LMFDB - Embedded newform 546.2.q.j.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, 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("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.q (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.3
Character	$\chi$	$=$	546.251
Dual form			546.2.q.j.335.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.48647 + 0.889052i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.655349i q^{5} +(0.0267080 + 1.73184i) q^{6} +(0.402891 + 2.61490i) q^{7} -1.00000 q^{8} +(1.41917 - 2.64309i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.48647 + 0.889052i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.655349i q^{5} +(0.0267080 + 1.73184i) q^{6} +(0.402891 + 2.61490i) q^{7} -1.00000 q^{8} +(1.41917 - 2.64309i) q^{9} +(-0.567549 - 0.327675i) q^{10} +(0.366849 - 0.635401i) q^{11} +(1.51318 + 0.842793i) q^{12} +(0.424437 + 3.58048i) q^{13} +(2.46601 + 0.958534i) q^{14} +(0.582640 + 0.974155i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.581815 - 1.00773i) q^{17} +(-1.57940 - 2.55059i) q^{18} +(2.51943 + 4.36378i) q^{19} +(-0.567549 + 0.327675i) q^{20} +(-2.92366 - 3.52877i) q^{21} +(-0.366849 - 0.635401i) q^{22} +(5.55559 + 3.20752i) q^{23} +(1.48647 - 0.889052i) q^{24} +4.57052 q^{25} +(3.31301 + 1.42267i) q^{26} +(0.240296 + 5.19059i) q^{27} +(2.06312 - 1.65636i) q^{28} +(-0.839009 - 0.484402i) q^{29} +(1.13496 - 0.0175031i) q^{30} +4.20440 q^{31} +(0.500000 + 0.866025i) q^{32} +(0.0195956 + 1.27065i) q^{33} -1.16363 q^{34} +(1.71367 - 0.264034i) q^{35} +(-2.99857 + 0.0925084i) q^{36} +(3.59978 + 2.07834i) q^{37} +5.03886 q^{38} +(-3.81415 - 4.94492i) q^{39} +0.655349i q^{40} +(-4.22814 - 2.44112i) q^{41} +(-4.51783 + 0.767584i) q^{42} +(3.81091 + 6.60069i) q^{43} -0.733697 q^{44} +(-1.73215 - 0.930053i) q^{45} +(5.55559 - 3.20752i) q^{46} -6.48204i q^{47} +(-0.0267080 - 1.73184i) q^{48} +(-6.67536 + 2.10704i) q^{49} +(2.28526 - 3.95818i) q^{50} +(1.76078 + 0.980698i) q^{51} +(2.88857 - 2.15781i) q^{52} +1.29577i q^{53} +(4.61533 + 2.38719i) q^{54} +(-0.416409 - 0.240414i) q^{55} +(-0.402891 - 2.61490i) q^{56} +(-7.62467 - 4.24671i) q^{57} +(-0.839009 + 0.484402i) q^{58} +(2.15803 - 1.24594i) q^{59} +(0.552323 - 0.991658i) q^{60} +(0.932808 - 0.538557i) q^{61} +(2.10220 - 3.64112i) q^{62} +(7.48319 + 2.64611i) q^{63} +1.00000 q^{64} +(2.34647 - 0.278155i) q^{65} +(1.11021 + 0.618355i) q^{66} +(-5.07874 - 2.93221i) q^{67} +(-0.581815 + 1.00773i) q^{68} +(-11.1099 + 0.171333i) q^{69} +(0.628174 - 1.61610i) q^{70} +(4.09978 + 7.10103i) q^{71} +(-1.41917 + 2.64309i) q^{72} -6.93011 q^{73} +(3.59978 - 2.07834i) q^{74} +(-6.79393 + 4.06343i) q^{75} +(2.51943 - 4.36378i) q^{76} +(1.80931 + 0.703274i) q^{77} +(-6.18950 + 0.830687i) q^{78} -13.1952 q^{79} +(0.567549 + 0.327675i) q^{80} +(-4.97190 - 7.50201i) q^{81} +(-4.22814 + 2.44112i) q^{82} +12.5007i q^{83} +(-1.59417 + 4.29635i) q^{84} +(-0.660417 + 0.381292i) q^{85} +7.62182 q^{86} +(1.67782 - 0.0258749i) q^{87} +(-0.366849 + 0.635401i) q^{88} +(-12.6797 - 7.32065i) q^{89} +(-1.67152 + 1.03506i) q^{90} +(-9.19158 + 2.55240i) q^{91} -6.41504i q^{92} +(-6.24970 + 3.73793i) q^{93} +(-5.61361 - 3.24102i) q^{94} +(2.85980 - 1.65110i) q^{95} +(-1.51318 - 0.842793i) q^{96} +(3.36975 + 5.83658i) q^{97} +(-1.51293 + 6.83455i) q^{98} +(-1.15880 - 1.87136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.48647	+	0.889052i	−0.858212	+	0.513295i
$3$	−1.48647	+	0.889052i	−0.858212	+	0.513295i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		−	0.655349i		−	0.293081i	−0.989205	−	0.146541i	$-0.953186\pi$
$5$		−	0.655349i		−	0.293081i	0.989205	−	0.146541i	$-0.0468139\pi$
$6$	0.0267080	+	1.73184i	0.0109035	+	0.707023i
$7$	0.402891	+	2.61490i	0.152279	+	0.988338i
$7$	0.402891	+	2.61490i	0.152279	+	0.988338i
$8$	−1.00000			−0.353553
$9$	1.41917	−	2.64309i	0.473057	−	0.881032i
$10$	−0.567549	−	0.327675i	−0.179475	−	0.103620i
$11$	0.366849	−	0.635401i	0.110609	−	0.191580i	−0.805407	−	0.592722i	$-0.798053\pi$
$11$	0.366849	−	0.635401i	0.110609	−	0.191580i	0.916016	+	0.401142i	$0.131387\pi$
$12$	1.51318	+	0.842793i	0.436816	+	0.243293i
$13$	0.424437	+	3.58048i	0.117718	+	0.993047i
$13$	0.424437	+	3.58048i	0.117718	+	0.993047i
$14$	2.46601	+	0.958534i	0.659069	+	0.256179i
$15$	0.582640	+	0.974155i	0.150437	+	0.251526i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.581815	−	1.00773i	−0.141111	−	0.244411i	0.786804	−	0.617202i	$-0.211734\pi$
$17$	−0.581815	−	1.00773i	−0.141111	−	0.244411i	−0.927915	+	0.372791i	$0.878401\pi$
$18$	−1.57940	−	2.55059i	−0.372268	−	0.601179i
$19$	2.51943	+	4.36378i	0.577996	+	1.00112i	0.995709	+	0.0925398i	$0.0294986\pi$
$19$	2.51943	+	4.36378i	0.577996	+	1.00112i	−0.417713	+	0.908579i	$0.637168\pi$
$20$	−0.567549	+	0.327675i	−0.126908	+	0.0732703i
$21$	−2.92366	−	3.52877i	−0.637996	−	0.770040i
$22$	−0.366849	−	0.635401i	−0.0782124	−	0.135468i
$23$	5.55559	+	3.20752i	1.15842	+	0.668815i	0.950925	−	0.309421i	$-0.100135\pi$
$23$	5.55559	+	3.20752i	1.15842	+	0.668815i	0.207496	+	0.978236i	$0.433469\pi$
$24$	1.48647	−	0.889052i	0.303424	−	0.181477i
$25$	4.57052			0.914104
$26$	3.31301	+	1.42267i	0.649734	+	0.279008i
$27$	0.240296	+	5.19059i	0.0462450	+	0.998930i
$28$	2.06312	−	1.65636i	0.389893	−	0.313023i
$29$	−0.839009	−	0.484402i	−0.155800	−	0.0899512i	0.420073	−	0.907490i	$-0.362004\pi$
$29$	−0.839009	−	0.484402i	−0.155800	−	0.0899512i	−0.575873	+	0.817539i	$0.695338\pi$
$30$	1.13496	−	0.0175031i	0.207215	−	0.00319561i
$31$	4.20440			0.755132			0.377566	−	0.925983i	$-0.376761\pi$
$31$	4.20440			0.755132			0.377566	+	0.925983i	$0.376761\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.0195956	+	1.27065i	0.00341116	+	0.221192i
$34$	−1.16363			−0.199561
$35$	1.71367	−	0.264034i	0.289663	−	0.0446300i
$36$	−2.99857	+	0.0925084i	−0.499762	+	0.0154181i
$37$	3.59978	+	2.07834i	0.591801	+	0.341676i	0.765809	−	0.643068i	$-0.222339\pi$
$37$	3.59978	+	2.07834i	0.591801	+	0.341676i	−0.174008	+	0.984744i	$0.555672\pi$
$38$	5.03886			0.817410
$39$	−3.81415	−	4.94492i	−0.610753	−	0.791822i
$40$			0.655349i			0.103620i
$41$	−4.22814	−	2.44112i	−0.660324	−	0.381238i	0.132076	−	0.991240i	$-0.457836\pi$
$41$	−4.22814	−	2.44112i	−0.660324	−	0.381238i	−0.792401	+	0.610001i	$0.791169\pi$
$42$	−4.51783	+	0.767584i	−0.697117	+	0.118441i
$43$	3.81091	+	6.60069i	0.581158	+	1.00660i	0.995342	+	0.0964026i	$0.0307336\pi$
$43$	3.81091	+	6.60069i	0.581158	+	1.00660i	−0.414184	+	0.910193i	$0.635933\pi$
$44$	−0.733697			−0.110609
$45$	−1.73215	−	0.930053i	−0.258214	−	0.138644i
$46$	5.55559	−	3.20752i	0.819127	−	0.472923i
$47$		−	6.48204i		−	0.945503i	−0.881196	−	0.472752i	$-0.843261\pi$
$47$		−	6.48204i		−	0.945503i	0.881196	−	0.472752i	$-0.156739\pi$
$48$	−0.0267080	−	1.73184i	−0.00385497	−	0.249970i
$49$	−6.67536	+	2.10704i	−0.953622	+	0.301005i
$50$	2.28526	−	3.95818i	0.323184	−	0.559772i
$51$	1.76078	+	0.980698i	0.246558	+	0.137325i
$52$	2.88857	−	2.15781i	0.400573	−	0.299235i
$53$			1.29577i			0.177987i	0.996032	+	0.0889937i	$0.0283651\pi$
$53$			1.29577i			0.177987i	−0.996032	+	0.0889937i	$0.971635\pi$
$54$	4.61533	+	2.38719i	0.628067	+	0.324856i
$55$	−0.416409	−	0.240414i	−0.0561486	−	0.0324174i
$56$	−0.402891	−	2.61490i	−0.0538386	−	0.349430i
$57$	−7.62467	−	4.24671i	−1.00991	−	0.562490i
$58$	−0.839009	+	0.484402i	−0.110167	+	0.0636051i
$59$	2.15803	−	1.24594i	0.280952	−	0.162208i	−0.352902	−	0.935660i	$-0.614805\pi$
$59$	2.15803	−	1.24594i	0.280952	−	0.162208i	0.633854	+	0.773452i	$0.281472\pi$
$60$	0.552323	−	0.991658i	0.0713046	−	0.128023i
$61$	0.932808	−	0.538557i	0.119434	−	0.0689551i	−0.439093	−	0.898442i	$-0.644700\pi$
$61$	0.932808	−	0.538557i	0.119434	−	0.0689551i	0.558527	+	0.829486i	$0.311367\pi$
$62$	2.10220	−	3.64112i	0.266980	−	0.462422i
$63$	7.48319	+	2.64611i	0.942793	+	0.333378i
$64$	1.00000			0.125000
$65$	2.34647	−	0.278155i	0.291043	−	0.0345008i
$66$	1.11021	+	0.618355i	0.136658	+	0.0761142i
$67$	−5.07874	−	2.93221i	−0.620466	−	0.358226i	0.156584	−	0.987665i	$-0.449952\pi$
$67$	−5.07874	−	2.93221i	−0.620466	−	0.358226i	−0.777051	+	0.629438i	$0.783285\pi$
$68$	−0.581815	+	1.00773i	−0.0705554	+	0.122205i
$69$	−11.1099	+	0.171333i	−1.33747	+	0.0206261i
$70$	0.628174	−	1.61610i	0.0750812	−	0.193161i
$71$	4.09978	+	7.10103i	0.486555	+	0.842738i	0.999881	−	0.0154562i	$-0.00492004\pi$
$71$	4.09978	+	7.10103i	0.486555	+	0.842738i	−0.513326	+	0.858194i	$0.671587\pi$
$72$	−1.41917	+	2.64309i	−0.167251	+	0.311492i
$73$	−6.93011			−0.811108			−0.405554	−	0.914071i	$-0.632921\pi$
$73$	−6.93011			−0.811108			−0.405554	+	0.914071i	$0.632921\pi$
$74$	3.59978	−	2.07834i	0.418466	−	0.241602i
$75$	−6.79393	+	4.06343i	−0.784495	+	0.469204i
$76$	2.51943	−	4.36378i	0.288998	−	0.500560i
$77$	1.80931	+	0.703274i	0.206190	+	0.0801455i
$78$	−6.18950	+	0.830687i	−0.700823	+	0.0940568i
$79$	−13.1952			−1.48457			−0.742287	−	0.670082i	$-0.766259\pi$
$79$	−13.1952			−1.48457			−0.742287	+	0.670082i	$0.766259\pi$
$80$	0.567549	+	0.327675i	0.0634539	+	0.0366351i
$81$	−4.97190	−	7.50201i	−0.552433	−	0.833557i
$82$	−4.22814	+	2.44112i	−0.466920	+	0.269576i
$83$			12.5007i			1.37213i	0.727539	+	0.686066i	$0.240664\pi$
$83$			12.5007i			1.37213i	−0.727539	+	0.686066i	$0.759336\pi$
$84$	−1.59417	+	4.29635i	−0.173938	+	0.468770i
$85$	−0.660417	+	0.381292i	−0.0716322	+	0.0413569i
$86$	7.62182			0.821882
$87$	1.67782	−	0.0258749i	0.179881	−	0.00277408i
$88$	−0.366849	+	0.635401i	−0.0391062	+	0.0677339i
$89$	−12.6797	−	7.32065i	−1.34405	−	0.775987i	−0.356650	−	0.934238i	$-0.616081\pi$
$89$	−12.6797	−	7.32065i	−1.34405	−	0.775987i	−0.987399	+	0.158251i	$0.949414\pi$
$90$	−1.67152	+	1.03506i	−0.176194	+	0.109105i
$91$	−9.19158	+	2.55240i	−0.963540	+	0.267565i
$92$		−	6.41504i		−	0.668815i
$93$	−6.24970	+	3.73793i	−0.648064	+	0.387605i
$94$	−5.61361	−	3.24102i	−0.579000	−	0.334286i
$95$	2.85980	−	1.65110i	0.293409	−	0.169400i
$96$	−1.51318	−	0.842793i	−0.154438	−	0.0860172i
$97$	3.36975	+	5.83658i	0.342146	+	0.592615i	0.984831	−	0.173516i	$-0.0555129\pi$
$97$	3.36975	+	5.83658i	0.342146	+	0.592615i	−0.642685	+	0.766131i	$0.722180\pi$
$98$	−1.51293	+	6.83455i	−0.152829	+	0.690394i
$99$	−1.15880	−	1.87136i	−0.116464	−	0.188079i
$100$	−2.28526	−	3.95818i	−0.228526	−	0.395818i
$101$	1.15739	−	2.00466i	0.115165	−	0.199471i	−0.802681	−	0.596409i	$-0.796594\pi$
$101$	1.15739	−	2.00466i	0.115165	−	0.199471i	0.917846	+	0.396938i	$0.129927\pi$
$102$	1.72970	−	1.03453i	0.171266	−	0.102433i
$103$		−	11.2924i		−	1.11268i	−0.830956	−	0.556338i	$-0.812206\pi$
$103$		−	11.2924i		−	1.11268i	0.830956	−	0.556338i	$-0.187794\pi$
$104$	−0.424437	−	3.58048i	−0.0416195	−	0.351095i
$105$	−2.31257	+	1.91602i	−0.225684	+	0.186984i
$106$	1.12217	+	0.647884i	0.108995	+	0.0629281i
$107$	5.35526	+	3.09186i	0.517713	+	0.298901i	0.735998	−	0.676983i	$-0.236713\pi$
$107$	5.35526	+	3.09186i	0.517713	+	0.298901i	−0.218286	+	0.975885i	$0.570046\pi$
$108$	4.37504	−	2.80340i	0.420988	−	0.269757i
$109$		−	16.2242i		−	1.55399i	−0.629504	−	0.776997i	$-0.716742\pi$
$109$		−	16.2242i		−	1.55399i	0.629504	−	0.776997i	$-0.283258\pi$
$110$	−0.416409	+	0.240414i	−0.0397031	+	0.0229226i
$111$	−7.19871	+	0.111017i	−0.683272	+	0.0105372i
$112$	−2.46601	−	0.958534i	−0.233016	−	0.0905729i
$113$	4.96016	−	2.86375i	0.466612	−	0.269399i	−0.248208	−	0.968707i	$-0.579842\pi$
$113$	4.96016	−	2.86375i	0.466612	−	0.269399i	0.714820	+	0.699308i	$0.246508\pi$
$114$	−7.49010	+	4.47981i	−0.701512	+	0.419572i
$115$	2.10205	−	3.64085i	0.196017	−	0.339511i
$116$			0.968804i			0.0899512i
$117$	10.0659	+	3.95949i	0.930593	+	0.366055i
$118$		−	2.49188i		−	0.229396i
$119$	2.40071	−	1.92739i	0.220072	−	0.176684i
$120$	−0.582640	−	0.974155i	−0.0531875	−	0.0889278i
$121$	5.23084	+	9.06009i	0.475531	+	0.823644i
$122$		−	1.07711i		−	0.0975173i
$123$	8.45527	−	0.130395i	0.762386	−	0.0117573i
$124$	−2.10220	−	3.64112i	−0.188783	−	0.326982i
$125$		−	6.27203i		−	0.560987i
$126$	6.03319	−	5.15758i	0.537479	−	0.459474i
$127$	3.74468	−	6.48598i	0.332287	−	0.575537i	−0.650673	−	0.759358i	$-0.725513\pi$
$127$	3.74468	−	6.48598i	0.332287	−	0.575537i	0.982960	+	0.183821i	$0.0588465\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−11.5332	−	6.42361i	−1.01544	−	0.565568i
$130$	0.932344	−	2.17118i	0.0817720	−	0.190425i
$131$	−12.5967			−1.10058			−0.550288	−	0.834975i	$-0.685482\pi$
$131$	−12.5967			−1.10058			−0.550288	+	0.834975i	$0.685482\pi$
$132$	1.09062	−	0.652295i	0.0949261	−	0.0567750i
$133$	−10.3958	+	8.34617i	−0.901427	+	0.723704i
$134$	−5.07874	+	2.93221i	−0.438736	+	0.253304i
$135$	3.40165	−	0.157478i	0.292767	−	0.0135535i
$136$	0.581815	+	1.00773i	0.0498902	+	0.0864123i
$137$	−11.1336	−	19.2839i	−0.951205	−	1.64753i	−0.742824	−	0.669487i	$-0.766514\pi$
$137$	−11.1336	−	19.2839i	−0.951205	−	1.64753i	−0.208381	−	0.978048i	$-0.566819\pi$
$138$	−5.40655	+	9.70709i	−0.460236	+	0.826322i
$139$	3.15133	−	1.81942i	0.267293	−	0.154321i	−0.360364	−	0.932812i	$-0.617348\pi$
$139$	3.15133	−	1.81942i	0.267293	−	0.154321i	0.627657	+	0.778490i	$0.284014\pi$
$140$	−1.08550	−	1.35206i	−0.0917411	−	0.114270i
$141$	5.76287	+	9.63535i	0.485322	+	0.811443i
$142$	8.19957			0.688092
$143$	2.43074	+	1.04381i	0.203269	+	0.0872876i
$144$	1.57940	+	2.55059i	0.131617	+	0.212549i
$145$	−0.317452	+	0.549844i	−0.0263630	+	0.0456620i
$146$	−3.46505	+	6.00165i	−0.286770	+	0.496700i
$147$	8.04944	−	9.06678i	0.663906	−	0.747816i
$148$		−	4.15667i		−	0.341676i
$149$	10.9093	+	18.8954i	0.893722	+	1.54797i	0.835378	+	0.549675i	$0.185249\pi$
$149$	10.9093	+	18.8954i	0.893722	+	1.54797i	0.0583437	+	0.998297i	$0.481418\pi$
$150$	0.122070	+	7.91543i	0.00996694	+	0.646292i
$151$		−	6.34819i		−	0.516608i	−0.966064	−	0.258304i	$-0.916836\pi$
$151$		−	6.34819i		−	0.516608i	0.966064	−	0.258304i	$-0.0831636\pi$
$152$	−2.51943	−	4.36378i	−0.204353	−	0.353949i
$153$	−3.48923	+	0.107645i	−0.282087	+	0.00870262i
$154$	1.51371	−	1.21527i	0.121978	−	0.0979291i
$155$		−	2.75535i		−	0.221315i
$156$	−2.37536	+	5.77561i	−0.190181	+	0.462419i
$157$			6.08218i			0.485411i	0.970100	+	0.242705i	$0.0780349\pi$
$157$			6.08218i			0.485411i	−0.970100	+	0.242705i	$0.921965\pi$
$158$	−6.59760	+	11.4274i	−0.524877	+	0.909113i
$159$	−1.15201	−	1.92612i	−0.0913600	−	0.152751i
$160$	0.567549	−	0.327675i	0.0448687	−	0.0259049i
$161$	−6.14904	+	15.8196i	−0.484612	+	1.24676i
$162$	−8.98288	+	0.554786i	−0.705762	+	0.0435881i
$163$	−8.79156	+	5.07581i	−0.688608	+	0.397568i	−0.803090	−	0.595857i	$-0.796812\pi$
$163$	−8.79156	+	5.07581i	−0.688608	+	0.397568i	0.114482	+	0.993425i	$0.463479\pi$
$164$			4.88223i			0.381238i
$165$	0.832719	−	0.0128420i	0.0648271	−	0.000999746i
$166$	10.8259	+	6.25036i	0.840256	+	0.485122i
$167$	18.4911	+	10.6759i	1.43089	+	0.826122i	0.997188	−	0.0749359i	$-0.0238752\pi$
$167$	18.4911	+	10.6759i	1.43089	+	0.826122i	0.433698	+	0.901058i	$0.357209\pi$
$168$	2.92366	+	3.52877i	0.225566	+	0.272250i
$169$	−12.6397	+	3.03938i	−0.972285	+	0.233799i
$170$			0.762583i			0.0584875i
$171$	15.1094	−	0.466136i	1.15544	−	0.0356463i
$172$	3.81091	−	6.60069i	0.290579	−	0.503298i
$173$	−3.66961	−	6.35595i	−0.278995	−	0.483234i	0.692140	−	0.721763i	$-0.256668\pi$
$173$	−3.66961	−	6.35595i	−0.278995	−	0.483234i	−0.971135	+	0.238529i	$0.923335\pi$
$174$	0.816501	−	1.46597i	0.0618988	−	0.111135i
$175$	1.84142	+	11.9514i	0.139198	+	0.903443i
$176$	0.366849	+	0.635401i	0.0276523	+	0.0478951i
$177$	−2.10014	+	3.77066i	−0.157856	+	0.283420i
$178$	−12.6797	+	7.32065i	−0.950386	+	0.548706i
$179$	2.15825	+	1.24607i	0.161315	+	0.0931353i	0.578484	−	0.815694i	$-0.303644\pi$
$179$	2.15825	+	1.24607i	0.161315	+	0.0931353i	−0.417169	+	0.908829i	$0.636978\pi$
$180$	0.0606253	+	1.96511i	0.00451874	+	0.146471i
$181$		−	19.3857i		−	1.44092i	−0.693494	−	0.720462i	$-0.743930\pi$
$181$		−	19.3857i		−	1.44092i	0.693494	−	0.720462i	$-0.256070\pi$
$182$	−2.38535	+	9.23635i	−0.176814	+	0.684644i
$183$	−0.907783	+	1.62986i	−0.0671053	+	0.120483i
$184$	−5.55559	−	3.20752i	−0.409564	−	0.236462i
$185$	1.36204	−	2.35912i	0.100139	−	0.173446i
$186$	0.112291	+	7.28137i	0.00823359	+	0.533896i
$187$	−0.853752			−0.0624325
$188$	−5.61361	+	3.24102i	−0.409415	+	0.236376i
$189$	−13.4760	+	2.71959i	−0.980238	+	0.197821i
$190$		−	3.30221i		−	0.239567i
$191$	11.8522	−	6.84286i	0.857594	−	0.495132i	−0.00561166	−	0.999984i	$-0.501786\pi$
$191$	11.8522	−	6.84286i	0.857594	−	0.495132i	0.863206	+	0.504852i	$0.168453\pi$
$192$	−1.48647	+	0.889052i	−0.107277	+	0.0641618i
$193$	18.7113	+	10.8030i	1.34687	+	0.777615i	0.987805	−	0.155698i	$-0.0497627\pi$
$193$	18.7113	+	10.8030i	1.34687	+	0.777615i	0.359064	+	0.933313i	$0.383096\pi$
$194$	6.73950			0.483868
$195$	−3.24065	+	2.49960i	−0.232068	+	0.179000i
$196$	5.16243	+	4.72751i	0.368745	+	0.337679i
$197$	−10.6029	+	18.3647i	−0.755423	+	1.30843i	0.189741	+	0.981834i	$0.439235\pi$
$197$	−10.6029	+	18.3647i	−0.755423	+	1.30843i	−0.945164	+	0.326596i	$0.894098\pi$
$198$	−2.20005	+	0.0678731i	−0.156350	+	0.00482353i
$199$	−2.97067	+	1.71512i	−0.210585	+	0.121581i	−0.601583	−	0.798810i	$-0.705463\pi$
$199$	−2.97067	+	1.71512i	−0.210585	+	0.121581i	0.390998	+	0.920391i	$0.372130\pi$
$200$	−4.57052			−0.323184
$201$	10.1563	−	0.156627i	0.716368	−	0.0110476i
$202$	−1.15739	−	2.00466i	−0.0814338	−	0.141047i
$203$	0.928631	−	2.38908i	0.0651771	−	0.167681i
$204$	−0.0310783	−	2.01523i	−0.00217591	−	0.141094i
$205$	−1.59978	+	2.77091i	−0.111734	+	0.193529i
$206$	−9.77953	−	5.64621i	−0.681372	−	0.393390i
$207$	16.3621	−	10.1319i	1.13725	−	0.704218i
$208$	−3.31301	−	1.42267i	−0.229716	−	0.0986442i
$209$	3.69699			0.255726
$210$	0.503035	+	2.96076i	0.0347127	+	0.204312i
$211$	12.4331	−	21.5347i	0.855929	−	1.48251i	−0.0198516	−	0.999803i	$-0.506319\pi$
$211$	12.4331	−	21.5347i	0.855929	−	1.48251i	0.875781	−	0.482710i	$-0.160347\pi$
$212$	1.12217	−	0.647884i	0.0770708	−	0.0444969i
$213$	−12.4074	−	6.91054i	−0.850140	−	0.473502i
$214$	5.35526	−	3.09186i	0.366078	−	0.211355i
$215$	4.32576	−	2.49748i	0.295014	−	0.170326i
$216$	−0.240296	−	5.19059i	−0.0163501	−	0.353175i
$217$	1.69392	+	10.9941i	0.114990	+	0.746326i
$218$	−14.0505	−	8.11209i	−0.951623	−	0.549420i
$219$	10.3014	−	6.16123i	0.696103	−	0.416337i
$220$			0.480828i			0.0324174i
$221$	3.36122	−	2.51090i	0.226100	−	0.168901i
$222$	−3.50321	+	6.28978i	−0.235120	+	0.422142i
$223$	4.26929	−	7.39463i	0.285893	−	0.495181i	−0.686932	−	0.726721i	$-0.741043\pi$
$223$	4.26929	−	7.39463i	0.285893	−	0.495181i	0.972825	+	0.231540i	$0.0743764\pi$
$224$	−2.06312	+	1.65636i	−0.137848	+	0.110670i
$225$	6.48635	−	12.0803i	0.432423	−	0.805354i
$226$		−	5.72749i		−	0.380987i
$227$	5.99732	−	3.46256i	0.398056	−	0.229818i	−0.287589	−	0.957754i	$-0.592854\pi$
$227$	5.99732	−	3.46256i	0.398056	−	0.229818i	0.685645	+	0.727936i	$0.259520\pi$
$228$	0.134578	+	8.72652i	0.00891264	+	0.577928i
$229$	−4.68499			−0.309593			−0.154796	−	0.987946i	$-0.549472\pi$
$229$	−4.68499			−0.309593			−0.154796	+	0.987946i	$0.549472\pi$
$230$	−2.10205	−	3.64085i	−0.138605	−	0.240071i
$231$	−3.31472	+	0.563174i	−0.218093	+	0.0370541i
$232$	0.839009	+	0.484402i	0.0550836	+	0.0318025i
$233$		−	8.61388i		−	0.564314i	−0.959368	−	0.282157i	$-0.908950\pi$
$233$		−	8.61388i		−	0.564314i	0.959368	−	0.282157i	$-0.0910499\pi$
$234$	8.46197	−	6.73758i	0.553176	−	0.440450i
$235$	−4.24800			−0.277109
$236$	−2.15803	−	1.24594i	−0.140476	−	0.0811039i
$237$	19.6142	−	11.7312i	1.27408	−	0.762024i
$238$	−0.468816	−	3.04277i	−0.0303888	−	0.197233i
$239$	−10.2610			−0.663727			−0.331864	−	0.943327i	$-0.607677\pi$
$239$	−10.2610			−0.663727			−0.331864	+	0.943327i	$0.607677\pi$
$240$	−1.13496	+	0.0175031i	−0.0732615	+	0.00112982i
$241$	8.05368	+	13.9494i	0.518783	+	0.898559i	0.999762	+	0.0218264i	$0.00694812\pi$
$241$	8.05368	+	13.9494i	0.518783	+	0.898559i	−0.480979	+	0.876732i	$0.659719\pi$
$242$	10.4617			0.672503
$243$	14.0603	+	6.73122i	0.901966	+	0.431808i
$244$	−0.932808	−	0.538557i	−0.0597169	−	0.0344776i
$245$	1.38084	+	4.37469i	0.0882189	+	0.279489i
$246$	4.11471	−	7.38768i	0.262344	−	0.471021i
$247$	−14.5551	+	10.8729i	−0.926118	+	0.691827i
$248$	−4.20440			−0.266980
$249$	−11.1138	−	18.5819i	−0.704308	−	1.17758i
$250$	−5.43174	−	3.13602i	−0.343533	−	0.198339i
$251$	10.4635	+	18.1234i	0.660453	+	1.14394i	0.980497	+	0.196535i	$0.0629689\pi$
$251$	10.4635	+	18.1234i	0.660453	+	1.14394i	−0.320044	+	0.947403i	$0.603698\pi$
$252$	−1.45000	−	7.80369i	−0.0913413	−	0.491586i
$253$	4.07612	−	2.35335i	0.256264	−	0.147954i
$254$	−3.74468	−	6.48598i	−0.234962	−	0.406966i
$255$	0.642700	−	1.15392i	0.0402474	−	0.0722614i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.7555	−	23.8253i	0.858047	−	1.48618i	−0.0157419	−	0.999876i	$-0.505011\pi$
$257$	13.7555	−	23.8253i	0.858047	−	1.48618i	0.873789	−	0.486305i	$-0.161656\pi$
$258$	−11.3296	+	6.77620i	−0.705349	+	0.421868i
$259$	−3.98431	+	10.2504i	−0.247573	+	0.636929i
$260$	−1.41412	−	1.89302i	−0.0877001	−	0.117400i
$261$	−2.47102	+	1.53013i	−0.152952	+	0.0947127i
$262$	−6.29833	+	10.9090i	−0.389112	+	0.673962i
$263$	−27.0282	−	15.6048i	−1.66663	−	0.962231i	−0.969434	−	0.245352i	$-0.921096\pi$
$263$	−27.0282	−	15.6048i	−1.66663	−	0.962231i	−0.697198	−	0.716878i	$-0.745570\pi$
$264$	−0.0195956	−	1.27065i	−0.00120603	−	0.0782031i
$265$	0.849181			0.0521647
$266$	2.03011	+	13.1761i	0.124474	+	0.807877i
$267$	25.3564	−	0.391040i	1.55179	−	0.0239313i
$268$			5.86442i			0.358226i
$269$	0.0309493	+	0.0536058i	0.00188701	+	0.00326841i	0.866967	−	0.498365i	$-0.166066\pi$
$269$	0.0309493	+	0.0536058i	0.00188701	+	0.00326841i	−0.865080	+	0.501633i	$0.832733\pi$
$270$	1.56445	−	3.02465i	0.0952091	−	0.184075i
$271$	−2.55715	+	4.42912i	−0.155336	+	0.269050i	−0.933181	−	0.359406i	$-0.882979\pi$
$271$	−2.55715	+	4.42912i	−0.155336	+	0.269050i	0.777845	+	0.628456i	$0.216313\pi$
$272$	1.16363			0.0705554
$273$	11.3938	−	11.9659i	0.689582	−	0.724207i
$274$	−22.2671			−1.34521
$275$	1.67669	−	2.90411i	0.101108	−	0.175124i
$276$	5.70331	+	9.53575i	0.343299	+	0.573985i
$277$	−7.08419	−	12.2702i	−0.425648	−	0.737244i	0.570833	−	0.821066i	$-0.306620\pi$
$277$	−7.08419	−	12.2702i	−0.425648	−	0.737244i	−0.996481	+	0.0838226i	$0.973287\pi$
$278$		−	3.63885i		−	0.218243i
$279$	5.96677	−	11.1126i	0.357221	−	0.665295i
$280$	−1.71367	+	0.264034i	−0.102411	+	0.0157791i
$281$	3.54138			0.211261			0.105630	−	0.994405i	$-0.466314\pi$
$281$	3.54138			0.211261			0.105630	+	0.994405i	$0.466314\pi$
$282$	11.2259	−	0.173123i	0.668492	−	0.0103093i
$283$	18.6608	+	10.7738i	1.10927	+	0.640438i	0.938640	−	0.344897i	$-0.112086\pi$
$283$	18.6608	+	10.7738i	1.10927	+	0.640438i	0.170631	+	0.985335i	$0.445420\pi$
$284$	4.09978	−	7.10103i	0.243277	−	0.421369i
$285$	−2.78308	+	4.99682i	−0.164855	+	0.295986i
$286$	2.11934	−	1.58318i	0.125319	−	0.0936156i
$287$	4.67979	−	12.0396i	0.276239	−	0.710678i
$288$	2.99857	−	0.0925084i	0.176693	−	0.00545111i
$289$	7.82298	−	13.5498i	0.460176	−	0.797047i
$290$	0.317452	+	0.549844i	0.0186414	+	0.0322879i
$291$	−10.1980	−	5.68000i	−0.597820	−	0.332967i
$292$	3.46505	+	6.00165i	0.202777	+	0.351220i
$293$	19.1717	−	11.0688i	1.12002	−	0.646645i	0.178615	−	0.983919i	$-0.442838\pi$
$293$	19.1717	−	11.0688i	1.12002	−	0.646645i	0.941406	+	0.337274i	$0.109505\pi$
$294$	−3.82735	−	11.5044i	−0.223215	−	0.670951i
$295$	−0.816527	−	1.41427i	−0.0475400	−	0.0823417i
$296$	−3.59978	−	2.07834i	−0.209233	−	0.120801i
$297$	3.38626	+	1.75148i	0.196491	+	0.101631i
$298$	21.8185			1.26391
$299$	−9.12647	+	21.2531i	−0.527798	+	1.22910i
$300$	6.91600	+	3.85200i	0.399295	+	0.222395i
$301$	−15.7247	+	12.6245i	−0.906358	+	0.727664i
$302$	−5.49769	−	3.17409i	−0.316357	−	0.182649i
$303$	0.0618233	+	4.00885i	0.00355166	+	0.230302i
$304$	−5.03886			−0.288998
$305$	−0.352943	−	0.611315i	−0.0202094	−	0.0350038i
$306$	−1.65139	+	3.07558i	−0.0944037	+	0.175819i
$307$	2.17640			0.124214			0.0621068	−	0.998070i	$-0.480218\pi$
$307$	2.17640			0.124214			0.0621068	+	0.998070i	$0.480218\pi$
$308$	−0.295600	−	1.91854i	−0.0168434	−	0.109319i
$309$	10.0396	+	16.7858i	0.571130	+	0.954912i
$310$	−2.38620	−	1.37767i	−0.135527	−	0.0782467i
$311$	−7.10285			−0.402766			−0.201383	−	0.979513i	$-0.564544\pi$
$311$	−7.10285			−0.402766			−0.201383	+	0.979513i	$0.564544\pi$
$312$	3.81415	+	4.94492i	0.215934	+	0.279951i
$313$		−	17.1322i		−	0.968368i	−0.874966	−	0.484184i	$-0.839117\pi$
$313$		−	17.1322i		−	0.968368i	0.874966	−	0.484184i	$-0.160883\pi$
$314$	5.26732	+	3.04109i	0.297252	+	0.171619i
$315$	1.73412	−	4.90410i	0.0977068	−	0.276315i
$316$	6.59760	+	11.4274i	0.371144	+	0.642840i
$317$	−24.6347			−1.38362			−0.691812	−	0.722078i	$-0.743187\pi$
$317$	−24.6347			−1.38362			−0.691812	+	0.722078i	$0.743187\pi$
$318$	−2.24407	+	0.0346074i	−0.125841	+	0.00194069i
$319$	−0.615579	+	0.355404i	−0.0344658	+	0.0198988i
$320$		−	0.655349i		−	0.0366351i
$321$	−10.7092	+	0.165155i	−0.597732	+	0.00921806i
$322$	10.6256	+	13.2350i	0.592143	+	0.737558i
$323$	2.93168	−	5.07782i	0.163123	−	0.282537i
$324$	−4.01098	+	8.05680i	−0.222832	+	0.447600i
$325$	1.93990	+	16.3647i	0.107606	+	0.907748i
$326$			10.1516i			0.562246i
$327$	14.4241	+	24.1167i	0.797657	+	1.33366i
$328$	4.22814	+	2.44112i	0.233460	+	0.134788i
$329$	16.9499	−	2.61156i	0.934476	−	0.143980i
$330$	0.405238	−	0.727577i	0.0223076	−	0.0400518i
$331$	−9.87158	+	5.69936i	−0.542591	+	0.313265i	−0.746128	−	0.665802i	$-0.768090\pi$
$331$	−9.87158	+	5.69936i	−0.542591	+	0.313265i	0.203537	+	0.979067i	$0.434756\pi$
$332$	10.8259	−	6.25036i	0.594151	−	0.343033i
$333$	10.6020	−	6.56505i	0.580983	−	0.359763i
$334$	18.4911	−	10.6759i	1.01179	−	0.584157i
$335$	−1.92162	+	3.32835i	−0.104989	+	0.181847i
$336$	4.51783	−	0.767584i	0.246468	−	0.0418751i
$337$	15.7709			0.859096			0.429548	−	0.903044i	$-0.358673\pi$
$337$	15.7709			0.859096			0.429548	+	0.903044i	$0.358673\pi$
$338$	−3.68767	+	12.4660i	−0.200583	+	0.678061i
$339$	−4.82709	+	8.66671i	−0.262172	+	0.470711i
$340$	0.660417	+	0.381292i	0.0358161	+	0.0206784i
$341$	1.54238	−	2.67148i	0.0835245	−	0.144669i
$342$	7.15100	−	13.3182i	0.386682	−	0.720164i
$343$	−8.19912	−	16.6065i	−0.442711	−	0.896664i
$344$	−3.81091	−	6.60069i	−0.205470	−	0.355885i
$345$	0.112283	+	7.28084i	0.00604512	+	0.391987i
$346$	−7.33922			−0.394559
$347$	−17.2114	+	9.93698i	−0.923954	+	0.533445i	−0.884894	−	0.465792i	$-0.845770\pi$
$347$	−17.2114	+	9.93698i	−0.923954	+	0.533445i	−0.0390595	+	0.999237i	$0.512436\pi$
$348$	−0.861317	−	1.44010i	−0.0461715	−	0.0771972i
$349$	8.02933	−	13.9072i	0.429800	−	0.744436i	−0.567055	−	0.823680i	$-0.691917\pi$
$349$	8.02933	−	13.9072i	0.429800	−	0.744436i	0.996855	+	0.0792439i	$0.0252506\pi$
$350$	11.2709	+	4.38100i	0.602458	+	0.234174i
$351$	−18.4828	+	3.06346i	−0.986541	+	0.163515i
$352$	0.733697			0.0391062
$353$	−23.2239	−	13.4084i	−1.23609	−	0.713655i	−0.267794	−	0.963476i	$-0.586295\pi$
$353$	−23.2239	−	13.4084i	−1.23609	−	0.713655i	−0.968292	+	0.249822i	$0.919628\pi$
$354$	2.21541	+	3.70410i	0.117748	+	0.196871i
$355$	4.65366	−	2.68679i	0.246990	−	0.142600i
$356$			14.6413i			0.775987i
$357$	−1.85502	+	4.99936i	−0.0981782	+	0.264594i
$358$	2.15825	−	1.24607i	0.114067	−	0.0658566i
$359$	−31.4068			−1.65759			−0.828795	−	0.559553i	$-0.810973\pi$
$359$	−31.4068			−1.65759			−0.828795	+	0.559553i	$0.810973\pi$
$360$	1.73215	+	0.930053i	0.0912923	+	0.0490181i
$361$	−3.19503	+	5.53396i	−0.168160	+	0.291261i
$362$	−16.7885	−	9.69283i	−0.882383	−	0.509444i
$363$	−15.8304	−	8.81703i	−0.830879	−	0.462774i
$364$	6.80624	+	6.68394i	0.356744	+	0.350334i
$365$			4.54164i			0.237720i
$366$	0.957610	+	1.60109i	0.0500551	+	0.0836905i
$367$	1.82808	+	1.05544i	0.0954251	+	0.0550937i	0.546953	−	0.837163i	$-0.315788\pi$
$367$	1.82808	+	1.05544i	0.0954251	+	0.0550937i	−0.451528	+	0.892257i	$0.649121\pi$
$368$	−5.55559	+	3.20752i	−0.289605	+	0.167204i
$369$	−12.4526	+	7.71101i	−0.648254	+	0.401419i
$370$	−1.36204	−	2.35912i	−0.0708089	−	0.122645i
$371$	−3.38830	+	0.522054i	−0.175912	+	0.0271037i
$372$	6.36199	+	3.54344i	0.329854	+	0.183719i
$373$	12.1368	+	21.0216i	0.628421	+	1.08846i	0.987869	+	0.155292i	$0.0496318\pi$
$373$	12.1368	+	21.0216i	0.628421	+	1.08846i	−0.359448	+	0.933165i	$0.617035\pi$
$374$	−0.426876	+	0.739371i	−0.0220732	+	0.0382319i
$375$	5.57616	+	9.32317i	0.287952	+	0.481446i
$376$			6.48204i			0.334286i
$377$	1.37829	−	3.20965i	0.0709853	−	0.165306i
$378$	−4.38279	+	13.0304i	−0.225426	+	0.670211i
$379$	8.39822	+	4.84872i	0.431388	+	0.249062i	0.699938	−	0.714204i	$-0.253211\pi$
$379$	8.39822	+	4.84872i	0.431388	+	0.249062i	−0.268550	+	0.963266i	$0.586544\pi$
$380$	−2.85980	−	1.65110i	−0.146705	−	0.0846999i
$381$	0.200026	+	12.9704i	0.0102477	+	0.664494i
$382$		−	13.6857i		−	0.700223i
$383$	23.5996	−	13.6253i	1.20589	−	0.696218i	0.244028	−	0.969768i	$-0.421531\pi$
$383$	23.5996	−	13.6253i	1.20589	−	0.696218i	0.961858	+	0.273550i	$0.0881979\pi$
$384$	0.0267080	+	1.73184i	0.00136294	+	0.0883778i
$385$	0.460890	−	1.18573i	0.0234891	−	0.0604303i
$386$	18.7113	−	10.8030i	0.952380	−	0.549857i
$387$	22.8546	−	0.705082i	1.16176	−	0.0358413i
$388$	3.36975	−	5.83658i	0.171073	−	0.296307i
$389$		−	16.2748i		−	0.825166i	−0.910920	−	0.412583i	$-0.864627\pi$
$389$		−	16.2748i		−	0.825166i	0.910920	−	0.412583i	$-0.135373\pi$
$390$	0.544390	+	4.05629i	0.0275663	+	0.205398i
$391$		−	7.46473i		−	0.377508i
$392$	6.67536	−	2.10704i	0.337156	−	0.106421i
$393$	18.7245	−	11.1991i	0.944527	−	0.564919i
$394$	10.6029	+	18.3647i	0.534165	+	0.925200i
$395$			8.64746i			0.435101i
$396$	−1.04124	+	1.93923i	−0.0523244	+	0.0974501i
$397$	10.1097	+	17.5105i	0.507390	+	0.878825i	0.999963	+	0.00855427i	$0.00272294\pi$
$397$	10.1097	+	17.5105i	0.507390	+	0.878825i	−0.492573	+	0.870271i	$0.663944\pi$
$398$			3.43023i			0.171942i
$399$	8.03279	−	21.6487i	0.402142	−	1.08379i
$400$	−2.28526	+	3.95818i	−0.114263	+	0.197909i
$401$	−16.5578	+	28.6789i	−0.826856	+	1.43216i	0.0736358	+	0.997285i	$0.476540\pi$
$401$	−16.5578	+	28.6789i	−0.826856	+	1.43216i	−0.900492	+	0.434872i	$0.856794\pi$
$402$	4.94249	−	8.87390i	0.246509	−	0.442590i
$403$	1.78450	+	15.0538i	0.0888925	+	0.749882i
$404$	−2.31478			−0.115165
$405$	−4.91644	+	3.25833i	−0.244300	+	0.161908i
$406$	−1.60469	−	1.99876i	−0.0796394	−	0.0991967i
$407$	2.64115	−	1.52487i	0.130917	−	0.0755850i
$408$	−1.76078	−	0.980698i	−0.0871714	−	0.0485518i
$409$	−18.8192	−	32.5957i	−0.930547	−	1.61175i	−0.782388	−	0.622791i	$-0.785999\pi$
$409$	−18.8192	−	32.5957i	−0.930547	−	1.61175i	−0.148159	−	0.988964i	$-0.547335\pi$
$410$	1.59978	+	2.77091i	0.0790077	+	0.136845i
$411$	33.6941	+	18.7666i	1.66201	+	0.925687i
$412$	−9.77953	+	5.64621i	−0.481803	+	0.278169i
$413$	4.12746	+	5.14105i	0.203099	+	0.252975i
$414$	−0.593445	−	19.2360i	−0.0291662	−	0.945397i
$415$	8.19234			0.402146
$416$	−2.88857	+	2.15781i	−0.141624	+	0.105796i
$417$	−3.06679	+	5.50621i	−0.150181	+	0.269640i
$418$	1.84850	−	3.20169i	0.0904130	−	0.156600i
$419$	−15.8330	+	27.4235i	−0.773492	+	1.33973i	0.162146	+	0.986767i	$0.448158\pi$
$419$	−15.8330	+	27.4235i	−0.773492	+	1.33973i	−0.935638	+	0.352961i	$0.885175\pi$
$420$	2.81561	+	1.04474i	0.137388	+	0.0509780i
$421$		−	3.23775i		−	0.157798i	−0.996883	−	0.0788991i	$-0.974860\pi$
$421$		−	3.23775i		−	0.157798i	0.996883	−	0.0788991i	$-0.0251405\pi$
$422$	−12.4331	−	21.5347i	−0.605233	−	1.04829i
$423$	−17.1327	−	9.19913i	−0.833018	−	0.447277i
$424$		−	1.29577i		−	0.0629281i
$425$	−2.65919	−	4.60586i	−0.128990	−	0.223417i
$426$	−12.1884	+	7.28984i	−0.590530	+	0.353194i
$427$	1.78409	+	2.22221i	0.0863381	+	0.107540i
$428$		−	6.18372i		−	0.298901i
$429$	−4.54122	+	0.609473i	−0.219252	+	0.0294256i
$430$		−	4.99495i		−	0.240878i
$431$	−1.47511	+	2.55497i	−0.0710536	+	0.123068i	−0.899363	−	0.437202i	$-0.855969\pi$
$431$	−1.47511	+	2.55497i	−0.0710536	+	0.123068i	0.828310	+	0.560270i	$0.189303\pi$
$432$	−4.61533	−	2.38719i	−0.222055	−	0.114854i
$433$	20.2415	−	11.6864i	0.972742	−	0.561613i	0.0726709	−	0.997356i	$-0.476848\pi$
$433$	20.2415	−	11.6864i	0.972742	−	0.561613i	0.900071	+	0.435743i	$0.143514\pi$
$434$	10.3681	+	4.03006i	0.497685	+	0.193449i
$435$	−0.0169571	−	1.09956i	−0.000813029	−	0.0527197i
$436$	−14.0505	+	8.11209i	−0.672899	+	0.388499i
$437$			32.3245i			1.54629i
$438$	−0.185090	−	12.0019i	−0.00884392	−	0.573472i
$439$	−15.3108	−	8.83972i	−0.730747	−	0.421897i	0.0879485	−	0.996125i	$-0.471969\pi$
$439$	−15.3108	−	8.83972i	−0.730747	−	0.421897i	−0.818695	+	0.574228i	$0.805302\pi$
$440$	0.416409	+	0.240414i	0.0198515	+	0.0114613i
$441$	−3.90438	+	20.6339i	−0.185923	+	0.982564i
$442$	−0.493888	−	4.16635i	−0.0234918	−	0.198173i
$443$		−	5.76939i		−	0.274112i	−0.990563	−	0.137056i	$-0.956236\pi$
$443$		−	5.76939i		−	0.274112i	0.990563	−	0.137056i	$-0.0437640\pi$
$444$	3.69550	+	6.17876i	0.175381	+	0.293231i
$445$	−4.79758	+	8.30965i	−0.227427	+	0.393915i
$446$	−4.26929	−	7.39463i	−0.202157	−	0.350146i
$447$	−33.0153	−	18.3885i	−1.56157	−	0.869746i
$448$	0.402891	+	2.61490i	0.0190348	+	0.123542i
$449$	6.85295	+	11.8697i	0.323411	+	0.560164i	0.981189	−	0.193047i	$-0.0618371\pi$
$449$	6.85295	+	11.8697i	0.323411	+	0.560164i	−0.657779	+	0.753211i	$0.728504\pi$
$450$	−7.21868	−	11.6575i	−0.340292	−	0.549540i
$451$	−3.10217	+	1.79104i	−0.146076	+	0.0843368i
$452$	−4.96016	−	2.86375i	−0.233306	−	0.134699i
$453$	5.64387	+	9.43637i	0.265172	+	0.443359i
$454$		−	6.92511i		−	0.325012i
$455$	1.67272	+	6.02370i	0.0784181	+	0.282395i
$456$	7.62467	+	4.24671i	0.357058	+	0.198870i
$457$	7.47187	+	4.31389i	0.349519	+	0.201795i	0.664474	−	0.747312i	$-0.268656\pi$
$457$	7.47187	+	4.31389i	0.349519	+	0.201795i	−0.314954	+	0.949107i	$0.601989\pi$
$458$	−2.34250	+	4.05732i	−0.109458	+	0.189586i
$459$	5.09092	−	3.26212i	0.237624	−	0.152263i
$460$	−4.20409			−0.196017
$461$	−28.5935	+	16.5084i	−1.33173	+	0.768875i	−0.985565	−	0.169299i	$-0.945850\pi$
$461$	−28.5935	+	16.5084i	−1.33173	+	0.768875i	−0.346165	+	0.938173i	$0.612516\pi$
$462$	−1.16964	+	3.15222i	−0.0544165	+	0.146655i
$463$			18.6394i			0.866246i	0.901335	+	0.433123i	$0.142589\pi$
$463$			18.6394i			0.866246i	−0.901335	+	0.433123i	$0.857411\pi$
$464$	0.839009	−	0.484402i	0.0389500	−	0.0224878i
$465$	2.44965	+	4.09574i	0.113600	+	0.189935i
$466$	−7.45984	−	4.30694i	−0.345570	−	0.199515i
$467$	−2.44186			−0.112996			−0.0564978	−	0.998403i	$-0.517993\pi$
$467$	−2.44186			−0.112996			−0.0564978	+	0.998403i	$0.517993\pi$
$468$	−1.60393	−	10.6971i	−0.0741418	−	0.494472i
$469$	5.62124	−	14.4617i	0.259565	−	0.667781i
$470$	−2.12400	+	3.67888i	−0.0979728	+	0.169694i
$471$	−5.40738	−	9.04097i	−0.249159	−	0.416586i
$472$	−2.15803	+	1.24594i	−0.0993316	+	0.0573491i
$473$	5.59211			0.257125
$474$	−0.352418	−	22.8520i	−0.0161871	−	1.04963i
$475$	11.5151	+	19.9447i	0.528348	+	0.915126i
$476$	−2.86952	−	1.11538i	−0.131524	−	0.0511233i
$477$	3.42484	+	1.83892i	0.156813	+	0.0841983i
$478$	−5.13049	+	8.88626i	−0.234663	+	0.406448i
$479$	−27.1685	−	15.6857i	−1.24136	−	0.716699i	−0.271989	−	0.962300i	$-0.587681\pi$
$479$	−27.1685	−	15.6857i	−1.24136	−	0.716699i	−0.969371	+	0.245601i	$0.921015\pi$
$480$	−0.552323	+	0.991658i	−0.0252100	+	0.0452628i
$481$	−5.91356	+	13.7711i	−0.269635	+	0.627907i
$482$	16.1074			0.733670
$483$	−4.92408	−	28.9821i	−0.224054	−	1.31873i
$484$	5.23084	−	9.06009i	0.237766	−	0.411822i
$485$	3.82500	−	2.20836i	0.173684	−	0.100277i
$486$	12.8595	−	8.81093i	0.583320	−	0.399672i
$487$	−10.1304	+	5.84880i	−0.459053	+	0.265035i	−0.711646	−	0.702538i	$-0.752050\pi$
$487$	−10.1304	+	5.84880i	−0.459053	+	0.265035i	0.252593	+	0.967573i	$0.418717\pi$
$488$	−0.932808	+	0.538557i	−0.0422262	+	0.0243793i
$489$	8.55571	−	15.3612i	0.386902	−	0.694656i
$490$	4.47901	+	0.991498i	0.202341	+	0.0447913i
$491$	35.7809	+	20.6581i	1.61477	+	0.932287i	0.988244	+	0.152886i	$0.0488569\pi$
$491$	35.7809	+	20.6581i	1.61477	+	0.932287i	0.626525	+	0.779401i	$0.284476\pi$
$492$	−4.34056	−	7.25728i	−0.195688	−	0.327184i
$493$			1.12733i			0.0507723i
$494$	2.13868	+	18.0415i	0.0962237	+	0.811727i
$495$	−1.22639	+	0.759420i	−0.0551223	+	0.0341334i
$496$	−2.10220	+	3.64112i	−0.0943915	+	0.163491i
$497$	−16.9167	+	13.5815i	−0.758818	+	0.609211i
$498$	−21.6493	+	0.333870i	−0.970129	+	0.0149611i
$499$		−	25.7632i		−	1.15332i	−0.816985	−	0.576660i	$-0.804356\pi$
$499$		−	25.7632i		−	1.15332i	0.816985	−	0.576660i	$-0.195644\pi$
$500$	−5.43174	+	3.13602i	−0.242915	+	0.140247i
$501$	−36.9779	+	0.570262i	−1.65205	+	0.0254774i
$502$	20.9271			0.934021
$503$	−5.86833	−	10.1642i	−0.261656	−	0.453201i	0.705026	−	0.709181i	$-0.250935\pi$
$503$	−5.86833	−	10.1642i	−0.261656	−	0.453201i	−0.966682	+	0.255980i	$0.917602\pi$
$504$	−7.48319	−	2.64611i	−0.333328	−	0.117867i
$505$	−1.31375	−	0.758496i	−0.0584612	−	0.0337526i
$506$		−	4.70670i		−	0.209238i
$507$	16.0863	−	15.7553i	0.714420	−	0.699717i
$508$	−7.48936			−0.332287
$509$	−33.3626	−	19.2619i	−1.47877	−	0.853768i	−0.479059	−	0.877783i	$-0.659022\pi$
$509$	−33.3626	−	19.2619i	−1.47877	−	0.853768i	−0.999712	+	0.0240145i	$0.992355\pi$
$510$	−0.677976	−	1.13356i	−0.0300213	−	0.0501947i
$511$	−2.79208	−	18.1215i	−0.123514	−	0.801648i
$512$	−1.00000			−0.0441942
$513$	−22.0452	+	14.1259i	−0.973319	+	0.623675i
$514$	−13.7555	−	23.8253i	−0.606731	−	1.05089i
$515$	−7.40048			−0.326104
$516$	0.203564	+	13.1998i	0.00896140	+	0.581089i
$517$	−4.11869	−	2.37793i	−0.181140	−	0.104581i
$518$	6.88495	+	8.57572i	0.302507	+	0.376795i
$519$	11.1055	+	6.18544i	0.487479	+	0.271511i
$520$	−2.34647	+	0.278155i	−0.102899	+	0.0121979i
$521$	38.0123			1.66535			0.832674	−	0.553763i	$-0.186809\pi$
$521$	38.0123			1.66535			0.832674	+	0.553763i	$0.186809\pi$
$522$	0.0896225	+	2.90503i	0.00392267	+	0.127150i
$523$	−29.6865	−	17.1395i	−1.29810	−	0.749458i	−0.318024	−	0.948083i	$-0.603019\pi$
$523$	−29.6865	−	17.1395i	−1.29810	−	0.749458i	−0.980076	+	0.198625i	$0.936353\pi$
$524$	6.29833	+	10.9090i	0.275144	+	0.476563i
$525$	−13.3627	−	16.1283i	−0.583194	−	0.703896i
$526$	−27.0282	+	15.6048i	−1.17849	+	0.680400i
$527$	−2.44618	−	4.23691i	−0.106557	−	0.184563i
$528$	−1.11021	−	0.618355i	−0.0483158	−	0.0269104i
$529$	9.07639	+	15.7208i	0.394626	+	0.683512i
$530$	0.424590	−	0.735412i	0.0184430	−	0.0319443i
$531$	−0.230520	−	7.47209i	−0.0100037	−	0.324261i
$532$	12.4259	+	4.82991i	0.538730	+	0.209403i
$533$	6.94580	−	16.1749i	0.300856	−	0.700612i
$534$	12.3396	−	22.1548i	0.533985	−	0.958734i
$535$	2.02625	−	3.50957i	0.0876024	−	0.151732i
$536$	5.07874	+	2.93221i	0.219368	+	0.126652i
$537$	−4.31598	+	0.0665599i	−0.186248	+	0.00287227i
$538$	0.0618987			0.00266864
$539$	−1.11003	+	5.01449i	−0.0478125	+	0.215989i
$540$	−1.83721	−	2.86718i	−0.0790607	−	0.123384i
$541$		−	20.6184i		−	0.886454i	−0.896410	−	0.443227i	$-0.853834\pi$
$541$		−	20.6184i		−	0.886454i	0.896410	−	0.443227i	$-0.146166\pi$
$542$	2.55715	+	4.42912i	0.109839	+	0.190247i
$543$	17.2349	+	28.8162i	0.739619	+	1.23662i
$544$	0.581815	−	1.00773i	0.0249451	−	0.0432062i
$545$	−10.6325			−0.455446
$546$	−4.66586	−	15.8502i	−0.199680	−	0.678327i
$547$	−27.3235			−1.16827			−0.584134	−	0.811658i	$-0.698566\pi$
$547$	−27.3235			−1.16827			−0.584134	+	0.811658i	$0.698566\pi$
$548$	−11.1336	+	19.2839i	−0.475602	+	0.823767i
$549$	−0.0996420	−	3.22980i	−0.00425262	−	0.137845i
$550$	−1.67669	−	2.90411i	−0.0714942	−	0.123832i
$551$		−	4.88166i		−	0.207966i
$552$	11.1099	−	0.171333i	0.472867	−	0.00729243i
$553$	−5.31623	−	34.5040i	−0.226069	−	1.46726i
$554$	−14.1684			−0.601957
$555$	0.0727546	+	4.71767i	0.00308826	+	0.200254i
$556$	−3.15133	−	1.81942i	−0.133646	−	0.0771607i
$557$	4.33794	−	7.51353i	0.183804	−	0.318358i	−0.759369	−	0.650661i	$-0.774492\pi$
$557$	4.33794	−	7.51353i	0.183804	−	0.318358i	0.943173	+	0.332302i	$0.107825\pi$
$558$	−6.64043	−	10.7237i	−0.281112	−	0.453970i
$559$	−22.0162	+	16.4465i	−0.931184	+	0.695612i
$560$	−0.628174	+	1.61610i	−0.0265452	+	0.0682926i
$561$	1.26907	−	0.759030i	0.0535804	−	0.0320463i
$562$	1.77069	−	3.06692i	0.0746920	−	0.129370i
$563$	−6.82336	−	11.8184i	−0.287570	−	0.498087i	0.685659	−	0.727923i	$-0.259514\pi$
$563$	−6.82336	−	11.8184i	−0.287570	−	0.498087i	−0.973229	+	0.229836i	$0.926181\pi$
$564$	5.46302	−	9.80847i	0.230035	−	0.413011i
$565$	−1.87675	−	3.25063i	−0.0789557	−	0.136755i
$566$	18.6608	−	10.7738i	0.784373	−	0.452858i
$567$	17.6138	−	16.0235i	0.739712	−	0.672924i
$568$	−4.09978	−	7.10103i	−0.172023	−	0.297953i
$569$	−22.2652	−	12.8548i	−0.933404	−	0.538901i	−0.0455175	−	0.998964i	$-0.514494\pi$
$569$	−22.2652	−	12.8548i	−0.933404	−	0.538901i	−0.887887	+	0.460062i	$0.847827\pi$
$570$	2.93584	+	4.90863i	0.122969	+	0.205600i
$571$	4.42968			0.185376			0.0926881	−	0.995695i	$-0.470454\pi$
$571$	4.42968			0.185376			0.0926881	+	0.995695i	$0.470454\pi$
$572$	−0.311409	−	2.62699i	−0.0130206	−	0.109840i
$573$	−11.5342	+	20.7089i	−0.481849	+	0.865127i
$574$	−8.08675	−	10.0726i	−0.337534	−	0.420424i
$575$	25.3919	+	14.6600i	1.05892	+	0.611366i
$576$	1.41917	−	2.64309i	0.0591322	−	0.110129i
$577$	24.2166			1.00815			0.504075	−	0.863660i	$-0.331834\pi$
$577$	24.2166			1.00815			0.504075	+	0.863660i	$0.331834\pi$
$578$	−7.82298	−	13.5498i	−0.325393	−	0.563598i
$579$	−37.4181	+	0.577052i	−1.55504	+	0.0239815i
$580$	0.634905			0.0263630
$581$	−32.6881	+	5.03643i	−1.35613	+	0.208946i
$582$	−10.0180	+	5.99177i	−0.415261	+	0.248367i
$583$	0.823332	+	0.475351i	0.0340989	+	0.0196870i
$584$	6.93011			0.286770
$585$	2.59485	−	6.59668i	0.107284	−	0.272739i
$586$		−	22.1375i		−	0.914494i
$587$	−16.9787	−	9.80266i	−0.700786	−	0.404599i	0.106854	−	0.994275i	$-0.465922\pi$
$587$	−16.9787	−	9.80266i	−0.700786	−	0.404599i	−0.807640	+	0.589676i	$0.799256\pi$
$588$	−11.8768	−	2.43763i	−0.489790	−	0.100526i
$589$	10.5927	+	18.3471i	0.436464	+	0.755977i
$590$	−1.63305			−0.0672317
$591$	−0.566363	−	36.7250i	−0.0232971	−	1.51067i
$592$	−3.59978	+	2.07834i	−0.147950	+	0.0854191i
$593$			7.95508i			0.326676i	0.986570	+	0.163338i	$0.0522261\pi$
$593$			7.95508i			0.326676i	−0.986570	+	0.163338i	$0.947774\pi$
$594$	3.20995	−	2.05685i	0.131706	−	0.0843934i
$595$	−1.26311	−	1.57330i	−0.0517826	−	0.0644991i
$596$	10.9093	−	18.8954i	0.446861	−	0.773986i
$597$	2.89098	−	5.19055i	0.118320	−	0.212435i
$598$	13.8425	+	18.5303i	0.566061	+	0.757760i
$599$			22.9488i			0.937662i	0.883288	+	0.468831i	$0.155325\pi$
$599$			22.9488i			0.937662i	−0.883288	+	0.468831i	$0.844675\pi$
$600$	6.79393	−	4.06343i	0.277361	−	0.165889i
$601$	6.23997	+	3.60265i	0.254534	+	0.146955i	0.621839	−	0.783145i	$-0.286386\pi$
$601$	6.23997	+	3.60265i	0.254534	+	0.146955i	−0.367305	+	0.930101i	$0.619719\pi$
$602$	3.07076	+	19.9303i	0.125155	+	0.812297i
$603$	−14.9577	+	9.26227i	−0.609125	+	0.377189i
$604$	−5.49769	+	3.17409i	−0.223698	+	0.129152i
$605$	5.93752	−	3.42803i	0.241395	−	0.139369i
$606$	3.50267	+	1.95088i	0.142286	+	0.0792492i
$607$	0.0665333	−	0.0384130i	0.00270050	−	0.00155914i	−0.498649	−	0.866804i	$-0.666170\pi$
$607$	0.0665333	−	0.0384130i	0.00270050	−	0.00155914i	0.501350	+	0.865245i	$0.332837\pi$
$608$	−2.51943	+	4.36378i	−0.102176	+	0.176975i
$609$	0.743638	+	4.37689i	0.0301337	+	0.177361i
$610$	−0.705885			−0.0285805
$611$	23.2088	−	2.75122i	0.938929	−	0.111303i
$612$	1.83784	+	2.96794i	0.0742902	+	0.119972i
$613$	−32.8419	−	18.9613i	−1.32647	−	0.765838i	−0.341718	−	0.939802i	$-0.611009\pi$
$613$	−32.8419	−	18.9613i	−1.32647	−	0.765838i	−0.984752	+	0.173965i	$0.944342\pi$
$614$	1.08820	−	1.88482i	0.0439161	−	0.0760650i
$615$	−0.0854542	−	5.54116i	−0.00344585	−	0.223441i
$616$	−1.80931	−	0.703274i	−0.0728990	−	0.0283357i
$617$	−1.59443	−	2.76163i	−0.0641892	−	0.111179i	0.832145	−	0.554558i	$-0.187113\pi$
$617$	−1.59443	−	2.76163i	−0.0641892	−	0.111179i	−0.896334	+	0.443379i	$0.853779\pi$
$618$	19.5567	−	0.301599i	0.786687	−	0.0121321i
$619$	−10.9786			−0.441267			−0.220634	−	0.975357i	$-0.570812\pi$
$619$	−10.9786			−0.441267			−0.220634	+	0.975357i	$0.570812\pi$
$620$	−2.38620	+	1.37767i	−0.0958322	+	0.0553287i
$621$	−15.3140	+	29.6076i	−0.614528	+	1.18811i
$622$	−3.55142	+	6.15125i	−0.142399	+	0.246643i
$623$	14.0342	−	36.1056i	0.562267	−	1.44654i
$624$	6.18950	−	0.830687i	0.247778	−	0.0332541i
$625$	18.7422			0.749689
$626$	−14.8369	−	8.56609i	−0.593002	−	0.342370i
$627$	−5.49546	+	3.28682i	−0.219468	+	0.131263i
$628$	5.26732	−	3.04109i	0.210189	−	0.121353i
$629$		−	4.83683i		−	0.192857i
$630$	−3.38001	−	3.95385i	−0.134663	−	0.157525i
$631$	2.23519	−	1.29049i	0.0889816	−	0.0513735i	−0.454849	−	0.890569i	$-0.650307\pi$
$631$	2.23519	−	1.29049i	0.0889816	−	0.0513735i	0.543831	+	0.839195i	$0.316973\pi$
$632$	13.1952			0.524877
$633$	0.664127	+	43.0644i	0.0263967	+	1.71165i
$634$	−12.3174	+	21.3343i	−0.489185	+	0.847293i
$635$	−4.25058	−	2.45407i	−0.168679	−	0.0973869i
$636$	−1.09206	+	1.96072i	−0.0433031	+	0.0777478i
$637$	−10.3775	−	23.0067i	−0.411171	−	0.911558i
$638$			0.710809i			0.0281412i
$639$	24.5870	−	0.758529i	0.972647	−	0.0300069i
$640$	−0.567549	−	0.327675i	−0.0224343	−	0.0129525i
$641$	21.6084	−	12.4756i	0.853482	−	0.492758i	−0.00834190	−	0.999965i	$-0.502655\pi$
$641$	21.6084	−	12.4756i	0.853482	−	0.492758i	0.861824	+	0.507207i	$0.169322\pi$
$642$	−5.21160	+	9.35706i	−0.205685	+	0.369294i
$643$	2.49176	+	4.31585i	0.0982653	+	0.170200i	0.910967	−	0.412480i	$-0.135337\pi$
$643$	2.49176	+	4.31585i	0.0982653	+	0.170200i	−0.812701	+	0.582680i	$0.802004\pi$
$644$	16.7747	−	2.58456i	0.661015	−	0.101846i
$645$	−4.20971	+	7.55824i	−0.165757	+	0.297605i
$646$	−2.93168	−	5.07782i	−0.115345	−	0.199784i
$647$	15.4932	−	26.8350i	0.609101	−	1.05499i	−0.382288	−	0.924043i	$-0.624864\pi$
$647$	15.4932	−	26.8350i	0.609101	−	1.05499i	0.991389	−	0.130951i	$-0.0418030\pi$
$648$	4.97190	+	7.50201i	0.195315	+	0.294707i
$649$		−	1.82829i		−	0.0717666i
$650$	15.1422	+	6.50233i	0.593924	+	0.255042i
$651$	−12.2922	−	14.8363i	−0.481771	−	0.581482i
$652$	8.79156	+	5.07581i	0.344304	+	0.198784i
$653$	22.3928	+	12.9285i	0.876299	+	0.505931i	0.869436	−	0.494045i	$-0.164482\pi$
$653$	22.3928	+	12.9285i	0.876299	+	0.505931i	0.00686241	+	0.999976i	$0.497816\pi$
$654$	28.0978	−	0.433316i	1.09871	−	0.0169440i
$655$			8.25521i			0.322558i
$656$	4.22814	−	2.44112i	0.165081	−	0.0953096i
$657$	−9.83502	+	18.3169i	−0.383701	+	0.714612i
$658$	6.21326	−	15.9848i	0.242218	−	0.623152i
$659$	−37.8578	+	21.8572i	−1.47473	+	0.851436i	−0.999594	−	0.0284766i	$-0.990934\pi$
$659$	−37.8578	+	21.8572i	−1.47473	+	0.851436i	−0.475136	+	0.879912i	$0.657601\pi$
$660$	−0.427481	−	0.714735i	−0.0166397	−	0.0278210i
$661$	16.3148	−	28.2581i	0.634573	−	1.09911i	−0.352032	−	0.935988i	$-0.614509\pi$
$661$	16.3148	−	28.2581i	0.634573	−	1.09911i	0.986605	−	0.163125i	$-0.0521575\pi$
$662$			11.3987i			0.443024i
$663$	−2.76403	+	6.72067i	−0.107346	+	0.261009i
$664$		−	12.5007i		−	0.485122i
$665$	5.46965	+	6.81286i	0.212104	+	0.264191i
$666$	−0.384527	−	12.4641i	−0.0149001	−	0.482974i
$667$	−3.10746	−	5.38228i	−0.120321	−	0.208403i
$668$		−	21.3517i		−	0.826122i
$669$	0.228049	+	14.7875i	0.00881688	+	0.571718i
$670$	1.92162	+	3.32835i	0.0742387	+	0.128585i
$671$		−	0.790275i		−	0.0305082i
$672$	1.59417	−	4.29635i	0.0614964	−	0.165735i
$673$	8.95203	−	15.5054i	0.345076	−	0.597688i	−0.640292	−	0.768132i	$-0.721187\pi$
$673$	8.95203	−	15.5054i	0.345076	−	0.597688i	0.985367	+	0.170443i	$0.0545200\pi$
$674$	7.88546	−	13.6580i	0.303736	−	0.526087i
$675$	1.09828	+	23.7237i	0.0422727	+	0.913126i
$676$	8.95203	+	9.42662i	0.344309	+	0.362562i
$677$	20.3466			0.781983			0.390992	−	0.920394i	$-0.372132\pi$
$677$	20.3466			0.781983			0.390992	+	0.920394i	$0.372132\pi$
$678$	5.09204	+	8.51374i	0.195559	+	0.326968i
$679$	−13.9044	+	11.1630i	−0.533602	+	0.428398i
$680$	0.660417	−	0.381292i	0.0253258	−	0.0146219i
$681$	−5.83643	+	10.4789i	−0.223653	+	0.401553i
$682$	−1.54238	−	2.67148i	−0.0590607	−	0.102296i
$683$	10.2174	+	17.6970i	0.390956	+	0.677156i	0.992576	−	0.121627i	$-0.0388111\pi$
$683$	10.2174	+	17.6970i	0.390956	+	0.677156i	−0.601620	+	0.798783i	$0.705478\pi$
$684$	−7.95837	−	12.8520i	−0.304296	−	0.491410i
$685$	−12.6377	+	7.29637i	−0.482861	+	0.278780i
$686$	−18.4812	−	1.20258i	−0.705615	−	0.0459147i
$687$	6.96409	−	4.16520i	0.265697	−	0.158912i
$688$	−7.62182			−0.290579
$689$	−4.63947	+	0.549972i	−0.176750	+	0.0209523i
$690$	6.36153	+	3.54318i	0.242179	+	0.134887i
$691$	−25.8706	+	44.8092i	−0.984165	+	1.70462i	−0.338573	+	0.940940i	$0.609944\pi$
$691$	−25.8706	+	44.8092i	−0.984165	+	1.70462i	−0.645591	+	0.763683i	$0.723389\pi$
$692$	−3.66961	+	6.35595i	−0.139498	+	0.241617i
$693$	4.42654	−	3.78410i	0.168150	−	0.143746i
$694$			19.8740i			0.754405i
$695$	−1.19236	−	2.06522i	−0.0452287	−	0.0783384i
$696$	−1.67782	+	0.0258749i	−0.0635975	+	0.000980784i
$697$			5.68111i			0.215187i
$698$	−8.02933	−	13.9072i	−0.303915	−	0.526396i
$699$	7.65819	+	12.8043i	0.289659	+	0.484301i
$700$	9.42953	−	7.57043i	0.356403	−	0.286135i
$701$		−	12.8757i		−	0.486308i	−0.969988	−	0.243154i	$-0.921818\pi$
$701$		−	12.8757i		−	0.486308i	0.969988	−	0.243154i	$-0.0781820\pi$
$702$	−6.58839	+	17.5383i	−0.248663	+	0.661942i
$703$			20.9449i			0.789951i
$704$	0.366849	−	0.635401i	0.0138261	−	0.0239476i
$705$	6.31452	−	3.77669i	0.237818	−	0.142239i
$706$	−23.2239	+	13.4084i	−0.874045	+	0.504630i
$707$	5.70828	+	2.21880i	0.214682	+	0.0834465i
$708$	4.31555	−	0.0665533i	0.162188	−	0.00250123i
$709$	13.9466	−	8.05207i	0.523776	−	0.302402i	−0.214702	−	0.976680i	$-0.568878\pi$
$709$	13.9466	−	8.05207i	0.523776	−	0.302402i	0.738478	+	0.674278i	$0.235545\pi$
$710$		−	5.37358i		−	0.201667i
$711$	−18.7262	+	34.8761i	−0.702289	+	1.30796i
$712$	12.6797	+	7.32065i	0.475193	+	0.274353i
$713$	23.3579	+	13.4857i	0.874761	+	0.505043i
$714$	3.40206	+	4.10618i	0.127319	+	0.153670i
$715$	0.684058	−	1.59299i	0.0255823	−	0.0595743i
$716$		−	2.49213i		−	0.0931353i
$717$	15.2526	−	9.12254i	0.569619	−	0.340687i
$718$	−15.7034	+	27.1991i	−0.586046	+	1.01506i
$719$	−13.1163	−	22.7181i	−0.489155	−	0.847241i	0.510768	−	0.859719i	$-0.329361\pi$
$719$	−13.1163	−	22.7181i	−0.489155	−	0.847241i	−0.999922	+	0.0124783i	$0.996028\pi$
$720$	1.67152	−	1.03506i	0.0622940	−	0.0385744i
$721$	29.5285	−	4.54962i	1.09970	−	0.169437i
$722$	3.19503	+	5.53396i	0.118907	+	0.205953i
$723$	−24.3733	−	13.5752i	−0.906451	−	0.504866i
$724$	−16.7885	+	9.69283i	−0.623939	+	0.360231i
$725$	−3.83470	−	2.21397i	−0.142417	−	0.0822247i
$726$	−15.5510	+	9.30099i	−0.577150	+	0.345192i
$727$			16.5596i			0.614161i	0.951683	+	0.307081i	$0.0993521\pi$
$727$			16.5596i			0.614161i	−0.951683	+	0.307081i	$0.900648\pi$
$728$	9.19158	−	2.55240i	0.340663	−	0.0945984i
$729$	−26.8845	+	2.49456i	−0.995723	+	0.0923911i
$730$	3.93318	+	2.27082i	0.145573	+	0.0840468i
$731$	4.43449	−	7.68075i	0.164015	−	0.284083i
$732$	1.86539	−	0.0287676i	0.0689469	−	0.00106328i
$733$	6.98748			0.258088			0.129044	−	0.991639i	$-0.458809\pi$
$733$	6.98748			0.258088			0.129044	+	0.991639i	$0.458809\pi$
$734$	1.82808	−	1.05544i	0.0674758	−	0.0389572i
$735$	−5.94191	−	5.27519i	−0.219171	−	0.194578i
$736$			6.41504i			0.236462i
$737$	−3.72626	+	2.15135i	−0.137258	+	0.0792462i
$738$	0.451648	+	14.6397i	0.0166254	+	0.538896i
$739$	6.55386	+	3.78387i	0.241087	+	0.139192i	0.615676	−	0.787999i	$-0.288883\pi$
$739$	6.55386	+	3.78387i	0.241087	+	0.139192i	−0.374589	+	0.927191i	$0.622216\pi$
$740$	−2.72407			−0.100139
$741$	11.9691	−	29.1025i	0.439695	−	1.06911i
$742$	−1.24204	+	3.19538i	−0.0455966	+	0.117306i
$743$	−14.6769	+	25.4211i	−0.538443	+	0.932610i	0.460545	+	0.887636i	$0.347654\pi$
$743$	−14.6769	+	25.4211i	−0.538443	+	0.932610i	−0.998988	+	0.0449741i	$0.985679\pi$
$744$	6.24970	−	3.73793i	0.229125	−	0.137039i
$745$	12.3831	−	7.14938i	0.453681	−	0.261933i
$746$	24.2736			0.888721
$747$	33.0406	+	17.7407i	1.20889	+	0.649097i
$748$	0.426876	+	0.739371i	0.0156081	+	0.0270341i
$749$	−5.92731	+	15.2491i	−0.216579	+	0.557191i
$750$	10.8622	−	0.167514i	0.396631	−	0.00611673i
$751$	22.9520	−	39.7541i	0.837531	−	1.45065i	−0.0544211	−	0.998518i	$-0.517331\pi$
$751$	22.9520	−	39.7541i	0.837531	−	1.45065i	0.891953	−	0.452129i	$-0.149335\pi$
$752$	5.61361	+	3.24102i	0.204707	+	0.118188i
$753$	−31.6663	−	17.6372i	−1.15399	−	0.642735i
$754$	−2.09050	−	2.79846i	−0.0761315	−	0.101914i
$755$	−4.16028			−0.151408
$756$	9.09326	+	10.3108i	0.330719	+	0.375000i
$757$	18.3065	−	31.7078i	0.665361	−	1.15244i	−0.313826	−	0.949481i	$-0.601611\pi$
$757$	18.3065	−	31.7078i	0.665361	−	1.15244i	0.979187	−	0.202959i	$-0.0650559\pi$
$758$	8.39822	−	4.84872i	0.305037	−	0.176113i
$759$	−3.96677	+	7.12206i	−0.143985	+	0.258515i
$760$	−2.85980	+	1.65110i	−0.103736	+	0.0598919i
$761$	4.69480	−	2.71054i	0.170186	−	0.0982571i	−0.412487	−	0.910963i	$-0.635340\pi$
$761$	4.69480	−	2.71054i	0.170186	−	0.0982571i	0.582674	+	0.812706i	$0.302007\pi$
$762$	11.3327	+	6.31198i	0.410541	+	0.228659i
$763$	42.4245	−	6.53658i	1.53587	−	0.236640i
$764$	−11.8522	−	6.84286i	−0.428797	−	0.247566i
$765$	0.0705453	+	2.28666i	0.00255057	+	0.0826744i
$766$		−	27.2505i		−	0.984601i
$767$	5.37702	+	7.19798i	0.194153	+	0.259904i
$768$	1.51318	+	0.842793i	0.0546020	+	0.0304117i
$769$	2.00109	−	3.46599i	0.0721612	−	0.124987i	−0.827687	−	0.561190i	$-0.810344\pi$
$769$	2.00109	−	3.46599i	0.0721612	−	0.124987i	0.899848	+	0.436203i	$0.143677\pi$
$770$	−0.796425	−	0.992006i	−0.0287012	−	0.0357494i
$771$	0.734767	+	47.6449i	0.0264620	+	1.71589i
$772$		−	21.6059i		−	0.777615i
$773$	−25.5699	+	14.7628i	−0.919686	+	0.530981i	−0.883535	−	0.468365i	$-0.844843\pi$
$773$	−25.5699	+	14.7628i	−0.919686	+	0.530981i	−0.0361510	+	0.999346i	$0.511510\pi$
$774$	10.8167	−	20.1452i	0.388797	−	0.724104i
$775$	19.2163			0.690269
$776$	−3.36975	−	5.83658i	−0.120967	−	0.209521i
$777$	−3.19059	−	18.7792i	−0.114462	−	0.673698i
$778$	−14.0944	−	8.13741i	−0.505309	−	0.291740i
$779$		−	24.6009i		−	0.881418i
$780$	3.78504	+	1.55669i	0.135526	+	0.0557383i
$781$	6.01600			0.215269
$782$	−6.46465	−	3.73237i	−0.231175	−	0.133469i
$783$	2.31272	−	4.47135i	0.0826500	−	0.159793i
$784$	1.51293	−	6.83455i	0.0540333	−	0.244091i
$785$	3.98595			0.142265
$786$	−0.336432	−	21.8155i	−0.0120001	−	0.778132i
$787$	20.6739	+	35.8082i	0.736945	+	1.27643i	0.953865	+	0.300236i	$0.0970655\pi$
$787$	20.6739	+	35.8082i	0.736945	+	1.27643i	−0.216920	+	0.976189i	$0.569601\pi$
$788$	21.2057			0.755423
$789$	54.0500	−	0.833545i	1.92423	−	0.0296750i
$790$	7.48892	+	4.32373i	0.266444	+	0.153831i
$791$	9.48680	+	11.8165i	0.337312	+	0.420147i
$792$	1.15880	+	1.87136i	0.0411763	+	0.0664958i
$793$	2.32421	+	3.11132i	0.0825352	+	0.110486i
$794$	20.2193			0.717558
$795$	−1.26228	+	0.754966i	−0.0447684	+	0.0267759i
$796$	2.97067	+	1.71512i	0.105293	+	0.0607907i
$797$	11.8501	+	20.5250i	0.419753	+	0.727034i	0.995914	−	0.0903022i	$-0.0287833\pi$
$797$	11.8501	+	20.5250i	0.419753	+	0.727034i	−0.576161	+	0.817336i	$0.695450\pi$
$798$	−14.7319	−	17.7809i	−0.521504	−	0.629439i
$799$	−6.53216	+	3.77135i	−0.231091	+	0.133421i
$800$	2.28526	+	3.95818i	0.0807961	+	0.139943i
$801$	−37.3439	+	23.1245i	−1.31948	+	0.817063i
$802$	16.5578	+	28.6789i	0.584676	+	1.01269i
$803$	−2.54230	+	4.40339i	−0.0897159	+	0.155392i
$804$	−5.21378	−	8.71727i	−0.183876	−	0.307434i
$805$	10.3673	+	4.02977i	0.365401	+	0.142031i
$806$	13.9292	+	5.98146i	0.490635	+	0.210688i
$807$	−0.0936636	−	0.0521678i	−0.00329711	−	0.00183639i
$808$	−1.15739	+	2.00466i	−0.0407169	+	0.0705237i
$809$	28.4068	+	16.4007i	0.998730	+	0.576617i	0.907872	−	0.419247i	$-0.137706\pi$
$809$	28.4068	+	16.4007i	0.998730	+	0.576617i	0.0908575	+	0.995864i	$0.471039\pi$
$810$	0.363579	+	5.88693i	0.0127749	+	0.206845i
$811$	−8.64443			−0.303547			−0.151774	−	0.988415i	$-0.548498\pi$
$811$	−8.64443			−0.303547			−0.151774	+	0.988415i	$0.548498\pi$
$812$	−2.53332	+	0.390323i	−0.0889021	+	0.0136976i
$813$	−0.136593	−	8.85719i	−0.00479053	−	0.310635i
$814$		−	3.04974i		−	0.106893i
$815$	3.32643	+	5.76154i	0.116520	+	0.201818i
$816$	−1.72970	+	1.03453i	−0.0605515	+	0.0362157i
$817$	−19.2026	+	33.2599i	−0.671815	+	1.16362i
$818$	−37.6383			−1.31599
$819$	−6.29819	+	27.9165i	−0.220077	+	0.975483i
$820$	3.19957			0.111734
$821$	12.8952	−	22.3352i	0.450046	−	0.779503i	−0.548342	−	0.836254i	$-0.684741\pi$
$821$	12.8952	−	22.3352i	0.450046	−	0.779503i	0.998388	+	0.0567514i	$0.0180742\pi$
$822$	33.0994	−	19.7966i	1.15447	−	0.690487i
$823$	−7.55953	−	13.0935i	−0.263509	−	0.456411i	0.703663	−	0.710534i	$-0.251546\pi$
$823$	−7.55953	−	13.0935i	−0.263509	−	0.456411i	−0.967172	+	0.254123i	$0.918213\pi$
$824$			11.2924i			0.393390i
$825$	0.0895621	+	5.80753i	0.00311815	+	0.202192i
$826$	6.51601	−	1.00396i	0.226721	−	0.0349322i
$827$	5.85211			0.203498			0.101749	−	0.994810i	$-0.467556\pi$
$827$	5.85211			0.203498			0.101749	+	0.994810i	$0.467556\pi$
$828$	−16.9556	−	9.10405i	−0.589247	−	0.316388i
$829$	12.2127	+	7.05100i	0.424164	+	0.244891i	0.696857	−	0.717210i	$-0.254581\pi$
$829$	12.2127	+	7.05100i	0.424164	+	0.244891i	−0.272693	+	0.962101i	$0.587914\pi$
$830$	4.09617	−	7.09477i	0.142180	−	0.246263i
$831$	21.4393	+	11.9410i	0.743720	+	0.414229i
$832$	0.424437	+	3.58048i	0.0147147	+	0.124131i
$833$	6.00715	+	5.50107i	0.208135	+	0.190601i
$834$	3.23512	+	5.40903i	0.112023	+	0.187299i
$835$	6.99641	−	12.1181i	0.242121	−	0.419366i
$836$	−1.84850	−	3.20169i	−0.0639316	−	0.110733i
$837$	1.01030	+	21.8233i	0.0349211	+	0.754324i
$838$	15.8330	+	27.4235i	0.546942	+	0.947331i
$839$	8.47056	−	4.89048i	0.292436	−	0.168838i	−0.346604	−	0.938012i	$-0.612665\pi$
$839$	8.47056	−	4.89048i	0.292436	−	0.168838i	0.639040	+	0.769174i	$0.279332\pi$
$840$	2.31257	−	1.91602i	0.0797914	−	0.0661090i
$841$	−14.0307	−	24.3019i	−0.483818	−	0.837997i
$842$	−2.80397	−	1.61887i	−0.0966312	−	0.0557901i
$843$	−5.26414	+	3.14847i	−0.181307	+	0.108439i
$844$	−24.8662			−0.855929
$845$	1.99186	+	8.28342i	0.0685219	+	0.284958i
$846$	−16.5330	+	10.2377i	−0.568417	+	0.351981i
$847$	−21.5837	+	17.3283i	−0.741625	+	0.595409i
$848$	−1.12217	−	0.647884i	−0.0385354	−	0.0222484i
$849$	−37.3172	+	0.575496i	−1.28072	+	0.0197510i
$850$	−5.31839			−0.182419
$851$	13.3326	+	23.0928i	0.457036	+	0.791610i
$852$	0.218994	+	14.2004i	0.00750262	+	0.486497i
$853$	−5.48095			−0.187664			−0.0938321	−	0.995588i	$-0.529912\pi$
$853$	−5.48095			−0.187664			−0.0938321	+	0.995588i	$0.529912\pi$
$854$	2.81654	−	0.433959i	0.0963800	−	0.0148498i
$855$	−0.305482	−	9.90192i	−0.0104473	−	0.338638i
$856$	−5.35526	−	3.09186i	−0.183039	−	0.105678i
$857$	−9.04966			−0.309130			−0.154565	−	0.987983i	$-0.549398\pi$
$857$	−9.04966			−0.309130			−0.154565	+	0.987983i	$0.549398\pi$
$858$	−1.74279	+	4.23755i	−0.0594979	+	0.144668i
$859$		−	4.33385i		−	0.147869i	−0.997263	−	0.0739346i	$-0.976444\pi$
$859$		−	4.33385i		−	0.147869i	0.997263	−	0.0739346i	$-0.0235556\pi$
$860$	−4.32576	−	2.49748i	−0.147507	−	0.0851632i
$861$	3.74752	+	22.0571i	0.127715	+	0.751705i
$862$	1.47511	+	2.55497i	0.0502425	+	0.0870225i
$863$	36.0591			1.22747			0.613733	−	0.789513i	$-0.289667\pi$
$863$	36.0591			1.22747			0.613733	+	0.789513i	$0.289667\pi$
$864$	−4.37504	+	2.80340i	−0.148842	+	0.0953736i
$865$	−4.16537	+	2.40488i	−0.141627	+	0.0817682i
$866$		−	23.3728i		−	0.794241i
$867$	0.417873	+	27.0964i	0.0141917	+	0.920242i
$868$	8.67418	−	6.96401i	0.294421	−	0.236374i
$869$	−4.84064	+	8.38423i	−0.164207	+	0.284416i
$870$	−0.960723	−	0.535093i	−0.0325715	−	0.0181414i
$871$	8.34312	−	19.4289i	0.282696	−	0.658322i
$872$			16.2242i			0.549420i
$873$	20.2089	−	0.623460i	0.683967	−	0.0211009i
$874$	27.9938	+	16.1622i	0.946905	+	0.546696i
$875$	16.4007	−	2.52695i	0.554445	−	0.0854264i
$876$	−10.4865	−	5.84064i	−0.354305	−	0.197337i
$877$	11.5032	−	6.64138i	0.388436	−	0.224264i	−0.293046	−	0.956098i	$-0.594669\pi$
$877$	11.5032	−	6.64138i	0.388436	−	0.224264i	0.681482	+	0.731835i	$0.261336\pi$
$878$	−15.3108	+	8.83972i	−0.516716	+	0.298326i
$879$	−18.6574	+	33.4980i	−0.629297	+	1.12986i
$880$	0.416409	−	0.240414i	0.0140372	−	0.00810435i
$881$	21.7703	−	37.7073i	0.733461	−	1.27039i	−0.221934	−	0.975062i	$-0.571237\pi$
$881$	21.7703	−	37.7073i	0.733461	−	1.27039i	0.955395	−	0.295331i	$-0.0954298\pi$
$882$	15.9172	+	13.6982i	0.535962	+	0.461243i
$883$	−45.0270			−1.51528			−0.757639	−	0.652674i	$-0.773647\pi$
$883$	−45.0270			−1.51528			−0.757639	+	0.652674i	$0.773647\pi$
$884$	−3.85511	−	1.65546i	−0.129661	−	0.0556791i
$885$	2.47110	+	1.37633i	0.0830650	+	0.0462647i
$886$	−4.99643	−	2.88469i	−0.167858	−	0.0969131i
$887$	18.2727	−	31.6493i	0.613537	−	1.06268i	−0.377102	−	0.926172i	$-0.623079\pi$
$887$	18.2727	−	31.6493i	0.613537	−	1.06268i	0.990639	−	0.136506i	$-0.0435874\pi$
$888$	7.19871	−	0.111017i	0.241573	−	0.00372547i
$889$	18.4689	+	7.17881i	0.619425	+	0.240769i
$890$	4.79758	+	8.30965i	0.160815	+	0.278540i
$891$	−6.59072	+	0.407045i	−0.220797	+	0.0136365i
$892$	−8.53859			−0.285893
$893$	28.2862	−	16.3310i	0.946561	−	0.546497i
$894$	−32.4325	+	19.3978i	−1.08471	+	0.648760i
$895$	0.816608	−	1.41441i	0.0272962	−	0.0472784i
$896$	2.46601	+	0.958534i	0.0823837	+	0.0320224i
$897$	−5.32890	−	39.7059i	−0.177927	−	1.32574i
$898$	13.7059			0.457372
$899$	−3.52753	−	2.03662i	−0.117650	−	0.0679250i
$900$	−13.7050	+	0.422811i	−0.456834	+	0.0140937i
$901$	1.30579	−	0.753897i	0.0435021	−	0.0251159i
$902$			3.58208i			0.119270i
$903$	12.1505	−	32.7460i	0.404342	−	1.08972i
$904$	−4.96016	+	2.86375i	−0.164972	+	0.0952468i
$905$	−12.7044			−0.422308
$906$	10.9941	−	0.169548i	0.365254	−	0.00563284i
$907$	2.29532	−	3.97562i	0.0762149	−	0.132008i	−0.825399	−	0.564550i	$-0.809050\pi$
$907$	2.29532	−	3.97562i	0.0762149	−	0.132008i	0.901614	+	0.432542i	$0.142383\pi$
$908$	−5.99732	−	3.46256i	−0.199028	−	0.114909i
$909$	−3.65597	−	5.90406i	−0.121261	−	0.195825i
$910$	6.05303	+	1.56323i	0.200656	+	0.0518207i
$911$		−	60.0679i		−	1.99014i	−0.0991827	−	0.995069i	$-0.531623\pi$
$911$		−	60.0679i		−	1.99014i	0.0991827	−	0.995069i	$-0.468377\pi$
$912$	7.49010	−	4.47981i	0.248022	−	0.148341i
$913$	7.94297	+	4.58587i	0.262874	+	0.151770i
$914$	7.47187	−	4.31389i	0.247148	−	0.142691i
$915$	1.06813	+	0.594915i	0.0353112	+	0.0196673i
$916$	2.34250	+	4.05732i	0.0773982	+	0.134058i
$917$	−5.07508	−	32.9389i	−0.167594	−	1.08774i
$918$	−0.279616	−	6.03993i	−0.00922869	−	0.199347i
$919$	−13.4861	−	23.3585i	−0.444864	−	0.770527i	0.553179	−	0.833063i	$-0.313415\pi$
$919$	−13.4861	−	23.3585i	−0.444864	−	0.770527i	−0.998043	+	0.0625354i	$0.980081\pi$
$920$	−2.10205	+	3.64085i	−0.0693024	+	0.120035i
$921$	−3.23515	+	1.93493i	−0.106602	+	0.0637582i
$922$			33.0169i			1.08735i
$923$	−23.6850	+	17.6931i	−0.779602	+	0.582377i
$924$	2.14508	+	2.58905i	0.0705681	+	0.0851734i
$925$	16.4529	+	9.49907i	0.540967	+	0.312328i
$926$	16.1422	+	9.31970i	0.530465	+	0.306264i
$927$	−29.8470	−	16.0259i	−0.980303	−	0.526359i
$928$		−	0.968804i		−	0.0318025i
$929$	−12.3212	+	7.11365i	−0.404246	+	0.233391i	−0.688314	−	0.725413i	$-0.741649\pi$
$929$	−12.3212	+	7.11365i	−0.404246	+	0.233391i	0.284069	+	0.958804i	$0.408316\pi$
$930$	4.77184	−	0.0735900i	0.156475	−	0.00241311i
$931$	−26.0127	−	23.8212i	−0.852532	−	0.780710i
$932$	−7.45984	+	4.30694i	−0.244355	+	0.141079i
$933$	10.5582	−	6.31480i	0.345658	−	0.206737i
$934$	−1.22093	+	2.11471i	−0.0399500	+	0.0691955i
$935$			0.559505i			0.0182978i
$936$	−10.0659	−	3.95949i	−0.329014	−	0.129420i
$937$			4.30558i			0.140657i	0.997524	+	0.0703287i	$0.0224048\pi$
$937$			4.30558i			0.140657i	−0.997524	+	0.0703287i	$0.977595\pi$
$938$	−9.71360	−	12.0990i	−0.317160	−	0.395046i
$939$	15.2314	+	25.4664i	0.497058	+	0.831065i
$940$	2.12400	+	3.67888i	0.0692773	+	0.119992i
$941$			10.9105i			0.355671i	0.984060	+	0.177835i	$0.0569095\pi$
$941$			10.9105i			0.355671i	−0.984060	+	0.177835i	$0.943091\pi$
$942$	−10.5334	+	0.162443i	−0.343197	+	0.00529268i
$943$	−15.6599	−	27.1237i	−0.509956	−	0.883269i
$944$			2.49188i			0.0811039i
$945$	1.78228	+	8.83151i	0.0579777	+	0.287289i
$946$	2.79605	−	4.84291i	0.0909076	−	0.157457i
$947$	2.65690	−	4.60188i	0.0863376	−	0.149541i	−0.819623	−	0.572904i	$-0.805817\pi$
$947$	2.65690	−	4.60188i	0.0863376	−	0.149541i	0.905960	+	0.423362i	$0.139150\pi$
$948$	−19.9666	−	11.1208i	−0.648486	−	0.361187i
$949$	−2.94140	−	24.8131i	−0.0954818	−	0.805468i
$950$	23.0302			0.747198
$951$	36.6187	−	21.9016i	1.18744	−	0.710206i
$952$	−2.40071	+	1.92739i	−0.0778074	+	0.0624671i
$953$	4.59073	−	2.65046i	0.148708	−	0.0858569i	−0.423800	−	0.905756i	$-0.639304\pi$
$953$	4.59073	−	2.65046i	0.148708	−	0.0858569i	0.572508	+	0.819899i	$0.305971\pi$
$954$	3.30497	−	2.04654i	0.107002	−	0.0662591i
$955$	−4.48447	−	7.76732i	−0.145114	−	0.251345i
$956$	5.13049	+	8.88626i	0.165932	+	0.287402i
$957$	0.599064	−	1.07558i	0.0193650	−	0.0347685i
$958$	−27.1685	+	15.6857i	−0.877774	+	0.506783i
$959$	45.9398	−	36.8824i	1.48347	−	1.19100i
$960$	0.582640	+	0.974155i	0.0188046	+	0.0314407i
$961$	−13.3230			−0.429775
$962$	8.96933	+	12.0068i	0.289183	+	0.387116i
$963$	15.7721	−	9.76658i	0.508249	−	0.314724i
$964$	8.05368	−	13.9494i	0.259392	−	0.449279i
$965$	7.07972	−	12.2624i	0.227904	−	0.394742i
$966$	−27.5613	−	10.2267i	−0.886769	−	0.329038i
$967$			5.42003i			0.174296i	0.996195	+	0.0871482i	$0.0277754\pi$
$967$			5.42003i			0.174296i	−0.996195	+	0.0871482i	$0.972225\pi$
$968$	−5.23084	−	9.06009i	−0.168126	−	0.291202i
$969$	0.156599	+	10.1544i	0.00503068	+	0.326207i
$970$		−	4.41672i		−	0.141812i
$971$	−29.9886	−	51.9418i	−0.962381	−	1.66689i	−0.716493	−	0.697594i	$-0.754254\pi$
$971$	−29.9886	−	51.9418i	−0.962381	−	1.66689i	−0.245888	−	0.969298i	$-0.579079\pi$
$972$	−1.20072	−	15.5421i	−0.0385131	−	0.498515i
$973$	6.02724	+	7.50738i	0.193225	+	0.240675i
$974$			11.6976i			0.374815i
$975$	−17.4326	−	22.6009i	−0.558291	−	0.723807i
$976$			1.07711i			0.0344776i
$977$	16.0567	−	27.8110i	0.513699	−	0.889753i	−0.486175	−	0.873862i	$-0.661608\pi$
$977$	16.0567	−	27.8110i	0.513699	−	0.889753i	0.999874	−	0.0158911i	$-0.00505852\pi$
$978$	−9.02532	−	15.0900i	−0.288598	−	0.482526i
$979$	−9.30308	+	5.37114i	−0.297328	+	0.171662i
$980$	3.09817	−	3.38319i	0.0989674	−	0.108072i
$981$	−42.8820	−	23.0249i	−1.36912	−	0.735128i
$982$	35.7809	−	20.6581i	1.14181	−	0.659227i
$983$			4.84635i			0.154574i	0.997009	+	0.0772872i	$0.0246258\pi$
$983$			4.84635i			0.154574i	−0.997009	+	0.0772872i	$0.975374\pi$
$984$	−8.45527	+	0.130395i	−0.269544	+	0.00415684i
$985$	12.0353	+	6.94858i	0.383476	+	0.221400i
$986$	0.976295	+	0.563664i	0.0310916	+	0.0179507i
$987$	−22.8736	+	18.9513i	−0.728075	+	0.603227i
$988$	16.6938	+	7.16862i	0.531099	+	0.228064i
$989$			48.8943i			1.55475i
$990$	0.0444806	+	1.44180i	0.00141369	+	0.0458233i
$991$	−24.0646	+	41.6810i	−0.764436	+	1.32404i	0.176108	+	0.984371i	$0.443649\pi$
$991$	−24.0646	+	41.6810i	−0.764436	+	1.32404i	−0.940544	+	0.339671i	$0.889684\pi$
$992$	2.10220	+	3.64112i	0.0667449	+	0.115606i
$993$	9.60676	−	17.2483i	0.304861	−	0.547357i
$994$	3.30353	+	21.4410i	0.104782	+	0.680068i
$995$	1.12400	+	1.94683i	0.0356332	+	0.0617185i
$996$	−10.5355	+	18.9158i	−0.333831	+	0.599370i
$997$	−42.7858	+	24.7024i	−1.35504	+	0.782332i	−0.988950	−	0.148248i	$-0.952637\pi$
$997$	−42.7858	+	24.7024i	−1.35504	+	0.782332i	−0.366089	+	0.930580i	$0.619303\pi$
$998$	−22.3116	−	12.8816i	−0.706261	−	0.407760i
$999$	−9.92278	+	19.1844i	−0.313943	+	0.606969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.j.251.3	yes	24
3.2	odd	2		546.2.q.i.251.7	yes	24
7.6	odd	2	inner	546.2.q.j.251.10	yes	24
13.10	even	6		546.2.q.i.335.6	yes	24
21.20	even	2		546.2.q.i.251.6	✓	24
39.23	odd	6	inner	546.2.q.j.335.10	yes	24
91.62	odd	6		546.2.q.i.335.7	yes	24
273.62	even	6	inner	546.2.q.j.335.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.6	✓	24	21.20	even	2
546.2.q.i.251.7	yes	24	3.2	odd	2
546.2.q.i.335.6	yes	24	13.10	even	6
546.2.q.i.335.7	yes	24	91.62	odd	6
546.2.q.j.251.3	yes	24	1.1	even	1	trivial
546.2.q.j.251.10	yes	24	7.6	odd	2	inner
546.2.q.j.335.3	yes	24	273.62	even	6	inner
546.2.q.j.335.10	yes	24	39.23	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.48647 + 0.889052i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.655349i q^{5} +(0.0267080 + 1.73184i) q^{6} +(0.402891 + 2.61490i) q^{7} -1.00000 q^{8} +(1.41917 - 2.64309i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.48647 + 0.889052i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.655349i q^{5} +(0.0267080 + 1.73184i) q^{6} +(0.402891 + 2.61490i) q^{7} -1.00000 q^{8} +(1.41917 - 2.64309i) q^{9} +(-0.567549 - 0.327675i) q^{10} +(0.366849 - 0.635401i) q^{11} +(1.51318 + 0.842793i) q^{12} +(0.424437 + 3.58048i) q^{13} +(2.46601 + 0.958534i) q^{14} +(0.582640 + 0.974155i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.581815 - 1.00773i) q^{17} +(-1.57940 - 2.55059i) q^{18} +(2.51943 + 4.36378i) q^{19} +(-0.567549 + 0.327675i) q^{20} +(-2.92366 - 3.52877i) q^{21} +(-0.366849 - 0.635401i) q^{22} +(5.55559 + 3.20752i) q^{23} +(1.48647 - 0.889052i) q^{24} +4.57052 q^{25} +(3.31301 + 1.42267i) q^{26} +(0.240296 + 5.19059i) q^{27} +(2.06312 - 1.65636i) q^{28} +(-0.839009 - 0.484402i) q^{29} +(1.13496 - 0.0175031i) q^{30} +4.20440 q^{31} +(0.500000 + 0.866025i) q^{32} +(0.0195956 + 1.27065i) q^{33} -1.16363 q^{34} +(1.71367 - 0.264034i) q^{35} +(-2.99857 + 0.0925084i) q^{36} +(3.59978 + 2.07834i) q^{37} +5.03886 q^{38} +(-3.81415 - 4.94492i) q^{39} +0.655349i q^{40} +(-4.22814 - 2.44112i) q^{41} +(-4.51783 + 0.767584i) q^{42} +(3.81091 + 6.60069i) q^{43} -0.733697 q^{44} +(-1.73215 - 0.930053i) q^{45} +(5.55559 - 3.20752i) q^{46} -6.48204i q^{47} +(-0.0267080 - 1.73184i) q^{48} +(-6.67536 + 2.10704i) q^{49} +(2.28526 - 3.95818i) q^{50} +(1.76078 + 0.980698i) q^{51} +(2.88857 - 2.15781i) q^{52} +1.29577i q^{53} +(4.61533 + 2.38719i) q^{54} +(-0.416409 - 0.240414i) q^{55} +(-0.402891 - 2.61490i) q^{56} +(-7.62467 - 4.24671i) q^{57} +(-0.839009 + 0.484402i) q^{58} +(2.15803 - 1.24594i) q^{59} +(0.552323 - 0.991658i) q^{60} +(0.932808 - 0.538557i) q^{61} +(2.10220 - 3.64112i) q^{62} +(7.48319 + 2.64611i) q^{63} +1.00000 q^{64} +(2.34647 - 0.278155i) q^{65} +(1.11021 + 0.618355i) q^{66} +(-5.07874 - 2.93221i) q^{67} +(-0.581815 + 1.00773i) q^{68} +(-11.1099 + 0.171333i) q^{69} +(0.628174 - 1.61610i) q^{70} +(4.09978 + 7.10103i) q^{71} +(-1.41917 + 2.64309i) q^{72} -6.93011 q^{73} +(3.59978 - 2.07834i) q^{74} +(-6.79393 + 4.06343i) q^{75} +(2.51943 - 4.36378i) q^{76} +(1.80931 + 0.703274i) q^{77} +(-6.18950 + 0.830687i) q^{78} -13.1952 q^{79} +(0.567549 + 0.327675i) q^{80} +(-4.97190 - 7.50201i) q^{81} +(-4.22814 + 2.44112i) q^{82} +12.5007i q^{83} +(-1.59417 + 4.29635i) q^{84} +(-0.660417 + 0.381292i) q^{85} +7.62182 q^{86} +(1.67782 - 0.0258749i) q^{87} +(-0.366849 + 0.635401i) q^{88} +(-12.6797 - 7.32065i) q^{89} +(-1.67152 + 1.03506i) q^{90} +(-9.19158 + 2.55240i) q^{91} -6.41504i q^{92} +(-6.24970 + 3.73793i) q^{93} +(-5.61361 - 3.24102i) q^{94} +(2.85980 - 1.65110i) q^{95} +(-1.51318 - 0.842793i) q^{96} +(3.36975 + 5.83658i) q^{97} +(-1.51293 + 6.83455i) q^{98} +(-1.15880 - 1.87136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

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