LMFDB - Embedded newform 572.2.s.a.439.63

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(43,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("572.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$80$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.63
Character	$\chi$	$=$	572.439
Dual form			572.2.s.a.43.63

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10302 - 0.885069i) q^{2} +(-2.39320 + 1.38172i) q^{3} +(0.433305 - 1.95250i) q^{4} +1.60862i q^{5} +(-1.41683 + 3.64221i) q^{6} +(-0.824322 - 0.475923i) q^{7} +(-1.25015 - 2.53715i) q^{8} +(2.31828 - 4.01537i) q^{9} +O(q^{10})$	\(q+(1.10302 - 0.885069i) q^{2} +(-2.39320 + 1.38172i) q^{3} +(0.433305 - 1.95250i) q^{4} +1.60862i q^{5} +(-1.41683 + 3.64221i) q^{6} +(-0.824322 - 0.475923i) q^{7} +(-1.25015 - 2.53715i) q^{8} +(2.31828 - 4.01537i) q^{9} +(1.42374 + 1.77434i) q^{10} +(-2.08622 + 2.57831i) q^{11} +(1.66081 + 5.27142i) q^{12} +(-0.449071 - 3.57748i) q^{13} +(-1.33047 + 0.204630i) q^{14} +(-2.22266 - 3.84975i) q^{15} +(-3.62449 - 1.69205i) q^{16} +(-3.08043 - 1.77849i) q^{17} +(-0.996779 - 6.48087i) q^{18} +(-5.85339 - 3.37945i) q^{19} +(3.14083 + 0.697023i) q^{20} +2.63036 q^{21} +(-0.0191506 + 4.69038i) q^{22} +(4.39537 - 2.53767i) q^{23} +(6.49748 + 4.34455i) q^{24} +2.41234 q^{25} +(-3.66165 - 3.54857i) q^{26} +4.52250i q^{27} +(-1.28642 + 1.40327i) q^{28} +(0.157432 - 0.0908935i) q^{29} +(-5.85893 - 2.27915i) q^{30} -10.5012 q^{31} +(-5.49547 + 1.34156i) q^{32} +(1.43024 - 9.05298i) q^{33} +(-4.97185 + 0.764687i) q^{34} +(0.765579 - 1.32602i) q^{35} +(-6.83548 - 6.26631i) q^{36} +(-10.2058 + 5.89234i) q^{37} +(-9.44745 + 1.45305i) q^{38} +(6.01777 + 7.94113i) q^{39} +(4.08131 - 2.01102i) q^{40} +(-1.77565 - 3.07552i) q^{41} +(2.90134 - 2.32805i) q^{42} +(-0.883307 + 1.52993i) q^{43} +(4.13019 + 5.19053i) q^{44} +(6.45921 + 3.72923i) q^{45} +(2.60217 - 6.68930i) q^{46} +0.738448 q^{47} +(11.0121 - 0.958598i) q^{48} +(-3.04700 - 5.27755i) q^{49} +(2.66086 - 2.13509i) q^{50} +9.82944 q^{51} +(-7.17960 - 0.673326i) q^{52} +6.34339 q^{53} +(4.00273 + 4.98841i) q^{54} +(-4.14753 - 3.35593i) q^{55} +(-0.176958 + 2.68640i) q^{56} +18.6778 q^{57} +(0.0932037 - 0.239596i) q^{58} +(-0.678136 + 1.17457i) q^{59} +(-8.47972 + 2.67161i) q^{60} +(6.60273 + 3.81209i) q^{61} +(-11.5831 + 9.29433i) q^{62} +(-3.82201 + 2.20664i) q^{63} +(-4.87424 + 6.34364i) q^{64} +(5.75480 - 0.722385i) q^{65} +(-6.43494 - 11.2515i) q^{66} +(5.28970 + 9.16202i) q^{67} +(-4.80725 + 5.24390i) q^{68} +(-7.01267 + 12.1463i) q^{69} +(-0.329173 - 2.14022i) q^{70} +(5.35114 - 9.26845i) q^{71} +(-13.0858 - 0.861982i) q^{72} +0.620466 q^{73} +(-6.04210 + 15.5322i) q^{74} +(-5.77322 + 3.33317i) q^{75} +(-9.13467 + 9.96439i) q^{76} +(2.94679 - 1.13248i) q^{77} +(13.6662 + 3.43308i) q^{78} +11.7178 q^{79} +(2.72187 - 5.83043i) q^{80} +(0.706020 + 1.22286i) q^{81} +(-4.68063 - 1.82078i) q^{82} -14.0859i q^{83} +(1.13975 - 5.13577i) q^{84} +(2.86091 - 4.95524i) q^{85} +(0.379792 + 2.46933i) q^{86} +(-0.251178 + 0.435053i) q^{87} +(9.14965 + 2.06975i) q^{88} +(-5.71451 + 3.29927i) q^{89} +(10.4253 - 1.60344i) q^{90} +(-1.33242 + 3.16272i) q^{91} +(-3.05025 - 9.68153i) q^{92} +(25.1316 - 14.5097i) q^{93} +(0.814523 - 0.653578i) q^{94} +(5.43626 - 9.41587i) q^{95} +(11.2981 - 10.8038i) q^{96} +(3.28725 + 1.89790i) q^{97} +(-8.03189 - 3.12444i) q^{98} +(5.51646 + 14.3542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{4} + 68 q^{9}+O(q^{10}) $ 160 * q - 2 * q^4 + 68 * q^9	$ 160 q - 2 q^{4} + 68 q^{9} - 36 q^{12} - 8 q^{14} - 6 q^{16} + 30 q^{20} - 20 q^{22} - 144 q^{25} - 40 q^{26} - 6 q^{33} + 46 q^{36} - 12 q^{37} - 56 q^{38} - 2 q^{42} + 48 q^{45} - 40 q^{48} + 44 q^{49} - 32 q^{53} + 30 q^{56} + 78 q^{58} + 64 q^{64} - 4 q^{66} - 44 q^{69} - 44 q^{77} + 16 q^{78} + 24 q^{80} - 40 q^{81} - 6 q^{82} - 10 q^{88} + 24 q^{89} - 24 q^{92} - 96 q^{93}+O(q^{100}) $ 160 * q - 2 * q^4 + 68 * q^9 - 36 * q^12 - 8 * q^14 - 6 * q^16 + 30 * q^20 - 20 * q^22 - 144 * q^25 - 40 * q^26 - 6 * q^33 + 46 * q^36 - 12 * q^37 - 56 * q^38 - 2 * q^42 + 48 * q^45 - 40 * q^48 + 44 * q^49 - 32 * q^53 + 30 * q^56 + 78 * q^58 + 64 * q^64 - 4 * q^66 - 44 * q^69 - 44 * q^77 + 16 * q^78 + 24 * q^80 - 40 * q^81 - 6 * q^82 - 10 * q^88 + 24 * q^89 - 24 * q^92 - 96 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.10302	−	0.885069i	0.779953	−	0.625839i
$2$	1.10302	−	0.885069i	0.779953	−	0.625839i
$3$	−2.39320	+	1.38172i	−1.38172	+	0.797734i	−0.992363	−	0.123355i	$-0.960635\pi$
$3$	−2.39320	+	1.38172i	−1.38172	+	0.797734i	−0.389353	+	0.921089i	$0.627301\pi$
$4$	0.433305	−	1.95250i	0.216652	−	0.976249i
$5$			1.60862i			0.719397i	0.933069	+	0.359698i	$0.117120\pi$
$5$			1.60862i			0.719397i	−0.933069	+	0.359698i	$0.882880\pi$
$6$	−1.41683	+	3.64221i	−0.578420	+	1.48693i
$7$	−0.824322	−	0.475923i	−0.311565	−	0.179882i	0.336062	−	0.941840i	$-0.390905\pi$
$7$	−0.824322	−	0.475923i	−0.311565	−	0.179882i	−0.647626	+	0.761958i	$0.724238\pi$
$8$	−1.25015	−	2.53715i	−0.441996	−	0.897017i
$9$	2.31828	−	4.01537i	0.772759	−	1.33846i
$10$	1.42374	+	1.77434i	0.450226	+	0.561095i
$11$	−2.08622	+	2.57831i	−0.629018	+	0.777391i
$11$	−2.08622	+	2.57831i	−0.629018	+	0.777391i
$12$	1.66081	+	5.27142i	0.479435	+	1.52173i
$13$	−0.449071	−	3.57748i	−0.124550	−	0.992213i
$13$	−0.449071	−	3.57748i	−0.124550	−	0.992213i
$14$	−1.33047	+	0.204630i	−0.355583	+	0.0546898i
$15$	−2.22266	−	3.84975i	−0.573887	−	0.994002i
$16$	−3.62449	−	1.69205i	−0.906124	−	0.423013i
$17$	−3.08043	−	1.77849i	−0.747113	−	0.431346i	0.0775366	−	0.996990i	$-0.475295\pi$
$17$	−3.08043	−	1.77849i	−0.747113	−	0.431346i	−0.824650	+	0.565643i	$0.808628\pi$
$18$	−0.996779	−	6.48087i	−0.234943	−	1.52756i
$19$	−5.85339	−	3.37945i	−1.34286	−	0.775300i	−0.355633	−	0.934626i	$-0.615735\pi$
$19$	−5.85339	−	3.37945i	−1.34286	−	0.775300i	−0.987226	+	0.159326i	$0.949068\pi$
$20$	3.14083	+	0.697023i	0.702310	+	0.155859i
$21$	2.63036			0.573992
$22$	−0.0191506	+	4.69038i	−0.00408292	+	0.999992i
$23$	4.39537	−	2.53767i	0.916497	−	0.529140i	0.0339814	−	0.999422i	$-0.489181\pi$
$23$	4.39537	−	2.53767i	0.916497	−	0.529140i	0.882516	+	0.470283i	$0.155848\pi$
$24$	6.49748	+	4.34455i	1.32629	+	0.886828i
$25$	2.41234			0.482468
$26$	−3.66165	−	3.54857i	−0.718108	−	0.695931i
$27$			4.52250i			0.870355i
$28$	−1.28642	+	1.40327i	−0.243111	+	0.265193i
$29$	0.157432	−	0.0908935i	0.0292344	−	0.0168785i	−0.485312	−	0.874341i	$-0.661294\pi$
$29$	0.157432	−	0.0908935i	0.0292344	−	0.0168785i	0.514546	+	0.857463i	$0.327960\pi$
$30$	−5.85893	−	2.27915i	−1.06969	−	0.416114i
$31$	−10.5012			−1.88608			−0.943039	−	0.332681i	$-0.892047\pi$
$31$	−10.5012			−1.88608			−0.943039	+	0.332681i	$0.892047\pi$
$32$	−5.49547	+	1.34156i	−0.971471	+	0.237157i
$33$	1.43024	−	9.05298i	0.248973	−	1.57592i
$34$	−4.97185	+	0.764687i	−0.852666	+	0.131143i
$35$	0.765579	−	1.32602i	0.129406	−	0.224139i
$36$	−6.83548	−	6.26631i	−1.13925	−	1.04438i
$37$	−10.2058	+	5.89234i	−1.67783	+	0.968694i	−0.714786	+	0.699343i	$0.753476\pi$
$37$	−10.2058	+	5.89234i	−1.67783	+	0.968694i	−0.963042	+	0.269351i	$0.913191\pi$
$38$	−9.44745	+	1.45305i	−1.53258	+	0.235716i
$39$	6.01777	+	7.94113i	0.963615	+	1.27160i
$40$	4.08131	−	2.01102i	0.645311	−	0.317970i
$41$	−1.77565	−	3.07552i	−0.277310	−	0.480316i	0.693405	−	0.720548i	$-0.256110\pi$
$41$	−1.77565	−	3.07552i	−0.277310	−	0.480316i	−0.970715	+	0.240232i	$0.922776\pi$
$42$	2.90134	−	2.32805i	0.447686	−	0.359226i
$43$	−0.883307	+	1.52993i	−0.134703	+	0.233313i	−0.925484	−	0.378787i	$-0.876341\pi$
$43$	−0.883307	+	1.52993i	−0.134703	+	0.233313i	0.790781	+	0.612099i	$0.209675\pi$
$44$	4.13019	+	5.19053i	0.622649	+	0.782501i
$45$	6.45921	+	3.72923i	0.962882	+	0.555920i
$46$	2.60217	−	6.68930i	0.383668	−	0.986283i
$47$	0.738448			0.107714			0.0538569	−	0.998549i	$-0.482849\pi$
$47$	0.738448			0.107714			0.0538569	+	0.998549i	$0.482849\pi$
$48$	11.0121	−	0.958598i	1.58946	−	0.138362i
$49$	−3.04700	−	5.27755i	−0.435285	−	0.753936i
$50$	2.66086	−	2.13509i	0.376302	−	0.301947i
$51$	9.82944			1.37640
$52$	−7.17960	−	0.673326i	−0.995631	−	0.0933735i
$53$	6.34339			0.871332			0.435666	−	0.900108i	$-0.356513\pi$
$53$	6.34339			0.871332			0.435666	+	0.900108i	$0.356513\pi$
$54$	4.00273	+	4.98841i	0.544702	+	0.678836i
$55$	−4.14753	−	3.35593i	−0.559253	−	0.452513i
$56$	−0.176958	+	2.68640i	−0.0236470	+	0.358986i
$57$	18.6778			2.47393
$58$	0.0932037	−	0.239596i	0.0122383	−	0.0314605i
$59$	−0.678136	+	1.17457i	−0.0882858	+	0.152916i	−0.906787	−	0.421590i	$-0.861472\pi$
$59$	−0.678136	+	1.17457i	−0.0882858	+	0.152916i	0.818501	+	0.574505i	$0.194806\pi$
$60$	−8.47972	+	2.67161i	−1.09473	+	0.344904i
$61$	6.60273	+	3.81209i	0.845392	+	0.488088i	0.859094	−	0.511819i	$-0.171028\pi$
$61$	6.60273	+	3.81209i	0.845392	+	0.488088i	−0.0137011	+	0.999906i	$0.504361\pi$
$62$	−11.5831	+	9.29433i	−1.47105	+	1.18038i
$63$	−3.82201	+	2.20664i	−0.481528	+	0.278011i
$64$	−4.87424	+	6.34364i	−0.609280	+	0.792955i
$65$	5.75480	−	0.722385i	0.713795	−	0.0896008i
$66$	−6.43494	−	11.2515i	−0.792086	−	1.38496i
$67$	5.28970	+	9.16202i	0.646239	+	1.11932i	0.984014	+	0.178092i	$0.0569925\pi$
$67$	5.28970	+	9.16202i	0.646239	+	1.11932i	−0.337775	+	0.941227i	$0.609674\pi$
$68$	−4.80725	+	5.24390i	−0.582965	+	0.635916i
$69$	−7.01267	+	12.1463i	−0.844226	+	1.46224i
$70$	−0.329173	−	2.14022i	−0.0393436	−	0.255805i
$71$	5.35114	−	9.26845i	0.635063	−	1.09996i	−0.351438	−	0.936211i	$-0.614307\pi$
$71$	5.35114	−	9.26845i	0.635063	−	1.09996i	0.986502	−	0.163751i	$-0.0523594\pi$
$72$	−13.0858	−	0.861982i	−1.54218	−	0.101586i
$73$	0.620466			0.0726200			0.0363100	−	0.999341i	$-0.488440\pi$
$73$	0.620466			0.0726200			0.0363100	+	0.999341i	$0.488440\pi$
$74$	−6.04210	+	15.5322i	−0.702380	+	1.80559i
$75$	−5.77322	+	3.33317i	−0.666634	+	0.384881i
$76$	−9.13467	+	9.96439i	−1.04782	+	1.14299i
$77$	2.94679	−	1.13248i	0.335818	−	0.129059i
$78$	13.6662	+	3.43308i	1.54739	+	0.388720i
$79$	11.7178			1.31835			0.659175	−	0.751989i	$-0.270906\pi$
$79$	11.7178			1.31835			0.659175	+	0.751989i	$0.270906\pi$
$80$	2.72187	−	5.83043i	0.304314	−	0.651862i
$81$	0.706020	+	1.22286i	0.0784467	+	0.135874i
$82$	−4.68063	−	1.82078i	−0.516889	−	0.201072i
$83$		−	14.0859i		−	1.54613i	−0.634326	−	0.773066i	$-0.718722\pi$
$83$		−	14.0859i		−	1.54613i	0.634326	−	0.773066i	$-0.281278\pi$
$84$	1.13975	−	5.13577i	0.124357	−	0.560359i
$85$	2.86091	−	4.95524i	0.310309	−	0.537471i
$86$	0.379792	+	2.46933i	0.0409540	+	0.266275i
$87$	−0.251178	+	0.435053i	−0.0269291	+	0.0466426i
$88$	9.14965	+	2.06975i	0.975356	+	0.220636i
$89$	−5.71451	+	3.29927i	−0.605737	+	0.349722i	−0.771295	−	0.636478i	$-0.780391\pi$
$89$	−5.71451	+	3.29927i	−0.605737	+	0.349722i	0.165558	+	0.986200i	$0.447057\pi$
$90$	10.4253	−	1.60344i	1.09892	−	0.169017i
$91$	−1.33242	+	3.16272i	−0.139676	+	0.331543i
$92$	−3.05025	−	9.68153i	−0.318011	−	1.00937i
$93$	25.1316	−	14.5097i	2.60602	−	1.50459i
$94$	0.814523	−	0.653578i	0.0840116	−	0.0674114i
$95$	5.43626	−	9.41587i	0.557748	−	0.966048i
$96$	11.2981	−	10.8038i	1.15311	−	1.10266i
$97$	3.28725	+	1.89790i	0.333770	+	0.192702i	0.657514	−	0.753443i	$-0.271608\pi$
$97$	3.28725	+	1.89790i	0.333770	+	0.192702i	−0.323744	+	0.946145i	$0.604942\pi$
$98$	−8.03189	−	3.12444i	−0.811344	−	0.315616i
$99$	5.51646	+	14.3542i	0.554426	+	1.44265i
$100$	1.04528	−	4.71009i	0.104528	−	0.471009i
$101$	−6.81733	+	3.93599i	−0.678349	+	0.391645i	−0.799233	−	0.601022i	$-0.794761\pi$
$101$	−6.81733	+	3.93599i	−0.678349	+	0.391645i	0.120884	+	0.992667i	$0.461427\pi$
$102$	10.8421	−	8.69974i	1.07352	−	0.861403i
$103$			8.70800i			0.858025i	0.903299	+	0.429012i	$0.141138\pi$
$103$			8.70800i			0.858025i	−0.903299	+	0.429012i	$0.858862\pi$
$104$	−8.51518	+	5.61175i	−0.834982	+	0.550277i
$105$			4.23125i			0.412928i
$106$	6.99689	−	5.61434i	0.679598	−	0.545313i
$107$	5.47243	+	9.47853i	0.529040	+	0.916324i	0.999426	+	0.0338634i	$0.0107811\pi$
$107$	5.47243	+	9.47853i	0.529040	+	0.916324i	−0.470387	+	0.882460i	$0.655886\pi$
$108$	8.83017	+	1.95962i	0.849683	+	0.188564i
$109$	−12.5881			−1.20572			−0.602862	−	0.797846i	$-0.705973\pi$
$109$	−12.5881			−1.20572			−0.602862	+	0.797846i	$0.705973\pi$
$110$	−7.54503	−	0.0308061i	−0.719391	−	0.00293724i
$111$	16.2831	−	28.2031i	1.54552	−	2.67692i
$112$	2.18247	+	3.11978i	0.206224	+	0.294791i
$113$	−0.773817	+	1.34029i	−0.0727945	+	0.126084i	−0.900125	−	0.435632i	$-0.856525\pi$
$113$	−0.773817	+	1.34029i	−0.0727945	+	0.126084i	0.827331	+	0.561715i	$0.189858\pi$
$114$	20.6020	−	16.5311i	1.92955	−	1.54828i
$115$	4.08214	+	7.07048i	0.380662	+	0.659325i
$116$	−0.109253	−	0.346771i	−0.0101439	−	0.0321968i
$117$	−15.4060	−	6.49039i	−1.42428	−	0.600037i
$118$	0.291575	+	1.89577i	0.0268417	+	0.174520i
$119$	1.69284	+	2.93209i	0.155183	+	0.268784i
$120$	−6.98873	+	10.4520i	−0.637981	+	0.954131i
$121$	−2.29541	−	10.7578i	−0.208673	−	0.977985i
$122$	10.6569	−	1.63907i	0.964830	−	0.148394i
$123$	8.49899	+	4.90689i	0.766328	+	0.442440i
$124$	−4.55024	+	20.5037i	−0.408623	+	1.84128i
$125$			11.9236i			1.06648i
$126$	−2.26273	+	5.81672i	−0.201580	+	0.518194i
$127$	−2.34055	−	4.05396i	−0.207691	−	0.359731i	0.743296	−	0.668963i	$-0.233261\pi$
$127$	−2.34055	−	4.05396i	−0.207691	−	0.359731i	−0.950987	+	0.309232i	$0.899928\pi$
$128$	0.238183	+	11.3112i	0.0210526	+	0.999778i
$129$		−	4.88192i		−	0.429829i
$130$	5.70830	−	5.89020i	0.500651	−	0.516605i
$131$	−12.0031			−1.04871			−0.524356	−	0.851499i	$-0.675694\pi$
$131$	−12.0031			−1.04871			−0.524356	+	0.851499i	$0.675694\pi$
$132$	−17.0562	−	6.71524i	−1.48455	−	0.584486i
$133$	3.21672	+	5.57152i	0.278925	+	0.483112i
$134$	13.9437	+	5.42414i	1.20455	+	0.468574i
$135$	−7.27498			−0.626131
$136$	−0.661277	+	10.0389i	−0.0567041	+	0.860827i
$137$	−9.62734	−	5.55835i	−0.822520	−	0.474882i	0.0287650	−	0.999586i	$-0.490843\pi$
$137$	−9.62734	−	5.55835i	−0.822520	−	0.474882i	−0.851285	+	0.524704i	$0.824176\pi$
$138$	3.01520	+	19.6043i	0.256671	+	1.66883i
$139$	4.58662	−	7.94425i	0.389032	−	0.673823i	−0.603288	−	0.797524i	$-0.706143\pi$
$139$	4.58662	−	7.94425i	0.389032	−	0.673823i	0.992320	+	0.123701i	$0.0394763\pi$
$140$	−2.25733	−	2.06936i	−0.190779	−	0.174893i
$141$	−1.76726	+	1.02033i	−0.148830	+	0.0859269i
$142$	−2.30081	−	14.9594i	−0.193079	−	1.25537i
$143$	10.1607	+	6.30554i	0.849682	+	0.527296i
$144$	−15.1968	+	10.6310i	−1.26640	+	0.885921i
$145$	0.146213	+	0.253249i	0.0121423	+	0.0210312i
$146$	0.684386	−	0.549155i	0.0566402	−	0.0454484i
$147$	14.5841	+	8.42016i	1.20288	+	0.694483i
$148$	7.08254	+	22.4800i	0.582182	+	1.84785i
$149$	−4.02189	+	6.96611i	−0.329486	+	0.570686i	−0.982410	−	0.186737i	$-0.940209\pi$
$149$	−4.02189	+	6.96611i	−0.329486	+	0.570686i	0.652924	+	0.757423i	$0.273542\pi$
$150$	−3.41789	+	8.78625i	−0.279069	+	0.717394i
$151$			3.53594i			0.287751i	0.989596	+	0.143875i	$0.0459564\pi$
$151$			3.53594i			0.287751i	−0.989596	+	0.143875i	$0.954044\pi$
$152$	−1.25655	+	19.0757i	−0.101920	+	1.54725i
$153$	−14.2826	+	8.24604i	−1.15468	+	0.666653i
$154$	2.24804	−	3.85727i	0.181152	−	0.310828i
$155$		−	16.8925i		−	1.35684i
$156$	18.1126	−	8.30876i	1.45017	−	0.665233i
$157$	−7.15070			−0.570688			−0.285344	−	0.958425i	$-0.592108\pi$
$157$	−7.15070			−0.570688			−0.285344	+	0.958425i	$0.592108\pi$
$158$	12.9249	−	10.3710i	1.02825	−	0.825074i
$159$	−15.1810	+	8.76477i	−1.20393	+	0.695091i
$160$	−2.15806	−	8.84013i	−0.170610	−	0.698873i
$161$	−4.83093			−0.380731
$162$	1.86107	+	0.723965i	0.146220	+	0.0568801i
$163$	9.19433	−	15.9250i	0.720155	−	1.24735i	−0.240782	−	0.970579i	$-0.577404\pi$
$163$	9.19433	−	15.9250i	0.720155	−	1.24735i	0.960937	−	0.276766i	$-0.0892628\pi$
$164$	−6.77434	+	2.13432i	−0.528987	+	0.166662i
$165$	14.5628	+	2.30071i	1.13371	+	0.179110i
$166$	−12.4670	−	15.5371i	−0.967629	−	1.20591i
$167$	7.07069	−	4.08226i	0.547146	−	0.315895i	−0.200824	−	0.979627i	$-0.564362\pi$
$167$	7.07069	−	4.08226i	0.547146	−	0.315895i	0.747970	+	0.663732i	$0.231029\pi$
$168$	−3.28835	−	6.67361i	−0.253702	−	0.514880i
$169$	−12.5967	+	3.21308i	−0.968975	+	0.247160i
$170$	−1.23009	−	7.99783i	−0.0943437	−	0.613405i
$171$	−27.1395	+	15.6690i	−2.07541	+	1.19824i
$172$	2.60445	+	2.38758i	0.198587	+	0.182051i
$173$	1.73573	+	1.00212i	0.131965	+	0.0761901i	0.564529	−	0.825413i	$-0.309058\pi$
$173$	1.73573	+	1.00212i	0.131965	+	0.0761901i	−0.432564	+	0.901603i	$0.642391\pi$
$174$	0.107998	+	0.702182i	0.00818730	+	0.0532323i
$175$	−1.98855	−	1.14809i	−0.150320	−	0.0867873i
$176$	11.9241	−	5.81510i	0.898814	−	0.438329i
$177$		−	3.74797i		−	0.281714i
$178$	−3.38313	+	8.69690i	−0.253576	+	0.651860i
$179$	−6.50643	+	3.75649i	−0.486313	+	0.280773i	−0.723044	−	0.690802i	$-0.757257\pi$
$179$	−6.50643	+	3.75649i	−0.486313	+	0.280773i	0.236731	+	0.971575i	$0.423924\pi$
$180$	10.0801	−	10.9957i	0.751327	−	0.819571i
$181$	−6.08545			−0.452328			−0.226164	−	0.974089i	$-0.572619\pi$
$181$	−6.08545			−0.452328			−0.226164	+	0.974089i	$0.572619\pi$
$182$	1.32954	+	4.66783i	0.0985517	+	0.346002i
$183$	−21.0689			−1.55746
$184$	−11.9333	−	7.97923i	−0.879735	−	0.588236i
$185$	−9.47853	−	16.4173i	−0.696876	−	1.20702i
$186$	14.8785	−	38.2477i	1.09095	−	2.80446i
$187$	11.0119	−	4.23200i	0.805272	−	0.309475i
$188$	0.319973	−	1.44182i	0.0233364	−	0.105155i
$189$	2.15236	−	3.72800i	0.156561	−	0.271172i
$190$	−2.33740	−	15.1974i	−0.169573	−	1.10253i
$191$	−19.6308	−	11.3339i	−1.42044	−	0.820089i	−0.424100	−	0.905615i	$-0.639409\pi$
$191$	−19.6308	−	11.3339i	−1.42044	−	0.820089i	−0.996336	+	0.0855264i	$0.972743\pi$
$192$	2.89992	−	21.9164i	0.209284	−	1.58168i
$193$	10.7987	+	18.7038i	0.777305	+	1.34633i	0.933490	+	0.358604i	$0.116747\pi$
$193$	10.7987	+	18.7038i	0.777305	+	1.34633i	−0.156184	+	0.987728i	$0.549919\pi$
$194$	5.30567	−	0.816030i	0.380925	−	0.0585875i
$195$	−12.7743	+	9.68031i	−0.914784	+	0.693221i
$196$	−11.6247	+	3.66246i	−0.830334	+	0.261605i
$197$	−4.70447	−	8.14838i	−0.335179	−	0.580548i	0.648340	−	0.761351i	$-0.275464\pi$
$197$	−4.70447	−	8.14838i	−0.335179	−	0.580548i	−0.983519	+	0.180803i	$0.942130\pi$
$198$	18.7892	+	10.9505i	1.33529	+	0.778217i
$199$	1.05311	+	0.608016i	0.0746533	+	0.0431011i	0.536862	−	0.843670i	$-0.319610\pi$
$199$	1.05311	+	0.608016i	0.0746533	+	0.0431011i	−0.462209	+	0.886771i	$0.652943\pi$
$200$	−3.01579	−	6.12047i	−0.213249	−	0.432782i
$201$	−25.3186	−	14.6177i	−1.78584	−	1.03105i
$202$	−4.03602	+	10.3753i	−0.283974	+	0.730002i
$203$	−0.173033			−0.0121446
$204$	4.25914	−	19.1920i	0.298200	−	1.34371i
$205$	4.94734	−	2.85635i	0.345538	−	0.199496i
$206$	7.70719	+	9.60510i	0.536985	+	0.669219i
$207$		−	23.5320i		−	1.63559i
$208$	−4.42562	+	13.7264i	−0.306862	+	0.951754i
$209$	20.9247	−	8.04159i	1.44739	−	0.556249i
$210$	3.74495	+	4.66715i	0.258426	+	0.322064i
$211$	−6.25551	−	10.8349i	−0.430647	−	0.745902i	0.566282	−	0.824211i	$-0.308381\pi$
$211$	−6.25551	−	10.8349i	−0.430647	−	0.745902i	−0.996929	+	0.0783091i	$0.975048\pi$
$212$	2.74862	−	12.3855i	0.188776	−	0.850637i
$213$			29.5750i			2.02645i
$214$	14.4254	+	5.61152i	0.986097	+	0.383596i
$215$	−2.46108	−	1.42091i	−0.167844	−	0.0969050i
$216$	11.4742	−	5.65381i	0.780724	−	0.384693i
$217$	8.65641	+	4.99778i	0.587635	+	0.339271i
$218$	−13.8849	+	11.1414i	−0.940407	+	0.754588i
$219$	−1.48490	+	0.857307i	−0.100340	+	0.0579314i
$220$	−8.34959	+	6.64390i	−0.562929	+	0.447932i
$221$	−4.97916	+	11.8188i	−0.334934	+	0.795020i
$222$	−7.00116	−	45.5202i	−0.469887	−	3.05512i
$223$	−1.21946	−	2.11216i	−0.0816608	−	0.141441i	0.822303	−	0.569050i	$-0.192689\pi$
$223$	−1.21946	−	2.11216i	−0.0816608	−	0.141441i	−0.903963	+	0.427610i	$0.859356\pi$
$224$	5.16852	+	1.50954i	0.345336	+	0.100860i
$225$	5.59247	−	9.68645i	0.372831	−	0.645763i
$226$	0.332714	+	2.16325i	0.0221318	+	0.143897i
$227$	16.8840	+	9.74800i	1.12063	+	0.646998i	0.941562	−	0.336838i	$-0.109358\pi$
$227$	16.8840	+	9.74800i	1.12063	+	0.646998i	0.179071	+	0.983836i	$0.442691\pi$
$228$	8.09317	−	36.4683i	0.535983	−	2.41517i
$229$		−	5.20421i		−	0.343904i	−0.985105	−	0.171952i	$-0.944993\pi$
$229$		−	5.20421i		−	0.343904i	0.985105	−	0.171952i	$-0.0550073\pi$
$230$	10.7605	+	4.18590i	0.709529	+	0.276010i
$231$	−5.48750	+	6.78189i	−0.361051	+	0.446216i
$232$	−0.427425	−	0.285798i	−0.0280618	−	0.0187636i
$233$		−	23.5497i		−	1.54279i	−0.636356	−	0.771395i	$-0.719559\pi$
$233$		−	23.5497i		−	1.54279i	0.636356	−	0.771395i	$-0.280441\pi$
$234$	−22.7375	+	6.47632i	−1.48640	+	0.423371i
$235$			1.18788i			0.0774890i
$236$	1.99950	+	1.83301i	0.130156	+	0.119318i
$237$	−28.0429	+	16.1906i	−1.82159	+	1.05169i
$238$	4.46234	+	1.73587i	0.289251	+	0.112520i
$239$		−	15.6845i		−	1.01455i	−0.861786	−	0.507273i	$-0.830654\pi$
$239$		−	15.6845i		−	1.01455i	0.861786	−	0.507273i	$-0.169346\pi$
$240$	1.54202	+	17.7143i	0.0995370	+	1.14345i
$241$	−4.31578	+	7.47514i	−0.278004	+	0.481516i	−0.970888	−	0.239532i	$-0.923006\pi$
$241$	−4.31578	+	7.47514i	−0.278004	+	0.481516i	0.692885	+	0.721048i	$0.256339\pi$
$242$	−12.0533	−	9.83452i	−0.774816	−	0.632187i
$243$	−15.1291	−	8.73479i	−0.970532	−	0.560337i
$244$	10.3041	−	11.2400i	0.659651	−	0.719568i
$245$	8.48957	−	4.90146i	0.542379	−	0.313143i
$246$	13.7175	−	2.10979i	0.874595	−	0.134516i
$247$	−9.46133	+	22.4580i	−0.602010	+	1.42897i
$248$	13.1282	+	26.6432i	0.833639	+	1.69185i
$249$	19.4627	+	33.7105i	1.23340	+	2.13631i
$250$	10.5532	+	13.1520i	0.667446	+	0.831806i
$251$	10.7330	+	6.19672i	0.677463	+	0.391134i	0.798899	−	0.601466i	$-0.205416\pi$
$251$	10.7330	+	6.19672i	0.677463	+	0.391134i	−0.121435	+	0.992599i	$0.538750\pi$
$252$	2.65236	+	8.41862i	0.167083	+	0.530323i
$253$	−2.62678	+	16.6268i	−0.165145	+	1.04532i
$254$	−6.16971	−	2.40004i	−0.387122	−	0.150592i
$255$			15.8118i			0.990176i
$256$	10.2739	+	12.2657i	0.642120	+	0.766604i
$257$	2.00958	+	3.48069i	0.125354	+	0.217120i	0.921871	−	0.387496i	$-0.126660\pi$
$257$	2.00958	+	3.48069i	0.125354	+	0.217120i	−0.796517	+	0.604616i	$0.793327\pi$
$258$	−4.32084	−	5.38485i	−0.269004	−	0.335246i
$259$	11.2172			0.697002
$260$	1.08313	−	11.5492i	0.0671726	−	0.716254i
$261$		−	0.842865i		−	0.0521720i
$262$	−13.2396	+	10.6235i	−0.817946	+	0.656325i
$263$	0.411333	+	0.712450i	0.0253639	+	0.0439315i	0.878429	−	0.477873i	$-0.158592\pi$
$263$	0.411333	+	0.712450i	0.0253639	+	0.0439315i	−0.853065	+	0.521805i	$0.825259\pi$
$264$	−24.7568	+	7.68888i	−1.52367	+	0.473218i
$265$			10.2041i			0.626834i
$266$	8.47928	+	3.29848i	0.519898	+	0.202243i
$267$	9.11732	−	15.7917i	0.557971	−	0.966434i
$268$	20.1809	−	6.35817i	1.23274	−	0.388387i
$269$	10.3006	−	17.8411i	0.628038	−	1.08779i	−0.359907	−	0.932988i	$-0.617192\pi$
$269$	10.3006	−	17.8411i	0.628038	−	1.08779i	0.987945	−	0.154805i	$-0.0494750\pi$
$270$	−8.02445	+	6.43887i	−0.488352	+	0.391857i
$271$	−24.5979	+	14.2016i	−1.49422	+	0.862686i	−0.999978	−	0.00663992i	$-0.997886\pi$
$271$	−24.5979	+	14.2016i	−1.49422	+	0.862686i	−0.494239	+	0.869326i	$0.664553\pi$
$272$	8.15570	+	11.6584i	0.494512	+	0.706892i
$273$	−1.18122	−	9.41005i	−0.0714906	−	0.569522i
$274$	−15.5387	+	2.38990i	−0.938726	+	0.144379i
$275$	−5.03266	+	6.21977i	−0.303481	+	0.375066i
$276$	20.6770	+	18.9553i	1.24461	+	1.14097i
$277$	17.1321	+	9.89125i	1.02937	+	0.594308i	0.916804	−	0.399337i	$-0.130759\pi$
$277$	17.1321	+	9.89125i	1.02937	+	0.594308i	0.112567	+	0.993644i	$0.464093\pi$
$278$	−1.97209	−	12.8221i	−0.118278	−	0.769021i
$279$	−24.3448	+	42.1664i	−1.45748	+	2.52444i
$280$	−4.32140	−	0.284658i	−0.258253	−	0.0170116i
$281$	−24.1510			−1.44073			−0.720363	−	0.693597i	$-0.756025\pi$
$281$	−24.1510			−1.44073			−0.720363	+	0.693597i	$0.756025\pi$
$282$	−1.04626	+	2.68958i	−0.0623038	+	0.160162i
$283$	3.90087	+	6.75651i	0.231883	+	0.401633i	0.958362	−	0.285555i	$-0.0921781\pi$
$283$	3.90087	+	6.75651i	0.231883	+	0.401633i	−0.726479	+	0.687188i	$0.758845\pi$
$284$	−15.7779	−	14.4641i	−0.936249	−	0.858289i
$285$			30.0454i			1.77974i
$286$	16.7883	−	2.03780i	0.992714	−	0.120498i
$287$			3.38029i			0.199532i
$288$	−7.35315	+	25.1765i	−0.433289	+	1.48354i
$289$	−2.17398	−	3.76544i	−0.127881	−	0.221497i
$290$	0.385419	+	0.149929i	0.0226326	+	0.00880416i
$291$	−10.4894			−0.614900
$292$	0.268851	−	1.21146i	0.0157333	−	0.0708952i
$293$	5.02023	−	8.69529i	0.293285	−	0.507984i	−0.681300	−	0.732005i	$-0.738585\pi$
$293$	5.02023	−	8.69529i	0.293285	−	0.507984i	0.974584	+	0.224020i	$0.0719182\pi$
$294$	23.5390	−	3.62038i	1.37282	−	0.211145i
$295$	−1.88943	−	1.09086i	−0.110007	−	0.0635126i
$296$	27.7086	+	18.5274i	1.61053	+	1.07688i
$297$	−11.6604	−	9.43491i	−0.676606	−	0.547469i
$298$	1.72927	+	11.2434i	0.100174	+	0.651313i
$299$	−11.0523	−	14.5847i	−0.639169	−	0.843456i
$300$	4.00644	+	12.7165i	0.231312	+	0.734186i
$301$	1.45626	−	0.840772i	0.0839374	−	0.0484613i
$302$	3.12955	+	3.90021i	0.180085	+	0.224432i
$303$	10.8768	−	18.8392i	0.624857	−	1.08228i
$304$	15.4973	+	22.1530i	0.888834	+	1.27056i
$305$	−6.13220	+	10.6213i	−0.351129	+	0.608173i
$306$	−8.45563	+	21.7366i	−0.483376	+	1.24260i
$307$		−	22.3978i		−	1.27831i	−0.769078	−	0.639155i	$-0.779284\pi$
$307$		−	22.3978i		−	1.27831i	0.769078	−	0.639155i	$-0.220716\pi$
$308$	−0.934314	−	6.24432i	−0.0532375	−	0.355803i
$309$	−12.0320	−	20.8400i	−0.684476	−	1.18555i
$310$	−14.9510	−	18.6328i	−0.849162	−	1.05827i
$311$		−	10.5680i		−	0.599253i	−0.954057	−	0.299627i	$-0.903138\pi$
$311$		−	10.5680i		−	0.599253i	0.954057	−	0.299627i	$-0.0968621\pi$
$312$	12.6247	−	25.1956i	0.714733	−	1.42642i
$313$	0.0258873			0.00146324			0.000731620	−	1.00000i	$-0.499767\pi$
$313$	0.0258873			0.00146324			0.000731620		1.00000i	$0.499767\pi$
$314$	−7.88736	+	6.32886i	−0.445109	+	0.357158i
$315$	−3.54965	−	6.14817i	−0.200000	−	0.346410i
$316$	5.07736	−	22.8789i	0.285624	−	1.28704i
$317$		−	9.47350i		−	0.532085i	−0.963961	−	0.266042i	$-0.914284\pi$
$317$		−	9.47350i		−	0.532085i	0.963961	−	0.266042i	$-0.0857162\pi$
$318$	−8.98754	+	23.1040i	−0.503996	+	1.29561i
$319$	−0.0940855	+	0.595533i	−0.00526778	+	0.0333435i
$320$	−10.2045	−	7.84080i	−0.570450	−	0.438314i
$321$	−26.1933	−	15.1227i	−1.46197	−	0.844066i
$322$	−5.32861	+	4.27571i	−0.296952	+	0.238276i
$323$	12.0206	+	20.8203i	0.668845	+	1.15847i
$324$	2.69356	−	0.848631i	0.149642	−	0.0471462i
$325$	−1.08331	−	8.63009i	−0.0600914	−	0.478711i
$326$	−3.95324	−	25.7033i	−0.218950	−	1.42357i
$327$	30.1259	−	17.3932i	1.66597	−	0.961847i
$328$	−5.58321	+	8.34996i	−0.308281	+	0.461050i
$329$	−0.608720	−	0.351444i	−0.0335598	−	0.0193758i
$330$	18.0994	−	10.3514i	0.996337	−	0.569824i
$331$	−0.808705	+	1.40072i	−0.0444504	+	0.0769904i	−0.887395	−	0.461011i	$-0.847487\pi$
$331$	−0.808705	+	1.40072i	−0.0444504	+	0.0769904i	0.842944	+	0.538001i	$0.180820\pi$
$332$	−27.5027	−	6.10350i	−1.50941	−	0.334973i
$333$			54.6403i			2.99427i
$334$	4.18602	−	10.7609i	0.229049	−	0.588809i
$335$	−14.7382	+	8.50911i	−0.805235	+	0.464902i
$336$	−9.53372	−	4.45071i	−0.520107	−	0.242806i
$337$			20.5930i			1.12177i	0.827892	+	0.560887i	$0.189540\pi$
$337$			20.5930i			1.12177i	−0.827892	+	0.560887i	$0.810460\pi$
$338$	−11.0506	+	14.6930i	−0.601072	+	0.799195i
$339$		−	4.27678i		−	0.232283i
$340$	−8.43544	−	7.73304i	−0.457476	−	0.419383i
$341$	21.9079	−	27.0755i	1.18638	−	1.46622i
$342$	−16.0673	+	41.3036i	−0.868818	+	2.23344i
$343$			12.4635i			0.672963i
$344$	4.98594	+	0.328432i	0.268824	+	0.0177079i
$345$	−19.5388	−	11.2807i	−1.05193	−	0.607333i
$346$	2.80149	−	0.430879i	0.150609	−	0.0231642i
$347$	8.46013	−	14.6534i	0.454164	−	0.786634i	−0.544476	−	0.838776i	$-0.683272\pi$
$347$	8.46013	−	14.6534i	0.454164	−	0.786634i	0.998640	+	0.0521420i	$0.0166048\pi$
$348$	0.740604	+	0.678935i	0.0397005	+	0.0363947i
$349$	−8.55551	−	14.8186i	−0.457966	−	0.793220i	0.540888	−	0.841095i	$-0.318088\pi$
$349$	−8.55551	−	14.8186i	−0.457966	−	0.793220i	−0.998853	+	0.0478749i	$0.984755\pi$
$350$	−3.20954	+	0.493638i	−0.171557	+	0.0263861i
$351$	16.1791	−	2.03092i	0.863578	−	0.108403i
$352$	8.00577	−	16.9678i	0.426709	−	0.904389i
$353$	21.9078	−	12.6484i	1.16603	−	0.673209i	0.213290	−	0.976989i	$-0.431582\pi$
$353$	21.9078	−	12.6484i	1.16603	−	0.673209i	0.952742	+	0.303780i	$0.0982488\pi$
$354$	−3.31721	−	4.13408i	−0.176308	−	0.219724i
$355$	14.9094	+	8.60795i	0.791309	+	0.456863i
$356$	3.96570	+	12.5872i	0.210182	+	0.667118i
$357$	−8.10263	−	4.67806i	−0.428837	−	0.247589i
$358$	−3.85196	+	9.90212i	−0.203583	+	0.523343i
$359$		−	0.247991i		−	0.0130885i	−0.999979	−	0.00654423i	$-0.997917\pi$
$359$		−	0.247991i		−	0.0130885i	0.999979	−	0.00654423i	$-0.00208311\pi$
$360$	1.38660	−	21.0501i	0.0730804	−	1.10944i
$361$	13.3414	+	23.1080i	0.702180	+	1.21621i
$362$	−6.71237	+	5.38604i	−0.352794	+	0.283084i
$363$	20.3576	+	22.5741i	1.06850	+	1.18483i
$364$	5.59785	+	3.97197i	0.293407	+	0.208188i
$365$			0.998094i			0.0522426i
$366$	−23.2394	+	18.6474i	−1.21474	+	0.974716i
$367$	2.02035	−	1.16645i	0.105461	−	0.0608881i	−0.446342	−	0.894863i	$-0.647273\pi$
$367$	2.02035	−	1.16645i	0.105461	−	0.0608881i	0.551803	+	0.833975i	$0.313940\pi$
$368$	−20.2248	+	1.76057i	−1.05429	+	0.0917758i
$369$	−16.4658			−0.857176
$370$	−24.9855	−	9.71945i	−1.29893	−	0.505290i
$371$	−5.22900	−	3.01897i	−0.271476	−	0.156737i
$372$	−17.4406	−	55.3565i	−0.904252	−	2.87010i
$373$	6.25582	+	3.61180i	0.323914	+	0.187012i	0.653136	−	0.757241i	$-0.273453\pi$
$373$	6.25582	+	3.61180i	0.323914	+	0.187012i	−0.329222	+	0.944253i	$0.606786\pi$
$374$	8.40076	−	14.4143i	0.434393	−	0.745346i
$375$	−16.4751	−	28.5357i	−0.850770	−	1.47358i
$376$	−0.923173	−	1.87355i	−0.0476090	−	0.0966211i
$377$	−0.395868	−	0.522392i	−0.0203882	−	0.0269046i
$378$	−0.925441	−	6.01704i	−0.0475995	−	0.309483i
$379$	10.3097	+	17.8569i	0.529573	+	0.917247i	0.999405	+	0.0344915i	$0.0109811\pi$
$379$	10.3097	+	17.8569i	0.529573	+	0.917247i	−0.469832	+	0.882756i	$0.655686\pi$
$380$	−16.0289	−	14.6942i	−0.822266	−	0.753798i
$381$	11.2028	+	6.46796i	0.573939	+	0.331364i
$382$	−31.6844	+	4.87317i	−1.62112	+	0.249333i
$383$	17.1044	−	29.6256i	0.873993	−	1.51380i	0.0161609	−	0.999869i	$-0.494856\pi$
$383$	17.1044	−	29.6256i	0.873993	−	1.51380i	0.857832	−	0.513930i	$-0.171811\pi$
$384$	−16.1989	−	26.7409i	−0.826646	−	1.36462i
$385$	1.82174	+	4.74027i	0.0928443	+	0.241587i
$386$	28.4653	+	11.0731i	1.44885	+	0.563608i
$387$	4.09550	+	7.09362i	0.208186	+	0.360589i
$388$	5.13002	−	5.59599i	0.260437	−	0.284093i
$389$	−20.5774			−1.04332			−0.521659	−	0.853154i	$-0.674687\pi$
$389$	−20.5774			−1.04332			−0.521659	+	0.853154i	$0.674687\pi$
$390$	−5.52252	+	21.9837i	−0.279644	+	1.11319i
$391$	−18.0528			−0.912970
$392$	−9.58072	+	14.3284i	−0.483899	+	0.723694i
$393$	28.7258	−	16.5848i	1.44902	−	0.836594i
$394$	−12.4010	−	4.82404i	−0.624753	−	0.243032i
$395$			18.8494i			0.948417i
$396$	30.4168	−	4.55115i	1.52850	−	0.228704i
$397$	−6.45317	−	3.72574i	−0.323875	−	0.186989i	0.329243	−	0.944245i	$-0.393206\pi$
$397$	−6.45317	−	3.72574i	−0.323875	−	0.186989i	−0.653119	+	0.757256i	$0.726540\pi$
$398$	1.69974	−	0.261426i	0.0852004	−	0.0131041i
$399$	−15.3965	−	8.88918i	−0.770789	−	0.445016i
$400$	−8.74352	−	4.08181i	−0.437176	−	0.204090i
$401$	15.0040	−	8.66255i	0.749262	−	0.432587i	−0.0761649	−	0.997095i	$-0.524268\pi$
$401$	15.0040	−	8.66255i	0.749262	−	0.432587i	0.825427	+	0.564508i	$0.190934\pi$
$402$	−40.8646	+	6.28511i	−2.03814	+	0.313473i
$403$	4.71581	+	37.5679i	0.234911	+	1.87139i
$404$	4.73102	+	15.0163i	0.235377	+	0.747089i
$405$	−1.96712	+	1.13572i	−0.0977471	+	0.0564343i
$406$	−0.190859	+	0.153146i	−0.00947217	+	0.00760053i
$407$	6.09927	−	38.6065i	0.302329	−	1.91365i
$408$	−12.2883	−	24.9388i	−0.608362	−	1.23465i
$409$	11.0134	−	19.0758i	0.544577	−	0.943236i	−0.454056	−	0.890973i	$-0.650023\pi$
$409$	11.0134	−	19.0758i	0.544577	−	0.943236i	0.998633	−	0.0522625i	$-0.0166432\pi$
$410$	2.92895	−	7.52935i	0.144651	−	0.371848i
$411$	30.7202			1.51532
$412$	17.0024	+	3.77322i	0.837646	+	0.185893i
$413$	1.11801	−	0.645481i	0.0550135	−	0.0317621i
$414$	−20.8275	−	25.9563i	−1.02362	−	1.27568i
$415$	22.6589			1.11228
$416$	7.26726	+	19.0575i	0.356307	+	0.934369i
$417$			25.3496i			1.24138i
$418$	15.9630	−	27.3899i	0.780776	−	1.33968i
$419$	8.16345	−	4.71317i	0.398811	−	0.230253i	−0.287160	−	0.957883i	$-0.592711\pi$
$419$	8.16345	−	4.71317i	0.398811	−	0.230253i	0.685971	+	0.727629i	$0.259378\pi$
$420$	8.26151	+	1.83342i	0.403120	+	0.0894617i
$421$		−	28.7395i		−	1.40068i	−0.713812	−	0.700338i	$-0.753033\pi$
$421$		−	28.7395i		−	1.40068i	0.713812	−	0.700338i	$-0.246967\pi$
$422$	−16.4895	−	6.41450i	−0.802699	−	0.312253i
$423$	1.71193	−	2.96515i	0.0832368	−	0.144170i
$424$	−7.93021	−	16.0941i	−0.385125	−	0.781600i
$425$	−7.43104	−	4.29031i	−0.360458	−	0.208111i
$426$	26.1759	+	32.6218i	1.26823	+	1.58053i
$427$	−3.62852	−	6.28478i	−0.175596	−	0.304142i
$428$	20.8780	−	6.57782i	1.00918	−	0.317951i
$429$	−33.0291	−	1.05121i	−1.59466	−	0.0507530i
$430$	−3.97222	+	0.610941i	−0.191558	+	0.0294622i
$431$	−13.2035	+	7.62302i	−0.635989	+	0.367188i	−0.783068	−	0.621937i	$-0.786346\pi$
$431$	−13.2035	+	7.62302i	−0.635989	+	0.367188i	0.147079	+	0.989125i	$0.453013\pi$
$432$	7.65231	−	16.3918i	0.368172	−	0.788650i
$433$	2.35340	−	4.07621i	0.113097	−	0.195890i	−0.803920	−	0.594737i	$-0.797256\pi$
$433$	2.35340	−	4.07621i	0.113097	−	0.195890i	0.917018	+	0.398847i	$0.130589\pi$
$434$	13.9716	−	2.14887i	0.670657	−	0.103149i
$435$	−0.699835	−	0.404050i	−0.0335545	−	0.0193727i
$436$	−5.45449	+	24.5783i	−0.261223	+	1.17709i
$437$	−34.3037			−1.64097
$438$	−0.879097	+	2.25987i	−0.0420049	+	0.107981i
$439$	−8.95996	−	15.5191i	−0.427636	−	0.740687i	0.569027	−	0.822319i	$-0.307320\pi$
$439$	−8.95996	−	15.5191i	−0.427636	−	0.740687i	−0.996663	+	0.0816322i	$0.973987\pi$
$440$	−3.32945	+	14.7183i	−0.158725	+	0.701668i
$441$	−28.2551			−1.34548
$442$	4.96837	+	17.4433i	0.236321	+	0.829693i
$443$			12.9132i			0.613527i	0.951786	+	0.306763i	$0.0992461\pi$
$443$			12.9132i			0.613527i	−0.951786	+	0.306763i	$0.900754\pi$
$444$	−48.0110	−	44.0132i	−2.27850	−	2.08877i
$445$	−5.30728	−	9.19248i	−0.251589	−	0.435765i
$446$	−3.21449	−	1.25045i	−0.152211	−	0.0592106i
$447$		−	22.2284i		−	1.05137i
$448$	7.03703	−	2.90945i	0.332468	−	0.137458i
$449$	33.2567	+	19.2008i	1.56948	+	0.906140i	0.996229	+	0.0867603i	$0.0276514\pi$
$449$	33.2567	+	19.2008i	1.56948	+	0.906140i	0.573251	+	0.819380i	$0.305682\pi$
$450$	−2.40457	−	15.6341i	−0.113352	−	0.736997i
$451$	11.6341	+	1.83801i	0.547826	+	0.0865485i
$452$	2.28161	+	2.09163i	0.107318	+	0.0983819i
$453$	−4.88566	−	8.46221i	−0.229548	−	0.397589i
$454$	27.2511	−	4.19130i	1.27896	−	0.196708i
$455$	−5.08761	−	2.14336i	−0.238511	−	0.100482i
$456$	−23.3501	−	47.3883i	−1.09347	−	2.21916i
$457$	−12.3099	−	21.3214i	−0.575833	−	0.997372i	−0.995951	−	0.0899026i	$-0.971344\pi$
$457$	−12.3099	−	21.3214i	−0.575833	−	0.997372i	0.420117	−	0.907470i	$-0.361989\pi$
$458$	−4.60608	−	5.74034i	−0.215228	−	0.268228i
$459$	8.04320	−	13.9312i	0.375424	−	0.650254i
$460$	15.5739	−	4.90670i	0.726137	−	0.228776i
$461$	9.09343	−	15.7503i	0.423523	−	0.733564i	−0.572758	−	0.819724i	$-0.694127\pi$
$461$	9.09343	−	15.7503i	0.423523	−	0.733564i	0.996281	+	0.0861608i	$0.0274599\pi$
$462$	−0.0503730	+	12.3374i	−0.00234356	+	0.573987i
$463$	−13.8077			−0.641699			−0.320849	−	0.947130i	$-0.603968\pi$
$463$	−13.8077			−0.641699			−0.320849	+	0.947130i	$0.603968\pi$
$464$	−0.724409	+	0.0630595i	−0.0336298	+	0.00292747i
$465$	23.3406	+	40.4272i	1.08240	+	1.87477i
$466$	−20.8431	−	25.9758i	−0.965538	−	1.20330i
$467$			0.736447i			0.0340787i	0.999855	+	0.0170393i	$0.00542405\pi$
$467$			0.736447i			0.0340787i	−0.999855	+	0.0170393i	$0.994576\pi$
$468$	−19.3479	+	27.2678i	−0.894359	+	1.26045i
$469$		−	10.0699i		−	0.464987i
$470$	1.05136	+	1.31026i	0.0484956	+	0.0604377i
$471$	17.1131	−	9.88023i	0.788528	−	0.455257i
$472$	3.82782	+	0.252145i	0.176190	+	0.0116059i
$473$	−2.10188	−	5.46922i	−0.0966445	−	0.251475i
$474$	−16.6021	+	42.6785i	−0.762560	+	1.96029i
$475$	−14.1204	−	8.15239i	−0.647887	−	0.374057i
$476$	6.45842	−	2.03478i	0.296021	−	0.0932642i
$477$	14.7057	−	25.4711i	0.673329	−	1.16624i
$478$	−13.8819	−	17.3003i	−0.634941	−	0.791297i
$479$	−12.6979	+	7.33115i	−0.580183	+	0.334969i	−0.761206	−	0.648510i	$-0.775392\pi$
$479$	−12.6979	+	7.33115i	−0.580183	+	0.334969i	0.181023	+	0.983479i	$0.442059\pi$
$480$	17.3792	+	18.1744i	0.793249	+	0.829543i
$481$	25.6628	+	33.8650i	1.17012	+	1.54411i
$482$	1.85563	+	12.0650i	0.0845218	+	0.549545i
$483$	11.5614	−	6.67497i	0.526062	−	0.303722i
$484$	−21.9993	−	0.179647i	−0.999967	−	0.00816578i
$485$	−3.05299	+	5.28794i	−0.138629	+	0.240113i
$486$	−24.4186	+	3.75566i	−1.10765	+	0.170360i
$487$	0.395882	−	0.685688i	0.0179391	−	0.0310715i	−0.856916	−	0.515455i	$-0.827623\pi$
$487$	0.395882	−	0.685688i	0.0179391	−	0.0310715i	0.874856	+	0.484384i	$0.160956\pi$
$488$	1.41741	−	21.5178i	0.0641632	−	0.974064i
$489$			50.8158i			2.29797i
$490$	5.02604	−	12.9203i	0.227053	−	0.583678i
$491$	14.3916	+	24.9269i	0.649482	+	1.12494i	0.983247	+	0.182279i	$0.0583474\pi$
$491$	14.3916	+	24.9269i	0.649482	+	1.12494i	−0.333765	+	0.942656i	$0.608319\pi$
$492$	13.2633	−	14.4681i	0.597958	−	0.652271i
$493$	−0.646611			−0.0291219
$494$	9.44082	+	33.1455i	0.424763	+	1.49129i
$495$	−23.0904	+	8.87390i	−1.03784	+	0.398852i
$496$	38.0617	+	17.7687i	1.70902	+	0.797836i
$497$	−8.82213	+	5.09346i	−0.395727	+	0.228473i
$498$	51.3039	+	19.9574i	2.29898	+	0.894314i
$499$	−39.4093			−1.76420			−0.882102	−	0.471059i	$-0.843872\pi$
$499$	−39.4093			−1.76420			−0.882102	+	0.471059i	$0.843872\pi$
$500$	23.2809	+	5.16657i	1.04115	+	0.231056i
$501$	−11.2811	+	19.5394i	−0.504001	+	0.872955i
$502$	17.3233	−	2.66438i	0.773176	−	0.118917i
$503$	−12.2195	+	21.1649i	−0.544843	+	0.943695i	0.453774	+	0.891117i	$0.350077\pi$
$503$	−12.2195	+	21.1649i	−0.544843	+	0.943695i	−0.998617	+	0.0525785i	$0.983256\pi$
$504$	10.3767	+	6.93838i	0.462214	+	0.309060i
$505$	−6.33151	−	10.9665i	−0.281748	−	0.488002i
$506$	11.8184	+	20.6645i	0.525394	+	0.918650i
$507$	25.7068	−	25.0946i	1.14168	−	1.11449i
$508$	−8.92952	+	2.81333i	−0.396183	+	0.124821i
$509$	19.7303	−	11.3913i	0.874529	−	0.504910i	0.00567839	−	0.999984i	$-0.498193\pi$
$509$	19.7303	−	11.3913i	0.874529	−	0.504910i	0.868851	+	0.495074i	$0.164859\pi$
$510$	13.9946	+	17.4408i	0.619690	+	0.772290i
$511$	−0.511464	−	0.295294i	−0.0226258	−	0.0130630i
$512$	22.1883	+	4.43614i	0.980594	+	0.196052i
$513$	15.2836	−	26.4719i	0.674786	−	1.16876i
$514$	5.29726	+	2.06066i	0.233652	+	0.0908916i
$515$	−14.0079			−0.617260
$516$	−9.53194	−	2.11536i	−0.419620	−	0.0931234i
$517$	−1.54056	+	1.90395i	−0.0677539	+	0.0837357i
$518$	12.3728	−	9.92799i	0.543629	−	0.436211i
$519$	−5.53860			−0.243118
$520$	−9.02718	−	13.6977i	−0.395868	−	0.600683i
$521$	10.0173			0.438865			0.219432	−	0.975628i	$-0.429579\pi$
$521$	10.0173			0.438865			0.219432	+	0.975628i	$0.429579\pi$
$522$	−0.745994	−	0.929697i	−0.0326513	−	0.0406917i
$523$	6.51984	+	11.2927i	0.285093	+	0.493795i	0.972632	−	0.232352i	$-0.0746423\pi$
$523$	6.51984	+	11.2927i	0.285093	+	0.493795i	−0.687539	+	0.726148i	$0.741309\pi$
$524$	−5.20098	+	23.4360i	−0.227206	+	1.02380i
$525$	6.34532			0.276933
$526$	1.08428	+	0.421788i	0.0472767	+	0.0183908i
$527$	32.3483	+	18.6763i	1.40911	+	0.813553i
$528$	−20.5020	+	30.3924i	−0.892236	+	1.32266i
$529$	1.37950	−	2.38936i	0.0599782	−	0.103885i
$530$	9.03135	+	11.2553i	0.392297	+	0.488901i
$531$	3.14422	+	5.44594i	0.136447	+	0.236334i
$532$	12.2722	−	3.86647i	0.532067	−	0.167633i
$533$	−10.2052	+	7.73348i	−0.442037	+	0.334974i
$534$	−3.92013	−	25.4880i	−0.169641	−	1.10297i
$535$	−15.2474	+	8.80306i	−0.659200	+	0.380590i
$536$	16.6325	−	24.8747i	0.718414	−	1.07442i
$537$	10.3808	−	17.9801i	0.447964	−	0.775897i
$538$	−4.42890	−	28.7959i	−0.190943	−	1.24148i
$539$	19.9639	+	3.15400i	0.859905	+	0.135852i
$540$	−3.15228	+	14.2044i	−0.135653	+	0.611260i
$541$	−7.99489			−0.343727			−0.171864	−	0.985121i	$-0.554979\pi$
$541$	−7.99489			−0.343727			−0.171864	+	0.985121i	$0.554979\pi$
$542$	−14.5626	+	37.4355i	−0.625516	+	1.60799i
$543$	14.5637	−	8.40836i	0.624988	−	0.360837i
$544$	19.3143	+	5.64103i	0.828096	+	0.241857i
$545$		−	20.2495i		−	0.867394i
$546$	−9.63145	−	9.33401i	−0.412188	−	0.399459i
$547$	−16.2568			−0.695091			−0.347546	−	0.937663i	$-0.612985\pi$
$547$	−16.2568			−0.695091			−0.347546	+	0.937663i	$0.612985\pi$
$548$	−15.0242	+	16.3889i	−0.641804	+	0.700100i
$549$	30.6139	−	17.6749i	1.30657	−	0.754348i
$550$	−0.0461978	+	11.3148i	−0.00196988	+	0.482464i
$551$	−1.22868			−0.0523436
$552$	39.5838	+	2.60745i	1.68480	+	0.110981i
$553$	−9.65921	−	5.57675i	−0.410751	−	0.237147i
$554$	27.6515	−	4.25290i	1.17480	−	0.180688i
$555$	45.3681	+	26.1933i	1.92577	+	1.11184i
$556$	−13.5237	−	12.3976i	−0.573534	−	0.525777i
$557$	−21.1192	−	36.5796i	−0.894851	−	1.54993i	−0.833989	−	0.551781i	$-0.813949\pi$
$557$	−21.1192	−	36.5796i	−0.894851	−	1.54993i	−0.0608616	−	0.998146i	$-0.519385\pi$
$558$	10.4674	+	68.0572i	0.443121	+	2.88109i
$559$	5.86997	+	2.47296i	0.248273	+	0.104595i
$560$	−5.01854	+	3.51076i	−0.212072	+	0.148357i
$561$	−20.5063	+	25.3434i	−0.865778	+	1.07000i
$562$	−26.6390	+	21.3753i	−1.12370	+	0.901662i
$563$	−18.9645	+	32.8475i	−0.799260	+	1.38436i	0.120838	+	0.992672i	$0.461442\pi$
$563$	−18.9645	+	32.8475i	−0.799260	+	1.38436i	−0.920099	+	0.391687i	$0.871892\pi$
$564$	1.22642	+	3.89268i	0.0516417	+	0.163911i
$565$	−2.15602	−	1.24478i	−0.0907043	−	0.0523682i
$566$	10.2827	+	4.00002i	0.432215	+	0.168133i
$567$		−	1.34404i		−	0.0564446i
$568$	−30.2052	−	1.98966i	−1.26738	−	0.0834844i
$569$	24.3711	−	14.0706i	1.02169	−	0.589872i	0.107096	−	0.994249i	$-0.465845\pi$
$569$	24.3711	−	14.0706i	1.02169	−	0.589872i	0.914593	+	0.404377i	$0.132511\pi$
$570$	26.5923	+	33.1407i	1.11383	+	1.38811i
$571$	−39.0776			−1.63535			−0.817674	−	0.575682i	$-0.804737\pi$
$571$	−39.0776			−1.63535			−0.817674	+	0.575682i	$0.804737\pi$
$572$	16.7142	−	17.1066i	0.698857	−	0.715261i
$573$	62.6407			2.61685
$574$	2.99179	+	3.72853i	0.124875	+	0.155626i
$575$	10.6031	−	6.12172i	0.442181	−	0.255293i
$576$	14.1723	+	34.2782i	0.590511	+	1.42826i
$577$			20.7539i			0.863995i	0.901875	+	0.431998i	$0.142191\pi$
$577$			20.7539i			0.863995i	−0.901875	+	0.431998i	$0.857809\pi$
$578$	−5.73062	−	2.22924i	−0.238362	−	0.0927240i
$579$	−51.6868	−	29.8414i	−2.14803	−	1.24017i
$580$	0.557822	−	0.175747i	0.0231623	−	0.00729750i
$581$	−6.70381	+	11.6113i	−0.278121	+	0.481720i
$582$	−11.5700	+	9.28386i	−0.479593	+	0.384828i
$583$	−13.2337	+	16.3553i	−0.548083	+	0.677366i
$584$	−0.775677	−	1.57421i	−0.0320977	−	0.0651414i
$585$	10.4406	−	24.7824i	0.431665	−	1.02462i
$586$	−2.15852	−	14.0343i	−0.0891678	−	0.579753i
$587$	11.5994	+	20.0907i	0.478757	+	0.829232i	0.999703	−	0.0243577i	$-0.00775408\pi$
$587$	11.5994	+	20.0907i	0.478757	+	0.829232i	−0.520946	+	0.853590i	$0.674421\pi$
$588$	22.7597	−	24.8270i	0.938595	−	1.02385i
$589$	61.4678	+	35.4885i	2.53274	+	1.46228i
$590$	−3.04957	+	0.469034i	−0.125549	+	0.0193098i
$591$	22.5175	+	13.0005i	0.926245	+	0.534768i
$592$	46.9611	−	4.08795i	1.93009	−	0.168014i
$593$	10.2825			0.422253			0.211127	−	0.977459i	$-0.432287\pi$
$593$	10.2825			0.422253			0.211127	+	0.977459i	$0.432287\pi$
$594$	−21.2122	−	0.0866086i	−0.870348	−	0.00355359i
$595$	−4.71662	+	2.72314i	−0.193363	+	0.111638i
$596$	11.8586	+	10.8712i	0.485748	+	0.445301i
$597$	−3.36042			−0.137533
$598$	−25.0994	−	6.30521i	−1.02639	−	0.257839i
$599$		−	41.0978i		−	1.67921i	−0.543198	−	0.839605i	$-0.682787\pi$
$599$		−	41.0978i		−	1.67921i	0.543198	−	0.839605i	$-0.317213\pi$
$600$	15.6741	+	10.4805i	0.639894	+	0.427866i
$601$	−25.3575	+	14.6401i	−1.03435	+	0.597184i	−0.918229	−	0.396051i	$-0.870380\pi$
$601$	−25.3575	+	14.6401i	−1.03435	+	0.597184i	−0.116124	+	0.993235i	$0.537047\pi$
$602$	0.862142	−	2.21628i	0.0351383	−	0.0903288i
$603$	49.0519			1.99755
$604$	6.90391	+	1.53214i	0.280916	+	0.0623418i
$605$	17.3053	−	3.69244i	0.703560	−	0.150119i
$606$	−4.67666	−	30.4068i	−0.189976	−	1.23519i
$607$	−5.15057	+	8.92105i	−0.209055	+	0.362094i	−0.951417	−	0.307905i	$-0.900372\pi$
$607$	−5.15057	+	8.92105i	−0.209055	+	0.362094i	0.742362	+	0.669999i	$0.233706\pi$
$608$	36.7009	+	10.7190i	1.48842	+	0.434713i
$609$	0.414103	−	0.239083i	0.0167803	−	0.00968812i
$610$	2.63663	+	17.1429i	0.106754	+	0.694096i
$611$	−0.331616	−	2.64178i	−0.0134157	−	0.106875i
$612$	9.91168	+	31.4597i	0.400656	+	1.27168i
$613$	−8.38415	−	14.5218i	−0.338633	−	0.586529i	0.645543	−	0.763724i	$-0.276631\pi$
$613$	−8.38415	−	14.5218i	−0.338633	−	0.586529i	−0.984176	+	0.177195i	$0.943298\pi$
$614$	−19.8236	−	24.7052i	−0.800016	−	0.997022i
$615$	−7.89333	+	13.6716i	−0.318290	+	0.551294i
$616$	−6.55722	−	6.06067i	−0.264198	−	0.244191i
$617$	36.2317	+	20.9184i	1.45863	+	0.842141i	0.998944	−	0.0459395i	$-0.0146282\pi$
$617$	36.2317	+	20.9184i	1.45863	+	0.842141i	0.459687	+	0.888081i	$0.347961\pi$
$618$	−31.7164	−	12.3378i	−1.27582	−	0.496299i
$619$	−4.91482			−0.197543			−0.0987716	−	0.995110i	$-0.531491\pi$
$619$	−4.91482			−0.197543			−0.0987716	+	0.995110i	$0.531491\pi$
$620$	−32.9826	−	7.31960i	−1.32461	−	0.293962i
$621$	11.4766	+	19.8780i	0.460540	+	0.797678i
$622$	−9.35337	−	11.6567i	−0.375036	−	0.467389i
$623$	6.28080			0.251635
$624$	−8.37457	−	38.9650i	−0.335251	−	1.55985i
$625$	−7.11891			−0.284756
$626$	0.0285543	−	0.0229121i	0.00114126	−	0.000915752i
$627$	−38.9659	+	48.1572i	−1.55615	+	1.92321i
$628$	−3.09843	+	13.9617i	−0.123641	+	0.557133i
$629$	41.9177			1.67137
$630$	−9.35689	−	3.63987i	−0.372787	−	0.145016i
$631$	−6.40958	+	11.1017i	−0.255161	+	0.441952i	−0.964939	−	0.262473i	$-0.915462\pi$
$631$	−6.40958	+	11.1017i	−0.255161	+	0.441952i	0.709778	+	0.704425i	$0.248795\pi$
$632$	−14.6490	−	29.7297i	−0.582705	−	1.18258i
$633$	29.9414	+	17.2867i	1.19006	+	0.687083i
$634$	−8.38471	−	10.4495i	−0.332999	−	0.415001i
$635$	6.52128	−	3.76506i	0.258789	−	0.149412i
$636$	10.5352	+	33.4387i	0.417747	+	1.32593i
$637$	−17.5120	+	13.2705i	−0.693850	+	0.525798i
$638$	0.423310	+	0.740157i	0.0167590	+	0.0293031i
$639$	−24.8108	−	42.9736i	−0.981502	−	1.70001i
$640$	−18.1954	+	0.383146i	−0.719237	+	0.0151452i
$641$	12.6719	−	21.9483i	0.500509	−	0.866908i	−0.499491	−	0.866319i	$-0.666479\pi$
$641$	12.6719	−	21.9483i	0.500509	−	0.866908i	1.00000		0.000588180i	$-0.000187224\pi$
$642$	−42.2763	+	6.50223i	−1.66851	+	0.256623i
$643$	19.4514	−	33.6908i	0.767088	−	1.32864i	−0.172047	−	0.985089i	$-0.555038\pi$
$643$	19.4514	−	33.6908i	0.767088	−	1.32864i	0.939135	−	0.343547i	$-0.111629\pi$
$644$	−2.09327	+	9.43238i	−0.0824862	+	0.371688i
$645$	7.85315			0.309218
$646$	31.6864	+	12.3261i	1.24668	+	0.484966i
$647$	−20.1991	+	11.6620i	−0.794109	+	0.458479i	−0.841407	−	0.540402i	$-0.818272\pi$
$647$	−20.1991	+	11.6620i	−0.794109	+	0.458479i	0.0472981	+	0.998881i	$0.484939\pi$
$648$	2.21995	−	3.32004i	0.0872079	−	0.130424i
$649$	−1.61366	−	4.19885i	−0.0633418	−	0.164819i
$650$	−8.83314	−	8.56035i	−0.346464	−	0.335765i
$651$	−27.6220			−1.08259
$652$	−27.1097	−	24.8523i	−1.06170	−	0.973291i
$653$	3.72303	+	6.44847i	0.145693	+	0.252348i	0.929631	−	0.368491i	$-0.120125\pi$
$653$	3.72303	+	6.44847i	0.145693	+	0.252348i	−0.783938	+	0.620839i	$0.786792\pi$
$654$	17.8353	−	45.8486i	0.697415	−	1.79282i
$655$		−	19.3084i		−	0.754441i
$656$	1.23190	+	14.1517i	0.0480977	+	0.552531i
$657$	1.43841	−	2.49140i	0.0561177	−	0.0971988i
$658$	−0.982482	+	0.151109i	−0.0383011	+	0.00589084i
$659$	0.138761	−	0.240340i	0.00540534	−	0.00936233i	−0.863310	−	0.504674i	$-0.831613\pi$
$659$	0.138761	−	0.240340i	0.00540534	−	0.00936233i	0.868715	+	0.495312i	$0.164946\pi$
$660$	10.8023	−	27.4369i	0.420478	−	1.06798i
$661$	−16.3367	+	9.43203i	−0.635426	+	0.366863i	−0.782850	−	0.622210i	$-0.786235\pi$
$661$	−16.3367	+	9.43203i	−0.635426	+	0.366863i	0.147425	+	0.989073i	$0.452902\pi$
$662$	0.347715	+	2.26078i	0.0135143	+	0.0878677i
$663$	−4.41412	−	35.1646i	−0.171430	−	1.36568i
$664$	−35.7381	+	17.6096i	−1.38691	+	0.683383i
$665$	−8.96246	+	5.17448i	−0.347549	+	0.200658i
$666$	48.3604	+	60.2693i	1.87393	+	2.33539i
$667$	0.461315	−	0.799021i	0.0178622	−	0.0309382i
$668$	−4.90685	−	15.5744i	−0.189852	−	0.602590i
$669$	5.83681	+	3.36988i	0.225664	+	0.130287i
$670$	−8.72538	+	22.4301i	−0.337091	+	0.866549i
$671$	−23.6035	+	9.07107i	−0.911202	+	0.350185i
$672$	−14.4551	+	3.52879i	−0.557616	+	0.136126i
$673$	17.3364	−	10.0092i	0.668269	−	0.385826i	−0.127151	−	0.991883i	$-0.540583\pi$
$673$	17.3364	−	10.0092i	0.668269	−	0.385826i	0.795421	+	0.606058i	$0.207250\pi$
$674$	18.2263	+	22.7145i	0.702050	+	0.874931i
$675$			10.9098i			0.419919i
$676$	0.815343	+	25.9872i	0.0313593	+	0.999508i
$677$		−	25.5410i		−	0.981621i	−0.871266	−	0.490811i	$-0.836701\pi$
$677$		−	25.5410i		−	0.981621i	0.871266	−	0.490811i	$-0.163299\pi$
$678$	−3.78524	−	4.71737i	−0.145371	−	0.181169i
$679$	−1.80650	−	3.12896i	−0.0693273	−	0.120078i
$680$	−16.1487	−	1.06374i	−0.619276	−	0.0407927i
$681$	−53.8759			−2.06453
$682$	0.201105	−	49.2548i	0.00770072	−	1.88606i
$683$	−5.68701	+	9.85020i	−0.217608	+	0.376907i	−0.954076	−	0.299565i	$-0.903159\pi$
$683$	−5.68701	+	9.85020i	−0.217608	+	0.376907i	0.736469	+	0.676472i	$0.236492\pi$
$684$	18.8340	+	59.7793i	0.720137	+	2.28572i
$685$	8.94127	−	15.4867i	0.341629	−	0.591718i
$686$	11.0310	+	13.7474i	0.421166	+	0.524880i
$687$	7.19073	+	12.4547i	0.274344	+	0.475177i
$688$	5.79027	−	4.05063i	0.220752	−	0.154429i
$689$	−2.84864	−	22.6933i	−0.108524	−	0.864547i
$690$	−31.5359	+	4.85032i	−1.20055	+	0.184648i
$691$	−17.1634	−	29.7279i	−0.652926	−	1.13090i	−0.982409	−	0.186740i	$-0.940208\pi$
$691$	−17.1634	−	29.7279i	−0.652926	−	1.13090i	0.329483	−	0.944161i	$-0.393125\pi$
$692$	2.70875	−	2.95478i	0.102971	−	0.112324i
$693$	2.28413	−	14.4579i	0.0867671	−	0.549209i
$694$	−3.63756	−	23.6508i	−0.138080	−	0.897771i
$695$	12.7793	+	7.37812i	0.484746	+	0.279868i
$696$	1.41780	+	0.0933931i	0.0537418	+	0.00354006i
$697$			12.6319i			0.478467i
$698$	−22.5524	−	8.77296i	−0.853619	−	0.332061i
$699$	32.5390	+	56.3591i	1.23074	+	2.13170i
$700$	−3.10329	+	3.38516i	−0.117293	+	0.127947i
$701$		−	42.3423i		−	1.59925i	−0.600503	−	0.799623i	$-0.705033\pi$
$701$		−	42.3423i		−	1.59925i	0.600503	−	0.799623i	$-0.294967\pi$
$702$	16.0484	−	16.5598i	0.605708	−	0.625010i
$703$	79.6515			3.00411
$704$	−6.18719	−	25.8015i	−0.233188	−	0.972432i
$705$	−1.64132	−	2.84284i	−0.0618156	−	0.107068i
$706$	12.9699	−	33.3414i	0.488130	−	1.25482i
$707$	7.49290			0.281800
$708$	−7.31790	−	1.62401i	−0.275023	−	0.0610341i
$709$	−24.3596	−	14.0640i	−0.914843	−	0.528185i	−0.0328566	−	0.999460i	$-0.510460\pi$
$709$	−24.3596	−	14.0640i	−0.914843	−	0.528185i	−0.881986	+	0.471275i	$0.843794\pi$
$710$	24.0640	−	3.70112i	0.903106	−	0.138901i
$711$	27.1650	−	47.0511i	1.01877	−	1.76456i
$712$	15.5148	+	10.3740i	0.581440	+	0.388781i
$713$	−46.1568	+	26.6486i	−1.72859	+	0.998000i
$714$	−13.0778	+	2.01140i	−0.489423	+	0.0752748i
$715$	−10.1432	+	16.3447i	−0.379335	+	0.611258i
$716$	4.51527	+	14.3315i	0.168743	+	0.535593i
$717$	21.6715	+	37.5361i	0.809337	+	1.40181i
$718$	−0.219489	−	0.273539i	−0.00819126	−	0.0102084i
$719$	28.2124	+	16.2884i	1.05215	+	0.607456i	0.923249	−	0.384202i	$-0.125523\pi$
$719$	28.2124	+	16.2884i	1.05215	+	0.607456i	0.128896	+	0.991658i	$0.458857\pi$
$720$	−17.1013	−	24.4459i	−0.637329	−	0.911044i
$721$	4.14434	−	7.17820i	0.154343	−	0.267330i
$722$	35.1680	+	13.6805i	1.30882	+	0.509136i
$723$		−	23.8527i		−	0.887091i
$724$	−2.63685	+	11.8818i	−0.0979979	+	0.441585i
$725$	0.379780	−	0.219266i	0.0141047	−	0.00814334i
$726$	42.4345	+	6.88173i	1.57489	+	0.255405i
$727$		−	8.23705i		−	0.305495i	−0.988265	−	0.152748i	$-0.951188\pi$
$727$		−	8.23705i		−	0.305495i	0.988265	−	0.152748i	$-0.0488122\pi$
$728$	9.69001	−	0.573324i	0.359136	−	0.0212488i
$729$	44.0398			1.63111
$730$	0.883382	+	1.10092i	0.0326954	+	0.0407468i
$731$	5.44193	−	3.14190i	0.201277	−	0.116207i
$732$	−9.12924	+	41.1369i	−0.337426	+	1.52046i
$733$	11.3540			0.419370			0.209685	−	0.977769i	$-0.432756\pi$
$733$	11.3540			0.419370			0.209685	+	0.977769i	$0.432756\pi$
$734$	1.19610	−	3.07476i	0.0441487	−	0.113492i
$735$	−13.5448	+	23.4604i	−0.499609	+	0.865348i
$736$	−20.7502	+	19.8423i	−0.764862	+	0.731398i
$737$	−34.6580	−	5.47546i	−1.27664	−	0.201691i
$738$	−18.1621	+	14.5734i	−0.668557	+	0.536454i
$739$	33.9664	−	19.6105i	1.24947	−	0.721383i	0.278468	−	0.960445i	$-0.410173\pi$
$739$	33.9664	−	19.6105i	1.24947	−	0.721383i	0.971004	+	0.239062i	$0.0768400\pi$
$740$	−36.1618	+	11.3931i	−1.32934	+	0.418820i
$741$	−8.38765	−	66.8193i	−0.308128	−	2.45467i
$742$	−8.43968	+	1.29805i	−0.309831	+	0.0476529i
$743$	−1.68344	+	0.971932i	−0.0617592	+	0.0356567i	−0.530562	−	0.847646i	$-0.678019\pi$
$743$	−1.68344	+	0.971932i	−0.0617592	+	0.0356567i	0.468802	+	0.883303i	$0.344686\pi$
$744$	−68.2316	−	45.6232i	−2.50149	−	1.67263i
$745$	−11.2058	−	6.46969i	−0.410550	−	0.237031i
$746$	10.0970	−	1.55295i	0.369677	−	0.0568575i
$747$	−56.5602	−	32.6551i	−2.06943	−	1.19479i
$748$	−3.49146	−	23.3345i	−0.127660	−	0.853194i
$749$		−	10.4178i		−	0.380659i
$750$	−43.4284	−	16.8938i	−1.58578	−	0.616875i
$751$	25.6066	−	14.7840i	0.934398	−	0.539475i	0.0461985	−	0.998932i	$-0.485289\pi$
$751$	25.6066	−	14.7840i	0.934398	−	0.539475i	0.888200	+	0.459457i	$0.151956\pi$
$752$	−2.67650	−	1.24949i	−0.0976020	−	0.0455643i
$753$	−34.2484			−1.24808
$754$	−0.899003	−	0.225839i	−0.0327398	−	0.00822456i
$755$	−5.68798			−0.207007
$756$	−6.34628	−	5.81784i	−0.230812	−	0.211593i
$757$	−5.53647	−	9.58945i	−0.201226	−	0.348534i	0.747697	−	0.664040i	$-0.231159\pi$
$757$	−5.53647	−	9.58945i	−0.201226	−	0.348534i	−0.948924	+	0.315505i	$0.897826\pi$
$758$	27.1764	+	10.5717i	0.987091	+	0.383982i
$759$	−16.6870	−	43.4206i	−0.605701	−	1.57607i
$760$	−30.6856	−	2.02131i	−1.11308	−	0.0733207i
$761$	−17.6723	+	30.6094i	−0.640621	+	1.10959i	0.344673	+	0.938723i	$0.387990\pi$
$761$	−17.6723	+	30.6094i	−0.640621	+	1.10959i	−0.985294	+	0.170866i	$0.945343\pi$
$762$	18.0815	−	2.78100i	0.655025	−	0.100745i
$763$	10.3767	+	5.99097i	0.375661	+	0.216888i
$764$	−30.6354	+	33.4181i	−1.10835	+	1.20902i
$765$	−13.2647	−	22.9752i	−0.479588	−	0.830671i
$766$	−7.35429	−	47.8162i	−0.265721	−	1.72767i
$767$	4.50652	+	1.89855i	0.162721	+	0.0685528i
$768$	−41.5352	−	15.1586i	−1.49877	−	0.546988i
$769$	13.7473	+	23.8110i	0.495740	+	0.858646i	0.999988	−	0.00491239i	$-0.00156367\pi$
$769$	13.7473	+	23.8110i	0.495740	+	0.858646i	−0.504248	+	0.863559i	$0.668230\pi$
$770$	6.20488	+	3.61625i	0.223608	+	0.130321i
$771$	−9.61865	−	5.55333i	−0.346407	−	0.199998i
$772$	41.1983	−	12.9799i	1.48276	−	0.467157i
$773$	−39.2485	−	22.6602i	−1.41167	−	0.815029i	−0.416126	−	0.909307i	$-0.636612\pi$
$773$	−39.2485	−	22.6602i	−1.41167	−	0.815029i	−0.995546	+	0.0942781i	$0.969946\pi$
$774$	10.7958	+	4.19960i	0.388046	+	0.150951i
$775$	−25.3326			−0.909973
$776$	0.705677	−	10.7129i	0.0253323	−	0.384571i
$777$	−26.8450	+	15.4990i	−0.963059	+	0.556022i
$778$	−22.6973	+	18.2125i	−0.813739	+	0.652949i
$779$			24.0029i			0.859995i
$780$	13.3656	+	29.1363i	0.478567	+	1.04325i
$781$	12.7333	+	33.1329i	0.455634	+	1.18559i
$782$	−19.9126	+	15.9780i	−0.712073	+	0.571372i
$783$	0.411066	+	0.711987i	0.0146903	+	0.0254443i
$784$	2.11392	+	24.2841i	0.0754973	+	0.867290i
$785$		−	11.5028i		−	0.410551i
$786$	17.0064	−	43.7177i	0.606597	−	1.55936i
$787$	10.7125	+	6.18484i	0.381858	+	0.220466i	0.678626	−	0.734484i	$-0.262576\pi$
$787$	10.7125	+	6.18484i	0.381858	+	0.220466i	−0.296769	+	0.954949i	$0.595909\pi$
$788$	−17.9482	+	5.65473i	−0.639376	+	0.201442i
$789$	−1.96881	−	1.13669i	−0.0700913	−	0.0404673i
$790$	16.6830	+	20.7913i	0.593556	+	0.739720i
$791$	1.27575	−	0.736554i	0.0453604	−	0.0261888i
$792$	29.5222	−	31.9410i	1.04903	−	1.13497i
$793$	10.6726	−	25.3330i	0.378993	−	0.899601i
$794$	−10.4155	+	1.60194i	−0.369632	+	0.0568507i
$795$	−14.0992	−	24.4205i	−0.500046	−	0.866106i
$796$	1.64347	−	1.79275i	0.0582512	−	0.0635423i
$797$	−10.5981	+	18.3564i	−0.375403	+	0.650217i	−0.990387	−	0.138323i	$-0.955829\pi$
$797$	−10.5981	+	18.3564i	−0.375403	+	0.650217i	0.614984	+	0.788539i	$0.289162\pi$
$798$	−24.8502	+	3.82204i	−0.879687	+	0.135299i
$799$	−2.27474	−	1.31332i	−0.0804744	−	0.0464619i
$800$	−13.2570	+	3.23630i	−0.468704	+	0.114421i
$801$			30.5945i			1.08100i
$802$	8.88272	−	22.8345i	0.313660	−	0.806315i
$803$	−1.29443	+	1.59976i	−0.0456793	+	0.0564541i
$804$	−39.5117	+	43.1006i	−1.39347	+	1.52004i
$805$		−	7.77114i		−	0.273897i
$806$	38.4519	+	37.2644i	1.35441	+	1.31258i
$807$			56.9299i			2.00403i
$808$	18.5089	+	12.3760i	0.651140	+	0.435386i
$809$	−11.9808	+	6.91713i	−0.421223	+	0.243193i	−0.695600	−	0.718429i	$-0.744862\pi$
$809$	−11.9808	+	6.91713i	−0.421223	+	0.243193i	0.274377	+	0.961622i	$0.411528\pi$
$810$	−1.16458	+	2.99376i	−0.0409193	+	0.105190i
$811$			43.9063i			1.54176i	0.636981	+	0.770879i	$0.280183\pi$
$811$			43.9063i			1.54176i	−0.636981	+	0.770879i	$0.719817\pi$
$812$	−0.0749761	+	0.337847i	−0.00263114	+	0.0118561i
$813$	39.2452	−	67.9746i	1.37639	−	2.38397i
$814$	−27.4418	−	47.9820i	−0.961836	−	1.68177i
$815$	25.6173	+	14.7902i	0.897337	+	0.518078i
$816$	−35.6268	−	16.6319i	−1.24719	−	0.582234i
$817$	10.3407	−	5.97019i	0.361775	−	0.208871i
$818$	−4.73538	−	30.7886i	−0.165569	−	1.07650i
$819$	9.61056	+	12.6822i	0.335820	+	0.443153i
$820$	−3.43331	−	10.8973i	−0.119896	−	0.380552i
$821$	−11.5385	−	19.9852i	−0.402695	−	0.697489i	0.591355	−	0.806411i	$-0.298593\pi$
$821$	−11.5385	−	19.9852i	−0.402695	−	0.697489i	−0.994050	+	0.108923i	$0.965260\pi$
$822$	33.8850	−	27.1895i	1.18188	−	0.948344i
$823$	−32.7233	−	18.8928i	−1.14066	−	0.658561i	−0.194067	−	0.980988i	$-0.562168\pi$
$823$	−32.7233	−	18.8928i	−1.14066	−	0.658561i	−0.946594	+	0.322427i	$0.895501\pi$
$824$	22.0935	−	10.8863i	0.769663	−	0.379243i
$825$	3.45022	−	21.8389i	0.120121	−	0.760332i
$826$	0.661887	−	1.70149i	0.0230300	−	0.0592025i
$827$		−	34.7836i		−	1.20954i	−0.796399	−	0.604772i	$-0.793264\pi$
$827$		−	34.7836i		−	1.20954i	0.796399	−	0.604772i	$-0.206736\pi$
$828$	−45.9463	−	10.1965i	−1.59674	−	0.354354i
$829$	5.73359	+	9.93087i	0.199136	+	0.344913i	0.948248	−	0.317529i	$-0.102853\pi$
$829$	5.73359	+	9.93087i	0.199136	+	0.344913i	−0.749113	+	0.662443i	$0.769520\pi$
$830$	24.9932	−	20.0547i	0.867527	−	0.696109i
$831$	−54.6676			−1.89640
$832$	24.8831	+	14.5887i	0.862667	+	0.505773i
$833$			21.6761i			0.751034i
$834$	22.4362	+	27.9611i	0.776900	+	0.968214i
$835$	6.56681	+	11.3741i	0.227254	+	0.393615i
$836$	−6.63442	−	44.3399i	−0.229456	−	1.53353i
$837$		−	47.4919i		−	1.64156i
$838$	4.83296	−	12.4239i	0.166952	−	0.429178i
$839$	−21.0855	+	36.5211i	−0.727951	+	1.26085i	0.229796	+	0.973239i	$0.426194\pi$
$839$	−21.0855	+	36.5211i	−0.727951	+	1.26085i	−0.957748	+	0.287610i	$0.907139\pi$
$840$	10.7353	−	5.28971i	0.370403	−	0.182512i
$841$	−14.4835	+	25.0861i	−0.499430	+	0.865039i
$842$	−25.4364	−	31.7002i	−0.876597	−	1.09246i
$843$	57.7981	−	33.3698i	1.99067	−	1.14932i
$844$	−23.8656	+	7.51907i	−0.821487	+	0.258817i
$845$	−5.16863	−	20.2633i	−0.177806	−	0.697077i
$846$	−0.736070	−	4.78579i	−0.0253066	−	0.164539i
$847$	−3.22775	+	9.96036i	−0.110907	+	0.342242i
$848$	−22.9916	−	10.7334i	−0.789535	−	0.368585i
$849$	−18.6712	−	10.7798i	−0.640792	−	0.369962i
$850$	−11.9938	+	1.84469i	−0.411384	+	0.0632722i
$851$	−29.9056	+	51.7980i	−1.02515	+	1.77561i
$852$	57.7451	+	12.8150i	1.97832	+	0.439034i
$853$	−44.5718			−1.52611			−0.763054	−	0.646335i	$-0.776301\pi$
$853$	−44.5718			−1.52611			−0.763054	+	0.646335i	$0.776301\pi$
$854$	−9.56479	−	3.72074i	−0.327300	−	0.127321i
$855$	−25.2055	−	43.6572i	−0.862010	−	1.49304i
$856$	17.2071	−	25.7340i	0.588125	−	0.879569i
$857$			34.8426i			1.19020i	0.803652	+	0.595100i	$0.202888\pi$
$857$			34.8426i			1.19020i	−0.803652	+	0.595100i	$0.797112\pi$
$858$	−37.3621	+	28.0735i	−1.27552	+	0.958415i
$859$		−	16.9614i		−	0.578717i	−0.957221	−	0.289358i	$-0.906558\pi$
$859$		−	16.9614i		−	0.578717i	0.957221	−	0.289358i	$-0.0934419\pi$
$860$	−3.84071	+	4.18957i	−0.130967	+	0.142863i
$861$	−4.67060	−	8.08973i	−0.159174	−	0.275697i
$862$	−7.81678	+	20.0943i	−0.266240	+	0.684416i
$863$	48.8497			1.66286			0.831431	−	0.555628i	$-0.187522\pi$
$863$	48.8497			1.66286			0.831431	+	0.555628i	$0.187522\pi$
$864$	−6.06721	−	24.8533i	−0.206411	−	0.845525i
$865$	−1.61204	+	2.79213i	−0.0548109	+	0.0949353i
$866$	−1.01188	−	6.57907i	−0.0343851	−	0.223566i
$867$	10.4055	+	6.00764i	0.353391	+	0.204030i
$868$	13.5090	−	14.7361i	0.458526	−	0.500174i
$869$	−24.4458	+	30.2120i	−0.829266	+	1.02487i
$870$	−1.12954	+	0.173728i	−0.0382951	+	0.00588992i
$871$	30.4015	−	23.0382i	1.03011	−	0.780618i
$872$	15.7371	+	31.9379i	0.532924	+	1.08155i
$873$	15.2415	−	8.79970i	0.515847	−	0.297825i
$874$	−37.8377	+	30.3612i	−1.27988	+	1.02698i
$875$	5.67473	−	9.82893i	0.191841	−	0.332278i
$876$	1.03048	+	3.27074i	0.0348166	+	0.110508i
$877$	−21.7158	+	37.6129i	−0.733290	+	1.27010i	0.222179	+	0.975006i	$0.428683\pi$
$877$	−21.7158	+	37.6129i	−0.733290	+	1.27010i	−0.955469	+	0.295090i	$0.904650\pi$
$878$	−23.6185	−	9.18770i	−0.797086	−	0.310070i
$879$			27.7461i			0.935853i
$880$	9.35428	+	19.1814i	0.315333	+	0.646604i
$881$	18.4678	+	31.9872i	0.622198	+	1.07768i	0.989076	+	0.147409i	$0.0470933\pi$
$881$	18.4678	+	31.9872i	0.622198	+	1.07768i	−0.366878	+	0.930269i	$0.619573\pi$
$882$	−31.1659	+	25.0077i	−1.04941	+	0.842054i
$883$			1.98337i			0.0667457i	0.999443	+	0.0333728i	$0.0106249\pi$
$883$			1.98337i			0.0667457i	−0.999443	+	0.0333728i	$0.989375\pi$
$884$	20.9187	+	14.8429i	0.703573	+	0.499222i
$885$	6.02906			0.202664
$886$	11.4291	+	14.2436i	0.383969	+	0.478522i
$887$	8.11250	+	14.0513i	0.272391	+	0.471795i	0.969474	−	0.245196i	$-0.0788522\pi$
$887$	8.11250	+	14.0513i	0.272391	+	0.471795i	−0.697083	+	0.716991i	$0.745519\pi$
$888$	−91.9118	−	6.05438i	−3.08436	−	0.203172i
$889$			4.45569i			0.149439i
$890$	−13.9900	−	5.44217i	−0.468946	−	0.182422i
$891$	−4.62584	−	0.730814i	−0.154971	−	0.0244832i
$892$	−4.65238	+	1.46578i	−0.155773	+	0.0490778i
$893$	−4.32242	−	2.49555i	−0.144644	−	0.0835105i
$894$	−19.6737	−	24.5184i	−0.657987	−	0.820017i
$895$	−6.04276	−	10.4664i	−0.201987	−	0.349852i
$896$	5.18692	−	9.43743i	0.173283	−	0.315283i
$897$	46.6023	+	19.6331i	1.55600	+	0.655530i
$898$	53.6768	−	8.25566i	1.79122	−	0.275495i
$899$	−1.65323	+	0.954495i	−0.0551384	+	0.0318342i
$900$	−16.4895	−	15.1165i	−0.549651	−	0.503882i
$901$	−19.5404	−	11.2816i	−0.650984	−	0.375846i
$902$	14.4594	−	8.26958i	0.481444	−	0.275347i
$903$	−2.32342	+	4.02428i	−0.0773185	+	0.133919i
$904$	4.36790	+	0.287721i	0.145274	+	0.00956945i
$905$		−	9.78918i		−	0.325403i
$906$	−12.8786	−	5.00984i	−0.427864	−	0.166441i
$907$	−24.2217	+	13.9844i	−0.804270	+	0.464345i	−0.844962	−	0.534826i	$-0.820377\pi$
$907$	−24.2217	+	13.9844i	−0.804270	+	0.464345i	0.0406922	+	0.999172i	$0.487044\pi$
$908$	26.3489	−	28.7422i	0.874419	−	0.953843i
$909$			36.4988i			1.21059i
$910$	−7.50876	+	2.13872i	−0.248913	+	0.0708978i
$911$		−	31.8948i		−	1.05672i	−0.849020	−	0.528361i	$-0.822807\pi$
$911$		−	31.8948i		−	1.05672i	0.849020	−	0.528361i	$-0.177193\pi$
$912$	−67.6975	−	31.6038i	−2.24169	−	1.04651i
$913$	36.3179	+	29.3863i	1.20195	+	0.972544i
$914$	−32.4490	−	12.6228i	−1.07332	−	0.417525i
$915$		−	33.8918i		−	1.12043i
$916$	−10.1612	−	2.25501i	−0.335735	−	0.0745075i
$917$	9.89440	+	5.71253i	0.326742	+	0.188644i
$918$	−3.45830	−	22.4852i	−0.114141	−	0.742122i
$919$	12.9721	−	22.4683i	0.427909	−	0.741161i	−0.568778	−	0.822491i	$-0.692584\pi$
$919$	12.9721	−	22.4683i	0.427909	−	0.741161i	0.996687	+	0.0813306i	$0.0259170\pi$
$920$	12.8355	−	19.1962i	0.423175	−	0.632879i
$921$	30.9474	+	53.6025i	1.01975	+	1.76626i
$922$	−3.90986	−	25.4212i	−0.128764	−	0.837202i
$923$	−35.5607	−	14.9814i	−1.17049	−	0.493118i
$924$	10.8639	+	13.6530i	0.357395	+	0.449149i
$925$	−24.6199	+	14.2143i	−0.809499	+	0.467364i
$926$	−15.2302	+	12.2208i	−0.500495	+	0.401600i
$927$	34.9659	+	20.1876i	1.14843	+	0.663046i
$928$	−0.743225	+	0.710708i	−0.0243976	+	0.0233301i
$929$	16.9563	+	9.78974i	0.556319	+	0.321191i	0.751667	−	0.659543i	$-0.229250\pi$
$929$	16.9563	+	9.78974i	0.556319	+	0.321191i	−0.195348	+	0.980734i	$0.562584\pi$
$930$	61.5261	+	23.9339i	2.01752	+	0.784823i
$931$			41.1887i			1.34991i
$932$	−45.9807	−	10.2042i	−1.50615	−	0.334249i
$933$	14.6019	+	25.2912i	0.478045	+	0.827998i
$934$	0.651806	+	0.812315i	0.0213278	+	0.0265798i
$935$	6.80769	+	17.7140i	0.222635	+	0.579310i
$936$	2.79273	+	47.2012i	0.0912833	+	1.54282i
$937$			4.07081i			0.132988i	0.997787	+	0.0664938i	$0.0211812\pi$
$937$			4.07081i			0.132988i	−0.997787	+	0.0664938i	$0.978819\pi$
$938$	−8.91260	−	11.1073i	−0.291007	−	0.362668i
$939$	−0.0619536	+	0.0357689i	−0.00202178	+	0.00116728i
$940$	2.31934	+	0.514715i	0.0756485	+	0.0167882i
$941$	33.7709			1.10090			0.550451	−	0.834868i	$-0.314456\pi$
$941$	33.7709			1.10090			0.550451	+	0.834868i	$0.314456\pi$
$942$	10.1314	−	26.0443i	0.330097	−	0.848570i
$943$	−15.6093	−	9.01203i	−0.508308	−	0.293472i
$944$	4.44533	−	3.10977i	0.144683	−	0.101214i
$945$	5.99693	+	3.46233i	0.195080	+	0.112630i
$946$	−7.15905	−	4.17234i	−0.232761	−	0.135655i
$947$	−22.5519	−	39.0611i	−0.732839	−	1.26931i	−0.955665	−	0.294456i	$-0.904862\pi$
$947$	−22.5519	−	39.0611i	−0.732839	−	1.26931i	0.222826	−	0.974858i	$-0.428472\pi$
$948$	19.4610	+	61.7692i	0.632063	+	2.00617i
$949$	−0.278633	−	2.21970i	−0.00904482	−	0.0720545i
$950$	−22.7905	+	3.50525i	−0.739420	+	0.113725i
$951$	13.0897	+	22.6720i	0.424462	+	0.735190i
$952$	5.32284	−	7.96055i	0.172514	−	0.258003i
$953$	−11.8146	−	6.82119i	−0.382714	−	0.220960i	0.296284	−	0.955100i	$-0.404252\pi$
$953$	−11.8146	−	6.82119i	−0.382714	−	0.220960i	−0.678998	+	0.734140i	$0.737586\pi$
$954$	−6.32296	−	41.1107i	−0.204713	−	1.33101i
$955$	18.2319	−	31.5785i	0.589969	−	1.02186i
$956$	−30.6239	−	6.79616i	−0.990448	−	0.219804i
$957$	−0.597692	−	1.55523i	−0.0193206	−	0.0502735i
$958$	−7.51748	+	19.3249i	−0.242879	+	0.624361i
$959$	5.29069	+	9.16375i	0.170845	+	0.295913i
$960$	35.2552	+	4.66488i	1.13786	+	0.150558i
$961$	79.2761			2.55729
$962$	58.2795	+	14.6404i	1.87901	+	0.472025i
$963$	50.7464			1.63528
$964$	12.7252	+	11.6656i	0.409850	+	0.375722i
$965$	−30.0874	+	17.3710i	−0.968547	+	0.559191i
$966$	6.84463	−	17.5953i	0.220222	−	0.566118i
$967$			34.6351i			1.11379i	0.830583	+	0.556895i	$0.188007\pi$
$967$			34.6351i			1.11379i	−0.830583	+	0.556895i	$0.811993\pi$
$968$	−24.4246	+	19.2727i	−0.785037	+	0.619449i
$969$	−57.5355	−	33.2181i	−1.84831	−	1.06712i
$970$	1.31268	+	8.53482i	0.0421477	+	0.274036i
$971$	−13.9749	−	8.06841i	−0.448476	−	0.258928i	0.258711	−	0.965955i	$-0.416702\pi$
$971$	−13.9749	−	8.06841i	−0.448476	−	0.258928i	−0.707186	+	0.707027i	$0.750036\pi$
$972$	−23.6102	+	25.7547i	−0.757296	+	0.826082i
$973$	−7.56170	+	4.36575i	−0.242417	+	0.139960i
$974$	−0.170216	−	1.10671i	−0.00545406	−	0.0354613i
$975$	14.5169	+	19.1567i	0.464913	+	0.613506i
$976$	−17.4813	−	24.9890i	−0.559563	−	0.799880i
$977$	15.2184	−	8.78635i	0.486880	−	0.281100i	−0.236399	−	0.971656i	$-0.575967\pi$
$977$	15.2184	−	8.78635i	0.486880	−	0.281100i	0.723279	+	0.690556i	$0.242634\pi$
$978$	44.9755	+	56.0508i	1.43816	+	1.79231i
$979$	3.41514	−	21.6168i	0.109148	−	0.690876i
$980$	−5.89151	−	18.6997i	−0.188198	−	0.597340i
$981$	−29.1827	+	50.5460i	−0.931733	+	1.61381i
$982$	37.9362	+	14.7573i	1.21059	+	0.470926i
$983$	−21.1110			−0.673338			−0.336669	−	0.941623i	$-0.609300\pi$
$983$	−21.1110			−0.673338			−0.336669	+	0.941623i	$0.609300\pi$
$984$	1.82448	−	27.6976i	0.0581624	−	0.882966i
$985$	13.1076	−	7.56770i	0.417644	−	0.241127i
$986$	−0.713225	+	0.572296i	−0.0227137	+	0.0182256i
$987$	1.94238			0.0618268
$988$	39.7495	+	28.2044i	1.26460	+	0.897300i
$989$			8.96616i			0.285107i
$990$	−17.6152	+	30.2247i	−0.559847	+	0.960604i
$991$	5.77778	−	3.33580i	0.183537	−	0.105965i	−0.405416	−	0.914132i	$-0.632873\pi$
$991$	5.77778	−	3.33580i	0.183537	−	0.105965i	0.588953	+	0.808167i	$0.299540\pi$
$992$	57.7093	−	14.0881i	1.83227	−	0.447297i
$993$		−	4.46960i		−	0.141839i
$994$	−5.22292	+	13.4264i	−0.165661	+	0.425859i
$995$	−0.978067	+	1.69406i	−0.0310068	+	0.0537054i
$996$	74.2529	−	23.3941i	2.35279	−	0.741269i
$997$	13.0606	+	7.54056i	0.413634	+	0.238812i	0.692350	−	0.721562i	$-0.256575\pi$
$997$	13.0606	+	7.54056i	0.413634	+	0.238812i	−0.278716	+	0.960374i	$0.589909\pi$
$998$	−43.4693	+	34.8800i	−1.37600	+	1.10411i
$999$	−26.6481	−	46.1559i	−0.843108	−	1.46031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.s.a.439.63	yes	160
4.3	odd	2	inner	572.2.s.a.439.10	yes	160
11.10	odd	2	inner	572.2.s.a.439.18	yes	160
13.4	even	6	inner	572.2.s.a.43.71	yes	160
44.43	even	2	inner	572.2.s.a.439.71	yes	160
52.43	odd	6	inner	572.2.s.a.43.18	yes	160
143.43	odd	6	inner	572.2.s.a.43.10	✓	160
572.43	even	6	inner	572.2.s.a.43.63	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.s.a.43.10	✓	160	143.43	odd	6	inner
572.2.s.a.43.18	yes	160	52.43	odd	6	inner
572.2.s.a.43.63	yes	160	572.43	even	6	inner
572.2.s.a.43.71	yes	160	13.4	even	6	inner
572.2.s.a.439.10	yes	160	4.3	odd	2	inner
572.2.s.a.439.18	yes	160	11.10	odd	2	inner
572.2.s.a.439.63	yes	160	1.1	even	1	trivial
572.2.s.a.439.71	yes	160	44.43	even	2	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10302 - 0.885069i) q^{2} +(-2.39320 + 1.38172i) q^{3} +(0.433305 - 1.95250i) q^{4} +1.60862i q^{5} +(-1.41683 + 3.64221i) q^{6} +(-0.824322 - 0.475923i) q^{7} +(-1.25015 - 2.53715i) q^{8} +(2.31828 - 4.01537i) q^{9} +O(q^{10})\)	\(q+(1.10302 - 0.885069i) q^{2} +(-2.39320 + 1.38172i) q^{3} +(0.433305 - 1.95250i) q^{4} +1.60862i q^{5} +(-1.41683 + 3.64221i) q^{6} +(-0.824322 - 0.475923i) q^{7} +(-1.25015 - 2.53715i) q^{8} +(2.31828 - 4.01537i) q^{9} +(1.42374 + 1.77434i) q^{10} +(-2.08622 + 2.57831i) q^{11} +(1.66081 + 5.27142i) q^{12} +(-0.449071 - 3.57748i) q^{13} +(-1.33047 + 0.204630i) q^{14} +(-2.22266 - 3.84975i) q^{15} +(-3.62449 - 1.69205i) q^{16} +(-3.08043 - 1.77849i) q^{17} +(-0.996779 - 6.48087i) q^{18} +(-5.85339 - 3.37945i) q^{19} +(3.14083 + 0.697023i) q^{20} +2.63036 q^{21} +(-0.0191506 + 4.69038i) q^{22} +(4.39537 - 2.53767i) q^{23} +(6.49748 + 4.34455i) q^{24} +2.41234 q^{25} +(-3.66165 - 3.54857i) q^{26} +4.52250i q^{27} +(-1.28642 + 1.40327i) q^{28} +(0.157432 - 0.0908935i) q^{29} +(-5.85893 - 2.27915i) q^{30} -10.5012 q^{31} +(-5.49547 + 1.34156i) q^{32} +(1.43024 - 9.05298i) q^{33} +(-4.97185 + 0.764687i) q^{34} +(0.765579 - 1.32602i) q^{35} +(-6.83548 - 6.26631i) q^{36} +(-10.2058 + 5.89234i) q^{37} +(-9.44745 + 1.45305i) q^{38} +(6.01777 + 7.94113i) q^{39} +(4.08131 - 2.01102i) q^{40} +(-1.77565 - 3.07552i) q^{41} +(2.90134 - 2.32805i) q^{42} +(-0.883307 + 1.52993i) q^{43} +(4.13019 + 5.19053i) q^{44} +(6.45921 + 3.72923i) q^{45} +(2.60217 - 6.68930i) q^{46} +0.738448 q^{47} +(11.0121 - 0.958598i) q^{48} +(-3.04700 - 5.27755i) q^{49} +(2.66086 - 2.13509i) q^{50} +9.82944 q^{51} +(-7.17960 - 0.673326i) q^{52} +6.34339 q^{53} +(4.00273 + 4.98841i) q^{54} +(-4.14753 - 3.35593i) q^{55} +(-0.176958 + 2.68640i) q^{56} +18.6778 q^{57} +(0.0932037 - 0.239596i) q^{58} +(-0.678136 + 1.17457i) q^{59} +(-8.47972 + 2.67161i) q^{60} +(6.60273 + 3.81209i) q^{61} +(-11.5831 + 9.29433i) q^{62} +(-3.82201 + 2.20664i) q^{63} +(-4.87424 + 6.34364i) q^{64} +(5.75480 - 0.722385i) q^{65} +(-6.43494 - 11.2515i) q^{66} +(5.28970 + 9.16202i) q^{67} +(-4.80725 + 5.24390i) q^{68} +(-7.01267 + 12.1463i) q^{69} +(-0.329173 - 2.14022i) q^{70} +(5.35114 - 9.26845i) q^{71} +(-13.0858 - 0.861982i) q^{72} +0.620466 q^{73} +(-6.04210 + 15.5322i) q^{74} +(-5.77322 + 3.33317i) q^{75} +(-9.13467 + 9.96439i) q^{76} +(2.94679 - 1.13248i) q^{77} +(13.6662 + 3.43308i) q^{78} +11.7178 q^{79} +(2.72187 - 5.83043i) q^{80} +(0.706020 + 1.22286i) q^{81} +(-4.68063 - 1.82078i) q^{82} -14.0859i q^{83} +(1.13975 - 5.13577i) q^{84} +(2.86091 - 4.95524i) q^{85} +(0.379792 + 2.46933i) q^{86} +(-0.251178 + 0.435053i) q^{87} +(9.14965 + 2.06975i) q^{88} +(-5.71451 + 3.29927i) q^{89} +(10.4253 - 1.60344i) q^{90} +(-1.33242 + 3.16272i) q^{91} +(-3.05025 - 9.68153i) q^{92} +(25.1316 - 14.5097i) q^{93} +(0.814523 - 0.653578i) q^{94} +(5.43626 - 9.41587i) q^{95} +(11.2981 - 10.8038i) q^{96} +(3.28725 + 1.89790i) q^{97} +(-8.03189 - 3.12444i) q^{98} +(5.51646 + 14.3542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{4} + 68 q^{9}+O(q^{10}) \) 160 * q - 2 * q^4 + 68 * q^9	\( 160 q - 2 q^{4} + 68 q^{9} - 36 q^{12} - 8 q^{14} - 6 q^{16} + 30 q^{20} - 20 q^{22} - 144 q^{25} - 40 q^{26} - 6 q^{33} + 46 q^{36} - 12 q^{37} - 56 q^{38} - 2 q^{42} + 48 q^{45} - 40 q^{48} + 44 q^{49} - 32 q^{53} + 30 q^{56} + 78 q^{58} + 64 q^{64} - 4 q^{66} - 44 q^{69} - 44 q^{77} + 16 q^{78} + 24 q^{80} - 40 q^{81} - 6 q^{82} - 10 q^{88} + 24 q^{89} - 24 q^{92} - 96 q^{93}+O(q^{100}) \) 160 * q - 2 * q^4 + 68 * q^9 - 36 * q^12 - 8 * q^14 - 6 * q^16 + 30 * q^20 - 20 * q^22 - 144 * q^25 - 40 * q^26 - 6 * q^33 + 46 * q^36 - 12 * q^37 - 56 * q^38 - 2 * q^42 + 48 * q^45 - 40 * q^48 + 44 * q^49 - 32 * q^53 + 30 * q^56 + 78 * q^58 + 64 * q^64 - 4 * q^66 - 44 * q^69 - 44 * q^77 + 16 * q^78 + 24 * q^80 - 40 * q^81 - 6 * q^82 - 10 * q^88 + 24 * q^89 - 24 * q^92 - 96 * q^93

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