LMFDB - Embedded newform 546.2.q.i.335.6

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			335.6
Character	$\chi$	$=$	546.335
Dual form			546.2.q.i.251.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.0267080 - 1.73184i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.655349i q^{5} +(-1.48647 + 0.889052i) q^{6} +(-2.06312 + 1.65636i) q^{7} +1.00000 q^{8} +(-2.99857 + 0.0925084i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.0267080 - 1.73184i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.655349i q^{5} +(-1.48647 + 0.889052i) q^{6} +(-2.06312 + 1.65636i) q^{7} +1.00000 q^{8} +(-2.99857 + 0.0925084i) 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} +(1.13496 - 0.0175031i) 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} +(-0.0267080 - 1.73184i) q^{24} +4.57052 q^{25} +(3.31301 - 1.42267i) q^{26} +(0.240296 + 5.19059i) q^{27} +(-0.402891 - 2.61490i) q^{28} +(0.839009 - 0.484402i) q^{29} +(-0.582640 - 0.974155i) q^{30} -4.20440 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.09062 + 0.652295i) q^{33} +1.16363 q^{34} +(-1.08550 - 1.35206i) q^{35} +(1.41917 - 2.64309i) q^{36} +(3.59978 - 2.07834i) q^{37} +5.03886 q^{38} +(6.21218 + 0.639432i) q^{39} +0.655349i q^{40} +(-4.22814 + 2.44112i) q^{41} +(1.59417 - 4.29635i) q^{42} +(3.81091 - 6.60069i) q^{43} +0.733697 q^{44} +(-0.0606253 - 1.96511i) q^{45} +(5.55559 + 3.20752i) q^{46} +6.48204i q^{47} +(-1.48647 + 0.889052i) q^{48} +(1.51293 - 6.83455i) q^{49} +(-2.28526 - 3.95818i) q^{50} +(1.76078 + 0.980698i) q^{51} +(-2.88857 - 2.15781i) q^{52} +1.29577i q^{53} +(4.37504 - 2.80340i) q^{54} +(0.416409 - 0.240414i) q^{55} +(-2.06312 + 1.65636i) 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} +(6.03319 - 5.15758i) 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} +(5.70331 + 9.53575i) q^{69} +(-0.628174 + 1.61610i) q^{70} +(-4.09978 + 7.10103i) q^{71} +(-2.99857 + 0.0925084i) q^{72} +6.93011 q^{73} +(-3.59978 - 2.07834i) q^{74} +(-0.122070 - 7.91543i) q^{75} +(-2.51943 - 4.36378i) q^{76} +(1.80931 + 0.703274i) q^{77} +(-2.55232 - 5.69962i) q^{78} -13.1952 q^{79} +(0.567549 - 0.327675i) q^{80} +(8.98288 - 0.554786i) q^{81} +(4.22814 + 2.44112i) q^{82} -12.5007i q^{83} +(-4.51783 + 0.767584i) q^{84} +(-0.660417 - 0.381292i) q^{85} -7.62182 q^{86} +(-0.861317 - 1.44010i) q^{87} +(-0.366849 - 0.635401i) q^{88} +(-12.6797 + 7.32065i) q^{89} +(-1.67152 + 1.03506i) q^{90} +(-5.05491 - 8.08999i) q^{91} -6.41504i q^{92} +(0.112291 + 7.28137i) 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} +(-6.67536 + 2.10704i) 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} - 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9	$ 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9} + 6 q^{15} - 12 q^{16} + 6 q^{18} - 12 q^{21} + 36 q^{23} - 12 q^{25} + 18 q^{28} - 12 q^{30} - 12 q^{32} + 36 q^{35} + 6 q^{36} + 36 q^{37} + 12 q^{39} + 24 q^{42} - 42 q^{43} - 36 q^{46} + 6 q^{50} + 12 q^{51} - 18 q^{56} + 36 q^{57} + 6 q^{60} + 24 q^{63} + 24 q^{64} - 66 q^{65} - 54 q^{67} - 48 q^{71} - 12 q^{72} - 36 q^{74} - 42 q^{78} - 48 q^{79} + 84 q^{81} - 12 q^{84} + 84 q^{86} + 36 q^{91} - 18 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 - 12 * q^9 + 6 * q^15 - 12 * q^16 + 6 * q^18 - 12 * q^21 + 36 * q^23 - 12 * q^25 + 18 * q^28 - 12 * q^30 - 12 * q^32 + 36 * q^35 + 6 * q^36 + 36 * q^37 + 12 * q^39 + 24 * q^42 - 42 * q^43 - 36 * q^46 + 6 * q^50 + 12 * q^51 - 18 * q^56 + 36 * q^57 + 6 * q^60 + 24 * q^63 + 24 * q^64 - 66 * q^65 - 54 * q^67 - 48 * q^71 - 12 * q^72 - 36 * q^74 - 42 * q^78 - 48 * q^79 + 84 * q^81 - 12 * q^84 + 84 * q^86 + 36 * q^91 - 18 * q^93 + 36 * q^95 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.0267080	−	1.73184i	−0.0154199	−	0.999881i
$3$	−0.0267080	−	1.73184i	−0.0154199	−	0.999881i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$			0.655349i			0.293081i	0.989205	+	0.146541i	$0.0468139\pi$
$5$			0.655349i			0.293081i	−0.989205	+	0.146541i	$0.953186\pi$
$6$	−1.48647	+	0.889052i	−0.606848	+	0.362954i
$7$	−2.06312	+	1.65636i	−0.779786	+	0.626046i
$7$	−2.06312	+	1.65636i	−0.779786	+	0.626046i
$8$	1.00000			0.353553
$9$	−2.99857	+	0.0925084i	−0.999524	+	0.0308361i
$10$	0.567549	−	0.327675i	0.179475	−	0.103620i
$11$	−0.366849	−	0.635401i	−0.110609	−	0.191580i	0.805407	−	0.592722i	$-0.201947\pi$
$11$	−0.366849	−	0.635401i	−0.110609	−	0.191580i	−0.916016	+	0.401142i	$0.868613\pi$
$12$	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
$15$	1.13496	−	0.0175031i	0.293046	−	0.00451928i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.581815	+	1.00773i	−0.141111	+	0.244411i	−0.927915	−	0.372791i	$-0.878401\pi$
$17$	−0.581815	+	1.00773i	−0.141111	+	0.244411i	0.786804	+	0.617202i	$0.211734\pi$
$18$	1.57940	+	2.55059i	0.372268	+	0.601179i
$19$	−2.51943	+	4.36378i	−0.577996	+	1.00112i	0.417713	+	0.908579i	$0.362832\pi$
$19$	−2.51943	+	4.36378i	−0.577996	+	1.00112i	−0.995709	+	0.0925398i	$0.970501\pi$
$20$	−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	$-0.899865\pi$
$23$	−5.55559	+	3.20752i	−1.15842	+	0.668815i	−0.207496	+	0.978236i	$0.566531\pi$
$24$	−0.0267080	−	1.73184i	−0.00545176	−	0.353511i
$25$	4.57052			0.914104
$26$	3.31301	−	1.42267i	0.649734	−	0.279008i
$27$	0.240296	+	5.19059i	0.0462450	+	0.998930i
$28$	−0.402891	−	2.61490i	−0.0761393	−	0.494169i
$29$	0.839009	−	0.484402i	0.155800	−	0.0899512i	−0.420073	−	0.907490i	$-0.637996\pi$
$29$	0.839009	−	0.484402i	0.155800	−	0.0899512i	0.575873	+	0.817539i	$0.304662\pi$
$30$	−0.582640	−	0.974155i	−0.106375	−	0.177856i
$31$	−4.20440			−0.755132			−0.377566	−	0.925983i	$-0.623239\pi$
$31$	−4.20440			−0.755132			−0.377566	+	0.925983i	$0.623239\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.09062	+	0.652295i	−0.189852	+	0.113550i
$34$	1.16363			0.199561
$35$	−1.08550	−	1.35206i	−0.183482	−	0.228541i
$36$	1.41917	−	2.64309i	0.236529	−	0.440516i
$37$	3.59978	−	2.07834i	0.591801	−	0.341676i	−0.174008	−	0.984744i	$-0.555672\pi$
$37$	3.59978	−	2.07834i	0.591801	−	0.341676i	0.765809	+	0.643068i	$0.222339\pi$
$38$	5.03886			0.817410
$39$	6.21218	+	0.639432i	0.994744	+	0.102391i
$40$			0.655349i			0.103620i
$41$	−4.22814	+	2.44112i	−0.660324	+	0.381238i	−0.792401	−	0.610001i	$-0.791169\pi$
$41$	−4.22814	+	2.44112i	−0.660324	+	0.381238i	0.132076	+	0.991240i	$0.457836\pi$
$42$	1.59417	−	4.29635i	0.245986	−	0.662941i
$43$	3.81091	−	6.60069i	0.581158	−	1.00660i	−0.414184	−	0.910193i	$-0.635933\pi$
$43$	3.81091	−	6.60069i	0.581158	−	1.00660i	0.995342	−	0.0964026i	$-0.0307336\pi$
$44$	0.733697			0.110609
$45$	−0.0606253	−	1.96511i	−0.00903748	−	0.292942i
$46$	5.55559	+	3.20752i	0.819127	+	0.472923i
$47$			6.48204i			0.945503i	0.881196	+	0.472752i	$0.156739\pi$
$47$			6.48204i			0.945503i	−0.881196	+	0.472752i	$0.843261\pi$
$48$	−1.48647	+	0.889052i	−0.214553	+	0.128324i
$49$	1.51293	−	6.83455i	0.216133	−	0.976364i
$50$	−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	$0.971635\pi$
$54$	4.37504	−	2.80340i	0.595367	−	0.381494i
$55$	0.416409	−	0.240414i	0.0561486	−	0.0324174i
$56$	−2.06312	+	1.65636i	−0.275696	+	0.221341i
$57$	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	0.633854	−	0.773452i	$-0.281472\pi$
$59$	2.15803	+	1.24594i	0.280952	+	0.162208i	−0.352902	+	0.935660i	$0.614805\pi$
$60$	−0.552323	+	0.991658i	−0.0713046	+	0.128023i
$61$	−0.932808	−	0.538557i	−0.119434	−	0.0689551i	0.439093	−	0.898442i	$-0.355300\pi$
$61$	−0.932808	−	0.538557i	−0.119434	−	0.0689551i	−0.558527	+	0.829486i	$0.688633\pi$
$62$	2.10220	+	3.64112i	0.266980	+	0.462422i
$63$	6.03319	−	5.15758i	0.760111	−	0.649794i
$64$	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	−0.777051	−	0.629438i	$-0.783285\pi$
$67$	−5.07874	+	2.93221i	−0.620466	+	0.358226i	0.156584	+	0.987665i	$0.449952\pi$
$68$	−0.581815	−	1.00773i	−0.0705554	−	0.122205i
$69$	5.70331	+	9.53575i	0.686598	+	1.14797i
$70$	−0.628174	+	1.61610i	−0.0750812	+	0.193161i
$71$	−4.09978	+	7.10103i	−0.486555	+	0.842738i	−0.999881	−	0.0154562i	$-0.995080\pi$
$71$	−4.09978	+	7.10103i	−0.486555	+	0.842738i	0.513326	+	0.858194i	$0.328413\pi$
$72$	−2.99857	+	0.0925084i	−0.353385	+	0.0109022i
$73$	6.93011			0.811108			0.405554	−	0.914071i	$-0.367079\pi$
$73$	6.93011			0.811108			0.405554	+	0.914071i	$0.367079\pi$
$74$	−3.59978	−	2.07834i	−0.418466	−	0.241602i
$75$	−0.122070	−	7.91543i	−0.0140954	−	0.913995i
$76$	−2.51943	−	4.36378i	−0.288998	−	0.500560i
$77$	1.80931	+	0.703274i	0.206190	+	0.0801455i
$78$	−2.55232	−	5.69962i	−0.288994	−	0.645355i
$79$	−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
$81$	8.98288	−	0.554786i	0.998098	−	0.0616429i
$82$	4.22814	+	2.44112i	0.466920	+	0.269576i
$83$		−	12.5007i		−	1.37213i	−0.727539	−	0.686066i	$-0.759336\pi$
$83$		−	12.5007i		−	1.37213i	0.727539	−	0.686066i	$-0.240664\pi$
$84$	−4.51783	+	0.767584i	−0.492936	+	0.0837503i
$85$	−0.660417	−	0.381292i	−0.0716322	−	0.0413569i
$86$	−7.62182			−0.821882
$87$	−0.861317	−	1.44010i	−0.0923429	−	0.154394i
$88$	−0.366849	−	0.635401i	−0.0391062	−	0.0677339i
$89$	−12.6797	+	7.32065i	−1.34405	+	0.775987i	−0.987399	−	0.158251i	$-0.949414\pi$
$89$	−12.6797	+	7.32065i	−1.34405	+	0.775987i	−0.356650	+	0.934238i	$0.616081\pi$
$90$	−1.67152	+	1.03506i	−0.176194	+	0.109105i
$91$	−5.05491	−	8.08999i	−0.529898	−	0.848061i
$92$		−	6.41504i		−	0.668815i
$93$	0.112291	+	7.28137i	0.0116441	+	0.755043i
$94$	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	$-0.944487\pi$
$97$	−3.36975	+	5.83658i	−0.342146	+	0.592615i	0.642685	+	0.766131i	$0.277820\pi$
$98$	−6.67536	+	2.10704i	−0.674313	+	0.212843i
$99$	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	0.917846	−	0.396938i	$-0.129927\pi$
$101$	1.15739	+	2.00466i	0.115165	+	0.199471i	−0.802681	+	0.596409i	$0.796594\pi$
$102$	−0.0310783	−	2.01523i	−0.00307721	−	0.199537i
$103$		−	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	$-0.763287\pi$
$107$	−5.35526	+	3.09186i	−0.517713	+	0.298901i	0.218286	+	0.975885i	$0.429954\pi$
$108$	−4.61533	−	2.38719i	−0.444111	−	0.229708i
$109$			16.2242i			1.55399i	0.629504	+	0.776997i	$0.283258\pi$
$109$			16.2242i			1.55399i	−0.629504	+	0.776997i	$0.716742\pi$
$110$	−0.416409	−	0.240414i	−0.0397031	−	0.0229226i
$111$	−3.69550	−	6.17876i	−0.350761	−	0.586462i
$112$	2.46601	+	0.958534i	0.233016	+	0.0905729i
$113$	−4.96016	−	2.86375i	−0.466612	−	0.269399i	0.248208	−	0.968707i	$-0.420158\pi$
$113$	−4.96016	−	2.86375i	−0.466612	−	0.269399i	−0.714820	+	0.699308i	$0.753492\pi$
$114$	−0.134578	−	8.72652i	−0.0126044	−	0.817313i
$115$	−2.10205	−	3.64085i	−0.196017	−	0.339511i
$116$			0.968804i			0.0899512i
$117$	0.941482	−	10.7756i	0.0870401	−	0.996205i
$118$		−	2.49188i		−	0.229396i
$119$	−0.468816	−	3.04277i	−0.0429763	−	0.278930i
$120$	1.13496	−	0.0175031i	0.103607	−	0.00159781i
$121$	5.23084	−	9.06009i	0.475531	−	0.823644i
$122$			1.07711i			0.0975173i
$123$	4.34056	+	7.25728i	0.391375	+	0.654367i
$124$	2.10220	−	3.64112i	0.188783	−	0.326982i
$125$			6.27203i			0.560987i
$126$	−7.48319	−	2.64611i	−0.666655	−	0.235734i
$127$	3.74468	+	6.48598i	0.332287	+	0.575537i	0.982960	−	0.183821i	$-0.0588465\pi$
$127$	3.74468	+	6.48598i	0.332287	+	0.575537i	−0.650673	+	0.759358i	$0.725513\pi$
$128$	−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	$0.685482\pi$
$132$	−0.0195956	−	1.27065i	−0.00170558	−	0.110596i
$133$	−2.03011	−	13.1761i	−0.176033	−	1.14251i
$134$	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	0.208381	−	0.978048i	$-0.433181\pi$
$137$	11.1336	−	19.2839i	0.951205	−	1.64753i	0.742824	−	0.669487i	$-0.233486\pi$
$138$	5.40655	−	9.70709i	0.460236	−	0.826322i
$139$	−3.15133	−	1.81942i	−0.267293	−	0.154321i	0.360364	−	0.932812i	$-0.382652\pi$
$139$	−3.15133	−	1.81942i	−0.267293	−	0.154321i	−0.627657	+	0.778490i	$0.715986\pi$
$140$	1.71367	−	0.264034i	0.144832	−	0.0223150i
$141$	11.2259	−	0.173123i	0.945391	−	0.0145796i
$142$	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
$147$	−11.8768	−	2.43763i	−0.979581	−	0.201052i
$148$			4.15667i			0.341676i
$149$	−10.9093	+	18.8954i	−0.893722	+	1.54797i	−0.0583437	+	0.998297i	$0.518582\pi$
$149$	−10.9093	+	18.8954i	−0.893722	+	1.54797i	−0.835378	+	0.549675i	$0.814751\pi$
$150$	−6.79393	+	4.06343i	−0.554722	+	0.331778i
$151$			6.34819i			0.516608i	0.966064	+	0.258304i	$0.0831636\pi$
$151$			6.34819i			0.516608i	−0.966064	+	0.258304i	$0.916836\pi$
$152$	−2.51943	+	4.36378i	−0.204353	+	0.353949i
$153$	1.65139	−	3.07558i	0.133507	−	0.248646i
$154$	−0.295600	−	1.91854i	−0.0238201	−	0.154601i
$155$		−	2.75535i		−	0.221315i
$156$	−3.65985	+	5.06019i	−0.293023	+	0.405139i
$157$			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
$159$	2.24407	−	0.0346074i	0.177966	−	0.00274455i
$160$	−0.567549	−	0.327675i	−0.0448687	−	0.0259049i
$161$	6.14904	−	15.8196i	0.484612	−	1.24676i
$162$	−4.97190	−	7.50201i	−0.390629	−	0.589414i
$163$	−8.79156	−	5.07581i	−0.688608	−	0.397568i	0.114482	−	0.993425i	$-0.463479\pi$
$163$	−8.79156	−	5.07581i	−0.688608	−	0.397568i	−0.803090	+	0.595857i	$0.796812\pi$
$164$		−	4.88223i		−	0.381238i
$165$	−0.427481	−	0.714735i	−0.0332794	−	0.0556421i
$166$	−10.8259	+	6.25036i	−0.840256	+	0.485122i
$167$	18.4911	−	10.6759i	1.43089	−	0.826122i	0.433698	−	0.901058i	$-0.357209\pi$
$167$	18.4911	−	10.6759i	1.43089	−	0.826122i	0.997188	+	0.0749359i	$0.0238752\pi$
$168$	2.92366	+	3.52877i	0.225566	+	0.272250i
$169$	−12.6397	−	3.03938i	−0.972285	−	0.233799i
$170$			0.762583i			0.0584875i
$171$	7.15100	−	13.3182i	0.546851	−	1.01847i
$172$	3.81091	+	6.60069i	0.290579	+	0.503298i
$173$	−3.66961	+	6.35595i	−0.278995	+	0.483234i	−0.971135	−	0.238529i	$-0.923335\pi$
$173$	−3.66961	+	6.35595i	−0.278995	+	0.483234i	0.692140	+	0.721763i	$0.256668\pi$
$174$	−0.816501	+	1.46597i	−0.0618988	+	0.111135i
$175$	−9.42953	+	7.57043i	−0.712805	+	0.572271i
$176$	−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	$-0.696356\pi$
$179$	−2.15825	+	1.24607i	−0.161315	+	0.0931353i	0.417169	+	0.908829i	$0.363022\pi$
$180$	1.73215	+	0.930053i	0.129107	+	0.0693221i
$181$		−	19.3857i		−	1.44092i	−0.693494	−	0.720462i	$-0.743930\pi$
$181$		−	19.3857i		−	1.44092i	0.693494	−	0.720462i	$-0.256070\pi$
$182$	−4.47868	+	8.42267i	−0.331982	+	0.624330i
$183$	−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
$186$	6.24970	−	3.73793i	0.458250	−	0.274078i
$187$	0.853752			0.0624325
$188$	−5.61361	−	3.24102i	−0.409415	−	0.236376i
$189$	−9.09326	−	10.3108i	−0.661437	−	0.750000i
$190$			3.30221i			0.239567i
$191$	−11.8522	−	6.84286i	−0.857594	−	0.495132i	0.00561166	−	0.999984i	$-0.498214\pi$
$191$	−11.8522	−	6.84286i	−0.857594	−	0.495132i	−0.863206	+	0.504852i	$0.831547\pi$
$192$	−0.0267080	−	1.73184i	−0.00192749	−	0.124985i
$193$	18.7113	−	10.8030i	1.34687	−	0.777615i	0.359064	−	0.933313i	$-0.383096\pi$
$193$	18.7113	−	10.8030i	1.34687	−	0.777615i	0.987805	+	0.155698i	$0.0497627\pi$
$194$	6.73950			0.483868
$195$	−0.419051	+	4.07114i	−0.0300089	+	0.291541i
$196$	5.16243	+	4.72751i	0.368745	+	0.337679i
$197$	10.6029	+	18.3647i	0.755423	+	1.30843i	0.945164	+	0.326596i	$0.105902\pi$
$197$	10.6029	+	18.3647i	0.755423	+	1.30843i	−0.189741	+	0.981834i	$0.560765\pi$
$198$	1.04124	−	1.93923i	0.0739979	−	0.137815i
$199$	2.97067	+	1.71512i	0.210585	+	0.121581i	0.601583	−	0.798810i	$-0.294537\pi$
$199$	2.97067	+	1.71512i	0.210585	+	0.121581i	−0.390998	+	0.920391i	$0.627870\pi$
$200$	4.57052			0.323184
$201$	5.21378	+	8.71727i	0.367751	+	0.614869i
$202$	1.15739	−	2.00466i	0.0814338	−	0.141047i
$203$	−0.928631	+	2.38908i	−0.0651771	+	0.167681i
$204$	−1.72970	+	1.03453i	−0.121103	+	0.0724314i
$205$	−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
$210$	2.81561	+	1.04474i	0.194295	+	0.0720937i
$211$	12.4331	+	21.5347i	0.855929	+	1.48251i	0.875781	+	0.482710i	$0.160347\pi$
$211$	12.4331	+	21.5347i	0.855929	+	1.48251i	−0.0198516	+	0.999803i	$0.506319\pi$
$212$	−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
$217$	8.67418	−	6.96401i	0.588842	−	0.472747i
$218$	14.0505	−	8.11209i	0.951623	−	0.549420i
$219$	−0.185090	−	12.0019i	−0.0125072	−	0.811011i
$220$			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	$-0.258957\pi$
$223$	−4.26929	−	7.39463i	−0.285893	−	0.495181i	−0.972825	+	0.231540i	$0.925624\pi$
$224$	−0.402891	−	2.61490i	−0.0269193	−	0.174715i
$225$	−13.7050	+	0.422811i	−0.913669	+	0.0281874i
$226$			5.72749i			0.380987i
$227$	5.99732	+	3.46256i	0.398056	+	0.229818i	0.685645	−	0.727936i	$-0.259520\pi$
$227$	5.99732	+	3.46256i	0.398056	+	0.229818i	−0.287589	+	0.957754i	$0.592854\pi$
$228$	−7.49010	+	4.47981i	−0.496044	+	0.296682i
$229$	4.68499			0.309593			0.154796	−	0.987946i	$-0.450528\pi$
$229$	4.68499			0.309593			0.154796	+	0.987946i	$0.450528\pi$
$230$	−2.10205	+	3.64085i	−0.138605	+	0.240071i
$231$	1.16964	−	3.15222i	0.0769565	−	0.207401i
$232$	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	$-0.0910499\pi$
$234$	−9.80269	+	4.57245i	−0.640822	+	0.298911i
$235$	−4.24800			−0.277109
$236$	−2.15803	+	1.24594i	−0.140476	+	0.0811039i
$237$	0.352418	+	22.8520i	0.0228920	+	1.48440i
$238$	−2.40071	+	1.92739i	−0.155615	+	0.124934i
$239$	10.2610			0.663727			0.331864	−	0.943327i	$-0.392323\pi$
$239$	10.2610			0.663727			0.331864	+	0.943327i	$0.392323\pi$
$240$	−0.582640	−	0.974155i	−0.0376092	−	0.0628815i
$241$	−8.05368	+	13.9494i	−0.518783	+	0.898559i	0.480979	+	0.876732i	$0.340281\pi$
$241$	−8.05368	+	13.9494i	−0.518783	+	0.898559i	−0.999762	+	0.0218264i	$0.993052\pi$
$242$	−10.4617			−0.672503
$243$	−1.20072	−	15.5421i	−0.0770262	−	0.997029i
$244$	0.932808	−	0.538557i	0.0597169	−	0.0344776i
$245$	4.47901	+	0.991498i	0.286154	+	0.0633445i
$246$	4.11471	−	7.38768i	0.262344	−	0.471021i
$247$	−14.5551	−	10.8729i	−0.926118	−	0.691827i
$248$	−4.20440			−0.266980
$249$	−21.6493	+	0.333870i	−1.37197	+	0.0211581i
$250$	5.43174	−	3.13602i	0.343533	−	0.198339i
$251$	10.4635	−	18.1234i	0.660453	−	1.14394i	−0.320044	−	0.947403i	$-0.603698\pi$
$251$	10.4635	−	18.1234i	0.660453	−	1.14394i	0.980497	−	0.196535i	$-0.0629689\pi$
$252$	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	0.873789	+	0.486305i	$0.161656\pi$
$257$	13.7555	+	23.8253i	0.858047	+	1.48618i	−0.0157419	+	0.999876i	$0.505011\pi$
$258$	0.203564	+	13.1998i	0.0126733	+	0.821784i
$259$	−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	0.697198	−	0.716878i	$-0.254430\pi$
$263$	27.0282	−	15.6048i	1.66663	−	0.962231i	0.969434	−	0.245352i	$-0.0789036\pi$
$264$	−1.09062	+	0.652295i	−0.0671229	+	0.0401460i
$265$	−0.849181			−0.0521647
$266$	−10.3958	+	8.34617i	−0.637405	+	0.511736i
$267$	13.0169	+	21.7638i	0.796620	+	1.33192i
$268$		−	5.86442i		−	0.358226i
$269$	0.0309493	−	0.0536058i	0.00188701	−	0.00326841i	−0.865080	−	0.501633i	$-0.832733\pi$
$269$	0.0309493	−	0.0536058i	0.00188701	−	0.00326841i	0.866967	+	0.498365i	$0.166066\pi$
$270$	1.83721	+	2.86718i	0.111809	+	0.174491i
$271$	2.55715	+	4.42912i	0.155336	+	0.269050i	0.933181	−	0.359406i	$-0.117021\pi$
$271$	2.55715	+	4.42912i	0.155336	+	0.269050i	−0.777845	+	0.628456i	$0.783687\pi$
$272$	1.16363			0.0705554
$273$	−13.8756	+	8.97038i	−0.839789	+	0.542912i
$274$	−22.2671			−1.34521
$275$	−1.67669	−	2.90411i	−0.101108	−	0.175124i
$276$	−11.1099	+	0.171333i	−0.668735	+	0.0103130i
$277$	−7.08419	+	12.2702i	−0.425648	+	0.737244i	−0.996481	−	0.0838226i	$-0.973287\pi$
$277$	−7.08419	+	12.2702i	−0.425648	+	0.737244i	0.570833	+	0.821066i	$0.306620\pi$
$278$			3.63885i			0.218243i
$279$	12.6072	−	0.388942i	0.754773	−	0.0232854i
$280$	−1.08550	−	1.35206i	−0.0648707	−	0.0808013i
$281$	−3.54138			−0.211261			−0.105630	−	0.994405i	$-0.533686\pi$
$281$	−3.54138			−0.211261			−0.105630	+	0.994405i	$0.533686\pi$
$282$	−5.76287	−	9.63535i	−0.343174	−	0.573777i
$283$	−18.6608	+	10.7738i	−1.10927	+	0.640438i	−0.938640	−	0.344897i	$-0.887914\pi$
$283$	−18.6608	+	10.7738i	−1.10927	+	0.640438i	−0.170631	+	0.985335i	$0.554580\pi$
$284$	−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
$288$	1.41917	−	2.64309i	0.0836255	−	0.155746i
$289$	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	0.941406	−	0.337274i	$-0.109505\pi$
$293$	19.1717	+	11.0688i	1.12002	+	0.646645i	0.178615	+	0.983919i	$0.442838\pi$
$294$	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
$297$	3.20995	−	2.05685i	0.186260	−	0.119350i
$298$	21.8185			1.26391
$299$	−9.12647	−	21.2531i	−0.527798	−	1.22910i
$300$	6.91600	+	3.85200i	0.399295	+	0.222395i
$301$	3.07076	+	19.9303i	0.176996	+	1.14876i
$302$	5.49769	−	3.17409i	0.316357	−	0.182649i
$303$	3.44085	−	2.05796i	0.197672	−	0.118227i
$304$	5.03886			0.288998
$305$	0.352943	−	0.611315i	0.0202094	−	0.0350038i
$306$	−3.48923	+	0.107645i	−0.199466	+	0.00615368i
$307$	−2.17640			−0.124214			−0.0621068	−	0.998070i	$-0.519782\pi$
$307$	−2.17640			−0.124214			−0.0621068	+	0.998070i	$0.519782\pi$
$308$	−1.51371	+	1.21527i	−0.0862514	+	0.0692463i
$309$	−19.5567	+	0.301599i	−1.11254	+	0.0171573i
$310$	−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	$0.564544\pi$
$312$	6.21218	+	0.639432i	0.351695	+	0.0362007i
$313$		−	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
$315$	3.38001	+	3.95385i	0.190442	+	0.222774i
$316$	6.59760	−	11.4274i	0.371144	−	0.642840i
$317$	24.6347			1.38362			0.691812	−	0.722078i	$-0.256813\pi$
$317$	24.6347			1.38362			0.691812	+	0.722078i	$0.256813\pi$
$318$	−1.15201	−	1.92612i	−0.0646013	−	0.108011i
$319$	−0.615579	−	0.355404i	−0.0344658	−	0.0198988i
$320$			0.655349i			0.0366351i
$321$	5.49765	+	9.19190i	0.306849	+	0.513042i
$322$	−16.7747	+	2.58456i	−0.934816	+	0.144032i
$323$	−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
$327$	28.0978	−	0.433316i	1.55381	−	0.0239624i
$328$	−4.22814	+	2.44112i	−0.233460	+	0.134788i
$329$	−10.7366	−	13.3732i	−0.591928	−	0.737290i
$330$	−0.405238	+	0.727577i	−0.0223076	+	0.0400518i
$331$	−9.87158	−	5.69936i	−0.542591	−	0.313265i	0.203537	−	0.979067i	$-0.434756\pi$
$331$	−9.87158	−	5.69936i	−0.542591	−	0.313265i	−0.746128	+	0.665802i	$0.768090\pi$
$332$	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
$336$	1.59417	−	4.29635i	0.0869691	−	0.234385i
$337$	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
$342$	−15.1094	+	0.466136i	−0.817022	+	0.0252058i
$343$	8.19912	+	16.6065i	0.442711	+	0.896664i
$344$	3.81091	−	6.60069i	0.205470	−	0.355885i
$345$	−6.24925	+	3.73766i	−0.336448	+	0.201229i
$346$	7.33922			0.394559
$347$	17.2114	+	9.93698i	0.923954	+	0.533445i	0.884894	−	0.465792i	$-0.154230\pi$
$347$	17.2114	+	9.93698i	0.923954	+	0.533445i	0.0390595	+	0.999237i	$0.487564\pi$
$348$	1.67782	−	0.0258749i	0.0899405	−	0.00138704i
$349$	−8.02933	−	13.9072i	−0.429800	−	0.744436i	0.567055	−	0.823680i	$-0.308083\pi$
$349$	−8.02933	−	13.9072i	−0.429800	−	0.744436i	−0.996855	+	0.0792439i	$0.974749\pi$
$350$	11.2709	+	4.38100i	0.602458	+	0.234174i
$351$	−18.6868	−	1.34271i	−0.997429	−	0.0716683i
$352$	0.733697			0.0391062
$353$	−23.2239	+	13.4084i	−1.23609	+	0.713655i	−0.968292	−	0.249822i	$-0.919628\pi$
$353$	−23.2239	+	13.4084i	−1.23609	+	0.713655i	−0.267794	+	0.963476i	$0.586295\pi$
$354$	−4.31555	+	0.0665533i	−0.229369	+	0.00353727i
$355$	−4.65366	−	2.68679i	−0.246990	−	0.142600i
$356$		−	14.6413i		−	0.775987i
$357$	−5.25708	+	0.893183i	−0.278234	+	0.0472722i
$358$	2.15825	+	1.24607i	0.114067	+	0.0658566i
$359$	31.4068			1.65759			0.828795	−	0.559553i	$-0.189027\pi$
$359$	31.4068			1.65759			0.828795	+	0.559553i	$0.189027\pi$
$360$	−0.0606253	−	1.96511i	−0.00319523	−	0.103571i
$361$	−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
$364$	9.53359	−	0.332685i	0.499696	−	0.0174374i
$365$			4.54164i			0.237720i
$366$	1.86539	−	0.0287676i	0.0975057	−	0.00150371i
$367$	−1.82808	+	1.05544i	−0.0954251	+	0.0550937i	−0.546953	−	0.837163i	$-0.684212\pi$
$367$	−1.82808	+	1.05544i	−0.0954251	+	0.0550937i	0.451528	+	0.892257i	$0.350879\pi$
$368$	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
$371$	−2.14626	−	2.67333i	−0.111428	−	0.138792i
$372$	−6.36199	−	3.54344i	−0.329854	−	0.183719i
$373$	12.1368	−	21.0216i	0.628421	−	1.08846i	−0.359448	−	0.933165i	$-0.617035\pi$
$373$	12.1368	−	21.0216i	0.628421	−	1.08846i	0.987869	−	0.155292i	$-0.0496318\pi$
$374$	−0.426876	−	0.739371i	−0.0220732	−	0.0382319i
$375$	10.8622	−	0.167514i	0.560921	−	0.00865037i
$376$			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	−0.268550	−	0.963266i	$-0.586544\pi$
$379$	8.39822	−	4.84872i	0.431388	−	0.249062i	0.699938	+	0.714204i	$0.253211\pi$
$380$	2.85980	−	1.65110i	0.146705	−	0.0846999i
$381$	11.1327	−	6.65843i	0.570345	−	0.341122i
$382$			13.6857i			0.700223i
$383$	23.5996	+	13.6253i	1.20589	+	0.696218i	0.961858	−	0.273550i	$-0.0881979\pi$
$383$	23.5996	+	13.6253i	1.20589	+	0.696218i	0.244028	+	0.969768i	$0.421531\pi$
$384$	−1.48647	+	0.889052i	−0.0758560	+	0.0453693i
$385$	−0.460890	+	1.18573i	−0.0234891	+	0.0604303i
$386$	−18.7113	−	10.8030i	−0.952380	−	0.549857i
$387$	−10.8167	+	20.1452i	−0.549842	+	1.02404i
$388$	−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	$-0.135373\pi$
$390$	3.73524	−	1.67266i	0.189141	−	0.0846986i
$391$		−	7.46473i		−	0.377508i
$392$	1.51293	−	6.83455i	0.0764146	−	0.345197i
$393$	0.336432	+	21.8155i	0.0169708	+	1.10044i
$394$	10.6029	−	18.3647i	0.534165	−	0.925200i
$395$		−	8.64746i		−	0.435101i
$396$	−2.20005	+	0.0678731i	−0.110556	+	0.00341075i
$397$	−10.1097	+	17.5105i	−0.507390	+	0.878825i	0.492573	+	0.870271i	$0.336056\pi$
$397$	−10.1097	+	17.5105i	−0.507390	+	0.878825i	−0.999963	+	0.00855427i	$0.997277\pi$
$398$		−	3.43023i		−	0.171942i
$399$	−22.7647	+	3.86774i	−1.13966	+	0.193629i
$400$	−2.28526	−	3.95818i	−0.114263	−	0.197909i
$401$	16.5578	+	28.6789i	0.826856	+	1.43216i	0.900492	+	0.434872i	$0.143206\pi$
$401$	16.5578	+	28.6789i	0.826856	+	1.43216i	−0.0736358	+	0.997285i	$0.523460\pi$
$402$	4.94249	−	8.87390i	0.246509	−	0.442590i
$403$	1.78450	−	15.0538i	0.0888925	−	0.749882i
$404$	−2.31478			−0.115165
$405$	0.363579	+	5.88693i	0.0180664	+	0.292524i
$406$	2.53332	−	0.390323i	0.125727	−	0.0193714i
$407$	−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	0.148159	−	0.988964i	$-0.452665\pi$
$409$	18.8192	−	32.5957i	0.930547	−	1.61175i	0.782388	−	0.622791i	$-0.214001\pi$
$410$	−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
$413$	−6.51601	+	1.00396i	−0.320632	+	0.0494015i
$414$	−16.9556	−	9.10405i	−0.833321	−	0.447440i
$415$	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	−0.935638	−	0.352961i	$-0.885175\pi$
$419$	−15.8330	−	27.4235i	−0.773492	−	1.33973i	0.162146	−	0.986767i	$-0.448158\pi$
$420$	−0.503035	−	2.96076i	−0.0245456	−	0.144470i
$421$			3.23775i			0.157798i	0.996883	+	0.0788991i	$0.0251405\pi$
$421$			3.23775i			0.157798i	−0.996883	+	0.0788991i	$0.974860\pi$
$422$	12.4331	−	21.5347i	0.605233	−	1.04829i
$423$	−0.599643	−	19.4369i	−0.0291556	−	0.945053i
$424$			1.29577i			0.0629281i
$425$	−2.65919	+	4.60586i	−0.128990	+	0.223417i
$426$	−0.218994	−	14.2004i	−0.0106103	−	0.688011i
$427$	2.81654	−	0.433959i	0.136302	−	0.0210008i
$428$		−	6.18372i		−	0.298901i
$429$	−1.87263	−	4.18179i	−0.0904116	−	0.201899i
$430$		−	4.99495i		−	0.240878i
$431$	1.47511	+	2.55497i	0.0710536	+	0.123068i	0.899363	−	0.437202i	$-0.144031\pi$
$431$	1.47511	+	2.55497i	0.0710536	+	0.123068i	−0.828310	+	0.560270i	$0.810697\pi$
$432$	4.37504	−	2.80340i	0.210494	−	0.134879i
$433$	−20.2415	−	11.6864i	−0.972742	−	0.561613i	−0.0726709	−	0.997356i	$-0.523152\pi$
$433$	−20.2415	−	11.6864i	−0.972742	−	0.561613i	−0.900071	+	0.435743i	$0.856486\pi$
$434$	−10.3681	−	4.03006i	−0.497685	−	0.193449i
$435$	0.943765	−	0.564464i	0.0452501	−	0.0270640i
$436$	−14.0505	−	8.11209i	−0.672899	−	0.388499i
$437$		−	32.3245i		−	1.54629i
$438$	−10.3014	+	6.16123i	−0.492219	+	0.294395i
$439$	15.3108	−	8.83972i	0.730747	−	0.421897i	−0.0879485	−	0.996125i	$-0.528031\pi$
$439$	15.3108	−	8.83972i	0.730747	−	0.421897i	0.818695	+	0.574228i	$0.194698\pi$
$440$	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	$-0.0437640\pi$
$444$	7.19871	−	0.111017i	0.341636	−	0.00526861i
$445$	−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
$448$	−2.06312	+	1.65636i	−0.0974733	+	0.0782557i
$449$	−6.85295	+	11.8697i	−0.323411	+	0.560164i	−0.981189	−	0.193047i	$-0.938163\pi$
$449$	−6.85295	+	11.8697i	−0.323411	+	0.560164i	0.657779	+	0.753211i	$0.271496\pi$
$450$	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
$453$	10.9941	−	0.169548i	0.516547	−	0.00796604i
$454$		−	6.92511i		−	0.325012i
$455$	5.30177	−	3.31273i	0.248551	−	0.155303i
$456$	7.62467	+	4.24671i	0.357058	+	0.198870i
$457$	7.47187	−	4.31389i	0.349519	−	0.201795i	−0.314954	−	0.949107i	$-0.601989\pi$
$457$	7.47187	−	4.31389i	0.349519	−	0.201795i	0.664474	+	0.747312i	$0.268656\pi$
$458$	−2.34250	−	4.05732i	−0.109458	−	0.189586i
$459$	−5.37054	−	2.77781i	−0.250675	−	0.129657i
$460$	4.20409			0.196017
$461$	−28.5935	−	16.5084i	−1.33173	−	0.768875i	−0.346165	−	0.938173i	$-0.612516\pi$
$461$	−28.5935	−	16.5084i	−1.33173	−	0.768875i	−0.985565	+	0.169299i	$0.945850\pi$
$462$	−3.31472	+	0.563174i	−0.154215	+	0.0262012i
$463$		−	18.6394i		−	0.866246i	−0.901335	−	0.433123i	$-0.857411\pi$
$463$		−	18.6394i		−	0.866246i	0.901335	−	0.433123i	$-0.142589\pi$
$464$	−0.839009	−	0.484402i	−0.0389500	−	0.0224878i
$465$	−4.77184	+	0.0735900i	−0.221289	+	0.00341265i
$466$	−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	$0.517993\pi$
$468$	8.86120	+	6.20315i	0.409609	+	0.286741i
$469$	5.62124	−	14.4617i	0.259565	−	0.667781i
$470$	2.12400	+	3.67888i	0.0979728	+	0.169694i
$471$	10.5334	−	0.162443i	0.485353	−	0.00748499i
$472$	2.15803	+	1.24594i	0.0993316	+	0.0573491i
$473$	−5.59211			−0.257125
$474$	19.6142	−	11.7312i	0.900911	−	0.538833i
$475$	−11.5151	+	19.9447i	−0.528348	+	0.915126i
$476$	2.86952	+	1.11538i	0.131524	+	0.0511233i
$477$	−0.119869	−	3.88546i	−0.00548844	−	0.177903i
$478$	−5.13049	−	8.88626i	−0.234663	−	0.406448i
$479$	−27.1685	+	15.6857i	−1.24136	+	0.716699i	−0.969371	−	0.245601i	$-0.921015\pi$
$479$	−27.1685	+	15.6857i	−1.24136	+	0.716699i	−0.271989	+	0.962300i	$0.587681\pi$
$480$	−0.552323	+	0.991658i	−0.0252100	+	0.0452628i
$481$	5.91356	+	13.7711i	0.269635	+	0.627907i
$482$	16.1074			0.733670
$483$	−27.5613	−	10.2267i	−1.25408	−	0.465329i
$484$	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	0.252593	−	0.967573i	$-0.418717\pi$
$487$	−10.1304	−	5.84880i	−0.459053	−	0.265035i	−0.711646	+	0.702538i	$0.752050\pi$
$488$	−0.932808	−	0.538557i	−0.0422262	−	0.0243793i
$489$	−8.55571	+	15.3612i	−0.386902	+	0.694656i
$490$	−1.38084	−	4.37469i	−0.0623802	−	0.197628i
$491$	−35.7809	+	20.6581i	−1.61477	+	0.932287i	−0.626525	+	0.779401i	$0.715524\pi$
$491$	−35.7809	+	20.6581i	−1.61477	+	0.932287i	−0.988244	+	0.152886i	$0.951143\pi$
$492$	−8.45527	+	0.130395i	−0.381193	+	0.00587866i
$493$			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
$497$	−3.30353	−	21.4410i	−0.148184	−	0.961761i
$498$	11.1138	+	18.5819i	0.498021	+	0.832676i
$499$			25.7632i			1.15332i	0.816985	+	0.576660i	$0.195644\pi$
$499$			25.7632i			1.15332i	−0.816985	+	0.576660i	$0.804356\pi$
$500$	−5.43174	−	3.13602i	−0.242915	−	0.140247i
$501$	−18.9828	−	31.7386i	−0.848088	−	1.41798i
$502$	−20.9271			−0.934021
$503$	−5.86833	+	10.1642i	−0.261656	+	0.453201i	−0.966682	−	0.255980i	$-0.917602\pi$
$503$	−5.86833	+	10.1642i	−0.261656	+	0.453201i	0.705026	+	0.709181i	$0.250935\pi$
$504$	6.03319	−	5.15758i	0.268740	−	0.229737i
$505$	−1.31375	+	0.758496i	−0.0584612	+	0.0337526i
$506$		−	4.70670i		−	0.209238i
$507$	−4.92616	+	21.9712i	−0.218778	+	0.975775i
$508$	−7.48936			−0.332287
$509$	−33.3626	+	19.2619i	−1.47877	+	0.853768i	−0.999712	−	0.0240145i	$-0.992355\pi$
$509$	−33.3626	+	19.2619i	−1.47877	+	0.853768i	−0.479059	+	0.877783i	$0.659022\pi$
$510$	1.32068	−	0.0203671i	0.0584805	−	0.000901871i
$511$	−14.2976	+	11.4788i	−0.632491	+	0.507791i
$512$	1.00000			0.0441942
$513$	−23.2560	−	12.0287i	−1.02678	−	0.531081i
$514$	13.7555	−	23.8253i	0.606731	−	1.05089i
$515$	7.40048			0.326104
$516$	11.3296	−	6.77620i	0.498757	−	0.298305i
$517$	4.11869	−	2.37793i	0.181140	−	0.104581i
$518$	10.8693	−	1.67469i	0.477568	−	0.0735815i
$519$	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	$0.186809\pi$
$522$	2.56064	+	1.37490i	0.112076	+	0.0601777i
$523$	29.6865	−	17.1395i	1.29810	−	0.749458i	0.318024	−	0.948083i	$-0.396981\pi$
$523$	29.6865	−	17.1395i	1.29810	−	0.749458i	0.980076	+	0.198625i	$0.0636474\pi$
$524$	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
$531$	−6.58628	−	3.53641i	−0.285820	−	0.153467i
$532$	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
$537$	2.21563	+	3.70447i	0.0956117	+	0.159860i
$538$	−0.0618987			−0.00266864
$539$	−4.89769	+	1.54593i	−0.210959	+	0.0665878i
$540$	1.56445	−	3.02465i	0.0673230	−	0.130160i
$541$			20.6184i			0.886454i	0.896410	+	0.443227i	$0.146166\pi$
$541$			20.6184i			0.886454i	−0.896410	+	0.443227i	$0.853834\pi$
$542$	2.55715	−	4.42912i	0.109839	−	0.190247i
$543$	−33.5730	+	0.517753i	−1.44075	+	0.0222189i
$544$	−0.581815	−	1.00773i	−0.0249451	−	0.0432062i
$545$	−10.6325			−0.455446
$546$	14.7064	+	7.53143i	0.629375	+	0.322315i
$547$	−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
$549$	2.84691	+	1.52861i	0.121503	+	0.0652395i
$550$	−1.67669	+	2.90411i	−0.0714942	+	0.123832i
$551$			4.88166i			0.207966i
$552$	5.70331	+	9.53575i	0.242749	+	0.405869i
$553$	27.2233	−	21.8560i	1.15765	−	0.929412i
$554$	14.1684			0.601957
$555$	4.04924	−	2.42184i	0.171881	−	0.102801i
$556$	3.15133	−	1.81942i	0.133646	−	0.0771607i
$557$	−4.33794	−	7.51353i	−0.183804	−	0.318358i	0.759369	−	0.650661i	$-0.225508\pi$
$557$	−4.33794	−	7.51353i	−0.183804	−	0.318358i	−0.943173	+	0.332302i	$0.892175\pi$
$558$	−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
$561$	−0.0228020	−	1.47857i	−0.000962703	−	0.0624251i
$562$	1.77069	+	3.06692i	0.0746920	+	0.129370i
$563$	−6.82336	+	11.8184i	−0.287570	+	0.498087i	−0.973229	−	0.229836i	$-0.926181\pi$
$563$	−6.82336	+	11.8184i	−0.287570	+	0.498087i	0.685659	+	0.727923i	$0.259514\pi$
$564$	−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	$-0.485506\pi$
$569$	22.2652	−	12.8548i	0.933404	−	0.538901i	0.887887	+	0.460062i	$0.152173\pi$
$570$	5.71891	−	0.0881955i	0.239539	−	0.00369410i
$571$	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
$574$	−12.7665	+	1.96701i	−0.532865	+	0.0821014i
$575$	−25.3919	+	14.6600i	−1.05892	+	0.611366i
$576$	−2.99857	+	0.0925084i	−0.124941	+	0.00385452i
$577$	−24.2166			−1.00815			−0.504075	−	0.863660i	$-0.668166\pi$
$577$	−24.2166			−1.00815			−0.504075	+	0.863660i	$0.668166\pi$
$578$	7.82298	−	13.5498i	0.325393	−	0.563598i
$579$	−19.2088	−	32.1165i	−0.798291	−	1.33472i
$580$	−0.634905			−0.0263630
$581$	20.7057	+	25.7905i	0.859018	+	1.06997i
$582$	−0.179999	−	11.6718i	−0.00746119	−	0.483810i
$583$	0.823332	−	0.475351i	0.0340989	−	0.0196870i
$584$	6.93011			0.286770
$585$	7.06178	+	0.617000i	0.291969	+	0.0255098i
$586$		−	22.1375i		−	0.914494i
$587$	−16.9787	+	9.80266i	−0.700786	+	0.404599i	−0.807640	−	0.589676i	$-0.799256\pi$
$587$	−16.9787	+	9.80266i	−0.700786	+	0.404599i	0.106854	+	0.994275i	$0.465922\pi$
$588$	8.04944	−	9.06678i	0.331953	−	0.373908i
$589$	10.5927	−	18.3471i	0.436464	−	0.755977i
$590$	1.63305			0.0672317
$591$	31.5216	−	18.8530i	1.29663	−	0.775509i
$592$	−3.59978	−	2.07834i	−0.147950	−	0.0854191i
$593$		−	7.95508i		−	0.326676i	−0.986570	−	0.163338i	$-0.947774\pi$
$593$		−	7.95508i		−	0.326676i	0.986570	−	0.163338i	$-0.0522261\pi$
$594$	−3.38626	−	1.75148i	−0.138940	−	0.0718640i
$595$	1.99408	−	0.307238i	0.0817491	−	0.0125955i
$596$	−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	$0.844675\pi$
$600$	−0.122070	−	7.91543i	−0.00498347	−	0.323146i
$601$	−6.23997	+	3.60265i	−0.254534	+	0.146955i	−0.621839	−	0.783145i	$-0.713614\pi$
$601$	−6.23997	+	3.60265i	−0.254534	+	0.146955i	0.367305	+	0.930101i	$0.380281\pi$
$602$	15.7247	−	12.6245i	0.640892	−	0.514536i
$603$	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	$-0.333830\pi$
$607$	−0.0665333	−	0.0384130i	−0.00270050	−	0.00155914i	−0.501350	+	0.865245i	$0.667163\pi$
$608$	−2.51943	−	4.36378i	−0.102176	−	0.176975i
$609$	4.16232	+	1.54444i	0.168666	+	0.0625838i
$610$	−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	−0.984752	−	0.173965i	$-0.944342\pi$
$613$	−32.8419	+	18.9613i	−1.32647	+	0.765838i	−0.341718	+	0.939802i	$0.611009\pi$
$614$	1.08820	+	1.88482i	0.0439161	+	0.0760650i
$615$	−4.75605	+	2.84458i	−0.191783	+	0.114705i
$616$	1.80931	+	0.703274i	0.0728990	+	0.0283357i
$617$	1.59443	−	2.76163i	0.0641892	−	0.111179i	−0.832145	−	0.554558i	$-0.812887\pi$
$617$	1.59443	−	2.76163i	0.0641892	−	0.111179i	0.896334	+	0.443379i	$0.146221\pi$
$618$	10.0396	+	16.7858i	0.403850	+	0.675225i
$619$	10.9786			0.441267			0.220634	−	0.975357i	$-0.429188\pi$
$619$	10.9786			0.441267			0.220634	+	0.975357i	$0.429188\pi$
$620$	2.38620	+	1.37767i	0.0958322	+	0.0553287i
$621$	−17.9839	−	28.0661i	−0.721670	−	1.12625i
$622$	3.55142	+	6.15125i	0.142399	+	0.246643i
$623$	14.0342	−	36.1056i	0.562267	−	1.44654i
$624$	−2.55232	−	5.69962i	−0.102175	−	0.228167i
$625$	18.7422			0.749689
$626$	−14.8369	+	8.56609i	−0.593002	+	0.342370i
$627$	−0.0987395	−	6.40262i	−0.00394328	−	0.255696i
$628$	−5.26732	−	3.04109i	−0.210189	−	0.121353i
$629$			4.83683i			0.192857i
$630$	1.73412	−	4.90410i	0.0690892	−	0.195384i
$631$	2.23519	+	1.29049i	0.0889816	+	0.0513735i	0.543831	−	0.839195i	$-0.316973\pi$
$631$	2.23519	+	1.29049i	0.0889816	+	0.0513735i	−0.454849	+	0.890569i	$0.650307\pi$
$632$	−13.1952			−0.524877
$633$	36.9628	−	22.1073i	1.46914	−	0.878687i
$634$	−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
$637$	23.8288	+	8.31786i	0.944133	+	0.329566i
$638$			0.710809i			0.0281412i
$639$	11.6366	−	21.6722i	0.460337	−	0.857340i
$640$	0.567549	−	0.327675i	0.0224343	−	0.0129525i
$641$	−21.6084	−	12.4756i	−0.853482	−	0.492758i	0.00834190	−	0.999965i	$-0.497345\pi$
$641$	−21.6084	−	12.4756i	−0.853482	−	0.492758i	−0.861824	+	0.507207i	$0.830678\pi$
$642$	5.21160	−	9.35706i	0.205685	−	0.369294i
$643$	−2.49176	+	4.31585i	−0.0982653	+	0.170200i	−0.910967	−	0.412480i	$-0.864663\pi$
$643$	−2.49176	+	4.31585i	−0.0982653	+	0.170200i	0.812701	+	0.582680i	$0.197996\pi$
$644$	10.6256	+	13.2350i	0.418709	+	0.521532i
$645$	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	0.991389	+	0.130951i	$0.0418030\pi$
$647$	15.4932	+	26.8350i	0.609101	+	1.05499i	−0.382288	+	0.924043i	$0.624864\pi$
$648$	8.98288	−	0.554786i	0.352881	−	0.0217941i
$649$		−	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	$-0.835518\pi$
$653$	−22.3928	+	12.9285i	−0.876299	+	0.505931i	−0.00686241	+	0.999976i	$0.502184\pi$
$654$	−14.4241	−	24.1167i	−0.564029	−	0.943038i
$655$		−	8.25521i		−	0.322558i
$656$	4.22814	+	2.44112i	0.165081	+	0.0953096i
$657$	−20.7804	+	0.641093i	−0.810722	+	0.0250114i
$658$	−6.21326	+	15.9848i	−0.242218	+	0.623152i
$659$	37.8578	+	21.8572i	1.47473	+	0.851436i	0.999594	−	0.0284766i	$-0.00906561\pi$
$659$	37.8578	+	21.8572i	1.47473	+	0.851436i	0.475136	+	0.879912i	$0.342399\pi$
$660$	0.832719	−	0.0128420i	0.0324136	−	0.000499873i
$661$	−16.3148	−	28.2581i	−0.634573	−	1.09911i	−0.986605	−	0.163125i	$-0.947842\pi$
$661$	−16.3148	−	28.2581i	−0.634573	−	1.09911i	0.352032	−	0.935988i	$-0.385491\pi$
$662$			11.3987i			0.443024i
$663$	−4.25871	+	5.88818i	−0.165395	+	0.228678i
$664$		−	12.5007i		−	0.485122i
$665$	8.63493	−	1.33043i	0.334848	−	0.0515919i
$666$	10.9865	+	5.89903i	0.425717	+	0.228583i
$667$	−3.10746	+	5.38228i	−0.120321	+	0.208403i
$668$			21.3517i			0.826122i
$669$	−12.6923	+	7.59125i	−0.490714	+	0.293495i
$670$	−1.92162	+	3.32835i	−0.0742387	+	0.128585i
$671$			0.790275i			0.0305082i
$672$	−4.51783	+	0.767584i	−0.174279	+	0.0296102i
$673$	8.95203	+	15.5054i	0.345076	+	0.597688i	0.985367	−	0.170443i	$-0.0545200\pi$
$673$	8.95203	+	15.5054i	0.345076	+	0.597688i	−0.640292	+	0.768132i	$0.721187\pi$
$674$	−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	$0.372132\pi$
$678$	9.91913	−	0.152970i	0.380942	−	0.00587478i
$679$	−2.71528	−	17.6231i	−0.104203	−	0.676312i
$680$	−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	$-0.961189\pi$
$683$	−10.2174	+	17.6970i	−0.390956	+	0.677156i	0.601620	+	0.798783i	$0.294522\pi$
$684$	7.95837	+	12.8520i	0.304296	+	0.491410i
$685$	12.6377	+	7.29637i	0.482861	+	0.278780i
$686$	10.2821	−	15.4039i	0.392571	−	0.588123i
$687$	−0.125127	−	8.11368i	−0.00477389	−	0.309556i
$688$	−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	0.645591	+	0.763683i	$0.276611\pi$
$691$	25.8706	+	44.8092i	0.984165	+	1.70462i	0.338573	+	0.940940i	$0.390056\pi$
$692$	−3.66961	−	6.35595i	−0.139498	−	0.241617i
$693$	−5.49040	−	1.94144i	−0.208563	−	0.0737493i
$694$		−	19.8740i		−	0.754405i
$695$	1.19236	−	2.06522i	0.0452287	−	0.0783384i
$696$	−0.861317	−	1.44010i	−0.0326481	−	0.0545867i
$697$		−	5.68111i		−	0.215187i
$698$	−8.02933	+	13.9072i	−0.303915	+	0.526396i
$699$	−14.9179	+	0.230060i	−0.564247	+	0.00870166i
$700$	−1.84142	−	11.9514i	−0.0695992	−	0.451721i
$701$		−	12.8757i		−	0.486308i	−0.969988	−	0.243154i	$-0.921818\pi$
$701$		−	12.8757i		−	0.486308i	0.969988	−	0.243154i	$-0.0781820\pi$
$702$	8.18059	+	16.8546i	0.308757	+	0.636136i
$703$			20.9449i			0.789951i
$704$	−0.366849	−	0.635401i	−0.0138261	−	0.0239476i
$705$	0.113456	+	7.35688i	0.00427299	+	0.277076i
$706$	23.2239	+	13.4084i	0.874045	+	0.504630i
$707$	−5.70828	−	2.21880i	−0.214682	−	0.0834465i
$708$	2.21541	+	3.70410i	0.0832604	+	0.139209i
$709$	13.9466	+	8.05207i	0.523776	+	0.302402i	0.738478	−	0.674278i	$-0.235545\pi$
$709$	13.9466	+	8.05207i	0.523776	+	0.302402i	−0.214702	+	0.976680i	$0.568878\pi$
$710$			5.37358i			0.201667i
$711$	39.5667	−	1.22067i	1.48387	−	0.0457785i
$712$	−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
$717$	−0.274050	−	17.7704i	−0.0102346	−	0.663648i
$718$	−15.7034	−	27.1991i	−0.586046	−	1.01506i
$719$	−13.1163	+	22.7181i	−0.489155	+	0.847241i	−0.999922	−	0.0124783i	$-0.996028\pi$
$719$	−13.1163	+	22.7181i	−0.489155	+	0.847241i	0.510768	+	0.859719i	$0.329361\pi$
$720$	−1.67152	+	1.03506i	−0.0622940	+	0.0385744i
$721$	18.7043	+	23.2976i	0.696586	+	0.867649i
$722$	−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
$726$	0.279411	+	18.1180i	0.0103699	+	0.672423i
$727$			16.5596i			0.614161i	0.951683	+	0.307081i	$0.0993521\pi$
$727$			16.5596i			0.614161i	−0.951683	+	0.307081i	$0.900648\pi$
$728$	−5.05491	−	8.08999i	−0.187347	−	0.299835i
$729$	−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
$732$	−0.957610	−	1.60109i	−0.0353943	−	0.0591781i
$733$	−6.98748			−0.258088			−0.129044	−	0.991639i	$-0.541191\pi$
$733$	−6.98748			−0.258088			−0.129044	+	0.991639i	$0.541191\pi$
$734$	1.82808	+	1.05544i	0.0674758	+	0.0389572i
$735$	1.59750	−	7.78344i	0.0589245	−	0.287096i
$736$		−	6.41504i		−	0.236462i
$737$	3.72626	+	2.15135i	0.137258	+	0.0792462i
$738$	−12.9042	−	6.92873i	−0.475010	−	0.255050i
$739$	6.55386	−	3.78387i	0.241087	−	0.139192i	−0.374589	−	0.927191i	$-0.622216\pi$
$739$	6.55386	−	3.78387i	0.241087	−	0.139192i	0.615676	+	0.787999i	$0.288883\pi$
$740$	−2.72407			−0.100139
$741$	−18.4415	+	25.4975i	−0.677464	+	0.936676i
$742$	−1.24204	+	3.19538i	−0.0455966	+	0.117306i
$743$	14.6769	+	25.4211i	0.538443	+	0.932610i	0.998988	+	0.0449741i	$0.0143205\pi$
$743$	14.6769	+	25.4211i	0.538443	+	0.932610i	−0.460545	+	0.887636i	$0.652346\pi$
$744$	0.112291	+	7.28137i	0.00411680	+	0.266948i
$745$	−12.3831	−	7.14938i	−0.453681	−	0.261933i
$746$	−24.2736			−0.888721
$747$	1.15642	+	37.4843i	0.0423112	+	1.37148i
$748$	−0.426876	+	0.739371i	−0.0156081	+	0.0270341i
$749$	5.92731	−	15.2491i	0.216579	−	0.557191i
$750$	−5.57616	−	9.32317i	−0.203613	−	0.340434i
$751$	22.9520	+	39.7541i	0.837531	+	1.45065i	0.891953	+	0.452129i	$0.149335\pi$
$751$	22.9520	+	39.7541i	0.837531	+	1.45065i	−0.0544211	+	0.998518i	$0.517331\pi$
$752$	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
$756$	13.4760	−	2.71959i	0.490119	−	0.0989107i
$757$	18.3065	+	31.7078i	0.665361	+	1.15244i	0.979187	+	0.202959i	$0.0650559\pi$
$757$	18.3065	+	31.7078i	0.665361	+	1.15244i	−0.313826	+	0.949481i	$0.601611\pi$
$758$	−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	0.582674	−	0.812706i	$-0.302007\pi$
$761$	4.69480	+	2.71054i	0.170186	+	0.0982571i	−0.412487	+	0.910963i	$0.635340\pi$
$762$	−11.3327	−	6.31198i	−0.410541	−	0.228659i
$763$	−26.8731	−	33.4724i	−0.972872	−	1.21178i
$764$	11.8522	−	6.84286i	0.428797	−	0.247566i
$765$	2.01558	+	1.08224i	0.0728735	+	0.0391284i
$766$		−	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	$-0.189656\pi$
$769$	−2.00109	−	3.46599i	−0.0721612	−	0.124987i	−0.899848	+	0.436203i	$0.856323\pi$
$770$	1.25731	−	0.193721i	0.0453105	−	0.00698123i
$771$	40.8943	−	24.4588i	1.47277	−	0.880862i
$772$			21.6059i			0.777615i
$773$	−25.5699	−	14.7628i	−0.919686	−	0.530981i	−0.0361510	−	0.999346i	$-0.511510\pi$
$773$	−25.5699	−	14.7628i	−0.919686	−	0.530981i	−0.883535	+	0.468365i	$0.844843\pi$
$774$	22.8546	−	0.705082i	0.821491	−	0.0253437i
$775$	−19.2163			−0.690269
$776$	−3.36975	+	5.83658i	−0.120967	+	0.209521i
$777$	17.8585	+	6.62644i	0.640671	+	0.237722i
$778$	−14.0944	+	8.13741i	−0.505309	+	0.291740i
$779$		−	24.6009i		−	0.881418i
$780$	−3.31619	−	2.39848i	−0.118739	−	0.0858794i
$781$	6.01600			0.215269
$782$	−6.46465	+	3.73237i	−0.231175	+	0.133469i
$783$	2.71594	+	4.23855i	0.0970599	+	0.151474i
$784$	−6.67536	+	2.10704i	−0.238406	+	0.0752513i
$785$	−3.98595			−0.142265
$786$	18.7245	−	11.1991i	0.667882	−	0.399458i
$787$	−20.6739	+	35.8082i	−0.736945	+	1.27643i	0.216920	+	0.976189i	$0.430399\pi$
$787$	−20.6739	+	35.8082i	−0.736945	+	1.27643i	−0.953865	+	0.300236i	$0.902934\pi$
$788$	−21.2057			−0.755423
$789$	−27.7469	−	46.3919i	−0.987816	−	1.65160i
$790$	−7.48892	+	4.32373i	−0.266444	+	0.153831i
$791$	14.9768	−	2.30756i	0.532514	−	0.0820473i
$792$	1.15880	+	1.87136i	0.0411763	+	0.0664958i
$793$	2.32421	−	3.11132i	0.0825352	−	0.110486i
$794$	20.2193			0.717558
$795$	0.0226799	+	1.47065i	0.000804375	+	0.0521585i
$796$	−2.97067	+	1.71512i	−0.105293	+	0.0607907i
$797$	11.8501	−	20.5250i	0.419753	−	0.727034i	−0.576161	−	0.817336i	$-0.695450\pi$
$797$	11.8501	−	20.5250i	0.419753	−	0.727034i	0.995914	+	0.0903022i	$0.0287833\pi$
$798$	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
$804$	−10.1563	+	0.156627i	−0.358184	+	0.00552381i
$805$	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	$-0.862294\pi$
$809$	−28.4068	+	16.4007i	−0.998730	+	0.576617i	−0.0908575	+	0.995864i	$0.528961\pi$
$810$	4.91644	−	3.25833i	0.172746	−	0.114486i
$811$	8.64443			0.303547			0.151774	−	0.988415i	$-0.451502\pi$
$811$	8.64443			0.303547			0.151774	+	0.988415i	$0.451502\pi$
$812$	−1.60469	−	1.99876i	−0.0563136	−	0.0701427i
$813$	7.60225	−	4.54689i	0.266623	−	0.159466i
$814$			3.04974i			0.106893i
$815$	3.32643	−	5.76154i	0.116520	−	0.201818i
$816$	−0.0310783	−	2.01523i	−0.00108796	−	0.0705470i
$817$	19.2026	+	33.2599i	0.671815	+	1.16362i
$818$	−37.6383			−1.31599
$819$	15.9059	+	23.7908i	0.555797	+	0.831318i
$820$	3.19957			0.111734
$821$	−12.8952	−	22.3352i	−0.450046	−	0.779503i	0.548342	−	0.836254i	$-0.315259\pi$
$821$	−12.8952	−	22.3352i	−0.450046	−	0.779503i	−0.998388	+	0.0567514i	$0.981926\pi$
$822$	0.594711	+	38.5632i	0.0207429	+	1.34505i
$823$	−7.55953	+	13.0935i	−0.263509	+	0.456411i	−0.967172	−	0.254123i	$-0.918213\pi$
$823$	−7.55953	+	13.0935i	−0.263509	+	0.456411i	0.703663	+	0.710534i	$0.251546\pi$
$824$		−	11.2924i		−	0.393390i
$825$	−4.98469	+	2.98133i	−0.173544	+	0.103796i
$826$	4.12746	+	5.14105i	0.143613	+	0.178880i
$827$	−5.85211			−0.203498			−0.101749	−	0.994810i	$-0.532444\pi$
$827$	−5.85211			−0.203498			−0.101749	+	0.994810i	$0.532444\pi$
$828$	0.593445	+	19.2360i	0.0206236	+	0.668496i
$829$	−12.2127	+	7.05100i	−0.424164	+	0.244891i	−0.696857	−	0.717210i	$-0.745419\pi$
$829$	−12.2127	+	7.05100i	−0.424164	+	0.244891i	0.272693	+	0.962101i	$0.412086\pi$
$830$	−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
$834$	6.30192	−	0.0971864i	0.218218	−	0.00336529i
$835$	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	0.639040	−	0.769174i	$-0.279332\pi$
$839$	8.47056	+	4.89048i	0.292436	+	0.168838i	−0.346604	+	0.938012i	$0.612665\pi$
$840$	−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
$843$	0.0945832	+	6.13311i	0.00325762	+	0.211236i
$844$	−24.8662			−0.855929
$845$	1.99186	−	8.28342i	0.0685219	−	0.284958i
$846$	−16.5330	+	10.2377i	−0.568417	+	0.351981i
$847$	4.21492	+	27.3562i	0.144826	+	0.939971i
$848$	1.12217	−	0.647884i	0.0385354	−	0.0222484i
$849$	19.1570	+	32.0299i	0.657467	+	1.09926i
$850$	5.31839			0.182419
$851$	−13.3326	+	23.0928i	−0.457036	+	0.791610i
$852$	−12.1884	+	7.28984i	−0.417567	+	0.249746i
$853$	5.48095			0.187664			0.0938321	−	0.995588i	$-0.470088\pi$
$853$	5.48095			0.187664			0.0938321	+	0.995588i	$0.470088\pi$
$854$	−1.78409	−	2.22221i	−0.0610503	−	0.0760426i
$855$	8.72805	+	4.68640i	0.298493	+	0.160272i
$856$	−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	$0.549398\pi$
$858$	−2.68522	+	3.71265i	−0.0916720	+	0.126748i
$859$		−	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
$861$	−20.9758	−	7.78311i	−0.714853	−	0.265248i
$862$	1.47511	−	2.55497i	0.0502425	−	0.0870225i
$863$	−36.0591			−1.22747			−0.613733	−	0.789513i	$-0.710333\pi$
$863$	−36.0591			−1.22747			−0.613733	+	0.789513i	$0.710333\pi$
$864$	−4.61533	−	2.38719i	−0.157017	−	0.0812140i
$865$	−4.16537	−	2.40488i	−0.141627	−	0.0817682i
$866$			23.3728i			0.794241i
$867$	23.2572	−	13.9101i	0.789857	−	0.472411i
$868$	1.69392	+	10.9941i	0.0574952	+	0.373163i
$869$	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
$873$	9.56451	−	17.8131i	0.323710	−	0.602883i
$874$	−27.9938	+	16.1622i	−0.946905	+	0.546696i
$875$	−10.3888	−	12.9400i	−0.351204	−	0.437450i
$876$	10.4865	+	5.84064i	0.354305	+	0.197337i
$877$	11.5032	+	6.64138i	0.388436	+	0.224264i	0.681482	−	0.731835i	$-0.261336\pi$
$877$	11.5032	+	6.64138i	0.388436	+	0.224264i	−0.293046	+	0.956098i	$0.594669\pi$
$878$	−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	0.955395	+	0.295331i	$0.0954298\pi$
$881$	21.7703	+	37.7073i	0.733461	+	1.27039i	−0.221934	+	0.975062i	$0.571237\pi$
$882$	19.8216	−	6.93563i	0.667429	−	0.233535i
$883$	−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	0.990639	+	0.136506i	$0.0435874\pi$
$887$	18.2727	+	31.6493i	0.613537	+	1.06268i	−0.377102	+	0.926172i	$0.623079\pi$
$888$	−3.69550	−	6.17876i	−0.124013	−	0.207346i
$889$	−18.4689	−	7.17881i	−0.619425	−	0.240769i
$890$	−4.79758	+	8.30965i	−0.160815	+	0.278540i
$891$	−3.64787	−	5.50421i	−0.122208	−	0.184398i
$892$	8.53859			0.285893
$893$	−28.2862	−	16.3310i	−0.946561	−	0.546497i
$894$	−0.582730	−	37.7863i	−0.0194894	−	1.26376i
$895$	−0.816608	−	1.41441i	−0.0272962	−	0.0472784i
$896$	2.46601	+	0.958534i	0.0823837	+	0.0320224i
$897$	−36.5633	+	16.3733i	−1.22081	+	0.546687i
$898$	13.7059			0.457372
$899$	−3.52753	+	2.03662i	−0.117650	+	0.0679250i
$900$	6.48635	−	12.0803i	0.216212	−	0.402677i
$901$	−1.30579	−	0.753897i	−0.0435021	−	0.0251159i
$902$		−	3.58208i		−	0.119270i
$903$	34.4341	−	5.85039i	1.14590	−	0.194689i
$904$	−4.96016	−	2.86375i	−0.164972	−	0.0952468i
$905$	12.7044			0.422308
$906$	−5.64387	−	9.43637i	−0.187505	−	0.313502i
$907$	2.29532	+	3.97562i	0.0762149	+	0.132008i	0.901614	−	0.432542i	$-0.142383\pi$
$907$	2.29532	+	3.97562i	0.0762149	+	0.132008i	−0.825399	+	0.564550i	$0.809050\pi$
$908$	−5.99732	+	3.46256i	−0.199028	+	0.114909i
$909$	−3.65597	−	5.90406i	−0.121261	−	0.195825i
$910$	−5.51979	−	2.93510i	−0.182979	−	0.0972976i
$911$		−	60.0679i		−	1.99014i	−0.0991827	−	0.995069i	$-0.531623\pi$
$911$		−	60.0679i		−	1.99014i	0.0991827	−	0.995069i	$-0.468377\pi$
$912$	−0.134578	−	8.72652i	−0.00445632	−	0.288964i
$913$	−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
$917$	25.9884	−	20.8646i	0.858213	−	0.689011i
$918$	0.279616	+	6.03993i	0.00922869	+	0.199347i
$919$	−13.4861	+	23.3585i	−0.444864	+	0.770527i	−0.998043	−	0.0625354i	$-0.980081\pi$
$919$	−13.4861	+	23.3585i	−0.444864	+	0.770527i	0.553179	+	0.833063i	$0.313415\pi$
$920$	−2.10205	−	3.64085i	−0.0693024	−	0.120035i
$921$	0.0581273	+	3.76918i	0.00191536	+	0.124199i
$922$			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
$927$	1.04464	+	33.8612i	0.0343106	+	1.11215i
$928$			0.968804i			0.0318025i
$929$	−12.3212	−	7.11365i	−0.404246	−	0.233391i	0.284069	−	0.958804i	$-0.408316\pi$
$929$	−12.3212	−	7.11365i	−0.404246	−	0.233391i	−0.688314	+	0.725413i	$0.741649\pi$
$930$	2.44965	+	4.09574i	0.0803272	+	0.134305i
$931$	26.0127	+	23.8212i	0.852532	+	0.780710i
$932$	7.45984	+	4.30694i	0.244355	+	0.141079i
$933$	0.189703	+	12.3010i	0.00621060	+	0.402718i
$934$	1.22093	+	2.11471i	0.0399500	+	0.0691955i
$935$			0.559505i			0.0182978i
$936$	0.941482	−	10.7756i	0.0307733	−	0.352212i
$937$			4.30558i			0.140657i	0.997524	+	0.0703287i	$0.0224048\pi$
$937$			4.30558i			0.140657i	−0.997524	+	0.0703287i	$0.977595\pi$
$938$	−15.3348	+	2.36272i	−0.500700	+	0.0771456i
$939$	−29.6703	+	0.457567i	−0.968253	+	0.0149321i
$940$	2.12400	−	3.67888i	0.0692773	−	0.119992i
$941$		−	10.9105i		−	0.355671i	−0.984060	−	0.177835i	$-0.943091\pi$
$941$		−	10.9105i		−	0.355671i	0.984060	−	0.177835i	$-0.0569095\pi$
$942$	−5.40738	−	9.04097i	−0.176182	−	0.294571i
$943$	15.6599	−	27.1237i	0.509956	−	0.883269i
$944$		−	2.49188i		−	0.0811039i
$945$	6.75717	−	5.95926i	0.219811	−	0.193855i
$946$	2.79605	+	4.84291i	0.0909076	+	0.157457i
$947$	−2.65690	−	4.60188i	−0.0863376	−	0.149541i	0.819623	−	0.572904i	$-0.194183\pi$
$947$	−2.65690	−	4.60188i	−0.0863376	−	0.149541i	−0.905960	+	0.423362i	$0.860850\pi$
$948$	−19.9666	−	11.1208i	−0.648486	−	0.361187i
$949$	−2.94140	+	24.8131i	−0.0954818	+	0.805468i
$950$	23.0302			0.747198
$951$	−0.657945	−	42.6635i	−0.0213353	−	1.38346i
$952$	−0.468816	−	3.04277i	−0.0151944	−	0.0986167i
$953$	−4.59073	−	2.65046i	−0.148708	−	0.0858569i	0.423800	−	0.905756i	$-0.360696\pi$
$953$	−4.59073	−	2.65046i	−0.148708	−	0.0858569i	−0.572508	+	0.819899i	$0.694029\pi$
$954$	−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
$959$	8.97123	+	58.2262i	0.289696	+	1.88022i
$960$	1.13496	−	0.0175031i	0.0366308	−	0.000564910i
$961$	−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
$966$	4.92408	+	28.9821i	0.158430	+	0.932484i
$967$		−	5.42003i		−	0.174296i	−0.996195	−	0.0871482i	$-0.972225\pi$
$967$		−	5.42003i		−	0.174296i	0.996195	−	0.0871482i	$-0.0277754\pi$
$968$	5.23084	−	9.06009i	0.168126	−	0.291202i
$969$	−8.71569	+	5.21283i	−0.279988	+	0.167460i
$970$			4.41672i			0.141812i
$971$	−29.9886	+	51.9418i	−0.962381	+	1.66689i	−0.245888	+	0.969298i	$0.579079\pi$
$971$	−29.9886	+	51.9418i	−0.962381	+	1.66689i	−0.716493	+	0.697594i	$0.754254\pi$
$972$	14.0603	+	6.73122i	0.450983	+	0.215904i
$973$	9.51520	−	1.46606i	0.305043	−	0.0469997i
$974$			11.6976i			0.374815i
$975$	28.3929	+	2.92254i	0.909299	+	0.0935960i
$976$			1.07711i			0.0344776i
$977$	−16.0567	−	27.8110i	−0.513699	−	0.889753i	−0.999874	−	0.0158911i	$-0.994941\pi$
$977$	−16.0567	−	27.8110i	−0.513699	−	0.889753i	0.486175	−	0.873862i	$-0.338392\pi$
$978$	17.5810	−	0.271130i	0.562179	−	0.00866977i
$979$	9.30308	+	5.37114i	0.297328	+	0.171662i
$980$	−3.09817	+	3.38319i	−0.0989674	+	0.108072i
$981$	−1.50087	−	48.6494i	−0.0479192	−	1.55326i
$982$	35.7809	+	20.6581i	1.14181	+	0.659227i
$983$		−	4.84635i		−	0.154574i	−0.997009	−	0.0772872i	$-0.975374\pi$
$983$		−	4.84635i		−	0.154574i	0.997009	−	0.0772872i	$-0.0246258\pi$
$984$	4.34056	+	7.25728i	0.138372	+	0.231354i
$985$	−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
$990$	1.27087	+	0.682378i	0.0403910	+	0.0216874i
$991$	−24.0646	−	41.6810i	−0.764436	−	1.32404i	−0.940544	−	0.339671i	$-0.889684\pi$
$991$	−24.0646	−	41.6810i	−0.764436	−	1.32404i	0.176108	−	0.984371i	$-0.443649\pi$
$992$	2.10220	−	3.64112i	0.0667449	−	0.115606i
$993$	−9.60676	+	17.2483i	−0.304861	+	0.547357i
$994$	−16.9167	+	13.5815i	−0.536565	+	0.430777i
$995$	−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	$-0.0473632\pi$
$997$	42.7858	+	24.7024i	1.35504	+	0.782332i	0.366089	+	0.930580i	$0.380697\pi$
$998$	22.3116	−	12.8816i	0.706261	−	0.407760i
$999$	11.6528	+	18.1856i	0.368679	+	0.575367i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.6	✓	24	273.251	even	6	inner
546.2.q.i.251.7	yes	24	39.17	odd	6	inner
546.2.q.i.335.6	yes	24	1.1	even	1	trivial
546.2.q.i.335.7	yes	24	7.6	odd	2	inner
546.2.q.j.251.3	yes	24	13.4	even	6
546.2.q.j.251.10	yes	24	91.69	odd	6
546.2.q.j.335.3	yes	24	21.20	even	2
546.2.q.j.335.10	yes	24	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.0267080 - 1.73184i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.655349i q^{5} +(-1.48647 + 0.889052i) q^{6} +(-2.06312 + 1.65636i) q^{7} +1.00000 q^{8} +(-2.99857 + 0.0925084i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.0267080 - 1.73184i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.655349i q^{5} +(-1.48647 + 0.889052i) q^{6} +(-2.06312 + 1.65636i) q^{7} +1.00000 q^{8} +(-2.99857 + 0.0925084i) 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} +(1.13496 - 0.0175031i) 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} +(-0.0267080 - 1.73184i) q^{24} +4.57052 q^{25} +(3.31301 - 1.42267i) q^{26} +(0.240296 + 5.19059i) q^{27} +(-0.402891 - 2.61490i) q^{28} +(0.839009 - 0.484402i) q^{29} +(-0.582640 - 0.974155i) q^{30} -4.20440 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.09062 + 0.652295i) q^{33} +1.16363 q^{34} +(-1.08550 - 1.35206i) q^{35} +(1.41917 - 2.64309i) q^{36} +(3.59978 - 2.07834i) q^{37} +5.03886 q^{38} +(6.21218 + 0.639432i) q^{39} +0.655349i q^{40} +(-4.22814 + 2.44112i) q^{41} +(1.59417 - 4.29635i) q^{42} +(3.81091 - 6.60069i) q^{43} +0.733697 q^{44} +(-0.0606253 - 1.96511i) q^{45} +(5.55559 + 3.20752i) q^{46} +6.48204i q^{47} +(-1.48647 + 0.889052i) q^{48} +(1.51293 - 6.83455i) q^{49} +(-2.28526 - 3.95818i) q^{50} +(1.76078 + 0.980698i) q^{51} +(-2.88857 - 2.15781i) q^{52} +1.29577i q^{53} +(4.37504 - 2.80340i) q^{54} +(0.416409 - 0.240414i) q^{55} +(-2.06312 + 1.65636i) 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} +(6.03319 - 5.15758i) 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} +(5.70331 + 9.53575i) q^{69} +(-0.628174 + 1.61610i) q^{70} +(-4.09978 + 7.10103i) q^{71} +(-2.99857 + 0.0925084i) q^{72} +6.93011 q^{73} +(-3.59978 - 2.07834i) q^{74} +(-0.122070 - 7.91543i) q^{75} +(-2.51943 - 4.36378i) q^{76} +(1.80931 + 0.703274i) q^{77} +(-2.55232 - 5.69962i) q^{78} -13.1952 q^{79} +(0.567549 - 0.327675i) q^{80} +(8.98288 - 0.554786i) q^{81} +(4.22814 + 2.44112i) q^{82} -12.5007i q^{83} +(-4.51783 + 0.767584i) q^{84} +(-0.660417 - 0.381292i) q^{85} -7.62182 q^{86} +(-0.861317 - 1.44010i) q^{87} +(-0.366849 - 0.635401i) q^{88} +(-12.6797 + 7.32065i) q^{89} +(-1.67152 + 1.03506i) q^{90} +(-5.05491 - 8.08999i) q^{91} -6.41504i q^{92} +(0.112291 + 7.28137i) 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} +(-6.67536 + 2.10704i) q^{98} +(1.15880 + 1.87136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9} + 6 q^{15} - 12 q^{16} + 6 q^{18} - 12 q^{21} + 36 q^{23} - 12 q^{25} + 18 q^{28} - 12 q^{30} - 12 q^{32} + 36 q^{35} + 6 q^{36} + 36 q^{37} + 12 q^{39} + 24 q^{42} - 42 q^{43} - 36 q^{46} + 6 q^{50} + 12 q^{51} - 18 q^{56} + 36 q^{57} + 6 q^{60} + 24 q^{63} + 24 q^{64} - 66 q^{65} - 54 q^{67} - 48 q^{71} - 12 q^{72} - 36 q^{74} - 42 q^{78} - 48 q^{79} + 84 q^{81} - 12 q^{84} + 84 q^{86} + 36 q^{91} - 18 q^{93} + 36 q^{95} - 36 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9 + 6 * q^15 - 12 * q^16 + 6 * q^18 - 12 * q^21 + 36 * q^23 - 12 * q^25 + 18 * q^28 - 12 * q^30 - 12 * q^32 + 36 * q^35 + 6 * q^36 + 36 * q^37 + 12 * q^39 + 24 * q^42 - 42 * q^43 - 36 * q^46 + 6 * q^50 + 12 * q^51 - 18 * q^56 + 36 * q^57 + 6 * q^60 + 24 * q^63 + 24 * q^64 - 66 * q^65 - 54 * q^67 - 48 * q^71 - 12 * q^72 - 36 * q^74 - 42 * q^78 - 48 * q^79 + 84 * q^81 - 12 * q^84 + 84 * q^86 + 36 * q^91 - 18 * q^93 + 36 * q^95 - 36 * q^99

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