LMFDB - Embedded newform 572.2.s.a.43.11

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			43.11
Character	$\chi$	$=$	572.43
Dual form			572.2.s.a.439.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30032 - 0.556038i) q^{2} +(0.593637 + 0.342737i) q^{3} +(1.38164 + 1.44605i) q^{4} -3.22106i q^{5} +(-0.581342 - 0.775751i) q^{6} +(-1.12143 + 0.647461i) q^{7} +(-0.992516 - 2.64857i) q^{8} +(-1.26506 - 2.19115i) q^{9} +O(q^{10})$	\(q+(-1.30032 - 0.556038i) q^{2} +(0.593637 + 0.342737i) q^{3} +(1.38164 + 1.44605i) q^{4} -3.22106i q^{5} +(-0.581342 - 0.775751i) q^{6} +(-1.12143 + 0.647461i) q^{7} +(-0.992516 - 2.64857i) q^{8} +(-1.26506 - 2.19115i) q^{9} +(-1.79103 + 4.18839i) q^{10} +(-2.18376 + 2.49623i) q^{11} +(0.324581 + 1.33197i) q^{12} +(-2.52218 - 2.57655i) q^{13} +(1.81823 - 0.218344i) q^{14} +(1.10398 - 1.91214i) q^{15} +(-0.182119 + 3.99585i) q^{16} +(-3.19737 + 1.84600i) q^{17} +(0.426618 + 3.55262i) q^{18} +(-4.91650 + 2.83855i) q^{19} +(4.65781 - 4.45036i) q^{20} -0.887634 q^{21} +(4.22758 - 2.03164i) q^{22} +(3.72964 + 2.15331i) q^{23} +(0.318567 - 1.91246i) q^{24} -5.37522 q^{25} +(1.84698 + 4.75275i) q^{26} -3.79075i q^{27} +(-2.48568 - 0.727090i) q^{28} +(8.37391 + 4.83468i) q^{29} +(-2.49874 + 1.87254i) q^{30} -9.61716 q^{31} +(2.45866 - 5.09461i) q^{32} +(-2.15191 + 0.733402i) q^{33} +(5.18404 - 0.622529i) q^{34} +(2.08551 + 3.61221i) q^{35} +(1.42065 - 4.85674i) q^{36} +(-1.65873 - 0.957668i) q^{37} +(7.97135 - 0.957244i) q^{38} +(-0.614186 - 2.39398i) q^{39} +(-8.53119 + 3.19695i) q^{40} +(3.51263 - 6.08406i) q^{41} +(1.15421 + 0.493558i) q^{42} +(-4.41995 - 7.65557i) q^{43} +(-6.62686 + 0.291078i) q^{44} +(-7.05783 + 4.07484i) q^{45} +(-3.65239 - 4.87380i) q^{46} +5.93650 q^{47} +(-1.47764 + 2.30967i) q^{48} +(-2.66159 + 4.61001i) q^{49} +(6.98949 + 2.98883i) q^{50} -2.53077 q^{51} +(0.241052 - 7.20707i) q^{52} -9.56469 q^{53} +(-2.10780 + 4.92918i) q^{54} +(8.04052 + 7.03403i) q^{55} +(2.82789 + 2.32758i) q^{56} -3.89149 q^{57} +(-8.20047 - 10.9428i) q^{58} +(-4.23935 - 7.34277i) q^{59} +(4.29035 - 1.04550i) q^{60} +(3.10829 - 1.79457i) q^{61} +(12.5053 + 5.34750i) q^{62} +(2.83737 + 1.63816i) q^{63} +(-6.02982 + 5.25749i) q^{64} +(-8.29921 + 8.12410i) q^{65} +(3.20597 + 0.242891i) q^{66} +(-3.57389 + 6.19016i) q^{67} +(-7.08705 - 2.07304i) q^{68} +(1.47603 + 2.55657i) q^{69} +(-0.703298 - 5.85663i) q^{70} +(-3.77721 - 6.54232i) q^{71} +(-4.54782 + 5.52536i) q^{72} +1.05134 q^{73} +(1.62437 + 2.16759i) q^{74} +(-3.19093 - 1.84229i) q^{75} +(-10.8975 - 3.18765i) q^{76} +(0.832734 - 4.21326i) q^{77} +(-0.532507 + 3.45444i) q^{78} +2.11291 q^{79} +(12.8709 + 0.586615i) q^{80} +(-2.49596 + 4.32313i) q^{81} +(-7.95050 + 5.95805i) q^{82} -5.83783i q^{83} +(-1.22639 - 1.28356i) q^{84} +(5.94609 + 10.2989i) q^{85} +(1.49054 + 12.4123i) q^{86} +(3.31404 + 5.74009i) q^{87} +(8.77886 + 3.30629i) q^{88} +(-7.82986 - 4.52057i) q^{89} +(11.4432 - 1.37416i) q^{90} +(4.49668 + 1.25641i) q^{91} +(2.03924 + 8.36834i) q^{92} +(-5.70910 - 3.29615i) q^{93} +(-7.71933 - 3.30092i) q^{94} +(9.14312 + 15.8363i) q^{95} +(3.20566 - 2.18168i) q^{96} +(14.2378 - 8.22017i) q^{97} +(6.02425 - 4.51452i) q^{98} +(8.23223 + 1.62707i) 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 $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.30032	−	0.556038i	−0.919462	−	0.393178i
$2$	−1.30032	−	0.556038i	−0.919462	−	0.393178i
$3$	0.593637	+	0.342737i	0.342737	+	0.197879i	0.661482	−	0.749961i	$-0.269928\pi$
$3$	0.593637	+	0.342737i	0.342737	+	0.197879i	−0.318745	+	0.947841i	$0.603261\pi$
$4$	1.38164	+	1.44605i	0.690822	+	0.723025i
$5$		−	3.22106i		−	1.44050i	−0.693714	−	0.720251i	$-0.744027\pi$
$5$		−	3.22106i		−	1.44050i	0.693714	−	0.720251i	$-0.255973\pi$
$6$	−0.581342	−	0.775751i	−0.237332	−	0.316699i
$7$	−1.12143	+	0.647461i	−0.423863	+	0.244717i	−0.696729	−	0.717335i	$-0.745362\pi$
$7$	−1.12143	+	0.647461i	−0.423863	+	0.244717i	0.272866	+	0.962052i	$0.412028\pi$
$8$	−0.992516	−	2.64857i	−0.350907	−	0.936410i
$9$	−1.26506	−	2.19115i	−0.421688	−	0.730385i
$10$	−1.79103	+	4.18839i	−0.566373	+	1.32449i
$11$	−2.18376	+	2.49623i	−0.658429	+	0.752643i
$11$	−2.18376	+	2.49623i	−0.658429	+	0.752643i
$12$	0.324581	+	1.33197i	0.0936986	+	0.384506i
$13$	−2.52218	−	2.57655i	−0.699528	−	0.714605i
$13$	−2.52218	−	2.57655i	−0.699528	−	0.714605i
$14$	1.81823	−	0.218344i	0.485943	−	0.0583548i
$15$	1.10398	−	1.91214i	0.285045	−	0.493713i
$16$	−0.182119	+	3.99585i	−0.0455297	+	0.998963i
$17$	−3.19737	+	1.84600i	−0.775477	+	0.447722i	−0.834825	−	0.550515i	$-0.814431\pi$
$17$	−3.19737	+	1.84600i	−0.775477	+	0.447722i	0.0593479	+	0.998237i	$0.481098\pi$
$18$	0.426618	+	3.55262i	0.100555	+	0.837359i
$19$	−4.91650	+	2.83855i	−1.12792	+	0.651207i	−0.943412	−	0.331623i	$-0.892404\pi$
$19$	−4.91650	+	2.83855i	−1.12792	+	0.651207i	−0.184512	+	0.982830i	$0.559070\pi$
$20$	4.65781	−	4.45036i	1.04152	−	0.995130i
$21$	−0.887634			−0.193698
$22$	4.22758	−	2.03164i	0.901323	−	0.433147i
$23$	3.72964	+	2.15331i	0.777683	+	0.448995i	0.835608	−	0.549326i	$-0.185115\pi$
$23$	3.72964	+	2.15331i	0.777683	+	0.448995i	−0.0579256	+	0.998321i	$0.518449\pi$
$24$	0.318567	−	1.91246i	0.0650272	−	0.390379i
$25$	−5.37522			−1.07504
$26$	1.84698	+	4.75275i	0.362223	+	0.932092i
$27$		−	3.79075i		−	0.729531i
$28$	−2.48568	−	0.727090i	−0.469750	−	0.137407i
$29$	8.37391	+	4.83468i	1.55500	+	0.897777i	0.997723	+	0.0674484i	$0.0214858\pi$
$29$	8.37391	+	4.83468i	1.55500	+	0.897777i	0.557273	+	0.830329i	$0.311848\pi$
$30$	−2.49874	+	1.87254i	−0.456205	+	0.341877i
$31$	−9.61716			−1.72729			−0.863646	−	0.504099i	$-0.831825\pi$
$31$	−9.61716			−1.72729			−0.863646	+	0.504099i	$0.831825\pi$
$32$	2.45866	−	5.09461i	0.434633	−	0.900608i
$33$	−2.15191	+	0.733402i	−0.374600	+	0.127669i
$34$	5.18404	−	0.622529i	0.889056	−	0.106763i
$35$	2.08551	+	3.61221i	0.352515	+	0.610575i
$36$	1.42065	−	4.85674i	0.236775	−	0.809456i
$37$	−1.65873	−	0.957668i	−0.272693	−	0.157440i	0.357418	−	0.933945i	$-0.383657\pi$
$37$	−1.65873	−	0.957668i	−0.272693	−	0.157440i	−0.630111	+	0.776505i	$0.716991\pi$
$38$	7.97135	−	0.957244i	1.29312	−	0.155286i
$39$	−0.614186	−	2.39398i	−0.0983484	−	0.383343i
$40$	−8.53119	+	3.19695i	−1.34890	+	0.505483i
$41$	3.51263	−	6.08406i	0.548581	−	0.950171i	−0.449791	−	0.893134i	$-0.648501\pi$
$41$	3.51263	−	6.08406i	0.548581	−	0.950171i	0.998372	−	0.0570368i	$-0.0181652\pi$
$42$	1.15421	+	0.493558i	0.178098	+	0.0761577i
$43$	−4.41995	−	7.65557i	−0.674036	−	1.16746i	−0.976750	−	0.214383i	$-0.931226\pi$
$43$	−4.41995	−	7.65557i	−0.674036	−	1.16746i	0.302714	−	0.953081i	$-0.402107\pi$
$44$	−6.62686	+	0.291078i	−0.999037	+	0.0438817i
$45$	−7.05783	+	4.07484i	−1.05212	+	0.607442i
$46$	−3.65239	−	4.87380i	−0.538515	−	0.718602i
$47$	5.93650			0.865927			0.432964	−	0.901411i	$-0.357468\pi$
$47$	5.93650			0.865927			0.432964	+	0.901411i	$0.357468\pi$
$48$	−1.47764	+	2.30967i	−0.213279	+	0.333372i
$49$	−2.66159	+	4.61001i	−0.380227	+	0.658573i
$50$	6.98949	+	2.98883i	0.988463	+	0.422684i
$51$	−2.53077			−0.354379
$52$	0.241052	−	7.20707i	0.0334279	−	0.999441i
$53$	−9.56469			−1.31381			−0.656906	−	0.753973i	$-0.728135\pi$
$53$	−9.56469			−1.31381			−0.656906	+	0.753973i	$0.728135\pi$
$54$	−2.10780	+	4.92918i	−0.286836	+	0.670776i
$55$	8.04052	+	7.03403i	1.08418	+	0.948468i
$56$	2.82789	+	2.32758i	0.377892	+	0.311036i
$57$	−3.89149			−0.515441
$58$	−8.20047	−	10.9428i	−1.07677	−	1.43686i
$59$	−4.23935	−	7.34277i	−0.551916	−	0.955947i	−0.998136	−	0.0610237i	$-0.980563\pi$
$59$	−4.23935	−	7.34277i	−0.551916	−	0.955947i	0.446220	−	0.894923i	$-0.352770\pi$
$60$	4.29035	−	1.04550i	0.553882	−	0.134973i
$61$	3.10829	−	1.79457i	0.397976	−	0.229771i	−0.287634	−	0.957740i	$-0.592869\pi$
$61$	3.10829	−	1.79457i	0.397976	−	0.229771i	0.685610	+	0.727969i	$0.259535\pi$
$62$	12.5053	+	5.34750i	1.58818	+	0.679133i
$63$	2.83737	+	1.63816i	0.357475	+	0.206388i
$64$	−6.02982	+	5.25749i	−0.753728	+	0.657187i
$65$	−8.29921	+	8.12410i	−1.02939	+	1.00767i
$66$	3.20597	+	0.242891i	0.394627	+	0.0298978i
$67$	−3.57389	+	6.19016i	−0.436620	+	0.756248i	−0.997426	−	0.0716991i	$-0.977158\pi$
$67$	−3.57389	+	6.19016i	−0.436620	+	0.756248i	0.560806	+	0.827947i	$0.310491\pi$
$68$	−7.08705	−	2.07304i	−0.859431	−	0.251393i
$69$	1.47603	+	2.55657i	0.177694	+	0.307774i
$70$	−0.703298	−	5.85663i	−0.0840601	−	0.700002i
$71$	−3.77721	−	6.54232i	−0.448272	−	0.776430i	0.550002	−	0.835164i	$-0.314627\pi$
$71$	−3.77721	−	6.54232i	−0.448272	−	0.776430i	−0.998274	+	0.0587335i	$0.981294\pi$
$72$	−4.54782	+	5.52536i	−0.535966	+	0.651170i
$73$	1.05134			0.123050			0.0615251	−	0.998106i	$-0.480404\pi$
$73$	1.05134			0.123050			0.0615251	+	0.998106i	$0.480404\pi$
$74$	1.62437	+	2.16759i	0.188830	+	0.251977i
$75$	−3.19093	−	1.84229i	−0.368457	−	0.212729i
$76$	−10.8975	−	3.18765i	−1.25003	−	0.365648i
$77$	0.832734	−	4.21326i	0.0948988	−	0.480146i
$78$	−0.532507	+	3.45444i	−0.0602945	+	0.391138i
$79$	2.11291			0.237721			0.118860	−	0.992911i	$-0.462076\pi$
$79$	2.11291			0.237721			0.118860	+	0.992911i	$0.462076\pi$
$80$	12.8709	+	0.586615i	1.43901	+	0.0655856i
$81$	−2.49596	+	4.32313i	−0.277329	+	0.480347i
$82$	−7.95050	+	5.95805i	−0.877986	+	0.657956i
$83$		−	5.83783i		−	0.640785i	−0.947285	−	0.320393i	$-0.896185\pi$
$83$		−	5.83783i		−	0.640785i	0.947285	−	0.320393i	$-0.103815\pi$
$84$	−1.22639	−	1.28356i	−0.133811	−	0.140048i
$85$	5.94609	+	10.2989i	0.644944	+	1.11708i
$86$	1.49054	+	12.4123i	0.160729	+	1.33846i
$87$	3.31404	+	5.74009i	0.355303	+	0.615403i
$88$	8.77886	+	3.30629i	0.935830	+	0.352452i
$89$	−7.82986	−	4.52057i	−0.829963	−	0.479179i	0.0238770	−	0.999715i	$-0.492399\pi$
$89$	−7.82986	−	4.52057i	−0.829963	−	0.479179i	−0.853840	+	0.520536i	$0.825732\pi$
$90$	11.4432	−	1.37416i	1.20622	−	0.144849i
$91$	4.49668	+	1.25641i	0.471380	+	0.131708i
$92$	2.03924	+	8.36834i	0.212606	+	0.872460i
$93$	−5.70910	−	3.29615i	−0.592006	−	0.341795i
$94$	−7.71933	−	3.30092i	−0.796188	−	0.340464i
$95$	9.14312	+	15.8363i	0.938064	+	1.62478i
$96$	3.20566	−	2.18168i	0.327176	−	0.222666i
$97$	14.2378	−	8.22017i	1.44563	−	0.834632i	0.447409	−	0.894330i	$-0.352347\pi$
$97$	14.2378	−	8.22017i	1.44563	−	0.834632i	0.998217	+	0.0596977i	$0.0190137\pi$
$98$	6.02425	−	4.51452i	0.608541	−	0.456036i
$99$	8.23223	+	1.62707i	0.827370	+	0.163526i
$100$	−7.42664	−	7.77284i	−0.742664	−	0.777284i
$101$	−3.60990	−	2.08418i	−0.359198	−	0.207383i	0.309531	−	0.950889i	$-0.399828\pi$
$101$	−3.60990	−	2.08418i	−0.359198	−	0.207383i	−0.668729	+	0.743506i	$0.733161\pi$
$102$	3.29081	+	1.40721i	0.325838	+	0.139334i
$103$			1.35975i			0.133980i	0.997754	+	0.0669898i	$0.0213395\pi$
$103$			1.35975i			0.133980i	−0.997754	+	0.0669898i	$0.978660\pi$
$104$	−4.32085	+	9.23744i	−0.423694	+	0.905805i
$105$			2.85912i			0.279022i
$106$	12.4371	+	5.31833i	1.20800	+	0.516562i
$107$	8.49287	−	14.7101i	0.821037	−	1.42208i	−0.0838734	−	0.996476i	$-0.526729\pi$
$107$	8.49287	−	14.7101i	0.821037	−	1.42208i	0.904911	−	0.425602i	$-0.139938\pi$
$108$	5.48162	−	5.23747i	0.527469	−	0.503976i
$109$	−12.0154			−1.15087			−0.575434	−	0.817848i	$-0.695167\pi$
$109$	−12.0154			−1.15087			−0.575434	+	0.817848i	$0.695167\pi$
$110$	−6.54403	−	13.6173i	−0.623949	−	1.29836i
$111$	−0.656456	−	1.13701i	−0.0623080	−	0.107921i
$112$	−2.38292	−	4.59900i	−0.225165	−	0.434565i
$113$	−0.644228	−	1.11584i	−0.0606039	−	0.104969i	0.834132	−	0.551565i	$-0.185969\pi$
$113$	−0.644228	−	1.11584i	−0.0606039	−	0.104969i	−0.894735	+	0.446596i	$0.852636\pi$
$114$	5.06017	+	2.16382i	0.473929	+	0.202660i
$115$	6.93593	−	12.0134i	0.646778	−	1.12025i
$116$	4.57858	+	18.7889i	0.425110	+	1.74451i
$117$	−2.45489	+	8.78599i	−0.226954	+	0.812265i
$118$	1.42964	+	11.9052i	0.131609	+	1.09596i
$119$	2.39043	−	4.14035i	0.219130	−	0.379545i
$120$	−6.16015	−	1.02612i	−0.562342	−	0.0936717i
$121$	−1.46236	−	10.9024i	−0.132942	−	0.991124i
$122$	−5.03961	+	0.605185i	−0.456265	+	0.0547909i
$123$	4.17046	−	2.40782i	0.376038	−	0.217106i
$124$	−13.2875	−	13.9069i	−1.19325	−	1.24887i
$125$			1.20861i			0.108101i
$126$	−2.77860	−	3.70781i	−0.247538	−	0.330318i
$127$	−0.662449	+	1.14739i	−0.0587828	+	0.101815i	−0.893919	−	0.448228i	$-0.852055\pi$
$127$	−0.662449	+	1.14739i	−0.0587828	+	0.101815i	0.835136	+	0.550043i	$0.185389\pi$
$128$	10.7640	−	3.48359i	0.951416	−	0.307909i
$129$		−	6.05951i		−	0.533510i
$130$	15.3089	−	5.94923i	1.34268	−	0.521782i
$131$	−1.87764			−0.164050			−0.0820249	−	0.996630i	$-0.526139\pi$
$131$	−1.87764			−0.164050			−0.0820249	+	0.996630i	$0.526139\pi$
$132$	−4.03371	−	2.09847i	−0.351090	−	0.182649i
$133$	3.67569	−	6.36649i	0.318723	−	0.552044i
$134$	8.08914	−	6.06194i	0.698796	−	0.523672i
$135$	−12.2102			−1.05089
$136$	8.06271	+	6.63627i	0.691372	+	0.569056i
$137$	16.2452	−	9.37916i	1.38792	−	0.801316i	0.394839	−	0.918750i	$-0.370800\pi$
$137$	16.2452	−	9.37916i	1.38792	−	0.801316i	0.993081	+	0.117434i	$0.0374669\pi$
$138$	−0.497764	−	4.14507i	−0.0423725	−	0.352852i
$139$	−9.27601	−	16.0665i	−0.786781	−	1.36274i	−0.927929	−	0.372756i	$-0.878413\pi$
$139$	−9.27601	−	16.0665i	−0.786781	−	1.36274i	0.141148	−	0.989988i	$-0.454921\pi$
$140$	−2.34200	+	8.00654i	−0.197935	+	0.676676i
$141$	3.52413	+	2.03466i	0.296785	+	0.171349i
$142$	1.27379	+	10.6073i	0.106894	+	0.890149i
$143$	11.9395	−	0.669397i	0.998432	−	0.0559778i
$144$	8.98592	−	4.65595i	0.748826	−	0.387996i
$145$	15.5728	−	26.9729i	1.29325	−	2.23997i
$146$	−1.36708	−	0.584585i	−0.113140	−	0.0483806i
$147$	−3.16004	+	1.82445i	−0.260636	+	0.150478i
$148$	−0.906939	−	3.72176i	−0.0745499	−	0.305927i
$149$	6.70209	+	11.6084i	0.549057	+	0.950994i	0.998339	+	0.0576044i	$0.0183462\pi$
$149$	6.70209	+	11.6084i	0.549057	+	0.950994i	−0.449283	+	0.893390i	$0.648320\pi$
$150$	3.12484	+	4.16983i	0.255142	+	0.340465i
$151$			1.22847i			0.0999711i	0.998750	+	0.0499856i	$0.0159175\pi$
$151$			1.22847i			0.0999711i	−0.998750	+	0.0499856i	$0.984082\pi$
$152$	12.3978	+	10.2044i	1.00559	+	0.827686i
$153$	8.08976	+	4.67062i	0.654018	+	0.377598i
$154$	−3.42555	+	5.01554i	−0.276039	+	0.404164i
$155$			30.9774i			2.48817i
$156$	2.61323	−	4.19577i	0.209226	−	0.335930i
$157$	13.6405			1.08863			0.544314	−	0.838881i	$-0.316790\pi$
$157$	13.6405			1.08863			0.544314	+	0.838881i	$0.316790\pi$
$158$	−2.74745	−	1.17486i	−0.218575	−	0.0934665i
$159$	−5.67796	−	3.27817i	−0.450291	−	0.259976i
$160$	−16.4100	−	7.91948i	−1.29733	−	0.626090i
$161$	−5.57673			−0.439508
$162$	5.64936	−	4.23359i	0.443855	−	0.332622i
$163$	−0.305624	−	0.529356i	−0.0239383	−	0.0414624i	0.853808	−	0.520588i	$-0.174287\pi$
$163$	−0.305624	−	0.529356i	−0.0239383	−	0.0414624i	−0.877746	+	0.479126i	$0.840954\pi$
$164$	13.6511	−	3.32656i	1.06597	−	0.259761i
$165$	2.36233	+	6.93144i	0.183907	+	0.539612i
$166$	−3.24605	+	7.59103i	−0.251943	+	0.589178i
$167$	−1.11839	−	0.645701i	−0.0865434	−	0.0499658i	0.456104	−	0.889927i	$-0.349245\pi$
$167$	−1.11839	−	0.645701i	−0.0865434	−	0.0499658i	−0.542647	+	0.839961i	$0.682578\pi$
$168$	0.880991	+	2.35096i	0.0679700	+	0.181380i
$169$	−0.277176	+	12.9970i	−0.0213212	+	0.999773i
$170$	−2.00520	−	16.6981i	−0.153792	−	1.28069i
$171$	12.4394	+	7.18188i	0.951263	+	0.549212i
$172$	4.96354	−	16.9687i	0.378467	−	1.29385i
$173$	−8.29276	+	4.78783i	−0.630487	+	0.364012i	−0.780941	−	0.624605i	$-0.785260\pi$
$173$	−8.29276	+	4.78783i	−0.630487	+	0.364012i	0.150454	+	0.988617i	$0.451927\pi$
$174$	−1.11760	−	9.30667i	−0.0847248	−	0.705537i
$175$	6.02796	−	3.48024i	0.455671	−	0.263082i
$176$	−9.57688	−	9.18060i	−0.721884	−	0.692014i
$177$		−	5.81192i		−	0.436851i
$178$	7.66768	+	10.2319i	0.574717	+	0.766911i
$179$	3.03156	+	1.75027i	0.226589	+	0.130821i	0.608998	−	0.793172i	$-0.291572\pi$
$179$	3.03156	+	1.75027i	0.226589	+	0.130821i	−0.382408	+	0.923993i	$0.624905\pi$
$180$	−15.6438	−	4.57600i	−1.16602	−	0.341075i
$181$	9.43478			0.701282			0.350641	−	0.936510i	$-0.385964\pi$
$181$	9.43478			0.701282			0.350641	+	0.936510i	$0.385964\pi$
$182$	−5.14849	−	4.13406i	−0.381631	−	0.306437i
$183$	2.46026			0.181868
$184$	2.00145	−	12.0154i	0.147549	−	0.885786i
$185$	−3.08470	+	5.34287i	−0.226792	+	0.392815i
$186$	5.59085	+	7.46052i	0.409941	+	0.547032i
$187$	2.37425	−	12.0126i	0.173622	−	0.878450i
$188$	8.20213	+	8.58447i	0.598202	+	0.626087i
$189$	2.45436	+	4.25108i	0.178529	+	0.309221i
$190$	−3.08334	−	25.6762i	−0.223689	−	1.86275i
$191$	16.5988	−	9.58334i	1.20105	−	0.693426i	0.240261	−	0.970708i	$-0.422767\pi$
$191$	16.5988	−	9.58334i	1.20105	−	0.693426i	0.960789	+	0.277282i	$0.0894336\pi$
$192$	−5.38146	+	1.05440i	−0.388374	+	0.0760949i
$193$	−10.0526	+	17.4116i	−0.723603	+	1.25332i	0.235943	+	0.971767i	$0.424182\pi$
$193$	−10.0526	+	17.4116i	−0.723603	+	1.25332i	−0.959546	+	0.281551i	$0.909151\pi$
$194$	−23.0843	+	2.77209i	−1.65736	+	0.199025i
$195$	−7.71115	+	1.97833i	−0.552207	+	0.141671i
$196$	−10.3437	+	2.52060i	−0.738833	+	0.180043i
$197$	7.48032	−	12.9563i	0.532951	−	0.923098i	−0.466309	−	0.884622i	$-0.654416\pi$
$197$	7.48032	−	12.9563i	0.532951	−	0.923098i	0.999260	−	0.0384757i	$-0.0122502\pi$
$198$	−9.79979	−	6.69313i	−0.696441	−	0.475660i
$199$	−13.0809	+	7.55228i	−0.927282	+	0.535367i	−0.885951	−	0.463779i	$-0.846493\pi$
$199$	−13.0809	+	7.55228i	−0.927282	+	0.535367i	−0.0413312	+	0.999146i	$0.513160\pi$
$200$	5.33499	+	14.2366i	0.377241	+	1.00668i
$201$	−4.24319	+	2.44981i	−0.299291	+	0.172796i
$202$	3.53513	+	4.71733i	0.248731	+	0.331910i
$203$	−12.5211			−0.878806
$204$	−3.49663	−	3.65962i	−0.244813	−	0.256225i
$205$	−19.5971	−	11.3144i	−1.36872	−	0.790232i
$206$	0.756070	−	1.76810i	0.0526779	−	0.123189i
$207$		−	10.8963i		−	0.757343i
$208$	10.7548	−	9.60904i	0.745713	−	0.666267i
$209$	3.65080	−	18.4715i	0.252531	−	1.27770i
$210$	1.58978	−	3.71776i	0.109705	−	0.256550i
$211$	−2.90823	+	5.03720i	−0.200211	+	0.346775i	−0.948596	−	0.316489i	$-0.897496\pi$
$211$	−2.90823	+	5.03720i	−0.200211	+	0.346775i	0.748386	+	0.663264i	$0.230829\pi$
$212$	−13.2150	−	13.8310i	−0.907610	−	0.949918i
$213$		−	5.17835i		−	0.354815i
$214$	−19.2228	+	14.4054i	−1.31404	+	0.984734i
$215$	−24.6591	+	14.2369i	−1.68173	+	0.970949i
$216$	−10.0401	+	3.76239i	−0.683140	+	0.255998i
$217$	10.7850	−	6.22673i	0.732134	−	0.422698i
$218$	15.6238	+	6.68102i	1.05818	+	0.452496i
$219$	0.624115	+	0.360333i	0.0421738	+	0.0243491i
$220$	0.937580	+	21.3455i	0.0632116	+	1.43911i
$221$	12.8207	+	3.58222i	0.862412	+	0.240966i
$222$	0.221377	+	1.84349i	0.0148579	+	0.123727i
$223$	2.28005	−	3.94916i	0.152683	−	0.264455i	−0.779530	−	0.626365i	$-0.784542\pi$
$223$	2.28005	−	3.94916i	0.152683	−	0.264455i	0.932213	+	0.361910i	$0.117875\pi$
$224$	0.541335	+	7.30515i	0.0361694	+	0.488096i
$225$	6.79999	+	11.7779i	0.453333	+	0.785196i
$226$	0.217253	+	1.80915i	0.0144515	+	0.120343i
$227$	−3.20282	+	1.84915i	−0.212578	+	0.122732i	−0.602509	−	0.798112i	$-0.705832\pi$
$227$	−3.20282	+	1.84915i	−0.212578	+	0.122732i	0.389931	+	0.920844i	$0.372499\pi$
$228$	−5.37666	−	5.62729i	−0.356078	−	0.372677i
$229$			13.5166i			0.893202i	0.894733	+	0.446601i	$0.147366\pi$
$229$			13.5166i			0.893202i	−0.894733	+	0.446601i	$0.852634\pi$
$230$	−15.6988	+	11.7646i	−1.03515	+	0.775732i
$231$	1.93838	−	2.21574i	0.127536	−	0.145785i
$232$	4.49373	−	26.9774i	0.295028	−	1.77115i
$233$			9.41814i			0.617003i	0.951224	+	0.308501i	$0.0998274\pi$
$233$			9.41814i			0.617003i	−0.951224	+	0.308501i	$0.900173\pi$
$234$	8.07747	−	10.0595i	0.528041	−	0.657613i
$235$		−	19.1218i		−	1.24737i
$236$	4.76073	−	16.2754i	0.309897	−	1.05944i
$237$	1.25430	+	0.724171i	0.0814756	+	0.0470399i
$238$	−5.41051	+	4.05459i	−0.350711	+	0.262820i
$239$			25.4881i			1.64869i	0.566089	+	0.824344i	$0.308456\pi$
$239$			25.4881i			1.64869i	−0.566089	+	0.824344i	$0.691544\pi$
$240$	7.43958	+	4.75956i	0.480223	+	0.307228i
$241$	15.3420	+	26.5731i	0.988264	+	1.71172i	0.626423	+	0.779483i	$0.284518\pi$
$241$	15.3420	+	26.5731i	0.988264	+	1.71172i	0.361841	+	0.932240i	$0.382148\pi$
$242$	−4.16059	+	14.9896i	−0.267453	+	0.963571i
$243$	−12.8121	+	7.39704i	−0.821894	+	0.474521i
$244$	6.88959	+	2.01528i	0.441061	+	0.129015i
$245$	14.8491	+	8.57314i	0.948675	+	0.547718i
$246$	−6.76176	+	0.811990i	−0.431114	+	0.0517706i
$247$	19.7140	+	5.50827i	1.25437	+	0.350483i
$248$	9.54518	+	25.4717i	0.606120	+	1.61745i
$249$	2.00084	−	3.46555i	0.126798	−	0.219621i
$250$	0.672031	−	1.57157i	0.0425030	−	0.0993949i
$251$	−22.5667	+	13.0289i	−1.42440	+	0.822377i	−0.996671	−	0.0815307i	$-0.974019\pi$
$251$	−22.5667	+	13.0289i	−1.42440	+	0.822377i	−0.427728	+	0.903908i	$0.640686\pi$
$252$	1.55138	+	6.36633i	0.0977279	+	0.401041i
$253$	−13.5198	+	4.60773i	−0.849982	+	0.289686i
$254$	1.49939	−	1.12363i	0.0940799	−	0.0705028i
$255$			8.15177i			0.510484i
$256$	−15.9337	−	1.45544i	−0.995854	−	0.0909649i
$257$	−0.0226647	+	0.0392564i	−0.00141378	+	0.00244875i	−0.866731	−	0.498775i	$-0.833783\pi$
$257$	−0.0226647	+	0.0392564i	−0.00141378	+	0.00244875i	0.865318	+	0.501224i	$0.167117\pi$
$258$	−3.36932	+	7.87928i	−0.209765	+	0.490543i
$259$	2.48021			0.154113
$260$	−23.2144	−	0.776443i	−1.43970	−	0.0481530i
$261$		−	24.4647i		−	1.51433i
$262$	2.44152	+	1.04404i	0.150838	+	0.0645008i
$263$	−11.1018	+	19.2289i	−0.684569	+	1.18571i	0.289004	+	0.957328i	$0.406676\pi$
$263$	−11.1018	+	19.2289i	−0.684569	+	1.18571i	−0.973572	+	0.228380i	$0.926657\pi$
$264$	4.07827	+	4.97158i	0.251000	+	0.305979i
$265$			30.8084i			1.89255i
$266$	−8.31957	+	6.23462i	−0.510106	+	0.382269i
$267$	−3.09873	−	5.36716i	−0.189639	−	0.328465i
$268$	−13.8891	+	3.38457i	−0.848413	+	0.206746i
$269$	−9.26213	−	16.0425i	−0.564722	−	0.978127i	−0.997075	−	0.0764230i	$-0.975650\pi$
$269$	−9.26213	−	16.0425i	−0.564722	−	0.978127i	0.432354	−	0.901704i	$-0.357683\pi$
$270$	15.8772	+	6.78936i	0.966254	+	0.413187i
$271$	−5.64802	−	3.26089i	−0.343093	−	0.198085i	0.318546	−	0.947907i	$-0.396805\pi$
$271$	−5.64802	−	3.26089i	−0.343093	−	0.198085i	−0.661639	+	0.749823i	$0.730139\pi$
$272$	−6.79406	−	13.1124i	−0.411950	−	0.795058i
$273$	2.23878	+	2.28703i	0.135497	+	0.138417i
$274$	−26.3391	+	3.16294i	−1.59120	+	0.191080i
$275$	11.7382	−	13.4178i	0.707840	−	0.809124i
$276$	−1.65757	+	5.66668i	−0.0997738	+	0.341094i
$277$	13.6698	−	7.89228i	0.821340	−	0.474201i	−0.0295383	−	0.999564i	$-0.509404\pi$
$277$	13.6698	−	7.89228i	0.821340	−	0.474201i	0.850878	+	0.525363i	$0.176070\pi$
$278$	3.12815	+	26.0494i	0.187614	+	1.56234i
$279$	12.1663	+	21.0727i	0.728378	+	1.26159i
$280$	7.49728	−	9.10879i	0.448048	−	0.544354i
$281$	−25.2351			−1.50540			−0.752699	−	0.658365i	$-0.771248\pi$
$281$	−25.2351			−1.50540			−0.752699	+	0.658365i	$0.771248\pi$
$282$	−3.45113	−	4.60524i	−0.205512	−	0.274238i
$283$	10.2160	−	17.6946i	0.607277	−	1.05183i	−0.384411	−	0.923162i	$-0.625595\pi$
$283$	10.2160	−	17.6946i	0.607277	−	1.05183i	0.991687	−	0.128672i	$-0.0410713\pi$
$284$	4.24176	−	14.5012i	0.251702	−	0.860487i
$285$			12.5347i			0.742493i
$286$	−15.8973	−	5.76839i	−0.940030	−	0.341092i
$287$			9.09717i			0.536989i
$288$	−14.2734	+	1.05770i	−0.841069	+	0.0623259i
$289$	−1.68453	+	2.91770i	−0.0990902	+	0.171629i
$290$	−35.2475	+	26.4142i	−2.06980	+	1.55109i
$291$	11.2694			0.660625
$292$	1.45258	+	1.52029i	0.0850057	+	0.0889683i
$293$	−2.05715	−	3.56309i	−0.120180	−	0.208158i	0.799658	−	0.600455i	$-0.205014\pi$
$293$	−2.05715	−	3.56309i	−0.120180	−	0.208158i	−0.919839	+	0.392297i	$0.871681\pi$
$294$	5.12351	−	0.615260i	0.298809	−	0.0358827i
$295$	−23.6515	+	13.6552i	−1.37704	+	0.795036i
$296$	−0.890133	+	5.34376i	−0.0517379	+	0.310600i
$297$	9.46261	+	8.27811i	0.549076	+	0.480344i
$298$	−2.26015	−	18.8212i	−0.130927	−	1.09028i
$299$	−3.85874	−	15.0406i	−0.223156	−	0.869821i
$300$	−1.74470	−	7.15963i	−0.100730	−	0.413361i
$301$	9.91337	+	5.72348i	0.571397	+	0.329896i
$302$	0.683073	−	1.59739i	0.0393064	−	0.0919197i
$303$	−1.42865	−	2.47449i	−0.0820736	−	0.142156i
$304$	−10.4470	−	20.1626i	−0.599178	−	1.15640i
$305$	−5.78042	−	10.0120i	−0.330986	−	0.573285i
$306$	−7.92220	−	10.5715i	−0.452882	−	0.604332i
$307$		−	16.5746i		−	0.945965i	−0.881072	−	0.472983i	$-0.843177\pi$
$307$		−	16.5746i		−	0.945965i	0.881072	−	0.472983i	$-0.156823\pi$
$308$	7.24313	−	4.61706i	0.412716	−	0.263081i
$309$	−0.466035	+	0.807195i	−0.0265118	+	0.0459197i
$310$	17.2246	−	40.2804i	0.978292	−	2.28778i
$311$		−	11.6004i		−	0.657800i	−0.944365	−	0.328900i	$-0.893322\pi$
$311$		−	11.6004i		−	0.657800i	0.944365	−	0.328900i	$-0.106678\pi$
$312$	−5.73103	+	4.00278i	−0.324455	+	0.226613i
$313$	−0.990980			−0.0560135			−0.0280067	−	0.999608i	$-0.508916\pi$
$313$	−0.990980			−0.0560135			−0.0280067	+	0.999608i	$0.508916\pi$
$314$	−17.7369	−	7.58462i	−1.00095	−	0.428025i
$315$	5.27660	−	9.13934i	0.297303	−	0.514944i
$316$	2.91929	+	3.05537i	0.164223	+	0.171878i
$317$		−	27.2597i		−	1.53106i	−0.643401	−	0.765529i	$-0.722477\pi$
$317$		−	27.2597i		−	1.53106i	0.643401	−	0.765529i	$-0.277523\pi$
$318$	5.56036	+	7.41982i	0.311809	+	0.416083i
$319$	−30.3551	+	10.3454i	−1.69956	+	0.579234i
$320$	16.9347	+	19.4224i	0.946678	+	1.08575i
$321$	10.0834	−	5.82164i	0.562799	−	0.324932i
$322$	7.25151	+	3.10087i	0.404111	+	0.172805i
$323$	10.4799	−	18.1518i	0.583119	−	1.00999i
$324$	−9.69998	+	2.36374i	−0.538888	+	0.131319i
$325$	13.5573	+	13.8495i	0.752023	+	0.768232i
$326$	0.103066	+	0.858269i	0.00570828	+	0.0475351i
$327$	−7.13280	−	4.11812i	−0.394445	−	0.227733i
$328$	−19.6004	−	3.26492i	−1.08225	−	0.180275i
$329$	−6.65740	+	3.84365i	−0.367034	+	0.211907i
$330$	0.782365	−	10.3266i	0.0430678	−	0.568461i
$331$	4.42735	+	7.66840i	0.243349	+	0.421493i	0.961666	−	0.274223i	$-0.0884206\pi$
$331$	4.42735	+	7.66840i	0.243349	+	0.421493i	−0.718317	+	0.695716i	$0.755087\pi$
$332$	8.44179	−	8.06581i	0.463304	−	0.442669i
$333$			4.84604i			0.265561i
$334$	1.09522	+	1.46148i	0.0599279	+	0.0799687i
$335$	19.9389	+	11.5117i	1.08938	+	0.628952i
$336$	0.161655	−	3.54685i	0.00881899	−	0.193497i
$337$		−	2.14984i		−	0.117109i	−0.998284	−	0.0585547i	$-0.981351\pi$
$337$		−	2.14984i		−	0.117109i	0.998284	−	0.0585547i	$-0.0186492\pi$
$338$	7.58726	−	16.7461i	0.412693	−	0.910870i
$339$		−	0.883202i		−	0.0479690i
$340$	−6.67738	+	22.8278i	−0.362132	+	1.23801i
$341$	21.0016	−	24.0067i	1.13730	−	1.30003i
$342$	−12.1817	−	16.2555i	−0.658712	−	0.878995i
$343$		−	15.9575i		−	0.861627i
$344$	−15.8894	+	19.3048i	−0.856701	+	1.04085i
$345$	8.23485	−	4.75439i	0.443349	−	0.255968i
$346$	13.4454	−	1.61460i	0.722831	−	0.0868016i
$347$	−7.71374	−	13.3606i	−0.414095	−	0.717234i	0.581238	−	0.813734i	$-0.302569\pi$
$347$	−7.71374	−	13.3606i	−0.414095	−	0.717234i	−0.995333	+	0.0964996i	$0.969235\pi$
$348$	−3.72163	+	12.7230i	−0.199500	+	0.682026i
$349$	−2.03254	+	3.52046i	−0.108799	+	0.188446i	−0.915284	−	0.402809i	$-0.868034\pi$
$349$	−2.03254	+	3.52046i	−0.108799	+	0.188446i	0.806485	+	0.591255i	$0.201367\pi$
$350$	−9.77340	+	1.17364i	−0.522410	+	0.0627340i
$351$	−9.76705	+	9.56098i	−0.521327	+	0.510327i
$352$	7.34821	+	17.2628i	0.391661	+	0.920110i
$353$	−8.46639	−	4.88807i	−0.450621	−	0.260166i	0.257472	−	0.966286i	$-0.417111\pi$
$353$	−8.46639	−	4.88807i	−0.450621	−	0.260166i	−0.708092	+	0.706120i	$0.750444\pi$
$354$	−3.23165	+	7.55734i	−0.171760	+	0.401668i
$355$	−21.0732	+	12.1666i	−1.11845	+	0.645737i
$356$	−4.28111	−	17.5682i	−0.226898	−	0.931112i
$357$	2.83810	−	1.63858i	0.150208	−	0.0867227i
$358$	−2.96877	−	3.96157i	−0.156904	−	0.209375i
$359$		−	6.52829i		−	0.344550i	−0.985049	−	0.172275i	$-0.944888\pi$
$359$		−	6.52829i		−	0.344550i	0.985049	−	0.172275i	$-0.0551117\pi$
$360$	17.7975	+	14.6488i	0.938011	+	0.772060i
$361$	6.61468	−	11.4570i	0.348141	−	0.602998i
$362$	−12.2682	−	5.24609i	−0.644802	−	0.275729i
$363$	2.86852	−	6.97326i	0.150559	−	0.366001i
$364$	4.39597	+	8.23833i	0.230412	+	0.431806i
$365$		−	3.38643i		−	0.177254i
$366$	−3.19912	−	1.36800i	−0.167221	−	0.0715065i
$367$	−0.837220	−	0.483369i	−0.0437025	−	0.0252317i	0.477990	−	0.878366i	$-0.341366\pi$
$367$	−0.837220	−	0.483369i	−0.0437025	−	0.0252317i	−0.521692	+	0.853134i	$0.674699\pi$
$368$	−9.28353	+	14.5109i	−0.483937	+	0.756434i
$369$	−17.7748			−0.925320
$370$	6.98193	−	5.23220i	0.362973	−	0.272009i
$371$	10.7262	−	6.19276i	0.556876	−	0.321512i
$372$	−3.12155	−	12.8098i	−0.161845	−	0.664155i
$373$	9.33128	−	5.38742i	0.483156	−	0.278950i	−0.238575	−	0.971124i	$-0.576680\pi$
$373$	9.33128	−	5.38742i	0.483156	−	0.278950i	0.721731	+	0.692174i	$0.243347\pi$
$374$	−9.76674	+	14.3000i	−0.505026	+	0.739438i
$375$	−0.414234	+	0.717474i	−0.0213910	+	0.0370502i
$376$	−5.89207	−	15.7232i	−0.303860	−	0.810863i
$377$	−8.66377	−	33.7697i	−0.446207	−	1.73923i
$378$	−0.827687	−	6.89247i	−0.0425716	−	0.354511i
$379$	6.37071	−	11.0344i	0.327241	−	0.566798i	−0.654722	−	0.755870i	$-0.727214\pi$
$379$	6.37071	−	11.0344i	0.327241	−	0.566798i	0.981963	+	0.189071i	$0.0605477\pi$
$380$	−10.2676	+	35.1016i	−0.526717	+	1.80067i
$381$	−0.786509	+	0.454091i	−0.0402941	+	0.0232638i
$382$	−26.9124	+	3.23180i	−1.37696	+	0.165353i
$383$	13.7507	+	23.8168i	0.702626	+	1.21698i	0.967542	+	0.252712i	$0.0813225\pi$
$383$	13.7507	+	23.8168i	0.702626	+	1.21698i	−0.264916	+	0.964272i	$0.585344\pi$
$384$	7.58389	+	1.62124i	0.387014	+	0.0827336i
$385$	−13.5712	−	2.68229i	−0.691651	−	0.136702i
$386$	22.7531	−	17.0510i	1.15810	−	0.867874i
$387$	−11.1830	+	19.3696i	−0.568465	+	0.984610i
$388$	31.5583	+	9.23115i	1.60213	+	0.468640i
$389$	1.91166			0.0969251			0.0484625	−	0.998825i	$-0.484568\pi$
$389$	1.91166			0.0969251			0.0484625	+	0.998825i	$0.484568\pi$
$390$	11.1270	+	1.71524i	0.563435	+	0.0868543i
$391$	−15.9001			−0.804100
$392$	14.8516	+	2.47389i	0.750118	+	0.124950i
$393$	−1.11463	−	0.643535i	−0.0562259	−	0.0324620i
$394$	−16.9310	+	12.6879i	−0.852970	+	0.639209i
$395$		−	6.80580i		−	0.342437i
$396$	9.02119	+	14.1522i	0.453332	+	0.711177i
$397$	−0.329561	+	0.190272i	−0.0165402	+	0.00954949i	−0.508247	−	0.861211i	$-0.669706\pi$
$397$	−0.329561	+	0.190272i	−0.0165402	+	0.00954949i	0.491707	+	0.870761i	$0.336373\pi$
$398$	21.2087	−	2.54686i	1.06310	−	0.127662i
$399$	4.36406	−	2.51959i	0.218476	−	0.126137i
$400$	0.978928	−	21.4786i	0.0489464	−	1.07393i
$401$	6.93436	+	4.00355i	0.346285	+	0.199928i	0.663048	−	0.748577i	$-0.269263\pi$
$401$	6.93436	+	4.00355i	0.346285	+	0.199928i	−0.316763	+	0.948505i	$0.602596\pi$
$402$	6.87967	−	0.826149i	0.343127	−	0.0412046i
$403$	24.2562	+	24.7790i	1.20829	+	1.23433i
$404$	−1.97377	−	8.09968i	−0.0981989	−	0.402974i
$405$	13.9250	+	8.03963i	0.691941	+	0.399492i
$406$	16.2813	+	6.96218i	0.808029	+	0.345527i
$407$	6.01283	−	2.04926i	0.298045	−	0.101578i
$408$	2.51183	+	6.70293i	0.124354	+	0.331844i
$409$	−11.7755	−	20.3958i	−0.582261	−	1.00851i	−0.995211	−	0.0977516i	$-0.968835\pi$
$409$	−11.7755	−	20.3958i	−0.582261	−	1.00851i	0.412950	−	0.910754i	$-0.364498\pi$
$410$	19.1912	+	25.6090i	0.947787	+	1.26474i
$411$	12.8583			0.634255
$412$	−1.96626	+	1.87868i	−0.0968706	+	0.0925561i
$413$	9.50831	+	5.48962i	0.467873	+	0.270127i
$414$	−6.05874	+	14.1686i	−0.297771	+	0.696349i
$415$	−18.8040			−0.923052
$416$	−19.3277	+	6.51469i	−0.947617	+	0.319409i
$417$		−	12.7169i		−	0.622750i
$418$	−15.0180	+	21.9887i	−0.734556	+	1.07550i
$419$	−11.7922	−	6.80825i	−0.576089	−	0.332605i	0.183489	−	0.983022i	$-0.441261\pi$
$419$	−11.7922	−	6.80825i	−0.576089	−	0.332605i	−0.759577	+	0.650417i	$0.774594\pi$
$420$	−4.13443	+	3.95029i	−0.201740	+	0.192754i
$421$			12.5205i			0.610211i	0.952319	+	0.305106i	$0.0986917\pi$
$421$			12.5205i			0.610211i	−0.952319	+	0.305106i	$0.901308\pi$
$422$	6.58249	−	4.93287i	0.320430	−	0.240128i
$423$	−7.51005	−	13.0078i	−0.365151	−	0.632460i
$424$	9.49311	+	25.3327i	0.461026	+	1.23027i
$425$	17.1866	−	9.92268i	0.833672	−	0.481321i
$426$	−2.87936	+	6.73349i	−0.139505	+	0.326239i
$427$	−2.32383	+	4.02499i	−0.112458	+	0.194783i
$428$	33.0057	−	8.04299i	1.59539	−	0.388773i
$429$	7.31717	+	3.69473i	0.353276	+	0.178383i
$430$	39.9808	−	4.80112i	1.92805	−	0.231531i
$431$	20.1904	+	11.6569i	0.972536	+	0.561494i	0.900008	−	0.435873i	$-0.143560\pi$
$431$	20.1904	+	11.6569i	0.972536	+	0.561494i	0.0725273	+	0.997366i	$0.476894\pi$
$432$	15.1473	+	0.690367i	0.728774	+	0.0332153i
$433$	−4.43396	−	7.67984i	−0.213082	−	0.369069i	0.739595	−	0.673052i	$-0.235017\pi$
$433$	−4.43396	−	7.67984i	−0.213082	−	0.369069i	−0.952678	+	0.303982i	$0.901684\pi$
$434$	−17.4862	+	2.09984i	−0.839366	+	0.100796i
$435$	18.4892	−	10.6747i	0.886488	−	0.511814i
$436$	−16.6010	−	17.3749i	−0.795045	−	0.832106i
$437$	−24.4490			−1.16956
$438$	−0.611188	−	0.815578i	−0.0292037	−	0.0389698i
$439$	−10.4155	+	18.0401i	−0.497103	+	0.861008i	−0.999994	−	0.00334199i	$-0.998936\pi$
$439$	−10.4155	+	18.0401i	−0.497103	+	0.861008i	0.502891	+	0.864350i	$0.332270\pi$
$440$	10.6498	−	28.2772i	0.507707	−	1.34806i
$441$	13.4683			0.641348
$442$	−14.6791	−	11.7868i	−0.698213	−	0.560641i
$443$		−	13.3924i		−	0.636292i	−0.948042	−	0.318146i	$-0.896940\pi$
$443$		−	13.3924i		−	0.636292i	0.948042	−	0.318146i	$-0.103060\pi$
$444$	0.737192	−	2.52022i	0.0349856	−	0.119604i
$445$	−14.5610	+	25.2204i	−0.690259	+	1.19556i
$446$	−5.16066	+	3.86736i	−0.244364	+	0.183125i
$447$			9.18821i			0.434587i
$448$	3.35803	−	9.80001i	0.158652	−	0.463007i
$449$	−4.64147	+	2.67975i	−0.219044	+	0.126465i	−0.605508	−	0.795839i	$-0.707030\pi$
$449$	−4.64147	+	2.67975i	−0.219044	+	0.126465i	0.386463	+	0.922305i	$0.373697\pi$
$450$	−2.29317	−	19.0961i	−0.108101	−	0.900198i
$451$	7.51648	+	22.0545i	0.353937	+	1.03851i
$452$	0.723460	−	2.47327i	0.0340287	−	0.116333i
$453$	−0.421040	+	0.729263i	−0.0197822	+	0.0342638i
$454$	5.19287	−	0.623589i	0.243713	−	0.0292665i
$455$	4.04698	−	14.4841i	0.189725	−	0.679023i
$456$	3.86237	+	10.3069i	0.180872	+	0.482664i
$457$	−10.9835	+	19.0239i	−0.513785	+	0.889902i	0.486087	+	0.873910i	$0.338424\pi$
$457$	−10.9835	+	19.0239i	−0.513785	+	0.889902i	−0.999872	+	0.0159913i	$0.994910\pi$
$458$	7.51574	−	17.5758i	0.351187	−	0.821265i
$459$	6.99775	+	12.1205i	0.326627	+	0.565735i
$460$	26.9549	−	6.56852i	1.25678	−	0.306259i
$461$	6.93570	+	12.0130i	0.323028	+	0.559501i	0.981111	−	0.193444i	$-0.0619659\pi$
$461$	6.93570	+	12.0130i	0.323028	+	0.559501i	−0.658083	+	0.752945i	$0.728633\pi$
$462$	−3.75255	+	1.80335i	−0.174584	+	0.0838995i
$463$	−11.6058			−0.539369			−0.269685	−	0.962949i	$-0.586919\pi$
$463$	−11.6058			−0.539369			−0.269685	+	0.962949i	$0.586919\pi$
$464$	−20.8437	+	32.5804i	−0.967645	+	1.51251i
$465$	−10.6171	+	18.3894i	−0.492356	+	0.852786i
$466$	5.23684	−	12.2466i	0.242592	−	0.567311i
$467$			17.9521i			0.830725i	0.909656	+	0.415362i	$0.136345\pi$
$467$			17.9521i			0.830725i	−0.909656	+	0.415362i	$0.863655\pi$
$468$	−16.0967	+	8.58922i	−0.744072	+	0.397037i
$469$		−	9.25581i		−	0.427394i
$470$	−10.6324	+	24.8644i	−0.490438	+	1.14691i
$471$	8.09749	+	4.67509i	0.373113	+	0.215417i
$472$	−15.2402	+	18.5160i	−0.701487	+	0.852269i
$473$	28.7622	+	5.68473i	1.32249	+	0.261384i
$474$	−1.22832	−	1.63909i	−0.0564186	−	0.0752859i
$475$	26.4273	−	15.2578i	1.21257	−	0.700076i
$476$	9.28987	−	2.26381i	0.425801	−	0.103761i
$477$	12.0999	+	20.9577i	0.554018	+	0.959588i
$478$	14.1723	−	33.1426i	0.648228	−	1.51591i
$479$	6.74529	+	3.89439i	0.308200	+	0.177939i	0.646121	−	0.763235i	$-0.276390\pi$
$479$	6.74529	+	3.89439i	0.308200	+	0.177939i	−0.337921	+	0.941175i	$0.609724\pi$
$480$	−7.02731	−	10.3256i	−0.320751	−	0.471298i
$481$	1.71615	+	6.68921i	0.0782495	+	0.305002i
$482$	−5.17379	−	43.0841i	−0.235659	−	1.96243i
$483$	−3.31055	−	1.91135i	−0.150635	−	0.0869694i
$484$	13.7449	−	17.1778i	0.624768	−	0.780811i
$485$	−26.4777	−	45.8606i	−1.20229	−	2.08242i
$486$	20.7728	−	2.49451i	0.942272	−	0.113153i
$487$	7.28893	+	12.6248i	0.330293	+	0.572084i	0.982569	−	0.185897i	$-0.0595191\pi$
$487$	7.28893	+	12.6248i	0.330293	+	0.572084i	−0.652276	+	0.757981i	$0.726186\pi$
$488$	−7.83808	−	6.45138i	−0.354813	−	0.292040i
$489$		−	0.418994i		−	0.0189476i
$490$	−14.5415	−	19.4044i	−0.656920	−	0.876604i
$491$	17.6897	−	30.6394i	0.798324	−	1.38274i	−0.122383	−	0.992483i	$-0.539054\pi$
$491$	17.6897	−	30.6394i	0.798324	−	1.38274i	0.920707	−	0.390255i	$-0.127613\pi$
$492$	9.24392	+	2.70395i	0.416748	+	0.121903i
$493$	−35.6994			−1.60782
$494$	−22.5716	−	18.1242i	−1.01554	−	0.815446i
$495$	5.24087	−	26.5165i	0.235560	−	1.19183i
$496$	1.75146	−	38.4287i	0.0786431	−	1.72550i
$497$	8.47179	+	4.89119i	0.380012	+	0.219400i
$498$	−4.52870	+	3.39378i	−0.202936	+	0.152079i
$499$	21.2279			0.950293			0.475147	−	0.879907i	$-0.342395\pi$
$499$	21.2279			0.950293			0.475147	+	0.879907i	$0.342395\pi$
$500$	−1.74771	+	1.66986i	−0.0781598	+	0.0746786i
$501$	−0.442611	−	0.766625i	−0.0197744	−	0.0342503i
$502$	36.5884	−	4.39374i	1.63302	−	0.196102i
$503$	1.89804	+	3.28751i	0.0846296	+	0.146583i	0.905233	−	0.424915i	$-0.139696\pi$
$503$	1.89804	+	3.28751i	0.0846296	+	0.146583i	−0.820604	+	0.571498i	$0.806363\pi$
$504$	1.52263	−	9.14087i	0.0678235	−	0.407167i
$505$	−6.71325	+	11.6277i	−0.298736	+	0.517426i
$506$	20.1421	+	1.52600i	0.895425	+	0.0678392i
$507$	−4.61911	+	7.62053i	−0.205142	+	0.338440i
$508$	−2.57446	+	0.627358i	−0.114223	+	0.0278345i
$509$	−10.9693	−	6.33315i	−0.486207	−	0.280712i	0.236792	−	0.971560i	$-0.423904\pi$
$509$	−10.9693	−	6.33315i	−0.486207	−	0.280712i	−0.723000	+	0.690848i	$0.757237\pi$
$510$	4.53269	−	10.5999i	0.200711	−	0.469371i
$511$	−1.17901	+	0.680702i	−0.0521563	+	0.0301125i
$512$	19.9095	+	10.7522i	0.879885	+	0.475187i
$513$	10.7602	+	18.6373i	0.475076	+	0.822855i
$514$	0.0512993	−	0.0384433i	0.00226271	−	0.00169566i
$515$	4.37982			0.192998
$516$	8.76236	−	8.37209i	0.385741	−	0.368561i
$517$	−12.9639	+	14.8189i	−0.570152	+	0.651734i
$518$	−3.22506	−	1.37909i	−0.141701	−	0.0605937i
$519$	−6.56386			−0.288121
$520$	29.7543	+	13.9177i	1.30481	+	0.610332i
$521$	−27.3357			−1.19760			−0.598800	−	0.800899i	$-0.704356\pi$
$521$	−27.3357			−1.19760			−0.598800	+	0.800899i	$0.704356\pi$
$522$	−13.6033	+	31.8118i	−0.595400	+	1.39237i
$523$	3.35462	−	5.81038i	0.146687	−	0.254070i	−0.783314	−	0.621626i	$-0.786472\pi$
$523$	3.35462	−	5.81038i	0.146687	−	0.254070i	0.930001	+	0.367556i	$0.119806\pi$
$524$	−2.59422	−	2.71515i	−0.113329	−	0.118612i
$525$	4.77123			0.208234
$526$	25.1279	−	18.8307i	1.09563	−	0.821056i
$527$	30.7496	−	17.7533i	1.33948	−	0.773346i
$528$	−2.53866	−	8.73229i	−0.110481	−	0.380024i
$529$	−2.22654	−	3.85649i	−0.0968063	−	0.167673i
$530$	17.1307	−	40.0607i	0.744108	−	1.74013i
$531$	−10.7261	+	18.5781i	−0.465473	+	0.806222i
$532$	14.2848	−	3.48099i	0.619323	−	0.150920i
$533$	−24.5354	+	6.29466i	−1.06274	+	0.272652i
$534$	1.04499	+	8.70201i	0.0452210	+	0.376573i
$535$	−47.3821	−	27.3560i	−2.04851	−	1.18271i
$536$	19.9422	+	3.32186i	0.861371	+	0.143482i
$537$	1.19976	+	2.07805i	0.0517736	+	0.0896746i
$538$	3.12347	+	26.0104i	0.134663	+	1.12139i
$539$	−5.69538	−	16.7111i	−0.245317	−	0.719798i
$540$	−16.8702	−	17.6566i	−0.725978	−	0.759820i
$541$	−34.6210			−1.48847			−0.744237	−	0.667915i	$-0.767187\pi$
$541$	−34.6210			−1.48847			−0.744237	+	0.667915i	$0.767187\pi$
$542$	5.53104	+	7.38069i	0.237578	+	0.317028i
$543$	5.60084	+	3.23365i	0.240355	+	0.138769i
$544$	1.54342	+	20.8281i	0.0661737	+	0.892995i
$545$			38.7023i			1.65783i
$546$	−1.63944	−	4.21871i	−0.0701617	−	0.180544i
$547$	13.8420			0.591843			0.295922	−	0.955212i	$-0.404373\pi$
$547$	13.8420			0.591843			0.295922	+	0.955212i	$0.404373\pi$
$548$	36.0078	+	10.5327i	1.53818	+	0.449934i
$549$	−7.86437	−	4.54049i	−0.335643	−	0.193784i
$550$	−22.7242	+	10.9205i	−0.968962	+	0.465652i
$551$	−54.8938			−2.33856
$552$	5.30625	−	6.44681i	0.225849	−	0.274394i
$553$	−2.36949	+	1.36802i	−0.100761	+	0.0581743i
$554$	−22.1635	+	2.66152i	−0.941637	+	0.113077i
$555$	−3.66239	+	2.11448i	−0.155460	+	0.0897548i
$556$	10.4168	−	35.6118i	0.441772	−	1.51028i
$557$	−11.5327	+	19.9752i	−0.488656	+	0.846377i	−0.999915	−	0.0130497i	$-0.995846\pi$
$557$	−11.5327	+	19.9752i	−0.488656	+	0.846377i	0.511259	+	0.859427i	$0.329179\pi$
$558$	−4.10285	−	34.1661i	−0.173688	−	1.44636i
$559$	−8.57701	+	30.6970i	−0.362769	+	1.29834i
$560$	−14.8137	+	7.67554i	−0.625991	+	0.324351i
$561$	5.52661	−	6.31740i	0.233334	−	0.266721i
$562$	32.8136	+	14.0317i	1.38416	+	0.591889i
$563$	−7.34039	−	12.7139i	−0.309361	−	0.535828i	0.668862	−	0.743387i	$-0.266782\pi$
$563$	−7.34039	−	12.7139i	−0.309361	−	0.535828i	−0.978223	+	0.207558i	$0.933448\pi$
$564$	1.92688	+	7.90723i	0.0811362	+	0.332955i
$565$	−3.59417	+	2.07510i	−0.151208	+	0.0872999i
$566$	−23.1228	+	17.3281i	−0.971926	+	0.728354i
$567$		−	6.46414i		−	0.271468i
$568$	−13.5788	+	16.4975i	−0.569755	+	0.692222i
$569$	−1.53536	−	0.886442i	−0.0643658	−	0.0371616i	0.467472	−	0.884008i	$-0.345165\pi$
$569$	−1.53536	−	0.886442i	−0.0643658	−	0.0371616i	−0.531838	+	0.846846i	$0.678498\pi$
$570$	6.96978	−	16.2991i	0.291932	−	0.682695i
$571$	15.8727			0.664252			0.332126	−	0.943235i	$-0.392234\pi$
$571$	15.8727			0.664252			0.332126	+	0.943235i	$0.392234\pi$
$572$	17.4641	+	16.3403i	0.730212	+	0.683220i
$573$	13.1383			0.548858
$574$	5.05837	−	11.8292i	0.211132	−	0.493741i
$575$	−20.0476	−	11.5745i	−0.836043	−	0.482690i
$576$	19.1481	+	6.56121i	0.797837	+	0.273384i
$577$		−	13.8096i		−	0.574901i	−0.957795	−	0.287451i	$-0.907192\pi$
$577$		−	13.8096i		−	0.574901i	0.957795	−	0.287451i	$-0.0928077\pi$
$578$	3.81278	−	2.85727i	0.158591	−	0.118847i
$579$	−11.9352	+	6.89080i	−0.496011	+	0.286372i
$580$	60.5201	−	14.7479i	2.51296	−	0.612372i
$581$	3.77977	+	6.54675i	0.156811	+	0.271605i
$582$	−14.6538	−	6.26622i	−0.607420	−	0.259743i
$583$	20.8870	−	23.8757i	0.865052	−	0.988831i
$584$	−1.04347	−	2.78455i	−0.0431792	−	0.115225i
$585$	28.3002	+	7.90733i	1.17007	+	0.326928i
$586$	0.693735	+	5.77700i	0.0286579	+	0.238646i
$587$	18.8408	−	32.6332i	0.777643	−	1.34692i	−0.155653	−	0.987812i	$-0.549748\pi$
$587$	18.8408	−	32.6332i	0.777643	−	1.34692i	0.933297	−	0.359106i	$-0.116918\pi$
$588$	−7.00429	−	2.04883i	−0.288852	−	0.0844924i
$589$	47.2828	−	27.2987i	1.94825	−	1.12482i
$590$	38.3472	−	4.60495i	1.57873	−	0.189583i
$591$	8.88119	−	5.12756i	0.365324	−	0.210920i
$592$	4.12878	−	6.45363i	0.169692	−	0.265242i
$593$	−30.5205			−1.25333			−0.626663	−	0.779291i	$-0.715580\pi$
$593$	−30.5205			−1.25333			−0.626663	+	0.779291i	$0.715580\pi$
$594$	−7.70144	−	16.0257i	−0.315994	−	0.657543i
$595$	−13.3363	−	7.69972i	−0.546735	−	0.315658i
$596$	−7.52636	+	25.7302i	−0.308292	+	1.05395i
$597$	−10.3538			−0.423752
$598$	−3.34557	+	21.7032i	−0.136811	+	0.887508i
$599$			0.459313i			0.0187670i	0.999956	+	0.00938351i	$0.00298691\pi$
$599$			0.459313i			0.0187670i	−0.999956	+	0.00938351i	$0.997013\pi$
$600$	−1.71237	+	10.2799i	−0.0699071	+	0.419675i
$601$	−4.44259	−	2.56493i	−0.181217	−	0.104626i	0.406647	−	0.913585i	$-0.366698\pi$
$601$	−4.44259	−	2.56493i	−0.181217	−	0.104626i	−0.587864	+	0.808959i	$0.700031\pi$
$602$	−9.70804	−	12.9545i	−0.395670	−	0.527988i
$603$	18.0848			0.736469
$604$	−1.77642	+	1.69730i	−0.0722816	+	0.0690622i
$605$	−35.1171	+	4.71036i	−1.42772	+	0.191503i
$606$	0.481783	+	4.01200i	0.0195711	+	0.162976i
$607$	14.8394	+	25.7026i	0.602312	+	1.04324i	0.992470	+	0.122487i	$0.0390871\pi$
$607$	14.8394	+	25.7026i	0.602312	+	1.04324i	−0.390158	+	0.920748i	$0.627580\pi$
$608$	2.37327	+	32.0267i	0.0962490	+	1.29885i
$609$	−7.43297	−	4.29143i	−0.301199	−	0.173897i
$610$	1.94934	+	16.2329i	0.0789263	+	0.657250i
$611$	−14.9729	−	15.2957i	−0.605740	−	0.618796i
$612$	4.42321	+	18.1513i	0.178798	+	0.733724i
$613$	−0.558090	+	0.966641i	−0.0225411	+	0.0390422i	−0.877076	−	0.480352i	$-0.840509\pi$
$613$	−0.558090	+	0.966641i	−0.0225411	+	0.0390422i	0.854535	+	0.519394i	$0.173842\pi$
$614$	−9.21613	+	21.5523i	−0.371933	+	0.869779i
$615$	−7.75572	−	13.4333i	−0.312741	−	0.541683i
$616$	−11.9856	+	1.97618i	−0.482914	+	0.0796226i
$617$	3.12636	−	1.80501i	0.125863	−	0.0726668i	−0.435747	−	0.900069i	$-0.643516\pi$
$617$	3.12636	−	1.80501i	0.125863	−	0.0726668i	0.561609	+	0.827402i	$0.310182\pi$
$618$	1.05482	−	0.790477i	0.0424312	−	0.0317976i
$619$	3.08023			0.123805			0.0619024	−	0.998082i	$-0.480283\pi$
$619$	3.08023			0.123805			0.0619024	+	0.998082i	$0.480283\pi$
$620$	−44.7949	+	42.7998i	−1.79901	+	1.71888i
$621$	8.16266	−	14.1381i	0.327556	−	0.567344i
$622$	−6.45028	+	15.0842i	−0.258633	+	0.604823i
$623$	11.7076			0.469054
$624$	9.67784	−	2.01821i	0.387424	−	0.0807930i
$625$	−22.9831			−0.919324
$626$	1.28859	+	0.551022i	0.0515023	+	0.0220233i
$627$	8.49810	−	9.71408i	0.339381	−	0.387943i
$628$	18.8463	+	19.7248i	0.752048	+	0.787105i
$629$	7.07144			0.281957
$630$	−11.9431	+	8.95004i	−0.475823	+	0.356578i
$631$	−2.24893	−	3.89527i	−0.0895287	−	0.155068i	0.817783	−	0.575526i	$-0.195203\pi$
$631$	−2.24893	−	3.89527i	−0.0895287	−	0.155068i	−0.907312	+	0.420458i	$0.861869\pi$
$632$	−2.09709	−	5.59618i	−0.0834179	−	0.222604i
$633$	−3.45286	+	1.99351i	−0.137239	+	0.0792350i
$634$	−15.1574	+	35.4463i	−0.601979	+	1.40775i
$635$	3.69583	+	2.13379i	0.146664	+	0.0846767i
$636$	−3.10452	−	12.7399i	−0.123102	−	0.505169i
$637$	18.5909	−	4.76958i	0.736599	−	0.188978i
$638$	45.2237	+	3.42624i	1.79042	+	0.135646i
$639$	−9.55681	+	16.5529i	−0.378062	+	0.654822i
$640$	−11.2209	−	34.6716i	−0.443543	−	1.37052i
$641$	4.84490	+	8.39161i	0.191362	+	0.331449i	0.945702	−	0.325035i	$-0.105376\pi$
$641$	4.84490	+	8.39161i	0.191362	+	0.331449i	−0.754340	+	0.656484i	$0.772043\pi$
$642$	−16.3486	+	1.96324i	−0.645229	+	0.0774827i
$643$	−17.1862	−	29.7674i	−0.677759	−	1.17391i	−0.975654	−	0.219314i	$-0.929618\pi$
$643$	−17.1862	−	29.7674i	−0.677759	−	1.17391i	0.297896	−	0.954598i	$-0.403715\pi$
$644$	−7.70505	−	8.06422i	−0.303621	−	0.317775i
$645$	−19.5180			−0.768522
$646$	−23.7203	+	17.7758i	−0.933263	+	0.699380i
$647$	25.1355	+	14.5120i	0.988178	+	0.570525i	0.904729	−	0.425988i	$-0.140073\pi$
$647$	25.1355	+	14.5120i	0.988178	+	0.570525i	0.0834485	+	0.996512i	$0.473407\pi$
$648$	13.9274	+	2.31994i	0.547119	+	0.0911359i
$649$	27.5870	+	5.45245i	1.08288	+	0.214028i
$650$	−9.92792	−	25.5471i	−0.389405	−	1.00204i
$651$	8.53652			0.334572
$652$	0.343212	−	1.17333i	0.0134412	−	0.0459511i
$653$	11.6483	−	20.1755i	0.455834	−	0.789528i	−0.542902	−	0.839796i	$-0.682674\pi$
$653$	11.6483	−	20.1755i	0.455834	−	0.789528i	0.998736	+	0.0502686i	$0.0160077\pi$
$654$	6.98506	+	9.32096i	0.273137	+	0.364479i
$655$			6.04797i			0.236314i
$656$	23.6713	+	15.1440i	0.924209	+	0.591273i
$657$	−1.33001	−	2.30365i	−0.0518887	−	0.0898739i
$658$	10.7939	−	1.29620i	0.420791	−	0.0505310i
$659$	−9.71580	−	16.8283i	−0.378474	−	0.655536i	0.612367	−	0.790574i	$-0.290218\pi$
$659$	−9.71580	−	16.8283i	−0.378474	−	0.655536i	−0.990840	+	0.135038i	$0.956884\pi$
$660$	−6.75931	+	12.9928i	−0.263106	+	0.505745i
$661$	−11.2194	−	6.47750i	−0.436382	−	0.251945i	0.265680	−	0.964061i	$-0.414404\pi$
$661$	−11.2194	−	6.47750i	−0.436382	−	0.251945i	−0.702062	+	0.712116i	$0.747737\pi$
$662$	−1.49304	−	12.4331i	−0.0580286	−	0.483227i
$663$	6.38308	+	6.52066i	0.247898	+	0.253241i
$664$	−15.4619	+	5.79414i	−0.600038	+	0.224856i
$665$	−20.5068	−	11.8396i	−0.795221	−	0.459121i
$666$	2.69458	−	6.30139i	0.104413	−	0.244174i
$667$	20.8211	+	36.0632i	0.806196	+	1.39637i
$668$	−0.611497	−	2.50937i	−0.0236595	−	0.0970905i
$669$	2.70704	−	1.56291i	0.104660	−	0.0604256i
$670$	−19.5259	−	26.0556i	−0.754350	−	1.00662i
$671$	−2.30810	+	11.6779i	−0.0891030	+	0.450822i
$672$	−2.18239	+	4.52215i	−0.0841874	+	0.174446i
$673$	−18.7807	−	10.8431i	−0.723944	−	0.417969i	0.0922584	−	0.995735i	$-0.470591\pi$
$673$	−18.7807	−	10.8431i	−0.723944	−	0.417969i	−0.816203	+	0.577766i	$0.803925\pi$
$674$	−1.19539	+	2.79547i	−0.0460448	+	0.107678i
$675$			20.3761i			0.784278i
$676$	−19.1773	+	17.5565i	−0.737590	+	0.675249i
$677$		−	22.5095i		−	0.865112i	−0.901607	−	0.432556i	$-0.857612\pi$
$677$		−	22.5095i		−	0.865112i	0.901607	−	0.432556i	$-0.142388\pi$
$678$	−0.491094	+	1.14844i	−0.0188603	+	0.0441056i
$679$	−10.6445	+	18.4368i	−0.408498	+	0.707538i
$680$	21.3758	−	25.9705i	0.819725	−	0.995922i
$681$	−2.53508			−0.0971445
$682$	−40.6573	+	19.5386i	−1.55685	+	0.748171i
$683$	−18.9713	−	32.8592i	−0.725915	−	1.25732i	−0.958596	−	0.284769i	$-0.908083\pi$
$683$	−18.9713	−	32.8592i	−0.725915	−	1.25732i	0.232681	−	0.972553i	$-0.425250\pi$
$684$	6.80144	+	27.9108i	0.260060	+	1.06719i
$685$	−30.2108	−	52.3267i	−1.15430	−	1.99930i
$686$	−8.87300	+	20.7499i	−0.338773	+	0.792233i
$687$	−4.63263	+	8.02396i	−0.176746	+	0.306133i
$688$	31.3955	−	16.2672i	1.19694	−	0.620182i
$689$	24.1239	+	24.6439i	0.919048	+	0.938857i
$690$	−13.3515	+	1.60333i	−0.508284	+	0.0610376i
$691$	−20.2204	+	35.0228i	−0.769222	+	1.33233i	0.168764	+	0.985657i	$0.446022\pi$
$691$	−20.2204	+	35.0228i	−0.769222	+	1.33233i	−0.937986	+	0.346674i	$0.887311\pi$
$692$	−18.3811	−	5.37667i	−0.698744	−	0.204390i
$693$	−10.2854	+	3.50540i	−0.390709	+	0.133159i
$694$	2.60131	+	21.6621i	0.0987444	+	0.822283i
$695$	−51.7512	+	29.8786i	−1.96304	+	1.13336i
$696$	11.9138	−	14.4746i	0.451591	−	0.548659i
$697$			25.9374i			0.982447i
$698$	4.60045	−	3.44754i	0.174130	−	0.130491i
$699$	−3.22794	+	5.59096i	−0.122092	+	0.211469i
$700$	13.3611	+	3.90827i	0.505002	+	0.147719i
$701$			46.9262i			1.77238i	0.463322	+	0.886190i	$0.346657\pi$
$701$			46.9262i			1.77238i	−0.463322	+	0.886190i	$0.653343\pi$
$702$	18.0165	−	7.00145i	0.679990	−	0.264253i
$703$	10.8735			0.410103
$704$	0.0437697	−	26.5330i	0.00164963	−	0.999999i
$705$	6.55375	−	11.3514i	0.246828	−	0.427519i
$706$	8.29103	+	11.0637i	0.312037	+	0.416387i
$707$	5.39769			0.203001
$708$	8.40433	−	8.03001i	0.315854	−	0.301786i
$709$	10.5731	−	6.10436i	0.397080	−	0.229254i	−0.288143	−	0.957587i	$-0.593038\pi$
$709$	10.5731	−	6.10436i	0.397080	−	0.229254i	0.685223	+	0.728333i	$0.259705\pi$
$710$	34.1669	−	4.10295i	1.28226	−	0.153981i
$711$	−2.67296	−	4.62970i	−0.100244	−	0.173627i
$712$	−4.20178	+	25.2246i	−0.157468	+	0.945333i
$713$	−35.8685	−	20.7087i	−1.34329	−	0.775546i
$714$	−4.60154	+	0.552578i	−0.172208	+	0.0206797i
$715$	−2.15617	−	38.4579i	−0.0806361	−	1.43824i
$716$	1.65756	+	6.80204i	0.0619458	+	0.254204i
$717$	−8.73571	+	15.1307i	−0.326241	+	0.565066i
$718$	−3.62997	+	8.48884i	−0.135469	+	0.316801i
$719$	31.4196	−	18.1401i	1.17175	−	0.676513i	0.217662	−	0.976024i	$-0.430157\pi$
$719$	31.4196	−	18.1401i	1.17175	−	0.676513i	0.954093	+	0.299511i	$0.0968237\pi$
$720$	−14.9971	−	28.9442i	−0.558909	−	1.07869i
$721$	−0.880382	−	1.52487i	−0.0327871	−	0.0567890i
$722$	−14.9717	+	11.2197i	−0.557188	+	0.417552i
$723$			21.0330i			0.782227i
$724$	13.0355	+	13.6432i	0.484461	+	0.507044i
$725$	−45.0116	−	25.9875i	−1.67169	−	0.965150i
$726$	−7.60738	+	7.47243i	−0.282336	+	0.277328i
$727$		−	34.7342i		−	1.28822i	−0.764932	−	0.644110i	$-0.777228\pi$
$727$		−	34.7342i		−	1.28822i	0.764932	−	0.644110i	$-0.222772\pi$
$728$	−1.13533	−	13.1568i	−0.0420781	−	0.487622i
$729$	4.83480			0.179067
$730$	−1.88298	+	4.40343i	−0.0696923	+	0.162978i
$731$	28.2644	+	16.3185i	1.04540	+	0.603561i
$732$	3.39921	+	3.55766i	0.125638	+	0.131495i
$733$	12.7042			0.469241			0.234621	−	0.972087i	$-0.424615\pi$
$733$	12.7042			0.469241			0.234621	+	0.972087i	$0.424615\pi$
$734$	0.819879	+	1.09406i	0.0302623	+	0.0403824i
$735$	5.87666	+	10.1787i	0.216764	+	0.375446i
$736$	20.1401	−	13.7068i	0.742375	−	0.505239i
$737$	−7.64755	−	22.4391i	−0.281701	−	0.826554i
$738$	23.1129	+	9.88347i	0.850797	+	0.363815i
$739$	−35.5313	−	20.5140i	−1.30704	−	0.754620i	−0.325439	−	0.945563i	$-0.605512\pi$
$739$	−35.5313	−	20.5140i	−1.30704	−	0.754620i	−0.981601	+	0.190943i	$0.938845\pi$
$740$	−11.9880	+	2.92130i	−0.440688	+	0.107389i
$741$	9.81506	+	10.0266i	0.360565	+	0.368337i
$742$	−17.3908	+	2.08839i	−0.638438	+	0.0766672i
$743$	42.4585	+	24.5135i	1.55765	+	0.899311i	0.997481	+	0.0709352i	$0.0225984\pi$
$743$	42.4585	+	24.5135i	1.55765	+	0.899311i	0.560172	+	0.828376i	$0.310735\pi$
$744$	−3.06371	+	18.3924i	−0.112321	+	0.674299i
$745$	37.3912	−	21.5878i	1.36991	−	0.790917i
$746$	−15.1292	+	1.81680i	−0.553920	+	0.0665179i
$747$	−12.7916	+	7.38523i	−0.468020	+	0.270211i
$748$	20.6512	−	13.1639i	0.755083	−	0.481320i
$749$			21.9952i			0.803688i
$750$	0.937578	−	0.702614i	0.0342355	−	0.0256558i
$751$	−16.0089	−	9.24274i	−0.584173	−	0.337272i	0.178617	−	0.983919i	$-0.442838\pi$
$751$	−16.0089	−	9.24274i	−0.584173	−	0.337272i	−0.762790	+	0.646646i	$0.776171\pi$
$752$	−1.08115	+	23.7214i	−0.0394254	+	0.865029i
$753$	−17.8619			−0.650925
$754$	−7.51159	+	48.7287i	−0.273556	+	1.77459i
$755$	3.95696			0.144009
$756$	−2.75622	+	9.42262i	−0.100243	+	0.342697i
$757$	−12.5133	+	21.6737i	−0.454805	+	0.787745i	−0.998677	−	0.0514233i	$-0.983624\pi$
$757$	−12.5133	+	21.6737i	−0.454805	+	0.787745i	0.543872	+	0.839168i	$0.316958\pi$
$758$	−14.4195	+	10.8058i	−0.523739	+	0.392486i
$759$	−9.60509	−	1.89841i	−0.348643	−	0.0689078i
$760$	32.8690	−	39.9340i	1.19228	−	1.44856i
$761$	−13.8047	−	23.9104i	−0.500420	−	0.866753i	−1.00000		0.000484935i	$-0.999846\pi$
$761$	−13.8047	−	23.9104i	−0.500420	−	0.866753i	0.499580	−	0.866268i	$-0.333488\pi$
$762$	1.27520	−	0.153133i	0.0461957	−	0.00554744i
$763$	13.4745	−	7.77951i	0.487810	−	0.281637i
$764$	36.7917	+	10.7620i	1.33108	+	0.389354i
$765$	15.0444	−	26.0576i	0.543930	−	0.942114i
$766$	−4.63714	−	38.6153i	−0.167547	−	1.39523i
$767$	−8.22656	+	29.4427i	−0.297044	+	1.06311i
$768$	−8.95999	−	6.32505i	−0.323316	−	0.228236i
$769$	−16.1673	+	28.0025i	−0.583006	+	1.00980i	0.412115	+	0.911132i	$0.364790\pi$
$769$	−16.1673	+	28.0025i	−0.583006	+	1.00980i	−0.995121	+	0.0986643i	$0.968543\pi$
$770$	16.1554	+	11.0339i	0.582199	+	0.397634i
$771$	−0.0269092	+	0.0155360i	−0.000969112	+	0.000559517i
$772$	−39.0673	+	9.52012i	−1.40606	+	0.342636i
$773$	2.50003	−	1.44339i	0.0899197	−	0.0519151i	−0.454366	−	0.890815i	$-0.650134\pi$
$773$	2.50003	−	1.44339i	0.0899197	−	0.0519151i	0.544286	+	0.838900i	$0.316801\pi$
$774$	25.3117	−	18.9684i	0.909809	−	0.681804i
$775$	51.6943			1.85692
$776$	−35.9029	−	29.5510i	−1.28884	−	1.06082i
$777$	1.47235	+	0.850059i	0.0528201	+	0.0304957i
$778$	−2.48576	−	1.06296i	−0.0891189	−	0.0381088i
$779$			39.8831i			1.42896i
$780$	−13.5148	−	8.41735i	−0.483908	−	0.301390i
$781$	24.5797	+	4.85807i	0.879530	+	0.173835i
$782$	20.6751	+	8.84103i	0.739340	+	0.316155i
$783$	18.3271	−	31.7434i	0.654956	−	1.13442i
$784$	−17.9362	−	11.4749i	−0.640578	−	0.409817i
$785$		−	43.9368i		−	1.56817i
$786$	1.09155	+	1.45658i	0.0389342	+	0.0519544i
$787$	−33.3159	+	19.2349i	−1.18758	+	0.685652i	−0.957757	−	0.287580i	$-0.907149\pi$
$787$	−33.3159	+	19.2349i	−1.18758	+	0.685652i	−0.229827	+	0.973232i	$0.573816\pi$
$788$	29.0706	−	7.08407i	1.03560	−	0.252360i
$789$	−13.1809	+	7.61001i	−0.469254	+	0.270924i
$790$	−3.78428	+	8.84969i	−0.134639	+	0.314858i
$791$	1.44492	+	0.834224i	0.0513754	+	0.0296616i
$792$	−3.86123	−	23.4185i	−0.137203	−	0.832140i
$793$	−12.4635	−	3.48241i	−0.442591	−	0.123664i
$794$	0.534332	−	0.0641656i	0.0189627	−	0.00227715i
$795$	−10.5592	+	18.2890i	−0.374496	+	0.648645i
$796$	−28.9941	−	8.48111i	−1.02767	−	0.300605i
$797$	8.43847	+	14.6159i	0.298906	+	0.517720i	0.975886	−	0.218281i	$-0.0700450\pi$
$797$	8.43847	+	14.6159i	0.298906	+	0.517720i	−0.676980	+	0.736001i	$0.736712\pi$
$798$	−7.07564	+	0.849683i	−0.250475	+	0.0300784i
$799$	−18.9812	+	10.9588i	−0.671507	+	0.387695i
$800$	−13.2158	+	27.3846i	−0.467250	+	0.968193i
$801$			22.8752i			0.808256i
$802$	−6.79073	−	9.06165i	−0.239789	−	0.319978i
$803$	−2.29588	+	2.62439i	−0.0810198	+	0.0926128i
$804$	−9.40511	−	2.75110i	−0.331693	−	0.0970238i
$805$			17.9630i			0.633111i
$806$	−17.7627	−	45.7080i	−0.625664	−	1.60999i
$807$		−	12.6979i		−	0.446987i
$808$	−1.93720	+	11.6296i	−0.0681504	+	0.409129i
$809$	−10.4919	−	6.05749i	−0.368875	−	0.212970i	0.304092	−	0.952643i	$-0.401647\pi$
$809$	−10.4919	−	6.05749i	−0.368875	−	0.212970i	−0.672967	+	0.739673i	$0.734980\pi$
$810$	−13.6366	−	18.1969i	−0.479142	−	0.639374i
$811$		−	17.4590i		−	0.613069i	−0.951859	−	0.306535i	$-0.900830\pi$
$811$		−	17.4590i		−	0.613069i	0.951859	−	0.306535i	$-0.0991695\pi$
$812$	−17.2997	−	18.1061i	−0.607099	−	0.635399i
$813$	−2.23525	−	3.87157i	−0.0783936	−	0.135782i
$814$	−8.95805	−	0.678680i	−0.313979	−	0.0237877i
$815$	−1.70509	+	0.984433i	−0.0597266	+	0.0344832i
$816$	0.460901	−	10.1126i	0.0161348	−	0.354012i
$817$	43.4614	+	25.0924i	1.52052	+	0.877873i
$818$	3.97106	+	33.0686i	0.138845	+	1.15621i
$819$	−2.93559	−	11.4424i	−0.102578	−	0.399828i
$820$	−10.7151	−	43.9709i	−0.374186	−	1.53553i
$821$	21.2342	−	36.7787i	0.741079	−	1.28359i	−0.210925	−	0.977502i	$-0.567648\pi$
$821$	21.2342	−	36.7787i	0.741079	−	1.28359i	0.952004	−	0.306085i	$-0.0990191\pi$
$822$	−16.7199	−	7.14972i	−0.583173	−	0.249375i
$823$	−2.54772	+	1.47093i	−0.0888079	+	0.0512733i	−0.543746	−	0.839250i	$-0.682995\pi$
$823$	−2.54772	+	1.47093i	−0.0888079	+	0.0512733i	0.454938	+	0.890523i	$0.349661\pi$
$824$	3.60138	−	1.34957i	0.125460	−	0.0470145i
$825$	11.5670	−	3.94220i	0.402712	−	0.137250i
$826$	−9.31137	−	12.4252i	−0.323984	−	0.432329i
$827$		−	22.9904i		−	0.799456i	−0.916634	−	0.399728i	$-0.869105\pi$
$827$		−	22.9904i		−	0.799456i	0.916634	−	0.399728i	$-0.130895\pi$
$828$	15.7566	−	15.0548i	0.547578	−	0.523190i
$829$	7.46575	−	12.9311i	0.259296	−	0.449114i	−0.706757	−	0.707456i	$-0.749843\pi$
$829$	7.46575	−	12.9311i	0.259296	−	0.449114i	0.966054	+	0.258342i	$0.0831760\pi$
$830$	24.4511	+	10.4557i	0.848712	+	0.362924i
$831$	10.8199			0.375338
$832$	28.7545	+	2.27575i	0.996883	+	0.0788975i
$833$		−	19.6532i		−	0.680944i
$834$	−7.07109	+	16.5360i	−0.244852	+	0.572595i
$835$	−2.07984	+	3.60239i	−0.0719759	+	0.124666i
$836$	31.7547	−	20.2417i	1.09826	−	0.700075i
$837$			36.4563i			1.26011i
$838$	11.5480	+	15.4098i	0.398919	+	0.532323i
$839$	3.77437	+	6.53740i	0.130306	+	0.225696i	0.923794	−	0.382889i	$-0.125071\pi$
$839$	3.77437	+	6.53740i	0.130306	+	0.225696i	−0.793489	+	0.608585i	$0.791737\pi$
$840$	7.57258	−	2.83772i	0.261279	−	0.0979108i
$841$	32.2483	+	55.8556i	1.11201	+	1.92606i
$842$	6.96186	−	16.2806i	0.239922	−	0.561066i
$843$	−14.9805	−	8.64899i	−0.515955	−	0.297887i
$844$	−11.3022	+	2.75417i	−0.389037	+	0.0948026i
$845$	41.8642	+	0.892801i	1.44017	+	0.0307133i
$846$	2.53262	+	21.0901i	0.0870732	+	0.725093i
$847$	8.69880	+	11.2795i	0.298894	+	0.387567i
$848$	1.74191	−	38.2191i	0.0598174	−	1.31245i
$849$	12.1292	−	7.00278i	0.416272	−	0.240335i
$850$	−27.8654	+	3.34623i	−0.955775	+	0.114775i
$851$	−4.12430	−	7.14351i	−0.141379	−	0.244876i
$852$	7.48815	−	7.15464i	0.256540	−	0.245114i
$853$	−23.2173			−0.794947			−0.397473	−	0.917614i	$-0.630113\pi$
$853$	−23.2173			−0.794947			−0.397473	+	0.917614i	$0.630113\pi$
$854$	5.25976	−	3.94163i	0.179985	−	0.134880i
$855$	23.1332	−	40.0680i	0.791140	−	1.37030i
$856$	−47.3900	−	7.89395i	−1.61976	−	0.269810i
$857$		−	12.4973i		−	0.426900i	−0.976954	−	0.213450i	$-0.931530\pi$
$857$		−	12.4973i		−	0.426900i	0.976954	−	0.213450i	$-0.0684701\pi$
$858$	−7.46022	−	8.87294i	−0.254688	−	0.302917i
$859$			24.0064i			0.819088i	0.912290	+	0.409544i	$0.134312\pi$
$859$			24.0064i			0.819088i	−0.912290	+	0.409544i	$0.865688\pi$
$860$	−54.6573	−	15.9879i	−1.86380	−	0.545182i
$861$	−3.11793	+	5.40042i	−0.106259	+	0.184046i
$862$	−19.7722	−	26.3843i	−0.673443	−	0.898652i
$863$	−20.8700			−0.710422			−0.355211	−	0.934786i	$-0.615591\pi$
$863$	−20.8700			−0.710422			−0.355211	+	0.934786i	$0.615591\pi$
$864$	−19.3124	−	9.32016i	−0.657021	−	0.317078i
$865$	15.4219	+	26.7115i	0.524360	+	0.908218i
$866$	1.49527	+	12.4517i	0.0508112	+	0.423125i
$867$	−2.00000	+	1.15470i	−0.0679237	+	0.0392158i
$868$	23.9052	+	6.99254i	0.811396	+	0.237342i
$869$	−4.61409	+	5.27431i	−0.156522	+	0.178919i
$870$	−29.9773	+	3.59985i	−1.01633	+	0.122046i
$871$	24.9632	−	6.40443i	0.845846	−	0.217006i
$872$	11.9255	+	31.8236i	0.403848	+	1.07768i
$873$	−36.0233	−	20.7981i	−1.21920	−	0.703908i
$874$	31.7915	+	13.5946i	1.07536	+	0.459844i
$875$	−0.782526	−	1.35537i	−0.0264542	−	0.0458200i
$876$	0.341246	+	1.40035i	0.0115296	+	0.0473136i
$877$	6.85628	+	11.8754i	0.231520	+	0.401004i	0.958256	−	0.285913i	$-0.0922968\pi$
$877$	6.85628	+	11.8754i	0.231520	+	0.401004i	−0.726736	+	0.686917i	$0.758963\pi$
$878$	23.5744	−	17.6665i	0.795597	−	0.596214i
$879$		−	2.82025i		−	0.0951246i
$880$	−29.5713	+	30.8477i	−0.996847	+	1.03988i
$881$	3.59517	−	6.22702i	0.121124	−	0.209794i	−0.799087	−	0.601216i	$-0.794683\pi$
$881$	3.59517	−	6.22702i	0.121124	−	0.209794i	0.920211	+	0.391422i	$0.128017\pi$
$882$	−17.5131	−	7.48889i	−0.589696	−	0.252164i
$883$			45.1512i			1.51946i	0.650239	+	0.759729i	$0.274669\pi$
$883$			45.1512i			1.51946i	−0.650239	+	0.759729i	$0.725331\pi$
$884$	12.5336	+	23.4887i	0.421549	+	0.790010i
$885$	−18.7205			−0.629284
$886$	−7.44668	+	17.4143i	−0.250176	+	0.585046i
$887$	−22.4120	+	38.8187i	−0.752521	+	1.30340i	0.194077	+	0.980986i	$0.437829\pi$
$887$	−22.4120	+	38.8187i	−0.752521	+	1.30340i	−0.946597	+	0.322418i	$0.895504\pi$
$888$	−2.35992	+	2.86717i	−0.0791937	+	0.0962160i
$889$		−	1.71564i		−	0.0575407i
$890$	32.9574	−	24.6981i	1.10474	−	0.827881i
$891$	−5.34096	−	15.6712i	−0.178929	−	0.525004i
$892$	8.86089	−	2.15927i	0.296685	−	0.0722977i
$893$	−29.1868	+	16.8510i	−0.976700	+	0.563898i
$894$	5.10899	−	11.9476i	0.170870	−	0.399587i
$895$	5.63773	−	9.76483i	0.188448	−	0.326402i
$896$	−9.81568	+	10.8759i	−0.327919	+	0.363339i
$897$	2.86428	−	10.2512i	0.0956355	−	0.342278i
$898$	7.52542	−	0.903695i	0.251127	−	0.0301567i
$899$	−80.5332	−	46.4959i	−2.68593	−	1.55072i
$900$	−7.63630	+	26.1060i	−0.254543	+	0.870201i
$901$	30.5819	−	17.6565i	1.01883	−	0.588222i
$902$	2.48933	−	32.8573i	0.0828857	−	1.09403i
$903$	3.92330	+	6.79535i	0.130559	+	0.226135i
$904$	−2.31596	+	2.81377i	−0.0770277	+	0.0935845i
$905$		−	30.3900i		−	1.01020i
$906$	0.952983	−	0.714158i	0.0316607	−	0.0237263i
$907$	−9.21795	−	5.32198i	−0.306077	−	0.176714i	0.339093	−	0.940753i	$-0.389880\pi$
$907$	−9.21795	−	5.32198i	−0.306077	−	0.176714i	−0.645170	+	0.764039i	$0.723213\pi$
$908$	−7.09911	−	2.07657i	−0.235592	−	0.0689133i
$909$			10.5465i			0.349804i
$910$	−13.3160	+	16.5836i	−0.441422	+	0.549741i
$911$		−	4.35218i		−	0.144194i	−0.997398	−	0.0720972i	$-0.977031\pi$
$911$		−	4.35218i		−	0.144194i	0.997398	−	0.0720972i	$-0.0229692\pi$
$912$	0.708714	−	15.5498i	0.0234679	−	0.514906i
$913$	14.5726	+	12.7484i	0.482282	+	0.421912i
$914$	24.8600	−	18.6299i	0.822296	−	0.616222i
$915$		−	7.92465i		−	0.261981i
$916$	−19.5457	+	18.6751i	−0.645807	+	0.617044i
$917$	2.10565	−	1.21570i	0.0695346	−	0.0401458i
$918$	−2.35986	−	19.6514i	−0.0778868	−	0.648594i
$919$	2.99709	+	5.19112i	0.0988650	+	0.171239i	0.911215	−	0.411931i	$-0.135145\pi$
$919$	2.99709	+	5.19112i	0.0988650	+	0.171239i	−0.812350	+	0.583170i	$0.801812\pi$
$920$	−38.7023	−	6.44680i	−1.27598	−	0.212545i
$921$	5.68074	−	9.83933i	0.187187	−	0.324217i
$922$	−2.33893	−	19.4772i	−0.0770286	−	0.641447i
$923$	−7.32976	+	26.2331i	−0.241262	+	0.863472i
$924$	5.88223	−	0.258371i	0.193511	−	0.00849978i
$925$	8.91604	+	5.14768i	0.293157	+	0.169255i
$926$	15.0913	+	6.45329i	0.495930	+	0.212068i
$927$	2.97941	−	1.72016i	0.0978567	−	0.0564976i
$928$	45.2194	−	30.7750i	1.48440	−	1.01024i
$929$	−8.16493	+	4.71403i	−0.267883	+	0.154662i	−0.627925	−	0.778274i	$-0.716096\pi$
$929$	−8.16493	+	4.71403i	−0.267883	+	0.154662i	0.360042	+	0.932936i	$0.382762\pi$
$930$	24.0308	−	18.0085i	0.788000	−	0.590521i
$931$		−	30.2202i		−	0.990426i
$932$	−13.6191	+	13.0125i	−0.446108	+	0.426239i
$933$	3.97589	−	6.88645i	0.130165	−	0.225452i
$934$	9.98205	−	23.3434i	0.326623	−	0.763820i
$935$	−38.6934	−	7.64758i	−1.26541	−	0.250103i
$936$	25.7068	−	2.21830i	0.840253	−	0.0725075i
$937$		−	26.2484i		−	0.857498i	−0.903424	−	0.428749i	$-0.858955\pi$
$937$		−	26.2484i		−	0.857498i	0.903424	−	0.428749i	$-0.141045\pi$
$938$	−5.14658	+	12.0355i	−0.168042	+	0.392972i
$939$	−0.588283	−	0.339645i	−0.0191979	−	0.0110839i
$940$	27.6511	−	26.4195i	0.901879	−	0.861710i
$941$	9.07272			0.295762			0.147881	−	0.989005i	$-0.452755\pi$
$941$	9.07272			0.295762			0.147881	+	0.989005i	$0.452755\pi$
$942$	−7.92978	−	10.5816i	−0.258366	−	0.344767i
$943$	26.2017	−	15.1276i	0.853245	−	0.492621i
$944$	30.1127	−	15.6026i	0.980084	−	0.507820i
$945$	13.6930	−	7.90565i	0.445433	−	0.257171i
$946$	−34.2390	−	23.3848i	−1.11321	−	0.760306i
$947$	−10.7999	+	18.7059i	−0.350948	+	0.607860i	−0.986416	−	0.164267i	$-0.947474\pi$
$947$	−10.7999	+	18.7059i	−0.350948	+	0.607860i	0.635468	+	0.772128i	$0.280807\pi$
$948$	0.685810	+	2.81433i	0.0222741	+	0.0914051i
$949$	−2.65167	−	2.70883i	−0.0860770	−	0.0879323i
$950$	−42.8478	+	5.14540i	−1.39016	+	0.166939i
$951$	9.34291	−	16.1824i	0.302964	−	0.524750i
$952$	−13.3385	−	2.22186i	−0.432304	−	0.0720108i
$953$	5.82462	−	3.36285i	0.188678	−	0.108933i	−0.402686	−	0.915338i	$-0.631923\pi$
$953$	5.82462	−	3.36285i	0.188678	−	0.108933i	0.591364	+	0.806405i	$0.298590\pi$
$954$	−4.08047	−	33.9797i	−0.132110	−	1.10013i
$955$	−30.8685	−	53.4658i	−0.998882	−	1.73011i
$956$	−36.8571	+	35.2155i	−1.19204	+	1.13895i
$957$	−21.5657	−	4.26237i	−0.697120	−	0.137783i
$958$	−6.60558	−	8.81457i	−0.213416	−	0.284786i
$959$	−12.1453	+	21.0362i	−0.392192	+	0.679296i
$960$	3.39629	+	17.3340i	0.109615	+	0.559453i
$961$	61.4897			1.98354
$962$	1.48792	−	9.65233i	0.0479724	−	0.311203i
$963$	−42.9761			−1.38489
$964$	−17.2288	+	58.8998i	−0.554904	+	1.89704i
$965$	56.0839	+	32.3801i	1.80541	+	1.04235i
$966$	3.24198	+	4.32615i	0.104309	+	0.139192i
$967$			36.1905i			1.16381i	0.813258	+	0.581903i	$0.197692\pi$
$967$			36.1905i			1.16381i	−0.813258	+	0.581903i	$0.802308\pi$
$968$	−27.4242	+	14.6939i	−0.881448	+	0.472281i
$969$	12.4426	−	7.18372i	0.399713	−	0.230774i
$970$	8.92908	+	74.3559i	0.286695	+	2.38742i
$971$	22.8380	−	13.1855i	0.732905	−	0.423143i	−0.0865787	−	0.996245i	$-0.527593\pi$
$971$	22.8380	−	13.1855i	0.732905	−	0.423143i	0.819484	+	0.573102i	$0.194260\pi$
$972$	−28.3982	−	8.30679i	−0.910873	−	0.266440i
$973$	20.8049	+	12.0117i	0.666974	+	0.385078i
$974$	−2.45805	−	20.4692i	−0.0787610	−	0.655874i
$975$	3.30138	+	12.8682i	0.105729	+	0.412111i
$976$	6.60477	+	12.7471i	0.211413	+	0.408025i
$977$	43.0842	+	24.8747i	1.37839	+	0.795812i	0.991965	−	0.126511i	$-0.0403777\pi$
$977$	43.0842	+	24.8747i	1.37839	+	0.795812i	0.386421	+	0.922322i	$0.373711\pi$
$978$	−0.232977	+	0.544825i	−0.00744977	+	0.0174216i
$979$	28.3829	−	9.67330i	0.907123	−	0.309160i
$980$	8.11900	+	33.3176i	0.259352	+	1.06429i
$981$	15.2003	+	26.3276i	0.485307	+	0.840576i
$982$	−40.0388	+	30.0048i	−1.27769	+	0.957492i
$983$	0.236712			0.00754993			0.00377497	−	0.999993i	$-0.498798\pi$
$983$	0.236712			0.00754993			0.00377497	+	0.999993i	$0.498798\pi$
$984$	−10.5165	−	8.65595i	−0.335254	−	0.275942i
$985$	−41.7330	−	24.0945i	−1.32972	−	0.767716i
$986$	46.4205	+	19.8502i	1.47833	+	0.632159i
$987$	−5.26944			−0.167728
$988$	19.2725	+	36.1178i	0.613139	+	1.14906i
$989$		−	38.0700i		−	1.21056i
$990$	−21.5590	+	31.5657i	−0.685189	+	1.00322i
$991$	32.4565	+	18.7388i	1.03102	+	0.595257i	0.917276	−	0.398253i	$-0.130383\pi$
$991$	32.4565	+	18.7388i	1.03102	+	0.595257i	0.113741	+	0.993510i	$0.463717\pi$
$992$	−23.6453	+	48.9956i	−0.750738	+	1.55561i
$993$			6.06966i			0.192615i
$994$	−8.29632	−	11.0707i	−0.263143	−	0.351142i
$995$	24.3263	+	42.1344i	0.771196	+	1.33575i
$996$	7.77581	−	1.89485i	0.246386	−	0.0600407i
$997$	−6.54003	+	3.77589i	−0.207125	+	0.119584i	−0.599975	−	0.800019i	$-0.704823\pi$
$997$	−6.54003	+	3.77589i	−0.207125	+	0.119584i	0.392850	+	0.919603i	$0.371489\pi$
$998$	−27.6030	−	11.8035i	−0.873759	−	0.373635i
$999$	−3.63028	+	6.28784i	−0.114857	+	0.198938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.s.a.43.11	✓	160
4.3	odd	2	inner	572.2.s.a.43.64	yes	160
11.10	odd	2	inner	572.2.s.a.43.70	yes	160
13.10	even	6	inner	572.2.s.a.439.17	yes	160
44.43	even	2	inner	572.2.s.a.43.17	yes	160
52.23	odd	6	inner	572.2.s.a.439.70	yes	160
143.10	odd	6	inner	572.2.s.a.439.64	yes	160
572.439	even	6	inner	572.2.s.a.439.11	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.s.a.43.11	✓	160	1.1	even	1	trivial
572.2.s.a.43.17	yes	160	44.43	even	2	inner
572.2.s.a.43.64	yes	160	4.3	odd	2	inner
572.2.s.a.43.70	yes	160	11.10	odd	2	inner
572.2.s.a.439.11	yes	160	572.439	even	6	inner
572.2.s.a.439.17	yes	160	13.10	even	6	inner
572.2.s.a.439.64	yes	160	143.10	odd	6	inner
572.2.s.a.439.70	yes	160	52.23	odd	6	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)

\(f(q)\)	\(=\)	\(q+(-1.30032 - 0.556038i) q^{2} +(0.593637 + 0.342737i) q^{3} +(1.38164 + 1.44605i) q^{4} -3.22106i q^{5} +(-0.581342 - 0.775751i) q^{6} +(-1.12143 + 0.647461i) q^{7} +(-0.992516 - 2.64857i) q^{8} +(-1.26506 - 2.19115i) q^{9} +O(q^{10})\)	\(q+(-1.30032 - 0.556038i) q^{2} +(0.593637 + 0.342737i) q^{3} +(1.38164 + 1.44605i) q^{4} -3.22106i q^{5} +(-0.581342 - 0.775751i) q^{6} +(-1.12143 + 0.647461i) q^{7} +(-0.992516 - 2.64857i) q^{8} +(-1.26506 - 2.19115i) q^{9} +(-1.79103 + 4.18839i) q^{10} +(-2.18376 + 2.49623i) q^{11} +(0.324581 + 1.33197i) q^{12} +(-2.52218 - 2.57655i) q^{13} +(1.81823 - 0.218344i) q^{14} +(1.10398 - 1.91214i) q^{15} +(-0.182119 + 3.99585i) q^{16} +(-3.19737 + 1.84600i) q^{17} +(0.426618 + 3.55262i) q^{18} +(-4.91650 + 2.83855i) q^{19} +(4.65781 - 4.45036i) q^{20} -0.887634 q^{21} +(4.22758 - 2.03164i) q^{22} +(3.72964 + 2.15331i) q^{23} +(0.318567 - 1.91246i) q^{24} -5.37522 q^{25} +(1.84698 + 4.75275i) q^{26} -3.79075i q^{27} +(-2.48568 - 0.727090i) q^{28} +(8.37391 + 4.83468i) q^{29} +(-2.49874 + 1.87254i) q^{30} -9.61716 q^{31} +(2.45866 - 5.09461i) q^{32} +(-2.15191 + 0.733402i) q^{33} +(5.18404 - 0.622529i) q^{34} +(2.08551 + 3.61221i) q^{35} +(1.42065 - 4.85674i) q^{36} +(-1.65873 - 0.957668i) q^{37} +(7.97135 - 0.957244i) q^{38} +(-0.614186 - 2.39398i) q^{39} +(-8.53119 + 3.19695i) q^{40} +(3.51263 - 6.08406i) q^{41} +(1.15421 + 0.493558i) q^{42} +(-4.41995 - 7.65557i) q^{43} +(-6.62686 + 0.291078i) q^{44} +(-7.05783 + 4.07484i) q^{45} +(-3.65239 - 4.87380i) q^{46} +5.93650 q^{47} +(-1.47764 + 2.30967i) q^{48} +(-2.66159 + 4.61001i) q^{49} +(6.98949 + 2.98883i) q^{50} -2.53077 q^{51} +(0.241052 - 7.20707i) q^{52} -9.56469 q^{53} +(-2.10780 + 4.92918i) q^{54} +(8.04052 + 7.03403i) q^{55} +(2.82789 + 2.32758i) q^{56} -3.89149 q^{57} +(-8.20047 - 10.9428i) q^{58} +(-4.23935 - 7.34277i) q^{59} +(4.29035 - 1.04550i) q^{60} +(3.10829 - 1.79457i) q^{61} +(12.5053 + 5.34750i) q^{62} +(2.83737 + 1.63816i) q^{63} +(-6.02982 + 5.25749i) q^{64} +(-8.29921 + 8.12410i) q^{65} +(3.20597 + 0.242891i) q^{66} +(-3.57389 + 6.19016i) q^{67} +(-7.08705 - 2.07304i) q^{68} +(1.47603 + 2.55657i) q^{69} +(-0.703298 - 5.85663i) q^{70} +(-3.77721 - 6.54232i) q^{71} +(-4.54782 + 5.52536i) q^{72} +1.05134 q^{73} +(1.62437 + 2.16759i) q^{74} +(-3.19093 - 1.84229i) q^{75} +(-10.8975 - 3.18765i) q^{76} +(0.832734 - 4.21326i) q^{77} +(-0.532507 + 3.45444i) q^{78} +2.11291 q^{79} +(12.8709 + 0.586615i) q^{80} +(-2.49596 + 4.32313i) q^{81} +(-7.95050 + 5.95805i) q^{82} -5.83783i q^{83} +(-1.22639 - 1.28356i) q^{84} +(5.94609 + 10.2989i) q^{85} +(1.49054 + 12.4123i) q^{86} +(3.31404 + 5.74009i) q^{87} +(8.77886 + 3.30629i) q^{88} +(-7.82986 - 4.52057i) q^{89} +(11.4432 - 1.37416i) q^{90} +(4.49668 + 1.25641i) q^{91} +(2.03924 + 8.36834i) q^{92} +(-5.70910 - 3.29615i) q^{93} +(-7.71933 - 3.30092i) q^{94} +(9.14312 + 15.8363i) q^{95} +(3.20566 - 2.18168i) q^{96} +(14.2378 - 8.22017i) q^{97} +(6.02425 - 4.51452i) q^{98} +(8.23223 + 1.62707i) 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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