.291741	+	0.127509i
$820$		−	0.337974i		−	0.0118026i
$821$	3.08239	−	5.33886i	0.107576	−	0.186328i	−0.807212	−	0.590262i	$-0.799024\pi$
$821$	3.08239	−	5.33886i	0.107576	−	0.186328i	0.914788	+	0.403935i	$0.132358\pi$
$822$	2.98768	+	4.56638i	0.104207	+	0.159271i
$823$	23.8434	+	41.2980i	0.831130	+	1.43956i	0.897143	+	0.441740i	$0.145639\pi$
$823$	23.8434	+	41.2980i	0.831130	+	1.43956i	−0.0660135	+	0.997819i	$0.521028\pi$
$824$	1.72620	−	2.98986i	0.0601349	−	0.104157i
$825$	1.22668	−	0.802591i	0.0427075	−	0.0279426i
$826$	−6.61328			−0.230105
$827$	32.8627	−	18.9733i	1.14275	−	0.659765i	0.195637	−	0.980676i	$-0.437323\pi$
$827$	32.8627	−	18.9733i	1.14275	−	0.659765i	0.947109	+	0.320911i	$0.103989\pi$
$828$	−13.4601	−	5.88289i	−0.467771	−	0.204445i
$829$	−7.07788	−	4.08641i	−0.245825	−	0.141927i	0.372026	−	0.928222i	$-0.378663\pi$
$829$	−7.07788	−	4.08641i	−0.245825	−	0.141927i	−0.617851	+	0.786295i	$0.711996\pi$
$830$	12.1327			0.421132
$831$	2.41201	−	4.77412i	0.0836718	−	0.165612i
$832$		−	1.73401i		−	0.0601160i
$833$		−	8.09446i		−	0.280457i
$834$	−11.3229	−	17.3059i	−0.392079	−	0.599255i
$835$	−0.352431			−0.0121964
$836$	−14.4463	−	8.34058i	−0.499636	−	0.288465i
$837$	−10.4759	+	28.1500i	−0.362099	+	0.973007i
$838$	−18.5847	+	10.7299i	−0.641998	+	0.370658i
$839$	−9.42368			−0.325342			−0.162671	−	0.986680i	$-0.552011\pi$
$839$	−9.42368			−0.325342			−0.162671	+	0.986680i	$0.552011\pi$
$840$	−5.96567	−	3.01402i	−0.205835	−	0.103994i
$841$	−8.39343	+	14.5378i	−0.289429	+	0.501305i
$842$	−7.40075	−	12.8185i	−0.255047	−	0.441754i
$843$	53.9388	−	3.01173i	1.85775	−	0.103729i
$844$	0.696105	−	1.20569i	0.0239609	−	0.0415015i
$845$		−	22.0162i		−	0.757382i
$846$	10.6946	−	7.88234i	0.367688	−	0.271001i
$847$	−19.6940	−	34.1109i	−0.676692	−	1.17207i
$848$	3.36414	−	5.82685i	0.115525	−	0.200095i
$849$	32.2082	−	1.79838i	1.10538	−	0.0617203i
$850$	−0.150539	+	0.260742i	−0.00516345	+	0.00894337i
$851$	−22.7324	+	19.2443i	−0.779256	+	0.659687i
$852$	12.1874	−	7.97396i	0.417534	−	0.273183i
$853$			39.4776i			1.35169i	0.737045	+	0.675843i	$0.236220\pi$
$853$			39.4776i			1.35169i	−0.737045	+	0.675843i	$0.763780\pi$
$854$	−5.11539	−	8.86012i	−0.175045	−	0.303187i
$855$	−11.3037	−	15.3367i	−0.386580	−	0.524503i
$856$	−1.67016	+	0.964265i	−0.0570848	+	0.0329579i
$857$	0.917467	−	0.529700i	0.0313401	−	0.0180942i	−0.484248	−	0.874931i	$-0.660907\pi$
$857$	0.917467	−	0.529700i	0.0313401	−	0.0180942i	0.515588	+	0.856837i	$0.327573\pi$
$858$	14.5437	−	9.51565i	0.496515	−	0.324859i
$859$	6.72949	+	3.88528i	0.229607	+	0.132564i	0.610391	−	0.792100i	$-0.291012\pi$
$859$	6.72949	+	3.88528i	0.229607	+	0.132564i	−0.380784	+	0.924664i	$0.624346\pi$
$860$	−2.12747	−	3.68488i	−0.0725460	−	0.125653i
$861$	0.415400	+	0.209871i	0.0141568	+	0.00715240i
$862$	−6.71993	−	11.6393i	−0.228882	−	0.396435i
$863$	−13.0631	+	22.6260i	−0.444674	+	0.770198i	−0.998029	−	0.0627471i	$-0.980014\pi$
$863$	−13.0631	+	22.6260i	−0.444674	+	0.770198i	0.553355	+	0.832945i	$0.313347\pi$
$864$	−5.12357	+	0.865442i	−0.174308	+	0.0294429i
$865$		−	51.1857i		−	1.74037i
$866$			9.82764i			0.333957i
$867$	18.4973	−	12.1024i	0.628201	−	0.411018i
$868$	−8.76836	+	5.06242i	−0.297618	+	0.171830i
$869$		−	56.9176i		−	1.93080i
$870$	7.30128	+	11.1593i	0.247537	+	0.378335i
$871$		−	20.8007i		−	0.704804i
$872$	−7.72301	+	13.3766i	−0.261534	+	0.452990i
$873$	−29.8191	+	21.9779i	−1.00922	+	0.743838i
$874$		−	14.1148i		−	0.477439i
$875$	17.1983	+	9.92947i	0.581410	+	0.335677i
$876$	0.847502	+	15.1784i	0.0286344	+	0.512831i
$877$	13.1774	−	22.8240i	0.444970	−	0.770711i	−0.553080	−	0.833128i	$-0.686548\pi$
$877$	13.1774	−	22.8240i	0.444970	−	0.770711i	0.998050	+	0.0624173i	$0.0198810\pi$
$878$	−15.3029	+	26.5054i	−0.516447	+	0.894513i
$879$	0.804299	+	14.4047i	0.0271283	+	0.485858i
$880$	−11.0410	+	6.37453i	−0.372193	+	0.214885i
$881$	20.1553	+	34.9100i	0.679050	+	1.17615i	0.975267	+	0.221028i	$0.0709412\pi$
$881$	20.1553	+	34.9100i	0.679050	+	1.17615i	−0.296218	+	0.955120i	$0.595725\pi$
$882$	−9.49559	+	6.99863i	−0.319733	+	0.235656i
$883$	−1.98311	+	1.14495i	−0.0667371	+	0.0385307i	−0.532997	−	0.846117i	$-0.678934\pi$
$883$	−1.98311	+	1.14495i	−0.0667371	+	0.0385307i	0.466260	+	0.884648i	$0.345601\pi$
$884$	−1.78482	+	3.09140i	−0.0600300	+	0.103975i
$885$	−12.0563	+	7.88817i	−0.405268	+	0.265158i
$886$	−33.0893	+	19.1041i	−1.11166	+	0.641815i
$887$	18.2765	−	31.6558i	0.613665	−	1.06290i	−0.376952	−	0.926233i	$-0.623028\pi$
$887$	18.2765	−	31.6558i	0.613665	−	1.06290i	0.990617	−	0.136666i	$-0.0436388\pi$
$888$	−3.00185	+	10.0990i	−0.100735	+	0.338899i
$889$	−3.88996	−	6.73761i	−0.130465	−	0.225972i
$890$	−26.9782	−	15.5759i	−0.904313	−	0.522105i
$891$	−35.3752	−	38.2239i	−1.18511	−	1.28055i
$892$	−8.33456	−	14.4359i	−0.279062	−	0.483349i
$893$	11.0554	+	6.38285i	0.369955	+	0.213594i
$894$	−17.2962	+	34.2345i	−0.578471	+	1.14497i
$895$	−49.1346			−1.64239
$896$	−1.51690	−	0.875783i	−0.0506761	−	0.0292578i
$897$	13.1260	+	6.63163i	0.438266	+	0.221424i
$898$	−12.2160	−	21.1587i	−0.407652	−	0.706075i
$899$	20.2011			0.673745
$900$	0.436034	−	0.0488451i	0.0145345	−	0.00162817i
$901$	−11.9952	+	6.92542i	−0.399617	+	0.230719i
$902$	0.768804	−	0.443869i	0.0255984	−	0.0147792i
$903$	5.85013	−	0.326648i	0.194680	−	0.0108702i
$904$	3.97274	+	6.88099i	0.132131	+	0.228858i
$905$	−26.8185	+	15.4837i	−0.891478	+	0.514695i
$906$	6.02057	−	11.9166i	0.200020	−	0.395901i
$907$	−20.4389	−	11.8004i	−0.678661	−	0.391825i	0.120689	−	0.992690i	$-0.461490\pi$
$907$	−20.4389	−	11.8004i	−0.678661	−	0.391825i	−0.799350	+	0.600865i	$0.794823\pi$
$908$	18.3649	+	10.6030i	0.609460	+	0.351872i
$909$	−0.261473	−	0.354761i	−0.00867251	−	0.0117667i
$910$	5.79492	+	3.34570i	0.192100	+	0.110909i
$911$	32.1141	−	18.5411i	1.06399	−	0.614293i	0.137454	−	0.990508i	$-0.456108\pi$
$911$	32.1141	−	18.5411i	1.06399	−	0.614293i	0.926532	+	0.376215i	$0.122775\pi$
$912$	−2.73359	−	4.17802i	−0.0905182	−	0.138348i
$913$	15.9341	+	27.5988i	0.527343	+	0.913385i
$914$	19.9925	−	34.6280i	0.661292	−	1.14539i
$915$	−19.8937	−	10.0508i	−0.657666	−	0.332271i
$916$	−7.52806			−0.248734
$917$			2.45589i			0.0811007i
$918$	10.0251	+	3.73079i	0.330878	+	0.123134i
$919$		−	37.1787i		−	1.22641i	−0.789923	−	0.613206i	$-0.789879\pi$
$919$		−	37.1787i		−	1.22641i	0.789923	−	0.613206i	$-0.210121\pi$
$920$	−9.34235	−	5.39381i	−0.308008	−	0.177829i
$921$	1.76224	+	31.5610i	0.0580678	+	1.03997i
$922$	−20.4189			−0.672459
$923$	−12.6273	+	7.29036i	−0.415632	+	0.239965i
$924$	−0.978735	−	17.5287i	−0.0321980	−	0.576653i
$925$	0.300621	−	0.837296i	0.00988437	−	0.0275301i
$926$	30.4512			1.00069
$927$	9.49034	+	4.14786i	0.311704	+	0.136234i
$928$	1.74737	+	3.02653i	0.0573601	+	0.0993506i
$929$	−3.71353	+	6.43202i	−0.121837	+	0.211028i	−0.920492	−	0.390761i	$-0.872212\pi$
$929$	−3.71353	+	6.43202i	−0.121837	+	0.211028i	0.798655	+	0.601789i	$0.205545\pi$
$930$	−9.94676	+	19.6877i	−0.326167	+	0.645585i
$931$	−9.81596	−	5.66724i	−0.321705	−	0.185736i
$932$	28.0205			0.917841
$933$	−21.6585	−	33.1029i	−0.709068	−	1.08374i
$934$	−32.7226			−1.07072
$935$	26.2453			0.858312
$936$	5.16970	−	0.579116i	0.168977	−	0.0189290i
$937$	−21.6216	+	37.4498i	−0.706348	+	1.22343i	0.259854	+	0.965648i	$0.416325\pi$
$937$	−21.6216	+	37.4498i	−0.706348	+	1.22343i	−0.966203	+	0.257783i	$0.917008\pi$
$938$	−18.1963	−	10.5056i	−0.594129	−	0.343021i
$939$	39.4680	−	2.20373i	1.28799	−	0.0719162i
$940$	8.44943	−	4.87828i	0.275590	−	0.159112i
$941$	24.0848	+	41.7160i	0.785141	+	1.35990i	0.928915	+	0.370294i	$0.120743\pi$
$941$	24.0848	+	41.7160i	0.785141	+	1.35990i	−0.143774	+	0.989611i	$0.545924\pi$
$942$	−13.8716	−	21.2014i	−0.451961	−	0.690777i
$943$	0.650523	+	0.375580i	0.0211840	+	0.0122306i
$944$	−3.26980	+	1.88782i	−0.106423	+	0.0614433i
$945$	6.99347	−	18.7924i	0.227498	−	0.611316i
$946$	5.58810	−	9.67887i	0.181685	−	0.314687i
$947$		−	49.2968i		−	1.60193i	−0.598710	−	0.800966i	$-0.704320\pi$
$947$		−	49.2968i		−	1.60193i	0.598710	−	0.800966i	$-0.295680\pi$
$948$	7.68225	−	15.2055i	0.249508	−	0.493853i
$949$		−	15.2193i		−	0.494038i
$950$	0.210797	+	0.365111i	0.00683915	+	0.0118457i
$951$	−1.82700	−	32.7209i	−0.0592446	−	1.06105i
$952$	1.80289	+	3.12269i	0.0584319	+	0.101207i
$953$	13.8020	−	23.9057i	0.447090	−	0.774382i	−0.551106	−	0.834436i	$-0.685794\pi$
$953$	13.8020	−	23.9057i	0.447090	−	0.774382i	0.998195	+	0.0600536i	$0.0191272\pi$
$954$	18.4954	+	8.08365i	0.598812	+	0.261718i
$955$	−12.1578	−	21.0580i	−0.393418	−	0.681420i
$956$	0.704600	−	0.406801i	0.0227884	−	0.0131569i
$957$	−15.7956	+	31.2643i	−0.510598	+	1.01063i
$958$	9.24633			0.298735
$959$	−5.51841			−0.178199
$960$	−3.80998	+	0.212734i	−0.122967	+	0.00686597i
$961$	1.20679	+	2.09023i	0.0389288	+	0.0674266i
$962$	3.56422	−	9.92712i	0.114915	−	0.320063i
$963$	−3.43261	−	4.65728i	−0.110614	−	0.150079i
$964$	9.61383	+	5.55055i	0.309641	+	0.178771i
$965$	−23.3311	+	40.4107i	−0.751055	+	1.30086i
$966$	12.4308	−	8.13317i	0.399953	−	0.261681i
$967$		−	14.9242i		−	0.479931i	−0.970781	−	0.239965i	$-0.922864\pi$
$967$		−	14.9242i		−	0.479931i	0.970781	−	0.239965i	$-0.0771361\pi$
$968$	−19.4745	−	11.2436i	−0.625935	−	0.361384i
$969$	0.573004	+	10.2623i	0.0184075	+	0.329672i
$970$	−23.5590	+	13.6018i	−0.756435	+	0.436728i
$971$	−28.9836	+	50.2010i	−0.930127	+	1.61103i	−0.147027	+	0.989132i	$0.546970\pi$
$971$	−28.9836	+	50.2010i	−0.930127	+	1.61103i	−0.783100	+	0.621895i	$0.786363\pi$
$972$	−4.29133	−	14.9861i	−0.137645	−	0.480681i
$973$	20.9140			0.670471
$974$	3.90658			0.125175
$975$	−0.438575	+	0.0244883i	−0.0140456	+	0.000784253i
$976$	−5.05840	−	2.92047i	−0.161916	−	0.0934820i
$977$	31.5437	−	18.2117i	1.00917	−	0.582645i	0.0982221	−	0.995165i	$-0.468684\pi$
$977$	31.5437	−	18.2117i	1.00917	−	0.582645i	0.910949	+	0.412519i	$0.135351\pi$
$978$	34.2715	+	17.3149i	1.09588	+	0.553669i
$979$		−	81.8247i		−	2.61513i
$980$	−7.50213	+	4.33136i	−0.239647	+	0.138360i
$981$	−42.4598	−	18.5575i	−1.35564	−	0.592497i
$982$	−4.05599	−	2.34173i	−0.129432	−	0.0747276i
$983$	−50.8849			−1.62298			−0.811489	−	0.584368i	$-0.801342\pi$
$983$	−50.8849			−1.62298			−0.811489	+	0.584368i	$0.801342\pi$
$984$	0.265296	−	0.0148130i	0.00845731	−	0.000472223i
$985$	22.2295	+	12.8342i	0.708292	+	0.408933i
$986$		−	7.19426i		−	0.229112i
$987$	0.749003	+	13.4143i	0.0238410	+	0.426983i
$988$	2.49924	+	4.32881i	0.0795115	+	0.137718i
$989$	9.45673			0.300707
$990$	−22.6921	−	30.7882i	−0.721204	−	0.978514i
$991$			16.4523i			0.522625i	0.965254	+	0.261313i	$0.0841554\pi$
$991$			16.4523i			0.522625i	−0.965254	+	0.261313i	$0.915845\pi$
$992$	−2.89022	+	5.00602i	−0.0917647	+	0.158941i
$993$	3.83817	−	0.214308i	0.121801	−	0.00680086i
$994$			14.7283i			0.467154i
$995$	8.08392			0.256277
$996$	0.531763	+	9.52366i	0.0168496	+	0.301769i
$997$			43.2567i			1.36995i	0.728564	+	0.684977i	$0.240188\pi$
$997$			43.2567i			1.36995i	−0.728564	+	0.684977i	$0.759812\pi$
$998$	−8.75225			−0.277048
$999$	−31.1111	−	5.57677i	−0.984311	−	0.176441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.10	✓	76
3.2	odd	2		1998.2.k.a.1063.35		76
9.2	odd	6		1998.2.t.a.397.23		76
9.7	even	3		666.2.t.a.619.16	yes	76
37.11	even	6		666.2.t.a.85.16	yes	76
111.11	odd	6		1998.2.t.a.307.23		76
333.11	odd	6		1998.2.k.a.1639.4		76
333.196	even	6	inner	666.2.k.a.529.29	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.10	✓	76	1.1	even	1	trivial
666.2.k.a.529.29	yes	76	333.196	even	6	inner
666.2.t.a.85.16	yes	76	37.11	even	6
666.2.t.a.619.16	yes	76	9.7	even	3
1998.2.k.a.1063.35		76	3.2	odd	2
1998.2.k.a.1639.4		76	333.11	odd	6
1998.2.t.a.307.23		76	111.11	odd	6
1998.2.t.a.397.23		76	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.0965604 + 1.72936i) q^{3} -1.00000 q^{4} -2.20312i q^{5} +(1.72936 - 0.0965604i) q^{6} +(-0.875783 + 1.51690i) q^{7} +1.00000i q^{8} +(-2.98135 + 0.333975i) q^{9} -2.20312 q^{10} +(-2.89341 - 5.01153i) q^{11} +(-0.0965604 - 1.72936i) q^{12} +1.73401i q^{13} +(1.51690 + 0.875783i) q^{14} +(3.80998 - 0.212734i) q^{15} +1.00000 q^{16} +(-1.78280 - 1.02930i) q^{17} +(0.333975 + 2.98135i) q^{18} +(-2.49642 + 1.44131i) q^{19} +2.20312i q^{20} +(-2.70783 - 1.36807i) q^{21} +(-5.01153 + 2.89341i) q^{22} +(-4.24050 - 2.44826i) q^{23} +(-1.72936 + 0.0965604i) q^{24} +0.146254 q^{25} +1.73401 q^{26} +(-0.865442 - 5.12357i) q^{27} +(0.875783 - 1.51690i) q^{28} +(-3.02653 + 1.74737i) q^{29} +(-0.212734 - 3.80998i) q^{30} +(-5.00602 - 2.89022i) q^{31} -1.00000i q^{32} +(8.38734 - 5.48765i) q^{33} +(-1.02930 + 1.78280i) q^{34} +(3.34192 + 1.92946i) q^{35} +(2.98135 - 0.333975i) q^{36} +(2.05548 - 5.72495i) q^{37} +(1.44131 + 2.49642i) q^{38} +(-2.99873 + 0.167437i) q^{39} +2.20312 q^{40} -0.153407 q^{41} +(-1.36807 + 2.70783i) q^{42} +(-1.67257 + 0.965660i) q^{43} +(2.89341 + 5.01153i) q^{44} +(0.735787 + 6.56828i) q^{45} +(-2.44826 + 4.24050i) q^{46} +(-2.21426 - 3.83521i) q^{47} +(0.0965604 + 1.72936i) q^{48} +(1.96601 + 3.40523i) q^{49} -0.146254i q^{50} +(1.60788 - 3.18249i) q^{51} -1.73401i q^{52} +(3.36414 - 5.82685i) q^{53} +(-5.12357 + 0.865442i) q^{54} +(-11.0410 + 6.37453i) q^{55} +(-1.51690 - 0.875783i) q^{56} +(-2.73359 - 4.17802i) q^{57} +(1.74737 + 3.02653i) q^{58} +(-3.26980 + 1.88782i) q^{59} +(-3.80998 + 0.212734i) q^{60} +(-5.05840 - 2.92047i) q^{61} +(-2.89022 + 5.00602i) q^{62} +(2.10441 - 4.81490i) q^{63} -1.00000 q^{64} +3.82024 q^{65} +(-5.48765 - 8.38734i) q^{66} -11.9957 q^{67} +(1.78280 + 1.02930i) q^{68} +(3.82444 - 7.56975i) q^{69} +(1.92946 - 3.34192i) q^{70} +(4.20433 + 7.28212i) q^{71} +(-0.333975 - 2.98135i) q^{72} -8.77691 q^{73} +(-5.72495 - 2.05548i) q^{74} +(0.0141223 + 0.252925i) q^{75} +(2.49642 - 1.44131i) q^{76} +10.1360 q^{77} +(0.167437 + 2.99873i) q^{78} +(8.51800 + 4.91787i) q^{79} -2.20312i q^{80} +(8.77692 - 1.99139i) q^{81} +0.153407i q^{82} -5.50705 q^{83} +(2.70783 + 1.36807i) q^{84} +(-2.26768 + 3.92773i) q^{85} +(0.965660 + 1.67257i) q^{86} +(-3.31406 - 5.06522i) q^{87} +(5.01153 - 2.89341i) q^{88} +(12.2455 + 7.06992i) q^{89} +(6.56828 - 0.735787i) q^{90} +(-2.63032 - 1.51862i) q^{91} +(4.24050 + 2.44826i) q^{92} +(4.51485 - 8.93627i) q^{93} +(-3.83521 + 2.21426i) q^{94} +(3.17537 + 5.49991i) q^{95} +(1.72936 - 0.0965604i) q^{96} +(10.6935 - 6.17388i) q^{97} +(3.40523 - 1.96601i) q^{98} +(10.3000 + 13.9748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

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